Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), 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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.14 | ||
Root | \(1.61360i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.7 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61360i | 0.806801i | 0.915023 | + | 0.403401i | \(0.132172\pi\) | ||||
−0.915023 | + | 0.403401i | \(0.867828\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 1.39629 | 0.349072 | ||||||||
\(5\) | −6.36659 | −1.27332 | −0.636659 | − | 0.771146i | \(-0.719684\pi\) | ||||
−0.636659 | + | 0.771146i | \(0.719684\pi\) | |||||||
\(6\) | 2.79484i | 0.465807i | ||||||||
\(7\) | 6.66564 | 0.952234 | 0.476117 | − | 0.879382i | \(-0.342044\pi\) | ||||
0.476117 | + | 0.879382i | \(0.342044\pi\) | |||||||
\(8\) | 8.70746i | 1.08843i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 10.2731i | − | 1.02731i | ||||||
\(11\) | 16.0509i | 1.45917i | 0.683890 | + | 0.729586i | \(0.260287\pi\) | ||||
−0.683890 | + | 0.729586i | \(0.739713\pi\) | |||||||
\(12\) | 2.41844 | 0.201537 | ||||||||
\(13\) | 7.84026i | 0.603097i | 0.953451 | + | 0.301548i | \(0.0975035\pi\) | ||||
−0.953451 | + | 0.301548i | \(0.902497\pi\) | |||||||
\(14\) | 10.7557i | 0.768263i | ||||||||
\(15\) | −11.0272 | −0.735150 | ||||||||
\(16\) | −8.46523 | −0.529077 | ||||||||
\(17\) | 18.9063 | 1.11213 | 0.556067 | − | 0.831137i | \(-0.312310\pi\) | ||||
0.556067 | + | 0.831137i | \(0.312310\pi\) | |||||||
\(18\) | 4.84081i | 0.268934i | ||||||||
\(19\) | 7.10898 | 0.374157 | 0.187078 | − | 0.982345i | \(-0.440098\pi\) | ||||
0.187078 | + | 0.982345i | \(0.440098\pi\) | |||||||
\(20\) | −8.88958 | −0.444479 | ||||||||
\(21\) | 11.5452 | 0.549772 | ||||||||
\(22\) | −25.8997 | −1.17726 | ||||||||
\(23\) | − | 33.6730i | − | 1.46404i | −0.681282 | − | 0.732021i | \(-0.738577\pi\) | ||
0.681282 | − | 0.732021i | \(-0.261423\pi\) | |||||||
\(24\) | 15.0818i | 0.628407i | ||||||||
\(25\) | 15.5334 | 0.621336 | ||||||||
\(26\) | −12.6511 | −0.486579 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 9.30714 | 0.332398 | ||||||||
\(29\) | −46.2052 | −1.59328 | −0.796642 | − | 0.604451i | \(-0.793392\pi\) | ||||
−0.796642 | + | 0.604451i | \(0.793392\pi\) | |||||||
\(30\) | − | 17.7936i | − | 0.593120i | ||||||
\(31\) | − | 29.5207i | − | 0.952280i | −0.879369 | − | 0.476140i | \(-0.842036\pi\) | ||
0.879369 | − | 0.476140i | \(-0.157964\pi\) | |||||||
\(32\) | 21.1703i | 0.661573i | ||||||||
\(33\) | 27.8009i | 0.842453i | ||||||||
\(34\) | 30.5072i | 0.897271i | ||||||||
\(35\) | −42.4373 | −1.21250 | ||||||||
\(36\) | 4.18886 | 0.116357 | ||||||||
\(37\) | − | 1.91983i | − | 0.0518873i | −0.999663 | − | 0.0259437i | \(-0.991741\pi\) | ||
0.999663 | − | 0.0259437i | \(-0.00825905\pi\) | |||||||
\(38\) | 11.4711i | 0.301870i | ||||||||
\(39\) | 13.5797i | 0.348198i | ||||||||
\(40\) | − | 55.4368i | − | 1.38592i | ||||||
\(41\) | 46.4596 | 1.13316 | 0.566580 | − | 0.824007i | \(-0.308266\pi\) | ||||
0.566580 | + | 0.824007i | \(0.308266\pi\) | |||||||
\(42\) | 18.6294i | 0.443557i | ||||||||
\(43\) | 21.6675i | 0.503895i | 0.967741 | + | 0.251947i | \(0.0810710\pi\) | ||||
−0.967741 | + | 0.251947i | \(0.918929\pi\) | |||||||
\(44\) | 22.4116i | 0.509355i | ||||||||
\(45\) | −19.0998 | −0.424439 | ||||||||
\(46\) | 54.3348 | 1.18119 | ||||||||
\(47\) | − | 75.3742i | − | 1.60371i | −0.597521 | − | 0.801853i | \(-0.703848\pi\) | ||
0.597521 | − | 0.801853i | \(-0.296152\pi\) | |||||||
\(48\) | −14.6622 | −0.305463 | ||||||||
\(49\) | −4.56931 | −0.0932512 | ||||||||
\(50\) | 25.0647i | 0.501295i | ||||||||
\(51\) | 32.7466 | 0.642091 | ||||||||
\(52\) | 10.9473i | 0.210524i | ||||||||
\(53\) | 19.5526 | 0.368916 | 0.184458 | − | 0.982840i | \(-0.440947\pi\) | ||||
0.184458 | + | 0.982840i | \(0.440947\pi\) | |||||||
\(54\) | 8.38452i | 0.155269i | ||||||||
\(55\) | − | 102.189i | − | 1.85799i | ||||||
\(56\) | 58.0408i | 1.03644i | ||||||||
\(57\) | 12.3131 | 0.216019 | ||||||||
\(58\) | − | 74.5569i | − | 1.28546i | ||||||
\(59\) | −4.68014 | − | 58.8141i | −0.0793243 | − | 0.996849i | ||||
\(60\) | −15.3972 | −0.256620 | ||||||||
\(61\) | − | 41.0613i | − | 0.673136i | −0.941659 | − | 0.336568i | \(-0.890734\pi\) | ||
0.941659 | − | 0.336568i | \(-0.109266\pi\) | |||||||
\(62\) | 47.6346 | 0.768301 | ||||||||
\(63\) | 19.9969 | 0.317411 | ||||||||
\(64\) | −68.0214 | −1.06283 | ||||||||
\(65\) | − | 49.9157i | − | 0.767934i | ||||||
\(66\) | −44.8597 | −0.679692 | ||||||||
\(67\) | − | 90.1839i | − | 1.34603i | −0.739630 | − | 0.673014i | \(-0.764999\pi\) | ||
0.739630 | − | 0.673014i | \(-0.235001\pi\) | |||||||
\(68\) | 26.3986 | 0.388215 | ||||||||
\(69\) | − | 58.3233i | − | 0.845266i | ||||||
\(70\) | − | 68.4770i | − | 0.978243i | ||||||
\(71\) | 57.1922 | 0.805523 | 0.402762 | − | 0.915305i | \(-0.368050\pi\) | ||||
0.402762 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(72\) | 26.1224i | 0.362811i | ||||||||
\(73\) | 69.6739i | 0.954436i | 0.878785 | + | 0.477218i | \(0.158355\pi\) | ||||
−0.878785 | + | 0.477218i | \(0.841645\pi\) | |||||||
\(74\) | 3.09784 | 0.0418628 | ||||||||
\(75\) | 26.9047 | 0.358729 | ||||||||
\(76\) | 9.92617 | 0.130608 | ||||||||
\(77\) | 106.989i | 1.38947i | ||||||||
\(78\) | −21.9123 | −0.280927 | ||||||||
\(79\) | 118.749 | 1.50315 | 0.751575 | − | 0.659647i | \(-0.229294\pi\) | ||||
0.751575 | + | 0.659647i | \(0.229294\pi\) | |||||||
\(80\) | 53.8946 | 0.673683 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 74.9673i | 0.914235i | ||||||||
\(83\) | 86.3181i | 1.03998i | 0.854173 | + | 0.519988i | \(0.174064\pi\) | ||||
−0.854173 | + | 0.519988i | \(0.825936\pi\) | |||||||
\(84\) | 16.1204 | 0.191910 | ||||||||
\(85\) | −120.368 | −1.41610 | ||||||||
\(86\) | −34.9627 | −0.406543 | ||||||||
\(87\) | −80.0298 | −0.919883 | ||||||||
\(88\) | −139.762 | −1.58821 | ||||||||
\(89\) | 38.4935i | 0.432512i | 0.976337 | + | 0.216256i | \(0.0693845\pi\) | ||||
−0.976337 | + | 0.216256i | \(0.930615\pi\) | |||||||
\(90\) | − | 30.8194i | − | 0.342438i | ||||||
\(91\) | 52.2603i | 0.574289i | ||||||||
\(92\) | − | 47.0172i | − | 0.511056i | ||||||
\(93\) | − | 51.1313i | − | 0.549799i | ||||||
\(94\) | 121.624 | 1.29387 | ||||||||
\(95\) | −45.2599 | −0.476420 | ||||||||
\(96\) | 36.6681i | 0.381959i | ||||||||
\(97\) | − | 24.0445i | − | 0.247881i | −0.992290 | − | 0.123941i | \(-0.960447\pi\) | ||
0.992290 | − | 0.123941i | \(-0.0395532\pi\) | |||||||
\(98\) | − | 7.37305i | − | 0.0752352i | ||||||
\(99\) | 48.1526i | 0.486390i | ||||||||
\(100\) | 21.6891 | 0.216891 | ||||||||
\(101\) | 56.4784i | 0.559192i | 0.960118 | + | 0.279596i | \(0.0902006\pi\) | ||||
−0.960118 | + | 0.279596i | \(0.909799\pi\) | |||||||
\(102\) | 52.8401i | 0.518040i | ||||||||
\(103\) | 99.6967i | 0.967929i | 0.875088 | + | 0.483964i | \(0.160804\pi\) | ||||
−0.875088 | + | 0.483964i | \(0.839196\pi\) | |||||||
\(104\) | −68.2688 | −0.656430 | ||||||||
\(105\) | −73.5036 | −0.700034 | ||||||||
\(106\) | 31.5500i | 0.297642i | ||||||||
\(107\) | −193.034 | −1.80406 | −0.902030 | − | 0.431673i | \(-0.857924\pi\) | ||||
−0.902030 | + | 0.431673i | \(0.857924\pi\) | |||||||
\(108\) | 7.25532 | 0.0671789 | ||||||||
\(109\) | − | 65.4956i | − | 0.600877i | −0.953801 | − | 0.300439i | \(-0.902867\pi\) | ||
0.953801 | − | 0.300439i | \(-0.0971330\pi\) | |||||||
\(110\) | 164.893 | 1.49903 | ||||||||
\(111\) | − | 3.32524i | − | 0.0299572i | ||||||
\(112\) | −56.4262 | −0.503805 | ||||||||
\(113\) | − | 169.975i | − | 1.50420i | −0.659048 | − | 0.752101i | \(-0.729041\pi\) | ||
0.659048 | − | 0.752101i | \(-0.270959\pi\) | |||||||
\(114\) | 19.8685i | 0.174285i | ||||||||
\(115\) | 214.382i | 1.86419i | ||||||||
\(116\) | −64.5158 | −0.556171 | ||||||||
\(117\) | 23.5208i | 0.201032i | ||||||||
\(118\) | 94.9025 | − | 7.55188i | 0.804259 | − | 0.0639990i | ||||
\(119\) | 126.022 | 1.05901 | ||||||||
\(120\) | − | 96.0194i | − | 0.800161i | ||||||
\(121\) | −136.631 | −1.12918 | ||||||||
\(122\) | 66.2566 | 0.543087 | ||||||||
\(123\) | 80.4704 | 0.654231 | ||||||||
\(124\) | − | 41.2194i | − | 0.332414i | ||||||
\(125\) | 60.2699 | 0.482159 | ||||||||
\(126\) | 32.2671i | 0.256088i | ||||||||
\(127\) | −166.750 | −1.31299 | −0.656495 | − | 0.754331i | \(-0.727962\pi\) | ||||
−0.656495 | + | 0.754331i | \(0.727962\pi\) | |||||||
\(128\) | − | 25.0782i | − | 0.195924i | ||||||
\(129\) | 37.5292i | 0.290924i | ||||||||
\(130\) | 80.5441 | 0.619570 | ||||||||
\(131\) | 45.5267i | 0.347532i | 0.984787 | + | 0.173766i | \(0.0555936\pi\) | ||||
−0.984787 | + | 0.173766i | \(0.944406\pi\) | |||||||
\(132\) | 38.8181i | 0.294077i | ||||||||
\(133\) | 47.3859 | 0.356285 | ||||||||
\(134\) | 145.521 | 1.08598 | ||||||||
\(135\) | −33.0817 | −0.245050 | ||||||||
\(136\) | 164.626i | 1.21048i | ||||||||
\(137\) | −106.697 | −0.778807 | −0.389404 | − | 0.921067i | \(-0.627319\pi\) | ||||
−0.389404 | + | 0.921067i | \(0.627319\pi\) | |||||||
\(138\) | 94.1107 | 0.681961 | ||||||||
\(139\) | −133.637 | −0.961414 | −0.480707 | − | 0.876881i | \(-0.659620\pi\) | ||||
−0.480707 | + | 0.876881i | \(0.659620\pi\) | |||||||
\(140\) | −59.2547 | −0.423248 | ||||||||
\(141\) | − | 130.552i | − | 0.925900i | ||||||
\(142\) | 92.2854i | 0.649897i | ||||||||
\(143\) | −125.843 | −0.880022 | ||||||||
\(144\) | −25.3957 | −0.176359 | ||||||||
\(145\) | 294.170 | 2.02876 | ||||||||
\(146\) | −112.426 | −0.770040 | ||||||||
\(147\) | −7.91428 | −0.0538386 | ||||||||
\(148\) | − | 2.68064i | − | 0.0181124i | ||||||
\(149\) | − | 118.228i | − | 0.793478i | −0.917931 | − | 0.396739i | \(-0.870142\pi\) | ||
0.917931 | − | 0.396739i | \(-0.129858\pi\) | |||||||
\(150\) | 43.4134i | 0.289423i | ||||||||
\(151\) | 221.371i | 1.46603i | 0.680212 | + | 0.733015i | \(0.261888\pi\) | ||||
−0.680212 | + | 0.733015i | \(0.738112\pi\) | |||||||
\(152\) | 61.9012i | 0.407244i | ||||||||
\(153\) | 56.7189 | 0.370711 | ||||||||
\(154\) | −172.638 | −1.12103 | ||||||||
\(155\) | 187.946i | 1.21255i | ||||||||
\(156\) | 18.9612i | 0.121546i | ||||||||
\(157\) | 13.3063i | 0.0847535i | 0.999102 | + | 0.0423768i | \(0.0134930\pi\) | ||||
−0.999102 | + | 0.0423768i | \(0.986507\pi\) | |||||||
\(158\) | 191.614i | 1.21274i | ||||||||
\(159\) | 33.8660 | 0.212994 | ||||||||
\(160\) | − | 134.783i | − | 0.842392i | ||||||
\(161\) | − | 224.452i | − | 1.39411i | ||||||
\(162\) | 14.5224i | 0.0896446i | ||||||||
\(163\) | 227.187 | 1.39378 | 0.696891 | − | 0.717177i | \(-0.254566\pi\) | ||||
0.696891 | + | 0.717177i | \(0.254566\pi\) | |||||||
\(164\) | 64.8709 | 0.395554 | ||||||||
\(165\) | − | 176.997i | − | 1.07271i | ||||||
\(166\) | −139.283 | −0.839055 | ||||||||
\(167\) | 176.740 | 1.05832 | 0.529162 | − | 0.848521i | \(-0.322506\pi\) | ||||
0.529162 | + | 0.848521i | \(0.322506\pi\) | |||||||
\(168\) | 100.530i | 0.598390i | ||||||||
\(169\) | 107.530 | 0.636274 | ||||||||
\(170\) | − | 194.227i | − | 1.14251i | ||||||
\(171\) | 21.3269 | 0.124719 | ||||||||
\(172\) | 30.2540i | 0.175895i | ||||||||
\(173\) | 184.896i | 1.06876i | 0.845244 | + | 0.534381i | \(0.179455\pi\) | ||||
−0.845244 | + | 0.534381i | \(0.820545\pi\) | |||||||
\(174\) | − | 129.136i | − | 0.742163i | ||||||
\(175\) | 103.540 | 0.591657 | ||||||||
\(176\) | − | 135.874i | − | 0.772014i | ||||||
\(177\) | −8.10623 | − | 101.869i | −0.0457979 | − | 0.575531i | ||||
\(178\) | −62.1133 | −0.348951 | ||||||||
\(179\) | − | 290.925i | − | 1.62528i | −0.582765 | − | 0.812641i | \(-0.698029\pi\) | ||
0.582765 | − | 0.812641i | \(-0.301971\pi\) | |||||||
\(180\) | −26.6687 | −0.148160 | ||||||||
\(181\) | 71.9948 | 0.397761 | 0.198881 | − | 0.980024i | \(-0.436269\pi\) | ||||
0.198881 | + | 0.980024i | \(0.436269\pi\) | |||||||
\(182\) | −84.3274 | −0.463337 | ||||||||
\(183\) | − | 71.1203i | − | 0.388635i | ||||||
\(184\) | 293.206 | 1.59351 | ||||||||
\(185\) | 12.2228i | 0.0660690i | ||||||||
\(186\) | 82.5056 | 0.443579 | ||||||||
\(187\) | 303.463i | 1.62279i | ||||||||
\(188\) | − | 105.244i | − | 0.559809i | ||||||
\(189\) | 34.6357 | 0.183257 | ||||||||
\(190\) | − | 73.0315i | − | 0.384376i | ||||||
\(191\) | − | 169.923i | − | 0.889651i | −0.895617 | − | 0.444825i | \(-0.853266\pi\) | ||
0.895617 | − | 0.444825i | \(-0.146734\pi\) | |||||||
\(192\) | −117.817 | −0.613628 | ||||||||
\(193\) | −15.6413 | −0.0810432 | −0.0405216 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405216 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(194\) | 38.7982 | 0.199991 | ||||||||
\(195\) | − | 86.4565i | − | 0.443367i | ||||||
\(196\) | −6.38007 | −0.0325514 | ||||||||
\(197\) | −100.597 | −0.510645 | −0.255323 | − | 0.966856i | \(-0.582182\pi\) | ||||
−0.255323 | + | 0.966856i | \(0.582182\pi\) | |||||||
\(198\) | −77.6992 | −0.392420 | ||||||||
\(199\) | −84.4909 | −0.424577 | −0.212289 | − | 0.977207i | \(-0.568092\pi\) | ||||
−0.212289 | + | 0.977207i | \(0.568092\pi\) | |||||||
\(200\) | 135.257i | 0.676283i | ||||||||
\(201\) | − | 156.203i | − | 0.777129i | ||||||
\(202\) | −91.1337 | −0.451157 | ||||||||
\(203\) | −307.987 | −1.51718 | ||||||||
\(204\) | 45.7237 | 0.224136 | ||||||||
\(205\) | −295.789 | −1.44287 | ||||||||
\(206\) | −160.871 | −0.780926 | ||||||||
\(207\) | − | 101.019i | − | 0.488014i | ||||||
\(208\) | − | 66.3696i | − | 0.319085i | ||||||
\(209\) | 114.105i | 0.545959i | ||||||||
\(210\) | − | 118.606i | − | 0.564789i | ||||||
\(211\) | 307.104i | 1.45547i | 0.685859 | + | 0.727735i | \(0.259427\pi\) | ||||
−0.685859 | + | 0.727735i | \(0.740573\pi\) | |||||||
\(212\) | 27.3010 | 0.128778 | ||||||||
\(213\) | 99.0597 | 0.465069 | ||||||||
\(214\) | − | 311.481i | − | 1.45552i | ||||||
\(215\) | − | 137.948i | − | 0.641618i | ||||||
\(216\) | 45.2453i | 0.209469i | ||||||||
\(217\) | − | 196.774i | − | 0.906793i | ||||||
\(218\) | 105.684 | 0.484788 | ||||||||
\(219\) | 120.679i | 0.551044i | ||||||||
\(220\) | − | 142.686i | − | 0.648571i | ||||||
\(221\) | 148.230i | 0.670725i | ||||||||
\(222\) | 5.36562 | 0.0241695 | ||||||||
\(223\) | −334.093 | −1.49818 | −0.749088 | − | 0.662471i | \(-0.769508\pi\) | ||||
−0.749088 | + | 0.662471i | \(0.769508\pi\) | |||||||
\(224\) | 141.114i | 0.629972i | ||||||||
\(225\) | 46.6002 | 0.207112 | ||||||||
\(226\) | 274.272 | 1.21359 | ||||||||
\(227\) | 194.419i | 0.856471i | 0.903667 | + | 0.428236i | \(0.140865\pi\) | ||||
−0.903667 | + | 0.428236i | \(0.859135\pi\) | |||||||
\(228\) | 17.1926 | 0.0754063 | ||||||||
\(229\) | − | 198.825i | − | 0.868230i | −0.900857 | − | 0.434115i | \(-0.857061\pi\) | ||
0.900857 | − | 0.434115i | \(-0.142939\pi\) | |||||||
\(230\) | −345.927 | −1.50403 | ||||||||
\(231\) | 185.311i | 0.802212i | ||||||||
\(232\) | − | 402.330i | − | 1.73418i | ||||||
\(233\) | − | 268.492i | − | 1.15233i | −0.817335 | − | 0.576163i | \(-0.804550\pi\) | ||
0.817335 | − | 0.576163i | \(-0.195450\pi\) | |||||||
\(234\) | −37.9532 | −0.162193 | ||||||||
\(235\) | 479.876i | 2.04203i | ||||||||
\(236\) | −6.53481 | − | 82.1213i | −0.0276899 | − | 0.347972i | ||||
\(237\) | 205.679 | 0.867844 | ||||||||
\(238\) | 203.350i | 0.854412i | ||||||||
\(239\) | 321.465 | 1.34504 | 0.672522 | − | 0.740077i | \(-0.265211\pi\) | ||||
0.672522 | + | 0.740077i | \(0.265211\pi\) | |||||||
\(240\) | 93.3482 | 0.388951 | ||||||||
\(241\) | −44.9975 | −0.186712 | −0.0933559 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933559 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(242\) | − | 220.468i | − | 0.911024i | ||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 57.3334i | − | 0.234973i | ||||||
\(245\) | 29.0909 | 0.118738 | ||||||||
\(246\) | 129.847i | 0.527834i | ||||||||
\(247\) | 55.7362i | 0.225653i | ||||||||
\(248\) | 257.050 | 1.03649 | ||||||||
\(249\) | 149.507i | 0.600431i | ||||||||
\(250\) | 97.2516i | 0.389006i | ||||||||
\(251\) | 307.277 | 1.22421 | 0.612105 | − | 0.790776i | \(-0.290323\pi\) | ||||
0.612105 | + | 0.790776i | \(0.290323\pi\) | |||||||
\(252\) | 27.9214 | 0.110799 | ||||||||
\(253\) | 540.481 | 2.13629 | ||||||||
\(254\) | − | 269.068i | − | 1.05932i | ||||||
\(255\) | −208.484 | −0.817586 | ||||||||
\(256\) | −231.619 | −0.904763 | ||||||||
\(257\) | −269.259 | −1.04770 | −0.523850 | − | 0.851811i | \(-0.675505\pi\) | ||||
−0.523850 | + | 0.851811i | \(0.675505\pi\) | |||||||
\(258\) | −60.5572 | −0.234718 | ||||||||
\(259\) | − | 12.7969i | − | 0.0494089i | ||||||
\(260\) | − | 69.6966i | − | 0.268064i | ||||||
\(261\) | −138.616 | −0.531095 | ||||||||
\(262\) | −73.4619 | −0.280389 | ||||||||
\(263\) | −294.101 | −1.11825 | −0.559127 | − | 0.829082i | \(-0.688864\pi\) | ||||
−0.559127 | + | 0.829082i | \(0.688864\pi\) | |||||||
\(264\) | −242.076 | −0.916953 | ||||||||
\(265\) | −124.483 | −0.469747 | ||||||||
\(266\) | 76.4619i | 0.287451i | ||||||||
\(267\) | 66.6728i | 0.249711i | ||||||||
\(268\) | − | 125.923i | − | 0.469860i | ||||||
\(269\) | − | 52.5633i | − | 0.195403i | −0.995216 | − | 0.0977013i | \(-0.968851\pi\) | ||
0.995216 | − | 0.0977013i | \(-0.0311490\pi\) | |||||||
\(270\) | − | 53.3808i | − | 0.197707i | ||||||
\(271\) | −63.5650 | −0.234557 | −0.117279 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117279 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(272\) | −160.046 | −0.588405 | ||||||||
\(273\) | 90.5175i | 0.331566i | ||||||||
\(274\) | − | 172.166i | − | 0.628343i | ||||||
\(275\) | 249.325i | 0.906636i | ||||||||
\(276\) | − | 81.4361i | − | 0.295058i | ||||||
\(277\) | −76.0155 | −0.274424 | −0.137212 | − | 0.990542i | \(-0.543814\pi\) | ||||
−0.137212 | + | 0.990542i | \(0.543814\pi\) | |||||||
\(278\) | − | 215.636i | − | 0.775670i | ||||||
\(279\) | − | 88.5620i | − | 0.317427i | ||||||
\(280\) | − | 369.521i | − | 1.31972i | ||||||
\(281\) | 146.718 | 0.522127 | 0.261063 | − | 0.965322i | \(-0.415927\pi\) | ||||
0.261063 | + | 0.965322i | \(0.415927\pi\) | |||||||
\(282\) | 210.659 | 0.747017 | ||||||||
\(283\) | 497.505i | 1.75797i | 0.476850 | + | 0.878985i | \(0.341779\pi\) | ||||
−0.476850 | + | 0.878985i | \(0.658221\pi\) | |||||||
\(284\) | 79.8567 | 0.281185 | ||||||||
\(285\) | −78.3925 | −0.275061 | ||||||||
\(286\) | − | 203.061i | − | 0.710002i | ||||||
\(287\) | 309.683 | 1.07903 | ||||||||
\(288\) | 63.5110i | 0.220524i | ||||||||
\(289\) | 68.4476 | 0.236843 | ||||||||
\(290\) | 474.673i | 1.63680i | ||||||||
\(291\) | − | 41.6462i | − | 0.143114i | ||||||
\(292\) | 97.2847i | 0.333167i | ||||||||
\(293\) | 158.624 | 0.541378 | 0.270689 | − | 0.962667i | \(-0.412749\pi\) | ||||
0.270689 | + | 0.962667i | \(0.412749\pi\) | |||||||
\(294\) | − | 12.7705i | − | 0.0434371i | ||||||
\(295\) | 29.7965 | + | 374.445i | 0.101005 | + | 1.26930i | ||||
\(296\) | 16.7169 | 0.0564759 | ||||||||
\(297\) | 83.4028i | 0.280818i | ||||||||
\(298\) | 190.773 | 0.640179 | ||||||||
\(299\) | 264.005 | 0.882960 | ||||||||
\(300\) | 37.5666 | 0.125222 | ||||||||
\(301\) | 144.428i | 0.479826i | ||||||||
\(302\) | −357.204 | −1.18280 | ||||||||
\(303\) | 97.8235i | 0.322850i | ||||||||
\(304\) | −60.1792 | −0.197958 | ||||||||
\(305\) | 261.420i | 0.857116i | ||||||||
\(306\) | 91.5217i | 0.299090i | ||||||||
\(307\) | 302.624 | 0.985747 | 0.492873 | − | 0.870101i | \(-0.335947\pi\) | ||||
0.492873 | + | 0.870101i | \(0.335947\pi\) | |||||||
\(308\) | 149.388i | 0.485025i | ||||||||
\(309\) | 172.680i | 0.558834i | ||||||||
\(310\) | −303.270 | −0.978290 | ||||||||
\(311\) | 545.048 | 1.75257 | 0.876283 | − | 0.481798i | \(-0.160016\pi\) | ||||
0.876283 | + | 0.481798i | \(0.160016\pi\) | |||||||
\(312\) | −118.245 | −0.378990 | ||||||||
\(313\) | − | 378.973i | − | 1.21078i | −0.795931 | − | 0.605388i | \(-0.793018\pi\) | ||
0.795931 | − | 0.605388i | \(-0.206982\pi\) | |||||||
\(314\) | −21.4711 | −0.0683792 | ||||||||
\(315\) | −127.312 | −0.404165 | ||||||||
\(316\) | 165.808 | 0.524708 | ||||||||
\(317\) | −400.912 | −1.26471 | −0.632354 | − | 0.774680i | \(-0.717911\pi\) | ||||
−0.632354 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(318\) | 54.6463i | 0.171844i | ||||||||
\(319\) | − | 741.635i | − | 2.32487i | ||||||
\(320\) | 433.064 | 1.35333 | ||||||||
\(321\) | −334.346 | −1.04157 | ||||||||
\(322\) | 362.176 | 1.12477 | ||||||||
\(323\) | 134.404 | 0.416113 | ||||||||
\(324\) | 12.5666 | 0.0387858 | ||||||||
\(325\) | 121.786i | 0.374726i | ||||||||
\(326\) | 366.589i | 1.12451i | ||||||||
\(327\) | − | 113.442i | − | 0.346917i | ||||||
\(328\) | 404.545i | 1.23337i | ||||||||
\(329\) | − | 502.417i | − | 1.52710i | ||||||
\(330\) | 285.603 | 0.865463 | ||||||||
\(331\) | −256.922 | −0.776199 | −0.388099 | − | 0.921618i | \(-0.626868\pi\) | ||||
−0.388099 | + | 0.921618i | \(0.626868\pi\) | |||||||
\(332\) | 120.525i | 0.363027i | ||||||||
\(333\) | − | 5.75949i | − | 0.0172958i | ||||||
\(334\) | 285.188i | 0.853857i | ||||||||
\(335\) | 574.163i | 1.71392i | ||||||||
\(336\) | −97.7330 | −0.290872 | ||||||||
\(337\) | 519.832i | 1.54253i | 0.636516 | + | 0.771264i | \(0.280375\pi\) | ||||
−0.636516 | + | 0.771264i | \(0.719625\pi\) | |||||||
\(338\) | 173.511i | 0.513347i | ||||||||
\(339\) | − | 294.405i | − | 0.868451i | ||||||
\(340\) | −168.069 | −0.494320 | ||||||||
\(341\) | 473.833 | 1.38954 | ||||||||
\(342\) | 34.4132i | 0.100623i | ||||||||
\(343\) | −357.073 | −1.04103 | ||||||||
\(344\) | −188.669 | −0.548456 | ||||||||
\(345\) | 371.320i | 1.07629i | ||||||||
\(346\) | −298.349 | −0.862279 | ||||||||
\(347\) | − | 144.710i | − | 0.417032i | −0.978019 | − | 0.208516i | \(-0.933137\pi\) | ||
0.978019 | − | 0.208516i | \(-0.0668633\pi\) | |||||||
\(348\) | −111.745 | −0.321105 | ||||||||
\(349\) | − | 444.542i | − | 1.27376i | −0.770963 | − | 0.636880i | \(-0.780225\pi\) | ||
0.770963 | − | 0.636880i | \(-0.219775\pi\) | |||||||
\(350\) | 167.072i | 0.477350i | ||||||||
\(351\) | 40.7392i | 0.116066i | ||||||||
\(352\) | −339.802 | −0.965348 | ||||||||
\(353\) | 625.820i | 1.77286i | 0.462863 | + | 0.886430i | \(0.346822\pi\) | ||||
−0.462863 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(354\) | 164.376 | − | 13.0802i | 0.464339 | − | 0.0369498i | ||||
\(355\) | −364.119 | −1.02569 | ||||||||
\(356\) | 53.7480i | 0.150978i | ||||||||
\(357\) | 218.277 | 0.611421 | ||||||||
\(358\) | 469.438 | 1.31128 | ||||||||
\(359\) | −351.287 | −0.978517 | −0.489258 | − | 0.872139i | \(-0.662732\pi\) | ||||
−0.489258 | + | 0.872139i | \(0.662732\pi\) | |||||||
\(360\) | − | 166.310i | − | 0.461973i | ||||||
\(361\) | −310.462 | −0.860007 | ||||||||
\(362\) | 116.171i | 0.320914i | ||||||||
\(363\) | −236.652 | −0.651933 | ||||||||
\(364\) | 72.9704i | 0.200468i | ||||||||
\(365\) | − | 443.585i | − | 1.21530i | ||||||
\(366\) | 114.760 | 0.313551 | ||||||||
\(367\) | 221.302i | 0.603002i | 0.953466 | + | 0.301501i | \(0.0974877\pi\) | ||||
−0.953466 | + | 0.301501i | \(0.902512\pi\) | |||||||
\(368\) | 285.050i | 0.774592i | ||||||||
\(369\) | 139.379 | 0.377720 | ||||||||
\(370\) | −19.7227 | −0.0533046 | ||||||||
\(371\) | 130.330 | 0.351294 | ||||||||
\(372\) | − | 71.3940i | − | 0.191919i | ||||||
\(373\) | −159.549 | −0.427745 | −0.213873 | − | 0.976862i | \(-0.568608\pi\) | ||||
−0.213873 | + | 0.976862i | \(0.568608\pi\) | |||||||
\(374\) | −489.668 | −1.30927 | ||||||||
\(375\) | 104.390 | 0.278375 | ||||||||
\(376\) | 656.318 | 1.74553 | ||||||||
\(377\) | − | 362.261i | − | 0.960905i | ||||||
\(378\) | 55.8882i | 0.147852i | ||||||||
\(379\) | 264.069 | 0.696752 | 0.348376 | − | 0.937355i | \(-0.386733\pi\) | ||||
0.348376 | + | 0.937355i | \(0.386733\pi\) | |||||||
\(380\) | −63.1958 | −0.166305 | ||||||||
\(381\) | −288.819 | −0.758055 | ||||||||
\(382\) | 274.189 | 0.717771 | ||||||||
\(383\) | −89.2279 | −0.232971 | −0.116486 | − | 0.993192i | \(-0.537163\pi\) | ||||
−0.116486 | + | 0.993192i | \(0.537163\pi\) | |||||||
\(384\) | − | 43.4368i | − | 0.113117i | ||||||
\(385\) | − | 681.157i | − | 1.76924i | ||||||
\(386\) | − | 25.2389i | − | 0.0653857i | ||||||
\(387\) | 65.0024i | 0.167965i | ||||||||
\(388\) | − | 33.5730i | − | 0.0865283i | ||||||
\(389\) | −161.318 | −0.414699 | −0.207350 | − | 0.978267i | \(-0.566484\pi\) | ||||
−0.207350 | + | 0.978267i | \(0.566484\pi\) | |||||||
\(390\) | 139.506 | 0.357709 | ||||||||
\(391\) | − | 636.631i | − | 1.62821i | ||||||
\(392\) | − | 39.7871i | − | 0.101498i | ||||||
\(393\) | 78.8545i | 0.200648i | ||||||||
\(394\) | − | 162.324i | − | 0.411989i | ||||||
\(395\) | −756.025 | −1.91399 | ||||||||
\(396\) | 67.2349i | 0.169785i | ||||||||
\(397\) | − | 519.713i | − | 1.30910i | −0.756018 | − | 0.654551i | \(-0.772858\pi\) | ||
0.756018 | − | 0.654551i | \(-0.227142\pi\) | |||||||
\(398\) | − | 136.335i | − | 0.342549i | ||||||
\(399\) | 82.0747 | 0.205701 | ||||||||
\(400\) | −131.494 | −0.328735 | ||||||||
\(401\) | 550.540i | 1.37292i | 0.727169 | + | 0.686459i | \(0.240836\pi\) | ||||
−0.727169 | + | 0.686459i | \(0.759164\pi\) | |||||||
\(402\) | 252.050 | 0.626989 | ||||||||
\(403\) | 231.450 | 0.574317 | ||||||||
\(404\) | 78.8601i | 0.195198i | ||||||||
\(405\) | −57.2993 | −0.141480 | ||||||||
\(406\) | − | 496.969i | − | 1.22406i | ||||||
\(407\) | 30.8150 | 0.0757125 | ||||||||
\(408\) | 285.140i | 0.698873i | ||||||||
\(409\) | − | 17.8723i | − | 0.0436976i | −0.999761 | − | 0.0218488i | \(-0.993045\pi\) | ||
0.999761 | − | 0.0218488i | \(-0.00695524\pi\) | |||||||
\(410\) | − | 477.286i | − | 1.16411i | ||||||
\(411\) | −184.804 | −0.449645 | ||||||||
\(412\) | 139.205i | 0.337877i | ||||||||
\(413\) | −31.1961 | − | 392.033i | −0.0755353 | − | 0.949233i | ||||
\(414\) | 163.004 | 0.393731 | ||||||||
\(415\) | − | 549.551i | − | 1.32422i | ||||||
\(416\) | −165.981 | −0.398992 | ||||||||
\(417\) | −231.465 | −0.555072 | ||||||||
\(418\) | −184.121 | −0.440480 | ||||||||
\(419\) | − | 18.7816i | − | 0.0448248i | −0.999749 | − | 0.0224124i | \(-0.992865\pi\) | ||
0.999749 | − | 0.0224124i | \(-0.00713469\pi\) | |||||||
\(420\) | −102.632 | −0.244362 | ||||||||
\(421\) | − | 561.743i | − | 1.33431i | −0.744920 | − | 0.667153i | \(-0.767513\pi\) | ||
0.744920 | − | 0.667153i | \(-0.232487\pi\) | |||||||
\(422\) | −495.544 | −1.17427 | ||||||||
\(423\) | − | 226.123i | − | 0.534569i | ||||||
\(424\) | 170.253i | 0.401540i | ||||||||
\(425\) | 293.679 | 0.691010 | ||||||||
\(426\) | 159.843i | 0.375218i | ||||||||
\(427\) | − | 273.700i | − | 0.640983i | ||||||
\(428\) | −269.532 | −0.629747 | ||||||||
\(429\) | −217.967 | −0.508081 | ||||||||
\(430\) | 222.593 | 0.517658 | ||||||||
\(431\) | 43.8318i | 0.101698i | 0.998706 | + | 0.0508490i | \(0.0161927\pi\) | ||||
−0.998706 | + | 0.0508490i | \(0.983807\pi\) | |||||||
\(432\) | −43.9866 | −0.101821 | ||||||||
\(433\) | 100.552 | 0.232221 | 0.116111 | − | 0.993236i | \(-0.462957\pi\) | ||||
0.116111 | + | 0.993236i | \(0.462957\pi\) | |||||||
\(434\) | 317.515 | 0.731602 | ||||||||
\(435\) | 509.517 | 1.17130 | ||||||||
\(436\) | − | 91.4507i | − | 0.209749i | ||||||
\(437\) | − | 239.381i | − | 0.547781i | ||||||
\(438\) | −194.727 | −0.444583 | ||||||||
\(439\) | 580.171 | 1.32157 | 0.660787 | − | 0.750573i | \(-0.270223\pi\) | ||||
0.660787 | + | 0.750573i | \(0.270223\pi\) | |||||||
\(440\) | 889.810 | 2.02229 | ||||||||
\(441\) | −13.7079 | −0.0310837 | ||||||||
\(442\) | −239.185 | −0.541142 | ||||||||
\(443\) | 763.409i | 1.72327i | 0.507528 | + | 0.861635i | \(0.330559\pi\) | ||||
−0.507528 | + | 0.861635i | \(0.669441\pi\) | |||||||
\(444\) | − | 4.64300i | − | 0.0104572i | ||||||
\(445\) | − | 245.072i | − | 0.550724i | ||||||
\(446\) | − | 539.093i | − | 1.20873i | ||||||
\(447\) | − | 204.777i | − | 0.458115i | ||||||
\(448\) | −453.406 | −1.01207 | ||||||||
\(449\) | 350.584 | 0.780810 | 0.390405 | − | 0.920643i | \(-0.372335\pi\) | ||||
0.390405 | + | 0.920643i | \(0.372335\pi\) | |||||||
\(450\) | 75.1942i | 0.167098i | ||||||||
\(451\) | 745.717i | 1.65348i | ||||||||
\(452\) | − | 237.334i | − | 0.525074i | ||||||
\(453\) | 383.425i | 0.846413i | ||||||||
\(454\) | −313.715 | −0.691002 | ||||||||
\(455\) | − | 332.720i | − | 0.731252i | ||||||
\(456\) | 107.216i | 0.235123i | ||||||||
\(457\) | 627.986i | 1.37415i | 0.726587 | + | 0.687075i | \(0.241106\pi\) | ||||
−0.726587 | + | 0.687075i | \(0.758894\pi\) | |||||||
\(458\) | 320.824 | 0.700489 | ||||||||
\(459\) | 98.2399 | 0.214030 | ||||||||
\(460\) | 299.339i | 0.650736i | ||||||||
\(461\) | 602.743 | 1.30747 | 0.653735 | − | 0.756724i | \(-0.273201\pi\) | ||||
0.653735 | + | 0.756724i | \(0.273201\pi\) | |||||||
\(462\) | −299.018 | −0.647226 | ||||||||
\(463\) | 340.754i | 0.735969i | 0.929832 | + | 0.367985i | \(0.119952\pi\) | ||||
−0.929832 | + | 0.367985i | \(0.880048\pi\) | |||||||
\(464\) | 391.138 | 0.842970 | ||||||||
\(465\) | 325.532i | 0.700069i | ||||||||
\(466\) | 433.239 | 0.929697 | ||||||||
\(467\) | − | 682.672i | − | 1.46182i | −0.682471 | − | 0.730912i | \(-0.739095\pi\) | ||
0.682471 | − | 0.730912i | \(-0.260905\pi\) | |||||||
\(468\) | 32.8418i | 0.0701747i | ||||||||
\(469\) | − | 601.133i | − | 1.28173i | ||||||
\(470\) | −774.329 | −1.64751 | ||||||||
\(471\) | 23.0472i | 0.0489325i | ||||||||
\(472\) | 512.121 | − | 40.7521i | 1.08500 | − | 0.0863392i | ||||
\(473\) | −347.782 | −0.735269 | ||||||||
\(474\) | 331.884i | 0.700178i | ||||||||
\(475\) | 110.427 | 0.232477 | ||||||||
\(476\) | 175.963 | 0.369671 | ||||||||
\(477\) | 58.6577 | 0.122972 | ||||||||
\(478\) | 518.717i | 1.08518i | ||||||||
\(479\) | −757.928 | −1.58231 | −0.791156 | − | 0.611614i | \(-0.790520\pi\) | ||||
−0.791156 | + | 0.611614i | \(0.790520\pi\) | |||||||
\(480\) | − | 233.450i | − | 0.486355i | ||||||
\(481\) | 15.0520 | 0.0312931 | ||||||||
\(482\) | − | 72.6081i | − | 0.150639i | ||||||
\(483\) | − | 388.762i | − | 0.804890i | ||||||
\(484\) | −190.776 | −0.394165 | ||||||||
\(485\) | 153.081i | 0.315631i | ||||||||
\(486\) | 25.1536i | 0.0517563i | ||||||||
\(487\) | −105.431 | −0.216491 | −0.108246 | − | 0.994124i | \(-0.534523\pi\) | ||||
−0.108246 | + | 0.994124i | \(0.534523\pi\) | |||||||
\(488\) | 357.540 | 0.732663 | ||||||||
\(489\) | 393.499 | 0.804701 | ||||||||
\(490\) | 46.9411i | 0.0957983i | ||||||||
\(491\) | −603.562 | −1.22925 | −0.614625 | − | 0.788820i | \(-0.710693\pi\) | ||||
−0.614625 | + | 0.788820i | \(0.710693\pi\) | |||||||
\(492\) | 112.360 | 0.228373 | ||||||||
\(493\) | −873.570 | −1.77195 | ||||||||
\(494\) | −89.9361 | −0.182057 | ||||||||
\(495\) | − | 306.568i | − | 0.619329i | ||||||
\(496\) | 249.899i | 0.503830i | ||||||||
\(497\) | 381.222 | 0.767046 | ||||||||
\(498\) | −241.245 | −0.484428 | ||||||||
\(499\) | 308.346 | 0.617928 | 0.308964 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308964 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(500\) | 84.1540 | 0.168308 | ||||||||
\(501\) | 306.123 | 0.611023 | ||||||||
\(502\) | 495.823i | 0.987695i | ||||||||
\(503\) | − | 6.39623i | − | 0.0127162i | −0.999980 | − | 0.00635809i | \(-0.997976\pi\) | ||
0.999980 | − | 0.00635809i | \(-0.00202386\pi\) | |||||||
\(504\) | 174.122i | 0.345481i | ||||||||
\(505\) | − | 359.575i | − | 0.712029i | ||||||
\(506\) | 872.122i | 1.72356i | ||||||||
\(507\) | 186.248 | 0.367353 | ||||||||
\(508\) | −232.830 | −0.458328 | ||||||||
\(509\) | 243.213i | 0.477826i | 0.971041 | + | 0.238913i | \(0.0767911\pi\) | ||||
−0.971041 | + | 0.238913i | \(0.923209\pi\) | |||||||
\(510\) | − | 336.411i | − | 0.659629i | ||||||
\(511\) | 464.420i | 0.908846i | ||||||||
\(512\) | − | 474.055i | − | 0.925888i | ||||||
\(513\) | 36.9393 | 0.0720065 | ||||||||
\(514\) | − | 434.477i | − | 0.845285i | ||||||
\(515\) | − | 634.727i | − | 1.23248i | ||||||
\(516\) | 52.4015i | 0.101553i | ||||||||
\(517\) | 1209.82 | 2.34008 | ||||||||
\(518\) | 20.6491 | 0.0398631 | ||||||||
\(519\) | 320.249i | 0.617050i | ||||||||
\(520\) | 434.639 | 0.835844 | ||||||||
\(521\) | −903.968 | −1.73506 | −0.867532 | − | 0.497382i | \(-0.834295\pi\) | ||||
−0.867532 | + | 0.497382i | \(0.834295\pi\) | |||||||
\(522\) | − | 223.671i | − | 0.428488i | ||||||
\(523\) | −860.311 | −1.64495 | −0.822477 | − | 0.568798i | \(-0.807408\pi\) | ||||
−0.822477 | + | 0.568798i | \(0.807408\pi\) | |||||||
\(524\) | 63.5683i | 0.121314i | ||||||||
\(525\) | 179.337 | 0.341594 | ||||||||
\(526\) | − | 474.562i | − | 0.902209i | ||||||
\(527\) | − | 558.126i | − | 1.05906i | ||||||
\(528\) | − | 235.341i | − | 0.445722i | ||||||
\(529\) | −604.870 | −1.14342 | ||||||||
\(530\) | − | 200.866i | − | 0.378993i | ||||||
\(531\) | −14.0404 | − | 176.442i | −0.0264414 | − | 0.332283i | ||||
\(532\) | 66.1643 | 0.124369 | ||||||||
\(533\) | 364.255i | 0.683406i | ||||||||
\(534\) | −107.583 | −0.201467 | ||||||||
\(535\) | 1228.97 | 2.29714 | ||||||||
\(536\) | 785.272 | 1.46506 | ||||||||
\(537\) | − | 503.898i | − | 0.938357i | ||||||
\(538\) | 84.8163 | 0.157651 | ||||||||
\(539\) | − | 73.3414i | − | 0.136069i | ||||||
\(540\) | −46.1916 | −0.0855400 | ||||||||
\(541\) | − | 562.764i | − | 1.04023i | −0.854097 | − | 0.520115i | \(-0.825889\pi\) | ||
0.854097 | − | 0.520115i | \(-0.174111\pi\) | |||||||
\(542\) | − | 102.569i | − | 0.189241i | ||||||
\(543\) | 124.699 | 0.229648 | ||||||||
\(544\) | 400.252i | 0.735758i | ||||||||
\(545\) | 416.983i | 0.765107i | ||||||||
\(546\) | −146.059 | −0.267508 | ||||||||
\(547\) | −186.037 | −0.340104 | −0.170052 | − | 0.985435i | \(-0.554394\pi\) | ||||
−0.170052 | + | 0.985435i | \(0.554394\pi\) | |||||||
\(548\) | −148.979 | −0.271860 | ||||||||
\(549\) | − | 123.184i | − | 0.224379i | ||||||
\(550\) | −402.311 | −0.731475 | ||||||||
\(551\) | −328.472 | −0.596138 | ||||||||
\(552\) | 507.848 | 0.920015 | ||||||||
\(553\) | 791.537 | 1.43135 | ||||||||
\(554\) | − | 122.659i | − | 0.221406i | ||||||
\(555\) | 21.1705i | 0.0381450i | ||||||||
\(556\) | −186.595 | −0.335602 | ||||||||
\(557\) | −206.473 | −0.370687 | −0.185343 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185343 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(558\) | 142.904 | 0.256100 | ||||||||
\(559\) | −169.879 | −0.303897 | ||||||||
\(560\) | 359.242 | 0.641503 | ||||||||
\(561\) | 525.613i | 0.936921i | ||||||||
\(562\) | 236.744i | 0.421252i | ||||||||
\(563\) | 560.271i | 0.995152i | 0.867420 | + | 0.497576i | \(0.165776\pi\) | ||||
−0.867420 | + | 0.497576i | \(0.834224\pi\) | |||||||
\(564\) | − | 182.288i | − | 0.323206i | ||||||
\(565\) | 1082.16i | 1.91533i | ||||||||
\(566\) | −802.776 | −1.41833 | ||||||||
\(567\) | 59.9907 | 0.105804 | ||||||||
\(568\) | 497.999i | 0.876758i | ||||||||
\(569\) | − | 694.519i | − | 1.22060i | −0.792172 | − | 0.610298i | \(-0.791050\pi\) | ||
0.792172 | − | 0.610298i | \(-0.208950\pi\) | |||||||
\(570\) | − | 126.494i | − | 0.221920i | ||||||
\(571\) | 344.549i | 0.603414i | 0.953401 | + | 0.301707i | \(0.0975564\pi\) | ||||
−0.953401 | + | 0.301707i | \(0.902444\pi\) | |||||||
\(572\) | −175.713 | −0.307191 | ||||||||
\(573\) | − | 294.316i | − | 0.513640i | ||||||
\(574\) | 499.705i | 0.870566i | ||||||||
\(575\) | − | 523.056i | − | 0.909663i | ||||||
\(576\) | −204.064 | −0.354278 | ||||||||
\(577\) | −543.385 | −0.941742 | −0.470871 | − | 0.882202i | \(-0.656060\pi\) | ||||
−0.470871 | + | 0.882202i | \(0.656060\pi\) | |||||||
\(578\) | 110.447i | 0.191085i | ||||||||
\(579\) | −27.0916 | −0.0467903 | ||||||||
\(580\) | 410.745 | 0.708182 | ||||||||
\(581\) | 575.365i | 0.990301i | ||||||||
\(582\) | 67.2005 | 0.115465 | ||||||||
\(583\) | 313.836i | 0.538312i | ||||||||
\(584\) | −606.682 | −1.03884 | ||||||||
\(585\) | − | 149.747i | − | 0.255978i | ||||||
\(586\) | 255.956i | 0.436784i | ||||||||
\(587\) | 995.683i | 1.69622i | 0.529818 | + | 0.848111i | \(0.322260\pi\) | ||||
−0.529818 | + | 0.848111i | \(0.677740\pi\) | |||||||
\(588\) | −11.0506 | −0.0187935 | ||||||||
\(589\) | − | 209.862i | − | 0.356302i | ||||||
\(590\) | −604.205 | + | 48.0797i | −1.02408 | + | 0.0814910i | ||||
\(591\) | −174.239 | −0.294821 | ||||||||
\(592\) | 16.2518i | 0.0274524i | ||||||||
\(593\) | 503.068 | 0.848345 | 0.424172 | − | 0.905581i | \(-0.360565\pi\) | ||||
0.424172 | + | 0.905581i | \(0.360565\pi\) | |||||||
\(594\) | −134.579 | −0.226564 | ||||||||
\(595\) | −802.332 | −1.34846 | ||||||||
\(596\) | − | 165.081i | − | 0.276981i | ||||||
\(597\) | −146.342 | −0.245130 | ||||||||
\(598\) | 425.999i | 0.712373i | ||||||||
\(599\) | −475.339 | −0.793554 | −0.396777 | − | 0.917915i | \(-0.629871\pi\) | ||||
−0.396777 | + | 0.917915i | \(0.629871\pi\) | |||||||
\(600\) | 234.271i | 0.390452i | ||||||||
\(601\) | − | 288.933i | − | 0.480754i | −0.970680 | − | 0.240377i | \(-0.922729\pi\) | ||
0.970680 | − | 0.240377i | \(-0.0772710\pi\) | |||||||
\(602\) | −233.049 | −0.387124 | ||||||||
\(603\) | − | 270.552i | − | 0.448676i | ||||||
\(604\) | 309.097i | 0.511750i | ||||||||
\(605\) | 869.872 | 1.43780 | ||||||||
\(606\) | −157.848 | −0.260476 | ||||||||
\(607\) | 76.8532 | 0.126612 | 0.0633058 | − | 0.997994i | \(-0.479836\pi\) | ||||
0.0633058 | + | 0.997994i | \(0.479836\pi\) | |||||||
\(608\) | 150.499i | 0.247532i | ||||||||
\(609\) | −533.450 | −0.875944 | ||||||||
\(610\) | −421.828 | −0.691522 | ||||||||
\(611\) | 590.953 | 0.967190 | ||||||||
\(612\) | 79.1958 | 0.129405 | ||||||||
\(613\) | − | 518.309i | − | 0.845529i | −0.906240 | − | 0.422765i | \(-0.861060\pi\) | ||
0.906240 | − | 0.422765i | \(-0.138940\pi\) | |||||||
\(614\) | 488.315i | 0.795302i | ||||||||
\(615\) | −512.321 | −0.833043 | ||||||||
\(616\) | −931.605 | −1.51235 | ||||||||
\(617\) | −440.167 | −0.713399 | −0.356699 | − | 0.934219i | \(-0.616098\pi\) | ||||
−0.356699 | + | 0.934219i | \(0.616098\pi\) | |||||||
\(618\) | −278.636 | −0.450868 | ||||||||
\(619\) | 624.254 | 1.00849 | 0.504244 | − | 0.863561i | \(-0.331771\pi\) | ||||
0.504244 | + | 0.863561i | \(0.331771\pi\) | |||||||
\(620\) | 262.427i | 0.423269i | ||||||||
\(621\) | − | 174.970i | − | 0.281755i | ||||||
\(622\) | 879.490i | 1.41397i | ||||||||
\(623\) | 256.584i | 0.411852i | ||||||||
\(624\) | − | 114.956i | − | 0.184224i | ||||||
\(625\) | −772.048 | −1.23528 | ||||||||
\(626\) | 611.511 | 0.976855 | ||||||||
\(627\) | 197.636i | 0.315209i | ||||||||
\(628\) | 18.5794i | 0.0295851i | ||||||||
\(629\) | − | 36.2969i | − | 0.0577057i | ||||||
\(630\) | − | 205.431i | − | 0.326081i | ||||||
\(631\) | −647.088 | −1.02550 | −0.512748 | − | 0.858539i | \(-0.671372\pi\) | ||||
−0.512748 | + | 0.858539i | \(0.671372\pi\) | |||||||
\(632\) | 1034.00i | 1.63608i | ||||||||
\(633\) | 531.920i | 0.840316i | ||||||||
\(634\) | − | 646.913i | − | 1.02037i | ||||||
\(635\) | 1061.63 | 1.67185 | ||||||||
\(636\) | 47.2867 | 0.0743501 | ||||||||
\(637\) | − | 35.8246i | − | 0.0562395i | ||||||
\(638\) | 1196.70 | 1.87571 | ||||||||
\(639\) | 171.576 | 0.268508 | ||||||||
\(640\) | 159.663i | 0.249473i | ||||||||
\(641\) | 463.987 | 0.723848 | 0.361924 | − | 0.932208i | \(-0.382120\pi\) | ||||
0.361924 | + | 0.932208i | \(0.382120\pi\) | |||||||
\(642\) | − | 539.501i | − | 0.840344i | ||||||
\(643\) | −12.4294 | −0.0193304 | −0.00966518 | − | 0.999953i | \(-0.503077\pi\) | ||||
−0.00966518 | + | 0.999953i | \(0.503077\pi\) | |||||||
\(644\) | − | 313.399i | − | 0.486645i | ||||||
\(645\) | − | 238.933i | − | 0.370438i | ||||||
\(646\) | 216.875i | 0.335720i | ||||||||
\(647\) | 879.244 | 1.35895 | 0.679477 | − | 0.733696i | \(-0.262207\pi\) | ||||
0.679477 | + | 0.733696i | \(0.262207\pi\) | |||||||
\(648\) | 78.3672i | 0.120937i | ||||||||
\(649\) | 944.018 | − | 75.1203i | 1.45457 | − | 0.115748i | ||||
\(650\) | −196.514 | −0.302329 | ||||||||
\(651\) | − | 340.823i | − | 0.523537i | ||||||
\(652\) | 317.218 | 0.486530 | ||||||||
\(653\) | 200.318 | 0.306766 | 0.153383 | − | 0.988167i | \(-0.450983\pi\) | ||||
0.153383 | + | 0.988167i | \(0.450983\pi\) | |||||||
\(654\) | 183.050 | 0.279893 | ||||||||
\(655\) | − | 289.849i | − | 0.442518i | ||||||
\(656\) | −393.291 | −0.599529 | ||||||||
\(657\) | 209.022i | 0.318145i | ||||||||
\(658\) | 810.701 | 1.23207 | ||||||||
\(659\) | − | 652.030i | − | 0.989423i | −0.869057 | − | 0.494712i | \(-0.835274\pi\) | ||
0.869057 | − | 0.494712i | \(-0.164726\pi\) | |||||||
\(660\) | − | 247.139i | − | 0.374453i | ||||||
\(661\) | −440.130 | −0.665855 | −0.332928 | − | 0.942952i | \(-0.608036\pi\) | ||||
−0.332928 | + | 0.942952i | \(0.608036\pi\) | |||||||
\(662\) | − | 414.570i | − | 0.626238i | ||||||
\(663\) | 256.742i | 0.387243i | ||||||||
\(664\) | −751.611 | −1.13194 | ||||||||
\(665\) | −301.686 | −0.453663 | ||||||||
\(666\) | 9.29353 | 0.0139543 | ||||||||
\(667\) | 1555.87i | 2.33264i | ||||||||
\(668\) | 246.780 | 0.369431 | ||||||||
\(669\) | −578.666 | −0.864972 | ||||||||
\(670\) | −926.471 | −1.38279 | ||||||||
\(671\) | 659.070 | 0.982221 | ||||||||
\(672\) | 244.416i | 0.363714i | ||||||||
\(673\) | 178.659i | 0.265466i | 0.991152 | + | 0.132733i | \(0.0423754\pi\) | ||||
−0.991152 | + | 0.132733i | \(0.957625\pi\) | |||||||
\(674\) | −838.802 | −1.24451 | ||||||||
\(675\) | 80.7140 | 0.119576 | ||||||||
\(676\) | 150.143 | 0.222105 | ||||||||
\(677\) | −890.544 | −1.31543 | −0.657713 | − | 0.753268i | \(-0.728476\pi\) | ||||
−0.657713 | + | 0.753268i | \(0.728476\pi\) | |||||||
\(678\) | 475.053 | 0.700667 | ||||||||
\(679\) | − | 160.272i | − | 0.236041i | ||||||
\(680\) | − | 1048.10i | − | 1.54133i | ||||||
\(681\) | 336.744i | 0.494484i | ||||||||
\(682\) | 764.578i | 1.12108i | ||||||||
\(683\) | − | 230.871i | − | 0.338025i | −0.985614 | − | 0.169013i | \(-0.945942\pi\) | ||
0.985614 | − | 0.169013i | \(-0.0540578\pi\) | |||||||
\(684\) | 29.7785 | 0.0435359 | ||||||||
\(685\) | 679.293 | 0.991669 | ||||||||
\(686\) | − | 576.175i | − | 0.839905i | ||||||
\(687\) | − | 344.374i | − | 0.501273i | ||||||
\(688\) | − | 183.420i | − | 0.266599i | ||||||
\(689\) | 153.297i | 0.222492i | ||||||||
\(690\) | −599.164 | −0.868353 | ||||||||
\(691\) | − | 305.505i | − | 0.442120i | −0.975260 | − | 0.221060i | \(-0.929048\pi\) | ||
0.975260 | − | 0.221060i | \(-0.0709516\pi\) | |||||||
\(692\) | 258.168i | 0.373075i | ||||||||
\(693\) | 320.968i | 0.463157i | ||||||||
\(694\) | 233.504 | 0.336462 | ||||||||
\(695\) | 850.808 | 1.22418 | ||||||||
\(696\) | − | 696.857i | − | 1.00123i | ||||||
\(697\) | 878.378 | 1.26023 | ||||||||
\(698\) | 717.315 | 1.02767 | ||||||||
\(699\) | − | 465.041i | − | 0.665295i | ||||||
\(700\) | 144.572 | 0.206531 | ||||||||
\(701\) | 309.337i | 0.441280i | 0.975355 | + | 0.220640i | \(0.0708146\pi\) | ||||
−0.975355 | + | 0.220640i | \(0.929185\pi\) | |||||||
\(702\) | −65.7368 | −0.0936422 | ||||||||
\(703\) | − | 13.6480i | − | 0.0194140i | ||||||
\(704\) | − | 1091.80i | − | 1.55086i | ||||||
\(705\) | 831.170i | 1.17896i | ||||||||
\(706\) | −1009.82 | −1.43035 | ||||||||
\(707\) | 376.465i | 0.532482i | ||||||||
\(708\) | −11.3186 | − | 142.238i | −0.0159868 | − | 0.200902i | ||||
\(709\) | −1363.47 | −1.92309 | −0.961543 | − | 0.274655i | \(-0.911436\pi\) | ||||
−0.961543 | + | 0.274655i | \(0.911436\pi\) | |||||||
\(710\) | − | 587.543i | − | 0.827525i | ||||||
\(711\) | 356.247 | 0.501050 | ||||||||
\(712\) | −335.181 | −0.470760 | ||||||||
\(713\) | −994.049 | −1.39418 | ||||||||
\(714\) | 352.213i | 0.493295i | ||||||||
\(715\) | 801.191 | 1.12055 | ||||||||
\(716\) | − | 406.215i | − | 0.567340i | ||||||
\(717\) | 556.794 | 0.776561 | ||||||||
\(718\) | − | 566.838i | − | 0.789468i | ||||||
\(719\) | 358.898i | 0.499162i | 0.968354 | + | 0.249581i | \(0.0802929\pi\) | ||||
−0.968354 | + | 0.249581i | \(0.919707\pi\) | |||||||
\(720\) | 161.684 | 0.224561 | ||||||||
\(721\) | 664.542i | 0.921694i | ||||||||
\(722\) | − | 500.963i | − | 0.693854i | ||||||
\(723\) | −77.9380 | −0.107798 | ||||||||
\(724\) | 100.525 | 0.138847 | ||||||||
\(725\) | −717.725 | −0.989966 | ||||||||
\(726\) | − | 381.861i | − | 0.525980i | ||||||
\(727\) | 123.204 | 0.169469 | 0.0847345 | − | 0.996404i | \(-0.472996\pi\) | ||||
0.0847345 | + | 0.996404i | \(0.472996\pi\) | |||||||
\(728\) | −455.055 | −0.625075 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 715.769 | 0.980506 | ||||||||
\(731\) | 409.652i | 0.560399i | ||||||||
\(732\) | − | 99.3043i | − | 0.135662i | ||||||
\(733\) | 505.875 | 0.690143 | 0.345071 | − | 0.938576i | \(-0.387855\pi\) | ||||
0.345071 | + | 0.938576i | \(0.387855\pi\) | |||||||
\(734\) | −357.093 | −0.486503 | ||||||||
\(735\) | 50.3869 | 0.0685536 | ||||||||
\(736\) | 712.868 | 0.968571 | ||||||||
\(737\) | 1447.53 | 1.96408 | ||||||||
\(738\) | 224.902i | 0.304745i | ||||||||
\(739\) | − | 214.823i | − | 0.290694i | −0.989381 | − | 0.145347i | \(-0.953570\pi\) | ||
0.989381 | − | 0.145347i | \(-0.0464298\pi\) | |||||||
\(740\) | 17.0665i | 0.0230628i | ||||||||
\(741\) | 96.5380i | 0.130281i | ||||||||
\(742\) | 210.301i | 0.283425i | ||||||||
\(743\) | −919.142 | −1.23707 | −0.618534 | − | 0.785758i | \(-0.712273\pi\) | ||||
−0.618534 | + | 0.785758i | \(0.712273\pi\) | |||||||
\(744\) | 445.224 | 0.598419 | ||||||||
\(745\) | 752.710i | 1.01035i | ||||||||
\(746\) | − | 257.448i | − | 0.345105i | ||||||
\(747\) | 258.954i | 0.346659i | ||||||||
\(748\) | 423.721i | 0.566472i | ||||||||
\(749\) | −1286.70 | −1.71789 | ||||||||
\(750\) | 168.445i | 0.224593i | ||||||||
\(751\) | − | 448.537i | − | 0.597254i | −0.954370 | − | 0.298627i | \(-0.903471\pi\) | ||
0.954370 | − | 0.298627i | \(-0.0965286\pi\) | |||||||
\(752\) | 638.060i | 0.848484i | ||||||||
\(753\) | 532.219 | 0.706798 | ||||||||
\(754\) | 584.545 | 0.775259 | ||||||||
\(755\) | − | 1409.37i | − | 1.86672i | ||||||
\(756\) | 48.3613 | 0.0639700 | ||||||||
\(757\) | −250.783 | −0.331286 | −0.165643 | − | 0.986186i | \(-0.552970\pi\) | ||||
−0.165643 | + | 0.986186i | \(0.552970\pi\) | |||||||
\(758\) | 426.102i | 0.562140i | ||||||||
\(759\) | 936.141 | 1.23339 | ||||||||
\(760\) | − | 394.099i | − | 0.518551i | ||||||
\(761\) | 746.517 | 0.980968 | 0.490484 | − | 0.871450i | \(-0.336820\pi\) | ||||
0.490484 | + | 0.871450i | \(0.336820\pi\) | |||||||
\(762\) | − | 466.039i | − | 0.611599i | ||||||
\(763\) | − | 436.570i | − | 0.572175i | ||||||
\(764\) | − | 237.262i | − | 0.310552i | ||||||
\(765\) | −361.105 | −0.472033 | ||||||||
\(766\) | − | 143.978i | − | 0.187961i | ||||||
\(767\) | 461.118 | − | 36.6935i | 0.601196 | − | 0.0478403i | ||||
\(768\) | −401.177 | −0.522365 | ||||||||
\(769\) | − | 1189.01i | − | 1.54618i | −0.634296 | − | 0.773091i | \(-0.718710\pi\) | ||
0.634296 | − | 0.773091i | \(-0.281290\pi\) | |||||||
\(770\) | 1099.12 | 1.42742 | ||||||||
\(771\) | −466.370 | −0.604889 | ||||||||
\(772\) | −21.8398 | −0.0282899 | ||||||||
\(773\) | − | 900.789i | − | 1.16532i | −0.812717 | − | 0.582658i | \(-0.802013\pi\) | ||
0.812717 | − | 0.582658i | \(-0.197987\pi\) | |||||||
\(774\) | −104.888 | −0.135514 | ||||||||
\(775\) | − | 458.557i | − | 0.591686i | ||||||
\(776\) | 209.366 | 0.269802 | ||||||||
\(777\) | − | 22.1649i | − | 0.0285262i | ||||||
\(778\) | − | 260.303i | − | 0.334580i | ||||||
\(779\) | 330.280 | 0.423980 | ||||||||
\(780\) | − | 120.718i | − | 0.154767i | ||||||
\(781\) | 917.985i | 1.17540i | ||||||||
\(782\) | 1027.27 | 1.31364 | ||||||||
\(783\) | −240.090 | −0.306628 | ||||||||
\(784\) | 38.6803 | 0.0493371 | ||||||||
\(785\) | − | 84.7157i | − | 0.107918i | ||||||
\(786\) | −127.240 | −0.161883 | ||||||||
\(787\) | −212.704 | −0.270272 | −0.135136 | − | 0.990827i | \(-0.543147\pi\) | ||||
−0.135136 | + | 0.990827i | \(0.543147\pi\) | |||||||
\(788\) | −140.463 | −0.178252 | ||||||||
\(789\) | −509.397 | −0.645624 | ||||||||
\(790\) | − | 1219.92i | − | 1.54421i | ||||||
\(791\) | − | 1132.99i | − | 1.43235i | ||||||
\(792\) | −419.287 | −0.529403 | ||||||||
\(793\) | 321.931 | 0.405966 | ||||||||
\(794\) | 838.610 | 1.05618 | ||||||||
\(795\) | −215.611 | −0.271209 | ||||||||
\(796\) | −117.974 | −0.148208 | ||||||||
\(797\) | − | 487.589i | − | 0.611780i | −0.952067 | − | 0.305890i | \(-0.901046\pi\) | ||
0.952067 | − | 0.305890i | \(-0.0989540\pi\) | |||||||
\(798\) | 132.436i | 0.165960i | ||||||||
\(799\) | − | 1425.05i | − | 1.78354i | ||||||
\(800\) | 328.847i | 0.411059i | ||||||||
\(801\) | 115.481i | 0.144171i | ||||||||
\(802\) | −888.353 | −1.10767 | ||||||||
\(803\) | −1118.33 | −1.39269 | ||||||||
\(804\) | − | 218.104i | − | 0.271274i | ||||||
\(805\) | 1428.99i | 1.77515i | ||||||||
\(806\) | 373.468i | 0.463360i | ||||||||
\(807\) | − | 91.0424i | − | 0.112816i | ||||||
\(808\) | −491.784 | −0.608643 | ||||||||
\(809\) | 913.419i | 1.12907i | 0.825408 | + | 0.564536i | \(0.190945\pi\) | ||||
−0.825408 | + | 0.564536i | \(0.809055\pi\) | |||||||
\(810\) | − | 92.4582i | − | 0.114146i | ||||||
\(811\) | − | 569.765i | − | 0.702547i | −0.936273 | − | 0.351273i | \(-0.885749\pi\) | ||
0.936273 | − | 0.351273i | \(-0.114251\pi\) | |||||||
\(812\) | −430.039 | −0.529604 | ||||||||
\(813\) | −110.098 | −0.135422 | ||||||||
\(814\) | 49.7231i | 0.0610849i | ||||||||
\(815\) | −1446.40 | −1.77473 | ||||||||
\(816\) | −277.208 | −0.339716 | ||||||||
\(817\) | 154.034i | 0.188536i | ||||||||
\(818\) | 28.8388 | 0.0352553 | ||||||||
\(819\) | 156.781i | 0.191430i | ||||||||
\(820\) | −413.006 | −0.503666 | ||||||||
\(821\) | 1353.27i | 1.64832i | 0.566359 | + | 0.824158i | \(0.308351\pi\) | ||||
−0.566359 | + | 0.824158i | \(0.691649\pi\) | |||||||
\(822\) | − | 298.200i | − | 0.362774i | ||||||
\(823\) | − | 1255.98i | − | 1.52610i | −0.646340 | − | 0.763049i | \(-0.723701\pi\) | ||
0.646340 | − | 0.763049i | \(-0.276299\pi\) | |||||||
\(824\) | −868.105 | −1.05353 | ||||||||
\(825\) | 431.843i | 0.523447i | ||||||||
\(826\) | 632.586 | − | 50.3381i | 0.765842 | − | 0.0609420i | ||||
\(827\) | −1318.17 | −1.59392 | −0.796961 | − | 0.604031i | \(-0.793560\pi\) | ||||
−0.796961 | + | 0.604031i | \(0.793560\pi\) | |||||||
\(828\) | − | 141.051i | − | 0.170352i | ||||||
\(829\) | −329.831 | −0.397866 | −0.198933 | − | 0.980013i | \(-0.563748\pi\) | ||||
−0.198933 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(830\) | 886.758 | 1.06838 | ||||||||
\(831\) | −131.663 | −0.158439 | ||||||||
\(832\) | − | 533.306i | − | 0.640992i | ||||||
\(833\) | −86.3887 | −0.103708 | ||||||||
\(834\) | − | 373.493i | − | 0.447833i | ||||||
\(835\) | −1125.23 | −1.34758 | ||||||||
\(836\) | 159.324i | 0.190579i | ||||||||
\(837\) | − | 153.394i | − | 0.183266i | ||||||
\(838\) | 30.3060 | 0.0361647 | ||||||||
\(839\) | 949.502i | 1.13171i | 0.824506 | + | 0.565853i | \(0.191453\pi\) | ||||
−0.824506 | + | 0.565853i | \(0.808547\pi\) | |||||||
\(840\) | − | 640.030i | − | 0.761940i | ||||||
\(841\) | 1293.92 | 1.53856 | ||||||||
\(842\) | 906.430 | 1.07652 | ||||||||
\(843\) | 254.122 | 0.301450 | ||||||||
\(844\) | 428.805i | 0.508063i | ||||||||
\(845\) | −684.601 | −0.810179 | ||||||||
\(846\) | 364.872 | 0.431291 | ||||||||
\(847\) | −910.731 | −1.07524 | ||||||||
\(848\) | −165.517 | −0.195185 | ||||||||
\(849\) | 861.705i | 1.01496i | ||||||||
\(850\) | 473.881i | 0.557507i | ||||||||
\(851\) | −64.6464 | −0.0759653 | ||||||||
\(852\) | 138.316 | 0.162343 | ||||||||
\(853\) | 442.888 | 0.519213 | 0.259606 | − | 0.965715i | \(-0.416407\pi\) | ||||
0.259606 | + | 0.965715i | \(0.416407\pi\) | |||||||
\(854\) | 441.642 | 0.517146 | ||||||||
\(855\) | −135.780 | −0.158807 | ||||||||
\(856\) | − | 1680.84i | − | 1.96360i | ||||||
\(857\) | − | 1181.30i | − | 1.37841i | −0.724567 | − | 0.689204i | \(-0.757960\pi\) | ||
0.724567 | − | 0.689204i | \(-0.242040\pi\) | |||||||
\(858\) | − | 351.711i | − | 0.409920i | ||||||
\(859\) | − | 822.613i | − | 0.957641i | −0.877913 | − | 0.478820i | \(-0.841065\pi\) | ||
0.877913 | − | 0.478820i | \(-0.158935\pi\) | |||||||
\(860\) | − | 192.615i | − | 0.223971i | ||||||
\(861\) | 536.386 | 0.622980 | ||||||||
\(862\) | −70.7271 | −0.0820500 | ||||||||
\(863\) | − | 220.298i | − | 0.255270i | −0.991821 | − | 0.127635i | \(-0.959261\pi\) | ||
0.991821 | − | 0.127635i | \(-0.0407385\pi\) | |||||||
\(864\) | 110.004i | 0.127320i | ||||||||
\(865\) | − | 1177.16i | − | 1.36087i | ||||||
\(866\) | 162.251i | 0.187356i | ||||||||
\(867\) | 118.555 | 0.136741 | ||||||||
\(868\) | − | 274.753i | − | 0.316536i | ||||||
\(869\) | 1906.02i | 2.19335i | ||||||||
\(870\) | 822.158i | 0.945009i | ||||||||
\(871\) | 707.065 | 0.811785 | ||||||||
\(872\) | 570.300 | 0.654014 | ||||||||
\(873\) | − | 72.1334i | − | 0.0826270i | ||||||
\(874\) | 386.265 | 0.441951 | ||||||||
\(875\) | 401.737 | 0.459128 | ||||||||
\(876\) | 168.502i | 0.192354i | ||||||||
\(877\) | 985.610 | 1.12384 | 0.561921 | − | 0.827191i | \(-0.310062\pi\) | ||||
0.561921 | + | 0.827191i | \(0.310062\pi\) | |||||||
\(878\) | 936.165i | 1.06625i | ||||||||
\(879\) | 274.744 | 0.312565 | ||||||||
\(880\) | 865.056i | 0.983019i | ||||||||
\(881\) | 444.402i | 0.504429i | 0.967671 | + | 0.252215i | \(0.0811589\pi\) | ||||
−0.967671 | + | 0.252215i | \(0.918841\pi\) | |||||||
\(882\) | − | 22.1191i | − | 0.0250784i | ||||||
\(883\) | 268.071 | 0.303592 | 0.151796 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151796 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(884\) | 206.972i | 0.234131i | ||||||||
\(885\) | 51.6090 | + | 648.558i | 0.0583153 | + | 0.732833i | ||||
\(886\) | −1231.84 | −1.39034 | ||||||||
\(887\) | 231.757i | 0.261282i | 0.991430 | + | 0.130641i | \(0.0417035\pi\) | ||||
−0.991430 | + | 0.130641i | \(0.958297\pi\) | |||||||
\(888\) | 28.9544 | 0.0326064 | ||||||||
\(889\) | −1111.49 | −1.25027 | ||||||||
\(890\) | 395.449 | 0.444325 | ||||||||
\(891\) | 144.458i | 0.162130i | ||||||||
\(892\) | −466.490 | −0.522971 | ||||||||
\(893\) | − | 535.833i | − | 0.600037i | ||||||
\(894\) | 330.429 | 0.369607 | ||||||||
\(895\) | 1852.20i | 2.06950i | ||||||||
\(896\) | − | 167.162i | − | 0.186565i | ||||||
\(897\) | 457.270 | 0.509777 | ||||||||
\(898\) | 565.703i | 0.629958i | ||||||||
\(899\) | 1364.01i | 1.51725i | ||||||||
\(900\) | 65.0673 | 0.0722970 | ||||||||
\(901\) | 369.666 | 0.410284 | ||||||||
\(902\) | −1203.29 | −1.33403 | ||||||||
\(903\) | 250.156i | 0.277027i | ||||||||
\(904\) | 1480.05 | 1.63722 | ||||||||
\(905\) | −458.361 | −0.506476 | ||||||||
\(906\) | −618.696 | −0.682887 | ||||||||
\(907\) | 569.019 | 0.627364 | 0.313682 | − | 0.949528i | \(-0.398437\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398437\pi\) | |||||||
\(908\) | 271.465i | 0.298970i | ||||||||
\(909\) | 169.435i | 0.186397i | ||||||||
\(910\) | 536.877 | 0.589975 | ||||||||
\(911\) | −557.041 | −0.611461 | −0.305730 | − | 0.952118i | \(-0.598901\pi\) | ||||
−0.305730 | + | 0.952118i | \(0.598901\pi\) | |||||||
\(912\) | −104.233 | −0.114291 | ||||||||
\(913\) | −1385.48 | −1.51750 | ||||||||
\(914\) | −1013.32 | −1.10867 | ||||||||
\(915\) | 452.793i | 0.494856i | ||||||||
\(916\) | − | 277.616i | − | 0.303075i | ||||||
\(917\) | 303.464i | 0.330931i | ||||||||
\(918\) | 158.520i | 0.172680i | ||||||||
\(919\) | 389.979i | 0.424351i | 0.977232 | + | 0.212176i | \(0.0680549\pi\) | ||||
−0.977232 | + | 0.212176i | \(0.931945\pi\) | |||||||
\(920\) | −1866.72 | −2.02905 | ||||||||
\(921\) | 524.161 | 0.569121 | ||||||||
\(922\) | 972.588i | 1.05487i | ||||||||
\(923\) | 448.401i | 0.485809i | ||||||||
\(924\) | 258.747i | 0.280030i | ||||||||
\(925\) | − | 29.8215i | − | 0.0322395i | ||||||
\(926\) | −549.841 | −0.593781 | ||||||||
\(927\) | 299.090i | 0.322643i | ||||||||
\(928\) | − | 978.180i | − | 1.05407i | ||||||
\(929\) | − | 235.870i | − | 0.253897i | −0.991909 | − | 0.126948i | \(-0.959482\pi\) | ||
0.991909 | − | 0.126948i | \(-0.0405183\pi\) | |||||||
\(930\) | −525.279 | −0.564816 | ||||||||
\(931\) | −32.4831 | −0.0348906 | ||||||||
\(932\) | − | 374.892i | − | 0.402244i | ||||||
\(933\) | 944.050 | 1.01184 | ||||||||
\(934\) | 1101.56 | 1.17940 | ||||||||
\(935\) | − | 1932.02i | − | 2.06633i | ||||||
\(936\) | −204.806 | −0.218810 | ||||||||
\(937\) | − | 772.809i | − | 0.824770i | −0.911010 | − | 0.412385i | \(-0.864696\pi\) | ||
0.911010 | − | 0.412385i | \(-0.135304\pi\) | |||||||
\(938\) | 969.989 | 1.03410 | ||||||||
\(939\) | − | 656.400i | − | 0.699042i | ||||||
\(940\) | 670.045i | 0.712814i | ||||||||
\(941\) | 1275.95i | 1.35595i | 0.735086 | + | 0.677974i | \(0.237142\pi\) | ||||
−0.735086 | + | 0.677974i | \(0.762858\pi\) | |||||||
\(942\) | −37.1890 | −0.0394788 | ||||||||
\(943\) | − | 1564.43i | − | 1.65900i | ||||||
\(944\) | 39.6184 | + | 497.875i | 0.0419687 | + | 0.527410i | ||||
\(945\) | −220.511 | −0.233345 | ||||||||
\(946\) | − | 561.182i | − | 0.593216i | ||||||
\(947\) | 1385.44 | 1.46297 | 0.731487 | − | 0.681855i | \(-0.238827\pi\) | ||||
0.731487 | + | 0.681855i | \(0.238827\pi\) | |||||||
\(948\) | 287.187 | 0.302940 | ||||||||
\(949\) | −546.261 | −0.575618 | ||||||||
\(950\) | 178.185i | 0.187563i | ||||||||
\(951\) | −694.401 | −0.730179 | ||||||||
\(952\) | 1097.34i | 1.15266i | ||||||||
\(953\) | −1150.91 | −1.20767 | −0.603835 | − | 0.797109i | \(-0.706362\pi\) | ||||
−0.603835 | + | 0.797109i | \(0.706362\pi\) | |||||||
\(954\) | 94.6501i | 0.0992140i | ||||||||
\(955\) | 1081.83i | 1.13281i | ||||||||
\(956\) | 448.858 | 0.469517 | ||||||||
\(957\) | − | 1284.55i | − | 1.34227i | ||||||
\(958\) | − | 1222.99i | − | 1.27661i | ||||||
\(959\) | −711.200 | −0.741606 | ||||||||
\(960\) | 750.089 | 0.781343 | ||||||||
\(961\) | 89.5293 | 0.0931626 | ||||||||
\(962\) | 24.2879i | 0.0252473i | ||||||||
\(963\) | −579.103 | −0.601354 | ||||||||
\(964\) | −62.8295 | −0.0651758 | ||||||||
\(965\) | 99.5819 | 0.103194 | ||||||||
\(966\) | 627.307 | 0.649386 | ||||||||
\(967\) | 876.840i | 0.906763i | 0.891317 | + | 0.453382i | \(0.149782\pi\) | ||||
−0.891317 | + | 0.453382i | \(0.850218\pi\) | |||||||
\(968\) | − | 1189.71i | − | 1.22904i | ||||||
\(969\) | 232.795 | 0.240243 | ||||||||
\(970\) | −247.012 | −0.254652 | ||||||||
\(971\) | 794.804 | 0.818542 | 0.409271 | − | 0.912413i | \(-0.365783\pi\) | ||||
0.409271 | + | 0.912413i | \(0.365783\pi\) | |||||||
\(972\) | 21.7660 | 0.0223930 | ||||||||
\(973\) | −890.772 | −0.915490 | ||||||||
\(974\) | − | 170.124i | − | 0.174665i | ||||||
\(975\) | 210.939i | 0.216348i | ||||||||
\(976\) | 347.594i | 0.356141i | ||||||||
\(977\) | 1736.90i | 1.77779i | 0.458114 | + | 0.888893i | \(0.348525\pi\) | ||||
−0.458114 | + | 0.888893i | \(0.651475\pi\) | |||||||
\(978\) | 634.950i | 0.649233i | ||||||||
\(979\) | −617.855 | −0.631108 | ||||||||
\(980\) | 40.6192 | 0.0414482 | ||||||||
\(981\) | − | 196.487i | − | 0.200292i | ||||||
\(982\) | − | 973.908i | − | 0.991760i | ||||||
\(983\) | 427.042i | 0.434427i | 0.976124 | + | 0.217214i | \(0.0696968\pi\) | ||||
−0.976124 | + | 0.217214i | \(0.930303\pi\) | |||||||
\(984\) | 700.693i | 0.712086i | ||||||||
\(985\) | 640.460 | 0.650214 | ||||||||
\(986\) | − | 1409.59i | − | 1.42961i | ||||||
\(987\) | − | 870.211i | − | 0.881673i | ||||||
\(988\) | 77.8238i | 0.0787690i | ||||||||
\(989\) | 729.609 | 0.737724 | ||||||||
\(990\) | 494.679 | 0.499676 | ||||||||
\(991\) | 1352.88i | 1.36517i | 0.730806 | + | 0.682585i | \(0.239144\pi\) | ||||
−0.730806 | + | 0.682585i | \(0.760856\pi\) | |||||||
\(992\) | 624.963 | 0.630003 | ||||||||
\(993\) | −445.002 | −0.448139 | ||||||||
\(994\) | 615.141i | 0.618854i | ||||||||
\(995\) | 537.918 | 0.540621 | ||||||||
\(996\) | 208.755i | 0.209594i | ||||||||
\(997\) | 1441.02 | 1.44535 | 0.722676 | − | 0.691187i | \(-0.242912\pi\) | ||||
0.722676 | + | 0.691187i | \(0.242912\pi\) | |||||||
\(998\) | 497.548i | 0.498545i | ||||||||
\(999\) | − | 9.97573i | − | 0.00998572i |
(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 | 177.3.c.a.58.14 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.7 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.7 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.14 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.7 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.14 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.7 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.14 | 20 | 177.176 | even | 2 |