Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,3,Mod(189,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.189");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.g (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: | \(10.3542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 44x^{8} - 270x^{6} + 36676x^{4} - 71664x^{2} + 687241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 189.6 | ||
Root | \(0.975196 + 4.19028i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.189 |
Dual form | 380.3.g.c.189.5 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.95039 | −0.650131 | −0.325065 | − | 0.945692i | \(-0.605386\pi\) | ||||
−0.325065 | + | 0.945692i | \(0.605386\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.75473 | + | 4.17271i | −0.550946 | + | 0.834541i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.18749i | − | 0.312499i | −0.987718 | − | 0.156249i | \(-0.950060\pi\) | ||
0.987718 | − | 0.156249i | \(-0.0499403\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.19597 | −0.577330 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.50946 | −0.864496 | −0.432248 | − | 0.901755i | \(-0.642280\pi\) | ||||
−0.432248 | + | 0.901755i | \(0.642280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.4976 | 1.57674 | 0.788368 | − | 0.615204i | \(-0.210926\pi\) | ||||
0.788368 | + | 0.615204i | \(0.210926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.37280 | − | 8.13841i | 0.358187 | − | 0.542561i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.15792i | − | 0.362231i | −0.983462 | − | 0.181115i | \(-0.942029\pi\) | ||
0.983462 | − | 0.181115i | \(-0.0579707\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.68651 | − | 16.3454i | 0.509816 | − | 0.860283i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.26647i | 0.203165i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 10.9375i | − | 0.475541i | −0.971321 | − | 0.237771i | \(-0.923583\pi\) | ||
0.971321 | − | 0.237771i | \(-0.0764167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.82294 | − | 22.9893i | −0.392918 | − | 0.919574i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.6877 | 1.02547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 28.4243i | 0.980148i | 0.871681 | + | 0.490074i | \(0.163030\pi\) | ||||
−0.871681 | + | 0.490074i | \(0.836970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 24.8098i | − | 0.800315i | −0.916446 | − | 0.400157i | \(-0.868955\pi\) | ||
0.916446 | − | 0.400157i | \(-0.131045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.5472 | 0.562035 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.12776 | + | 6.02594i | 0.260793 | + | 0.172170i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.4397 | 1.01188 | 0.505941 | − | 0.862568i | \(-0.331145\pi\) | ||||
0.505941 | + | 0.862568i | \(0.331145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.9783 | −1.02508 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 81.6583i | − | 1.99167i | −0.0911903 | − | 0.995833i | \(-0.529067\pi\) | ||
0.0911903 | − | 0.995833i | \(-0.470933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 70.8743i | − | 1.64824i | −0.566415 | − | 0.824120i | \(-0.691670\pi\) | ||
0.566415 | − | 0.824120i | \(-0.308330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.3135 | − | 21.6813i | 0.318077 | − | 0.481806i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.1193i | 0.981261i | 0.871368 | + | 0.490631i | \(0.163234\pi\) | ||||
−0.871368 | + | 0.490631i | \(0.836766\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.2149 | 0.902345 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0104i | 0.235497i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32.1999 | −0.607546 | −0.303773 | − | 0.952745i | \(-0.598246\pi\) | ||||
−0.303773 | + | 0.952745i | \(0.598246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.1960 | − | 39.6802i | 0.476290 | − | 0.721458i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.8925 | + | 31.8799i | −0.331447 | + | 0.559297i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 94.3206i | − | 1.59865i | −0.600896 | − | 0.799327i | \(-0.705189\pi\) | ||
0.600896 | − | 0.799327i | \(-0.294811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.566 | −1.68141 | −0.840707 | − | 0.541491i | \(-0.817860\pi\) | ||||
−0.840707 | + | 0.541491i | \(0.817860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.3661i | 0.180415i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −56.4652 | + | 85.5303i | −0.868696 | + | 1.31585i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.0282 | 1.03027 | 0.515136 | − | 0.857109i | \(-0.327742\pi\) | ||||
0.515136 | + | 0.857109i | \(0.327742\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.3323i | 0.309164i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 40.5718i | − | 0.571433i | −0.958314 | − | 0.285717i | \(-0.907768\pi\) | ||
0.958314 | − | 0.285717i | \(-0.0922316\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 102.209i | 1.40012i | 0.714082 | + | 0.700062i | \(0.246844\pi\) | ||||
−0.714082 | + | 0.700062i | \(0.753156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 19.1586 | + | 44.8382i | 0.255448 | + | 0.597843i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.8018i | 0.270154i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 73.9145i | 0.935626i | 0.883827 | + | 0.467813i | \(0.154958\pi\) | ||||
−0.883827 | + | 0.467813i | \(0.845042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.23816 | −0.0893600 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 91.9574i | − | 1.10792i | −0.832543 | − | 0.553960i | \(-0.813116\pi\) | ||
0.832543 | − | 0.553960i | \(-0.186884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.6952 | + | 16.9634i | 0.302296 | + | 0.199569i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 55.4385i | − | 0.637224i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 57.3634i | 0.644533i | 0.946649 | + | 0.322266i | \(0.104445\pi\) | ||||
−0.946649 | + | 0.322266i | \(0.895555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 44.8382i | − | 0.492728i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.3888i | 0.520309i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 41.5207 | + | 85.4461i | 0.437060 | + | 0.899432i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −84.3229 | −0.869308 | −0.434654 | − | 0.900598i | \(-0.643129\pi\) | ||||
−0.434654 | + | 0.900598i | \(0.643129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 49.4109 | 0.499100 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 69.2688 | 0.685830 | 0.342915 | − | 0.939366i | \(-0.388586\pi\) | ||||
0.342915 | + | 0.939366i | \(0.388586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 100.192 | 0.972739 | 0.486369 | − | 0.873753i | \(-0.338321\pi\) | ||||
0.486369 | + | 0.873753i | \(0.338321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.8027 | − | 11.7530i | −0.169550 | − | 0.111933i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −52.7344 | −0.492845 | −0.246422 | − | 0.969163i | \(-0.579255\pi\) | ||||
−0.246422 | + | 0.969163i | \(0.579255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 76.7400i | 0.704036i | 0.935993 | + | 0.352018i | \(0.114504\pi\) | ||||
−0.935993 | + | 0.352018i | \(0.885496\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −73.0220 | −0.657856 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −210.252 | −1.86064 | −0.930320 | − | 0.366749i | \(-0.880471\pi\) | ||||
−0.930320 | + | 0.366749i | \(0.880471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 45.6388 | + | 30.1297i | 0.396859 | + | 0.261998i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −106.505 | −0.910297 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.4704 | −0.113197 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.5702 | −0.252647 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 159.266i | 1.29484i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 122.987 | + | 22.3411i | 0.983898 | + | 0.178729i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9230 | 0.156874 | 0.0784371 | − | 0.996919i | \(-0.475007\pi\) | ||||
0.0784371 | + | 0.996919i | \(0.475007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 138.233i | 1.07157i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.29737 | −0.0251708 | −0.0125854 | − | 0.999921i | \(-0.504006\pi\) | ||||
−0.0125854 | + | 0.999921i | \(0.504006\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −35.7554 | − | 21.1892i | −0.268837 | − | 0.159317i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −76.2721 | + | 115.533i | −0.564979 | + | 0.855797i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 148.188i | 1.08166i | 0.841131 | + | 0.540831i | \(0.181890\pi\) | ||||
−0.841131 | + | 0.540831i | \(0.818110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −54.2729 | −0.390452 | −0.195226 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195226 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 89.9507i | − | 0.637948i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −194.921 | −1.36308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −118.606 | − | 78.3012i | −0.817974 | − | 0.540008i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −86.2364 | −0.586642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 160.700 | 1.07852 | 0.539262 | − | 0.842138i | \(-0.318703\pi\) | ||||
0.539262 | + | 0.842138i | \(0.318703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 285.273i | − | 1.88922i | −0.328192 | − | 0.944611i | \(-0.606439\pi\) | ||
0.328192 | − | 0.944611i | \(-0.393561\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.9964i | 0.209127i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 103.524 | + | 68.3441i | 0.667896 | + | 0.440930i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 189.486i | − | 1.20692i | −0.797394 | − | 0.603459i | \(-0.793789\pi\) | ||
0.797394 | − | 0.603459i | \(-0.206211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 62.8025 | 0.394984 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.9256 | −0.148606 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 152.943i | − | 0.938302i | −0.883118 | − | 0.469151i | \(-0.844560\pi\) | ||
0.883118 | − | 0.469151i | \(-0.155440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.0924 | + | 77.3919i | −0.309651 | + | 0.469042i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 89.7126 | 0.537201 | 0.268601 | − | 0.963252i | \(-0.413439\pi\) | ||||
0.268601 | + | 0.963252i | \(0.413439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 251.150 | 1.48610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −50.3308 | + | 84.9301i | −0.294332 | + | 0.496667i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 154.463 | 0.892851 | 0.446425 | − | 0.894821i | \(-0.352697\pi\) | ||||
0.446425 | + | 0.894821i | \(0.352697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −50.2890 | + | 21.4876i | −0.287366 | + | 0.122786i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 183.962i | 1.03933i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 138.885i | 0.775892i | 0.921682 | + | 0.387946i | \(0.126815\pi\) | ||||
−0.921682 | + | 0.387946i | \(0.873185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 106.605i | − | 0.588979i | −0.955655 | − | 0.294490i | \(-0.904850\pi\) | ||
0.955655 | − | 0.294490i | \(-0.0951496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 200.044 | 1.09314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −103.136 | + | 156.225i | −0.557493 | + | 0.844458i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 58.5585i | 0.313147i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 60.5666i | − | 0.320458i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −262.954 | −1.37672 | −0.688362 | − | 0.725367i | \(-0.741670\pi\) | ||||
−0.688362 | + | 0.725367i | \(0.741670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −34.0711 | −0.176534 | −0.0882670 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882670 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 110.129 | − | 166.818i | 0.564766 | − | 0.855475i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 293.544i | − | 1.49007i | −0.667026 | − | 0.745035i | \(-0.732433\pi\) | ||
0.667026 | − | 0.745035i | \(-0.267567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −144.876 | −0.728018 | −0.364009 | − | 0.931395i | \(-0.618592\pi\) | ||||
−0.364009 | + | 0.931395i | \(0.618592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −134.632 | −0.669811 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 62.1779 | 0.306295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 340.736 | + | 224.947i | 1.66213 | + | 1.09730i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 56.8307i | 0.274544i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −92.1135 | + | 155.436i | −0.440734 | + | 0.743711i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 355.298i | − | 1.68388i | −0.539573 | − | 0.841939i | \(-0.681414\pi\) | ||
0.539573 | − | 0.841939i | \(-0.318586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 79.1309i | 0.371506i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 295.738 | + | 195.239i | 1.37552 | + | 0.908091i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −54.2711 | −0.250097 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 199.348i | − | 0.910264i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 126.222i | − | 0.571142i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.367 | 1.48147 | 0.740734 | − | 0.671798i | \(-0.234478\pi\) | ||||
0.740734 | + | 0.671798i | \(0.234478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.0397 | + | 119.452i | 0.226843 | + | 0.530897i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4416 | −0.103267 | −0.0516335 | − | 0.998666i | \(-0.516443\pi\) | ||||
−0.0516335 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −183.710 | −0.802229 | −0.401114 | − | 0.916028i | \(-0.631377\pi\) | ||||
−0.401114 | + | 0.916028i | \(0.631377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 40.5718i | − | 0.175635i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 143.648i | − | 0.616515i | −0.951303 | − | 0.308258i | \(-0.900254\pi\) | ||
0.951303 | − | 0.308258i | \(-0.0997459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −192.442 | − | 127.046i | −0.818903 | − | 0.540622i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 144.162i | − | 0.608279i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −79.5051 | −0.332657 | −0.166329 | − | 0.986070i | \(-0.553191\pi\) | ||||
−0.166329 | + | 0.986070i | \(0.553191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 122.504i | − | 0.508317i | −0.967163 | − | 0.254158i | \(-0.918202\pi\) | ||
0.967163 | − | 0.254158i | \(-0.0817984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −235.072 | −0.967375 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −121.800 | + | 184.496i | −0.497143 | + | 0.753044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 198.550 | − | 335.040i | 0.803846 | − | 1.35644i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 179.353i | 0.720293i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2335 | 0.0766274 | 0.0383137 | − | 0.999266i | \(-0.487801\pi\) | ||||
0.0383137 | + | 0.999266i | \(0.487801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 104.009i | 0.411104i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −50.1157 | − | 33.0853i | −0.196532 | − | 0.129746i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 60.4198 | 0.235097 | 0.117548 | − | 0.993067i | \(-0.462497\pi\) | ||||
0.117548 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 81.8989i | − | 0.316212i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 147.692i | − | 0.565869i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 23.1886i | − | 0.0881694i | −0.999028 | − | 0.0440847i | \(-0.985963\pi\) | ||
0.999028 | − | 0.0440847i | \(-0.0140371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 88.7020 | − | 134.361i | 0.334725 | − | 0.507022i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 111.881i | − | 0.419030i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 211.221i | − | 0.785208i | −0.919708 | − | 0.392604i | \(-0.871574\pi\) | ||
0.919708 | − | 0.392604i | \(-0.128426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −371.216 | −1.36980 | −0.684901 | − | 0.728637i | \(-0.740154\pi\) | ||||
−0.684901 | + | 0.728637i | \(0.740154\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 87.4521i | 0.320337i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 93.4109 | + | 218.616i | 0.339676 | + | 0.794968i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.90841i | − | 0.0249401i | −0.999922 | − | 0.0124701i | \(-0.996031\pi\) | ||
0.999922 | − | 0.0124701i | \(-0.00396944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 128.911i | 0.462046i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.46967i | 0.0265825i | 0.999912 | + | 0.0132912i | \(0.00423086\pi\) | ||||
−0.999912 | + | 0.0132912i | \(0.995769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 64.0548i | 0.226342i | 0.993576 | + | 0.113171i | \(0.0361008\pi\) | ||||
−0.993576 | + | 0.113171i | \(0.963899\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −80.9817 | − | 166.653i | −0.284146 | − | 0.584748i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −178.627 | −0.622393 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 251.080 | 0.868789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 164.463 | 0.565164 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 527.510 | 1.80038 | 0.900188 | − | 0.435502i | \(-0.143429\pi\) | ||||
0.900188 | + | 0.435502i | \(0.143429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 393.572 | + | 259.828i | 1.33414 | + | 0.880772i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −263.295 | −0.886515 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 224.191i | − | 0.749803i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −155.037 | −0.515073 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −135.101 | −0.445879 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 282.542 | − | 427.979i | 0.926367 | − | 1.40321i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 385.063 | 1.25428 | 0.627139 | − | 0.778908i | \(-0.284226\pi\) | ||||
0.627139 | + | 0.778908i | \(0.284226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −195.414 | −0.632407 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 107.903 | 0.346956 | 0.173478 | − | 0.984838i | \(-0.444499\pi\) | ||||
0.173478 | + | 0.984838i | \(0.444499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 311.071i | − | 0.993838i | −0.867797 | − | 0.496919i | \(-0.834465\pi\) | ||
0.867797 | − | 0.496919i | \(-0.165535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −47.4275 | − | 31.3106i | −0.150564 | − | 0.0993988i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 213.771 | 0.674356 | 0.337178 | − | 0.941441i | \(-0.390528\pi\) | ||||
0.337178 | + | 0.941441i | \(0.390528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 270.300i | − | 0.847334i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 102.853 | 0.320413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −100.654 | − | 59.6488i | −0.311621 | − | 0.184671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −201.346 | − | 471.225i | −0.619527 | − | 1.44992i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 149.673i | − | 0.457716i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 100.886 | 0.306643 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 248.075i | 0.749471i | 0.927132 | + | 0.374735i | \(0.122266\pi\) | ||||
−0.927132 | + | 0.374735i | \(0.877734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −194.535 | −0.584190 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −190.154 | + | 288.034i | −0.567623 | + | 0.859804i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 160.776 | 0.477080 | 0.238540 | − | 0.971133i | \(-0.423331\pi\) | ||||
0.238540 | + | 0.971133i | \(0.423331\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 410.074 | 1.20966 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 235.927i | 0.691869i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 203.907i | − | 0.594480i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −89.0135 | − | 58.7648i | −0.258010 | − | 0.170333i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 245.342i | − | 0.707038i | −0.935427 | − | 0.353519i | \(-0.884985\pi\) | ||
0.935427 | − | 0.353519i | \(-0.115015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −220.492 | −0.631782 | −0.315891 | − | 0.948796i | \(-0.602303\pi\) | ||||
−0.315891 | + | 0.948796i | \(0.602303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 567.531 | 1.61690 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 414.946i | 1.17548i | 0.809048 | + | 0.587742i | \(0.199983\pi\) | ||||
−0.809048 | + | 0.587742i | \(0.800017\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 169.294 | + | 111.764i | 0.476885 | + | 0.314829i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.2726 | 0.0735926 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −130.150 | −0.362533 | −0.181267 | − | 0.983434i | \(-0.558020\pi\) | ||||
−0.181267 | + | 0.983434i | \(0.558020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −173.343 | − | 316.659i | −0.480174 | − | 0.877173i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 59.6239 | 0.164253 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −426.488 | − | 281.558i | −1.16846 | − | 0.771392i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 625.628i | 1.70471i | 0.522965 | + | 0.852354i | \(0.324826\pi\) | ||||
−0.522965 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 424.294i | 1.14985i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 70.4370i | 0.189857i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 282.836 | 0.758273 | 0.379137 | − | 0.925341i | \(-0.376221\pi\) | ||||
0.379137 | + | 0.925341i | \(0.376221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −239.873 | − | 43.5740i | −0.639663 | − | 0.116197i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 582.629i | 1.54543i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 60.1889i | 0.158810i | 0.996842 | + | 0.0794049i | \(0.0253020\pi\) | ||||
−0.996842 | + | 0.0794049i | \(0.974698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.8577 | −0.101989 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −747.259 | −1.95107 | −0.975534 | − | 0.219848i | \(-0.929444\pi\) | ||||
−0.975534 | + | 0.219848i | \(0.929444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −86.8000 | − | 57.3034i | −0.225455 | − | 0.148840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 368.261i | 0.951578i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 160.723 | 0.413170 | 0.206585 | − | 0.978429i | \(-0.433765\pi\) | ||||
0.206585 | + | 0.978429i | \(0.433765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −67.3520 | −0.172256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.43117 | 0.0163643 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −308.423 | − | 203.614i | −0.780818 | − | 0.515479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 394.796i | 0.994449i | 0.867622 | + | 0.497224i | \(0.165647\pi\) | ||||
−0.867622 | + | 0.497224i | \(0.834353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 69.7370 | + | 41.3272i | 0.174779 | + | 0.103577i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 206.496i | 0.514953i | 0.966285 | + | 0.257477i | \(0.0828910\pi\) | ||||
−0.966285 | + | 0.257477i | \(0.917109\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 508.540i | − | 1.26188i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.9392 | − | 30.2027i | 0.0492325 | − | 0.0745746i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −356.031 | −0.874769 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 588.126i | 1.43796i | 0.695031 | + | 0.718980i | \(0.255391\pi\) | ||||
−0.695031 | + | 0.718980i | \(0.744609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 289.024i | − | 0.703222i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −206.326 | −0.499578 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 383.711 | + | 253.318i | 0.924605 | + | 0.610404i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 105.853 | 0.253845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −573.699 | −1.36921 | −0.684605 | − | 0.728914i | \(-0.740025\pi\) | ||||
−0.684605 | + | 0.728914i | \(0.740025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8321i | 0.0423566i | 0.999776 | + | 0.0211783i | \(0.00674176\pi\) | ||||
−0.999776 | + | 0.0211783i | \(0.993258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 239.634i | − | 0.566512i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −141.567 | + | 60.4889i | −0.333098 | + | 0.142327i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 224.363i | 0.525439i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 380.172 | 0.886181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 424.809i | 0.985636i | 0.870132 | + | 0.492818i | \(0.164033\pi\) | ||||
−0.870132 | + | 0.492818i | \(0.835967\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −309.312 | −0.714346 | −0.357173 | − | 0.934038i | \(-0.616259\pi\) | ||||
−0.357173 | + | 0.934038i | \(0.616259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 231.329 | + | 152.718i | 0.531790 | + | 0.351076i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −178.777 | − | 105.946i | −0.409100 | − | 0.242439i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 126.062i | − | 0.287158i | −0.989639 | − | 0.143579i | \(-0.954139\pi\) | ||
0.989639 | − | 0.143579i | \(-0.0458612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −229.739 | −0.520951 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 602.717i | 1.36054i | 0.732964 | + | 0.680268i | \(0.238137\pi\) | ||||
−0.732964 | + | 0.680268i | \(0.761863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −239.361 | − | 158.021i | −0.537889 | − | 0.355102i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −313.428 | −0.701182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 174.732i | − | 0.389157i | −0.980887 | − | 0.194579i | \(-0.937666\pi\) | ||
0.980887 | − | 0.194579i | \(-0.0623339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 776.527i | 1.72179i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 556.393i | 1.22824i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 187.097 | + | 123.517i | 0.411202 | + | 0.271466i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 766.792i | − | 1.67788i | −0.544223 | − | 0.838941i | \(-0.683175\pi\) | ||
0.544223 | − | 0.838941i | \(-0.316825\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 170.499i | − | 0.371457i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −192.820 | −0.418264 | −0.209132 | − | 0.977887i | \(-0.567064\pi\) | ||||
−0.209132 | + | 0.977887i | \(0.567064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 440.773i | − | 0.951994i | −0.879447 | − | 0.475997i | \(-0.842087\pi\) | ||
0.879447 | − | 0.475997i | \(-0.157913\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −201.912 | − | 133.298i | −0.434219 | − | 0.286662i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 450.985i | 0.965707i | 0.875701 | + | 0.482853i | \(0.160400\pi\) | ||||
−0.875701 | + | 0.482853i | \(0.839600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 150.998i | − | 0.321958i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 369.572i | 0.784654i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 673.976i | 1.42490i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −470.920 | − | 62.1268i | −0.991410 | − | 0.130793i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 167.310 | 0.350754 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 493.345 | 1.02995 | 0.514974 | − | 0.857206i | \(-0.327802\pi\) | ||||
0.514974 | + | 0.857206i | \(0.327802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 767.422 | 1.59547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 46.6643 | 0.0966134 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 232.287 | − | 351.854i | 0.478941 | − | 0.725473i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 111.096 | 0.228124 | 0.114062 | − | 0.993474i | \(-0.463614\pi\) | ||||
0.114062 | + | 0.993474i | \(0.463614\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 298.299i | 0.610019i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 671.679 | 1.36798 | 0.683990 | − | 0.729491i | \(-0.260243\pi\) | ||||
0.683990 | + | 0.729491i | \(0.260243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 175.035 | 0.355040 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −136.113 | + | 206.177i | −0.274977 | + | 0.416519i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −88.7504 | −0.178572 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −813.880 | −1.63102 | −0.815511 | − | 0.578741i | \(-0.803544\pi\) | ||||
−0.815511 | + | 0.578741i | \(0.803544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −174.975 | −0.349251 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 901.318i | 1.79189i | 0.444170 | + | 0.895943i | \(0.353499\pi\) | ||||
−0.444170 | + | 0.895943i | \(0.646501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −190.817 | + | 289.038i | −0.377855 | + | 0.572353i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −489.841 | −0.966156 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 92.1471i | 0.181035i | 0.995895 | + | 0.0905177i | \(0.0288522\pi\) | ||||
−0.995895 | + | 0.0905177i | \(0.971148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 223.581 | 0.437537 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 268.197 | − | 452.566i | 0.522802 | − | 0.882195i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −276.002 | + | 418.072i | −0.535926 | + | 0.811790i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 438.569i | − | 0.848297i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −301.264 | −0.580470 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 235.653i | 0.452309i | 0.974091 | + | 0.226155i | \(0.0726154\pi\) | ||||
−0.974091 | + | 0.226155i | \(0.927385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −290.076 | −0.554639 | −0.277320 | − | 0.960778i | \(-0.589446\pi\) | ||||
−0.277320 | + | 0.960778i | \(0.589446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 98.0832 | − | 41.9092i | 0.186825 | − | 0.0798271i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −152.776 | −0.289898 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409.372 | 0.773860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 490.087i | 0.922951i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1673.80i | − | 3.14033i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 145.269 | − | 220.045i | 0.271531 | − | 0.411299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 270.880i | − | 0.504431i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −420.460 | −0.780073 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 352.993 | 0.652483 | 0.326242 | − | 0.945286i | \(-0.394218\pi\) | ||||
0.326242 | + | 0.945286i | \(0.394218\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 207.922i | 0.382913i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −320.213 | − | 211.398i | −0.587547 | − | 0.387886i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 571.004 | 1.04388 | 0.521942 | − | 0.852981i | \(-0.325208\pi\) | ||||
0.521942 | + | 0.852981i | \(0.325208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 532.931 | 0.970730 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 464.606 | + | 275.332i | 0.843205 | + | 0.499696i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 161.687 | 0.292382 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 201.156 | − | 304.699i | 0.362443 | − | 0.549008i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 245.730i | 0.441166i | 0.975368 | + | 0.220583i | \(0.0707960\pi\) | ||||
−0.975368 | + | 0.220583i | \(0.929204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1452.75i | − | 2.59884i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 114.212i | − | 0.203586i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −623.923 | −1.10821 | −0.554106 | − | 0.832446i | \(-0.686940\pi\) | ||||
−0.554106 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 579.188 | − | 877.321i | 1.02511 | − | 1.55278i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.8334i | 0.0279249i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 286.095i | − | 0.502804i | −0.967883 | − | 0.251402i | \(-0.919108\pi\) | ||
0.967883 | − | 0.251402i | \(-0.0808915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 213.683 | 0.374226 | 0.187113 | − | 0.982338i | \(-0.440087\pi\) | ||||
0.187113 | + | 0.982338i | \(0.440087\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 512.864 | 0.895051 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −251.445 | + | 107.438i | −0.437295 | + | 0.186849i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 521.531i | 0.903866i | 0.892052 | + | 0.451933i | \(0.149265\pi\) | ||||
−0.892052 | + | 0.451933i | \(0.850735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 66.4519 | 0.114770 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −201.156 | −0.346224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 306.204 | 0.525221 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 293.392 | − | 444.413i | 0.501524 | − | 0.759680i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 195.026i | 0.332243i | 0.986105 | + | 0.166121i | \(0.0531244\pi\) | ||||
−0.986105 | + | 0.166121i | \(0.946876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −405.525 | − | 240.320i | −0.688497 | − | 0.408014i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 572.525i | 0.968740i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 333.768i | − | 0.562847i | −0.959584 | − | 0.281423i | \(-0.909193\pi\) | ||
0.959584 | − | 0.281423i | \(-0.0908065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.1073 | − | 56.2080i | 0.0623652 | − | 0.0944672i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 282.564 | 0.473307 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 556.121i | − | 0.928415i | −0.885726 | − | 0.464208i | \(-0.846339\pi\) | ||
0.885726 | − | 0.464208i | \(-0.153661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1015.58i | 1.68981i | 0.534916 | + | 0.844905i | \(0.320343\pi\) | ||||
−0.534916 | + | 0.844905i | \(0.679657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −358.668 | −0.594806 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 84.2127 | − | 127.561i | 0.139195 | − | 0.210844i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −916.408 | −1.50973 | −0.754867 | − | 0.655878i | \(-0.772298\pi\) | ||||
−0.754867 | + | 0.655878i | \(0.772298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −121.271 | −0.199132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 945.333i | 1.54719i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 265.921i | − | 0.433802i | −0.976194 | − | 0.216901i | \(-0.930405\pi\) | ||
0.976194 | − | 0.216901i | \(-0.0695949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −664.569 | − | 438.734i | −1.08060 | − | 0.713389i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.9941i | − | 0.0405091i | −0.999795 | − | 0.0202545i | \(-0.993552\pi\) | ||
0.999795 | − | 0.0202545i | \(-0.00644766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 52.7690 | 0.0852488 | 0.0426244 | − | 0.999091i | \(-0.486428\pi\) | ||||
0.0426244 | + | 0.999091i | \(0.486428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 302.833i | − | 0.487654i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 125.482 | 0.201416 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −432.020 | + | 451.646i | −0.691231 | + | 0.722634i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 179.657 | − | 303.161i | 0.286535 | − | 0.483510i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 230.551i | − | 0.366535i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −439.188 | −0.696019 | −0.348010 | − | 0.937491i | \(-0.613142\pi\) | ||||
−0.348010 | + | 0.937491i | \(0.613142\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 692.971i | 1.09474i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −54.8825 | + | 83.1329i | −0.0864292 | + | 0.130918i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 906.297 | 1.42276 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 210.810i | 0.329906i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 795.892i | − | 1.24164i | −0.783953 | − | 0.620821i | \(-0.786799\pi\) | ||
0.783953 | − | 0.620821i | \(-0.213201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 927.013i | 1.44170i | 0.693092 | + | 0.720850i | \(0.256248\pi\) | ||||
−0.693092 | + | 0.720850i | \(0.743752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −576.804 | − | 380.794i | −0.894270 | − | 0.590378i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 128.287i | − | 0.198280i | −0.995073 | − | 0.0991401i | \(-0.968391\pi\) | ||
0.995073 | − | 0.0991401i | \(-0.0316092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 896.938i | 1.38203i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 105.850 | 0.162596 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 745.488i | − | 1.14164i | −0.821077 | − | 0.570818i | \(-0.806626\pi\) | ||
0.821077 | − | 0.570818i | \(-0.193374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.08337 | − | 13.7590i | 0.0138677 | − | 0.0210061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 531.075i | − | 0.808334i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 563.842i | − | 0.855602i | −0.903873 | − | 0.427801i | \(-0.859288\pi\) | ||
0.903873 | − | 0.427801i | \(-0.140712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 219.673i | − | 0.332335i | −0.986098 | − | 0.166167i | \(-0.946861\pi\) | ||
0.986098 | − | 0.166167i | \(-0.0531392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 246.183i | 0.371317i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 186.912 | − | 90.8263i | 0.281071 | − | 0.136581i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 310.889 | 0.466101 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −644.346 | −0.963148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 975.349 | 1.45357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −145.649 | −0.216418 | −0.108209 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108209 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −271.975 | − | 636.522i | −0.402926 | − | 0.942996i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1031.23 | 1.52323 | 0.761616 | − | 0.648029i | \(-0.224406\pi\) | ||||
0.761616 | + | 0.648029i | \(0.224406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 184.455i | 0.271658i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.7203 | 0.0671370 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1266.00 | 1.85358 | 0.926791 | − | 0.375577i | \(-0.122555\pi\) | ||||
0.926791 | + | 0.375577i | \(0.122555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −618.344 | − | 408.217i | −0.902692 | − | 0.595937i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 358.307 | 0.521553 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −660.020 | −0.957939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −458.754 | −0.663899 | −0.331949 | − | 0.943297i | \(-0.607706\pi\) | ||||
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 108.086i | − | 0.155968i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 149.507 | − | 226.465i | 0.215118 | − | 0.325848i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −502.846 | −0.721443 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 280.170i | 0.400815i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 790.423 | 1.12756 | 0.563782 | − | 0.825923i | \(-0.309346\pi\) | ||||
0.563782 | + | 0.825923i | \(0.309346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 362.660 | − | 611.966i | 0.515875 | − | 0.870506i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 375.338 | + | 247.790i | 0.532394 | + | 0.351475i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 151.525i | − | 0.214321i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −131.077 | −0.184875 | −0.0924377 | − | 0.995718i | \(-0.529466\pi\) | ||||
−0.0924377 | + | 0.995718i | \(0.529466\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 384.057i | − | 0.540165i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −271.356 | −0.380583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 536.954 | − | 813.347i | 0.750984 | − | 1.13755i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 155.066 | 0.216271 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −820.977 | −1.14183 | −0.570916 | − | 0.821008i | \(-0.693412\pi\) | ||||
−0.570916 | + | 0.821008i | \(0.693412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 219.169i | − | 0.303980i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 238.931i | 0.330472i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 653.456 | − | 279.210i | 0.901318 | − | 0.385118i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1121.14i | − | 1.54214i | −0.636749 | − | 0.771071i | \(-0.719721\pi\) | ||
0.636749 | − | 0.771071i | \(-0.280279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 523.626 | 0.718280 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −436.438 | −0.597043 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 97.7494i | − | 0.133355i | −0.997775 | − | 0.0666777i | \(-0.978760\pi\) | ||
0.997775 | − | 0.0666777i | \(-0.0212399\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 237.558 | − | 359.839i | 0.323208 | − | 0.489577i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −656.420 | −0.890665 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 520.032 | 0.703697 | 0.351849 | − | 0.936057i | \(-0.385553\pi\) | ||||
0.351849 | + | 0.936057i | \(0.385553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −387.250 | + | 653.460i | −0.522605 | + | 0.881863i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1357.00 | 1.82638 | 0.913189 | − | 0.407535i | \(-0.133612\pi\) | ||||
0.913189 | + | 0.407535i | \(0.133612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −442.685 | + | 670.554i | −0.594208 | + | 0.900073i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 477.808i | 0.639635i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 115.356i | 0.154013i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 431.283i | 0.574278i | 0.957889 | + | 0.287139i | \(0.0927042\pi\) | ||||
−0.957889 | + | 0.287139i | \(0.907296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.5128 | −0.0498178 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1190.36 | + | 785.848i | 1.57663 | + | 1.04086i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 665.943i | 0.879713i | 0.898068 | + | 0.439857i | \(0.144971\pi\) | ||||
−0.898068 | + | 0.439857i | \(0.855029\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 202.859i | − | 0.267271i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −792.938 | −1.04197 | −0.520984 | − | 0.853566i | \(-0.674435\pi\) | ||||
−0.520984 | + | 0.853566i | \(0.674435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 167.868 | 0.220010 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −133.511 | − | 88.1413i | −0.174525 | − | 0.115217i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1933.34i | − | 2.52066i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1263.74 | 1.64336 | 0.821678 | − | 0.569953i | \(-0.193038\pi\) | ||||
0.821678 | + | 0.569953i | \(0.193038\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −117.842 | −0.152843 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −441.297 | −0.570889 | −0.285445 | − | 0.958395i | \(-0.592141\pi\) | ||||
−0.285445 | + | 0.958395i | \(0.592141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −570.360 | + | 243.705i | −0.735948 | + | 0.314458i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 159.735i | 0.205579i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1334.74 | − | 790.985i | −1.71340 | − | 1.01538i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 385.815i | 0.494002i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 787.004i | 1.00511i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 790.670 | + | 521.983i | 1.00722 | + | 0.664946i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −367.069 | −0.466415 | −0.233207 | − | 0.972427i | \(-0.574922\pi\) | ||||
−0.233207 | + | 0.972427i | \(0.574922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.2268i | 0.0573216i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 459.925i | 0.581447i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2102.36 | −2.65114 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −173.004 | + | 262.056i | −0.217615 | + | 0.329630i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 923.535 | 1.15876 | 0.579382 | − | 0.815056i | \(-0.303294\pi\) | ||||
0.579382 | + | 0.815056i | \(0.303294\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 283.999 | 0.355443 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 298.059i | − | 0.372108i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 971.953i | − | 1.21040i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 65.9085 | − | 99.8344i | 0.0818739 | − | 0.124018i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 411.964i | 0.510488i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 823.083 | 1.01741 | 0.508704 | − | 0.860942i | \(-0.330125\pi\) | ||||
0.508704 | + | 0.860942i | \(0.330125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 125.683i | − | 0.154973i | −0.996993 | − | 0.0774866i | \(-0.975311\pi\) | ||
0.996993 | − | 0.0774866i | \(-0.0246895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 724.017 | 0.890550 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 638.187 | + | 421.317i | 0.783051 | + | 0.516953i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1158.47 | − | 686.525i | −1.41795 | − | 0.840300i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 232.978i | 0.284467i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 713.601 | 0.869185 | 0.434592 | − | 0.900627i | \(-0.356892\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 823.797i | 1.00097i | 0.865746 | + | 0.500484i | \(0.166845\pi\) | ||||
−0.865746 | + | 0.500484i | \(0.833155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −182.188 | − | 426.387i | −0.220834 | − | 0.516833i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −654.261 | −0.791125 | −0.395563 | − | 0.918439i | \(-0.629450\pi\) | ||||
−0.395563 | + | 0.918439i | \(0.629450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 530.752i | 0.640231i | 0.947379 | + | 0.320116i | \(0.103722\pi\) | ||||
−0.947379 | + | 0.320116i | \(0.896278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4741i | 0.0162143i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 272.272i | − | 0.326857i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −247.134 | + | 374.344i | −0.295969 | + | 0.448316i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 686.925i | − | 0.820699i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 917.949i | − | 1.09410i | −0.837100 | − | 0.547049i | \(-0.815751\pi\) | ||
0.837100 | − | 0.547049i | \(-0.184249\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0594 | 0.0393097 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 14.5688i | − | 0.0172821i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −691.850 | + | 1047.98i | −0.818758 | + | 1.24021i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 66.8721i | 0.0789517i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 124.932i | − | 0.147152i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 409.495i | − | 0.481192i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 600.529i | 0.704020i | 0.935996 | + | 0.352010i | \(0.114502\pi\) | ||||
−0.935996 | + | 0.352010i | \(0.885498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −215.741 | − | 443.975i | −0.252328 | − | 0.519269i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1059.28 | −1.23603 | −0.618015 | − | 0.786167i | \(-0.712063\pi\) | ||||
−0.618015 | + | 0.786167i | \(0.712063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 734.054 | 0.854545 | 0.427272 | − | 0.904123i | \(-0.359475\pi\) | ||||
0.427272 | + | 0.904123i | \(0.359475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 348.392 | 0.404637 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −714.413 | −0.827825 | −0.413912 | − | 0.910317i | \(-0.635838\pi\) | ||||
−0.413912 | + | 0.910317i | \(0.635838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −425.504 | + | 644.529i | −0.491912 | + | 0.745121i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −489.705 | −0.564826 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 702.886i | − | 0.808845i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1414.91 | 1.62447 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 438.139 | 0.501878 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 48.8710 | − | 269.034i | 0.0558526 | − | 0.307467i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1129.51 | −1.28792 | −0.643961 | − | 0.765059i | \(-0.722710\pi\) | ||||
−0.643961 | + | 0.765059i | \(0.722710\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1028.85 | −1.17048 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 161.933 | 0.183806 | 0.0919029 | − | 0.995768i | \(-0.470705\pi\) | ||||
0.0919029 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 199.206i | − | 0.225602i | −0.993618 | − | 0.112801i | \(-0.964018\pi\) | ||
0.993618 | − | 0.112801i | \(-0.0359822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −767.620 | − | 506.766i | −0.867367 | − | 0.572617i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 727.670 | 0.820373 | 0.410186 | − | 0.912002i | \(-0.365464\pi\) | ||||
0.410186 | + | 0.912002i | \(0.365464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 43.5814i | − | 0.0490230i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 68.8310 | 0.0772514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 753.837 | + | 446.735i | 0.844163 | + | 0.500263i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −579.525 | − | 382.589i | −0.647514 | − | 0.427474i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 437.261i | 0.487470i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 705.200 | 0.784427 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 198.285i | 0.220072i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 302.383 | 0.334865 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 444.832 | + | 293.668i | 0.491527 | + | 0.324495i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1249.33 | 1.37743 | 0.688716 | − | 0.725031i | \(-0.258174\pi\) | ||||
0.688716 | + | 0.725031i | \(0.258174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −359.919 | −0.395950 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 813.909i | 0.893423i | 0.894678 | + | 0.446712i | \(0.147405\pi\) | ||||
−0.894678 | + | 0.446712i | \(0.852595\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 874.465i | 0.957793i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −551.068 | + | 834.726i | −0.602260 | + | 0.912269i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.21297i | 0.00786584i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −442.339 | −0.481327 | −0.240663 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240663 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −751.024 | −0.815444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 831.622i | − | 0.900999i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −367.768 | − | 860.713i | −0.397587 | − | 0.930501i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −520.595 | −0.561591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −514.468 | −0.553786 | −0.276893 | − | 0.960901i | \(-0.589305\pi\) | ||||
−0.276893 | + | 0.960901i | \(0.589305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 428.288 | − | 722.709i | 0.460030 | − | 0.776272i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −210.454 | −0.225567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −244.347 | − | 161.313i | −0.261334 | − | 0.172527i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1147.17i | 1.22430i | 0.790743 | + | 0.612149i | \(0.209695\pi\) | ||||
−0.790743 | + | 0.612149i | \(0.790305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 606.711i | 0.646124i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1355.11i | 1.44008i | 0.693934 | + | 0.720039i | \(0.255876\pi\) | ||||
−0.693934 | + | 0.720039i | \(0.744124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −893.134 | −0.947120 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 252.727 | + | 166.845i | 0.267436 | + | 0.176555i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1560.15i | 1.64746i | 0.566980 | + | 0.823732i | \(0.308112\pi\) | ||||
−0.566980 | + | 0.823732i | \(0.691888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2095.04i | 2.20763i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −416.937 | −0.438420 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −643.715 | −0.675461 | −0.337731 | − | 0.941243i | \(-0.609659\pi\) | ||||
−0.337731 | + | 0.941243i | \(0.609659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 724.368 | − | 1097.23i | 0.758501 | − | 1.14893i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 527.190i | 0.550878i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 324.159 | 0.338018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 345.476 | 0.359496 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 274.006 | 0.284534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 93.8565 | − | 142.169i | 0.0972607 | − | 0.147325i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 570.639i | − | 0.590113i | −0.955480 | − | 0.295056i | \(-0.904662\pi\) | ||
0.955480 | − | 0.295056i | \(-0.0953384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 196.314 | + | 116.339i | 0.202594 | + | 0.120060i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 516.280i | 0.531699i | 0.964015 | + | 0.265850i | \(0.0856525\pi\) | ||||
−0.964015 | + | 0.265850i | \(0.914348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 118.721i | 0.122016i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 392.704 | + | 919.074i | 0.402774 | + | 0.942640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 432.740 | 0.442927 | 0.221464 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 545.495i | − | 0.557196i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 398.739i | − | 0.406461i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1116.57 | −1.13588 | −0.567940 | − | 0.823070i | \(-0.692260\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1224.87 | + | 808.633i | 1.24352 | + | 0.820947i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −196.766 | −0.199358 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −775.185 | −0.783806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1158.19i | − | 1.16871i | −0.811499 | − | 0.584354i | \(-0.801348\pi\) | ||
0.811499 | − | 0.584354i | \(-0.198652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 483.843i | − | 0.487254i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 399.093 | − | 604.523i | 0.401099 | − | 0.607561i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 76.0503i | − | 0.0762792i | −0.999272 | − | 0.0381396i | \(-0.987857\pi\) | ||
0.999272 | − | 0.0381396i | \(-0.0121432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1036.62 | 1.03766 |
(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 | 380.3.g.c.189.6 | yes | 12 | |
3.2 | odd | 2 | 3420.3.h.e.2089.10 | 12 | |||
5.2 | odd | 4 | 1900.3.e.e.1101.8 | 12 | |||
5.3 | odd | 4 | 1900.3.e.e.1101.5 | 12 | |||
5.4 | even | 2 | inner | 380.3.g.c.189.7 | yes | 12 | |
15.14 | odd | 2 | 3420.3.h.e.2089.11 | 12 | |||
19.18 | odd | 2 | inner | 380.3.g.c.189.8 | yes | 12 | |
57.56 | even | 2 | 3420.3.h.e.2089.9 | 12 | |||
95.18 | even | 4 | 1900.3.e.e.1101.7 | 12 | |||
95.37 | even | 4 | 1900.3.e.e.1101.6 | 12 | |||
95.94 | odd | 2 | inner | 380.3.g.c.189.5 | ✓ | 12 | |
285.284 | even | 2 | 3420.3.h.e.2089.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.g.c.189.5 | ✓ | 12 | 95.94 | odd | 2 | inner | |
380.3.g.c.189.6 | yes | 12 | 1.1 | even | 1 | trivial | |
380.3.g.c.189.7 | yes | 12 | 5.4 | even | 2 | inner | |
380.3.g.c.189.8 | yes | 12 | 19.18 | odd | 2 | inner | |
1900.3.e.e.1101.5 | 12 | 5.3 | odd | 4 | |||
1900.3.e.e.1101.6 | 12 | 95.37 | even | 4 | |||
1900.3.e.e.1101.7 | 12 | 95.18 | even | 4 | |||
1900.3.e.e.1101.8 | 12 | 5.2 | odd | 4 | |||
3420.3.h.e.2089.9 | 12 | 57.56 | even | 2 | |||
3420.3.h.e.2089.10 | 12 | 3.2 | odd | 2 | |||
3420.3.h.e.2089.11 | 12 | 15.14 | odd | 2 | |||
3420.3.h.e.2089.12 | 12 | 285.284 | even | 2 |