Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.e (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: | \(51.7712502285\) |
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: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.6 | ||
Root | \(-4.19028 + 0.975196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.e.1101.8 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.95039i | − | 0.650131i | −0.945692 | − | 0.325065i | \(-0.894614\pi\) | ||
0.945692 | − | 0.325065i | \(-0.105386\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18749 | 0.312499 | 0.156249 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156249 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 20.4976i | 1.57674i | 0.615204 | + | 0.788368i | \(0.289074\pi\) | ||||
−0.615204 | + | 0.788368i | \(0.710926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.15792 | 0.362231 | 0.181115 | − | 0.983462i | \(-0.442029\pi\) | ||||
0.181115 | + | 0.983462i | \(0.442029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.68651 | − | 16.3454i | −0.509816 | − | 0.860283i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.26647i | − | 0.203165i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.9375 | −0.475541 | −0.237771 | − | 0.971321i | \(-0.576417\pi\) | ||||
−0.237771 | + | 0.971321i | \(0.576417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.6877i | − | 1.02547i | ||||||
\(28\) | 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 | \(0.131045\pi\) | ||||
−0.916446 | + | 0.400157i | \(0.868955\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.5472i | 0.562035i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 37.4397i | − | 1.01188i | −0.862568 | − | 0.505941i | \(-0.831145\pi\) | ||
0.862568 | − | 0.505941i | \(-0.168855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.9783 | 1.02508 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 81.6583i | 1.99167i | 0.0911903 | + | 0.995833i | \(0.470933\pi\) | ||||
−0.0911903 | + | 0.995833i | \(0.529067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −70.8743 | −1.64824 | −0.824120 | − | 0.566415i | \(-0.808330\pi\) | ||||
−0.824120 | + | 0.566415i | \(0.808330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −46.1193 | −0.981261 | −0.490631 | − | 0.871368i | \(-0.663234\pi\) | ||||
−0.490631 | + | 0.871368i | \(0.663234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.2149 | −0.902345 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 12.0104i | − | 0.235497i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 32.1999i | − | 0.607546i | −0.952745 | − | 0.303773i | \(-0.901754\pi\) | ||
0.952745 | − | 0.303773i | \(-0.0982464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31.8799 | + | 18.8925i | −0.559297 | + | 0.331447i | ||||
\(58\) | 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 | ||||||||
\(63\) | 11.3661 | 0.180415 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 69.0282i | − | 1.03027i | −0.857109 | − | 0.515136i | \(-0.827742\pi\) | ||
0.857109 | − | 0.515136i | \(-0.172258\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.3323i | 0.309164i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.5718i | 0.571433i | 0.958314 | + | 0.285717i | \(0.0922316\pi\) | ||||
−0.958314 | + | 0.285717i | \(0.907768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 102.209 | 1.40012 | 0.700062 | − | 0.714082i | \(-0.253156\pi\) | ||||
0.700062 | + | 0.714082i | \(0.253156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20.8018 | −0.270154 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | −91.9574 | −1.10792 | −0.553960 | − | 0.832543i | \(-0.686884\pi\) | ||||
−0.553960 | + | 0.832543i | \(0.686884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 55.4385 | 0.637224 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 48.3888 | 0.520309 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84.3229i | 0.869308i | 0.900598 | + | 0.434654i | \(0.143129\pi\) | ||||
−0.900598 | + | 0.434654i | \(0.856871\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 100.192i | 0.972739i | 0.873753 | + | 0.486369i | \(0.161679\pi\) | ||||
−0.873753 | + | 0.486369i | \(0.838321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 52.7344i | 0.492845i | 0.969163 | + | 0.246422i | \(0.0792550\pi\) | ||||
−0.969163 | + | 0.246422i | \(0.920745\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | − | 210.252i | − | 1.86064i | −0.366749 | − | 0.930320i | \(-0.619529\pi\) | ||
0.366749 | − | 0.930320i | \(-0.380471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 106.505i | 0.910297i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.4704 | 0.113197 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.5702 | −0.252647 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 159.266 | 1.29484 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.9230i | − | 0.156874i | −0.996919 | − | 0.0784371i | \(-0.975007\pi\) | ||
0.996919 | − | 0.0784371i | \(-0.0249930\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −21.1892 | − | 35.7554i | −0.159317 | − | 0.268837i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −148.188 | −1.08166 | −0.540831 | − | 0.841131i | \(-0.681890\pi\) | ||||
−0.540831 | + | 0.841131i | \(0.681890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 54.2729 | 0.390452 | 0.195226 | − | 0.980758i | \(-0.437456\pi\) | ||||
0.195226 | + | 0.980758i | \(0.437456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 89.9507i | 0.637948i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 194.921i | − | 1.36308i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 86.2364i | 0.586642i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −160.700 | −1.07852 | −0.539262 | − | 0.842138i | \(-0.681297\pi\) | ||||
−0.539262 | + | 0.842138i | \(0.681297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 285.273i | 1.88922i | 0.328192 | + | 0.944611i | \(0.393561\pi\) | ||||
−0.328192 | + | 0.944611i | \(0.606439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.9964 | 0.209127 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 189.486 | 1.20692 | 0.603459 | − | 0.797394i | \(-0.293789\pi\) | ||||
0.603459 | + | 0.797394i | \(0.293789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −62.8025 | −0.394984 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.9256 | −0.148606 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −152.943 | −0.938302 | −0.469151 | − | 0.883118i | \(-0.655440\pi\) | ||||
−0.469151 | + | 0.883118i | \(0.655440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 89.7126i | − | 0.537201i | −0.963252 | − | 0.268601i | \(-0.913439\pi\) | ||
0.963252 | − | 0.268601i | \(-0.0865612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −251.150 | −1.48610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −50.3308 | − | 84.9301i | −0.294332 | − | 0.496667i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 154.463i | 0.892851i | 0.894821 | + | 0.446425i | \(0.147303\pi\) | ||||
−0.894821 | + | 0.446425i | \(0.852697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −183.962 | −1.03933 | ||||||||
\(178\) | 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 | \(0.0951496\pi\) | ||||
−0.955655 | + | 0.294490i | \(0.904850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 200.044i | 1.09314i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −58.5585 | −0.313147 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | − | 34.0711i | − | 0.176534i | −0.996097 | − | 0.0882670i | \(-0.971867\pi\) | ||
0.996097 | − | 0.0882670i | \(-0.0281329\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 293.544 | 1.49007 | 0.745035 | − | 0.667026i | \(-0.232433\pi\) | ||||
0.745035 | + | 0.667026i | \(0.232433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 144.876 | 0.728018 | 0.364009 | − | 0.931395i | \(-0.381408\pi\) | ||||
0.364009 | + | 0.931395i | \(0.381408\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −134.632 | −0.669811 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 62.1779i | 0.306295i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −56.8307 | −0.274544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 92.1135 | + | 155.436i | 0.440734 | + | 0.743711i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 355.298i | 1.68388i | 0.539573 | + | 0.841939i | \(0.318586\pi\) | ||||
−0.539573 | + | 0.841939i | \(0.681414\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 79.1309 | 0.371506 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 54.2711i | 0.250097i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 199.348i | − | 0.910264i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 126.222i | 0.571142i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.367i | 1.48147i | 0.671798 | + | 0.740734i | \(0.265522\pi\) | ||||
−0.671798 | + | 0.740734i | \(0.734478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.4416i | 0.103267i | 0.998666 | + | 0.0516335i | \(0.0164428\pi\) | ||||
−0.998666 | + | 0.0516335i | \(0.983557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 183.710 | 0.802229 | 0.401114 | − | 0.916028i | \(-0.368623\pi\) | ||||
0.401114 | + | 0.916028i | \(0.368623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 40.5718i | 0.175635i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −143.648 | −0.616515 | −0.308258 | − | 0.951303i | \(-0.599746\pi\) | ||||
−0.308258 | + | 0.951303i | \(0.599746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 144.162 | 0.608279 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 79.5051 | 0.332657 | 0.166329 | − | 0.986070i | \(-0.446809\pi\) | ||||
0.166329 | + | 0.986070i | \(0.446809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 122.504i | 0.508317i | 0.967163 | + | 0.254158i | \(0.0817984\pi\) | ||||
−0.967163 | + | 0.254158i | \(0.918202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 235.072i | − | 0.967375i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 335.040 | − | 198.550i | 1.35644 | − | 0.803846i | ||||
\(248\) | 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 | ||||||||
\(253\) | 104.009 | 0.411104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 60.4198i | − | 0.235097i | −0.993067 | − | 0.117548i | \(-0.962497\pi\) | ||
0.993067 | − | 0.117548i | \(-0.0375035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 81.8989i | − | 0.316212i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 147.692i | 0.565869i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.1886 | −0.0881694 | −0.0440847 | − | 0.999028i | \(-0.514037\pi\) | ||||
−0.0440847 | + | 0.999028i | \(0.514037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 111.881 | 0.419030 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | 87.4521 | 0.320337 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.90841 | 0.0249401 | 0.0124701 | − | 0.999922i | \(-0.496031\pi\) | ||||
0.0124701 | + | 0.999922i | \(0.496031\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 128.911i | 0.462046i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.46967i | − | 0.0265825i | −0.999912 | − | 0.0132912i | \(-0.995769\pi\) | ||
0.999912 | − | 0.0132912i | \(-0.00423086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 64.0548 | 0.226342 | 0.113171 | − | 0.993576i | \(-0.463899\pi\) | ||||
0.113171 | + | 0.993576i | \(0.463899\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 178.627i | 0.622393i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −251.080 | −0.868789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 164.463 | 0.565164 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 527.510i | 1.80038i | 0.435502 | + | 0.900188i | \(0.356571\pi\) | ||||
−0.435502 | + | 0.900188i | \(0.643429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 263.295i | 0.886515i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 224.191i | − | 0.749803i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −155.037 | −0.515073 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 135.101i | − | 0.445879i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 385.063i | − | 1.25428i | −0.778908 | − | 0.627139i | \(-0.784226\pi\) | ||
0.778908 | − | 0.627139i | \(-0.215774\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −311.071 | −0.993838 | −0.496919 | − | 0.867797i | \(-0.665535\pi\) | ||||
−0.496919 | + | 0.867797i | \(0.665535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 213.771i | − | 0.674356i | −0.941441 | − | 0.337178i | \(-0.890528\pi\) | ||
0.941441 | − | 0.337178i | \(-0.109472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 270.300i | − | 0.847334i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 102.853 | 0.320413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −59.6488 | − | 100.654i | −0.184671 | − | 0.311621i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 149.673 | 0.457716 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −100.886 | −0.306643 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 248.075i | − | 0.749471i | −0.927132 | − | 0.374735i | \(-0.877734\pi\) | ||
0.927132 | − | 0.374735i | \(-0.122266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 194.535i | − | 0.584190i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 160.776i | − | 0.477080i | −0.971133 | − | 0.238540i | \(-0.923331\pi\) | ||
0.971133 | − | 0.238540i | \(-0.0766688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −410.074 | −1.20966 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 235.927i | − | 0.691869i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −203.907 | −0.594480 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 245.342 | 0.707038 | 0.353519 | − | 0.935427i | \(-0.384985\pi\) | ||||
0.353519 | + | 0.935427i | \(0.384985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 220.492 | 0.631782 | 0.315891 | − | 0.948796i | \(-0.397697\pi\) | ||||
0.315891 | + | 0.948796i | \(0.397697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 567.531 | 1.61690 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 414.946 | 1.17548 | 0.587742 | − | 0.809048i | \(-0.300017\pi\) | ||||
0.587742 | + | 0.809048i | \(0.300017\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 26.2726i | − | 0.0735926i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 130.150 | 0.362533 | 0.181267 | − | 0.983434i | \(-0.441980\pi\) | ||||
0.181267 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −173.343 | + | 316.659i | −0.480174 | + | 0.877173i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 59.6239i | 0.164253i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −625.628 | −1.70471 | −0.852354 | − | 0.522965i | \(-0.824826\pi\) | ||||
−0.852354 | + | 0.522965i | \(0.824826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 424.294i | 1.14985i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 70.4370i | − | 0.189857i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 282.836i | 0.758273i | 0.925341 | + | 0.379137i | \(0.123779\pi\) | ||||
−0.925341 | + | 0.379137i | \(0.876221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −582.629 | −1.54543 | ||||||||
\(378\) | 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 | ||||||||
\(383\) | − | 747.259i | − | 1.95107i | −0.219848 | − | 0.975534i | \(-0.570556\pi\) | ||
0.219848 | − | 0.975534i | \(-0.429444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −368.261 | −0.951578 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −160.723 | −0.413170 | −0.206585 | − | 0.978429i | \(-0.566235\pi\) | ||||
−0.206585 | + | 0.978429i | \(0.566235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −67.3520 | −0.172256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.43117i | 0.0163643i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −394.796 | −0.994449 | −0.497224 | − | 0.867622i | \(-0.665647\pi\) | ||||
−0.497224 | + | 0.867622i | \(0.665647\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −69.7370 | + | 41.3272i | −0.174779 | + | 0.103577i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 206.496i | − | 0.514953i | −0.966285 | − | 0.257477i | \(-0.917109\pi\) | ||
0.966285 | − | 0.257477i | \(-0.0828910\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −508.540 | −1.26188 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 356.031i | 0.874769i | ||||||||
\(408\) | 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 | ||||||||
\(413\) | − | 206.326i | − | 0.499578i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 105.853i | − | 0.253845i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 573.699 | 1.36921 | 0.684605 | − | 0.728914i | \(-0.259975\pi\) | ||||
0.684605 | + | 0.728914i | \(0.259975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.8321i | − | 0.0423566i | −0.999776 | − | 0.0211783i | \(-0.993258\pi\) | ||
0.999776 | − | 0.0211783i | \(-0.00674176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −239.634 | −0.566512 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −224.363 | −0.525439 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −380.172 | −0.886181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 424.809i | − | 0.985636i | −0.870132 | − | 0.492818i | \(-0.835967\pi\) | ||
0.870132 | − | 0.492818i | \(-0.164033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 309.312i | − | 0.714346i | −0.934038 | − | 0.357173i | \(-0.883741\pi\) | ||
0.934038 | − | 0.357173i | \(-0.116259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 105.946 | + | 178.777i | 0.242439 | + | 0.409100i | ||||
\(438\) | 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 | ||||||||
\(443\) | 602.717 | 1.36054 | 0.680268 | − | 0.732964i | \(-0.261863\pi\) | ||||
0.680268 | + | 0.732964i | \(0.261863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 313.428i | 0.701182i | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 556.393 | 1.22824 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 766.792 | 1.67788 | 0.838941 | − | 0.544223i | \(-0.183175\pi\) | ||||
0.838941 | + | 0.544223i | \(0.183175\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −440.773 | −0.951994 | −0.475997 | − | 0.879447i | \(-0.657913\pi\) | ||||
−0.475997 | + | 0.879447i | \(0.657913\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −450.985 | −0.965707 | −0.482853 | − | 0.875701i | \(-0.660400\pi\) | ||||
−0.482853 | + | 0.875701i | \(0.660400\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 150.998i | − | 0.321958i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 369.572i | − | 0.784654i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 673.976 | 1.42490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 167.310i | − | 0.350754i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −493.345 | −1.02995 | −0.514974 | − | 0.857206i | \(-0.672198\pi\) | ||||
−0.514974 | + | 0.857206i | \(0.672198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 767.422 | 1.59547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 46.6643i | 0.0966134i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 111.096i | − | 0.228124i | −0.993474 | − | 0.114062i | \(-0.963614\pi\) | ||
0.993474 | − | 0.114062i | \(-0.0363862\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 175.035i | 0.355040i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 88.7504i | 0.178572i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 813.880 | 1.63102 | 0.815511 | − | 0.578741i | \(-0.196456\pi\) | ||||
0.815511 | + | 0.578741i | \(0.196456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −174.975 | −0.349251 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 901.318 | 1.79189 | 0.895943 | − | 0.444170i | \(-0.146501\pi\) | ||||
0.895943 | + | 0.444170i | \(0.146501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 489.841i | 0.966156i | ||||||||
\(508\) | 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 | ||||||||
\(513\) | −452.566 | + | 268.197i | −0.882195 | + | 0.522802i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 438.569 | 0.848297 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 301.264 | 0.580470 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 235.653i | − | 0.452309i | −0.974091 | − | 0.226155i | \(-0.927385\pi\) | ||
0.974091 | − | 0.226155i | \(-0.0726154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 290.076i | − | 0.554639i | −0.960778 | − | 0.277320i | \(-0.910554\pi\) | ||
0.960778 | − | 0.277320i | \(-0.0894461\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 152.776i | 0.289898i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −409.372 | −0.773860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 490.087i | − | 0.922951i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1673.80 | −3.14033 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 270.880 | 0.504431 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 207.922 | 0.382913 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 571.004i | − | 1.04388i | −0.852981 | − | 0.521942i | \(-0.825208\pi\) | ||
0.852981 | − | 0.521942i | \(-0.174792\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −532.931 | −0.970730 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 464.606 | − | 275.332i | 0.843205 | − | 0.499696i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 161.687i | 0.292382i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −245.730 | −0.441166 | −0.220583 | − | 0.975368i | \(-0.570796\pi\) | ||||
−0.220583 | + | 0.975368i | \(0.570796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1452.75i | − | 2.59884i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 114.212i | 0.203586i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 623.923i | − | 1.10821i | −0.832446 | − | 0.554106i | \(-0.813060\pi\) | ||
0.832446 | − | 0.554106i | \(-0.186940\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.8334 | −0.0279249 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | 512.864i | 0.895051i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −521.531 | −0.903866 | −0.451933 | − | 0.892052i | \(-0.649265\pi\) | ||||
−0.451933 | + | 0.892052i | \(0.649265\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −66.4519 | −0.114770 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −201.156 | −0.346224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 306.204i | 0.525221i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −195.026 | −0.332243 | −0.166121 | − | 0.986105i | \(-0.553124\pi\) | ||||
−0.166121 | + | 0.986105i | \(0.553124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 405.525 | − | 240.320i | 0.688497 | − | 0.408014i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 572.525i | − | 0.968740i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −333.768 | −0.562847 | −0.281423 | − | 0.959584i | \(-0.590807\pi\) | ||||
−0.281423 | + | 0.959584i | \(0.590807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 282.564i | − | 0.473307i | ||||||
\(598\) | 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 | \(-0.679657\pi\) | ||
0.534916 | − | 0.844905i | \(-0.320343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 358.668i | − | 0.594806i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 916.408i | 1.50973i | 0.655878 | + | 0.754867i | \(0.272298\pi\) | ||||
−0.655878 | + | 0.754867i | \(0.727702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 121.271 | 0.199132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 945.333i | − | 1.54719i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −265.921 | −0.433802 | −0.216901 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216901 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.9941 | 0.0405091 | 0.0202545 | − | 0.999795i | \(-0.493552\pi\) | ||||
0.0202545 | + | 0.999795i | \(0.493552\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −52.7690 | −0.0852488 | −0.0426244 | − | 0.999091i | \(-0.513572\pi\) | ||||
−0.0426244 | + | 0.999091i | \(0.513572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 302.833i | 0.487654i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 125.482i | 0.201416i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 303.161 | − | 179.657i | 0.483510 | − | 0.286535i | ||||
\(628\) | 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 | ||||||||
\(633\) | 692.971 | 1.09474 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 906.297i | − | 1.42276i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 210.810i | 0.329906i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 795.892i | 1.24164i | 0.783953 | + | 0.620821i | \(0.213201\pi\) | ||||
−0.783953 | + | 0.620821i | \(0.786799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 927.013 | 1.44170 | 0.720850 | − | 0.693092i | \(-0.243752\pi\) | ||||
0.720850 | + | 0.693092i | \(0.243752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 128.287 | 0.198280 | 0.0991401 | − | 0.995073i | \(-0.468391\pi\) | ||||
0.0991401 | + | 0.995073i | \(0.468391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 896.938i | 1.38203i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 105.850 | 0.162596 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −745.488 | −1.14164 | −0.570818 | − | 0.821077i | \(-0.693374\pi\) | ||||
−0.570818 | + | 0.821077i | \(0.693374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 531.075 | 0.808334 | ||||||||
\(658\) | 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 | \(0.0531392\pi\) | ||||
−0.986098 | + | 0.166167i | \(0.946861\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 246.183 | 0.371317 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 310.889i | − | 0.466101i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 644.346 | 0.963148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 975.349 | 1.45357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 145.649i | − | 0.216418i | −0.994128 | − | 0.108209i | \(-0.965488\pi\) | ||
0.994128 | − | 0.108209i | \(-0.0345115\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1031.23i | − | 1.52323i | −0.648029 | − | 0.761616i | \(-0.724406\pi\) | ||
0.648029 | − | 0.761616i | \(-0.275594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 184.455i | 0.271658i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.7203 | 0.0671370 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1266.00i | 1.85358i | 0.375577 | + | 0.926791i | \(0.377445\pi\) | ||||
−0.375577 | + | 0.926791i | \(0.622555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 358.307i | − | 0.521553i | ||||||
\(688\) | 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 | ||||||||
\(693\) | −108.086 | −0.155968 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 502.846i | 0.721443i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −611.966 | + | 362.660i | −0.870506 | + | 0.515875i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 151.525 | 0.214321 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 131.077 | 0.184875 | 0.0924377 | − | 0.995718i | \(-0.470534\pi\) | ||||
0.0924377 | + | 0.995718i | \(0.470534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 384.057i | 0.540165i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 271.356i | − | 0.380583i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 155.066i | − | 0.216271i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 820.977 | 1.14183 | 0.570916 | − | 0.821008i | \(-0.306588\pi\) | ||||
0.570916 | + | 0.821008i | \(0.306588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 219.169i | 0.303980i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 238.931 | 0.330472 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1121.14 | 1.54214 | 0.771071 | − | 0.636749i | \(-0.219721\pi\) | ||||
0.771071 | + | 0.636749i | \(0.219721\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −523.626 | −0.718280 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −436.438 | −0.597043 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −97.7494 | −0.133355 | −0.0666777 | − | 0.997775i | \(-0.521240\pi\) | ||||
−0.0666777 | + | 0.997775i | \(0.521240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 656.420i | 0.890665i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −520.032 | −0.703697 | −0.351849 | − | 0.936057i | \(-0.614447\pi\) | ||||
−0.351849 | + | 0.936057i | \(0.614447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −387.250 | − | 653.460i | −0.522605 | − | 0.881863i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1357.00i | 1.82638i | 0.407535 | + | 0.913189i | \(0.366388\pi\) | ||||
−0.407535 | + | 0.913189i | \(0.633612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −477.808 | −0.639635 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 115.356i | 0.154013i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 431.283i | − | 0.574278i | −0.957889 | − | 0.287139i | \(-0.907296\pi\) | ||
0.957889 | − | 0.287139i | \(-0.0927042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 37.5128i | − | 0.0498178i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −665.943 | −0.879713 | −0.439857 | − | 0.898068i | \(-0.644971\pi\) | ||||
−0.439857 | + | 0.898068i | \(0.644971\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 167.868i | 0.220010i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1933.34 | 2.52066 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1263.74 | −1.64336 | −0.821678 | − | 0.569953i | \(-0.806962\pi\) | ||||
−0.821678 | + | 0.569953i | \(0.806962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −117.842 | −0.152843 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 441.297i | − | 0.570889i | −0.958395 | − | 0.285445i | \(-0.907859\pi\) | ||
0.958395 | − | 0.285445i | \(-0.0921412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −159.735 | −0.205579 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1334.74 | − | 790.985i | 1.71340 | − | 1.01538i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 385.815i | − | 0.494002i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 787.004 | 1.00511 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 367.069i | 0.466415i | 0.972427 | + | 0.233207i | \(0.0749221\pi\) | ||||
−0.972427 | + | 0.233207i | \(0.925078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.2268i | 0.0573216i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 459.925i | − | 0.581447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2102.36i | − | 2.65114i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 923.535i | − | 1.15876i | −0.815056 | − | 0.579382i | \(-0.803294\pi\) | ||
0.815056 | − | 0.579382i | \(-0.196706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −283.999 | −0.355443 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 298.059i | 0.372108i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −971.953 | −1.21040 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −411.964 | −0.510488 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −823.083 | −1.01741 | −0.508704 | − | 0.860942i | \(-0.669875\pi\) | ||||
−0.508704 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 125.683i | 0.154973i | 0.996993 | + | 0.0774866i | \(0.0246895\pi\) | ||||
−0.996993 | + | 0.0774866i | \(0.975311\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 724.017i | 0.890550i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 686.525 | + | 1158.47i | 0.840300 | + | 1.41795i | ||||
\(818\) | 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 | ||||||||
\(823\) | 823.797 | 1.00097 | 0.500484 | − | 0.865746i | \(-0.333155\pi\) | ||||
0.500484 | + | 0.865746i | \(0.333155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 654.261i | 0.791125i | 0.918439 | + | 0.395563i | \(0.129450\pi\) | ||||
−0.918439 | + | 0.395563i | \(0.870550\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | −272.272 | −0.326857 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 686.925 | 0.820699 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −14.5688 | −0.0172821 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −66.8721 | −0.0789517 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 124.932i | − | 0.147152i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 409.495i | 0.481192i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 600.529 | 0.704020 | 0.352010 | − | 0.935996i | \(-0.385498\pi\) | ||||
0.352010 | + | 0.935996i | \(0.385498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1059.28i | 1.23603i | 0.786167 | + | 0.618015i | \(0.212063\pi\) | ||||
−0.786167 | + | 0.618015i | \(0.787937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −734.054 | −0.854545 | −0.427272 | − | 0.904123i | \(-0.640525\pi\) | ||||
−0.427272 | + | 0.904123i | \(0.640525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 348.392 | 0.404637 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 714.413i | − | 0.827825i | −0.910317 | − | 0.413912i | \(-0.864162\pi\) | ||
0.910317 | − | 0.413912i | \(-0.135838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 489.705i | 0.564826i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 702.886i | − | 0.808845i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1414.91 | 1.62447 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 438.139i | 0.501878i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1129.51i | 1.28792i | 0.765059 | + | 0.643961i | \(0.222710\pi\) | ||||
−0.765059 | + | 0.643961i | \(0.777290\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −199.206 | −0.225602 | −0.112801 | − | 0.993618i | \(-0.535982\pi\) | ||||
−0.112801 | + | 0.993618i | \(0.535982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 727.670i | − | 0.820373i | −0.912002 | − | 0.410186i | \(-0.865464\pi\) | ||
0.912002 | − | 0.410186i | \(-0.134536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 43.5814i | − | 0.0490230i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 68.8310 | 0.0772514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 446.735 | + | 753.837i | 0.500263 | + | 0.844163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −437.261 | −0.487470 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −705.200 | −0.784427 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 198.285i | − | 0.220072i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 302.383i | 0.334865i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1249.33i | − | 1.37743i | −0.725031 | − | 0.688716i | \(-0.758174\pi\) | ||
0.725031 | − | 0.688716i | \(-0.241826\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 359.919 | 0.395950 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 813.909i | − | 0.893423i | −0.894678 | − | 0.446712i | \(-0.852595\pi\) | ||
0.894678 | − | 0.446712i | \(-0.147405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 874.465 | 0.957793 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.21297 | −0.00786584 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 442.339 | 0.481327 | 0.240663 | − | 0.970609i | \(-0.422635\pi\) | ||||
0.240663 | + | 0.970609i | \(0.422635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −751.024 | −0.815444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −831.622 | −0.900999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 520.595i | 0.561591i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 514.468 | 0.553786 | 0.276893 | − | 0.960901i | \(-0.410695\pi\) | ||||
0.276893 | + | 0.960901i | \(0.410695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 428.288 | + | 722.709i | 0.460030 | + | 0.776272i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 210.454i | − | 0.225567i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1147.17 | −1.22430 | −0.612149 | − | 0.790743i | \(-0.709695\pi\) | ||||
−0.612149 | + | 0.790743i | \(0.709695\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 606.711i | 0.646124i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1355.11i | − | 1.44008i | −0.693934 | − | 0.720039i | \(-0.744124\pi\) | ||
0.693934 | − | 0.720039i | \(-0.255876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 893.134i | − | 0.947120i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1560.15 | −1.64746 | −0.823732 | − | 0.566980i | \(-0.808112\pi\) | ||||
−0.823732 | + | 0.566980i | \(0.808112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2095.04i | 2.20763i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −416.937 | −0.438420 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 643.715i | − | 0.675461i | −0.941243 | − | 0.337731i | \(-0.890341\pi\) | ||
0.941243 | − | 0.337731i | \(-0.109659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −527.190 | −0.550878 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −324.159 | −0.338018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 345.476 | 0.359496 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 274.006i | 0.284534i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 570.639 | 0.590113 | 0.295056 | − | 0.955480i | \(-0.404662\pi\) | ||||
0.295056 | + | 0.955480i | \(0.404662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −196.314 | + | 116.339i | −0.202594 | + | 0.120060i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 516.280i | − | 0.531699i | −0.964015 | − | 0.265850i | \(-0.914348\pi\) | ||
0.964015 | − | 0.265850i | \(-0.0856525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 118.721 | 0.122016 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 432.740i | − | 0.442927i | −0.975169 | − | 0.221464i | \(-0.928917\pi\) | ||
0.975169 | − | 0.221464i | \(-0.0710834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 545.495i | − | 0.557196i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 398.739i | 0.406461i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1116.57i | − | 1.13588i | −0.823070 | − | 0.567940i | \(-0.807740\pi\) | ||
0.823070 | − | 0.567940i | \(-0.192260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 196.766i | 0.199358i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 775.185 | 0.783806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1158.19i | 1.16871i | 0.811499 | + | 0.584354i | \(0.198652\pi\) | ||||
−0.811499 | + | 0.584354i | \(0.801348\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −483.843 | −0.487254 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 76.0503 | 0.0762792 | 0.0381396 | − | 0.999272i | \(-0.487857\pi\) | ||||
0.0381396 | + | 0.999272i | \(0.487857\pi\) | |||||||
\(998\) | 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 | 1900.3.e.e.1101.6 | 12 | ||
5.2 | odd | 4 | 380.3.g.c.189.5 | ✓ | 12 | ||
5.3 | odd | 4 | 380.3.g.c.189.8 | yes | 12 | ||
5.4 | even | 2 | inner | 1900.3.e.e.1101.7 | 12 | ||
15.2 | even | 4 | 3420.3.h.e.2089.12 | 12 | |||
15.8 | even | 4 | 3420.3.h.e.2089.9 | 12 | |||
19.18 | odd | 2 | inner | 1900.3.e.e.1101.8 | 12 | ||
95.18 | even | 4 | 380.3.g.c.189.6 | yes | 12 | ||
95.37 | even | 4 | 380.3.g.c.189.7 | yes | 12 | ||
95.94 | odd | 2 | inner | 1900.3.e.e.1101.5 | 12 | ||
285.113 | odd | 4 | 3420.3.h.e.2089.10 | 12 | |||
285.227 | odd | 4 | 3420.3.h.e.2089.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.g.c.189.5 | ✓ | 12 | 5.2 | odd | 4 | ||
380.3.g.c.189.6 | yes | 12 | 95.18 | even | 4 | ||
380.3.g.c.189.7 | yes | 12 | 95.37 | even | 4 | ||
380.3.g.c.189.8 | yes | 12 | 5.3 | odd | 4 | ||
1900.3.e.e.1101.5 | 12 | 95.94 | odd | 2 | inner | ||
1900.3.e.e.1101.6 | 12 | 1.1 | even | 1 | trivial | ||
1900.3.e.e.1101.7 | 12 | 5.4 | even | 2 | inner | ||
1900.3.e.e.1101.8 | 12 | 19.18 | odd | 2 | inner | ||
3420.3.h.e.2089.9 | 12 | 15.8 | even | 4 | |||
3420.3.h.e.2089.10 | 12 | 285.113 | odd | 4 | |||
3420.3.h.e.2089.11 | 12 | 285.227 | odd | 4 | |||
3420.3.h.e.2089.12 | 12 | 15.2 | even | 4 |