Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.2 | ||
Root | \(-1.27069 - 2.20090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.j.1471.4 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.08276 | 1.81655 | 0.908276 | − | 0.418371i | \(-0.137399\pi\) | ||||
0.908276 | + | 0.418371i | \(0.137399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 8.80360i | − 0.800328i | −0.916444 | − | 0.400164i | \(-0.868953\pi\) | ||||
0.916444 | − | 0.400164i | \(-0.131047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 15.7318i | − 1.04879i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.91724 | −0.171602 | −0.0858011 | − | 0.996312i | \(-0.527345\pi\) | ||||
−0.0858011 | + | 0.996312i | \(0.527345\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.6072i | 0.926695i | 0.886177 | + | 0.463348i | \(0.153352\pi\) | ||||
−0.886177 | + | 0.463348i | \(0.846648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.5882i | 1.28644i | 0.765680 | + | 0.643222i | \(0.222403\pi\) | ||||
−0.765680 | + | 0.643222i | \(0.777597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 57.4966 | 2.29986 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 48.4966 | 1.67230 | 0.836148 | − | 0.548504i | \(-0.184803\pi\) | ||||
0.836148 | + | 0.548504i | \(0.184803\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.3918i | 1.23845i | 0.785215 | + | 0.619223i | \(0.212552\pi\) | ||||
−0.785215 | + | 0.619223i | \(0.787448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.2483 | −0.462069 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.4966 | −0.553961 | −0.276981 | − | 0.960875i | \(-0.589334\pi\) | ||||
−0.276981 | + | 0.960875i | \(0.589334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 26.9172 | 0.656518 | 0.328259 | − | 0.944588i | \(-0.393538\pi\) | ||||
0.328259 | + | 0.944588i | \(0.393538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 27.7128i | − 0.644484i | −0.946657 | − | 0.322242i | \(-0.895564\pi\) | ||||
0.946657 | − | 0.322242i | \(-0.104436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.2483 | −0.605518 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 62.9272i | − 1.33888i | −0.742867 | − | 0.669439i | \(-0.766535\pi\) | ||||
0.742867 | − | 0.669439i | \(-0.233465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.05280i | 0.0990746i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 84.4966 | 1.59428 | 0.797138 | − | 0.603798i | \(-0.206347\pi\) | ||||
0.797138 | + | 0.603798i | \(0.206347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 79.9610i | − 1.45384i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.4966 | 0.535028 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 42.1426i | − 0.714282i | −0.934051 | − | 0.357141i | \(-0.883752\pi\) | ||||
0.934051 | − | 0.357141i | \(-0.116248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 102.497 | 1.68027 | 0.840136 | − | 0.542376i | \(-0.182475\pi\) | ||||
0.840136 | + | 0.542376i | \(0.182475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 52.8216i | − 0.788382i | −0.919028 | − | 0.394191i | \(-0.871025\pi\) | ||||
0.919028 | − | 0.394191i | \(-0.128975\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 51.2483 | 0.742729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 64.8026i | − 0.912713i | −0.889797 | − | 0.456357i | \(-0.849154\pi\) | ||||
0.889797 | − | 0.456357i | \(-0.150846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.4966 | 0.417761 | 0.208881 | − | 0.977941i | \(-0.433018\pi\) | ||||
0.208881 | + | 0.977941i | \(0.433018\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 99.5870i | − 1.32783i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 149.816i | 1.89641i | 0.317658 | + | 0.948205i | \(0.397104\pi\) | ||||
−0.317658 | + | 0.948205i | \(0.602896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.573396i | 0.00690838i | 0.999994 | + | 0.00345419i | \(0.00109951\pi\) | ||||
−0.999994 | + | 0.00345419i | \(0.998900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.4966 | −0.311724 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 83.9985i | − 0.965500i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0759 | −0.113213 | −0.0566063 | − | 0.998397i | \(-0.518028\pi\) | ||||
−0.0566063 | + | 0.998397i | \(0.518028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 66.4966 | 0.715017 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 159.922i | 1.68339i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 113.503 | 1.17014 | 0.585069 | − | 0.810983i | \(-0.301067\pi\) | ||||
0.585069 | + | 0.810983i | \(0.301067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.4108i | 0.266776i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −142.076 | −1.40669 | −0.703346 | − | 0.710848i | \(-0.748312\pi\) | ||||
−0.703346 | + | 0.710848i | \(0.748312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 185.604i | 1.80198i | 0.433837 | + | 0.900992i | \(0.357160\pi\) | ||||
−0.433837 | + | 0.900992i | \(0.642840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 120.802i | − 1.12899i | −0.825437 | − | 0.564494i | \(-0.809071\pi\) | ||||
0.825437 | − | 0.564494i | \(-0.190929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −142.993 | −1.31186 | −0.655932 | − | 0.754820i | \(-0.727724\pi\) | ||||
−0.655932 | + | 0.754820i | \(0.727724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.5011i | 0.319830i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −114.993 | −1.01764 | −0.508819 | − | 0.860873i | \(-0.669918\pi\) | ||||
−0.508819 | + | 0.860873i | \(0.669918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 268.743i | 2.33689i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43.4966 | 0.359476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 46.6220i | − 0.379041i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 295.159 | 2.36127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 38.9652i | 0.306813i | 0.988163 | + | 0.153406i | \(0.0490243\pi\) | ||||
−0.988163 | + | 0.153406i | \(0.950976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −48.0000 | −0.372093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 187.061i | − 1.42795i | −0.700171 | − | 0.713975i | \(-0.746893\pi\) | ||||
0.700171 | − | 0.713975i | \(-0.253107\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 47.1954i | 0.349596i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −139.986 | −1.02180 | −0.510899 | − | 0.859641i | \(-0.670687\pi\) | ||||
−0.510899 | + | 0.859641i | \(0.670687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 209.566i | − 1.50767i | −0.657063 | − | 0.753836i | \(-0.728202\pi\) | ||||
0.657063 | − | 0.753836i | \(-0.271798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −108.993 | −0.773001 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 440.483 | 3.03781 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84.4966 | 0.567091 | 0.283546 | − | 0.958959i | \(-0.408489\pi\) | ||||
0.283546 | + | 0.958959i | \(0.408489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 238.999i | 1.58278i | 0.611314 | + | 0.791388i | \(0.290641\pi\) | ||||
−0.611314 | + | 0.791388i | \(0.709359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.75171 | 0.0572007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 348.704i | 2.24970i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 80.4829 | 0.512630 | 0.256315 | − | 0.966593i | \(-0.417492\pi\) | ||||
0.256315 | + | 0.966593i | \(0.417492\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 146.352i | − 0.920455i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 297.029i | − 1.82226i | −0.412115 | − | 0.911132i | \(-0.635210\pi\) | ||||
0.412115 | − | 0.911132i | \(-0.364790\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −138.497 | −0.839373 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 229.204i | − 1.37248i | −0.727375 | − | 0.686240i | \(-0.759260\pi\) | ||||
0.727375 | − | 0.686240i | \(-0.240740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 52.8216i | − 0.308898i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 206.917 | 1.19605 | 0.598027 | − | 0.801476i | \(-0.295952\pi\) | ||||
0.598027 | + | 0.801476i | \(0.295952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −72.9932 | −0.412391 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 56.7276i | 0.316914i | 0.987366 | + | 0.158457i | \(0.0506519\pi\) | ||||
−0.987366 | + | 0.158457i | \(0.949348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0137 | 0.121623 | 0.0608113 | − | 0.998149i | \(-0.480631\pi\) | ||||
0.0608113 | + | 0.998149i | \(0.480631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 177.529i | − 0.970105i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −186.166 | −1.00630 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.6822i | 0.137338i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 140.129i | 0.733660i | 0.930288 | + | 0.366830i | \(0.119557\pi\) | ||||
−0.930288 | + | 0.366830i | \(0.880443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −149.490 | −0.774558 | −0.387279 | − | 0.921963i | \(-0.626585\pi\) | ||||
−0.387279 | + | 0.921963i | \(0.626585\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 106.510 | 0.540661 | 0.270331 | − | 0.962768i | \(-0.412867\pi\) | ||||
0.270331 | + | 0.962768i | \(0.412867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 111.998i | 0.562804i | 0.959590 | + | 0.281402i | \(0.0907995\pi\) | ||||
−0.959590 | + | 0.281402i | \(0.909201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −91.4897 | −0.455173 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 244.483 | 1.19260 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 88.7646i | − 0.428815i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 155.007 | 0.741660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 105.643i | − 0.500679i | −0.968158 | − | 0.250339i | \(-0.919458\pi\) | ||||
0.968158 | − | 0.250339i | \(-0.0805422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −112.241 | −0.526955 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 251.709i | − 1.17074i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 52.8216i | − 0.241195i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 255.770i | − 1.14695i | −0.819223 | − | 0.573476i | \(-0.805595\pi\) | ||||
0.819223 | − | 0.573476i | \(-0.194405\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −172.490 | −0.766621 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 81.4183i | 0.358671i | 0.983788 | + | 0.179335i | \(0.0573947\pi\) | ||||
−0.983788 | + | 0.179335i | \(0.942605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −38.9795 | −0.170216 | −0.0851080 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851080 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −306.000 | −1.31330 | −0.656652 | − | 0.754193i | \(-0.728028\pi\) | ||||
−0.656652 | + | 0.754193i | \(0.728028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 571.553i | − 2.43214i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 259.490 | 1.09489 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 243.789i | 1.02004i | 0.860163 | + | 0.510019i | \(0.170362\pi\) | ||||
−0.860163 | + | 0.510019i | \(0.829638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −357.476 | −1.48330 | −0.741652 | − | 0.670785i | \(-0.765957\pi\) | ||||
−0.741652 | + | 0.670785i | \(0.765957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.993150 | 0.00398856 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 189.355i | 0.754403i | 0.926131 | + | 0.377201i | \(0.123114\pi\) | ||||
−0.926131 | + | 0.377201i | \(0.876886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 260.483 | 1.02958 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 45.8934i | 0.179974i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 207.910 | 0.808990 | 0.404495 | − | 0.914540i | \(-0.367447\pi\) | ||||
0.404495 | + | 0.914540i | \(0.367447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −145.490 | −0.557432 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 237.434i | 0.902792i | 0.892324 | + | 0.451396i | \(0.149074\pi\) | ||||
−0.892324 | + | 0.451396i | \(0.850926\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 767.462 | 2.89608 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.4520i | 0.0653633i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 83.0691 | 0.308807 | 0.154403 | − | 0.988008i | \(-0.450654\pi\) | ||||
0.154403 | + | 0.988008i | \(0.450654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 239.883i | − 0.885178i | −0.896725 | − | 0.442589i | \(-0.854060\pi\) | ||||
0.896725 | − | 0.442589i | \(-0.145940\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 506.177i | − 1.84064i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 78.4829 | 0.283332 | 0.141666 | − | 0.989915i | \(-0.454754\pi\) | ||||
0.141666 | + | 0.989915i | \(0.454754\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 115.175i | − 0.412815i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 380.979 | 1.35580 | 0.677899 | − | 0.735155i | \(-0.262890\pi\) | ||||
0.677899 | + | 0.735155i | \(0.262890\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 49.3812i | 0.174492i | 0.996187 | + | 0.0872460i | \(0.0278066\pi\) | ||||
−0.996187 | + | 0.0872460i | \(0.972193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 276.993 | 0.971906 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −280.490 | −0.970553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 196.594i | − 0.675580i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 217.924 | 0.743768 | 0.371884 | − | 0.928279i | \(-0.378712\pi\) | ||||
0.371884 | + | 0.928279i | \(0.378712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 382.771i | − 1.29753i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 45.7449 | 0.154023 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 246.083i | 0.812154i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 930.952 | 3.05230 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 164.820i | 0.536872i | 0.963298 | + | 0.268436i | \(0.0865068\pi\) | ||||
−0.963298 | + | 0.268436i | \(0.913493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 321.476 | 1.04038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 353.912i | − 1.13798i | −0.822344 | − | 0.568990i | \(-0.807334\pi\) | ||||
0.822344 | − | 0.568990i | \(-0.192666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 265.986 | 0.849796 | 0.424898 | − | 0.905241i | \(-0.360310\pi\) | ||||
0.424898 | + | 0.905241i | \(0.360310\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −292.469 | −0.922616 | −0.461308 | − | 0.887240i | \(-0.652620\pi\) | ||||
−0.461308 | + | 0.887240i | \(0.652620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 426.945i | − 1.33838i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −209.235 | −0.651821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 51.3644i | − 0.159023i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 247.671i | 0.757405i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 538.632i | 1.62729i | 0.581364 | + | 0.813644i | \(0.302519\pi\) | ||||
−0.581364 | + | 0.813644i | \(0.697481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 61.4897 | 0.184654 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 479.766i | − 1.43214i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135.986 | 0.403520 | 0.201760 | − | 0.979435i | \(-0.435334\pi\) | ||||
0.201760 | + | 0.979435i | \(0.435334\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 199.174i | 0.587534i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 337.986 | 0.991162 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 465.476 | 1.34921 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 312.498i | 0.900570i | 0.892885 | + | 0.450285i | \(0.148678\pi\) | ||||
−0.892885 | + | 0.450285i | \(0.851322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −407.462 | −1.16751 | −0.583757 | − | 0.811928i | \(-0.698418\pi\) | ||||
−0.583757 | + | 0.811928i | \(0.698418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 154.076 | 0.436476 | 0.218238 | − | 0.975896i | \(-0.429969\pi\) | ||||
0.218238 | + | 0.975896i | \(0.429969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 588.587i | − 1.65799i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 413.506i | − 1.15183i | −0.817510 | − | 0.575914i | \(-0.804646\pi\) | ||||
0.817510 | − | 0.575914i | \(-0.195354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.9863 | 0.141236 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 75.3383i | − 0.207543i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 276.993 | 0.758885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 639.688i | − 1.74302i | −0.490378 | − | 0.871510i | \(-0.663141\pi\) | ||||
0.490378 | − | 0.871510i | \(-0.336859\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −80.7517 | −0.218839 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −265.973 | −0.713063 | −0.356532 | − | 0.934283i | \(-0.616041\pi\) | ||||
−0.356532 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 511.230i | − 1.36328i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 32.9208i | − 0.0868623i | −0.999056 | − | 0.0434312i | \(-0.986171\pi\) | ||||
0.999056 | − | 0.0434312i | \(-0.0138289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 67.4897 | 0.177138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 673.135i | 1.75753i | 0.477252 | + | 0.878766i | \(0.341633\pi\) | ||||
−0.477252 | + | 0.878766i | \(0.658367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 83.1384i | 0.214828i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 236.524 | 0.608031 | 0.304015 | − | 0.952667i | \(-0.401673\pi\) | ||||
0.304015 | + | 0.952667i | \(0.401673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 86.3158i | − 0.220757i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −324.000 | −0.824427 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1360.75i | 3.44493i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −695.462 | −1.75179 | −0.875897 | − | 0.482498i | \(-0.839730\pi\) | ||||
−0.875897 | + | 0.482498i | \(0.839730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −184.014 | −0.458887 | −0.229444 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229444 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 81.7449 | 0.201839 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 180.444i | 0.443351i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −257.503 | −0.629593 | −0.314796 | − | 0.949159i | \(-0.601936\pi\) | ||||
−0.314796 | + | 0.949159i | \(0.601936\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 242.463i | 0.589935i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.20802i | 0.0125494i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −362.979 | −0.870454 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 361.366i | − 0.862448i | −0.902245 | − | 0.431224i | \(-0.858082\pi\) | ||||
0.902245 | − | 0.431224i | \(-0.141918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −191.476 | −0.454812 | −0.227406 | − | 0.973800i | \(-0.573025\pi\) | ||||
−0.227406 | + | 0.973800i | \(0.573025\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 188.782i | 0.446292i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −167.731 | −0.394662 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 299.525i | 0.694954i | 0.937689 | + | 0.347477i | \(0.112962\pi\) | ||||
−0.937689 | + | 0.347477i | \(0.887038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 448.966 | 1.03687 | 0.518436 | − | 0.855116i | \(-0.326514\pi\) | ||||
0.518436 | + | 0.855116i | \(0.326514\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 762.939i | − 1.75388i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −520.966 | −1.19214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 486.647i | − 1.10854i | −0.832339 | − | 0.554268i | \(-0.812998\pi\) | ||||
0.832339 | − | 0.554268i | \(-0.187002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 367.303i | 0.829125i | 0.910021 | + | 0.414563i | \(0.136065\pi\) | ||||
−0.910021 | + | 0.414563i | \(0.863935\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −91.5171 | −0.205656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 146.352i | − 0.327410i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 306.000 | 0.681514 | 0.340757 | − | 0.940151i | \(-0.389317\pi\) | ||||
0.340757 | + | 0.940151i | \(0.389317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 236.969i | − 0.525429i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 413.959 | 0.913817 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 152.014 | 0.332634 | 0.166317 | − | 0.986072i | \(-0.446813\pi\) | ||||
0.166317 | + | 0.986072i | \(0.446813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 15.1584i | − 0.0330249i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 103.883 | 0.225343 | 0.112671 | − | 0.993632i | \(-0.464059\pi\) | ||||
0.112671 | + | 0.993632i | \(0.464059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 189.618i | 0.409542i | 0.978810 | + | 0.204771i | \(0.0656450\pi\) | ||||
−0.978810 | + | 0.204771i | \(0.934355\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 603.973 | 1.29887 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 187.061i | − 0.400560i | −0.979739 | − | 0.200280i | \(-0.935815\pi\) | ||||
0.979739 | − | 0.200280i | \(-0.0641852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 139.400i | − 0.295967i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −243.973 | −0.515798 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1012.35i | 2.13127i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −253.490 | −0.531425 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 416.839i | − 0.870228i | −0.900375 | − | 0.435114i | \(-0.856708\pi\) | ||||
0.900375 | − | 0.435114i | \(-0.143292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1030.92 | 2.12562 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 105.643i | 0.216927i | 0.994100 | + | 0.108463i | \(0.0345930\pi\) | ||||
−0.994100 | + | 0.108463i | \(0.965407\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −514.469 | −1.05208 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 920.412i | 1.87457i | 0.348569 | + | 0.937283i | \(0.386668\pi\) | ||||
−0.348569 | + | 0.937283i | \(0.613332\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −141.476 | −0.286970 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 239.883i | 0.484612i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 337.762i | 0.676877i | 0.940988 | + | 0.338439i | \(0.109899\pi\) | ||||
−0.940988 | + | 0.338439i | \(0.890101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −396.993 | −0.792401 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 612.501i | 1.21770i | 0.793287 | + | 0.608848i | \(0.208368\pi\) | ||||
−0.793287 | + | 0.608848i | \(0.791632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1290.44 | −2.55533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 292.717i | 0.577350i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 181.055 | 0.355708 | 0.177854 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177854 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −91.4897 | −0.178343 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1685.80i | 3.27340i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −553.986 | −1.07154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 358.391i | − 0.690542i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 878.049 | 1.68531 | 0.842657 | − | 0.538451i | \(-0.180990\pi\) | ||||
0.842657 | + | 0.538451i | \(0.180990\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 456.067i | − 0.872021i | −0.899941 | − | 0.436011i | \(-0.856391\pi\) | ||||
0.899941 | − | 0.436011i | \(-0.143609\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 111.998i | − 0.212520i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −346.462 | −0.654938 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 126.428i | 0.238094i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1097.21i | − 2.05086i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 98.2551 | 0.182970 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 558.483 | 1.03232 | 0.516158 | − | 0.856493i | \(-0.327362\pi\) | ||||
0.516158 | + | 0.856493i | \(0.327362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 38.1288i | − 0.0702189i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1298.77 | −2.38307 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 579.365i | − 1.05917i | −0.848257 | − | 0.529584i | \(-0.822348\pi\) | ||||
0.848257 | − | 0.529584i | \(-0.177652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −307.490 | −0.560091 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 853.889i | 1.54971i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 322.448i | 0.580988i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.4760 | −0.0277846 | −0.0138923 | − | 0.999903i | \(-0.504422\pi\) | ||||
−0.0138923 | + | 0.999903i | \(0.504422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.4829 | 0.0792921 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 715.278i | − 1.27048i | −0.772317 | − | 0.635238i | \(-0.780902\pi\) | ||||
0.772317 | − | 0.635238i | \(-0.219098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1044.46 | −1.84859 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −660.952 | −1.16160 | −0.580801 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580801 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 281.405i | 0.492828i | 0.969165 | + | 0.246414i | \(0.0792523\pi\) | ||||
−0.969165 | + | 0.246414i | \(0.920748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 242.711 | 0.423579 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1701.22i | 2.95865i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −570.952 | −0.989518 | −0.494759 | − | 0.869030i | \(-0.664744\pi\) | ||||
−0.494759 | + | 0.869030i | \(0.664744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 258.924i | 0.447191i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 743.874i | − 1.27594i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 455.541i | 0.776050i | 0.921649 | + | 0.388025i | \(0.126843\pi\) | ||||
−0.921649 | + | 0.388025i | \(0.873157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −675.973 | −1.14766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 184.481i | − 0.312151i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1038.89 | −1.75192 | −0.875961 | − | 0.482382i | \(-0.839772\pi\) | ||||
−0.875961 | + | 0.482382i | \(0.839772\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 193.986 | 0.324935 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 884.935i | 1.47735i | 0.674060 | + | 0.738677i | \(0.264549\pi\) | ||||
−0.674060 | + | 0.738677i | \(0.735451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 282.952 | 0.470802 | 0.235401 | − | 0.971898i | \(-0.424360\pi\) | ||||
0.235401 | + | 0.971898i | \(0.424360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 158.465i | 0.262794i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 395.069 | 0.653007 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 185.341i | 0.305340i | 0.988277 | + | 0.152670i | \(0.0487871\pi\) | ||||
−0.988277 | + | 0.152670i | \(0.951213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −849.945 | −1.38653 | −0.693267 | − | 0.720681i | \(-0.743829\pi\) | ||||
−0.693267 | + | 0.720681i | \(0.743829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 423.457i | − 0.688548i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.0342 | 0.0600231 | 0.0300115 | − | 0.999550i | \(-0.490446\pi\) | ||||
0.0300115 | + | 0.999550i | \(0.490446\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 554.830i | 0.896332i | 0.893950 | + | 0.448166i | \(0.147923\pi\) | ||||
−0.893950 | + | 0.448166i | \(0.852077\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −153.745 | −0.247576 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1243.44 | 1.98951 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 268.480i | − 0.428197i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 59.7934 | 0.0950610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 633.023i | − 1.00321i | −0.865098 | − | 0.501603i | \(-0.832744\pi\) | ||||
0.865098 | − | 0.501603i | \(-0.167256\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −182.979 | −0.289067 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 353.912i | 0.557341i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 194.408i | 0.304238i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −228.952 | −0.357179 | −0.178590 | − | 0.983924i | \(-0.557153\pi\) | ||||
−0.178590 | + | 0.983924i | \(0.557153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 724.284i | 1.12641i | 0.826316 | + | 0.563207i | \(0.190433\pi\) | ||||
−0.826316 | + | 0.563207i | \(0.809567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −435.973 | −0.675927 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 739.503i | 1.14297i | 0.820612 | + | 0.571486i | \(0.193633\pi\) | ||||
−0.820612 | + | 0.571486i | \(0.806367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −371.007 | −0.571659 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −195.476 | −0.299351 | −0.149675 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149675 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1699.04i | − 2.59395i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −91.4897 | −0.139254 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 706.737i | − 1.07244i | −0.844079 | − | 0.536219i | \(-0.819852\pi\) | ||||
0.844079 | − | 0.536219i | \(-0.180148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1210.47 | 1.83127 | 0.915635 | − | 0.402011i | \(-0.131689\pi\) | ||||
0.915635 | + | 0.402011i | \(0.131689\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1434.93i | 2.15131i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −443.007 | −0.662193 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 902.339i | − 1.34477i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 515.449 | 0.765897 | 0.382948 | − | 0.923770i | \(-0.374909\pi\) | ||||
0.382948 | + | 0.923770i | \(0.374909\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 298.761i | 0.442609i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 179.856 | 0.265666 | 0.132833 | − | 0.991138i | \(-0.457593\pi\) | ||||
0.132833 | + | 0.991138i | \(0.457593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 141.021 | 0.207079 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 753.609i | 1.10338i | 0.834049 | + | 0.551690i | \(0.186017\pi\) | ||||
−0.834049 | + | 0.551690i | \(0.813983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1271.46 | −1.85615 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.5144i | 0.0982742i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 235.511i | 0.340827i | 0.985373 | + | 0.170413i | \(0.0545103\pi\) | ||||
−0.985373 | + | 0.170413i | \(0.945490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1903.44i | − 2.73876i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −78.5240 | −0.112660 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 530.008i | 0.758237i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −195.476 | −0.278853 | −0.139427 | − | 0.990232i | \(-0.544526\pi\) | ||||
−0.139427 | + | 0.990232i | \(0.544526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 360.887i | − 0.513353i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −989.959 | −1.40420 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −958.993 | −1.35260 | −0.676300 | − | 0.736626i | \(-0.736418\pi\) | ||||
−0.676300 | + | 0.736626i | \(0.736418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 449.449i | − 0.632137i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1135.95 | −1.59319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 422.255 | 0.588919 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 549.574i | − 0.764359i | −0.924088 | − | 0.382180i | \(-0.875174\pi\) | ||||
0.924088 | − | 0.382180i | \(-0.124826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 619.167i | 0.856385i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2788.39 | 3.84605 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 761.219i | − 1.04707i | −0.852005 | − | 0.523534i | \(-0.824613\pi\) | ||||
0.852005 | − | 0.523534i | \(-0.175387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 80.8449i | 0.110595i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −476.027 | −0.649423 | −0.324712 | − | 0.945813i | \(-0.605267\pi\) | ||||
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −465.021 | −0.630964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 686.681i | 0.929203i | 0.885520 | + | 0.464602i | \(0.153802\pi\) | ||||
−0.885520 | + | 0.464602i | \(0.846198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 423.302i | − 0.569719i | −0.958569 | − | 0.284860i | \(-0.908053\pi\) | ||||
0.958569 | − | 0.284860i | \(-0.0919470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 767.462 | 1.03015 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.72019i | − 0.00230279i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 748.246i | 0.996333i | 0.867081 | + | 0.498166i | \(0.165993\pi\) | ||||
−0.867081 | + | 0.498166i | \(0.834007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 327.973 | 0.435555 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2170.77i | 2.87520i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1264.90 | 1.67093 | 0.835467 | − | 0.549540i | \(-0.185197\pi\) | ||||
0.835467 | + | 0.549540i | \(0.185197\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 451.170i | − 0.594426i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.1170 | −0.0369475 | −0.0184737 | − | 0.999829i | \(-0.505881\pi\) | ||||
−0.0184737 | + | 0.999829i | \(0.505881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 79.4897 | 0.103908 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1334.98 | −1.73599 | −0.867997 | − | 0.496569i | \(-0.834593\pi\) | ||||
−0.867997 | + | 0.496569i | \(0.834593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 360.111i | − 0.467070i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 969.869 | 1.25468 | 0.627341 | − | 0.778745i | \(-0.284143\pi\) | ||||
0.627341 | + | 0.778745i | \(0.284143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2207.40i | 2.84826i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 473.937i | 0.608392i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −570.497 | −0.730469 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 251.996i | 0.321833i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 731.007 | 0.931219 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1047.83i | 1.33142i | 0.746208 | + | 0.665712i | \(0.231872\pi\) | ||||
−0.746208 | + | 0.665712i | \(0.768128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 411.248 | 0.521227 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1329.28i | − 1.67206i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −548.090 | −0.687691 | −0.343845 | − | 0.939026i | \(-0.611730\pi\) | ||||
−0.343845 | + | 0.939026i | \(0.611730\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 183.574i | 0.229754i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.2277 | 0.0377375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 268.480i | − 0.334346i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 143.880i | − 0.178290i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −203.048 | −0.250986 | −0.125493 | − | 0.992094i | \(-0.540051\pi\) | ||||
−0.125493 | + | 0.992094i | \(0.540051\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 279.469i | 0.344598i | 0.985045 | + | 0.172299i | \(0.0551196\pi\) | ||||
−0.985045 | + | 0.172299i | \(0.944880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −415.490 | −0.511057 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2697.84i | − 3.31024i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 487.945 | 0.597240 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1201.41 | −1.46335 | −0.731673 | − | 0.681655i | \(-0.761260\pi\) | ||||
−0.731673 | + | 0.681655i | \(0.761260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 731.786i | − 0.889168i | −0.895737 | − | 0.444584i | \(-0.853351\pi\) | ||||
0.895737 | − | 0.444584i | \(-0.146649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −876.724 | −1.06270 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1164.93i | 1.40862i | 0.709892 | + | 0.704311i | \(0.248744\pi\) | ||||
−0.709892 | + | 0.704311i | \(0.751256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0137 | −0.0265545 | −0.0132773 | − | 0.999912i | \(-0.504226\pi\) | ||||
−0.0132773 | + | 0.999912i | \(0.504226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 135.936i | − 0.163582i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2081.81i | − 2.49318i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −199.490 | −0.238339 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 293.278i | − 0.349557i | −0.984608 | − | 0.174778i | \(-0.944079\pi\) | ||||
0.984608 | − | 0.174778i | \(-0.0559209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1510.92 | 1.79657 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 659.876i | − 0.782771i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1534.99 | −1.81655 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 85.5308 | 0.100743 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 606.457i | − 0.712640i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −495.517 | −0.580911 | −0.290456 | − | 0.956888i | \(-0.593807\pi\) | ||||
−0.290456 | + | 0.956888i | \(0.593807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 479.766i | − 0.561130i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1029.99 | −1.20186 | −0.600930 | − | 0.799302i | \(-0.705203\pi\) | ||||
−0.600930 | + | 0.799302i | \(0.705203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 769.294i | 0.895569i | 0.894142 | + | 0.447784i | \(0.147787\pi\) | ||||
−0.894142 | + | 0.447784i | \(0.852213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 170.972i | 0.198113i | 0.995082 | + | 0.0990567i | \(0.0315825\pi\) | ||||
−0.995082 | + | 0.0990567i | \(0.968417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1879.38 | 2.17269 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 485.822i | 0.560349i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1318.92 | 1.51775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −340.510 | −0.390046 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −919.959 | −1.04898 | −0.524492 | − | 0.851415i | \(-0.675745\pi\) | ||||
−0.524492 | + | 0.851415i | \(0.675745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 377.456i | − 0.429415i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1179.95 | 1.33933 | 0.669667 | − | 0.742662i | \(-0.266437\pi\) | ||||
0.669667 | + | 0.742662i | \(0.266437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1453.16i | − 1.64570i | −0.568257 | − | 0.822851i | \(-0.692382\pi\) | ||||
0.568257 | − | 0.822851i | \(-0.307618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −662.979 | −0.749129 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1017.87i | 1.14755i | 0.819015 | + | 0.573773i | \(0.194521\pi\) | ||||
−0.819015 | + | 0.573773i | \(0.805479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 79.2324i | − 0.0889253i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1107.97 | 1.24073 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 515.244i | 0.575691i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1861.87i | 2.07105i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −246.497 | −0.273581 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 199.945 | 0.220934 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 720.533i | − 0.794414i | −0.917729 | − | 0.397207i | \(-0.869980\pi\) | ||||
0.917729 | − | 0.397207i | \(-0.130020\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 426.228 | 0.468897 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1067.36i | 1.17164i | 0.810442 | + | 0.585819i | \(0.199227\pi\) | ||||
−0.810442 | + | 0.585819i | \(0.800773\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.04795 | 0.00552897 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1612.46i | − 1.76225i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 389.652i | 0.423996i | 0.977270 | + | 0.211998i | \(0.0679970\pi\) | ||||
−0.977270 | + | 0.211998i | \(0.932003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 285.476 | 0.309963 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1178.48 | −1.27404 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 556.813i | − 0.600661i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1268.01 | −1.36492 | −0.682458 | − | 0.730925i | \(-0.739089\pi\) | ||||
−0.682458 | + | 0.730925i | \(0.739089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −612.993 | −0.657013 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 233.265i | 0.249482i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 121.986 | 0.130188 | 0.0650941 | − | 0.997879i | \(-0.479265\pi\) | ||||
0.0650941 | + | 0.997879i | \(0.479265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 460.702i | − 0.490630i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1160.79 | −1.23357 | −0.616787 | − | 0.787130i | \(-0.711566\pi\) | ||||
−0.616787 | + | 0.787130i | \(0.711566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 796.433i | 0.844574i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 59.6421i | − 0.0629800i | −0.999504 | − | 0.0314900i | \(-0.989975\pi\) | ||||
0.999504 | − | 0.0314900i | \(-0.0100252\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 506.571i | 0.532672i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 959.959 | 1.00730 | 0.503651 | − | 0.863907i | \(-0.331990\pi\) | ||||
0.503651 | + | 0.863907i | \(0.331990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1272.76i | 1.33273i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −739.490 | −0.772717 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −512.932 | −0.533748 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 362.405i | 0.376329i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1357.78 | −1.40703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 629.488i | − 0.650970i | −0.945547 | − | 0.325485i | \(-0.894472\pi\) | ||||
0.945547 | − | 0.325485i | \(-0.105528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −88.9658 | −0.0918119 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1048.98i | − 1.08031i | −0.841566 | − | 0.540154i | \(-0.818366\pi\) | ||||
0.841566 | − | 0.540154i | \(-0.181634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −793.945 | −0.812636 | −0.406318 | − | 0.913732i | \(-0.633187\pi\) | ||||
−0.406318 | + | 0.913732i | \(0.633187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 88.7043i | 0.0906071i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 428.979 | 0.437288 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1271.87i | − 1.29387i | −0.762545 | − | 0.646935i | \(-0.776050\pi\) | ||||
0.762545 | − | 0.646935i | \(-0.223950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 967.408 | 0.982140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 819.973 | 0.829093 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 677.196i | − 0.683346i | −0.939819 | − | 0.341673i | \(-0.889006\pi\) | ||||
0.939819 | − | 0.341673i | \(-0.110994\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 932.938 | 0.939515 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1017.25i | 1.02236i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1876.35 | 1.88199 | 0.940996 | − | 0.338418i | \(-0.109892\pi\) | ||||
0.940996 | + | 0.338418i | \(0.109892\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 106.503i | − 0.106610i |
(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 | 2352.3.m.j.1471.2 | yes | 4 | |
4.3 | odd | 2 | inner | 2352.3.m.j.1471.4 | yes | 4 | |
7.6 | odd | 2 | 2352.3.m.e.1471.3 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.e.1471.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.3.m.e.1471.1 | ✓ | 4 | 28.27 | even | 2 | ||
2352.3.m.e.1471.3 | yes | 4 | 7.6 | odd | 2 | ||
2352.3.m.j.1471.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.3.m.j.1471.4 | yes | 4 | 4.3 | odd | 2 | inner |