Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(257,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.257 |
Dual form | 600.2.r.e.593.1 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0.292893 | − | 1.70711i | 0.169102 | − | 0.985599i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 2.00000i | 0.755929 | + | 0.755929i | 0.975579 | − | 0.219650i | \(-0.0704915\pi\) |
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | − | 1.00000i | −0.942809 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.65685i | − | 1.70561i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||
0.522233 | − | 0.852803i | \(-0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 2.82843i | 0.872872 | − | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | + | 4.24264i | 0.884652 | + | 0.884652i | 0.994003 | − | 0.109351i | \(-0.0348774\pi\) |
−0.109351 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.53553 | + | 4.53553i | −0.487964 | + | 0.872864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.65685 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.65685 | − | 1.65685i | −1.68104 | − | 0.288421i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00000 | − | 8.00000i | −1.31519 | − | 1.31519i | −0.917534 | − | 0.397658i | \(-0.869823\pi\) |
−0.397658 | − | 0.917534i | \(-0.630177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 2.00000i | 0.304997 | − | 0.304997i | −0.537968 | − | 0.842965i | \(-0.680808\pi\) |
0.842965 | + | 0.537968i | \(0.180808\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.41421 | + | 1.41421i | −0.206284 | + | 0.206284i | −0.802686 | − | 0.596402i | \(-0.796597\pi\) |
0.596402 | + | 0.802686i | \(0.296597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | − | 5.65685i | −0.560112 | − | 0.792118i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685 | + | 5.65685i | 0.777029 | + | 0.777029i | 0.979324 | − | 0.202296i | \(-0.0648402\pi\) |
−0.202296 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.82843 | − | 1.17157i | −0.904447 | − | 0.155179i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | −0.736460 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.65685 | − | 7.65685i | −0.460720 | − | 0.964673i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | + | 6.00000i | 0.733017 | + | 0.733017i | 0.971216 | − | 0.238200i | \(-0.0765572\pi\) |
−0.238200 | + | 0.971216i | \(0.576557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.48528 | − | 6.00000i | 1.02151 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137i | 1.34269i | 0.741145 | + | 0.671345i | \(0.234283\pi\) | ||||
−0.741145 | + | 0.671345i | \(0.765717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | + | 8.00000i | −0.936329 | + | 0.936329i | −0.998091 | − | 0.0617617i | \(-0.980328\pi\) |
0.0617617 | + | 0.998091i | \(0.480328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137 | − | 11.3137i | 1.28932 | − | 1.28932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89949 | + | 9.89949i | 1.08661 | + | 1.08661i | 0.995875 | + | 0.0907357i | \(0.0289219\pi\) |
0.0907357 | + | 0.995875i | \(0.471078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.65685 | + | 9.65685i | −0.177633 | + | 1.03532i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3137 | 1.19925 | 0.599625 | − | 0.800281i | \(-0.295316\pi\) | ||||
0.599625 | + | 0.800281i | \(0.295316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34315 | − | 13.6569i | 0.242973 | − | 1.41615i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | + | 8.00000i | 0.812277 | + | 0.812277i | 0.984975 | − | 0.172698i | \(-0.0552484\pi\) |
−0.172698 | + | 0.984975i | \(0.555248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | + | 16.0000i | −0.568535 | + | 1.60806i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65685i | 0.562878i | 0.959579 | + | 0.281439i | \(0.0908117\pi\) | ||||
−0.959579 | + | 0.281439i | \(0.909188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | − | 6.00000i | 0.591198 | − | 0.591198i | −0.346757 | − | 0.937955i | \(-0.612717\pi\) |
0.937955 | + | 0.346757i | \(0.112717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24264 | − | 4.24264i | 0.410152 | − | 0.410152i | −0.471640 | − | 0.881791i | \(-0.656338\pi\) |
0.881791 | + | 0.471640i | \(0.156338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0000 | + | 11.3137i | −1.51865 | + | 1.07385i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.82843 | − | 2.82843i | −0.266076 | − | 0.266076i | 0.561441 | − | 0.827517i | \(-0.310247\pi\) |
−0.827517 | + | 0.561441i | \(0.810247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3137 | 1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.65685 | − | 1.65685i | −0.870729 | − | 0.149394i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | − | 2.00000i | −0.177471 | − | 0.177471i | 0.612781 | − | 0.790253i | \(-0.290051\pi\) |
−0.790253 | + | 0.612781i | \(0.790051\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.82843 | − | 4.00000i | −0.249029 | − | 0.352180i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685i | 0.494242i | 0.968985 | + | 0.247121i | \(0.0794845\pi\) | ||||
−0.968985 | + | 0.247121i | \(0.920516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | − | 8.00000i | 0.693688 | − | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.48528 | + | 8.48528i | −0.724947 | + | 0.724947i | −0.969608 | − | 0.244662i | \(-0.921323\pi\) |
0.244662 | + | 0.969608i | \(0.421323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | + | 2.82843i | 0.168430 | + | 0.238197i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.70711 | + | 0.292893i | 0.140800 | + | 0.0241574i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.3137 | 0.926855 | 0.463428 | − | 0.886135i | \(-0.346619\pi\) | ||||
0.463428 | + | 0.886135i | \(0.346619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.8284 | + | 5.17157i | −0.875426 | + | 0.418097i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00000 | − | 8.00000i | −0.638470 | − | 0.638470i | 0.311708 | − | 0.950178i | \(-0.399099\pi\) |
−0.950178 | + | 0.311708i | \(0.899099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.3137 | − | 8.00000i | 0.897235 | − | 0.634441i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.9706i | 1.33747i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 2.00000i | −0.156652 | + | 0.156652i | −0.781081 | − | 0.624429i | \(-0.785332\pi\) |
0.624429 | + | 0.781081i | \(0.285332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.07107 | − | 7.07107i | 0.547176 | − | 0.547176i | −0.378447 | − | 0.925623i | \(-0.623542\pi\) |
0.925623 | + | 0.378447i | \(0.123542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | + | 11.3137i | −0.305888 | + | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9706 | + | 16.9706i | 1.29025 | + | 1.29025i | 0.934632 | + | 0.355616i | \(0.115729\pi\) |
0.355616 | + | 0.934632i | \(0.384271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.65685 | + | 9.65685i | −0.124537 | + | 0.725854i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.65685 | 0.422813 | 0.211407 | − | 0.977398i | \(-0.432196\pi\) | ||||
0.211407 | + | 0.977398i | \(0.432196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75736 | + | 10.2426i | −0.129908 | + | 0.757158i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0000 | − | 16.0000i | −1.17004 | − | 1.17004i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.1421 | + | 4.00000i | −1.02869 | + | 0.290957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | + | 8.00000i | −0.575853 | + | 0.575853i | −0.933758 | − | 0.357905i | \(-0.883491\pi\) |
0.357905 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | − | 8.48528i | 0.846415 | − | 0.598506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3137 | − | 11.3137i | −0.794067 | − | 0.794067i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.75736 | − | 16.2426i | −0.539174 | − | 1.12894i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.6274 | −1.56517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.3137 | + | 3.31371i | 1.32335 | + | 0.227052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | + | 16.0000i | 1.08615 | + | 1.08615i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3137 | + | 16.0000i | 0.764510 | + | 1.08118i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.0000 | + | 18.0000i | −1.20537 | + | 1.20537i | −0.232859 | + | 0.972511i | \(0.574808\pi\) |
−0.972511 | + | 0.232859i | \(0.925192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.89949 | + | 9.89949i | −0.657053 | + | 0.657053i | −0.954682 | − | 0.297629i | \(-0.903804\pi\) |
0.297629 | + | 0.954682i | \(0.403804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0000 | − | 22.6274i | −1.05272 | − | 1.48877i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1421 | − | 14.1421i | −0.926482 | − | 0.926482i | 0.0709946 | − | 0.997477i | \(-0.477383\pi\) |
−0.997477 | + | 0.0709946i | \(0.977383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7071 | − | 10.2929i | 0.751011 | − | 0.660289i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.7990 | − | 14.0000i | 1.25471 | − | 0.887214i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.65685i | − | 0.357057i | −0.983935 | − | 0.178529i | \(-0.942866\pi\) | ||
0.983935 | − | 0.178529i | \(-0.0571337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | − | 24.0000i | 1.50887 | − | 1.50887i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.48528 | + | 8.48528i | −0.529297 | + | 0.529297i | −0.920363 | − | 0.391066i | \(-0.872107\pi\) |
0.391066 | + | 0.920363i | \(0.372107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 32.0000i | − | 1.98838i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.0000 | + | 5.65685i | 0.990375 | + | 0.350150i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.24264 | − | 4.24264i | −0.261612 | − | 0.261612i | 0.564096 | − | 0.825709i | \(-0.309225\pi\) |
−0.825709 | + | 0.564096i | \(0.809225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.31371 | − | 19.3137i | 0.202796 | − | 1.18198i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.3137 | −0.689809 | −0.344904 | − | 0.938638i | \(-0.612089\pi\) | ||||
−0.344904 | + | 0.938638i | \(0.612089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | + | 8.00000i | 0.480673 | + | 0.480673i | 0.905347 | − | 0.424673i | \(-0.139611\pi\) |
−0.424673 | + | 0.905347i | \(0.639611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.6274 | − | 8.00000i | −1.35467 | − | 0.478947i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.9706i | − | 1.01238i | −0.862422 | − | 0.506189i | \(-0.831054\pi\) | ||
0.862422 | − | 0.506189i | \(-0.168946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | + | 6.00000i | −0.356663 | + | 0.356663i | −0.862581 | − | 0.505918i | \(-0.831154\pi\) |
0.505918 | + | 0.862581i | \(0.331154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3137 | − | 11.3137i | 0.667827 | − | 0.667827i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.0000 | − | 11.3137i | 0.937937 | − | 0.663221i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.65685 | − | 5.65685i | −0.330477 | − | 0.330477i | 0.522291 | − | 0.852768i | \(-0.325078\pi\) |
−0.852768 | + | 0.522291i | \(0.825078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.6569 | + | 14.3431i | 1.48876 | + | 0.832274i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.65685 | + | 1.65685i | 0.554772 | + | 0.0951838i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | + | 10.0000i | 0.570730 | + | 0.570730i | 0.932332 | − | 0.361602i | \(-0.117770\pi\) |
−0.361602 | + | 0.932332i | \(0.617770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.48528 | − | 12.0000i | −0.482711 | − | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.3137i | − | 0.641542i | −0.947157 | − | 0.320771i | \(-0.896058\pi\) | ||
0.947157 | − | 0.320771i | \(-0.103942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.6274 | + | 22.6274i | −1.27088 | + | 1.27088i | −0.325257 | + | 0.945626i | \(0.605451\pi\) |
−0.945626 | + | 0.325257i | \(0.894549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.0000i | 1.79166i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | − | 8.48528i | −0.334887 | − | 0.473602i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3137 | − | 11.3137i | −0.629512 | − | 0.629512i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.0711 | + | 2.92893i | 0.944032 | + | 0.161970i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.6274 | + | 30.6274i | 0.801578 | + | 1.67837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.65685 | + | 4.00000i | −0.307238 | + | 0.217250i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 45.2548i | − | 2.45069i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5563 | − | 15.5563i | 0.835109 | − | 0.835109i | −0.153102 | − | 0.988210i | \(-0.548926\pi\) |
0.988210 | + | 0.153102i | \(0.0489263\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.82843 | − | 2.82843i | −0.150542 | − | 0.150542i | 0.627818 | − | 0.778360i | \(-0.283948\pi\) |
−0.778360 | + | 0.627818i | \(0.783948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.31371 | − | 19.3137i | 0.175380 | − | 1.02219i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.6274 | −1.19423 | −0.597115 | − | 0.802156i | \(-0.703686\pi\) | ||||
−0.597115 | + | 0.802156i | \(0.703686\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.15076 | + | 35.8492i | −0.322831 | + | 1.88160i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0000 | − | 18.0000i | −0.939592 | − | 0.939592i | 0.0586842 | − | 0.998277i | \(-0.481309\pi\) |
−0.998277 | + | 0.0586842i | \(0.981309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.65685 | + | 16.0000i | −0.294484 | + | 0.832927i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.6274i | 1.17476i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.00000 | − | 8.00000i | 0.414224 | − | 0.414224i | −0.468983 | − | 0.883207i | \(-0.655379\pi\) |
0.883207 | + | 0.468983i | \(0.155379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.0000i | − | 1.84920i | −0.380945 | − | 0.924598i | \(-0.624401\pi\) | ||
0.380945 | − | 0.924598i | \(-0.375599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | + | 2.82843i | −0.204926 | + | 0.144905i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.2132 | − | 21.2132i | −1.08394 | − | 1.08394i | −0.996138 | − | 0.0878065i | \(-0.972014\pi\) |
−0.0878065 | − | 0.996138i | \(-0.527986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.65685 | + | 3.65685i | −0.389220 | + | 0.185888i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9411 | 1.72088 | 0.860442 | − | 0.509549i | \(-0.170188\pi\) | ||||
0.860442 | + | 0.509549i | \(0.170188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.65685 | + | 1.65685i | 0.487124 | + | 0.0835772i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.3137 | − | 16.0000i | −0.566394 | − | 0.801002i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.2548 | + | 45.2548i | −2.24320 | + | 2.24320i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.0000i | − | 1.48340i | −0.670729 | − | 0.741702i | \(-0.734019\pi\) | ||
0.670729 | − | 0.741702i | \(-0.265981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | + | 16.9706i | 0.591916 | + | 0.837096i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3137 | − | 11.3137i | −0.556711 | − | 0.556711i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.82843 | − | 1.17157i | −0.334390 | − | 0.0573722i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9706 | 0.829066 | 0.414533 | − | 0.910034i | \(-0.363945\pi\) | ||||
0.414533 | + | 0.910034i | \(0.363945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.41421 | − | 2.58579i | 0.263248 | − | 0.125725i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | − | 12.0000i | −0.580721 | − | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.6274i | − | 1.08992i | −0.838461 | − | 0.544962i | \(-0.816544\pi\) | ||
0.838461 | − | 0.544962i | \(-0.183456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.0000 | + | 24.0000i | −1.15337 | + | 1.15337i | −0.167493 | + | 0.985873i | \(0.553567\pi\) |
−0.985873 | + | 0.167493i | \(0.946433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.9706 | − | 16.9706i | 0.811812 | − | 0.811812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000i | 1.52728i | 0.645644 | + | 0.763638i | \(0.276589\pi\) | ||||
−0.645644 | + | 0.763638i | \(0.723411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 2.82843i | 0.0476190 | − | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.07107 | + | 7.07107i | 0.335957 | + | 0.335957i | 0.854843 | − | 0.518887i | \(-0.173653\pi\) |
−0.518887 | + | 0.854843i | \(0.673653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.31371 | − | 19.3137i | 0.156733 | − | 0.913507i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685 | 0.266963 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.0000 | −1.50682 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.34315 | − | 13.6569i | 0.110091 | − | 0.641655i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0000 | − | 16.0000i | −0.748448 | − | 0.748448i | 0.225739 | − | 0.974188i | \(-0.427520\pi\) |
−0.974188 | + | 0.225739i | \(0.927520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.65685 | + | 20.0000i | 0.264039 | + | 0.933520i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.5980i | 1.84426i | 0.386878 | + | 0.922131i | \(0.373553\pi\) | ||||
−0.386878 | + | 0.922131i | \(0.626447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.00000 | + | 6.00000i | −0.278844 | + | 0.278844i | −0.832647 | − | 0.553804i | \(-0.813176\pi\) |
0.553804 | + | 0.832647i | \(0.313176\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.89949 | + | 9.89949i | −0.458094 | + | 0.458094i | −0.898029 | − | 0.439935i | \(-0.855001\pi\) |
0.439935 | + | 0.898029i | \(0.355001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.0000 | + | 11.3137i | −0.737241 | + | 0.521308i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.3137 | − | 11.3137i | −0.520205 | − | 0.520205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3431 | − | 21.6569i | −0.473580 | − | 0.991599i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.9706 | + | 4.97056i | 1.31821 | + | 0.226168i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000 | + | 18.0000i | 0.815658 | + | 0.815658i | 0.985476 | − | 0.169818i | \(-0.0543179\pi\) |
−0.169818 | + | 0.985476i | \(0.554318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.82843 | + | 4.00000i | 0.127906 | + | 0.180886i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.65685i | 0.255290i | 0.991820 | + | 0.127645i | \(0.0407419\pi\) | ||||
−0.991820 | + | 0.127645i | \(0.959258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0000 | + | 16.0000i | −0.720604 | + | 0.720604i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.6274 | + | 22.6274i | −1.01498 | + | 1.01498i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0000 | − | 14.1421i | −0.446767 | − | 0.631824i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.24264 | + | 4.24264i | 0.189170 | + | 0.189170i | 0.795337 | − | 0.606167i | \(-0.207294\pi\) |
−0.606167 | + | 0.795337i | \(0.707294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.1924 | + | 3.80761i | 0.985599 | + | 0.169102i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9706 | −0.752207 | −0.376103 | − | 0.926578i | \(-0.622736\pi\) | ||||
−0.376103 | + | 0.926578i | \(0.622736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.0000 | −1.41560 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.1421 | + | 10.1421i | 0.800995 | + | 0.447786i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 8.00000i | 0.351840 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.9411 | − | 24.0000i | 1.48985 | − | 1.05348i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9411i | 1.48699i | 0.668743 | + | 0.743494i | \(0.266833\pi\) | ||||
−0.668743 | + | 0.743494i | \(0.733167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.00000 | − | 6.00000i | 0.262362 | − | 0.262362i | −0.563651 | − | 0.826013i | \(-0.690604\pi\) |
0.826013 | + | 0.563651i | \(0.190604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.6274 | − | 22.6274i | 0.985666 | − | 0.985666i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.0000 | + | 5.65685i | 0.694341 | + | 0.245487i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.65685 | − | 9.65685i | 0.0714985 | − | 0.416724i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.65685 | 0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0000 | 1.46177 | 0.730887 | − | 0.682498i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682498i | \(0.239107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.92893 | + | 17.0711i | −0.125693 | + | 0.732590i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0000 | + | 30.0000i | 1.28271 | + | 1.28271i | 0.939121 | + | 0.343586i | \(0.111642\pi\) |
0.343586 | + | 0.939121i | \(0.388358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.9706 | + | 6.00000i | 0.724286 | + | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6274i | 0.963960i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.9706 | − | 16.9706i | 0.719066 | − | 0.719066i | −0.249348 | − | 0.968414i | \(-0.580216\pi\) |
0.968414 | + | 0.249348i | \(0.0802163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.0000 | + | 22.6274i | −1.35104 | + | 0.955330i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.89949 | − | 9.89949i | −0.417214 | − | 0.417214i | 0.467028 | − | 0.884242i | \(-0.345325\pi\) |
−0.884242 | + | 0.467028i | \(0.845325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.68629 | + | 25.3137i | 0.112814 | + | 1.06308i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2843 | 1.18574 | 0.592869 | − | 0.805299i | \(-0.297995\pi\) | ||||
0.592869 | + | 0.805299i | \(0.297995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.3137 | − | 3.31371i | −0.806842 | − | 0.138432i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0000 | − | 16.0000i | −0.666089 | − | 0.666089i | 0.290720 | − | 0.956808i | \(-0.406105\pi\) |
−0.956808 | + | 0.290720i | \(0.906105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3137 | + | 16.0000i | 0.470182 | + | 0.664937i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.5980i | 1.64280i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.0000 | − | 32.0000i | 1.32530 | − | 1.32530i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5563 | + | 15.5563i | −0.642079 | + | 0.642079i | −0.951066 | − | 0.308987i | \(-0.900010\pi\) |
0.308987 | + | 0.951066i | \(0.400010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 32.0000i | − | 1.31854i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.48528 | − | 8.48528i | −0.348449 | − | 0.348449i | 0.511083 | − | 0.859532i | \(-0.329245\pi\) |
−0.859532 | + | 0.511083i | \(0.829245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.2548 | 1.84906 | 0.924531 | − | 0.381106i | \(-0.124457\pi\) | ||||
0.924531 | + | 0.381106i | \(0.124457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9706 | − | 22.9706i | −0.446756 | − | 0.935434i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0000 | + | 10.0000i | 0.405887 | + | 0.405887i | 0.880302 | − | 0.474414i | \(-0.157340\pi\) |
−0.474414 | + | 0.880302i | \(0.657340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.6274 | + | 16.0000i | −0.916909 | + | 0.648353i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.4558 | − | 25.4558i | 1.02481 | − | 1.02481i | 0.0251295 | − | 0.999684i | \(-0.492000\pi\) |
0.999684 | − | 0.0251295i | \(-0.00799981\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.0000i | − | 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.0000 | + | 8.48528i | −1.20386 | + | 0.340503i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.6274 | + | 22.6274i | 0.906548 | + | 0.906548i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.62742 | + | 38.6274i | −0.264674 | + | 1.54263i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.2548 | −1.80443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.17157 | − | 6.82843i | 0.0465658 | − | 0.271406i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3137 | − | 32.0000i | 0.447563 | − | 1.26590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.2843i | − | 1.11716i | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||
0.829450 | − | 0.558581i | \(-0.188654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0000 | − | 22.0000i | 0.867595 | − | 0.867595i | −0.124610 | − | 0.992206i | \(-0.539768\pi\) |
0.992206 | + | 0.124610i | \(0.0397681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.24264 | + | 4.24264i | −0.166795 | + | 0.166795i | −0.785569 | − | 0.618774i | \(-0.787630\pi\) |
0.618774 | + | 0.785569i | \(0.287630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000i | 1.25611i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.0000 | − | 22.6274i | 1.25418 | − | 0.886838i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.9706 | − | 16.9706i | −0.664109 | − | 0.664109i | 0.292237 | − | 0.956346i | \(-0.405601\pi\) |
−0.956346 | + | 0.292237i | \(0.905601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.6274 | − | 14.6274i | 1.19489 | − | 0.570670i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9706 | −0.661079 | −0.330540 | − | 0.943792i | \(-0.607231\pi\) | ||||
−0.330540 | + | 0.943792i | \(0.607231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.0000 | −1.32245 | −0.661223 | − | 0.750189i | \(-0.729962\pi\) | ||||
−0.661223 | + | 0.750189i | \(0.729962\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | − | 24.0000i | −0.929284 | − | 0.929284i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.4558 | + | 36.0000i | 0.984180 | + | 1.39184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.9411i | 1.31028i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | − | 24.0000i | 0.925132 | − | 0.925132i | −0.0722542 | − | 0.997386i | \(-0.523019\pi\) |
0.997386 | + | 0.0722542i | \(0.0230193\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9706 | + | 16.9706i | −0.652232 | + | 0.652232i | −0.953530 | − | 0.301298i | \(-0.902580\pi\) |
0.301298 | + | 0.953530i | \(0.402580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.0000i | 1.22805i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | + | 19.7990i | 0.536481 | + | 0.758699i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.24264 | − | 4.24264i | −0.162340 | − | 0.162340i | 0.621262 | − | 0.783603i | \(-0.286620\pi\) |
−0.783603 | + | 0.621262i | \(0.786620\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.2426 | − | 1.75736i | −0.390781 | − | 0.0670474i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −43.3137 | + | 20.6863i | −1.64535 | + | 0.785807i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | − | 16.0000i | −0.606043 | − | 0.606043i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.2843 | + | 20.0000i | −1.06981 | + | 0.756469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.6274i | − | 0.854626i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) | ||
0.904104 | − | 0.427313i | \(-0.140540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.0000 | + | 32.0000i | −1.20690 | + | 1.20690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.3137 | + | 11.3137i | −0.425496 | + | 0.425496i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.00000i | − | 0.225335i | −0.993633 | − | 0.112667i | \(-0.964061\pi\) | ||
0.993633 | − | 0.112667i | \(-0.0359394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.9411 | + | 33.9411i | 1.27111 | + | 1.27111i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.31371 | + | 19.3137i | −0.123753 | + | 0.721284i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.2548 | 1.68772 | 0.843860 | − | 0.536563i | \(-0.180278\pi\) | ||||
0.843860 | + | 0.536563i | \(0.180278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.92893 | − | 17.0711i | 0.108928 | − | 0.634880i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.0000 | + | 30.0000i | 1.11264 | + | 1.11264i | 0.992793 | + | 0.119846i | \(0.0382401\pi\) |
0.119846 | + | 0.992793i | \(0.461760\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.3137i | − | 0.418453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0000 | + | 24.0000i | −0.886460 | + | 0.886460i | −0.994181 | − | 0.107721i | \(-0.965645\pi\) |
0.107721 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9411 | − | 33.9411i | 1.25024 | − | 1.25024i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.00000i | − | 0.147142i | −0.997290 | − | 0.0735712i | \(-0.976560\pi\) | ||
0.997290 | − | 0.0735712i | \(-0.0234396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3848 | + | 18.3848i | 0.674472 | + | 0.674472i | 0.958744 | − | 0.284272i | \(-0.0917518\pi\) |
−0.284272 | + | 0.958744i | \(0.591752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.1005 | − | 37.8995i | −0.662263 | − | 1.38667i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706 | 0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.65685 | − | 1.65685i | −0.351915 | − | 0.0603791i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0000 | − | 24.0000i | −0.872295 | − | 0.872295i | 0.120427 | − | 0.992722i | \(-0.461574\pi\) |
−0.992722 | + | 0.120427i | \(0.961574\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.9411 | − | 48.0000i | −1.23198 | − | 1.74229i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.6274i | − | 0.820243i | −0.912031 | − | 0.410122i | \(-0.865486\pi\) | ||
0.912031 | − | 0.410122i | \(-0.134514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | + | 20.0000i | −0.724049 | + | 0.724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 50.0000i | − | 1.80305i | −0.432731 | − | 0.901523i | \(-0.642450\pi\) | ||
0.432731 | − | 0.901523i | \(-0.357550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | + | 16.9706i | 0.432169 | + | 0.611180i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.3137 | + | 11.3137i | 0.406926 | + | 0.406926i | 0.880665 | − | 0.473739i | \(-0.157096\pi\) |
−0.473739 | + | 0.880665i | \(0.657096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −54.6274 | − | 9.37258i | −1.95975 | − | 0.336240i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6274 | −0.810711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.0000 | 2.29010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.3431 | − | 25.6569i | 0.512582 | − | 0.916901i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0000 | + | 22.0000i | 0.784215 | + | 0.784215i | 0.980539 | − | 0.196324i | \(-0.0629004\pi\) |
−0.196324 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.48528 | + | 6.00000i | −0.302084 | + | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.3137i | − | 0.402269i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0000 | − | 11.3137i | −1.13066 | − | 0.399750i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 45.2548 | + | 45.2548i | 1.59701 | + | 1.59701i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.31371 | + | 19.3137i | −0.116648 | + | 0.679875i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.3137 | 0.397769 | 0.198884 | − | 0.980023i | \(-0.436268\pi\) | ||||
0.198884 | + | 0.980023i | \(0.436268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.68629 | − | 27.3137i | 0.164355 | − | 0.957934i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 8.00000i | −0.279885 | − | 0.279885i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.6274i | − | 0.789702i | −0.918745 | − | 0.394851i | \(-0.870796\pi\) | ||
0.918745 | − | 0.394851i | \(-0.129204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.00000 | + | 6.00000i | −0.209147 | + | 0.209147i | −0.803905 | − | 0.594758i | \(-0.797248\pi\) |
0.594758 | + | 0.803905i | \(0.297248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6985 | − | 29.6985i | 1.03272 | − | 1.03272i | 0.0332711 | − | 0.999446i | \(-0.489408\pi\) |
0.999446 | − | 0.0332711i | \(-0.0105925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.0000i | − | 0.903017i | −0.892267 | − | 0.451509i | \(-0.850886\pi\) | ||
0.892267 | − | 0.451509i | \(-0.149114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.0000 | − | 11.3137i | 0.555034 | − | 0.392468i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.82843 | + | 2.82843i | 0.0979992 | + | 0.0979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.2843 | + | 36.2843i | −0.701127 | + | 1.25417i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.2548 | −1.56237 | −0.781185 | − | 0.624299i | \(-0.785385\pi\) | ||||
−0.781185 | + | 0.624299i | \(0.785385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9706 | − | 4.97056i | −0.997799 | − | 0.171195i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.0000 | − | 42.0000i | −1.44314 | − | 1.44314i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.48528 | + | 12.0000i | 0.291214 | + | 0.411839i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 67.8823i | − | 2.32697i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.0000 | + | 32.0000i | −1.09566 | + | 1.09566i | −0.100747 | + | 0.994912i | \(0.532123\pi\) |
−0.994912 | + | 0.100747i | \(0.967877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.48528 | + | 8.48528i | −0.289852 | + | 0.289852i | −0.837022 | − | 0.547170i | \(-0.815705\pi\) |
0.547170 | + | 0.837022i | \(0.315705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000i | 0.682391i | 0.939992 | + | 0.341196i | \(0.110832\pi\) | ||||
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | − | 22.6274i | −0.545279 | − | 0.771140i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.5269 | − | 32.5269i | −1.10723 | − | 1.10723i | −0.993513 | − | 0.113716i | \(-0.963725\pi\) |
−0.113716 | − | 0.993513i | \(-0.536275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.70711 | + | 0.292893i | 0.0579764 | + | 0.00994718i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6274 | − | 30.6274i | −0.495063 | − | 1.03658i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0000 | + | 24.0000i | 0.810422 | + | 0.810422i | 0.984697 | − | 0.174275i | \(-0.0557581\pi\) |
−0.174275 | + | 0.984697i | \(0.555758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.3137 | + | 8.00000i | −0.381602 | + | 0.269833i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.65685i | − | 0.190584i | −0.995449 | − | 0.0952921i | \(-0.969621\pi\) | ||
0.995449 | − | 0.0952921i | \(-0.0303785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | − | 2.00000i | 0.0673054 | − | 0.0673054i | −0.672653 | − | 0.739958i | \(-0.734845\pi\) |
0.739958 | + | 0.672653i | \(0.234845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.5563 | − | 15.5563i | 0.522331 | − | 0.522331i | −0.395944 | − | 0.918275i | \(-0.629582\pi\) |
0.918275 | + | 0.395944i | \(0.129582\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.00000i | − | 0.268311i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.0000 | − | 39.5980i | 1.07204 | − | 1.32658i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.65685 | + | 5.65685i | 0.189299 | + | 0.189299i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.2548 | −1.50933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000 | 1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.34315 | − | 13.6569i | 0.0779750 | − | 0.454472i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | + | 6.00000i | 0.199227 | + | 0.199227i | 0.799668 | − | 0.600442i | \(-0.205009\pi\) |
−0.600442 | + | 0.799668i | \(0.705009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.65685 | − | 16.0000i | 0.187626 | − | 0.530687i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6274i | 0.749680i | 0.927090 | + | 0.374840i | \(0.122302\pi\) | ||||
−0.927090 | + | 0.374840i | \(0.877698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.0000 | − | 56.0000i | 1.85333 | − | 1.85333i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.3137 | + | 11.3137i | −0.373612 | + | 0.373612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000i | 0.263896i | 0.991257 | + | 0.131948i | \(0.0421231\pi\) | ||||
−0.991257 | + | 0.131948i | \(0.957877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.0000 | − | 14.1421i | 0.659022 | − | 0.465999i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.9706 | + | 10.9706i | −0.754452 | + | 0.360321i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.65685 | −0.185595 | −0.0927977 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927977 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.3137 | − | 3.31371i | −0.632302 | − | 0.108486i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.0000 | + | 24.0000i | 0.784046 | + | 0.784046i | 0.980511 | − | 0.196465i | \(-0.0629462\pi\) |
−0.196465 | + | 0.980511i | \(0.562946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 16.9706i | − | 0.553225i | −0.960982 | − | 0.276612i | \(-0.910788\pi\) | ||
0.960982 | − | 0.276612i | \(-0.0892118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | − | 24.0000i | 0.781548 | − | 0.781548i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7279 | + | 12.7279i | −0.413602 | + | 0.413602i | −0.882991 | − | 0.469389i | \(-0.844474\pi\) |
0.469389 | + | 0.882991i | \(0.344474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.0000 | + | 45.2548i | 1.03767 | + | 1.46749i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.4264 | + | 42.4264i | 1.37433 | + | 1.37433i | 0.853917 | + | 0.520409i | \(0.174220\pi\) |
0.520409 | + | 0.853917i | \(0.325780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 54.6274 | + | 9.37258i | 1.76585 | + | 0.302973i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.9411 | −1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2426 | + | 7.75736i | −0.523412 | + | 0.249977i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0000 | − | 10.0000i | −0.321578 | − | 0.321578i | 0.527794 | − | 0.849372i | \(-0.323019\pi\) |
−0.849372 | + | 0.527794i | \(0.823019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.6274 | + | 16.0000i | −0.726897 | + | 0.513994i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.65685i | 0.181537i | 0.995872 | + | 0.0907685i | \(0.0289323\pi\) | ||||
−0.995872 | + | 0.0907685i | \(0.971068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | − | 8.00000i | 0.256468 | − | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.4264 | − | 42.4264i | 1.35734 | − | 1.35734i | 0.480160 | − | 0.877181i | \(-0.340579\pi\) |
0.877181 | − | 0.480160i | \(-0.159421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 64.0000i | − | 2.04545i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | − | 28.2843i | 0.319275 | − | 0.903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.5563 | + | 15.5563i | 0.496170 | + | 0.496170i | 0.910244 | − | 0.414073i | \(-0.135894\pi\) |
−0.414073 | + | 0.910244i | \(0.635894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.65685 | + | 9.65685i | −0.0527383 | + | 0.307381i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.17157 | − | 6.82843i | 0.0371787 | − | 0.216694i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0000 | + | 16.0000i | 0.506725 | + | 0.506725i | 0.913520 | − | 0.406795i | \(-0.133354\pi\) |
−0.406795 | + | 0.913520i | \(0.633354\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 56.5685 | − | 16.0000i | 1.78975 | − | 0.506218i |
(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 | 600.2.r.e.257.1 | yes | 4 | |
3.2 | odd | 2 | inner | 600.2.r.e.257.2 | yes | 4 | |
4.3 | odd | 2 | 1200.2.v.a.257.2 | 4 | |||
5.2 | odd | 4 | 600.2.r.a.593.1 | yes | 4 | ||
5.3 | odd | 4 | inner | 600.2.r.e.593.2 | yes | 4 | |
5.4 | even | 2 | 600.2.r.a.257.2 | yes | 4 | ||
12.11 | even | 2 | 1200.2.v.a.257.1 | 4 | |||
15.2 | even | 4 | 600.2.r.a.593.2 | yes | 4 | ||
15.8 | even | 4 | inner | 600.2.r.e.593.1 | yes | 4 | |
15.14 | odd | 2 | 600.2.r.a.257.1 | ✓ | 4 | ||
20.3 | even | 4 | 1200.2.v.a.593.1 | 4 | |||
20.7 | even | 4 | 1200.2.v.k.593.2 | 4 | |||
20.19 | odd | 2 | 1200.2.v.k.257.1 | 4 | |||
60.23 | odd | 4 | 1200.2.v.a.593.2 | 4 | |||
60.47 | odd | 4 | 1200.2.v.k.593.1 | 4 | |||
60.59 | even | 2 | 1200.2.v.k.257.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.r.a.257.1 | ✓ | 4 | 15.14 | odd | 2 | ||
600.2.r.a.257.2 | yes | 4 | 5.4 | even | 2 | ||
600.2.r.a.593.1 | yes | 4 | 5.2 | odd | 4 | ||
600.2.r.a.593.2 | yes | 4 | 15.2 | even | 4 | ||
600.2.r.e.257.1 | yes | 4 | 1.1 | even | 1 | trivial | |
600.2.r.e.257.2 | yes | 4 | 3.2 | odd | 2 | inner | |
600.2.r.e.593.1 | yes | 4 | 15.8 | even | 4 | inner | |
600.2.r.e.593.2 | yes | 4 | 5.3 | odd | 4 | inner | |
1200.2.v.a.257.1 | 4 | 12.11 | even | 2 | |||
1200.2.v.a.257.2 | 4 | 4.3 | odd | 2 | |||
1200.2.v.a.593.1 | 4 | 20.3 | even | 4 | |||
1200.2.v.a.593.2 | 4 | 60.23 | odd | 4 | |||
1200.2.v.k.257.1 | 4 | 20.19 | odd | 2 | |||
1200.2.v.k.257.2 | 4 | 60.59 | even | 2 | |||
1200.2.v.k.593.1 | 4 | 60.47 | odd | 4 | |||
1200.2.v.k.593.2 | 4 | 20.7 | even | 4 |