Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.1 | ||
Root | \(-1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1801 |
Dual form | 2100.2.q.i.1201.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32288 | − | 2.29129i | −0.500000 | − | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.177124 | + | 0.306788i | 0.0534050 | + | 0.0925002i | 0.891492 | − | 0.453036i | \(-0.149659\pi\) |
−0.838087 | + | 0.545537i | \(0.816326\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.82288 | − | 3.15731i | −0.442112 | − | 0.765761i | 0.555734 | − | 0.831360i | \(-0.312437\pi\) |
−0.997846 | + | 0.0655994i | \(0.979104\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.322876 | + | 0.559237i | −0.0740728 | + | 0.128298i | −0.900683 | − | 0.434478i | \(-0.856933\pi\) |
0.826610 | + | 0.562775i | \(0.190266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32288 | − | 2.29129i | 0.288675 | − | 0.500000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.29150 | −0.611217 | −0.305608 | − | 0.952157i | \(-0.598860\pi\) | ||||
−0.305608 | + | 0.952157i | \(0.598860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.177124 | + | 0.306788i | −0.0308334 | + | 0.0534050i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.14575 | − | 1.98450i | 0.188360 | − | 0.326250i | −0.756343 | − | 0.654175i | \(-0.773016\pi\) |
0.944704 | + | 0.327925i | \(0.106349\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.64575 | −0.881718 | −0.440859 | − | 0.897576i | \(-0.645326\pi\) | ||||
−0.440859 | + | 0.897576i | \(0.645326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29150 | 0.501949 | 0.250975 | − | 0.967994i | \(-0.419249\pi\) | ||||
0.250975 | + | 0.967994i | \(0.419249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.46863 | − | 11.2040i | 0.943546 | − | 1.63427i | 0.184910 | − | 0.982755i | \(-0.440801\pi\) |
0.758636 | − | 0.651515i | \(-0.225866\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.82288 | − | 3.15731i | 0.255254 | − | 0.442112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.82288 | − | 6.62141i | −0.525112 | − | 0.909521i | −0.999572 | − | 0.0292442i | \(-0.990690\pi\) |
0.474460 | − | 0.880277i | \(-0.342643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.645751 | −0.0855319 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.468627 | + | 0.811686i | 0.0610100 | + | 0.105672i | 0.894917 | − | 0.446232i | \(-0.147235\pi\) |
−0.833907 | + | 0.551905i | \(0.813901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.79150 | − | 10.0312i | 0.741526 | − | 1.28436i | −0.210274 | − | 0.977642i | \(-0.567436\pi\) |
0.951800 | − | 0.306718i | \(-0.0992309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.64575 | 0.333333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96863 | − | 6.87386i | −0.484845 | − | 0.839776i | 0.515003 | − | 0.857188i | \(-0.327791\pi\) |
−0.999848 | + | 0.0174120i | \(0.994457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.29150 | −0.865342 | −0.432671 | − | 0.901552i | \(-0.642429\pi\) | ||||
−0.432671 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.14575 | − | 3.71655i | −0.251141 | − | 0.434989i | 0.712699 | − | 0.701470i | \(-0.247473\pi\) |
−0.963840 | + | 0.266481i | \(0.914139\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.468627 | − | 0.811686i | 0.0534050 | − | 0.0925002i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.677124 | − | 1.17281i | 0.0761824 | − | 0.131952i | −0.825417 | − | 0.564523i | \(-0.809060\pi\) |
0.901600 | + | 0.432571i | \(0.142394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.64575 | −0.180645 | −0.0903223 | − | 0.995913i | \(-0.528790\pi\) | ||||
−0.0903223 | + | 0.995913i | \(0.528790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.64575 | − | 2.85052i | −0.176443 | − | 0.305608i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46863 | + | 6.00784i | −0.367674 | + | 0.636830i | −0.989201 | − | 0.146563i | \(-0.953179\pi\) |
0.621528 | + | 0.783392i | \(0.286512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32288 | − | 2.29129i | −0.138675 | − | 0.240192i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.70850 | 0.376541 | 0.188270 | − | 0.982117i | \(-0.439712\pi\) | ||||
0.188270 | + | 0.982117i | \(0.439712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.354249 | −0.0356033 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46863 | − | 4.27579i | −0.245638 | − | 0.425457i | 0.716673 | − | 0.697409i | \(-0.245664\pi\) |
−0.962311 | + | 0.271953i | \(0.912331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0313730 | + | 0.0543397i | −0.00309128 | + | 0.00535425i | −0.867567 | − | 0.497320i | \(-0.834317\pi\) |
0.864476 | + | 0.502675i | \(0.167651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.11438 | − | 14.0545i | 0.784447 | − | 1.35870i | −0.144883 | − | 0.989449i | \(-0.546280\pi\) |
0.929329 | − | 0.369252i | \(-0.120386\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.79150 | + | 10.0312i | 0.554725 | + | 0.960812i | 0.997925 | + | 0.0643895i | \(0.0205100\pi\) |
−0.443200 | + | 0.896423i | \(0.646157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29150 | 0.217500 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.58301 | −0.807421 | −0.403711 | − | 0.914887i | \(-0.632280\pi\) | ||||
−0.403711 | + | 0.914887i | \(0.632280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.82288 | + | 8.35347i | −0.442112 | + | 0.765761i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.43725 | − | 9.41760i | 0.494296 | − | 0.856145i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.82288 | − | 4.88936i | −0.254530 | − | 0.440859i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.35425 | −0.120170 | −0.0600851 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600851 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.64575 | + | 2.85052i | 0.144900 | + | 0.250975i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.291503 | + | 0.504897i | −0.0254687 | + | 0.0441131i | −0.878479 | − | 0.477781i | \(-0.841441\pi\) |
0.853010 | + | 0.521894i | \(0.174774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70850 | 0.148146 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.645751 | − | 1.11847i | −0.0551703 | − | 0.0955577i | 0.837121 | − | 0.547017i | \(-0.184237\pi\) |
−0.892292 | + | 0.451460i | \(0.850903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9373 | 1.35178 | 0.675890 | − | 0.737002i | \(-0.263759\pi\) | ||||
0.675890 | + | 0.737002i | \(0.263759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9373 | 1.08951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.177124 | + | 0.306788i | 0.0148119 | + | 0.0256549i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.46863 | + | 4.27579i | −0.202238 | + | 0.350286i | −0.949249 | − | 0.314525i | \(-0.898155\pi\) |
0.747011 | + | 0.664811i | \(0.231488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67712 | + | 9.83307i | 0.461998 | + | 0.800204i | 0.999060 | − | 0.0433387i | \(-0.0137995\pi\) |
−0.537063 | + | 0.843542i | \(0.680466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.64575 | 0.294742 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.50000 | − | 14.7224i | −0.678374 | − | 1.17498i | −0.975470 | − | 0.220131i | \(-0.929352\pi\) |
0.297097 | − | 0.954847i | \(-0.403982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.82288 | − | 6.62141i | 0.303174 | − | 0.525112i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.29150 | −0.417029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.61438 | − | 14.9205i | 0.674730 | − | 1.16867i | −0.301818 | − | 0.953366i | \(-0.597593\pi\) |
0.976548 | − | 0.215301i | \(-0.0690733\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5203 | 1.51052 | 0.755262 | − | 0.655424i | \(-0.227510\pi\) | ||||
0.755262 | + | 0.655424i | \(0.227510\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.322876 | − | 0.559237i | −0.0246909 | − | 0.0427659i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2915 | + | 17.8254i | −0.782448 | + | 1.35524i | 0.148063 | + | 0.988978i | \(0.452696\pi\) |
−0.930512 | + | 0.366263i | \(0.880637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.468627 | + | 0.811686i | −0.0352242 | + | 0.0610100i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6458 | + | 20.1710i | 0.870444 | + | 1.50765i | 0.861538 | + | 0.507693i | \(0.169502\pi\) |
0.00890653 | + | 0.999960i | \(0.497165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5830 | 1.08395 | 0.541973 | − | 0.840396i | \(-0.317677\pi\) | ||||
0.541973 | + | 0.840396i | \(0.317677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5830 | 0.856240 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.645751 | − | 1.11847i | 0.0472220 | − | 0.0817909i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.32288 | + | 2.29129i | 0.0962250 | + | 0.166667i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76013 | + | 11.7089i | −0.489146 | + | 0.847225i | −0.999922 | − | 0.0124883i | \(-0.996025\pi\) |
0.510776 | + | 0.859714i | \(0.329358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | − | 13.8564i | −0.575853 | − | 0.997406i | −0.995948 | − | 0.0899262i | \(-0.971337\pi\) |
0.420096 | − | 0.907480i | \(-0.361996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.70850 | −0.620455 | −0.310227 | − | 0.950662i | \(-0.600405\pi\) | ||||
−0.310227 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.322876 | − | 0.559237i | −0.0228880 | − | 0.0396433i | 0.854355 | − | 0.519691i | \(-0.173953\pi\) |
−0.877243 | + | 0.480047i | \(0.840619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.96863 | − | 6.87386i | 0.279925 | − | 0.484845i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.35425 | + | 7.54178i | 0.305608 | + | 0.529329i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | + | 1.73205i | 0.0695048 | + | 0.120386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.228757 | −0.0158234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.06275 | −0.142005 | −0.0710026 | − | 0.997476i | \(-0.522620\pi\) | ||||
−0.0710026 | + | 0.997476i | \(0.522620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.64575 | − | 6.31463i | −0.249803 | − | 0.432671i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.29150 | + | 9.16515i | −0.359211 | + | 0.622171i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.14575 | − | 3.71655i | 0.144996 | − | 0.251141i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.82288 | − | 3.15731i | −0.122620 | − | 0.212384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9373 | 0.933308 | 0.466654 | − | 0.884440i | \(-0.345459\pi\) | ||||
0.466654 | + | 0.884440i | \(0.345459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.35425 | + | 7.54178i | 0.289002 | + | 0.500566i | 0.973572 | − | 0.228382i | \(-0.0733434\pi\) |
−0.684570 | + | 0.728947i | \(0.740010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1458 | − | 17.5730i | 0.670450 | − | 1.16125i | −0.307326 | − | 0.951604i | \(-0.599434\pi\) |
0.977777 | − | 0.209650i | \(-0.0672323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.937254 | 0.0616668 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1144 | + | 20.9827i | −0.793639 | + | 1.37462i | 0.130060 | + | 0.991506i | \(0.458483\pi\) |
−0.923700 | + | 0.383118i | \(0.874850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.35425 | 0.0879679 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.41699 | −0.609135 | −0.304567 | − | 0.952491i | \(-0.598512\pi\) | ||||
−0.304567 | + | 0.952491i | \(0.598512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.145751 | + | 0.252449i | 0.00938867 | + | 0.0162616i | 0.870682 | − | 0.491847i | \(-0.163678\pi\) |
−0.861293 | + | 0.508109i | \(0.830345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.322876 | + | 0.559237i | −0.0205441 | + | 0.0355834i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.822876 | − | 1.42526i | −0.0521476 | − | 0.0903223i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.8118 | −1.81858 | −0.909291 | − | 0.416161i | \(-0.863375\pi\) | ||||
−0.909291 | + | 0.416161i | \(0.863375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.708497 | 0.0445428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.82288 | − | 15.2817i | 0.550356 | − | 0.953244i | −0.447893 | − | 0.894087i | \(-0.647825\pi\) |
0.998249 | − | 0.0591571i | \(-0.0188413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.06275 | −0.376721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.64575 | − | 2.85052i | 0.101869 | − | 0.176443i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.93725 | −0.424553 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1144 | − | 17.5186i | −0.616685 | − | 1.06813i | −0.990086 | − | 0.140459i | \(-0.955142\pi\) |
0.373402 | − | 0.927670i | \(-0.378191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35425 | − | 2.34563i | 0.0822647 | − | 0.142487i | −0.821958 | − | 0.569549i | \(-0.807118\pi\) |
0.904222 | + | 0.427062i | \(0.140451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.32288 | − | 2.29129i | 0.0800641 | − | 0.138675i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5000 | + | 21.6506i | 0.751052 | + | 1.30086i | 0.947313 | + | 0.320309i | \(0.103787\pi\) |
−0.196261 | + | 0.980552i | \(0.562880\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2288 | −1.32606 | −0.663028 | − | 0.748594i | \(-0.730729\pi\) | ||||
−0.663028 | + | 0.748594i | \(0.730729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.26013 | + | 5.64671i | 0.193795 | + | 0.335662i | 0.946505 | − | 0.322690i | \(-0.104587\pi\) |
−0.752710 | + | 0.658352i | \(0.771254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.46863 | + | 12.9360i | 0.440859 | + | 0.763590i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.85425 | − | 3.21165i | 0.109073 | − | 0.188921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.85425 | + | 3.21165i | 0.108698 | + | 0.188270i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.87451 | −0.576875 | −0.288437 | − | 0.957499i | \(-0.593136\pi\) | ||||
−0.288437 | + | 0.957499i | \(0.593136\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.177124 | − | 0.306788i | −0.0102778 | − | 0.0178017i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.35425 | − | 7.54178i | −0.250975 | − | 0.434701i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.46863 | − | 4.27579i | 0.141819 | − | 0.245638i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.87451 | −0.106984 | −0.0534919 | − | 0.998568i | \(-0.517035\pi\) | ||||
−0.0534919 | + | 0.998568i | \(0.517035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0627461 | −0.00356950 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.64575 | + | 11.5108i | 0.376846 | + | 0.652716i | 0.990601 | − | 0.136780i | \(-0.0436753\pi\) |
−0.613755 | + | 0.789496i | \(0.710342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.64575 | + | 16.7069i | −0.545210 | + | 0.944332i | 0.453384 | + | 0.891316i | \(0.350217\pi\) |
−0.998594 | + | 0.0530161i | \(0.983117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.29150 | + | 7.43310i | −0.241035 | + | 0.417485i | −0.961009 | − | 0.276516i | \(-0.910820\pi\) |
0.719975 | + | 0.694000i | \(0.244153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.583005 | − | 1.00979i | −0.0326420 | − | 0.0565376i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.2288 | 0.905801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.35425 | 0.130994 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.79150 | + | 10.0312i | −0.320271 | + | 0.554725i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.2288 | −1.88709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.67712 | − | 2.90486i | 0.0921831 | − | 0.159666i | −0.816246 | − | 0.577704i | \(-0.803949\pi\) |
0.908429 | + | 0.418038i | \(0.137282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.14575 | + | 1.98450i | 0.0627868 | + | 0.108750i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2915 | −1.05088 | −0.525438 | − | 0.850832i | \(-0.676098\pi\) | ||||
−0.525438 | + | 0.850832i | \(0.676098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.29150 | − | 7.43310i | −0.233082 | − | 0.403711i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.708497 | − | 1.22715i | 0.0383673 | − | 0.0664541i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.76013 | + | 9.97684i | 0.309220 | + | 0.535585i | 0.978192 | − | 0.207703i | \(-0.0665987\pi\) |
−0.668972 | + | 0.743288i | \(0.733265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.70850 | 0.252040 | 0.126020 | − | 0.992028i | \(-0.459780\pi\) | ||||
0.126020 | + | 0.992028i | \(0.459780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.46863 | + | 14.6681i | 0.450740 | + | 0.780704i | 0.998432 | − | 0.0559759i | \(-0.0178270\pi\) |
−0.547693 | + | 0.836680i | \(0.684494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.64575 | −0.510507 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.4686 | − | 21.5963i | 0.658069 | − | 1.13981i | −0.323046 | − | 0.946383i | \(-0.604707\pi\) |
0.981115 | − | 0.193426i | \(-0.0619598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.29150 | + | 16.0934i | 0.489026 | + | 0.847019i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8745 | 0.570764 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.93725 | + | 10.2836i | 0.309922 | + | 0.536801i | 0.978345 | − | 0.206981i | \(-0.0663637\pi\) |
−0.668423 | + | 0.743781i | \(0.733030\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.82288 | − | 4.88936i | 0.146953 | − | 0.254530i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1144 | + | 17.5186i | −0.525112 | + | 0.909521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.7915 | + | 20.4235i | −0.610541 | + | 1.05749i | 0.380608 | + | 0.924736i | \(0.375715\pi\) |
−0.991149 | + | 0.132752i | \(0.957619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.29150 | −0.169521 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3542 | −0.788695 | −0.394347 | − | 0.918961i | \(-0.629029\pi\) | ||||
−0.394347 | + | 0.918961i | \(0.629029\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.677124 | − | 1.17281i | −0.0346901 | − | 0.0600851i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.64575 | + | 8.04668i | −0.237387 | + | 0.411166i | −0.959964 | − | 0.280125i | \(-0.909624\pi\) |
0.722577 | + | 0.691291i | \(0.242958\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.64575 | + | 2.85052i | −0.0836582 | + | 0.144900i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.239870 | + | 0.415468i | 0.0121619 | + | 0.0210651i | 0.872042 | − | 0.489430i | \(-0.162795\pi\) |
−0.859880 | + | 0.510496i | \(0.829462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.29150 | −0.368747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.583005 | −0.0294087 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2288 | + | 17.7167i | −0.513367 | + | 0.889177i | 0.486513 | + | 0.873673i | \(0.338269\pi\) |
−0.999880 | + | 0.0155038i | \(0.995065\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.854249 | + | 1.47960i | 0.0427659 | + | 0.0740728i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7601 | + | 30.7614i | −0.886899 | + | 1.53615i | −0.0433765 | + | 0.999059i | \(0.513812\pi\) |
−0.843522 | + | 0.537095i | \(0.819522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.811762 | 0.0402375 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.79150 | − | 6.56708i | −0.187478 | − | 0.324721i | 0.756931 | − | 0.653495i | \(-0.226698\pi\) |
−0.944409 | + | 0.328774i | \(0.893365\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.645751 | − | 1.11847i | 0.0318526 | − | 0.0551703i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.23987 | − | 2.14752i | 0.0610100 | − | 0.105672i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.96863 | + | 13.8021i | 0.390225 | + | 0.675890i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6458 | 1.54600 | 0.772998 | − | 0.634408i | \(-0.218756\pi\) | ||||
0.772998 | + | 0.634408i | \(0.218756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8745 | 1.40726 | 0.703629 | − | 0.710568i | \(-0.251562\pi\) | ||||
0.703629 | + | 0.710568i | \(0.251562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.46863 | + | 11.2040i | 0.314515 | + | 0.544757i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.6458 | −1.48305 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.177124 | + | 0.306788i | −0.00855164 | + | 0.0148119i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9373 | + | 24.1400i | 0.671334 | + | 1.16278i | 0.977526 | + | 0.210815i | \(0.0676117\pi\) |
−0.306192 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.29150 | −0.158180 | −0.0790898 | − | 0.996867i | \(-0.525201\pi\) | ||||
−0.0790898 | + | 0.996867i | \(0.525201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.645751 | + | 1.11847i | 0.0308905 | + | 0.0535039i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.9059 | − | 34.4780i | 0.950056 | − | 1.64555i | 0.204759 | − | 0.978812i | \(-0.434359\pi\) |
0.745297 | − | 0.666733i | \(-0.232308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.50000 | − | 6.06218i | −0.166667 | − | 0.288675i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.35425 | − | 5.80973i | 0.159365 | − | 0.276029i | −0.775275 | − | 0.631624i | \(-0.782389\pi\) |
0.934640 | + | 0.355596i | \(0.115722\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.93725 | −0.233524 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.1033 | −1.51505 | −0.757523 | − | 0.652808i | \(-0.773591\pi\) | ||||
−0.757523 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.67712 | + | 9.83307i | −0.266735 | + | 0.461998i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.08301 | + | 7.07197i | −0.190995 | + | 0.330813i | −0.945580 | − | 0.325389i | \(-0.894505\pi\) |
0.754585 | + | 0.656202i | \(0.227838\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.82288 | + | 3.15731i | 0.0850845 | + | 0.147371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7085 | 0.498744 | 0.249372 | − | 0.968408i | \(-0.419776\pi\) | ||||
0.249372 | + | 0.968408i | \(0.419776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.9373 | 1.57720 | 0.788599 | − | 0.614908i | \(-0.210807\pi\) | ||||
0.788599 | + | 0.614908i | \(0.210807\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3542 | − | 19.6661i | 0.525412 | − | 0.910040i | −0.474150 | − | 0.880444i | \(-0.657245\pi\) |
0.999562 | − | 0.0295961i | \(-0.00942212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5000 | + | 18.1865i | −0.484845 | + | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.50000 | − | 14.7224i | 0.391659 | − | 0.678374i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.583005 | + | 1.00979i | 0.0268066 | + | 0.0464304i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.64575 | 0.350075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8229 | − | 22.2099i | −0.585892 | − | 1.01479i | −0.994764 | − | 0.102203i | \(-0.967411\pi\) |
0.408871 | − | 0.912592i | \(-0.365922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.14575 | − | 1.98450i | 0.0522418 | − | 0.0904854i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.64575 | − | 4.58258i | −0.120386 | − | 0.208514i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2288 | + | 35.0372i | 0.916652 | + | 1.58769i | 0.804464 | + | 0.594002i | \(0.202453\pi\) |
0.112189 | + | 0.993687i | \(0.464214\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.2288 | 0.779111 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4575 | −1.55505 | −0.777523 | − | 0.628855i | \(-0.783524\pi\) | ||||
−0.777523 | + | 0.628855i | \(0.783524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 10.3923i | 0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.64575 | + | 16.7069i | 0.432671 | + | 0.749408i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.90588 | − | 17.1575i | 0.443448 | − | 0.768075i | −0.554495 | − | 0.832187i | \(-0.687088\pi\) |
0.997943 | + | 0.0641127i | \(0.0204217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.76013 | + | 16.9050i | 0.436050 | + | 0.755262i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.7085 | −0.744995 | −0.372498 | − | 0.928033i | \(-0.621498\pi\) | ||||
−0.372498 | + | 0.928033i | \(0.621498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9373 | − | 22.4080i | 0.573434 | − | 0.993216i | −0.422776 | − | 0.906234i | \(-0.638944\pi\) |
0.996210 | − | 0.0869822i | \(-0.0277223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.67712 | + | 9.83307i | −0.251141 | + | 0.434989i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.322876 | − | 0.559237i | 0.0142553 | − | 0.0246909i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.58301 | 0.201560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.5830 | −0.903494 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.93725 | + | 13.7477i | 0.347737 | + | 0.602299i | 0.985847 | − | 0.167647i | \(-0.0536167\pi\) |
−0.638110 | + | 0.769945i | \(0.720283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.06275 | + | 8.76893i | −0.221378 | + | 0.383439i | −0.955227 | − | 0.295875i | \(-0.904389\pi\) |
0.733848 | + | 0.679313i | \(0.237722\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.29150 | + | 12.6293i | −0.317623 | + | 0.550139i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.937254 | −0.0406734 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.64575 | −0.244545 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6458 | + | 20.1710i | −0.502551 | + | 0.870444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.47974 | −0.106810 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4373 | + | 23.2740i | −0.577713 | + | 1.00063i | 0.418028 | + | 0.908434i | \(0.362721\pi\) |
−0.995741 | + | 0.0921937i | \(0.970612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.29150 | + | 12.6293i | 0.312908 | + | 0.541973i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.125492 | 0.00536566 | 0.00268283 | − | 0.999996i | \(-0.499146\pi\) | ||||
0.00268283 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.79150 | + | 10.0312i | 0.247175 | + | 0.428120i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.06275 | − | 1.84073i | 0.0452745 | − | 0.0784177i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.58301 | −0.152365 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.35425 | + | 14.4700i | 0.353981 | + | 0.613113i | 0.986943 | − | 0.161070i | \(-0.0514945\pi\) |
−0.632962 | + | 0.774183i | \(0.718161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.29150 | 0.139216 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29150 | 0.0545273 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.76013 | − | 4.78068i | −0.116326 | − | 0.201482i | 0.801983 | − | 0.597346i | \(-0.203778\pi\) |
−0.918309 | + | 0.395865i | \(0.870445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.32288 | + | 2.29129i | −0.0555556 | + | 0.0962250i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.46863 | + | 4.27579i | −0.103490 | + | 0.179250i | −0.913120 | − | 0.407690i | \(-0.866334\pi\) |
0.809630 | + | 0.586940i | \(0.199668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.96863 | − | 5.14181i | −0.124233 | − | 0.215178i | 0.797200 | − | 0.603716i | \(-0.206314\pi\) |
−0.921433 | + | 0.388537i | \(0.872980\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5203 | −0.564817 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.29150 | + | 3.96900i | 0.0953965 | + | 0.165232i | 0.909774 | − | 0.415104i | \(-0.136255\pi\) |
−0.814378 | + | 0.580335i | \(0.802921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00000 | − | 13.8564i | 0.332469 | − | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.17712 | + | 3.77089i | 0.0903223 | + | 0.156443i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.35425 | − | 2.34563i | 0.0560872 | − | 0.0971460i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.00000 | 0.247647 | 0.123823 | − | 0.992304i | \(-0.460484\pi\) | ||||
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.58301 | 0.106431 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.35425 | − | 7.54178i | −0.179110 | − | 0.310227i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.291503 | + | 0.504897i | −0.0119706 | + | 0.0207336i | −0.871949 | − | 0.489597i | \(-0.837144\pi\) |
0.859978 | + | 0.510331i | \(0.170477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.322876 | − | 0.559237i | 0.0132144 | − | 0.0228880i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.4686 | + | 28.5245i | 0.672890 | + | 1.16548i | 0.977081 | + | 0.212868i | \(0.0682806\pi\) |
−0.304191 | + | 0.952611i | \(0.598386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2915 | 0.582963 | 0.291481 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291481 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.93725 | 0.323230 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.32288 | − | 14.4156i | 0.337815 | − | 0.585113i | −0.646206 | − | 0.763163i | \(-0.723645\pi\) |
0.984021 | + | 0.178050i | \(0.0569788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.35425 | + | 7.54178i | −0.176443 | + | 0.305608i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.46863 | − | 11.2040i | 0.261693 | − | 0.453265i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6458 | − | 30.5633i | −0.712705 | − | 1.23444i | −0.963838 | − | 0.266489i | \(-0.914136\pi\) |
0.251133 | − | 0.967953i | \(-0.419197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.8745 | −1.68580 | −0.842902 | − | 0.538067i | \(-0.819155\pi\) | ||||
−0.842902 | + | 0.538067i | \(0.819155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.3542 | − | 21.3982i | −0.496559 | − | 0.860066i | 0.503433 | − | 0.864034i | \(-0.332070\pi\) |
−0.999992 | + | 0.00396857i | \(0.998737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | + | 1.73205i | −0.0401286 | + | 0.0695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.3542 | 0.735347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.114378 | − | 0.198109i | −0.00456783 | − | 0.00791171i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.35425 | −0.333106 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35425 | −0.0539118 | −0.0269559 | − | 0.999637i | \(-0.508581\pi\) | ||||
−0.0269559 | + | 0.999637i | \(0.508581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.03137 | − | 1.78639i | −0.0409934 | − | 0.0710026i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.50000 | + | 6.06218i | −0.138675 | + | 0.240192i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.64575 | − | 6.31463i | 0.144224 | − | 0.249803i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.3542 | −1.07875 | −0.539373 | − | 0.842067i | \(-0.681339\pi\) | ||||
−0.539373 | + | 0.842067i | \(0.681339\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.3431 | + | 43.8956i | 0.996341 | + | 1.72571i | 0.572183 | + | 0.820126i | \(0.306097\pi\) |
0.424159 | + | 0.905588i | \(0.360570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.166010 | + | 0.287539i | −0.00651648 | + | 0.0112869i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5830 | −0.414781 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.11438 | + | 14.0545i | −0.317540 | + | 0.549996i | −0.979974 | − | 0.199125i | \(-0.936190\pi\) |
0.662434 | + | 0.749120i | \(0.269523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.29150 | 0.167427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.1033 | 1.56220 | 0.781101 | − | 0.624405i | \(-0.214659\pi\) | ||||
0.781101 | + | 0.624405i | \(0.214659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.854249 | − | 1.47960i | −0.0332264 | − | 0.0575499i | 0.848934 | − | 0.528499i | \(-0.177245\pi\) |
−0.882160 | + | 0.470949i | \(0.843912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.82288 | − | 3.15731i | 0.0707946 | − | 0.122620i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.29150 | + | 5.70105i | −0.127447 | + | 0.220746i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.96863 | + | 12.0700i | 0.269423 | + | 0.466654i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.10326 | 0.158405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.29150 | 0.0883309 | 0.0441655 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441655 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.3542 | − | 33.5225i | 0.743844 | − | 1.28838i | −0.206889 | − | 0.978365i | \(-0.566334\pi\) |
0.950733 | − | 0.310011i | \(-0.100333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.90588 | − | 8.49723i | −0.188270 | − | 0.326094i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.35425 | + | 7.54178i | −0.166855 | + | 0.289002i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0516 | − | 17.4099i | −0.384615 | − | 0.666173i | 0.607101 | − | 0.794625i | \(-0.292332\pi\) |
−0.991716 | + | 0.128452i | \(0.958999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.2915 | 0.774169 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.82288 | − | 6.62141i | −0.145640 | − | 0.252256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.61438 | + | 13.1885i | −0.289665 | + | 0.501714i | −0.973730 | − | 0.227707i | \(-0.926877\pi\) |
0.684065 | + | 0.729421i | \(0.260210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.468627 | + | 0.811686i | 0.0178017 | + | 0.0308334i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.2915 | + | 17.8254i | 0.389818 | + | 0.675185i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.2288 | −0.916416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0627 | −0.946607 | −0.473303 | − | 0.880899i | \(-0.656939\pi\) | ||||
−0.473303 | + | 0.880899i | \(0.656939\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.739870 | + | 1.28149i | 0.0279047 | + | 0.0483324i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.53137 | + | 11.3127i | −0.245638 | + | 0.425457i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.08301 | − | 5.33992i | 0.115785 | − | 0.200545i | −0.802308 | − | 0.596910i | \(-0.796395\pi\) |
0.918093 | + | 0.396365i | \(0.129728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.677124 | + | 1.17281i | 0.0253941 | + | 0.0439840i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.70850 | − | 8.15536i | −0.175842 | − | 0.304567i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11438 | + | 1.93016i | −0.0415593 | + | 0.0719828i | −0.886057 | − | 0.463577i | \(-0.846566\pi\) |
0.844498 | + | 0.535559i | \(0.179899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.166010 | 0.00618255 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.145751 | + | 0.252449i | −0.00542055 | + | 0.00938867i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.1033 | 1.00520 | 0.502602 | − | 0.864518i | \(-0.332376\pi\) | ||||
0.502602 | + | 0.864518i | \(0.332376\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0203 | + | 27.7479i | −0.591722 | + | 1.02489i | 0.402279 | + | 0.915517i | \(0.368218\pi\) |
−0.994001 | + | 0.109375i | \(0.965115\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.40588 | − | 2.43506i | 0.0517863 | − | 0.0896965i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.2601 | + | 43.7518i | 0.929209 | + | 1.60944i | 0.784648 | + | 0.619941i | \(0.212843\pi\) |
0.144560 | + | 0.989496i | \(0.453823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.645751 | −0.0237223 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.4170 | −0.418849 | −0.209424 | − | 0.977825i | \(-0.567159\pi\) | ||||
−0.209424 | + | 0.977825i | \(0.567159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.822876 | − | 1.42526i | 0.0301074 | − | 0.0521476i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.9373 | −1.56889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6771 | − | 28.8856i | 0.608557 | − | 1.05405i | −0.382922 | − | 0.923781i | \(-0.625082\pi\) |
0.991478 | − | 0.130271i | \(-0.0415846\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.4059 | − | 24.9517i | −0.524979 | − | 0.909291i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0000 | 0.399802 | 0.199901 | − | 0.979816i | \(-0.435938\pi\) | ||||
0.199901 | + | 0.979816i | \(0.435938\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.354249 | + | 0.613577i | 0.0128584 | + | 0.0222714i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1771 | − | 38.4119i | 0.803920 | − | 1.39243i | −0.113098 | − | 0.993584i | \(-0.536077\pi\) |
0.917018 | − | 0.398847i | \(-0.130589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.3229 | − | 26.5400i | 0.554725 | − | 0.960812i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.468627 | + | 0.811686i | 0.0169211 | + | 0.0293083i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.00000 | 0.144244 | 0.0721218 | − | 0.997396i | \(-0.477023\pi\) | ||||
0.0721218 | + | 0.997396i | \(0.477023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6458 | 0.635496 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2915 | + | 23.0216i | 0.478062 | + | 0.828028i | 0.999684 | − | 0.0251491i | \(-0.00800604\pi\) |
−0.521622 | + | 0.853177i | \(0.674673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.03137 | − | 5.25049i | −0.108750 | − | 0.188360i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.82288 | − | 3.15731i | 0.0653113 | − | 0.113122i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29150 | − | 2.23695i | −0.0462136 | − | 0.0800443i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.29150 | 0.117629 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.4889 | − | 38.9519i | −0.801642 | − | 1.38849i | −0.918535 | − | 0.395340i | \(-0.870627\pi\) |
0.116892 | − | 0.993145i | \(-0.462707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3542 | + | 19.6661i | 0.403711 | + | 0.699247i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.79150 | − | 10.0312i | 0.205662 | − | 0.356218i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.87451 | −0.137242 | −0.0686211 | − | 0.997643i | \(-0.521860\pi\) | ||||
−0.0686211 | + | 0.997643i | \(0.521860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.1660 | −1.66861 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.46863 | − | 6.00784i | −0.122558 | − | 0.212277i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.760130 | − | 1.31658i | 0.0268244 | − | 0.0464612i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.1144 | − | 17.5186i | 0.356043 | − | 0.616685i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.3542 | + | 30.0584i | 0.610143 | + | 1.05680i | 0.991216 | + | 0.132254i | \(0.0422213\pi\) |
−0.381073 | + | 0.924545i | \(0.624445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.93725 | −0.278715 | −0.139357 | − | 0.990242i | \(-0.544504\pi\) | ||||
−0.139357 | + | 0.990242i | \(0.544504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.70850 | 0.0949912 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.06275 | + | 1.84073i | −0.0371808 | + | 0.0643990i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.64575 | 0.0924500 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.69738 | − | 15.0643i | 0.303541 | − | 0.525748i | −0.673395 | − | 0.739283i | \(-0.735164\pi\) |
0.976935 | + | 0.213535i | \(0.0684978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.26013 | + | 14.3070i | 0.287930 | + | 0.498709i | 0.973315 | − | 0.229471i | \(-0.0736996\pi\) |
−0.685385 | + | 0.728180i | \(0.740366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.5830 | −1.48076 | −0.740378 | − | 0.672191i | \(-0.765354\pi\) | ||||
−0.740378 | + | 0.672191i | \(0.765354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.6660 | + | 34.0625i | 0.683029 | + | 1.18304i | 0.974052 | + | 0.226325i | \(0.0726710\pi\) |
−0.291023 | + | 0.956716i | \(0.593996\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.5000 | + | 21.6506i | −0.433620 | + | 0.751052i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.5203 | 0.884225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000 | + | 3.46410i | 0.0691301 | + | 0.119737i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1660 | 0.661684 | 0.330842 | − | 0.943686i | \(-0.392667\pi\) | ||||
0.330842 | + | 0.943686i | \(0.392667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1660 | −0.626414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1144 | − | 19.2507i | −0.382800 | − | 0.663028i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.7712 | −0.988592 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.26013 | + | 5.64671i | −0.111887 | + | 0.193795i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.29150 | − | 3.96900i | −0.0785517 | − | 0.136056i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.00000 | −0.0684787 | −0.0342393 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342393 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5830 | − | 23.5265i | −0.463987 | − | 0.803648i | 0.535169 | − | 0.844745i | \(-0.320248\pi\) |
−0.999155 | + | 0.0410969i | \(0.986915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5830 | − | 35.6508i | 0.702283 | − | 1.21639i | −0.265380 | − | 0.964144i | \(-0.585497\pi\) |
0.967663 | − | 0.252246i | \(-0.0811692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.46863 | + | 12.9360i | −0.254530 | + | 0.440859i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.05163 | − | 5.28558i | 0.103879 | − | 0.179923i | −0.809401 | − | 0.587257i | \(-0.800208\pi\) |
0.913280 | + | 0.407333i | \(0.133541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.70850 | 0.125947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.479741 | 0.0162741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.96863 | − | 6.87386i | −0.134472 | − | 0.232912i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.85425 | + | 3.21165i | −0.0627568 | + | 0.108698i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3745 | − | 38.7538i | 0.755533 | − | 1.30862i | −0.189575 | − | 0.981866i | \(-0.560711\pi\) |
0.945109 | − | 0.326756i | \(-0.105956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.93725 | − | 8.55157i | −0.166529 | − | 0.288437i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7085 | 1.50627 | 0.753134 | − | 0.657867i | \(-0.228541\pi\) | ||||
0.753134 | + | 0.657867i | \(0.228541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.3542 | 0.785933 | 0.392967 | − | 0.919553i | \(-0.371449\pi\) | ||||
0.392967 | + | 0.919553i | \(0.371449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.6458 | − | 35.7595i | 0.693216 | − | 1.20069i | −0.277562 | − | 0.960708i | \(-0.589526\pi\) |
0.970778 | − | 0.239978i | \(-0.0771404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.79150 | + | 3.10297i | 0.0600851 | + | 0.104070i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.177124 | − | 0.306788i | 0.00593389 | − | 0.0102778i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.17712 | + | 7.23499i | 0.139782 | + | 0.242110i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.00000 | 0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.58301 | + | 11.4021i | 0.219556 | + | 0.380281i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.9373 | + | 24.1400i | −0.464317 | + | 0.804221i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.35425 | − | 7.54178i | 0.144900 | − | 0.250975i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4889 | − | 26.8275i | −0.514300 | − | 0.890794i | −0.999862 | − | 0.0165917i | \(-0.994718\pi\) |
0.485562 | − | 0.874202i | \(-0.338615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.93725 | 0.163758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3320 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.291503 | − | 0.504897i | −0.00964733 | − | 0.0167097i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.54249 | 0.0509374 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.4575 | + | 42.3617i | −0.806779 | + | 1.39738i | 0.108305 | + | 0.994118i | \(0.465458\pi\) |
−0.915084 | + | 0.403264i | \(0.867876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.937254 | − | 1.62337i | −0.0308836 | − | 0.0534919i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.29150 | −0.240003 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0313730 | − | 0.0543397i | −0.00103043 | − | 0.00178475i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.17712 | + | 2.03884i | −0.0386202 | + | 0.0668921i | −0.884689 | − | 0.466181i | \(-0.845630\pi\) |
0.846069 | + | 0.533073i | \(0.178963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.26013 | − | 3.91466i | −0.0740728 | − | 0.128298i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.64575 | + | 11.5108i | −0.217572 | + | 0.376846i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.2915 | −0.629554 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.87451 | − | 11.9070i | −0.224103 | − | 0.388157i | 0.731947 | − | 0.681361i | \(-0.238612\pi\) |
−0.956050 | + | 0.293204i | \(0.905278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.64575 | + | 9.77873i | −0.183851 | + | 0.318439i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.3542 | + | 23.1302i | −0.433955 | + | 0.751632i | −0.997210 | − | 0.0746515i | \(-0.976216\pi\) |
0.563255 | + | 0.826283i | \(0.309549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.14575 | − | 3.71655i | −0.0696540 | − | 0.120644i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.58301 | −0.278323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.5203 | 1.53933 | 0.769666 | − | 0.638447i | \(-0.220423\pi\) | ||||
0.769666 | + | 0.638447i | \(0.220423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.583005 | − | 1.00979i | 0.0188459 | − | 0.0326420i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.70850 | + | 2.95920i | −0.0551703 | + | 0.0955577i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.11438 | + | 14.0545i | 0.261482 | + | 0.452900i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9373 | 0.962717 | 0.481359 | − | 0.876524i | \(-0.340143\pi\) | ||||
0.481359 | + | 0.876524i | \(0.340143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.17712 | + | 2.03884i | 0.0378147 | + | 0.0654970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.2804 | − | 45.5190i | 0.843378 | − | 1.46077i | −0.0436447 | − | 0.999047i | \(-0.513897\pi\) |
0.887023 | − | 0.461726i | \(-0.152770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.0830 | − | 36.5168i | −0.675890 | − | 1.17068i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3431 | − | 21.3789i | −0.394892 | − | 0.683973i | 0.598196 | − | 0.801350i | \(-0.295885\pi\) |
−0.993087 | + | 0.117377i | \(0.962551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.45751 | −0.0785425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.5830 | −0.369817 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.82288 | + | 4.88936i | 0.0900358 | + | 0.155946i | 0.907526 | − | 0.419996i | \(-0.137969\pi\) |
−0.817490 | + | 0.575943i | \(0.804635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.1144 | − | 29.6430i | −0.544757 | − | 0.943546i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.29150 | − | 5.70105i | 0.104664 | − | 0.181283i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9373 | + | 20.6759i | 0.379199 | + | 0.656793i | 0.990946 | − | 0.134261i | \(-0.0428661\pi\) |
−0.611747 | + | 0.791054i | \(0.709533\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.35425 | 0.106444 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.3745 | − | 42.2179i | −0.771948 | − | 1.33705i | −0.936494 | − | 0.350684i | \(-0.885949\pi\) |
0.164545 | − | 0.986370i | \(-0.447384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.14575 | + | 1.98450i | −0.0362500 | + | 0.0627868i |
(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 | 2100.2.q.i.1801.1 | yes | 4 | |
5.2 | odd | 4 | 2100.2.bc.h.1549.4 | 8 | |||
5.3 | odd | 4 | 2100.2.bc.h.1549.1 | 8 | |||
5.4 | even | 2 | 2100.2.q.g.1801.2 | yes | 4 | ||
7.4 | even | 3 | inner | 2100.2.q.i.1201.1 | yes | 4 | |
35.4 | even | 6 | 2100.2.q.g.1201.2 | ✓ | 4 | ||
35.18 | odd | 12 | 2100.2.bc.h.949.4 | 8 | |||
35.32 | odd | 12 | 2100.2.bc.h.949.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.g.1201.2 | ✓ | 4 | 35.4 | even | 6 | ||
2100.2.q.g.1801.2 | yes | 4 | 5.4 | even | 2 | ||
2100.2.q.i.1201.1 | yes | 4 | 7.4 | even | 3 | inner | |
2100.2.q.i.1801.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2100.2.bc.h.949.1 | 8 | 35.32 | odd | 12 | |||
2100.2.bc.h.949.4 | 8 | 35.18 | odd | 12 | |||
2100.2.bc.h.1549.1 | 8 | 5.3 | odd | 4 | |||
2100.2.bc.h.1549.4 | 8 | 5.2 | odd | 4 |