Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,4,Mod(177,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.177");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.i (of order \(3\), degree \(2\), not 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: | \(23.1287487223\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11163123.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 14x^{4} + 49x^{2} + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.3 | ||
Root | \(0.821510i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.177 |
Dual form | 392.4.i.m.361.3 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.40222 | + | 2.42872i | 0.269858 | + | 0.467408i | 0.968825 | − | 0.247746i | \(-0.0796899\pi\) |
−0.698967 | + | 0.715154i | \(0.746357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.34580 | + | 5.79509i | −0.299257 | + | 0.518328i | −0.975966 | − | 0.217922i | \(-0.930072\pi\) |
0.676709 | + | 0.736250i | \(0.263405\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.56754 | − | 16.5715i | 0.354353 | − | 0.613758i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.7441 | − | 27.2695i | −0.431546 | − | 0.747460i | 0.565460 | − | 0.824776i | \(-0.308699\pi\) |
−0.997007 | + | 0.0773151i | \(0.975365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.6837 | −0.398609 | −0.199304 | − | 0.979938i | \(-0.563868\pi\) | ||||
−0.199304 | + | 0.979938i | \(0.563868\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.7662 | −0.323028 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −43.9769 | − | 76.1703i | −0.627410 | − | 1.08671i | −0.988070 | − | 0.154008i | \(-0.950782\pi\) |
0.360660 | − | 0.932698i | \(-0.382552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.54850 | − | 11.3423i | 0.0790700 | − | 0.136953i | −0.823779 | − | 0.566911i | \(-0.808138\pi\) |
0.902849 | + | 0.429958i | \(0.141472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.68840 | − | 8.12055i | 0.0425043 | − | 0.0736197i | −0.843991 | − | 0.536358i | \(-0.819800\pi\) |
0.886495 | + | 0.462738i | \(0.153133\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.1113 | + | 69.4748i | 0.320890 | + | 0.555799i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 129.383 | 0.922216 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.11923 | −0.0327799 | −0.0163900 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163900 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.706 | − | 222.925i | −0.745685 | − | 1.29156i | −0.949874 | − | 0.312633i | \(-0.898789\pi\) |
0.204189 | − | 0.978932i | \(-0.434544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 44.1533 | − | 76.4758i | 0.232912 | − | 0.403416i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 190.107 | − | 329.276i | 0.844688 | − | 1.46304i | −0.0412040 | − | 0.999151i | \(-0.513119\pi\) |
0.885892 | − | 0.463892i | \(-0.153547\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −26.1987 | − | 45.3774i | −0.107568 | − | 0.186313i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 217.959 | 0.830230 | 0.415115 | − | 0.909769i | \(-0.363741\pi\) | ||||
0.415115 | + | 0.909769i | \(0.363741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 377.049 | 1.33720 | 0.668598 | − | 0.743624i | \(-0.266895\pi\) | ||||
0.668598 | + | 0.743624i | \(0.266895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 64.0221 | + | 110.889i | 0.212086 | + | 0.367343i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −178.855 | + | 309.786i | −0.555079 | + | 0.961425i | 0.442818 | + | 0.896611i | \(0.353979\pi\) |
−0.997897 | + | 0.0648137i | \(0.979355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 123.331 | − | 213.615i | 0.338623 | − | 0.586512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −382.195 | − | 661.981i | −0.990538 | − | 1.71566i | −0.614122 | − | 0.789211i | \(-0.710490\pi\) |
−0.376415 | − | 0.926451i | \(-0.622843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 210.706 | 0.516573 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 36.7298 | 0.0853506 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −225.336 | − | 390.293i | −0.497224 | − | 0.861216i | 0.502771 | − | 0.864419i | \(-0.332314\pi\) |
−0.999995 | + | 0.00320303i | \(0.998980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −87.0388 | + | 150.756i | −0.182691 | + | 0.316431i | −0.942796 | − | 0.333370i | \(-0.891814\pi\) |
0.760105 | + | 0.649801i | \(0.225148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62.5117 | − | 108.273i | 0.119287 | − | 0.206610i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 248.617 | + | 430.617i | 0.453334 | + | 0.785198i | 0.998591 | − | 0.0530711i | \(-0.0169010\pi\) |
−0.545256 | + | 0.838269i | \(0.683568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 26.2967 | 0.0458805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 350.238 | 0.585432 | 0.292716 | − | 0.956199i | \(-0.405441\pi\) | ||||
0.292716 | + | 0.956199i | \(0.405441\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −531.343 | − | 920.312i | −0.851903 | − | 1.47554i | −0.879488 | − | 0.475920i | \(-0.842115\pi\) |
0.0275851 | − | 0.999619i | \(-0.491218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −112.490 | + | 194.838i | −0.173190 | + | 0.299973i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −280.224 | + | 485.363i | −0.399085 | + | 0.691235i | −0.993613 | − | 0.112839i | \(-0.964005\pi\) |
0.594528 | + | 0.804075i | \(0.297339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −76.8993 | − | 133.194i | −0.105486 | − | 0.182707i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1105.27 | 1.46168 | 0.730840 | − | 0.682549i | \(-0.239129\pi\) | ||||
0.730840 | + | 0.682549i | \(0.239129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 588.551 | 0.751027 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.17830 | − | 12.4332i | −0.00884592 | − | 0.0153216i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 603.357 | − | 1045.04i | 0.718604 | − | 1.24466i | −0.242950 | − | 0.970039i | \(-0.578115\pi\) |
0.961553 | − | 0.274619i | \(-0.0885517\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 360.948 | − | 625.181i | 0.402458 | − | 0.697078i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 43.8199 | + | 75.8983i | 0.0473245 | + | 0.0819684i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1442.99 | −1.51045 | −0.755226 | − | 0.655465i | \(-0.772473\pi\) | ||||
−0.755226 | + | 0.655465i | \(0.772473\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −602.528 | −0.611680 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 155.961 | + | 270.133i | 0.153651 | + | 0.266131i | 0.932567 | − | 0.360997i | \(-0.117564\pi\) |
−0.778916 | + | 0.627128i | \(0.784230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −290.816 | + | 503.708i | −0.278203 | + | 0.481862i | −0.970938 | − | 0.239330i | \(-0.923072\pi\) |
0.692735 | + | 0.721192i | \(0.256406\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 587.738 | − | 1017.99i | 0.531016 | − | 0.919748i | −0.468328 | − | 0.883555i | \(-0.655144\pi\) |
0.999345 | − | 0.0361930i | \(-0.0115231\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −168.526 | − | 291.896i | −0.148091 | − | 0.256500i | 0.782431 | − | 0.622737i | \(-0.213979\pi\) |
−0.930522 | + | 0.366237i | \(0.880646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1066.29 | 0.911783 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1168.16 | −0.972487 | −0.486243 | − | 0.873823i | \(-0.661633\pi\) | ||||
−0.486243 | + | 0.873823i | \(0.661633\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.3729 | + | 54.3394i | 0.0254394 | + | 0.0440624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −178.757 | + | 309.616i | −0.141248 | + | 0.244649i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 169.749 | − | 294.015i | 0.127535 | − | 0.220898i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 305.627 | + | 529.361i | 0.224044 | + | 0.388056i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1373.27 | −0.982629 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23.4734 | 0.0164010 | 0.00820049 | − | 0.999966i | \(-0.497390\pi\) | ||||
0.00820049 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 528.707 | + | 915.747i | 0.360853 | + | 0.625016i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −186.991 | + | 323.878i | −0.124713 | + | 0.216010i | −0.921621 | − | 0.388091i | \(-0.873135\pi\) |
0.796907 | + | 0.604101i | \(0.206468\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −432.890 | + | 749.788i | −0.275980 | + | 0.478011i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −569.069 | − | 985.656i | −0.354882 | − | 0.614674i | 0.632216 | − | 0.774792i | \(-0.282146\pi\) |
−0.987098 | + | 0.160119i | \(0.948812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1229.46 | 0.750224 | 0.375112 | − | 0.926979i | \(-0.377604\pi\) | ||||
0.375112 | + | 0.926979i | \(0.377604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1003.18 | −0.599170 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 294.157 | + | 509.494i | 0.172018 | + | 0.297944i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.1279 | − | 29.6664i | 0.00980962 | − | 0.0169908i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1481.38 | + | 2565.82i | −0.814492 | + | 1.41074i | 0.0952006 | + | 0.995458i | \(0.469651\pi\) |
−0.909692 | + | 0.415283i | \(0.863683\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1298.85 | + | 2249.68i | 0.699993 | + | 1.21242i | 0.968468 | + | 0.249137i | \(0.0801471\pi\) |
−0.268475 | + | 0.963287i | \(0.586520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1683.00 | −0.889299 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1722.49 | 0.892606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 682.492 | + | 1182.11i | 0.346935 | + | 0.600909i | 0.985703 | − | 0.168490i | \(-0.0538891\pi\) |
−0.638768 | + | 0.769399i | \(0.720556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1071.84 | − | 1856.49i | 0.534609 | − | 0.925970i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1658.74 | + | 2873.02i | −0.797071 | + | 1.38057i | 0.124445 | + | 0.992227i | \(0.460285\pi\) |
−0.921516 | + | 0.388341i | \(0.873048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 295.456 | + | 511.745i | 0.139401 | + | 0.241450i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3803.96 | −1.76263 | −0.881315 | − | 0.472530i | \(-0.843341\pi\) | ||||
−0.881315 | + | 0.472530i | \(0.843341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1847.92 | −0.841111 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −125.306 | − | 217.037i | −0.0560374 | − | 0.0970597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1261.15 | − | 2184.37i | 0.554239 | − | 0.959970i | −0.443723 | − | 0.896164i | \(-0.646343\pi\) |
0.997962 | − | 0.0638064i | \(-0.0203240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 631.941 | − | 1094.55i | 0.268359 | − | 0.464812i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 93.5182 | + | 161.978i | 0.0390496 | + | 0.0676359i | 0.884890 | − | 0.465801i | \(-0.154234\pi\) |
−0.845840 | + | 0.533437i | \(0.820900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 457.654 | 0.187940 | 0.0939701 | − | 0.995575i | \(-0.470044\pi\) | ||||
0.0939701 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −488.191 | −0.197203 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1272.12 | + | 2203.38i | 0.505558 | + | 0.875652i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1384.75 | + | 2398.46i | −0.541513 | + | 0.937928i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1445.80 | + | 2504.19i | −0.547719 | + | 0.948676i | 0.450712 | + | 0.892670i | \(0.351170\pi\) |
−0.998430 | + | 0.0560069i | \(0.982163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −573.946 | − | 994.104i | −0.214060 | − | 0.370762i | 0.738922 | − | 0.673791i | \(-0.235335\pi\) |
−0.952981 | + | 0.303029i | \(0.902002\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 350.621 | 0.128762 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1638.22 | 0.592481 | 0.296240 | − | 0.955113i | \(-0.404267\pi\) | ||||
0.296240 | + | 0.955113i | \(0.404267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2655.64 | + | 4599.70i | 0.945996 | + | 1.63851i | 0.753745 | + | 0.657167i | \(0.228245\pi\) |
0.192251 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −697.233 | + | 1207.64i | −0.244672 | + | 0.423784i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −729.245 | + | 1263.09i | −0.248452 | + | 0.430332i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −89.7130 | − | 155.387i | −0.0301231 | − | 0.0521748i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −412.400 | −0.136489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1505.74 | −0.491277 | −0.245639 | − | 0.969361i | \(-0.578998\pi\) | ||||
−0.245639 | + | 0.969361i | \(0.578998\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 491.112 | + | 850.632i | 0.157983 | + | 0.273635i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1261.53 | + | 2185.03i | −0.400165 | + | 0.693107i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1490.12 | − | 2580.97i | 0.459786 | − | 0.796372i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 821.650 | + | 1423.14i | 0.250091 | + | 0.433171i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2520.23 | 0.756802 | 0.378401 | − | 0.925642i | \(-0.376474\pi\) | ||||
0.378401 | + | 0.925642i | \(0.376474\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1535.07 | 0.454834 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −769.019 | − | 1331.98i | −0.224853 | − | 0.389456i | 0.731423 | − | 0.681925i | \(-0.238857\pi\) |
−0.956275 | + | 0.292468i | \(0.905523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 285.842 | − | 495.092i | 0.0824845 | − | 0.142867i | −0.821832 | − | 0.569730i | \(-0.807048\pi\) |
0.904317 | + | 0.426863i | \(0.140381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 802.101 | − | 1389.28i | 0.225525 | − | 0.390621i | −0.730952 | − | 0.682429i | \(-0.760923\pi\) |
0.956477 | + | 0.291808i | \(0.0942568\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1196.83 | − | 2072.96i | −0.332223 | − | 0.575426i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1571.75 | −0.430785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4699.38 | −1.27187 | −0.635936 | − | 0.771742i | \(-0.719386\pi\) | ||||
−0.635936 | + | 0.771742i | \(0.719386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −436.304 | − | 755.700i | −0.116617 | − | 0.201987i | 0.801808 | − | 0.597582i | \(-0.203872\pi\) |
−0.918425 | + | 0.395595i | \(0.870538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1962.34 | − | 3398.86i | 0.518041 | − | 0.897273i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −122.350 | + | 211.916i | −0.0315180 | + | 0.0545908i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1549.84 | + | 2684.40i | 0.394446 | + | 0.683200i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3126.30 | −0.786176 | −0.393088 | − | 0.919501i | \(-0.628593\pi\) | ||||
−0.393088 | + | 0.919501i | \(0.628593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −295.258 | −0.0733704 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 825.280 | + | 1429.43i | 0.202671 | + | 0.351036i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 452.007 | − | 782.900i | 0.109710 | − | 0.190023i | −0.805943 | − | 0.591993i | \(-0.798341\pi\) |
0.915653 | + | 0.401970i | \(0.131674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.9785 | + | 84.8332i | −0.0116157 | + | 0.0201189i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 46.3184 | + | 80.2258i | 0.0108598 | + | 0.0188096i | 0.871404 | − | 0.490566i | \(-0.163210\pi\) |
−0.860544 | + | 0.509375i | \(0.829876\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5114.98 | 1.18570 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3384.16 | 0.775683 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2025.89 | − | 3508.94i | −0.459184 | − | 0.795330i | 0.539734 | − | 0.841836i | \(-0.318525\pi\) |
−0.998918 | + | 0.0465054i | \(0.985192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1395.65 | − | 2417.34i | 0.312840 | − | 0.541855i | −0.666136 | − | 0.745830i | \(-0.732053\pi\) |
0.978976 | + | 0.203975i | \(0.0653863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1263.03 | − | 2187.63i | 0.276958 | − | 0.479706i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1290.33 | + | 2234.92i | 0.279886 | + | 0.484777i | 0.971356 | − | 0.237628i | \(-0.0763699\pi\) |
−0.691470 | + | 0.722405i | \(0.743037\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4925.59 | −1.05694 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −919.487 | −0.195203 | −0.0976014 | − | 0.995226i | \(-0.531117\pi\) | ||||
−0.0976014 | + | 0.995226i | \(0.531117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4136.00 | − | 7163.77i | −0.868762 | − | 1.50474i | −0.863262 | − | 0.504756i | \(-0.831583\pi\) |
−0.00550035 | − | 0.999985i | \(-0.501751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −122.891 | + | 212.853i | −0.0255418 | + | 0.0442396i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1411.44 | + | 2444.68i | −0.287286 | + | 0.497595i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2023.40 | − | 3504.63i | −0.407607 | − | 0.705997i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2859.38 | 0.570126 | 0.285063 | − | 0.958509i | \(-0.407986\pi\) | ||||
0.285063 | + | 0.958509i | \(0.407986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3015.71 | 0.595191 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2037.02 | − | 3528.22i | −0.397979 | − | 0.689320i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −87.5965 | + | 151.722i | −0.0169426 | + | 0.0293455i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −437.385 | + | 757.573i | −0.0829277 | + | 0.143635i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −582.428 | − | 1008.79i | −0.109343 | − | 0.189388i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3542.86 | 0.658638 | 0.329319 | − | 0.944219i | \(-0.393181\pi\) | ||||
0.329319 | + | 0.944219i | \(0.393181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1631.15 | −0.300301 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −311.274 | − | 539.143i | −0.0567548 | − | 0.0983022i | 0.836252 | − | 0.548345i | \(-0.184742\pi\) |
−0.893007 | + | 0.450043i | \(0.851409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3532.42 | + | 6118.34i | −0.637905 | + | 1.10488i | 0.347986 | + | 0.937500i | \(0.386866\pi\) |
−0.985892 | + | 0.167385i | \(0.946468\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3229.60 | − | 5593.84i | 0.572217 | − | 0.991108i | −0.424121 | − | 0.905605i | \(-0.639417\pi\) |
0.996338 | − | 0.0855029i | \(-0.0272497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80.5975 | + | 139.599i | 0.0141461 | + | 0.0245017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3296.56 | 0.573196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1151.93 | −0.198437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −749.426 | − | 1298.04i | −0.127910 | − | 0.221546i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 472.622 | − | 818.606i | 0.0799268 | − | 0.138437i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4167.61 | − | 7218.51i | 0.692062 | − | 1.19869i | −0.279099 | − | 0.960262i | \(-0.590036\pi\) |
0.971161 | − | 0.238424i | \(-0.0766308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3637.72 | − | 6300.72i | −0.598636 | − | 1.03687i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3327.29 | −0.542654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5853.18 | 0.946122 | 0.473061 | − | 0.881030i | \(-0.343149\pi\) | ||||
0.473061 | + | 0.881030i | \(0.343149\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1638.02 | − | 2837.13i | −0.262433 | − | 0.454548i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4052.70 | + | 7019.49i | −0.643596 | + | 1.11474i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −87.9835 | + | 152.392i | −0.0137301 | + | 0.0237812i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3587.90 | − | 6214.43i | −0.555069 | − | 0.961407i | −0.997898 | − | 0.0648013i | \(-0.979359\pi\) |
0.442830 | − | 0.896606i | \(-0.353975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10302.4 | 1.58016 | 0.790081 | − | 0.613003i | \(-0.210039\pi\) | ||||
0.790081 | + | 0.613003i | \(0.210039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2417.35 | −0.367604 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 550.560 | + | 953.599i | 0.0830124 | + | 0.143782i | 0.904543 | − | 0.426383i | \(-0.140213\pi\) |
−0.821530 | + | 0.570165i | \(0.806879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1171.83 | + | 2029.66i | −0.175195 | + | 0.303446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2816.47 | − | 4878.26i | 0.414060 | − | 0.717172i | −0.581270 | − | 0.813711i | \(-0.697444\pi\) |
0.995329 | + | 0.0965388i | \(0.0307772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3343.73 | + | 5791.52i | 0.487496 | + | 0.844368i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 952.106 | 0.137666 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7111.05 | 1.01975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1598.23 | + | 2768.22i | 0.227322 | + | 0.393733i | 0.957013 | − | 0.290044i | \(-0.0936698\pi\) |
−0.729692 | + | 0.683776i | \(0.760336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2085.33 | − | 3611.90i | 0.294195 | − | 0.509560i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −457.697 | + | 792.755i | −0.0635353 | + | 0.110046i | −0.896043 | − | 0.443967i | \(-0.853571\pi\) |
0.832508 | + | 0.554013i | \(0.186904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1925.62 | − | 3335.28i | −0.265170 | − | 0.459288i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 95.6460 | 0.0130664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11767.5 | 1.59487 | 0.797437 | − | 0.603402i | \(-0.206188\pi\) | ||||
0.797437 | + | 0.603402i | \(0.206188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.9149 | + | 57.0103i | 0.00442594 | + | 0.00766595i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4207.56 | − | 7287.71i | 0.561348 | − | 0.972283i | −0.436031 | − | 0.899932i | \(-0.643616\pi\) |
0.997379 | − | 0.0723518i | \(-0.0230504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3607.43 | − | 6248.26i | 0.473840 | − | 0.820715i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1681.19 | + | 2911.91i | 0.219125 | + | 0.379536i | 0.954541 | − | 0.298080i | \(-0.0963463\pi\) |
−0.735415 | + | 0.677616i | \(0.763013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −824.726 | −0.106671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1048.81 | −0.134620 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1875.15 | − | 3247.85i | −0.238858 | − | 0.413714i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2431.72 | + | 4211.86i | −0.307417 | + | 0.532462i | −0.977797 | − | 0.209557i | \(-0.932798\pi\) |
0.670380 | + | 0.742018i | \(0.266131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1869.43 | + | 3237.94i | −0.232805 | + | 0.403229i | −0.958632 | − | 0.284647i | \(-0.908124\pi\) |
0.725828 | + | 0.687876i | \(0.241457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2404.70 | + | 4165.06i | 0.297237 | + | 0.514829i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1029.16 | 0.126270 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11972.2 | −1.45809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7006.64 | − | 12135.9i | −0.847081 | − | 1.46719i | −0.883802 | − | 0.467862i | \(-0.845024\pi\) |
0.0367205 | − | 0.999326i | \(-0.488309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1595.92 | − | 2764.22i | 0.191535 | − | 0.331749i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3698.01 | + | 6405.15i | −0.437418 | + | 0.757630i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1723.97 | + | 2986.01i | 0.202454 | + | 0.350661i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8043.46 | 0.937826 | 0.468913 | − | 0.883244i | \(-0.344646\pi\) | ||||
0.468913 | + | 0.883244i | \(0.344646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1832.27 | 0.212112 | 0.106056 | − | 0.994360i | \(-0.466178\pi\) | ||||
0.106056 | + | 0.994360i | \(0.466178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3422.41 | + | 5927.79i | 0.393388 | + | 0.681368i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3527.94 | − | 6110.58i | 0.402660 | − | 0.697427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −824.946 | + | 1428.85i | −0.0928410 | + | 0.160805i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1431.63 | − | 2479.65i | −0.159998 | − | 0.277124i | 0.774870 | − | 0.632121i | \(-0.217815\pi\) |
−0.934868 | + | 0.354997i | \(0.884482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6856.23 | 0.760946 | 0.380473 | − | 0.924792i | \(-0.375761\pi\) | ||||
0.380473 | + | 0.924792i | \(0.375761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 96.0685 | 0.0105888 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −61.4040 | − | 106.355i | −0.00672163 | − | 0.0116422i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2037.21 | + | 3528.55i | −0.221482 | + | 0.383618i | −0.955258 | − | 0.295773i | \(-0.904423\pi\) |
0.733776 | + | 0.679391i | \(0.237756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1248.96 | − | 2163.27i | 0.133950 | − | 0.232009i | −0.791246 | − | 0.611498i | \(-0.790567\pi\) |
0.925196 | + | 0.379490i | \(0.123900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4037.42 | + | 6993.01i | 0.430094 | + | 0.744945i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8308.89 | −0.879188 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9529.68 | 1.00163 | 0.500817 | − | 0.865553i | \(-0.333033\pi\) | ||||
0.500817 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3431.55 | − | 5943.62i | −0.358283 | − | 0.620564i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3642.56 | + | 6309.09i | −0.377797 | + | 0.654364i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5275.95 | + | 9138.22i | −0.540041 | + | 0.935379i | 0.458860 | + | 0.888509i | \(0.348258\pi\) |
−0.998901 | + | 0.0468699i | \(0.985075\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5689.88 | − | 9855.16i | −0.578608 | − | 1.00218i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13103.5 | −1.32384 | −0.661922 | − | 0.749573i | \(-0.730259\pi\) | ||||
−0.661922 | + | 0.749573i | \(0.730259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −816.035 | −0.0819101 | −0.0409550 | − | 0.999161i | \(-0.513040\pi\) | ||||
−0.0409550 | + | 0.999161i | \(0.513040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2415.32 | + | 4183.46i | 0.240877 | + | 0.417211i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2294.16 | + | 3973.61i | −0.227326 | + | 0.393740i | −0.957015 | − | 0.290039i | \(-0.906332\pi\) |
0.729689 | + | 0.683779i | \(0.239665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1914.01 | + | 3315.17i | −0.187246 | + | 0.324320i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5936.28 | − | 10281.9i | −0.577062 | − | 0.999501i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1050.68 | 0.101491 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14626.7 | −1.40400 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8690.77 | + | 15052.9i | 0.829001 | + | 1.43587i | 0.898822 | + | 0.438313i | \(0.144424\pi\) |
−0.0698212 | + | 0.997560i | \(0.522243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3551.90 | + | 6152.07i | −0.336700 | + | 0.583182i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4827.96 | − | 8362.28i | 0.452013 | − | 0.782910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8176.24 | + | 14161.7i | 0.760781 | + | 1.31771i | 0.942448 | + | 0.334352i | \(0.108517\pi\) |
−0.181667 | + | 0.983360i | \(0.558149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9303.70 | −0.860384 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13094.7 | −1.20358 | −0.601789 | − | 0.798655i | \(-0.705545\pi\) | ||||
−0.601789 | + | 0.798655i | \(0.705545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 225.128 | + | 389.933i | 0.0205664 | + | 0.0356221i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2015.93 | − | 3491.70i | 0.183050 | − | 0.317051i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4880.53 | − | 8453.32i | 0.437840 | − | 0.758362i | −0.559682 | − | 0.828707i | \(-0.689077\pi\) |
0.997523 | + | 0.0703455i | \(0.0224102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5334.00 | − | 9238.75i | −0.475660 | − | 0.823866i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14229.0 | −1.26131 | −0.630657 | − | 0.776061i | \(-0.717215\pi\) | ||||
−0.630657 | + | 0.776061i | \(0.717215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2087.26 | −0.183924 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2591.20 | − | 4488.08i | −0.226980 | − | 0.393142i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10160.2 | − | 17597.9i | 0.884757 | − | 1.53244i | 0.0387650 | − | 0.999248i | \(-0.487658\pi\) |
0.845992 | − | 0.533196i | \(-0.179009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 847.267 | − | 1467.51i | 0.0729196 | − | 0.126300i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1946.02 | − | 3370.61i | −0.166509 | − | 0.288401i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11263.6 | 0.958170 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7073.65 | 0.598263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10092.7 | + | 17481.0i | 0.848692 | + | 1.46998i | 0.882376 | + | 0.470544i | \(0.155942\pi\) |
−0.0336847 | + | 0.999433i | \(0.510724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1355.34 | + | 2347.51i | −0.113317 | + | 0.196271i | −0.917106 | − | 0.398644i | \(-0.869481\pi\) |
0.803789 | + | 0.594915i | \(0.202814\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11320.2 | + | 19607.1i | −0.935701 | + | 1.62068i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6039.54 | + | 10460.8i | 0.496387 | + | 0.859767i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8623.63 | −0.704771 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4072.27 | −0.330937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3932.90 | + | 6811.99i | 0.317821 | + | 0.550482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −262.267 | + | 454.259i | −0.0210757 | + | 0.0365042i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1828.34 | + | 3166.77i | −0.145298 | + | 0.251664i | −0.929484 | − | 0.368862i | \(-0.879747\pi\) |
0.784186 | + | 0.620526i | \(0.213081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 641.733 | + | 1111.51i | 0.0507171 | + | 0.0878447i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2255.42 | 0.177269 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 787.130 | 0.0615269 | 0.0307635 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307635 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1665.49 | + | 2884.72i | 0.129475 | + | 0.224257i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.5233 | + | 58.0640i | −0.00259191 | + | 0.00448931i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3567.59 | + | 6179.25i | −0.272857 | + | 0.472603i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6228.68 | + | 10788.4i | 0.473820 | + | 0.820680i | 0.999551 | − | 0.0299707i | \(-0.00954140\pi\) |
−0.525731 | + | 0.850651i | \(0.676208\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7044.66 | −0.533018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7766.91 | −0.584526 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7959.35 | − | 13786.0i | −0.595820 | − | 1.03199i | −0.993431 | − | 0.114436i | \(-0.963494\pi\) |
0.397611 | − | 0.917554i | \(-0.369839\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3908.42 | − | 6769.57i | 0.291023 | − | 0.504067i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3908.25 | − | 6769.28i | 0.287948 | − | 0.498740i | −0.685372 | − | 0.728193i | \(-0.740360\pi\) |
0.973320 | + | 0.229453i | \(0.0736937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10918.9 | + | 18912.1i | 0.800248 | + | 1.38607i | 0.919453 | + | 0.393200i | \(0.128632\pi\) |
−0.119206 | + | 0.992870i | \(0.538035\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8109.32 | −0.591225 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 752.232 | 0.0545569 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7592.30 | + | 13150.3i | 0.547785 | + | 0.948791i | 0.998426 | + | 0.0560856i | \(0.0178620\pi\) |
−0.450641 | + | 0.892705i | \(0.648805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1609.60 | − | 2787.91i | 0.115531 | − | 0.200106i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12034.6 | + | 20844.5i | −0.854926 | + | 1.48078i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1196.17 | − | 2071.82i | −0.0845392 | − | 0.146426i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21861.6 | 1.53718 | 0.768591 | − | 0.639740i | \(-0.220958\pi\) | ||||
0.768591 | + | 0.639740i | \(0.220958\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3371.32 | −0.235845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2297.16 | + | 3978.79i | 0.159886 | + | 0.276930i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −136.751 | + | 236.860i | −0.00946997 | + | 0.0164025i | −0.870722 | − | 0.491776i | \(-0.836348\pi\) |
0.861252 | + | 0.508179i | \(0.169681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7447.59 | + | 12899.6i | −0.510569 | + | 0.884331i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1221.81 | + | 2116.24i | 0.0833421 | + | 0.144353i | 0.904684 | − | 0.426084i | \(-0.140107\pi\) |
−0.821341 | + | 0.570437i | \(0.806774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1107.14 | 0.0751431 | 0.0375716 | − | 0.999294i | \(-0.488038\pi\) | ||||
0.0375716 | + | 0.999294i | \(0.488038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9514.62 | 0.642562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1135.89 | + | 1967.43i | 0.0763317 | + | 0.132210i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −709.429 | + | 1228.77i | −0.0474379 | + | 0.0821649i | −0.888769 | − | 0.458355i | \(-0.848439\pi\) |
0.841331 | + | 0.540520i | \(0.181772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3341.67 | − | 5787.94i | 0.221259 | − | 0.383233i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4701.49 | − | 8143.22i | −0.309774 | − | 0.536544i | 0.668539 | − | 0.743677i | \(-0.266920\pi\) |
−0.978313 | + | 0.207133i | \(0.933587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4090.26 | −0.268187 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11223.0 | −0.732284 | −0.366142 | − | 0.930559i | \(-0.619322\pi\) | ||||
−0.366142 | + | 0.930559i | \(0.619322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7939.57 | + | 13751.7i | 0.515538 | + | 0.892938i | 0.999837 | + | 0.0180360i | \(0.00574133\pi\) |
−0.484299 | + | 0.874903i | \(0.660925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 606.601 | − | 1050.66i | 0.0391982 | − | 0.0678932i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −419.247 | + | 726.156i | −0.0268318 | + | 0.0464740i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −578.277 | − | 1001.60i | −0.0368328 | − | 0.0637962i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33441.3 | −2.11986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9079.04 | −0.572791 | −0.286395 | − | 0.958112i | \(-0.592457\pi\) | ||||
−0.286395 | + | 0.958112i | \(0.592457\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2111.38 | − | 3657.03i | −0.132575 | − | 0.229627i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −78.5371 | + | 136.030i | −0.00490811 | + | 0.00850110i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3350.92 | − | 5803.97i | 0.207450 | − | 0.359314i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4967.58 | − | 8604.10i | −0.306096 | − | 0.530174i | 0.671409 | − | 0.741087i | \(-0.265689\pi\) |
−0.977505 | + | 0.210913i | \(0.932356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21282.8 | 1.30531 | 0.652653 | − | 0.757657i | \(-0.273656\pi\) | ||||
0.652653 | + | 0.757657i | \(0.273656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7075.78 | −0.431951 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3438.07 | + | 5954.91i | 0.208910 | + | 0.361842i | 0.951371 | − | 0.308046i | \(-0.0996752\pi\) |
−0.742462 | + | 0.669888i | \(0.766342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7095.39 | + | 12289.6i | −0.429150 | + | 0.743310i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 701.120 | − | 1214.38i | 0.0420168 | − | 0.0727752i | −0.844252 | − | 0.535946i | \(-0.819955\pi\) |
0.886269 | + | 0.463171i | \(0.153288\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1251.27 | − | 2167.26i | −0.0746428 | − | 0.129285i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20334.6 | −1.20750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19975.7 | 1.18079 | 0.590395 | − | 0.807114i | \(-0.298972\pi\) | ||||
0.590395 | + | 0.807114i | \(0.298972\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 328.416 | + | 568.832i | 0.0193251 | + | 0.0334720i | 0.875526 | − | 0.483171i | \(-0.160515\pi\) |
−0.856201 | + | 0.516643i | \(0.827182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2304.27 | + | 3991.12i | −0.134978 | + | 0.233789i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0010 | + | 41.5710i | −0.00139329 | + | 0.00241325i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3533.92 | + | 6120.93i | 0.204229 | + | 0.353735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5481.37 | 0.315359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14668.1 | 0.840140 | 0.420070 | − | 0.907492i | \(-0.362006\pi\) | ||||
0.420070 | + | 0.907492i | \(0.362006\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5189.73 | + | 8988.88i | 0.295930 | + | 0.512566i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9605.04 | − | 16636.4i | 0.545276 | − | 0.944446i | −0.453314 | − | 0.891351i | \(-0.649758\pi\) |
0.998589 | − | 0.0530944i | \(-0.0169084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2156.67 | − | 3735.46i | 0.121357 | − | 0.210196i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9223.01 | − | 15974.7i | −0.516704 | − | 0.894957i | −0.999812 | − | 0.0193965i | \(-0.993826\pi\) |
0.483108 | − | 0.875561i | \(-0.339508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7615.95 | 0.424804 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1603.25 | 0.0890364 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7140.80 | + | 12368.2i | 0.394837 | + | 0.683878i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12451.0 | + | 21565.7i | −0.685467 | + | 1.18726i | 0.287822 | + | 0.957684i | \(0.407069\pi\) |
−0.973290 | + | 0.229581i | \(0.926265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4113.51 | + | 7124.81i | −0.224510 | + | 0.388863i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9585.15 | − | 16602.0i | −0.520894 | − | 0.902216i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4498.90 | 0.243439 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22637.7 | 1.21970 | 0.609852 | − | 0.792515i | \(-0.291229\pi\) | ||||
0.609852 | + | 0.792515i | \(0.291229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2489.84 | − | 4312.52i | −0.133579 | − | 0.231365i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3356.43 | − | 5813.51i | 0.179306 | − | 0.310567i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.49494 | + | 6.05341i | −0.000185127 | + | 0.000320650i | −0.866118 | − | 0.499840i | \(-0.833392\pi\) |
0.865933 | + | 0.500160i | \(0.166726\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5362.12 | + | 9287.46i | 0.282834 | + | 0.489883i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2413.70 | −0.126779 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3936.75 | −0.205911 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6589.57 | − | 11413.5i | −0.343225 | − | 0.594483i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9509.80 | + | 16471.5i | −0.493262 | + | 0.854355i | −0.999970 | − | 0.00776257i | \(-0.997529\pi\) |
0.506708 | + | 0.862118i | \(0.330862\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1223.59 | − | 2119.32i | 0.0629402 | − | 0.109016i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −205.339 | − | 355.658i | −0.0105188 | − | 0.0182190i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33880.6 | 1.72842 | 0.864210 | − | 0.503130i | \(-0.167818\pi\) | ||||
0.864210 | + | 0.503130i | \(0.167818\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6853.96 | 0.348217 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16581.5 | − | 28719.9i | −0.838970 | − | 1.45314i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5222.71 | + | 9045.99i | −0.263172 | + | 0.455827i | −0.967083 | − | 0.254461i | \(-0.918102\pi\) |
0.703911 | + | 0.710288i | \(0.251435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7828.48 | − | 13559.3i | 0.391270 | − | 0.677699i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12837.3 | + | 22234.8i | 0.639007 | + | 1.10679i | 0.985651 | + | 0.168796i | \(0.0539880\pi\) |
−0.346644 | + | 0.937997i | \(0.612679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −686.248 | −0.0340215 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30646.2 | −1.51319 | −0.756596 | − | 0.653883i | \(-0.773139\pi\) | ||||
−0.756596 | + | 0.653883i | \(0.773139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9912.78 | − | 17169.4i | −0.487485 | − | 0.844348i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10574.7 | − | 18316.0i | 0.517951 | − | 0.897118i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4355.95 | − | 7544.73i | 0.211652 | − | 0.366593i | −0.740579 | − | 0.671969i | \(-0.765449\pi\) |
0.952232 | + | 0.305376i | \(0.0987822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4383.77 | − | 7592.91i | −0.212156 | − | 0.367465i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17382.8 | −0.837912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18830.7 | −0.904114 | −0.452057 | − | 0.891989i | \(-0.649310\pi\) | ||||
−0.452057 | + | 0.891989i | \(0.649310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −414.017 | − | 717.099i | −0.0197996 | − | 0.0342939i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10900.3 | − | 18879.9i | 0.519232 | − | 0.899336i | −0.480518 | − | 0.876985i | \(-0.659551\pi\) |
0.999750 | − | 0.0223513i | \(-0.00711523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5630.99 | − | 9753.16i | 0.266129 | − | 0.460949i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4210.09 | + | 7292.10i | 0.198198 | + | 0.343289i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4412.21 | −0.206903 | −0.103452 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103452 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2535.26 | 0.118424 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15223.4 | − | 26367.7i | −0.708342 | − | 1.22688i | −0.965472 | − | 0.260507i | \(-0.916110\pi\) |
0.257130 | − | 0.966377i | \(-0.417223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10325.1 | − | 17883.6i | 0.478567 | − | 0.828902i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1427.30 | − | 2472.16i | 0.0656462 | − | 0.113703i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5514.17 | − | 9550.83i | −0.252641 | − | 0.437587i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −662.343 | −0.0302302 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9133.92 | −0.415291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5606.01 | − | 9709.90i | −0.253917 | − | 0.439797i | 0.710684 | − | 0.703512i | \(-0.248386\pi\) |
−0.964601 | + | 0.263714i | \(0.915052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −129.897 | + | 224.989i | −0.00586118 | + | 0.0101519i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1626.20 | − | 2816.67i | 0.0728224 | − | 0.126132i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7172.35 | + | 12422.9i | 0.319971 | + | 0.554206i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11809.3 | 0.524852 | 0.262426 | − | 0.964952i | \(-0.415477\pi\) | ||||
0.262426 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31462.0 | 1.39305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11545.3 | − | 19997.0i | −0.509279 | − | 0.882097i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16731.0 | + | 28978.9i | −0.735272 | + | 1.27353i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5681.49 | − | 9840.63i | 0.247829 | − | 0.429252i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7163.83 | − | 12408.1i | −0.311331 | − | 0.539241i | 0.667320 | − | 0.744771i | \(-0.267441\pi\) |
−0.978651 | + | 0.205530i | \(0.934108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32413.9 | 1.40346 | 0.701730 | − | 0.712443i | \(-0.252411\pi\) | ||||
0.701730 | + | 0.712443i | \(0.252411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7828.05 | 0.337690 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11099.6 | − | 19225.1i | −0.477058 | − | 0.826289i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2469.11 | − | 4276.62i | 0.105732 | − | 0.183133i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1203.08 | + | 2083.80i | −0.0511423 | + | 0.0885810i | −0.890463 | − | 0.455055i | \(-0.849620\pi\) |
0.839321 | + | 0.543636i | \(0.182953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 980.182 | + | 1697.72i | 0.0415152 | + | 0.0719064i | 0.886036 | − | 0.463616i | \(-0.153448\pi\) |
−0.844521 | + | 0.535522i | \(0.820115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7084.19 | 0.298958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17517.2 | 0.736557 | 0.368278 | − | 0.929716i | \(-0.379947\pi\) | ||||
0.368278 | + | 0.929716i | \(0.379947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16749.4 | + | 29010.8i | 0.701724 | + | 1.21542i | 0.967861 | + | 0.251487i | \(0.0809195\pi\) |
−0.266136 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3618.67 | + | 6267.71i | −0.151059 | + | 0.261642i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12727.3 | − | 22044.3i | 0.527479 | − | 0.913621i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16652.4 | − | 28842.8i | −0.687683 | − | 1.19110i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1609.45 | 0.0662268 | 0.0331134 | − | 0.999452i | \(-0.489458\pi\) | ||||
0.0331134 | + | 0.999452i | \(0.489458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24362.8 | −0.998925 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1289.33 | − | 2233.18i | −0.0526770 | − | 0.0912393i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6182.76 | − | 10708.9i | 0.251708 | − | 0.435972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11599.2 | − | 20090.4i | 0.468885 | − | 0.812132i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1782.60 | − | 3087.55i | −0.0718058 | − | 0.124371i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20446.9 | 0.820739 | 0.410369 | − | 0.911919i | \(-0.365400\pi\) | ||||
0.410369 | + | 0.911919i | \(0.365400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1676.99 | 0.0670784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2892.11 | − | 5009.28i | −0.115277 | − | 0.199666i | 0.802613 | − | 0.596500i | \(-0.203442\pi\) |
−0.917891 | + | 0.396834i | \(0.870109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16180.7 | − | 28025.7i | 0.642697 | − | 1.11318i | −0.342131 | − | 0.939652i | \(-0.611149\pi\) |
0.984828 | − | 0.173532i | \(-0.0555179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14415.6 | − | 24968.6i | 0.568614 | − | 0.984868i | −0.428089 | − | 0.903736i | \(-0.640813\pi\) |
0.996703 | − | 0.0811320i | \(-0.0258535\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8439.09 | + | 14616.9i | 0.331720 | + | 0.574556i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7916.60 | −0.310106 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17647.5 | 0.688895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4645.08 | − | 8045.51i | −0.180703 | − | 0.312987i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13805.9 | + | 23912.5i | −0.535234 | + | 0.927052i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6552.70 | − | 11349.6i | 0.252302 | − | 0.437000i | −0.711857 | − | 0.702324i | \(-0.752146\pi\) |
0.964159 | + | 0.265324i | \(0.0854790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4009.49 | + | 6944.64i | 0.153853 | + | 0.266481i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3089.10 | 0.118132 | 0.0590661 | − | 0.998254i | \(-0.481188\pi\) | ||||
0.0590661 | + | 0.998254i | \(0.481188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1601.96 | 0.0610536 | 0.0305268 | − | 0.999534i | \(-0.490282\pi\) | ||||
0.0305268 | + | 0.999534i | \(0.490282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4228.69 | + | 7324.31i | 0.160617 | + | 0.278197i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11285.2 | + | 19546.6i | −0.427194 | + | 0.739921i | −0.996622 | − | 0.0821197i | \(-0.973831\pi\) |
0.569429 | + | 0.822041i | \(0.307164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2421.42 | + | 4194.01i | −0.0910443 | + | 0.157693i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2342.47 | + | 4057.27i | 0.0877801 | + | 0.152040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1251.57 | −0.0467435 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −491.320 | −0.0182884 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 658.875 | + | 1141.20i | 0.0244435 | + | 0.0423374i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33615.5 | + | 58223.8i | −1.24295 | + | 2.15285i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1531.22 | + | 2652.15i | −0.0562424 | + | 0.0974147i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24172.1 | − | 41867.4i | −0.884920 | − | 1.53273i | −0.845805 | − | 0.533492i | \(-0.820880\pi\) |
−0.0391146 | − | 0.999235i | \(-0.512454\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5968.66 | 0.217787 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14697.9 | 0.534539 | 0.267269 | − | 0.963622i | \(-0.413879\pi\) | ||||
0.267269 | + | 0.963622i | \(0.413879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17401.5 | − | 30140.2i | −0.630783 | − | 1.09255i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1633.39 | − | 2829.11i | 0.0590143 | − | 0.102216i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7665.28 | + | 13276.7i | −0.275141 | + | 0.476558i | −0.970171 | − | 0.242423i | \(-0.922058\pi\) |
0.695030 | + | 0.718981i | \(0.255391\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4967.88 | + | 8604.63i | 0.177739 | + | 0.307852i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6543.74 | −0.233358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30501.8 | 1.08421 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5564.79 | + | 9638.49i | 0.197165 | + | 0.341499i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27955.2 | − | 48419.7i | 0.987275 | − | 1.71001i | 0.355922 | − | 0.934516i | \(-0.384167\pi\) |
0.631353 | − | 0.775495i | \(-0.282500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 872.952 | − | 1512.00i | 0.0306315 | − | 0.0530553i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9266.18 | − | 16049.5i | −0.324103 | − | 0.561363i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18627.7 | −0.649457 | −0.324728 | − | 0.945807i | \(-0.605273\pi\) | ||||
−0.324728 | + | 0.945807i | \(0.605273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19813.0 | −0.688575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20282.3 | + | 35130.0i | 0.702641 | + | 1.21701i | 0.967536 | + | 0.252732i | \(0.0813292\pi\) |
−0.264896 | + | 0.964277i | \(0.585337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1021.88 | − | 1769.94i | 0.0352884 | − | 0.0611212i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13345.1 | + | 23114.3i | −0.457926 | + | 0.793151i | −0.998851 | − | 0.0479196i | \(-0.984741\pi\) |
0.540925 | + | 0.841071i | \(0.318074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9927.43 | + | 17194.8i | 0.339576 | + | 0.588163i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18114.5 | 0.617669 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7182.06 | −0.244123 | −0.122062 | − | 0.992523i | \(-0.538951\pi\) | ||||
−0.122062 | + | 0.992523i | \(0.538951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9674.69 | − | 16757.0i | −0.327817 | − | 0.567796i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −226.031 | + | 391.498i | −0.00763485 | + | 0.0132239i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18234.9 | + | 31583.7i | −0.612093 | + | 1.06018i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11246.4 | − | 19479.4i | −0.376335 | − | 0.651831i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7681.22 | 0.256236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18129.4 | 0.602898 | 0.301449 | − | 0.953482i | \(-0.402530\pi\) | ||||
0.301449 | + | 0.953482i | \(0.402530\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1615.26 | − | 2797.72i | −0.0535498 | − | 0.0927510i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10488.0 | + | 18165.8i | −0.346629 | + | 0.600378i | −0.985648 | − | 0.168812i | \(-0.946007\pi\) |
0.639020 | + | 0.769190i | \(0.279340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2101.73 | − | 3640.29i | 0.0690349 | − | 0.119572i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22347.4 | + | 38706.8i | 0.731786 | + | 1.26749i | 0.956119 | + | 0.292979i | \(0.0946465\pi\) |
−0.224333 | + | 0.974513i | \(0.572020\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37997.1 | −1.24044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6449.52 | −0.209906 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7713.11 | + | 13359.5i | 0.250265 | + | 0.433471i | 0.963599 | − | 0.267353i | \(-0.0861490\pi\) |
−0.713334 | + | 0.700824i | \(0.752816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5481.17 | + | 9493.66i | −0.177304 | + | 0.307100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1767.76 | − | 3061.85i | 0.0568366 | − | 0.0984439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14124.0 | − | 24463.5i | −0.452739 | − | 0.784167i | 0.545816 | − | 0.837905i | \(-0.316220\pi\) |
−0.998555 | + | 0.0537377i | \(0.982887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23375.7 | 0.747034 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35540.9 | −1.13238 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18560.8 | − | 32148.2i | −0.589594 | − | 1.02121i | −0.994285 | − | 0.106754i | \(-0.965954\pi\) |
0.404691 | − | 0.914453i | \(-0.367379\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24596.7 | − | 42602.8i | 0.778985 | − | 1.34924i |
(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 | 392.4.i.m.177.3 | 6 | ||
7.2 | even | 3 | 392.4.a.l.1.1 | 3 | |||
7.3 | odd | 6 | 56.4.i.b.25.1 | yes | 6 | ||
7.4 | even | 3 | inner | 392.4.i.m.361.3 | 6 | ||
7.5 | odd | 6 | 392.4.a.i.1.3 | 3 | |||
7.6 | odd | 2 | 56.4.i.b.9.1 | ✓ | 6 | ||
21.17 | even | 6 | 504.4.s.h.361.2 | 6 | |||
21.20 | even | 2 | 504.4.s.h.289.2 | 6 | |||
28.3 | even | 6 | 112.4.i.e.81.3 | 6 | |||
28.19 | even | 6 | 784.4.a.be.1.1 | 3 | |||
28.23 | odd | 6 | 784.4.a.bb.1.3 | 3 | |||
28.27 | even | 2 | 112.4.i.e.65.3 | 6 | |||
56.3 | even | 6 | 448.4.i.m.193.1 | 6 | |||
56.13 | odd | 2 | 448.4.i.j.65.3 | 6 | |||
56.27 | even | 2 | 448.4.i.m.65.1 | 6 | |||
56.45 | odd | 6 | 448.4.i.j.193.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.4.i.b.9.1 | ✓ | 6 | 7.6 | odd | 2 | ||
56.4.i.b.25.1 | yes | 6 | 7.3 | odd | 6 | ||
112.4.i.e.65.3 | 6 | 28.27 | even | 2 | |||
112.4.i.e.81.3 | 6 | 28.3 | even | 6 | |||
392.4.a.i.1.3 | 3 | 7.5 | odd | 6 | |||
392.4.a.l.1.1 | 3 | 7.2 | even | 3 | |||
392.4.i.m.177.3 | 6 | 1.1 | even | 1 | trivial | ||
392.4.i.m.361.3 | 6 | 7.4 | even | 3 | inner | ||
448.4.i.j.65.3 | 6 | 56.13 | odd | 2 | |||
448.4.i.j.193.3 | 6 | 56.45 | odd | 6 | |||
448.4.i.m.65.1 | 6 | 56.27 | even | 2 | |||
448.4.i.m.193.1 | 6 | 56.3 | even | 6 | |||
504.4.s.h.289.2 | 6 | 21.20 | even | 2 | |||
504.4.s.h.361.2 | 6 | 21.17 | even | 6 | |||
784.4.a.bb.1.3 | 3 | 28.23 | odd | 6 | |||
784.4.a.be.1.1 | 3 | 28.19 | even | 6 |