Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (of order \(6\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1279.8 | ||
Root | \(1.63139 - 1.15696i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1279 |
Dual form | 1728.3.o.g.127.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.07403 | − | 5.32438i | 0.614806 | − | 1.06488i | −0.375612 | − | 0.926777i | \(-0.622568\pi\) |
0.990418 | − | 0.138099i | \(-0.0440991\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.511543 | − | 0.295340i | 0.0730776 | − | 0.0421914i | −0.463016 | − | 0.886350i | \(-0.653233\pi\) |
0.536094 | + | 0.844159i | \(0.319899\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.1205 | − | 8.72982i | 1.37459 | − | 0.793620i | 0.383088 | − | 0.923712i | \(-0.374861\pi\) |
0.991502 | + | 0.130092i | \(0.0415274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.892255 | − | 1.54543i | 0.0686350 | − | 0.118879i | −0.829666 | − | 0.558261i | \(-0.811469\pi\) |
0.898301 | + | 0.439381i | \(0.144802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.9171 | 0.995123 | 0.497562 | − | 0.867429i | \(-0.334229\pi\) | ||||
0.497562 | + | 0.867429i | \(0.334229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.5058i | − | 1.02662i | −0.858203 | − | 0.513310i | \(-0.828419\pi\) | ||
0.858203 | − | 0.513310i | \(-0.171581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.86778 | + | 3.96511i | 0.298599 | + | 0.172396i | 0.641813 | − | 0.766861i | \(-0.278182\pi\) |
−0.343214 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.39933 | − | 11.0840i | −0.255973 | − | 0.443359i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17517 | + | 5.49956i | 0.109489 | + | 0.189640i | 0.915563 | − | 0.402174i | \(-0.131745\pi\) |
−0.806075 | + | 0.591814i | \(0.798412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27.6558 | + | 15.9671i | 0.892124 | + | 0.515068i | 0.874637 | − | 0.484779i | \(-0.161100\pi\) |
0.0174873 | + | 0.999847i | \(0.494433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.63153i | − | 0.103758i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −58.2834 | −1.57523 | −0.787614 | − | 0.616169i | \(-0.788684\pi\) | ||||
−0.787614 | + | 0.616169i | \(0.788684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66948 | − | 4.62368i | 0.0651093 | − | 0.112773i | −0.831633 | − | 0.555325i | \(-0.812594\pi\) |
0.896742 | + | 0.442553i | \(0.145927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.9324 | − | 19.5909i | 0.789126 | − | 0.455602i | −0.0505290 | − | 0.998723i | \(-0.516091\pi\) |
0.839655 | + | 0.543121i | \(0.182757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.64117 | − | 5.56633i | 0.205131 | − | 0.118433i | −0.393915 | − | 0.919147i | \(-0.628880\pi\) |
0.599047 | + | 0.800714i | \(0.295546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.3255 | + | 42.1331i | −0.496440 | + | 0.859859i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.8770 | 0.676925 | 0.338462 | − | 0.940980i | \(-0.390093\pi\) | ||||
0.338462 | + | 0.940980i | \(0.390093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 107.343i | − | 1.95169i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20.8974 | − | 12.0651i | −0.354194 | − | 0.204494i | 0.312337 | − | 0.949971i | \(-0.398888\pi\) |
−0.666531 | + | 0.745477i | \(0.732222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.9460 | + | 65.7244i | 0.622066 | + | 1.07745i | 0.989100 | + | 0.147243i | \(0.0470398\pi\) |
−0.367034 | + | 0.930207i | \(0.619627\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.48564 | − | 9.50141i | −0.0843944 | − | 0.146175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31.8200 | + | 18.3713i | 0.474925 | + | 0.274198i | 0.718299 | − | 0.695734i | \(-0.244921\pi\) |
−0.243374 | + | 0.969933i | \(0.578254\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 87.8370i | − | 1.23714i | −0.785730 | − | 0.618570i | \(-0.787712\pi\) | ||
0.785730 | − | 0.618570i | \(-0.212288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.15652 | − | 8.93136i | 0.0669678 | − | 0.115992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.1841 | − | 18.5815i | 0.407394 | − | 0.235209i | −0.282275 | − | 0.959333i | \(-0.591089\pi\) |
0.689669 | + | 0.724124i | \(0.257756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −66.0281 | + | 38.1214i | −0.795520 | + | 0.459294i | −0.841902 | − | 0.539630i | \(-0.818564\pi\) |
0.0463824 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 52.0037 | − | 90.0730i | 0.611808 | − | 1.05968i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 27.5873 | 0.309969 | 0.154985 | − | 0.987917i | \(-0.450467\pi\) | ||||
0.154985 | + | 0.987917i | \(0.450467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.05407i | − | 0.0115832i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −103.856 | − | 59.9614i | −1.09322 | − | 0.631172i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0585 | + | 22.6180i | 0.134624 | + | 0.233176i | 0.925454 | − | 0.378861i | \(-0.123684\pi\) |
−0.790830 | + | 0.612036i | \(0.790351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.8831 | − | 22.3142i | −0.127556 | − | 0.220933i | 0.795173 | − | 0.606382i | \(-0.207380\pi\) |
−0.922729 | + | 0.385449i | \(0.874047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9947 | − | 9.81187i | −0.164997 | − | 0.0952609i | 0.415228 | − | 0.909717i | \(-0.363702\pi\) |
−0.580225 | + | 0.814457i | \(0.697035\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 183.200i | − | 1.71215i | −0.516850 | − | 0.856076i | \(-0.672895\pi\) | ||
0.516850 | − | 0.856076i | \(-0.327105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −100.841 | −0.925147 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.12484 | − | 15.8047i | 0.0807508 | − | 0.139865i | −0.822822 | − | 0.568299i | \(-0.807602\pi\) |
0.903573 | + | 0.428435i | \(0.140935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.2235 | − | 24.3778i | 0.367161 | − | 0.211981i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.65383 | − | 4.99629i | 0.0727212 | − | 0.0419856i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 91.9194 | − | 159.209i | 0.759664 | − | 1.31578i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 75.0146 | 0.600117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.386i | 1.29438i | 0.762331 | + | 0.647188i | \(0.224055\pi\) | ||||
−0.762331 | + | 0.647188i | \(0.775945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −123.421 | − | 71.2570i | −0.942143 | − | 0.543947i | −0.0515116 | − | 0.998672i | \(-0.516404\pi\) |
−0.890631 | + | 0.454726i | \(0.849737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.76083 | − | 9.97805i | −0.0433145 | − | 0.0750229i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08176 | + | 5.33777i | 0.0224946 | + | 0.0389618i | 0.877054 | − | 0.480393i | \(-0.159506\pi\) |
−0.854559 | + | 0.519354i | \(0.826172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −103.168 | − | 59.5642i | −0.742218 | − | 0.428519i | 0.0806575 | − | 0.996742i | \(-0.474298\pi\) |
−0.822875 | + | 0.568222i | \(0.807631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 31.1569i | − | 0.217880i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −103.365 | + | 179.034i | −0.693726 | + | 1.20157i | 0.276882 | + | 0.960904i | \(0.410699\pi\) |
−0.970608 | + | 0.240665i | \(0.922634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 127.422 | − | 73.5670i | 0.843853 | − | 0.487199i | −0.0147190 | − | 0.999892i | \(-0.504685\pi\) |
0.858572 | + | 0.512693i | \(0.171352\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 170.030 | − | 98.1668i | 1.09697 | − | 0.633334i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.4395 | + | 54.4548i | −0.200251 | + | 0.346846i | −0.948609 | − | 0.316449i | \(-0.897509\pi\) |
0.748358 | + | 0.663295i | \(0.230843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.68422 | 0.0290946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 143.325i | − | 0.879292i | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||
0.898171 | − | 0.439646i | \(-0.144896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −150.531 | − | 86.9089i | −0.901381 | − | 0.520413i | −0.0237332 | − | 0.999718i | \(-0.507555\pi\) |
−0.877648 | + | 0.479306i | \(0.840889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.9078 | + | 143.600i | 0.490578 | + | 0.849707i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −125.806 | − | 217.902i | −0.727201 | − | 1.25955i | −0.958062 | − | 0.286562i | \(-0.907488\pi\) |
0.230861 | − | 0.972987i | \(-0.425846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.54707 | − | 3.77995i | −0.0374118 | − | 0.0215997i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 96.0059i | − | 0.536346i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||
0.963371 | − | 0.268173i | \(-0.0864199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 328.757 | 1.81634 | 0.908170 | − | 0.418603i | \(-0.137480\pi\) | ||||
0.908170 | + | 0.418603i | \(0.137480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −179.165 | + | 310.323i | −0.968460 | + | 1.67742i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 255.795 | − | 147.683i | 1.36789 | − | 0.789749i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.351914 | − | 0.203178i | 0.00184248 | − | 0.00106376i | −0.499078 | − | 0.866557i | \(-0.666328\pi\) |
0.500921 | + | 0.865493i | \(0.332995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.2230 | + | 54.0798i | −0.161777 | + | 0.280206i | −0.935506 | − | 0.353311i | \(-0.885056\pi\) |
0.773729 | + | 0.633517i | \(0.218389\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −207.861 | −1.05513 | −0.527566 | − | 0.849514i | \(-0.676895\pi\) | ||||
−0.527566 | + | 0.849514i | \(0.676895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 299.128i | − | 1.50316i | −0.659643 | − | 0.751579i | \(-0.729293\pi\) | ||
0.659643 | − | 0.751579i | \(-0.270707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.24848 | + | 1.87551i | 0.0160024 | + | 0.00923896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.4121 | − | 28.4266i | −0.0800592 | − | 0.138667i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −170.282 | − | 294.937i | −0.814746 | − | 1.41118i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.744 | + | 81.8360i | 0.671773 | + | 0.387848i | 0.796748 | − | 0.604311i | \(-0.206552\pi\) |
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 240.892i | − | 1.12043i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0944 | − | 26.1442i | 0.0683003 | − | 0.118300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.681 | − | 190.919i | 1.48287 | − | 0.856138i | 0.483063 | − | 0.875586i | \(-0.339524\pi\) |
0.999811 | + | 0.0194478i | \(0.00619081\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −51.5472 | + | 29.7608i | −0.227080 | + | 0.131105i | −0.609224 | − | 0.792998i | \(-0.708519\pi\) |
0.382144 | + | 0.924103i | \(0.375186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −64.4366 | + | 111.608i | −0.281383 | + | 0.487369i | −0.971726 | − | 0.236113i | \(-0.924126\pi\) |
0.690343 | + | 0.723482i | \(0.257460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9939 | −0.0643513 | −0.0321757 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321757 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 68.4443i | − | 0.291252i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 315.244 | + | 182.006i | 1.31901 | + | 0.761532i | 0.983570 | − | 0.180529i | \(-0.0577811\pi\) |
0.335442 | + | 0.942061i | \(0.391114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −40.5235 | − | 70.1888i | −0.168147 | − | 0.291240i | 0.769621 | − | 0.638501i | \(-0.220445\pi\) |
−0.937769 | + | 0.347261i | \(0.887112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 149.555 | + | 259.037i | 0.610428 | + | 1.05729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.1448 | − | 17.4041i | −0.122044 | − | 0.0704620i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 281.883i | 1.12304i | 0.827463 | + | 0.561520i | \(0.189783\pi\) | ||||
−0.827463 | + | 0.561520i | \(0.810217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 138.459 | 0.547268 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 37.6564 | − | 65.2227i | 0.146523 | − | 0.253785i | −0.783417 | − | 0.621496i | \(-0.786525\pi\) |
0.929940 | + | 0.367711i | \(0.119858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.8145 | + | 17.2134i | −0.115114 | + | 0.0664610i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 105.914 | − | 61.1497i | 0.402716 | − | 0.232508i | −0.284939 | − | 0.958546i | \(-0.591973\pi\) |
0.687655 | + | 0.726037i | \(0.258640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.287 | − | 191.023i | 0.416178 | − | 0.720841i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 280.452 | 1.04257 | 0.521287 | − | 0.853382i | \(-0.325452\pi\) | ||||
0.521287 | + | 0.853382i | \(0.325452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 81.4468i | − | 0.300542i | −0.988645 | − | 0.150271i | \(-0.951985\pi\) | ||
0.988645 | − | 0.150271i | \(-0.0480146\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −193.522 | − | 111.730i | −0.703716 | − | 0.406291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −224.861 | − | 389.471i | −0.811774 | − | 1.40603i | −0.911622 | − | 0.411031i | \(-0.865169\pi\) |
0.0998479 | − | 0.995003i | \(-0.468164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 37.8649 | + | 65.5838i | 0.134750 | + | 0.233394i | 0.925502 | − | 0.378743i | \(-0.123643\pi\) |
−0.790752 | + | 0.612137i | \(0.790310\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 322.061 | + | 185.942i | 1.13803 | + | 0.657039i | 0.945941 | − | 0.324339i | \(-0.105142\pi\) |
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.15361i | − | 0.0109882i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −66.3946 | + | 114.999i | −0.226603 | + | 0.392488i | −0.956799 | − | 0.290750i | \(-0.906095\pi\) |
0.730196 | + | 0.683237i | \(0.239429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.479 | + | 74.1772i | −0.435521 | + | 0.251448i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.2556 | − | 7.07579i | 0.0409887 | − | 0.0236648i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5719 | − | 20.0432i | 0.0384450 | − | 0.0665886i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 466.589 | 1.52980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 336.514i | − | 1.09614i | −0.836434 | − | 0.548068i | \(-0.815363\pi\) | ||
0.836434 | − | 0.548068i | \(-0.184637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −304.206 | − | 175.634i | −0.978156 | − | 0.564738i | −0.0764428 | − | 0.997074i | \(-0.524356\pi\) |
−0.901713 | + | 0.432336i | \(0.857690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −95.4299 | − | 165.289i | −0.304888 | − | 0.528081i | 0.672349 | − | 0.740235i | \(-0.265286\pi\) |
−0.977236 | + | 0.212154i | \(0.931952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −202.797 | − | 351.255i | −0.639738 | − | 1.10806i | −0.985490 | − | 0.169733i | \(-0.945709\pi\) |
0.345752 | − | 0.938326i | \(-0.387624\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.0203 | + | 55.4374i | 0.301004 | + | 0.173785i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 329.981i | − | 1.02161i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.8393 | −0.0702749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.28792 | − | 5.69484i | 0.00999368 | − | 0.0173096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −384.104 | + | 221.763i | −1.16044 | + | 0.669978i | −0.951408 | − | 0.307932i | \(-0.900363\pi\) |
−0.209027 | + | 0.977910i | \(0.567030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 195.631 | − | 112.948i | 0.583974 | − | 0.337158i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −254.239 | + | 440.356i | −0.754420 | + | 1.30669i | 0.191243 | + | 0.981543i | \(0.438748\pi\) |
−0.945662 | + | 0.325150i | \(0.894585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 557.560 | 1.63507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 57.6805i | 0.168165i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 492.773 | + | 284.503i | 1.42010 | + | 0.819893i | 0.996307 | − | 0.0858678i | \(-0.0273663\pi\) |
0.423790 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 206.901 | + | 358.363i | 0.592840 | + | 1.02683i | 0.993848 | + | 0.110754i | \(0.0353266\pi\) |
−0.401008 | + | 0.916074i | \(0.631340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −62.3070 | − | 107.919i | −0.176507 | − | 0.305719i | 0.764175 | − | 0.645009i | \(-0.223147\pi\) |
−0.940682 | + | 0.339290i | \(0.889813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −467.677 | − | 270.014i | −1.31740 | − | 0.760602i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 303.196i | 0.844557i | 0.906466 | + | 0.422278i | \(0.138770\pi\) | ||||
−0.906466 | + | 0.422278i | \(0.861230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −184.572 | + | 319.688i | −0.505677 | + | 0.875858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −615.571 | + | 355.400i | −1.67730 | + | 0.968392i | −0.713936 | + | 0.700211i | \(0.753089\pi\) |
−0.963369 | + | 0.268181i | \(0.913578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.3527 | − | 10.5959i | 0.0494681 | − | 0.0285604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −166.740 | + | 288.803i | −0.447025 | + | 0.774271i | −0.998191 | − | 0.0601254i | \(-0.980850\pi\) |
0.551166 | + | 0.834396i | \(0.314183\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3323 | 0.0300590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 662.686i | 1.74851i | 0.485465 | + | 0.874256i | \(0.338650\pi\) | ||||
−0.485465 | + | 0.874256i | \(0.661350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 69.9008 | + | 40.3572i | 0.182509 | + | 0.105371i | 0.588471 | − | 0.808518i | \(-0.299730\pi\) |
−0.405962 | + | 0.913890i | \(0.633064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.7026 | − | 54.9106i | −0.0823445 | − | 0.142625i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −346.006 | − | 599.301i | −0.889476 | − | 1.54062i | −0.840495 | − | 0.541819i | \(-0.817736\pi\) |
−0.0489809 | − | 0.998800i | \(-0.515597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 116.183 | + | 67.0782i | 0.297143 | + | 0.171556i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 228.481i | − | 0.578432i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −657.713 | −1.65671 | −0.828354 | − | 0.560206i | \(-0.810722\pi\) | ||||
−0.828354 | + | 0.560206i | \(0.810722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −296.433 | + | 513.437i | −0.739235 | + | 1.28039i | 0.213606 | + | 0.976920i | \(0.431479\pi\) |
−0.952840 | + | 0.303472i | \(0.901854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.3521 | − | 28.4935i | 0.122462 | − | 0.0707034i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −881.274 | + | 508.804i | −2.16529 | + | 1.25013i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −161.594 | + | 279.889i | −0.395095 | + | 0.684325i | −0.993113 | − | 0.117157i | \(-0.962622\pi\) |
0.598018 | + | 0.801483i | \(0.295955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.2533 | −0.0345115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 468.745i | 1.12951i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −222.744 | − | 128.601i | −0.531608 | − | 0.306924i | 0.210063 | − | 0.977688i | \(-0.432633\pi\) |
−0.741671 | + | 0.670764i | \(0.765967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −41.9905 | − | 72.7297i | −0.0997400 | − | 0.172755i | 0.811837 | − | 0.583884i | \(-0.198468\pi\) |
−0.911577 | + | 0.411129i | \(0.865134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −108.258 | − | 187.509i | −0.254725 | − | 0.441197i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.8221 | + | 22.4139i | 0.0909182 | + | 0.0524917i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 144.348i | 0.334914i | 0.985879 | + | 0.167457i | \(0.0535555\pi\) | ||||
−0.985879 | + | 0.167457i | \(0.946445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 77.3426 | − | 133.961i | 0.176985 | − | 0.306548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −194.776 | + | 112.454i | −0.443682 | + | 0.256160i | −0.705158 | − | 0.709050i | \(-0.749124\pi\) |
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −369.184 | + | 213.148i | −0.833373 | + | 0.481148i | −0.855006 | − | 0.518618i | \(-0.826447\pi\) |
0.0216335 | + | 0.999766i | \(0.493113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 84.8041 | − | 146.885i | 0.190571 | − | 0.330079i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 406.744 | 0.905888 | 0.452944 | − | 0.891539i | \(-0.350374\pi\) | ||||
0.452944 | + | 0.891539i | \(0.350374\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93.2163i | − | 0.206688i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.61228 | − | 3.24025i | −0.0123347 | − | 0.00712144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −159.600 | − | 276.435i | −0.349234 | − | 0.604891i | 0.636879 | − | 0.770963i | \(-0.280225\pi\) |
−0.986114 | + | 0.166072i | \(0.946892\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 293.888 | + | 509.029i | 0.637501 | + | 1.10418i | 0.985979 | + | 0.166867i | \(0.0533652\pi\) |
−0.348478 | + | 0.937317i | \(0.613302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 230.088 | + | 132.841i | 0.496950 | + | 0.286914i | 0.727453 | − | 0.686157i | \(-0.240704\pi\) |
−0.230503 | + | 0.973072i | \(0.574037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 794.598i | 1.70149i | 0.525575 | + | 0.850747i | \(0.323850\pi\) | ||||
−0.525575 | + | 0.850747i | \(0.676150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.7031 | 0.0462752 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 342.050 | − | 592.447i | 0.723149 | − | 1.25253i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −216.201 | + | 124.824i | −0.455161 | + | 0.262787i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 572.964 | − | 330.801i | 1.19617 | − | 0.690607i | 0.236468 | − | 0.971639i | \(-0.424010\pi\) |
0.959698 | + | 0.281033i | \(0.0906769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.0037 | + | 90.0730i | −0.108116 | + | 0.187262i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 160.569 | 0.331071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.1525i | 0.117356i | 0.998277 | + | 0.0586781i | \(0.0186886\pi\) | ||||
−0.998277 | + | 0.0586781i | \(0.981311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 48.6600 | + | 28.0939i | 0.0991040 | + | 0.0572177i | 0.548733 | − | 0.835998i | \(-0.315110\pi\) |
−0.449629 | + | 0.893215i | \(0.648444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.7147 | + | 93.0366i | 0.108955 | + | 0.188715i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9417 | − | 44.9324i | −0.0521967 | − | 0.0904073i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −522.225 | − | 301.507i | −1.04654 | − | 0.604222i | −0.124863 | − | 0.992174i | \(-0.539849\pi\) |
−0.921679 | + | 0.387952i | \(0.873183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 549.354i | 1.09216i | 0.837734 | + | 0.546078i | \(0.183880\pi\) | ||||
−0.837734 | + | 0.546078i | \(0.816120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −119.464 | + | 206.918i | −0.234704 | + | 0.406519i | −0.959187 | − | 0.282774i | \(-0.908745\pi\) |
0.724483 | + | 0.689293i | \(0.242079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.7143 | + | 17.7329i | −0.0601062 | + | 0.0347023i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −104.484 | + | 60.3240i | −0.202882 | + | 0.117134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 97.1862 | − | 168.331i | 0.187981 | − | 0.325593i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 567.711 | 1.08966 | 0.544828 | − | 0.838548i | \(-0.316595\pi\) | ||||
0.544828 | + | 0.838548i | \(0.316595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 941.999i | 1.80114i | 0.434706 | + | 0.900572i | \(0.356852\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 467.856 | + | 270.117i | 0.887773 | + | 0.512556i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −233.056 | − | 403.664i | −0.440559 | − | 0.763071i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.76372 | − | 8.25100i | −0.00893755 | − | 0.0154803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −975.428 | − | 563.163i | −1.82323 | − | 1.05264i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 849.430i | 1.57594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 242.245 | 0.447772 | 0.223886 | − | 0.974615i | \(-0.428126\pi\) | ||||
0.223886 | + | 0.974615i | \(0.428126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −309.988 | + | 536.915i | −0.568786 | + | 0.985166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 170.503 | − | 98.4402i | 0.311706 | − | 0.179964i | −0.335983 | − | 0.941868i | \(-0.609069\pi\) |
0.647690 | + | 0.761904i | \(0.275735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 107.273 | − | 61.9342i | 0.194688 | − | 0.112403i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9757 | − | 19.0105i | 0.0198476 | − | 0.0343770i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 958.121 | 1.72015 | 0.860073 | − | 0.510171i | \(-0.170418\pi\) | ||||
0.860073 | + | 0.510171i | \(0.170418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 69.9202i | − | 0.125081i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 165.774 | + | 95.7097i | 0.294448 | + | 0.169999i | 0.639946 | − | 0.768420i | \(-0.278957\pi\) |
−0.345498 | + | 0.938419i | \(0.612290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.1001 | − | 97.1682i | −0.0992922 | − | 0.171979i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −228.215 | − | 395.280i | −0.401081 | − | 0.694693i | 0.592775 | − | 0.805368i | \(-0.298032\pi\) |
−0.993857 | + | 0.110675i | \(0.964699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 842.764 | + | 486.570i | 1.47594 | + | 0.852136i | 0.999632 | − | 0.0271399i | \(-0.00863995\pi\) |
0.476312 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 101.496i | − | 0.176515i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.5175 | + | 39.0015i | −0.0387565 | + | 0.0671282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 542.478 | − | 313.200i | 0.930494 | − | 0.537221i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 620.808 | − | 358.424i | 1.05759 | − | 0.610602i | 0.132829 | − | 0.991139i | \(-0.457594\pi\) |
0.924766 | + | 0.380537i | \(0.124261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 311.451 | − | 539.449i | 0.528779 | − | 0.915872i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −542.129 | −0.914214 | −0.457107 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457107 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 61.4350i | − | 0.103252i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 245.527 | + | 141.755i | 0.409895 | + | 0.236653i | 0.690744 | − | 0.723099i | \(-0.257283\pi\) |
−0.280850 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 377.424 | + | 653.717i | 0.627993 | + | 1.08772i | 0.987954 | + | 0.154748i | \(0.0494567\pi\) |
−0.359961 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −565.126 | − | 978.827i | −0.934093 | − | 1.61790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 77.2227 | + | 44.5845i | 0.127220 | + | 0.0734506i | 0.562260 | − | 0.826961i | \(-0.309932\pi\) |
−0.435039 | + | 0.900411i | \(0.643266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 19.8664i | − | 0.0325145i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 316.779 | 0.516769 | 0.258385 | − | 0.966042i | \(-0.416810\pi\) | ||||
0.258385 | + | 0.966042i | \(0.416810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −534.934 | + | 926.533i | −0.866992 | + | 1.50167i | −0.00193565 | + | 0.999998i | \(0.500616\pi\) |
−0.865056 | + | 0.501675i | \(0.832717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −578.542 | + | 334.021i | −0.934640 | + | 0.539615i | −0.888276 | − | 0.459310i | \(-0.848097\pi\) |
−0.0463638 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1121 | − | 8.14762i | 0.0226518 | − | 0.0130780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.580 | − | 676.505i | 0.624929 | − | 1.08241i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −985.986 | −1.56755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 150.631i | 0.238718i | 0.992851 | + | 0.119359i | \(0.0380839\pi\) | ||||
−0.992851 | + | 0.119359i | \(0.961916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 875.252 | + | 505.327i | 1.37835 | + | 0.795790i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.4092 | + | 75.1869i | 0.0681463 | + | 0.118033i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −351.521 | − | 608.852i | −0.548395 | − | 0.949847i | −0.998385 | − | 0.0568139i | \(-0.981906\pi\) |
0.449990 | − | 0.893034i | \(-0.351427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −742.057 | − | 428.427i | −1.15405 | − | 0.666293i | −0.204182 | − | 0.978933i | \(-0.565454\pi\) |
−0.949872 | + | 0.312639i | \(0.898787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 156.257i | − | 0.241510i | −0.992682 | − | 0.120755i | \(-0.961468\pi\) | ||
0.992682 | − | 0.120755i | \(-0.0385316\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −441.773 | + | 765.173i | −0.676528 | + | 1.17178i | 0.299492 | + | 0.954099i | \(0.403183\pi\) |
−0.976020 | + | 0.217682i | \(0.930151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −758.798 | + | 438.092i | −1.15847 | + | 0.668843i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −379.533 | + | 219.123i | −0.575922 | + | 0.332509i | −0.759511 | − | 0.650494i | \(-0.774562\pi\) |
0.183589 | + | 0.983003i | \(0.441228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −233.924 | + | 405.168i | −0.353894 | + | 0.612963i | −0.986928 | − | 0.161161i | \(-0.948476\pi\) |
0.633034 | + | 0.774124i | \(0.281809\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −70.8359 | −0.106520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.3597i | 0.0755018i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1147.52 | + | 662.524i | 1.71017 | + | 0.987368i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 273.302 | + | 473.372i | 0.406094 | + | 0.703376i | 0.994448 | − | 0.105227i | \(-0.0335571\pi\) |
−0.588354 | + | 0.808604i | \(0.700224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 227.606 | + | 394.225i | 0.336198 | + | 0.582312i | 0.983714 | − | 0.179740i | \(-0.0575255\pi\) |
−0.647516 | + | 0.762052i | \(0.724192\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3600 | + | 7.71341i | 0.0196760 | + | 0.0113600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 123.214i | 0.180400i | 0.995924 | + | 0.0902002i | \(0.0287507\pi\) | ||||
−0.995924 | + | 0.0902002i | \(0.971249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.8937 | 0.0553193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.0115 | − | 55.4455i | 0.0464607 | − | 0.0804724i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 163.326 | − | 94.2965i | 0.236362 | − | 0.136464i | −0.377141 | − | 0.926156i | \(-0.623093\pi\) |
0.613504 | + | 0.789692i | \(0.289760\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −634.285 | + | 366.204i | −0.912640 | + | 0.526913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.1599 | − | 78.2192i | 0.0647918 | − | 0.112223i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −810.064 | −1.15558 | −0.577792 | − | 0.816184i | \(-0.696085\pi\) | ||||
−0.577792 | + | 0.816184i | \(0.696085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1136.86i | 1.61716i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.1806 | − | 7.60980i | −0.0186429 | − | 0.0107635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 651.819 | + | 1128.98i | 0.919349 | + | 1.59236i | 0.800406 | + | 0.599459i | \(0.204618\pi\) |
0.118944 | + | 0.992901i | \(0.462049\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 126.623 | + | 219.317i | 0.177592 | + | 0.307598i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −165.891 | − | 95.7772i | −0.232015 | − | 0.133954i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 788.981i | 1.09733i | 0.836042 | + | 0.548666i | \(0.184864\pi\) | ||||
−0.836042 | + | 0.548666i | \(0.815136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.6380 | − | 70.3870i | 0.0560524 | − | 0.0970856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −232.676 | + | 134.335i | −0.320049 | + | 0.184780i | −0.651414 | − | 0.758722i | \(-0.725824\pi\) |
0.331365 | + | 0.943502i | \(0.392491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 574.038 | − | 331.421i | 0.785277 | − | 0.453380i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.8343 | − | 63.7989i | 0.0502514 | − | 0.0870380i | −0.839806 | − | 0.542887i | \(-0.817331\pi\) |
0.890057 | + | 0.455849i | \(0.150664\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 641.512 | 0.870437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 448.249i | − | 0.606562i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) | ||
0.952901 | − | 0.303281i | \(-0.0980820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −656.602 | − | 379.089i | −0.883718 | − | 0.510215i | −0.0118352 | − | 0.999930i | \(-0.503767\pi\) |
−0.871882 | + | 0.489715i | \(0.837101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 635.496 | + | 1100.71i | 0.853015 | + | 1.47746i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.1063 | − | 93.7149i | −0.0722381 | − | 0.125120i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1141.58 | + | 659.091i | 1.52008 | + | 0.877618i | 0.999720 | + | 0.0236697i | \(0.00753501\pi\) |
0.520358 | + | 0.853948i | \(0.325798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 904.589i | − | 1.19813i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −587.874 | −0.776583 | −0.388292 | − | 0.921537i | \(-0.626935\pi\) | ||||
−0.388292 | + | 0.921537i | \(0.626935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 188.496 | − | 326.485i | 0.247695 | − | 0.429021i | −0.715191 | − | 0.698929i | \(-0.753660\pi\) |
0.962886 | + | 0.269908i | \(0.0869934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.5845 | + | 29.7823i | −0.0676075 | + | 0.0390332i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.2917 | + | 21.5304i | −0.0486202 | + | 0.0280709i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 643.939 | − | 1115.34i | 0.837372 | − | 1.45037i | −0.0547122 | − | 0.998502i | \(-0.517424\pi\) |
0.892084 | − | 0.451869i | \(-0.149243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 778.578 | 1.00722 | 0.503608 | − | 0.863932i | \(-0.332006\pi\) | ||||
0.503608 | + | 0.863932i | \(0.332006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 408.715i | − | 0.527375i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −90.1884 | − | 52.0703i | −0.115775 | − | 0.0668425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −766.801 | − | 1328.14i | −0.981819 | − | 1.70056i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 193.292 | + | 334.791i | 0.246232 | + | 0.426486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 390.283 | + | 225.330i | 0.495913 | + | 0.286315i | 0.727024 | − | 0.686612i | \(-0.240903\pi\) |
−0.231111 | + | 0.972927i | \(0.574236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.7797i | − | 0.0136280i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −182.891 | + | 316.776i | −0.229474 | + | 0.397461i | −0.957652 | − | 0.287927i | \(-0.907034\pi\) |
0.728178 | + | 0.685388i | \(0.240367\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 163.101 | − | 94.1662i | 0.204131 | − | 0.117855i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −907.869 | + | 524.158i | −1.13060 | + | 0.652750i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.3994 | − | 24.9406i | 0.0178875 | − | 0.0309821i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1167.70 | −1.44339 | −0.721695 | − | 0.692212i | \(-0.756636\pi\) | ||||
−0.721695 | + | 0.692212i | \(0.756636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 810.121i | − | 0.998916i | −0.866338 | − | 0.499458i | \(-0.833533\pi\) | ||
0.866338 | − | 0.499458i | \(-0.166467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −763.114 | − | 440.584i | −0.936336 | − | 0.540594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −382.135 | − | 661.878i | −0.467730 | − | 0.810132i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −280.513 | − | 485.862i | −0.341672 | − | 0.591793i | 0.643071 | − | 0.765806i | \(-0.277660\pi\) |
−0.984743 | + | 0.174013i | \(0.944327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1016.04 | − | 586.612i | −1.23456 | − | 0.712773i | −0.266583 | − | 0.963812i | \(-0.585895\pi\) |
−0.967977 | + | 0.251039i | \(0.919228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 267.739i | 0.323747i | 0.986811 | + | 0.161874i | \(0.0517537\pi\) | ||||
−0.986811 | + | 0.161874i | \(0.948246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 432.474 | 0.521682 | 0.260841 | − | 0.965382i | \(-0.416000\pi\) | ||||
0.260841 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −411.518 | + | 712.769i | −0.494019 | + | 0.855665i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −925.472 | + | 534.321i | −1.10835 | + | 0.639906i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 459.103 | − | 265.063i | 0.547202 | − | 0.315927i | −0.200790 | − | 0.979634i | \(-0.564351\pi\) |
0.747993 | + | 0.663707i | \(0.231018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 400.337 | − | 693.403i | 0.476024 | − | 0.824499i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1019.44 | 1.20644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 108.590i | − | 0.128205i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −400.278 | − | 231.100i | −0.470361 | − | 0.271563i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −88.3868 | − | 153.090i | −0.103619 | − | 0.179473i | 0.809554 | − | 0.587045i | \(-0.199709\pi\) |
−0.913173 | + | 0.407572i | \(0.866376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 194.859 | + | 337.505i | 0.227373 | + | 0.393821i | 0.957029 | − | 0.289993i | \(-0.0936531\pi\) |
−0.729656 | + | 0.683815i | \(0.760320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 503.279 | + | 290.568i | 0.585889 | + | 0.338263i | 0.763470 | − | 0.645843i | \(-0.223494\pi\) |
−0.177581 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 827.326i | 0.958663i | 0.877634 | + | 0.479331i | \(0.159121\pi\) | ||||
−0.877634 | + | 0.479331i | \(0.840879\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 324.426 | − | 561.923i | 0.373333 | − | 0.646632i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.7831 | − | 32.7837i | 0.0651930 | − | 0.0376392i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.3732 | − | 22.1548i | 0.0438551 | − | 0.0253198i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 279.815 | − | 484.653i | 0.319059 | − | 0.552626i | −0.661233 | − | 0.750181i | \(-0.729967\pi\) |
0.980292 | + | 0.197554i | \(0.0632999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 957.127 | 1.08641 | 0.543205 | − | 0.839600i | \(-0.317211\pi\) | ||||
0.543205 | + | 0.839600i | \(0.317211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 625.252i | 0.708100i | 0.935227 | + | 0.354050i | \(0.115196\pi\) | ||||
−0.935227 | + | 0.354050i | \(0.884804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −921.187 | − | 531.847i | −1.03854 | − | 0.599602i | −0.119122 | − | 0.992880i | \(-0.538008\pi\) |
−0.919420 | + | 0.393277i | \(0.871341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.5496 | + | 84.0904i | 0.0546115 | + | 0.0945899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −108.576 | − | 188.059i | −0.121585 | − | 0.210592i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −511.172 | − | 295.125i | −0.571142 | − | 0.329749i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 202.793i | 0.225577i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 606.935 | 0.673624 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1010.61 | − | 1750.43i | 1.11670 | − | 1.93418i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −207.207 | + | 119.631i | −0.228453 | + | 0.131898i | −0.609858 | − | 0.792510i | \(-0.708774\pi\) |
0.381405 | + | 0.924408i | \(0.375440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −175.804 | + | 101.501i | −0.192980 | + | 0.111417i | −0.593377 | − | 0.804925i | \(-0.702206\pi\) |
0.400397 | + | 0.916342i | \(0.368872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −665.585 | + | 1152.83i | −0.729009 | + | 1.26268i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −84.1801 | −0.0917994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 878.708i | − | 0.956156i | −0.878317 | − | 0.478078i | \(-0.841334\pi\) | ||
0.878317 | − | 0.478078i | \(-0.158666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −135.746 | − | 78.3730i | −0.147070 | − | 0.0849111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 372.975 | + | 646.011i | 0.403216 | + | 0.698391i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −300.259 | − | 520.064i | −0.323207 | − | 0.559810i | 0.657941 | − | 0.753069i | \(-0.271428\pi\) |
−0.981148 | + | 0.193259i | \(0.938094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 821.838 | + | 474.489i | 0.882748 | + | 0.509655i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1815.93i | − | 1.94217i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −377.587 | + | 653.999i | −0.401261 | + | 0.695005i | −0.993878 | − | 0.110479i | \(-0.964761\pi\) |
0.592617 | + | 0.805484i | \(0.298095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6668 | − | 21.1696i | 0.0388831 | − | 0.0224492i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −769.965 | + | 444.539i | −0.813057 | + | 0.469419i | −0.848016 | − | 0.529970i | \(-0.822203\pi\) |
0.0349595 | + | 0.999389i | \(0.488870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.5731 | + | 92.7913i | −0.0564521 | + | 0.0977779i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.5920 | −0.0163610 | −0.00818050 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818050 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.49830i | − | 0.00261602i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.15291 | + | 1.82033i | 0.00328770 | + | 0.00189816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3970 | + | 50.9172i | 0.0305900 | + | 0.0529835i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 191.961 | + | 332.486i | 0.198923 | + | 0.344545i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 847.921 | + | 489.548i | 0.876858 | + | 0.506254i | 0.869621 | − | 0.493720i | \(-0.164363\pi\) |
0.00723669 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 67.3838i | − | 0.0693963i | −0.999398 | − | 0.0346982i | \(-0.988953\pi\) | ||
0.999398 | − | 0.0346982i | \(-0.0110470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −70.3667 | −0.0723193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −353.710 | + | 612.644i | −0.362037 | + | 0.627067i | −0.988296 | − | 0.152549i | \(-0.951252\pi\) |
0.626259 | + | 0.779615i | \(0.284585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 417.133 | − | 240.832i | 0.426081 | − | 0.245998i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 338.829 | − | 195.623i | 0.344689 | − | 0.199006i | −0.317655 | − | 0.948206i | \(-0.602895\pi\) |
0.662343 | + | 0.749200i | \(0.269562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −638.971 | + | 1106.73i | −0.648701 | + | 1.12358i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 310.720 | 0.314176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 104.988i | − | 0.105941i | −0.998596 | − | 0.0529706i | \(-0.983131\pi\) | ||
0.998596 | − | 0.0529706i | \(-0.0168690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1592.67 | − | 919.530i | −1.60068 | − | 0.924151i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0028 | + | 67.5547i | 0.0391201 | + | 0.0677580i | 0.884923 | − | 0.465738i | \(-0.154211\pi\) |
−0.845802 | + | 0.533496i | \(0.820878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1728.3.o.g.1279.8 | 16 | ||
3.2 | odd | 2 | 576.3.o.g.319.7 | 16 | |||
4.3 | odd | 2 | inner | 1728.3.o.g.1279.7 | 16 | ||
8.3 | odd | 2 | 108.3.f.c.91.6 | 16 | |||
8.5 | even | 2 | 108.3.f.c.91.5 | 16 | |||
9.2 | odd | 6 | 576.3.o.g.511.2 | 16 | |||
9.7 | even | 3 | inner | 1728.3.o.g.127.7 | 16 | ||
12.11 | even | 2 | 576.3.o.g.319.2 | 16 | |||
24.5 | odd | 2 | 36.3.f.c.31.4 | yes | 16 | ||
24.11 | even | 2 | 36.3.f.c.31.3 | yes | 16 | ||
36.7 | odd | 6 | inner | 1728.3.o.g.127.8 | 16 | ||
36.11 | even | 6 | 576.3.o.g.511.7 | 16 | |||
72.5 | odd | 6 | 324.3.d.i.163.8 | 8 | |||
72.11 | even | 6 | 36.3.f.c.7.4 | yes | 16 | ||
72.13 | even | 6 | 324.3.d.g.163.1 | 8 | |||
72.29 | odd | 6 | 36.3.f.c.7.3 | ✓ | 16 | ||
72.43 | odd | 6 | 108.3.f.c.19.5 | 16 | |||
72.59 | even | 6 | 324.3.d.i.163.7 | 8 | |||
72.61 | even | 6 | 108.3.f.c.19.6 | 16 | |||
72.67 | odd | 6 | 324.3.d.g.163.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 72.29 | odd | 6 | ||
36.3.f.c.7.4 | yes | 16 | 72.11 | even | 6 | ||
36.3.f.c.31.3 | yes | 16 | 24.11 | even | 2 | ||
36.3.f.c.31.4 | yes | 16 | 24.5 | odd | 2 | ||
108.3.f.c.19.5 | 16 | 72.43 | odd | 6 | |||
108.3.f.c.19.6 | 16 | 72.61 | even | 6 | |||
108.3.f.c.91.5 | 16 | 8.5 | even | 2 | |||
108.3.f.c.91.6 | 16 | 8.3 | odd | 2 | |||
324.3.d.g.163.1 | 8 | 72.13 | even | 6 | |||
324.3.d.g.163.2 | 8 | 72.67 | odd | 6 | |||
324.3.d.i.163.7 | 8 | 72.59 | even | 6 | |||
324.3.d.i.163.8 | 8 | 72.5 | odd | 6 | |||
576.3.o.g.319.2 | 16 | 12.11 | even | 2 | |||
576.3.o.g.319.7 | 16 | 3.2 | odd | 2 | |||
576.3.o.g.511.2 | 16 | 9.2 | odd | 6 | |||
576.3.o.g.511.7 | 16 | 36.11 | even | 6 | |||
1728.3.o.g.127.7 | 16 | 9.7 | even | 3 | inner | ||
1728.3.o.g.127.8 | 16 | 36.7 | odd | 6 | inner | ||
1728.3.o.g.1279.7 | 16 | 4.3 | odd | 2 | inner | ||
1728.3.o.g.1279.8 | 16 | 1.1 | even | 1 | trivial |