Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(289,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.289 |
Dual form | 504.2.s.i.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.13746 | + | 3.70219i | −0.955901 | + | 1.65567i | −0.223607 | + | 0.974679i | \(0.571783\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 2.17945i | −0.566947 | − | 0.823754i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.13746 | − | 3.70219i | −0.644468 | − | 1.11625i | −0.984424 | − | 0.175810i | \(-0.943746\pi\) |
0.339956 | − | 0.940441i | \(-0.389588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.27492 | −0.353598 | −0.176799 | − | 0.984247i | \(-0.556574\pi\) | ||||
−0.176799 | + | 0.984247i | \(0.556574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.637459 | + | 1.10411i | −0.146243 | + | 0.253300i | −0.929836 | − | 0.367974i | \(-0.880051\pi\) |
0.783593 | + | 0.621275i | \(0.213385\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.63746 | − | 11.4964i | −1.32749 | − | 2.29928i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27492 | 0.422442 | 0.211221 | − | 0.977438i | \(-0.432256\pi\) | ||||
0.211221 | + | 0.977438i | \(0.432256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.2749 | − | 0.894797i | 1.90581 | − | 0.151248i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.63746 | + | 4.56821i | −0.433596 | + | 0.751009i | −0.997180 | − | 0.0750491i | \(-0.976089\pi\) |
0.563584 | + | 0.826059i | \(0.309422\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5498 | −1.64761 | −0.823804 | − | 0.566875i | \(-0.808152\pi\) | ||||
−0.823804 | + | 0.566875i | \(0.808152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27492 | −1.10941 | −0.554707 | − | 0.832046i | \(-0.687170\pi\) | ||||
−0.554707 | + | 0.832046i | \(0.687170\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.50000 | + | 6.53835i | −0.357143 | + | 0.934050i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.862541 | + | 1.49397i | 0.118479 | + | 0.205212i | 0.919165 | − | 0.393872i | \(-0.128865\pi\) |
−0.800686 | + | 0.599084i | \(0.795531\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.2749 | 2.46419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13746 | + | 5.43424i | 0.408462 | + | 0.707477i | 0.994718 | − | 0.102649i | \(-0.0327318\pi\) |
−0.586255 | + | 0.810126i | \(0.699398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.72508 | − | 4.71998i | 0.338005 | − | 0.585442i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.63746 | − | 6.30026i | −0.444386 | − | 0.769700i | 0.553623 | − | 0.832767i | \(-0.313245\pi\) |
−0.998009 | + | 0.0630678i | \(0.979912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.63746 | − | 2.83616i | −0.191650 | − | 0.331948i | 0.754147 | − | 0.656705i | \(-0.228051\pi\) |
−0.945797 | + | 0.324758i | \(0.894717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.86254 | + | 10.2118i | −0.554138 | + | 1.16374i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77492 | − | 3.07425i | 0.199694 | − | 0.345880i | −0.748735 | − | 0.662869i | \(-0.769339\pi\) |
0.948429 | + | 0.316989i | \(0.102672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.274917 | 0.0301761 | 0.0150880 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150880 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.0997 | 1.85472 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.27492 | − | 3.94027i | 0.241141 | − | 0.417668i | −0.719899 | − | 0.694079i | \(-0.755812\pi\) |
0.961040 | + | 0.276411i | \(0.0891451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.91238 | + | 2.77862i | 0.200471 | + | 0.291278i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.72508 | − | 4.71998i | −0.279588 | − | 0.484260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2749 | 1.65247 | 0.826234 | − | 0.563327i | \(-0.190479\pi\) | ||||
0.826234 | + | 0.563327i | \(0.190479\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.91238 | − | 10.2405i | 0.582564 | − | 1.00903i | −0.412611 | − | 0.910907i | \(-0.635383\pi\) |
0.995174 | − | 0.0981224i | \(-0.0312837\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.41238 | − | 5.91041i | 0.329887 | − | 0.571381i | −0.652602 | − | 0.757701i | \(-0.726323\pi\) |
0.982489 | + | 0.186320i | \(0.0596561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.91238 | + | 5.04438i | 0.278955 | + | 0.483164i | 0.971125 | − | 0.238570i | \(-0.0766786\pi\) |
−0.692170 | + | 0.721734i | \(0.743345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5498 | −0.992445 | −0.496222 | − | 0.868195i | \(-0.665280\pi\) | ||||
−0.496222 | + | 0.868195i | \(0.665280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.54983 | + | 14.8087i | 0.797276 | + | 1.38092i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.54983 | + | 9.55505i | −0.417083 | + | 0.875910i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.63746 | + | 6.30026i | −0.330678 | + | 0.572751i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 35.3746 | 3.16400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5498 | −1.91224 | −0.956119 | − | 0.292978i | \(-0.905354\pi\) | ||||
−0.956119 | + | 0.292978i | \(0.905354\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.137459 | + | 0.238085i | −0.0120098 | + | 0.0208016i | −0.871968 | − | 0.489563i | \(-0.837156\pi\) |
0.859958 | + | 0.510365i | \(0.170490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36254 | − | 0.266857i | 0.291569 | − | 0.0231395i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.27492 | + | 14.3326i | 0.706974 | + | 1.22451i | 0.965974 | + | 0.258638i | \(0.0832735\pi\) |
−0.259001 | + | 0.965877i | \(0.583393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.725083 | 0.0615007 | 0.0307504 | − | 0.999527i | \(-0.490210\pi\) | ||||
0.0307504 | + | 0.999527i | \(0.490210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.72508 | + | 4.71998i | 0.227883 | + | 0.394705i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.86254 | + | 8.42217i | −0.403812 | + | 0.699423i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.274917 | − | 0.476171i | 0.0225221 | − | 0.0390094i | −0.854545 | − | 0.519378i | \(-0.826164\pi\) |
0.877067 | + | 0.480368i | \(0.159497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.68729 | + | 13.3148i | 0.625583 | + | 1.08354i | 0.988428 | + | 0.151692i | \(0.0484722\pi\) |
−0.362845 | + | 0.931850i | \(0.618194\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.27492 | −0.343370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.27492 | − | 12.6005i | −0.580602 | − | 1.00563i | −0.995408 | − | 0.0957218i | \(-0.969484\pi\) |
0.414807 | − | 0.909910i | \(-0.363849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5498 | + | 0.837253i | −0.831443 | + | 0.0659848i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 10.3923i | 0.469956 | − | 0.813988i | −0.529454 | − | 0.848339i | \(-0.677603\pi\) |
0.999410 | + | 0.0343508i | \(0.0109363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3746 | −0.874968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.72508 | + | 6.45203i | −0.283213 | + | 0.490539i | −0.972174 | − | 0.234259i | \(-0.924734\pi\) |
0.688961 | + | 0.724798i | \(0.258067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.0997 | + | 31.7106i | −1.14143 | + | 2.39710i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.725083 | − | 1.25588i | −0.0541952 | − | 0.0938689i | 0.837655 | − | 0.546200i | \(-0.183926\pi\) |
−0.891850 | + | 0.452331i | \(0.850593\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.82475 | 0.284292 | 0.142146 | − | 0.989846i | \(-0.454600\pi\) | ||||
0.142146 | + | 0.989846i | \(0.454600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2749 | − | 19.5287i | −0.828948 | − | 1.43578i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.54983 | + | 14.8087i | −0.625226 | + | 1.08292i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.27492 | + | 9.13642i | −0.381680 | + | 0.661088i | −0.991302 | − | 0.131603i | \(-0.957988\pi\) |
0.609623 | + | 0.792692i | \(0.291321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.77492 | − | 13.4666i | −0.559651 | − | 0.969344i | −0.997525 | − | 0.0703075i | \(-0.977602\pi\) |
0.437875 | − | 0.899036i | \(-0.355731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5498 | 1.17913 | 0.589563 | − | 0.807722i | \(-0.299300\pi\) | ||||
0.589563 | + | 0.807722i | \(0.299300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5498 | − | 21.7370i | −0.889634 | − | 1.54089i | −0.840308 | − | 0.542109i | \(-0.817626\pi\) |
−0.0493259 | − | 0.998783i | \(-0.515707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.41238 | − | 4.95807i | −0.239502 | − | 0.347988i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.5498 | − | 39.0575i | 1.57495 | − | 2.72789i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.45017 | 0.376996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6495 | 1.21504 | 0.607521 | − | 0.794304i | \(-0.292164\pi\) | ||||
0.607521 | + | 0.794304i | \(0.292164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.5498 | − | 26.9331i | 1.06049 | − | 1.83682i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.13746 | − | 2.38876i | 0.0772157 | − | 0.162160i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.54983 | + | 4.41644i | 0.171520 | + | 0.297082i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.27492 | 0.420200 | 0.210100 | − | 0.977680i | \(-0.432621\pi\) | ||||
0.210100 | + | 0.977680i | \(0.432621\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.86254 | − | 3.22602i | −0.123621 | − | 0.214118i | 0.797572 | − | 0.603224i | \(-0.206117\pi\) |
−0.921193 | + | 0.389106i | \(0.872784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.36254 | + | 9.28819i | −0.354367 | + | 0.613781i | −0.987009 | − | 0.160663i | \(-0.948637\pi\) |
0.632643 | + | 0.774444i | \(0.281970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.27492 | − | 12.6005i | 0.476596 | − | 0.825488i | −0.523045 | − | 0.852305i | \(-0.675204\pi\) |
0.999640 | + | 0.0268173i | \(0.00853725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8248 | − | 22.2131i | −0.836595 | − | 1.44902i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.5498 | −1.97610 | −0.988052 | − | 0.154119i | \(-0.950746\pi\) | ||||
−0.988052 | + | 0.154119i | \(0.950746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41238 | + | 11.1066i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976343i | \(-0.0311275\pi\) |
−0.582165 | + | 0.813071i | \(0.697794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.8625 | − | 23.2309i | −1.20508 | − | 1.48417i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.812707 | − | 1.40765i | 0.0517113 | − | 0.0895666i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.3746 | −1.22291 | −0.611457 | − | 0.791278i | \(-0.709416\pi\) | ||||
−0.611457 | + | 0.791278i | \(0.709416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0997 | −1.07505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.54983 | + | 16.5408i | −0.595702 | + | 1.03179i | 0.397745 | + | 0.917496i | \(0.369793\pi\) |
−0.993447 | + | 0.114291i | \(0.963540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.9124 | − | 1.10411i | 0.864473 | − | 0.0686061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2749 | − | 21.2608i | −0.756904 | − | 1.31100i | −0.944422 | − | 0.328735i | \(-0.893378\pi\) |
0.187518 | − | 0.982261i | \(-0.439956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.37459 | −0.453017 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1375 | + | 24.4868i | 0.861976 | + | 1.49299i | 0.870019 | + | 0.493019i | \(0.164107\pi\) |
−0.00804266 | + | 0.999968i | \(0.502560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.13746 | − | 5.43424i | 0.190587 | − | 0.330106i | −0.754858 | − | 0.655888i | \(-0.772294\pi\) |
0.945445 | + | 0.325782i | \(0.105628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.3746 | + | 49.1462i | −1.71105 | + | 2.96363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.08762 | + | 3.61587i | 0.125433 | + | 0.217257i | 0.921902 | − | 0.387423i | \(-0.126635\pi\) |
−0.796469 | + | 0.604679i | \(0.793301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4502 | 0.683060 | 0.341530 | − | 0.939871i | \(-0.389055\pi\) | ||||
0.341530 | + | 0.939871i | \(0.389055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4622 | − | 23.3172i | −0.800245 | − | 1.38607i | −0.919454 | − | 0.393196i | \(-0.871369\pi\) |
0.119209 | − | 0.992869i | \(-0.461964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.8248 | + | 22.9928i | 0.934106 | + | 1.35722i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.17525 | 0.302341 | 0.151171 | − | 0.988508i | \(-0.451696\pi\) | ||||
0.151171 | + | 0.988508i | \(0.451696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.8248 | −1.56180 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.54983 | + | 4.41644i | −0.147461 | + | 0.255409i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9124 | + | 15.8553i | 0.628979 | + | 0.913885i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.3746 | − | 37.0219i | −1.22391 | − | 2.11987i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3746 | −1.50528 | −0.752639 | − | 0.658434i | \(-0.771219\pi\) | ||||
−0.752639 | + | 0.658434i | \(0.771219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.27492 | + | 9.13642i | 0.299113 | + | 0.518079i | 0.975933 | − | 0.218069i | \(-0.0699759\pi\) |
−0.676820 | + | 0.736148i | \(0.736643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.22508 | − | 3.85396i | 0.125769 | − | 0.217838i | −0.796264 | − | 0.604949i | \(-0.793193\pi\) |
0.922033 | + | 0.387111i | \(0.126527\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.58762 | + | 4.48190i | −0.145335 | + | 0.251728i | −0.929498 | − | 0.368827i | \(-0.879759\pi\) |
0.784163 | + | 0.620555i | \(0.213093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.86254 | − | 8.42217i | −0.272250 | − | 0.471551i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.09967 | 0.283753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.46221 | + | 14.6570i | 0.469399 | + | 0.813023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.8248 | − | 1.25588i | 0.872447 | − | 0.0692389i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9124 | + | 20.6328i | −0.654763 | + | 1.13408i | 0.327190 | + | 0.944959i | \(0.393898\pi\) |
−0.981953 | + | 0.189125i | \(0.939435\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.0997 | 1.69916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.09967 | 0.332270 | 0.166135 | − | 0.986103i | \(-0.446871\pi\) | ||||
0.166135 | + | 0.986103i | \(0.446871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.13746 | − | 3.70219i | 0.115750 | − | 0.200485i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0000 | − | 4.35890i | 0.971909 | − | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0997 | − | 26.1534i | −0.810593 | − | 1.40399i | −0.912450 | − | 0.409189i | \(-0.865812\pi\) |
0.101857 | − | 0.994799i | \(-0.467522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.72508 | − | 4.71998i | −0.145042 | − | 0.251219i | 0.784347 | − | 0.620322i | \(-0.212998\pi\) |
−0.929388 | + | 0.369103i | \(0.879665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.27492 | − | 7.40437i | 0.226889 | − | 0.392983i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.8248 | − | 22.2131i | 0.676865 | − | 1.17236i | −0.299056 | − | 0.954236i | \(-0.596672\pi\) |
0.975920 | − | 0.218128i | \(-0.0699950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68729 | + | 15.0468i | 0.457226 | + | 0.791939i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.04983 | + | 7.01452i | 0.211400 | + | 0.366155i | 0.952153 | − | 0.305622i | \(-0.0988645\pi\) |
−0.740753 | + | 0.671777i | \(0.765531\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.96221 | − | 4.12081i | 0.101873 | − | 0.213942i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.637459 | + | 1.10411i | −0.0330064 | + | 0.0571687i | −0.882057 | − | 0.471143i | \(-0.843841\pi\) |
0.849050 | + | 0.528312i | \(0.177175\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.90033 | −0.149375 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8248 | 1.84019 | 0.920097 | − | 0.391691i | \(-0.128110\pi\) | ||||
0.920097 | + | 0.391691i | \(0.128110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.27492 | + | 3.94027i | −0.116243 | + | 0.201339i | −0.918276 | − | 0.395941i | \(-0.870418\pi\) |
0.802033 | + | 0.597280i | \(0.203752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.4124 | − | 39.8293i | −1.39706 | − | 2.02989i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00000 | − | 1.73205i | −0.0507020 | − | 0.0878185i | 0.839561 | − | 0.543266i | \(-0.182813\pi\) |
−0.890263 | + | 0.455448i | \(0.849479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.58762 | + | 13.1422i | 0.381775 | + | 0.661253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.1873 | + | 29.7693i | −0.862606 | + | 1.49408i | 0.00679974 | + | 0.999977i | \(0.497836\pi\) |
−0.869405 | + | 0.494100i | \(0.835498\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | − | 20.7846i | 0.599251 | − | 1.03793i | −0.393680 | − | 0.919247i | \(-0.628798\pi\) |
0.992932 | − | 0.118686i | \(-0.0378683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.637459 | − | 1.10411i | −0.0317541 | − | 0.0549997i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.5498 | 1.11775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7749 | − | 22.1268i | −0.631679 | − | 1.09410i | −0.987208 | − | 0.159435i | \(-0.949033\pi\) |
0.355529 | − | 0.934665i | \(-0.384301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.13746 | − | 14.9893i | 0.351211 | − | 0.737575i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.587624 | + | 1.01779i | −0.0288453 | + | 0.0499616i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4502 | −0.657084 | −0.328542 | − | 0.944489i | \(-0.606557\pi\) | ||||
−0.328542 | + | 0.944489i | \(0.606557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8248 | −0.673777 | −0.336889 | − | 0.941545i | \(-0.609375\pi\) | ||||
−0.336889 | + | 0.941545i | \(0.609375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.5498 | + | 45.9857i | −1.28786 | + | 2.23063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.3746 | − | 2.09313i | 1.27636 | − | 0.101294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8248 | + | 23.9452i | 0.665915 | + | 1.15340i | 0.979036 | + | 0.203685i | \(0.0652919\pi\) |
−0.313122 | + | 0.949713i | \(0.601375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.8248 | 1.24106 | 0.620529 | − | 0.784183i | \(-0.286918\pi\) | ||||
0.620529 | + | 0.784183i | \(0.286918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.54983 | + | 4.41644i | 0.121975 | + | 0.211267i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.86254 | + | 8.42217i | −0.232076 | + | 0.401968i | −0.958419 | − | 0.285365i | \(-0.907885\pi\) |
0.726343 | + | 0.687333i | \(0.241219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6873 | − | 27.1712i | 0.745326 | − | 1.29094i | −0.204717 | − | 0.978821i | \(-0.565627\pi\) |
0.950042 | − | 0.312121i | \(-0.101039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.72508 | + | 16.8443i | 0.461013 | + | 0.798498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45017 | −0.257209 | −0.128605 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128605 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5498 | + | 39.0575i | 1.06183 | + | 1.83914i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.3746 | + | 1.14079i | −0.673891 | + | 0.0534812i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.32475 | − | 7.49069i | 0.202303 | − | 0.350400i | −0.746967 | − | 0.664861i | \(-0.768491\pi\) |
0.949270 | + | 0.314462i | \(0.101824\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.6495 | −1.93981 | −0.969905 | − | 0.243482i | \(-0.921710\pi\) | ||||
−0.969905 | + | 0.243482i | \(0.921710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8248 | 1.66492 | 0.832459 | − | 0.554087i | \(-0.186933\pi\) | ||||
0.832459 | + | 0.554087i | \(0.186933\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7251 | − | 22.0405i | 0.588847 | − | 1.01991i | −0.405537 | − | 0.914079i | \(-0.632916\pi\) |
0.994384 | − | 0.105834i | \(-0.0337511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.27492 | + | 17.3781i | −0.382100 | + | 0.802444i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5498 | + | 26.9331i | 0.714982 | + | 1.23839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9244 | 0.776546 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2749 | − | 17.7967i | −0.469473 | − | 0.813151i | 0.529918 | − | 0.848049i | \(-0.322223\pi\) |
−0.999391 | + | 0.0348979i | \(0.988889\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.36254 | − | 5.82409i | 0.153319 | − | 0.265556i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.7870 | + | 60.2528i | −1.57959 | + | 2.73594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | − | 0.866025i | −0.0226572 | − | 0.0392434i | 0.854475 | − | 0.519493i | \(-0.173879\pi\) |
−0.877132 | + | 0.480250i | \(0.840546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9244 | 0.718659 | 0.359330 | − | 0.933211i | \(-0.383005\pi\) | ||||
0.359330 | + | 0.933211i | \(0.383005\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.54983 | − | 7.88054i | −0.204914 | − | 0.354922i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | + | 4.35890i | 0.134568 | + | 0.195523i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3625 | + | 21.4125i | −0.553423 | + | 0.958557i | 0.444601 | + | 0.895729i | \(0.353345\pi\) |
−0.998024 | + | 0.0628286i | \(0.979988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.64950 | −0.341074 | −0.170537 | − | 0.985351i | \(-0.554550\pi\) | ||||
−0.170537 | + | 0.985351i | \(0.554550\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6495 | 1.14139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.86254 | + | 3.22602i | −0.0825557 | + | 0.142991i | −0.904347 | − | 0.426798i | \(-0.859642\pi\) |
0.821791 | + | 0.569789i | \(0.192975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.72508 | + | 7.82300i | −0.164788 | + | 0.346069i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.2749 | + | 43.7774i | 1.11375 | + | 1.92906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.6495 | 1.12806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.274917 | + | 0.476171i | 0.0120443 | + | 0.0208614i | 0.871985 | − | 0.489533i | \(-0.162833\pi\) |
−0.859940 | + | 0.510394i | \(0.829499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.6375 | − | 21.8887i | 0.552597 | − | 0.957127i | −0.445489 | − | 0.895288i | \(-0.646970\pi\) |
0.998086 | − | 0.0618393i | \(-0.0196966\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | − | 3.46410i | 0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4502 | 0.582591 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.5876 | + | 25.2665i | 0.630678 | + | 1.09237i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.5498 | − | 4.71998i | 1.27280 | − | 0.203304i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.362541 | − | 0.627940i | 0.0155869 | − | 0.0269973i | −0.858127 | − | 0.513438i | \(-0.828372\pi\) |
0.873714 | + | 0.486441i | \(0.161705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.9003 | −1.06661 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.45017 | + | 2.51176i | −0.0617791 | + | 0.107005i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.36254 | + | 0.743028i | −0.398136 | + | 0.0315968i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.58762 | − | 6.21395i | −0.152013 | − | 0.263293i | 0.779955 | − | 0.625836i | \(-0.215242\pi\) |
−0.931967 | + | 0.362543i | \(0.881909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.27492 | 0.392287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.86254 | + | 6.69012i | 0.162787 | + | 0.281955i | 0.935867 | − | 0.352353i | \(-0.114618\pi\) |
−0.773080 | + | 0.634308i | \(0.781285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5498 | − | 39.0575i | 0.948679 | − | 1.64316i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2749 | − | 22.9928i | 0.556513 | − | 0.963910i | −0.441271 | − | 0.897374i | \(-0.645472\pi\) |
0.997784 | − | 0.0665355i | \(-0.0211946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.362541 | − | 0.627940i | −0.0151719 | − | 0.0262785i | 0.858340 | − | 0.513082i | \(-0.171496\pi\) |
−0.873512 | + | 0.486803i | \(0.838163\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −53.0997 | −2.21441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5000 | + | 21.6506i | 0.520382 | + | 0.901328i | 0.999719 | + | 0.0236970i | \(0.00754370\pi\) |
−0.479337 | + | 0.877631i | \(0.659123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.412376 | − | 0.599168i | −0.0171082 | − | 0.0248577i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.68729 | − | 6.38658i | 0.152712 | − | 0.264505i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.72508 | −0.0712018 | −0.0356009 | − | 0.999366i | \(-0.511335\pi\) | ||||
−0.0356009 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.27492 | −0.0525320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.27492 | − | 12.6005i | 0.298745 | − | 0.517442i | −0.677104 | − | 0.735887i | \(-0.736765\pi\) |
0.975849 | + | 0.218446i | \(0.0700986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.6495 | − | 37.2679i | −1.05153 | − | 1.52783i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.72508 | + | 6.45203i | 0.152203 | + | 0.263623i | 0.932037 | − | 0.362363i | \(-0.118030\pi\) |
−0.779834 | + | 0.625986i | \(0.784697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0997 | −1.06463 | −0.532314 | − | 0.846547i | \(-0.678677\pi\) | ||||
−0.532314 | + | 0.846547i | \(0.678677\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5498 | − | 26.9331i | −0.632191 | − | 1.09499i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50000 | − | 6.06218i | 0.142061 | − | 0.246056i | −0.786212 | − | 0.617957i | \(-0.787961\pi\) |
0.928272 | + | 0.371901i | \(0.121294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.82475 | − | 6.62466i | 0.154733 | − | 0.268005i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.27492 | − | 5.67232i | −0.132273 | − | 0.229103i | 0.792280 | − | 0.610158i | \(-0.208894\pi\) |
−0.924552 | + | 0.381055i | \(0.875561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.08762 | − | 5.34792i | −0.124102 | − | 0.214951i | 0.797280 | − | 0.603610i | \(-0.206272\pi\) |
−0.921382 | + | 0.388659i | \(0.872938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | + | 0.952341i | −0.480770 | + | 0.0381547i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −42.4244 | + | 73.4813i | −1.69698 | + | 2.93925i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0997 | 0.841299 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.82475 | −0.112452 | −0.0562258 | − | 0.998418i | \(-0.517907\pi\) | ||||
−0.0562258 | + | 0.998418i | \(0.517907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.0619 | − | 79.7815i | 1.82791 | − | 3.16603i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.18729 | − | 8.33585i | 0.126285 | − | 0.330279i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.8248 | + | 36.0695i | 0.822528 | + | 1.42466i | 0.903794 | + | 0.427968i | \(0.140770\pi\) |
−0.0812655 | + | 0.996692i | \(0.525896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.3746 | −1.27673 | −0.638365 | − | 0.769734i | \(-0.720389\pi\) | ||||
−0.638365 | + | 0.769734i | \(0.720389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0000 | − | 29.4449i | −0.668339 | − | 1.15760i | −0.978368 | − | 0.206870i | \(-0.933672\pi\) |
0.310029 | − | 0.950727i | \(-0.399661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4124 | − | 23.2309i | 0.526482 | − | 0.911893i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.9622 | − | 39.7717i | 0.898581 | − | 1.55639i | 0.0692713 | − | 0.997598i | \(-0.477933\pi\) |
0.829309 | − | 0.558790i | \(-0.188734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.587624 | − | 1.01779i | −0.0229604 | − | 0.0397685i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.1993 | −0.708946 | −0.354473 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354473 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9124 | − | 25.8290i | −0.580024 | − | 1.00463i | −0.995476 | − | 0.0950161i | \(-0.969710\pi\) |
0.415452 | − | 0.909615i | \(-0.363624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.19934 | + | 13.0192i | −0.240400 | + | 0.504861i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.54983 | − | 7.88054i | 0.176170 | − | 0.305136i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.7492 | 1.65031 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.4502 | 1.01958 | 0.509789 | − | 0.860299i | \(-0.329723\pi\) | ||||
0.509789 | + | 0.860299i | \(0.329723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.86254 | + | 4.95807i | −0.110016 | + | 0.190554i | −0.915777 | − | 0.401688i | \(-0.868424\pi\) |
0.805760 | + | 0.592242i | \(0.201757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.4124 | − | 35.4704i | −0.936861 | − | 1.36123i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4124 | + | 30.1591i | 0.666266 | + | 1.15401i | 0.978940 | + | 0.204146i | \(0.0654418\pi\) |
−0.312674 | + | 0.949860i | \(0.601225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −70.7492 | −2.70319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.09967 | − | 1.90468i | −0.0418940 | − | 0.0725626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.91238 | + | 10.2405i | −0.224917 | + | 0.389568i | −0.956295 | − | 0.292405i | \(-0.905545\pi\) |
0.731377 | + | 0.681973i | \(0.238878\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.54983 | + | 2.68439i | −0.0587886 | + | 0.101825i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.0997 | + | 36.5457i | 0.799207 | + | 1.38427i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.9244 | −1.50792 | −0.753962 | − | 0.656918i | \(-0.771860\pi\) | ||||
−0.753962 | + | 0.656918i | \(0.771860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.36254 | − | 5.82409i | −0.126821 | − | 0.219660i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.82475 | + | 14.3326i | −0.256671 | + | 0.539032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0997 | + | 27.8854i | −0.604636 | + | 1.04726i | 0.387473 | + | 0.921881i | \(0.373348\pi\) |
−0.992109 | + | 0.125379i | \(0.959985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.2990 | −0.871333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0997 | + | 27.8854i | −0.600416 | + | 1.03995i | 0.392342 | + | 0.919820i | \(0.371665\pi\) |
−0.992758 | + | 0.120132i | \(0.961668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.1873 | + | 2.47508i | −1.16148 | + | 0.0921767i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0997 | − | 26.1534i | −0.560788 | − | 0.971313i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4502 | 0.610103 | 0.305051 | − | 0.952336i | \(-0.401326\pi\) | ||||
0.305051 | + | 0.952336i | \(0.401326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5498 | + | 25.2011i | 0.538145 | + | 0.932095i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4622 | − | 40.6377i | 0.866597 | − | 1.50099i | 0.00114334 | − | 0.999999i | \(-0.499636\pi\) |
0.865453 | − | 0.500990i | \(-0.167031\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.5498 | + | 26.9331i | −0.572786 | + | 0.992094i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.1873 | + | 31.5013i | 0.669030 | + | 1.15879i | 0.978176 | + | 0.207780i | \(0.0666237\pi\) |
−0.309145 | + | 0.951015i | \(0.600043\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.1993 | −0.594296 | −0.297148 | − | 0.954831i | \(-0.596035\pi\) | ||||
−0.297148 | + | 0.954831i | \(0.596035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.17525 | + | 2.03559i | 0.0430578 | + | 0.0745782i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 1.42851i | −0.657706 | + | 0.0521967i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7749 | − | 22.1268i | 0.466163 | − | 0.807419i | −0.533090 | − | 0.846059i | \(-0.678969\pi\) |
0.999253 | + | 0.0386400i | \(0.0123026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −65.7251 | −2.39198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.54983 | − | 4.41644i | 0.0924314 | − | 0.160096i | −0.816102 | − | 0.577907i | \(-0.803869\pi\) |
0.908534 | + | 0.417812i | \(0.137203\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.62541 | − | 13.9140i | 0.239856 | − | 0.503719i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | − | 6.92820i | −0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.6495 | 0.456153 | 0.228076 | − | 0.973643i | \(-0.426756\pi\) | ||||
0.228076 | + | 0.973643i | \(0.426756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5498 | − | 23.4690i | −0.487354 | − | 0.844121i | 0.512541 | − | 0.858663i | \(-0.328704\pi\) |
−0.999894 | + | 0.0145417i | \(0.995371\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.63746 | − | 11.4964i | 0.238425 | − | 0.412963i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.72508 | − | 11.6482i | 0.240951 | − | 0.417340i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.27492 | + | 7.40437i | 0.152969 | + | 0.264949i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 62.1993 | 2.21999 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.27492 | + | 10.8685i | 0.223677 | + | 0.387419i | 0.955922 | − | 0.293622i | \(-0.0948607\pi\) |
−0.732245 | + | 0.681041i | \(0.761527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8248 | + | 22.9928i | 0.562663 | + | 0.817531i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.37459 | − | 11.0411i | 0.226368 | − | 0.392081i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.4743 | −1.29198 | −0.645992 | − | 0.763344i | \(-0.723556\pi\) | ||||
−0.645992 | + | 0.763344i | \(0.723556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.00000 | + | 12.1244i | −0.247025 | + | 0.427859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.4502 | − | 40.8471i | 0.685528 | − | 1.43967i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.82475 | + | 13.5529i | 0.275104 | + | 0.476493i | 0.970161 | − | 0.242461i | \(-0.0779545\pi\) |
−0.695058 | + | 0.718954i | \(0.744621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4502 | −0.963906 | −0.481953 | − | 0.876197i | \(-0.660072\pi\) | ||||
−0.481953 | + | 0.876197i | \(0.660072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.6495 | + | 44.4262i | 0.898463 | + | 1.55618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.63746 | − | 8.03231i | 0.162244 | − | 0.281015i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.1375 | − | 17.5586i | 0.353800 | − | 0.612799i | −0.633112 | − | 0.774060i | \(-0.718223\pi\) |
0.986912 | + | 0.161261i | \(0.0515561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0997 | − | 22.6893i | −0.456626 | − | 0.790899i | 0.542154 | − | 0.840279i | \(-0.317609\pi\) |
−0.998780 | + | 0.0493799i | \(0.984275\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.0241 | −1.35700 | −0.678500 | − | 0.734600i | \(-0.737370\pi\) | ||||
−0.678500 | + | 0.734600i | \(0.737370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3625 | − | 19.6805i | −0.394637 | − | 0.683532i | 0.598417 | − | 0.801184i | \(-0.295796\pi\) |
−0.993055 | + | 0.117652i | \(0.962463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.6495 | − | 4.41644i | 0.957999 | − | 0.153021i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.8248 | + | 22.2131i | −0.443819 | + | 0.768717i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1993 | −1.04260 | −0.521298 | − | 0.853374i | \(-0.674552\pi\) | ||||
−0.521298 | + | 0.853374i | \(0.674552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8248 | −0.821543 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.3127 | − | 42.1108i | 0.836383 | − | 1.44866i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.1873 | − | 1.52274i | 0.659283 | − | 0.0523219i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5498 | + | 18.2728i | 0.361644 | + | 0.626385i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.3746 | −0.834570 | −0.417285 | − | 0.908776i | \(-0.637018\pi\) | ||||
−0.417285 | + | 0.908776i | \(0.637018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2749 | − | 24.7249i | −0.487622 | − | 0.844586i | 0.512277 | − | 0.858820i | \(-0.328802\pi\) |
−0.999899 | + | 0.0142345i | \(0.995469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.17525 | − | 8.96379i | 0.176577 | − | 0.305841i | −0.764129 | − | 0.645064i | \(-0.776831\pi\) |
0.940706 | + | 0.339223i | \(0.110164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.54983 | + | 9.61260i | −0.188919 | + | 0.327217i | −0.944890 | − | 0.327388i | \(-0.893832\pi\) |
0.755971 | + | 0.654605i | \(0.227165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9244 | − | 27.5819i | −0.541447 | − | 0.937813i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1752 | −0.514785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.63746 | + | 8.03231i | 0.157134 | + | 0.272165i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −53.0619 | − | 77.0971i | −1.79382 | − | 2.60636i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3746 | − | 24.8975i | 0.485395 | − | 0.840729i | −0.514464 | − | 0.857512i | \(-0.672009\pi\) |
0.999859 | + | 0.0167828i | \(0.00534237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5498 | −0.827105 | −0.413552 | − | 0.910480i | \(-0.635712\pi\) | ||||
−0.413552 | + | 0.910480i | \(0.635712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.3746 | −1.02219 | −0.511093 | − | 0.859525i | \(-0.670759\pi\) | ||||
−0.511093 | + | 0.859525i | \(0.670759\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.82475 | + | 10.0888i | −0.195576 | + | 0.338748i | −0.947089 | − | 0.320970i | \(-0.895991\pi\) |
0.751513 | + | 0.659718i | \(0.229324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.3248 | + | 46.9668i | 1.08414 | + | 1.57522i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.82475 | − | 6.62466i | −0.127990 | − | 0.221686i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19934 | 0.207221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.13746 | + | 1.97014i | 0.0379364 | + | 0.0657077i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.45017 | − | 5.97586i | 0.114942 | − | 0.199085i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.17525 | + | 14.1599i | −0.271754 | + | 0.470693i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.6375 | + | 32.2810i | 0.618847 | + | 1.07187i | 0.989697 | + | 0.143181i | \(0.0457331\pi\) |
−0.370850 | + | 0.928693i | \(0.620934\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.8488 | 1.71783 | 0.858914 | − | 0.512119i | \(-0.171139\pi\) | ||||
0.858914 | + | 0.512119i | \(0.171139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.587624 | − | 1.01779i | −0.0194475 | − | 0.0336841i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.725083 | − | 0.0575438i | 0.0239443 | − | 0.00190027i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.91238 | + | 17.1687i | −0.326979 | + | 0.566344i | −0.981911 | − | 0.189344i | \(-0.939364\pi\) |
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.54983 | 0.0839288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.0241 | 2.30238 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0997 | − | 17.4931i | 0.331359 | − | 0.573931i | −0.651419 | − | 0.758718i | \(-0.725826\pi\) |
0.982779 | + | 0.184787i | \(0.0591594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.62541 | − | 6.92820i | −0.184365 | − | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.5498 | − | 63.3062i | −1.19531 | − | 2.07033i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.0997 | 0.787302 | 0.393651 | − | 0.919260i | \(-0.371212\pi\) | ||||
0.393651 | + | 0.919260i | \(0.371212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.5876 | + | 25.2665i | 0.475543 | + | 0.823665i | 0.999608 | − | 0.0280140i | \(-0.00891829\pi\) |
−0.524065 | + | 0.851679i | \(0.675585\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0997 | + | 36.5457i | −0.687100 | + | 1.19009i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2749 | + | 29.9210i | −0.561359 | + | 0.972303i | 0.436019 | + | 0.899938i | \(0.356388\pi\) |
−0.997378 | + | 0.0723654i | \(0.976945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.08762 | + | 3.61587i | 0.0677671 | + | 0.117376i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3505 | −0.335285 | −0.167643 | − | 0.985848i | \(-0.553616\pi\) | ||||
−0.167643 | + | 0.985848i | \(0.553616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5498 | − | 39.0575i | −0.729696 | − | 1.26387i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.8248 | − | 39.5336i | 0.607883 | − | 1.27661i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66.4743 | 2.13988 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.4502 | −1.23647 | −0.618237 | − | 0.785992i | \(-0.712153\pi\) | ||||
−0.618237 | + | 0.785992i | \(0.712153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.7870 | + | 36.0041i | −0.667085 | + | 1.15543i | 0.311630 | + | 0.950204i | \(0.399125\pi\) |
−0.978715 | + | 0.205222i | \(0.934208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.08762 | − | 1.58028i | −0.0348676 | − | 0.0506615i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.5498 | + | 33.8613i | 0.625455 | + | 1.08332i | 0.988453 | + | 0.151529i | \(0.0484198\pi\) |
−0.362998 | + | 0.931790i | \(0.618247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.4502 | −0.621630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6495 | − | 44.4262i | −0.818092 | − | 1.41698i | −0.907086 | − | 0.420945i | \(-0.861699\pi\) |
0.0889941 | − | 0.996032i | \(-0.471635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.3746 | + | 61.2706i | −1.12713 | + | 1.95224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5498 | + | 25.2011i | −0.462658 | + | 0.801347i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.04983 | − | 13.9427i | −0.255711 | − | 0.442905i | 0.709377 | − | 0.704829i | \(-0.248976\pi\) |
−0.965089 | + | 0.261924i | \(0.915643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 107.299 | 3.40161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0876 | + | 19.2043i | 0.351149 | + | 0.608207i | 0.986451 | − | 0.164056i | \(-0.0524579\pi\) |
−0.635302 | + | 0.772263i | \(0.719125\pi\) | |||||||
\(998\) | 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 twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.q.c.25.2 | ✓ | 4 | 21.11 | odd | 6 | ||
168.2.q.c.121.2 | yes | 4 | 3.2 | odd | 2 | ||
336.2.q.g.193.2 | 4 | 84.11 | even | 6 | |||
336.2.q.g.289.2 | 4 | 12.11 | even | 2 | |||
504.2.s.i.289.1 | 4 | 1.1 | even | 1 | trivial | ||
504.2.s.i.361.1 | 4 | 7.4 | even | 3 | inner | ||
1008.2.s.r.289.1 | 4 | 4.3 | odd | 2 | |||
1008.2.s.r.865.1 | 4 | 28.11 | odd | 6 | |||
1176.2.a.k.1.1 | 2 | 21.2 | odd | 6 | |||
1176.2.a.n.1.2 | 2 | 21.5 | even | 6 | |||
1176.2.q.l.361.1 | 4 | 21.17 | even | 6 | |||
1176.2.q.l.961.1 | 4 | 21.20 | even | 2 | |||
1344.2.q.w.193.1 | 4 | 168.53 | odd | 6 | |||
1344.2.q.w.961.1 | 4 | 24.5 | odd | 2 | |||
1344.2.q.x.193.1 | 4 | 168.11 | even | 6 | |||
1344.2.q.x.961.1 | 4 | 24.11 | even | 2 | |||
2352.2.a.ba.1.2 | 2 | 84.47 | odd | 6 | |||
2352.2.a.bf.1.1 | 2 | 84.23 | even | 6 | |||
2352.2.q.bf.961.1 | 4 | 84.83 | odd | 2 | |||
2352.2.q.bf.1537.1 | 4 | 84.59 | odd | 6 | |||
3528.2.a.bd.1.1 | 2 | 7.5 | odd | 6 | |||
3528.2.a.bk.1.2 | 2 | 7.2 | even | 3 | |||
3528.2.s.bk.361.2 | 4 | 7.3 | odd | 6 | |||
3528.2.s.bk.3313.2 | 4 | 7.6 | odd | 2 | |||
7056.2.a.ch.1.1 | 2 | 28.19 | even | 6 | |||
7056.2.a.cu.1.2 | 2 | 28.23 | odd | 6 | |||
9408.2.a.dj.1.1 | 2 | 168.5 | even | 6 | |||
9408.2.a.dp.1.2 | 2 | 168.107 | even | 6 | |||
9408.2.a.dw.1.1 | 2 | 168.131 | odd | 6 | |||
9408.2.a.ec.1.2 | 2 | 168.149 | odd | 6 |