Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(361,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.39040727770\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-1.63746 - 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.361 |
Dual form | 1176.2.q.l.961.1 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.13746 | − | 3.70219i | −0.955901 | − | 1.65567i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
−0.223607 | − | 0.974679i | \(-0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.13746 | − | 3.70219i | 0.644468 | − | 1.11625i | −0.339956 | − | 0.940441i | \(-0.610412\pi\) |
0.984424 | − | 0.175810i | \(-0.0562545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.27492 | 0.353598 | 0.176799 | − | 0.984247i | \(-0.443426\pi\) | ||||
0.176799 | + | 0.984247i | \(0.443426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.27492 | 1.10378 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.637459 | + | 1.10411i | 0.146243 | + | 0.253300i | 0.929836 | − | 0.367974i | \(-0.119949\pi\) |
−0.783593 | + | 0.621275i | \(0.786615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.63746 | + | 11.4964i | −1.32749 | + | 2.29928i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27492 | −0.422442 | −0.211221 | − | 0.977438i | \(-0.567744\pi\) | ||||
−0.211221 | + | 0.977438i | \(0.567744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.0898027 | + | 0.155543i | −0.907428 | − | 0.420208i | \(-0.861957\pi\) |
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.13746 | + | 3.70219i | 0.372084 | + | 0.644468i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.63746 | − | 4.56821i | −0.433596 | − | 0.751009i | 0.563584 | − | 0.826059i | \(-0.309422\pi\) |
−0.997180 | + | 0.0750491i | \(0.976089\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.637459 | + | 1.10411i | −0.102075 | + | 0.176799i | ||||
\(40\) | 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 | ||||||||
\(45\) | −2.13746 | + | 3.70219i | −0.318634 | + | 0.551889i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.862541 | + | 1.49397i | −0.118479 | + | 0.205212i | −0.919165 | − | 0.393872i | \(-0.871135\pi\) |
0.800686 | + | 0.599084i | \(0.204469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.2749 | −2.46419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.27492 | −0.168867 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13746 | − | 5.43424i | 0.408462 | − | 0.707477i | −0.586255 | − | 0.810126i | \(-0.699398\pi\) |
0.994718 | + | 0.102649i | \(0.0327318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 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 | −0.998009 | − | 0.0630678i | \(-0.979912\pi\) |
0.553623 | + | 0.832767i | \(0.313245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.63746 | − | 2.83616i | 0.191650 | − | 0.331948i | −0.754147 | − | 0.656705i | \(-0.771949\pi\) |
0.945797 | + | 0.324758i | \(0.105283\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.63746 | − | 11.4964i | −0.766428 | − | 1.32749i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77492 | + | 3.07425i | 0.199694 | + | 0.345880i | 0.948429 | − | 0.316989i | \(-0.102672\pi\) |
−0.748735 | + | 0.662869i | \(0.769339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | 1.13746 | − | 1.97014i | 0.121948 | − | 0.211221i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.27492 | + | 3.94027i | 0.241141 | + | 0.417668i | 0.961040 | − | 0.276411i | \(-0.0891451\pi\) |
−0.719899 | + | 0.694079i | \(0.755812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.500000 | − | 0.866025i | −0.0518476 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.72508 | − | 4.71998i | 0.279588 | − | 0.484260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2749 | −1.65247 | −0.826234 | − | 0.563327i | \(-0.809521\pi\) | ||||
−0.826234 | + | 0.563327i | \(0.809521\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.27492 | −0.429645 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.91238 | − | 10.2405i | −0.582564 | − | 1.00903i | −0.995174 | − | 0.0981224i | \(-0.968716\pi\) |
0.412611 | − | 0.910907i | \(-0.364617\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.41238 | − | 5.91041i | −0.329887 | − | 0.571381i | 0.652602 | − | 0.757701i | \(-0.273677\pi\) |
−0.982489 | + | 0.186320i | \(0.940344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.91238 | − | 5.04438i | 0.278955 | − | 0.483164i | −0.692170 | − | 0.721734i | \(-0.743345\pi\) |
0.971125 | + | 0.238570i | \(0.0766786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.27492 | 0.500673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5498 | 0.992445 | 0.496222 | − | 0.868195i | \(-0.334720\pi\) | ||||
0.496222 | + | 0.868195i | \(0.334720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.54983 | + | 14.8087i | −0.797276 | + | 1.38092i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.637459 | − | 1.10411i | −0.0589331 | − | 0.102075i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.63746 | − | 6.30026i | −0.330678 | − | 0.572751i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.27492 | − | 9.13642i | 0.475623 | − | 0.823804i | ||||
\(124\) | 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 | ||||||||
\(129\) | 3.63746 | − | 6.30026i | 0.320260 | − | 0.554707i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.137459 | − | 0.238085i | −0.0120098 | − | 0.0208016i | 0.859958 | − | 0.510365i | \(-0.170490\pi\) |
−0.871968 | + | 0.489563i | \(0.837156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13746 | − | 3.70219i | −0.183963 | − | 0.318634i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.27492 | + | 14.3326i | −0.706974 | + | 1.22451i | 0.259001 | + | 0.965877i | \(0.416607\pi\) |
−0.965974 | + | 0.258638i | \(0.916726\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.725083 | −0.0615007 | −0.0307504 | − | 0.999527i | \(-0.509790\pi\) | ||||
−0.0307504 | + | 0.999527i | \(0.509790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 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 | \(-0.173836\pi\) |
−0.877067 | + | 0.480368i | \(0.840503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.68729 | − | 13.3148i | 0.625583 | − | 1.08354i | −0.362845 | − | 0.931850i | \(-0.618194\pi\) |
0.988428 | − | 0.151692i | \(-0.0484722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.27492 | 0.343370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.27492 | − | 12.6005i | 0.580602 | − | 1.00563i | −0.414807 | − | 0.909910i | \(-0.636151\pi\) |
0.995408 | − | 0.0957218i | \(-0.0305159\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.862541 | − | 1.49397i | −0.0684040 | − | 0.118479i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 10.3923i | 0.469956 | + | 0.813988i | 0.999410 | − | 0.0343508i | \(-0.0109363\pi\) |
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.13746 | − | 15.8265i | 0.711350 | − | 1.23209i | ||||
\(166\) | 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 | ||||||||
\(171\) | 0.637459 | − | 1.10411i | 0.0487477 | − | 0.0844335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.72508 | − | 6.45203i | −0.283213 | − | 0.490539i | 0.688961 | − | 0.724798i | \(-0.258067\pi\) |
−0.972174 | + | 0.234259i | \(0.924734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.13746 | + | 5.43424i | 0.235826 | + | 0.408462i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.725083 | − | 1.25588i | 0.0541952 | − | 0.0938689i | −0.837655 | − | 0.546200i | \(-0.816074\pi\) |
0.891850 | + | 0.452331i | \(0.149407\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.82475 | −0.284292 | −0.142146 | − | 0.989846i | \(-0.545400\pi\) | ||||
−0.142146 | + | 0.989846i | \(0.545400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 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 | \(-0.0420124\pi\) |
−0.609623 | + | 0.792692i | \(0.708679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.77492 | + | 13.4666i | −0.559651 | + | 0.969344i | 0.437875 | + | 0.899036i | \(0.355731\pi\) |
−0.997525 | + | 0.0703075i | \(0.977602\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.45017 | 0.390294 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.5498 | −1.17913 | −0.589563 | − | 0.807722i | \(-0.700700\pi\) | ||||
−0.589563 | + | 0.807722i | \(0.700700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5498 | − | 21.7370i | 0.889634 | − | 1.54089i | 0.0493259 | − | 0.998783i | \(-0.484293\pi\) |
0.840308 | − | 0.542109i | \(-0.182374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.63746 | − | 6.30026i | −0.256567 | − | 0.444386i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.5498 | + | 39.0575i | 1.57495 | + | 2.72789i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | + | 3.46410i | −0.139010 | + | 0.240772i | ||||
\(208\) | 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 | ||||||||
\(213\) | −1.00000 | + | 1.73205i | −0.0685189 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.5498 | + | 26.9331i | 1.06049 | + | 1.83682i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.63746 | + | 2.83616i | 0.110649 | + | 0.191650i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.54983 | + | 4.41644i | −0.171520 | + | 0.297082i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.27492 | −0.420200 | −0.210100 | − | 0.977680i | \(-0.567379\pi\) | ||||
−0.210100 | + | 0.977680i | \(0.567379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.2749 | 0.884994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.86254 | + | 3.22602i | −0.123621 | + | 0.214118i | −0.921193 | − | 0.389106i | \(-0.872784\pi\) |
0.797572 | + | 0.603224i | \(0.206117\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.36254 | + | 9.28819i | 0.354367 | + | 0.613781i | 0.987009 | − | 0.160663i | \(-0.0513631\pi\) |
−0.632643 | + | 0.774444i | \(0.718030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.27492 | − | 12.6005i | −0.476596 | − | 0.825488i | 0.523045 | − | 0.852305i | \(-0.324796\pi\) |
−0.999640 | + | 0.0268173i | \(0.991463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8248 | + | 22.2131i | −0.836595 | + | 1.44902i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.54983 | −0.230587 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.5498 | 1.97610 | 0.988052 | − | 0.154119i | \(-0.0492540\pi\) | ||||
0.988052 | + | 0.154119i | \(0.0492540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.41238 | + | 11.1066i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976343i | \(-0.968872\pi\) |
0.582165 | + | 0.813071i | \(0.302206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.812707 | + | 1.40765i | 0.0517113 | + | 0.0895666i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.137459 | + | 0.238085i | −0.00871109 | + | 0.0150880i | ||||
\(250\) | 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 | ||||||||
\(255\) | −8.54983 | + | 14.8087i | −0.535411 | + | 0.927360i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.54983 | − | 16.5408i | −0.595702 | − | 1.03179i | −0.993447 | − | 0.114291i | \(-0.963540\pi\) |
0.397745 | − | 0.917496i | \(-0.369793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.13746 | + | 1.97014i | 0.0704069 | + | 0.121948i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2749 | − | 21.2608i | 0.756904 | − | 1.31100i | −0.187518 | − | 0.982261i | \(-0.560044\pi\) |
0.944422 | − | 0.328735i | \(-0.106622\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.37459 | 0.453017 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.54983 | −0.278445 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1375 | − | 24.4868i | 0.861976 | − | 1.49299i | −0.00804266 | − | 0.999968i | \(-0.502560\pi\) |
0.870019 | − | 0.493019i | \(-0.164107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.13746 | − | 5.43424i | −0.190587 | − | 0.330106i | 0.754858 | − | 0.655888i | \(-0.227706\pi\) |
−0.945445 | + | 0.325782i | \(0.894372\pi\) | |||||||
\(272\) | 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 | −0.796469 | − | 0.604679i | \(-0.793301\pi\) |
0.921902 | + | 0.387423i | \(0.126635\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4502 | −0.683060 | −0.341530 | − | 0.939871i | \(-0.610945\pi\) | ||||
−0.341530 | + | 0.939871i | \(0.610945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4622 | − | 23.3172i | 0.800245 | − | 1.38607i | −0.119209 | − | 0.992869i | \(-0.538036\pi\) |
0.919454 | − | 0.393196i | \(-0.128631\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.72508 | + | 4.71998i | 0.161420 | + | 0.279588i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.13746 | − | 14.0945i | 0.477026 | − | 0.826234i | ||||
\(292\) | 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 | ||||||||
\(297\) | 2.13746 | − | 3.70219i | 0.124028 | − | 0.214823i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.54983 | − | 4.41644i | −0.147461 | − | 0.255409i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | − | 5.19615i | −0.172345 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.3746 | − | 37.0219i | 1.22391 | − | 2.11987i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3746 | 1.50528 | 0.752639 | − | 0.658434i | \(-0.228781\pi\) | ||||
0.752639 | + | 0.658434i | \(0.228781\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.8248 | 0.672687 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.27492 | − | 9.13642i | 0.299113 | − | 0.518079i | −0.676820 | − | 0.736148i | \(-0.736643\pi\) |
0.975933 | + | 0.218069i | \(0.0699759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.22508 | − | 3.85396i | −0.125769 | − | 0.217838i | 0.796264 | − | 0.604949i | \(-0.206807\pi\) |
−0.922033 | + | 0.387111i | \(0.873473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.58762 | + | 4.48190i | 0.145335 | + | 0.251728i | 0.929498 | − | 0.368827i | \(-0.120241\pi\) |
−0.784163 | + | 0.620555i | \(0.786907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.86254 | + | 8.42217i | −0.272250 | + | 0.471551i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.82475 | 0.380920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.09967 | −0.283753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.46221 | + | 14.6570i | −0.469399 | + | 0.813023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.91238 | + | 5.04438i | 0.161055 | + | 0.278955i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9124 | − | 20.6328i | −0.654763 | − | 1.13408i | −0.981953 | − | 0.189125i | \(-0.939435\pi\) |
0.327190 | − | 0.944959i | \(-0.393898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.63746 | + | 4.56821i | −0.144532 | + | 0.250336i | ||||
\(334\) | 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 | ||||||||
\(339\) | −5.27492 | + | 9.13642i | −0.286494 | + | 0.496222i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.13746 | + | 3.70219i | 0.115750 | + | 0.200485i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.54983 | − | 14.8087i | −0.460308 | − | 0.797276i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0997 | − | 26.1534i | 0.810593 | − | 1.40399i | −0.101857 | − | 0.994799i | \(-0.532478\pi\) |
0.912450 | − | 0.409189i | \(-0.134188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.27492 | 0.0680500 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.72508 | + | 4.71998i | −0.145042 | + | 0.251219i | −0.929388 | − | 0.369103i | \(-0.879665\pi\) |
0.784347 | + | 0.620322i | \(0.212998\pi\) | |||||||
\(354\) | 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 | −0.975920 | − | 0.218128i | \(-0.930005\pi\) |
0.299056 | − | 0.954236i | \(-0.403328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68729 | − | 15.0468i | 0.457226 | − | 0.791939i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.27492 | 0.381834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.04983 | + | 7.01452i | −0.211400 | + | 0.366155i | −0.952153 | − | 0.305622i | \(-0.901135\pi\) |
0.740753 | + | 0.671777i | \(0.234469\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.27492 | + | 9.13642i | 0.274601 | + | 0.475623i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.637459 | − | 1.10411i | −0.0330064 | − | 0.0571687i | 0.849050 | − | 0.528312i | \(-0.177175\pi\) |
−0.882057 | + | 0.471143i | \(0.843841\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.6873 | + | 30.6353i | −0.913368 | + | 1.58200i | ||||
\(376\) | 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 | ||||||||
\(381\) | 10.7749 | − | 18.6627i | 0.552016 | − | 0.956119i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.27492 | − | 3.94027i | −0.116243 | − | 0.201339i | 0.802033 | − | 0.597280i | \(-0.203752\pi\) |
−0.918276 | + | 0.395941i | \(0.870418\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.63746 | + | 6.30026i | 0.184902 | + | 0.320260i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00000 | − | 1.73205i | 0.0507020 | − | 0.0878185i | −0.839561 | − | 0.543266i | \(-0.817187\pi\) |
0.890263 | + | 0.455448i | \(0.150521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.274917 | 0.0138677 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.58762 | − | 13.1422i | 0.381775 | − | 0.661253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.1873 | + | 29.7693i | 0.862606 | + | 1.49408i | 0.869405 | + | 0.494100i | \(0.164502\pi\) |
−0.00679974 | + | 0.999977i | \(0.502164\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.637459 | + | 1.10411i | −0.0317541 | + | 0.0549997i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.27492 | 0.212422 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.5498 | −1.11775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7749 | − | 22.1268i | 0.631679 | − | 1.09410i | −0.355529 | − | 0.934665i | \(-0.615699\pi\) |
0.987208 | − | 0.159435i | \(-0.0509673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.27492 | − | 14.3326i | −0.408172 | − | 0.706974i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.587624 | − | 1.01779i | −0.0288453 | − | 0.0499616i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.362541 | − | 0.627940i | 0.0177537 | − | 0.0307504i | ||||
\(418\) | 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 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.5498 | − | 45.9857i | −1.28786 | − | 2.23063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.72508 | + | 4.71998i | 0.131568 | + | 0.227883i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.8248 | + | 23.9452i | −0.665915 | + | 1.15340i | 0.313122 | + | 0.949713i | \(0.398625\pi\) |
−0.979036 | + | 0.203685i | \(0.934708\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8248 | −1.24106 | −0.620529 | − | 0.784183i | \(-0.713082\pi\) | ||||
−0.620529 | + | 0.784183i | \(0.713082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.72508 | −0.466282 | ||||||||
\(436\) | 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 | \(-0.0921147\pi\) |
−0.726343 | + | 0.687333i | \(0.758781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6873 | − | 27.1712i | −0.745326 | − | 1.29094i | −0.950042 | − | 0.312121i | \(-0.898961\pi\) |
0.204717 | − | 0.978821i | \(-0.434373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.72508 | − | 16.8443i | 0.461013 | − | 0.798498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.549834 | 0.0260063 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.45017 | 0.257209 | 0.128605 | − | 0.991696i | \(-0.458950\pi\) | ||||
0.128605 | + | 0.991696i | \(0.458950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5498 | + | 39.0575i | −1.06183 | + | 1.83914i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.68729 | + | 13.3148i | 0.361181 | + | 0.625583i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.32475 | + | 7.49069i | 0.202303 | + | 0.350400i | 0.949270 | − | 0.314462i | \(-0.101824\pi\) |
−0.746967 | + | 0.664861i | \(0.768491\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 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 | ||||||||
\(465\) | −2.13746 | + | 3.70219i | −0.0991223 | + | 0.171685i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7251 | + | 22.0405i | 0.588847 | + | 1.01991i | 0.994384 | + | 0.105834i | \(0.0337511\pi\) |
−0.405537 | + | 0.914079i | \(0.632916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.27492 | + | 12.6005i | 0.335210 | + | 0.580602i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.5498 | + | 26.9331i | −0.714982 | + | 1.23839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9244 | −0.776546 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.72508 | 0.0789861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2749 | + | 17.7967i | −0.469473 | + | 0.813151i | −0.999391 | − | 0.0348979i | \(-0.988889\pi\) |
0.529918 | + | 0.848049i | \(0.322223\pi\) | |||||||
\(480\) | 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 | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9244 | −0.718659 | −0.359330 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.54983 | − | 7.88054i | 0.204914 | − | 0.354922i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.13746 | + | 15.8265i | 0.410698 | + | 0.711350i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3625 | − | 21.4125i | −0.553423 | − | 0.958557i | −0.998024 | − | 0.0628286i | \(-0.979988\pi\) |
0.444601 | − | 0.895729i | \(-0.353345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.00000 | + | 5.19615i | −0.134030 | + | 0.232147i | ||||
\(502\) | 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 | ||||||||
\(507\) | 5.68729 | − | 9.85068i | 0.252582 | − | 0.437484i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.86254 | − | 3.22602i | −0.0825557 | − | 0.142991i | 0.821791 | − | 0.569789i | \(-0.192975\pi\) |
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.637459 | + | 1.10411i | 0.0281445 | + | 0.0487477i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.2749 | + | 43.7774i | −1.11375 | + | 1.92906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.6495 | −1.12806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.45017 | 0.327026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.274917 | − | 0.476171i | 0.0120443 | − | 0.0208614i | −0.859940 | − | 0.510394i | \(-0.829499\pi\) |
0.871985 | + | 0.489533i | \(0.162833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6375 | − | 21.8887i | −0.552597 | − | 0.957127i | −0.998086 | − | 0.0618393i | \(-0.980303\pi\) |
0.445489 | − | 0.895288i | \(-0.353030\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | −6.27492 | −0.272308 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.4502 | −0.582591 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5876 | + | 25.2665i | −0.630678 | + | 1.09237i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.725083 | + | 1.25588i | 0.0312896 | + | 0.0541952i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.362541 | + | 0.627940i | 0.0155869 | + | 0.0269973i | 0.873714 | − | 0.486441i | \(-0.161705\pi\) |
−0.858127 | + | 0.513438i | \(0.828372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.91238 | − | 3.31233i | 0.0820679 | − | 0.142146i | ||||
\(544\) | 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 | ||||||||
\(549\) | 5.00000 | − | 8.66025i | 0.213395 | − | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.45017 | − | 2.51176i | −0.0617791 | − | 0.107005i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.2749 | − | 19.5287i | −0.478594 | − | 0.828948i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.58762 | − | 6.21395i | 0.152013 | − | 0.263293i | −0.779955 | − | 0.625836i | \(-0.784758\pi\) |
0.931967 | + | 0.362543i | \(0.118091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.27492 | −0.392287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0997 | −0.721949 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.86254 | − | 6.69012i | 0.162787 | − | 0.281955i | −0.773080 | − | 0.634308i | \(-0.781285\pi\) |
0.935867 | + | 0.352353i | \(0.114618\pi\) | |||||||
\(564\) | 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 | −0.997784 | − | 0.0665355i | \(-0.978805\pi\) |
0.441271 | − | 0.897374i | \(-0.354528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.362541 | + | 0.627940i | −0.0151719 | + | 0.0262785i | −0.873512 | − | 0.486803i | \(-0.838163\pi\) |
0.858340 | + | 0.513082i | \(0.171496\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.5498 | −0.440726 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.0997 | 2.21441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5000 | + | 21.6506i | −0.520382 | + | 0.901328i | 0.479337 | + | 0.877631i | \(0.340877\pi\) |
−0.999719 | + | 0.0236970i | \(0.992456\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.77492 | − | 13.4666i | −0.323115 | − | 0.559651i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.68729 | + | 6.38658i | 0.152712 | + | 0.264505i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.72508 | + | 4.71998i | −0.112668 | + | 0.195147i | ||||
\(586\) | 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 | ||||||||
\(591\) | 8.27492 | − | 14.3326i | 0.340385 | − | 0.589563i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.27492 | + | 12.6005i | 0.298745 | + | 0.517442i | 0.975849 | − | 0.218446i | \(-0.0700986\pi\) |
−0.677104 | + | 0.735887i | \(0.736765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.5498 | + | 21.7370i | 0.513631 | + | 0.889634i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.72508 | + | 6.45203i | −0.152203 | + | 0.263623i | −0.932037 | − | 0.362363i | \(-0.881970\pi\) |
0.779834 | + | 0.625986i | \(0.215303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0997 | 1.06463 | 0.532314 | − | 0.846547i | \(-0.321323\pi\) | ||||
0.532314 | + | 0.846547i | \(0.321323\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.27492 | 0.296258 | ||||||||
\(604\) | 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 | \(-0.212039\pi\) |
−0.928272 | + | 0.371901i | \(0.878706\pi\) | |||||||
\(608\) | 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 | −0.924552 | − | 0.381055i | \(-0.875561\pi\) |
0.792280 | + | 0.610158i | \(0.208894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −45.0997 | −1.81859 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.08762 | − | 5.34792i | 0.124102 | − | 0.214951i | −0.797280 | − | 0.603610i | \(-0.793728\pi\) |
0.921382 | + | 0.388659i | \(0.127062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −42.4244 | − | 73.4813i | −1.69698 | − | 2.93925i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.72508 | + | 4.71998i | −0.108829 | + | 0.188498i | ||||
\(628\) | 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 | ||||||||
\(633\) | −8.82475 | + | 15.2849i | −0.350752 | + | 0.607521i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.0619 | + | 79.7815i | 1.82791 | + | 3.16603i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8248 | + | 36.0695i | −0.822528 | + | 1.42466i | 0.0812655 | + | 0.996692i | \(0.474104\pi\) |
−0.903794 | + | 0.427968i | \(0.859230\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.3746 | 1.27673 | 0.638365 | − | 0.769734i | \(-0.279611\pi\) | ||||
0.638365 | + | 0.769734i | \(0.279611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.0997 | −1.22455 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0000 | + | 29.4449i | −0.668339 | + | 1.15760i | 0.310029 | + | 0.950727i | \(0.399661\pi\) |
−0.978368 | + | 0.206870i | \(0.933672\pi\) | |||||||
\(648\) | 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 | −0.829309 | − | 0.558790i | \(-0.811266\pi\) |
−0.0692713 | − | 0.997598i | \(-0.522067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.587624 | + | 1.01779i | −0.0229604 | + | 0.0397685i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.27492 | −0.127767 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1993 | 0.708946 | 0.354473 | − | 0.935066i | \(-0.384660\pi\) | ||||
0.354473 | + | 0.935066i | \(0.384660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9124 | − | 25.8290i | 0.580024 | − | 1.00463i | −0.415452 | − | 0.909615i | \(-0.636376\pi\) |
0.995476 | − | 0.0950161i | \(-0.0302902\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.54983 | − | 4.41644i | −0.0990274 | − | 0.171520i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.54983 | + | 7.88054i | 0.176170 | + | 0.305136i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.13746 | − | 5.43424i | 0.121301 | − | 0.210100i | ||||
\(670\) | 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 | ||||||||
\(675\) | −6.63746 | + | 11.4964i | −0.255476 | + | 0.442497i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.86254 | − | 4.95807i | −0.110016 | − | 0.190554i | 0.805760 | − | 0.592242i | \(-0.201757\pi\) |
−0.915777 | + | 0.401688i | \(0.868424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.86254 | − | 3.22602i | −0.0713727 | − | 0.123621i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.4124 | + | 30.1591i | −0.666266 | + | 1.15401i | 0.312674 | + | 0.949860i | \(0.398775\pi\) |
−0.978940 | + | 0.204146i | \(0.934558\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.7492 | 2.70319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7251 | −0.409187 | ||||||||
\(688\) | 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 | \(-0.0944554\pi\) |
−0.731377 | + | 0.681973i | \(0.761122\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 14.5498 | 0.550325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.9244 | 1.50792 | 0.753962 | − | 0.656918i | \(-0.228140\pi\) | ||||
0.753962 | + | 0.656918i | \(0.228140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.36254 | − | 5.82409i | 0.126821 | − | 0.219660i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.8248 | − | 22.2131i | −0.483008 | − | 0.836595i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0997 | − | 27.8854i | −0.604636 | − | 1.04726i | −0.992109 | − | 0.125379i | \(-0.959985\pi\) |
0.387473 | − | 0.921881i | \(-0.373348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.77492 | − | 3.07425i | 0.0665646 | − | 0.115293i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.2990 | −0.871333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2749 | + | 26.4569i | −0.570452 | + | 0.988052i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0997 | − | 27.8854i | −0.600416 | − | 1.03995i | −0.992758 | − | 0.120132i | \(-0.961668\pi\) |
0.392342 | − | 0.919820i | \(-0.371665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.41238 | − | 11.1066i | −0.238479 | − | 0.413057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0997 | − | 26.1534i | 0.560788 | − | 0.971313i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4502 | −0.610103 | −0.305051 | − | 0.952336i | \(-0.598674\pi\) | ||||
−0.305051 | + | 0.952336i | \(0.598674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5498 | − | 25.2011i | 0.538145 | − | 0.932095i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.4622 | − | 40.6377i | −0.866597 | − | 1.50099i | −0.865453 | − | 0.500990i | \(-0.832969\pi\) |
−0.00114334 | − | 0.999999i | \(-0.500364\pi\) | |||||||
\(734\) | 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 | −0.309145 | − | 0.951015i | \(-0.600043\pi\) |
0.978176 | − | 0.207780i | \(-0.0666237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.62541 | −0.0597111 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1993 | 0.594296 | 0.297148 | − | 0.954831i | \(-0.403965\pi\) | ||||
0.297148 | + | 0.954831i | \(0.403965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.17525 | + | 2.03559i | −0.0430578 | + | 0.0745782i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.137459 | − | 0.238085i | −0.00502935 | − | 0.00871109i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7749 | + | 22.1268i | 0.466163 | + | 0.807419i | 0.999253 | − | 0.0386400i | \(-0.0123026\pi\) |
−0.533090 | + | 0.846059i | \(0.678969\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.68729 | − | 16.7789i | 0.353025 | − | 0.611457i | ||||
\(754\) | 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 | ||||||||
\(759\) | 8.54983 | − | 14.8087i | 0.310339 | − | 0.537523i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.54983 | + | 4.41644i | 0.0924314 | + | 0.160096i | 0.908534 | − | 0.417812i | \(-0.137203\pi\) |
−0.816102 | + | 0.577907i | \(0.803869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.54983 | − | 14.8087i | −0.309120 | − | 0.535411i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | − | 6.92820i | 0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6495 | −0.456153 | −0.228076 | − | 0.973643i | \(-0.573244\pi\) | ||||
−0.228076 | + | 0.973643i | \(0.573244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.0997 | 0.687858 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5498 | + | 23.4690i | −0.487354 | + | 0.844121i | −0.999894 | − | 0.0145417i | \(-0.995371\pi\) |
0.512541 | + | 0.858663i | \(0.328704\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | −2.27492 | −0.0812989 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.1993 | −2.21999 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.27492 | + | 10.8685i | −0.223677 | + | 0.387419i | −0.955922 | − | 0.293622i | \(-0.905139\pi\) |
0.732245 | + | 0.681041i | \(0.238473\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.2749 | + | 21.2608i | 0.436999 | + | 0.756904i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.37459 | + | 11.0411i | 0.226368 | + | 0.392081i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.68729 | + | 6.38658i | −0.130775 | + | 0.226509i | ||||
\(796\) | 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 | ||||||||
\(801\) | 2.27492 | − | 3.94027i | 0.0803802 | − | 0.139223i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.00000 | − | 12.1244i | −0.247025 | − | 0.427859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1375 | + | 24.4868i | 0.497662 | + | 0.861976i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.82475 | + | 13.5529i | −0.275104 | + | 0.476493i | −0.970161 | − | 0.242461i | \(-0.922045\pi\) |
0.695058 | + | 0.718954i | \(0.255379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.4502 | 0.963906 | 0.481953 | − | 0.876197i | \(-0.339928\pi\) | ||||
0.481953 | + | 0.876197i | \(0.339928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.27492 | 0.220071 | ||||||||
\(814\) | 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 | \(-0.281777\pi\) |
−0.986912 | + | 0.161261i | \(0.948444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0997 | + | 22.6893i | −0.456626 | + | 0.790899i | −0.998780 | − | 0.0493799i | \(-0.984275\pi\) |
0.542154 | + | 0.840279i | \(0.317609\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −56.7492 | −1.97575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.0241 | 1.35700 | 0.678500 | − | 0.734600i | \(-0.262630\pi\) | ||||
0.678500 | + | 0.734600i | \(0.262630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3625 | − | 19.6805i | 0.394637 | − | 0.683532i | −0.598417 | − | 0.801184i | \(-0.704204\pi\) |
0.993055 | + | 0.117652i | \(0.0375369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.08762 | + | 3.61587i | 0.0724189 | + | 0.125433i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.8248 | − | 22.2131i | −0.443819 | − | 0.768717i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.500000 | + | 0.866025i | −0.0172825 | + | 0.0299342i | ||||
\(838\) | 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 | ||||||||
\(843\) | 5.72508 | − | 9.91613i | 0.197182 | − | 0.341530i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.3127 | + | 42.1108i | 0.836383 | + | 1.44866i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.4622 | + | 23.3172i | 0.462022 | + | 0.800245i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5498 | + | 18.2728i | −0.361644 | + | 0.626385i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3746 | 0.834570 | 0.417285 | − | 0.908776i | \(-0.362982\pi\) | ||||
0.417285 | + | 0.908776i | \(0.362982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.45017 | −0.186392 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2749 | + | 24.7249i | −0.487622 | + | 0.844586i | −0.999899 | − | 0.0142345i | \(-0.995469\pi\) |
0.512277 | + | 0.858820i | \(0.328802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17525 | − | 8.96379i | −0.176577 | − | 0.305841i | 0.764129 | − | 0.645064i | \(-0.223169\pi\) |
−0.940706 | + | 0.339223i | \(0.889836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.54983 | + | 9.61260i | 0.188919 | + | 0.327217i | 0.944890 | − | 0.327388i | \(-0.106168\pi\) |
−0.755971 | + | 0.654605i | \(0.772835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9244 | + | 27.5819i | −0.541447 | + | 0.937813i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.1752 | 0.514785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.63746 | + | 8.03231i | −0.157134 | + | 0.272165i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.13746 | + | 14.0945i | 0.275411 | + | 0.477026i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3746 | + | 24.8975i | 0.485395 | + | 0.840729i | 0.999859 | − | 0.0167828i | \(-0.00534237\pi\) |
−0.514464 | + | 0.857512i | \(0.672009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.58762 | + | 4.48190i | −0.0872784 | + | 0.151171i | ||||
\(880\) | 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 | ||||||||
\(885\) | 13.4124 | − | 23.2309i | 0.450852 | − | 0.780899i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.82475 | − | 10.0888i | −0.195576 | − | 0.338748i | 0.751513 | − | 0.659718i | \(-0.229324\pi\) |
−0.947089 | + | 0.320970i | \(0.895991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.13746 | + | 3.70219i | 0.0716076 | + | 0.124028i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.82475 | − | 6.62466i | 0.127990 | − | 0.221686i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.19934 | −0.207221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.09967 | 0.170273 | ||||||||
\(898\) | 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 | −0.370850 | − | 0.928693i | \(-0.620934\pi\) |
0.989697 | − | 0.143181i | \(-0.0457331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8488 | −1.71783 | −0.858914 | − | 0.512119i | \(-0.828861\pi\) | ||||
−0.858914 | + | 0.512119i | \(0.828861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.587624 | − | 1.01779i | 0.0194475 | − | 0.0336841i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.3746 | + | 37.0219i | 0.706622 | + | 1.22391i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.91238 | − | 17.1687i | −0.326979 | − | 0.566344i | 0.654932 | − | 0.755688i | \(-0.272697\pi\) |
−0.981911 | + | 0.189344i | \(0.939364\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.1873 | + | 22.8411i | −0.434536 | + | 0.752639i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.54983 | 0.0839288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.0241 | 2.30238 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.91238 | + | 10.2405i | −0.194188 | + | 0.336343i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0997 | + | 17.4931i | 0.331359 | + | 0.573931i | 0.982779 | − | 0.184787i | \(-0.0591594\pi\) |
−0.651419 | + | 0.758718i | \(0.725826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.27492 | + | 9.13642i | 0.172693 | + | 0.299113i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.5498 | − | 63.3062i | 1.19531 | − | 2.07033i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0997 | −0.787302 | −0.393651 | − | 0.919260i | \(-0.628788\pi\) | ||||
−0.393651 | + | 0.919260i | \(0.628788\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.45017 | 0.145226 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.5876 | − | 25.2665i | 0.475543 | − | 0.823665i | −0.524065 | − | 0.851679i | \(-0.675585\pi\) |
0.999608 | + | 0.0280140i | \(0.00891829\pi\) | |||||||
\(942\) | 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 | 0.997378 | + | 0.0723654i | \(0.0230548\pi\) |
−0.436019 | + | 0.899938i | \(0.643612\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.08762 | − | 3.61587i | 0.0677671 | − | 0.117376i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.17525 | −0.167819 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3505 | 0.335285 | 0.167643 | − | 0.985848i | \(-0.446384\pi\) | ||||
0.167643 | + | 0.985848i | \(0.446384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5498 | − | 39.0575i | 0.729696 | − | 1.26387i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.86254 | − | 8.42217i | −0.157184 | − | 0.272250i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.41238 | + | 5.91041i | −0.109962 | + | 0.190460i | ||||
\(964\) | 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 | ||||||||
\(969\) | 2.54983 | − | 4.41644i | 0.0819125 | − | 0.141877i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.7870 | − | 36.0041i | −0.667085 | − | 1.15543i | −0.978715 | − | 0.205222i | \(-0.934208\pi\) |
0.311630 | − | 0.950204i | \(-0.399125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.46221 | − | 14.6570i | −0.271008 | − | 0.469399i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5498 | + | 33.8613i | −0.625455 | + | 1.08332i | 0.362998 | + | 0.931790i | \(0.381753\pi\) |
−0.988453 | + | 0.151529i | \(0.951580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.4502 | 0.621630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.82475 | −0.185970 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6495 | + | 44.4262i | −0.818092 | + | 1.41698i | 0.0889941 | + | 0.996032i | \(0.471635\pi\) |
−0.907086 | + | 0.420945i | \(0.861699\pi\) | |||||||
\(984\) | 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 | −0.965089 | − | 0.261924i | \(-0.915643\pi\) |
0.709377 | + | 0.704829i | \(0.248976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.8248 | 0.756056 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −107.299 | −3.40161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0876 | + | 19.2043i | −0.351149 | + | 0.608207i | −0.986451 | − | 0.164056i | \(-0.947542\pi\) |
0.635302 | + | 0.772263i | \(0.280875\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.63746 | − | 4.56821i | −0.0834455 | − | 0.144532i |
(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 | 1176.2.q.l.361.1 | 4 | ||
3.2 | odd | 2 | 3528.2.s.bk.361.2 | 4 | |||
4.3 | odd | 2 | 2352.2.q.bf.1537.1 | 4 | |||
7.2 | even | 3 | inner | 1176.2.q.l.961.1 | 4 | ||
7.3 | odd | 6 | 1176.2.a.k.1.1 | 2 | |||
7.4 | even | 3 | 1176.2.a.n.1.2 | 2 | |||
7.5 | odd | 6 | 168.2.q.c.121.2 | yes | 4 | ||
7.6 | odd | 2 | 168.2.q.c.25.2 | ✓ | 4 | ||
21.2 | odd | 6 | 3528.2.s.bk.3313.2 | 4 | |||
21.5 | even | 6 | 504.2.s.i.289.1 | 4 | |||
21.11 | odd | 6 | 3528.2.a.bd.1.1 | 2 | |||
21.17 | even | 6 | 3528.2.a.bk.1.2 | 2 | |||
21.20 | even | 2 | 504.2.s.i.361.1 | 4 | |||
28.3 | even | 6 | 2352.2.a.bf.1.1 | 2 | |||
28.11 | odd | 6 | 2352.2.a.ba.1.2 | 2 | |||
28.19 | even | 6 | 336.2.q.g.289.2 | 4 | |||
28.23 | odd | 6 | 2352.2.q.bf.961.1 | 4 | |||
28.27 | even | 2 | 336.2.q.g.193.2 | 4 | |||
56.3 | even | 6 | 9408.2.a.dp.1.2 | 2 | |||
56.5 | odd | 6 | 1344.2.q.w.961.1 | 4 | |||
56.11 | odd | 6 | 9408.2.a.dw.1.1 | 2 | |||
56.13 | odd | 2 | 1344.2.q.w.193.1 | 4 | |||
56.19 | even | 6 | 1344.2.q.x.961.1 | 4 | |||
56.27 | even | 2 | 1344.2.q.x.193.1 | 4 | |||
56.45 | odd | 6 | 9408.2.a.ec.1.2 | 2 | |||
56.53 | even | 6 | 9408.2.a.dj.1.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.ch.1.1 | 2 | |||
84.47 | odd | 6 | 1008.2.s.r.289.1 | 4 | |||
84.59 | odd | 6 | 7056.2.a.cu.1.2 | 2 | |||
84.83 | odd | 2 | 1008.2.s.r.865.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.q.c.25.2 | ✓ | 4 | 7.6 | odd | 2 | ||
168.2.q.c.121.2 | yes | 4 | 7.5 | odd | 6 | ||
336.2.q.g.193.2 | 4 | 28.27 | even | 2 | |||
336.2.q.g.289.2 | 4 | 28.19 | even | 6 | |||
504.2.s.i.289.1 | 4 | 21.5 | even | 6 | |||
504.2.s.i.361.1 | 4 | 21.20 | even | 2 | |||
1008.2.s.r.289.1 | 4 | 84.47 | odd | 6 | |||
1008.2.s.r.865.1 | 4 | 84.83 | odd | 2 | |||
1176.2.a.k.1.1 | 2 | 7.3 | odd | 6 | |||
1176.2.a.n.1.2 | 2 | 7.4 | even | 3 | |||
1176.2.q.l.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1176.2.q.l.961.1 | 4 | 7.2 | even | 3 | inner | ||
1344.2.q.w.193.1 | 4 | 56.13 | odd | 2 | |||
1344.2.q.w.961.1 | 4 | 56.5 | odd | 6 | |||
1344.2.q.x.193.1 | 4 | 56.27 | even | 2 | |||
1344.2.q.x.961.1 | 4 | 56.19 | even | 6 | |||
2352.2.a.ba.1.2 | 2 | 28.11 | odd | 6 | |||
2352.2.a.bf.1.1 | 2 | 28.3 | even | 6 | |||
2352.2.q.bf.961.1 | 4 | 28.23 | odd | 6 | |||
2352.2.q.bf.1537.1 | 4 | 4.3 | odd | 2 | |||
3528.2.a.bd.1.1 | 2 | 21.11 | odd | 6 | |||
3528.2.a.bk.1.2 | 2 | 21.17 | even | 6 | |||
3528.2.s.bk.361.2 | 4 | 3.2 | odd | 2 | |||
3528.2.s.bk.3313.2 | 4 | 21.2 | odd | 6 | |||
7056.2.a.ch.1.1 | 2 | 84.11 | even | 6 | |||
7056.2.a.cu.1.2 | 2 | 84.59 | odd | 6 | |||
9408.2.a.dj.1.1 | 2 | 56.53 | even | 6 | |||
9408.2.a.dp.1.2 | 2 | 56.3 | even | 6 | |||
9408.2.a.dw.1.1 | 2 | 56.11 | odd | 6 | |||
9408.2.a.ec.1.2 | 2 | 56.45 | odd | 6 |