Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(17,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.cx (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Character | \(\chi\) | \(=\) | 1512.17 |
Dual form | 1512.2.cx.a.89.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −3.53401 | −1.58046 | −0.790229 | − | 0.612812i | \(-0.790038\pi\) | ||||
−0.790229 | + | 0.612812i | \(0.790038\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30083 | + | 2.30388i | 0.491667 | + | 0.870783i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.81827i | − | 0.548230i | −0.961697 | − | 0.274115i | \(-0.911615\pi\) | ||
0.961697 | − | 0.274115i | \(-0.0883849\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.78280 | + | 1.60665i | 0.771809 | + | 0.445604i | 0.833519 | − | 0.552490i | \(-0.186322\pi\) |
−0.0617107 | + | 0.998094i | \(0.519656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.93434 | − | 5.08242i | 0.711682 | − | 1.23267i | −0.252544 | − | 0.967585i | \(-0.581267\pi\) |
0.964225 | − | 0.265083i | \(-0.0853995\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09143 | + | 1.20749i | −0.479807 | + | 0.277017i | −0.720336 | − | 0.693625i | \(-0.756012\pi\) |
0.240529 | + | 0.970642i | \(0.422679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.84871i | 0.802512i | 0.915966 | + | 0.401256i | \(0.131426\pi\) | ||||
−0.915966 | + | 0.401256i | \(0.868574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.48923 | 1.49785 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.79110 | + | 3.34349i | −1.07538 | + | 0.620871i | −0.929647 | − | 0.368452i | \(-0.879888\pi\) |
−0.145734 | + | 0.989324i | \(0.546554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.21959 | + | 2.43618i | −0.757861 | + | 0.437551i | −0.828527 | − | 0.559949i | \(-0.810821\pi\) |
0.0706663 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.59714 | − | 8.14192i | −0.777059 | − | 1.37624i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.905385 | − | 1.56817i | −0.148844 | − | 0.257806i | 0.781956 | − | 0.623333i | \(-0.214222\pi\) |
−0.930801 | + | 0.365527i | \(0.880889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.03152 | + | 8.71485i | −0.785792 | + | 1.36103i | 0.142733 | + | 0.989761i | \(0.454411\pi\) |
−0.928525 | + | 0.371270i | \(0.878922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.36232 | − | 4.09166i | −0.360251 | − | 0.623973i | 0.627751 | − | 0.778414i | \(-0.283976\pi\) |
−0.988002 | + | 0.154441i | \(0.950642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.96076 | + | 6.86023i | −0.577736 | + | 1.00067i | 0.418003 | + | 0.908446i | \(0.362730\pi\) |
−0.995738 | + | 0.0922218i | \(0.970603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.61569 | + | 5.99390i | −0.516527 | + | 0.856271i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.26517 | − | 1.30780i | −0.311146 | − | 0.179640i | 0.336293 | − | 0.941757i | \(-0.390827\pi\) |
−0.647439 | + | 0.762117i | \(0.724160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.42580i | 0.866454i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.40604 | − | 7.63149i | −0.573618 | − | 0.993535i | −0.996190 | − | 0.0872059i | \(-0.972206\pi\) |
0.422573 | − | 0.906329i | \(-0.361127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.98447 | − | 5.18718i | −1.15034 | − | 0.664151i | −0.201372 | − | 0.979515i | \(-0.564540\pi\) |
−0.948971 | + | 0.315364i | \(0.897873\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.83443 | − | 5.67791i | −1.21981 | − | 0.704258i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.92384 | + | 6.79630i | 0.479374 | + | 0.830300i | 0.999720 | − | 0.0236554i | \(-0.00753044\pi\) |
−0.520346 | + | 0.853955i | \(0.674197\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.62952i | 0.905458i | 0.891648 | + | 0.452729i | \(0.149549\pi\) | ||||
−0.891648 | + | 0.452729i | \(0.850451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7672 | − | 6.79382i | −1.37725 | − | 0.795156i | −0.385423 | − | 0.922740i | \(-0.625945\pi\) |
−0.991828 | + | 0.127584i | \(0.959278\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.18907 | − | 2.36526i | 0.477389 | − | 0.269547i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.921268 | − | 1.59568i | 0.103651 | − | 0.179528i | −0.809535 | − | 0.587071i | \(-0.800281\pi\) |
0.913186 | + | 0.407543i | \(0.133614\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.61748 | + | 9.72975i | 0.616598 | + | 1.06798i | 0.990102 | + | 0.140351i | \(0.0448230\pi\) |
−0.373504 | + | 0.927629i | \(0.621844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3700 | + | 17.9613i | −1.12478 | + | 1.94818i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.89792 | + | 11.9475i | 0.731178 | + | 1.26644i | 0.956380 | + | 0.292125i | \(0.0943624\pi\) |
−0.225202 | + | 0.974312i | \(0.572304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0815748 | + | 8.50119i | −0.00855137 | + | 0.891167i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.39114 | − | 4.26728i | 0.758315 | − | 0.437813i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7982 | + | 7.96638i | −1.40099 | + | 0.808863i | −0.994494 | − | 0.104789i | \(-0.966583\pi\) |
−0.406497 | + | 0.913652i | \(0.633250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1250 | −1.10698 | −0.553489 | − | 0.832856i | \(-0.686704\pi\) | ||||
−0.553489 | + | 0.832856i | \(0.686704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.603028i | − | 0.0594181i | −0.999559 | − | 0.0297091i | \(-0.990542\pi\) | ||
0.999559 | − | 0.0297091i | \(-0.00945808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3342 | − | 6.54381i | 1.09572 | − | 0.632614i | 0.160627 | − | 0.987015i | \(-0.448649\pi\) |
0.935094 | + | 0.354401i | \(0.115315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.37061 | + | 2.37396i | −0.131280 | + | 0.227384i | −0.924170 | − | 0.381981i | \(-0.875242\pi\) |
0.792890 | + | 0.609365i | \(0.208575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.65125 | − | 3.84010i | −0.625697 | − | 0.361246i | 0.153387 | − | 0.988166i | \(-0.450982\pi\) |
−0.779084 | + | 0.626920i | \(0.784315\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.6014i | − | 1.26834i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.5263 | + | 0.148986i | 1.42330 | + | 0.0136575i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.69388 | 0.699444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.79697 | −0.786825 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9246 | 1.59055 | 0.795277 | − | 0.606246i | \(-0.207325\pi\) | ||||
0.795277 | + | 0.606246i | \(0.207325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9707 | −1.48273 | −0.741367 | − | 0.671100i | \(-0.765822\pi\) | ||||
−0.741367 | + | 0.671100i | \(0.765822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50250 | − | 3.24766i | −0.477127 | − | 0.281608i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.56139i | 0.475142i | 0.971370 | + | 0.237571i | \(0.0763512\pi\) | ||||
−0.971370 | + | 0.237571i | \(0.923649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4503 | − | 7.18817i | −1.05602 | − | 0.609693i | −0.131690 | − | 0.991291i | \(-0.542040\pi\) |
−0.924328 | + | 0.381598i | \(0.875374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.92132 | − | 5.05988i | 0.244293 | − | 0.423129i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.4658 | − | 11.8159i | 1.69959 | − | 0.981261i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.42112i | 0.526039i | 0.964791 | + | 0.263019i | \(0.0847184\pi\) | ||||
−0.964791 | + | 0.263019i | \(0.915282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.9925 | 1.30145 | 0.650727 | − | 0.759312i | \(-0.274464\pi\) | ||||
0.650727 | + | 0.759312i | \(0.274464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.9121 | − | 8.60949i | 1.19777 | − | 0.691531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0612 | + | 6.96356i | −0.962592 | + | 0.555753i | −0.896970 | − | 0.442092i | \(-0.854236\pi\) |
−0.0656219 | + | 0.997845i | \(0.520903\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.86696 | + | 5.00652i | −0.698814 | + | 0.394569i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.79498 | + | 13.5013i | 0.610550 | + | 1.05750i | 0.991148 | + | 0.132762i | \(0.0423847\pi\) |
−0.380598 | + | 0.924740i | \(0.624282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.58728 | − | 11.4095i | 0.509739 | − | 0.882893i | −0.490198 | − | 0.871611i | \(-0.663075\pi\) |
0.999936 | − | 0.0112821i | \(-0.00359127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33736 | − | 2.31638i | −0.102874 | − | 0.178183i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.60402 | − | 9.70645i | 0.426066 | − | 0.737968i | −0.570453 | − | 0.821330i | \(-0.693233\pi\) |
0.996519 | + | 0.0833623i | \(0.0265659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.74221 | + | 17.2543i | 0.736442 | + | 1.30430i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.22783 | − | 5.32769i | −0.689721 | − | 0.398210i | 0.113787 | − | 0.993505i | \(-0.463702\pi\) |
−0.803507 | + | 0.595295i | \(0.797035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8897i | 0.883754i | 0.897076 | + | 0.441877i | \(0.145687\pi\) | ||||
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.19964 | + | 5.54194i | 0.235242 | + | 0.407451i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.24123 | − | 5.33543i | −0.675786 | − | 0.390165i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.193961 | − | 0.111983i | −0.0140345 | − | 0.00810283i | 0.492966 | − | 0.870048i | \(-0.335913\pi\) |
−0.507001 | + | 0.861946i | \(0.669246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0373 | − | 22.5812i | −0.938442 | − | 1.62543i | −0.768378 | − | 0.639996i | \(-0.778936\pi\) |
−0.170064 | − | 0.985433i | \(-0.554398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.56289i | − | 0.111352i | −0.998449 | − | 0.0556758i | \(-0.982269\pi\) | ||
0.998449 | − | 0.0556758i | \(-0.0177313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4725 | + | 7.77832i | 0.955037 | + | 0.551391i | 0.894642 | − | 0.446784i | \(-0.147431\pi\) |
0.0603949 | + | 0.998175i | \(0.480764\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2362 | − | 8.99266i | −1.06937 | − | 0.631161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.7815 | − | 30.7984i | 1.24191 | − | 2.15105i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.19554 | + | 3.80279i | 0.151869 | + | 0.263045i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98216 | − | 12.0935i | 0.480672 | − | 0.832548i | −0.519082 | − | 0.854724i | \(-0.673726\pi\) |
0.999754 | + | 0.0221763i | \(0.00705950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.34848 | + | 14.4600i | 0.569361 | + | 0.986163i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1016 | − | 6.55236i | −0.753628 | − | 0.444803i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3313 | − | 9.42890i | 1.09856 | − | 0.634256i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4242 | + | 12.3693i | −1.43467 | + | 0.828307i | −0.997472 | − | 0.0710586i | \(-0.977362\pi\) |
−0.437198 | + | 0.899366i | \(0.644029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.24153 | 0.414265 | 0.207132 | − | 0.978313i | \(-0.433587\pi\) | ||||
0.207132 | + | 0.978313i | \(0.433587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8574i | 1.04789i | 0.851753 | + | 0.523943i | \(0.175540\pi\) | ||||
−0.851753 | + | 0.523943i | \(0.824460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.94574 | + | 1.70072i | −0.192982 | + | 0.111418i | −0.593378 | − | 0.804924i | \(-0.702206\pi\) |
0.400396 | + | 0.916342i | \(0.368873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9974 | − | 24.2441i | 0.913087 | − | 1.58151i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3482 | + | 9.43864i | 1.05748 | + | 0.610535i | 0.924733 | − | 0.380615i | \(-0.124288\pi\) |
0.132744 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.1845i | − | 0.720460i | −0.932864 | − | 0.360230i | \(-0.882698\pi\) | ||
0.932864 | − | 0.360230i | \(-0.117302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7779 | − | 21.1825i | 0.816348 | − | 1.35330i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.76003 | −0.493759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.4537 | −0.975431 | −0.487716 | − | 0.873003i | \(-0.662170\pi\) | ||||
−0.487716 | + | 0.873003i | \(0.662170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99801 | 0.439961 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6448 | 0.664002 | 0.332001 | − | 0.943279i | \(-0.392276\pi\) | ||||
0.332001 | + | 0.943279i | \(0.392276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.43512 | − | 4.12582i | 0.151311 | − | 0.256366i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0875i | 0.683685i | 0.939757 | + | 0.341842i | \(0.111051\pi\) | ||||
−0.939757 | + | 0.341842i | \(0.888949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00515 | + | 4.62178i | 0.491753 | + | 0.283913i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.14147 | − | 5.44119i | 0.191539 | − | 0.331755i | −0.754221 | − | 0.656620i | \(-0.771986\pi\) |
0.945760 | + | 0.324865i | \(0.105319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.954533 | − | 0.551100i | 0.0579838 | − | 0.0334769i | −0.470728 | − | 0.882278i | \(-0.656009\pi\) |
0.528712 | + | 0.848802i | \(0.322675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 13.6175i | − | 0.821164i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3616 | −0.922990 | −0.461495 | − | 0.887143i | \(-0.652687\pi\) | ||||
−0.461495 | + | 0.887143i | \(0.652687\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9133 | + | 10.9196i | −1.12827 | + | 0.651407i | −0.943499 | − | 0.331374i | \(-0.892488\pi\) |
−0.184771 | + | 0.982782i | \(0.559154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.59426 | + | 5.53925i | −0.570320 | + | 0.329274i | −0.757277 | − | 0.653094i | \(-0.773471\pi\) |
0.186957 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.6231 | − | 0.255467i | −1.57151 | − | 0.0150797i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.72069 | − | 15.1047i | −0.512982 | − | 0.888511i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6330 | + | 21.8810i | −0.738027 | + | 1.27830i | 0.215355 | + | 0.976536i | \(0.430909\pi\) |
−0.953382 | + | 0.301765i | \(0.902424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5710 | + | 26.9698i | 0.906578 | + | 1.57024i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.18353 | + | 10.7102i | −0.357603 | + | 0.619386i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.35371 | − | 10.7651i | 0.366222 | − | 0.620488i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.7512 | + | 18.3316i | 1.81807 | + | 1.04966i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.2163i | − | 0.697219i | −0.937268 | − | 0.348610i | \(-0.886654\pi\) | ||
0.937268 | − | 0.348610i | \(-0.113346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.74484 | + | 8.21830i | 0.269055 | + | 0.466017i | 0.968618 | − | 0.248554i | \(-0.0799553\pi\) |
−0.699563 | + | 0.714571i | \(0.746622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7358 | + | 6.77564i | 0.663344 | + | 0.382982i | 0.793550 | − | 0.608505i | \(-0.208231\pi\) |
−0.130206 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.7559 | − | 7.94197i | −0.772608 | − | 0.446065i | 0.0611961 | − | 0.998126i | \(-0.480508\pi\) |
−0.833804 | + | 0.552060i | \(0.813842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.07939 | + | 10.5298i | 0.340380 | + | 0.589556i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.1727i | 0.788591i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.8410 | + | 12.0326i | 1.15605 | + | 0.667446i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.9574 | − | 0.201101i | −1.15542 | − | 0.0110870i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.48697 | + | 9.50372i | −0.301591 | + | 0.522371i | −0.976497 | − | 0.215533i | \(-0.930851\pi\) |
0.674905 | + | 0.737904i | \(0.264184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.8669 | − | 24.0182i | −0.757630 | − | 1.31225i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.80751 | − | 4.86275i | 0.152935 | − | 0.264891i | −0.779370 | − | 0.626564i | \(-0.784461\pi\) |
0.932305 | + | 0.361673i | \(0.117794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.42964 | + | 7.67237i | 0.239879 | + | 0.415482i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5126 | − | 0.533054i | −0.999586 | − | 0.0287822i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.18003 | − | 2.41334i | 0.224396 | − | 0.129555i | −0.383588 | − | 0.923504i | \(-0.625312\pi\) |
0.607984 | + | 0.793949i | \(0.291978\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.7167 | − | 13.1155i | 1.21600 | − | 0.702056i | 0.251937 | − | 0.967744i | \(-0.418932\pi\) |
0.964059 | + | 0.265688i | \(0.0855991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.9914 | 1.86240 | 0.931201 | − | 0.364505i | \(-0.118762\pi\) | ||||
0.931201 | + | 0.364505i | \(0.118762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26.9628i | − | 1.43104i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.6396 | − | 12.4936i | 1.14209 | − | 0.659388i | 0.195146 | − | 0.980774i | \(-0.437482\pi\) |
0.946948 | + | 0.321386i | \(0.104149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58394 | + | 11.4037i | −0.346523 | + | 0.600196i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.5855 | + | 24.0094i | 2.17669 | + | 1.25671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.6067i | − | 1.28446i | −0.766512 | − | 0.642230i | \(-0.778009\pi\) | ||
0.766512 | − | 0.642230i | \(-0.221991\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0664013 | − | 6.91990i | 0.00344738 | − | 0.359264i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.4374 | −0.540428 | −0.270214 | − | 0.962800i | \(-0.587094\pi\) | ||||
−0.270214 | + | 0.962800i | \(0.587094\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.4873 | −1.10665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8728 | 1.63719 | 0.818597 | − | 0.574368i | \(-0.194752\pi\) | ||||
0.818597 | + | 0.574368i | \(0.194752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7719 | 1.26579 | 0.632893 | − | 0.774239i | \(-0.281867\pi\) | ||||
0.632893 | + | 0.774239i | \(0.281867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.8042 | + | 8.35886i | −0.754494 | + | 0.426007i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.0227i | 1.16729i | 0.812007 | + | 0.583647i | \(0.198375\pi\) | ||||
−0.812007 | + | 0.583647i | \(0.801625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5608 | + | 11.2934i | 0.989232 | + | 0.571133i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.25577 | + | 5.63916i | −0.163816 | + | 0.283737i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9247 | − | 13.8129i | 1.20075 | − | 0.693251i | 0.240025 | − | 0.970767i | \(-0.422844\pi\) |
0.960721 | + | 0.277515i | \(0.0895109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.32384i | − | 0.265860i | −0.991125 | − | 0.132930i | \(-0.957561\pi\) | ||
0.991125 | − | 0.132930i | \(-0.0424385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6563 | −0.779898 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.85137 | + | 1.64624i | −0.141337 | + | 0.0816009i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.11912 | − | 3.53288i | 0.302571 | − | 0.174690i | −0.341026 | − | 0.940054i | \(-0.610774\pi\) |
0.643597 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.8505 | − | 20.0782i | 0.583124 | − | 0.987985i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.8522 | − | 34.3851i | −0.974507 | − | 1.68790i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.94504 | − | 3.36891i | 0.0950215 | − | 0.164582i | −0.814596 | − | 0.580029i | \(-0.803041\pi\) |
0.909618 | + | 0.415447i | \(0.136375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.18533 | − | 3.78510i | −0.106506 | − | 0.184475i | 0.807846 | − | 0.589393i | \(-0.200633\pi\) |
−0.914353 | + | 0.404919i | \(0.867300\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.9759 | − | 38.0634i | 1.06599 | − | 1.84635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.263371 | − | 27.4467i | 0.0127454 | − | 1.32824i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7505 | − | 6.20681i | −0.517834 | − | 0.298971i | 0.218214 | − | 0.975901i | \(-0.429977\pi\) |
−0.736048 | + | 0.676929i | \(0.763310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2979i | 1.21574i | 0.794036 | + | 0.607870i | \(0.207976\pi\) | ||||
−0.794036 | + | 0.607870i | \(0.792024\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.64728 | − | 8.04932i | −0.222309 | − | 0.385051i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.2408 | − | 13.4181i | −1.10922 | − | 0.640410i | −0.170595 | − | 0.985341i | \(-0.554569\pi\) |
−0.938628 | + | 0.344931i | \(0.887902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3051 | + | 6.52699i | 0.537120 | + | 0.310107i | 0.743911 | − | 0.668279i | \(-0.232969\pi\) |
−0.206791 | + | 0.978385i | \(0.566302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.3773 | − | 42.2227i | −1.15560 | − | 2.00155i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.468645i | 0.0221167i | 0.999939 | + | 0.0110584i | \(0.00352006\pi\) | ||||
−0.999939 | + | 0.0110584i | \(0.996480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8460 | + | 9.14868i | 0.746158 | + | 0.430795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.288286 | − | 30.0433i | 0.0135151 | − | 1.40845i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.06486 | − | 3.57644i | 0.0965901 | − | 0.167299i | −0.813681 | − | 0.581312i | \(-0.802540\pi\) |
0.910271 | + | 0.414013i | \(0.135873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9115 | − | 22.3633i | −0.601347 | − | 1.04156i | −0.992617 | − | 0.121288i | \(-0.961298\pi\) |
0.391271 | − | 0.920276i | \(-0.372036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.56402 | + | 4.44101i | −0.119160 | + | 0.206391i | −0.919435 | − | 0.393242i | \(-0.871353\pi\) |
0.800275 | + | 0.599633i | \(0.204687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.26091 | + | 2.18396i | 0.0583480 | + | 0.101062i | 0.893724 | − | 0.448617i | \(-0.148083\pi\) |
−0.835376 | + | 0.549679i | \(0.814750\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5536 | + | 17.8809i | −0.487319 | + | 0.825662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.43976 | + | 4.29535i | −0.342081 | + | 0.197500i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.6632 | + | 9.04316i | −0.718677 | + | 0.414929i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4924 | 0.525103 | 0.262552 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262552 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.81854i | − | 0.265303i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.7629 | − | 28.1533i | 2.21421 | − | 1.27837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8463 | + | 18.7864i | −0.491493 | + | 0.851292i | −0.999952 | − | 0.00979483i | \(-0.996882\pi\) |
0.508459 | + | 0.861086i | \(0.330215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3592 | + | 11.1771i | 0.873669 | + | 0.504413i | 0.868566 | − | 0.495574i | \(-0.165042\pi\) |
0.00510349 | + | 0.999987i | \(0.498376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.2438i | 1.76745i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.5775 | + | 9.92470i | −0.788457 | + | 0.445184i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5246 | 0.784510 | 0.392255 | − | 0.919857i | \(-0.371695\pi\) | ||||
0.392255 | + | 0.919857i | \(0.371695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.60926 | 0.339280 | 0.169640 | − | 0.985506i | \(-0.445739\pi\) | ||||
0.169640 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.3159 | 1.74953 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.78746 | 0.300849 | 0.150424 | − | 0.988622i | \(-0.451936\pi\) | ||||
0.150424 | + | 0.988622i | \(0.451936\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.344945 | − | 35.9479i | 0.0152595 | − | 1.59024i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.13111i | 0.0939078i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4738 | + | 7.20174i | 0.548596 | + | 0.316732i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8435 | − | 23.9777i | 0.606497 | − | 1.05048i | −0.385316 | − | 0.922785i | \(-0.625908\pi\) |
0.991813 | − | 0.127698i | \(-0.0407590\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.834923 | + | 0.482043i | −0.0365086 | + | 0.0210783i | −0.518143 | − | 0.855294i | \(-0.673377\pi\) |
0.481635 | + | 0.876372i | \(0.340043\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.5943i | 1.24559i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.18740 | 0.355974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.0034 | + | 16.1678i | −1.21296 | + | 0.700304i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.0552 | + | 23.1259i | −1.73174 | + | 0.999820i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.8985 | + | 6.57430i | 0.469433 | + | 0.283175i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.36867 | + | 4.10266i | 0.101837 | + | 0.176387i | 0.912442 | − | 0.409207i | \(-0.134195\pi\) |
−0.810604 | + | 0.585594i | \(0.800861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84374 | − | 8.38960i | 0.207483 | − | 0.359371i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.840875 | − | 1.45644i | −0.0359532 | − | 0.0622728i | 0.847489 | − | 0.530813i | \(-0.178113\pi\) |
−0.883442 | + | 0.468540i | \(0.844780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.07446 | − | 13.9854i | 0.343984 | − | 0.595797i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.87467 | + | 0.0467758i | 0.207292 | + | 0.00198911i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.14983 | − | 4.70530i | −0.345319 | − | 0.199370i | 0.317303 | − | 0.948324i | \(-0.397223\pi\) |
−0.662622 | + | 0.748954i | \(0.730556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.1817i | − | 0.642117i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5319 | + | 26.9020i | 0.654591 | + | 1.13378i | 0.981996 | + | 0.188901i | \(0.0604924\pi\) |
−0.327405 | + | 0.944884i | \(0.606174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.5056 | + | 13.5710i | 0.988888 | + | 0.570935i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4099 | − | 10.0516i | −0.729859 | − | 0.421384i | 0.0885114 | − | 0.996075i | \(-0.471789\pi\) |
−0.818371 | + | 0.574691i | \(0.805122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.93707 | + | 6.81920i | 0.164761 | + | 0.285375i | 0.936570 | − | 0.350479i | \(-0.113981\pi\) |
−0.771809 | + | 0.635854i | \(0.780648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.8239i | 1.20204i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.77842 | − | 1.60412i | −0.115667 | − | 0.0667805i | 0.441050 | − | 0.897482i | \(-0.354606\pi\) |
−0.556717 | + | 0.830702i | \(0.687939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1088 | + | 25.5987i | −0.626817 | + | 1.06201i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.37794 | + | 4.11871i | −0.0984840 | + | 0.170579i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37708 | + | 4.11722i | 0.0981125 | + | 0.169936i | 0.910903 | − | 0.412620i | \(-0.135386\pi\) |
−0.812791 | + | 0.582556i | \(0.802053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.88332 | − | 10.1902i | 0.242418 | − | 0.419880i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0354 | − | 22.5780i | −0.535300 | − | 0.927166i | −0.999149 | − | 0.0412519i | \(-0.986865\pi\) |
0.463849 | − | 0.885914i | \(-0.346468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −54.8703 | − | 0.526519i | −2.24946 | − | 0.0215852i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.8178 | − | 13.7512i | 0.973168 | − | 0.561859i | 0.0729672 | − | 0.997334i | \(-0.476753\pi\) |
0.900200 | + | 0.435476i | \(0.143420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8647 | + | 15.5104i | −1.09584 | + | 0.632681i | −0.935124 | − | 0.354320i | \(-0.884712\pi\) |
−0.160712 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.1903 | −1.10544 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2304i | 1.59231i | 0.605092 | + | 0.796156i | \(0.293136\pi\) | ||||
−0.605092 | + | 0.796156i | \(0.706864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.0440 | + | 12.7271i | −0.891803 | + | 0.514883i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5364 | + | 19.9817i | −0.465951 | + | 0.807051i | −0.999244 | − | 0.0388795i | \(-0.987621\pi\) |
0.533293 | + | 0.845931i | \(0.320954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.15715 | − | 2.97748i | −0.207619 | − | 0.119869i | 0.392585 | − | 0.919716i | \(-0.371581\pi\) |
−0.600204 | + | 0.799847i | \(0.704914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.3650i | − | 1.30086i | −0.759567 | − | 0.650429i | \(-0.774589\pi\) | ||
0.759567 | − | 0.650429i | \(-0.225411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.5526 | + | 31.4337i | −0.743296 | + | 1.25936i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.35758 | −0.254303 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.6268 | −0.423719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.6689 | −1.41996 | −0.709978 | − | 0.704224i | \(-0.751295\pi\) | ||||
−0.709978 | + | 0.704224i | \(0.751295\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −63.3459 | −2.51380 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.6918 | + | 10.8707i | −0.780218 | + | 0.430711i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.8536i | 0.981659i | 0.871256 | + | 0.490829i | \(0.163306\pi\) | ||||
−0.871256 | + | 0.490829i | \(0.836694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8270 | + | 8.56038i | 0.584720 | + | 0.337588i | 0.763007 | − | 0.646390i | \(-0.223722\pi\) |
−0.178287 | + | 0.983979i | \(0.557056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.7208 | + | 28.9613i | −0.657363 | + | 1.13859i | 0.323933 | + | 0.946080i | \(0.394995\pi\) |
−0.981296 | + | 0.192506i | \(0.938339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8761 | + | 8.01138i | −0.544686 | + | 0.314474i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 26.4238i | − | 1.03404i | −0.855972 | − | 0.517022i | \(-0.827041\pi\) | ||
0.855972 | − | 0.517022i | \(-0.172959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 59.9745 | 2.34340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.8862 | + | 14.9454i | −1.00838 | + | 0.582191i | −0.910718 | − | 0.413029i | \(-0.864471\pi\) |
−0.0976658 | + | 0.995219i | \(0.531138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.92629 | + | 2.26684i | −0.152715 | + | 0.0881699i | −0.574410 | − | 0.818568i | \(-0.694769\pi\) |
0.421695 | + | 0.906738i | \(0.361435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.4459 | + | 11.4773i | 0.754079 | + | 0.445069i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8682 | − | 22.2883i | −0.498257 | − | 0.863006i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.43172 | + | 16.3362i | −0.364107 | + | 0.630652i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.12239 | + | 7.14019i | 0.158907 | + | 0.275234i | 0.934475 | − | 0.356030i | \(-0.115870\pi\) |
−0.775568 | + | 0.631264i | \(0.782536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.75631 | + | 4.77407i | −0.105934 | + | 0.183483i | −0.914119 | − | 0.405445i | \(-0.867116\pi\) |
0.808186 | + | 0.588928i | \(0.200450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.3026 | − | 21.4264i | −1.39317 | − | 0.822268i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0097 | − | 13.8620i | −0.918706 | − | 0.530415i | −0.0354840 | − | 0.999370i | \(-0.511297\pi\) |
−0.883222 | + | 0.468955i | \(0.844631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 19.6540i | − | 0.750942i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.20235 | − | 7.27868i | −0.160097 | − | 0.277296i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.5312 | + | 21.0913i | 1.38971 | + | 0.802351i | 0.993283 | − | 0.115714i | \(-0.0369157\pi\) |
0.396430 | + | 0.918065i | \(0.370249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.9994 | + | 25.4031i | 1.66899 | + | 0.963593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.5284 | + | 51.1447i | 1.11847 | + | 1.93724i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.07738i | − | 0.0406922i | −0.999793 | − | 0.0203461i | \(-0.993523\pi\) | ||
0.999793 | − | 0.0203461i | \(-0.00647681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.78710 | + | 2.18648i | 0.142833 | + | 0.0824648i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4717 | − | 25.6306i | −0.544265 | − | 0.963938i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.9806 | − | 19.0189i | 0.412385 | − | 0.714271i | −0.582765 | − | 0.812640i | \(-0.698029\pi\) |
0.995150 | + | 0.0983694i | \(0.0313627\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.37617 | − | 16.2400i | −0.351140 | − | 0.608193i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.3240 | + | 17.8817i | −0.386095 | + | 0.668737i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89267 | + | 10.2064i | 0.219760 | + | 0.380635i | 0.954734 | − | 0.297460i | \(-0.0961394\pi\) |
−0.734975 | + | 0.678094i | \(0.762806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.38930 | − | 0.784436i | 0.0517403 | − | 0.0292139i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −43.3709 | + | 25.0402i | −1.61075 | + | 0.929970i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1963 | + | 5.88682i | −0.378159 | + | 0.218330i | −0.677017 | − | 0.735967i | \(-0.736728\pi\) |
0.298858 | + | 0.954298i | \(0.403394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.7274 | −1.02554 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.7655i | 1.61652i | 0.588829 | + | 0.808258i | \(0.299589\pi\) | ||||
−0.588829 | + | 0.808258i | \(0.700411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.3575 | − | 7.13462i | 0.455195 | − | 0.262807i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.9728 | − | 24.2016i | 0.513998 | − | 0.890270i | −0.485870 | − | 0.874031i | \(-0.661497\pi\) |
0.999868 | − | 0.0162393i | \(-0.00516935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.0951 | − | 17.9528i | −1.14077 | − | 0.658623i | −0.194147 | − | 0.980972i | \(-0.562194\pi\) |
−0.946621 | + | 0.322350i | \(0.895527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 22.6923i | − | 0.831382i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.8200 | + | 17.6002i | 1.08960 | + | 0.643099i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.35031 | −0.0857642 | −0.0428821 | − | 0.999080i | \(-0.513654\pi\) | ||||
−0.0428821 | + | 0.999080i | \(0.513654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −56.5178 | −2.05689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.88061 | 0.322771 | 0.161386 | − | 0.986891i | \(-0.448404\pi\) | ||||
0.161386 | + | 0.986891i | \(0.448404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.9766 | −0.977902 | −0.488951 | − | 0.872311i | \(-0.662620\pi\) | ||||
−0.488951 | + | 0.872311i | \(0.662620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.25223 | − | 0.0695902i | −0.262548 | − | 0.00251933i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 28.3158i | − | 1.02243i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.88232 | + | 4.55086i | 0.284244 | + | 0.164108i | 0.635343 | − | 0.772230i | \(-0.280859\pi\) |
−0.351099 | + | 0.936338i | \(0.614192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.46864 | − | 11.2040i | 0.232661 | − | 0.402980i | −0.725929 | − | 0.687769i | \(-0.758590\pi\) |
0.958590 | + | 0.284789i | \(0.0919235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.6015 | + | 18.2451i | −1.13516 | + | 0.655384i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.3020i | − | 0.870710i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8726 | 0.496399 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.6245 | − | 24.6093i | 1.52134 | − | 0.878343i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5265 | − | 12.4283i | 0.767336 | − | 0.443022i | −0.0645875 | − | 0.997912i | \(-0.520573\pi\) |
0.831923 | + | 0.554890i | \(0.187240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.194975 | − | 20.3190i | 0.00693250 | − | 0.722460i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6680 | − | 28.8697i | −0.591896 | − | 1.02519i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.71671 | + | 11.6337i | −0.237918 | + | 0.412086i | −0.960117 | − | 0.279600i | \(-0.909798\pi\) |
0.722199 | + | 0.691686i | \(0.243132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2444 | + | 40.2605i | 0.822328 | + | 1.42431i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.3530 | + | 21.3961i | −0.435928 | + | 0.755050i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.3359 | − | 17.6931i | 1.10445 | − | 0.623600i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.38524 | + | 5.41857i | 0.329967 | + | 0.190507i | 0.655827 | − | 0.754912i | \(-0.272320\pi\) |
−0.325859 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.3334i | 1.24072i | 0.784316 | + | 0.620361i | \(0.213014\pi\) | ||||
−0.784316 | + | 0.620361i | \(0.786986\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.5475 | − | 47.7137i | −0.964948 | − | 1.67134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.88127 | + | 5.70496i | 0.345702 | + | 0.199591i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6412 | + | 9.60782i | 0.580783 | + | 0.335315i | 0.761445 | − | 0.648230i | \(-0.224490\pi\) |
−0.180661 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.9074 | − | 25.8204i | −0.519639 | − | 0.900041i | −0.999739 | − | 0.0228278i | \(-0.992733\pi\) |
0.480100 | − | 0.877214i | \(-0.340600\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.356137i | 0.0123841i | 0.999981 | + | 0.00619205i | \(0.00197100\pi\) | ||||
−0.999981 | + | 0.00619205i | \(0.998029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5571 | − | 10.1366i | −0.609783 | − | 0.352058i | 0.163098 | − | 0.986610i | \(-0.447851\pi\) |
−0.772880 | + | 0.634552i | \(0.781185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.8539 | + | 35.9646i | 0.687896 | + | 1.24610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.2795 | + | 40.3213i | −0.805620 | + | 1.39538i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.662663 | + | 1.14777i | 0.0228777 | + | 0.0396253i | 0.877238 | − | 0.480056i | \(-0.159384\pi\) |
−0.854360 | + | 0.519682i | \(0.826051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.85791 | − | 13.6103i | 0.270962 | − | 0.469321i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.72626 | + | 8.18612i | 0.162588 | + | 0.281611i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0084 | + | 17.7258i | 0.343894 | + | 0.609064i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.03545 | − | 3.48457i | 0.206893 | − | 0.119449i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.7558 | + | 24.1077i | −1.42969 | + | 0.825432i | −0.997096 | − | 0.0761571i | \(-0.975735\pi\) |
−0.432594 | + | 0.901589i | \(0.642402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.8773 | 0.713155 | 0.356578 | − | 0.934266i | \(-0.383944\pi\) | ||||
0.356578 | + | 0.934266i | \(0.383944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.7094i | − | 0.467758i | −0.972266 | − | 0.233879i | \(-0.924858\pi\) | ||
0.972266 | − | 0.233879i | \(-0.0751419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.1125 | + | 16.2307i | −0.956959 | + | 0.552501i | −0.895236 | − | 0.445593i | \(-0.852993\pi\) |
−0.0617233 | + | 0.998093i | \(0.519660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8047 | + | 34.3027i | −0.673379 | + | 1.16633i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.90139 | − | 1.67512i | −0.0984228 | − | 0.0568244i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.2169i | 0.854444i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.4434 | − | 20.2671i | −0.386856 | − | 0.685154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.9338 | 0.740653 | 0.370326 | − | 0.928902i | \(-0.379246\pi\) | ||||
0.370326 | + | 0.928902i | \(0.379246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.8019 | −0.734526 | −0.367263 | − | 0.930117i | \(-0.619705\pi\) | ||||
−0.367263 | + | 0.930117i | \(0.619705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4085 | −0.821411 | −0.410705 | − | 0.911768i | \(-0.634717\pi\) | ||||
−0.410705 | + | 0.911768i | \(0.634717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.7444 | 1.13303 | 0.566513 | − | 0.824053i | \(-0.308292\pi\) | ||||
0.566513 | + | 0.824053i | \(0.308292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3169 | + | 41.2961i | 0.782024 | + | 1.38503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 19.1303i | − | 0.640170i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.6113 | + | 18.8281i | 1.09007 | + | 0.629355i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.2907 | − | 28.2164i | 0.543326 | − | 0.941068i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2936 | + | 7.67505i | −0.442873 | + | 0.255693i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 42.0183i | − | 1.39674i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0566 | 0.499948 | 0.249974 | − | 0.968253i | \(-0.419578\pi\) | ||||
0.249974 | + | 0.968253i | \(0.419578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5047 | − | 12.4157i | 0.712481 | − | 0.411351i | −0.0994977 | − | 0.995038i | \(-0.531724\pi\) |
0.811979 | + | 0.583686i | \(0.198390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6913 | − | 10.2141i | 0.585498 | − | 0.338038i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.0759 | − | 39.0983i | −0.729012 | − | 1.29114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0689 | − | 20.9039i | −0.398115 | − | 0.689555i | 0.595378 | − | 0.803445i | \(-0.297002\pi\) |
−0.993493 | + | 0.113890i | \(0.963669\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2580 | + | 21.2314i | −0.403476 | + | 0.698840i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78064 | − | 11.7444i | −0.222946 | − | 0.386154i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.3310 | − | 23.0900i | 0.437376 | − | 0.757558i | −0.560110 | − | 0.828418i | \(-0.689241\pi\) |
0.997486 | + | 0.0708606i | \(0.0225745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.324397 | − | 16.9017i | 0.0106317 | − | 0.553932i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.6586 | + | 18.8555i | 1.06805 | + | 0.616640i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.17165i | 0.266956i | 0.991052 | + | 0.133478i | \(0.0426146\pi\) | ||||
−0.991052 | + | 0.133478i | \(0.957385\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.0136 | − | 27.7363i | −0.522028 | − | 0.904179i | −0.999672 | − | 0.0256254i | \(-0.991842\pi\) |
0.477644 | − | 0.878554i | \(-0.341491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.5410 | − | 19.3649i | −1.09224 | − | 0.630608i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5020 | + | 8.95009i | 0.503748 | + | 0.290839i | 0.730260 | − | 0.683169i | \(-0.239399\pi\) |
−0.226512 | + | 0.974008i | \(0.572732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.8305 | − | 37.8116i | −0.708650 | − | 1.22742i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2737i | 0.365191i | 0.983188 | + | 0.182596i | \(0.0584499\pi\) | ||||
−0.983188 | + | 0.182596i | \(0.941550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.685459 | + | 0.395750i | 0.0221809 | + | 0.0128062i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.8128 | + | 7.23442i | −0.413746 | + | 0.233612i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.63003 | + | 6.28740i | −0.117098 | + | 0.202819i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.0738 | + | 79.8022i | 1.48317 | + | 2.56892i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3313 | − | 26.5546i | 0.493022 | − | 0.853939i | −0.506946 | − | 0.861978i | \(-0.669226\pi\) |
0.999968 | + | 0.00803913i | \(0.00255896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0807 | − | 33.0488i | −0.612330 | − | 1.06059i | −0.990847 | − | 0.134992i | \(-0.956899\pi\) |
0.378517 | − | 0.925595i | \(-0.376434\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.364967 | − | 38.0345i | 0.0117003 | − | 1.21933i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.5862 | + | 15.3496i | −0.850568 | + | 0.491076i | −0.860842 | − | 0.508872i | \(-0.830063\pi\) |
0.0102745 | + | 0.999947i | \(0.496729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7239 | − | 12.5423i | 0.694299 | − | 0.400854i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.8057 | −0.823073 | −0.411536 | − | 0.911393i | \(-0.635008\pi\) | ||||
−0.411536 | + | 0.911393i | \(0.635008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.52328i | 0.175986i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7476 | − | 9.09191i | 0.500746 | − | 0.289106i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4388 | + | 19.8126i | −0.363366 | + | 0.629369i | −0.988513 | − | 0.151139i | \(-0.951706\pi\) |
0.625146 | + | 0.780508i | \(0.285039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.6118 | − | 27.4887i | −1.50940 | − | 0.871450i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 41.5407i | − | 1.31561i | −0.753189 | − | 0.657804i | \(-0.771486\pi\) | ||
0.753189 | − | 0.657804i | \(-0.228514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.cx.a.17.3 | 48 | ||
3.2 | odd | 2 | 504.2.cx.a.185.7 | yes | 48 | ||
4.3 | odd | 2 | 3024.2.df.e.17.3 | 48 | |||
7.5 | odd | 6 | 1512.2.bs.a.1097.3 | 48 | |||
9.2 | odd | 6 | 1512.2.bs.a.521.3 | 48 | |||
9.7 | even | 3 | 504.2.bs.a.353.1 | yes | 48 | ||
12.11 | even | 2 | 1008.2.df.e.689.18 | 48 | |||
21.5 | even | 6 | 504.2.bs.a.257.1 | ✓ | 48 | ||
28.19 | even | 6 | 3024.2.ca.e.2609.3 | 48 | |||
36.7 | odd | 6 | 1008.2.ca.e.353.24 | 48 | |||
36.11 | even | 6 | 3024.2.ca.e.2033.3 | 48 | |||
63.47 | even | 6 | inner | 1512.2.cx.a.89.3 | 48 | ||
63.61 | odd | 6 | 504.2.cx.a.425.7 | yes | 48 | ||
84.47 | odd | 6 | 1008.2.ca.e.257.24 | 48 | |||
252.47 | odd | 6 | 3024.2.df.e.1601.3 | 48 | |||
252.187 | even | 6 | 1008.2.df.e.929.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.1 | ✓ | 48 | 21.5 | even | 6 | ||
504.2.bs.a.353.1 | yes | 48 | 9.7 | even | 3 | ||
504.2.cx.a.185.7 | yes | 48 | 3.2 | odd | 2 | ||
504.2.cx.a.425.7 | yes | 48 | 63.61 | odd | 6 | ||
1008.2.ca.e.257.24 | 48 | 84.47 | odd | 6 | |||
1008.2.ca.e.353.24 | 48 | 36.7 | odd | 6 | |||
1008.2.df.e.689.18 | 48 | 12.11 | even | 2 | |||
1008.2.df.e.929.18 | 48 | 252.187 | even | 6 | |||
1512.2.bs.a.521.3 | 48 | 9.2 | odd | 6 | |||
1512.2.bs.a.1097.3 | 48 | 7.5 | odd | 6 | |||
1512.2.cx.a.17.3 | 48 | 1.1 | even | 1 | trivial | ||
1512.2.cx.a.89.3 | 48 | 63.47 | even | 6 | inner | ||
3024.2.ca.e.2033.3 | 48 | 36.11 | even | 6 | |||
3024.2.ca.e.2609.3 | 48 | 28.19 | even | 6 | |||
3024.2.df.e.17.3 | 48 | 4.3 | odd | 2 | |||
3024.2.df.e.1601.3 | 48 | 252.47 | odd | 6 |