Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.7 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.11231 | − | 1.32769i | −0.642195 | − | 0.766542i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.53401 | 1.58046 | 0.790229 | − | 0.612812i | \(-0.209962\pi\) | ||||
0.790229 | + | 0.612812i | \(0.209962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30083 | + | 2.30388i | 0.491667 | + | 0.870783i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.525517 | + | 2.95361i | −0.175172 | + | 0.984538i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.81827i | 0.548230i | 0.961697 | + | 0.274115i | \(0.0883849\pi\) | ||||
−0.961697 | + | 0.274115i | \(0.911615\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −3.93093 | − | 4.69207i | −1.01496 | − | 1.21149i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.93434 | + | 5.08242i | −0.711682 | + | 1.23267i | 0.252544 | + | 0.967585i | \(0.418733\pi\) |
−0.964225 | + | 0.265083i | \(0.914600\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 1.61190 | − | 4.28973i | 0.351746 | − | 0.936096i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.84871i | − | 0.802512i | −0.915966 | − | 0.401256i | \(-0.868574\pi\) | ||
0.915966 | − | 0.401256i | \(-0.131426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.48923 | 1.49785 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.50602 | − | 2.58762i | 0.867184 | − | 0.497988i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.79110 | − | 3.34349i | 1.07538 | − | 0.620871i | 0.145734 | − | 0.989324i | \(-0.453446\pi\) |
0.929647 | + | 0.368452i | \(0.120112\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 2.41410 | − | 2.02249i | 0.420241 | − | 0.352070i | ||||
\(34\) | 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 | ||||||||
\(39\) | −0.962213 | − | 5.48178i | −0.154077 | − | 0.877788i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.03152 | − | 8.71485i | 0.785792 | − | 1.36103i | −0.142733 | − | 0.989761i | \(-0.545589\pi\) |
0.928525 | − | 0.371270i | \(-0.121078\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −1.85718 | + | 10.4381i | −0.276852 | + | 1.55602i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.96076 | − | 6.86023i | 0.577736 | − | 1.00067i | −0.418003 | − | 0.908446i | \(-0.637270\pi\) |
0.995738 | − | 0.0922218i | \(-0.0293969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.61569 | + | 5.99390i | −0.516527 | + | 0.856271i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0118 | − | 1.75736i | 1.40193 | − | 0.246080i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.26517 | + | 1.30780i | 0.311146 | + | 0.179640i | 0.647439 | − | 0.762117i | \(-0.275840\pi\) |
−0.336293 | + | 0.941757i | \(0.609173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.42580i | 0.866454i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.92950 | + | 1.43366i | 0.520474 | + | 0.189893i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.40604 | + | 7.63149i | 0.573618 | + | 0.993535i | 0.996190 | + | 0.0872059i | \(0.0277938\pi\) |
−0.422573 | + | 0.906329i | \(0.638873\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −7.48837 | + | 2.63142i | −0.943445 | + | 0.331528i | ||||
\(64\) | 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 | ||||||||
\(69\) | −5.10990 | + | 4.28098i | −0.615159 | + | 0.515369i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.62952i | − | 0.905458i | −0.891648 | − | 0.452729i | \(-0.850451\pi\) | ||
0.891648 | − | 0.452729i | \(-0.149549\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | −8.33037 | − | 9.94337i | −0.961909 | − | 1.14816i | ||||
\(76\) | 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 | ||||||||
\(81\) | −8.44766 | − | 3.10435i | −0.938629 | − | 0.344927i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.61748 | − | 9.72975i | −0.616598 | − | 1.06798i | −0.990102 | − | 0.140351i | \(-0.955177\pi\) |
0.373504 | − | 0.927629i | \(-0.378156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3700 | + | 17.9613i | −1.12478 | + | 1.94818i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.8806 | − | 3.96977i | −1.16653 | − | 0.425604i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.89792 | − | 11.9475i | −0.731178 | − | 1.26644i | −0.956380 | − | 0.292125i | \(-0.905638\pi\) |
0.225202 | − | 0.974312i | \(-0.427696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0815748 | + | 8.50119i | −0.00855137 | + | 0.891167i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.92800 | + | 2.89251i | 0.822095 | + | 0.299939i | ||||
\(94\) | 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 | ||||||||
\(99\) | −5.37048 | − | 0.955533i | −0.539753 | − | 0.0960346i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1250 | 1.10698 | 0.553489 | − | 0.832856i | \(-0.313296\pi\) | ||||
0.553489 | + | 0.832856i | \(0.313296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.603028i | − | 0.0594181i | −0.999559 | − | 0.0297091i | \(-0.990542\pi\) | ||
0.999559 | − | 0.0297091i | \(-0.00945808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.69647 | − | 15.1599i | 0.555919 | − | 1.47946i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3342 | + | 6.54381i | −1.09572 | + | 0.632614i | −0.935094 | − | 0.354401i | \(-0.884685\pi\) |
−0.160627 | + | 0.987015i | \(0.551351\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −1.07497 | + | 2.94637i | −0.102032 | + | 0.279657i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.65125 | + | 3.84010i | 0.625697 | + | 0.361246i | 0.779084 | − | 0.626920i | \(-0.215685\pi\) |
−0.153387 | + | 0.988166i | \(0.549018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.6014i | − | 1.26834i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.20782 | + | 7.37498i | −0.573913 | + | 0.681817i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.5263 | − | 0.148986i | −1.42330 | − | 0.0136575i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.69388 | 0.699444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.1672 | + | 3.01335i | −1.54792 | + | 0.271705i | ||||
\(124\) | 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 | ||||||||
\(129\) | −2.80481 | + | 7.68765i | −0.246950 | + | 0.676859i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9707 | 1.48273 | 0.741367 | − | 0.671100i | \(-0.234178\pi\) | ||||
0.741367 | + | 0.671100i | \(0.234178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50250 | − | 3.24766i | −0.477127 | − | 0.281608i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.9243 | − | 9.14468i | 1.37055 | − | 0.787049i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.56139i | − | 0.475142i | −0.971370 | − | 0.237571i | \(-0.923649\pi\) | ||
0.971370 | − | 0.237571i | \(-0.0763512\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −13.5139 | + | 2.37208i | −1.13807 | + | 0.199765i | ||||
\(142\) | 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 | ||||||||
\(147\) | 11.9798 | − | 1.86659i | 0.988078 | − | 0.153954i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.42112i | − | 0.526039i | −0.964791 | − | 0.263019i | \(-0.915282\pi\) | ||
0.964791 | − | 0.263019i | \(-0.0847184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.9925 | 1.30145 | 0.650727 | − | 0.759312i | \(-0.274464\pi\) | ||||
0.650727 | + | 0.759312i | \(0.274464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.4695 | − | 11.3378i | −1.08894 | − | 0.916607i | ||||
\(154\) | 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 | ||||||||
\(159\) | −0.783234 | − | 4.46213i | −0.0621145 | − | 0.353870i | ||||
\(160\) | 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 | ||||||||
\(165\) | 8.53146 | − | 7.14750i | 0.664173 | − | 0.556432i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.58728 | + | 11.4095i | −0.509739 | + | 0.882893i | 0.490198 | + | 0.871611i | \(0.336925\pi\) |
−0.999936 | + | 0.0112821i | \(0.996409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33736 | − | 2.31638i | −0.102874 | − | 0.178183i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.46737 | − | 6.81183i | −0.188685 | − | 0.520914i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.60402 | + | 9.70645i | −0.426066 | + | 0.737968i | −0.996519 | − | 0.0833623i | \(-0.973434\pi\) |
0.570453 | + | 0.821330i | \(0.306767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.74221 | + | 17.2543i | 0.736442 | + | 1.30430i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.23134 | − | 14.3385i | 0.393212 | − | 1.07774i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.22783 | + | 5.32769i | 0.689721 | + | 0.398210i | 0.803507 | − | 0.595295i | \(-0.202965\pi\) |
−0.113787 | + | 0.993505i | \(0.536298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8897i | 0.883754i | 0.897076 | + | 0.441877i | \(0.145687\pi\) | ||||
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.10658 | + | 17.6984i | 0.229645 | + | 1.30830i | ||||
\(184\) | 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 | ||||||||
\(189\) | 11.8231 | + | 7.01525i | 0.860006 | + | 0.510285i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.193961 | + | 0.111983i | 0.0140345 | + | 0.00810283i | 0.507001 | − | 0.861946i | \(-0.330754\pi\) |
−0.492966 | + | 0.870048i | \(0.664087\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −3.40047 | − | 19.3727i | −0.243513 | − | 1.38731i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.56289i | 0.111352i | 0.998449 | + | 0.0556758i | \(0.0177313\pi\) | ||||
−0.998449 | + | 0.0556758i | \(0.982269\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 4.65883 | − | 12.7693i | 0.328608 | − | 0.900674i | ||||
\(202\) | 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 | ||||||||
\(207\) | 11.3676 | + | 2.02256i | 0.790104 | + | 0.140578i | ||||
\(208\) | 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 | ||||||||
\(213\) | −10.1296 | + | 8.48642i | −0.694071 | + | 0.581480i | ||||
\(214\) | 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 | ||||||||
\(219\) | 4.06878 | + | 23.1801i | 0.274943 | + | 1.56637i | ||||
\(220\) | 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 | ||||||||
\(225\) | −3.93571 | + | 22.1203i | −0.262381 | + | 1.47469i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.24153 | −0.414265 | −0.207132 | − | 0.978313i | \(-0.566413\pi\) | ||||
−0.207132 | + | 0.978313i | \(0.566413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8574i | 1.04789i | 0.851753 | + | 0.523943i | \(0.175540\pi\) | ||||
−0.851753 | + | 0.523943i | \(0.824460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.79990 | + | 2.93087i | 0.513196 | + | 0.192837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.94574 | − | 1.70072i | 0.192982 | − | 0.111418i | −0.400396 | − | 0.916342i | \(-0.631127\pi\) |
0.593378 | + | 0.804924i | \(0.297794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9974 | − | 24.2441i | 0.913087 | − | 1.58151i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.14331 | + | 0.551742i | −0.204180 | + | 0.0358395i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3482 | − | 9.43864i | −1.05748 | − | 0.610535i | −0.132744 | − | 0.991150i | \(-0.542379\pi\) |
−0.924733 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.1845i | − | 0.720460i | −0.932864 | − | 0.360230i | \(-0.882698\pi\) | ||
0.932864 | − | 0.360230i | \(-0.117302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.27485 | + | 14.6689i | 0.338382 | + | 0.941009i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.7779 | + | 21.1825i | −0.816348 | + | 1.35330i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.76003 | −0.493759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.66969 | + | 18.2808i | −0.422675 | + | 1.15850i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4537 | 0.975431 | 0.487716 | − | 0.873003i | \(-0.337830\pi\) | ||||
0.487716 | + | 0.873003i | \(0.337830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99801 | 0.439961 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 35.3818 | − | 6.21053i | 2.21569 | − | 0.388918i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.6448 | −0.664002 | −0.332001 | − | 0.943279i | \(-0.607724\pi\) | ||||
−0.332001 | + | 0.943279i | \(0.607724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.43512 | − | 4.12582i | 0.151311 | − | 0.256366i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.83207 | + | 18.8617i | 0.422895 | + | 1.16751i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.0875i | − | 0.683685i | −0.939757 | − | 0.341842i | \(-0.888949\pi\) | ||
0.939757 | − | 0.341842i | \(-0.111051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00515 | + | 4.62178i | 0.491753 | + | 0.283913i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.18998 | + | 22.4477i | −0.501218 | + | 1.37378i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.14147 | + | 5.44119i | −0.191539 | + | 0.331755i | −0.945760 | − | 0.324865i | \(-0.894681\pi\) |
0.754221 | + | 0.656620i | \(0.228014\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 11.3777 | − | 9.34768i | 0.688608 | − | 0.565748i | ||||
\(274\) | 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 | ||||||||
\(279\) | −4.97807 | − | 13.7433i | −0.298030 | − | 0.822790i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9133 | − | 10.9196i | 1.12827 | − | 0.651407i | 0.184771 | − | 0.982782i | \(-0.440846\pi\) |
0.943499 | + | 0.331374i | \(0.107512\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 13.8869 | + | 5.06658i | 0.822588 | + | 0.300119i | ||||
\(286\) | 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 | ||||||||
\(291\) | 25.9248 | + | 9.45857i | 1.51974 | + | 0.554471i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6330 | − | 21.8810i | 0.738027 | − | 1.27830i | −0.215355 | − | 0.976536i | \(-0.569091\pi\) |
0.953382 | − | 0.301765i | \(-0.0975757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5710 | + | 26.9698i | 0.906578 | + | 1.57024i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.70500 | + | 8.19317i | 0.273012 | + | 0.475416i | ||||
\(298\) | 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 | ||||||||
\(303\) | −12.3745 | − | 14.7705i | −0.710896 | − | 0.848545i | ||||
\(304\) | 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 | ||||||||
\(309\) | −0.800634 | + | 0.670756i | −0.0455465 | + | 0.0381580i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.74484 | − | 8.21830i | −0.269055 | − | 0.466017i | 0.699563 | − | 0.714571i | \(-0.253378\pi\) |
−0.968618 | + | 0.248554i | \(0.920045\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −26.4640 | + | 9.29947i | −1.49108 | + | 0.523966i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7559 | + | 7.94197i | 0.772608 | + | 0.446065i | 0.833804 | − | 0.552060i | \(-0.186158\pi\) |
−0.0611961 | + | 0.998126i | \(0.519492\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.07939 | + | 10.5298i | 0.340380 | + | 0.589556i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.2954 | + | 7.76954i | 1.18859 | + | 0.433654i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14.1727i | − | 0.788591i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.8410 | + | 12.0326i | 1.15605 | + | 0.667446i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.67642 | − | 0.820849i | 0.258607 | − | 0.0453930i | ||||
\(328\) | 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 | ||||||||
\(333\) | 5.10757 | − | 1.85006i | 0.279893 | − | 0.101382i | ||||
\(334\) | 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 | ||||||||
\(339\) | −2.29982 | − | 13.1022i | −0.124909 | − | 0.711613i | ||||
\(340\) | 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 | ||||||||
\(345\) | −18.0584 | + | 15.1290i | −0.972233 | + | 0.814519i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.18003 | + | 2.41334i | −0.224396 | + | 0.129555i | −0.607984 | − | 0.793949i | \(-0.708022\pi\) |
0.383588 | + | 0.923504i | \(0.374688\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 16.6967 | + | 0.0387633i | 0.891206 | + | 0.00206903i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.9914 | −1.86240 | −0.931201 | − | 0.364505i | \(-0.881238\pi\) | ||||
−0.931201 | + | 0.364505i | \(0.881238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26.9628i | − | 1.43104i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.0724 | + | 20.7799i | 0.903565 | + | 1.09979i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.6396 | + | 12.4936i | −1.14209 | + | 0.659388i | −0.946948 | − | 0.321386i | \(-0.895851\pi\) |
−0.195146 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58394 | + | 11.4037i | −0.346523 | + | 0.600196i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.55801 | − | 10.2151i | −0.449179 | − | 0.536153i | ||||
\(364\) | 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 | ||||||||
\(369\) | 23.0962 | + | 19.4410i | 1.20234 | + | 1.01206i | ||||
\(370\) | 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 | ||||||||
\(375\) | −9.78499 | − | 11.6796i | −0.505295 | − | 0.603134i | ||||
\(376\) | 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 | ||||||||
\(381\) | −19.9378 | − | 23.7983i | −1.02145 | − | 1.21923i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.7719 | −1.26579 | −0.632893 | − | 0.774239i | \(-0.718133\pi\) | ||||
−0.632893 | + | 0.774239i | \(0.718133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.8042 | + | 8.35886i | −0.754494 | + | 0.426007i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.3266 | − | 4.82715i | 0.677431 | − | 0.245378i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.0227i | − | 1.16729i | −0.812007 | − | 0.583647i | \(-0.801625\pi\) | ||
0.812007 | − | 0.583647i | \(-0.198375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5608 | + | 11.2934i | 0.989232 | + | 0.571133i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8767 | − | 22.5318i | −0.952204 | − | 1.13658i | ||||
\(394\) | 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 | ||||||||
\(399\) | 1.80862 | + | 10.9180i | 0.0905442 | + | 0.546585i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.32384i | 0.265860i | 0.991125 | + | 0.132930i | \(0.0424385\pi\) | ||||
−0.991125 | + | 0.132930i | \(0.957561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6563 | −0.779898 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −29.8541 | − | 10.9708i | −1.48346 | − | 0.545143i | ||||
\(406\) | 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 | ||||||||
\(411\) | −7.38380 | + | 6.18602i | −0.364216 | + | 0.305134i | ||||
\(412\) | 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 | ||||||||
\(417\) | 4.30496 | + | 24.5256i | 0.210815 | + | 1.20102i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.94504 | + | 3.36891i | −0.0950215 | + | 0.164582i | −0.909618 | − | 0.415447i | \(-0.863625\pi\) |
0.814596 | + | 0.580029i | \(0.196959\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 18.1810 | + | 15.3037i | 0.883992 | + | 0.744092i | ||||
\(424\) | 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 | ||||||||
\(429\) | 9.96738 | − | 1.74957i | 0.481230 | − | 0.0844698i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7505 | + | 6.20681i | 0.517834 | + | 0.298971i | 0.736048 | − | 0.676929i | \(-0.236690\pi\) |
−0.218214 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2979i | 1.21574i | 0.794036 | + | 0.607870i | \(0.207976\pi\) | ||||
−0.794036 | + | 0.607870i | \(0.792024\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.4523 | − | 14.0292i | −1.84365 | − | 0.672649i | ||||
\(436\) | 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 | ||||||||
\(441\) | −15.8036 | − | 13.8292i | −0.752550 | − | 0.658535i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3051 | − | 6.52699i | −0.537120 | − | 0.310107i | 0.206791 | − | 0.978385i | \(-0.433698\pi\) |
−0.743911 | + | 0.668279i | \(0.767031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.3773 | − | 42.2227i | −1.15560 | − | 2.00155i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.52526 | + | 7.14230i | −0.403231 | + | 0.337819i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.468645i | − | 0.0221167i | −0.999939 | − | 0.0110584i | \(-0.996480\pi\) | ||
0.999939 | − | 0.0110584i | \(-0.00352006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8460 | + | 9.14868i | 0.746158 | + | 0.430795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.7887 | − | 21.2331i | −0.835787 | − | 0.997618i | ||||
\(454\) | 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 | ||||||||
\(459\) | −0.0707962 | + | 30.4945i | −0.00330448 | + | 1.42336i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9115 | + | 22.3633i | 0.601347 | + | 1.04156i | 0.992617 | + | 0.121288i | \(0.0387023\pi\) |
−0.391271 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 28.0176 | + | 10.2221i | 1.29929 | + | 0.474041i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.26091 | − | 2.18396i | −0.0583480 | − | 0.101062i | 0.835376 | − | 0.549679i | \(-0.185250\pi\) |
−0.893724 | + | 0.448617i | \(0.851917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5536 | + | 17.8809i | −0.487319 | + | 0.825662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.6613 | + | 8.26791i | 1.04418 | + | 0.380965i | ||||
\(472\) | 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 | ||||||||
\(477\) | −5.05312 | + | 6.00318i | −0.231366 | + | 0.274867i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.4924 | −0.525103 | −0.262552 | − | 0.964918i | \(-0.584564\pi\) | ||||
−0.262552 | + | 0.964918i | \(0.584564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.81854i | − | 0.265303i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.5099 | − | 6.20374i | −0.751228 | − | 0.282280i | ||||
\(484\) | 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 | ||||||||
\(489\) | 9.25506 | − | 25.3670i | 0.418528 | − | 1.14713i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3592 | − | 11.1771i | −0.873669 | − | 0.504413i | −0.00510349 | − | 0.999987i | \(-0.501624\pi\) |
−0.868566 | + | 0.495574i | \(0.834958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.2438i | 1.76745i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.9793 | − | 3.37686i | −0.853057 | − | 0.151779i | ||||
\(496\) | 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 | ||||||||
\(501\) | 22.4754 | − | 3.94508i | 1.00413 | − | 0.176253i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.60926 | −0.339280 | −0.169640 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169640 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.3159 | 1.74953 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.58787 | + | 4.35215i | −0.0705197 | + | 0.193286i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.78746 | −0.300849 | −0.150424 | − | 0.988622i | \(-0.548064\pi\) | ||||
−0.150424 | + | 0.988622i | \(0.548064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.344945 | − | 35.9479i | 0.0152595 | − | 1.59024i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.29951 | + | 10.8528i | −0.278130 | + | 0.479163i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 2.13111i | − | 0.0939078i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4738 | + | 7.20174i | 0.548596 | + | 0.316732i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1206 | − | 3.35622i | 0.839300 | − | 0.147322i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8435 | + | 23.9777i | −0.606497 | + | 1.05048i | 0.385316 | + | 0.922785i | \(0.374092\pi\) |
−0.991813 | + | 0.127698i | \(0.959241\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | 12.0719 | − | 32.1268i | 0.526861 | − | 1.40213i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 28.5943i | − | 1.24559i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.18740 | 0.355974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.8559 | + | 9.00327i | −1.07865 | + | 0.390709i | ||||
\(532\) | 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 | ||||||||
\(537\) | −3.19073 | − | 18.1778i | −0.137690 | − | 0.784428i | ||||
\(538\) | 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 | ||||||||
\(543\) | 15.7858 | − | 13.2251i | 0.677435 | − | 0.567542i | ||||
\(544\) | 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 | ||||||||
\(549\) | 20.0424 | − | 23.8107i | 0.855390 | − | 1.01622i | ||||
\(550\) | 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 | ||||||||
\(555\) | −3.79897 | + | 10.4125i | −0.161257 | + | 0.441986i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.14983 | + | 4.70530i | 0.345319 | + | 0.199370i | 0.662622 | − | 0.748954i | \(-0.269444\pi\) |
−0.317303 | + | 0.948324i | \(0.602777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.1817i | − | 0.642117i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.19536 | + | 18.2042i | 0.134908 | + | 0.768580i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.5319 | − | 26.9020i | −0.654591 | − | 1.13378i | −0.981996 | − | 0.188901i | \(-0.939508\pi\) |
0.327405 | − | 0.944884i | \(-0.393826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.5056 | + | 13.5710i | 0.988888 | + | 0.570935i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.83694 | − | 23.5006i | −0.161136 | − | 0.986932i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.4099 | + | 10.0516i | 0.729859 | + | 0.421384i | 0.818371 | − | 0.574691i | \(-0.194878\pi\) |
−0.0885114 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −0.0670662 | − | 0.382080i | −0.00280173 | − | 0.0159616i | ||||
\(574\) | 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 | ||||||||
\(579\) | −15.4793 | + | 42.4268i | −0.643297 | + | 1.76320i | ||||
\(580\) | 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 | ||||||||
\(585\) | −21.9385 | + | 26.0633i | −0.907046 | + | 1.07758i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.37708 | − | 4.11722i | −0.0981125 | − | 0.169936i | 0.812791 | − | 0.582556i | \(-0.197947\pi\) |
−0.910903 | + | 0.412620i | \(0.864614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.88332 | − | 10.1902i | 0.242418 | − | 0.419880i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.07504 | − | 1.73843i | 0.0853556 | − | 0.0715094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0354 | + | 22.5780i | 0.535300 | + | 0.927166i | 0.999149 | + | 0.0412519i | \(0.0131346\pi\) |
−0.463849 | + | 0.885914i | \(0.653532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −54.8703 | − | 0.526519i | −2.24946 | − | 0.0215852i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.65840 | − | 26.5392i | −0.190656 | − | 1.08618i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.8178 | + | 13.7512i | −0.973168 | + | 0.561859i | −0.900200 | − | 0.435476i | \(-0.856580\pi\) |
−0.0729672 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −22.1357 | + | 8.01795i | −0.901435 | + | 0.326516i | ||||
\(604\) | 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 | ||||||||
\(609\) | −5.00801 | − | 30.2316i | −0.202935 | − | 1.22505i | ||||
\(610\) | 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 | ||||||||
\(615\) | −60.6692 | + | 10.6492i | −2.44642 | + | 0.429418i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.15715 | + | 2.97748i | 0.207619 | + | 0.119869i | 0.600204 | − | 0.799847i | \(-0.295086\pi\) |
−0.392585 | + | 0.919716i | \(0.628419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.3650i | − | 1.30086i | −0.759567 | − | 0.650429i | \(-0.774589\pi\) | ||
0.759567 | − | 0.650429i | \(-0.225411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.95902 | − | 17.3424i | −0.399642 | − | 0.695926i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.5526 | − | 31.4337i | 0.743296 | − | 1.25936i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.35758 | −0.254303 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.60679 | + | 7.14490i | −0.104105 | + | 0.285340i | ||||
\(628\) | 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 | ||||||||
\(633\) | −23.8227 | + | 4.18158i | −0.946868 | + | 0.166203i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.3459 | 2.51380 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.6918 | + | 10.8707i | −0.780218 | + | 0.430711i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.5347 | + | 4.00944i | 0.891457 | + | 0.158611i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.8536i | − | 0.981659i | −0.871256 | − | 0.490829i | \(-0.836694\pi\) | ||
0.871256 | − | 0.490829i | \(-0.163306\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −9.91224 | + | 27.1682i | −0.390294 | + | 1.06975i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.7208 | − | 28.9613i | 0.657363 | − | 1.13859i | −0.323933 | − | 0.946080i | \(-0.605005\pi\) |
0.981296 | − | 0.192506i | \(-0.0616614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8761 | + | 8.01138i | −0.544686 | + | 0.314474i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.64900 | + | 22.0278i | 0.143016 | + | 0.863337i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.4238i | 1.03404i | 0.855972 | + | 0.517022i | \(0.172959\pi\) | ||||
−0.855972 | + | 0.517022i | \(0.827041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 59.9745 | 2.34340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.2502 | − | 31.1856i | 1.02412 | − | 1.21667i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8862 | − | 14.9454i | 1.00838 | − | 0.582191i | 0.0976658 | − | 0.995219i | \(-0.468862\pi\) |
0.910718 | + | 0.413029i | \(0.135529\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 30.6842 | + | 11.1950i | 1.19168 | + | 0.434779i | ||||
\(664\) | 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 | ||||||||
\(669\) | 40.2529 | + | 14.6862i | 1.55627 | + | 0.567800i | ||||
\(670\) | 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 | ||||||||
\(675\) | 33.7466 | − | 19.3793i | 1.29891 | − | 0.745910i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.75631 | − | 4.77407i | 0.105934 | − | 0.183483i | −0.808186 | − | 0.588928i | \(-0.799550\pi\) |
0.914119 | + | 0.405445i | \(0.132884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.3026 | − | 21.4264i | −1.39317 | − | 0.822268i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.94253 | + | 8.28680i | 0.266038 | + | 0.317551i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0097 | + | 13.8620i | 0.918706 | + | 0.530415i | 0.883222 | − | 0.468955i | \(-0.155369\pi\) |
0.0354840 | + | 0.999370i | \(0.488703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 19.6540i | − | 0.750942i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.0537 | − | 17.6384i | 0.803248 | − | 0.672947i | ||||
\(688\) | 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 | ||||||||
\(693\) | −4.78464 | − | 13.6159i | −0.181754 | − | 0.517225i | ||||
\(694\) | 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 | ||||||||
\(699\) | −5.53461 | − | 2.01929i | −0.209338 | − | 0.0763764i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.07738i | 0.0406922i | 0.999793 | + | 0.0203461i | \(0.00647681\pi\) | ||||
−0.999793 | + | 0.0203461i | \(0.993523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.78710 | + | 2.18648i | 0.142833 | + | 0.0824648i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −47.7581 | + | 8.38294i | −1.79867 | + | 0.315720i | ||||
\(706\) | 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 | ||||||||
\(711\) | 4.22889 | + | 3.55963i | 0.158596 | + | 0.133496i | ||||
\(712\) | 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 | ||||||||
\(717\) | 5.65275 | + | 32.2041i | 0.211106 | + | 1.20268i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.89267 | − | 10.2064i | −0.219760 | − | 0.380635i | 0.734975 | − | 0.678094i | \(-0.237194\pi\) |
−0.954734 | + | 0.297460i | \(0.903861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.38930 | − | 0.784436i | 0.0517403 | − | 0.0292139i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.8496 | + | 12.4407i | −0.552263 | + | 0.462676i | ||||
\(724\) | 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 | ||||||||
\(729\) | 13.6084 | − | 23.3198i | 0.504016 | − | 0.863694i | ||||
\(730\) | 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 | ||||||||
\(735\) | 42.3368 | − | 6.59654i | 1.56162 | − | 0.243317i | ||||
\(736\) | 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 | ||||||||
\(741\) | 8.63159 | + | 10.3029i | 0.317089 | + | 0.378487i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0951 | + | 17.9528i | 1.14077 | + | 0.658623i | 0.946621 | − | 0.322350i | \(-0.104473\pi\) |
0.194147 | + | 0.980972i | \(0.437806\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 22.6923i | − | 0.831382i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.6900 | − | 11.4787i | 1.15948 | − | 0.419984i | ||||
\(748\) | 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 | ||||||||
\(753\) | −17.1894 | − | 20.5178i | −0.626417 | − | 0.747709i | ||||
\(754\) | 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 | ||||||||
\(759\) | −7.78399 | − | 9.29119i | −0.282541 | − | 0.337249i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9766 | 0.977902 | 0.488951 | − | 0.872311i | \(-0.337380\pi\) | ||||
0.488951 | + | 0.872311i | \(0.337380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.25223 | − | 0.0695902i | −0.262548 | − | 0.00251933i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −47.6013 | − | 40.0679i | −1.72103 | − | 1.44866i | ||||
\(766\) | 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 | ||||||||
\(771\) | 11.8403 | + | 14.1329i | 0.426419 | + | 0.508985i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.46864 | + | 11.2040i | −0.232661 | + | 0.402980i | −0.958590 | − | 0.284789i | \(-0.908077\pi\) |
0.725929 | + | 0.687769i | \(0.241410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.6015 | + | 18.2451i | −1.13516 | + | 0.655384i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.18643 | + | 1.35612i | −0.293686 | + | 0.0486505i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.3020i | 0.870710i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8726 | 0.496399 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.4431 | − | 30.0510i | 0.623366 | − | 1.07394i | ||||
\(784\) | 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 | ||||||||
\(789\) | −14.7208 | + | 12.3328i | −0.524073 | + | 0.439059i | ||||
\(790\) | 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 | ||||||||
\(795\) | −2.76796 | − | 15.7692i | −0.0981693 | − | 0.559277i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.71671 | − | 11.6337i | 0.237918 | − | 0.412086i | −0.722199 | − | 0.691686i | \(-0.756868\pi\) |
0.960117 | + | 0.279600i | \(0.0902017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2444 | + | 40.2605i | 0.822328 | + | 1.42431i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.9134 | − | 14.0951i | 1.37494 | − | 0.498028i | ||||
\(802\) | 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 | ||||||||
\(807\) | 10.7185 | − | 1.88141i | 0.377309 | − | 0.0662288i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.38524 | − | 5.41857i | −0.329967 | − | 0.190507i | 0.325859 | − | 0.945418i | \(-0.394346\pi\) |
−0.655827 | + | 0.754912i | \(0.727680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.3334i | 1.24072i | 0.784316 | + | 0.620361i | \(0.213014\pi\) | ||||
−0.784316 | + | 0.620361i | \(0.786986\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.79343 | − | 0.654327i | −0.0628983 | − | 0.0229483i | ||||
\(814\) | 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 | ||||||||
\(819\) | −25.0664 | − | 4.70846i | −0.875890 | − | 0.164527i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6412 | − | 9.60782i | −0.580783 | − | 0.335315i | 0.180661 | − | 0.983545i | \(-0.442176\pi\) |
−0.761445 | + | 0.648230i | \(0.775510\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 18.0798 | − | 15.1469i | 0.629456 | − | 0.527347i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.356137i | − | 0.0123841i | −0.999981 | − | 0.00619205i | \(-0.998029\pi\) | ||
0.999981 | − | 0.00619205i | \(-0.00197100\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 17.0869 | + | 20.3955i | 0.592739 | + | 0.707510i | ||||
\(832\) | 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 | ||||||||
\(837\) | −12.7096 | + | 21.8962i | −0.439309 | + | 0.756843i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.662663 | − | 1.14777i | −0.0228777 | − | 0.0396253i | 0.854360 | − | 0.519682i | \(-0.173949\pi\) |
−0.877238 | + | 0.480056i | \(0.840616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.85791 | − | 13.6103i | 0.270962 | − | 0.469321i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.5353 | − | 12.9649i | −1.22390 | − | 0.446536i | ||||
\(844\) | 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 | ||||||||
\(849\) | 18.0262 | + | 6.57681i | 0.618659 | + | 0.225716i | ||||
\(850\) | 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 | ||||||||
\(855\) | −8.71972 | − | 24.0731i | −0.298208 | − | 0.823282i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.8773 | −0.713155 | −0.356578 | − | 0.934266i | \(-0.616056\pi\) | ||||
−0.356578 | + | 0.934266i | \(0.616056\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.7094i | − | 0.467758i | −0.972266 | − | 0.233879i | \(-0.924858\pi\) | ||
0.972266 | − | 0.233879i | \(-0.0751419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.2740 | − | 35.6313i | −0.997657 | − | 1.21431i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.1125 | − | 16.2307i | 0.956959 | − | 0.552501i | 0.0617233 | − | 0.998093i | \(-0.480340\pi\) |
0.895236 | + | 0.445593i | \(0.147007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8047 | + | 34.3027i | −0.673379 | + | 1.16633i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.3542 | + | 28.3795i | −0.351646 | + | 0.963819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.90139 | + | 1.67512i | 0.0984228 | + | 0.0568244i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.2169i | 0.854444i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.2784 | − | 44.9409i | −0.550941 | − | 1.52102i | ||||
\(874\) | 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 | ||||||||
\(879\) | −43.1030 | + | 7.56583i | −1.45383 | + | 0.255189i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.8019 | 0.734526 | 0.367263 | − | 0.930117i | \(-0.380295\pi\) | ||||
0.367263 | + | 0.930117i | \(0.380295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4085 | −0.821411 | −0.410705 | − | 0.911768i | \(-0.634717\pi\) | ||||
−0.410705 | + | 0.911768i | \(0.634717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.4876 | − | 50.6723i | 0.621454 | − | 1.70333i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.7444 | −1.13303 | −0.566513 | − | 0.824053i | \(-0.691708\pi\) | ||||
−0.566513 | + | 0.824053i | \(0.691708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3169 | + | 41.2961i | 0.782024 | + | 1.38503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.64455 | − | 15.3602i | 0.189099 | − | 0.514585i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.1303i | 0.640170i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.6113 | + | 18.8281i | 1.09007 | + | 0.629355i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.0978 | + | 3.70328i | −0.704436 | + | 0.123649i | ||||
\(898\) | 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 | ||||||||
\(903\) | −21.3600 | + | 3.53837i | −0.710815 | + | 0.117750i | ||||
\(904\) | 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 | ||||||||
\(909\) | −5.84637 | + | 32.8589i | −0.193912 | + | 1.08986i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5047 | + | 12.4157i | −0.712481 | + | 0.411351i | −0.811979 | − | 0.583686i | \(-0.801610\pi\) |
0.0994977 | + | 0.995038i | \(0.468276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6913 | − | 10.2141i | 0.585498 | − | 0.338038i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.9787 | + | 62.5462i | 0.362944 | + | 2.06771i | ||||
\(916\) | 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 | ||||||||
\(921\) | −16.2194 | + | 13.5883i | −0.534447 | + | 0.447750i | ||||
\(922\) | 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 | ||||||||
\(927\) | 1.78111 | + | 0.316901i | 0.0584994 | + | 0.0104084i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.3310 | + | 23.0900i | −0.437376 | + | 0.757558i | −0.997486 | − | 0.0708606i | \(-0.977425\pi\) |
0.560110 | + | 0.828418i | \(0.310759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.324397 | − | 16.9017i | 0.0106317 | − | 0.553932i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.63360 | + | 15.4410i | −0.184436 | + | 0.505515i | ||||
\(934\) | 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 | ||||||||
\(939\) | −4.05790 | − | 23.1181i | −0.132424 | − | 0.754430i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.0136 | + | 27.7363i | 0.522028 | + | 0.904179i | 0.999672 | + | 0.0256254i | \(0.00815770\pi\) |
−0.477644 | + | 0.878554i | \(0.658509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.5410 | − | 19.3649i | −1.09224 | − | 0.630608i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.7830 | + | 24.7920i | 1.35920 | + | 0.806483i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5020 | − | 8.95009i | −0.503748 | − | 0.290839i | 0.226512 | − | 0.974008i | \(-0.427268\pi\) |
−0.730260 | + | 0.683169i | \(0.760601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.8305 | − | 37.8116i | −0.708650 | − | 1.22742i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.75640 | − | 27.0975i | −0.154237 | − | 0.878697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.2737i | − | 0.365191i | −0.983188 | − | 0.182596i | \(-0.941550\pi\) | ||
0.983188 | − | 0.182596i | \(-0.0584499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.685459 | + | 0.395750i | 0.0221809 | + | 0.0128062i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.21812 | − | 19.7840i | 0.233329 | − | 0.639525i | ||||
\(958\) | 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 | ||||||||
\(963\) | −13.3716 | − | 36.9158i | −0.430893 | − | 1.18959i | ||||
\(964\) | 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 | ||||||||
\(969\) | −18.8170 | + | 15.7645i | −0.604488 | + | 0.506429i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0807 | + | 33.0488i | 0.612330 | + | 1.06059i | 0.990847 | + | 0.134992i | \(0.0431010\pi\) |
−0.378517 | + | 0.925595i | \(0.623566\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.364967 | − | 38.0345i | 0.0117003 | − | 1.21933i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.20624 | − | 41.0543i | −0.230784 | − | 1.31479i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.5862 | − | 15.3496i | 0.850568 | − | 0.491076i | −0.0102745 | − | 0.999947i | \(-0.503271\pi\) |
0.860842 | + | 0.508872i | \(0.169937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7239 | − | 12.5423i | 0.694299 | − | 0.400854i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.29148 | − | 5.29580i | −0.200872 | − | 0.169082i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8057 | 0.823073 | 0.411536 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411536 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.52328i | 0.175986i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.0442 | − | 28.0486i | −0.733505 | − | 0.892796i | ||||
\(988\) | 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 | ||||||||
\(993\) | 18.7212 | − | 3.28612i | 0.594100 | − | 0.104282i | ||||
\(994\) | 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 | ||||||||
\(999\) | −8.13752 | − | 4.72342i | −0.257460 | − | 0.149443i |
(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 | 504.2.cx.a.185.7 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.3 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.18 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.1 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.1 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.3 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.3 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.3 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.24 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.3 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.24 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.7 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.3 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.3 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.18 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.1 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.1 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.7 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.7 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.24 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.24 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.18 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.18 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.3 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.3 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.3 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.3 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.3 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.3 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.3 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.3 | 48 | 252.187 | even | 6 |