Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.h.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35757 | − | 2.35137i | −0.959944 | − | 1.66267i | −0.722624 | − | 0.691241i | \(-0.757064\pi\) |
−0.237320 | − | 0.971432i | \(-0.576269\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.68597 | + | 4.65224i | −1.34299 | + | 2.32612i | ||||
\(5\) | 1.58639 | 0.709457 | 0.354728 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354728 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.15528 | 3.23688 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.15363 | − | 3.73020i | −0.681039 | − | 1.17959i | ||||
\(11\) | 1.34875 | 0.406664 | 0.203332 | − | 0.979110i | \(-0.434823\pi\) | ||||
0.203332 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58916 | + | 2.75251i | 0.440754 | + | 0.763409i | 0.997746 | − | 0.0671096i | \(-0.0213777\pi\) |
−0.556991 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.05696 | − | 12.2230i | −1.76424 | − | 3.05575i | ||||
\(17\) | 1.40027 | + | 2.42534i | 0.339615 | + | 0.588230i | 0.984360 | − | 0.176167i | \(-0.0563699\pi\) |
−0.644745 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.312846 | + | 0.541866i | −0.0717719 | + | 0.124313i | −0.899678 | − | 0.436554i | \(-0.856199\pi\) |
0.827906 | + | 0.560867i | \(0.189532\pi\) | |||||||
\(20\) | −4.26101 | + | 7.38028i | −0.952791 | + | 1.65028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.83102 | − | 3.17142i | −0.390375 | − | 0.676149i | ||||
\(23\) | 0.284867 | 0.0593989 | 0.0296995 | − | 0.999559i | \(-0.490545\pi\) | ||||
0.0296995 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.48336 | −0.496671 | ||||||||
\(26\) | 4.31479 | − | 7.47343i | 0.846199 | − | 1.46566i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27396 | + | 3.93861i | −0.422264 | + | 0.731382i | −0.996161 | − | 0.0875454i | \(-0.972098\pi\) |
0.573897 | + | 0.818928i | \(0.305431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.71502 | + | 6.43461i | −0.667238 | + | 1.15569i | 0.311435 | + | 0.950267i | \(0.399190\pi\) |
−0.978673 | + | 0.205423i | \(0.934143\pi\) | |||||||
\(32\) | −10.0053 | + | 17.3297i | −1.76870 | + | 3.06348i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.80191 | − | 6.58511i | 0.652023 | − | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.01126 | + | 6.94770i | −0.659447 | + | 1.14220i | 0.321312 | + | 0.946973i | \(0.395876\pi\) |
−0.980759 | + | 0.195222i | \(0.937457\pi\) | |||||||
\(38\) | 1.69884 | 0.275588 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.5239 | 2.29643 | ||||||||
\(41\) | −5.01329 | − | 8.68327i | −0.782944 | − | 1.35610i | −0.930219 | − | 0.367004i | \(-0.880384\pi\) |
0.147275 | − | 0.989096i | \(-0.452950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | + | 5.42022i | −0.477224 | + | 0.826576i | −0.999659 | − | 0.0261027i | \(-0.991690\pi\) |
0.522435 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(44\) | −3.62271 | + | 6.27472i | −0.546144 | + | 0.945950i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.386726 | − | 0.669829i | −0.0570197 | − | 0.0987609i | ||||
\(47\) | 5.57383 | + | 9.65415i | 0.813026 | + | 1.40820i | 0.910737 | + | 0.412988i | \(0.135515\pi\) |
−0.0977106 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.37132 | + | 5.83930i | 0.476777 | + | 0.825802i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.0738 | −2.36771 | ||||||||
\(53\) | 1.39349 | + | 2.41359i | 0.191410 | + | 0.331532i | 0.945718 | − | 0.324989i | \(-0.105361\pi\) |
−0.754308 | + | 0.656521i | \(0.772027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13965 | 0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.3482 | 1.62140 | ||||||||
\(59\) | 2.28734 | − | 3.96180i | 0.297787 | − | 0.515782i | −0.677842 | − | 0.735207i | \(-0.737085\pi\) |
0.975629 | + | 0.219425i | \(0.0704182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.192507 | + | 0.333432i | 0.0246480 | + | 0.0426916i | 0.878086 | − | 0.478502i | \(-0.158820\pi\) |
−0.853438 | + | 0.521194i | \(0.825487\pi\) | |||||||
\(62\) | 20.1736 | 2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | 2.52104 | + | 4.36656i | 0.312696 | + | 0.541605i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.26958 | − | 2.19898i | 0.155104 | − | 0.268648i | −0.777993 | − | 0.628273i | \(-0.783762\pi\) |
0.933097 | + | 0.359625i | \(0.117095\pi\) | |||||||
\(68\) | −15.0443 | −1.82439 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.45208 | 0.172330 | 0.0861651 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861651 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.234067 | + | 0.405416i | 0.0273955 | + | 0.0474503i | 0.879398 | − | 0.476087i | \(-0.157945\pi\) |
−0.852003 | + | 0.523538i | \(0.824612\pi\) | |||||||
\(74\) | 21.7822 | 2.53213 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.68059 | − | 2.91087i | −0.192777 | − | 0.333900i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.85620 | + | 13.6073i | 0.883892 | + | 1.53095i | 0.846978 | + | 0.531627i | \(0.178419\pi\) |
0.0369135 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(80\) | −11.1951 | − | 19.3905i | −1.25165 | − | 2.16792i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.6117 | + | 23.5762i | −1.50317 | + | 2.60356i | ||||
\(83\) | 6.99338 | − | 12.1129i | 0.767623 | − | 1.32956i | −0.171225 | − | 0.985232i | \(-0.554772\pi\) |
0.938848 | − | 0.344331i | \(-0.111894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22138 | + | 3.84754i | 0.240942 | + | 0.417324i | ||||
\(86\) | 16.9933 | 1.83243 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.3482 | 1.31632 | ||||||||
\(89\) | −1.29353 | + | 2.24046i | −0.137114 | + | 0.237488i | −0.926403 | − | 0.376534i | \(-0.877116\pi\) |
0.789289 | + | 0.614022i | \(0.210449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.765146 | + | 1.32527i | −0.0797719 | + | 0.138169i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.1337 | − | 26.2123i | 1.56092 | − | 2.70359i | ||||
\(95\) | −0.496297 | + | 0.859612i | −0.0509190 | + | 0.0881944i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.22962 | − | 12.5221i | 0.734057 | − | 1.27142i | −0.221079 | − | 0.975256i | \(-0.570958\pi\) |
0.955136 | − | 0.296168i | \(-0.0957089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.67023 | − | 11.5532i | 0.667023 | − | 1.15532i | ||||
\(101\) | −9.83776 | −0.978894 | −0.489447 | − | 0.872033i | \(-0.662801\pi\) | ||||
−0.489447 | + | 0.872033i | \(0.662801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0579 | 1.08957 | 0.544786 | − | 0.838575i | \(-0.316611\pi\) | ||||
0.544786 | + | 0.838575i | \(0.316611\pi\) | |||||||
\(104\) | 14.5492 | + | 25.2000i | 1.42667 | + | 2.47106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78350 | − | 6.55322i | 0.367486 | − | 0.636505i | ||||
\(107\) | −0.962153 | + | 1.66650i | −0.0930149 | + | 0.161106i | −0.908778 | − | 0.417279i | \(-0.862984\pi\) |
0.815764 | + | 0.578386i | \(0.196317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.30341 | + | 16.1140i | 0.891105 | + | 1.54344i | 0.838553 | + | 0.544821i | \(0.183402\pi\) |
0.0525523 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(110\) | −2.90472 | − | 5.03112i | −0.276954 | − | 0.479698i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.59338 | − | 2.75982i | −0.149893 | − | 0.259622i | 0.781295 | − | 0.624162i | \(-0.214560\pi\) |
−0.931188 | + | 0.364540i | \(0.881226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.451911 | 0.0421410 | ||||||||
\(116\) | −12.2156 | − | 21.1580i | −1.13419 | − | 1.96447i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4209 | −1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.18087 | −0.834624 | ||||||||
\(122\) | 0.522682 | − | 0.905312i | 0.0473214 | − | 0.0819631i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −19.9569 | − | 34.5664i | −1.79218 | − | 3.10415i | ||||
\(125\) | −11.8715 | −1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | −15.4267 | − | 26.7199i | −1.36354 | − | 2.36173i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.84495 | − | 11.8558i | 0.600341 | − | 1.03982i | ||||
\(131\) | 11.9726 | 1.04605 | 0.523024 | − | 0.852318i | \(-0.324804\pi\) | ||||
0.523024 | + | 0.852318i | \(0.324804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.89415 | −0.595564 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.8199 | + | 22.2046i | 1.09929 | + | 1.90403i | ||||
\(137\) | −16.5505 | −1.41401 | −0.707003 | − | 0.707211i | \(-0.749953\pi\) | ||||
−0.707003 | + | 0.707211i | \(0.749953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.95119 | + | 6.84367i | 0.335136 | + | 0.580472i | 0.983511 | − | 0.180849i | \(-0.0578845\pi\) |
−0.648375 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.97130 | − | 3.41438i | −0.165427 | − | 0.286529i | ||||
\(143\) | 2.14339 | + | 3.71245i | 0.179239 | + | 0.310451i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.60739 | + | 6.24819i | −0.299578 | + | 0.518884i | ||||
\(146\) | 0.635523 | − | 1.10076i | 0.0525962 | − | 0.0910994i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.5483 | − | 37.3227i | −1.77126 | − | 3.06791i | ||||
\(149\) | 13.6685 | 1.11977 | 0.559885 | − | 0.828570i | \(-0.310845\pi\) | ||||
0.559885 | + | 0.828570i | \(0.310845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.89963 | 0.317348 | 0.158674 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(152\) | −2.86420 | + | 4.96093i | −0.232317 | + | 0.402385i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.89349 | + | 10.2078i | −0.473376 | + | 0.819912i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.147176 | − | 0.254917i | 0.0117459 | − | 0.0203446i | −0.860093 | − | 0.510138i | \(-0.829594\pi\) |
0.871839 | + | 0.489793i | \(0.162928\pi\) | |||||||
\(158\) | 21.3306 | − | 36.9457i | 1.69697 | − | 2.93925i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.8723 | + | 27.4917i | −1.25482 | + | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.35455 | + | 9.27436i | −0.419401 | + | 0.726424i | −0.995879 | − | 0.0906886i | \(-0.971093\pi\) |
0.576478 | + | 0.817112i | \(0.304427\pi\) | |||||||
\(164\) | 53.8622 | 4.20593 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.9759 | −2.94750 | ||||||||
\(167\) | −1.59872 | − | 2.76907i | −0.123713 | − | 0.214277i | 0.797516 | − | 0.603298i | \(-0.206147\pi\) |
−0.921229 | + | 0.389020i | \(0.872814\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | − | 2.50997i | 0.111472 | − | 0.193074i | ||||
\(170\) | 6.03133 | − | 10.4466i | 0.462582 | − | 0.801215i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.8108 | − | 29.1171i | −1.28181 | − | 2.22016i | ||||
\(173\) | −5.71875 | − | 9.90517i | −0.434789 | − | 0.753076i | 0.562490 | − | 0.826804i | \(-0.309844\pi\) |
−0.997278 | + | 0.0737284i | \(0.976510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.51809 | − | 16.4858i | −0.717453 | − | 1.24266i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.02421 | 0.526487 | ||||||||
\(179\) | 0.549275 | + | 0.951372i | 0.0410547 | + | 0.0711089i | 0.885823 | − | 0.464024i | \(-0.153595\pi\) |
−0.844768 | + | 0.535133i | \(0.820262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.19013 | 0.237120 | 0.118560 | − | 0.992947i | \(-0.462172\pi\) | ||||
0.118560 | + | 0.992947i | \(0.462172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.60804 | 0.192267 | ||||||||
\(185\) | −6.36343 | + | 11.0218i | −0.467849 | + | 0.810338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88861 | + | 3.27118i | 0.138109 | + | 0.239212i | ||||
\(188\) | −59.8846 | −4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | 1.93407 | + | 3.34992i | 0.139945 | + | 0.242391i | 0.927475 | − | 0.373884i | \(-0.121974\pi\) |
−0.787531 | + | 0.616275i | \(0.788641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.06793 | − | 3.58175i | 0.148853 | − | 0.257820i | −0.781951 | − | 0.623340i | \(-0.785775\pi\) |
0.930804 | + | 0.365520i | \(0.119109\pi\) | |||||||
\(194\) | −39.2588 | −2.81862 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.889267 | 0.0633576 | 0.0316788 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316788 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.16193 | − | 5.47663i | −0.224143 | − | 0.388228i | 0.731919 | − | 0.681392i | \(-0.238625\pi\) |
−0.956062 | + | 0.293164i | \(0.905292\pi\) | |||||||
\(200\) | −22.7358 | −1.60767 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.3554 | + | 23.1323i | 0.939684 | + | 1.62758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.95305 | − | 13.7751i | −0.555465 | − | 0.962093i | ||||
\(206\) | −15.0119 | − | 26.0014i | −1.04593 | − | 1.81160i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.4293 | − | 38.8487i | 1.55519 | − | 2.69367i | ||||
\(209\) | −0.421952 | + | 0.730843i | −0.0291870 | + | 0.0505535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71291 | + | 9.89505i | 0.393293 | + | 0.681204i | 0.992882 | − | 0.119105i | \(-0.0380025\pi\) |
−0.599589 | + | 0.800308i | \(0.704669\pi\) | |||||||
\(212\) | −14.9715 | −1.02825 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.22475 | 0.357156 | ||||||||
\(215\) | −4.96441 | + | 8.59860i | −0.338570 | + | 0.586420i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.2600 | − | 43.7516i | 1.71082 | − | 2.96323i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.74705 | + | 9.95417i | −0.387466 | + | 0.671110i | ||||
\(221\) | −4.45051 | + | 7.70850i | −0.299373 | + | 0.518530i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.35953 | − | 14.4791i | 0.559796 | − | 0.969595i | −0.437717 | − | 0.899113i | \(-0.644213\pi\) |
0.997513 | − | 0.0704822i | \(-0.0224538\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.32625 | + | 7.49328i | −0.287778 | + | 0.498446i | ||||
\(227\) | −17.0700 | −1.13298 | −0.566489 | − | 0.824070i | \(-0.691698\pi\) | ||||
−0.566489 | + | 0.824070i | \(0.691698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7894 | 1.30772 | 0.653861 | − | 0.756615i | \(-0.273148\pi\) | ||||
0.653861 | + | 0.756615i | \(0.273148\pi\) | |||||||
\(230\) | −0.613500 | − | 1.06261i | −0.0404530 | − | 0.0700666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8187 | + | 36.0591i | −1.36682 | + | 2.36740i | ||||
\(233\) | 2.96579 | − | 5.13691i | 0.194296 | − | 0.336530i | −0.752374 | − | 0.658736i | \(-0.771091\pi\) |
0.946669 | + | 0.322207i | \(0.104425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.84228 | + | 15.3153i | 0.576807 | + | 0.999058i | ||||
\(236\) | 12.2875 | + | 21.2826i | 0.799847 | + | 1.38538i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0277 | + | 17.3685i | 0.648637 | + | 1.12347i | 0.983449 | + | 0.181187i | \(0.0579939\pi\) |
−0.334812 | + | 0.942285i | \(0.608673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.2887 | 1.88665 | 0.943326 | − | 0.331869i | \(-0.107679\pi\) | ||||
0.943326 | + | 0.331869i | \(0.107679\pi\) | |||||||
\(242\) | 12.4636 | + | 21.5877i | 0.801193 | + | 1.38771i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.06827 | −0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.98865 | −0.126535 | ||||||||
\(248\) | −34.0121 | + | 58.9107i | −2.15977 | + | 3.74083i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.1164 | + | 27.9144i | 1.01929 | + | 1.76546i | ||||
\(251\) | 22.7856 | 1.43821 | 0.719106 | − | 0.694901i | \(-0.244552\pi\) | ||||
0.719106 | + | 0.694901i | \(0.244552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | 11.3681 | + | 19.6901i | 0.713297 | + | 1.23547i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7821 | + | 27.3354i | −0.986381 | + | 1.70846i | ||||
\(257\) | 24.2889 | 1.51510 | 0.757550 | − | 0.652778i | \(-0.226396\pi\) | ||||
0.757550 | + | 0.652778i | \(0.226396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.0857 | −1.67979 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.2536 | − | 28.1520i | −1.00415 | − | 1.73924i | ||||
\(263\) | 8.61155 | 0.531011 | 0.265506 | − | 0.964109i | \(-0.414461\pi\) | ||||
0.265506 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.21062 | + | 3.82890i | 0.135797 | + | 0.235208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.82011 | + | 11.8128i | 0.416605 | + | 0.721581i | ||||
\(269\) | −7.61561 | − | 13.1906i | −0.464332 | − | 0.804247i | 0.534839 | − | 0.844954i | \(-0.320372\pi\) |
−0.999171 | + | 0.0407073i | \(0.987039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.33910 | − | 4.05144i | 0.142090 | − | 0.246108i | −0.786193 | − | 0.617981i | \(-0.787951\pi\) |
0.928284 | + | 0.371873i | \(0.121284\pi\) | |||||||
\(272\) | 19.7633 | − | 34.2310i | 1.19832 | − | 2.07556i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.4684 | + | 38.9164i | 1.35737 | + | 2.35103i | ||||
\(275\) | −3.34943 | −0.201978 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3907 | −0.984824 | −0.492412 | − | 0.870362i | \(-0.663885\pi\) | ||||
−0.492412 | + | 0.870362i | \(0.663885\pi\) | |||||||
\(278\) | 10.7280 | − | 18.5815i | 0.643423 | − | 1.11444i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75702 | + | 3.04325i | −0.104815 | + | 0.181545i | −0.913663 | − | 0.406473i | \(-0.866758\pi\) |
0.808848 | + | 0.588018i | \(0.200092\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0354 | + | 22.5780i | −0.774874 | + | 1.34212i | 0.159992 | + | 0.987118i | \(0.448853\pi\) |
−0.934865 | + | 0.355002i | \(0.884480\pi\) | |||||||
\(284\) | −3.90025 | + | 6.75543i | −0.231437 | + | 0.400861i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.81958 | − | 10.0798i | 0.344119 | − | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.57850 | − | 7.93019i | 0.269323 | − | 0.466482i | ||||
\(290\) | 19.5891 | 1.15031 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.51479 | −0.147167 | ||||||||
\(293\) | 9.44192 | + | 16.3539i | 0.551603 | + | 0.955404i | 0.998159 | + | 0.0606487i | \(0.0193169\pi\) |
−0.446556 | + | 0.894756i | \(0.647350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | − | 6.28497i | 0.211267 | − | 0.365925i | ||||
\(296\) | −36.7242 | + | 63.6082i | −2.13455 | + | 3.69715i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.5559 | − | 32.1398i | −1.07492 | − | 1.86181i | ||||
\(299\) | 0.452700 | + | 0.784099i | 0.0261803 | + | 0.0453456i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.29401 | − | 9.16950i | −0.304636 | − | 0.527645i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.83097 | 0.506491 | ||||||||
\(305\) | 0.305392 | + | 0.528954i | 0.0174867 | + | 0.0302878i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6407 | −1.23510 | −0.617551 | − | 0.786531i | \(-0.711875\pi\) | ||||
−0.617551 | + | 0.786531i | \(0.711875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 32.0032 | 1.81766 | ||||||||
\(311\) | 2.24724 | − | 3.89234i | 0.127429 | − | 0.220714i | −0.795251 | − | 0.606281i | \(-0.792661\pi\) |
0.922680 | + | 0.385567i | \(0.125994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.30102 | − | 7.44958i | −0.243108 | − | 0.421075i | 0.718490 | − | 0.695537i | \(-0.244834\pi\) |
−0.961598 | + | 0.274462i | \(0.911500\pi\) | |||||||
\(314\) | −0.799206 | −0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | −4.03128 | − | 6.98237i | −0.226419 | − | 0.392169i | 0.730325 | − | 0.683100i | \(-0.239369\pi\) |
−0.956744 | + | 0.290930i | \(0.906035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.06701 | + | 5.31221i | −0.171719 | + | 0.297427i | ||||
\(320\) | 41.4105 | 2.31492 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.75228 | −0.0974992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.94646 | − | 6.83546i | −0.218910 | − | 0.379163i | ||||
\(326\) | 29.0766 | 1.61041 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −45.8981 | − | 79.4978i | −2.53430 | − | 4.38953i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4513 | + | 19.8342i | 0.629419 | + | 1.09019i | 0.987668 | + | 0.156560i | \(0.0500405\pi\) |
−0.358249 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(332\) | 37.5681 | + | 65.0698i | 2.06182 | + | 3.57117i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.34075 | + | 7.51840i | −0.237515 | + | 0.411388i | ||||
\(335\) | 2.01405 | − | 3.48844i | 0.110039 | − | 0.190594i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81891 | − | 11.8107i | −0.371450 | − | 0.643369i | 0.618339 | − | 0.785911i | \(-0.287806\pi\) |
−0.989789 | + | 0.142542i | \(0.954472\pi\) | |||||||
\(338\) | −7.86916 | −0.428026 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.8662 | −1.29433 | ||||||||
\(341\) | −5.01065 | + | 8.67869i | −0.271342 | + | 0.469978i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −28.6502 | + | 49.6237i | −1.54472 | + | 2.67553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5272 | + | 26.8938i | −0.834746 | + | 1.44582i | ||||
\(347\) | −1.41282 | + | 2.44707i | −0.0758440 | + | 0.131366i | −0.901453 | − | 0.432877i | \(-0.857498\pi\) |
0.825609 | + | 0.564243i | \(0.190832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81202 | + | 3.13851i | −0.0969951 | + | 0.168000i | −0.910440 | − | 0.413642i | \(-0.864256\pi\) |
0.813444 | + | 0.581643i | \(0.197590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.4947 | + | 23.3734i | −0.719268 | + | 1.24581i | ||||
\(353\) | 2.75401 | 0.146581 | 0.0732907 | − | 0.997311i | \(-0.476650\pi\) | ||||
0.0732907 | + | 0.997311i | \(0.476650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.30357 | 0.122261 | ||||||||
\(356\) | −6.94877 | − | 12.0356i | −0.368284 | − | 0.637887i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.49135 | − | 2.58310i | 0.0788205 | − | 0.136521i | ||||
\(359\) | −8.40076 | + | 14.5505i | −0.443375 | + | 0.767948i | −0.997937 | − | 0.0641941i | \(-0.979552\pi\) |
0.554562 | + | 0.832142i | \(0.312886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.30425 | + | 16.1154i | 0.489698 | + | 0.848181i | ||||
\(362\) | −4.33081 | − | 7.50119i | −0.227622 | − | 0.394254i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.371322 | + | 0.643149i | 0.0194359 | + | 0.0336640i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.9339 | −1.24934 | −0.624670 | − | 0.780889i | \(-0.714767\pi\) | ||||
−0.624670 | + | 0.780889i | \(0.714767\pi\) | |||||||
\(368\) | −2.01030 | − | 3.48193i | −0.104794 | − | 0.181508i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.5551 | 1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1606 | −0.992098 | −0.496049 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496049 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(374\) | 5.12784 | − | 8.88168i | 0.265154 | − | 0.459261i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 51.0299 | + | 88.3865i | 2.63167 | + | 4.55818i | ||||
\(377\) | −14.4548 | −0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | −2.66608 | − | 4.61779i | −0.136767 | − | 0.236888i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.25127 | − | 9.09546i | 0.268678 | − | 0.465364i | ||||
\(383\) | 20.1435 | 1.02929 | 0.514643 | − | 0.857405i | \(-0.327925\pi\) | ||||
0.514643 | + | 0.857405i | \(0.327925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2294 | −0.571561 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 38.8372 | + | 67.2679i | 1.97166 | + | 3.41501i | ||||
\(389\) | −13.3947 | −0.679139 | −0.339570 | − | 0.940581i | \(-0.610281\pi\) | ||||
−0.339570 | + | 0.940581i | \(0.610281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.398891 | + | 0.690899i | 0.0201728 | + | 0.0349402i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.20724 | − | 2.09100i | −0.0608198 | − | 0.105343i | ||||
\(395\) | 12.4630 | + | 21.5866i | 0.627083 | + | 1.08614i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00664 | − | 15.6000i | 0.452031 | − | 0.782940i | −0.546482 | − | 0.837471i | \(-0.684033\pi\) |
0.998512 | + | 0.0545313i | \(0.0173665\pi\) | |||||||
\(398\) | −8.58506 | + | 14.8698i | −0.430330 | + | 0.745354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5249 | + | 30.3541i | 0.876247 | + | 1.51770i | ||||
\(401\) | −28.8675 | −1.44157 | −0.720787 | − | 0.693157i | \(-0.756219\pi\) | ||||
−0.720787 | + | 0.693157i | \(0.756219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.6151 | −1.17635 | ||||||||
\(404\) | 26.4240 | − | 45.7676i | 1.31464 | − | 2.27703i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.41019 | + | 9.37073i | −0.268173 | + | 0.464490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.42937 | − | 9.40395i | 0.268465 | − | 0.464995i | −0.700000 | − | 0.714142i | \(-0.746817\pi\) |
0.968466 | + | 0.249147i | \(0.0801502\pi\) | |||||||
\(410\) | −21.5936 | + | 37.4012i | −1.06643 | + | 1.84711i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.7014 | + | 51.4443i | −1.46328 | + | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0943 | − | 19.2158i | 0.544595 | − | 0.943267i | ||||
\(416\) | −63.6001 | −3.11825 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.29131 | 0.112072 | ||||||||
\(419\) | 0.247572 | + | 0.428807i | 0.0120947 | + | 0.0209486i | 0.872009 | − | 0.489489i | \(-0.162817\pi\) |
−0.859915 | + | 0.510438i | \(0.829483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | − | 16.4600i | 0.463158 | − | 0.802212i | −0.535959 | − | 0.844244i | \(-0.680050\pi\) |
0.999116 | + | 0.0420318i | \(0.0133831\pi\) | |||||||
\(422\) | 15.5113 | − | 26.8664i | 0.755079 | − | 1.30784i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.7578 | + | 22.0971i | 0.619572 | + | 1.07313i | ||||
\(425\) | −3.47737 | − | 6.02298i | −0.168677 | − | 0.292157i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.16864 | − | 8.95234i | −0.249835 | − | 0.432728i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.9580 | 1.30003 | ||||||||
\(431\) | −8.46073 | − | 14.6544i | −0.407539 | − | 0.705878i | 0.587074 | − | 0.809533i | \(-0.300280\pi\) |
−0.994613 | + | 0.103655i | \(0.966946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.4740 | −1.60866 | −0.804330 | − | 0.594183i | \(-0.797476\pi\) | ||||
−0.804330 | + | 0.594183i | \(0.797476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −99.9548 | −4.78697 | ||||||||
\(437\) | −0.0891197 | + | 0.154360i | −0.00426317 | + | 0.00738403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4657 | − | 18.1272i | −0.499502 | − | 0.865163i | 0.500498 | − | 0.865738i | \(-0.333150\pi\) |
−1.00000 | 0.000574559i | \(0.999817\pi\) | ||||||||
\(440\) | 19.5891 | 0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | −15.4290 | − | 26.7238i | −0.733054 | − | 1.26969i | −0.955572 | − | 0.294759i | \(-0.904761\pi\) |
0.222517 | − | 0.974929i | \(-0.428573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.05205 | + | 3.55425i | −0.0972763 | + | 0.168487i | ||||
\(446\) | −45.3945 | −2.14949 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.2789 | 1.57053 | 0.785263 | − | 0.619162i | \(-0.212528\pi\) | ||||
0.785263 | + | 0.619162i | \(0.212528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.76168 | − | 11.7116i | −0.318395 | − | 0.551477i | ||||
\(452\) | 17.1191 | 0.805217 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.1737 | + | 40.1380i | 1.08760 | + | 1.88377i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8952 | − | 20.6031i | −0.556434 | − | 0.963772i | −0.997790 | − | 0.0664402i | \(-0.978836\pi\) |
0.441356 | − | 0.897332i | \(-0.354498\pi\) | |||||||
\(458\) | −26.8654 | − | 46.5323i | −1.25534 | − | 2.17431i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.21382 | + | 2.10240i | −0.0565947 | + | 0.0980249i | ||||
\(461\) | −8.53122 | + | 14.7765i | −0.397339 | + | 0.688211i | −0.993397 | − | 0.114731i | \(-0.963400\pi\) |
0.596058 | + | 0.802941i | \(0.296733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | + | 31.3922i | 0.842306 | + | 1.45892i | 0.887940 | + | 0.459959i | \(0.152136\pi\) |
−0.0456338 | + | 0.998958i | \(0.514531\pi\) | |||||||
\(464\) | 64.1889 | 2.97990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1051 | −0.746052 | ||||||||
\(467\) | −4.09580 | + | 7.09413i | −0.189531 | + | 0.328277i | −0.945094 | − | 0.326799i | \(-0.894030\pi\) |
0.755563 | + | 0.655076i | \(0.227363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.0080 | − | 41.5830i | 1.10740 | − | 1.91808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.9413 | − | 36.2714i | 0.963900 | − | 1.66952i | ||||
\(473\) | −4.22074 | + | 7.31054i | −0.194070 | + | 0.336139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.776909 | − | 1.34565i | 0.0356470 | − | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.2265 | − | 47.1577i | 1.24531 | − | 2.15694i | ||||
\(479\) | 25.5549 | 1.16763 | 0.583817 | − | 0.811885i | \(-0.301559\pi\) | ||||
0.583817 | + | 0.811885i | \(0.301559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4982 | −1.16262 | ||||||||
\(482\) | −39.7614 | − | 68.8687i | −1.81108 | − | 3.13688i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.6596 | − | 42.7116i | 1.12089 | − | 1.94144i | ||||
\(485\) | 11.4690 | − | 19.8649i | 0.520782 | − | 0.902020i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.46140 | + | 5.99533i | 0.156851 | + | 0.271674i | 0.933732 | − | 0.357974i | \(-0.116532\pi\) |
−0.776880 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(488\) | 1.76246 | + | 3.05266i | 0.0797826 | + | 0.138188i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7262 | − | 32.4348i | −0.845103 | − | 1.46376i | −0.885532 | − | 0.464578i | \(-0.846206\pi\) |
0.0404294 | − | 0.999182i | \(-0.487127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7366 | −0.573628 | ||||||||
\(494\) | 2.69973 | + | 4.67607i | 0.121467 | + | 0.210386i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 104.867 | 4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6250 | 1.14713 | 0.573566 | − | 0.819159i | \(-0.305560\pi\) | ||||
0.573566 | + | 0.819159i | \(0.305560\pi\) | |||||||
\(500\) | 31.8867 | − | 55.2293i | 1.42601 | − | 2.46993i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.9329 | − | 53.5774i | −1.38060 | − | 2.39127i | ||||
\(503\) | 5.79692 | 0.258472 | 0.129236 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129236 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | −0.521598 | − | 0.903434i | −0.0231878 | − | 0.0401625i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.4920 | − | 38.9573i | 0.997921 | − | 1.72845i | ||||
\(509\) | −25.1395 | −1.11429 | −0.557144 | − | 0.830416i | \(-0.688103\pi\) | ||||
−0.557144 | + | 0.830416i | \(0.688103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 23.9940 | 1.06039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −32.9738 | − | 57.1123i | −1.45441 | − | 2.51911i | ||||
\(515\) | 17.5423 | 0.773004 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.51771 | + | 13.0211i | 0.330629 | + | 0.572665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.0808 | + | 39.9771i | 1.01216 | + | 1.75311i | ||||
\(521\) | 3.64828 | + | 6.31900i | 0.159834 | + | 0.276841i | 0.934809 | − | 0.355152i | \(-0.115571\pi\) |
−0.774975 | + | 0.631992i | \(0.782237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.38637 | + | 14.5256i | −0.366710 | + | 0.635161i | −0.989049 | − | 0.147587i | \(-0.952849\pi\) |
0.622339 | + | 0.782748i | \(0.286183\pi\) | |||||||
\(524\) | −32.1580 | + | 55.6993i | −1.40483 | + | 2.43324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6908 | − | 20.2490i | −0.509741 | − | 0.882898i | ||||
\(527\) | −20.8081 | −0.906416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9189 | −0.996472 | ||||||||
\(530\) | 6.00212 | − | 10.3960i | 0.260716 | − | 0.451573i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9339 | − | 27.5982i | 0.690172 | − | 1.19541i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.52635 | + | 2.64372i | −0.0659900 | + | 0.114298i | ||||
\(536\) | 11.6234 | − | 20.1322i | 0.502053 | − | 0.869581i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.6774 | + | 35.8143i | −0.891466 | + | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.64908 | − | 4.58834i | 0.113893 | − | 0.197268i | −0.803444 | − | 0.595381i | \(-0.797001\pi\) |
0.917337 | + | 0.398112i | \(0.130335\pi\) | |||||||
\(542\) | −12.7019 | −0.545595 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −56.0404 | −2.40271 | ||||||||
\(545\) | 14.7589 | + | 25.5631i | 0.632200 | + | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | − | 28.4619i | 0.702603 | − | 1.21694i | −0.264947 | − | 0.964263i | \(-0.585354\pi\) |
0.967550 | − | 0.252681i | \(-0.0813123\pi\) | |||||||
\(548\) | 44.4542 | − | 76.9970i | 1.89899 | − | 3.28915i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.54708 | + | 7.87577i | 0.193888 | + | 0.335824i | ||||
\(551\) | −1.42280 | − | 2.46436i | −0.0606133 | − | 0.104985i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.2515 | + | 38.5408i | 0.945376 | + | 1.63744i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −42.4512 | −1.80033 | ||||||||
\(557\) | −9.40798 | − | 16.2951i | −0.398629 | − | 0.690446i | 0.594928 | − | 0.803779i | \(-0.297181\pi\) |
−0.993557 | + | 0.113333i | \(0.963847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8923 | −0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.54108 | 0.402466 | ||||||||
\(563\) | 13.8325 | − | 23.9586i | 0.582970 | − | 1.00973i | −0.412155 | − | 0.911114i | \(-0.635224\pi\) |
0.995125 | − | 0.0986197i | \(-0.0314427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.52773 | − | 4.37816i | −0.106343 | − | 0.184191i | ||||
\(566\) | 70.7856 | 2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | −20.0916 | − | 34.7996i | −0.842282 | − | 1.45888i | −0.887961 | − | 0.459920i | \(-0.847878\pi\) |
0.0456782 | − | 0.998956i | \(-0.485455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.40565 | − | 5.89875i | 0.142522 | − | 0.246855i | −0.785924 | − | 0.618323i | \(-0.787812\pi\) |
0.928446 | + | 0.371468i | \(0.121146\pi\) | |||||||
\(572\) | −23.0283 | −0.962862 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.707427 | −0.0295017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2111 | + | 31.5425i | 0.758138 | + | 1.31313i | 0.943799 | + | 0.330519i | \(0.107224\pi\) |
−0.185661 | + | 0.982614i | \(0.559443\pi\) | |||||||
\(578\) | −24.8625 | −1.03414 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.3787 | − | 33.5649i | −0.804658 | − | 1.39371i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.87947 | + | 3.25534i | 0.0778397 | + | 0.134822i | ||||
\(584\) | 2.14295 | + | 3.71170i | 0.0886759 | + | 0.153591i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.6361 | − | 44.4030i | 1.05902 | − | 1.83427i | ||||
\(587\) | −5.57943 | + | 9.66385i | −0.230288 | + | 0.398870i | −0.957893 | − | 0.287126i | \(-0.907300\pi\) |
0.727605 | + | 0.685996i | \(0.240633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32446 | − | 4.02609i | −0.0957779 | − | 0.165892i | ||||
\(590\) | −19.7044 | −0.811218 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 113.229 | 4.65369 | ||||||||
\(593\) | 9.90427 | − | 17.1547i | 0.406720 | − | 0.704459i | −0.587800 | − | 0.809006i | \(-0.700006\pi\) |
0.994520 | + | 0.104547i | \(0.0333392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.7133 | + | 63.5893i | −1.50384 | + | 2.60472i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.22914 | − | 2.12893i | 0.0502633 | − | 0.0870586i | ||||
\(599\) | −9.06600 | + | 15.7028i | −0.370427 | + | 0.641598i | −0.989631 | − | 0.143632i | \(-0.954122\pi\) |
0.619204 | + | 0.785230i | \(0.287455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3285 | + | 21.3536i | −0.502889 | + | 0.871030i | 0.497105 | + | 0.867690i | \(0.334396\pi\) |
−0.999994 | + | 0.00333942i | \(0.998937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.4743 | + | 18.1420i | −0.426194 | + | 0.738189i | ||||
\(605\) | −14.5645 | −0.592130 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2775 | 0.701273 | 0.350637 | − | 0.936512i | \(-0.385965\pi\) | ||||
0.350637 | + | 0.936512i | \(0.385965\pi\) | |||||||
\(608\) | −6.26024 | − | 10.8431i | −0.253886 | − | 0.439744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.829179 | − | 1.43618i | 0.0335725 | − | 0.0581492i | ||||
\(611\) | −17.7154 | + | 30.6840i | −0.716689 | + | 1.24134i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.77828 | − | 16.9365i | −0.394941 | − | 0.684058i | 0.598153 | − | 0.801382i | \(-0.295902\pi\) |
−0.993094 | + | 0.117324i | \(0.962568\pi\) | |||||||
\(614\) | 29.3787 | + | 50.8855i | 1.18563 | + | 2.05357i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8723 | − | 18.8314i | −0.437702 | − | 0.758122i | 0.559810 | − | 0.828621i | \(-0.310874\pi\) |
−0.997512 | + | 0.0704988i | \(0.977541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.8048 | 1.35873 | 0.679366 | − | 0.733800i | \(-0.262255\pi\) | ||||
0.679366 | + | 0.733800i | \(0.262255\pi\) | |||||||
\(620\) | −31.6595 | − | 54.8359i | −1.27148 | − | 2.20226i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.2031 | −0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.41615 | −0.256646 | ||||||||
\(626\) | −11.6778 | + | 20.2266i | −0.466740 | + | 0.808418i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.790623 | + | 1.36940i | 0.0315493 | + | 0.0546450i | ||||
\(629\) | −22.4674 | −0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | 71.9258 | + | 124.579i | 2.86105 | + | 4.95549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.9454 | + | 18.9581i | −0.434699 | + | 0.752921i | ||||
\(635\) | −13.2843 | −0.527169 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6547 | 0.659365 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.4729 | − | 42.3883i | −0.967375 | − | 1.67554i | ||||
\(641\) | −15.9180 | −0.628724 | −0.314362 | − | 0.949303i | \(-0.601791\pi\) | ||||
−0.314362 | + | 0.949303i | \(0.601791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.2527 | − | 22.9544i | −0.522636 | − | 0.905231i | −0.999653 | − | 0.0263376i | \(-0.991616\pi\) |
0.477017 | − | 0.878894i | \(-0.341718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.37883 | + | 4.12026i | 0.0935938 | + | 0.162109i | ||||
\(647\) | 0.00801958 | + | 0.0138903i | 0.000315282 | + | 0.000546085i | 0.866183 | − | 0.499727i | \(-0.166566\pi\) |
−0.865868 | + | 0.500273i | \(0.833233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.08506 | − | 5.34348i | 0.121099 | − | 0.209750i | ||||
\(650\) | −10.7152 | + | 18.5592i | −0.420283 | + | 0.727951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.7644 | − | 49.8214i | −1.12650 | − | 1.95115i | ||||
\(653\) | 33.2879 | 1.30266 | 0.651328 | − | 0.758796i | \(-0.274212\pi\) | ||||
0.651328 | + | 0.758796i | \(0.274212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9932 | 0.742126 | ||||||||
\(656\) | −70.7571 | + | 122.555i | −2.76260 | + | 4.78497i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4156 | + | 33.6288i | −0.756324 | + | 1.30999i | 0.188389 | + | 0.982094i | \(0.439673\pi\) |
−0.944713 | + | 0.327897i | \(0.893660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.65322 | + | 4.59551i | −0.103198 | + | 0.178745i | −0.913001 | − | 0.407958i | \(-0.866241\pi\) |
0.809802 | + | 0.586703i | \(0.199574\pi\) | |||||||
\(662\) | 31.0917 | − | 53.8525i | 1.20842 | − | 2.09304i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64.0264 | − | 110.897i | 2.48471 | − | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.647777 | + | 1.12198i | −0.0250820 | + | 0.0434433i | ||||
\(668\) | 17.1765 | 0.664579 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.9368 | −0.422527 | ||||||||
\(671\) | 0.259644 | + | 0.449717i | 0.0100235 | + | 0.0173611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03565 | + | 5.25789i | −0.117016 | + | 0.202677i | −0.918584 | − | 0.395227i | \(-0.870666\pi\) |
0.801568 | + | 0.597903i | \(0.203999\pi\) | |||||||
\(674\) | −18.5142 | + | 32.0676i | −0.713142 | + | 1.23520i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.78465 | + | 13.4834i | 0.299410 | + | 0.518593i | ||||
\(677\) | −17.3925 | − | 30.1247i | −0.668449 | − | 1.15779i | −0.978338 | − | 0.207014i | \(-0.933625\pi\) |
0.309889 | − | 0.950773i | \(-0.399708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.3373 | + | 35.2253i | 0.779901 | + | 1.35083i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.2091 | 1.04189 | ||||||||
\(683\) | 9.71206 | + | 16.8218i | 0.371622 | + | 0.643667i | 0.989815 | − | 0.142358i | \(-0.0454686\pi\) |
−0.618194 | + | 0.786026i | \(0.712135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.2556 | −1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 88.3352 | 3.36775 | ||||||||
\(689\) | −4.42895 | + | 7.67117i | −0.168730 | + | 0.292248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.31837 | + | 5.74759i | 0.126237 | + | 0.218649i | 0.922216 | − | 0.386676i | \(-0.126377\pi\) |
−0.795979 | + | 0.605324i | \(0.793043\pi\) | |||||||
\(692\) | 61.4416 | 2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | 6.26814 | + | 10.8567i | 0.237764 | + | 0.411820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0399 | − | 24.3178i | 0.531799 | − | 0.921103i | ||||
\(698\) | 9.83974 | 0.372440 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9153 | 0.525574 | 0.262787 | − | 0.964854i | \(-0.415358\pi\) | ||||
0.262787 | + | 0.964854i | \(0.415358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.50982 | − | 4.34713i | −0.0946595 | − | 0.163955i | ||||
\(704\) | 35.2072 | 1.32692 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.73876 | − | 6.47571i | −0.140710 | − | 0.243717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0778 | − | 29.5796i | −0.641370 | − | 1.11089i | −0.985127 | − | 0.171827i | \(-0.945033\pi\) |
0.343757 | − | 0.939059i | \(-0.388300\pi\) | |||||||
\(710\) | −3.12725 | − | 5.41655i | −0.117364 | − | 0.203280i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.8426 | + | 20.5120i | −0.443821 | + | 0.768721i | ||||
\(713\) | −1.05829 | + | 1.83301i | −0.0396332 | + | 0.0686467i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.40025 | + | 5.88941i | 0.127162 | + | 0.220251i | ||||
\(716\) | −5.90135 | −0.220544 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 45.6183 | 1.70246 | ||||||||
\(719\) | −22.1450 | + | 38.3563i | −0.825870 | + | 1.43045i | 0.0753825 | + | 0.997155i | \(0.475982\pi\) |
−0.901253 | + | 0.433294i | \(0.857351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.2623 | − | 43.7556i | 0.940165 | − | 1.62841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.56860 | + | 14.8413i | −0.318450 | + | 0.551571i | ||||
\(725\) | 5.64705 | − | 9.78099i | 0.209726 | − | 0.363257i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1247 | − | 24.4647i | 0.523857 | − | 0.907346i | −0.475758 | − | 0.879576i | \(-0.657826\pi\) |
0.999614 | − | 0.0277700i | \(-0.00884060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.00819 | − | 1.74623i | 0.0373147 | − | 0.0646310i | ||||
\(731\) | −17.5278 | −0.648290 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0169 | −0.924020 | −0.462010 | − | 0.886875i | \(-0.652872\pi\) | ||||
−0.462010 | + | 0.886875i | \(0.652872\pi\) | |||||||
\(734\) | 32.4919 | + | 56.2776i | 1.19930 | + | 2.07724i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.85018 | + | 4.93666i | −0.105059 | + | 0.181968i | ||||
\(737\) | 1.71235 | − | 2.96587i | 0.0630752 | − | 0.109249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0115 | − | 27.7327i | −0.588992 | − | 1.02016i | −0.994365 | − | 0.106013i | \(-0.966192\pi\) |
0.405373 | − | 0.914151i | \(-0.367142\pi\) | |||||||
\(740\) | −34.1840 | − | 59.2084i | −1.25663 | − | 2.17655i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4031 | − | 33.6072i | −0.711833 | − | 1.23293i | −0.964169 | − | 0.265290i | \(-0.914532\pi\) |
0.252336 | − | 0.967640i | \(-0.418801\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.6837 | 0.794428 | ||||||||
\(746\) | 26.0118 | + | 45.0537i | 0.952359 | + | 1.64953i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.2911 | −0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6991 | 0.791811 | 0.395905 | − | 0.918291i | \(-0.370431\pi\) | ||||
0.395905 | + | 0.918291i | \(0.370431\pi\) | |||||||
\(752\) | 78.6685 | − | 136.258i | 2.86874 | − | 4.96881i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.6233 | + | 33.9885i | 0.714638 | + | 1.23779i | ||||
\(755\) | 6.18635 | 0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | −13.6802 | − | 23.6949i | −0.496889 | − | 0.860637i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.54374 | + | 7.86999i | −0.164819 | + | 0.285475i | ||||
\(761\) | 13.3210 | 0.482884 | 0.241442 | − | 0.970415i | \(-0.422380\pi\) | ||||
0.241442 | + | 0.970415i | \(0.422380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.7795 | −0.751775 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.3462 | − | 47.3649i | −0.988057 | − | 1.71137i | ||||
\(767\) | 14.5398 | 0.525003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.3568 | + | 47.3833i | 0.986510 | + | 1.70869i | 0.635022 | + | 0.772494i | \(0.280991\pi\) |
0.351488 | + | 0.936192i | \(0.385676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.1088 | + | 19.2410i | 0.399814 | + | 0.692498i | ||||
\(773\) | 1.18021 | + | 2.04418i | 0.0424491 | + | 0.0735240i | 0.886469 | − | 0.462787i | \(-0.153151\pi\) |
−0.844020 | + | 0.536311i | \(0.819817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.22573 | − | 15.9794i | 0.331398 | − | 0.573998i | ||||
\(776\) | 66.1892 | − | 114.643i | 2.37606 | − | 4.11545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1842 | + | 31.4960i | 0.651936 | + | 1.12919i | ||||
\(779\) | 6.27356 | 0.224774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.95850 | 0.0700805 | ||||||||
\(782\) | 1.08304 | − | 1.87588i | 0.0387295 | − | 0.0670814i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.233479 | − | 0.404398i | 0.00833323 | − | 0.0144336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.833971 | − | 1.44448i | 0.0297278 | − | 0.0514901i | −0.850779 | − | 0.525524i | \(-0.823869\pi\) |
0.880507 | + | 0.474034i | \(0.157203\pi\) | |||||||
\(788\) | −2.38855 | + | 4.13708i | −0.0850884 | + | 0.147377i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.8388 | − | 58.6105i | 1.20393 | − | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.611849 | + | 1.05975i | −0.0217274 | + | 0.0376330i | ||||
\(794\) | −48.9085 | −1.73570 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.9715 | 1.20409 | ||||||||
\(797\) | 14.3148 | + | 24.7939i | 0.507055 | + | 0.878244i | 0.999967 | + | 0.00816511i | \(0.00259906\pi\) |
−0.492912 | + | 0.870079i | \(0.664068\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | + | 27.0368i | −0.552232 | + | 0.956493i | ||||
\(800\) | 24.8467 | − | 43.0358i | 0.878464 | − | 1.52154i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.1895 | + | 67.8783i | 1.38383 | + | 2.39687i | ||||
\(803\) | 0.315698 | + | 0.546805i | 0.0111408 | + | 0.0192963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0591 | + | 55.5279i | 1.12923 | + | 1.95589i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −90.0675 | −3.16856 | ||||||||
\(809\) | −1.42846 | − | 2.47416i | −0.0502219 | − | 0.0869868i | 0.839822 | − | 0.542862i | \(-0.182660\pi\) |
−0.890043 | + | 0.455876i | \(0.849326\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.2917 | 0.923225 | 0.461613 | − | 0.887082i | \(-0.347271\pi\) | ||||
0.461613 | + | 0.887082i | \(0.347271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.3788 | 1.02973 | ||||||||
\(815\) | −8.49443 | + | 14.7128i | −0.297547 | + | 0.515366i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.95802 | − | 3.39139i | −0.0685025 | − | 0.118650i | ||||
\(818\) | −29.4829 | −1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | −1.32925 | − | 2.30232i | −0.0463910 | − | 0.0803517i | 0.841897 | − | 0.539638i | \(-0.181439\pi\) |
−0.888289 | + | 0.459286i | \(0.848105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.10769 | − | 10.5788i | 0.212901 | − | 0.368755i | −0.739721 | − | 0.672914i | \(-0.765042\pi\) |
0.952621 | + | 0.304160i | \(0.0983756\pi\) | |||||||
\(824\) | 101.239 | 3.52681 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.15812 | −0.318459 | −0.159230 | − | 0.987242i | \(-0.550901\pi\) | ||||
−0.159230 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.17156 | − | 15.8856i | −0.318541 | − | 0.551730i | 0.661642 | − | 0.749819i | \(-0.269860\pi\) |
−0.980184 | + | 0.198089i | \(0.936526\pi\) | |||||||
\(830\) | −60.2447 | −2.09113 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.4828 | + | 71.8503i | 1.43816 | + | 2.49096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.53620 | − | 4.39284i | −0.0877690 | − | 0.152020i | ||||
\(836\) | −2.26670 | − | 3.92605i | −0.0783956 | − | 0.135785i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.672190 | − | 1.16427i | 0.0232204 | − | 0.0402190i | ||||
\(839\) | 9.47055 | − | 16.4035i | 0.326960 | − | 0.566311i | −0.654947 | − | 0.755675i | \(-0.727309\pi\) |
0.981907 | + | 0.189364i | \(0.0606425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15821 | + | 7.20224i | 0.143387 | + | 0.248353i | ||||
\(842\) | −51.6049 | −1.77842 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −61.3789 | −2.11275 | ||||||||
\(845\) | 2.29889 | − | 3.98179i | 0.0790842 | − | 0.136978i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.6676 | − | 34.0652i | 0.675387 | − | 1.16980i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.44151 | + | 16.3532i | −0.323841 | + | 0.560909i | ||||
\(851\) | −1.14268 | + | 1.97917i | −0.0391704 | + | 0.0678452i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.97922 | + | 17.2845i | −0.341682 | + | 0.591811i | −0.984745 | − | 0.174002i | \(-0.944330\pi\) |
0.643063 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.80878 | + | 15.2573i | −0.301078 | + | 0.521482i | ||||
\(857\) | 16.4000 | 0.560214 | 0.280107 | − | 0.959969i | \(-0.409630\pi\) | ||||
0.280107 | + | 0.959969i | \(0.409630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7151 | 1.15034 | 0.575172 | − | 0.818033i | \(-0.304935\pi\) | ||||
0.575172 | + | 0.818033i | \(0.304935\pi\) | |||||||
\(860\) | −26.6685 | − | 46.1912i | −0.909389 | − | 1.57511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.9720 | + | 39.7887i | −0.782429 | + | 1.35521i | ||||
\(863\) | −14.3415 | + | 24.8403i | −0.488191 | + | 0.845572i | −0.999908 | − | 0.0135822i | \(-0.995677\pi\) |
0.511716 | + | 0.859154i | \(0.329010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.07219 | − | 15.7135i | −0.308464 | − | 0.534275i | ||||
\(866\) | 45.4432 | + | 78.7100i | 1.54422 | + | 2.67467i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.5961 | + | 18.3529i | 0.359447 | + | 0.622581i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.07027 | 0.273451 | ||||||||
\(872\) | 85.1753 | + | 147.528i | 2.88440 | + | 4.99593i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.483944 | 0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5243 | −0.996964 | −0.498482 | − | 0.866900i | \(-0.666109\pi\) | ||||
−0.498482 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(878\) | −28.4159 | + | 49.2177i | −0.958989 | + | 1.66102i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.0994 | − | 26.1530i | −0.509001 | − | 0.881616i | ||||
\(881\) | −57.5032 | −1.93733 | −0.968666 | − | 0.248366i | \(-0.920107\pi\) | ||||
−0.968666 | + | 0.248366i | \(0.920107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | −23.9079 | − | 41.4097i | −0.804109 | − | 1.39276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.8918 | + | 72.5587i | −1.40738 | + | 2.43766i | ||||
\(887\) | −37.0951 | −1.24553 | −0.622766 | − | 0.782408i | \(-0.713991\pi\) | ||||
−0.622766 | + | 0.782408i | \(0.713991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.1432 | 0.373519 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.9070 | + | 77.7812i | 1.50360 | + | 2.60431i | ||||
\(893\) | −6.97501 | −0.233410 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.871366 | + | 1.50925i | 0.0291266 | + | 0.0504487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.1783 | − | 78.2511i | −1.50762 | − | 2.61127i | ||||
\(899\) | −16.8956 | − | 29.2641i | −0.563501 | − | 0.976012i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.90251 | + | 6.75935i | −0.130012 | + | 0.225187i | ||||
\(902\) | −18.3589 | + | 31.7985i | −0.611284 | + | 1.05877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5879 | − | 25.2669i | −0.485185 | − | 0.840366i | ||||
\(905\) | 5.06080 | 0.168227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4088 | 0.810479 | 0.405240 | − | 0.914210i | \(-0.367188\pi\) | ||||
0.405240 | + | 0.914210i | \(0.367188\pi\) | |||||||
\(908\) | 45.8496 | − | 79.4139i | 1.52157 | − | 2.63544i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5493 | − | 21.7360i | 0.415776 | − | 0.720146i | −0.579733 | − | 0.814806i | \(-0.696843\pi\) |
0.995510 | + | 0.0946604i | \(0.0301765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.43234 | − | 16.3373i | 0.312165 | − | 0.540685i | ||||
\(914\) | −32.2971 | + | 55.9401i | −1.06829 | + | 1.85034i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.1538 | + | 92.0652i | −1.75625 | + | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2988 | − | 24.7662i | 0.471674 | − | 0.816963i | −0.527801 | − | 0.849368i | \(-0.676983\pi\) |
0.999475 | + | 0.0324050i | \(0.0103167\pi\) | |||||||
\(920\) | 4.13738 | 0.136405 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46.3268 | 1.52569 | ||||||||
\(923\) | 2.30759 | + | 3.99686i | 0.0759553 | + | 0.131558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96139 | − | 17.2536i | 0.327528 | − | 0.567296i | ||||
\(926\) | 49.2098 | − | 85.2339i | 1.61713 | − | 2.80096i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.5033 | − | 78.8140i | −1.49372 | − | 2.58720i | ||||
\(929\) | −22.7285 | − | 39.3669i | −0.745698 | − | 1.29159i | −0.949868 | − | 0.312651i | \(-0.898783\pi\) |
0.204170 | − | 0.978935i | \(-0.434550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.9321 | + | 27.5952i | 0.521873 | + | 0.903910i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.2413 | 0.727757 | ||||||||
\(935\) | 2.99609 | + | 5.18937i | 0.0979825 | + | 0.169711i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0083 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −95.0005 | −3.09857 | ||||||||
\(941\) | 6.35657 | − | 11.0099i | 0.207218 | − | 0.358912i | −0.743619 | − | 0.668604i | \(-0.766892\pi\) |
0.950837 | + | 0.309691i | \(0.100226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.42812 | − | 2.47358i | −0.0465060 | − | 0.0805508i | ||||
\(944\) | −64.5667 | −2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | 23.7724 | + | 41.1749i | 0.772498 | + | 1.33801i | 0.936190 | + | 0.351494i | \(0.114326\pi\) |
−0.163692 | + | 0.986511i | \(0.552340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.743940 | + | 1.28854i | −0.0241493 | + | 0.0418279i | ||||
\(950\) | −4.21882 | −0.136877 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.2355 | −1.23857 | −0.619285 | − | 0.785166i | \(-0.712577\pi\) | ||||
−0.619285 | + | 0.785166i | \(0.712577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.06820 | + | 5.31428i | 0.0992847 | + | 0.171966i | ||||
\(956\) | −107.736 | −3.48444 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.6925 | − | 60.0891i | −1.12086 | − | 1.94139i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1028 | − | 20.9627i | −0.390413 | − | 0.676215i | ||||
\(962\) | 34.6154 | + | 59.9557i | 1.11605 | + | 1.93305i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −78.6687 | + | 136.258i | −2.53375 | + | 4.38858i | ||||
\(965\) | 3.28054 | − | 5.68207i | 0.105604 | − | 0.182912i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4093 | − | 35.3499i | −0.656317 | − | 1.13678i | −0.981562 | − | 0.191145i | \(-0.938780\pi\) |
0.325244 | − | 0.945630i | \(-0.394553\pi\) | |||||||
\(968\) | −84.0534 | −2.70158 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −62.2799 | −1.99969 | ||||||||
\(971\) | 22.4735 | − | 38.9253i | 0.721210 | − | 1.24917i | −0.239305 | − | 0.970944i | \(-0.576920\pi\) |
0.960515 | − | 0.278228i | \(-0.0897470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.39817 | − | 16.2781i | 0.301137 | − | 0.521584i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.71703 | − | 4.70603i | 0.0869699 | − | 0.150636i | ||||
\(977\) | 26.7552 | − | 46.3414i | 0.855974 | − | 1.48259i | −0.0197635 | − | 0.999805i | \(-0.506291\pi\) |
0.875738 | − | 0.482787i | \(-0.160375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.74465 | + | 3.02182i | −0.0557593 | + | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −50.8442 | + | 88.0647i | −1.62250 | + | 2.81026i | ||||
\(983\) | −11.6056 | −0.370160 | −0.185080 | − | 0.982723i | \(-0.559254\pi\) | ||||
−0.185080 | + | 0.982723i | \(0.559254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.41073 | 0.0449495 | ||||||||
\(986\) | 17.2908 | + | 29.9485i | 0.550651 | + | 0.953756i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.34147 | − | 9.25170i | 0.169935 | − | 0.294336i | ||||
\(989\) | −0.891454 | + | 1.54404i | −0.0283466 | + | 0.0490977i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0046 | − | 22.5246i | −0.413104 | − | 0.715517i | 0.582123 | − | 0.813100i | \(-0.302222\pi\) |
−0.995227 | + | 0.0975835i | \(0.968889\pi\) | |||||||
\(992\) | −74.3398 | − | 128.760i | −2.36029 | − | 4.08814i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.01607 | − | 8.68808i | −0.159020 | − | 0.275431i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.8998 | −1.48533 | −0.742666 | − | 0.669662i | \(-0.766439\pi\) | ||||
−0.742666 | + | 0.669662i | \(0.766439\pi\) | |||||||
\(998\) | −34.7876 | − | 60.2539i | −1.10118 | − | 1.90731i | ||||
\(999\) | 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 | 1323.2.g.h.667.1 | 24 | ||
3.2 | odd | 2 | 441.2.g.h.79.11 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.883.2 | 24 | |||
7.3 | odd | 6 | 1323.2.h.h.802.11 | 24 | |||
7.4 | even | 3 | 1323.2.h.h.802.12 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.883.1 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.g.h.667.2 | 24 | ||
9.4 | even | 3 | 1323.2.h.h.226.12 | 24 | |||
9.5 | odd | 6 | 441.2.h.h.373.2 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.295.12 | yes | 24 | ||
21.5 | even | 6 | 441.2.f.h.295.11 | yes | 24 | ||
21.11 | odd | 6 | 441.2.h.h.214.2 | 24 | |||
21.17 | even | 6 | 441.2.h.h.214.1 | 24 | |||
21.20 | even | 2 | 441.2.g.h.79.12 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bh.1.1 | 12 | |||
63.4 | even | 3 | inner | 1323.2.g.h.361.1 | 24 | ||
63.5 | even | 6 | 441.2.f.h.148.11 | ✓ | 24 | ||
63.13 | odd | 6 | 1323.2.h.h.226.11 | 24 | |||
63.16 | even | 3 | 3969.2.a.bi.1.12 | 12 | |||
63.23 | odd | 6 | 441.2.f.h.148.12 | yes | 24 | ||
63.31 | odd | 6 | inner | 1323.2.g.h.361.2 | 24 | ||
63.32 | odd | 6 | 441.2.g.h.67.11 | 24 | |||
63.40 | odd | 6 | 1323.2.f.h.442.1 | 24 | |||
63.41 | even | 6 | 441.2.h.h.373.1 | 24 | |||
63.47 | even | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.58 | even | 3 | 1323.2.f.h.442.2 | 24 | |||
63.59 | even | 6 | 441.2.g.h.67.12 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bi.1.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 63.5 | even | 6 | ||
441.2.f.h.148.12 | yes | 24 | 63.23 | odd | 6 | ||
441.2.f.h.295.11 | yes | 24 | 21.5 | even | 6 | ||
441.2.f.h.295.12 | yes | 24 | 21.2 | odd | 6 | ||
441.2.g.h.67.11 | 24 | 63.32 | odd | 6 | |||
441.2.g.h.67.12 | 24 | 63.59 | even | 6 | |||
441.2.g.h.79.11 | 24 | 3.2 | odd | 2 | |||
441.2.g.h.79.12 | 24 | 21.20 | even | 2 | |||
441.2.h.h.214.1 | 24 | 21.17 | even | 6 | |||
441.2.h.h.214.2 | 24 | 21.11 | odd | 6 | |||
441.2.h.h.373.1 | 24 | 63.41 | even | 6 | |||
441.2.h.h.373.2 | 24 | 9.5 | odd | 6 | |||
1323.2.f.h.442.1 | 24 | 63.40 | odd | 6 | |||
1323.2.f.h.442.2 | 24 | 63.58 | even | 3 | |||
1323.2.f.h.883.1 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.883.2 | 24 | 7.2 | even | 3 | |||
1323.2.g.h.361.1 | 24 | 63.4 | even | 3 | inner | ||
1323.2.g.h.361.2 | 24 | 63.31 | odd | 6 | inner | ||
1323.2.g.h.667.1 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.g.h.667.2 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.226.11 | 24 | 63.13 | odd | 6 | |||
1323.2.h.h.226.12 | 24 | 9.4 | even | 3 | |||
1323.2.h.h.802.11 | 24 | 7.3 | odd | 6 | |||
1323.2.h.h.802.12 | 24 | 7.4 | even | 3 | |||
3969.2.a.bh.1.1 | 12 | 63.2 | odd | 6 | |||
3969.2.a.bh.1.2 | 12 | 63.47 | even | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.61 | odd | 6 | |||
3969.2.a.bi.1.12 | 12 | 63.16 | even | 3 |