Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 897.4 | ||
Root | \(-0.793353 - 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.897 |
Dual form | 1024.2.g.f.129.4 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.12197 | + | 2.70868i | 0.647770 | + | 1.56386i | 0.815965 | + | 0.578102i | \(0.196206\pi\) |
−0.168194 | + | 0.985754i | \(0.553794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.366025 | − | 0.151613i | −0.163692 | − | 0.0678033i | 0.299333 | − | 0.954149i | \(-0.403236\pi\) |
−0.463025 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.06528 | − | 3.06528i | −1.15857 | − | 1.15857i | −0.984784 | − | 0.173784i | \(-0.944401\pi\) |
−0.173784 | − | 0.984784i | \(-0.555599\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.95680 | + | 3.95680i | −1.31893 | + | 1.31893i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.51815 | + | 3.66515i | −0.457741 | + | 1.10508i | 0.511569 | + | 0.859242i | \(0.329064\pi\) |
−0.969310 | + | 0.245842i | \(0.920936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88366 | + | 0.780239i | −0.522434 | + | 0.216399i | −0.628286 | − | 0.777983i | \(-0.716243\pi\) |
0.105852 | + | 0.994382i | \(0.466243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.16155i | − | 0.299911i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.54587i | − | 1.10253i | −0.834329 | − | 0.551267i | \(-0.814144\pi\) | ||
0.834329 | − | 0.551267i | \(-0.185856\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.534684 | + | 0.221474i | −0.122665 | + | 0.0508095i | −0.443172 | − | 0.896437i | \(-0.646147\pi\) |
0.320507 | + | 0.947246i | \(0.396147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.86370 | − | 11.7420i | 1.06135 | − | 2.56232i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.41794 | + | 4.41794i | −0.921203 | + | 0.921203i | −0.997115 | − | 0.0759114i | \(-0.975813\pi\) |
0.0759114 | + | 0.997115i | \(0.475813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.42455 | − | 3.42455i | −0.684909 | − | 0.684909i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.03106 | − | 2.91236i | −1.35313 | − | 0.560484i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.96642 | − | 4.74737i | −0.365156 | − | 0.881564i | −0.994529 | − | 0.104461i | \(-0.966688\pi\) |
0.629373 | − | 0.777103i | \(-0.283312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0539984 | 0.00969841 | 0.00484920 | − | 0.999988i | \(-0.498456\pi\) | ||||
0.00484920 | + | 0.999988i | \(0.498456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.6310 | −2.02470 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.657235 | + | 1.58671i | 0.111093 | + | 0.268202i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.798499 | + | 0.330749i | 0.131272 | + | 0.0543748i | 0.447353 | − | 0.894358i | \(-0.352367\pi\) |
−0.316080 | + | 0.948732i | \(0.602367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.22683 | − | 4.22683i | −0.676835 | − | 0.676835i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.621063 | + | 0.621063i | −0.0969937 | + | 0.0969937i | −0.753939 | − | 0.656945i | \(-0.771848\pi\) |
0.656945 | + | 0.753939i | \(0.271848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.857104 | − | 2.06923i | 0.130707 | − | 0.315555i | −0.844954 | − | 0.534839i | \(-0.820372\pi\) |
0.975661 | + | 0.219284i | \(0.0703722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.04819 | − | 0.848387i | 0.305326 | − | 0.126470i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.44387i | 1.37753i | 0.724984 | + | 0.688765i | \(0.241847\pi\) | ||||
−0.724984 | + | 0.688765i | \(0.758153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7919i | 1.68456i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.3133 | − | 5.10033i | 1.72420 | − | 0.714189i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.16622 | + | 10.0582i | −0.572275 | + | 1.38159i | 0.327339 | + | 0.944907i | \(0.393848\pi\) |
−0.899614 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.11137 | − | 1.11137i | 0.149857 | − | 0.149857i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19980 | − | 1.19980i | −0.158918 | − | 0.158918i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.17877 | − | 2.97354i | −0.934596 | − | 0.387123i | −0.137176 | − | 0.990547i | \(-0.543803\pi\) |
−0.797420 | + | 0.603424i | \(0.793803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.02993 | − | 9.72911i | −0.515979 | − | 1.24568i | −0.940354 | − | 0.340198i | \(-0.889506\pi\) |
0.424375 | − | 0.905487i | \(-0.360494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.2574 | 3.05614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.807763 | 0.100191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12265 | + | 7.53875i | 0.381493 | + | 0.921004i | 0.991678 | + | 0.128746i | \(0.0410951\pi\) |
−0.610185 | + | 0.792259i | \(0.708905\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.9236 | − | 7.00997i | −2.03736 | − | 0.843901i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.99152 | + | 2.99152i | 0.355028 | + | 0.355028i | 0.861976 | − | 0.506948i | \(-0.169227\pi\) |
−0.506948 | + | 0.861976i | \(0.669227\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.91724 | − | 2.91724i | 0.341437 | − | 0.341437i | −0.515470 | − | 0.856907i | \(-0.672383\pi\) |
0.856907 | + | 0.515470i | \(0.172383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.43375 | − | 13.1182i | 0.627435 | − | 1.51476i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.8883 | − | 6.58114i | 1.81064 | − | 0.749991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.74836i | − | 0.646741i | −0.946272 | − | 0.323370i | \(-0.895184\pi\) | ||
0.946272 | − | 0.323370i | \(-0.104816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 5.52520i | − | 0.613911i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.30517 | − | 1.36905i | 0.362790 | − | 0.150272i | −0.193840 | − | 0.981033i | \(-0.562094\pi\) |
0.556630 | + | 0.830761i | \(0.312094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.689211 | + | 1.66390i | −0.0747554 | + | 0.180476i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.6528 | − | 10.6528i | 1.14210 | − | 1.14210i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.38134 | − | 2.38134i | −0.252422 | − | 0.252422i | 0.569541 | − | 0.821963i | \(-0.307121\pi\) |
−0.821963 | + | 0.569541i | \(0.807121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.16561 | + | 3.38231i | 0.855989 | + | 0.354562i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0605847 | + | 0.146264i | 0.00628234 | + | 0.0151669i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.229286 | 0.0235243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2672 | −1.34708 | −0.673541 | − | 0.739150i | \(-0.735228\pi\) | ||||
−0.673541 | + | 0.739150i | \(0.735228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.49522 | − | 20.5093i | −0.853801 | − | 2.06126i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6610 | + | 5.65855i | 1.35932 | + | 0.563047i | 0.938870 | − | 0.344271i | \(-0.111874\pi\) |
0.420446 | + | 0.907318i | \(0.361874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.66978 | + | 4.66978i | 0.460127 | + | 0.460127i | 0.898697 | − | 0.438570i | \(-0.144515\pi\) |
−0.438570 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.56048 | + | 3.56048i | −0.347467 | + | 0.347467i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.16083 | + | 7.63093i | −0.305569 | + | 0.737710i | 0.694269 | + | 0.719716i | \(0.255728\pi\) |
−0.999838 | + | 0.0179938i | \(0.994272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.46240 | − | 1.01996i | 0.235855 | − | 0.0976945i | −0.261625 | − | 0.965169i | \(-0.584259\pi\) |
0.497481 | + | 0.867475i | \(0.334259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.53397i | 0.240514i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.96472i | 0.467042i | 0.972352 | + | 0.233521i | \(0.0750247\pi\) | ||||
−0.972352 | + | 0.233521i | \(0.924975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.28689 | − | 0.947262i | 0.213254 | − | 0.0883326i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.36603 | − | 10.5405i | 0.403639 | − | 0.974471i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.9344 | + | 13.9344i | −1.27736 | + | 1.27736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.35034 | − | 3.35034i | −0.304577 | − | 0.304577i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.37907 | − | 0.985444i | −0.214514 | − | 0.0888545i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.49233 | + | 3.60280i | 0.133478 | + | 0.322244i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4530 | −1.37123 | −0.685614 | − | 0.727965i | \(-0.740466\pi\) | ||||
−0.685614 | + | 0.727965i | \(0.740466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.56653 | 0.578151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00352 | + | 9.66535i | 0.349789 | + | 0.844465i | 0.996644 | + | 0.0818527i | \(0.0260837\pi\) |
−0.646855 | + | 0.762613i | \(0.723916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.31784 | + | 0.960080i | 0.200982 | + | 0.0832495i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.13200 | + | 2.13200i | 0.183493 | + | 0.183493i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4887 | − | 11.4887i | 0.981544 | − | 0.981544i | −0.0182885 | − | 0.999833i | \(-0.505822\pi\) |
0.999833 | + | 0.0182885i | \(0.00582173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.86897 | + | 6.92630i | −0.243343 | + | 0.587481i | −0.997611 | − | 0.0690854i | \(-0.977992\pi\) |
0.754268 | + | 0.656567i | \(0.227992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.5804 | + | 10.5958i | −2.15426 | + | 0.892323i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.08843i | − | 0.676388i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.03579i | 0.169063i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −31.9405 | + | 13.2302i | −2.63441 | + | 1.09121i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.42248 | + | 5.84839i | −0.198457 | + | 0.479119i | −0.991509 | − | 0.130035i | \(-0.958491\pi\) |
0.793052 | + | 0.609154i | \(0.208491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.57293 | + | 7.57293i | −0.616276 | + | 0.616276i | −0.944574 | − | 0.328298i | \(-0.893525\pi\) |
0.328298 | + | 0.944574i | \(0.393525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.9871 | + | 17.9871i | 1.45417 | + | 1.45417i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0197648 | − | 0.00818685i | −0.00158755 | − | 0.000657583i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.12025 | + | 7.53295i | 0.249023 | + | 0.601195i | 0.998122 | − | 0.0612635i | \(-0.0195130\pi\) |
−0.749098 | + | 0.662459i | \(0.769513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −31.9187 | −2.53132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.0844 | 2.13455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.28073 | + | 5.50617i | 0.178640 | + | 0.431276i | 0.987682 | − | 0.156475i | \(-0.0500132\pi\) |
−0.809041 | + | 0.587752i | \(0.800013\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.25725 | + | 1.76341i | 0.331427 | + | 0.137281i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4145 | − | 14.4145i | −1.11543 | − | 1.11543i | −0.992404 | − | 0.123021i | \(-0.960742\pi\) |
−0.123021 | − | 0.992404i | \(-0.539258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.25297 | + | 6.25297i | −0.480998 | + | 0.480998i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.23931 | − | 2.99196i | 0.0947725 | − | 0.228801i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.0158 | + | 6.63397i | −1.21766 | + | 0.504372i | −0.896665 | − | 0.442709i | \(-0.854018\pi\) |
−0.320996 | + | 0.947081i | \(0.604018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.9944i | 1.58703i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 22.7812i | − | 1.71234i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.69109 | − | 3.59997i | 0.649602 | − | 0.269074i | −0.0334535 | − | 0.999440i | \(-0.510651\pi\) |
0.683056 | + | 0.730366i | \(0.260651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.276217 | + | 0.666847i | −0.0205310 | + | 0.0495663i | −0.933813 | − | 0.357763i | \(-0.883540\pi\) |
0.913282 | + | 0.407329i | \(0.133540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.8316 | − | 21.8316i | 1.61383 | − | 1.61383i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.242125 | − | 0.242125i | −0.0178014 | − | 0.0178014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.6613 | + | 6.90133i | 1.21839 | + | 0.504675i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.6250 | + | 30.4794i | 0.918332 | + | 2.21705i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1746 | 0.736209 | 0.368105 | − | 0.929784i | \(-0.380007\pi\) | ||||
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7515 | 0.845889 | 0.422945 | − | 0.906156i | \(-0.360996\pi\) | ||||
0.422945 | + | 0.906156i | \(0.360996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.906286 | + | 2.18797i | 0.0649005 | + | 0.156684i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5064 | + | 6.00875i | 1.03354 | + | 0.428106i | 0.833988 | − | 0.551782i | \(-0.186052\pi\) |
0.199550 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.32691 | − | 2.32691i | −0.164951 | − | 0.164951i | 0.619805 | − | 0.784756i | \(-0.287212\pi\) |
−0.784756 | + | 0.619805i | \(0.787212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.9165 | + | 16.9165i | −1.19320 | + | 1.19320i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.52437 | + | 20.5797i | −0.598294 | + | 1.44441i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.321486 | − | 0.133164i | 0.0224535 | − | 0.00930056i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 34.9617i | − | 2.43001i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.29593i | − | 0.158813i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9059 | + | 7.00267i | −1.16385 | + | 0.482083i | −0.879156 | − | 0.476534i | \(-0.841893\pi\) |
−0.284696 | + | 0.958618i | \(0.591893\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.74666 | + | 11.4595i | −0.325236 | + | 0.785189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.627444 | + | 0.627444i | −0.0427913 | + | 0.0427913i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.165520 | − | 0.165520i | −0.0112363 | − | 0.0112363i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1749 | + | 4.62880i | 0.755131 | + | 0.312786i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.54686 | + | 8.56288i | 0.238588 | + | 0.576002i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6471 | −1.44959 | −0.724797 | − | 0.688962i | \(-0.758066\pi\) | ||||
−0.724797 | + | 0.688962i | \(0.758066\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 27.1005 | 1.80670 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.67176 | − | 8.86440i | −0.243703 | − | 0.588351i | 0.753942 | − | 0.656941i | \(-0.228150\pi\) |
−0.997645 | + | 0.0685901i | \(0.978150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.5787 | − | 11.0093i | −1.75637 | − | 0.727513i | −0.997046 | − | 0.0768003i | \(-0.975530\pi\) |
−0.759324 | − | 0.650712i | \(-0.774470\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 35.6524 | + | 35.6524i | 2.34575 | + | 2.34575i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0722 | − | 18.0722i | 1.18395 | − | 1.18395i | 0.205239 | − | 0.978712i | \(-0.434203\pi\) |
0.978712 | − | 0.205239i | \(-0.0657972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.43181 | − | 3.45670i | 0.0934011 | − | 0.225490i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5704 | − | 6.44949i | 1.01141 | − | 0.418939i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.0765i | − | 1.55738i | −0.627409 | − | 0.778690i | \(-0.715884\pi\) | ||
0.627409 | − | 0.778690i | \(-0.284116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.3823i | − | 0.668785i | −0.942434 | − | 0.334393i | \(-0.891469\pi\) | ||
0.942434 | − | 0.334393i | \(-0.108531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.12719 | + | 2.53797i | −0.393060 | + | 0.162811i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.78780 | − | 4.31614i | 0.114219 | − | 0.275748i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.834363 | − | 0.834363i | 0.0530893 | − | 0.0530893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.41662 | + | 7.41662i | 0.470009 | + | 0.470009i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.0365 | + | 9.54203i | 1.45405 | + | 0.602288i | 0.963159 | − | 0.268933i | \(-0.0866710\pi\) |
0.490892 | + | 0.871221i | \(0.336671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.48528 | − | 22.8995i | −0.596335 | − | 1.43968i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.28025 | −0.330662 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7121 | −1.16723 | −0.583613 | − | 0.812032i | \(-0.698362\pi\) | ||||
−0.583613 | + | 0.812032i | \(0.698362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.43379 | − | 3.46146i | −0.0890911 | − | 0.215085i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.5651 | + | 11.0036i | 1.64434 | + | 0.681107i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.884682 | − | 0.884682i | −0.0545518 | − | 0.0545518i | 0.679305 | − | 0.733856i | \(-0.262282\pi\) |
−0.733856 | + | 0.679305i | \(0.762282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.04989 | − | 3.04989i | 0.187353 | − | 0.187353i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.77849 | − | 9.12208i | 0.231240 | − | 0.558262i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1421 | − | 5.44363i | 0.801286 | − | 0.331904i | 0.0558149 | − | 0.998441i | \(-0.482224\pi\) |
0.745472 | + | 0.666537i | \(0.232224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5598i | 1.06668i | 0.845900 | + | 0.533341i | \(0.179064\pi\) | ||||
−0.845900 | + | 0.533341i | \(0.820936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.9129i | 1.56832i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.7505 | − | 7.35248i | 1.07039 | − | 0.443371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0964 | + | 24.3747i | −0.606631 | + | 1.46454i | 0.260011 | + | 0.965606i | \(0.416274\pi\) |
−0.866642 | + | 0.498931i | \(0.833726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.213661 | + | 0.213661i | −0.0127915 | + | 0.0127915i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.9764 | − | 16.9764i | −1.01273 | − | 1.01273i | −0.999918 | − | 0.0128071i | \(-0.995923\pi\) |
−0.0128071 | − | 0.999918i | \(-0.504077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.25301 | − | 1.34744i | −0.193372 | − | 0.0800972i | 0.283896 | − | 0.958855i | \(-0.408373\pi\) |
−0.477268 | + | 0.878758i | \(0.658373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.257253 | + | 0.621063i | 0.0152383 | + | 0.0367886i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.80746 | 0.224747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.66490 | −0.215582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8854 | − | 35.9366i | −0.872600 | − | 2.10664i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.88607 | + | 1.19545i | 0.168606 | + | 0.0698388i | 0.465390 | − | 0.885106i | \(-0.345914\pi\) |
−0.296784 | + | 0.954945i | \(0.595914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.17679 | + | 2.17679i | 0.126737 | + | 0.126737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.3485 | − | 21.3485i | 1.23876 | − | 1.23876i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.87486 | − | 11.7689i | 0.281920 | − | 0.680616i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.97005 | + | 3.71552i | −0.517025 | + | 0.214159i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.3519i | 2.49050i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.17209i | 0.238893i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.87800 | + | 3.26318i | −0.449621 | + | 0.186239i | −0.595992 | − | 0.802991i | \(-0.703241\pi\) |
0.146370 | + | 0.989230i | \(0.453241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.40957 | + | 17.8883i | −0.421516 | + | 1.01763i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.38586 | + | 3.38586i | −0.191995 | + | 0.191995i | −0.796557 | − | 0.604563i | \(-0.793348\pi\) |
0.604563 | + | 0.796557i | \(0.293348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0698 | + | 21.0698i | 1.19094 | + | 1.19094i | 0.976805 | + | 0.214132i | \(0.0686923\pi\) |
0.214132 | + | 0.976805i | \(0.431308\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.87882 | − | 3.67773i | −0.500265 | − | 0.207216i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7863 | + | 26.0404i | 0.605818 | + | 1.46258i | 0.867508 | + | 0.497423i | \(0.165720\pi\) |
−0.261690 | + | 0.965152i | \(0.584280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.3851 | 1.14135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2161 | −1.35161 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.00679 | + | 2.43060i | 0.0560192 | + | 0.135242i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.12266 | + | 3.77873i | 0.506034 | + | 0.209606i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.52549 | + | 5.52549i | 0.305560 | + | 0.305560i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.9481 | − | 28.9481i | 1.59596 | − | 1.59596i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0060 | − | 28.9852i | 0.659912 | − | 1.59317i | −0.138026 | − | 0.990429i | \(-0.544076\pi\) |
0.797938 | − | 0.602740i | \(-0.205924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.46821 | + | 1.85079i | −0.244856 | + | 0.101423i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.23281i | − | 0.176627i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.6957i | 1.94447i | 0.234010 | + | 0.972234i | \(0.424815\pi\) | ||||
−0.234010 | + | 0.972234i | \(0.575185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4478 | + | 5.57028i | −0.730386 | + | 0.302536i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0819780 | + | 0.197912i | −0.00443935 | + | 0.0107176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.6885 | − | 14.6885i | 0.793107 | − | 0.793107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.13165 | + | 5.13165i | 0.276279 | + | 0.276279i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.1047 | − | 10.8129i | −1.40137 | − | 0.580468i | −0.451266 | − | 0.892389i | \(-0.649027\pi\) |
−0.950108 | + | 0.311921i | \(0.899027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.99757 | − | 12.0652i | −0.267514 | − | 0.645836i | 0.731851 | − | 0.681464i | \(-0.238657\pi\) |
−0.999365 | + | 0.0356289i | \(0.988657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.5165 | 0.828209 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.4488 | 0.875479 | 0.437740 | − | 0.899102i | \(-0.355779\pi\) | ||||
0.437740 | + | 0.899102i | \(0.355779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.641420 | − | 1.54852i | −0.0340430 | − | 0.0821871i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −53.3776 | − | 22.1097i | −2.82504 | − | 1.17017i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.92378 | − | 3.92378i | −0.207089 | − | 0.207089i | 0.595940 | − | 0.803029i | \(-0.296780\pi\) |
−0.803029 | + | 0.595940i | \(0.796780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1982 | + | 13.1982i | −0.694642 | + | 0.694642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.31601 | − | 12.8340i | 0.279018 | − | 0.673610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.51007 | + | 0.625493i | −0.0790409 | + | 0.0327398i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.9285i | − | 0.988061i | −0.869444 | − | 0.494031i | \(-0.835523\pi\) | ||
0.869444 | − | 0.494031i | \(-0.164477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.91484i | − | 0.255856i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 43.6017 | − | 18.0604i | 2.26369 | − | 0.937651i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.92159 | − | 14.2960i | 0.306608 | − | 0.740218i | −0.693202 | − | 0.720743i | \(-0.743801\pi\) |
0.999810 | − | 0.0194748i | \(-0.00619941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.08448 | + | 8.08448i | −0.417481 | + | 0.417481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.40816 | + | 7.40816i | 0.381540 | + | 0.381540i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.8882 | − | 8.23798i | −1.02159 | − | 0.423157i | −0.191920 | − | 0.981411i | \(-0.561471\pi\) |
−0.829670 | + | 0.558254i | \(0.811471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3378 | − | 41.8571i | −0.888241 | − | 2.14440i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8953 | 0.761113 | 0.380556 | − | 0.924758i | \(-0.375732\pi\) | ||||
0.380556 | + | 0.924758i | \(0.375732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.81330 | −0.347238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.79614 | + | 11.5789i | 0.243802 | + | 0.588589i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3896 | + | 7.61723i | 0.932390 | + | 0.386209i | 0.796585 | − | 0.604527i | \(-0.206638\pi\) |
0.135805 | + | 0.990736i | \(0.456638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0833 | + | 20.0833i | 1.01566 | + | 1.01566i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.6885 | + | 21.6885i | −1.09404 | + | 1.09404i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.871524 | + | 2.10404i | −0.0438511 | + | 0.105866i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0423 | − | 6.23072i | 0.754951 | − | 0.312711i | 0.0281913 | − | 0.999603i | \(-0.491025\pi\) |
0.726760 | + | 0.686891i | \(0.241025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.35546i | 0.368233i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 26.1297i | − | 1.30485i | −0.757852 | − | 0.652427i | \(-0.773751\pi\) | ||
0.757852 | − | 0.652427i | \(-0.226249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.101715 | + | 0.0421317i | −0.00506678 | + | 0.00209873i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.837691 | + | 2.02236i | −0.0416252 | + | 0.100492i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.42449 | + | 2.42449i | −0.120177 | + | 0.120177i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4495 | − | 15.4495i | −0.763928 | − | 0.763928i | 0.213102 | − | 0.977030i | \(-0.431643\pi\) |
−0.977030 | + | 0.213102i | \(0.931643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.0091 | + | 18.2292i | 2.17081 | + | 0.899179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.8902 | + | 31.1197i | 0.634286 | + | 1.53130i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.41734 | −0.0695746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.9800 | −1.07637 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.26299 | + | 10.2918i | 0.208261 | + | 0.502786i | 0.993149 | − | 0.116851i | \(-0.0372799\pi\) |
−0.784889 | + | 0.619637i | \(0.787280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2514 | + | 10.0453i | 1.18194 | + | 0.489576i | 0.885123 | − | 0.465357i | \(-0.154074\pi\) |
0.296819 | + | 0.954934i | \(0.404074\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.3675 | − | 37.3675i | −1.81687 | − | 1.81687i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.5675 | + | 15.5675i | −0.755136 | + | 0.755136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4696 | + | 42.1753i | −0.845413 | + | 2.04101i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.9089 | − | 9.07498i | 1.05777 | − | 0.438144i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11.4592i | − | 0.551972i | −0.961162 | − | 0.275986i | \(-0.910996\pi\) | ||
0.961162 | − | 0.275986i | \(-0.0890043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.0019i | − | 0.720946i | −0.932770 | − | 0.360473i | \(-0.882615\pi\) | ||
0.932770 | − | 0.360473i | \(-0.117385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.51430 | + | 2.28410i | −0.264391 | + | 0.109514i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.38375 | − | 3.34066i | 0.0661935 | − | 0.159805i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9503 | − | 13.9503i | 0.665812 | − | 0.665812i | −0.290932 | − | 0.956744i | \(-0.593965\pi\) |
0.956744 | + | 0.290932i | \(0.0939653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.6582 | − | 46.6582i | −2.22182 | − | 2.22182i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8126 | − | 4.47872i | −0.513722 | − | 0.212791i | 0.110735 | − | 0.993850i | \(-0.464680\pi\) |
−0.624457 | + | 0.781059i | \(0.714680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.510590 | + | 1.23267i | 0.0242043 | + | 0.0584343i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.5594 | −0.877827 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.74061 | 0.223723 | 0.111862 | − | 0.993724i | \(-0.464319\pi\) | ||||
0.111862 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33342 | − | 3.21916i | −0.0627882 | − | 0.151584i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.0092 | − | 12.0160i | −1.36297 | − | 0.564562i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.47602 | − | 2.47602i | −0.116078 | − | 0.116078i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.1910 | + | 15.1910i | −0.710605 | + | 0.710605i | −0.966662 | − | 0.256057i | \(-0.917577\pi\) |
0.256057 | + | 0.966662i | \(0.417577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.2392 | + | 31.9623i | −0.617953 | + | 1.49187i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.8912 | − | 6.16815i | 0.693554 | − | 0.287279i | −0.00792626 | − | 0.999969i | \(-0.502523\pi\) |
0.701480 | + | 0.712689i | \(0.252523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.4145i | − | 0.530477i | −0.964183 | − | 0.265238i | \(-0.914549\pi\) | ||
0.964183 | − | 0.265238i | \(-0.0854506\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.0627219i | − | 0.00290866i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.38825 | − | 2.64610i | 0.295613 | − | 0.122447i | −0.229948 | − | 0.973203i | \(-0.573856\pi\) |
0.525561 | + | 0.850756i | \(0.323856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5366 | − | 32.6802i | 0.625061 | − | 1.50903i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9035 | + | 16.9035i | −0.778873 | + | 0.778873i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.28283 | + | 6.28283i | 0.288885 | + | 0.288885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.58950 | + | 1.07260i | 0.118814 | + | 0.0492145i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.3132 | − | 56.2830i | −1.06744 | − | 2.57702i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.2733 | 0.743545 | 0.371772 | − | 0.928324i | \(-0.378750\pi\) | ||||
0.371772 | + | 0.928324i | \(0.378750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.76217 | −0.0803479 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.3880 | + | 73.3630i | 1.38270 | + | 3.33813i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.85614 | + | 2.01148i | 0.220506 | + | 0.0913366i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0573 | − | 13.0573i | −0.591683 | − | 0.591683i | 0.346403 | − | 0.938086i | \(-0.387403\pi\) |
−0.938086 | + | 0.346403i | \(0.887403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.3555 | + | 12.3555i | −0.558736 | + | 0.558736i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.48577 | + | 13.2438i | −0.247569 | + | 0.597686i | −0.997997 | − | 0.0632676i | \(-0.979848\pi\) |
0.750427 | + | 0.660953i | \(0.229848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.5809 | + | 8.93910i | −0.971955 | + | 0.402597i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.79490i | 0.395301i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 18.3397i | − | 0.822648i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7784 | + | 9.43511i | −1.01970 | + | 0.422374i | −0.828984 | − | 0.559272i | \(-0.811081\pi\) |
−0.190716 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.8715 | − | 55.2168i | 1.02182 | − | 2.46690i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.0166 | + | 29.0166i | −1.29378 | + | 1.29378i | −0.361357 | + | 0.932428i | \(0.617686\pi\) |
−0.932428 | + | 0.361357i | \(0.882314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.14235 | − | 4.14235i | −0.184332 | − | 0.184332i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.9529 | − | 9.92163i | −1.06379 | − | 0.440635i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0998009 | − | 0.240941i | −0.00442360 | − | 0.0106795i | 0.921652 | − | 0.388017i | \(-0.126840\pi\) |
−0.926076 | + | 0.377337i | \(0.876840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8843 | −0.791156 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.40441 | 0.194459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.00126 | − | 2.41726i | −0.0441208 | − | 0.106517i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.6132 | − | 14.3373i | −1.52229 | − | 0.630552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.9386 | − | 35.9386i | −1.57753 | − | 1.57753i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.59451 | + | 6.59451i | −0.288911 | + | 0.288911i | −0.836649 | − | 0.547739i | \(-0.815489\pi\) |
0.547739 | + | 0.836649i | \(0.315489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.4900 | − | 30.1535i | 0.546148 | − | 1.31852i | −0.374174 | − | 0.927358i | \(-0.622074\pi\) |
0.920323 | − | 0.391160i | \(-0.127926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −56.8671 | + | 23.5551i | −2.48188 | + | 1.02803i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.245470i | − | 0.0106928i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.0363i | − | 0.697231i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.1706 | − | 16.6392i | 1.74326 | − | 0.722081i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.685296 | − | 1.65445i | 0.0296835 | − | 0.0716622i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.31389 | − | 2.31389i | 0.100038 | − | 0.100038i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.5023 | + | 19.5023i | 0.841586 | + | 0.841586i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −43.2191 | − | 17.9019i | −1.86158 | − | 0.771091i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.46141 | + | 13.1850i | 0.234804 | + | 0.566867i | 0.996731 | − | 0.0807961i | \(-0.0257463\pi\) |
−0.761926 | + | 0.647664i | \(0.775746\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.11618 | −0.0908140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.05594 | −0.0452315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.46669 | − | 22.8546i | −0.404766 | − | 0.977192i | −0.986492 | − | 0.163807i | \(-0.947622\pi\) |
0.581726 | − | 0.813385i | \(-0.302378\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 54.4417 | + | 22.5505i | 2.32351 | + | 0.962431i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.10283 | + | 2.10283i | 0.0895837 | + | 0.0895837i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.6203 | + | 17.6203i | −0.749293 | + | 0.749293i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.384182 | − | 0.927497i | 0.0163076 | − | 0.0393700i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.6576 | + | 7.31400i | −0.748175 | + | 0.309904i | −0.723997 | − | 0.689804i | \(-0.757697\pi\) |
−0.0241782 | + | 0.999708i | \(0.507697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56648i | 0.193142i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.8731i | 2.23230i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.0826 | + | 12.0464i | −1.22568 | + | 0.507695i | −0.899213 | − | 0.437512i | \(-0.855860\pi\) |
−0.326472 | + | 0.945207i | \(0.605860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.752715 | − | 1.81722i | 0.0316670 | − | 0.0764508i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.9363 | + | 16.9363i | −0.711258 | + | 0.711258i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.1317 | + | 18.1317i | 0.760118 | + | 0.760118i | 0.976344 | − | 0.216225i | \(-0.0693745\pi\) |
−0.216225 | + | 0.976344i | \(0.569375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.77020 | − | 3.21852i | −0.325173 | − | 0.134691i | 0.214125 | − | 0.976806i | \(-0.431310\pi\) |
−0.539297 | + | 0.842115i | \(0.681310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.4156 | + | 27.5597i | 0.476894 | + | 1.15133i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2588 | 1.26188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2275 | −0.550669 | −0.275335 | − | 0.961348i | \(-0.588789\pi\) | ||||
−0.275335 | + | 0.961348i | \(0.588789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1848 | + | 31.8309i | 0.547942 | + | 1.32285i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.3278 | − | 5.93477i | −0.594418 | − | 0.246216i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.5397 | − | 30.5397i | −1.26482 | − | 1.26482i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.19615 | + | 3.19615i | −0.132145 | + | 0.132145i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.2730 | + | 32.0438i | −0.547835 | + | 1.32259i | 0.371251 | + | 0.928533i | \(0.378929\pi\) |
−0.919086 | + | 0.394058i | \(0.871071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0288721 | + | 0.0119592i | −0.00118966 | + | 0.000492771i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.0348i | 1.89362i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 37.4869i | − | 1.53940i | −0.638405 | − | 0.769700i | \(-0.720406\pi\) | ||
0.638405 | − | 0.769700i | \(-0.279594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.21296 | − | 2.98770i | 0.295702 | − | 0.122484i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.69213 | − | 8.91359i | 0.151109 | − | 0.364809i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.05549 | − | 4.05549i | 0.165703 | − | 0.165703i | −0.619385 | − | 0.785088i | \(-0.712618\pi\) |
0.785088 | + | 0.619385i | \(0.212618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.796070 | − | 0.796070i | −0.0324724 | − | 0.0324724i | 0.690684 | − | 0.723157i | \(-0.257309\pi\) |
−0.723157 | + | 0.690684i | \(0.757309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.1850 | − | 17.4736i | −1.71790 | − | 0.711579i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.718357 | + | 1.73427i | 0.0292053 | + | 0.0705079i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8854 | 0.563591 | 0.281795 | − | 0.959475i | \(-0.409070\pi\) | ||||
0.281795 | + | 0.959475i | \(0.409070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −65.3078 | −2.64640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.36848 | − | 17.7891i | −0.298097 | − | 0.719669i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.46292 | − | 3.91967i | −0.382204 | − | 0.158314i | 0.183305 | − | 0.983056i | \(-0.441320\pi\) |
−0.565509 | + | 0.824742i | \(0.691320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.721395 | + | 0.721395i | 0.0290895 | + | 0.0290895i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.39736 | + | 5.39736i | −0.217290 | + | 0.217290i | −0.807355 | − | 0.590066i | \(-0.799102\pi\) |
0.590066 | + | 0.807355i | \(0.299102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.9301 | − | 31.2161i | 0.519706 | − | 1.25468i | −0.418379 | − | 0.908273i | \(-0.637401\pi\) |
0.938084 | − | 0.346408i | \(-0.112599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.9294 | − | 18.1962i | 1.76283 | − | 0.730186i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.5990i | 0.584895i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.6702i | 0.906809i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.21893 | − | 2.57597i | 0.248360 | − | 0.102874i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.50354 | − | 3.62987i | 0.0599501 | − | 0.144732i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8697 | − | 21.8697i | 0.870620 | − | 0.870620i | −0.121920 | − | 0.992540i | \(-0.538905\pi\) |
0.992540 | + | 0.121920i | \(0.0389050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.9359 | − | 37.9359i | −1.50782 | − | 1.50782i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.65618 | + | 2.34286i | 0.224458 | + | 0.0929737i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.20050 | − | 22.2120i | −0.364537 | − | 0.880071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.6737 | −0.936515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.0037 | 1.34307 | 0.671533 | − | 0.740975i | \(-0.265636\pi\) | ||||
0.671533 | + | 0.740975i | \(0.265636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.89697 | − | 9.40811i | −0.153681 | − | 0.371020i | 0.828223 | − | 0.560399i | \(-0.189352\pi\) |
−0.981904 | + | 0.189380i | \(0.939352\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.40352 | − | 0.995569i | −0.0946384 | − | 0.0392005i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9528 | + | 11.9528i | 0.469914 | + | 0.469914i | 0.901887 | − | 0.431973i | \(-0.142182\pi\) |
−0.431973 | + | 0.901887i | \(0.642182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.7970 | − | 21.7970i | 0.855606 | − | 0.855606i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.262632 | − | 0.634051i | 0.0102934 | − | 0.0248504i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9705 | − | 6.61520i | 0.624974 | − | 0.258873i | −0.0476419 | − | 0.998864i | \(-0.515171\pi\) |
0.672616 | + | 0.739992i | \(0.265171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.14475i | − | 0.161949i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.0858i | 0.900665i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.12170 | + | 1.29305i | −0.121604 | + | 0.0503701i | −0.442656 | − | 0.896692i | \(-0.645964\pi\) |
0.321052 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.7729 | − | 42.9077i | 0.691287 | − | 1.66892i | −0.0508836 | − | 0.998705i | \(-0.516204\pi\) |
0.742171 | − | 0.670211i | \(-0.233796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.2146 | + | 19.2146i | −0.746234 | + | 0.746234i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.702827 | − | 0.702827i | −0.0272545 | − | 0.0272545i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.6611 | + | 12.2860i | 1.14848 | + | 0.475717i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.2874 | − | 58.6349i | −0.939004 | − | 2.26696i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.7767 | 1.61277 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.107425 | −0.00414091 | −0.00207046 | − | 0.999998i | \(-0.500659\pi\) | ||||
−0.00207046 | + | 0.999998i | \(0.500659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.1047 | + | 34.0517i | 0.542889 | + | 1.31065i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.2485 | + | 4.24507i | 0.393882 | + | 0.163151i | 0.570829 | − | 0.821069i | \(-0.306622\pi\) |
−0.176947 | + | 0.984220i | \(0.556622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.6678 | + | 40.6678i | 1.56069 | + | 1.56069i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8912 | − | 19.8912i | 0.762233 | − | 0.762233i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.4720 | − | 25.2815i | 0.400698 | − | 0.967371i | −0.586799 | − | 0.809733i | \(-0.699612\pi\) |
0.987497 | − | 0.157638i | \(-0.0503879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.94698 | + | 2.46332i | −0.227222 | + | 0.0941186i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 84.3452i | − | 3.21797i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 22.1968i | − | 0.845632i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0716 | − | 11.6277i | 1.06790 | − | 0.442337i | 0.221648 | − | 0.975127i | \(-0.428856\pi\) |
0.846248 | + | 0.532790i | \(0.178856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −36.8265 | + | 88.9069i | −1.39892 | + | 3.37729i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.10023 | − | 2.10023i | 0.0796663 | − | 0.0796663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.82327 | + | 2.82327i | 0.106939 | + | 0.106939i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 69.2284 | + | 28.6753i | 2.61846 | + | 1.08460i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4808 | − | 25.3030i | −0.395855 | − | 0.955679i | −0.988638 | − | 0.150317i | \(-0.951971\pi\) |
0.592783 | − | 0.805363i | \(-0.298029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.500197 | −0.0188653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9695 | 0.413136 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.5296 | − | 59.2198i | −0.922531 | − | 2.22719i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.0598 | − | 18.2502i | −1.65470 | − | 0.685400i | −0.657047 | − | 0.753850i | \(-0.728195\pi\) |
−0.997655 | + | 0.0684496i | \(0.978195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.7451 | + | 22.7451i | 0.853007 | + | 0.853007i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.238562 | + | 0.238562i | −0.00893420 | + | 0.00893420i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22631 | + | 2.96057i | −0.0458613 | + | 0.110719i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 65.2155 | − | 27.0132i | 2.43552 | − | 1.00882i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5621i | 0.766835i | 0.923575 | + | 0.383418i | \(0.125253\pi\) | ||||
−0.923575 | + | 0.383418i | \(0.874747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 28.6284i | − | 1.06618i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.1224 | − | 11.6487i | 1.04588 | − | 0.433219i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.52347 | + | 22.9917i | −0.353693 | + | 0.853890i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.98129 | + | 2.98129i | −0.110570 | + | 0.110570i | −0.760227 | − | 0.649657i | \(-0.774912\pi\) |
0.649657 | + | 0.760227i | \(0.274912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.4698 | − | 25.4698i | −0.943326 | − | 0.943326i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.40645 | − | 3.89628i | −0.347910 | − | 0.144109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.3350 | + | 44.2647i | 0.677220 | + | 1.63495i | 0.769057 | + | 0.639180i | \(0.220726\pi\) |
−0.0918368 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.6969 | 0.505217 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.3713 | −1.19241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.44435 | + | 15.5580i | 0.237059 | + | 0.572312i | 0.996976 | − | 0.0777085i | \(-0.0247603\pi\) |
−0.759917 | + | 0.650020i | \(0.774760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.19615 | + | 1.32389i | 0.117414 | + | 0.0486343i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2184 | − | 15.2184i | −0.558309 | − | 0.558309i | 0.370516 | − | 0.928826i | \(-0.379181\pi\) |
−0.928826 | + | 0.370516i | \(0.879181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.77338 | − | 1.77338i | 0.0649716 | − | 0.0649716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.66085 | + | 18.4949i | −0.280296 | + | 0.676694i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.0798 | − | 13.7021i | 1.20871 | − | 0.500664i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.40389i | − | 0.160700i | −0.996767 | − | 0.0803501i | \(-0.974396\pi\) | ||
0.996767 | − | 0.0803501i | \(-0.0256038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 73.1043i | 2.66407i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.92004 | − | 1.62373i | 0.142665 | − | 0.0590937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.26500 | + | 22.3677i | −0.336742 | + | 0.812968i | 0.661282 | + | 0.750137i | \(0.270013\pi\) |
−0.998024 | + | 0.0628304i | \(0.979987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.3851 | − | 51.3851i | 1.86516 | − | 1.86516i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.81382 | + | 6.81382i | 0.247001 | + | 0.247001i | 0.819739 | − | 0.572738i | \(-0.194119\pi\) |
−0.572738 | + | 0.819739i | \(0.694119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6744 | − | 4.42149i | −0.386440 | − | 0.160069i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.85666 | − | 9.31079i | −0.139438 | − | 0.336632i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.8425 | 0.572038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.7366 | −0.603538 | −0.301769 | − | 0.953381i | \(-0.597577\pi\) | ||||
−0.301769 | + | 0.953381i | \(0.597577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.9944 | − | 50.6850i | −0.756095 | − | 1.82537i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.6437 | + | 5.65140i | 0.490730 | + | 0.203267i | 0.614305 | − | 0.789068i | \(-0.289436\pi\) |
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.184920 | − | 0.184920i | −0.00664253 | − | 0.00664253i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.76733 | − | 7.76733i | 0.278651 | − | 0.278651i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.194524 | − | 0.469621i | 0.00696953 | − | 0.0168259i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.5059 | + | 6.42277i | −0.554846 | + | 0.229825i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.1060i | 1.39753i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.23032i | − | 0.115295i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.06441 | − | 3.75460i | 0.323111 | − | 0.133837i | −0.215231 | − | 0.976563i | \(-0.569051\pi\) |
0.538343 | + | 0.842726i | \(0.319051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.40373 | − | 3.38891i | 0.0499741 | − | 0.120648i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2183 | − | 15.2183i | 0.541100 | − | 0.541100i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1821 | + | 15.1821i | 0.539131 | + | 0.539131i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.6830 | + | 4.83928i | 0.414355 | + | 0.171631i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4147 | + | 34.8002i | 0.510595 | + | 1.23269i | 0.943538 | + | 0.331264i | \(0.107475\pi\) |
−0.432943 | + | 0.901421i | \(0.642525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.9306 | 1.51878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.8450 | 0.665854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.26330 | + | 15.1209i | 0.221027 | + | 0.533606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.91359 | − | 4.10634i | −0.349408 | − | 0.144730i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.4901 | + | 29.4901i | 1.03810 | + | 1.03810i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.59383 | − | 6.59383i | 0.231827 | − | 0.231827i | −0.581628 | − | 0.813455i | \(-0.697584\pi\) |
0.813455 | + | 0.581628i | \(0.197584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0137 | − | 29.0036i | 0.421857 | − | 1.01845i | −0.559942 | − | 0.828532i | \(-0.689177\pi\) |
0.981799 | − | 0.189922i | \(-0.0608234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47.5638 | + | 19.7016i | −1.66814 | + | 0.690965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.36118i | − | 0.0827087i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29621i | 0.0453487i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.6928 | + | 18.9266i | −1.59663 | + | 0.661348i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1833 | + | 26.9988i | −0.390299 | + | 0.942265i | 0.599575 | + | 0.800318i | \(0.295336\pi\) |
−0.989874 | + | 0.141947i | \(0.954664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.497968 | + | 0.497968i | −0.0173581 | + | 0.0173581i | −0.715733 | − | 0.698374i | \(-0.753907\pi\) |
0.698374 | + | 0.715733i | \(0.253907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 39.8310 | + | 39.8310i | 1.38674 | + | 1.38674i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.8102 | − | 18.1468i | −1.52343 | − | 0.631025i | −0.545154 | − | 0.838336i | \(-0.683529\pi\) |
−0.978275 | + | 0.207311i | \(0.933529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0186 | + | 29.0154i | 0.417422 | + | 1.00774i | 0.983092 | + | 0.183113i | \(0.0586175\pi\) |
−0.565670 | + | 0.824632i | \(0.691382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −77.3512 | −2.68328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 53.6044 | 1.85728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.09065 | + | 7.46148i | 0.106956 | + | 0.258215i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.379666 | − | 0.157263i | −0.0131232 | − | 0.00543580i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.1636 | + | 28.1636i | 0.972317 | + | 0.972317i | 0.999627 | − | 0.0273102i | \(-0.00869417\pi\) |
−0.0273102 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.83543 | − | 1.83543i | 0.0632906 | − | 0.0632906i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.9365 | − | 65.0305i | 0.927743 | − | 2.23977i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.23678 | − | 1.34072i | 0.111349 | − | 0.0461221i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.5395i | 0.705746i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 10.3232i | − | 0.354290i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.98895 | + | 2.06649i | −0.171019 | + | 0.0708383i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.15715 | + | 7.62203i | −0.108099 | + | 0.260973i | −0.968668 | − | 0.248361i | \(-0.920108\pi\) |
0.860569 | + | 0.509334i | \(0.170108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.907239 | + | 0.907239i | −0.0310269 | + | 0.0310269i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.53805 | − | 8.53805i | −0.291654 | − | 0.291654i | 0.546079 | − | 0.837734i | \(-0.316120\pi\) |
−0.837734 | + | 0.546079i | \(0.816120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.10474 | + | 3.77131i | 0.310650 | + | 0.128675i | 0.532561 | − | 0.846392i | \(-0.321230\pi\) |
−0.221912 | + | 0.975067i | \(0.571230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.27186 | + | 10.3132i | 0.145585 | + | 0.351473i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.7816 | −0.605294 | −0.302647 | − | 0.953103i | \(-0.597870\pi\) | ||||
−0.302647 | + | 0.953103i | \(0.597870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.86800 | 0.233519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.11191 | − | 9.92703i | −0.139648 | − | 0.337140i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0686 | + | 8.72689i | 0.714703 | + | 0.296040i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.7640 | − | 11.7640i | −0.398610 | − | 0.398610i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 52.4957 | − | 52.4957i | 1.77671 | − | 1.77671i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.46919 | − | 15.6180i | 0.218699 | − | 0.527985i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.4212 | + | 8.87297i | −0.723344 | + | 0.299619i | −0.713814 | − | 0.700336i | \(-0.753034\pi\) |
−0.00953022 | + | 0.999955i | \(0.503034\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.15869i | 0.308915i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.5225i | − | 0.725113i | −0.931962 | − | 0.362557i | \(-0.881904\pi\) | ||
0.931962 | − | 0.362557i | \(-0.118096\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.8481 | + | 11.5351i | −0.937165 | + | 0.388186i | −0.798392 | − | 0.602138i | \(-0.794316\pi\) |
−0.138773 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.45392 | + | 8.33850i | −0.116102 | + | 0.280296i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.2963 | + | 25.2963i | −0.849368 | + | 0.849368i | −0.990054 | − | 0.140686i | \(-0.955069\pi\) |
0.140686 | + | 0.990054i | \(0.455069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.3677 | + | 47.3677i | 1.58866 | + | 1.58866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.2507 | + | 8.38811i | 0.678423 | + | 0.281012i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.09157 | − | 5.04949i | −0.0699917 | − | 0.168975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.72696 | −0.124579 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.3477 | 1.24700 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.106184 | − | 0.256350i | −0.00354143 | − | 0.00854976i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.7230 | + | 18.9391i | 1.52325 | + | 0.630953i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.1283 | − | 20.1283i | −0.669827 | − | 0.669827i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.202205 | − | 0.202205i | 0.00672152 | − | 0.00672152i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.69269 | + | 18.5718i | −0.255432 | + | 0.616666i | −0.998626 | − | 0.0524095i | \(-0.983310\pi\) |
0.743194 | + | 0.669076i | \(0.233310\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −76.4434 | + | 31.6639i | −2.53547 | + | 1.05022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 57.0332i | − | 1.88960i | −0.327655 | − | 0.944798i | \(-0.606258\pi\) | ||
0.327655 | − | 0.944798i | \(-0.393742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1924i | 0.469699i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.3008 | + | 4.68096i | −0.373594 | + | 0.154748i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.3551 | − | 41.8989i | 0.573116 | − | 1.38362i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.18487 | − | 7.18487i | 0.237007 | − | 0.237007i | −0.578603 | − | 0.815610i | \(-0.696402\pi\) |
0.815610 | + | 0.578603i | \(0.196402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.6778 | − | 17.6778i | −0.582503 | − | 0.582503i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.96911 | − | 3.30092i | −0.262307 | − | 0.108651i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.60183 | − | 3.86716i | −0.0526679 | − | 0.127152i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.9547 | −1.21375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.2751 | −0.763630 | −0.381815 | − | 0.924239i | \(-0.624701\pi\) | ||||
−0.381815 | + | 0.924239i | \(0.624701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.61160 | − | 6.30495i | −0.0855916 | − | 0.206636i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9700 | − | 5.37237i | −0.424620 | − | 0.175883i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.05212 | − | 5.05212i | −0.165222 | − | 0.165222i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.60456 | + | 7.60456i | −0.248430 | + | 0.248430i | −0.820326 | − | 0.571896i | \(-0.806208\pi\) |
0.571896 | + | 0.820326i | \(0.306208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.4316 | + | 80.7111i | −1.09100 | + | 2.63391i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.74672 | + | 1.13773i | −0.0895406 | + | 0.0370889i | −0.427004 | − | 0.904250i | \(-0.640431\pi\) |
0.337464 | + | 0.941339i | \(0.390431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.48763i | − | 0.178702i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 13.0703i | − | 0.425178i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.7202 | + | 8.99679i | −0.705811 | + | 0.292357i | −0.706570 | − | 0.707643i | \(-0.749758\pi\) |
0.000758845 | 1.00000i | \(0.499758\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.21895 | + | 7.77124i | −0.104492 | + | 0.252265i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −58.4332 | + | 58.4332i | −1.89483 | + | 1.89483i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.594510 | + | 0.594510i | 0.0192581 | + | 0.0192581i | 0.716670 | − | 0.697412i | \(-0.245665\pi\) |
−0.697412 | + | 0.716670i | \(0.745665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.72417 | − | 1.54260i | −0.120511 | − | 0.0499174i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.8715 | + | 55.2168i | 0.739332 | + | 1.78490i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.4321 | −2.27437 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9971 | −0.999906 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.6872 | − | 42.7008i | −0.569964 | − | 1.37601i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.30134 | − | 1.78167i | −0.138465 | − | 0.0573541i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.28012 | + | 5.28012i | 0.169797 | + | 0.169797i | 0.786890 | − | 0.617093i | \(-0.211690\pi\) |
−0.617093 | + | 0.786890i | \(0.711690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.45413 | + | 5.45413i | −0.175212 | + | 0.175212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.9737 | + | 45.8066i | −0.608895 | + | 1.47000i | 0.255308 | + | 0.966860i | \(0.417823\pi\) |
−0.864203 | + | 0.503143i | \(0.832177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0253 | − | 12.4369i | 0.962566 | − | 0.398708i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.9500i | 0.927141i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.5870i | 0.882586i | 0.897363 | + | 0.441293i | \(0.145480\pi\) | ||||
−0.897363 | + | 0.441293i | \(0.854520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3432 | − | 5.11273i | 0.394491 | − | 0.163403i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.70745 | + | 13.7790i | −0.182225 | + | 0.439929i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.4856 | − | 32.4856i | 1.03613 | − | 1.03613i | 0.0368067 | − | 0.999322i | \(-0.488281\pi\) |
0.999322 | − | 0.0368067i | \(-0.0117186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.39871 | − | 4.39871i | −0.140155 | − | 0.140155i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 110.890 | + | 45.9322i | 3.52967 | + | 1.46204i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.35510 | + | 12.9284i | 0.170282 | + | 0.411098i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.6148 | −1.38547 | −0.692735 | − | 0.721192i | \(-0.743595\pi\) | ||||
−0.692735 | + | 0.721192i | \(0.743595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 91.9819 | 2.91896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.498920 | + | 1.20450i | 0.0158168 | + | 0.0381852i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.4769 | + | 12.6240i | 0.965214 | + | 0.399805i | 0.808928 | − | 0.587907i | \(-0.200048\pi\) |
0.156286 | + | 0.987712i | \(0.450048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.65104 | − | 4.65104i | −0.147152 | − | 0.147152i |
(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 | 1024.2.g.f.897.4 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.f.897.1 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.a.897.4 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.a.897.1 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.d.385.4 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.g.385.4 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.g.385.1 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.d.385.1 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.a.129.4 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.d.641.1 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.g.641.1 | yes | 16 | ||
32.13 | even | 8 | inner | 1024.2.g.f.129.4 | yes | 16 | |
32.19 | odd | 8 | inner | 1024.2.g.f.129.1 | yes | 16 | |
32.21 | even | 8 | 1024.2.g.g.641.4 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.d.641.4 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.a.129.1 | ✓ | 16 | ||
64.13 | even | 16 | 4096.2.a.s.1.7 | 8 | |||
64.19 | odd | 16 | 4096.2.a.s.1.8 | 8 | |||
64.45 | even | 16 | 4096.2.a.i.1.2 | 8 | |||
64.51 | odd | 16 | 4096.2.a.i.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.129.1 | ✓ | 16 | 32.29 | even | 8 | ||
1024.2.g.a.129.4 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.a.897.1 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.a.897.4 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.d.385.1 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.d.385.4 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.d.641.1 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.d.641.4 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.f.129.1 | yes | 16 | 32.19 | odd | 8 | inner | |
1024.2.g.f.129.4 | yes | 16 | 32.13 | even | 8 | inner | |
1024.2.g.f.897.1 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.f.897.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.g.385.1 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.g.385.4 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.g.641.1 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.g.641.4 | yes | 16 | 32.21 | even | 8 | ||
4096.2.a.i.1.1 | 8 | 64.51 | odd | 16 | |||
4096.2.a.i.1.2 | 8 | 64.45 | even | 16 | |||
4096.2.a.s.1.7 | 8 | 64.13 | even | 16 | |||
4096.2.a.s.1.8 | 8 | 64.19 | odd | 16 |