Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.c.1349.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | + | 0.189469i | −0.997433 | + | 0.0716124i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44829 | + | 1.99087i | 1.03970 | + | 0.600270i | 0.919748 | − | 0.392510i | \(-0.128393\pi\) |
0.119950 | + | 0.992780i | \(0.461727\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0681483 | −0.0189010 | −0.00945048 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00945048 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(14\) | 1.48356 | + | 2.19067i | 0.396499 | + | 0.585481i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.34607 | − | 3.66390i | −1.53915 | − | 0.888627i | −0.998889 | − | 0.0471274i | \(-0.984993\pi\) |
−0.540258 | − | 0.841499i | \(-0.681673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.76260 | − | 1.01764i | 0.404368 | − | 0.233462i | −0.283999 | − | 0.958825i | \(-0.591661\pi\) |
0.688367 | + | 0.725362i | \(0.258328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.98174i | − | 0.848910i | ||||||
\(23\) | 1.86603 | + | 3.23205i | 0.389093 | + | 0.673929i | 0.992328 | − | 0.123635i | \(-0.0394551\pi\) |
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0340742 | + | 0.0590182i | 0.00668250 | + | 0.0115744i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.15539 | − | 2.38014i | 0.218349 | − | 0.449804i | ||||
\(29\) | − | 0.898979i | − | 0.166936i | −0.996510 | − | 0.0834681i | \(-0.973400\pi\) | ||
0.996510 | − | 0.0834681i | \(-0.0265997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18154 | − | 2.41421i | −0.751027 | − | 0.433606i | 0.0750380 | − | 0.997181i | \(-0.476092\pi\) |
−0.826065 | + | 0.563575i | \(0.809426\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.32780i | 1.25671i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.52312 | − | 2.03407i | 0.579197 | − | 0.334400i | −0.181617 | − | 0.983369i | \(-0.558133\pi\) |
0.760814 | + | 0.648970i | \(0.224800\pi\) | |||||||
\(38\) | −1.76260 | − | 1.01764i | −0.285932 | − | 0.165083i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68921 | 0.263810 | 0.131905 | − | 0.991262i | \(-0.457891\pi\) | ||||
0.131905 | + | 0.991262i | \(0.457891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.964724i | − | 0.147119i | −0.997291 | − | 0.0735595i | \(-0.976564\pi\) | ||
0.997291 | − | 0.0735595i | \(-0.0234359\pi\) | |||||||
\(44\) | −3.44829 | + | 1.99087i | −0.519849 | + | 0.300135i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86603 | − | 3.23205i | 0.275130 | − | 0.476540i | ||||
\(47\) | −1.43890 | + | 0.830749i | −0.209885 | + | 0.121177i | −0.601258 | − | 0.799055i | \(-0.705334\pi\) |
0.391373 | + | 0.920232i | \(0.372000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0340742 | − | 0.0590182i | 0.00472524 | − | 0.00818435i | ||||
\(53\) | −6.61339 | + | 11.4547i | −0.908419 | + | 1.57343i | −0.0921588 | + | 0.995744i | \(0.529377\pi\) |
−0.816260 | + | 0.577684i | \(0.803957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63896 | + | 0.189469i | −0.352646 | + | 0.0253188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.778539 | + | 0.449490i | −0.102227 | + | 0.0590209i | ||||
\(59\) | 5.32112 | − | 9.21645i | 0.692751 | − | 1.19988i | −0.278182 | − | 0.960528i | \(-0.589732\pi\) |
0.970933 | − | 0.239352i | \(-0.0769348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.51299 | − | 3.76028i | 0.833903 | − | 0.481454i | −0.0212839 | − | 0.999773i | \(-0.506775\pi\) |
0.855187 | + | 0.518319i | \(0.173442\pi\) | |||||||
\(62\) | 4.82843i | 0.613211i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.23435 | + | 5.33145i | 1.12816 | + | 0.651341i | 0.943470 | − | 0.331457i | \(-0.107540\pi\) |
0.184685 | + | 0.982798i | \(0.440874\pi\) | |||||||
\(68\) | 6.34607 | − | 3.66390i | 0.769573 | − | 0.444313i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.93426i | 1.17898i | 0.807776 | + | 0.589490i | \(0.200671\pi\) | ||||
−0.807776 | + | 0.589490i | \(0.799329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.82843 | − | 10.0951i | 0.682166 | − | 1.18155i | −0.292153 | − | 0.956372i | \(-0.594372\pi\) |
0.974319 | − | 0.225174i | \(-0.0722951\pi\) | |||||||
\(74\) | −3.52312 | − | 2.03407i | −0.409554 | − | 0.236456i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.03528i | 0.233462i | ||||||||
\(77\) | −9.47710 | − | 4.60048i | −1.08002 | − | 0.524273i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.77489 | + | 15.1986i | 0.987252 | + | 1.70997i | 0.631465 | + | 0.775404i | \(0.282454\pi\) |
0.355787 | + | 0.934567i | \(0.384213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.844605 | − | 1.46290i | −0.0932711 | − | 0.161550i | ||||
\(83\) | − | 14.3490i | − | 1.57501i | −0.616311 | − | 0.787503i | \(-0.711374\pi\) | ||
0.616311 | − | 0.787503i | \(-0.288626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.835475 | + | 0.482362i | −0.0900916 | + | 0.0520144i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.44829 | + | 1.99087i | 0.367589 | + | 0.212227i | ||||
\(89\) | 0.913956 | + | 1.58302i | 0.0968791 | + | 0.167800i | 0.910391 | − | 0.413748i | \(-0.135781\pi\) |
−0.813512 | + | 0.581548i | \(0.802447\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.179841 | − | 0.0129120i | 0.0188524 | − | 0.00135354i | ||||
\(92\) | −3.73205 | −0.389093 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.43890 | + | 0.830749i | 0.148411 | + | 0.0856852i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1502 | 1.74134 | 0.870668 | − | 0.491870i | \(-0.163687\pi\) | ||||
0.870668 | + | 0.491870i | \(0.163687\pi\) | |||||||
\(98\) | −4.33013 | − | 5.50000i | −0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.36773 | + | 5.83307i | −0.335101 | + | 0.580412i | −0.983504 | − | 0.180885i | \(-0.942104\pi\) |
0.648403 | + | 0.761297i | \(0.275437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.260021 | + | 0.450370i | 0.0256206 | + | 0.0443762i | 0.878551 | − | 0.477648i | \(-0.158510\pi\) |
−0.852931 | + | 0.522024i | \(0.825177\pi\) | |||||||
\(104\) | −0.0681483 | −0.00668250 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.2268 | 1.28470 | ||||||||
\(107\) | −3.06350 | − | 5.30614i | −0.296160 | − | 0.512964i | 0.679094 | − | 0.734051i | \(-0.262373\pi\) |
−0.975254 | + | 0.221087i | \(0.929040\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.77729 | − | 11.7386i | 0.649147 | − | 1.12436i | −0.334180 | − | 0.942509i | \(-0.608459\pi\) |
0.983327 | − | 0.181846i | \(-0.0582074\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.48356 | + | 2.19067i | 0.140184 | + | 0.206999i | ||||
\(113\) | −11.6982 | −1.10047 | −0.550236 | − | 0.835009i | \(-0.685462\pi\) | ||||
−0.550236 | + | 0.835009i | \(0.685462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.778539 | + | 0.449490i | 0.0722855 | + | 0.0417341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.6422 | −0.979698 | ||||||||
\(119\) | 17.4412 | + | 8.46651i | 1.59883 | + | 0.776123i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.42713 | + | 4.20390i | 0.220648 | + | 0.382173i | ||||
\(122\) | −6.51299 | − | 3.76028i | −0.589659 | − | 0.340440i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.18154 | − | 2.41421i | 0.375513 | − | 0.216803i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.7530i | − | 0.954173i | −0.878856 | − | 0.477086i | \(-0.841693\pi\) | ||
0.878856 | − | 0.477086i | \(-0.158307\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.85457 | + | 3.21221i | 0.162035 | + | 0.280653i | 0.935598 | − | 0.353066i | \(-0.114861\pi\) |
−0.773564 | + | 0.633719i | \(0.781528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.45862 | + | 3.01946i | −0.386611 | + | 0.261821i | ||||
\(134\) | − | 10.6629i | − | 0.921135i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.34607 | − | 3.66390i | −0.544171 | − | 0.314177i | ||||
\(137\) | 6.76028 | − | 11.7091i | 0.577570 | − | 1.00038i | −0.418188 | − | 0.908361i | \(-0.637335\pi\) |
0.995757 | − | 0.0920192i | \(-0.0293321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.06251i | − | 0.768672i | −0.923193 | − | 0.384336i | \(-0.874430\pi\) | ||
0.923193 | − | 0.384336i | \(-0.125570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.60332 | − | 4.96713i | 0.721974 | − | 0.416832i | ||||
\(143\) | −0.234995 | − | 0.135674i | −0.0196513 | − | 0.0113457i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.6569 | −0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.06815i | 0.334400i | ||||||||
\(149\) | 13.2385 | − | 7.64324i | 1.08454 | − | 0.626158i | 0.152421 | − | 0.988316i | \(-0.451293\pi\) |
0.932117 | + | 0.362157i | \(0.117960\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.93942 | − | 8.55532i | 0.401964 | − | 0.696222i | −0.591999 | − | 0.805939i | \(-0.701661\pi\) |
0.993963 | + | 0.109717i | \(0.0349944\pi\) | |||||||
\(152\) | 1.76260 | − | 1.01764i | 0.142966 | − | 0.0825413i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.754415 | + | 10.5076i | 0.0607925 | + | 0.846730i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.14418 | − | 12.3741i | 0.570168 | − | 0.987560i | −0.426380 | − | 0.904544i | \(-0.640212\pi\) |
0.996548 | − | 0.0830157i | \(-0.0264552\pi\) | |||||||
\(158\) | 8.77489 | − | 15.1986i | 0.698093 | − | 1.20913i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.53674 | − | 8.17569i | −0.436356 | − | 0.644335i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.64083 | − | 4.98879i | 0.676802 | − | 0.390752i | −0.121847 | − | 0.992549i | \(-0.538882\pi\) |
0.798649 | + | 0.601797i | \(0.205548\pi\) | |||||||
\(164\) | −0.844605 | + | 1.46290i | −0.0659526 | + | 0.114233i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.4266 | + | 7.17449i | −0.964490 | + | 0.556849i | ||||
\(167\) | 13.7778i | 1.06616i | 0.846065 | + | 0.533079i | \(0.178965\pi\) | ||||
−0.846065 | + | 0.533079i | \(0.821035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9954 | −0.999643 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.835475 | + | 0.482362i | 0.0637044 | + | 0.0367798i | ||||
\(173\) | 7.16442 | − | 4.13638i | 0.544701 | − | 0.314483i | −0.202281 | − | 0.979327i | \(-0.564836\pi\) |
0.746982 | + | 0.664844i | \(0.231502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.98174i | − | 0.300135i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.913956 | − | 1.58302i | 0.0685039 | − | 0.118652i | ||||
\(179\) | 9.97501 | + | 5.75908i | 0.745568 | + | 0.430454i | 0.824090 | − | 0.566459i | \(-0.191687\pi\) |
−0.0785226 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5924i | 1.23330i | 0.787237 | + | 0.616650i | \(0.211511\pi\) | ||||
−0.787237 | + | 0.616650i | \(0.788489\pi\) | |||||||
\(182\) | −0.101102 | − | 0.149291i | −0.00749421 | − | 0.0110662i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.86603 | + | 3.23205i | 0.137565 | + | 0.238270i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.5887 | − | 25.2684i | −1.06683 | − | 1.84781i | ||||
\(188\) | − | 1.66150i | − | 0.121177i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9640 | − | 9.21682i | 1.15511 | − | 0.666905i | 0.204986 | − | 0.978765i | \(-0.434285\pi\) |
0.950128 | + | 0.311859i | \(0.100952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50643 | + | 3.17914i | 0.396361 | + | 0.228839i | 0.684913 | − | 0.728625i | \(-0.259840\pi\) |
−0.288552 | + | 0.957464i | \(0.593174\pi\) | |||||||
\(194\) | −8.57509 | − | 14.8525i | −0.615656 | − | 1.06635i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.59808 | + | 6.50000i | −0.185577 | + | 0.464286i | ||||
\(197\) | −12.8389 | −0.914734 | −0.457367 | − | 0.889278i | \(-0.651208\pi\) | ||||
−0.457367 | + | 0.889278i | \(0.651208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.33950 | + | 4.81481i | 0.591171 | + | 0.341313i | 0.765561 | − | 0.643364i | \(-0.222462\pi\) |
−0.174389 | + | 0.984677i | \(0.555795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.73545 | 0.473905 | ||||||||
\(203\) | 0.170328 | + | 2.37237i | 0.0119547 | + | 0.166508i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.260021 | − | 0.450370i | 0.0181165 | − | 0.0313787i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0340742 | + | 0.0590182i | 0.00236262 | + | 0.00409218i | ||||
\(209\) | 8.10394 | 0.560561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5619 | −1.00248 | −0.501241 | − | 0.865308i | \(-0.667123\pi\) | ||||
−0.501241 | + | 0.865308i | \(0.667123\pi\) | |||||||
\(212\) | −6.61339 | − | 11.4547i | −0.454210 | − | 0.786714i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.06350 | + | 5.30614i | −0.209417 | + | 0.362721i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4923 | + | 5.57874i | 0.780150 | + | 0.378709i | ||||
\(218\) | −13.5546 | −0.918033 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.432474 | + | 0.249689i | 0.0290913 | + | 0.0167959i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6609 | 1.58445 | 0.792227 | − | 0.610227i | \(-0.208922\pi\) | ||||
0.792227 | + | 0.610227i | \(0.208922\pi\) | |||||||
\(224\) | 1.15539 | − | 2.38014i | 0.0771980 | − | 0.159030i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.84909 | + | 10.1309i | 0.389076 | + | 0.673899i | ||||
\(227\) | 7.48288 | + | 4.32024i | 0.496656 | + | 0.286744i | 0.727332 | − | 0.686286i | \(-0.240760\pi\) |
−0.230676 | + | 0.973031i | \(0.574094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1896 | − | 7.03768i | 0.805513 | − | 0.465063i | −0.0398824 | − | 0.999204i | \(-0.512698\pi\) |
0.845395 | + | 0.534141i | \(0.179365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 0.898979i | − | 0.0590209i | ||||||
\(233\) | 10.0988 | + | 17.4916i | 0.661593 | + | 1.14591i | 0.980197 | + | 0.198025i | \(0.0634527\pi\) |
−0.318604 | + | 0.947888i | \(0.603214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.32112 | + | 9.21645i | 0.346375 | + | 0.599940i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.38839 | − | 19.3378i | −0.0899959 | − | 1.25348i | ||||
\(239\) | − | 23.5040i | − | 1.52035i | −0.649721 | − | 0.760173i | \(-0.725114\pi\) | ||
0.649721 | − | 0.760173i | \(-0.274886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8765 | − | 7.43426i | −0.829449 | − | 0.478883i | 0.0242151 | − | 0.999707i | \(-0.492291\pi\) |
−0.853664 | + | 0.520824i | \(0.825625\pi\) | |||||||
\(242\) | 2.42713 | − | 4.20390i | 0.156022 | − | 0.270237i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.52056i | 0.481454i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.120118 | + | 0.0693504i | −0.00764295 | + | 0.00441266i | ||||
\(248\) | −4.18154 | − | 2.41421i | −0.265528 | − | 0.153303i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.31736 | −0.272509 | −0.136255 | − | 0.990674i | \(-0.543507\pi\) | ||||
−0.136255 | + | 0.990674i | \(0.543507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.8601i | 0.934244i | ||||||||
\(254\) | −9.31236 | + | 5.37649i | −0.584309 | + | 0.337351i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.18570 | − | 2.41662i | 0.261097 | − | 0.150744i | −0.363738 | − | 0.931501i | \(-0.618500\pi\) |
0.624835 | + | 0.780757i | \(0.285166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.91197 | + | 6.03536i | −0.553763 | + | 0.375019i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.85457 | − | 3.21221i | 0.114576 | − | 0.198451i | ||||
\(263\) | −3.33245 | + | 5.77197i | −0.205488 | + | 0.355915i | −0.950288 | − | 0.311372i | \(-0.899211\pi\) |
0.744800 | + | 0.667287i | \(0.232545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.84424 | + | 2.35155i | 0.297019 | + | 0.144183i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.23435 | + | 5.33145i | −0.564078 | + | 0.325670i | ||||
\(269\) | −15.8700 | + | 27.4877i | −0.967612 | + | 1.67595i | −0.265186 | + | 0.964197i | \(0.585433\pi\) |
−0.702426 | + | 0.711757i | \(0.747900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1244 | − | 8.73205i | 0.918739 | − | 0.530434i | 0.0355066 | − | 0.999369i | \(-0.488696\pi\) |
0.883233 | + | 0.468935i | \(0.155362\pi\) | |||||||
\(272\) | 7.32780i | 0.444313i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.5206 | −0.816807 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3557 | − | 11.7524i | −1.22305 | − | 0.706130i | −0.257486 | − | 0.966282i | \(-0.582894\pi\) |
−0.965568 | + | 0.260152i | \(0.916227\pi\) | |||||||
\(278\) | −7.84836 | + | 4.53125i | −0.470714 | + | 0.271767i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4159i | 0.919635i | 0.888013 | + | 0.459817i | \(0.152085\pi\) | ||||
−0.888013 | + | 0.459817i | \(0.847915\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8554 | − | 23.9983i | 0.823619 | − | 1.42655i | −0.0793517 | − | 0.996847i | \(-0.525285\pi\) |
0.902970 | − | 0.429703i | \(-0.141382\pi\) | |||||||
\(284\) | −8.60332 | − | 4.96713i | −0.510513 | − | 0.294745i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.271349i | 0.0160452i | ||||||||
\(287\) | −4.45776 | + | 0.320053i | −0.263133 | + | 0.0188921i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.3484 | + | 31.7803i | 1.07932 | + | 1.86943i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.82843 | + | 10.0951i | 0.341083 | + | 0.590773i | ||||
\(293\) | 2.84377i | 0.166135i | 0.996544 | + | 0.0830673i | \(0.0264717\pi\) | ||||
−0.996544 | + | 0.0830673i | \(0.973528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.52312 | − | 2.03407i | 0.204777 | − | 0.118228i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.2385 | − | 7.64324i | −0.766884 | − | 0.442761i | ||||
\(299\) | −0.127167 | − | 0.220259i | −0.00735423 | − | 0.0127379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.182785 | + | 2.54587i | 0.0105355 | + | 0.146741i | ||||
\(302\) | −9.87883 | −0.568463 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.76260 | − | 1.01764i | −0.101092 | − | 0.0583655i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.52180 | −0.143927 | −0.0719634 | − | 0.997407i | \(-0.522926\pi\) | ||||
−0.0719634 | + | 0.997407i | \(0.522926\pi\) | |||||||
\(308\) | 8.72268 | − | 5.90717i | 0.497021 | − | 0.336592i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.49697 | − | 9.52104i | 0.311705 | − | 0.539889i | −0.667027 | − | 0.745034i | \(-0.732433\pi\) |
0.978732 | + | 0.205145i | \(0.0657667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4731 | + | 21.6040i | 0.705020 | + | 1.22113i | 0.966684 | + | 0.255971i | \(0.0823952\pi\) |
−0.261665 | + | 0.965159i | \(0.584271\pi\) | |||||||
\(314\) | −14.2884 | −0.806339 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5498 | −0.987252 | ||||||||
\(317\) | −7.53465 | − | 13.0504i | −0.423188 | − | 0.732984i | 0.573061 | − | 0.819513i | \(-0.305756\pi\) |
−0.996249 | + | 0.0865290i | \(0.972422\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.78975 | − | 3.09994i | 0.100207 | − | 0.173563i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.31199 | + | 8.88280i | −0.240298 | + | 0.495019i | ||||
\(323\) | −14.9141 | −0.829843 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.64083 | − | 4.98879i | −0.478572 | − | 0.276303i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.68921 | 0.0932711 | ||||||||
\(329\) | 3.63980 | − | 2.46494i | 0.200668 | − | 0.135896i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0904 | − | 26.1373i | −0.829444 | − | 1.43664i | −0.898475 | − | 0.439024i | \(-0.855324\pi\) |
0.0690315 | − | 0.997614i | \(-0.478009\pi\) | |||||||
\(332\) | 12.4266 | + | 7.17449i | 0.681997 | + | 0.393751i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.9319 | − | 6.88891i | 0.652886 | − | 0.376944i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5911i | 1.17614i | 0.808809 | + | 0.588071i | \(0.200113\pi\) | ||||
−0.808809 | + | 0.588071i | \(0.799887\pi\) | |||||||
\(338\) | 6.49768 | + | 11.2543i | 0.353427 | + | 0.612154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.61277 | − | 16.6498i | −0.520561 | − | 0.901638i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | − | 0.964724i | − | 0.0520144i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.16442 | − | 4.13638i | −0.385161 | − | 0.222373i | ||||
\(347\) | 11.5921 | − | 20.0781i | 0.622297 | − | 1.07785i | −0.366760 | − | 0.930316i | \(-0.619533\pi\) |
0.989057 | − | 0.147534i | \(-0.0471336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.7287i | − | 0.574292i | −0.957887 | − | 0.287146i | \(-0.907294\pi\) | ||
0.957887 | − | 0.287146i | \(-0.0927064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.44829 | + | 1.99087i | −0.183794 | + | 0.106114i | ||||
\(353\) | 7.57561 | + | 4.37378i | 0.403209 | + | 0.232793i | 0.687868 | − | 0.725836i | \(-0.258547\pi\) |
−0.284659 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.82791 | −0.0968791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 11.5182i | − | 0.608753i | ||||||
\(359\) | 22.3059 | − | 12.8783i | 1.17726 | − | 0.679691i | 0.221881 | − | 0.975074i | \(-0.428780\pi\) |
0.955379 | + | 0.295382i | \(0.0954470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.42883 | + | 12.8671i | −0.390991 | + | 0.677216i | ||||
\(362\) | 14.3694 | − | 8.29618i | 0.755239 | − | 0.436037i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0787382 | + | 0.162203i | −0.00412700 | + | 0.00850172i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.96885 | − | 17.2665i | 0.520369 | − | 0.901306i | −0.479350 | − | 0.877624i | \(-0.659128\pi\) |
0.999720 | − | 0.0236826i | \(-0.00753911\pi\) | |||||||
\(368\) | 1.86603 | − | 3.23205i | 0.0972733 | − | 0.168482i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.2822 | − | 31.4816i | 0.793410 | − | 1.63444i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.893327 | − | 0.515762i | 0.0462547 | − | 0.0267052i | −0.476694 | − | 0.879069i | \(-0.658165\pi\) |
0.522949 | + | 0.852364i | \(0.324832\pi\) | |||||||
\(374\) | −14.5887 | + | 25.2684i | −0.754364 | + | 1.30660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43890 | + | 0.830749i | −0.0742056 | + | 0.0428426i | ||||
\(377\) | 0.0612640i | 0.00315525i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.09497 | −0.261711 | −0.130855 | − | 0.991401i | \(-0.541772\pi\) | ||||
−0.130855 | + | 0.991401i | \(0.541772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.9640 | − | 9.21682i | −0.816789 | − | 0.471573i | ||||
\(383\) | 7.33307 | − | 4.23375i | 0.374702 | − | 0.216335i | −0.300808 | − | 0.953685i | \(-0.597256\pi\) |
0.675511 | + | 0.737350i | \(0.263923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.35827i | − | 0.323628i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.57509 | + | 14.8525i | −0.435334 | + | 0.754021i | ||||
\(389\) | −4.97229 | − | 2.87075i | −0.252105 | − | 0.145553i | 0.368623 | − | 0.929579i | \(-0.379829\pi\) |
−0.620728 | + | 0.784026i | \(0.713163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.3477i | − | 1.38303i | ||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.41946 | + | 11.1188i | 0.323407 | + | 0.560158i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.43791 | − | 14.6149i | −0.423487 | − | 0.733501i | 0.572791 | − | 0.819701i | \(-0.305861\pi\) |
−0.996278 | + | 0.0862009i | \(0.972527\pi\) | |||||||
\(398\) | − | 9.62962i | − | 0.482689i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.63572 | + | 0.944382i | −0.0816838 | + | 0.0471602i | −0.540286 | − | 0.841482i | \(-0.681684\pi\) |
0.458602 | + | 0.888642i | \(0.348350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.284965 | + | 0.164525i | 0.0141951 | + | 0.00819556i | ||||
\(404\) | −3.36773 | − | 5.83307i | −0.167551 | − | 0.290206i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.96937 | − | 1.33369i | 0.0977381 | − | 0.0661901i | ||||
\(407\) | 16.1983 | 0.802920 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.5617 | − | 16.4901i | −1.41228 | − | 0.815382i | −0.416681 | − | 0.909053i | \(-0.636807\pi\) |
−0.995603 | + | 0.0936705i | \(0.970140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.520042 | −0.0256206 | ||||||||
\(413\) | −12.2960 | + | 25.3300i | −0.605046 | + | 1.24641i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.0340742 | − | 0.0590182i | 0.00167062 | − | 0.00289361i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.05197 | − | 7.01822i | −0.198188 | − | 0.343272i | ||||
\(419\) | −0.300470 | −0.0146789 | −0.00733945 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733945 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8625 | 1.40667 | 0.703335 | − | 0.710858i | \(-0.251693\pi\) | ||||
0.703335 | + | 0.710858i | \(0.251693\pi\) | |||||||
\(422\) | 7.28094 | + | 12.6110i | 0.354431 | + | 0.613892i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.61339 | + | 11.4547i | −0.321175 | + | 0.556291i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.4751 | + | 11.1572i | −0.797284 | + | 0.539936i | ||||
\(428\) | 6.12701 | 0.296160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.0895 | − | 16.7948i | −1.40119 | − | 0.808978i | −0.406677 | − | 0.913572i | \(-0.633312\pi\) |
−0.994515 | + | 0.104594i | \(0.966646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.2207 | −0.539234 | −0.269617 | − | 0.962968i | \(-0.586897\pi\) | ||||
−0.269617 | + | 0.962968i | \(0.586897\pi\) | |||||||
\(434\) | −0.914836 | − | 12.7420i | −0.0439135 | − | 0.611636i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.77729 | + | 11.7386i | 0.324574 | + | 0.562178i | ||||
\(437\) | 6.57812 | + | 3.79788i | 0.314674 | + | 0.181677i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6075 | − | 8.43363i | 0.697177 | − | 0.402515i | −0.109118 | − | 0.994029i | \(-0.534803\pi\) |
0.806295 | + | 0.591513i | \(0.201469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.499378i | − | 0.0237530i | ||||||
\(443\) | −1.02823 | − | 1.78094i | −0.0488526 | − | 0.0846152i | 0.840565 | − | 0.541711i | \(-0.182223\pi\) |
−0.889418 | + | 0.457095i | \(0.848890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.8305 | − | 20.4910i | −0.560189 | − | 0.970276i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.63896 | + | 0.189469i | −0.124679 | + | 0.00895155i | ||||
\(449\) | − | 12.5892i | − | 0.594122i | −0.954858 | − | 0.297061i | \(-0.903994\pi\) | ||
0.954858 | − | 0.297061i | \(-0.0960065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.82489 | + | 3.36300i | 0.274283 | + | 0.158357i | ||||
\(452\) | 5.84909 | − | 10.1309i | 0.275118 | − | 0.476519i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 8.64048i | − | 0.405518i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.2701 | + | 17.4765i | −1.41598 | + | 0.817515i | −0.995942 | − | 0.0899930i | \(-0.971316\pi\) |
−0.420035 | + | 0.907508i | \(0.637982\pi\) | |||||||
\(458\) | −12.1896 | − | 7.03768i | −0.569584 | − | 0.328849i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3750 | 1.08868 | 0.544341 | − | 0.838864i | \(-0.316780\pi\) | ||||
0.544341 | + | 0.838864i | \(0.316780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.35693i | − | 0.295431i | −0.989030 | − | 0.147716i | \(-0.952808\pi\) | ||
0.989030 | − | 0.147716i | \(-0.0471921\pi\) | |||||||
\(464\) | −0.778539 | + | 0.449490i | −0.0361428 | + | 0.0208670i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0988 | − | 17.4916i | 0.467817 | − | 0.810283i | ||||
\(467\) | 6.74907 | − | 3.89658i | 0.312310 | − | 0.180312i | −0.335650 | − | 0.941987i | \(-0.608956\pi\) |
0.647960 | + | 0.761675i | \(0.275623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3792 | − | 12.3199i | −1.17190 | − | 0.568878i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.32112 | − | 9.21645i | 0.244924 | − | 0.424222i | ||||
\(473\) | 1.92064 | − | 3.32665i | 0.0883111 | − | 0.152959i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.0528 | + | 10.8713i | −0.735779 | + | 0.498284i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.3550 | + | 11.7520i | −0.931018 | + | 0.537523i | ||||
\(479\) | −13.7520 | + | 23.8191i | −0.628344 | + | 1.08832i | 0.359540 | + | 0.933130i | \(0.382934\pi\) |
−0.987884 | + | 0.155194i | \(0.950400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.240095 | + | 0.138619i | −0.0109474 | + | 0.00632047i | ||||
\(482\) | 14.8685i | 0.677242i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.85425 | −0.220648 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.6978 | + | 17.7234i | 1.39105 | + | 0.803124i | 0.993432 | − | 0.114427i | \(-0.0365032\pi\) |
0.397619 | + | 0.917551i | \(0.369836\pi\) | |||||||
\(488\) | 6.51299 | − | 3.76028i | 0.294829 | − | 0.170220i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.64349i | 0.0741695i | 0.999312 | + | 0.0370848i | \(0.0118072\pi\) | ||||
−0.999312 | + | 0.0370848i | \(0.988193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.29377 | + | 5.70498i | −0.148344 | + | 0.256939i | ||||
\(494\) | 0.120118 | + | 0.0693504i | 0.00540438 | + | 0.00312022i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.82843i | 0.216803i | ||||||||
\(497\) | −1.88223 | − | 26.2161i | −0.0844296 | − | 1.17595i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3665 | − | 30.0796i | −0.777430 | − | 1.34655i | −0.933418 | − | 0.358790i | \(-0.883189\pi\) |
0.155988 | − | 0.987759i | \(-0.450144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.15868 | + | 3.73894i | 0.0963465 | + | 0.166877i | ||||
\(503\) | 28.9613i | 1.29132i | 0.763625 | + | 0.645660i | \(0.223418\pi\) | ||||
−0.763625 | + | 0.645660i | \(0.776582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.8692 | − | 7.43003i | 0.572105 | − | 0.330305i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.31236 | + | 5.37649i | 0.413169 | + | 0.238543i | ||||
\(509\) | 10.7311 | + | 18.5867i | 0.475646 | + | 0.823842i | 0.999611 | − | 0.0278973i | \(-0.00888113\pi\) |
−0.523965 | + | 0.851740i | \(0.675548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4683 | + | 27.7449i | −0.595801 | + | 1.22736i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.18570 | − | 2.41662i | −0.184624 | − | 0.106592i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.61565 | −0.290956 | ||||||||
\(518\) | 9.68276 | + | 4.70032i | 0.425436 | + | 0.206520i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.1218 | + | 34.8520i | −0.881552 | + | 1.52689i | −0.0319362 | + | 0.999490i | \(0.510167\pi\) |
−0.849616 | + | 0.527403i | \(0.823166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.8444 | + | 25.7113i | 0.649102 | + | 1.12428i | 0.983338 | + | 0.181789i | \(0.0581887\pi\) |
−0.334235 | + | 0.942490i | \(0.608478\pi\) | |||||||
\(524\) | −3.70915 | −0.162035 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.66490 | 0.290603 | ||||||||
\(527\) | 17.6909 | + | 30.6415i | 0.770627 | + | 1.33477i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.53590 | − | 7.85641i | 0.197213 | − | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.385621 | − | 5.37101i | −0.0167188 | − | 0.232863i | ||||
\(533\) | −0.115117 | −0.00498627 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.23435 | + | 5.33145i | 0.398863 | + | 0.230284i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.7400 | 1.36841 | ||||||||
\(539\) | 25.8813 | + | 10.3449i | 1.11479 | + | 0.445585i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.62914 | + | 14.9461i | 0.370996 | + | 0.642584i | 0.989719 | − | 0.143026i | \(-0.0456831\pi\) |
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(542\) | −15.1244 | − | 8.73205i | −0.649647 | − | 0.375074i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.34607 | − | 3.66390i | 0.272085 | − | 0.157089i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9703i | 0.768354i | 0.923260 | + | 0.384177i | \(0.125515\pi\) | ||||
−0.923260 | + | 0.384177i | \(0.874485\pi\) | |||||||
\(548\) | 6.76028 | + | 11.7091i | 0.288785 | + | 0.500190i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.914836 | − | 1.58454i | −0.0389733 | − | 0.0675038i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0362 | − | 38.4458i | −1.10717 | − | 1.63488i | ||||
\(554\) | 23.5047i | 0.998619i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.84836 | + | 4.53125i | 0.332845 | + | 0.192168i | ||||
\(557\) | −22.6273 | + | 39.1916i | −0.958748 | + | 1.66060i | −0.233201 | + | 0.972428i | \(0.574920\pi\) |
−0.725547 | + | 0.688172i | \(0.758413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0657443i | 0.00278069i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.3506 | − | 7.70794i | 0.563159 | − | 0.325140i | ||||
\(563\) | −13.7410 | − | 7.93336i | −0.579114 | − | 0.334351i | 0.181667 | − | 0.983360i | \(-0.441851\pi\) |
−0.760781 | + | 0.649009i | \(0.775184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.7108 | −1.16477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.93426i | 0.416832i | ||||||||
\(569\) | 0.0524375 | − | 0.0302748i | 0.00219829 | − | 0.00126918i | −0.498900 | − | 0.866659i | \(-0.666263\pi\) |
0.501099 | + | 0.865390i | \(0.332929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.78245 | − | 11.7476i | 0.283837 | − | 0.491620i | −0.688490 | − | 0.725246i | \(-0.741726\pi\) |
0.972326 | + | 0.233626i | \(0.0750592\pi\) | |||||||
\(572\) | 0.234995 | − | 0.135674i | 0.00982564 | − | 0.00567284i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.50605 | + | 3.70050i | 0.104601 | + | 0.154456i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8384 | + | 37.8252i | −0.909144 | + | 1.57468i | −0.0938887 | + | 0.995583i | \(0.529930\pi\) |
−0.815256 | + | 0.579101i | \(0.803404\pi\) | |||||||
\(578\) | 18.3484 | − | 31.7803i | 0.763191 | − | 1.32189i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.71868 | + | 37.8664i | 0.112790 | + | 1.57096i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.6098 | + | 26.3328i | −1.88896 | + | 1.09059i | ||||
\(584\) | 5.82843 | − | 10.0951i | 0.241182 | − | 0.417740i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.46278 | − | 1.42188i | 0.101736 | − | 0.0587375i | ||||
\(587\) | 45.4100i | 1.87427i | 0.348967 | + | 0.937135i | \(0.386532\pi\) | ||||
−0.348967 | + | 0.937135i | \(0.613468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.82718 | −0.404922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.52312 | − | 2.03407i | −0.144799 | − | 0.0835999i | ||||
\(593\) | 22.2579 | − | 12.8506i | 0.914022 | − | 0.527711i | 0.0322991 | − | 0.999478i | \(-0.489717\pi\) |
0.881723 | + | 0.471767i | \(0.156384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2865i | 0.626158i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.127167 | + | 0.220259i | −0.00520023 | + | 0.00900706i | ||||
\(599\) | −23.0347 | − | 13.2991i | −0.941173 | − | 0.543386i | −0.0508450 | − | 0.998707i | \(-0.516191\pi\) |
−0.890328 | + | 0.455320i | \(0.849525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9681i | 0.528979i | 0.964389 | + | 0.264489i | \(0.0852034\pi\) | ||||
−0.964389 | + | 0.264489i | \(0.914797\pi\) | |||||||
\(602\) | 2.11339 | − | 1.43123i | 0.0861354 | − | 0.0583326i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.93942 | + | 8.55532i | 0.200982 | + | 0.348111i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.15576 | + | 14.1262i | 0.331032 | + | 0.573364i | 0.982714 | − | 0.185128i | \(-0.0592698\pi\) |
−0.651682 | + | 0.758492i | \(0.725937\pi\) | |||||||
\(608\) | 2.03528i | 0.0825413i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0980586 | − | 0.0566142i | 0.00396703 | − | 0.00229036i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4603 | + | 7.19395i | 0.503267 | + | 0.290561i | 0.730062 | − | 0.683381i | \(-0.239491\pi\) |
−0.226795 | + | 0.973943i | \(0.572825\pi\) | |||||||
\(614\) | 1.26090 | + | 2.18394i | 0.0508858 | + | 0.0881368i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47710 | − | 4.60048i | −0.381843 | − | 0.185359i | ||||
\(617\) | −8.65760 | −0.348542 | −0.174271 | − | 0.984698i | \(-0.555757\pi\) | ||||
−0.174271 | + | 0.984698i | \(0.555757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.8459 | − | 22.4277i | −1.56135 | − | 0.901444i | −0.997121 | − | 0.0758230i | \(-0.975842\pi\) |
−0.564225 | − | 0.825621i | \(-0.690825\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.9939 | −0.440817 | ||||||||
\(623\) | −2.71182 | − | 4.00435i | −0.108647 | − | 0.160431i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.4731 | − | 21.6040i | 0.498524 | − | 0.863469i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.14418 | + | 12.3741i | 0.285084 | + | 0.493780i | ||||
\(629\) | −29.8106 | −1.18863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1878 | −1.52023 | −0.760116 | − | 0.649788i | \(-0.774858\pi\) | ||||
−0.760116 | + | 0.649788i | \(0.774858\pi\) | |||||||
\(632\) | 8.77489 | + | 15.1986i | 0.349046 | + | 0.604566i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.53465 | + | 13.0504i | −0.299239 | + | 0.518298i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.472146 | + | 0.0681483i | −0.0187071 | + | 0.00270014i | ||||
\(638\) | −3.57950 | −0.141714 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.40533 | + | 4.27547i | 0.292493 | + | 0.168871i | 0.639066 | − | 0.769152i | \(-0.279321\pi\) |
−0.346573 | + | 0.938023i | \(0.612655\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.75058 | −0.108472 | −0.0542361 | − | 0.998528i | \(-0.517272\pi\) | ||||
−0.0542361 | + | 0.998528i | \(0.517272\pi\) | |||||||
\(644\) | 9.84873 | − | 0.707107i | 0.388094 | − | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.45705 | + | 12.9160i | 0.293394 | + | 0.508173i | ||||
\(647\) | 24.0431 | + | 13.8813i | 0.945234 | + | 0.545731i | 0.891597 | − | 0.452830i | \(-0.149585\pi\) |
0.0536365 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.6975 | − | 21.1873i | 1.44050 | − | 0.831675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.97758i | 0.390752i | ||||||||
\(653\) | −7.05994 | − | 12.2282i | −0.276277 | − | 0.478525i | 0.694180 | − | 0.719802i | \(-0.255767\pi\) |
−0.970456 | + | 0.241276i | \(0.922434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.844605 | − | 1.46290i | −0.0329763 | − | 0.0571166i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.95460 | − | 1.91969i | −0.154166 | − | 0.0748372i | ||||
\(659\) | 9.92570i | 0.386650i | 0.981135 | + | 0.193325i | \(0.0619272\pi\) | ||||
−0.981135 | + | 0.193325i | \(0.938073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9029 | + | 9.18154i | 0.618551 | + | 0.357121i | 0.776305 | − | 0.630358i | \(-0.217092\pi\) |
−0.157754 | + | 0.987478i | \(0.550425\pi\) | |||||||
\(662\) | −15.0904 | + | 26.1373i | −0.586505 | + | 1.01586i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.3490i | − | 0.556849i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.90555 | − | 1.67752i | 0.112503 | − | 0.0649538i | ||||
\(668\) | −11.9319 | − | 6.88891i | −0.461660 | − | 0.266540i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.9449 | 1.15601 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32.6050i | − | 1.25683i | −0.777878 | − | 0.628415i | \(-0.783704\pi\) | ||
0.777878 | − | 0.628415i | \(-0.216296\pi\) | |||||||
\(674\) | 18.6984 | − | 10.7956i | 0.720237 | − | 0.415829i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.49768 | − | 11.2543i | 0.249911 | − | 0.432858i | ||||
\(677\) | 15.8816 | − | 9.16923i | 0.610378 | − | 0.352402i | −0.162735 | − | 0.986670i | \(-0.552032\pi\) |
0.773113 | + | 0.634268i | \(0.218698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.2586 | + | 3.24942i | −1.73687 | + | 0.124701i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.61277 | + | 16.6498i | −0.368092 | + | 0.637554i | ||||
\(683\) | −12.2385 | + | 21.1977i | −0.468294 | + | 0.811108i | −0.999343 | − | 0.0362323i | \(-0.988464\pi\) |
0.531050 | + | 0.847341i | \(0.321798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.4691 | + | 13.6938i | 0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.835475 | + | 0.482362i | −0.0318522 | + | 0.0183899i | ||||
\(689\) | 0.450692 | − | 0.780621i | 0.0171700 | − | 0.0297393i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9118 | + | 9.18670i | −0.605315 | + | 0.349479i | −0.771129 | − | 0.636678i | \(-0.780308\pi\) |
0.165815 | + | 0.986157i | \(0.446975\pi\) | |||||||
\(692\) | 8.27276i | 0.314483i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.1842 | −0.880061 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.7198 | − | 6.18910i | −0.406043 | − | 0.234429i | ||||
\(698\) | −9.29128 | + | 5.36433i | −0.351680 | + | 0.203043i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.2399i | − | 0.537834i | −0.963163 | − | 0.268917i | \(-0.913334\pi\) | ||
0.963163 | − | 0.268917i | \(-0.0866658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.13990 | − | 7.17052i | 0.156139 | − | 0.270441i | ||||
\(704\) | 3.44829 | + | 1.99087i | 0.129962 | + | 0.0750337i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 8.74756i | − | 0.329219i | ||||||
\(707\) | 7.78210 | − | 16.0313i | 0.292676 | − | 0.602920i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7586 | + | 32.4908i | 0.704492 | + | 1.22022i | 0.966874 | + | 0.255252i | \(0.0821586\pi\) |
−0.262382 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.913956 | + | 1.58302i | 0.0342519 | + | 0.0593261i | ||||
\(713\) | − | 18.0199i | − | 0.674852i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.97501 | + | 5.75908i | −0.372784 | + | 0.215227i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.3059 | − | 12.8783i | −0.832449 | − | 0.480614i | ||||
\(719\) | −2.65733 | − | 4.60264i | −0.0991019 | − | 0.171649i | 0.812211 | − | 0.583363i | \(-0.198264\pi\) |
−0.911313 | + | 0.411714i | \(0.864930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.771516 | − | 1.13924i | −0.0287327 | − | 0.0424276i | ||||
\(722\) | 14.8577 | 0.552945 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.3694 | − | 8.29618i | −0.534035 | − | 0.308325i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.93413 | −0.108821 | −0.0544104 | − | 0.998519i | \(-0.517328\pi\) | ||||
−0.0544104 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(728\) | 0.179841 | − | 0.0129120i | 0.00666534 | − | 0.000478550i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.53465 | + | 6.12220i | −0.130734 | + | 0.226438i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.82411 | + | 11.8197i | 0.252054 | + | 0.436570i | 0.964091 | − | 0.265571i | \(-0.0855606\pi\) |
−0.712037 | + | 0.702142i | \(0.752227\pi\) | |||||||
\(734\) | −19.9377 | −0.735914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.73205 | −0.137565 | ||||||||
\(737\) | 21.2285 | + | 36.7688i | 0.781960 | + | 1.35440i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.6650 | − | 27.1325i | 0.576246 | − | 0.998087i | −0.419659 | − | 0.907682i | \(-0.637851\pi\) |
0.995905 | − | 0.0904051i | \(-0.0288162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.9049 | + | 2.50606i | −1.28140 | + | 0.0920004i | ||||
\(743\) | 4.72061 | 0.173182 | 0.0865911 | − | 0.996244i | \(-0.472403\pi\) | ||||
0.0865911 | + | 0.996244i | \(0.472403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.893327 | − | 0.515762i | −0.0327070 | − | 0.0188834i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29.1774 | 1.06683 | ||||||||
\(749\) | 9.08981 | + | 13.4223i | 0.332134 | + | 0.490439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8394 | + | 22.2385i | 0.468516 | + | 0.811494i | 0.999352 | − | 0.0359807i | \(-0.0114555\pi\) |
−0.530836 | + | 0.847474i | \(0.678122\pi\) | |||||||
\(752\) | 1.43890 | + | 0.830749i | 0.0524713 | + | 0.0302943i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0530562 | − | 0.0306320i | 0.00193219 | − | 0.00111555i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8781i | 1.37670i | 0.725377 | + | 0.688352i | \(0.241665\pi\) | ||||
−0.725377 | + | 0.688352i | \(0.758335\pi\) | |||||||
\(758\) | 2.54748 | + | 4.41237i | 0.0925288 | + | 0.160265i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.3533 | + | 17.9325i | 0.375308 | + | 0.650052i | 0.990373 | − | 0.138424i | \(-0.0442038\pi\) |
−0.615065 | + | 0.788476i | \(0.710870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.6609 | + | 32.2618i | −0.566963 | + | 1.16796i | ||||
\(764\) | 18.4336i | 0.666905i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.33307 | − | 4.23375i | −0.264955 | − | 0.152972i | ||||
\(767\) | −0.362626 | + | 0.628086i | −0.0130937 | + | 0.0226789i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.34563i | 0.120647i | 0.998179 | + | 0.0603233i | \(0.0192132\pi\) | ||||
−0.998179 | + | 0.0603233i | \(0.980787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50643 | + | 3.17914i | −0.198181 | + | 0.114420i | ||||
\(773\) | 24.8778 | + | 14.3632i | 0.894793 | + | 0.516609i | 0.875507 | − | 0.483205i | \(-0.160527\pi\) |
0.0192861 | + | 0.999814i | \(0.493861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.1502 | 0.615656 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.74150i | 0.205843i | ||||||||
\(779\) | 2.97740 | − | 1.71901i | 0.106677 | − | 0.0615898i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7778 | + | 34.2562i | −0.707706 | + | 1.22578i | ||||
\(782\) | −23.6838 | + | 13.6739i | −0.846932 | + | 0.488977i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.33013 | − | 5.50000i | −0.154647 | − | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.74515 | + | 4.75474i | −0.0978541 | + | 0.169488i | −0.910796 | − | 0.412856i | \(-0.864531\pi\) |
0.812942 | + | 0.582345i | \(0.197865\pi\) | |||||||
\(788\) | 6.41946 | − | 11.1188i | 0.228684 | − | 0.396092i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.8710 | − | 2.21644i | 1.09765 | − | 0.0788075i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.443850 | + | 0.256257i | −0.0157616 | + | 0.00909995i | ||||
\(794\) | −8.43791 | + | 14.6149i | −0.299450 | + | 0.518663i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.33950 | + | 4.81481i | −0.295586 | + | 0.170656i | ||||
\(797\) | − | 50.8854i | − | 1.80245i | −0.433347 | − | 0.901227i | \(-0.642668\pi\) | ||
0.433347 | − | 0.901227i | \(-0.357332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.1751 | 0.430725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.63572 | + | 0.944382i | 0.0577592 | + | 0.0333473i | ||||
\(803\) | 40.1962 | − | 23.2073i | 1.41849 | − | 0.818967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 0.329049i | − | 0.0115903i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.36773 | + | 5.83307i | −0.118476 | + | 0.205207i | ||||
\(809\) | 1.80508 | + | 1.04217i | 0.0634634 | + | 0.0366406i | 0.531396 | − | 0.847124i | \(-0.321668\pi\) |
−0.467933 | + | 0.883764i | \(0.655001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.0199i | − | 0.948797i | −0.880310 | − | 0.474398i | \(-0.842666\pi\) | ||
0.880310 | − | 0.474398i | \(-0.157334\pi\) | |||||||
\(812\) | −2.13970 | − | 1.03868i | −0.0750886 | − | 0.0364504i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.09915 | − | 14.0281i | −0.283875 | − | 0.491686i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.981740 | − | 1.70042i | −0.0343467 | − | 0.0594903i | ||||
\(818\) | 32.9802i | 1.15312i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.06085 | + | 4.65393i | −0.281326 | + | 0.162423i | −0.634023 | − | 0.773314i | \(-0.718598\pi\) |
0.352698 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.0901 | + | 20.2593i | 1.22316 | + | 0.706195i | 0.965591 | − | 0.260064i | \(-0.0837437\pi\) |
0.257573 | + | 0.966259i | \(0.417077\pi\) | |||||||
\(824\) | 0.260021 | + | 0.450370i | 0.00905826 | + | 0.0156894i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.0844 | − | 2.01637i | 0.977182 | − | 0.0701585i | ||||
\(827\) | −14.0131 | −0.487284 | −0.243642 | − | 0.969865i | \(-0.578342\pi\) | ||||
−0.243642 | + | 0.969865i | \(0.578342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.8540 | − | 10.8854i | −0.654827 | − | 0.378064i | 0.135476 | − | 0.990781i | \(-0.456744\pi\) |
−0.790303 | + | 0.612716i | \(0.790077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0681483 | −0.00236262 | ||||||||
\(833\) | −47.6307 | − | 19.0382i | −1.65031 | − | 0.659634i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.05197 | + | 7.01822i | −0.140140 | + | 0.242730i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.150235 | + | 0.260214i | 0.00518978 | + | 0.00898896i | ||||
\(839\) | −53.7026 | −1.85402 | −0.927009 | − | 0.375039i | \(-0.877629\pi\) | ||||
−0.927009 | + | 0.375039i | \(0.877629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1918 | 0.972132 | ||||||||
\(842\) | −14.4312 | − | 24.9956i | −0.497333 | − | 0.861406i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.28094 | − | 12.6110i | 0.250620 | − | 0.434087i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.20159 | − | 10.6341i | −0.247450 | − | 0.365391i | ||||
\(848\) | 13.2268 | 0.454210 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1485 | + | 7.59127i | 0.450723 | + | 0.260225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.95355 | −0.272324 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(854\) | 17.9000 | + | 8.68921i | 0.612525 | + | 0.297339i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.06350 | − | 5.30614i | −0.104708 | − | 0.181360i | ||||
\(857\) | 1.98582 | + | 1.14651i | 0.0678343 | + | 0.0391641i | 0.533534 | − | 0.845779i | \(-0.320864\pi\) |
−0.465699 | + | 0.884943i | \(0.654197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1054 | − | 22.0002i | 1.30014 | − | 0.750636i | 0.319712 | − | 0.947515i | \(-0.396414\pi\) |
0.980428 | + | 0.196879i | \(0.0630806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.5897i | 1.14407i | ||||||||
\(863\) | 16.5676 | + | 28.6959i | 0.563968 | + | 0.976821i | 0.997145 | + | 0.0755122i | \(0.0240592\pi\) |
−0.433177 | + | 0.901309i | \(0.642607\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.61037 | + | 9.71744i | 0.190648 | + | 0.330212i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.5775 | + | 7.16328i | −0.359024 | + | 0.243138i | ||||
\(869\) | 69.8787i | 2.37047i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.629306 | − | 0.363330i | −0.0213232 | − | 0.0123110i | ||||
\(872\) | 6.77729 | − | 11.7386i | 0.229508 | − | 0.397520i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.59575i | − | 0.256930i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.92657 | − | 2.84436i | 0.166358 | − | 0.0960471i | −0.414509 | − | 0.910045i | \(-0.636047\pi\) |
0.580868 | + | 0.813998i | \(0.302713\pi\) | |||||||
\(878\) | −14.6075 | − | 8.43363i | −0.492979 | − | 0.284621i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.4073 | −0.754923 | −0.377461 | − | 0.926025i | \(-0.623203\pi\) | ||||
−0.377461 | + | 0.926025i | \(0.623203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.7564i | − | 0.631204i | −0.948892 | − | 0.315602i | \(-0.897794\pi\) | ||
0.948892 | − | 0.315602i | \(-0.102206\pi\) | |||||||
\(884\) | −0.432474 | + | 0.249689i | −0.0145457 | + | 0.00839795i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.02823 | + | 1.78094i | −0.0345440 | + | 0.0598320i | ||||
\(887\) | −1.27384 | + | 0.735451i | −0.0427713 | + | 0.0246940i | −0.521233 | − | 0.853414i | \(-0.674528\pi\) |
0.478462 | + | 0.878108i | \(0.341194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.03735 | + | 28.3767i | 0.0683306 | + | 0.951723i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.8305 | + | 20.4910i | −0.396113 | + | 0.686088i | ||||
\(893\) | −1.69080 | + | 2.92856i | −0.0565806 | + | 0.0980005i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.48356 | + | 2.19067i | 0.0495624 | + | 0.0731852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.9026 | + | 6.29461i | −0.363824 | + | 0.210054i | ||||
\(899\) | −2.17033 | + | 3.75912i | −0.0723845 | + | 0.125374i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.9380 | − | 48.4616i | 2.79638 | − | 1.61449i | ||||
\(902\) | − | 6.72600i | − | 0.223951i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.6982 | −0.389076 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3210 | + | 9.42294i | 0.541930 | + | 0.312883i | 0.745861 | − | 0.666102i | \(-0.232038\pi\) |
−0.203931 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(908\) | −7.48288 | + | 4.32024i | −0.248328 | + | 0.143372i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.45859i | − | 0.180851i | −0.995903 | − | 0.0904256i | \(-0.971177\pi\) | ||
0.995903 | − | 0.0904256i | \(-0.0288227\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.5670 | − | 49.4794i | 0.945428 | − | 1.63753i | ||||
\(914\) | 30.2701 | + | 17.4765i | 1.00125 | + | 0.578070i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0754i | 0.465063i | ||||||||
\(917\) | −5.50276 | − | 8.12552i | −0.181717 | − | 0.268328i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.9805 | + | 25.9470i | 0.494162 | + | 0.855914i | 0.999977 | − | 0.00672796i | \(-0.00214159\pi\) |
−0.505815 | + | 0.862642i | \(0.668808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.6875 | − | 20.2433i | −0.384907 | − | 0.666678i | ||||
\(923\) | − | 0.677003i | − | 0.0222838i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.50526 | + | 3.17846i | −0.180914 | + | 0.104451i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.778539 | + | 0.449490i | 0.0255568 | + | 0.0147552i | ||||
\(929\) | −23.3931 | − | 40.5181i | −0.767504 | − | 1.32936i | −0.938912 | − | 0.344156i | \(-0.888165\pi\) |
0.171408 | − | 0.985200i | \(-0.445168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1940 | − | 8.81300i | 0.366869 | − | 0.288835i | ||||
\(932\) | −20.1976 | −0.661593 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.74907 | − | 3.89658i | −0.220836 | − | 0.127500i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1632 | −0.626036 | −0.313018 | − | 0.949747i | \(-0.601340\pi\) | ||||
−0.313018 | + | 0.949747i | \(0.601340\pi\) | |||||||
\(938\) | 2.02029 | + | 28.1390i | 0.0659647 | + | 0.918770i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2474 | + | 43.7299i | −0.823043 | + | 1.42555i | 0.0803623 | + | 0.996766i | \(0.474392\pi\) |
−0.903406 | + | 0.428787i | \(0.858941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.15211 | + | 5.45962i | 0.102647 | + | 0.177790i | ||||
\(944\) | −10.6422 | −0.346375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.84128 | −0.124891 | ||||||||
\(947\) | −18.0309 | − | 31.2304i | −0.585925 | − | 1.01485i | −0.994759 | − | 0.102244i | \(-0.967398\pi\) |
0.408834 | − | 0.912609i | \(-0.365936\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.397198 | + | 0.687967i | −0.0128936 | + | 0.0223323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.4412 | + | 8.46651i | 0.565272 | + | 0.274401i | ||||
\(953\) | 29.7944 | 0.965137 | 0.482568 | − | 0.875858i | \(-0.339704\pi\) | ||||
0.482568 | + | 0.875858i | \(0.339704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.3550 | + | 11.7520i | 0.658329 | + | 0.380086i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.5040 | 0.888613 | ||||||||
\(959\) | −15.6216 | + | 32.1808i | −0.504447 | + | 1.03917i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84315 | − | 6.65652i | −0.123972 | − | 0.214727i | ||||
\(962\) | 0.240095 | + | 0.138619i | 0.00774097 | + | 0.00446925i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.8765 | − | 7.43426i | 0.414724 | − | 0.239441i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5198i | 0.370453i | 0.982696 | + | 0.185226i | \(0.0593018\pi\) | ||||
−0.982696 | + | 0.185226i | \(0.940698\pi\) | |||||||
\(968\) | 2.42713 | + | 4.20390i | 0.0780108 | + | 0.135119i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2347 | − | 36.7795i | −0.681453 | − | 1.18031i | −0.974537 | − | 0.224225i | \(-0.928015\pi\) |
0.293084 | − | 0.956087i | \(-0.405318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.71706 | + | 23.9156i | 0.0550465 | + | 0.766698i | ||||
\(974\) | − | 35.4468i | − | 1.13579i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.51299 | − | 3.76028i | −0.208476 | − | 0.120364i | ||||
\(977\) | −9.08052 | + | 15.7279i | −0.290512 | + | 0.503181i | −0.973931 | − | 0.226845i | \(-0.927159\pi\) |
0.683419 | + | 0.730026i | \(0.260492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.27827i | 0.232614i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.42330 | − | 0.821743i | 0.0454194 | − | 0.0262229i | ||||
\(983\) | 10.7385 | + | 6.19988i | 0.342505 | + | 0.197746i | 0.661379 | − | 0.750052i | \(-0.269971\pi\) |
−0.318874 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.58755 | 0.209790 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.138701i | − | 0.00441266i | ||||||
\(989\) | 3.11804 | − | 1.80020i | 0.0991478 | − | 0.0572430i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8601 | + | 18.8102i | −0.344981 | + | 0.597525i | −0.985350 | − | 0.170543i | \(-0.945448\pi\) |
0.640369 | + | 0.768067i | \(0.278781\pi\) | |||||||
\(992\) | 4.18154 | − | 2.41421i | 0.132764 | − | 0.0766514i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.7627 | + | 14.7381i | −0.690270 | + | 0.467464i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.2381 | + | 36.7856i | −0.672619 | + | 1.16501i | 0.304540 | + | 0.952500i | \(0.401497\pi\) |
−0.977159 | + | 0.212510i | \(0.931836\pi\) | |||||||
\(998\) | −17.3665 | + | 30.0796i | −0.549726 | + | 0.952154i | ||||
\(999\) | 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 | 3150.2.bp.c.899.1 | 8 | ||
3.2 | odd | 2 | 3150.2.bp.d.899.1 | 8 | |||
5.2 | odd | 4 | 630.2.be.b.521.3 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.bf.c.1151.2 | 8 | |||
5.4 | even | 2 | 3150.2.bp.f.899.4 | 8 | |||
7.5 | odd | 6 | 3150.2.bp.a.1349.4 | 8 | |||
15.2 | even | 4 | 630.2.be.a.521.1 | yes | 8 | ||
15.8 | even | 4 | 3150.2.bf.b.1151.4 | 8 | |||
15.14 | odd | 2 | 3150.2.bp.a.899.4 | 8 | |||
21.5 | even | 6 | 3150.2.bp.f.1349.4 | 8 | |||
35.12 | even | 12 | 630.2.be.a.341.1 | ✓ | 8 | ||
35.17 | even | 12 | 4410.2.b.e.881.5 | 8 | |||
35.19 | odd | 6 | 3150.2.bp.d.1349.1 | 8 | |||
35.32 | odd | 12 | 4410.2.b.b.881.5 | 8 | |||
35.33 | even | 12 | 3150.2.bf.b.1601.4 | 8 | |||
105.17 | odd | 12 | 4410.2.b.b.881.4 | 8 | |||
105.32 | even | 12 | 4410.2.b.e.881.4 | 8 | |||
105.47 | odd | 12 | 630.2.be.b.341.3 | yes | 8 | ||
105.68 | odd | 12 | 3150.2.bf.c.1601.2 | 8 | |||
105.89 | even | 6 | inner | 3150.2.bp.c.1349.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.1 | ✓ | 8 | 35.12 | even | 12 | ||
630.2.be.a.521.1 | yes | 8 | 15.2 | even | 4 | ||
630.2.be.b.341.3 | yes | 8 | 105.47 | odd | 12 | ||
630.2.be.b.521.3 | yes | 8 | 5.2 | odd | 4 | ||
3150.2.bf.b.1151.4 | 8 | 15.8 | even | 4 | |||
3150.2.bf.b.1601.4 | 8 | 35.33 | even | 12 | |||
3150.2.bf.c.1151.2 | 8 | 5.3 | odd | 4 | |||
3150.2.bf.c.1601.2 | 8 | 105.68 | odd | 12 | |||
3150.2.bp.a.899.4 | 8 | 15.14 | odd | 2 | |||
3150.2.bp.a.1349.4 | 8 | 7.5 | odd | 6 | |||
3150.2.bp.c.899.1 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bp.c.1349.1 | 8 | 105.89 | even | 6 | inner | ||
3150.2.bp.d.899.1 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.d.1349.1 | 8 | 35.19 | odd | 6 | |||
3150.2.bp.f.899.4 | 8 | 5.4 | even | 2 | |||
3150.2.bp.f.1349.4 | 8 | 21.5 | even | 6 | |||
4410.2.b.b.881.4 | 8 | 105.17 | odd | 12 | |||
4410.2.b.b.881.5 | 8 | 35.32 | odd | 12 | |||
4410.2.b.e.881.4 | 8 | 105.32 | even | 12 | |||
4410.2.b.e.881.5 | 8 | 35.17 | even | 12 |