Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
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.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
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 | 1601.4 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.b.1151.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.189469 | − | 2.63896i | 0.0716124 | − | 0.997433i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.44829 | + | 1.99087i | −1.03970 | + | 0.600270i | −0.919748 | − | 0.392510i | \(-0.871607\pi\) |
−0.119950 | + | 0.992780i | \(0.538273\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0681483i | 0.0189010i | 0.999955 | + | 0.00945048i | \(0.00300822\pi\) | ||||
−0.999955 | + | 0.00945048i | \(0.996992\pi\) | |||||||
\(14\) | 1.48356 | − | 2.19067i | 0.396499 | − | 0.585481i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.66390 | + | 6.34607i | 0.888627 | + | 1.53915i | 0.841499 | + | 0.540258i | \(0.181673\pi\) |
0.0471274 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.76260 | − | 1.01764i | −0.404368 | − | 0.233462i | 0.283999 | − | 0.958825i | \(-0.408339\pi\) |
−0.688367 | + | 0.725362i | \(0.741672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.98174 | −0.848910 | ||||||||
\(23\) | 3.23205 | + | 1.86603i | 0.673929 | + | 0.389093i | 0.797564 | − | 0.603235i | \(-0.206122\pi\) |
−0.123635 | + | 0.992328i | \(0.539455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0340742 | + | 0.0590182i | −0.00668250 | + | 0.0115744i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.38014 | − | 1.15539i | 0.449804 | − | 0.218349i | ||||
\(29\) | 0.898979i | 0.166936i | 0.996510 | + | 0.0834681i | \(0.0265997\pi\) | ||||
−0.996510 | + | 0.0834681i | \(0.973400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18154 | + | 2.41421i | −0.751027 | + | 0.433606i | −0.826065 | − | 0.563575i | \(-0.809426\pi\) |
0.0750380 | + | 0.997181i | \(0.476092\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.32780i | 1.25671i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.03407 | + | 3.52312i | −0.334400 | + | 0.579197i | −0.983369 | − | 0.181617i | \(-0.941867\pi\) |
0.648970 | + | 0.760814i | \(0.275200\pi\) | |||||||
\(38\) | −1.01764 | − | 1.76260i | −0.165083 | − | 0.285932i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.68921 | −0.263810 | −0.131905 | − | 0.991262i | \(-0.542109\pi\) | ||||
−0.131905 | + | 0.991262i | \(0.542109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.964724 | 0.147119 | 0.0735595 | − | 0.997291i | \(-0.476564\pi\) | ||||
0.0735595 | + | 0.997291i | \(0.476564\pi\) | |||||||
\(44\) | −3.44829 | − | 1.99087i | −0.519849 | − | 0.300135i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86603 | + | 3.23205i | 0.275130 | + | 0.476540i | ||||
\(47\) | −0.830749 | + | 1.43890i | −0.121177 | + | 0.209885i | −0.920232 | − | 0.391373i | \(-0.872000\pi\) |
0.799055 | + | 0.601258i | \(0.205334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92820 | − | 1.00000i | −0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0590182 | + | 0.0340742i | −0.00818435 | + | 0.00472524i | ||||
\(53\) | 11.4547 | − | 6.61339i | 1.57343 | − | 0.908419i | 0.577684 | − | 0.816260i | \(-0.303957\pi\) |
0.995744 | − | 0.0921588i | \(-0.0293767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.63896 | + | 0.189469i | 0.352646 | + | 0.0253188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.449490 | + | 0.778539i | −0.0590209 | + | 0.102227i | ||||
\(59\) | 5.32112 | + | 9.21645i | 0.692751 | + | 1.19988i | 0.970933 | + | 0.239352i | \(0.0769348\pi\) |
−0.278182 | + | 0.960528i | \(0.589732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.51299 | + | 3.76028i | 0.833903 | + | 0.481454i | 0.855187 | − | 0.518319i | \(-0.173442\pi\) |
−0.0212839 | + | 0.999773i | \(0.506775\pi\) | |||||||
\(62\) | −4.82843 | −0.613211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.33145 | + | 9.23435i | 0.651341 | + | 1.12816i | 0.982798 | + | 0.184685i | \(0.0591264\pi\) |
−0.331457 | + | 0.943470i | \(0.607540\pi\) | |||||||
\(68\) | −3.66390 | + | 6.34607i | −0.444313 | + | 0.769573i | ||||
\(69\) | 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 | ||||||||
\(73\) | 10.0951 | − | 5.82843i | 1.18155 | − | 0.682166i | 0.225174 | − | 0.974319i | \(-0.427705\pi\) |
0.956372 | + | 0.292153i | \(0.0943716\pi\) | |||||||
\(74\) | −3.52312 | + | 2.03407i | −0.409554 | + | 0.236456i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.03528i | − | 0.233462i | ||||||
\(77\) | 4.60048 | + | 9.47710i | 0.524273 | + | 1.08002i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.77489 | + | 15.1986i | −0.987252 | + | 1.70997i | −0.355787 | + | 0.934567i | \(0.615787\pi\) |
−0.631465 | + | 0.775404i | \(0.717546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.46290 | − | 0.844605i | −0.161550 | − | 0.0932711i | ||||
\(83\) | −14.3490 | −1.57501 | −0.787503 | − | 0.616311i | \(-0.788626\pi\) | ||||
−0.787503 | + | 0.616311i | \(0.788626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.835475 | + | 0.482362i | 0.0900916 | + | 0.0520144i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.99087 | − | 3.44829i | −0.212227 | − | 0.367589i | ||||
\(89\) | 0.913956 | − | 1.58302i | 0.0968791 | − | 0.167800i | −0.813512 | − | 0.581548i | \(-0.802447\pi\) |
0.910391 | + | 0.413748i | \(0.135781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.179841 | + | 0.0129120i | 0.0188524 | + | 0.00135354i | ||||
\(92\) | 3.73205i | 0.389093i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.43890 | + | 0.830749i | −0.148411 | + | 0.0856852i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1502i | 1.74134i | 0.491870 | + | 0.870668i | \(0.336313\pi\) | ||||
−0.491870 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(98\) | −5.50000 | − | 4.33013i | −0.555584 | − | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36773 | + | 5.83307i | 0.335101 | + | 0.580412i | 0.983504 | − | 0.180885i | \(-0.0578962\pi\) |
−0.648403 | + | 0.761297i | \(0.724563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.450370 | − | 0.260021i | −0.0443762 | − | 0.0256206i | 0.477648 | − | 0.878551i | \(-0.341490\pi\) |
−0.522024 | + | 0.852931i | \(0.674823\pi\) | |||||||
\(104\) | −0.0681483 | −0.00668250 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.2268 | 1.28470 | ||||||||
\(107\) | 5.30614 | + | 3.06350i | 0.512964 | + | 0.296160i | 0.734051 | − | 0.679094i | \(-0.237627\pi\) |
−0.221087 | + | 0.975254i | \(0.570960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.77729 | − | 11.7386i | −0.649147 | − | 1.12436i | −0.983327 | − | 0.181846i | \(-0.941793\pi\) |
0.334180 | − | 0.942509i | \(-0.391541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.19067 | + | 1.48356i | 0.206999 | + | 0.140184i | ||||
\(113\) | − | 11.6982i | − | 1.10047i | −0.835009 | − | 0.550236i | \(-0.814538\pi\) | ||
0.835009 | − | 0.550236i | \(-0.185462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.778539 | + | 0.449490i | −0.0722855 | + | 0.0417341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.6422i | 0.979698i | ||||||||
\(119\) | 17.4412 | − | 8.46651i | 1.59883 | − | 0.776123i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.42713 | − | 4.20390i | 0.220648 | − | 0.382173i | ||||
\(122\) | 3.76028 | + | 6.51299i | 0.340440 | + | 0.589659i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.18154 | − | 2.41421i | −0.375513 | − | 0.216803i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7530 | −0.954173 | −0.477086 | − | 0.878856i | \(-0.658307\pi\) | ||||
−0.477086 | + | 0.878856i | \(0.658307\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.85457 | + | 3.21221i | −0.162035 | + | 0.280653i | −0.935598 | − | 0.353066i | \(-0.885139\pi\) |
0.773564 | + | 0.633719i | \(0.218472\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.01946 | + | 4.45862i | −0.261821 | + | 0.386611i | ||||
\(134\) | 10.6629i | 0.921135i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.34607 | + | 3.66390i | −0.544171 | + | 0.314177i | ||||
\(137\) | 11.7091 | − | 6.76028i | 1.00038 | − | 0.577570i | 0.0920192 | − | 0.995757i | \(-0.470668\pi\) |
0.908361 | + | 0.418188i | \(0.137335\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −4.96713 | + | 8.60332i | −0.416832 | + | 0.721974i | ||||
\(143\) | −0.135674 | − | 0.234995i | −0.0113457 | − | 0.0196513i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.6569 | 0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.06815 | −0.334400 | ||||||||
\(149\) | 13.2385 | + | 7.64324i | 1.08454 | + | 0.626158i | 0.932117 | − | 0.362157i | \(-0.117960\pi\) |
0.152421 | + | 0.988316i | \(0.451293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.93942 | + | 8.55532i | 0.401964 | + | 0.696222i | 0.993963 | − | 0.109717i | \(-0.0349944\pi\) |
−0.591999 | + | 0.805939i | \(0.701661\pi\) | |||||||
\(152\) | 1.01764 | − | 1.76260i | 0.0825413 | − | 0.142966i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.754415 | + | 10.5076i | −0.0607925 | + | 0.846730i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3741 | + | 7.14418i | −0.987560 | + | 0.570168i | −0.904544 | − | 0.426380i | \(-0.859788\pi\) |
−0.0830157 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(158\) | −15.1986 | + | 8.77489i | −1.20913 | + | 0.698093i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.53674 | − | 8.17569i | 0.436356 | − | 0.644335i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.98879 | − | 8.64083i | 0.390752 | − | 0.676802i | −0.601797 | − | 0.798649i | \(-0.705548\pi\) |
0.992549 | + | 0.121847i | \(0.0388817\pi\) | |||||||
\(164\) | −0.844605 | − | 1.46290i | −0.0659526 | − | 0.114233i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.4266 | − | 7.17449i | −0.964490 | − | 0.556849i | ||||
\(167\) | −13.7778 | −1.06616 | −0.533079 | − | 0.846065i | \(-0.678965\pi\) | ||||
−0.533079 | + | 0.846065i | \(0.678965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9954 | 0.999643 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.482362 | + | 0.835475i | 0.0367798 | + | 0.0637044i | ||||
\(173\) | −4.13638 | + | 7.16442i | −0.314483 | + | 0.544701i | −0.979327 | − | 0.202281i | \(-0.935164\pi\) |
0.664844 | + | 0.746982i | \(0.268498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.98174i | − | 0.300135i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.58302 | − | 0.913956i | 0.118652 | − | 0.0685039i | ||||
\(179\) | 9.97501 | − | 5.75908i | 0.745568 | − | 0.430454i | −0.0785226 | − | 0.996912i | \(-0.525020\pi\) |
0.824090 | + | 0.566459i | \(0.191687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.5924i | − | 1.23330i | −0.787237 | − | 0.616650i | \(-0.788489\pi\) | ||
0.787237 | − | 0.616650i | \(-0.211511\pi\) | |||||||
\(182\) | 0.149291 | + | 0.101102i | 0.0110662 | + | 0.00749421i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.86603 | + | 3.23205i | −0.137565 | + | 0.238270i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.2684 | − | 14.5887i | −1.84781 | − | 1.06683i | ||||
\(188\) | −1.66150 | −0.121177 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.9640 | − | 9.21682i | −1.15511 | − | 0.666905i | −0.204986 | − | 0.978765i | \(-0.565715\pi\) |
−0.950128 | + | 0.311859i | \(0.899048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.17914 | − | 5.50643i | −0.228839 | − | 0.396361i | 0.728625 | − | 0.684913i | \(-0.240160\pi\) |
−0.957464 | + | 0.288552i | \(0.906826\pi\) | |||||||
\(194\) | −8.57509 | + | 14.8525i | −0.615656 | + | 1.06635i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.59808 | − | 6.50000i | −0.185577 | − | 0.464286i | ||||
\(197\) | 12.8389i | 0.914734i | 0.889278 | + | 0.457367i | \(0.151208\pi\) | ||||
−0.889278 | + | 0.457367i | \(0.848792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.33950 | + | 4.81481i | −0.591171 | + | 0.341313i | −0.765561 | − | 0.643364i | \(-0.777538\pi\) |
0.174389 | + | 0.984677i | \(0.444205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.73545i | 0.473905i | ||||||||
\(203\) | 2.37237 | + | 0.170328i | 0.166508 | + | 0.0119547i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.260021 | − | 0.450370i | −0.0181165 | − | 0.0313787i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.0590182 | − | 0.0340742i | −0.00409218 | − | 0.00236262i | ||||
\(209\) | 8.10394 | 0.560561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5619 | −1.00248 | −0.501241 | − | 0.865308i | \(-0.667123\pi\) | ||||
−0.501241 | + | 0.865308i | \(0.667123\pi\) | |||||||
\(212\) | 11.4547 | + | 6.61339i | 0.786714 | + | 0.454210i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.06350 | + | 5.30614i | 0.209417 | + | 0.362721i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.57874 | + | 11.4923i | 0.378709 | + | 0.780150i | ||||
\(218\) | − | 13.5546i | − | 0.918033i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.432474 | + | 0.249689i | −0.0290913 | + | 0.0167959i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.6609i | − | 1.58445i | −0.610227 | − | 0.792227i | \(-0.708922\pi\) | ||
0.610227 | − | 0.792227i | \(-0.291078\pi\) | |||||||
\(224\) | 1.15539 | + | 2.38014i | 0.0771980 | + | 0.159030i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.84909 | − | 10.1309i | 0.389076 | − | 0.673899i | ||||
\(227\) | −4.32024 | − | 7.48288i | −0.286744 | − | 0.496656i | 0.686286 | − | 0.727332i | \(-0.259240\pi\) |
−0.973031 | + | 0.230676i | \(0.925906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1896 | − | 7.03768i | −0.805513 | − | 0.465063i | 0.0398824 | − | 0.999204i | \(-0.487302\pi\) |
−0.845395 | + | 0.534141i | \(0.820635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.898979 | −0.0590209 | ||||||||
\(233\) | 17.4916 | + | 10.0988i | 1.14591 | + | 0.661593i | 0.947888 | − | 0.318604i | \(-0.103214\pi\) |
0.198025 | + | 0.980197i | \(0.436547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.32112 | + | 9.21645i | −0.346375 | + | 0.599940i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 19.3378 | + | 1.38839i | 1.25348 | + | 0.0899959i | ||||
\(239\) | 23.5040i | 1.52035i | 0.649721 | + | 0.760173i | \(0.274886\pi\) | ||||
−0.649721 | + | 0.760173i | \(0.725114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8765 | + | 7.43426i | −0.829449 | + | 0.478883i | −0.853664 | − | 0.520824i | \(-0.825625\pi\) |
0.0242151 | + | 0.999707i | \(0.492291\pi\) | |||||||
\(242\) | 4.20390 | − | 2.42713i | 0.270237 | − | 0.156022i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.52056i | 0.481454i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0693504 | − | 0.120118i | 0.00441266 | − | 0.00764295i | ||||
\(248\) | −2.41421 | − | 4.18154i | −0.153303 | − | 0.265528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.31736 | 0.272509 | 0.136255 | − | 0.990674i | \(-0.456493\pi\) | ||||
0.136255 | + | 0.990674i | \(0.456493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8601 | −0.934244 | ||||||||
\(254\) | −9.31236 | − | 5.37649i | −0.584309 | − | 0.337351i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.41662 | − | 4.18570i | 0.150744 | − | 0.261097i | −0.780757 | − | 0.624835i | \(-0.785166\pi\) |
0.931501 | + | 0.363738i | \(0.118500\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.91197 | + | 6.03536i | 0.553763 | + | 0.375019i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.21221 | + | 1.85457i | −0.198451 | + | 0.114576i | ||||
\(263\) | 5.77197 | − | 3.33245i | 0.355915 | − | 0.205488i | −0.311372 | − | 0.950288i | \(-0.600789\pi\) |
0.667287 | + | 0.744800i | \(0.267455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.84424 | + | 2.35155i | −0.297019 | + | 0.144183i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.33145 | + | 9.23435i | −0.325670 | + | 0.564078i | ||||
\(269\) | −15.8700 | − | 27.4877i | −0.967612 | − | 1.67595i | −0.702426 | − | 0.711757i | \(-0.747900\pi\) |
−0.265186 | − | 0.964197i | \(-0.585433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1244 | + | 8.73205i | 0.918739 | + | 0.530434i | 0.883233 | − | 0.468935i | \(-0.155362\pi\) |
0.0355066 | + | 0.999369i | \(0.488696\pi\) | |||||||
\(272\) | −7.32780 | −0.444313 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.5206 | 0.816807 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.7524 | − | 20.3557i | −0.706130 | − | 1.22305i | −0.966282 | − | 0.257486i | \(-0.917106\pi\) |
0.260152 | − | 0.965568i | \(-0.416227\pi\) | |||||||
\(278\) | 4.53125 | − | 7.84836i | 0.271767 | − | 0.470714i | ||||
\(279\) | 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 | ||||||||
\(283\) | 23.9983 | − | 13.8554i | 1.42655 | − | 0.823619i | 0.429703 | − | 0.902970i | \(-0.358618\pi\) |
0.996847 | + | 0.0793517i | \(0.0252850\pi\) | |||||||
\(284\) | −8.60332 | + | 4.96713i | −0.510513 | + | 0.294745i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.271349i | − | 0.0160452i | ||||||
\(287\) | −0.320053 | + | 4.45776i | −0.0188921 | + | 0.263133i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.3484 | + | 31.7803i | −1.07932 | + | 1.86943i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.0951 | + | 5.82843i | 0.590773 | + | 0.341083i | ||||
\(293\) | 2.84377 | 0.166135 | 0.0830673 | − | 0.996544i | \(-0.473528\pi\) | ||||
0.0830673 | + | 0.996544i | \(0.473528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.52312 | − | 2.03407i | −0.204777 | − | 0.118228i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.64324 | + | 13.2385i | 0.442761 | + | 0.766884i | ||||
\(299\) | −0.127167 | + | 0.220259i | −0.00735423 | + | 0.0127379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.182785 | − | 2.54587i | 0.0105355 | − | 0.146741i | ||||
\(302\) | 9.87883i | 0.568463i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.76260 | − | 1.01764i | 0.101092 | − | 0.0583655i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.52180i | − | 0.143927i | −0.997407 | − | 0.0719634i | \(-0.977074\pi\) | ||
0.997407 | − | 0.0719634i | \(-0.0229265\pi\) | |||||||
\(308\) | −5.90717 | + | 8.72268i | −0.336592 | + | 0.497021i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.49697 | − | 9.52104i | −0.311705 | − | 0.539889i | 0.667027 | − | 0.745034i | \(-0.267567\pi\) |
−0.978732 | + | 0.205145i | \(0.934233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6040 | − | 12.4731i | −1.22113 | − | 0.705020i | −0.255971 | − | 0.966684i | \(-0.582395\pi\) |
−0.965159 | + | 0.261665i | \(0.915729\pi\) | |||||||
\(314\) | −14.2884 | −0.806339 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5498 | −0.987252 | ||||||||
\(317\) | 13.0504 | + | 7.53465i | 0.732984 | + | 0.423188i | 0.819513 | − | 0.573061i | \(-0.194244\pi\) |
−0.0865290 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.78975 | − | 3.09994i | −0.100207 | − | 0.173563i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.88280 | − | 4.31199i | 0.495019 | − | 0.240298i | ||||
\(323\) | − | 14.9141i | − | 0.829843i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.64083 | − | 4.98879i | 0.478572 | − | 0.276303i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1.68921i | − | 0.0932711i | ||||||
\(329\) | 3.63980 | + | 2.46494i | 0.200668 | + | 0.135896i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0904 | + | 26.1373i | −0.829444 | + | 1.43664i | 0.0690315 | + | 0.997614i | \(0.478009\pi\) |
−0.898475 | + | 0.439024i | \(0.855324\pi\) | |||||||
\(332\) | −7.17449 | − | 12.4266i | −0.393751 | − | 0.681997i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.9319 | − | 6.88891i | −0.652886 | − | 0.376944i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5911 | 1.17614 | 0.588071 | − | 0.808809i | \(-0.299887\pi\) | ||||
0.588071 | + | 0.808809i | \(0.299887\pi\) | |||||||
\(338\) | 11.2543 | + | 6.49768i | 0.612154 | + | 0.353427i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.61277 | − | 16.6498i | 0.520561 | − | 0.901638i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.95164 | + | 18.0938i | −0.213368 | + | 0.976972i | ||||
\(344\) | 0.964724i | 0.0520144i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.16442 | + | 4.13638i | −0.385161 | + | 0.222373i | ||||
\(347\) | 20.0781 | − | 11.5921i | 1.07785 | − | 0.622297i | 0.147534 | − | 0.989057i | \(-0.452866\pi\) |
0.930316 | + | 0.366760i | \(0.119533\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 1.99087 | − | 3.44829i | 0.106114 | − | 0.183794i | ||||
\(353\) | 4.37378 | + | 7.57561i | 0.232793 | + | 0.403209i | 0.958629 | − | 0.284659i | \(-0.0918803\pi\) |
−0.725836 | + | 0.687868i | \(0.758547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.82791 | 0.0968791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.5182 | 0.608753 | ||||||||
\(359\) | 22.3059 | + | 12.8783i | 1.17726 | + | 0.679691i | 0.955379 | − | 0.295382i | \(-0.0954470\pi\) |
0.221881 | + | 0.975074i | \(0.428780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.42883 | − | 12.8671i | −0.390991 | − | 0.677216i | ||||
\(362\) | 8.29618 | − | 14.3694i | 0.436037 | − | 0.755239i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0787382 | + | 0.162203i | 0.00412700 | + | 0.00850172i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2665 | + | 9.96885i | −0.901306 | + | 0.520369i | −0.877624 | − | 0.479350i | \(-0.840872\pi\) |
−0.0236826 | + | 0.999720i | \(0.507539\pi\) | |||||||
\(368\) | −3.23205 | + | 1.86603i | −0.168482 | + | 0.0972733i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.2822 | − | 31.4816i | −0.793410 | − | 1.63444i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.515762 | − | 0.893327i | 0.0267052 | − | 0.0462547i | −0.852364 | − | 0.522949i | \(-0.824832\pi\) |
0.879069 | + | 0.476694i | \(0.158165\pi\) | |||||||
\(374\) | −14.5887 | − | 25.2684i | −0.754364 | − | 1.30660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43890 | − | 0.830749i | −0.0742056 | − | 0.0428426i | ||||
\(377\) | −0.0612640 | −0.00315525 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.09497 | 0.261711 | 0.130855 | − | 0.991401i | \(-0.458228\pi\) | ||||
0.130855 | + | 0.991401i | \(0.458228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.21682 | − | 15.9640i | −0.471573 | − | 0.816789i | ||||
\(383\) | −4.23375 | + | 7.33307i | −0.216335 | + | 0.374702i | −0.953685 | − | 0.300808i | \(-0.902744\pi\) |
0.737350 | + | 0.675511i | \(0.236077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.35827i | − | 0.323628i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.8525 | + | 8.57509i | −0.754021 | + | 0.435334i | ||||
\(389\) | −4.97229 | + | 2.87075i | −0.252105 | + | 0.145553i | −0.620728 | − | 0.784026i | \(-0.713163\pi\) |
0.368623 | + | 0.929579i | \(0.379829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.3477i | 1.38303i | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.41946 | + | 11.1188i | −0.323407 | + | 0.560158i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6149 | − | 8.43791i | −0.733501 | − | 0.423487i | 0.0862009 | − | 0.996278i | \(-0.472527\pi\) |
−0.819701 | + | 0.572791i | \(0.805861\pi\) | |||||||
\(398\) | −9.62962 | −0.482689 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.63572 | + | 0.944382i | 0.0816838 | + | 0.0471602i | 0.540286 | − | 0.841482i | \(-0.318316\pi\) |
−0.458602 | + | 0.888642i | \(0.651650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.164525 | − | 0.284965i | −0.00819556 | − | 0.0141951i | ||||
\(404\) | −3.36773 | + | 5.83307i | −0.167551 | + | 0.290206i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.96937 | + | 1.33369i | 0.0977381 | + | 0.0661901i | ||||
\(407\) | − | 16.1983i | − | 0.802920i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5617 | − | 16.4901i | 1.41228 | − | 0.815382i | 0.416681 | − | 0.909053i | \(-0.363193\pi\) |
0.995603 | + | 0.0936705i | \(0.0298600\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 0.520042i | − | 0.0256206i | ||||||
\(413\) | 25.3300 | − | 12.2960i | 1.24641 | − | 0.605046i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0340742 | − | 0.0590182i | −0.00167062 | − | 0.00289361i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.01822 | + | 4.05197i | 0.343272 | + | 0.198188i | ||||
\(419\) | −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 | \(0.251693\pi\) | |||||||
\(422\) | −12.6110 | − | 7.28094i | −0.613892 | − | 0.354431i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.61339 | + | 11.4547i | 0.321175 | + | 0.556291i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1572 | − | 16.4751i | 0.539936 | − | 0.797284i | ||||
\(428\) | 6.12701i | 0.296160i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.0895 | − | 16.7948i | 1.40119 | − | 0.808978i | 0.406677 | − | 0.913572i | \(-0.366688\pi\) |
0.994515 | + | 0.104594i | \(0.0333543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2207i | 0.539234i | 0.962968 | + | 0.269617i | \(0.0868971\pi\) | ||||
−0.962968 | + | 0.269617i | \(0.913103\pi\) | |||||||
\(434\) | −0.914836 | + | 12.7420i | −0.0439135 | + | 0.611636i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.77729 | − | 11.7386i | 0.324574 | − | 0.562178i | ||||
\(437\) | −3.79788 | − | 6.57812i | −0.181677 | − | 0.314674i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6075 | − | 8.43363i | −0.697177 | − | 0.402515i | 0.109118 | − | 0.994029i | \(-0.465197\pi\) |
−0.806295 | + | 0.591513i | \(0.798531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.499378 | −0.0237530 | ||||||||
\(443\) | −1.78094 | − | 1.02823i | −0.0846152 | − | 0.0488526i | 0.457095 | − | 0.889418i | \(-0.348890\pi\) |
−0.541711 | + | 0.840565i | \(0.682223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.8305 | − | 20.4910i | 0.560189 | − | 0.970276i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.189469 | + | 2.63896i | −0.00895155 | + | 0.124679i | ||||
\(449\) | 12.5892i | 0.594122i | 0.954858 | + | 0.297061i | \(0.0960065\pi\) | ||||
−0.954858 | + | 0.297061i | \(0.903994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.82489 | − | 3.36300i | 0.274283 | − | 0.158357i | ||||
\(452\) | 10.1309 | − | 5.84909i | 0.476519 | − | 0.275118i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 8.64048i | − | 0.405518i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4765 | − | 30.2701i | 0.817515 | − | 1.41598i | −0.0899930 | − | 0.995942i | \(-0.528684\pi\) |
0.907508 | − | 0.420035i | \(-0.137982\pi\) | |||||||
\(458\) | −7.03768 | − | 12.1896i | −0.328849 | − | 0.569584i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.3750 | −1.08868 | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||||
−0.544341 | + | 0.838864i | \(0.683220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.35693 | 0.295431 | 0.147716 | − | 0.989030i | \(-0.452808\pi\) | ||||
0.147716 | + | 0.989030i | \(0.452808\pi\) | |||||||
\(464\) | −0.778539 | − | 0.449490i | −0.0361428 | − | 0.0208670i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0988 | + | 17.4916i | 0.467817 | + | 0.810283i | ||||
\(467\) | 3.89658 | − | 6.74907i | 0.180312 | − | 0.312310i | −0.761675 | − | 0.647960i | \(-0.775623\pi\) |
0.941987 | + | 0.335650i | \(0.108956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.3792 | − | 12.3199i | 1.17190 | − | 0.568878i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.21645 | + | 5.32112i | −0.424222 | + | 0.244924i | ||||
\(473\) | −3.32665 | + | 1.92064i | −0.152959 | + | 0.0883111i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 16.0528 | + | 10.8713i | 0.735779 | + | 0.498284i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.7520 | + | 20.3550i | −0.537523 | + | 0.931018i | ||||
\(479\) | −13.7520 | − | 23.8191i | −0.628344 | − | 1.08832i | −0.987884 | − | 0.155194i | \(-0.950400\pi\) |
0.359540 | − | 0.933130i | \(-0.382934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.240095 | − | 0.138619i | −0.0109474 | − | 0.00632047i | ||||
\(482\) | −14.8685 | −0.677242 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.85425 | 0.220648 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7234 | + | 30.6978i | 0.803124 | + | 1.39105i | 0.917551 | + | 0.397619i | \(0.130164\pi\) |
−0.114427 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(488\) | −3.76028 | + | 6.51299i | −0.170220 | + | 0.294829i | ||||
\(489\) | 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 | ||||||||
\(493\) | −5.70498 | + | 3.29377i | −0.256939 | + | 0.148344i | ||||
\(494\) | 0.120118 | − | 0.0693504i | 0.00540438 | − | 0.00312022i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.82843i | − | 0.216803i | ||||||
\(497\) | 26.2161 | + | 1.88223i | 1.17595 | + | 0.0844296i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3665 | − | 30.0796i | 0.777430 | − | 1.34655i | −0.155988 | − | 0.987759i | \(-0.549856\pi\) |
0.933418 | − | 0.358790i | \(-0.116811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.73894 | + | 2.15868i | 0.166877 | + | 0.0963465i | ||||
\(503\) | 28.9613 | 1.29132 | 0.645660 | − | 0.763625i | \(-0.276582\pi\) | ||||
0.645660 | + | 0.763625i | \(0.276582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.8692 | − | 7.43003i | −0.572105 | − | 0.330305i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.37649 | − | 9.31236i | −0.238543 | − | 0.413169i | ||||
\(509\) | 10.7311 | − | 18.5867i | 0.475646 | − | 0.823842i | −0.523965 | − | 0.851740i | \(-0.675548\pi\) |
0.999611 | + | 0.0278973i | \(0.00888113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4683 | − | 27.7449i | −0.595801 | − | 1.22736i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.18570 | − | 2.41662i | 0.184624 | − | 0.106592i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.61565i | − | 0.290956i | ||||||
\(518\) | 4.70032 | + | 9.68276i | 0.206520 | + | 0.425436i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1218 | + | 34.8520i | 0.881552 | + | 1.52689i | 0.849616 | + | 0.527403i | \(0.176834\pi\) |
0.0319362 | + | 0.999490i | \(0.489833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7113 | − | 14.8444i | −1.12428 | − | 0.649102i | −0.181789 | − | 0.983338i | \(-0.558189\pi\) |
−0.942490 | + | 0.334235i | \(0.891522\pi\) | |||||||
\(524\) | −3.70915 | −0.162035 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.66490 | 0.290603 | ||||||||
\(527\) | −30.6415 | − | 17.6909i | −1.33477 | − | 0.770627i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.53590 | − | 7.85641i | −0.197213 | − | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.37101 | − | 0.385621i | −0.232863 | − | 0.0167188i | ||||
\(533\) | − | 0.115117i | − | 0.00498627i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.23435 | + | 5.33145i | −0.398863 | + | 0.230284i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 31.7400i | − | 1.36841i | ||||||
\(539\) | 25.8813 | − | 10.3449i | 1.11479 | − | 0.445585i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.62914 | − | 14.9461i | 0.370996 | − | 0.642584i | −0.618723 | − | 0.785609i | \(-0.712350\pi\) |
0.989719 | + | 0.143026i | \(0.0456831\pi\) | |||||||
\(542\) | 8.73205 | + | 15.1244i | 0.375074 | + | 0.649647i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.34607 | − | 3.66390i | −0.272085 | − | 0.157089i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9703 | 0.768354 | 0.384177 | − | 0.923260i | \(-0.374485\pi\) | ||||
0.384177 | + | 0.923260i | \(0.374485\pi\) | |||||||
\(548\) | 11.7091 | + | 6.76028i | 0.500190 | + | 0.288785i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.914836 | − | 1.58454i | 0.0389733 | − | 0.0675038i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.4458 | + | 26.0362i | 1.63488 | + | 1.10717i | ||||
\(554\) | − | 23.5047i | − | 0.998619i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.84836 | − | 4.53125i | 0.332845 | − | 0.192168i | ||||
\(557\) | −39.1916 | + | 22.6273i | −1.66060 | + | 0.958748i | −0.688172 | + | 0.725547i | \(0.741587\pi\) |
−0.972428 | + | 0.233201i | \(0.925080\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0657443i | 0.00278069i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.70794 | + | 13.3506i | −0.325140 | + | 0.563159i | ||||
\(563\) | −7.93336 | − | 13.7410i | −0.334351 | − | 0.579114i | 0.649009 | − | 0.760781i | \(-0.275184\pi\) |
−0.983360 | + | 0.181667i | \(0.941851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.7108 | 1.16477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.93426 | −0.416832 | ||||||||
\(569\) | 0.0524375 | + | 0.0302748i | 0.00219829 | + | 0.00126918i | 0.501099 | − | 0.865390i | \(-0.332929\pi\) |
−0.498900 | + | 0.866659i | \(0.666263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.78245 | + | 11.7476i | 0.283837 | + | 0.491620i | 0.972326 | − | 0.233626i | \(-0.0750592\pi\) |
−0.688490 | + | 0.725246i | \(0.741726\pi\) | |||||||
\(572\) | 0.135674 | − | 0.234995i | 0.00567284 | − | 0.00982564i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.50605 | + | 3.70050i | −0.104601 | + | 0.154456i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.8252 | − | 21.8384i | 1.57468 | − | 0.909144i | 0.579101 | − | 0.815256i | \(-0.303404\pi\) |
0.995583 | − | 0.0938887i | \(-0.0299298\pi\) | |||||||
\(578\) | −31.7803 | + | 18.3484i | −1.32189 | + | 0.763191i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.71868 | + | 37.8664i | −0.112790 | + | 1.57096i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.3328 | + | 45.6098i | −1.09059 | + | 1.88896i | ||||
\(584\) | 5.82843 | + | 10.0951i | 0.241182 | + | 0.417740i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.46278 | + | 1.42188i | 0.101736 | + | 0.0587375i | ||||
\(587\) | −45.4100 | −1.87427 | −0.937135 | − | 0.348967i | \(-0.886532\pi\) | ||||
−0.937135 | + | 0.348967i | \(0.886532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.82718 | 0.404922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.03407 | − | 3.52312i | −0.0835999 | − | 0.144799i | ||||
\(593\) | −12.8506 | + | 22.2579i | −0.527711 | + | 0.914022i | 0.471767 | + | 0.881723i | \(0.343616\pi\) |
−0.999478 | + | 0.0322991i | \(0.989717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2865i | 0.626158i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.220259 | + | 0.127167i | −0.00900706 | + | 0.00520023i | ||||
\(599\) | −23.0347 | + | 13.2991i | −0.941173 | + | 0.543386i | −0.890328 | − | 0.455320i | \(-0.849525\pi\) |
−0.0508450 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.9681i | − | 0.528979i | −0.964389 | − | 0.264489i | \(-0.914797\pi\) | ||
0.964389 | − | 0.264489i | \(-0.0852034\pi\) | |||||||
\(602\) | 1.43123 | − | 2.11339i | 0.0583326 | − | 0.0861354i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.93942 | + | 8.55532i | −0.200982 | + | 0.348111i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1262 | + | 8.15576i | 0.573364 | + | 0.331032i | 0.758492 | − | 0.651682i | \(-0.225937\pi\) |
−0.185128 | + | 0.982714i | \(0.559270\pi\) | |||||||
\(608\) | 2.03528 | 0.0825413 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0980586 | − | 0.0566142i | −0.00396703 | − | 0.00229036i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.19395 | − | 12.4603i | −0.290561 | − | 0.503267i | 0.683381 | − | 0.730062i | \(-0.260509\pi\) |
−0.973943 | + | 0.226795i | \(0.927175\pi\) | |||||||
\(614\) | 1.26090 | − | 2.18394i | 0.0508858 | − | 0.0881368i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47710 | + | 4.60048i | −0.381843 | + | 0.185359i | ||||
\(617\) | 8.65760i | 0.348542i | 0.984698 | + | 0.174271i | \(0.0557569\pi\) | ||||
−0.984698 | + | 0.174271i | \(0.944243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.8459 | − | 22.4277i | 1.56135 | − | 0.901444i | 0.564225 | − | 0.825621i | \(-0.309175\pi\) |
0.997121 | − | 0.0758230i | \(-0.0241584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.9939i | − | 0.440817i | ||||||
\(623\) | −4.00435 | − | 2.71182i | −0.160431 | − | 0.108647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.4731 | − | 21.6040i | −0.498524 | − | 0.863469i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.3741 | − | 7.14418i | −0.493780 | − | 0.285084i | ||||
\(629\) | −29.8106 | −1.18863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1878 | −1.52023 | −0.760116 | − | 0.649788i | \(-0.774858\pi\) | ||||
−0.760116 | + | 0.649788i | \(0.774858\pi\) | |||||||
\(632\) | −15.1986 | − | 8.77489i | −0.604566 | − | 0.349046i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.53465 | + | 13.0504i | 0.299239 | + | 0.518298i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0681483 | − | 0.472146i | 0.00270014 | − | 0.0187071i | ||||
\(638\) | − | 3.57950i | − | 0.141714i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.40533 | + | 4.27547i | −0.292493 | + | 0.168871i | −0.639066 | − | 0.769152i | \(-0.720679\pi\) |
0.346573 | + | 0.938023i | \(0.387345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.75058i | 0.108472i | 0.998528 | + | 0.0542361i | \(0.0172724\pi\) | ||||
−0.998528 | + | 0.0542361i | \(0.982728\pi\) | |||||||
\(644\) | 9.84873 | + | 0.707107i | 0.388094 | + | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.45705 | − | 12.9160i | 0.293394 | − | 0.508173i | ||||
\(647\) | −13.8813 | − | 24.0431i | −0.545731 | − | 0.945234i | −0.998561 | − | 0.0536365i | \(-0.982919\pi\) |
0.452830 | − | 0.891597i | \(-0.350415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.6975 | − | 21.1873i | −1.44050 | − | 0.831675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.97758 | 0.390752 | ||||||||
\(653\) | −12.2282 | − | 7.05994i | −0.478525 | − | 0.276277i | 0.241276 | − | 0.970456i | \(-0.422434\pi\) |
−0.719802 | + | 0.694180i | \(0.755767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.844605 | − | 1.46290i | 0.0329763 | − | 0.0571166i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.91969 | + | 3.95460i | 0.0748372 | + | 0.154166i | ||||
\(659\) | − | 9.92570i | − | 0.386650i | −0.981135 | − | 0.193325i | \(-0.938073\pi\) | ||
0.981135 | − | 0.193325i | \(-0.0619272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9029 | − | 9.18154i | 0.618551 | − | 0.357121i | −0.157754 | − | 0.987478i | \(-0.550425\pi\) |
0.776305 | + | 0.630358i | \(0.217092\pi\) | |||||||
\(662\) | −26.1373 | + | 15.0904i | −1.01586 | + | 0.586505i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.3490i | − | 0.556849i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.67752 | + | 2.90555i | −0.0649538 | + | 0.112503i | ||||
\(668\) | −6.88891 | − | 11.9319i | −0.266540 | − | 0.461660i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.9449 | −1.15601 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6050 | 1.25683 | 0.628415 | − | 0.777878i | \(-0.283704\pi\) | ||||
0.628415 | + | 0.777878i | \(0.283704\pi\) | |||||||
\(674\) | 18.6984 | + | 10.7956i | 0.720237 | + | 0.415829i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.49768 | + | 11.2543i | 0.249911 | + | 0.432858i | ||||
\(677\) | 9.16923 | − | 15.8816i | 0.352402 | − | 0.610378i | −0.634268 | − | 0.773113i | \(-0.718698\pi\) |
0.986670 | + | 0.162735i | \(0.0520317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.2586 | + | 3.24942i | 1.73687 | + | 0.124701i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.6498 | − | 9.61277i | 0.637554 | − | 0.368092i | ||||
\(683\) | 21.1977 | − | 12.2385i | 0.811108 | − | 0.468294i | −0.0362323 | − | 0.999343i | \(-0.511536\pi\) |
0.847341 | + | 0.531050i | \(0.178202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.4691 | + | 13.6938i | −0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.482362 | + | 0.835475i | −0.0183899 | + | 0.0318522i | ||||
\(689\) | 0.450692 | + | 0.780621i | 0.0171700 | + | 0.0297393i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9118 | − | 9.18670i | −0.605315 | − | 0.349479i | 0.165815 | − | 0.986157i | \(-0.446975\pi\) |
−0.771129 | + | 0.636678i | \(0.780308\pi\) | |||||||
\(692\) | −8.27276 | −0.314483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.1842 | 0.880061 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.18910 | − | 10.7198i | −0.234429 | − | 0.406043i | ||||
\(698\) | 5.36433 | − | 9.29128i | 0.203043 | − | 0.351680i | ||||
\(699\) | 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 | ||||||||
\(703\) | 7.17052 | − | 4.13990i | 0.270441 | − | 0.156139i | ||||
\(704\) | 3.44829 | − | 1.99087i | 0.129962 | − | 0.0750337i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.74756i | 0.329219i | ||||||||
\(707\) | 16.0313 | − | 7.78210i | 0.602920 | − | 0.292676i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7586 | + | 32.4908i | −0.704492 | + | 1.22022i | 0.262382 | + | 0.964964i | \(0.415492\pi\) |
−0.966874 | + | 0.255252i | \(0.917841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.58302 | + | 0.913956i | 0.0593261 | + | 0.0342519i | ||||
\(713\) | −18.0199 | −0.674852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.97501 | + | 5.75908i | 0.372784 | + | 0.215227i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.8783 | + | 22.3059i | 0.480614 | + | 0.832449i | ||||
\(719\) | −2.65733 | + | 4.60264i | −0.0991019 | + | 0.171649i | −0.911313 | − | 0.411714i | \(-0.864930\pi\) |
0.812211 | + | 0.583363i | \(0.198264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.771516 | + | 1.13924i | −0.0287327 | + | 0.0424276i | ||||
\(722\) | − | 14.8577i | − | 0.552945i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.3694 | − | 8.29618i | 0.534035 | − | 0.308325i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.93413i | − | 0.108821i | −0.998519 | − | 0.0544104i | \(-0.982672\pi\) | ||
0.998519 | − | 0.0544104i | \(-0.0173279\pi\) | |||||||
\(728\) | −0.0129120 | + | 0.179841i | −0.000478550 | + | 0.00666534i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.53465 | + | 6.12220i | 0.130734 | + | 0.226438i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.8197 | − | 6.82411i | −0.436570 | − | 0.252054i | 0.265571 | − | 0.964091i | \(-0.414439\pi\) |
−0.702142 | + | 0.712037i | \(0.747773\pi\) | |||||||
\(734\) | −19.9377 | −0.735914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.73205 | −0.137565 | ||||||||
\(737\) | −36.7688 | − | 21.2285i | −1.35440 | − | 0.781960i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.6650 | − | 27.1325i | −0.576246 | − | 0.998087i | −0.995905 | − | 0.0904051i | \(-0.971184\pi\) |
0.419659 | − | 0.907682i | \(-0.362149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.50606 | − | 34.9049i | 0.0920004 | − | 1.28140i | ||||
\(743\) | 4.72061i | 0.173182i | 0.996244 | + | 0.0865911i | \(0.0275974\pi\) | ||||
−0.996244 | + | 0.0865911i | \(0.972403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.893327 | − | 0.515762i | 0.0327070 | − | 0.0188834i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 29.1774i | − | 1.06683i | ||||||
\(749\) | 9.08981 | − | 13.4223i | 0.332134 | − | 0.490439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8394 | − | 22.2385i | 0.468516 | − | 0.811494i | −0.530836 | − | 0.847474i | \(-0.678122\pi\) |
0.999352 | + | 0.0359807i | \(0.0114555\pi\) | |||||||
\(752\) | −0.830749 | − | 1.43890i | −0.0302943 | − | 0.0524713i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0530562 | − | 0.0306320i | −0.00193219 | − | 0.00111555i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8781 | 1.37670 | 0.688352 | − | 0.725377i | \(-0.258335\pi\) | ||||
0.688352 | + | 0.725377i | \(0.258335\pi\) | |||||||
\(758\) | 4.41237 | + | 2.54748i | 0.160265 | + | 0.0925288i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3533 | + | 17.9325i | −0.375308 | + | 0.650052i | −0.990373 | − | 0.138424i | \(-0.955796\pi\) |
0.615065 | + | 0.788476i | \(0.289130\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.2618 | + | 15.6609i | −1.16796 | + | 0.566963i | ||||
\(764\) | − | 18.4336i | − | 0.666905i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.33307 | + | 4.23375i | −0.264955 | + | 0.152972i | ||||
\(767\) | −0.628086 | + | 0.362626i | −0.0226789 | + | 0.0130937i | ||||
\(768\) | 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 | ||||||||
\(772\) | 3.17914 | − | 5.50643i | 0.114420 | − | 0.198181i | ||||
\(773\) | 14.3632 | + | 24.8778i | 0.516609 | + | 0.894793i | 0.999814 | + | 0.0192861i | \(0.00613933\pi\) |
−0.483205 | + | 0.875507i | \(0.660527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.1502 | −0.615656 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.74150 | −0.205843 | ||||||||
\(779\) | 2.97740 | + | 1.71901i | 0.106677 | + | 0.0615898i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7778 | − | 34.2562i | −0.707706 | − | 1.22578i | ||||
\(782\) | −13.6739 | + | 23.6838i | −0.488977 | + | 0.846932i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.33013 | − | 5.50000i | 0.154647 | − | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.75474 | − | 2.74515i | 0.169488 | − | 0.0978541i | −0.412856 | − | 0.910796i | \(-0.635469\pi\) |
0.582345 | + | 0.812942i | \(0.302135\pi\) | |||||||
\(788\) | −11.1188 | + | 6.41946i | −0.396092 | + | 0.228684i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.8710 | − | 2.21644i | −1.09765 | − | 0.0788075i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.256257 | + | 0.443850i | −0.00909995 | + | 0.0157616i | ||||
\(794\) | −8.43791 | − | 14.6149i | −0.299450 | − | 0.518663i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.33950 | − | 4.81481i | −0.295586 | − | 0.170656i | ||||
\(797\) | 50.8854 | 1.80245 | 0.901227 | − | 0.433347i | \(-0.142668\pi\) | ||||
0.901227 | + | 0.433347i | \(0.142668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.1751 | −0.430725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.944382 | + | 1.63572i | 0.0333473 | + | 0.0577592i | ||||
\(803\) | −23.2073 | + | 40.1962i | −0.818967 | + | 1.41849i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 0.329049i | − | 0.0115903i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.83307 | + | 3.36773i | −0.205207 | + | 0.118476i | ||||
\(809\) | 1.80508 | − | 1.04217i | 0.0634634 | − | 0.0366406i | −0.467933 | − | 0.883764i | \(-0.655001\pi\) |
0.531396 | + | 0.847124i | \(0.321668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0199i | 0.948797i | 0.880310 | + | 0.474398i | \(0.157334\pi\) | ||||
−0.880310 | + | 0.474398i | \(0.842666\pi\) | |||||||
\(812\) | 1.03868 | + | 2.13970i | 0.0364504 | + | 0.0750886i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.09915 | − | 14.0281i | 0.283875 | − | 0.491686i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.70042 | − | 0.981740i | −0.0594903 | − | 0.0343467i | ||||
\(818\) | 32.9802 | 1.15312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.06085 | + | 4.65393i | 0.281326 | + | 0.162423i | 0.634023 | − | 0.773314i | \(-0.281402\pi\) |
−0.352698 | + | 0.935737i | \(0.614736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2593 | − | 35.0901i | −0.706195 | − | 1.22316i | −0.966259 | − | 0.257573i | \(-0.917077\pi\) |
0.260064 | − | 0.965591i | \(-0.416256\pi\) | |||||||
\(824\) | 0.260021 | − | 0.450370i | 0.00905826 | − | 0.0156894i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.0844 | + | 2.01637i | 0.977182 | + | 0.0701585i | ||||
\(827\) | 14.0131i | 0.487284i | 0.969865 | + | 0.243642i | \(0.0783423\pi\) | ||||
−0.969865 | + | 0.243642i | \(0.921658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.8540 | − | 10.8854i | 0.654827 | − | 0.378064i | −0.135476 | − | 0.990781i | \(-0.543256\pi\) |
0.790303 | + | 0.612716i | \(0.209923\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.0681483i | − | 0.00236262i | ||||||
\(833\) | −19.0382 | − | 47.6307i | −0.659634 | − | 1.65031i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.05197 | + | 7.01822i | 0.140140 | + | 0.242730i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.260214 | − | 0.150235i | −0.00898896 | − | 0.00518978i | ||||
\(839\) | −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 | ||||||||
\(842\) | 24.9956 | + | 14.4312i | 0.861406 | + | 0.497333i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.28094 | − | 12.6110i | −0.250620 | − | 0.434087i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6341 | − | 7.20159i | −0.365391 | − | 0.247450i | ||||
\(848\) | 13.2268i | 0.454210i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1485 | + | 7.59127i | −0.450723 | + | 0.260225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.95355i | 0.272324i | 0.990687 | + | 0.136162i | \(0.0434768\pi\) | ||||
−0.990687 | + | 0.136162i | \(0.956523\pi\) | |||||||
\(854\) | 17.9000 | − | 8.68921i | 0.612525 | − | 0.297339i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.06350 | + | 5.30614i | −0.104708 | + | 0.181360i | ||||
\(857\) | −1.14651 | − | 1.98582i | −0.0391641 | − | 0.0678343i | 0.845779 | − | 0.533534i | \(-0.179136\pi\) |
−0.884943 | + | 0.465699i | \(0.845803\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1054 | − | 22.0002i | −1.30014 | − | 0.750636i | −0.319712 | − | 0.947515i | \(-0.603586\pi\) |
−0.980428 | + | 0.196879i | \(0.936919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.5897 | 1.14407 | ||||||||
\(863\) | 28.6959 | + | 16.5676i | 0.976821 | + | 0.563968i | 0.901309 | − | 0.433177i | \(-0.142607\pi\) |
0.0755122 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.61037 | + | 9.71744i | −0.190648 | + | 0.330212i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.16328 | + | 10.5775i | −0.243138 | + | 0.359024i | ||||
\(869\) | − | 69.8787i | − | 2.37047i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.629306 | + | 0.363330i | −0.0213232 | + | 0.0123110i | ||||
\(872\) | 11.7386 | − | 6.77729i | 0.397520 | − | 0.229508i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.59575i | − | 0.256930i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.84436 | + | 4.92657i | −0.0960471 | + | 0.166358i | −0.910045 | − | 0.414509i | \(-0.863953\pi\) |
0.813998 | + | 0.580868i | \(0.197287\pi\) | |||||||
\(878\) | −8.43363 | − | 14.6075i | −0.284621 | − | 0.492979i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4073 | 0.754923 | 0.377461 | − | 0.926025i | \(-0.376797\pi\) | ||||
0.377461 | + | 0.926025i | \(0.376797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.7564 | 0.631204 | 0.315602 | − | 0.948892i | \(-0.397794\pi\) | ||||
0.315602 | + | 0.948892i | \(0.397794\pi\) | |||||||
\(884\) | −0.432474 | − | 0.249689i | −0.0145457 | − | 0.00839795i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.02823 | − | 1.78094i | −0.0345440 | − | 0.0598320i | ||||
\(887\) | −0.735451 | + | 1.27384i | −0.0246940 | + | 0.0427713i | −0.878108 | − | 0.478462i | \(-0.841194\pi\) |
0.853414 | + | 0.521233i | \(0.174528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.03735 | + | 28.3767i | −0.0683306 | + | 0.951723i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.4910 | − | 11.8305i | 0.686088 | − | 0.396113i | ||||
\(893\) | 2.92856 | − | 1.69080i | 0.0980005 | − | 0.0565806i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.48356 | + | 2.19067i | −0.0495624 | + | 0.0731852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.29461 | + | 10.9026i | −0.210054 | + | 0.363824i | ||||
\(899\) | −2.17033 | − | 3.75912i | −0.0723845 | − | 0.125374i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.9380 | + | 48.4616i | 2.79638 | + | 1.61449i | ||||
\(902\) | 6.72600 | 0.223951 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.6982 | 0.389076 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.42294 | + | 16.3210i | 0.312883 | + | 0.541930i | 0.978985 | − | 0.203931i | \(-0.0653717\pi\) |
−0.666102 | + | 0.745861i | \(0.732038\pi\) | |||||||
\(908\) | 4.32024 | − | 7.48288i | 0.143372 | − | 0.248328i | ||||
\(909\) | 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 | ||||||||
\(913\) | 49.4794 | − | 28.5670i | 1.63753 | − | 0.945428i | ||||
\(914\) | 30.2701 | − | 17.4765i | 1.00125 | − | 0.578070i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 14.0754i | − | 0.465063i | ||||||
\(917\) | 8.12552 | + | 5.50276i | 0.268328 | + | 0.181717i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.9805 | + | 25.9470i | −0.494162 | + | 0.855914i | −0.999977 | − | 0.00672796i | \(-0.997858\pi\) |
0.505815 | + | 0.862642i | \(0.331192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.2433 | − | 11.6875i | −0.666678 | − | 0.384907i | ||||
\(923\) | −0.677003 | −0.0222838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.50526 | + | 3.17846i | 0.180914 | + | 0.104451i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.449490 | − | 0.778539i | −0.0147552 | − | 0.0255568i | ||||
\(929\) | −23.3931 | + | 40.5181i | −0.767504 | + | 1.32936i | 0.171408 | + | 0.985200i | \(0.445168\pi\) |
−0.938912 | + | 0.344156i | \(0.888165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1940 | + | 8.81300i | 0.366869 | + | 0.288835i | ||||
\(932\) | 20.1976i | 0.661593i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.74907 | − | 3.89658i | 0.220836 | − | 0.127500i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.1632i | − | 0.626036i | −0.949747 | − | 0.313018i | \(-0.898660\pi\) | ||
0.949747 | − | 0.313018i | \(-0.101340\pi\) | |||||||
\(938\) | 28.1390 | + | 2.02029i | 0.918770 | + | 0.0659647i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2474 | + | 43.7299i | 0.823043 | + | 1.42555i | 0.903406 | + | 0.428787i | \(0.141059\pi\) |
−0.0803623 | + | 0.996766i | \(0.525608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.45962 | − | 3.15211i | −0.177790 | − | 0.102647i | ||||
\(944\) | −10.6422 | −0.346375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.84128 | −0.124891 | ||||||||
\(947\) | 31.2304 | + | 18.0309i | 1.01485 | + | 0.585925i | 0.912609 | − | 0.408834i | \(-0.134064\pi\) |
0.102244 | + | 0.994759i | \(0.467398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.397198 | + | 0.687967i | 0.0128936 | + | 0.0223323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.46651 | + | 17.4412i | 0.274401 | + | 0.565272i | ||||
\(953\) | 29.7944i | 0.965137i | 0.875858 | + | 0.482568i | \(0.160296\pi\) | ||||
−0.875858 | + | 0.482568i | \(0.839704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.3550 | + | 11.7520i | −0.658329 | + | 0.380086i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 27.5040i | − | 0.888613i | ||||||
\(959\) | −15.6216 | − | 32.1808i | −0.504447 | − | 1.03917i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84315 | + | 6.65652i | −0.123972 | + | 0.214727i | ||||
\(962\) | −0.138619 | − | 0.240095i | −0.00446925 | − | 0.00774097i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.8765 | − | 7.43426i | −0.414724 | − | 0.239441i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5198 | 0.370453 | 0.185226 | − | 0.982696i | \(-0.440698\pi\) | ||||
0.185226 | + | 0.982696i | \(0.440698\pi\) | |||||||
\(968\) | 4.20390 | + | 2.42713i | 0.135119 | + | 0.0780108i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2347 | − | 36.7795i | 0.681453 | − | 1.18031i | −0.293084 | − | 0.956087i | \(-0.594682\pi\) |
0.974537 | − | 0.224225i | \(-0.0719849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.9156 | − | 1.71706i | −0.766698 | − | 0.0550465i | ||||
\(974\) | 35.4468i | 1.13579i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.51299 | + | 3.76028i | −0.208476 | + | 0.120364i | ||||
\(977\) | −15.7279 | + | 9.08052i | −0.503181 | + | 0.290512i | −0.730026 | − | 0.683419i | \(-0.760492\pi\) |
0.226845 | + | 0.973931i | \(0.427159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.27827i | 0.232614i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.821743 | + | 1.42330i | −0.0262229 | + | 0.0454194i | ||||
\(983\) | 6.19988 | + | 10.7385i | 0.197746 | + | 0.342505i | 0.947797 | − | 0.318874i | \(-0.103305\pi\) |
−0.750052 | + | 0.661379i | \(0.769971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.58755 | −0.209790 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.138701 | 0.00441266 | ||||||||
\(989\) | 3.11804 | + | 1.80020i | 0.0991478 | + | 0.0572430i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8601 | − | 18.8102i | −0.344981 | − | 0.597525i | 0.640369 | − | 0.768067i | \(-0.278781\pi\) |
−0.985350 | + | 0.170543i | \(0.945448\pi\) | |||||||
\(992\) | 2.41421 | − | 4.18154i | 0.0766514 | − | 0.132764i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.7627 | + | 14.7381i | 0.690270 | + | 0.467464i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7856 | − | 21.2381i | 1.16501 | − | 0.672619i | 0.212510 | − | 0.977159i | \(-0.431836\pi\) |
0.952500 | + | 0.304540i | \(0.0985027\pi\) | |||||||
\(998\) | 30.0796 | − | 17.3665i | 0.952154 | − | 0.549726i | ||||
\(999\) | 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.bf.b.1601.4 | 8 | ||
3.2 | odd | 2 | 3150.2.bf.c.1601.2 | 8 | |||
5.2 | odd | 4 | 3150.2.bp.a.1349.4 | 8 | |||
5.3 | odd | 4 | 3150.2.bp.d.1349.1 | 8 | |||
5.4 | even | 2 | 630.2.be.a.341.1 | ✓ | 8 | ||
7.3 | odd | 6 | 3150.2.bf.c.1151.2 | 8 | |||
15.2 | even | 4 | 3150.2.bp.f.1349.4 | 8 | |||
15.8 | even | 4 | 3150.2.bp.c.1349.1 | 8 | |||
15.14 | odd | 2 | 630.2.be.b.341.3 | yes | 8 | ||
21.17 | even | 6 | inner | 3150.2.bf.b.1151.4 | 8 | ||
35.3 | even | 12 | 3150.2.bp.f.899.4 | 8 | |||
35.9 | even | 6 | 4410.2.b.e.881.5 | 8 | |||
35.17 | even | 12 | 3150.2.bp.c.899.1 | 8 | |||
35.19 | odd | 6 | 4410.2.b.b.881.5 | 8 | |||
35.24 | odd | 6 | 630.2.be.b.521.3 | yes | 8 | ||
105.17 | odd | 12 | 3150.2.bp.d.899.1 | 8 | |||
105.38 | odd | 12 | 3150.2.bp.a.899.4 | 8 | |||
105.44 | odd | 6 | 4410.2.b.b.881.4 | 8 | |||
105.59 | even | 6 | 630.2.be.a.521.1 | yes | 8 | ||
105.89 | even | 6 | 4410.2.b.e.881.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.1 | ✓ | 8 | 5.4 | even | 2 | ||
630.2.be.a.521.1 | yes | 8 | 105.59 | even | 6 | ||
630.2.be.b.341.3 | yes | 8 | 15.14 | odd | 2 | ||
630.2.be.b.521.3 | yes | 8 | 35.24 | odd | 6 | ||
3150.2.bf.b.1151.4 | 8 | 21.17 | even | 6 | inner | ||
3150.2.bf.b.1601.4 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bf.c.1151.2 | 8 | 7.3 | odd | 6 | |||
3150.2.bf.c.1601.2 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.a.899.4 | 8 | 105.38 | odd | 12 | |||
3150.2.bp.a.1349.4 | 8 | 5.2 | odd | 4 | |||
3150.2.bp.c.899.1 | 8 | 35.17 | even | 12 | |||
3150.2.bp.c.1349.1 | 8 | 15.8 | even | 4 | |||
3150.2.bp.d.899.1 | 8 | 105.17 | odd | 12 | |||
3150.2.bp.d.1349.1 | 8 | 5.3 | odd | 4 | |||
3150.2.bp.f.899.4 | 8 | 35.3 | even | 12 | |||
3150.2.bp.f.1349.4 | 8 | 15.2 | even | 4 | |||
4410.2.b.b.881.4 | 8 | 105.44 | odd | 6 | |||
4410.2.b.b.881.5 | 8 | 35.19 | odd | 6 | |||
4410.2.b.e.881.4 | 8 | 105.89 | even | 6 | |||
4410.2.b.e.881.5 | 8 | 35.9 | even | 6 |