Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(49,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.z (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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.3 | ||
Root | \(-1.56631 + 0.739379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.69 |
Dual form | 260.2.z.a.49.3 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.28064 | − | 0.739379i | −0.739379 | − | 0.426881i | 0.0824643 | − | 0.996594i | \(-0.473721\pi\) |
−0.821844 | + | 0.569713i | \(0.807054\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.494086 | + | 2.18080i | −0.220962 | + | 0.975282i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56631 | − | 2.71292i | −0.592008 | − | 1.02539i | −0.993962 | − | 0.109729i | \(-0.965002\pi\) |
0.401953 | − | 0.915660i | \(-0.368331\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.406637 | − | 0.704315i | −0.135546 | − | 0.234772i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.01176 | − | 2.31619i | −1.20959 | − | 0.698358i | −0.246921 | − | 0.969036i | \(-0.579419\pi\) |
−0.962670 | + | 0.270678i | \(0.912752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44512 | − | 2.64979i | 0.678155 | − | 0.734919i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.24518 | − | 2.42751i | 0.579704 | − | 0.626779i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.87021 | + | 3.38917i | −1.42373 | + | 0.821994i | −0.996616 | − | 0.0822017i | \(-0.973805\pi\) |
−0.427119 | + | 0.904195i | \(0.640471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.45442 | − | 0.839708i | 0.333666 | − | 0.192642i | −0.323802 | − | 0.946125i | \(-0.604961\pi\) |
0.657468 | + | 0.753483i | \(0.271628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.63238i | 1.01087i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.79118 | − | 2.76619i | −0.999030 | − | 0.576790i | −0.0910690 | − | 0.995845i | \(-0.529028\pi\) |
−0.907961 | + | 0.419054i | \(0.862362\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51176 | − | 2.15500i | −0.902352 | − | 0.431000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63891i | 1.08521i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87062 | − | 6.70410i | 0.718755 | − | 1.24492i | −0.242738 | − | 0.970092i | \(-0.578045\pi\) |
0.961493 | − | 0.274829i | \(-0.0886212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46127i | 0.262451i | 0.991353 | + | 0.131226i | \(0.0418912\pi\) | ||||
−0.991353 | + | 0.131226i | \(0.958109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.42509 | + | 5.93242i | 0.596231 | + | 1.03270i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.69023 | − | 2.07538i | 1.13085 | − | 0.350804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.72577 | + | 6.45322i | −0.612512 | + | 1.06090i | 0.378303 | + | 0.925682i | \(0.376508\pi\) |
−0.990816 | + | 0.135220i | \(0.956826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.09053 | + | 1.58556i | −0.815137 | + | 0.253892i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.78901 | + | 2.76494i | 0.747918 | + | 0.431811i | 0.824941 | − | 0.565219i | \(-0.191208\pi\) |
−0.0770232 | + | 0.997029i | \(0.524542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7707 | − | 6.21849i | 1.64252 | − | 0.948311i | 0.662591 | − | 0.748982i | \(-0.269457\pi\) |
0.979933 | − | 0.199329i | \(-0.0638764\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.73688 | − | 0.538800i | 0.258919 | − | 0.0803196i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.97634 | 0.288279 | 0.144140 | − | 0.989557i | \(-0.453959\pi\) | ||||
0.144140 | + | 0.989557i | \(0.453959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.40664 | + | 2.43637i | −0.200948 | + | 0.348052i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0235 | 1.40357 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65865i | 0.777276i | 0.921391 | + | 0.388638i | \(0.127054\pi\) | ||||
−0.921391 | + | 0.388638i | \(0.872946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.03329 | − | 7.60444i | 0.948369 | − | 1.02538i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.48345 | −0.328941 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.27725 | − | 1.31477i | 0.296473 | − | 0.171169i | −0.344384 | − | 0.938829i | \(-0.611912\pi\) |
0.640857 | + | 0.767660i | \(0.278579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.87062 | − | 8.43615i | −0.623618 | − | 1.08014i | −0.988806 | − | 0.149205i | \(-0.952329\pi\) |
0.365188 | − | 0.930934i | \(-0.381005\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.27384 | + | 2.20635i | −0.160488 | + | 0.277974i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.57055 | + | 6.64154i | 0.566907 | + | 0.823782i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.317776 | − | 0.550404i | 0.0388225 | − | 0.0672426i | −0.845961 | − | 0.533244i | \(-0.820973\pi\) |
0.884784 | + | 0.466002i | \(0.154306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.09053 | + | 7.08500i | 0.492441 | + | 0.852934i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0089 | + | 6.93335i | −1.42520 | + | 0.822838i | −0.996737 | − | 0.0807229i | \(-0.974277\pi\) |
−0.428460 | + | 0.903561i | \(0.640944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89025 | 0.572360 | 0.286180 | − | 0.958176i | \(-0.407614\pi\) | ||||
0.286180 | + | 0.958176i | \(0.407614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.18459 | + | 6.09569i | 0.483194 | + | 0.703869i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.5115i | 1.65373i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.21024 | −0.698707 | −0.349354 | − | 0.936991i | \(-0.613599\pi\) | ||||
−0.349354 | + | 0.936991i | \(0.613599\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.94938 | − | 5.10848i | 0.327709 | − | 0.567609i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.33075 | −0.365597 | −0.182798 | − | 0.983150i | \(-0.558516\pi\) | ||||
−0.182798 | + | 0.983150i | \(0.558516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.49070 | − | 14.4763i | −0.487085 | − | 1.57017i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.91375 | + | 5.72371i | −1.06287 | + | 0.613646i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.27725 | − | 1.31477i | −0.241388 | − | 0.139366i | 0.374426 | − | 0.927257i | \(-0.377840\pi\) |
−0.615815 | + | 0.787891i | \(0.711173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0185 | − | 2.48305i | −1.15505 | − | 0.260294i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.08043 | − | 1.87136i | 0.112035 | − | 0.194051i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.11263 | + | 3.58668i | 0.114153 | + | 0.367985i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.13942 | − | 5.43764i | −0.318760 | − | 0.552108i | 0.661470 | − | 0.749972i | \(-0.269933\pi\) |
−0.980230 | + | 0.197864i | \(0.936600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.76739i | 0.378637i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.41840 | − | 14.5811i | 0.837662 | − | 1.45087i | −0.0541831 | − | 0.998531i | \(-0.517255\pi\) |
0.891845 | − | 0.452342i | \(-0.149411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.86212i | − | 0.971744i | −0.874030 | − | 0.485872i | \(-0.838502\pi\) | ||
0.874030 | − | 0.485872i | \(-0.161498\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.1023 | − | 2.28879i | −0.985882 | − | 0.223363i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.53096 | + | 2.03860i | 0.341351 | + | 0.197079i | 0.660869 | − | 0.750501i | \(-0.270188\pi\) |
−0.319519 | + | 0.947580i | \(0.603521\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6762i | 1.11837i | 0.829042 | + | 0.559186i | \(0.188886\pi\) | ||||
−0.829042 | + | 0.559186i | \(0.811114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.54275 | − | 5.50951i | 0.905757 | − | 0.522939i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.30892 | − | 1.91041i | 0.311277 | − | 0.179716i | −0.336221 | − | 0.941783i | \(-0.609149\pi\) |
0.647498 | + | 0.762067i | \(0.275815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.39975 | − | 9.08186i | 0.783281 | − | 0.846888i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.86056 | − | 0.644637i | −0.264459 | − | 0.0595967i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.3891 | + | 10.6170i | 1.68573 | + | 0.973254i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.22947 | + | 9.05771i | 0.475407 | + | 0.823428i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.08867 | − | 7.08179i | −0.368663 | − | 0.638544i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92882 | − | 8.77448i | 0.619732 | − | 0.784813i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.91375 | − | 5.72371i | −0.879703 | − | 0.507897i | −0.00914258 | − | 0.999958i | \(-0.502910\pi\) |
−0.870561 | + | 0.492061i | \(0.836244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.3913 | −1.61926 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.36778 | −0.381615 | −0.190807 | − | 0.981628i | \(-0.561111\pi\) | ||||
−0.190807 | + | 0.981628i | \(0.561111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.55613 | − | 2.63048i | −0.395066 | − | 0.228092i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.2973 | − | 2.78610i | −1.05839 | − | 0.239790i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.76290 | − | 4.78548i | −0.236050 | − | 0.408851i | 0.723527 | − | 0.690296i | \(-0.242520\pi\) |
−0.959577 | + | 0.281445i | \(0.909186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.64787 | − | 9.78240i | −0.479046 | − | 0.829732i | 0.520665 | − | 0.853761i | \(-0.325684\pi\) |
−0.999711 | + | 0.0240289i | \(0.992351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.53099 | − | 1.46127i | −0.213148 | − | 0.123061i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.9467 | + | 4.96694i | −1.33353 | + | 0.415356i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.7079 | + | 11.7534i | 1.05533 | + | 0.976069i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.60280 | − | 2.08008i | 0.297154 | − | 0.171562i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.25802 | + | 3.03572i | −0.430754 | + | 0.248696i | −0.699668 | − | 0.714468i | \(-0.746669\pi\) |
0.268914 | + | 0.963164i | \(0.413335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1403i | 1.23210i | 0.787708 | + | 0.616048i | \(0.211267\pi\) | ||||
−0.787708 | + | 0.616048i | \(0.788733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.77408 | + | 2.75632i | 0.385962 | + | 0.222835i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.18673 | − | 0.721991i | −0.255964 | − | 0.0579917i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.3218i | − | 1.54205i | −0.636804 | − | 0.771026i | \(-0.719744\pi\) | ||
0.636804 | − | 0.771026i | \(-0.280256\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.18389 | − | 7.24671i | 0.331804 | − | 0.574701i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.3308i | 1.36586i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.278858 | + | 0.482997i | 0.0218419 | + | 0.0378312i | 0.876740 | − | 0.480965i | \(-0.159714\pi\) |
−0.854898 | + | 0.518796i | \(0.826380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.6297 | + | 4.53830i | −1.13892 | + | 0.353306i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.16473 | + | 5.48147i | −0.244894 | + | 0.424169i | −0.962102 | − | 0.272691i | \(-0.912086\pi\) |
0.717208 | + | 0.696859i | \(0.245420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.04275 | − | 12.9581i | −0.0802113 | − | 0.996778i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.18284 | − | 0.682912i | −0.0904539 | − | 0.0522236i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.62192 | − | 3.82317i | 0.503455 | − | 0.290670i | −0.226684 | − | 0.973968i | \(-0.572788\pi\) |
0.730139 | + | 0.683298i | \(0.239455\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.22045 | + | 15.6155i | 0.0922571 | + | 1.18042i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.88846 | −0.292275 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.27725 | − | 3.94432i | 0.170210 | − | 0.294812i | −0.768283 | − | 0.640110i | \(-0.778889\pi\) |
0.938493 | + | 0.345298i | \(0.112222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.76475 | −0.577149 | −0.288575 | − | 0.957457i | \(-0.593181\pi\) | ||||
−0.288575 | + | 0.957457i | \(0.593181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.4049i | 1.06484i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.2323 | − | 11.3136i | −0.899337 | − | 0.831791i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.3998 | 2.29618 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.2979 | − | 8.83227i | 1.11276 | − | 0.642453i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.71991 | − | 9.90717i | −0.413878 | − | 0.716858i | 0.581432 | − | 0.813595i | \(-0.302493\pi\) |
−0.995310 | + | 0.0967371i | \(0.969159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58132 | − | 2.73893i | 0.113826 | − | 0.197153i | −0.803484 | − | 0.595327i | \(-0.797023\pi\) |
0.917310 | + | 0.398174i | \(0.130356\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.942624 | − | 11.8848i | −0.0675027 | − | 0.851089i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5791 | − | 20.0556i | 0.824978 | − | 1.42890i | −0.0769575 | − | 0.997034i | \(-0.524521\pi\) |
0.901936 | − | 0.431870i | \(-0.142146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.01176 | + | 5.21652i | 0.213498 | + | 0.369789i | 0.952807 | − | 0.303577i | \(-0.0981810\pi\) |
−0.739309 | + | 0.673366i | \(0.764848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.813915 | + | 0.469914i | −0.0574091 | + | 0.0331452i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.2503 | −1.70204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.39595 | + | 9.07775i | −0.586399 | + | 0.634018i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.49934i | 0.312725i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.77969 | −0.538132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56910 | − | 4.44981i | 0.176864 | − | 0.306338i | −0.763941 | − | 0.645287i | \(-0.776738\pi\) |
0.940805 | + | 0.338949i | \(0.110071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.5055 | 1.40501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.23961 | + | 26.5613i | 0.561936 | + | 1.81146i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.96430 | − | 2.28879i | 0.269115 | − | 0.155373i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.26266 | − | 3.61575i | −0.423191 | − | 0.244330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.37281 | + | 23.8417i | −0.361414 | + | 1.60377i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.31533 | + | 14.4026i | −0.556836 | + | 0.964468i | 0.440922 | + | 0.897545i | \(0.354651\pi\) |
−0.997758 | + | 0.0669227i | \(0.978682\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.316846 | + | 4.05400i | 0.0211231 | + | 0.270267i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.22129 | + | 12.5076i | 0.479294 | + | 0.830161i | 0.999718 | − | 0.0237467i | \(-0.00755951\pi\) |
−0.520424 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00567i | 0.264702i | 0.991203 | + | 0.132351i | \(0.0422526\pi\) | ||||
−0.991203 | + | 0.132351i | \(0.957747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7295 | − | 18.5840i | 0.705948 | − | 1.22274i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.48148i | − | 0.228079i | −0.993476 | − | 0.114040i | \(-0.963621\pi\) | ||
0.993476 | − | 0.114040i | \(-0.0363791\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.976482 | + | 4.31000i | −0.0636987 | + | 0.281154i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.95310 | + | 4.59173i | 0.516610 | + | 0.298265i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.1155i | − | 1.23648i | −0.785990 | − | 0.618239i | \(-0.787846\pi\) | ||
0.785990 | − | 0.618239i | \(-0.212154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.3464 | − | 11.1696i | 1.24621 | − | 0.719499i | 0.275857 | − | 0.961199i | \(-0.411038\pi\) |
0.970351 | + | 0.241700i | \(0.0777050\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.09611 | − | 4.09694i | 0.455216 | − | 0.262819i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.61822 | − | 4.27136i | −0.295047 | − | 0.272887i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.33118 | − | 5.90708i | 0.0847010 | − | 0.375859i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.26549 | + | 2.46268i | 0.270315 | + | 0.156066i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.37281 | + | 14.5021i | 0.528487 | + | 0.915367i | 0.999448 | + | 0.0332127i | \(0.0105739\pi\) |
−0.470961 | + | 0.882154i | \(0.656093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.8140 | + | 22.1946i | 0.805612 | + | 1.39536i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.95248 | + | 21.8593i | −0.310136 | + | 1.36888i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6560 | + | 7.88431i | 0.851839 | + | 0.491810i | 0.861271 | − | 0.508146i | \(-0.169669\pi\) |
−0.00943181 | + | 0.999956i | \(0.503002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.3428 | 1.45045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.29574 | −0.389696 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6443 | − | 6.14549i | −0.656355 | − | 0.378947i | 0.134532 | − | 0.990909i | \(-0.457047\pi\) |
−0.790887 | + | 0.611962i | \(0.790380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.3404 | − | 2.79586i | −0.758063 | − | 0.171748i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.94423 | + | 3.36751i | 0.118985 | + | 0.206088i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.82503 | + | 11.8213i | 0.416130 | + | 0.720758i | 0.995546 | − | 0.0942739i | \(-0.0300529\pi\) |
−0.579417 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.54558 | − | 0.892343i | −0.0938875 | − | 0.0542060i | 0.452321 | − | 0.891855i | \(-0.350596\pi\) |
−0.546209 | + | 0.837649i | \(0.683929\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.2748 | + | 11.3267i | 0.742906 | + | 0.685525i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1087 | + | 19.0954i | 0.790484 | + | 1.15150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9723 | + | 9.79899i | −1.01977 | + | 0.588764i | −0.914037 | − | 0.405631i | \(-0.867052\pi\) |
−0.105732 | + | 0.994395i | \(0.533719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.02919 | − | 0.594204i | 0.0616161 | − | 0.0355741i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0710i | − | 1.07803i | −0.842297 | − | 0.539013i | \(-0.818797\pi\) | ||
0.842297 | − | 0.539013i | \(-0.181203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.31095 | + | 3.64363i | 0.375147 | + | 0.216591i | 0.675705 | − | 0.737172i | \(-0.263839\pi\) |
−0.300558 | + | 0.953764i | \(0.597173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.22704 | − | 5.41590i | 0.0726834 | − | 0.320810i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.3230i | − | 1.02254i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4729 | − | 25.0678i | 0.851347 | − | 1.47458i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.28489i | 0.544290i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.14226 | − | 10.6387i | −0.358835 | − | 0.621520i | 0.628932 | − | 0.777461i | \(-0.283492\pi\) |
−0.987766 | + | 0.155941i | \(0.950159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.74210 | + | 5.61584i | 0.101429 | + | 0.326967i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.0608 | − | 22.6219i | 0.757864 | − | 1.31266i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.0448 | + | 5.93194i | −1.10139 | + | 0.343053i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.7406 | − | 19.4801i | −1.94478 | − | 1.12282i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.5619 | + | 12.4488i | −1.23870 | + | 0.715163i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.8040 | − | 6.45365i | 1.19124 | − | 0.369535i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1511 | 1.77789 | 0.888943 | − | 0.458018i | \(-0.151440\pi\) | ||||
0.888943 | + | 0.458018i | \(0.151440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.29185 | + | 12.6299i | −0.414819 | + | 0.718487i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.694196 | 0.0393643 | 0.0196821 | − | 0.999806i | \(-0.493735\pi\) | ||||
0.0196821 | + | 0.999806i | \(0.493735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.5944i | − | 0.824925i | −0.910975 | − | 0.412463i | \(-0.864669\pi\) | ||
0.910975 | − | 0.412463i | \(-0.135331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.18222 | − | 3.86810i | −0.235641 | − | 0.217943i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5641 | 0.817999 | 0.408999 | − | 0.912535i | \(-0.365878\pi\) | ||||
0.408999 | + | 0.912535i | \(0.365878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.0560 | + | 17.9302i | −1.73880 | + | 1.00390i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.01460 | − | 5.22143i | −0.168258 | − | 0.291432i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.69182 | + | 9.85852i | −0.316701 | + | 0.548543i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.7421 | + | 6.68596i | −0.928685 | + | 0.370870i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.63311 | − | 14.9530i | 0.477412 | − | 0.826902i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.09556 | − | 5.36167i | −0.170664 | − | 0.295598i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.71991 | + | 5.03444i | −0.479290 | + | 0.276718i | −0.720120 | − | 0.693849i | \(-0.755913\pi\) |
0.240831 | + | 0.970567i | \(0.422580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.06013 | 0.332093 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.04331 | + | 0.964952i | 0.0570022 | + | 0.0527210i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.974536i | 0.0530863i | 0.999648 | + | 0.0265432i | \(0.00844995\pi\) | ||||
−0.999648 | + | 0.0265432i | \(0.991550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.65006 | −0.306869 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.38457 | − | 5.86225i | 0.183285 | − | 0.317459i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.1154 | −0.708165 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.4720 | + | 5.42002i | −0.940662 | + | 0.291804i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.29440 | + | 4.21142i | −0.391584 | + | 0.226081i | −0.682846 | − | 0.730562i | \(-0.739258\pi\) |
0.291262 | + | 0.956643i | \(0.405925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.51639 | + | 2.03019i | 0.188228 | + | 0.108674i | 0.591153 | − | 0.806560i | \(-0.298673\pi\) |
−0.402925 | + | 0.915233i | \(0.632006\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.9419 | + | 13.7878i | 0.797540 | + | 0.735940i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.95925 | + | 3.39351i | −0.104280 | + | 0.180618i | −0.913444 | − | 0.406965i | \(-0.866587\pi\) |
0.809164 | + | 0.587583i | \(0.199921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.18681 | − | 29.6147i | −0.487585 | − | 1.57179i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6999 | − | 27.1930i | −0.830927 | − | 1.43921i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.23682i | 0.223611i | 0.993730 | + | 0.111805i | \(0.0356633\pi\) | ||||
−0.993730 | + | 0.111805i | \(0.964337\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.08978 | + | 14.0119i | −0.425778 | + | 0.737469i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.4663i | − | 0.811768i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.41620 | + | 10.6646i | −0.126470 | + | 0.558213i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.9499 | − | 11.5181i | −1.04138 | − | 0.601238i | −0.121153 | − | 0.992634i | \(-0.538659\pi\) |
−0.920222 | + | 0.391396i | \(0.871992\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.49730i | − | 0.234120i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.3515 | − | 8.86319i | 0.797010 | − | 0.460154i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.2984 | + | 11.7193i | −1.05101 | + | 0.606801i | −0.922932 | − | 0.384964i | \(-0.874214\pi\) |
−0.128078 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.3610 | + | 6.11395i | −0.793239 | + | 0.315723i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.30032 | − | 26.6487i | −0.427488 | − | 1.37248i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8942 | + | 10.9086i | 0.970532 | + | 0.560337i | 0.899398 | − | 0.437130i | \(-0.144005\pi\) |
0.0711334 | + | 0.997467i | \(0.477338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.46398 | + | 14.6600i | 0.433623 | + | 0.751057i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.94924 | − | 12.0364i | −0.355089 | − | 0.615033i | 0.632044 | − | 0.774933i | \(-0.282216\pi\) |
−0.987133 | + | 0.159900i | \(0.948883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.6466 | − | 7.16990i | −1.61286 | − | 0.365412i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.75956 | − | 5.05733i | −0.445273 | − | 0.257079i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.66919 | −0.338141 | −0.169071 | − | 0.985604i | \(-0.554077\pi\) | ||||
−0.169071 | + | 0.985604i | \(0.554077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.5003 | 1.89647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.59356 | + | 3.22945i | 0.282158 | + | 0.162904i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.06839 | − | 13.5433i | 0.154388 | − | 0.681437i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66745 | + | 2.88812i | 0.0836871 | + | 0.144950i | 0.904831 | − | 0.425771i | \(-0.139997\pi\) |
−0.821144 | + | 0.570721i | \(0.806664\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.88984 | + | 6.73741i | 0.194736 | + | 0.337292i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1405 | − | 9.89607i | −0.855956 | − | 0.494186i | 0.00670012 | − | 0.999978i | \(-0.497867\pi\) |
−0.862656 | + | 0.505791i | \(0.831201\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.87205 | + | 3.57298i | 0.192880 | + | 0.177983i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.68332 | + | 8.95604i | 0.481168 | + | 0.445029i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.8937 | − | 17.2592i | 1.48178 | − | 0.855505i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.06018 | − | 2.92150i | 0.250210 | − | 0.144459i | −0.369651 | − | 0.929171i | \(-0.620523\pi\) |
0.619860 | + | 0.784712i | \(0.287189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.17132i | 0.403062i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.13375 | − | 4.11868i | −0.351029 | − | 0.202667i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.64567 | − | 7.26368i | 0.0807829 | − | 0.356560i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.7037i | 0.817982i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.8553 | + | 30.9262i | −0.872287 | + | 1.51085i | −0.0126627 | + | 0.999920i | \(0.504031\pi\) |
−0.859625 | + | 0.510926i | \(0.829303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9384i | 1.21542i | 0.794159 | + | 0.607711i | \(0.207912\pi\) | ||||
−0.794159 | + | 0.607711i | \(0.792088\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.803653 | − | 1.39197i | −0.0390750 | − | 0.0676798i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.7886 | − | 2.64079i | 1.63899 | − | 0.128097i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.2578 | + | 26.4272i | −0.738375 | + | 1.27890i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0944 | + | 5.42975i | 1.16329 | + | 0.262151i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.2773 | − | 15.1712i | −1.26573 | − | 0.730770i | −0.291553 | − | 0.956555i | \(-0.594172\pi\) |
−0.974177 | + | 0.225785i | \(0.927505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.1016 | − | 5.83216i | 0.485452 | − | 0.280276i | −0.237234 | − | 0.971453i | \(-0.576241\pi\) |
0.722686 | + | 0.691177i | \(0.242907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.58401 | − | 24.4479i | −0.363625 | − | 1.17219i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.29116 | −0.444457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.74627 | − | 3.02462i | 0.0833447 | − | 0.144357i | −0.821340 | − | 0.570439i | \(-0.806773\pi\) |
0.904685 | + | 0.426082i | \(0.140106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.28796 | 0.108950 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 27.7833i | − | 1.32002i | −0.751255 | − | 0.660012i | \(-0.770551\pi\) | ||
0.751255 | − | 0.660012i | \(-0.229449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.99241 | − | 4.31662i | 0.189258 | − | 0.204627i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.97820 | 0.424654 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.16257 | + | 1.82591i | −0.149251 | + | 0.0861700i | −0.572766 | − | 0.819719i | \(-0.694129\pi\) |
0.423515 | + | 0.905889i | \(0.360796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8082 | − | 22.1845i | −0.603116 | − | 1.04463i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1944 | − | 19.3893i | 0.525958 | − | 0.910987i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.8591 | − | 22.8022i | 0.509083 | − | 1.06899i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1718 | + | 36.6706i | −0.990374 | + | 1.71538i | −0.375313 | + | 0.926898i | \(0.622465\pi\) |
−0.615061 | + | 0.788480i | \(0.710869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.1112 | − | 33.1016i | −0.892035 | − | 1.54505i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.87450 | − | 1.65960i | 0.133879 | − | 0.0772951i | −0.431565 | − | 0.902082i | \(-0.642038\pi\) |
0.565444 | + | 0.824787i | \(0.308705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2130 | 1.21822 | 0.609111 | − | 0.793085i | \(-0.291526\pi\) | ||||
0.609111 | + | 0.793085i | \(0.291526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.54723 | + | 3.28081i | 0.164499 | + | 0.152144i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.45243i | 0.113485i | 0.998389 | + | 0.0567424i | \(0.0180714\pi\) | ||||
−0.998389 | + | 0.0567424i | \(0.981929\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.99094 | −0.0919330 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2862 | + | 24.7444i | −0.658272 | + | 1.14016i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.6128 | −2.64904 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.37155 | + | 0.654289i | −0.384113 | + | 0.0300208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.98548 | − | 2.30102i | 0.182482 | − | 0.105356i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.89707 | + | 1.09528i | 0.0866795 | + | 0.0500444i | 0.542713 | − | 0.839918i | \(-0.317397\pi\) |
−0.456034 | + | 0.889962i | \(0.650730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.98969 | + | 25.6514i | 0.364299 | + | 1.16960i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.8140 | − | 22.1946i | 0.583059 | − | 1.00989i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.4095 | − | 4.15979i | 0.608895 | − | 0.188886i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.75727 | − | 16.9001i | −0.442144 | − | 0.765816i | 0.555704 | − | 0.831380i | \(-0.312449\pi\) |
−0.997848 | + | 0.0655640i | \(0.979115\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.824728i | − | 0.0372955i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6383 | − | 27.0863i | 0.705747 | − | 1.22239i | −0.260674 | − | 0.965427i | \(-0.583945\pi\) |
0.966421 | − | 0.256963i | \(-0.0827217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.4727i | 2.36325i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.21592 | − | 1.86141i | −0.369278 | − | 0.0836643i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.6193 | + | 21.7195i | 1.68746 | + | 0.974254i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5312i | 1.41153i | 0.708445 | + | 0.705766i | \(0.249397\pi\) | ||||
−0.708445 | + | 0.705766i | \(0.750603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.10576 | − | 4.67986i | 0.362139 | − | 0.209081i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.86709 | − | 2.81002i | 0.217013 | − | 0.125293i | −0.387553 | − | 0.921847i | \(-0.626680\pi\) |
0.604566 | + | 0.796555i | \(0.293346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.6390 | + | 25.5631i | 1.22992 | + | 1.13754i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.24557 | + | 17.3657i | −0.366199 | + | 0.771238i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.7002 | − | 7.90980i | −0.607250 | − | 0.350596i | 0.164639 | − | 0.986354i | \(-0.447354\pi\) |
−0.771888 | + | 0.635758i | \(0.780688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.65963 | − | 13.2669i | −0.338842 | − | 0.586892i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.73504 | + | 8.20132i | 0.209057 | + | 0.362097i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.5073 | + | 4.87273i | 0.947725 | + | 0.214718i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.92861 | − | 4.57758i | −0.348700 | − | 0.201322i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.3071 | −0.496326 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6030 | 0.552149 | 0.276074 | − | 0.961136i | \(-0.410966\pi\) | ||||
0.276074 | + | 0.961136i | \(0.410966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8881 | + | 13.7918i | 1.04456 | + | 0.603074i | 0.921120 | − | 0.389278i | \(-0.127276\pi\) |
0.123435 | + | 0.992353i | \(0.460609\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.98279 | − | 20.9002i | 0.435685 | − | 0.912159i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.95248 | − | 8.57794i | −0.215733 | − | 0.373661i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.80361 | + | 6.58804i | 0.165374 | + | 0.286437i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.85203 | − | 1.06927i | −0.0803712 | − | 0.0464023i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.0362 | − | 5.92925i | 0.824550 | − | 0.256824i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.19037 | + | 6.69306i | −0.267633 | + | 0.289366i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.83269 | + | 3.36751i | −0.251699 | + | 0.145319i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2862 | − | 6.51608i | 0.486130 | − | 0.280667i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.6835i | − | 1.19021i | −0.803650 | − | 0.595103i | \(-0.797111\pi\) | ||
0.803650 | − | 0.595103i | \(-0.202889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.94387 | + | 5.74110i | 0.426732 | + | 0.246374i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.4633 | − | 5.76902i | −1.09073 | − | 0.247118i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.7863i | 1.05979i | 0.848064 | + | 0.529893i | \(0.177768\pi\) | ||||
−0.848064 | + | 0.529893i | \(0.822232\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.96114 | + | 6.86090i | −0.169057 | + | 0.292816i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.0007i | − | 0.553850i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.72715 | + | 16.8479i | 0.413641 | + | 0.716446i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.30019 | + | 23.5330i | 0.309876 | + | 0.998919i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.3096 | + | 28.2490i | −0.691058 | + | 1.19695i | 0.280433 | + | 0.959874i | \(0.409522\pi\) |
−0.971491 | + | 0.237075i | \(0.923811\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.85811 | − | 43.7452i | 0.416954 | − | 1.85022i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −40.2119 | − | 23.2164i | −1.69775 | − | 0.980196i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.6082 | + | 17.0943i | −1.24783 | + | 0.720438i | −0.970677 | − | 0.240387i | \(-0.922726\pi\) |
−0.277158 | + | 0.960824i | \(0.589392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.53132 | + | 8.16000i | 0.106494 | + | 0.343294i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.4786 | −0.776027 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.1721 | + | 17.6186i | −0.426438 | + | 0.738612i | −0.996554 | − | 0.0829524i | \(-0.973565\pi\) |
0.570116 | + | 0.821564i | \(0.306898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.7490 | 1.95639 | 0.978193 | − | 0.207700i | \(-0.0665978\pi\) | ||||
0.978193 | + | 0.207700i | \(0.0665978\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9167i | 0.706707i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6555 | + | 22.8054i | 0.652880 | + | 0.951050i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8607 | −0.493768 | −0.246884 | − | 0.969045i | \(-0.579407\pi\) | ||||
−0.246884 | + | 0.969045i | \(0.579407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.05022 | + | 2.33839i | −0.168321 | + | 0.0971803i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.21697 | + | 9.03606i | 0.216436 | + | 0.374879i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1065 | − | 22.7011i | 0.542816 | − | 0.940185i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.81919 | − | 5.91980i | 0.116559 | − | 0.244754i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.59483 | − | 9.69054i | 0.230924 | − | 0.399971i | −0.727157 | − | 0.686472i | \(-0.759159\pi\) |
0.958080 | + | 0.286500i | \(0.0924920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.22704 | + | 2.12529i | 0.0505592 | + | 0.0875710i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.6574 | + | 17.1227i | −1.21994 | + | 0.704335i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.6058 | 1.13363 | 0.566817 | − | 0.823844i | \(-0.308175\pi\) | ||||
0.566817 | + | 0.823844i | \(0.308175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.2392 | + | 34.8572i | −1.32168 | + | 1.42901i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.90733i | − | 0.364553i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.3193 | 1.19795 | 0.598976 | − | 0.800767i | \(-0.295574\pi\) | ||||
0.598976 | + | 0.800767i | \(0.295574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1764 | + | 28.0184i | −0.659850 | + | 1.14289i | 0.320804 | + | 0.947146i | \(0.396047\pi\) |
−0.980654 | + | 0.195748i | \(0.937287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.516878 | −0.0210489 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.3368 | + | 6.92914i | −0.908122 | + | 0.281710i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4492 | − | 8.91963i | 0.627066 | − | 0.362036i | −0.152549 | − | 0.988296i | \(-0.548748\pi\) |
0.779615 | + | 0.626259i | \(0.215415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.0560 | + | 17.9302i | 1.25845 | + | 0.726567i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.83240 | − | 5.23689i | 0.195498 | − | 0.211862i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8288 | − | 23.9523i | 0.558542 | − | 0.967423i | −0.439077 | − | 0.898450i | \(-0.644694\pi\) |
0.997619 | − | 0.0689733i | \(-0.0219723\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.4641 | − | 5.41756i | 0.704221 | − | 0.218457i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8577 | + | 27.4664i | 0.638408 | + | 1.10575i | 0.985782 | + | 0.168028i | \(0.0537400\pi\) |
−0.347374 | + | 0.937727i | \(0.612927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 47.4958i | − | 1.90902i | −0.298186 | − | 0.954508i | \(-0.596382\pi\) | ||
0.298186 | − | 0.954508i | \(-0.403618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.5983 | − | 27.0170i | 0.625938 | − | 1.08416i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.23735i | 0.330022i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.7119 | + | 19.4457i | 0.628478 | + | 0.777828i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.96300 | + | 5.75214i | 0.397884 | + | 0.229718i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 50.5090i | − | 2.01392i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.47459 | + | 4.31546i | −0.297559 | + | 0.171796i | −0.641346 | − | 0.767252i | \(-0.721624\pi\) |
0.343787 | + | 0.939048i | \(0.388290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.58020 | + | 3.79908i | −0.261540 | + | 0.151000i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.3805 | − | 18.7919i | 0.689724 | − | 0.745733i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.01645 | + | 9.68450i | 0.119516 | + | 0.383714i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.76654 | + | 5.63871i | 0.386358 | + | 0.223064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.59556 | + | 13.1559i | 0.300007 | + | 0.519627i | 0.976137 | − | 0.217155i | \(-0.0696778\pi\) |
−0.676131 | + | 0.736782i | \(0.736344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.80445 | + | 11.7856i | 0.268341 | + | 0.464781i | 0.968434 | − | 0.249272i | \(-0.0801912\pi\) |
−0.700092 | + | 0.714052i | \(0.746858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.08687 | − | 40.1077i | 0.357795 | − | 1.57924i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.95677 | − | 4.01649i | −0.273499 | − | 0.157905i | 0.356978 | − | 0.934113i | \(-0.383807\pi\) |
−0.630477 | + | 0.776208i | \(0.717140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.1811 | −0.478148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.76914 | −0.265304 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.3286 | − | 18.6649i | −1.26512 | − | 0.730415i | −0.291055 | − | 0.956706i | \(-0.594006\pi\) |
−0.974060 | + | 0.226292i | \(0.927340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15806 | − | 9.52524i | 0.0843222 | − | 0.372182i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.98855 | − | 3.44428i | −0.0775809 | − | 0.134374i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.72275 | + | 6.44799i | 0.145018 | + | 0.251178i | 0.929380 | − | 0.369126i | \(-0.120343\pi\) |
−0.784362 | + | 0.620303i | \(0.787009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.5907 | + | 25.1671i | 1.69548 | + | 0.978888i | 0.949941 | + | 0.312429i | \(0.101142\pi\) |
0.745542 | + | 0.666459i | \(0.232191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.5087 | − | 26.5602i | 0.951840 | − | 1.03151i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.98766 | − | 8.63631i | 0.309748 | − | 0.334902i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.0896 | + | 21.4137i | −1.43612 | + | 0.829142i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.2979 | − | 12.2964i | 0.823426 | − | 0.475405i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.1251i | 1.74203i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7485 | + | 7.36034i | 0.491418 | + | 0.283720i | 0.725163 | − | 0.688578i | \(-0.241765\pi\) |
−0.233744 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.1519 | − | 25.4414i | 0.467725 | − | 0.979240i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.0788i | 0.848559i | 0.905531 | + | 0.424279i | \(0.139473\pi\) | ||||
−0.905531 | + | 0.424279i | \(0.860527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.83460 | + | 17.0340i | −0.377417 | + | 0.653706i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 21.3571i | − | 0.818405i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.9013 | − | 34.4700i | −0.761501 | − | 1.31896i | −0.942077 | − | 0.335397i | \(-0.891130\pi\) |
0.180576 | − | 0.983561i | \(-0.442204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.8013 | − | 3.66089i | 0.450904 | − | 0.139875i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.96171 | − | 5.12983i | 0.112996 | − | 0.195715i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.9942 | + | 13.8361i | 0.571234 | + | 0.527113i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.6907 | − | 20.0287i | −1.31970 | − | 0.761927i | −0.336017 | − | 0.941856i | \(-0.609080\pi\) |
−0.983680 | + | 0.179928i | \(0.942413\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.2206 | − | 5.90089i | 0.388250 | − | 0.224156i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.1240 | − | 7.48352i | 0.915074 | − | 0.283866i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.4833 | −1.41978 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.57413 | + | 4.45853i | −0.0973627 | + | 0.168637i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1911 | 0.460452 | 0.230226 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230226 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5142i | 0.471983i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.43725 | − | 4.79758i | 0.167117 | − | 0.180687i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.7432 | −1.98361 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7237 | + | 10.8101i | −0.703183 | + | 0.405983i | −0.808532 | − | 0.588452i | \(-0.799737\pi\) |
0.105349 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.52531 | + | 4.37397i | 0.0947066 | + | 0.164037i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.04214 | − | 7.00119i | 0.151379 | − | 0.262197i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.95288 | − | 37.2305i | −0.110431 | − | 1.39234i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.1336 | + | 24.4801i | −0.527829 | + | 0.914227i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.39194 | − | 2.41091i | −0.0519105 | − | 0.0899117i | 0.838903 | − | 0.544282i | \(-0.183198\pi\) |
−0.890813 | + | 0.454370i | \(0.849864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.7552 | + | 15.4471i | −0.996415 | + | 0.575281i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.0343 | −1.22856 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.9106 | + | 21.9061i | −1.18513 | + | 0.813573i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5075i | 0.834756i | 0.908733 | + | 0.417378i | \(0.137051\pi\) | ||||
−0.908733 | + | 0.417378i | \(0.862949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.8131 | −1.10419 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.1510 | + | 73.0077i | −1.55901 | + | 2.70029i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.58058 | 0.316931 | 0.158465 | − | 0.987365i | \(-0.449345\pi\) | ||||
0.158465 | + | 0.987365i | \(0.449345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75614 | + | 8.88471i | 0.101662 | + | 0.327717i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.54968 | + | 1.47206i | −0.0939187 | + | 0.0542240i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.98591 | − | 2.87861i | −0.183410 | − | 0.105892i | 0.405484 | − | 0.914102i | \(-0.367103\pi\) |
−0.588894 | + | 0.808211i | \(0.700436\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.07234 | + | 6.58061i | −0.223073 | + | 0.241745i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.3320 | + | 23.0918i | −0.489105 | + | 0.847154i | −0.999921 | − | 0.0125354i | \(-0.996010\pi\) |
0.510817 | + | 0.859690i | \(0.329343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.02238 | − | 12.9666i | −0.147369 | − | 0.475059i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.35440 | + | 2.34590i | 0.0495550 | + | 0.0858318i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 12.7723i | − | 0.466689i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8390 | − | 37.8262i | 0.796916 | − | 1.38030i | −0.124699 | − | 0.992195i | \(-0.539797\pi\) |
0.921615 | − | 0.388104i | \(-0.126870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 24.7627i | − | 0.902404i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.0178 | − | 7.48058i | −1.20164 | − | 0.272246i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.9105 | − | 16.1141i | −1.01442 | − | 0.585678i | −0.101941 | − | 0.994790i | \(-0.532505\pi\) |
−0.912484 | + | 0.409112i | \(0.865838\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 37.8977i | − | 1.37560i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4017 | − | 6.00543i | 0.377062 | − | 0.217697i | −0.299477 | − | 0.954103i | \(-0.596812\pi\) |
0.676539 | + | 0.736407i | \(0.263479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.6765 | − | 18.2884i | 1.14677 | − | 0.662086i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.36978 | + | 9.04946i | −0.302610 | + | 0.327184i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.08430 | − | 9.24902i | 0.0752596 | − | 0.333963i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.3628 | − | 25.0355i | −1.56370 | − | 0.902804i | −0.996877 | − | 0.0789667i | \(-0.974838\pi\) |
−0.566826 | − | 0.823838i | \(-0.691829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6590 | − | 20.1940i | −0.419888 | − | 0.727268i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.3030 | − | 42.0940i | −0.874118 | − | 1.51402i | −0.857700 | − | 0.514151i | \(-0.828107\pi\) |
−0.0164180 | − | 0.999865i | \(-0.505226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.14903 | − | 6.59288i | 0.113117 | − | 0.236823i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29.8937 | − | 17.2592i | −1.07243 | − | 0.619169i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.28695 | 0.332740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.2359 | 2.29854 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.8038 | + | 21.8261i | 1.35100 | + | 0.780000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.1370 | + | 9.54665i | 1.50394 | + | 0.340734i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3298 | + | 35.2122i | 0.724679 | + | 1.25518i | 0.959106 | + | 0.283047i | \(0.0913452\pi\) |
−0.234427 | + | 0.972134i | \(0.575321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.08769 | + | 15.7403i | 0.323530 | + | 0.560371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3656 | − | 5.98457i | −0.368558 | − | 0.212787i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.2633 | − | 7.72134i | −1.21672 | − | 0.274193i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.7364 | + | 12.7047i | 0.487180 | + | 0.450590i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.2116 | − | 9.93712i | 0.609666 | − | 0.351991i | −0.163169 | − | 0.986598i | \(-0.552171\pi\) |
0.772835 | + | 0.634607i | \(0.218838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6015 | + | 6.69815i | −0.410433 | + | 0.236964i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.13854i | 0.0755616i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.6185 | − | 11.3267i | −0.692321 | − | 0.399712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.7950 | − | 8.56290i | −1.33210 | − | 0.301803i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 20.1851i | − | 0.710551i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.94549 | − | 5.10175i | 0.103558 | − | 0.179368i | −0.809590 | − | 0.586996i | \(-0.800311\pi\) |
0.913148 | + | 0.407628i | \(0.133644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.4566i | 1.28016i | 0.768306 | + | 0.640082i | \(0.221100\pi\) | ||||
−0.768306 | + | 0.640082i | \(0.778900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.31956 | + | 2.28555i | 0.0462790 | + | 0.0801576i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.19110 | + | 0.369492i | −0.0417223 | + | 0.0129427i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4434 | − | 18.0886i | 0.365369 | − | 0.632838i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.73167 | + | 8.77019i | 0.0954522 | + | 0.306455i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.1856 | − | 18.0050i | −1.08838 | − | 0.628379i | −0.155238 | − | 0.987877i | \(-0.549615\pi\) |
−0.933146 | + | 0.359498i | \(0.882948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.19441 | + | 2.99899i | −0.181066 | + | 0.104538i | −0.587793 | − | 0.809011i | \(-0.700003\pi\) |
0.406728 | + | 0.913549i | \(0.366670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.66878 | − | 34.1467i | −0.0929151 | − | 1.18884i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.98279 | −0.347135 | −0.173568 | − | 0.984822i | \(-0.555530\pi\) | ||||
−0.173568 | + | 0.984822i | \(0.555530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1400 | + | 40.0797i | −0.803685 | + | 1.39202i | 0.113490 | + | 0.993539i | \(0.463797\pi\) |
−0.917175 | + | 0.398485i | \(0.869536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.9807 | 1.00533 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 19.0693i | − | 0.660712i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3903 | − | 9.60994i | −0.359572 | − | 0.332566i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.23995 | −0.284814 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.3449 | + | 7.12733i | −0.426193 | + | 0.246063i | −0.697724 | − | 0.716367i | \(-0.745804\pi\) |
0.271530 | + | 0.962430i | \(0.412470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4633 | − | 26.7833i | −0.533219 | − | 0.923562i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.3613 | + | 23.1425i | −0.460189 | + | 0.797071i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.7742 | + | 4.12840i | 0.989864 | + | 0.142021i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.3819 | − | 28.3743i | 0.562890 | − | 0.974953i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.38805 | − | 9.33238i | −0.184917 | − | 0.320286i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7016 | − | 20.6123i | 1.22384 | − | 0.706582i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1321 | −0.963225 | −0.481613 | − | 0.876384i | \(-0.659949\pi\) | ||||
−0.481613 | + | 0.876384i | \(0.659949\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.07372 | − | 2.24211i | 0.0709196 | − | 0.0766787i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 25.1192i | − | 0.858054i | −0.903292 | − | 0.429027i | \(-0.858857\pi\) | ||
0.903292 | − | 0.429027i | \(-0.141143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.9680 | 1.87549 | 0.937743 | − | 0.347331i | \(-0.112912\pi\) | ||||
0.937743 | + | 0.347331i | \(0.112912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.8082 | + | 22.1845i | −0.436504 | + | 0.756047i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.9445 | 1.93841 | 0.969206 | − | 0.246252i | \(-0.0791990\pi\) | ||||
0.969206 | + | 0.246252i | \(0.0791990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.06576 | + | 16.3300i | 0.172241 | + | 0.555238i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.0692 | + | 21.4019i | −1.25894 | + | 0.726847i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.9140 | + | 14.3841i | 0.845150 | + | 0.487947i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.681453 | − | 2.18784i | −0.0230901 | − | 0.0741323i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.55321 | + | 4.42228i | −0.0864130 | + | 0.149672i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.6571 | − | 5.05382i | −1.17163 | − | 0.170850i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.56089 | + | 13.0958i | 0.255313 | + | 0.442215i | 0.964980 | − | 0.262322i | \(-0.0844882\pi\) |
−0.709667 | + | 0.704537i | \(0.751155\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.1658i | 0.612719i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8443 | − | 27.4431i | 0.533807 | − | 0.924580i | −0.465413 | − | 0.885093i | \(-0.654094\pi\) |
0.999220 | − | 0.0394869i | \(-0.0125723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.8901i | − | 0.904924i | −0.891784 | − | 0.452462i | \(-0.850546\pi\) | ||
0.891784 | − | 0.452462i | \(-0.149454\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.92123 | − | 8.47995i | 0.0645815 | − | 0.285050i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.2524 | − | 9.96070i | −0.579280 | − | 0.334448i | 0.181567 | − | 0.983379i | \(-0.441883\pi\) |
−0.760847 | + | 0.648931i | \(0.775216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.8603i | 1.20272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.6644 | + | 13.6627i | −0.792788 | + | 0.457716i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.87442 | − | 1.65955i | 0.0961889 | − | 0.0555347i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.47660 | + | 6.91506i | 0.249915 | + | 0.231145i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.7756 | + | 6.48467i | 0.960789 | + | 0.216517i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.79648 | + | 5.65600i | 0.326731 | + | 0.188638i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.1781 | − | 33.2175i | −0.638916 | − | 1.10663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.8064 | + | 49.8942i | 0.958618 | + | 1.66037i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.83645 | − | 16.9334i | 0.127528 | − | 0.562884i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.4739 | + | 22.7903i | 1.31071 | + | 0.756739i | 0.982214 | − | 0.187766i | \(-0.0601247\pi\) |
0.328497 | + | 0.944505i | \(0.393458\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6929 | −0.454165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.88950 | 0.261391 | 0.130695 | − | 0.991423i | \(-0.458279\pi\) | ||||
0.130695 | + | 0.991423i | \(0.458279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.3621 | + | 7.71464i | 0.442223 | + | 0.255317i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.4142 | − | 7.11727i | −1.03852 | − | 0.235290i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.84128 | + | 11.8495i | 0.225919 | + | 0.391303i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8457 | + | 37.8379i | 0.720624 | + | 1.24816i | 0.960750 | + | 0.277415i | \(0.0894777\pi\) |
−0.240127 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.8934 | − | 23.0325i | −1.31453 | − | 0.758945i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9914 | + | 48.7740i | −0.361786 | + | 1.60542i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.7164 | − | 21.0863i | 1.00995 | − | 0.693314i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.94604 | + | 4.01030i | −0.228138 | + | 0.131716i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.8952 | − | 14.3732i | 0.816785 | − | 0.471571i | −0.0325218 | − | 0.999471i | \(-0.510354\pi\) |
0.849306 | + | 0.527900i | \(0.177021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.72465i | 0.154844i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.889017 | − | 0.513274i | −0.0291051 | − | 0.0168038i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.5142 | + | 68.4767i | −0.507368 | + | 2.23943i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 43.1084i | − | 1.40829i | −0.710056 | − | 0.704145i | \(-0.751330\pi\) | ||
0.710056 | − | 0.704145i | \(-0.248670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7908 | + | 18.6902i | −0.352145 | + | 0.609932i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8675i | 0.549866i | 0.961463 | + | 0.274933i | \(0.0886557\pi\) | ||||
−0.961463 | + | 0.274933i | \(0.911344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.2967 | − | 26.4946i | −0.498128 | − | 0.862784i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.7029 | + | 37.7256i | 0.380695 | + | 1.22721i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9396 | − | 29.3402i | 0.550461 | − | 0.953427i | −0.447780 | − | 0.894144i | \(-0.647785\pi\) |
0.998241 | − | 0.0592833i | \(-0.0188815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9573 | − | 12.9581i | 0.388149 | − | 0.420638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.6513 | − | 10.7684i | −0.604811 | − | 0.349188i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3445 | + | 10.5912i | −0.594236 | + | 0.343083i | −0.766771 | − | 0.641921i | \(-0.778138\pi\) |
0.172534 | + | 0.985003i | \(0.444804\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.4317 | − | 7.57898i | 0.790590 | − | 0.245250i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.0288 | 1.71418 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.65510 | + | 14.9911i | −0.279488 | + | 0.484087i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8647 | 0.931119 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3.31588i | − | 0.106853i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.19174 | + | 4.80181i | 0.167128 | + | 0.154576i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.6488 | −0.953442 | −0.476721 | − | 0.879055i | \(-0.658175\pi\) | ||||
−0.476721 | + | 0.879055i | \(0.658175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5784 | − | 8.41682i | 0.468325 | − | 0.270387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.4640 | − | 19.8562i | −0.367897 | − | 0.637216i | 0.621340 | − | 0.783541i | \(-0.286589\pi\) |
−0.989236 | + | 0.146326i | \(0.953255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.6926 | + | 30.6445i | −0.567199 | + | 0.982417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.3841 | + | 3.81644i | 0.844968 | + | 0.122224i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.3631 | + | 47.3942i | −0.875423 | + | 1.51628i | −0.0191106 | + | 0.999817i | \(0.506083\pi\) |
−0.856312 | + | 0.516459i | \(0.827250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.09053 | + | 10.5491i | 0.194654 | + | 0.337151i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.22370 | − | 4.74795i | 0.262562 | − | 0.151590i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.1492 | 1.15298 | 0.576490 | − | 0.817104i | \(-0.304422\pi\) | ||||
0.576490 | + | 0.817104i | \(0.304422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.0162 | + | 35.1609i | 1.21130 | + | 1.12032i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.15517i | 0.291412i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.8061 | −2.18791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0324 | − | 27.7690i | 0.509287 | − | 0.882111i | −0.490655 | − | 0.871354i | \(-0.663242\pi\) |
0.999942 | − | 0.0107574i | \(-0.00342424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8894 | 0.472502 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.8642 | + | 3.99063i | −0.407824 | + | 0.126511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8308 | − | 14.9134i | 0.818070 | − | 0.472313i | −0.0316805 | − | 0.999498i | \(-0.510086\pi\) |
0.849750 | + | 0.527185i | \(0.176753\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.3891 | − | 21.0093i | −1.15130 | − | 0.664703i |
(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 | 260.2.z.a.69.3 | yes | 16 | |
3.2 | odd | 2 | 2340.2.cr.a.1369.5 | 16 | |||
4.3 | odd | 2 | 1040.2.df.d.849.6 | 16 | |||
5.2 | odd | 4 | 1300.2.y.e.901.3 | 16 | |||
5.3 | odd | 4 | 1300.2.y.e.901.6 | 16 | |||
5.4 | even | 2 | inner | 260.2.z.a.69.6 | yes | 16 | |
13.4 | even | 6 | 3380.2.d.d.1689.12 | 16 | |||
13.6 | odd | 12 | 3380.2.c.e.2029.12 | 16 | |||
13.7 | odd | 12 | 3380.2.c.e.2029.11 | 16 | |||
13.9 | even | 3 | 3380.2.d.d.1689.11 | 16 | |||
13.10 | even | 6 | inner | 260.2.z.a.49.6 | yes | 16 | |
15.14 | odd | 2 | 2340.2.cr.a.1369.4 | 16 | |||
20.19 | odd | 2 | 1040.2.df.d.849.3 | 16 | |||
39.23 | odd | 6 | 2340.2.cr.a.829.4 | 16 | |||
52.23 | odd | 6 | 1040.2.df.d.49.3 | 16 | |||
65.4 | even | 6 | 3380.2.d.d.1689.5 | 16 | |||
65.9 | even | 6 | 3380.2.d.d.1689.6 | 16 | |||
65.19 | odd | 12 | 3380.2.c.e.2029.6 | 16 | |||
65.23 | odd | 12 | 1300.2.y.e.101.6 | 16 | |||
65.49 | even | 6 | inner | 260.2.z.a.49.3 | ✓ | 16 | |
65.59 | odd | 12 | 3380.2.c.e.2029.5 | 16 | |||
65.62 | odd | 12 | 1300.2.y.e.101.3 | 16 | |||
195.179 | odd | 6 | 2340.2.cr.a.829.5 | 16 | |||
260.179 | odd | 6 | 1040.2.df.d.49.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.z.a.49.3 | ✓ | 16 | 65.49 | even | 6 | inner | |
260.2.z.a.49.6 | yes | 16 | 13.10 | even | 6 | inner | |
260.2.z.a.69.3 | yes | 16 | 1.1 | even | 1 | trivial | |
260.2.z.a.69.6 | yes | 16 | 5.4 | even | 2 | inner | |
1040.2.df.d.49.3 | 16 | 52.23 | odd | 6 | |||
1040.2.df.d.49.6 | 16 | 260.179 | odd | 6 | |||
1040.2.df.d.849.3 | 16 | 20.19 | odd | 2 | |||
1040.2.df.d.849.6 | 16 | 4.3 | odd | 2 | |||
1300.2.y.e.101.3 | 16 | 65.62 | odd | 12 | |||
1300.2.y.e.101.6 | 16 | 65.23 | odd | 12 | |||
1300.2.y.e.901.3 | 16 | 5.2 | odd | 4 | |||
1300.2.y.e.901.6 | 16 | 5.3 | odd | 4 | |||
2340.2.cr.a.829.4 | 16 | 39.23 | odd | 6 | |||
2340.2.cr.a.829.5 | 16 | 195.179 | odd | 6 | |||
2340.2.cr.a.1369.4 | 16 | 15.14 | odd | 2 | |||
2340.2.cr.a.1369.5 | 16 | 3.2 | odd | 2 | |||
3380.2.c.e.2029.5 | 16 | 65.59 | odd | 12 | |||
3380.2.c.e.2029.6 | 16 | 65.19 | odd | 12 | |||
3380.2.c.e.2029.11 | 16 | 13.7 | odd | 12 | |||
3380.2.c.e.2029.12 | 16 | 13.6 | odd | 12 | |||
3380.2.d.d.1689.5 | 16 | 65.4 | even | 6 | |||
3380.2.d.d.1689.6 | 16 | 65.9 | even | 6 | |||
3380.2.d.d.1689.11 | 16 | 13.9 | even | 3 | |||
3380.2.d.d.1689.12 | 16 | 13.4 | even | 6 |