Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (of order \(2\), degree \(1\), 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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.3 | ||
Root | \(-0.282359 - 0.282359i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.p.1999.8 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.70518 | − | 1.44650i | −0.762579 | − | 0.646895i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.83227i | − | 0.692532i | −0.938136 | − | 0.346266i | \(-0.887449\pi\) | ||
0.938136 | − | 0.346266i | \(-0.112551\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.44650 | + | 1.70518i | −0.457424 | + | 0.539225i | ||||
\(11\) | −4.19017 | −1.26338 | −0.631692 | − | 0.775219i | \(-0.717639\pi\) | ||||
−0.631692 | + | 0.775219i | \(0.717639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.369454i | 0.102468i | 0.998687 | + | 0.0512340i | \(0.0163154\pi\) | ||||
−0.998687 | + | 0.0512340i | \(0.983685\pi\) | |||||||
\(14\) | −1.83227 | −0.489694 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.08317i | 1.23285i | 0.787414 | + | 0.616425i | \(0.211420\pi\) | ||||
−0.787414 | + | 0.616425i | \(0.788580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.55963 | −0.816634 | −0.408317 | − | 0.912840i | \(-0.633884\pi\) | ||||
−0.408317 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(20\) | 1.70518 | + | 1.44650i | 0.381290 | + | 0.323447i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.19017i | 0.893348i | ||||||||
\(23\) | 5.62036i | 1.17193i | 0.810338 | + | 0.585963i | \(0.199284\pi\) | ||||
−0.810338 | + | 0.585963i | \(0.800716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.815273 | + | 4.93309i | 0.163055 | + | 0.986617i | ||||
\(26\) | 0.369454 | 0.0724559 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.83227i | 0.346266i | ||||||||
\(29\) | 1.20681 | 0.224100 | 0.112050 | − | 0.993703i | \(-0.464258\pi\) | ||||
0.112050 | + | 0.993703i | \(0.464258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1030 | 1.81455 | 0.907276 | − | 0.420535i | \(-0.138158\pi\) | ||||
0.907276 | + | 0.420535i | \(0.138158\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.08317 | 0.871757 | ||||||||
\(35\) | −2.65038 | + | 3.12434i | −0.447995 | + | 0.528111i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 3.55963i | 0.577447i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.44650 | − | 1.70518i | 0.228712 | − | 0.269613i | ||||
\(41\) | 8.01447 | 1.25165 | 0.625825 | − | 0.779964i | \(-0.284762\pi\) | ||||
0.625825 | + | 0.779964i | \(0.284762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27264i | 0.346575i | 0.984871 | + | 0.173287i | \(0.0554389\pi\) | ||||
−0.984871 | + | 0.173287i | \(0.944561\pi\) | |||||||
\(44\) | 4.19017 | 0.631692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.62036 | 0.828677 | ||||||||
\(47\) | − | 10.9154i | − | 1.59218i | −0.605178 | − | 0.796090i | \(-0.706898\pi\) | ||
0.605178 | − | 0.796090i | \(-0.293102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.64280 | 0.520400 | ||||||||
\(50\) | 4.93309 | − | 0.815273i | 0.697644 | − | 0.115297i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.369454i | − | 0.0512340i | ||||||
\(53\) | − | 9.94355i | − | 1.36585i | −0.730488 | − | 0.682926i | \(-0.760707\pi\) | ||
0.730488 | − | 0.682926i | \(-0.239293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.14499 | + | 6.06108i | 0.963431 | + | 0.817276i | ||||
\(56\) | 1.83227 | 0.244847 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.20681i | − | 0.158463i | ||||||
\(59\) | −5.34563 | −0.695941 | −0.347971 | − | 0.937505i | \(-0.613129\pi\) | ||||
−0.347971 | + | 0.937505i | \(0.613129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.79428 | −1.25403 | −0.627015 | − | 0.779008i | \(-0.715723\pi\) | ||||
−0.627015 | + | 0.779008i | \(0.715723\pi\) | |||||||
\(62\) | − | 10.1030i | − | 1.28308i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.534415 | − | 0.629985i | 0.0662861 | − | 0.0781401i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.85073i | 0.226103i | 0.993589 | + | 0.113052i | \(0.0360625\pi\) | ||||
−0.993589 | + | 0.113052i | \(0.963937\pi\) | |||||||
\(68\) | − | 5.08317i | − | 0.616425i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.12434 | + | 2.65038i | 0.373431 | + | 0.316780i | ||||
\(71\) | −2.86038 | −0.339464 | −0.169732 | − | 0.985490i | \(-0.554290\pi\) | ||||
−0.169732 | + | 0.985490i | \(0.554290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.09942i | 0.947966i | 0.880534 | + | 0.473983i | \(0.157184\pi\) | ||||
−0.880534 | + | 0.473983i | \(0.842816\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.55963 | 0.408317 | ||||||||
\(77\) | 7.67751i | 0.874934i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.06361 | −0.682209 | −0.341105 | − | 0.940025i | \(-0.610801\pi\) | ||||
−0.341105 | + | 0.940025i | \(0.610801\pi\) | |||||||
\(80\) | −1.70518 | − | 1.44650i | −0.190645 | − | 0.161724i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 8.01447i | − | 0.885050i | ||||||
\(83\) | − | 8.93200i | − | 0.980414i | −0.871606 | − | 0.490207i | \(-0.836921\pi\) | ||
0.871606 | − | 0.490207i | \(-0.163079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.35281 | − | 8.66772i | 0.797524 | − | 0.940146i | ||||
\(86\) | 2.27264 | 0.245065 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.19017i | − | 0.446674i | ||||||
\(89\) | 11.4773 | 1.21659 | 0.608295 | − | 0.793711i | \(-0.291854\pi\) | ||||
0.608295 | + | 0.793711i | \(0.291854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.676938 | 0.0709624 | ||||||||
\(92\) | − | 5.62036i | − | 0.585963i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.9154 | −1.12584 | ||||||||
\(95\) | 6.06980 | + | 5.14900i | 0.622748 | + | 0.528276i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.05864i | 0.615162i | 0.951522 | + | 0.307581i | \(0.0995195\pi\) | ||||
−0.951522 | + | 0.307581i | \(0.900480\pi\) | |||||||
\(98\) | − | 3.64280i | − | 0.367978i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.815273 | − | 4.93309i | −0.0815273 | − | 0.493309i | ||||
\(101\) | −4.96528 | −0.494064 | −0.247032 | − | 0.969007i | \(-0.579455\pi\) | ||||
−0.247032 | + | 0.969007i | \(0.579455\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.33338i | 0.722579i | 0.932454 | + | 0.361289i | \(0.117663\pi\) | ||||
−0.932454 | + | 0.361289i | \(0.882337\pi\) | |||||||
\(104\) | −0.369454 | −0.0362279 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.94355 | −0.965803 | ||||||||
\(107\) | 8.21182i | 0.793867i | 0.917847 | + | 0.396933i | \(0.129926\pi\) | ||||
−0.917847 | + | 0.396933i | \(0.870074\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.5503 | 1.96836 | 0.984179 | − | 0.177175i | \(-0.0566960\pi\) | ||||
0.984179 | + | 0.177175i | \(0.0566960\pi\) | |||||||
\(110\) | 6.06108 | − | 7.14499i | 0.577902 | − | 0.681248i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.83227i | − | 0.173133i | ||||||
\(113\) | − | 0.652984i | − | 0.0614276i | −0.999528 | − | 0.0307138i | \(-0.990222\pi\) | ||
0.999528 | − | 0.0307138i | \(-0.00977804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.12985 | − | 9.58372i | 0.758113 | − | 0.893686i | ||||
\(116\) | −1.20681 | −0.112050 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.34563i | 0.492105i | ||||||||
\(119\) | 9.31373 | 0.853788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.55754 | 0.596140 | ||||||||
\(122\) | 9.79428i | 0.886733i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.1030 | −0.907276 | ||||||||
\(125\) | 5.74552 | − | 9.59109i | 0.513895 | − | 0.857853i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.2856i | − | 1.71132i | −0.517539 | − | 0.855660i | \(-0.673152\pi\) | ||
0.517539 | − | 0.855660i | \(-0.326848\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.629985 | − | 0.534415i | −0.0552534 | − | 0.0468713i | ||||
\(131\) | 8.82072 | 0.770670 | 0.385335 | − | 0.922777i | \(-0.374086\pi\) | ||||
0.385335 | + | 0.922777i | \(0.374086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.52218i | 0.565545i | ||||||||
\(134\) | 1.85073 | 0.159879 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.08317 | −0.435878 | ||||||||
\(137\) | − | 4.66126i | − | 0.398239i | −0.979975 | − | 0.199119i | \(-0.936192\pi\) | ||
0.979975 | − | 0.199119i | \(-0.0638081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4050 | −1.39145 | −0.695727 | − | 0.718306i | \(-0.744918\pi\) | ||||
−0.695727 | + | 0.718306i | \(0.744918\pi\) | |||||||
\(140\) | 2.65038 | − | 3.12434i | 0.223998 | − | 0.264055i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.86038i | 0.240037i | ||||||||
\(143\) | − | 1.54808i | − | 0.129457i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.05784 | − | 1.74566i | −0.170894 | − | 0.144969i | ||||
\(146\) | 8.09942 | 0.670313 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −5.86259 | −0.480282 | −0.240141 | − | 0.970738i | \(-0.577194\pi\) | ||||
−0.240141 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1460 | 1.06981 | 0.534903 | − | 0.844913i | \(-0.320348\pi\) | ||||
0.534903 | + | 0.844913i | \(0.320348\pi\) | |||||||
\(152\) | − | 3.55963i | − | 0.288724i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.67751 | 0.618672 | ||||||||
\(155\) | −17.2274 | − | 14.6140i | −1.38374 | − | 1.17382i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.33629i | − | 0.585500i | −0.956189 | − | 0.292750i | \(-0.905430\pi\) | ||
0.956189 | − | 0.292750i | \(-0.0945704\pi\) | |||||||
\(158\) | 6.06361i | 0.482395i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.44650 | + | 1.70518i | −0.114356 | + | 0.134806i | ||||
\(161\) | 10.2980 | 0.811596 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7968i | 1.47228i | 0.676831 | + | 0.736138i | \(0.263353\pi\) | ||||
−0.676831 | + | 0.736138i | \(0.736647\pi\) | |||||||
\(164\) | −8.01447 | −0.625825 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.93200 | −0.693257 | ||||||||
\(167\) | 5.92772i | 0.458700i | 0.973344 | + | 0.229350i | \(0.0736601\pi\) | ||||
−0.973344 | + | 0.229350i | \(0.926340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8635 | 0.989500 | ||||||||
\(170\) | −8.66772 | − | 7.35281i | −0.664784 | − | 0.563935i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.27264i | − | 0.173287i | ||||||
\(173\) | 5.78242i | 0.439629i | 0.975542 | + | 0.219815i | \(0.0705453\pi\) | ||||
−0.975542 | + | 0.219815i | \(0.929455\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.03873 | − | 1.49380i | 0.683264 | − | 0.112921i | ||||
\(176\) | −4.19017 | −0.315846 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 11.4773i | − | 0.860259i | ||||||
\(179\) | 7.13581 | 0.533355 | 0.266678 | − | 0.963786i | \(-0.414074\pi\) | ||||
0.266678 | + | 0.963786i | \(0.414074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5365 | 0.857503 | 0.428752 | − | 0.903422i | \(-0.358954\pi\) | ||||
0.428752 | + | 0.903422i | \(0.358954\pi\) | |||||||
\(182\) | − | 0.676938i | − | 0.0501780i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.62036 | −0.414338 | ||||||||
\(185\) | 1.44650 | − | 1.70518i | 0.106349 | − | 0.125367i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.2994i | − | 1.55756i | ||||||
\(188\) | 10.9154i | 0.796090i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.14900 | − | 6.06980i | 0.373548 | − | 0.440350i | ||||
\(191\) | 20.6048 | 1.49091 | 0.745456 | − | 0.666555i | \(-0.232232\pi\) | ||||
0.745456 | + | 0.666555i | \(0.232232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.1663i | 1.88349i | 0.336321 | + | 0.941747i | \(0.390817\pi\) | ||||
−0.336321 | + | 0.941747i | \(0.609183\pi\) | |||||||
\(194\) | 6.05864 | 0.434985 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.64280 | −0.260200 | ||||||||
\(197\) | − | 14.6067i | − | 1.04069i | −0.853957 | − | 0.520343i | \(-0.825804\pi\) | ||
0.853957 | − | 0.520343i | \(-0.174196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.81275 | −0.412055 | −0.206027 | − | 0.978546i | \(-0.566054\pi\) | ||||
−0.206027 | + | 0.978546i | \(0.566054\pi\) | |||||||
\(200\) | −4.93309 | + | 0.815273i | −0.348822 | + | 0.0576485i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.96528i | 0.349356i | ||||||||
\(203\) | − | 2.21121i | − | 0.155196i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6661 | − | 11.5929i | −0.954482 | − | 0.809685i | ||||
\(206\) | 7.33338 | 0.510940 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.369454i | 0.0256170i | ||||||||
\(209\) | 14.9154 | 1.03172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0976 | 1.10821 | 0.554104 | − | 0.832448i | \(-0.313061\pi\) | ||||
0.554104 | + | 0.832448i | \(0.313061\pi\) | |||||||
\(212\) | 9.94355i | 0.682926i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.21182 | 0.561349 | ||||||||
\(215\) | 3.28738 | − | 3.87526i | 0.224197 | − | 0.264291i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 18.5114i | − | 1.25664i | ||||||
\(218\) | − | 20.5503i | − | 1.39184i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.14499 | − | 6.06108i | −0.481715 | − | 0.408638i | ||||
\(221\) | −1.87800 | −0.126328 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.3608i | − | 1.69828i | −0.528164 | − | 0.849142i | \(-0.677119\pi\) | ||
0.528164 | − | 0.849142i | \(-0.322881\pi\) | |||||||
\(224\) | −1.83227 | −0.122423 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.652984 | −0.0434359 | ||||||||
\(227\) | 5.57339i | 0.369919i | 0.982746 | + | 0.184960i | \(0.0592154\pi\) | ||||
−0.982746 | + | 0.184960i | \(0.940785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.02035 | −0.596081 | −0.298041 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298041 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(230\) | −9.58372 | − | 8.12985i | −0.631932 | − | 0.536067i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.20681i | 0.0792313i | ||||||||
\(233\) | 11.8100i | 0.773696i | 0.922144 | + | 0.386848i | \(0.126436\pi\) | ||||
−0.922144 | + | 0.386848i | \(0.873564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7892 | + | 18.6128i | −1.02997 | + | 1.21416i | ||||
\(236\) | 5.34563 | 0.347971 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 9.31373i | − | 0.603719i | ||||||
\(239\) | 0.907160 | 0.0586793 | 0.0293396 | − | 0.999569i | \(-0.490660\pi\) | ||||
0.0293396 | + | 0.999569i | \(0.490660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.15616 | −0.267722 | −0.133861 | − | 0.991000i | \(-0.542738\pi\) | ||||
−0.133861 | + | 0.991000i | \(0.542738\pi\) | |||||||
\(242\) | − | 6.55754i | − | 0.421534i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.79428 | 0.627015 | ||||||||
\(245\) | −6.21162 | − | 5.26931i | −0.396846 | − | 0.336644i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.31512i | − | 0.0836789i | ||||||
\(248\) | 10.1030i | 0.641541i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.59109 | − | 5.74552i | −0.606594 | − | 0.363379i | ||||
\(251\) | −9.31888 | −0.588203 | −0.294101 | − | 0.955774i | \(-0.595020\pi\) | ||||
−0.294101 | + | 0.955774i | \(0.595020\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 23.5503i | − | 1.48059i | ||||||
\(254\) | −19.2856 | −1.21009 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6312i | 0.850294i | 0.905124 | + | 0.425147i | \(0.139778\pi\) | ||||
−0.905124 | + | 0.425147i | \(0.860222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.83227 | 0.113852 | ||||||||
\(260\) | −0.534415 | + | 0.629985i | −0.0331430 | + | 0.0390700i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 8.82072i | − | 0.544946i | ||||||
\(263\) | 27.2170i | 1.67827i | 0.543921 | + | 0.839137i | \(0.316939\pi\) | ||||
−0.543921 | + | 0.839137i | \(0.683061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.3833 | + | 16.9555i | −0.883562 | + | 1.04157i | ||||
\(266\) | 6.52218 | 0.399901 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 1.85073i | − | 0.113052i | ||||||
\(269\) | 23.0550 | 1.40569 | 0.702845 | − | 0.711343i | \(-0.251913\pi\) | ||||
0.702845 | + | 0.711343i | \(0.251913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.9320 | 1.39302 | 0.696510 | − | 0.717547i | \(-0.254735\pi\) | ||||
0.696510 | + | 0.717547i | \(0.254735\pi\) | |||||||
\(272\) | 5.08317i | 0.308213i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.66126 | −0.281597 | ||||||||
\(275\) | −3.41613 | − | 20.6705i | −0.206001 | − | 1.24648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.7534i | − | 0.706192i | −0.935587 | − | 0.353096i | \(-0.885129\pi\) | ||
0.935587 | − | 0.353096i | \(-0.114871\pi\) | |||||||
\(278\) | 16.4050i | 0.983906i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.12434 | − | 2.65038i | −0.186715 | − | 0.158390i | ||||
\(281\) | 29.0962 | 1.73573 | 0.867865 | − | 0.496799i | \(-0.165492\pi\) | ||||
0.867865 | + | 0.496799i | \(0.165492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1829i | 0.605311i | 0.953100 | + | 0.302655i | \(0.0978731\pi\) | ||||
−0.953100 | + | 0.302655i | \(0.902127\pi\) | |||||||
\(284\) | 2.86038 | 0.169732 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.54808 | −0.0915396 | ||||||||
\(287\) | − | 14.6846i | − | 0.866807i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.83864 | −0.519920 | ||||||||
\(290\) | −1.74566 | + | 2.05784i | −0.102509 | + | 0.120840i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 8.09942i | − | 0.473983i | ||||||
\(293\) | 18.1243i | 1.05883i | 0.848363 | + | 0.529415i | \(0.177589\pi\) | ||||
−0.848363 | + | 0.529415i | \(0.822411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.11525 | + | 7.73245i | 0.530711 | + | 0.450201i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.86259i | 0.339611i | ||||||||
\(299\) | −2.07646 | −0.120085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.16409 | 0.240014 | ||||||||
\(302\) | − | 13.1460i | − | 0.756467i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.55963 | −0.204159 | ||||||||
\(305\) | 16.7010 | + | 14.1674i | 0.956297 | + | 0.811225i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.15561i | − | 0.351319i | −0.984451 | − | 0.175660i | \(-0.943794\pi\) | ||
0.984451 | − | 0.175660i | \(-0.0562058\pi\) | |||||||
\(308\) | − | 7.67751i | − | 0.437467i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.6140 | + | 17.2274i | −0.830019 | + | 0.978452i | ||||
\(311\) | 29.4512 | 1.67002 | 0.835011 | − | 0.550234i | \(-0.185461\pi\) | ||||
0.835011 | + | 0.550234i | \(0.185461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.0102i | − | 0.735378i | −0.929949 | − | 0.367689i | \(-0.880149\pi\) | ||
0.929949 | − | 0.367689i | \(-0.119851\pi\) | |||||||
\(314\) | −7.33629 | −0.414011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.06361 | 0.341105 | ||||||||
\(317\) | 7.39826i | 0.415528i | 0.978179 | + | 0.207764i | \(0.0666186\pi\) | ||||
−0.978179 | + | 0.207764i | \(0.933381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.05676 | −0.283124 | ||||||||
\(320\) | 1.70518 | + | 1.44650i | 0.0953224 | + | 0.0808618i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 10.2980i | − | 0.573885i | ||||||
\(323\) | − | 18.0942i | − | 1.00679i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.82255 | + | 0.301206i | −0.101097 | + | 0.0167079i | ||||
\(326\) | 18.7968 | 1.04106 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.01447i | 0.442525i | ||||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.2545 | 1.82783 | 0.913916 | − | 0.405903i | \(-0.133043\pi\) | ||||
0.913916 | + | 0.405903i | \(0.133043\pi\) | |||||||
\(332\) | 8.93200i | 0.490207i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.92772 | 0.324350 | ||||||||
\(335\) | 2.67709 | − | 3.15583i | 0.146265 | − | 0.172422i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6288i | 1.23267i | 0.787485 | + | 0.616334i | \(0.211383\pi\) | ||||
−0.787485 | + | 0.616334i | \(0.788617\pi\) | |||||||
\(338\) | − | 12.8635i | − | 0.699682i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.35281 | + | 8.66772i | −0.398762 | + | 0.470073i | ||||
\(341\) | −42.3333 | −2.29248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5004i | − | 1.05293i | ||||||
\(344\) | −2.27264 | −0.122533 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.78242 | 0.310865 | ||||||||
\(347\) | 24.1396i | 1.29588i | 0.761691 | + | 0.647941i | \(0.224370\pi\) | ||||
−0.761691 | + | 0.647941i | \(0.775630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3702 | 0.555102 | 0.277551 | − | 0.960711i | \(-0.410477\pi\) | ||||
0.277551 | + | 0.960711i | \(0.410477\pi\) | |||||||
\(350\) | −1.49380 | − | 9.03873i | −0.0798469 | − | 0.483140i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.19017i | 0.223337i | ||||||||
\(353\) | − | 3.92699i | − | 0.209013i | −0.994524 | − | 0.104506i | \(-0.966674\pi\) | ||
0.994524 | − | 0.104506i | \(-0.0333262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.87745 | + | 4.13753i | 0.258868 | + | 0.219598i | ||||
\(356\) | −11.4773 | −0.608295 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7.13581i | − | 0.377139i | ||||||
\(359\) | −9.85179 | −0.519957 | −0.259979 | − | 0.965614i | \(-0.583716\pi\) | ||||
−0.259979 | + | 0.965614i | \(0.583716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32907 | −0.333109 | ||||||||
\(362\) | − | 11.5365i | − | 0.606346i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.676938 | −0.0354812 | ||||||||
\(365\) | 11.7158 | − | 13.8110i | 0.613234 | − | 0.722899i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.2559i | 1.73594i | 0.496614 | + | 0.867972i | \(0.334577\pi\) | ||||
−0.496614 | + | 0.867972i | \(0.665423\pi\) | |||||||
\(368\) | 5.62036i | 0.292981i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.70518 | − | 1.44650i | −0.0886481 | − | 0.0752000i | ||||
\(371\) | −18.2192 | −0.945896 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.5387i | 1.47768i | 0.673882 | + | 0.738839i | \(0.264625\pi\) | ||||
−0.673882 | + | 0.738839i | \(0.735375\pi\) | |||||||
\(374\) | −21.2994 | −1.10136 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9154 | 0.562921 | ||||||||
\(377\) | 0.445862i | 0.0229631i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.476554 | −0.0244789 | −0.0122395 | − | 0.999925i | \(-0.503896\pi\) | ||||
−0.0122395 | + | 0.999925i | \(0.503896\pi\) | |||||||
\(380\) | −6.06980 | − | 5.14900i | −0.311374 | − | 0.264138i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 20.6048i | − | 1.05423i | ||||||
\(383\) | 7.13962i | 0.364818i | 0.983223 | + | 0.182409i | \(0.0583895\pi\) | ||||
−0.983223 | + | 0.182409i | \(0.941611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.1055 | − | 13.0915i | 0.565990 | − | 0.667206i | ||||
\(386\) | 26.1663 | 1.33183 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 6.05864i | − | 0.307581i | ||||||
\(389\) | −24.2060 | −1.22729 | −0.613646 | − | 0.789581i | \(-0.710298\pi\) | ||||
−0.613646 | + | 0.789581i | \(0.710298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.5693 | −1.44481 | ||||||||
\(392\) | 3.64280i | 0.183989i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.6067 | −0.735876 | ||||||||
\(395\) | 10.3395 | + | 8.77101i | 0.520239 | + | 0.441318i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7491i | 1.04137i | 0.853750 | + | 0.520684i | \(0.174323\pi\) | ||||
−0.853750 | + | 0.520684i | \(0.825677\pi\) | |||||||
\(398\) | 5.81275i | 0.291367i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.815273 | + | 4.93309i | 0.0407637 | + | 0.246654i | ||||
\(401\) | 34.8410 | 1.73988 | 0.869939 | − | 0.493159i | \(-0.164158\pi\) | ||||
0.869939 | + | 0.493159i | \(0.164158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.73259i | 0.185934i | ||||||||
\(404\) | 4.96528 | 0.247032 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.21121 | −0.109740 | ||||||||
\(407\) | − | 4.19017i | − | 0.207699i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2132 | −1.24671 | −0.623356 | − | 0.781938i | \(-0.714231\pi\) | ||||
−0.623356 | + | 0.781938i | \(0.714231\pi\) | |||||||
\(410\) | −11.5929 | + | 13.6661i | −0.572534 | + | 0.674921i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 7.33338i | − | 0.361289i | ||||||
\(413\) | 9.79462i | 0.481962i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.9201 | + | 15.2307i | −0.634225 | + | 0.747644i | ||||
\(416\) | 0.369454 | 0.0181140 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 14.9154i | − | 0.729538i | ||||||
\(419\) | 5.69695 | 0.278314 | 0.139157 | − | 0.990270i | \(-0.455561\pi\) | ||||
0.139157 | + | 0.990270i | \(0.455561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38092 | 0.164776 | 0.0823880 | − | 0.996600i | \(-0.473745\pi\) | ||||
0.0823880 | + | 0.996600i | \(0.473745\pi\) | |||||||
\(422\) | − | 16.0976i | − | 0.783621i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.94355 | 0.482901 | ||||||||
\(425\) | −25.0757 | + | 4.14417i | −1.21635 | + | 0.201022i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9457i | 0.868455i | ||||||||
\(428\) | − | 8.21182i | − | 0.396933i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.87526 | − | 3.28738i | −0.186882 | − | 0.158531i | ||||
\(431\) | 0.381731 | 0.0183873 | 0.00919367 | − | 0.999958i | \(-0.497074\pi\) | ||||
0.00919367 | + | 0.999958i | \(0.497074\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6393i | 1.03992i | 0.854192 | + | 0.519958i | \(0.174052\pi\) | ||||
−0.854192 | + | 0.519958i | \(0.825948\pi\) | |||||||
\(434\) | −18.5114 | −0.888575 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.5503 | −0.984179 | ||||||||
\(437\) | − | 20.0064i | − | 0.957035i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.4663 | −1.26317 | −0.631583 | − | 0.775308i | \(-0.717595\pi\) | ||||
−0.631583 | + | 0.775308i | \(0.717595\pi\) | |||||||
\(440\) | −6.06108 | + | 7.14499i | −0.288951 | + | 0.340624i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.87800i | 0.0893273i | ||||||||
\(443\) | − | 4.65489i | − | 0.221161i | −0.993867 | − | 0.110580i | \(-0.964729\pi\) | ||
0.993867 | − | 0.110580i | \(-0.0352709\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.5708 | − | 16.6019i | −0.927746 | − | 0.787005i | ||||
\(446\) | −25.3608 | −1.20087 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.83227i | 0.0865665i | ||||||||
\(449\) | −26.5531 | −1.25312 | −0.626558 | − | 0.779375i | \(-0.715537\pi\) | ||||
−0.626558 | + | 0.779375i | \(0.715537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.5820 | −1.58131 | ||||||||
\(452\) | 0.652984i | 0.0307138i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.57339 | 0.261572 | ||||||||
\(455\) | −1.15430 | − | 0.979192i | −0.0541145 | − | 0.0459052i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.27264i | 0.199866i | 0.994994 | + | 0.0999329i | \(0.0318628\pi\) | ||||
−0.994994 | + | 0.0999329i | \(0.968137\pi\) | |||||||
\(458\) | 9.02035i | 0.421493i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.12985 | + | 9.58372i | −0.379056 | + | 0.446843i | ||||
\(461\) | −32.1873 | −1.49911 | −0.749555 | − | 0.661942i | \(-0.769733\pi\) | ||||
−0.749555 | + | 0.661942i | \(0.769733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.4014i | − | 0.855186i | −0.903971 | − | 0.427593i | \(-0.859362\pi\) | ||
0.903971 | − | 0.427593i | \(-0.140638\pi\) | |||||||
\(464\) | 1.20681 | 0.0560250 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.8100 | 0.547086 | ||||||||
\(467\) | 3.06777i | 0.141959i | 0.997478 | + | 0.0709797i | \(0.0226125\pi\) | ||||
−0.997478 | + | 0.0709797i | \(0.977387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.39104 | 0.156584 | ||||||||
\(470\) | 18.6128 | + | 15.7892i | 0.858544 | + | 0.728301i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 5.34563i | − | 0.246052i | ||||||
\(473\) | − | 9.52276i | − | 0.437857i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.90207 | − | 17.5599i | −0.133156 | − | 0.805705i | ||||
\(476\) | −9.31373 | −0.426894 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 0.907160i | − | 0.0414925i | ||||||
\(479\) | 8.78798 | 0.401533 | 0.200767 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200767 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.369454 | −0.0168457 | ||||||||
\(482\) | 4.15616i | 0.189308i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.55754 | −0.298070 | ||||||||
\(485\) | 8.76383 | − | 10.3311i | 0.397945 | − | 0.469110i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.4814i | − | 1.01873i | −0.860550 | − | 0.509366i | \(-0.829880\pi\) | ||
0.860550 | − | 0.509366i | \(-0.170120\pi\) | |||||||
\(488\) | − | 9.79428i | − | 0.443366i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.26931 | + | 6.21162i | −0.238043 | + | 0.280613i | ||||
\(491\) | 0.0441752 | 0.00199360 | 0.000996799 | − | 1.00000i | \(-0.499683\pi\) | ||||
0.000996799 | 1.00000i | \(0.499683\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.13445i | 0.276282i | ||||||||
\(494\) | −1.31512 | −0.0591699 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.1030 | 0.453638 | ||||||||
\(497\) | 5.24097i | 0.235090i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2445 | −1.26440 | −0.632199 | − | 0.774806i | \(-0.717847\pi\) | ||||
−0.632199 | + | 0.774806i | \(0.717847\pi\) | |||||||
\(500\) | −5.74552 | + | 9.59109i | −0.256948 | + | 0.428926i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.31888i | 0.415922i | ||||||||
\(503\) | − | 19.7713i | − | 0.881560i | −0.897615 | − | 0.440780i | \(-0.854702\pi\) | ||
0.897615 | − | 0.440780i | \(-0.145298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.46670 | + | 7.18229i | 0.376763 | + | 0.319608i | ||||
\(506\) | −23.5503 | −1.04694 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2856i | 0.855660i | ||||||||
\(509\) | 43.4809 | 1.92726 | 0.963628 | − | 0.267247i | \(-0.0861141\pi\) | ||||
0.963628 | + | 0.267247i | \(0.0861141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8403 | 0.656496 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.6312 | 0.601249 | ||||||||
\(515\) | 10.6077 | − | 12.5047i | 0.467432 | − | 0.551024i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.7376i | 2.01154i | ||||||||
\(518\) | − | 1.83227i | − | 0.0805052i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.629985 | + | 0.534415i | 0.0276267 | + | 0.0234357i | ||||
\(521\) | 18.0325 | 0.790019 | 0.395009 | − | 0.918677i | \(-0.370741\pi\) | ||||
0.395009 | + | 0.918677i | \(0.370741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.6788i | − | 1.38522i | −0.721313 | − | 0.692610i | \(-0.756461\pi\) | ||
0.721313 | − | 0.692610i | \(-0.243539\pi\) | |||||||
\(524\) | −8.82072 | −0.385335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.2170 | 1.18672 | ||||||||
\(527\) | 51.3553i | 2.23707i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.58844 | −0.373410 | ||||||||
\(530\) | 16.9555 | + | 14.3833i | 0.736501 | + | 0.624773i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 6.52218i | − | 0.282773i | ||||||
\(533\) | 2.96098i | 0.128254i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.8784 | − | 14.0026i | 0.513548 | − | 0.605387i | ||||
\(536\) | −1.85073 | −0.0799395 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 23.0550i | − | 0.993973i | ||||||
\(539\) | −15.2639 | −0.657465 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.39442 | 0.403898 | 0.201949 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201949 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(542\) | − | 22.9320i | − | 0.985014i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.08317 | 0.217939 | ||||||||
\(545\) | −35.0419 | − | 29.7260i | −1.50103 | − | 1.27332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.7824i | 1.05962i | 0.848117 | + | 0.529809i | \(0.177737\pi\) | ||||
−0.848117 | + | 0.529809i | \(0.822263\pi\) | |||||||
\(548\) | 4.66126i | 0.199119i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.6705 | + | 3.41613i | −0.881392 | + | 0.145664i | ||||
\(551\) | −4.29581 | −0.183008 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1102i | 0.472452i | ||||||||
\(554\) | −11.7534 | −0.499353 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4050 | 0.695727 | ||||||||
\(557\) | 22.1627i | 0.939062i | 0.882916 | + | 0.469531i | \(0.155577\pi\) | ||||
−0.882916 | + | 0.469531i | \(0.844423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.839637 | −0.0355128 | ||||||||
\(560\) | −2.65038 | + | 3.12434i | −0.111999 | + | 0.132028i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 29.0962i | − | 1.22735i | ||||||
\(563\) | 6.46846i | 0.272613i | 0.990667 | + | 0.136306i | \(0.0435232\pi\) | ||||
−0.990667 | + | 0.136306i | \(0.956477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.944542 | + | 1.11346i | −0.0397372 | + | 0.0468434i | ||||
\(566\) | 10.1829 | 0.428019 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.86038i | − | 0.120019i | ||||||
\(569\) | 8.26550 | 0.346508 | 0.173254 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173254 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5179 | 1.44453 | 0.722264 | − | 0.691618i | \(-0.243102\pi\) | ||||
0.722264 | + | 0.691618i | \(0.243102\pi\) | |||||||
\(572\) | 1.54808i | 0.0647283i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.6846 | −0.612925 | ||||||||
\(575\) | −27.7257 | + | 4.58213i | −1.15624 | + | 0.191088i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.05347i | − | 0.127117i | −0.997978 | − | 0.0635587i | \(-0.979755\pi\) | ||
0.997978 | − | 0.0635587i | \(-0.0202450\pi\) | |||||||
\(578\) | 8.83864i | 0.367639i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.05784 | + | 1.74566i | 0.0854470 | + | 0.0724845i | ||||
\(581\) | −16.3658 | −0.678968 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.6652i | 1.72559i | ||||||||
\(584\) | −8.09942 | −0.335156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.1243 | 0.748706 | ||||||||
\(587\) | 35.1344i | 1.45015i | 0.688668 | + | 0.725076i | \(0.258196\pi\) | ||||
−0.688668 | + | 0.725076i | \(0.741804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.9629 | −1.48183 | ||||||||
\(590\) | 7.73245 | − | 9.11525i | 0.318340 | − | 0.375269i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − | 12.0400i | − | 0.494424i | −0.968961 | − | 0.247212i | \(-0.920486\pi\) | ||
0.968961 | − | 0.247212i | \(-0.0795144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.8816 | − | 13.4723i | −0.651081 | − | 0.552311i | ||||
\(596\) | 5.86259 | 0.240141 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.07646i | 0.0849129i | ||||||||
\(599\) | −17.4701 | −0.713810 | −0.356905 | − | 0.934141i | \(-0.616168\pi\) | ||||
−0.356905 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.7044 | 1.57878 | 0.789392 | − | 0.613890i | \(-0.210396\pi\) | ||||
0.789392 | + | 0.613890i | \(0.210396\pi\) | |||||||
\(602\) | − | 4.16409i | − | 0.169716i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.1460 | −0.534903 | ||||||||
\(605\) | −11.1818 | − | 9.48548i | −0.454604 | − | 0.385639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 28.7903i | − | 1.16856i | −0.811551 | − | 0.584282i | \(-0.801376\pi\) | ||
0.811551 | − | 0.584282i | \(-0.198624\pi\) | |||||||
\(608\) | 3.55963i | 0.144362i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.1674 | − | 16.7010i | 0.573623 | − | 0.676204i | ||||
\(611\) | 4.03275 | 0.163148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.66539i | 0.309602i | 0.987946 | + | 0.154801i | \(0.0494737\pi\) | ||||
−0.987946 | + | 0.154801i | \(0.950526\pi\) | |||||||
\(614\) | −6.15561 | −0.248420 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.67751 | −0.309336 | ||||||||
\(617\) | − | 36.5388i | − | 1.47100i | −0.677527 | − | 0.735498i | \(-0.736948\pi\) | ||
0.677527 | − | 0.735498i | \(-0.263052\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.8085 | 1.84120 | 0.920599 | − | 0.390510i | \(-0.127701\pi\) | ||||
0.920599 | + | 0.390510i | \(0.127701\pi\) | |||||||
\(620\) | 17.2274 | + | 14.6140i | 0.691870 | + | 0.586912i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 29.4512i | − | 1.18088i | ||||||
\(623\) | − | 21.0294i | − | 0.842527i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6707 | + | 8.04362i | −0.946826 | + | 0.321745i | ||||
\(626\) | −13.0102 | −0.519991 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.33629i | 0.292750i | ||||||||
\(629\) | −5.08317 | −0.202679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.42682 | 0.136420 | 0.0682098 | − | 0.997671i | \(-0.478271\pi\) | ||||
0.0682098 | + | 0.997671i | \(0.478271\pi\) | |||||||
\(632\) | − | 6.06361i | − | 0.241197i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.39826 | 0.293823 | ||||||||
\(635\) | −27.8966 | + | 32.8854i | −1.10704 | + | 1.30502i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.34585i | 0.0533244i | ||||||||
\(638\) | 5.05676i | 0.200199i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.44650 | − | 1.70518i | 0.0571779 | − | 0.0674031i | ||||
\(641\) | −38.3241 | −1.51371 | −0.756855 | − | 0.653583i | \(-0.773265\pi\) | ||||
−0.756855 | + | 0.653583i | \(0.773265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.36660i | − | 0.0538935i | −0.999637 | − | 0.0269468i | \(-0.991422\pi\) | ||
0.999637 | − | 0.0269468i | \(-0.00857846\pi\) | |||||||
\(644\) | −10.2980 | −0.405798 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.0942 | −0.711906 | ||||||||
\(647\) | − | 11.2690i | − | 0.443028i | −0.975157 | − | 0.221514i | \(-0.928900\pi\) | ||
0.975157 | − | 0.221514i | \(-0.0710999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3991 | 0.879241 | ||||||||
\(650\) | 0.301206 | + | 1.82255i | 0.0118143 | + | 0.0714862i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 18.7968i | − | 0.736138i | ||||||
\(653\) | − | 29.5439i | − | 1.15614i | −0.815987 | − | 0.578070i | \(-0.803806\pi\) | ||
0.815987 | − | 0.578070i | \(-0.196194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0409 | − | 12.7592i | −0.587697 | − | 0.498542i | ||||
\(656\) | 8.01447 | 0.312912 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.0000i | 0.779681i | ||||||||
\(659\) | −49.9126 | −1.94432 | −0.972159 | − | 0.234324i | \(-0.924712\pi\) | ||||
−0.972159 | + | 0.234324i | \(0.924712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9950 | 1.01109 | 0.505545 | − | 0.862800i | \(-0.331292\pi\) | ||||
0.505545 | + | 0.862800i | \(0.331292\pi\) | |||||||
\(662\) | − | 33.2545i | − | 1.29247i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.93200 | 0.346629 | ||||||||
\(665\) | 9.43434 | − | 11.1215i | 0.365848 | − | 0.431273i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.78273i | 0.262628i | ||||||||
\(668\) | − | 5.92772i | − | 0.229350i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.15583 | − | 2.67709i | −0.121920 | − | 0.103425i | ||||
\(671\) | 41.0397 | 1.58432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.91054i | − | 0.266382i | −0.991090 | − | 0.133191i | \(-0.957478\pi\) | ||
0.991090 | − | 0.133191i | \(-0.0425223\pi\) | |||||||
\(674\) | 22.6288 | 0.871627 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8635 | −0.494750 | ||||||||
\(677\) | 15.6913i | 0.603065i | 0.953456 | + | 0.301532i | \(0.0974982\pi\) | ||||
−0.953456 | + | 0.301532i | \(0.902502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.1011 | 0.426019 | ||||||||
\(680\) | 8.66772 | + | 7.35281i | 0.332392 | + | 0.281967i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42.3333i | 1.62103i | ||||||||
\(683\) | − | 18.2002i | − | 0.696412i | −0.937418 | − | 0.348206i | \(-0.886791\pi\) | ||
0.937418 | − | 0.348206i | \(-0.113209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.74252 | + | 7.94829i | −0.257618 | + | 0.303689i | ||||
\(686\) | −19.5004 | −0.744531 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.27264i | 0.0866437i | ||||||||
\(689\) | 3.67368 | 0.139956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.58658 | −0.0983982 | −0.0491991 | − | 0.998789i | \(-0.515667\pi\) | ||||
−0.0491991 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(692\) | − | 5.78242i | − | 0.219815i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.1396 | 0.916327 | ||||||||
\(695\) | 27.9735 | + | 23.7298i | 1.06109 | + | 0.900124i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.7389i | 1.54310i | ||||||||
\(698\) | − | 10.3702i | − | 0.392516i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.03873 | + | 1.49380i | −0.341632 | + | 0.0564603i | ||||
\(701\) | 26.5092 | 1.00124 | 0.500620 | − | 0.865667i | \(-0.333105\pi\) | ||||
0.500620 | + | 0.865667i | \(0.333105\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.55963i | − | 0.134254i | ||||||
\(704\) | 4.19017 | 0.157923 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.92699 | −0.147794 | ||||||||
\(707\) | 9.09773i | 0.342155i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0474 | 0.940674 | 0.470337 | − | 0.882487i | \(-0.344132\pi\) | ||||
0.470337 | + | 0.882487i | \(0.344132\pi\) | |||||||
\(710\) | 4.13753 | − | 4.87745i | 0.155279 | − | 0.183048i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.4773i | 0.430129i | ||||||||
\(713\) | 56.7825i | 2.12652i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.23929 | + | 2.63975i | −0.0837448 | + | 0.0987209i | ||||
\(716\) | −7.13581 | −0.266678 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.85179i | 0.367665i | ||||||||
\(719\) | 24.9551 | 0.930668 | 0.465334 | − | 0.885135i | \(-0.345934\pi\) | ||||
0.465334 | + | 0.885135i | \(0.345934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4367 | 0.500409 | ||||||||
\(722\) | 6.32907i | 0.235544i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5365 | −0.428752 | ||||||||
\(725\) | 0.983883 | + | 5.95332i | 0.0365405 | + | 0.221101i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.6774i | − | 0.803970i | −0.915646 | − | 0.401985i | \(-0.868320\pi\) | ||
0.915646 | − | 0.401985i | \(-0.131680\pi\) | |||||||
\(728\) | 0.676938i | 0.0250890i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.8110 | − | 11.7158i | −0.511167 | − | 0.433622i | ||||
\(731\) | −11.5522 | −0.427275 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.33267i | − | 0.233903i | −0.993138 | − | 0.116951i | \(-0.962688\pi\) | ||
0.993138 | − | 0.116951i | \(-0.0373122\pi\) | |||||||
\(734\) | 33.2559 | 1.22750 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.62036 | 0.207169 | ||||||||
\(737\) | − | 7.75489i | − | 0.285655i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8076 | −0.471136 | −0.235568 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235568 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(740\) | −1.44650 | + | 1.70518i | −0.0531744 | + | 0.0626836i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.2192i | 0.668849i | ||||||||
\(743\) | 11.0694i | 0.406097i | 0.979169 | + | 0.203048i | \(0.0650848\pi\) | ||||
−0.979169 | + | 0.203048i | \(0.934915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.99677 | + | 8.48024i | 0.366253 | + | 0.310692i | ||||
\(746\) | 28.5387 | 1.04488 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.2994i | 0.778782i | ||||||||
\(749\) | 15.0463 | 0.549778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.5316 | −1.69796 | −0.848981 | − | 0.528423i | \(-0.822784\pi\) | ||||
−0.848981 | + | 0.528423i | \(0.822784\pi\) | |||||||
\(752\) | − | 10.9154i | − | 0.398045i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.445862 | 0.0162374 | ||||||||
\(755\) | −22.4163 | − | 19.0157i | −0.815812 | − | 0.692052i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.9872i | 1.19894i | 0.800397 | + | 0.599470i | \(0.204622\pi\) | ||||
−0.800397 | + | 0.599470i | \(0.795378\pi\) | |||||||
\(758\) | 0.476554i | 0.0173092i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.14900 | + | 6.06980i | −0.186774 | + | 0.220175i | ||||
\(761\) | −28.7913 | −1.04369 | −0.521843 | − | 0.853042i | \(-0.674755\pi\) | ||||
−0.521843 | + | 0.853042i | \(0.674755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 37.6536i | − | 1.36315i | ||||||
\(764\) | −20.6048 | −0.745456 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.13962 | 0.257965 | ||||||||
\(767\) | − | 1.97496i | − | 0.0713118i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.9025 | −1.51104 | −0.755521 | − | 0.655124i | \(-0.772616\pi\) | ||||
−0.755521 | + | 0.655124i | \(0.772616\pi\) | |||||||
\(770\) | −13.0915 | − | 11.1055i | −0.471786 | − | 0.400215i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 26.1663i | − | 0.941747i | ||||||
\(773\) | 31.0931i | 1.11834i | 0.829052 | + | 0.559171i | \(0.188881\pi\) | ||||
−0.829052 | + | 0.559171i | \(0.811119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.23670 | + | 49.8390i | 0.295871 | + | 1.79027i | ||||
\(776\) | −6.05864 | −0.217493 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.2060i | 0.867827i | ||||||||
\(779\) | −28.5285 | −1.02214 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.9855 | 0.428874 | ||||||||
\(782\) | 28.5693i | 1.02163i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.64280 | 0.130100 | ||||||||
\(785\) | −10.6120 | + | 12.5097i | −0.378757 | + | 0.446490i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.2842i | − | 0.651760i | −0.945411 | − | 0.325880i | \(-0.894339\pi\) | ||
0.945411 | − | 0.325880i | \(-0.105661\pi\) | |||||||
\(788\) | 14.6067i | 0.520343i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.77101 | − | 10.3395i | 0.312059 | − | 0.367864i | ||||
\(791\) | −1.19644 | −0.0425406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.61854i | − | 0.128498i | ||||||
\(794\) | 20.7491 | 0.736358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.81275 | 0.206027 | ||||||||
\(797\) | 40.6025i | 1.43821i | 0.694900 | + | 0.719106i | \(0.255449\pi\) | ||||
−0.694900 | + | 0.719106i | \(0.744551\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.4851 | 1.96292 | ||||||||
\(800\) | 4.93309 | − | 0.815273i | 0.174411 | − | 0.0288243i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 34.8410i | − | 1.23028i | ||||||
\(803\) | − | 33.9380i | − | 1.19764i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.5599 | − | 14.8961i | −0.618906 | − | 0.525017i | ||||
\(806\) | 3.73259 | 0.131475 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.96528i | − | 0.174678i | ||||||
\(809\) | 41.1512 | 1.44680 | 0.723400 | − | 0.690429i | \(-0.242578\pi\) | ||||
0.723400 | + | 0.690429i | \(0.242578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.71866 | −0.235924 | −0.117962 | − | 0.993018i | \(-0.537636\pi\) | ||||
−0.117962 | + | 0.993018i | \(0.537636\pi\) | |||||||
\(812\) | 2.21121i | 0.0775981i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.19017 | −0.146865 | ||||||||
\(815\) | 27.1895 | − | 32.0519i | 0.952408 | − | 1.12273i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.08975i | − | 0.283025i | ||||||
\(818\) | 25.2132i | 0.881558i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.6661 | + | 11.5929i | 0.477241 | + | 0.404843i | ||||
\(821\) | 11.5263 | 0.402272 | 0.201136 | − | 0.979563i | \(-0.435537\pi\) | ||||
0.201136 | + | 0.979563i | \(0.435537\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.69569i | 0.163681i | 0.996645 | + | 0.0818407i | \(0.0260799\pi\) | ||||
−0.996645 | + | 0.0818407i | \(0.973920\pi\) | |||||||
\(824\) | −7.33338 | −0.255470 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.79462 | 0.340798 | ||||||||
\(827\) | 28.4859i | 0.990550i | 0.868736 | + | 0.495275i | \(0.164933\pi\) | ||||
−0.868736 | + | 0.495275i | \(0.835067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.2771 | 1.39888 | 0.699441 | − | 0.714691i | \(-0.253433\pi\) | ||||
0.699441 | + | 0.714691i | \(0.253433\pi\) | |||||||
\(830\) | 15.2307 | + | 12.9201i | 0.528664 | + | 0.448465i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.369454i | − | 0.0128085i | ||||||
\(833\) | 18.5170i | 0.641575i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.57444 | − | 10.1078i | 0.296731 | − | 0.349796i | ||||
\(836\) | −14.9154 | −0.515861 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 5.69695i | − | 0.196798i | ||||||
\(839\) | −9.99007 | −0.344895 | −0.172448 | − | 0.985019i | \(-0.555168\pi\) | ||||
−0.172448 | + | 0.985019i | \(0.555168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5436 | −0.949779 | ||||||||
\(842\) | − | 3.38092i | − | 0.116514i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0976 | −0.554104 | ||||||||
\(845\) | −21.9346 | − | 18.6071i | −0.754573 | − | 0.640102i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.0152i | − | 0.412846i | ||||||
\(848\) | − | 9.94355i | − | 0.341463i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.14417 | + | 25.0757i | 0.142144 | + | 0.860090i | ||||
\(851\) | −5.62036 | −0.192663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0500i | 0.618019i | 0.951059 | + | 0.309010i | \(0.0999975\pi\) | ||||
−0.951059 | + | 0.309010i | \(0.900002\pi\) | |||||||
\(854\) | 17.9457 | 0.614091 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.21182 | −0.280674 | ||||||||
\(857\) | − | 24.3118i | − | 0.830474i | −0.909713 | − | 0.415237i | \(-0.863699\pi\) | ||
0.909713 | − | 0.415237i | \(-0.136301\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.2112 | −1.20139 | −0.600696 | − | 0.799477i | \(-0.705110\pi\) | ||||
−0.600696 | + | 0.799477i | \(0.705110\pi\) | |||||||
\(860\) | −3.28738 | + | 3.87526i | −0.112099 | + | 0.132145i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 0.381731i | − | 0.0130018i | ||||||
\(863\) | 23.2986i | 0.793093i | 0.918015 | + | 0.396546i | \(0.129791\pi\) | ||||
−0.918015 | + | 0.396546i | \(0.870209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.36428 | − | 9.86007i | 0.284394 | − | 0.335252i | ||||
\(866\) | 21.6393 | 0.735332 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.5114i | 0.628318i | ||||||||
\(869\) | 25.4076 | 0.861893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.683761 | −0.0231684 | ||||||||
\(872\) | 20.5503i | 0.695920i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.0064 | −0.676726 | ||||||||
\(875\) | −17.5734 | − | 10.5273i | −0.594091 | − | 0.355889i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.8713i | 1.61650i | 0.588839 | + | 0.808250i | \(0.299585\pi\) | ||||
−0.588839 | + | 0.808250i | \(0.700415\pi\) | |||||||
\(878\) | 26.4663i | 0.893194i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.14499 | + | 6.06108i | 0.240858 | + | 0.204319i | ||||
\(881\) | 40.1274 | 1.35193 | 0.675963 | − | 0.736936i | \(-0.263728\pi\) | ||||
0.675963 | + | 0.736936i | \(0.263728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.6747i | − | 1.53708i | −0.639803 | − | 0.768539i | \(-0.720984\pi\) | ||
0.639803 | − | 0.768539i | \(-0.279016\pi\) | |||||||
\(884\) | 1.87800 | 0.0631639 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.65489 | −0.156384 | ||||||||
\(887\) | 17.5417i | 0.588992i | 0.955653 | + | 0.294496i | \(0.0951517\pi\) | ||||
−0.955653 | + | 0.294496i | \(0.904848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.3364 | −1.18514 | ||||||||
\(890\) | −16.6019 | + | 19.5708i | −0.556497 | + | 0.656015i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.3608i | 0.849142i | ||||||||
\(893\) | 38.8549i | 1.30023i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1678 | − | 10.3220i | −0.406726 | − | 0.345025i | ||||
\(896\) | 1.83227 | 0.0612117 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.5531i | 0.886087i | ||||||||
\(899\) | 12.1924 | 0.406641 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.5448 | 1.68389 | ||||||||
\(902\) | 33.5820i | 1.11816i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.652984 | 0.0217179 | ||||||||
\(905\) | −19.6718 | − | 16.6876i | −0.653914 | − | 0.554714i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.04294i | − | 0.0678347i | −0.999425 | − | 0.0339173i | \(-0.989202\pi\) | ||
0.999425 | − | 0.0339173i | \(-0.0107983\pi\) | |||||||
\(908\) | − | 5.57339i | − | 0.184960i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.979192 | + | 1.15430i | −0.0324599 | + | 0.0382647i | ||||
\(911\) | −54.3145 | −1.79952 | −0.899760 | − | 0.436385i | \(-0.856258\pi\) | ||||
−0.899760 | + | 0.436385i | \(0.856258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.4266i | 1.23864i | ||||||||
\(914\) | 4.27264 | 0.141326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.02035 | 0.298041 | ||||||||
\(917\) | − | 16.1619i | − | 0.533713i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.9771 | −1.35171 | −0.675855 | − | 0.737034i | \(-0.736226\pi\) | ||||
−0.675855 | + | 0.737034i | \(0.736226\pi\) | |||||||
\(920\) | 9.58372 | + | 8.12985i | 0.315966 | + | 0.268033i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.1873i | 1.06003i | ||||||||
\(923\) | − | 1.05678i | − | 0.0347842i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.93309 | + | 0.815273i | −0.162199 | + | 0.0268060i | ||||
\(926\) | −18.4014 | −0.604708 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 1.20681i | − | 0.0396156i | ||||||
\(929\) | −22.2458 | −0.729860 | −0.364930 | − | 0.931035i | \(-0.618907\pi\) | ||||
−0.364930 | + | 0.931035i | \(0.618907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9670 | −0.424976 | ||||||||
\(932\) | − | 11.8100i | − | 0.386848i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.06777 | 0.100380 | ||||||||
\(935\) | −30.8095 | + | 36.3192i | −1.00758 | + | 1.18777i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.989771i | − | 0.0323344i | −0.999869 | − | 0.0161672i | \(-0.994854\pi\) | ||
0.999869 | − | 0.0161672i | \(-0.00514640\pi\) | |||||||
\(938\) | − | 3.39104i | − | 0.110721i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.7892 | − | 18.6128i | 0.514987 | − | 0.607082i | ||||
\(941\) | −0.255111 | −0.00831639 | −0.00415820 | − | 0.999991i | \(-0.501324\pi\) | ||||
−0.00415820 | + | 0.999991i | \(0.501324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.0442i | 1.46684i | ||||||||
\(944\) | −5.34563 | −0.173985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.52276 | −0.309612 | ||||||||
\(947\) | − | 58.4983i | − | 1.90094i | −0.310819 | − | 0.950469i | \(-0.600603\pi\) | ||
0.310819 | − | 0.950469i | \(-0.399397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.99236 | −0.0971362 | ||||||||
\(950\) | −17.5599 | + | 2.90207i | −0.569720 | + | 0.0941555i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.31373i | 0.301860i | ||||||||
\(953\) | 34.4365i | 1.11551i | 0.830006 | + | 0.557755i | \(0.188337\pi\) | ||||
−0.830006 | + | 0.557755i | \(0.811663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.1349 | − | 29.8049i | −1.13694 | − | 0.964463i | ||||
\(956\) | −0.907160 | −0.0293396 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 8.78798i | − | 0.283927i | ||||||
\(959\) | −8.54068 | −0.275793 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.0706 | 2.29260 | ||||||||
\(962\) | 0.369454i | 0.0119117i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.15616 | 0.133861 | ||||||||
\(965\) | 37.8496 | − | 44.6183i | 1.21842 | − | 1.43631i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0310i | 0.611997i | 0.952032 | + | 0.305998i | \(0.0989902\pi\) | ||||
−0.952032 | + | 0.305998i | \(0.901010\pi\) | |||||||
\(968\) | 6.55754i | 0.210767i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.3311 | − | 8.76383i | −0.331711 | − | 0.281390i | ||||
\(971\) | −50.9856 | −1.63621 | −0.818103 | − | 0.575071i | \(-0.804974\pi\) | ||||
−0.818103 | + | 0.575071i | \(0.804974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0583i | 0.963626i | ||||||||
\(974\) | −22.4814 | −0.720352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.79428 | −0.313507 | ||||||||
\(977\) | 26.8574i | 0.859245i | 0.903009 | + | 0.429622i | \(0.141353\pi\) | ||||
−0.903009 | + | 0.429622i | \(0.858647\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.0918 | −1.53702 | ||||||||
\(980\) | 6.21162 | + | 5.26931i | 0.198423 | + | 0.168322i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 0.0441752i | − | 0.00140969i | ||||||
\(983\) | − | 7.09389i | − | 0.226260i | −0.993580 | − | 0.113130i | \(-0.963912\pi\) | ||
0.993580 | − | 0.113130i | \(-0.0360877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.1286 | + | 24.9071i | −0.673214 | + | 0.793605i | ||||
\(986\) | 6.13445 | 0.195361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.31512i | 0.0418395i | ||||||||
\(989\) | −12.7731 | −0.406160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.2573 | −0.865856 | −0.432928 | − | 0.901429i | \(-0.642520\pi\) | ||||
−0.432928 | + | 0.901429i | \(0.642520\pi\) | |||||||
\(992\) | − | 10.1030i | − | 0.320771i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.24097 | 0.166234 | ||||||||
\(995\) | 9.91178 | + | 8.40814i | 0.314224 | + | 0.266556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 24.6984i | − | 0.782207i | −0.920347 | − | 0.391103i | \(-0.872094\pi\) | ||
0.920347 | − | 0.391103i | \(-0.127906\pi\) | |||||||
\(998\) | 28.2445i | 0.894064i | ||||||||
\(999\) | 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 | 3330.2.d.p.1999.3 | 10 | ||
3.2 | odd | 2 | 370.2.b.d.149.6 | yes | 10 | ||
5.4 | even | 2 | inner | 3330.2.d.p.1999.8 | 10 | ||
15.2 | even | 4 | 1850.2.a.bd.1.1 | 5 | |||
15.8 | even | 4 | 1850.2.a.be.1.5 | 5 | |||
15.14 | odd | 2 | 370.2.b.d.149.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.d.149.5 | ✓ | 10 | 15.14 | odd | 2 | ||
370.2.b.d.149.6 | yes | 10 | 3.2 | odd | 2 | ||
1850.2.a.bd.1.1 | 5 | 15.2 | even | 4 | |||
1850.2.a.be.1.5 | 5 | 15.8 | even | 4 | |||
3330.2.d.p.1999.3 | 10 | 1.1 | even | 1 | trivial | ||
3330.2.d.p.1999.8 | 10 | 5.4 | even | 2 | inner |