Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(37,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.i (of order \(3\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 565.4 | ||
Root | \(1.69181 - 2.93030i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.565 |
Dual form | 804.2.i.d.37.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.38361 | 1.51320 | 0.756599 | − | 0.653879i | \(-0.226859\pi\) | ||||
0.756599 | + | 0.653879i | \(0.226859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69181 | + | 2.93030i | 0.639443 | + | 1.10755i | 0.985555 | + | 0.169355i | \(0.0541684\pi\) |
−0.346112 | + | 0.938193i | \(0.612498\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.53262 | − | 2.65457i | 0.425071 | − | 0.736245i | −0.571356 | − | 0.820703i | \(-0.693582\pi\) |
0.996427 | + | 0.0844572i | \(0.0269156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.38361 | −0.873646 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.03262 | + | 1.78855i | −0.250446 | + | 0.433786i | −0.963649 | − | 0.267172i | \(-0.913911\pi\) |
0.713202 | + | 0.700958i | \(0.247244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.72442 | + | 6.45089i | −0.854442 | + | 1.47994i | 0.0227206 | + | 0.999742i | \(0.492767\pi\) |
−0.877162 | + | 0.480194i | \(0.840566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69181 | − | 2.93030i | −0.369183 | − | 0.639443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.11036 | − | 1.92321i | 0.231527 | − | 0.401016i | −0.726731 | − | 0.686922i | \(-0.758961\pi\) |
0.958258 | + | 0.285906i | \(0.0922946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.44885 | 1.28977 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.80217 | − | 4.85350i | −0.520350 | − | 0.901273i | −0.999720 | − | 0.0236598i | \(-0.992468\pi\) |
0.479370 | − | 0.877613i | \(-0.340865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.99398 | − | 5.18572i | −0.537734 | − | 0.931383i | −0.999026 | − | 0.0441344i | \(-0.985947\pi\) |
0.461291 | − | 0.887249i | \(-0.347386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.72442 | + | 9.91499i | 0.967604 | + | 1.67594i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.14298 | + | 5.44380i | −0.516703 | + | 0.894955i | 0.483109 | + | 0.875560i | \(0.339507\pi\) |
−0.999812 | + | 0.0193953i | \(0.993826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.53262 | + | 2.65457i | −0.245415 | + | 0.425071i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92225 | + | 3.32944i | 0.300206 | + | 0.519971i | 0.976182 | − | 0.216952i | \(-0.0696114\pi\) |
−0.675977 | + | 0.736923i | \(0.736278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.92272 | 0.903207 | 0.451603 | − | 0.892219i | \(-0.350852\pi\) | ||||
0.451603 | + | 0.892219i | \(0.350852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.38361 | 0.504400 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.92225 | + | 3.32944i | 0.280390 | + | 0.485649i | 0.971481 | − | 0.237119i | \(-0.0762030\pi\) |
−0.691091 | + | 0.722768i | \(0.742870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.22442 | + | 3.85282i | −0.317775 | + | 0.550402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.03262 | − | 1.78855i | 0.144595 | − | 0.250446i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.93477 | 0.265761 | 0.132880 | − | 0.991132i | \(-0.457577\pi\) | ||||
0.132880 | + | 0.991132i | \(0.457577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.38361 | + | 5.86059i | 0.456247 | + | 0.790242i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.72442 | − | 6.45089i | 0.493312 | − | 0.854442i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6696 | 1.51925 | 0.759625 | − | 0.650362i | \(-0.225383\pi\) | ||||
0.759625 | + | 0.650362i | \(0.225383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.98379 | − | 8.63218i | 0.638109 | − | 1.10524i | −0.347738 | − | 0.937592i | \(-0.613050\pi\) |
0.985847 | − | 0.167645i | \(-0.0536164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.69181 | + | 2.93030i | 0.213148 | + | 0.369183i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.18579 | − | 8.98204i | 0.643218 | − | 1.11409i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.80587 | + | 2.46342i | −0.953639 | + | 0.300954i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.11036 | + | 1.92321i | −0.133672 | + | 0.231527i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.65687 | + | 11.5300i | 0.790025 | + | 1.36836i | 0.925951 | + | 0.377644i | \(0.123266\pi\) |
−0.135926 | + | 0.990719i | \(0.543401\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.80587 | − | 4.85991i | 0.328402 | − | 0.568809i | −0.653793 | − | 0.756674i | \(-0.726823\pi\) |
0.982195 | + | 0.187864i | \(0.0601566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.44885 | −0.744649 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.38361 | + | 5.86059i | −0.385599 | + | 0.667877i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.29985 | − | 10.9117i | −0.708788 | − | 1.22766i | −0.965307 | − | 0.261118i | \(-0.915909\pi\) |
0.256519 | − | 0.966539i | \(-0.417424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.03262 | + | 3.52060i | −0.223109 | + | 0.386436i | −0.955750 | − | 0.294179i | \(-0.904954\pi\) |
0.732642 | + | 0.680615i | \(0.238287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.49398 | + | 6.05175i | −0.378975 | + | 0.656404i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.80217 | + | 4.85350i | 0.300424 | + | 0.520350i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.837112 | −0.0887337 | −0.0443668 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443668 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3716 | 1.08724 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.99398 | + | 5.18572i | 0.310461 | + | 0.537734i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6020 | + | 21.8273i | −1.29294 | + | 2.23944i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.08144 | − | 5.33722i | 0.312873 | − | 0.541912i | −0.666110 | − | 0.745854i | \(-0.732042\pi\) |
0.978983 | + | 0.203941i | \(0.0653752\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | + | 1.73205i | 0.100504 | + | 0.174078i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.09785 | + | 8.82974i | 0.507255 | + | 0.878592i | 0.999965 | + | 0.00839785i | \(0.00267315\pi\) |
−0.492710 | + | 0.870194i | \(0.663994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.65919 | − | 2.87380i | −0.163485 | − | 0.283164i | 0.772631 | − | 0.634855i | \(-0.218940\pi\) |
−0.936116 | + | 0.351691i | \(0.885607\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.72442 | − | 9.91499i | −0.558647 | − | 0.967604i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.15084 | 0.787972 | 0.393986 | − | 0.919116i | \(-0.371096\pi\) | ||||
0.393986 | + | 0.919116i | \(0.371096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3063 | −1.65765 | −0.828823 | − | 0.559511i | \(-0.810989\pi\) | ||||
−0.828823 | + | 0.559511i | \(0.810989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.14298 | − | 5.44380i | 0.298318 | − | 0.516703i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.14066 | − | 10.6359i | −0.577664 | − | 1.00054i | −0.995747 | − | 0.0921348i | \(-0.970631\pi\) |
0.418082 | − | 0.908409i | \(-0.362702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.75704 | − | 6.50739i | 0.350346 | − | 0.606817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.53262 | − | 2.65457i | 0.141690 | − | 0.245415i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.98796 | −0.640585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.92225 | − | 3.32944i | −0.173324 | − | 0.300206i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.90235 | 0.438479 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.49768 | − | 16.4505i | −0.842782 | − | 1.45974i | −0.887533 | − | 0.460744i | \(-0.847583\pi\) |
0.0447507 | − | 0.998998i | \(-0.485751\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.92272 | −0.521467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.87732 | −0.600874 | −0.300437 | − | 0.953802i | \(-0.597133\pi\) | ||||
−0.300437 | + | 0.953802i | \(0.597133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.2040 | −2.18547 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.38361 | −0.291215 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.51873 | 0.129754 | 0.0648770 | − | 0.997893i | \(-0.479335\pi\) | ||||
0.0648770 | + | 0.997893i | \(0.479335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9301 | −0.927080 | −0.463540 | − | 0.886076i | \(-0.653421\pi\) | ||||
−0.463540 | + | 0.886076i | \(0.653421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.92225 | − | 3.32944i | −0.161883 | − | 0.280390i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.13047 | 0.512655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.48147 | − | 16.4224i | −0.787393 | − | 1.36380i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.22442 | − | 3.85282i | 0.183467 | − | 0.317775i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.0365 | 1.96915 | 0.984573 | − | 0.174973i | \(-0.0559837\pi\) | ||||
0.984573 | + | 0.174973i | \(0.0559837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.90604 | + | 3.30136i | −0.155112 | + | 0.268661i | −0.933100 | − | 0.359618i | \(-0.882907\pi\) |
0.777988 | + | 0.628279i | \(0.216240\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.03262 | + | 1.78855i | −0.0834821 | + | 0.144595i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.1305 | − | 17.5465i | −0.813699 | − | 1.40937i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.83711 | + | 3.18197i | −0.146617 | + | 0.253949i | −0.929975 | − | 0.367622i | \(-0.880172\pi\) |
0.783358 | + | 0.621571i | \(0.213505\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.93477 | −0.153437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.51408 | 0.592193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.03631 | − | 12.1873i | −0.551127 | − | 0.954579i | −0.998194 | − | 0.0600790i | \(-0.980865\pi\) |
0.447067 | − | 0.894501i | \(-0.352469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.38361 | − | 5.86059i | −0.263414 | − | 0.456247i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.1835 | − | 19.3703i | −0.865402 | − | 1.49892i | −0.866647 | − | 0.498921i | \(-0.833730\pi\) |
0.00124506 | − | 0.999999i | \(-0.499604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.80217 | + | 3.12145i | 0.138629 | + | 0.240112i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.72442 | + | 6.45089i | −0.284814 | + | 0.493312i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.30819 | − | 3.99791i | 0.175489 | − | 0.303955i | −0.764842 | − | 0.644218i | \(-0.777183\pi\) |
0.940330 | + | 0.340263i | \(0.110516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9102 | + | 18.8970i | 0.824734 | + | 1.42848i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.6696 | −0.877139 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.37157 | 0.625721 | 0.312860 | − | 0.949799i | \(-0.398713\pi\) | ||||
0.312860 | + | 0.949799i | \(0.398713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.70802 | − | 2.95837i | −0.126956 | − | 0.219894i | 0.795540 | − | 0.605901i | \(-0.207187\pi\) |
−0.922496 | + | 0.386007i | \(0.873854\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98379 | + | 8.63218i | −0.368412 | + | 0.638109i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.6346 | + | 18.4197i | −0.781874 | + | 1.35425i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.13047 | −0.302050 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.69181 | − | 2.93030i | −0.123061 | − | 0.213148i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.36119 | − | 7.55380i | 0.315564 | − | 0.546573i | −0.663993 | − | 0.747739i | \(-0.731140\pi\) |
0.979557 | + | 0.201165i | \(0.0644729\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.69460 | −0.337925 | −0.168962 | − | 0.985623i | \(-0.554042\pi\) | ||||
−0.168962 | + | 0.985623i | \(0.554042\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.18579 | + | 8.98204i | −0.371362 | + | 0.643218i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.47128 | − | 11.2086i | −0.461059 | − | 0.798578i | 0.537955 | − | 0.842974i | \(-0.319197\pi\) |
−0.999014 | + | 0.0443955i | \(0.985864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.87343 | − | 3.24487i | 0.132804 | − | 0.230023i | −0.791953 | − | 0.610583i | \(-0.790935\pi\) |
0.924756 | + | 0.380560i | \(0.124269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.80587 | − | 2.46342i | 0.550584 | − | 0.173756i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.48147 | − | 16.4224i | 0.665468 | − | 1.15263i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.50417 | + | 11.2655i | 0.454271 | + | 0.786820i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.11036 | − | 1.92321i | 0.0771756 | − | 0.133672i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.8977 | −1.03050 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.77325 | + | 13.4637i | −0.535133 | + | 0.926877i | 0.464024 | + | 0.885823i | \(0.346405\pi\) |
−0.999157 | + | 0.0410545i | \(0.986928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.65687 | − | 11.5300i | −0.456121 | − | 0.790025i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.0402 | 1.36673 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1305 | − | 17.5465i | 0.687701 | − | 1.19113i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.80587 | + | 4.85991i | −0.189603 | + | 0.328402i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.16521 | + | 5.48231i | 0.212915 | + | 0.368780i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.514083 | 0.0344255 | 0.0172128 | − | 0.999852i | \(-0.494521\pi\) | ||||
0.0172128 | + | 0.999852i | \(0.494521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.44885 | 0.429923 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9981 | − | 24.2455i | −0.929089 | − | 1.60923i | −0.784849 | − | 0.619688i | \(-0.787259\pi\) |
−0.144241 | − | 0.989543i | \(-0.546074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.75334 | − | 6.50098i | 0.248028 | − | 0.429597i | −0.714951 | − | 0.699175i | \(-0.753551\pi\) |
0.962979 | + | 0.269578i | \(0.0868842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.38361 | − | 5.86059i | 0.222626 | − | 0.385599i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.95534 | + | 15.5111i | 0.586684 | + | 1.01617i | 0.994663 | + | 0.103175i | \(0.0329002\pi\) |
−0.407979 | + | 0.912991i | \(0.633767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.50417 | + | 11.2655i | 0.424285 | + | 0.734883i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.29985 | + | 10.9117i | 0.409219 | + | 0.708788i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.65919 | − | 6.33790i | −0.236693 | − | 0.409965i | 0.723070 | − | 0.690775i | \(-0.242730\pi\) |
−0.959763 | + | 0.280810i | \(0.909397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.9833 | 1.93139 | 0.965697 | − | 0.259670i | \(-0.0836139\pi\) | ||||
0.965697 | + | 0.259670i | \(0.0836139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.52659 | + | 13.0364i | −0.480857 | + | 0.832868i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4162 | + | 19.7735i | 0.726397 | + | 1.25816i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.03262 | − | 3.52060i | 0.128812 | − | 0.223109i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4917 | + | 23.3682i | −0.851586 | + | 1.47499i | 0.0281911 | + | 0.999603i | \(0.491025\pi\) |
−0.879777 | + | 0.475387i | \(0.842308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44145 | 0.279232 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.49398 | − | 6.05175i | 0.218801 | − | 0.378975i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.6221 | + | 21.8622i | 0.787346 | + | 1.36372i | 0.927587 | + | 0.373606i | \(0.121879\pi\) |
−0.140241 | + | 0.990117i | \(0.544788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.2693 | −1.32161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.80217 | − | 4.85350i | −0.173450 | − | 0.300424i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0532 | 0.681569 | 0.340784 | − | 0.940141i | \(-0.389307\pi\) | ||||
0.340784 | + | 0.940141i | \(0.389307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.54650 | 0.402148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.837112 | 0.0512304 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.0161 | −1.22040 | −0.610202 | − | 0.792246i | \(-0.708912\pi\) | ||||
−0.610202 | + | 0.792246i | \(0.708912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8736 | −1.45022 | −0.725109 | − | 0.688634i | \(-0.758211\pi\) | ||||
−0.725109 | + | 0.688634i | \(0.758211\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3716 | −0.627716 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.44885 | + | 11.1697i | 0.388880 | + | 0.673560i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8325 | −1.07145 | −0.535724 | − | 0.844393i | \(-0.679961\pi\) | ||||
−0.535724 | + | 0.844393i | \(0.679961\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.99398 | − | 5.18572i | −0.179245 | − | 0.310461i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.63649 | + | 9.76269i | −0.336245 | + | 0.582393i | −0.983723 | − | 0.179691i | \(-0.942490\pi\) |
0.647478 | + | 0.762084i | \(0.275824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.5673 | −1.10371 | −0.551855 | − | 0.833940i | \(-0.686080\pi\) | ||||
−0.551855 | + | 0.833940i | \(0.686080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.6020 | − | 21.8273i | 0.746479 | − | 1.29294i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.50417 | + | 11.2655i | −0.383929 | + | 0.664984i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.36740 | + | 11.0287i | 0.374553 | + | 0.648745i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.08144 | + | 5.33722i | −0.180637 | + | 0.312873i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.8000 | −1.97462 | −0.987310 | − | 0.158806i | \(-0.949236\pi\) | ||||
−0.987310 | + | 0.158806i | \(0.949236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.4853 | 2.29893 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.40352 | − | 5.89507i | −0.196831 | − | 0.340921i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0201 | + | 17.3553i | 0.577549 | + | 1.00034i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.09785 | − | 8.82974i | −0.292864 | − | 0.507255i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8632 | − | 29.2080i | 0.965585 | − | 1.67244i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.95117 | − | 3.37953i | 0.111359 | − | 0.192880i | −0.804959 | − | 0.593330i | \(-0.797813\pi\) |
0.916319 | + | 0.400450i | \(0.131146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.65919 | + | 2.87380i | 0.0943880 | + | 0.163485i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.6071 | 1.50875 | 0.754375 | − | 0.656444i | \(-0.227940\pi\) | ||||
0.754375 | + | 0.656444i | \(0.227940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8482 | 1.17841 | 0.589205 | − | 0.807984i | \(-0.299441\pi\) | ||||
0.589205 | + | 0.807984i | \(0.299441\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.72442 | + | 9.91499i | 0.322535 | + | 0.558647i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.90002 | − | 6.75504i | 0.219047 | − | 0.379401i | −0.735470 | − | 0.677557i | \(-0.763039\pi\) |
0.954517 | + | 0.298157i | \(0.0963719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.60434 | − | 9.70700i | 0.313783 | − | 0.543488i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.15084 | −0.454936 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.69181 | − | 13.3226i | −0.427984 | − | 0.741289i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.88361 | − | 17.1189i | 0.548244 | − | 0.949587i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3063 | 0.957043 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.50417 | + | 11.2655i | −0.358586 | + | 0.621090i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0569 | + | 17.4190i | 0.552777 | + | 0.957437i | 0.998073 | + | 0.0620538i | \(0.0197650\pi\) |
−0.445296 | + | 0.895383i | \(0.646902\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.14298 | + | 5.44380i | −0.172234 | + | 0.298318i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.4121 | + | 8.33525i | −1.44304 | + | 0.455403i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0819 | − | 20.9265i | 0.658144 | − | 1.13994i | −0.322952 | − | 0.946415i | \(-0.604675\pi\) |
0.981096 | − | 0.193523i | \(-0.0619914\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.14066 | + | 10.6359i | 0.333515 | + | 0.577664i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.98796 | − | 10.3714i | 0.324266 | − | 0.561645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.63211 | 0.466090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.75704 | + | 6.50739i | −0.202272 | + | 0.350346i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.04048 | − | 10.4624i | −0.324270 | − | 0.561652i | 0.657094 | − | 0.753808i | \(-0.271785\pi\) |
−0.981364 | + | 0.192156i | \(0.938452\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.09026 | 0.165418 | 0.0827089 | − | 0.996574i | \(-0.473643\pi\) | ||||
0.0827089 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.53262 | + | 2.65457i | −0.0818050 | + | 0.141690i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.31606 | + | 2.27948i | −0.0700466 | + | 0.121324i | −0.898922 | − | 0.438110i | \(-0.855648\pi\) |
0.828875 | + | 0.559434i | \(0.188981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.5243 | + | 39.0132i | 1.19546 | + | 2.07060i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.98796 | 0.369842 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1017 | −0.955373 | −0.477686 | − | 0.878530i | \(-0.658524\pi\) | ||||
−0.477686 | + | 0.878530i | \(0.658524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2427 | − | 31.5972i | −0.960141 | − | 1.66301i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.50000 | + | 6.06218i | −0.183702 | + | 0.318182i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.49398 | − | 16.4441i | 0.496938 | − | 0.860721i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.61685 | − | 2.80047i | −0.0843991 | − | 0.146183i | 0.820736 | − | 0.571308i | \(-0.193564\pi\) |
−0.905135 | + | 0.425124i | \(0.860230\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.92225 | + | 3.32944i | 0.100069 | + | 0.173324i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.27325 | + | 5.66944i | 0.169939 | + | 0.294343i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9241 | − | 25.8493i | −0.772740 | − | 1.33843i | −0.936056 | − | 0.351852i | \(-0.885552\pi\) |
0.163315 | − | 0.986574i | \(-0.447781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.90235 | −0.253156 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.1786 | −0.884744 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0717 | + | 19.1768i | −0.568716 | + | 0.985045i | 0.427977 | + | 0.903790i | \(0.359226\pi\) |
−0.996693 | + | 0.0812559i | \(0.974107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.49768 | + | 16.4505i | 0.486581 | + | 0.842782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0731 | − | 26.1074i | 0.770199 | − | 1.33402i | −0.167254 | − | 0.985914i | \(-0.553490\pi\) |
0.937453 | − | 0.348111i | \(-0.113177\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.4488 | + | 19.8300i | −0.583487 | + | 1.01063i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.92272 | 0.301069 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.31838 | − | 5.74760i | 0.168249 | − | 0.291415i | −0.769556 | − | 0.638580i | \(-0.779522\pi\) |
0.937804 | + | 0.347165i | \(0.112856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.29316 | + | 3.97187i | 0.115970 | + | 0.200866i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.87732 | 0.346915 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.3163 | − | 36.9208i | −1.07254 | − | 1.85769i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.518731 | 0.0260344 | 0.0130172 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130172 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.2040 | 1.26178 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.6973 | −0.534200 | −0.267100 | − | 0.963669i | \(-0.586065\pi\) | ||||
−0.267100 | + | 0.963669i | \(0.586065\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.3545 | −0.914302 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.38361 | 0.168133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.5719 | −0.623167 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.12795 | + | 8.88187i | 0.253561 | + | 0.439180i | 0.964504 | − | 0.264070i | \(-0.0850649\pi\) |
−0.710943 | + | 0.703250i | \(0.751732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.51873 | −0.0749135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.7427 | + | 34.1953i | 0.971473 | + | 1.68264i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.87759 | + | 11.9123i | −0.337608 | + | 0.584754i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9301 | 0.535250 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.41391 | − | 12.8413i | 0.362193 | − | 0.627337i | −0.626128 | − | 0.779720i | \(-0.715361\pi\) |
0.988321 | + | 0.152383i | \(0.0486948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.44468 | + | 9.43047i | −0.265358 | + | 0.459613i | −0.967657 | − | 0.252269i | \(-0.918823\pi\) |
0.702300 | + | 0.711881i | \(0.252157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.92225 | + | 3.32944i | 0.0934632 | + | 0.161883i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.65919 | + | 11.5341i | −0.323018 | + | 0.559484i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.7264 | 1.63214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.13047 | −0.295982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4671 | + | 31.9860i | 0.889529 | + | 1.54071i | 0.840433 | + | 0.541915i | \(0.182301\pi\) |
0.0490954 | + | 0.998794i | \(0.484366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1913 | − | 33.2404i | −0.922276 | − | 1.59743i | −0.795884 | − | 0.605449i | \(-0.792994\pi\) |
−0.126392 | − | 0.991980i | \(-0.540340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.48147 | + | 16.4224i | 0.454601 | + | 0.787393i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.27093 | + | 14.3257i | 0.395652 | + | 0.685290i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5308 | − | 18.2398i | 0.502606 | − | 0.870539i | −0.497390 | − | 0.867527i | \(-0.665708\pi\) |
0.999995 | − | 0.00301154i | \(-0.000958603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.22442 | + | 3.85282i | −0.105925 | + | 0.183467i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.91993 | − | 11.9857i | −0.328776 | − | 0.569456i | 0.653493 | − | 0.756932i | \(-0.273303\pi\) |
−0.982269 | + | 0.187476i | \(0.939969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.83246 | −0.134272 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0365 | −1.13689 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6900 | + | 25.4437i | 0.693262 | + | 1.20076i | 0.970763 | + | 0.240039i | \(0.0771603\pi\) |
−0.277502 | + | 0.960725i | \(0.589506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.84451 | + | 6.65888i | −0.181031 | + | 0.313555i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.90604 | − | 3.30136i | 0.0895537 | − | 0.155112i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.0934 | 1.64520 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.94079 | + | 3.36154i | 0.0907862 | + | 0.157246i | 0.907842 | − | 0.419312i | \(-0.137729\pi\) |
−0.817056 | + | 0.576558i | \(0.804395\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.03262 | − | 1.78855i | 0.0481984 | − | 0.0834821i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.40399 | 0.158540 | 0.0792698 | − | 0.996853i | \(-0.474741\pi\) | ||||
0.0792698 | + | 0.996853i | \(0.474741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.3894 | + | 26.6551i | −0.715204 | + | 1.23877i | 0.247677 | + | 0.968843i | \(0.420333\pi\) |
−0.962881 | + | 0.269927i | \(0.913001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1305 | + | 17.5465i | 0.469789 | + | 0.813699i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.0983 | + | 22.6870i | −0.606118 | + | 1.04983i | 0.385756 | + | 0.922601i | \(0.373941\pi\) |
−0.991874 | + | 0.127226i | \(0.959393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.4246 | − | 18.7059i | −0.943119 | − | 0.863757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.83711 | − | 3.18197i | 0.0846496 | − | 0.146617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.92272 | + | 10.2585i | 0.272327 | + | 0.471684i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.0182 | + | 41.6008i | −1.10203 | + | 1.90878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.93477 | 0.0885869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.4666 | − | 31.9851i | 0.843762 | − | 1.46144i | −0.0429303 | − | 0.999078i | \(-0.513669\pi\) |
0.886692 | − | 0.462360i | \(-0.152997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.63397 | + | 16.6865i | 0.439271 | + | 0.760840i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.51408 | −0.341903 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4264 | − | 18.0591i | 0.473439 | − | 0.820021i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.84313 | − | 11.8527i | 0.310092 | − | 0.537095i | −0.668290 | − | 0.743901i | \(-0.732973\pi\) |
0.978382 | + | 0.206806i | \(0.0663068\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.03631 | + | 12.1873i | 0.318193 | + | 0.551127i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.727413 | 0.0328277 | 0.0164138 | − | 0.999865i | \(-0.494775\pi\) | ||||
0.0164138 | + | 0.999865i | \(0.494775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5743 | 0.521279 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.38361 | + | 5.86059i | 0.152082 | + | 0.263414i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5243 | + | 39.0132i | −1.01035 | + | 1.74998i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2087 | − | 22.8781i | 0.591302 | − | 1.02416i | −0.402756 | − | 0.915308i | \(-0.631948\pi\) |
0.994057 | − | 0.108857i | \(-0.0347191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1835 | + | 19.3703i | 0.499640 | + | 0.865402i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6346 | − | 27.0800i | −0.697114 | − | 1.20744i | −0.969463 | − | 0.245238i | \(-0.921134\pi\) |
0.272349 | − | 0.962199i | \(-0.412199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.2492 | + | 29.8764i | 0.767578 | + | 1.32948i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.80217 | − | 3.12145i | −0.0800372 | − | 0.138629i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.7505 | 1.67326 | 0.836632 | − | 0.547766i | \(-0.184522\pi\) | ||||
0.836632 | + | 0.547766i | \(0.184522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9880 | 0.839978 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.72442 | − | 6.45089i | 0.164437 | − | 0.284814i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.61406 | − | 9.72384i | −0.247385 | − | 0.428484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.84451 | + | 6.65888i | −0.169081 | + | 0.292857i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.30819 | + | 3.99791i | −0.101318 | + | 0.175489i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2860 | −0.450636 | −0.225318 | − | 0.974285i | \(-0.572342\pi\) | ||||
−0.225318 | + | 0.974285i | \(0.572342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.64947 | + | 6.32107i | −0.159580 | + | 0.276401i | −0.934717 | − | 0.355392i | \(-0.884347\pi\) |
0.775137 | + | 0.631793i | \(0.217681\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.9102 | − | 18.8970i | −0.476161 | − | 0.824734i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.3665 | 0.538694 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.03419 | + | 15.6477i | 0.392791 | + | 0.680334i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6696 | 0.506416 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7843 | 0.510435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.5793 | 1.19236 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.37157 | −0.361260 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.89770 | −0.383251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.2485 | −1.21450 | −0.607249 | − | 0.794512i | \(-0.707727\pi\) | ||||
−0.607249 | + | 0.794512i | \(0.707727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.70802 | + | 2.95837i | 0.0732981 | + | 0.126956i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −58.5580 | −2.50835 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.13444 | − | 1.96490i | −0.0485050 | − | 0.0840132i | 0.840754 | − | 0.541418i | \(-0.182112\pi\) |
−0.889259 | + | 0.457405i | \(0.848779\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.98379 | − | 8.63218i | 0.212703 | − | 0.368412i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.7459 | 1.77843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.3163 | − | 36.9208i | 0.906459 | − | 1.57003i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.6346 | − | 18.4197i | 0.451415 | − | 0.781874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2711 | + | 21.2542i | 0.519944 | + | 0.900570i | 0.999731 | + | 0.0231848i | \(0.00738060\pi\) |
−0.479787 | + | 0.877385i | \(0.659286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.07726 | − | 15.7223i | 0.383927 | − | 0.664982i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13047 | 0.174388 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9509 | −1.17799 | −0.588995 | − | 0.808137i | \(-0.700476\pi\) | ||||
−0.588995 | + | 0.808137i | \(0.700476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.7776 | − | 35.9879i | −0.874121 | − | 1.51402i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.69181 | + | 2.93030i | 0.0710492 | + | 0.123061i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.28317 | − | 12.6148i | −0.305326 | − | 0.528841i | 0.672008 | − | 0.740544i | \(-0.265432\pi\) |
−0.977334 | + | 0.211704i | \(0.932099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2529 | − | 19.4905i | −0.470918 | − | 0.815653i | 0.528529 | − | 0.848915i | \(-0.322744\pi\) |
−0.999447 | + | 0.0332620i | \(0.989410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.36119 | + | 7.55380i | −0.182191 | + | 0.315564i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.16056 | − | 12.4025i | 0.298616 | − | 0.517218i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5833 | + | 20.0628i | 0.482219 | + | 0.835227i | 0.999792 | − | 0.0204120i | \(-0.00649779\pi\) |
−0.517573 | + | 0.855639i | \(0.673164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.69460 | 0.195101 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.7552 | −0.570661 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93477 | + | 3.35111i | 0.0801298 | + | 0.138789i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.18579 | − | 8.98204i | 0.214406 | − | 0.371362i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.22859 | + | 10.7882i | −0.257081 | + | 0.445278i | −0.965459 | − | 0.260556i | \(-0.916094\pi\) |
0.708377 | + | 0.705834i | \(0.249428\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.6034 | 1.83785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.47128 | + | 11.2086i | 0.266193 | + | 0.461059i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9181 | − | 29.3030i | 0.694742 | − | 1.20333i | −0.275526 | − | 0.961294i | \(-0.588852\pi\) |
0.970268 | − | 0.242035i | \(-0.0778148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.6446 | −0.969332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.87343 | + | 3.24487i | −0.0766742 | + | 0.132804i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0349 | − | 24.3092i | −0.573452 | − | 0.993248i | −0.996208 | − | 0.0870046i | \(-0.972271\pi\) |
0.422756 | − | 0.906244i | \(-0.361063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.7059 | + | 25.4713i | −0.599866 | + | 1.03900i | 0.392975 | + | 0.919549i | \(0.371446\pi\) |
−0.992840 | + | 0.119449i | \(0.961887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.80587 | + | 2.46342i | −0.317880 | + | 0.100318i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8427 | − | 20.5121i | 0.481472 | − | 0.833934i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.59553 | + | 16.6199i | 0.389470 | + | 0.674583i | 0.992378 | − | 0.123228i | \(-0.0393247\pi\) |
−0.602908 | + | 0.797811i | \(0.705991\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.48147 | + | 16.4224i | −0.384208 | + | 0.665468i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.7843 | 0.476742 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0574 | + | 26.0801i | −0.608161 | + | 1.05337i | 0.383382 | + | 0.923590i | \(0.374759\pi\) |
−0.991543 | + | 0.129776i | \(0.958574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.50417 | − | 11.2655i | −0.262273 | − | 0.454271i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.7579 | −0.835683 | −0.417841 | − | 0.908520i | \(-0.637213\pi\) | ||||
−0.417841 | + | 0.908520i | \(0.637213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.359344 | − | 0.622402i | 0.0144433 | − | 0.0250165i | −0.858713 | − | 0.512456i | \(-0.828736\pi\) |
0.873157 | + | 0.487440i | \(0.162069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.11036 | + | 1.92321i | −0.0445573 | + | 0.0771756i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.41623 | − | 2.45299i | −0.0567401 | − | 0.0982768i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.6566 | −0.626264 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.8977 | 0.594957 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.49099 | − | 11.2427i | −0.258813 | − | 0.448277i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.85257 | − | 11.8690i | 0.272796 | − | 0.472497i | −0.696780 | − | 0.717285i | \(-0.745385\pi\) |
0.969577 | + | 0.244787i | \(0.0787181\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.77325 | − | 13.4637i | 0.308959 | − | 0.535133i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.1365 | − | 55.6620i | −1.27530 | − | 2.20888i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.81838 | + | 11.8098i | 0.270154 | + | 0.467921i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.65687 | + | 11.5300i | 0.263342 | + | 0.456121i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.61658 | − | 7.99615i | −0.182344 | − | 0.315829i | 0.760334 | − | 0.649532i | \(-0.225035\pi\) |
−0.942678 | + | 0.333703i | \(0.891702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.2031 | −0.441807 | −0.220904 | − | 0.975296i | \(-0.570901\pi\) | ||||
−0.220904 | + | 0.975296i | \(0.570901\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.0402 | −0.789082 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.1839 | − | 26.2993i | 0.596942 | − | 1.03393i | −0.396328 | − | 0.918109i | \(-0.629716\pi\) |
0.993270 | − | 0.115825i | \(-0.0369510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.6696 | + | 20.2123i | 0.458071 | + | 0.793402i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.1305 | + | 17.5465i | −0.397044 | + | 0.687701i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.2388 | + | 36.7866i | −0.831138 | + | 1.43957i | 0.0659991 | + | 0.997820i | \(0.478977\pi\) |
−0.897137 | + | 0.441753i | \(0.854357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.2702 | −0.909242 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.80587 | − | 4.85991i | 0.109467 | − | 0.189603i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.62611 | − | 13.2088i | −0.297071 | − | 0.514542i | 0.678394 | − | 0.734699i | \(-0.262676\pi\) |
−0.975465 | + | 0.220157i | \(0.929343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7218 | 1.23384 | 0.616918 | − | 0.787027i | \(-0.288381\pi\) | ||||
0.616918 | + | 0.787027i | \(0.288381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.16521 | − | 5.48231i | −0.122927 | − | 0.212915i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −85.2807 | −3.30705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.4457 | −0.481900 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.514083 | −0.0198756 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.9352 | 0.769588 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7904 | −0.878504 | −0.439252 | − | 0.898364i | \(-0.644756\pi\) | ||||
−0.439252 | + | 0.898364i | \(0.644756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.44885 | −0.248216 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5164 | + | 23.4111i | 0.519478 | + | 0.899762i | 0.999744 | + | 0.0226389i | \(0.00720680\pi\) |
−0.480266 | + | 0.877123i | \(0.659460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.8528 | 0.800259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.9981 | + | 24.2455i | 0.536410 | + | 0.929089i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.05784 | + | 3.56428i | −0.0787410 | + | 0.136383i | −0.902707 | − | 0.430256i | \(-0.858423\pi\) |
0.823966 | + | 0.566639i | \(0.191757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.13880 | 0.196343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.75334 | + | 6.50098i | −0.143199 | + | 0.248028i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.96526 | − | 5.13597i | 0.112967 | − | 0.195665i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.82692 | − | 6.62843i | −0.145583 | − | 0.252157i | 0.784007 | − | 0.620752i | \(-0.213172\pi\) |
−0.929590 | + | 0.368594i | \(0.879839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.38361 | + | 5.86059i | −0.128533 | + | 0.222626i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.9833 | −1.40286 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.93981 | −0.300742 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.95534 | − | 15.5111i | −0.338722 | − | 0.586684i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9558 | − | 22.4401i | −0.489334 | − | 0.847551i | 0.510591 | − | 0.859824i | \(-0.329427\pi\) |
−0.999925 | + | 0.0122725i | \(0.996093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.4116 | − | 40.5501i | −0.882985 | − | 1.52937i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.50417 | − | 11.2655i | −0.244961 | − | 0.424285i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2492 | + | 29.8764i | −0.648722 | + | 1.12362i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.0204 | + | 19.0879i | −0.413879 | + | 0.716859i | −0.995310 | − | 0.0967363i | \(-0.969160\pi\) |
0.581431 | + | 0.813596i | \(0.302493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.29985 | − | 10.9117i | −0.236263 | − | 0.409219i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.2976 | −0.497999 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.7431 | 0.775749 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.65919 | + | 6.33790i | 0.136655 | + | 0.236693i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1705 | − | 21.0799i | 0.453882 | − | 0.786147i | −0.544741 | − | 0.838604i | \(-0.683372\pi\) |
0.998623 | + | 0.0524572i | \(0.0167053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.61406 | − | 9.72384i | 0.209079 | − | 0.362135i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.9833 | −1.11509 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0708 | − | 31.2995i | −0.671132 | − | 1.16243i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4773 | − | 19.8793i | 0.425669 | − | 0.737281i | −0.570813 | − | 0.821080i | \(-0.693372\pi\) |
0.996483 | + | 0.0837988i | \(0.0267053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.11590 | + | 10.5931i | −0.226205 | + | 0.391798i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.3815 | + | 21.4454i | 0.457321 | + | 0.792103i | 0.998818 | − | 0.0485996i | \(-0.0154758\pi\) |
−0.541498 | + | 0.840702i | \(0.682143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.52659 | − | 13.0364i | 0.277623 | − | 0.480857i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0726 | − | 11.0567i | −0.444701 | − | 0.407280i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.47591 | + | 16.4128i | −0.348577 | + | 0.603753i | −0.985997 | − | 0.166763i | \(-0.946668\pi\) |
0.637420 | + | 0.770517i | \(0.280002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.4162 | − | 19.7735i | −0.419386 | − | 0.726397i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.3637 | + | 17.9505i | −0.380208 | + | 0.658539i | −0.991092 | − | 0.133181i | \(-0.957481\pi\) |
0.610884 | + | 0.791720i | \(0.290814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 81.3302 | 2.97971 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.03262 | + | 3.52060i | −0.0743696 | + | 0.128812i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7897 | + | 23.8844i | 0.503863 | + | 0.872717i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0241 | 1.35103 | 0.675514 | − | 0.737348i | \(-0.263922\pi\) | ||||
0.675514 | + | 0.737348i | \(0.263922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4917 | − | 23.3682i | 0.491663 | − | 0.851586i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.44932 | + | 11.1705i | −0.234715 | + | 0.406538i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.58301 | − | 13.1342i | −0.275609 | − | 0.477369i | 0.694679 | − | 0.719320i | \(-0.255546\pi\) |
−0.970289 | + | 0.241950i | \(0.922213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.44145 | −0.161215 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.28871 | −0.119216 | −0.0596078 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596078 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.2790 | − | 50.7127i | −1.05997 | − | 1.83592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.49398 | + | 6.05175i | −0.126325 | + | 0.218801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.8850 | − | 30.9777i | 0.645790 | − | 1.11854i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0391 | + | 24.3164i | 0.506263 | + | 0.876874i | 0.999974 | + | 0.00724723i | \(0.00230689\pi\) |
−0.493711 | + | 0.869626i | \(0.664360\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.6221 | − | 21.8622i | −0.454575 | − | 0.787346i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.88983 | − | 6.73739i | −0.139908 | − | 0.242327i | 0.787554 | − | 0.616246i | \(-0.211347\pi\) |
−0.927461 | + | 0.373919i | \(0.878014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.3077 | − | 33.4419i | −0.693553 | − | 1.20127i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.2693 | 0.763031 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6372 | −1.02603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3137 | + | 23.0601i | −0.476403 | + | 0.825154i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.80217 | + | 4.85350i | 0.100141 | + | 0.173450i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.21608 | + | 10.7666i | −0.221861 | + | 0.384275i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.27372 | − | 10.8664i | 0.223634 | − | 0.387345i | −0.732275 | − | 0.681009i | \(-0.761541\pi\) |
0.955909 | + | 0.293664i | \(0.0948747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0532 | −0.393504 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7776 | − | 35.9879i | 0.738767 | − | 1.27958i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2765 | − | 26.4596i | −0.542484 | − | 0.939609i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.54650 | −0.232181 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5574 | + | 30.4102i | 0.621913 | + | 1.07719i | 0.989129 | + | 0.147050i | \(0.0469778\pi\) |
−0.367216 | + | 0.930136i | \(0.619689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.93981 | −0.280890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.837112 | −0.0295779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.2235 | 0.396068 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.4248 | 0.896105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0161 | 0.704601 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.5539 | −0.757795 | −0.378897 | − | 0.925439i | \(-0.623697\pi\) | ||||
−0.378897 | + | 0.925439i | \(0.623697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2003 | + | 26.3278i | 0.533756 | + | 0.924492i | 0.999222 | + | 0.0394270i | \(0.0125532\pi\) |
−0.465466 | + | 0.885066i | \(0.654113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.8736 | 0.837284 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8082 | − | 41.2370i | −0.833964 | − | 1.44447i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0587 | + | 38.2068i | −0.771737 | + | 1.33669i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3716 | 0.362412 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.88778 | + | 6.73383i | −0.135684 | + | 0.235012i | −0.925859 | − | 0.377870i | \(-0.876657\pi\) |
0.790174 | + | 0.612882i | \(0.209990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.2001 | + | 38.4518i | −0.773848 | + | 1.34034i | 0.161591 | + | 0.986858i | \(0.448337\pi\) |
−0.935440 | + | 0.353487i | \(0.884996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.44885 | − | 11.1697i | −0.224520 | − | 0.388880i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8026 | + | 25.6389i | −0.514738 | + | 0.891553i | 0.485116 | + | 0.874450i | \(0.338778\pi\) |
−0.999854 | + | 0.0171026i | \(0.994556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.7352 | −1.41479 | −0.707396 | − | 0.706817i | \(-0.750130\pi\) | ||||
−0.707396 | + | 0.706817i | \(0.750130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8325 | 0.618601 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.59396 | − | 7.95697i | −0.159171 | − | 0.275693i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.8405 | − | 65.5417i | −1.30953 | − | 2.26816i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.99398 | + | 5.18572i | 0.103487 | + | 0.179245i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1286 | + | 38.3279i | 0.763965 | + | 1.32323i | 0.940792 | + | 0.338984i | \(0.110083\pi\) |
−0.176828 | + | 0.984242i | \(0.556584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20432 | + | 2.08594i | −0.0415283 | + | 0.0719291i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.63649 | − | 9.76269i | 0.194131 | − | 0.336245i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.09785 | + | 10.5618i | 0.209772 | + | 0.363337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.6853 | 0.813837 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.5673 | 0.637227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.97970 | + | 12.0892i | 0.239261 | + | 0.414412i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.4431 | + | 21.5521i | −0.426044 | + | 0.737929i | −0.996517 | − | 0.0833868i | \(-0.973426\pi\) |
0.570474 | + | 0.821316i | \(0.306760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6020 | + | 21.8273i | −0.430980 | + | 0.746479i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.9870 | 1.50257 | 0.751284 | − | 0.659980i | \(-0.229435\pi\) | ||||
0.751284 | + | 0.659980i | \(0.229435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.8042 | + | 42.9622i | 0.846309 | + | 1.46585i | 0.884480 | + | 0.466578i | \(0.154513\pi\) |
−0.0381711 | + | 0.999271i | \(0.512153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.50417 | − | 11.2655i | 0.221661 | − | 0.383929i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.8616 | −1.69731 | −0.848654 | − | 0.528949i | \(-0.822586\pi\) | ||||
−0.848654 | + | 0.528949i | \(0.822586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.81003 | − | 13.5274i | 0.265549 | − | 0.459945i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.36740 | − | 11.0287i | −0.216248 | − | 0.374553i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5997 | − | 21.8233i | 0.427415 | − | 0.740305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.42410 | + | 24.4967i | −0.183788 | + | 0.830039i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.08144 | − | 5.33722i | 0.104291 | − | 0.180637i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.29382 | + | 14.3653i | 0.280382 | + | 0.485637i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.54699 | + | 6.14356i | −0.119773 | + | 0.207453i | −0.919678 | − | 0.392674i | \(-0.871550\pi\) |
0.799905 | + | 0.600127i | \(0.204883\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.8000 | 1.14005 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6150 | − | 23.5819i | 0.458701 | − | 0.794493i | −0.540192 | − | 0.841542i | \(-0.681648\pi\) |
0.998893 | + | 0.0470487i | \(0.0149816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.42363 | − | 4.19785i | −0.0815616 | − | 0.141269i | 0.822359 | − | 0.568969i | \(-0.192657\pi\) |
−0.903921 | + | 0.427700i | \(0.859324\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.4853 | −1.32729 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7369 | − | 25.5251i | 0.494818 | − | 0.857050i | −0.505164 | − | 0.863023i | \(-0.668568\pi\) |
0.999982 | + | 0.00597347i | \(0.00190142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.1365 | − | 55.6620i | 1.07782 | − | 1.86684i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.6372 | −0.958306 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.3262 | 0.946839 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.40352 | + | 5.89507i | 0.113640 | + | 0.196831i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.7793 | + | 29.0626i | −0.559620 | + | 0.969290i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.99787 | + | 3.46042i | −0.0665588 | + | 0.115283i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.0201 | − | 17.3553i | −0.333448 | − | 0.577549i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.77927 | − | 10.0100i | −0.192110 | − | 0.332744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0039 | − | 48.5041i | −0.929854 | − | 1.61055i | −0.783563 | − | 0.621312i | \(-0.786600\pi\) |
−0.146290 | − | 0.989242i | \(-0.546733\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.09785 | + | 8.82974i | 0.169085 | + | 0.292864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.1837 | 1.56326 | 0.781632 | − | 0.623740i | \(-0.214387\pi\) | ||||
0.781632 | + | 0.623740i | \(0.214387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.13047 | −0.269079 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.8632 | + | 29.2080i | −0.557481 | + | 0.965585i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.6351 | − | 20.1526i | −0.384225 | − | 0.665497i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0286 | + | 41.6188i | −0.792631 | + | 1.37288i | 0.131701 | + | 0.991290i | \(0.457956\pi\) |
−0.924332 | + | 0.381588i | \(0.875377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.95117 | + | 3.37953i | −0.0642933 | + | 0.111359i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.8097 | 1.34327 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.2686 | + | 35.1063i | −0.666428 | + | 1.15429i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.65919 | − | 2.87380i | −0.0544950 | − | 0.0943880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.3314 | 0.667050 | 0.333525 | − | 0.942741i | \(-0.391762\pi\) | ||||
0.333525 | + | 0.942741i | \(0.391762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5694 | − | 28.6990i | −0.543040 | − | 0.940573i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.6071 | −0.871077 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.9759 | −0.457061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.5904 | −1.13002 | −0.565009 | − | 0.825084i | \(-0.691128\pi\) | ||||
−0.565009 | + | 0.825084i | \(0.691128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.8482 | −0.680355 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.9125 | 1.39891 | 0.699454 | − | 0.714678i | \(-0.253427\pi\) | ||||
0.699454 | + | 0.714678i | \(0.253427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.53760 | 0.278022 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.72442 | − | 9.91499i | −0.186216 | − | 0.322535i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6482 | 1.12592 | 0.562958 | − | 0.826485i | \(-0.309663\pi\) | ||||
0.562958 | + | 0.826485i | \(0.309663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.60064 | − | 14.8968i | −0.279189 | − | 0.483569i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.90002 | + | 6.75504i | −0.126467 | + | 0.219047i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.9023 | −0.936239 | −0.468119 | − | 0.883665i | \(-0.655068\pi\) | ||||
−0.468119 | + | 0.883665i | \(0.655068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7566 | − | 25.5591i | 0.477511 | − | 0.827074i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.60434 | + | 9.70700i | −0.181163 | + | 0.313783i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.56940 | + | 4.45033i | 0.0829703 | + | 0.143709i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.42781 | + | 4.20509i | −0.0783164 | + | 0.135648i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.15084 | 0.262657 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.8847 | −0.511347 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6309 | − | 25.3415i | −0.470499 | − | 0.814928i | 0.528932 | − | 0.848664i | \(-0.322593\pi\) |
−0.999431 | + | 0.0337360i | \(0.989259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.69181 | + | 13.3226i | 0.247096 | + | 0.427984i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0761 | − | 29.5766i | −0.547998 | − | 0.949160i | −0.998412 | − | 0.0563400i | \(-0.982057\pi\) |
0.450414 | − | 0.892820i | \(-0.351276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4917 | − | 32.0285i | −0.592815 | − | 1.02679i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.88361 | + | 17.1189i | −0.316529 | + | 0.548244i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.4134 | + | 21.5007i | −0.397141 | + | 0.687869i | −0.993372 | − | 0.114944i | \(-0.963331\pi\) |
0.596231 | + | 0.802813i | \(0.296664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.837112 | − | 1.44992i | −0.0267542 | − | 0.0463396i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3063 | −0.552549 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.1920 | −0.325074 | −0.162537 | − | 0.986702i | \(-0.551968\pi\) | ||||
−0.162537 | + | 0.986702i | \(0.551968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8963 | − | 37.9255i | −0.697674 | − | 1.20841i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.50417 | − | 11.2655i | 0.207030 | − | 0.358586i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.57637 | − | 11.3906i | 0.209116 | − | 0.362200i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.25260 | 0.103322 | 0.0516612 | − | 0.998665i | \(-0.483548\pi\) | ||||
0.0516612 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0569 | − | 17.4190i | −0.319146 | − | 0.552777i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.33895 | − | 10.9794i | 0.200958 | − | 0.348070i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0619 | 1.39545 | 0.697727 | − | 0.716363i | \(-0.254195\pi\) | ||||
0.697727 | + | 0.716363i | \(0.254195\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.14298 | − | 5.44380i | 0.0994395 | − | 0.172234i |
(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 | 804.2.i.d.565.4 | yes | 8 | |
3.2 | odd | 2 | 2412.2.l.e.1369.1 | 8 | |||
67.37 | even | 3 | inner | 804.2.i.d.37.4 | ✓ | 8 | |
201.104 | odd | 6 | 2412.2.l.e.37.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.i.d.37.4 | ✓ | 8 | 67.37 | even | 3 | inner | |
804.2.i.d.565.4 | yes | 8 | 1.1 | even | 1 | trivial | |
2412.2.l.e.37.1 | 8 | 201.104 | odd | 6 | |||
2412.2.l.e.1369.1 | 8 | 3.2 | odd | 2 |