Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(1249,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, 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("1300.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(0.675970 - 0.675970i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.1249 |
Dual form | 1300.2.c.f.1249.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.35194i | 0.780542i | 0.920700 | + | 0.390271i | \(0.127619\pi\) | ||||
−0.920700 | + | 0.390271i | \(0.872381\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.17226i | − 1.57697i | −0.615056 | − | 0.788483i | \(-0.710867\pi\) | ||||
0.615056 | − | 0.788483i | \(-0.289133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.17226 | 0.390753 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.52420 | −1.66561 | −0.832804 | − | 0.553567i | \(-0.813266\pi\) | ||||
−0.832804 | + | 0.553567i | \(0.813266\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.703878i | 0.170716i | 0.996350 | + | 0.0853578i | \(0.0272033\pi\) | ||||
−0.996350 | + | 0.0853578i | \(0.972797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82032 | −1.56469 | −0.782344 | − | 0.622846i | \(-0.785976\pi\) | ||||
−0.782344 | + | 0.622846i | \(0.785976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.64064 | 1.23089 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2.64806i | − 0.552159i | −0.961135 | − | 0.276079i | \(-0.910965\pi\) | ||||
0.961135 | − | 0.276079i | \(-0.0890353\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64064i | 1.08554i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.17226 | −1.51755 | −0.758775 | − | 0.651352i | \(-0.774202\pi\) | ||||
−0.758775 | + | 0.651352i | \(0.774202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.52420 | −1.71060 | −0.855298 | − | 0.518136i | \(-0.826626\pi\) | ||||
−0.855298 | + | 0.518136i | \(0.826626\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 7.46838i | − 1.30008i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.87614i | 1.13043i | 0.824944 | + | 0.565215i | \(0.191207\pi\) | ||||
−0.824944 | + | 0.565215i | \(0.808793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.35194 | −0.216484 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.703878 | 0.109927 | 0.0549637 | − | 0.998488i | \(-0.482496\pi\) | ||||
0.0549637 | + | 0.998488i | \(0.482496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.35194i | − 0.206169i | −0.994673 | − | 0.103084i | \(-0.967129\pi\) | ||||
0.994673 | − | 0.103084i | \(-0.0328712\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.17226i | 1.19205i | 0.802967 | + | 0.596023i | \(0.203253\pi\) | ||||
−0.802967 | + | 0.596023i | \(0.796747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.4078 | −1.48682 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.951601 | −0.133251 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.04840i | 0.693451i | 0.937967 | + | 0.346725i | \(0.112706\pi\) | ||||
−0.937967 | + | 0.346725i | \(0.887294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 9.22066i | − 1.22131i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2281 | 1.59196 | 0.795980 | − | 0.605323i | \(-0.206956\pi\) | ||||
0.795980 | + | 0.605323i | \(0.206956\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.172260 | −0.0220557 | −0.0110278 | − | 0.999939i | \(-0.503510\pi\) | ||||
−0.0110278 | + | 0.999939i | \(0.503510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.89098i | − 0.616205i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.8761i | − 1.32873i | −0.747407 | − | 0.664366i | \(-0.768702\pi\) | ||||
0.747407 | − | 0.664366i | \(-0.231298\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.58002 | 0.430983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.52420 | −0.655602 | −0.327801 | − | 0.944747i | \(-0.606308\pi\) | ||||
−0.327801 | + | 0.944747i | \(0.606308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11.2207i | − 1.31328i | −0.754205 | − | 0.656639i | \(-0.771977\pi\) | ||||
0.754205 | − | 0.656639i | \(-0.228023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.0484i | 2.62661i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.29612 | −0.145825 | −0.0729125 | − | 0.997338i | \(-0.523229\pi\) | ||||
−0.0729125 | + | 0.997338i | \(0.523229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.10902 | −0.456558 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.58002i | − 1.05154i | −0.850626 | − | 0.525772i | \(-0.823777\pi\) | ||||
0.850626 | − | 0.525772i | \(-0.176223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 11.0484i | − 1.18451i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7523 | −1.24574 | −0.622869 | − | 0.782326i | \(-0.714033\pi\) | ||||
−0.622869 | + | 0.782326i | \(0.714033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17226 | 0.437372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 12.8761i | − 1.33519i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 18.3445i | − 1.86260i | −0.364248 | − | 0.931302i | \(-0.618674\pi\) | ||||
0.364248 | − | 0.931302i | \(-0.381326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.47580 | −0.650842 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.9926i | − 1.08313i | −0.840658 | − | 0.541566i | \(-0.817832\pi\) | ||||
0.840658 | − | 0.541566i | \(-0.182168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 6.99258i | − 0.675998i | −0.941146 | − | 0.337999i | \(-0.890250\pi\) | ||||
0.941146 | − | 0.337999i | \(-0.109750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40776 | −0.326404 | −0.163202 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163202 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.29612 | −0.882349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.64064i | 0.342483i | 0.985229 | + | 0.171241i | \(0.0547778\pi\) | ||||
−0.985229 | + | 0.171241i | \(0.945222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17226i | 0.108376i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.93676 | 0.269213 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5168 | 1.77425 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.951601i | 0.0858030i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.69646i | 0.505479i | 0.967534 | + | 0.252740i | \(0.0813316\pi\) | ||||
−0.967534 | + | 0.252740i | \(0.918668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.82774 | 0.160923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7523 | 1.55102 | 0.775512 | − | 0.631333i | \(-0.217492\pi\) | ||||
0.775512 | + | 0.631333i | \(0.217492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.4562i | 2.46746i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.93676i | 0.763519i | 0.924262 | + | 0.381760i | \(0.124682\pi\) | ||||
−0.924262 | + | 0.381760i | \(0.875318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2961 | −1.12776 | −0.563881 | − | 0.825856i | \(-0.690692\pi\) | ||||
−0.563881 | + | 0.825856i | \(0.690692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0484 | −0.930443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.52420i | − 0.461957i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 14.0707i | − 1.16053i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.93676 | 0.732128 | 0.366064 | − | 0.930590i | \(-0.380705\pi\) | ||||
0.366064 | + | 0.930590i | \(0.380705\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.93196 | 0.238599 | 0.119300 | − | 0.992858i | \(-0.461935\pi\) | ||||
0.119300 | + | 0.992858i | \(0.461935\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.825129i | 0.0667077i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.592243i | − 0.0472662i | −0.999721 | − | 0.0236331i | \(-0.992477\pi\) | ||||
0.999721 | − | 0.0236331i | \(-0.00752334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82513 | −0.541268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0484 | −0.870736 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6284i | 1.30244i | 0.758890 | + | 0.651219i | \(0.225742\pi\) | ||||
−0.758890 | + | 0.651219i | \(0.774258\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.82774i | 0.296199i | 0.988972 | + | 0.148100i | \(0.0473156\pi\) | ||||
−0.988972 | + | 0.148100i | \(0.952684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.99519 | −0.611408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1116i | 1.07289i | 0.843936 | + | 0.536444i | \(0.180233\pi\) | ||||
−0.843936 | + | 0.536444i | \(0.819767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.5316i | 1.24259i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.75228 | −0.429945 | −0.214973 | − | 0.976620i | \(-0.568966\pi\) | ||||
−0.214973 | + | 0.976620i | \(0.568966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.76450 | 0.205484 | 0.102742 | − | 0.994708i | \(-0.467238\pi\) | ||||
0.102742 | + | 0.994708i | \(0.467238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 0.232886i | − 0.0172154i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.88836i | − 0.284345i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.5342 | 1.71186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 14.3445i | − 1.03254i | −0.856426 | − | 0.516271i | \(-0.827320\pi\) | ||||
0.856426 | − | 0.516271i | \(-0.172680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.40776i | 0.527781i | 0.964553 | + | 0.263890i | \(0.0850057\pi\) | ||||
−0.964553 | + | 0.263890i | \(0.914994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.75228 | −0.124216 | −0.0621078 | − | 0.998069i | \(-0.519782\pi\) | ||||
−0.0621078 | + | 0.998069i | \(0.519782\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.7039 | 1.03713 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.0968i | 2.39313i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.10422i | − 0.215758i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.6768 | 2.60616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.75228 | −0.671374 | −0.335687 | − | 0.941974i | \(-0.608969\pi\) | ||||
−0.335687 | + | 0.941974i | \(0.608969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 7.46838i | − 0.511725i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 39.7374i | 2.69755i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1696 | 1.02507 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.703878 | −0.0473480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.76450i | 0.185125i | 0.995707 | + | 0.0925624i | \(0.0295058\pi\) | ||||
−0.995707 | + | 0.0925624i | \(0.970494\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 17.8129i | − 1.18228i | −0.806568 | − | 0.591142i | \(-0.798677\pi\) | ||||
0.806568 | − | 0.591142i | \(-0.201323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1116 | −0.668196 | −0.334098 | − | 0.942538i | \(-0.608432\pi\) | ||||
−0.334098 | + | 0.942538i | \(0.608432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −31.1600 | −2.05018 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6.00000i | − 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.75228i | − 0.113823i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.86872 | −0.638354 | −0.319177 | − | 0.947695i | \(-0.603407\pi\) | ||||
−0.319177 | + | 0.947695i | \(0.603407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.88836 | −0.121640 | −0.0608201 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608201 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3668i | 0.729179i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.82032i | − 0.433967i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9516 | 0.820774 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.35936 | 0.148921 | 0.0744607 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744607 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6284i | 0.919681i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.65548i | 0.103266i | 0.998666 | + | 0.0516330i | \(0.0164426\pi\) | ||||
−0.998666 | + | 0.0516330i | \(0.983557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.6890 | 1.78265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.58002 | −0.592988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 16.6332i | − 1.02565i | −0.858494 | − | 0.512824i | \(-0.828599\pi\) | ||||
0.858494 | − | 0.512824i | \(-0.171401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 15.8884i | − 0.972352i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0968 | −0.981439 | −0.490720 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490720 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4758 | −0.636360 | −0.318180 | − | 0.948030i | \(-0.603072\pi\) | ||||
−0.318180 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.64064i | 0.341387i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 17.3929i | − 1.04504i | −0.852627 | − | 0.522520i | \(-0.824992\pi\) | ||||
0.852627 | − | 0.522520i | \(-0.175008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.1648 | −0.668422 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2961 | 0.673870 | 0.336935 | − | 0.941528i | \(-0.390610\pi\) | ||||
0.336935 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.24030i | 0.549279i | 0.961547 | + | 0.274640i | \(0.0885585\pi\) | ||||
−0.961547 | + | 0.274640i | \(0.911441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.93676i | − 0.173352i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5046 | 0.970856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.8007 | 1.45384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 16.4051i | − 0.958399i | −0.877706 | − | 0.479199i | \(-0.840927\pi\) | ||||
0.877706 | − | 0.479199i | \(-0.159073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 31.1600i | − 1.80809i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.64806 | 0.153141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.64064 | −0.325121 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.11164i | 0.466001i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.1090i | 0.862318i | 0.902276 | + | 0.431159i | \(0.141895\pi\) | ||||
−0.902276 | + | 0.431159i | \(0.858105\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8613 | 0.845430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.11164 | −0.459969 | −0.229984 | − | 0.973194i | \(-0.573867\pi\) | ||||
−0.229984 | + | 0.973194i | \(0.573867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.39292i | − 0.0787325i | −0.999225 | − | 0.0393662i | \(-0.987466\pi\) | ||||
0.999225 | − | 0.0393662i | \(-0.0125339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.8129i | 1.67446i | 0.546851 | + | 0.837230i | \(0.315826\pi\) | ||||
−0.546851 | + | 0.837230i | \(0.684174\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.1452 | 2.52765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.45355 | 0.527645 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.80068i | − 0.267117i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4.60708i | − 0.254772i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.0968 | 1.87982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1648 | −1.05339 | −0.526697 | − | 0.850053i | \(-0.676570\pi\) | ||||
−0.526697 | + | 0.850053i | \(0.676570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.06063i | 0.441720i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 11.6406i | − 0.634106i | −0.948408 | − | 0.317053i | \(-0.897307\pi\) | ||||
0.948408 | − | 0.317053i | \(-0.102693\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.92193 | −0.267322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52.6136 | 2.84919 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2180i | 0.767702i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.7597i | 1.22180i | 0.791706 | + | 0.610902i | \(0.209193\pi\) | ||||
−0.791706 | + | 0.610902i | \(0.790807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.04840 | −0.0561195 | −0.0280598 | − | 0.999606i | \(-0.508933\pi\) | ||||
−0.0280598 | + | 0.999606i | \(0.508933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.64064 | −0.301075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40515i | 0.234462i | 0.993105 | + | 0.117231i | \(0.0374018\pi\) | ||||
−0.993105 | + | 0.117231i | \(0.962598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.97033i | 0.210132i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2281 | −1.27871 | −0.639355 | − | 0.768912i | \(-0.720798\pi\) | ||||
−0.639355 | + | 0.768912i | \(0.720798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.5168 | 1.44825 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.3855i | 1.38488i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3371i | 1.42699i | 0.700663 | + | 0.713493i | \(0.252888\pi\) | ||||
−0.700663 | + | 0.713493i | \(0.747112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.825129 | 0.0429545 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.0632 | 1.09355 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6890i | 1.17479i | 0.809299 | + | 0.587397i | \(0.199847\pi\) | ||||
−0.809299 | + | 0.587397i | \(0.800153\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 8.17226i | − 0.420893i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.3249 | −1.55768 | −0.778842 | − | 0.627220i | \(-0.784193\pi\) | ||||
−0.778842 | + | 0.627220i | \(0.784193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.70127 | −0.394548 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 5.23550i | − 0.267521i | −0.991014 | − | 0.133761i | \(-0.957295\pi\) | ||||
0.991014 | − | 0.133761i | \(-0.0427053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.58482i | − 0.0805612i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8735 | −1.21044 | −0.605218 | − | 0.796060i | \(-0.706914\pi\) | ||||
−0.605218 | + | 0.796060i | \(0.706914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.86391 | 0.0942621 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000i | 1.21064i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 39.2207i | − 1.96843i | −0.176981 | − | 0.984214i | \(-0.556633\pi\) | ||||
0.176981 | − | 0.984214i | \(-0.443367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −38.4710 | −1.92596 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0336 | 1.54974 | 0.774871 | − | 0.632119i | \(-0.217815\pi\) | ||||
0.774871 | + | 0.632119i | \(0.217815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.52420i | − 0.474434i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 37.9852i | − 1.88285i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1116 | 0.895563 | 0.447781 | − | 0.894143i | \(-0.352214\pi\) | ||||
0.447781 | + | 0.894143i | \(0.352214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0820 | −0.595959 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 51.0187i | − 2.51047i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 17.9755i | − 0.880266i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0484 | 1.12599 | 0.562994 | − | 0.826461i | \(-0.309649\pi\) | ||||
0.562994 | + | 0.826461i | \(0.309649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.9123 | −1.70152 | −0.850761 | − | 0.525553i | \(-0.823859\pi\) | ||||
−0.850761 | + | 0.525553i | \(0.823859\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.58002i | 0.465796i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.718715i | 0.0347811i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.46838 | 0.360577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.47580 | 0.311928 | 0.155964 | − | 0.987763i | \(-0.450152\pi\) | ||||
0.155964 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 24.8155i | − 1.19256i | −0.802777 | − | 0.596279i | \(-0.796645\pi\) | ||||
0.802777 | − | 0.596279i | \(-0.203355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0606i | 0.863957i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8155 | −0.516196 | −0.258098 | − | 0.966119i | \(-0.583096\pi\) | ||||
−0.258098 | + | 0.966119i | \(0.583096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.2006 | −0.580981 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0410i | 0.857153i | 0.903506 | + | 0.428576i | \(0.140985\pi\) | ||||
−0.903506 | + | 0.428576i | \(0.859015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0820i | 0.571457i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1452 | −1.28106 | −0.640531 | − | 0.767933i | \(-0.721286\pi\) | ||||
−0.640531 | + | 0.767933i | \(0.721286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88836 | −0.183096 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.96383i | 0.186237i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.75228i | 0.175524i | 0.996141 | + | 0.0877621i | \(0.0279715\pi\) | ||||
−0.996141 | + | 0.0877621i | \(0.972028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.97033 | −0.185319 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.3297 | 1.69204 | 0.846021 | − | 0.533150i | \(-0.178992\pi\) | ||||
0.846021 | + | 0.533150i | \(0.178992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 29.4684i | − 1.36951i | −0.728772 | − | 0.684756i | \(-0.759909\pi\) | ||||
0.728772 | − | 0.684756i | \(-0.240091\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5848i | 0.813729i | 0.913489 | + | 0.406864i | \(0.133378\pi\) | ||||
−0.913489 | + | 0.406864i | \(0.866622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.3781 | −2.09537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.800677 | 0.0368932 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.46838i | 0.343397i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.91804i | 0.270968i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.2765 | 0.515235 | 0.257618 | − | 0.966247i | \(-0.417062\pi\) | ||||
0.257618 | + | 0.966247i | \(0.417062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.87614 | −0.313525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 14.9368i | − 0.679646i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1574i | 1.18531i | 0.805458 | + | 0.592653i | \(0.201919\pi\) | ||||
−0.805458 | + | 0.592653i | \(0.798081\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.4806 | −1.01661 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.456156 | 0.0205860 | 0.0102930 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102930 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.75228i | − 0.259070i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0484i | 1.03386i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4610 | 0.557829 | 0.278915 | − | 0.960316i | \(-0.410025\pi\) | ||||
0.278915 | + | 0.960316i | \(0.410025\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.17487 | −0.231196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 11.7933i | − 0.525835i | −0.964818 | − | 0.262918i | \(-0.915315\pi\) | ||||
0.964818 | − | 0.262918i | \(-0.0846848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.35194i | − 0.0600417i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.0484 | 1.28755 | 0.643774 | − | 0.765216i | \(-0.277368\pi\) | ||||
0.643774 | + | 0.765216i | \(0.277368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.8155 | −2.07100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 38.4710i | − 1.69854i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 45.1452i | − 1.98548i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.0781 | −0.837434 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3323 | −0.671720 | −0.335860 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335860 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4487i | 0.675526i | 0.941231 | + | 0.337763i | \(0.109670\pi\) | ||||
−0.941231 | + | 0.337763i | \(0.890330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.70388i | − 0.292026i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9878 | 0.695121 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3345 | 0.622064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.703878i | 0.0304884i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 7.77673i | − 0.335591i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.4945 | 2.47646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.8007 | −1.66817 | −0.834086 | − | 0.551635i | \(-0.814004\pi\) | ||||
−0.834086 | + | 0.551635i | \(0.814004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.73744i | 0.160389i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 14.9926i | − 0.641036i | −0.947242 | − | 0.320518i | \(-0.896143\pi\) | ||||
0.947242 | − | 0.320518i | \(-0.103857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.201934 | −0.00861833 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.7374 | 2.37449 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.40776i | 0.229961i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3807i | 1.11779i | 0.829240 | + | 0.558893i | \(0.188774\pi\) | ||||
−0.829240 | + | 0.558893i | \(0.811226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.35194 | 0.0571809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.25683 | 0.221944 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 42.0410i | − 1.77182i | −0.463861 | − | 0.885908i | \(-0.653536\pi\) | ||||
0.463861 | − | 0.885908i | \(-0.346464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.1439i | 0.719977i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.2691 | −1.26894 | −0.634472 | − | 0.772945i | \(-0.718783\pi\) | ||||
−0.634472 | + | 0.772945i | \(0.718783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1116 | −0.506856 | −0.253428 | − | 0.967354i | \(-0.581558\pi\) | ||||
−0.253428 | + | 0.967354i | \(0.581558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2233i | 0.677737i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.40515i | 0.349911i | 0.984576 | + | 0.174955i | \(0.0559781\pi\) | ||||
−0.984576 | + | 0.174955i | \(0.944022\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.3929 | 0.805942 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.9703 | −1.65825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 27.8884i | − 1.15502i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 47.4439i | − 1.95822i | −0.203330 | − | 0.979110i | \(-0.565176\pi\) | ||||
0.203330 | − | 0.979110i | \(-0.434824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.9581 | 2.67655 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0148 | −0.411955 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.4413i | 1.33221i | 0.745860 | + | 0.666103i | \(0.232039\pi\) | ||||
−0.745860 | + | 0.666103i | \(0.767961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 2.36897i | − 0.0969556i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.6742 | 1.41675 | 0.708375 | − | 0.705836i | \(-0.249429\pi\) | ||||
0.708375 | + | 0.705836i | \(0.249429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 12.7497i | − 0.519207i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.30354i | 0.0934978i | 0.998907 | + | 0.0467489i | \(0.0148861\pi\) | ||||
−0.998907 | + | 0.0467489i | \(0.985114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −46.0968 | −1.86794 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.17226 | −0.330614 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 15.8735i | − 0.641126i | −0.947227 | − | 0.320563i | \(-0.896128\pi\) | ||||
0.947227 | − | 0.320563i | \(-0.103872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 10.3445i | − 0.416455i | −0.978080 | − | 0.208227i | \(-0.933231\pi\) | ||||
0.978080 | − | 0.208227i | \(-0.0667694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.1500 | −1.49318 | −0.746592 | − | 0.665282i | \(-0.768311\pi\) | ||||
−0.746592 | + | 0.665282i | \(0.768311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.9368 | 0.599392 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 49.0336i | 1.96449i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 50.9368i | 2.03422i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.83997 | −0.192982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2132 | 0.406583 | 0.203291 | − | 0.979118i | \(-0.434836\pi\) | ||||
0.203291 | + | 0.979118i | \(0.434836\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 13.1845i | − 0.524036i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 10.4078i | − 0.412370i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.47580 | −0.256179 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0968 | −0.635785 | −0.317893 | − | 0.948127i | \(-0.602975\pi\) | ||||
−0.317893 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 18.0458i | − 0.711656i | −0.934551 | − | 0.355828i | \(-0.884199\pi\) | ||||
0.934551 | − | 0.355828i | \(-0.115801\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.5700i | 1.71291i | 0.516219 | + | 0.856456i | \(0.327339\pi\) | ||||
−0.516219 | + | 0.856456i | \(0.672661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −67.5503 | −2.65158 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.7226 | −2.10555 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 22.3445i | − 0.874409i | −0.899362 | − | 0.437204i | \(-0.855969\pi\) | ||||
0.899362 | − | 0.437204i | \(-0.144031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 13.1535i | − 0.513168i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.9219 | −1.12664 | −0.563319 | − | 0.826239i | \(-0.690476\pi\) | ||||
−0.563319 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6890 | −0.726919 | −0.363460 | − | 0.931610i | \(-0.618405\pi\) | ||||
−0.363460 | + | 0.931610i | \(0.618405\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.951601i | − 0.0369571i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6406i | 0.837929i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.73744 | −0.144498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.951601 | 0.0367361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5194i | 0.906606i | 0.891357 | + | 0.453303i | \(0.149754\pi\) | ||||
−0.891357 | + | 0.453303i | \(0.850246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.35936i | 0.321276i | 0.987013 | + | 0.160638i | \(0.0513552\pi\) | ||||
−0.987013 | + | 0.160638i | \(0.948645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −76.5381 | −2.93726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0820 | 0.922823 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 11.9394i | − 0.456847i | −0.973562 | − | 0.228424i | \(-0.926643\pi\) | ||||
0.973562 | − | 0.228424i | \(-0.0733572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 13.6703i | − 0.521555i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.04840 | −0.192329 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4274 | 0.586886 | 0.293443 | − | 0.955977i | \(-0.405199\pi\) | ||||
0.293443 | + | 0.955977i | \(0.405199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.0187i | 1.02636i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.495445i | 0.0187663i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.11164 | 0.306810 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.2813 | 1.40809 | 0.704047 | − | 0.710153i | \(-0.251374\pi\) | ||||
0.704047 | + | 0.710153i | \(0.251374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 46.8975i | − 1.76877i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 25.0336i | − 0.941484i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9852 | 0.450112 | 0.225056 | − | 0.974346i | \(-0.427743\pi\) | ||||
0.225056 | + | 0.974346i | \(0.427743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.51939 | −0.0569817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.2207i | 0.944521i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 13.3419i | − 0.498263i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6258 | −0.881094 | −0.440547 | − | 0.897730i | \(-0.645215\pi\) | ||||
−0.440547 | + | 0.897730i | \(0.645215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.8639 | −1.70806 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.55295i | − 0.0949454i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 22.1526i | − 0.821595i | −0.911727 | − | 0.410798i | \(-0.865250\pi\) | ||||
0.911727 | − | 0.410798i | \(-0.134750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.6943 | −1.02571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.951601 | 0.0351962 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 10.0000i | − 0.369358i | −0.982799 | − | 0.184679i | \(-0.940875\pi\) | ||||
0.982799 | − | 0.184679i | \(-0.0591246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.0820i | 2.21315i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0436 | 0.700530 | 0.350265 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350265 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.22066 | 0.338729 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.26906i | 0.229989i | 0.993366 | + | 0.114995i | \(0.0366851\pi\) | ||||
−0.993366 | + | 0.114995i | \(0.963315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 11.2303i | − 0.410894i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.1749 | −1.06603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.9219 | −0.763452 | −0.381726 | − | 0.924276i | \(-0.624670\pi\) | ||||
−0.381726 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.18971i | 0.116239i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.8975i | 1.77721i | 0.458674 | + | 0.888604i | \(0.348324\pi\) | ||||
−0.458674 | + | 0.888604i | \(0.651676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.7767 | −0.717850 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.09680 | −0.148509 | −0.0742544 | − | 0.997239i | \(-0.523658\pi\) | ||||
−0.0742544 | + | 0.997239i | \(0.523658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2180i | 0.514728i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2281i | 0.441530i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.7858 | 1.03804 | 0.519022 | − | 0.854761i | \(-0.326296\pi\) | ||||
0.519022 | + | 0.854761i | \(0.326296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.23811 | −0.0806035 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.22066i | 0.259709i | 0.991533 | + | 0.129855i | \(0.0414510\pi\) | ||||
−0.991533 | + | 0.129855i | \(0.958549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.7858i | 1.39143i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.80068 | −0.172002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.5168 | 1.09198 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 46.0968i | − 1.64737i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 41.5800i | − 1.48217i | −0.671413 | − | 0.741084i | \(-0.734312\pi\) | ||||
0.671413 | − | 0.741084i | \(-0.265688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.4871 | 0.800562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1897 | 0.540084 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 0.172260i | − 0.00611715i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.4078i | − 0.687458i | −0.939069 | − | 0.343729i | \(-0.888310\pi\) | ||||
0.939069 | − | 0.343729i | \(-0.111690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.75228 | −0.203501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.7767 | −0.486777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 61.9852i | 2.18741i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 21.7619i | − 0.766055i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.7981 | −1.53986 | −0.769929 | − | 0.638130i | \(-0.779708\pi\) | ||||
−0.769929 | + | 0.638130i | \(0.779708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.75709 | −0.202159 | −0.101079 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101079 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.1626i | − 0.496706i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.22066i | 0.322590i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.89098 | 0.170905 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.9368 | −1.14950 | −0.574750 | − | 0.818329i | \(-0.694901\pi\) | ||||
−0.574750 | + | 0.818329i | \(0.694901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 57.0894i | − 1.99001i | −0.0998217 | − | 0.995005i | \(-0.531827\pi\) | ||||
0.0998217 | − | 0.995005i | \(-0.468173\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4535i | 0.954653i | 0.878726 | + | 0.477327i | \(0.158394\pi\) | ||||
−0.878726 | + | 0.477327i | \(0.841606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4200 | −0.361901 | −0.180950 | − | 0.983492i | \(-0.557917\pi\) | ||||
−0.180950 | + | 0.983492i | \(0.557917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.5142 | 0.815698 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 7.32580i | − 0.253824i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 53.7226i | − 1.85692i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.1984 | −1.38780 | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||||
−0.693902 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7858 | 1.30296 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.2717i | 0.525984i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 81.4291i | − 2.79794i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.4923 | −0.428736 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.2084 | 0.624177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.8761i | 1.19414i | 0.802191 | + | 0.597068i | \(0.203668\pi\) | ||||
−0.802191 | + | 0.597068i | \(0.796332\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 25.1600i | − 0.859450i | −0.902960 | − | 0.429725i | \(-0.858610\pi\) | ||||
0.902960 | − | 0.429725i | \(-0.141390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0484 | 0.513445 | 0.256722 | − | 0.966485i | \(-0.417357\pi\) | ||||
0.256722 | + | 0.966485i | \(0.417357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.97033 | 0.135308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.29873i | 0.0782498i | 0.999234 | + | 0.0391249i | \(0.0124570\pi\) | ||||
−0.999234 | + | 0.0391249i | \(0.987543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.3132i | 0.757794i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.16003 | 0.242888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8761 | 0.368524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 21.5046i | − 0.727819i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0000i | 0.337676i | 0.985644 | + | 0.168838i | \(0.0540015\pi\) | ||||
−0.985644 | + | 0.168838i | \(0.945999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1788 | 0.748071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1426 | −1.62196 | −0.810982 | − | 0.585070i | \(-0.801067\pi\) | ||||
−0.810982 | + | 0.585070i | \(0.801067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12.8565i | − 0.432655i | −0.976321 | − | 0.216328i | \(-0.930592\pi\) | ||||
0.976321 | − | 0.216328i | \(-0.0694080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.5216i | 1.09197i | 0.837796 | + | 0.545984i | \(0.183844\pi\) | ||||
−0.837796 | + | 0.545984i | \(0.816156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.7671 | 0.797123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.6991 | 0.760447 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 55.7374i | − 1.86518i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.58002i | 0.119533i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 77.8342 | 2.59592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.55346 | −0.118383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 7.62581i | − 0.253771i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0894i | 0.700261i | 0.936701 | + | 0.350131i | \(0.113863\pi\) | ||||
−0.936701 | + | 0.350131i | \(0.886137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.03356 | 0.233289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.1600 | 1.42996 | 0.714978 | − | 0.699147i | \(-0.246437\pi\) | ||||
0.714978 | + | 0.699147i | \(0.246437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.9219i | 1.75146i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 74.0671i | − 2.44591i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8884 | −0.392161 | −0.196080 | − | 0.980588i | \(-0.562821\pi\) | ||||
−0.196080 | + | 0.980588i | \(0.562821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.4265 | −0.673075 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.52420i | − 0.181831i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 12.8862i | − 0.423237i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.4265 | 1.12950 | 0.564748 | − | 0.825263i | \(-0.308973\pi\) | ||||
0.564748 | + | 0.825263i | \(0.308973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70.9842 | 2.32641 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 10.9664i | − 0.359025i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 26.0000i | − 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.88314 | 0.0614541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.1116 | −1.24240 | −0.621202 | − | 0.783651i | \(-0.713355\pi\) | ||||
−0.621202 | + | 0.783651i | \(0.713355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.86391i | − 0.0606974i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 13.9245i | − 0.452487i | −0.974071 | − | 0.226243i | \(-0.927356\pi\) | ||||
0.974071 | − | 0.226243i | \(-0.0726445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2207 | 0.364238 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.3052 | −1.30699 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 23.7523i | − 0.769412i | −0.923039 | − | 0.384706i | \(-0.874303\pi\) | ||||
0.923039 | − | 0.384706i | \(-0.125697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 61.0336i | 1.97293i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.2865 | 1.20404 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.7104 | 1.92614 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 8.19713i | − 0.264149i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.87614i | 0.221122i | 0.993869 | + | 0.110561i | \(0.0352647\pi\) | ||||
−0.993869 | + | 0.110561i | \(0.964735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.49022 | 0.208496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.24772 | 0.200499 | 0.100249 | − | 0.994962i | \(-0.468036\pi\) | ||||
0.100249 | + | 0.994962i | \(0.468036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.4749i | 1.77844i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.5316i | 1.10476i | 0.833591 | + | 0.552382i | \(0.186281\pi\) | ||||
−0.833591 | + | 0.552382i | \(0.813719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.9219 | 2.07491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.99478 | −0.127543 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 11.5652i | − 0.368872i | −0.982845 | − | 0.184436i | \(-0.940954\pi\) | ||||
0.982845 | − | 0.184436i | \(-0.0590458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.0968i | 1.46728i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.58002 | −0.113838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.77673 | 0.119972 | 0.0599859 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599859 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 25.9097i | − 0.822220i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 54.4265i | − 1.72370i | −0.507160 | − | 0.861852i | \(-0.669305\pi\) | ||||
0.507160 | − | 0.861852i | \(-0.330695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.7858 | −1.22713 |
(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 | 1300.2.c.f.1249.4 | 6 | ||
5.2 | odd | 4 | 260.2.a.b.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 1300.2.a.i.1.2 | 3 | |||
5.4 | even | 2 | inner | 1300.2.c.f.1249.3 | 6 | ||
15.2 | even | 4 | 2340.2.a.n.1.3 | 3 | |||
20.3 | even | 4 | 5200.2.a.ci.1.2 | 3 | |||
20.7 | even | 4 | 1040.2.a.o.1.2 | 3 | |||
40.27 | even | 4 | 4160.2.a.br.1.2 | 3 | |||
40.37 | odd | 4 | 4160.2.a.bo.1.2 | 3 | |||
60.47 | odd | 4 | 9360.2.a.da.1.1 | 3 | |||
65.12 | odd | 4 | 3380.2.a.o.1.2 | 3 | |||
65.47 | even | 4 | 3380.2.f.h.3041.4 | 6 | |||
65.57 | even | 4 | 3380.2.f.h.3041.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.a.b.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
1040.2.a.o.1.2 | 3 | 20.7 | even | 4 | |||
1300.2.a.i.1.2 | 3 | 5.3 | odd | 4 | |||
1300.2.c.f.1249.3 | 6 | 5.4 | even | 2 | inner | ||
1300.2.c.f.1249.4 | 6 | 1.1 | even | 1 | trivial | ||
2340.2.a.n.1.3 | 3 | 15.2 | even | 4 | |||
3380.2.a.o.1.2 | 3 | 65.12 | odd | 4 | |||
3380.2.f.h.3041.3 | 6 | 65.57 | even | 4 | |||
3380.2.f.h.3041.4 | 6 | 65.47 | even | 4 | |||
4160.2.a.bo.1.2 | 3 | 40.37 | odd | 4 | |||
4160.2.a.br.1.2 | 3 | 40.27 | even | 4 | |||
5200.2.a.ci.1.2 | 3 | 20.3 | even | 4 | |||
9360.2.a.da.1.1 | 3 | 60.47 | odd | 4 |