Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.11667456256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 13x^{6} + 44x^{4} + 21x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-2.74108i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.g.337.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.74108i | − 1.93824i | −0.246594 | − | 0.969119i | \(-0.579311\pi\) | ||||
0.246594 | − | 0.969119i | \(-0.420689\pi\) | |||||||
\(3\) | 1.36482 | 0.787979 | 0.393989 | − | 0.919115i | \(-0.371095\pi\) | ||||
0.393989 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(4\) | −5.51353 | −2.75677 | ||||||||
\(5\) | 0.741082i | 0.331422i | 0.986174 | + | 0.165711i | \(0.0529919\pi\) | ||||
−0.986174 | + | 0.165711i | \(0.947008\pi\) | |||||||
\(6\) | − 3.74108i | − 1.52729i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 9.63087i | 3.40503i | ||||||||
\(9\) | −1.13727 | −0.379089 | ||||||||
\(10\) | 2.03137 | 0.642374 | ||||||||
\(11\) | 1.36482i | 0.411509i | 0.978604 | + | 0.205754i | \(0.0659648\pi\) | ||||
−0.978604 | + | 0.205754i | \(0.934035\pi\) | |||||||
\(12\) | −7.52497 | −2.17227 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.74108 | 0.732585 | ||||||||
\(15\) | 1.01144i | 0.261153i | ||||||||
\(16\) | 15.3720 | 3.84299 | ||||||||
\(17\) | 4.14871 | 1.00621 | 0.503105 | − | 0.864225i | \(-0.332191\pi\) | ||||
0.503105 | + | 0.864225i | \(0.332191\pi\) | |||||||
\(18\) | 3.11734i | 0.734765i | ||||||||
\(19\) | 7.26606i | 1.66695i | 0.552559 | + | 0.833474i | \(0.313651\pi\) | ||||
−0.552559 | + | 0.833474i | \(0.686349\pi\) | |||||||
\(20\) | − 4.08598i | − 0.913652i | ||||||||
\(21\) | 1.36482i | 0.297828i | ||||||||
\(22\) | 3.74108 | 0.797601 | ||||||||
\(23\) | 2.33345 | 0.486559 | 0.243279 | − | 0.969956i | \(-0.421777\pi\) | ||||
0.243279 | + | 0.969956i | \(0.421777\pi\) | |||||||
\(24\) | 13.1444i | 2.68309i | ||||||||
\(25\) | 4.45080 | 0.890159 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64662 | −1.08669 | ||||||||
\(28\) | − 5.51353i | − 1.04196i | ||||||||
\(29\) | −0.407629 | −0.0756948 | −0.0378474 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378474 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(30\) | 2.77245 | 0.506178 | ||||||||
\(31\) | − 2.77245i | − 0.497946i | −0.968510 | − | 0.248973i | \(-0.919907\pi\) | ||||
0.968510 | − | 0.248973i | \(-0.0800931\pi\) | |||||||
\(32\) | − 22.8740i | − 4.04360i | ||||||||
\(33\) | 1.86273i | 0.324260i | ||||||||
\(34\) | − 11.3720i | − 1.95027i | ||||||||
\(35\) | −0.741082 | −0.125266 | ||||||||
\(36\) | 6.27036 | 1.04506 | ||||||||
\(37\) | 6.10590i | 1.00380i | 0.864924 | + | 0.501902i | \(0.167366\pi\) | ||||
−0.864924 | + | 0.501902i | \(0.832634\pi\) | |||||||
\(38\) | 19.9169 | 3.23094 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.13727 | −1.12850 | ||||||||
\(41\) | 1.25461i | 0.195938i | 0.995189 | + | 0.0979688i | \(0.0312345\pi\) | ||||
−0.995189 | + | 0.0979688i | \(0.968765\pi\) | |||||||
\(42\) | 3.74108 | 0.577261 | ||||||||
\(43\) | 1.74108 | 0.265513 | 0.132756 | − | 0.991149i | \(-0.457617\pi\) | ||||
0.132756 | + | 0.991149i | \(0.457617\pi\) | |||||||
\(44\) | − 7.52497i | − 1.13443i | ||||||||
\(45\) | − 0.842809i | − 0.125639i | ||||||||
\(46\) | − 6.39619i | − 0.943066i | ||||||||
\(47\) | 5.85843i | 0.854539i | 0.904124 | + | 0.427270i | \(0.140525\pi\) | ||||
−0.904124 | + | 0.427270i | \(0.859475\pi\) | |||||||
\(48\) | 20.9799 | 3.02819 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − 12.2000i | − 1.72534i | ||||||||
\(51\) | 5.66224 | 0.792872 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.56778 | 0.627433 | 0.313717 | − | 0.949517i | \(-0.398426\pi\) | ||||
0.313717 | + | 0.949517i | \(0.398426\pi\) | |||||||
\(54\) | 15.4779i | 2.10627i | ||||||||
\(55\) | −1.01144 | −0.136383 | ||||||||
\(56\) | −9.63087 | −1.28698 | ||||||||
\(57\) | 9.91685i | 1.31352i | ||||||||
\(58\) | 1.11734i | 0.146715i | ||||||||
\(59\) | 10.9843i | 1.43003i | 0.699110 | + | 0.715014i | \(0.253580\pi\) | ||||
−0.699110 | + | 0.715014i | \(0.746420\pi\) | |||||||
\(60\) | − 5.57662i | − 0.719939i | ||||||||
\(61\) | 6.52497 | 0.835437 | 0.417719 | − | 0.908576i | \(-0.362830\pi\) | ||||
0.417719 | + | 0.908576i | \(0.362830\pi\) | |||||||
\(62\) | −7.59951 | −0.965139 | ||||||||
\(63\) | − 1.13727i | − 0.143282i | ||||||||
\(64\) | −31.9557 | −3.99446 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.10590 | 0.628493 | ||||||||
\(67\) | − 13.7597i | − 1.68101i | −0.541804 | − | 0.840505i | \(-0.682258\pi\) | ||||
0.541804 | − | 0.840505i | \(-0.317742\pi\) | |||||||
\(68\) | −22.8740 | −2.77389 | ||||||||
\(69\) | 3.18474 | 0.383398 | ||||||||
\(70\) | 2.03137i | 0.242795i | ||||||||
\(71\) | − 4.81526i | − 0.571466i | −0.958309 | − | 0.285733i | \(-0.907763\pi\) | ||||
0.958309 | − | 0.285733i | \(-0.0922370\pi\) | |||||||
\(72\) | − 10.9529i | − 1.29081i | ||||||||
\(73\) | − 6.06987i | − 0.710425i | −0.934786 | − | 0.355212i | \(-0.884409\pi\) | ||||
0.934786 | − | 0.355212i | \(-0.115591\pi\) | |||||||
\(74\) | 16.7368 | 1.94561 | ||||||||
\(75\) | 6.07453 | 0.701427 | ||||||||
\(76\) | − 40.0616i | − 4.59538i | ||||||||
\(77\) | −1.36482 | −0.155536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.12582 | −1.02674 | −0.513368 | − | 0.858169i | \(-0.671602\pi\) | ||||
−0.513368 | + | 0.858169i | \(0.671602\pi\) | |||||||
\(80\) | 11.3919i | 1.27365i | ||||||||
\(81\) | −4.29482 | −0.477202 | ||||||||
\(82\) | 3.43900 | 0.379774 | ||||||||
\(83\) | 11.7368i | 1.28828i | 0.764908 | + | 0.644139i | \(0.222784\pi\) | ||||
−0.764908 | + | 0.644139i | \(0.777216\pi\) | |||||||
\(84\) | − 7.52497i | − 0.821042i | ||||||||
\(85\) | 3.07453i | 0.333480i | ||||||||
\(86\) | − 4.77245i | − 0.514626i | ||||||||
\(87\) | −0.556340 | −0.0596459 | ||||||||
\(88\) | −13.1444 | −1.40120 | ||||||||
\(89\) | 1.76101i | 0.186666i | 0.995635 | + | 0.0933331i | \(0.0297522\pi\) | ||||
−0.995635 | + | 0.0933331i | \(0.970248\pi\) | |||||||
\(90\) | −2.31021 | −0.243517 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.8656 | −1.34133 | ||||||||
\(93\) | − 3.78389i | − 0.392371i | ||||||||
\(94\) | 16.0584 | 1.65630 | ||||||||
\(95\) | −5.38474 | −0.552463 | ||||||||
\(96\) | − 31.2189i | − 3.18627i | ||||||||
\(97\) | 9.53381i | 0.968012i | 0.875065 | + | 0.484006i | \(0.160819\pi\) | ||||
−0.875065 | + | 0.484006i | \(0.839181\pi\) | |||||||
\(98\) | 2.74108i | 0.276891i | ||||||||
\(99\) | − 1.55217i | − 0.155998i | ||||||||
\(100\) | −24.5396 | −2.45396 | ||||||||
\(101\) | 7.49361 | 0.745642 | 0.372821 | − | 0.927903i | \(-0.378391\pi\) | ||||
0.372821 | + | 0.927903i | \(0.378391\pi\) | |||||||
\(102\) | − 15.5207i | − 1.53678i | ||||||||
\(103\) | −2.80848 | −0.276728 | −0.138364 | − | 0.990381i | \(-0.544184\pi\) | ||||
−0.138364 | + | 0.990381i | \(0.544184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.01144 | −0.0987067 | ||||||||
\(106\) | − 12.5207i | − 1.21611i | ||||||||
\(107\) | 1.48647 | 0.143702 | 0.0718512 | − | 0.997415i | \(-0.477109\pi\) | ||||
0.0718512 | + | 0.997415i | \(0.477109\pi\) | |||||||
\(108\) | 31.1328 | 2.99576 | ||||||||
\(109\) | 2.87121i | 0.275012i | 0.990501 | + | 0.137506i | \(0.0439087\pi\) | ||||
−0.990501 | + | 0.137506i | \(0.956091\pi\) | |||||||
\(110\) | 2.77245i | 0.264343i | ||||||||
\(111\) | 8.33345i | 0.790976i | ||||||||
\(112\) | 15.3720i | 1.45251i | ||||||||
\(113\) | −12.4194 | −1.16832 | −0.584161 | − | 0.811638i | \(-0.698576\pi\) | ||||
−0.584161 | + | 0.811638i | \(0.698576\pi\) | |||||||
\(114\) | 27.1829 | 2.54591 | ||||||||
\(115\) | 1.72928i | 0.161256i | ||||||||
\(116\) | 2.24747 | 0.208673 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30.1087 | 2.77173 | ||||||||
\(119\) | 4.14871i | 0.380312i | ||||||||
\(120\) | −9.74108 | −0.889235 | ||||||||
\(121\) | 9.13727 | 0.830661 | ||||||||
\(122\) | − 17.8855i | − 1.61928i | ||||||||
\(123\) | 1.71232i | 0.154395i | ||||||||
\(124\) | 15.2860i | 1.37272i | ||||||||
\(125\) | 7.00382i | 0.626440i | ||||||||
\(126\) | −3.11734 | −0.277715 | ||||||||
\(127\) | −5.43052 | −0.481880 | −0.240940 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240940 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(128\) | 41.8452i | 3.69862i | ||||||||
\(129\) | 2.37626 | 0.209218 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3220 | −0.989209 | −0.494604 | − | 0.869118i | \(-0.664687\pi\) | ||||
−0.494604 | + | 0.869118i | \(0.664687\pi\) | |||||||
\(132\) | − 10.2702i | − 0.893909i | ||||||||
\(133\) | −7.26606 | −0.630047 | ||||||||
\(134\) | −37.7164 | −3.25820 | ||||||||
\(135\) | − 4.18461i | − 0.360154i | ||||||||
\(136\) | 39.9557i | 3.42617i | ||||||||
\(137\) | 13.9754i | 1.19400i | 0.802241 | + | 0.597000i | \(0.203641\pi\) | ||||
−0.802241 | + | 0.597000i | \(0.796359\pi\) | |||||||
\(138\) | − 8.72964i | − 0.743116i | ||||||||
\(139\) | 10.4309 | 0.884735 | 0.442368 | − | 0.896834i | \(-0.354139\pi\) | ||||
0.442368 | + | 0.896834i | \(0.354139\pi\) | |||||||
\(140\) | 4.08598 | 0.345328 | ||||||||
\(141\) | 7.99569i | 0.673359i | ||||||||
\(142\) | −13.1990 | −1.10764 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −17.4820 | −1.45684 | ||||||||
\(145\) | − 0.302087i | − 0.0250869i | ||||||||
\(146\) | −16.6380 | −1.37697 | ||||||||
\(147\) | −1.36482 | −0.112568 | ||||||||
\(148\) | − 33.6651i | − 2.76725i | ||||||||
\(149\) | 8.16433i | 0.668848i | 0.942423 | + | 0.334424i | \(0.108542\pi\) | ||||
−0.942423 | + | 0.334424i | \(0.891458\pi\) | |||||||
\(150\) | − 16.6508i | − 1.35953i | ||||||||
\(151\) | 2.46188i | 0.200345i | 0.994970 | + | 0.100173i | \(0.0319395\pi\) | ||||
−0.994970 | + | 0.100173i | \(0.968061\pi\) | |||||||
\(152\) | −69.9785 | −5.67600 | ||||||||
\(153\) | −4.71820 | −0.381444 | ||||||||
\(154\) | 3.74108i | 0.301465i | ||||||||
\(155\) | 2.05461 | 0.165030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9198 | −1.03111 | −0.515557 | − | 0.856855i | \(-0.672415\pi\) | ||||
−0.515557 | + | 0.856855i | \(0.672415\pi\) | |||||||
\(158\) | 25.0146i | 1.99006i | ||||||||
\(159\) | 6.23420 | 0.494404 | ||||||||
\(160\) | 16.9515 | 1.34014 | ||||||||
\(161\) | 2.33345i | 0.183902i | ||||||||
\(162\) | 11.7724i | 0.924931i | ||||||||
\(163\) | 6.02742i | 0.472104i | 0.971740 | + | 0.236052i | \(0.0758536\pi\) | ||||
−0.971740 | + | 0.236052i | \(0.924146\pi\) | |||||||
\(164\) | − 6.91734i | − 0.540154i | ||||||||
\(165\) | −1.38044 | −0.107467 | ||||||||
\(166\) | 32.1715 | 2.49699 | ||||||||
\(167\) | − 7.65116i | − 0.592064i | −0.955178 | − | 0.296032i | \(-0.904336\pi\) | ||||
0.955178 | − | 0.296032i | \(-0.0956636\pi\) | |||||||
\(168\) | −13.1444 | −1.01411 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.42755 | 0.646364 | ||||||||
\(171\) | − 8.26345i | − 0.631922i | ||||||||
\(172\) | −9.59951 | −0.731956 | ||||||||
\(173\) | 0.164460 | 0.0125036 | 0.00625182 | − | 0.999980i | \(-0.498010\pi\) | ||||
0.00625182 | + | 0.999980i | \(0.498010\pi\) | |||||||
\(174\) | 1.52497i | 0.115608i | ||||||||
\(175\) | 4.45080i | 0.336449i | ||||||||
\(176\) | 20.9799i | 1.58142i | ||||||||
\(177\) | 14.9915i | 1.12683i | ||||||||
\(178\) | 4.82706 | 0.361803 | ||||||||
\(179\) | −0.768633 | −0.0574503 | −0.0287252 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287252 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(180\) | 4.64685i | 0.346356i | ||||||||
\(181\) | 9.92152 | 0.737461 | 0.368730 | − | 0.929536i | \(-0.379793\pi\) | ||||
0.368730 | + | 0.929536i | \(0.379793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.90541 | 0.658307 | ||||||||
\(184\) | 22.4732i | 1.65675i | ||||||||
\(185\) | −4.52497 | −0.332683 | ||||||||
\(186\) | −10.3720 | −0.760509 | ||||||||
\(187\) | 5.66224i | 0.414064i | ||||||||
\(188\) | − 32.3006i | − 2.35576i | ||||||||
\(189\) | − 5.64662i | − 0.410731i | ||||||||
\(190\) | 14.7600i | 1.07080i | ||||||||
\(191\) | 9.89693 | 0.716117 | 0.358058 | − | 0.933699i | \(-0.383439\pi\) | ||||
0.358058 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(192\) | −43.6138 | −3.14755 | ||||||||
\(193\) | − 8.70075i | − 0.626293i | −0.949705 | − | 0.313147i | \(-0.898617\pi\) | ||||
0.949705 | − | 0.313147i | \(-0.101383\pi\) | |||||||
\(194\) | 26.1330 | 1.87624 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.51353 | 0.393824 | ||||||||
\(197\) | − 26.0186i | − 1.85375i | −0.375374 | − | 0.926874i | \(-0.622486\pi\) | ||||
0.375374 | − | 0.926874i | \(-0.377514\pi\) | |||||||
\(198\) | −4.25461 | −0.302362 | ||||||||
\(199\) | −10.1330 | −0.718307 | −0.359153 | − | 0.933279i | \(-0.616934\pi\) | ||||
−0.359153 | + | 0.933279i | \(0.616934\pi\) | |||||||
\(200\) | 42.8651i | 3.03102i | ||||||||
\(201\) | − 18.7795i | − 1.32460i | ||||||||
\(202\) | − 20.5406i | − 1.44523i | ||||||||
\(203\) | − 0.407629i | − 0.0286099i | ||||||||
\(204\) | −31.2189 | −2.18576 | ||||||||
\(205\) | −0.929771 | −0.0649380 | ||||||||
\(206\) | 7.69827i | 0.536364i | ||||||||
\(207\) | −2.65376 | −0.184449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.91685 | −0.685963 | ||||||||
\(210\) | 2.77245i | 0.191317i | ||||||||
\(211\) | 16.6782 | 1.14818 | 0.574088 | − | 0.818794i | \(-0.305357\pi\) | ||||
0.574088 | + | 0.818794i | \(0.305357\pi\) | |||||||
\(212\) | −25.1846 | −1.72969 | ||||||||
\(213\) | − 6.57196i | − 0.450303i | ||||||||
\(214\) | − 4.07453i | − 0.278529i | ||||||||
\(215\) | 1.29028i | 0.0879967i | ||||||||
\(216\) | − 54.3819i | − 3.70022i | ||||||||
\(217\) | 2.77245 | 0.188206 | ||||||||
\(218\) | 7.87023 | 0.533039 | ||||||||
\(219\) | − 8.28428i | − 0.559800i | ||||||||
\(220\) | 5.57662 | 0.375976 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 22.8427 | 1.53310 | ||||||||
\(223\) | 1.07036i | 0.0716766i | 0.999358 | + | 0.0358383i | \(0.0114101\pi\) | ||||
−0.999358 | + | 0.0358383i | \(0.988590\pi\) | |||||||
\(224\) | 22.8740 | 1.52834 | ||||||||
\(225\) | −5.06175 | −0.337450 | ||||||||
\(226\) | 34.0427i | 2.26449i | ||||||||
\(227\) | − 24.4664i | − 1.62389i | −0.583732 | − | 0.811947i | \(-0.698408\pi\) | ||||
0.583732 | − | 0.811947i | \(-0.301592\pi\) | |||||||
\(228\) | − 54.6769i | − 3.62106i | ||||||||
\(229\) | − 4.72964i | − 0.312543i | −0.987714 | − | 0.156272i | \(-0.950052\pi\) | ||||
0.987714 | − | 0.156272i | \(-0.0499475\pi\) | |||||||
\(230\) | 4.74010 | 0.312553 | ||||||||
\(231\) | −1.86273 | −0.122559 | ||||||||
\(232\) | − 3.92582i | − 0.257743i | ||||||||
\(233\) | −20.5507 | −1.34632 | −0.673160 | − | 0.739497i | \(-0.735064\pi\) | ||||
−0.673160 | + | 0.739497i | \(0.735064\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.34157 | −0.283213 | ||||||||
\(236\) | − 60.5620i | − 3.94225i | ||||||||
\(237\) | −12.4551 | −0.809046 | ||||||||
\(238\) | 11.3720 | 0.737134 | ||||||||
\(239\) | 6.25461i | 0.404577i | 0.979326 | + | 0.202289i | \(0.0648379\pi\) | ||||
−0.979326 | + | 0.202289i | \(0.935162\pi\) | |||||||
\(240\) | 15.5479i | 1.00361i | ||||||||
\(241\) | 12.1444i | 0.782290i | 0.920329 | + | 0.391145i | \(0.127921\pi\) | ||||
−0.920329 | + | 0.391145i | \(0.872079\pi\) | |||||||
\(242\) | − 25.0460i | − 1.61002i | ||||||||
\(243\) | 11.0782 | 0.710668 | ||||||||
\(244\) | −35.9756 | −2.30310 | ||||||||
\(245\) | − 0.741082i | − 0.0473460i | ||||||||
\(246\) | 4.69361 | 0.299254 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 26.7011 | 1.69552 | ||||||||
\(249\) | 16.0186i | 1.01514i | ||||||||
\(250\) | 19.1980 | 1.21419 | ||||||||
\(251\) | 6.31438 | 0.398560 | 0.199280 | − | 0.979943i | \(-0.436140\pi\) | ||||
0.199280 | + | 0.979943i | \(0.436140\pi\) | |||||||
\(252\) | 6.27036i | 0.394996i | ||||||||
\(253\) | 3.18474i | 0.200223i | ||||||||
\(254\) | 14.8855i | 0.933999i | ||||||||
\(255\) | 4.19619i | 0.262775i | ||||||||
\(256\) | 50.7896 | 3.17435 | ||||||||
\(257\) | −24.3562 | −1.51930 | −0.759649 | − | 0.650333i | \(-0.774629\pi\) | ||||
−0.759649 | + | 0.650333i | \(0.774629\pi\) | |||||||
\(258\) | − 6.51353i | − 0.405515i | ||||||||
\(259\) | −6.10590 | −0.379402 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.463583 | 0.0286951 | ||||||||
\(262\) | 31.0346i | 1.91732i | ||||||||
\(263\) | −9.57910 | −0.590672 | −0.295336 | − | 0.955393i | \(-0.595432\pi\) | ||||
−0.295336 | + | 0.955393i | \(0.595432\pi\) | |||||||
\(264\) | −17.9397 | −1.10411 | ||||||||
\(265\) | 3.38510i | 0.207945i | ||||||||
\(266\) | 19.9169i | 1.22118i | ||||||||
\(267\) | 2.40345i | 0.147089i | ||||||||
\(268\) | 75.8643i | 4.63415i | ||||||||
\(269\) | 29.3990 | 1.79249 | 0.896245 | − | 0.443560i | \(-0.146285\pi\) | ||||
0.896245 | + | 0.443560i | \(0.146285\pi\) | |||||||
\(270\) | −11.4704 | −0.698064 | ||||||||
\(271\) | 0.300385i | 0.0182471i | 0.999958 | + | 0.00912354i | \(0.00290415\pi\) | ||||
−0.999958 | + | 0.00912354i | \(0.997096\pi\) | |||||||
\(272\) | 63.7738 | 3.86686 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 38.3078 | 2.31426 | ||||||||
\(275\) | 6.07453i | 0.366308i | ||||||||
\(276\) | −17.5592 | −1.05694 | ||||||||
\(277\) | 32.7710 | 1.96902 | 0.984509 | − | 0.175337i | \(-0.0561014\pi\) | ||||
0.984509 | + | 0.175337i | \(0.0561014\pi\) | |||||||
\(278\) | − 28.5919i | − 1.71483i | ||||||||
\(279\) | 3.15302i | 0.188766i | ||||||||
\(280\) | − 7.13727i | − 0.426533i | ||||||||
\(281\) | − 4.29482i | − 0.256207i | −0.991761 | − | 0.128104i | \(-0.959111\pi\) | ||||
0.991761 | − | 0.128104i | \(-0.0408890\pi\) | |||||||
\(282\) | 21.9169 | 1.30513 | ||||||||
\(283\) | 21.1003 | 1.25428 | 0.627140 | − | 0.778907i | \(-0.284225\pi\) | ||||
0.627140 | + | 0.778907i | \(0.284225\pi\) | |||||||
\(284\) | 26.5491i | 1.57540i | ||||||||
\(285\) | −7.34920 | −0.435329 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.25461 | −0.0740574 | ||||||||
\(288\) | 26.0139i | 1.53288i | ||||||||
\(289\) | 0.211803 | 0.0124590 | ||||||||
\(290\) | −0.828044 | −0.0486244 | ||||||||
\(291\) | 13.0119i | 0.762773i | ||||||||
\(292\) | 33.4664i | 1.95847i | ||||||||
\(293\) | − 17.7638i | − 1.03777i | −0.854843 | − | 0.518887i | \(-0.826346\pi\) | ||||
0.854843 | − | 0.518887i | \(-0.173654\pi\) | |||||||
\(294\) | 3.74108i | 0.218184i | ||||||||
\(295\) | −8.14023 | −0.473943 | ||||||||
\(296\) | −58.8052 | −3.41798 | ||||||||
\(297\) | − 7.70662i | − 0.447184i | ||||||||
\(298\) | 22.3791 | 1.29639 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −33.4921 | −1.93367 | ||||||||
\(301\) | 1.74108i | 0.100354i | ||||||||
\(302\) | 6.74822 | 0.388316 | ||||||||
\(303\) | 10.2274 | 0.587550 | ||||||||
\(304\) | 111.693i | 6.40606i | ||||||||
\(305\) | 4.83554i | 0.276882i | ||||||||
\(306\) | 12.9330i | 0.739328i | ||||||||
\(307\) | − 18.0156i | − 1.02821i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) | ||||
0.857729 | − | 0.514103i | \(-0.171875\pi\) | |||||||
\(308\) | 7.52497 | 0.428775 | ||||||||
\(309\) | −3.83307 | −0.218056 | ||||||||
\(310\) | − 5.63186i | − 0.319868i | ||||||||
\(311\) | −17.2545 | −0.978412 | −0.489206 | − | 0.872168i | \(-0.662713\pi\) | ||||
−0.489206 | + | 0.872168i | \(0.662713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.81526 | 0.385221 | 0.192611 | − | 0.981275i | \(-0.438305\pi\) | ||||
0.192611 | + | 0.981275i | \(0.438305\pi\) | |||||||
\(314\) | 35.4143i | 1.99854i | ||||||||
\(315\) | 0.842809 | 0.0474869 | ||||||||
\(316\) | 50.3155 | 2.83047 | ||||||||
\(317\) | − 25.0770i | − 1.40847i | −0.709969 | − | 0.704233i | \(-0.751291\pi\) | ||||
0.709969 | − | 0.704233i | \(-0.248709\pi\) | |||||||
\(318\) | − 17.0885i | − 0.958273i | ||||||||
\(319\) | − 0.556340i | − 0.0311491i | ||||||||
\(320\) | − 23.6818i | − 1.32385i | ||||||||
\(321\) | 2.02876 | 0.113234 | ||||||||
\(322\) | 6.39619 | 0.356446 | ||||||||
\(323\) | 30.1448i | 1.67730i | ||||||||
\(324\) | 23.6796 | 1.31553 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.5217 | 0.915050 | ||||||||
\(327\) | 3.91869i | 0.216704i | ||||||||
\(328\) | −12.0830 | −0.667173 | ||||||||
\(329\) | −5.85843 | −0.322986 | ||||||||
\(330\) | 3.78389i | 0.208296i | ||||||||
\(331\) | − 2.99534i | − 0.164639i | −0.996606 | − | 0.0823193i | \(-0.973767\pi\) | ||||
0.996606 | − | 0.0823193i | \(-0.0262327\pi\) | |||||||
\(332\) | − 64.7111i | − 3.55148i | ||||||||
\(333\) | − 6.94405i | − 0.380531i | ||||||||
\(334\) | −20.9724 | −1.14756 | ||||||||
\(335\) | 10.1970 | 0.557124 | ||||||||
\(336\) | 20.9799i | 1.14455i | ||||||||
\(337\) | 29.4888 | 1.60636 | 0.803179 | − | 0.595738i | \(-0.203140\pi\) | ||||
0.803179 | + | 0.595738i | \(0.203140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.9503 | −0.920613 | ||||||||
\(340\) | − 16.9515i | − 0.919326i | ||||||||
\(341\) | 3.78389 | 0.204909 | ||||||||
\(342\) | −22.6508 | −1.22481 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 16.7681i | 0.904078i | ||||||||
\(345\) | 2.36015i | 0.127066i | ||||||||
\(346\) | − 0.450797i | − 0.0242350i | ||||||||
\(347\) | −5.98686 | −0.321391 | −0.160696 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160696 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(348\) | 3.06740 | 0.164430 | ||||||||
\(349\) | 30.3362i | 1.62386i | 0.583757 | + | 0.811929i | \(0.301582\pi\) | ||||
−0.583757 | + | 0.811929i | \(0.698418\pi\) | |||||||
\(350\) | 12.2000 | 0.652117 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 31.2189 | 1.66398 | ||||||||
\(353\) | − 28.6063i | − 1.52256i | −0.648424 | − | 0.761280i | \(-0.724572\pi\) | ||||
0.648424 | − | 0.761280i | \(-0.275428\pi\) | |||||||
\(354\) | 41.0930 | 2.18407 | ||||||||
\(355\) | 3.56850 | 0.189396 | ||||||||
\(356\) | − 9.70936i | − 0.514595i | ||||||||
\(357\) | 5.66224i | 0.299678i | ||||||||
\(358\) | 2.10689i | 0.111352i | ||||||||
\(359\) | − 23.4618i | − 1.23826i | −0.785287 | − | 0.619132i | \(-0.787485\pi\) | ||||
0.785287 | − | 0.619132i | \(-0.212515\pi\) | |||||||
\(360\) | 8.11699 | 0.427803 | ||||||||
\(361\) | −33.7956 | −1.77871 | ||||||||
\(362\) | − 27.1957i | − 1.42937i | ||||||||
\(363\) | 12.4707 | 0.654543 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.49827 | 0.235450 | ||||||||
\(366\) | − 24.4105i | − 1.27596i | ||||||||
\(367\) | 36.5197 | 1.90631 | 0.953156 | − | 0.302479i | \(-0.0978143\pi\) | ||||
0.953156 | + | 0.302479i | \(0.0978143\pi\) | |||||||
\(368\) | 35.8697 | 1.86984 | ||||||||
\(369\) | − 1.42683i | − 0.0742778i | ||||||||
\(370\) | 12.4033i | 0.644818i | ||||||||
\(371\) | 4.56778i | 0.237147i | ||||||||
\(372\) | 20.8626i | 1.08168i | ||||||||
\(373\) | −13.0498 | −0.675694 | −0.337847 | − | 0.941201i | \(-0.609699\pi\) | ||||
−0.337847 | + | 0.941201i | \(0.609699\pi\) | |||||||
\(374\) | 15.5207 | 0.802555 | ||||||||
\(375\) | 9.55894i | 0.493622i | ||||||||
\(376\) | −56.4218 | −2.90973 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −15.4779 | −0.796095 | ||||||||
\(379\) | 30.6037i | 1.57201i | 0.618223 | + | 0.786003i | \(0.287853\pi\) | ||||
−0.618223 | + | 0.786003i | \(0.712147\pi\) | |||||||
\(380\) | 29.6889 | 1.52301 | ||||||||
\(381\) | −7.41167 | −0.379711 | ||||||||
\(382\) | − 27.1283i | − 1.38800i | ||||||||
\(383\) | − 4.88598i | − 0.249662i | −0.992178 | − | 0.124831i | \(-0.960161\pi\) | ||||
0.992178 | − | 0.124831i | \(-0.0398388\pi\) | |||||||
\(384\) | 57.1111i | 2.91444i | ||||||||
\(385\) | − 1.01144i | − 0.0515479i | ||||||||
\(386\) | −23.8495 | −1.21391 | ||||||||
\(387\) | −1.98008 | −0.100653 | ||||||||
\(388\) | − 52.5650i | − 2.66858i | ||||||||
\(389\) | 1.85425 | 0.0940143 | 0.0470072 | − | 0.998895i | \(-0.485032\pi\) | ||||
0.0470072 | + | 0.998895i | \(0.485032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.68082 | 0.489580 | ||||||||
\(392\) | − 9.63087i | − 0.486433i | ||||||||
\(393\) | −15.4525 | −0.779475 | ||||||||
\(394\) | −71.3191 | −3.59300 | ||||||||
\(395\) | − 6.76298i | − 0.340283i | ||||||||
\(396\) | 8.55791i | 0.430051i | ||||||||
\(397\) | − 21.5134i | − 1.07973i | −0.841753 | − | 0.539863i | \(-0.818476\pi\) | ||||
0.841753 | − | 0.539863i | \(-0.181524\pi\) | |||||||
\(398\) | 27.7753i | 1.39225i | ||||||||
\(399\) | −9.91685 | −0.496464 | ||||||||
\(400\) | 68.4175 | 3.42087 | ||||||||
\(401\) | 14.5653i | 0.727357i | 0.931525 | + | 0.363678i | \(0.118479\pi\) | ||||
−0.931525 | + | 0.363678i | \(0.881521\pi\) | |||||||
\(402\) | −51.4760 | −2.56739 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −41.3162 | −2.05556 | ||||||||
\(405\) | − 3.18281i | − 0.158155i | ||||||||
\(406\) | −1.11734 | −0.0554529 | ||||||||
\(407\) | −8.33345 | −0.413074 | ||||||||
\(408\) | 54.5323i | 2.69975i | ||||||||
\(409\) | − 22.1290i | − 1.09421i | −0.837064 | − | 0.547105i | \(-0.815730\pi\) | ||||
0.837064 | − | 0.547105i | \(-0.184270\pi\) | |||||||
\(410\) | 2.54858i | 0.125865i | ||||||||
\(411\) | 19.0739i | 0.940847i | ||||||||
\(412\) | 15.4846 | 0.762873 | ||||||||
\(413\) | −10.9843 | −0.540500 | ||||||||
\(414\) | 7.27418i | 0.357506i | ||||||||
\(415\) | −8.69791 | −0.426964 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2363 | 0.697153 | ||||||||
\(418\) | 27.1829i | 1.32956i | ||||||||
\(419\) | 3.37590 | 0.164924 | 0.0824618 | − | 0.996594i | \(-0.473722\pi\) | ||||
0.0824618 | + | 0.996594i | \(0.473722\pi\) | |||||||
\(420\) | 5.57662 | 0.272111 | ||||||||
\(421\) | − 25.1101i | − 1.22379i | −0.790939 | − | 0.611895i | \(-0.790407\pi\) | ||||
0.790939 | − | 0.611895i | \(-0.209593\pi\) | |||||||
\(422\) | − 45.7164i | − 2.22544i | ||||||||
\(423\) | − 6.66260i | − 0.323947i | ||||||||
\(424\) | 43.9917i | 2.13643i | ||||||||
\(425\) | 18.4651 | 0.895688 | ||||||||
\(426\) | −18.0143 | −0.872794 | ||||||||
\(427\) | 6.52497i | 0.315766i | ||||||||
\(428\) | −8.19570 | −0.396154 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.53678 | 0.170558 | ||||||||
\(431\) | 10.7948i | 0.519969i | 0.965613 | + | 0.259985i | \(0.0837175\pi\) | ||||
−0.965613 | + | 0.259985i | \(0.916282\pi\) | |||||||
\(432\) | −86.7997 | −4.17615 | ||||||||
\(433\) | 14.5182 | 0.697700 | 0.348850 | − | 0.937179i | \(-0.386572\pi\) | ||||
0.348850 | + | 0.937179i | \(0.386572\pi\) | |||||||
\(434\) | − 7.59951i | − 0.364788i | ||||||||
\(435\) | − 0.412294i | − 0.0197680i | ||||||||
\(436\) | − 15.8305i | − 0.758144i | ||||||||
\(437\) | 16.9550i | 0.811068i | ||||||||
\(438\) | −22.7079 | −1.08502 | ||||||||
\(439\) | 14.4309 | 0.688748 | 0.344374 | − | 0.938833i | \(-0.388091\pi\) | ||||
0.344374 | + | 0.938833i | \(0.388091\pi\) | |||||||
\(440\) | − 9.74108i | − 0.464388i | ||||||||
\(441\) | 1.13727 | 0.0541556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.2430 | −1.43689 | −0.718445 | − | 0.695584i | \(-0.755146\pi\) | ||||
−0.718445 | + | 0.695584i | \(0.755146\pi\) | |||||||
\(444\) | − 45.9467i | − 2.18054i | ||||||||
\(445\) | −1.30505 | −0.0618653 | ||||||||
\(446\) | 2.93395 | 0.138926 | ||||||||
\(447\) | 11.1428i | 0.527038i | ||||||||
\(448\) | − 31.9557i | − 1.50977i | ||||||||
\(449\) | − 31.2760i | − 1.47601i | −0.674797 | − | 0.738003i | \(-0.735769\pi\) | ||||
0.674797 | − | 0.738003i | \(-0.264231\pi\) | |||||||
\(450\) | 13.8747i | 0.654058i | ||||||||
\(451\) | −1.71232 | −0.0806300 | ||||||||
\(452\) | 68.4749 | 3.22079 | ||||||||
\(453\) | 3.36002i | 0.157868i | ||||||||
\(454\) | −67.0645 | −3.14749 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −95.5080 | −4.47257 | ||||||||
\(457\) | 20.6466i | 0.965808i | 0.875673 | + | 0.482904i | \(0.160418\pi\) | ||||
−0.875673 | + | 0.482904i | \(0.839582\pi\) | |||||||
\(458\) | −12.9643 | −0.605783 | ||||||||
\(459\) | −23.4262 | −1.09344 | ||||||||
\(460\) | − 9.53444i | − 0.444545i | ||||||||
\(461\) | 27.2961i | 1.27131i | 0.771975 | + | 0.635653i | \(0.219269\pi\) | ||||
−0.771975 | + | 0.635653i | \(0.780731\pi\) | |||||||
\(462\) | 5.10590i | 0.237548i | ||||||||
\(463\) | − 5.65977i | − 0.263032i | −0.991314 | − | 0.131516i | \(-0.958016\pi\) | ||||
0.991314 | − | 0.131516i | \(-0.0419844\pi\) | |||||||
\(464\) | −6.26606 | −0.290894 | ||||||||
\(465\) | 2.80417 | 0.130040 | ||||||||
\(466\) | 56.3311i | 2.60949i | ||||||||
\(467\) | −42.2145 | −1.95345 | −0.976727 | − | 0.214486i | \(-0.931192\pi\) | ||||
−0.976727 | + | 0.214486i | \(0.931192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7597 | 0.635362 | ||||||||
\(470\) | 11.9006i | 0.548934i | ||||||||
\(471\) | −17.6332 | −0.812496 | ||||||||
\(472\) | −105.788 | −4.86929 | ||||||||
\(473\) | 2.37626i | 0.109261i | ||||||||
\(474\) | 34.1405i | 1.56812i | ||||||||
\(475\) | 32.3397i | 1.48385i | ||||||||
\(476\) | − 22.8740i | − 1.04843i | ||||||||
\(477\) | −5.19479 | −0.237853 | ||||||||
\(478\) | 17.1444 | 0.784167 | ||||||||
\(479\) | − 32.5316i | − 1.48641i | −0.669065 | − | 0.743204i | \(-0.733305\pi\) | ||||
0.669065 | − | 0.743204i | \(-0.266695\pi\) | |||||||
\(480\) | 23.1358 | 1.05600 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 33.2888 | 1.51626 | ||||||||
\(483\) | 3.18474i | 0.144911i | ||||||||
\(484\) | −50.3786 | −2.28994 | ||||||||
\(485\) | −7.06534 | −0.320820 | ||||||||
\(486\) | − 30.3663i | − 1.37744i | ||||||||
\(487\) | 26.8583i | 1.21707i | 0.793529 | + | 0.608533i | \(0.208242\pi\) | ||||
−0.793529 | + | 0.608533i | \(0.791758\pi\) | |||||||
\(488\) | 62.8412i | 2.84469i | ||||||||
\(489\) | 8.22634i | 0.372008i | ||||||||
\(490\) | −2.03137 | −0.0917678 | ||||||||
\(491\) | −43.6878 | −1.97160 | −0.985802 | − | 0.167912i | \(-0.946298\pi\) | ||||
−0.985802 | + | 0.167912i | \(0.946298\pi\) | |||||||
\(492\) | − 9.44093i | − 0.425630i | ||||||||
\(493\) | −1.69113 | −0.0761649 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.15028 | 0.0517013 | ||||||||
\(496\) | − 42.6180i | − 1.91360i | ||||||||
\(497\) | 4.81526 | 0.215994 | ||||||||
\(498\) | 43.9082 | 1.96758 | ||||||||
\(499\) | − 18.1020i | − 0.810355i | −0.914238 | − | 0.405177i | \(-0.867210\pi\) | ||||
0.914238 | − | 0.405177i | \(-0.132790\pi\) | |||||||
\(500\) | − 38.6158i | − 1.72695i | ||||||||
\(501\) | − 10.4424i | − 0.466534i | ||||||||
\(502\) | − 17.3082i | − 0.772505i | ||||||||
\(503\) | −28.4155 | −1.26698 | −0.633492 | − | 0.773749i | \(-0.718379\pi\) | ||||
−0.633492 | + | 0.773749i | \(0.718379\pi\) | |||||||
\(504\) | 10.9529 | 0.487880 | ||||||||
\(505\) | 5.55338i | 0.247122i | ||||||||
\(506\) | 8.72964 | 0.388080 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.9413 | 1.32843 | ||||||||
\(509\) | 17.4791i | 0.774748i | 0.921923 | + | 0.387374i | \(0.126618\pi\) | ||||
−0.921923 | + | 0.387374i | \(0.873382\pi\) | |||||||
\(510\) | 11.5021 | 0.509321 | ||||||||
\(511\) | 6.06987 | 0.268515 | ||||||||
\(512\) | − 55.5280i | − 2.45402i | ||||||||
\(513\) | − 41.0287i | − 1.81146i | ||||||||
\(514\) | 66.7624i | 2.94476i | ||||||||
\(515\) | − 2.08131i | − 0.0917136i | ||||||||
\(516\) | −13.1016 | −0.576766 | ||||||||
\(517\) | −7.99569 | −0.351650 | ||||||||
\(518\) | 16.7368i | 0.735372i | ||||||||
\(519\) | 0.224458 | 0.00985260 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3087 | 0.845931 | 0.422966 | − | 0.906146i | \(-0.360989\pi\) | ||||
0.422966 | + | 0.906146i | \(0.360989\pi\) | |||||||
\(522\) | − 1.27072i | − 0.0556179i | ||||||||
\(523\) | −10.0229 | −0.438270 | −0.219135 | − | 0.975695i | \(-0.570324\pi\) | ||||
−0.219135 | + | 0.975695i | \(0.570324\pi\) | |||||||
\(524\) | 62.4242 | 2.72702 | ||||||||
\(525\) | 6.07453i | 0.265114i | ||||||||
\(526\) | 26.2571i | 1.14486i | ||||||||
\(527\) | − 11.5021i | − 0.501039i | ||||||||
\(528\) | 28.6338i | 1.24613i | ||||||||
\(529\) | −17.5550 | −0.763261 | ||||||||
\(530\) | 9.27884 | 0.403047 | ||||||||
\(531\) | − 12.4920i | − 0.542108i | ||||||||
\(532\) | 40.0616 | 1.73689 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.58807 | 0.285093 | ||||||||
\(535\) | 1.10160i | 0.0476261i | ||||||||
\(536\) | 132.518 | 5.72389 | ||||||||
\(537\) | −1.04904 | −0.0452696 | ||||||||
\(538\) | − 80.5851i | − 3.47427i | ||||||||
\(539\) | − 1.36482i | − 0.0587869i | ||||||||
\(540\) | 23.0720i | 0.992860i | ||||||||
\(541\) | − 17.6153i | − 0.757339i | −0.925532 | − | 0.378670i | \(-0.876382\pi\) | ||||
0.925532 | − | 0.378670i | \(-0.123618\pi\) | |||||||
\(542\) | 0.823379 | 0.0353672 | ||||||||
\(543\) | 13.5411 | 0.581103 | ||||||||
\(544\) | − 94.8978i | − 4.06871i | ||||||||
\(545\) | −2.12780 | −0.0911451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.98425 | 0.127597 | 0.0637987 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0637987 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(548\) | − 77.0539i | − 3.29158i | ||||||||
\(549\) | −7.42064 | −0.316705 | ||||||||
\(550\) | 16.6508 | 0.709992 | ||||||||
\(551\) | − 2.96185i | − 0.126179i | ||||||||
\(552\) | 30.6719i | 1.30548i | ||||||||
\(553\) | − 9.12582i | − 0.388070i | ||||||||
\(554\) | − 89.8279i | − 3.81642i | ||||||||
\(555\) | −6.17577 | −0.262147 | ||||||||
\(556\) | −57.5109 | −2.43901 | ||||||||
\(557\) | − 7.25596i | − 0.307445i | −0.988114 | − | 0.153722i | \(-0.950874\pi\) | ||||
0.988114 | − | 0.153722i | \(-0.0491261\pi\) | |||||||
\(558\) | 8.64268 | 0.365874 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −11.3919 | −0.481395 | ||||||||
\(561\) | 7.72794i | 0.326274i | ||||||||
\(562\) | −11.7724 | −0.496591 | ||||||||
\(563\) | −4.27933 | −0.180352 | −0.0901762 | − | 0.995926i | \(-0.528743\pi\) | ||||
−0.0901762 | + | 0.995926i | \(0.528743\pi\) | |||||||
\(564\) | − 44.0845i | − 1.85629i | ||||||||
\(565\) | − 9.20382i | − 0.387207i | ||||||||
\(566\) | − 57.8375i | − 2.43109i | ||||||||
\(567\) | − 4.29482i | − 0.180365i | ||||||||
\(568\) | 46.3751 | 1.94586 | ||||||||
\(569\) | 19.7626 | 0.828492 | 0.414246 | − | 0.910165i | \(-0.364045\pi\) | ||||
0.414246 | + | 0.910165i | \(0.364045\pi\) | |||||||
\(570\) | 20.1448i | 0.843771i | ||||||||
\(571\) | 19.9236 | 0.833778 | 0.416889 | − | 0.908957i | \(-0.363120\pi\) | ||||
0.416889 | + | 0.908957i | \(0.363120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5075 | 0.564285 | ||||||||
\(574\) | 3.43900i | 0.143541i | ||||||||
\(575\) | 10.3857 | 0.433115 | ||||||||
\(576\) | 36.3422 | 1.51426 | ||||||||
\(577\) | − 28.7300i | − 1.19605i | −0.801479 | − | 0.598023i | \(-0.795953\pi\) | ||||
0.801479 | − | 0.598023i | \(-0.204047\pi\) | |||||||
\(578\) | − 0.580569i | − 0.0241485i | ||||||||
\(579\) | − 11.8749i | − 0.493506i | ||||||||
\(580\) | 1.66556i | 0.0691587i | ||||||||
\(581\) | −11.7368 | −0.486924 | ||||||||
\(582\) | 35.6668 | 1.47844 | ||||||||
\(583\) | 6.23420i | 0.258194i | ||||||||
\(584\) | 58.4582 | 2.41902 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.6921 | −2.01145 | ||||||||
\(587\) | 31.5388i | 1.30174i | 0.759188 | + | 0.650872i | \(0.225597\pi\) | ||||
−0.759188 | + | 0.650872i | \(0.774403\pi\) | |||||||
\(588\) | 7.52497 | 0.310325 | ||||||||
\(589\) | 20.1448 | 0.830051 | ||||||||
\(590\) | 22.3130i | 0.918613i | ||||||||
\(591\) | − 35.5107i | − 1.46071i | ||||||||
\(592\) | 93.8597i | 3.85761i | ||||||||
\(593\) | 11.1181i | 0.456564i | 0.973595 | + | 0.228282i | \(0.0733108\pi\) | ||||
−0.973595 | + | 0.228282i | \(0.926689\pi\) | |||||||
\(594\) | −21.1245 | −0.866748 | ||||||||
\(595\) | −3.07453 | −0.126044 | ||||||||
\(596\) | − 45.0143i | − 1.84386i | ||||||||
\(597\) | −13.8297 | −0.566010 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.29572 | −0.298095 | −0.149048 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149048 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(600\) | 58.5031i | 2.38838i | ||||||||
\(601\) | −1.17258 | −0.0478306 | −0.0239153 | − | 0.999714i | \(-0.507613\pi\) | ||||
−0.0239153 | + | 0.999714i | \(0.507613\pi\) | |||||||
\(602\) | 4.77245 | 0.194510 | ||||||||
\(603\) | 15.6484i | 0.637253i | ||||||||
\(604\) | − 13.5737i | − 0.552304i | ||||||||
\(605\) | 6.77146i | 0.275299i | ||||||||
\(606\) | − 28.0342i | − 1.13881i | ||||||||
\(607\) | 0.633838 | 0.0257267 | 0.0128633 | − | 0.999917i | \(-0.495905\pi\) | ||||
0.0128633 | + | 0.999917i | \(0.495905\pi\) | |||||||
\(608\) | 166.204 | 6.74047 | ||||||||
\(609\) | − 0.556340i | − 0.0225440i | ||||||||
\(610\) | 13.2546 | 0.536664 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 26.0139 | 1.05155 | ||||||||
\(613\) | − 30.8550i | − 1.24622i | −0.782134 | − | 0.623110i | \(-0.785869\pi\) | ||||
0.782134 | − | 0.623110i | \(-0.214131\pi\) | |||||||
\(614\) | −49.3823 | −1.99291 | ||||||||
\(615\) | −1.26897 | −0.0511698 | ||||||||
\(616\) | − 13.1444i | − 0.529603i | ||||||||
\(617\) | 33.8209i | 1.36158i | 0.732479 | + | 0.680790i | \(0.238363\pi\) | ||||
−0.732479 | + | 0.680790i | \(0.761637\pi\) | |||||||
\(618\) | 10.5068i | 0.422644i | ||||||||
\(619\) | 0.404797i | 0.0162702i | 0.999967 | + | 0.00813509i | \(0.00258951\pi\) | ||||
−0.999967 | + | 0.00813509i | \(0.997410\pi\) | |||||||
\(620\) | −11.3282 | −0.454950 | ||||||||
\(621\) | −13.1761 | −0.528740 | ||||||||
\(622\) | 47.2959i | 1.89639i | ||||||||
\(623\) | −1.76101 | −0.0705532 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0636 | 0.682543 | ||||||||
\(626\) | − 18.6812i | − 0.746650i | ||||||||
\(627\) | −13.5347 | −0.540524 | ||||||||
\(628\) | 71.2338 | 2.84254 | ||||||||
\(629\) | 25.3316i | 1.01004i | ||||||||
\(630\) | − 2.31021i | − 0.0920409i | ||||||||
\(631\) | − 30.4508i | − 1.21223i | −0.795378 | − | 0.606114i | \(-0.792728\pi\) | ||||
0.795378 | − | 0.606114i | \(-0.207272\pi\) | |||||||
\(632\) | − 87.8897i | − 3.49606i | ||||||||
\(633\) | 22.7628 | 0.904738 | ||||||||
\(634\) | −68.7381 | −2.72994 | ||||||||
\(635\) | − 4.02446i | − 0.159706i | ||||||||
\(636\) | −34.3724 | −1.36296 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.52497 | −0.0603743 | ||||||||
\(639\) | 5.47624i | 0.216637i | ||||||||
\(640\) | −31.0107 | −1.22581 | ||||||||
\(641\) | −9.64564 | −0.380980 | −0.190490 | − | 0.981689i | \(-0.561008\pi\) | ||||
−0.190490 | + | 0.981689i | \(0.561008\pi\) | |||||||
\(642\) | − 5.56100i | − 0.219475i | ||||||||
\(643\) | 8.13296i | 0.320733i | 0.987058 | + | 0.160366i | \(0.0512676\pi\) | ||||
−0.987058 | + | 0.160366i | \(0.948732\pi\) | |||||||
\(644\) | − 12.8656i | − 0.506974i | ||||||||
\(645\) | 1.76101i | 0.0693395i | ||||||||
\(646\) | 82.6293 | 3.25101 | ||||||||
\(647\) | 11.5227 | 0.453005 | 0.226503 | − | 0.974011i | \(-0.427271\pi\) | ||||
0.226503 | + | 0.974011i | \(0.427271\pi\) | |||||||
\(648\) | − 41.3629i | − 1.62489i | ||||||||
\(649\) | −14.9915 | −0.588469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.78389 | 0.148302 | ||||||||
\(652\) | − 33.2324i | − 1.30148i | ||||||||
\(653\) | 42.4039 | 1.65939 | 0.829697 | − | 0.558215i | \(-0.188513\pi\) | ||||
0.829697 | + | 0.558215i | \(0.188513\pi\) | |||||||
\(654\) | 10.7414 | 0.420024 | ||||||||
\(655\) | − 8.39054i | − 0.327845i | ||||||||
\(656\) | 19.2858i | 0.752986i | ||||||||
\(657\) | 6.90307i | 0.269314i | ||||||||
\(658\) | 16.0584i | 0.626023i | ||||||||
\(659\) | −2.50088 | −0.0974203 | −0.0487101 | − | 0.998813i | \(-0.515511\pi\) | ||||
−0.0487101 | + | 0.998813i | \(0.515511\pi\) | |||||||
\(660\) | 7.61108 | 0.296261 | ||||||||
\(661\) | − 14.8394i | − 0.577184i | −0.957452 | − | 0.288592i | \(-0.906813\pi\) | ||||
0.957452 | − | 0.288592i | \(-0.0931871\pi\) | |||||||
\(662\) | −8.21046 | −0.319109 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −113.035 | −4.38663 | ||||||||
\(665\) | − 5.38474i | − 0.208811i | ||||||||
\(666\) | −19.0342 | −0.737560 | ||||||||
\(667\) | −0.951183 | −0.0368300 | ||||||||
\(668\) | 42.1849i | 1.63218i | ||||||||
\(669\) | 1.46085i | 0.0564797i | ||||||||
\(670\) | − 27.9509i | − 1.07984i | ||||||||
\(671\) | 8.90541i | 0.343790i | ||||||||
\(672\) | 31.2189 | 1.20430 | ||||||||
\(673\) | −39.6091 | −1.52682 | −0.763410 | − | 0.645915i | \(-0.776476\pi\) | ||||
−0.763410 | + | 0.645915i | \(0.776476\pi\) | |||||||
\(674\) | − 80.8313i | − 3.11350i | ||||||||
\(675\) | −25.1320 | −0.967330 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.0321 | 0.654596 | 0.327298 | − | 0.944921i | \(-0.393862\pi\) | ||||
0.327298 | + | 0.944921i | \(0.393862\pi\) | |||||||
\(678\) | 46.4621i | 1.78437i | ||||||||
\(679\) | −9.53381 | −0.365874 | ||||||||
\(680\) | −29.6105 | −1.13551 | ||||||||
\(681\) | − 33.3922i | − 1.27959i | ||||||||
\(682\) | − 10.3720i | − 0.397163i | ||||||||
\(683\) | − 32.8912i | − 1.25854i | −0.777185 | − | 0.629272i | \(-0.783353\pi\) | ||||
0.777185 | − | 0.629272i | \(-0.216647\pi\) | |||||||
\(684\) | 45.5608i | 1.74206i | ||||||||
\(685\) | −10.3569 | −0.395718 | ||||||||
\(686\) | −2.74108 | −0.104655 | ||||||||
\(687\) | − 6.45510i | − 0.246278i | ||||||||
\(688\) | 26.7638 | 1.02036 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.46938 | 0.246285 | ||||||||
\(691\) | − 23.7922i | − 0.905099i | −0.891739 | − | 0.452550i | \(-0.850514\pi\) | ||||
0.891739 | − | 0.452550i | \(-0.149486\pi\) | |||||||
\(692\) | −0.906754 | −0.0344696 | ||||||||
\(693\) | 1.55217 | 0.0589619 | ||||||||
\(694\) | 16.4105i | 0.622933i | ||||||||
\(695\) | 7.73013i | 0.293221i | ||||||||
\(696\) | − 5.35804i | − 0.203096i | ||||||||
\(697\) | 5.20502i | 0.197154i | ||||||||
\(698\) | 83.1539 | 3.14742 | ||||||||
\(699\) | −28.0480 | −1.06087 | ||||||||
\(700\) | − 24.5396i | − 0.927510i | ||||||||
\(701\) | −29.7796 | −1.12476 | −0.562380 | − | 0.826879i | \(-0.690114\pi\) | ||||
−0.562380 | + | 0.826879i | \(0.690114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.3658 | −1.67329 | ||||||||
\(704\) | − 43.6138i | − 1.64376i | ||||||||
\(705\) | −5.92547 | −0.223166 | ||||||||
\(706\) | −78.4122 | −2.95108 | ||||||||
\(707\) | 7.49361i | 0.281826i | ||||||||
\(708\) | − 82.6562i | − 3.10641i | ||||||||
\(709\) | − 11.9304i | − 0.448054i | −0.974583 | − | 0.224027i | \(-0.928080\pi\) | ||||
0.974583 | − | 0.224027i | \(-0.0719204\pi\) | |||||||
\(710\) | − 9.78155i | − 0.367095i | ||||||||
\(711\) | 10.3785 | 0.389224 | ||||||||
\(712\) | −16.9600 | −0.635604 | ||||||||
\(713\) | − 6.46938i | − 0.242280i | ||||||||
\(714\) | 15.5207 | 0.580846 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.23788 | 0.158377 | ||||||||
\(717\) | 8.53642i | 0.318798i | ||||||||
\(718\) | −64.3106 | −2.40005 | ||||||||
\(719\) | −32.3638 | −1.20697 | −0.603484 | − | 0.797375i | \(-0.706221\pi\) | ||||
−0.603484 | + | 0.797375i | \(0.706221\pi\) | |||||||
\(720\) | − 12.9556i | − 0.482827i | ||||||||
\(721\) | − 2.80848i | − 0.104593i | ||||||||
\(722\) | 92.6364i | 3.44757i | ||||||||
\(723\) | 16.5749i | 0.616428i | ||||||||
\(724\) | −54.7026 | −2.03301 | ||||||||
\(725\) | −1.81427 | −0.0673805 | ||||||||
\(726\) | − 34.1833i | − 1.26866i | ||||||||
\(727\) | 31.4897 | 1.16789 | 0.583943 | − | 0.811794i | \(-0.301509\pi\) | ||||
0.583943 | + | 0.811794i | \(0.301509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.0042 | 1.03719 | ||||||||
\(730\) | − 12.3301i | − 0.456359i | ||||||||
\(731\) | 7.22325 | 0.267161 | ||||||||
\(732\) | −49.1003 | −1.81480 | ||||||||
\(733\) | 2.66224i | 0.0983321i | 0.998791 | + | 0.0491661i | \(0.0156564\pi\) | ||||
−0.998791 | + | 0.0491661i | \(0.984344\pi\) | |||||||
\(734\) | − 100.103i | − 3.69489i | ||||||||
\(735\) | − 1.01144i | − 0.0373076i | ||||||||
\(736\) | − 53.3755i | − 1.96745i | ||||||||
\(737\) | 18.7795 | 0.691750 | ||||||||
\(738\) | −3.91106 | −0.143968 | ||||||||
\(739\) | 35.5828i | 1.30893i | 0.756091 | + | 0.654467i | \(0.227107\pi\) | ||||
−0.756091 | + | 0.654467i | \(0.772893\pi\) | |||||||
\(740\) | 24.9486 | 0.917128 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.5207 | 0.459648 | ||||||||
\(743\) | 24.2406i | 0.889300i | 0.895704 | + | 0.444650i | \(0.146672\pi\) | ||||
−0.895704 | + | 0.444650i | \(0.853328\pi\) | |||||||
\(744\) | 36.4422 | 1.33604 | ||||||||
\(745\) | −6.05044 | −0.221671 | ||||||||
\(746\) | 35.7706i | 1.30966i | ||||||||
\(747\) | − 13.3479i | − 0.488373i | ||||||||
\(748\) | − 31.2189i | − 1.14148i | ||||||||
\(749\) | 1.48647i | 0.0543144i | ||||||||
\(750\) | 26.2018 | 0.956756 | ||||||||
\(751\) | 29.1410 | 1.06337 | 0.531684 | − | 0.846943i | \(-0.321559\pi\) | ||||
0.531684 | + | 0.846943i | \(0.321559\pi\) | |||||||
\(752\) | 90.0555i | 3.28399i | ||||||||
\(753\) | 8.61799 | 0.314057 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.82446 | −0.0663988 | ||||||||
\(756\) | 31.1328i | 1.13229i | ||||||||
\(757\) | −4.98990 | −0.181361 | −0.0906805 | − | 0.995880i | \(-0.528904\pi\) | ||||
−0.0906805 | + | 0.995880i | \(0.528904\pi\) | |||||||
\(758\) | 83.8872 | 3.04692 | ||||||||
\(759\) | 4.34660i | 0.157772i | ||||||||
\(760\) | − 51.8598i | − 1.88115i | ||||||||
\(761\) | 11.8372i | 0.429097i | 0.976713 | + | 0.214548i | \(0.0688280\pi\) | ||||
−0.976713 | + | 0.214548i | \(0.931172\pi\) | |||||||
\(762\) | 20.3160i | 0.735971i | ||||||||
\(763\) | −2.87121 | −0.103945 | ||||||||
\(764\) | −54.5670 | −1.97417 | ||||||||
\(765\) | − 3.49657i | − 0.126419i | ||||||||
\(766\) | −13.3929 | −0.483904 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 69.3186 | 2.50132 | ||||||||
\(769\) | − 35.8183i | − 1.29164i | −0.763489 | − | 0.645821i | \(-0.776515\pi\) | ||||
0.763489 | − | 0.645821i | \(-0.223485\pi\) | |||||||
\(770\) | −2.77245 | −0.0999121 | ||||||||
\(771\) | −33.2418 | −1.19718 | ||||||||
\(772\) | 47.9718i | 1.72654i | ||||||||
\(773\) | − 19.9534i | − 0.717673i | −0.933400 | − | 0.358837i | \(-0.883174\pi\) | ||||
0.933400 | − | 0.358837i | \(-0.116826\pi\) | |||||||
\(774\) | 5.42755i | 0.195089i | ||||||||
\(775\) | − 12.3396i | − 0.443252i | ||||||||
\(776\) | −91.8190 | −3.29611 | ||||||||
\(777\) | −8.33345 | −0.298961 | ||||||||
\(778\) | − 5.08266i | − 0.182222i | ||||||||
\(779\) | −9.11608 | −0.326618 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.57196 | 0.235163 | ||||||||
\(782\) | − 26.5359i | − 0.948923i | ||||||||
\(783\) | 2.30173 | 0.0822570 | ||||||||
\(784\) | −15.3720 | −0.548998 | ||||||||
\(785\) | − 9.57464i | − 0.341734i | ||||||||
\(786\) | 42.3566i | 1.51081i | ||||||||
\(787\) | − 2.79619i | − 0.0996733i | −0.998757 | − | 0.0498367i | \(-0.984130\pi\) | ||||
0.998757 | − | 0.0498367i | \(-0.0158701\pi\) | |||||||
\(788\) | 143.454i | 5.11035i | ||||||||
\(789\) | −13.0737 | −0.465437 | ||||||||
\(790\) | −18.5379 | −0.659549 | ||||||||
\(791\) | − 12.4194i | − 0.441584i | ||||||||
\(792\) | 14.9487 | 0.531179 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −58.9700 | −2.09277 | ||||||||
\(795\) | 4.62005i | 0.163856i | ||||||||
\(796\) | 55.8684 | 1.98020 | ||||||||
\(797\) | −1.68562 | −0.0597076 | −0.0298538 | − | 0.999554i | \(-0.509504\pi\) | ||||
−0.0298538 | + | 0.999554i | \(0.509504\pi\) | |||||||
\(798\) | 27.1829i | 0.962265i | ||||||||
\(799\) | 24.3049i | 0.859846i | ||||||||
\(800\) | − 101.808i | − 3.59945i | ||||||||
\(801\) | − 2.00273i | − 0.0707632i | ||||||||
\(802\) | 39.9247 | 1.40979 | ||||||||
\(803\) | 8.28428 | 0.292346 | ||||||||
\(804\) | 103.541i | 3.65161i | ||||||||
\(805\) | −1.72928 | −0.0609491 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.1244 | 1.41244 | ||||||||
\(808\) | 72.1700i | 2.53893i | ||||||||
\(809\) | −43.4372 | −1.52717 | −0.763585 | − | 0.645708i | \(-0.776562\pi\) | ||||
−0.763585 | + | 0.645708i | \(0.776562\pi\) | |||||||
\(810\) | −8.72435 | −0.306542 | ||||||||
\(811\) | 5.60812i | 0.196928i | 0.995141 | + | 0.0984639i | \(0.0313929\pi\) | ||||
−0.995141 | + | 0.0984639i | \(0.968607\pi\) | |||||||
\(812\) | 2.24747i | 0.0788709i | ||||||||
\(813\) | 0.409971i | 0.0143783i | ||||||||
\(814\) | 22.8427i | 0.800635i | ||||||||
\(815\) | −4.46681 | −0.156466 | ||||||||
\(816\) | 87.0397 | 3.04700 | ||||||||
\(817\) | 12.6508i | 0.442595i | ||||||||
\(818\) | −60.6574 | −2.12084 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.12632 | 0.179019 | ||||||||
\(821\) | − 23.9448i | − 0.835678i | −0.908521 | − | 0.417839i | \(-0.862788\pi\) | ||||
0.908521 | − | 0.417839i | \(-0.137212\pi\) | |||||||
\(822\) | 52.2832 | 1.82358 | ||||||||
\(823\) | −35.4117 | −1.23437 | −0.617187 | − | 0.786817i | \(-0.711728\pi\) | ||||
−0.617187 | + | 0.786817i | \(0.711728\pi\) | |||||||
\(824\) | − 27.0481i | − 0.942266i | ||||||||
\(825\) | 8.29064i | 0.288643i | ||||||||
\(826\) | 30.1087i | 1.04762i | ||||||||
\(827\) | 16.1563i | 0.561811i | 0.959735 | + | 0.280905i | \(0.0906347\pi\) | ||||
−0.959735 | + | 0.280905i | \(0.909365\pi\) | |||||||
\(828\) | 14.6316 | 0.508483 | ||||||||
\(829\) | 52.7010 | 1.83038 | 0.915190 | − | 0.403022i | \(-0.132040\pi\) | ||||
0.915190 | + | 0.403022i | \(0.132040\pi\) | |||||||
\(830\) | 23.8417i | 0.827557i | ||||||||
\(831\) | 44.7265 | 1.55154 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.14871 | −0.143744 | ||||||||
\(834\) | − 39.0228i | − 1.35125i | ||||||||
\(835\) | 5.67013 | 0.196223 | ||||||||
\(836\) | 54.6769 | 1.89104 | ||||||||
\(837\) | 15.6550i | 0.541115i | ||||||||
\(838\) | − 9.25363i | − 0.319661i | ||||||||
\(839\) | 22.4338i | 0.774502i | 0.921974 | + | 0.387251i | \(0.126575\pi\) | ||||
−0.921974 | + | 0.387251i | \(0.873425\pi\) | |||||||
\(840\) | − 9.74108i | − 0.336099i | ||||||||
\(841\) | −28.8338 | −0.994270 | ||||||||
\(842\) | −68.8288 | −2.37200 | ||||||||
\(843\) | − 5.86165i | − 0.201886i | ||||||||
\(844\) | −91.9559 | −3.16525 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.2627 | −0.627886 | ||||||||
\(847\) | 9.13727i | 0.313960i | ||||||||
\(848\) | 70.2158 | 2.41122 | ||||||||
\(849\) | 28.7980 | 0.988346 | ||||||||
\(850\) | − 50.6143i | − 1.73606i | ||||||||
\(851\) | 14.2478i | 0.488409i | ||||||||
\(852\) | 36.2347i | 1.24138i | ||||||||
\(853\) | − 30.8521i | − 1.05635i | −0.849134 | − | 0.528177i | \(-0.822876\pi\) | ||||
0.849134 | − | 0.528177i | \(-0.177124\pi\) | |||||||
\(854\) | 17.8855 | 0.612029 | ||||||||
\(855\) | 6.12390 | 0.209433 | ||||||||
\(856\) | 14.3160i | 0.489311i | ||||||||
\(857\) | −26.7400 | −0.913420 | −0.456710 | − | 0.889616i | \(-0.650972\pi\) | ||||
−0.456710 | + | 0.889616i | \(0.650972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.15804 | −0.175990 | −0.0879950 | − | 0.996121i | \(-0.528046\pi\) | ||||
−0.0879950 | + | 0.996121i | \(0.528046\pi\) | |||||||
\(860\) | − 7.11402i | − 0.242586i | ||||||||
\(861\) | −1.71232 | −0.0583557 | ||||||||
\(862\) | 29.5896 | 1.00782 | ||||||||
\(863\) | 8.16814i | 0.278047i | 0.990289 | + | 0.139023i | \(0.0443963\pi\) | ||||
−0.990289 | + | 0.139023i | \(0.955604\pi\) | |||||||
\(864\) | 129.161i | 4.39415i | ||||||||
\(865\) | 0.121878i | 0.00414398i | ||||||||
\(866\) | − 39.7956i | − 1.35231i | ||||||||
\(867\) | 0.289073 | 0.00981742 | ||||||||
\(868\) | −15.2860 | −0.518840 | ||||||||
\(869\) | − 12.4551i | − 0.422510i | ||||||||
\(870\) | −1.13013 | −0.0383150 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −27.6523 | −0.936425 | ||||||||
\(873\) | − 10.8425i | − 0.366963i | ||||||||
\(874\) | 46.4750 | 1.57204 | ||||||||
\(875\) | −7.00382 | −0.236772 | ||||||||
\(876\) | 45.6756i | 1.54324i | ||||||||
\(877\) | 15.6184i | 0.527398i | 0.964605 | + | 0.263699i | \(0.0849425\pi\) | ||||
−0.964605 | + | 0.263699i | \(0.915058\pi\) | |||||||
\(878\) | − 39.5562i | − 1.33496i | ||||||||
\(879\) | − 24.2444i | − 0.817744i | ||||||||
\(880\) | −15.5479 | −0.524118 | ||||||||
\(881\) | 46.4375 | 1.56452 | 0.782260 | − | 0.622952i | \(-0.214067\pi\) | ||||
0.782260 | + | 0.622952i | \(0.214067\pi\) | |||||||
\(882\) | − 3.11734i | − 0.104966i | ||||||||
\(883\) | −15.6588 | −0.526960 | −0.263480 | − | 0.964665i | \(-0.584870\pi\) | ||||
−0.263480 | + | 0.964665i | \(0.584870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.1099 | −0.373457 | ||||||||
\(886\) | 82.8986i | 2.78503i | ||||||||
\(887\) | 31.5107 | 1.05803 | 0.529013 | − | 0.848614i | \(-0.322562\pi\) | ||||
0.529013 | + | 0.848614i | \(0.322562\pi\) | |||||||
\(888\) | −80.2584 | −2.69330 | ||||||||
\(889\) | − 5.43052i | − 0.182134i | ||||||||
\(890\) | 3.57725i | 0.119910i | ||||||||
\(891\) | − 5.86165i | − 0.196373i | ||||||||
\(892\) | − 5.90146i | − 0.197596i | ||||||||
\(893\) | −42.5677 | −1.42447 | ||||||||
\(894\) | 30.5434 | 1.02152 | ||||||||
\(895\) | − 0.569620i | − 0.0190403i | ||||||||
\(896\) | −41.8452 | −1.39795 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −85.7301 | −2.86085 | ||||||||
\(899\) | 1.13013i | 0.0376920i | ||||||||
\(900\) | 27.9081 | 0.930270 | ||||||||
\(901\) | 18.9504 | 0.631330 | ||||||||
\(902\) | 4.69361i | 0.156280i | ||||||||
\(903\) | 2.37626i | 0.0790771i | ||||||||
\(904\) | − 119.610i | − 3.97817i | ||||||||
\(905\) | 7.35266i | 0.244411i | ||||||||
\(906\) | 9.21010 | 0.305985 | ||||||||
\(907\) | 0.747991 | 0.0248366 | 0.0124183 | − | 0.999923i | \(-0.496047\pi\) | ||||
0.0124183 | + | 0.999923i | \(0.496047\pi\) | |||||||
\(908\) | 134.896i | 4.47669i | ||||||||
\(909\) | −8.52224 | −0.282665 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9000 | 0.824973 | 0.412486 | − | 0.910964i | \(-0.364660\pi\) | ||||
0.412486 | + | 0.910964i | \(0.364660\pi\) | |||||||
\(912\) | 152.441i | 5.04784i | ||||||||
\(913\) | −16.0186 | −0.530138 | ||||||||
\(914\) | 56.5941 | 1.87197 | ||||||||
\(915\) | 6.59964i | 0.218177i | ||||||||
\(916\) | 26.0770i | 0.861609i | ||||||||
\(917\) | − 11.3220i | − 0.373886i | ||||||||
\(918\) | 64.2132i | 2.11935i | ||||||||
\(919\) | 0.586495 | 0.0193467 | 0.00967334 | − | 0.999953i | \(-0.496921\pi\) | ||||
0.00967334 | + | 0.999953i | \(0.496921\pi\) | |||||||
\(920\) | −16.6545 | −0.549082 | ||||||||
\(921\) | − 24.5881i | − 0.810204i | ||||||||
\(922\) | 74.8208 | 2.46409 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10.2702 | 0.337866 | ||||||||
\(925\) | 27.1761i | 0.893546i | ||||||||
\(926\) | −15.5139 | −0.509818 | ||||||||
\(927\) | 3.19399 | 0.104905 | ||||||||
\(928\) | 9.32412i | 0.306079i | ||||||||
\(929\) | − 50.1949i | − 1.64684i | −0.567431 | − | 0.823421i | \(-0.692062\pi\) | ||||
0.567431 | − | 0.823421i | \(-0.307938\pi\) | |||||||
\(930\) | − 7.68647i | − 0.252049i | ||||||||
\(931\) | − 7.26606i | − 0.238135i | ||||||||
\(932\) | 113.307 | 3.71149 | ||||||||
\(933\) | −23.5493 | −0.770968 | ||||||||
\(934\) | 115.713i | 3.78626i | ||||||||
\(935\) | −4.19619 | −0.137230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.7130 | 0.742003 | 0.371001 | − | 0.928632i | \(-0.379015\pi\) | ||||
0.371001 | + | 0.928632i | \(0.379015\pi\) | |||||||
\(938\) | − 37.7164i | − 1.23148i | ||||||||
\(939\) | 9.30160 | 0.303546 | ||||||||
\(940\) | 23.9374 | 0.780752 | ||||||||
\(941\) | − 49.8734i | − 1.62583i | −0.582384 | − | 0.812914i | \(-0.697880\pi\) | ||||
0.582384 | − | 0.812914i | \(-0.302120\pi\) | |||||||
\(942\) | 48.3341i | 1.57481i | ||||||||
\(943\) | 2.92758i | 0.0953351i | ||||||||
\(944\) | 168.849i | 5.49558i | ||||||||
\(945\) | 4.18461 | 0.136125 | ||||||||
\(946\) | 6.51353 | 0.211773 | ||||||||
\(947\) | − 0.266414i | − 0.00865731i | −0.999991 | − | 0.00432865i | \(-0.998622\pi\) | ||||
0.999991 | − | 0.00432865i | \(-0.00137786\pi\) | |||||||
\(948\) | 68.6716 | 2.23035 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 88.6459 | 2.87605 | ||||||||
\(951\) | − 34.2256i | − 1.10984i | ||||||||
\(952\) | −39.9557 | −1.29497 | ||||||||
\(953\) | −7.82029 | −0.253324 | −0.126662 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126662 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(954\) | 14.2394i | 0.461016i | ||||||||
\(955\) | 7.33444i | 0.237337i | ||||||||
\(956\) | − 34.4850i | − 1.11532i | ||||||||
\(957\) | − 0.759304i | − 0.0245448i | ||||||||
\(958\) | −89.1718 | −2.88101 | ||||||||
\(959\) | −13.9754 | −0.451290 | ||||||||
\(960\) | − 32.3214i | − 1.04317i | ||||||||
\(961\) | 23.3135 | 0.752049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.69051 | −0.0544761 | ||||||||
\(964\) | − 66.9585i | − 2.15659i | ||||||||
\(965\) | 6.44797 | 0.207567 | ||||||||
\(966\) | 8.72964 | 0.280872 | ||||||||
\(967\) | 39.8224i | 1.28060i | 0.768124 | + | 0.640301i | \(0.221190\pi\) | ||||
−0.768124 | + | 0.640301i | \(0.778810\pi\) | |||||||
\(968\) | 87.9999i | 2.82842i | ||||||||
\(969\) | 41.1422i | 1.32168i | ||||||||
\(970\) | 19.3667i | 0.621826i | ||||||||
\(971\) | −45.9295 | −1.47395 | −0.736974 | − | 0.675921i | \(-0.763746\pi\) | ||||
−0.736974 | + | 0.675921i | \(0.763746\pi\) | |||||||
\(972\) | −61.0801 | −1.95915 | ||||||||
\(973\) | 10.4309i | 0.334398i | ||||||||
\(974\) | 73.6208 | 2.35896 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 100.302 | 3.21058 | ||||||||
\(977\) | − 28.6627i | − 0.917002i | −0.888694 | − | 0.458501i | \(-0.848387\pi\) | ||||
0.888694 | − | 0.458501i | \(-0.151613\pi\) | |||||||
\(978\) | 22.5491 | 0.721040 | ||||||||
\(979\) | −2.40345 | −0.0768147 | ||||||||
\(980\) | 4.08598i | 0.130522i | ||||||||
\(981\) | − 3.26534i | − 0.104254i | ||||||||
\(982\) | 119.752i | 3.82144i | ||||||||
\(983\) | 46.1200i | 1.47100i | 0.677524 | + | 0.735500i | \(0.263053\pi\) | ||||
−0.677524 | + | 0.735500i | \(0.736947\pi\) | |||||||
\(984\) | −16.4911 | −0.525718 | ||||||||
\(985\) | 19.2819 | 0.614372 | ||||||||
\(986\) | 4.63554i | 0.147626i | ||||||||
\(987\) | −7.99569 | −0.254506 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.06273 | 0.129187 | ||||||||
\(990\) | − 3.15302i | − 0.100209i | ||||||||
\(991\) | 37.8249 | 1.20155 | 0.600773 | − | 0.799419i | \(-0.294859\pi\) | ||||
0.600773 | + | 0.799419i | \(0.294859\pi\) | |||||||
\(992\) | −63.4171 | −2.01350 | ||||||||
\(993\) | − 4.08809i | − 0.129732i | ||||||||
\(994\) | − 13.1990i | − 0.418647i | ||||||||
\(995\) | − 7.50936i | − 0.238063i | ||||||||
\(996\) | − 88.3189i | − 2.79849i | ||||||||
\(997\) | 38.3748 | 1.21534 | 0.607671 | − | 0.794189i | \(-0.292104\pi\) | ||||
0.607671 | + | 0.794189i | \(0.292104\pi\) | |||||||
\(998\) | −49.6189 | −1.57066 | ||||||||
\(999\) | − 34.4777i | − 1.09083i |
(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 | 1183.2.c.g.337.1 | 8 | ||
13.2 | odd | 12 | 91.2.f.c.22.4 | ✓ | 8 | ||
13.5 | odd | 4 | 1183.2.a.k.1.1 | 4 | |||
13.6 | odd | 12 | 91.2.f.c.29.4 | yes | 8 | ||
13.8 | odd | 4 | 1183.2.a.l.1.4 | 4 | |||
13.12 | even | 2 | inner | 1183.2.c.g.337.8 | 8 | ||
39.2 | even | 12 | 819.2.o.h.568.1 | 8 | |||
39.32 | even | 12 | 819.2.o.h.757.1 | 8 | |||
52.15 | even | 12 | 1456.2.s.q.113.3 | 8 | |||
52.19 | even | 12 | 1456.2.s.q.1121.3 | 8 | |||
91.2 | odd | 12 | 637.2.h.h.165.1 | 8 | |||
91.6 | even | 12 | 637.2.f.i.393.4 | 8 | |||
91.19 | even | 12 | 637.2.g.j.263.4 | 8 | |||
91.32 | odd | 12 | 637.2.h.h.471.1 | 8 | |||
91.34 | even | 4 | 8281.2.a.bt.1.4 | 4 | |||
91.41 | even | 12 | 637.2.f.i.295.4 | 8 | |||
91.45 | even | 12 | 637.2.h.i.471.1 | 8 | |||
91.54 | even | 12 | 637.2.h.i.165.1 | 8 | |||
91.58 | odd | 12 | 637.2.g.k.263.4 | 8 | |||
91.67 | odd | 12 | 637.2.g.k.373.4 | 8 | |||
91.80 | even | 12 | 637.2.g.j.373.4 | 8 | |||
91.83 | even | 4 | 8281.2.a.bp.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.c.22.4 | ✓ | 8 | 13.2 | odd | 12 | ||
91.2.f.c.29.4 | yes | 8 | 13.6 | odd | 12 | ||
637.2.f.i.295.4 | 8 | 91.41 | even | 12 | |||
637.2.f.i.393.4 | 8 | 91.6 | even | 12 | |||
637.2.g.j.263.4 | 8 | 91.19 | even | 12 | |||
637.2.g.j.373.4 | 8 | 91.80 | even | 12 | |||
637.2.g.k.263.4 | 8 | 91.58 | odd | 12 | |||
637.2.g.k.373.4 | 8 | 91.67 | odd | 12 | |||
637.2.h.h.165.1 | 8 | 91.2 | odd | 12 | |||
637.2.h.h.471.1 | 8 | 91.32 | odd | 12 | |||
637.2.h.i.165.1 | 8 | 91.54 | even | 12 | |||
637.2.h.i.471.1 | 8 | 91.45 | even | 12 | |||
819.2.o.h.568.1 | 8 | 39.2 | even | 12 | |||
819.2.o.h.757.1 | 8 | 39.32 | even | 12 | |||
1183.2.a.k.1.1 | 4 | 13.5 | odd | 4 | |||
1183.2.a.l.1.4 | 4 | 13.8 | odd | 4 | |||
1183.2.c.g.337.1 | 8 | 1.1 | even | 1 | trivial | ||
1183.2.c.g.337.8 | 8 | 13.12 | even | 2 | inner | ||
1456.2.s.q.113.3 | 8 | 52.15 | even | 12 | |||
1456.2.s.q.1121.3 | 8 | 52.19 | even | 12 | |||
8281.2.a.bp.1.1 | 4 | 91.83 | even | 4 | |||
8281.2.a.bt.1.4 | 4 | 91.34 | even | 4 |