Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(85,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(1.10050 - 0.888196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.253 |
Dual form | 336.2.w.a.85.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33348 | − | 0.470984i | −0.942914 | − | 0.333036i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.55635 | + | 1.25610i | 0.778174 | + | 0.628049i | ||||
\(5\) | 2.01011 | − | 2.01011i | 0.898949 | − | 0.898949i | −0.0963939 | − | 0.995343i | \(-0.530731\pi\) |
0.995343 | + | 0.0963939i | \(0.0307308\pi\) | |||||||
\(6\) | 0.609878 | + | 1.27595i | 0.248982 | + | 0.520905i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −1.48376 | − | 2.40800i | −0.524588 | − | 0.851356i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −3.62718 | + | 1.73372i | −1.14701 | + | 0.548249i | ||||
\(11\) | 1.19999 | − | 1.19999i | 0.361810 | − | 0.361810i | −0.502669 | − | 0.864479i | \(-0.667649\pi\) |
0.864479 | + | 0.502669i | \(0.167649\pi\) | |||||||
\(12\) | −0.212308 | − | 1.98870i | −0.0612880 | − | 0.574088i | ||||
\(13\) | 1.92519 | + | 1.92519i | 0.533951 | + | 0.533951i | 0.921746 | − | 0.387795i | \(-0.126763\pi\) |
−0.387795 | + | 0.921746i | \(0.626763\pi\) | |||||||
\(14\) | −0.470984 | + | 1.33348i | −0.125876 | + | 0.356388i | ||||
\(15\) | −2.84273 | −0.733989 | ||||||||
\(16\) | 0.844433 | + | 3.90985i | 0.211108 | + | 0.977463i | ||||
\(17\) | 1.24973 | 0.303105 | 0.151553 | − | 0.988449i | \(-0.451573\pi\) | ||||
0.151553 | + | 0.988449i | \(0.451573\pi\) | |||||||
\(18\) | 0.470984 | − | 1.33348i | 0.111012 | − | 0.314305i | ||||
\(19\) | −0.720066 | − | 0.720066i | −0.165195 | − | 0.165195i | 0.619669 | − | 0.784863i | \(-0.287267\pi\) |
−0.784863 | + | 0.619669i | \(0.787267\pi\) | |||||||
\(20\) | 5.65333 | − | 0.603534i | 1.26412 | − | 0.134954i | ||||
\(21\) | −0.707107 | + | 0.707107i | −0.154303 | + | 0.154303i | ||||
\(22\) | −2.16534 | + | 1.03499i | −0.461651 | + | 0.220660i | ||||
\(23\) | − | 8.18862i | − | 1.70744i | −0.520729 | − | 0.853722i | \(-0.674340\pi\) | ||
0.520729 | − | 0.853722i | \(-0.325660\pi\) | |||||||
\(24\) | −0.653538 | + | 2.75189i | −0.133403 | + | 0.561727i | ||||
\(25\) | − | 3.08110i | − | 0.616220i | ||||||
\(26\) | −1.66047 | − | 3.47394i | −0.325645 | − | 0.681295i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 1.25610 | − | 1.55635i | 0.237380 | − | 0.294122i | ||||
\(29\) | −1.27746 | − | 1.27746i | −0.237218 | − | 0.237218i | 0.578479 | − | 0.815697i | \(-0.303646\pi\) |
−0.815697 | + | 0.578479i | \(0.803646\pi\) | |||||||
\(30\) | 3.79073 | + | 1.33888i | 0.692089 | + | 0.244445i | ||||
\(31\) | −10.8193 | −1.94320 | −0.971599 | − | 0.236635i | \(-0.923955\pi\) | ||||
−0.971599 | + | 0.236635i | \(0.923955\pi\) | |||||||
\(32\) | 0.715443 | − | 5.61143i | 0.126474 | − | 0.991970i | ||||
\(33\) | −1.69704 | −0.295416 | ||||||||
\(34\) | −1.66650 | − | 0.588605i | −0.285802 | − | 0.100945i | ||||
\(35\) | −2.01011 | − | 2.01011i | −0.339771 | − | 0.339771i | ||||
\(36\) | −1.25610 | + | 1.55635i | −0.209350 | + | 0.259391i | ||||
\(37\) | 5.38468 | − | 5.38468i | 0.885236 | − | 0.885236i | −0.108825 | − | 0.994061i | \(-0.534709\pi\) |
0.994061 | + | 0.108825i | \(0.0347087\pi\) | |||||||
\(38\) | 0.621055 | + | 1.29934i | 0.100748 | + | 0.210780i | ||||
\(39\) | − | 2.72263i | − | 0.435969i | ||||||
\(40\) | −7.82287 | − | 1.85783i | −1.23690 | − | 0.293749i | ||||
\(41\) | − | 4.30290i | − | 0.672000i | −0.941862 | − | 0.336000i | \(-0.890926\pi\) | ||
0.941862 | − | 0.336000i | \(-0.109074\pi\) | |||||||
\(42\) | 1.27595 | − | 0.609878i | 0.196883 | − | 0.0941062i | ||||
\(43\) | 0.310922 | − | 0.310922i | 0.0474152 | − | 0.0474152i | −0.683002 | − | 0.730417i | \(-0.739326\pi\) |
0.730417 | + | 0.683002i | \(0.239326\pi\) | |||||||
\(44\) | 3.37490 | − | 0.360295i | 0.508785 | − | 0.0543165i | ||||
\(45\) | 2.01011 | + | 2.01011i | 0.299650 | + | 0.299650i | ||||
\(46\) | −3.85671 | + | 10.9194i | −0.568641 | + | 1.60997i | ||||
\(47\) | 6.10797 | 0.890939 | 0.445470 | − | 0.895297i | \(-0.353037\pi\) | ||||
0.445470 | + | 0.895297i | \(0.353037\pi\) | |||||||
\(48\) | 2.16758 | − | 3.36179i | 0.312863 | − | 0.485232i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.45115 | + | 4.10859i | −0.205224 | + | 0.581042i | ||||
\(51\) | −0.883695 | − | 0.883695i | −0.123742 | − | 0.123742i | ||||
\(52\) | 0.578035 | + | 5.41448i | 0.0801590 | + | 0.750854i | ||||
\(53\) | −1.34951 | + | 1.34951i | −0.185370 | + | 0.185370i | −0.793691 | − | 0.608321i | \(-0.791843\pi\) |
0.608321 | + | 0.793691i | \(0.291843\pi\) | |||||||
\(54\) | −1.27595 | + | 0.609878i | −0.173635 | + | 0.0829938i | ||||
\(55\) | − | 4.82422i | − | 0.650497i | ||||||
\(56\) | −2.40800 | + | 1.48376i | −0.321783 | + | 0.198275i | ||||
\(57\) | 1.01833i | 0.134881i | ||||||||
\(58\) | 1.10180 | + | 2.30513i | 0.144674 | + | 0.302678i | ||||
\(59\) | −10.2730 | + | 10.2730i | −1.33743 | + | 1.33743i | −0.438882 | + | 0.898545i | \(0.644625\pi\) |
−0.898545 | + | 0.438882i | \(0.855375\pi\) | |||||||
\(60\) | −4.42427 | − | 3.57075i | −0.571171 | − | 0.460981i | ||||
\(61\) | 10.2386 | + | 10.2386i | 1.31092 | + | 1.31092i | 0.920740 | + | 0.390178i | \(0.127586\pi\) |
0.390178 | + | 0.920740i | \(0.372414\pi\) | |||||||
\(62\) | 14.4273 | + | 5.09571i | 1.83227 | + | 0.647155i | ||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −3.59693 | + | 7.14578i | −0.449616 | + | 0.893222i | ||||
\(65\) | 7.73968 | 0.959990 | ||||||||
\(66\) | 2.26297 | + | 0.799279i | 0.278552 | + | 0.0983844i | ||||
\(67\) | 1.99158 | + | 1.99158i | 0.243310 | + | 0.243310i | 0.818218 | − | 0.574908i | \(-0.194962\pi\) |
−0.574908 | + | 0.818218i | \(0.694962\pi\) | |||||||
\(68\) | 1.94502 | + | 1.56979i | 0.235868 | + | 0.190365i | ||||
\(69\) | −5.79023 | + | 5.79023i | −0.697061 | + | 0.697061i | ||||
\(70\) | 1.73372 | + | 3.62718i | 0.207219 | + | 0.433531i | ||||
\(71\) | 4.97742i | 0.590711i | 0.955387 | + | 0.295356i | \(0.0954381\pi\) | ||||
−0.955387 | + | 0.295356i | \(0.904562\pi\) | |||||||
\(72\) | 2.40800 | − | 1.48376i | 0.283785 | − | 0.174863i | ||||
\(73\) | − | 9.75342i | − | 1.14155i | −0.821106 | − | 0.570776i | \(-0.806643\pi\) | ||
0.821106 | − | 0.570776i | \(-0.193357\pi\) | |||||||
\(74\) | −9.71648 | + | 4.64427i | −1.12952 | + | 0.539886i | ||||
\(75\) | −2.17867 | + | 2.17867i | −0.251571 | + | 0.251571i | ||||
\(76\) | −0.216199 | − | 2.02515i | −0.0247997 | − | 0.232300i | ||||
\(77\) | −1.19999 | − | 1.19999i | −0.136751 | − | 0.136751i | ||||
\(78\) | −1.28231 | + | 3.63057i | −0.145194 | + | 0.411081i | ||||
\(79\) | 15.7018 | 1.76660 | 0.883298 | − | 0.468813i | \(-0.155318\pi\) | ||||
0.883298 | + | 0.468813i | \(0.155318\pi\) | |||||||
\(80\) | 9.55664 | + | 6.16183i | 1.06847 | + | 0.688914i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −2.02660 | + | 5.73784i | −0.223800 | + | 0.633638i | ||||
\(83\) | 3.53556 | + | 3.53556i | 0.388078 | + | 0.388078i | 0.874002 | − | 0.485923i | \(-0.161516\pi\) |
−0.485923 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(84\) | −1.98870 | + | 0.212308i | −0.216985 | + | 0.0231647i | ||||
\(85\) | 2.51211 | − | 2.51211i | 0.272476 | − | 0.272476i | ||||
\(86\) | −0.561049 | + | 0.268170i | −0.0604994 | + | 0.0289175i | ||||
\(87\) | 1.80660i | 0.193687i | ||||||||
\(88\) | −4.67006 | − | 1.10908i | −0.497830 | − | 0.118228i | ||||
\(89\) | − | 2.86694i | − | 0.303895i | −0.988389 | − | 0.151947i | \(-0.951446\pi\) | ||
0.988389 | − | 0.151947i | \(-0.0485544\pi\) | |||||||
\(90\) | −1.73372 | − | 3.62718i | −0.182750 | − | 0.382338i | ||||
\(91\) | 1.92519 | − | 1.92519i | 0.201814 | − | 0.201814i | ||||
\(92\) | 10.2857 | − | 12.7443i | 1.07236 | − | 1.32869i | ||||
\(93\) | 7.65037 | + | 7.65037i | 0.793307 | + | 0.793307i | ||||
\(94\) | −8.14487 | − | 2.87676i | −0.840079 | − | 0.296715i | ||||
\(95\) | −2.89483 | −0.297003 | ||||||||
\(96\) | −4.47377 | + | 3.46199i | −0.456603 | + | 0.353337i | ||||
\(97\) | −8.40145 | −0.853038 | −0.426519 | − | 0.904478i | \(-0.640260\pi\) | ||||
−0.426519 | + | 0.904478i | \(0.640260\pi\) | |||||||
\(98\) | 1.33348 | + | 0.470984i | 0.134702 | + | 0.0475766i | ||||
\(99\) | 1.19999 | + | 1.19999i | 0.120603 | + | 0.120603i | ||||
\(100\) | 3.87017 | − | 4.79526i | 0.387017 | − | 0.479526i | ||||
\(101\) | −7.84089 | + | 7.84089i | −0.780198 | + | 0.780198i | −0.979864 | − | 0.199666i | \(-0.936014\pi\) |
0.199666 | + | 0.979864i | \(0.436014\pi\) | |||||||
\(102\) | 0.762185 | + | 1.59460i | 0.0754676 | + | 0.157889i | ||||
\(103\) | 4.47471i | 0.440906i | 0.975398 | + | 0.220453i | \(0.0707536\pi\) | ||||
−0.975398 | + | 0.220453i | \(0.929246\pi\) | |||||||
\(104\) | 1.77934 | − | 7.49236i | 0.174479 | − | 0.734687i | ||||
\(105\) | 2.84273i | 0.277422i | ||||||||
\(106\) | 2.43515 | − | 1.16395i | 0.236523 | − | 0.113053i | ||||
\(107\) | −6.88767 | + | 6.88767i | −0.665856 | + | 0.665856i | −0.956754 | − | 0.290898i | \(-0.906046\pi\) |
0.290898 | + | 0.956754i | \(0.406046\pi\) | |||||||
\(108\) | 1.98870 | − | 0.212308i | 0.191363 | − | 0.0204293i | ||||
\(109\) | 14.1226 | + | 14.1226i | 1.35270 | + | 1.35270i | 0.882633 | + | 0.470062i | \(0.155769\pi\) |
0.470062 | + | 0.882633i | \(0.344231\pi\) | |||||||
\(110\) | −2.27213 | + | 6.43301i | −0.216639 | + | 0.613363i | ||||
\(111\) | −7.61509 | −0.722792 | ||||||||
\(112\) | 3.90985 | − | 0.844433i | 0.369446 | − | 0.0797914i | ||||
\(113\) | −7.45355 | −0.701171 | −0.350585 | − | 0.936531i | \(-0.614017\pi\) | ||||
−0.350585 | + | 0.936531i | \(0.614017\pi\) | |||||||
\(114\) | 0.479616 | − | 1.35792i | 0.0449202 | − | 0.127181i | ||||
\(115\) | −16.4600 | − | 16.4600i | −1.53491 | − | 1.53491i | ||||
\(116\) | −0.383555 | − | 3.59278i | −0.0356122 | − | 0.333581i | ||||
\(117\) | −1.92519 | + | 1.92519i | −0.177984 | + | 0.177984i | ||||
\(118\) | 18.5372 | − | 8.86041i | 1.70649 | − | 0.815667i | ||||
\(119\) | − | 1.24973i | − | 0.114563i | ||||||
\(120\) | 4.21792 | + | 6.84529i | 0.385042 | + | 0.624886i | ||||
\(121\) | 8.12006i | 0.738187i | ||||||||
\(122\) | −8.83076 | − | 18.4752i | −0.799499 | − | 1.67267i | ||||
\(123\) | −3.04261 | + | 3.04261i | −0.274343 | + | 0.274343i | ||||
\(124\) | −16.8385 | − | 13.5901i | −1.51214 | − | 1.22042i | ||||
\(125\) | 3.85720 | + | 3.85720i | 0.344999 | + | 0.344999i | ||||
\(126\) | −1.33348 | − | 0.470984i | −0.118796 | − | 0.0419586i | ||||
\(127\) | 14.8202 | 1.31508 | 0.657539 | − | 0.753421i | \(-0.271598\pi\) | ||||
0.657539 | + | 0.753421i | \(0.271598\pi\) | |||||||
\(128\) | 8.16199 | − | 7.83467i | 0.721424 | − | 0.692493i | ||||
\(129\) | −0.439710 | −0.0387144 | ||||||||
\(130\) | −10.3207 | − | 3.64527i | −0.905188 | − | 0.319711i | ||||
\(131\) | −2.59589 | − | 2.59589i | −0.226804 | − | 0.226804i | 0.584552 | − | 0.811356i | \(-0.301270\pi\) |
−0.811356 | + | 0.584552i | \(0.801270\pi\) | |||||||
\(132\) | −2.64118 | − | 2.13165i | −0.229885 | − | 0.185536i | ||||
\(133\) | −0.720066 | + | 0.720066i | −0.0624377 | + | 0.0624377i | ||||
\(134\) | −1.71773 | − | 3.59374i | −0.148389 | − | 0.310452i | ||||
\(135\) | − | 2.84273i | − | 0.244663i | ||||||
\(136\) | −1.85430 | − | 3.00936i | −0.159005 | − | 0.258050i | ||||
\(137\) | 4.13193i | 0.353015i | 0.984299 | + | 0.176507i | \(0.0564799\pi\) | ||||
−0.984299 | + | 0.176507i | \(0.943520\pi\) | |||||||
\(138\) | 10.4483 | − | 4.99405i | 0.889416 | − | 0.425122i | ||||
\(139\) | 5.21659 | − | 5.21659i | 0.442465 | − | 0.442465i | −0.450374 | − | 0.892840i | \(-0.648709\pi\) |
0.892840 | + | 0.450374i | \(0.148709\pi\) | |||||||
\(140\) | −0.603534 | − | 5.65333i | −0.0510079 | − | 0.477794i | ||||
\(141\) | −4.31899 | − | 4.31899i | −0.363724 | − | 0.363724i | ||||
\(142\) | 2.34429 | − | 6.63730i | 0.196728 | − | 0.556990i | ||||
\(143\) | 4.62040 | 0.386377 | ||||||||
\(144\) | −3.90985 | + | 0.844433i | −0.325821 | + | 0.0703694i | ||||
\(145\) | −5.13566 | −0.426493 | ||||||||
\(146\) | −4.59371 | + | 13.0060i | −0.380178 | + | 1.07638i | ||||
\(147\) | 0.707107 | + | 0.707107i | 0.0583212 | + | 0.0583212i | ||||
\(148\) | 15.1441 | − | 1.61674i | 1.24484 | − | 0.132896i | ||||
\(149\) | −0.139187 | + | 0.139187i | −0.0114027 | + | 0.0114027i | −0.712785 | − | 0.701382i | \(-0.752567\pi\) |
0.701382 | + | 0.712785i | \(0.252567\pi\) | |||||||
\(150\) | 3.93133 | − | 1.87909i | 0.320992 | − | 0.153427i | ||||
\(151\) | − | 9.05020i | − | 0.736495i | −0.929728 | − | 0.368247i | \(-0.879958\pi\) | ||
0.929728 | − | 0.368247i | \(-0.120042\pi\) | |||||||
\(152\) | −0.665515 | + | 2.80232i | −0.0539804 | + | 0.227298i | ||||
\(153\) | 1.24973i | 0.101035i | ||||||||
\(154\) | 1.03499 | + | 2.16534i | 0.0834015 | + | 0.174488i | ||||
\(155\) | −21.7479 | + | 21.7479i | −1.74684 | + | 1.74684i | ||||
\(156\) | 3.41989 | − | 4.23735i | 0.273810 | − | 0.339260i | ||||
\(157\) | 9.76247 | + | 9.76247i | 0.779130 | + | 0.779130i | 0.979683 | − | 0.200553i | \(-0.0642738\pi\) |
−0.200553 | + | 0.979683i | \(0.564274\pi\) | |||||||
\(158\) | −20.9381 | − | 7.39532i | −1.66575 | − | 0.588340i | ||||
\(159\) | 1.90850 | 0.151354 | ||||||||
\(160\) | −9.84148 | − | 12.7177i | −0.778037 | − | 1.00542i | ||||
\(161\) | −8.18862 | −0.645353 | ||||||||
\(162\) | 1.33348 | + | 0.470984i | 0.104768 | + | 0.0370040i | ||||
\(163\) | −5.52971 | − | 5.52971i | −0.433121 | − | 0.433121i | 0.456568 | − | 0.889689i | \(-0.349079\pi\) |
−0.889689 | + | 0.456568i | \(0.849079\pi\) | |||||||
\(164\) | 5.40487 | − | 6.69681i | 0.422049 | − | 0.522933i | ||||
\(165\) | −3.41124 | + | 3.41124i | −0.265564 | + | 0.265564i | ||||
\(166\) | −3.04941 | − | 6.37980i | −0.236680 | − | 0.495169i | ||||
\(167\) | − | 3.97093i | − | 0.307280i | −0.988127 | − | 0.153640i | \(-0.950900\pi\) | ||
0.988127 | − | 0.153640i | \(-0.0490996\pi\) | |||||||
\(168\) | 2.75189 | + | 0.653538i | 0.212313 | + | 0.0504215i | ||||
\(169\) | − | 5.58731i | − | 0.429793i | ||||||
\(170\) | −4.53301 | + | 2.16668i | −0.347666 | + | 0.166177i | ||||
\(171\) | 0.720066 | − | 0.720066i | 0.0550648 | − | 0.0550648i | ||||
\(172\) | 0.874452 | − | 0.0933540i | 0.0666763 | − | 0.00711818i | ||||
\(173\) | −12.8323 | − | 12.8323i | −0.975619 | − | 0.975619i | 0.0240906 | − | 0.999710i | \(-0.492331\pi\) |
−0.999710 | + | 0.0240906i | \(0.992331\pi\) | |||||||
\(174\) | 0.850879 | − | 2.40906i | 0.0645050 | − | 0.182631i | ||||
\(175\) | −3.08110 | −0.232909 | ||||||||
\(176\) | 5.70508 | + | 3.67846i | 0.430037 | + | 0.277275i | ||||
\(177\) | 14.5282 | 1.09200 | ||||||||
\(178\) | −1.35028 | + | 3.82301i | −0.101208 | + | 0.286547i | ||||
\(179\) | 16.0865 | + | 16.0865i | 1.20236 | + | 1.20236i | 0.973446 | + | 0.228917i | \(0.0735183\pi\) |
0.228917 | + | 0.973446i | \(0.426482\pi\) | |||||||
\(180\) | 0.603534 | + | 5.65333i | 0.0449847 | + | 0.421374i | ||||
\(181\) | −5.13842 | + | 5.13842i | −0.381936 | + | 0.381936i | −0.871799 | − | 0.489863i | \(-0.837047\pi\) |
0.489863 | + | 0.871799i | \(0.337047\pi\) | |||||||
\(182\) | −3.47394 | + | 1.66047i | −0.257505 | + | 0.123082i | ||||
\(183\) | − | 14.4796i | − | 1.07036i | ||||||
\(184\) | −19.7182 | + | 12.1499i | −1.45364 | + | 0.895704i | ||||
\(185\) | − | 21.6476i | − | 1.59157i | ||||||
\(186\) | −6.59843 | − | 13.8048i | −0.483820 | − | 1.01222i | ||||
\(187\) | 1.49967 | − | 1.49967i | 0.109666 | − | 0.109666i | ||||
\(188\) | 9.50612 | + | 7.67221i | 0.693305 | + | 0.559554i | ||||
\(189\) | −0.707107 | − | 0.707107i | −0.0514344 | − | 0.0514344i | ||||
\(190\) | 3.86020 | + | 1.36342i | 0.280048 | + | 0.0989128i | ||||
\(191\) | 21.8736 | 1.58272 | 0.791358 | − | 0.611354i | \(-0.209375\pi\) | ||||
0.791358 | + | 0.611354i | \(0.209375\pi\) | |||||||
\(192\) | 7.59624 | − | 2.50942i | 0.548211 | − | 0.181102i | ||||
\(193\) | −4.53207 | −0.326225 | −0.163113 | − | 0.986607i | \(-0.552153\pi\) | ||||
−0.163113 | + | 0.986607i | \(0.552153\pi\) | |||||||
\(194\) | 11.2032 | + | 3.95695i | 0.804342 | + | 0.284093i | ||||
\(195\) | −5.47278 | − | 5.47278i | −0.391914 | − | 0.391914i | ||||
\(196\) | −1.55635 | − | 1.25610i | −0.111168 | − | 0.0897213i | ||||
\(197\) | 16.9905 | − | 16.9905i | 1.21052 | − | 1.21052i | 0.239666 | − | 0.970855i | \(-0.422962\pi\) |
0.970855 | − | 0.239666i | \(-0.0770379\pi\) | |||||||
\(198\) | −1.03499 | − | 2.16534i | −0.0735532 | − | 0.153884i | ||||
\(199\) | 4.63377i | 0.328479i | 0.986420 | + | 0.164240i | \(0.0525170\pi\) | ||||
−0.986420 | + | 0.164240i | \(0.947483\pi\) | |||||||
\(200\) | −7.41929 | + | 4.57161i | −0.524623 | + | 0.323261i | ||||
\(201\) | − | 2.81652i | − | 0.198662i | ||||||
\(202\) | 14.1486 | − | 6.76275i | 0.995494 | − | 0.475825i | ||||
\(203\) | −1.27746 | + | 1.27746i | −0.0896599 | + | 0.0896599i | ||||
\(204\) | −0.265328 | − | 2.48535i | −0.0185767 | − | 0.174009i | ||||
\(205\) | −8.64931 | − | 8.64931i | −0.604094 | − | 0.604094i | ||||
\(206\) | 2.10752 | − | 5.96694i | 0.146838 | − | 0.415737i | ||||
\(207\) | 8.18862 | 0.569148 | ||||||||
\(208\) | −5.90150 | + | 9.15289i | −0.409196 | + | 0.634639i | ||||
\(209\) | −1.72814 | −0.119538 | ||||||||
\(210\) | 1.33888 | − | 3.79073i | 0.0923915 | − | 0.261585i | ||||
\(211\) | 1.26697 | + | 1.26697i | 0.0872219 | + | 0.0872219i | 0.749372 | − | 0.662150i | \(-0.230356\pi\) |
−0.662150 | + | 0.749372i | \(0.730356\pi\) | |||||||
\(212\) | −3.79543 | + | 0.405189i | −0.260671 | + | 0.0278285i | ||||
\(213\) | 3.51957 | − | 3.51957i | 0.241157 | − | 0.241157i | ||||
\(214\) | 12.4286 | − | 5.94060i | 0.849599 | − | 0.406091i | ||||
\(215\) | − | 1.24998i | − | 0.0852477i | ||||||
\(216\) | −2.75189 | − | 0.653538i | −0.187242 | − | 0.0444676i | ||||
\(217\) | 10.8193i | 0.734459i | ||||||||
\(218\) | −12.1807 | − | 25.4837i | −0.824979 | − | 1.72597i | ||||
\(219\) | −6.89671 | + | 6.89671i | −0.466036 | + | 0.466036i | ||||
\(220\) | 6.05969 | − | 7.50816i | 0.408544 | − | 0.506200i | ||||
\(221\) | 2.40597 | + | 2.40597i | 0.161843 | + | 0.161843i | ||||
\(222\) | 10.1546 | + | 3.58659i | 0.681531 | + | 0.240716i | ||||
\(223\) | −6.29832 | −0.421767 | −0.210884 | − | 0.977511i | \(-0.567634\pi\) | ||||
−0.210884 | + | 0.977511i | \(0.567634\pi\) | |||||||
\(224\) | −5.61143 | − | 0.715443i | −0.374929 | − | 0.0478025i | ||||
\(225\) | 3.08110 | 0.205407 | ||||||||
\(226\) | 9.93917 | + | 3.51051i | 0.661144 | + | 0.233515i | ||||
\(227\) | 17.8116 | + | 17.8116i | 1.18220 | + | 1.18220i | 0.979173 | + | 0.203025i | \(0.0650774\pi\) |
0.203025 | + | 0.979173i | \(0.434923\pi\) | |||||||
\(228\) | −1.27912 | + | 1.58487i | −0.0847117 | + | 0.104961i | ||||
\(229\) | 1.15235 | − | 1.15235i | 0.0761496 | − | 0.0761496i | −0.668006 | − | 0.744156i | \(-0.732852\pi\) |
0.744156 | + | 0.668006i | \(0.232852\pi\) | |||||||
\(230\) | 14.1967 | + | 29.7016i | 0.936105 | + | 1.95846i | ||||
\(231\) | 1.69704i | 0.111657i | ||||||||
\(232\) | −1.18068 | + | 4.97155i | −0.0775154 | + | 0.326398i | ||||
\(233\) | 11.7361i | 0.768857i | 0.923155 | + | 0.384429i | \(0.125602\pi\) | ||||
−0.923155 | + | 0.384429i | \(0.874398\pi\) | |||||||
\(234\) | 3.47394 | − | 1.66047i | 0.227098 | − | 0.108548i | ||||
\(235\) | 12.2777 | − | 12.2777i | 0.800909 | − | 0.800909i | ||||
\(236\) | −28.8922 | + | 3.08445i | −1.88072 | + | 0.200780i | ||||
\(237\) | −11.1029 | − | 11.1029i | −0.721209 | − | 0.721209i | ||||
\(238\) | −0.588605 | + | 1.66650i | −0.0381536 | + | 0.108023i | ||||
\(239\) | −15.4758 | −1.00105 | −0.500524 | − | 0.865723i | \(-0.666859\pi\) | ||||
−0.500524 | + | 0.865723i | \(0.666859\pi\) | |||||||
\(240\) | −2.40049 | − | 11.1146i | −0.154951 | − | 0.717447i | ||||
\(241\) | −17.3101 | −1.11504 | −0.557522 | − | 0.830162i | \(-0.688248\pi\) | ||||
−0.557522 | + | 0.830162i | \(0.688248\pi\) | |||||||
\(242\) | 3.82442 | − | 10.8280i | 0.245843 | − | 0.696047i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 3.07412 | + | 28.7955i | 0.196801 | + | 1.84344i | ||||
\(245\) | −2.01011 | + | 2.01011i | −0.128421 | + | 0.128421i | ||||
\(246\) | 5.49029 | − | 2.62424i | 0.350048 | − | 0.167316i | ||||
\(247\) | − | 2.77252i | − | 0.176412i | ||||||
\(248\) | 16.0532 | + | 26.0528i | 1.01938 | + | 1.65435i | ||||
\(249\) | − | 5.00004i | − | 0.316865i | ||||||
\(250\) | −3.32683 | − | 6.96019i | −0.210407 | − | 0.440201i | ||||
\(251\) | −4.97541 | + | 4.97541i | −0.314045 | + | 0.314045i | −0.846475 | − | 0.532429i | \(-0.821279\pi\) |
0.532429 | + | 0.846475i | \(0.321279\pi\) | |||||||
\(252\) | 1.55635 | + | 1.25610i | 0.0980407 | + | 0.0791268i | ||||
\(253\) | −9.82624 | − | 9.82624i | −0.617770 | − | 0.617770i | ||||
\(254\) | −19.7624 | − | 6.98007i | −1.24000 | − | 0.437969i | ||||
\(255\) | −3.55265 | −0.222476 | ||||||||
\(256\) | −14.5739 | + | 6.60322i | −0.910867 | + | 0.412701i | ||||
\(257\) | −17.6065 | −1.09827 | −0.549133 | − | 0.835735i | \(-0.685042\pi\) | ||||
−0.549133 | + | 0.835735i | \(0.685042\pi\) | |||||||
\(258\) | 0.586346 | + | 0.207097i | 0.0365043 | + | 0.0128933i | ||||
\(259\) | −5.38468 | − | 5.38468i | −0.334588 | − | 0.334588i | ||||
\(260\) | 12.0456 | + | 9.72181i | 0.747039 | + | 0.602921i | ||||
\(261\) | 1.27746 | − | 1.27746i | 0.0790726 | − | 0.0790726i | ||||
\(262\) | 2.23895 | + | 4.68419i | 0.138323 | + | 0.289391i | ||||
\(263\) | 31.6849i | 1.95377i | 0.213759 | + | 0.976886i | \(0.431429\pi\) | ||||
−0.213759 | + | 0.976886i | \(0.568571\pi\) | |||||||
\(264\) | 2.51799 | + | 4.08647i | 0.154972 | + | 0.251505i | ||||
\(265\) | 5.42534i | 0.333276i | ||||||||
\(266\) | 1.29934 | − | 0.621055i | 0.0796673 | − | 0.0380793i | ||||
\(267\) | −2.02723 | + | 2.02723i | −0.124064 | + | 0.124064i | ||||
\(268\) | 0.597969 | + | 5.60121i | 0.0365268 | + | 0.342148i | ||||
\(269\) | 5.40521 | + | 5.40521i | 0.329561 | + | 0.329561i | 0.852420 | − | 0.522858i | \(-0.175134\pi\) |
−0.522858 | + | 0.852420i | \(0.675134\pi\) | |||||||
\(270\) | −1.33888 | + | 3.79073i | −0.0814817 | + | 0.230696i | ||||
\(271\) | 11.1293 | 0.676057 | 0.338028 | − | 0.941136i | \(-0.390240\pi\) | ||||
0.338028 | + | 0.941136i | \(0.390240\pi\) | |||||||
\(272\) | 1.05532 | + | 4.88627i | 0.0639880 | + | 0.296274i | ||||
\(273\) | −2.72263 | −0.164781 | ||||||||
\(274\) | 1.94607 | − | 5.50985i | 0.117567 | − | 0.332862i | ||||
\(275\) | −3.69728 | − | 3.69728i | −0.222954 | − | 0.222954i | ||||
\(276\) | −16.2847 | + | 1.73851i | −0.980223 | + | 0.104646i | ||||
\(277\) | 16.4865 | − | 16.4865i | 0.990580 | − | 0.990580i | −0.00937626 | − | 0.999956i | \(-0.502985\pi\) |
0.999956 | + | 0.00937626i | \(0.00298460\pi\) | |||||||
\(278\) | −9.41316 | + | 4.49929i | −0.564564 | + | 0.269850i | ||||
\(279\) | − | 10.8193i | − | 0.647732i | ||||||
\(280\) | −1.85783 | + | 7.82287i | −0.111027 | + | 0.467506i | ||||
\(281\) | − | 16.9337i | − | 1.01018i | −0.863067 | − | 0.505089i | \(-0.831460\pi\) | ||
0.863067 | − | 0.505089i | \(-0.168540\pi\) | |||||||
\(282\) | 3.72512 | + | 7.79347i | 0.221827 | + | 0.464094i | ||||
\(283\) | −4.26162 | + | 4.26162i | −0.253327 | + | 0.253327i | −0.822333 | − | 0.569006i | \(-0.807328\pi\) |
0.569006 | + | 0.822333i | \(0.307328\pi\) | |||||||
\(284\) | −6.25213 | + | 7.74659i | −0.370996 | + | 0.459676i | ||||
\(285\) | 2.04695 | + | 2.04695i | 0.121251 | + | 0.121251i | ||||
\(286\) | −6.16122 | − | 2.17614i | −0.364321 | − | 0.128678i | ||||
\(287\) | −4.30290 | −0.253992 | ||||||||
\(288\) | 5.61143 | + | 0.715443i | 0.330657 | + | 0.0421579i | ||||
\(289\) | −15.4382 | −0.908127 | ||||||||
\(290\) | 6.84831 | + | 2.41882i | 0.402147 | + | 0.142038i | ||||
\(291\) | 5.94073 | + | 5.94073i | 0.348252 | + | 0.348252i | ||||
\(292\) | 12.2513 | − | 15.1797i | 0.716950 | − | 0.888325i | ||||
\(293\) | −10.5179 | + | 10.5179i | −0.614464 | + | 0.614464i | −0.944106 | − | 0.329642i | \(-0.893072\pi\) |
0.329642 | + | 0.944106i | \(0.393072\pi\) | |||||||
\(294\) | −0.609878 | − | 1.27595i | −0.0355688 | − | 0.0744149i | ||||
\(295\) | 41.2996i | 2.40456i | ||||||||
\(296\) | −20.9559 | − | 4.97675i | −1.21804 | − | 0.289268i | ||||
\(297\) | − | 1.69704i | − | 0.0984722i | ||||||
\(298\) | 0.251159 | − | 0.120049i | 0.0145492 | − | 0.00695423i | ||||
\(299\) | 15.7646 | − | 15.7646i | 0.911691 | − | 0.911691i | ||||
\(300\) | −6.12738 | + | 0.654142i | −0.353765 | + | 0.0377669i | ||||
\(301\) | −0.310922 | − | 0.310922i | −0.0179213 | − | 0.0179213i | ||||
\(302\) | −4.26250 | + | 12.0683i | −0.245279 | + | 0.694451i | ||||
\(303\) | 11.0887 | 0.637029 | ||||||||
\(304\) | 2.20730 | − | 3.42340i | 0.126598 | − | 0.196345i | ||||
\(305\) | 41.1614 | 2.35690 | ||||||||
\(306\) | 0.588605 | − | 1.66650i | 0.0336483 | − | 0.0952673i | ||||
\(307\) | 12.5856 | + | 12.5856i | 0.718300 | + | 0.718300i | 0.968257 | − | 0.249957i | \(-0.0804164\pi\) |
−0.249957 | + | 0.968257i | \(0.580416\pi\) | |||||||
\(308\) | −0.360295 | − | 3.37490i | −0.0205297 | − | 0.192303i | ||||
\(309\) | 3.16410 | − | 3.16410i | 0.179999 | − | 0.179999i | ||||
\(310\) | 39.2434 | − | 18.7575i | 2.22888 | − | 1.06536i | ||||
\(311\) | 7.29408i | 0.413609i | 0.978382 | + | 0.206805i | \(0.0663064\pi\) | ||||
−0.978382 | + | 0.206805i | \(0.933694\pi\) | |||||||
\(312\) | −6.55608 | + | 4.03972i | −0.371165 | + | 0.228704i | ||||
\(313\) | 17.6793i | 0.999293i | 0.866229 | + | 0.499646i | \(0.166537\pi\) | ||||
−0.866229 | + | 0.499646i | \(0.833463\pi\) | |||||||
\(314\) | −8.42010 | − | 17.6160i | −0.475174 | − | 0.994131i | ||||
\(315\) | 2.01011 | − | 2.01011i | 0.113257 | − | 0.113257i | ||||
\(316\) | 24.4375 | + | 19.7231i | 1.37472 | + | 1.10951i | ||||
\(317\) | −17.1763 | − | 17.1763i | −0.964714 | − | 0.964714i | 0.0346839 | − | 0.999398i | \(-0.488958\pi\) |
−0.999398 | + | 0.0346839i | \(0.988958\pi\) | |||||||
\(318\) | −2.54495 | − | 0.898874i | −0.142714 | − | 0.0504063i | ||||
\(319\) | −3.06586 | −0.171655 | ||||||||
\(320\) | 7.13359 | + | 21.5940i | 0.398780 | + | 1.20714i | ||||
\(321\) | 9.74064 | 0.543669 | ||||||||
\(322\) | 10.9194 | + | 3.85671i | 0.608513 | + | 0.214926i | ||||
\(323\) | −0.899891 | − | 0.899891i | −0.0500713 | − | 0.0500713i | ||||
\(324\) | −1.55635 | − | 1.25610i | −0.0864637 | − | 0.0697832i | ||||
\(325\) | 5.93170 | − | 5.93170i | 0.329031 | − | 0.329031i | ||||
\(326\) | 4.76936 | + | 9.97818i | 0.264151 | + | 0.552640i | ||||
\(327\) | − | 19.9723i | − | 1.10447i | ||||||
\(328\) | −10.3614 | + | 6.38446i | −0.572112 | + | 0.352523i | ||||
\(329\) | − | 6.10797i | − | 0.336743i | ||||||
\(330\) | 6.15546 | − | 2.94218i | 0.338847 | − | 0.161962i | ||||
\(331\) | −1.24559 | + | 1.24559i | −0.0684641 | + | 0.0684641i | −0.740510 | − | 0.672046i | \(-0.765416\pi\) |
0.672046 | + | 0.740510i | \(0.265416\pi\) | |||||||
\(332\) | 1.06155 | + | 9.94358i | 0.0582600 | + | 0.545725i | ||||
\(333\) | 5.38468 | + | 5.38468i | 0.295079 | + | 0.295079i | ||||
\(334\) | −1.87025 | + | 5.29516i | −0.102335 | + | 0.289738i | ||||
\(335\) | 8.00659 | 0.437447 | ||||||||
\(336\) | −3.36179 | − | 2.16758i | −0.183400 | − | 0.118251i | ||||
\(337\) | 21.7737 | 1.18609 | 0.593045 | − | 0.805169i | \(-0.297925\pi\) | ||||
0.593045 | + | 0.805169i | \(0.297925\pi\) | |||||||
\(338\) | −2.63154 | + | 7.45057i | −0.143137 | + | 0.405258i | ||||
\(339\) | 5.27046 | + | 5.27046i | 0.286252 | + | 0.286252i | ||||
\(340\) | 7.06516 | − | 0.754256i | 0.383162 | − | 0.0409053i | ||||
\(341\) | −12.9830 | + | 12.9830i | −0.703068 | + | 0.703068i | ||||
\(342\) | −1.29934 | + | 0.621055i | −0.0702600 | + | 0.0335828i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −1.21003 | − | 0.287367i | −0.0652407 | − | 0.0154938i | ||||
\(345\) | 23.2780i | 1.25325i | ||||||||
\(346\) | 11.0678 | + | 23.1554i | 0.595008 | + | 1.24484i | ||||
\(347\) | 20.7830 | − | 20.7830i | 1.11569 | − | 1.11569i | 0.123321 | − | 0.992367i | \(-0.460645\pi\) |
0.992367 | − | 0.123321i | \(-0.0393546\pi\) | |||||||
\(348\) | −2.26926 | + | 2.81169i | −0.121645 | + | 0.150722i | ||||
\(349\) | −9.63121 | − | 9.63121i | −0.515547 | − | 0.515547i | 0.400674 | − | 0.916221i | \(-0.368776\pi\) |
−0.916221 | + | 0.400674i | \(0.868776\pi\) | |||||||
\(350\) | 4.10859 | + | 1.45115i | 0.219613 | + | 0.0775673i | ||||
\(351\) | 2.72263 | 0.145323 | ||||||||
\(352\) | −5.87512 | − | 7.59217i | −0.313145 | − | 0.404664i | ||||
\(353\) | −35.5556 | −1.89243 | −0.946217 | − | 0.323531i | \(-0.895130\pi\) | ||||
−0.946217 | + | 0.323531i | \(0.895130\pi\) | |||||||
\(354\) | −19.3730 | − | 6.84254i | −1.02967 | − | 0.363677i | ||||
\(355\) | 10.0052 | + | 10.0052i | 0.531019 | + | 0.531019i | ||||
\(356\) | 3.60115 | − | 4.46195i | 0.190861 | − | 0.236483i | ||||
\(357\) | −0.883695 | + | 0.883695i | −0.0467701 | + | 0.0467701i | ||||
\(358\) | −13.8746 | − | 29.0276i | −0.733294 | − | 1.53415i | ||||
\(359\) | − | 14.5283i | − | 0.766776i | −0.923587 | − | 0.383388i | \(-0.874757\pi\) | ||
0.923587 | − | 0.383388i | \(-0.125243\pi\) | |||||||
\(360\) | 1.85783 | − | 7.82287i | 0.0979162 | − | 0.412301i | ||||
\(361\) | − | 17.9630i | − | 0.945422i | ||||||
\(362\) | 9.27211 | − | 4.43188i | 0.487331 | − | 0.232934i | ||||
\(363\) | 5.74175 | − | 5.74175i | 0.301364 | − | 0.301364i | ||||
\(364\) | 5.41448 | − | 0.578035i | 0.283796 | − | 0.0302973i | ||||
\(365\) | −19.6055 | − | 19.6055i | −1.02620 | − | 1.02620i | ||||
\(366\) | −6.81965 | + | 19.3082i | −0.356469 | + | 1.00926i | ||||
\(367\) | −19.1601 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(368\) | 32.0163 | − | 6.91474i | 1.66896 | − | 0.360456i | ||||
\(369\) | 4.30290 | 0.224000 | ||||||||
\(370\) | −10.1957 | + | 28.8667i | −0.530049 | + | 1.50071i | ||||
\(371\) | 1.34951 | + | 1.34951i | 0.0700632 | + | 0.0700632i | ||||
\(372\) | 2.29702 | + | 21.5163i | 0.119095 | + | 1.11557i | ||||
\(373\) | −23.3748 | + | 23.3748i | −1.21030 | + | 1.21030i | −0.239374 | + | 0.970927i | \(0.576942\pi\) |
−0.970927 | + | 0.239374i | \(0.923058\pi\) | |||||||
\(374\) | −2.70610 | + | 1.29346i | −0.139929 | + | 0.0668831i | ||||
\(375\) | − | 5.45491i | − | 0.281690i | ||||||
\(376\) | −9.06275 | − | 14.7080i | −0.467376 | − | 0.758507i | ||||
\(377\) | − | 4.91869i | − | 0.253325i | ||||||
\(378\) | 0.609878 | + | 1.27595i | 0.0313687 | + | 0.0656278i | ||||
\(379\) | −5.03700 | + | 5.03700i | −0.258734 | + | 0.258734i | −0.824539 | − | 0.565805i | \(-0.808565\pi\) |
0.565805 | + | 0.824539i | \(0.308565\pi\) | |||||||
\(380\) | −4.50536 | − | 3.63619i | −0.231120 | − | 0.186533i | ||||
\(381\) | −10.4794 | − | 10.4794i | −0.536878 | − | 0.536878i | ||||
\(382\) | −29.1680 | − | 10.3021i | −1.49236 | − | 0.527102i | ||||
\(383\) | −4.80910 | −0.245734 | −0.122867 | − | 0.992423i | \(-0.539209\pi\) | ||||
−0.122867 | + | 0.992423i | \(0.539209\pi\) | |||||||
\(384\) | −11.3113 | − | 0.231450i | −0.577229 | − | 0.0118111i | ||||
\(385\) | −4.82422 | −0.245865 | ||||||||
\(386\) | 6.04343 | + | 2.13453i | 0.307602 | + | 0.108645i | ||||
\(387\) | 0.310922 | + | 0.310922i | 0.0158051 | + | 0.0158051i | ||||
\(388\) | −13.0756 | − | 10.5531i | −0.663812 | − | 0.535750i | ||||
\(389\) | 18.7727 | − | 18.7727i | 0.951813 | − | 0.951813i | −0.0470783 | − | 0.998891i | \(-0.514991\pi\) |
0.998891 | + | 0.0470783i | \(0.0149910\pi\) | |||||||
\(390\) | 4.72026 | + | 9.87545i | 0.239020 | + | 0.500063i | ||||
\(391\) | − | 10.2336i | − | 0.517535i | ||||||
\(392\) | 1.48376 | + | 2.40800i | 0.0749411 | + | 0.121622i | ||||
\(393\) | 3.67114i | 0.185185i | ||||||||
\(394\) | −30.6587 | + | 14.6542i | −1.54457 | + | 0.738270i | ||||
\(395\) | 31.5625 | − | 31.5625i | 1.58808 | − | 1.58808i | ||||
\(396\) | 0.360295 | + | 3.37490i | 0.0181055 | + | 0.169595i | ||||
\(397\) | 24.8947 | + | 24.8947i | 1.24943 | + | 1.24943i | 0.955973 | + | 0.293455i | \(0.0948051\pi\) |
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(398\) | 2.18243 | − | 6.17905i | 0.109396 | − | 0.309728i | ||||
\(399\) | 1.01833 | 0.0509801 | ||||||||
\(400\) | 12.0466 | − | 2.60178i | 0.602332 | − | 0.130089i | ||||
\(401\) | −2.62482 | −0.131077 | −0.0655386 | − | 0.997850i | \(-0.520877\pi\) | ||||
−0.0655386 | + | 0.997850i | \(0.520877\pi\) | |||||||
\(402\) | −1.32654 | + | 3.75578i | −0.0661616 | + | 0.187321i | ||||
\(403\) | −20.8291 | − | 20.8291i | −1.03757 | − | 1.03757i | ||||
\(404\) | −22.0521 | + | 2.35422i | −1.09713 | + | 0.117127i | ||||
\(405\) | −2.01011 | + | 2.01011i | −0.0998833 | + | 0.0998833i | ||||
\(406\) | 2.30513 | − | 1.10180i | 0.114402 | − | 0.0546816i | ||||
\(407\) | − | 12.9231i | − | 0.640574i | ||||||
\(408\) | −0.816749 | + | 3.43913i | −0.0404351 | + | 0.170262i | ||||
\(409\) | − | 16.5394i | − | 0.817822i | −0.912574 | − | 0.408911i | \(-0.865909\pi\) | ||
0.912574 | − | 0.408911i | \(-0.134091\pi\) | |||||||
\(410\) | 7.46001 | + | 15.6074i | 0.368423 | + | 0.770794i | ||||
\(411\) | 2.92172 | − | 2.92172i | 0.144118 | − | 0.144118i | ||||
\(412\) | −5.62068 | + | 6.96420i | −0.276911 | + | 0.343102i | ||||
\(413\) | 10.2730 | + | 10.2730i | 0.505500 | + | 0.505500i | ||||
\(414\) | −10.9194 | − | 3.85671i | −0.536658 | − | 0.189547i | ||||
\(415\) | 14.2138 | 0.697726 | ||||||||
\(416\) | 12.1804 | − | 9.42569i | 0.597194 | − | 0.462133i | ||||
\(417\) | −7.37737 | −0.361271 | ||||||||
\(418\) | 2.30444 | + | 0.813927i | 0.112714 | + | 0.0398105i | ||||
\(419\) | −4.06764 | − | 4.06764i | −0.198717 | − | 0.198717i | 0.600733 | − | 0.799450i | \(-0.294876\pi\) |
−0.799450 | + | 0.600733i | \(0.794876\pi\) | |||||||
\(420\) | −3.57075 | + | 4.42427i | −0.174235 | + | 0.215882i | ||||
\(421\) | 13.2281 | − | 13.2281i | 0.644699 | − | 0.644699i | −0.307008 | − | 0.951707i | \(-0.599328\pi\) |
0.951707 | + | 0.307008i | \(0.0993279\pi\) | |||||||
\(422\) | −1.09276 | − | 2.28621i | −0.0531947 | − | 0.111291i | ||||
\(423\) | 6.10797i | 0.296980i | ||||||||
\(424\) | 5.25198 | + | 1.24728i | 0.255059 | + | 0.0605731i | ||||
\(425\) | − | 3.85056i | − | 0.186779i | ||||||
\(426\) | −6.35094 | + | 3.03562i | −0.307704 | + | 0.147076i | ||||
\(427\) | 10.2386 | − | 10.2386i | 0.495480 | − | 0.495480i | ||||
\(428\) | −19.3712 | + | 2.06801i | −0.936342 | + | 0.0999612i | ||||
\(429\) | −3.26712 | − | 3.26712i | −0.157738 | − | 0.157738i | ||||
\(430\) | −0.588720 | + | 1.66682i | −0.0283906 | + | 0.0803813i | ||||
\(431\) | −25.5013 | −1.22836 | −0.614178 | − | 0.789167i | \(-0.710512\pi\) | ||||
−0.614178 | + | 0.789167i | \(0.710512\pi\) | |||||||
\(432\) | 3.36179 | + | 2.16758i | 0.161744 | + | 0.104288i | ||||
\(433\) | −38.3125 | −1.84118 | −0.920592 | − | 0.390526i | \(-0.872293\pi\) | ||||
−0.920592 | + | 0.390526i | \(0.872293\pi\) | |||||||
\(434\) | 5.09571 | − | 14.4273i | 0.244602 | − | 0.692532i | ||||
\(435\) | 3.63146 | + | 3.63146i | 0.174115 | + | 0.174115i | ||||
\(436\) | 4.24028 | + | 39.7189i | 0.203073 | + | 1.90219i | ||||
\(437\) | −5.89635 | + | 5.89635i | −0.282060 | + | 0.282060i | ||||
\(438\) | 12.4449 | − | 5.94839i | 0.594639 | − | 0.284225i | ||||
\(439\) | 15.1503i | 0.723082i | 0.932356 | + | 0.361541i | \(0.117749\pi\) | ||||
−0.932356 | + | 0.361541i | \(0.882251\pi\) | |||||||
\(440\) | −11.6167 | + | 7.15797i | −0.553805 | + | 0.341243i | ||||
\(441\) | − | 1.00000i | − | 0.0476190i | ||||||
\(442\) | −2.07514 | − | 4.34150i | −0.0987046 | − | 0.206504i | ||||
\(443\) | −2.78395 | + | 2.78395i | −0.132270 | + | 0.132270i | −0.770142 | − | 0.637872i | \(-0.779815\pi\) |
0.637872 | + | 0.770142i | \(0.279815\pi\) | |||||||
\(444\) | −11.8517 | − | 9.56530i | −0.562458 | − | 0.453949i | ||||
\(445\) | −5.76286 | − | 5.76286i | −0.273186 | − | 0.273186i | ||||
\(446\) | 8.39870 | + | 2.96641i | 0.397690 | + | 0.140464i | ||||
\(447\) | 0.196840 | 0.00931023 | ||||||||
\(448\) | 7.14578 | + | 3.59693i | 0.337606 | + | 0.169939i | ||||
\(449\) | 17.0189 | 0.803172 | 0.401586 | − | 0.915821i | \(-0.368459\pi\) | ||||
0.401586 | + | 0.915821i | \(0.368459\pi\) | |||||||
\(450\) | −4.10859 | − | 1.45115i | −0.193681 | − | 0.0684079i | ||||
\(451\) | −5.16343 | − | 5.16343i | −0.243136 | − | 0.243136i | ||||
\(452\) | −11.6003 | − | 9.36239i | −0.545633 | − | 0.440370i | ||||
\(453\) | −6.39946 | + | 6.39946i | −0.300673 | + | 0.300673i | ||||
\(454\) | −15.3625 | − | 32.1405i | −0.720997 | − | 1.50843i | ||||
\(455\) | − | 7.73968i | − | 0.362842i | ||||||
\(456\) | 2.45213 | − | 1.51095i | 0.114832 | − | 0.0707568i | ||||
\(457\) | − | 12.0596i | − | 0.564123i | −0.959396 | − | 0.282061i | \(-0.908982\pi\) | ||
0.959396 | − | 0.282061i | \(-0.0910182\pi\) | |||||||
\(458\) | −2.07938 | + | 0.993901i | −0.0971631 | + | 0.0464419i | ||||
\(459\) | 0.883695 | − | 0.883695i | 0.0412474 | − | 0.0412474i | ||||
\(460\) | −4.94210 | − | 46.2930i | −0.230427 | − | 2.15842i | ||||
\(461\) | 5.72644 | + | 5.72644i | 0.266707 | + | 0.266707i | 0.827772 | − | 0.561065i | \(-0.189608\pi\) |
−0.561065 | + | 0.827772i | \(0.689608\pi\) | |||||||
\(462\) | 0.799279 | − | 2.26297i | 0.0371858 | − | 0.105283i | ||||
\(463\) | −35.9237 | −1.66952 | −0.834758 | − | 0.550618i | \(-0.814392\pi\) | ||||
−0.834758 | + | 0.550618i | \(0.814392\pi\) | |||||||
\(464\) | 3.91594 | − | 6.07339i | 0.181793 | − | 0.281950i | ||||
\(465\) | 30.7562 | 1.42629 | ||||||||
\(466\) | 5.52752 | − | 15.6499i | 0.256057 | − | 0.724966i | ||||
\(467\) | 0.383033 | + | 0.383033i | 0.0177247 | + | 0.0177247i | 0.715914 | − | 0.698189i | \(-0.246010\pi\) |
−0.698189 | + | 0.715914i | \(0.746010\pi\) | |||||||
\(468\) | −5.41448 | + | 0.578035i | −0.250285 | + | 0.0267197i | ||||
\(469\) | 1.99158 | − | 1.99158i | 0.0919626 | − | 0.0919626i | ||||
\(470\) | −22.1547 | + | 10.5895i | −1.02192 | + | 0.488457i | ||||
\(471\) | − | 13.8062i | − | 0.636157i | ||||||
\(472\) | 39.9799 | + | 9.49471i | 1.84022 | + | 0.437029i | ||||
\(473\) | − | 0.746206i | − | 0.0343106i | ||||||
\(474\) | 9.57620 | + | 20.0348i | 0.439850 | + | 0.920227i | ||||
\(475\) | −2.21860 | + | 2.21860i | −0.101796 | + | 0.101796i | ||||
\(476\) | 1.56979 | − | 1.94502i | 0.0719512 | − | 0.0891499i | ||||
\(477\) | −1.34951 | − | 1.34951i | −0.0617899 | − | 0.0617899i | ||||
\(478\) | 20.6367 | + | 7.28888i | 0.943903 | + | 0.333385i | ||||
\(479\) | 40.7375 | 1.86135 | 0.930673 | − | 0.365853i | \(-0.119223\pi\) | ||||
0.930673 | + | 0.365853i | \(0.119223\pi\) | |||||||
\(480\) | −2.03381 | + | 15.9518i | −0.0928302 | + | 0.728095i | ||||
\(481\) | 20.7330 | 0.945345 | ||||||||
\(482\) | 23.0828 | + | 8.15281i | 1.05139 | + | 0.371350i | ||||
\(483\) | 5.79023 | + | 5.79023i | 0.263464 | + | 0.263464i | ||||
\(484\) | −10.1996 | + | 12.6376i | −0.463618 | + | 0.574438i | ||||
\(485\) | −16.8879 | + | 16.8879i | −0.766838 | + | 0.766838i | ||||
\(486\) | −0.609878 | − | 1.27595i | −0.0276646 | − | 0.0578783i | ||||
\(487\) | 17.2478i | 0.781573i | 0.920481 | + | 0.390786i | \(0.127797\pi\) | ||||
−0.920481 | + | 0.390786i | \(0.872203\pi\) | |||||||
\(488\) | 9.46294 | − | 39.8461i | 0.428367 | − | 1.80375i | ||||
\(489\) | 7.82020i | 0.353641i | ||||||||
\(490\) | 3.62718 | − | 1.73372i | 0.163859 | − | 0.0783213i | ||||
\(491\) | −12.5443 | + | 12.5443i | −0.566118 | + | 0.566118i | −0.931039 | − | 0.364921i | \(-0.881096\pi\) |
0.364921 | + | 0.931039i | \(0.381096\pi\) | |||||||
\(492\) | −8.55717 | + | 0.913540i | −0.385787 | + | 0.0411855i | ||||
\(493\) | −1.59648 | − | 1.59648i | −0.0719019 | − | 0.0719019i | ||||
\(494\) | −1.30582 | + | 3.69711i | −0.0587514 | + | 0.166341i | ||||
\(495\) | 4.82422 | 0.216832 | ||||||||
\(496\) | −9.13615 | − | 42.3017i | −0.410225 | − | 1.89940i | ||||
\(497\) | 4.97742 | 0.223268 | ||||||||
\(498\) | −2.35494 | + | 6.66746i | −0.105527 | + | 0.298776i | ||||
\(499\) | −8.56236 | − | 8.56236i | −0.383304 | − | 0.383304i | 0.488987 | − | 0.872291i | \(-0.337366\pi\) |
−0.872291 | + | 0.488987i | \(0.837366\pi\) | |||||||
\(500\) | 1.15812 | + | 10.8482i | 0.0517927 | + | 0.485145i | ||||
\(501\) | −2.80787 | + | 2.80787i | −0.125446 | + | 0.125446i | ||||
\(502\) | 8.97796 | − | 4.29128i | 0.400706 | − | 0.191529i | ||||
\(503\) | − | 21.5863i | − | 0.962488i | −0.876587 | − | 0.481244i | \(-0.840185\pi\) | ||
0.876587 | − | 0.481244i | \(-0.159815\pi\) | |||||||
\(504\) | −1.48376 | − | 2.40800i | −0.0660918 | − | 0.107261i | ||||
\(505\) | 31.5221i | 1.40272i | ||||||||
\(506\) | 8.47510 | + | 17.7311i | 0.376764 | + | 0.788244i | ||||
\(507\) | −3.95082 | + | 3.95082i | −0.175462 | + | 0.175462i | ||||
\(508\) | 23.0653 | + | 18.6156i | 1.02336 | + | 0.825933i | ||||
\(509\) | 13.1322 | + | 13.1322i | 0.582074 | + | 0.582074i | 0.935473 | − | 0.353398i | \(-0.114974\pi\) |
−0.353398 | + | 0.935473i | \(0.614974\pi\) | |||||||
\(510\) | 4.73740 | + | 1.67324i | 0.209776 | + | 0.0740925i | ||||
\(511\) | −9.75342 | −0.431466 | ||||||||
\(512\) | 22.5440 | − | 1.94120i | 0.996313 | − | 0.0857899i | ||||
\(513\) | −1.01833 | −0.0449602 | ||||||||
\(514\) | 23.4780 | + | 8.29241i | 1.03557 | + | 0.365762i | ||||
\(515\) | 8.99467 | + | 8.99467i | 0.396352 | + | 0.396352i | ||||
\(516\) | −0.684342 | − | 0.552320i | −0.0301265 | − | 0.0243145i | ||||
\(517\) | 7.32949 | − | 7.32949i | 0.322351 | − | 0.322351i | ||||
\(518\) | 4.64427 | + | 9.71648i | 0.204058 | + | 0.426917i | ||||
\(519\) | 18.1476i | 0.796590i | ||||||||
\(520\) | −11.4838 | − | 18.6372i | −0.503599 | − | 0.817293i | ||||
\(521\) | − | 11.9641i | − | 0.524155i | −0.965047 | − | 0.262077i | \(-0.915592\pi\) | ||
0.965047 | − | 0.262077i | \(-0.0844076\pi\) | |||||||
\(522\) | −2.30513 | + | 1.10180i | −0.100893 | + | 0.0482246i | ||||
\(523\) | 28.2756 | − | 28.2756i | 1.23640 | − | 1.23640i | 0.274943 | − | 0.961461i | \(-0.411341\pi\) |
0.961461 | − | 0.274943i | \(-0.0886590\pi\) | |||||||
\(524\) | −0.779413 | − | 7.30080i | −0.0340488 | − | 0.318937i | ||||
\(525\) | 2.17867 | + | 2.17867i | 0.0950848 | + | 0.0950848i | ||||
\(526\) | 14.9231 | − | 42.2512i | 0.650677 | − | 1.84224i | ||||
\(527\) | −13.5212 | −0.588993 | ||||||||
\(528\) | −1.43304 | − | 6.63517i | −0.0623649 | − | 0.288759i | ||||
\(529\) | −44.0534 | −1.91537 | ||||||||
\(530\) | 2.55525 | − | 7.23460i | 0.110993 | − | 0.314251i | ||||
\(531\) | −10.2730 | − | 10.2730i | −0.445809 | − | 0.445809i | ||||
\(532\) | −2.02515 | + | 0.216199i | −0.0878013 | + | 0.00937341i | ||||
\(533\) | 8.28389 | − | 8.28389i | 0.358815 | − | 0.358815i | ||||
\(534\) | 3.65807 | − | 1.74848i | 0.158300 | − | 0.0756642i | ||||
\(535\) | 27.6900i | 1.19714i | ||||||||
\(536\) | 1.84070 | − | 7.75074i | 0.0795062 | − | 0.334781i | ||||
\(537\) | − | 22.7498i | − | 0.981725i | ||||||
\(538\) | −4.66198 | − | 9.75352i | −0.200992 | − | 0.420504i | ||||
\(539\) | −1.19999 | + | 1.19999i | −0.0516871 | + | 0.0516871i | ||||
\(540\) | 3.57075 | − | 4.42427i | 0.153660 | − | 0.190390i | ||||
\(541\) | −25.0102 | − | 25.0102i | −1.07527 | − | 1.07527i | −0.996926 | − | 0.0783484i | \(-0.975035\pi\) |
−0.0783484 | − | 0.996926i | \(-0.524965\pi\) | |||||||
\(542\) | −14.8407 | − | 5.24173i | −0.637463 | − | 0.225151i | ||||
\(543\) | 7.26683 | 0.311849 | ||||||||
\(544\) | 0.894113 | − | 7.01279i | 0.0383348 | − | 0.300671i | ||||
\(545\) | 56.7758 | 2.43201 | ||||||||
\(546\) | 3.63057 | + | 1.28231i | 0.155374 | + | 0.0548780i | ||||
\(547\) | 8.31314 | + | 8.31314i | 0.355444 | + | 0.355444i | 0.862130 | − | 0.506686i | \(-0.169130\pi\) |
−0.506686 | + | 0.862130i | \(0.669130\pi\) | |||||||
\(548\) | −5.19011 | + | 6.43072i | −0.221711 | + | 0.274707i | ||||
\(549\) | −10.2386 | + | 10.2386i | −0.436972 | + | 0.436972i | ||||
\(550\) | 3.18890 | + | 6.67162i | 0.135975 | + | 0.284479i | ||||
\(551\) | 1.83971i | 0.0783741i | ||||||||
\(552\) | 22.5342 | + | 5.35157i | 0.959117 | + | 0.227778i | ||||
\(553\) | − | 15.7018i | − | 0.667710i | ||||||
\(554\) | −29.7494 | + | 14.2196i | −1.26393 | + | 0.604132i | ||||
\(555\) | −15.3072 | + | 15.3072i | −0.649754 | + | 0.649754i | ||||
\(556\) | 14.6714 | − | 1.56627i | 0.622205 | − | 0.0664248i | ||||
\(557\) | −16.8478 | − | 16.8478i | −0.713866 | − | 0.713866i | 0.253476 | − | 0.967342i | \(-0.418426\pi\) |
−0.967342 | + | 0.253476i | \(0.918426\pi\) | |||||||
\(558\) | −5.09571 | + | 14.4273i | −0.215718 | + | 0.610756i | ||||
\(559\) | 1.19717 | 0.0506348 | ||||||||
\(560\) | 6.16183 | − | 9.55664i | 0.260385 | − | 0.403842i | ||||
\(561\) | −2.12085 | −0.0895422 | ||||||||
\(562\) | −7.97550 | + | 22.5807i | −0.336426 | + | 0.952511i | ||||
\(563\) | −14.8909 | − | 14.8909i | −0.627577 | − | 0.627577i | 0.319881 | − | 0.947458i | \(-0.396357\pi\) |
−0.947458 | + | 0.319881i | \(0.896357\pi\) | |||||||
\(564\) | −1.29677 | − | 12.1469i | −0.0546039 | − | 0.511478i | ||||
\(565\) | −14.9825 | + | 14.9825i | −0.630317 | + | 0.630317i | ||||
\(566\) | 7.68994 | − | 3.67563i | 0.323232 | − | 0.154498i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 11.9856 | − | 7.38528i | 0.502906 | − | 0.309880i | ||||
\(569\) | 37.7158i | 1.58113i | 0.612380 | + | 0.790564i | \(0.290212\pi\) | ||||
−0.612380 | + | 0.790564i | \(0.709788\pi\) | |||||||
\(570\) | −1.76549 | − | 3.69366i | −0.0739483 | − | 0.154710i | ||||
\(571\) | −21.6472 | + | 21.6472i | −0.905906 | + | 0.905906i | −0.995939 | − | 0.0900329i | \(-0.971303\pi\) |
0.0900329 | + | 0.995939i | \(0.471303\pi\) | |||||||
\(572\) | 7.19095 | + | 5.80368i | 0.300669 | + | 0.242664i | ||||
\(573\) | −15.4669 | − | 15.4669i | −0.646141 | − | 0.646141i | ||||
\(574\) | 5.73784 | + | 2.02660i | 0.239493 | + | 0.0845886i | ||||
\(575\) | −25.2299 | −1.05216 | ||||||||
\(576\) | −7.14578 | − | 3.59693i | −0.297741 | − | 0.149872i | ||||
\(577\) | 22.0735 | 0.918934 | 0.459467 | − | 0.888195i | \(-0.348041\pi\) | ||||
0.459467 | + | 0.888195i | \(0.348041\pi\) | |||||||
\(578\) | 20.5865 | + | 7.27114i | 0.856286 | + | 0.302439i | ||||
\(579\) | 3.20466 | + | 3.20466i | 0.133181 | + | 0.133181i | ||||
\(580\) | −7.99287 | − | 6.45090i | −0.331886 | − | 0.267859i | ||||
\(581\) | 3.53556 | − | 3.53556i | 0.146680 | − | 0.146680i | ||||
\(582\) | −5.12386 | − | 10.7198i | −0.212391 | − | 0.444352i | ||||
\(583\) | 3.23880i | 0.134137i | ||||||||
\(584\) | −23.4862 | + | 14.4717i | −0.971867 | + | 0.598843i | ||||
\(585\) | 7.73968i | 0.319997i | ||||||||
\(586\) | 18.9792 | − | 9.07169i | 0.784026 | − | 0.374748i | ||||
\(587\) | −15.9766 | + | 15.9766i | −0.659426 | + | 0.659426i | −0.955244 | − | 0.295818i | \(-0.904408\pi\) |
0.295818 | + | 0.955244i | \(0.404408\pi\) | |||||||
\(588\) | 0.212308 | + | 1.98870i | 0.00875543 | + | 0.0820126i | ||||
\(589\) | 7.79059 | + | 7.79059i | 0.321005 | + | 0.321005i | ||||
\(590\) | 19.4515 | − | 55.0723i | 0.800805 | − | 2.26729i | ||||
\(591\) | −24.0282 | −0.988387 | ||||||||
\(592\) | 25.6003 | + | 16.5063i | 1.05217 | + | 0.678405i | ||||
\(593\) | −2.13357 | −0.0876150 | −0.0438075 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438075 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(594\) | −0.799279 | + | 2.26297i | −0.0327948 | + | 0.0928508i | ||||
\(595\) | −2.51211 | − | 2.51211i | −0.102986 | − | 0.102986i | ||||
\(596\) | −0.391457 | + | 0.0417908i | −0.0160347 | + | 0.00171182i | ||||
\(597\) | 3.27657 | − | 3.27657i | 0.134101 | − | 0.134101i | ||||
\(598\) | −28.4467 | + | 13.5969i | −1.16327 | + | 0.556020i | ||||
\(599\) | 16.0735i | 0.656743i | 0.944549 | + | 0.328372i | \(0.106500\pi\) | ||||
−0.944549 | + | 0.328372i | \(0.893500\pi\) | |||||||
\(600\) | 8.47884 | + | 2.01362i | 0.346147 | + | 0.0822055i | ||||
\(601\) | 38.7107i | 1.57904i | 0.613722 | + | 0.789522i | \(0.289672\pi\) | ||||
−0.613722 | + | 0.789522i | \(0.710328\pi\) | |||||||
\(602\) | 0.268170 | + | 0.561049i | 0.0109298 | + | 0.0228666i | ||||
\(603\) | −1.99158 | + | 1.99158i | −0.0811034 | + | 0.0811034i | ||||
\(604\) | 11.3679 | − | 14.0852i | 0.462555 | − | 0.573121i | ||||
\(605\) | 16.3222 | + | 16.3222i | 0.663593 | + | 0.663593i | ||||
\(606\) | −14.7866 | − | 5.22260i | −0.600663 | − | 0.212154i | ||||
\(607\) | −0.471089 | −0.0191209 | −0.00956045 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00956045 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(608\) | −4.55577 | + | 3.52543i | −0.184761 | + | 0.142975i | ||||
\(609\) | 1.80660 | 0.0732070 | ||||||||
\(610\) | −54.8880 | − | 19.3864i | −2.22235 | − | 0.784932i | ||||
\(611\) | 11.7590 | + | 11.7590i | 0.475718 | + | 0.475718i | ||||
\(612\) | −1.56979 | + | 1.94502i | −0.0634550 | + | 0.0786228i | ||||
\(613\) | −12.2091 | + | 12.2091i | −0.493120 | + | 0.493120i | −0.909288 | − | 0.416168i | \(-0.863373\pi\) |
0.416168 | + | 0.909288i | \(0.363373\pi\) | |||||||
\(614\) | −10.8551 | − | 22.7104i | −0.438075 | − | 0.916516i | ||||
\(615\) | 12.2320i | 0.493241i | ||||||||
\(616\) | −1.10908 | + | 4.67006i | −0.0446861 | + | 0.188162i | ||||
\(617\) | − | 15.2964i | − | 0.615808i | −0.951417 | − | 0.307904i | \(-0.900372\pi\) | ||
0.951417 | − | 0.307904i | \(-0.0996275\pi\) | |||||||
\(618\) | −5.70951 | + | 2.72903i | −0.229670 | + | 0.109777i | ||||
\(619\) | 1.21290 | − | 1.21290i | 0.0487507 | − | 0.0487507i | −0.682311 | − | 0.731062i | \(-0.739025\pi\) |
0.731062 | + | 0.682311i | \(0.239025\pi\) | |||||||
\(620\) | −61.1649 | + | 6.52979i | −2.45644 | + | 0.262243i | ||||
\(621\) | −5.79023 | − | 5.79023i | −0.232354 | − | 0.232354i | ||||
\(622\) | 3.43540 | − | 9.72652i | 0.137747 | − | 0.389998i | ||||
\(623\) | −2.86694 | −0.114861 | ||||||||
\(624\) | 10.6451 | − | 2.29908i | 0.426144 | − | 0.0920367i | ||||
\(625\) | 30.9123 | 1.23649 | ||||||||
\(626\) | 8.32667 | − | 23.5750i | 0.332801 | − | 0.942247i | ||||
\(627\) | 1.22198 | + | 1.22198i | 0.0488012 | + | 0.0488012i | ||||
\(628\) | 2.93117 | + | 27.4564i | 0.116966 | + | 1.09563i | ||||
\(629\) | 6.72942 | − | 6.72942i | 0.268320 | − | 0.268320i | ||||
\(630\) | −3.62718 | + | 1.73372i | −0.144510 | + | 0.0690729i | ||||
\(631\) | 27.4265i | 1.09183i | 0.837841 | + | 0.545915i | \(0.183818\pi\) | ||||
−0.837841 | + | 0.545915i | \(0.816182\pi\) | |||||||
\(632\) | −23.2977 | − | 37.8100i | −0.926734 | − | 1.50400i | ||||
\(633\) | − | 1.79177i | − | 0.0712164i | ||||||
\(634\) | 14.8145 | + | 30.9940i | 0.588358 | + | 1.23093i | ||||
\(635\) | 29.7902 | − | 29.7902i | 1.18219 | − | 1.18219i | ||||
\(636\) | 2.97029 | + | 2.39726i | 0.117780 | + | 0.0950577i | ||||
\(637\) | −1.92519 | − | 1.92519i | −0.0762787 | − | 0.0762787i | ||||
\(638\) | 4.08827 | + | 1.44397i | 0.161856 | + | 0.0571675i | ||||
\(639\) | −4.97742 | −0.196904 | ||||||||
\(640\) | 0.657948 | − | 32.1551i | 0.0260077 | − | 1.27104i | ||||
\(641\) | 43.1622 | 1.70480 | 0.852401 | − | 0.522888i | \(-0.175145\pi\) | ||||
0.852401 | + | 0.522888i | \(0.175145\pi\) | |||||||
\(642\) | −12.9890 | − | 4.58769i | −0.512633 | − | 0.181062i | ||||
\(643\) | −11.6984 | − | 11.6984i | −0.461342 | − | 0.461342i | 0.437753 | − | 0.899095i | \(-0.355774\pi\) |
−0.899095 | + | 0.437753i | \(0.855774\pi\) | |||||||
\(644\) | −12.7443 | − | 10.2857i | −0.502197 | − | 0.405314i | ||||
\(645\) | −0.883867 | + | 0.883867i | −0.0348022 | + | 0.0348022i | ||||
\(646\) | 0.776154 | + | 1.62382i | 0.0305374 | + | 0.0638885i | ||||
\(647\) | 9.25148i | 0.363713i | 0.983325 | + | 0.181857i | \(0.0582107\pi\) | ||||
−0.983325 | + | 0.181857i | \(0.941789\pi\) | |||||||
\(648\) | 1.48376 | + | 2.40800i | 0.0582875 | + | 0.0945952i | ||||
\(649\) | 24.6549i | 0.967788i | ||||||||
\(650\) | −10.7035 | + | 5.11607i | −0.419828 | + | 0.200669i | ||||
\(651\) | 7.65037 | − | 7.65037i | 0.299842 | − | 0.299842i | ||||
\(652\) | −1.66029 | − | 15.5520i | −0.0650219 | − | 0.609064i | ||||
\(653\) | −18.0872 | − | 18.0872i | −0.707808 | − | 0.707808i | 0.258266 | − | 0.966074i | \(-0.416849\pi\) |
−0.966074 | + | 0.258266i | \(0.916849\pi\) | |||||||
\(654\) | −9.40665 | + | 26.6327i | −0.367829 | + | 1.04142i | ||||
\(655\) | −10.4361 | −0.407770 | ||||||||
\(656\) | 16.8237 | − | 3.63351i | 0.656855 | − | 0.141865i | ||||
\(657\) | 9.75342 | 0.380517 | ||||||||
\(658\) | −2.87676 | + | 8.14487i | −0.112148 | + | 0.317520i | ||||
\(659\) | −14.5814 | − | 14.5814i | −0.568011 | − | 0.568011i | 0.363560 | − | 0.931571i | \(-0.381561\pi\) |
−0.931571 | + | 0.363560i | \(0.881561\pi\) | |||||||
\(660\) | −9.59392 | + | 1.02422i | −0.373443 | + | 0.0398677i | ||||
\(661\) | 20.4492 | − | 20.4492i | 0.795382 | − | 0.795382i | −0.186982 | − | 0.982363i | \(-0.559871\pi\) |
0.982363 | + | 0.186982i | \(0.0598705\pi\) | |||||||
\(662\) | 2.24763 | − | 1.07432i | 0.0873568 | − | 0.0417547i | ||||
\(663\) | − | 3.40256i | − | 0.132144i | ||||||
\(664\) | 3.26772 | − | 13.7596i | 0.126812 | − | 0.533974i | ||||
\(665\) | 2.89483i | 0.112257i | ||||||||
\(666\) | −4.64427 | − | 9.71648i | −0.179962 | − | 0.376506i | ||||
\(667\) | −10.4606 | + | 10.4606i | −0.405036 | + | 0.405036i | ||||
\(668\) | 4.98788 | − | 6.18015i | 0.192987 | − | 0.239117i | ||||
\(669\) | 4.45359 | + | 4.45359i | 0.172186 | + | 0.172186i | ||||
\(670\) | −10.6766 | − | 3.77098i | −0.412475 | − | 0.145686i | ||||
\(671\) | 24.5724 | 0.948606 | ||||||||
\(672\) | 3.46199 | + | 4.47377i | 0.133549 | + | 0.172580i | ||||
\(673\) | −19.3984 | −0.747755 | −0.373878 | − | 0.927478i | \(-0.621972\pi\) | ||||
−0.373878 | + | 0.927478i | \(0.621972\pi\) | |||||||
\(674\) | −29.0349 | − | 10.2551i | −1.11838 | − | 0.395011i | ||||
\(675\) | −2.17867 | − | 2.17867i | −0.0838569 | − | 0.0838569i | ||||
\(676\) | 7.01821 | − | 8.69579i | 0.269931 | − | 0.334453i | ||||
\(677\) | −0.258487 | + | 0.258487i | −0.00993446 | + | 0.00993446i | −0.712057 | − | 0.702122i | \(-0.752236\pi\) |
0.702122 | + | 0.712057i | \(0.252236\pi\) | |||||||
\(678\) | −4.54575 | − | 9.51036i | −0.174579 | − | 0.365243i | ||||
\(679\) | 8.40145i | 0.322418i | ||||||||
\(680\) | −9.77651 | − | 2.32179i | −0.374912 | − | 0.0890367i | ||||
\(681\) | − | 25.1894i | − | 0.965261i | ||||||
\(682\) | 23.4274 | − | 11.1978i | 0.897080 | − | 0.428785i | ||||
\(683\) | −1.04397 | + | 1.04397i | −0.0399462 | + | 0.0399462i | −0.726798 | − | 0.686852i | \(-0.758992\pi\) |
0.686852 | + | 0.726798i | \(0.258992\pi\) | |||||||
\(684\) | 2.02515 | − | 0.216199i | 0.0774334 | − | 0.00826657i | ||||
\(685\) | 8.30564 | + | 8.30564i | 0.317342 | + | 0.317342i | ||||
\(686\) | 0.470984 | − | 1.33348i | 0.0179823 | − | 0.0509126i | ||||
\(687\) | −1.62967 | −0.0621759 | ||||||||
\(688\) | 1.47821 | + | 0.953107i | 0.0563563 | + | 0.0363368i | ||||
\(689\) | −5.19613 | −0.197957 | ||||||||
\(690\) | 10.9636 | − | 31.0408i | 0.417376 | − | 1.18170i | ||||
\(691\) | −18.2172 | − | 18.2172i | −0.693013 | − | 0.693013i | 0.269880 | − | 0.962894i | \(-0.413016\pi\) |
−0.962894 | + | 0.269880i | \(0.913016\pi\) | |||||||
\(692\) | −3.85287 | − | 36.0901i | −0.146464 | − | 1.37194i | ||||
\(693\) | 1.19999 | − | 1.19999i | 0.0455838 | − | 0.0455838i | ||||
\(694\) | −37.5022 | + | 17.9253i | −1.42356 | + | 0.680433i | ||||
\(695\) | − | 20.9719i | − | 0.795508i | ||||||
\(696\) | 4.35028 | − | 2.68055i | 0.164897 | − | 0.101606i | ||||
\(697\) | − | 5.37748i | − | 0.203687i | ||||||
\(698\) | 8.30689 | + | 17.3792i | 0.314420 | + | 0.657812i | ||||
\(699\) | 8.29867 | − | 8.29867i | 0.313885 | − | 0.313885i | ||||
\(700\) | −4.79526 | − | 3.87017i | −0.181244 | − | 0.146278i | ||||
\(701\) | 21.2401 | + | 21.2401i | 0.802226 | + | 0.802226i | 0.983443 | − | 0.181217i | \(-0.0580037\pi\) |
−0.181217 | + | 0.983443i | \(0.558004\pi\) | |||||||
\(702\) | −3.63057 | − | 1.28231i | −0.137027 | − | 0.0483978i | ||||
\(703\) | −7.75465 | −0.292472 | ||||||||
\(704\) | 4.25858 | + | 12.8911i | 0.160501 | + | 0.485852i | ||||
\(705\) | −17.3633 | −0.653940 | ||||||||
\(706\) | 47.4128 | + | 16.7461i | 1.78440 | + | 0.630250i | ||||
\(707\) | 7.84089 | + | 7.84089i | 0.294887 | + | 0.294887i | ||||
\(708\) | 22.6109 | + | 18.2488i | 0.849769 | + | 0.685832i | ||||
\(709\) | 23.9787 | − | 23.9787i | 0.900539 | − | 0.900539i | −0.0949439 | − | 0.995483i | \(-0.530267\pi\) |
0.995483 | + | 0.0949439i | \(0.0302672\pi\) | |||||||
\(710\) | −8.62943 | − | 18.0540i | −0.323857 | − | 0.677554i | ||||
\(711\) | 15.7018i | 0.588865i | ||||||||
\(712\) | −6.90358 | + | 4.25384i | −0.258723 | + | 0.159419i | ||||
\(713\) | 88.5948i | 3.31790i | ||||||||
\(714\) | 1.59460 | − | 0.762185i | 0.0596764 | − | 0.0285241i | ||||
\(715\) | 9.28752 | − | 9.28752i | 0.347334 | − | 0.347334i | ||||
\(716\) | 4.82996 | + | 45.2425i | 0.180504 | + | 1.69079i | ||||
\(717\) | 10.9431 | + | 10.9431i | 0.408676 | + | 0.408676i | ||||
\(718\) | −6.84262 | + | 19.3733i | −0.255364 | + | 0.723004i | ||||
\(719\) | −45.9476 | −1.71356 | −0.856779 | − | 0.515684i | \(-0.827538\pi\) | ||||
−0.856779 | + | 0.515684i | \(0.827538\pi\) | |||||||
\(720\) | −6.16183 | + | 9.55664i | −0.229638 | + | 0.356155i | ||||
\(721\) | 4.47471 | 0.166647 | ||||||||
\(722\) | −8.46030 | + | 23.9533i | −0.314860 | + | 0.891451i | ||||
\(723\) | 12.2401 | + | 12.2401i | 0.455215 | + | 0.455215i | ||||
\(724\) | −14.4515 | + | 1.54281i | −0.537087 | + | 0.0573379i | ||||
\(725\) | −3.93597 | + | 3.93597i | −0.146178 | + | 0.146178i | ||||
\(726\) | −10.3608 | + | 4.95224i | −0.384525 | + | 0.183795i | ||||
\(727\) | − | 14.9397i | − | 0.554082i | −0.960858 | − | 0.277041i | \(-0.910646\pi\) | ||
0.960858 | − | 0.277041i | \(-0.0893538\pi\) | |||||||
\(728\) | −7.49236 | − | 1.77934i | −0.277685 | − | 0.0659467i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 16.9097 | + | 35.3774i | 0.625854 | + | 1.30938i | ||||
\(731\) | 0.388570 | − | 0.388570i | 0.0143718 | − | 0.0143718i | ||||
\(732\) | 18.1877 | − | 22.5352i | 0.672238 | − | 0.832925i | ||||
\(733\) | 25.5679 | + | 25.5679i | 0.944371 | + | 0.944371i | 0.998532 | − | 0.0541608i | \(-0.0172483\pi\) |
−0.0541608 | + | 0.998532i | \(0.517248\pi\) | |||||||
\(734\) | 25.5496 | + | 9.02411i | 0.943055 | + | 0.333086i | ||||
\(735\) | 2.84273 | 0.104856 | ||||||||
\(736\) | −45.9498 | − | 5.85849i | −1.69373 | − | 0.215947i | ||||
\(737\) | 4.77974 | 0.176064 | ||||||||
\(738\) | −5.73784 | − | 2.02660i | −0.211213 | − | 0.0746001i | ||||
\(739\) | 19.6495 | + | 19.6495i | 0.722819 | + | 0.722819i | 0.969178 | − | 0.246360i | \(-0.0792344\pi\) |
−0.246360 | + | 0.969178i | \(0.579234\pi\) | |||||||
\(740\) | 27.1916 | − | 33.6912i | 0.999581 | − | 1.23851i | ||||
\(741\) | −1.96047 | + | 1.96047i | −0.0720197 | + | 0.0720197i | ||||
\(742\) | −1.16395 | − | 2.43515i | −0.0427300 | − | 0.0893972i | ||||
\(743\) | − | 26.0555i | − | 0.955885i | −0.878391 | − | 0.477942i | \(-0.841383\pi\) | ||
0.878391 | − | 0.477942i | \(-0.158617\pi\) | |||||||
\(744\) | 7.07080 | − | 29.7734i | 0.259228 | − | 1.09155i | ||||
\(745\) | 0.559564i | 0.0205008i | ||||||||
\(746\) | 42.1791 | − | 20.1607i | 1.54428 | − | 0.738136i | ||||
\(747\) | −3.53556 | + | 3.53556i | −0.129359 | + | 0.129359i | ||||
\(748\) | 4.21773 | − | 0.450273i | 0.154215 | − | 0.0164636i | ||||
\(749\) | 6.88767 | + | 6.88767i | 0.251670 | + | 0.251670i | ||||
\(750\) | −2.56918 | + | 7.27402i | −0.0938131 | + | 0.265610i | ||||
\(751\) | −34.2020 | −1.24805 | −0.624024 | − | 0.781405i | \(-0.714503\pi\) | ||||
−0.624024 | + | 0.781405i | \(0.714503\pi\) | |||||||
\(752\) | 5.15777 | + | 23.8813i | 0.188085 | + | 0.870860i | ||||
\(753\) | 7.03630 | 0.256417 | ||||||||
\(754\) | −2.31663 | + | 6.55898i | −0.0843665 | + | 0.238864i | ||||
\(755\) | −18.1919 | − | 18.1919i | −0.662071 | − | 0.662071i | ||||
\(756\) | −0.212308 | − | 1.98870i | −0.00772156 | − | 0.0723283i | ||||
\(757\) | −23.5059 | + | 23.5059i | −0.854337 | + | 0.854337i | −0.990664 | − | 0.136327i | \(-0.956470\pi\) |
0.136327 | + | 0.990664i | \(0.456470\pi\) | |||||||
\(758\) | 9.08910 | − | 4.34440i | 0.330131 | − | 0.157796i | ||||
\(759\) | 13.8964i | 0.504407i | ||||||||
\(760\) | 4.29522 | + | 6.97074i | 0.155804 | + | 0.252855i | ||||
\(761\) | 19.1706i | 0.694932i | 0.937692 | + | 0.347466i | \(0.112958\pi\) | ||||
−0.937692 | + | 0.347466i | \(0.887042\pi\) | |||||||
\(762\) | 9.03849 | + | 18.9098i | 0.327430 | + | 0.685030i | ||||
\(763\) | 14.1226 | − | 14.1226i | 0.511271 | − | 0.511271i | ||||
\(764\) | 34.0429 | + | 27.4753i | 1.23163 | + | 0.994023i | ||||
\(765\) | 2.51211 | + | 2.51211i | 0.0908254 | + | 0.0908254i | ||||
\(766\) | 6.41285 | + | 2.26501i | 0.231706 | + | 0.0818383i | ||||
\(767\) | −39.5548 | −1.42824 | ||||||||
\(768\) | 14.9745 | + | 5.63610i | 0.540344 | + | 0.203375i | ||||
\(769\) | 10.8534 | 0.391385 | 0.195692 | − | 0.980665i | \(-0.437305\pi\) | ||||
0.195692 | + | 0.980665i | \(0.437305\pi\) | |||||||
\(770\) | 6.43301 | + | 2.27213i | 0.231829 | + | 0.0818820i | ||||
\(771\) | 12.4497 | + | 12.4497i | 0.448365 | + | 0.448365i | ||||
\(772\) | −7.05347 | − | 5.69272i | −0.253860 | − | 0.204886i | ||||
\(773\) | −3.57093 | + | 3.57093i | −0.128437 | + | 0.128437i | −0.768403 | − | 0.639966i | \(-0.778948\pi\) |
0.639966 | + | 0.768403i | \(0.278948\pi\) | |||||||
\(774\) | −0.268170 | − | 0.561049i | −0.00963916 | − | 0.0201665i | ||||
\(775\) | 33.3352i | 1.19744i | ||||||||
\(776\) | 12.4657 | + | 20.2307i | 0.447493 | + | 0.726240i | ||||
\(777\) | 7.61509i | 0.273190i | ||||||||
\(778\) | −33.8747 | + | 16.1914i | −1.21447 | + | 0.580489i | ||||
\(779\) | −3.09837 | + | 3.09837i | −0.111011 | + | 0.111011i | ||||
\(780\) | −1.64320 | − | 15.3919i | −0.0588359 | − | 0.551119i | ||||
\(781\) | 5.97284 | + | 5.97284i | 0.213725 | + | 0.213725i | ||||
\(782\) | −4.81986 | + | 13.6463i | −0.172358 | + | 0.487991i | ||||
\(783\) | −1.80660 | −0.0645625 | ||||||||
\(784\) | −0.844433 | − | 3.90985i | −0.0301583 | − | 0.139638i | ||||
\(785\) | 39.2473 | 1.40080 | ||||||||
\(786\) | 1.72905 | − | 4.89540i | 0.0616732 | − | 0.174613i | ||||
\(787\) | 21.8242 | + | 21.8242i | 0.777950 | + | 0.777950i | 0.979482 | − | 0.201532i | \(-0.0645919\pi\) |
−0.201532 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(788\) | 47.7848 | − | 5.10137i | 1.70226 | − | 0.181729i | ||||
\(789\) | 22.4046 | − | 22.4046i | 0.797624 | − | 0.797624i | ||||
\(790\) | −56.9534 | + | 27.2225i | −2.02631 | + | 0.968534i | ||||
\(791\) | 7.45355i | 0.265018i | ||||||||
\(792\) | 1.10908 | − | 4.67006i | 0.0394094 | − | 0.165943i | ||||
\(793\) | 39.4224i | 1.39993i | ||||||||
\(794\) | −21.4716 | − | 44.9216i | −0.761998 | − | 1.59421i | ||||
\(795\) | 3.83630 | − | 3.83630i | 0.136059 | − | 0.136059i | ||||
\(796\) | −5.82047 | + | 7.21175i | −0.206301 | + | 0.255614i | ||||
\(797\) | −25.5382 | − | 25.5382i | −0.904610 | − | 0.904610i | 0.0912205 | − | 0.995831i | \(-0.470923\pi\) |
−0.995831 | + | 0.0912205i | \(0.970923\pi\) | |||||||
\(798\) | −1.35792 | − | 0.479616i | −0.0480699 | − | 0.0169782i | ||||
\(799\) | 7.63334 | 0.270048 | ||||||||
\(800\) | −17.2894 | − | 2.20435i | −0.611272 | − | 0.0779356i | ||||
\(801\) | 2.86694 | 0.101298 | ||||||||
\(802\) | 3.50015 | + | 1.23625i | 0.123595 | + | 0.0436535i | ||||
\(803\) | −11.7040 | − | 11.7040i | −0.413024 | − | 0.413024i | ||||
\(804\) | 3.53782 | − | 4.38348i | 0.124769 | − | 0.154593i | ||||
\(805\) | −16.4600 | + | 16.4600i | −0.580140 | + | 0.580140i | ||||
\(806\) | 17.9651 | + | 37.5854i | 0.632792 | + | 1.32389i | ||||
\(807\) | − | 7.64412i | − | 0.269086i | ||||||
\(808\) | 30.5148 | + | 7.24688i | 1.07351 | + | 0.254944i | ||||
\(809\) | 32.2906i | 1.13528i | 0.823278 | + | 0.567638i | \(0.192143\pi\) | ||||
−0.823278 | + | 0.567638i | \(0.807857\pi\) | |||||||
\(810\) | 3.62718 | − | 1.73372i | 0.127446 | − | 0.0609166i | ||||
\(811\) | −5.25871 | + | 5.25871i | −0.184658 | + | 0.184658i | −0.793382 | − | 0.608724i | \(-0.791682\pi\) |
0.608724 | + | 0.793382i | \(0.291682\pi\) | |||||||
\(812\) | −3.59278 | + | 0.383555i | −0.126082 | + | 0.0134601i | ||||
\(813\) | −7.86960 | − | 7.86960i | −0.275999 | − | 0.275999i | ||||
\(814\) | −6.08658 | + | 17.2327i | −0.213335 | + | 0.604007i | ||||
\(815\) | −22.2307 | −0.778707 | ||||||||
\(816\) | 2.70890 | − | 4.20134i | 0.0948303 | − | 0.147076i | ||||
\(817\) | −0.447769 | −0.0156655 | ||||||||
\(818\) | −7.78981 | + | 22.0550i | −0.272364 | + | 0.771136i | ||||
\(819\) | 1.92519 | + | 1.92519i | 0.0672715 | + | 0.0672715i | ||||
\(820\) | −2.59694 | − | 24.3257i | −0.0906892 | − | 0.849491i | ||||
\(821\) | −6.11075 | + | 6.11075i | −0.213267 | + | 0.213267i | −0.805654 | − | 0.592387i | \(-0.798186\pi\) |
0.592387 | + | 0.805654i | \(0.298186\pi\) | |||||||
\(822\) | −5.27214 | + | 2.51997i | −0.183887 | + | 0.0878941i | ||||
\(823\) | − | 37.3133i | − | 1.30066i | −0.759652 | − | 0.650330i | \(-0.774631\pi\) | ||
0.759652 | − | 0.650330i | \(-0.225369\pi\) | |||||||
\(824\) | 10.7751 | − | 6.63938i | 0.375368 | − | 0.231294i | ||||
\(825\) | 5.22875i | 0.182042i | ||||||||
\(826\) | −8.86041 | − | 18.5372i | −0.308293 | − | 0.644992i | ||||
\(827\) | −21.0461 | + | 21.0461i | −0.731846 | + | 0.731846i | −0.970985 | − | 0.239139i | \(-0.923135\pi\) |
0.239139 | + | 0.970985i | \(0.423135\pi\) | |||||||
\(828\) | 12.7443 | + | 10.2857i | 0.442896 | + | 0.357453i | ||||
\(829\) | 11.5168 | + | 11.5168i | 0.399995 | + | 0.399995i | 0.878231 | − | 0.478236i | \(-0.158724\pi\) |
−0.478236 | + | 0.878231i | \(0.658724\pi\) | |||||||
\(830\) | −18.9538 | − | 6.69446i | −0.657895 | − | 0.232368i | ||||
\(831\) | −23.3155 | −0.808805 | ||||||||
\(832\) | −20.6817 | + | 6.83220i | −0.717009 | + | 0.236864i | ||||
\(833\) | −1.24973 | −0.0433007 | ||||||||
\(834\) | 9.83759 | + | 3.47463i | 0.340648 | + | 0.120317i | ||||
\(835\) | −7.98202 | − | 7.98202i | −0.276229 | − | 0.276229i | ||||
\(836\) | −2.68959 | − | 2.17071i | −0.0930213 | − | 0.0750757i | ||||
\(837\) | −7.65037 | + | 7.65037i | −0.264436 | + | 0.264436i | ||||
\(838\) | 3.50832 | + | 7.33991i | 0.121193 | + | 0.253553i | ||||
\(839\) | 18.3880i | 0.634824i | 0.948288 | + | 0.317412i | \(0.102814\pi\) | ||||
−0.948288 | + | 0.317412i | \(0.897186\pi\) | |||||||
\(840\) | 6.84529 | − | 4.21792i | 0.236185 | − | 0.145532i | ||||
\(841\) | − | 25.7362i | − | 0.887455i | ||||||
\(842\) | −23.8697 | + | 11.4092i | −0.822604 | + | 0.393187i | ||||
\(843\) | −11.9739 | + | 11.9739i | −0.412403 | + | 0.412403i | ||||
\(844\) | 0.380406 | + | 3.56329i | 0.0130941 | + | 0.122653i | ||||
\(845\) | −11.2311 | − | 11.2311i | −0.386362 | − | 0.386362i | ||||
\(846\) | 2.87676 | − | 8.14487i | 0.0989050 | − | 0.280026i | ||||
\(847\) | 8.12006 | 0.279009 | ||||||||
\(848\) | −6.41597 | − | 4.13682i | −0.220325 | − | 0.142059i | ||||
\(849\) | 6.02684 | 0.206841 | ||||||||
\(850\) | −1.81355 | + | 5.13465i | −0.0622043 | + | 0.176117i | ||||
\(851\) | −44.0931 | − | 44.0931i | −1.51149 | − | 1.51149i | ||||
\(852\) | 9.89859 | − | 1.05675i | 0.339120 | − | 0.0362035i | ||||
\(853\) | 25.9771 | − | 25.9771i | 0.889439 | − | 0.889439i | −0.105030 | − | 0.994469i | \(-0.533494\pi\) |
0.994469 | + | 0.105030i | \(0.0334938\pi\) | |||||||
\(854\) | −18.4752 | + | 8.83076i | −0.632208 | + | 0.302182i | ||||
\(855\) | − | 2.89483i | − | 0.0990010i | ||||||
\(856\) | 26.8051 | + | 6.36587i | 0.916181 | + | 0.217581i | ||||
\(857\) | 26.4386i | 0.903126i | 0.892239 | + | 0.451563i | \(0.149133\pi\) | ||||
−0.892239 | + | 0.451563i | \(0.850867\pi\) | |||||||
\(858\) | 2.81788 | + | 5.89540i | 0.0962008 | + | 0.201266i | ||||
\(859\) | 16.9656 | − | 16.9656i | 0.578860 | − | 0.578860i | −0.355729 | − | 0.934589i | \(-0.615768\pi\) |
0.934589 | + | 0.355729i | \(0.115768\pi\) | |||||||
\(860\) | 1.57009 | − | 1.94540i | 0.0535398 | − | 0.0663375i | ||||
\(861\) | 3.04261 | + | 3.04261i | 0.103692 | + | 0.103692i | ||||
\(862\) | 34.0056 | + | 12.0107i | 1.15823 | + | 0.409087i | ||||
\(863\) | 35.3210 | 1.20234 | 0.601171 | − | 0.799121i | \(-0.294701\pi\) | ||||
0.601171 | + | 0.799121i | \(0.294701\pi\) | |||||||
\(864\) | −3.46199 | − | 4.47377i | −0.117779 | − | 0.152201i | ||||
\(865\) | −51.5886 | −1.75406 | ||||||||
\(866\) | 51.0891 | + | 18.0446i | 1.73608 | + | 0.613181i | ||||
\(867\) | 10.9164 | + | 10.9164i | 0.370741 | + | 0.370741i | ||||
\(868\) | −13.5901 | + | 16.8385i | −0.461277 | + | 0.571537i | ||||
\(869\) | 18.8420 | − | 18.8420i | 0.639171 | − | 0.639171i | ||||
\(870\) | −3.13213 | − | 6.55285i | −0.106189 | − | 0.222162i | ||||
\(871\) | 7.66833i | 0.259831i | ||||||||
\(872\) | 13.0527 | − | 54.9616i | 0.442019 | − | 1.86123i | ||||
\(873\) | − | 8.40145i | − | 0.284346i | ||||||
\(874\) | 10.6398 | − | 5.08558i | 0.359895 | − | 0.172022i | ||||
\(875\) | 3.85720 | − | 3.85720i | 0.130397 | − | 0.130397i | ||||
\(876\) | −19.3966 | + | 2.07073i | −0.655351 | + | 0.0699634i | ||||
\(877\) | −18.3579 | − | 18.3579i | −0.619902 | − | 0.619902i | 0.325604 | − | 0.945506i | \(-0.394432\pi\) |
−0.945506 | + | 0.325604i | \(0.894432\pi\) | |||||||
\(878\) | 7.13554 | − | 20.2026i | 0.240813 | − | 0.681804i | ||||
\(879\) | 14.8746 | 0.501708 | ||||||||
\(880\) | 18.8620 | − | 4.07373i | 0.635837 | − | 0.137325i | ||||
\(881\) | −26.3703 | −0.888438 | −0.444219 | − | 0.895918i | \(-0.646519\pi\) | ||||
−0.444219 | + | 0.895918i | \(0.646519\pi\) | |||||||
\(882\) | −0.470984 | + | 1.33348i | −0.0158589 | + | 0.0449007i | ||||
\(883\) | −1.91831 | − | 1.91831i | −0.0645564 | − | 0.0645564i | 0.674091 | − | 0.738648i | \(-0.264535\pi\) |
−0.738648 | + | 0.674091i | \(0.764535\pi\) | |||||||
\(884\) | 0.722390 | + | 6.76667i | 0.0242966 | + | 0.227588i | ||||
\(885\) | 29.2032 | − | 29.2032i | 0.981656 | − | 0.981656i | ||||
\(886\) | 5.02355 | − | 2.40115i | 0.168769 | − | 0.0806683i | ||||
\(887\) | − | 44.2379i | − | 1.48536i | −0.669644 | − | 0.742682i | \(-0.733553\pi\) | ||
0.669644 | − | 0.742682i | \(-0.266447\pi\) | |||||||
\(888\) | 11.2989 | + | 18.3371i | 0.379168 | + | 0.615354i | ||||
\(889\) | − | 14.8202i | − | 0.497053i | ||||||
\(890\) | 4.97045 | + | 10.3989i | 0.166610 | + | 0.348572i | ||||
\(891\) | −1.19999 | + | 1.19999i | −0.0402011 | + | 0.0402011i | ||||
\(892\) | −9.80238 | − | 7.91132i | −0.328208 | − | 0.264890i | ||||
\(893\) | −4.39814 | − | 4.39814i | −0.147178 | − | 0.147178i | ||||
\(894\) | −0.262483 | − | 0.0927088i | −0.00877875 | − | 0.00310065i | ||||
\(895\) | 64.6714 | 2.16173 | ||||||||
\(896\) | −7.83467 | − | 8.16199i | −0.261738 | − | 0.272673i | ||||
\(897\) | −22.2945 | −0.744393 | ||||||||
\(898\) | −22.6944 | − | 8.01564i | −0.757322 | − | 0.267486i | ||||
\(899\) | 13.8211 | + | 13.8211i | 0.460961 | + | 0.460961i | ||||
\(900\) | 4.79526 | + | 3.87017i | 0.159842 | + | 0.129006i | ||||
\(901\) | −1.68653 | + | 1.68653i | −0.0561865 | + | 0.0561865i | ||||
\(902\) | 4.45344 | + | 9.31723i | 0.148283 | + | 0.310230i | ||||
\(903\) | 0.439710i | 0.0146326i | ||||||||
\(904\) | 11.0593 | + | 17.9481i | 0.367826 | + | 0.596946i | ||||
\(905\) | 20.6576i | 0.686682i | ||||||||
\(906\) | 11.5476 | − | 5.51951i | 0.383643 | − | 0.183374i | ||||
\(907\) | 5.39604 | − | 5.39604i | 0.179173 | − | 0.179173i | −0.611822 | − | 0.790995i | \(-0.709563\pi\) |
0.790995 | + | 0.611822i | \(0.209563\pi\) | |||||||
\(908\) | 5.34792 | + | 50.0942i | 0.177477 | + | 1.66244i | ||||
\(909\) | −7.84089 | − | 7.84089i | −0.260066 | − | 0.260066i | ||||
\(910\) | −3.64527 | + | 10.3207i | −0.120840 | + | 0.342129i | ||||
\(911\) | 26.8905 | 0.890924 | 0.445462 | − | 0.895301i | \(-0.353040\pi\) | ||||
0.445462 | + | 0.895301i | \(0.353040\pi\) | |||||||
\(912\) | −3.98151 | + | 0.859909i | −0.131841 | + | 0.0284744i | ||||
\(913\) | 8.48526 | 0.280821 | ||||||||
\(914\) | −5.67987 | + | 16.0812i | −0.187873 | + | 0.531919i | ||||
\(915\) | −29.1055 | − | 29.1055i | −0.962199 | − | 0.962199i | ||||
\(916\) | 3.24093 | − | 0.345992i | 0.107083 | − | 0.0114319i | ||||
\(917\) | −2.59589 | + | 2.59589i | −0.0857238 | + | 0.0857238i | ||||
\(918\) | −1.59460 | + | 0.762185i | −0.0526296 | + | 0.0251559i | ||||
\(919\) | − | 33.9472i | − | 1.11981i | −0.828555 | − | 0.559907i | \(-0.810837\pi\) | ||
0.828555 | − | 0.559907i | \(-0.189163\pi\) | |||||||
\(920\) | −15.2131 | + | 64.0585i | −0.501560 | + | 2.11195i | ||||
\(921\) | − | 17.7988i | − | 0.586490i | ||||||
\(922\) | −4.93904 | − | 10.3332i | −0.162659 | − | 0.340305i | ||||
\(923\) | −9.58246 | + | 9.58246i | −0.315411 | + | 0.315411i | ||||
\(924\) | −2.13165 | + | 2.64118i | −0.0701261 | + | 0.0868885i | ||||
\(925\) | −16.5907 | − | 16.5907i | −0.545500 | − | 0.545500i | ||||
\(926\) | 47.9036 | + | 16.9195i | 1.57421 | + | 0.556009i | ||||
\(927\) | −4.47471 | −0.146969 | ||||||||
\(928\) | −8.08231 | + | 6.25441i | −0.265315 | + | 0.205311i | ||||
\(929\) | −19.8940 | −0.652700 | −0.326350 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326350 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(930\) | −41.0129 | − | 14.4857i | −1.34486 | − | 0.475005i | ||||
\(931\) | 0.720066 | + | 0.720066i | 0.0235992 | + | 0.0235992i | ||||
\(932\) | −14.7417 | + | 18.2654i | −0.482880 | + | 0.598304i | ||||
\(933\) | 5.15769 | − | 5.15769i | 0.168855 | − | 0.168855i | ||||
\(934\) | −0.330365 | − | 0.691171i | −0.0108099 | − | 0.0226158i | ||||
\(935\) | − | 6.02899i | − | 0.197169i | ||||||
\(936\) | 7.49236 | + | 1.77934i | 0.244896 | + | 0.0581595i | ||||
\(937\) | 7.81612i | 0.255341i | 0.991817 | + | 0.127671i | \(0.0407501\pi\) | ||||
−0.991817 | + | 0.127671i | \(0.959250\pi\) | |||||||
\(938\) | −3.59374 | + | 1.71773i | −0.117340 | + | 0.0560859i | ||||
\(939\) | 12.5011 | − | 12.5011i | 0.407960 | − | 0.407960i | ||||
\(940\) | 34.5304 | − | 3.68637i | 1.12626 | − | 0.120236i | ||||
\(941\) | −9.80534 | − | 9.80534i | −0.319645 | − | 0.319645i | 0.528986 | − | 0.848631i | \(-0.322573\pi\) |
−0.848631 | + | 0.528986i | \(0.822573\pi\) | |||||||
\(942\) | −6.50251 | + | 18.4103i | −0.211863 | + | 0.599841i | ||||
\(943\) | −35.2348 | −1.14740 | ||||||||
\(944\) | −48.8406 | − | 31.4909i | −1.58963 | − | 1.02494i | ||||
\(945\) | −2.84273 | −0.0924739 | ||||||||
\(946\) | −0.351451 | + | 0.995052i | −0.0114267 | + | 0.0323519i | ||||
\(947\) | 4.80786 | + | 4.80786i | 0.156235 | + | 0.156235i | 0.780896 | − | 0.624661i | \(-0.214763\pi\) |
−0.624661 | + | 0.780896i | \(0.714763\pi\) | |||||||
\(948\) | −3.33363 | − | 31.2262i | −0.108271 | − | 1.01418i | ||||
\(949\) | 18.7772 | − | 18.7772i | 0.609532 | − | 0.609532i | ||||
\(950\) | 4.00338 | − | 1.91353i | 0.129887 | − | 0.0620832i | ||||
\(951\) | 24.2909i | 0.787686i | ||||||||
\(952\) | −3.00936 | + | 1.85430i | −0.0975339 | + | 0.0600983i | ||||
\(953\) | − | 23.2445i | − | 0.752963i | −0.926424 | − | 0.376482i | \(-0.877134\pi\) | ||
0.926424 | − | 0.376482i | \(-0.122866\pi\) | |||||||
\(954\) | 1.16395 | + | 2.43515i | 0.0376843 | + | 0.0788409i | ||||
\(955\) | 43.9683 | − | 43.9683i | 1.42278 | − | 1.42278i | ||||
\(956\) | −24.0858 | − | 19.4392i | −0.778989 | − | 0.628708i | ||||
\(957\) | 2.16789 | + | 2.16789i | 0.0700780 | + | 0.0700780i | ||||
\(958\) | −54.3228 | − | 19.1867i | −1.75509 | − | 0.619896i | ||||
\(959\) | 4.13193 | 0.133427 | ||||||||
\(960\) | 10.2251 | − | 20.3135i | 0.330013 | − | 0.655615i | ||||
\(961\) | 86.0565 | 2.77602 | ||||||||
\(962\) | −27.6471 | − | 9.76494i | −0.891379 | − | 0.314834i | ||||
\(963\) | −6.88767 | − | 6.88767i | −0.221952 | − | 0.221952i | ||||
\(964\) | −26.9406 | − | 21.7432i | −0.867698 | − | 0.700303i | ||||
\(965\) | −9.10996 | + | 9.10996i | −0.293260 | + | 0.293260i | ||||
\(966\) | −4.99405 | − | 10.4483i | −0.160681 | − | 0.336167i | ||||
\(967\) | − | 26.3657i | − | 0.847865i | −0.905694 | − | 0.423932i | \(-0.860649\pi\) | ||
0.905694 | − | 0.423932i | \(-0.139351\pi\) | |||||||
\(968\) | 19.5531 | − | 12.0482i | 0.628461 | − | 0.387244i | ||||
\(969\) | 1.27264i | 0.0408830i | ||||||||
\(970\) | 30.4736 | − | 14.5657i | 0.978448 | − | 0.467678i | ||||
\(971\) | 6.90103 | − | 6.90103i | 0.221464 | − | 0.221464i | −0.587650 | − | 0.809115i | \(-0.699947\pi\) |
0.809115 | + | 0.587650i | \(0.199947\pi\) | |||||||
\(972\) | 0.212308 | + | 1.98870i | 0.00680978 | + | 0.0637876i | ||||
\(973\) | −5.21659 | − | 5.21659i | −0.167236 | − | 0.167236i | ||||
\(974\) | 8.12345 | − | 22.9996i | 0.260292 | − | 0.736956i | ||||
\(975\) | −8.38868 | −0.268653 | ||||||||
\(976\) | −31.3856 | + | 48.6772i | −1.00463 | + | 1.55812i | ||||
\(977\) | −51.4493 | −1.64601 | −0.823004 | − | 0.568035i | \(-0.807704\pi\) | ||||
−0.823004 | + | 0.568035i | \(0.807704\pi\) | |||||||
\(978\) | 3.68319 | − | 10.4281i | 0.117775 | − | 0.333453i | ||||
\(979\) | −3.44029 | − | 3.44029i | −0.109952 | − | 0.109952i | ||||
\(980\) | −5.65333 | + | 0.603534i | −0.180589 | + | 0.0192792i | ||||
\(981\) | −14.1226 | + | 14.1226i | −0.450898 | + | 0.450898i | ||||
\(982\) | 22.6358 | − | 10.8194i | 0.722338 | − | 0.345262i | ||||
\(983\) | − | 15.4509i | − | 0.492807i | −0.969167 | − | 0.246403i | \(-0.920751\pi\) | ||
0.969167 | − | 0.246403i | \(-0.0792488\pi\) | |||||||
\(984\) | 11.8411 | + | 2.81211i | 0.377480 | + | 0.0896467i | ||||
\(985\) | − | 68.3055i | − | 2.17639i | ||||||
\(986\) | 1.37696 | + | 2.88080i | 0.0438514 | + | 0.0917432i | ||||
\(987\) | −4.31899 | + | 4.31899i | −0.137475 | + | 0.137475i | ||||
\(988\) | 3.48256 | − | 4.31501i | 0.110795 | − | 0.137279i | ||||
\(989\) | −2.54602 | − | 2.54602i | −0.0809588 | − | 0.0809588i | ||||
\(990\) | −6.43301 | − | 2.27213i | −0.204454 | − | 0.0722131i | ||||
\(991\) | 19.5894 | 0.622279 | 0.311140 | − | 0.950364i | \(-0.399289\pi\) | ||||
0.311140 | + | 0.950364i | \(0.399289\pi\) | |||||||
\(992\) | −7.74056 | + | 60.7115i | −0.245763 | + | 1.92759i | ||||
\(993\) | 1.76154 | 0.0559007 | ||||||||
\(994\) | −6.63730 | − | 2.34429i | −0.210522 | − | 0.0743563i | ||||
\(995\) | 9.31440 | + | 9.31440i | 0.295286 | + | 0.295286i | ||||
\(996\) | 6.28054 | − | 7.78180i | 0.199007 | − | 0.246576i | ||||
\(997\) | 30.4417 | − | 30.4417i | 0.964097 | − | 0.964097i | −0.0352807 | − | 0.999377i | \(-0.511233\pi\) |
0.999377 | + | 0.0352807i | \(0.0112325\pi\) | |||||||
\(998\) | 7.38501 | + | 15.4505i | 0.233768 | + | 0.489077i | ||||
\(999\) | − | 7.61509i | − | 0.240931i |
(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 | 336.2.w.a.253.1 | yes | 20 | |
4.3 | odd | 2 | 1344.2.w.a.337.10 | 20 | |||
8.3 | odd | 2 | 2688.2.w.b.673.1 | 20 | |||
8.5 | even | 2 | 2688.2.w.a.673.6 | 20 | |||
16.3 | odd | 4 | 2688.2.w.b.2017.1 | 20 | |||
16.5 | even | 4 | inner | 336.2.w.a.85.1 | ✓ | 20 | |
16.11 | odd | 4 | 1344.2.w.a.1009.10 | 20 | |||
16.13 | even | 4 | 2688.2.w.a.2017.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.w.a.85.1 | ✓ | 20 | 16.5 | even | 4 | inner | |
336.2.w.a.253.1 | yes | 20 | 1.1 | even | 1 | trivial | |
1344.2.w.a.337.10 | 20 | 4.3 | odd | 2 | |||
1344.2.w.a.1009.10 | 20 | 16.11 | odd | 4 | |||
2688.2.w.a.673.6 | 20 | 8.5 | even | 2 | |||
2688.2.w.a.2017.6 | 20 | 16.13 | even | 4 | |||
2688.2.w.b.673.1 | 20 | 8.3 | odd | 2 | |||
2688.2.w.b.2017.1 | 20 | 16.3 | odd | 4 |