Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.6 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.b.91.5 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32949 | + | 0.482147i | −0.940089 | + | 0.340929i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.53507 | − | 1.28202i | 0.767534 | − | 0.641008i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.482147 | + | 1.32949i | 0.196836 | + | 0.542761i | ||||
\(7\) | 4.27008 | 1.61394 | 0.806968 | − | 0.590595i | \(-0.201107\pi\) | ||||
0.806968 | + | 0.590595i | \(0.201107\pi\) | |||||||
\(8\) | −1.42273 | + | 2.44455i | −0.503012 | + | 0.864280i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.482147 | − | 1.32949i | −0.152468 | − | 0.420421i | ||||
\(11\) | 6.33992 | 1.91156 | 0.955779 | − | 0.294085i | \(-0.0950148\pi\) | ||||
0.955779 | + | 0.294085i | \(0.0950148\pi\) | |||||||
\(12\) | −1.28202 | − | 1.53507i | −0.370086 | − | 0.443136i | ||||
\(13\) | 5.06818 | 1.40566 | 0.702829 | − | 0.711358i | \(-0.251920\pi\) | ||||
0.702829 | + | 0.711358i | \(0.251920\pi\) | |||||||
\(14\) | −5.67701 | + | 2.05880i | −1.51724 | + | 0.550239i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0.712870 | − | 3.93596i | 0.178217 | − | 0.983991i | ||||
\(17\) | 2.28607i | 0.554454i | 0.960804 | + | 0.277227i | \(0.0894153\pi\) | ||||
−0.960804 | + | 0.277227i | \(0.910585\pi\) | |||||||
\(18\) | 1.32949 | − | 0.482147i | 0.313363 | − | 0.113643i | ||||
\(19\) | 2.14696 | 0.492546 | 0.246273 | − | 0.969200i | \(-0.420794\pi\) | ||||
0.246273 | + | 0.969200i | \(0.420794\pi\) | |||||||
\(20\) | 1.28202 | + | 1.53507i | 0.286667 | + | 0.343252i | ||||
\(21\) | − | 4.27008i | − | 0.931807i | ||||||
\(22\) | −8.42884 | + | 3.05678i | −1.79704 | + | 0.651707i | ||||
\(23\) | −4.21933 | − | 2.27976i | −0.879790 | − | 0.475362i | ||||
\(24\) | 2.44455 | + | 1.42273i | 0.498992 | + | 0.290414i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −6.73807 | + | 2.44361i | −1.32144 | + | 0.479231i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 6.55486 | − | 5.47430i | 1.23875 | − | 1.03455i | ||||
\(29\) | −0.184440 | −0.0342497 | −0.0171249 | − | 0.999853i | \(-0.505451\pi\) | ||||
−0.0171249 | + | 0.999853i | \(0.505451\pi\) | |||||||
\(30\) | −1.32949 | + | 0.482147i | −0.242730 | + | 0.0880276i | ||||
\(31\) | 6.08631i | 1.09313i | 0.837415 | + | 0.546567i | \(0.184066\pi\) | ||||
−0.837415 | + | 0.546567i | \(0.815934\pi\) | |||||||
\(32\) | 0.949963 | + | 5.57652i | 0.167931 | + | 0.985799i | ||||
\(33\) | − | 6.33992i | − | 1.10364i | ||||||
\(34\) | −1.10222 | − | 3.03930i | −0.189030 | − | 0.521236i | ||||
\(35\) | 4.27008i | 0.721774i | ||||||||
\(36\) | −1.53507 | + | 1.28202i | −0.255845 | + | 0.213669i | ||||
\(37\) | 0.639401i | 0.105117i | 0.998618 | + | 0.0525584i | \(0.0167376\pi\) | ||||
−0.998618 | + | 0.0525584i | \(0.983262\pi\) | |||||||
\(38\) | −2.85435 | + | 1.03515i | −0.463037 | + | 0.167924i | ||||
\(39\) | − | 5.06818i | − | 0.811558i | ||||||
\(40\) | −2.44455 | − | 1.42273i | −0.386518 | − | 0.224954i | ||||
\(41\) | −9.20080 | −1.43692 | −0.718462 | − | 0.695566i | \(-0.755154\pi\) | ||||
−0.718462 | + | 0.695566i | \(0.755154\pi\) | |||||||
\(42\) | 2.05880 | + | 5.67701i | 0.317680 | + | 0.875981i | ||||
\(43\) | −5.56828 | −0.849155 | −0.424578 | − | 0.905392i | \(-0.639577\pi\) | ||||
−0.424578 | + | 0.905392i | \(0.639577\pi\) | |||||||
\(44\) | 9.73221 | − | 8.12788i | 1.46719 | − | 1.22532i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 6.70871 | + | 0.996570i | 0.989146 | + | 0.146936i | ||||
\(47\) | 13.4174i | 1.95713i | 0.205942 | + | 0.978564i | \(0.433974\pi\) | ||||
−0.205942 | + | 0.978564i | \(0.566026\pi\) | |||||||
\(48\) | −3.93596 | − | 0.712870i | −0.568108 | − | 0.102894i | ||||
\(49\) | 11.2335 | 1.60479 | ||||||||
\(50\) | 1.32949 | − | 0.482147i | 0.188018 | − | 0.0681859i | ||||
\(51\) | 2.28607 | 0.320114 | ||||||||
\(52\) | 7.78000 | − | 6.49748i | 1.07889 | − | 0.901039i | ||||
\(53\) | 1.68353i | 0.231251i | 0.993293 | + | 0.115626i | \(0.0368873\pi\) | ||||
−0.993293 | + | 0.115626i | \(0.963113\pi\) | |||||||
\(54\) | −0.482147 | − | 1.32949i | −0.0656119 | − | 0.180920i | ||||
\(55\) | 6.33992i | 0.854875i | ||||||||
\(56\) | −6.07517 | + | 10.4384i | −0.811829 | + | 1.39489i | ||||
\(57\) | − | 2.14696i | − | 0.284372i | ||||||
\(58\) | 0.245211 | − | 0.0889274i | 0.0321978 | − | 0.0116767i | ||||
\(59\) | 6.99605i | 0.910808i | 0.890285 | + | 0.455404i | \(0.150505\pi\) | ||||
−0.890285 | + | 0.455404i | \(0.849495\pi\) | |||||||
\(60\) | 1.53507 | − | 1.28202i | 0.198176 | − | 0.165508i | ||||
\(61\) | − | 10.7249i | − | 1.37319i | −0.727041 | − | 0.686594i | \(-0.759105\pi\) | ||
0.727041 | − | 0.686594i | \(-0.240895\pi\) | |||||||
\(62\) | −2.93450 | − | 8.09167i | −0.372682 | − | 1.02764i | ||||
\(63\) | −4.27008 | −0.537979 | ||||||||
\(64\) | −3.95167 | − | 6.95589i | −0.493958 | − | 0.869486i | ||||
\(65\) | 5.06818i | 0.628630i | ||||||||
\(66\) | 3.05678 | + | 8.42884i | 0.376263 | + | 1.03752i | ||||
\(67\) | −11.6198 | −1.41959 | −0.709795 | − | 0.704409i | \(-0.751212\pi\) | ||||
−0.709795 | + | 0.704409i | \(0.751212\pi\) | |||||||
\(68\) | 2.93078 | + | 3.50928i | 0.355409 | + | 0.425562i | ||||
\(69\) | −2.27976 | + | 4.21933i | −0.274450 | + | 0.507947i | ||||
\(70\) | −2.05880 | − | 5.67701i | −0.246074 | − | 0.678532i | ||||
\(71\) | − | 14.8246i | − | 1.75936i | −0.475569 | − | 0.879678i | \(-0.657758\pi\) | ||
0.475569 | − | 0.879678i | \(-0.342242\pi\) | |||||||
\(72\) | 1.42273 | − | 2.44455i | 0.167671 | − | 0.288093i | ||||
\(73\) | 4.06642 | 0.475938 | 0.237969 | − | 0.971273i | \(-0.423518\pi\) | ||||
0.237969 | + | 0.971273i | \(0.423518\pi\) | |||||||
\(74\) | −0.308285 | − | 0.850075i | −0.0358374 | − | 0.0988192i | ||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 3.29573 | − | 2.75244i | 0.378046 | − | 0.315726i | ||||
\(77\) | 27.0719 | 3.08513 | ||||||||
\(78\) | 2.44361 | + | 6.73807i | 0.276684 | + | 0.762936i | ||||
\(79\) | −3.65467 | −0.411182 | −0.205591 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205591 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(80\) | 3.93596 | + | 0.712870i | 0.440054 | + | 0.0797013i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.2323 | − | 4.43614i | 1.35084 | − | 0.489890i | ||||
\(83\) | −1.98859 | −0.218276 | −0.109138 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109138 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(84\) | −5.47430 | − | 6.55486i | −0.597296 | − | 0.715194i | ||||
\(85\) | −2.28607 | −0.247959 | ||||||||
\(86\) | 7.40296 | − | 2.68473i | 0.798281 | − | 0.289502i | ||||
\(87\) | 0.184440i | 0.0197741i | ||||||||
\(88\) | −9.02001 | + | 15.4983i | −0.961537 | + | 1.65212i | ||||
\(89\) | − | 13.1874i | − | 1.39786i | −0.715191 | − | 0.698930i | \(-0.753660\pi\) | ||
0.715191 | − | 0.698930i | \(-0.246340\pi\) | |||||||
\(90\) | 0.482147 | + | 1.32949i | 0.0508228 | + | 0.140140i | ||||
\(91\) | 21.6415 | 2.26864 | ||||||||
\(92\) | −9.39964 | + | 1.90966i | −0.979980 | + | 0.199096i | ||||
\(93\) | 6.08631 | 0.631121 | ||||||||
\(94\) | −6.46916 | − | 17.8382i | −0.667243 | − | 1.83987i | ||||
\(95\) | 2.14696i | 0.220273i | ||||||||
\(96\) | 5.57652 | − | 0.949963i | 0.569151 | − | 0.0969552i | ||||
\(97\) | 8.73755i | 0.887164i | 0.896234 | + | 0.443582i | \(0.146293\pi\) | ||||
−0.896234 | + | 0.443582i | \(0.853707\pi\) | |||||||
\(98\) | −14.9348 | + | 5.41622i | −1.50865 | + | 0.547121i | ||||
\(99\) | −6.33992 | −0.637186 | ||||||||
\(100\) | −1.53507 | + | 1.28202i | −0.153507 | + | 0.128202i | ||||
\(101\) | −1.23440 | −0.122827 | −0.0614135 | − | 0.998112i | \(-0.519561\pi\) | ||||
−0.0614135 | + | 0.998112i | \(0.519561\pi\) | |||||||
\(102\) | −3.03930 | + | 1.10222i | −0.300936 | + | 0.109136i | ||||
\(103\) | −5.53812 | −0.545687 | −0.272844 | − | 0.962058i | \(-0.587964\pi\) | ||||
−0.272844 | + | 0.962058i | \(0.587964\pi\) | |||||||
\(104\) | −7.21066 | + | 12.3894i | −0.707063 | + | 1.21488i | ||||
\(105\) | 4.27008 | 0.416717 | ||||||||
\(106\) | −0.811711 | − | 2.23824i | −0.0788403 | − | 0.217397i | ||||
\(107\) | 8.82985 | 0.853614 | 0.426807 | − | 0.904343i | \(-0.359638\pi\) | ||||
0.426807 | + | 0.904343i | \(0.359638\pi\) | |||||||
\(108\) | 1.28202 | + | 1.53507i | 0.123362 | + | 0.147712i | ||||
\(109\) | − | 13.7436i | − | 1.31640i | −0.752843 | − | 0.658200i | \(-0.771318\pi\) | ||
0.752843 | − | 0.658200i | \(-0.228682\pi\) | |||||||
\(110\) | −3.05678 | − | 8.42884i | −0.291452 | − | 0.803658i | ||||
\(111\) | 0.639401 | 0.0606892 | ||||||||
\(112\) | 3.04401 | − | 16.8069i | 0.287632 | − | 1.58810i | ||||
\(113\) | − | 9.28660i | − | 0.873610i | −0.899556 | − | 0.436805i | \(-0.856110\pi\) | ||
0.899556 | − | 0.436805i | \(-0.143890\pi\) | |||||||
\(114\) | 1.03515 | + | 2.85435i | 0.0969507 | + | 0.267335i | ||||
\(115\) | 2.27976 | − | 4.21933i | 0.212588 | − | 0.393454i | ||||
\(116\) | −0.283129 | + | 0.236456i | −0.0262878 | + | 0.0219543i | ||||
\(117\) | −5.06818 | −0.468553 | ||||||||
\(118\) | −3.37312 | − | 9.30115i | −0.310521 | − | 0.856240i | ||||
\(119\) | 9.76170i | 0.894853i | ||||||||
\(120\) | −1.42273 | + | 2.44455i | −0.129877 | + | 0.223156i | ||||
\(121\) | 29.1946 | 2.65406 | ||||||||
\(122\) | 5.17100 | + | 14.2587i | 0.468161 | + | 1.29092i | ||||
\(123\) | 9.20080i | 0.829609i | ||||||||
\(124\) | 7.80275 | + | 9.34291i | 0.700708 | + | 0.839018i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 5.67701 | − | 2.05880i | 0.505748 | − | 0.183413i | ||||
\(127\) | 1.34406i | 0.119266i | 0.998220 | + | 0.0596328i | \(0.0189930\pi\) | ||||
−0.998220 | + | 0.0596328i | \(0.981007\pi\) | |||||||
\(128\) | 8.60745 | + | 7.34247i | 0.760798 | + | 0.648989i | ||||
\(129\) | 5.56828i | 0.490260i | ||||||||
\(130\) | −2.44361 | − | 6.73807i | −0.214318 | − | 0.590968i | ||||
\(131\) | − | 4.08505i | − | 0.356913i | −0.983948 | − | 0.178456i | \(-0.942890\pi\) | ||
0.983948 | − | 0.178456i | \(-0.0571103\pi\) | |||||||
\(132\) | −8.12788 | − | 9.73221i | −0.707441 | − | 0.847081i | ||||
\(133\) | 9.16768 | 0.794939 | ||||||||
\(134\) | 15.4484 | − | 5.60247i | 1.33454 | − | 0.483980i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −5.58842 | − | 3.25247i | −0.479203 | − | 0.278897i | ||||
\(137\) | − | 4.20683i | − | 0.359413i | −0.983720 | − | 0.179707i | \(-0.942485\pi\) | ||
0.983720 | − | 0.179707i | \(-0.0575149\pi\) | |||||||
\(138\) | 0.996570 | − | 6.70871i | 0.0848337 | − | 0.571084i | ||||
\(139\) | 3.26694i | 0.277098i | 0.990356 | + | 0.138549i | \(0.0442439\pi\) | ||||
−0.990356 | + | 0.138549i | \(0.955756\pi\) | |||||||
\(140\) | 5.47430 | + | 6.55486i | 0.462663 | + | 0.553987i | ||||
\(141\) | 13.4174 | 1.12995 | ||||||||
\(142\) | 7.14764 | + | 19.7091i | 0.599817 | + | 1.65395i | ||||
\(143\) | 32.1318 | 2.68700 | ||||||||
\(144\) | −0.712870 | + | 3.93596i | −0.0594058 | + | 0.327997i | ||||
\(145\) | − | 0.184440i | − | 0.0153169i | ||||||
\(146\) | −5.40625 | + | 1.96061i | −0.447424 | + | 0.162261i | ||||
\(147\) | − | 11.2335i | − | 0.926527i | ||||||
\(148\) | 0.819722 | + | 0.981524i | 0.0673807 | + | 0.0806808i | ||||
\(149\) | 4.04197i | 0.331131i | 0.986199 | + | 0.165566i | \(0.0529450\pi\) | ||||
−0.986199 | + | 0.165566i | \(0.947055\pi\) | |||||||
\(150\) | −0.482147 | − | 1.32949i | −0.0393671 | − | 0.108552i | ||||
\(151\) | − | 13.1086i | − | 1.06676i | −0.845874 | − | 0.533382i | \(-0.820921\pi\) | ||
0.845874 | − | 0.533382i | \(-0.179079\pi\) | |||||||
\(152\) | −3.05455 | + | 5.24835i | −0.247757 | + | 0.425698i | ||||
\(153\) | − | 2.28607i | − | 0.184818i | ||||||
\(154\) | −35.9918 | + | 13.0527i | −2.90030 | + | 1.05181i | ||||
\(155\) | −6.08631 | −0.488864 | ||||||||
\(156\) | −6.49748 | − | 7.78000i | −0.520215 | − | 0.622898i | ||||
\(157\) | 5.45303i | 0.435200i | 0.976038 | + | 0.217600i | \(0.0698228\pi\) | ||||
−0.976038 | + | 0.217600i | \(0.930177\pi\) | |||||||
\(158\) | 4.85883 | − | 1.76209i | 0.386548 | − | 0.140184i | ||||
\(159\) | 1.68353 | 0.133513 | ||||||||
\(160\) | −5.57652 | + | 0.949963i | −0.440863 | + | 0.0751012i | ||||
\(161\) | −18.0168 | − | 9.73473i | −1.41993 | − | 0.767204i | ||||
\(162\) | −1.32949 | + | 0.482147i | −0.104454 | + | 0.0378811i | ||||
\(163\) | 11.4235i | 0.894754i | 0.894345 | + | 0.447377i | \(0.147642\pi\) | ||||
−0.894345 | + | 0.447377i | \(0.852358\pi\) | |||||||
\(164\) | −14.1239 | + | 11.7956i | −1.10289 | + | 0.921080i | ||||
\(165\) | 6.33992 | 0.493562 | ||||||||
\(166\) | 2.64380 | − | 0.958792i | 0.205199 | − | 0.0744167i | ||||
\(167\) | 20.6429i | 1.59739i | 0.601734 | + | 0.798697i | \(0.294477\pi\) | ||||
−0.601734 | + | 0.798697i | \(0.705523\pi\) | |||||||
\(168\) | 10.4384 | + | 6.07517i | 0.805342 | + | 0.468710i | ||||
\(169\) | 12.6864 | 0.975877 | ||||||||
\(170\) | 3.03930 | − | 1.10222i | 0.233104 | − | 0.0845366i | ||||
\(171\) | −2.14696 | −0.164182 | ||||||||
\(172\) | −8.54769 | + | 7.13863i | −0.651756 | + | 0.544315i | ||||
\(173\) | −5.69694 | −0.433131 | −0.216565 | − | 0.976268i | \(-0.569485\pi\) | ||||
−0.216565 | + | 0.976268i | \(0.569485\pi\) | |||||||
\(174\) | −0.0889274 | − | 0.245211i | −0.00674157 | − | 0.0185894i | ||||
\(175\) | −4.27008 | −0.322787 | ||||||||
\(176\) | 4.51954 | − | 24.9537i | 0.340673 | − | 1.88096i | ||||
\(177\) | 6.99605 | 0.525855 | ||||||||
\(178\) | 6.35825 | + | 17.5324i | 0.476571 | + | 1.31411i | ||||
\(179\) | 4.11047i | 0.307231i | 0.988131 | + | 0.153615i | \(0.0490917\pi\) | ||||
−0.988131 | + | 0.153615i | \(0.950908\pi\) | |||||||
\(180\) | −1.28202 | − | 1.53507i | −0.0955558 | − | 0.114417i | ||||
\(181\) | − | 11.3771i | − | 0.845655i | −0.906210 | − | 0.422827i | \(-0.861038\pi\) | ||
0.906210 | − | 0.422827i | \(-0.138962\pi\) | |||||||
\(182\) | −28.7721 | + | 10.4344i | −2.13273 | + | 0.773448i | ||||
\(183\) | −10.7249 | −0.792811 | ||||||||
\(184\) | 11.5760 | − | 7.07088i | 0.853391 | − | 0.521272i | ||||
\(185\) | −0.639401 | −0.0470097 | ||||||||
\(186\) | −8.09167 | + | 2.93450i | −0.593310 | + | 0.215168i | ||||
\(187\) | 14.4935i | 1.05987i | ||||||||
\(188\) | 17.2013 | + | 20.5966i | 1.25454 | + | 1.50216i | ||||
\(189\) | 4.27008i | 0.310602i | ||||||||
\(190\) | −1.03515 | − | 2.85435i | −0.0750977 | − | 0.207077i | ||||
\(191\) | 6.76632 | 0.489593 | 0.244797 | − | 0.969574i | \(-0.421279\pi\) | ||||
0.244797 | + | 0.969574i | \(0.421279\pi\) | |||||||
\(192\) | −6.95589 | + | 3.95167i | −0.501998 | + | 0.285187i | ||||
\(193\) | −22.6747 | −1.63216 | −0.816079 | − | 0.577941i | \(-0.803857\pi\) | ||||
−0.816079 | + | 0.577941i | \(0.803857\pi\) | |||||||
\(194\) | −4.21279 | − | 11.6165i | −0.302460 | − | 0.834013i | ||||
\(195\) | 5.06818 | 0.362940 | ||||||||
\(196\) | 17.2443 | − | 14.4016i | 1.23173 | − | 1.02868i | ||||
\(197\) | −18.6303 | −1.32735 | −0.663677 | − | 0.748019i | \(-0.731005\pi\) | ||||
−0.663677 | + | 0.748019i | \(0.731005\pi\) | |||||||
\(198\) | 8.42884 | − | 3.05678i | 0.599012 | − | 0.217236i | ||||
\(199\) | 8.02404 | 0.568809 | 0.284405 | − | 0.958704i | \(-0.408204\pi\) | ||||
0.284405 | + | 0.958704i | \(0.408204\pi\) | |||||||
\(200\) | 1.42273 | − | 2.44455i | 0.100602 | − | 0.172856i | ||||
\(201\) | 11.6198i | 0.819600i | ||||||||
\(202\) | 1.64111 | − | 0.595160i | 0.115468 | − | 0.0418753i | ||||
\(203\) | −0.787574 | −0.0552769 | ||||||||
\(204\) | 3.50928 | − | 2.93078i | 0.245698 | − | 0.205196i | ||||
\(205\) | − | 9.20080i | − | 0.642612i | ||||||
\(206\) | 7.36286 | − | 2.67019i | 0.512994 | − | 0.186041i | ||||
\(207\) | 4.21933 | + | 2.27976i | 0.293263 | + | 0.158454i | ||||
\(208\) | 3.61295 | − | 19.9482i | 0.250513 | − | 1.38316i | ||||
\(209\) | 13.6116 | 0.941531 | ||||||||
\(210\) | −5.67701 | + | 2.05880i | −0.391751 | + | 0.142071i | ||||
\(211\) | 19.6771i | 1.35463i | 0.735694 | + | 0.677314i | \(0.236856\pi\) | ||||
−0.735694 | + | 0.677314i | \(0.763144\pi\) | |||||||
\(212\) | 2.15832 | + | 2.58434i | 0.148234 | + | 0.177493i | ||||
\(213\) | −14.8246 | −1.01577 | ||||||||
\(214\) | −11.7392 | + | 4.25729i | −0.802473 | + | 0.291022i | ||||
\(215\) | − | 5.56828i | − | 0.379754i | ||||||
\(216\) | −2.44455 | − | 1.42273i | −0.166331 | − | 0.0968047i | ||||
\(217\) | 25.9890i | 1.76425i | ||||||||
\(218\) | 6.62644 | + | 18.2719i | 0.448799 | + | 1.23753i | ||||
\(219\) | − | 4.06642i | − | 0.274783i | ||||||
\(220\) | 8.12788 | + | 9.73221i | 0.547982 | + | 0.656146i | ||||
\(221\) | 11.5862i | 0.779373i | ||||||||
\(222\) | −0.850075 | + | 0.308285i | −0.0570533 | + | 0.0206908i | ||||
\(223\) | − | 21.7302i | − | 1.45516i | −0.686022 | − | 0.727581i | \(-0.740644\pi\) | ||
0.686022 | − | 0.727581i | \(-0.259356\pi\) | |||||||
\(224\) | 4.05641 | + | 23.8122i | 0.271031 | + | 1.59102i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.47751 | + | 12.3464i | 0.297839 | + | 0.821271i | ||||
\(227\) | −19.5294 | −1.29621 | −0.648106 | − | 0.761550i | \(-0.724438\pi\) | ||||
−0.648106 | + | 0.761550i | \(0.724438\pi\) | |||||||
\(228\) | −2.75244 | − | 3.29573i | −0.182285 | − | 0.218265i | ||||
\(229\) | 6.03097i | 0.398538i | 0.979945 | + | 0.199269i | \(0.0638567\pi\) | ||||
−0.979945 | + | 0.199269i | \(0.936143\pi\) | |||||||
\(230\) | −0.996570 | + | 6.70871i | −0.0657119 | + | 0.442360i | ||||
\(231\) | − | 27.0719i | − | 1.78120i | ||||||
\(232\) | 0.262409 | − | 0.450874i | 0.0172280 | − | 0.0296013i | ||||
\(233\) | 15.5780 | 1.02055 | 0.510275 | − | 0.860011i | \(-0.329544\pi\) | ||||
0.510275 | + | 0.860011i | \(0.329544\pi\) | |||||||
\(234\) | 6.73807 | − | 2.44361i | 0.440481 | − | 0.159744i | ||||
\(235\) | −13.4174 | −0.875254 | ||||||||
\(236\) | 8.96904 | + | 10.7394i | 0.583835 | + | 0.699076i | ||||
\(237\) | 3.65467i | 0.237396i | ||||||||
\(238\) | −4.70657 | − | 12.9780i | −0.305082 | − | 0.841241i | ||||
\(239\) | − | 29.6232i | − | 1.91616i | −0.286496 | − | 0.958081i | \(-0.592491\pi\) | ||
0.286496 | − | 0.958081i | \(-0.407509\pi\) | |||||||
\(240\) | 0.712870 | − | 3.93596i | 0.0460155 | − | 0.254065i | ||||
\(241\) | − | 1.02822i | − | 0.0662336i | −0.999451 | − | 0.0331168i | \(-0.989457\pi\) | ||
0.999451 | − | 0.0331168i | \(-0.0105433\pi\) | |||||||
\(242\) | −38.8139 | + | 14.0761i | −2.49505 | + | 0.904846i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −13.7496 | − | 16.4635i | −0.880225 | − | 1.05397i | ||||
\(245\) | 11.2335i | 0.717685i | ||||||||
\(246\) | −4.43614 | − | 12.2323i | −0.282838 | − | 0.779906i | ||||
\(247\) | 10.8812 | 0.692352 | ||||||||
\(248\) | −14.8783 | − | 8.65919i | −0.944773 | − | 0.549859i | ||||
\(249\) | 1.98859i | 0.126022i | ||||||||
\(250\) | 0.482147 | + | 1.32949i | 0.0304937 | + | 0.0840841i | ||||
\(251\) | 7.72202 | 0.487410 | 0.243705 | − | 0.969849i | \(-0.421637\pi\) | ||||
0.243705 | + | 0.969849i | \(0.421637\pi\) | |||||||
\(252\) | −6.55486 | + | 5.47430i | −0.412917 | + | 0.344849i | ||||
\(253\) | −26.7502 | − | 14.4535i | −1.68177 | − | 0.908683i | ||||
\(254\) | −0.648033 | − | 1.78690i | −0.0406612 | − | 0.112120i | ||||
\(255\) | 2.28607i | 0.143159i | ||||||||
\(256\) | −14.9836 | − | 5.61166i | −0.936477 | − | 0.350729i | ||||
\(257\) | 15.8364 | 0.987846 | 0.493923 | − | 0.869506i | \(-0.335563\pi\) | ||||
0.493923 | + | 0.869506i | \(0.335563\pi\) | |||||||
\(258\) | −2.68473 | − | 7.40296i | −0.167144 | − | 0.460888i | ||||
\(259\) | 2.73029i | 0.169652i | ||||||||
\(260\) | 6.49748 | + | 7.78000i | 0.402957 | + | 0.482495i | ||||
\(261\) | 0.184440 | 0.0114166 | ||||||||
\(262\) | 1.96960 | + | 5.43102i | 0.121682 | + | 0.335530i | ||||
\(263\) | 18.7282 | 1.15483 | 0.577414 | − | 0.816452i | \(-0.304062\pi\) | ||||
0.577414 | + | 0.816452i | \(0.304062\pi\) | |||||||
\(264\) | 15.4983 | + | 9.02001i | 0.953853 | + | 0.555143i | ||||
\(265\) | −1.68353 | −0.103419 | ||||||||
\(266\) | −12.1883 | + | 4.42017i | −0.747313 | + | 0.271018i | ||||
\(267\) | −13.1874 | −0.807054 | ||||||||
\(268\) | −17.8372 | + | 14.8968i | −1.08958 | + | 0.909968i | ||||
\(269\) | −7.39847 | −0.451093 | −0.225546 | − | 0.974232i | \(-0.572417\pi\) | ||||
−0.225546 | + | 0.974232i | \(0.572417\pi\) | |||||||
\(270\) | 1.32949 | − | 0.482147i | 0.0809100 | − | 0.0293425i | ||||
\(271\) | 6.22206i | 0.377963i | 0.981981 | + | 0.188982i | \(0.0605186\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(272\) | 8.99789 | + | 1.62967i | 0.545577 | + | 0.0988133i | ||||
\(273\) | − | 21.6415i | − | 1.30980i | ||||||
\(274\) | 2.02831 | + | 5.59292i | 0.122535 | + | 0.337880i | ||||
\(275\) | −6.33992 | −0.382312 | ||||||||
\(276\) | 1.90966 | + | 9.39964i | 0.114948 | + | 0.565792i | ||||
\(277\) | −11.9387 | −0.717326 | −0.358663 | − | 0.933467i | \(-0.616767\pi\) | ||||
−0.358663 | + | 0.933467i | \(0.616767\pi\) | |||||||
\(278\) | −1.57514 | − | 4.34335i | −0.0944709 | − | 0.260497i | ||||
\(279\) | − | 6.08631i | − | 0.364378i | ||||||
\(280\) | −10.4384 | − | 6.07517i | −0.623815 | − | 0.363061i | ||||
\(281\) | − | 28.3633i | − | 1.69201i | −0.533174 | − | 0.846006i | \(-0.679001\pi\) | ||
0.533174 | − | 0.846006i | \(-0.320999\pi\) | |||||||
\(282\) | −17.8382 | + | 6.46916i | −1.06225 | + | 0.385233i | ||||
\(283\) | 11.4358 | 0.679788 | 0.339894 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339894 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(284\) | −19.0054 | − | 22.7568i | −1.12776 | − | 1.35037i | ||||
\(285\) | 2.14696 | 0.127175 | ||||||||
\(286\) | −42.7188 | + | 15.4923i | −2.52602 | + | 0.916077i | ||||
\(287\) | −39.2881 | −2.31910 | ||||||||
\(288\) | −0.949963 | − | 5.57652i | −0.0559771 | − | 0.328600i | ||||
\(289\) | 11.7739 | 0.692581 | ||||||||
\(290\) | 0.0889274 | + | 0.245211i | 0.00522200 | + | 0.0143993i | ||||
\(291\) | 8.73755 | 0.512205 | ||||||||
\(292\) | 6.24223 | − | 5.21322i | 0.365299 | − | 0.305080i | ||||
\(293\) | − | 21.5790i | − | 1.26066i | −0.776327 | − | 0.630330i | \(-0.782920\pi\) | ||
0.776327 | − | 0.630330i | \(-0.217080\pi\) | |||||||
\(294\) | 5.41622 | + | 14.9348i | 0.315880 | + | 0.871018i | ||||
\(295\) | −6.99605 | −0.407326 | ||||||||
\(296\) | −1.56305 | − | 0.909696i | −0.0908504 | − | 0.0528750i | ||||
\(297\) | 6.33992i | 0.367880i | ||||||||
\(298\) | −1.94882 | − | 5.37375i | −0.112892 | − | 0.311293i | ||||
\(299\) | −21.3843 | − | 11.5542i | −1.23668 | − | 0.668197i | ||||
\(300\) | 1.28202 | + | 1.53507i | 0.0740172 | + | 0.0886272i | ||||
\(301\) | −23.7770 | −1.37048 | ||||||||
\(302\) | 6.32029 | + | 17.4277i | 0.363692 | + | 1.00285i | ||||
\(303\) | 1.23440i | 0.0709142i | ||||||||
\(304\) | 1.53050 | − | 8.45036i | 0.0877804 | − | 0.484661i | ||||
\(305\) | 10.7249 | 0.614109 | ||||||||
\(306\) | 1.10222 | + | 3.03930i | 0.0630099 | + | 0.173745i | ||||
\(307\) | − | 5.89225i | − | 0.336289i | −0.985762 | − | 0.168144i | \(-0.946223\pi\) | ||
0.985762 | − | 0.168144i | \(-0.0537775\pi\) | |||||||
\(308\) | 41.5573 | − | 34.7067i | 2.36795 | − | 1.97760i | ||||
\(309\) | 5.53812i | 0.315053i | ||||||||
\(310\) | 8.09167 | − | 2.93450i | 0.459576 | − | 0.166668i | ||||
\(311\) | − | 10.5498i | − | 0.598224i | −0.954218 | − | 0.299112i | \(-0.903310\pi\) | ||
0.954218 | − | 0.299112i | \(-0.0966905\pi\) | |||||||
\(312\) | 12.3894 | + | 7.21066i | 0.701413 | + | 0.408223i | ||||
\(313\) | − | 22.2836i | − | 1.25954i | −0.776781 | − | 0.629771i | \(-0.783149\pi\) | ||
0.776781 | − | 0.629771i | \(-0.216851\pi\) | |||||||
\(314\) | −2.62916 | − | 7.24974i | −0.148372 | − | 0.409126i | ||||
\(315\) | − | 4.27008i | − | 0.240591i | ||||||
\(316\) | −5.61017 | + | 4.68534i | −0.315597 | + | 0.263571i | ||||
\(317\) | 4.20644 | 0.236257 | 0.118129 | − | 0.992998i | \(-0.462310\pi\) | ||||
0.118129 | + | 0.992998i | \(0.462310\pi\) | |||||||
\(318\) | −2.23824 | + | 0.811711i | −0.125514 | + | 0.0455185i | ||||
\(319\) | −1.16934 | −0.0654703 | ||||||||
\(320\) | 6.95589 | − | 3.95167i | 0.388846 | − | 0.220905i | ||||
\(321\) | − | 8.82985i | − | 0.492834i | ||||||
\(322\) | 28.6467 | + | 4.25543i | 1.59642 | + | 0.237146i | ||||
\(323\) | 4.90810i | 0.273094i | ||||||||
\(324\) | 1.53507 | − | 1.28202i | 0.0852816 | − | 0.0712231i | ||||
\(325\) | −5.06818 | −0.281132 | ||||||||
\(326\) | −5.50779 | − | 15.1873i | −0.305048 | − | 0.841149i | ||||
\(327\) | −13.7436 | −0.760023 | ||||||||
\(328\) | 13.0903 | − | 22.4918i | 0.722790 | − | 1.24190i | ||||
\(329\) | 57.2933i | 3.15868i | ||||||||
\(330\) | −8.42884 | + | 3.05678i | −0.463992 | + | 0.168270i | ||||
\(331\) | 16.0620i | 0.882847i | 0.897299 | + | 0.441423i | \(0.145526\pi\) | ||||
−0.897299 | + | 0.441423i | \(0.854474\pi\) | |||||||
\(332\) | −3.05262 | + | 2.54940i | −0.167534 | + | 0.139917i | ||||
\(333\) | − | 0.639401i | − | 0.0350390i | ||||||
\(334\) | −9.95290 | − | 27.4444i | −0.544598 | − | 1.50169i | ||||
\(335\) | − | 11.6198i | − | 0.634860i | ||||||
\(336\) | −16.8069 | − | 3.04401i | −0.916890 | − | 0.166064i | ||||
\(337\) | 3.96429i | 0.215948i | 0.994154 | + | 0.107974i | \(0.0344364\pi\) | ||||
−0.994154 | + | 0.107974i | \(0.965564\pi\) | |||||||
\(338\) | −16.8664 | + | 6.11671i | −0.917411 | + | 0.332705i | ||||
\(339\) | −9.28660 | −0.504379 | ||||||||
\(340\) | −3.50928 | + | 2.93078i | −0.190317 | + | 0.158944i | ||||
\(341\) | 38.5868i | 2.08959i | ||||||||
\(342\) | 2.85435 | − | 1.03515i | 0.154346 | − | 0.0559745i | ||||
\(343\) | 18.0775 | 0.976096 | ||||||||
\(344\) | 7.92217 | − | 13.6120i | 0.427135 | − | 0.733907i | ||||
\(345\) | −4.21933 | − | 2.27976i | −0.227161 | − | 0.122738i | ||||
\(346\) | 7.57401 | − | 2.74677i | 0.407181 | − | 0.147667i | ||||
\(347\) | − | 7.81164i | − | 0.419351i | −0.977771 | − | 0.209675i | \(-0.932759\pi\) | ||
0.977771 | − | 0.209675i | \(-0.0672408\pi\) | |||||||
\(348\) | 0.236456 | + | 0.283129i | 0.0126753 | + | 0.0151773i | ||||
\(349\) | −33.4169 | −1.78876 | −0.894382 | − | 0.447305i | \(-0.852384\pi\) | ||||
−0.894382 | + | 0.447305i | \(0.852384\pi\) | |||||||
\(350\) | 5.67701 | − | 2.05880i | 0.303449 | − | 0.110048i | ||||
\(351\) | 5.06818i | 0.270519i | ||||||||
\(352\) | 6.02269 | + | 35.3547i | 0.321011 | + | 1.88441i | ||||
\(353\) | −0.0557663 | −0.00296814 | −0.00148407 | − | 0.999999i | \(-0.500472\pi\) | ||||
−0.00148407 | + | 0.999999i | \(0.500472\pi\) | |||||||
\(354\) | −9.30115 | + | 3.37312i | −0.494350 | + | 0.179279i | ||||
\(355\) | 14.8246 | 0.786808 | ||||||||
\(356\) | −16.9064 | − | 20.2435i | −0.896039 | − | 1.07290i | ||||
\(357\) | 9.76170 | 0.516644 | ||||||||
\(358\) | −1.98185 | − | 5.46481i | −0.104744 | − | 0.288824i | ||||
\(359\) | −10.1353 | −0.534923 | −0.267462 | − | 0.963569i | \(-0.586185\pi\) | ||||
−0.267462 | + | 0.963569i | \(0.586185\pi\) | |||||||
\(360\) | 2.44455 | + | 1.42273i | 0.128839 | + | 0.0749846i | ||||
\(361\) | −14.3906 | −0.757398 | ||||||||
\(362\) | 5.48545 | + | 15.1257i | 0.288309 | + | 0.794991i | ||||
\(363\) | − | 29.1946i | − | 1.53232i | ||||||
\(364\) | 33.2212 | − | 27.7447i | 1.74126 | − | 1.45422i | ||||
\(365\) | 4.06642i | 0.212846i | ||||||||
\(366\) | 14.2587 | − | 5.17100i | 0.745313 | − | 0.270293i | ||||
\(367\) | 26.4828 | 1.38239 | 0.691195 | − | 0.722668i | \(-0.257085\pi\) | ||||
0.691195 | + | 0.722668i | \(0.257085\pi\) | |||||||
\(368\) | −11.9809 | + | 14.9819i | −0.624546 | + | 0.780988i | ||||
\(369\) | 9.20080 | 0.478975 | ||||||||
\(370\) | 0.850075 | − | 0.308285i | 0.0441933 | − | 0.0160270i | ||||
\(371\) | 7.18881i | 0.373225i | ||||||||
\(372\) | 9.34291 | − | 7.80275i | 0.484407 | − | 0.404554i | ||||
\(373\) | − | 22.9313i | − | 1.18734i | −0.804710 | − | 0.593668i | \(-0.797679\pi\) | ||
0.804710 | − | 0.593668i | \(-0.202321\pi\) | |||||||
\(374\) | −6.98801 | − | 19.2689i | −0.361341 | − | 0.996373i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −32.7995 | − | 19.0894i | −1.69151 | − | 0.984459i | ||||
\(377\) | −0.934776 | −0.0481434 | ||||||||
\(378\) | −2.05880 | − | 5.67701i | −0.105893 | − | 0.291994i | ||||
\(379\) | 17.6902 | 0.908686 | 0.454343 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454343 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(380\) | 2.75244 | + | 3.29573i | 0.141197 | + | 0.169067i | ||||
\(381\) | 1.34406 | 0.0688581 | ||||||||
\(382\) | −8.99572 | + | 3.26236i | −0.460261 | + | 0.166917i | ||||
\(383\) | −34.2904 | −1.75216 | −0.876079 | − | 0.482167i | \(-0.839850\pi\) | ||||
−0.876079 | + | 0.482167i | \(0.839850\pi\) | |||||||
\(384\) | 7.34247 | − | 8.60745i | 0.374694 | − | 0.439247i | ||||
\(385\) | 27.0719i | 1.37971i | ||||||||
\(386\) | 30.1457 | − | 10.9325i | 1.53437 | − | 0.556451i | ||||
\(387\) | 5.56828 | 0.283052 | ||||||||
\(388\) | 11.2017 | + | 13.4127i | 0.568679 | + | 0.680929i | ||||
\(389\) | 0.380521i | 0.0192932i | 0.999953 | + | 0.00964660i | \(0.00307066\pi\) | ||||
−0.999953 | + | 0.00964660i | \(0.996929\pi\) | |||||||
\(390\) | −6.73807 | + | 2.44361i | −0.341195 | + | 0.123737i | ||||
\(391\) | 5.21169 | − | 9.64568i | 0.263566 | − | 0.487803i | ||||
\(392\) | −15.9823 | + | 27.4610i | −0.807229 | + | 1.38699i | ||||
\(393\) | −4.08505 | −0.206064 | ||||||||
\(394\) | 24.7687 | − | 8.98254i | 1.24783 | − | 0.452534i | ||||
\(395\) | − | 3.65467i | − | 0.183886i | ||||||
\(396\) | −9.73221 | + | 8.12788i | −0.489062 | + | 0.408441i | ||||
\(397\) | −13.1522 | −0.660089 | −0.330045 | − | 0.943965i | \(-0.607064\pi\) | ||||
−0.330045 | + | 0.943965i | \(0.607064\pi\) | |||||||
\(398\) | −10.6679 | + | 3.86877i | −0.534731 | + | 0.193924i | ||||
\(399\) | − | 9.16768i | − | 0.458958i | ||||||
\(400\) | −0.712870 | + | 3.93596i | −0.0356435 | + | 0.196798i | ||||
\(401\) | 7.17569i | 0.358337i | 0.983818 | + | 0.179169i | \(0.0573407\pi\) | ||||
−0.983818 | + | 0.179169i | \(0.942659\pi\) | |||||||
\(402\) | −5.60247 | − | 15.4484i | −0.279426 | − | 0.770497i | ||||
\(403\) | 30.8465i | 1.53657i | ||||||||
\(404\) | −1.89488 | + | 1.58252i | −0.0942739 | + | 0.0787331i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 1.04707 | − | 0.379727i | 0.0519652 | − | 0.0188455i | ||||
\(407\) | 4.05375i | 0.200937i | ||||||||
\(408\) | −3.25247 | + | 5.58842i | −0.161021 | + | 0.276668i | ||||
\(409\) | 0.900619 | 0.0445327 | 0.0222664 | − | 0.999752i | \(-0.492912\pi\) | ||||
0.0222664 | + | 0.999752i | \(0.492912\pi\) | |||||||
\(410\) | 4.43614 | + | 12.2323i | 0.219085 | + | 0.604112i | ||||
\(411\) | −4.20683 | −0.207507 | ||||||||
\(412\) | −8.50139 | + | 7.09996i | −0.418834 | + | 0.349790i | ||||
\(413\) | 29.8736i | 1.46999i | ||||||||
\(414\) | −6.70871 | − | 0.996570i | −0.329715 | − | 0.0489787i | ||||
\(415\) | − | 1.98859i | − | 0.0976160i | ||||||
\(416\) | 4.81458 | + | 28.2628i | 0.236054 | + | 1.38570i | ||||
\(417\) | 3.26694 | 0.159983 | ||||||||
\(418\) | −18.0964 | + | 6.56277i | −0.885123 | + | 0.320996i | ||||
\(419\) | −3.26664 | −0.159586 | −0.0797929 | − | 0.996811i | \(-0.525426\pi\) | ||||
−0.0797929 | + | 0.996811i | \(0.525426\pi\) | |||||||
\(420\) | 6.55486 | − | 5.47430i | 0.319844 | − | 0.267119i | ||||
\(421\) | 4.17945i | 0.203694i | 0.994800 | + | 0.101847i | \(0.0324752\pi\) | ||||
−0.994800 | + | 0.101847i | \(0.967525\pi\) | |||||||
\(422\) | −9.48726 | − | 26.1604i | −0.461833 | − | 1.27347i | ||||
\(423\) | − | 13.4174i | − | 0.652376i | ||||||
\(424\) | −4.11548 | − | 2.39522i | −0.199866 | − | 0.116322i | ||||
\(425\) | − | 2.28607i | − | 0.110891i | ||||||
\(426\) | 19.7091 | − | 7.14764i | 0.954909 | − | 0.346304i | ||||
\(427\) | − | 45.7963i | − | 2.21624i | ||||||
\(428\) | 13.5544 | − | 11.3200i | 0.655178 | − | 0.547173i | ||||
\(429\) | − | 32.1318i | − | 1.55134i | ||||||
\(430\) | 2.68473 | + | 7.40296i | 0.129469 | + | 0.357002i | ||||
\(431\) | −17.2005 | −0.828520 | −0.414260 | − | 0.910159i | \(-0.635960\pi\) | ||||
−0.414260 | + | 0.910159i | \(0.635960\pi\) | |||||||
\(432\) | 3.93596 | + | 0.712870i | 0.189369 | + | 0.0342980i | ||||
\(433\) | 16.2997i | 0.783313i | 0.920111 | + | 0.391657i | \(0.128098\pi\) | ||||
−0.920111 | + | 0.391657i | \(0.871902\pi\) | |||||||
\(434\) | −12.5305 | − | 34.5520i | −0.601485 | − | 1.65855i | ||||
\(435\) | −0.184440 | −0.00884324 | ||||||||
\(436\) | −17.6195 | − | 21.0974i | −0.843822 | − | 1.01038i | ||||
\(437\) | −9.05872 | − | 4.89455i | −0.433337 | − | 0.234138i | ||||
\(438\) | 1.96061 | + | 5.40625i | 0.0936817 | + | 0.258321i | ||||
\(439\) | 6.44669i | 0.307684i | 0.988095 | + | 0.153842i | \(0.0491647\pi\) | ||||
−0.988095 | + | 0.153842i | \(0.950835\pi\) | |||||||
\(440\) | −15.4983 | − | 9.02001i | −0.738851 | − | 0.430012i | ||||
\(441\) | −11.2335 | −0.534931 | ||||||||
\(442\) | −5.58626 | − | 15.4037i | −0.265711 | − | 0.732680i | ||||
\(443\) | − | 21.1812i | − | 1.00635i | −0.864185 | − | 0.503175i | \(-0.832165\pi\) | ||
0.864185 | − | 0.503175i | \(-0.167835\pi\) | |||||||
\(444\) | 0.981524 | − | 0.819722i | 0.0465811 | − | 0.0389023i | ||||
\(445\) | 13.1874 | 0.625142 | ||||||||
\(446\) | 10.4772 | + | 28.8900i | 0.496108 | + | 1.36798i | ||||
\(447\) | 4.04197 | 0.191179 | ||||||||
\(448\) | −16.8739 | − | 29.7022i | −0.797217 | − | 1.40329i | ||||
\(449\) | −10.8884 | −0.513855 | −0.256927 | − | 0.966431i | \(-0.582710\pi\) | ||||
−0.256927 | + | 0.966431i | \(0.582710\pi\) | |||||||
\(450\) | −1.32949 | + | 0.482147i | −0.0626726 | + | 0.0227286i | ||||
\(451\) | −58.3324 | −2.74676 | ||||||||
\(452\) | −11.9056 | − | 14.2556i | −0.559991 | − | 0.670526i | ||||
\(453\) | −13.1086 | −0.615897 | ||||||||
\(454\) | 25.9641 | − | 9.41604i | 1.21855 | − | 0.441917i | ||||
\(455\) | 21.6415i | 1.01457i | ||||||||
\(456\) | 5.24835 | + | 3.05455i | 0.245777 | + | 0.143042i | ||||
\(457\) | − | 19.9654i | − | 0.933942i | −0.884273 | − | 0.466971i | \(-0.845345\pi\) | ||
0.884273 | − | 0.466971i | \(-0.154655\pi\) | |||||||
\(458\) | −2.90782 | − | 8.01810i | −0.135873 | − | 0.374661i | ||||
\(459\) | −2.28607 | −0.106705 | ||||||||
\(460\) | −1.90966 | − | 9.39964i | −0.0890384 | − | 0.438260i | ||||
\(461\) | −23.0529 | −1.07368 | −0.536840 | − | 0.843684i | \(-0.680382\pi\) | ||||
−0.536840 | + | 0.843684i | \(0.680382\pi\) | |||||||
\(462\) | 13.0527 | + | 35.9918i | 0.607265 | + | 1.67449i | ||||
\(463\) | 31.1058i | 1.44561i | 0.691053 | + | 0.722804i | \(0.257147\pi\) | ||||
−0.691053 | + | 0.722804i | \(0.742853\pi\) | |||||||
\(464\) | −0.131482 | + | 0.725951i | −0.00610390 | + | 0.0337014i | ||||
\(465\) | 6.08631i | 0.282246i | ||||||||
\(466\) | −20.7108 | + | 7.51090i | −0.959408 | + | 0.347936i | ||||
\(467\) | −35.4360 | −1.63978 | −0.819891 | − | 0.572520i | \(-0.805966\pi\) | ||||
−0.819891 | + | 0.572520i | \(0.805966\pi\) | |||||||
\(468\) | −7.78000 | + | 6.49748i | −0.359630 | + | 0.300346i | ||||
\(469\) | −49.6176 | −2.29113 | ||||||||
\(470\) | 17.8382 | − | 6.46916i | 0.822817 | − | 0.298400i | ||||
\(471\) | 5.45303 | 0.251263 | ||||||||
\(472\) | −17.1022 | − | 9.95350i | −0.787192 | − | 0.458147i | ||||
\(473\) | −35.3025 | −1.62321 | ||||||||
\(474\) | −1.76209 | − | 4.85883i | −0.0809354 | − | 0.223174i | ||||
\(475\) | −2.14696 | −0.0985093 | ||||||||
\(476\) | 12.5146 | + | 14.9849i | 0.573608 | + | 0.686830i | ||||
\(477\) | − | 1.68353i | − | 0.0770837i | ||||||
\(478\) | 14.2827 | + | 39.3836i | 0.653276 | + | 1.80136i | ||||
\(479\) | 29.2482 | 1.33638 | 0.668192 | − | 0.743989i | \(-0.267068\pi\) | ||||
0.668192 | + | 0.743989i | \(0.267068\pi\) | |||||||
\(480\) | 0.949963 | + | 5.57652i | 0.0433597 | + | 0.254532i | ||||
\(481\) | 3.24060i | 0.147758i | ||||||||
\(482\) | 0.495754 | + | 1.36701i | 0.0225810 | + | 0.0622655i | ||||
\(483\) | −9.73473 | + | 18.0168i | −0.442946 | + | 0.819795i | ||||
\(484\) | 44.8157 | − | 37.4280i | 2.03708 | − | 1.70127i | ||||
\(485\) | −8.73755 | −0.396752 | ||||||||
\(486\) | 0.482147 | + | 1.32949i | 0.0218706 | + | 0.0603067i | ||||
\(487\) | − | 13.0759i | − | 0.592526i | −0.955106 | − | 0.296263i | \(-0.904260\pi\) | ||
0.955106 | − | 0.296263i | \(-0.0957405\pi\) | |||||||
\(488\) | 26.2177 | + | 15.2587i | 1.18682 | + | 0.690730i | ||||
\(489\) | 11.4235 | 0.516587 | ||||||||
\(490\) | −5.41622 | − | 14.9348i | −0.244680 | − | 0.674687i | ||||
\(491\) | 16.4461i | 0.742203i | 0.928592 | + | 0.371102i | \(0.121020\pi\) | ||||
−0.928592 | + | 0.371102i | \(0.878980\pi\) | |||||||
\(492\) | 11.7956 | + | 14.1239i | 0.531786 | + | 0.636753i | ||||
\(493\) | − | 0.421644i | − | 0.0189899i | ||||||
\(494\) | −14.4664 | + | 5.24632i | −0.650873 | + | 0.236043i | ||||
\(495\) | − | 6.33992i | − | 0.284958i | ||||||
\(496\) | 23.9555 | + | 4.33875i | 1.07563 | + | 0.194816i | ||||
\(497\) | − | 63.3022i | − | 2.83949i | ||||||
\(498\) | −0.958792 | − | 2.64380i | −0.0429645 | − | 0.118472i | ||||
\(499\) | 33.1788i | 1.48529i | 0.669686 | + | 0.742644i | \(0.266429\pi\) | ||||
−0.669686 | + | 0.742644i | \(0.733571\pi\) | |||||||
\(500\) | −1.28202 | − | 1.53507i | −0.0573335 | − | 0.0686503i | ||||
\(501\) | 20.6429 | 0.922255 | ||||||||
\(502\) | −10.2663 | + | 3.72315i | −0.458209 | + | 0.166172i | ||||
\(503\) | 5.75291 | 0.256510 | 0.128255 | − | 0.991741i | \(-0.459062\pi\) | ||||
0.128255 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(504\) | 6.07517 | − | 10.4384i | 0.270610 | − | 0.464964i | ||||
\(505\) | − | 1.23440i | − | 0.0549299i | ||||||
\(506\) | 42.5327 | + | 6.31818i | 1.89081 | + | 0.280877i | ||||
\(507\) | − | 12.6864i | − | 0.563423i | ||||||
\(508\) | 1.72310 | + | 2.06322i | 0.0764503 | + | 0.0915405i | ||||
\(509\) | 33.4402 | 1.48221 | 0.741105 | − | 0.671389i | \(-0.234302\pi\) | ||||
0.741105 | + | 0.671389i | \(0.234302\pi\) | |||||||
\(510\) | −1.10222 | − | 3.03930i | −0.0488072 | − | 0.134582i | ||||
\(511\) | 17.3639 | 0.768134 | ||||||||
\(512\) | 22.6262 | + | 0.236311i | 0.999945 | + | 0.0104436i | ||||
\(513\) | 2.14696i | 0.0947906i | ||||||||
\(514\) | −21.0542 | + | 7.63546i | −0.928663 | + | 0.336786i | ||||
\(515\) | − | 5.53812i | − | 0.244039i | ||||||
\(516\) | 7.13863 | + | 8.54769i | 0.314261 | + | 0.376291i | ||||
\(517\) | 85.0653i | 3.74117i | ||||||||
\(518\) | −1.31640 | − | 3.62988i | −0.0578394 | − | 0.159488i | ||||
\(519\) | 5.69694i | 0.250068i | ||||||||
\(520\) | −12.3894 | − | 7.21066i | −0.543312 | − | 0.316208i | ||||
\(521\) | − | 42.6418i | − | 1.86817i | −0.357050 | − | 0.934085i | \(-0.616217\pi\) | ||
0.357050 | − | 0.934085i | \(-0.383783\pi\) | |||||||
\(522\) | −0.245211 | + | 0.0889274i | −0.0107326 | + | 0.00389225i | ||||
\(523\) | 23.8459 | 1.04271 | 0.521353 | − | 0.853341i | \(-0.325427\pi\) | ||||
0.521353 | + | 0.853341i | \(0.325427\pi\) | |||||||
\(524\) | −5.23710 | − | 6.27083i | −0.228784 | − | 0.273943i | ||||
\(525\) | 4.27008i | 0.186361i | ||||||||
\(526\) | −24.8988 | + | 9.02972i | −1.08564 | + | 0.393715i | ||||
\(527\) | −13.9137 | −0.606092 | ||||||||
\(528\) | −24.9537 | − | 4.51954i | −1.08597 | − | 0.196688i | ||||
\(529\) | 12.6054 | + | 19.2381i | 0.548062 | + | 0.836438i | ||||
\(530\) | 2.23824 | − | 0.811711i | 0.0972227 | − | 0.0352585i | ||||
\(531\) | − | 6.99605i | − | 0.303603i | ||||||
\(532\) | 14.0730 | − | 11.7531i | 0.610143 | − | 0.509562i | ||||
\(533\) | −46.6313 | −2.01983 | ||||||||
\(534\) | 17.5324 | − | 6.35825i | 0.758703 | − | 0.275149i | ||||
\(535\) | 8.82985i | 0.381748i | ||||||||
\(536\) | 16.5319 | − | 28.4053i | 0.714070 | − | 1.22692i | ||||
\(537\) | 4.11047 | 0.177380 | ||||||||
\(538\) | 9.83617 | − | 3.56715i | 0.424067 | − | 0.153791i | ||||
\(539\) | 71.2198 | 3.06765 | ||||||||
\(540\) | −1.53507 | + | 1.28202i | −0.0660588 | + | 0.0551692i | ||||
\(541\) | −21.7135 | −0.933535 | −0.466768 | − | 0.884380i | \(-0.654582\pi\) | ||||
−0.466768 | + | 0.884380i | \(0.654582\pi\) | |||||||
\(542\) | −2.99995 | − | 8.27214i | −0.128859 | − | 0.355319i | ||||
\(543\) | −11.3771 | −0.488239 | ||||||||
\(544\) | −12.7483 | + | 2.17168i | −0.546580 | + | 0.0931101i | ||||
\(545\) | 13.7436 | 0.588712 | ||||||||
\(546\) | 10.4344 | + | 28.7721i | 0.446550 | + | 1.23133i | ||||
\(547\) | − | 0.483696i | − | 0.0206813i | −0.999947 | − | 0.0103407i | \(-0.996708\pi\) | ||
0.999947 | − | 0.0103407i | \(-0.00329159\pi\) | |||||||
\(548\) | −5.39322 | − | 6.45776i | −0.230387 | − | 0.275862i | ||||
\(549\) | 10.7249i | 0.457730i | ||||||||
\(550\) | 8.42884 | − | 3.05678i | 0.359407 | − | 0.130341i | ||||
\(551\) | −0.395986 | −0.0168696 | ||||||||
\(552\) | −7.07088 | − | 11.5760i | −0.300956 | − | 0.492705i | ||||
\(553\) | −15.6057 | −0.663622 | ||||||||
\(554\) | 15.8723 | − | 5.75620i | 0.674350 | − | 0.244557i | ||||
\(555\) | 0.639401i | 0.0271411i | ||||||||
\(556\) | 4.18827 | + | 5.01497i | 0.177622 | + | 0.212682i | ||||
\(557\) | 44.9485i | 1.90453i | 0.305272 | + | 0.952265i | \(0.401252\pi\) | ||||
−0.305272 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(558\) | 2.93450 | + | 8.09167i | 0.124227 | + | 0.342548i | ||||
\(559\) | −28.2210 | −1.19362 | ||||||||
\(560\) | 16.8069 | + | 3.04401i | 0.710220 | + | 0.128633i | ||||
\(561\) | 14.4935 | 0.611917 | ||||||||
\(562\) | 13.6753 | + | 37.7086i | 0.576857 | + | 1.59064i | ||||
\(563\) | 33.9938 | 1.43267 | 0.716334 | − | 0.697757i | \(-0.245819\pi\) | ||||
0.716334 | + | 0.697757i | \(0.245819\pi\) | |||||||
\(564\) | 20.5966 | − | 17.2013i | 0.867274 | − | 0.724306i | ||||
\(565\) | 9.28660 | 0.390690 | ||||||||
\(566\) | −15.2038 | + | 5.51374i | −0.639061 | + | 0.231760i | ||||
\(567\) | 4.27008 | 0.179326 | ||||||||
\(568\) | 36.2395 | + | 21.0914i | 1.52058 | + | 0.884977i | ||||
\(569\) | − | 11.3973i | − | 0.477801i | −0.971044 | − | 0.238900i | \(-0.923213\pi\) | ||
0.971044 | − | 0.238900i | \(-0.0767870\pi\) | |||||||
\(570\) | −2.85435 | + | 1.03515i | −0.119556 | + | 0.0433577i | ||||
\(571\) | 21.2400 | 0.888866 | 0.444433 | − | 0.895812i | \(-0.353405\pi\) | ||||
0.444433 | + | 0.895812i | \(0.353405\pi\) | |||||||
\(572\) | 49.3246 | − | 41.1935i | 2.06236 | − | 1.72239i | ||||
\(573\) | − | 6.76632i | − | 0.282667i | ||||||
\(574\) | 52.2330 | − | 18.9427i | 2.18016 | − | 0.790651i | ||||
\(575\) | 4.21933 | + | 2.27976i | 0.175958 | + | 0.0950724i | ||||
\(576\) | 3.95167 | + | 6.95589i | 0.164653 | + | 0.289829i | ||||
\(577\) | 31.9987 | 1.33212 | 0.666062 | − | 0.745896i | \(-0.267978\pi\) | ||||
0.666062 | + | 0.745896i | \(0.267978\pi\) | |||||||
\(578\) | −15.6532 | + | 5.67674i | −0.651088 | + | 0.236121i | ||||
\(579\) | 22.6747i | 0.942327i | ||||||||
\(580\) | −0.236456 | − | 0.283129i | −0.00981828 | − | 0.0117563i | ||||
\(581\) | −8.49142 | −0.352284 | ||||||||
\(582\) | −11.6165 | + | 4.21279i | −0.481518 | + | 0.174626i | ||||
\(583\) | 10.6735i | 0.442050i | ||||||||
\(584\) | −5.78543 | + | 9.94057i | −0.239403 | + | 0.411344i | ||||
\(585\) | − | 5.06818i | − | 0.209543i | ||||||
\(586\) | 10.4043 | + | 28.6890i | 0.429796 | + | 1.18513i | ||||
\(587\) | − | 41.5654i | − | 1.71559i | −0.513994 | − | 0.857794i | \(-0.671835\pi\) | ||
0.513994 | − | 0.857794i | \(-0.328165\pi\) | |||||||
\(588\) | −14.4016 | − | 17.2443i | −0.593911 | − | 0.711141i | ||||
\(589\) | 13.0671i | 0.538419i | ||||||||
\(590\) | 9.30115 | − | 3.37312i | 0.382922 | − | 0.138869i | ||||
\(591\) | 18.6303i | 0.766348i | ||||||||
\(592\) | 2.51666 | + | 0.455810i | 0.103434 | + | 0.0187337i | ||||
\(593\) | 40.3723 | 1.65789 | 0.828945 | − | 0.559330i | \(-0.188942\pi\) | ||||
0.828945 | + | 0.559330i | \(0.188942\pi\) | |||||||
\(594\) | −3.05678 | − | 8.42884i | −0.125421 | − | 0.345840i | ||||
\(595\) | −9.76170 | −0.400190 | ||||||||
\(596\) | 5.18187 | + | 6.20470i | 0.212258 | + | 0.254155i | ||||
\(597\) | − | 8.02404i | − | 0.328402i | ||||||
\(598\) | 34.0009 | + | 5.05079i | 1.39040 | + | 0.206542i | ||||
\(599\) | − | 2.25262i | − | 0.0920395i | −0.998941 | − | 0.0460198i | \(-0.985346\pi\) | ||
0.998941 | − | 0.0460198i | \(-0.0146537\pi\) | |||||||
\(600\) | −2.44455 | − | 1.42273i | −0.0997984 | − | 0.0580828i | ||||
\(601\) | −0.510957 | −0.0208424 | −0.0104212 | − | 0.999946i | \(-0.503317\pi\) | ||||
−0.0104212 | + | 0.999946i | \(0.503317\pi\) | |||||||
\(602\) | 31.6112 | − | 11.4640i | 1.28838 | − | 0.467238i | ||||
\(603\) | 11.6198 | 0.473196 | ||||||||
\(604\) | −16.8055 | − | 20.1226i | −0.683805 | − | 0.818779i | ||||
\(605\) | 29.1946i | 1.18693i | ||||||||
\(606\) | −0.595160 | − | 1.64111i | −0.0241767 | − | 0.0666656i | ||||
\(607\) | 47.9293i | 1.94539i | 0.232083 | + | 0.972696i | \(0.425446\pi\) | ||||
−0.232083 | + | 0.972696i | \(0.574554\pi\) | |||||||
\(608\) | 2.03953 | + | 11.9726i | 0.0827140 | + | 0.485552i | ||||
\(609\) | 0.787574i | 0.0319141i | ||||||||
\(610\) | −14.2587 | + | 5.17100i | −0.577317 | + | 0.209368i | ||||
\(611\) | 68.0017i | 2.75106i | ||||||||
\(612\) | −2.93078 | − | 3.50928i | −0.118470 | − | 0.141854i | ||||
\(613\) | 13.6334i | 0.550649i | 0.961351 | + | 0.275325i | \(0.0887854\pi\) | ||||
−0.961351 | + | 0.275325i | \(0.911215\pi\) | |||||||
\(614\) | 2.84093 | + | 7.83367i | 0.114651 | + | 0.316141i | ||||
\(615\) | −9.20080 | −0.371012 | ||||||||
\(616\) | −38.5161 | + | 66.1788i | −1.55186 | + | 2.66642i | ||||
\(617\) | − | 44.3044i | − | 1.78363i | −0.452402 | − | 0.891814i | \(-0.649433\pi\) | ||
0.452402 | − | 0.891814i | \(-0.350567\pi\) | |||||||
\(618\) | −2.67019 | − | 7.36286i | −0.107411 | − | 0.296177i | ||||
\(619\) | 26.7059 | 1.07340 | 0.536700 | − | 0.843773i | \(-0.319671\pi\) | ||||
0.536700 | + | 0.843773i | \(0.319671\pi\) | |||||||
\(620\) | −9.34291 | + | 7.80275i | −0.375220 | + | 0.313366i | ||||
\(621\) | 2.27976 | − | 4.21933i | 0.0914835 | − | 0.169316i | ||||
\(622\) | 5.08656 | + | 14.0258i | 0.203952 | + | 0.562384i | ||||
\(623\) | − | 56.3111i | − | 2.25606i | ||||||
\(624\) | −19.9482 | − | 3.61295i | −0.798565 | − | 0.144634i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.7440 | + | 29.6257i | 0.429415 | + | 1.18408i | ||||
\(627\) | − | 13.6116i | − | 0.543593i | ||||||
\(628\) | 6.99088 | + | 8.37078i | 0.278966 | + | 0.334031i | ||||
\(629\) | −1.46172 | −0.0582824 | ||||||||
\(630\) | 2.05880 | + | 5.67701i | 0.0820247 | + | 0.226177i | ||||
\(631\) | −29.7923 | −1.18601 | −0.593006 | − | 0.805198i | \(-0.702059\pi\) | ||||
−0.593006 | + | 0.805198i | \(0.702059\pi\) | |||||||
\(632\) | 5.19962 | − | 8.93403i | 0.206830 | − | 0.355377i | ||||
\(633\) | 19.6771 | 0.782095 | ||||||||
\(634\) | −5.59241 | + | 2.02812i | −0.222103 | + | 0.0805471i | ||||
\(635\) | −1.34406 | −0.0533372 | ||||||||
\(636\) | 2.58434 | − | 2.15832i | 0.102476 | − | 0.0855828i | ||||
\(637\) | 56.9336 | 2.25579 | ||||||||
\(638\) | 1.55462 | − | 0.563793i | 0.0615479 | − | 0.0223208i | ||||
\(639\) | 14.8246i | 0.586452i | ||||||||
\(640\) | −7.34247 | + | 8.60745i | −0.290237 | + | 0.340239i | ||||
\(641\) | − | 16.6470i | − | 0.657517i | −0.944414 | − | 0.328758i | \(-0.893370\pi\) | ||
0.944414 | − | 0.328758i | \(-0.106630\pi\) | |||||||
\(642\) | 4.25729 | + | 11.7392i | 0.168022 | + | 0.463308i | ||||
\(643\) | −19.8644 | −0.783375 | −0.391687 | − | 0.920098i | \(-0.628109\pi\) | ||||
−0.391687 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(644\) | −40.1372 | + | 8.15439i | −1.58163 | + | 0.321328i | ||||
\(645\) | −5.56828 | −0.219251 | ||||||||
\(646\) | −2.36643 | − | 6.52526i | −0.0931058 | − | 0.256733i | ||||
\(647\) | − | 3.09993i | − | 0.121871i | −0.998142 | − | 0.0609354i | \(-0.980592\pi\) | ||
0.998142 | − | 0.0609354i | \(-0.0194083\pi\) | |||||||
\(648\) | −1.42273 | + | 2.44455i | −0.0558902 | + | 0.0960311i | ||||
\(649\) | 44.3544i | 1.74106i | ||||||||
\(650\) | 6.73807 | − | 2.44361i | 0.264289 | − | 0.0958461i | ||||
\(651\) | 25.9890 | 1.01859 | ||||||||
\(652\) | 14.6451 | + | 17.5358i | 0.573545 | + | 0.686755i | ||||
\(653\) | 10.1831 | 0.398497 | 0.199249 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199249 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(654\) | 18.2719 | − | 6.62644i | 0.714490 | − | 0.259114i | ||||
\(655\) | 4.08505 | 0.159616 | ||||||||
\(656\) | −6.55898 | + | 36.2140i | −0.256085 | + | 1.41392i | ||||
\(657\) | −4.06642 | −0.158646 | ||||||||
\(658\) | −27.6238 | − | 76.1707i | −1.07689 | − | 2.96944i | ||||
\(659\) | 34.4249 | 1.34100 | 0.670501 | − | 0.741908i | \(-0.266079\pi\) | ||||
0.670501 | + | 0.741908i | \(0.266079\pi\) | |||||||
\(660\) | 9.73221 | − | 8.12788i | 0.378826 | − | 0.316377i | ||||
\(661\) | 36.0651i | 1.40277i | 0.712783 | + | 0.701385i | \(0.247435\pi\) | ||||
−0.712783 | + | 0.701385i | \(0.752565\pi\) | |||||||
\(662\) | −7.74424 | − | 21.3542i | −0.300989 | − | 0.829955i | ||||
\(663\) | 11.5862 | 0.449971 | ||||||||
\(664\) | 2.82923 | − | 4.86121i | 0.109795 | − | 0.188651i | ||||
\(665\) | 9.16768i | 0.355507i | ||||||||
\(666\) | 0.308285 | + | 0.850075i | 0.0119458 | + | 0.0329397i | ||||
\(667\) | 0.778214 | + | 0.420479i | 0.0301326 | + | 0.0162810i | ||||
\(668\) | 26.4645 | + | 31.6882i | 1.02394 | + | 1.22605i | ||||
\(669\) | −21.7302 | −0.840138 | ||||||||
\(670\) | 5.60247 | + | 15.4484i | 0.216442 | + | 0.596824i | ||||
\(671\) | − | 67.9953i | − | 2.62493i | ||||||
\(672\) | 23.8122 | − | 4.05641i | 0.918574 | − | 0.156480i | ||||
\(673\) | 17.8360 | 0.687527 | 0.343764 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343764 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(674\) | −1.91137 | − | 5.27047i | −0.0736232 | − | 0.203011i | ||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 19.4745 | − | 16.2642i | 0.749019 | − | 0.625545i | ||||
\(677\) | − | 31.3870i | − | 1.20630i | −0.797627 | − | 0.603151i | \(-0.793912\pi\) | ||
0.797627 | − | 0.603151i | \(-0.206088\pi\) | |||||||
\(678\) | 12.3464 | − | 4.47751i | 0.474161 | − | 0.171958i | ||||
\(679\) | 37.3100i | 1.43183i | ||||||||
\(680\) | 3.25247 | − | 5.58842i | 0.124726 | − | 0.214306i | ||||
\(681\) | 19.5294i | 0.748368i | ||||||||
\(682\) | −18.6045 | − | 51.3006i | −0.712403 | − | 1.96440i | ||||
\(683\) | 27.7435i | 1.06157i | 0.847505 | + | 0.530787i | \(0.178104\pi\) | ||||
−0.847505 | + | 0.530787i | \(0.821896\pi\) | |||||||
\(684\) | −3.29573 | + | 2.75244i | −0.126015 | + | 0.105242i | ||||
\(685\) | 4.20683 | 0.160735 | ||||||||
\(686\) | −24.0338 | + | 8.71603i | −0.917617 | + | 0.332780i | ||||
\(687\) | 6.03097 | 0.230096 | ||||||||
\(688\) | −3.96946 | + | 21.9166i | −0.151334 | + | 0.835561i | ||||
\(689\) | 8.53244i | 0.325060i | ||||||||
\(690\) | 6.70871 | + | 0.996570i | 0.255396 | + | 0.0379388i | ||||
\(691\) | 0.927373i | 0.0352789i | 0.999844 | + | 0.0176395i | \(0.00561511\pi\) | ||||
−0.999844 | + | 0.0176395i | \(0.994385\pi\) | |||||||
\(692\) | −8.74520 | + | 7.30357i | −0.332443 | + | 0.277640i | ||||
\(693\) | −27.0719 | −1.02838 | ||||||||
\(694\) | 3.76636 | + | 10.3855i | 0.142969 | + | 0.394227i | ||||
\(695\) | −3.26694 | −0.123922 | ||||||||
\(696\) | −0.450874 | − | 0.262409i | −0.0170903 | − | 0.00994660i | ||||
\(697\) | − | 21.0337i | − | 0.796708i | ||||||
\(698\) | 44.4273 | − | 16.1118i | 1.68160 | − | 0.609842i | ||||
\(699\) | − | 15.5780i | − | 0.589215i | ||||||
\(700\) | −6.55486 | + | 5.47430i | −0.247750 | + | 0.206909i | ||||
\(701\) | − | 11.5413i | − | 0.435910i | −0.975959 | − | 0.217955i | \(-0.930061\pi\) | ||
0.975959 | − | 0.217955i | \(-0.0699385\pi\) | |||||||
\(702\) | −2.44361 | − | 6.73807i | −0.0922280 | − | 0.254312i | ||||
\(703\) | 1.37277i | 0.0517749i | ||||||||
\(704\) | −25.0533 | − | 44.0998i | −0.944230 | − | 1.66207i | ||||
\(705\) | 13.4174i | 0.505328i | ||||||||
\(706\) | 0.0741406 | − | 0.0268876i | 0.00279032 | − | 0.00101193i | ||||
\(707\) | −5.27096 | −0.198235 | ||||||||
\(708\) | 10.7394 | − | 8.96904i | 0.403612 | − | 0.337077i | ||||
\(709\) | 46.1072i | 1.73159i | 0.500398 | + | 0.865796i | \(0.333187\pi\) | ||||
−0.500398 | + | 0.865796i | \(0.666813\pi\) | |||||||
\(710\) | −19.7091 | + | 7.14764i | −0.739670 | + | 0.268246i | ||||
\(711\) | 3.65467 | 0.137061 | ||||||||
\(712\) | 32.2372 | + | 18.7621i | 1.20814 | + | 0.703140i | ||||
\(713\) | 13.8753 | − | 25.6801i | 0.519635 | − | 0.961729i | ||||
\(714\) | −12.9780 | + | 4.70657i | −0.485691 | + | 0.176139i | ||||
\(715\) | 32.1318i | 1.20166i | ||||||||
\(716\) | 5.26969 | + | 6.30985i | 0.196938 | + | 0.235810i | ||||
\(717\) | −29.6232 | −1.10630 | ||||||||
\(718\) | 13.4748 | − | 4.88673i | 0.502875 | − | 0.182371i | ||||
\(719\) | 11.3976i | 0.425058i | 0.977155 | + | 0.212529i | \(0.0681700\pi\) | ||||
−0.977155 | + | 0.212529i | \(0.931830\pi\) | |||||||
\(720\) | −3.93596 | − | 0.712870i | −0.146685 | − | 0.0265671i | ||||
\(721\) | −23.6482 | −0.880705 | ||||||||
\(722\) | 19.1321 | − | 6.93837i | 0.712021 | − | 0.258219i | ||||
\(723\) | −1.02822 | −0.0382400 | ||||||||
\(724\) | −14.5857 | − | 17.4647i | −0.542072 | − | 0.649069i | ||||
\(725\) | 0.184440 | 0.00684994 | ||||||||
\(726\) | 14.0761 | + | 38.8139i | 0.522413 | + | 1.44052i | ||||
\(727\) | 20.4020 | 0.756668 | 0.378334 | − | 0.925669i | \(-0.376497\pi\) | ||||
0.378334 | + | 0.925669i | \(0.376497\pi\) | |||||||
\(728\) | −30.7900 | + | 52.9037i | −1.14115 | + | 1.96074i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.96061 | − | 5.40625i | −0.0725655 | − | 0.200094i | ||||
\(731\) | − | 12.7295i | − | 0.470817i | ||||||
\(732\) | −16.4635 | + | 13.7496i | −0.608509 | + | 0.508198i | ||||
\(733\) | − | 14.1545i | − | 0.522807i | −0.965230 | − | 0.261403i | \(-0.915815\pi\) | ||
0.965230 | − | 0.261403i | \(-0.0841853\pi\) | |||||||
\(734\) | −35.2085 | + | 12.7686i | −1.29957 | + | 0.471297i | ||||
\(735\) | 11.2335 | 0.414355 | ||||||||
\(736\) | 8.70490 | − | 25.6948i | 0.320867 | − | 0.947124i | ||||
\(737\) | −73.6689 | −2.71363 | ||||||||
\(738\) | −12.2323 | + | 4.43614i | −0.450279 | + | 0.163297i | ||||
\(739\) | − | 20.9145i | − | 0.769354i | −0.923051 | − | 0.384677i | \(-0.874313\pi\) | ||
0.923051 | − | 0.384677i | \(-0.125687\pi\) | |||||||
\(740\) | −0.981524 | + | 0.819722i | −0.0360815 | + | 0.0301336i | ||||
\(741\) | − | 10.8812i | − | 0.399730i | ||||||
\(742\) | −3.46607 | − | 9.55743i | −0.127243 | − | 0.350864i | ||||
\(743\) | −42.2593 | −1.55034 | −0.775171 | − | 0.631752i | \(-0.782336\pi\) | ||||
−0.775171 | + | 0.631752i | \(0.782336\pi\) | |||||||
\(744\) | −8.65919 | + | 14.8783i | −0.317461 | + | 0.545465i | ||||
\(745\) | −4.04197 | −0.148086 | ||||||||
\(746\) | 11.0563 | + | 30.4868i | 0.404798 | + | 1.11620i | ||||
\(747\) | 1.98859 | 0.0727587 | ||||||||
\(748\) | 18.5809 | + | 22.2485i | 0.679386 | + | 0.813487i | ||||
\(749\) | 37.7041 | 1.37768 | ||||||||
\(750\) | 1.32949 | − | 0.482147i | 0.0485460 | − | 0.0176055i | ||||
\(751\) | −2.04064 | −0.0744641 | −0.0372320 | − | 0.999307i | \(-0.511854\pi\) | ||||
−0.0372320 | + | 0.999307i | \(0.511854\pi\) | |||||||
\(752\) | 52.8104 | + | 9.56486i | 1.92580 | + | 0.348794i | ||||
\(753\) | − | 7.72202i | − | 0.281406i | ||||||
\(754\) | 1.24277 | − | 0.450700i | 0.0452591 | − | 0.0164135i | ||||
\(755\) | 13.1086 | 0.477072 | ||||||||
\(756\) | 5.47430 | + | 6.55486i | 0.199099 | + | 0.238398i | ||||
\(757\) | − | 16.9083i | − | 0.614544i | −0.951622 | − | 0.307272i | \(-0.900584\pi\) | ||
0.951622 | − | 0.307272i | \(-0.0994161\pi\) | |||||||
\(758\) | −23.5189 | + | 8.52930i | −0.854246 | + | 0.309798i | ||||
\(759\) | −14.4535 | + | 26.7502i | −0.524628 | + | 0.970971i | ||||
\(760\) | −5.24835 | − | 3.05455i | −0.190378 | − | 0.110800i | ||||
\(761\) | 15.7867 | 0.572269 | 0.286134 | − | 0.958189i | \(-0.407630\pi\) | ||||
0.286134 | + | 0.958189i | \(0.407630\pi\) | |||||||
\(762\) | −1.78690 | + | 0.648033i | −0.0647327 | + | 0.0234757i | ||||
\(763\) | − | 58.6863i | − | 2.12459i | ||||||
\(764\) | 10.3868 | − | 8.67452i | 0.375780 | − | 0.313833i | ||||
\(765\) | 2.28607 | 0.0826531 | ||||||||
\(766\) | 45.5886 | − | 16.5330i | 1.64718 | − | 0.597362i | ||||
\(767\) | 35.4572i | 1.28028i | ||||||||
\(768\) | −5.61166 | + | 14.9836i | −0.202493 | + | 0.540675i | ||||
\(769\) | − | 2.35009i | − | 0.0847464i | −0.999102 | − | 0.0423732i | \(-0.986508\pi\) | ||
0.999102 | − | 0.0423732i | \(-0.0134919\pi\) | |||||||
\(770\) | −13.0527 | − | 35.9918i | −0.470385 | − | 1.29705i | ||||
\(771\) | − | 15.8364i | − | 0.570333i | ||||||
\(772\) | −34.8072 | + | 29.0693i | −1.25274 | + | 1.04623i | ||||
\(773\) | − | 37.8489i | − | 1.36133i | −0.732595 | − | 0.680665i | \(-0.761691\pi\) | ||
0.732595 | − | 0.680665i | \(-0.238309\pi\) | |||||||
\(774\) | −7.40296 | + | 2.68473i | −0.266094 | + | 0.0965007i | ||||
\(775\) | − | 6.08631i | − | 0.218627i | ||||||
\(776\) | −21.3594 | − | 12.4312i | −0.766758 | − | 0.446254i | ||||
\(777\) | 2.73029 | 0.0979486 | ||||||||
\(778\) | −0.183467 | − | 0.505898i | −0.00657762 | − | 0.0181373i | ||||
\(779\) | −19.7538 | −0.707752 | ||||||||
\(780\) | 7.78000 | − | 6.49748i | 0.278569 | − | 0.232647i | ||||
\(781\) | − | 93.9868i | − | 3.36311i | ||||||
\(782\) | −2.27823 | + | 15.3366i | −0.0814693 | + | 0.548436i | ||||
\(783\) | − | 0.184440i | − | 0.00659136i | ||||||
\(784\) | 8.00805 | − | 44.2148i | 0.286002 | − | 1.57910i | ||||
\(785\) | −5.45303 | −0.194627 | ||||||||
\(786\) | 5.43102 | − | 1.96960i | 0.193718 | − | 0.0702532i | ||||
\(787\) | 7.72930 | 0.275520 | 0.137760 | − | 0.990466i | \(-0.456010\pi\) | ||||
0.137760 | + | 0.990466i | \(0.456010\pi\) | |||||||
\(788\) | −28.5988 | + | 23.8843i | −1.01879 | + | 0.850844i | ||||
\(789\) | − | 18.7282i | − | 0.666740i | ||||||
\(790\) | 1.76209 | + | 4.85883i | 0.0626923 | + | 0.172870i | ||||
\(791\) | − | 39.6545i | − | 1.40995i | ||||||
\(792\) | 9.02001 | − | 15.4983i | 0.320512 | − | 0.550707i | ||||
\(793\) | − | 54.3559i | − | 1.93023i | ||||||
\(794\) | 17.4857 | − | 6.34129i | 0.620543 | − | 0.225044i | ||||
\(795\) | 1.68353i | 0.0597088i | ||||||||
\(796\) | 12.3175 | − | 10.2870i | 0.436581 | − | 0.364611i | ||||
\(797\) | 42.3887i | 1.50149i | 0.660594 | + | 0.750743i | \(0.270304\pi\) | ||||
−0.660594 | + | 0.750743i | \(0.729696\pi\) | |||||||
\(798\) | 4.42017 | + | 12.1883i | 0.156472 | + | 0.431461i | ||||
\(799\) | −30.6731 | −1.08514 | ||||||||
\(800\) | −0.949963 | − | 5.57652i | −0.0335863 | − | 0.197160i | ||||
\(801\) | 13.1874i | 0.465953i | ||||||||
\(802\) | −3.45974 | − | 9.53999i | −0.122168 | − | 0.336869i | ||||
\(803\) | 25.7808 | 0.909784 | ||||||||
\(804\) | 14.8968 | + | 17.8372i | 0.525370 | + | 0.629071i | ||||
\(805\) | 9.73473 | − | 18.0168i | 0.343104 | − | 0.635010i | ||||
\(806\) | −14.8725 | − | 41.0100i | −0.523863 | − | 1.44452i | ||||
\(807\) | 7.39847i | 0.260439i | ||||||||
\(808\) | 1.75621 | − | 3.01754i | 0.0617834 | − | 0.106157i | ||||
\(809\) | 20.6701 | 0.726720 | 0.363360 | − | 0.931649i | \(-0.381629\pi\) | ||||
0.363360 | + | 0.931649i | \(0.381629\pi\) | |||||||
\(810\) | −0.482147 | − | 1.32949i | −0.0169409 | − | 0.0467134i | ||||
\(811\) | 30.9310i | 1.08613i | 0.839689 | + | 0.543067i | \(0.182737\pi\) | ||||
−0.839689 | + | 0.543067i | \(0.817263\pi\) | |||||||
\(812\) | −1.20898 | + | 1.00968i | −0.0424269 | + | 0.0354329i | ||||
\(813\) | 6.22206 | 0.218217 | ||||||||
\(814\) | −1.95450 | − | 5.38941i | −0.0685054 | − | 0.188899i | ||||
\(815\) | −11.4235 | −0.400146 | ||||||||
\(816\) | 1.62967 | − | 8.99789i | 0.0570499 | − | 0.314989i | ||||
\(817\) | −11.9549 | −0.418248 | ||||||||
\(818\) | −1.19736 | + | 0.434231i | −0.0418647 | + | 0.0151825i | ||||
\(819\) | −21.6415 | −0.756215 | ||||||||
\(820\) | −11.7956 | − | 14.1239i | −0.411919 | − | 0.493227i | ||||
\(821\) | 2.34307 | 0.0817735 | 0.0408868 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408868 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(822\) | 5.59292 | − | 2.02831i | 0.195075 | − | 0.0707454i | ||||
\(823\) | − | 38.8494i | − | 1.35420i | −0.735889 | − | 0.677102i | \(-0.763236\pi\) | ||
0.735889 | − | 0.677102i | \(-0.236764\pi\) | |||||||
\(824\) | 7.87926 | − | 13.5382i | 0.274487 | − | 0.471626i | ||||
\(825\) | 6.33992i | 0.220728i | ||||||||
\(826\) | −14.4035 | − | 39.7166i | −0.501161 | − | 1.38192i | ||||
\(827\) | 0.484323 | 0.0168415 | 0.00842077 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00842077 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(828\) | 9.39964 | − | 1.90966i | 0.326660 | − | 0.0663653i | ||||
\(829\) | 21.9471 | 0.762255 | 0.381128 | − | 0.924522i | \(-0.375536\pi\) | ||||
0.381128 | + | 0.924522i | \(0.375536\pi\) | |||||||
\(830\) | 0.958792 | + | 2.64380i | 0.0332802 | + | 0.0917677i | ||||
\(831\) | 11.9387i | 0.414148i | ||||||||
\(832\) | −20.0277 | − | 35.2536i | −0.694337 | − | 1.22220i | ||||
\(833\) | 25.6807i | 0.889783i | ||||||||
\(834\) | −4.34335 | + | 1.57514i | −0.150398 | + | 0.0545428i | ||||
\(835\) | −20.6429 | −0.714376 | ||||||||
\(836\) | 20.8947 | − | 17.4502i | 0.722657 | − | 0.603529i | ||||
\(837\) | −6.08631 | −0.210374 | ||||||||
\(838\) | 4.34295 | − | 1.57500i | 0.150025 | − | 0.0544075i | ||||
\(839\) | −41.6416 | −1.43763 | −0.718813 | − | 0.695203i | \(-0.755314\pi\) | ||||
−0.718813 | + | 0.695203i | \(0.755314\pi\) | |||||||
\(840\) | −6.07517 | + | 10.4384i | −0.209613 | + | 0.360160i | ||||
\(841\) | −28.9660 | −0.998827 | ||||||||
\(842\) | −2.01511 | − | 5.55652i | −0.0694452 | − | 0.191490i | ||||
\(843\) | −28.3633 | −0.976883 | ||||||||
\(844\) | 25.2264 | + | 30.2057i | 0.868327 | + | 1.03972i | ||||
\(845\) | 12.6864i | 0.436425i | ||||||||
\(846\) | 6.46916 | + | 17.8382i | 0.222414 | + | 0.613292i | ||||
\(847\) | 124.663 | 4.28348 | ||||||||
\(848\) | 6.62633 | + | 1.20014i | 0.227549 | + | 0.0412130i | ||||
\(849\) | − | 11.4358i | − | 0.392476i | ||||||
\(850\) | 1.10222 | + | 3.03930i | 0.0378059 | + | 0.104247i | ||||
\(851\) | 1.45768 | − | 2.69784i | 0.0499686 | − | 0.0924808i | ||||
\(852\) | −22.7568 | + | 19.0054i | −0.779634 | + | 0.651114i | ||||
\(853\) | −25.8101 | −0.883721 | −0.441860 | − | 0.897084i | \(-0.645681\pi\) | ||||
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(854\) | 22.0806 | + | 60.8856i | 0.755581 | + | 2.08346i | ||||
\(855\) | − | 2.14696i | − | 0.0734245i | ||||||
\(856\) | −12.5625 | + | 21.5850i | −0.429378 | + | 0.737761i | ||||
\(857\) | −0.817165 | −0.0279138 | −0.0139569 | − | 0.999903i | \(-0.504443\pi\) | ||||
−0.0139569 | + | 0.999903i | \(0.504443\pi\) | |||||||
\(858\) | 15.4923 | + | 42.7188i | 0.528897 | + | 1.45840i | ||||
\(859\) | − | 5.27081i | − | 0.179838i | −0.995949 | − | 0.0899189i | \(-0.971339\pi\) | ||
0.995949 | − | 0.0899189i | \(-0.0286608\pi\) | |||||||
\(860\) | −7.13863 | − | 8.54769i | −0.243425 | − | 0.291474i | ||||
\(861\) | 39.2881i | 1.33894i | ||||||||
\(862\) | 22.8679 | − | 8.29318i | 0.778882 | − | 0.282467i | ||||
\(863\) | − | 3.58063i | − | 0.121886i | −0.998141 | − | 0.0609430i | \(-0.980589\pi\) | ||
0.998141 | − | 0.0609430i | \(-0.0194108\pi\) | |||||||
\(864\) | −5.57652 | + | 0.949963i | −0.189717 | + | 0.0323184i | ||||
\(865\) | − | 5.69694i | − | 0.193702i | ||||||
\(866\) | −7.85885 | − | 21.6702i | −0.267055 | − | 0.736384i | ||||
\(867\) | − | 11.7739i | − | 0.399862i | ||||||
\(868\) | 33.3183 | + | 39.8949i | 1.13090 | + | 1.35412i | ||||
\(869\) | −23.1703 | −0.785999 | ||||||||
\(870\) | 0.245211 | − | 0.0889274i | 0.00831343 | − | 0.00301492i | ||||
\(871\) | −58.8914 | −1.99546 | ||||||||
\(872\) | 33.5970 | + | 19.5535i | 1.13774 | + | 0.662164i | ||||
\(873\) | − | 8.73755i | − | 0.295721i | ||||||
\(874\) | 14.4033 | + | 2.13960i | 0.487200 | + | 0.0723729i | ||||
\(875\) | − | 4.27008i | − | 0.144355i | ||||||
\(876\) | −5.21322 | − | 6.24223i | −0.176138 | − | 0.210905i | ||||
\(877\) | −43.6993 | −1.47562 | −0.737810 | − | 0.675008i | \(-0.764140\pi\) | ||||
−0.737810 | + | 0.675008i | \(0.764140\pi\) | |||||||
\(878\) | −3.10825 | − | 8.57079i | −0.104899 | − | 0.289250i | ||||
\(879\) | −21.5790 | −0.727842 | ||||||||
\(880\) | 24.9537 | + | 4.51954i | 0.841189 | + | 0.152354i | ||||
\(881\) | 21.6563i | 0.729620i | 0.931082 | + | 0.364810i | \(0.118866\pi\) | ||||
−0.931082 | + | 0.364810i | \(0.881134\pi\) | |||||||
\(882\) | 14.9348 | − | 5.41622i | 0.502882 | − | 0.182374i | ||||
\(883\) | 37.3040i | 1.25538i | 0.778464 | + | 0.627689i | \(0.215999\pi\) | ||||
−0.778464 | + | 0.627689i | \(0.784001\pi\) | |||||||
\(884\) | 14.8537 | + | 17.7856i | 0.499584 | + | 0.598195i | ||||
\(885\) | 6.99605i | 0.235170i | ||||||||
\(886\) | 10.2125 | + | 28.1601i | 0.343094 | + | 0.946058i | ||||
\(887\) | 6.79994i | 0.228320i | 0.993462 | + | 0.114160i | \(0.0364176\pi\) | ||||
−0.993462 | + | 0.114160i | \(0.963582\pi\) | |||||||
\(888\) | −0.909696 | + | 1.56305i | −0.0305274 | + | 0.0524525i | ||||
\(889\) | 5.73922i | 0.192487i | ||||||||
\(890\) | −17.5324 | + | 6.35825i | −0.587689 | + | 0.213129i | ||||
\(891\) | 6.33992 | 0.212395 | ||||||||
\(892\) | −27.8585 | − | 33.3574i | −0.932771 | − | 1.11689i | ||||
\(893\) | 28.8066i | 0.963977i | ||||||||
\(894\) | −5.37375 | + | 1.94882i | −0.179725 | + | 0.0651784i | ||||
\(895\) | −4.11047 | −0.137398 | ||||||||
\(896\) | 36.7544 | + | 31.3529i | 1.22788 | + | 1.04743i | ||||
\(897\) | −11.5542 | + | 21.3843i | −0.385784 | + | 0.714000i | ||||
\(898\) | 14.4760 | − | 5.24980i | 0.483069 | − | 0.175188i | ||||
\(899\) | − | 1.12256i | − | 0.0374395i | ||||||
\(900\) | 1.53507 | − | 1.28202i | 0.0511689 | − | 0.0427339i | ||||
\(901\) | −3.84868 | −0.128218 | ||||||||
\(902\) | 77.5521 | − | 28.1248i | 2.58220 | − | 0.936453i | ||||
\(903\) | 23.7770i | 0.791248i | ||||||||
\(904\) | 22.7016 | + | 13.2124i | 0.755043 | + | 0.439436i | ||||
\(905\) | 11.3771 | 0.378188 | ||||||||
\(906\) | 17.4277 | − | 6.32029i | 0.578998 | − | 0.209977i | ||||
\(907\) | −29.6090 | −0.983151 | −0.491575 | − | 0.870835i | \(-0.663579\pi\) | ||||
−0.491575 | + | 0.870835i | \(0.663579\pi\) | |||||||
\(908\) | −29.9789 | + | 25.0370i | −0.994886 | + | 0.830882i | ||||
\(909\) | 1.23440 | 0.0409423 | ||||||||
\(910\) | −10.4344 | − | 28.7721i | −0.345896 | − | 0.953785i | ||||
\(911\) | −44.4726 | −1.47344 | −0.736721 | − | 0.676196i | \(-0.763627\pi\) | ||||
−0.736721 | + | 0.676196i | \(0.763627\pi\) | |||||||
\(912\) | −8.45036 | − | 1.53050i | −0.279819 | − | 0.0506800i | ||||
\(913\) | −12.6075 | −0.417247 | ||||||||
\(914\) | 9.62626 | + | 26.5437i | 0.318408 | + | 0.877989i | ||||
\(915\) | − | 10.7249i | − | 0.354556i | ||||||
\(916\) | 7.73180 | + | 9.25795i | 0.255466 | + | 0.305891i | ||||
\(917\) | − | 17.4435i | − | 0.576035i | ||||||
\(918\) | 3.03930 | − | 1.10222i | 0.100312 | − | 0.0363788i | ||||
\(919\) | −25.2267 | −0.832153 | −0.416076 | − | 0.909330i | \(-0.636595\pi\) | ||||
−0.416076 | + | 0.909330i | \(0.636595\pi\) | |||||||
\(920\) | 7.07088 | + | 11.5760i | 0.233120 | + | 0.381648i | ||||
\(921\) | −5.89225 | −0.194156 | ||||||||
\(922\) | 30.6485 | − | 11.1149i | 1.00935 | − | 0.366049i | ||||
\(923\) | − | 75.1337i | − | 2.47306i | ||||||
\(924\) | −34.7067 | − | 41.5573i | −1.14177 | − | 1.36713i | ||||
\(925\) | − | 0.639401i | − | 0.0210234i | ||||||
\(926\) | −14.9976 | − | 41.3547i | −0.492850 | − | 1.35900i | ||||
\(927\) | 5.53812 | 0.181896 | ||||||||
\(928\) | −0.175212 | − | 1.02854i | −0.00575160 | − | 0.0337633i | ||||
\(929\) | −7.22571 | −0.237068 | −0.118534 | − | 0.992950i | \(-0.537819\pi\) | ||||
−0.118534 | + | 0.992950i | \(0.537819\pi\) | |||||||
\(930\) | −2.93450 | − | 8.09167i | −0.0962260 | − | 0.265336i | ||||
\(931\) | 24.1180 | 0.790434 | ||||||||
\(932\) | 23.9133 | − | 19.9713i | 0.783307 | − | 0.654181i | ||||
\(933\) | −10.5498 | −0.345385 | ||||||||
\(934\) | 47.1116 | − | 17.0853i | 1.54154 | − | 0.559050i | ||||
\(935\) | −14.4935 | −0.473989 | ||||||||
\(936\) | 7.21066 | − | 12.3894i | 0.235688 | − | 0.404961i | ||||
\(937\) | 5.18714i | 0.169457i | 0.996404 | + | 0.0847283i | \(0.0270022\pi\) | ||||
−0.996404 | + | 0.0847283i | \(0.972998\pi\) | |||||||
\(938\) | 65.9659 | − | 23.9230i | 2.15386 | − | 0.781113i | ||||
\(939\) | −22.2836 | −0.727197 | ||||||||
\(940\) | −20.5966 | + | 17.2013i | −0.671788 | + | 0.561045i | ||||
\(941\) | − | 5.57594i | − | 0.181770i | −0.995861 | − | 0.0908852i | \(-0.971030\pi\) | ||
0.995861 | − | 0.0908852i | \(-0.0289696\pi\) | |||||||
\(942\) | −7.24974 | + | 2.62916i | −0.236209 | + | 0.0856628i | ||||
\(943\) | 38.8212 | + | 20.9756i | 1.26419 | + | 0.683059i | ||||
\(944\) | 27.5362 | + | 4.98727i | 0.896227 | + | 0.162322i | ||||
\(945\) | −4.27008 | −0.138906 | ||||||||
\(946\) | 46.9342 | − | 17.0210i | 1.52596 | − | 0.553400i | ||||
\(947\) | 16.3670i | 0.531856i | 0.963993 | + | 0.265928i | \(0.0856783\pi\) | ||||
−0.963993 | + | 0.265928i | \(0.914322\pi\) | |||||||
\(948\) | 4.68534 | + | 5.61017i | 0.152173 | + | 0.182210i | ||||
\(949\) | 20.6093 | 0.669007 | ||||||||
\(950\) | 2.85435 | − | 1.03515i | 0.0926075 | − | 0.0335847i | ||||
\(951\) | − | 4.20644i | − | 0.136403i | ||||||
\(952\) | −23.8630 | − | 13.8883i | −0.773403 | − | 0.450122i | ||||
\(953\) | − | 28.4543i | − | 0.921727i | −0.887471 | − | 0.460863i | \(-0.847540\pi\) | ||
0.887471 | − | 0.460863i | \(-0.152460\pi\) | |||||||
\(954\) | 0.811711 | + | 2.23824i | 0.0262801 | + | 0.0724655i | ||||
\(955\) | 6.76632i | 0.218953i | ||||||||
\(956\) | −37.9774 | − | 45.4736i | −1.22828 | − | 1.47072i | ||||
\(957\) | 1.16934i | 0.0377993i | ||||||||
\(958\) | −38.8851 | + | 14.1019i | −1.25632 | + | 0.455613i | ||||
\(959\) | − | 17.9635i | − | 0.580070i | ||||||
\(960\) | −3.95167 | − | 6.95589i | −0.127539 | − | 0.224500i | ||||
\(961\) | −6.04320 | −0.194942 | ||||||||
\(962\) | −1.56244 | − | 4.30833i | −0.0503752 | − | 0.138906i | ||||
\(963\) | −8.82985 | −0.284538 | ||||||||
\(964\) | −1.31820 | − | 1.57839i | −0.0424563 | − | 0.0508366i | ||||
\(965\) | − | 22.6747i | − | 0.729923i | ||||||
\(966\) | 4.25543 | − | 28.6467i | 0.136916 | − | 0.921693i | ||||
\(967\) | 29.3267i | 0.943085i | 0.881843 | + | 0.471542i | \(0.156303\pi\) | ||||
−0.881843 | + | 0.471542i | \(0.843697\pi\) | |||||||
\(968\) | −41.5361 | + | 71.3678i | −1.33502 | + | 2.29385i | ||||
\(969\) | 4.90810 | 0.157671 | ||||||||
\(970\) | 11.6165 | − | 4.21279i | 0.372982 | − | 0.135264i | ||||
\(971\) | −23.4011 | −0.750977 | −0.375488 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375488 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(972\) | −1.28202 | − | 1.53507i | −0.0411207 | − | 0.0492373i | ||||
\(973\) | 13.9501i | 0.447219i | ||||||||
\(974\) | 6.30451 | + | 17.3842i | 0.202010 | + | 0.557027i | ||||
\(975\) | 5.06818i | 0.162312i | ||||||||
\(976\) | −42.2130 | − | 7.64549i | −1.35121 | − | 0.244726i | ||||
\(977\) | 53.5732i | 1.71396i | 0.515351 | + | 0.856979i | \(0.327662\pi\) | ||||
−0.515351 | + | 0.856979i | \(0.672338\pi\) | |||||||
\(978\) | −15.1873 | + | 5.50779i | −0.485637 | + | 0.176120i | ||||
\(979\) | − | 83.6069i | − | 2.67209i | ||||||
\(980\) | 14.4016 | + | 17.2443i | 0.460042 | + | 0.550848i | ||||
\(981\) | 13.7436i | 0.438800i | ||||||||
\(982\) | −7.92945 | − | 21.8649i | −0.253039 | − | 0.697737i | ||||
\(983\) | 31.8612 | 1.01622 | 0.508108 | − | 0.861294i | \(-0.330345\pi\) | ||||
0.508108 | + | 0.861294i | \(0.330345\pi\) | |||||||
\(984\) | −22.4918 | − | 13.0903i | −0.717014 | − | 0.417303i | ||||
\(985\) | − | 18.6303i | − | 0.593611i | ||||||
\(986\) | 0.203294 | + | 0.560570i | 0.00647421 | + | 0.0178522i | ||||
\(987\) | 57.2933 | 1.82367 | ||||||||
\(988\) | 16.7033 | − | 13.9498i | 0.531404 | − | 0.443803i | ||||
\(989\) | 23.4944 | + | 12.6943i | 0.747078 | + | 0.403656i | ||||
\(990\) | 3.05678 | + | 8.42884i | 0.0971507 | + | 0.267886i | ||||
\(991\) | 20.7723i | 0.659855i | 0.944006 | + | 0.329928i | \(0.107024\pi\) | ||||
−0.944006 | + | 0.329928i | \(0.892976\pi\) | |||||||
\(992\) | −33.9404 | + | 5.78177i | −1.07761 | + | 0.183571i | ||||
\(993\) | 16.0620 | 0.509712 | ||||||||
\(994\) | 30.5210 | + | 84.1594i | 0.968066 | + | 2.66937i | ||||
\(995\) | 8.02404i | 0.254379i | ||||||||
\(996\) | 2.54940 | + | 3.05262i | 0.0807809 | + | 0.0967259i | ||||
\(997\) | −23.2860 | −0.737475 | −0.368737 | − | 0.929534i | \(-0.620210\pi\) | ||||
−0.368737 | + | 0.929534i | \(0.620210\pi\) | |||||||
\(998\) | −15.9971 | − | 44.1108i | −0.506379 | − | 1.39630i | ||||
\(999\) | −0.639401 | −0.0202297 |
(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 | 1380.2.p.b.91.6 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.a.91.5 | ✓ | 48 | ||
23.22 | odd | 2 | 1380.2.p.a.91.6 | yes | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.b.91.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.5 | ✓ | 48 | 4.3 | odd | 2 | ||
1380.2.p.a.91.6 | yes | 48 | 23.22 | odd | 2 | ||
1380.2.p.b.91.5 | yes | 48 | 92.91 | even | 2 | inner | |
1380.2.p.b.91.6 | yes | 48 | 1.1 | even | 1 | trivial |