Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(139,336)]
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([2, 1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.u (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: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 139.15 | ||
Character | \(\chi\) | \(=\) | 336.139 |
Dual form | 336.2.u.a.307.15 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.135637 | − | 1.40769i | −0.0959095 | − | 0.995390i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.96321 | + | 0.381870i | −0.981603 | + | 0.190935i | ||||
\(5\) | 2.46638 | − | 2.46638i | 1.10300 | − | 1.10300i | 0.108949 | − | 0.994047i | \(-0.465251\pi\) |
0.994047 | − | 0.108949i | \(-0.0347486\pi\) | |||||||
\(6\) | 1.09130 | + | 0.899481i | 0.445521 | + | 0.367211i | ||||
\(7\) | −2.50032 | − | 0.865115i | −0.945030 | − | 0.326983i | ||||
\(8\) | 0.803838 | + | 2.71180i | 0.284200 | + | 0.958765i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −3.80643 | − | 3.13737i | −1.20370 | − | 0.992124i | ||||
\(11\) | 0.244455 | − | 0.244455i | 0.0737061 | − | 0.0737061i | −0.669293 | − | 0.742999i | \(-0.733403\pi\) |
0.742999 | + | 0.669293i | \(0.233403\pi\) | |||||||
\(12\) | 1.11817 | − | 1.65822i | 0.322789 | − | 0.478686i | ||||
\(13\) | −2.35087 | − | 2.35087i | −0.652014 | − | 0.652014i | 0.301464 | − | 0.953478i | \(-0.402525\pi\) |
−0.953478 | + | 0.301464i | \(0.902525\pi\) | |||||||
\(14\) | −0.878683 | + | 3.63702i | −0.234838 | + | 0.972035i | ||||
\(15\) | 3.48798i | 0.900593i | ||||||||
\(16\) | 3.70835 | − | 1.49938i | 0.927088 | − | 0.374844i | ||||
\(17\) | − | 5.19171i | − | 1.25918i | −0.776930 | − | 0.629588i | \(-0.783224\pi\) | ||
0.776930 | − | 0.629588i | \(-0.216776\pi\) | |||||||
\(18\) | −1.40769 | + | 0.135637i | −0.331797 | + | 0.0319698i | ||||
\(19\) | 1.43102 | − | 1.43102i | 0.328298 | − | 0.328298i | −0.523641 | − | 0.851939i | \(-0.675427\pi\) |
0.851939 | + | 0.523641i | \(0.175427\pi\) | |||||||
\(20\) | −3.90017 | + | 5.78384i | −0.872104 | + | 1.29330i | ||||
\(21\) | 2.37972 | − | 1.15626i | 0.519297 | − | 0.252317i | ||||
\(22\) | −0.377275 | − | 0.310961i | −0.0804354 | − | 0.0662972i | ||||
\(23\) | −6.61525 | −1.37937 | −0.689687 | − | 0.724108i | \(-0.742252\pi\) | ||||
−0.689687 | + | 0.724108i | \(0.742252\pi\) | |||||||
\(24\) | −2.48593 | − | 1.34913i | −0.507438 | − | 0.275390i | ||||
\(25\) | − | 7.16602i | − | 1.43320i | ||||||
\(26\) | −2.99044 | + | 3.62817i | −0.586474 | + | 0.711542i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 5.23899 | + | 0.743604i | 0.990077 | + | 0.140528i | ||||
\(29\) | −5.09187 | + | 5.09187i | −0.945537 | + | 0.945537i | −0.998592 | − | 0.0530544i | \(-0.983104\pi\) |
0.0530544 | + | 0.998592i | \(0.483104\pi\) | |||||||
\(30\) | 4.91001 | − | 0.473098i | 0.896441 | − | 0.0863755i | ||||
\(31\) | −1.53315 | −0.275363 | −0.137681 | − | 0.990477i | \(-0.543965\pi\) | ||||
−0.137681 | + | 0.990477i | \(0.543965\pi\) | |||||||
\(32\) | −2.61365 | − | 5.01685i | −0.462033 | − | 0.886863i | ||||
\(33\) | 0.345712i | 0.0601807i | ||||||||
\(34\) | −7.30834 | + | 0.704186i | −1.25337 | + | 0.120767i | ||||
\(35\) | −8.30041 | + | 4.03302i | −1.40303 | + | 0.681704i | ||||
\(36\) | 0.381870 | + | 1.96321i | 0.0636449 | + | 0.327201i | ||||
\(37\) | −2.40835 | − | 2.40835i | −0.395930 | − | 0.395930i | 0.480865 | − | 0.876795i | \(-0.340323\pi\) |
−0.876795 | + | 0.480865i | \(0.840323\pi\) | |||||||
\(38\) | −2.20854 | − | 1.82034i | −0.358272 | − | 0.295298i | ||||
\(39\) | 3.32463 | 0.532367 | ||||||||
\(40\) | 8.67088 | + | 4.70574i | 1.37099 | + | 0.744043i | ||||
\(41\) | 9.55090 | 1.49160 | 0.745800 | − | 0.666170i | \(-0.232068\pi\) | ||||
0.745800 | + | 0.666170i | \(0.232068\pi\) | |||||||
\(42\) | −1.95044 | − | 3.19308i | −0.300959 | − | 0.492704i | ||||
\(43\) | 6.80405 | − | 6.80405i | 1.03761 | − | 1.03761i | 0.0383425 | − | 0.999265i | \(-0.487792\pi\) |
0.999265 | − | 0.0383425i | \(-0.0122078\pi\) | |||||||
\(44\) | −0.386566 | + | 0.573266i | −0.0582770 | + | 0.0864231i | ||||
\(45\) | −2.46638 | − | 2.46638i | −0.367666 | − | 0.367666i | ||||
\(46\) | 0.897269 | + | 9.31224i | 0.132295 | + | 1.37302i | ||||
\(47\) | 7.20043 | 1.05029 | 0.525145 | − | 0.851013i | \(-0.324011\pi\) | ||||
0.525145 | + | 0.851013i | \(0.324011\pi\) | |||||||
\(48\) | −1.56198 | + | 3.68242i | −0.225452 | + | 0.531512i | ||||
\(49\) | 5.50315 | + | 4.32612i | 0.786165 | + | 0.618017i | ||||
\(50\) | −10.0876 | + | 0.971974i | −1.42660 | + | 0.137458i | ||||
\(51\) | 3.67109 | + | 3.67109i | 0.514056 | + | 0.514056i | ||||
\(52\) | 5.51296 | + | 3.71751i | 0.764510 | + | 0.515526i | ||||
\(53\) | 5.49720 | + | 5.49720i | 0.755099 | + | 0.755099i | 0.975426 | − | 0.220327i | \(-0.0707126\pi\) |
−0.220327 | + | 0.975426i | \(0.570713\pi\) | |||||||
\(54\) | 0.899481 | − | 1.09130i | 0.122404 | − | 0.148507i | ||||
\(55\) | − | 1.20584i | − | 0.162595i | ||||||
\(56\) | 0.336168 | − | 7.47576i | 0.0449224 | − | 0.998990i | ||||
\(57\) | 2.02377i | 0.268055i | ||||||||
\(58\) | 7.85844 | + | 6.47716i | 1.03186 | + | 0.850492i | ||||
\(59\) | −3.45643 | − | 3.45643i | −0.449988 | − | 0.449988i | 0.445362 | − | 0.895351i | \(-0.353075\pi\) |
−0.895351 | + | 0.445362i | \(0.853075\pi\) | |||||||
\(60\) | −1.33195 | − | 6.84762i | −0.171955 | − | 0.884025i | ||||
\(61\) | −1.27576 | − | 1.27576i | −0.163344 | − | 0.163344i | 0.620702 | − | 0.784046i | \(-0.286848\pi\) |
−0.784046 | + | 0.620702i | \(0.786848\pi\) | |||||||
\(62\) | 0.207952 | + | 2.15821i | 0.0264099 | + | 0.274093i | ||||
\(63\) | −0.865115 | + | 2.50032i | −0.108994 | + | 0.315010i | ||||
\(64\) | −6.70769 | + | 4.35969i | −0.838461 | + | 0.544961i | ||||
\(65\) | −11.5962 | −1.43834 | ||||||||
\(66\) | 0.486657 | − | 0.0468912i | 0.0599033 | − | 0.00577191i | ||||
\(67\) | 3.83774 | + | 3.83774i | 0.468855 | + | 0.468855i | 0.901543 | − | 0.432689i | \(-0.142435\pi\) |
−0.432689 | + | 0.901543i | \(0.642435\pi\) | |||||||
\(68\) | 1.98256 | + | 10.1924i | 0.240420 | + | 1.23601i | ||||
\(69\) | 4.67768 | − | 4.67768i | 0.563127 | − | 0.563127i | ||||
\(70\) | 6.80309 | + | 11.1374i | 0.813125 | + | 1.33118i | ||||
\(71\) | 16.0833 | 1.90874 | 0.954368 | − | 0.298632i | \(-0.0965304\pi\) | ||||
0.954368 | + | 0.298632i | \(0.0965304\pi\) | |||||||
\(72\) | 2.71180 | − | 0.803838i | 0.319588 | − | 0.0947332i | ||||
\(73\) | 6.68392 | 0.782293 | 0.391147 | − | 0.920328i | \(-0.372079\pi\) | ||||
0.391147 | + | 0.920328i | \(0.372079\pi\) | |||||||
\(74\) | −3.06356 | + | 3.71688i | −0.356131 | + | 0.432078i | ||||
\(75\) | 5.06714 | + | 5.06714i | 0.585103 | + | 0.585103i | ||||
\(76\) | −2.26292 | + | 3.35585i | −0.259575 | + | 0.384942i | ||||
\(77\) | −0.822697 | + | 0.399733i | −0.0937551 | + | 0.0455539i | ||||
\(78\) | −0.450941 | − | 4.68006i | −0.0510591 | − | 0.529913i | ||||
\(79\) | − | 4.09727i | − | 0.460979i | −0.973075 | − | 0.230490i | \(-0.925967\pi\) | ||
0.973075 | − | 0.230490i | \(-0.0740328\pi\) | |||||||
\(80\) | 5.44816 | − | 12.8442i | 0.609123 | − | 1.43603i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.29545 | − | 13.4447i | −0.143059 | − | 1.48472i | ||||
\(83\) | −9.70907 | + | 9.70907i | −1.06571 | + | 1.06571i | −0.0680257 | + | 0.997684i | \(0.521670\pi\) |
−0.997684 | + | 0.0680257i | \(0.978330\pi\) | |||||||
\(84\) | −4.23034 | + | 3.17872i | −0.461567 | + | 0.346827i | ||||
\(85\) | −12.8047 | − | 12.8047i | −1.38887 | − | 1.38887i | ||||
\(86\) | −10.5009 | − | 8.65514i | −1.13234 | − | 0.933307i | ||||
\(87\) | − | 7.20100i | − | 0.772028i | ||||||
\(88\) | 0.859416 | + | 0.466411i | 0.0916140 | + | 0.0497196i | ||||
\(89\) | 11.5562 | 1.22495 | 0.612477 | − | 0.790489i | \(-0.290173\pi\) | ||||
0.612477 | + | 0.790489i | \(0.290173\pi\) | |||||||
\(90\) | −3.13737 | + | 3.80643i | −0.330708 | + | 0.401233i | ||||
\(91\) | 3.84414 | + | 7.91168i | 0.402975 | + | 0.829370i | ||||
\(92\) | 12.9871 | − | 2.52616i | 1.35400 | − | 0.263370i | ||||
\(93\) | 1.08410 | − | 1.08410i | 0.112416 | − | 0.112416i | ||||
\(94\) | −0.976641 | − | 10.1360i | −0.100733 | − | 1.04545i | ||||
\(95\) | − | 7.05886i | − | 0.724224i | ||||||
\(96\) | 5.39558 | + | 1.69932i | 0.550684 | + | 0.173436i | ||||
\(97\) | − | 16.7160i | − | 1.69725i | −0.528995 | − | 0.848625i | \(-0.677431\pi\) | ||
0.528995 | − | 0.848625i | \(-0.322569\pi\) | |||||||
\(98\) | 5.34343 | − | 8.33353i | 0.539768 | − | 0.841814i | ||||
\(99\) | −0.244455 | − | 0.244455i | −0.0245687 | − | 0.0245687i | ||||
\(100\) | 2.73648 | + | 14.0684i | 0.273648 | + | 1.40684i | ||||
\(101\) | −10.5198 | + | 10.5198i | −1.04676 | + | 1.04676i | −0.0479051 | + | 0.998852i | \(0.515255\pi\) |
−0.998852 | + | 0.0479051i | \(0.984745\pi\) | |||||||
\(102\) | 4.66984 | − | 5.66571i | 0.462383 | − | 0.560989i | ||||
\(103\) | − | 5.39742i | − | 0.531824i | −0.963997 | − | 0.265912i | \(-0.914327\pi\) | ||
0.963997 | − | 0.265912i | \(-0.0856730\pi\) | |||||||
\(104\) | 4.48536 | − | 8.26480i | 0.439826 | − | 0.810430i | ||||
\(105\) | 3.01751 | − | 8.72105i | 0.294478 | − | 0.851088i | ||||
\(106\) | 6.99276 | − | 8.48400i | 0.679196 | − | 0.824039i | ||||
\(107\) | −5.63948 | + | 5.63948i | −0.545189 | + | 0.545189i | −0.925045 | − | 0.379857i | \(-0.875973\pi\) |
0.379857 | + | 0.925045i | \(0.375973\pi\) | |||||||
\(108\) | −1.65822 | − | 1.11817i | −0.159562 | − | 0.107596i | ||||
\(109\) | 1.70321 | − | 1.70321i | 0.163138 | − | 0.163138i | −0.620817 | − | 0.783955i | \(-0.713199\pi\) |
0.783955 | + | 0.620817i | \(0.213199\pi\) | |||||||
\(110\) | −1.69745 | + | 0.163556i | −0.161846 | + | 0.0155944i | ||||
\(111\) | 3.40592 | 0.323275 | ||||||||
\(112\) | −10.5692 | + | 0.540765i | −0.998694 | + | 0.0510974i | ||||
\(113\) | 5.88021 | 0.553163 | 0.276582 | − | 0.960990i | \(-0.410798\pi\) | ||||
0.276582 | + | 0.960990i | \(0.410798\pi\) | |||||||
\(114\) | 2.84885 | − | 0.274497i | 0.266819 | − | 0.0257090i | ||||
\(115\) | −16.3157 | + | 16.3157i | −1.52144 | + | 1.52144i | ||||
\(116\) | 8.05196 | − | 11.9408i | 0.747606 | − | 1.10868i | ||||
\(117\) | −2.35087 | + | 2.35087i | −0.217338 | + | 0.217338i | ||||
\(118\) | −4.39677 | + | 5.33441i | −0.404756 | + | 0.491072i | ||||
\(119\) | −4.49143 | + | 12.9809i | −0.411729 | + | 1.18996i | ||||
\(120\) | −9.45870 | + | 2.80377i | −0.863457 | + | 0.255948i | ||||
\(121\) | 10.8805i | 0.989135i | ||||||||
\(122\) | −1.62283 | + | 1.96891i | −0.146925 | + | 0.178257i | ||||
\(123\) | −6.75350 | + | 6.75350i | −0.608943 | + | 0.608943i | ||||
\(124\) | 3.00990 | − | 0.585465i | 0.270297 | − | 0.0525763i | ||||
\(125\) | −5.34221 | − | 5.34221i | −0.477822 | − | 0.477822i | ||||
\(126\) | 3.63702 | + | 0.878683i | 0.324012 | + | 0.0782793i | ||||
\(127\) | − | 2.54065i | − | 0.225446i | −0.993626 | − | 0.112723i | \(-0.964043\pi\) | ||
0.993626 | − | 0.112723i | \(-0.0359573\pi\) | |||||||
\(128\) | 7.04692 | + | 8.85104i | 0.622866 | + | 0.782329i | ||||
\(129\) | 9.62237i | 0.847203i | ||||||||
\(130\) | 1.57288 | + | 16.3240i | 0.137950 | + | 1.43171i | ||||
\(131\) | 1.36457 | − | 1.36457i | 0.119223 | − | 0.119223i | −0.644978 | − | 0.764201i | \(-0.723134\pi\) |
0.764201 | + | 0.644978i | \(0.223134\pi\) | |||||||
\(132\) | −0.132017 | − | 0.678704i | −0.0114906 | − | 0.0590736i | ||||
\(133\) | −4.81600 | + | 2.34000i | −0.417600 | + | 0.202904i | ||||
\(134\) | 4.88183 | − | 5.92290i | 0.421726 | − | 0.511661i | ||||
\(135\) | 3.48798 | 0.300198 | ||||||||
\(136\) | 14.0789 | − | 4.17330i | 1.20725 | − | 0.357857i | ||||
\(137\) | 8.81747i | 0.753327i | 0.926350 | + | 0.376664i | \(0.122929\pi\) | ||||
−0.926350 | + | 0.376664i | \(0.877071\pi\) | |||||||
\(138\) | −7.21921 | − | 5.95028i | −0.614540 | − | 0.506522i | ||||
\(139\) | −0.409417 | − | 0.409417i | −0.0347263 | − | 0.0347263i | 0.689530 | − | 0.724257i | \(-0.257817\pi\) |
−0.724257 | + | 0.689530i | \(0.757817\pi\) | |||||||
\(140\) | 14.7553 | − | 11.0873i | 1.24705 | − | 0.937049i | ||||
\(141\) | −5.09147 | + | 5.09147i | −0.428779 | + | 0.428779i | ||||
\(142\) | −2.18148 | − | 22.6404i | −0.183066 | − | 1.89994i | ||||
\(143\) | −1.14936 | −0.0961147 | ||||||||
\(144\) | −1.49938 | − | 3.70835i | −0.124948 | − | 0.309029i | ||||
\(145\) | 25.1169i | 2.08585i | ||||||||
\(146\) | −0.906583 | − | 9.40891i | −0.0750294 | − | 0.778687i | ||||
\(147\) | −6.95035 | + | 0.832287i | −0.573255 | + | 0.0686459i | ||||
\(148\) | 5.64776 | + | 3.80841i | 0.464243 | + | 0.313049i | ||||
\(149\) | 8.59190 | + | 8.59190i | 0.703876 | + | 0.703876i | 0.965240 | − | 0.261364i | \(-0.0841724\pi\) |
−0.261364 | + | 0.965240i | \(0.584172\pi\) | |||||||
\(150\) | 6.44569 | − | 7.82027i | 0.526289 | − | 0.638522i | ||||
\(151\) | −15.8215 | −1.28753 | −0.643767 | − | 0.765222i | \(-0.722629\pi\) | ||||
−0.643767 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(152\) | 5.03094 | + | 2.73033i | 0.408063 | + | 0.221459i | ||||
\(153\) | −5.19171 | −0.419725 | ||||||||
\(154\) | 0.674290 | + | 1.10389i | 0.0543359 | + | 0.0889538i | ||||
\(155\) | −3.78134 | + | 3.78134i | −0.303724 | + | 0.303724i | ||||
\(156\) | −6.52693 | + | 1.26958i | −0.522573 | + | 0.101647i | ||||
\(157\) | −13.3568 | − | 13.3568i | −1.06599 | − | 1.06599i | −0.997663 | − | 0.0683267i | \(-0.978234\pi\) |
−0.0683267 | − | 0.997663i | \(-0.521766\pi\) | |||||||
\(158\) | −5.76771 | + | 0.555740i | −0.458854 | + | 0.0442123i | ||||
\(159\) | −7.77422 | −0.616535 | ||||||||
\(160\) | −18.8197 | − | 5.92720i | −1.48783 | − | 0.468586i | ||||
\(161\) | 16.5402 | + | 5.72295i | 1.30355 | + | 0.451031i | ||||
\(162\) | 0.135637 | + | 1.40769i | 0.0106566 | + | 0.110599i | ||||
\(163\) | 11.2072 | + | 11.2072i | 0.877815 | + | 0.877815i | 0.993308 | − | 0.115493i | \(-0.0368449\pi\) |
−0.115493 | + | 0.993308i | \(0.536845\pi\) | |||||||
\(164\) | −18.7504 | + | 3.64720i | −1.46416 | + | 0.284798i | ||||
\(165\) | 0.852656 | + | 0.852656i | 0.0663792 | + | 0.0663792i | ||||
\(166\) | 14.9843 | + | 12.3505i | 1.16301 | + | 0.958585i | ||||
\(167\) | − | 15.6103i | − | 1.20796i | −0.796998 | − | 0.603981i | \(-0.793580\pi\) | ||
0.796998 | − | 0.603981i | \(-0.206420\pi\) | |||||||
\(168\) | 5.04845 | + | 5.52387i | 0.389497 | + | 0.426176i | ||||
\(169\) | − | 1.94683i | − | 0.149756i | ||||||
\(170\) | −16.2883 | + | 19.7619i | −1.24926 | + | 1.51567i | ||||
\(171\) | −1.43102 | − | 1.43102i | −0.109433 | − | 0.109433i | ||||
\(172\) | −10.7595 | + | 15.9560i | −0.820403 | + | 1.21663i | ||||
\(173\) | −6.62694 | − | 6.62694i | −0.503837 | − | 0.503837i | 0.408791 | − | 0.912628i | \(-0.365950\pi\) |
−0.912628 | + | 0.408791i | \(0.865950\pi\) | |||||||
\(174\) | −10.1368 | + | 0.976718i | −0.768469 | + | 0.0740448i | ||||
\(175\) | −6.19943 | + | 17.9173i | −0.468633 | + | 1.35442i | ||||
\(176\) | 0.539996 | − | 1.27306i | 0.0407037 | − | 0.0959603i | ||||
\(177\) | 4.88812 | 0.367414 | ||||||||
\(178\) | −1.56744 | − | 16.2676i | −0.117485 | − | 1.21931i | ||||
\(179\) | −1.58460 | − | 1.58460i | −0.118439 | − | 0.118439i | 0.645403 | − | 0.763842i | \(-0.276689\pi\) |
−0.763842 | + | 0.645403i | \(0.776689\pi\) | |||||||
\(180\) | 5.78384 | + | 3.90017i | 0.431102 | + | 0.290701i | ||||
\(181\) | 7.37897 | − | 7.37897i | 0.548475 | − | 0.548475i | −0.377525 | − | 0.925999i | \(-0.623225\pi\) |
0.925999 | + | 0.377525i | \(0.123225\pi\) | |||||||
\(182\) | 10.6158 | − | 6.48449i | 0.786897 | − | 0.480662i | ||||
\(183\) | 1.80419 | 0.133370 | ||||||||
\(184\) | −5.31759 | − | 17.9392i | −0.392018 | − | 1.32250i | ||||
\(185\) | −11.8798 | −0.873419 | ||||||||
\(186\) | −1.67313 | − | 1.37904i | −0.122680 | − | 0.101116i | ||||
\(187\) | −1.26914 | − | 1.26914i | −0.0928088 | − | 0.0928088i | ||||
\(188\) | −14.1359 | + | 2.74962i | −1.03097 | + | 0.200537i | ||||
\(189\) | −1.15626 | − | 2.37972i | −0.0841056 | − | 0.173099i | ||||
\(190\) | −9.93672 | + | 0.957440i | −0.720885 | + | 0.0694600i | ||||
\(191\) | − | 24.9642i | − | 1.80635i | −0.429274 | − | 0.903174i | \(-0.641231\pi\) | ||
0.429274 | − | 0.903174i | \(-0.358769\pi\) | |||||||
\(192\) | 1.66028 | − | 7.82582i | 0.119821 | − | 0.564780i | ||||
\(193\) | −9.84108 | −0.708376 | −0.354188 | − | 0.935174i | \(-0.615243\pi\) | ||||
−0.354188 | + | 0.935174i | \(0.615243\pi\) | |||||||
\(194\) | −23.5310 | + | 2.26730i | −1.68943 | + | 0.162782i | ||||
\(195\) | 8.19979 | − | 8.19979i | 0.587199 | − | 0.587199i | ||||
\(196\) | −12.4558 | − | 6.39158i | −0.889702 | − | 0.456541i | ||||
\(197\) | 6.20883 | + | 6.20883i | 0.442360 | + | 0.442360i | 0.892805 | − | 0.450444i | \(-0.148734\pi\) |
−0.450444 | + | 0.892805i | \(0.648734\pi\) | |||||||
\(198\) | −0.310961 | + | 0.377275i | −0.0220991 | + | 0.0268118i | ||||
\(199\) | 10.1707i | 0.720981i | 0.932763 | + | 0.360491i | \(0.117391\pi\) | ||||
−0.932763 | + | 0.360491i | \(0.882609\pi\) | |||||||
\(200\) | 19.4328 | − | 5.76032i | 1.37411 | − | 0.407316i | ||||
\(201\) | −5.42739 | −0.382818 | ||||||||
\(202\) | 16.2355 | + | 13.3818i | 1.14233 | + | 0.941538i | ||||
\(203\) | 17.1363 | − | 8.32623i | 1.20274 | − | 0.584387i | ||||
\(204\) | −8.60899 | − | 5.80523i | −0.602750 | − | 0.406448i | ||||
\(205\) | 23.5561 | − | 23.5561i | 1.64523 | − | 1.64523i | ||||
\(206\) | −7.59792 | + | 0.732088i | −0.529372 | + | 0.0510070i | ||||
\(207\) | 6.61525i | 0.459791i | ||||||||
\(208\) | −12.2427 | − | 5.19301i | −0.848877 | − | 0.360070i | ||||
\(209\) | − | 0.699641i | − | 0.0483952i | ||||||
\(210\) | −12.6859 | − | 3.06483i | −0.875407 | − | 0.211493i | ||||
\(211\) | −5.69803 | − | 5.69803i | −0.392269 | − | 0.392269i | 0.483227 | − | 0.875495i | \(-0.339465\pi\) |
−0.875495 | + | 0.483227i | \(0.839465\pi\) | |||||||
\(212\) | −12.8913 | − | 8.69292i | −0.885381 | − | 0.597032i | ||||
\(213\) | −11.3726 | + | 11.3726i | −0.779238 | + | 0.779238i | ||||
\(214\) | 8.70358 | + | 7.17374i | 0.594964 | + | 0.490387i | ||||
\(215\) | − | 33.5627i | − | 2.28895i | ||||||
\(216\) | −1.34913 | + | 2.48593i | −0.0917967 | + | 0.169146i | ||||
\(217\) | 3.83337 | + | 1.32636i | 0.260226 | + | 0.0900389i | ||||
\(218\) | −2.62862 | − | 2.16658i | −0.178033 | − | 0.146740i | ||||
\(219\) | −4.72624 | + | 4.72624i | −0.319370 | + | 0.319370i | ||||
\(220\) | 0.460473 | + | 2.36731i | 0.0310451 | + | 0.159604i | ||||
\(221\) | −12.2050 | + | 12.2050i | −0.820999 | + | 0.820999i | ||||
\(222\) | −0.461967 | − | 4.79449i | −0.0310052 | − | 0.321785i | ||||
\(223\) | 5.26554 | 0.352607 | 0.176303 | − | 0.984336i | \(-0.443586\pi\) | ||||
0.176303 | + | 0.984336i | \(0.443586\pi\) | |||||||
\(224\) | 2.19480 | + | 14.8048i | 0.146646 | + | 0.989189i | ||||
\(225\) | −7.16602 | −0.477734 | ||||||||
\(226\) | −0.797571 | − | 8.27753i | −0.0530536 | − | 0.550613i | ||||
\(227\) | 11.3768 | − | 11.3768i | 0.755102 | − | 0.755102i | −0.220325 | − | 0.975427i | \(-0.570712\pi\) |
0.975427 | + | 0.220325i | \(0.0707117\pi\) | |||||||
\(228\) | −0.772815 | − | 3.97307i | −0.0511809 | − | 0.263123i | ||||
\(229\) | −14.8763 | + | 14.8763i | −0.983051 | + | 0.983051i | −0.999859 | − | 0.0168077i | \(-0.994650\pi\) |
0.0168077 | + | 0.999859i | \(0.494650\pi\) | |||||||
\(230\) | 25.1805 | + | 20.7545i | 1.66035 | + | 1.36851i | ||||
\(231\) | 0.299081 | − | 0.864389i | 0.0196781 | − | 0.0568726i | ||||
\(232\) | −17.9012 | − | 9.71509i | −1.17527 | − | 0.637827i | ||||
\(233\) | − | 2.12538i | − | 0.139238i | −0.997574 | − | 0.0696190i | \(-0.977822\pi\) | ||
0.997574 | − | 0.0696190i | \(-0.0221783\pi\) | |||||||
\(234\) | 3.62817 | + | 2.99044i | 0.237181 | + | 0.195491i | ||||
\(235\) | 17.7590 | − | 17.7590i | 1.15847 | − | 1.15847i | ||||
\(236\) | 8.10558 | + | 5.46577i | 0.527628 | + | 0.355791i | ||||
\(237\) | 2.89721 | + | 2.89721i | 0.188194 | + | 0.188194i | ||||
\(238\) | 18.8824 | + | 4.56187i | 1.22396 | + | 0.295702i | ||||
\(239\) | 8.94355i | 0.578510i | 0.957252 | + | 0.289255i | \(0.0934076\pi\) | ||||
−0.957252 | + | 0.289255i | \(0.906592\pi\) | |||||||
\(240\) | 5.22980 | + | 12.9347i | 0.337582 | + | 0.834929i | ||||
\(241\) | − | 4.16309i | − | 0.268168i | −0.990970 | − | 0.134084i | \(-0.957191\pi\) | ||
0.990970 | − | 0.134084i | \(-0.0428092\pi\) | |||||||
\(242\) | 15.3164 | − | 1.47579i | 0.984575 | − | 0.0948675i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 2.99174 | + | 2.01740i | 0.191527 | + | 0.129151i | ||||
\(245\) | 24.2427 | − | 2.90300i | 1.54881 | − | 0.185466i | ||||
\(246\) | 10.4229 | + | 8.59084i | 0.664539 | + | 0.547732i | ||||
\(247\) | −6.72828 | −0.428110 | ||||||||
\(248\) | −1.23241 | − | 4.15761i | −0.0782580 | − | 0.264008i | ||||
\(249\) | − | 13.7307i | − | 0.870148i | ||||||
\(250\) | −6.79560 | + | 8.24480i | −0.429791 | + | 0.521447i | ||||
\(251\) | −0.848419 | − | 0.848419i | −0.0535518 | − | 0.0535518i | 0.679824 | − | 0.733376i | \(-0.262056\pi\) |
−0.733376 | + | 0.679824i | \(0.762056\pi\) | |||||||
\(252\) | 0.743604 | − | 5.23899i | 0.0468427 | − | 0.330026i | ||||
\(253\) | −1.61713 | + | 1.61713i | −0.101668 | + | 0.101668i | ||||
\(254\) | −3.57646 | + | 0.344605i | −0.224407 | + | 0.0216224i | ||||
\(255\) | 18.1086 | 1.13400 | ||||||||
\(256\) | 11.5037 | − | 11.1204i | 0.718984 | − | 0.695027i | ||||
\(257\) | 20.1074i | 1.25426i | 0.778913 | + | 0.627132i | \(0.215772\pi\) | ||||
−0.778913 | + | 0.627132i | \(0.784228\pi\) | |||||||
\(258\) | 13.5454 | − | 1.30515i | 0.843297 | − | 0.0812548i | ||||
\(259\) | 3.93813 | + | 8.10513i | 0.244703 | + | 0.503628i | ||||
\(260\) | 22.7658 | − | 4.42826i | 1.41188 | − | 0.274629i | ||||
\(261\) | 5.09187 | + | 5.09187i | 0.315179 | + | 0.315179i | ||||
\(262\) | −2.10598 | − | 1.73581i | −0.130108 | − | 0.107239i | ||||
\(263\) | −6.57887 | −0.405671 | −0.202835 | − | 0.979213i | \(-0.565016\pi\) | ||||
−0.202835 | + | 0.979213i | \(0.565016\pi\) | |||||||
\(264\) | −0.937501 | + | 0.277897i | −0.0576992 | + | 0.0171033i | ||||
\(265\) | 27.1163 | 1.66574 | ||||||||
\(266\) | 3.94723 | + | 6.46206i | 0.242020 | + | 0.396214i | ||||
\(267\) | −8.17146 | + | 8.17146i | −0.500085 | + | 0.500085i | ||||
\(268\) | −8.99979 | − | 6.06876i | −0.549750 | − | 0.370708i | ||||
\(269\) | 18.5658 | + | 18.5658i | 1.13198 | + | 1.13198i | 0.989848 | + | 0.142129i | \(0.0453949\pi\) |
0.142129 | + | 0.989848i | \(0.454605\pi\) | |||||||
\(270\) | −0.473098 | − | 4.91001i | −0.0287918 | − | 0.298814i | ||||
\(271\) | 22.1109 | 1.34314 | 0.671569 | − | 0.740942i | \(-0.265621\pi\) | ||||
0.671569 | + | 0.740942i | \(0.265621\pi\) | |||||||
\(272\) | −7.78433 | − | 19.2527i | −0.471995 | − | 1.16737i | ||||
\(273\) | −8.31262 | − | 2.87619i | −0.503103 | − | 0.174075i | ||||
\(274\) | 12.4123 | − | 1.19597i | 0.749854 | − | 0.0722513i | ||||
\(275\) | −1.75177 | − | 1.75177i | −0.105636 | − | 0.105636i | ||||
\(276\) | −7.39699 | + | 10.9695i | −0.445247 | + | 0.660288i | ||||
\(277\) | −14.1965 | − | 14.1965i | −0.852983 | − | 0.852983i | 0.137516 | − | 0.990499i | \(-0.456088\pi\) |
−0.990499 | + | 0.137516i | \(0.956088\pi\) | |||||||
\(278\) | −0.520802 | + | 0.631866i | −0.0312356 | + | 0.0378968i | ||||
\(279\) | 1.53315i | 0.0917876i | ||||||||
\(280\) | −17.6089 | − | 19.2671i | −1.05233 | − | 1.15143i | ||||
\(281\) | − | 0.533748i | − | 0.0318407i | −0.999873 | − | 0.0159204i | \(-0.994932\pi\) | ||
0.999873 | − | 0.0159204i | \(-0.00506782\pi\) | |||||||
\(282\) | 7.85782 | + | 6.47664i | 0.467927 | + | 0.385678i | ||||
\(283\) | −19.5036 | − | 19.5036i | −1.15937 | − | 1.15937i | −0.984612 | − | 0.174754i | \(-0.944087\pi\) |
−0.174754 | − | 0.984612i | \(-0.555913\pi\) | |||||||
\(284\) | −31.5748 | + | 6.14172i | −1.87362 | + | 0.364444i | ||||
\(285\) | 4.99137 | + | 4.99137i | 0.295663 | + | 0.295663i | ||||
\(286\) | 0.155896 | + | 1.61795i | 0.00921832 | + | 0.0956716i | ||||
\(287\) | −23.8802 | − | 8.26262i | −1.40961 | − | 0.487727i | ||||
\(288\) | −5.01685 | + | 2.61365i | −0.295621 | + | 0.154011i | ||||
\(289\) | −9.95388 | −0.585522 | ||||||||
\(290\) | 35.3570 | − | 3.40678i | 2.07623 | − | 0.200053i | ||||
\(291\) | 11.8200 | + | 11.8200i | 0.692899 | + | 0.692899i | ||||
\(292\) | −13.1219 | + | 2.55238i | −0.767901 | + | 0.149367i | ||||
\(293\) | 13.2601 | − | 13.2601i | 0.774661 | − | 0.774661i | −0.204256 | − | 0.978917i | \(-0.565478\pi\) |
0.978917 | + | 0.204256i | \(0.0654775\pi\) | |||||||
\(294\) | 2.11433 | + | 9.67107i | 0.123310 | + | 0.564028i | ||||
\(295\) | −17.0497 | −0.992671 | ||||||||
\(296\) | 4.59503 | − | 8.46687i | 0.267081 | − | 0.492127i | ||||
\(297\) | 0.345712 | 0.0200602 | ||||||||
\(298\) | 10.9294 | − | 13.2601i | 0.633123 | − | 0.768139i | ||||
\(299\) | 15.5516 | + | 15.5516i | 0.899371 | + | 0.899371i | ||||
\(300\) | −11.8828 | − | 8.01285i | −0.686055 | − | 0.462622i | ||||
\(301\) | −22.8985 | + | 11.1260i | −1.31985 | + | 0.641291i | ||||
\(302\) | 2.14597 | + | 22.2718i | 0.123487 | + | 1.28160i | ||||
\(303\) | − | 14.8772i | − | 0.854674i | ||||||
\(304\) | 3.16109 | − | 7.45236i | 0.181301 | − | 0.427422i | ||||
\(305\) | −6.29298 | −0.360335 | ||||||||
\(306\) | 0.704186 | + | 7.30834i | 0.0402556 | + | 0.417790i | ||||
\(307\) | 8.75073 | − | 8.75073i | 0.499430 | − | 0.499430i | −0.411830 | − | 0.911261i | \(-0.635110\pi\) |
0.911261 | + | 0.411830i | \(0.135110\pi\) | |||||||
\(308\) | 1.46248 | − | 1.09892i | 0.0833324 | − | 0.0626169i | ||||
\(309\) | 3.81655 | + | 3.81655i | 0.217116 | + | 0.217116i | ||||
\(310\) | 5.83585 | + | 4.81008i | 0.331454 | + | 0.273194i | ||||
\(311\) | 12.5063i | 0.709170i | 0.935024 | + | 0.354585i | \(0.115378\pi\) | ||||
−0.935024 | + | 0.354585i | \(0.884622\pi\) | |||||||
\(312\) | 2.67246 | + | 9.01572i | 0.151298 | + | 0.510415i | ||||
\(313\) | −30.6740 | −1.73380 | −0.866899 | − | 0.498484i | \(-0.833890\pi\) | ||||
−0.866899 | + | 0.498484i | \(0.833890\pi\) | |||||||
\(314\) | −16.9906 | + | 20.6140i | −0.958837 | + | 1.16331i | ||||
\(315\) | 4.03302 | + | 8.30041i | 0.227235 | + | 0.467675i | ||||
\(316\) | 1.56462 | + | 8.04379i | 0.0880170 | + | 0.452498i | ||||
\(317\) | −6.56844 | + | 6.56844i | −0.368920 | + | 0.368920i | −0.867083 | − | 0.498163i | \(-0.834008\pi\) |
0.498163 | + | 0.867083i | \(0.334008\pi\) | |||||||
\(318\) | 1.05447 | + | 10.9437i | 0.0591316 | + | 0.613693i | ||||
\(319\) | 2.48947i | 0.139384i | ||||||||
\(320\) | −5.79104 | + | 27.2963i | −0.323729 | + | 1.52591i | ||||
\(321\) | − | 7.97542i | − | 0.445145i | ||||||
\(322\) | 5.81270 | − | 24.0598i | 0.323929 | − | 1.34080i | ||||
\(323\) | −7.42944 | − | 7.42944i | −0.413385 | − | 0.413385i | ||||
\(324\) | 1.96321 | − | 0.381870i | 0.109067 | − | 0.0212150i | ||||
\(325\) | −16.8464 | + | 16.8464i | −0.934468 | + | 0.934468i | ||||
\(326\) | 14.2562 | − | 17.2964i | 0.789577 | − | 0.957959i | ||||
\(327\) | 2.40871i | 0.133202i | ||||||||
\(328\) | 7.67737 | + | 25.9001i | 0.423912 | + | 1.43009i | ||||
\(329\) | −18.0033 | − | 6.22920i | −0.992556 | − | 0.343427i | ||||
\(330\) | 1.08463 | − | 1.31593i | 0.0597068 | − | 0.0724396i | ||||
\(331\) | 2.86508 | − | 2.86508i | 0.157479 | − | 0.157479i | −0.623969 | − | 0.781449i | \(-0.714481\pi\) |
0.781449 | + | 0.623969i | \(0.214481\pi\) | |||||||
\(332\) | 15.3533 | − | 22.7685i | 0.842622 | − | 1.24958i | ||||
\(333\) | −2.40835 | + | 2.40835i | −0.131977 | + | 0.131977i | ||||
\(334\) | −21.9746 | + | 2.11733i | −1.20239 | + | 0.115855i | ||||
\(335\) | 18.9306 | 1.03429 | ||||||||
\(336\) | 7.09116 | − | 7.85592i | 0.386855 | − | 0.428575i | ||||
\(337\) | 23.4976 | 1.28000 | 0.639999 | − | 0.768376i | \(-0.278935\pi\) | ||||
0.639999 | + | 0.768376i | \(0.278935\pi\) | |||||||
\(338\) | −2.74055 | + | 0.264062i | −0.149066 | + | 0.0143631i | ||||
\(339\) | −4.15793 | + | 4.15793i | −0.225828 | + | 0.225828i | ||||
\(340\) | 30.0280 | + | 20.2485i | 1.62850 | + | 1.09813i | ||||
\(341\) | −0.374788 | + | 0.374788i | −0.0202959 | + | 0.0202959i | ||||
\(342\) | −1.82034 | + | 2.20854i | −0.0984327 | + | 0.119424i | ||||
\(343\) | −10.0170 | − | 15.5775i | −0.540868 | − | 0.841107i | ||||
\(344\) | 23.9205 | + | 12.9818i | 1.28971 | + | 0.699934i | ||||
\(345\) | − | 23.0739i | − | 1.24225i | ||||||
\(346\) | −8.42985 | + | 10.2276i | −0.453191 | + | 0.549837i | ||||
\(347\) | 7.30416 | − | 7.30416i | 0.392108 | − | 0.392108i | −0.483330 | − | 0.875438i | \(-0.660573\pi\) |
0.875438 | + | 0.483330i | \(0.160573\pi\) | |||||||
\(348\) | 2.74984 | + | 14.1370i | 0.147407 | + | 0.757825i | ||||
\(349\) | 10.4160 | + | 10.4160i | 0.557555 | + | 0.557555i | 0.928611 | − | 0.371055i | \(-0.121004\pi\) |
−0.371055 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(350\) | 26.0629 | + | 6.29666i | 1.39312 | + | 0.336571i | ||||
\(351\) | − | 3.32463i | − | 0.177456i | ||||||
\(352\) | −1.86532 | − | 0.587476i | −0.0994218 | − | 0.0313126i | ||||
\(353\) | 0.352884i | 0.0187821i | 0.999956 | + | 0.00939107i | \(0.00298931\pi\) | ||||
−0.999956 | + | 0.00939107i | \(0.997011\pi\) | |||||||
\(354\) | −0.663008 | − | 6.88098i | −0.0352385 | − | 0.365720i | ||||
\(355\) | 39.6675 | − | 39.6675i | 2.10533 | − | 2.10533i | ||||
\(356\) | −22.6872 | + | 4.41296i | −1.20242 | + | 0.233886i | ||||
\(357\) | −6.00297 | − | 12.3548i | −0.317711 | − | 0.653886i | ||||
\(358\) | −2.01571 | + | 2.44557i | −0.106533 | + | 0.129252i | ||||
\(359\) | 2.93757 | 0.155039 | 0.0775194 | − | 0.996991i | \(-0.475300\pi\) | ||||
0.0775194 | + | 0.996991i | \(0.475300\pi\) | |||||||
\(360\) | 4.70574 | − | 8.67088i | 0.248014 | − | 0.456995i | ||||
\(361\) | 14.9044i | 0.784440i | ||||||||
\(362\) | −11.3882 | − | 9.38647i | −0.598550 | − | 0.493342i | ||||
\(363\) | −7.69366 | − | 7.69366i | −0.403813 | − | 0.403813i | ||||
\(364\) | −10.5681 | − | 14.0643i | −0.553917 | − | 0.737170i | ||||
\(365\) | 16.4850 | − | 16.4850i | 0.862867 | − | 0.862867i | ||||
\(366\) | −0.244714 | − | 2.53975i | −0.0127914 | − | 0.132755i | ||||
\(367\) | 33.3562 | 1.74118 | 0.870589 | − | 0.492010i | \(-0.163738\pi\) | ||||
0.870589 | + | 0.492010i | \(0.163738\pi\) | |||||||
\(368\) | −24.5317 | + | 9.91875i | −1.27880 | + | 0.517050i | ||||
\(369\) | − | 9.55090i | − | 0.497200i | ||||||
\(370\) | 1.61133 | + | 16.7231i | 0.0837692 | + | 0.869392i | ||||
\(371\) | −8.98902 | − | 18.5004i | −0.466687 | − | 0.960495i | ||||
\(372\) | −1.71433 | + | 2.54231i | −0.0888840 | + | 0.131812i | ||||
\(373\) | 19.0617 | + | 19.0617i | 0.986977 | + | 0.986977i | 0.999916 | − | 0.0129389i | \(-0.00411870\pi\) |
−0.0129389 | + | 0.999916i | \(0.504119\pi\) | |||||||
\(374\) | −1.61442 | + | 1.95871i | −0.0834797 | + | 0.101282i | ||||
\(375\) | 7.55502 | 0.390140 | ||||||||
\(376\) | 5.78798 | + | 19.5261i | 0.298492 | + | 1.00698i | ||||
\(377\) | 23.9407 | 1.23301 | ||||||||
\(378\) | −3.19308 | + | 1.95044i | −0.164235 | + | 0.100320i | ||||
\(379\) | −8.93678 | + | 8.93678i | −0.459051 | + | 0.459051i | −0.898344 | − | 0.439293i | \(-0.855229\pi\) |
0.439293 | + | 0.898344i | \(0.355229\pi\) | |||||||
\(380\) | 2.69557 | + | 13.8580i | 0.138280 | + | 0.710900i | ||||
\(381\) | 1.79651 | + | 1.79651i | 0.0920381 | + | 0.0920381i | ||||
\(382\) | −35.1420 | + | 3.38606i | −1.79802 | + | 0.173246i | ||||
\(383\) | −30.1669 | −1.54145 | −0.770727 | − | 0.637165i | \(-0.780107\pi\) | ||||
−0.770727 | + | 0.637165i | \(0.780107\pi\) | |||||||
\(384\) | −11.2416 | − | 1.27571i | −0.573668 | − | 0.0651006i | ||||
\(385\) | −1.04319 | + | 3.01497i | −0.0531658 | + | 0.153657i | ||||
\(386\) | 1.33481 | + | 13.8532i | 0.0679400 | + | 0.705111i | ||||
\(387\) | −6.80405 | − | 6.80405i | −0.345869 | − | 0.345869i | ||||
\(388\) | 6.38332 | + | 32.8169i | 0.324064 | + | 1.66602i | ||||
\(389\) | 9.88128 | + | 9.88128i | 0.501001 | + | 0.501001i | 0.911749 | − | 0.410748i | \(-0.134732\pi\) |
−0.410748 | + | 0.911749i | \(0.634732\pi\) | |||||||
\(390\) | −12.6550 | − | 10.4306i | −0.640810 | − | 0.528174i | ||||
\(391\) | 34.3445i | 1.73687i | ||||||||
\(392\) | −7.30792 | + | 18.4009i | −0.369106 | + | 0.929387i | ||||
\(393\) | 1.92979i | 0.0973451i | ||||||||
\(394\) | 7.89798 | − | 9.58227i | 0.397895 | − | 0.482748i | ||||
\(395\) | −10.1054 | − | 10.1054i | −0.508459 | − | 0.508459i | ||||
\(396\) | 0.573266 | + | 0.386566i | 0.0288077 | + | 0.0194257i | ||||
\(397\) | 5.73434 | + | 5.73434i | 0.287798 | + | 0.287798i | 0.836209 | − | 0.548411i | \(-0.184767\pi\) |
−0.548411 | + | 0.836209i | \(0.684767\pi\) | |||||||
\(398\) | 14.3172 | − | 1.37952i | 0.717657 | − | 0.0691490i | ||||
\(399\) | 1.75079 | − | 5.06006i | 0.0876492 | − | 0.253320i | ||||
\(400\) | −10.7446 | − | 26.5741i | −0.537228 | − | 1.32871i | ||||
\(401\) | 10.0283 | 0.500789 | 0.250394 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250394 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(402\) | 0.736152 | + | 7.64010i | 0.0367159 | + | 0.381053i | ||||
\(403\) | 3.60425 | + | 3.60425i | 0.179540 | + | 0.179540i | ||||
\(404\) | 16.6353 | − | 24.6697i | 0.827637 | − | 1.22736i | ||||
\(405\) | −2.46638 | + | 2.46638i | −0.122555 | + | 0.122555i | ||||
\(406\) | −14.0451 | − | 22.9934i | −0.697047 | − | 1.14114i | ||||
\(407\) | −1.17747 | −0.0583649 | ||||||||
\(408\) | −7.00430 | + | 12.9062i | −0.346764 | + | 0.638954i | ||||
\(409\) | 16.0808 | 0.795145 | 0.397572 | − | 0.917571i | \(-0.369853\pi\) | ||||
0.397572 | + | 0.917571i | \(0.369853\pi\) | |||||||
\(410\) | −36.3548 | − | 29.9647i | −1.79544 | − | 1.47985i | ||||
\(411\) | −6.23489 | − | 6.23489i | −0.307545 | − | 0.307545i | ||||
\(412\) | 2.06111 | + | 10.5962i | 0.101544 | + | 0.522040i | ||||
\(413\) | 5.65195 | + | 11.6324i | 0.278114 | + | 0.572391i | ||||
\(414\) | 9.31224 | − | 0.897269i | 0.457672 | − | 0.0440984i | ||||
\(415\) | 47.8924i | 2.35095i | ||||||||
\(416\) | −5.64961 | + | 17.9383i | −0.276995 | + | 0.879498i | ||||
\(417\) | 0.579003 | 0.0283539 | ||||||||
\(418\) | −0.984880 | + | 0.0948969i | −0.0481721 | + | 0.00464156i | ||||
\(419\) | −6.59346 | + | 6.59346i | −0.322112 | + | 0.322112i | −0.849577 | − | 0.527465i | \(-0.823143\pi\) |
0.527465 | + | 0.849577i | \(0.323143\pi\) | |||||||
\(420\) | −2.59368 | + | 18.2735i | −0.126559 | + | 0.891656i | ||||
\(421\) | −4.63581 | − | 4.63581i | −0.225936 | − | 0.225936i | 0.585057 | − | 0.810992i | \(-0.301072\pi\) |
−0.810992 | + | 0.585057i | \(0.801072\pi\) | |||||||
\(422\) | −7.24822 | + | 8.79395i | −0.352838 | + | 0.428083i | ||||
\(423\) | − | 7.20043i | − | 0.350097i | ||||||
\(424\) | −10.4884 | + | 19.3262i | −0.509363 | + | 0.938561i | ||||
\(425\) | −37.2039 | −1.80465 | ||||||||
\(426\) | 17.5517 | + | 14.4666i | 0.850383 | + | 0.700910i | ||||
\(427\) | 2.08612 | + | 4.29347i | 0.100954 | + | 0.207775i | ||||
\(428\) | 8.91791 | − | 13.2250i | 0.431063 | − | 0.639254i | ||||
\(429\) | 0.812724 | − | 0.812724i | 0.0392387 | − | 0.0392387i | ||||
\(430\) | −47.2460 | + | 4.55232i | −2.27840 | + | 0.219533i | ||||
\(431\) | − | 9.22678i | − | 0.444438i | −0.974997 | − | 0.222219i | \(-0.928670\pi\) | ||
0.974997 | − | 0.222219i | \(-0.0713301\pi\) | |||||||
\(432\) | 3.68242 | + | 1.56198i | 0.177171 | + | 0.0751508i | ||||
\(433\) | − | 20.5961i | − | 0.989786i | −0.868954 | − | 0.494893i | \(-0.835207\pi\) | ||
0.868954 | − | 0.494893i | \(-0.164793\pi\) | |||||||
\(434\) | 1.34716 | − | 5.57611i | 0.0646656 | − | 0.267662i | ||||
\(435\) | −17.7604 | − | 17.7604i | −0.851544 | − | 0.851544i | ||||
\(436\) | −2.69335 | + | 3.99416i | −0.128988 | + | 0.191286i | ||||
\(437\) | −9.46655 | + | 9.46655i | −0.452846 | + | 0.452846i | ||||
\(438\) | 7.29415 | + | 6.01205i | 0.348528 | + | 0.287267i | ||||
\(439\) | − | 30.5005i | − | 1.45571i | −0.685731 | − | 0.727855i | \(-0.740517\pi\) | ||
0.685731 | − | 0.727855i | \(-0.259483\pi\) | |||||||
\(440\) | 3.26999 | − | 0.969298i | 0.155890 | − | 0.0462095i | ||||
\(441\) | 4.32612 | − | 5.50315i | 0.206006 | − | 0.262055i | ||||
\(442\) | 18.8364 | + | 15.5255i | 0.895956 | + | 0.738473i | ||||
\(443\) | −16.6469 | + | 16.6469i | −0.790916 | + | 0.790916i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.190727 | + | 0.981643i | \(0.438916\pi\) | |||||||
\(444\) | −6.68652 | + | 1.30062i | −0.317328 | + | 0.0617245i | ||||
\(445\) | 28.5019 | − | 28.5019i | 1.35112 | − | 1.35112i | ||||
\(446\) | −0.714200 | − | 7.41228i | −0.0338184 | − | 0.350981i | ||||
\(447\) | −12.1508 | −0.574712 | ||||||||
\(448\) | 20.5430 | − | 5.09768i | 0.970564 | − | 0.240843i | ||||
\(449\) | 10.8337 | 0.511272 | 0.255636 | − | 0.966773i | \(-0.417715\pi\) | ||||
0.255636 | + | 0.966773i | \(0.417715\pi\) | |||||||
\(450\) | 0.971974 | + | 10.0876i | 0.0458193 | + | 0.475532i | ||||
\(451\) | 2.33477 | − | 2.33477i | 0.109940 | − | 0.109940i | ||||
\(452\) | −11.5441 | + | 2.24547i | −0.542987 | + | 0.105618i | ||||
\(453\) | 11.1875 | − | 11.1875i | 0.525633 | − | 0.525633i | ||||
\(454\) | −17.5581 | − | 14.4719i | −0.824043 | − | 0.679200i | ||||
\(455\) | 28.9943 | + | 10.0321i | 1.35927 | + | 0.470312i | ||||
\(456\) | −5.48805 | + | 1.62678i | −0.257001 | + | 0.0761810i | ||||
\(457\) | 35.1980i | 1.64650i | 0.567683 | + | 0.823248i | \(0.307840\pi\) | ||||
−0.567683 | + | 0.823248i | \(0.692160\pi\) | |||||||
\(458\) | 22.9590 | + | 18.9235i | 1.07280 | + | 0.884235i | ||||
\(459\) | 3.67109 | − | 3.67109i | 0.171352 | − | 0.171352i | ||||
\(460\) | 25.8006 | − | 38.2615i | 1.20296 | − | 1.78395i | ||||
\(461\) | −27.0443 | − | 27.0443i | −1.25958 | − | 1.25958i | −0.951294 | − | 0.308286i | \(-0.900245\pi\) |
−0.308286 | − | 0.951294i | \(-0.599755\pi\) | |||||||
\(462\) | −1.25736 | − | 0.303771i | −0.0584978 | − | 0.0141327i | ||||
\(463\) | − | 18.6030i | − | 0.864556i | −0.901740 | − | 0.432278i | \(-0.857710\pi\) | ||
0.901740 | − | 0.432278i | \(-0.142290\pi\) | |||||||
\(464\) | −11.2478 | + | 26.5171i | −0.522167 | + | 1.23103i | ||||
\(465\) | − | 5.34762i | − | 0.247990i | ||||||
\(466\) | −2.99188 | + | 0.288279i | −0.138596 | + | 0.0133542i | ||||
\(467\) | 10.0714 | − | 10.0714i | 0.466047 | − | 0.466047i | −0.434584 | − | 0.900631i | \(-0.643105\pi\) |
0.900631 | + | 0.434584i | \(0.143105\pi\) | |||||||
\(468\) | 3.71751 | − | 5.51296i | 0.171842 | − | 0.254837i | ||||
\(469\) | −6.27547 | − | 12.9156i | −0.289774 | − | 0.596389i | ||||
\(470\) | −27.4079 | − | 22.5904i | −1.26423 | − | 1.04202i | ||||
\(471\) | 18.8894 | 0.870377 | ||||||||
\(472\) | 6.59472 | − | 12.1515i | 0.303547 | − | 0.559320i | ||||
\(473\) | − | 3.32657i | − | 0.152956i | ||||||
\(474\) | 3.68542 | − | 4.47135i | 0.169277 | − | 0.205376i | ||||
\(475\) | −10.2547 | − | 10.2547i | −0.470518 | − | 0.470518i | ||||
\(476\) | 3.86058 | − | 27.1993i | 0.176949 | − | 1.24668i | ||||
\(477\) | 5.49720 | − | 5.49720i | 0.251700 | − | 0.251700i | ||||
\(478\) | 12.5898 | − | 1.21307i | 0.575843 | − | 0.0554847i | ||||
\(479\) | 8.19876 | 0.374611 | 0.187305 | − | 0.982302i | \(-0.440025\pi\) | ||||
0.187305 | + | 0.982302i | \(0.440025\pi\) | |||||||
\(480\) | 17.4987 | − | 9.11637i | 0.798702 | − | 0.416103i | ||||
\(481\) | 11.3234i | 0.516303i | ||||||||
\(482\) | −5.86036 | + | 0.564667i | −0.266932 | + | 0.0257199i | ||||
\(483\) | −15.7424 | + | 7.64895i | −0.716305 | + | 0.348039i | ||||
\(484\) | −4.15493 | − | 21.3606i | −0.188860 | − | 0.970937i | ||||
\(485\) | −41.2279 | − | 41.2279i | −1.87206 | − | 1.87206i | ||||
\(486\) | −1.09130 | − | 0.899481i | −0.0495024 | − | 0.0408013i | ||||
\(487\) | 18.4865 | 0.837705 | 0.418852 | − | 0.908054i | \(-0.362432\pi\) | ||||
0.418852 | + | 0.908054i | \(0.362432\pi\) | |||||||
\(488\) | 2.43409 | − | 4.48509i | 0.110186 | − | 0.203031i | ||||
\(489\) | −15.8494 | −0.716733 | ||||||||
\(490\) | −7.37473 | − | 33.7325i | −0.333156 | − | 1.52388i | ||||
\(491\) | −7.92543 | + | 7.92543i | −0.357670 | + | 0.357670i | −0.862953 | − | 0.505284i | \(-0.831388\pi\) |
0.505284 | + | 0.862953i | \(0.331388\pi\) | |||||||
\(492\) | 10.6796 | − | 15.8375i | 0.481472 | − | 0.714008i | ||||
\(493\) | 26.4355 | + | 26.4355i | 1.19060 | + | 1.19060i | ||||
\(494\) | 0.912601 | + | 9.47136i | 0.0410598 | + | 0.426137i | ||||
\(495\) | −1.20584 | −0.0541984 | ||||||||
\(496\) | −5.68548 | + | 2.29878i | −0.255285 | + | 0.103218i | ||||
\(497\) | −40.2133 | − | 13.9139i | −1.80381 | − | 0.624124i | ||||
\(498\) | −19.3286 | + | 1.86239i | −0.866137 | + | 0.0834555i | ||||
\(499\) | −2.98057 | − | 2.98057i | −0.133429 | − | 0.133429i | 0.637238 | − | 0.770667i | \(-0.280077\pi\) |
−0.770667 | + | 0.637238i | \(0.780077\pi\) | |||||||
\(500\) | 12.5279 | + | 8.44783i | 0.560264 | + | 0.377798i | ||||
\(501\) | 11.0382 | + | 11.0382i | 0.493149 | + | 0.493149i | ||||
\(502\) | −1.07924 | + | 1.30939i | −0.0481688 | + | 0.0584410i | ||||
\(503\) | − | 4.63846i | − | 0.206819i | −0.994639 | − | 0.103409i | \(-0.967025\pi\) | ||
0.994639 | − | 0.103409i | \(-0.0329751\pi\) | |||||||
\(504\) | −7.47576 | − | 0.336168i | −0.332997 | − | 0.0149741i | ||||
\(505\) | 51.8914i | 2.30914i | ||||||||
\(506\) | 2.49577 | + | 2.05709i | 0.110950 | + | 0.0914486i | ||||
\(507\) | 1.37662 | + | 1.37662i | 0.0611378 | + | 0.0611378i | ||||
\(508\) | 0.970197 | + | 4.98782i | 0.0430455 | + | 0.221299i | ||||
\(509\) | 6.96054 | + | 6.96054i | 0.308520 | + | 0.308520i | 0.844335 | − | 0.535815i | \(-0.179996\pi\) |
−0.535815 | + | 0.844335i | \(0.679996\pi\) | |||||||
\(510\) | −2.45619 | − | 25.4914i | −0.108762 | − | 1.12878i | ||||
\(511\) | −16.7119 | − | 5.78236i | −0.739291 | − | 0.255796i | ||||
\(512\) | −17.2145 | − | 14.6854i | −0.760780 | − | 0.649009i | ||||
\(513\) | 2.02377 | 0.0893515 | ||||||||
\(514\) | 28.3051 | − | 2.72730i | 1.24848 | − | 0.120296i | ||||
\(515\) | −13.3121 | − | 13.3121i | −0.586600 | − | 0.586600i | ||||
\(516\) | −3.67449 | − | 18.8907i | −0.161760 | − | 0.831616i | ||||
\(517\) | 1.76018 | − | 1.76018i | 0.0774127 | − | 0.0774127i | ||||
\(518\) | 10.8754 | − | 6.64303i | 0.477837 | − | 0.291878i | ||||
\(519\) | 9.37191 | 0.411381 | ||||||||
\(520\) | −9.32151 | − | 31.4467i | −0.408775 | − | 1.37903i | ||||
\(521\) | −11.4231 | −0.500457 | −0.250229 | − | 0.968187i | \(-0.580506\pi\) | ||||
−0.250229 | + | 0.968187i | \(0.580506\pi\) | |||||||
\(522\) | 6.47716 | − | 7.85844i | 0.283497 | − | 0.343955i | ||||
\(523\) | −6.27518 | − | 6.27518i | −0.274394 | − | 0.274394i | 0.556472 | − | 0.830866i | \(-0.312155\pi\) |
−0.830866 | + | 0.556472i | \(0.812155\pi\) | |||||||
\(524\) | −2.15784 | + | 3.20002i | −0.0942658 | + | 0.139793i | ||||
\(525\) | −8.28579 | − | 17.0531i | −0.361621 | − | 0.744258i | ||||
\(526\) | 0.892335 | + | 9.26104i | 0.0389077 | + | 0.403800i | ||||
\(527\) | 7.95970i | 0.346730i | ||||||||
\(528\) | 0.518353 | + | 1.28202i | 0.0225584 | + | 0.0557928i | ||||
\(529\) | 20.7615 | 0.902673 | ||||||||
\(530\) | −3.67796 | − | 38.1715i | −0.159761 | − | 1.65806i | ||||
\(531\) | −3.45643 | + | 3.45643i | −0.149996 | + | 0.149996i | ||||
\(532\) | 8.56121 | − | 6.43299i | 0.371176 | − | 0.278906i | ||||
\(533\) | −22.4529 | − | 22.4529i | −0.972543 | − | 0.972543i | ||||
\(534\) | 12.6113 | + | 10.3946i | 0.545743 | + | 0.449817i | ||||
\(535\) | 27.8181i | 1.20268i | ||||||||
\(536\) | −7.32225 | + | 13.4921i | −0.316273 | + | 0.582770i | ||||
\(537\) | 2.24097 | 0.0967049 | ||||||||
\(538\) | 23.6168 | − | 28.6532i | 1.01819 | − | 1.23533i | ||||
\(539\) | 2.40282 | − | 0.287732i | 0.103497 | − | 0.0123935i | ||||
\(540\) | −6.84762 | + | 1.33195i | −0.294675 | + | 0.0573182i | ||||
\(541\) | −28.9885 | + | 28.9885i | −1.24631 | + | 1.24631i | −0.288978 | + | 0.957336i | \(0.593315\pi\) |
−0.957336 | + | 0.288978i | \(0.906685\pi\) | |||||||
\(542\) | −2.99904 | − | 31.1253i | −0.128820 | − | 1.33695i | ||||
\(543\) | 10.4354i | 0.447828i | ||||||||
\(544\) | −26.0461 | + | 13.5693i | −1.11672 | + | 0.581780i | ||||
\(545\) | − | 8.40153i | − | 0.359882i | ||||||
\(546\) | −2.92130 | + | 12.0917i | −0.125020 | + | 0.517479i | ||||
\(547\) | 1.24129 | + | 1.24129i | 0.0530738 | + | 0.0530738i | 0.733146 | − | 0.680072i | \(-0.238051\pi\) |
−0.680072 | + | 0.733146i | \(0.738051\pi\) | |||||||
\(548\) | −3.36712 | − | 17.3105i | −0.143836 | − | 0.739468i | ||||
\(549\) | −1.27576 | + | 1.27576i | −0.0544479 | + | 0.0544479i | ||||
\(550\) | −2.22835 | + | 2.70356i | −0.0950173 | + | 0.115280i | ||||
\(551\) | 14.5731i | 0.620837i | ||||||||
\(552\) | 16.4450 | + | 8.92483i | 0.699947 | + | 0.379866i | ||||
\(553\) | −3.54461 | + | 10.2445i | −0.150732 | + | 0.435639i | ||||
\(554\) | −18.0587 | + | 21.9098i | −0.767242 | + | 0.930860i | ||||
\(555\) | 8.40027 | − | 8.40027i | 0.356572 | − | 0.356572i | ||||
\(556\) | 0.960114 | + | 0.647426i | 0.0407179 | + | 0.0274570i | ||||
\(557\) | −18.6847 | + | 18.6847i | −0.791695 | + | 0.791695i | −0.981770 | − | 0.190075i | \(-0.939127\pi\) |
0.190075 | + | 0.981770i | \(0.439127\pi\) | |||||||
\(558\) | 2.15821 | − | 0.207952i | 0.0913644 | − | 0.00880330i | ||||
\(559\) | −31.9908 | −1.35307 | ||||||||
\(560\) | −24.7338 | + | 27.4013i | −1.04520 | + | 1.15792i | ||||
\(561\) | 1.79484 | 0.0757781 | ||||||||
\(562\) | −0.751354 | + | 0.0723957i | −0.0316939 | + | 0.00305383i | ||||
\(563\) | 0.450781 | − | 0.450781i | 0.0189981 | − | 0.0189981i | −0.697544 | − | 0.716542i | \(-0.745724\pi\) |
0.716542 | + | 0.697544i | \(0.245724\pi\) | |||||||
\(564\) | 8.05132 | − | 11.9399i | 0.339022 | − | 0.502760i | ||||
\(565\) | 14.5028 | − | 14.5028i | 0.610137 | − | 0.610137i | ||||
\(566\) | −24.8097 | + | 30.1004i | −1.04283 | + | 1.26522i | ||||
\(567\) | 2.50032 | + | 0.865115i | 0.105003 | + | 0.0363314i | ||||
\(568\) | 12.9284 | + | 43.6146i | 0.542462 | + | 1.83003i | ||||
\(569\) | − | 19.8762i | − | 0.833254i | −0.909077 | − | 0.416627i | \(-0.863212\pi\) | ||
0.909077 | − | 0.416627i | \(-0.136788\pi\) | |||||||
\(570\) | 6.34931 | − | 7.70333i | 0.265943 | − | 0.322657i | ||||
\(571\) | 0.229081 | − | 0.229081i | 0.00958675 | − | 0.00958675i | −0.702297 | − | 0.711884i | \(-0.747842\pi\) |
0.711884 | + | 0.702297i | \(0.247842\pi\) | |||||||
\(572\) | 2.25644 | − | 0.438907i | 0.0943465 | − | 0.0183516i | ||||
\(573\) | 17.6524 | + | 17.6524i | 0.737439 | + | 0.737439i | ||||
\(574\) | −8.39221 | + | 34.7368i | −0.350284 | + | 1.44989i | ||||
\(575\) | 47.4050i | 1.97692i | ||||||||
\(576\) | 4.35969 | + | 6.70769i | 0.181654 | + | 0.279487i | ||||
\(577\) | − | 44.9253i | − | 1.87026i | −0.354300 | − | 0.935132i | \(-0.615281\pi\) | ||
0.354300 | − | 0.935132i | \(-0.384719\pi\) | |||||||
\(578\) | 1.35011 | + | 14.0120i | 0.0561572 | + | 0.582823i | ||||
\(579\) | 6.95869 | − | 6.95869i | 0.289193 | − | 0.289193i | ||||
\(580\) | −9.59140 | − | 49.3097i | −0.398261 | − | 2.04747i | ||||
\(581\) | 32.6752 | − | 15.8763i | 1.35560 | − | 0.658659i | ||||
\(582\) | 15.0357 | − | 18.2421i | 0.623249 | − | 0.756161i | ||||
\(583\) | 2.68764 | 0.111311 | ||||||||
\(584\) | 5.37279 | + | 18.1254i | 0.222327 | + | 0.750035i | ||||
\(585\) | 11.5962i | 0.479446i | ||||||||
\(586\) | −20.4647 | − | 16.8676i | −0.845388 | − | 0.696793i | ||||
\(587\) | 22.6986 | + | 22.6986i | 0.936871 | + | 0.936871i | 0.998122 | − | 0.0612514i | \(-0.0195092\pi\) |
−0.0612514 | + | 0.998122i | \(0.519509\pi\) | |||||||
\(588\) | 13.3271 | − | 4.28808i | 0.549602 | − | 0.176837i | ||||
\(589\) | −2.19397 | + | 2.19397i | −0.0904011 | + | 0.0904011i | ||||
\(590\) | 2.31256 | + | 24.0007i | 0.0952066 | + | 0.988095i | ||||
\(591\) | −8.78060 | −0.361186 | ||||||||
\(592\) | −12.5420 | − | 5.31998i | −0.515474 | − | 0.218650i | ||||
\(593\) | 17.6514i | 0.724855i | 0.932012 | + | 0.362427i | \(0.118052\pi\) | ||||
−0.932012 | + | 0.362427i | \(0.881948\pi\) | |||||||
\(594\) | −0.0468912 | − | 0.486657i | −0.00192397 | − | 0.0199678i | ||||
\(595\) | 20.9383 | + | 43.0934i | 0.858385 | + | 1.76666i | ||||
\(596\) | −20.1486 | − | 13.5867i | −0.825321 | − | 0.556532i | ||||
\(597\) | −7.19176 | − | 7.19176i | −0.294339 | − | 0.294339i | ||||
\(598\) | 19.7825 | − | 24.0012i | 0.808966 | − | 0.981483i | ||||
\(599\) | 13.0847 | 0.534627 | 0.267314 | − | 0.963610i | \(-0.413864\pi\) | ||||
0.267314 | + | 0.963610i | \(0.413864\pi\) | |||||||
\(600\) | −9.66789 | + | 17.8142i | −0.394690 | + | 0.727262i | ||||
\(601\) | −42.5370 | −1.73512 | −0.867560 | − | 0.497333i | \(-0.834313\pi\) | ||||
−0.867560 | + | 0.497333i | \(0.834313\pi\) | |||||||
\(602\) | 18.7679 | + | 30.7251i | 0.764920 | + | 1.25226i | ||||
\(603\) | 3.83774 | − | 3.83774i | 0.156285 | − | 0.156285i | ||||
\(604\) | 31.0608 | − | 6.04174i | 1.26385 | − | 0.245835i | ||||
\(605\) | 26.8354 | + | 26.8354i | 1.09101 | + | 1.09101i | ||||
\(606\) | −20.9426 | + | 2.01789i | −0.850734 | + | 0.0819713i | ||||
\(607\) | −29.5855 | −1.20084 | −0.600419 | − | 0.799686i | \(-0.704999\pi\) | ||||
−0.600419 | + | 0.799686i | \(0.704999\pi\) | |||||||
\(608\) | −10.9194 | − | 3.43903i | −0.442840 | − | 0.139471i | ||||
\(609\) | −6.22969 | + | 18.0048i | −0.252440 | + | 0.729590i | ||||
\(610\) | 0.853559 | + | 8.85860i | 0.0345596 | + | 0.358674i | ||||
\(611\) | −16.9273 | − | 16.9273i | −0.684804 | − | 0.684804i | ||||
\(612\) | 10.1924 | − | 1.98256i | 0.412003 | − | 0.0801401i | ||||
\(613\) | −20.2489 | − | 20.2489i | −0.817847 | − | 0.817847i | 0.167949 | − | 0.985796i | \(-0.446286\pi\) |
−0.985796 | + | 0.167949i | \(0.946286\pi\) | |||||||
\(614\) | −13.5053 | − | 11.1314i | −0.545028 | − | 0.449228i | ||||
\(615\) | 33.3133i | 1.34332i | ||||||||
\(616\) | −1.74531 | − | 1.90967i | −0.0703206 | − | 0.0769427i | ||||
\(617\) | − | 32.9416i | − | 1.32618i | −0.748541 | − | 0.663089i | \(-0.769245\pi\) | ||
0.748541 | − | 0.663089i | \(-0.230755\pi\) | |||||||
\(618\) | 4.85488 | − | 5.89021i | 0.195292 | − | 0.236939i | ||||
\(619\) | 20.5109 | + | 20.5109i | 0.824404 | + | 0.824404i | 0.986736 | − | 0.162333i | \(-0.0519017\pi\) |
−0.162333 | + | 0.986736i | \(0.551902\pi\) | |||||||
\(620\) | 5.97956 | − | 8.86752i | 0.240145 | − | 0.356128i | ||||
\(621\) | −4.67768 | − | 4.67768i | −0.187709 | − | 0.187709i | ||||
\(622\) | 17.6051 | − | 1.69632i | 0.705901 | − | 0.0680161i | ||||
\(623\) | −28.8941 | − | 9.99743i | −1.15762 | − | 0.400539i | ||||
\(624\) | 12.3289 | − | 4.98487i | 0.493551 | − | 0.199555i | ||||
\(625\) | 9.47829 | 0.379132 | ||||||||
\(626\) | 4.16052 | + | 43.1796i | 0.166288 | + | 1.72581i | ||||
\(627\) | 0.494721 | + | 0.494721i | 0.0197572 | + | 0.0197572i | ||||
\(628\) | 31.3227 | + | 21.1216i | 1.24991 | + | 0.842844i | ||||
\(629\) | −12.5034 | + | 12.5034i | −0.498545 | + | 0.498545i | ||||
\(630\) | 11.1374 | − | 6.80309i | 0.443725 | − | 0.271042i | ||||
\(631\) | −1.92496 | −0.0766314 | −0.0383157 | − | 0.999266i | \(-0.512199\pi\) | ||||
−0.0383157 | + | 0.999266i | \(0.512199\pi\) | |||||||
\(632\) | 11.1110 | − | 3.29354i | 0.441971 | − | 0.131010i | ||||
\(633\) | 8.05823 | 0.320286 | ||||||||
\(634\) | 10.1373 | + | 8.35544i | 0.402603 | + | 0.331837i | ||||
\(635\) | −6.26620 | − | 6.26620i | −0.248666 | − | 0.248666i | ||||
\(636\) | 15.2624 | − | 2.96874i | 0.605193 | − | 0.117718i | ||||
\(637\) | −2.76705 | − | 23.1073i | −0.109634 | − | 0.915546i | ||||
\(638\) | 3.50441 | − | 0.337663i | 0.138741 | − | 0.0133682i | ||||
\(639\) | − | 16.0833i | − | 0.636246i | ||||||
\(640\) | 39.2103 | + | 4.44964i | 1.54992 | + | 0.175887i | ||||
\(641\) | 0.665171 | 0.0262727 | 0.0131363 | − | 0.999914i | \(-0.495818\pi\) | ||||
0.0131363 | + | 0.999914i | \(0.495818\pi\) | |||||||
\(642\) | −11.2270 | + | 1.08176i | −0.443093 | + | 0.0426936i | ||||
\(643\) | −10.5926 | + | 10.5926i | −0.417733 | + | 0.417733i | −0.884422 | − | 0.466689i | \(-0.845447\pi\) |
0.466689 | + | 0.884422i | \(0.345447\pi\) | |||||||
\(644\) | −34.6572 | − | 4.91912i | −1.36569 | − | 0.193841i | ||||
\(645\) | 23.7324 | + | 23.7324i | 0.934462 | + | 0.934462i | ||||
\(646\) | −9.45068 | + | 11.4661i | −0.371832 | + | 0.451127i | ||||
\(647\) | 40.4129i | 1.58880i | 0.607397 | + | 0.794398i | \(0.292214\pi\) | ||||
−0.607397 | + | 0.794398i | \(0.707786\pi\) | |||||||
\(648\) | −0.803838 | − | 2.71180i | −0.0315777 | − | 0.106529i | ||||
\(649\) | −1.68988 | −0.0663337 | ||||||||
\(650\) | 25.9995 | + | 21.4295i | 1.01978 | + | 0.840536i | ||||
\(651\) | −3.64848 | + | 1.77273i | −0.142995 | + | 0.0694787i | ||||
\(652\) | −26.2817 | − | 17.7223i | −1.02927 | − | 0.694060i | ||||
\(653\) | 6.72324 | − | 6.72324i | 0.263101 | − | 0.263101i | −0.563212 | − | 0.826313i | \(-0.690435\pi\) |
0.826313 | + | 0.563212i | \(0.190435\pi\) | |||||||
\(654\) | 3.39072 | − | 0.326709i | 0.132588 | − | 0.0127753i | ||||
\(655\) | − | 6.73108i | − | 0.263005i | ||||||
\(656\) | 35.4181 | − | 14.3204i | 1.38284 | − | 0.559117i | ||||
\(657\) | − | 6.68392i | − | 0.260764i | ||||||
\(658\) | −6.32689 | + | 26.1881i | −0.246648 | + | 1.02092i | ||||
\(659\) | 33.6058 | + | 33.6058i | 1.30910 | + | 1.30910i | 0.922067 | + | 0.387029i | \(0.126499\pi\) |
0.387029 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(660\) | −1.99954 | − | 1.34834i | −0.0778321 | − | 0.0524839i | ||||
\(661\) | −8.66416 | + | 8.66416i | −0.336997 | + | 0.336997i | −0.855236 | − | 0.518239i | \(-0.826588\pi\) |
0.518239 | + | 0.855236i | \(0.326588\pi\) | |||||||
\(662\) | −4.42177 | − | 3.64455i | −0.171857 | − | 0.141650i | ||||
\(663\) | − | 17.2605i | − | 0.670343i | ||||||
\(664\) | −34.1336 | − | 18.5245i | −1.32464 | − | 0.718891i | ||||
\(665\) | −6.10673 | + | 17.6494i | −0.236809 | + | 0.684414i | ||||
\(666\) | 3.71688 | + | 3.06356i | 0.144026 | + | 0.118710i | ||||
\(667\) | 33.6840 | − | 33.6840i | 1.30425 | − | 1.30425i | ||||
\(668\) | 5.96111 | + | 30.6463i | 0.230642 | + | 1.18574i | ||||
\(669\) | −3.72330 | + | 3.72330i | −0.143951 | + | 0.143951i | ||||
\(670\) | −2.56768 | − | 26.6485i | −0.0991983 | − | 1.02952i | ||||
\(671\) | −0.623731 | −0.0240789 | ||||||||
\(672\) | −12.0205 | − | 8.91664i | −0.463703 | − | 0.343967i | ||||
\(673\) | 5.60669 | 0.216122 | 0.108061 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108061 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(674\) | −3.18714 | − | 33.0775i | −0.122764 | − | 1.27410i | ||||
\(675\) | 5.06714 | − | 5.06714i | 0.195034 | − | 0.195034i | ||||
\(676\) | 0.743437 | + | 3.82203i | 0.0285937 | + | 0.147001i | ||||
\(677\) | −1.76989 | + | 1.76989i | −0.0680223 | + | 0.0680223i | −0.740300 | − | 0.672277i | \(-0.765316\pi\) |
0.672277 | + | 0.740300i | \(0.265316\pi\) | |||||||
\(678\) | 6.41707 | + | 5.28913i | 0.246446 | + | 0.203128i | ||||
\(679\) | −14.4612 | + | 41.7952i | −0.554971 | + | 1.60395i | ||||
\(680\) | 24.4309 | − | 45.0167i | 0.936881 | − | 1.72631i | ||||
\(681\) | 16.0892i | 0.616538i | ||||||||
\(682\) | 0.578422 | + | 0.476752i | 0.0221489 | + | 0.0182558i | ||||
\(683\) | −28.4450 | + | 28.4450i | −1.08842 | + | 1.08842i | −0.0927272 | + | 0.995692i | \(0.529558\pi\) |
−0.995692 | + | 0.0927272i | \(0.970442\pi\) | |||||||
\(684\) | 3.35585 | + | 2.26292i | 0.128314 | + | 0.0865250i | ||||
\(685\) | 21.7472 | + | 21.7472i | 0.830917 | + | 0.830917i | ||||
\(686\) | −20.5697 | + | 16.2138i | −0.785355 | + | 0.619045i | ||||
\(687\) | − | 21.0382i | − | 0.802658i | ||||||
\(688\) | 15.0300 | − | 35.4336i | 0.573012 | − | 1.35089i | ||||
\(689\) | − | 25.8464i | − | 0.984669i | ||||||
\(690\) | −32.4809 | + | 3.12966i | −1.23653 | + | 0.119144i | ||||
\(691\) | −10.4240 | + | 10.4240i | −0.396547 | + | 0.396547i | −0.877013 | − | 0.480466i | \(-0.840467\pi\) |
0.480466 | + | 0.877013i | \(0.340467\pi\) | |||||||
\(692\) | 15.5407 | + | 10.4794i | 0.590768 | + | 0.398368i | ||||
\(693\) | 0.399733 | + | 0.822697i | 0.0151846 | + | 0.0312517i | ||||
\(694\) | −11.2727 | − | 9.29132i | −0.427907 | − | 0.352694i | ||||
\(695\) | −2.01955 | −0.0766060 | ||||||||
\(696\) | 19.5276 | − | 5.78843i | 0.740193 | − | 0.219410i | ||||
\(697\) | − | 49.5855i | − | 1.87818i | ||||||
\(698\) | 13.2497 | − | 16.0753i | 0.501510 | − | 0.608460i | ||||
\(699\) | 1.50287 | + | 1.50287i | 0.0568437 | + | 0.0568437i | ||||
\(700\) | 5.32868 | − | 37.5427i | 0.201405 | − | 1.41898i | ||||
\(701\) | 37.1588 | − | 37.1588i | 1.40347 | − | 1.40347i | 0.614732 | − | 0.788736i | \(-0.289264\pi\) |
0.788736 | − | 0.614732i | \(-0.210736\pi\) | |||||||
\(702\) | −4.68006 | + | 0.450941i | −0.176638 | + | 0.0170197i | ||||
\(703\) | −6.89278 | −0.259966 | ||||||||
\(704\) | −0.573981 | + | 2.70548i | −0.0216327 | + | 0.101967i | ||||
\(705\) | 25.1150i | 0.945884i | ||||||||
\(706\) | 0.496753 | − | 0.0478640i | 0.0186956 | − | 0.00180139i | ||||
\(707\) | 35.4036 | − | 17.2019i | 1.33149 | − | 0.646946i | ||||
\(708\) | −9.59639 | + | 1.86663i | −0.360655 | + | 0.0701521i | ||||
\(709\) | −2.24522 | − | 2.24522i | −0.0843210 | − | 0.0843210i | 0.663688 | − | 0.748009i | \(-0.268990\pi\) |
−0.748009 | + | 0.663688i | \(0.768990\pi\) | |||||||
\(710\) | −61.2200 | − | 50.4593i | −2.29755 | − | 1.89370i | ||||
\(711\) | −4.09727 | −0.153660 | ||||||||
\(712\) | 9.28930 | + | 31.3380i | 0.348131 | + | 1.17444i | ||||
\(713\) | 10.1422 | 0.379828 | ||||||||
\(714\) | −16.5776 | + | 10.1261i | −0.620400 | + | 0.378960i | ||||
\(715\) | −2.83477 | + | 2.83477i | −0.106014 | + | 0.106014i | ||||
\(716\) | 3.71601 | + | 2.50579i | 0.138874 | + | 0.0936457i | ||||
\(717\) | −6.32405 | − | 6.32405i | −0.236176 | − | 0.236176i | ||||
\(718\) | −0.398441 | − | 4.13519i | −0.0148697 | − | 0.154324i | ||||
\(719\) | 19.0248 | 0.709506 | 0.354753 | − | 0.934960i | \(-0.384565\pi\) | ||||
0.354753 | + | 0.934960i | \(0.384565\pi\) | |||||||
\(720\) | −12.8442 | − | 5.44816i | −0.478676 | − | 0.203041i | ||||
\(721\) | −4.66939 | + | 13.4953i | −0.173897 | + | 0.502590i | ||||
\(722\) | 20.9808 | − | 2.02158i | 0.780824 | − | 0.0752353i | ||||
\(723\) | 2.94375 | + | 2.94375i | 0.109479 | + | 0.109479i | ||||
\(724\) | −11.6686 | + | 17.3042i | −0.433661 | + | 0.643107i | ||||
\(725\) | 36.4884 | + | 36.4884i | 1.35515 | + | 1.35515i | ||||
\(726\) | −9.78678 | + | 11.8739i | −0.363222 | + | 0.440681i | ||||
\(727\) | 40.7707i | 1.51210i | 0.654513 | + | 0.756050i | \(0.272874\pi\) | ||||
−0.654513 | + | 0.756050i | \(0.727126\pi\) | |||||||
\(728\) | −18.3648 | + | 16.7842i | −0.680645 | + | 0.622065i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −25.4419 | − | 20.9699i | −0.941646 | − | 0.776132i | ||||
\(731\) | −35.3246 | − | 35.3246i | −1.30653 | − | 1.30653i | ||||
\(732\) | −3.54200 | + | 0.688966i | −0.130916 | + | 0.0254649i | ||||
\(733\) | −6.53739 | − | 6.53739i | −0.241464 | − | 0.241464i | 0.575992 | − | 0.817456i | \(-0.304616\pi\) |
−0.817456 | + | 0.575992i | \(0.804616\pi\) | |||||||
\(734\) | −4.52432 | − | 46.9553i | −0.166996 | − | 1.73315i | ||||
\(735\) | −15.0894 | + | 19.1949i | −0.556582 | + | 0.708014i | ||||
\(736\) | 17.2899 | + | 33.1877i | 0.637316 | + | 1.22332i | ||||
\(737\) | 1.87631 | 0.0691149 | ||||||||
\(738\) | −13.4447 | + | 1.29545i | −0.494908 | + | 0.0476862i | ||||
\(739\) | −25.7167 | − | 25.7167i | −0.946003 | − | 0.946003i | 0.0526125 | − | 0.998615i | \(-0.483245\pi\) |
−0.998615 | + | 0.0526125i | \(0.983245\pi\) | |||||||
\(740\) | 23.3224 | − | 4.53653i | 0.857350 | − | 0.166766i | ||||
\(741\) | 4.75761 | − | 4.75761i | 0.174775 | − | 0.174775i | ||||
\(742\) | −24.8237 | + | 15.1631i | −0.911308 | + | 0.556656i | ||||
\(743\) | 9.46009 | 0.347057 | 0.173529 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173529 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(744\) | 3.81131 | + | 2.06843i | 0.139730 | + | 0.0758322i | ||||
\(745\) | 42.3817 | 1.55275 | ||||||||
\(746\) | 24.2476 | − | 29.4185i | 0.887767 | − | 1.07709i | ||||
\(747\) | 9.70907 | + | 9.70907i | 0.355236 | + | 0.355236i | ||||
\(748\) | 2.97623 | + | 2.00694i | 0.108822 | + | 0.0733810i | ||||
\(749\) | 18.9793 | − | 9.22167i | 0.693487 | − | 0.336953i | ||||
\(750\) | −1.02474 | − | 10.6352i | −0.0374181 | − | 0.388341i | ||||
\(751\) | 26.5634i | 0.969313i | 0.874705 | + | 0.484656i | \(0.161055\pi\) | ||||
−0.874705 | + | 0.484656i | \(0.838945\pi\) | |||||||
\(752\) | 26.7017 | − | 10.7962i | 0.973711 | − | 0.393695i | ||||
\(753\) | 1.19985 | 0.0437248 | ||||||||
\(754\) | −3.24723 | − | 33.7011i | −0.118257 | − | 1.22732i | ||||
\(755\) | −39.0217 | + | 39.0217i | −1.42015 | + | 1.42015i | ||||
\(756\) | 3.17872 | + | 4.23034i | 0.115609 | + | 0.153856i | ||||
\(757\) | 7.83618 | + | 7.83618i | 0.284811 | + | 0.284811i | 0.835024 | − | 0.550213i | \(-0.185454\pi\) |
−0.550213 | + | 0.835024i | \(0.685454\pi\) | |||||||
\(758\) | 13.7924 | + | 11.3681i | 0.500963 | + | 0.412908i | ||||
\(759\) | − | 2.28697i | − | 0.0830118i | ||||||
\(760\) | 19.1422 | − | 5.67418i | 0.694361 | − | 0.205824i | ||||
\(761\) | −22.5355 | −0.816910 | −0.408455 | − | 0.912778i | \(-0.633932\pi\) | ||||
−0.408455 | + | 0.912778i | \(0.633932\pi\) | |||||||
\(762\) | 2.28527 | − | 2.77261i | 0.0827864 | − | 0.100441i | ||||
\(763\) | −5.73204 | + | 2.78509i | −0.207514 | + | 0.100827i | ||||
\(764\) | 9.53308 | + | 49.0099i | 0.344895 | + | 1.77312i | ||||
\(765\) | −12.8047 | + | 12.8047i | −0.462955 | + | 0.462955i | ||||
\(766\) | 4.09173 | + | 42.4657i | 0.147840 | + | 1.53435i | ||||
\(767\) | 16.2512i | 0.586797i | ||||||||
\(768\) | −0.271038 | + | 15.9977i | −0.00978023 | + | 0.577267i | ||||
\(769\) | − | 5.25162i | − | 0.189378i | −0.995507 | − | 0.0946892i | \(-0.969814\pi\) | ||
0.995507 | − | 0.0946892i | \(-0.0301857\pi\) | |||||||
\(770\) | 4.38565 | + | 1.05955i | 0.158048 | + | 0.0381835i | ||||
\(771\) | −14.2181 | − | 14.2181i | −0.512052 | − | 0.512052i | ||||
\(772\) | 19.3201 | − | 3.75801i | 0.695344 | − | 0.135254i | ||||
\(773\) | −10.2035 | + | 10.2035i | −0.366995 | + | 0.366995i | −0.866380 | − | 0.499385i | \(-0.833559\pi\) |
0.499385 | + | 0.866380i | \(0.333559\pi\) | |||||||
\(774\) | −8.65514 | + | 10.5009i | −0.311102 | + | 0.377447i | ||||
\(775\) | 10.9866i | 0.394651i | ||||||||
\(776\) | 45.3303 | − | 13.4369i | 1.62726 | − | 0.482358i | ||||
\(777\) | −8.51587 | − | 2.94651i | −0.305505 | − | 0.105705i | ||||
\(778\) | 12.5696 | − | 15.2501i | 0.450641 | − | 0.546742i | ||||
\(779\) | 13.6675 | − | 13.6675i | 0.489690 | − | 0.489690i | ||||
\(780\) | −12.9666 | + | 19.2291i | −0.464279 | + | 0.688513i | ||||
\(781\) | 3.93165 | − | 3.93165i | 0.140685 | − | 0.140685i | ||||
\(782\) | 48.3465 | − | 4.65836i | 1.72887 | − | 0.166583i | ||||
\(783\) | −7.20100 | −0.257343 | ||||||||
\(784\) | 26.8941 | + | 7.79147i | 0.960504 | + | 0.278267i | ||||
\(785\) | −65.8858 | −2.35157 | ||||||||
\(786\) | 2.71656 | − | 0.261750i | 0.0968964 | − | 0.00933633i | ||||
\(787\) | 9.39612 | − | 9.39612i | 0.334936 | − | 0.334936i | −0.519522 | − | 0.854457i | \(-0.673890\pi\) |
0.854457 | + | 0.519522i | \(0.173890\pi\) | |||||||
\(788\) | −14.5602 | − | 9.81824i | −0.518684 | − | 0.349760i | ||||
\(789\) | 4.65196 | − | 4.65196i | 0.165614 | − | 0.165614i | ||||
\(790\) | −12.8547 | + | 15.5960i | −0.457349 | + | 0.554881i | ||||
\(791\) | −14.7024 | − | 5.08706i | −0.522756 | − | 0.180875i | ||||
\(792\) | 0.466411 | − | 0.859416i | 0.0165732 | − | 0.0305380i | ||||
\(793\) | 5.99827i | 0.213005i | ||||||||
\(794\) | 7.29441 | − | 8.84998i | 0.258869 | − | 0.314074i | ||||
\(795\) | −19.1741 | + | 19.1741i | −0.680036 | + | 0.680036i | ||||
\(796\) | −3.88388 | − | 19.9672i | −0.137660 | − | 0.707717i | ||||
\(797\) | 15.0117 | + | 15.0117i | 0.531741 | + | 0.531741i | 0.921090 | − | 0.389349i | \(-0.127300\pi\) |
−0.389349 | + | 0.921090i | \(0.627300\pi\) | |||||||
\(798\) | −7.36048 | − | 1.77825i | −0.260558 | − | 0.0629494i | ||||
\(799\) | − | 37.3825i | − | 1.32250i | ||||||
\(800\) | −35.9509 | + | 18.7295i | −1.27105 | + | 0.662187i | ||||
\(801\) | − | 11.5562i | − | 0.408318i | ||||||
\(802\) | −1.36020 | − | 14.1168i | −0.0480304 | − | 0.498480i | ||||
\(803\) | 1.63392 | − | 1.63392i | 0.0576597 | − | 0.0576597i | ||||
\(804\) | 10.6551 | − | 2.07255i | 0.375775 | − | 0.0730933i | ||||
\(805\) | 54.9093 | − | 26.6794i | 1.93530 | − | 0.940325i | ||||
\(806\) | 4.58481 | − | 5.56254i | 0.161493 | − | 0.195932i | ||||
\(807\) | −26.2560 | −0.924256 | ||||||||
\(808\) | −36.9837 | − | 20.0713i | −1.30108 | − | 0.706106i | ||||
\(809\) | 9.85392i | 0.346445i | 0.984883 | + | 0.173223i | \(0.0554180\pi\) | ||||
−0.984883 | + | 0.173223i | \(0.944582\pi\) | |||||||
\(810\) | 3.80643 | + | 3.13737i | 0.133744 | + | 0.110236i | ||||
\(811\) | −5.99202 | − | 5.99202i | −0.210408 | − | 0.210408i | 0.594033 | − | 0.804441i | \(-0.297535\pi\) |
−0.804441 | + | 0.594033i | \(0.797535\pi\) | |||||||
\(812\) | −30.4626 | + | 22.8900i | −1.06903 | + | 0.803280i | ||||
\(813\) | −15.6347 | + | 15.6347i | −0.548334 | + | 0.548334i | ||||
\(814\) | 0.159708 | + | 1.65751i | 0.00559775 | + | 0.0580958i | ||||
\(815\) | 55.2823 | 1.93645 | ||||||||
\(816\) | 19.1181 | + | 8.10935i | 0.669266 | + | 0.283884i | ||||
\(817\) | − | 19.4734i | − | 0.681290i | ||||||
\(818\) | −2.18114 | − | 22.6369i | −0.0762619 | − | 0.791479i | ||||
\(819\) | 7.91168 | − | 3.84414i | 0.276457 | − | 0.134325i | ||||
\(820\) | −37.2501 | + | 55.2408i | −1.30083 | + | 1.92909i | ||||
\(821\) | 7.92158 | + | 7.92158i | 0.276465 | + | 0.276465i | 0.831696 | − | 0.555231i | \(-0.187370\pi\) |
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(822\) | −7.93114 | + | 9.62250i | −0.276630 | + | 0.335623i | ||||
\(823\) | −31.5025 | −1.09811 | −0.549055 | − | 0.835786i | \(-0.685012\pi\) | ||||
−0.549055 | + | 0.835786i | \(0.685012\pi\) | |||||||
\(824\) | 14.6367 | − | 4.33865i | 0.509894 | − | 0.151144i | ||||
\(825\) | 2.47738 | 0.0862512 | ||||||||
\(826\) | 15.6082 | − | 9.53399i | 0.543079 | − | 0.331730i | ||||
\(827\) | 2.82748 | − | 2.82748i | 0.0983211 | − | 0.0983211i | −0.656235 | − | 0.754556i | \(-0.727852\pi\) |
0.754556 | + | 0.656235i | \(0.227852\pi\) | |||||||
\(828\) | −2.52616 | − | 12.9871i | −0.0877902 | − | 0.451332i | ||||
\(829\) | −5.54898 | − | 5.54898i | −0.192724 | − | 0.192724i | 0.604148 | − | 0.796872i | \(-0.293514\pi\) |
−0.796872 | + | 0.604148i | \(0.793514\pi\) | |||||||
\(830\) | 67.4179 | − | 6.49597i | 2.34011 | − | 0.225478i | ||||
\(831\) | 20.0768 | 0.696458 | ||||||||
\(832\) | 26.0180 | + | 5.51983i | 0.902010 | + | 0.191366i | ||||
\(833\) | 22.4600 | − | 28.5708i | 0.778192 | − | 0.989919i | ||||
\(834\) | −0.0785340 | − | 0.815060i | −0.00271941 | − | 0.0282232i | ||||
\(835\) | −38.5009 | − | 38.5009i | −1.33238 | − | 1.33238i | ||||
\(836\) | 0.267172 | + | 1.37354i | 0.00924032 | + | 0.0475048i | ||||
\(837\) | −1.08410 | − | 1.08410i | −0.0374721 | − | 0.0374721i | ||||
\(838\) | 10.1759 | + | 8.38726i | 0.351520 | + | 0.289733i | ||||
\(839\) | 25.5143i | 0.880850i | 0.897789 | + | 0.440425i | \(0.145172\pi\) | ||||
−0.897789 | + | 0.440425i | \(0.854828\pi\) | |||||||
\(840\) | 26.0753 | + | 1.17255i | 0.899684 | + | 0.0404568i | ||||
\(841\) | − | 22.8544i | − | 0.788081i | ||||||
\(842\) | −5.89702 | + | 7.15459i | −0.203225 | + | 0.246563i | ||||
\(843\) | 0.377417 | + | 0.377417i | 0.0129989 | + | 0.0129989i | ||||
\(844\) | 13.3623 | + | 9.01050i | 0.459950 | + | 0.310154i | ||||
\(845\) | −4.80162 | − | 4.80162i | −0.165181 | − | 0.165181i | ||||
\(846\) | −10.1360 | + | 0.976641i | −0.348483 | + | 0.0335776i | ||||
\(847\) | 9.41287 | − | 27.2046i | 0.323430 | − | 0.934762i | ||||
\(848\) | 28.6279 | + | 12.1432i | 0.983087 | + | 0.416998i | ||||
\(849\) | 27.5822 | 0.946619 | ||||||||
\(850\) | 5.04621 | + | 52.3717i | 0.173084 | + | 1.79633i | ||||
\(851\) | 15.9318 | + | 15.9318i | 0.546135 | + | 0.546135i | ||||
\(852\) | 17.9839 | − | 26.6696i | 0.616119 | − | 0.913686i | ||||
\(853\) | 9.34018 | − | 9.34018i | 0.319802 | − | 0.319802i | −0.528889 | − | 0.848691i | \(-0.677391\pi\) |
0.848691 | + | 0.528889i | \(0.177391\pi\) | |||||||
\(854\) | 5.76093 | − | 3.51896i | 0.197135 | − | 0.120416i | ||||
\(855\) | −7.05886 | −0.241408 | ||||||||
\(856\) | −19.8263 | − | 10.7599i | −0.677650 | − | 0.367765i | ||||
\(857\) | 14.6466 | 0.500317 | 0.250159 | − | 0.968205i | \(-0.419517\pi\) | ||||
0.250159 | + | 0.968205i | \(0.419517\pi\) | |||||||
\(858\) | −1.25430 | − | 1.03383i | −0.0428211 | − | 0.0352944i | ||||
\(859\) | 35.4037 | + | 35.4037i | 1.20796 | + | 1.20796i | 0.971687 | + | 0.236272i | \(0.0759257\pi\) |
0.236272 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(860\) | 12.8166 | + | 65.8904i | 0.437041 | + | 2.24684i | ||||
\(861\) | 22.7284 | − | 11.0433i | 0.774583 | − | 0.376356i | ||||
\(862\) | −12.9885 | + | 1.25149i | −0.442390 | + | 0.0426259i | ||||
\(863\) | 31.2983i | 1.06541i | 0.846302 | + | 0.532703i | \(0.178824\pi\) | ||||
−0.846302 | + | 0.532703i | \(0.821176\pi\) | |||||||
\(864\) | 1.69932 | − | 5.39558i | 0.0578120 | − | 0.183561i | ||||
\(865\) | −32.6890 | −1.11146 | ||||||||
\(866\) | −28.9930 | + | 2.79359i | −0.985223 | + | 0.0949299i | ||||
\(867\) | 7.03845 | − | 7.03845i | 0.239038 | − | 0.239038i | ||||
\(868\) | −8.03219 | − | 1.14006i | −0.272630 | − | 0.0386962i | ||||
\(869\) | −1.00160 | − | 1.00160i | −0.0339770 | − | 0.0339770i | ||||
\(870\) | −22.5922 | + | 27.4101i | −0.765947 | + | 0.929290i | ||||
\(871\) | − | 18.0440i | − | 0.611399i | ||||||
\(872\) | 5.98788 | + | 3.24966i | 0.202775 | + | 0.110047i | ||||
\(873\) | −16.7160 | −0.565750 | ||||||||
\(874\) | 14.6100 | + | 12.0420i | 0.494191 | + | 0.407326i | ||||
\(875\) | 8.73558 | + | 17.9788i | 0.295317 | + | 0.607795i | ||||
\(876\) | 7.47378 | − | 11.0834i | 0.252516 | − | 0.374473i | ||||
\(877\) | 14.5201 | − | 14.5201i | 0.490310 | − | 0.490310i | −0.418094 | − | 0.908404i | \(-0.637302\pi\) |
0.908404 | + | 0.418094i | \(0.137302\pi\) | |||||||
\(878\) | −42.9354 | + | 4.13698i | −1.44900 | + | 0.139616i | ||||
\(879\) | 18.7526i | 0.632508i | ||||||||
\(880\) | −1.80800 | − | 4.47167i | −0.0609478 | − | 0.150740i | ||||
\(881\) | − | 10.6714i | − | 0.359529i | −0.983710 | − | 0.179764i | \(-0.942466\pi\) | ||
0.983710 | − | 0.179764i | \(-0.0575335\pi\) | |||||||
\(882\) | −8.33353 | − | 5.34343i | −0.280605 | − | 0.179923i | ||||
\(883\) | 35.8490 | + | 35.8490i | 1.20641 | + | 1.20641i | 0.972180 | + | 0.234235i | \(0.0752585\pi\) |
0.234235 | + | 0.972180i | \(0.424742\pi\) | |||||||
\(884\) | 19.3003 | − | 28.6217i | 0.649138 | − | 0.962653i | ||||
\(885\) | 12.0560 | − | 12.0560i | 0.405256 | − | 0.405256i | ||||
\(886\) | 25.6916 | + | 21.1758i | 0.863127 | + | 0.711414i | ||||
\(887\) | − | 4.16513i | − | 0.139852i | −0.997552 | − | 0.0699258i | \(-0.977724\pi\) | ||
0.997552 | − | 0.0699258i | \(-0.0222762\pi\) | |||||||
\(888\) | 2.73781 | + | 9.23616i | 0.0918748 | + | 0.309945i | ||||
\(889\) | −2.19795 | + | 6.35243i | −0.0737170 | + | 0.213054i | ||||
\(890\) | −43.9879 | − | 36.2561i | −1.47448 | − | 1.21531i | ||||
\(891\) | −0.244455 | + | 0.244455i | −0.00818956 | + | 0.00818956i | ||||
\(892\) | −10.3373 | + | 2.01075i | −0.346120 | + | 0.0673249i | ||||
\(893\) | 10.3040 | − | 10.3040i | 0.344809 | − | 0.344809i | ||||
\(894\) | 1.64809 | + | 17.1046i | 0.0551204 | + | 0.572063i | ||||
\(895\) | −7.81645 | −0.261275 | ||||||||
\(896\) | −9.96235 | − | 28.2268i | −0.332819 | − | 0.942991i | ||||
\(897\) | −21.9932 | −0.734333 | ||||||||
\(898\) | −1.46944 | − | 15.2505i | −0.0490359 | − | 0.508915i | ||||
\(899\) | 7.80663 | − | 7.80663i | 0.260366 | − | 0.260366i | ||||
\(900\) | 14.0684 | − | 2.73648i | 0.468945 | − | 0.0912161i | ||||
\(901\) | 28.5399 | − | 28.5399i | 0.950801 | − | 0.950801i | ||||
\(902\) | −3.60332 | − | 2.96996i | −0.119977 | − | 0.0988888i | ||||
\(903\) | 8.32446 | − | 24.0590i | 0.277021 | − | 0.800632i | ||||
\(904\) | 4.72673 | + | 15.9459i | 0.157209 | + | 0.530354i | ||||
\(905\) | − | 36.3986i | − | 1.20993i | ||||||
\(906\) | −17.2660 | − | 14.2311i | −0.573624 | − | 0.472797i | ||||
\(907\) | 7.88170 | − | 7.88170i | 0.261708 | − | 0.261708i | −0.564040 | − | 0.825747i | \(-0.690754\pi\) |
0.825747 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(908\) | −17.9905 | + | 26.6794i | −0.597035 | + | 0.885385i | ||||
\(909\) | 10.5198 | + | 10.5198i | 0.348919 | + | 0.348919i | ||||
\(910\) | 10.1894 | − | 42.1758i | 0.337776 | − | 1.39811i | ||||
\(911\) | − | 22.4309i | − | 0.743169i | −0.928399 | − | 0.371585i | \(-0.878815\pi\) | ||
0.928399 | − | 0.371585i | \(-0.121185\pi\) | |||||||
\(912\) | 3.03439 | + | 7.50484i | 0.100479 | + | 0.248510i | ||||
\(913\) | 4.74687i | 0.157098i | ||||||||
\(914\) | 49.5481 | − | 4.77414i | 1.63890 | − | 0.157915i | ||||
\(915\) | 4.44981 | − | 4.44981i | 0.147106 | − | 0.147106i | ||||
\(916\) | 23.5244 | − | 34.8860i | 0.777267 | − | 1.15266i | ||||
\(917\) | −4.59236 | + | 2.23134i | −0.151653 | + | 0.0736855i | ||||
\(918\) | −5.66571 | − | 4.66984i | −0.186996 | − | 0.154128i | ||||
\(919\) | 38.3187 | 1.26402 | 0.632009 | − | 0.774961i | \(-0.282230\pi\) | ||||
0.632009 | + | 0.774961i | \(0.282230\pi\) | |||||||
\(920\) | −57.3600 | − | 31.1297i | −1.89110 | − | 1.02631i | ||||
\(921\) | 12.3754i | 0.407783i | ||||||||
\(922\) | −34.4019 | + | 41.7383i | −1.13297 | + | 1.37458i | ||||
\(923\) | −37.8097 | − | 37.8097i | −1.24452 | − | 1.24452i | ||||
\(924\) | −0.257073 | + | 1.81118i | −0.00845708 | + | 0.0595836i | ||||
\(925\) | −17.2583 | + | 17.2583i | −0.567448 | + | 0.567448i | ||||
\(926\) | −26.1874 | + | 2.52325i | −0.860571 | + | 0.0829192i | ||||
\(927\) | −5.39742 | −0.177275 | ||||||||
\(928\) | 38.8536 | + | 12.2368i | 1.27543 | + | 0.401693i | ||||
\(929\) | 28.5117i | 0.935438i | 0.883877 | + | 0.467719i | \(0.154924\pi\) | ||||
−0.883877 | + | 0.467719i | \(0.845076\pi\) | |||||||
\(930\) | −7.52781 | + | 0.725332i | −0.246847 | + | 0.0237846i | ||||
\(931\) | 14.0659 | − | 1.68436i | 0.460991 | − | 0.0552025i | ||||
\(932\) | 0.811616 | + | 4.17255i | 0.0265854 | + | 0.136676i | ||||
\(933\) | −8.84332 | − | 8.84332i | −0.289517 | − | 0.289517i | ||||
\(934\) | −15.5434 | − | 12.8113i | −0.508597 | − | 0.419200i | ||||
\(935\) | −6.26036 | −0.204736 | ||||||||
\(936\) | −8.26480 | − | 4.48536i | −0.270143 | − | 0.146609i | ||||
\(937\) | −16.8510 | −0.550499 | −0.275250 | − | 0.961373i | \(-0.588760\pi\) | ||||
−0.275250 | + | 0.961373i | \(0.588760\pi\) | |||||||
\(938\) | −17.3301 | + | 10.5858i | −0.565848 | + | 0.345638i | ||||
\(939\) | 21.6898 | − | 21.6898i | 0.707820 | − | 0.707820i | ||||
\(940\) | −28.0829 | + | 41.6461i | −0.915962 | + | 1.35835i | ||||
\(941\) | −28.9571 | − | 28.9571i | −0.943975 | − | 0.943975i | 0.0545372 | − | 0.998512i | \(-0.482632\pi\) |
−0.998512 | + | 0.0545372i | \(0.982632\pi\) | |||||||
\(942\) | −2.56209 | − | 26.5905i | −0.0834774 | − | 0.866365i | ||||
\(943\) | −63.1815 | −2.05747 | ||||||||
\(944\) | −18.0001 | − | 7.63516i | −0.585854 | − | 0.248503i | ||||
\(945\) | −8.72105 | − | 3.01751i | −0.283696 | − | 0.0981595i | ||||
\(946\) | −4.68279 | + | 0.451205i | −0.152251 | + | 0.0146699i | ||||
\(947\) | 42.0974 | + | 42.0974i | 1.36798 | + | 1.36798i | 0.863315 | + | 0.504666i | \(0.168384\pi\) |
0.504666 | + | 0.863315i | \(0.331616\pi\) | |||||||
\(948\) | −6.79417 | − | 4.58146i | −0.220665 | − | 0.148799i | ||||
\(949\) | −15.7130 | − | 15.7130i | −0.510066 | − | 0.510066i | ||||
\(950\) | −13.0446 | + | 15.8264i | −0.423222 | + | 0.513476i | ||||
\(951\) | − | 9.28918i | − | 0.301222i | ||||||
\(952\) | −38.8120 | − | 1.74529i | −1.25790 | − | 0.0565651i | ||||
\(953\) | − | 20.9090i | − | 0.677308i | −0.940911 | − | 0.338654i | \(-0.890028\pi\) | ||
0.940911 | − | 0.338654i | \(-0.109972\pi\) | |||||||
\(954\) | −8.48400 | − | 6.99276i | −0.274680 | − | 0.226399i | ||||
\(955\) | −61.5712 | − | 61.5712i | −1.99240 | − | 1.99240i | ||||
\(956\) | −3.41527 | − | 17.5580i | −0.110458 | − | 0.567867i | ||||
\(957\) | −1.76032 | − | 1.76032i | −0.0569031 | − | 0.0569031i | ||||
\(958\) | −1.11205 | − | 11.5413i | −0.0359288 | − | 0.372884i | ||||
\(959\) | 7.62812 | − | 22.0465i | 0.246325 | − | 0.711917i | ||||
\(960\) | −15.2065 | − | 23.3963i | −0.490788 | − | 0.755112i | ||||
\(961\) | −28.6494 | −0.924175 | ||||||||
\(962\) | 15.9399 | − | 1.53587i | 0.513923 | − | 0.0495184i | ||||
\(963\) | 5.63948 | + | 5.63948i | 0.181730 | + | 0.181730i | ||||
\(964\) | 1.58976 | + | 8.17300i | 0.0512026 | + | 0.263235i | ||||
\(965\) | −24.2718 | + | 24.2718i | −0.781337 | + | 0.781337i | ||||
\(966\) | 12.9026 | + | 21.1230i | 0.415135 | + | 0.679623i | ||||
\(967\) | −19.1350 | −0.615340 | −0.307670 | − | 0.951493i | \(-0.599549\pi\) | ||||
−0.307670 | + | 0.951493i | \(0.599549\pi\) | |||||||
\(968\) | −29.5057 | + | 8.74615i | −0.948348 | + | 0.281112i | ||||
\(969\) | 10.5068 | 0.337528 | ||||||||
\(970\) | −52.4442 | + | 63.6282i | −1.68388 | + | 2.04298i | ||||
\(971\) | 13.3830 | + | 13.3830i | 0.429480 | + | 0.429480i | 0.888451 | − | 0.458971i | \(-0.151782\pi\) |
−0.458971 | + | 0.888451i | \(0.651782\pi\) | |||||||
\(972\) | −1.11817 | + | 1.65822i | −0.0358654 | + | 0.0531874i | ||||
\(973\) | 0.669479 | + | 1.37787i | 0.0214625 | + | 0.0441723i | ||||
\(974\) | −2.50745 | − | 26.0234i | −0.0803439 | − | 0.833843i | ||||
\(975\) | − | 23.8244i | − | 0.762990i | ||||||
\(976\) | −6.64379 | − | 2.81811i | −0.212662 | − | 0.0902055i | ||||
\(977\) | 36.3850 | 1.16406 | 0.582029 | − | 0.813168i | \(-0.302259\pi\) | ||||
0.582029 | + | 0.813168i | \(0.302259\pi\) | |||||||
\(978\) | 2.14975 | + | 22.3111i | 0.0687415 | + | 0.713429i | ||||
\(979\) | 2.82497 | − | 2.82497i | 0.0902865 | − | 0.0902865i | ||||
\(980\) | −46.4848 | + | 14.9567i | −1.48490 | + | 0.477775i | ||||
\(981\) | −1.70321 | − | 1.70321i | −0.0543794 | − | 0.0543794i | ||||
\(982\) | 12.2316 | + | 10.0816i | 0.390325 | + | 0.321717i | ||||
\(983\) | − | 13.6512i | − | 0.435406i | −0.976015 | − | 0.217703i | \(-0.930144\pi\) | ||
0.976015 | − | 0.217703i | \(-0.0698563\pi\) | |||||||
\(984\) | −23.7429 | − | 12.8854i | −0.756894 | − | 0.410772i | ||||
\(985\) | 30.6266 | 0.975844 | ||||||||
\(986\) | 33.6275 | − | 40.7988i | 1.07092 | − | 1.29930i | ||||
\(987\) | 17.1350 | − | 8.32557i | 0.545413 | − | 0.265006i | ||||
\(988\) | 13.2090 | − | 2.56932i | 0.420234 | − | 0.0817411i | ||||
\(989\) | −45.0104 | + | 45.0104i | −1.43125 | + | 1.43125i | ||||
\(990\) | 0.163556 | + | 1.69745i | 0.00519814 | + | 0.0539485i | ||||
\(991\) | − | 14.6044i | − | 0.463926i | −0.972725 | − | 0.231963i | \(-0.925485\pi\) | ||
0.972725 | − | 0.231963i | \(-0.0745148\pi\) | |||||||
\(992\) | 4.00713 | + | 7.69161i | 0.127227 | + | 0.244209i | ||||
\(993\) | 4.05184i | 0.128581i | ||||||||
\(994\) | −14.1321 | + | 58.4953i | −0.448244 | + | 1.85536i | ||||
\(995\) | 25.0847 | + | 25.0847i | 0.795240 | + | 0.795240i | ||||
\(996\) | 5.24334 | + | 26.9562i | 0.166142 | + | 0.854140i | ||||
\(997\) | −33.5387 | + | 33.5387i | −1.06218 | + | 1.06218i | −0.0642464 | + | 0.997934i | \(0.520464\pi\) |
−0.997934 | + | 0.0642464i | \(0.979536\pi\) | |||||||
\(998\) | −3.79146 | + | 4.60001i | −0.120017 | + | 0.145611i | ||||
\(999\) | − | 3.40592i | − | 0.107758i |
(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.u.a.139.15 | ✓ | 64 | |
4.3 | odd | 2 | 1344.2.u.a.1231.18 | 64 | |||
7.6 | odd | 2 | inner | 336.2.u.a.139.16 | yes | 64 | |
16.3 | odd | 4 | inner | 336.2.u.a.307.16 | yes | 64 | |
16.13 | even | 4 | 1344.2.u.a.559.15 | 64 | |||
28.27 | even | 2 | 1344.2.u.a.1231.15 | 64 | |||
112.13 | odd | 4 | 1344.2.u.a.559.18 | 64 | |||
112.83 | even | 4 | inner | 336.2.u.a.307.15 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.15 | ✓ | 64 | 1.1 | even | 1 | trivial | |
336.2.u.a.139.16 | yes | 64 | 7.6 | odd | 2 | inner | |
336.2.u.a.307.15 | yes | 64 | 112.83 | even | 4 | inner | |
336.2.u.a.307.16 | yes | 64 | 16.3 | odd | 4 | inner | |
1344.2.u.a.559.15 | 64 | 16.13 | even | 4 | |||
1344.2.u.a.559.18 | 64 | 112.13 | odd | 4 | |||
1344.2.u.a.1231.15 | 64 | 28.27 | even | 2 | |||
1344.2.u.a.1231.18 | 64 | 4.3 | odd | 2 |