Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), 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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.191 |
Dual form | 418.2.f.c.267.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | −0.999773 | − | 0.0213149i | \(-0.993215\pi\) |
0.821362 | + | 0.570408i | \(0.193215\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 0.309017 | − | 0.224514i | 0.138197 | − | 0.100406i | −0.516539 | − | 0.856264i | \(-0.672780\pi\) |
0.654736 | + | 0.755858i | \(0.272780\pi\) | |||||||
\(6\) | 0.809017 | − | 0.587785i | 0.330280 | − | 0.239962i | ||||
\(7\) | −0.190983 | − | 0.587785i | −0.0721848 | − | 0.222162i | 0.908455 | − | 0.417983i | \(-0.137263\pi\) |
−0.980640 | + | 0.195821i | \(0.937263\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | 1.61803 | + | 1.17557i | 0.539345 | + | 0.391857i | ||||
\(10\) | −0.381966 | −0.120788 | ||||||||
\(11\) | −2.19098 | + | 2.48990i | −0.660606 | + | 0.750733i | ||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.50000 | + | 1.08981i | 0.416025 | + | 0.302260i | 0.776037 | − | 0.630688i | \(-0.217227\pi\) |
−0.360011 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(14\) | −0.190983 | + | 0.587785i | −0.0510424 | + | 0.157092i | ||||
\(15\) | 0.118034 | + | 0.363271i | 0.0304762 | + | 0.0937962i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 3.42705 | − | 2.48990i | 0.831182 | − | 0.603889i | −0.0887115 | − | 0.996057i | \(-0.528275\pi\) |
0.919893 | + | 0.392168i | \(0.128275\pi\) | |||||||
\(18\) | −0.618034 | − | 1.90211i | −0.145672 | − | 0.448332i | ||||
\(19\) | −0.309017 | + | 0.951057i | −0.0708934 | + | 0.218187i | ||||
\(20\) | 0.309017 | + | 0.224514i | 0.0690983 | + | 0.0502029i | ||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | 3.23607 | − | 0.726543i | 0.689932 | − | 0.154899i | ||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | 0.809017 | + | 0.587785i | 0.165140 | + | 0.119981i | ||||
\(25\) | −1.50000 | + | 4.61653i | −0.300000 | + | 0.923305i | ||||
\(26\) | −0.572949 | − | 1.76336i | −0.112365 | − | 0.345823i | ||||
\(27\) | −4.04508 | + | 2.93893i | −0.778477 | + | 0.565597i | ||||
\(28\) | 0.500000 | − | 0.363271i | 0.0944911 | − | 0.0686518i | ||||
\(29\) | 2.76393 | + | 8.50651i | 0.513249 | + | 1.57962i | 0.786445 | + | 0.617660i | \(0.211919\pi\) |
−0.273196 | + | 0.961958i | \(0.588081\pi\) | |||||||
\(30\) | 0.118034 | − | 0.363271i | 0.0215500 | − | 0.0663240i | ||||
\(31\) | 3.80902 | + | 2.76741i | 0.684120 | + | 0.497042i | 0.874722 | − | 0.484625i | \(-0.161044\pi\) |
−0.190602 | + | 0.981667i | \(0.561044\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.69098 | − | 2.85317i | −0.294362 | − | 0.496673i | ||||
\(34\) | −4.23607 | −0.726480 | ||||||||
\(35\) | −0.190983 | − | 0.138757i | −0.0322820 | − | 0.0234543i | ||||
\(36\) | −0.618034 | + | 1.90211i | −0.103006 | + | 0.317019i | ||||
\(37\) | 3.59017 | + | 11.0494i | 0.590220 | + | 1.81651i | 0.577210 | + | 0.816596i | \(0.304142\pi\) |
0.0130106 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(38\) | 0.809017 | − | 0.587785i | 0.131240 | − | 0.0953514i | ||||
\(39\) | −1.50000 | + | 1.08981i | −0.240192 | + | 0.174510i | ||||
\(40\) | −0.118034 | − | 0.363271i | −0.0186628 | − | 0.0574382i | ||||
\(41\) | 1.57295 | − | 4.84104i | 0.245653 | − | 0.756043i | −0.749875 | − | 0.661580i | \(-0.769886\pi\) |
0.995528 | − | 0.0944637i | \(-0.0301136\pi\) | |||||||
\(42\) | −0.500000 | − | 0.363271i | −0.0771517 | − | 0.0560540i | ||||
\(43\) | 5.70820 | 0.870493 | 0.435246 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435246 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(44\) | −3.04508 | − | 1.31433i | −0.459064 | − | 0.198142i | ||||
\(45\) | 0.763932 | 0.113880 | ||||||||
\(46\) | 0.809017 | + | 0.587785i | 0.119283 | + | 0.0866642i | ||||
\(47\) | 1.45492 | − | 4.47777i | 0.212221 | − | 0.653150i | −0.787118 | − | 0.616802i | \(-0.788428\pi\) |
0.999339 | − | 0.0363472i | \(-0.0115722\pi\) | |||||||
\(48\) | −0.309017 | − | 0.951057i | −0.0446028 | − | 0.137273i | ||||
\(49\) | 5.35410 | − | 3.88998i | 0.764872 | − | 0.555712i | ||||
\(50\) | 3.92705 | − | 2.85317i | 0.555369 | − | 0.403499i | ||||
\(51\) | 1.30902 | + | 4.02874i | 0.183299 | + | 0.564136i | ||||
\(52\) | −0.572949 | + | 1.76336i | −0.0794537 | + | 0.244533i | ||||
\(53\) | −10.8992 | − | 7.91872i | −1.49712 | − | 1.08772i | −0.971511 | − | 0.236993i | \(-0.923838\pi\) |
−0.525607 | − | 0.850727i | \(-0.676162\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | −0.118034 | + | 1.26133i | −0.0159157 | + | 0.170077i | ||||
\(56\) | −0.618034 | −0.0825883 | ||||||||
\(57\) | −0.809017 | − | 0.587785i | −0.107157 | − | 0.0778541i | ||||
\(58\) | 2.76393 | − | 8.50651i | 0.362922 | − | 1.11696i | ||||
\(59\) | 0.263932 | + | 0.812299i | 0.0343610 | + | 0.105752i | 0.966766 | − | 0.255663i | \(-0.0822937\pi\) |
−0.932405 | + | 0.361415i | \(0.882294\pi\) | |||||||
\(60\) | −0.309017 | + | 0.224514i | −0.0398939 | + | 0.0289846i | ||||
\(61\) | 4.50000 | − | 3.26944i | 0.576166 | − | 0.418609i | −0.261174 | − | 0.965292i | \(-0.584110\pi\) |
0.837340 | + | 0.546683i | \(0.184110\pi\) | |||||||
\(62\) | −1.45492 | − | 4.47777i | −0.184774 | − | 0.568677i | ||||
\(63\) | 0.381966 | − | 1.17557i | 0.0481232 | − | 0.148108i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 0.708204 | 0.0878419 | ||||||||
\(66\) | −0.309017 | + | 3.30220i | −0.0380374 | + | 0.406472i | ||||
\(67\) | −3.38197 | −0.413173 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(68\) | 3.42705 | + | 2.48990i | 0.415591 | + | 0.301945i | ||||
\(69\) | 0.309017 | − | 0.951057i | 0.0372013 | − | 0.114494i | ||||
\(70\) | 0.0729490 | + | 0.224514i | 0.00871908 | + | 0.0268346i | ||||
\(71\) | −11.5172 | + | 8.36775i | −1.36684 | + | 0.993069i | −0.368866 | + | 0.929482i | \(0.620254\pi\) |
−0.997976 | + | 0.0635869i | \(0.979746\pi\) | |||||||
\(72\) | 1.61803 | − | 1.17557i | 0.190687 | − | 0.138542i | ||||
\(73\) | 0.809017 | + | 2.48990i | 0.0946883 | + | 0.291421i | 0.987172 | − | 0.159658i | \(-0.0510393\pi\) |
−0.892484 | + | 0.451079i | \(0.851039\pi\) | |||||||
\(74\) | 3.59017 | − | 11.0494i | 0.417349 | − | 1.28447i | ||||
\(75\) | −3.92705 | − | 2.85317i | −0.453457 | − | 0.329456i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 1.88197 | + | 0.812299i | 0.214470 | + | 0.0925701i | ||||
\(78\) | 1.85410 | 0.209936 | ||||||||
\(79\) | −12.1353 | − | 8.81678i | −1.36532 | − | 0.991965i | −0.998086 | − | 0.0618376i | \(-0.980304\pi\) |
−0.367237 | − | 0.930128i | \(-0.619696\pi\) | |||||||
\(80\) | −0.118034 | + | 0.363271i | −0.0131966 | + | 0.0406150i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −4.11803 | + | 2.99193i | −0.454761 | + | 0.330403i | ||||
\(83\) | 12.7812 | − | 9.28605i | 1.40291 | − | 1.01928i | 0.408608 | − | 0.912710i | \(-0.366014\pi\) |
0.994306 | − | 0.106567i | \(-0.0339858\pi\) | |||||||
\(84\) | 0.190983 | + | 0.587785i | 0.0208380 | + | 0.0641326i | ||||
\(85\) | 0.500000 | − | 1.53884i | 0.0542326 | − | 0.166911i | ||||
\(86\) | −4.61803 | − | 3.35520i | −0.497975 | − | 0.361800i | ||||
\(87\) | −8.94427 | −0.958927 | ||||||||
\(88\) | 1.69098 | + | 2.85317i | 0.180259 | + | 0.304149i | ||||
\(89\) | −8.41641 | −0.892137 | −0.446069 | − | 0.894999i | \(-0.647176\pi\) | ||||
−0.446069 | + | 0.894999i | \(0.647176\pi\) | |||||||
\(90\) | −0.618034 | − | 0.449028i | −0.0651465 | − | 0.0473317i | ||||
\(91\) | 0.354102 | − | 1.08981i | 0.0371200 | − | 0.114244i | ||||
\(92\) | −0.309017 | − | 0.951057i | −0.0322172 | − | 0.0991545i | ||||
\(93\) | −3.80902 | + | 2.76741i | −0.394977 | + | 0.286967i | ||||
\(94\) | −3.80902 | + | 2.76741i | −0.392870 | + | 0.285437i | ||||
\(95\) | 0.118034 | + | 0.363271i | 0.0121100 | + | 0.0372708i | ||||
\(96\) | −0.309017 | + | 0.951057i | −0.0315389 | + | 0.0970668i | ||||
\(97\) | 10.6631 | + | 7.74721i | 1.08268 | + | 0.786610i | 0.978148 | − | 0.207912i | \(-0.0666668\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(98\) | −6.61803 | −0.668522 | ||||||||
\(99\) | −6.47214 | + | 1.45309i | −0.650474 | + | 0.146041i | ||||
\(100\) | −4.85410 | −0.485410 | ||||||||
\(101\) | −10.6631 | − | 7.74721i | −1.06102 | − | 0.770876i | −0.0867432 | − | 0.996231i | \(-0.527646\pi\) |
−0.974277 | + | 0.225355i | \(0.927646\pi\) | |||||||
\(102\) | 1.30902 | − | 4.02874i | 0.129612 | − | 0.398905i | ||||
\(103\) | −1.95492 | − | 6.01661i | −0.192624 | − | 0.592834i | −0.999996 | − | 0.00279224i | \(-0.999111\pi\) |
0.807373 | − | 0.590042i | \(-0.200889\pi\) | |||||||
\(104\) | 1.50000 | − | 1.08981i | 0.147087 | − | 0.106865i | ||||
\(105\) | 0.190983 | − | 0.138757i | 0.0186380 | − | 0.0135413i | ||||
\(106\) | 4.16312 | + | 12.8128i | 0.404358 | + | 1.24449i | ||||
\(107\) | 3.16312 | − | 9.73508i | 0.305790 | − | 0.941126i | −0.673591 | − | 0.739104i | \(-0.735249\pi\) |
0.979381 | − | 0.202021i | \(-0.0647510\pi\) | |||||||
\(108\) | −4.04508 | − | 2.93893i | −0.389238 | − | 0.282798i | ||||
\(109\) | 1.90983 | 0.182929 | 0.0914643 | − | 0.995808i | \(-0.470845\pi\) | ||||
0.0914643 | + | 0.995808i | \(0.470845\pi\) | |||||||
\(110\) | 0.836881 | − | 0.951057i | 0.0797935 | − | 0.0906797i | ||||
\(111\) | −11.6180 | −1.10273 | ||||||||
\(112\) | 0.500000 | + | 0.363271i | 0.0472456 | + | 0.0343259i | ||||
\(113\) | 4.69098 | − | 14.4374i | 0.441291 | − | 1.35815i | −0.445210 | − | 0.895426i | \(-0.646871\pi\) |
0.886501 | − | 0.462727i | \(-0.153129\pi\) | |||||||
\(114\) | 0.309017 | + | 0.951057i | 0.0289421 | + | 0.0890746i | ||||
\(115\) | −0.309017 | + | 0.224514i | −0.0288160 | + | 0.0209360i | ||||
\(116\) | −7.23607 | + | 5.25731i | −0.671852 | + | 0.488129i | ||||
\(117\) | 1.14590 | + | 3.52671i | 0.105938 | + | 0.326045i | ||||
\(118\) | 0.263932 | − | 0.812299i | 0.0242969 | − | 0.0747782i | ||||
\(119\) | −2.11803 | − | 1.53884i | −0.194160 | − | 0.141065i | ||||
\(120\) | 0.381966 | 0.0348686 | ||||||||
\(121\) | −1.39919 | − | 10.9106i | −0.127199 | − | 0.991877i | ||||
\(122\) | −5.56231 | −0.503588 | ||||||||
\(123\) | 4.11803 | + | 2.99193i | 0.371311 | + | 0.269773i | ||||
\(124\) | −1.45492 | + | 4.47777i | −0.130655 | + | 0.402115i | ||||
\(125\) | 1.16312 | + | 3.57971i | 0.104033 | + | 0.320179i | ||||
\(126\) | −1.00000 | + | 0.726543i | −0.0890871 | + | 0.0647256i | ||||
\(127\) | −1.04508 | + | 0.759299i | −0.0927363 | + | 0.0673769i | −0.633187 | − | 0.773999i | \(-0.718254\pi\) |
0.540451 | + | 0.841376i | \(0.318254\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | −1.76393 | + | 5.42882i | −0.155306 | + | 0.477981i | ||||
\(130\) | −0.572949 | − | 0.416272i | −0.0502510 | − | 0.0365095i | ||||
\(131\) | −15.2361 | −1.33118 | −0.665591 | − | 0.746317i | \(-0.731820\pi\) | ||||
−0.665591 | + | 0.746317i | \(0.731820\pi\) | |||||||
\(132\) | 2.19098 | − | 2.48990i | 0.190701 | − | 0.216718i | ||||
\(133\) | 0.618034 | 0.0535903 | ||||||||
\(134\) | 2.73607 | + | 1.98787i | 0.236360 | + | 0.171726i | ||||
\(135\) | −0.590170 | + | 1.81636i | −0.0507937 | + | 0.156327i | ||||
\(136\) | −1.30902 | − | 4.02874i | −0.112247 | − | 0.345462i | ||||
\(137\) | 9.28115 | − | 6.74315i | 0.792942 | − | 0.576106i | −0.115893 | − | 0.993262i | \(-0.536973\pi\) |
0.908835 | + | 0.417155i | \(0.136973\pi\) | |||||||
\(138\) | −0.809017 | + | 0.587785i | −0.0688681 | + | 0.0500356i | ||||
\(139\) | 5.42705 | + | 16.7027i | 0.460316 | + | 1.41671i | 0.864778 | + | 0.502154i | \(0.167459\pi\) |
−0.404462 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(140\) | 0.0729490 | − | 0.224514i | 0.00616532 | − | 0.0189749i | ||||
\(141\) | 3.80902 | + | 2.76741i | 0.320777 | + | 0.233058i | ||||
\(142\) | 14.2361 | 1.19466 | ||||||||
\(143\) | −6.00000 | + | 1.34708i | −0.501745 | + | 0.112649i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 2.76393 | + | 2.00811i | 0.229532 | + | 0.166765i | ||||
\(146\) | 0.809017 | − | 2.48990i | 0.0669547 | − | 0.206065i | ||||
\(147\) | 2.04508 | + | 6.29412i | 0.168676 | + | 0.519131i | ||||
\(148\) | −9.39919 | + | 6.82891i | −0.772608 | + | 0.561333i | ||||
\(149\) | 11.2812 | − | 8.19624i | 0.924188 | − | 0.671462i | −0.0203749 | − | 0.999792i | \(-0.506486\pi\) |
0.944563 | + | 0.328330i | \(0.106486\pi\) | |||||||
\(150\) | 1.50000 | + | 4.61653i | 0.122474 | + | 0.376938i | ||||
\(151\) | 1.47214 | − | 4.53077i | 0.119801 | − | 0.368709i | −0.873117 | − | 0.487510i | \(-0.837905\pi\) |
0.992918 | + | 0.118801i | \(0.0379052\pi\) | |||||||
\(152\) | 0.809017 | + | 0.587785i | 0.0656199 | + | 0.0476757i | ||||
\(153\) | 8.47214 | 0.684932 | ||||||||
\(154\) | −1.04508 | − | 1.76336i | −0.0842153 | − | 0.142095i | ||||
\(155\) | 1.79837 | 0.144449 | ||||||||
\(156\) | −1.50000 | − | 1.08981i | −0.120096 | − | 0.0872549i | ||||
\(157\) | 0.236068 | − | 0.726543i | 0.0188403 | − | 0.0579844i | −0.941194 | − | 0.337866i | \(-0.890295\pi\) |
0.960035 | + | 0.279881i | \(0.0902951\pi\) | |||||||
\(158\) | 4.63525 | + | 14.2658i | 0.368761 | + | 1.13493i | ||||
\(159\) | 10.8992 | − | 7.91872i | 0.864362 | − | 0.627996i | ||||
\(160\) | 0.309017 | − | 0.224514i | 0.0244299 | − | 0.0177494i | ||||
\(161\) | 0.190983 | + | 0.587785i | 0.0150516 | + | 0.0463240i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −3.50000 | − | 2.54290i | −0.274141 | − | 0.199175i | 0.442217 | − | 0.896908i | \(-0.354192\pi\) |
−0.716358 | + | 0.697733i | \(0.754192\pi\) | |||||||
\(164\) | 5.09017 | 0.397475 | ||||||||
\(165\) | −1.16312 | − | 0.502029i | −0.0905487 | − | 0.0390829i | ||||
\(166\) | −15.7984 | −1.22619 | ||||||||
\(167\) | −3.11803 | − | 2.26538i | −0.241281 | − | 0.175301i | 0.460573 | − | 0.887622i | \(-0.347644\pi\) |
−0.701854 | + | 0.712321i | \(0.747644\pi\) | |||||||
\(168\) | 0.190983 | − | 0.587785i | 0.0147347 | − | 0.0453486i | ||||
\(169\) | −2.95492 | − | 9.09429i | −0.227301 | − | 0.699561i | ||||
\(170\) | −1.30902 | + | 0.951057i | −0.100397 | + | 0.0729427i | ||||
\(171\) | −1.61803 | + | 1.17557i | −0.123734 | + | 0.0898981i | ||||
\(172\) | 1.76393 | + | 5.42882i | 0.134499 | + | 0.413944i | ||||
\(173\) | 4.59017 | − | 14.1271i | 0.348984 | − | 1.07406i | −0.610432 | − | 0.792069i | \(-0.709004\pi\) |
0.959416 | − | 0.281994i | \(-0.0909959\pi\) | |||||||
\(174\) | 7.23607 | + | 5.25731i | 0.548565 | + | 0.398556i | ||||
\(175\) | 3.00000 | 0.226779 | ||||||||
\(176\) | 0.309017 | − | 3.30220i | 0.0232930 | − | 0.248913i | ||||
\(177\) | −0.854102 | −0.0641982 | ||||||||
\(178\) | 6.80902 | + | 4.94704i | 0.510357 | + | 0.370796i | ||||
\(179\) | −0.527864 | + | 1.62460i | −0.0394544 | + | 0.121428i | −0.968844 | − | 0.247673i | \(-0.920334\pi\) |
0.929389 | + | 0.369101i | \(0.120334\pi\) | |||||||
\(180\) | 0.236068 | + | 0.726543i | 0.0175955 | + | 0.0541533i | ||||
\(181\) | −20.1353 | + | 14.6291i | −1.49664 | + | 1.08737i | −0.524947 | + | 0.851135i | \(0.675915\pi\) |
−0.971695 | + | 0.236239i | \(0.924085\pi\) | |||||||
\(182\) | −0.927051 | + | 0.673542i | −0.0687176 | + | 0.0499263i | ||||
\(183\) | 1.71885 | + | 5.29007i | 0.127061 | + | 0.391053i | ||||
\(184\) | −0.309017 | + | 0.951057i | −0.0227810 | + | 0.0701128i | ||||
\(185\) | 3.59017 | + | 2.60841i | 0.263955 | + | 0.191774i | ||||
\(186\) | 4.70820 | 0.345222 | ||||||||
\(187\) | −1.30902 | + | 13.9883i | −0.0957248 | + | 1.02293i | ||||
\(188\) | 4.70820 | 0.343381 | ||||||||
\(189\) | 2.50000 | + | 1.81636i | 0.181848 | + | 0.132120i | ||||
\(190\) | 0.118034 | − | 0.363271i | 0.00856309 | − | 0.0263545i | ||||
\(191\) | −1.45492 | − | 4.47777i | −0.105274 | − | 0.324000i | 0.884521 | − | 0.466501i | \(-0.154486\pi\) |
−0.989795 | + | 0.142501i | \(0.954486\pi\) | |||||||
\(192\) | 0.809017 | − | 0.587785i | 0.0583858 | − | 0.0424197i | ||||
\(193\) | 5.54508 | − | 4.02874i | 0.399144 | − | 0.289995i | −0.370048 | − | 0.929013i | \(-0.620659\pi\) |
0.769192 | + | 0.639017i | \(0.220659\pi\) | |||||||
\(194\) | −4.07295 | − | 12.5352i | −0.292421 | − | 0.899978i | ||||
\(195\) | −0.218847 | + | 0.673542i | −0.0156720 | + | 0.0482333i | ||||
\(196\) | 5.35410 | + | 3.88998i | 0.382436 | + | 0.277856i | ||||
\(197\) | 23.0000 | 1.63868 | 0.819341 | − | 0.573306i | \(-0.194340\pi\) | ||||
0.819341 | + | 0.573306i | \(0.194340\pi\) | |||||||
\(198\) | 6.09017 | + | 2.62866i | 0.432810 | + | 0.186810i | ||||
\(199\) | 23.4164 | 1.65995 | 0.829973 | − | 0.557804i | \(-0.188356\pi\) | ||||
0.829973 | + | 0.557804i | \(0.188356\pi\) | |||||||
\(200\) | 3.92705 | + | 2.85317i | 0.277684 | + | 0.201750i | ||||
\(201\) | 1.04508 | − | 3.21644i | 0.0737146 | − | 0.226870i | ||||
\(202\) | 4.07295 | + | 12.5352i | 0.286572 | + | 0.881977i | ||||
\(203\) | 4.47214 | − | 3.24920i | 0.313882 | − | 0.228049i | ||||
\(204\) | −3.42705 | + | 2.48990i | −0.239942 | + | 0.174328i | ||||
\(205\) | −0.600813 | − | 1.84911i | −0.0419626 | − | 0.129148i | ||||
\(206\) | −1.95492 | + | 6.01661i | −0.136205 | + | 0.419197i | ||||
\(207\) | −1.61803 | − | 1.17557i | −0.112461 | − | 0.0817078i | ||||
\(208\) | −1.85410 | −0.128559 | ||||||||
\(209\) | −1.69098 | − | 2.85317i | −0.116968 | − | 0.197358i | ||||
\(210\) | −0.236068 | −0.0162902 | ||||||||
\(211\) | −2.57295 | − | 1.86936i | −0.177129 | − | 0.128692i | 0.495688 | − | 0.868501i | \(-0.334916\pi\) |
−0.672817 | + | 0.739809i | \(0.734916\pi\) | |||||||
\(212\) | 4.16312 | − | 12.8128i | 0.285924 | − | 0.879984i | ||||
\(213\) | −4.39919 | − | 13.5393i | −0.301427 | − | 0.927698i | ||||
\(214\) | −8.28115 | + | 6.01661i | −0.566088 | + | 0.411287i | ||||
\(215\) | 1.76393 | − | 1.28157i | 0.120299 | − | 0.0874025i | ||||
\(216\) | 1.54508 | + | 4.75528i | 0.105130 | + | 0.323556i | ||||
\(217\) | 0.899187 | − | 2.76741i | 0.0610408 | − | 0.187864i | ||||
\(218\) | −1.54508 | − | 1.12257i | −0.104646 | − | 0.0760300i | ||||
\(219\) | −2.61803 | −0.176910 | ||||||||
\(220\) | −1.23607 | + | 0.277515i | −0.0833357 | + | 0.0187100i | ||||
\(221\) | 7.85410 | 0.528324 | ||||||||
\(222\) | 9.39919 | + | 6.82891i | 0.630832 | + | 0.458326i | ||||
\(223\) | −1.52786 | + | 4.70228i | −0.102313 | + | 0.314888i | −0.989091 | − | 0.147309i | \(-0.952939\pi\) |
0.886777 | + | 0.462197i | \(0.152939\pi\) | |||||||
\(224\) | −0.190983 | − | 0.587785i | −0.0127606 | − | 0.0392731i | ||||
\(225\) | −7.85410 | + | 5.70634i | −0.523607 | + | 0.380423i | ||||
\(226\) | −12.2812 | + | 8.92278i | −0.816930 | + | 0.593534i | ||||
\(227\) | 7.37132 | + | 22.6866i | 0.489252 | + | 1.50576i | 0.825727 | + | 0.564070i | \(0.190765\pi\) |
−0.336475 | + | 0.941692i | \(0.609235\pi\) | |||||||
\(228\) | 0.309017 | − | 0.951057i | 0.0204652 | − | 0.0629853i | ||||
\(229\) | 2.07295 | + | 1.50609i | 0.136984 | + | 0.0995249i | 0.654167 | − | 0.756350i | \(-0.273019\pi\) |
−0.517183 | + | 0.855875i | \(0.673019\pi\) | |||||||
\(230\) | 0.381966 | 0.0251861 | ||||||||
\(231\) | −1.35410 | + | 1.53884i | −0.0890934 | + | 0.101248i | ||||
\(232\) | 8.94427 | 0.587220 | ||||||||
\(233\) | 10.2812 | + | 7.46969i | 0.673541 | + | 0.489356i | 0.871209 | − | 0.490913i | \(-0.163337\pi\) |
−0.197668 | + | 0.980269i | \(0.563337\pi\) | |||||||
\(234\) | 1.14590 | − | 3.52671i | 0.0749097 | − | 0.230548i | ||||
\(235\) | −0.555728 | − | 1.71036i | −0.0362517 | − | 0.111571i | ||||
\(236\) | −0.690983 | + | 0.502029i | −0.0449792 | + | 0.0326793i | ||||
\(237\) | 12.1353 | − | 8.81678i | 0.788270 | − | 0.572711i | ||||
\(238\) | 0.809017 | + | 2.48990i | 0.0524408 | + | 0.161396i | ||||
\(239\) | −3.19098 | + | 9.82084i | −0.206408 | + | 0.635257i | 0.793245 | + | 0.608902i | \(0.208390\pi\) |
−0.999653 | + | 0.0263546i | \(0.991610\pi\) | |||||||
\(240\) | −0.309017 | − | 0.224514i | −0.0199470 | − | 0.0144923i | ||||
\(241\) | 5.09017 | 0.327887 | 0.163943 | − | 0.986470i | \(-0.447579\pi\) | ||||
0.163943 | + | 0.986470i | \(0.447579\pi\) | |||||||
\(242\) | −5.28115 | + | 9.64932i | −0.339485 | + | 0.620282i | ||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 4.50000 | + | 3.26944i | 0.288083 | + | 0.209305i | ||||
\(245\) | 0.781153 | − | 2.40414i | 0.0499060 | − | 0.153595i | ||||
\(246\) | −1.57295 | − | 4.84104i | −0.100288 | − | 0.308653i | ||||
\(247\) | −1.50000 | + | 1.08981i | −0.0954427 | + | 0.0693432i | ||||
\(248\) | 3.80902 | − | 2.76741i | 0.241873 | − | 0.175731i | ||||
\(249\) | 4.88197 | + | 15.0251i | 0.309382 | + | 0.952180i | ||||
\(250\) | 1.16312 | − | 3.57971i | 0.0735621 | − | 0.226401i | ||||
\(251\) | 9.23607 | + | 6.71040i | 0.582975 | + | 0.423556i | 0.839796 | − | 0.542903i | \(-0.182675\pi\) |
−0.256820 | + | 0.966459i | \(0.582675\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | 2.19098 | − | 2.48990i | 0.137746 | − | 0.156539i | ||||
\(254\) | 1.29180 | 0.0810545 | ||||||||
\(255\) | 1.30902 | + | 0.951057i | 0.0819738 | + | 0.0595575i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −5.02786 | − | 15.4742i | −0.313630 | − | 0.965252i | −0.976315 | − | 0.216355i | \(-0.930583\pi\) |
0.662685 | − | 0.748898i | \(-0.269417\pi\) | |||||||
\(258\) | 4.61803 | − | 3.35520i | 0.287506 | − | 0.208886i | ||||
\(259\) | 5.80902 | − | 4.22050i | 0.360955 | − | 0.262249i | ||||
\(260\) | 0.218847 | + | 0.673542i | 0.0135723 | + | 0.0417713i | ||||
\(261\) | −5.52786 | + | 17.0130i | −0.342166 | + | 1.05308i | ||||
\(262\) | 12.3262 | + | 8.95554i | 0.761518 | + | 0.553275i | ||||
\(263\) | −14.6180 | −0.901387 | −0.450693 | − | 0.892679i | \(-0.648823\pi\) | ||||
−0.450693 | + | 0.892679i | \(0.648823\pi\) | |||||||
\(264\) | −3.23607 | + | 0.726543i | −0.199166 | + | 0.0447156i | ||||
\(265\) | −5.14590 | −0.316110 | ||||||||
\(266\) | −0.500000 | − | 0.363271i | −0.0306570 | − | 0.0222736i | ||||
\(267\) | 2.60081 | − | 8.00448i | 0.159167 | − | 0.489866i | ||||
\(268\) | −1.04508 | − | 3.21644i | −0.0638387 | − | 0.196475i | ||||
\(269\) | −8.51722 | + | 6.18812i | −0.519304 | + | 0.377297i | −0.816342 | − | 0.577569i | \(-0.804001\pi\) |
0.297038 | + | 0.954866i | \(0.404001\pi\) | |||||||
\(270\) | 1.54508 | − | 1.12257i | 0.0940309 | − | 0.0683174i | ||||
\(271\) | 2.52786 | + | 7.77997i | 0.153557 | + | 0.472599i | 0.998012 | − | 0.0630273i | \(-0.0200755\pi\) |
−0.844455 | + | 0.535627i | \(0.820076\pi\) | |||||||
\(272\) | −1.30902 | + | 4.02874i | −0.0793708 | + | 0.244278i | ||||
\(273\) | 0.927051 | + | 0.673542i | 0.0561077 | + | 0.0407646i | ||||
\(274\) | −11.4721 | −0.693057 | ||||||||
\(275\) | −8.20820 | − | 13.8496i | −0.494973 | − | 0.835161i | ||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −19.2984 | − | 14.0211i | −1.15953 | − | 0.842446i | −0.169809 | − | 0.985477i | \(-0.554315\pi\) |
−0.989718 | + | 0.143031i | \(0.954315\pi\) | |||||||
\(278\) | 5.42705 | − | 16.7027i | 0.325493 | − | 1.00176i | ||||
\(279\) | 2.90983 | + | 8.95554i | 0.174207 | + | 0.536154i | ||||
\(280\) | −0.190983 | + | 0.138757i | −0.0114134 | + | 0.00829233i | ||||
\(281\) | −22.5344 | + | 16.3722i | −1.34429 | + | 0.976685i | −0.345018 | + | 0.938596i | \(0.612127\pi\) |
−0.999274 | + | 0.0380892i | \(0.987873\pi\) | |||||||
\(282\) | −1.45492 | − | 4.47777i | −0.0866389 | − | 0.266647i | ||||
\(283\) | 1.60081 | − | 4.92680i | 0.0951585 | − | 0.292868i | −0.892136 | − | 0.451766i | \(-0.850794\pi\) |
0.987295 | + | 0.158898i | \(0.0507942\pi\) | |||||||
\(284\) | −11.5172 | − | 8.36775i | −0.683421 | − | 0.496535i | ||||
\(285\) | −0.381966 | −0.0226257 | ||||||||
\(286\) | 5.64590 | + | 2.43690i | 0.333849 | + | 0.144097i | ||||
\(287\) | −3.14590 | −0.185696 | ||||||||
\(288\) | 1.61803 | + | 1.17557i | 0.0953436 | + | 0.0692712i | ||||
\(289\) | 0.291796 | − | 0.898056i | 0.0171645 | − | 0.0528268i | ||||
\(290\) | −1.05573 | − | 3.24920i | −0.0619945 | − | 0.190799i | ||||
\(291\) | −10.6631 | + | 7.74721i | −0.625083 | + | 0.454149i | ||||
\(292\) | −2.11803 | + | 1.53884i | −0.123949 | + | 0.0900539i | ||||
\(293\) | 0.746711 | + | 2.29814i | 0.0436233 | + | 0.134259i | 0.970496 | − | 0.241117i | \(-0.0775137\pi\) |
−0.926873 | + | 0.375376i | \(0.877514\pi\) | |||||||
\(294\) | 2.04508 | − | 6.29412i | 0.119272 | − | 0.367081i | ||||
\(295\) | 0.263932 | + | 0.191758i | 0.0153667 | + | 0.0111646i | ||||
\(296\) | 11.6180 | 0.675285 | ||||||||
\(297\) | 1.54508 | − | 16.5110i | 0.0896549 | − | 0.958065i | ||||
\(298\) | −13.9443 | −0.807770 | ||||||||
\(299\) | −1.50000 | − | 1.08981i | −0.0867472 | − | 0.0630256i | ||||
\(300\) | 1.50000 | − | 4.61653i | 0.0866025 | − | 0.266535i | ||||
\(301\) | −1.09017 | − | 3.35520i | −0.0628364 | − | 0.193390i | ||||
\(302\) | −3.85410 | + | 2.80017i | −0.221779 | + | 0.161132i | ||||
\(303\) | 10.6631 | − | 7.74721i | 0.612580 | − | 0.445066i | ||||
\(304\) | −0.309017 | − | 0.951057i | −0.0177233 | − | 0.0545468i | ||||
\(305\) | 0.656541 | − | 2.02063i | 0.0375934 | − | 0.115701i | ||||
\(306\) | −6.85410 | − | 4.97980i | −0.391823 | − | 0.284676i | ||||
\(307\) | 23.0000 | 1.31268 | 0.656340 | − | 0.754466i | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(308\) | −0.190983 | + | 2.04087i | −0.0108823 | + | 0.116289i | ||||
\(309\) | 6.32624 | 0.359887 | ||||||||
\(310\) | −1.45492 | − | 1.05706i | −0.0826336 | − | 0.0600368i | ||||
\(311\) | 0.618034 | − | 1.90211i | 0.0350455 | − | 0.107859i | −0.932004 | − | 0.362449i | \(-0.881941\pi\) |
0.967049 | + | 0.254590i | \(0.0819406\pi\) | |||||||
\(312\) | 0.572949 | + | 1.76336i | 0.0324369 | + | 0.0998304i | ||||
\(313\) | 1.66312 | − | 1.20833i | 0.0940050 | − | 0.0682987i | −0.539790 | − | 0.841800i | \(-0.681496\pi\) |
0.633795 | + | 0.773501i | \(0.281496\pi\) | |||||||
\(314\) | −0.618034 | + | 0.449028i | −0.0348777 | + | 0.0253401i | ||||
\(315\) | −0.145898 | − | 0.449028i | −0.00822042 | − | 0.0252999i | ||||
\(316\) | 4.63525 | − | 14.2658i | 0.260753 | − | 0.802517i | ||||
\(317\) | 13.7533 | + | 9.99235i | 0.772462 | + | 0.561226i | 0.902707 | − | 0.430256i | \(-0.141577\pi\) |
−0.130245 | + | 0.991482i | \(0.541577\pi\) | |||||||
\(318\) | −13.4721 | −0.755480 | ||||||||
\(319\) | −27.2361 | − | 11.7557i | −1.52493 | − | 0.658193i | ||||
\(320\) | −0.381966 | −0.0213525 | ||||||||
\(321\) | 8.28115 | + | 6.01661i | 0.462209 | + | 0.335814i | ||||
\(322\) | 0.190983 | − | 0.587785i | 0.0106431 | − | 0.0327560i | ||||
\(323\) | 1.30902 | + | 4.02874i | 0.0728357 | + | 0.224165i | ||||
\(324\) | −0.809017 | + | 0.587785i | −0.0449454 | + | 0.0326547i | ||||
\(325\) | −7.28115 | + | 5.29007i | −0.403886 | + | 0.293440i | ||||
\(326\) | 1.33688 | + | 4.11450i | 0.0740430 | + | 0.227881i | ||||
\(327\) | −0.590170 | + | 1.81636i | −0.0326365 | + | 0.100445i | ||||
\(328\) | −4.11803 | − | 2.99193i | −0.227380 | − | 0.165202i | ||||
\(329\) | −2.90983 | −0.160424 | ||||||||
\(330\) | 0.645898 | + | 1.08981i | 0.0355555 | + | 0.0599923i | ||||
\(331\) | −1.81966 | −0.100018 | −0.0500088 | − | 0.998749i | \(-0.515925\pi\) | ||||
−0.0500088 | + | 0.998749i | \(0.515925\pi\) | |||||||
\(332\) | 12.7812 | + | 9.28605i | 0.701457 | + | 0.509638i | ||||
\(333\) | −7.18034 | + | 22.0988i | −0.393480 | + | 1.21101i | ||||
\(334\) | 1.19098 | + | 3.66547i | 0.0651677 | + | 0.200566i | ||||
\(335\) | −1.04508 | + | 0.759299i | −0.0570991 | + | 0.0414849i | ||||
\(336\) | −0.500000 | + | 0.363271i | −0.0272772 | + | 0.0198181i | ||||
\(337\) | −2.16312 | − | 6.65740i | −0.117833 | − | 0.362651i | 0.874695 | − | 0.484674i | \(-0.161062\pi\) |
−0.992527 | + | 0.122023i | \(0.961062\pi\) | |||||||
\(338\) | −2.95492 | + | 9.09429i | −0.160726 | + | 0.494664i | ||||
\(339\) | 12.2812 | + | 8.92278i | 0.667021 | + | 0.484619i | ||||
\(340\) | 1.61803 | 0.0877502 | ||||||||
\(341\) | −15.2361 | + | 3.42071i | −0.825079 | + | 0.185242i | ||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | −6.80902 | − | 4.94704i | −0.367652 | − | 0.267115i | ||||
\(344\) | 1.76393 | − | 5.42882i | 0.0951048 | − | 0.292703i | ||||
\(345\) | −0.118034 | − | 0.363271i | −0.00635474 | − | 0.0195579i | ||||
\(346\) | −12.0172 | + | 8.73102i | −0.646050 | + | 0.469383i | ||||
\(347\) | −15.0902 | + | 10.9637i | −0.810083 | + | 0.588560i | −0.913855 | − | 0.406042i | \(-0.866909\pi\) |
0.103772 | + | 0.994601i | \(0.466909\pi\) | |||||||
\(348\) | −2.76393 | − | 8.50651i | −0.148162 | − | 0.455997i | ||||
\(349\) | 9.57295 | − | 29.4625i | 0.512428 | − | 1.57709i | −0.275485 | − | 0.961305i | \(-0.588838\pi\) |
0.787913 | − | 0.615786i | \(-0.211162\pi\) | |||||||
\(350\) | −2.42705 | − | 1.76336i | −0.129731 | − | 0.0942553i | ||||
\(351\) | −9.27051 | −0.494823 | ||||||||
\(352\) | −2.19098 | + | 2.48990i | −0.116780 | + | 0.132712i | ||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 0.690983 | + | 0.502029i | 0.0367253 | + | 0.0266825i | ||||
\(355\) | −1.68034 | + | 5.17155i | −0.0891832 | + | 0.274478i | ||||
\(356\) | −2.60081 | − | 8.00448i | −0.137843 | − | 0.424237i | ||||
\(357\) | 2.11803 | − | 1.53884i | 0.112098 | − | 0.0814441i | ||||
\(358\) | 1.38197 | − | 1.00406i | 0.0730392 | − | 0.0530661i | ||||
\(359\) | −3.55573 | − | 10.9434i | −0.187664 | − | 0.577571i | 0.812320 | − | 0.583212i | \(-0.198204\pi\) |
−0.999984 | + | 0.00564120i | \(0.998204\pi\) | |||||||
\(360\) | 0.236068 | − | 0.726543i | 0.0124419 | − | 0.0382922i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.0425798 | − | 0.0309361i | ||||
\(362\) | 24.8885 | 1.30811 | ||||||||
\(363\) | 10.8090 | + | 2.04087i | 0.567326 | + | 0.107118i | ||||
\(364\) | 1.14590 | 0.0600614 | ||||||||
\(365\) | 0.809017 | + | 0.587785i | 0.0423459 | + | 0.0307661i | ||||
\(366\) | 1.71885 | − | 5.29007i | 0.0898456 | − | 0.276516i | ||||
\(367\) | −7.75329 | − | 23.8622i | −0.404718 | − | 1.24560i | −0.921130 | − | 0.389255i | \(-0.872733\pi\) |
0.516412 | − | 0.856340i | \(-0.327267\pi\) | |||||||
\(368\) | 0.809017 | − | 0.587785i | 0.0421729 | − | 0.0306404i | ||||
\(369\) | 8.23607 | − | 5.98385i | 0.428753 | − | 0.311507i | ||||
\(370\) | −1.37132 | − | 4.22050i | −0.0712917 | − | 0.219413i | ||||
\(371\) | −2.57295 | + | 7.91872i | −0.133581 | + | 0.411120i | ||||
\(372\) | −3.80902 | − | 2.76741i | −0.197488 | − | 0.143484i | ||||
\(373\) | 16.7639 | 0.868003 | 0.434002 | − | 0.900912i | \(-0.357101\pi\) | ||||
0.434002 | + | 0.900912i | \(0.357101\pi\) | |||||||
\(374\) | 9.28115 | − | 10.5474i | 0.479917 | − | 0.545392i | ||||
\(375\) | −3.76393 | −0.194369 | ||||||||
\(376\) | −3.80902 | − | 2.76741i | −0.196435 | − | 0.142718i | ||||
\(377\) | −5.12461 | + | 15.7719i | −0.263931 | + | 0.812296i | ||||
\(378\) | −0.954915 | − | 2.93893i | −0.0491155 | − | 0.151162i | ||||
\(379\) | 24.6353 | − | 17.8986i | 1.26543 | − | 0.919387i | 0.266417 | − | 0.963858i | \(-0.414160\pi\) |
0.999011 | + | 0.0444705i | \(0.0141601\pi\) | |||||||
\(380\) | −0.309017 | + | 0.224514i | −0.0158522 | + | 0.0115173i | ||||
\(381\) | −0.399187 | − | 1.22857i | −0.0204510 | − | 0.0629416i | ||||
\(382\) | −1.45492 | + | 4.47777i | −0.0744399 | + | 0.229103i | ||||
\(383\) | 1.07295 | + | 0.779543i | 0.0548251 | + | 0.0398328i | 0.614860 | − | 0.788636i | \(-0.289212\pi\) |
−0.560035 | + | 0.828469i | \(0.689212\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0.763932 | − | 0.171513i | 0.0389336 | − | 0.00874113i | ||||
\(386\) | −6.85410 | −0.348865 | ||||||||
\(387\) | 9.23607 | + | 6.71040i | 0.469496 | + | 0.341109i | ||||
\(388\) | −4.07295 | + | 12.5352i | −0.206773 | + | 0.636381i | ||||
\(389\) | −1.18034 | − | 3.63271i | −0.0598456 | − | 0.184186i | 0.916664 | − | 0.399658i | \(-0.130871\pi\) |
−0.976510 | + | 0.215472i | \(0.930871\pi\) | |||||||
\(390\) | 0.572949 | − | 0.416272i | 0.0290124 | − | 0.0210787i | ||||
\(391\) | −3.42705 | + | 2.48990i | −0.173313 | + | 0.125920i | ||||
\(392\) | −2.04508 | − | 6.29412i | −0.103292 | − | 0.317901i | ||||
\(393\) | 4.70820 | − | 14.4904i | 0.237497 | − | 0.730942i | ||||
\(394\) | −18.6074 | − | 13.5191i | −0.937427 | − | 0.681080i | ||||
\(395\) | −5.72949 | −0.288282 | ||||||||
\(396\) | −3.38197 | − | 5.70634i | −0.169950 | − | 0.286754i | ||||
\(397\) | −33.1803 | −1.66527 | −0.832637 | − | 0.553819i | \(-0.813170\pi\) | ||||
−0.832637 | + | 0.553819i | \(0.813170\pi\) | |||||||
\(398\) | −18.9443 | − | 13.7638i | −0.949591 | − | 0.689918i | ||||
\(399\) | −0.190983 | + | 0.587785i | −0.00956111 | + | 0.0294261i | ||||
\(400\) | −1.50000 | − | 4.61653i | −0.0750000 | − | 0.230826i | ||||
\(401\) | 26.3713 | − | 19.1599i | 1.31692 | − | 0.956799i | 0.316956 | − | 0.948440i | \(-0.397339\pi\) |
0.999965 | − | 0.00835887i | \(-0.00266074\pi\) | |||||||
\(402\) | −2.73607 | + | 1.98787i | −0.136463 | + | 0.0991459i | ||||
\(403\) | 2.69756 | + | 8.30224i | 0.134375 | + | 0.413564i | ||||
\(404\) | 4.07295 | − | 12.5352i | 0.202637 | − | 0.623652i | ||||
\(405\) | 0.309017 | + | 0.224514i | 0.0153552 | + | 0.0111562i | ||||
\(406\) | −5.52786 | −0.274343 | ||||||||
\(407\) | −35.3779 | − | 15.2699i | −1.75362 | − | 0.756901i | ||||
\(408\) | 4.23607 | 0.209717 | ||||||||
\(409\) | −13.5172 | − | 9.82084i | −0.668384 | − | 0.485609i | 0.201100 | − | 0.979571i | \(-0.435548\pi\) |
−0.869484 | + | 0.493962i | \(0.835548\pi\) | |||||||
\(410\) | −0.600813 | + | 1.84911i | −0.0296720 | + | 0.0913212i | ||||
\(411\) | 3.54508 | + | 10.9106i | 0.174866 | + | 0.538183i | ||||
\(412\) | 5.11803 | − | 3.71847i | 0.252147 | − | 0.183196i | ||||
\(413\) | 0.427051 | − | 0.310271i | 0.0210138 | − | 0.0152674i | ||||
\(414\) | 0.618034 | + | 1.90211i | 0.0303747 | + | 0.0934838i | ||||
\(415\) | 1.86475 | − | 5.73910i | 0.0915367 | − | 0.281721i | ||||
\(416\) | 1.50000 | + | 1.08981i | 0.0735436 | + | 0.0534325i | ||||
\(417\) | −17.5623 | −0.860030 | ||||||||
\(418\) | −0.309017 | + | 3.30220i | −0.0151145 | + | 0.161516i | ||||
\(419\) | 34.4721 | 1.68407 | 0.842037 | − | 0.539420i | \(-0.181356\pi\) | ||||
0.842037 | + | 0.539420i | \(0.181356\pi\) | |||||||
\(420\) | 0.190983 | + | 0.138757i | 0.00931902 | + | 0.00677066i | ||||
\(421\) | −3.36475 | + | 10.3556i | −0.163988 | + | 0.504702i | −0.998960 | − | 0.0455894i | \(-0.985483\pi\) |
0.834973 | + | 0.550291i | \(0.185483\pi\) | |||||||
\(422\) | 0.982779 | + | 3.02468i | 0.0478409 | + | 0.147239i | ||||
\(423\) | 7.61803 | − | 5.53483i | 0.370401 | − | 0.269112i | ||||
\(424\) | −10.8992 | + | 7.91872i | −0.529311 | + | 0.384567i | ||||
\(425\) | 6.35410 | + | 19.5559i | 0.308219 | + | 0.948601i | ||||
\(426\) | −4.39919 | + | 13.5393i | −0.213141 | + | 0.655981i | ||||
\(427\) | −2.78115 | − | 2.02063i | −0.134589 | − | 0.0977849i | ||||
\(428\) | 10.2361 | 0.494779 | ||||||||
\(429\) | 0.572949 | − | 6.12261i | 0.0276622 | − | 0.295602i | ||||
\(430\) | −2.18034 | −0.105145 | ||||||||
\(431\) | −17.5344 | − | 12.7395i | −0.844604 | − | 0.613641i | 0.0790487 | − | 0.996871i | \(-0.474812\pi\) |
−0.923653 | + | 0.383230i | \(0.874812\pi\) | |||||||
\(432\) | 1.54508 | − | 4.75528i | 0.0743379 | − | 0.228789i | ||||
\(433\) | 3.67376 | + | 11.3067i | 0.176550 | + | 0.543364i | 0.999701 | − | 0.0244581i | \(-0.00778604\pi\) |
−0.823151 | + | 0.567822i | \(0.807786\pi\) | |||||||
\(434\) | −2.35410 | + | 1.71036i | −0.113001 | + | 0.0820997i | ||||
\(435\) | −2.76393 | + | 2.00811i | −0.132520 | + | 0.0962817i | ||||
\(436\) | 0.590170 | + | 1.81636i | 0.0282640 | + | 0.0869877i | ||||
\(437\) | 0.309017 | − | 0.951057i | 0.0147823 | − | 0.0454952i | ||||
\(438\) | 2.11803 | + | 1.53884i | 0.101204 | + | 0.0735287i | ||||
\(439\) | 4.14590 | 0.197873 | 0.0989365 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989365 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(440\) | 1.16312 | + | 0.502029i | 0.0554495 | + | 0.0239333i | ||||
\(441\) | 13.2361 | 0.630289 | ||||||||
\(442\) | −6.35410 | − | 4.61653i | −0.302234 | − | 0.219586i | ||||
\(443\) | 4.26393 | − | 13.1230i | 0.202586 | − | 0.623494i | −0.797218 | − | 0.603691i | \(-0.793696\pi\) |
0.999804 | − | 0.0198031i | \(-0.00630393\pi\) | |||||||
\(444\) | −3.59017 | − | 11.0494i | −0.170382 | − | 0.524382i | ||||
\(445\) | −2.60081 | + | 1.88960i | −0.123290 | + | 0.0895757i | ||||
\(446\) | 4.00000 | − | 2.90617i | 0.189405 | − | 0.137611i | ||||
\(447\) | 4.30902 | + | 13.2618i | 0.203810 | + | 0.627261i | ||||
\(448\) | −0.190983 | + | 0.587785i | −0.00902310 | + | 0.0277702i | ||||
\(449\) | 18.5172 | + | 13.4535i | 0.873882 | + | 0.634912i | 0.931626 | − | 0.363419i | \(-0.118391\pi\) |
−0.0577440 | + | 0.998331i | \(0.518391\pi\) | |||||||
\(450\) | 9.70820 | 0.457649 | ||||||||
\(451\) | 8.60739 | + | 14.5231i | 0.405306 | + | 0.683867i | ||||
\(452\) | 15.1803 | 0.714023 | ||||||||
\(453\) | 3.85410 | + | 2.80017i | 0.181082 | + | 0.131563i | ||||
\(454\) | 7.37132 | − | 22.6866i | 0.345953 | − | 1.06473i | ||||
\(455\) | −0.135255 | − | 0.416272i | −0.00634085 | − | 0.0195151i | ||||
\(456\) | −0.809017 | + | 0.587785i | −0.0378857 | + | 0.0275256i | ||||
\(457\) | 12.8992 | − | 9.37181i | 0.603399 | − | 0.438395i | −0.243685 | − | 0.969854i | \(-0.578356\pi\) |
0.847084 | + | 0.531460i | \(0.178356\pi\) | |||||||
\(458\) | −0.791796 | − | 2.43690i | −0.0369982 | − | 0.113869i | ||||
\(459\) | −6.54508 | + | 20.1437i | −0.305498 | + | 0.940227i | ||||
\(460\) | −0.309017 | − | 0.224514i | −0.0144080 | − | 0.0104680i | ||||
\(461\) | −15.7639 | −0.734200 | −0.367100 | − | 0.930182i | \(-0.619649\pi\) | ||||
−0.367100 | + | 0.930182i | \(0.619649\pi\) | |||||||
\(462\) | 2.00000 | − | 0.449028i | 0.0930484 | − | 0.0208907i | ||||
\(463\) | 23.1459 | 1.07568 | 0.537841 | − | 0.843047i | \(-0.319240\pi\) | ||||
0.537841 | + | 0.843047i | \(0.319240\pi\) | |||||||
\(464\) | −7.23607 | − | 5.25731i | −0.335926 | − | 0.244065i | ||||
\(465\) | −0.555728 | + | 1.71036i | −0.0257713 | + | 0.0793158i | ||||
\(466\) | −3.92705 | − | 12.0862i | −0.181917 | − | 0.559883i | ||||
\(467\) | −10.7812 | + | 7.83297i | −0.498892 | + | 0.362466i | −0.808594 | − | 0.588367i | \(-0.799771\pi\) |
0.309701 | + | 0.950834i | \(0.399771\pi\) | |||||||
\(468\) | −3.00000 | + | 2.17963i | −0.138675 | + | 0.100753i | ||||
\(469\) | 0.645898 | + | 1.98787i | 0.0298248 | + | 0.0917913i | ||||
\(470\) | −0.555728 | + | 1.71036i | −0.0256338 | + | 0.0788928i | ||||
\(471\) | 0.618034 | + | 0.449028i | 0.0284775 | + | 0.0206901i | ||||
\(472\) | 0.854102 | 0.0393132 | ||||||||
\(473\) | −12.5066 | + | 14.2128i | −0.575053 | + | 0.653507i | ||||
\(474\) | −15.0000 | −0.688973 | ||||||||
\(475\) | −3.92705 | − | 2.85317i | −0.180185 | − | 0.130912i | ||||
\(476\) | 0.809017 | − | 2.48990i | 0.0370812 | − | 0.114124i | ||||
\(477\) | −8.32624 | − | 25.6255i | −0.381232 | − | 1.17331i | ||||
\(478\) | 8.35410 | − | 6.06961i | 0.382108 | − | 0.277618i | ||||
\(479\) | 6.80902 | − | 4.94704i | 0.311112 | − | 0.226036i | −0.421262 | − | 0.906939i | \(-0.638413\pi\) |
0.732373 | + | 0.680903i | \(0.238413\pi\) | |||||||
\(480\) | 0.118034 | + | 0.363271i | 0.00538749 | + | 0.0165810i | ||||
\(481\) | −6.65654 | + | 20.4867i | −0.303512 | + | 0.934114i | ||||
\(482\) | −4.11803 | − | 2.99193i | −0.187571 | − | 0.136279i | ||||
\(483\) | −0.618034 | −0.0281215 | ||||||||
\(484\) | 9.94427 | − | 4.70228i | 0.452012 | − | 0.213740i | ||||
\(485\) | 5.03444 | 0.228602 | ||||||||
\(486\) | 12.9443 | + | 9.40456i | 0.587164 | + | 0.426600i | ||||
\(487\) | 7.51064 | − | 23.1154i | 0.340340 | − | 1.04746i | −0.623692 | − | 0.781670i | \(-0.714368\pi\) |
0.964032 | − | 0.265788i | \(-0.0856320\pi\) | |||||||
\(488\) | −1.71885 | − | 5.29007i | −0.0778086 | − | 0.239470i | ||||
\(489\) | 3.50000 | − | 2.54290i | 0.158275 | − | 0.114994i | ||||
\(490\) | −2.04508 | + | 1.48584i | −0.0923875 | + | 0.0671235i | ||||
\(491\) | −4.28115 | − | 13.1760i | −0.193206 | − | 0.594626i | −0.999993 | − | 0.00378385i | \(-0.998796\pi\) |
0.806787 | − | 0.590842i | \(-0.201204\pi\) | |||||||
\(492\) | −1.57295 | + | 4.84104i | −0.0709140 | + | 0.218251i | ||||
\(493\) | 30.6525 | + | 22.2703i | 1.38052 | + | 1.00301i | ||||
\(494\) | 1.85410 | 0.0834200 | ||||||||
\(495\) | −1.67376 | + | 1.90211i | −0.0752300 | + | 0.0854936i | ||||
\(496\) | −4.70820 | −0.211405 | ||||||||
\(497\) | 7.11803 | + | 5.17155i | 0.319287 | + | 0.231976i | ||||
\(498\) | 4.88197 | − | 15.0251i | 0.218766 | − | 0.673293i | ||||
\(499\) | 0.892609 | + | 2.74717i | 0.0399587 | + | 0.122980i | 0.969046 | − | 0.246880i | \(-0.0794055\pi\) |
−0.929087 | + | 0.369861i | \(0.879405\pi\) | |||||||
\(500\) | −3.04508 | + | 2.21238i | −0.136180 | + | 0.0989408i | ||||
\(501\) | 3.11803 | − | 2.26538i | 0.139303 | − | 0.101210i | ||||
\(502\) | −3.52786 | − | 10.8576i | −0.157456 | − | 0.484601i | ||||
\(503\) | 6.17376 | − | 19.0009i | 0.275274 | − | 0.847208i | −0.713872 | − | 0.700276i | \(-0.753060\pi\) |
0.989147 | − | 0.146932i | \(-0.0469397\pi\) | |||||||
\(504\) | −1.00000 | − | 0.726543i | −0.0445435 | − | 0.0323628i | ||||
\(505\) | −5.03444 | −0.224030 | ||||||||
\(506\) | −3.23607 | + | 0.726543i | −0.143861 | + | 0.0322988i | ||||
\(507\) | 9.56231 | 0.424677 | ||||||||
\(508\) | −1.04508 | − | 0.759299i | −0.0463681 | − | 0.0336884i | ||||
\(509\) | −11.0172 | + | 33.9075i | −0.488330 | + | 1.50292i | 0.338770 | + | 0.940869i | \(0.389989\pi\) |
−0.827100 | + | 0.562055i | \(0.810011\pi\) | |||||||
\(510\) | −0.500000 | − | 1.53884i | −0.0221404 | − | 0.0681411i | ||||
\(511\) | 1.30902 | − | 0.951057i | 0.0579075 | − | 0.0420723i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | −1.54508 | − | 4.75528i | −0.0682172 | − | 0.209951i | ||||
\(514\) | −5.02786 | + | 15.4742i | −0.221770 | + | 0.682537i | ||||
\(515\) | −1.95492 | − | 1.42033i | −0.0861438 | − | 0.0625872i | ||||
\(516\) | −5.70820 | −0.251290 | ||||||||
\(517\) | 7.96149 | + | 13.4333i | 0.350146 | + | 0.590796i | ||||
\(518\) | −7.18034 | −0.315486 | ||||||||
\(519\) | 12.0172 | + | 8.73102i | 0.527497 | + | 0.383249i | ||||
\(520\) | 0.218847 | − | 0.673542i | 0.00959708 | − | 0.0295368i | ||||
\(521\) | 11.6353 | + | 35.8096i | 0.509750 | + | 1.56885i | 0.792636 | + | 0.609695i | \(0.208708\pi\) |
−0.282886 | + | 0.959153i | \(0.591292\pi\) | |||||||
\(522\) | 14.4721 | − | 10.5146i | 0.633428 | − | 0.460213i | ||||
\(523\) | −28.7254 | + | 20.8702i | −1.25608 | + | 0.912592i | −0.998558 | − | 0.0536818i | \(-0.982904\pi\) |
−0.257517 | + | 0.966274i | \(0.582904\pi\) | |||||||
\(524\) | −4.70820 | − | 14.4904i | −0.205679 | − | 0.633014i | ||||
\(525\) | −0.927051 | + | 2.85317i | −0.0404598 | + | 0.124523i | ||||
\(526\) | 11.8262 | + | 8.59226i | 0.515648 | + | 0.374641i | ||||
\(527\) | 19.9443 | 0.868786 | ||||||||
\(528\) | 3.04508 | + | 1.31433i | 0.132520 | + | 0.0571988i | ||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 4.16312 | + | 3.02468i | 0.180834 | + | 0.131384i | ||||
\(531\) | −0.527864 | + | 1.62460i | −0.0229073 | + | 0.0705016i | ||||
\(532\) | 0.190983 | + | 0.587785i | 0.00828016 | + | 0.0254837i | ||||
\(533\) | 7.63525 | − | 5.54734i | 0.330720 | − | 0.240282i | ||||
\(534\) | −6.80902 | + | 4.94704i | −0.294655 | + | 0.214079i | ||||
\(535\) | −1.20820 | − | 3.71847i | −0.0522352 | − | 0.160763i | ||||
\(536\) | −1.04508 | + | 3.21644i | −0.0451408 | + | 0.138929i | ||||
\(537\) | −1.38197 | − | 1.00406i | −0.0596362 | − | 0.0433283i | ||||
\(538\) | 10.5279 | 0.453888 | ||||||||
\(539\) | −2.04508 | + | 21.8541i | −0.0880880 | + | 0.941321i | ||||
\(540\) | −1.90983 | −0.0821860 | ||||||||
\(541\) | −15.7254 | − | 11.4252i | −0.676089 | − | 0.491207i | 0.195969 | − | 0.980610i | \(-0.437215\pi\) |
−0.872058 | + | 0.489403i | \(0.837215\pi\) | |||||||
\(542\) | 2.52786 | − | 7.77997i | 0.108581 | − | 0.334178i | ||||
\(543\) | −7.69098 | − | 23.6704i | −0.330052 | − | 1.01579i | ||||
\(544\) | 3.42705 | − | 2.48990i | 0.146934 | − | 0.106754i | ||||
\(545\) | 0.590170 | − | 0.428784i | 0.0252801 | − | 0.0183671i | ||||
\(546\) | −0.354102 | − | 1.08981i | −0.0151542 | − | 0.0466397i | ||||
\(547\) | 4.11803 | − | 12.6740i | 0.176074 | − | 0.541901i | −0.823606 | − | 0.567162i | \(-0.808041\pi\) |
0.999681 | + | 0.0252603i | \(0.00804147\pi\) | |||||||
\(548\) | 9.28115 | + | 6.74315i | 0.396471 | + | 0.288053i | ||||
\(549\) | 11.1246 | 0.474787 | ||||||||
\(550\) | −1.50000 | + | 16.0292i | −0.0639602 | + | 0.683488i | ||||
\(551\) | −8.94427 | −0.381039 | ||||||||
\(552\) | −0.809017 | − | 0.587785i | −0.0344340 | − | 0.0250178i | ||||
\(553\) | −2.86475 | + | 8.81678i | −0.121821 | + | 0.374928i | ||||
\(554\) | 7.37132 | + | 22.6866i | 0.313178 | + | 0.963861i | ||||
\(555\) | −3.59017 | + | 2.60841i | −0.152394 | + | 0.110721i | ||||
\(556\) | −14.2082 | + | 10.3229i | −0.602562 | + | 0.437787i | ||||
\(557\) | −6.14590 | − | 18.9151i | −0.260410 | − | 0.801460i | −0.992715 | − | 0.120483i | \(-0.961556\pi\) |
0.732305 | − | 0.680976i | \(-0.238444\pi\) | |||||||
\(558\) | 2.90983 | − | 8.95554i | 0.123183 | − | 0.379118i | ||||
\(559\) | 8.56231 | + | 6.22088i | 0.362147 | + | 0.263115i | ||||
\(560\) | 0.236068 | 0.00997569 | ||||||||
\(561\) | −12.8992 | − | 5.56758i | −0.544604 | − | 0.235063i | ||||
\(562\) | 27.8541 | 1.17495 | ||||||||
\(563\) | −1.95492 | − | 1.42033i | −0.0823898 | − | 0.0598597i | 0.545828 | − | 0.837897i | \(-0.316215\pi\) |
−0.628218 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(564\) | −1.45492 | + | 4.47777i | −0.0612630 | + | 0.188548i | ||||
\(565\) | −1.79180 | − | 5.51458i | −0.0753814 | − | 0.232000i | ||||
\(566\) | −4.19098 | + | 3.04493i | −0.176160 | + | 0.127988i | ||||
\(567\) | 0.500000 | − | 0.363271i | 0.0209980 | − | 0.0152560i | ||||
\(568\) | 4.39919 | + | 13.5393i | 0.184586 | + | 0.568097i | ||||
\(569\) | −6.18034 | + | 19.0211i | −0.259093 | + | 0.797407i | 0.733902 | + | 0.679255i | \(0.237697\pi\) |
−0.992996 | + | 0.118152i | \(0.962303\pi\) | |||||||
\(570\) | 0.309017 | + | 0.224514i | 0.0129433 | + | 0.00940386i | ||||
\(571\) | −25.3607 | −1.06131 | −0.530656 | − | 0.847587i | \(-0.678054\pi\) | ||||
−0.530656 | + | 0.847587i | \(0.678054\pi\) | |||||||
\(572\) | −3.13525 | − | 5.29007i | −0.131092 | − | 0.221189i | ||||
\(573\) | 4.70820 | 0.196688 | ||||||||
\(574\) | 2.54508 | + | 1.84911i | 0.106230 | + | 0.0771805i | ||||
\(575\) | 1.50000 | − | 4.61653i | 0.0625543 | − | 0.192522i | ||||
\(576\) | −0.618034 | − | 1.90211i | −0.0257514 | − | 0.0792547i | ||||
\(577\) | 2.30902 | − | 1.67760i | 0.0961256 | − | 0.0698394i | −0.538684 | − | 0.842508i | \(-0.681078\pi\) |
0.634810 | + | 0.772668i | \(0.281078\pi\) | |||||||
\(578\) | −0.763932 | + | 0.555029i | −0.0317754 | + | 0.0230862i | ||||
\(579\) | 2.11803 | + | 6.51864i | 0.0880225 | + | 0.270905i | ||||
\(580\) | −1.05573 | + | 3.24920i | −0.0438367 | + | 0.134916i | ||||
\(581\) | −7.89919 | − | 5.73910i | −0.327713 | − | 0.238098i | ||||
\(582\) | 13.1803 | 0.546343 | ||||||||
\(583\) | 43.5967 | − | 9.78808i | 1.80559 | − | 0.405381i | ||||
\(584\) | 2.61803 | 0.108335 | ||||||||
\(585\) | 1.14590 | + | 0.832544i | 0.0473771 | + | 0.0344214i | ||||
\(586\) | 0.746711 | − | 2.29814i | 0.0308464 | − | 0.0949353i | ||||
\(587\) | 12.6353 | + | 38.8873i | 0.521513 | + | 1.60505i | 0.771110 | + | 0.636702i | \(0.219702\pi\) |
−0.249597 | + | 0.968350i | \(0.580298\pi\) | |||||||
\(588\) | −5.35410 | + | 3.88998i | −0.220799 | + | 0.160420i | ||||
\(589\) | −3.80902 | + | 2.76741i | −0.156948 | + | 0.114029i | ||||
\(590\) | −0.100813 | − | 0.310271i | −0.00415041 | − | 0.0127736i | ||||
\(591\) | −7.10739 | + | 21.8743i | −0.292359 | + | 0.899788i | ||||
\(592\) | −9.39919 | − | 6.82891i | −0.386304 | − | 0.280666i | ||||
\(593\) | −2.05573 | −0.0844186 | −0.0422093 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422093 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(594\) | −10.9549 | + | 12.4495i | −0.449486 | + | 0.510809i | ||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 11.2812 | + | 8.19624i | 0.462094 | + | 0.335731i | ||||
\(597\) | −7.23607 | + | 22.2703i | −0.296153 | + | 0.911464i | ||||
\(598\) | 0.572949 | + | 1.76336i | 0.0234296 | + | 0.0721090i | ||||
\(599\) | 15.5902 | − | 11.3269i | 0.636997 | − | 0.462805i | −0.221820 | − | 0.975088i | \(-0.571200\pi\) |
0.858817 | + | 0.512282i | \(0.171200\pi\) | |||||||
\(600\) | −3.92705 | + | 2.85317i | −0.160321 | + | 0.116480i | ||||
\(601\) | −12.4098 | − | 38.1935i | −0.506208 | − | 1.55795i | −0.798731 | − | 0.601688i | \(-0.794495\pi\) |
0.292524 | − | 0.956258i | \(-0.405505\pi\) | |||||||
\(602\) | −1.09017 | + | 3.35520i | −0.0444320 | + | 0.136748i | ||||
\(603\) | −5.47214 | − | 3.97574i | −0.222843 | − | 0.161905i | ||||
\(604\) | 4.76393 | 0.193842 | ||||||||
\(605\) | −2.88197 | − | 3.05744i | −0.117169 | − | 0.124303i | ||||
\(606\) | −13.1803 | −0.535415 | ||||||||
\(607\) | −31.3713 | − | 22.7926i | −1.27332 | − | 0.925123i | −0.273993 | − | 0.961732i | \(-0.588345\pi\) |
−0.999330 | + | 0.0366086i | \(0.988345\pi\) | |||||||
\(608\) | −0.309017 | + | 0.951057i | −0.0125323 | + | 0.0385704i | ||||
\(609\) | 1.70820 | + | 5.25731i | 0.0692199 | + | 0.213037i | ||||
\(610\) | −1.71885 | + | 1.24882i | −0.0695941 | + | 0.0505631i | ||||
\(611\) | 7.06231 | − | 5.13107i | 0.285710 | − | 0.207581i | ||||
\(612\) | 2.61803 | + | 8.05748i | 0.105828 | + | 0.325704i | ||||
\(613\) | −2.38197 | + | 7.33094i | −0.0962067 | + | 0.296094i | −0.987566 | − | 0.157203i | \(-0.949752\pi\) |
0.891360 | + | 0.453297i | \(0.149752\pi\) | |||||||
\(614\) | −18.6074 | − | 13.5191i | −0.750933 | − | 0.545585i | ||||
\(615\) | 1.94427 | 0.0784006 | ||||||||
\(616\) | 1.35410 | − | 1.53884i | 0.0545583 | − | 0.0620017i | ||||
\(617\) | −11.2705 | −0.453734 | −0.226867 | − | 0.973926i | \(-0.572848\pi\) | ||||
−0.226867 | + | 0.973926i | \(0.572848\pi\) | |||||||
\(618\) | −5.11803 | − | 3.71847i | −0.205878 | − | 0.149579i | ||||
\(619\) | 0.791796 | − | 2.43690i | 0.0318250 | − | 0.0979472i | −0.933882 | − | 0.357581i | \(-0.883602\pi\) |
0.965707 | + | 0.259633i | \(0.0836017\pi\) | |||||||
\(620\) | 0.555728 | + | 1.71036i | 0.0223186 | + | 0.0686895i | ||||
\(621\) | 4.04508 | − | 2.93893i | 0.162324 | − | 0.117935i | ||||
\(622\) | −1.61803 | + | 1.17557i | −0.0648773 | + | 0.0471361i | ||||
\(623\) | 1.60739 | + | 4.94704i | 0.0643988 | + | 0.198199i | ||||
\(624\) | 0.572949 | − | 1.76336i | 0.0229363 | − | 0.0705907i | ||||
\(625\) | −18.4721 | − | 13.4208i | −0.738885 | − | 0.536832i | ||||
\(626\) | −2.05573 | −0.0821634 | ||||||||
\(627\) | 3.23607 | − | 0.726543i | 0.129236 | − | 0.0290153i | ||||
\(628\) | 0.763932 | 0.0304842 | ||||||||
\(629\) | 39.8156 | + | 28.9277i | 1.58755 | + | 1.15342i | ||||
\(630\) | −0.145898 | + | 0.449028i | −0.00581272 | + | 0.0178897i | ||||
\(631\) | 9.29837 | + | 28.6175i | 0.370162 | + | 1.13924i | 0.946685 | + | 0.322161i | \(0.104409\pi\) |
−0.576522 | + | 0.817081i | \(0.695591\pi\) | |||||||
\(632\) | −12.1353 | + | 8.81678i | −0.482715 | + | 0.350713i | ||||
\(633\) | 2.57295 | − | 1.86936i | 0.102266 | − | 0.0743003i | ||||
\(634\) | −5.25329 | − | 16.1680i | −0.208635 | − | 0.642112i | ||||
\(635\) | −0.152476 | + | 0.469272i | −0.00605082 | + | 0.0186225i | ||||
\(636\) | 10.8992 | + | 7.91872i | 0.432181 | + | 0.313998i | ||||
\(637\) | 12.2705 | 0.486175 | ||||||||
\(638\) | 15.1246 | + | 25.5195i | 0.598789 | + | 1.01033i | ||||
\(639\) | −28.4721 | −1.12634 | ||||||||
\(640\) | 0.309017 | + | 0.224514i | 0.0122150 | + | 0.00887469i | ||||
\(641\) | −2.67376 | + | 8.22899i | −0.105607 | + | 0.325026i | −0.989872 | − | 0.141959i | \(-0.954660\pi\) |
0.884265 | + | 0.466985i | \(0.154660\pi\) | |||||||
\(642\) | −3.16312 | − | 9.73508i | −0.124838 | − | 0.384213i | ||||
\(643\) | 28.2705 | − | 20.5397i | 1.11488 | − | 0.810008i | 0.131455 | − | 0.991322i | \(-0.458035\pi\) |
0.983425 | + | 0.181314i | \(0.0580352\pi\) | |||||||
\(644\) | −0.500000 | + | 0.363271i | −0.0197028 | + | 0.0143149i | ||||
\(645\) | 0.673762 | + | 2.07363i | 0.0265294 | + | 0.0816490i | ||||
\(646\) | 1.30902 | − | 4.02874i | 0.0515026 | − | 0.158509i | ||||
\(647\) | −13.8713 | − | 10.0781i | −0.545338 | − | 0.396211i | 0.280726 | − | 0.959788i | \(-0.409425\pi\) |
−0.826064 | + | 0.563577i | \(0.809425\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.60081 | − | 1.12257i | −0.102091 | − | 0.0440647i | ||||
\(650\) | 9.00000 | 0.353009 | ||||||||
\(651\) | 2.35410 | + | 1.71036i | 0.0922645 | + | 0.0670341i | ||||
\(652\) | 1.33688 | − | 4.11450i | 0.0523563 | − | 0.161136i | ||||
\(653\) | 6.70163 | + | 20.6255i | 0.262255 | + | 0.807138i | 0.992313 | + | 0.123753i | \(0.0394929\pi\) |
−0.730058 | + | 0.683385i | \(0.760507\pi\) | |||||||
\(654\) | 1.54508 | − | 1.12257i | 0.0604176 | − | 0.0438960i | ||||
\(655\) | −4.70820 | + | 3.42071i | −0.183965 | + | 0.133658i | ||||
\(656\) | 1.57295 | + | 4.84104i | 0.0614133 | + | 0.189011i | ||||
\(657\) | −1.61803 | + | 4.97980i | −0.0631255 | + | 0.194280i | ||||
\(658\) | 2.35410 | + | 1.71036i | 0.0917724 | + | 0.0666766i | ||||
\(659\) | 15.6525 | 0.609734 | 0.304867 | − | 0.952395i | \(-0.401388\pi\) | ||||
0.304867 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(660\) | 0.118034 | − | 1.26133i | 0.00459447 | − | 0.0490971i | ||||
\(661\) | −17.1459 | −0.666898 | −0.333449 | − | 0.942768i | \(-0.608213\pi\) | ||||
−0.333449 | + | 0.942768i | \(0.608213\pi\) | |||||||
\(662\) | 1.47214 | + | 1.06957i | 0.0572162 | + | 0.0415700i | ||||
\(663\) | −2.42705 | + | 7.46969i | −0.0942588 | + | 0.290099i | ||||
\(664\) | −4.88197 | − | 15.0251i | −0.189457 | − | 0.583089i | ||||
\(665\) | 0.190983 | − | 0.138757i | 0.00740600 | − | 0.00538078i | ||||
\(666\) | 18.7984 | − | 13.6578i | 0.728422 | − | 0.529230i | ||||
\(667\) | −2.76393 | − | 8.50651i | −0.107020 | − | 0.329373i | ||||
\(668\) | 1.19098 | − | 3.66547i | 0.0460805 | − | 0.141821i | ||||
\(669\) | −4.00000 | − | 2.90617i | −0.154649 | − | 0.112359i | ||||
\(670\) | 1.29180 | 0.0499064 | ||||||||
\(671\) | −1.71885 | + | 18.3678i | −0.0663554 | + | 0.709082i | ||||
\(672\) | 0.618034 | 0.0238412 | ||||||||
\(673\) | 1.07295 | + | 0.779543i | 0.0413591 | + | 0.0300492i | 0.608273 | − | 0.793728i | \(-0.291863\pi\) |
−0.566914 | + | 0.823777i | \(0.691863\pi\) | |||||||
\(674\) | −2.16312 | + | 6.65740i | −0.0833202 | + | 0.256433i | ||||
\(675\) | −7.50000 | − | 23.0826i | −0.288675 | − | 0.888451i | ||||
\(676\) | 7.73607 | − | 5.62058i | 0.297541 | − | 0.216176i | ||||
\(677\) | −9.66312 | + | 7.02067i | −0.371384 | + | 0.269826i | −0.757785 | − | 0.652505i | \(-0.773718\pi\) |
0.386401 | + | 0.922331i | \(0.373718\pi\) | |||||||
\(678\) | −4.69098 | − | 14.4374i | −0.180156 | − | 0.554464i | ||||
\(679\) | 2.51722 | − | 7.74721i | 0.0966021 | − | 0.297311i | ||||
\(680\) | −1.30902 | − | 0.951057i | −0.0501985 | − | 0.0364714i | ||||
\(681\) | −23.8541 | −0.914091 | ||||||||
\(682\) | 14.3369 | + | 6.18812i | 0.548988 | + | 0.236955i | ||||
\(683\) | 44.9787 | 1.72106 | 0.860531 | − | 0.509398i | \(-0.170132\pi\) | ||||
0.860531 | + | 0.509398i | \(0.170132\pi\) | |||||||
\(684\) | −1.61803 | − | 1.17557i | −0.0618671 | − | 0.0449491i | ||||
\(685\) | 1.35410 | − | 4.16750i | 0.0517376 | − | 0.159232i | ||||
\(686\) | 2.60081 | + | 8.00448i | 0.0992995 | + | 0.305612i | ||||
\(687\) | −2.07295 | + | 1.50609i | −0.0790879 | + | 0.0574608i | ||||
\(688\) | −4.61803 | + | 3.35520i | −0.176061 | + | 0.127916i | ||||
\(689\) | −7.71885 | − | 23.7562i | −0.294065 | − | 0.905038i | ||||
\(690\) | −0.118034 | + | 0.363271i | −0.00449348 | + | 0.0138295i | ||||
\(691\) | 30.4164 | + | 22.0988i | 1.15709 | + | 0.840678i | 0.989408 | − | 0.145162i | \(-0.0463703\pi\) |
0.167687 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(692\) | 14.8541 | 0.564668 | ||||||||
\(693\) | 2.09017 | + | 3.52671i | 0.0793990 | + | 0.133969i | ||||
\(694\) | 18.6525 | 0.708038 | ||||||||
\(695\) | 5.42705 | + | 3.94298i | 0.205860 | + | 0.149566i | ||||
\(696\) | −2.76393 | + | 8.50651i | −0.104767 | + | 0.322438i | ||||
\(697\) | −6.66312 | − | 20.5070i | −0.252384 | − | 0.776757i | ||||
\(698\) | −25.0623 | + | 18.2088i | −0.948622 | + | 0.689214i | ||||
\(699\) | −10.2812 | + | 7.46969i | −0.388869 | + | 0.282530i | ||||
\(700\) | 0.927051 | + | 2.85317i | 0.0350392 | + | 0.107840i | ||||
\(701\) | −2.24671 | + | 6.91467i | −0.0848571 | + | 0.261163i | −0.984478 | − | 0.175509i | \(-0.943843\pi\) |
0.899621 | + | 0.436672i | \(0.143843\pi\) | |||||||
\(702\) | 7.50000 | + | 5.44907i | 0.283069 | + | 0.205662i | ||||
\(703\) | −11.6180 | −0.438182 | ||||||||
\(704\) | 3.23607 | − | 0.726543i | 0.121964 | − | 0.0273826i | ||||
\(705\) | 1.79837 | 0.0677307 | ||||||||
\(706\) | 21.0344 | + | 15.2824i | 0.791642 | + | 0.575161i | ||||
\(707\) | −2.51722 | + | 7.74721i | −0.0946698 | + | 0.291364i | ||||
\(708\) | −0.263932 | − | 0.812299i | −0.00991917 | − | 0.0305281i | ||||
\(709\) | 17.4615 | − | 12.6865i | 0.655780 | − | 0.476452i | −0.209455 | − | 0.977818i | \(-0.567169\pi\) |
0.865235 | + | 0.501366i | \(0.167169\pi\) | |||||||
\(710\) | 4.39919 | − | 3.19620i | 0.165099 | − | 0.119951i | ||||
\(711\) | −9.27051 | − | 28.5317i | −0.347671 | − | 1.07002i | ||||
\(712\) | −2.60081 | + | 8.00448i | −0.0974696 | + | 0.299981i | ||||
\(713\) | −3.80902 | − | 2.76741i | −0.142649 | − | 0.103640i | ||||
\(714\) | −2.61803 | −0.0979775 | ||||||||
\(715\) | −1.55166 | + | 1.76336i | −0.0580289 | + | 0.0659458i | ||||
\(716\) | −1.70820 | −0.0638386 | ||||||||
\(717\) | −8.35410 | − | 6.06961i | −0.311990 | − | 0.226674i | ||||
\(718\) | −3.55573 | + | 10.9434i | −0.132699 | + | 0.408404i | ||||
\(719\) | −3.51722 | − | 10.8249i | −0.131170 | − | 0.403700i | 0.863804 | − | 0.503827i | \(-0.168075\pi\) |
−0.994975 | + | 0.100127i | \(0.968075\pi\) | |||||||
\(720\) | −0.618034 | + | 0.449028i | −0.0230328 | + | 0.0167343i | ||||
\(721\) | −3.16312 | + | 2.29814i | −0.117801 | + | 0.0855872i | ||||
\(722\) | 0.309017 | + | 0.951057i | 0.0115004 | + | 0.0353947i | ||||
\(723\) | −1.57295 | + | 4.84104i | −0.0584986 | + | 0.180040i | ||||
\(724\) | −20.1353 | − | 14.6291i | −0.748321 | − | 0.543687i | ||||
\(725\) | −43.4164 | −1.61244 | ||||||||
\(726\) | −7.54508 | − | 8.00448i | −0.280024 | − | 0.297074i | ||||
\(727\) | 44.7082 | 1.65814 | 0.829068 | − | 0.559148i | \(-0.188872\pi\) | ||||
0.829068 | + | 0.559148i | \(0.188872\pi\) | |||||||
\(728\) | −0.927051 | − | 0.673542i | −0.0343588 | − | 0.0249631i | ||||
\(729\) | 4.01722 | − | 12.3637i | 0.148786 | − | 0.457916i | ||||
\(730\) | −0.309017 | − | 0.951057i | −0.0114372 | − | 0.0352002i | ||||
\(731\) | 19.5623 | − | 14.2128i | 0.723538 | − | 0.525681i | ||||
\(732\) | −4.50000 | + | 3.26944i | −0.166325 | + | 0.120842i | ||||
\(733\) | 3.37132 | + | 10.3759i | 0.124523 | + | 0.383241i | 0.993814 | − | 0.111059i | \(-0.0354243\pi\) |
−0.869291 | + | 0.494300i | \(0.835424\pi\) | |||||||
\(734\) | −7.75329 | + | 23.8622i | −0.286179 | + | 0.880769i | ||||
\(735\) | 2.04508 | + | 1.48584i | 0.0754341 | + | 0.0548061i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 7.40983 | − | 8.42075i | 0.272945 | − | 0.310182i | ||||
\(738\) | −10.1803 | −0.374743 | ||||||||
\(739\) | 14.7984 | + | 10.7516i | 0.544367 | + | 0.395506i | 0.825704 | − | 0.564103i | \(-0.190778\pi\) |
−0.281337 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(740\) | −1.37132 | + | 4.22050i | −0.0504108 | + | 0.155149i | ||||
\(741\) | −0.572949 | − | 1.76336i | −0.0210478 | − | 0.0647785i | ||||
\(742\) | 6.73607 | − | 4.89404i | 0.247289 | − | 0.179666i | ||||
\(743\) | 13.4721 | − | 9.78808i | 0.494245 | − | 0.359090i | −0.312570 | − | 0.949895i | \(-0.601190\pi\) |
0.806814 | + | 0.590805i | \(0.201190\pi\) | |||||||
\(744\) | 1.45492 | + | 4.47777i | 0.0533398 | + | 0.164163i | ||||
\(745\) | 1.64590 | − | 5.06555i | 0.0603010 | − | 0.185588i | ||||
\(746\) | −13.5623 | − | 9.85359i | −0.496551 | − | 0.360766i | ||||
\(747\) | 31.5967 | 1.15606 | ||||||||
\(748\) | −13.7082 | + | 3.07768i | −0.501222 | + | 0.112531i | ||||
\(749\) | −6.32624 | −0.231156 | ||||||||
\(750\) | 3.04508 | + | 2.21238i | 0.111191 | + | 0.0807848i | ||||
\(751\) | 0.781153 | − | 2.40414i | 0.0285047 | − | 0.0877284i | −0.935792 | − | 0.352552i | \(-0.885314\pi\) |
0.964297 | + | 0.264824i | \(0.0853138\pi\) | |||||||
\(752\) | 1.45492 | + | 4.47777i | 0.0530553 | + | 0.163287i | ||||
\(753\) | −9.23607 | + | 6.71040i | −0.336581 | + | 0.244540i | ||||
\(754\) | 13.4164 | − | 9.74759i | 0.488597 | − | 0.354986i | ||||
\(755\) | −0.562306 | − | 1.73060i | −0.0204644 | − | 0.0629830i | ||||
\(756\) | −0.954915 | + | 2.93893i | −0.0347299 | + | 0.106888i | ||||
\(757\) | 8.48936 | + | 6.16788i | 0.308551 | + | 0.224175i | 0.731274 | − | 0.682083i | \(-0.238926\pi\) |
−0.422724 | + | 0.906259i | \(0.638926\pi\) | |||||||
\(758\) | −30.4508 | −1.10602 | ||||||||
\(759\) | 1.69098 | + | 2.85317i | 0.0613788 | + | 0.103563i | ||||
\(760\) | 0.381966 | 0.0138554 | ||||||||
\(761\) | 12.2254 | + | 8.88229i | 0.443171 | + | 0.321983i | 0.786894 | − | 0.617088i | \(-0.211688\pi\) |
−0.343722 | + | 0.939071i | \(0.611688\pi\) | |||||||
\(762\) | −0.399187 | + | 1.22857i | −0.0144610 | + | 0.0445064i | ||||
\(763\) | −0.364745 | − | 1.12257i | −0.0132047 | − | 0.0406398i | ||||
\(764\) | 3.80902 | − | 2.76741i | 0.137805 | − | 0.100121i | ||||
\(765\) | 2.61803 | − | 1.90211i | 0.0946552 | − | 0.0687710i | ||||
\(766\) | −0.409830 | − | 1.26133i | −0.0148078 | − | 0.0455736i | ||||
\(767\) | −0.489357 | + | 1.50609i | −0.0176697 | + | 0.0543816i | ||||
\(768\) | 0.809017 | + | 0.587785i | 0.0291929 | + | 0.0212099i | ||||
\(769\) | 16.7082 | 0.602513 | 0.301257 | − | 0.953543i | \(-0.402594\pi\) | ||||
0.301257 | + | 0.953543i | \(0.402594\pi\) | |||||||
\(770\) | −0.718847 | − | 0.310271i | −0.0259054 | − | 0.0111814i | ||||
\(771\) | 16.2705 | 0.585968 | ||||||||
\(772\) | 5.54508 | + | 4.02874i | 0.199572 | + | 0.144998i | ||||
\(773\) | −11.9164 | + | 36.6749i | −0.428603 | + | 1.31911i | 0.470898 | + | 0.882188i | \(0.343930\pi\) |
−0.899501 | + | 0.436918i | \(0.856070\pi\) | |||||||
\(774\) | −3.52786 | − | 10.8576i | −0.126806 | − | 0.390270i | ||||
\(775\) | −18.4894 | + | 13.4333i | −0.664157 | + | 0.482539i | ||||
\(776\) | 10.6631 | − | 7.74721i | 0.382784 | − | 0.278109i | ||||
\(777\) | 2.21885 | + | 6.82891i | 0.0796007 | + | 0.244986i | ||||
\(778\) | −1.18034 | + | 3.63271i | −0.0423172 | + | 0.130239i | ||||
\(779\) | 4.11803 | + | 2.99193i | 0.147544 | + | 0.107197i | ||||
\(780\) | −0.708204 | −0.0253578 | ||||||||
\(781\) | 4.39919 | − | 47.0103i | 0.157415 | − | 1.68216i | ||||
\(782\) | 4.23607 | 0.151481 | ||||||||
\(783\) | −36.1803 | − | 26.2866i | −1.29298 | − | 0.939405i | ||||
\(784\) | −2.04508 | + | 6.29412i | −0.0730387 | + | 0.224790i | ||||
\(785\) | −0.0901699 | − | 0.277515i | −0.00321830 | − | 0.00990492i | ||||
\(786\) | −12.3262 | + | 8.95554i | −0.439662 | + | 0.319433i | ||||
\(787\) | 40.0344 | − | 29.0867i | 1.42707 | − | 1.03683i | 0.436521 | − | 0.899694i | \(-0.356210\pi\) |
0.990552 | − | 0.137136i | \(-0.0437897\pi\) | |||||||
\(788\) | 7.10739 | + | 21.8743i | 0.253190 | + | 0.779240i | ||||
\(789\) | 4.51722 | − | 13.9026i | 0.160817 | − | 0.494945i | ||||
\(790\) | 4.63525 | + | 3.36771i | 0.164915 | + | 0.119818i | ||||
\(791\) | −9.38197 | −0.333584 | ||||||||
\(792\) | −0.618034 | + | 6.60440i | −0.0219609 | + | 0.234677i | ||||
\(793\) | 10.3131 | 0.366228 | ||||||||
\(794\) | 26.8435 | + | 19.5029i | 0.952639 | + | 0.692133i | ||||
\(795\) | 1.59017 | − | 4.89404i | 0.0563975 | − | 0.173574i | ||||
\(796\) | 7.23607 | + | 22.2703i | 0.256476 | + | 0.789351i | ||||
\(797\) | −4.50000 | + | 3.26944i | −0.159398 | + | 0.115810i | −0.664625 | − | 0.747177i | \(-0.731409\pi\) |
0.505227 | + | 0.862986i | \(0.331409\pi\) | |||||||
\(798\) | 0.500000 | − | 0.363271i | 0.0176998 | − | 0.0128597i | ||||
\(799\) | −6.16312 | − | 18.9681i | −0.218035 | − | 0.671044i | ||||
\(800\) | −1.50000 | + | 4.61653i | −0.0530330 | + | 0.163219i | ||||
\(801\) | −13.6180 | − | 9.89408i | −0.481170 | − | 0.349590i | ||||
\(802\) | −32.5967 | −1.15103 | ||||||||
\(803\) | −7.97214 | − | 3.44095i | −0.281331 | − | 0.121429i | ||||
\(804\) | 3.38197 | 0.119273 | ||||||||
\(805\) | 0.190983 | + | 0.138757i | 0.00673127 | + | 0.00489055i | ||||
\(806\) | 2.69756 | − | 8.30224i | 0.0950175 | − | 0.292434i | ||||
\(807\) | −3.25329 | − | 10.0126i | −0.114521 | − | 0.352460i | ||||
\(808\) | −10.6631 | + | 7.74721i | −0.375127 | + | 0.272546i | ||||
\(809\) | −14.4721 | + | 10.5146i | −0.508813 | + | 0.369674i | −0.812373 | − | 0.583138i | \(-0.801825\pi\) |
0.303560 | + | 0.952812i | \(0.401825\pi\) | |||||||
\(810\) | −0.118034 | − | 0.363271i | −0.00414729 | − | 0.0127641i | ||||
\(811\) | 5.41641 | − | 16.6700i | 0.190196 | − | 0.585362i | −0.809803 | − | 0.586701i | \(-0.800426\pi\) |
0.999999 | + | 0.00133898i | \(0.000426209\pi\) | |||||||
\(812\) | 4.47214 | + | 3.24920i | 0.156941 | + | 0.114024i | ||||
\(813\) | −8.18034 | −0.286897 | ||||||||
\(814\) | 19.6459 | + | 33.1482i | 0.688588 | + | 1.16184i | ||||
\(815\) | −1.65248 | −0.0578837 | ||||||||
\(816\) | −3.42705 | − | 2.48990i | −0.119971 | − | 0.0871639i | ||||
\(817\) | −1.76393 | + | 5.42882i | −0.0617122 | + | 0.189931i | ||||
\(818\) | 5.16312 | + | 15.8904i | 0.180524 | + | 0.555596i | ||||
\(819\) | 1.85410 | − | 1.34708i | 0.0647876 | − | 0.0470709i | ||||
\(820\) | 1.57295 | − | 1.14281i | 0.0549298 | − | 0.0399088i | ||||
\(821\) | −2.20820 | − | 6.79615i | −0.0770668 | − | 0.237187i | 0.905100 | − | 0.425199i | \(-0.139796\pi\) |
−0.982167 | + | 0.188011i | \(0.939796\pi\) | |||||||
\(822\) | 3.54508 | − | 10.9106i | 0.123649 | − | 0.380553i | ||||
\(823\) | 6.23607 | + | 4.53077i | 0.217376 | + | 0.157933i | 0.691145 | − | 0.722717i | \(-0.257107\pi\) |
−0.473769 | + | 0.880649i | \(0.657107\pi\) | |||||||
\(824\) | −6.32624 | −0.220385 | ||||||||
\(825\) | 15.7082 | − | 3.52671i | 0.546889 | − | 0.122784i | ||||
\(826\) | −0.527864 | −0.0183667 | ||||||||
\(827\) | −15.6803 | − | 11.3924i | −0.545259 | − | 0.396154i | 0.280776 | − | 0.959773i | \(-0.409408\pi\) |
−0.826034 | + | 0.563620i | \(0.809408\pi\) | |||||||
\(828\) | 0.618034 | − | 1.90211i | 0.0214782 | − | 0.0661030i | ||||
\(829\) | −5.12461 | − | 15.7719i | −0.177985 | − | 0.547782i | 0.821772 | − | 0.569816i | \(-0.192986\pi\) |
−0.999757 | + | 0.0220344i | \(0.992986\pi\) | |||||||
\(830\) | −4.88197 | + | 3.54696i | −0.169456 | + | 0.123117i | ||||
\(831\) | 19.2984 | − | 14.0211i | 0.669453 | − | 0.486386i | ||||
\(832\) | −0.572949 | − | 1.76336i | −0.0198634 | − | 0.0611334i | ||||
\(833\) | 8.66312 | − | 26.6623i | 0.300159 | − | 0.923795i | ||||
\(834\) | 14.2082 | + | 10.3229i | 0.491990 | + | 0.357452i | ||||
\(835\) | −1.47214 | −0.0509454 | ||||||||
\(836\) | 2.19098 | − | 2.48990i | 0.0757767 | − | 0.0861149i | ||||
\(837\) | −23.5410 | −0.813697 | ||||||||
\(838\) | −27.8885 | − | 20.2622i | −0.963394 | − | 0.699947i | ||||
\(839\) | −0.263932 | + | 0.812299i | −0.00911195 | + | 0.0280437i | −0.955509 | − | 0.294962i | \(-0.904693\pi\) |
0.946397 | + | 0.323005i | \(0.104693\pi\) | |||||||
\(840\) | −0.0729490 | − | 0.224514i | −0.00251698 | − | 0.00774647i | ||||
\(841\) | −41.2599 | + | 29.9770i | −1.42275 | + | 1.03369i | ||||
\(842\) | 8.80902 | − | 6.40013i | 0.303579 | − | 0.220563i | ||||
\(843\) | −8.60739 | − | 26.4908i | −0.296454 | − | 0.912392i | ||||
\(844\) | 0.982779 | − | 3.02468i | 0.0338287 | − | 0.104114i | ||||
\(845\) | −2.95492 | − | 2.14687i | −0.101652 | − | 0.0738546i | ||||
\(846\) | −9.41641 | −0.323743 | ||||||||
\(847\) | −6.14590 | + | 2.90617i | −0.211176 | + | 0.0998572i | ||||
\(848\) | 13.4721 | 0.462635 | ||||||||
\(849\) | 4.19098 | + | 3.04493i | 0.143834 | + | 0.104502i | ||||
\(850\) | 6.35410 | − | 19.5559i | 0.217944 | − | 0.670762i | ||||
\(851\) | −3.59017 | − | 11.0494i | −0.123069 | − | 0.378769i | ||||
\(852\) | 11.5172 | − | 8.36775i | 0.394573 | − | 0.286674i | ||||
\(853\) | −24.1525 | + | 17.5478i | −0.826965 | + | 0.600825i | −0.918699 | − | 0.394958i | \(-0.870759\pi\) |
0.0917340 | + | 0.995784i | \(0.470759\pi\) | |||||||
\(854\) | 1.06231 | + | 3.26944i | 0.0363514 | + | 0.111878i | ||||
\(855\) | −0.236068 | + | 0.726543i | −0.00807335 | + | 0.0248472i | ||||
\(856\) | −8.28115 | − | 6.01661i | −0.283044 | − | 0.205643i | ||||
\(857\) | 27.1459 | 0.927286 | 0.463643 | − | 0.886022i | \(-0.346542\pi\) | ||||
0.463643 | + | 0.886022i | \(0.346542\pi\) | |||||||
\(858\) | −4.06231 | + | 4.61653i | −0.138685 | + | 0.157606i | ||||
\(859\) | 46.3050 | 1.57990 | 0.789952 | − | 0.613168i | \(-0.210105\pi\) | ||||
0.789952 | + | 0.613168i | \(0.210105\pi\) | |||||||
\(860\) | 1.76393 | + | 1.28157i | 0.0601496 | + | 0.0437012i | ||||
\(861\) | 0.972136 | − | 2.99193i | 0.0331303 | − | 0.101965i | ||||
\(862\) | 6.69756 | + | 20.6130i | 0.228120 | + | 0.702081i | ||||
\(863\) | 2.61803 | − | 1.90211i | 0.0891189 | − | 0.0647487i | −0.542334 | − | 0.840163i | \(-0.682459\pi\) |
0.631452 | + | 0.775415i | \(0.282459\pi\) | |||||||
\(864\) | −4.04508 | + | 2.93893i | −0.137617 | + | 0.0999843i | ||||
\(865\) | −1.75329 | − | 5.39607i | −0.0596136 | − | 0.183472i | ||||
\(866\) | 3.67376 | − | 11.3067i | 0.124840 | − | 0.384217i | ||||
\(867\) | 0.763932 | + | 0.555029i | 0.0259445 | + | 0.0188498i | ||||
\(868\) | 2.90983 | 0.0987661 | ||||||||
\(869\) | 48.5410 | − | 10.8981i | 1.64664 | − | 0.369694i | ||||
\(870\) | 3.41641 | 0.115827 | ||||||||
\(871\) | −5.07295 | − | 3.68571i | −0.171890 | − | 0.124886i | ||||
\(872\) | 0.590170 | − | 1.81636i | 0.0199857 | − | 0.0615096i | ||||
\(873\) | 8.14590 | + | 25.0705i | 0.275697 | + | 0.848508i | ||||
\(874\) | −0.809017 | + | 0.587785i | −0.0273654 | + | 0.0198821i | ||||
\(875\) | 1.88197 | − | 1.36733i | 0.0636221 | − | 0.0462241i | ||||
\(876\) | −0.809017 | − | 2.48990i | −0.0273342 | − | 0.0841259i | ||||
\(877\) | 8.26393 | − | 25.4338i | 0.279053 | − | 0.858837i | −0.709065 | − | 0.705143i | \(-0.750883\pi\) |
0.988118 | − | 0.153694i | \(-0.0491171\pi\) | |||||||
\(878\) | −3.35410 | − | 2.43690i | −0.113195 | − | 0.0822413i | ||||
\(879\) | −2.41641 | −0.0815034 | ||||||||
\(880\) | −0.645898 | − | 1.08981i | −0.0217732 | − | 0.0367376i | ||||
\(881\) | −4.58359 | −0.154425 | −0.0772126 | − | 0.997015i | \(-0.524602\pi\) | ||||
−0.0772126 | + | 0.997015i | \(0.524602\pi\) | |||||||
\(882\) | −10.7082 | − | 7.77997i | −0.360564 | − | 0.261965i | ||||
\(883\) | −4.49342 | + | 13.8293i | −0.151216 | + | 0.465394i | −0.997758 | − | 0.0669277i | \(-0.978680\pi\) |
0.846542 | + | 0.532322i | \(0.178680\pi\) | |||||||
\(884\) | 2.42705 | + | 7.46969i | 0.0816306 | + | 0.251233i | ||||
\(885\) | −0.263932 | + | 0.191758i | −0.00887198 | + | 0.00644587i | ||||
\(886\) | −11.1631 | + | 8.11048i | −0.375032 | + | 0.272477i | ||||
\(887\) | −10.9828 | − | 33.8015i | −0.368766 | − | 1.13494i | −0.947589 | − | 0.319491i | \(-0.896488\pi\) |
0.578824 | − | 0.815453i | \(-0.303512\pi\) | |||||||
\(888\) | −3.59017 | + | 11.0494i | −0.120478 | + | 0.370794i | ||||
\(889\) | 0.645898 | + | 0.469272i | 0.0216627 | + | 0.0157389i | ||||
\(890\) | 3.21478 | 0.107760 | ||||||||
\(891\) | −3.04508 | − | 1.31433i | −0.102014 | − | 0.0440316i | ||||
\(892\) | −4.94427 | −0.165546 | ||||||||
\(893\) | 3.80902 | + | 2.76741i | 0.127464 | + | 0.0926079i | ||||
\(894\) | 4.30902 | − | 13.2618i | 0.144115 | − | 0.443541i | ||||
\(895\) | 0.201626 | + | 0.620541i | 0.00673962 | + | 0.0207424i | ||||
\(896\) | 0.500000 | − | 0.363271i | 0.0167038 | − | 0.0121360i | ||||
\(897\) | 1.50000 | − | 1.08981i | 0.0500835 | − | 0.0363878i | ||||
\(898\) | −7.07295 | − | 21.7683i | −0.236027 | − | 0.726418i | ||||
\(899\) | −13.0132 | + | 40.0504i | −0.434013 | + | 1.33575i | ||||
\(900\) | −7.85410 | − | 5.70634i | −0.261803 | − | 0.190211i | ||||
\(901\) | −57.0689 | −1.90124 | ||||||||
\(902\) | 1.57295 | − | 16.8087i | 0.0523735 | − | 0.559670i | ||||
\(903\) | 3.52786 | 0.117400 | ||||||||
\(904\) | −12.2812 | − | 8.92278i | −0.408465 | − | 0.296767i | ||||
\(905\) | −2.93769 | + | 9.04129i | −0.0976523 | + | 0.300543i | ||||
\(906\) | −1.47214 | − | 4.53077i | −0.0489084 | − | 0.150525i | ||||
\(907\) | 0.826238 | − | 0.600297i | 0.0274348 | − | 0.0199325i | −0.573983 | − | 0.818867i | \(-0.694603\pi\) |
0.601418 | + | 0.798934i | \(0.294603\pi\) | |||||||
\(908\) | −19.2984 | + | 14.0211i | −0.640439 | + | 0.465306i | ||||
\(909\) | −8.14590 | − | 25.0705i | −0.270182 | − | 0.831536i | ||||
\(910\) | −0.135255 | + | 0.416272i | −0.00448366 | + | 0.0137993i | ||||
\(911\) | −25.8885 | − | 18.8091i | −0.857726 | − | 0.623174i | 0.0695396 | − | 0.997579i | \(-0.477847\pi\) |
−0.927265 | + | 0.374405i | \(0.877847\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −4.88197 | + | 52.1694i | −0.161569 | + | 1.72655i | ||||
\(914\) | −15.9443 | −0.527390 | ||||||||
\(915\) | 1.71885 | + | 1.24882i | 0.0568233 | + | 0.0412846i | ||||
\(916\) | −0.791796 | + | 2.43690i | −0.0261617 | + | 0.0805174i | ||||
\(917\) | 2.90983 | + | 8.95554i | 0.0960911 | + | 0.295738i | ||||
\(918\) | 17.1353 | − | 12.4495i | 0.565548 | − | 0.410894i | ||||
\(919\) | −41.4058 | + | 30.0830i | −1.36585 | + | 0.992348i | −0.367802 | + | 0.929904i | \(0.619889\pi\) |
−0.998048 | + | 0.0624440i | \(0.980111\pi\) | |||||||
\(920\) | 0.118034 | + | 0.363271i | 0.00389147 | + | 0.0119767i | ||||
\(921\) | −7.10739 | + | 21.8743i | −0.234196 | + | 0.720783i | ||||
\(922\) | 12.7533 | + | 9.26581i | 0.420007 | + | 0.305153i | ||||
\(923\) | −26.3951 | −0.868806 | ||||||||
\(924\) | −1.88197 | − | 0.812299i | −0.0619121 | − | 0.0267227i | ||||
\(925\) | −56.3951 | −1.85426 | ||||||||
\(926\) | −18.7254 | − | 13.6048i | −0.615356 | − | 0.447082i | ||||
\(927\) | 3.90983 | − | 12.0332i | 0.128416 | − | 0.395223i | ||||
\(928\) | 2.76393 | + | 8.50651i | 0.0907305 | + | 0.279240i | ||||
\(929\) | 24.8992 | − | 18.0903i | 0.816916 | − | 0.593524i | −0.0989116 | − | 0.995096i | \(-0.531536\pi\) |
0.915827 | + | 0.401572i | \(0.131536\pi\) | |||||||
\(930\) | 1.45492 | − | 1.05706i | 0.0477085 | − | 0.0346623i | ||||
\(931\) | 2.04508 | + | 6.29412i | 0.0670250 | + | 0.206282i | ||||
\(932\) | −3.92705 | + | 12.0862i | −0.128635 | + | 0.395897i | ||||
\(933\) | 1.61803 | + | 1.17557i | 0.0529721 | + | 0.0384865i | ||||
\(934\) | 13.3262 | 0.436048 | ||||||||
\(935\) | 2.73607 | + | 4.61653i | 0.0894790 | + | 0.150977i | ||||
\(936\) | 3.70820 | 0.121206 | ||||||||
\(937\) | −32.3262 | − | 23.4864i | −1.05605 | − | 0.767267i | −0.0826982 | − | 0.996575i | \(-0.526354\pi\) |
−0.973354 | + | 0.229308i | \(0.926354\pi\) | |||||||
\(938\) | 0.645898 | − | 1.98787i | 0.0210893 | − | 0.0649062i | ||||
\(939\) | 0.635255 | + | 1.95511i | 0.0207308 | + | 0.0638027i | ||||
\(940\) | 1.45492 | − | 1.05706i | 0.0474541 | − | 0.0344774i | ||||
\(941\) | 44.7877 | − | 32.5402i | 1.46004 | − | 1.06078i | 0.476685 | − | 0.879074i | \(-0.341838\pi\) |
0.983353 | − | 0.181706i | \(-0.0581619\pi\) | |||||||
\(942\) | −0.236068 | − | 0.726543i | −0.00769151 | − | 0.0236720i | ||||
\(943\) | −1.57295 | + | 4.84104i | −0.0512223 | + | 0.157646i | ||||
\(944\) | −0.690983 | − | 0.502029i | −0.0224896 | − | 0.0163396i | ||||
\(945\) | 1.18034 | 0.0383965 | ||||||||
\(946\) | 18.4721 | − | 4.14725i | 0.600581 | − | 0.134839i | ||||
\(947\) | −14.8885 | −0.483813 | −0.241906 | − | 0.970300i | \(-0.577773\pi\) | ||||
−0.241906 | + | 0.970300i | \(0.577773\pi\) | |||||||
\(948\) | 12.1353 | + | 8.81678i | 0.394135 | + | 0.286356i | ||||
\(949\) | −1.50000 | + | 4.61653i | −0.0486921 | + | 0.149859i | ||||
\(950\) | 1.50000 | + | 4.61653i | 0.0486664 | + | 0.149780i | ||||
\(951\) | −13.7533 | + | 9.99235i | −0.445981 | + | 0.324024i | ||||
\(952\) | −2.11803 | + | 1.53884i | −0.0686459 | + | 0.0498741i | ||||
\(953\) | −6.85410 | − | 21.0948i | −0.222026 | − | 0.683326i | −0.998580 | − | 0.0532752i | \(-0.983034\pi\) |
0.776554 | − | 0.630051i | \(-0.216966\pi\) | |||||||
\(954\) | −8.32624 | + | 25.6255i | −0.269572 | + | 0.829657i | ||||
\(955\) | −1.45492 | − | 1.05706i | −0.0470799 | − | 0.0342056i | ||||
\(956\) | −10.3262 | −0.333974 | ||||||||
\(957\) | 19.5967 | − | 22.2703i | 0.633473 | − | 0.719897i | ||||
\(958\) | −8.41641 | −0.271922 | ||||||||
\(959\) | −5.73607 | − | 4.16750i | −0.185227 | − | 0.134576i | ||||
\(960\) | 0.118034 | − | 0.363271i | 0.00380953 | − | 0.0117245i | ||||
\(961\) | −2.72949 | − | 8.40051i | −0.0880481 | − | 0.270984i | ||||
\(962\) | 17.4271 | − | 12.6615i | 0.561871 | − | 0.408223i | ||||
\(963\) | 16.5623 | − | 12.0332i | 0.533713 | − | 0.387765i | ||||
\(964\) | 1.57295 | + | 4.84104i | 0.0506613 | + | 0.155919i | ||||
\(965\) | 0.809017 | − | 2.48990i | 0.0260432 | − | 0.0801527i | ||||
\(966\) | 0.500000 | + | 0.363271i | 0.0160872 | + | 0.0116881i | ||||
\(967\) | −30.7426 | −0.988617 | −0.494308 | − | 0.869287i | \(-0.664579\pi\) | ||||
−0.494308 | + | 0.869287i | \(0.664579\pi\) | |||||||
\(968\) | −10.8090 | − | 2.04087i | −0.347415 | − | 0.0655961i | ||||
\(969\) | −4.23607 | −0.136082 | ||||||||
\(970\) | −4.07295 | − | 2.95917i | −0.130775 | − | 0.0950132i | ||||
\(971\) | −17.7361 | + | 54.5860i | −0.569178 | + | 1.75175i | 0.0860229 | + | 0.996293i | \(0.472584\pi\) |
−0.655200 | + | 0.755455i | \(0.727416\pi\) | |||||||
\(972\) | −4.94427 | − | 15.2169i | −0.158588 | − | 0.488082i | ||||
\(973\) | 8.78115 | − | 6.37988i | 0.281511 | − | 0.204530i | ||||
\(974\) | −19.6631 | + | 14.2861i | −0.630047 | + | 0.457756i | ||||
\(975\) | −2.78115 | − | 8.55951i | −0.0890682 | − | 0.274124i | ||||
\(976\) | −1.71885 | + | 5.29007i | −0.0550190 | + | 0.169331i | ||||
\(977\) | −0.618034 | − | 0.449028i | −0.0197727 | − | 0.0143657i | 0.577855 | − | 0.816139i | \(-0.303890\pi\) |
−0.597628 | + | 0.801774i | \(0.703890\pi\) | |||||||
\(978\) | −4.32624 | −0.138338 | ||||||||
\(979\) | 18.4402 | − | 20.9560i | 0.589352 | − | 0.669757i | ||||
\(980\) | 2.52786 | 0.0807497 | ||||||||
\(981\) | 3.09017 | + | 2.24514i | 0.0986615 | + | 0.0716818i | ||||
\(982\) | −4.28115 | + | 13.1760i | −0.136617 | + | 0.420464i | ||||
\(983\) | 7.94427 | + | 24.4500i | 0.253383 | + | 0.779832i | 0.994144 | + | 0.108064i | \(0.0344651\pi\) |
−0.740761 | + | 0.671769i | \(0.765535\pi\) | |||||||
\(984\) | 4.11803 | − | 2.99193i | 0.131278 | − | 0.0953791i | ||||
\(985\) | 7.10739 | − | 5.16382i | 0.226460 | − | 0.164533i | ||||
\(986\) | −11.7082 | − | 36.0341i | −0.372865 | − | 1.14756i | ||||
\(987\) | 0.899187 | − | 2.76741i | 0.0286214 | − | 0.0880877i | ||||
\(988\) | −1.50000 | − | 1.08981i | −0.0477214 | − | 0.0346716i | ||||
\(989\) | −5.70820 | −0.181510 | ||||||||
\(990\) | 2.47214 | − | 0.555029i | 0.0785696 | − | 0.0176400i | ||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | 3.80902 | + | 2.76741i | 0.120936 | + | 0.0878654i | ||||
\(993\) | 0.562306 | − | 1.73060i | 0.0178442 | − | 0.0549189i | ||||
\(994\) | −2.71885 | − | 8.36775i | −0.0862366 | − | 0.265409i | ||||
\(995\) | 7.23607 | − | 5.25731i | 0.229399 | − | 0.166668i | ||||
\(996\) | −12.7812 | + | 9.28605i | −0.404986 | + | 0.294240i | ||||
\(997\) | −1.63525 | − | 5.03280i | −0.0517890 | − | 0.159390i | 0.921817 | − | 0.387625i | \(-0.126705\pi\) |
−0.973606 | + | 0.228235i | \(0.926705\pi\) | |||||||
\(998\) | 0.892609 | − | 2.74717i | 0.0282550 | − | 0.0869601i | ||||
\(999\) | −46.9959 | − | 34.1445i | −1.48689 | − | 1.08029i |
(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 | 418.2.f.c.191.1 | ✓ | 4 | |
11.3 | even | 5 | inner | 418.2.f.c.267.1 | yes | 4 | |
11.5 | even | 5 | 4598.2.a.bd.1.2 | 2 | |||
11.6 | odd | 10 | 4598.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.c.191.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
418.2.f.c.267.1 | yes | 4 | 11.3 | even | 5 | inner | |
4598.2.a.u.1.2 | 2 | 11.6 | odd | 10 | |||
4598.2.a.bd.1.2 | 2 | 11.5 | even | 5 |