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 | 115.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.115 |
Dual form | 418.2.f.d.229.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | 1.61803 | + | 1.17557i | 0.934172 | + | 0.678716i | 0.947011 | − | 0.321202i | \(-0.104087\pi\) |
−0.0128385 | + | 0.999918i | \(0.504087\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0.500000 | − | 1.53884i | 0.223607 | − | 0.688191i | −0.774823 | − | 0.632178i | \(-0.782161\pi\) |
0.998430 | − | 0.0560130i | \(-0.0178388\pi\) | |||||||
\(6\) | −0.618034 | + | 1.90211i | −0.252311 | + | 0.776534i | ||||
\(7\) | 3.92705 | − | 2.85317i | 1.48429 | − | 1.07840i | 0.508142 | − | 0.861274i | \(-0.330333\pi\) |
0.976144 | − | 0.217123i | \(-0.0696673\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 1.61803 | 0.511667 | ||||||||
\(11\) | −0.809017 | + | 3.21644i | −0.243928 | + | 0.969793i | ||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0.763932 | + | 2.35114i | 0.211877 | + | 0.652089i | 0.999361 | + | 0.0357541i | \(0.0113833\pi\) |
−0.787484 | + | 0.616335i | \(0.788617\pi\) | |||||||
\(14\) | 3.92705 | + | 2.85317i | 1.04955 | + | 0.762542i | ||||
\(15\) | 2.61803 | − | 1.90211i | 0.675973 | − | 0.491123i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 1.04508 | − | 3.21644i | 0.253470 | − | 0.780101i | −0.740657 | − | 0.671883i | \(-0.765486\pi\) |
0.994127 | − | 0.108218i | \(-0.0345144\pi\) | |||||||
\(18\) | −0.809017 | + | 0.587785i | −0.190687 | + | 0.138542i | ||||
\(19\) | −0.809017 | − | 0.587785i | −0.185601 | − | 0.134847i | ||||
\(20\) | 0.500000 | + | 1.53884i | 0.111803 | + | 0.344095i | ||||
\(21\) | 9.70820 | 2.11850 | ||||||||
\(22\) | −3.30902 | + | 0.224514i | −0.705485 | + | 0.0478665i | ||||
\(23\) | −7.85410 | −1.63769 | −0.818847 | − | 0.574012i | \(-0.805386\pi\) | ||||
−0.818847 | + | 0.574012i | \(0.805386\pi\) | |||||||
\(24\) | −0.618034 | − | 1.90211i | −0.126156 | − | 0.388267i | ||||
\(25\) | 1.92705 | + | 1.40008i | 0.385410 | + | 0.280017i | ||||
\(26\) | −2.00000 | + | 1.45309i | −0.392232 | + | 0.284973i | ||||
\(27\) | 1.23607 | − | 3.80423i | 0.237881 | − | 0.732124i | ||||
\(28\) | −1.50000 | + | 4.61653i | −0.283473 | + | 0.872441i | ||||
\(29\) | −8.47214 | + | 6.15537i | −1.57324 | + | 1.14302i | −0.649264 | + | 0.760563i | \(0.724923\pi\) |
−0.923972 | + | 0.382460i | \(0.875077\pi\) | |||||||
\(30\) | 2.61803 | + | 1.90211i | 0.477985 | + | 0.347277i | ||||
\(31\) | 0.618034 | + | 1.90211i | 0.111002 | + | 0.341630i | 0.991092 | − | 0.133177i | \(-0.0425179\pi\) |
−0.880090 | + | 0.474807i | \(0.842518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.09017 | + | 4.25325i | −0.886085 | + | 0.740396i | ||||
\(34\) | 3.38197 | 0.580002 | ||||||||
\(35\) | −2.42705 | − | 7.46969i | −0.410246 | − | 1.26261i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | −3.23607 | + | 2.35114i | −0.532006 | + | 0.386525i | −0.821108 | − | 0.570773i | \(-0.806644\pi\) |
0.289101 | + | 0.957298i | \(0.406644\pi\) | |||||||
\(38\) | 0.309017 | − | 0.951057i | 0.0501292 | − | 0.154282i | ||||
\(39\) | −1.52786 | + | 4.70228i | −0.244654 | + | 0.752968i | ||||
\(40\) | −1.30902 | + | 0.951057i | −0.206974 | + | 0.150375i | ||||
\(41\) | 3.85410 | + | 2.80017i | 0.601910 | + | 0.437313i | 0.846556 | − | 0.532299i | \(-0.178672\pi\) |
−0.244647 | + | 0.969612i | \(0.578672\pi\) | |||||||
\(42\) | 3.00000 | + | 9.23305i | 0.462910 | + | 1.42469i | ||||
\(43\) | −9.09017 | −1.38624 | −0.693119 | − | 0.720823i | \(-0.743764\pi\) | ||||
−0.693119 | + | 0.720823i | \(0.743764\pi\) | |||||||
\(44\) | −1.23607 | − | 3.07768i | −0.186344 | − | 0.463978i | ||||
\(45\) | 1.61803 | 0.241202 | ||||||||
\(46\) | −2.42705 | − | 7.46969i | −0.357849 | − | 1.10135i | ||||
\(47\) | −1.11803 | − | 0.812299i | −0.163082 | − | 0.118486i | 0.503251 | − | 0.864140i | \(-0.332137\pi\) |
−0.666333 | + | 0.745654i | \(0.732137\pi\) | |||||||
\(48\) | 1.61803 | − | 1.17557i | 0.233543 | − | 0.169679i | ||||
\(49\) | 5.11803 | − | 15.7517i | 0.731148 | − | 2.25024i | ||||
\(50\) | −0.736068 | + | 2.26538i | −0.104096 | + | 0.320374i | ||||
\(51\) | 5.47214 | − | 3.97574i | 0.766252 | − | 0.556715i | ||||
\(52\) | −2.00000 | − | 1.45309i | −0.277350 | − | 0.201507i | ||||
\(53\) | −1.47214 | − | 4.53077i | −0.202213 | − | 0.622349i | −0.999816 | − | 0.0191660i | \(-0.993899\pi\) |
0.797603 | − | 0.603183i | \(-0.206101\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 4.54508 | + | 2.85317i | 0.612859 | + | 0.384721i | ||||
\(56\) | −4.85410 | −0.648657 | ||||||||
\(57\) | −0.618034 | − | 1.90211i | −0.0818606 | − | 0.251941i | ||||
\(58\) | −8.47214 | − | 6.15537i | −1.11245 | − | 0.808239i | ||||
\(59\) | 2.85410 | − | 2.07363i | 0.371572 | − | 0.269963i | −0.386290 | − | 0.922377i | \(-0.626244\pi\) |
0.757863 | + | 0.652414i | \(0.226244\pi\) | |||||||
\(60\) | −1.00000 | + | 3.07768i | −0.129099 | + | 0.397327i | ||||
\(61\) | −2.95492 | + | 9.09429i | −0.378338 | + | 1.16440i | 0.562861 | + | 0.826552i | \(0.309701\pi\) |
−0.941199 | + | 0.337853i | \(0.890299\pi\) | |||||||
\(62\) | −1.61803 | + | 1.17557i | −0.205491 | + | 0.149298i | ||||
\(63\) | 3.92705 | + | 2.85317i | 0.494762 | + | 0.359466i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | −5.61803 | − | 3.52671i | −0.691532 | − | 0.434108i | ||||
\(67\) | 2.76393 | 0.337668 | 0.168834 | − | 0.985644i | \(-0.446000\pi\) | ||||
0.168834 | + | 0.985644i | \(0.446000\pi\) | |||||||
\(68\) | 1.04508 | + | 3.21644i | 0.126735 | + | 0.390051i | ||||
\(69\) | −12.7082 | − | 9.23305i | −1.52989 | − | 1.11153i | ||||
\(70\) | 6.35410 | − | 4.61653i | 0.759460 | − | 0.551780i | ||||
\(71\) | 1.52786 | − | 4.70228i | 0.181324 | − | 0.558058i | −0.818542 | − | 0.574447i | \(-0.805217\pi\) |
0.999866 | + | 0.0163891i | \(0.00521704\pi\) | |||||||
\(72\) | 0.309017 | − | 0.951057i | 0.0364180 | − | 0.112083i | ||||
\(73\) | 11.3262 | − | 8.22899i | 1.32564 | − | 0.963131i | 0.325792 | − | 0.945441i | \(-0.394369\pi\) |
0.999844 | − | 0.0176895i | \(-0.00563103\pi\) | |||||||
\(74\) | −3.23607 | − | 2.35114i | −0.376185 | − | 0.273315i | ||||
\(75\) | 1.47214 | + | 4.53077i | 0.169988 | + | 0.523168i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 6.00000 | + | 14.9394i | 0.683763 | + | 1.70250i | ||||
\(78\) | −4.94427 | −0.559829 | ||||||||
\(79\) | 1.14590 | + | 3.52671i | 0.128924 | + | 0.396786i | 0.994596 | − | 0.103826i | \(-0.0331084\pi\) |
−0.865672 | + | 0.500612i | \(0.833108\pi\) | |||||||
\(80\) | −1.30902 | − | 0.951057i | −0.146353 | − | 0.106331i | ||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | −1.47214 | + | 4.53077i | −0.162570 | + | 0.500340i | ||||
\(83\) | −4.26393 | + | 13.1230i | −0.468027 | + | 1.44044i | 0.387108 | + | 0.922035i | \(0.373474\pi\) |
−0.855135 | + | 0.518405i | \(0.826526\pi\) | |||||||
\(84\) | −7.85410 | + | 5.70634i | −0.856953 | + | 0.622613i | ||||
\(85\) | −4.42705 | − | 3.21644i | −0.480181 | − | 0.348872i | ||||
\(86\) | −2.80902 | − | 8.64527i | −0.302904 | − | 0.932243i | ||||
\(87\) | −20.9443 | −2.24546 | ||||||||
\(88\) | 2.54508 | − | 2.12663i | 0.271307 | − | 0.226699i | ||||
\(89\) | 11.2361 | 1.19102 | 0.595510 | − | 0.803348i | \(-0.296950\pi\) | ||||
0.595510 | + | 0.803348i | \(0.296950\pi\) | |||||||
\(90\) | 0.500000 | + | 1.53884i | 0.0527046 | + | 0.162208i | ||||
\(91\) | 9.70820 | + | 7.05342i | 1.01770 | + | 0.739400i | ||||
\(92\) | 6.35410 | − | 4.61653i | 0.662461 | − | 0.481306i | ||||
\(93\) | −1.23607 | + | 3.80423i | −0.128174 | + | 0.394480i | ||||
\(94\) | 0.427051 | − | 1.31433i | 0.0440469 | − | 0.135563i | ||||
\(95\) | −1.30902 | + | 0.951057i | −0.134302 | + | 0.0975763i | ||||
\(96\) | 1.61803 | + | 1.17557i | 0.165140 | + | 0.119981i | ||||
\(97\) | −2.85410 | − | 8.78402i | −0.289790 | − | 0.891882i | −0.984922 | − | 0.173000i | \(-0.944654\pi\) |
0.695132 | − | 0.718882i | \(-0.255346\pi\) | |||||||
\(98\) | 16.5623 | 1.67305 | ||||||||
\(99\) | −3.30902 | + | 0.224514i | −0.332569 | + | 0.0225645i | ||||
\(100\) | −2.38197 | −0.238197 | ||||||||
\(101\) | −4.50000 | − | 13.8496i | −0.447767 | − | 1.37808i | −0.879421 | − | 0.476045i | \(-0.842070\pi\) |
0.431654 | − | 0.902039i | \(-0.357930\pi\) | |||||||
\(102\) | 5.47214 | + | 3.97574i | 0.541822 | + | 0.393657i | ||||
\(103\) | 3.85410 | − | 2.80017i | 0.379756 | − | 0.275909i | −0.381489 | − | 0.924373i | \(-0.624589\pi\) |
0.761245 | + | 0.648465i | \(0.224589\pi\) | |||||||
\(104\) | 0.763932 | − | 2.35114i | 0.0749097 | − | 0.230548i | ||||
\(105\) | 4.85410 | − | 14.9394i | 0.473712 | − | 1.45794i | ||||
\(106\) | 3.85410 | − | 2.80017i | 0.374343 | − | 0.271976i | ||||
\(107\) | −4.85410 | − | 3.52671i | −0.469264 | − | 0.340940i | 0.327891 | − | 0.944716i | \(-0.393662\pi\) |
−0.797154 | + | 0.603776i | \(0.793662\pi\) | |||||||
\(108\) | 1.23607 | + | 3.80423i | 0.118941 | + | 0.366062i | ||||
\(109\) | 3.23607 | 0.309959 | 0.154980 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154980 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(110\) | −1.30902 | + | 5.20431i | −0.124810 | + | 0.496212i | ||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | −1.50000 | − | 4.61653i | −0.141737 | − | 0.436221i | ||||
\(113\) | −4.47214 | − | 3.24920i | −0.420703 | − | 0.305659i | 0.357218 | − | 0.934021i | \(-0.383725\pi\) |
−0.777921 | + | 0.628362i | \(0.783725\pi\) | |||||||
\(114\) | 1.61803 | − | 1.17557i | 0.151543 | − | 0.110102i | ||||
\(115\) | −3.92705 | + | 12.0862i | −0.366199 | + | 1.12705i | ||||
\(116\) | 3.23607 | − | 9.95959i | 0.300461 | − | 0.924725i | ||||
\(117\) | −2.00000 | + | 1.45309i | −0.184900 | + | 0.134338i | ||||
\(118\) | 2.85410 | + | 2.07363i | 0.262741 | + | 0.190893i | ||||
\(119\) | −5.07295 | − | 15.6129i | −0.465036 | − | 1.43124i | ||||
\(120\) | −3.23607 | −0.295411 | ||||||||
\(121\) | −9.69098 | − | 5.20431i | −0.880998 | − | 0.473119i | ||||
\(122\) | −9.56231 | −0.865730 | ||||||||
\(123\) | 2.94427 | + | 9.06154i | 0.265476 | + | 0.817051i | ||||
\(124\) | −1.61803 | − | 1.17557i | −0.145304 | − | 0.105569i | ||||
\(125\) | 9.66312 | − | 7.02067i | 0.864296 | − | 0.627948i | ||||
\(126\) | −1.50000 | + | 4.61653i | −0.133631 | + | 0.411273i | ||||
\(127\) | −6.00000 | + | 18.4661i | −0.532414 | + | 1.63860i | 0.216758 | + | 0.976225i | \(0.430452\pi\) |
−0.749172 | + | 0.662376i | \(0.769548\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | −14.7082 | − | 10.6861i | −1.29499 | − | 0.940862i | ||||
\(130\) | 1.23607 | + | 3.80423i | 0.108410 | + | 0.333653i | ||||
\(131\) | −12.0902 | −1.05632 | −0.528162 | − | 0.849144i | \(-0.677118\pi\) | ||||
−0.528162 | + | 0.849144i | \(0.677118\pi\) | |||||||
\(132\) | 1.61803 | − | 6.43288i | 0.140832 | − | 0.559910i | ||||
\(133\) | −4.85410 | −0.420904 | ||||||||
\(134\) | 0.854102 | + | 2.62866i | 0.0737832 | + | 0.227081i | ||||
\(135\) | −5.23607 | − | 3.80423i | −0.450649 | − | 0.327416i | ||||
\(136\) | −2.73607 | + | 1.98787i | −0.234616 | + | 0.170458i | ||||
\(137\) | −1.20820 | + | 3.71847i | −0.103224 | + | 0.317690i | −0.989309 | − | 0.145831i | \(-0.953414\pi\) |
0.886086 | + | 0.463522i | \(0.153414\pi\) | |||||||
\(138\) | 4.85410 | − | 14.9394i | 0.413209 | − | 1.27173i | ||||
\(139\) | 8.35410 | − | 6.06961i | 0.708586 | − | 0.514818i | −0.174131 | − | 0.984722i | \(-0.555712\pi\) |
0.882717 | + | 0.469905i | \(0.155712\pi\) | |||||||
\(140\) | 6.35410 | + | 4.61653i | 0.537020 | + | 0.390168i | ||||
\(141\) | −0.854102 | − | 2.62866i | −0.0719284 | − | 0.221373i | ||||
\(142\) | 4.94427 | 0.414914 | ||||||||
\(143\) | −8.18034 | + | 0.555029i | −0.684074 | + | 0.0464139i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.23607 | + | 16.1150i | 0.434832 | + | 1.33827i | ||||
\(146\) | 11.3262 | + | 8.22899i | 0.937366 | + | 0.681036i | ||||
\(147\) | 26.7984 | − | 19.4702i | 2.21029 | − | 1.60587i | ||||
\(148\) | 1.23607 | − | 3.80423i | 0.101604 | − | 0.312705i | ||||
\(149\) | −3.56231 | + | 10.9637i | −0.291835 | + | 0.898177i | 0.692431 | + | 0.721484i | \(0.256540\pi\) |
−0.984266 | + | 0.176693i | \(0.943460\pi\) | |||||||
\(150\) | −3.85410 | + | 2.80017i | −0.314686 | + | 0.228633i | ||||
\(151\) | 11.0902 | + | 8.05748i | 0.902505 | + | 0.655708i | 0.939108 | − | 0.343621i | \(-0.111654\pi\) |
−0.0366030 | + | 0.999330i | \(0.511654\pi\) | |||||||
\(152\) | 0.309017 | + | 0.951057i | 0.0250646 | + | 0.0771409i | ||||
\(153\) | 3.38197 | 0.273416 | ||||||||
\(154\) | −12.3541 | + | 10.3229i | −0.995522 | + | 0.831840i | ||||
\(155\) | 3.23607 | 0.259927 | ||||||||
\(156\) | −1.52786 | − | 4.70228i | −0.122327 | − | 0.376484i | ||||
\(157\) | −18.8713 | − | 13.7108i | −1.50610 | − | 1.09424i | −0.967873 | − | 0.251440i | \(-0.919096\pi\) |
−0.538223 | − | 0.842803i | \(-0.680904\pi\) | |||||||
\(158\) | −3.00000 | + | 2.17963i | −0.238667 | + | 0.173402i | ||||
\(159\) | 2.94427 | − | 9.06154i | 0.233496 | − | 0.718627i | ||||
\(160\) | 0.500000 | − | 1.53884i | 0.0395285 | − | 0.121656i | ||||
\(161\) | −30.8435 | + | 22.4091i | −2.43081 | + | 1.76608i | ||||
\(162\) | 8.89919 | + | 6.46564i | 0.699186 | + | 0.507988i | ||||
\(163\) | −0.208204 | − | 0.640786i | −0.0163078 | − | 0.0501902i | 0.942571 | − | 0.334005i | \(-0.108400\pi\) |
−0.958879 | + | 0.283814i | \(0.908400\pi\) | |||||||
\(164\) | −4.76393 | −0.372001 | ||||||||
\(165\) | 4.00000 | + | 9.95959i | 0.311400 | + | 0.775353i | ||||
\(166\) | −13.7984 | −1.07096 | ||||||||
\(167\) | 0.437694 | + | 1.34708i | 0.0338698 | + | 0.104240i | 0.966562 | − | 0.256432i | \(-0.0825471\pi\) |
−0.932692 | + | 0.360673i | \(0.882547\pi\) | |||||||
\(168\) | −7.85410 | − | 5.70634i | −0.605957 | − | 0.440254i | ||||
\(169\) | 5.57295 | − | 4.04898i | 0.428688 | − | 0.311460i | ||||
\(170\) | 1.69098 | − | 5.20431i | 0.129692 | − | 0.399152i | ||||
\(171\) | 0.309017 | − | 0.951057i | 0.0236311 | − | 0.0727291i | ||||
\(172\) | 7.35410 | − | 5.34307i | 0.560745 | − | 0.407405i | ||||
\(173\) | 16.9443 | + | 12.3107i | 1.28825 | + | 0.935968i | 0.999768 | − | 0.0215179i | \(-0.00684990\pi\) |
0.288481 | + | 0.957486i | \(0.406850\pi\) | |||||||
\(174\) | −6.47214 | − | 19.9192i | −0.490651 | − | 1.51007i | ||||
\(175\) | 11.5623 | 0.874028 | ||||||||
\(176\) | 2.80902 | + | 1.76336i | 0.211738 | + | 0.132918i | ||||
\(177\) | 7.05573 | 0.530341 | ||||||||
\(178\) | 3.47214 | + | 10.6861i | 0.260248 | + | 0.800960i | ||||
\(179\) | −1.76393 | − | 1.28157i | −0.131842 | − | 0.0957892i | 0.519909 | − | 0.854221i | \(-0.325966\pi\) |
−0.651752 | + | 0.758432i | \(0.725966\pi\) | |||||||
\(180\) | −1.30902 | + | 0.951057i | −0.0975684 | + | 0.0708876i | ||||
\(181\) | −0.0901699 | + | 0.277515i | −0.00670228 | + | 0.0206275i | −0.954352 | − | 0.298685i | \(-0.903452\pi\) |
0.947649 | + | 0.319313i | \(0.103452\pi\) | |||||||
\(182\) | −3.70820 | + | 11.4127i | −0.274870 | + | 0.845964i | ||||
\(183\) | −15.4721 | + | 11.2412i | −1.14373 | + | 0.830971i | ||||
\(184\) | 6.35410 | + | 4.61653i | 0.468431 | + | 0.340335i | ||||
\(185\) | 2.00000 | + | 6.15537i | 0.147043 | + | 0.452552i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 9.50000 | + | 5.96361i | 0.694709 | + | 0.436102i | ||||
\(188\) | 1.38197 | 0.100790 | ||||||||
\(189\) | −6.00000 | − | 18.4661i | −0.436436 | − | 1.34321i | ||||
\(190\) | −1.30902 | − | 0.951057i | −0.0949661 | − | 0.0689969i | ||||
\(191\) | −4.07295 | + | 2.95917i | −0.294708 | + | 0.214118i | −0.725307 | − | 0.688425i | \(-0.758302\pi\) |
0.430599 | + | 0.902543i | \(0.358302\pi\) | |||||||
\(192\) | −0.618034 | + | 1.90211i | −0.0446028 | + | 0.137273i | ||||
\(193\) | 5.90983 | − | 18.1886i | 0.425399 | − | 1.30924i | −0.477213 | − | 0.878788i | \(-0.658353\pi\) |
0.902612 | − | 0.430455i | \(-0.141647\pi\) | |||||||
\(194\) | 7.47214 | − | 5.42882i | 0.536468 | − | 0.389767i | ||||
\(195\) | 6.47214 | + | 4.70228i | 0.463479 | + | 0.336737i | ||||
\(196\) | 5.11803 | + | 15.7517i | 0.365574 | + | 1.12512i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | −1.23607 | − | 3.07768i | −0.0878435 | − | 0.218721i | ||||
\(199\) | 14.5623 | 1.03229 | 0.516147 | − | 0.856500i | \(-0.327366\pi\) | ||||
0.516147 | + | 0.856500i | \(0.327366\pi\) | |||||||
\(200\) | −0.736068 | − | 2.26538i | −0.0520479 | − | 0.160187i | ||||
\(201\) | 4.47214 | + | 3.24920i | 0.315440 | + | 0.229181i | ||||
\(202\) | 11.7812 | − | 8.55951i | 0.828919 | − | 0.602245i | ||||
\(203\) | −15.7082 | + | 48.3449i | −1.10250 | + | 3.39315i | ||||
\(204\) | −2.09017 | + | 6.43288i | −0.146341 | + | 0.450392i | ||||
\(205\) | 6.23607 | − | 4.53077i | 0.435546 | − | 0.316443i | ||||
\(206\) | 3.85410 | + | 2.80017i | 0.268528 | + | 0.195097i | ||||
\(207\) | −2.42705 | − | 7.46969i | −0.168692 | − | 0.519180i | ||||
\(208\) | 2.47214 | 0.171412 | ||||||||
\(209\) | 2.54508 | − | 2.12663i | 0.176047 | − | 0.147102i | ||||
\(210\) | 15.7082 | 1.08397 | ||||||||
\(211\) | 4.76393 | + | 14.6619i | 0.327963 | + | 1.00937i | 0.970086 | + | 0.242763i | \(0.0780539\pi\) |
−0.642123 | + | 0.766602i | \(0.721946\pi\) | |||||||
\(212\) | 3.85410 | + | 2.80017i | 0.264701 | + | 0.192316i | ||||
\(213\) | 8.00000 | − | 5.81234i | 0.548151 | − | 0.398255i | ||||
\(214\) | 1.85410 | − | 5.70634i | 0.126744 | − | 0.390077i | ||||
\(215\) | −4.54508 | + | 13.9883i | −0.309972 | + | 0.953996i | ||||
\(216\) | −3.23607 | + | 2.35114i | −0.220187 | + | 0.159975i | ||||
\(217\) | 7.85410 | + | 5.70634i | 0.533171 | + | 0.387372i | ||||
\(218\) | 1.00000 | + | 3.07768i | 0.0677285 | + | 0.208447i | ||||
\(219\) | 28.0000 | 1.89206 | ||||||||
\(220\) | −5.35410 | + | 0.363271i | −0.360973 | + | 0.0244917i | ||||
\(221\) | 8.36068 | 0.562400 | ||||||||
\(222\) | −2.47214 | − | 7.60845i | −0.165919 | − | 0.510646i | ||||
\(223\) | 7.85410 | + | 5.70634i | 0.525950 | + | 0.382125i | 0.818840 | − | 0.574021i | \(-0.194617\pi\) |
−0.292891 | + | 0.956146i | \(0.594617\pi\) | |||||||
\(224\) | 3.92705 | − | 2.85317i | 0.262387 | − | 0.190635i | ||||
\(225\) | −0.736068 | + | 2.26538i | −0.0490712 | + | 0.151026i | ||||
\(226\) | 1.70820 | − | 5.25731i | 0.113628 | − | 0.349711i | ||||
\(227\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(228\) | 1.61803 | + | 1.17557i | 0.107157 | + | 0.0778541i | ||||
\(229\) | −2.86475 | − | 8.81678i | −0.189308 | − | 0.582629i | 0.810688 | − | 0.585478i | \(-0.199093\pi\) |
−0.999996 | + | 0.00284891i | \(0.999093\pi\) | |||||||
\(230\) | −12.7082 | −0.837954 | ||||||||
\(231\) | −7.85410 | + | 31.2259i | −0.516762 | + | 2.05451i | ||||
\(232\) | 10.4721 | 0.687529 | ||||||||
\(233\) | 1.79180 | + | 5.51458i | 0.117384 | + | 0.361272i | 0.992437 | − | 0.122756i | \(-0.0391732\pi\) |
−0.875052 | + | 0.484028i | \(0.839173\pi\) | |||||||
\(234\) | −2.00000 | − | 1.45309i | −0.130744 | − | 0.0949911i | ||||
\(235\) | −1.80902 | + | 1.31433i | −0.118007 | + | 0.0857373i | ||||
\(236\) | −1.09017 | + | 3.35520i | −0.0709640 | + | 0.218405i | ||||
\(237\) | −2.29180 | + | 7.05342i | −0.148868 | + | 0.458169i | ||||
\(238\) | 13.2812 | − | 9.64932i | 0.860889 | − | 0.625473i | ||||
\(239\) | −14.8262 | − | 10.7719i | −0.959030 | − | 0.696776i | −0.00610444 | − | 0.999981i | \(-0.501943\pi\) |
−0.952925 | + | 0.303206i | \(0.901943\pi\) | |||||||
\(240\) | −1.00000 | − | 3.07768i | −0.0645497 | − | 0.198664i | ||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 1.95492 | − | 10.8249i | 0.125667 | − | 0.695850i | ||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | −2.95492 | − | 9.09429i | −0.189169 | − | 0.582202i | ||||
\(245\) | −21.6803 | − | 15.7517i | −1.38511 | − | 1.00634i | ||||
\(246\) | −7.70820 | + | 5.60034i | −0.491457 | + | 0.357065i | ||||
\(247\) | 0.763932 | − | 2.35114i | 0.0486078 | − | 0.149600i | ||||
\(248\) | 0.618034 | − | 1.90211i | 0.0392452 | − | 0.120784i | ||||
\(249\) | −22.3262 | + | 16.2210i | −1.41487 | + | 1.02796i | ||||
\(250\) | 9.66312 | + | 7.02067i | 0.611149 | + | 0.444026i | ||||
\(251\) | 1.28115 | + | 3.94298i | 0.0808657 | + | 0.248879i | 0.983313 | − | 0.181921i | \(-0.0582315\pi\) |
−0.902448 | + | 0.430800i | \(0.858231\pi\) | |||||||
\(252\) | −4.85410 | −0.305780 | ||||||||
\(253\) | 6.35410 | − | 25.2623i | 0.399479 | − | 1.58822i | ||||
\(254\) | −19.4164 | −1.21829 | ||||||||
\(255\) | −3.38197 | − | 10.4086i | −0.211787 | − | 0.651813i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −5.61803 | + | 4.08174i | −0.350443 | + | 0.254612i | −0.749055 | − | 0.662508i | \(-0.769492\pi\) |
0.398612 | + | 0.917120i | \(0.369492\pi\) | |||||||
\(258\) | 5.61803 | − | 17.2905i | 0.349764 | − | 1.07646i | ||||
\(259\) | −6.00000 | + | 18.4661i | −0.372822 | + | 1.14743i | ||||
\(260\) | −3.23607 | + | 2.35114i | −0.200692 | + | 0.145812i | ||||
\(261\) | −8.47214 | − | 6.15537i | −0.524412 | − | 0.381008i | ||||
\(262\) | −3.73607 | − | 11.4984i | −0.230815 | − | 0.710376i | ||||
\(263\) | −2.47214 | −0.152438 | −0.0762192 | − | 0.997091i | \(-0.524285\pi\) | ||||
−0.0762192 | + | 0.997091i | \(0.524285\pi\) | |||||||
\(264\) | 6.61803 | − | 0.449028i | 0.407312 | − | 0.0276358i | ||||
\(265\) | −7.70820 | −0.473511 | ||||||||
\(266\) | −1.50000 | − | 4.61653i | −0.0919709 | − | 0.283057i | ||||
\(267\) | 18.1803 | + | 13.2088i | 1.11262 | + | 0.808365i | ||||
\(268\) | −2.23607 | + | 1.62460i | −0.136590 | + | 0.0992381i | ||||
\(269\) | −3.90983 | + | 12.0332i | −0.238387 | + | 0.733678i | 0.758268 | + | 0.651943i | \(0.226046\pi\) |
−0.996654 | + | 0.0817349i | \(0.973954\pi\) | |||||||
\(270\) | 2.00000 | − | 6.15537i | 0.121716 | − | 0.374604i | ||||
\(271\) | −16.3541 | + | 11.8820i | −0.993441 | + | 0.721777i | −0.960672 | − | 0.277686i | \(-0.910433\pi\) |
−0.0327690 | + | 0.999463i | \(0.510433\pi\) | |||||||
\(272\) | −2.73607 | − | 1.98787i | −0.165898 | − | 0.120532i | ||||
\(273\) | 7.41641 | + | 22.8254i | 0.448861 | + | 1.38145i | ||||
\(274\) | −3.90983 | −0.236201 | ||||||||
\(275\) | −6.06231 | + | 5.06555i | −0.365571 | + | 0.305464i | ||||
\(276\) | 15.7082 | 0.945523 | ||||||||
\(277\) | −3.85410 | − | 11.8617i | −0.231571 | − | 0.712701i | −0.997558 | − | 0.0698451i | \(-0.977749\pi\) |
0.765987 | − | 0.642856i | \(-0.222251\pi\) | |||||||
\(278\) | 8.35410 | + | 6.06961i | 0.501046 | + | 0.364031i | ||||
\(279\) | −1.61803 | + | 1.17557i | −0.0968692 | + | 0.0703796i | ||||
\(280\) | −2.42705 | + | 7.46969i | −0.145044 | + | 0.446400i | ||||
\(281\) | −8.23607 | + | 25.3480i | −0.491323 | + | 1.51214i | 0.331288 | + | 0.943530i | \(0.392517\pi\) |
−0.822610 | + | 0.568606i | \(0.807483\pi\) | |||||||
\(282\) | 2.23607 | − | 1.62460i | 0.133156 | − | 0.0967434i | ||||
\(283\) | −8.54508 | − | 6.20837i | −0.507953 | − | 0.369049i | 0.304094 | − | 0.952642i | \(-0.401646\pi\) |
−0.812046 | + | 0.583593i | \(0.801646\pi\) | |||||||
\(284\) | 1.52786 | + | 4.70228i | 0.0906621 | + | 0.279029i | ||||
\(285\) | −3.23607 | −0.191688 | ||||||||
\(286\) | −3.05573 | − | 7.60845i | −0.180689 | − | 0.449897i | ||||
\(287\) | 23.1246 | 1.36500 | ||||||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | 4.50000 | + | 3.26944i | 0.264706 | + | 0.192320i | ||||
\(290\) | −13.7082 | + | 9.95959i | −0.804973 | + | 0.584847i | ||||
\(291\) | 5.70820 | − | 17.5680i | 0.334621 | − | 1.02986i | ||||
\(292\) | −4.32624 | + | 13.3148i | −0.253174 | + | 0.779189i | ||||
\(293\) | 24.7984 | − | 18.0171i | 1.44874 | − | 1.05257i | 0.462612 | − | 0.886561i | \(-0.346912\pi\) |
0.986124 | − | 0.166008i | \(-0.0530877\pi\) | |||||||
\(294\) | 26.7984 | + | 19.4702i | 1.56291 | + | 1.13552i | ||||
\(295\) | −1.76393 | − | 5.42882i | −0.102700 | − | 0.316078i | ||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 11.2361 | + | 7.05342i | 0.651983 | + | 0.409281i | ||||
\(298\) | −11.5279 | −0.667791 | ||||||||
\(299\) | −6.00000 | − | 18.4661i | −0.346989 | − | 1.06792i | ||||
\(300\) | −3.85410 | − | 2.80017i | −0.222517 | − | 0.161668i | ||||
\(301\) | −35.6976 | + | 25.9358i | −2.05757 | + | 1.49491i | ||||
\(302\) | −4.23607 | + | 13.0373i | −0.243758 | + | 0.750211i | ||||
\(303\) | 9.00000 | − | 27.6992i | 0.517036 | − | 1.59127i | ||||
\(304\) | −0.809017 | + | 0.587785i | −0.0464003 | + | 0.0337118i | ||||
\(305\) | 12.5172 | + | 9.09429i | 0.716734 | + | 0.520738i | ||||
\(306\) | 1.04508 | + | 3.21644i | 0.0597435 | + | 0.183872i | ||||
\(307\) | −0.583592 | −0.0333074 | −0.0166537 | − | 0.999861i | \(-0.505301\pi\) | ||||
−0.0166537 | + | 0.999861i | \(0.505301\pi\) | |||||||
\(308\) | −13.6353 | − | 8.55951i | −0.776941 | − | 0.487723i | ||||
\(309\) | 9.52786 | 0.542021 | ||||||||
\(310\) | 1.00000 | + | 3.07768i | 0.0567962 | + | 0.174801i | ||||
\(311\) | 23.2984 | + | 16.9273i | 1.32113 | + | 0.959857i | 0.999917 | + | 0.0128496i | \(0.00409025\pi\) |
0.321212 | + | 0.947007i | \(0.395910\pi\) | |||||||
\(312\) | 4.00000 | − | 2.90617i | 0.226455 | − | 0.164529i | ||||
\(313\) | 3.42705 | − | 10.5474i | 0.193708 | − | 0.596173i | −0.806281 | − | 0.591533i | \(-0.798523\pi\) |
0.999989 | − | 0.00464017i | \(-0.00147702\pi\) | |||||||
\(314\) | 7.20820 | − | 22.1846i | 0.406782 | − | 1.25195i | ||||
\(315\) | 6.35410 | − | 4.61653i | 0.358013 | − | 0.260112i | ||||
\(316\) | −3.00000 | − | 2.17963i | −0.168763 | − | 0.122614i | ||||
\(317\) | −6.23607 | − | 19.1926i | −0.350252 | − | 1.07797i | −0.958711 | − | 0.284381i | \(-0.908212\pi\) |
0.608459 | − | 0.793585i | \(-0.291788\pi\) | |||||||
\(318\) | 9.52786 | 0.534296 | ||||||||
\(319\) | −12.9443 | − | 32.2299i | −0.724740 | − | 1.80453i | ||||
\(320\) | 1.61803 | 0.0904508 | ||||||||
\(321\) | −3.70820 | − | 11.4127i | −0.206972 | − | 0.636994i | ||||
\(322\) | −30.8435 | − | 22.4091i | −1.71884 | − | 1.24881i | ||||
\(323\) | −2.73607 | + | 1.98787i | −0.152239 | + | 0.110608i | ||||
\(324\) | −3.39919 | + | 10.4616i | −0.188844 | + | 0.581201i | ||||
\(325\) | −1.81966 | + | 5.60034i | −0.100937 | + | 0.310651i | ||||
\(326\) | 0.545085 | − | 0.396027i | 0.0301895 | − | 0.0219339i | ||||
\(327\) | 5.23607 | + | 3.80423i | 0.289555 | + | 0.210374i | ||||
\(328\) | −1.47214 | − | 4.53077i | −0.0812851 | − | 0.250170i | ||||
\(329\) | −6.70820 | −0.369835 | ||||||||
\(330\) | −8.23607 | + | 6.88191i | −0.453381 | + | 0.378837i | ||||
\(331\) | 3.70820 | 0.203821 | 0.101911 | − | 0.994794i | \(-0.467504\pi\) | ||||
0.101911 | + | 0.994794i | \(0.467504\pi\) | |||||||
\(332\) | −4.26393 | − | 13.1230i | −0.234014 | − | 0.720220i | ||||
\(333\) | −3.23607 | − | 2.35114i | −0.177335 | − | 0.128842i | ||||
\(334\) | −1.14590 | + | 0.832544i | −0.0627008 | + | 0.0455548i | ||||
\(335\) | 1.38197 | − | 4.25325i | 0.0755049 | − | 0.232380i | ||||
\(336\) | 3.00000 | − | 9.23305i | 0.163663 | − | 0.503704i | ||||
\(337\) | 28.2705 | − | 20.5397i | 1.53999 | − | 1.11887i | 0.589653 | − | 0.807657i | \(-0.299265\pi\) |
0.950340 | − | 0.311213i | \(-0.100735\pi\) | |||||||
\(338\) | 5.57295 | + | 4.04898i | 0.303128 | + | 0.220236i | ||||
\(339\) | −3.41641 | − | 10.5146i | −0.185554 | − | 0.571076i | ||||
\(340\) | 5.47214 | 0.296768 | ||||||||
\(341\) | −6.61803 | + | 0.449028i | −0.358387 | + | 0.0243162i | ||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −14.3435 | − | 44.1446i | −0.774474 | − | 2.38359i | ||||
\(344\) | 7.35410 | + | 5.34307i | 0.396507 | + | 0.288079i | ||||
\(345\) | −20.5623 | + | 14.9394i | −1.10704 | + | 0.804310i | ||||
\(346\) | −6.47214 | + | 19.9192i | −0.347944 | + | 1.07086i | ||||
\(347\) | −3.57295 | + | 10.9964i | −0.191806 | + | 0.590318i | 0.808193 | + | 0.588918i | \(0.200446\pi\) |
−0.999999 | + | 0.00140040i | \(0.999554\pi\) | |||||||
\(348\) | 16.9443 | − | 12.3107i | 0.908308 | − | 0.659925i | ||||
\(349\) | 21.0172 | + | 15.2699i | 1.12503 | + | 0.817379i | 0.984963 | − | 0.172763i | \(-0.0552696\pi\) |
0.140063 | + | 0.990143i | \(0.455270\pi\) | |||||||
\(350\) | 3.57295 | + | 10.9964i | 0.190982 | + | 0.587783i | ||||
\(351\) | 9.88854 | 0.527811 | ||||||||
\(352\) | −0.809017 | + | 3.21644i | −0.0431208 | + | 0.171437i | ||||
\(353\) | 17.6180 | 0.937713 | 0.468857 | − | 0.883274i | \(-0.344666\pi\) | ||||
0.468857 | + | 0.883274i | \(0.344666\pi\) | |||||||
\(354\) | 2.18034 | + | 6.71040i | 0.115884 | + | 0.356654i | ||||
\(355\) | −6.47214 | − | 4.70228i | −0.343505 | − | 0.249571i | ||||
\(356\) | −9.09017 | + | 6.60440i | −0.481778 | + | 0.350032i | ||||
\(357\) | 10.1459 | − | 31.2259i | 0.536978 | − | 1.65265i | ||||
\(358\) | 0.673762 | − | 2.07363i | 0.0356094 | − | 0.109595i | ||||
\(359\) | −4.11803 | + | 2.99193i | −0.217342 | + | 0.157908i | −0.691129 | − | 0.722731i | \(-0.742886\pi\) |
0.473788 | + | 0.880639i | \(0.342886\pi\) | |||||||
\(360\) | −1.30902 | − | 0.951057i | −0.0689913 | − | 0.0501251i | ||||
\(361\) | 0.309017 | + | 0.951057i | 0.0162641 | + | 0.0500556i | ||||
\(362\) | −0.291796 | −0.0153365 | ||||||||
\(363\) | −9.56231 | − | 19.8132i | −0.501891 | − | 1.03992i | ||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | −7.00000 | − | 21.5438i | −0.366397 | − | 1.12765i | ||||
\(366\) | −15.4721 | − | 11.2412i | −0.808742 | − | 0.587585i | ||||
\(367\) | 1.16312 | − | 0.845055i | 0.0607143 | − | 0.0441115i | −0.557014 | − | 0.830503i | \(-0.688053\pi\) |
0.617728 | + | 0.786391i | \(0.288053\pi\) | |||||||
\(368\) | −2.42705 | + | 7.46969i | −0.126519 | + | 0.389385i | ||||
\(369\) | −1.47214 | + | 4.53077i | −0.0766363 | + | 0.235862i | ||||
\(370\) | −5.23607 | + | 3.80423i | −0.272210 | + | 0.197772i | ||||
\(371\) | −18.7082 | − | 13.5923i | −0.971282 | − | 0.705677i | ||||
\(372\) | −1.23607 | − | 3.80423i | −0.0640871 | − | 0.197240i | ||||
\(373\) | 14.3607 | 0.743568 | 0.371784 | − | 0.928319i | \(-0.378746\pi\) | ||||
0.371784 | + | 0.928319i | \(0.378746\pi\) | |||||||
\(374\) | −2.73607 | + | 10.8779i | −0.141479 | + | 0.562482i | ||||
\(375\) | 23.8885 | 1.23360 | ||||||||
\(376\) | 0.427051 | + | 1.31433i | 0.0220235 | + | 0.0677813i | ||||
\(377\) | −20.9443 | − | 15.2169i | −1.07868 | − | 0.783710i | ||||
\(378\) | 15.7082 | − | 11.4127i | 0.807943 | − | 0.587005i | ||||
\(379\) | −1.00000 | + | 3.07768i | −0.0513665 | + | 0.158090i | −0.973449 | − | 0.228903i | \(-0.926486\pi\) |
0.922083 | + | 0.386993i | \(0.126486\pi\) | |||||||
\(380\) | 0.500000 | − | 1.53884i | 0.0256495 | − | 0.0789409i | ||||
\(381\) | −31.4164 | + | 22.8254i | −1.60951 | + | 1.16938i | ||||
\(382\) | −4.07295 | − | 2.95917i | −0.208390 | − | 0.151404i | ||||
\(383\) | −0.909830 | − | 2.80017i | −0.0464901 | − | 0.143082i | 0.925117 | − | 0.379682i | \(-0.123967\pi\) |
−0.971607 | + | 0.236601i | \(0.923967\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 25.9894 | − | 1.76336i | 1.32454 | − | 0.0898689i | ||||
\(386\) | 19.1246 | 0.973417 | ||||||||
\(387\) | −2.80902 | − | 8.64527i | −0.142790 | − | 0.439464i | ||||
\(388\) | 7.47214 | + | 5.42882i | 0.379340 | + | 0.275607i | ||||
\(389\) | 12.9721 | − | 9.42481i | 0.657713 | − | 0.477857i | −0.208177 | − | 0.978091i | \(-0.566753\pi\) |
0.865890 | + | 0.500235i | \(0.166753\pi\) | |||||||
\(390\) | −2.47214 | + | 7.60845i | −0.125181 | + | 0.385269i | ||||
\(391\) | −8.20820 | + | 25.2623i | −0.415107 | + | 1.27757i | ||||
\(392\) | −13.3992 | + | 9.73508i | −0.676761 | + | 0.491696i | ||||
\(393\) | −19.5623 | − | 14.2128i | −0.986788 | − | 0.716943i | ||||
\(394\) | −5.56231 | − | 17.1190i | −0.280225 | − | 0.862444i | ||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 2.54508 | − | 2.12663i | 0.127895 | − | 0.106867i | ||||
\(397\) | 14.1459 | 0.709962 | 0.354981 | − | 0.934873i | \(-0.384487\pi\) | ||||
0.354981 | + | 0.934873i | \(0.384487\pi\) | |||||||
\(398\) | 4.50000 | + | 13.8496i | 0.225565 | + | 0.694217i | ||||
\(399\) | −7.85410 | − | 5.70634i | −0.393197 | − | 0.285674i | ||||
\(400\) | 1.92705 | − | 1.40008i | 0.0963525 | − | 0.0700042i | ||||
\(401\) | 1.09017 | − | 3.35520i | 0.0544405 | − | 0.167551i | −0.920139 | − | 0.391591i | \(-0.871925\pi\) |
0.974580 | + | 0.224040i | \(0.0719248\pi\) | |||||||
\(402\) | −1.70820 | + | 5.25731i | −0.0851975 | + | 0.262211i | ||||
\(403\) | −4.00000 | + | 2.90617i | −0.199254 | + | 0.144767i | ||||
\(404\) | 11.7812 | + | 8.55951i | 0.586134 | + | 0.425851i | ||||
\(405\) | −5.50000 | − | 16.9273i | −0.273297 | − | 0.841122i | ||||
\(406\) | −50.8328 | −2.52279 | ||||||||
\(407\) | −4.94427 | − | 12.3107i | −0.245078 | − | 0.610220i | ||||
\(408\) | −6.76393 | −0.334865 | ||||||||
\(409\) | −1.56231 | − | 4.80828i | −0.0772511 | − | 0.237754i | 0.904972 | − | 0.425471i | \(-0.139891\pi\) |
−0.982223 | + | 0.187716i | \(0.939891\pi\) | |||||||
\(410\) | 6.23607 | + | 4.53077i | 0.307977 | + | 0.223759i | ||||
\(411\) | −6.32624 | + | 4.59628i | −0.312050 | + | 0.226718i | ||||
\(412\) | −1.47214 | + | 4.53077i | −0.0725269 | + | 0.223215i | ||||
\(413\) | 5.29180 | − | 16.2865i | 0.260392 | − | 0.801405i | ||||
\(414\) | 6.35410 | − | 4.61653i | 0.312287 | − | 0.226890i | ||||
\(415\) | 18.0623 | + | 13.1230i | 0.886644 | + | 0.644184i | ||||
\(416\) | 0.763932 | + | 2.35114i | 0.0374548 | + | 0.115274i | ||||
\(417\) | 20.6525 | 1.01136 | ||||||||
\(418\) | 2.80902 | + | 1.76336i | 0.137394 | + | 0.0862485i | ||||
\(419\) | −6.32624 | −0.309057 | −0.154528 | − | 0.987988i | \(-0.549386\pi\) | ||||
−0.154528 | + | 0.987988i | \(0.549386\pi\) | |||||||
\(420\) | 4.85410 | + | 14.9394i | 0.236856 | + | 0.728968i | ||||
\(421\) | −22.6525 | − | 16.4580i | −1.10401 | − | 0.802113i | −0.122304 | − | 0.992493i | \(-0.539028\pi\) |
−0.981711 | + | 0.190380i | \(0.939028\pi\) | |||||||
\(422\) | −12.4721 | + | 9.06154i | −0.607134 | + | 0.441109i | ||||
\(423\) | 0.427051 | − | 1.31433i | 0.0207639 | − | 0.0639048i | ||||
\(424\) | −1.47214 | + | 4.53077i | −0.0714932 | + | 0.220034i | ||||
\(425\) | 6.51722 | − | 4.73504i | 0.316132 | − | 0.229683i | ||||
\(426\) | 8.00000 | + | 5.81234i | 0.387601 | + | 0.281609i | ||||
\(427\) | 14.3435 | + | 44.1446i | 0.694129 | + | 2.13631i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | −13.8885 | − | 8.71851i | −0.670545 | − | 0.420934i | ||||
\(430\) | −14.7082 | −0.709293 | ||||||||
\(431\) | 0.0344419 | + | 0.106001i | 0.00165901 | + | 0.00510589i | 0.951883 | − | 0.306463i | \(-0.0991456\pi\) |
−0.950224 | + | 0.311569i | \(0.899146\pi\) | |||||||
\(432\) | −3.23607 | − | 2.35114i | −0.155695 | − | 0.113119i | ||||
\(433\) | −11.7082 | + | 8.50651i | −0.562660 | + | 0.408797i | −0.832432 | − | 0.554128i | \(-0.813052\pi\) |
0.269771 | + | 0.962924i | \(0.413052\pi\) | |||||||
\(434\) | −3.00000 | + | 9.23305i | −0.144005 | + | 0.443201i | ||||
\(435\) | −10.4721 | + | 32.2299i | −0.502100 | + | 1.54531i | ||||
\(436\) | −2.61803 | + | 1.90211i | −0.125381 | + | 0.0910947i | ||||
\(437\) | 6.35410 | + | 4.61653i | 0.303958 | + | 0.220838i | ||||
\(438\) | 8.65248 | + | 26.6296i | 0.413431 | + | 1.27241i | ||||
\(439\) | −17.1246 | −0.817313 | −0.408657 | − | 0.912688i | \(-0.634003\pi\) | ||||
−0.408657 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(440\) | −2.00000 | − | 4.97980i | −0.0953463 | − | 0.237402i | ||||
\(441\) | 16.5623 | 0.788681 | ||||||||
\(442\) | 2.58359 | + | 7.95148i | 0.122889 | + | 0.378213i | ||||
\(443\) | 30.1074 | + | 21.8743i | 1.43045 | + | 1.03928i | 0.989934 | + | 0.141532i | \(0.0452030\pi\) |
0.440512 | + | 0.897747i | \(0.354797\pi\) | |||||||
\(444\) | 6.47214 | − | 4.70228i | 0.307154 | − | 0.223160i | ||||
\(445\) | 5.61803 | − | 17.2905i | 0.266320 | − | 0.819650i | ||||
\(446\) | −3.00000 | + | 9.23305i | −0.142054 | + | 0.437198i | ||||
\(447\) | −18.6525 | + | 13.5518i | −0.882232 | + | 0.640979i | ||||
\(448\) | 3.92705 | + | 2.85317i | 0.185536 | + | 0.134800i | ||||
\(449\) | 4.38197 | + | 13.4863i | 0.206798 | + | 0.636458i | 0.999635 | + | 0.0270243i | \(0.00860316\pi\) |
−0.792837 | + | 0.609434i | \(0.791397\pi\) | |||||||
\(450\) | −2.38197 | −0.112287 | ||||||||
\(451\) | −12.1246 | + | 10.1311i | −0.570926 | + | 0.477055i | ||||
\(452\) | 5.52786 | 0.260009 | ||||||||
\(453\) | 8.47214 | + | 26.0746i | 0.398056 | + | 1.22509i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.7082 | − | 11.4127i | 0.736412 | − | 0.535035i | ||||
\(456\) | −0.618034 | + | 1.90211i | −0.0289421 | + | 0.0890746i | ||||
\(457\) | −7.91641 | + | 24.3642i | −0.370314 | + | 1.13971i | 0.576272 | + | 0.817258i | \(0.304507\pi\) |
−0.946586 | + | 0.322451i | \(0.895493\pi\) | |||||||
\(458\) | 7.50000 | − | 5.44907i | 0.350452 | − | 0.254618i | ||||
\(459\) | −10.9443 | − | 7.95148i | −0.510835 | − | 0.371143i | ||||
\(460\) | −3.92705 | − | 12.0862i | −0.183100 | − | 0.563523i | ||||
\(461\) | 29.7984 | 1.38785 | 0.693924 | − | 0.720048i | \(-0.255880\pi\) | ||||
0.693924 | + | 0.720048i | \(0.255880\pi\) | |||||||
\(462\) | −32.1246 | + | 2.17963i | −1.49457 | + | 0.101405i | ||||
\(463\) | −21.7984 | −1.01306 | −0.506528 | − | 0.862223i | \(-0.669071\pi\) | ||||
−0.506528 | + | 0.862223i | \(0.669071\pi\) | |||||||
\(464\) | 3.23607 | + | 9.95959i | 0.150231 | + | 0.462363i | ||||
\(465\) | 5.23607 | + | 3.80423i | 0.242817 | + | 0.176417i | ||||
\(466\) | −4.69098 | + | 3.40820i | −0.217306 | + | 0.157882i | ||||
\(467\) | 6.15248 | − | 18.9354i | 0.284703 | − | 0.876225i | −0.701785 | − | 0.712389i | \(-0.747613\pi\) |
0.986488 | − | 0.163836i | \(-0.0523867\pi\) | |||||||
\(468\) | 0.763932 | − | 2.35114i | 0.0353128 | − | 0.108682i | ||||
\(469\) | 10.8541 | − | 7.88597i | 0.501196 | − | 0.364140i | ||||
\(470\) | −1.80902 | − | 1.31433i | −0.0834437 | − | 0.0606254i | ||||
\(471\) | −14.4164 | − | 44.3691i | −0.664273 | − | 2.04442i | ||||
\(472\) | −3.52786 | −0.162383 | ||||||||
\(473\) | 7.35410 | − | 29.2380i | 0.338142 | − | 1.34436i | ||||
\(474\) | −7.41641 | −0.340647 | ||||||||
\(475\) | −0.736068 | − | 2.26538i | −0.0337731 | − | 0.103943i | ||||
\(476\) | 13.2812 | + | 9.64932i | 0.608741 | + | 0.442276i | ||||
\(477\) | 3.85410 | − | 2.80017i | 0.176467 | − | 0.128211i | ||||
\(478\) | 5.66312 | − | 17.4293i | 0.259025 | − | 0.797197i | ||||
\(479\) | 0.336881 | − | 1.03681i | 0.0153925 | − | 0.0473732i | −0.943065 | − | 0.332608i | \(-0.892071\pi\) |
0.958458 | + | 0.285235i | \(0.0920715\pi\) | |||||||
\(480\) | 2.61803 | − | 1.90211i | 0.119496 | − | 0.0868192i | ||||
\(481\) | −8.00000 | − | 5.81234i | −0.364769 | − | 0.265020i | ||||
\(482\) | 3.09017 | + | 9.51057i | 0.140753 | + | 0.433194i | ||||
\(483\) | −76.2492 | −3.46946 | ||||||||
\(484\) | 10.8992 | − | 1.48584i | 0.495418 | − | 0.0675382i | ||||
\(485\) | −14.9443 | −0.678584 | ||||||||
\(486\) | 3.09017 | + | 9.51057i | 0.140173 | + | 0.431408i | ||||
\(487\) | −8.09017 | − | 5.87785i | −0.366601 | − | 0.266351i | 0.389199 | − | 0.921154i | \(-0.372752\pi\) |
−0.755800 | + | 0.654803i | \(0.772752\pi\) | |||||||
\(488\) | 7.73607 | − | 5.62058i | 0.350195 | − | 0.254432i | ||||
\(489\) | 0.416408 | − | 1.28157i | 0.0188306 | − | 0.0579547i | ||||
\(490\) | 8.28115 | − | 25.4868i | 0.374104 | − | 1.15137i | ||||
\(491\) | 13.6353 | − | 9.90659i | 0.615350 | − | 0.447078i | −0.235944 | − | 0.971767i | \(-0.575818\pi\) |
0.851294 | + | 0.524688i | \(0.175818\pi\) | |||||||
\(492\) | −7.70820 | − | 5.60034i | −0.347513 | − | 0.252483i | ||||
\(493\) | 10.9443 | + | 33.6830i | 0.492905 | + | 1.51701i | ||||
\(494\) | 2.47214 | 0.111227 | ||||||||
\(495\) | −1.30902 | + | 5.20431i | −0.0588359 | + | 0.233916i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −7.41641 | − | 22.8254i | −0.332671 | − | 1.02386i | ||||
\(498\) | −22.3262 | − | 16.2210i | −1.00046 | − | 0.726879i | ||||
\(499\) | 2.07295 | − | 1.50609i | 0.0927979 | − | 0.0674217i | −0.540419 | − | 0.841396i | \(-0.681734\pi\) |
0.633217 | + | 0.773975i | \(0.281734\pi\) | |||||||
\(500\) | −3.69098 | + | 11.3597i | −0.165066 | + | 0.508020i | ||||
\(501\) | −0.875388 | + | 2.69417i | −0.0391095 | + | 0.120367i | ||||
\(502\) | −3.35410 | + | 2.43690i | −0.149701 | + | 0.108764i | ||||
\(503\) | −26.9443 | − | 19.5762i | −1.20139 | − | 0.872858i | −0.206965 | − | 0.978348i | \(-0.566359\pi\) |
−0.994420 | + | 0.105490i | \(0.966359\pi\) | |||||||
\(504\) | −1.50000 | − | 4.61653i | −0.0668153 | − | 0.205636i | ||||
\(505\) | −23.5623 | −1.04851 | ||||||||
\(506\) | 25.9894 | − | 1.76336i | 1.15537 | − | 0.0783907i | ||||
\(507\) | 13.7771 | 0.611862 | ||||||||
\(508\) | −6.00000 | − | 18.4661i | −0.266207 | − | 0.819301i | ||||
\(509\) | −27.2705 | − | 19.8132i | −1.20874 | − | 0.878204i | −0.213628 | − | 0.976915i | \(-0.568528\pi\) |
−0.995116 | + | 0.0987111i | \(0.968528\pi\) | |||||||
\(510\) | 8.85410 | − | 6.43288i | 0.392066 | − | 0.284853i | ||||
\(511\) | 21.0000 | − | 64.6314i | 0.928985 | − | 2.85912i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −3.23607 | + | 2.35114i | −0.142876 | + | 0.103805i | ||||
\(514\) | −5.61803 | − | 4.08174i | −0.247801 | − | 0.180038i | ||||
\(515\) | −2.38197 | − | 7.33094i | −0.104962 | − | 0.323040i | ||||
\(516\) | 18.1803 | 0.800345 | ||||||||
\(517\) | 3.51722 | − | 2.93893i | 0.154687 | − | 0.129254i | ||||
\(518\) | −19.4164 | −0.853108 | ||||||||
\(519\) | 12.9443 | + | 39.8384i | 0.568190 | + | 1.74871i | ||||
\(520\) | −3.23607 | − | 2.35114i | −0.141911 | − | 0.103104i | ||||
\(521\) | 16.3262 | − | 11.8617i | 0.715265 | − | 0.519671i | −0.169603 | − | 0.985513i | \(-0.554248\pi\) |
0.884868 | + | 0.465842i | \(0.154248\pi\) | |||||||
\(522\) | 3.23607 | − | 9.95959i | 0.141639 | − | 0.435920i | ||||
\(523\) | 3.43769 | − | 10.5801i | 0.150320 | − | 0.462637i | −0.847337 | − | 0.531056i | \(-0.821795\pi\) |
0.997657 | + | 0.0684189i | \(0.0217954\pi\) | |||||||
\(524\) | 9.78115 | − | 7.10642i | 0.427292 | − | 0.310446i | ||||
\(525\) | 18.7082 | + | 13.5923i | 0.816493 | + | 0.593217i | ||||
\(526\) | −0.763932 | − | 2.35114i | −0.0333090 | − | 0.102515i | ||||
\(527\) | 6.76393 | 0.294642 | ||||||||
\(528\) | 2.47214 | + | 6.15537i | 0.107586 | + | 0.267878i | ||||
\(529\) | 38.6869 | 1.68204 | ||||||||
\(530\) | −2.38197 | − | 7.33094i | −0.103466 | − | 0.318436i | ||||
\(531\) | 2.85410 | + | 2.07363i | 0.123857 | + | 0.0899877i | ||||
\(532\) | 3.92705 | − | 2.85317i | 0.170259 | − | 0.123701i | ||||
\(533\) | −3.63932 | + | 11.2007i | −0.157636 | + | 0.485155i | ||||
\(534\) | −6.94427 | + | 21.3723i | −0.300508 | + | 0.924869i | ||||
\(535\) | −7.85410 | + | 5.70634i | −0.339562 | + | 0.246707i | ||||
\(536\) | −2.23607 | − | 1.62460i | −0.0965834 | − | 0.0701720i | ||||
\(537\) | −1.34752 | − | 4.14725i | −0.0581500 | − | 0.178967i | ||||
\(538\) | −12.6525 | −0.545487 | ||||||||
\(539\) | 46.5238 | + | 29.2052i | 2.00392 | + | 1.25796i | ||||
\(540\) | 6.47214 | 0.278516 | ||||||||
\(541\) | 10.4615 | + | 32.1972i | 0.449775 | + | 1.38426i | 0.877162 | + | 0.480195i | \(0.159434\pi\) |
−0.427387 | + | 0.904069i | \(0.640566\pi\) | |||||||
\(542\) | −16.3541 | − | 11.8820i | −0.702469 | − | 0.510373i | ||||
\(543\) | −0.472136 | + | 0.343027i | −0.0202613 | + | 0.0147207i | ||||
\(544\) | 1.04508 | − | 3.21644i | 0.0448076 | − | 0.137904i | ||||
\(545\) | 1.61803 | − | 4.97980i | 0.0693090 | − | 0.213311i | ||||
\(546\) | −19.4164 | + | 14.1068i | −0.830946 | + | 0.603717i | ||||
\(547\) | −15.9443 | − | 11.5842i | −0.681728 | − | 0.495304i | 0.192203 | − | 0.981355i | \(-0.438437\pi\) |
−0.873930 | + | 0.486051i | \(0.838437\pi\) | |||||||
\(548\) | −1.20820 | − | 3.71847i | −0.0516119 | − | 0.158845i | ||||
\(549\) | −9.56231 | −0.408109 | ||||||||
\(550\) | −6.69098 | − | 4.20025i | −0.285304 | − | 0.179099i | ||||
\(551\) | 10.4721 | 0.446128 | ||||||||
\(552\) | 4.85410 | + | 14.9394i | 0.206604 | + | 0.635863i | ||||
\(553\) | 14.5623 | + | 10.5801i | 0.619252 | + | 0.449913i | ||||
\(554\) | 10.0902 | − | 7.33094i | 0.428690 | − | 0.311462i | ||||
\(555\) | −4.00000 | + | 12.3107i | −0.169791 | + | 0.522562i | ||||
\(556\) | −3.19098 | + | 9.82084i | −0.135328 | + | 0.416496i | ||||
\(557\) | 16.5451 | − | 12.0207i | 0.701038 | − | 0.509334i | −0.179232 | − | 0.983807i | \(-0.557361\pi\) |
0.880270 | + | 0.474473i | \(0.157361\pi\) | |||||||
\(558\) | −1.61803 | − | 1.17557i | −0.0684968 | − | 0.0497659i | ||||
\(559\) | −6.94427 | − | 21.3723i | −0.293711 | − | 0.903951i | ||||
\(560\) | −7.85410 | −0.331896 | ||||||||
\(561\) | 8.36068 | + | 20.8172i | 0.352988 | + | 0.878905i | ||||
\(562\) | −26.6525 | −1.12427 | ||||||||
\(563\) | 1.14590 | + | 3.52671i | 0.0482938 | + | 0.148633i | 0.972295 | − | 0.233756i | \(-0.0751015\pi\) |
−0.924002 | + | 0.382389i | \(0.875102\pi\) | |||||||
\(564\) | 2.23607 | + | 1.62460i | 0.0941554 | + | 0.0684079i | ||||
\(565\) | −7.23607 | + | 5.25731i | −0.304424 | + | 0.221177i | ||||
\(566\) | 3.26393 | − | 10.0453i | 0.137193 | − | 0.422238i | ||||
\(567\) | 16.5000 | − | 50.7818i | 0.692935 | − | 2.13263i | ||||
\(568\) | −4.00000 | + | 2.90617i | −0.167836 | + | 0.121940i | ||||
\(569\) | −11.8541 | − | 8.61251i | −0.496950 | − | 0.361055i | 0.310901 | − | 0.950442i | \(-0.399369\pi\) |
−0.807851 | + | 0.589387i | \(0.799369\pi\) | |||||||
\(570\) | −1.00000 | − | 3.07768i | −0.0418854 | − | 0.128910i | ||||
\(571\) | 12.8541 | 0.537927 | 0.268964 | − | 0.963150i | \(-0.413319\pi\) | ||||
0.268964 | + | 0.963150i | \(0.413319\pi\) | |||||||
\(572\) | 6.29180 | − | 5.25731i | 0.263073 | − | 0.219819i | ||||
\(573\) | −10.0689 | −0.420634 | ||||||||
\(574\) | 7.14590 | + | 21.9928i | 0.298264 | + | 0.917962i | ||||
\(575\) | −15.1353 | − | 10.9964i | −0.631184 | − | 0.458582i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 1.09017 | − | 3.35520i | 0.0453844 | − | 0.139679i | −0.925797 | − | 0.378022i | \(-0.876604\pi\) |
0.971181 | + | 0.238343i | \(0.0766043\pi\) | |||||||
\(578\) | −1.71885 | + | 5.29007i | −0.0714946 | + | 0.220038i | ||||
\(579\) | 30.9443 | − | 22.4823i | 1.28600 | − | 0.934334i | ||||
\(580\) | −13.7082 | − | 9.95959i | −0.569202 | − | 0.413550i | ||||
\(581\) | 20.6976 | + | 63.7005i | 0.858680 | + | 2.64274i | ||||
\(582\) | 18.4721 | 0.765695 | ||||||||
\(583\) | 15.7639 | − | 1.06957i | 0.652875 | − | 0.0442970i | ||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 1.23607 | + | 3.80423i | 0.0511051 | + | 0.157285i | ||||
\(586\) | 24.7984 | + | 18.0171i | 1.02441 | + | 0.744278i | ||||
\(587\) | −8.94427 | + | 6.49839i | −0.369170 | + | 0.268217i | −0.756867 | − | 0.653569i | \(-0.773271\pi\) |
0.387697 | + | 0.921787i | \(0.373271\pi\) | |||||||
\(588\) | −10.2361 | + | 31.5034i | −0.422128 | + | 1.29918i | ||||
\(589\) | 0.618034 | − | 1.90211i | 0.0254656 | − | 0.0783752i | ||||
\(590\) | 4.61803 | − | 3.35520i | 0.190121 | − | 0.138131i | ||||
\(591\) | −29.1246 | − | 21.1603i | −1.19803 | − | 0.870417i | ||||
\(592\) | 1.23607 | + | 3.80423i | 0.0508021 | + | 0.156353i | ||||
\(593\) | 11.4508 | 0.470230 | 0.235115 | − | 0.971968i | \(-0.424453\pi\) | ||||
0.235115 | + | 0.971968i | \(0.424453\pi\) | |||||||
\(594\) | −3.23607 | + | 12.8658i | −0.132777 | + | 0.527889i | ||||
\(595\) | −26.5623 | −1.08895 | ||||||||
\(596\) | −3.56231 | − | 10.9637i | −0.145918 | − | 0.449089i | ||||
\(597\) | 23.5623 | + | 17.1190i | 0.964341 | + | 0.700635i | ||||
\(598\) | 15.7082 | − | 11.4127i | 0.642356 | − | 0.466699i | ||||
\(599\) | −10.3820 | + | 31.9524i | −0.424196 | + | 1.30554i | 0.479567 | + | 0.877505i | \(0.340794\pi\) |
−0.903762 | + | 0.428035i | \(0.859206\pi\) | |||||||
\(600\) | 1.47214 | − | 4.53077i | 0.0600997 | − | 0.184968i | ||||
\(601\) | −14.7984 | + | 10.7516i | −0.603638 | + | 0.438569i | −0.847168 | − | 0.531324i | \(-0.821695\pi\) |
0.243530 | + | 0.969893i | \(0.421695\pi\) | |||||||
\(602\) | −35.6976 | − | 25.9358i | −1.45492 | − | 1.05706i | ||||
\(603\) | 0.854102 | + | 2.62866i | 0.0347817 | + | 0.107047i | ||||
\(604\) | −13.7082 | −0.557779 | ||||||||
\(605\) | −12.8541 | + | 12.3107i | −0.522594 | + | 0.500503i | ||||
\(606\) | 29.1246 | 1.18311 | ||||||||
\(607\) | 2.18034 | + | 6.71040i | 0.0884973 | + | 0.272367i | 0.985505 | − | 0.169649i | \(-0.0542635\pi\) |
−0.897007 | + | 0.442016i | \(0.854263\pi\) | |||||||
\(608\) | −0.809017 | − | 0.587785i | −0.0328100 | − | 0.0238378i | ||||
\(609\) | −82.2492 | + | 59.7576i | −3.33291 | + | 2.42150i | ||||
\(610\) | −4.78115 | + | 14.7149i | −0.193583 | + | 0.595788i | ||||
\(611\) | 1.05573 | − | 3.24920i | 0.0427102 | − | 0.131448i | ||||
\(612\) | −2.73607 | + | 1.98787i | −0.110599 | + | 0.0803549i | ||||
\(613\) | 33.3885 | + | 24.2582i | 1.34855 | + | 0.979779i | 0.999082 | + | 0.0428311i | \(0.0136377\pi\) |
0.349468 | + | 0.936948i | \(0.386362\pi\) | |||||||
\(614\) | −0.180340 | − | 0.555029i | −0.00727793 | − | 0.0223992i | ||||
\(615\) | 15.4164 | 0.621650 | ||||||||
\(616\) | 3.92705 | − | 15.6129i | 0.158225 | − | 0.629063i | ||||
\(617\) | −46.7214 | −1.88093 | −0.940466 | − | 0.339889i | \(-0.889610\pi\) | ||||
−0.940466 | + | 0.339889i | \(0.889610\pi\) | |||||||
\(618\) | 2.94427 | + | 9.06154i | 0.118436 | + | 0.364508i | ||||
\(619\) | 6.11803 | + | 4.44501i | 0.245905 | + | 0.178660i | 0.703910 | − | 0.710289i | \(-0.251436\pi\) |
−0.458005 | + | 0.888949i | \(0.651436\pi\) | |||||||
\(620\) | −2.61803 | + | 1.90211i | −0.105143 | + | 0.0763907i | ||||
\(621\) | −9.70820 | + | 29.8788i | −0.389577 | + | 1.19899i | ||||
\(622\) | −8.89919 | + | 27.3889i | −0.356825 | + | 1.09819i | ||||
\(623\) | 44.1246 | − | 32.0584i | 1.76782 | − | 1.28439i | ||||
\(624\) | 4.00000 | + | 2.90617i | 0.160128 | + | 0.116340i | ||||
\(625\) | −2.29180 | − | 7.05342i | −0.0916718 | − | 0.282137i | ||||
\(626\) | 11.0902 | 0.443252 | ||||||||
\(627\) | 6.61803 | − | 0.449028i | 0.264299 | − | 0.0179325i | ||||
\(628\) | 23.3262 | 0.930818 | ||||||||
\(629\) | 4.18034 | + | 12.8658i | 0.166681 | + | 0.512992i | ||||
\(630\) | 6.35410 | + | 4.61653i | 0.253153 | + | 0.183927i | ||||
\(631\) | −16.4721 | + | 11.9677i | −0.655745 | + | 0.476427i | −0.865223 | − | 0.501386i | \(-0.832824\pi\) |
0.209478 | + | 0.977813i | \(0.432824\pi\) | |||||||
\(632\) | 1.14590 | − | 3.52671i | 0.0455814 | − | 0.140285i | ||||
\(633\) | −9.52786 | + | 29.3238i | −0.378699 | + | 1.16551i | ||||
\(634\) | 16.3262 | − | 11.8617i | 0.648398 | − | 0.471089i | ||||
\(635\) | 25.4164 | + | 18.4661i | 1.00862 | + | 0.732805i | ||||
\(636\) | 2.94427 | + | 9.06154i | 0.116748 | + | 0.359313i | ||||
\(637\) | 40.9443 | 1.62227 | ||||||||
\(638\) | 26.6525 | − | 22.2703i | 1.05518 | − | 0.881691i | ||||
\(639\) | 4.94427 | 0.195592 | ||||||||
\(640\) | 0.500000 | + | 1.53884i | 0.0197642 | + | 0.0608281i | ||||
\(641\) | 33.4164 | + | 24.2784i | 1.31987 | + | 0.958941i | 0.999934 | + | 0.0115013i | \(0.00366104\pi\) |
0.319935 | + | 0.947440i | \(0.396339\pi\) | |||||||
\(642\) | 9.70820 | − | 7.05342i | 0.383152 | − | 0.278376i | ||||
\(643\) | −13.5729 | + | 41.7732i | −0.535265 | + | 1.64738i | 0.207811 | + | 0.978169i | \(0.433366\pi\) |
−0.743076 | + | 0.669207i | \(0.766634\pi\) | |||||||
\(644\) | 11.7812 | − | 36.2587i | 0.464242 | − | 1.42879i | ||||
\(645\) | −23.7984 | + | 17.2905i | −0.937060 | + | 0.680814i | ||||
\(646\) | −2.73607 | − | 1.98787i | −0.107649 | − | 0.0782117i | ||||
\(647\) | −3.70820 | − | 11.4127i | −0.145785 | − | 0.448679i | 0.851327 | − | 0.524636i | \(-0.175799\pi\) |
−0.997111 | + | 0.0759575i | \(0.975799\pi\) | |||||||
\(648\) | −11.0000 | −0.432121 | ||||||||
\(649\) | 4.36068 | + | 10.8576i | 0.171172 | + | 0.426200i | ||||
\(650\) | −5.88854 | −0.230968 | ||||||||
\(651\) | 6.00000 | + | 18.4661i | 0.235159 | + | 0.723744i | ||||
\(652\) | 0.545085 | + | 0.396027i | 0.0213472 | + | 0.0155096i | ||||
\(653\) | −0.500000 | + | 0.363271i | −0.0195665 | + | 0.0142159i | −0.597526 | − | 0.801850i | \(-0.703849\pi\) |
0.577959 | + | 0.816066i | \(0.303849\pi\) | |||||||
\(654\) | −2.00000 | + | 6.15537i | −0.0782062 | + | 0.240694i | ||||
\(655\) | −6.04508 | + | 18.6049i | −0.236201 | + | 0.726952i | ||||
\(656\) | 3.85410 | − | 2.80017i | 0.150477 | − | 0.109328i | ||||
\(657\) | 11.3262 | + | 8.22899i | 0.441879 | + | 0.321044i | ||||
\(658\) | −2.07295 | − | 6.37988i | −0.0808120 | − | 0.248714i | ||||
\(659\) | 33.7082 | 1.31309 | 0.656543 | − | 0.754289i | \(-0.272018\pi\) | ||||
0.656543 | + | 0.754289i | \(0.272018\pi\) | |||||||
\(660\) | −9.09017 | − | 5.70634i | −0.353834 | − | 0.222119i | ||||
\(661\) | −29.5967 | −1.15118 | −0.575590 | − | 0.817738i | \(-0.695228\pi\) | ||||
−0.575590 | + | 0.817738i | \(0.695228\pi\) | |||||||
\(662\) | 1.14590 | + | 3.52671i | 0.0445366 | + | 0.137070i | ||||
\(663\) | 13.5279 | + | 9.82857i | 0.525379 | + | 0.381710i | ||||
\(664\) | 11.1631 | − | 8.11048i | 0.433213 | − | 0.314748i | ||||
\(665\) | −2.42705 | + | 7.46969i | −0.0941170 | + | 0.289662i | ||||
\(666\) | 1.23607 | − | 3.80423i | 0.0478967 | − | 0.147411i | ||||
\(667\) | 66.5410 | − | 48.3449i | 2.57648 | − | 1.87192i | ||||
\(668\) | −1.14590 | − | 0.832544i | −0.0443361 | − | 0.0322121i | ||||
\(669\) | 6.00000 | + | 18.4661i | 0.231973 | + | 0.713941i | ||||
\(670\) | 4.47214 | 0.172774 | ||||||||
\(671\) | −26.8607 | − | 16.8617i | −1.03695 | − | 0.650941i | ||||
\(672\) | 9.70820 | 0.374502 | ||||||||
\(673\) | 9.58359 | + | 29.4953i | 0.369420 | + | 1.13696i | 0.947166 | + | 0.320742i | \(0.103932\pi\) |
−0.577746 | + | 0.816217i | \(0.696068\pi\) | |||||||
\(674\) | 28.2705 | + | 20.5397i | 1.08894 | + | 0.791161i | ||||
\(675\) | 7.70820 | − | 5.60034i | 0.296689 | − | 0.215557i | ||||
\(676\) | −2.12868 | + | 6.55139i | −0.0818722 | + | 0.251977i | ||||
\(677\) | 6.27051 | − | 19.2986i | 0.240995 | − | 0.741707i | −0.755274 | − | 0.655409i | \(-0.772496\pi\) |
0.996269 | − | 0.0862981i | \(-0.0275038\pi\) | |||||||
\(678\) | 8.94427 | − | 6.49839i | 0.343503 | − | 0.249569i | ||||
\(679\) | −36.2705 | − | 26.3521i | −1.39193 | − | 1.01130i | ||||
\(680\) | 1.69098 | + | 5.20431i | 0.0648462 | + | 0.199576i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.47214 | − | 6.15537i | −0.0946630 | − | 0.235701i | ||||
\(683\) | 38.0689 | 1.45667 | 0.728333 | − | 0.685224i | \(-0.240296\pi\) | ||||
0.728333 | + | 0.685224i | \(0.240296\pi\) | |||||||
\(684\) | 0.309017 | + | 0.951057i | 0.0118156 | + | 0.0363646i | ||||
\(685\) | 5.11803 | + | 3.71847i | 0.195550 | + | 0.142075i | ||||
\(686\) | 37.5517 | − | 27.2829i | 1.43373 | − | 1.04167i | ||||
\(687\) | 5.72949 | − | 17.6336i | 0.218594 | − | 0.672762i | ||||
\(688\) | −2.80902 | + | 8.64527i | −0.107093 | + | 0.329598i | ||||
\(689\) | 9.52786 | − | 6.92240i | 0.362983 | − | 0.263722i | ||||
\(690\) | −20.5623 | − | 14.9394i | −0.782794 | − | 0.568733i | ||||
\(691\) | −1.44427 | − | 4.44501i | −0.0549427 | − | 0.169096i | 0.919820 | − | 0.392342i | \(-0.128335\pi\) |
−0.974762 | + | 0.223245i | \(0.928335\pi\) | |||||||
\(692\) | −20.9443 | −0.796182 | ||||||||
\(693\) | −12.3541 | + | 10.3229i | −0.469294 | + | 0.392133i | ||||
\(694\) | −11.5623 | −0.438899 | ||||||||
\(695\) | −5.16312 | − | 15.8904i | −0.195848 | − | 0.602759i | ||||
\(696\) | 16.9443 | + | 12.3107i | 0.642271 | + | 0.466637i | ||||
\(697\) | 13.0344 | − | 9.47008i | 0.493715 | − | 0.358705i | ||||
\(698\) | −8.02786 | + | 24.7072i | −0.303859 | + | 0.935182i | ||||
\(699\) | −3.58359 | + | 11.0292i | −0.135544 | + | 0.417161i | ||||
\(700\) | −9.35410 | + | 6.79615i | −0.353552 | + | 0.256870i | ||||
\(701\) | 22.4443 | + | 16.3067i | 0.847708 | + | 0.615896i | 0.924513 | − | 0.381150i | \(-0.124472\pi\) |
−0.0768048 | + | 0.997046i | \(0.524472\pi\) | |||||||
\(702\) | 3.05573 | + | 9.40456i | 0.115331 | + | 0.354952i | ||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | −3.30902 | + | 0.224514i | −0.124713 | + | 0.00846169i | ||||
\(705\) | −4.47214 | −0.168430 | ||||||||
\(706\) | 5.44427 | + | 16.7557i | 0.204898 | + | 0.630611i | ||||
\(707\) | −57.1869 | − | 41.5487i | −2.15074 | − | 1.56260i | ||||
\(708\) | −5.70820 | + | 4.14725i | −0.214527 | + | 0.155863i | ||||
\(709\) | 9.20820 | − | 28.3399i | 0.345821 | − | 1.06433i | −0.615321 | − | 0.788276i | \(-0.710974\pi\) |
0.961143 | − | 0.276052i | \(-0.0890263\pi\) | |||||||
\(710\) | 2.47214 | − | 7.60845i | 0.0927776 | − | 0.285540i | ||||
\(711\) | −3.00000 | + | 2.17963i | −0.112509 | + | 0.0817424i | ||||
\(712\) | −9.09017 | − | 6.60440i | −0.340669 | − | 0.247510i | ||||
\(713\) | −4.85410 | − | 14.9394i | −0.181788 | − | 0.559485i | ||||
\(714\) | 32.8328 | 1.22874 | ||||||||
\(715\) | −3.23607 | + | 12.8658i | −0.121022 | + | 0.481152i | ||||
\(716\) | 2.18034 | 0.0814831 | ||||||||
\(717\) | −11.3262 | − | 34.8586i | −0.422986 | − | 1.30182i | ||||
\(718\) | −4.11803 | − | 2.99193i | −0.153684 | − | 0.111658i | ||||
\(719\) | 3.78115 | − | 2.74717i | 0.141013 | − | 0.102452i | −0.515042 | − | 0.857165i | \(-0.672224\pi\) |
0.656055 | + | 0.754713i | \(0.272224\pi\) | |||||||
\(720\) | 0.500000 | − | 1.53884i | 0.0186339 | − | 0.0573492i | ||||
\(721\) | 7.14590 | − | 21.9928i | 0.266127 | − | 0.819055i | ||||
\(722\) | −0.809017 | + | 0.587785i | −0.0301085 | + | 0.0218751i | ||||
\(723\) | 16.1803 | + | 11.7557i | 0.601753 | + | 0.437199i | ||||
\(724\) | −0.0901699 | − | 0.277515i | −0.00335114 | − | 0.0103137i | ||||
\(725\) | −24.9443 | −0.926407 | ||||||||
\(726\) | 15.8885 | − | 15.2169i | 0.589679 | − | 0.564752i | ||||
\(727\) | 12.1459 | 0.450466 | 0.225233 | − | 0.974305i | \(-0.427686\pi\) | ||||
0.225233 | + | 0.974305i | \(0.427686\pi\) | |||||||
\(728\) | −3.70820 | − | 11.4127i | −0.137435 | − | 0.422982i | ||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | 18.3262 | − | 13.3148i | 0.678284 | − | 0.492803i | ||||
\(731\) | −9.50000 | + | 29.2380i | −0.351370 | + | 1.08141i | ||||
\(732\) | 5.90983 | − | 18.1886i | 0.218434 | − | 0.672270i | ||||
\(733\) | −23.1976 | + | 16.8540i | −0.856821 | + | 0.622517i | −0.927018 | − | 0.375016i | \(-0.877637\pi\) |
0.0701969 | + | 0.997533i | \(0.477637\pi\) | |||||||
\(734\) | 1.16312 | + | 0.845055i | 0.0429315 | + | 0.0311916i | ||||
\(735\) | −16.5623 | − | 50.9735i | −0.610910 | − | 1.88019i | ||||
\(736\) | −7.85410 | −0.289506 | ||||||||
\(737\) | −2.23607 | + | 8.89002i | −0.0823666 | + | 0.327468i | ||||
\(738\) | −4.76393 | −0.175363 | ||||||||
\(739\) | 3.84752 | + | 11.8415i | 0.141533 | + | 0.435595i | 0.996549 | − | 0.0830073i | \(-0.0264525\pi\) |
−0.855015 | + | 0.518602i | \(0.826452\pi\) | |||||||
\(740\) | −5.23607 | − | 3.80423i | −0.192482 | − | 0.139846i | ||||
\(741\) | 4.00000 | − | 2.90617i | 0.146944 | − | 0.106761i | ||||
\(742\) | 7.14590 | − | 21.9928i | 0.262334 | − | 0.807382i | ||||
\(743\) | −0.819660 | + | 2.52265i | −0.0300704 | + | 0.0925472i | −0.964965 | − | 0.262377i | \(-0.915493\pi\) |
0.934895 | + | 0.354925i | \(0.115493\pi\) | |||||||
\(744\) | 3.23607 | − | 2.35114i | 0.118640 | − | 0.0861970i | ||||
\(745\) | 15.0902 | + | 10.9637i | 0.552861 | + | 0.401677i | ||||
\(746\) | 4.43769 | + | 13.6578i | 0.162476 | + | 0.500048i | ||||
\(747\) | −13.7984 | −0.504856 | ||||||||
\(748\) | −11.1910 | + | 0.759299i | −0.409183 | + | 0.0277627i | ||||
\(749\) | −29.1246 | −1.06419 | ||||||||
\(750\) | 7.38197 | + | 22.7194i | 0.269551 | + | 0.829594i | ||||
\(751\) | 8.56231 | + | 6.22088i | 0.312443 | + | 0.227003i | 0.732944 | − | 0.680289i | \(-0.238146\pi\) |
−0.420501 | + | 0.907292i | \(0.638146\pi\) | |||||||
\(752\) | −1.11803 | + | 0.812299i | −0.0407705 | + | 0.0296215i | ||||
\(753\) | −2.56231 | + | 7.88597i | −0.0933756 | + | 0.287381i | ||||
\(754\) | 8.00000 | − | 24.6215i | 0.291343 | − | 0.896661i | ||||
\(755\) | 17.9443 | − | 13.0373i | 0.653059 | − | 0.474475i | ||||
\(756\) | 15.7082 | + | 11.4127i | 0.571302 | + | 0.415075i | ||||
\(757\) | −7.85410 | − | 24.1724i | −0.285462 | − | 0.878562i | −0.986260 | − | 0.165202i | \(-0.947172\pi\) |
0.700798 | − | 0.713360i | \(-0.252828\pi\) | |||||||
\(758\) | −3.23607 | −0.117539 | ||||||||
\(759\) | 39.9787 | − | 33.4055i | 1.45114 | − | 1.21254i | ||||
\(760\) | 1.61803 | 0.0586923 | ||||||||
\(761\) | −3.49342 | − | 10.7516i | −0.126636 | − | 0.389747i | 0.867559 | − | 0.497334i | \(-0.165688\pi\) |
−0.994196 | + | 0.107587i | \(0.965688\pi\) | |||||||
\(762\) | −31.4164 | − | 22.8254i | −1.13810 | − | 0.826875i | ||||
\(763\) | 12.7082 | − | 9.23305i | 0.460068 | − | 0.334259i | ||||
\(764\) | 1.55573 | − | 4.78804i | 0.0562843 | − | 0.173225i | ||||
\(765\) | 1.69098 | − | 5.20431i | 0.0611376 | − | 0.188162i | ||||
\(766\) | 2.38197 | − | 1.73060i | 0.0860639 | − | 0.0625291i | ||||
\(767\) | 7.05573 | + | 5.12629i | 0.254768 | + | 0.185099i | ||||
\(768\) | −0.618034 | − | 1.90211i | −0.0223014 | − | 0.0686366i | ||||
\(769\) | −3.50658 | −0.126450 | −0.0632252 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632252 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(770\) | 9.70820 | + | 24.1724i | 0.349859 | + | 0.871114i | ||||
\(771\) | −13.8885 | −0.500184 | ||||||||
\(772\) | 5.90983 | + | 18.1886i | 0.212699 | + | 0.654622i | ||||
\(773\) | −12.6180 | − | 9.16754i | −0.453839 | − | 0.329733i | 0.337271 | − | 0.941408i | \(-0.390496\pi\) |
−0.791110 | + | 0.611674i | \(0.790496\pi\) | |||||||
\(774\) | 7.35410 | − | 5.34307i | 0.264338 | − | 0.192053i | ||||
\(775\) | −1.47214 | + | 4.53077i | −0.0528807 | + | 0.162750i | ||||
\(776\) | −2.85410 | + | 8.78402i | −0.102456 | + | 0.315328i | ||||
\(777\) | −31.4164 | + | 22.8254i | −1.12706 | + | 0.818855i | ||||
\(778\) | 12.9721 | + | 9.42481i | 0.465074 | + | 0.337896i | ||||
\(779\) | −1.47214 | − | 4.53077i | −0.0527447 | − | 0.162332i | ||||
\(780\) | −8.00000 | −0.286446 | ||||||||
\(781\) | 13.8885 | + | 8.71851i | 0.496971 | + | 0.311973i | ||||
\(782\) | −26.5623 | −0.949866 | ||||||||
\(783\) | 12.9443 | + | 39.8384i | 0.462591 | + | 1.42371i | ||||
\(784\) | −13.3992 | − | 9.73508i | −0.478542 | − | 0.347681i | ||||
\(785\) | −30.5344 | + | 22.1846i | −1.08982 | + | 0.791801i | ||||
\(786\) | 7.47214 | − | 22.9969i | 0.266522 | − | 0.820271i | ||||
\(787\) | −7.74265 | + | 23.8294i | −0.275996 | + | 0.849427i | 0.712959 | + | 0.701206i | \(0.247355\pi\) |
−0.988954 | + | 0.148221i | \(0.952645\pi\) | |||||||
\(788\) | 14.5623 | − | 10.5801i | 0.518761 | − | 0.376902i | ||||
\(789\) | −4.00000 | − | 2.90617i | −0.142404 | − | 0.103462i | ||||
\(790\) | 1.85410 | + | 5.70634i | 0.0659660 | + | 0.203022i | ||||
\(791\) | −26.8328 | −0.954065 | ||||||||
\(792\) | 2.80902 | + | 1.76336i | 0.0998141 | + | 0.0626581i | ||||
\(793\) | −23.6393 | −0.839457 | ||||||||
\(794\) | 4.37132 | + | 13.4535i | 0.155132 | + | 0.477449i | ||||
\(795\) | −12.4721 | − | 9.06154i | −0.442341 | − | 0.321380i | ||||
\(796\) | −11.7812 | + | 8.55951i | −0.417572 | + | 0.303384i | ||||
\(797\) | 5.49342 | − | 16.9070i | 0.194587 | − | 0.598877i | −0.805394 | − | 0.592740i | \(-0.798046\pi\) |
0.999981 | − | 0.00613760i | \(-0.00195367\pi\) | |||||||
\(798\) | 3.00000 | − | 9.23305i | 0.106199 | − | 0.326846i | ||||
\(799\) | −3.78115 | + | 2.74717i | −0.133768 | + | 0.0971878i | ||||
\(800\) | 1.92705 | + | 1.40008i | 0.0681315 | + | 0.0495005i | ||||
\(801\) | 3.47214 | + | 10.6861i | 0.122682 | + | 0.377576i | ||||
\(802\) | 3.52786 | 0.124573 | ||||||||
\(803\) | 17.3050 | + | 43.0876i | 0.610678 | + | 1.52053i | ||||
\(804\) | −5.52786 | −0.194953 | ||||||||
\(805\) | 19.0623 | + | 58.6677i | 0.671858 | + | 2.06777i | ||||
\(806\) | −4.00000 | − | 2.90617i | −0.140894 | − | 0.102365i | ||||
\(807\) | −20.4721 | + | 14.8739i | −0.720653 | + | 0.523585i | ||||
\(808\) | −4.50000 | + | 13.8496i | −0.158309 | + | 0.487226i | ||||
\(809\) | −4.50000 | + | 13.8496i | −0.158212 | + | 0.486925i | −0.998472 | − | 0.0552577i | \(-0.982402\pi\) |
0.840261 | + | 0.542183i | \(0.182402\pi\) | |||||||
\(810\) | 14.3992 | − | 10.4616i | 0.505936 | − | 0.367584i | ||||
\(811\) | −32.5623 | − | 23.6579i | −1.14342 | − | 0.830741i | −0.155826 | − | 0.987785i | \(-0.549804\pi\) |
−0.987592 | + | 0.157043i | \(0.949804\pi\) | |||||||
\(812\) | −15.7082 | − | 48.3449i | −0.551250 | − | 1.69657i | ||||
\(813\) | −40.4296 | −1.41793 | ||||||||
\(814\) | 10.1803 | − | 8.50651i | 0.356821 | − | 0.298153i | ||||
\(815\) | −1.09017 | −0.0381870 | ||||||||
\(816\) | −2.09017 | − | 6.43288i | −0.0731706 | − | 0.225196i | ||||
\(817\) | 7.35410 | + | 5.34307i | 0.257287 | + | 0.186930i | ||||
\(818\) | 4.09017 | − | 2.97168i | 0.143009 | − | 0.103902i | ||||
\(819\) | −3.70820 | + | 11.4127i | −0.129575 | + | 0.398791i | ||||
\(820\) | −2.38197 | + | 7.33094i | −0.0831819 | + | 0.256007i | ||||
\(821\) | −12.2082 | + | 8.86978i | −0.426069 | + | 0.309557i | −0.780075 | − | 0.625686i | \(-0.784819\pi\) |
0.354006 | + | 0.935243i | \(0.384819\pi\) | |||||||
\(822\) | −6.32624 | − | 4.59628i | −0.220653 | − | 0.160314i | ||||
\(823\) | 2.20820 | + | 6.79615i | 0.0769732 | + | 0.236899i | 0.982138 | − | 0.188161i | \(-0.0602528\pi\) |
−0.905165 | + | 0.425060i | \(0.860253\pi\) | |||||||
\(824\) | −4.76393 | −0.165959 | ||||||||
\(825\) | −15.7639 | + | 1.06957i | −0.548830 | + | 0.0372376i | ||||
\(826\) | 17.1246 | 0.595841 | ||||||||
\(827\) | −16.1459 | − | 49.6920i | −0.561448 | − | 1.72796i | −0.678276 | − | 0.734807i | \(-0.737273\pi\) |
0.116829 | − | 0.993152i | \(-0.462727\pi\) | |||||||
\(828\) | 6.35410 | + | 4.61653i | 0.220820 | + | 0.160435i | ||||
\(829\) | −28.1803 | + | 20.4742i | −0.978744 | + | 0.711099i | −0.957427 | − | 0.288674i | \(-0.906786\pi\) |
−0.0213162 | + | 0.999773i | \(0.506786\pi\) | |||||||
\(830\) | −6.89919 | + | 21.2335i | −0.239474 | + | 0.737026i | ||||
\(831\) | 7.70820 | − | 23.7234i | 0.267395 | − | 0.822956i | ||||
\(832\) | −2.00000 | + | 1.45309i | −0.0693375 | + | 0.0503767i | ||||
\(833\) | −45.3156 | − | 32.9237i | −1.57009 | − | 1.14074i | ||||
\(834\) | 6.38197 | + | 19.6417i | 0.220989 | + | 0.680135i | ||||
\(835\) | 2.29180 | 0.0793109 | ||||||||
\(836\) | −0.809017 | + | 3.21644i | −0.0279804 | + | 0.111243i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −1.95492 | − | 6.01661i | −0.0675314 | − | 0.207840i | ||||
\(839\) | 1.47214 | + | 1.06957i | 0.0508238 | + | 0.0369256i | 0.612907 | − | 0.790155i | \(-0.290000\pi\) |
−0.562083 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(840\) | −12.7082 | + | 9.23305i | −0.438475 | + | 0.318571i | ||||
\(841\) | 24.9271 | − | 76.7176i | 0.859553 | − | 2.64543i | ||||
\(842\) | 8.65248 | − | 26.6296i | 0.298184 | − | 0.917716i | ||||
\(843\) | −43.1246 | + | 31.3319i | −1.48529 | + | 1.07913i | ||||
\(844\) | −12.4721 | − | 9.06154i | −0.429309 | − | 0.311911i | ||||
\(845\) | −3.44427 | − | 10.6004i | −0.118487 | − | 0.364664i | ||||
\(846\) | 1.38197 | 0.0475130 | ||||||||
\(847\) | −52.9058 | + | 7.21242i | −1.81786 | + | 0.247822i | ||||
\(848\) | −4.76393 | −0.163594 | ||||||||
\(849\) | −6.52786 | − | 20.0907i | −0.224036 | − | 0.689511i | ||||
\(850\) | 6.51722 | + | 4.73504i | 0.223539 | + | 0.162410i | ||||
\(851\) | 25.4164 | − | 18.4661i | 0.871263 | − | 0.633010i | ||||
\(852\) | −3.05573 | + | 9.40456i | −0.104688 | + | 0.322195i | ||||
\(853\) | 9.04508 | − | 27.8379i | 0.309698 | − | 0.953152i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.977882 | − | 0.209156i | \(-0.0670717\pi\) | |||||||
\(854\) | −37.5517 | + | 27.2829i | −1.28499 | + | 0.933601i | ||||
\(855\) | −1.30902 | − | 0.951057i | −0.0447674 | − | 0.0325254i | ||||
\(856\) | 1.85410 | + | 5.70634i | 0.0633719 | + | 0.195039i | ||||
\(857\) | 57.0132 | 1.94753 | 0.973766 | − | 0.227551i | \(-0.0730719\pi\) | ||||
0.973766 | + | 0.227551i | \(0.0730719\pi\) | |||||||
\(858\) | 4.00000 | − | 15.9030i | 0.136558 | − | 0.542918i | ||||
\(859\) | −26.6869 | −0.910546 | −0.455273 | − | 0.890352i | \(-0.650458\pi\) | ||||
−0.455273 | + | 0.890352i | \(0.650458\pi\) | |||||||
\(860\) | −4.54508 | − | 13.9883i | −0.154986 | − | 0.476998i | ||||
\(861\) | 37.4164 | + | 27.1846i | 1.27515 | + | 0.926449i | ||||
\(862\) | −0.0901699 | + | 0.0655123i | −0.00307120 | + | 0.00223136i | ||||
\(863\) | 7.97871 | − | 24.5560i | 0.271599 | − | 0.835894i | −0.718501 | − | 0.695526i | \(-0.755171\pi\) |
0.990099 | − | 0.140368i | \(-0.0448287\pi\) | |||||||
\(864\) | 1.23607 | − | 3.80423i | 0.0420519 | − | 0.129422i | ||||
\(865\) | 27.4164 | − | 19.9192i | 0.932186 | − | 0.677273i | ||||
\(866\) | −11.7082 | − | 8.50651i | −0.397861 | − | 0.289063i | ||||
\(867\) | 3.43769 | + | 10.5801i | 0.116750 | + | 0.359320i | ||||
\(868\) | −9.70820 | −0.329518 | ||||||||
\(869\) | −12.2705 | + | 0.832544i | −0.416249 | + | 0.0282421i | ||||
\(870\) | −33.8885 | −1.14893 | ||||||||
\(871\) | 2.11146 | + | 6.49839i | 0.0715440 | + | 0.220190i | ||||
\(872\) | −2.61803 | − | 1.90211i | −0.0886578 | − | 0.0644137i | ||||
\(873\) | 7.47214 | − | 5.42882i | 0.252893 | − | 0.183738i | ||||
\(874\) | −2.42705 | + | 7.46969i | −0.0820962 | + | 0.252666i | ||||
\(875\) | 17.9164 | − | 55.1410i | 0.605685 | − | 1.86411i | ||||
\(876\) | −22.6525 | + | 16.4580i | −0.765356 | + | 0.556064i | ||||
\(877\) | 33.5066 | + | 24.3440i | 1.13144 | + | 0.822037i | 0.985903 | − | 0.167316i | \(-0.0535101\pi\) |
0.145533 | + | 0.989353i | \(0.453510\pi\) | |||||||
\(878\) | −5.29180 | − | 16.2865i | −0.178589 | − | 0.549642i | ||||
\(879\) | 61.3050 | 2.06776 | ||||||||
\(880\) | 4.11803 | − | 3.44095i | 0.138819 | − | 0.115995i | ||||
\(881\) | −1.41641 | −0.0477200 | −0.0238600 | − | 0.999715i | \(-0.507596\pi\) | ||||
−0.0238600 | + | 0.999715i | \(0.507596\pi\) | |||||||
\(882\) | 5.11803 | + | 15.7517i | 0.172333 | + | 0.530387i | ||||
\(883\) | −39.9615 | − | 29.0337i | −1.34481 | − | 0.977063i | −0.999252 | − | 0.0386656i | \(-0.987689\pi\) |
−0.345559 | − | 0.938397i | \(-0.612311\pi\) | |||||||
\(884\) | −6.76393 | + | 4.91428i | −0.227496 | + | 0.165285i | ||||
\(885\) | 3.52786 | − | 10.8576i | 0.118588 | − | 0.364976i | ||||
\(886\) | −11.5000 | + | 35.3934i | −0.386350 | + | 1.18906i | ||||
\(887\) | −38.7426 | + | 28.1482i | −1.30085 | + | 0.945123i | −0.999964 | − | 0.00853637i | \(-0.997283\pi\) |
−0.300887 | + | 0.953660i | \(0.597283\pi\) | |||||||
\(888\) | 6.47214 | + | 4.70228i | 0.217191 | + | 0.157798i | ||||
\(889\) | 29.1246 | + | 89.6363i | 0.976808 | + | 3.00631i | ||||
\(890\) | 18.1803 | 0.609406 | ||||||||
\(891\) | 13.5967 | + | 33.8545i | 0.455508 | + | 1.13417i | ||||
\(892\) | −9.70820 | −0.325055 | ||||||||
\(893\) | 0.427051 | + | 1.31433i | 0.0142907 | + | 0.0439823i | ||||
\(894\) | −18.6525 | − | 13.5518i | −0.623832 | − | 0.453241i | ||||
\(895\) | −2.85410 | + | 2.07363i | −0.0954021 | + | 0.0693137i | ||||
\(896\) | −1.50000 | + | 4.61653i | −0.0501115 | + | 0.154227i | ||||
\(897\) | 12.0000 | − | 36.9322i | 0.400668 | − | 1.23313i | ||||
\(898\) | −11.4721 | + | 8.33499i | −0.382830 | + | 0.278142i | ||||
\(899\) | −16.9443 | − | 12.3107i | −0.565123 | − | 0.410586i | ||||
\(900\) | −0.736068 | − | 2.26538i | −0.0245356 | − | 0.0755128i | ||||
\(901\) | −16.1115 | −0.536750 | ||||||||
\(902\) | −13.3820 | − | 8.40051i | −0.445571 | − | 0.279706i | ||||
\(903\) | −88.2492 | −2.93675 | ||||||||
\(904\) | 1.70820 | + | 5.25731i | 0.0568140 | + | 0.174856i | ||||
\(905\) | 0.381966 | + | 0.277515i | 0.0126970 | + | 0.00922490i | ||||
\(906\) | −22.1803 | + | 16.1150i | −0.736892 | + | 0.535384i | ||||
\(907\) | 7.05573 | − | 21.7153i | 0.234282 | − | 0.721045i | −0.762934 | − | 0.646476i | \(-0.776242\pi\) |
0.997216 | − | 0.0745686i | \(-0.0237580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.7812 | − | 8.55951i | 0.390756 | − | 0.283901i | ||||
\(910\) | 15.7082 | + | 11.4127i | 0.520722 | + | 0.378327i | ||||
\(911\) | −4.14590 | − | 12.7598i | −0.137360 | − | 0.422750i | 0.858590 | − | 0.512663i | \(-0.171341\pi\) |
−0.995950 | + | 0.0899133i | \(0.971341\pi\) | |||||||
\(912\) | −2.00000 | −0.0662266 | ||||||||
\(913\) | −38.7599 | − | 24.3314i | −1.28276 | − | 0.805253i | ||||
\(914\) | −25.6180 | −0.847369 | ||||||||
\(915\) | 9.56231 | + | 29.4298i | 0.316120 | + | 0.972918i | ||||
\(916\) | 7.50000 | + | 5.44907i | 0.247807 | + | 0.180042i | ||||
\(917\) | −47.4787 | + | 34.4953i | −1.56789 | + | 1.13914i | ||||
\(918\) | 4.18034 | − | 12.8658i | 0.137972 | − | 0.424633i | ||||
\(919\) | 9.79180 | − | 30.1360i | 0.323002 | − | 0.994097i | −0.649333 | − | 0.760504i | \(-0.724952\pi\) |
0.972335 | − | 0.233592i | \(-0.0750481\pi\) | |||||||
\(920\) | 10.2812 | − | 7.46969i | 0.338960 | − | 0.246269i | ||||
\(921\) | −0.944272 | − | 0.686054i | −0.0311148 | − | 0.0226062i | ||||
\(922\) | 9.20820 | + | 28.3399i | 0.303256 | + | 0.933326i | ||||
\(923\) | 12.2229 | 0.402322 | ||||||||
\(924\) | −12.0000 | − | 29.8788i | −0.394771 | − | 0.982940i | ||||
\(925\) | −9.52786 | −0.313274 | ||||||||
\(926\) | −6.73607 | − | 20.7315i | −0.221361 | − | 0.681279i | ||||
\(927\) | 3.85410 | + | 2.80017i | 0.126585 | + | 0.0919696i | ||||
\(928\) | −8.47214 | + | 6.15537i | −0.278111 | + | 0.202060i | ||||
\(929\) | 4.55166 | − | 14.0086i | 0.149335 | − | 0.459607i | −0.848208 | − | 0.529664i | \(-0.822318\pi\) |
0.997543 | + | 0.0700571i | \(0.0223182\pi\) | |||||||
\(930\) | −2.00000 | + | 6.15537i | −0.0655826 | + | 0.201842i | ||||
\(931\) | −13.3992 | + | 9.73508i | −0.439141 | + | 0.319054i | ||||
\(932\) | −4.69098 | − | 3.40820i | −0.153658 | − | 0.111639i | ||||
\(933\) | 17.7984 | + | 54.7778i | 0.582693 | + | 1.79334i | ||||
\(934\) | 19.9098 | 0.651470 | ||||||||
\(935\) | 13.9271 | − | 11.6372i | 0.455463 | − | 0.380577i | ||||
\(936\) | 2.47214 | 0.0808043 | ||||||||
\(937\) | −13.5385 | − | 41.6672i | −0.442284 | − | 1.36121i | −0.885435 | − | 0.464763i | \(-0.846140\pi\) |
0.443152 | − | 0.896447i | \(-0.353860\pi\) | |||||||
\(938\) | 10.8541 | + | 7.88597i | 0.354399 | + | 0.257486i | ||||
\(939\) | 17.9443 | − | 13.0373i | 0.585589 | − | 0.425455i | ||||
\(940\) | 0.690983 | − | 2.12663i | 0.0225374 | − | 0.0693629i | ||||
\(941\) | −2.76393 | + | 8.50651i | −0.0901016 | + | 0.277304i | −0.985946 | − | 0.167063i | \(-0.946572\pi\) |
0.895845 | + | 0.444368i | \(0.146572\pi\) | |||||||
\(942\) | 37.7426 | − | 27.4216i | 1.22972 | − | 0.893445i | ||||
\(943\) | −30.2705 | − | 21.9928i | −0.985743 | − | 0.716185i | ||||
\(944\) | −1.09017 | − | 3.35520i | −0.0354820 | − | 0.109202i | ||||
\(945\) | −31.4164 | −1.02198 | ||||||||
\(946\) | 30.0795 | − | 2.04087i | 0.977970 | − | 0.0663544i | ||||
\(947\) | 26.9230 | 0.874879 | 0.437440 | − | 0.899248i | \(-0.355885\pi\) | ||||
0.437440 | + | 0.899248i | \(0.355885\pi\) | |||||||
\(948\) | −2.29180 | − | 7.05342i | −0.0744341 | − | 0.229085i | ||||
\(949\) | 28.0000 | + | 20.3432i | 0.908918 | + | 0.660368i | ||||
\(950\) | 1.92705 | − | 1.40008i | 0.0625218 | − | 0.0454247i | ||||
\(951\) | 12.4721 | − | 38.3853i | 0.404437 | − | 1.24473i | ||||
\(952\) | −5.07295 | + | 15.6129i | −0.164415 | + | 0.506018i | ||||
\(953\) | 17.6180 | − | 12.8003i | 0.570704 | − | 0.414641i | −0.264657 | − | 0.964343i | \(-0.585259\pi\) |
0.835361 | + | 0.549702i | \(0.185259\pi\) | |||||||
\(954\) | 3.85410 | + | 2.80017i | 0.124781 | + | 0.0906588i | ||||
\(955\) | 2.51722 | + | 7.74721i | 0.0814554 | + | 0.250694i | ||||
\(956\) | 18.3262 | 0.592713 | ||||||||
\(957\) | 16.9443 | − | 67.3660i | 0.547731 | − | 2.17763i | ||||
\(958\) | 1.09017 | 0.0352218 | ||||||||
\(959\) | 5.86475 | + | 18.0498i | 0.189382 | + | 0.582859i | ||||
\(960\) | 2.61803 | + | 1.90211i | 0.0844967 | + | 0.0613904i | ||||
\(961\) | 21.8435 | − | 15.8702i | 0.704628 | − | 0.511942i | ||||
\(962\) | 3.05573 | − | 9.40456i | 0.0985206 | − | 0.303215i | ||||
\(963\) | 1.85410 | − | 5.70634i | 0.0597476 | − | 0.183884i | ||||
\(964\) | −8.09017 | + | 5.87785i | −0.260567 | + | 0.189313i | ||||
\(965\) | −25.0344 | − | 18.1886i | −0.805887 | − | 0.585511i | ||||
\(966\) | −23.5623 | − | 72.5173i | −0.758105 | − | 2.33321i | ||||
\(967\) | −24.7295 | −0.795247 | −0.397623 | − | 0.917549i | \(-0.630165\pi\) | ||||
−0.397623 | + | 0.917549i | \(0.630165\pi\) | |||||||
\(968\) | 4.78115 | + | 9.90659i | 0.153672 | + | 0.318410i | ||||
\(969\) | −6.76393 | −0.217289 | ||||||||
\(970\) | −4.61803 | − | 14.2128i | −0.148276 | − | 0.456347i | ||||
\(971\) | −8.38197 | − | 6.08985i | −0.268990 | − | 0.195433i | 0.445111 | − | 0.895475i | \(-0.353164\pi\) |
−0.714101 | + | 0.700043i | \(0.753164\pi\) | |||||||
\(972\) | −8.09017 | + | 5.87785i | −0.259492 | + | 0.188532i | ||||
\(973\) | 15.4894 | − | 47.6713i | 0.496566 | − | 1.52827i | ||||
\(974\) | 3.09017 | − | 9.51057i | 0.0990154 | − | 0.304738i | ||||
\(975\) | −9.52786 | + | 6.92240i | −0.305136 | + | 0.221694i | ||||
\(976\) | 7.73607 | + | 5.62058i | 0.247626 | + | 0.179910i | ||||
\(977\) | −13.8541 | − | 42.6385i | −0.443232 | − | 1.36413i | −0.884411 | − | 0.466709i | \(-0.845440\pi\) |
0.441179 | − | 0.897419i | \(-0.354560\pi\) | |||||||
\(978\) | 1.34752 | 0.0430891 | ||||||||
\(979\) | −9.09017 | + | 36.1401i | −0.290523 | + | 1.15504i | ||||
\(980\) | 26.7984 | 0.856043 | ||||||||
\(981\) | 1.00000 | + | 3.07768i | 0.0319275 | + | 0.0982629i | ||||
\(982\) | 13.6353 | + | 9.90659i | 0.435118 | + | 0.316132i | ||||
\(983\) | −47.0344 | + | 34.1725i | −1.50017 | + | 1.08993i | −0.529850 | + | 0.848091i | \(0.677752\pi\) |
−0.970315 | + | 0.241843i | \(0.922248\pi\) | |||||||
\(984\) | 2.94427 | − | 9.06154i | 0.0938600 | − | 0.288871i | ||||
\(985\) | −9.00000 | + | 27.6992i | −0.286764 | + | 0.882568i | ||||
\(986\) | −28.6525 | + | 20.8172i | −0.912481 | + | 0.662956i | ||||
\(987\) | −10.8541 | − | 7.88597i | −0.345490 | − | 0.251013i | ||||
\(988\) | 0.763932 | + | 2.35114i | 0.0243039 | + | 0.0747998i | ||||
\(989\) | 71.3951 | 2.27023 | ||||||||
\(990\) | −5.35410 | + | 0.363271i | −0.170165 | + | 0.0115455i | ||||
\(991\) | 18.3607 | 0.583246 | 0.291623 | − | 0.956533i | \(-0.405805\pi\) | ||||
0.291623 | + | 0.956533i | \(0.405805\pi\) | |||||||
\(992\) | 0.618034 | + | 1.90211i | 0.0196226 | + | 0.0603921i | ||||
\(993\) | 6.00000 | + | 4.35926i | 0.190404 | + | 0.138337i | ||||
\(994\) | 19.4164 | − | 14.1068i | 0.615851 | − | 0.447442i | ||||
\(995\) | 7.28115 | − | 22.4091i | 0.230828 | − | 0.710416i | ||||
\(996\) | 8.52786 | − | 26.2461i | 0.270216 | − | 0.831638i | ||||
\(997\) | −9.92705 | + | 7.21242i | −0.314393 | + | 0.228420i | −0.733779 | − | 0.679388i | \(-0.762245\pi\) |
0.419386 | + | 0.907808i | \(0.362245\pi\) | |||||||
\(998\) | 2.07295 | + | 1.50609i | 0.0656181 | + | 0.0476743i | ||||
\(999\) | 4.94427 | + | 15.2169i | 0.156430 | + | 0.481442i |
(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.d.115.1 | ✓ | 4 | |
11.3 | even | 5 | 4598.2.a.bb.1.2 | 2 | |||
11.8 | odd | 10 | 4598.2.a.t.1.2 | 2 | |||
11.9 | even | 5 | inner | 418.2.f.d.229.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.d.115.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
418.2.f.d.229.1 | yes | 4 | 11.9 | even | 5 | inner | |
4598.2.a.t.1.2 | 2 | 11.8 | odd | 10 | |||
4598.2.a.bb.1.2 | 2 | 11.3 | even | 5 |