Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (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: | \(3.68908857338\) |
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 | 169.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.169 |
Dual form | 462.2.j.a.421.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 1.30902 | − | 0.951057i | 0.585410 | − | 0.425325i | −0.255260 | − | 0.966872i | \(-0.582161\pi\) |
0.840670 | + | 0.541547i | \(0.182161\pi\) | |||||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | −3.04508 | − | 1.31433i | −0.918128 | − | 0.396285i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.00000 | − | 1.45309i | −0.554700 | − | 0.403013i | 0.274815 | − | 0.961497i | \(-0.411383\pi\) |
−0.829515 | + | 0.558484i | \(0.811383\pi\) | |||||||
\(14\) | −0.309017 | + | 0.951057i | −0.0825883 | + | 0.254181i | ||||
\(15\) | −0.500000 | − | 1.53884i | −0.129099 | − | 0.397327i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 6.35410 | − | 4.61653i | 1.54110 | − | 1.11967i | 0.591452 | − | 0.806340i | \(-0.298555\pi\) |
0.949644 | − | 0.313332i | \(-0.101445\pi\) | |||||||
\(18\) | 0.309017 | + | 0.951057i | 0.0728360 | + | 0.224166i | ||||
\(19\) | −0.427051 | + | 1.31433i | −0.0979722 | + | 0.301527i | −0.988017 | − | 0.154346i | \(-0.950673\pi\) |
0.890045 | + | 0.455873i | \(0.150673\pi\) | |||||||
\(20\) | 1.30902 | + | 0.951057i | 0.292705 | + | 0.212663i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.69098 | + | 2.85317i | 0.360519 | + | 0.608298i | ||||
\(23\) | 1.38197 | 0.288160 | 0.144080 | − | 0.989566i | \(-0.453978\pi\) | ||||
0.144080 | + | 0.989566i | \(0.453978\pi\) | |||||||
\(24\) | −0.809017 | − | 0.587785i | −0.165140 | − | 0.119981i | ||||
\(25\) | −0.736068 | + | 2.26538i | −0.147214 | + | 0.453077i | ||||
\(26\) | 0.763932 | + | 2.35114i | 0.149819 | + | 0.461097i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0.809017 | − | 0.587785i | 0.152890 | − | 0.111081i | ||||
\(29\) | −2.85410 | − | 8.78402i | −0.529993 | − | 1.63115i | −0.754225 | − | 0.656616i | \(-0.771987\pi\) |
0.224231 | − | 0.974536i | \(-0.428013\pi\) | |||||||
\(30\) | −0.500000 | + | 1.53884i | −0.0912871 | + | 0.280953i | ||||
\(31\) | −1.69098 | − | 1.22857i | −0.303710 | − | 0.220658i | 0.425483 | − | 0.904966i | \(-0.360104\pi\) |
−0.729193 | + | 0.684308i | \(0.760104\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.19098 | + | 2.48990i | −0.381401 | + | 0.433436i | ||||
\(34\) | −7.85410 | −1.34697 | ||||||||
\(35\) | −1.30902 | − | 0.951057i | −0.221264 | − | 0.160758i | ||||
\(36\) | 0.309017 | − | 0.951057i | 0.0515028 | − | 0.158509i | ||||
\(37\) | −0.354102 | − | 1.08981i | −0.0582140 | − | 0.179164i | 0.917721 | − | 0.397225i | \(-0.130027\pi\) |
−0.975935 | + | 0.218061i | \(0.930027\pi\) | |||||||
\(38\) | 1.11803 | − | 0.812299i | 0.181369 | − | 0.131772i | ||||
\(39\) | −2.00000 | + | 1.45309i | −0.320256 | + | 0.232680i | ||||
\(40\) | −0.500000 | − | 1.53884i | −0.0790569 | − | 0.243312i | ||||
\(41\) | 1.64590 | − | 5.06555i | 0.257046 | − | 0.791107i | −0.736374 | − | 0.676575i | \(-0.763463\pi\) |
0.993420 | − | 0.114531i | \(-0.0365366\pi\) | |||||||
\(42\) | 0.809017 | + | 0.587785i | 0.124834 | + | 0.0906972i | ||||
\(43\) | −1.52786 | −0.232997 | −0.116499 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116499 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(44\) | 0.309017 | − | 3.30220i | 0.0465861 | − | 0.497825i | ||||
\(45\) | −1.61803 | −0.241202 | ||||||||
\(46\) | −1.11803 | − | 0.812299i | −0.164845 | − | 0.119767i | ||||
\(47\) | −2.38197 | + | 7.33094i | −0.347445 | + | 1.06933i | 0.612816 | + | 0.790226i | \(0.290037\pi\) |
−0.960262 | + | 0.279102i | \(0.909963\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 1.92705 | − | 1.40008i | 0.272526 | − | 0.198002i | ||||
\(51\) | −2.42705 | − | 7.46969i | −0.339855 | − | 1.04597i | ||||
\(52\) | 0.763932 | − | 2.35114i | 0.105938 | − | 0.326045i | ||||
\(53\) | 3.00000 | + | 2.17963i | 0.412082 | + | 0.299395i | 0.774444 | − | 0.632642i | \(-0.218030\pi\) |
−0.362362 | + | 0.932037i | \(0.618030\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.23607 | + | 1.17557i | −0.706031 | + | 0.158514i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.11803 | + | 0.812299i | 0.148087 | + | 0.107592i | ||||
\(58\) | −2.85410 | + | 8.78402i | −0.374762 | + | 1.15340i | ||||
\(59\) | 1.09017 | + | 3.35520i | 0.141928 | + | 0.436810i | 0.996603 | − | 0.0823536i | \(-0.0262437\pi\) |
−0.854675 | + | 0.519163i | \(0.826244\pi\) | |||||||
\(60\) | 1.30902 | − | 0.951057i | 0.168993 | − | 0.122781i | ||||
\(61\) | −2.85410 | + | 2.07363i | −0.365430 | + | 0.265501i | −0.755313 | − | 0.655364i | \(-0.772515\pi\) |
0.389883 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(62\) | 0.645898 | + | 1.98787i | 0.0820291 | + | 0.252460i | ||||
\(63\) | −0.309017 | + | 0.951057i | −0.0389325 | + | 0.119822i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 3.23607 | − | 0.726543i | 0.398332 | − | 0.0894312i | ||||
\(67\) | −3.52786 | −0.430997 | −0.215499 | − | 0.976504i | \(-0.569138\pi\) | ||||
−0.215499 | + | 0.976504i | \(0.569138\pi\) | |||||||
\(68\) | 6.35410 | + | 4.61653i | 0.770548 | + | 0.559836i | ||||
\(69\) | 0.427051 | − | 1.31433i | 0.0514109 | − | 0.158226i | ||||
\(70\) | 0.500000 | + | 1.53884i | 0.0597614 | + | 0.183927i | ||||
\(71\) | 9.70820 | − | 7.05342i | 1.15215 | − | 0.837087i | 0.163386 | − | 0.986562i | \(-0.447758\pi\) |
0.988766 | + | 0.149475i | \(0.0477583\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | −0.909830 | − | 2.80017i | −0.106488 | − | 0.327735i | 0.883589 | − | 0.468263i | \(-0.155120\pi\) |
−0.990077 | + | 0.140528i | \(0.955120\pi\) | |||||||
\(74\) | −0.354102 | + | 1.08981i | −0.0411635 | + | 0.126688i | ||||
\(75\) | 1.92705 | + | 1.40008i | 0.222517 | + | 0.161668i | ||||
\(76\) | −1.38197 | −0.158522 | ||||||||
\(77\) | −0.309017 | + | 3.30220i | −0.0352158 | + | 0.376320i | ||||
\(78\) | 2.47214 | 0.279914 | ||||||||
\(79\) | 4.23607 | + | 3.07768i | 0.476595 | + | 0.346266i | 0.800006 | − | 0.599992i | \(-0.204830\pi\) |
−0.323411 | + | 0.946259i | \(0.604830\pi\) | |||||||
\(80\) | −0.500000 | + | 1.53884i | −0.0559017 | + | 0.172048i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −4.30902 | + | 3.13068i | −0.475851 | + | 0.345726i | ||||
\(83\) | 9.23607 | − | 6.71040i | 1.01379 | − | 0.736562i | 0.0487895 | − | 0.998809i | \(-0.484464\pi\) |
0.965001 | + | 0.262247i | \(0.0844637\pi\) | |||||||
\(84\) | −0.309017 | − | 0.951057i | −0.0337165 | − | 0.103769i | ||||
\(85\) | 3.92705 | − | 12.0862i | 0.425948 | − | 1.31093i | ||||
\(86\) | 1.23607 | + | 0.898056i | 0.133289 | + | 0.0968399i | ||||
\(87\) | −9.23607 | −0.990210 | ||||||||
\(88\) | −2.19098 | + | 2.48990i | −0.233560 | + | 0.265424i | ||||
\(89\) | 11.8541 | 1.25653 | 0.628266 | − | 0.777998i | \(-0.283765\pi\) | ||||
0.628266 | + | 0.777998i | \(0.283765\pi\) | |||||||
\(90\) | 1.30902 | + | 0.951057i | 0.137983 | + | 0.100250i | ||||
\(91\) | −0.763932 | + | 2.35114i | −0.0800818 | + | 0.246467i | ||||
\(92\) | 0.427051 | + | 1.31433i | 0.0445231 | + | 0.137028i | ||||
\(93\) | −1.69098 | + | 1.22857i | −0.175347 | + | 0.127397i | ||||
\(94\) | 6.23607 | − | 4.53077i | 0.643201 | − | 0.467313i | ||||
\(95\) | 0.690983 | + | 2.12663i | 0.0708934 | + | 0.218187i | ||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | 10.4721 | + | 7.60845i | 1.06328 | + | 0.772521i | 0.974693 | − | 0.223547i | \(-0.0717636\pi\) |
0.0885911 | + | 0.996068i | \(0.471764\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.69098 | + | 2.85317i | 0.169950 | + | 0.286754i | ||||
\(100\) | −2.38197 | −0.238197 | ||||||||
\(101\) | 0.690983 | + | 0.502029i | 0.0687554 | + | 0.0499537i | 0.621632 | − | 0.783309i | \(-0.286470\pi\) |
−0.552877 | + | 0.833263i | \(0.686470\pi\) | |||||||
\(102\) | −2.42705 | + | 7.46969i | −0.240314 | + | 0.739610i | ||||
\(103\) | 3.04508 | + | 9.37181i | 0.300041 | + | 0.923432i | 0.981481 | + | 0.191558i | \(0.0613540\pi\) |
−0.681440 | + | 0.731874i | \(0.738646\pi\) | |||||||
\(104\) | −2.00000 | + | 1.45309i | −0.196116 | + | 0.142487i | ||||
\(105\) | −1.30902 | + | 0.951057i | −0.127747 | + | 0.0928136i | ||||
\(106\) | −1.14590 | − | 3.52671i | −0.111299 | − | 0.342545i | ||||
\(107\) | −5.51722 | + | 16.9803i | −0.533370 | + | 1.64154i | 0.213775 | + | 0.976883i | \(0.431424\pi\) |
−0.747145 | + | 0.664661i | \(0.768576\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 16.5623 | 1.58638 | 0.793191 | − | 0.608973i | \(-0.208418\pi\) | ||||
0.793191 | + | 0.608973i | \(0.208418\pi\) | |||||||
\(110\) | 4.92705 | + | 2.12663i | 0.469776 | + | 0.202766i | ||||
\(111\) | −1.14590 | −0.108764 | ||||||||
\(112\) | 0.809017 | + | 0.587785i | 0.0764449 | + | 0.0555405i | ||||
\(113\) | 1.61803 | − | 4.97980i | 0.152212 | − | 0.468460i | −0.845656 | − | 0.533728i | \(-0.820790\pi\) |
0.997868 | + | 0.0652686i | \(0.0207904\pi\) | |||||||
\(114\) | −0.427051 | − | 1.31433i | −0.0399970 | − | 0.123098i | ||||
\(115\) | 1.80902 | − | 1.31433i | 0.168692 | − | 0.122562i | ||||
\(116\) | 7.47214 | − | 5.42882i | 0.693770 | − | 0.504054i | ||||
\(117\) | 0.763932 | + | 2.35114i | 0.0706255 | + | 0.217363i | ||||
\(118\) | 1.09017 | − | 3.35520i | 0.100358 | − | 0.308871i | ||||
\(119\) | −6.35410 | − | 4.61653i | −0.582480 | − | 0.423196i | ||||
\(120\) | −1.61803 | −0.147706 | ||||||||
\(121\) | 7.54508 | + | 8.00448i | 0.685917 | + | 0.727680i | ||||
\(122\) | 3.52786 | 0.319398 | ||||||||
\(123\) | −4.30902 | − | 3.13068i | −0.388531 | − | 0.282284i | ||||
\(124\) | 0.645898 | − | 1.98787i | 0.0580034 | − | 0.178516i | ||||
\(125\) | 3.69098 | + | 11.3597i | 0.330132 | + | 1.01604i | ||||
\(126\) | 0.809017 | − | 0.587785i | 0.0720730 | − | 0.0523641i | ||||
\(127\) | 13.3262 | − | 9.68208i | 1.18251 | − | 0.859146i | 0.190060 | − | 0.981773i | \(-0.439132\pi\) |
0.992453 | + | 0.122627i | \(0.0391319\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | −0.472136 | + | 1.45309i | −0.0415693 | + | 0.127937i | ||||
\(130\) | 3.23607 | + | 2.35114i | 0.283822 | + | 0.206209i | ||||
\(131\) | −18.9443 | −1.65517 | −0.827584 | − | 0.561341i | \(-0.810285\pi\) | ||||
−0.827584 | + | 0.561341i | \(0.810285\pi\) | |||||||
\(132\) | −3.04508 | − | 1.31433i | −0.265041 | − | 0.114398i | ||||
\(133\) | 1.38197 | 0.119832 | ||||||||
\(134\) | 2.85410 | + | 2.07363i | 0.246557 | + | 0.179134i | ||||
\(135\) | −0.500000 | + | 1.53884i | −0.0430331 | + | 0.132442i | ||||
\(136\) | −2.42705 | − | 7.46969i | −0.208118 | − | 0.640521i | ||||
\(137\) | −3.61803 | + | 2.62866i | −0.309110 | + | 0.224581i | −0.731514 | − | 0.681826i | \(-0.761186\pi\) |
0.422405 | + | 0.906407i | \(0.361186\pi\) | |||||||
\(138\) | −1.11803 | + | 0.812299i | −0.0951734 | + | 0.0691475i | ||||
\(139\) | 5.95492 | + | 18.3273i | 0.505089 | + | 1.55451i | 0.800620 | + | 0.599172i | \(0.204503\pi\) |
−0.295531 | + | 0.955333i | \(0.595497\pi\) | |||||||
\(140\) | 0.500000 | − | 1.53884i | 0.0422577 | − | 0.130056i | ||||
\(141\) | 6.23607 | + | 4.53077i | 0.525172 | + | 0.381560i | ||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 4.18034 | + | 7.05342i | 0.349578 | + | 0.589837i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.0902 | − | 8.78402i | −1.00403 | − | 0.729473i | ||||
\(146\) | −0.909830 | + | 2.80017i | −0.0752981 | + | 0.231744i | ||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | 0.927051 | − | 0.673542i | 0.0762031 | − | 0.0553648i | ||||
\(149\) | 11.7082 | − | 8.50651i | 0.959173 | − | 0.696880i | 0.00621481 | − | 0.999981i | \(-0.498022\pi\) |
0.952959 | + | 0.303100i | \(0.0980218\pi\) | |||||||
\(150\) | −0.736068 | − | 2.26538i | −0.0600997 | − | 0.184968i | ||||
\(151\) | −1.47214 | + | 4.53077i | −0.119801 | + | 0.368709i | −0.992918 | − | 0.118801i | \(-0.962095\pi\) |
0.873117 | + | 0.487510i | \(0.162095\pi\) | |||||||
\(152\) | 1.11803 | + | 0.812299i | 0.0906845 | + | 0.0658862i | ||||
\(153\) | −7.85410 | −0.634967 | ||||||||
\(154\) | 2.19098 | − | 2.48990i | 0.176554 | − | 0.200642i | ||||
\(155\) | −3.38197 | −0.271646 | ||||||||
\(156\) | −2.00000 | − | 1.45309i | −0.160128 | − | 0.116340i | ||||
\(157\) | 3.00000 | − | 9.23305i | 0.239426 | − | 0.736878i | −0.757077 | − | 0.653325i | \(-0.773373\pi\) |
0.996503 | − | 0.0835524i | \(-0.0266266\pi\) | |||||||
\(158\) | −1.61803 | − | 4.97980i | −0.128724 | − | 0.396171i | ||||
\(159\) | 3.00000 | − | 2.17963i | 0.237915 | − | 0.172856i | ||||
\(160\) | 1.30902 | − | 0.951057i | 0.103487 | − | 0.0751876i | ||||
\(161\) | −0.427051 | − | 1.31433i | −0.0336563 | − | 0.103584i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | 12.0902 | + | 8.78402i | 0.946975 | + | 0.688018i | 0.950090 | − | 0.311977i | \(-0.100991\pi\) |
−0.00311433 | + | 0.999995i | \(0.500991\pi\) | |||||||
\(164\) | 5.32624 | 0.415909 | ||||||||
\(165\) | −0.500000 | + | 5.34307i | −0.0389249 | + | 0.415957i | ||||
\(166\) | −11.4164 | −0.886085 | ||||||||
\(167\) | −18.9443 | − | 13.7638i | −1.46595 | − | 1.06508i | −0.981762 | − | 0.190113i | \(-0.939114\pi\) |
−0.484190 | − | 0.874963i | \(-0.660886\pi\) | |||||||
\(168\) | −0.309017 | + | 0.951057i | −0.0238412 | + | 0.0733756i | ||||
\(169\) | −2.12868 | − | 6.55139i | −0.163744 | − | 0.503953i | ||||
\(170\) | −10.2812 | + | 7.46969i | −0.788528 | + | 0.572899i | ||||
\(171\) | 1.11803 | − | 0.812299i | 0.0854982 | − | 0.0621181i | ||||
\(172\) | −0.472136 | − | 1.45309i | −0.0360000 | − | 0.110797i | ||||
\(173\) | −6.66312 | + | 20.5070i | −0.506588 | + | 1.55912i | 0.291498 | + | 0.956572i | \(0.405846\pi\) |
−0.798085 | + | 0.602545i | \(0.794154\pi\) | |||||||
\(174\) | 7.47214 | + | 5.42882i | 0.566461 | + | 0.411558i | ||||
\(175\) | 2.38197 | 0.180060 | ||||||||
\(176\) | 3.23607 | − | 0.726543i | 0.243928 | − | 0.0547652i | ||||
\(177\) | 3.52786 | 0.265170 | ||||||||
\(178\) | −9.59017 | − | 6.96767i | −0.718814 | − | 0.522249i | ||||
\(179\) | 5.88197 | − | 18.1028i | 0.439639 | − | 1.35307i | −0.448619 | − | 0.893723i | \(-0.648084\pi\) |
0.888258 | − | 0.459346i | \(-0.151916\pi\) | |||||||
\(180\) | −0.500000 | − | 1.53884i | −0.0372678 | − | 0.114698i | ||||
\(181\) | −6.61803 | + | 4.80828i | −0.491915 | + | 0.357397i | −0.805920 | − | 0.592024i | \(-0.798329\pi\) |
0.314006 | + | 0.949421i | \(0.398329\pi\) | |||||||
\(182\) | 2.00000 | − | 1.45309i | 0.148250 | − | 0.107710i | ||||
\(183\) | 1.09017 | + | 3.35520i | 0.0805877 | + | 0.248023i | ||||
\(184\) | 0.427051 | − | 1.31433i | 0.0314826 | − | 0.0968935i | ||||
\(185\) | −1.50000 | − | 1.08981i | −0.110282 | − | 0.0801247i | ||||
\(186\) | 2.09017 | 0.153259 | ||||||||
\(187\) | −25.4164 | + | 5.70634i | −1.85863 | + | 0.417289i | ||||
\(188\) | −7.70820 | −0.562179 | ||||||||
\(189\) | 0.809017 | + | 0.587785i | 0.0588473 | + | 0.0427551i | ||||
\(190\) | 0.690983 | − | 2.12663i | 0.0501292 | − | 0.154282i | ||||
\(191\) | 1.20820 | + | 3.71847i | 0.0874226 | + | 0.269059i | 0.985205 | − | 0.171380i | \(-0.0548227\pi\) |
−0.897782 | + | 0.440439i | \(0.854823\pi\) | |||||||
\(192\) | −0.809017 | + | 0.587785i | −0.0583858 | + | 0.0424197i | ||||
\(193\) | 15.7812 | − | 11.4657i | 1.13595 | − | 0.825318i | 0.149402 | − | 0.988777i | \(-0.452265\pi\) |
0.986550 | + | 0.163459i | \(0.0522651\pi\) | |||||||
\(194\) | −4.00000 | − | 12.3107i | −0.287183 | − | 0.883859i | ||||
\(195\) | −1.23607 | + | 3.80423i | −0.0885167 | + | 0.272426i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | −11.8885 | −0.847024 | −0.423512 | − | 0.905891i | \(-0.639203\pi\) | ||||
−0.423512 | + | 0.905891i | \(0.639203\pi\) | |||||||
\(198\) | 0.309017 | − | 3.30220i | 0.0219609 | − | 0.234677i | ||||
\(199\) | −0.326238 | −0.0231264 | −0.0115632 | − | 0.999933i | \(-0.503681\pi\) | ||||
−0.0115632 | + | 0.999933i | \(0.503681\pi\) | |||||||
\(200\) | 1.92705 | + | 1.40008i | 0.136263 | + | 0.0990009i | ||||
\(201\) | −1.09017 | + | 3.35520i | −0.0768947 | + | 0.236657i | ||||
\(202\) | −0.263932 | − | 0.812299i | −0.0185702 | − | 0.0571532i | ||||
\(203\) | −7.47214 | + | 5.42882i | −0.524441 | + | 0.381029i | ||||
\(204\) | 6.35410 | − | 4.61653i | 0.444876 | − | 0.323221i | ||||
\(205\) | −2.66312 | − | 8.19624i | −0.186000 | − | 0.572450i | ||||
\(206\) | 3.04508 | − | 9.37181i | 0.212161 | − | 0.652965i | ||||
\(207\) | −1.11803 | − | 0.812299i | −0.0777087 | − | 0.0564587i | ||||
\(208\) | 2.47214 | 0.171412 | ||||||||
\(209\) | 3.02786 | − | 3.44095i | 0.209442 | − | 0.238016i | ||||
\(210\) | 1.61803 | 0.111655 | ||||||||
\(211\) | 2.00000 | + | 1.45309i | 0.137686 | + | 0.100035i | 0.654496 | − | 0.756065i | \(-0.272881\pi\) |
−0.516810 | + | 0.856100i | \(0.672881\pi\) | |||||||
\(212\) | −1.14590 | + | 3.52671i | −0.0787006 | + | 0.242216i | ||||
\(213\) | −3.70820 | − | 11.4127i | −0.254082 | − | 0.781984i | ||||
\(214\) | 14.4443 | − | 10.4944i | 0.987390 | − | 0.717381i | ||||
\(215\) | −2.00000 | + | 1.45309i | −0.136399 | + | 0.0990996i | ||||
\(216\) | 0.309017 | + | 0.951057i | 0.0210259 | + | 0.0647112i | ||||
\(217\) | −0.645898 | + | 1.98787i | −0.0438464 | + | 0.134945i | ||||
\(218\) | −13.3992 | − | 9.73508i | −0.907507 | − | 0.659343i | ||||
\(219\) | −2.94427 | −0.198955 | ||||||||
\(220\) | −2.73607 | − | 4.61653i | −0.184466 | − | 0.311246i | ||||
\(221\) | −19.4164 | −1.30609 | ||||||||
\(222\) | 0.927051 | + | 0.673542i | 0.0622196 | + | 0.0452052i | ||||
\(223\) | −0.753289 | + | 2.31838i | −0.0504440 | + | 0.155251i | −0.973105 | − | 0.230361i | \(-0.926009\pi\) |
0.922661 | + | 0.385611i | \(0.126009\pi\) | |||||||
\(224\) | −0.309017 | − | 0.951057i | −0.0206471 | − | 0.0635451i | ||||
\(225\) | 1.92705 | − | 1.40008i | 0.128470 | − | 0.0933390i | ||||
\(226\) | −4.23607 | + | 3.07768i | −0.281779 | + | 0.204724i | ||||
\(227\) | 3.94427 | + | 12.1392i | 0.261791 | + | 0.805708i | 0.992415 | + | 0.122929i | \(0.0392288\pi\) |
−0.730625 | + | 0.682779i | \(0.760771\pi\) | |||||||
\(228\) | −0.427051 | + | 1.31433i | −0.0282821 | + | 0.0870435i | ||||
\(229\) | 4.61803 | + | 3.35520i | 0.305168 | + | 0.221718i | 0.729820 | − | 0.683639i | \(-0.239604\pi\) |
−0.424652 | + | 0.905357i | \(0.639604\pi\) | |||||||
\(230\) | −2.23607 | −0.147442 | ||||||||
\(231\) | 3.04508 | + | 1.31433i | 0.200352 | + | 0.0864764i | ||||
\(232\) | −9.23607 | −0.606378 | ||||||||
\(233\) | 12.9443 | + | 9.40456i | 0.848007 | + | 0.616113i | 0.924596 | − | 0.380949i | \(-0.124403\pi\) |
−0.0765885 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(234\) | 0.763932 | − | 2.35114i | 0.0499398 | − | 0.153699i | ||||
\(235\) | 3.85410 | + | 11.8617i | 0.251414 | + | 0.773772i | ||||
\(236\) | −2.85410 | + | 2.07363i | −0.185786 | + | 0.134982i | ||||
\(237\) | 4.23607 | − | 3.07768i | 0.275162 | − | 0.199917i | ||||
\(238\) | 2.42705 | + | 7.46969i | 0.157322 | + | 0.484188i | ||||
\(239\) | 6.42705 | − | 19.7804i | 0.415731 | − | 1.27949i | −0.495864 | − | 0.868400i | \(-0.665148\pi\) |
0.911595 | − | 0.411089i | \(-0.134852\pi\) | |||||||
\(240\) | 1.30902 | + | 0.951057i | 0.0844967 | + | 0.0613904i | ||||
\(241\) | −4.47214 | −0.288076 | −0.144038 | − | 0.989572i | \(-0.546009\pi\) | ||||
−0.144038 | + | 0.989572i | \(0.546009\pi\) | |||||||
\(242\) | −1.39919 | − | 10.9106i | −0.0899431 | − | 0.701363i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.85410 | − | 2.07363i | −0.182715 | − | 0.132750i | ||||
\(245\) | −0.500000 | + | 1.53884i | −0.0319438 | + | 0.0983130i | ||||
\(246\) | 1.64590 | + | 5.06555i | 0.104939 | + | 0.322968i | ||||
\(247\) | 2.76393 | − | 2.00811i | 0.175865 | − | 0.127773i | ||||
\(248\) | −1.69098 | + | 1.22857i | −0.107378 | + | 0.0780143i | ||||
\(249\) | −3.52786 | − | 10.8576i | −0.223569 | − | 0.688076i | ||||
\(250\) | 3.69098 | − | 11.3597i | 0.233438 | − | 0.718449i | ||||
\(251\) | −12.7082 | − | 9.23305i | −0.802135 | − | 0.582785i | 0.109405 | − | 0.993997i | \(-0.465105\pi\) |
−0.911540 | + | 0.411212i | \(0.865105\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −4.20820 | − | 1.81636i | −0.264568 | − | 0.114193i | ||||
\(254\) | −16.4721 | −1.03355 | ||||||||
\(255\) | −10.2812 | − | 7.46969i | −0.643831 | − | 0.467770i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 4.42705 | + | 13.6251i | 0.276152 | + | 0.849908i | 0.988912 | + | 0.148500i | \(0.0474447\pi\) |
−0.712760 | + | 0.701408i | \(0.752555\pi\) | |||||||
\(258\) | 1.23607 | − | 0.898056i | 0.0769542 | − | 0.0559105i | ||||
\(259\) | −0.927051 | + | 0.673542i | −0.0576041 | + | 0.0418519i | ||||
\(260\) | −1.23607 | − | 3.80423i | −0.0766577 | − | 0.235928i | ||||
\(261\) | −2.85410 | + | 8.78402i | −0.176664 | + | 0.543717i | ||||
\(262\) | 15.3262 | + | 11.1352i | 0.946858 | + | 0.687933i | ||||
\(263\) | −26.6180 | −1.64134 | −0.820669 | − | 0.571404i | \(-0.806399\pi\) | ||||
−0.820669 | + | 0.571404i | \(0.806399\pi\) | |||||||
\(264\) | 1.69098 | + | 2.85317i | 0.104073 | + | 0.175600i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −1.11803 | − | 0.812299i | −0.0685511 | − | 0.0498053i | ||||
\(267\) | 3.66312 | − | 11.2739i | 0.224179 | − | 0.689953i | ||||
\(268\) | −1.09017 | − | 3.35520i | −0.0665927 | − | 0.204951i | ||||
\(269\) | 0.854102 | − | 0.620541i | 0.0520755 | − | 0.0378351i | −0.561443 | − | 0.827515i | \(-0.689754\pi\) |
0.613519 | + | 0.789680i | \(0.289754\pi\) | |||||||
\(270\) | 1.30902 | − | 0.951057i | 0.0796642 | − | 0.0578795i | ||||
\(271\) | −9.64590 | − | 29.6870i | −0.585947 | − | 1.80336i | −0.595435 | − | 0.803403i | \(-0.703020\pi\) |
0.00948887 | − | 0.999955i | \(-0.496980\pi\) | |||||||
\(272\) | −2.42705 | + | 7.46969i | −0.147162 | + | 0.452917i | ||||
\(273\) | 2.00000 | + | 1.45309i | 0.121046 | + | 0.0879447i | ||||
\(274\) | 4.47214 | 0.270172 | ||||||||
\(275\) | 5.21885 | − | 5.93085i | 0.314708 | − | 0.357644i | ||||
\(276\) | 1.38197 | 0.0831846 | ||||||||
\(277\) | −15.5902 | − | 11.3269i | −0.936723 | − | 0.680569i | 0.0109070 | − | 0.999941i | \(-0.496528\pi\) |
−0.947630 | + | 0.319372i | \(0.896528\pi\) | |||||||
\(278\) | 5.95492 | − | 18.3273i | 0.357152 | − | 1.09920i | ||||
\(279\) | 0.645898 | + | 1.98787i | 0.0386689 | + | 0.119011i | ||||
\(280\) | −1.30902 | + | 0.951057i | −0.0782287 | + | 0.0568365i | ||||
\(281\) | 4.47214 | − | 3.24920i | 0.266785 | − | 0.193831i | −0.446348 | − | 0.894860i | \(-0.647276\pi\) |
0.713133 | + | 0.701029i | \(0.247276\pi\) | |||||||
\(282\) | −2.38197 | − | 7.33094i | −0.141844 | − | 0.436551i | ||||
\(283\) | −0.972136 | + | 2.99193i | −0.0577875 | + | 0.177852i | −0.975784 | − | 0.218737i | \(-0.929806\pi\) |
0.917996 | + | 0.396589i | \(0.129806\pi\) | |||||||
\(284\) | 9.70820 | + | 7.05342i | 0.576076 | + | 0.418544i | ||||
\(285\) | 2.23607 | 0.132453 | ||||||||
\(286\) | 0.763932 | − | 8.16348i | 0.0451722 | − | 0.482717i | ||||
\(287\) | −5.32624 | −0.314398 | ||||||||
\(288\) | −0.809017 | − | 0.587785i | −0.0476718 | − | 0.0346356i | ||||
\(289\) | 13.8090 | − | 42.4998i | 0.812295 | − | 2.49999i | ||||
\(290\) | 4.61803 | + | 14.2128i | 0.271180 | + | 0.834607i | ||||
\(291\) | 10.4721 | − | 7.60845i | 0.613887 | − | 0.446015i | ||||
\(292\) | 2.38197 | − | 1.73060i | 0.139394 | − | 0.101276i | ||||
\(293\) | −0.736068 | − | 2.26538i | −0.0430016 | − | 0.132345i | 0.927251 | − | 0.374441i | \(-0.122165\pi\) |
−0.970252 | + | 0.242096i | \(0.922165\pi\) | |||||||
\(294\) | 0.309017 | − | 0.951057i | 0.0180222 | − | 0.0554667i | ||||
\(295\) | 4.61803 | + | 3.35520i | 0.268872 | + | 0.195347i | ||||
\(296\) | −1.14590 | −0.0666040 | ||||||||
\(297\) | 3.23607 | − | 0.726543i | 0.187776 | − | 0.0421583i | ||||
\(298\) | −14.4721 | −0.838348 | ||||||||
\(299\) | −2.76393 | − | 2.00811i | −0.159842 | − | 0.116132i | ||||
\(300\) | −0.736068 | + | 2.26538i | −0.0424969 | + | 0.130792i | ||||
\(301\) | 0.472136 | + | 1.45309i | 0.0272135 | + | 0.0837544i | ||||
\(302\) | 3.85410 | − | 2.80017i | 0.221779 | − | 0.161132i | ||||
\(303\) | 0.690983 | − | 0.502029i | 0.0396959 | − | 0.0288408i | ||||
\(304\) | −0.427051 | − | 1.31433i | −0.0244931 | − | 0.0753819i | ||||
\(305\) | −1.76393 | + | 5.42882i | −0.101002 | + | 0.310854i | ||||
\(306\) | 6.35410 | + | 4.61653i | 0.363240 | + | 0.263909i | ||||
\(307\) | −12.8541 | −0.733622 | −0.366811 | − | 0.930295i | \(-0.619550\pi\) | ||||
−0.366811 | + | 0.930295i | \(0.619550\pi\) | |||||||
\(308\) | −3.23607 | + | 0.726543i | −0.184392 | + | 0.0413986i | ||||
\(309\) | 9.85410 | 0.560580 | ||||||||
\(310\) | 2.73607 | + | 1.98787i | 0.155398 | + | 0.112903i | ||||
\(311\) | −9.14590 | + | 28.1482i | −0.518616 | + | 1.59614i | 0.257988 | + | 0.966148i | \(0.416941\pi\) |
−0.776604 | + | 0.629989i | \(0.783059\pi\) | |||||||
\(312\) | 0.763932 | + | 2.35114i | 0.0432491 | + | 0.133107i | ||||
\(313\) | −9.47214 | + | 6.88191i | −0.535397 | + | 0.388989i | −0.822373 | − | 0.568949i | \(-0.807350\pi\) |
0.286976 | + | 0.957938i | \(0.407350\pi\) | |||||||
\(314\) | −7.85410 | + | 5.70634i | −0.443233 | + | 0.322027i | ||||
\(315\) | 0.500000 | + | 1.53884i | 0.0281718 | + | 0.0867039i | ||||
\(316\) | −1.61803 | + | 4.97980i | −0.0910215 | + | 0.280135i | ||||
\(317\) | 7.00000 | + | 5.08580i | 0.393159 | + | 0.285647i | 0.766749 | − | 0.641947i | \(-0.221873\pi\) |
−0.373590 | + | 0.927594i | \(0.621873\pi\) | |||||||
\(318\) | −3.70820 | −0.207946 | ||||||||
\(319\) | −2.85410 | + | 30.4993i | −0.159799 | + | 1.70763i | ||||
\(320\) | −1.61803 | −0.0904508 | ||||||||
\(321\) | 14.4443 | + | 10.4944i | 0.806201 | + | 0.585739i | ||||
\(322\) | −0.427051 | + | 1.31433i | −0.0237986 | + | 0.0732446i | ||||
\(323\) | 3.35410 | + | 10.3229i | 0.186627 | + | 0.574380i | ||||
\(324\) | −0.809017 | + | 0.587785i | −0.0449454 | + | 0.0326547i | ||||
\(325\) | 4.76393 | − | 3.46120i | 0.264255 | − | 0.191993i | ||||
\(326\) | −4.61803 | − | 14.2128i | −0.255769 | − | 0.787177i | ||||
\(327\) | 5.11803 | − | 15.7517i | 0.283028 | − | 0.871070i | ||||
\(328\) | −4.30902 | − | 3.13068i | −0.237926 | − | 0.172863i | ||||
\(329\) | 7.70820 | 0.424967 | ||||||||
\(330\) | 3.54508 | − | 4.02874i | 0.195151 | − | 0.221775i | ||||
\(331\) | −17.8885 | −0.983243 | −0.491622 | − | 0.870809i | \(-0.663596\pi\) | ||||
−0.491622 | + | 0.870809i | \(0.663596\pi\) | |||||||
\(332\) | 9.23607 | + | 6.71040i | 0.506895 | + | 0.368281i | ||||
\(333\) | −0.354102 | + | 1.08981i | −0.0194047 | + | 0.0597214i | ||||
\(334\) | 7.23607 | + | 22.2703i | 0.395940 | + | 1.21858i | ||||
\(335\) | −4.61803 | + | 3.35520i | −0.252310 | + | 0.183314i | ||||
\(336\) | 0.809017 | − | 0.587785i | 0.0441355 | − | 0.0320663i | ||||
\(337\) | 11.0279 | + | 33.9403i | 0.600726 | + | 1.84884i | 0.523862 | + | 0.851803i | \(0.324491\pi\) |
0.0768638 | + | 0.997042i | \(0.475509\pi\) | |||||||
\(338\) | −2.12868 | + | 6.55139i | −0.115785 | + | 0.356349i | ||||
\(339\) | −4.23607 | − | 3.07768i | −0.230072 | − | 0.167157i | ||||
\(340\) | 12.7082 | 0.689199 | ||||||||
\(341\) | 3.53444 | + | 5.96361i | 0.191401 | + | 0.322948i | ||||
\(342\) | −1.38197 | −0.0747282 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −0.472136 | + | 1.45309i | −0.0254559 | + | 0.0783451i | ||||
\(345\) | −0.690983 | − | 2.12663i | −0.0372013 | − | 0.114494i | ||||
\(346\) | 17.4443 | − | 12.6740i | 0.937810 | − | 0.681359i | ||||
\(347\) | −0.781153 | + | 0.567541i | −0.0419345 | + | 0.0304672i | −0.608555 | − | 0.793512i | \(-0.708251\pi\) |
0.566621 | + | 0.823979i | \(0.308251\pi\) | |||||||
\(348\) | −2.85410 | − | 8.78402i | −0.152996 | − | 0.470873i | ||||
\(349\) | −1.85410 | + | 5.70634i | −0.0992478 | + | 0.305453i | −0.988337 | − | 0.152280i | \(-0.951338\pi\) |
0.889090 | + | 0.457733i | \(0.151338\pi\) | |||||||
\(350\) | −1.92705 | − | 1.40008i | −0.103005 | − | 0.0748377i | ||||
\(351\) | 2.47214 | 0.131953 | ||||||||
\(352\) | −3.04508 | − | 1.31433i | −0.162304 | − | 0.0700539i | ||||
\(353\) | −2.58359 | −0.137511 | −0.0687554 | − | 0.997634i | \(-0.521903\pi\) | ||||
−0.0687554 | + | 0.997634i | \(0.521903\pi\) | |||||||
\(354\) | −2.85410 | − | 2.07363i | −0.151694 | − | 0.110212i | ||||
\(355\) | 6.00000 | − | 18.4661i | 0.318447 | − | 0.980079i | ||||
\(356\) | 3.66312 | + | 11.2739i | 0.194145 | + | 0.597517i | ||||
\(357\) | −6.35410 | + | 4.61653i | −0.336295 | + | 0.244332i | ||||
\(358\) | −15.3992 | + | 11.1882i | −0.813872 | + | 0.591313i | ||||
\(359\) | 1.02786 | + | 3.16344i | 0.0542486 | + | 0.166960i | 0.974510 | − | 0.224344i | \(-0.0720240\pi\) |
−0.920261 | + | 0.391304i | \(0.872024\pi\) | |||||||
\(360\) | −0.500000 | + | 1.53884i | −0.0263523 | + | 0.0811041i | ||||
\(361\) | 13.8262 | + | 10.0453i | 0.727697 | + | 0.528703i | ||||
\(362\) | 8.18034 | 0.429949 | ||||||||
\(363\) | 9.94427 | − | 4.70228i | 0.521939 | − | 0.246806i | ||||
\(364\) | −2.47214 | −0.129575 | ||||||||
\(365\) | −3.85410 | − | 2.80017i | −0.201733 | − | 0.146568i | ||||
\(366\) | 1.09017 | − | 3.35520i | 0.0569841 | − | 0.175379i | ||||
\(367\) | 4.29837 | + | 13.2290i | 0.224373 | + | 0.690550i | 0.998355 | + | 0.0573416i | \(0.0182624\pi\) |
−0.773981 | + | 0.633208i | \(0.781738\pi\) | |||||||
\(368\) | −1.11803 | + | 0.812299i | −0.0582816 | + | 0.0423440i | ||||
\(369\) | −4.30902 | + | 3.13068i | −0.224318 | + | 0.162977i | ||||
\(370\) | 0.572949 | + | 1.76336i | 0.0297862 | + | 0.0916725i | ||||
\(371\) | 1.14590 | − | 3.52671i | 0.0594921 | − | 0.183098i | ||||
\(372\) | −1.69098 | − | 1.22857i | −0.0876734 | − | 0.0636984i | ||||
\(373\) | 19.0344 | 0.985566 | 0.492783 | − | 0.870152i | \(-0.335980\pi\) | ||||
0.492783 | + | 0.870152i | \(0.335980\pi\) | |||||||
\(374\) | 23.9164 | + | 10.3229i | 1.23669 | + | 0.533783i | ||||
\(375\) | 11.9443 | 0.616800 | ||||||||
\(376\) | 6.23607 | + | 4.53077i | 0.321601 | + | 0.233657i | ||||
\(377\) | −7.05573 | + | 21.7153i | −0.363388 | + | 1.11839i | ||||
\(378\) | −0.309017 | − | 0.951057i | −0.0158941 | − | 0.0489171i | ||||
\(379\) | −24.7984 | + | 18.0171i | −1.27381 | + | 0.925475i | −0.999347 | − | 0.0361237i | \(-0.988499\pi\) |
−0.274460 | + | 0.961599i | \(0.588499\pi\) | |||||||
\(380\) | −1.80902 | + | 1.31433i | −0.0928006 | + | 0.0674236i | ||||
\(381\) | −5.09017 | − | 15.6659i | −0.260777 | − | 0.802590i | ||||
\(382\) | 1.20820 | − | 3.71847i | 0.0618171 | − | 0.190253i | ||||
\(383\) | −8.85410 | − | 6.43288i | −0.452423 | − | 0.328705i | 0.338128 | − | 0.941100i | \(-0.390206\pi\) |
−0.790552 | + | 0.612395i | \(0.790206\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.73607 | + | 4.61653i | 0.139443 | + | 0.235280i | ||||
\(386\) | −19.5066 | −0.992859 | ||||||||
\(387\) | 1.23607 | + | 0.898056i | 0.0628329 | + | 0.0456507i | ||||
\(388\) | −4.00000 | + | 12.3107i | −0.203069 | + | 0.624983i | ||||
\(389\) | −11.4164 | − | 35.1361i | −0.578835 | − | 1.78147i | −0.622733 | − | 0.782434i | \(-0.713978\pi\) |
0.0438980 | − | 0.999036i | \(-0.486022\pi\) | |||||||
\(390\) | 3.23607 | − | 2.35114i | 0.163865 | − | 0.119055i | ||||
\(391\) | 8.78115 | − | 6.37988i | 0.444082 | − | 0.322644i | ||||
\(392\) | 0.309017 | + | 0.951057i | 0.0156077 | + | 0.0480356i | ||||
\(393\) | −5.85410 | + | 18.0171i | −0.295300 | + | 0.908841i | ||||
\(394\) | 9.61803 | + | 6.98791i | 0.484550 | + | 0.352046i | ||||
\(395\) | 8.47214 | 0.426279 | ||||||||
\(396\) | −2.19098 | + | 2.48990i | −0.110101 | + | 0.125122i | ||||
\(397\) | −11.7082 | −0.587618 | −0.293809 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293809 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(398\) | 0.263932 | + | 0.191758i | 0.0132297 | + | 0.00961195i | ||||
\(399\) | 0.427051 | − | 1.31433i | 0.0213793 | − | 0.0657987i | ||||
\(400\) | −0.736068 | − | 2.26538i | −0.0368034 | − | 0.113269i | ||||
\(401\) | −1.14590 | + | 0.832544i | −0.0572234 | + | 0.0415752i | −0.616029 | − | 0.787723i | \(-0.711260\pi\) |
0.558806 | + | 0.829299i | \(0.311260\pi\) | |||||||
\(402\) | 2.85410 | − | 2.07363i | 0.142350 | − | 0.103423i | ||||
\(403\) | 1.59675 | + | 4.91428i | 0.0795397 | + | 0.244798i | ||||
\(404\) | −0.263932 | + | 0.812299i | −0.0131311 | + | 0.0404134i | ||||
\(405\) | 1.30902 | + | 0.951057i | 0.0650456 | + | 0.0472584i | ||||
\(406\) | 9.23607 | 0.458378 | ||||||||
\(407\) | −0.354102 | + | 3.78398i | −0.0175522 | + | 0.187565i | ||||
\(408\) | −7.85410 | −0.388836 | ||||||||
\(409\) | 7.09017 | + | 5.15131i | 0.350586 | + | 0.254716i | 0.749115 | − | 0.662440i | \(-0.230479\pi\) |
−0.398529 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(410\) | −2.66312 | + | 8.19624i | −0.131522 | + | 0.404783i | ||||
\(411\) | 1.38197 | + | 4.25325i | 0.0681674 | + | 0.209798i | ||||
\(412\) | −7.97214 | + | 5.79210i | −0.392759 | + | 0.285356i | ||||
\(413\) | 2.85410 | − | 2.07363i | 0.140441 | − | 0.102036i | ||||
\(414\) | 0.427051 | + | 1.31433i | 0.0209884 | + | 0.0645957i | ||||
\(415\) | 5.70820 | − | 17.5680i | 0.280205 | − | 0.862381i | ||||
\(416\) | −2.00000 | − | 1.45309i | −0.0980581 | − | 0.0712434i | ||||
\(417\) | 19.2705 | 0.943681 | ||||||||
\(418\) | −4.47214 | + | 1.00406i | −0.218739 | + | 0.0491100i | ||||
\(419\) | 38.6525 | 1.88830 | 0.944149 | − | 0.329520i | \(-0.106887\pi\) | ||||
0.944149 | + | 0.329520i | \(0.106887\pi\) | |||||||
\(420\) | −1.30902 | − | 0.951057i | −0.0638735 | − | 0.0464068i | ||||
\(421\) | 11.9549 | − | 36.7934i | 0.582647 | − | 1.79320i | −0.0258743 | − | 0.999665i | \(-0.508237\pi\) |
0.608521 | − | 0.793538i | \(-0.291763\pi\) | |||||||
\(422\) | −0.763932 | − | 2.35114i | −0.0371876 | − | 0.114452i | ||||
\(423\) | 6.23607 | − | 4.53077i | 0.303208 | − | 0.220294i | ||||
\(424\) | 3.00000 | − | 2.17963i | 0.145693 | − | 0.105852i | ||||
\(425\) | 5.78115 | + | 17.7926i | 0.280427 | + | 0.863066i | ||||
\(426\) | −3.70820 | + | 11.4127i | −0.179663 | + | 0.552946i | ||||
\(427\) | 2.85410 | + | 2.07363i | 0.138120 | + | 0.100350i | ||||
\(428\) | −17.8541 | −0.863011 | ||||||||
\(429\) | 8.00000 | − | 1.79611i | 0.386244 | − | 0.0867171i | ||||
\(430\) | 2.47214 | 0.119217 | ||||||||
\(431\) | −21.0172 | − | 15.2699i | −1.01236 | − | 0.735525i | −0.0476603 | − | 0.998864i | \(-0.515177\pi\) |
−0.964704 | + | 0.263338i | \(0.915177\pi\) | |||||||
\(432\) | 0.309017 | − | 0.951057i | 0.0148676 | − | 0.0457577i | ||||
\(433\) | 6.94427 | + | 21.3723i | 0.333720 | + | 1.02709i | 0.967349 | + | 0.253448i | \(0.0815648\pi\) |
−0.633629 | + | 0.773637i | \(0.718435\pi\) | |||||||
\(434\) | 1.69098 | − | 1.22857i | 0.0811698 | − | 0.0589733i | ||||
\(435\) | −12.0902 | + | 8.78402i | −0.579679 | + | 0.421162i | ||||
\(436\) | 5.11803 | + | 15.7517i | 0.245109 | + | 0.754369i | ||||
\(437\) | −0.590170 | + | 1.81636i | −0.0282317 | + | 0.0868881i | ||||
\(438\) | 2.38197 | + | 1.73060i | 0.113815 | + | 0.0826912i | ||||
\(439\) | 28.5623 | 1.36320 | 0.681602 | − | 0.731723i | \(-0.261283\pi\) | ||||
0.681602 | + | 0.731723i | \(0.261283\pi\) | |||||||
\(440\) | −0.500000 | + | 5.34307i | −0.0238366 | + | 0.254721i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 15.7082 | + | 11.4127i | 0.747163 | + | 0.542846i | ||||
\(443\) | 4.07953 | − | 12.5555i | 0.193824 | − | 0.596529i | −0.806164 | − | 0.591692i | \(-0.798460\pi\) |
0.999988 | − | 0.00483748i | \(-0.00153982\pi\) | |||||||
\(444\) | −0.354102 | − | 1.08981i | −0.0168049 | − | 0.0517203i | ||||
\(445\) | 15.5172 | − | 11.2739i | 0.735587 | − | 0.534435i | ||||
\(446\) | 1.97214 | − | 1.43284i | 0.0933833 | − | 0.0678470i | ||||
\(447\) | −4.47214 | − | 13.7638i | −0.211525 | − | 0.651006i | ||||
\(448\) | −0.309017 | + | 0.951057i | −0.0145997 | + | 0.0449332i | ||||
\(449\) | −13.0902 | − | 9.51057i | −0.617763 | − | 0.448831i | 0.234376 | − | 0.972146i | \(-0.424695\pi\) |
−0.852140 | + | 0.523315i | \(0.824695\pi\) | |||||||
\(450\) | −2.38197 | −0.112287 | ||||||||
\(451\) | −11.6697 | + | 13.2618i | −0.549505 | + | 0.624473i | ||||
\(452\) | 5.23607 | 0.246284 | ||||||||
\(453\) | 3.85410 | + | 2.80017i | 0.181082 | + | 0.131563i | ||||
\(454\) | 3.94427 | − | 12.1392i | 0.185114 | − | 0.569722i | ||||
\(455\) | 1.23607 | + | 3.80423i | 0.0579478 | + | 0.178345i | ||||
\(456\) | 1.11803 | − | 0.812299i | 0.0523567 | − | 0.0380394i | ||||
\(457\) | −4.38197 | + | 3.18368i | −0.204980 | + | 0.148926i | −0.685539 | − | 0.728036i | \(-0.740434\pi\) |
0.480560 | + | 0.876962i | \(0.340434\pi\) | |||||||
\(458\) | −1.76393 | − | 5.42882i | −0.0824231 | − | 0.253672i | ||||
\(459\) | −2.42705 | + | 7.46969i | −0.113285 | + | 0.348655i | ||||
\(460\) | 1.80902 | + | 1.31433i | 0.0843459 | + | 0.0612808i | ||||
\(461\) | −30.3607 | −1.41404 | −0.707019 | − | 0.707195i | \(-0.749960\pi\) | ||||
−0.707019 | + | 0.707195i | \(0.749960\pi\) | |||||||
\(462\) | −1.69098 | − | 2.85317i | −0.0786716 | − | 0.132741i | ||||
\(463\) | 2.18034 | 0.101329 | 0.0506645 | − | 0.998716i | \(-0.483866\pi\) | ||||
0.0506645 | + | 0.998716i | \(0.483866\pi\) | |||||||
\(464\) | 7.47214 | + | 5.42882i | 0.346885 | + | 0.252027i | ||||
\(465\) | −1.04508 | + | 3.21644i | −0.0484647 | + | 0.149159i | ||||
\(466\) | −4.94427 | − | 15.2169i | −0.229039 | − | 0.704909i | ||||
\(467\) | 22.4164 | − | 16.2865i | 1.03731 | − | 0.753648i | 0.0675495 | − | 0.997716i | \(-0.478482\pi\) |
0.969758 | + | 0.244068i | \(0.0784819\pi\) | |||||||
\(468\) | −2.00000 | + | 1.45309i | −0.0924500 | + | 0.0671689i | ||||
\(469\) | 1.09017 | + | 3.35520i | 0.0503394 | + | 0.154929i | ||||
\(470\) | 3.85410 | − | 11.8617i | 0.177776 | − | 0.547140i | ||||
\(471\) | −7.85410 | − | 5.70634i | −0.361898 | − | 0.262934i | ||||
\(472\) | 3.52786 | 0.162383 | ||||||||
\(473\) | 4.65248 | + | 2.00811i | 0.213921 | + | 0.0923332i | ||||
\(474\) | −5.23607 | −0.240501 | ||||||||
\(475\) | −2.66312 | − | 1.93487i | −0.122192 | − | 0.0887779i | ||||
\(476\) | 2.42705 | − | 7.46969i | 0.111244 | − | 0.342373i | ||||
\(477\) | −1.14590 | − | 3.52671i | −0.0524671 | − | 0.161477i | ||||
\(478\) | −16.8262 | + | 12.2250i | −0.769614 | + | 0.559157i | ||||
\(479\) | 14.1803 | − | 10.3026i | 0.647916 | − | 0.470739i | −0.214644 | − | 0.976692i | \(-0.568859\pi\) |
0.862561 | + | 0.505954i | \(0.168859\pi\) | |||||||
\(480\) | −0.500000 | − | 1.53884i | −0.0228218 | − | 0.0702382i | ||||
\(481\) | −0.875388 | + | 2.69417i | −0.0399143 | + | 0.122843i | ||||
\(482\) | 3.61803 | + | 2.62866i | 0.164797 | + | 0.119732i | ||||
\(483\) | −1.38197 | −0.0628816 | ||||||||
\(484\) | −5.28115 | + | 9.64932i | −0.240052 | + | 0.438606i | ||||
\(485\) | 20.9443 | 0.951030 | ||||||||
\(486\) | −0.809017 | − | 0.587785i | −0.0366978 | − | 0.0266625i | ||||
\(487\) | 0.965558 | − | 2.97168i | 0.0437536 | − | 0.134660i | −0.926793 | − | 0.375572i | \(-0.877446\pi\) |
0.970547 | + | 0.240912i | \(0.0774464\pi\) | |||||||
\(488\) | 1.09017 | + | 3.35520i | 0.0493497 | + | 0.151883i | ||||
\(489\) | 12.0902 | − | 8.78402i | 0.546736 | − | 0.397227i | ||||
\(490\) | 1.30902 | − | 0.951057i | 0.0591354 | − | 0.0429644i | ||||
\(491\) | 7.51722 | + | 23.1356i | 0.339247 | + | 1.04410i | 0.964592 | + | 0.263747i | \(0.0849585\pi\) |
−0.625344 | + | 0.780349i | \(0.715041\pi\) | |||||||
\(492\) | 1.64590 | − | 5.06555i | 0.0742028 | − | 0.228373i | ||||
\(493\) | −58.6869 | − | 42.6385i | −2.64313 | − | 1.92034i | ||||
\(494\) | −3.41641 | −0.153711 | ||||||||
\(495\) | 4.92705 | + | 2.12663i | 0.221454 | + | 0.0955848i | ||||
\(496\) | 2.09017 | 0.0938514 | ||||||||
\(497\) | −9.70820 | − | 7.05342i | −0.435472 | − | 0.316389i | ||||
\(498\) | −3.52786 | + | 10.8576i | −0.158087 | + | 0.486543i | ||||
\(499\) | −4.76393 | − | 14.6619i | −0.213263 | − | 0.656356i | −0.999272 | − | 0.0381412i | \(-0.987856\pi\) |
0.786009 | − | 0.618214i | \(-0.212144\pi\) | |||||||
\(500\) | −9.66312 | + | 7.02067i | −0.432148 | + | 0.313974i | ||||
\(501\) | −18.9443 | + | 13.7638i | −0.846368 | + | 0.614922i | ||||
\(502\) | 4.85410 | + | 14.9394i | 0.216649 | + | 0.666778i | ||||
\(503\) | 7.38197 | − | 22.7194i | 0.329146 | − | 1.01301i | −0.640389 | − | 0.768051i | \(-0.721227\pi\) |
0.969534 | − | 0.244955i | \(-0.0787732\pi\) | |||||||
\(504\) | 0.809017 | + | 0.587785i | 0.0360365 | + | 0.0261820i | ||||
\(505\) | 1.38197 | 0.0614967 | ||||||||
\(506\) | 2.33688 | + | 3.94298i | 0.103887 | + | 0.175287i | ||||
\(507\) | −6.88854 | −0.305931 | ||||||||
\(508\) | 13.3262 | + | 9.68208i | 0.591256 | + | 0.429573i | ||||
\(509\) | 4.73607 | − | 14.5761i | 0.209923 | − | 0.646075i | −0.789553 | − | 0.613683i | \(-0.789687\pi\) |
0.999475 | − | 0.0323923i | \(-0.0103126\pi\) | |||||||
\(510\) | 3.92705 | + | 12.0862i | 0.173893 | + | 0.535187i | ||||
\(511\) | −2.38197 | + | 1.73060i | −0.105372 | + | 0.0765572i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | −0.427051 | − | 1.31433i | −0.0188548 | − | 0.0580290i | ||||
\(514\) | 4.42705 | − | 13.6251i | 0.195269 | − | 0.600976i | ||||
\(515\) | 12.8992 | + | 9.37181i | 0.568406 | + | 0.412971i | ||||
\(516\) | −1.52786 | −0.0672605 | ||||||||
\(517\) | 16.8885 | − | 19.1926i | 0.742757 | − | 0.844092i | ||||
\(518\) | 1.14590 | 0.0503479 | ||||||||
\(519\) | 17.4443 | + | 12.6740i | 0.765719 | + | 0.556327i | ||||
\(520\) | −1.23607 | + | 3.80423i | −0.0542052 | + | 0.166826i | ||||
\(521\) | 11.7705 | + | 36.2259i | 0.515675 | + | 1.58709i | 0.782050 | + | 0.623216i | \(0.214174\pi\) |
−0.266374 | + | 0.963870i | \(0.585826\pi\) | |||||||
\(522\) | 7.47214 | − | 5.42882i | 0.327047 | − | 0.237613i | ||||
\(523\) | −16.0623 | + | 11.6699i | −0.702356 | + | 0.510291i | −0.880699 | − | 0.473677i | \(-0.842926\pi\) |
0.178343 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(524\) | −5.85410 | − | 18.0171i | −0.255738 | − | 0.787079i | ||||
\(525\) | 0.736068 | − | 2.26538i | 0.0321246 | − | 0.0988695i | ||||
\(526\) | 21.5344 | + | 15.6457i | 0.938946 | + | 0.682184i | ||||
\(527\) | −16.4164 | −0.715110 | ||||||||
\(528\) | 0.309017 | − | 3.30220i | 0.0134482 | − | 0.143710i | ||||
\(529\) | −21.0902 | −0.916964 | ||||||||
\(530\) | −4.85410 | − | 3.52671i | −0.210849 | − | 0.153191i | ||||
\(531\) | 1.09017 | − | 3.35520i | 0.0473093 | − | 0.145603i | ||||
\(532\) | 0.427051 | + | 1.31433i | 0.0185150 | + | 0.0569833i | ||||
\(533\) | −10.6525 | + | 7.73948i | −0.461410 | + | 0.335234i | ||||
\(534\) | −9.59017 | + | 6.96767i | −0.415007 | + | 0.301520i | ||||
\(535\) | 8.92705 | + | 27.4746i | 0.385950 | + | 1.18783i | ||||
\(536\) | −1.09017 | + | 3.35520i | −0.0470882 | + | 0.144922i | ||||
\(537\) | −15.3992 | − | 11.1882i | −0.664524 | − | 0.482805i | ||||
\(538\) | −1.05573 | −0.0455157 | ||||||||
\(539\) | 3.23607 | − | 0.726543i | 0.139387 | − | 0.0312944i | ||||
\(540\) | −1.61803 | −0.0696291 | ||||||||
\(541\) | −26.0172 | − | 18.9026i | −1.11857 | − | 0.812687i | −0.134576 | − | 0.990903i | \(-0.542967\pi\) |
−0.983991 | + | 0.178216i | \(0.942967\pi\) | |||||||
\(542\) | −9.64590 | + | 29.6870i | −0.414327 | + | 1.27517i | ||||
\(543\) | 2.52786 | + | 7.77997i | 0.108481 | + | 0.333870i | ||||
\(544\) | 6.35410 | − | 4.61653i | 0.272430 | − | 0.197932i | ||||
\(545\) | 21.6803 | − | 15.7517i | 0.928684 | − | 0.674728i | ||||
\(546\) | −0.763932 | − | 2.35114i | −0.0326933 | − | 0.100620i | ||||
\(547\) | −1.11146 | + | 3.42071i | −0.0475224 | + | 0.146259i | −0.972002 | − | 0.234973i | \(-0.924500\pi\) |
0.924480 | + | 0.381232i | \(0.124500\pi\) | |||||||
\(548\) | −3.61803 | − | 2.62866i | −0.154555 | − | 0.112291i | ||||
\(549\) | 3.52786 | 0.150566 | ||||||||
\(550\) | −7.70820 | + | 1.73060i | −0.328679 | + | 0.0737930i | ||||
\(551\) | 12.7639 | 0.543762 | ||||||||
\(552\) | −1.11803 | − | 0.812299i | −0.0475867 | − | 0.0345738i | ||||
\(553\) | 1.61803 | − | 4.97980i | 0.0688058 | − | 0.211762i | ||||
\(554\) | 5.95492 | + | 18.3273i | 0.253000 | + | 0.778654i | ||||
\(555\) | −1.50000 | + | 1.08981i | −0.0636715 | + | 0.0462600i | ||||
\(556\) | −15.5902 | + | 11.3269i | −0.661170 | + | 0.480368i | ||||
\(557\) | −9.09017 | − | 27.9767i | −0.385163 | − | 1.18541i | −0.936362 | − | 0.351036i | \(-0.885830\pi\) |
0.551199 | − | 0.834374i | \(-0.314170\pi\) | |||||||
\(558\) | 0.645898 | − | 1.98787i | 0.0273430 | − | 0.0841532i | ||||
\(559\) | 3.05573 | + | 2.22012i | 0.129244 | + | 0.0939009i | ||||
\(560\) | 1.61803 | 0.0683744 | ||||||||
\(561\) | −2.42705 | + | 25.9358i | −0.102470 | + | 1.09501i | ||||
\(562\) | −5.52786 | −0.233179 | ||||||||
\(563\) | −12.2361 | − | 8.89002i | −0.515689 | − | 0.374670i | 0.299289 | − | 0.954163i | \(-0.403251\pi\) |
−0.814977 | + | 0.579493i | \(0.803251\pi\) | |||||||
\(564\) | −2.38197 | + | 7.33094i | −0.100299 | + | 0.308688i | ||||
\(565\) | −2.61803 | − | 8.05748i | −0.110142 | − | 0.338981i | ||||
\(566\) | 2.54508 | − | 1.84911i | 0.106978 | − | 0.0777240i | ||||
\(567\) | 0.809017 | − | 0.587785i | 0.0339755 | − | 0.0246847i | ||||
\(568\) | −3.70820 | − | 11.4127i | −0.155593 | − | 0.478865i | ||||
\(569\) | −10.9443 | + | 33.6830i | −0.458808 | + | 1.41207i | 0.407798 | + | 0.913072i | \(0.366297\pi\) |
−0.866606 | + | 0.498993i | \(0.833703\pi\) | |||||||
\(570\) | −1.80902 | − | 1.31433i | −0.0757714 | − | 0.0550511i | ||||
\(571\) | 2.29180 | 0.0959087 | 0.0479543 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479543 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(572\) | −5.41641 | + | 6.15537i | −0.226471 | + | 0.257369i | ||||
\(573\) | 3.90983 | 0.163335 | ||||||||
\(574\) | 4.30902 | + | 3.13068i | 0.179855 | + | 0.130672i | ||||
\(575\) | −1.01722 | + | 3.13068i | −0.0424210 | + | 0.130559i | ||||
\(576\) | 0.309017 | + | 0.951057i | 0.0128757 | + | 0.0396274i | ||||
\(577\) | −21.1803 | + | 15.3884i | −0.881749 | + | 0.640628i | −0.933714 | − | 0.358021i | \(-0.883452\pi\) |
0.0519646 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(578\) | −36.1525 | + | 26.2663i | −1.50374 | + | 1.09253i | ||||
\(579\) | −6.02786 | − | 18.5519i | −0.250509 | − | 0.770989i | ||||
\(580\) | 4.61803 | − | 14.2128i | 0.191753 | − | 0.590156i | ||||
\(581\) | −9.23607 | − | 6.71040i | −0.383177 | − | 0.278394i | ||||
\(582\) | −12.9443 | −0.536557 | ||||||||
\(583\) | −6.27051 | − | 10.5801i | −0.259698 | − | 0.438184i | ||||
\(584\) | −2.94427 | −0.121835 | ||||||||
\(585\) | 3.23607 | + | 2.35114i | 0.133795 | + | 0.0972077i | ||||
\(586\) | −0.736068 | + | 2.26538i | −0.0304067 | + | 0.0935822i | ||||
\(587\) | −6.61803 | − | 20.3682i | −0.273155 | − | 0.840686i | −0.989702 | − | 0.143146i | \(-0.954278\pi\) |
0.716546 | − | 0.697540i | \(-0.245722\pi\) | |||||||
\(588\) | −0.809017 | + | 0.587785i | −0.0333633 | + | 0.0242399i | ||||
\(589\) | 2.33688 | − | 1.69784i | 0.0962895 | − | 0.0699584i | ||||
\(590\) | −1.76393 | − | 5.42882i | −0.0726199 | − | 0.223501i | ||||
\(591\) | −3.67376 | + | 11.3067i | −0.151118 | + | 0.465095i | ||||
\(592\) | 0.927051 | + | 0.673542i | 0.0381016 | + | 0.0276824i | ||||
\(593\) | 31.9787 | 1.31321 | 0.656604 | − | 0.754235i | \(-0.271992\pi\) | ||||
0.656604 | + | 0.754235i | \(0.271992\pi\) | |||||||
\(594\) | −3.04508 | − | 1.31433i | −0.124941 | − | 0.0539275i | ||||
\(595\) | −12.7082 | −0.520986 | ||||||||
\(596\) | 11.7082 | + | 8.50651i | 0.479587 | + | 0.348440i | ||||
\(597\) | −0.100813 | + | 0.310271i | −0.00412600 | + | 0.0126985i | ||||
\(598\) | 1.05573 | + | 3.24920i | 0.0431719 | + | 0.132870i | ||||
\(599\) | 16.5902 | − | 12.0535i | 0.677856 | − | 0.492491i | −0.194790 | − | 0.980845i | \(-0.562402\pi\) |
0.872646 | + | 0.488354i | \(0.162402\pi\) | |||||||
\(600\) | 1.92705 | − | 1.40008i | 0.0786715 | − | 0.0571582i | ||||
\(601\) | −1.09017 | − | 3.35520i | −0.0444690 | − | 0.136861i | 0.926357 | − | 0.376647i | \(-0.122923\pi\) |
−0.970826 | + | 0.239785i | \(0.922923\pi\) | |||||||
\(602\) | 0.472136 | − | 1.45309i | 0.0192428 | − | 0.0592233i | ||||
\(603\) | 2.85410 | + | 2.07363i | 0.116228 | + | 0.0844446i | ||||
\(604\) | −4.76393 | −0.193842 | ||||||||
\(605\) | 17.4894 | + | 3.30220i | 0.711043 | + | 0.134253i | ||||
\(606\) | −0.854102 | −0.0346955 | ||||||||
\(607\) | 8.97214 | + | 6.51864i | 0.364168 | + | 0.264583i | 0.754788 | − | 0.655968i | \(-0.227740\pi\) |
−0.390621 | + | 0.920552i | \(0.627740\pi\) | |||||||
\(608\) | −0.427051 | + | 1.31433i | −0.0173192 | + | 0.0533030i | ||||
\(609\) | 2.85410 | + | 8.78402i | 0.115654 | + | 0.355947i | ||||
\(610\) | 4.61803 | − | 3.35520i | 0.186979 | − | 0.135848i | ||||
\(611\) | 15.4164 | − | 11.2007i | 0.623681 | − | 0.453131i | ||||
\(612\) | −2.42705 | − | 7.46969i | −0.0981077 | − | 0.301945i | ||||
\(613\) | −8.80902 | + | 27.1114i | −0.355793 | + | 1.09502i | 0.599755 | + | 0.800183i | \(0.295265\pi\) |
−0.955548 | + | 0.294834i | \(0.904735\pi\) | |||||||
\(614\) | 10.3992 | + | 7.55545i | 0.419677 | + | 0.304913i | ||||
\(615\) | −8.61803 | −0.347513 | ||||||||
\(616\) | 3.04508 | + | 1.31433i | 0.122690 | + | 0.0529558i | ||||
\(617\) | −27.0132 | −1.08751 | −0.543754 | − | 0.839244i | \(-0.682998\pi\) | ||||
−0.543754 | + | 0.839244i | \(0.682998\pi\) | |||||||
\(618\) | −7.97214 | − | 5.79210i | −0.320686 | − | 0.232992i | ||||
\(619\) | 1.97214 | − | 6.06961i | 0.0792668 | − | 0.243958i | −0.903568 | − | 0.428444i | \(-0.859062\pi\) |
0.982835 | + | 0.184486i | \(0.0590619\pi\) | |||||||
\(620\) | −1.04508 | − | 3.21644i | −0.0419716 | − | 0.129175i | ||||
\(621\) | −1.11803 | + | 0.812299i | −0.0448652 | + | 0.0325964i | ||||
\(622\) | 23.9443 | − | 17.3965i | 0.960078 | − | 0.697537i | ||||
\(623\) | −3.66312 | − | 11.2739i | −0.146760 | − | 0.451680i | ||||
\(624\) | 0.763932 | − | 2.35114i | 0.0305818 | − | 0.0941210i | ||||
\(625\) | 6.00000 | + | 4.35926i | 0.240000 | + | 0.174370i | ||||
\(626\) | 11.7082 | 0.467954 | ||||||||
\(627\) | −2.33688 | − | 3.94298i | −0.0933260 | − | 0.157468i | ||||
\(628\) | 9.70820 | 0.387400 | ||||||||
\(629\) | −7.28115 | − | 5.29007i | −0.290319 | − | 0.210929i | ||||
\(630\) | 0.500000 | − | 1.53884i | 0.0199205 | − | 0.0613089i | ||||
\(631\) | 0.326238 | + | 1.00406i | 0.0129873 | + | 0.0399709i | 0.957340 | − | 0.288963i | \(-0.0933106\pi\) |
−0.944353 | + | 0.328934i | \(0.893311\pi\) | |||||||
\(632\) | 4.23607 | − | 3.07768i | 0.168502 | − | 0.122424i | ||||
\(633\) | 2.00000 | − | 1.45309i | 0.0794929 | − | 0.0577549i | ||||
\(634\) | −2.67376 | − | 8.22899i | −0.106189 | − | 0.326815i | ||||
\(635\) | 8.23607 | − | 25.3480i | 0.326838 | − | 1.00591i | ||||
\(636\) | 3.00000 | + | 2.17963i | 0.118958 | + | 0.0864279i | ||||
\(637\) | 2.47214 | 0.0979496 | ||||||||
\(638\) | 20.2361 | − | 22.9969i | 0.801154 | − | 0.910455i | ||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 1.30902 | + | 0.951057i | 0.0517434 | + | 0.0375938i | ||||
\(641\) | −9.56231 | + | 29.4298i | −0.377688 | + | 1.16241i | 0.563959 | + | 0.825803i | \(0.309278\pi\) |
−0.941647 | + | 0.336602i | \(0.890722\pi\) | |||||||
\(642\) | −5.51722 | − | 16.9803i | −0.217747 | − | 0.670157i | ||||
\(643\) | −6.59017 | + | 4.78804i | −0.259891 | + | 0.188822i | −0.710099 | − | 0.704102i | \(-0.751350\pi\) |
0.450208 | + | 0.892924i | \(0.351350\pi\) | |||||||
\(644\) | 1.11803 | − | 0.812299i | 0.0440567 | − | 0.0320091i | ||||
\(645\) | 0.763932 | + | 2.35114i | 0.0300798 | + | 0.0925761i | ||||
\(646\) | 3.35410 | − | 10.3229i | 0.131965 | − | 0.406148i | ||||
\(647\) | −3.00000 | − | 2.17963i | −0.117942 | − | 0.0856900i | 0.527251 | − | 0.849710i | \(-0.323223\pi\) |
−0.645193 | + | 0.764020i | \(0.723223\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.09017 | − | 11.6497i | 0.0427929 | − | 0.457291i | ||||
\(650\) | −5.88854 | −0.230968 | ||||||||
\(651\) | 1.69098 | + | 1.22857i | 0.0662748 | + | 0.0481515i | ||||
\(652\) | −4.61803 | + | 14.2128i | −0.180856 | + | 0.556618i | ||||
\(653\) | −4.27051 | − | 13.1433i | −0.167118 | − | 0.514336i | 0.832068 | − | 0.554673i | \(-0.187157\pi\) |
−0.999186 | + | 0.0403372i | \(0.987157\pi\) | |||||||
\(654\) | −13.3992 | + | 9.73508i | −0.523950 | + | 0.380672i | ||||
\(655\) | −24.7984 | + | 18.0171i | −0.968953 | + | 0.703985i | ||||
\(656\) | 1.64590 | + | 5.06555i | 0.0642615 | + | 0.197777i | ||||
\(657\) | −0.909830 | + | 2.80017i | −0.0354959 | + | 0.109245i | ||||
\(658\) | −6.23607 | − | 4.53077i | −0.243107 | − | 0.176628i | ||||
\(659\) | 5.72949 | 0.223189 | 0.111595 | − | 0.993754i | \(-0.464404\pi\) | ||||
0.111595 | + | 0.993754i | \(0.464404\pi\) | |||||||
\(660\) | −5.23607 | + | 1.17557i | −0.203814 | + | 0.0457590i | ||||
\(661\) | −37.1246 | −1.44398 | −0.721990 | − | 0.691903i | \(-0.756772\pi\) | ||||
−0.721990 | + | 0.691903i | \(0.756772\pi\) | |||||||
\(662\) | 14.4721 | + | 10.5146i | 0.562476 | + | 0.408662i | ||||
\(663\) | −6.00000 | + | 18.4661i | −0.233021 | + | 0.717164i | ||||
\(664\) | −3.52786 | − | 10.8576i | −0.136908 | − | 0.421359i | ||||
\(665\) | 1.80902 | − | 1.31433i | 0.0701507 | − | 0.0509674i | ||||
\(666\) | 0.927051 | − | 0.673542i | 0.0359225 | − | 0.0260992i | ||||
\(667\) | −3.94427 | − | 12.1392i | −0.152723 | − | 0.470033i | ||||
\(668\) | 7.23607 | − | 22.2703i | 0.279972 | − | 0.861665i | ||||
\(669\) | 1.97214 | + | 1.43284i | 0.0762472 | + | 0.0553968i | ||||
\(670\) | 5.70820 | 0.220527 | ||||||||
\(671\) | 11.4164 | − | 2.56314i | 0.440726 | − | 0.0989490i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −19.3262 | − | 14.0413i | −0.744972 | − | 0.541254i | 0.149292 | − | 0.988793i | \(-0.452300\pi\) |
−0.894264 | + | 0.447539i | \(0.852300\pi\) | |||||||
\(674\) | 11.0279 | − | 33.9403i | 0.424777 | − | 1.30733i | ||||
\(675\) | −0.736068 | − | 2.26538i | −0.0283313 | − | 0.0871947i | ||||
\(676\) | 5.57295 | − | 4.04898i | 0.214344 | − | 0.155730i | ||||
\(677\) | −14.0902 | + | 10.2371i | −0.541529 | + | 0.393444i | −0.824653 | − | 0.565639i | \(-0.808629\pi\) |
0.283123 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(678\) | 1.61803 | + | 4.97980i | 0.0621402 | + | 0.191248i | ||||
\(679\) | 4.00000 | − | 12.3107i | 0.153506 | − | 0.472443i | ||||
\(680\) | −10.2812 | − | 7.46969i | −0.394264 | − | 0.286450i | ||||
\(681\) | 12.7639 | 0.489115 | ||||||||
\(682\) | 0.645898 | − | 6.90215i | 0.0247327 | − | 0.264297i | ||||
\(683\) | 40.7426 | 1.55897 | 0.779487 | − | 0.626418i | \(-0.215480\pi\) | ||||
0.779487 | + | 0.626418i | \(0.215480\pi\) | |||||||
\(684\) | 1.11803 | + | 0.812299i | 0.0427491 | + | 0.0310590i | ||||
\(685\) | −2.23607 | + | 6.88191i | −0.0854358 | + | 0.262944i | ||||
\(686\) | −0.309017 | − | 0.951057i | −0.0117983 | − | 0.0363115i | ||||
\(687\) | 4.61803 | − | 3.35520i | 0.176189 | − | 0.128009i | ||||
\(688\) | 1.23607 | − | 0.898056i | 0.0471246 | − | 0.0342381i | ||||
\(689\) | −2.83282 | − | 8.71851i | −0.107922 | − | 0.332149i | ||||
\(690\) | −0.690983 | + | 2.12663i | −0.0263053 | + | 0.0809593i | ||||
\(691\) | −9.82624 | − | 7.13918i | −0.373808 | − | 0.271587i | 0.384980 | − | 0.922925i | \(-0.374208\pi\) |
−0.758788 | + | 0.651338i | \(0.774208\pi\) | |||||||
\(692\) | −21.5623 | −0.819676 | ||||||||
\(693\) | 2.19098 | − | 2.48990i | 0.0832286 | − | 0.0945834i | ||||
\(694\) | 0.965558 | 0.0366521 | ||||||||
\(695\) | 25.2254 | + | 18.3273i | 0.956855 | + | 0.695196i | ||||
\(696\) | −2.85410 | + | 8.78402i | −0.108184 | + | 0.332958i | ||||
\(697\) | −12.9271 | − | 39.7854i | −0.489647 | − | 1.50698i | ||||
\(698\) | 4.85410 | − | 3.52671i | 0.183730 | − | 0.133488i | ||||
\(699\) | 12.9443 | − | 9.40456i | 0.489597 | − | 0.355713i | ||||
\(700\) | 0.736068 | + | 2.26538i | 0.0278208 | + | 0.0856235i | ||||
\(701\) | −2.23607 | + | 6.88191i | −0.0844551 | + | 0.259926i | −0.984362 | − | 0.176155i | \(-0.943634\pi\) |
0.899907 | + | 0.436081i | \(0.143634\pi\) | |||||||
\(702\) | −2.00000 | − | 1.45309i | −0.0754851 | − | 0.0548432i | ||||
\(703\) | 1.58359 | 0.0597263 | ||||||||
\(704\) | 1.69098 | + | 2.85317i | 0.0637313 | + | 0.107533i | ||||
\(705\) | 12.4721 | 0.469728 | ||||||||
\(706\) | 2.09017 | + | 1.51860i | 0.0786646 | + | 0.0571532i | ||||
\(707\) | 0.263932 | − | 0.812299i | 0.00992619 | − | 0.0305497i | ||||
\(708\) | 1.09017 | + | 3.35520i | 0.0409711 | + | 0.126096i | ||||
\(709\) | −9.39919 | + | 6.82891i | −0.352994 | + | 0.256465i | −0.750124 | − | 0.661297i | \(-0.770006\pi\) |
0.397130 | + | 0.917762i | \(0.370006\pi\) | |||||||
\(710\) | −15.7082 | + | 11.4127i | −0.589518 | + | 0.428310i | ||||
\(711\) | −1.61803 | − | 4.97980i | −0.0606810 | − | 0.186757i | ||||
\(712\) | 3.66312 | − | 11.2739i | 0.137281 | − | 0.422508i | ||||
\(713\) | −2.33688 | − | 1.69784i | −0.0875169 | − | 0.0635847i | ||||
\(714\) | 7.85410 | 0.293932 | ||||||||
\(715\) | 12.1803 | + | 5.25731i | 0.455519 | + | 0.196612i | ||||
\(716\) | 19.0344 | 0.711350 | ||||||||
\(717\) | −16.8262 | − | 12.2250i | −0.628387 | − | 0.456550i | ||||
\(718\) | 1.02786 | − | 3.16344i | 0.0383595 | − | 0.118059i | ||||
\(719\) | −3.18034 | − | 9.78808i | −0.118607 | − | 0.365034i | 0.874076 | − | 0.485790i | \(-0.161468\pi\) |
−0.992682 | + | 0.120756i | \(0.961468\pi\) | |||||||
\(720\) | 1.30902 | − | 0.951057i | 0.0487842 | − | 0.0354438i | ||||
\(721\) | 7.97214 | − | 5.79210i | 0.296898 | − | 0.215709i | ||||
\(722\) | −5.28115 | − | 16.2537i | −0.196544 | − | 0.604901i | ||||
\(723\) | −1.38197 | + | 4.25325i | −0.0513959 | + | 0.158180i | ||||
\(724\) | −6.61803 | − | 4.80828i | −0.245957 | − | 0.178698i | ||||
\(725\) | 22.0000 | 0.817059 | ||||||||
\(726\) | −10.8090 | − | 2.04087i | −0.401160 | − | 0.0757438i | ||||
\(727\) | 23.4508 | 0.869744 | 0.434872 | − | 0.900492i | \(-0.356794\pi\) | ||||
0.434872 | + | 0.900492i | \(0.356794\pi\) | |||||||
\(728\) | 2.00000 | + | 1.45309i | 0.0741249 | + | 0.0538549i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 1.47214 | + | 4.53077i | 0.0544862 | + | 0.167691i | ||||
\(731\) | −9.70820 | + | 7.05342i | −0.359071 | + | 0.260880i | ||||
\(732\) | −2.85410 | + | 2.07363i | −0.105491 | + | 0.0766434i | ||||
\(733\) | −7.09017 | − | 21.8213i | −0.261881 | − | 0.805988i | −0.992395 | − | 0.123090i | \(-0.960719\pi\) |
0.730514 | − | 0.682898i | \(-0.239281\pi\) | |||||||
\(734\) | 4.29837 | − | 13.2290i | 0.158656 | − | 0.488293i | ||||
\(735\) | 1.30902 | + | 0.951057i | 0.0482838 | + | 0.0350802i | ||||
\(736\) | 1.38197 | 0.0509399 | ||||||||
\(737\) | 10.7426 | + | 4.63677i | 0.395710 | + | 0.170798i | ||||
\(738\) | 5.32624 | 0.196062 | ||||||||
\(739\) | 16.7082 | + | 12.1392i | 0.614621 | + | 0.446548i | 0.851039 | − | 0.525103i | \(-0.175973\pi\) |
−0.236417 | + | 0.971652i | \(0.575973\pi\) | |||||||
\(740\) | 0.572949 | − | 1.76336i | 0.0210620 | − | 0.0648222i | ||||
\(741\) | −1.05573 | − | 3.24920i | −0.0387831 | − | 0.119362i | ||||
\(742\) | −3.00000 | + | 2.17963i | −0.110133 | + | 0.0800166i | ||||
\(743\) | −18.2533 | + | 13.2618i | −0.669648 | + | 0.486528i | −0.869907 | − | 0.493215i | \(-0.835822\pi\) |
0.200259 | + | 0.979743i | \(0.435822\pi\) | |||||||
\(744\) | 0.645898 | + | 1.98787i | 0.0236798 | + | 0.0728788i | ||||
\(745\) | 7.23607 | − | 22.2703i | 0.265109 | − | 0.815922i | ||||
\(746\) | −15.3992 | − | 11.1882i | −0.563804 | − | 0.409628i | ||||
\(747\) | −11.4164 | −0.417705 | ||||||||
\(748\) | −13.2812 | − | 22.4091i | −0.485607 | − | 0.819357i | ||||
\(749\) | 17.8541 | 0.652375 | ||||||||
\(750\) | −9.66312 | − | 7.02067i | −0.352847 | − | 0.256359i | ||||
\(751\) | 9.43769 | − | 29.0462i | 0.344386 | − | 1.05991i | −0.617525 | − | 0.786551i | \(-0.711865\pi\) |
0.961911 | − | 0.273361i | \(-0.0881354\pi\) | |||||||
\(752\) | −2.38197 | − | 7.33094i | −0.0868614 | − | 0.267332i | ||||
\(753\) | −12.7082 | + | 9.23305i | −0.463113 | + | 0.336471i | ||||
\(754\) | 18.4721 | − | 13.4208i | 0.672716 | − | 0.488756i | ||||
\(755\) | 2.38197 | + | 7.33094i | 0.0866886 | + | 0.266800i | ||||
\(756\) | −0.309017 | + | 0.951057i | −0.0112388 | + | 0.0345896i | ||||
\(757\) | −37.5344 | − | 27.2704i | −1.36421 | − | 0.991158i | −0.998164 | − | 0.0605625i | \(-0.980711\pi\) |
−0.366048 | − | 0.930596i | \(-0.619289\pi\) | |||||||
\(758\) | 30.6525 | 1.11335 | ||||||||
\(759\) | −3.02786 | + | 3.44095i | −0.109905 | + | 0.124899i | ||||
\(760\) | 2.23607 | 0.0811107 | ||||||||
\(761\) | −4.56231 | − | 3.31471i | −0.165383 | − | 0.120158i | 0.502015 | − | 0.864859i | \(-0.332592\pi\) |
−0.667399 | + | 0.744701i | \(0.732592\pi\) | |||||||
\(762\) | −5.09017 | + | 15.6659i | −0.184397 | + | 0.567517i | ||||
\(763\) | −5.11803 | − | 15.7517i | −0.185285 | − | 0.570249i | ||||
\(764\) | −3.16312 | + | 2.29814i | −0.114438 | + | 0.0831438i | ||||
\(765\) | −10.2812 | + | 7.46969i | −0.371716 | + | 0.270067i | ||||
\(766\) | 3.38197 | + | 10.4086i | 0.122195 | + | 0.376079i | ||||
\(767\) | 2.69505 | − | 8.29451i | 0.0973126 | − | 0.299497i | ||||
\(768\) | −0.809017 | − | 0.587785i | −0.0291929 | − | 0.0212099i | ||||
\(769\) | 29.1246 | 1.05026 | 0.525130 | − | 0.851022i | \(-0.324017\pi\) | ||||
0.525130 | + | 0.851022i | \(0.324017\pi\) | |||||||
\(770\) | 0.500000 | − | 5.34307i | 0.0180187 | − | 0.192551i | ||||
\(771\) | 14.3262 | 0.515947 | ||||||||
\(772\) | 15.7812 | + | 11.4657i | 0.567976 | + | 0.412659i | ||||
\(773\) | −10.3262 | + | 31.7809i | −0.371409 | + | 1.14308i | 0.574461 | + | 0.818532i | \(0.305212\pi\) |
−0.945870 | + | 0.324547i | \(0.894788\pi\) | |||||||
\(774\) | −0.472136 | − | 1.45309i | −0.0169706 | − | 0.0522301i | ||||
\(775\) | 4.02786 | − | 2.92641i | 0.144685 | − | 0.105120i | ||||
\(776\) | 10.4721 | − | 7.60845i | 0.375928 | − | 0.273128i | ||||
\(777\) | 0.354102 | + | 1.08981i | 0.0127033 | + | 0.0390969i | ||||
\(778\) | −11.4164 | + | 35.1361i | −0.409298 | + | 1.25969i | ||||
\(779\) | 5.95492 | + | 4.32650i | 0.213357 | + | 0.155013i | ||||
\(780\) | −4.00000 | −0.143223 | ||||||||
\(781\) | −38.8328 | + | 8.71851i | −1.38955 | + | 0.311973i | ||||
\(782\) | −10.8541 | −0.388142 | ||||||||
\(783\) | 7.47214 | + | 5.42882i | 0.267032 | + | 0.194010i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | −4.85410 | − | 14.9394i | −0.173250 | − | 0.533210i | ||||
\(786\) | 15.3262 | − | 11.1352i | 0.546669 | − | 0.397178i | ||||
\(787\) | 24.7254 | − | 17.9641i | 0.881366 | − | 0.640350i | −0.0522464 | − | 0.998634i | \(-0.516638\pi\) |
0.933613 | + | 0.358284i | \(0.116638\pi\) | |||||||
\(788\) | −3.67376 | − | 11.3067i | −0.130872 | − | 0.402784i | ||||
\(789\) | −8.22542 | + | 25.3153i | −0.292833 | + | 0.901247i | ||||
\(790\) | −6.85410 | − | 4.97980i | −0.243858 | − | 0.177173i | ||||
\(791\) | −5.23607 | −0.186173 | ||||||||
\(792\) | 3.23607 | − | 0.726543i | 0.114989 | − | 0.0258166i | ||||
\(793\) | 8.72136 | 0.309705 | ||||||||
\(794\) | 9.47214 | + | 6.88191i | 0.336154 | + | 0.244230i | ||||
\(795\) | 1.85410 | − | 5.70634i | 0.0657582 | − | 0.202383i | ||||
\(796\) | −0.100813 | − | 0.310271i | −0.00357322 | − | 0.0109973i | ||||
\(797\) | −22.5451 | + | 16.3800i | −0.798588 | + | 0.580208i | −0.910500 | − | 0.413510i | \(-0.864303\pi\) |
0.111912 | + | 0.993718i | \(0.464303\pi\) | |||||||
\(798\) | −1.11803 | + | 0.812299i | −0.0395780 | + | 0.0287551i | ||||
\(799\) | 18.7082 | + | 57.5779i | 0.661849 | + | 2.03696i | ||||
\(800\) | −0.736068 | + | 2.26538i | −0.0260239 | + | 0.0800934i | ||||
\(801\) | −9.59017 | − | 6.96767i | −0.338852 | − | 0.246190i | ||||
\(802\) | 1.41641 | 0.0500151 | ||||||||
\(803\) | −0.909830 | + | 9.72257i | −0.0321072 | + | 0.343102i | ||||
\(804\) | −3.52786 | −0.124418 | ||||||||
\(805\) | −1.80902 | − | 1.31433i | −0.0637595 | − | 0.0463240i | ||||
\(806\) | 1.59675 | − | 4.91428i | 0.0562430 | − | 0.173098i | ||||
\(807\) | −0.326238 | − | 1.00406i | −0.0114841 | − | 0.0353445i | ||||
\(808\) | 0.690983 | − | 0.502029i | 0.0243087 | − | 0.0176613i | ||||
\(809\) | −29.1246 | + | 21.1603i | −1.02397 | + | 0.743955i | −0.967092 | − | 0.254426i | \(-0.918114\pi\) |
−0.0568745 | + | 0.998381i | \(0.518114\pi\) | |||||||
\(810\) | −0.500000 | − | 1.53884i | −0.0175682 | − | 0.0540694i | ||||
\(811\) | −13.4164 | + | 41.2915i | −0.471114 | + | 1.44994i | 0.380014 | + | 0.924981i | \(0.375919\pi\) |
−0.851128 | + | 0.524958i | \(0.824081\pi\) | |||||||
\(812\) | −7.47214 | − | 5.42882i | −0.262221 | − | 0.190514i | ||||
\(813\) | −31.2148 | −1.09475 | ||||||||
\(814\) | 2.51064 | − | 2.85317i | 0.0879980 | − | 0.100004i | ||||
\(815\) | 24.1803 | 0.847000 | ||||||||
\(816\) | 6.35410 | + | 4.61653i | 0.222438 | + | 0.161611i | ||||
\(817\) | 0.652476 | − | 2.00811i | 0.0228272 | − | 0.0702550i | ||||
\(818\) | −2.70820 | − | 8.33499i | −0.0946901 | − | 0.291426i | ||||
\(819\) | 2.00000 | − | 1.45309i | 0.0698857 | − | 0.0507749i | ||||
\(820\) | 6.97214 | − | 5.06555i | 0.243478 | − | 0.176897i | ||||
\(821\) | −1.61803 | − | 4.97980i | −0.0564698 | − | 0.173796i | 0.918843 | − | 0.394622i | \(-0.129125\pi\) |
−0.975313 | + | 0.220826i | \(0.929125\pi\) | |||||||
\(822\) | 1.38197 | − | 4.25325i | 0.0482016 | − | 0.148349i | ||||
\(823\) | 42.9787 | + | 31.2259i | 1.49814 | + | 1.08847i | 0.971113 | + | 0.238619i | \(0.0766946\pi\) |
0.527030 | + | 0.849846i | \(0.323305\pi\) | |||||||
\(824\) | 9.85410 | 0.343284 | ||||||||
\(825\) | −4.02786 | − | 6.79615i | −0.140232 | − | 0.236612i | ||||
\(826\) | −3.52786 | −0.122750 | ||||||||
\(827\) | 37.1525 | + | 26.9929i | 1.29192 | + | 0.938633i | 0.999842 | − | 0.0177616i | \(-0.00565400\pi\) |
0.292076 | + | 0.956395i | \(0.405654\pi\) | |||||||
\(828\) | 0.427051 | − | 1.31433i | 0.0148410 | − | 0.0456760i | ||||
\(829\) | −3.76393 | − | 11.5842i | −0.130727 | − | 0.402336i | 0.864174 | − | 0.503193i | \(-0.167841\pi\) |
−0.994901 | + | 0.100857i | \(0.967841\pi\) | |||||||
\(830\) | −14.9443 | + | 10.8576i | −0.518723 | + | 0.376875i | ||||
\(831\) | −15.5902 | + | 11.3269i | −0.540817 | + | 0.392927i | ||||
\(832\) | 0.763932 | + | 2.35114i | 0.0264846 | + | 0.0815111i | ||||
\(833\) | −2.42705 | + | 7.46969i | −0.0840923 | + | 0.258810i | ||||
\(834\) | −15.5902 | − | 11.3269i | −0.539843 | − | 0.392219i | ||||
\(835\) | −37.8885 | −1.31119 | ||||||||
\(836\) | 4.20820 | + | 1.81636i | 0.145544 | + | 0.0628200i | ||||
\(837\) | 2.09017 | 0.0722468 | ||||||||
\(838\) | −31.2705 | − | 22.7194i | −1.08022 | − | 0.784827i | ||||
\(839\) | 10.8885 | − | 33.5115i | 0.375914 | − | 1.15695i | −0.566945 | − | 0.823755i | \(-0.691875\pi\) |
0.942860 | − | 0.333190i | \(-0.108125\pi\) | |||||||
\(840\) | 0.500000 | + | 1.53884i | 0.0172516 | + | 0.0530951i | ||||
\(841\) | −45.5517 | + | 33.0952i | −1.57075 | + | 1.14121i | ||||
\(842\) | −31.2984 | + | 22.7396i | −1.07861 | + | 0.783658i | ||||
\(843\) | −1.70820 | − | 5.25731i | −0.0588337 | − | 0.181071i | ||||
\(844\) | −0.763932 | + | 2.35114i | −0.0262956 | + | 0.0809296i | ||||
\(845\) | −9.01722 | − | 6.55139i | −0.310202 | − | 0.225375i | ||||
\(846\) | −7.70820 | −0.265014 | ||||||||
\(847\) | 5.28115 | − | 9.64932i | 0.181463 | − | 0.331555i | ||||
\(848\) | −3.70820 | −0.127340 | ||||||||
\(849\) | 2.54508 | + | 1.84911i | 0.0873471 | + | 0.0634614i | ||||
\(850\) | 5.78115 | − | 17.7926i | 0.198292 | − | 0.610280i | ||||
\(851\) | −0.489357 | − | 1.50609i | −0.0167749 | − | 0.0516280i | ||||
\(852\) | 9.70820 | − | 7.05342i | 0.332598 | − | 0.241646i | ||||
\(853\) | 5.47214 | − | 3.97574i | 0.187362 | − | 0.136127i | −0.490150 | − | 0.871638i | \(-0.663058\pi\) |
0.677512 | + | 0.735511i | \(0.263058\pi\) | |||||||
\(854\) | −1.09017 | − | 3.35520i | −0.0373048 | − | 0.114813i | ||||
\(855\) | 0.690983 | − | 2.12663i | 0.0236311 | − | 0.0727291i | ||||
\(856\) | 14.4443 | + | 10.4944i | 0.493695 | + | 0.358690i | ||||
\(857\) | 23.8885 | 0.816017 | 0.408009 | − | 0.912978i | \(-0.366223\pi\) | ||||
0.408009 | + | 0.912978i | \(0.366223\pi\) | |||||||
\(858\) | −7.52786 | − | 3.24920i | −0.256997 | − | 0.110926i | ||||
\(859\) | 32.9443 | 1.12404 | 0.562022 | − | 0.827122i | \(-0.310024\pi\) | ||||
0.562022 | + | 0.827122i | \(0.310024\pi\) | |||||||
\(860\) | −2.00000 | − | 1.45309i | −0.0681994 | − | 0.0495498i | ||||
\(861\) | −1.64590 | + | 5.06555i | −0.0560921 | + | 0.172634i | ||||
\(862\) | 8.02786 | + | 24.7072i | 0.273430 | + | 0.841531i | ||||
\(863\) | 11.9271 | − | 8.66551i | 0.406002 | − | 0.294977i | −0.365980 | − | 0.930623i | \(-0.619266\pi\) |
0.771981 | + | 0.635646i | \(0.219266\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | 10.7812 | + | 33.1810i | 0.366570 | + | 1.12819i | ||||
\(866\) | 6.94427 | − | 21.3723i | 0.235976 | − | 0.726259i | ||||
\(867\) | −36.1525 | − | 26.2663i | −1.22780 | − | 0.892051i | ||||
\(868\) | −2.09017 | −0.0709450 | ||||||||
\(869\) | −8.85410 | − | 14.9394i | −0.300355 | − | 0.506784i | ||||
\(870\) | 14.9443 | 0.506658 | ||||||||
\(871\) | 7.05573 | + | 5.12629i | 0.239074 | + | 0.173698i | ||||
\(872\) | 5.11803 | − | 15.7517i | 0.173319 | − | 0.533419i | ||||
\(873\) | −4.00000 | − | 12.3107i | −0.135379 | − | 0.416655i | ||||
\(874\) | 1.54508 | − | 1.12257i | 0.0522633 | − | 0.0379715i | ||||
\(875\) | 9.66312 | − | 7.02067i | 0.326673 | − | 0.237342i | ||||
\(876\) | −0.909830 | − | 2.80017i | −0.0307403 | − | 0.0946089i | ||||
\(877\) | −13.3820 | + | 41.1855i | −0.451877 | + | 1.39073i | 0.422886 | + | 0.906183i | \(0.361017\pi\) |
−0.874763 | + | 0.484551i | \(0.838983\pi\) | |||||||
\(878\) | −23.1074 | − | 16.7885i | −0.779837 | − | 0.566585i | ||||
\(879\) | −2.38197 | −0.0803417 | ||||||||
\(880\) | 3.54508 | − | 4.02874i | 0.119505 | − | 0.135809i | ||||
\(881\) | 15.9230 | 0.536459 | 0.268230 | − | 0.963355i | \(-0.413561\pi\) | ||||
0.268230 | + | 0.963355i | \(0.413561\pi\) | |||||||
\(882\) | −0.809017 | − | 0.587785i | −0.0272410 | − | 0.0197918i | ||||
\(883\) | 0.416408 | − | 1.28157i | 0.0140132 | − | 0.0431283i | −0.943805 | − | 0.330502i | \(-0.892782\pi\) |
0.957819 | + | 0.287373i | \(0.0927821\pi\) | |||||||
\(884\) | −6.00000 | − | 18.4661i | −0.201802 | − | 0.621082i | ||||
\(885\) | 4.61803 | − | 3.35520i | 0.155234 | − | 0.112784i | ||||
\(886\) | −10.6803 | + | 7.75972i | −0.358813 | + | 0.260693i | ||||
\(887\) | −2.90983 | − | 8.95554i | −0.0977025 | − | 0.300697i | 0.890246 | − | 0.455480i | \(-0.150532\pi\) |
−0.987949 | + | 0.154782i | \(0.950532\pi\) | |||||||
\(888\) | −0.354102 | + | 1.08981i | −0.0118829 | + | 0.0365718i | ||||
\(889\) | −13.3262 | − | 9.68208i | −0.446948 | − | 0.324726i | ||||
\(890\) | −19.1803 | −0.642926 | ||||||||
\(891\) | 0.309017 | − | 3.30220i | 0.0103525 | − | 0.110628i | ||||
\(892\) | −2.43769 | −0.0816200 | ||||||||
\(893\) | −8.61803 | − | 6.26137i | −0.288392 | − | 0.209529i | ||||
\(894\) | −4.47214 | + | 13.7638i | −0.149571 | + | 0.460331i | ||||
\(895\) | −9.51722 | − | 29.2910i | −0.318126 | − | 0.979090i | ||||
\(896\) | 0.809017 | − | 0.587785i | 0.0270274 | − | 0.0196365i | ||||
\(897\) | −2.76393 | + | 2.00811i | −0.0922850 | + | 0.0670490i | ||||
\(898\) | 5.00000 | + | 15.3884i | 0.166852 | + | 0.513518i | ||||
\(899\) | −5.96556 | + | 18.3601i | −0.198963 | + | 0.612344i | ||||
\(900\) | 1.92705 | + | 1.40008i | 0.0642350 | + | 0.0466695i | ||||
\(901\) | 29.1246 | 0.970281 | ||||||||
\(902\) | 17.2361 | − | 3.86974i | 0.573898 | − | 0.128848i | ||||
\(903\) | 1.52786 | 0.0508441 | ||||||||
\(904\) | −4.23607 | − | 3.07768i | −0.140890 | − | 0.102362i | ||||
\(905\) | −4.09017 | + | 12.5882i | −0.135962 | + | 0.418448i | ||||
\(906\) | −1.47214 | − | 4.53077i | −0.0489084 | − | 0.150525i | ||||
\(907\) | −3.38197 | + | 2.45714i | −0.112296 | + | 0.0815881i | −0.642516 | − | 0.766272i | \(-0.722109\pi\) |
0.530220 | + | 0.847860i | \(0.322109\pi\) | |||||||
\(908\) | −10.3262 | + | 7.50245i | −0.342688 | + | 0.248978i | ||||
\(909\) | −0.263932 | − | 0.812299i | −0.00875407 | − | 0.0269423i | ||||
\(910\) | 1.23607 | − | 3.80423i | 0.0409753 | − | 0.126109i | ||||
\(911\) | −4.47214 | − | 3.24920i | −0.148168 | − | 0.107651i | 0.511231 | − | 0.859443i | \(-0.329190\pi\) |
−0.659400 | + | 0.751792i | \(0.729190\pi\) | |||||||
\(912\) | −1.38197 | −0.0457615 | ||||||||
\(913\) | −36.9443 | + | 8.29451i | −1.22268 | + | 0.274508i | ||||
\(914\) | 5.41641 | 0.179159 | ||||||||
\(915\) | 4.61803 | + | 3.35520i | 0.152667 | + | 0.110919i | ||||
\(916\) | −1.76393 | + | 5.42882i | −0.0582820 | + | 0.179373i | ||||
\(917\) | 5.85410 | + | 18.0171i | 0.193319 | + | 0.594976i | ||||
\(918\) | 6.35410 | − | 4.61653i | 0.209717 | − | 0.152368i | ||||
\(919\) | −27.0344 | + | 19.6417i | −0.891784 | + | 0.647919i | −0.936343 | − | 0.351088i | \(-0.885812\pi\) |
0.0445586 | + | 0.999007i | \(0.485812\pi\) | |||||||
\(920\) | −0.690983 | − | 2.12663i | −0.0227810 | − | 0.0701128i | ||||
\(921\) | −3.97214 | + | 12.2250i | −0.130886 | + | 0.402827i | ||||
\(922\) | 24.5623 | + | 17.8456i | 0.808916 | + | 0.587712i | ||||
\(923\) | −29.6656 | −0.976456 | ||||||||
\(924\) | −0.309017 | + | 3.30220i | −0.0101659 | + | 0.108634i | ||||
\(925\) | 2.72949 | 0.0897451 | ||||||||
\(926\) | −1.76393 | − | 1.28157i | −0.0579664 | − | 0.0421151i | ||||
\(927\) | 3.04508 | − | 9.37181i | 0.100014 | − | 0.307811i | ||||
\(928\) | −2.85410 | − | 8.78402i | −0.0936905 | − | 0.288350i | ||||
\(929\) | 13.8262 | − | 10.0453i | 0.453624 | − | 0.329577i | −0.337401 | − | 0.941361i | \(-0.609548\pi\) |
0.791025 | + | 0.611784i | \(0.209548\pi\) | |||||||
\(930\) | 2.73607 | − | 1.98787i | 0.0897192 | − | 0.0651848i | ||||
\(931\) | −0.427051 | − | 1.31433i | −0.0139960 | − | 0.0430754i | ||||
\(932\) | −4.94427 | + | 15.2169i | −0.161955 | + | 0.498446i | ||||
\(933\) | 23.9443 | + | 17.3965i | 0.783900 | + | 0.569537i | ||||
\(934\) | −27.7082 | −0.906640 | ||||||||
\(935\) | −27.8435 | + | 31.6421i | −0.910578 | + | 1.03481i | ||||
\(936\) | 2.47214 | 0.0808043 | ||||||||
\(937\) | 41.7984 | + | 30.3683i | 1.36549 | + | 0.992089i | 0.998074 | + | 0.0620336i | \(0.0197586\pi\) |
0.367419 | + | 0.930055i | \(0.380241\pi\) | |||||||
\(938\) | 1.09017 | − | 3.35520i | 0.0355953 | − | 0.109551i | ||||
\(939\) | 3.61803 | + | 11.1352i | 0.118070 | + | 0.363382i | ||||
\(940\) | −10.0902 | + | 7.33094i | −0.329105 | + | 0.239109i | ||||
\(941\) | 17.9721 | − | 13.0575i | 0.585875 | − | 0.425663i | −0.254962 | − | 0.966951i | \(-0.582063\pi\) |
0.840837 | + | 0.541288i | \(0.182063\pi\) | |||||||
\(942\) | 3.00000 | + | 9.23305i | 0.0977453 | + | 0.300829i | ||||
\(943\) | 2.27458 | − | 7.00042i | 0.0740704 | − | 0.227965i | ||||
\(944\) | −2.85410 | − | 2.07363i | −0.0928931 | − | 0.0674908i | ||||
\(945\) | 1.61803 | 0.0526346 | ||||||||
\(946\) | −2.58359 | − | 4.35926i | −0.0839998 | − | 0.141732i | ||||
\(947\) | 50.6312 | 1.64529 | 0.822646 | − | 0.568553i | \(-0.192497\pi\) | ||||
0.822646 | + | 0.568553i | \(0.192497\pi\) | |||||||
\(948\) | 4.23607 | + | 3.07768i | 0.137581 | + | 0.0999585i | ||||
\(949\) | −2.24922 | + | 6.92240i | −0.0730129 | + | 0.224711i | ||||
\(950\) | 1.01722 | + | 3.13068i | 0.0330030 | + | 0.101573i | ||||
\(951\) | 7.00000 | − | 5.08580i | 0.226991 | − | 0.164918i | ||||
\(952\) | −6.35410 | + | 4.61653i | −0.205938 | + | 0.149622i | ||||
\(953\) | 0.965558 | + | 2.97168i | 0.0312775 | + | 0.0962622i | 0.965477 | − | 0.260490i | \(-0.0838841\pi\) |
−0.934199 | + | 0.356752i | \(0.883884\pi\) | |||||||
\(954\) | −1.14590 | + | 3.52671i | −0.0370998 | + | 0.114182i | ||||
\(955\) | 5.11803 | + | 3.71847i | 0.165616 | + | 0.120327i | ||||
\(956\) | 20.7984 | 0.672667 | ||||||||
\(957\) | 28.1246 | + | 12.1392i | 0.909140 | + | 0.392405i | ||||
\(958\) | −17.5279 | −0.566300 | ||||||||
\(959\) | 3.61803 | + | 2.62866i | 0.116832 | + | 0.0848837i | ||||
\(960\) | −0.500000 | + | 1.53884i | −0.0161374 | + | 0.0496659i | ||||
\(961\) | −8.22949 | − | 25.3278i | −0.265467 | − | 0.817025i | ||||
\(962\) | 2.29180 | − | 1.66509i | 0.0738905 | − | 0.0536846i | ||||
\(963\) | 14.4443 | − | 10.4944i | 0.465460 | − | 0.338177i | ||||
\(964\) | −1.38197 | − | 4.25325i | −0.0445101 | − | 0.136988i | ||||
\(965\) | 9.75329 | − | 30.0175i | 0.313969 | − | 0.966299i | ||||
\(966\) | 1.11803 | + | 0.812299i | 0.0359722 | + | 0.0261353i | ||||
\(967\) | 21.7082 | 0.698089 | 0.349044 | − | 0.937106i | \(-0.386506\pi\) | ||||
0.349044 | + | 0.937106i | \(0.386506\pi\) | |||||||
\(968\) | 9.94427 | − | 4.70228i | 0.319621 | − | 0.151137i | ||||
\(969\) | 10.8541 | 0.348684 | ||||||||
\(970\) | −16.9443 | − | 12.3107i | −0.544048 | − | 0.395274i | ||||
\(971\) | −4.36068 | + | 13.4208i | −0.139941 | + | 0.430694i | −0.996326 | − | 0.0856442i | \(-0.972705\pi\) |
0.856385 | + | 0.516338i | \(0.172705\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | 15.5902 | − | 11.3269i | 0.499798 | − | 0.363124i | ||||
\(974\) | −2.52786 | + | 1.83660i | −0.0809980 | + | 0.0588485i | ||||
\(975\) | −1.81966 | − | 5.60034i | −0.0582758 | − | 0.179354i | ||||
\(976\) | 1.09017 | − | 3.35520i | 0.0348955 | − | 0.107397i | ||||
\(977\) | 42.1246 | + | 30.6053i | 1.34769 | + | 0.979151i | 0.999123 | + | 0.0418654i | \(0.0133301\pi\) |
0.348562 | + | 0.937286i | \(0.386670\pi\) | |||||||
\(978\) | −14.9443 | −0.477865 | ||||||||
\(979\) | −36.0967 | − | 15.5802i | −1.15366 | − | 0.497945i | ||||
\(980\) | −1.61803 | −0.0516862 | ||||||||
\(981\) | −13.3992 | − | 9.73508i | −0.427803 | − | 0.310817i | ||||
\(982\) | 7.51722 | − | 23.1356i | 0.239884 | − | 0.738288i | ||||
\(983\) | −2.61803 | − | 8.05748i | −0.0835023 | − | 0.256994i | 0.900585 | − | 0.434680i | \(-0.143139\pi\) |
−0.984087 | + | 0.177687i | \(0.943139\pi\) | |||||||
\(984\) | −4.30902 | + | 3.13068i | −0.137366 | + | 0.0998026i | ||||
\(985\) | −15.5623 | + | 11.3067i | −0.495856 | + | 0.360261i | ||||
\(986\) | 22.4164 | + | 68.9906i | 0.713884 | + | 2.19711i | ||||
\(987\) | 2.38197 | − | 7.33094i | 0.0758188 | − | 0.233346i | ||||
\(988\) | 2.76393 | + | 2.00811i | 0.0879324 | + | 0.0638866i | ||||
\(989\) | −2.11146 | −0.0671404 | ||||||||
\(990\) | −2.73607 | − | 4.61653i | −0.0869579 | − | 0.146723i | ||||
\(991\) | −40.1803 | −1.27637 | −0.638185 | − | 0.769883i | \(-0.720315\pi\) | ||||
−0.638185 | + | 0.769883i | \(0.720315\pi\) | |||||||
\(992\) | −1.69098 | − | 1.22857i | −0.0536888 | − | 0.0390072i | ||||
\(993\) | −5.52786 | + | 17.0130i | −0.175421 | + | 0.539892i | ||||
\(994\) | 3.70820 | + | 11.4127i | 0.117617 | + | 0.361988i | ||||
\(995\) | −0.427051 | + | 0.310271i | −0.0135384 | + | 0.00983624i | ||||
\(996\) | 9.23607 | − | 6.71040i | 0.292656 | − | 0.212627i | ||||
\(997\) | 15.7082 | + | 48.3449i | 0.497484 | + | 1.53110i | 0.813050 | + | 0.582194i | \(0.197806\pi\) |
−0.315566 | + | 0.948904i | \(0.602194\pi\) | |||||||
\(998\) | −4.76393 | + | 14.6619i | −0.150800 | + | 0.464114i | ||||
\(999\) | 0.927051 | + | 0.673542i | 0.0293306 | + | 0.0213099i |
(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 | 462.2.j.a.169.1 | ✓ | 4 | |
11.3 | even | 5 | inner | 462.2.j.a.421.1 | yes | 4 | |
11.5 | even | 5 | 5082.2.a.bt.1.1 | 2 | |||
11.6 | odd | 10 | 5082.2.a.bj.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.a.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
462.2.j.a.421.1 | yes | 4 | 11.3 | even | 5 | inner | |
5082.2.a.bj.1.1 | 2 | 11.6 | odd | 10 | |||
5082.2.a.bt.1.1 | 2 | 11.5 | even | 5 |