Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(68,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.l (of order \(12\), degree \(4\), not 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: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 117.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.117 |
Dual form | 245.2.l.b.178.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.133975i | 0.353553 | − | 0.0947343i | −0.0776710 | − | 0.996979i | \(-0.524748\pi\) |
0.431224 | + | 0.902245i | \(0.358082\pi\) | |||||||
\(3\) | 0.133975 | − | 0.500000i | 0.0773503 | − | 0.288675i | −0.916406 | − | 0.400251i | \(-0.868923\pi\) |
0.993756 | + | 0.111576i | \(0.0355897\pi\) | |||||||
\(4\) | −1.50000 | + | 0.866025i | −0.750000 | + | 0.433013i | ||||
\(5\) | −0.133975 | + | 2.23205i | −0.0599153 | + | 0.998203i | ||||
\(6\) | − | 0.267949i | − | 0.109390i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.36603 | + | 1.36603i | −0.482963 | + | 0.482963i | ||||
\(9\) | 2.36603 | + | 1.36603i | 0.788675 | + | 0.455342i | ||||
\(10\) | 0.232051 | + | 1.13397i | 0.0733809 | + | 0.358594i | ||||
\(11\) | 1.36603 | + | 2.36603i | 0.411872 | + | 0.713384i | 0.995094 | − | 0.0989291i | \(-0.0315417\pi\) |
−0.583222 | + | 0.812313i | \(0.698208\pi\) | |||||||
\(12\) | 0.232051 | + | 0.866025i | 0.0669873 | + | 0.250000i | ||||
\(13\) | 2.00000 | + | 2.00000i | 0.554700 | + | 0.554700i | 0.927794 | − | 0.373094i | \(-0.121703\pi\) |
−0.373094 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.09808 | + | 0.366025i | 0.283522 | + | 0.0945074i | ||||
\(16\) | 1.23205 | − | 2.13397i | 0.308013 | − | 0.533494i | ||||
\(17\) | −3.73205 | − | 1.00000i | −0.905155 | − | 0.242536i | −0.223926 | − | 0.974606i | \(-0.571888\pi\) |
−0.681229 | + | 0.732070i | \(0.738554\pi\) | |||||||
\(18\) | 1.36603 | + | 0.366025i | 0.321975 | + | 0.0862730i | ||||
\(19\) | −0.366025 | + | 0.633975i | −0.0839720 | + | 0.145444i | −0.904953 | − | 0.425512i | \(-0.860094\pi\) |
0.820981 | + | 0.570956i | \(0.193427\pi\) | |||||||
\(20\) | −1.73205 | − | 3.46410i | −0.387298 | − | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | + | 1.00000i | 0.213201 | + | 0.213201i | ||||
\(23\) | 0.0358984 | + | 0.133975i | 0.00748533 | + | 0.0279356i | 0.969567 | − | 0.244824i | \(-0.0787302\pi\) |
−0.962082 | + | 0.272760i | \(0.912064\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | 1.26795 | + | 0.732051i | 0.248665 | + | 0.143567i | ||||
\(27\) | 2.09808 | − | 2.09808i | 0.403775 | − | 0.403775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 0.598076 | + | 0.0358984i | 0.109193 | + | 0.00655412i | ||||
\(31\) | 6.46410 | − | 3.73205i | 1.16099 | − | 0.670296i | 0.209447 | − | 0.977820i | \(-0.432834\pi\) |
0.951540 | + | 0.307524i | \(0.0995004\pi\) | |||||||
\(32\) | 1.33013 | − | 4.96410i | 0.235135 | − | 0.877537i | ||||
\(33\) | 1.36603 | − | 0.366025i | 0.237795 | − | 0.0637168i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.73205 | −0.788675 | ||||||||
\(37\) | −4.73205 | + | 1.26795i | −0.777944 | + | 0.208450i | −0.625878 | − | 0.779921i | \(-0.715259\pi\) |
−0.152066 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(38\) | −0.0980762 | + | 0.366025i | −0.0159101 | + | 0.0593772i | ||||
\(39\) | 1.26795 | − | 0.732051i | 0.203034 | − | 0.117222i | ||||
\(40\) | −2.86603 | − | 3.23205i | −0.453158 | − | 0.511032i | ||||
\(41\) | 6.46410i | 1.00952i | 0.863259 | + | 0.504762i | \(0.168420\pi\) | ||||
−0.863259 | + | 0.504762i | \(0.831580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.83013 | − | 2.83013i | 0.431590 | − | 0.431590i | −0.457579 | − | 0.889169i | \(-0.651283\pi\) |
0.889169 | + | 0.457579i | \(0.151283\pi\) | |||||||
\(44\) | −4.09808 | − | 2.36603i | −0.617808 | − | 0.356692i | ||||
\(45\) | −3.36603 | + | 5.09808i | −0.501777 | + | 0.759976i | ||||
\(46\) | 0.0358984 | + | 0.0621778i | 0.00529293 | + | 0.00916762i | ||||
\(47\) | −2.36603 | − | 8.83013i | −0.345120 | − | 1.28801i | −0.892472 | − | 0.451103i | \(-0.851031\pi\) |
0.547351 | − | 0.836903i | \(-0.315636\pi\) | |||||||
\(48\) | −0.901924 | − | 0.901924i | −0.130181 | − | 0.130181i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.56218 | + | 0.366025i | −0.362347 | + | 0.0517638i | ||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | −4.73205 | − | 1.26795i | −0.656217 | − | 0.175833i | ||||
\(53\) | 6.83013 | + | 1.83013i | 0.938190 | + | 0.251387i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(54\) | 0.767949 | − | 1.33013i | 0.104505 | − | 0.181007i | ||||
\(55\) | −5.46410 | + | 2.73205i | −0.736779 | + | 0.368390i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.267949 | + | 0.267949i | 0.0354907 | + | 0.0354907i | ||||
\(58\) | −0.401924 | − | 1.50000i | −0.0527752 | − | 0.196960i | ||||
\(59\) | 4.09808 | + | 7.09808i | 0.533524 | + | 0.924091i | 0.999233 | + | 0.0391530i | \(0.0124660\pi\) |
−0.465709 | + | 0.884938i | \(0.654201\pi\) | |||||||
\(60\) | −1.96410 | + | 0.401924i | −0.253564 | + | 0.0518881i | ||||
\(61\) | −1.33013 | − | 0.767949i | −0.170305 | − | 0.0983258i | 0.412424 | − | 0.910992i | \(-0.364682\pi\) |
−0.582730 | + | 0.812666i | \(0.698015\pi\) | |||||||
\(62\) | 2.73205 | − | 2.73205i | 0.346971 | − | 0.346971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.26795i | 0.283494i | ||||||||
\(65\) | −4.73205 | + | 4.19615i | −0.586939 | + | 0.520469i | ||||
\(66\) | 0.633975 | − | 0.366025i | 0.0780369 | − | 0.0450546i | ||||
\(67\) | 2.86603 | − | 10.6962i | 0.350141 | − | 1.30674i | −0.536350 | − | 0.843996i | \(-0.680197\pi\) |
0.886490 | − | 0.462747i | \(-0.153136\pi\) | |||||||
\(68\) | 6.46410 | − | 1.73205i | 0.783887 | − | 0.210042i | ||||
\(69\) | 0.0717968 | 0.00864332 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26795 | 0.150478 | 0.0752389 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752389 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(72\) | −5.09808 | + | 1.36603i | −0.600814 | + | 0.160988i | ||||
\(73\) | 3.46410 | − | 12.9282i | 0.405442 | − | 1.51313i | −0.397796 | − | 0.917474i | \(-0.630225\pi\) |
0.803238 | − | 0.595658i | \(-0.203109\pi\) | |||||||
\(74\) | −2.19615 | + | 1.26795i | −0.255298 | + | 0.147396i | ||||
\(75\) | −0.964102 | + | 2.40192i | −0.111325 | + | 0.277350i | ||||
\(76\) | − | 1.26795i | − | 0.145444i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.535898 | − | 0.535898i | 0.0606785 | − | 0.0606785i | ||||
\(79\) | 2.83013 | + | 1.63397i | 0.318414 | + | 0.183837i | 0.650686 | − | 0.759347i | \(-0.274482\pi\) |
−0.332271 | + | 0.943184i | \(0.607815\pi\) | |||||||
\(80\) | 4.59808 | + | 3.03590i | 0.514081 | + | 0.339424i | ||||
\(81\) | 3.33013 | + | 5.76795i | 0.370014 | + | 0.640883i | ||||
\(82\) | 0.866025 | + | 3.23205i | 0.0956365 | + | 0.356920i | ||||
\(83\) | 2.09808 | + | 2.09808i | 0.230294 | + | 0.230294i | 0.812815 | − | 0.582522i | \(-0.197934\pi\) |
−0.582522 | + | 0.812815i | \(0.697934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.73205 | − | 8.19615i | 0.296333 | − | 0.888998i | ||||
\(86\) | 1.03590 | − | 1.79423i | 0.111704 | − | 0.193477i | ||||
\(87\) | −1.50000 | − | 0.401924i | −0.160817 | − | 0.0430908i | ||||
\(88\) | −5.09808 | − | 1.36603i | −0.543457 | − | 0.145619i | ||||
\(89\) | 0.330127 | − | 0.571797i | 0.0349934 | − | 0.0606103i | −0.847998 | − | 0.529999i | \(-0.822192\pi\) |
0.882992 | + | 0.469389i | \(0.155526\pi\) | |||||||
\(90\) | −1.00000 | + | 3.00000i | −0.105409 | + | 0.316228i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.169873 | − | 0.169873i | −0.0177105 | − | 0.0177105i | ||||
\(93\) | −1.00000 | − | 3.73205i | −0.103695 | − | 0.386996i | ||||
\(94\) | −2.36603 | − | 4.09808i | −0.244037 | − | 0.422684i | ||||
\(95\) | −1.36603 | − | 0.901924i | −0.140151 | − | 0.0925354i | ||||
\(96\) | −2.30385 | − | 1.33013i | −0.235135 | − | 0.135756i | ||||
\(97\) | 5.92820 | − | 5.92820i | 0.601918 | − | 0.601918i | −0.338903 | − | 0.940821i | \(-0.610056\pi\) |
0.940821 | + | 0.338903i | \(0.110056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.46410i | 0.750170i | ||||||||
\(100\) | 7.96410 | − | 3.40192i | 0.796410 | − | 0.340192i | ||||
\(101\) | −7.16025 | + | 4.13397i | −0.712472 | + | 0.411346i | −0.811976 | − | 0.583691i | \(-0.801608\pi\) |
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | −0.267949 | + | 1.00000i | −0.0265309 | + | 0.0990148i | ||||
\(103\) | −4.59808 | + | 1.23205i | −0.453062 | + | 0.121398i | −0.478132 | − | 0.878288i | \(-0.658686\pi\) |
0.0250698 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.66025 | 0.355515 | ||||||||
\(107\) | 12.6962 | − | 3.40192i | 1.22738 | − | 0.328876i | 0.413823 | − | 0.910357i | \(-0.364193\pi\) |
0.813560 | + | 0.581481i | \(0.197526\pi\) | |||||||
\(108\) | −1.33013 | + | 4.96410i | −0.127992 | + | 0.477671i | ||||
\(109\) | −8.76795 | + | 5.06218i | −0.839817 | + | 0.484869i | −0.857202 | − | 0.514980i | \(-0.827799\pi\) |
0.0173849 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(110\) | −2.36603 | + | 2.09808i | −0.225592 | + | 0.200044i | ||||
\(111\) | 2.53590i | 0.240697i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.73205 | + | 7.73205i | −0.727370 | + | 0.727370i | −0.970095 | − | 0.242725i | \(-0.921959\pi\) |
0.242725 | + | 0.970095i | \(0.421959\pi\) | |||||||
\(114\) | 0.169873 | + | 0.0980762i | 0.0159101 | + | 0.00918568i | ||||
\(115\) | −0.303848 | + | 0.0621778i | −0.0283339 | + | 0.00579811i | ||||
\(116\) | 2.59808 | + | 4.50000i | 0.241225 | + | 0.417815i | ||||
\(117\) | 2.00000 | + | 7.46410i | 0.184900 | + | 0.690056i | ||||
\(118\) | 3.00000 | + | 3.00000i | 0.276172 | + | 0.276172i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | + | 1.00000i | −0.182574 | + | 0.0912871i | ||||
\(121\) | 1.76795 | − | 3.06218i | 0.160723 | − | 0.278380i | ||||
\(122\) | −0.767949 | − | 0.205771i | −0.0695269 | − | 0.0186297i | ||||
\(123\) | 3.23205 | + | 0.866025i | 0.291424 | + | 0.0780869i | ||||
\(124\) | −6.46410 | + | 11.1962i | −0.580493 | + | 1.00544i | ||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.464102 | + | 0.464102i | 0.0411824 | + | 0.0411824i | 0.727398 | − | 0.686216i | \(-0.240729\pi\) |
−0.686216 | + | 0.727398i | \(0.740729\pi\) | |||||||
\(128\) | 2.96410 | + | 11.0622i | 0.261992 | + | 0.977768i | ||||
\(129\) | −1.03590 | − | 1.79423i | −0.0912058 | − | 0.157973i | ||||
\(130\) | −1.80385 | + | 2.73205i | −0.158208 | + | 0.239617i | ||||
\(131\) | 13.3923 | + | 7.73205i | 1.17009 | + | 0.675552i | 0.953702 | − | 0.300755i | \(-0.0972385\pi\) |
0.216390 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(132\) | −1.73205 | + | 1.73205i | −0.150756 | + | 0.150756i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 5.73205i | − | 0.495174i | ||||||
\(135\) | 4.40192 | + | 4.96410i | 0.378857 | + | 0.427242i | ||||
\(136\) | 6.46410 | − | 3.73205i | 0.554292 | − | 0.320021i | ||||
\(137\) | −3.53590 | + | 13.1962i | −0.302092 | + | 1.12742i | 0.633327 | + | 0.773884i | \(0.281689\pi\) |
−0.935420 | + | 0.353539i | \(0.884978\pi\) | |||||||
\(138\) | 0.0358984 | − | 0.00961894i | 0.00305587 | − | 0.000818819i | ||||
\(139\) | 5.66025 | 0.480096 | 0.240048 | − | 0.970761i | \(-0.422837\pi\) | ||||
0.240048 | + | 0.970761i | \(0.422837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.73205 | −0.398511 | ||||||||
\(142\) | 0.633975 | − | 0.169873i | 0.0532020 | − | 0.0142554i | ||||
\(143\) | −2.00000 | + | 7.46410i | −0.167248 | + | 0.624180i | ||||
\(144\) | 5.83013 | − | 3.36603i | 0.485844 | − | 0.280502i | ||||
\(145\) | 6.69615 | + | 0.401924i | 0.556085 | + | 0.0333780i | ||||
\(146\) | − | 6.92820i | − | 0.573382i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | − | 6.00000i | 0.493197 | − | 0.493197i | ||||
\(149\) | 0.696152 | + | 0.401924i | 0.0570310 | + | 0.0329269i | 0.528244 | − | 0.849092i | \(-0.322850\pi\) |
−0.471213 | + | 0.882019i | \(0.656184\pi\) | |||||||
\(150\) | −0.160254 | + | 1.33013i | −0.0130847 | + | 0.108604i | ||||
\(151\) | −6.92820 | − | 12.0000i | −0.563809 | − | 0.976546i | −0.997159 | − | 0.0753205i | \(-0.976002\pi\) |
0.433350 | − | 0.901226i | \(-0.357331\pi\) | |||||||
\(152\) | −0.366025 | − | 1.36603i | −0.0296886 | − | 0.110799i | ||||
\(153\) | −7.46410 | − | 7.46410i | −0.603437 | − | 0.603437i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.46410 | + | 14.9282i | 0.599531 | + | 1.19906i | ||||
\(156\) | −1.26795 | + | 2.19615i | −0.101517 | + | 0.175833i | ||||
\(157\) | 4.63397 | + | 1.24167i | 0.369831 | + | 0.0990960i | 0.438948 | − | 0.898513i | \(-0.355351\pi\) |
−0.0691164 | + | 0.997609i | \(0.522018\pi\) | |||||||
\(158\) | 1.63397 | + | 0.437822i | 0.129992 | + | 0.0348313i | ||||
\(159\) | 1.83013 | − | 3.16987i | 0.145139 | − | 0.251387i | ||||
\(160\) | 10.9019 | + | 3.63397i | 0.861873 | + | 0.287291i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.43782 | + | 2.43782i | 0.191533 | + | 0.191533i | ||||
\(163\) | −3.63397 | − | 13.5622i | −0.284635 | − | 1.06227i | −0.949106 | − | 0.314958i | \(-0.898010\pi\) |
0.664471 | − | 0.747314i | \(-0.268657\pi\) | |||||||
\(164\) | −5.59808 | − | 9.69615i | −0.437136 | − | 0.757142i | ||||
\(165\) | 0.633975 | + | 3.09808i | 0.0493549 | + | 0.241185i | ||||
\(166\) | 1.33013 | + | 0.767949i | 0.103238 | + | 0.0596044i | ||||
\(167\) | −11.7583 | + | 11.7583i | −0.909887 | + | 0.909887i | −0.996263 | − | 0.0863757i | \(-0.972471\pi\) |
0.0863757 | + | 0.996263i | \(0.472471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0.267949 | − | 4.46410i | 0.0205508 | − | 0.342381i | ||||
\(171\) | −1.73205 | + | 1.00000i | −0.132453 | + | 0.0764719i | ||||
\(172\) | −1.79423 | + | 6.69615i | −0.136809 | + | 0.510577i | ||||
\(173\) | −19.9282 | + | 5.33975i | −1.51511 | + | 0.405973i | −0.918130 | − | 0.396280i | \(-0.870301\pi\) |
−0.596984 | + | 0.802253i | \(0.703634\pi\) | |||||||
\(174\) | −0.803848 | −0.0609395 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.73205 | 0.507447 | ||||||||
\(177\) | 4.09808 | − | 1.09808i | 0.308030 | − | 0.0825365i | ||||
\(178\) | 0.0884573 | − | 0.330127i | 0.00663015 | − | 0.0247441i | ||||
\(179\) | 6.80385 | − | 3.92820i | 0.508543 | − | 0.293608i | −0.223691 | − | 0.974660i | \(-0.571811\pi\) |
0.732235 | + | 0.681052i | \(0.238477\pi\) | |||||||
\(180\) | 0.633975 | − | 10.5622i | 0.0472537 | − | 0.787258i | ||||
\(181\) | 1.19615i | 0.0889093i | 0.999011 | + | 0.0444547i | \(0.0141550\pi\) | ||||
−0.999011 | + | 0.0444547i | \(0.985845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.562178 | + | 0.562178i | −0.0415574 | + | 0.0415574i | ||||
\(184\) | −0.232051 | − | 0.133975i | −0.0171070 | − | 0.00987674i | ||||
\(185\) | −2.19615 | − | 10.7321i | −0.161464 | − | 0.789036i | ||||
\(186\) | −1.00000 | − | 1.73205i | −0.0733236 | − | 0.127000i | ||||
\(187\) | −2.73205 | − | 10.1962i | −0.199787 | − | 0.745617i | ||||
\(188\) | 11.1962 | + | 11.1962i | 0.816563 | + | 0.816563i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.803848 | − | 0.267949i | −0.0583172 | − | 0.0194391i | ||||
\(191\) | −6.63397 | + | 11.4904i | −0.480018 | + | 0.831415i | −0.999737 | − | 0.0229220i | \(-0.992703\pi\) |
0.519720 | + | 0.854337i | \(0.326036\pi\) | |||||||
\(192\) | 1.13397 | + | 0.303848i | 0.0818376 | + | 0.0219283i | ||||
\(193\) | −7.83013 | − | 2.09808i | −0.563625 | − | 0.151023i | −0.0342537 | − | 0.999413i | \(-0.510905\pi\) |
−0.529371 | + | 0.848390i | \(0.677572\pi\) | |||||||
\(194\) | 2.16987 | − | 3.75833i | 0.155788 | − | 0.269832i | ||||
\(195\) | 1.46410 | + | 2.92820i | 0.104846 | + | 0.209693i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1244 | − | 10.1244i | −0.721330 | − | 0.721330i | 0.247546 | − | 0.968876i | \(-0.420376\pi\) |
−0.968876 | + | 0.247546i | \(0.920376\pi\) | |||||||
\(198\) | 1.00000 | + | 3.73205i | 0.0710669 | + | 0.265225i | ||||
\(199\) | 5.53590 | + | 9.58846i | 0.392429 | + | 0.679708i | 0.992769 | − | 0.120037i | \(-0.0383014\pi\) |
−0.600340 | + | 0.799745i | \(0.704968\pi\) | |||||||
\(200\) | 7.59808 | − | 5.96410i | 0.537265 | − | 0.421726i | ||||
\(201\) | −4.96410 | − | 2.86603i | −0.350141 | − | 0.202154i | ||||
\(202\) | −3.02628 | + | 3.02628i | −0.212928 | + | 0.212928i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 3.46410i | − | 0.242536i | ||||||
\(205\) | −14.4282 | − | 0.866025i | −1.00771 | − | 0.0604858i | ||||
\(206\) | −2.13397 | + | 1.23205i | −0.148681 | + | 0.0858410i | ||||
\(207\) | −0.0980762 | + | 0.366025i | −0.00681677 | + | 0.0254405i | ||||
\(208\) | 6.73205 | − | 1.80385i | 0.466784 | − | 0.125074i | ||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.196152 | −0.0135037 | −0.00675184 | − | 0.999977i | \(-0.502149\pi\) | ||||
−0.00675184 | + | 0.999977i | \(0.502149\pi\) | |||||||
\(212\) | −11.8301 | + | 3.16987i | −0.812496 | + | 0.217708i | ||||
\(213\) | 0.169873 | − | 0.633975i | 0.0116395 | − | 0.0434392i | ||||
\(214\) | 5.89230 | − | 3.40192i | 0.402790 | − | 0.232551i | ||||
\(215\) | 5.93782 | + | 6.69615i | 0.404956 | + | 0.456674i | ||||
\(216\) | 5.73205i | 0.390017i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.70577 | + | 3.70577i | −0.250987 | + | 0.250987i | ||||
\(219\) | −6.00000 | − | 3.46410i | −0.405442 | − | 0.234082i | ||||
\(220\) | 5.83013 | − | 8.83013i | 0.393067 | − | 0.595327i | ||||
\(221\) | −5.46410 | − | 9.46410i | −0.367555 | − | 0.636624i | ||||
\(222\) | 0.339746 | + | 1.26795i | 0.0228023 | + | 0.0850992i | ||||
\(223\) | −18.1244 | − | 18.1244i | −1.21370 | − | 1.21370i | −0.969802 | − | 0.243895i | \(-0.921575\pi\) |
−0.243895 | − | 0.969802i | \(-0.578425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.9282 | − | 8.19615i | −0.728547 | − | 0.546410i | ||||
\(226\) | −2.83013 | + | 4.90192i | −0.188257 | + | 0.326071i | ||||
\(227\) | 19.0263 | + | 5.09808i | 1.26282 | + | 0.338371i | 0.827275 | − | 0.561797i | \(-0.189890\pi\) |
0.435543 | + | 0.900168i | \(0.356556\pi\) | |||||||
\(228\) | −0.633975 | − | 0.169873i | −0.0419860 | − | 0.0112501i | ||||
\(229\) | 9.19615 | − | 15.9282i | 0.607699 | − | 1.05257i | −0.383920 | − | 0.923366i | \(-0.625426\pi\) |
0.991619 | − | 0.129199i | \(-0.0412406\pi\) | |||||||
\(230\) | −0.143594 | + | 0.0717968i | −0.00946828 | + | 0.00473414i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.09808 | + | 4.09808i | 0.269052 | + | 0.269052i | ||||
\(233\) | −1.73205 | − | 6.46410i | −0.113470 | − | 0.423477i | 0.885698 | − | 0.464263i | \(-0.153681\pi\) |
−0.999168 | + | 0.0407854i | \(0.987014\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 20.0263 | − | 4.09808i | 1.30637 | − | 0.267329i | ||||
\(236\) | −12.2942 | − | 7.09808i | −0.800286 | − | 0.462045i | ||||
\(237\) | 1.19615 | − | 1.19615i | 0.0776984 | − | 0.0776984i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.39230i | 0.154745i | 0.997002 | + | 0.0773727i | \(0.0246531\pi\) | ||||
−0.997002 | + | 0.0773727i | \(0.975347\pi\) | |||||||
\(240\) | 2.13397 | − | 1.89230i | 0.137747 | − | 0.122148i | ||||
\(241\) | −21.4641 | + | 12.3923i | −1.38262 | + | 0.798259i | −0.992470 | − | 0.122491i | \(-0.960912\pi\) |
−0.390155 | + | 0.920749i | \(0.627578\pi\) | |||||||
\(242\) | 0.473721 | − | 1.76795i | 0.0304519 | − | 0.113648i | ||||
\(243\) | 11.9282 | − | 3.19615i | 0.765195 | − | 0.205033i | ||||
\(244\) | 2.66025 | 0.170305 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.73205 | 0.110432 | ||||||||
\(247\) | −2.00000 | + | 0.535898i | −0.127257 | + | 0.0340984i | ||||
\(248\) | −3.73205 | + | 13.9282i | −0.236985 | + | 0.884442i | ||||
\(249\) | 1.33013 | − | 0.767949i | 0.0842934 | − | 0.0486668i | ||||
\(250\) | −0.473721 | − | 5.76795i | −0.0299607 | − | 0.364797i | ||||
\(251\) | − | 21.8564i | − | 1.37956i | −0.724017 | − | 0.689782i | \(-0.757706\pi\) | ||
0.724017 | − | 0.689782i | \(-0.242294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.267949 | + | 0.267949i | −0.0168458 | + | 0.0168458i | ||||
\(254\) | 0.294229 | + | 0.169873i | 0.0184615 | + | 0.0106588i | ||||
\(255\) | −3.73205 | − | 2.46410i | −0.233710 | − | 0.154308i | ||||
\(256\) | 0.696152 | + | 1.20577i | 0.0435095 | + | 0.0753607i | ||||
\(257\) | 0.732051 | + | 2.73205i | 0.0456641 | + | 0.170421i | 0.984992 | − | 0.172600i | \(-0.0552167\pi\) |
−0.939328 | + | 0.343020i | \(0.888550\pi\) | |||||||
\(258\) | −0.758330 | − | 0.758330i | −0.0472116 | − | 0.0472116i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.46410 | − | 10.3923i | 0.214834 | − | 0.644503i | ||||
\(261\) | 4.09808 | − | 7.09808i | 0.253665 | − | 0.439360i | ||||
\(262\) | 7.73205 | + | 2.07180i | 0.477688 | + | 0.127996i | ||||
\(263\) | −15.1603 | − | 4.06218i | −0.934821 | − | 0.250485i | −0.240912 | − | 0.970547i | \(-0.577447\pi\) |
−0.693909 | + | 0.720062i | \(0.744113\pi\) | |||||||
\(264\) | −1.36603 | + | 2.36603i | −0.0840731 | + | 0.145619i | ||||
\(265\) | −5.00000 | + | 15.0000i | −0.307148 | + | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.241670 | − | 0.241670i | −0.0147899 | − | 0.0147899i | ||||
\(268\) | 4.96410 | + | 18.5263i | 0.303231 | + | 1.13167i | ||||
\(269\) | −11.4282 | − | 19.7942i | −0.696790 | − | 1.20688i | −0.969574 | − | 0.244800i | \(-0.921278\pi\) |
0.272784 | − | 0.962075i | \(-0.412056\pi\) | |||||||
\(270\) | 2.86603 | + | 1.89230i | 0.174421 | + | 0.115162i | ||||
\(271\) | −18.4186 | − | 10.6340i | −1.11885 | − | 0.645968i | −0.177742 | − | 0.984077i | \(-0.556879\pi\) |
−0.941107 | + | 0.338109i | \(0.890213\pi\) | |||||||
\(272\) | −6.73205 | + | 6.73205i | −0.408191 | + | 0.408191i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.07180i | 0.427223i | ||||||||
\(275\) | −5.36603 | − | 12.5622i | −0.323584 | − | 0.757528i | ||||
\(276\) | −0.107695 | + | 0.0621778i | −0.00648249 | + | 0.00374267i | ||||
\(277\) | −1.39230 | + | 5.19615i | −0.0836555 | + | 0.312207i | −0.995056 | − | 0.0993135i | \(-0.968335\pi\) |
0.911401 | + | 0.411520i | \(0.135002\pi\) | |||||||
\(278\) | 2.83013 | − | 0.758330i | 0.169740 | − | 0.0454816i | ||||
\(279\) | 20.3923 | 1.22086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.928203 | −0.0553720 | −0.0276860 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276860 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(282\) | −2.36603 | + | 0.633975i | −0.140895 | + | 0.0377526i | ||||
\(283\) | 0.509619 | − | 1.90192i | 0.0302937 | − | 0.113058i | −0.949123 | − | 0.314904i | \(-0.898028\pi\) |
0.979417 | + | 0.201847i | \(0.0646943\pi\) | |||||||
\(284\) | −1.90192 | + | 1.09808i | −0.112858 | + | 0.0651588i | ||||
\(285\) | −0.633975 | + | 0.562178i | −0.0375534 | + | 0.0333005i | ||||
\(286\) | 4.00000i | 0.236525i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.92820 | − | 9.92820i | 0.585025 | − | 0.585025i | ||||
\(289\) | −1.79423 | − | 1.03590i | −0.105543 | − | 0.0609352i | ||||
\(290\) | 3.40192 | − | 0.696152i | 0.199768 | − | 0.0408795i | ||||
\(291\) | −2.16987 | − | 3.75833i | −0.127200 | − | 0.220317i | ||||
\(292\) | 6.00000 | + | 22.3923i | 0.351123 | + | 1.31041i | ||||
\(293\) | 2.39230 | + | 2.39230i | 0.139760 | + | 0.139760i | 0.773525 | − | 0.633765i | \(-0.218492\pi\) |
−0.633765 | + | 0.773525i | \(0.718492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.3923 | + | 8.19615i | −0.954397 | + | 0.477198i | ||||
\(296\) | 4.73205 | − | 8.19615i | 0.275045 | − | 0.476392i | ||||
\(297\) | 7.83013 | + | 2.09808i | 0.454350 | + | 0.121743i | ||||
\(298\) | 0.401924 | + | 0.107695i | 0.0232828 | + | 0.00623861i | ||||
\(299\) | −0.196152 | + | 0.339746i | −0.0113438 | + | 0.0196480i | ||||
\(300\) | −0.633975 | − | 4.43782i | −0.0366025 | − | 0.256218i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.07180 | − | 5.07180i | −0.291849 | − | 0.291849i | ||||
\(303\) | 1.10770 | + | 4.13397i | 0.0636354 | + | 0.237491i | ||||
\(304\) | 0.901924 | + | 1.56218i | 0.0517289 | + | 0.0895970i | ||||
\(305\) | 1.89230 | − | 2.86603i | 0.108353 | − | 0.164108i | ||||
\(306\) | −4.73205 | − | 2.73205i | −0.270513 | − | 0.156181i | ||||
\(307\) | −6.29423 | + | 6.29423i | −0.359231 | + | 0.359231i | −0.863529 | − | 0.504299i | \(-0.831751\pi\) |
0.504299 | + | 0.863529i | \(0.331751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.46410i | 0.140178i | ||||||||
\(310\) | 5.73205 | + | 6.46410i | 0.325559 | + | 0.367136i | ||||
\(311\) | 13.2224 | − | 7.63397i | 0.749775 | − | 0.432883i | −0.0758374 | − | 0.997120i | \(-0.524163\pi\) |
0.825613 | + | 0.564237i | \(0.190830\pi\) | |||||||
\(312\) | −0.732051 | + | 2.73205i | −0.0414442 | + | 0.154672i | ||||
\(313\) | 5.19615 | − | 1.39230i | 0.293704 | − | 0.0786977i | −0.108958 | − | 0.994046i | \(-0.534752\pi\) |
0.402662 | + | 0.915349i | \(0.368085\pi\) | |||||||
\(314\) | 2.48334 | 0.140143 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.66025 | −0.318414 | ||||||||
\(317\) | 9.19615 | − | 2.46410i | 0.516507 | − | 0.138398i | 0.00885679 | − | 0.999961i | \(-0.497181\pi\) |
0.507651 | + | 0.861563i | \(0.330514\pi\) | |||||||
\(318\) | 0.490381 | − | 1.83013i | 0.0274992 | − | 0.102628i | ||||
\(319\) | 7.09808 | − | 4.09808i | 0.397416 | − | 0.229448i | ||||
\(320\) | −5.06218 | − | 0.303848i | −0.282984 | − | 0.0169856i | ||||
\(321\) | − | 6.80385i | − | 0.379754i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | − | 2.00000i | 0.111283 | − | 0.111283i | ||||
\(324\) | −9.99038 | − | 5.76795i | −0.555021 | − | 0.320442i | ||||
\(325\) | −8.73205 | − | 11.1244i | −0.484367 | − | 0.617068i | ||||
\(326\) | −3.63397 | − | 6.29423i | −0.201267 | − | 0.348605i | ||||
\(327\) | 1.35641 | + | 5.06218i | 0.0750094 | + | 0.279939i | ||||
\(328\) | −8.83013 | − | 8.83013i | −0.487562 | − | 0.487562i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.732051 | + | 1.46410i | 0.0402981 | + | 0.0805961i | ||||
\(331\) | 0.928203 | − | 1.60770i | 0.0510187 | − | 0.0883669i | −0.839388 | − | 0.543532i | \(-0.817087\pi\) |
0.890407 | + | 0.455165i | \(0.150420\pi\) | |||||||
\(332\) | −4.96410 | − | 1.33013i | −0.272440 | − | 0.0730002i | ||||
\(333\) | −12.9282 | − | 3.46410i | −0.708461 | − | 0.189832i | ||||
\(334\) | −4.30385 | + | 7.45448i | −0.235496 | + | 0.407891i | ||||
\(335\) | 23.4904 | + | 7.83013i | 1.28342 | + | 0.427806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.53590 | + | 9.53590i | 0.519453 | + | 0.519453i | 0.917406 | − | 0.397953i | \(-0.130279\pi\) |
−0.397953 | + | 0.917406i | \(0.630279\pi\) | |||||||
\(338\) | −0.669873 | − | 2.50000i | −0.0364363 | − | 0.135982i | ||||
\(339\) | 2.83013 | + | 4.90192i | 0.153711 | + | 0.266236i | ||||
\(340\) | 3.00000 | + | 14.6603i | 0.162698 | + | 0.795064i | ||||
\(341\) | 17.6603 | + | 10.1962i | 0.956356 | + | 0.552153i | ||||
\(342\) | −0.732051 | + | 0.732051i | −0.0395848 | + | 0.0395848i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.73205i | 0.416884i | ||||||||
\(345\) | −0.00961894 | + | 0.160254i | −0.000517866 | + | 0.00862779i | ||||
\(346\) | −9.24871 | + | 5.33975i | −0.497214 | + | 0.287067i | ||||
\(347\) | −7.79423 | + | 29.0885i | −0.418416 | + | 1.56155i | 0.359477 | + | 0.933154i | \(0.382955\pi\) |
−0.777893 | + | 0.628396i | \(0.783712\pi\) | |||||||
\(348\) | 2.59808 | − | 0.696152i | 0.139272 | − | 0.0373177i | ||||
\(349\) | −6.26795 | −0.335516 | −0.167758 | − | 0.985828i | \(-0.553653\pi\) | ||||
−0.167758 | + | 0.985828i | \(0.553653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.39230 | 0.447948 | ||||||||
\(352\) | 13.5622 | − | 3.63397i | 0.722867 | − | 0.193691i | ||||
\(353\) | −3.63397 | + | 13.5622i | −0.193417 | + | 0.721842i | 0.799254 | + | 0.600993i | \(0.205228\pi\) |
−0.992671 | + | 0.120849i | \(0.961438\pi\) | |||||||
\(354\) | 1.90192 | − | 1.09808i | 0.101086 | − | 0.0583621i | ||||
\(355\) | −0.169873 | + | 2.83013i | −0.00901592 | + | 0.150208i | ||||
\(356\) | 1.14359i | 0.0606103i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.87564 | − | 2.87564i | 0.151983 | − | 0.151983i | ||||
\(359\) | 29.6603 | + | 17.1244i | 1.56541 | + | 0.903789i | 0.996693 | + | 0.0812542i | \(0.0258926\pi\) |
0.568715 | + | 0.822535i | \(0.307441\pi\) | |||||||
\(360\) | −2.36603 | − | 11.5622i | −0.124700 | − | 0.609380i | ||||
\(361\) | 9.23205 | + | 15.9904i | 0.485897 | + | 0.841599i | ||||
\(362\) | 0.160254 | + | 0.598076i | 0.00842277 | + | 0.0314342i | ||||
\(363\) | −1.29423 | − | 1.29423i | −0.0679294 | − | 0.0679294i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.3923 | + | 9.46410i | 1.48612 | + | 0.495374i | ||||
\(366\) | −0.205771 | + | 0.356406i | −0.0107558 | + | 0.0186297i | ||||
\(367\) | −0.500000 | − | 0.133975i | −0.0260998 | − | 0.00699342i | 0.245746 | − | 0.969334i | \(-0.420967\pi\) |
−0.271845 | + | 0.962341i | \(0.587634\pi\) | |||||||
\(368\) | 0.330127 | + | 0.0884573i | 0.0172091 | + | 0.00461115i | ||||
\(369\) | −8.83013 | + | 15.2942i | −0.459678 | + | 0.796186i | ||||
\(370\) | −2.53590 | − | 5.07180i | −0.131835 | − | 0.263670i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.73205 | + | 4.73205i | 0.245345 | + | 0.245345i | ||||
\(373\) | 2.07180 | + | 7.73205i | 0.107274 | + | 0.400350i | 0.998593 | − | 0.0530251i | \(-0.0168863\pi\) |
−0.891320 | + | 0.453376i | \(0.850220\pi\) | |||||||
\(374\) | −2.73205 | − | 4.73205i | −0.141271 | − | 0.244689i | ||||
\(375\) | −5.23205 | − | 2.47372i | −0.270182 | − | 0.127742i | ||||
\(376\) | 15.2942 | + | 8.83013i | 0.788740 | + | 0.455379i | ||||
\(377\) | 6.00000 | − | 6.00000i | 0.309016 | − | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.33975i | 0.120185i | 0.998193 | + | 0.0600923i | \(0.0191395\pi\) | ||||
−0.998193 | + | 0.0600923i | \(0.980860\pi\) | |||||||
\(380\) | 2.83013 | + | 0.169873i | 0.145182 | + | 0.00871430i | ||||
\(381\) | 0.294229 | − | 0.169873i | 0.0150738 | − | 0.00870286i | ||||
\(382\) | −1.77757 | + | 6.63397i | −0.0909483 | + | 0.339424i | ||||
\(383\) | −30.5526 | + | 8.18653i | −1.56116 | + | 0.418312i | −0.933031 | − | 0.359795i | \(-0.882847\pi\) |
−0.628131 | + | 0.778107i | \(0.716180\pi\) | |||||||
\(384\) | 5.92820 | 0.302522 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.19615 | −0.213579 | ||||||||
\(387\) | 10.5622 | − | 2.83013i | 0.536906 | − | 0.143863i | ||||
\(388\) | −3.75833 | + | 14.0263i | −0.190800 | + | 0.712076i | ||||
\(389\) | −4.26795 | + | 2.46410i | −0.216394 | + | 0.124935i | −0.604279 | − | 0.796773i | \(-0.706539\pi\) |
0.387886 | + | 0.921707i | \(0.373206\pi\) | |||||||
\(390\) | 1.12436 | + | 1.26795i | 0.0569340 | + | 0.0642051i | ||||
\(391\) | − | 0.535898i | − | 0.0271015i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.66025 | − | 5.66025i | 0.285522 | − | 0.285522i | ||||
\(394\) | −6.41858 | − | 3.70577i | −0.323364 | − | 0.186694i | ||||
\(395\) | −4.02628 | + | 6.09808i | −0.202584 | + | 0.306828i | ||||
\(396\) | −6.46410 | − | 11.1962i | −0.324833 | − | 0.562628i | ||||
\(397\) | 0.973721 | + | 3.63397i | 0.0488696 | + | 0.182384i | 0.986046 | − | 0.166471i | \(-0.0532372\pi\) |
−0.937177 | + | 0.348855i | \(0.886571\pi\) | |||||||
\(398\) | 4.05256 | + | 4.05256i | 0.203136 | + | 0.203136i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.39230 | + | 9.85641i | −0.369615 | + | 0.492820i | ||||
\(401\) | −5.50000 | + | 9.52628i | −0.274657 | + | 0.475720i | −0.970049 | − | 0.242911i | \(-0.921898\pi\) |
0.695392 | + | 0.718631i | \(0.255231\pi\) | |||||||
\(402\) | −2.86603 | − | 0.767949i | −0.142944 | − | 0.0383018i | ||||
\(403\) | 20.3923 | + | 5.46410i | 1.01581 | + | 0.272186i | ||||
\(404\) | 7.16025 | − | 12.4019i | 0.356236 | − | 0.617019i | ||||
\(405\) | −13.3205 | + | 6.66025i | −0.661901 | + | 0.330951i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.46410 | − | 9.46410i | −0.469118 | − | 0.469118i | ||||
\(408\) | −1.00000 | − | 3.73205i | −0.0495074 | − | 0.184764i | ||||
\(409\) | 10.4282 | + | 18.0622i | 0.515641 | + | 0.893117i | 0.999835 | + | 0.0181564i | \(0.00577967\pi\) |
−0.484194 | + | 0.874961i | \(0.660887\pi\) | |||||||
\(410\) | −7.33013 | + | 1.50000i | −0.362009 | + | 0.0740797i | ||||
\(411\) | 6.12436 | + | 3.53590i | 0.302092 | + | 0.174413i | ||||
\(412\) | 5.83013 | − | 5.83013i | 0.287230 | − | 0.287230i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.196152i | 0.00964037i | ||||||||
\(415\) | −4.96410 | + | 4.40192i | −0.243678 | + | 0.216082i | ||||
\(416\) | 12.5885 | − | 7.26795i | 0.617200 | − | 0.356341i | ||||
\(417\) | 0.758330 | − | 2.83013i | 0.0371356 | − | 0.138592i | ||||
\(418\) | −1.00000 | + | 0.267949i | −0.0489116 | + | 0.0131058i | ||||
\(419\) | −23.8564 | −1.16546 | −0.582731 | − | 0.812665i | \(-0.698016\pi\) | ||||
−0.582731 | + | 0.812665i | \(0.698016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3397 | −0.845088 | −0.422544 | − | 0.906343i | \(-0.638863\pi\) | ||||
−0.422544 | + | 0.906343i | \(0.638863\pi\) | |||||||
\(422\) | −0.0980762 | + | 0.0262794i | −0.00477428 | + | 0.00127926i | ||||
\(423\) | 6.46410 | − | 24.1244i | 0.314295 | − | 1.17297i | ||||
\(424\) | −11.8301 | + | 6.83013i | −0.574522 | + | 0.331700i | ||||
\(425\) | 17.9282 | + | 7.19615i | 0.869646 | + | 0.349065i | ||||
\(426\) | − | 0.339746i | − | 0.0164607i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.0981 | + | 16.0981i | −0.778130 | + | 0.778130i | ||||
\(429\) | 3.46410 | + | 2.00000i | 0.167248 | + | 0.0965609i | ||||
\(430\) | 3.86603 | + | 2.55256i | 0.186436 | + | 0.123095i | ||||
\(431\) | −3.09808 | − | 5.36603i | −0.149229 | − | 0.258472i | 0.781714 | − | 0.623637i | \(-0.214346\pi\) |
−0.930943 | + | 0.365165i | \(0.881013\pi\) | |||||||
\(432\) | −1.89230 | − | 7.06218i | −0.0910436 | − | 0.339779i | ||||
\(433\) | 17.5359 | + | 17.5359i | 0.842721 | + | 0.842721i | 0.989212 | − | 0.146491i | \(-0.0467978\pi\) |
−0.146491 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.09808 | − | 3.29423i | 0.0526487 | − | 0.157946i | ||||
\(436\) | 8.76795 | − | 15.1865i | 0.419909 | − | 0.727303i | ||||
\(437\) | −0.0980762 | − | 0.0262794i | −0.00469162 | − | 0.00125712i | ||||
\(438\) | −3.46410 | − | 0.928203i | −0.165521 | − | 0.0443513i | ||||
\(439\) | −1.66025 | + | 2.87564i | −0.0792396 | + | 0.137247i | −0.902922 | − | 0.429804i | \(-0.858583\pi\) |
0.823682 | + | 0.567051i | \(0.191916\pi\) | |||||||
\(440\) | 3.73205 | − | 11.1962i | 0.177919 | − | 0.533756i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | − | 4.00000i | −0.190261 | − | 0.190261i | ||||
\(443\) | −3.50000 | − | 13.0622i | −0.166290 | − | 0.620603i | −0.997872 | − | 0.0652010i | \(-0.979231\pi\) |
0.831582 | − | 0.555402i | \(-0.187436\pi\) | |||||||
\(444\) | −2.19615 | − | 3.80385i | −0.104225 | − | 0.180523i | ||||
\(445\) | 1.23205 | + | 0.813467i | 0.0584048 | + | 0.0385620i | ||||
\(446\) | −11.4904 | − | 6.63397i | −0.544085 | − | 0.314128i | ||||
\(447\) | 0.294229 | − | 0.294229i | 0.0139165 | − | 0.0139165i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.0526i | − | 1.55985i | −0.625875 | − | 0.779923i | \(-0.715258\pi\) | ||
0.625875 | − | 0.779923i | \(-0.284742\pi\) | |||||||
\(450\) | −6.56218 | − | 2.63397i | −0.309344 | − | 0.124167i | ||||
\(451\) | −15.2942 | + | 8.83013i | −0.720177 | + | 0.415794i | ||||
\(452\) | 4.90192 | − | 18.2942i | 0.230567 | − | 0.860488i | ||||
\(453\) | −6.92820 | + | 1.85641i | −0.325515 | + | 0.0872216i | ||||
\(454\) | 10.1962 | 0.478529 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.732051 | −0.0342814 | ||||||||
\(457\) | −11.7321 | + | 3.14359i | −0.548802 | + | 0.147051i | −0.522557 | − | 0.852604i | \(-0.675022\pi\) |
−0.0262453 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(458\) | 2.46410 | − | 9.19615i | 0.115140 | − | 0.429708i | ||||
\(459\) | −9.92820 | + | 5.73205i | −0.463409 | + | 0.267549i | ||||
\(460\) | 0.401924 | − | 0.356406i | 0.0187398 | − | 0.0166175i | ||||
\(461\) | 5.60770i | 0.261176i | 0.991437 | + | 0.130588i | \(0.0416866\pi\) | ||||
−0.991437 | + | 0.130588i | \(0.958313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.75833 | + | 4.75833i | −0.221138 | + | 0.221138i | −0.808978 | − | 0.587839i | \(-0.799979\pi\) |
0.587839 | + | 0.808978i | \(0.299979\pi\) | |||||||
\(464\) | −6.40192 | − | 3.69615i | −0.297202 | − | 0.171590i | ||||
\(465\) | 8.46410 | − | 1.73205i | 0.392513 | − | 0.0803219i | ||||
\(466\) | −1.73205 | − | 3.00000i | −0.0802357 | − | 0.138972i | ||||
\(467\) | −3.64359 | − | 13.5981i | −0.168605 | − | 0.629244i | −0.997553 | − | 0.0699173i | \(-0.977726\pi\) |
0.828947 | − | 0.559327i | \(-0.188940\pi\) | |||||||
\(468\) | −9.46410 | − | 9.46410i | −0.437478 | − | 0.437478i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.46410 | − | 4.73205i | 0.436546 | − | 0.218273i | ||||
\(471\) | 1.24167 | − | 2.15064i | 0.0572131 | − | 0.0990960i | ||||
\(472\) | −15.2942 | − | 4.09808i | −0.703974 | − | 0.188629i | ||||
\(473\) | 10.5622 | + | 2.83013i | 0.485649 | + | 0.130129i | ||||
\(474\) | 0.437822 | − | 0.758330i | 0.0201098 | − | 0.0348313i | ||||
\(475\) | 2.19615 | − | 2.92820i | 0.100766 | − | 0.134355i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.6603 | + | 13.6603i | 0.625460 | + | 0.625460i | ||||
\(478\) | 0.320508 | + | 1.19615i | 0.0146597 | + | 0.0547107i | ||||
\(479\) | −6.53590 | − | 11.3205i | −0.298633 | − | 0.517247i | 0.677191 | − | 0.735808i | \(-0.263197\pi\) |
−0.975823 | + | 0.218560i | \(0.929864\pi\) | |||||||
\(480\) | 3.27757 | − | 4.96410i | 0.149600 | − | 0.226579i | ||||
\(481\) | −12.0000 | − | 6.92820i | −0.547153 | − | 0.315899i | ||||
\(482\) | −9.07180 | + | 9.07180i | −0.413209 | + | 0.413209i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.12436i | 0.278380i | ||||||||
\(485\) | 12.4378 | + | 14.0263i | 0.564772 | + | 0.636901i | ||||
\(486\) | 5.53590 | − | 3.19615i | 0.251113 | − | 0.144980i | ||||
\(487\) | 7.29423 | − | 27.2224i | 0.330533 | − | 1.23357i | −0.578098 | − | 0.815967i | \(-0.696205\pi\) |
0.908631 | − | 0.417599i | \(-0.137128\pi\) | |||||||
\(488\) | 2.86603 | − | 0.767949i | 0.129739 | − | 0.0347634i | ||||
\(489\) | −7.26795 | −0.328668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.7128 | 1.70196 | 0.850978 | − | 0.525202i | \(-0.176010\pi\) | ||||
0.850978 | + | 0.525202i | \(0.176010\pi\) | |||||||
\(492\) | −5.59808 | + | 1.50000i | −0.252381 | + | 0.0676252i | ||||
\(493\) | −3.00000 | + | 11.1962i | −0.135113 | + | 0.504249i | ||||
\(494\) | −0.928203 | + | 0.535898i | −0.0417618 | + | 0.0241112i | ||||
\(495\) | −16.6603 | − | 1.00000i | −0.748823 | − | 0.0449467i | ||||
\(496\) | − | 18.3923i | − | 0.825839i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.562178 | − | 0.562178i | 0.0251918 | − | 0.0251918i | ||||
\(499\) | −9.97372 | − | 5.75833i | −0.446485 | − | 0.257778i | 0.259860 | − | 0.965646i | \(-0.416324\pi\) |
−0.706345 | + | 0.707868i | \(0.749657\pi\) | |||||||
\(500\) | 6.52628 | + | 18.2321i | 0.291864 | + | 0.815362i | ||||
\(501\) | 4.30385 | + | 7.45448i | 0.192282 | + | 0.333042i | ||||
\(502\) | −2.92820 | − | 10.9282i | −0.130692 | − | 0.487750i | ||||
\(503\) | 17.6340 | + | 17.6340i | 0.786260 | + | 0.786260i | 0.980879 | − | 0.194619i | \(-0.0623470\pi\) |
−0.194619 | + | 0.980879i | \(0.562347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.26795 | − | 16.5359i | −0.367919 | − | 0.735838i | ||||
\(506\) | −0.0980762 | + | 0.169873i | −0.00436002 | + | 0.00755178i | ||||
\(507\) | −2.50000 | − | 0.669873i | −0.111029 | − | 0.0297501i | ||||
\(508\) | −1.09808 | − | 0.294229i | −0.0487193 | − | 0.0130543i | ||||
\(509\) | 19.4545 | − | 33.6962i | 0.862305 | − | 1.49356i | −0.00739389 | − | 0.999973i | \(-0.502354\pi\) |
0.869699 | − | 0.493583i | \(-0.164313\pi\) | |||||||
\(510\) | −2.19615 | − | 0.732051i | −0.0972473 | − | 0.0324158i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.6865 | − | 15.6865i | −0.693253 | − | 0.693253i | ||||
\(513\) | 0.562178 | + | 2.09808i | 0.0248208 | + | 0.0926323i | ||||
\(514\) | 0.732051 | + | 1.26795i | 0.0322894 | + | 0.0559268i | ||||
\(515\) | −2.13397 | − | 10.4282i | −0.0940342 | − | 0.459522i | ||||
\(516\) | 3.10770 | + | 1.79423i | 0.136809 | + | 0.0789865i | ||||
\(517\) | 17.6603 | − | 17.6603i | 0.776697 | − | 0.776697i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.6795i | 0.468778i | ||||||||
\(520\) | 0.732051 | − | 12.1962i | 0.0321026 | − | 0.534837i | ||||
\(521\) | 20.6603 | − | 11.9282i | 0.905142 | − | 0.522584i | 0.0262772 | − | 0.999655i | \(-0.491635\pi\) |
0.878865 | + | 0.477071i | \(0.158301\pi\) | |||||||
\(522\) | 1.09808 | − | 4.09808i | 0.0480615 | − | 0.179368i | ||||
\(523\) | 42.8827 | − | 11.4904i | 1.87513 | − | 0.502439i | 0.875307 | − | 0.483568i | \(-0.160659\pi\) |
0.999822 | − | 0.0188717i | \(-0.00600740\pi\) | |||||||
\(524\) | −26.7846 | −1.17009 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.12436 | −0.354239 | ||||||||
\(527\) | −27.8564 | + | 7.46410i | −1.21344 | + | 0.325141i | ||||
\(528\) | 0.901924 | − | 3.36603i | 0.0392512 | − | 0.146487i | ||||
\(529\) | 19.9019 | − | 11.4904i | 0.865301 | − | 0.499582i | ||||
\(530\) | −0.490381 | + | 8.16987i | −0.0213008 | + | 0.354877i | ||||
\(531\) | 22.3923i | 0.971743i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9282 | + | 12.9282i | −0.559983 | + | 0.559983i | ||||
\(534\) | −0.153212 | − | 0.0884573i | −0.00663015 | − | 0.00382792i | ||||
\(535\) | 5.89230 | + | 28.7942i | 0.254747 | + | 1.24488i | ||||
\(536\) | 10.6962 | + | 18.5263i | 0.462003 | + | 0.800213i | ||||
\(537\) | −1.05256 | − | 3.92820i | −0.0454213 | − | 0.169514i | ||||
\(538\) | −8.36603 | − | 8.36603i | −0.360685 | − | 0.360685i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.9019 | − | 3.63397i | −0.469144 | − | 0.156381i | ||||
\(541\) | −18.3564 | + | 31.7942i | −0.789204 | + | 1.36694i | 0.137252 | + | 0.990536i | \(0.456173\pi\) |
−0.926455 | + | 0.376404i | \(0.877160\pi\) | |||||||
\(542\) | −10.6340 | − | 2.84936i | −0.456768 | − | 0.122391i | ||||
\(543\) | 0.598076 | + | 0.160254i | 0.0256659 | + | 0.00687716i | ||||
\(544\) | −9.92820 | + | 17.1962i | −0.425668 | + | 0.737279i | ||||
\(545\) | −10.1244 | − | 20.2487i | −0.433680 | − | 0.867359i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7583 | − | 16.7583i | −0.716534 | − | 0.716534i | 0.251359 | − | 0.967894i | \(-0.419122\pi\) |
−0.967894 | + | 0.251359i | \(0.919122\pi\) | |||||||
\(548\) | −6.12436 | − | 22.8564i | −0.261620 | − | 0.976377i | ||||
\(549\) | −2.09808 | − | 3.63397i | −0.0895437 | − | 0.155094i | ||||
\(550\) | −4.36603 | − | 5.56218i | −0.186168 | − | 0.237172i | ||||
\(551\) | 1.90192 | + | 1.09808i | 0.0810247 | + | 0.0467796i | ||||
\(552\) | −0.0980762 | + | 0.0980762i | −0.00417440 | + | 0.00417440i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.78461i | 0.118307i | ||||||||
\(555\) | −5.66025 | − | 0.339746i | −0.240264 | − | 0.0144214i | ||||
\(556\) | −8.49038 | + | 4.90192i | −0.360072 | + | 0.207888i | ||||
\(557\) | 8.36603 | − | 31.2224i | 0.354480 | − | 1.32294i | −0.526658 | − | 0.850077i | \(-0.676555\pi\) |
0.881138 | − | 0.472860i | \(-0.156778\pi\) | |||||||
\(558\) | 10.1962 | − | 2.73205i | 0.431638 | − | 0.115657i | ||||
\(559\) | 11.3205 | 0.478806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.46410 | −0.230695 | ||||||||
\(562\) | −0.464102 | + | 0.124356i | −0.0195769 | + | 0.00524563i | ||||
\(563\) | 6.35641 | − | 23.7224i | 0.267891 | − | 0.999781i | −0.692567 | − | 0.721354i | \(-0.743520\pi\) |
0.960457 | − | 0.278427i | \(-0.0898132\pi\) | |||||||
\(564\) | 7.09808 | − | 4.09808i | 0.298883 | − | 0.172560i | ||||
\(565\) | −16.2224 | − | 18.2942i | −0.682483 | − | 0.769644i | ||||
\(566\) | − | 1.01924i | − | 0.0428418i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.73205 | + | 1.73205i | −0.0726752 | + | 0.0726752i | ||||
\(569\) | −25.0526 | − | 14.4641i | −1.05026 | − | 0.606367i | −0.127536 | − | 0.991834i | \(-0.540707\pi\) |
−0.922722 | + | 0.385467i | \(0.874040\pi\) | |||||||
\(570\) | −0.241670 | + | 0.366025i | −0.0101224 | + | 0.0153311i | ||||
\(571\) | 9.02628 | + | 15.6340i | 0.377738 | + | 0.654261i | 0.990733 | − | 0.135826i | \(-0.0433687\pi\) |
−0.612995 | + | 0.790087i | \(0.710035\pi\) | |||||||
\(572\) | −3.46410 | − | 12.9282i | −0.144841 | − | 0.540555i | ||||
\(573\) | 4.85641 | + | 4.85641i | 0.202879 | + | 0.202879i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0980762 | − | 0.686533i | −0.00409006 | − | 0.0286304i | ||||
\(576\) | −3.09808 | + | 5.36603i | −0.129087 | + | 0.223584i | ||||
\(577\) | −5.63397 | − | 1.50962i | −0.234545 | − | 0.0628463i | 0.139632 | − | 0.990204i | \(-0.455408\pi\) |
−0.374177 | + | 0.927357i | \(0.622075\pi\) | |||||||
\(578\) | −1.03590 | − | 0.277568i | −0.0430877 | − | 0.0115453i | ||||
\(579\) | −2.09808 | + | 3.63397i | −0.0871931 | + | 0.151023i | ||||
\(580\) | −10.3923 | + | 5.19615i | −0.431517 | + | 0.215758i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.58846 | − | 1.58846i | −0.0658437 | − | 0.0658437i | ||||
\(583\) | 5.00000 | + | 18.6603i | 0.207079 | + | 0.772829i | ||||
\(584\) | 12.9282 | + | 22.3923i | 0.534973 | + | 0.926600i | ||||
\(585\) | −16.9282 | + | 3.46410i | −0.699895 | + | 0.143223i | ||||
\(586\) | 1.51666 | + | 0.875644i | 0.0626527 | + | 0.0361725i | ||||
\(587\) | −15.7846 | + | 15.7846i | −0.651501 | + | 0.651501i | −0.953354 | − | 0.301854i | \(-0.902395\pi\) |
0.301854 | + | 0.953354i | \(0.402395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.46410i | 0.225144i | ||||||||
\(590\) | −7.09808 | + | 6.29423i | −0.292223 | + | 0.259129i | ||||
\(591\) | −6.41858 | + | 3.70577i | −0.264025 | + | 0.152435i | ||||
\(592\) | −3.12436 | + | 11.6603i | −0.128410 | + | 0.479233i | ||||
\(593\) | −20.7583 | + | 5.56218i | −0.852442 | + | 0.228411i | −0.658481 | − | 0.752598i | \(-0.728801\pi\) |
−0.193962 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(594\) | 4.19615 | 0.172170 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.39230 | −0.0570310 | ||||||||
\(597\) | 5.53590 | − | 1.48334i | 0.226569 | − | 0.0607090i | ||||
\(598\) | −0.0525589 | + | 0.196152i | −0.00214929 | + | 0.00802127i | ||||
\(599\) | −15.3397 | + | 8.85641i | −0.626765 | + | 0.361863i | −0.779498 | − | 0.626405i | \(-0.784526\pi\) |
0.152733 | + | 0.988267i | \(0.451193\pi\) | |||||||
\(600\) | −1.96410 | − | 4.59808i | −0.0801841 | − | 0.187716i | ||||
\(601\) | 41.1769i | 1.67964i | 0.542864 | + | 0.839821i | \(0.317340\pi\) | ||||
−0.542864 | + | 0.839821i | \(0.682660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3923 | − | 21.3923i | 0.871162 | − | 0.871162i | ||||
\(604\) | 20.7846 | + | 12.0000i | 0.845714 | + | 0.488273i | ||||
\(605\) | 6.59808 | + | 4.35641i | 0.268250 | + | 0.177113i | ||||
\(606\) | 1.10770 | + | 1.91858i | 0.0449970 | + | 0.0779372i | ||||
\(607\) | −3.40192 | − | 12.6962i | −0.138080 | − | 0.515321i | −0.999966 | − | 0.00821951i | \(-0.997384\pi\) |
0.861886 | − | 0.507101i | \(-0.169283\pi\) | |||||||
\(608\) | 2.66025 | + | 2.66025i | 0.107888 | + | 0.107888i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.562178 | − | 1.68653i | 0.0227619 | − | 0.0682857i | ||||
\(611\) | 12.9282 | − | 22.3923i | 0.523019 | − | 0.905896i | ||||
\(612\) | 17.6603 | + | 4.73205i | 0.713873 | + | 0.191282i | ||||
\(613\) | 24.3923 | + | 6.53590i | 0.985196 | + | 0.263982i | 0.715231 | − | 0.698888i | \(-0.246321\pi\) |
0.269965 | + | 0.962870i | \(0.412988\pi\) | |||||||
\(614\) | −2.30385 | + | 3.99038i | −0.0929757 | + | 0.161039i | ||||
\(615\) | −2.36603 | + | 7.09808i | −0.0954074 | + | 0.286222i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9090 | + | 33.9090i | 1.36512 | + | 1.36512i | 0.867249 | + | 0.497874i | \(0.165886\pi\) |
0.497874 | + | 0.867249i | \(0.334114\pi\) | |||||||
\(618\) | 0.330127 | + | 1.23205i | 0.0132797 | + | 0.0495604i | ||||
\(619\) | −5.09808 | − | 8.83013i | −0.204909 | − | 0.354913i | 0.745195 | − | 0.666847i | \(-0.232357\pi\) |
−0.950104 | + | 0.311934i | \(0.899023\pi\) | |||||||
\(620\) | −24.1244 | − | 15.9282i | −0.968857 | − | 0.639692i | ||||
\(621\) | 0.356406 | + | 0.205771i | 0.0143021 | + | 0.00825732i | ||||
\(622\) | 5.58846 | − | 5.58846i | 0.224077 | − | 0.224077i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 3.60770i | − | 0.144423i | ||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 2.41154 | − | 1.39230i | 0.0963846 | − | 0.0556477i | ||||
\(627\) | −0.267949 | + | 1.00000i | −0.0107009 | + | 0.0399362i | ||||
\(628\) | −8.02628 | + | 2.15064i | −0.320283 | + | 0.0858197i | ||||
\(629\) | 18.9282 | 0.754717 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.58846 | −0.182664 | −0.0913318 | − | 0.995821i | \(-0.529112\pi\) | ||||
−0.0913318 | + | 0.995821i | \(0.529112\pi\) | |||||||
\(632\) | −6.09808 | + | 1.63397i | −0.242568 | + | 0.0649960i | ||||
\(633\) | −0.0262794 | + | 0.0980762i | −0.00104451 | + | 0.00389818i | ||||
\(634\) | 4.26795 | − | 2.46410i | 0.169502 | − | 0.0978620i | ||||
\(635\) | −1.09808 | + | 0.973721i | −0.0435758 | + | 0.0386409i | ||||
\(636\) | 6.33975i | 0.251387i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.00000 | − | 3.00000i | 0.118771 | − | 0.118771i | ||||
\(639\) | 3.00000 | + | 1.73205i | 0.118678 | + | 0.0685189i | ||||
\(640\) | −25.0885 | + | 5.13397i | −0.991708 | + | 0.202938i | ||||
\(641\) | −5.33013 | − | 9.23205i | −0.210527 | − | 0.364644i | 0.741352 | − | 0.671116i | \(-0.234185\pi\) |
−0.951880 | + | 0.306472i | \(0.900851\pi\) | |||||||
\(642\) | −0.911543 | − | 3.40192i | −0.0359757 | − | 0.134263i | ||||
\(643\) | −17.5359 | − | 17.5359i | −0.691548 | − | 0.691548i | 0.271024 | − | 0.962573i | \(-0.412638\pi\) |
−0.962573 | + | 0.271024i | \(0.912638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.14359 | − | 2.07180i | 0.163154 | − | 0.0815769i | ||||
\(646\) | 0.732051 | − | 1.26795i | 0.0288022 | − | 0.0498868i | ||||
\(647\) | −39.5526 | − | 10.5981i | −1.55497 | − | 0.416653i | −0.623904 | − | 0.781501i | \(-0.714454\pi\) |
−0.931067 | + | 0.364847i | \(0.881121\pi\) | |||||||
\(648\) | −12.4282 | − | 3.33013i | −0.488226 | − | 0.130820i | ||||
\(649\) | −11.1962 | + | 19.3923i | −0.439487 | + | 0.761215i | ||||
\(650\) | −5.85641 | − | 4.39230i | −0.229707 | − | 0.172280i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.1962 | + | 17.1962i | 0.673453 | + | 0.673453i | ||||
\(653\) | −5.26795 | − | 19.6603i | −0.206151 | − | 0.769365i | −0.989096 | − | 0.147274i | \(-0.952950\pi\) |
0.782945 | − | 0.622091i | \(-0.213717\pi\) | |||||||
\(654\) | 1.35641 | + | 2.34936i | 0.0530397 | + | 0.0918674i | ||||
\(655\) | −19.0526 | + | 28.8564i | −0.744445 | + | 1.12751i | ||||
\(656\) | 13.7942 | + | 7.96410i | 0.538574 | + | 0.310946i | ||||
\(657\) | 25.8564 | − | 25.8564i | 1.00875 | − | 1.00875i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27.6603i | − | 1.07749i | −0.842469 | − | 0.538745i | \(-0.818899\pi\) | ||
0.842469 | − | 0.538745i | \(-0.181101\pi\) | |||||||
\(660\) | −3.63397 | − | 4.09808i | −0.141452 | − | 0.159517i | ||||
\(661\) | 41.7224 | − | 24.0885i | 1.62281 | − | 0.936932i | 0.636652 | − | 0.771151i | \(-0.280319\pi\) |
0.986163 | − | 0.165781i | \(-0.0530145\pi\) | |||||||
\(662\) | 0.248711 | − | 0.928203i | 0.00966644 | − | 0.0360756i | ||||
\(663\) | −5.46410 | + | 1.46410i | −0.212208 | + | 0.0568610i | ||||
\(664\) | −5.73205 | −0.222447 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.92820 | −0.268462 | ||||||||
\(667\) | 0.401924 | − | 0.107695i | 0.0155626 | − | 0.00416997i | ||||
\(668\) | 7.45448 | − | 27.8205i | 0.288423 | − | 1.07641i | ||||
\(669\) | −11.4904 | + | 6.63397i | −0.444244 | + | 0.256484i | ||||
\(670\) | 12.7942 | + | 0.767949i | 0.494284 | + | 0.0296685i | ||||
\(671\) | − | 4.19615i | − | 0.161991i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.39230 | − | 4.39230i | 0.169311 | − | 0.169311i | −0.617366 | − | 0.786676i | \(-0.711800\pi\) |
0.786676 | + | 0.617366i | \(0.211800\pi\) | |||||||
\(674\) | 6.04552 | + | 3.49038i | 0.232865 | + | 0.134444i | ||||
\(675\) | −11.6699 | + | 9.16025i | −0.449174 | + | 0.352578i | ||||
\(676\) | 4.33013 | + | 7.50000i | 0.166543 | + | 0.288462i | ||||
\(677\) | 6.92820 | + | 25.8564i | 0.266272 | + | 0.993742i | 0.961467 | + | 0.274921i | \(0.0886516\pi\) |
−0.695194 | + | 0.718822i | \(0.744682\pi\) | |||||||
\(678\) | 2.07180 | + | 2.07180i | 0.0795669 | + | 0.0795669i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.46410 | + | 14.9282i | 0.286235 | + | 0.572470i | ||||
\(681\) | 5.09808 | − | 8.83013i | 0.195359 | − | 0.338371i | ||||
\(682\) | 10.1962 | + | 2.73205i | 0.390431 | + | 0.104616i | ||||
\(683\) | 17.0622 | + | 4.57180i | 0.652866 | + | 0.174935i | 0.570024 | − | 0.821628i | \(-0.306934\pi\) |
0.0828417 | + | 0.996563i | \(0.473600\pi\) | |||||||
\(684\) | 1.73205 | − | 3.00000i | 0.0662266 | − | 0.114708i | ||||
\(685\) | −28.9808 | − | 9.66025i | −1.10730 | − | 0.369099i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.73205 | − | 6.73205i | −0.256844 | − | 0.256844i | ||||
\(688\) | −2.55256 | − | 9.52628i | −0.0973154 | − | 0.363186i | ||||
\(689\) | 10.0000 | + | 17.3205i | 0.380970 | + | 0.659859i | ||||
\(690\) | 0.0166605 | + | 0.0814157i | 0.000634254 | + | 0.00309944i | ||||
\(691\) | 44.0263 | + | 25.4186i | 1.67484 | + | 0.966969i | 0.964867 | + | 0.262738i | \(0.0846255\pi\) |
0.709971 | + | 0.704231i | \(0.248708\pi\) | |||||||
\(692\) | 25.2679 | − | 25.2679i | 0.960543 | − | 0.960543i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.5885i | 0.591730i | ||||||||
\(695\) | −0.758330 | + | 12.6340i | −0.0287651 | + | 0.479234i | ||||
\(696\) | 2.59808 | − | 1.50000i | 0.0984798 | − | 0.0568574i | ||||
\(697\) | 6.46410 | − | 24.1244i | 0.244845 | − | 0.913775i | ||||
\(698\) | −3.13397 | + | 0.839746i | −0.118623 | + | 0.0317849i | ||||
\(699\) | −3.46410 | −0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.2679 | −0.765510 | −0.382755 | − | 0.923850i | \(-0.625025\pi\) | ||||
−0.382755 | + | 0.923850i | \(0.625025\pi\) | |||||||
\(702\) | 4.19615 | − | 1.12436i | 0.158374 | − | 0.0424361i | ||||
\(703\) | 0.928203 | − | 3.46410i | 0.0350078 | − | 0.130651i | ||||
\(704\) | −5.36603 | + | 3.09808i | −0.202240 | + | 0.116763i | ||||
\(705\) | 0.633975 | − | 10.5622i | 0.0238769 | − | 0.397795i | ||||
\(706\) | 7.26795i | 0.273533i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.19615 | + | 5.19615i | −0.195283 | + | 0.195283i | ||||
\(709\) | 18.9904 | + | 10.9641i | 0.713199 | + | 0.411765i | 0.812244 | − | 0.583317i | \(-0.198246\pi\) |
−0.0990456 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(710\) | 0.294229 | + | 1.43782i | 0.0110422 | + | 0.0539605i | ||||
\(711\) | 4.46410 | + | 7.73205i | 0.167417 | + | 0.289975i | ||||
\(712\) | 0.330127 | + | 1.23205i | 0.0123720 | + | 0.0461731i | ||||
\(713\) | 0.732051 | + | 0.732051i | 0.0274155 | + | 0.0274155i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.3923 | − | 5.46410i | −0.613037 | − | 0.204346i | ||||
\(716\) | −6.80385 | + | 11.7846i | −0.254272 | + | 0.440412i | ||||
\(717\) | 1.19615 | + | 0.320508i | 0.0446711 | + | 0.0119696i | ||||
\(718\) | 17.1244 | + | 4.58846i | 0.639075 | + | 0.171240i | ||||
\(719\) | −19.2942 | + | 33.4186i | −0.719553 | + | 1.24630i | 0.241624 | + | 0.970370i | \(0.422320\pi\) |
−0.961177 | + | 0.275933i | \(0.911013\pi\) | |||||||
\(720\) | 6.73205 | + | 13.4641i | 0.250889 | + | 0.501777i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.75833 | + | 6.75833i | 0.251519 | + | 0.251519i | ||||
\(723\) | 3.32051 | + | 12.3923i | 0.123491 | + | 0.460875i | ||||
\(724\) | −1.03590 | − | 1.79423i | −0.0384989 | − | 0.0666820i | ||||
\(725\) | −1.79423 | + | 14.8923i | −0.0666360 | + | 0.553086i | ||||
\(726\) | −0.820508 | − | 0.473721i | −0.0304519 | − | 0.0175814i | ||||
\(727\) | 10.0981 | − | 10.0981i | 0.374517 | − | 0.374517i | −0.494602 | − | 0.869119i | \(-0.664686\pi\) |
0.869119 | + | 0.494602i | \(0.164686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5885i | 0.503276i | ||||||||
\(730\) | 15.4641 | + | 0.928203i | 0.572352 | + | 0.0343543i | ||||
\(731\) | −13.3923 | + | 7.73205i | −0.495332 | + | 0.285980i | ||||
\(732\) | 0.356406 | − | 1.33013i | 0.0131732 | − | 0.0491629i | ||||
\(733\) | 4.36603 | − | 1.16987i | 0.161263 | − | 0.0432102i | −0.177284 | − | 0.984160i | \(-0.556731\pi\) |
0.338547 | + | 0.940949i | \(0.390065\pi\) | |||||||
\(734\) | −0.267949 | −0.00989019 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.712813 | 0.0262746 | ||||||||
\(737\) | 29.2224 | − | 7.83013i | 1.07642 | − | 0.288426i | ||||
\(738\) | −2.36603 | + | 8.83013i | −0.0870946 | + | 0.325041i | ||||
\(739\) | −19.5622 | + | 11.2942i | −0.719606 | + | 0.415465i | −0.814608 | − | 0.580012i | \(-0.803048\pi\) |
0.0950014 | + | 0.995477i | \(0.469714\pi\) | |||||||
\(740\) | 12.5885 | + | 14.1962i | 0.462761 | + | 0.521861i | ||||
\(741\) | 1.07180i | 0.0393734i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.16987 | + | 6.16987i | −0.226351 | + | 0.226351i | −0.811166 | − | 0.584816i | \(-0.801167\pi\) |
0.584816 | + | 0.811166i | \(0.301167\pi\) | |||||||
\(744\) | 6.46410 | + | 3.73205i | 0.236985 | + | 0.136824i | ||||
\(745\) | −0.990381 | + | 1.50000i | −0.0362848 | + | 0.0549557i | ||||
\(746\) | 2.07180 | + | 3.58846i | 0.0758539 | + | 0.131383i | ||||
\(747\) | 2.09808 | + | 7.83013i | 0.0767646 | + | 0.286489i | ||||
\(748\) | 12.9282 | + | 12.9282i | 0.472702 | + | 0.472702i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.94744 | − | 0.535898i | −0.107625 | − | 0.0195682i | ||||
\(751\) | 3.19615 | − | 5.53590i | 0.116629 | − | 0.202008i | −0.801801 | − | 0.597592i | \(-0.796124\pi\) |
0.918430 | + | 0.395584i | \(0.129458\pi\) | |||||||
\(752\) | −21.7583 | − | 5.83013i | −0.793445 | − | 0.212603i | ||||
\(753\) | −10.9282 | − | 2.92820i | −0.398246 | − | 0.106710i | ||||
\(754\) | 2.19615 | − | 3.80385i | 0.0799792 | − | 0.138528i | ||||
\(755\) | 27.7128 | − | 13.8564i | 1.00857 | − | 0.504286i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7321 | + | 12.7321i | 0.462754 | + | 0.462754i | 0.899557 | − | 0.436803i | \(-0.143889\pi\) |
−0.436803 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(758\) | 0.313467 | + | 1.16987i | 0.0113856 | + | 0.0424917i | ||||
\(759\) | 0.0980762 | + | 0.169873i | 0.00355994 | + | 0.00616600i | ||||
\(760\) | 3.09808 | − | 0.633975i | 0.112379 | − | 0.0229967i | ||||
\(761\) | −24.9282 | − | 14.3923i | −0.903647 | − | 0.521721i | −0.0252651 | − | 0.999681i | \(-0.508043\pi\) |
−0.878382 | + | 0.477960i | \(0.841376\pi\) | |||||||
\(762\) | 0.124356 | − | 0.124356i | 0.00450493 | − | 0.00450493i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 22.9808i | − | 0.831415i | ||||||
\(765\) | 17.6603 | − | 15.6603i | 0.638508 | − | 0.566198i | ||||
\(766\) | −14.1795 | + | 8.18653i | −0.512326 | + | 0.295791i | ||||
\(767\) | −6.00000 | + | 22.3923i | −0.216647 | + | 0.808539i | ||||
\(768\) | 0.696152 | − | 0.186533i | 0.0251202 | − | 0.00673095i | ||||
\(769\) | −15.1769 | −0.547294 | −0.273647 | − | 0.961830i | \(-0.588230\pi\) | ||||
−0.273647 | + | 0.961830i | \(0.588230\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.46410 | 0.0527283 | ||||||||
\(772\) | 13.5622 | − | 3.63397i | 0.488113 | − | 0.130790i | ||||
\(773\) | −4.07180 | + | 15.1962i | −0.146452 | + | 0.546568i | 0.853234 | + | 0.521528i | \(0.174638\pi\) |
−0.999686 | + | 0.0250395i | \(0.992029\pi\) | |||||||
\(774\) | 4.90192 | − | 2.83013i | 0.176196 | − | 0.101727i | ||||
\(775\) | −34.3205 | + | 14.6603i | −1.23283 | + | 0.526612i | ||||
\(776\) | 16.1962i | 0.581408i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.80385 | + | 1.80385i | −0.0646711 | + | 0.0646711i | ||||
\(779\) | −4.09808 | − | 2.36603i | −0.146829 | − | 0.0847717i | ||||
\(780\) | −4.73205 | − | 3.12436i | −0.169435 | − | 0.111870i | ||||
\(781\) | 1.73205 | + | 3.00000i | 0.0619777 | + | 0.107348i | ||||
\(782\) | −0.0717968 | − | 0.267949i | −0.00256745 | − | 0.00958184i | ||||
\(783\) | −6.29423 | − | 6.29423i | −0.224937 | − | 0.224937i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.39230 | + | 10.1769i | −0.121077 | + | 0.363230i | ||||
\(786\) | 2.07180 | − | 3.58846i | 0.0738985 | − | 0.127996i | ||||
\(787\) | −31.1865 | − | 8.35641i | −1.11168 | − | 0.297874i | −0.344168 | − | 0.938908i | \(-0.611839\pi\) |
−0.767512 | + | 0.641034i | \(0.778506\pi\) | |||||||
\(788\) | 23.9545 | + | 6.41858i | 0.853343 | + | 0.228653i | ||||
\(789\) | −4.06218 | + | 7.03590i | −0.144617 | + | 0.250485i | ||||
\(790\) | −1.19615 | + | 3.58846i | −0.0425572 | + | 0.127672i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.1962 | − | 10.1962i | −0.362305 | − | 0.362305i | ||||
\(793\) | −1.12436 | − | 4.19615i | −0.0399270 | − | 0.149010i | ||||
\(794\) | 0.973721 | + | 1.68653i | 0.0345560 | + | 0.0598528i | ||||
\(795\) | 6.83013 | + | 4.50962i | 0.242240 | + | 0.159940i | ||||
\(796\) | −16.6077 | − | 9.58846i | −0.588644 | − | 0.339854i | ||||
\(797\) | −22.5359 | + | 22.5359i | −0.798262 | + | 0.798262i | −0.982821 | − | 0.184559i | \(-0.940914\pi\) |
0.184559 | + | 0.982821i | \(0.440914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.3205i | 1.24955i | ||||||||
\(800\) | −9.57180 | + | 23.8468i | −0.338414 | + | 0.843111i | ||||
\(801\) | 1.56218 | − | 0.901924i | 0.0551968 | − | 0.0318679i | ||||
\(802\) | −1.47372 | + | 5.50000i | −0.0520389 | + | 0.194212i | ||||
\(803\) | 35.3205 | − | 9.46410i | 1.24643 | − | 0.333981i | ||||
\(804\) | 9.92820 | 0.350141 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.9282 | 0.384930 | ||||||||
\(807\) | −11.4282 | + | 3.06218i | −0.402292 | + | 0.107794i | ||||
\(808\) | 4.13397 | − | 15.4282i | 0.145433 | − | 0.542762i | ||||
\(809\) | −3.99038 | + | 2.30385i | −0.140294 | + | 0.0809990i | −0.568504 | − | 0.822680i | \(-0.692478\pi\) |
0.428210 | + | 0.903679i | \(0.359144\pi\) | |||||||
\(810\) | −5.76795 | + | 5.11474i | −0.202665 | + | 0.179714i | ||||
\(811\) | − | 42.9282i | − | 1.50741i | −0.657211 | − | 0.753707i | \(-0.728264\pi\) | ||
0.657211 | − | 0.753707i | \(-0.271736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.78461 | + | 7.78461i | −0.273018 | + | 0.273018i | ||||
\(814\) | −6.00000 | − | 3.46410i | −0.210300 | − | 0.121417i | ||||
\(815\) | 30.7583 | − | 6.29423i | 1.07742 | − | 0.220477i | ||||
\(816\) | 2.46410 | + | 4.26795i | 0.0862608 | + | 0.149408i | ||||
\(817\) | 0.758330 | + | 2.83013i | 0.0265306 | + | 0.0990136i | ||||
\(818\) | 7.63397 | + | 7.63397i | 0.266916 | + | 0.266916i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.3923 | − | 11.1962i | 0.781973 | − | 0.390987i | ||||
\(821\) | 24.6603 | − | 42.7128i | 0.860649 | − | 1.49069i | −0.0106549 | − | 0.999943i | \(-0.503392\pi\) |
0.871304 | − | 0.490744i | \(-0.163275\pi\) | |||||||
\(822\) | 3.53590 | + | 0.947441i | 0.123329 | + | 0.0330458i | ||||
\(823\) | −53.3827 | − | 14.3038i | −1.86080 | − | 0.498601i | −0.860856 | − | 0.508849i | \(-0.830071\pi\) |
−0.999947 | + | 0.0102479i | \(0.996738\pi\) | |||||||
\(824\) | 4.59808 | − | 7.96410i | 0.160182 | − | 0.277443i | ||||
\(825\) | −7.00000 | + | 1.00000i | −0.243709 | + | 0.0348155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.2224 | − | 33.2224i | −1.15526 | − | 1.15526i | −0.985483 | − | 0.169774i | \(-0.945696\pi\) |
−0.169774 | − | 0.985483i | \(-0.554304\pi\) | |||||||
\(828\) | −0.169873 | − | 0.633975i | −0.00590349 | − | 0.0220321i | ||||
\(829\) | 7.26795 | + | 12.5885i | 0.252426 | + | 0.437215i | 0.964193 | − | 0.265200i | \(-0.0854381\pi\) |
−0.711767 | + | 0.702416i | \(0.752105\pi\) | |||||||
\(830\) | −1.89230 | + | 2.86603i | −0.0656829 | + | 0.0994812i | ||||
\(831\) | 2.41154 | + | 1.39230i | 0.0836555 | + | 0.0482985i | ||||
\(832\) | −4.53590 | + | 4.53590i | −0.157254 | + | 0.157254i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 1.51666i | − | 0.0525177i | ||||||
\(835\) | −24.6699 | − | 27.8205i | −0.853736 | − | 0.962768i | ||||
\(836\) | 3.00000 | − | 1.73205i | 0.103757 | − | 0.0599042i | ||||
\(837\) | 5.73205 | − | 21.3923i | 0.198129 | − | 0.739426i | ||||
\(838\) | −11.9282 | + | 3.19615i | −0.412053 | + | 0.110409i | ||||
\(839\) | −6.87564 | −0.237374 | −0.118687 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118687 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −8.66987 | + | 2.32309i | −0.298784 | + | 0.0800588i | ||||
\(843\) | −0.124356 | + | 0.464102i | −0.00428304 | + | 0.0159845i | ||||
\(844\) | 0.294229 | − | 0.169873i | 0.0101278 | − | 0.00584727i | ||||
\(845\) | 11.1603 | + | 0.669873i | 0.383924 | + | 0.0230443i | ||||
\(846\) | − | 12.9282i | − | 0.444481i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.3205 | − | 12.3205i | 0.423088 | − | 0.423088i | ||||
\(849\) | −0.882686 | − | 0.509619i | −0.0302937 | − | 0.0174901i | ||||
\(850\) | 9.92820 | + | 1.19615i | 0.340535 | + | 0.0410277i | ||||
\(851\) | −0.339746 | − | 0.588457i | −0.0116463 | − | 0.0201721i | ||||
\(852\) | 0.294229 | + | 1.09808i | 0.0100801 | + | 0.0376195i | ||||
\(853\) | 18.1244 | + | 18.1244i | 0.620566 | + | 0.620566i | 0.945676 | − | 0.325110i | \(-0.105401\pi\) |
−0.325110 | + | 0.945676i | \(0.605401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00000 | − | 4.00000i | −0.0683986 | − | 0.136797i | ||||
\(856\) | −12.6962 | + | 21.9904i | −0.433946 | + | 0.751616i | ||||
\(857\) | 11.0981 | + | 2.97372i | 0.379103 | + | 0.101580i | 0.443338 | − | 0.896354i | \(-0.353794\pi\) |
−0.0642351 | + | 0.997935i | \(0.520461\pi\) | |||||||
\(858\) | 2.00000 | + | 0.535898i | 0.0682789 | + | 0.0182953i | ||||
\(859\) | 17.4641 | − | 30.2487i | 0.595867 | − | 1.03207i | −0.397556 | − | 0.917578i | \(-0.630142\pi\) |
0.993424 | − | 0.114495i | \(-0.0365250\pi\) | |||||||
\(860\) | −14.7058 | − | 4.90192i | −0.501463 | − | 0.167154i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.26795 | − | 2.26795i | −0.0772467 | − | 0.0772467i | ||||
\(863\) | 13.3827 | + | 49.9449i | 0.455552 | + | 1.70014i | 0.686460 | + | 0.727167i | \(0.259164\pi\) |
−0.230908 | + | 0.972976i | \(0.574170\pi\) | |||||||
\(864\) | −7.62436 | − | 13.2058i | −0.259386 | − | 0.449269i | ||||
\(865\) | −9.24871 | − | 45.1962i | −0.314466 | − | 1.53672i | ||||
\(866\) | 11.1173 | + | 6.41858i | 0.377782 | + | 0.218112i | ||||
\(867\) | −0.758330 | + | 0.758330i | −0.0257542 | + | 0.0257542i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.92820i | 0.302869i | ||||||||
\(870\) | 0.107695 | − | 1.79423i | 0.00365121 | − | 0.0608300i | ||||
\(871\) | 27.1244 | − | 15.6603i | 0.919074 | − | 0.530627i | ||||
\(872\) | 5.06218 | − | 18.8923i | 0.171427 | − | 0.639774i | ||||
\(873\) | 22.1244 | − | 5.92820i | 0.748796 | − | 0.200639i | ||||
\(874\) | −0.0525589 | −0.00177783 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | −39.1506 | + | 10.4904i | −1.32202 | + | 0.354235i | −0.849735 | − | 0.527209i | \(-0.823238\pi\) |
−0.472288 | + | 0.881444i | \(0.656572\pi\) | |||||||
\(878\) | −0.444864 | + | 1.66025i | −0.0150134 | + | 0.0560309i | ||||
\(879\) | 1.51666 | − | 0.875644i | 0.0511557 | − | 0.0295348i | ||||
\(880\) | −0.901924 | + | 15.0263i | −0.0304038 | + | 0.506536i | ||||
\(881\) | − | 25.1436i | − | 0.847109i | −0.905871 | − | 0.423555i | \(-0.860782\pi\) | ||
0.905871 | − | 0.423555i | \(-0.139218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.07180 | − | 8.07180i | 0.271638 | − | 0.271638i | −0.558122 | − | 0.829759i | \(-0.688478\pi\) |
0.829759 | + | 0.558122i | \(0.188478\pi\) | |||||||
\(884\) | 16.3923 | + | 9.46410i | 0.551333 | + | 0.318312i | ||||
\(885\) | 1.90192 | + | 9.29423i | 0.0639325 | + | 0.312422i | ||||
\(886\) | −3.50000 | − | 6.06218i | −0.117585 | − | 0.203663i | ||||
\(887\) | −2.91858 | − | 10.8923i | −0.0979965 | − | 0.365728i | 0.899460 | − | 0.437003i | \(-0.143960\pi\) |
−0.997457 | + | 0.0712748i | \(0.977293\pi\) | |||||||
\(888\) | −3.46410 | − | 3.46410i | −0.116248 | − | 0.116248i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.725009 | + | 0.241670i | 0.0243024 | + | 0.00810079i | ||||
\(891\) | −9.09808 | + | 15.7583i | −0.304797 | + | 0.527924i | ||||
\(892\) | 42.8827 | + | 11.4904i | 1.43582 | + | 0.384726i | ||||
\(893\) | 6.46410 | + | 1.73205i | 0.216313 | + | 0.0579609i | ||||
\(894\) | 0.107695 | − | 0.186533i | 0.00360186 | − | 0.00623861i | ||||
\(895\) | 7.85641 | + | 15.7128i | 0.262611 | + | 0.525221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.143594 | + | 0.143594i | 0.00479445 | + | 0.00479445i | ||||
\(898\) | −4.42820 | − | 16.5263i | −0.147771 | − | 0.551489i | ||||
\(899\) | −11.1962 | − | 19.3923i | −0.373413 | − | 0.646770i | ||||
\(900\) | 23.4904 | + | 2.83013i | 0.783013 | + | 0.0943376i | ||||
\(901\) | −23.6603 | − | 13.6603i | −0.788237 | − | 0.455089i | ||||
\(902\) | −6.46410 | + | 6.46410i | −0.215231 | + | 0.215231i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 21.1244i | − | 0.702586i | ||||||
\(905\) | −2.66987 | − | 0.160254i | −0.0887496 | − | 0.00532702i | ||||
\(906\) | −3.21539 | + | 1.85641i | −0.106824 | + | 0.0616750i | ||||
\(907\) | −8.69615 | + | 32.4545i | −0.288751 | + | 1.07763i | 0.657304 | + | 0.753626i | \(0.271697\pi\) |
−0.946055 | + | 0.324007i | \(0.894970\pi\) | |||||||
\(908\) | −32.9545 | + | 8.83013i | −1.09363 | + | 0.293038i | ||||
\(909\) | −22.5885 | −0.749212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.51666 | −0.249038 | −0.124519 | − | 0.992217i | \(-0.539739\pi\) | ||||
−0.124519 | + | 0.992217i | \(0.539739\pi\) | |||||||
\(912\) | 0.901924 | − | 0.241670i | 0.0298657 | − | 0.00800249i | ||||
\(913\) | −2.09808 | + | 7.83013i | −0.0694362 | + | 0.259139i | ||||
\(914\) | −5.44486 | + | 3.14359i | −0.180100 | + | 0.103981i | ||||
\(915\) | −1.17949 | − | 1.33013i | −0.0389928 | − | 0.0439726i | ||||
\(916\) | 31.8564i | 1.05257i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.19615 | + | 4.19615i | −0.138494 | + | 0.138494i | ||||
\(919\) | −48.6673 | − | 28.0981i | −1.60539 | − | 0.926870i | −0.990384 | − | 0.138344i | \(-0.955822\pi\) |
−0.615002 | − | 0.788526i | \(-0.710845\pi\) | |||||||
\(920\) | 0.330127 | − | 0.500000i | 0.0108840 | − | 0.0164845i | ||||
\(921\) | 2.30385 | + | 3.99038i | 0.0759144 | + | 0.131488i | ||||
\(922\) | 0.751289 | + | 2.80385i | 0.0247424 | + | 0.0923398i | ||||
\(923\) | 2.53590 | + | 2.53590i | 0.0834701 | + | 0.0834701i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.2487 | − | 3.46410i | 0.797293 | − | 0.113899i | ||||
\(926\) | −1.74167 | + | 3.01666i | −0.0572348 | + | 0.0991336i | ||||
\(927\) | −12.5622 | − | 3.36603i | −0.412596 | − | 0.110555i | ||||
\(928\) | −14.8923 | − | 3.99038i | −0.488864 | − | 0.130991i | ||||
\(929\) | 18.1603 | − | 31.4545i | 0.595819 | − | 1.03199i | −0.397612 | − | 0.917554i | \(-0.630161\pi\) |
0.993431 | − | 0.114435i | \(-0.0365056\pi\) | |||||||
\(930\) | 4.00000 | − | 2.00000i | 0.131165 | − | 0.0655826i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.19615 | + | 8.19615i | 0.268474 | + | 0.268474i | ||||
\(933\) | −2.04552 | − | 7.63397i | −0.0669672 | − | 0.249925i | ||||
\(934\) | −3.64359 | − | 6.31089i | −0.119222 | − | 0.206499i | ||||
\(935\) | 23.1244 | − | 4.73205i | 0.756247 | − | 0.154755i | ||||
\(936\) | −12.9282 | − | 7.46410i | −0.422572 | − | 0.243972i | ||||
\(937\) | −17.0718 | + | 17.0718i | −0.557711 | + | 0.557711i | −0.928655 | − | 0.370944i | \(-0.879034\pi\) |
0.370944 | + | 0.928655i | \(0.379034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.78461i | − | 0.0908723i | ||||||
\(940\) | −26.4904 | + | 23.4904i | −0.864021 | + | 0.766172i | ||||
\(941\) | −35.1962 | + | 20.3205i | −1.14736 | + | 0.662430i | −0.948243 | − | 0.317546i | \(-0.897141\pi\) |
−0.199119 | + | 0.979975i | \(0.563808\pi\) | |||||||
\(942\) | 0.332704 | − | 1.24167i | 0.0108401 | − | 0.0404558i | ||||
\(943\) | −0.866025 | + | 0.232051i | −0.0282017 | + | 0.00755661i | ||||
\(944\) | 20.1962 | 0.657329 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.66025 | 0.184031 | ||||||||
\(947\) | −1.30385 | + | 0.349365i | −0.0423694 | + | 0.0113528i | −0.279941 | − | 0.960017i | \(-0.590315\pi\) |
0.237572 | + | 0.971370i | \(0.423648\pi\) | |||||||
\(948\) | −0.758330 | + | 2.83013i | −0.0246294 | + | 0.0919183i | ||||
\(949\) | 32.7846 | − | 18.9282i | 1.06423 | − | 0.614435i | ||||
\(950\) | 0.705771 | − | 1.75833i | 0.0228982 | − | 0.0570478i | ||||
\(951\) | − | 4.92820i | − | 0.159808i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.8564 | + | 37.8564i | −1.22629 | + | 1.22629i | −0.260932 | + | 0.965357i | \(0.584030\pi\) |
−0.965357 | + | 0.260932i | \(0.915970\pi\) | |||||||
\(954\) | 8.66025 | + | 5.00000i | 0.280386 | + | 0.161881i | ||||
\(955\) | −24.7583 | − | 16.3468i | −0.801161 | − | 0.528970i | ||||
\(956\) | −2.07180 | − | 3.58846i | −0.0670067 | − | 0.116059i | ||||
\(957\) | −1.09808 | − | 4.09808i | −0.0354958 | − | 0.132472i | ||||
\(958\) | −4.78461 | − | 4.78461i | −0.154584 | − | 0.154584i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.830127 | + | 2.49038i | −0.0267922 | + | 0.0803767i | ||||
\(961\) | 12.3564 | − | 21.4019i | 0.398594 | − | 0.690385i | ||||
\(962\) | −6.92820 | − | 1.85641i | −0.223374 | − | 0.0598529i | ||||
\(963\) | 34.6865 | + | 9.29423i | 1.11776 | + | 0.299502i | ||||
\(964\) | 21.4641 | − | 37.1769i | 0.691312 | − | 1.19739i | ||||
\(965\) | 5.73205 | − | 17.1962i | 0.184521 | − | 0.553564i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5622 | − | 13.5622i | −0.436130 | − | 0.436130i | 0.454577 | − | 0.890707i | \(-0.349790\pi\) |
−0.890707 | + | 0.454577i | \(0.849790\pi\) | |||||||
\(968\) | 1.76795 | + | 6.59808i | 0.0568240 | + | 0.212070i | ||||
\(969\) | −0.732051 | − | 1.26795i | −0.0235169 | − | 0.0407324i | ||||
\(970\) | 8.09808 | + | 5.34679i | 0.260014 | + | 0.171675i | ||||
\(971\) | −29.0718 | − | 16.7846i | −0.932958 | − | 0.538644i | −0.0452124 | − | 0.998977i | \(-0.514396\pi\) |
−0.887746 | + | 0.460334i | \(0.847730\pi\) | |||||||
\(972\) | −15.1244 | + | 15.1244i | −0.485114 | + | 0.485114i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 14.5885i | − | 0.467444i | ||||||
\(975\) | −6.73205 | + | 2.87564i | −0.215598 | + | 0.0920943i | ||||
\(976\) | −3.27757 | + | 1.89230i | −0.104912 | + | 0.0605712i | ||||
\(977\) | −0.150635 | + | 0.562178i | −0.00481924 | + | 0.0179857i | −0.968294 | − | 0.249815i | \(-0.919630\pi\) |
0.963474 | + | 0.267801i | \(0.0862969\pi\) | |||||||
\(978\) | −3.63397 | + | 0.973721i | −0.116202 | + | 0.0311362i | ||||
\(979\) | 1.80385 | 0.0576512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.6603 | −0.883124 | ||||||||
\(982\) | 18.8564 | − | 5.05256i | 0.601732 | − | 0.161234i | ||||
\(983\) | −14.5000 | + | 54.1147i | −0.462478 | + | 1.72599i | 0.202639 | + | 0.979253i | \(0.435048\pi\) |
−0.665118 | + | 0.746739i | \(0.731619\pi\) | |||||||
\(984\) | −5.59808 | + | 3.23205i | −0.178460 | + | 0.103034i | ||||
\(985\) | 23.9545 | − | 21.2417i | 0.763253 | − | 0.676816i | ||||
\(986\) | 6.00000i | 0.191079i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.53590 | − | 2.53590i | 0.0806777 | − | 0.0806777i | ||||
\(989\) | 0.480762 | + | 0.277568i | 0.0152873 | + | 0.00882615i | ||||
\(990\) | −8.46410 | + | 1.73205i | −0.269007 | + | 0.0550482i | ||||
\(991\) | −15.8564 | − | 27.4641i | −0.503695 | − | 0.872426i | −0.999991 | − | 0.00427229i | \(-0.998640\pi\) |
0.496296 | − | 0.868154i | \(-0.334693\pi\) | |||||||
\(992\) | −9.92820 | − | 37.0526i | −0.315221 | − | 1.17642i | ||||
\(993\) | −0.679492 | − | 0.679492i | −0.0215630 | − | 0.0215630i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.1436 | + | 11.0718i | −0.701999 | + | 0.351000i | ||||
\(996\) | −1.33013 | + | 2.30385i | −0.0421467 | + | 0.0730002i | ||||
\(997\) | 39.8827 | + | 10.6865i | 1.26310 | + | 0.338446i | 0.827382 | − | 0.561639i | \(-0.189829\pi\) |
0.435715 | + | 0.900085i | \(0.356496\pi\) | |||||||
\(998\) | −5.75833 | − | 1.54294i | −0.182277 | − | 0.0488409i | ||||
\(999\) | −7.26795 | + | 12.5885i | −0.229948 | + | 0.398281i |
(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 | 245.2.l.b.117.1 | 4 | ||
5.3 | odd | 4 | 245.2.l.a.68.1 | 4 | |||
7.2 | even | 3 | 245.2.f.a.97.1 | 4 | |||
7.3 | odd | 6 | 245.2.l.a.227.1 | 4 | |||
7.4 | even | 3 | 35.2.k.a.17.1 | ✓ | 4 | ||
7.5 | odd | 6 | 245.2.f.b.97.1 | 4 | |||
7.6 | odd | 2 | 35.2.k.b.12.1 | yes | 4 | ||
21.11 | odd | 6 | 315.2.bz.b.262.1 | 4 | |||
21.20 | even | 2 | 315.2.bz.a.82.1 | 4 | |||
28.11 | odd | 6 | 560.2.ci.a.17.1 | 4 | |||
28.27 | even | 2 | 560.2.ci.b.257.1 | 4 | |||
35.3 | even | 12 | inner | 245.2.l.b.178.1 | 4 | ||
35.4 | even | 6 | 175.2.o.b.157.1 | 4 | |||
35.13 | even | 4 | 35.2.k.a.33.1 | yes | 4 | ||
35.18 | odd | 12 | 35.2.k.b.3.1 | yes | 4 | ||
35.23 | odd | 12 | 245.2.f.b.48.1 | 4 | |||
35.27 | even | 4 | 175.2.o.b.68.1 | 4 | |||
35.32 | odd | 12 | 175.2.o.a.143.1 | 4 | |||
35.33 | even | 12 | 245.2.f.a.48.1 | 4 | |||
35.34 | odd | 2 | 175.2.o.a.82.1 | 4 | |||
105.53 | even | 12 | 315.2.bz.a.73.1 | 4 | |||
105.83 | odd | 4 | 315.2.bz.b.208.1 | 4 | |||
140.83 | odd | 4 | 560.2.ci.a.33.1 | 4 | |||
140.123 | even | 12 | 560.2.ci.b.353.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.k.a.17.1 | ✓ | 4 | 7.4 | even | 3 | ||
35.2.k.a.33.1 | yes | 4 | 35.13 | even | 4 | ||
35.2.k.b.3.1 | yes | 4 | 35.18 | odd | 12 | ||
35.2.k.b.12.1 | yes | 4 | 7.6 | odd | 2 | ||
175.2.o.a.82.1 | 4 | 35.34 | odd | 2 | |||
175.2.o.a.143.1 | 4 | 35.32 | odd | 12 | |||
175.2.o.b.68.1 | 4 | 35.27 | even | 4 | |||
175.2.o.b.157.1 | 4 | 35.4 | even | 6 | |||
245.2.f.a.48.1 | 4 | 35.33 | even | 12 | |||
245.2.f.a.97.1 | 4 | 7.2 | even | 3 | |||
245.2.f.b.48.1 | 4 | 35.23 | odd | 12 | |||
245.2.f.b.97.1 | 4 | 7.5 | odd | 6 | |||
245.2.l.a.68.1 | 4 | 5.3 | odd | 4 | |||
245.2.l.a.227.1 | 4 | 7.3 | odd | 6 | |||
245.2.l.b.117.1 | 4 | 1.1 | even | 1 | trivial | ||
245.2.l.b.178.1 | 4 | 35.3 | even | 12 | inner | ||
315.2.bz.a.73.1 | 4 | 105.53 | even | 12 | |||
315.2.bz.a.82.1 | 4 | 21.20 | even | 2 | |||
315.2.bz.b.208.1 | 4 | 105.83 | odd | 4 | |||
315.2.bz.b.262.1 | 4 | 21.11 | odd | 6 | |||
560.2.ci.a.17.1 | 4 | 28.11 | odd | 6 | |||
560.2.ci.a.33.1 | 4 | 140.83 | odd | 4 | |||
560.2.ci.b.257.1 | 4 | 28.27 | even | 2 | |||
560.2.ci.b.353.1 | 4 | 140.123 | even | 12 |