Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(31,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.523596960000.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.4 | ||
Root | \(1.76021 - 3.04878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.61 |
Dual form | 105.3.n.a.31.4 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76021 | − | 3.04878i | 0.880107 | − | 1.52439i | 0.0288858 | − | 0.999583i | \(-0.490804\pi\) |
0.851221 | − | 0.524807i | \(-0.175863\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | −4.19671 | − | 7.26891i | −1.04918 | − | 1.81723i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.387298 | − | 0.223607i | ||||
\(6\) | 6.09756i | 1.01626i | ||||||||
\(7\) | 0.244004 | − | 6.99575i | 0.0348577 | − | 0.999392i | ||||
\(8\) | −15.4667 | −1.93334 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | −6.81728 | + | 3.93596i | −0.681728 | + | 0.393596i | ||||
\(11\) | −1.29685 | − | 2.24621i | −0.117896 | − | 0.204201i | 0.801038 | − | 0.598614i | \(-0.204281\pi\) |
−0.918934 | + | 0.394412i | \(0.870948\pi\) | |||||||
\(12\) | 12.5901 | + | 7.26891i | 1.04918 | + | 0.605742i | ||||
\(13\) | 11.5763i | 0.890485i | 0.895410 | + | 0.445242i | \(0.146883\pi\) | ||||
−0.895410 | + | 0.445242i | \(0.853117\pi\) | |||||||
\(14\) | −20.8990 | − | 13.0579i | −1.49278 | − | 0.932709i | ||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | −10.4379 | + | 18.0789i | −0.652366 | + | 1.12993i | ||||
\(17\) | 20.0957 | − | 11.6023i | 1.18210 | − | 0.682486i | 0.225600 | − | 0.974220i | \(-0.427566\pi\) |
0.956499 | + | 0.291734i | \(0.0942323\pi\) | |||||||
\(18\) | −5.28064 | − | 9.14634i | −0.293369 | − | 0.508130i | ||||
\(19\) | 25.9538 | + | 14.9844i | 1.36599 | + | 0.788654i | 0.990413 | − | 0.138137i | \(-0.0441115\pi\) |
0.375576 | + | 0.926791i | \(0.377445\pi\) | |||||||
\(20\) | 18.7682i | 0.938412i | ||||||||
\(21\) | 5.69249 | + | 10.7049i | 0.271071 | + | 0.509759i | ||||
\(22\) | −9.13094 | −0.415043 | ||||||||
\(23\) | 17.5542 | − | 30.4048i | 0.763226 | − | 1.32195i | −0.177953 | − | 0.984039i | \(-0.556947\pi\) |
0.941179 | − | 0.337908i | \(-0.109719\pi\) | |||||||
\(24\) | 23.2000 | − | 13.3945i | 0.966668 | − | 0.558106i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | 35.2936 | + | 20.3768i | 1.35745 | + | 0.783722i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −51.8754 | + | 27.5854i | −1.85269 | + | 0.985194i | ||||
\(29\) | −24.4905 | −0.844499 | −0.422250 | − | 0.906480i | \(-0.638759\pi\) | ||||
−0.422250 | + | 0.906480i | \(0.638759\pi\) | |||||||
\(30\) | 6.81728 | − | 11.8079i | 0.227243 | − | 0.393596i | ||||
\(31\) | −32.4355 | + | 18.7266i | −1.04631 | + | 0.604085i | −0.921613 | − | 0.388110i | \(-0.873128\pi\) |
−0.124693 | + | 0.992195i | \(0.539795\pi\) | |||||||
\(32\) | 5.81233 | + | 10.0673i | 0.181635 | + | 0.314602i | ||||
\(33\) | 3.89055 | + | 2.24621i | 0.117896 | + | 0.0680670i | ||||
\(34\) | − | 81.6898i | − | 2.40264i | ||||||
\(35\) | −8.29399 | + | 13.2744i | −0.236971 | + | 0.379269i | ||||
\(36\) | −25.1802 | −0.699451 | ||||||||
\(37\) | −12.8743 | + | 22.2990i | −0.347954 | + | 0.602675i | −0.985886 | − | 0.167418i | \(-0.946457\pi\) |
0.637932 | + | 0.770093i | \(0.279790\pi\) | |||||||
\(38\) | 91.3685 | − | 52.7516i | 2.40443 | − | 1.38820i | ||||
\(39\) | −10.0254 | − | 17.3645i | −0.257061 | − | 0.445242i | ||||
\(40\) | 29.9511 | + | 17.2923i | 0.748778 | + | 0.432307i | ||||
\(41\) | 3.71113i | 0.0905155i | 0.998975 | + | 0.0452577i | \(0.0144109\pi\) | ||||
−0.998975 | + | 0.0452577i | \(0.985589\pi\) | |||||||
\(42\) | 42.6570 | + | 1.48783i | 1.01564 | + | 0.0354245i | ||||
\(43\) | 74.2225 | 1.72611 | 0.863053 | − | 0.505114i | \(-0.168549\pi\) | ||||
0.863053 | + | 0.505114i | \(0.168549\pi\) | |||||||
\(44\) | −10.8850 | + | 18.8534i | −0.247386 | + | 0.428486i | ||||
\(45\) | −5.80948 | + | 3.35410i | −0.129099 | + | 0.0745356i | ||||
\(46\) | −61.7983 | − | 107.038i | −1.34344 | − | 2.32691i | ||||
\(47\) | 2.92646 | + | 1.68959i | 0.0622652 | + | 0.0359488i | 0.530809 | − | 0.847491i | \(-0.321888\pi\) |
−0.468544 | + | 0.883440i | \(0.655221\pi\) | |||||||
\(48\) | − | 36.1578i | − | 0.753287i | ||||||
\(49\) | −48.8809 | − | 3.41398i | −0.997570 | − | 0.0696731i | ||||
\(50\) | 17.6021 | 0.352043 | ||||||||
\(51\) | −20.0957 | + | 34.8068i | −0.394033 | + | 0.682486i | ||||
\(52\) | 84.1471 | − | 48.5823i | 1.61821 | − | 0.934276i | ||||
\(53\) | 20.0193 | + | 34.6744i | 0.377722 | + | 0.654234i | 0.990730 | − | 0.135843i | \(-0.0433741\pi\) |
−0.613008 | + | 0.790076i | \(0.710041\pi\) | |||||||
\(54\) | 15.8419 | + | 9.14634i | 0.293369 | + | 0.169377i | ||||
\(55\) | 5.79969i | 0.105449i | ||||||||
\(56\) | −3.77394 | + | 108.201i | −0.0673917 | + | 1.93216i | ||||
\(57\) | −51.9076 | −0.910660 | ||||||||
\(58\) | −43.1085 | + | 74.6661i | −0.743250 | + | 1.28735i | ||||
\(59\) | −42.7180 | + | 24.6632i | −0.724033 | + | 0.418021i | −0.816235 | − | 0.577720i | \(-0.803943\pi\) |
0.0922022 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(60\) | −16.2538 | − | 28.1524i | −0.270896 | − | 0.469206i | ||||
\(61\) | −0.765094 | − | 0.441727i | −0.0125425 | − | 0.00724143i | 0.493716 | − | 0.869623i | \(-0.335638\pi\) |
−0.506258 | + | 0.862382i | \(0.668972\pi\) | |||||||
\(62\) | 131.852i | 2.12664i | ||||||||
\(63\) | −17.8095 | − | 11.1276i | −0.282690 | − | 0.176628i | ||||
\(64\) | −42.5790 | −0.665297 | ||||||||
\(65\) | 12.9427 | − | 22.4174i | 0.199118 | − | 0.344883i | ||||
\(66\) | 13.6964 | − | 7.90763i | 0.207521 | − | 0.119813i | ||||
\(67\) | 32.5272 | + | 56.3388i | 0.485481 | + | 0.840877i | 0.999861 | − | 0.0166850i | \(-0.00531125\pi\) |
−0.514380 | + | 0.857562i | \(0.671978\pi\) | |||||||
\(68\) | −168.671 | − | 97.3825i | −2.48046 | − | 1.43210i | ||||
\(69\) | 60.8096i | 0.881298i | ||||||||
\(70\) | 25.8715 | + | 48.6523i | 0.369593 | + | 0.695033i | ||||
\(71\) | 86.0786 | 1.21237 | 0.606187 | − | 0.795322i | \(-0.292698\pi\) | ||||
0.606187 | + | 0.795322i | \(0.292698\pi\) | |||||||
\(72\) | −23.2000 | + | 40.1836i | −0.322223 | + | 0.558106i | ||||
\(73\) | −53.3274 | + | 30.7886i | −0.730512 | + | 0.421761i | −0.818609 | − | 0.574350i | \(-0.805255\pi\) |
0.0880974 | + | 0.996112i | \(0.471921\pi\) | |||||||
\(74\) | 45.3231 | + | 78.5019i | 0.612474 | + | 1.06084i | ||||
\(75\) | −7.50000 | − | 4.33013i | −0.100000 | − | 0.0577350i | ||||
\(76\) | − | 251.541i | − | 3.30975i | ||||||
\(77\) | −16.0304 | + | 8.52436i | −0.208187 | + | 0.110706i | ||||
\(78\) | −70.5872 | −0.904964 | ||||||||
\(79\) | −13.7718 | + | 23.8534i | −0.174326 | + | 0.301942i | −0.939928 | − | 0.341373i | \(-0.889108\pi\) |
0.765602 | + | 0.643315i | \(0.222441\pi\) | |||||||
\(80\) | 40.4256 | − | 23.3397i | 0.505320 | − | 0.291747i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 11.3144 | + | 6.53239i | 0.137981 | + | 0.0796633i | ||||
\(83\) | − | 131.445i | − | 1.58367i | −0.610732 | − | 0.791837i | \(-0.709125\pi\) | ||
0.610732 | − | 0.791837i | \(-0.290875\pi\) | |||||||
\(84\) | 53.9235 | − | 86.3036i | 0.641946 | − | 1.02742i | ||||
\(85\) | −51.8869 | −0.610434 | ||||||||
\(86\) | 130.648 | − | 226.288i | 1.51916 | − | 2.63126i | ||||
\(87\) | 36.7357 | − | 21.2094i | 0.422250 | − | 0.243786i | ||||
\(88\) | 20.0580 | + | 34.7415i | 0.227932 | + | 0.394789i | ||||
\(89\) | −56.5108 | − | 32.6265i | −0.634953 | − | 0.366590i | 0.147715 | − | 0.989030i | \(-0.452808\pi\) |
−0.782668 | + | 0.622440i | \(0.786142\pi\) | |||||||
\(90\) | 23.6157i | 0.262397i | ||||||||
\(91\) | 80.9849 | + | 2.82467i | 0.889944 | + | 0.0310403i | ||||
\(92\) | −294.679 | −3.20304 | ||||||||
\(93\) | 32.4355 | − | 56.1799i | 0.348769 | − | 0.604085i | ||||
\(94\) | 10.3024 | − | 5.94809i | 0.109600 | − | 0.0632776i | ||||
\(95\) | −33.5062 | − | 58.0345i | −0.352697 | − | 0.610889i | ||||
\(96\) | −17.4370 | − | 10.0673i | −0.181635 | − | 0.104867i | ||||
\(97\) | 42.2375i | 0.435438i | 0.976011 | + | 0.217719i | \(0.0698616\pi\) | ||||
−0.976011 | + | 0.217719i | \(0.930138\pi\) | |||||||
\(98\) | −96.4494 | + | 143.018i | −0.984177 | + | 1.45937i | ||||
\(99\) | −7.78111 | −0.0785970 | ||||||||
\(100\) | 20.9835 | − | 36.3445i | 0.209835 | − | 0.363445i | ||||
\(101\) | −129.874 | + | 74.9830i | −1.28589 | + | 0.742406i | −0.977918 | − | 0.208991i | \(-0.932982\pi\) |
−0.307968 | + | 0.951397i | \(0.599649\pi\) | |||||||
\(102\) | 70.7454 | + | 122.535i | 0.693583 | + | 1.20132i | ||||
\(103\) | 120.964 | + | 69.8388i | 1.17441 | + | 0.678047i | 0.954715 | − | 0.297521i | \(-0.0961599\pi\) |
0.219697 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(104\) | − | 179.047i | − | 1.72161i | ||||||
\(105\) | 0.945024 | − | 27.0944i | 0.00900023 | − | 0.258042i | ||||
\(106\) | 140.953 | 1.32974 | ||||||||
\(107\) | 90.6198 | − | 156.958i | 0.846914 | − | 1.46690i | −0.0370350 | − | 0.999314i | \(-0.511791\pi\) |
0.883949 | − | 0.467584i | \(-0.154875\pi\) | |||||||
\(108\) | 37.7703 | − | 21.8067i | 0.349725 | − | 0.201914i | ||||
\(109\) | 36.9049 | + | 63.9212i | 0.338577 | + | 0.586433i | 0.984165 | − | 0.177253i | \(-0.0567211\pi\) |
−0.645588 | + | 0.763686i | \(0.723388\pi\) | |||||||
\(110\) | 17.6820 | + | 10.2087i | 0.160745 | + | 0.0928064i | ||||
\(111\) | − | 44.5979i | − | 0.401783i | ||||||
\(112\) | 123.928 | + | 77.4319i | 1.10650 | + | 0.691356i | ||||
\(113\) | 7.38562 | 0.0653595 | 0.0326797 | − | 0.999466i | \(-0.489596\pi\) | ||||
0.0326797 | + | 0.999466i | \(0.489596\pi\) | |||||||
\(114\) | −91.3685 | + | 158.255i | −0.801478 | + | 1.38820i | ||||
\(115\) | −67.9872 | + | 39.2524i | −0.591193 | + | 0.341325i | ||||
\(116\) | 102.779 | + | 178.019i | 0.886029 | + | 1.53465i | ||||
\(117\) | 30.0761 | + | 17.3645i | 0.257061 | + | 0.148414i | ||||
\(118\) | 173.650i | 1.47161i | ||||||||
\(119\) | −76.2630 | − | 143.415i | −0.640866 | − | 1.20517i | ||||
\(120\) | −59.9022 | −0.499185 | ||||||||
\(121\) | 57.1364 | − | 98.9631i | 0.472201 | − | 0.817877i | ||||
\(122\) | −2.69346 | + | 1.55507i | −0.0220775 | + | 0.0127465i | ||||
\(123\) | −3.21394 | − | 5.56670i | −0.0261296 | − | 0.0452577i | ||||
\(124\) | 272.244 | + | 157.180i | 2.19552 | + | 1.26758i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −65.2740 | + | 34.7103i | −0.518047 | + | 0.275478i | ||||
\(127\) | −208.640 | −1.64283 | −0.821416 | − | 0.570329i | \(-0.806816\pi\) | ||||
−0.821416 | + | 0.570329i | \(0.806816\pi\) | |||||||
\(128\) | −98.1975 | + | 170.083i | −0.767168 | + | 1.32877i | ||||
\(129\) | −111.334 | + | 64.2786i | −0.863053 | + | 0.498284i | ||||
\(130\) | −45.5638 | − | 78.9189i | −0.350491 | − | 0.607068i | ||||
\(131\) | 94.8997 | + | 54.7904i | 0.724425 | + | 0.418247i | 0.816379 | − | 0.577516i | \(-0.195978\pi\) |
−0.0919540 | + | 0.995763i | \(0.529311\pi\) | |||||||
\(132\) | − | 37.7068i | − | 0.285657i | ||||||
\(133\) | 111.160 | − | 177.910i | 0.835790 | − | 1.33767i | ||||
\(134\) | 229.019 | 1.70910 | ||||||||
\(135\) | 5.80948 | − | 10.0623i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | −310.814 | + | 179.448i | −2.28540 | + | 1.31947i | ||||
\(137\) | 88.7262 | + | 153.678i | 0.647637 | + | 1.12174i | 0.983686 | + | 0.179895i | \(0.0575758\pi\) |
−0.336049 | + | 0.941844i | \(0.609091\pi\) | |||||||
\(138\) | 185.395 | + | 107.038i | 1.34344 | + | 0.775636i | ||||
\(139\) | − | 169.894i | − | 1.22226i | −0.791532 | − | 0.611128i | \(-0.790716\pi\) | ||
0.791532 | − | 0.611128i | \(-0.209284\pi\) | |||||||
\(140\) | 131.298 | + | 4.57953i | 0.937842 | + | 0.0327109i | ||||
\(141\) | −5.85293 | −0.0415101 | ||||||||
\(142\) | 151.517 | − | 262.435i | 1.06702 | − | 1.84813i | ||||
\(143\) | 26.0028 | − | 15.0127i | 0.181838 | − | 0.104984i | ||||
\(144\) | 31.3136 | + | 54.2367i | 0.217455 | + | 0.376644i | ||||
\(145\) | 47.4256 | + | 27.3812i | 0.327073 | + | 0.188836i | ||||
\(146\) | 216.778i | 1.48478i | ||||||||
\(147\) | 76.2780 | − | 37.2111i | 0.518898 | − | 0.253137i | ||||
\(148\) | 216.119 | 1.46026 | ||||||||
\(149\) | −42.6928 | + | 73.9461i | −0.286529 | + | 0.496283i | −0.972979 | − | 0.230894i | \(-0.925835\pi\) |
0.686450 | + | 0.727177i | \(0.259168\pi\) | |||||||
\(150\) | −26.4032 | + | 15.2439i | −0.176021 | + | 0.101626i | ||||
\(151\) | 68.9977 | + | 119.507i | 0.456938 | + | 0.791440i | 0.998797 | − | 0.0490293i | \(-0.0156128\pi\) |
−0.541859 | + | 0.840469i | \(0.682279\pi\) | |||||||
\(152\) | −401.419 | − | 231.760i | −2.64092 | − | 1.52473i | ||||
\(153\) | − | 69.6135i | − | 0.454990i | ||||||
\(154\) | −2.22799 | + | 63.8777i | −0.0144675 | + | 0.414791i | ||||
\(155\) | 83.7481 | 0.540310 | ||||||||
\(156\) | −84.1471 | + | 145.747i | −0.539404 | + | 0.934276i | ||||
\(157\) | 5.94674 | − | 3.43335i | 0.0378773 | − | 0.0218685i | −0.480942 | − | 0.876753i | \(-0.659705\pi\) |
0.518819 | + | 0.854884i | \(0.326372\pi\) | |||||||
\(158\) | 48.4825 | + | 83.9742i | 0.306851 | + | 0.531482i | ||||
\(159\) | −60.0578 | − | 34.6744i | −0.377722 | − | 0.218078i | ||||
\(160\) | − | 25.9935i | − | 0.162460i | ||||||
\(161\) | −208.421 | − | 130.224i | −1.29454 | − | 0.808843i | ||||
\(162\) | −31.6838 | −0.195579 | ||||||||
\(163\) | 138.363 | − | 239.652i | 0.848854 | − | 1.47026i | −0.0333772 | − | 0.999443i | \(-0.510626\pi\) |
0.882231 | − | 0.470816i | \(-0.156040\pi\) | |||||||
\(164\) | 26.9759 | − | 15.5745i | 0.164487 | − | 0.0949667i | ||||
\(165\) | −5.02268 | − | 8.69954i | −0.0304405 | − | 0.0527245i | ||||
\(166\) | −400.747 | − | 231.371i | −2.41414 | − | 1.39380i | ||||
\(167\) | − | 42.3799i | − | 0.253772i | −0.991917 | − | 0.126886i | \(-0.959502\pi\) | ||
0.991917 | − | 0.126886i | \(-0.0404982\pi\) | |||||||
\(168\) | −88.0439 | − | 165.570i | −0.524071 | − | 0.985535i | ||||
\(169\) | 34.9892 | 0.207036 | ||||||||
\(170\) | −91.3320 | + | 158.192i | −0.537247 | + | 0.930539i | ||||
\(171\) | 77.8614 | − | 44.9533i | 0.455330 | − | 0.262885i | ||||
\(172\) | −311.490 | − | 539.517i | −1.81099 | − | 3.13673i | ||||
\(173\) | 25.5999 | + | 14.7801i | 0.147976 | + | 0.0854342i | 0.572160 | − | 0.820142i | \(-0.306106\pi\) |
−0.424184 | + | 0.905576i | \(0.639439\pi\) | |||||||
\(174\) | − | 149.332i | − | 0.858231i | ||||||
\(175\) | 30.9025 | − | 16.4328i | 0.176586 | − | 0.0939017i | ||||
\(176\) | 54.1454 | 0.307644 | ||||||||
\(177\) | 42.7180 | − | 73.9897i | 0.241344 | − | 0.418021i | ||||
\(178\) | −198.942 | + | 114.859i | −1.11765 | + | 0.645277i | ||||
\(179\) | 74.3408 | + | 128.762i | 0.415312 | + | 0.719341i | 0.995461 | − | 0.0951690i | \(-0.0303392\pi\) |
−0.580149 | + | 0.814510i | \(0.697006\pi\) | |||||||
\(180\) | 48.7613 | + | 28.1524i | 0.270896 | + | 0.156402i | ||||
\(181\) | 257.302i | 1.42156i | 0.703414 | + | 0.710780i | \(0.251658\pi\) | ||||
−0.703414 | + | 0.710780i | \(0.748342\pi\) | |||||||
\(182\) | 151.163 | − | 241.933i | 0.830563 | − | 1.32930i | ||||
\(183\) | 1.53019 | 0.00836168 | ||||||||
\(184\) | −271.505 | + | 470.261i | −1.47557 | + | 2.55577i | ||||
\(185\) | 49.8620 | − | 28.7878i | 0.269524 | − | 0.155610i | ||||
\(186\) | −114.187 | − | 197.777i | −0.613908 | − | 1.06332i | ||||
\(187\) | −52.1223 | − | 30.0928i | −0.278729 | − | 0.160924i | ||||
\(188\) | − | 28.3629i | − | 0.150867i | ||||||
\(189\) | 36.3510 | + | 1.26788i | 0.192333 | + | 0.00670837i | ||||
\(190\) | −235.912 | −1.24164 | ||||||||
\(191\) | −60.8021 | + | 105.312i | −0.318336 | + | 0.551373i | −0.980141 | − | 0.198302i | \(-0.936457\pi\) |
0.661805 | + | 0.749676i | \(0.269791\pi\) | |||||||
\(192\) | 63.8685 | − | 36.8745i | 0.332649 | − | 0.192055i | ||||
\(193\) | −121.266 | − | 210.039i | −0.628323 | − | 1.08829i | −0.987888 | − | 0.155167i | \(-0.950408\pi\) |
0.359566 | − | 0.933120i | \(-0.382925\pi\) | |||||||
\(194\) | 128.773 | + | 74.3470i | 0.663777 | + | 0.383232i | ||||
\(195\) | 44.8348i | 0.229922i | ||||||||
\(196\) | 180.323 | + | 369.638i | 0.920015 | + | 1.88591i | ||||
\(197\) | −98.9929 | −0.502502 | −0.251251 | − | 0.967922i | \(-0.580842\pi\) | ||||
−0.251251 | + | 0.967922i | \(0.580842\pi\) | |||||||
\(198\) | −13.6964 | + | 23.7229i | −0.0691738 | + | 0.119813i | ||||
\(199\) | 68.2115 | − | 39.3819i | 0.342772 | − | 0.197899i | −0.318725 | − | 0.947847i | \(-0.603255\pi\) |
0.661497 | + | 0.749948i | \(0.269921\pi\) | |||||||
\(200\) | −38.6667 | − | 66.9727i | −0.193334 | − | 0.334864i | ||||
\(201\) | −97.5816 | − | 56.3388i | −0.485481 | − | 0.280292i | ||||
\(202\) | 527.945i | 2.61359i | ||||||||
\(203\) | −5.97578 | + | 171.329i | −0.0294373 | + | 0.843986i | ||||
\(204\) | 337.343 | 1.65364 | ||||||||
\(205\) | 4.14917 | − | 7.18658i | 0.0202399 | − | 0.0350565i | ||||
\(206\) | 425.846 | − | 245.863i | 2.06722 | − | 1.19351i | ||||
\(207\) | −52.6626 | − | 91.2143i | −0.254409 | − | 0.440649i | ||||
\(208\) | −209.287 | − | 120.832i | −1.00619 | − | 0.580922i | ||||
\(209\) | − | 77.7303i | − | 0.371915i | ||||||
\(210\) | −80.9414 | − | 50.5731i | −0.385435 | − | 0.240824i | ||||
\(211\) | −107.144 | −0.507790 | −0.253895 | − | 0.967232i | \(-0.581712\pi\) | ||||
−0.253895 | + | 0.967232i | \(0.581712\pi\) | |||||||
\(212\) | 168.030 | − | 291.036i | 0.792594 | − | 1.37281i | ||||
\(213\) | −129.118 | + | 74.5462i | −0.606187 | + | 0.349982i | ||||
\(214\) | −319.020 | − | 552.559i | −1.49075 | − | 2.58205i | ||||
\(215\) | −143.731 | − | 82.9833i | −0.668518 | − | 0.385969i | ||||
\(216\) | − | 80.3673i | − | 0.372071i | ||||||
\(217\) | 123.092 | + | 231.480i | 0.567246 | + | 1.06673i | ||||
\(218\) | 259.842 | 1.19194 | ||||||||
\(219\) | 53.3274 | − | 92.3657i | 0.243504 | − | 0.421761i | ||||
\(220\) | 42.1574 | − | 24.3396i | 0.191625 | − | 0.110635i | ||||
\(221\) | 134.311 | + | 232.634i | 0.607743 | + | 1.05264i | ||||
\(222\) | −135.969 | − | 78.5019i | −0.612474 | − | 0.353612i | ||||
\(223\) | − | 8.72021i | − | 0.0391041i | −0.999809 | − | 0.0195520i | \(-0.993776\pi\) | ||
0.999809 | − | 0.0195520i | \(-0.00622400\pi\) | |||||||
\(224\) | 71.8462 | − | 38.2051i | 0.320742 | − | 0.170559i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 13.0003 | − | 22.5171i | 0.0575233 | − | 0.0996333i | ||||
\(227\) | −219.123 | + | 126.511i | −0.965299 | + | 0.557316i | −0.897800 | − | 0.440404i | \(-0.854835\pi\) |
−0.0674992 | + | 0.997719i | \(0.521502\pi\) | |||||||
\(228\) | 217.841 | + | 377.312i | 0.955443 | + | 1.65488i | ||||
\(229\) | 125.988 | + | 72.7394i | 0.550167 | + | 0.317639i | 0.749189 | − | 0.662356i | \(-0.230443\pi\) |
−0.199022 | + | 0.979995i | \(0.563777\pi\) | |||||||
\(230\) | 276.370i | 1.20161i | ||||||||
\(231\) | 16.6632 | − | 26.6692i | 0.0721352 | − | 0.115451i | ||||
\(232\) | 378.787 | 1.63270 | ||||||||
\(233\) | −128.758 | + | 223.015i | −0.552609 | + | 0.957146i | 0.445477 | + | 0.895294i | \(0.353034\pi\) |
−0.998085 | + | 0.0618526i | \(0.980299\pi\) | |||||||
\(234\) | 105.881 | − | 61.1303i | 0.452482 | − | 0.261241i | ||||
\(235\) | −3.77805 | − | 6.54377i | −0.0160768 | − | 0.0278458i | ||||
\(236\) | 358.549 | + | 207.009i | 1.51928 | + | 0.877155i | ||||
\(237\) | − | 47.7068i | − | 0.201295i | ||||||
\(238\) | −571.481 | − | 19.9326i | −2.40118 | − | 0.0837506i | ||||
\(239\) | −128.682 | −0.538418 | −0.269209 | − | 0.963082i | \(-0.586762\pi\) | ||||
−0.269209 | + | 0.963082i | \(0.586762\pi\) | |||||||
\(240\) | −40.4256 | + | 70.0192i | −0.168440 | + | 0.291747i | ||||
\(241\) | −8.02227 | + | 4.63166i | −0.0332874 | + | 0.0192185i | −0.516551 | − | 0.856256i | \(-0.672784\pi\) |
0.483264 | + | 0.875475i | \(0.339451\pi\) | |||||||
\(242\) | −201.144 | − | 348.392i | −0.831175 | − | 1.43964i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 7.41519i | 0.0303901i | ||||||||
\(245\) | 90.8406 | + | 61.2617i | 0.370778 | + | 0.250048i | ||||
\(246\) | −22.6289 | −0.0919872 | ||||||||
\(247\) | −173.464 | + | 300.449i | −0.702285 | + | 1.21639i | ||||
\(248\) | 501.670 | − | 289.639i | 2.02286 | − | 1.16790i | ||||
\(249\) | 113.835 | + | 197.167i | 0.457167 | + | 0.791837i | ||||
\(250\) | −34.0864 | − | 19.6798i | −0.136346 | − | 0.0787192i | ||||
\(251\) | − | 29.9212i | − | 0.119208i | −0.998222 | − | 0.0596040i | \(-0.981016\pi\) | ||
0.998222 | − | 0.0596040i | \(-0.0189838\pi\) | |||||||
\(252\) | −6.14408 | + | 176.155i | −0.0243813 | + | 0.699026i | ||||
\(253\) | −91.0608 | −0.359924 | ||||||||
\(254\) | −367.251 | + | 636.097i | −1.44587 | + | 2.50432i | ||||
\(255\) | 77.8303 | − | 44.9353i | 0.305217 | − | 0.176217i | ||||
\(256\) | 260.539 | + | 451.267i | 1.01773 | + | 1.76276i | ||||
\(257\) | 83.7338 | + | 48.3438i | 0.325813 | + | 0.188108i | 0.653980 | − | 0.756511i | \(-0.273098\pi\) |
−0.328168 | + | 0.944619i | \(0.606431\pi\) | |||||||
\(258\) | 452.576i | 1.75417i | ||||||||
\(259\) | 152.857 | + | 95.5065i | 0.590180 | + | 0.368751i | ||||
\(260\) | −217.267 | −0.835642 | ||||||||
\(261\) | −36.7357 | + | 63.6281i | −0.140750 | + | 0.243786i | ||||
\(262\) | 334.088 | − | 192.886i | 1.27514 | − | 0.736204i | ||||
\(263\) | −32.1231 | − | 55.6388i | −0.122141 | − | 0.211554i | 0.798471 | − | 0.602034i | \(-0.205643\pi\) |
−0.920612 | + | 0.390479i | \(0.872309\pi\) | |||||||
\(264\) | −60.1740 | − | 34.7415i | −0.227932 | − | 0.131596i | ||||
\(265\) | − | 89.5289i | − | 0.337845i | ||||||
\(266\) | −346.743 | − | 652.062i | −1.30354 | − | 2.45136i | ||||
\(267\) | 113.022 | 0.423302 | ||||||||
\(268\) | 273.014 | − | 472.875i | 1.01871 | − | 1.76446i | ||||
\(269\) | −171.096 | + | 98.7823i | −0.636044 | + | 0.367220i | −0.783089 | − | 0.621910i | \(-0.786357\pi\) |
0.147045 | + | 0.989130i | \(0.453024\pi\) | |||||||
\(270\) | −20.4518 | − | 35.4236i | −0.0757475 | − | 0.131199i | ||||
\(271\) | −133.483 | − | 77.0667i | −0.492559 | − | 0.284379i | 0.233077 | − | 0.972458i | \(-0.425121\pi\) |
−0.725635 | + | 0.688080i | \(0.758454\pi\) | |||||||
\(272\) | 484.410i | 1.78092i | ||||||||
\(273\) | −123.924 | + | 65.8980i | −0.453932 | + | 0.241385i | ||||
\(274\) | 624.708 | 2.27996 | ||||||||
\(275\) | 6.48426 | − | 11.2311i | 0.0235791 | − | 0.0408402i | ||||
\(276\) | 442.019 | − | 255.200i | 1.60152 | − | 0.924637i | ||||
\(277\) | −169.602 | − | 293.758i | −0.612280 | − | 1.06050i | −0.990855 | − | 0.134929i | \(-0.956919\pi\) |
0.378575 | − | 0.925570i | \(-0.376414\pi\) | |||||||
\(278\) | −517.968 | − | 299.049i | −1.86320 | − | 1.07572i | ||||
\(279\) | 112.360i | 0.402724i | ||||||||
\(280\) | 128.281 | − | 205.311i | 0.458145 | − | 0.733253i | ||||
\(281\) | −111.976 | −0.398492 | −0.199246 | − | 0.979949i | \(-0.563849\pi\) | ||||
−0.199246 | + | 0.979949i | \(0.563849\pi\) | |||||||
\(282\) | −10.3024 | + | 17.8443i | −0.0365333 | + | 0.0632776i | ||||
\(283\) | −56.6453 | + | 32.7042i | −0.200160 | + | 0.115563i | −0.596730 | − | 0.802442i | \(-0.703534\pi\) |
0.396570 | + | 0.918004i | \(0.370200\pi\) | |||||||
\(284\) | −361.246 | − | 625.697i | −1.27199 | − | 2.20316i | ||||
\(285\) | 100.519 | + | 58.0345i | 0.352697 | + | 0.203630i | ||||
\(286\) | − | 105.703i | − | 0.369589i | ||||||
\(287\) | 25.9622 | + | 0.905532i | 0.0904605 | + | 0.00315516i | ||||
\(288\) | 34.8740 | 0.121090 | ||||||||
\(289\) | 124.725 | − | 216.029i | 0.431573 | − | 0.747507i | ||||
\(290\) | 166.958 | − | 96.3935i | 0.575719 | − | 0.332391i | ||||
\(291\) | −36.5787 | − | 63.3562i | −0.125700 | − | 0.217719i | ||||
\(292\) | 447.599 | + | 258.421i | 1.53287 | + | 0.885004i | ||||
\(293\) | − | 100.992i | − | 0.344681i | −0.985037 | − | 0.172341i | \(-0.944867\pi\) | ||
0.985037 | − | 0.172341i | \(-0.0551330\pi\) | |||||||
\(294\) | 20.8170 | − | 298.054i | 0.0708060 | − | 1.01379i | ||||
\(295\) | 110.297 | 0.373889 | ||||||||
\(296\) | 199.123 | − | 344.891i | 0.672713 | − | 1.16517i | ||||
\(297\) | 11.6717 | − | 6.73864i | 0.0392985 | − | 0.0226890i | ||||
\(298\) | 150.297 | + | 260.322i | 0.504352 | + | 0.873564i | ||||
\(299\) | 351.975 | + | 203.213i | 1.17717 | + | 0.679642i | ||||
\(300\) | 72.6891i | 0.242297i | ||||||||
\(301\) | 18.1106 | − | 519.242i | 0.0601681 | − | 1.72506i | ||||
\(302\) | 485.802 | 1.60862 | ||||||||
\(303\) | 129.874 | − | 224.949i | 0.428628 | − | 0.742406i | ||||
\(304\) | −541.804 | + | 312.811i | −1.78225 | + | 1.02898i | ||||
\(305\) | 0.987732 | + | 1.71080i | 0.00323846 | + | 0.00560918i | ||||
\(306\) | −212.236 | − | 122.535i | −0.693583 | − | 0.400440i | ||||
\(307\) | 400.388i | 1.30420i | 0.758135 | + | 0.652098i | \(0.226111\pi\) | ||||
−0.758135 | + | 0.652098i | \(0.773889\pi\) | |||||||
\(308\) | 129.237 | + | 80.7490i | 0.419602 | + | 0.262172i | ||||
\(309\) | −241.929 | −0.782941 | ||||||||
\(310\) | 147.415 | − | 255.330i | 0.475531 | − | 0.823644i | ||||
\(311\) | −31.1758 | + | 17.9993i | −0.100244 | + | 0.0578757i | −0.549284 | − | 0.835636i | \(-0.685099\pi\) |
0.449040 | + | 0.893512i | \(0.351766\pi\) | |||||||
\(312\) | 155.059 | + | 268.571i | 0.496985 | + | 0.860803i | ||||
\(313\) | −99.1558 | − | 57.2476i | −0.316792 | − | 0.182900i | 0.333170 | − | 0.942867i | \(-0.391882\pi\) |
−0.649962 | + | 0.759967i | \(0.725215\pi\) | |||||||
\(314\) | − | 24.1737i | − | 0.0769864i | ||||||
\(315\) | 22.0469 | + | 41.4600i | 0.0699902 | + | 0.131619i | ||||
\(316\) | 231.184 | 0.731596 | ||||||||
\(317\) | −2.01608 | + | 3.49195i | −0.00635987 | + | 0.0110156i | −0.869188 | − | 0.494482i | \(-0.835358\pi\) |
0.862828 | + | 0.505498i | \(0.168691\pi\) | |||||||
\(318\) | −211.429 | + | 122.069i | −0.664872 | + | 0.383864i | ||||
\(319\) | 31.7605 | + | 55.0108i | 0.0995627 | + | 0.172448i | ||||
\(320\) | 82.4539 | + | 47.6048i | 0.257669 | + | 0.148765i | ||||
\(321\) | 313.916i | 0.977932i | ||||||||
\(322\) | −763.888 | + | 406.208i | −2.37232 | + | 1.26151i | ||||
\(323\) | 695.413 | 2.15298 | ||||||||
\(324\) | −37.7703 | + | 65.4202i | −0.116575 | + | 0.201914i | ||||
\(325\) | −50.1269 | + | 28.9408i | −0.154237 | + | 0.0890485i | ||||
\(326\) | −487.098 | − | 843.678i | −1.49417 | − | 2.58797i | ||||
\(327\) | −110.715 | − | 63.9212i | −0.338577 | − | 0.195478i | ||||
\(328\) | − | 57.3989i | − | 0.174997i | ||||||
\(329\) | 12.5340 | − | 20.0605i | 0.0380974 | − | 0.0609742i | ||||
\(330\) | −35.3640 | −0.107164 | ||||||||
\(331\) | −253.691 | + | 439.406i | −0.766439 | + | 1.32751i | 0.173043 | + | 0.984914i | \(0.444640\pi\) |
−0.939482 | + | 0.342598i | \(0.888693\pi\) | |||||||
\(332\) | −955.461 | + | 551.636i | −2.87790 | + | 1.66155i | ||||
\(333\) | 38.6229 | + | 66.8969i | 0.115985 | + | 0.200892i | ||||
\(334\) | −129.207 | − | 74.5976i | −0.386847 | − | 0.223346i | ||||
\(335\) | − | 145.466i | − | 0.434227i | ||||||
\(336\) | −252.951 | − | 8.82265i | −0.752829 | − | 0.0262579i | ||||
\(337\) | −264.279 | −0.784210 | −0.392105 | − | 0.919921i | \(-0.628253\pi\) | ||||
−0.392105 | + | 0.919921i | \(0.628253\pi\) | |||||||
\(338\) | 61.5884 | − | 106.674i | 0.182214 | − | 0.315604i | ||||
\(339\) | −11.0784 | + | 6.39614i | −0.0326797 | + | 0.0188677i | ||||
\(340\) | 217.754 | + | 377.161i | 0.640453 | + | 1.10930i | ||||
\(341\) | 84.1280 | + | 48.5713i | 0.246710 | + | 0.142438i | ||||
\(342\) | − | 316.510i | − | 0.925467i | ||||||
\(343\) | −35.8105 | + | 341.126i | −0.104404 | + | 0.994535i | ||||
\(344\) | −1147.98 | −3.33714 | ||||||||
\(345\) | 67.9872 | − | 117.757i | 0.197064 | − | 0.341325i | ||||
\(346\) | 90.1226 | − | 52.0323i | 0.260470 | − | 0.150382i | ||||
\(347\) | 117.234 | + | 203.055i | 0.337849 | + | 0.585172i | 0.984028 | − | 0.178014i | \(-0.0569673\pi\) |
−0.646179 | + | 0.763186i | \(0.723634\pi\) | |||||||
\(348\) | −308.338 | − | 178.019i | −0.886029 | − | 0.511549i | ||||
\(349\) | 54.2133i | 0.155339i | 0.996979 | + | 0.0776695i | \(0.0247479\pi\) | ||||
−0.996979 | + | 0.0776695i | \(0.975252\pi\) | |||||||
\(350\) | 4.29499 | − | 123.140i | 0.0122714 | − | 0.351829i | ||||
\(351\) | −60.1522 | −0.171374 | ||||||||
\(352\) | 15.0755 | − | 26.1115i | 0.0428280 | − | 0.0741803i | ||||
\(353\) | −451.914 | + | 260.913i | −1.28021 | + | 0.739129i | −0.976886 | − | 0.213759i | \(-0.931429\pi\) |
−0.303322 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(354\) | −150.385 | − | 260.475i | −0.424818 | − | 0.735806i | ||||
\(355\) | −166.690 | − | 96.2388i | −0.469551 | − | 0.271095i | ||||
\(356\) | 547.696i | 1.53847i | ||||||||
\(357\) | 238.596 | + | 149.077i | 0.668336 | + | 0.417584i | ||||
\(358\) | 523.423 | 1.46208 | ||||||||
\(359\) | 233.973 | − | 405.253i | 0.651735 | − | 1.12884i | −0.330967 | − | 0.943642i | \(-0.607375\pi\) |
0.982702 | − | 0.185196i | \(-0.0592919\pi\) | |||||||
\(360\) | 89.8533 | − | 51.8768i | 0.249593 | − | 0.144102i | ||||
\(361\) | 268.566 | + | 465.171i | 0.743951 | + | 1.28856i | ||||
\(362\) | 784.458 | + | 452.907i | 2.16701 | + | 1.25112i | ||||
\(363\) | 197.926i | 0.545251i | ||||||||
\(364\) | −319.337 | − | 600.526i | −0.877301 | − | 1.64980i | ||||
\(365\) | 137.691 | 0.377235 | ||||||||
\(366\) | 2.69346 | − | 4.66520i | 0.00735917 | − | 0.0127465i | ||||
\(367\) | −149.151 | + | 86.1123i | −0.406406 | + | 0.234638i | −0.689244 | − | 0.724529i | \(-0.742057\pi\) |
0.282839 | + | 0.959168i | \(0.408724\pi\) | |||||||
\(368\) | 366.456 | + | 634.721i | 0.995806 | + | 1.72479i | ||||
\(369\) | 9.64181 | + | 5.56670i | 0.0261296 | + | 0.0150859i | ||||
\(370\) | − | 202.691i | − | 0.547814i | ||||||
\(371\) | 247.458 | − | 131.589i | 0.667003 | − | 0.354687i | ||||
\(372\) | −544.489 | −1.46368 | ||||||||
\(373\) | 230.486 | − | 399.213i | 0.617924 | − | 1.07028i | −0.371940 | − | 0.928257i | \(-0.621307\pi\) |
0.989864 | − | 0.142019i | \(-0.0453593\pi\) | |||||||
\(374\) | −183.493 | + | 105.940i | −0.490622 | + | 0.283261i | ||||
\(375\) | 9.68246 | + | 16.7705i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −45.2627 | − | 26.1324i | −0.120379 | − | 0.0695011i | ||||
\(377\) | − | 283.509i | − | 0.752014i | ||||||
\(378\) | 67.8510 | − | 108.594i | 0.179500 | − | 0.287287i | ||||
\(379\) | 444.638 | 1.17319 | 0.586594 | − | 0.809881i | \(-0.300468\pi\) | ||||
0.586594 | + | 0.809881i | \(0.300468\pi\) | |||||||
\(380\) | −281.231 | + | 487.107i | −0.740083 | + | 1.28186i | ||||
\(381\) | 312.960 | − | 180.687i | 0.821416 | − | 0.474245i | ||||
\(382\) | 214.049 | + | 370.744i | 0.560339 | + | 0.970535i | ||||
\(383\) | −458.528 | − | 264.731i | −1.19720 | − | 0.691205i | −0.237271 | − | 0.971443i | \(-0.576253\pi\) |
−0.959930 | + | 0.280239i | \(0.909586\pi\) | |||||||
\(384\) | − | 340.166i | − | 0.885849i | ||||||
\(385\) | 40.5732 | + | 1.41515i | 0.105385 | + | 0.00367571i | ||||
\(386\) | −853.818 | −2.21196 | ||||||||
\(387\) | 111.334 | − | 192.836i | 0.287684 | − | 0.498284i | ||||
\(388\) | 307.020 | − | 177.258i | 0.791290 | − | 0.456851i | ||||
\(389\) | −97.7554 | − | 169.317i | −0.251299 | − | 0.435263i | 0.712585 | − | 0.701586i | \(-0.247524\pi\) |
−0.963884 | + | 0.266323i | \(0.914191\pi\) | |||||||
\(390\) | 136.692 | + | 78.9189i | 0.350491 | + | 0.202356i | ||||
\(391\) | − | 814.674i | − | 2.08356i | ||||||
\(392\) | 756.026 | + | 52.8030i | 1.92864 | + | 0.134701i | ||||
\(393\) | −189.799 | −0.482950 | ||||||||
\(394\) | −174.249 | + | 301.808i | −0.442256 | + | 0.766009i | ||||
\(395\) | 53.3378 | − | 30.7946i | 0.135032 | − | 0.0779610i | ||||
\(396\) | 32.6550 | + | 56.5601i | 0.0824622 | + | 0.142829i | ||||
\(397\) | 25.3358 | + | 14.6276i | 0.0638181 | + | 0.0368454i | 0.531570 | − | 0.847015i | \(-0.321602\pi\) |
−0.467751 | + | 0.883860i | \(0.654936\pi\) | |||||||
\(398\) | − | 277.283i | − | 0.696690i | ||||||
\(399\) | −12.6657 | + | 363.132i | −0.0317435 | + | 0.910106i | ||||
\(400\) | −104.379 | −0.260946 | ||||||||
\(401\) | −105.396 | + | 182.551i | −0.262833 | + | 0.455241i | −0.966994 | − | 0.254800i | \(-0.917990\pi\) |
0.704160 | + | 0.710041i | \(0.251324\pi\) | |||||||
\(402\) | −343.529 | + | 198.337i | −0.854550 | + | 0.493375i | ||||
\(403\) | −216.785 | − | 375.483i | −0.537929 | − | 0.931720i | ||||
\(404\) | 1090.09 | + | 629.363i | 2.69824 | + | 1.55783i | ||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 511.826 | + | 319.795i | 1.26066 | + | 0.787672i | ||||
\(407\) | 66.7843 | 0.164089 | ||||||||
\(408\) | 310.814 | − | 538.345i | 0.761799 | − | 1.31947i | ||||
\(409\) | 281.014 | − | 162.244i | 0.687077 | − | 0.396684i | −0.115439 | − | 0.993315i | \(-0.536828\pi\) |
0.802516 | + | 0.596631i | \(0.203494\pi\) | |||||||
\(410\) | −14.6069 | − | 25.2998i | −0.0356265 | − | 0.0617069i | ||||
\(411\) | −266.179 | − | 153.678i | −0.647637 | − | 0.373913i | ||||
\(412\) | − | 1172.37i | − | 2.84556i | ||||||
\(413\) | 162.114 | + | 304.862i | 0.392529 | + | 0.738164i | ||||
\(414\) | −370.790 | −0.895628 | ||||||||
\(415\) | −146.960 | + | 254.542i | −0.354120 | + | 0.613355i | ||||
\(416\) | −116.542 | + | 67.2853i | −0.280148 | + | 0.161744i | ||||
\(417\) | 147.132 | + | 254.841i | 0.352835 | + | 0.611128i | ||||
\(418\) | −236.983 | − | 136.822i | −0.566944 | − | 0.327325i | ||||
\(419\) | − | 693.958i | − | 1.65622i | −0.560563 | − | 0.828112i | \(-0.689415\pi\) | ||
0.560563 | − | 0.828112i | \(-0.310585\pi\) | |||||||
\(420\) | −200.913 | + | 106.838i | −0.478364 | + | 0.254376i | ||||
\(421\) | −341.554 | −0.811292 | −0.405646 | − | 0.914030i | \(-0.632953\pi\) | ||||
−0.405646 | + | 0.914030i | \(0.632953\pi\) | |||||||
\(422\) | −188.596 | + | 326.657i | −0.446909 | + | 0.774070i | ||||
\(423\) | 8.77939 | − | 5.06878i | 0.0207551 | − | 0.0119829i | ||||
\(424\) | −309.632 | − | 536.298i | −0.730264 | − | 1.26485i | ||||
\(425\) | 100.478 | + | 58.0113i | 0.236420 | + | 0.136497i | ||||
\(426\) | 524.869i | 1.23209i | ||||||||
\(427\) | −3.27690 | + | 5.24462i | −0.00767423 | + | 0.0122825i | ||||
\(428\) | −1521.22 | −3.55425 | ||||||||
\(429\) | −26.0028 | + | 45.0382i | −0.0606127 | + | 0.104984i | ||||
\(430\) | −505.996 | + | 292.137i | −1.17673 | + | 0.679388i | ||||
\(431\) | 205.726 | + | 356.328i | 0.477323 | + | 0.826748i | 0.999662 | − | 0.0259902i | \(-0.00827387\pi\) |
−0.522339 | + | 0.852738i | \(0.674941\pi\) | |||||||
\(432\) | −93.9407 | − | 54.2367i | −0.217455 | − | 0.125548i | ||||
\(433\) | − | 443.458i | − | 1.02415i | −0.858940 | − | 0.512077i | \(-0.828876\pi\) | ||
0.858940 | − | 0.512077i | \(-0.171124\pi\) | |||||||
\(434\) | 922.400 | + | 32.1723i | 2.12535 | + | 0.0741298i | ||||
\(435\) | −94.8512 | −0.218049 | ||||||||
\(436\) | 309.758 | − | 536.517i | 0.710454 | − | 1.23054i | ||||
\(437\) | 911.197 | − | 526.080i | 2.08512 | − | 1.20384i | ||||
\(438\) | −187.735 | − | 325.167i | −0.428619 | − | 0.742390i | ||||
\(439\) | −268.002 | − | 154.731i | −0.610484 | − | 0.352463i | 0.162671 | − | 0.986680i | \(-0.447989\pi\) |
−0.773155 | + | 0.634217i | \(0.781322\pi\) | |||||||
\(440\) | − | 89.7021i | − | 0.203868i | ||||||
\(441\) | −82.1912 | + | 121.875i | −0.186375 | + | 0.276361i | ||||
\(442\) | 945.666 | 2.13952 | ||||||||
\(443\) | −409.330 | + | 708.981i | −0.923996 | + | 1.60041i | −0.130829 | + | 0.991405i | \(0.541764\pi\) |
−0.793167 | + | 0.609004i | \(0.791569\pi\) | |||||||
\(444\) | −324.178 | + | 187.164i | −0.730131 | + | 0.421541i | ||||
\(445\) | 72.9552 | + | 126.362i | 0.163944 | + | 0.283960i | ||||
\(446\) | −26.5860 | − | 15.3494i | −0.0596099 | − | 0.0344158i | ||||
\(447\) | − | 147.892i | − | 0.330855i | ||||||
\(448\) | −10.3895 | + | 297.872i | −0.0231908 | + | 0.664893i | ||||
\(449\) | 315.756 | 0.703243 | 0.351621 | − | 0.936142i | \(-0.385630\pi\) | ||||
0.351621 | + | 0.936142i | \(0.385630\pi\) | |||||||
\(450\) | 26.4032 | − | 45.7317i | 0.0586738 | − | 0.101626i | ||||
\(451\) | 8.33600 | − | 4.81279i | 0.0184834 | − | 0.0106714i | ||||
\(452\) | −30.9953 | − | 53.6854i | −0.0685736 | − | 0.118773i | ||||
\(453\) | −206.993 | − | 119.507i | −0.456938 | − | 0.263813i | ||||
\(454\) | 890.743i | 1.96199i | ||||||||
\(455\) | −153.668 | − | 96.0138i | −0.337733 | − | 0.211019i | ||||
\(456\) | 802.839 | 1.76061 | ||||||||
\(457\) | 93.6533 | − | 162.212i | 0.204931 | − | 0.354950i | −0.745180 | − | 0.666863i | \(-0.767636\pi\) |
0.950111 | + | 0.311913i | \(0.100970\pi\) | |||||||
\(458\) | 443.533 | − | 256.074i | 0.968412 | − | 0.559113i | ||||
\(459\) | 60.2871 | + | 104.420i | 0.131344 | + | 0.227495i | ||||
\(460\) | 570.644 | + | 329.462i | 1.24053 | + | 0.716221i | ||||
\(461\) | − | 8.27599i | − | 0.0179523i | −0.999960 | − | 0.00897613i | \(-0.997143\pi\) | ||
0.999960 | − | 0.00897613i | \(-0.00285723\pi\) | |||||||
\(462\) | −51.9778 | − | 97.7461i | −0.112506 | − | 0.211572i | ||||
\(463\) | −472.925 | −1.02144 | −0.510718 | − | 0.859748i | \(-0.670620\pi\) | ||||
−0.510718 | + | 0.859748i | \(0.670620\pi\) | |||||||
\(464\) | 255.628 | − | 442.761i | 0.550922 | − | 0.954226i | ||||
\(465\) | −125.622 | + | 72.5280i | −0.270155 | + | 0.155974i | ||||
\(466\) | 453.283 | + | 785.108i | 0.972709 | + | 1.68478i | ||||
\(467\) | −620.865 | − | 358.456i | −1.32948 | − | 0.767573i | −0.344257 | − | 0.938876i | \(-0.611869\pi\) |
−0.985218 | + | 0.171303i | \(0.945202\pi\) | |||||||
\(468\) | − | 291.494i | − | 0.622851i | ||||||
\(469\) | 402.069 | − | 213.805i | 0.857289 | − | 0.455875i | ||||
\(470\) | −26.6007 | −0.0565972 | ||||||||
\(471\) | −5.94674 | + | 10.3001i | −0.0126258 | + | 0.0218685i | ||||
\(472\) | 660.705 | − | 381.458i | 1.39980 | − | 0.808174i | ||||
\(473\) | −96.2556 | − | 166.720i | −0.203500 | − | 0.352473i | ||||
\(474\) | −145.448 | − | 83.9742i | −0.306851 | − | 0.177161i | ||||
\(475\) | 149.844i | 0.315462i | ||||||||
\(476\) | −722.420 | + | 1156.22i | −1.51769 | + | 2.42904i | ||||
\(477\) | 120.116 | 0.251815 | ||||||||
\(478\) | −226.508 | + | 392.323i | −0.473866 | + | 0.820759i | ||||
\(479\) | 178.320 | − | 102.953i | 0.372276 | − | 0.214933i | −0.302177 | − | 0.953252i | \(-0.597713\pi\) |
0.674452 | + | 0.738319i | \(0.264380\pi\) | |||||||
\(480\) | 22.5111 | + | 38.9903i | 0.0468981 | + | 0.0812298i | ||||
\(481\) | −258.140 | − | 149.037i | −0.536673 | − | 0.309848i | ||||
\(482\) | 32.6108i | 0.0676573i | ||||||||
\(483\) | 425.408 | + | 14.8378i | 0.880762 | + | 0.0307201i | ||||
\(484\) | −959.138 | −1.98169 | ||||||||
\(485\) | 47.2230 | − | 81.7926i | 0.0973669 | − | 0.168644i | ||||
\(486\) | 47.5258 | − | 27.4390i | 0.0977897 | − | 0.0564589i | ||||
\(487\) | −161.439 | − | 279.621i | −0.331498 | − | 0.574171i | 0.651308 | − | 0.758813i | \(-0.274221\pi\) |
−0.982806 | + | 0.184643i | \(0.940887\pi\) | |||||||
\(488\) | 11.8335 | + | 6.83205i | 0.0242489 | + | 0.0140001i | ||||
\(489\) | 479.304i | 0.980172i | ||||||||
\(490\) | 346.672 | − | 169.119i | 0.707494 | − | 0.345141i | ||||
\(491\) | 272.380 | 0.554745 | 0.277372 | − | 0.960763i | \(-0.410536\pi\) | ||||
0.277372 | + | 0.960763i | \(0.410536\pi\) | |||||||
\(492\) | −26.9759 | + | 46.7236i | −0.0548290 | + | 0.0949667i | ||||
\(493\) | −492.153 | + | 284.145i | −0.998282 | + | 0.576359i | ||||
\(494\) | 610.669 | + | 1057.71i | 1.23617 | + | 2.14111i | ||||
\(495\) | 15.0680 | + | 8.69954i | 0.0304405 | + | 0.0175748i | ||||
\(496\) | − | 781.864i | − | 1.57634i | ||||||
\(497\) | 21.0035 | − | 602.184i | 0.0422606 | − | 1.21164i | ||||
\(498\) | 801.494 | 1.60943 | ||||||||
\(499\) | −264.597 | + | 458.296i | −0.530255 | + | 0.918429i | 0.469122 | + | 0.883134i | \(0.344571\pi\) |
−0.999377 | + | 0.0352954i | \(0.988763\pi\) | |||||||
\(500\) | −81.2689 | + | 46.9206i | −0.162538 | + | 0.0938412i | ||||
\(501\) | 36.7020 | + | 63.5698i | 0.0732576 | + | 0.126886i | ||||
\(502\) | −91.2231 | − | 52.6677i | −0.181719 | − | 0.104916i | ||||
\(503\) | − | 204.695i | − | 0.406948i | −0.979080 | − | 0.203474i | \(-0.934777\pi\) | ||
0.979080 | − | 0.203474i | \(-0.0652232\pi\) | |||||||
\(504\) | 275.454 | + | 172.106i | 0.546535 | + | 0.341481i | ||||
\(505\) | 335.334 | 0.664028 | ||||||||
\(506\) | −160.286 | + | 277.624i | −0.316772 | + | 0.548665i | ||||
\(507\) | −52.4837 | + | 30.3015i | −0.103518 | + | 0.0597663i | ||||
\(508\) | 875.599 | + | 1516.58i | 1.72362 | + | 2.98540i | ||||
\(509\) | −473.892 | − | 273.602i | −0.931026 | − | 0.537528i | −0.0438903 | − | 0.999036i | \(-0.513975\pi\) |
−0.887136 | + | 0.461508i | \(0.847309\pi\) | |||||||
\(510\) | − | 316.383i | − | 0.620359i | ||||||
\(511\) | 202.377 | + | 380.577i | 0.396041 | + | 0.744770i | ||||
\(512\) | 1048.84 | 2.04851 | ||||||||
\(513\) | −77.8614 | + | 134.860i | −0.151777 | + | 0.262885i | ||||
\(514\) | 294.779 | − | 170.191i | 0.573500 | − | 0.331110i | ||||
\(515\) | −156.164 | − | 270.485i | −0.303232 | − | 0.525213i | ||||
\(516\) | 934.470 | + | 539.517i | 1.81099 | + | 1.04558i | ||||
\(517\) | − | 8.76461i | − | 0.0169528i | ||||||
\(518\) | 560.238 | − | 297.914i | 1.08154 | − | 0.575124i | ||||
\(519\) | −51.1998 | −0.0986509 | ||||||||
\(520\) | −200.181 | + | 346.723i | −0.384963 | + | 0.666775i | ||||
\(521\) | 30.1482 | − | 17.4061i | 0.0578660 | − | 0.0334090i | −0.470788 | − | 0.882246i | \(-0.656030\pi\) |
0.528654 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(522\) | 129.325 | + | 223.998i | 0.247750 | + | 0.429115i | ||||
\(523\) | 720.290 | + | 415.860i | 1.37723 | + | 0.795143i | 0.991825 | − | 0.127606i | \(-0.0407292\pi\) |
0.385403 | + | 0.922748i | \(0.374062\pi\) | |||||||
\(524\) | − | 919.756i | − | 1.75526i | ||||||
\(525\) | −32.1225 | + | 51.4115i | −0.0611857 | + | 0.0979267i | ||||
\(526\) | −226.174 | −0.429989 | ||||||||
\(527\) | −434.543 | + | 752.650i | −0.824559 | + | 1.42818i | ||||
\(528\) | −81.2180 | + | 46.8913i | −0.153822 | + | 0.0888092i | ||||
\(529\) | −351.800 | − | 609.336i | −0.665029 | − | 1.15186i | ||||
\(530\) | −272.954 | − | 157.590i | −0.515007 | − | 0.297340i | ||||
\(531\) | 147.979i | 0.278680i | ||||||||
\(532\) | −1759.72 | − | 61.3770i | −3.30774 | − | 0.115370i | ||||
\(533\) | −42.9612 | −0.0806027 | ||||||||
\(534\) | 198.942 | − | 344.578i | 0.372551 | − | 0.645277i | ||||
\(535\) | −350.969 | + | 202.632i | −0.656017 | + | 0.378751i | ||||
\(536\) | −503.088 | − | 871.374i | −0.938597 | − | 1.62570i | ||||
\(537\) | −223.022 | − | 128.762i | −0.415312 | − | 0.239780i | ||||
\(538\) | 695.512i | 1.29277i | ||||||||
\(539\) | 55.7228 | + | 114.224i | 0.103382 | + | 0.211919i | ||||
\(540\) | −97.5226 | −0.180597 | ||||||||
\(541\) | 112.177 | − | 194.296i | 0.207351 | − | 0.359143i | −0.743528 | − | 0.668705i | \(-0.766849\pi\) |
0.950879 | + | 0.309562i | \(0.100182\pi\) | |||||||
\(542\) | −469.919 | + | 271.308i | −0.867008 | + | 0.500568i | ||||
\(543\) | −222.830 | − | 385.954i | −0.410369 | − | 0.710780i | ||||
\(544\) | 233.606 | + | 134.872i | 0.429422 | + | 0.247927i | ||||
\(545\) | − | 165.044i | − | 0.302833i | ||||||
\(546\) | −17.2236 | + | 493.810i | −0.0315450 | + | 0.904414i | ||||
\(547\) | −456.739 | −0.834989 | −0.417495 | − | 0.908679i | \(-0.637092\pi\) | ||||
−0.417495 | + | 0.908679i | \(0.637092\pi\) | |||||||
\(548\) | 744.716 | − | 1289.89i | 1.35897 | − | 2.35381i | ||||
\(549\) | −2.29528 | + | 1.32518i | −0.00418084 | + | 0.00241381i | ||||
\(550\) | −22.8274 | − | 39.5381i | −0.0415043 | − | 0.0718875i | ||||
\(551\) | −635.621 | − | 366.976i | −1.15358 | − | 0.666018i | ||||
\(552\) | − | 940.522i | − | 1.70384i | ||||||
\(553\) | 163.512 | + | 102.164i | 0.295682 | + | 0.184745i | ||||
\(554\) | −1194.14 | −2.15549 | ||||||||
\(555\) | −49.8620 | + | 86.3635i | −0.0898414 | + | 0.155610i | ||||
\(556\) | −1234.94 | + | 712.994i | −2.22112 | + | 1.28236i | ||||
\(557\) | 388.525 | + | 672.945i | 0.697532 | + | 1.20816i | 0.969320 | + | 0.245803i | \(0.0790516\pi\) |
−0.271788 | + | 0.962357i | \(0.587615\pi\) | |||||||
\(558\) | 342.561 | + | 197.777i | 0.613908 | + | 0.354440i | ||||
\(559\) | 859.223i | 1.53707i | ||||||||
\(560\) | −153.415 | − | 288.502i | −0.273955 | − | 0.515183i | ||||
\(561\) | 104.245 | 0.185819 | ||||||||
\(562\) | −197.102 | + | 341.391i | −0.350716 | + | 0.607457i | ||||
\(563\) | −72.2428 | + | 41.7094i | −0.128318 | + | 0.0740842i | −0.562785 | − | 0.826603i | \(-0.690270\pi\) |
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(564\) | 24.5630 | + | 42.5444i | 0.0435514 | + | 0.0754333i | ||||
\(565\) | −14.3022 | − | 8.25738i | −0.0253136 | − | 0.0146148i | ||||
\(566\) | 230.265i | 0.406829i | ||||||||
\(567\) | −55.6245 | + | 29.5790i | −0.0981031 | + | 0.0521676i | ||||
\(568\) | −1331.35 | −2.34393 | ||||||||
\(569\) | 111.671 | − | 193.421i | 0.196259 | − | 0.339931i | −0.751053 | − | 0.660241i | \(-0.770454\pi\) |
0.947313 | + | 0.320311i | \(0.103787\pi\) | |||||||
\(570\) | 353.869 | − | 204.306i | 0.620822 | − | 0.358432i | ||||
\(571\) | −88.3631 | − | 153.049i | −0.154751 | − | 0.268037i | 0.778217 | − | 0.627995i | \(-0.216124\pi\) |
−0.932969 | + | 0.359958i | \(0.882791\pi\) | |||||||
\(572\) | −218.252 | − | 126.008i | −0.381560 | − | 0.220294i | ||||
\(573\) | − | 210.625i | − | 0.367582i | ||||||
\(574\) | 48.4597 | − | 77.5590i | 0.0844246 | − | 0.135120i | ||||
\(575\) | 175.542 | 0.305291 | ||||||||
\(576\) | −63.8685 | + | 110.624i | −0.110883 | + | 0.192055i | ||||
\(577\) | 780.812 | − | 450.802i | 1.35323 | − | 0.781286i | 0.364527 | − | 0.931193i | \(-0.381231\pi\) |
0.988700 | + | 0.149907i | \(0.0478975\pi\) | |||||||
\(578\) | −439.084 | − | 760.516i | −0.759661 | − | 1.31577i | ||||
\(579\) | 363.799 | + | 210.039i | 0.628323 | + | 0.362762i | ||||
\(580\) | − | 459.643i | − | 0.792488i | ||||||
\(581\) | −919.556 | − | 32.0731i | −1.58271 | − | 0.0552033i | ||||
\(582\) | −257.546 | −0.442518 | ||||||||
\(583\) | 51.9240 | − | 89.9351i | 0.0890635 | − | 0.154263i | ||||
\(584\) | 824.798 | − | 476.197i | 1.41233 | − | 0.815406i | ||||
\(585\) | −38.8281 | − | 67.2523i | −0.0663728 | − | 0.114961i | ||||
\(586\) | −307.901 | − | 177.767i | −0.525429 | − | 0.303356i | ||||
\(587\) | − | 163.544i | − | 0.278610i | −0.990250 | − | 0.139305i | \(-0.955513\pi\) | ||
0.990250 | − | 0.139305i | \(-0.0444868\pi\) | |||||||
\(588\) | −590.601 | − | 398.293i | −1.00442 | − | 0.677370i | ||||
\(589\) | −1122.43 | −1.90566 | ||||||||
\(590\) | 194.147 | − | 336.272i | 0.329062 | − | 0.569953i | ||||
\(591\) | 148.489 | − | 85.7304i | 0.251251 | − | 0.145060i | ||||
\(592\) | −268.760 | − | 465.507i | −0.453987 | − | 0.786329i | ||||
\(593\) | 1004.47 | + | 579.932i | 1.69388 | + | 0.977964i | 0.951329 | + | 0.308177i | \(0.0997190\pi\) |
0.742554 | + | 0.669786i | \(0.233614\pi\) | |||||||
\(594\) | − | 47.4458i | − | 0.0798750i | ||||||
\(595\) | −12.6606 | + | 362.987i | −0.0212783 | + | 0.610063i | ||||
\(596\) | 716.677 | 1.20248 | ||||||||
\(597\) | −68.2115 | + | 118.146i | −0.114257 | + | 0.197899i | ||||
\(598\) | 1239.10 | − | 715.396i | 2.07208 | − | 1.19631i | ||||
\(599\) | −16.3990 | − | 28.4039i | −0.0273773 | − | 0.0474188i | 0.852012 | − | 0.523522i | \(-0.175382\pi\) |
−0.879389 | + | 0.476103i | \(0.842049\pi\) | |||||||
\(600\) | 116.000 | + | 66.9727i | 0.193334 | + | 0.111621i | ||||
\(601\) | − | 796.834i | − | 1.32585i | −0.748687 | − | 0.662924i | \(-0.769315\pi\) | ||
0.748687 | − | 0.662924i | \(-0.230685\pi\) | |||||||
\(602\) | −1551.18 | − | 969.192i | −2.57670 | − | 1.60995i | ||||
\(603\) | 195.163 | 0.323654 | ||||||||
\(604\) | 579.126 | − | 1003.08i | 0.958817 | − | 1.66072i | ||||
\(605\) | −221.288 | + | 127.761i | −0.365766 | + | 0.211175i | ||||
\(606\) | −457.214 | − | 791.917i | −0.754478 | − | 1.30679i | ||||
\(607\) | −453.877 | − | 262.046i | −0.747739 | − | 0.431707i | 0.0771375 | − | 0.997020i | \(-0.475422\pi\) |
−0.824876 | + | 0.565313i | \(0.808755\pi\) | |||||||
\(608\) | 348.378i | 0.572990i | ||||||||
\(609\) | −139.412 | − | 262.169i | −0.228919 | − | 0.430491i | ||||
\(610\) | 6.95448 | 0.0114008 | ||||||||
\(611\) | −19.5593 | + | 33.8776i | −0.0320119 | + | 0.0554462i | ||||
\(612\) | −506.014 | + | 292.147i | −0.826821 | + | 0.477365i | ||||
\(613\) | 126.866 | + | 219.738i | 0.206959 | + | 0.358463i | 0.950755 | − | 0.309944i | \(-0.100310\pi\) |
−0.743796 | + | 0.668406i | \(0.766977\pi\) | |||||||
\(614\) | 1220.69 | + | 704.769i | 1.98810 | + | 1.14783i | ||||
\(615\) | 14.3732i | 0.0233710i | ||||||||
\(616\) | 247.937 | − | 131.844i | 0.402495 | − | 0.214032i | ||||
\(617\) | 620.813 | 1.00618 | 0.503090 | − | 0.864234i | \(-0.332196\pi\) | ||||
0.503090 | + | 0.864234i | \(0.332196\pi\) | |||||||
\(618\) | −425.846 | + | 737.588i | −0.689072 | + | 1.19351i | ||||
\(619\) | 555.643 | − | 320.801i | 0.897647 | − | 0.518257i | 0.0212107 | − | 0.999775i | \(-0.493248\pi\) |
0.876436 | + | 0.481519i | \(0.159915\pi\) | |||||||
\(620\) | −351.466 | − | 608.757i | −0.566881 | − | 0.981866i | ||||
\(621\) | 157.988 | + | 91.2143i | 0.254409 | + | 0.146883i | ||||
\(622\) | 126.731i | 0.203747i | ||||||||
\(623\) | −242.036 | + | 387.374i | −0.388501 | + | 0.621789i | ||||
\(624\) | 418.573 | 0.670791 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −349.071 | + | 201.536i | −0.557621 | + | 0.321943i | ||||
\(627\) | 67.3164 | + | 116.595i | 0.107363 | + | 0.185958i | ||||
\(628\) | −49.9134 | − | 28.8175i | −0.0794800 | − | 0.0458878i | ||||
\(629\) | 597.484i | 0.949896i | ||||||||
\(630\) | 165.210 | + | 5.76234i | 0.262238 | + | 0.00914657i | ||||
\(631\) | −166.338 | −0.263610 | −0.131805 | − | 0.991276i | \(-0.542077\pi\) | ||||
−0.131805 | + | 0.991276i | \(0.542077\pi\) | |||||||
\(632\) | 213.004 | − | 368.933i | 0.337031 | − | 0.583755i | ||||
\(633\) | 160.715 | − | 92.7891i | 0.253895 | − | 0.146586i | ||||
\(634\) | 7.09746 | + | 12.2932i | 0.0111947 | + | 0.0193899i | ||||
\(635\) | 404.029 | + | 233.266i | 0.636266 | + | 0.367348i | ||||
\(636\) | 582.073i | 0.915209i | ||||||||
\(637\) | 39.5213 | − | 565.860i | 0.0620429 | − | 0.888321i | ||||
\(638\) | 223.621 | 0.350503 | ||||||||
\(639\) | 129.118 | − | 223.639i | 0.202062 | − | 0.349982i | ||||
\(640\) | 380.317 | − | 219.576i | 0.594246 | − | 0.343088i | ||||
\(641\) | −68.5302 | − | 118.698i | −0.106911 | − | 0.185176i | 0.807606 | − | 0.589722i | \(-0.200763\pi\) |
−0.914518 | + | 0.404546i | \(0.867429\pi\) | |||||||
\(642\) | 957.061 | + | 552.559i | 1.49075 | + | 0.860685i | ||||
\(643\) | 812.010i | 1.26285i | 0.775438 | + | 0.631423i | \(0.217529\pi\) | ||||
−0.775438 | + | 0.631423i | \(0.782471\pi\) | |||||||
\(644\) | −71.9030 | + | 2061.50i | −0.111651 | + | 3.20109i | ||||
\(645\) | 287.463 | 0.445679 | ||||||||
\(646\) | 1224.08 | − | 2120.16i | 1.89485 | − | 3.28198i | ||||
\(647\) | −197.709 | + | 114.148i | −0.305579 | + | 0.176426i | −0.644946 | − | 0.764228i | \(-0.723120\pi\) |
0.339368 | + | 0.940654i | \(0.389787\pi\) | |||||||
\(648\) | 69.6001 | + | 120.551i | 0.107408 | + | 0.186035i | ||||
\(649\) | 110.798 | + | 63.9691i | 0.170721 | + | 0.0985656i | ||||
\(650\) | 203.768i | 0.313489i | ||||||||
\(651\) | −385.106 | − | 240.619i | −0.591561 | − | 0.369614i | ||||
\(652\) | −2322.68 | −3.56239 | ||||||||
\(653\) | 435.557 | − | 754.406i | 0.667009 | − | 1.15529i | −0.311728 | − | 0.950171i | \(-0.600908\pi\) |
0.978736 | − | 0.205122i | \(-0.0657590\pi\) | |||||||
\(654\) | −389.763 | + | 225.030i | −0.595968 | + | 0.344082i | ||||
\(655\) | −122.515 | − | 212.202i | −0.187046 | − | 0.323973i | ||||
\(656\) | −67.0932 | − | 38.7363i | −0.102276 | − | 0.0590492i | ||||
\(657\) | 184.731i | 0.281174i | ||||||||
\(658\) | −39.0975 | − | 73.5243i | −0.0594187 | − | 0.111739i | ||||
\(659\) | −677.945 | −1.02875 | −0.514374 | − | 0.857566i | \(-0.671976\pi\) | ||||
−0.514374 | + | 0.857566i | \(0.671976\pi\) | |||||||
\(660\) | −42.1574 | + | 73.0188i | −0.0638749 | + | 0.110635i | ||||
\(661\) | 608.681 | − | 351.422i | 0.920849 | − | 0.531652i | 0.0369430 | − | 0.999317i | \(-0.488238\pi\) |
0.883906 | + | 0.467665i | \(0.154905\pi\) | |||||||
\(662\) | 893.102 | + | 1546.90i | 1.34910 | + | 2.33670i | ||||
\(663\) | −402.934 | − | 232.634i | −0.607743 | − | 0.350881i | ||||
\(664\) | 2033.02i | 3.06177i | ||||||||
\(665\) | −414.170 | + | 220.240i | −0.622812 | + | 0.331188i | ||||
\(666\) | 271.939 | 0.408316 | ||||||||
\(667\) | −429.911 | + | 744.628i | −0.644544 | + | 1.11638i | ||||
\(668\) | −308.055 | + | 177.856i | −0.461161 | + | 0.266251i | ||||
\(669\) | 7.55192 | + | 13.0803i | 0.0112884 | + | 0.0195520i | ||||
\(670\) | −443.494 | − | 256.051i | −0.661932 | − | 0.382166i | ||||
\(671\) | 2.29142i | 0.00341493i | ||||||||
\(672\) | −74.6827 | + | 119.528i | −0.111135 | + | 0.177870i | ||||
\(673\) | 612.283 | 0.909782 | 0.454891 | − | 0.890547i | \(-0.349678\pi\) | ||||
0.454891 | + | 0.890547i | \(0.349678\pi\) | |||||||
\(674\) | −465.187 | + | 805.727i | −0.690188 | + | 1.19544i | ||||
\(675\) | −22.5000 | + | 12.9904i | −0.0333333 | + | 0.0192450i | ||||
\(676\) | −146.839 | − | 254.333i | −0.217218 | − | 0.376232i | ||||
\(677\) | −5.01270 | − | 2.89408i | −0.00740428 | − | 0.00427487i | 0.496293 | − | 0.868155i | \(-0.334694\pi\) |
−0.503698 | + | 0.863880i | \(0.668027\pi\) | |||||||
\(678\) | 45.0343i | 0.0664222i | ||||||||
\(679\) | 295.483 | + | 10.3061i | 0.435173 | + | 0.0151784i | ||||
\(680\) | 802.518 | 1.18017 | ||||||||
\(681\) | 219.123 | − | 379.532i | 0.321766 | − | 0.557316i | ||||
\(682\) | 296.167 | − | 170.992i | 0.434262 | − | 0.250721i | ||||
\(683\) | 58.3832 | + | 101.123i | 0.0854806 | + | 0.148057i | 0.905596 | − | 0.424142i | \(-0.139424\pi\) |
−0.820115 | + | 0.572198i | \(0.806091\pi\) | |||||||
\(684\) | −653.523 | − | 377.312i | −0.955443 | − | 0.551625i | ||||
\(685\) | − | 396.796i | − | 0.579264i | ||||||
\(686\) | 976.982 | + | 709.632i | 1.42417 | + | 1.03445i | ||||
\(687\) | −251.977 | −0.366778 | ||||||||
\(688\) | −774.724 | + | 1341.86i | −1.12605 | + | 1.95038i | ||||
\(689\) | −401.401 | + | 231.749i | −0.582585 | + | 0.336356i | ||||
\(690\) | −239.344 | − | 414.556i | −0.346875 | − | 0.600805i | ||||
\(691\) | 820.541 | + | 473.740i | 1.18747 | + | 0.685585i | 0.957730 | − | 0.287667i | \(-0.0928796\pi\) |
0.229738 | + | 0.973252i | \(0.426213\pi\) | |||||||
\(692\) | − | 248.111i | − | 0.358542i | ||||||
\(693\) | −1.89862 | + | 54.4346i | −0.00273971 | + | 0.0785493i | ||||
\(694\) | 825.425 | 1.18937 | ||||||||
\(695\) | −189.947 | + | 328.998i | −0.273305 | + | 0.473378i | ||||
\(696\) | −568.180 | + | 328.039i | −0.816350 | + | 0.471320i | ||||
\(697\) | 43.0575 | + | 74.5778i | 0.0617755 | + | 0.106998i | ||||
\(698\) | 165.284 | + | 95.4270i | 0.236797 | + | 0.136715i | ||||
\(699\) | − | 446.030i | − | 0.638097i | ||||||
\(700\) | −249.137 | − | 155.664i | −0.355910 | − | 0.222377i | ||||
\(701\) | 1168.56 | 1.66700 | 0.833498 | − | 0.552523i | \(-0.186335\pi\) | ||||
0.833498 | + | 0.552523i | \(0.186335\pi\) | |||||||
\(702\) | −105.881 | + | 183.391i | −0.150827 | + | 0.261241i | ||||
\(703\) | −668.275 | + | 385.829i | −0.950604 | + | 0.548832i | ||||
\(704\) | 55.2187 | + | 95.6415i | 0.0784356 | + | 0.135854i | ||||
\(705\) | 11.3341 | + | 6.54377i | 0.0160768 | + | 0.00928194i | ||||
\(706\) | 1837.05i | 2.60205i | ||||||||
\(707\) | 492.872 | + | 926.865i | 0.697132 | + | 1.31098i | ||||
\(708\) | −717.099 | −1.01285 | ||||||||
\(709\) | −334.781 | + | 579.857i | −0.472187 | + | 0.817852i | −0.999494 | − | 0.0318230i | \(-0.989869\pi\) |
0.527306 | + | 0.849675i | \(0.323202\pi\) | |||||||
\(710\) | −586.822 | + | 338.802i | −0.826509 | + | 0.477185i | ||||
\(711\) | 41.3153 | + | 71.5602i | 0.0581087 | + | 0.100647i | ||||
\(712\) | 874.035 | + | 504.625i | 1.22758 | + | 0.708742i | ||||
\(713\) | 1314.93i | 1.84422i | ||||||||
\(714\) | 874.484 | − | 465.018i | 1.22477 | − | 0.651286i | ||||
\(715\) | −67.1390 | −0.0939008 | ||||||||
\(716\) | 623.973 | − | 1080.75i | 0.871471 | − | 1.50943i | ||||
\(717\) | 193.023 | − | 111.442i | 0.269209 | − | 0.155428i | ||||
\(718\) | −823.685 | − | 1426.66i | −1.14719 | − | 1.98700i | ||||
\(719\) | −805.983 | − | 465.334i | −1.12098 | − | 0.647196i | −0.179327 | − | 0.983790i | \(-0.557392\pi\) |
−0.941650 | + | 0.336593i | \(0.890725\pi\) | |||||||
\(720\) | − | 140.038i | − | 0.194498i | ||||||
\(721\) | 518.091 | − | 829.195i | 0.718572 | − | 1.15006i | ||||
\(722\) | 1890.94 | 2.61903 | ||||||||
\(723\) | 8.02227 | − | 13.8950i | 0.0110958 | − | 0.0192185i | ||||
\(724\) | 1870.31 | − | 1079.82i | 2.58330 | − | 1.49147i | ||||
\(725\) | −61.2262 | − | 106.047i | −0.0844499 | − | 0.146272i | ||||
\(726\) | 603.433 | + | 348.392i | 0.831175 | + | 0.479879i | ||||
\(727\) | − | 290.932i | − | 0.400182i | −0.979777 | − | 0.200091i | \(-0.935876\pi\) | ||
0.979777 | − | 0.200091i | \(-0.0641238\pi\) | |||||||
\(728\) | −1252.57 | − | 43.6882i | −1.72056 | − | 0.0600113i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 242.365 | − | 419.789i | 0.332007 | − | 0.575053i | ||||
\(731\) | 1491.55 | − | 861.149i | 2.04043 | − | 1.17804i | ||||
\(732\) | −6.42174 | − | 11.1228i | −0.00877288 | − | 0.0151951i | ||||
\(733\) | −0.836082 | − | 0.482712i | −0.00114063 | − | 0.000658543i | 0.499430 | − | 0.866354i | \(-0.333543\pi\) |
−0.500570 | + | 0.865696i | \(0.666876\pi\) | |||||||
\(734\) | 606.304i | 0.826027i | ||||||||
\(735\) | −189.315 | − | 13.2223i | −0.257571 | − | 0.0179895i | ||||
\(736\) | 408.124 | 0.554516 | ||||||||
\(737\) | 84.3659 | − | 146.126i | 0.114472 | − | 0.198271i | ||||
\(738\) | 33.9433 | − | 19.5972i | 0.0459936 | − | 0.0265544i | ||||
\(739\) | 49.9365 | + | 86.4925i | 0.0675731 | + | 0.117040i | 0.897832 | − | 0.440337i | \(-0.145141\pi\) |
−0.830259 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(740\) | −418.512 | − | 241.628i | −0.565557 | − | 0.326525i | ||||
\(741\) | − | 600.898i | − | 0.810929i | ||||||
\(742\) | 34.3931 | − | 986.070i | 0.0463518 | − | 1.32894i | ||||
\(743\) | 890.635 | 1.19870 | 0.599351 | − | 0.800486i | \(-0.295425\pi\) | ||||
0.599351 | + | 0.800486i | \(0.295425\pi\) | |||||||
\(744\) | −501.670 | + | 868.917i | −0.674287 | + | 1.16790i | ||||
\(745\) | 165.349 | − | 95.4640i | 0.221944 | − | 0.128140i | ||||
\(746\) | −811.408 | − | 1405.40i | −1.08768 | − | 1.88391i | ||||
\(747\) | −341.504 | − | 197.167i | −0.457167 | − | 0.263946i | ||||
\(748\) | 505.162i | 0.675351i | ||||||||
\(749\) | −1075.93 | − | 672.251i | −1.43648 | − | 0.897532i | ||||
\(750\) | 68.1728 | 0.0908971 | ||||||||
\(751\) | −310.537 | + | 537.867i | −0.413499 | + | 0.716200i | −0.995270 | − | 0.0971521i | \(-0.969027\pi\) |
0.581771 | + | 0.813353i | \(0.302360\pi\) | |||||||
\(752\) | −61.0920 | + | 35.2715i | −0.0812393 | + | 0.0469035i | ||||
\(753\) | 25.9125 | + | 44.8818i | 0.0344124 | + | 0.0596040i | ||||
\(754\) | −864.357 | − | 499.037i | −1.14636 | − | 0.661853i | ||||
\(755\) | − | 308.567i | − | 0.408698i | ||||||
\(756\) | −143.338 | − | 269.553i | −0.189601 | − | 0.356551i | ||||
\(757\) | 675.637 | 0.892519 | 0.446259 | − | 0.894904i | \(-0.352756\pi\) | ||||
0.446259 | + | 0.894904i | \(0.352756\pi\) | |||||||
\(758\) | 782.658 | − | 1355.60i | 1.03253 | − | 1.78840i | ||||
\(759\) | 136.591 | − | 78.8609i | 0.179962 | − | 0.103901i | ||||
\(760\) | 518.230 | + | 897.601i | 0.681882 | + | 1.18105i | ||||
\(761\) | 549.336 | + | 317.159i | 0.721861 | + | 0.416766i | 0.815437 | − | 0.578846i | \(-0.196497\pi\) |
−0.0935765 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(762\) | − | 1272.19i | − | 1.66954i | ||||||
\(763\) | 456.181 | − | 242.580i | 0.597878 | − | 0.317930i | ||||
\(764\) | 1020.67 | 1.33596 | ||||||||
\(765\) | −77.8303 | + | 134.806i | −0.101739 | + | 0.176217i | ||||
\(766\) | −1614.22 | + | 931.967i | −2.10733 | + | 1.21667i | ||||
\(767\) | −285.509 | − | 494.516i | −0.372241 | − | 0.644741i | ||||
\(768\) | −781.618 | − | 451.267i | −1.01773 | − | 0.587587i | ||||
\(769\) | 17.8434i | 0.0232033i | 0.999933 | + | 0.0116017i | \(0.00369301\pi\) | ||||
−0.999933 | + | 0.0116017i | \(0.996307\pi\) | |||||||
\(770\) | 75.7320 | − | 121.208i | 0.0983532 | − | 0.157413i | ||||
\(771\) | −167.468 | −0.217208 | ||||||||
\(772\) | −1017.84 | + | 1762.95i | −1.31844 | + | 2.28361i | ||||
\(773\) | −223.935 | + | 129.289i | −0.289697 | + | 0.167256i | −0.637805 | − | 0.770198i | \(-0.720157\pi\) |
0.348108 | + | 0.937454i | \(0.386824\pi\) | |||||||
\(774\) | −391.943 | − | 678.865i | −0.506386 | − | 0.877086i | ||||
\(775\) | −162.178 | − | 93.6332i | −0.209261 | − | 0.120817i | ||||
\(776\) | − | 653.274i | − | 0.841848i | ||||||
\(777\) | −311.996 | − | 10.8821i | −0.401539 | − | 0.0140053i | ||||
\(778\) | −688.281 | −0.884680 | ||||||||
\(779\) | −55.6092 | + | 96.3180i | −0.0713854 | + | 0.123643i | ||||
\(780\) | 325.900 | − | 188.159i | 0.417821 | − | 0.241229i | ||||
\(781\) | −111.631 | − | 193.351i | −0.142934 | − | 0.247568i | ||||
\(782\) | −2483.76 | − | 1434.00i | −3.17616 | − | 1.83376i | ||||
\(783\) | − | 127.256i | − | 0.162524i | ||||||
\(784\) | 571.933 | − | 848.078i | 0.729506 | − | 1.08173i | ||||
\(785\) | −15.3544 | −0.0195598 | ||||||||
\(786\) | −334.088 | + | 578.657i | −0.425048 | + | 0.736204i | ||||
\(787\) | 936.494 | − | 540.685i | 1.18995 | − | 0.687020i | 0.231658 | − | 0.972797i | \(-0.425585\pi\) |
0.958296 | + | 0.285777i | \(0.0922517\pi\) | |||||||
\(788\) | 415.444 | + | 719.570i | 0.527213 | + | 0.913160i | ||||
\(789\) | 96.3693 | + | 55.6388i | 0.122141 | + | 0.0705182i | ||||
\(790\) | − | 216.820i | − | 0.274456i | ||||||
\(791\) | 1.80212 | − | 51.6679i | 0.00227828 | − | 0.0653198i | ||||
\(792\) | 120.348 | 0.151954 | ||||||||
\(793\) | 5.11357 | − | 8.85696i | 0.00644838 | − | 0.0111689i | ||||
\(794\) | 89.1928 | − | 51.4955i | 0.112333 | − | 0.0648558i | ||||
\(795\) | 77.5343 | + | 134.293i | 0.0975274 | + | 0.168922i | ||||
\(796\) | −572.527 | − | 330.549i | −0.719256 | − | 0.415262i | ||||
\(797\) | 145.723i | 0.182839i | 0.995812 | + | 0.0914195i | \(0.0291404\pi\) | ||||
−0.995812 | + | 0.0914195i | \(0.970860\pi\) | |||||||
\(798\) | 1084.82 | + | 677.805i | 1.35942 | + | 0.849380i | ||||
\(799\) | 78.4124 | 0.0981382 | ||||||||
\(800\) | −29.0617 | + | 50.3363i | −0.0363271 | + | 0.0629203i | ||||
\(801\) | −169.533 | + | 97.8796i | −0.211651 | + | 0.122197i | ||||
\(802\) | 371.040 | + | 642.659i | 0.462643 | + | 0.801321i | ||||
\(803\) | 138.315 | + | 79.8564i | 0.172248 | + | 0.0994476i | ||||
\(804\) | 945.749i | 1.17630i | ||||||||
\(805\) | 258.011 | + | 485.199i | 0.320510 | + | 0.602731i | ||||
\(806\) | −1526.35 | −1.89374 | ||||||||
\(807\) | 171.096 | − | 296.347i | 0.212015 | − | 0.367220i | ||||
\(808\) | 2008.73 | − | 1159.74i | 2.48605 | − | 1.43532i | ||||
\(809\) | 108.425 | + | 187.797i | 0.134023 | + | 0.232134i | 0.925224 | − | 0.379422i | \(-0.123877\pi\) |
−0.791201 | + | 0.611556i | \(0.790544\pi\) | |||||||
\(810\) | 61.3555 | + | 35.4236i | 0.0757475 | + | 0.0437329i | ||||
\(811\) | − | 8.20233i | − | 0.0101139i | −0.999987 | − | 0.00505693i | \(-0.998390\pi\) | ||
0.999987 | − | 0.00505693i | \(-0.00160968\pi\) | |||||||
\(812\) | 1270.45 | − | 675.581i | 1.56460 | − | 0.831996i | ||||
\(813\) | 266.967 | 0.328372 | ||||||||
\(814\) | 117.555 | − | 203.611i | 0.144416 | − | 0.250136i | ||||
\(815\) | −535.879 | + | 309.390i | −0.657520 | + | 0.379619i | ||||
\(816\) | −419.512 | − | 726.616i | −0.514108 | − | 0.890460i | ||||
\(817\) | 1926.36 | + | 1112.18i | 2.35784 | + | 1.36130i | ||||
\(818\) | − | 1142.33i | − | 1.39650i | ||||||
\(819\) | 128.816 | − | 206.168i | 0.157285 | − | 0.251731i | ||||
\(820\) | −69.6514 | −0.0849408 | ||||||||
\(821\) | −786.474 | + | 1362.21i | −0.957946 | + | 1.65921i | −0.230469 | + | 0.973080i | \(0.574026\pi\) |
−0.727477 | + | 0.686132i | \(0.759307\pi\) | |||||||
\(822\) | −937.063 | + | 541.013i | −1.13998 | + | 0.658167i | ||||
\(823\) | −499.339 | − | 864.881i | −0.606731 | − | 1.05089i | −0.991775 | − | 0.127991i | \(-0.959147\pi\) |
0.385045 | − | 0.922898i | \(-0.374186\pi\) | |||||||
\(824\) | −1870.92 | − | 1080.18i | −2.27053 | − | 1.31089i | ||||
\(825\) | 22.4621i | 0.0272268i | ||||||||
\(826\) | 1214.81 | + | 42.3714i | 1.47072 | + | 0.0512970i | ||||
\(827\) | −1344.24 | −1.62544 | −0.812718 | − | 0.582658i | \(-0.802013\pi\) | ||||
−0.812718 | + | 0.582658i | \(0.802013\pi\) | |||||||
\(828\) | −442.019 | + | 765.599i | −0.533839 | + | 0.924637i | ||||
\(829\) | −1312.22 | + | 757.611i | −1.58290 | + | 0.913885i | −0.588462 | + | 0.808525i | \(0.700266\pi\) |
−0.994434 | + | 0.105360i | \(0.966400\pi\) | |||||||
\(830\) | 517.362 | + | 896.097i | 0.623328 | + | 1.07964i | ||||
\(831\) | 508.805 | + | 293.758i | 0.612280 | + | 0.353500i | ||||
\(832\) | − | 492.908i | − | 0.592437i | ||||||
\(833\) | −1021.91 | + | 498.523i | −1.22678 | + | 0.598467i | ||||
\(834\) | 1035.94 | 1.24213 | ||||||||
\(835\) | −47.3821 | + | 82.0682i | −0.0567451 | + | 0.0982853i | ||||
\(836\) | −565.014 | + | 326.211i | −0.675855 | + | 0.390205i | ||||
\(837\) | −97.3065 | − | 168.540i | −0.116256 | − | 0.201362i | ||||
\(838\) | −2115.72 | − | 1221.51i | −2.52473 | − | 1.45765i | ||||
\(839\) | 439.769i | 0.524159i | 0.965046 | + | 0.262079i | \(0.0844082\pi\) | ||||
−0.965046 | + | 0.262079i | \(0.915592\pi\) | |||||||
\(840\) | −14.6164 | + | 419.061i | −0.0174005 | + | 0.498882i | ||||
\(841\) | −241.217 | −0.286821 | ||||||||
\(842\) | −601.208 | + | 1041.32i | −0.714024 | + | 1.23673i | ||||
\(843\) | 167.964 | − | 96.9743i | 0.199246 | − | 0.115035i | ||||
\(844\) | 449.650 | + | 778.817i | 0.532761 | + | 0.922769i | ||||
\(845\) | −67.7562 | − | 39.1191i | −0.0801849 | − | 0.0462948i | ||||
\(846\) | − | 35.6886i | − | 0.0421851i | ||||||
\(847\) | −678.379 | − | 423.859i | −0.800920 | − | 0.500424i | ||||
\(848\) | −835.833 | −0.985652 | ||||||||
\(849\) | 56.6453 | − | 98.1126i | 0.0667201 | − | 0.115563i | ||||
\(850\) | 353.727 | − | 204.224i | 0.416150 | − | 0.240264i | ||||
\(851\) | 451.997 | + | 782.881i | 0.531136 | + | 0.919955i | ||||
\(852\) | 1083.74 | + | 625.697i | 1.27199 | + | 0.734386i | ||||
\(853\) | 222.026i | 0.260288i | 0.991495 | + | 0.130144i | \(0.0415439\pi\) | ||||
−0.991495 | + | 0.130144i | \(0.958456\pi\) | |||||||
\(854\) | 10.2216 | + | 19.2222i | 0.0119691 | + | 0.0225084i | ||||
\(855\) | −201.037 | −0.235131 | ||||||||
\(856\) | −1401.59 | + | 2427.62i | −1.63737 | + | 2.83601i | ||||
\(857\) | −902.699 | + | 521.173i | −1.05332 | + | 0.608137i | −0.923578 | − | 0.383410i | \(-0.874750\pi\) |
−0.129746 | + | 0.991547i | \(0.541416\pi\) | |||||||
\(858\) | 91.5411 | + | 158.554i | 0.106691 | + | 0.184795i | ||||
\(859\) | 132.904 | + | 76.7321i | 0.154719 | + | 0.0893272i | 0.575361 | − | 0.817900i | \(-0.304862\pi\) |
−0.420642 | + | 0.907227i | \(0.638195\pi\) | |||||||
\(860\) | 1393.03i | 1.61980i | ||||||||
\(861\) | −39.7274 | + | 21.1256i | −0.0461410 | + | 0.0245361i | ||||
\(862\) | 1448.49 | 1.68038 | ||||||||
\(863\) | 401.493 | − | 695.406i | 0.465229 | − | 0.805800i | −0.533983 | − | 0.845495i | \(-0.679305\pi\) |
0.999212 | + | 0.0396949i | \(0.0126386\pi\) | |||||||
\(864\) | −52.3110 | + | 30.2018i | −0.0605451 | + | 0.0349557i | ||||
\(865\) | −33.0493 | − | 57.2431i | −0.0382073 | − | 0.0661770i | ||||
\(866\) | −1352.01 | − | 780.582i | −1.56121 | − | 0.901365i | ||||
\(867\) | 432.059i | 0.498338i | ||||||||
\(868\) | 1166.02 | − | 1866.20i | 1.34334 | − | 2.15000i | ||||
\(869\) | 71.4397 | 0.0822091 | ||||||||
\(870\) | −166.958 | + | 289.180i | −0.191906 | + | 0.332391i | ||||
\(871\) | −652.195 | + | 376.545i | −0.748789 | + | 0.432313i | ||||
\(872\) | −570.797 | − | 988.649i | −0.654583 | − | 1.13377i | ||||
\(873\) | 109.736 | + | 63.3562i | 0.125700 | + | 0.0725730i | ||||
\(874\) | − | 3704.05i | − | 4.23804i | ||||||
\(875\) | −78.2148 | − | 2.72805i | −0.0893884 | − | 0.00311777i | ||||
\(876\) | −895.197 | −1.02191 | ||||||||
\(877\) | 672.328 | − | 1164.51i | 0.766622 | − | 1.32783i | −0.172763 | − | 0.984963i | \(-0.555269\pi\) |
0.939385 | − | 0.342865i | \(-0.111397\pi\) | |||||||
\(878\) | −943.483 | + | 544.720i | −1.07458 | + | 0.620410i | ||||
\(879\) | 87.4613 | + | 151.487i | 0.0995009 | + | 0.172341i | ||||
\(880\) | −104.852 | − | 60.5364i | −0.119150 | − | 0.0687913i | ||||
\(881\) | − | 1052.91i | − | 1.19513i | −0.801822 | − | 0.597563i | \(-0.796136\pi\) | ||
0.801822 | − | 0.597563i | \(-0.203864\pi\) | |||||||
\(882\) | 226.897 | + | 465.110i | 0.257253 | + | 0.527335i | ||||
\(883\) | 1372.84 | 1.55475 | 0.777375 | − | 0.629037i | \(-0.216551\pi\) | ||||
0.777375 | + | 0.629037i | \(0.216551\pi\) | |||||||
\(884\) | 1127.33 | − | 1952.59i | 1.27526 | − | 2.20881i | ||||
\(885\) | −165.446 | + | 95.5202i | −0.186945 | + | 0.107932i | ||||
\(886\) | 1441.02 | + | 2495.92i | 1.62643 | + | 2.81706i | ||||
\(887\) | −544.825 | − | 314.555i | −0.614233 | − | 0.354628i | 0.160387 | − | 0.987054i | \(-0.448726\pi\) |
−0.774620 | + | 0.632427i | \(0.782059\pi\) | |||||||
\(888\) | 689.782i | 0.776782i | ||||||||
\(889\) | −50.9090 | + | 1459.59i | −0.0572654 | + | 1.64183i | ||||
\(890\) | 513.667 | 0.577154 | ||||||||
\(891\) | −11.6717 | + | 20.2159i | −0.0130995 | + | 0.0226890i | ||||
\(892\) | −63.3864 | + | 36.5962i | −0.0710610 | + | 0.0410271i | ||||
\(893\) | 50.6352 | + | 87.7028i | 0.0567024 | + | 0.0982114i | ||||
\(894\) | −450.891 | − | 260.322i | −0.504352 | − | 0.291188i | ||||
\(895\) | − | 332.462i | − | 0.371466i | ||||||
\(896\) | 1165.90 | + | 728.466i | 1.30122 | + | 0.813020i | ||||
\(897\) | −703.950 | −0.784783 | ||||||||
\(898\) | 555.798 | − | 962.671i | 0.618929 | − | 1.07202i | ||||
\(899\) | 794.361 | − | 458.624i | 0.883605 | − | 0.510150i | ||||
\(900\) | −62.9506 | − | 109.034i | −0.0699451 | − | 0.121148i | ||||
\(901\) | 804.602 | + | 464.537i | 0.893010 | + | 0.515580i | ||||
\(902\) | − | 33.8862i | − | 0.0375678i | ||||||
\(903\) | 422.511 | + | 794.547i | 0.467897 | + | 0.879897i | ||||
\(904\) | −114.231 | −0.126362 | ||||||||
\(905\) | 287.673 | − | 498.264i | 0.317870 | − | 0.550568i | ||||
\(906\) | −728.704 | + | 420.717i | −0.804309 | + | 0.464368i | ||||
\(907\) | 29.8954 | + | 51.7804i | 0.0329608 | + | 0.0570897i | 0.882035 | − | 0.471183i | \(-0.156173\pi\) |
−0.849074 | + | 0.528273i | \(0.822840\pi\) | |||||||
\(908\) | 1839.19 | + | 1061.86i | 2.02554 | + | 1.16944i | ||||
\(909\) | 449.898i | 0.494938i | ||||||||
\(910\) | −563.214 | + | 299.497i | −0.618917 | + | 0.329117i | ||||
\(911\) | −850.964 | −0.934099 | −0.467050 | − | 0.884231i | \(-0.654683\pi\) | ||||
−0.467050 | + | 0.884231i | \(0.654683\pi\) | |||||||
\(912\) | 541.804 | − | 938.432i | 0.594083 | − | 1.02898i | ||||
\(913\) | −295.253 | + | 170.465i | −0.323388 | + | 0.186708i | ||||
\(914\) | −329.700 | − | 571.057i | −0.360722 | − | 0.624788i | ||||
\(915\) | −2.96319 | − | 1.71080i | −0.00323846 | − | 0.00186973i | ||||
\(916\) | − | 1221.06i | − | 1.33304i | ||||||
\(917\) | 406.455 | − | 650.525i | 0.443245 | − | 0.709406i | ||||
\(918\) | 424.473 | 0.462389 | ||||||||
\(919\) | −330.505 | + | 572.452i | −0.359636 | + | 0.622908i | −0.987900 | − | 0.155093i | \(-0.950432\pi\) |
0.628264 | + | 0.778000i | \(0.283766\pi\) | |||||||
\(920\) | 1051.54 | − | 607.105i | 1.14297 | − | 0.659896i | ||||
\(921\) | −346.746 | − | 600.582i | −0.376489 | − | 0.652098i | ||||
\(922\) | −25.2317 | − | 14.5675i | −0.0273662 | − | 0.0157999i | ||||
\(923\) | 996.472i | 1.07960i | ||||||||
\(924\) | −263.787 | − | 9.20061i | −0.285484 | − | 0.00995737i | ||||
\(925\) | −128.743 | −0.139182 | ||||||||
\(926\) | −832.448 | + | 1441.84i | −0.898972 | + | 1.55707i | ||||
\(927\) | 362.893 | − | 209.517i | 0.391471 | − | 0.226016i | ||||
\(928\) | −142.347 | − | 246.552i | −0.153391 | − | 0.265681i | ||||
\(929\) | −231.638 | − | 133.736i | −0.249341 | − | 0.143957i | 0.370122 | − | 0.928983i | \(-0.379316\pi\) |
−0.619462 | + | 0.785026i | \(0.712649\pi\) | |||||||
\(930\) | 510.659i | 0.549096i | ||||||||
\(931\) | −1217.49 | − | 821.059i | −1.30772 | − | 0.881911i | ||||
\(932\) | 2161.43 | 2.31914 | ||||||||
\(933\) | 31.1758 | − | 53.9980i | 0.0334145 | − | 0.0578757i | ||||
\(934\) | −2185.71 | + | 1261.92i | −2.34016 | + | 1.35109i | ||||
\(935\) | 67.2895 | + | 116.549i | 0.0719674 | + | 0.124651i | ||||
\(936\) | −465.178 | − | 268.571i | −0.496985 | − | 0.286934i | ||||
\(937\) | 1625.83i | 1.73515i | 0.497309 | + | 0.867573i | \(0.334321\pi\) | ||||
−0.497309 | + | 0.867573i | \(0.665679\pi\) | |||||||
\(938\) | 55.8817 | − | 1602.16i | 0.0595754 | − | 1.70806i | ||||
\(939\) | 198.312 | 0.211194 | ||||||||
\(940\) | −31.7107 | + | 54.9245i | −0.0337348 | + | 0.0584304i | ||||
\(941\) | −257.993 | + | 148.952i | −0.274168 | + | 0.158291i | −0.630780 | − | 0.775961i | \(-0.717265\pi\) |
0.356612 | + | 0.934253i | \(0.383932\pi\) | |||||||
\(942\) | 20.9351 | + | 36.2606i | 0.0222241 | + | 0.0384932i | ||||
\(943\) | 112.836 | + | 65.1460i | 0.119657 | + | 0.0690838i | ||||
\(944\) | − | 1029.72i | − | 1.09081i | ||||||
\(945\) | −68.9758 | − | 43.0969i | −0.0729903 | − | 0.0456051i | ||||
\(946\) | −677.722 | −0.716408 | ||||||||
\(947\) | 456.876 | − | 791.333i | 0.482446 | − | 0.835621i | −0.517351 | − | 0.855773i | \(-0.673082\pi\) |
0.999797 | + | 0.0201524i | \(0.00641516\pi\) | |||||||
\(948\) | −346.776 | + | 200.211i | −0.365798 | + | 0.211193i | ||||
\(949\) | −356.418 | − | 617.334i | −0.375572 | − | 0.650510i | ||||
\(950\) | 456.842 | + | 263.758i | 0.480887 | + | 0.277640i | ||||
\(951\) | − | 6.98391i | − | 0.00734375i | ||||||
\(952\) | 1179.54 | + | 2218.16i | 1.23901 | + | 2.33000i | ||||
\(953\) | −1451.89 | −1.52349 | −0.761746 | − | 0.647875i | \(-0.775658\pi\) | ||||
−0.761746 | + | 0.647875i | \(0.775658\pi\) | |||||||
\(954\) | 211.429 | − | 366.206i | 0.221624 | − | 0.383864i | ||||
\(955\) | 235.486 | − | 135.958i | 0.246582 | − | 0.142364i | ||||
\(956\) | 540.040 | + | 935.377i | 0.564896 | + | 0.978428i | ||||
\(957\) | −95.2815 | − | 55.0108i | −0.0995627 | − | 0.0574826i | ||||
\(958\) | − | 724.878i | − | 0.756657i | ||||||
\(959\) | 1096.74 | − | 583.208i | 1.14363 | − | 0.608142i | ||||
\(960\) | −164.908 | −0.171779 | ||||||||
\(961\) | 220.874 | − | 382.566i | 0.229838 | − | 0.398091i | ||||
\(962\) | −908.762 | + | 524.674i | −0.944659 | + | 0.545399i | ||||
\(963\) | −271.859 | − | 470.874i | −0.282305 | − | 0.488966i | ||||
\(964\) | 67.3342 | + | 38.8754i | 0.0698487 | + | 0.0403272i | ||||
\(965\) | 542.319i | 0.561989i | ||||||||
\(966\) | 794.047 | − | 1270.86i | 0.821994 | − | 1.31559i | ||||
\(967\) | 235.985 | 0.244039 | 0.122019 | − | 0.992528i | \(-0.461063\pi\) | ||||
0.122019 | + | 0.992528i | \(0.461063\pi\) | |||||||
\(968\) | −883.710 | + | 1530.63i | −0.912924 | + | 1.58123i | ||||
\(969\) | −1043.12 | + | 602.245i | −1.07649 | + | 0.621512i | ||||
\(970\) | −166.245 | − | 287.945i | −0.171387 | − | 0.296850i | ||||
\(971\) | −555.872 | − | 320.933i | −0.572474 | − | 0.330518i | 0.185663 | − | 0.982613i | \(-0.440557\pi\) |
−0.758137 | + | 0.652096i | \(0.773890\pi\) | |||||||
\(972\) | − | 130.840i | − | 0.134609i | ||||||
\(973\) | −1188.53 | − | 41.4548i | −1.22151 | − | 0.0426051i | ||||
\(974\) | −1136.67 | −1.16701 | ||||||||
\(975\) | 50.1269 | − | 86.8223i | 0.0514122 | − | 0.0890485i | ||||
\(976\) | 15.9719 | − | 9.22136i | 0.0163646 | − | 0.00944812i | ||||
\(977\) | −320.423 | − | 554.990i | −0.327967 | − | 0.568055i | 0.654142 | − | 0.756372i | \(-0.273030\pi\) |
−0.982108 | + | 0.188317i | \(0.939697\pi\) | |||||||
\(978\) | 1461.29 | + | 843.678i | 1.49417 | + | 0.862657i | ||||
\(979\) | 169.247i | 0.172878i | ||||||||
\(980\) | 64.0744 | − | 917.409i | 0.0653821 | − | 0.936131i | ||||
\(981\) | 221.429 | 0.225718 | ||||||||
\(982\) | 479.446 | − | 830.425i | 0.488235 | − | 0.845647i | ||||
\(983\) | −368.692 | + | 212.865i | −0.375068 | + | 0.216546i | −0.675670 | − | 0.737204i | \(-0.736146\pi\) |
0.300602 | + | 0.953750i | \(0.402812\pi\) | |||||||
\(984\) | 49.7089 | + | 86.0984i | 0.0505172 | + | 0.0874984i | ||||
\(985\) | 191.699 | + | 110.677i | 0.194618 | + | 0.112363i | ||||
\(986\) | 2000.62i | 2.02903i | ||||||||
\(987\) | −1.42814 | + | 40.9456i | −0.00144695 | + | 0.0414849i | ||||
\(988\) | 2911.92 | 2.94728 | ||||||||
\(989\) | 1302.92 | − | 2256.72i | 1.31741 | − | 2.28182i | ||||
\(990\) | 53.0460 | − | 30.6261i | 0.0535818 | − | 0.0309355i | ||||
\(991\) | 548.625 | + | 950.247i | 0.553608 | + | 0.958877i | 0.998010 | + | 0.0630498i | \(0.0200827\pi\) |
−0.444402 | + | 0.895827i | \(0.646584\pi\) | |||||||
\(992\) | −377.052 | − | 217.691i | −0.380093 | − | 0.219447i | ||||
\(993\) | − | 878.813i | − | 0.885008i | ||||||
\(994\) | −1798.96 | − | 1124.01i | −1.80981 | − | 1.13079i | ||||
\(995\) | −176.121 | −0.177006 | ||||||||
\(996\) | 955.461 | − | 1654.91i | 0.959299 | − | 1.66155i | ||||
\(997\) | −1104.16 | + | 637.487i | −1.10748 | + | 0.639405i | −0.938176 | − | 0.346159i | \(-0.887486\pi\) |
−0.169306 | + | 0.985564i | \(0.554153\pi\) | |||||||
\(998\) | 931.496 | + | 1613.40i | 0.933362 | + | 1.61663i | ||||
\(999\) | −115.869 | − | 66.8969i | −0.115985 | − | 0.0669639i |
(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 | 105.3.n.a.61.4 | yes | 8 | |
3.2 | odd | 2 | 315.3.w.a.271.1 | 8 | |||
5.2 | odd | 4 | 525.3.s.h.124.8 | 16 | |||
5.3 | odd | 4 | 525.3.s.h.124.1 | 16 | |||
5.4 | even | 2 | 525.3.o.l.376.1 | 8 | |||
7.2 | even | 3 | 735.3.h.a.391.1 | 8 | |||
7.3 | odd | 6 | inner | 105.3.n.a.31.4 | ✓ | 8 | |
7.5 | odd | 6 | 735.3.h.a.391.2 | 8 | |||
21.17 | even | 6 | 315.3.w.a.136.1 | 8 | |||
35.3 | even | 12 | 525.3.s.h.199.8 | 16 | |||
35.17 | even | 12 | 525.3.s.h.199.1 | 16 | |||
35.24 | odd | 6 | 525.3.o.l.451.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.n.a.31.4 | ✓ | 8 | 7.3 | odd | 6 | inner | |
105.3.n.a.61.4 | yes | 8 | 1.1 | even | 1 | trivial | |
315.3.w.a.136.1 | 8 | 21.17 | even | 6 | |||
315.3.w.a.271.1 | 8 | 3.2 | odd | 2 | |||
525.3.o.l.376.1 | 8 | 5.4 | even | 2 | |||
525.3.o.l.451.1 | 8 | 35.24 | odd | 6 | |||
525.3.s.h.124.1 | 16 | 5.3 | odd | 4 | |||
525.3.s.h.124.8 | 16 | 5.2 | odd | 4 | |||
525.3.s.h.199.1 | 16 | 35.17 | even | 12 | |||
525.3.s.h.199.8 | 16 | 35.3 | even | 12 | |||
735.3.h.a.391.1 | 8 | 7.2 | even | 3 | |||
735.3.h.a.391.2 | 8 | 7.5 | odd | 6 |