Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.100088711424.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.3 | ||
Root | \(-2.49541 - 1.44073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.165 |
Dual form | 637.2.h.j.471.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30278 | 1.62831 | 0.814154 | − | 0.580649i | \(-0.197201\pi\) | ||||
0.814154 | + | 0.580649i | \(0.197201\pi\) | |||||||
\(3\) | −1.08365 | − | 1.87694i | −0.625648 | − | 1.08365i | −0.988415 | − | 0.151774i | \(-0.951501\pi\) |
0.362767 | − | 0.931880i | \(-0.381832\pi\) | |||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | −1.08365 | − | 1.87694i | −0.484625 | − | 0.839395i | 0.515219 | − | 0.857058i | \(-0.327711\pi\) |
−0.999844 | + | 0.0176637i | \(0.994377\pi\) | |||||||
\(6\) | −2.49541 | − | 4.32218i | −1.01875 | − | 1.76452i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −0.848612 | + | 1.46984i | −0.282871 | + | 0.489946i | ||||
\(10\) | −2.49541 | − | 4.32218i | −0.789119 | − | 1.36679i | ||||
\(11\) | −2.45416 | − | 4.25074i | −0.739958 | − | 1.28165i | −0.952514 | − | 0.304496i | \(-0.901512\pi\) |
0.212555 | − | 0.977149i | \(-0.431821\pi\) | |||||||
\(12\) | −3.57907 | − | 6.19912i | −1.03319 | − | 1.78953i | ||||
\(13\) | −1.41176 | + | 3.31767i | −0.391551 | + | 0.920156i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34861 | + | 4.06792i | −0.606409 | + | 1.05033i | ||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | 7.15813 | 1.73610 | 0.868051 | − | 0.496475i | \(-0.165373\pi\) | ||||
0.868051 | + | 0.496475i | \(0.165373\pi\) | |||||||
\(18\) | −1.95416 | + | 3.38471i | −0.460601 | + | 0.797784i | ||||
\(19\) | −1.08365 | + | 1.87694i | −0.248607 | + | 0.430600i | −0.963140 | − | 0.269002i | \(-0.913306\pi\) |
0.714532 | + | 0.699602i | \(0.246640\pi\) | |||||||
\(20\) | −3.57907 | − | 6.19912i | −0.800304 | − | 1.38617i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.65139 | − | 9.78849i | −1.20488 | − | 2.08691i | ||||
\(23\) | −0.605551 | −0.126266 | −0.0631331 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631331 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(24\) | −3.25096 | − | 5.63083i | −0.663600 | − | 1.14939i | ||||
\(25\) | 0.151388 | − | 0.262211i | 0.0302776 | − | 0.0524423i | ||||
\(26\) | −3.25096 | + | 7.63985i | −0.637566 | + | 1.49830i | ||||
\(27\) | −2.82352 | −0.543386 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15139 | − | 1.99426i | 0.213807 | − | 0.370325i | −0.739096 | − | 0.673601i | \(-0.764747\pi\) |
0.952903 | + | 0.303275i | \(0.0980802\pi\) | |||||||
\(30\) | −5.40833 | + | 9.36750i | −0.987421 | + | 1.71026i | ||||
\(31\) | 3.57907 | − | 6.19912i | 0.642819 | − | 1.11340i | −0.341981 | − | 0.939707i | \(-0.611098\pi\) |
0.984801 | − | 0.173689i | \(-0.0555687\pi\) | |||||||
\(32\) | −5.30278 | −0.937407 | ||||||||
\(33\) | −5.31893 | + | 9.21265i | −0.925907 | + | 1.60372i | ||||
\(34\) | 16.4836 | 2.82691 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.80278 | + | 4.85455i | −0.467129 | + | 0.809092i | ||||
\(37\) | 8.60555 | 1.41474 | 0.707372 | − | 0.706842i | \(-0.249881\pi\) | ||||
0.707372 | + | 0.706842i | \(0.249881\pi\) | |||||||
\(38\) | −2.49541 | + | 4.32218i | −0.404809 | + | 0.701150i | ||||
\(39\) | 7.75694 | − | 0.945417i | 1.24210 | − | 0.151388i | ||||
\(40\) | −3.25096 | − | 5.63083i | −0.514022 | − | 0.890313i | ||||
\(41\) | 4.99082 | − | 8.64436i | 0.779436 | − | 1.35002i | −0.152832 | − | 0.988252i | \(-0.548839\pi\) |
0.932267 | − | 0.361770i | \(-0.117827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.25694 | + | 10.8373i | 0.954174 | + | 1.65268i | 0.736247 | + | 0.676713i | \(0.236596\pi\) |
0.217928 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(44\) | −8.10555 | − | 14.0392i | −1.22196 | − | 2.11649i | ||||
\(45\) | 3.67841 | 0.548345 | ||||||||
\(46\) | −1.39445 | −0.205600 | ||||||||
\(47\) | 0.755550 | + | 1.30865i | 0.110208 | + | 0.190886i | 0.915854 | − | 0.401511i | \(-0.131515\pi\) |
−0.805646 | + | 0.592397i | \(0.798182\pi\) | |||||||
\(48\) | −0.328104 | − | 0.568293i | −0.0473577 | − | 0.0820260i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.348612 | − | 0.603814i | 0.0493012 | − | 0.0853922i | ||||
\(51\) | −7.75694 | − | 13.4354i | −1.08619 | − | 1.88133i | ||||
\(52\) | −4.66272 | + | 10.9575i | −0.646603 | + | 1.51953i | ||||
\(53\) | −1.19722 | + | 2.07365i | −0.164451 | + | 0.284838i | −0.936460 | − | 0.350773i | \(-0.885919\pi\) |
0.772009 | + | 0.635612i | \(0.219252\pi\) | |||||||
\(54\) | −6.50192 | −0.884800 | ||||||||
\(55\) | −5.31893 | + | 9.21265i | −0.717204 | + | 1.24223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.69722 | 0.622163 | ||||||||
\(58\) | 2.65139 | − | 4.59234i | 0.348144 | − | 0.603004i | ||||
\(59\) | −2.82352 | −0.367590 | −0.183795 | − | 0.982965i | \(-0.558838\pi\) | ||||
−0.183795 | + | 0.982965i | \(0.558838\pi\) | |||||||
\(60\) | −7.75694 | + | 13.4354i | −1.00142 | + | 1.73450i | ||||
\(61\) | −2.16731 | + | 3.75389i | −0.277495 | + | 0.480636i | −0.970762 | − | 0.240045i | \(-0.922838\pi\) |
0.693266 | + | 0.720682i | \(0.256171\pi\) | |||||||
\(62\) | 8.24179 | − | 14.2752i | 1.04671 | − | 1.81295i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | 7.75694 | − | 0.945417i | 0.962130 | − | 0.117265i | ||||
\(66\) | −12.2483 | + | 21.2147i | −1.50766 | + | 2.61135i | ||||
\(67\) | −0.500000 | − | 0.866025i | −0.0610847 | − | 0.105802i | 0.833866 | − | 0.551967i | \(-0.186123\pi\) |
−0.894951 | + | 0.446165i | \(0.852789\pi\) | |||||||
\(68\) | 23.6417 | 2.86698 | ||||||||
\(69\) | 0.656208 | + | 1.13659i | 0.0789982 | + | 0.136829i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | − | 3.46410i | −0.237356 | − | 0.411113i | 0.722599 | − | 0.691268i | \(-0.242948\pi\) |
−0.959955 | + | 0.280155i | \(0.909614\pi\) | |||||||
\(72\) | −2.54584 | + | 4.40952i | −0.300030 | + | 0.519667i | ||||
\(73\) | 2.16731 | − | 3.75389i | 0.253664 | − | 0.439359i | −0.710868 | − | 0.703326i | \(-0.751698\pi\) |
0.964532 | + | 0.263967i | \(0.0850308\pi\) | |||||||
\(74\) | 19.8167 | 2.30364 | ||||||||
\(75\) | −0.656208 | −0.0757724 | ||||||||
\(76\) | −3.57907 | + | 6.19912i | −0.410547 | + | 0.711088i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.8625 | − | 2.17708i | 2.02253 | − | 0.246506i | ||||
\(79\) | 3.30278 | + | 5.72058i | 0.371591 | + | 0.643615i | 0.989811 | − | 0.142391i | \(-0.0454789\pi\) |
−0.618219 | + | 0.786006i | \(0.712146\pi\) | |||||||
\(80\) | −0.328104 | − | 0.568293i | −0.0366831 | − | 0.0635371i | ||||
\(81\) | 5.60555 | + | 9.70910i | 0.622839 | + | 1.07879i | ||||
\(82\) | 11.4927 | − | 19.9060i | 1.26916 | − | 2.19825i | ||||
\(83\) | 2.82352 | 0.309921 | 0.154961 | − | 0.987921i | \(-0.450475\pi\) | ||||
0.154961 | + | 0.987921i | \(0.450475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.75694 | − | 13.4354i | −0.841358 | − | 1.45728i | ||||
\(86\) | 14.4083 | + | 24.9560i | 1.55369 | + | 2.69107i | ||||
\(87\) | −4.99082 | −0.535073 | ||||||||
\(88\) | −7.36249 | − | 12.7522i | −0.784844 | − | 1.35939i | ||||
\(89\) | 6.50192 | 0.689203 | 0.344601 | − | 0.938749i | \(-0.388014\pi\) | ||||
0.344601 | + | 0.938749i | \(0.388014\pi\) | |||||||
\(90\) | 8.47055 | 0.892874 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −15.5139 | −1.60871 | ||||||||
\(94\) | 1.73986 | + | 3.01353i | 0.179453 | + | 0.310822i | ||||
\(95\) | 4.69722 | 0.481925 | ||||||||
\(96\) | 5.74637 | + | 9.95301i | 0.586487 | + | 1.01583i | ||||
\(97\) | 6.83003 | + | 11.8300i | 0.693484 | + | 1.20115i | 0.970689 | + | 0.240339i | \(0.0772587\pi\) |
−0.277205 | + | 0.960811i | \(0.589408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.33053 | 0.837250 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 3.25096 | + | 5.63083i | 0.323483 | + | 0.560289i | 0.981204 | − | 0.192973i | \(-0.0618129\pi\) |
−0.657721 | + | 0.753261i | \(0.728480\pi\) | |||||||
\(102\) | −17.8625 | − | 30.9387i | −1.76865 | − | 3.06339i | ||||
\(103\) | −5.74637 | − | 9.95301i | −0.566207 | − | 0.980699i | −0.996936 | − | 0.0782182i | \(-0.975077\pi\) |
0.430729 | − | 0.902481i | \(-0.358256\pi\) | |||||||
\(104\) | −4.23527 | + | 9.95301i | −0.415303 | + | 0.975973i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.75694 | + | 4.77516i | −0.267778 | + | 0.463804i | ||||
\(107\) | 5.69722 | 0.550771 | 0.275386 | − | 0.961334i | \(-0.411194\pi\) | ||||
0.275386 | + | 0.961334i | \(0.411194\pi\) | |||||||
\(108\) | −9.32544 | −0.897341 | ||||||||
\(109\) | −4.10555 | + | 7.11102i | −0.393240 | + | 0.681113i | −0.992875 | − | 0.119162i | \(-0.961979\pi\) |
0.599634 | + | 0.800274i | \(0.295313\pi\) | |||||||
\(110\) | −12.2483 | + | 21.2147i | −1.16783 | + | 2.02274i | ||||
\(111\) | −9.32544 | − | 16.1521i | −0.885132 | − | 1.53309i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.40833 | − | 5.90340i | −0.320628 | − | 0.555345i | 0.659989 | − | 0.751275i | \(-0.270561\pi\) |
−0.980618 | + | 0.195930i | \(0.937227\pi\) | |||||||
\(114\) | 10.8167 | 1.01307 | ||||||||
\(115\) | 0.656208 | + | 1.13659i | 0.0611917 | + | 0.105987i | ||||
\(116\) | 3.80278 | − | 6.58660i | 0.353079 | − | 0.611551i | ||||
\(117\) | −3.67841 | − | 4.89047i | −0.340069 | − | 0.452124i | ||||
\(118\) | −6.50192 | −0.598551 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.04584 | + | 12.2037i | −0.643194 | + | 1.11404i | ||||
\(121\) | −6.54584 | + | 11.3377i | −0.595076 | + | 1.03070i | ||||
\(122\) | −4.99082 | + | 8.64436i | −0.451848 | + | 0.782624i | ||||
\(123\) | −21.6333 | −1.95061 | ||||||||
\(124\) | 11.8209 | − | 20.4743i | 1.06154 | − | 1.83865i | ||||
\(125\) | −11.4927 | −1.02794 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.95416 | + | 6.84881i | −0.350875 | + | 0.607734i | −0.986403 | − | 0.164344i | \(-0.947449\pi\) |
0.635528 | + | 0.772078i | \(0.280783\pi\) | |||||||
\(128\) | −18.9083 | −1.67128 | ||||||||
\(129\) | 13.5607 | − | 23.4878i | 1.19395 | − | 2.06799i | ||||
\(130\) | 17.8625 | − | 2.17708i | 1.56664 | − | 0.190943i | ||||
\(131\) | 5.31893 | + | 9.21265i | 0.464717 | + | 0.804913i | 0.999189 | − | 0.0402730i | \(-0.0128228\pi\) |
−0.534472 | + | 0.845186i | \(0.679489\pi\) | |||||||
\(132\) | −17.5672 | + | 30.4273i | −1.52903 | + | 2.64836i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.15139 | − | 1.99426i | −0.0994648 | − | 0.172278i | ||||
\(135\) | 3.05971 | + | 5.29958i | 0.263338 | + | 0.456115i | ||||
\(136\) | 21.4744 | 1.84141 | ||||||||
\(137\) | 6.30278 | 0.538482 | 0.269241 | − | 0.963073i | \(-0.413227\pi\) | ||||
0.269241 | + | 0.963073i | \(0.413227\pi\) | |||||||
\(138\) | 1.51110 | + | 2.61730i | 0.128633 | + | 0.222800i | ||||
\(139\) | 5.31893 | + | 9.21265i | 0.451146 | + | 0.781407i | 0.998457 | − | 0.0555216i | \(-0.0176822\pi\) |
−0.547312 | + | 0.836929i | \(0.684349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.63751 | − | 2.83625i | 0.137903 | − | 0.238855i | ||||
\(142\) | −4.60555 | − | 7.97705i | −0.386489 | − | 0.669419i | ||||
\(143\) | 17.5672 | − | 2.14110i | 1.46905 | − | 0.179047i | ||||
\(144\) | −0.256939 | + | 0.445032i | −0.0214116 | + | 0.0370860i | ||||
\(145\) | −4.99082 | −0.414465 | ||||||||
\(146\) | 4.99082 | − | 8.64436i | 0.413044 | − | 0.715412i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.4222 | 2.33629 | ||||||||
\(149\) | 8.75694 | − | 15.1675i | 0.717396 | − | 1.24257i | −0.244632 | − | 0.969616i | \(-0.578667\pi\) |
0.962028 | − | 0.272951i | \(-0.0879997\pi\) | |||||||
\(150\) | −1.51110 | −0.123381 | ||||||||
\(151\) | −4.10555 | + | 7.11102i | −0.334105 | + | 0.578687i | −0.983313 | − | 0.181924i | \(-0.941767\pi\) |
0.649207 | + | 0.760611i | \(0.275101\pi\) | |||||||
\(152\) | −3.25096 | + | 5.63083i | −0.263688 | + | 0.456721i | ||||
\(153\) | −6.07448 | + | 10.5213i | −0.491092 | + | 0.850597i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5139 | −1.24610 | ||||||||
\(156\) | 25.6194 | − | 3.12250i | 2.05120 | − | 0.250000i | ||||
\(157\) | 0.328104 | − | 0.568293i | 0.0261856 | − | 0.0453547i | −0.852636 | − | 0.522506i | \(-0.824997\pi\) |
0.878821 | + | 0.477151i | \(0.158331\pi\) | |||||||
\(158\) | 7.60555 | + | 13.1732i | 0.605065 | + | 1.04800i | ||||
\(159\) | 5.18951 | 0.411555 | ||||||||
\(160\) | 5.74637 | + | 9.95301i | 0.454291 | + | 0.786855i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.9083 | + | 22.3579i | 1.01417 | + | 1.75660i | ||||
\(163\) | 1.39445 | − | 2.41526i | 0.109222 | − | 0.189177i | −0.806234 | − | 0.591597i | \(-0.798498\pi\) |
0.915455 | + | 0.402420i | \(0.131831\pi\) | |||||||
\(164\) | 16.4836 | − | 28.5504i | 1.28715 | − | 2.22941i | ||||
\(165\) | 23.0555 | 1.79487 | ||||||||
\(166\) | 6.50192 | 0.504647 | ||||||||
\(167\) | −5.74637 | + | 9.95301i | −0.444668 | + | 0.770187i | −0.998029 | − | 0.0627542i | \(-0.980012\pi\) |
0.553361 | + | 0.832941i | \(0.313345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.01388 | − | 9.36750i | −0.693375 | − | 0.720577i | ||||
\(170\) | −17.8625 | − | 30.9387i | −1.36999 | − | 2.37289i | ||||
\(171\) | −1.83920 | − | 3.18559i | −0.140647 | − | 0.243609i | ||||
\(172\) | 20.6653 | + | 35.7933i | 1.57571 | + | 2.72921i | ||||
\(173\) | −5.09017 | + | 8.81643i | −0.386998 | + | 0.670300i | −0.992044 | − | 0.125890i | \(-0.959821\pi\) |
0.605046 | + | 0.796190i | \(0.293155\pi\) | |||||||
\(174\) | −11.4927 | −0.871263 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.743061 | − | 1.28702i | −0.0560103 | − | 0.0970127i | ||||
\(177\) | 3.05971 | + | 5.29958i | 0.229982 | + | 0.398341i | ||||
\(178\) | 14.9725 | 1.12223 | ||||||||
\(179\) | −10.8028 | − | 18.7110i | −0.807437 | − | 1.39852i | −0.914633 | − | 0.404285i | \(-0.867521\pi\) |
0.107196 | − | 0.994238i | \(-0.465813\pi\) | |||||||
\(180\) | 12.1490 | 0.905530 | ||||||||
\(181\) | −24.2979 | −1.80605 | −0.903025 | − | 0.429588i | \(-0.858659\pi\) | ||||
−0.903025 | + | 0.429588i | \(0.858659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.39445 | 0.694458 | ||||||||
\(184\) | −1.81665 | −0.133925 | ||||||||
\(185\) | −9.32544 | − | 16.1521i | −0.685620 | − | 1.18753i | ||||
\(186\) | −35.7250 | −2.61948 | ||||||||
\(187\) | −17.5672 | − | 30.4273i | −1.28464 | − | 2.22507i | ||||
\(188\) | 2.49541 | + | 4.32218i | 0.181997 | + | 0.315227i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8167 | 0.784723 | ||||||||
\(191\) | −7.84861 | + | 13.5942i | −0.567906 | + | 0.983641i | 0.428867 | + | 0.903368i | \(0.358913\pi\) |
−0.996773 | + | 0.0802739i | \(0.974421\pi\) | |||||||
\(192\) | 13.8888 | + | 24.0561i | 1.00234 | + | 1.73610i | ||||
\(193\) | −9.90833 | − | 17.1617i | −0.713217 | − | 1.23533i | −0.963643 | − | 0.267192i | \(-0.913904\pi\) |
0.250426 | − | 0.968136i | \(-0.419429\pi\) | |||||||
\(194\) | 15.7280 | + | 27.2417i | 1.12921 | + | 1.95584i | ||||
\(195\) | −10.1803 | − | 13.5348i | −0.729029 | − | 0.969250i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.545837 | − | 0.945417i | 0.0388892 | − | 0.0673581i | −0.845926 | − | 0.533301i | \(-0.820951\pi\) |
0.884815 | + | 0.465943i | \(0.154285\pi\) | |||||||
\(198\) | 19.1833 | 1.36330 | ||||||||
\(199\) | −7.15813 | −0.507427 | −0.253713 | − | 0.967279i | \(-0.581652\pi\) | ||||
−0.253713 | + | 0.967279i | \(0.581652\pi\) | |||||||
\(200\) | 0.454163 | − | 0.786634i | 0.0321142 | − | 0.0556234i | ||||
\(201\) | −1.08365 | + | 1.87694i | −0.0764351 | + | 0.132389i | ||||
\(202\) | 7.48624 | + | 12.9665i | 0.526730 | + | 0.912323i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −25.6194 | − | 44.3742i | −1.79372 | − | 3.10681i | ||||
\(205\) | −21.6333 | −1.51094 | ||||||||
\(206\) | −13.2326 | − | 22.9196i | −0.921960 | − | 1.59688i | ||||
\(207\) | 0.513878 | − | 0.890063i | 0.0357170 | − | 0.0618637i | ||||
\(208\) | −0.427446 | + | 1.00451i | −0.0296380 | + | 0.0696502i | ||||
\(209\) | 10.6379 | 0.735836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | + | 12.9904i | −0.516321 | + | 0.894295i | 0.483499 | + | 0.875345i | \(0.339366\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(212\) | −3.95416 | + | 6.84881i | −0.271573 | + | 0.470378i | ||||
\(213\) | −4.33462 | + | 7.50778i | −0.297003 | + | 0.514424i | ||||
\(214\) | 13.1194 | 0.896826 | ||||||||
\(215\) | 13.5607 | − | 23.4878i | 0.924833 | − | 1.60186i | ||||
\(216\) | −8.47055 | −0.576348 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.45416 | + | 16.3751i | −0.640317 | + | 1.10906i | ||||
\(219\) | −9.39445 | −0.634818 | ||||||||
\(220\) | −17.5672 | + | 30.4273i | −1.18438 | + | 2.05141i | ||||
\(221\) | −10.1056 | + | 23.7483i | −0.679773 | + | 1.59749i | ||||
\(222\) | −21.4744 | − | 37.1947i | −1.44127 | − | 2.49635i | ||||
\(223\) | 8.99734 | − | 15.5838i | 0.602506 | − | 1.04357i | −0.389934 | − | 0.920843i | \(-0.627502\pi\) |
0.992440 | − | 0.122729i | \(-0.0391645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.256939 | + | 0.445032i | 0.0171293 | + | 0.0296688i | ||||
\(226\) | −7.84861 | − | 13.5942i | −0.522082 | − | 0.904272i | ||||
\(227\) | −18.4522 | −1.22472 | −0.612358 | − | 0.790581i | \(-0.709779\pi\) | ||||
−0.612358 | + | 0.790581i | \(0.709779\pi\) | |||||||
\(228\) | 15.5139 | 1.02743 | ||||||||
\(229\) | 7.81434 | + | 13.5348i | 0.516386 | + | 0.894407i | 0.999819 | + | 0.0190256i | \(0.00605640\pi\) |
−0.483433 | + | 0.875381i | \(0.660610\pi\) | |||||||
\(230\) | 1.51110 | + | 2.61730i | 0.0996390 | + | 0.172580i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.45416 | − | 5.98279i | 0.226777 | − | 0.392789i | ||||
\(233\) | 6.54584 | + | 11.3377i | 0.428832 | + | 0.742759i | 0.996770 | − | 0.0803127i | \(-0.0255919\pi\) |
−0.567938 | + | 0.823072i | \(0.692259\pi\) | |||||||
\(234\) | −8.47055 | − | 11.2617i | −0.553737 | − | 0.736198i | ||||
\(235\) | 1.63751 | − | 2.83625i | 0.106819 | − | 0.185017i | ||||
\(236\) | −9.32544 | −0.607034 | ||||||||
\(237\) | 7.15813 | − | 12.3982i | 0.464971 | − | 0.805353i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.39445 | 0.284253 | 0.142127 | − | 0.989848i | \(-0.454606\pi\) | ||||
0.142127 | + | 0.989848i | \(0.454606\pi\) | |||||||
\(240\) | −0.711103 | + | 1.23167i | −0.0459015 | + | 0.0795037i | ||||
\(241\) | −9.32544 | −0.600704 | −0.300352 | − | 0.953828i | \(-0.597104\pi\) | ||||
−0.300352 | + | 0.953828i | \(0.597104\pi\) | |||||||
\(242\) | −15.0736 | + | 26.1082i | −0.968967 | + | 1.67830i | ||||
\(243\) | 7.91368 | − | 13.7069i | 0.507663 | − | 0.879298i | ||||
\(244\) | −7.15813 | + | 12.3982i | −0.458252 | + | 0.793717i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −49.8167 | −3.17619 | ||||||||
\(247\) | −4.69722 | − | 6.24500i | −0.298877 | − | 0.397360i | ||||
\(248\) | 10.7372 | − | 18.5974i | 0.681813 | − | 1.18093i | ||||
\(249\) | −3.05971 | − | 5.29958i | −0.193902 | − | 0.335847i | ||||
\(250\) | −26.4652 | −1.67381 | ||||||||
\(251\) | −14.9725 | − | 25.9331i | −0.945054 | − | 1.63688i | −0.755643 | − | 0.654984i | \(-0.772675\pi\) |
−0.189411 | − | 0.981898i | \(-0.560658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.48612 | + | 2.57404i | 0.0934317 | + | 0.161828i | ||||
\(254\) | −9.10555 | + | 15.7713i | −0.571333 | + | 0.989578i | ||||
\(255\) | −16.8117 | + | 29.1187i | −1.05279 | + | 1.82348i | ||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | 6.30324 | 0.393185 | 0.196593 | − | 0.980485i | \(-0.437012\pi\) | ||||
0.196593 | + | 0.980485i | \(0.437012\pi\) | |||||||
\(258\) | 31.2273 | − | 54.0872i | 1.94413 | − | 3.36732i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 25.6194 | − | 3.12250i | 1.58885 | − | 0.193649i | ||||
\(261\) | 1.95416 | + | 3.38471i | 0.120960 | + | 0.209508i | ||||
\(262\) | 12.2483 | + | 21.2147i | 0.756702 | + | 1.31065i | ||||
\(263\) | −7.71110 | − | 13.3560i | −0.475487 | − | 0.823568i | 0.524119 | − | 0.851645i | \(-0.324395\pi\) |
−0.999606 | + | 0.0280776i | \(0.991061\pi\) | |||||||
\(264\) | −15.9568 | + | 27.6380i | −0.982072 | + | 1.70100i | ||||
\(265\) | 5.18951 | 0.318789 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.04584 | − | 12.2037i | −0.431198 | − | 0.746857i | ||||
\(268\) | −1.65139 | − | 2.86029i | −0.100875 | − | 0.174720i | ||||
\(269\) | −0.656208 | −0.0400097 | −0.0200049 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200049 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(270\) | 7.04584 | + | 12.2037i | 0.428796 | + | 0.742696i | ||||
\(271\) | 14.5149 | 0.881720 | 0.440860 | − | 0.897576i | \(-0.354673\pi\) | ||||
0.440860 | + | 0.897576i | \(0.354673\pi\) | |||||||
\(272\) | 2.16731 | 0.131412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5139 | 0.876815 | ||||||||
\(275\) | −1.48612 | −0.0896165 | ||||||||
\(276\) | 2.16731 | + | 3.75389i | 0.130457 | + | 0.225957i | ||||
\(277\) | −0.211103 | −0.0126839 | −0.00634196 | − | 0.999980i | \(-0.502019\pi\) | ||||
−0.00634196 | + | 0.999980i | \(0.502019\pi\) | |||||||
\(278\) | 12.2483 | + | 21.2147i | 0.734604 | + | 1.27237i | ||||
\(279\) | 6.07448 | + | 10.5213i | 0.363670 | + | 0.629894i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8167 | 1.42078 | 0.710391 | − | 0.703807i | \(-0.248518\pi\) | ||||
0.710391 | + | 0.703807i | \(0.248518\pi\) | |||||||
\(282\) | 3.77082 | − | 6.53125i | 0.224549 | − | 0.388930i | ||||
\(283\) | −9.32544 | − | 16.1521i | −0.554340 | − | 0.960145i | −0.997955 | − | 0.0639272i | \(-0.979637\pi\) |
0.443615 | − | 0.896218i | \(-0.353696\pi\) | |||||||
\(284\) | −6.60555 | − | 11.4412i | −0.391967 | − | 0.678907i | ||||
\(285\) | −5.09017 | − | 8.81643i | −0.301515 | − | 0.522240i | ||||
\(286\) | 40.4534 | − | 4.93046i | 2.39206 | − | 0.291544i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.50000 | − | 7.79423i | 0.265165 | − | 0.459279i | ||||
\(289\) | 34.2389 | 2.01405 | ||||||||
\(290\) | −11.4927 | −0.674877 | ||||||||
\(291\) | 14.8028 | − | 25.6392i | 0.867754 | − | 1.50299i | ||||
\(292\) | 7.15813 | − | 12.3982i | 0.418898 | − | 0.725553i | ||||
\(293\) | 14.3163 | + | 24.7965i | 0.836365 | + | 1.44863i | 0.892914 | + | 0.450227i | \(0.148657\pi\) |
−0.0565490 | + | 0.998400i | \(0.518010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.05971 | + | 5.29958i | 0.178143 | + | 0.308554i | ||||
\(296\) | 25.8167 | 1.50056 | ||||||||
\(297\) | 6.92937 | + | 12.0020i | 0.402083 | + | 0.696428i | ||||
\(298\) | 20.1653 | − | 34.9273i | 1.16814 | − | 2.02328i | ||||
\(299\) | 0.854892 | − | 2.00902i | 0.0494397 | − | 0.116185i | ||||
\(300\) | −2.16731 | −0.125130 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.45416 | + | 16.3751i | −0.544026 | + | 0.942281i | ||||
\(303\) | 7.04584 | − | 12.2037i | 0.404773 | − | 0.701087i | ||||
\(304\) | −0.328104 | + | 0.568293i | −0.0188181 | + | 0.0325938i | ||||
\(305\) | 9.39445 | 0.537925 | ||||||||
\(306\) | −13.9882 | + | 24.2282i | −0.799650 | + | 1.38503i | ||||
\(307\) | 3.67841 | 0.209938 | 0.104969 | − | 0.994476i | \(-0.466526\pi\) | ||||
0.104969 | + | 0.994476i | \(0.466526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4542 | + | 21.5712i | −0.708493 | + | 1.22715i | ||||
\(310\) | −35.7250 | −2.02904 | ||||||||
\(311\) | −5.31893 | + | 9.21265i | −0.301609 | + | 0.522402i | −0.976501 | − | 0.215515i | \(-0.930857\pi\) |
0.674892 | + | 0.737917i | \(0.264190\pi\) | |||||||
\(312\) | 23.2708 | − | 2.83625i | 1.31745 | − | 0.160571i | ||||
\(313\) | 2.82352 | + | 4.89047i | 0.159595 | + | 0.276426i | 0.934723 | − | 0.355378i | \(-0.115648\pi\) |
−0.775128 | + | 0.631804i | \(0.782315\pi\) | |||||||
\(314\) | 0.755550 | − | 1.30865i | 0.0426382 | − | 0.0738514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.9083 | + | 18.8938i | 0.613641 | + | 1.06286i | ||||
\(317\) | 3.10555 | + | 5.37897i | 0.174425 | + | 0.302113i | 0.939962 | − | 0.341279i | \(-0.110860\pi\) |
−0.765537 | + | 0.643392i | \(0.777527\pi\) | |||||||
\(318\) | 11.9503 | 0.670138 | ||||||||
\(319\) | −11.3028 | −0.632834 | ||||||||
\(320\) | 13.8888 | + | 24.0561i | 0.776409 | + | 1.34478i | ||||
\(321\) | −6.17382 | − | 10.6934i | −0.344589 | − | 0.596846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.75694 | + | 13.4354i | −0.431608 | + | 0.747566i | ||||
\(324\) | 18.5139 | + | 32.0670i | 1.02855 | + | 1.78150i | ||||
\(325\) | 0.656208 | + | 0.872434i | 0.0363999 | + | 0.0483939i | ||||
\(326\) | 3.21110 | − | 5.56179i | 0.177847 | − | 0.308039i | ||||
\(327\) | 17.7960 | 0.984120 | ||||||||
\(328\) | 14.9725 | − | 25.9331i | 0.826717 | − | 1.43192i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 53.0917 | 2.92260 | ||||||||
\(331\) | −2.15139 | + | 3.72631i | −0.118251 | + | 0.204817i | −0.919075 | − | 0.394084i | \(-0.871062\pi\) |
0.800824 | + | 0.598900i | \(0.204395\pi\) | |||||||
\(332\) | 9.32544 | 0.511800 | ||||||||
\(333\) | −7.30278 | + | 12.6488i | −0.400190 | + | 0.693149i | ||||
\(334\) | −13.2326 | + | 22.9196i | −0.724056 | + | 1.25410i | ||||
\(335\) | −1.08365 | + | 1.87694i | −0.0592063 | + | 0.102548i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1194 | 0.987028 | 0.493514 | − | 0.869738i | \(-0.335712\pi\) | ||||
0.493514 | + | 0.869738i | \(0.335712\pi\) | |||||||
\(338\) | −20.7569 | − | 21.5712i | −1.12903 | − | 1.17332i | ||||
\(339\) | −7.38689 | + | 12.7945i | −0.401201 | + | 0.694901i | ||||
\(340\) | −25.6194 | − | 44.3742i | −1.38941 | − | 2.40653i | ||||
\(341\) | −35.1345 | −1.90264 | ||||||||
\(342\) | −4.23527 | − | 7.33571i | −0.229017 | − | 0.396670i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.7708 | + | 32.5120i | 1.01205 | + | 1.75293i | ||||
\(345\) | 1.42221 | − | 2.46333i | 0.0765689 | − | 0.132621i | ||||
\(346\) | −11.7215 | + | 20.3023i | −0.630152 | + | 1.09146i | ||||
\(347\) | 15.2111 | 0.816575 | 0.408287 | − | 0.912853i | \(-0.366126\pi\) | ||||
0.408287 | + | 0.912853i | \(0.366126\pi\) | |||||||
\(348\) | −16.4836 | −0.883612 | ||||||||
\(349\) | −5.09017 | + | 8.81643i | −0.272470 | + | 0.471932i | −0.969494 | − | 0.245116i | \(-0.921174\pi\) |
0.697023 | + | 0.717048i | \(0.254507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.98612 | − | 9.36750i | 0.212763 | − | 0.500000i | ||||
\(352\) | 13.0139 | + | 22.5407i | 0.693642 | + | 1.20142i | ||||
\(353\) | 13.2326 | + | 22.9196i | 0.704301 | + | 1.21988i | 0.966943 | + | 0.254992i | \(0.0820727\pi\) |
−0.262642 | + | 0.964893i | \(0.584594\pi\) | |||||||
\(354\) | 7.04584 | + | 12.2037i | 0.374482 | + | 0.648622i | ||||
\(355\) | −4.33462 | + | 7.50778i | −0.230058 | + | 0.398471i | ||||
\(356\) | 21.4744 | 1.13814 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.8764 | − | 43.0871i | −1.31476 | − | 2.27723i | ||||
\(359\) | 6.04584 | + | 10.4717i | 0.319087 | + | 0.552675i | 0.980298 | − | 0.197525i | \(-0.0632904\pi\) |
−0.661211 | + | 0.750200i | \(0.729957\pi\) | |||||||
\(360\) | 11.0352 | 0.581607 | ||||||||
\(361\) | 7.15139 | + | 12.3866i | 0.376389 | + | 0.651925i | ||||
\(362\) | −55.9526 | −2.94081 | ||||||||
\(363\) | 28.3737 | 1.48923 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.39445 | −0.491728 | ||||||||
\(366\) | 21.6333 | 1.13079 | ||||||||
\(367\) | −12.8052 | − | 22.1792i | −0.668424 | − | 1.15774i | −0.978345 | − | 0.206982i | \(-0.933636\pi\) |
0.309921 | − | 0.950762i | \(-0.399698\pi\) | |||||||
\(368\) | −0.183346 | −0.00955758 | ||||||||
\(369\) | 8.47055 | + | 14.6714i | 0.440959 | + | 0.763764i | ||||
\(370\) | −21.4744 | − | 37.1947i | −1.11640 | − | 1.93366i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −51.2389 | −2.65661 | ||||||||
\(373\) | 6.34861 | − | 10.9961i | 0.328719 | − | 0.569357i | −0.653539 | − | 0.756893i | \(-0.726717\pi\) |
0.982258 | + | 0.187535i | \(0.0600499\pi\) | |||||||
\(374\) | −40.4534 | − | 70.0673i | −2.09179 | − | 3.62309i | ||||
\(375\) | 12.4542 | + | 21.5712i | 0.643130 | + | 1.11393i | ||||
\(376\) | 2.26665 | + | 3.92595i | 0.116894 | + | 0.202466i | ||||
\(377\) | 4.99082 | + | 6.63534i | 0.257041 | + | 0.341737i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.05971 | − | 10.4957i | 0.311267 | − | 0.539130i | −0.667370 | − | 0.744726i | \(-0.732580\pi\) |
0.978637 | + | 0.205596i | \(0.0659134\pi\) | |||||||
\(380\) | 15.5139 | 0.795845 | ||||||||
\(381\) | 17.1398 | 0.878098 | ||||||||
\(382\) | −18.0736 | + | 31.3044i | −0.924725 | + | 1.60167i | ||||
\(383\) | 11.1646 | − | 19.3377i | 0.570487 | − | 0.988112i | −0.426029 | − | 0.904709i | \(-0.640088\pi\) |
0.996516 | − | 0.0834025i | \(-0.0265787\pi\) | |||||||
\(384\) | 20.4901 | + | 35.4899i | 1.04563 | + | 1.81108i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.8167 | − | 39.5196i | −1.16134 | − | 2.01149i | ||||
\(387\) | −21.2389 | −1.07963 | ||||||||
\(388\) | 22.5581 | + | 39.0717i | 1.14521 | + | 1.98356i | ||||
\(389\) | −14.5139 | + | 25.1388i | −0.735883 | + | 1.27459i | 0.218452 | + | 0.975848i | \(0.429899\pi\) |
−0.954335 | + | 0.298739i | \(0.903434\pi\) | |||||||
\(390\) | −23.4430 | − | 31.1677i | −1.18708 | − | 1.57824i | ||||
\(391\) | −4.33462 | −0.219211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5278 | − | 19.9667i | 0.581498 | − | 1.00718i | ||||
\(394\) | 1.25694 | − | 2.17708i | 0.0633237 | − | 0.109680i | ||||
\(395\) | 7.15813 | − | 12.3982i | 0.360165 | − | 0.623824i | ||||
\(396\) | 27.5139 | 1.38262 | ||||||||
\(397\) | −2.16731 | + | 3.75389i | −0.108774 | + | 0.188402i | −0.915274 | − | 0.402832i | \(-0.868026\pi\) |
0.806500 | + | 0.591234i | \(0.201359\pi\) | |||||||
\(398\) | −16.4836 | −0.826247 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0458365 | − | 0.0793912i | 0.00229183 | − | 0.00396956i | ||||
\(401\) | −10.1194 | −0.505340 | −0.252670 | − | 0.967552i | \(-0.581309\pi\) | ||||
−0.252670 | + | 0.967552i | \(0.581309\pi\) | |||||||
\(402\) | −2.49541 | + | 4.32218i | −0.124460 | + | 0.215571i | ||||
\(403\) | 15.5139 | + | 20.6258i | 0.772801 | + | 1.02745i | ||||
\(404\) | 10.7372 | + | 18.5974i | 0.534196 | + | 0.925254i | ||||
\(405\) | 12.1490 | − | 21.0426i | 0.603687 | − | 1.04562i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1194 | − | 36.5799i | −1.04685 | − | 1.81320i | ||||
\(408\) | −23.2708 | − | 40.3062i | −1.15208 | − | 1.99546i | ||||
\(409\) | 3.47972 | 0.172061 | 0.0860306 | − | 0.996292i | \(-0.472582\pi\) | ||||
0.0860306 | + | 0.996292i | \(0.472582\pi\) | |||||||
\(410\) | −49.8167 | −2.46027 | ||||||||
\(411\) | −6.83003 | − | 11.8300i | −0.336900 | − | 0.583529i | ||||
\(412\) | −18.9790 | − | 32.8726i | −0.935027 | − | 1.61952i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.18335 | − | 2.04962i | 0.0581583 | − | 0.100733i | ||||
\(415\) | −3.05971 | − | 5.29958i | −0.150195 | − | 0.260146i | ||||
\(416\) | 7.48624 | − | 17.5929i | 0.367043 | − | 0.862561i | ||||
\(417\) | 11.5278 | − | 19.9667i | 0.564517 | − | 0.977772i | ||||
\(418\) | 24.4966 | 1.19817 | ||||||||
\(419\) | 8.56989 | − | 14.8435i | 0.418667 | − | 0.725152i | −0.577139 | − | 0.816646i | \(-0.695831\pi\) |
0.995806 | + | 0.0914942i | \(0.0291643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.02776 | 0.245038 | 0.122519 | − | 0.992466i | \(-0.460903\pi\) | ||||
0.122519 | + | 0.992466i | \(0.460903\pi\) | |||||||
\(422\) | −17.2708 | + | 29.9139i | −0.840730 | + | 1.45619i | ||||
\(423\) | −2.56468 | −0.124699 | ||||||||
\(424\) | −3.59167 | + | 6.22096i | −0.174427 | + | 0.302117i | ||||
\(425\) | 1.08365 | − | 1.87694i | 0.0525649 | − | 0.0910452i | ||||
\(426\) | −9.98165 | + | 17.2887i | −0.483612 | + | 0.837641i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.8167 | 0.909537 | ||||||||
\(429\) | −23.0555 | − | 30.6525i | −1.11313 | − | 1.47992i | ||||
\(430\) | 31.2273 | − | 54.0872i | 1.50591 | − | 2.60832i | ||||
\(431\) | 10.4680 | + | 18.1312i | 0.504228 | + | 0.873348i | 0.999988 | + | 0.00488877i | \(0.00155615\pi\) |
−0.495760 | + | 0.868459i | \(0.665111\pi\) | |||||||
\(432\) | −0.854892 | −0.0411310 | ||||||||
\(433\) | −8.56989 | − | 14.8435i | −0.411843 | − | 0.713332i | 0.583249 | − | 0.812294i | \(-0.301781\pi\) |
−0.995091 | + | 0.0989613i | \(0.968448\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.40833 | + | 9.36750i | 0.259309 | + | 0.449137i | ||||
\(436\) | −13.5597 | + | 23.4861i | −0.649393 | + | 1.12478i | ||||
\(437\) | 0.656208 | − | 1.13659i | 0.0313907 | − | 0.0543703i | ||||
\(438\) | −21.6333 | −1.03368 | ||||||||
\(439\) | −3.67841 | −0.175561 | −0.0877804 | − | 0.996140i | \(-0.527977\pi\) | ||||
−0.0877804 | + | 0.996140i | \(0.527977\pi\) | |||||||
\(440\) | −15.9568 | + | 27.6380i | −0.760710 | + | 1.31759i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.2708 | + | 54.6871i | −1.10688 | + | 2.60120i | ||||
\(443\) | 10.1194 | + | 17.5274i | 0.480789 | + | 0.832750i | 0.999757 | − | 0.0220431i | \(-0.00701711\pi\) |
−0.518968 | + | 0.854793i | \(0.673684\pi\) | |||||||
\(444\) | −30.7998 | − | 53.3469i | −1.46170 | − | 2.53173i | ||||
\(445\) | −7.04584 | − | 12.2037i | −0.334005 | − | 0.578513i | ||||
\(446\) | 20.7188 | − | 35.8861i | 0.981066 | − | 1.69926i | ||||
\(447\) | −37.9580 | −1.79535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2111 | + | 17.6861i | 0.481892 | + | 0.834661i | 0.999784 | − | 0.0207849i | \(-0.00661652\pi\) |
−0.517892 | + | 0.855446i | \(0.673283\pi\) | |||||||
\(450\) | 0.591673 | + | 1.02481i | 0.0278917 | + | 0.0483099i | ||||
\(451\) | −48.9932 | −2.30700 | ||||||||
\(452\) | −11.2569 | − | 19.4976i | −0.529482 | − | 0.917090i | ||||
\(453\) | 17.7960 | 0.836129 | ||||||||
\(454\) | −42.4913 | −1.99421 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.0917 | 0.659903 | ||||||||
\(457\) | 20.6056 | 0.963887 | 0.481944 | − | 0.876202i | \(-0.339931\pi\) | ||||
0.481944 | + | 0.876202i | \(0.339931\pi\) | |||||||
\(458\) | 17.9947 | + | 31.1677i | 0.840836 | + | 1.45637i | ||||
\(459\) | −20.2111 | −0.943373 | ||||||||
\(460\) | 2.16731 | + | 3.75389i | 0.101051 | + | 0.175026i | ||||
\(461\) | 12.5764 | + | 21.7830i | 0.585741 | + | 1.01453i | 0.994783 | + | 0.102018i | \(0.0325299\pi\) |
−0.409041 | + | 0.912516i | \(0.634137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7889 | −0.640824 | −0.320412 | − | 0.947278i | \(-0.603821\pi\) | ||||
−0.320412 | + | 0.947278i | \(0.603821\pi\) | |||||||
\(464\) | 0.348612 | − | 0.603814i | 0.0161839 | − | 0.0280314i | ||||
\(465\) | 16.8117 | + | 29.1187i | 0.779623 | + | 1.35035i | ||||
\(466\) | 15.0736 | + | 26.1082i | 0.698271 | + | 1.20944i | ||||
\(467\) | −6.40258 | − | 11.0896i | −0.296276 | − | 0.513165i | 0.679005 | − | 0.734134i | \(-0.262412\pi\) |
−0.975281 | + | 0.220968i | \(0.929078\pi\) | |||||||
\(468\) | −12.1490 | − | 16.1521i | −0.561586 | − | 0.746633i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.77082 | − | 6.53125i | 0.173935 | − | 0.301264i | ||||
\(471\) | −1.42221 | −0.0655318 | ||||||||
\(472\) | −8.47055 | −0.389889 | ||||||||
\(473\) | 30.7111 | − | 53.1932i | 1.41210 | − | 2.44583i | ||||
\(474\) | 16.4836 | − | 28.5504i | 0.757116 | − | 1.31136i | ||||
\(475\) | 0.328104 | + | 0.568293i | 0.0150544 | + | 0.0260751i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.03196 | − | 3.51946i | −0.0930370 | − | 0.161145i | ||||
\(478\) | 10.1194 | 0.462852 | ||||||||
\(479\) | 8.24179 | + | 14.2752i | 0.376577 | + | 0.652250i | 0.990562 | − | 0.137068i | \(-0.0437678\pi\) |
−0.613985 | + | 0.789318i | \(0.710434\pi\) | |||||||
\(480\) | 12.4542 | − | 21.5712i | 0.568452 | − | 0.984588i | ||||
\(481\) | −12.1490 | + | 28.5504i | −0.553945 | + | 1.30179i | ||||
\(482\) | −21.4744 | −0.978132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.6194 | + | 37.4460i | −0.982701 | + | 1.70209i | ||||
\(485\) | 14.8028 | − | 25.6392i | 0.672159 | − | 1.16421i | ||||
\(486\) | 18.2234 | − | 31.5639i | 0.826632 | − | 1.43177i | ||||
\(487\) | −31.3028 | −1.41846 | −0.709232 | − | 0.704975i | \(-0.750958\pi\) | ||||
−0.709232 | + | 0.704975i | \(0.750958\pi\) | |||||||
\(488\) | −6.50192 | + | 11.2617i | −0.294328 | + | 0.509792i | ||||
\(489\) | −6.04440 | −0.273337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.86249 | + | 17.0823i | −0.445088 | + | 0.770915i | −0.998058 | − | 0.0622859i | \(-0.980161\pi\) |
0.552970 | + | 0.833201i | \(0.313494\pi\) | |||||||
\(492\) | −71.4500 | −3.22121 | ||||||||
\(493\) | 8.24179 | − | 14.2752i | 0.371191 | − | 0.642922i | ||||
\(494\) | −10.8167 | − | 14.3808i | −0.486664 | − | 0.647024i | ||||
\(495\) | −9.02741 | − | 15.6359i | −0.405752 | − | 0.702783i | ||||
\(496\) | 1.08365 | − | 1.87694i | 0.0486575 | − | 0.0842773i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.04584 | − | 12.2037i | −0.315731 | − | 0.546863i | ||||
\(499\) | 4.16527 | + | 7.21445i | 0.186463 | + | 0.322963i | 0.944069 | − | 0.329749i | \(-0.106964\pi\) |
−0.757606 | + | 0.652713i | \(0.773631\pi\) | |||||||
\(500\) | −37.9580 | −1.69753 | ||||||||
\(501\) | 24.9083 | 1.11282 | ||||||||
\(502\) | −34.4782 | − | 59.7181i | −1.53884 | − | 2.66535i | ||||
\(503\) | 9.75289 | + | 16.8925i | 0.434860 | + | 0.753199i | 0.997284 | − | 0.0736495i | \(-0.0234646\pi\) |
−0.562424 | + | 0.826849i | \(0.690131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.04584 | − | 12.2037i | 0.313536 | − | 0.543060i | ||||
\(506\) | 3.42221 | + | 5.92743i | 0.152136 | + | 0.263507i | ||||
\(507\) | −7.81434 | + | 27.0697i | −0.347047 | + | 1.20221i | ||||
\(508\) | −13.0597 | + | 22.6201i | −0.579431 | + | 1.00360i | ||||
\(509\) | 21.4744 | 0.951836 | 0.475918 | − | 0.879490i | \(-0.342116\pi\) | ||||
0.475918 | + | 0.879490i | \(0.342116\pi\) | |||||||
\(510\) | −38.7135 | + | 67.0538i | −1.71426 | + | 2.96919i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.42221 | −0.151242 | ||||||||
\(513\) | 3.05971 | − | 5.29958i | 0.135090 | − | 0.233982i | ||||
\(514\) | 14.5149 | 0.640227 | ||||||||
\(515\) | −12.4542 | + | 21.5712i | −0.548796 | + | 0.950543i | ||||
\(516\) | 44.7880 | − | 77.5751i | 1.97168 | − | 3.41505i | ||||
\(517\) | 3.70849 | − | 6.42329i | 0.163099 | − | 0.282496i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0639 | 0.968498 | ||||||||
\(520\) | 23.2708 | − | 2.83625i | 1.02049 | − | 0.124378i | ||||
\(521\) | 10.8365 | − | 18.7694i | 0.474757 | − | 0.822304i | −0.524825 | − | 0.851210i | \(-0.675869\pi\) |
0.999582 | + | 0.0289063i | \(0.00920245\pi\) | |||||||
\(522\) | 4.50000 | + | 7.79423i | 0.196960 | + | 0.341144i | ||||
\(523\) | 24.2979 | 1.06247 | 0.531237 | − | 0.847223i | \(-0.321727\pi\) | ||||
0.531237 | + | 0.847223i | \(0.321727\pi\) | |||||||
\(524\) | 17.5672 | + | 30.4273i | 0.767428 | + | 1.32922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.7569 | − | 30.7559i | −0.774239 | − | 1.34102i | ||||
\(527\) | 25.6194 | − | 44.3742i | 1.11600 | − | 1.93297i | ||||
\(528\) | −1.61044 | + | 2.78937i | −0.0700855 | + | 0.121392i | ||||
\(529\) | −22.6333 | −0.984057 | ||||||||
\(530\) | 11.9503 | 0.519087 | ||||||||
\(531\) | 2.39607 | − | 4.15012i | 0.103981 | − | 0.180100i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.6333 | + | 28.7617i | 0.937043 | + | 1.24581i | ||||
\(534\) | −16.2250 | − | 28.1025i | −0.702124 | − | 1.21611i | ||||
\(535\) | −6.17382 | − | 10.6934i | −0.266918 | − | 0.462315i | ||||
\(536\) | −1.50000 | − | 2.59808i | −0.0647901 | − | 0.112220i | ||||
\(537\) | −23.4129 | + | 40.5524i | −1.01034 | + | 1.74997i | ||||
\(538\) | −1.51110 | −0.0651481 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.1056 | + | 17.5033i | 0.434874 | + | 0.753223i | ||||
\(541\) | −13.9680 | − | 24.1934i | −0.600533 | − | 1.04015i | −0.992740 | − | 0.120277i | \(-0.961622\pi\) |
0.392207 | − | 0.919877i | \(-0.371712\pi\) | |||||||
\(542\) | 33.4247 | 1.43571 | ||||||||
\(543\) | 26.3305 | + | 45.6058i | 1.12995 | + | 1.95713i | ||||
\(544\) | −37.9580 | −1.62743 | ||||||||
\(545\) | 17.7960 | 0.762296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0000 | 1.23995 | 0.619975 | − | 0.784621i | \(-0.287143\pi\) | ||||
0.619975 | + | 0.784621i | \(0.287143\pi\) | |||||||
\(548\) | 20.8167 | 0.889243 | ||||||||
\(549\) | −3.67841 | − | 6.37119i | −0.156991 | − | 0.271916i | ||||
\(550\) | −3.42221 | −0.145923 | ||||||||
\(551\) | 2.49541 | + | 4.32218i | 0.106308 | + | 0.184131i | ||||
\(552\) | 1.96862 | + | 3.40976i | 0.0837902 | + | 0.145129i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.486122 | −0.0206533 | ||||||||
\(555\) | −20.2111 | + | 35.0067i | −0.857914 | + | 1.48595i | ||||
\(556\) | 17.5672 | + | 30.4273i | 0.745016 | + | 1.29041i | ||||
\(557\) | −3.04584 | − | 5.27554i | −0.129056 | − | 0.223532i | 0.794255 | − | 0.607585i | \(-0.207861\pi\) |
−0.923311 | + | 0.384053i | \(0.874528\pi\) | |||||||
\(558\) | 13.9882 | + | 24.2282i | 0.592166 | + | 1.02566i | ||||
\(559\) | −44.7880 | + | 5.45877i | −1.89433 | + | 0.230881i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.0736 | + | 65.9454i | −1.60747 | + | 2.78422i | ||||
\(562\) | 54.8444 | 2.31347 | ||||||||
\(563\) | 1.31242 | 0.0553117 | 0.0276559 | − | 0.999618i | \(-0.491196\pi\) | ||||
0.0276559 | + | 0.999618i | \(0.491196\pi\) | |||||||
\(564\) | 5.40833 | − | 9.36750i | 0.227732 | − | 0.394443i | ||||
\(565\) | −7.38689 | + | 12.7945i | −0.310769 | + | 0.538268i | ||||
\(566\) | −21.4744 | − | 37.1947i | −0.902636 | − | 1.56341i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | − | 10.3923i | −0.251754 | − | 0.436051i | ||||
\(569\) | −34.6056 | −1.45074 | −0.725370 | − | 0.688359i | \(-0.758331\pi\) | ||||
−0.725370 | + | 0.688359i | \(0.758331\pi\) | |||||||
\(570\) | −11.7215 | − | 20.3023i | −0.490960 | − | 0.850368i | ||||
\(571\) | 5.36249 | − | 9.28811i | 0.224413 | − | 0.388695i | −0.731730 | − | 0.681595i | \(-0.761287\pi\) |
0.956143 | + | 0.292899i | \(0.0946201\pi\) | |||||||
\(572\) | 58.0206 | − | 7.07156i | 2.42596 | − | 0.295677i | ||||
\(573\) | 34.0207 | 1.42124 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0916731 | + | 0.158782i | −0.00382303 | + | 0.00662169i | ||||
\(576\) | 10.8764 | − | 18.8384i | 0.453182 | − | 0.784934i | ||||
\(577\) | −16.5829 | + | 28.7225i | −0.690356 | + | 1.19573i | 0.281366 | + | 0.959601i | \(0.409213\pi\) |
−0.971721 | + | 0.236131i | \(0.924121\pi\) | |||||||
\(578\) | 78.8444 | 3.27950 | ||||||||
\(579\) | −21.4744 | + | 37.1947i | −0.892445 | + | 1.54576i | ||||
\(580\) | −16.4836 | −0.684443 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 34.0875 | − | 59.0412i | 1.41297 | − | 2.44734i | ||||
\(583\) | 11.7527 | 0.486749 | ||||||||
\(584\) | 6.50192 | − | 11.2617i | 0.269052 | − | 0.466011i | ||||
\(585\) | −5.19302 | + | 12.2037i | −0.214705 | + | 0.504563i | ||||
\(586\) | 32.9671 | + | 57.1008i | 1.36186 | + | 2.35881i | ||||
\(587\) | −0.984312 | + | 1.70488i | −0.0406269 | + | 0.0703679i | −0.885624 | − | 0.464403i | \(-0.846269\pi\) |
0.844997 | + | 0.534771i | \(0.179602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.75694 | + | 13.4354i | 0.319619 | + | 0.553597i | ||||
\(590\) | 7.04584 | + | 12.2037i | 0.290072 | + | 0.502420i | ||||
\(591\) | −2.36599 | −0.0973239 | ||||||||
\(592\) | 2.60555 | 0.107087 | ||||||||
\(593\) | −3.15162 | − | 5.45877i | −0.129422 | − | 0.224165i | 0.794031 | − | 0.607877i | \(-0.207979\pi\) |
−0.923453 | + | 0.383712i | \(0.874645\pi\) | |||||||
\(594\) | 15.9568 | + | 27.6380i | 0.654715 | + | 1.13400i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.9222 | − | 50.0947i | 1.18470 | − | 2.05196i | ||||
\(597\) | 7.75694 | + | 13.4354i | 0.317470 | + | 0.549875i | ||||
\(598\) | 1.96862 | − | 4.62632i | 0.0805030 | − | 0.189184i | ||||
\(599\) | 5.25694 | − | 9.10529i | 0.214793 | − | 0.372032i | −0.738416 | − | 0.674346i | \(-0.764426\pi\) |
0.953208 | + | 0.302314i | \(0.0977591\pi\) | |||||||
\(600\) | −1.96862 | −0.0803687 | ||||||||
\(601\) | −4.56338 | + | 7.90400i | −0.186144 | + | 0.322411i | −0.943961 | − | 0.330056i | \(-0.892932\pi\) |
0.757817 | + | 0.652467i | \(0.226266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.69722 | 0.0691163 | ||||||||
\(604\) | −13.5597 | + | 23.4861i | −0.551737 | + | 0.955636i | ||||
\(605\) | 28.3737 | 1.15355 | ||||||||
\(606\) | 16.2250 | − | 28.1025i | 0.659095 | − | 1.14159i | ||||
\(607\) | −19.4064 | + | 33.6129i | −0.787683 | + | 1.36431i | 0.139701 | + | 0.990194i | \(0.455386\pi\) |
−0.927383 | + | 0.374113i | \(0.877947\pi\) | |||||||
\(608\) | 5.74637 | − | 9.95301i | 0.233046 | − | 0.403648i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.6333 | 0.875907 | ||||||||
\(611\) | −5.40833 | + | 0.659168i | −0.218797 | + | 0.0266671i | ||||
\(612\) | −20.0626 | + | 34.7495i | −0.810984 | + | 1.40467i | ||||
\(613\) | −15.9542 | − | 27.6334i | −0.644383 | − | 1.11610i | −0.984444 | − | 0.175700i | \(-0.943781\pi\) |
0.340061 | − | 0.940403i | \(-0.389552\pi\) | |||||||
\(614\) | 8.47055 | 0.341844 | ||||||||
\(615\) | 23.4430 | + | 40.6045i | 0.945314 | + | 1.63733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.92221 | − | 13.7217i | −0.318936 | − | 0.552413i | 0.661330 | − | 0.750095i | \(-0.269992\pi\) |
−0.980266 | + | 0.197681i | \(0.936659\pi\) | |||||||
\(618\) | −28.6791 | + | 49.6737i | −1.15364 | + | 1.99817i | ||||
\(619\) | 14.9725 | − | 25.9331i | 0.601794 | − | 1.04234i | −0.390755 | − | 0.920495i | \(-0.627786\pi\) |
0.992549 | − | 0.121844i | \(-0.0388807\pi\) | |||||||
\(620\) | −51.2389 | −2.05780 | ||||||||
\(621\) | 1.70978 | 0.0686113 | ||||||||
\(622\) | −12.2483 | + | 21.2147i | −0.491112 | + | 0.850631i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.34861 | − | 0.286249i | 0.0940197 | − | 0.0114591i | ||||
\(625\) | 11.6972 | + | 20.2602i | 0.467889 | + | 0.810407i | ||||
\(626\) | 6.50192 | + | 11.2617i | 0.259869 | + | 0.450107i | ||||
\(627\) | −11.5278 | − | 19.9667i | −0.460374 | − | 0.797392i | ||||
\(628\) | 1.08365 | − | 1.87694i | 0.0432425 | − | 0.0748982i | ||||
\(629\) | 61.5997 | 2.45614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4542 | − | 19.8392i | −0.455983 | − | 0.789786i | 0.542761 | − | 0.839887i | \(-0.317379\pi\) |
−0.998744 | + | 0.0501013i | \(0.984046\pi\) | |||||||
\(632\) | 9.90833 | + | 17.1617i | 0.394132 | + | 0.682657i | ||||
\(633\) | 32.5096 | 1.29214 | ||||||||
\(634\) | 7.15139 | + | 12.3866i | 0.284018 | + | 0.491933i | ||||
\(635\) | 17.1398 | 0.680171 | ||||||||
\(636\) | 17.1398 | 0.679637 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −26.0278 | −1.03045 | ||||||||
\(639\) | 6.78890 | 0.268565 | ||||||||
\(640\) | 20.4901 | + | 35.4899i | 0.809942 | + | 1.40286i | ||||
\(641\) | −14.5139 | −0.573264 | −0.286632 | − | 0.958041i | \(-0.592536\pi\) | ||||
−0.286632 | + | 0.958041i | \(0.592536\pi\) | |||||||
\(642\) | −14.2169 | − | 24.6244i | −0.561097 | − | 0.971849i | ||||
\(643\) | −8.56989 | − | 14.8435i | −0.337963 | − | 0.585370i | 0.646086 | − | 0.763265i | \(-0.276405\pi\) |
−0.984050 | + | 0.177895i | \(0.943071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −58.7805 | −2.31448 | ||||||||
\(646\) | −17.8625 | + | 30.9387i | −0.702790 | + | 1.21727i | ||||
\(647\) | 16.4836 | + | 28.5504i | 0.648036 | + | 1.12243i | 0.983591 | + | 0.180411i | \(0.0577428\pi\) |
−0.335555 | + | 0.942021i | \(0.608924\pi\) | |||||||
\(648\) | 16.8167 | + | 29.1273i | 0.660621 | + | 1.14423i | ||||
\(649\) | 6.92937 | + | 12.0020i | 0.272002 | + | 0.471121i | ||||
\(650\) | 1.51110 | + | 2.00902i | 0.0592702 | + | 0.0788002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.60555 | − | 7.97705i | 0.180367 | − | 0.312405i | ||||
\(653\) | −46.7527 | −1.82958 | −0.914788 | − | 0.403934i | \(-0.867642\pi\) | ||||
−0.914788 | + | 0.403934i | \(0.867642\pi\) | |||||||
\(654\) | 40.9802 | 1.60245 | ||||||||
\(655\) | 11.5278 | − | 19.9667i | 0.450427 | − | 0.780162i | ||||
\(656\) | 1.51110 | − | 2.61730i | 0.0589985 | − | 0.102188i | ||||
\(657\) | 3.67841 | + | 6.37119i | 0.143508 | + | 0.248564i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.81665 | + | 17.0029i | 0.382403 | + | 0.662341i | 0.991405 | − | 0.130828i | \(-0.0417634\pi\) |
−0.609003 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(660\) | 76.1472 | 2.96403 | ||||||||
\(661\) | 11.4927 | + | 19.9060i | 0.447016 | + | 0.774255i | 0.998190 | − | 0.0601356i | \(-0.0191533\pi\) |
−0.551174 | + | 0.834390i | \(0.685820\pi\) | |||||||
\(662\) | −4.95416 | + | 8.58086i | −0.192549 | + | 0.333505i | ||||
\(663\) | 55.5252 | − | 6.76742i | 2.15642 | − | 0.262825i | ||||
\(664\) | 8.47055 | 0.328721 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.8167 | + | 29.1273i | −0.651632 | + | 1.12866i | ||||
\(667\) | −0.697224 | + | 1.20763i | −0.0269966 | + | 0.0467595i | ||||
\(668\) | −18.9790 | + | 32.8726i | −0.734319 | + | 1.27188i | ||||
\(669\) | −39.0000 | −1.50783 | ||||||||
\(670\) | −2.49541 | + | 4.32218i | −0.0964062 | + | 0.166980i | ||||
\(671\) | 21.2757 | 0.821340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.10555 | − | 1.91487i | 0.0426159 | − | 0.0738129i | −0.843931 | − | 0.536452i | \(-0.819764\pi\) |
0.886547 | + | 0.462639i | \(0.153098\pi\) | |||||||
\(674\) | 41.7250 | 1.60719 | ||||||||
\(675\) | −0.427446 | + | 0.740358i | −0.0164524 | + | 0.0284964i | ||||
\(676\) | −29.7708 | − | 30.9387i | −1.14503 | − | 1.18995i | ||||
\(677\) | 13.2326 | + | 22.9196i | 0.508571 | + | 0.880870i | 0.999951 | + | 0.00992485i | \(0.00315923\pi\) |
−0.491380 | + | 0.870945i | \(0.663507\pi\) | |||||||
\(678\) | −17.0104 | + | 29.4628i | −0.653279 | + | 1.13151i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.2708 | − | 40.3062i | −0.892395 | − | 1.54567i | ||||
\(681\) | 19.9958 | + | 34.6337i | 0.766241 | + | 1.32717i | ||||
\(682\) | −80.9068 | −3.09808 | ||||||||
\(683\) | −3.60555 | −0.137963 | −0.0689813 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689813 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(684\) | −6.07448 | − | 10.5213i | −0.232263 | − | 0.402292i | ||||
\(685\) | −6.83003 | − | 11.8300i | −0.260962 | − | 0.451999i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9361 | − | 29.3342i | 0.646152 | − | 1.11917i | ||||
\(688\) | 1.89445 | + | 3.28128i | 0.0722252 | + | 0.125098i | ||||
\(689\) | −5.18951 | − | 6.89949i | −0.197705 | − | 0.262850i | ||||
\(690\) | 3.27502 | − | 5.67250i | 0.124678 | − | 0.215948i | ||||
\(691\) | −37.7593 | −1.43643 | −0.718215 | − | 0.695821i | \(-0.755041\pi\) | ||||
−0.718215 | + | 0.695821i | \(0.755041\pi\) | |||||||
\(692\) | −16.8117 | + | 29.1187i | −0.639084 | + | 1.10693i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.0278 | 1.32964 | ||||||||
\(695\) | 11.5278 | − | 19.9667i | 0.437273 | − | 0.757379i | ||||
\(696\) | −14.9725 | −0.567530 | ||||||||
\(697\) | 35.7250 | − | 61.8775i | 1.35318 | − | 2.34378i | ||||
\(698\) | −11.7215 | + | 20.3023i | −0.443666 | + | 0.768452i | ||||
\(699\) | 14.1868 | − | 24.5723i | 0.536596 | − | 0.929411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.02776 | 0.340974 | 0.170487 | − | 0.985360i | \(-0.445466\pi\) | ||||
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(702\) | 9.17914 | − | 21.5712i | 0.346444 | − | 0.814154i | ||||
\(703\) | −9.32544 | + | 16.1521i | −0.351716 | + | 0.609189i | ||||
\(704\) | 31.4542 | + | 54.4802i | 1.18547 | + | 2.05330i | ||||
\(705\) | −7.09798 | −0.267325 | ||||||||
\(706\) | 30.4717 | + | 52.7786i | 1.14682 | + | 1.98635i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.1056 | + | 17.5033i | 0.379790 | + | 0.657815i | ||||
\(709\) | −16.3625 | + | 28.3407i | −0.614506 | + | 1.06436i | 0.375965 | + | 0.926634i | \(0.377311\pi\) |
−0.990471 | + | 0.137722i | \(0.956022\pi\) | |||||||
\(710\) | −9.98165 | + | 17.2887i | −0.374605 | + | 0.648834i | ||||
\(711\) | −11.2111 | −0.420449 | ||||||||
\(712\) | 19.5058 | 0.731010 | ||||||||
\(713\) | −2.16731 | + | 3.75389i | −0.0811663 | + | 0.140584i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.0555 | − | 30.6525i | −0.862227 | − | 1.14634i | ||||
\(716\) | −35.6791 | − | 61.7981i | −1.33339 | − | 2.30950i | ||||
\(717\) | −4.76206 | − | 8.24813i | −0.177842 | − | 0.308032i | ||||
\(718\) | 13.9222 | + | 24.1140i | 0.519572 | + | 0.899925i | ||||
\(719\) | 11.3934 | − | 19.7340i | 0.424902 | − | 0.735952i | −0.571509 | − | 0.820596i | \(-0.693642\pi\) |
0.996411 | + | 0.0846433i | \(0.0269751\pi\) | |||||||
\(720\) | 1.11373 | 0.0415064 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.4680 | + | 28.5235i | 0.612877 | + | 1.06153i | ||||
\(723\) | 10.1056 | + | 17.5033i | 0.375829 | + | 0.650956i | ||||
\(724\) | −80.2506 | −2.98249 | ||||||||
\(725\) | −0.348612 | − | 0.603814i | −0.0129471 | − | 0.0224251i | ||||
\(726\) | 65.3382 | 2.42493 | ||||||||
\(727\) | 37.1031 | 1.37608 | 0.688038 | − | 0.725674i | \(-0.258472\pi\) | ||||
0.688038 | + | 0.725674i | \(0.258472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.669468 | −0.0247951 | ||||||||
\(730\) | −21.6333 | −0.800685 | ||||||||
\(731\) | 44.7880 | + | 77.5751i | 1.65654 | + | 2.86922i | ||||
\(732\) | 31.0278 | 1.14682 | ||||||||
\(733\) | 3.35030 | + | 5.80290i | 0.123746 | + | 0.214335i | 0.921242 | − | 0.388990i | \(-0.127176\pi\) |
−0.797496 | + | 0.603324i | \(0.793842\pi\) | |||||||
\(734\) | −29.4874 | − | 51.0737i | −1.08840 | − | 1.88517i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.21110 | 0.118363 | ||||||||
\(737\) | −2.45416 | + | 4.25074i | −0.0904003 | + | 0.156578i | ||||
\(738\) | 19.5058 | + | 33.7850i | 0.718017 | + | 1.24364i | ||||
\(739\) | 16.6056 | + | 28.7617i | 0.610845 | + | 1.05801i | 0.991098 | + | 0.133132i | \(0.0425035\pi\) |
−0.380253 | + | 0.924882i | \(0.624163\pi\) | |||||||
\(740\) | −30.7998 | − | 53.3469i | −1.13222 | − | 1.96107i | ||||
\(741\) | −6.63134 | + | 15.5838i | −0.243609 | + | 0.572487i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.6514 | − | 35.7693i | 0.757626 | − | 1.31225i | −0.186432 | − | 0.982468i | \(-0.559692\pi\) |
0.944058 | − | 0.329779i | \(-0.106974\pi\) | |||||||
\(744\) | −46.5416 | −1.70630 | ||||||||
\(745\) | −37.9580 | −1.39067 | ||||||||
\(746\) | 14.6194 | − | 25.3216i | 0.535255 | − | 0.927089i | ||||
\(747\) | −2.39607 | + | 4.15012i | −0.0876676 | + | 0.151845i | ||||
\(748\) | −58.0206 | − | 100.495i | −2.12144 | − | 3.67445i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 28.6791 | + | 49.6737i | 1.04721 | + | 1.81383i | ||||
\(751\) | −11.6056 | −0.423493 | −0.211746 | − | 0.977325i | \(-0.567915\pi\) | ||||
−0.211746 | + | 0.977325i | \(0.567915\pi\) | |||||||
\(752\) | 0.228762 | + | 0.396228i | 0.00834210 | + | 0.0144489i | ||||
\(753\) | −32.4500 | + | 56.2050i | −1.18254 | + | 2.04822i | ||||
\(754\) | 11.4927 | + | 15.2797i | 0.418541 | + | 0.556454i | ||||
\(755\) | 17.7960 | 0.647662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.11943 | + | 5.40301i | −0.113378 | + | 0.196376i | −0.917130 | − | 0.398588i | \(-0.869500\pi\) |
0.803752 | + | 0.594964i | \(0.202834\pi\) | |||||||
\(758\) | 13.9542 | − | 24.1693i | 0.506838 | − | 0.877869i | ||||
\(759\) | 3.22088 | − | 5.57873i | 0.116911 | − | 0.202495i | ||||
\(760\) | 14.0917 | 0.511159 | ||||||||
\(761\) | 21.1463 | − | 36.6265i | 0.766553 | − | 1.32771i | −0.172869 | − | 0.984945i | \(-0.555304\pi\) |
0.939422 | − | 0.342763i | \(-0.111363\pi\) | |||||||
\(762\) | 39.4691 | 1.42981 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.9222 | + | 44.8986i | −0.937832 | + | 1.62437i | ||||
\(765\) | 26.3305 | 0.951982 | ||||||||
\(766\) | 25.7097 | − | 44.5305i | 0.928928 | − | 1.60895i | ||||
\(767\) | 3.98612 | − | 9.36750i | 0.143931 | − | 0.338241i | ||||
\(768\) | 19.4064 | + | 33.6129i | 0.700269 | + | 1.21290i | ||||
\(769\) | −23.5424 | + | 40.7766i | −0.848959 | + | 1.47044i | 0.0331785 | + | 0.999449i | \(0.489437\pi\) |
−0.882138 | + | 0.470991i | \(0.843896\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.83053 | − | 11.8308i | −0.245996 | − | 0.426077i | ||||
\(772\) | −32.7250 | − | 56.6813i | −1.17780 | − | 2.04001i | ||||
\(773\) | 28.4338 | 1.02269 | 0.511347 | − | 0.859374i | \(-0.329147\pi\) | ||||
0.511347 | + | 0.859374i | \(0.329147\pi\) | |||||||
\(774\) | −48.9083 | −1.75797 | ||||||||
\(775\) | −1.08365 | − | 1.87694i | −0.0389260 | − | 0.0674218i | ||||
\(776\) | 20.4901 | + | 35.4899i | 0.735551 | + | 1.27401i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.4222 | + | 57.8890i | −1.19824 | + | 2.07542i | ||||
\(779\) | 10.8167 | + | 18.7350i | 0.387547 | + | 0.671251i | ||||
\(780\) | −33.6234 | − | 44.7025i | −1.20391 | − | 1.60061i | ||||
\(781\) | −9.81665 | + | 17.0029i | −0.351267 | + | 0.608413i | ||||
\(782\) | −9.98165 | −0.356943 | ||||||||
\(783\) | −3.25096 | + | 5.63083i | −0.116180 | + | 0.201230i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.42221 | −0.0507607 | ||||||||
\(786\) | 26.5458 | − | 45.9787i | 0.946859 | − | 1.64001i | ||||
\(787\) | −31.2574 | −1.11420 | −0.557102 | − | 0.830444i | \(-0.688087\pi\) | ||||
−0.557102 | + | 0.830444i | \(0.688087\pi\) | |||||||
\(788\) | 1.80278 | − | 3.12250i | 0.0642212 | − | 0.111234i | ||||
\(789\) | −16.7123 | + | 28.9466i | −0.594975 | + | 1.03053i | ||||
\(790\) | 16.4836 | − | 28.5504i | 0.586459 | − | 1.01578i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.9916 | 0.888038 | ||||||||
\(793\) | −9.39445 | − | 12.4900i | −0.333607 | − | 0.443533i | ||||
\(794\) | −4.99082 | + | 8.64436i | −0.177118 | + | 0.306777i | ||||
\(795\) | −5.62363 | − | 9.74042i | −0.199450 | − | 0.345457i | ||||
\(796\) | −23.6417 | −0.837958 | ||||||||
\(797\) | −13.0038 | − | 22.5233i | −0.460620 | − | 0.797817i | 0.538372 | − | 0.842707i | \(-0.319040\pi\) |
−0.998992 | + | 0.0448902i | \(0.985706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.40833 | + | 9.36750i | 0.191333 | + | 0.331398i | ||||
\(800\) | −0.802776 | + | 1.39045i | −0.0283824 | + | 0.0491598i | ||||
\(801\) | −5.51761 | + | 9.55678i | −0.194955 | + | 0.337672i | ||||
\(802\) | −23.3028 | −0.822850 | ||||||||
\(803\) | −21.2757 | −0.750804 | ||||||||
\(804\) | −3.57907 | + | 6.19912i | −0.126224 | + | 0.218626i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.7250 | + | 47.4967i | 1.25836 | + | 1.67300i | ||||
\(807\) | 0.711103 | + | 1.23167i | 0.0250320 | + | 0.0433567i | ||||
\(808\) | 9.75289 | + | 16.8925i | 0.343105 | + | 0.594276i | ||||
\(809\) | −10.0139 | − | 17.3445i | −0.352069 | − | 0.609802i | 0.634543 | − | 0.772888i | \(-0.281188\pi\) |
−0.986612 | + | 0.163086i | \(0.947855\pi\) | |||||||
\(810\) | 27.9763 | − | 48.4564i | 0.982988 | − | 1.70258i | ||||
\(811\) | 0.854892 | 0.0300193 | 0.0150097 | − | 0.999887i | \(-0.495222\pi\) | ||||
0.0150097 | + | 0.999887i | \(0.495222\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.7292 | − | 27.2437i | −0.551647 | − | 0.955480i | ||||
\(814\) | −48.6333 | − | 84.2354i | −1.70460 | − | 2.95245i | ||||
\(815\) | −6.04440 | −0.211726 | ||||||||
\(816\) | −2.34861 | − | 4.06792i | −0.0822179 | − | 0.142406i | ||||
\(817\) | −27.1214 | −0.948859 | ||||||||
\(818\) | 8.01302 | 0.280169 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −71.4500 | −2.49514 | ||||||||
\(821\) | −55.8444 | −1.94898 | −0.974492 | − | 0.224424i | \(-0.927950\pi\) | ||||
−0.974492 | + | 0.224424i | \(0.927950\pi\) | |||||||
\(822\) | −15.7280 | − | 27.2417i | −0.548578 | − | 0.950165i | ||||
\(823\) | 42.2666 | 1.47332 | 0.736661 | − | 0.676262i | \(-0.236401\pi\) | ||||
0.736661 | + | 0.676262i | \(0.236401\pi\) | |||||||
\(824\) | −17.2391 | − | 29.8590i | −0.600553 | − | 1.04019i | ||||
\(825\) | 1.61044 | + | 2.78937i | 0.0560684 | + | 0.0971133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7527 | −0.582550 | −0.291275 | − | 0.956639i | \(-0.594079\pi\) | ||||
−0.291275 | + | 0.956639i | \(0.594079\pi\) | |||||||
\(828\) | 1.69722 | − | 2.93968i | 0.0589826 | − | 0.102161i | ||||
\(829\) | −25.3816 | − | 43.9622i | −0.881538 | − | 1.52687i | −0.849631 | − | 0.527378i | \(-0.823175\pi\) |
−0.0319077 | − | 0.999491i | \(-0.510158\pi\) | |||||||
\(830\) | −7.04584 | − | 12.2037i | −0.244565 | − | 0.423598i | ||||
\(831\) | 0.228762 | + | 0.396228i | 0.00793567 | + | 0.0137450i | ||||
\(832\) | 18.0940 | − | 42.5214i | 0.627297 | − | 1.47417i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 26.5458 | − | 45.9787i | 0.919207 | − | 1.59211i | ||||
\(835\) | 24.9083 | 0.861988 | ||||||||
\(836\) | 35.1345 | 1.21515 | ||||||||
\(837\) | −10.1056 | + | 17.5033i | −0.349299 | + | 0.605004i | ||||
\(838\) | 19.7345 | − | 34.1812i | 0.681718 | − | 1.18077i | ||||
\(839\) | −6.73069 | − | 11.6579i | −0.232369 | − | 0.402475i | 0.726136 | − | 0.687551i | \(-0.241314\pi\) |
−0.958505 | + | 0.285076i | \(0.907981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8486 | + | 20.5224i | 0.408573 | + | 0.707669i | ||||
\(842\) | 11.5778 | 0.398997 | ||||||||
\(843\) | −25.8090 | − | 44.7025i | −0.888910 | − | 1.53964i | ||||
\(844\) | −24.7708 | + | 42.9043i | −0.852647 | + | 1.47683i | ||||
\(845\) | −7.81434 | + | 27.0697i | −0.268821 | + | 0.931225i | ||||
\(846\) | −5.90587 | −0.203048 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.362490 | + | 0.627852i | −0.0124480 | + | 0.0215605i | ||||
\(849\) | −20.2111 | + | 35.0067i | −0.693643 | + | 1.20143i | ||||
\(850\) | 2.49541 | − | 4.32218i | 0.0855919 | − | 0.148250i | ||||
\(851\) | −5.21110 | −0.178634 | ||||||||
\(852\) | −14.3163 | + | 24.7965i | −0.490467 | + | 0.849514i | ||||
\(853\) | 12.8052 | 0.438440 | 0.219220 | − | 0.975675i | \(-0.429649\pi\) | ||||
0.219220 | + | 0.975675i | \(0.429649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.98612 | + | 6.90417i | −0.136322 | + | 0.236117i | ||||
\(856\) | 17.0917 | 0.584181 | ||||||||
\(857\) | −1.64052 | + | 2.84146i | −0.0560391 | + | 0.0970626i | −0.892684 | − | 0.450683i | \(-0.851180\pi\) |
0.836645 | + | 0.547746i | \(0.184514\pi\) | |||||||
\(858\) | −53.0917 | − | 70.5858i | −1.81252 | − | 2.40976i | ||||
\(859\) | −1.51110 | − | 2.61730i | −0.0515581 | − | 0.0893012i | 0.839095 | − | 0.543986i | \(-0.183085\pi\) |
−0.890653 | + | 0.454684i | \(0.849752\pi\) | |||||||
\(860\) | 44.7880 | − | 77.5751i | 1.52726 | − | 2.64529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.1056 | + | 41.7520i | 0.821038 | + | 1.42208i | ||||
\(863\) | −4.90833 | − | 8.50147i | −0.167081 | − | 0.289393i | 0.770311 | − | 0.637668i | \(-0.220101\pi\) |
−0.937392 | + | 0.348275i | \(0.886768\pi\) | |||||||
\(864\) | 14.9725 | 0.509374 | ||||||||
\(865\) | 22.0639 | 0.750196 | ||||||||
\(866\) | −19.7345 | − | 34.1812i | −0.670607 | − | 1.16153i | ||||
\(867\) | −37.1031 | − | 64.2644i | −1.26009 | − | 2.18253i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.2111 | − | 28.0785i | 0.549924 | − | 0.952496i | ||||
\(870\) | 12.4542 | + | 21.5712i | 0.422236 | + | 0.731334i | ||||
\(871\) | 3.57907 | − | 0.436217i | 0.121272 | − | 0.0147806i | ||||
\(872\) | −12.3167 | + | 21.3331i | −0.417095 | + | 0.722429i | ||||
\(873\) | −23.1842 | −0.784666 | ||||||||
\(874\) | 1.51110 | − | 2.61730i | 0.0511137 | − | 0.0885316i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.0278 | −1.04833 | ||||||||
\(877\) | 22.8028 | − | 39.4956i | 0.769995 | − | 1.33367i | −0.167570 | − | 0.985860i | \(-0.553592\pi\) |
0.937565 | − | 0.347810i | \(-0.113075\pi\) | |||||||
\(878\) | −8.47055 | −0.285867 | ||||||||
\(879\) | 31.0278 | − | 53.7417i | 1.04654 | − | 1.81266i | ||||
\(880\) | −1.61044 | + | 2.78937i | −0.0542880 | + | 0.0940295i | ||||
\(881\) | −9.42478 | + | 16.3242i | −0.317529 | + | 0.549976i | −0.979972 | − | 0.199136i | \(-0.936186\pi\) |
0.662443 | + | 0.749112i | \(0.269520\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3944 | −0.820939 | −0.410469 | − | 0.911874i | \(-0.634635\pi\) | ||||
−0.410469 | + | 0.911874i | \(0.634635\pi\) | |||||||
\(884\) | −33.3764 | + | 78.4354i | −1.12257 | + | 2.63807i | ||||
\(885\) | 6.63134 | − | 11.4858i | 0.222910 | − | 0.386092i | ||||
\(886\) | 23.3028 | + | 40.3616i | 0.782872 | + | 1.35597i | ||||
\(887\) | 34.6769 | 1.16434 | 0.582169 | − | 0.813068i | \(-0.302204\pi\) | ||||
0.582169 | + | 0.813068i | \(0.302204\pi\) | |||||||
\(888\) | −27.9763 | − | 48.4564i | −0.938824 | − | 1.62609i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.2250 | − | 28.1025i | −0.543863 | − | 0.941998i | ||||
\(891\) | 27.5139 | − | 47.6554i | 0.921750 | − | 1.59652i | ||||
\(892\) | 29.7162 | − | 51.4699i | 0.994971 | − | 1.72334i | ||||
\(893\) | −3.27502 | −0.109594 | ||||||||
\(894\) | −87.4087 | −2.92338 | ||||||||
\(895\) | −23.4129 | + | 40.5524i | −0.782608 | + | 1.35552i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.69722 | + | 0.572498i | −0.156836 | + | 0.0191152i | ||||
\(898\) | 23.5139 | + | 40.7272i | 0.784668 | + | 1.35909i | ||||
\(899\) | −8.24179 | − | 14.2752i | −0.274879 | − | 0.476104i | ||||
\(900\) | 0.848612 | + | 1.46984i | 0.0282871 | + | 0.0489946i | ||||
\(901\) | −8.56989 | + | 14.8435i | −0.285504 | + | 0.494508i | ||||
\(902\) | −112.820 | −3.75651 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2250 | − | 17.7102i | −0.340078 | − | 0.589032i | ||||
\(905\) | 26.3305 | + | 45.6058i | 0.875256 | + | 1.51599i | ||||
\(906\) | 40.9802 | 1.36147 | ||||||||
\(907\) | 19.4222 | + | 33.6402i | 0.644904 | + | 1.11701i | 0.984324 | + | 0.176371i | \(0.0564359\pi\) |
−0.339420 | + | 0.940635i | \(0.610231\pi\) | |||||||
\(908\) | −60.9435 | −2.02248 | ||||||||
\(909\) | −11.0352 | −0.366015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.9361 | 1.19062 | 0.595308 | − | 0.803498i | \(-0.297030\pi\) | ||||
0.595308 | + | 0.803498i | \(0.297030\pi\) | |||||||
\(912\) | 1.42221 | 0.0470939 | ||||||||
\(913\) | −6.92937 | − | 12.0020i | −0.229329 | − | 0.397209i | ||||
\(914\) | 47.4500 | 1.56951 | ||||||||
\(915\) | −10.1803 | − | 17.6329i | −0.336551 | − | 0.582924i | ||||
\(916\) | 25.8090 | + | 44.7025i | 0.852754 | + | 1.47701i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −46.5416 | −1.53610 | ||||||||
\(919\) | −26.7250 | + | 46.2890i | −0.881576 | + | 1.52693i | −0.0319871 | + | 0.999488i | \(0.510184\pi\) |
−0.849589 | + | 0.527446i | \(0.823150\pi\) | |||||||
\(920\) | 1.96862 | + | 3.40976i | 0.0649036 | + | 0.112416i | ||||
\(921\) | −3.98612 | − | 6.90417i | −0.131347 | − | 0.227500i | ||||
\(922\) | 28.9606 | + | 50.1613i | 0.953768 | + | 1.65197i | ||||
\(923\) | 14.3163 | − | 1.74487i | 0.471226 | − | 0.0574330i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.30278 | − | 2.25647i | 0.0428350 | − | 0.0741924i | ||||
\(926\) | −31.7527 | −1.04346 | ||||||||
\(927\) | 19.5058 | 0.640654 | ||||||||
\(928\) | −6.10555 | + | 10.5751i | −0.200425 | + | 0.347145i | ||||
\(929\) | 8.56989 | − | 14.8435i | 0.281169 | − | 0.486999i | −0.690504 | − | 0.723329i | \(-0.742611\pi\) |
0.971673 | + | 0.236330i | \(0.0759445\pi\) | |||||||
\(930\) | 38.7135 | + | 67.0538i | 1.26947 | + | 2.19878i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.6194 | + | 37.4460i | 0.708168 | + | 1.22658i | ||||
\(933\) | 23.0555 | 0.754804 | ||||||||
\(934\) | −14.7437 | − | 25.5369i | −0.482429 | − | 0.835591i | ||||
\(935\) | −38.0736 | + | 65.9454i | −1.24514 | + | 2.15665i | ||||
\(936\) | −11.0352 | − | 14.6714i | −0.360698 | − | 0.479550i | ||||
\(937\) | −19.7646 | −0.645682 | −0.322841 | − | 0.946453i | \(-0.604638\pi\) | ||||
−0.322841 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.11943 | − | 10.5992i | 0.199700 | − | 0.345891i | ||||
\(940\) | 5.40833 | − | 9.36750i | 0.176400 | − | 0.305534i | ||||
\(941\) | 2.72417 | − | 4.71841i | 0.0888055 | − | 0.153816i | −0.818201 | − | 0.574932i | \(-0.805028\pi\) |
0.907006 | + | 0.421117i | \(0.138362\pi\) | |||||||
\(942\) | −3.27502 | −0.106706 | ||||||||
\(943\) | −3.02220 | + | 5.23460i | −0.0984164 | + | 0.170462i | ||||
\(944\) | −0.854892 | −0.0278244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.7208 | − | 122.492i | 2.29933 | − | 3.98256i | ||||
\(947\) | 27.8806 | 0.905997 | 0.452998 | − | 0.891511i | \(-0.350354\pi\) | ||||
0.452998 | + | 0.891511i | \(0.350354\pi\) | |||||||
\(948\) | 23.6417 | − | 40.9486i | 0.767847 | − | 1.32995i | ||||
\(949\) | 9.39445 | + | 12.4900i | 0.304957 | + | 0.405442i | ||||
\(950\) | 0.755550 | + | 1.30865i | 0.0245133 | + | 0.0424582i | ||||
\(951\) | 6.73069 | − | 11.6579i | 0.218257 | − | 0.378033i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1972 | − | 29.7865i | −0.557073 | − | 0.964878i | −0.997739 | − | 0.0672073i | \(-0.978591\pi\) |
0.440666 | − | 0.897671i | \(-0.354742\pi\) | |||||||
\(954\) | −4.67914 | − | 8.10452i | −0.151493 | − | 0.262393i | ||||
\(955\) | 34.0207 | 1.10088 | ||||||||
\(956\) | 14.5139 | 0.469412 | ||||||||
\(957\) | 12.2483 | + | 21.2147i | 0.395931 | + | 0.685773i | ||||
\(958\) | 18.9790 | + | 32.8726i | 0.613183 | + | 1.06206i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.1013 | − | 52.1371i | 0.971517 | − | 1.68272i | ||||
\(961\) | −10.1194 | − | 17.5274i | −0.326433 | − | 0.565399i | ||||
\(962\) | −27.9763 | + | 65.7451i | −0.901993 | + | 2.11971i | ||||
\(963\) | −4.83473 | + | 8.37400i | −0.155797 | + | 0.269849i | ||||
\(964\) | −30.7998 | −0.991996 | ||||||||
\(965\) | −21.4744 | + | 37.1947i | −0.691285 | + | 1.19734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4500 | −1.36510 | −0.682549 | − | 0.730839i | \(-0.739129\pi\) | ||||
−0.682549 | + | 0.730839i | \(0.739129\pi\) | |||||||
\(968\) | −19.6375 | + | 34.0132i | −0.631173 | + | 1.09322i | ||||
\(969\) | 33.6234 | 1.08014 | ||||||||
\(970\) | 34.0875 | − | 59.0412i | 1.09448 | − | 1.89570i | ||||
\(971\) | 15.7280 | − | 27.2417i | 0.504736 | − | 0.874229i | −0.495249 | − | 0.868751i | \(-0.664923\pi\) |
0.999985 | − | 0.00547764i | \(-0.00174359\pi\) | |||||||
\(972\) | 26.1371 | − | 45.2708i | 0.838348 | − | 1.45206i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.0833 | −2.30970 | ||||||||
\(975\) | 0.926407 | − | 2.17708i | 0.0296688 | − | 0.0697224i | ||||
\(976\) | −0.656208 | + | 1.13659i | −0.0210047 | + | 0.0363812i | ||||
\(977\) | 1.98612 | + | 3.44006i | 0.0635417 | + | 0.110057i | 0.896046 | − | 0.443961i | \(-0.146427\pi\) |
−0.832504 | + | 0.554018i | \(0.813094\pi\) | |||||||
\(978\) | −13.9189 | −0.445077 | ||||||||
\(979\) | −15.9568 | − | 27.6380i | −0.509981 | − | 0.883313i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.96804 | − | 12.0690i | −0.222472 | − | 0.385334i | ||||
\(982\) | −22.7111 | + | 39.3368i | −0.724740 | + | 1.25529i | ||||
\(983\) | −14.6444 | + | 25.3648i | −0.467083 | + | 0.809011i | −0.999293 | − | 0.0376012i | \(-0.988028\pi\) |
0.532210 | + | 0.846612i | \(0.321362\pi\) | |||||||
\(984\) | −64.8999 | −2.06893 | ||||||||
\(985\) | −2.36599 | −0.0753868 | ||||||||
\(986\) | 18.9790 | − | 32.8726i | 0.604414 | − | 1.04688i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.5139 | − | 20.6258i | −0.493562 | − | 0.656195i | ||||
\(989\) | −3.78890 | − | 6.56256i | −0.120480 | − | 0.208677i | ||||
\(990\) | −20.7881 | − | 36.0061i | −0.660690 | − | 1.14435i | ||||
\(991\) | 3.33473 | + | 5.77593i | 0.105931 | + | 0.183478i | 0.914118 | − | 0.405448i | \(-0.132884\pi\) |
−0.808187 | + | 0.588926i | \(0.799551\pi\) | |||||||
\(992\) | −18.9790 | + | 32.8726i | −0.602583 | + | 1.04371i | ||||
\(993\) | 9.32544 | 0.295934 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.75694 | + | 13.4354i | 0.245912 | + | 0.425931i | ||||
\(996\) | −10.1056 | − | 17.5033i | −0.320207 | − | 0.554614i | ||||
\(997\) | 52.7318 | 1.67003 | 0.835016 | − | 0.550226i | \(-0.185458\pi\) | ||||
0.835016 | + | 0.550226i | \(0.185458\pi\) | |||||||
\(998\) | 9.59167 | + | 16.6133i | 0.303619 | + | 0.525884i | ||||
\(999\) | −24.2979 | −0.768752 |
(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 | 637.2.h.j.165.3 | 8 | ||
7.2 | even | 3 | 637.2.g.i.373.2 | 8 | |||
7.3 | odd | 6 | 637.2.f.h.295.2 | yes | 8 | ||
7.4 | even | 3 | 637.2.f.h.295.1 | ✓ | 8 | ||
7.5 | odd | 6 | 637.2.g.i.373.1 | 8 | |||
7.6 | odd | 2 | inner | 637.2.h.j.165.4 | 8 | ||
13.3 | even | 3 | 637.2.g.i.263.2 | 8 | |||
91.3 | odd | 6 | 637.2.f.h.393.2 | yes | 8 | ||
91.4 | even | 6 | 8281.2.a.bo.1.2 | 4 | |||
91.16 | even | 3 | inner | 637.2.h.j.471.3 | 8 | ||
91.17 | odd | 6 | 8281.2.a.bo.1.1 | 4 | |||
91.55 | odd | 6 | 637.2.g.i.263.1 | 8 | |||
91.68 | odd | 6 | inner | 637.2.h.j.471.4 | 8 | ||
91.74 | even | 3 | 8281.2.a.bu.1.4 | 4 | |||
91.81 | even | 3 | 637.2.f.h.393.1 | yes | 8 | ||
91.87 | odd | 6 | 8281.2.a.bu.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.h.295.1 | ✓ | 8 | 7.4 | even | 3 | ||
637.2.f.h.295.2 | yes | 8 | 7.3 | odd | 6 | ||
637.2.f.h.393.1 | yes | 8 | 91.81 | even | 3 | ||
637.2.f.h.393.2 | yes | 8 | 91.3 | odd | 6 | ||
637.2.g.i.263.1 | 8 | 91.55 | odd | 6 | |||
637.2.g.i.263.2 | 8 | 13.3 | even | 3 | |||
637.2.g.i.373.1 | 8 | 7.5 | odd | 6 | |||
637.2.g.i.373.2 | 8 | 7.2 | even | 3 | |||
637.2.h.j.165.3 | 8 | 1.1 | even | 1 | trivial | ||
637.2.h.j.165.4 | 8 | 7.6 | odd | 2 | inner | ||
637.2.h.j.471.3 | 8 | 91.16 | even | 3 | inner | ||
637.2.h.j.471.4 | 8 | 91.68 | odd | 6 | inner | ||
8281.2.a.bo.1.1 | 4 | 91.17 | odd | 6 | |||
8281.2.a.bo.1.2 | 4 | 91.4 | even | 6 | |||
8281.2.a.bu.1.3 | 4 | 91.87 | odd | 6 | |||
8281.2.a.bu.1.4 | 4 | 91.74 | even | 3 |