Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (of order \(2\), degree \(1\), 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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.3 | ||
Root | \(1.40680 + 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.ba.1849.4 |
$q$-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 \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 3.10278i | 1.79139i | 0.444671 | + | 0.895694i | \(0.353321\pi\) | ||||
−0.444671 | + | 0.895694i | \(0.646679\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.10278 | 1.26670 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −6.62721 | −2.20907 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − 3.10278i | − 0.895694i | ||||||||
\(13\) | − 3.62721i | − 1.00601i | −0.864284 | − | 0.503004i | \(-0.832228\pi\) | ||||
0.864284 | − | 0.503004i | \(-0.167772\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.20555i | 1.02000i | 0.860176 | + | 0.509998i | \(0.170354\pi\) | ||||
−0.860176 | + | 0.509998i | \(0.829646\pi\) | |||||||
\(18\) | 6.62721i | 1.56205i | ||||||||
\(19\) | 8.15165 | 1.87012 | 0.935058 | − | 0.354493i | \(-0.115347\pi\) | ||||
0.935058 | + | 0.354493i | \(0.115347\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.10278 | −0.677081 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | 0.897225i | 0.187084i | 0.995615 | + | 0.0935422i | \(0.0298190\pi\) | ||||
−0.995615 | + | 0.0935422i | \(0.970181\pi\) | |||||||
\(24\) | −3.10278 | −0.633351 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.62721 | −0.711355 | ||||||||
\(27\) | − 11.2544i | − 2.16592i | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | 7.30833 | 1.35712 | 0.678561 | − | 0.734544i | \(-0.262604\pi\) | ||||
0.678561 | + | 0.734544i | \(0.262604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.42166 | −0.614549 | −0.307274 | − | 0.951621i | \(-0.599417\pi\) | ||||
−0.307274 | + | 0.951621i | \(0.599417\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 3.10278i | 0.540124i | ||||||||
\(34\) | 4.20555 | 0.721246 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.62721 | 1.10454 | ||||||||
\(37\) | 1.10278i | 0.181295i | 0.995883 | + | 0.0906476i | \(0.0288937\pi\) | ||||
−0.995883 | + | 0.0906476i | \(0.971106\pi\) | |||||||
\(38\) | − 8.15165i | − 1.32237i | ||||||||
\(39\) | 11.2544 | 1.80215 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3572 | 1.92987 | 0.964935 | − | 0.262488i | \(-0.0845430\pi\) | ||||
0.964935 | + | 0.262488i | \(0.0845430\pi\) | |||||||
\(42\) | 3.10278i | 0.478769i | ||||||||
\(43\) | 10.6761i | 1.62809i | 0.580803 | + | 0.814044i | \(0.302739\pi\) | ||||
−0.580803 | + | 0.814044i | \(0.697261\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.897225 | 0.132289 | ||||||||
\(47\) | 1.15667i | 0.168718i | 0.996435 | + | 0.0843591i | \(0.0268843\pi\) | ||||
−0.996435 | + | 0.0843591i | \(0.973116\pi\) | |||||||
\(48\) | 3.10278i | 0.447847i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0489 | −1.82721 | ||||||||
\(52\) | 3.62721i | 0.503004i | ||||||||
\(53\) | 11.3083i | 1.55332i | 0.629921 | + | 0.776659i | \(0.283087\pi\) | ||||
−0.629921 | + | 0.776659i | \(0.716913\pi\) | |||||||
\(54\) | −11.2544 | −1.53153 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 25.2927i | 3.35011i | ||||||||
\(58\) | − 7.30833i | − 0.959630i | ||||||||
\(59\) | −7.25443 | −0.944446 | −0.472223 | − | 0.881479i | \(-0.656548\pi\) | ||||
−0.472223 | + | 0.881479i | \(0.656548\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.15667 | −0.404171 | −0.202085 | − | 0.979368i | \(-0.564772\pi\) | ||||
−0.202085 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(62\) | 3.42166i | 0.434552i | ||||||||
\(63\) | − 6.62721i | − 0.834950i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.10278 | 0.381925 | ||||||||
\(67\) | 8.41110i | 1.02758i | 0.857916 | + | 0.513790i | \(0.171759\pi\) | ||||
−0.857916 | + | 0.513790i | \(0.828241\pi\) | |||||||
\(68\) | − 4.20555i | − 0.509998i | ||||||||
\(69\) | −2.78389 | −0.335141 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0489 | −1.54862 | −0.774308 | − | 0.632809i | \(-0.781902\pi\) | ||||
−0.774308 | + | 0.632809i | \(0.781902\pi\) | |||||||
\(72\) | − 6.62721i | − 0.781025i | ||||||||
\(73\) | 0.205550i | 0.0240578i | 0.999928 | + | 0.0120289i | \(0.00382901\pi\) | ||||
−0.999928 | + | 0.0120289i | \(0.996171\pi\) | |||||||
\(74\) | 1.10278 | 0.128195 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.15165 | −0.935058 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | − 11.2544i | − 1.27431i | ||||||||
\(79\) | −12.1517 | −1.36717 | −0.683584 | − | 0.729872i | \(-0.739580\pi\) | ||||
−0.683584 | + | 0.729872i | \(0.739580\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.0383 | 1.67092 | ||||||||
\(82\) | − 12.3572i | − 1.36462i | ||||||||
\(83\) | 2.20555i | 0.242091i | 0.992647 | + | 0.121045i | \(0.0386246\pi\) | ||||
−0.992647 | + | 0.121045i | \(0.961375\pi\) | |||||||
\(84\) | 3.10278 | 0.338541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.6761 | 1.15123 | ||||||||
\(87\) | 22.6761i | 2.43113i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | 7.45998 | 0.790756 | 0.395378 | − | 0.918519i | \(-0.370614\pi\) | ||||
0.395378 | + | 0.918519i | \(0.370614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.62721 | 0.380235 | ||||||||
\(92\) | − 0.897225i | − 0.0935422i | ||||||||
\(93\) | − 10.6167i | − 1.10090i | ||||||||
\(94\) | 1.15667 | 0.119302 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.10278 | 0.316676 | ||||||||
\(97\) | − 2.25945i | − 0.229412i | −0.993399 | − | 0.114706i | \(-0.963407\pi\) | ||||
0.993399 | − | 0.114706i | \(-0.0365926\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −6.62721 | −0.666060 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6655 | 1.35977 | 0.679885 | − | 0.733318i | \(-0.262030\pi\) | ||||
0.679885 | + | 0.733318i | \(0.262030\pi\) | |||||||
\(102\) | 13.0489i | 1.29203i | ||||||||
\(103\) | − 5.04888i | − 0.497481i | −0.968570 | − | 0.248740i | \(-0.919983\pi\) | ||||
0.968570 | − | 0.248740i | \(-0.0800166\pi\) | |||||||
\(104\) | 3.62721 | 0.355677 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.3083 | 1.09836 | ||||||||
\(107\) | − 12.9894i | − 1.25574i | −0.778320 | − | 0.627868i | \(-0.783928\pi\) | ||||
0.778320 | − | 0.627868i | \(-0.216072\pi\) | |||||||
\(108\) | 11.2544i | 1.08296i | ||||||||
\(109\) | −5.10278 | −0.488757 | −0.244379 | − | 0.969680i | \(-0.578584\pi\) | ||||
−0.244379 | + | 0.969680i | \(0.578584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42166 | −0.324770 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − 10.4111i | − 0.979394i | −0.871893 | − | 0.489697i | \(-0.837107\pi\) | ||||
0.871893 | − | 0.489697i | \(-0.162893\pi\) | |||||||
\(114\) | 25.2927 | 2.36888 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.30833 | −0.678561 | ||||||||
\(117\) | 24.0383i | 2.22234i | ||||||||
\(118\) | 7.25443i | 0.667824i | ||||||||
\(119\) | −4.20555 | −0.385522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.15667i | 0.285792i | ||||||||
\(123\) | 38.3416i | 3.45715i | ||||||||
\(124\) | 3.42166 | 0.307274 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.62721 | −0.590399 | ||||||||
\(127\) | − 3.25443i | − 0.288784i | −0.989521 | − | 0.144392i | \(-0.953877\pi\) | ||||
0.989521 | − | 0.144392i | \(-0.0461226\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −33.1255 | −2.91654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3083 | −1.51224 | −0.756118 | − | 0.654436i | \(-0.772906\pi\) | ||||
−0.756118 | + | 0.654436i | \(0.772906\pi\) | |||||||
\(132\) | − 3.10278i | − 0.270062i | ||||||||
\(133\) | 8.15165i | 0.706838i | ||||||||
\(134\) | 8.41110 | 0.726608 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.20555 | −0.360623 | ||||||||
\(137\) | − 10.0000i | − 0.854358i | −0.904167 | − | 0.427179i | \(-0.859507\pi\) | ||||
0.904167 | − | 0.427179i | \(-0.140493\pi\) | |||||||
\(138\) | 2.78389i | 0.236980i | ||||||||
\(139\) | −13.2005 | −1.11965 | −0.559827 | − | 0.828609i | \(-0.689132\pi\) | ||||
−0.559827 | + | 0.828609i | \(0.689132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.58890 | −0.302240 | ||||||||
\(142\) | 13.0489i | 1.09504i | ||||||||
\(143\) | − 3.62721i | − 0.303323i | ||||||||
\(144\) | −6.62721 | −0.552268 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.205550 | 0.0170114 | ||||||||
\(147\) | − 3.10278i | − 0.255913i | ||||||||
\(148\) | − 1.10278i | − 0.0906476i | ||||||||
\(149\) | 23.6116 | 1.93434 | 0.967170 | − | 0.254131i | \(-0.0817893\pi\) | ||||
0.967170 | + | 0.254131i | \(0.0817893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5139 | 0.936986 | 0.468493 | − | 0.883467i | \(-0.344797\pi\) | ||||
0.468493 | + | 0.883467i | \(0.344797\pi\) | |||||||
\(152\) | 8.15165i | 0.661186i | ||||||||
\(153\) | − 27.8711i | − 2.25324i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.2544 | −0.901075 | ||||||||
\(157\) | 16.2056i | 1.29334i | 0.762768 | + | 0.646672i | \(0.223840\pi\) | ||||
−0.762768 | + | 0.646672i | \(0.776160\pi\) | |||||||
\(158\) | 12.1517i | 0.966733i | ||||||||
\(159\) | −35.0872 | −2.78260 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.897225 | −0.0707112 | ||||||||
\(162\) | − 15.0383i | − 1.18152i | ||||||||
\(163\) | 6.31335i | 0.494500i | 0.968952 | + | 0.247250i | \(0.0795268\pi\) | ||||
−0.968952 | + | 0.247250i | \(0.920473\pi\) | |||||||
\(164\) | −12.3572 | −0.964935 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.20555 | 0.171184 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | − 3.10278i | − 0.239384i | ||||||||
\(169\) | −0.156674 | −0.0120519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −54.0227 | −4.13122 | ||||||||
\(172\) | − 10.6761i | − 0.814044i | ||||||||
\(173\) | 9.25443i | 0.703601i | 0.936075 | + | 0.351800i | \(0.114430\pi\) | ||||
−0.936075 | + | 0.351800i | \(0.885570\pi\) | |||||||
\(174\) | 22.6761 | 1.71907 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | − 22.5089i | − 1.69187i | ||||||||
\(178\) | − 7.45998i | − 0.559149i | ||||||||
\(179\) | −4.98944 | −0.372928 | −0.186464 | − | 0.982462i | \(-0.559703\pi\) | ||||
−0.186464 | + | 0.982462i | \(0.559703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.66553 | −0.718433 | −0.359216 | − | 0.933254i | \(-0.616956\pi\) | ||||
−0.359216 | + | 0.933254i | \(0.616956\pi\) | |||||||
\(182\) | − 3.62721i | − 0.268867i | ||||||||
\(183\) | − 9.79445i | − 0.724027i | ||||||||
\(184\) | −0.897225 | −0.0661443 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.6167 | −0.778451 | ||||||||
\(187\) | 4.20555i | 0.307540i | ||||||||
\(188\) | − 1.15667i | − 0.0843591i | ||||||||
\(189\) | 11.2544 | 0.818639 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.15667 | −0.662554 | −0.331277 | − | 0.943534i | \(-0.607479\pi\) | ||||
−0.331277 | + | 0.943534i | \(0.607479\pi\) | |||||||
\(192\) | − 3.10278i | − 0.223924i | ||||||||
\(193\) | 1.52946i | 0.110093i | 0.998484 | + | 0.0550465i | \(0.0175307\pi\) | ||||
−0.998484 | + | 0.0550465i | \(0.982469\pi\) | |||||||
\(194\) | −2.25945 | −0.162219 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − 14.3033i | − 1.01907i | −0.860451 | − | 0.509534i | \(-0.829818\pi\) | ||||
0.860451 | − | 0.509534i | \(-0.170182\pi\) | |||||||
\(198\) | 6.62721i | 0.470976i | ||||||||
\(199\) | 10.0978 | 0.715811 | 0.357905 | − | 0.933758i | \(-0.383491\pi\) | ||||
0.357905 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.0978 | −1.84079 | ||||||||
\(202\) | − 13.6655i | − 0.961503i | ||||||||
\(203\) | 7.30833i | 0.512944i | ||||||||
\(204\) | 13.0489 | 0.913604 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.04888 | −0.351772 | ||||||||
\(207\) | − 5.94610i | − 0.413283i | ||||||||
\(208\) | − 3.62721i | − 0.251502i | ||||||||
\(209\) | 8.15165 | 0.563861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8433 | 0.746485 | 0.373243 | − | 0.927734i | \(-0.378246\pi\) | ||||
0.373243 | + | 0.927734i | \(0.378246\pi\) | |||||||
\(212\) | − 11.3083i | − 0.776659i | ||||||||
\(213\) | − 40.4877i | − 2.77417i | ||||||||
\(214\) | −12.9894 | −0.887940 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.2544 | 0.765767 | ||||||||
\(217\) | − 3.42166i | − 0.232278i | ||||||||
\(218\) | 5.10278i | 0.345604i | ||||||||
\(219\) | −0.637776 | −0.0430969 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.2544 | 1.02612 | ||||||||
\(222\) | 3.42166i | 0.229647i | ||||||||
\(223\) | − 9.45998i | − 0.633487i | −0.948511 | − | 0.316743i | \(-0.897411\pi\) | ||||
0.948511 | − | 0.316743i | \(-0.102589\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4111 | −0.692536 | ||||||||
\(227\) | 17.5678i | 1.16601i | 0.812467 | + | 0.583007i | \(0.198124\pi\) | ||||
−0.812467 | + | 0.583007i | \(0.801876\pi\) | |||||||
\(228\) | − 25.2927i | − 1.67505i | ||||||||
\(229\) | −25.7250 | −1.69995 | −0.849977 | − | 0.526820i | \(-0.823384\pi\) | ||||
−0.849977 | + | 0.526820i | \(0.823384\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.10278 | −0.204148 | ||||||||
\(232\) | 7.30833i | 0.479815i | ||||||||
\(233\) | 19.1567i | 1.25500i | 0.778618 | + | 0.627498i | \(0.215921\pi\) | ||||
−0.778618 | + | 0.627498i | \(0.784079\pi\) | |||||||
\(234\) | 24.0383 | 1.57143 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.25443 | 0.472223 | ||||||||
\(237\) | − 37.7038i | − 2.44913i | ||||||||
\(238\) | 4.20555i | 0.272605i | ||||||||
\(239\) | 18.0539 | 1.16781 | 0.583905 | − | 0.811822i | \(-0.301524\pi\) | ||||
0.583905 | + | 0.811822i | \(0.301524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.15165 | 0.396263 | 0.198131 | − | 0.980175i | \(-0.436513\pi\) | ||||
0.198131 | + | 0.980175i | \(0.436513\pi\) | |||||||
\(242\) | − 1.00000i | − 0.0642824i | ||||||||
\(243\) | 12.8972i | 0.827357i | ||||||||
\(244\) | 3.15667 | 0.202085 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 38.3416 | 2.44457 | ||||||||
\(247\) | − 29.5678i | − 1.88135i | ||||||||
\(248\) | − 3.42166i | − 0.217276i | ||||||||
\(249\) | −6.84333 | −0.433678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.9789 | −1.89225 | −0.946125 | − | 0.323802i | \(-0.895039\pi\) | ||||
−0.946125 | + | 0.323802i | \(0.895039\pi\) | |||||||
\(252\) | 6.62721i | 0.417475i | ||||||||
\(253\) | 0.897225i | 0.0564080i | ||||||||
\(254\) | −3.25443 | −0.204201 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 4.05390i | − 0.252875i | −0.991975 | − | 0.126438i | \(-0.959646\pi\) | ||||
0.991975 | − | 0.126438i | \(-0.0403544\pi\) | |||||||
\(258\) | 33.1255i | 2.06230i | ||||||||
\(259\) | −1.10278 | −0.0685231 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.4338 | −2.99798 | ||||||||
\(262\) | 17.3083i | 1.06931i | ||||||||
\(263\) | − 14.5089i | − 0.894654i | −0.894370 | − | 0.447327i | \(-0.852376\pi\) | ||||
0.894370 | − | 0.447327i | \(-0.147624\pi\) | |||||||
\(264\) | −3.10278 | −0.190963 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.15165 | 0.499810 | ||||||||
\(267\) | 23.1466i | 1.41655i | ||||||||
\(268\) | − 8.41110i | − 0.513790i | ||||||||
\(269\) | −4.37279 | −0.266614 | −0.133307 | − | 0.991075i | \(-0.542560\pi\) | ||||
−0.133307 | + | 0.991075i | \(0.542560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6167 | −0.644916 | −0.322458 | − | 0.946584i | \(-0.604509\pi\) | ||||
−0.322458 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(272\) | 4.20555i | 0.254999i | ||||||||
\(273\) | 11.2544i | 0.681149i | ||||||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.78389 | 0.167570 | ||||||||
\(277\) | 19.7633i | 1.18746i | 0.804664 | + | 0.593730i | \(0.202345\pi\) | ||||
−0.804664 | + | 0.593730i | \(0.797655\pi\) | |||||||
\(278\) | 13.2005i | 0.791715i | ||||||||
\(279\) | 22.6761 | 1.35758 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0489 | −1.61360 | −0.806800 | − | 0.590824i | \(-0.798803\pi\) | ||||
−0.806800 | + | 0.590824i | \(0.798803\pi\) | |||||||
\(282\) | 3.58890i | 0.213716i | ||||||||
\(283\) | 27.6655i | 1.64454i | 0.569094 | + | 0.822272i | \(0.307294\pi\) | ||||
−0.569094 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(284\) | 13.0489 | 0.774308 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.62721 | −0.214482 | ||||||||
\(287\) | 12.3572i | 0.729423i | ||||||||
\(288\) | 6.62721i | 0.390512i | ||||||||
\(289\) | −0.686652 | −0.0403913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.01056 | 0.410966 | ||||||||
\(292\) | − 0.205550i | − 0.0120289i | ||||||||
\(293\) | − 8.37279i | − 0.489143i | −0.969631 | − | 0.244572i | \(-0.921353\pi\) | ||||
0.969631 | − | 0.244572i | \(-0.0786474\pi\) | |||||||
\(294\) | −3.10278 | −0.180958 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.10278 | −0.0640975 | ||||||||
\(297\) | − 11.2544i | − 0.653048i | ||||||||
\(298\) | − 23.6116i | − 1.36778i | ||||||||
\(299\) | 3.25443 | 0.188208 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6761 | −0.615360 | ||||||||
\(302\) | − 11.5139i | − 0.662549i | ||||||||
\(303\) | 42.4011i | 2.43588i | ||||||||
\(304\) | 8.15165 | 0.467529 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −27.8711 | −1.59328 | ||||||||
\(307\) | 10.2056i | 0.582462i | 0.956653 | + | 0.291231i | \(0.0940647\pi\) | ||||
−0.956653 | + | 0.291231i | \(0.905935\pi\) | |||||||
\(308\) | − 1.00000i | − 0.0569803i | ||||||||
\(309\) | 15.6655 | 0.891181 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.16724 | −0.463122 | −0.231561 | − | 0.972820i | \(-0.574383\pi\) | ||||
−0.231561 | + | 0.972820i | \(0.574383\pi\) | |||||||
\(312\) | 11.2544i | 0.637156i | ||||||||
\(313\) | 34.5628i | 1.95360i | 0.214149 | + | 0.976801i | \(0.431302\pi\) | ||||
−0.214149 | + | 0.976801i | \(0.568698\pi\) | |||||||
\(314\) | 16.2056 | 0.914532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1517 | 0.683584 | ||||||||
\(317\) | − 9.21057i | − 0.517317i | −0.965969 | − | 0.258659i | \(-0.916720\pi\) | ||||
0.965969 | − | 0.258659i | \(-0.0832805\pi\) | |||||||
\(318\) | 35.0872i | 1.96759i | ||||||||
\(319\) | 7.30833 | 0.409188 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.3033 | 2.24951 | ||||||||
\(322\) | 0.897225i | 0.0500004i | ||||||||
\(323\) | 34.2822i | 1.90751i | ||||||||
\(324\) | −15.0383 | −0.835462 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.31335 | 0.349664 | ||||||||
\(327\) | − 15.8328i | − 0.875554i | ||||||||
\(328\) | 12.3572i | 0.682312i | ||||||||
\(329\) | −1.15667 | −0.0637695 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2439 | 0.892843 | 0.446422 | − | 0.894823i | \(-0.352698\pi\) | ||||
0.446422 | + | 0.894823i | \(0.352698\pi\) | |||||||
\(332\) | − 2.20555i | − 0.121045i | ||||||||
\(333\) | − 7.30833i | − 0.400494i | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.10278 | −0.169270 | ||||||||
\(337\) | 1.25443i | 0.0683329i | 0.999416 | + | 0.0341665i | \(0.0108776\pi\) | ||||
−0.999416 | + | 0.0341665i | \(0.989122\pi\) | |||||||
\(338\) | 0.156674i | 0.00852195i | ||||||||
\(339\) | 32.3033 | 1.75447 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.42166 | −0.185293 | ||||||||
\(342\) | 54.0227i | 2.92121i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | −10.6761 | −0.575616 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.25443 | 0.497521 | ||||||||
\(347\) | − 7.42166i | − 0.398416i | −0.979957 | − | 0.199208i | \(-0.936163\pi\) | ||||
0.979957 | − | 0.199208i | \(-0.0638369\pi\) | |||||||
\(348\) | − 22.6761i | − 1.21557i | ||||||||
\(349\) | 18.3033 | 0.979753 | 0.489877 | − | 0.871792i | \(-0.337042\pi\) | ||||
0.489877 | + | 0.871792i | \(0.337042\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −40.8222 | −2.17893 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | 28.8761i | 1.53692i | 0.639898 | + | 0.768460i | \(0.278977\pi\) | ||||
−0.639898 | + | 0.768460i | \(0.721023\pi\) | |||||||
\(354\) | −22.5089 | −1.19633 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.45998 | −0.395378 | ||||||||
\(357\) | − 13.0489i | − 0.690620i | ||||||||
\(358\) | 4.98944i | 0.263700i | ||||||||
\(359\) | −4.15165 | −0.219116 | −0.109558 | − | 0.993980i | \(-0.534943\pi\) | ||||
−0.109558 | + | 0.993980i | \(0.534943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.4494 | 2.49734 | ||||||||
\(362\) | 9.66553i | 0.508009i | ||||||||
\(363\) | 3.10278i | 0.162853i | ||||||||
\(364\) | −3.62721 | −0.190118 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.79445 | −0.511964 | ||||||||
\(367\) | 5.26447i | 0.274803i | 0.990515 | + | 0.137402i | \(0.0438751\pi\) | ||||
−0.990515 | + | 0.137402i | \(0.956125\pi\) | |||||||
\(368\) | 0.897225i | 0.0467711i | ||||||||
\(369\) | −81.8938 | −4.26322 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3083 | −0.587099 | ||||||||
\(372\) | 10.6167i | 0.550448i | ||||||||
\(373\) | 35.8711i | 1.85733i | 0.370915 | + | 0.928667i | \(0.379044\pi\) | ||||
−0.370915 | + | 0.928667i | \(0.620956\pi\) | |||||||
\(374\) | 4.20555 | 0.217464 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.15667 | −0.0596509 | ||||||||
\(377\) | − 26.5089i | − 1.36528i | ||||||||
\(378\) | − 11.2544i | − 0.578865i | ||||||||
\(379\) | 33.0177 | 1.69601 | 0.848003 | − | 0.529992i | \(-0.177805\pi\) | ||||
0.848003 | + | 0.529992i | \(0.177805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0978 | 0.517323 | ||||||||
\(382\) | 9.15667i | 0.468496i | ||||||||
\(383\) | 2.95112i | 0.150795i | 0.997154 | + | 0.0753977i | \(0.0240226\pi\) | ||||
−0.997154 | + | 0.0753977i | \(0.975977\pi\) | |||||||
\(384\) | −3.10278 | −0.158338 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.52946 | 0.0778475 | ||||||||
\(387\) | − 70.7527i | − 3.59656i | ||||||||
\(388\) | 2.25945i | 0.114706i | ||||||||
\(389\) | −1.89220 | −0.0959384 | −0.0479692 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479692 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.77332 | −0.190825 | ||||||||
\(392\) | − 1.00000i | − 0.0505076i | ||||||||
\(393\) | − 53.7038i | − 2.70900i | ||||||||
\(394\) | −14.3033 | −0.720590 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.62721 | 0.333030 | ||||||||
\(397\) | − 5.36222i | − 0.269122i | −0.990905 | − | 0.134561i | \(-0.957038\pi\) | ||||
0.990905 | − | 0.134561i | \(-0.0429625\pi\) | |||||||
\(398\) | − 10.0978i | − 0.506155i | ||||||||
\(399\) | −25.2927 | −1.26622 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7038 | 1.18371 | 0.591857 | − | 0.806043i | \(-0.298395\pi\) | ||||
0.591857 | + | 0.806043i | \(0.298395\pi\) | |||||||
\(402\) | 26.0978i | 1.30164i | ||||||||
\(403\) | 12.4111i | 0.618241i | ||||||||
\(404\) | −13.6655 | −0.679885 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.30833 | 0.362706 | ||||||||
\(407\) | 1.10278i | 0.0546625i | ||||||||
\(408\) | − 13.0489i | − 0.646016i | ||||||||
\(409\) | −27.0816 | −1.33910 | −0.669551 | − | 0.742766i | \(-0.733513\pi\) | ||||
−0.669551 | + | 0.742766i | \(0.733513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.0278 | 1.53049 | ||||||||
\(412\) | 5.04888i | 0.248740i | ||||||||
\(413\) | − 7.25443i | − 0.356967i | ||||||||
\(414\) | −5.94610 | −0.292235 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.62721 | −0.177839 | ||||||||
\(417\) | − 40.9583i | − 2.00573i | ||||||||
\(418\) | − 8.15165i | − 0.398710i | ||||||||
\(419\) | 3.05892 | 0.149438 | 0.0747191 | − | 0.997205i | \(-0.476194\pi\) | ||||
0.0747191 | + | 0.997205i | \(0.476194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6655 | 1.05591 | 0.527957 | − | 0.849271i | \(-0.322958\pi\) | ||||
0.527957 | + | 0.849271i | \(0.322958\pi\) | |||||||
\(422\) | − 10.8433i | − 0.527845i | ||||||||
\(423\) | − 7.66553i | − 0.372711i | ||||||||
\(424\) | −11.3083 | −0.549181 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −40.4877 | −1.96164 | ||||||||
\(427\) | − 3.15667i | − 0.152762i | ||||||||
\(428\) | 12.9894i | 0.627868i | ||||||||
\(429\) | 11.2544 | 0.543369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.3260 | −1.65343 | −0.826713 | − | 0.562623i | \(-0.809792\pi\) | ||||
−0.826713 | + | 0.562623i | \(0.809792\pi\) | |||||||
\(432\) | − 11.2544i | − 0.541479i | ||||||||
\(433\) | − 0.0538991i | − 0.00259023i | −0.999999 | − | 0.00129511i | \(-0.999588\pi\) | ||||
0.999999 | − | 0.00129511i | \(-0.000412248\pi\) | |||||||
\(434\) | −3.42166 | −0.164245 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.10278 | 0.244379 | ||||||||
\(437\) | 7.31386i | 0.349870i | ||||||||
\(438\) | 0.637776i | 0.0304741i | ||||||||
\(439\) | 7.14663 | 0.341090 | 0.170545 | − | 0.985350i | \(-0.445447\pi\) | ||||
0.170545 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.62721 | 0.315582 | ||||||||
\(442\) | − 15.2544i | − 0.725579i | ||||||||
\(443\) | 8.74557i | 0.415515i | 0.978180 | + | 0.207757i | \(0.0666165\pi\) | ||||
−0.978180 | + | 0.207757i | \(0.933384\pi\) | |||||||
\(444\) | 3.42166 | 0.162385 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.45998 | −0.447943 | ||||||||
\(447\) | 73.2616i | 3.46515i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | −39.7038 | −1.87374 | −0.936870 | − | 0.349678i | \(-0.886291\pi\) | ||||
−0.936870 | + | 0.349678i | \(0.886291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.3572 | 0.581878 | ||||||||
\(452\) | 10.4111i | 0.489697i | ||||||||
\(453\) | 35.7250i | 1.67851i | ||||||||
\(454\) | 17.5678 | 0.824497 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −25.2927 | −1.18444 | ||||||||
\(457\) | − 12.3133i | − 0.575994i | −0.957631 | − | 0.287997i | \(-0.907011\pi\) | ||||
0.957631 | − | 0.287997i | \(-0.0929893\pi\) | |||||||
\(458\) | 25.7250i | 1.20205i | ||||||||
\(459\) | 47.3311 | 2.20922 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0489 | −0.700896 | −0.350448 | − | 0.936582i | \(-0.613971\pi\) | ||||
−0.350448 | + | 0.936582i | \(0.613971\pi\) | |||||||
\(462\) | 3.10278i | 0.144354i | ||||||||
\(463\) | 31.4061i | 1.45956i | 0.683680 | + | 0.729782i | \(0.260378\pi\) | ||||
−0.683680 | + | 0.729782i | \(0.739622\pi\) | |||||||
\(464\) | 7.30833 | 0.339280 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.1567 | 0.887416 | ||||||||
\(467\) | 19.0716i | 0.882529i | 0.897377 | + | 0.441264i | \(0.145470\pi\) | ||||
−0.897377 | + | 0.441264i | \(0.854530\pi\) | |||||||
\(468\) | − 24.0383i | − 1.11117i | ||||||||
\(469\) | −8.41110 | −0.388389 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.2822 | −2.31688 | ||||||||
\(472\) | − 7.25443i | − 0.333912i | ||||||||
\(473\) | 10.6761i | 0.490887i | ||||||||
\(474\) | −37.7038 | −1.73179 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.20555 | 0.192761 | ||||||||
\(477\) | − 74.9427i | − 3.43139i | ||||||||
\(478\) | − 18.0539i | − 0.825766i | ||||||||
\(479\) | 9.49115 | 0.433662 | 0.216831 | − | 0.976209i | \(-0.430428\pi\) | ||||
0.216831 | + | 0.976209i | \(0.430428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | − 6.15165i | − 0.280200i | ||||||||
\(483\) | − 2.78389i | − 0.126671i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.8972 | 0.585030 | ||||||||
\(487\) | − 0.0438527i | − 0.00198715i | −1.00000 | 0.000993577i | \(-0.999684\pi\) | |||||
1.00000 | 0.000993577i | \(-0.000316266\pi\) | ||||||||
\(488\) | − 3.15667i | − 0.142896i | ||||||||
\(489\) | −19.5889 | −0.885841 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.56777 | 0.0707527 | 0.0353763 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353763 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(492\) | − 38.3416i | − 1.72857i | ||||||||
\(493\) | 30.7355i | 1.38426i | ||||||||
\(494\) | −29.5678 | −1.33032 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.42166 | −0.153637 | ||||||||
\(497\) | − 13.0489i | − 0.585322i | ||||||||
\(498\) | 6.84333i | 0.306657i | ||||||||
\(499\) | 42.3416 | 1.89547 | 0.947736 | − | 0.319057i | \(-0.103366\pi\) | ||||
0.947736 | + | 0.319057i | \(0.103366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.8222 | −1.10897 | ||||||||
\(502\) | 29.9789i | 1.33802i | ||||||||
\(503\) | − 36.4111i | − 1.62349i | −0.584012 | − | 0.811745i | \(-0.698518\pi\) | ||||
0.584012 | − | 0.811745i | \(-0.301482\pi\) | |||||||
\(504\) | 6.62721 | 0.295200 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.897225 | 0.0398865 | ||||||||
\(507\) | − 0.486125i | − 0.0215896i | ||||||||
\(508\) | 3.25443i | 0.144392i | ||||||||
\(509\) | 30.0766 | 1.33312 | 0.666562 | − | 0.745450i | \(-0.267765\pi\) | ||||
0.666562 | + | 0.745450i | \(0.267765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.205550 | −0.00909300 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 91.7422i | − 4.05051i | ||||||||
\(514\) | −4.05390 | −0.178810 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33.1255 | 1.45827 | ||||||||
\(517\) | 1.15667i | 0.0508705i | ||||||||
\(518\) | 1.10278i | 0.0484532i | ||||||||
\(519\) | −28.7144 | −1.26042 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.2233 | −1.45554 | −0.727769 | − | 0.685823i | \(-0.759443\pi\) | ||||
−0.727769 | + | 0.685823i | \(0.759443\pi\) | |||||||
\(522\) | 48.4338i | 2.11989i | ||||||||
\(523\) | − 15.5577i | − 0.680292i | −0.940373 | − | 0.340146i | \(-0.889524\pi\) | ||||
0.940373 | − | 0.340146i | \(-0.110476\pi\) | |||||||
\(524\) | 17.3083 | 0.756118 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.5089 | −0.632616 | ||||||||
\(527\) | − 14.3900i | − 0.626837i | ||||||||
\(528\) | 3.10278i | 0.135031i | ||||||||
\(529\) | 22.1950 | 0.964999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.0766 | 2.08635 | ||||||||
\(532\) | − 8.15165i | − 0.353419i | ||||||||
\(533\) | − 44.8222i | − 1.94147i | ||||||||
\(534\) | 23.1466 | 1.00165 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.41110 | −0.363304 | ||||||||
\(537\) | − 15.4811i | − 0.668059i | ||||||||
\(538\) | 4.37279i | 0.188524i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.4161 | 1.00674 | 0.503369 | − | 0.864072i | \(-0.332094\pi\) | ||||
0.503369 | + | 0.864072i | \(0.332094\pi\) | |||||||
\(542\) | 10.6167i | 0.456024i | ||||||||
\(543\) | − 29.9900i | − 1.28699i | ||||||||
\(544\) | 4.20555 | 0.180311 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.2544 | 0.481645 | ||||||||
\(547\) | 8.41110i | 0.359633i | 0.983700 | + | 0.179816i | \(0.0575503\pi\) | ||||
−0.983700 | + | 0.179816i | \(0.942450\pi\) | |||||||
\(548\) | 10.0000i | 0.427179i | ||||||||
\(549\) | 20.9200 | 0.892842 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 59.5749 | 2.53798 | ||||||||
\(552\) | − 2.78389i | − 0.118490i | ||||||||
\(553\) | − 12.1517i | − 0.516741i | ||||||||
\(554\) | 19.7633 | 0.839661 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.2005 | 0.559827 | ||||||||
\(557\) | − 37.0278i | − 1.56892i | −0.620182 | − | 0.784458i | \(-0.712941\pi\) | ||||
0.620182 | − | 0.784458i | \(-0.287059\pi\) | |||||||
\(558\) | − 22.6761i | − 0.959955i | ||||||||
\(559\) | 38.7244 | 1.63787 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.0489 | −0.550924 | ||||||||
\(562\) | 27.0489i | 1.14099i | ||||||||
\(563\) | 22.9200i | 0.965961i | 0.875631 | + | 0.482980i | \(0.160446\pi\) | ||||
−0.875631 | + | 0.482980i | \(0.839554\pi\) | |||||||
\(564\) | 3.58890 | 0.151120 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.6655 | 1.16287 | ||||||||
\(567\) | 15.0383i | 0.631550i | ||||||||
\(568\) | − 13.0489i | − 0.547519i | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3033 | 0.849667 | 0.424833 | − | 0.905272i | \(-0.360333\pi\) | ||||
0.424833 | + | 0.905272i | \(0.360333\pi\) | |||||||
\(572\) | 3.62721i | 0.151661i | ||||||||
\(573\) | − 28.4111i | − 1.18689i | ||||||||
\(574\) | 12.3572 | 0.515780 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.62721 | 0.276134 | ||||||||
\(577\) | − 16.4650i | − 0.685447i | −0.939436 | − | 0.342723i | \(-0.888651\pi\) | ||||
0.939436 | − | 0.342723i | \(-0.111349\pi\) | |||||||
\(578\) | 0.686652i | 0.0285609i | ||||||||
\(579\) | −4.74557 | −0.197219 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.20555 | −0.0915016 | ||||||||
\(582\) | − 7.01056i | − 0.290597i | ||||||||
\(583\) | 11.3083i | 0.468343i | ||||||||
\(584\) | −0.205550 | −0.00850572 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.37279 | −0.345877 | ||||||||
\(587\) | 30.6605i | 1.26549i | 0.774358 | + | 0.632747i | \(0.218073\pi\) | ||||
−0.774358 | + | 0.632747i | \(0.781927\pi\) | |||||||
\(588\) | 3.10278i | 0.127956i | ||||||||
\(589\) | −27.8922 | −1.14928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.3799 | 1.82555 | ||||||||
\(592\) | 1.10278i | 0.0453238i | ||||||||
\(593\) | 18.3033i | 0.751627i | 0.926695 | + | 0.375813i | \(0.122637\pi\) | ||||
−0.926695 | + | 0.375813i | \(0.877363\pi\) | |||||||
\(594\) | −11.2544 | −0.461775 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −23.6116 | −0.967170 | ||||||||
\(597\) | 31.3311i | 1.28229i | ||||||||
\(598\) | − 3.25443i | − 0.133083i | ||||||||
\(599\) | −29.6555 | −1.21169 | −0.605845 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605845 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7783 | 0.765985 | 0.382992 | − | 0.923751i | \(-0.374894\pi\) | ||||
0.382992 | + | 0.923751i | \(0.374894\pi\) | |||||||
\(602\) | 10.6761i | 0.435125i | ||||||||
\(603\) | − 55.7422i | − 2.27000i | ||||||||
\(604\) | −11.5139 | −0.468493 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 42.4011 | 1.72243 | ||||||||
\(607\) | − 14.6761i | − 0.595684i | −0.954615 | − | 0.297842i | \(-0.903733\pi\) | ||||
0.954615 | − | 0.297842i | \(-0.0962669\pi\) | |||||||
\(608\) | − 8.15165i | − 0.330593i | ||||||||
\(609\) | −22.6761 | −0.918881 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.19550 | 0.169732 | ||||||||
\(612\) | 27.8711i | 1.12662i | ||||||||
\(613\) | − 5.28560i | − 0.213483i | −0.994287 | − | 0.106742i | \(-0.965958\pi\) | ||||
0.994287 | − | 0.106742i | \(-0.0340418\pi\) | |||||||
\(614\) | 10.2056 | 0.411862 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 44.6933i | 1.79928i | 0.436629 | + | 0.899642i | \(0.356172\pi\) | ||||
−0.436629 | + | 0.899642i | \(0.643828\pi\) | |||||||
\(618\) | − 15.6655i | − 0.630160i | ||||||||
\(619\) | 17.5678 | 0.706108 | 0.353054 | − | 0.935603i | \(-0.385143\pi\) | ||||
0.353054 | + | 0.935603i | \(0.385143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0978 | 0.405209 | ||||||||
\(622\) | 8.16724i | 0.327476i | ||||||||
\(623\) | 7.45998i | 0.298878i | ||||||||
\(624\) | 11.2544 | 0.450538 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.5628 | 1.38141 | ||||||||
\(627\) | 25.2927i | 1.01009i | ||||||||
\(628\) | − 16.2056i | − 0.646672i | ||||||||
\(629\) | −4.63778 | −0.184920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.74557 | 0.188918 | 0.0944592 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944592 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(632\) | − 12.1517i | − 0.483367i | ||||||||
\(633\) | 33.6444i | 1.33724i | ||||||||
\(634\) | −9.21057 | −0.365799 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 35.0872 | 1.39130 | ||||||||
\(637\) | 3.62721i | 0.143715i | ||||||||
\(638\) | − 7.30833i | − 0.289339i | ||||||||
\(639\) | 86.4777 | 3.42100 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.52998 | −0.0999281 | −0.0499641 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499641 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(642\) | − 40.3033i | − 1.59064i | ||||||||
\(643\) | − 0.670549i | − 0.0264439i | −0.999913 | − | 0.0132219i | \(-0.995791\pi\) | ||||
0.999913 | − | 0.0132219i | \(-0.00420880\pi\) | |||||||
\(644\) | 0.897225 | 0.0353556 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.2822 | 1.34881 | ||||||||
\(647\) | − 11.8922i | − 0.467531i | −0.972293 | − | 0.233765i | \(-0.924895\pi\) | ||||
0.972293 | − | 0.233765i | \(-0.0751048\pi\) | |||||||
\(648\) | 15.0383i | 0.590761i | ||||||||
\(649\) | −7.25443 | −0.284761 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.6167 | 0.416099 | ||||||||
\(652\) | − 6.31335i | − 0.247250i | ||||||||
\(653\) | − 11.4161i | − 0.446747i | −0.974733 | − | 0.223374i | \(-0.928293\pi\) | ||||
0.974733 | − | 0.223374i | \(-0.0717070\pi\) | |||||||
\(654\) | −15.8328 | −0.619110 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.3572 | 0.482468 | ||||||||
\(657\) | − 1.36222i | − 0.0531454i | ||||||||
\(658\) | 1.15667i | 0.0450919i | ||||||||
\(659\) | −1.87108 | −0.0728868 | −0.0364434 | − | 0.999336i | \(-0.511603\pi\) | ||||
−0.0364434 | + | 0.999336i | \(0.511603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1355 | 1.28882 | 0.644412 | − | 0.764679i | \(-0.277102\pi\) | ||||
0.644412 | + | 0.764679i | \(0.277102\pi\) | |||||||
\(662\) | − 16.2439i | − 0.631336i | ||||||||
\(663\) | 47.3311i | 1.83819i | ||||||||
\(664\) | −2.20555 | −0.0855919 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.30833 | −0.283192 | ||||||||
\(667\) | 6.55721i | 0.253896i | ||||||||
\(668\) | − 8.00000i | − 0.309529i | ||||||||
\(669\) | 29.3522 | 1.13482 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15667 | −0.121862 | ||||||||
\(672\) | 3.10278i | 0.119692i | ||||||||
\(673\) | − 18.1955i | − 0.701385i | −0.936491 | − | 0.350693i | \(-0.885946\pi\) | ||||
0.936491 | − | 0.350693i | \(-0.114054\pi\) | |||||||
\(674\) | 1.25443 | 0.0483187 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.156674 | 0.00602593 | ||||||||
\(677\) | − 15.9789i | − 0.614118i | −0.951690 | − | 0.307059i | \(-0.900655\pi\) | ||||
0.951690 | − | 0.307059i | \(-0.0993449\pi\) | |||||||
\(678\) | − 32.3033i | − 1.24060i | ||||||||
\(679\) | 2.25945 | 0.0867097 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.5089 | −2.08878 | ||||||||
\(682\) | 3.42166i | 0.131022i | ||||||||
\(683\) | − 17.8711i | − 0.683818i | −0.939733 | − | 0.341909i | \(-0.888927\pi\) | ||||
0.939733 | − | 0.341909i | \(-0.111073\pi\) | |||||||
\(684\) | 54.0227 | 2.06561 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | − 79.8188i | − 3.04528i | ||||||||
\(688\) | 10.6761i | 0.407022i | ||||||||
\(689\) | 41.0177 | 1.56265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.20555 | −0.0839031 | −0.0419515 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419515 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(692\) | − 9.25443i | − 0.351800i | ||||||||
\(693\) | − 6.62721i | − 0.251747i | ||||||||
\(694\) | −7.42166 | −0.281722 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −22.6761 | −0.859535 | ||||||||
\(697\) | 51.9688i | 1.96846i | ||||||||
\(698\) | − 18.3033i | − 0.692790i | ||||||||
\(699\) | −59.4389 | −2.24818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.6217 | −0.967717 | −0.483859 | − | 0.875146i | \(-0.660765\pi\) | ||||
−0.483859 | + | 0.875146i | \(0.660765\pi\) | |||||||
\(702\) | 40.8222i | 1.54073i | ||||||||
\(703\) | 8.98944i | 0.339043i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.8761 | 1.08677 | ||||||||
\(707\) | 13.6655i | 0.513945i | ||||||||
\(708\) | 22.5089i | 0.845934i | ||||||||
\(709\) | −5.48110 | −0.205847 | −0.102924 | − | 0.994689i | \(-0.532820\pi\) | ||||
−0.102924 | + | 0.994689i | \(0.532820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 80.5316 | 3.02017 | ||||||||
\(712\) | 7.45998i | 0.279574i | ||||||||
\(713\) | − 3.07000i | − 0.114972i | ||||||||
\(714\) | −13.0489 | −0.488342 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.98944 | 0.186464 | ||||||||
\(717\) | 56.0172i | 2.09200i | ||||||||
\(718\) | 4.15165i | 0.154938i | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.04888 | 0.188030 | ||||||||
\(722\) | − 47.4494i | − 1.76588i | ||||||||
\(723\) | 19.0872i | 0.709860i | ||||||||
\(724\) | 9.66553 | 0.359216 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.10278 | 0.115155 | ||||||||
\(727\) | − 18.5855i | − 0.689297i | −0.938732 | − | 0.344649i | \(-0.887998\pi\) | ||||
0.938732 | − | 0.344649i | \(-0.112002\pi\) | |||||||
\(728\) | 3.62721i | 0.134433i | ||||||||
\(729\) | 5.09775 | 0.188806 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.8988 | −1.66064 | ||||||||
\(732\) | 9.79445i | 0.362013i | ||||||||
\(733\) | − 42.0000i | − 1.55131i | −0.631160 | − | 0.775653i | \(-0.717421\pi\) | ||||
0.631160 | − | 0.775653i | \(-0.282579\pi\) | |||||||
\(734\) | 5.26447 | 0.194315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.897225 | 0.0330722 | ||||||||
\(737\) | 8.41110i | 0.309827i | ||||||||
\(738\) | 81.8938i | 3.01455i | ||||||||
\(739\) | −5.97887 | −0.219936 | −0.109968 | − | 0.993935i | \(-0.535075\pi\) | ||||
−0.109968 | + | 0.993935i | \(0.535075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 91.7422 | 3.37023 | ||||||||
\(742\) | 11.3083i | 0.415142i | ||||||||
\(743\) | − 50.0978i | − 1.83791i | −0.394364 | − | 0.918954i | \(-0.629035\pi\) | ||||
0.394364 | − | 0.918954i | \(-0.370965\pi\) | |||||||
\(744\) | 10.6167 | 0.389225 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 35.8711 | 1.31333 | ||||||||
\(747\) | − 14.6167i | − 0.534795i | ||||||||
\(748\) | − 4.20555i | − 0.153770i | ||||||||
\(749\) | 12.9894 | 0.474624 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.63778 | −0.315197 | −0.157598 | − | 0.987503i | \(-0.550375\pi\) | ||||
−0.157598 | + | 0.987503i | \(0.550375\pi\) | |||||||
\(752\) | 1.15667i | 0.0421796i | ||||||||
\(753\) | − 93.0177i | − 3.38975i | ||||||||
\(754\) | −26.5089 | −0.965395 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.2544 | −0.409320 | ||||||||
\(757\) | − 25.5139i | − 0.927318i | −0.886014 | − | 0.463659i | \(-0.846536\pi\) | ||||
0.886014 | − | 0.463659i | \(-0.153464\pi\) | |||||||
\(758\) | − 33.0177i | − 1.19926i | ||||||||
\(759\) | −2.78389 | −0.101049 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.6605 | −1.18394 | −0.591971 | − | 0.805959i | \(-0.701650\pi\) | ||||
−0.591971 | + | 0.805959i | \(0.701650\pi\) | |||||||
\(762\) | − 10.0978i | − 0.365803i | ||||||||
\(763\) | − 5.10278i | − 0.184733i | ||||||||
\(764\) | 9.15667 | 0.331277 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.95112 | 0.106628 | ||||||||
\(767\) | 26.3133i | 0.950120i | ||||||||
\(768\) | 3.10278i | 0.111962i | ||||||||
\(769\) | −16.7683 | −0.604680 | −0.302340 | − | 0.953200i | \(-0.597768\pi\) | ||||
−0.302340 | + | 0.953200i | \(0.597768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.5783 | 0.452998 | ||||||||
\(772\) | − 1.52946i | − 0.0550465i | ||||||||
\(773\) | − 2.82220i | − 0.101507i | −0.998711 | − | 0.0507537i | \(-0.983838\pi\) | ||||
0.998711 | − | 0.0507537i | \(-0.0161624\pi\) | |||||||
\(774\) | −70.7527 | −2.54315 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.25945 | 0.0811095 | ||||||||
\(777\) | − 3.42166i | − 0.122751i | ||||||||
\(778\) | 1.89220i | 0.0678387i | ||||||||
\(779\) | 100.732 | 3.60908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.0489 | −0.466925 | ||||||||
\(782\) | 3.77332i | 0.134934i | ||||||||
\(783\) | − 82.2510i | − 2.93941i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −53.7038 | −1.91555 | ||||||||
\(787\) | 4.82220i | 0.171893i | 0.996300 | + | 0.0859464i | \(0.0273914\pi\) | ||||
−0.996300 | + | 0.0859464i | \(0.972609\pi\) | |||||||
\(788\) | 14.3033i | 0.509534i | ||||||||
\(789\) | 45.0177 | 1.60267 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.4111 | 0.370176 | ||||||||
\(792\) | − 6.62721i | − 0.235488i | ||||||||
\(793\) | 11.4499i | 0.406599i | ||||||||
\(794\) | −5.36222 | −0.190298 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0978 | −0.357905 | ||||||||
\(797\) | 0.540024i | 0.0191286i | 0.999954 | + | 0.00956431i | \(0.00304446\pi\) | ||||
−0.999954 | + | 0.00956431i | \(0.996956\pi\) | |||||||
\(798\) | 25.2927i | 0.895353i | ||||||||
\(799\) | −4.86445 | −0.172092 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −49.4389 | −1.74684 | ||||||||
\(802\) | − 23.7038i | − 0.837012i | ||||||||
\(803\) | 0.205550i | 0.00725371i | ||||||||
\(804\) | 26.0978 | 0.920397 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4111 | 0.437162 | ||||||||
\(807\) | − 13.5678i | − 0.477608i | ||||||||
\(808\) | 13.6655i | 0.480752i | ||||||||
\(809\) | 17.8922 | 0.629056 | 0.314528 | − | 0.949248i | \(-0.398154\pi\) | ||||
0.314528 | + | 0.949248i | \(0.398154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.2283 | −0.429393 | −0.214696 | − | 0.976681i | \(-0.568876\pi\) | ||||
−0.214696 | + | 0.976681i | \(0.568876\pi\) | |||||||
\(812\) | − 7.30833i | − 0.256472i | ||||||||
\(813\) | − 32.9411i | − 1.15529i | ||||||||
\(814\) | 1.10278 | 0.0386522 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.0489 | −0.456802 | ||||||||
\(817\) | 87.0278i | 3.04472i | ||||||||
\(818\) | 27.0816i | 0.946888i | ||||||||
\(819\) | −24.0383 | −0.839967 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5316 | 1.34476 | 0.672381 | − | 0.740206i | \(-0.265272\pi\) | ||||
0.672381 | + | 0.740206i | \(0.265272\pi\) | |||||||
\(822\) | − 31.0278i | − 1.08222i | ||||||||
\(823\) | 21.9461i | 0.764993i | 0.923957 | + | 0.382496i | \(0.124936\pi\) | ||||
−0.923957 | + | 0.382496i | \(0.875064\pi\) | |||||||
\(824\) | 5.04888 | 0.175886 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.25443 | −0.252414 | ||||||||
\(827\) | − 9.68665i | − 0.336838i | −0.985716 | − | 0.168419i | \(-0.946134\pi\) | ||||
0.985716 | − | 0.168419i | \(-0.0538661\pi\) | |||||||
\(828\) | 5.94610i | 0.206641i | ||||||||
\(829\) | −31.0771 | −1.07935 | −0.539677 | − | 0.841872i | \(-0.681454\pi\) | ||||
−0.539677 | + | 0.841872i | \(0.681454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −61.3210 | −2.12720 | ||||||||
\(832\) | 3.62721i | 0.125751i | ||||||||
\(833\) | − 4.20555i | − 0.145714i | ||||||||
\(834\) | −40.9583 | −1.41827 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.15165 | −0.281931 | ||||||||
\(837\) | 38.5089i | 1.33106i | ||||||||
\(838\) | − 3.05892i | − 0.105669i | ||||||||
\(839\) | 24.7738 | 0.855288 | 0.427644 | − | 0.903947i | \(-0.359344\pi\) | ||||
0.427644 | + | 0.903947i | \(0.359344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.4116 | 0.841780 | ||||||||
\(842\) | − 21.6655i | − 0.746643i | ||||||||
\(843\) | − 83.9266i | − 2.89058i | ||||||||
\(844\) | −10.8433 | −0.373243 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.66553 | −0.263546 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 11.3083i | 0.388329i | ||||||||
\(849\) | −85.8399 | −2.94602 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.989437 | −0.0339175 | ||||||||
\(852\) | 40.4877i | 1.38709i | ||||||||
\(853\) | 1.58890i | 0.0544029i | 0.999630 | + | 0.0272014i | \(0.00865956\pi\) | ||||
−0.999630 | + | 0.0272014i | \(0.991340\pi\) | |||||||
\(854\) | −3.15667 | −0.108019 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9894 | 0.443970 | ||||||||
\(857\) | − 19.1255i | − 0.653315i | −0.945143 | − | 0.326657i | \(-0.894078\pi\) | ||||
0.945143 | − | 0.326657i | \(-0.105922\pi\) | |||||||
\(858\) | − 11.2544i | − 0.384220i | ||||||||
\(859\) | −4.94108 | −0.168587 | −0.0842937 | − | 0.996441i | \(-0.526863\pi\) | ||||
−0.0842937 | + | 0.996441i | \(0.526863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.3416 | −1.30668 | ||||||||
\(862\) | 34.3260i | 1.16915i | ||||||||
\(863\) | − 19.3295i | − 0.657982i | −0.944333 | − | 0.328991i | \(-0.893291\pi\) | ||||
0.944333 | − | 0.328991i | \(-0.106709\pi\) | |||||||
\(864\) | −11.2544 | −0.382883 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.0538991 | −0.00183157 | ||||||||
\(867\) | − 2.13053i | − 0.0723564i | ||||||||
\(868\) | 3.42166i | 0.116139i | ||||||||
\(869\) | −12.1517 | −0.412217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.5089 | 1.03375 | ||||||||
\(872\) | − 5.10278i | − 0.172802i | ||||||||
\(873\) | 14.9739i | 0.506788i | ||||||||
\(874\) | 7.31386 | 0.247395 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.637776 | 0.0215484 | ||||||||
\(877\) | − 16.4011i | − 0.553824i | −0.960895 | − | 0.276912i | \(-0.910689\pi\) | ||||
0.960895 | − | 0.276912i | \(-0.0893111\pi\) | |||||||
\(878\) | − 7.14663i | − 0.241187i | ||||||||
\(879\) | 25.9789 | 0.876246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.5678 | 1.33307 | 0.666536 | − | 0.745473i | \(-0.267776\pi\) | ||||
0.666536 | + | 0.745473i | \(0.267776\pi\) | |||||||
\(882\) | − 6.62721i | − 0.223150i | ||||||||
\(883\) | 55.4389i | 1.86567i | 0.360309 | + | 0.932833i | \(0.382671\pi\) | ||||
−0.360309 | + | 0.932833i | \(0.617329\pi\) | |||||||
\(884\) | −15.2544 | −0.513062 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.74557 | 0.293813 | ||||||||
\(887\) | − 44.1955i | − 1.48394i | −0.670433 | − | 0.741970i | \(-0.733892\pi\) | ||||
0.670433 | − | 0.741970i | \(-0.266108\pi\) | |||||||
\(888\) | − 3.42166i | − 0.114823i | ||||||||
\(889\) | 3.25443 | 0.109150 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0383 | 0.503802 | ||||||||
\(892\) | 9.45998i | 0.316743i | ||||||||
\(893\) | 9.42880i | 0.315523i | ||||||||
\(894\) | 73.2616 | 2.45023 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 10.0978i | 0.337154i | ||||||||
\(898\) | 39.7038i | 1.32493i | ||||||||
\(899\) | −25.0066 | −0.834018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.5577 | −1.58438 | ||||||||
\(902\) | − 12.3572i | − 0.411450i | ||||||||
\(903\) | − 33.1255i | − 1.10235i | ||||||||
\(904\) | 10.4111 | 0.346268 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.7250 | 1.18688 | ||||||||
\(907\) | − 9.26447i | − 0.307622i | −0.988100 | − | 0.153811i | \(-0.950845\pi\) | ||||
0.988100 | − | 0.153811i | \(-0.0491547\pi\) | |||||||
\(908\) | − 17.5678i | − 0.583007i | ||||||||
\(909\) | −90.5644 | −3.00383 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.0489 | −1.22748 | −0.613742 | − | 0.789507i | \(-0.710336\pi\) | ||||
−0.613742 | + | 0.789507i | \(0.710336\pi\) | |||||||
\(912\) | 25.2927i | 0.837526i | ||||||||
\(913\) | 2.20555i | 0.0729931i | ||||||||
\(914\) | −12.3133 | −0.407289 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.7250 | 0.849977 | ||||||||
\(917\) | − 17.3083i | − 0.571571i | ||||||||
\(918\) | − 47.3311i | − 1.56216i | ||||||||
\(919\) | 13.9149 | 0.459011 | 0.229506 | − | 0.973307i | \(-0.426289\pi\) | ||||
0.229506 | + | 0.973307i | \(0.426289\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6655 | −1.04341 | ||||||||
\(922\) | 15.0489i | 0.495608i | ||||||||
\(923\) | 47.3311i | 1.55792i | ||||||||
\(924\) | 3.10278 | 0.102074 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.4061 | 1.03207 | ||||||||
\(927\) | 33.4600i | 1.09897i | ||||||||
\(928\) | − 7.30833i | − 0.239908i | ||||||||
\(929\) | 32.0666 | 1.05207 | 0.526035 | − | 0.850463i | \(-0.323678\pi\) | ||||
0.526035 | + | 0.850463i | \(0.323678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.15165 | −0.267160 | ||||||||
\(932\) | − 19.1567i | − 0.627498i | ||||||||
\(933\) | − 25.3411i | − 0.829630i | ||||||||
\(934\) | 19.0716 | 0.624042 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24.0383 | −0.785717 | ||||||||
\(937\) | − 25.4499i | − 0.831413i | −0.909499 | − | 0.415706i | \(-0.863534\pi\) | ||||
0.909499 | − | 0.415706i | \(-0.136466\pi\) | |||||||
\(938\) | 8.41110i | 0.274632i | ||||||||
\(939\) | −107.240 | −3.49966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.49115 | −0.113808 | −0.0569041 | − | 0.998380i | \(-0.518123\pi\) | ||||
−0.0569041 | + | 0.998380i | \(0.518123\pi\) | |||||||
\(942\) | 50.2822i | 1.63828i | ||||||||
\(943\) | 11.0872i | 0.361049i | ||||||||
\(944\) | −7.25443 | −0.236111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.6761 | 0.347110 | ||||||||
\(947\) | − 30.6167i | − 0.994907i | −0.867491 | − | 0.497454i | \(-0.834268\pi\) | ||||
0.867491 | − | 0.497454i | \(-0.165732\pi\) | |||||||
\(948\) | 37.7038i | 1.22456i | ||||||||
\(949\) | 0.745574 | 0.0242024 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.5783 | 0.926716 | ||||||||
\(952\) | − 4.20555i | − 0.136303i | ||||||||
\(953\) | − 33.9406i | − 1.09944i | −0.835348 | − | 0.549721i | \(-0.814734\pi\) | ||||
0.835348 | − | 0.549721i | \(-0.185266\pi\) | |||||||
\(954\) | −74.9427 | −2.42636 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0539 | −0.583905 | ||||||||
\(957\) | 22.6761i | 0.733014i | ||||||||
\(958\) | − 9.49115i | − 0.306645i | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2922 | −0.622330 | ||||||||
\(962\) | − 4.00000i | − 0.128965i | ||||||||
\(963\) | 86.0838i | 2.77401i | ||||||||
\(964\) | −6.15165 | −0.198131 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.78389 | −0.0895701 | ||||||||
\(967\) | 60.8021i | 1.95526i | 0.210323 | + | 0.977632i | \(0.432548\pi\) | ||||
−0.210323 | + | 0.977632i | \(0.567452\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | −106.370 | −3.41709 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.2933 | 1.61399 | 0.806994 | − | 0.590560i | \(-0.201093\pi\) | ||||
0.806994 | + | 0.590560i | \(0.201093\pi\) | |||||||
\(972\) | − 12.8972i | − 0.413679i | ||||||||
\(973\) | − 13.2005i | − 0.423189i | ||||||||
\(974\) | −0.0438527 | −0.00140513 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.15667 | −0.101043 | ||||||||
\(977\) | − 28.0978i | − 0.898927i | −0.893299 | − | 0.449463i | \(-0.851615\pi\) | ||||
0.893299 | − | 0.449463i | \(-0.148385\pi\) | |||||||
\(978\) | 19.5889i | 0.626384i | ||||||||
\(979\) | 7.45998 | 0.238422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.8172 | 1.07970 | ||||||||
\(982\) | − 1.56777i | − 0.0500297i | ||||||||
\(983\) | − 21.0489i | − 0.671355i | −0.941977 | − | 0.335677i | \(-0.891035\pi\) | ||||
0.941977 | − | 0.335677i | \(-0.108965\pi\) | |||||||
\(984\) | −38.3416 | −1.22229 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.7355 | 0.978819 | ||||||||
\(987\) | − 3.58890i | − 0.114236i | ||||||||
\(988\) | 29.5678i | 0.940676i | ||||||||
\(989\) | −9.57885 | −0.304590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.6832 | −1.41941 | −0.709705 | − | 0.704499i | \(-0.751172\pi\) | ||||
−0.709705 | + | 0.704499i | \(0.751172\pi\) | |||||||
\(992\) | 3.42166i | 0.108638i | ||||||||
\(993\) | 50.4011i | 1.59943i | ||||||||
\(994\) | −13.0489 | −0.413885 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.84333 | 0.216839 | ||||||||
\(997\) | − 9.47002i | − 0.299919i | −0.988692 | − | 0.149959i | \(-0.952086\pi\) | ||||
0.988692 | − | 0.149959i | \(-0.0479143\pi\) | |||||||
\(998\) | − 42.3416i | − 1.34030i | ||||||||
\(999\) | 12.4111 | 0.392670 |
(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 | 3850.2.c.ba.1849.3 | 6 | ||
5.2 | odd | 4 | 770.2.a.m.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 3850.2.a.bt.1.1 | 3 | |||
5.4 | even | 2 | inner | 3850.2.c.ba.1849.4 | 6 | ||
15.2 | even | 4 | 6930.2.a.ce.1.1 | 3 | |||
20.7 | even | 4 | 6160.2.a.bf.1.1 | 3 | |||
35.27 | even | 4 | 5390.2.a.ca.1.1 | 3 | |||
55.32 | even | 4 | 8470.2.a.ci.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.m.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
3850.2.a.bt.1.1 | 3 | 5.3 | odd | 4 | |||
3850.2.c.ba.1849.3 | 6 | 1.1 | even | 1 | trivial | ||
3850.2.c.ba.1849.4 | 6 | 5.4 | even | 2 | inner | ||
5390.2.a.ca.1.1 | 3 | 35.27 | even | 4 | |||
6160.2.a.bf.1.1 | 3 | 20.7 | even | 4 | |||
6930.2.a.ce.1.1 | 3 | 15.2 | even | 4 | |||
8470.2.a.ci.1.3 | 3 | 55.32 | even | 4 |