Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(0.500000 + 1.72434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.199 |
Dual form | 1950.2.y.m.49.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | 1.79518 | + | 3.10934i | 0.678514 | + | 1.17522i | 0.975428 | + | 0.220317i | \(0.0707092\pi\) |
−0.296914 | + | 0.954904i | \(0.595957\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.72163 | − | 2.72603i | −1.42362 | − | 0.821930i | −0.427018 | − | 0.904243i | \(-0.640436\pi\) |
−0.996607 | + | 0.0823128i | \(0.973769\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −3.60494 | − | 0.0664404i | −0.999830 | − | 0.0184272i | ||||
\(14\) | −3.59036 | −0.959564 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.33097 | − | 3.65519i | 1.53549 | − | 0.886514i | 0.536392 | − | 0.843969i | \(-0.319787\pi\) |
0.999095 | − | 0.0425445i | \(-0.0135464\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.34713 | − | 1.93247i | 0.767884 | − | 0.443338i | −0.0642352 | − | 0.997935i | \(-0.520461\pi\) |
0.832119 | + | 0.554597i | \(0.187127\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.59036i | − | 0.783481i | ||||||
\(22\) | 4.72163 | − | 2.72603i | 1.00665 | − | 0.581192i | ||||
\(23\) | 1.60934 | + | 0.929155i | 0.335571 | + | 0.193742i | 0.658312 | − | 0.752745i | \(-0.271271\pi\) |
−0.322741 | + | 0.946487i | \(0.604604\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.86001 | − | 3.08875i | 0.364778 | − | 0.605753i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.79518 | − | 3.10934i | 0.339257 | − | 0.587611i | ||||
\(29\) | −2.67578 | + | 4.63459i | −0.496881 | + | 0.860622i | −0.999994 | − | 0.00359821i | \(-0.998855\pi\) |
0.503113 | + | 0.864221i | \(0.332188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.23338i | 0.401127i | 0.979681 | + | 0.200563i | \(0.0642773\pi\) | ||||
−0.979681 | + | 0.200563i | \(0.935723\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.72603 | + | 4.72163i | 0.474542 | + | 0.821930i | ||||
\(34\) | 7.31038i | 1.25372i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 1.06644 | − | 1.84713i | 0.175322 | − | 0.303666i | −0.764951 | − | 0.644089i | \(-0.777237\pi\) |
0.940273 | + | 0.340423i | \(0.110570\pi\) | |||||||
\(38\) | 3.86493i | 0.626975i | ||||||||
\(39\) | 3.08875 | + | 1.86001i | 0.494596 | + | 0.297840i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.33097 | − | 3.65519i | −0.988732 | − | 0.570845i | −0.0838369 | − | 0.996479i | \(-0.526717\pi\) |
−0.904895 | + | 0.425635i | \(0.860051\pi\) | |||||||
\(42\) | 3.10934 | + | 1.79518i | 0.479782 | + | 0.277002i | ||||
\(43\) | 7.10996 | − | 4.10494i | 1.08426 | − | 0.625997i | 0.152217 | − | 0.988347i | \(-0.451359\pi\) |
0.932042 | + | 0.362350i | \(0.118025\pi\) | |||||||
\(44\) | 5.45207i | 0.821930i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.60934 | + | 0.929155i | −0.237285 | + | 0.136996i | ||||
\(47\) | 5.07700 | 0.740556 | 0.370278 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370278 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | −2.94535 | + | 5.10149i | −0.420764 | + | 0.728784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.31038 | −1.02366 | ||||||||
\(52\) | 1.74493 | + | 3.15519i | 0.241978 | + | 0.437546i | ||||
\(53\) | − | 2.23338i | − | 0.306778i | −0.988166 | − | 0.153389i | \(-0.950981\pi\) | ||
0.988166 | − | 0.153389i | \(-0.0490188\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.79518 | + | 3.10934i | 0.239891 | + | 0.415504i | ||||
\(57\) | −3.86493 | −0.511923 | ||||||||
\(58\) | −2.67578 | − | 4.63459i | −0.351348 | − | 0.608552i | ||||
\(59\) | 0.237785 | − | 0.137285i | 0.0309570 | − | 0.0178730i | −0.484442 | − | 0.874824i | \(-0.660977\pi\) |
0.515399 | + | 0.856951i | \(0.327644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.06644 | + | 3.57918i | 0.264581 | + | 0.458267i | 0.967454 | − | 0.253048i | \(-0.0814332\pi\) |
−0.702873 | + | 0.711315i | \(0.748100\pi\) | |||||||
\(62\) | −1.93416 | − | 1.11669i | −0.245639 | − | 0.141820i | ||||
\(63\) | −1.79518 | + | 3.10934i | −0.226171 | + | 0.391740i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.45207 | −0.671103 | ||||||||
\(67\) | −7.39851 | + | 12.8146i | −0.903872 | + | 1.56555i | −0.0814466 | + | 0.996678i | \(0.525954\pi\) |
−0.822425 | + | 0.568874i | \(0.807379\pi\) | |||||||
\(68\) | −6.33097 | − | 3.65519i | −0.767743 | − | 0.443257i | ||||
\(69\) | −0.929155 | − | 1.60934i | −0.111857 | − | 0.193742i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3804 | − | 7.14784i | 1.46929 | − | 0.848293i | 0.469879 | − | 0.882731i | \(-0.344297\pi\) |
0.999407 | + | 0.0344378i | \(0.0109641\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 14.8975 | 1.74362 | 0.871811 | − | 0.489842i | \(-0.162946\pi\) | ||||
0.871811 | + | 0.489842i | \(0.162946\pi\) | |||||||
\(74\) | 1.06644 | + | 1.84713i | 0.123971 | + | 0.214724i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.34713 | − | 1.93247i | −0.383942 | − | 0.221669i | ||||
\(77\) | − | 19.5749i | − | 2.23077i | ||||||
\(78\) | −3.15519 | + | 1.74493i | −0.357255 | + | 0.197574i | ||||
\(79\) | −2.62105 | −0.294891 | −0.147446 | − | 0.989070i | \(-0.547105\pi\) | ||||
−0.147446 | + | 0.989070i | \(0.547105\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.33097 | − | 3.65519i | 0.699139 | − | 0.403648i | ||||
\(83\) | 7.15988 | 0.785899 | 0.392949 | − | 0.919560i | \(-0.371455\pi\) | ||||
0.392949 | + | 0.919560i | \(0.371455\pi\) | |||||||
\(84\) | −3.10934 | + | 1.79518i | −0.339257 | + | 0.195870i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.20988i | 0.885294i | ||||||||
\(87\) | 4.63459 | − | 2.67578i | 0.496881 | − | 0.286874i | ||||
\(88\) | −4.72163 | − | 2.72603i | −0.503327 | − | 0.290596i | ||||
\(89\) | −8.30844 | − | 4.79688i | −0.880693 | − | 0.508468i | −0.00980594 | − | 0.999952i | \(-0.503121\pi\) |
−0.870887 | + | 0.491484i | \(0.836455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.26493 | − | 11.3283i | −0.656743 | − | 1.18753i | ||||
\(92\) | − | 1.85831i | − | 0.193742i | ||||||
\(93\) | 1.11669 | − | 1.93416i | 0.115795 | − | 0.200563i | ||||
\(94\) | −2.53850 | + | 4.39681i | −0.261826 | + | 0.453496i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −0.954155 | − | 1.65264i | −0.0968797 | − | 0.167801i | 0.813512 | − | 0.581548i | \(-0.197553\pi\) |
−0.910392 | + | 0.413748i | \(0.864220\pi\) | |||||||
\(98\) | −2.94535 | − | 5.10149i | −0.297525 | − | 0.515328i | ||||
\(99\) | − | 5.45207i | − | 0.547953i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.12785 | − | 14.0779i | 0.808752 | − | 1.40080i | −0.104978 | − | 0.994475i | \(-0.533477\pi\) |
0.913729 | − | 0.406324i | \(-0.133190\pi\) | |||||||
\(102\) | 3.65519 | − | 6.33097i | 0.361918 | − | 0.626860i | ||||
\(103\) | 12.9760i | 1.27857i | 0.768971 | + | 0.639284i | \(0.220769\pi\) | ||||
−0.768971 | + | 0.639284i | \(0.779231\pi\) | |||||||
\(104\) | −3.60494 | − | 0.0664404i | −0.353493 | − | 0.00651501i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.93416 | + | 1.11669i | 0.187863 | + | 0.108463i | ||||
\(107\) | 8.58814 | + | 4.95837i | 0.830247 | + | 0.479343i | 0.853937 | − | 0.520376i | \(-0.174208\pi\) |
−0.0236901 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 7.41088i | 0.709833i | 0.934898 | + | 0.354917i | \(0.115491\pi\) | ||||
−0.934898 | + | 0.354917i | \(0.884509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.84713 | + | 1.06644i | −0.175322 | + | 0.101222i | ||||
\(112\) | −3.59036 | −0.339257 | ||||||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 1.93247 | − | 3.34713i | 0.180992 | − | 0.313487i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.35157 | 0.496881 | ||||||||
\(117\) | −1.74493 | − | 3.15519i | −0.161319 | − | 0.291697i | ||||
\(118\) | 0.274571i | 0.0252763i | ||||||||
\(119\) | 22.7305 | + | 13.1234i | 2.08370 | + | 1.20302i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.36252 | + | 16.2164i | 0.851138 | + | 1.47421i | ||||
\(122\) | −4.13288 | −0.374173 | ||||||||
\(123\) | 3.65519 | + | 6.33097i | 0.329577 | + | 0.570845i | ||||
\(124\) | 1.93416 | − | 1.11669i | 0.173693 | − | 0.100282i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.79518 | − | 3.10934i | −0.159927 | − | 0.277002i | ||||
\(127\) | 15.5772 | + | 8.99351i | 1.38225 | + | 0.798045i | 0.992426 | − | 0.122843i | \(-0.0392011\pi\) |
0.389828 | + | 0.920888i | \(0.372534\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −8.20988 | −0.722839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3462 | 1.77765 | 0.888827 | − | 0.458242i | \(-0.151521\pi\) | ||||
0.888827 | + | 0.458242i | \(0.151521\pi\) | |||||||
\(132\) | 2.72603 | − | 4.72163i | 0.237271 | − | 0.410965i | ||||
\(133\) | 12.0174 | + | 6.93825i | 1.04204 | + | 0.601623i | ||||
\(134\) | −7.39851 | − | 12.8146i | −0.639134 | − | 1.10701i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.33097 | − | 3.65519i | 0.542876 | − | 0.313430i | ||||
\(137\) | 5.52037 | + | 9.56156i | 0.471637 | + | 0.816899i | 0.999473 | − | 0.0324469i | \(-0.0103300\pi\) |
−0.527837 | + | 0.849346i | \(0.676997\pi\) | |||||||
\(138\) | 1.85831 | 0.158190 | ||||||||
\(139\) | 4.85096 | + | 8.40212i | 0.411453 | + | 0.712658i | 0.995049 | − | 0.0993864i | \(-0.0316880\pi\) |
−0.583596 | + | 0.812044i | \(0.698355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39681 | − | 2.53850i | −0.370278 | − | 0.213780i | ||||
\(142\) | 14.2957i | 1.19967i | ||||||||
\(143\) | 16.8401 | + | 10.1409i | 1.40824 | + | 0.848024i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.44876 | + | 12.9016i | −0.616464 | + | 1.06775i | ||||
\(147\) | 5.10149 | − | 2.94535i | 0.420764 | − | 0.242928i | ||||
\(148\) | −2.13288 | −0.175322 | ||||||||
\(149\) | 4.70959 | − | 2.71908i | 0.385825 | − | 0.222756i | −0.294525 | − | 0.955644i | \(-0.595161\pi\) |
0.680350 | + | 0.732888i | \(0.261828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.8010i | − | 1.44862i | −0.689472 | − | 0.724312i | \(-0.742157\pi\) | ||
0.689472 | − | 0.724312i | \(-0.257843\pi\) | |||||||
\(152\) | 3.34713 | − | 1.93247i | 0.271488 | − | 0.156744i | ||||
\(153\) | 6.33097 | + | 3.65519i | 0.511829 | + | 0.295505i | ||||
\(154\) | 16.9524 | + | 9.78745i | 1.36606 | + | 0.788695i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0664404 | − | 3.60494i | 0.00531949 | − | 0.288626i | ||||
\(157\) | 5.93652i | 0.473786i | 0.971536 | + | 0.236893i | \(0.0761290\pi\) | ||||
−0.971536 | + | 0.236893i | \(0.923871\pi\) | |||||||
\(158\) | 1.31052 | − | 2.26990i | 0.104260 | − | 0.180583i | ||||
\(159\) | −1.11669 | + | 1.93416i | −0.0885593 | + | 0.153389i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.67200i | 0.525828i | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −7.79688 | − | 13.5046i | −0.610699 | − | 1.05776i | −0.991123 | − | 0.132949i | \(-0.957555\pi\) |
0.380424 | − | 0.924812i | \(-0.375778\pi\) | |||||||
\(164\) | 7.31038i | 0.570845i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.57994 | + | 6.20064i | −0.277857 | + | 0.481263i | ||||
\(167\) | 0.929155 | − | 1.60934i | 0.0719002 | − | 0.124535i | −0.827834 | − | 0.560973i | \(-0.810427\pi\) |
0.899734 | + | 0.436439i | \(0.143760\pi\) | |||||||
\(168\) | − | 3.59036i | − | 0.277002i | ||||||
\(169\) | 12.9912 | + | 0.479027i | 0.999321 | + | 0.0368482i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34713 | + | 1.93247i | 0.255961 | + | 0.147779i | ||||
\(172\) | −7.10996 | − | 4.10494i | −0.542130 | − | 0.312999i | ||||
\(173\) | 21.0768 | − | 12.1687i | 1.60244 | − | 0.925168i | 0.611441 | − | 0.791290i | \(-0.290590\pi\) |
0.990998 | − | 0.133878i | \(-0.0427430\pi\) | |||||||
\(174\) | 5.35157i | 0.405701i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.72163 | − | 2.72603i | 0.355906 | − | 0.205483i | ||||
\(177\) | −0.274571 | −0.0206380 | ||||||||
\(178\) | 8.30844 | − | 4.79688i | 0.622744 | − | 0.359541i | ||||
\(179\) | −1.53429 | + | 2.65746i | −0.114678 | + | 0.198628i | −0.917651 | − | 0.397387i | \(-0.869917\pi\) |
0.802973 | + | 0.596015i | \(0.203250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.59376 | −0.341451 | −0.170726 | − | 0.985319i | \(-0.554611\pi\) | ||||
−0.170726 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(182\) | 12.9430 | + | 0.238545i | 0.959401 | + | 0.0176821i | ||||
\(183\) | − | 4.13288i | − | 0.305511i | ||||||
\(184\) | 1.60934 | + | 0.929155i | 0.118642 | + | 0.0684982i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.11669 | + | 1.93416i | 0.0818797 | + | 0.141820i | ||||
\(187\) | −39.8567 | −2.91461 | ||||||||
\(188\) | −2.53850 | − | 4.39681i | −0.185139 | − | 0.320670i | ||||
\(189\) | 3.10934 | − | 1.79518i | 0.226171 | − | 0.130580i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.03007 | − | 12.1764i | −0.508678 | − | 0.881056i | −0.999950 | − | 0.0100494i | \(-0.996801\pi\) |
0.491272 | − | 0.871006i | \(-0.336532\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −12.5444 | + | 21.7276i | −0.902966 | + | 1.56398i | −0.0793424 | + | 0.996847i | \(0.525282\pi\) |
−0.823624 | + | 0.567136i | \(0.808051\pi\) | |||||||
\(194\) | 1.90831 | 0.137009 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.89069 | 0.420764 | ||||||||
\(197\) | 4.59737 | − | 7.96287i | 0.327549 | − | 0.567331i | −0.654476 | − | 0.756083i | \(-0.727111\pi\) |
0.982025 | + | 0.188752i | \(0.0604441\pi\) | |||||||
\(198\) | 4.72163 | + | 2.72603i | 0.335552 | + | 0.193731i | ||||
\(199\) | 11.8396 | + | 20.5068i | 0.839286 | + | 1.45369i | 0.890492 | + | 0.454998i | \(0.150360\pi\) |
−0.0512060 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8146 | − | 7.39851i | 0.903872 | − | 0.521850i | ||||
\(202\) | 8.12785 | + | 14.0779i | 0.571874 | + | 0.990514i | ||||
\(203\) | −19.2141 | −1.34856 | ||||||||
\(204\) | 3.65519 | + | 6.33097i | 0.255914 | + | 0.443257i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2376 | − | 6.48802i | −0.782960 | − | 0.452042i | ||||
\(207\) | 1.85831i | 0.129161i | ||||||||
\(208\) | 1.86001 | − | 3.08875i | 0.128968 | − | 0.214166i | ||||
\(209\) | −21.0719 | −1.45757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.99303 | − | 8.64818i | 0.343734 | − | 0.595366i | −0.641389 | − | 0.767216i | \(-0.721641\pi\) |
0.985123 | + | 0.171851i | \(0.0549747\pi\) | |||||||
\(212\) | −1.93416 | + | 1.11669i | −0.132839 | + | 0.0766946i | ||||
\(213\) | −14.2957 | −0.979524 | ||||||||
\(214\) | −8.58814 | + | 4.95837i | −0.587073 | + | 0.338947i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −6.94435 | + | 4.00932i | −0.471413 | + | 0.272170i | ||||
\(218\) | −6.41801 | − | 3.70544i | −0.434682 | − | 0.250964i | ||||
\(219\) | −12.9016 | − | 7.44876i | −0.871811 | − | 0.503340i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.0656 | + | 12.7561i | −1.55156 | + | 0.858068i | ||||
\(222\) | − | 2.13288i | − | 0.143150i | ||||||
\(223\) | 11.1910 | − | 19.3833i | 0.749404 | − | 1.29801i | −0.198705 | − | 0.980059i | \(-0.563674\pi\) |
0.948109 | − | 0.317946i | \(-0.102993\pi\) | |||||||
\(224\) | 1.79518 | − | 3.10934i | 0.119946 | − | 0.207752i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.49265 | − | 11.2456i | −0.430933 | − | 0.746397i | 0.566021 | − | 0.824391i | \(-0.308482\pi\) |
−0.996954 | + | 0.0779935i | \(0.975149\pi\) | |||||||
\(228\) | 1.93247 | + | 3.34713i | 0.127981 | + | 0.221669i | ||||
\(229\) | − | 14.4455i | − | 0.954587i | −0.878744 | − | 0.477293i | \(-0.841618\pi\) | ||
0.878744 | − | 0.477293i | \(-0.158382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.78745 | + | 16.9524i | −0.643967 | + | 1.11538i | ||||
\(232\) | −2.67578 | + | 4.63459i | −0.175674 | + | 0.304276i | ||||
\(233\) | 12.4374i | 0.814800i | 0.913250 | + | 0.407400i | \(0.133564\pi\) | ||||
−0.913250 | + | 0.407400i | \(0.866436\pi\) | |||||||
\(234\) | 3.60494 | + | 0.0664404i | 0.235662 | + | 0.00434334i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.237785 | − | 0.137285i | −0.0154785 | − | 0.00893652i | ||||
\(237\) | 2.26990 | + | 1.31052i | 0.147446 | + | 0.0851277i | ||||
\(238\) | −22.7305 | + | 13.1234i | −1.47340 | + | 0.850667i | ||||
\(239\) | − | 4.16983i | − | 0.269724i | −0.990864 | − | 0.134862i | \(-0.956941\pi\) | ||
0.990864 | − | 0.134862i | \(-0.0430591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.63165 | − | 0.942035i | 0.105104 | − | 0.0606818i | −0.446527 | − | 0.894770i | \(-0.647339\pi\) |
0.551631 | + | 0.834089i | \(0.314006\pi\) | |||||||
\(242\) | −18.7250 | −1.20369 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 2.06644 | − | 3.57918i | 0.132290 | − | 0.229134i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.31038 | −0.466093 | ||||||||
\(247\) | −12.1946 | + | 6.74404i | −0.775923 | + | 0.429113i | ||||
\(248\) | 2.23338i | 0.141820i | ||||||||
\(249\) | −6.20064 | − | 3.57994i | −0.392949 | − | 0.226869i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.57502 | + | 6.19212i | 0.225653 | + | 0.390843i | 0.956515 | − | 0.291682i | \(-0.0942150\pi\) |
−0.730862 | + | 0.682525i | \(0.760882\pi\) | |||||||
\(252\) | 3.59036 | 0.226171 | ||||||||
\(253\) | −5.06582 | − | 8.77425i | −0.318485 | − | 0.551632i | ||||
\(254\) | −15.5772 | + | 8.99351i | −0.977401 | + | 0.564303i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −17.7517 | − | 10.2489i | −1.10732 | − | 0.639312i | −0.169186 | − | 0.985584i | \(-0.554114\pi\) |
−0.938134 | + | 0.346272i | \(0.887447\pi\) | |||||||
\(258\) | 4.10494 | − | 7.10996i | 0.255562 | − | 0.442647i | ||||
\(259\) | 7.65781 | 0.475833 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.35157 | −0.331254 | ||||||||
\(262\) | −10.1731 | + | 17.6203i | −0.628496 | + | 1.08859i | ||||
\(263\) | 15.3313 | + | 8.85153i | 0.945369 | + | 0.545809i | 0.891639 | − | 0.452747i | \(-0.149556\pi\) |
0.0537296 | + | 0.998556i | \(0.482889\pi\) | |||||||
\(264\) | 2.72603 | + | 4.72163i | 0.167776 | + | 0.290596i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0174 | + | 6.93825i | −0.736834 | + | 0.425411i | ||||
\(267\) | 4.79688 | + | 8.30844i | 0.293564 | + | 0.508468i | ||||
\(268\) | 14.7970 | 0.903872 | ||||||||
\(269\) | −9.09319 | − | 15.7499i | −0.554421 | − | 0.960286i | −0.997948 | − | 0.0640250i | \(-0.979606\pi\) |
0.443527 | − | 0.896261i | \(-0.353727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7188 | + | 11.3847i | 1.19783 | + | 0.691569i | 0.960072 | − | 0.279754i | \(-0.0902529\pi\) |
0.237762 | + | 0.971324i | \(0.423586\pi\) | |||||||
\(272\) | 7.31038i | 0.443257i | ||||||||
\(273\) | −0.238545 | + | 12.9430i | −0.0144374 | + | 0.783348i | ||||
\(274\) | −11.0407 | −0.666995 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.929155 | + | 1.60934i | −0.0559286 | + | 0.0968711i | ||||
\(277\) | −14.1649 | + | 8.17814i | −0.851089 | + | 0.491377i | −0.861018 | − | 0.508574i | \(-0.830173\pi\) |
0.00992898 | + | 0.999951i | \(0.496839\pi\) | |||||||
\(278\) | −9.70193 | −0.581883 | ||||||||
\(279\) | −1.93416 | + | 1.11669i | −0.115795 | + | 0.0668545i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.82221i | 0.466634i | 0.972401 | + | 0.233317i | \(0.0749580\pi\) | ||||
−0.972401 | + | 0.233317i | \(0.925042\pi\) | |||||||
\(282\) | 4.39681 | − | 2.53850i | 0.261826 | − | 0.151165i | ||||
\(283\) | 6.01483 | + | 3.47266i | 0.357544 | + | 0.206428i | 0.668003 | − | 0.744159i | \(-0.267149\pi\) |
−0.310459 | + | 0.950587i | \(0.600483\pi\) | |||||||
\(284\) | −12.3804 | − | 7.14784i | −0.734643 | − | 0.424146i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.2023 | + | 9.51348i | −1.01719 | + | 0.562544i | ||||
\(287\) | − | 26.2469i | − | 1.54931i | ||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 18.2208 | − | 31.5594i | 1.07181 | − | 1.85643i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.90831i | 0.111867i | ||||||||
\(292\) | −7.44876 | − | 12.9016i | −0.435906 | − | 0.755011i | ||||
\(293\) | −13.2122 | − | 22.8841i | −0.771863 | − | 1.33691i | −0.936541 | − | 0.350558i | \(-0.885992\pi\) |
0.164678 | − | 0.986347i | \(-0.447341\pi\) | |||||||
\(294\) | 5.89069i | 0.343552i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.06644 | − | 1.84713i | 0.0619856 | − | 0.107362i | ||||
\(297\) | −2.72603 | + | 4.72163i | −0.158181 | + | 0.273977i | ||||
\(298\) | 5.43817i | 0.315025i | ||||||||
\(299\) | −5.73985 | − | 3.45647i | −0.331944 | − | 0.199893i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.5273 | + | 14.7382i | 1.47137 | + | 0.849496i | ||||
\(302\) | 15.4161 | + | 8.90050i | 0.887098 | + | 0.512166i | ||||
\(303\) | −14.0779 | + | 8.12785i | −0.808752 | + | 0.466933i | ||||
\(304\) | 3.86493i | 0.221669i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.33097 | + | 3.65519i | −0.361918 | + | 0.208953i | ||||
\(307\) | −7.08581 | −0.404408 | −0.202204 | − | 0.979343i | \(-0.564810\pi\) | ||||
−0.202204 | + | 0.979343i | \(0.564810\pi\) | |||||||
\(308\) | −16.9524 | + | 9.78745i | −0.965950 | + | 0.557691i | ||||
\(309\) | 6.48802 | − | 11.2376i | 0.369091 | − | 0.639284i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.83017 | −0.103780 | −0.0518898 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518898 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(312\) | 3.08875 | + | 1.86001i | 0.174866 | + | 0.105302i | ||||
\(313\) | − | 12.2499i | − | 0.692403i | −0.938160 | − | 0.346201i | \(-0.887471\pi\) | ||
0.938160 | − | 0.346201i | \(-0.112529\pi\) | |||||||
\(314\) | −5.14117 | − | 2.96826i | −0.290133 | − | 0.167509i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.31052 | + | 2.26990i | 0.0737228 | + | 0.127692i | ||||
\(317\) | −6.25100 | −0.351091 | −0.175546 | − | 0.984471i | \(-0.556169\pi\) | ||||
−0.175546 | + | 0.984471i | \(0.556169\pi\) | |||||||
\(318\) | −1.11669 | − | 1.93416i | −0.0626209 | − | 0.108463i | ||||
\(319\) | 25.2681 | − | 14.5886i | 1.41474 | − | 0.816802i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.95837 | − | 8.58814i | −0.276749 | − | 0.479343i | ||||
\(322\) | −5.77812 | − | 3.33600i | −0.322002 | − | 0.185908i | ||||
\(323\) | 14.1271 | − | 24.4688i | 0.786050 | − | 1.36148i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5938 | 0.863658 | ||||||||
\(327\) | 3.70544 | − | 6.41801i | 0.204911 | − | 0.354917i | ||||
\(328\) | −6.33097 | − | 3.65519i | −0.349570 | − | 0.201824i | ||||
\(329\) | 9.11413 | + | 15.7861i | 0.502478 | + | 0.870318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6067 | + | 9.58790i | −0.912789 | + | 0.526999i | −0.881327 | − | 0.472506i | \(-0.843349\pi\) |
−0.0314613 | + | 0.999505i | \(0.510016\pi\) | |||||||
\(332\) | −3.57994 | − | 6.20064i | −0.196475 | − | 0.340304i | ||||
\(333\) | 2.13288 | 0.116881 | ||||||||
\(334\) | 0.929155 | + | 1.60934i | 0.0508411 | + | 0.0880594i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.10934 | + | 1.79518i | 0.169629 | + | 0.0979351i | ||||
\(337\) | 16.5450i | 0.901262i | 0.892710 | + | 0.450631i | \(0.148801\pi\) | ||||
−0.892710 | + | 0.450631i | \(0.851199\pi\) | |||||||
\(338\) | −6.91044 | + | 11.0112i | −0.375878 | + | 0.598929i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.08827 | − | 10.5452i | 0.329698 | − | 0.571054i | ||||
\(342\) | −3.34713 | + | 1.93247i | −0.180992 | + | 0.104496i | ||||
\(343\) | 3.98282 | 0.215052 | ||||||||
\(344\) | 7.10996 | − | 4.10494i | 0.383344 | − | 0.221323i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.3374i | 1.30839i | ||||||||
\(347\) | −5.16489 | + | 2.98195i | −0.277266 | + | 0.160079i | −0.632185 | − | 0.774818i | \(-0.717842\pi\) |
0.354919 | + | 0.934897i | \(0.384508\pi\) | |||||||
\(348\) | −4.63459 | − | 2.67578i | −0.248440 | − | 0.143437i | ||||
\(349\) | −2.76302 | − | 1.59523i | −0.147901 | − | 0.0853906i | 0.424223 | − | 0.905558i | \(-0.360547\pi\) |
−0.572124 | + | 0.820167i | \(0.693880\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0664404 | + | 3.60494i | −0.00354632 | + | 0.192417i | ||||
\(352\) | 5.45207i | 0.290596i | ||||||||
\(353\) | −14.0524 | + | 24.3395i | −0.747934 | + | 1.29546i | 0.200877 | + | 0.979616i | \(0.435621\pi\) |
−0.948811 | + | 0.315844i | \(0.897712\pi\) | |||||||
\(354\) | 0.137285 | − | 0.237785i | 0.00729663 | − | 0.0126381i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.59376i | 0.508468i | ||||||||
\(357\) | −13.1234 | − | 22.7305i | −0.694566 | − | 1.20302i | ||||
\(358\) | −1.53429 | − | 2.65746i | −0.0810895 | − | 0.140451i | ||||
\(359\) | 22.7404i | 1.20019i | 0.799927 | + | 0.600097i | \(0.204872\pi\) | ||||
−0.799927 | + | 0.600097i | \(0.795128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03115 | + | 3.51806i | −0.106903 | + | 0.185161i | ||||
\(362\) | 2.29688 | − | 3.97831i | 0.120721 | − | 0.209095i | ||||
\(363\) | − | 18.7250i | − | 0.982810i | ||||||
\(364\) | −6.67810 | + | 11.0897i | −0.350028 | + | 0.581259i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.57918 | + | 2.06644i | 0.187087 | + | 0.108015i | ||||
\(367\) | 26.1824 | + | 15.1164i | 1.36671 | + | 0.789072i | 0.990507 | − | 0.137464i | \(-0.0438952\pi\) |
0.376206 | + | 0.926536i | \(0.377229\pi\) | |||||||
\(368\) | −1.60934 | + | 0.929155i | −0.0838928 | + | 0.0484356i | ||||
\(369\) | − | 7.31038i | − | 0.380563i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.94435 | − | 4.00932i | 0.360533 | − | 0.208154i | ||||
\(372\) | −2.23338 | −0.115795 | ||||||||
\(373\) | 4.04965 | − | 2.33807i | 0.209683 | − | 0.121061i | −0.391481 | − | 0.920186i | \(-0.628037\pi\) |
0.601164 | + | 0.799126i | \(0.294704\pi\) | |||||||
\(374\) | 19.9283 | − | 34.5169i | 1.03047 | − | 1.78483i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.07700 | 0.261826 | ||||||||
\(377\) | 9.95396 | − | 16.5296i | 0.512655 | − | 0.851320i | ||||
\(378\) | 3.59036i | 0.184668i | ||||||||
\(379\) | −18.5598 | − | 10.7155i | −0.953353 | − | 0.550419i | −0.0592321 | − | 0.998244i | \(-0.518865\pi\) |
−0.894121 | + | 0.447826i | \(0.852199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.99351 | − | 15.5772i | −0.460751 | − | 0.798045i | ||||
\(382\) | 14.0601 | 0.719379 | ||||||||
\(383\) | 0.0256044 | + | 0.0443481i | 0.00130832 | + | 0.00226608i | 0.866679 | − | 0.498867i | \(-0.166250\pi\) |
−0.865371 | + | 0.501133i | \(0.832917\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.5444 | − | 21.7276i | −0.638494 | − | 1.10590i | ||||
\(387\) | 7.10996 | + | 4.10494i | 0.361420 | + | 0.208666i | ||||
\(388\) | −0.954155 | + | 1.65264i | −0.0484399 | + | 0.0839003i | ||||
\(389\) | 5.35157 | 0.271335 | 0.135668 | − | 0.990754i | \(-0.456682\pi\) | ||||
0.135668 | + | 0.990754i | \(0.456682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5849 | 0.687020 | ||||||||
\(392\) | −2.94535 | + | 5.10149i | −0.148762 | + | 0.257664i | ||||
\(393\) | −17.6203 | − | 10.1731i | −0.888827 | − | 0.513165i | ||||
\(394\) | 4.59737 | + | 7.96287i | 0.231612 | + | 0.401164i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.72163 | + | 2.72603i | −0.237271 | + | 0.136988i | ||||
\(397\) | −4.25359 | − | 7.36744i | −0.213482 | − | 0.369761i | 0.739320 | − | 0.673354i | \(-0.235147\pi\) |
−0.952802 | + | 0.303593i | \(0.901814\pi\) | |||||||
\(398\) | −23.6792 | −1.18693 | ||||||||
\(399\) | −6.93825 | − | 12.0174i | −0.347347 | − | 0.601623i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2467 | − | 11.6894i | −1.01107 | − | 0.583741i | −0.0995649 | − | 0.995031i | \(-0.531745\pi\) |
−0.911505 | + | 0.411290i | \(0.865078\pi\) | |||||||
\(402\) | 14.7970i | 0.738008i | ||||||||
\(403\) | 0.148387 | − | 8.05120i | 0.00739166 | − | 0.401059i | ||||
\(404\) | −16.2557 | −0.808752 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.60703 | − | 16.6399i | 0.476789 | − | 0.825823i | ||||
\(407\) | −10.0707 | + | 5.81431i | −0.499185 | + | 0.288204i | ||||
\(408\) | −7.31038 | −0.361918 | ||||||||
\(409\) | 4.51511 | − | 2.60680i | 0.223258 | − | 0.128898i | −0.384200 | − | 0.923250i | \(-0.625523\pi\) |
0.607458 | + | 0.794352i | \(0.292189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 11.0407i | − | 0.544599i | ||||||
\(412\) | 11.2376 | − | 6.48802i | 0.553636 | − | 0.319642i | ||||
\(413\) | 0.853735 | + | 0.492904i | 0.0420095 | + | 0.0242542i | ||||
\(414\) | −1.60934 | − | 0.929155i | −0.0790949 | − | 0.0456655i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.74493 | + | 3.15519i | 0.0855523 | + | 0.154696i | ||||
\(417\) | − | 9.70193i | − | 0.475105i | ||||||
\(418\) | 10.5359 | − | 18.2488i | 0.515329 | − | 0.892577i | ||||
\(419\) | 9.10066 | − | 15.7628i | 0.444596 | − | 0.770064i | −0.553428 | − | 0.832897i | \(-0.686680\pi\) |
0.998024 | + | 0.0628337i | \(0.0200138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.6463i | − | 1.24992i | −0.780656 | − | 0.624961i | \(-0.785115\pi\) | ||
0.780656 | − | 0.624961i | \(-0.214885\pi\) | |||||||
\(422\) | 4.99303 | + | 8.64818i | 0.243057 | + | 0.420987i | ||||
\(423\) | 2.53850 | + | 4.39681i | 0.123426 | + | 0.213780i | ||||
\(424\) | − | 2.23338i | − | 0.108463i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.14784 | − | 12.3804i | 0.346314 | − | 0.599834i | ||||
\(427\) | −7.41927 | + | 12.8505i | −0.359043 | + | 0.621882i | ||||
\(428\) | − | 9.91673i | − | 0.479343i | ||||||
\(429\) | −9.51348 | − | 17.2023i | −0.459315 | − | 0.830535i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.79193 | − | 1.03457i | −0.0863142 | − | 0.0498335i | 0.456222 | − | 0.889866i | \(-0.349202\pi\) |
−0.542536 | + | 0.840033i | \(0.682536\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 0.815649 | − | 0.470915i | 0.0391976 | − | 0.0226307i | −0.480273 | − | 0.877119i | \(-0.659462\pi\) |
0.519471 | + | 0.854488i | \(0.326129\pi\) | |||||||
\(434\) | − | 8.01864i | − | 0.384907i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.41801 | − | 3.70544i | 0.307367 | − | 0.177458i | ||||
\(437\) | 7.18224 | 0.343573 | ||||||||
\(438\) | 12.9016 | − | 7.44876i | 0.616464 | − | 0.355915i | ||||
\(439\) | 1.80132 | − | 3.11997i | 0.0859722 | − | 0.148908i | −0.819833 | − | 0.572603i | \(-0.805934\pi\) |
0.905805 | + | 0.423695i | \(0.139267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89069 | −0.280509 | ||||||||
\(442\) | 0.485704 | − | 26.3535i | 0.0231026 | − | 1.25351i | ||||
\(443\) | − | 5.05095i | − | 0.239978i | −0.992775 | − | 0.119989i | \(-0.961714\pi\) | ||
0.992775 | − | 0.119989i | \(-0.0382859\pi\) | |||||||
\(444\) | 1.84713 | + | 1.06644i | 0.0876609 | + | 0.0506110i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1910 | + | 19.3833i | 0.529908 | + | 0.917828i | ||||
\(447\) | −5.43817 | −0.257217 | ||||||||
\(448\) | 1.79518 | + | 3.10934i | 0.0848143 | + | 0.146903i | ||||
\(449\) | 4.70017 | − | 2.71364i | 0.221815 | − | 0.128065i | −0.384976 | − | 0.922927i | \(-0.625790\pi\) |
0.606790 | + | 0.794862i | \(0.292457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9283 | + | 34.5169i | 0.938389 | + | 1.62534i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.90050 | + | 15.4161i | −0.418182 | + | 0.724312i | ||||
\(454\) | 12.9853 | 0.609431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.86493 | −0.180992 | ||||||||
\(457\) | 10.8416 | − | 18.7782i | 0.507147 | − | 0.878405i | −0.492818 | − | 0.870132i | \(-0.664033\pi\) |
0.999966 | − | 0.00827291i | \(-0.00263338\pi\) | |||||||
\(458\) | 12.5102 | + | 7.22276i | 0.584562 | + | 0.337497i | ||||
\(459\) | −3.65519 | − | 6.33097i | −0.170610 | − | 0.295505i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.6364 | + | 14.8012i | −1.19401 | + | 0.689359i | −0.959212 | − | 0.282686i | \(-0.908775\pi\) |
−0.234793 | + | 0.972045i | \(0.575441\pi\) | |||||||
\(462\) | −9.78745 | − | 16.9524i | −0.455353 | − | 0.788695i | ||||
\(463\) | −28.2075 | −1.31091 | −0.655457 | − | 0.755232i | \(-0.727524\pi\) | ||||
−0.655457 | + | 0.755232i | \(0.727524\pi\) | |||||||
\(464\) | −2.67578 | − | 4.63459i | −0.124220 | − | 0.215156i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7711 | − | 6.21869i | −0.498961 | − | 0.288075i | ||||
\(467\) | 8.17371i | 0.378234i | 0.981955 | + | 0.189117i | \(0.0605626\pi\) | ||||
−0.981955 | + | 0.189117i | \(0.939437\pi\) | |||||||
\(468\) | −1.86001 | + | 3.08875i | −0.0859789 | + | 0.142777i | ||||
\(469\) | −53.1266 | −2.45316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.96826 | − | 5.14117i | 0.136770 | − | 0.236893i | ||||
\(472\) | 0.237785 | − | 0.137285i | 0.0109450 | − | 0.00631907i | ||||
\(473\) | −44.7608 | −2.05810 | ||||||||
\(474\) | −2.26990 | + | 1.31052i | −0.104260 | + | 0.0601944i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 26.2469i | − | 1.20302i | ||||||
\(477\) | 1.93416 | − | 1.11669i | 0.0885593 | − | 0.0511297i | ||||
\(478\) | 3.61118 | + | 2.08491i | 0.165171 | + | 0.0953618i | ||||
\(479\) | −10.1231 | − | 5.84458i | −0.462537 | − | 0.267046i | 0.250573 | − | 0.968098i | \(-0.419381\pi\) |
−0.713110 | + | 0.701052i | \(0.752714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.96718 | + | 6.58793i | −0.180888 | + | 0.300384i | ||||
\(482\) | 1.88407i | 0.0858170i | ||||||||
\(483\) | 3.33600 | − | 5.77812i | 0.151793 | − | 0.262914i | ||||
\(484\) | 9.36252 | − | 16.2164i | 0.425569 | − | 0.737107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 15.9438 | + | 27.6154i | 0.722481 | + | 1.25137i | 0.960003 | + | 0.279991i | \(0.0903316\pi\) |
−0.237522 | + | 0.971382i | \(0.576335\pi\) | |||||||
\(488\) | 2.06644 | + | 3.57918i | 0.0935434 | + | 0.162022i | ||||
\(489\) | 15.5938i | 0.705174i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.77506 | − | 16.9309i | 0.441142 | − | 0.764080i | −0.556632 | − | 0.830759i | \(-0.687907\pi\) |
0.997775 | + | 0.0666784i | \(0.0212402\pi\) | |||||||
\(492\) | 3.65519 | − | 6.33097i | 0.164789 | − | 0.285422i | ||||
\(493\) | 39.1220i | 1.76197i | ||||||||
\(494\) | 0.256787 | − | 13.9328i | 0.0115534 | − | 0.626868i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.93416 | − | 1.11669i | −0.0868465 | − | 0.0501409i | ||||
\(497\) | 44.4502 | + | 25.6633i | 1.99386 | + | 1.15116i | ||||
\(498\) | 6.20064 | − | 3.57994i | 0.277857 | − | 0.160421i | ||||
\(499\) | − | 39.3428i | − | 1.76123i | −0.473836 | − | 0.880613i | \(-0.657131\pi\) | ||
0.473836 | − | 0.880613i | \(-0.342869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.60934 | + | 0.929155i | −0.0719002 | + | 0.0415116i | ||||
\(502\) | −7.15005 | −0.319122 | ||||||||
\(503\) | −12.4127 | + | 7.16650i | −0.553457 | + | 0.319538i | −0.750515 | − | 0.660853i | \(-0.770194\pi\) |
0.197058 | + | 0.980392i | \(0.436861\pi\) | |||||||
\(504\) | −1.79518 | + | 3.10934i | −0.0799637 | + | 0.138501i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1316 | 0.450406 | ||||||||
\(507\) | −11.0112 | − | 6.91044i | −0.489023 | − | 0.306903i | ||||
\(508\) | − | 17.9870i | − | 0.798045i | ||||||
\(509\) | 3.23839 | + | 1.86968i | 0.143539 | + | 0.0828723i | 0.570050 | − | 0.821610i | \(-0.306924\pi\) |
−0.426511 | + | 0.904483i | \(0.640257\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.7437 | + | 46.3215i | 1.18307 | + | 2.04914i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.93247 | − | 3.34713i | −0.0853204 | − | 0.147779i | ||||
\(514\) | 17.7517 | − | 10.2489i | 0.782994 | − | 0.452062i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.10494 | + | 7.10996i | 0.180710 | + | 0.312999i | ||||
\(517\) | −23.9717 | − | 13.8401i | −1.05427 | − | 0.608685i | ||||
\(518\) | −3.82891 | + | 6.63186i | −0.168232 | + | 0.291387i | ||||
\(519\) | −24.3374 | −1.06829 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.2722 | −1.76436 | −0.882178 | − | 0.470915i | \(-0.843924\pi\) | ||||
−0.882178 | + | 0.470915i | \(0.843924\pi\) | |||||||
\(522\) | 2.67578 | − | 4.63459i | 0.117116 | − | 0.202851i | ||||
\(523\) | −19.7853 | − | 11.4230i | −0.865150 | − | 0.499495i | 0.000583330 | − | 1.00000i | \(-0.499814\pi\) |
−0.865734 | + | 0.500505i | \(0.833148\pi\) | |||||||
\(524\) | −10.1731 | − | 17.6203i | −0.444414 | − | 0.769747i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.3313 | + | 8.85153i | −0.668477 | + | 0.385945i | ||||
\(527\) | 8.16343 | + | 14.1395i | 0.355605 | + | 0.615925i | ||||
\(528\) | −5.45207 | −0.237271 | ||||||||
\(529\) | −9.77334 | − | 16.9279i | −0.424928 | − | 0.735997i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.237785 | + | 0.137285i | 0.0103190 | + | 0.00595768i | ||||
\(532\) | − | 13.8765i | − | 0.601623i | ||||||
\(533\) | 22.5799 | + | 13.5974i | 0.978045 | + | 0.588967i | ||||
\(534\) | −9.59376 | −0.415163 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.39851 | + | 12.8146i | −0.319567 | + | 0.553506i | ||||
\(537\) | 2.65746 | − | 1.53429i | 0.114678 | − | 0.0662093i | ||||
\(538\) | 18.1864 | 0.784070 | ||||||||
\(539\) | 27.8137 | − | 16.0582i | 1.19802 | − | 0.691677i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 18.9610i | − | 0.815196i | −0.913162 | − | 0.407598i | \(-0.866367\pi\) | ||
0.913162 | − | 0.407598i | \(-0.133633\pi\) | |||||||
\(542\) | −19.7188 | + | 11.3847i | −0.846996 | + | 0.489013i | ||||
\(543\) | 3.97831 | + | 2.29688i | 0.170726 | + | 0.0985685i | ||||
\(544\) | −6.33097 | − | 3.65519i | −0.271438 | − | 0.156715i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0897 | − | 6.67810i | −0.474596 | − | 0.285796i | ||||
\(547\) | − | 26.7863i | − | 1.14530i | −0.819801 | − | 0.572649i | \(-0.805916\pi\) | ||
0.819801 | − | 0.572649i | \(-0.194084\pi\) | |||||||
\(548\) | 5.52037 | − | 9.56156i | 0.235818 | − | 0.408450i | ||||
\(549\) | −2.06644 | + | 3.57918i | −0.0881935 | + | 0.152756i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.6834i | 0.881144i | ||||||||
\(552\) | −0.929155 | − | 1.60934i | −0.0395475 | − | 0.0684982i | ||||
\(553\) | −4.70526 | − | 8.14974i | −0.200088 | − | 0.346562i | ||||
\(554\) | − | 16.3563i | − | 0.694911i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.85096 | − | 8.40212i | 0.205727 | − | 0.356329i | ||||
\(557\) | −13.1189 | + | 22.7227i | −0.555867 | + | 0.962791i | 0.441968 | + | 0.897031i | \(0.354280\pi\) |
−0.997835 | + | 0.0657599i | \(0.979053\pi\) | |||||||
\(558\) | − | 2.23338i | − | 0.0945465i | ||||||
\(559\) | −25.9037 | + | 14.3257i | −1.09561 | + | 0.605911i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.5169 | + | 19.9283i | 1.45730 | + | 0.841375i | ||||
\(562\) | −6.77423 | − | 3.91110i | −0.285754 | − | 0.164980i | ||||
\(563\) | −14.0452 | + | 8.10900i | −0.591935 | + | 0.341754i | −0.765862 | − | 0.643005i | \(-0.777688\pi\) |
0.173927 | + | 0.984758i | \(0.444354\pi\) | |||||||
\(564\) | 5.07700i | 0.213780i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.01483 | + | 3.47266i | −0.252822 | + | 0.145967i | ||||
\(567\) | −3.59036 | −0.150781 | ||||||||
\(568\) | 12.3804 | − | 7.14784i | 0.519471 | − | 0.299917i | ||||
\(569\) | −17.1092 | + | 29.6340i | −0.717255 | + | 1.24232i | 0.244829 | + | 0.969566i | \(0.421268\pi\) |
−0.962083 | + | 0.272755i | \(0.912065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.151070 | 0.00632206 | 0.00316103 | − | 0.999995i | \(-0.498994\pi\) | ||||
0.00316103 | + | 0.999995i | \(0.498994\pi\) | |||||||
\(572\) | 0.362237 | − | 19.6544i | 0.0151459 | − | 0.821791i | ||||
\(573\) | 14.0601i | 0.587371i | ||||||||
\(574\) | 22.7305 | + | 13.1234i | 0.948752 | + | 0.547762i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −33.7742 | −1.40604 | −0.703019 | − | 0.711171i | \(-0.748165\pi\) | ||||
−0.703019 | + | 0.711171i | \(0.748165\pi\) | |||||||
\(578\) | 18.2208 | + | 31.5594i | 0.757886 | + | 1.31270i | ||||
\(579\) | 21.7276 | − | 12.5444i | 0.902966 | − | 0.521328i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8533 | + | 22.2625i | 0.533244 | + | 0.923605i | ||||
\(582\) | −1.65264 | − | 0.954155i | −0.0685043 | − | 0.0395510i | ||||
\(583\) | −6.08827 | + | 10.5452i | −0.252150 | + | 0.436737i | ||||
\(584\) | 14.8975 | 0.616464 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.4243 | 1.09158 | ||||||||
\(587\) | −16.8030 | + | 29.1037i | −0.693535 | + | 1.20124i | 0.277137 | + | 0.960831i | \(0.410615\pi\) |
−0.970672 | + | 0.240408i | \(0.922719\pi\) | |||||||
\(588\) | −5.10149 | − | 2.94535i | −0.210382 | − | 0.121464i | ||||
\(589\) | 4.31593 | + | 7.47541i | 0.177835 | + | 0.308019i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.96287 | + | 4.59737i | −0.327549 | + | 0.189110i | ||||
\(592\) | 1.06644 | + | 1.84713i | 0.0438304 | + | 0.0759165i | ||||
\(593\) | 36.7529 | 1.50926 | 0.754630 | − | 0.656150i | \(-0.227816\pi\) | ||||
0.754630 | + | 0.656150i | \(0.227816\pi\) | |||||||
\(594\) | −2.72603 | − | 4.72163i | −0.111851 | − | 0.193731i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.70959 | − | 2.71908i | −0.192912 | − | 0.111378i | ||||
\(597\) | − | 23.6792i | − | 0.969124i | ||||||
\(598\) | 5.86332 | − | 3.24262i | 0.239769 | − | 0.132601i | ||||
\(599\) | 24.5241 | 1.00203 | 0.501015 | − | 0.865439i | \(-0.332960\pi\) | ||||
0.501015 | + | 0.865439i | \(0.332960\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7548 | − | 32.4843i | 0.765025 | − | 1.32506i | −0.175208 | − | 0.984531i | \(-0.556060\pi\) |
0.940233 | − | 0.340531i | \(-0.110607\pi\) | |||||||
\(602\) | −25.5273 | + | 14.7382i | −1.04042 | + | 0.600685i | ||||
\(603\) | −14.7970 | −0.602581 | ||||||||
\(604\) | −15.4161 | + | 8.90050i | −0.627273 | + | 0.362156i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 16.2557i | − | 0.660343i | ||||||
\(607\) | 40.2796 | − | 23.2554i | 1.63490 | − | 0.943909i | 0.652346 | − | 0.757921i | \(-0.273785\pi\) |
0.982552 | − | 0.185988i | \(-0.0595484\pi\) | |||||||
\(608\) | −3.34713 | − | 1.93247i | −0.135744 | − | 0.0783718i | ||||
\(609\) | 16.6399 | + | 9.60703i | 0.674281 | + | 0.389297i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3023 | − | 0.337318i | −0.740430 | − | 0.0136464i | ||||
\(612\) | − | 7.31038i | − | 0.295505i | ||||||
\(613\) | −5.14785 | + | 8.91634i | −0.207920 | + | 0.360128i | −0.951059 | − | 0.309009i | \(-0.900003\pi\) |
0.743139 | + | 0.669137i | \(0.233336\pi\) | |||||||
\(614\) | 3.54290 | − | 6.13649i | 0.142980 | − | 0.247649i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 19.5749i | − | 0.788695i | ||||||
\(617\) | −17.8404 | − | 30.9005i | −0.718228 | − | 1.24401i | −0.961701 | − | 0.274100i | \(-0.911620\pi\) |
0.243473 | − | 0.969908i | \(-0.421713\pi\) | |||||||
\(618\) | 6.48802 | + | 11.2376i | 0.260987 | + | 0.452042i | ||||
\(619\) | 12.9815i | 0.521772i | 0.965370 | + | 0.260886i | \(0.0840146\pi\) | ||||
−0.965370 | + | 0.260886i | \(0.915985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.929155 | − | 1.60934i | 0.0372857 | − | 0.0645807i | ||||
\(622\) | 0.915086 | − | 1.58498i | 0.0366916 | − | 0.0635517i | ||||
\(623\) | − | 34.4451i | − | 1.38001i | ||||||
\(624\) | −3.15519 | + | 1.74493i | −0.126309 | + | 0.0698531i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.6087 | + | 6.12493i | 0.424008 | + | 0.244801i | ||||
\(627\) | 18.2488 | + | 10.5359i | 0.728786 | + | 0.420765i | ||||
\(628\) | 5.14117 | − | 2.96826i | 0.205155 | − | 0.118446i | ||||
\(629\) | − | 15.5922i | − | 0.621700i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4953 | + | 10.6783i | −0.736287 | + | 0.425096i | −0.820718 | − | 0.571334i | \(-0.806426\pi\) |
0.0844307 | + | 0.996429i | \(0.473093\pi\) | |||||||
\(632\) | −2.62105 | −0.104260 | ||||||||
\(633\) | −8.64818 | + | 4.99303i | −0.343734 | + | 0.198455i | ||||
\(634\) | 3.12550 | − | 5.41352i | 0.124129 | − | 0.214999i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.23338 | 0.0885593 | ||||||||
\(637\) | 10.9567 | − | 18.1949i | 0.434122 | − | 0.720907i | ||||
\(638\) | 29.1771i | 1.15513i | ||||||||
\(639\) | 12.3804 | + | 7.14784i | 0.489762 | + | 0.282764i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.49169 | − | 11.2439i | −0.256407 | − | 0.444109i | 0.708870 | − | 0.705339i | \(-0.249205\pi\) |
−0.965277 | + | 0.261230i | \(0.915872\pi\) | |||||||
\(642\) | 9.91673 | 0.391382 | ||||||||
\(643\) | 7.90323 | + | 13.6888i | 0.311673 | + | 0.539834i | 0.978725 | − | 0.205178i | \(-0.0657773\pi\) |
−0.667052 | + | 0.745012i | \(0.732444\pi\) | |||||||
\(644\) | 5.77812 | − | 3.33600i | 0.227690 | − | 0.131457i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.1271 | + | 24.4688i | 0.555822 | + | 0.962711i | ||||
\(647\) | −19.8219 | − | 11.4442i | −0.779277 | − | 0.449916i | 0.0568967 | − | 0.998380i | \(-0.481879\pi\) |
−0.836174 | + | 0.548464i | \(0.815213\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −1.49698 | −0.0587615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.01864 | 0.314275 | ||||||||
\(652\) | −7.79688 | + | 13.5046i | −0.305349 | + | 0.528881i | ||||
\(653\) | 1.87183 | + | 1.08070i | 0.0732504 | + | 0.0422911i | 0.536178 | − | 0.844105i | \(-0.319868\pi\) |
−0.462927 | + | 0.886396i | \(0.653201\pi\) | |||||||
\(654\) | 3.70544 | + | 6.41801i | 0.144894 | + | 0.250964i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.33097 | − | 3.65519i | 0.247183 | − | 0.142711i | ||||
\(657\) | 7.44876 | + | 12.9016i | 0.290604 | + | 0.503340i | ||||
\(658\) | −18.2283 | −0.710611 | ||||||||
\(659\) | 9.79863 | + | 16.9717i | 0.381700 | + | 0.661124i | 0.991305 | − | 0.131581i | \(-0.0420053\pi\) |
−0.609605 | + | 0.792705i | \(0.708672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8286 | − | 14.3348i | −0.965719 | − | 0.557558i | −0.0677909 | − | 0.997700i | \(-0.521595\pi\) |
−0.897929 | + | 0.440141i | \(0.854928\pi\) | |||||||
\(662\) | − | 19.1758i | − | 0.745289i | ||||||
\(663\) | 26.3535 | + | 0.485704i | 1.02348 | + | 0.0188632i | ||||
\(664\) | 7.15988 | 0.277857 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.06644 | + | 1.84713i | −0.0413237 | + | 0.0715748i | ||||
\(667\) | −8.61251 | + | 4.97244i | −0.333478 | + | 0.192534i | ||||
\(668\) | −1.85831 | −0.0719002 | ||||||||
\(669\) | −19.3833 | + | 11.1910i | −0.749404 | + | 0.432668i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.5327i | − | 0.869867i | ||||||
\(672\) | −3.10934 | + | 1.79518i | −0.119946 | + | 0.0692506i | ||||
\(673\) | −44.0166 | − | 25.4130i | −1.69672 | − | 0.979599i | −0.948838 | − | 0.315763i | \(-0.897740\pi\) |
−0.747878 | − | 0.663837i | \(-0.768927\pi\) | |||||||
\(674\) | −14.3284 | − | 8.27248i | −0.551908 | − | 0.318644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.08074 | − | 11.4902i | −0.233874 | − | 0.441931i | ||||
\(677\) | − | 15.4058i | − | 0.592093i | −0.955174 | − | 0.296046i | \(-0.904332\pi\) | ||
0.955174 | − | 0.296046i | \(-0.0956683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.42576 | − | 5.93359i | 0.131469 | − | 0.227710i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9853i | 0.497598i | ||||||||
\(682\) | 6.08827 | + | 10.5452i | 0.233132 | + | 0.403796i | ||||
\(683\) | 11.1227 | + | 19.2650i | 0.425597 | + | 0.737155i | 0.996476 | − | 0.0838788i | \(-0.0267309\pi\) |
−0.570879 | + | 0.821034i | \(0.693398\pi\) | |||||||
\(684\) | − | 3.86493i | − | 0.147779i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.99141 | + | 3.44922i | −0.0760324 | + | 0.131692i | ||||
\(687\) | −7.22276 | + | 12.5102i | −0.275565 | + | 0.477293i | ||||
\(688\) | 8.20988i | 0.312999i | ||||||||
\(689\) | −0.148387 | + | 8.05120i | −0.00565308 | + | 0.306726i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.31663 | + | 3.06956i | 0.202254 | + | 0.116771i | 0.597706 | − | 0.801715i | \(-0.296079\pi\) |
−0.395452 | + | 0.918486i | \(0.629412\pi\) | |||||||
\(692\) | −21.0768 | − | 12.1687i | −0.801219 | − | 0.462584i | ||||
\(693\) | 16.9524 | − | 9.78745i | 0.643967 | − | 0.371794i | ||||
\(694\) | − | 5.96390i | − | 0.226387i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.63459 | − | 2.67578i | 0.175674 | − | 0.101425i | ||||
\(697\) | −53.4416 | −2.02425 | ||||||||
\(698\) | 2.76302 | − | 1.59523i | 0.104582 | − | 0.0603803i | ||||
\(699\) | 6.21869 | − | 10.7711i | 0.235212 | − | 0.407400i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.7793 | −0.935902 | −0.467951 | − | 0.883754i | \(-0.655008\pi\) | ||||
−0.467951 | + | 0.883754i | \(0.655008\pi\) | |||||||
\(702\) | −3.08875 | − | 1.86001i | −0.116577 | − | 0.0702015i | ||||
\(703\) | − | 8.24344i | − | 0.310907i | ||||||
\(704\) | −4.72163 | − | 2.72603i | −0.177953 | − | 0.102741i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0524 | − | 24.3395i | −0.528869 | − | 0.916029i | ||||
\(707\) | 58.3638 | 2.19500 | ||||||||
\(708\) | 0.137285 | + | 0.237785i | 0.00515950 | + | 0.00893652i | ||||
\(709\) | −22.3507 | + | 12.9042i | −0.839398 | + | 0.484627i | −0.857060 | − | 0.515217i | \(-0.827711\pi\) |
0.0176613 | + | 0.999844i | \(0.494378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.31052 | − | 2.26990i | −0.0491485 | − | 0.0851277i | ||||
\(712\) | −8.30844 | − | 4.79688i | −0.311372 | − | 0.179771i | ||||
\(713\) | −2.07516 | + | 3.59428i | −0.0777152 | + | 0.134607i | ||||
\(714\) | 26.2469 | 0.982265 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.06857 | 0.114678 | ||||||||
\(717\) | −2.08491 | + | 3.61118i | −0.0778625 | + | 0.134862i | ||||
\(718\) | −19.6938 | − | 11.3702i | −0.734966 | − | 0.424333i | ||||
\(719\) | 11.7949 | + | 20.4293i | 0.439874 | + | 0.761884i | 0.997679 | − | 0.0680879i | \(-0.0216898\pi\) |
−0.557806 | + | 0.829972i | \(0.688357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.3470 | + | 23.2943i | −1.50260 | + | 0.867527i | ||||
\(722\) | −2.03115 | − | 3.51806i | −0.0755917 | − | 0.130929i | ||||
\(723\) | −1.88407 | −0.0700693 | ||||||||
\(724\) | 2.29688 | + | 3.97831i | 0.0853628 | + | 0.147853i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.2164 | + | 9.36252i | 0.601846 | + | 0.347476i | ||||
\(727\) | 31.4651i | 1.16698i | 0.812121 | + | 0.583489i | \(0.198313\pi\) | ||||
−0.812121 | + | 0.583489i | \(0.801687\pi\) | |||||||
\(728\) | −6.26493 | − | 11.3283i | −0.232194 | − | 0.419854i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0087 | − | 51.9765i | 1.10991 | − | 1.92242i | ||||
\(732\) | −3.57918 | + | 2.06644i | −0.132290 | + | 0.0763778i | ||||
\(733\) | 32.2822 | 1.19237 | 0.596186 | − | 0.802847i | \(-0.296682\pi\) | ||||
0.596186 | + | 0.802847i | \(0.296682\pi\) | |||||||
\(734\) | −26.1824 | + | 15.1164i | −0.966412 | + | 0.557958i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.85831i | − | 0.0684982i | ||||||
\(737\) | 69.8660 | − | 40.3372i | 2.57355 | − | 1.48584i | ||||
\(738\) | 6.33097 | + | 3.65519i | 0.233046 | + | 0.134549i | ||||
\(739\) | 13.2643 | + | 7.65817i | 0.487936 | + | 0.281710i | 0.723718 | − | 0.690096i | \(-0.242432\pi\) |
−0.235782 | + | 0.971806i | \(0.575765\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.9328 | + | 0.256787i | 0.511836 | + | 0.00943332i | ||||
\(742\) | 8.01864i | 0.294374i | ||||||||
\(743\) | 12.6161 | − | 21.8518i | 0.462841 | − | 0.801663i | −0.536261 | − | 0.844052i | \(-0.680164\pi\) |
0.999101 | + | 0.0423891i | \(0.0134969\pi\) | |||||||
\(744\) | 1.11669 | − | 1.93416i | 0.0409399 | − | 0.0709099i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.67614i | 0.171206i | ||||||||
\(747\) | 3.57994 | + | 6.20064i | 0.130983 | + | 0.226869i | ||||
\(748\) | 19.9283 | + | 34.5169i | 0.728652 | + | 1.26206i | ||||
\(749\) | 35.6047i | 1.30097i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.69444 | − | 13.3272i | 0.280774 | − | 0.486315i | −0.690802 | − | 0.723044i | \(-0.742742\pi\) |
0.971576 | + | 0.236729i | \(0.0760755\pi\) | |||||||
\(752\) | −2.53850 | + | 4.39681i | −0.0925695 | + | 0.160335i | ||||
\(753\) | − | 7.15005i | − | 0.260562i | ||||||
\(754\) | 9.33811 | + | 16.8852i | 0.340074 | + | 0.614923i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.10934 | − | 1.79518i | −0.113086 | − | 0.0652901i | ||||
\(757\) | 31.4879 | + | 18.1796i | 1.14445 | + | 0.660747i | 0.947528 | − | 0.319673i | \(-0.103573\pi\) |
0.196920 | + | 0.980420i | \(0.436906\pi\) | |||||||
\(758\) | 18.5598 | − | 10.7155i | 0.674122 | − | 0.389205i | ||||
\(759\) | 10.1316i | 0.367755i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.4056 | + | 15.8226i | −0.993453 | + | 0.573570i | −0.906305 | − | 0.422625i | \(-0.861109\pi\) |
−0.0871481 | + | 0.996195i | \(0.527775\pi\) | |||||||
\(762\) | 17.9870 | 0.651601 | ||||||||
\(763\) | −23.0430 | + | 13.3039i | −0.834211 | + | 0.481632i | ||||
\(764\) | −7.03007 | + | 12.1764i | −0.254339 | + | 0.440528i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.0512087 | −0.00185025 | ||||||||
\(767\) | −0.866322 | + | 0.479107i | −0.0312811 | + | 0.0172995i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 10.0722 | + | 5.81521i | 0.363214 | + | 0.209702i | 0.670490 | − | 0.741919i | \(-0.266084\pi\) |
−0.307276 | + | 0.951621i | \(0.599417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.2489 | + | 17.7517i | 0.369107 | + | 0.639312i | ||||
\(772\) | 25.0888 | 0.902966 | ||||||||
\(773\) | 14.5823 | + | 25.2573i | 0.524490 | + | 0.908443i | 0.999593 | + | 0.0285128i | \(0.00907714\pi\) |
−0.475104 | + | 0.879930i | \(0.657590\pi\) | |||||||
\(774\) | −7.10996 | + | 4.10494i | −0.255562 | + | 0.147549i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.954155 | − | 1.65264i | −0.0342522 | − | 0.0593265i | ||||
\(777\) | −6.63186 | − | 3.82891i | −0.237917 | − | 0.137361i | ||||
\(778\) | −2.67578 | + | 4.63459i | −0.0959315 | + | 0.166158i | ||||
\(779\) | −28.2541 | −1.01231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −77.9410 | −2.78895 | ||||||||
\(782\) | −6.79247 | + | 11.7649i | −0.242898 | + | 0.420712i | ||||
\(783\) | 4.63459 | + | 2.67578i | 0.165627 | + | 0.0956247i | ||||
\(784\) | −2.94535 | − | 5.10149i | −0.105191 | − | 0.182196i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.6203 | − | 10.1731i | 0.628496 | − | 0.362862i | ||||
\(787\) | 8.03414 | + | 13.9155i | 0.286386 | + | 0.496035i | 0.972944 | − | 0.231039i | \(-0.0742127\pi\) |
−0.686558 | + | 0.727075i | \(0.740879\pi\) | |||||||
\(788\) | −9.19473 | −0.327549 | ||||||||
\(789\) | −8.85153 | − | 15.3313i | −0.315123 | − | 0.545809i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5.45207i | − | 0.193731i | ||||||
\(793\) | −7.21159 | − | 13.0400i | −0.256091 | − | 0.463065i | ||||
\(794\) | 8.50719 | 0.301909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8396 | − | 20.5068i | 0.419643 | − | 0.726843i | ||||
\(797\) | −33.8249 | + | 19.5288i | −1.19814 | + | 0.691745i | −0.960140 | − | 0.279520i | \(-0.909825\pi\) |
−0.237998 | + | 0.971266i | \(0.576491\pi\) | |||||||
\(798\) | 13.8765 | 0.491223 | ||||||||
\(799\) | 32.1423 | − | 18.5574i | 1.13711 | − | 0.656513i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.59376i | − | 0.338979i | ||||||
\(802\) | 20.2467 | − | 11.6894i | 0.714934 | − | 0.412767i | ||||
\(803\) | −70.3405 | − | 40.6111i | −2.48226 | − | 1.43314i | ||||
\(804\) | −12.8146 | − | 7.39851i | −0.451936 | − | 0.260925i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.89835 | + | 4.15411i | 0.242984 | + | 0.146322i | ||||
\(807\) | 18.1864i | 0.640191i | ||||||||
\(808\) | 8.12785 | − | 14.0779i | 0.285937 | − | 0.495257i | ||||
\(809\) | 7.04891 | − | 12.2091i | 0.247827 | − | 0.429248i | −0.715096 | − | 0.699026i | \(-0.753617\pi\) |
0.962923 | + | 0.269778i | \(0.0869503\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3869i | 0.399846i | 0.979812 | + | 0.199923i | \(0.0640693\pi\) | ||||
−0.979812 | + | 0.199923i | \(0.935931\pi\) | |||||||
\(812\) | 9.60703 | + | 16.6399i | 0.337141 | + | 0.583945i | ||||
\(813\) | −11.3847 | − | 19.7188i | −0.399278 | − | 0.691569i | ||||
\(814\) | − | 11.6286i | − | 0.407583i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.65519 | − | 6.33097i | 0.127957 | − | 0.221628i | ||||
\(817\) | 15.8653 | − | 27.4795i | 0.555057 | − | 0.961387i | ||||
\(818\) | 5.21360i | 0.182289i | ||||||||
\(819\) | 6.67810 | − | 11.0897i | 0.233352 | − | 0.387506i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2924 | + | 14.6026i | 0.882710 | + | 0.509633i | 0.871551 | − | 0.490305i | \(-0.163114\pi\) |
0.0111593 | + | 0.999938i | \(0.496448\pi\) | |||||||
\(822\) | 9.56156 | + | 5.52037i | 0.333498 | + | 0.192545i | ||||
\(823\) | 24.4617 | − | 14.1230i | 0.852681 | − | 0.492296i | −0.00887332 | − | 0.999961i | \(-0.502825\pi\) |
0.861555 | + | 0.507665i | \(0.169491\pi\) | |||||||
\(824\) | 12.9760i | 0.452042i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.853735 | + | 0.492904i | −0.0297052 | + | 0.0171503i | ||||
\(827\) | −37.3963 | −1.30040 | −0.650198 | − | 0.759765i | \(-0.725314\pi\) | ||||
−0.650198 | + | 0.759765i | \(0.725314\pi\) | |||||||
\(828\) | 1.60934 | − | 0.929155i | 0.0559286 | − | 0.0322904i | ||||
\(829\) | 0.925320 | − | 1.60270i | 0.0321377 | − | 0.0556641i | −0.849509 | − | 0.527574i | \(-0.823102\pi\) |
0.881647 | + | 0.471910i | \(0.156435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.3563 | 0.567393 | ||||||||
\(832\) | −3.60494 | − | 0.0664404i | −0.124979 | − | 0.00230341i | ||||
\(833\) | 43.0632i | 1.49205i | ||||||||
\(834\) | 8.40212 | + | 4.85096i | 0.290941 | + | 0.167975i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.5359 | + | 18.2488i | 0.364393 | + | 0.631147i | ||||
\(837\) | 2.23338 | 0.0771969 | ||||||||
\(838\) | 9.10066 | + | 15.7628i | 0.314377 | + | 0.544517i | ||||
\(839\) | 38.8940 | − | 22.4555i | 1.34277 | − | 0.775249i | 0.355557 | − | 0.934655i | \(-0.384291\pi\) |
0.987213 | + | 0.159406i | \(0.0509578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.180359 | + | 0.312392i | 0.00621929 | + | 0.0107721i | ||||
\(842\) | 22.2103 | + | 12.8231i | 0.765418 | + | 0.441914i | ||||
\(843\) | 3.91110 | − | 6.77423i | 0.134706 | − | 0.233317i | ||||
\(844\) | −9.98606 | −0.343734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.07700 | −0.174551 | ||||||||
\(847\) | −33.6148 | + | 58.2226i | −1.15502 | + | 2.00055i | ||||
\(848\) | 1.93416 | + | 1.11669i | 0.0664195 | + | 0.0383473i | ||||
\(849\) | −3.47266 | − | 6.01483i | −0.119181 | − | 0.206428i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.43254 | − | 1.98178i | 0.117666 | − | 0.0679344i | ||||
\(852\) | 7.14784 | + | 12.3804i | 0.244881 | + | 0.424146i | ||||
\(853\) | 6.75772 | 0.231380 | 0.115690 | − | 0.993285i | \(-0.463092\pi\) | ||||
0.115690 | + | 0.993285i | \(0.463092\pi\) | |||||||
\(854\) | −7.41927 | − | 12.8505i | −0.253882 | − | 0.439737i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.58814 | + | 4.95837i | 0.293537 | + | 0.169474i | ||||
\(857\) | − | 9.16177i | − | 0.312960i | −0.987681 | − | 0.156480i | \(-0.949985\pi\) | ||
0.987681 | − | 0.156480i | \(-0.0500147\pi\) | |||||||
\(858\) | 19.6544 | + | 0.362237i | 0.670989 | + | 0.0123666i | ||||
\(859\) | −11.9538 | −0.407857 | −0.203928 | − | 0.978986i | \(-0.565371\pi\) | ||||
−0.203928 | + | 0.978986i | \(0.565371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.1234 | + | 22.7305i | −0.447246 | + | 0.774653i | ||||
\(862\) | 1.79193 | − | 1.03457i | 0.0610334 | − | 0.0352376i | ||||
\(863\) | 31.6465 | 1.07726 | 0.538630 | − | 0.842542i | \(-0.318942\pi\) | ||||
0.538630 | + | 0.842542i | \(0.318942\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.941830i | 0.0320047i | ||||||||
\(867\) | −31.5594 | + | 18.2208i | −1.07181 | + | 0.618811i | ||||
\(868\) | 6.94435 | + | 4.00932i | 0.235707 | + | 0.136085i | ||||
\(869\) | 12.3756 | + | 7.14507i | 0.419814 | + | 0.242380i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5226 | − | 45.7043i | 0.932567 | − | 1.54863i | ||||
\(872\) | 7.41088i | 0.250964i | ||||||||
\(873\) | 0.954155 | − | 1.65264i | 0.0322932 | − | 0.0559335i | ||||
\(874\) | −3.59112 | + | 6.22000i | −0.121471 | + | 0.210395i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.8975i | 0.503340i | ||||||||
\(877\) | −7.06515 | − | 12.2372i | −0.238573 | − | 0.413221i | 0.721732 | − | 0.692173i | \(-0.243346\pi\) |
−0.960305 | + | 0.278952i | \(0.910013\pi\) | |||||||
\(878\) | 1.80132 | + | 3.11997i | 0.0607915 | + | 0.105294i | ||||
\(879\) | 26.4243i | 0.891270i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.56417 | + | 16.5656i | −0.322225 | + | 0.558110i | −0.980947 | − | 0.194276i | \(-0.937764\pi\) |
0.658722 | + | 0.752387i | \(0.271097\pi\) | |||||||
\(882\) | 2.94535 | − | 5.10149i | 0.0991749 | − | 0.171776i | ||||
\(883\) | − | 7.19528i | − | 0.242140i | −0.992644 | − | 0.121070i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121070i | \(-0.0386326\pi\) | |||||||
\(884\) | 22.5799 | + | 13.5974i | 0.759445 | + | 0.457329i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.37425 | + | 2.52548i | 0.146956 | + | 0.0848451i | ||||
\(887\) | 24.9453 | + | 14.4022i | 0.837580 | + | 0.483577i | 0.856441 | − | 0.516245i | \(-0.172671\pi\) |
−0.0188611 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(888\) | −1.84713 | + | 1.06644i | −0.0619856 | + | 0.0357874i | ||||
\(889\) | 64.5799i | 2.16594i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.72163 | − | 2.72603i | 0.158181 | − | 0.0913256i | ||||
\(892\) | −22.3820 | −0.749404 | ||||||||
\(893\) | 16.9934 | − | 9.81112i | 0.568661 | − | 0.328317i | ||||
\(894\) | 2.71908 | − | 4.70959i | 0.0909398 | − | 0.157512i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.59036 | −0.119946 | ||||||||
\(897\) | 3.24262 | + | 5.86332i | 0.108268 | + | 0.195771i | ||||
\(898\) | 5.42729i | 0.181111i | ||||||||
\(899\) | −10.3508 | − | 5.97604i | −0.345219 | − | 0.199312i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.16343 | − | 14.1395i | −0.271963 | − | 0.471054i | ||||
\(902\) | −39.8567 | −1.32708 | ||||||||
\(903\) | −14.7382 | − | 25.5273i | −0.490457 | − | 0.849496i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.90050 | − | 15.4161i | −0.295699 | − | 0.512166i | ||||
\(907\) | 33.9233 | + | 19.5856i | 1.12641 | + | 0.650331i | 0.943029 | − | 0.332712i | \(-0.107964\pi\) |
0.183377 | + | 0.983043i | \(0.441297\pi\) | |||||||
\(908\) | −6.49265 | + | 11.2456i | −0.215466 | + | 0.373199i | ||||
\(909\) | 16.2557 | 0.539168 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3352 | 0.872526 | 0.436263 | − | 0.899819i | \(-0.356302\pi\) | ||||
0.436263 | + | 0.899819i | \(0.356302\pi\) | |||||||
\(912\) | 1.93247 | − | 3.34713i | 0.0639903 | − | 0.110835i | ||||
\(913\) | −33.8063 | − | 19.5181i | −1.11883 | − | 0.645954i | ||||
\(914\) | 10.8416 | + | 18.7782i | 0.358607 | + | 0.621126i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5102 | + | 7.22276i | −0.413348 | + | 0.238647i | ||||
\(917\) | 36.5251 | + | 63.2633i | 1.20616 | + | 2.08914i | ||||
\(918\) | 7.31038 | 0.241278 | ||||||||
\(919\) | 4.85456 | + | 8.40834i | 0.160137 | + | 0.277365i | 0.934918 | − | 0.354865i | \(-0.115473\pi\) |
−0.774781 | + | 0.632230i | \(0.782140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.13649 | + | 3.54290i | 0.202204 | + | 0.116743i | ||||
\(922\) | − | 29.6023i | − | 0.974901i | ||||||
\(923\) | −45.1056 | + | 24.9450i | −1.48467 | + | 0.821074i | ||||
\(924\) | 19.5749 | 0.643967 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.1038 | − | 24.4284i | 0.463478 | − | 0.802768i | ||||
\(927\) | −11.2376 | + | 6.48802i | −0.369091 | + | 0.213095i | ||||
\(928\) | 5.35157 | 0.175674 | ||||||||
\(929\) | −2.68782 | + | 1.55181i | −0.0881844 | + | 0.0509133i | −0.543444 | − | 0.839446i | \(-0.682880\pi\) |
0.455259 | + | 0.890359i | \(0.349547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.7671i | 0.746162i | ||||||||
\(932\) | 10.7711 | − | 6.21869i | 0.352819 | − | 0.203700i | ||||
\(933\) | 1.58498 | + | 0.915086i | 0.0518898 | + | 0.0299586i | ||||
\(934\) | −7.07864 | − | 4.08685i | −0.231620 | − | 0.133726i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.74493 | − | 3.15519i | −0.0570348 | − | 0.103131i | ||||
\(937\) | − | 53.5929i | − | 1.75080i | −0.483396 | − | 0.875402i | \(-0.660597\pi\) | ||
0.483396 | − | 0.875402i | \(-0.339403\pi\) | |||||||
\(938\) | 26.5633 | − | 46.0090i | 0.867323 | − | 1.50225i | ||||
\(939\) | −6.12493 | + | 10.6087i | −0.199880 | + | 0.346201i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.9758i | 1.40097i | 0.713667 | + | 0.700485i | \(0.247033\pi\) | ||||
−0.713667 | + | 0.700485i | \(0.752967\pi\) | |||||||
\(942\) | 2.96826 | + | 5.14117i | 0.0967111 | + | 0.167509i | ||||
\(943\) | −6.79247 | − | 11.7649i | −0.221193 | − | 0.383118i | ||||
\(944\) | 0.274571i | 0.00893652i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.3804 | − | 38.7640i | 0.727650 | − | 1.26033i | ||||
\(947\) | 5.54457 | − | 9.60349i | 0.180174 | − | 0.312071i | −0.761765 | − | 0.647853i | \(-0.775667\pi\) |
0.941940 | + | 0.335782i | \(0.109000\pi\) | |||||||
\(948\) | − | 2.62105i | − | 0.0851277i | ||||||
\(949\) | −53.7046 | − | 0.989796i | −1.74333 | − | 0.0321301i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.41352 | + | 3.12550i | 0.175546 | + | 0.101351i | ||||
\(952\) | 22.7305 | + | 13.1234i | 0.736699 | + | 0.425333i | ||||
\(953\) | 49.9313 | − | 28.8278i | 1.61743 | − | 0.933825i | 0.629852 | − | 0.776715i | \(-0.283116\pi\) |
0.987581 | − | 0.157110i | \(-0.0502177\pi\) | |||||||
\(954\) | 2.23338i | 0.0723084i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.61118 | + | 2.08491i | −0.116794 | + | 0.0674309i | ||||
\(957\) | −29.1771 | −0.943162 | ||||||||
\(958\) | 10.1231 | − | 5.84458i | 0.327063 | − | 0.188830i | ||||
\(959\) | −19.8201 | + | 34.3294i | −0.640025 | + | 1.10856i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0120 | 0.839097 | ||||||||
\(962\) | −3.72173 | − | 6.72964i | −0.119993 | − | 0.216972i | ||||
\(963\) | 9.91673i | 0.319562i | ||||||||
\(964\) | −1.63165 | − | 0.942035i | −0.0525520 | − | 0.0303409i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.33600 | + | 5.77812i | 0.107334 | + | 0.185908i | ||||
\(967\) | −30.5218 | −0.981516 | −0.490758 | − | 0.871296i | \(-0.663280\pi\) | ||||
−0.490758 | + | 0.871296i | \(0.663280\pi\) | |||||||
\(968\) | 9.36252 | + | 16.2164i | 0.300923 | + | 0.521214i | ||||
\(969\) | −24.4688 | + | 14.1271i | −0.786050 | + | 0.453826i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.9787 | − | 24.2119i | −0.448599 | − | 0.776996i | 0.549696 | − | 0.835365i | \(-0.314743\pi\) |
−0.998295 | + | 0.0583686i | \(0.981410\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | −17.4167 | + | 30.1666i | −0.558354 | + | 0.967098i | ||||
\(974\) | −31.8875 | −1.02174 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.13288 | −0.132290 | ||||||||
\(977\) | 0.986516 | − | 1.70870i | 0.0315614 | − | 0.0546660i | −0.849813 | − | 0.527084i | \(-0.823285\pi\) |
0.881375 | + | 0.472418i | \(0.156619\pi\) | |||||||
\(978\) | −13.5046 | − | 7.79688i | −0.431829 | − | 0.249317i | ||||
\(979\) | 26.1529 | + | 45.2982i | 0.835851 | + | 1.44774i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.41801 | + | 3.70544i | −0.204911 | + | 0.118306i | ||||
\(982\) | 9.77506 | + | 16.9309i | 0.311935 | + | 0.540286i | ||||
\(983\) | −8.00792 | −0.255413 | −0.127707 | − | 0.991812i | \(-0.540762\pi\) | ||||
−0.127707 | + | 0.991812i | \(0.540762\pi\) | |||||||
\(984\) | 3.65519 | + | 6.33097i | 0.116523 | + | 0.201824i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33.8806 | − | 19.5610i | −1.07898 | − | 0.622949i | ||||
\(987\) | − | 18.2283i | − | 0.580212i | ||||||
\(988\) | 11.9378 | + | 7.18881i | 0.379792 | + | 0.228706i | ||||
\(989\) | 15.2565 | 0.485128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0138 | + | 31.2007i | −0.572226 | + | 0.991124i | 0.424111 | + | 0.905610i | \(0.360587\pi\) |
−0.996337 | + | 0.0855139i | \(0.972747\pi\) | |||||||
\(992\) | 1.93416 | − | 1.11669i | 0.0614098 | − | 0.0354550i | ||||
\(993\) | 19.1758 | 0.608526 | ||||||||
\(994\) | −44.4502 | + | 25.6633i | −1.40987 | + | 0.813992i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.15988i | 0.226869i | ||||||||
\(997\) | 44.3242 | − | 25.5906i | 1.40376 | − | 0.810463i | 0.408986 | − | 0.912541i | \(-0.365883\pi\) |
0.994776 | + | 0.102078i | \(0.0325492\pi\) | |||||||
\(998\) | 34.0719 | + | 19.6714i | 1.07853 | + | 0.622688i | ||||
\(999\) | −1.84713 | − | 1.06644i | −0.0584406 | − | 0.0337407i |
(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 | 1950.2.y.m.199.3 | 12 | ||
5.2 | odd | 4 | 1950.2.bc.h.901.1 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.bc.k.901.6 | yes | 12 | ||
5.4 | even | 2 | 1950.2.y.n.199.4 | 12 | |||
13.10 | even | 6 | 1950.2.y.n.49.4 | 12 | |||
65.23 | odd | 12 | 1950.2.bc.k.751.6 | yes | 12 | ||
65.49 | even | 6 | inner | 1950.2.y.m.49.3 | 12 | ||
65.62 | odd | 12 | 1950.2.bc.h.751.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.3 | 12 | 65.49 | even | 6 | inner | ||
1950.2.y.m.199.3 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.y.n.49.4 | 12 | 13.10 | even | 6 | |||
1950.2.y.n.199.4 | 12 | 5.4 | even | 2 | |||
1950.2.bc.h.751.1 | ✓ | 12 | 65.62 | odd | 12 | ||
1950.2.bc.h.901.1 | yes | 12 | 5.2 | odd | 4 | ||
1950.2.bc.k.751.6 | yes | 12 | 65.23 | odd | 12 | ||
1950.2.bc.k.901.6 | yes | 12 | 5.3 | odd | 4 |