Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(208,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.208");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.n (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(256\) |
Relative dimension: | \(64\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 608.62 | ||
Character | \(\chi\) | \(=\) | 731.608 |
Dual form | 731.2.n.a.208.3 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67476i | 1.89134i | 0.325123 | + | 0.945672i | \(0.394594\pi\) | ||||
−0.325123 | + | 0.945672i | \(0.605406\pi\) | |||||||
\(3\) | −2.11059 | + | 0.565531i | −1.21855 | + | 0.326509i | −0.810111 | − | 0.586277i | \(-0.800593\pi\) |
−0.408438 | + | 0.912786i | \(0.633927\pi\) | |||||||
\(4\) | −5.15436 | −2.57718 | ||||||||
\(5\) | 2.13934 | − | 0.573235i | 0.956744 | − | 0.256359i | 0.253522 | − | 0.967330i | \(-0.418411\pi\) |
0.703221 | + | 0.710971i | \(0.251744\pi\) | |||||||
\(6\) | −1.51266 | − | 5.64533i | −0.617541 | − | 2.30469i | ||||
\(7\) | 0.737688 | + | 0.197663i | 0.278820 | + | 0.0747095i | 0.395519 | − | 0.918458i | \(-0.370565\pi\) |
−0.116699 | + | 0.993167i | \(0.537231\pi\) | |||||||
\(8\) | − | 8.43716i | − | 2.98299i | ||||||
\(9\) | 1.53669 | − | 0.887206i | 0.512229 | − | 0.295735i | ||||
\(10\) | 1.53327 | + | 5.72224i | 0.484862 | + | 1.80953i | ||||
\(11\) | 4.20765 | − | 4.20765i | 1.26865 | − | 1.26865i | 0.321870 | − | 0.946784i | \(-0.395689\pi\) |
0.946784 | − | 0.321870i | \(-0.104311\pi\) | |||||||
\(12\) | 10.8787 | − | 2.91495i | 3.14042 | − | 0.841473i | ||||
\(13\) | 2.31304 | + | 4.00631i | 0.641522 | + | 1.11115i | 0.985093 | + | 0.172023i | \(0.0550302\pi\) |
−0.343571 | + | 0.939127i | \(0.611636\pi\) | |||||||
\(14\) | −0.528701 | + | 1.97314i | −0.141301 | + | 0.527344i | ||||
\(15\) | −4.19109 | + | 2.41973i | −1.08214 | + | 0.624771i | ||||
\(16\) | 12.2587 | 3.06467 | ||||||||
\(17\) | 1.61094 | − | 3.79538i | 0.390709 | − | 0.920514i | ||||
\(18\) | 2.37307 | + | 4.11027i | 0.559337 | + | 0.968800i | ||||
\(19\) | 3.64127 | + | 2.10229i | 0.835365 | + | 0.482298i | 0.855686 | − | 0.517495i | \(-0.173135\pi\) |
−0.0203209 | + | 0.999794i | \(0.506469\pi\) | |||||||
\(20\) | −11.0269 | + | 2.95466i | −2.46570 | + | 0.660682i | ||||
\(21\) | −1.66874 | −0.364149 | ||||||||
\(22\) | 11.2545 | + | 11.2545i | 2.39946 | + | 2.39946i | ||||
\(23\) | −1.79603 | − | 6.70287i | −0.374498 | − | 1.39764i | −0.854077 | − | 0.520146i | \(-0.825878\pi\) |
0.479580 | − | 0.877498i | \(-0.340789\pi\) | |||||||
\(24\) | 4.77147 | + | 17.8074i | 0.973973 | + | 3.63492i | ||||
\(25\) | −0.0819346 | + | 0.0473049i | −0.0163869 | + | 0.00946099i | ||||
\(26\) | −10.7159 | + | 6.18684i | −2.10156 | + | 1.21334i | ||||
\(27\) | 1.89361 | − | 1.89361i | 0.364424 | − | 0.364424i | ||||
\(28\) | −3.80231 | − | 1.01883i | −0.718569 | − | 0.192540i | ||||
\(29\) | −0.860862 | + | 3.21278i | −0.159858 | + | 0.596598i | 0.838782 | + | 0.544467i | \(0.183268\pi\) |
−0.998640 | + | 0.0521311i | \(0.983399\pi\) | |||||||
\(30\) | −6.47220 | − | 11.2102i | −1.18166 | − | 2.04669i | ||||
\(31\) | 3.46139 | − | 0.927476i | 0.621683 | − | 0.166580i | 0.0657904 | − | 0.997833i | \(-0.479043\pi\) |
0.555893 | + | 0.831254i | \(0.312376\pi\) | |||||||
\(32\) | 15.9148i | 2.81336i | ||||||||
\(33\) | −6.50106 | + | 11.2602i | −1.13169 | + | 1.96014i | ||||
\(34\) | 10.1517 | + | 4.30887i | 1.74101 | + | 0.738965i | ||||
\(35\) | 1.69148 | 0.285912 | ||||||||
\(36\) | −7.92063 | + | 4.57298i | −1.32011 | + | 0.762163i | ||||
\(37\) | −5.62546 | + | 1.50734i | −0.924819 | + | 0.247805i | −0.689644 | − | 0.724148i | \(-0.742233\pi\) |
−0.235175 | + | 0.971953i | \(0.575566\pi\) | |||||||
\(38\) | −5.62313 | + | 9.73954i | −0.912192 | + | 1.57996i | ||||
\(39\) | −7.14757 | − | 7.14757i | −1.14453 | − | 1.14453i | ||||
\(40\) | −4.83648 | − | 18.0500i | −0.764715 | − | 2.85395i | ||||
\(41\) | 7.28041 | − | 7.28041i | 1.13701 | − | 1.13701i | 0.148025 | − | 0.988984i | \(-0.452708\pi\) |
0.988984 | − | 0.148025i | \(-0.0472915\pi\) | |||||||
\(42\) | − | 4.46349i | − | 0.688731i | ||||||
\(43\) | 2.18587 | + | 6.18239i | 0.333342 | + | 0.942806i | ||||
\(44\) | −21.6877 | + | 21.6877i | −3.26955 | + | 3.26955i | ||||
\(45\) | 2.77892 | − | 2.77892i | 0.414257 | − | 0.414257i | ||||
\(46\) | 17.9286 | − | 4.80395i | 2.64342 | − | 0.708304i | ||||
\(47\) | 3.34796 | 0.488350 | 0.244175 | − | 0.969731i | \(-0.421483\pi\) | ||||
0.244175 | + | 0.969731i | \(0.421483\pi\) | |||||||
\(48\) | −25.8731 | + | 6.93267i | −3.73446 | + | 1.00064i | ||||
\(49\) | −5.55707 | − | 3.20837i | −0.793866 | − | 0.458339i | ||||
\(50\) | −0.126530 | − | 0.219156i | −0.0178940 | − | 0.0309933i | ||||
\(51\) | −1.25362 | + | 8.92152i | −0.175542 | + | 1.24926i | ||||
\(52\) | −11.9222 | − | 20.6499i | −1.65332 | − | 2.86363i | ||||
\(53\) | 3.31602 | + | 1.91451i | 0.455490 | + | 0.262978i | 0.710146 | − | 0.704054i | \(-0.248629\pi\) |
−0.254656 | + | 0.967032i | \(0.581962\pi\) | |||||||
\(54\) | 5.06495 | + | 5.06495i | 0.689252 | + | 0.689252i | ||||
\(55\) | 6.58963 | − | 11.4136i | 0.888546 | − | 1.53901i | ||||
\(56\) | 1.66771 | − | 6.22399i | 0.222858 | − | 0.831716i | ||||
\(57\) | −8.87414 | − | 2.37782i | −1.17541 | − | 0.314950i | ||||
\(58\) | −8.59342 | − | 2.30260i | −1.12837 | − | 0.302346i | ||||
\(59\) | − | 2.62780i | − | 0.342111i | −0.985261 | − | 0.171055i | \(-0.945282\pi\) | ||
0.985261 | − | 0.171055i | \(-0.0547177\pi\) | |||||||
\(60\) | 21.6024 | − | 12.4722i | 2.78886 | − | 1.61015i | ||||
\(61\) | −8.13243 | − | 2.17908i | −1.04125 | − | 0.279002i | −0.302619 | − | 0.953111i | \(-0.597861\pi\) |
−0.738632 | + | 0.674109i | \(0.764528\pi\) | |||||||
\(62\) | 2.48078 | + | 9.25839i | 0.315059 | + | 1.17582i | ||||
\(63\) | 1.30896 | − | 0.350735i | 0.164914 | − | 0.0441885i | ||||
\(64\) | −18.0509 | −2.25636 | ||||||||
\(65\) | 7.24495 | + | 7.24495i | 0.898625 | + | 0.898625i | ||||
\(66\) | −30.1183 | − | 17.3888i | −3.70731 | − | 2.14041i | ||||
\(67\) | −1.09504 | + | 1.89667i | −0.133781 | + | 0.231715i | −0.925131 | − | 0.379648i | \(-0.876045\pi\) |
0.791350 | + | 0.611363i | \(0.209378\pi\) | |||||||
\(68\) | −8.30334 | + | 19.5627i | −1.00693 | + | 2.37233i | ||||
\(69\) | 7.58135 | + | 13.1313i | 0.912688 | + | 1.58082i | ||||
\(70\) | 4.52430i | 0.540757i | ||||||||
\(71\) | 2.02816 | − | 7.56919i | 0.240698 | − | 0.898297i | −0.734799 | − | 0.678285i | \(-0.762724\pi\) |
0.975497 | − | 0.220012i | \(-0.0706098\pi\) | |||||||
\(72\) | −7.48550 | − | 12.9653i | −0.882175 | − | 1.52797i | ||||
\(73\) | −0.0701783 | + | 0.261909i | −0.00821375 | + | 0.0306541i | −0.969911 | − | 0.243459i | \(-0.921718\pi\) |
0.961697 | + | 0.274114i | \(0.0883844\pi\) | |||||||
\(74\) | −4.03177 | − | 15.0468i | −0.468684 | − | 1.74915i | ||||
\(75\) | 0.146178 | − | 0.146178i | 0.0168792 | − | 0.0168792i | ||||
\(76\) | −18.7684 | − | 10.8360i | −2.15289 | − | 1.24297i | ||||
\(77\) | 3.93563 | − | 2.27224i | 0.448506 | − | 0.258945i | ||||
\(78\) | 19.1181 | − | 19.1181i | 2.16469 | − | 2.16469i | ||||
\(79\) | 4.92133 | + | 1.31867i | 0.553693 | + | 0.148362i | 0.524807 | − | 0.851221i | \(-0.324137\pi\) |
0.0288859 | + | 0.999583i | \(0.490804\pi\) | |||||||
\(80\) | 26.2256 | − | 7.02712i | 2.93211 | − | 0.785656i | ||||
\(81\) | −5.58735 | + | 9.67757i | −0.620817 | + | 1.07529i | ||||
\(82\) | 19.4734 | + | 19.4734i | 2.15047 | + | 2.15047i | ||||
\(83\) | 9.48994 | + | 5.47902i | 1.04166 | + | 0.601400i | 0.920302 | − | 0.391209i | \(-0.127943\pi\) |
0.121354 | + | 0.992609i | \(0.461276\pi\) | |||||||
\(84\) | 8.60129 | 0.938477 | ||||||||
\(85\) | 1.27070 | − | 9.04306i | 0.137827 | − | 0.980858i | ||||
\(86\) | −16.5364 | + | 5.84668i | −1.78317 | + | 0.630463i | ||||
\(87\) | − | 7.26770i | − | 0.779179i | ||||||
\(88\) | −35.5006 | − | 35.5006i | −3.78438 | − | 3.78438i | ||||
\(89\) | −8.82669 | + | 15.2883i | −0.935627 | + | 1.62055i | −0.162116 | + | 0.986772i | \(0.551832\pi\) |
−0.773511 | + | 0.633782i | \(0.781501\pi\) | |||||||
\(90\) | 7.43296 | + | 7.43296i | 0.783502 | + | 0.783502i | ||||
\(91\) | 0.914405 | + | 3.41261i | 0.0958557 | + | 0.357738i | ||||
\(92\) | 9.25737 | + | 34.5490i | 0.965147 | + | 3.60198i | ||||
\(93\) | −6.78105 | + | 3.91504i | −0.703162 | + | 0.405971i | ||||
\(94\) | 8.95499i | 0.923637i | ||||||||
\(95\) | 8.99504 | + | 2.41021i | 0.922872 | + | 0.247283i | ||||
\(96\) | −9.00030 | − | 33.5896i | −0.918589 | − | 3.42822i | ||||
\(97\) | 6.04978 | + | 6.04978i | 0.614262 | + | 0.614262i | 0.944054 | − | 0.329791i | \(-0.106978\pi\) |
−0.329791 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(98\) | 8.58164 | − | 14.8638i | 0.866876 | − | 1.50147i | ||||
\(99\) | 2.73278 | − | 10.1989i | 0.274655 | − | 1.02503i | ||||
\(100\) | 0.422320 | − | 0.243827i | 0.0422320 | − | 0.0243827i | ||||
\(101\) | 6.00112 | + | 10.3942i | 0.597134 | + | 1.03427i | 0.993242 | + | 0.116062i | \(0.0370271\pi\) |
−0.396108 | + | 0.918204i | \(0.629640\pi\) | |||||||
\(102\) | −23.8629 | − | 3.35314i | −2.36278 | − | 0.332010i | ||||
\(103\) | 6.27549 | + | 10.8695i | 0.618343 | + | 1.07100i | 0.989788 | + | 0.142546i | \(0.0455289\pi\) |
−0.371446 | + | 0.928455i | \(0.621138\pi\) | |||||||
\(104\) | 33.8019 | − | 19.5155i | 3.31454 | − | 1.91365i | ||||
\(105\) | −3.57001 | + | 0.956581i | −0.348397 | + | 0.0933528i | ||||
\(106\) | −5.12085 | + | 8.86957i | −0.497381 | + | 0.861489i | ||||
\(107\) | 4.86252 | + | 4.86252i | 0.470077 | + | 0.470077i | 0.901940 | − | 0.431862i | \(-0.142143\pi\) |
−0.431862 | + | 0.901940i | \(0.642143\pi\) | |||||||
\(108\) | −9.76032 | + | 9.76032i | −0.939187 | + | 0.939187i | ||||
\(109\) | −2.01588 | − | 7.52337i | −0.193086 | − | 0.720608i | −0.992754 | − | 0.120165i | \(-0.961658\pi\) |
0.799668 | − | 0.600443i | \(-0.205009\pi\) | |||||||
\(110\) | 30.5286 | + | 17.6257i | 2.91079 | + | 1.68055i | ||||
\(111\) | 11.0206 | − | 6.36274i | 1.04603 | − | 0.603924i | ||||
\(112\) | 9.04309 | + | 2.42309i | 0.854492 | + | 0.228960i | ||||
\(113\) | −0.329473 | + | 0.329473i | −0.0309942 | + | 0.0309942i | −0.722434 | − | 0.691440i | \(-0.756977\pi\) |
0.691440 | + | 0.722434i | \(0.256977\pi\) | |||||||
\(114\) | 6.36010 | − | 23.7362i | 0.595678 | − | 2.22310i | ||||
\(115\) | −7.68464 | − | 13.3102i | −0.716596 | − | 1.24118i | ||||
\(116\) | 4.43719 | − | 16.5598i | 0.411983 | − | 1.53754i | ||||
\(117\) | 7.10884 | + | 4.10429i | 0.657212 | + | 0.379442i | ||||
\(118\) | 7.02875 | 0.647049 | ||||||||
\(119\) | 1.93857 | − | 2.48138i | 0.177709 | − | 0.227468i | ||||
\(120\) | 20.4156 | + | 35.3609i | 1.86368 | + | 3.22800i | ||||
\(121\) | − | 24.4086i | − | 2.21897i | ||||||
\(122\) | 5.82852 | − | 21.7523i | 0.527689 | − | 1.96936i | ||||
\(123\) | −11.2487 | + | 19.4832i | −1.01426 | + | 1.75674i | ||||
\(124\) | −17.8412 | + | 4.78054i | −1.60219 | + | 0.429305i | ||||
\(125\) | −7.97871 | + | 7.97871i | −0.713638 | + | 0.713638i | ||||
\(126\) | 0.938134 | + | 3.50116i | 0.0835756 | + | 0.311909i | ||||
\(127\) | 6.67518i | 0.592327i | 0.955137 | + | 0.296163i | \(0.0957073\pi\) | ||||
−0.955137 | + | 0.296163i | \(0.904293\pi\) | |||||||
\(128\) | − | 16.4523i | − | 1.45419i | ||||||
\(129\) | −8.10980 | − | 11.8123i | −0.714028 | − | 1.04002i | ||||
\(130\) | −19.3785 | + | 19.3785i | −1.69961 | + | 1.69961i | ||||
\(131\) | −15.3696 | − | 15.3696i | −1.34285 | − | 1.34285i | −0.893214 | − | 0.449632i | \(-0.851555\pi\) |
−0.449632 | − | 0.893214i | \(-0.648445\pi\) | |||||||
\(132\) | 33.5088 | − | 58.0390i | 2.91657 | − | 5.05164i | ||||
\(133\) | 2.27058 | + | 2.27058i | 0.196884 | + | 0.196884i | ||||
\(134\) | −5.07314 | − | 2.92898i | −0.438252 | − | 0.253025i | ||||
\(135\) | 2.96559 | − | 5.13655i | 0.255237 | − | 0.442084i | ||||
\(136\) | −32.0222 | − | 13.5917i | −2.74588 | − | 1.16548i | ||||
\(137\) | −10.1612 | −0.868131 | −0.434065 | − | 0.900881i | \(-0.642921\pi\) | ||||
−0.434065 | + | 0.900881i | \(0.642921\pi\) | |||||||
\(138\) | −35.1231 | + | 20.2783i | −2.98988 | + | 1.72621i | ||||
\(139\) | 15.8927 | − | 4.25843i | 1.34800 | − | 0.361195i | 0.488603 | − | 0.872506i | \(-0.337507\pi\) |
0.859396 | + | 0.511311i | \(0.170840\pi\) | |||||||
\(140\) | −8.71847 | −0.736845 | ||||||||
\(141\) | −7.06616 | + | 1.89337i | −0.595078 | + | 0.159451i | ||||
\(142\) | 20.2458 | + | 5.42484i | 1.69899 | + | 0.455243i | ||||
\(143\) | 26.5896 | + | 7.12466i | 2.22353 | + | 0.595794i | ||||
\(144\) | 18.8378 | − | 10.8760i | 1.56981 | − | 0.906332i | ||||
\(145\) | 7.36672i | 0.611772i | ||||||||
\(146\) | −0.700545 | − | 0.187710i | −0.0579775 | − | 0.0155350i | ||||
\(147\) | 13.5431 | + | 3.62887i | 1.11702 | + | 0.299304i | ||||
\(148\) | 28.9956 | − | 7.76935i | 2.38343 | − | 0.638637i | ||||
\(149\) | 6.39101 | − | 11.0696i | 0.523572 | − | 0.906853i | −0.476052 | − | 0.879417i | \(-0.657932\pi\) |
0.999624 | − | 0.0274359i | \(-0.00873423\pi\) | |||||||
\(150\) | 0.390991 | + | 0.390991i | 0.0319243 | + | 0.0319243i | ||||
\(151\) | − | 4.65503i | − | 0.378821i | −0.981898 | − | 0.189410i | \(-0.939342\pi\) | ||
0.981898 | − | 0.189410i | \(-0.0606577\pi\) | |||||||
\(152\) | 17.7374 | − | 30.7220i | 1.43869 | − | 2.49188i | ||||
\(153\) | −0.891779 | − | 7.26153i | −0.0720961 | − | 0.587060i | ||||
\(154\) | 6.07769 | + | 10.5269i | 0.489754 | + | 0.848280i | ||||
\(155\) | 6.87343 | − | 3.96838i | 0.552087 | − | 0.318748i | ||||
\(156\) | 36.8411 | + | 36.8411i | 2.94965 | + | 2.94965i | ||||
\(157\) | −1.77230 | − | 3.06972i | −0.141445 | − | 0.244990i | 0.786596 | − | 0.617468i | \(-0.211842\pi\) |
−0.928041 | + | 0.372478i | \(0.878508\pi\) | |||||||
\(158\) | −3.52712 | + | 13.1634i | −0.280603 | + | 1.04722i | ||||
\(159\) | −8.08147 | − | 2.16542i | −0.640902 | − | 0.171729i | ||||
\(160\) | 9.12292 | + | 34.0472i | 0.721230 | + | 2.69167i | ||||
\(161\) | − | 5.29963i | − | 0.417669i | ||||||
\(162\) | −25.8852 | − | 14.9448i | −2.03373 | − | 1.17418i | ||||
\(163\) | 2.64985 | + | 0.710024i | 0.207552 | + | 0.0556134i | 0.361097 | − | 0.932528i | \(-0.382402\pi\) |
−0.153545 | + | 0.988142i | \(0.549069\pi\) | |||||||
\(164\) | −37.5258 | + | 37.5258i | −2.93027 | + | 2.93027i | ||||
\(165\) | −7.45328 | + | 27.8160i | −0.580237 | + | 2.16547i | ||||
\(166\) | −14.6551 | + | 25.3833i | −1.13745 | + | 1.97013i | ||||
\(167\) | −7.77708 | + | 2.08386i | −0.601809 | + | 0.161254i | −0.546845 | − | 0.837234i | \(-0.684171\pi\) |
−0.0549643 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(168\) | 14.0794i | 1.08625i | ||||||||
\(169\) | −4.20033 | + | 7.27518i | −0.323102 | + | 0.559629i | ||||
\(170\) | 24.1880 | + | 3.39882i | 1.85514 | + | 0.260678i | ||||
\(171\) | 7.46066 | 0.570531 | ||||||||
\(172\) | −11.2667 | − | 31.8663i | −0.859081 | − | 2.42978i | ||||
\(173\) | 4.78034 | + | 4.78034i | 0.363442 | + | 0.363442i | 0.865079 | − | 0.501636i | \(-0.167268\pi\) |
−0.501636 | + | 0.865079i | \(0.667268\pi\) | |||||||
\(174\) | 19.4394 | 1.47370 | ||||||||
\(175\) | −0.0697926 | + | 0.0187009i | −0.00527582 | + | 0.00141365i | ||||
\(176\) | 51.5803 | − | 51.5803i | 3.88801 | − | 3.88801i | ||||
\(177\) | 1.48610 | + | 5.54621i | 0.111702 | + | 0.416879i | ||||
\(178\) | −40.8925 | − | 23.6093i | −3.06502 | − | 1.76959i | ||||
\(179\) | −7.61387 | + | 4.39587i | −0.569087 | + | 0.328563i | −0.756785 | − | 0.653664i | \(-0.773231\pi\) |
0.187698 | + | 0.982227i | \(0.439898\pi\) | |||||||
\(180\) | −14.3236 | + | 14.3236i | −1.06761 | + | 1.06761i | ||||
\(181\) | 12.4748 | + | 3.34260i | 0.927242 | + | 0.248454i | 0.690678 | − | 0.723162i | \(-0.257312\pi\) |
0.236564 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(182\) | −9.12791 | + | 2.44582i | −0.676606 | + | 0.181296i | ||||
\(183\) | 18.3966 | 1.35991 | ||||||||
\(184\) | −56.5532 | + | 15.1534i | −4.16915 | + | 1.11712i | ||||
\(185\) | −11.1707 | + | 6.44942i | −0.821288 | + | 0.474171i | ||||
\(186\) | −10.4718 | − | 18.1377i | −0.767830 | − | 1.32992i | ||||
\(187\) | −9.19136 | − | 22.7479i | −0.672139 | − | 1.66349i | ||||
\(188\) | −17.2566 | −1.25856 | ||||||||
\(189\) | 1.77119 | − | 1.02259i | 0.128835 | − | 0.0743828i | ||||
\(190\) | −6.44675 | + | 24.0596i | −0.467697 | + | 1.74547i | ||||
\(191\) | 9.70094 | − | 16.8025i | 0.701935 | − | 1.21579i | −0.265851 | − | 0.964014i | \(-0.585653\pi\) |
0.967786 | − | 0.251773i | \(-0.0810138\pi\) | |||||||
\(192\) | 38.0980 | − | 10.2083i | 2.74949 | − | 0.736723i | ||||
\(193\) | −6.33852 | + | 6.33852i | −0.456257 | + | 0.456257i | −0.897425 | − | 0.441168i | \(-0.854564\pi\) |
0.441168 | + | 0.897425i | \(0.354564\pi\) | |||||||
\(194\) | −16.1817 | + | 16.1817i | −1.16178 | + | 1.16178i | ||||
\(195\) | −19.3883 | − | 11.1939i | −1.38843 | − | 0.801610i | ||||
\(196\) | 28.6431 | + | 16.5371i | 2.04594 | + | 1.18122i | ||||
\(197\) | 12.3569 | + | 3.31101i | 0.880391 | + | 0.235900i | 0.670576 | − | 0.741841i | \(-0.266047\pi\) |
0.209815 | + | 0.977741i | \(0.432714\pi\) | |||||||
\(198\) | 27.2796 | + | 7.30955i | 1.93868 | + | 0.519467i | ||||
\(199\) | 5.38622 | + | 5.38622i | 0.381819 | + | 0.381819i | 0.871757 | − | 0.489938i | \(-0.162981\pi\) |
−0.489938 | + | 0.871757i | \(0.662981\pi\) | |||||||
\(200\) | 0.399119 | + | 0.691295i | 0.0282220 | + | 0.0488820i | ||||
\(201\) | 1.23856 | − | 4.62237i | 0.0873613 | − | 0.326037i | ||||
\(202\) | −27.8021 | + | 16.0516i | −1.95615 | + | 1.12938i | ||||
\(203\) | −1.27009 | + | 2.19987i | −0.0891432 | + | 0.154400i | ||||
\(204\) | 6.46162 | − | 45.9847i | 0.452404 | − | 3.21957i | ||||
\(205\) | 11.4019 | − | 19.7487i | 0.796343 | − | 1.37931i | ||||
\(206\) | −29.0733 | + | 16.7855i | −2.02563 | + | 1.16950i | ||||
\(207\) | −8.70675 | − | 8.70675i | −0.605161 | − | 0.605161i | ||||
\(208\) | 28.3549 | + | 49.1121i | 1.96606 | + | 3.40531i | ||||
\(209\) | 24.1669 | − | 6.47550i | 1.67166 | − | 0.447920i | ||||
\(210\) | −2.55863 | − | 9.54893i | −0.176562 | − | 0.658939i | ||||
\(211\) | −14.2548 | + | 14.2548i | −0.981343 | + | 0.981343i | −0.999829 | − | 0.0184858i | \(-0.994115\pi\) |
0.0184858 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(212\) | −17.0920 | − | 9.86805i | −1.17388 | − | 0.677740i | ||||
\(213\) | 17.1224i | 1.17321i | ||||||||
\(214\) | −13.0061 | + | 13.0061i | −0.889077 | + | 0.889077i | ||||
\(215\) | 8.22029 | + | 11.9732i | 0.560619 | + | 0.816569i | ||||
\(216\) | −15.9767 | − | 15.9767i | −1.08707 | − | 1.08707i | ||||
\(217\) | 2.73675 | 0.185783 | ||||||||
\(218\) | 20.1232 | − | 5.39200i | 1.36292 | − | 0.365193i | ||||
\(219\) | − | 0.592470i | − | 0.0400354i | ||||||
\(220\) | −33.9653 | + | 58.8297i | −2.28994 | + | 3.96630i | ||||
\(221\) | 18.9316 | − | 2.32496i | 1.27348 | − | 0.156394i | ||||
\(222\) | 17.0188 | + | 29.4774i | 1.14223 | + | 1.97840i | ||||
\(223\) | − | 12.8830i | − | 0.862709i | −0.902182 | − | 0.431355i | \(-0.858036\pi\) | ||
0.902182 | − | 0.431355i | \(-0.141964\pi\) | |||||||
\(224\) | −3.14576 | + | 11.7401i | −0.210185 | + | 0.784421i | ||||
\(225\) | −0.0839385 | + | 0.145386i | −0.00559590 | + | 0.00969238i | ||||
\(226\) | −0.881262 | − | 0.881262i | −0.0586206 | − | 0.0586206i | ||||
\(227\) | −0.114873 | − | 0.428713i | −0.00762440 | − | 0.0284547i | 0.962009 | − | 0.273018i | \(-0.0880220\pi\) |
−0.969633 | + | 0.244564i | \(0.921355\pi\) | |||||||
\(228\) | 45.7405 | + | 12.2561i | 3.02924 | + | 0.811682i | ||||
\(229\) | −1.43458 | + | 0.828255i | −0.0947997 | + | 0.0547326i | −0.546650 | − | 0.837361i | \(-0.684097\pi\) |
0.451851 | + | 0.892094i | \(0.350764\pi\) | |||||||
\(230\) | 35.6016 | − | 20.5546i | 2.34750 | − | 1.35533i | ||||
\(231\) | −7.02147 | + | 7.02147i | −0.461979 | + | 0.461979i | ||||
\(232\) | 27.1067 | + | 7.26323i | 1.77964 | + | 0.476854i | ||||
\(233\) | 2.58046 | − | 9.63040i | 0.169051 | − | 0.630909i | −0.828437 | − | 0.560082i | \(-0.810770\pi\) |
0.997489 | − | 0.0708267i | \(-0.0225637\pi\) | |||||||
\(234\) | −10.9780 | + | 19.0145i | −0.717654 | + | 1.24301i | ||||
\(235\) | 7.16243 | − | 1.91917i | 0.467225 | − | 0.125193i | ||||
\(236\) | 13.5446i | 0.881681i | ||||||||
\(237\) | −11.1327 | −0.723144 | ||||||||
\(238\) | 6.63711 | + | 5.18522i | 0.430220 | + | 0.336108i | ||||
\(239\) | 7.19121 | − | 12.4555i | 0.465160 | − | 0.805682i | −0.534048 | − | 0.845454i | \(-0.679330\pi\) |
0.999209 | + | 0.0397724i | \(0.0126633\pi\) | |||||||
\(240\) | −51.3773 | + | 29.6627i | −3.31639 | + | 1.91472i | ||||
\(241\) | −3.97275 | + | 14.8265i | −0.255907 | + | 0.955059i | 0.711676 | + | 0.702508i | \(0.247936\pi\) |
−0.967583 | + | 0.252551i | \(0.918730\pi\) | |||||||
\(242\) | 65.2873 | 4.19682 | ||||||||
\(243\) | 4.24031 | − | 15.8251i | 0.272016 | − | 1.01518i | ||||
\(244\) | 41.9175 | + | 11.2318i | 2.68349 | + | 0.719039i | ||||
\(245\) | −13.7276 | − | 3.67831i | −0.877026 | − | 0.234998i | ||||
\(246\) | −52.1131 | − | 30.0875i | −3.32261 | − | 1.91831i | ||||
\(247\) | 19.4507i | 1.23762i | ||||||||
\(248\) | −7.82526 | − | 29.2043i | −0.496905 | − | 1.85447i | ||||
\(249\) | −23.1279 | − | 6.19710i | −1.46567 | − | 0.392726i | ||||
\(250\) | −21.3412 | − | 21.3412i | −1.34973 | − | 1.34973i | ||||
\(251\) | −10.3482 | − | 17.9235i | −0.653170 | − | 1.13132i | −0.982349 | − | 0.187056i | \(-0.940105\pi\) |
0.329180 | − | 0.944267i | \(-0.393228\pi\) | |||||||
\(252\) | −6.74686 | + | 1.80782i | −0.425012 | + | 0.113882i | ||||
\(253\) | −35.7604 | − | 20.6463i | −2.24823 | − | 1.29802i | ||||
\(254\) | −17.8545 | −1.12029 | ||||||||
\(255\) | 2.43220 | + | 19.8048i | 0.152310 | + | 1.24023i | ||||
\(256\) | 7.90418 | 0.494011 | ||||||||
\(257\) | 9.26127i | 0.577702i | 0.957374 | + | 0.288851i | \(0.0932732\pi\) | ||||
−0.957374 | + | 0.288851i | \(0.906727\pi\) | |||||||
\(258\) | 31.5952 | − | 21.6918i | 1.96703 | − | 1.35047i | ||||
\(259\) | −4.44778 | −0.276371 | ||||||||
\(260\) | −37.3431 | − | 37.3431i | −2.31592 | − | 2.31592i | ||||
\(261\) | 1.52752 | + | 5.70079i | 0.0945513 | + | 0.352870i | ||||
\(262\) | 41.1100 | − | 41.1100i | 2.53978 | − | 2.53978i | ||||
\(263\) | 6.90215 | + | 3.98496i | 0.425605 | + | 0.245723i | 0.697472 | − | 0.716612i | \(-0.254308\pi\) |
−0.271868 | + | 0.962335i | \(0.587641\pi\) | |||||||
\(264\) | 95.0039 | + | 54.8505i | 5.84709 | + | 3.37582i | ||||
\(265\) | 8.19157 | + | 2.19492i | 0.503204 | + | 0.134833i | ||||
\(266\) | −6.07326 | + | 6.07326i | −0.372375 | + | 0.372375i | ||||
\(267\) | 9.98353 | − | 37.2590i | 0.610982 | − | 2.28022i | ||||
\(268\) | 5.64424 | − | 9.77611i | 0.344777 | − | 0.597171i | ||||
\(269\) | −18.7851 | − | 18.7851i | −1.14535 | − | 1.14535i | −0.987456 | − | 0.157891i | \(-0.949530\pi\) |
−0.157891 | − | 0.987456i | \(-0.550470\pi\) | |||||||
\(270\) | 13.7391 | + | 7.93225i | 0.836133 | + | 0.482742i | ||||
\(271\) | −12.8013 | − | 22.1724i | −0.777621 | − | 1.34688i | −0.933310 | − | 0.359073i | \(-0.883093\pi\) |
0.155689 | − | 0.987806i | \(-0.450240\pi\) | |||||||
\(272\) | 19.7480 | − | 46.5264i | 1.19740 | − | 2.82108i | ||||
\(273\) | −3.85987 | − | 6.68549i | −0.233610 | − | 0.404624i | ||||
\(274\) | − | 27.1788i | − | 1.64193i | ||||||
\(275\) | −0.145709 | + | 0.543794i | −0.00878660 | + | 0.0327920i | ||||
\(276\) | −39.0770 | − | 67.6834i | −2.35216 | − | 4.07406i | ||||
\(277\) | 14.7367 | − | 3.94870i | 0.885445 | − | 0.237254i | 0.212690 | − | 0.977120i | \(-0.431777\pi\) |
0.672755 | + | 0.739865i | \(0.265111\pi\) | |||||||
\(278\) | 11.3903 | + | 42.5091i | 0.683144 | + | 2.54953i | ||||
\(279\) | 4.49620 | − | 4.49620i | 0.269181 | − | 0.269181i | ||||
\(280\) | − | 14.2713i | − | 0.852870i | ||||||
\(281\) | 0.959298 | + | 0.553851i | 0.0572269 | + | 0.0330400i | 0.528340 | − | 0.849033i | \(-0.322814\pi\) |
−0.471114 | + | 0.882073i | \(0.656148\pi\) | |||||||
\(282\) | −5.06432 | − | 18.9003i | −0.301576 | − | 1.12550i | ||||
\(283\) | −31.9662 | − | 8.56531i | −1.90019 | − | 0.509155i | −0.996761 | − | 0.0804207i | \(-0.974374\pi\) |
−0.903431 | − | 0.428734i | \(-0.858960\pi\) | |||||||
\(284\) | −10.4539 | + | 39.0143i | −0.620322 | + | 2.31507i | ||||
\(285\) | −20.3479 | −1.20530 | ||||||||
\(286\) | −19.0568 | + | 71.1209i | −1.12685 | + | 4.20547i | ||||
\(287\) | 6.80973 | − | 3.93160i | 0.401966 | − | 0.232075i | ||||
\(288\) | 14.1197 | + | 24.4560i | 0.832011 | + | 1.44108i | ||||
\(289\) | −11.8098 | − | 12.2282i | −0.694692 | − | 0.719307i | ||||
\(290\) | −19.7042 | −1.15707 | ||||||||
\(291\) | −16.1899 | − | 9.34727i | −0.949071 | − | 0.547947i | ||||
\(292\) | 0.361724 | − | 1.34997i | 0.0211683 | − | 0.0790012i | ||||
\(293\) | 8.09992 | 0.473202 | 0.236601 | − | 0.971607i | \(-0.423967\pi\) | ||||
0.236601 | + | 0.971607i | \(0.423967\pi\) | |||||||
\(294\) | −9.70636 | + | 36.2246i | −0.566086 | + | 2.11266i | ||||
\(295\) | −1.50635 | − | 5.62178i | −0.0877031 | − | 0.327312i | ||||
\(296\) | 12.7176 | + | 47.4629i | 0.739198 | + | 2.75872i | ||||
\(297\) | − | 15.9353i | − | 0.924657i | ||||||
\(298\) | 29.6084 | + | 17.0944i | 1.71517 | + | 0.990254i | ||||
\(299\) | 22.6994 | − | 22.6994i | 1.31274 | − | 1.31274i | ||||
\(300\) | −0.753453 | + | 0.753453i | −0.0435006 | + | 0.0435006i | ||||
\(301\) | 0.390458 | + | 4.99274i | 0.0225056 | + | 0.287777i | ||||
\(302\) | 12.4511 | 0.716480 | ||||||||
\(303\) | −18.5442 | − | 18.5442i | −1.06533 | − | 1.06533i | ||||
\(304\) | 44.6373 | + | 25.7713i | 2.56012 | + | 1.47809i | ||||
\(305\) | −18.6472 | −1.06774 | ||||||||
\(306\) | 19.4229 | − | 2.38530i | 1.11033 | − | 0.136358i | ||||
\(307\) | 13.2167 | − | 22.8920i | 0.754317 | − | 1.30652i | −0.191396 | − | 0.981513i | \(-0.561302\pi\) |
0.945713 | − | 0.325003i | \(-0.105365\pi\) | |||||||
\(308\) | −20.2856 | + | 11.7119i | −1.15588 | + | 0.667348i | ||||
\(309\) | −19.3920 | − | 19.3920i | −1.10317 | − | 1.10317i | ||||
\(310\) | 10.6145 | + | 18.3848i | 0.602861 | + | 1.04419i | ||||
\(311\) | −2.14386 | + | 0.574446i | −0.121567 | + | 0.0325739i | −0.319090 | − | 0.947724i | \(-0.603377\pi\) |
0.197522 | + | 0.980298i | \(0.436710\pi\) | |||||||
\(312\) | −60.3052 | + | 60.3052i | −3.41411 | + | 3.41411i | ||||
\(313\) | −0.892434 | − | 3.33061i | −0.0504434 | − | 0.188257i | 0.936107 | − | 0.351716i | \(-0.114402\pi\) |
−0.986550 | + | 0.163459i | \(0.947735\pi\) | |||||||
\(314\) | 8.21078 | − | 4.74049i | 0.463361 | − | 0.267522i | ||||
\(315\) | 2.59927 | − | 1.50069i | 0.146452 | − | 0.0845541i | ||||
\(316\) | −25.3663 | − | 6.79688i | −1.42697 | − | 0.382355i | ||||
\(317\) | −23.1870 | + | 23.1870i | −1.30231 | + | 1.30231i | −0.375480 | + | 0.926831i | \(0.622522\pi\) |
−0.926831 | + | 0.375480i | \(0.877478\pi\) | |||||||
\(318\) | 5.79199 | − | 21.6160i | 0.324799 | − | 1.21217i | ||||
\(319\) | 9.89604 | + | 17.1405i | 0.554072 | + | 0.959681i | ||||
\(320\) | −38.6170 | + | 10.3474i | −2.15876 | + | 0.578438i | ||||
\(321\) | −13.0127 | − | 7.51287i | −0.726297 | − | 0.419328i | ||||
\(322\) | 14.1753 | 0.789956 | ||||||||
\(323\) | 13.8448 | − | 10.4333i | 0.770347 | − | 0.580527i | ||||
\(324\) | 28.7992 | − | 49.8817i | 1.59996 | − | 2.77120i | ||||
\(325\) | −0.379036 | − | 0.218837i | −0.0210251 | − | 0.0121389i | ||||
\(326\) | −1.89915 | + | 7.08771i | −0.105184 | + | 0.392552i | ||||
\(327\) | 8.50939 | + | 14.7387i | 0.470571 | + | 0.815052i | ||||
\(328\) | −61.4260 | − | 61.4260i | −3.39168 | − | 3.39168i | ||||
\(329\) | 2.46975 | + | 0.661767i | 0.136162 | + | 0.0364844i | ||||
\(330\) | −74.4013 | − | 19.9358i | −4.09565 | − | 1.09743i | ||||
\(331\) | 6.61757 | − | 3.82066i | 0.363735 | − | 0.210002i | −0.306983 | − | 0.951715i | \(-0.599319\pi\) |
0.670718 | + | 0.741713i | \(0.265986\pi\) | |||||||
\(332\) | −48.9145 | − | 28.2408i | −2.68453 | − | 1.54992i | ||||
\(333\) | −7.30724 | + | 7.30724i | −0.400434 | + | 0.400434i | ||||
\(334\) | −5.57384 | − | 20.8019i | −0.304987 | − | 1.13823i | ||||
\(335\) | −1.25543 | + | 4.68534i | −0.0685917 | + | 0.255988i | ||||
\(336\) | −20.4566 | −1.11600 | ||||||||
\(337\) | 0.203233 | − | 0.758476i | 0.0110708 | − | 0.0413168i | −0.960169 | − | 0.279418i | \(-0.909858\pi\) |
0.971240 | + | 0.238101i | \(0.0765251\pi\) | |||||||
\(338\) | −19.4594 | − | 11.2349i | −1.05845 | − | 0.611097i | ||||
\(339\) | 0.509055 | − | 0.881709i | 0.0276481 | − | 0.0478878i | ||||
\(340\) | −6.54965 | + | 46.6112i | −0.355205 | + | 2.52785i | ||||
\(341\) | 10.6618 | − | 18.4668i | 0.577369 | − | 1.00003i | ||||
\(342\) | 19.9555i | 1.07907i | ||||||||
\(343\) | −7.24538 | − | 7.24538i | −0.391214 | − | 0.391214i | ||||
\(344\) | 52.1619 | − | 18.4425i | 2.81238 | − | 0.994354i | ||||
\(345\) | 23.7464 | + | 23.7464i | 1.27847 | + | 1.27847i | ||||
\(346\) | −12.7863 | + | 12.7863i | −0.687394 | + | 0.687394i | ||||
\(347\) | 8.11157 | + | 30.2728i | 0.435452 | + | 1.62513i | 0.739983 | + | 0.672625i | \(0.234833\pi\) |
−0.304531 | + | 0.952502i | \(0.598500\pi\) | |||||||
\(348\) | 37.4603i | 2.00808i | ||||||||
\(349\) | −0.390111 | − | 0.225231i | −0.0208822 | − | 0.0120563i | 0.489523 | − | 0.871991i | \(-0.337171\pi\) |
−0.510405 | + | 0.859934i | \(0.670504\pi\) | |||||||
\(350\) | −0.0500204 | − | 0.186679i | −0.00267370 | − | 0.00997839i | ||||
\(351\) | 11.9663 | + | 3.20637i | 0.638716 | + | 0.171144i | ||||
\(352\) | 66.9638 | + | 66.9638i | 3.56918 | + | 3.56918i | ||||
\(353\) | 5.72111 | + | 9.90926i | 0.304504 | + | 0.527417i | 0.977151 | − | 0.212547i | \(-0.0681759\pi\) |
−0.672647 | + | 0.739964i | \(0.734843\pi\) | |||||||
\(354\) | −14.8348 | + | 3.97498i | −0.788461 | + | 0.211268i | ||||
\(355\) | − | 17.3557i | − | 0.921145i | ||||||
\(356\) | 45.4959 | − | 78.8013i | 2.41128 | − | 4.17646i | ||||
\(357\) | −2.68823 | + | 6.33350i | −0.142276 | + | 0.335204i | ||||
\(358\) | −11.7579 | − | 20.3653i | −0.621425 | − | 1.07634i | ||||
\(359\) | −24.4774 | + | 14.1320i | −1.29187 | + | 0.745859i | −0.978985 | − | 0.203933i | \(-0.934627\pi\) |
−0.312881 | + | 0.949792i | \(0.601294\pi\) | |||||||
\(360\) | −23.4462 | − | 23.4462i | −1.23572 | − | 1.23572i | ||||
\(361\) | −0.660754 | − | 1.14446i | −0.0347765 | − | 0.0602347i | ||||
\(362\) | −8.94067 | + | 33.3670i | −0.469911 | + | 1.75373i | ||||
\(363\) | 13.8038 | + | 51.5166i | 0.724513 | + | 2.70392i | ||||
\(364\) | −4.71317 | − | 17.5898i | −0.247037 | − | 0.921956i | ||||
\(365\) | 0.600542i | 0.0314338i | ||||||||
\(366\) | 49.2064i | 2.57206i | ||||||||
\(367\) | 0.679296 | + | 2.53517i | 0.0354590 | + | 0.132335i | 0.981386 | − | 0.192044i | \(-0.0615115\pi\) |
−0.945927 | + | 0.324378i | \(0.894845\pi\) | |||||||
\(368\) | −22.0170 | − | 82.1684i | −1.14771 | − | 4.28332i | ||||
\(369\) | 4.72848 | − | 17.6469i | 0.246155 | − | 0.918662i | ||||
\(370\) | −17.2507 | − | 29.8790i | −0.896820 | − | 1.55334i | ||||
\(371\) | 2.06776 | + | 2.06776i | 0.107353 | + | 0.107353i | ||||
\(372\) | 34.9520 | − | 20.1795i | 1.81217 | − | 1.04626i | ||||
\(373\) | −2.35626 | − | 4.08117i | −0.122003 | − | 0.211315i | 0.798555 | − | 0.601922i | \(-0.205598\pi\) |
−0.920557 | + | 0.390607i | \(0.872265\pi\) | |||||||
\(374\) | 60.8452 | − | 24.5847i | 3.14623 | − | 1.27125i | ||||
\(375\) | 12.3276 | − | 21.3520i | 0.636593 | − | 1.10261i | ||||
\(376\) | − | 28.2472i | − | 1.45674i | ||||||
\(377\) | −14.8626 | + | 3.98242i | −0.765462 | + | 0.205105i | ||||
\(378\) | 2.73520 | + | 4.73750i | 0.140683 | + | 0.243671i | ||||
\(379\) | 26.2502 | + | 26.2502i | 1.34838 | + | 1.34838i | 0.887420 | + | 0.460962i | \(0.152496\pi\) |
0.460962 | + | 0.887420i | \(0.347504\pi\) | |||||||
\(380\) | −46.3637 | − | 12.4231i | −2.37841 | − | 0.637292i | ||||
\(381\) | −3.77502 | − | 14.0886i | −0.193400 | − | 0.721779i | ||||
\(382\) | 44.9428 | + | 25.9477i | 2.29947 | + | 1.32760i | ||||
\(383\) | − | 12.3318i | − | 0.630124i | −0.949071 | − | 0.315062i | \(-0.897975\pi\) | ||
0.949071 | − | 0.315062i | \(-0.102025\pi\) | |||||||
\(384\) | 9.30427 | + | 34.7240i | 0.474806 | + | 1.77200i | ||||
\(385\) | 7.11713 | − | 7.11713i | 0.362723 | − | 0.362723i | ||||
\(386\) | −16.9540 | − | 16.9540i | −0.862938 | − | 0.862938i | ||||
\(387\) | 8.84405 | + | 7.56108i | 0.449568 | + | 0.384351i | ||||
\(388\) | −31.1828 | − | 31.1828i | −1.58306 | − | 1.58306i | ||||
\(389\) | − | 1.10448i | − | 0.0559992i | −0.999608 | − | 0.0279996i | \(-0.991086\pi\) | ||
0.999608 | − | 0.0279996i | \(-0.00891371\pi\) | |||||||
\(390\) | 29.9409 | − | 51.8592i | 1.51612 | − | 2.62599i | ||||
\(391\) | −28.3332 | − | 3.98129i | −1.43287 | − | 0.201342i | ||||
\(392\) | −27.0696 | + | 46.8859i | −1.36722 | + | 2.36809i | ||||
\(393\) | 41.1308 | + | 23.7469i | 2.07478 | + | 1.19787i | ||||
\(394\) | −8.85618 | + | 33.0517i | −0.446168 | + | 1.66512i | ||||
\(395\) | 11.2843 | 0.567776 | ||||||||
\(396\) | −14.0857 | + | 52.5687i | −0.707835 | + | 2.64168i | ||||
\(397\) | 4.89505 | + | 18.2686i | 0.245676 | + | 0.916874i | 0.973043 | + | 0.230625i | \(0.0740772\pi\) |
−0.727367 | + | 0.686249i | \(0.759256\pi\) | |||||||
\(398\) | −14.4069 | + | 14.4069i | −0.722151 | + | 0.722151i | ||||
\(399\) | −6.07634 | − | 3.50818i | −0.304197 | − | 0.175628i | ||||
\(400\) | −1.00441 | + | 0.579897i | −0.0502205 | + | 0.0289948i | ||||
\(401\) | −19.0250 | − | 5.09772i | −0.950061 | − | 0.254568i | −0.249673 | − | 0.968330i | \(-0.580323\pi\) |
−0.700388 | + | 0.713762i | \(0.746990\pi\) | |||||||
\(402\) | 12.3637 | + | 3.31285i | 0.616647 | + | 0.165230i | ||||
\(403\) | 11.7221 | + | 11.7221i | 0.583918 | + | 0.583918i | ||||
\(404\) | −30.9319 | − | 53.5756i | −1.53892 | − | 2.66549i | ||||
\(405\) | −6.40573 | + | 23.9065i | −0.318303 | + | 1.18792i | ||||
\(406\) | −5.88413 | − | 3.39720i | −0.292024 | − | 0.168600i | ||||
\(407\) | −17.3276 | + | 30.0123i | −0.858897 | + | 1.48765i | ||||
\(408\) | 75.2723 | + | 10.5770i | 3.72653 | + | 0.523640i | ||||
\(409\) | −17.0586 | −0.843493 | −0.421746 | − | 0.906714i | \(-0.638583\pi\) | ||||
−0.421746 | + | 0.906714i | \(0.638583\pi\) | |||||||
\(410\) | 52.8230 | + | 30.4974i | 2.60874 | + | 1.50616i | ||||
\(411\) | 21.4461 | − | 5.74648i | 1.05786 | − | 0.283453i | ||||
\(412\) | −32.3461 | − | 56.0251i | −1.59358 | − | 2.76016i | ||||
\(413\) | 0.519419 | − | 1.93850i | 0.0255590 | − | 0.0953873i | ||||
\(414\) | 23.2885 | − | 23.2885i | 1.14457 | − | 1.14457i | ||||
\(415\) | 23.4430 | + | 6.28153i | 1.15077 | + | 0.308348i | ||||
\(416\) | −63.7595 | + | 36.8116i | −3.12607 | + | 1.80483i | ||||
\(417\) | −31.1346 | + | 17.9756i | −1.52467 | + | 0.880268i | ||||
\(418\) | 17.3204 | + | 64.6407i | 0.847170 | + | 3.16168i | ||||
\(419\) | −14.9771 | + | 14.9771i | −0.731680 | + | 0.731680i | −0.970952 | − | 0.239273i | \(-0.923091\pi\) |
0.239273 | + | 0.970952i | \(0.423091\pi\) | |||||||
\(420\) | 18.4011 | − | 4.93056i | 0.897882 | − | 0.240587i | ||||
\(421\) | 16.6092 | + | 28.7680i | 0.809483 | + | 1.40207i | 0.913223 | + | 0.407461i | \(0.133586\pi\) |
−0.103740 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(422\) | −38.1283 | − | 38.1283i | −1.85606 | − | 1.85606i | ||||
\(423\) | 5.14476 | − | 2.97033i | 0.250147 | − | 0.144422i | ||||
\(424\) | 16.1530 | − | 27.9778i | 0.784459 | − | 1.35872i | ||||
\(425\) | 0.0475488 | + | 0.387178i | 0.00230645 | + | 0.0187809i | ||||
\(426\) | −45.7985 | −2.21894 | ||||||||
\(427\) | −5.56847 | − | 3.21496i | −0.269477 | − | 0.155583i | ||||
\(428\) | −25.0632 | − | 25.0632i | −1.21147 | − | 1.21147i | ||||
\(429\) | −60.1489 | −2.90402 | ||||||||
\(430\) | −32.0256 | + | 21.9873i | −1.54441 | + | 1.06032i | ||||
\(431\) | 12.8003 | − | 12.8003i | 0.616571 | − | 0.616571i | −0.328080 | − | 0.944650i | \(-0.606401\pi\) |
0.944650 | + | 0.328080i | \(0.106401\pi\) | |||||||
\(432\) | 23.2131 | − | 23.2131i | 1.11684 | − | 1.11684i | ||||
\(433\) | 5.58480 | + | 3.22439i | 0.268388 | + | 0.154954i | 0.628155 | − | 0.778088i | \(-0.283810\pi\) |
−0.359767 | + | 0.933042i | \(0.617144\pi\) | |||||||
\(434\) | 7.32016i | 0.351379i | ||||||||
\(435\) | −4.16610 | − | 15.5481i | −0.199749 | − | 0.745475i | ||||
\(436\) | 10.3906 | + | 38.7781i | 0.497618 | + | 1.85714i | ||||
\(437\) | 7.55154 | − | 28.1827i | 0.361239 | − | 1.34816i | ||||
\(438\) | 1.58472 | 0.0757208 | ||||||||
\(439\) | −0.502776 | + | 1.87639i | −0.0239962 | + | 0.0895550i | −0.976885 | − | 0.213763i | \(-0.931428\pi\) |
0.952889 | + | 0.303318i | \(0.0980945\pi\) | |||||||
\(440\) | −96.2982 | − | 55.5978i | −4.59084 | − | 2.65052i | ||||
\(441\) | −11.3860 | −0.542188 | ||||||||
\(442\) | 6.21873 | + | 50.6376i | 0.295795 | + | 2.40858i | ||||
\(443\) | −7.28829 | − | 12.6237i | −0.346277 | − | 0.599770i | 0.639308 | − | 0.768951i | \(-0.279221\pi\) |
−0.985585 | + | 0.169181i | \(0.945888\pi\) | |||||||
\(444\) | −56.8040 | + | 32.7958i | −2.69580 | + | 1.55642i | ||||
\(445\) | −10.1195 | + | 37.7666i | −0.479712 | + | 1.79031i | ||||
\(446\) | 34.4590 | 1.63168 | ||||||||
\(447\) | −7.22863 | + | 26.9776i | −0.341902 | + | 1.27600i | ||||
\(448\) | −13.3159 | − | 3.56799i | −0.629118 | − | 0.168572i | ||||
\(449\) | −8.22192 | − | 30.6846i | −0.388016 | − | 1.44810i | −0.833357 | − | 0.552735i | \(-0.813584\pi\) |
0.445340 | − | 0.895361i | \(-0.353083\pi\) | |||||||
\(450\) | −0.388872 | − | 0.224516i | −0.0183316 | − | 0.0105838i | ||||
\(451\) | − | 61.2668i | − | 2.88494i | ||||||
\(452\) | 1.69822 | − | 1.69822i | 0.0798776 | − | 0.0798776i | ||||
\(453\) | 2.63256 | + | 9.82486i | 0.123689 | + | 0.461612i | ||||
\(454\) | 1.14670 | − | 0.307259i | 0.0538175 | − | 0.0144204i | ||||
\(455\) | 3.91245 | + | 6.77657i | 0.183419 | + | 0.317690i | ||||
\(456\) | −20.0620 | + | 74.8726i | −0.939491 | + | 3.50623i | ||||
\(457\) | 29.0589i | 1.35932i | 0.733528 | + | 0.679659i | \(0.237872\pi\) | ||||
−0.733528 | + | 0.679659i | \(0.762128\pi\) | |||||||
\(458\) | −2.21539 | − | 3.83716i | −0.103518 | − | 0.179299i | ||||
\(459\) | −4.13647 | − | 10.2374i | −0.193074 | − | 0.477842i | ||||
\(460\) | 39.6094 | + | 68.6055i | 1.84680 | + | 3.19875i | ||||
\(461\) | 8.76661 | + | 5.06141i | 0.408302 | + | 0.235733i | 0.690060 | − | 0.723752i | \(-0.257584\pi\) |
−0.281758 | + | 0.959485i | \(0.590918\pi\) | |||||||
\(462\) | −18.7808 | − | 18.7808i | −0.873761 | − | 0.873761i | ||||
\(463\) | −12.8343 | + | 22.2297i | −0.596461 | + | 1.03310i | 0.396878 | + | 0.917871i | \(0.370094\pi\) |
−0.993339 | + | 0.115229i | \(0.963240\pi\) | |||||||
\(464\) | −10.5530 | + | 39.3845i | −0.489913 | + | 1.82838i | ||||
\(465\) | −12.2628 | + | 12.2628i | −0.568672 | + | 0.568672i | ||||
\(466\) | 25.7591 | + | 6.90212i | 1.19327 | + | 0.319734i | ||||
\(467\) | −9.55639 | − | 5.51738i | −0.442217 | − | 0.255314i | 0.262321 | − | 0.964981i | \(-0.415512\pi\) |
−0.704538 | + | 0.709667i | \(0.748846\pi\) | |||||||
\(468\) | −36.6415 | − | 21.1550i | −1.69375 | − | 0.977889i | ||||
\(469\) | −1.18270 | + | 1.18270i | −0.0546120 | + | 0.0546120i | ||||
\(470\) | 5.13332 | + | 19.1578i | 0.236782 | + | 0.883683i | ||||
\(471\) | 5.47663 | + | 5.47663i | 0.252350 | + | 0.252350i | ||||
\(472\) | −22.1712 | −1.02051 | ||||||||
\(473\) | 35.2107 | + | 16.8160i | 1.61899 | + | 0.773199i | ||||
\(474\) | − | 29.7772i | − | 1.36771i | ||||||
\(475\) | −0.397795 | −0.0182521 | ||||||||
\(476\) | −9.99210 | + | 12.7899i | −0.457987 | + | 0.586225i | ||||
\(477\) | 6.79424 | 0.311087 | ||||||||
\(478\) | 33.3156 | + | 19.2348i | 1.52382 | + | 0.879778i | ||||
\(479\) | −25.9717 | + | 6.95910i | −1.18668 | + | 0.317969i | −0.797572 | − | 0.603223i | \(-0.793883\pi\) |
−0.389106 | + | 0.921193i | \(0.627216\pi\) | |||||||
\(480\) | −38.5095 | − | 66.7003i | −1.75771 | − | 3.04444i | ||||
\(481\) | −19.0508 | − | 19.0508i | −0.868640 | − | 0.868640i | ||||
\(482\) | −39.6574 | − | 10.6262i | −1.80634 | − | 0.484009i | ||||
\(483\) | 2.99710 | + | 11.1853i | 0.136373 | + | 0.508951i | ||||
\(484\) | 125.811i | 5.71867i | ||||||||
\(485\) | 16.4105 | + | 9.47462i | 0.745163 | + | 0.430220i | ||||
\(486\) | 42.3283 | + | 11.3418i | 1.92005 | + | 0.514476i | ||||
\(487\) | −28.3580 | − | 7.59850i | −1.28502 | − | 0.344321i | −0.449255 | − | 0.893404i | \(-0.648310\pi\) |
−0.835768 | + | 0.549083i | \(0.814977\pi\) | |||||||
\(488\) | −18.3852 | + | 68.6146i | −0.832261 | + | 3.10604i | ||||
\(489\) | −5.99428 | −0.271071 | ||||||||
\(490\) | 9.83860 | − | 36.7181i | 0.444463 | − | 1.65876i | ||||
\(491\) | −14.8147 | + | 8.55325i | −0.668576 | + | 0.386003i | −0.795537 | − | 0.605905i | \(-0.792811\pi\) |
0.126961 | + | 0.991908i | \(0.459478\pi\) | |||||||
\(492\) | 57.9796 | − | 100.424i | 2.61392 | − | 4.52745i | ||||
\(493\) | 10.8069 | + | 8.44288i | 0.486719 | + | 0.380248i | ||||
\(494\) | −52.0261 | −2.34077 | ||||||||
\(495\) | − | 23.3855i | − | 1.05110i | ||||||
\(496\) | 42.4321 | − | 11.3696i | 1.90526 | − | 0.510512i | ||||
\(497\) | 2.99230 | − | 5.18281i | 0.134223 | − | 0.232481i | ||||
\(498\) | 16.5758 | − | 61.8617i | 0.742779 | − | 2.77209i | ||||
\(499\) | 25.5213 | + | 6.83842i | 1.14249 | + | 0.306130i | 0.779953 | − | 0.625838i | \(-0.215243\pi\) |
0.362540 | + | 0.931968i | \(0.381910\pi\) | |||||||
\(500\) | 41.1251 | − | 41.1251i | 1.83917 | − | 1.83917i | ||||
\(501\) | 15.2357 | − | 8.79636i | 0.680683 | − | 0.392992i | ||||
\(502\) | 47.9412 | − | 27.6789i | 2.13972 | − | 1.23537i | ||||
\(503\) | 13.6634 | + | 3.66109i | 0.609220 | + | 0.163240i | 0.550222 | − | 0.835018i | \(-0.314543\pi\) |
0.0589975 | + | 0.998258i | \(0.481210\pi\) | |||||||
\(504\) | −2.95921 | − | 11.0439i | −0.131814 | − | 0.491936i | ||||
\(505\) | 18.7968 | + | 18.7968i | 0.836447 | + | 0.836447i | ||||
\(506\) | 55.2238 | − | 95.6505i | 2.45500 | − | 4.25218i | ||||
\(507\) | 4.75083 | − | 17.7303i | 0.210992 | − | 0.787431i | ||||
\(508\) | − | 34.4063i | − | 1.52653i | ||||||
\(509\) | 6.22378 | + | 10.7799i | 0.275864 | + | 0.477811i | 0.970353 | − | 0.241693i | \(-0.0777027\pi\) |
−0.694489 | + | 0.719504i | \(0.744369\pi\) | |||||||
\(510\) | −52.9732 | + | 6.50556i | −2.34569 | + | 0.288071i | ||||
\(511\) | −0.103539 | + | 0.179335i | −0.00458031 | + | 0.00793333i | ||||
\(512\) | − | 11.7627i | − | 0.519845i | ||||||
\(513\) | 10.8760 | − | 2.91423i | 0.480189 | − | 0.128666i | ||||
\(514\) | −24.7717 | −1.09263 | ||||||||
\(515\) | 19.6562 | + | 19.6562i | 0.866156 | + | 0.866156i | ||||
\(516\) | 41.8008 | + | 60.8849i | 1.84018 | + | 2.68031i | ||||
\(517\) | 14.0870 | − | 14.0870i | 0.619547 | − | 0.619547i | ||||
\(518\) | − | 11.8967i | − | 0.522713i | ||||||
\(519\) | −12.7928 | − | 7.38590i | −0.561540 | − | 0.324205i | ||||
\(520\) | 61.1268 | − | 61.1268i | 2.68059 | − | 2.68059i | ||||
\(521\) | 3.77338 | + | 14.0824i | 0.165315 | + | 0.616963i | 0.998000 | + | 0.0632161i | \(0.0201357\pi\) |
−0.832685 | + | 0.553747i | \(0.813198\pi\) | |||||||
\(522\) | −15.2483 | + | 4.08576i | −0.667399 | + | 0.178829i | ||||
\(523\) | −10.6922 | − | 18.5194i | −0.467536 | − | 0.809797i | 0.531776 | − | 0.846885i | \(-0.321525\pi\) |
−0.999312 | + | 0.0370886i | \(0.988192\pi\) | |||||||
\(524\) | 79.2203 | + | 79.2203i | 3.46076 | + | 3.46076i | ||||
\(525\) | 0.136728 | − | 0.0789397i | 0.00596728 | − | 0.00344521i | ||||
\(526\) | −10.6588 | + | 18.4616i | −0.464747 | + | 0.804965i | ||||
\(527\) | 2.05595 | − | 14.6314i | 0.0895586 | − | 0.637352i | ||||
\(528\) | −79.6946 | + | 138.035i | −3.46826 | + | 6.00720i | ||||
\(529\) | −21.7841 | + | 12.5771i | −0.947135 | + | 0.546829i | ||||
\(530\) | −5.87090 | + | 21.9105i | −0.255016 | + | 0.951732i | ||||
\(531\) | −2.33140 | − | 4.03811i | −0.101174 | − | 0.175239i | ||||
\(532\) | −11.7034 | − | 11.7034i | −0.507406 | − | 0.507406i | ||||
\(533\) | 46.0074 | + | 12.3277i | 1.99280 | + | 0.533970i | ||||
\(534\) | 99.6591 | + | 26.7036i | 4.31267 | + | 1.15558i | ||||
\(535\) | 13.1900 | + | 7.61523i | 0.570252 | + | 0.329235i | ||||
\(536\) | 16.0025 | + | 9.23905i | 0.691203 | + | 0.399066i | ||||
\(537\) | 13.5837 | − | 13.5837i | 0.586182 | − | 0.586182i | ||||
\(538\) | 50.2457 | − | 50.2457i | 2.16625 | − | 2.16625i | ||||
\(539\) | −36.8819 | + | 9.88247i | −1.58862 | + | 0.425668i | ||||
\(540\) | −15.2857 | + | 26.4756i | −0.657793 | + | 1.13933i | ||||
\(541\) | 4.85763 | − | 18.1289i | 0.208846 | − | 0.779423i | −0.779397 | − | 0.626530i | \(-0.784475\pi\) |
0.988243 | − | 0.152892i | \(-0.0488588\pi\) | |||||||
\(542\) | 59.3060 | − | 34.2403i | 2.54741 | − | 1.47075i | ||||
\(543\) | −28.2195 | −1.21101 | ||||||||
\(544\) | 60.4026 | + | 25.6377i | 2.58974 | + | 1.09921i | ||||
\(545\) | −8.62532 | − | 14.9395i | −0.369468 | − | 0.639938i | ||||
\(546\) | 17.8821 | − | 10.3242i | 0.765283 | − | 0.441836i | ||||
\(547\) | 16.0340 | − | 4.29629i | 0.685563 | − | 0.183696i | 0.100808 | − | 0.994906i | \(-0.467857\pi\) |
0.584755 | + | 0.811210i | \(0.301191\pi\) | |||||||
\(548\) | 52.3745 | 2.23733 | ||||||||
\(549\) | −14.4303 | + | 3.86658i | −0.615870 | + | 0.165022i | ||||
\(550\) | −1.45452 | − | 0.389738i | −0.0620210 | − | 0.0166185i | ||||
\(551\) | −9.88883 | + | 9.88883i | −0.421278 | + | 0.421278i | ||||
\(552\) | 110.791 | − | 63.9651i | 4.71557 | − | 2.72254i | ||||
\(553\) | 3.36976 | + | 1.94553i | 0.143297 | + | 0.0827323i | ||||
\(554\) | 10.5618 | + | 39.4173i | 0.448729 | + | 1.67468i | ||||
\(555\) | 19.9295 | − | 19.9295i | 0.845959 | − | 0.845959i | ||||
\(556\) | −81.9165 | + | 21.9495i | −3.47403 | + | 0.930865i | ||||
\(557\) | 20.7992 | 0.881290 | 0.440645 | − | 0.897681i | \(-0.354750\pi\) | ||||
0.440645 | + | 0.897681i | \(0.354750\pi\) | |||||||
\(558\) | 12.0263 | + | 12.0263i | 0.509113 | + | 0.509113i | ||||
\(559\) | −19.7126 | + | 23.0574i | −0.833752 | + | 0.975224i | ||||
\(560\) | 20.7353 | 0.876225 | ||||||||
\(561\) | 32.2638 | + | 42.8134i | 1.36218 | + | 1.80758i | ||||
\(562\) | −1.48142 | + | 2.56590i | −0.0624899 | + | 0.108236i | ||||
\(563\) | − | 6.03091i | − | 0.254172i | −0.991892 | − | 0.127086i | \(-0.959438\pi\) | ||
0.991892 | − | 0.127086i | \(-0.0405625\pi\) | |||||||
\(564\) | 36.4215 | − | 9.75912i | 1.53362 | − | 0.410933i | ||||
\(565\) | −0.515990 | + | 0.893721i | −0.0217079 | + | 0.0375991i | ||||
\(566\) | 22.9102 | − | 85.5019i | 0.962987 | − | 3.59391i | ||||
\(567\) | −6.03462 | + | 6.03462i | −0.253430 | + | 0.253430i | ||||
\(568\) | −63.8625 | − | 17.1119i | −2.67961 | − | 0.717999i | ||||
\(569\) | 0.273649 | + | 0.157992i | 0.0114720 | + | 0.00662335i | 0.505725 | − | 0.862695i | \(-0.331225\pi\) |
−0.494253 | + | 0.869318i | \(0.664558\pi\) | |||||||
\(570\) | − | 54.4258i | − | 2.27965i | ||||||
\(571\) | −1.67066 | − | 6.23498i | −0.0699148 | − | 0.260926i | 0.922117 | − | 0.386910i | \(-0.126458\pi\) |
−0.992032 | + | 0.125985i | \(0.959791\pi\) | |||||||
\(572\) | −137.052 | − | 36.7231i | −5.73044 | − | 1.53547i | ||||
\(573\) | −10.9724 | + | 40.9494i | −0.458377 | + | 1.71069i | ||||
\(574\) | 10.5161 | + | 18.2144i | 0.438934 | + | 0.760255i | ||||
\(575\) | 0.464235 | + | 0.464235i | 0.0193600 | + | 0.0193600i | ||||
\(576\) | −27.7385 | + | 16.0149i | −1.15577 | + | 0.667286i | ||||
\(577\) | 7.17721 | + | 12.4313i | 0.298791 | + | 0.517522i | 0.975860 | − | 0.218398i | \(-0.0700832\pi\) |
−0.677068 | + | 0.735920i | \(0.736750\pi\) | |||||||
\(578\) | 32.7076 | − | 31.5883i | 1.36046 | − | 1.31390i | ||||
\(579\) | 9.79339 | − | 16.9626i | 0.406999 | − | 0.704944i | ||||
\(580\) | − | 37.9707i | − | 1.57665i | ||||||
\(581\) | 5.91761 | + | 5.91761i | 0.245504 | + | 0.245504i | ||||
\(582\) | 25.0017 | − | 43.3043i | 1.03636 | − | 1.79502i | ||||
\(583\) | 22.0082 | − | 5.89708i | 0.911487 | − | 0.244232i | ||||
\(584\) | 2.20977 | + | 0.592106i | 0.0914409 | + | 0.0245015i | ||||
\(585\) | 17.5610 | + | 4.70545i | 0.726057 | + | 0.194546i | ||||
\(586\) | 21.6654i | 0.894988i | ||||||||
\(587\) | −11.3675 | + | 6.56301i | −0.469186 | + | 0.270885i | −0.715899 | − | 0.698204i | \(-0.753983\pi\) |
0.246713 | + | 0.969089i | \(0.420649\pi\) | |||||||
\(588\) | −69.8061 | − | 18.7045i | −2.87875 | − | 0.771360i | ||||
\(589\) | 14.5537 | + | 3.89965i | 0.599674 | + | 0.160682i | ||||
\(590\) | 15.0369 | − | 4.02913i | 0.619060 | − | 0.165877i | ||||
\(591\) | −27.9528 | −1.14982 | ||||||||
\(592\) | −68.9607 | + | 18.4780i | −2.83427 | + | 0.759440i | ||||
\(593\) | 12.5797 | − | 7.26291i | 0.516588 | − | 0.298252i | −0.218950 | − | 0.975736i | \(-0.570263\pi\) |
0.735538 | + | 0.677484i | \(0.236930\pi\) | |||||||
\(594\) | 42.6230 | 1.74884 | ||||||||
\(595\) | 2.72486 | − | 6.41979i | 0.111708 | − | 0.263186i | ||||
\(596\) | −32.9416 | + | 57.0565i | −1.34934 | + | 2.33712i | ||||
\(597\) | −14.4142 | − | 8.32203i | −0.589933 | − | 0.340598i | ||||
\(598\) | 60.7156 | + | 60.7156i | 2.48285 | + | 2.48285i | ||||
\(599\) | −16.6942 | + | 28.9152i | −0.682107 | + | 1.18144i | 0.292229 | + | 0.956348i | \(0.405603\pi\) |
−0.974337 | + | 0.225096i | \(0.927730\pi\) | |||||||
\(600\) | −1.23333 | − | 1.23333i | −0.0503503 | − | 0.0503503i | ||||
\(601\) | −21.5843 | + | 21.5843i | −0.880443 | + | 0.880443i | −0.993579 | − | 0.113137i | \(-0.963910\pi\) |
0.113137 | + | 0.993579i | \(0.463910\pi\) | |||||||
\(602\) | −13.3544 | + | 1.04438i | −0.544285 | + | 0.0425659i | ||||
\(603\) | 3.88611i | 0.158255i | ||||||||
\(604\) | 23.9937i | 0.976290i | ||||||||
\(605\) | −13.9919 | − | 52.2184i | −0.568851 | − | 2.12298i | ||||
\(606\) | 49.6012 | − | 49.6012i | 2.01491 | − | 2.01491i | ||||
\(607\) | −22.2409 | + | 5.95942i | −0.902729 | + | 0.241886i | −0.680188 | − | 0.733038i | \(-0.738102\pi\) |
−0.222541 | + | 0.974923i | \(0.571435\pi\) | |||||||
\(608\) | −33.4575 | + | 57.9501i | −1.35688 | + | 2.35019i | ||||
\(609\) | 1.43655 | − | 5.36130i | 0.0582121 | − | 0.217251i | ||||
\(610\) | − | 49.8768i | − | 2.01945i | ||||||
\(611\) | 7.74396 | + | 13.4129i | 0.313287 | + | 0.542629i | ||||
\(612\) | 4.59655 | + | 37.4286i | 0.185804 | + | 1.51296i | ||||
\(613\) | 47.5199 | 1.91931 | 0.959655 | − | 0.281180i | \(-0.0907258\pi\) | ||||
0.959655 | + | 0.281180i | \(0.0907258\pi\) | |||||||
\(614\) | 61.2307 | + | 35.3515i | 2.47107 | + | 1.42667i | ||||
\(615\) | −12.8963 | + | 48.1295i | −0.520027 | + | 1.94077i | ||||
\(616\) | −19.1712 | − | 33.2055i | −0.772430 | − | 1.33789i | ||||
\(617\) | −3.48424 | + | 13.0034i | −0.140270 | + | 0.523495i | 0.859650 | + | 0.510883i | \(0.170681\pi\) |
−0.999920 | + | 0.0126125i | \(0.995985\pi\) | |||||||
\(618\) | 51.8690 | − | 51.8690i | 2.08648 | − | 2.08648i | ||||
\(619\) | −21.9650 | − | 5.88549i | −0.882846 | − | 0.236558i | −0.211212 | − | 0.977440i | \(-0.567741\pi\) |
−0.671635 | + | 0.740882i | \(0.734408\pi\) | |||||||
\(620\) | −35.4281 | + | 20.4544i | −1.42283 | + | 0.821470i | ||||
\(621\) | −16.0935 | − | 9.29161i | −0.645812 | − | 0.372860i | ||||
\(622\) | −1.53651 | − | 5.73433i | −0.0616084 | − | 0.229926i | ||||
\(623\) | −9.53327 | + | 9.53327i | −0.381942 | + | 0.381942i | ||||
\(624\) | −87.6199 | − | 87.6199i | −3.50760 | − | 3.50760i | ||||
\(625\) | −12.2590 | + | 21.2332i | −0.490360 | + | 0.849328i | ||||
\(626\) | 8.90859 | − | 2.38705i | 0.356059 | − | 0.0954057i | ||||
\(627\) | −47.3443 | + | 27.3342i | −1.89075 | + | 1.09162i | ||||
\(628\) | 9.13509 | + | 15.8224i | 0.364530 | + | 0.631384i | ||||
\(629\) | −3.34134 | + | 23.7789i | −0.133228 | + | 0.948129i | ||||
\(630\) | 4.01398 | + | 6.95242i | 0.159921 | + | 0.276991i | ||||
\(631\) | −12.7546 | + | 7.36388i | −0.507753 | + | 0.293151i | −0.731910 | − | 0.681402i | \(-0.761371\pi\) |
0.224156 | + | 0.974553i | \(0.428037\pi\) | |||||||
\(632\) | 11.1258 | − | 41.5221i | 0.442561 | − | 1.65166i | ||||
\(633\) | 22.0246 | − | 38.1476i | 0.875397 | − | 1.51623i | ||||
\(634\) | −62.0197 | − | 62.0197i | −2.46312 | − | 2.46312i | ||||
\(635\) | 3.82645 | + | 14.2805i | 0.151848 | + | 0.566705i | ||||
\(636\) | 41.6548 | + | 11.1614i | 1.65172 | + | 0.442577i | ||||
\(637\) | − | 29.6844i | − | 1.17614i | ||||||
\(638\) | −45.8466 | + | 26.4696i | −1.81509 | + | 1.04794i | ||||
\(639\) | −3.59879 | − | 13.4309i | −0.142366 | − | 0.531317i | ||||
\(640\) | −9.43103 | − | 35.1971i | −0.372794 | − | 1.39129i | ||||
\(641\) | 24.7530 | + | 24.7530i | 0.977685 | + | 0.977685i | 0.999756 | − | 0.0220715i | \(-0.00702615\pi\) |
−0.0220715 | + | 0.999756i | \(0.507026\pi\) | |||||||
\(642\) | 20.0952 | − | 34.8058i | 0.793093 | − | 1.37368i | ||||
\(643\) | −4.89106 | − | 4.89106i | −0.192885 | − | 0.192885i | 0.604057 | − | 0.796941i | \(-0.293550\pi\) |
−0.796941 | + | 0.604057i | \(0.793550\pi\) | |||||||
\(644\) | 27.3162i | 1.07641i | ||||||||
\(645\) | −24.1209 | − | 20.6218i | −0.949759 | − | 0.811982i | ||||
\(646\) | 27.9067 | + | 37.0317i | 1.09798 | + | 1.45699i | ||||
\(647\) | −44.8618 | −1.76370 | −0.881850 | − | 0.471529i | \(-0.843702\pi\) | ||||
−0.881850 | + | 0.471529i | \(0.843702\pi\) | |||||||
\(648\) | 81.6512 | + | 47.1414i | 3.20756 | + | 1.85189i | ||||
\(649\) | −11.0569 | − | 11.0569i | −0.434020 | − | 0.434020i | ||||
\(650\) | 0.585336 | − | 1.01383i | 0.0229588 | − | 0.0397658i | ||||
\(651\) | −5.77616 | + | 1.54772i | −0.226385 | + | 0.0606598i | ||||
\(652\) | −13.6583 | − | 3.65972i | −0.534899 | − | 0.143326i | ||||
\(653\) | −9.54757 | + | 9.54757i | −0.373625 | + | 0.373625i | −0.868796 | − | 0.495171i | \(-0.835106\pi\) |
0.495171 | + | 0.868796i | \(0.335106\pi\) | |||||||
\(654\) | −39.4225 | + | 22.7606i | −1.54154 | + | 0.890010i | ||||
\(655\) | −41.6912 | − | 24.0704i | −1.62901 | − | 0.940509i | ||||
\(656\) | 89.2483 | − | 89.2483i | 3.48456 | − | 3.48456i | ||||
\(657\) | 0.124525 | + | 0.464735i | 0.00485819 | + | 0.0181310i | ||||
\(658\) | −1.77007 | + | 6.60599i | −0.0690045 | + | 0.257528i | ||||
\(659\) | 6.90456 | + | 11.9591i | 0.268964 | + | 0.465859i | 0.968594 | − | 0.248646i | \(-0.0799855\pi\) |
−0.699631 | + | 0.714504i | \(0.746652\pi\) | |||||||
\(660\) | 38.4169 | − | 143.374i | 1.49537 | − | 5.58082i | ||||
\(661\) | − | 25.3741i | − | 0.986937i | −0.869764 | − | 0.493469i | \(-0.835729\pi\) | ||
0.869764 | − | 0.493469i | \(-0.164271\pi\) | |||||||
\(662\) | 10.2194 | + | 17.7004i | 0.397187 | + | 0.687947i | ||||
\(663\) | −38.6420 | + | 15.6134i | −1.50073 | + | 0.606376i | ||||
\(664\) | 46.2274 | − | 80.0681i | 1.79397 | − | 3.10725i | ||||
\(665\) | 6.15912 | + | 3.55597i | 0.238841 | + | 0.137895i | ||||
\(666\) | −19.5451 | − | 19.5451i | −0.757359 | − | 0.757359i | ||||
\(667\) | 23.0810 | 0.893698 | ||||||||
\(668\) | 40.0859 | − | 10.7410i | 1.55097 | − | 0.415581i | ||||
\(669\) | 7.28573 | + | 27.1907i | 0.281683 | + | 1.05125i | ||||
\(670\) | −12.5322 | − | 3.35799i | −0.484160 | − | 0.129730i | ||||
\(671\) | −43.3872 | + | 25.0496i | −1.67494 | + | 0.967030i | ||||
\(672\) | − | 26.5576i | − | 1.02448i | ||||||
\(673\) | 0.764159 | + | 0.204756i | 0.0294562 | + | 0.00789275i | 0.273517 | − | 0.961867i | \(-0.411813\pi\) |
−0.244061 | + | 0.969760i | \(0.578480\pi\) | |||||||
\(674\) | 2.02874 | + | 0.543600i | 0.0781442 | + | 0.0209387i | ||||
\(675\) | −0.0655748 | + | 0.244729i | −0.00252398 | + | 0.00941961i | ||||
\(676\) | 21.6500 | − | 37.4989i | 0.832692 | − | 1.44226i | ||||
\(677\) | −19.1915 | − | 19.1915i | −0.737589 | − | 0.737589i | 0.234522 | − | 0.972111i | \(-0.424648\pi\) |
−0.972111 | + | 0.234522i | \(0.924648\pi\) | |||||||
\(678\) | 2.35836 | + | 1.36160i | 0.0905723 | + | 0.0522920i | ||||
\(679\) | 3.26703 | + | 5.65867i | 0.125377 | + | 0.217160i | ||||
\(680\) | −76.2978 | − | 10.7211i | −2.92589 | − | 0.411136i | ||||
\(681\) | 0.484900 | + | 0.839872i | 0.0185814 | + | 0.0321840i | ||||
\(682\) | 49.3943 | + | 28.5178i | 1.89140 | + | 1.09200i | ||||
\(683\) | −13.2466 | + | 3.54942i | −0.506868 | + | 0.135815i | −0.503186 | − | 0.864178i | \(-0.667839\pi\) |
−0.00368233 | + | 0.999993i | \(0.501172\pi\) | |||||||
\(684\) | −38.4549 | −1.47036 | ||||||||
\(685\) | −21.7383 | + | 5.82477i | −0.830579 | + | 0.222553i | ||||
\(686\) | 19.3797 | − | 19.3797i | 0.739919 | − | 0.739919i | ||||
\(687\) | 2.55940 | − | 2.55940i | 0.0976474 | − | 0.0976474i | ||||
\(688\) | 26.7959 | + | 75.7881i | 1.02158 | + | 2.88939i | ||||
\(689\) | 17.7133i | 0.674824i | ||||||||
\(690\) | −63.5161 | + | 63.5161i | −2.41802 | + | 2.41802i | ||||
\(691\) | 0.373287 | + | 1.39313i | 0.0142005 | + | 0.0529971i | 0.972663 | − | 0.232223i | \(-0.0745999\pi\) |
−0.958462 | + | 0.285220i | \(0.907933\pi\) | |||||||
\(692\) | −24.6396 | − | 24.6396i | −0.936656 | − | 0.936656i | ||||
\(693\) | 4.03188 | − | 6.98342i | 0.153159 | − | 0.265278i | ||||
\(694\) | −80.9725 | + | 21.6965i | −3.07367 | + | 0.823589i | ||||
\(695\) | 31.5588 | − | 18.2205i | 1.19709 | − | 0.691142i | ||||
\(696\) | −61.3188 | −2.32428 | ||||||||
\(697\) | −15.9036 | − | 39.3601i | −0.602392 | − | 1.49087i | ||||
\(698\) | 0.602439 | − | 1.04346i | 0.0228027 | − | 0.0394954i | ||||
\(699\) | 21.7852i | 0.823990i | ||||||||
\(700\) | 0.359736 | − | 0.0963910i | 0.0135967 | − | 0.00364324i | ||||
\(701\) | 4.72775 | + | 8.18871i | 0.178565 | + | 0.309283i | 0.941389 | − | 0.337323i | \(-0.109521\pi\) |
−0.762824 | + | 0.646606i | \(0.776188\pi\) | |||||||
\(702\) | −8.57629 | + | 32.0072i | −0.323691 | + | 1.20803i | ||||
\(703\) | −23.6527 | − | 6.33772i | −0.892078 | − | 0.239031i | ||||
\(704\) | −75.9518 | + | 75.9518i | −2.86254 | + | 2.86254i | ||||
\(705\) | −14.0316 | + | 8.10115i | −0.528461 | + | 0.305107i | ||||
\(706\) | −26.5049 | + | 15.3026i | −0.997526 | + | 0.575922i | ||||
\(707\) | 2.37240 | + | 8.85390i | 0.0892231 | + | 0.332985i | ||||
\(708\) | −7.65991 | − | 28.5872i | −0.287877 | − | 1.07437i | ||||
\(709\) | −6.18171 | − | 6.18171i | −0.232159 | − | 0.232159i | 0.581434 | − | 0.813593i | \(-0.302492\pi\) |
−0.813593 | + | 0.581434i | \(0.802492\pi\) | |||||||
\(710\) | 46.4224 | 1.74220 | ||||||||
\(711\) | 8.73247 | − | 2.33986i | 0.327493 | − | 0.0877516i | ||||
\(712\) | 128.990 | + | 74.4722i | 4.83409 | + | 2.79096i | ||||
\(713\) | −12.4335 | − | 21.5354i | −0.465638 | − | 0.806508i | ||||
\(714\) | −16.9406 | − | 7.19039i | −0.633986 | − | 0.269094i | ||||
\(715\) | 60.9684 | 2.28009 | ||||||||
\(716\) | 39.2446 | − | 22.6579i | 1.46664 | − | 0.846765i | ||||
\(717\) | −8.13370 | + | 30.3554i | −0.303758 | + | 1.13364i | ||||
\(718\) | −37.7998 | − | 65.4712i | −1.41068 | − | 2.44336i | ||||
\(719\) | 24.3831 | − | 6.53342i | 0.909335 | − | 0.243655i | 0.226314 | − | 0.974054i | \(-0.427333\pi\) |
0.683021 | + | 0.730399i | \(0.260666\pi\) | |||||||
\(720\) | 34.0659 | − | 34.0659i | 1.26956 | − | 1.26956i | ||||
\(721\) | 2.48086 | + | 9.25871i | 0.0923922 | + | 0.344812i | ||||
\(722\) | 3.06116 | − | 1.76736i | 0.113925 | − | 0.0657744i | ||||
\(723\) | − | 33.5394i | − | 1.24734i | ||||||
\(724\) | −64.2994 | − | 17.2290i | −2.38967 | − | 0.640310i | ||||
\(725\) | −0.0814460 | − | 0.303961i | −0.00302483 | − | 0.0112888i | ||||
\(726\) | −137.795 | + | 36.9220i | −5.11404 | + | 1.37030i | ||||
\(727\) | −33.2171 | −1.23195 | −0.615977 | − | 0.787764i | \(-0.711239\pi\) | ||||
−0.615977 | + | 0.787764i | \(0.711239\pi\) | |||||||
\(728\) | 28.7927 | − | 7.71498i | 1.06713 | − | 0.285936i | ||||
\(729\) | 2.27413i | 0.0842272i | ||||||||
\(730\) | −1.60631 | −0.0594521 | ||||||||
\(731\) | 26.9858 | + | 1.66325i | 0.998106 | + | 0.0615174i | ||||
\(732\) | −94.8225 | −3.50474 | ||||||||
\(733\) | 5.88153i | 0.217239i | 0.994083 | + | 0.108620i | \(0.0346431\pi\) | ||||
−0.994083 | + | 0.108620i | \(0.965357\pi\) | |||||||
\(734\) | −6.78097 | + | 1.81696i | −0.250290 | + | 0.0670651i | ||||
\(735\) | 31.0536 | 1.14543 | ||||||||
\(736\) | 106.675 | − | 28.5834i | 3.93208 | − | 1.05360i | ||||
\(737\) | 3.37296 | + | 12.5881i | 0.124245 | + | 0.463687i | ||||
\(738\) | 47.2013 | + | 12.6476i | 1.73750 | + | 0.465563i | ||||
\(739\) | − | 11.1907i | − | 0.411655i | −0.978588 | − | 0.205828i | \(-0.934011\pi\) | ||
0.978588 | − | 0.205828i | \(-0.0659886\pi\) | |||||||
\(740\) | 57.5779 | − | 33.2426i | 2.11661 | − | 1.22202i | ||||
\(741\) | −11.0000 | − | 41.0525i | −0.404095 | − | 1.50810i | ||||
\(742\) | −5.53077 | + | 5.53077i | −0.203041 | + | 0.203041i | ||||
\(743\) | 43.2803 | − | 11.5969i | 1.58780 | − | 0.425450i | 0.646470 | − | 0.762939i | \(-0.276244\pi\) |
0.941329 | + | 0.337490i | \(0.109578\pi\) | |||||||
\(744\) | 33.0318 | + | 57.2128i | 1.21101 | + | 2.09752i | ||||
\(745\) | 7.32711 | − | 27.3451i | 0.268444 | − | 1.00185i | ||||
\(746\) | 10.9162 | − | 6.30245i | 0.399669 | − | 0.230749i | ||||
\(747\) | 19.4441 | 0.711421 | ||||||||
\(748\) | 47.3756 | + | 117.251i | 1.73222 | + | 4.28711i | ||||
\(749\) | 2.62588 | + | 4.54816i | 0.0959476 | + | 0.166186i | ||||
\(750\) | 57.1115 | + | 32.9733i | 2.08542 | + | 1.20402i | ||||
\(751\) | −37.8568 | + | 10.1437i | −1.38142 | + | 0.370149i | −0.871635 | − | 0.490155i | \(-0.836940\pi\) |
−0.509781 | + | 0.860304i | \(0.670273\pi\) | |||||||
\(752\) | 41.0416 | 1.49663 | ||||||||
\(753\) | 31.9770 | + | 31.9770i | 1.16531 | + | 1.16531i | ||||
\(754\) | −10.6520 | − | 39.7539i | −0.387924 | − | 1.44775i | ||||
\(755\) | −2.66843 | − | 9.95871i | −0.0971140 | − | 0.362435i | ||||
\(756\) | −9.12932 | + | 5.27082i | −0.332030 | + | 0.191698i | ||||
\(757\) | −30.5313 | + | 17.6273i | −1.10968 | + | 0.640674i | −0.938746 | − | 0.344609i | \(-0.888012\pi\) |
−0.170933 | + | 0.985283i | \(0.554678\pi\) | |||||||
\(758\) | −70.2131 | + | 70.2131i | −2.55025 | + | 2.55025i | ||||
\(759\) | 87.1515 | + | 23.3522i | 3.16340 | + | 0.847630i | ||||
\(760\) | 20.3354 | − | 75.8926i | 0.737641 | − | 2.75291i | ||||
\(761\) | 25.3463 | + | 43.9011i | 0.918803 | + | 1.59141i | 0.801236 | + | 0.598348i | \(0.204176\pi\) |
0.117566 | + | 0.993065i | \(0.462491\pi\) | |||||||
\(762\) | 37.6836 | − | 10.0973i | 1.36513 | − | 0.365786i | ||||
\(763\) | − | 5.94836i | − | 0.215345i | ||||||
\(764\) | −50.0021 | + | 86.6062i | −1.80901 | + | 3.13330i | ||||
\(765\) | −6.07039 | − | 15.0237i | −0.219475 | − | 0.543184i | ||||
\(766\) | 32.9846 | 1.19178 | ||||||||
\(767\) | 10.5278 | − | 6.07822i | 0.380136 | − | 0.219472i | ||||
\(768\) | −16.6825 | + | 4.47006i | −0.601977 | + | 0.161299i | ||||
\(769\) | 8.28292 | − | 14.3464i | 0.298690 | − | 0.517346i | −0.677147 | − | 0.735848i | \(-0.736784\pi\) |
0.975836 | + | 0.218502i | \(0.0701171\pi\) | |||||||
\(770\) | 19.0366 | + | 19.0366i | 0.686033 | + | 0.686033i | ||||
\(771\) | −5.23753 | − | 19.5467i | −0.188625 | − | 0.703958i | ||||
\(772\) | 32.6710 | − | 32.6710i | 1.17586 | − | 1.17586i | ||||
\(773\) | − | 39.1455i | − | 1.40797i | −0.710216 | − | 0.703984i | \(-0.751403\pi\) | ||
0.710216 | − | 0.703984i | \(-0.248597\pi\) | |||||||
\(774\) | −20.2241 | + | 23.6557i | −0.726940 | + | 0.850288i | ||||
\(775\) | −0.239733 | + | 0.239733i | −0.00861146 | + | 0.00861146i | ||||
\(776\) | 51.0430 | − | 51.0430i | 1.83234 | − | 1.83234i | ||||
\(777\) | 9.38743 | − | 2.51535i | 0.336772 | − | 0.0902378i | ||||
\(778\) | 2.95421 | 0.105914 | ||||||||
\(779\) | 41.8155 | − | 11.2044i | 1.49819 | − | 0.401440i | ||||
\(780\) | 99.9345 | + | 57.6972i | 3.57823 | + | 2.06589i | ||||
\(781\) | −23.3147 | − | 40.3823i | −0.834266 | − | 1.44499i | ||||
\(782\) | 10.6490 | − | 75.7846i | 0.380807 | − | 2.71005i | ||||
\(783\) | 4.45360 | + | 7.71387i | 0.159159 | + | 0.275671i | ||||
\(784\) | −68.1224 | − | 39.3305i | −2.43294 | − | 1.40466i | ||||
\(785\) | −5.55124 | − | 5.55124i | −0.198132 | − | 0.198132i | ||||
\(786\) | −63.5173 | + | 110.015i | −2.26559 | + | 3.92411i | ||||
\(787\) | 10.7223 | − | 40.0160i | 0.382207 | − | 1.42642i | −0.460315 | − | 0.887756i | \(-0.652263\pi\) |
0.842522 | − | 0.538662i | \(-0.181070\pi\) | |||||||
\(788\) | −63.6918 | − | 17.0662i | −2.26892 | − | 0.607957i | ||||
\(789\) | −16.8212 | − | 4.50723i | −0.598851 | − | 0.160462i | ||||
\(790\) | 30.1829i | 1.07386i | ||||||||
\(791\) | −0.308173 | + | 0.177924i | −0.0109574 | + | 0.00632623i | ||||
\(792\) | −86.0497 | − | 23.0569i | −3.05764 | − | 0.819293i | ||||
\(793\) | −10.0806 | − | 37.6213i | −0.357973 | − | 1.33597i | ||||
\(794\) | −48.8642 | + | 13.0931i | −1.73412 | + | 0.464657i | ||||
\(795\) | −18.5303 | −0.657203 | ||||||||
\(796\) | −27.7625 | − | 27.7625i | −0.984016 | − | 0.984016i | ||||
\(797\) | 10.2210 | + | 5.90108i | 0.362045 | + | 0.209027i | 0.669978 | − | 0.742381i | \(-0.266304\pi\) |
−0.307932 | + | 0.951408i | \(0.599637\pi\) | |||||||
\(798\) | 9.38354 | − | 16.2528i | 0.332174 | − | 0.575342i | ||||
\(799\) | 5.39334 | − | 12.7068i | 0.190803 | − | 0.449533i | ||||
\(800\) | −0.752848 | − | 1.30397i | −0.0266172 | − | 0.0461023i | ||||
\(801\) | 31.3244i | 1.10679i | ||||||||
\(802\) | 13.6352 | − | 50.8873i | 0.481476 | − | 1.79689i | ||||
\(803\) | 0.806735 | + | 1.39731i | 0.0284691 | + | 0.0493099i | ||||
\(804\) | −6.38398 | + | 23.8253i | −0.225146 | + | 0.840255i | ||||
\(805\) | −3.03794 | − | 11.3377i | −0.107073 | − | 0.399603i | ||||
\(806\) | −31.3538 | + | 31.3538i | −1.10439 | + | 1.10439i | ||||
\(807\) | 50.2712 | + | 29.0241i | 1.76963 | + | 1.02170i | ||||
\(808\) | 87.6979 | − | 50.6324i | 3.08520 | − | 1.78124i | ||||
\(809\) | −2.96495 | + | 2.96495i | −0.104242 | + | 0.104242i | −0.757304 | − | 0.653062i | \(-0.773484\pi\) |
0.653062 | + | 0.757304i | \(0.273484\pi\) | |||||||
\(810\) | −63.9443 | − | 17.1338i | −2.24677 | − | 0.602021i | ||||
\(811\) | 1.19314 | − | 0.319700i | 0.0418967 | − | 0.0112262i | −0.237810 | − | 0.971312i | \(-0.576430\pi\) |
0.279707 | + | 0.960086i | \(0.409763\pi\) | |||||||
\(812\) | 6.54652 | − | 11.3389i | 0.229738 | − | 0.397918i | ||||
\(813\) | 39.5574 | + | 39.5574i | 1.38734 | + | 1.38734i | ||||
\(814\) | −80.2758 | − | 46.3472i | −2.81366 | − | 1.62447i | ||||
\(815\) | 6.07594 | 0.212831 | ||||||||
\(816\) | −15.3678 | + | 109.366i | −0.537979 | + | 3.82858i | ||||
\(817\) | −5.03784 | + | 27.1071i | −0.176252 | + | 0.948358i | ||||
\(818\) | − | 45.6277i | − | 1.59533i | ||||||
\(819\) | 4.43284 | + | 4.43284i | 0.154896 | + | 0.154896i | ||||
\(820\) | −58.7695 | + | 101.792i | −2.05232 | + | 3.55472i | ||||
\(821\) | −21.8935 | − | 21.8935i | −0.764089 | − | 0.764089i | 0.212970 | − | 0.977059i | \(-0.431686\pi\) |
−0.977059 | + | 0.212970i | \(0.931686\pi\) | |||||||
\(822\) | 15.3705 | + | 57.3633i | 0.536106 | + | 2.00078i | ||||
\(823\) | 3.70395 | + | 13.8233i | 0.129112 | + | 0.481851i | 0.999953 | − | 0.00971340i | \(-0.00309192\pi\) |
−0.870841 | + | 0.491564i | \(0.836425\pi\) | |||||||
\(824\) | 91.7075 | − | 52.9473i | 3.19478 | − | 1.84451i | ||||
\(825\) | − | 1.23013i | − | 0.0428276i | ||||||
\(826\) | 5.18503 | + | 1.38932i | 0.180410 | + | 0.0483407i | ||||
\(827\) | −1.89816 | − | 7.08404i | −0.0660056 | − | 0.246336i | 0.925038 | − | 0.379874i | \(-0.124033\pi\) |
−0.991044 | + | 0.133538i | \(0.957366\pi\) | |||||||
\(828\) | 44.8777 | + | 44.8777i | 1.55961 | + | 1.55961i | ||||
\(829\) | 8.87807 | − | 15.3773i | 0.308348 | − | 0.534074i | −0.669653 | − | 0.742674i | \(-0.733557\pi\) |
0.978001 | + | 0.208600i | \(0.0668905\pi\) | |||||||
\(830\) | −16.8016 | + | 62.7045i | −0.583192 | + | 2.17650i | ||||
\(831\) | −28.8701 | + | 16.6682i | −1.00149 | + | 0.578212i | ||||
\(832\) | −41.7524 | − | 72.3174i | −1.44751 | − | 2.50715i | ||||
\(833\) | −21.1291 | + | 15.9227i | −0.732079 | + | 0.551688i | ||||
\(834\) | −48.0804 | − | 83.2778i | −1.66489 | − | 2.88367i | ||||
\(835\) | −15.4433 | + | 8.91620i | −0.534438 | + | 0.308558i | ||||
\(836\) | −124.565 | + | 33.3770i | −4.30817 | + | 1.15437i | ||||
\(837\) | 4.79823 | − | 8.31077i | 0.165851 | − | 0.287262i | ||||
\(838\) | −40.0602 | − | 40.0602i | −1.38386 | − | 1.38386i | ||||
\(839\) | −1.09359 | + | 1.09359i | −0.0377548 | + | 0.0377548i | −0.725732 | − | 0.687977i | \(-0.758499\pi\) |
0.687977 | + | 0.725732i | \(0.258499\pi\) | |||||||
\(840\) | 8.07083 | + | 30.1208i | 0.278470 | + | 1.03926i | ||||
\(841\) | 15.5339 | + | 8.96848i | 0.535651 | + | 0.309258i | ||||
\(842\) | −76.9475 | + | 44.4257i | −2.65179 | + | 1.53101i | ||||
\(843\) | −2.33790 | − | 0.626440i | −0.0805217 | − | 0.0215757i | ||||
\(844\) | 73.4745 | − | 73.4745i | 2.52910 | − | 2.52910i | ||||
\(845\) | −4.81555 | + | 17.9719i | −0.165660 | + | 0.618251i | ||||
\(846\) | 7.94492 | + | 13.7610i | 0.273152 | + | 0.473113i | ||||
\(847\) | 4.82468 | − | 18.0059i | 0.165778 | − | 0.618691i | ||||
\(848\) | 40.6501 | + | 23.4693i | 1.39593 | + | 0.805940i | ||||
\(849\) | 72.3114 | 2.48172 | ||||||||
\(850\) | −1.03561 | + | 0.127182i | −0.0355211 | + | 0.00436230i | ||||
\(851\) | 20.2069 | + | 34.9995i | 0.692685 | + | 1.19977i | ||||
\(852\) | − | 88.2552i | − | 3.02357i | ||||||
\(853\) | 4.30612 | − | 16.0706i | 0.147439 | − | 0.550248i | −0.852196 | − | 0.523223i | \(-0.824730\pi\) |
0.999635 | − | 0.0270259i | \(-0.00860367\pi\) | |||||||
\(854\) | 8.59926 | − | 14.8943i | 0.294260 | − | 0.509674i | ||||
\(855\) | 15.9609 | − | 4.27671i | 0.545852 | − | 0.146260i | ||||
\(856\) | 41.0258 | − | 41.0258i | 1.40223 | − | 1.40223i | ||||
\(857\) | 3.76156 | + | 14.0383i | 0.128493 | + | 0.479541i | 0.999940 | − | 0.0109479i | \(-0.00348491\pi\) |
−0.871447 | + | 0.490489i | \(0.836818\pi\) | |||||||
\(858\) | − | 160.884i | − | 5.49249i | ||||||
\(859\) | − | 6.47666i | − | 0.220981i | −0.993877 | − | 0.110490i | \(-0.964758\pi\) | ||
0.993877 | − | 0.110490i | \(-0.0352421\pi\) | |||||||
\(860\) | −42.3703 | − | 61.7144i | −1.44482 | − | 2.10444i | ||||
\(861\) | −12.1491 | + | 12.1491i | −0.414041 | + | 0.414041i | ||||
\(862\) | 34.2379 | + | 34.2379i | 1.16615 | + | 1.16615i | ||||
\(863\) | −19.3989 | + | 33.5999i | −0.660347 | + | 1.14375i | 0.320178 | + | 0.947357i | \(0.396257\pi\) |
−0.980525 | + | 0.196396i | \(0.937076\pi\) | |||||||
\(864\) | 30.1363 | + | 30.1363i | 1.02526 | + | 1.02526i | ||||
\(865\) | 12.9670 | + | 7.48653i | 0.440893 | + | 0.254550i | ||||
\(866\) | −8.62447 | + | 14.9380i | −0.293071 | + | 0.507614i | ||||
\(867\) | 31.8410 | + | 19.1300i | 1.08138 | + | 0.649687i | ||||
\(868\) | −14.1062 | −0.478795 | ||||||||
\(869\) | 26.2557 | − | 15.1588i | 0.890665 | − | 0.514225i | ||||
\(870\) | 41.5875 | − | 11.1433i | 1.40995 | − | 0.377795i | ||||
\(871\) | −10.1315 | −0.343293 | ||||||||
\(872\) | −63.4759 | + | 17.0083i | −2.14956 | + | 0.575974i | ||||
\(873\) | 14.6640 | + | 3.92921i | 0.496302 | + | 0.132984i | ||||
\(874\) | 75.3821 | + | 20.1986i | 2.54984 | + | 0.683227i | ||||
\(875\) | −7.46289 | + | 4.30870i | −0.252292 | + | 0.145661i | ||||
\(876\) | 3.05380i | 0.103178i | ||||||||
\(877\) | −30.0964 | − | 8.06429i | −1.01628 | − | 0.272312i | −0.288030 | − | 0.957621i | \(-0.593000\pi\) |
−0.728252 | + | 0.685310i | \(0.759667\pi\) | |||||||
\(878\) | −5.01889 | − | 1.34481i | −0.169379 | − | 0.0453851i | ||||
\(879\) | −17.0956 | + | 4.58075i | −0.576620 | + | 0.154505i | ||||
\(880\) | 80.7803 | − | 139.916i | 2.72310 | − | 4.71655i | ||||
\(881\) | −29.8835 | − | 29.8835i | −1.00680 | − | 1.00680i | −0.999977 | − | 0.00682261i | \(-0.997828\pi\) |
−0.00682261 | − | 0.999977i | \(-0.502172\pi\) | |||||||
\(882\) | − | 30.4547i | − | 1.02546i | ||||||
\(883\) | −10.7193 | + | 18.5663i | −0.360732 | + | 0.624807i | −0.988082 | − | 0.153931i | \(-0.950807\pi\) |
0.627349 | + | 0.778738i | \(0.284140\pi\) | |||||||
\(884\) | −97.5803 | + | 11.9837i | −3.28198 | + | 0.403055i | ||||
\(885\) | 6.35857 | + | 11.0134i | 0.213741 | + | 0.370210i | ||||
\(886\) | 33.7654 | − | 19.4945i | 1.13437 | − | 0.654929i | ||||
\(887\) | −15.9799 | − | 15.9799i | −0.536554 | − | 0.536554i | 0.385961 | − | 0.922515i | \(-0.373870\pi\) |
−0.922515 | + | 0.385961i | \(0.873870\pi\) | |||||||
\(888\) | −53.6834 | − | 92.9824i | −1.80150 | − | 3.12029i | ||||
\(889\) | −1.31944 | + | 4.92420i | −0.0442525 | + | 0.165152i | ||||
\(890\) | −101.017 | − | 27.0674i | −3.38609 | − | 0.907301i | ||||
\(891\) | 17.2102 | + | 64.2294i | 0.576564 | + | 2.15177i | ||||
\(892\) | 66.4036i | 2.22336i | ||||||||
\(893\) | 12.1908 | + | 7.03837i | 0.407950 | + | 0.235530i | ||||
\(894\) | −72.1587 | − | 19.3349i | −2.41335 | − | 0.646655i | ||||
\(895\) | −13.7688 | + | 13.7688i | −0.460241 | + | 0.460241i | ||||
\(896\) | 3.25200 | − | 12.1366i | 0.108642 | − | 0.405457i | ||||
\(897\) | −35.0720 | + | 60.7464i | −1.17102 | + | 2.02826i | ||||
\(898\) | 82.0741 | − | 21.9917i | 2.73885 | − | 0.733872i | ||||
\(899\) | 11.9191i | 0.397524i | ||||||||
\(900\) | 0.432649 | − | 0.749370i | 0.0144216 | − | 0.0249790i | ||||
\(901\) | 12.6082 | − | 9.50140i | 0.420039 | − | 0.316538i | ||||
\(902\) | 163.874 | 5.45641 | ||||||||
\(903\) | −3.64765 | − | 10.3168i | −0.121386 | − | 0.343322i | ||||
\(904\) | 2.77982 | + | 2.77982i | 0.0924553 | + | 0.0924553i | ||||
\(905\) | 28.6039 | 0.950826 | ||||||||
\(906\) | −26.2792 | + | 7.04148i | −0.873067 | + | 0.233938i | ||||
\(907\) | −2.83554 | + | 2.83554i | −0.0941524 | + | 0.0941524i | −0.752614 | − | 0.658462i | \(-0.771207\pi\) |
0.658462 | + | 0.752614i | \(0.271207\pi\) | |||||||
\(908\) | 0.592098 | + | 2.20974i | 0.0196495 | + | 0.0733328i | ||||
\(909\) | 18.4437 | + | 10.6485i | 0.611738 | + | 0.353187i | ||||
\(910\) | −18.1257 | + | 10.4649i | −0.600862 | + | 0.346908i | ||||
\(911\) | 34.9063 | − | 34.9063i | 1.15650 | − | 1.15650i | 0.171275 | − | 0.985223i | \(-0.445211\pi\) |
0.985223 | − | 0.171275i | \(-0.0547886\pi\) | |||||||
\(912\) | −108.785 | − | 29.1490i | −3.60224 | − | 0.965218i | ||||
\(913\) | 62.9841 | − | 16.8765i | 2.08447 | − | 0.558532i | ||||
\(914\) | −77.7257 | −2.57094 | ||||||||
\(915\) | 39.3566 | − | 10.5456i | 1.30109 | − | 0.348625i | ||||
\(916\) | 7.39434 | − | 4.26912i | 0.244316 | − | 0.141056i | ||||
\(917\) | −8.29996 | − | 14.3759i | −0.274089 | − | 0.474736i | ||||
\(918\) | 27.3827 | − | 11.0641i | 0.903763 | − | 0.365169i | ||||
\(919\) | 24.8264 | 0.818948 | 0.409474 | − | 0.912322i | \(-0.365712\pi\) | ||||
0.409474 | + | 0.912322i | \(0.365712\pi\) | |||||||
\(920\) | −112.300 | + | 64.8366i | −3.70243 | + | 2.13760i | ||||
\(921\) | −14.9489 | + | 55.7901i | −0.492583 | + | 1.83834i | ||||
\(922\) | −13.5381 | + | 23.4486i | −0.445852 | + | 0.772239i | ||||
\(923\) | 35.0157 | − | 9.38243i | 1.15256 | − | 0.308826i | ||||
\(924\) | 36.1912 | − | 36.1912i | 1.19060 | − | 1.19060i | ||||
\(925\) | 0.389615 | − | 0.389615i | 0.0128105 | − | 0.0128105i | ||||
\(926\) | −59.4591 | − | 34.3287i | −1.95395 | − | 1.12811i | ||||
\(927\) | 19.2869 | + | 11.1353i | 0.633466 | + | 0.365732i | ||||
\(928\) | −51.1307 | − | 13.7004i | −1.67845 | − | 0.449738i | ||||
\(929\) | −7.98039 | − | 2.13834i | −0.261828 | − | 0.0701567i | 0.125517 | − | 0.992091i | \(-0.459941\pi\) |
−0.387345 | + | 0.921935i | \(0.626608\pi\) | |||||||
\(930\) | −32.8000 | − | 32.8000i | −1.07555 | − | 1.07555i | ||||
\(931\) | −13.4899 | − | 23.3651i | −0.442112 | − | 0.765761i | ||||
\(932\) | −13.3006 | + | 49.6386i | −0.435676 | + | 1.62596i | ||||
\(933\) | 4.19995 | − | 2.42484i | 0.137500 | − | 0.0793857i | ||||
\(934\) | 14.7577 | − | 25.5611i | 0.482887 | − | 0.836384i | ||||
\(935\) | −32.7034 | − | 43.3967i | −1.06951 | − | 1.41922i | ||||
\(936\) | 34.6286 | − | 59.9784i | 1.13187 | − | 1.96046i | ||||
\(937\) | 0.529514 | − | 0.305715i | 0.0172985 | − | 0.00998727i | −0.491326 | − | 0.870976i | \(-0.663488\pi\) |
0.508624 | + | 0.860989i | \(0.330154\pi\) | |||||||
\(938\) | −3.16344 | − | 3.16344i | −0.103290 | − | 0.103290i | ||||
\(939\) | 3.76712 | + | 6.52485i | 0.122935 | + | 0.212930i | ||||
\(940\) | −36.9177 | + | 9.89207i | −1.20412 | + | 0.322644i | ||||
\(941\) | −11.1335 | − | 41.5509i | −0.362942 | − | 1.35452i | −0.870189 | − | 0.492718i | \(-0.836003\pi\) |
0.507247 | − | 0.861801i | \(-0.330663\pi\) | |||||||
\(942\) | −14.6487 | + | 14.6487i | −0.477280 | + | 0.477280i | ||||
\(943\) | −61.8754 | − | 35.7238i | −2.01494 | − | 1.16333i | ||||
\(944\) | − | 32.2134i | − | 1.04846i | ||||||
\(945\) | 3.20299 | − | 3.20299i | 0.104193 | − | 0.104193i | ||||
\(946\) | −44.9788 | + | 94.1803i | −1.46239 | + | 3.06207i | ||||
\(947\) | −23.9053 | − | 23.9053i | −0.776819 | − | 0.776819i | 0.202469 | − | 0.979289i | \(-0.435103\pi\) |
−0.979289 | + | 0.202469i | \(0.935103\pi\) | |||||||
\(948\) | 57.3817 | 1.86367 | ||||||||
\(949\) | −1.21161 | + | 0.324651i | −0.0393306 | + | 0.0105386i | ||||
\(950\) | − | 1.06401i | − | 0.0345209i | ||||||
\(951\) | 35.8252 | − | 62.0511i | 1.16171 | − | 2.01215i | ||||
\(952\) | −20.9358 | − | 16.3561i | −0.678534 | − | 0.530103i | ||||
\(953\) | −23.3806 | − | 40.4963i | −0.757371 | − | 1.31180i | −0.944187 | − | 0.329410i | \(-0.893150\pi\) |
0.186816 | − | 0.982395i | \(-0.440183\pi\) | |||||||
\(954\) | 18.1730i | 0.588372i | ||||||||
\(955\) | 11.1218 | − | 41.5073i | 0.359894 | − | 1.34314i | ||||
\(956\) | −37.0661 | + | 64.2003i | −1.19880 | + | 2.07639i | ||||
\(957\) | −30.5799 | − | 30.5799i | −0.988509 | − | 0.988509i | ||||
\(958\) | −18.6140 | − | 69.4682i | −0.601389 | − | 2.24442i | ||||
\(959\) | −7.49580 | − | 2.00849i | −0.242052 | − | 0.0648577i | ||||
\(960\) | 75.6529 | − | 43.6782i | 2.44169 | − | 1.40971i | ||||
\(961\) | −15.7258 | + | 9.07930i | −0.507284 | + | 0.292881i | ||||
\(962\) | 50.9563 | − | 50.9563i | 1.64290 | − | 1.64290i | ||||
\(963\) | 11.7862 | + | 3.15811i | 0.379805 | + | 0.101769i | ||||
\(964\) | 20.4770 | − | 76.4211i | 0.659519 | − | 2.46136i | ||||
\(965\) | −9.92681 | + | 17.1937i | −0.319555 | + | 0.553486i | ||||
\(966\) | −29.9181 | + | 8.01654i | −0.962601 | + | 0.257928i | ||||
\(967\) | 2.78729i | 0.0896331i | 0.998995 | + | 0.0448166i | \(0.0142703\pi\) | ||||
−0.998995 | + | 0.0448166i | \(0.985730\pi\) | |||||||
\(968\) | −205.939 | −6.61914 | ||||||||
\(969\) | −23.3204 | + | 29.8502i | −0.749159 | + | 0.958926i | ||||
\(970\) | −25.3424 | + | 43.8942i | −0.813694 | + | 1.40936i | ||||
\(971\) | −0.533459 | + | 0.307993i | −0.0171195 | + | 0.00988396i | −0.508535 | − | 0.861041i | \(-0.669813\pi\) |
0.491416 | + | 0.870925i | \(0.336480\pi\) | |||||||
\(972\) | −21.8561 | + | 81.5680i | −0.701034 | + | 2.61630i | ||||
\(973\) | 12.5656 | 0.402834 | ||||||||
\(974\) | 20.3242 | − | 75.8509i | 0.651229 | − | 2.43042i | ||||
\(975\) | 0.923749 | + | 0.247518i | 0.0295836 | + | 0.00792691i | ||||
\(976\) | −99.6930 | − | 26.7127i | −3.19110 | − | 0.855051i | ||||
\(977\) | 8.67796 | + | 5.01022i | 0.277633 | + | 0.160291i | 0.632351 | − | 0.774682i | \(-0.282090\pi\) |
−0.354719 | + | 0.934973i | \(0.615423\pi\) | |||||||
\(978\) | − | 16.0333i | − | 0.512687i | ||||||
\(979\) | 27.1881 | + | 101.467i | 0.868935 | + | 3.24291i | ||||
\(980\) | 70.7571 | + | 18.9593i | 2.26025 | + | 0.605633i | ||||
\(981\) | −9.77256 | − | 9.77256i | −0.312014 | − | 0.312014i | ||||
\(982\) | −22.8779 | − | 39.6257i | −0.730063 | − | 1.26451i | ||||
\(983\) | 50.6813 | − | 13.5800i | 1.61648 | − | 0.433135i | 0.666518 | − | 0.745489i | \(-0.267784\pi\) |
0.949966 | + | 0.312354i | \(0.101117\pi\) | |||||||
\(984\) | 164.383 | + | 94.9067i | 5.24035 | + | 3.02552i | ||||
\(985\) | 28.3336 | 0.902783 | ||||||||
\(986\) | −22.5827 | + | 28.9059i | −0.719179 | + | 0.920553i | ||||
\(987\) | −5.58687 | −0.177832 | ||||||||
\(988\) | − | 100.256i | − | 3.18957i | ||||||
\(989\) | 37.5139 | − | 25.7553i | 1.19287 | − | 0.818972i | ||||
\(990\) | 62.5505 | 1.98799 | ||||||||
\(991\) | 24.9378 | + | 24.9378i | 0.792174 | + | 0.792174i | 0.981847 | − | 0.189673i | \(-0.0607428\pi\) |
−0.189673 | + | 0.981847i | \(0.560743\pi\) | |||||||
\(992\) | 14.7606 | + | 55.0872i | 0.468649 | + | 1.74902i | ||||
\(993\) | −11.8063 | + | 11.8063i | −0.374661 | + | 0.374661i | ||||
\(994\) | 13.8628 | + | 8.00368i | 0.439701 | + | 0.253861i | ||||
\(995\) | 14.6106 | + | 8.43541i | 0.463186 | + | 0.267420i | ||||
\(996\) | 119.210 | + | 31.9421i | 3.77730 | + | 1.01212i | ||||
\(997\) | −28.6831 | + | 28.6831i | −0.908404 | + | 0.908404i | −0.996143 | − | 0.0877391i | \(-0.972036\pi\) |
0.0877391 | + | 0.996143i | \(0.472036\pi\) | |||||||
\(998\) | −18.2912 | + | 68.2636i | −0.578997 | + | 2.16085i | ||||
\(999\) | −7.79809 | + | 13.5067i | −0.246721 | + | 0.427333i |
(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 | 731.2.n.a.608.62 | yes | 256 | |
17.4 | even | 4 | inner | 731.2.n.a.565.3 | yes | 256 | |
43.36 | even | 3 | inner | 731.2.n.a.251.62 | yes | 256 | |
731.208 | even | 12 | inner | 731.2.n.a.208.3 | ✓ | 256 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.n.a.208.3 | ✓ | 256 | 731.208 | even | 12 | inner | |
731.2.n.a.251.62 | yes | 256 | 43.36 | even | 3 | inner | |
731.2.n.a.565.3 | yes | 256 | 17.4 | even | 4 | inner | |
731.2.n.a.608.62 | yes | 256 | 1.1 | even | 1 | trivial |