Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(689,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.h (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.10 | ||
Character | \(\chi\) | \(=\) | 690.689 |
Dual form | 690.2.h.b.689.12 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.571841 | − | 1.63493i | −0.330152 | − | 0.943928i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.12720 | − | 0.689226i | 0.951311 | − | 0.308231i | ||||
\(6\) | −0.571841 | − | 1.63493i | −0.233453 | − | 0.667458i | ||||
\(7\) | 1.28874 | 0.487099 | 0.243550 | − | 0.969888i | \(-0.421688\pi\) | ||||
0.243550 | + | 0.969888i | \(0.421688\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.34600 | + | 1.86984i | −0.781999 | + | 0.623280i | ||||
\(10\) | 2.12720 | − | 0.689226i | 0.672679 | − | 0.217953i | ||||
\(11\) | 4.52819 | 1.36530 | 0.682650 | − | 0.730745i | \(-0.260827\pi\) | ||||
0.682650 | + | 0.730745i | \(0.260827\pi\) | |||||||
\(12\) | −0.571841 | − | 1.63493i | −0.165076 | − | 0.471964i | ||||
\(13\) | 3.04015i | 0.843186i | 0.906785 | + | 0.421593i | \(0.138529\pi\) | ||||
−0.906785 | + | 0.421593i | \(0.861471\pi\) | |||||||
\(14\) | 1.28874 | 0.344431 | ||||||||
\(15\) | −2.34326 | − | 3.08369i | −0.605026 | − | 0.796206i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.73191i | − | 1.39019i | −0.718917 | − | 0.695096i | \(-0.755362\pi\) | ||
0.718917 | − | 0.695096i | \(-0.244638\pi\) | |||||||
\(18\) | −2.34600 | + | 1.86984i | −0.552957 | + | 0.440726i | ||||
\(19\) | 3.52988i | 0.809811i | 0.914359 | + | 0.404905i | \(0.132696\pi\) | ||||
−0.914359 | + | 0.404905i | \(0.867304\pi\) | |||||||
\(20\) | 2.12720 | − | 0.689226i | 0.475656 | − | 0.154116i | ||||
\(21\) | −0.736956 | − | 2.10701i | −0.160817 | − | 0.459786i | ||||
\(22\) | 4.52819 | 0.965413 | ||||||||
\(23\) | −4.79401 | − | 0.132152i | −0.999620 | − | 0.0275555i | ||||
\(24\) | −0.571841 | − | 1.63493i | −0.116727 | − | 0.333729i | ||||
\(25\) | 4.04993 | − | 2.93224i | 0.809987 | − | 0.586448i | ||||
\(26\) | 3.04015i | 0.596223i | ||||||||
\(27\) | 4.39860 | + | 2.76629i | 0.846510 | + | 0.532373i | ||||
\(28\) | 1.28874 | 0.243550 | ||||||||
\(29\) | 3.03143i | 0.562923i | 0.959572 | + | 0.281462i | \(0.0908192\pi\) | ||||
−0.959572 | + | 0.281462i | \(0.909181\pi\) | |||||||
\(30\) | −2.34326 | − | 3.08369i | −0.427818 | − | 0.563002i | ||||
\(31\) | −7.30904 | −1.31274 | −0.656371 | − | 0.754438i | \(-0.727909\pi\) | ||||
−0.656371 | + | 0.754438i | \(0.727909\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.58940 | − | 7.40327i | −0.450757 | − | 1.28874i | ||||
\(34\) | − | 5.73191i | − | 0.983014i | ||||||
\(35\) | 2.74141 | − | 0.888236i | 0.463383 | − | 0.150139i | ||||
\(36\) | −2.34600 | + | 1.86984i | −0.390999 | + | 0.311640i | ||||
\(37\) | −8.69205 | −1.42896 | −0.714482 | − | 0.699654i | \(-0.753338\pi\) | ||||
−0.714482 | + | 0.699654i | \(0.753338\pi\) | |||||||
\(38\) | 3.52988i | 0.572623i | ||||||||
\(39\) | 4.97044 | − | 1.73848i | 0.795907 | − | 0.278380i | ||||
\(40\) | 2.12720 | − | 0.689226i | 0.336339 | − | 0.108976i | ||||
\(41\) | − | 12.7037i | − | 1.98399i | −0.126290 | − | 0.991993i | \(-0.540307\pi\) | ||
0.126290 | − | 0.991993i | \(-0.459693\pi\) | |||||||
\(42\) | −0.736956 | − | 2.10701i | −0.113715 | − | 0.325118i | ||||
\(43\) | 8.85037 | 1.34967 | 0.674834 | − | 0.737969i | \(-0.264215\pi\) | ||||
0.674834 | + | 0.737969i | \(0.264215\pi\) | |||||||
\(44\) | 4.52819 | 0.682650 | ||||||||
\(45\) | −3.70165 | + | 5.59444i | −0.551810 | + | 0.833970i | ||||
\(46\) | −4.79401 | − | 0.132152i | −0.706838 | − | 0.0194847i | ||||
\(47\) | −3.48815 | −0.508799 | −0.254400 | − | 0.967099i | \(-0.581878\pi\) | ||||
−0.254400 | + | 0.967099i | \(0.581878\pi\) | |||||||
\(48\) | −0.571841 | − | 1.63493i | −0.0825381 | − | 0.235982i | ||||
\(49\) | −5.33914 | −0.762734 | ||||||||
\(50\) | 4.04993 | − | 2.93224i | 0.572747 | − | 0.414681i | ||||
\(51\) | −9.37127 | + | 3.27774i | −1.31224 | + | 0.458975i | ||||
\(52\) | 3.04015i | 0.421593i | ||||||||
\(53\) | − | 4.54605i | − | 0.624448i | −0.950008 | − | 0.312224i | \(-0.898926\pi\) | ||
0.950008 | − | 0.312224i | \(-0.101074\pi\) | |||||||
\(54\) | 4.39860 | + | 2.76629i | 0.598573 | + | 0.376444i | ||||
\(55\) | 9.63235 | − | 3.12095i | 1.29883 | − | 0.420829i | ||||
\(56\) | 1.28874 | 0.172216 | ||||||||
\(57\) | 5.77111 | − | 2.01853i | 0.764403 | − | 0.267361i | ||||
\(58\) | 3.03143i | 0.398047i | ||||||||
\(59\) | 12.7816i | 1.66402i | 0.554757 | + | 0.832012i | \(0.312811\pi\) | ||||
−0.554757 | + | 0.832012i | \(0.687189\pi\) | |||||||
\(60\) | −2.34326 | − | 3.08369i | −0.302513 | − | 0.398103i | ||||
\(61\) | 3.04124i | 0.389391i | 0.980864 | + | 0.194696i | \(0.0623719\pi\) | ||||
−0.980864 | + | 0.194696i | \(0.937628\pi\) | |||||||
\(62\) | −7.30904 | −0.928249 | ||||||||
\(63\) | −3.02339 | + | 2.40974i | −0.380911 | + | 0.303599i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.09535 | + | 6.46700i | 0.259897 | + | 0.802133i | ||||
\(66\) | −2.58940 | − | 7.40327i | −0.318734 | − | 0.911280i | ||||
\(67\) | 3.98470 | 0.486808 | 0.243404 | − | 0.969925i | \(-0.421736\pi\) | ||||
0.243404 | + | 0.969925i | \(0.421736\pi\) | |||||||
\(68\) | − | 5.73191i | − | 0.695096i | ||||||
\(69\) | 2.52535 | + | 7.91344i | 0.304017 | + | 0.952667i | ||||
\(70\) | 2.74141 | − | 0.888236i | 0.327661 | − | 0.106165i | ||||
\(71\) | − | 5.30287i | − | 0.629335i | −0.949202 | − | 0.314667i | \(-0.898107\pi\) | ||
0.949202 | − | 0.314667i | \(-0.101893\pi\) | |||||||
\(72\) | −2.34600 | + | 1.86984i | −0.276478 | + | 0.220363i | ||||
\(73\) | 9.43385i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186164\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813836\pi\) | |||||||
\(74\) | −8.69205 | −1.01043 | ||||||||
\(75\) | −7.10993 | − | 4.94459i | −0.820984 | − | 0.570952i | ||||
\(76\) | 3.52988i | 0.404905i | ||||||||
\(77\) | 5.83567 | 0.665037 | ||||||||
\(78\) | 4.97044 | − | 1.73848i | 0.562791 | − | 0.196844i | ||||
\(79\) | 16.0456i | 1.80527i | 0.430410 | + | 0.902633i | \(0.358369\pi\) | ||||
−0.430410 | + | 0.902633i | \(0.641631\pi\) | |||||||
\(80\) | 2.12720 | − | 0.689226i | 0.237828 | − | 0.0770579i | ||||
\(81\) | 2.00739 | − | 8.77328i | 0.223044 | − | 0.974808i | ||||
\(82\) | − | 12.7037i | − | 1.40289i | ||||||
\(83\) | − | 8.09448i | − | 0.888484i | −0.895907 | − | 0.444242i | \(-0.853473\pi\) | ||
0.895907 | − | 0.444242i | \(-0.146527\pi\) | |||||||
\(84\) | −0.736956 | − | 2.10701i | −0.0804085 | − | 0.229893i | ||||
\(85\) | −3.95058 | − | 12.1929i | −0.428501 | − | 1.32250i | ||||
\(86\) | 8.85037 | 0.954360 | ||||||||
\(87\) | 4.95619 | − | 1.73350i | 0.531359 | − | 0.185851i | ||||
\(88\) | 4.52819 | 0.482707 | ||||||||
\(89\) | 6.63721 | 0.703543 | 0.351772 | − | 0.936086i | \(-0.385579\pi\) | ||||
0.351772 | + | 0.936086i | \(0.385579\pi\) | |||||||
\(90\) | −3.70165 | + | 5.59444i | −0.390188 | + | 0.589706i | ||||
\(91\) | 3.91797i | 0.410715i | ||||||||
\(92\) | −4.79401 | − | 0.132152i | −0.499810 | − | 0.0137778i | ||||
\(93\) | 4.17961 | + | 11.9498i | 0.433405 | + | 1.23913i | ||||
\(94\) | −3.48815 | −0.359776 | ||||||||
\(95\) | 2.43289 | + | 7.50876i | 0.249609 | + | 0.770382i | ||||
\(96\) | −0.571841 | − | 1.63493i | −0.0583633 | − | 0.166864i | ||||
\(97\) | 0.0268467 | 0.00272587 | 0.00136294 | − | 0.999999i | \(-0.499566\pi\) | ||||
0.00136294 | + | 0.999999i | \(0.499566\pi\) | |||||||
\(98\) | −5.33914 | −0.539335 | ||||||||
\(99\) | −10.6231 | + | 8.46699i | −1.06766 | + | 0.850965i | ||||
\(100\) | 4.04993 | − | 2.93224i | 0.404993 | − | 0.293224i | ||||
\(101\) | − | 1.23854i | − | 0.123239i | −0.998100 | − | 0.0616195i | \(-0.980373\pi\) | ||
0.998100 | − | 0.0616195i | \(-0.0196265\pi\) | |||||||
\(102\) | −9.37127 | + | 3.27774i | −0.927894 | + | 0.324544i | ||||
\(103\) | −15.0918 | −1.48704 | −0.743520 | − | 0.668714i | \(-0.766845\pi\) | ||||
−0.743520 | + | 0.668714i | \(0.766845\pi\) | |||||||
\(104\) | 3.04015i | 0.298111i | ||||||||
\(105\) | −3.01986 | − | 3.97409i | −0.294708 | − | 0.387831i | ||||
\(106\) | − | 4.54605i | − | 0.441552i | ||||||
\(107\) | 16.5225i | 1.59729i | 0.601802 | + | 0.798645i | \(0.294450\pi\) | ||||
−0.601802 | + | 0.798645i | \(0.705550\pi\) | |||||||
\(108\) | 4.39860 | + | 2.76629i | 0.423255 | + | 0.266186i | ||||
\(109\) | − | 17.0974i | − | 1.63764i | −0.574053 | − | 0.818818i | \(-0.694630\pi\) | ||
0.574053 | − | 0.818818i | \(-0.305370\pi\) | |||||||
\(110\) | 9.63235 | − | 3.12095i | 0.918409 | − | 0.297571i | ||||
\(111\) | 4.97047 | + | 14.2109i | 0.471776 | + | 1.34884i | ||||
\(112\) | 1.28874 | 0.121775 | ||||||||
\(113\) | 17.3017i | 1.62761i | 0.581139 | + | 0.813804i | \(0.302607\pi\) | ||||
−0.581139 | + | 0.813804i | \(0.697393\pi\) | |||||||
\(114\) | 5.77111 | − | 2.01853i | 0.540514 | − | 0.189053i | ||||
\(115\) | −10.2889 | + | 3.02305i | −0.959444 | + | 0.281901i | ||||
\(116\) | 3.03143i | 0.281462i | ||||||||
\(117\) | −5.68460 | − | 7.13218i | −0.525541 | − | 0.659371i | ||||
\(118\) | 12.7816i | 1.17664i | ||||||||
\(119\) | − | 7.38696i | − | 0.677161i | ||||||
\(120\) | −2.34326 | − | 3.08369i | −0.213909 | − | 0.281501i | ||||
\(121\) | 9.50450 | 0.864045 | ||||||||
\(122\) | 3.04124i | 0.275341i | ||||||||
\(123\) | −20.7697 | + | 7.26450i | −1.87274 | + | 0.655018i | ||||
\(124\) | −7.30904 | −0.656371 | ||||||||
\(125\) | 6.59403 | − | 9.02878i | 0.589788 | − | 0.807558i | ||||
\(126\) | −3.02339 | + | 2.40974i | −0.269345 | + | 0.214677i | ||||
\(127\) | 6.86184i | 0.608890i | 0.952530 | + | 0.304445i | \(0.0984709\pi\) | ||||
−0.952530 | + | 0.304445i | \(0.901529\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.06100 | − | 14.4697i | −0.445596 | − | 1.27399i | ||||
\(130\) | 2.09535 | + | 6.46700i | 0.183775 | + | 0.567193i | ||||
\(131\) | 0.675240i | 0.0589960i | 0.999565 | + | 0.0294980i | \(0.00939087\pi\) | ||||
−0.999565 | + | 0.0294980i | \(0.990609\pi\) | |||||||
\(132\) | −2.58940 | − | 7.40327i | −0.225379 | − | 0.644372i | ||||
\(133\) | 4.54911i | 0.394458i | ||||||||
\(134\) | 3.98470 | 0.344225 | ||||||||
\(135\) | 11.2633 | + | 2.85281i | 0.969389 | + | 0.245531i | ||||
\(136\) | − | 5.73191i | − | 0.491507i | ||||||
\(137\) | 6.14111i | 0.524670i | 0.964977 | + | 0.262335i | \(0.0844926\pi\) | ||||
−0.964977 | + | 0.262335i | \(0.915507\pi\) | |||||||
\(138\) | 2.52535 | + | 7.91344i | 0.214972 | + | 0.673637i | ||||
\(139\) | −13.8754 | −1.17689 | −0.588447 | − | 0.808536i | \(-0.700261\pi\) | ||||
−0.588447 | + | 0.808536i | \(0.700261\pi\) | |||||||
\(140\) | 2.74141 | − | 0.888236i | 0.231692 | − | 0.0750697i | ||||
\(141\) | 1.99467 | + | 5.70289i | 0.167981 | + | 0.480270i | ||||
\(142\) | − | 5.30287i | − | 0.445007i | ||||||
\(143\) | 13.7664i | 1.15120i | ||||||||
\(144\) | −2.34600 | + | 1.86984i | −0.195500 | + | 0.155820i | ||||
\(145\) | 2.08935 | + | 6.44846i | 0.173511 | + | 0.535515i | ||||
\(146\) | 9.43385i | 0.780751i | ||||||||
\(147\) | 3.05314 | + | 8.72912i | 0.251819 | + | 0.719966i | ||||
\(148\) | −8.69205 | −0.714482 | ||||||||
\(149\) | 12.8749 | 1.05475 | 0.527377 | − | 0.849631i | \(-0.323175\pi\) | ||||
0.527377 | + | 0.849631i | \(0.323175\pi\) | |||||||
\(150\) | −7.10993 | − | 4.94459i | −0.580523 | − | 0.403724i | ||||
\(151\) | −4.34447 | −0.353548 | −0.176774 | − | 0.984251i | \(-0.556566\pi\) | ||||
−0.176774 | + | 0.984251i | \(0.556566\pi\) | |||||||
\(152\) | 3.52988i | 0.286311i | ||||||||
\(153\) | 10.7177 | + | 13.4470i | 0.866479 | + | 1.08713i | ||||
\(154\) | 5.83567 | 0.470252 | ||||||||
\(155\) | −15.5478 | + | 5.03758i | −1.24883 | + | 0.404628i | ||||
\(156\) | 4.97044 | − | 1.73848i | 0.397953 | − | 0.139190i | ||||
\(157\) | −11.9565 | −0.954234 | −0.477117 | − | 0.878840i | \(-0.658318\pi\) | ||||
−0.477117 | + | 0.878840i | \(0.658318\pi\) | |||||||
\(158\) | 16.0456i | 1.27652i | ||||||||
\(159\) | −7.43248 | + | 2.59962i | −0.589434 | + | 0.206163i | ||||
\(160\) | 2.12720 | − | 0.689226i | 0.168170 | − | 0.0544881i | ||||
\(161\) | −6.17825 | − | 0.170309i | −0.486914 | − | 0.0134223i | ||||
\(162\) | 2.00739 | − | 8.77328i | 0.157716 | − | 0.689294i | ||||
\(163\) | 4.08030i | 0.319594i | 0.987150 | + | 0.159797i | \(0.0510839\pi\) | ||||
−0.987150 | + | 0.159797i | \(0.948916\pi\) | |||||||
\(164\) | − | 12.7037i | − | 0.991993i | ||||||
\(165\) | −10.6107 | − | 13.9635i | −0.826042 | − | 1.08706i | ||||
\(166\) | − | 8.09448i | − | 0.628253i | ||||||
\(167\) | 5.57148 | 0.431134 | 0.215567 | − | 0.976489i | \(-0.430840\pi\) | ||||
0.215567 | + | 0.976489i | \(0.430840\pi\) | |||||||
\(168\) | −0.736956 | − | 2.10701i | −0.0568574 | − | 0.162559i | ||||
\(169\) | 3.75748 | 0.289037 | ||||||||
\(170\) | −3.95058 | − | 12.1929i | −0.302996 | − | 0.935152i | ||||
\(171\) | −6.60032 | − | 8.28109i | −0.504739 | − | 0.633271i | ||||
\(172\) | 8.85037 | 0.674834 | ||||||||
\(173\) | 11.6414 | 0.885082 | 0.442541 | − | 0.896748i | \(-0.354077\pi\) | ||||
0.442541 | + | 0.896748i | \(0.354077\pi\) | |||||||
\(174\) | 4.95619 | − | 1.73350i | 0.375727 | − | 0.131416i | ||||
\(175\) | 5.21933 | − | 3.77891i | 0.394544 | − | 0.285658i | ||||
\(176\) | 4.52819 | 0.341325 | ||||||||
\(177\) | 20.8971 | − | 7.30905i | 1.57072 | − | 0.549382i | ||||
\(178\) | 6.63721 | 0.497480 | ||||||||
\(179\) | 6.37813i | 0.476724i | 0.971176 | + | 0.238362i | \(0.0766104\pi\) | ||||
−0.971176 | + | 0.238362i | \(0.923390\pi\) | |||||||
\(180\) | −3.70165 | + | 5.59444i | −0.275905 | + | 0.416985i | ||||
\(181\) | − | 7.84733i | − | 0.583287i | −0.956527 | − | 0.291644i | \(-0.905798\pi\) | ||
0.956527 | − | 0.291644i | \(-0.0942022\pi\) | |||||||
\(182\) | 3.91797i | 0.290420i | ||||||||
\(183\) | 4.97222 | − | 1.73911i | 0.367557 | − | 0.128559i | ||||
\(184\) | −4.79401 | − | 0.132152i | −0.353419 | − | 0.00974234i | ||||
\(185\) | −18.4897 | + | 5.99079i | −1.35939 | + | 0.440452i | ||||
\(186\) | 4.17961 | + | 11.9498i | 0.306464 | + | 0.876200i | ||||
\(187\) | − | 25.9552i | − | 1.89803i | ||||||
\(188\) | −3.48815 | −0.254400 | ||||||||
\(189\) | 5.66866 | + | 3.56504i | 0.412334 | + | 0.259318i | ||||
\(190\) | 2.43289 | + | 7.50876i | 0.176500 | + | 0.544742i | ||||
\(191\) | −6.06089 | −0.438550 | −0.219275 | − | 0.975663i | \(-0.570369\pi\) | ||||
−0.219275 | + | 0.975663i | \(0.570369\pi\) | |||||||
\(192\) | −0.571841 | − | 1.63493i | −0.0412691 | − | 0.117991i | ||||
\(193\) | 4.83220i | 0.347829i | 0.984761 | + | 0.173915i | \(0.0556417\pi\) | ||||
−0.984761 | + | 0.173915i | \(0.944358\pi\) | |||||||
\(194\) | 0.0268467 | 0.00192748 | ||||||||
\(195\) | 9.37489 | − | 7.12385i | 0.671350 | − | 0.510150i | ||||
\(196\) | −5.33914 | −0.381367 | ||||||||
\(197\) | −12.3455 | −0.879581 | −0.439790 | − | 0.898101i | \(-0.644947\pi\) | ||||
−0.439790 | + | 0.898101i | \(0.644947\pi\) | |||||||
\(198\) | −10.6231 | + | 8.46699i | −0.754952 | + | 0.601723i | ||||
\(199\) | − | 4.31745i | − | 0.306056i | −0.988222 | − | 0.153028i | \(-0.951098\pi\) | ||
0.988222 | − | 0.153028i | \(-0.0489024\pi\) | |||||||
\(200\) | 4.04993 | − | 2.93224i | 0.286374 | − | 0.207341i | ||||
\(201\) | −2.27861 | − | 6.51470i | −0.160721 | − | 0.459512i | ||||
\(202\) | − | 1.23854i | − | 0.0871431i | ||||||
\(203\) | 3.90674i | 0.274200i | ||||||||
\(204\) | −9.37127 | + | 3.27774i | −0.656120 | + | 0.229488i | ||||
\(205\) | −8.75574 | − | 27.0233i | −0.611527 | − | 1.88739i | ||||
\(206\) | −15.0918 | −1.05150 | ||||||||
\(207\) | 11.4938 | − | 8.65401i | 0.798877 | − | 0.601495i | ||||
\(208\) | 3.04015i | 0.210797i | ||||||||
\(209\) | 15.9840i | 1.10563i | ||||||||
\(210\) | −3.01986 | − | 3.97409i | −0.208390 | − | 0.274238i | ||||
\(211\) | 21.0772 | 1.45101 | 0.725507 | − | 0.688214i | \(-0.241605\pi\) | ||||
0.725507 | + | 0.688214i | \(0.241605\pi\) | |||||||
\(212\) | − | 4.54605i | − | 0.312224i | ||||||
\(213\) | −8.66982 | + | 3.03240i | −0.594047 | + | 0.207776i | ||||
\(214\) | 16.5225i | 1.12945i | ||||||||
\(215\) | 18.8265 | − | 6.09991i | 1.28396 | − | 0.416010i | ||||
\(216\) | 4.39860 | + | 2.76629i | 0.299287 | + | 0.188222i | ||||
\(217\) | −9.41947 | −0.639436 | ||||||||
\(218\) | − | 17.0974i | − | 1.15798i | ||||||
\(219\) | 15.4237 | − | 5.39466i | 1.04224 | − | 0.364538i | ||||
\(220\) | 9.63235 | − | 3.12095i | 0.649413 | − | 0.210414i | ||||
\(221\) | 17.4259 | 1.17219 | ||||||||
\(222\) | 4.97047 | + | 14.2109i | 0.333596 | + | 0.953773i | ||||
\(223\) | 20.9973i | 1.40608i | 0.711149 | + | 0.703042i | \(0.248175\pi\) | ||||
−0.711149 | + | 0.703042i | \(0.751825\pi\) | |||||||
\(224\) | 1.28874 | 0.0861078 | ||||||||
\(225\) | −4.01831 | + | 14.4518i | −0.267887 | + | 0.963450i | ||||
\(226\) | 17.3017i | 1.15089i | ||||||||
\(227\) | − | 5.88743i | − | 0.390762i | −0.980727 | − | 0.195381i | \(-0.937406\pi\) | ||
0.980727 | − | 0.195381i | \(-0.0625944\pi\) | |||||||
\(228\) | 5.77111 | − | 2.01853i | 0.382201 | − | 0.133680i | ||||
\(229\) | − | 22.8454i | − | 1.50967i | −0.655916 | − | 0.754834i | \(-0.727718\pi\) | ||
0.655916 | − | 0.754834i | \(-0.272282\pi\) | |||||||
\(230\) | −10.2889 | + | 3.02305i | −0.678429 | + | 0.199334i | ||||
\(231\) | −3.33708 | − | 9.54092i | −0.219564 | − | 0.627747i | ||||
\(232\) | 3.03143i | 0.199023i | ||||||||
\(233\) | −1.99467 | −0.130675 | −0.0653375 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653375 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(234\) | −5.68460 | − | 7.13218i | −0.371614 | − | 0.466245i | ||||
\(235\) | −7.41999 | + | 2.40413i | −0.484027 | + | 0.156828i | ||||
\(236\) | 12.7816i | 0.832012i | ||||||||
\(237\) | 26.2334 | − | 9.17551i | 1.70404 | − | 0.596013i | ||||
\(238\) | − | 7.38696i | − | 0.478825i | ||||||
\(239\) | − | 16.2137i | − | 1.04878i | −0.851479 | − | 0.524388i | \(-0.824294\pi\) | ||
0.851479 | − | 0.524388i | \(-0.175706\pi\) | |||||||
\(240\) | −2.34326 | − | 3.08369i | −0.151256 | − | 0.199051i | ||||
\(241\) | − | 19.7040i | − | 1.26924i | −0.772823 | − | 0.634622i | \(-0.781156\pi\) | ||
0.772823 | − | 0.634622i | \(-0.218844\pi\) | |||||||
\(242\) | 9.50450 | 0.610972 | ||||||||
\(243\) | −15.4916 | + | 1.73497i | −0.993787 | + | 0.111298i | ||||
\(244\) | 3.04124i | 0.194696i | ||||||||
\(245\) | −11.3574 | + | 3.67988i | −0.725598 | + | 0.235099i | ||||
\(246\) | −20.7697 | + | 7.26450i | −1.32423 | + | 0.463168i | ||||
\(247\) | −10.7314 | −0.682821 | ||||||||
\(248\) | −7.30904 | −0.464124 | ||||||||
\(249\) | −13.2339 | + | 4.62875i | −0.838665 | + | 0.293335i | ||||
\(250\) | 6.59403 | − | 9.02878i | 0.417043 | − | 0.571030i | ||||
\(251\) | 5.44250 | 0.343527 | 0.171764 | − | 0.985138i | \(-0.445053\pi\) | ||||
0.171764 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(252\) | −3.02339 | + | 2.40974i | −0.190455 | + | 0.151800i | ||||
\(253\) | −21.7082 | − | 0.598407i | −1.36478 | − | 0.0376215i | ||||
\(254\) | 6.86184i | 0.430550i | ||||||||
\(255\) | −17.6754 | + | 13.4313i | −1.10688 | + | 0.841102i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.2937 | −0.642105 | −0.321052 | − | 0.947061i | \(-0.604037\pi\) | ||||
−0.321052 | + | 0.947061i | \(0.604037\pi\) | |||||||
\(258\) | −5.06100 | − | 14.4697i | −0.315084 | − | 0.900847i | ||||
\(259\) | −11.2018 | −0.696047 | ||||||||
\(260\) | 2.09535 | + | 6.46700i | 0.129948 | + | 0.401066i | ||||
\(261\) | −5.66830 | − | 7.11173i | −0.350859 | − | 0.440205i | ||||
\(262\) | 0.675240i | 0.0417165i | ||||||||
\(263\) | − | 18.0484i | − | 1.11291i | −0.830877 | − | 0.556457i | \(-0.812161\pi\) | ||
0.830877 | − | 0.556457i | \(-0.187839\pi\) | |||||||
\(264\) | −2.58940 | − | 7.40327i | −0.159367 | − | 0.455640i | ||||
\(265\) | −3.13326 | − | 9.67035i | −0.192475 | − | 0.594045i | ||||
\(266\) | 4.54911i | 0.278924i | ||||||||
\(267\) | −3.79543 | − | 10.8514i | −0.232277 | − | 0.664094i | ||||
\(268\) | 3.98470 | 0.243404 | ||||||||
\(269\) | − | 5.62437i | − | 0.342924i | −0.985191 | − | 0.171462i | \(-0.945151\pi\) | ||
0.985191 | − | 0.171462i | \(-0.0548491\pi\) | |||||||
\(270\) | 11.2633 | + | 2.85281i | 0.685461 | + | 0.173617i | ||||
\(271\) | 19.4771 | 1.18315 | 0.591575 | − | 0.806250i | \(-0.298506\pi\) | ||||
0.591575 | + | 0.806250i | \(0.298506\pi\) | |||||||
\(272\) | − | 5.73191i | − | 0.347548i | ||||||
\(273\) | 6.40562 | − | 2.24046i | 0.387686 | − | 0.135599i | ||||
\(274\) | 6.14111i | 0.370998i | ||||||||
\(275\) | 18.3389 | − | 13.2777i | 1.10588 | − | 0.800678i | ||||
\(276\) | 2.52535 | + | 7.91344i | 0.152008 | + | 0.476333i | ||||
\(277\) | − | 1.53636i | − | 0.0923111i | −0.998934 | − | 0.0461555i | \(-0.985303\pi\) | ||
0.998934 | − | 0.0461555i | \(-0.0146970\pi\) | |||||||
\(278\) | −13.8754 | −0.832190 | ||||||||
\(279\) | 17.1470 | − | 13.6667i | 1.02656 | − | 0.818206i | ||||
\(280\) | 2.74141 | − | 0.888236i | 0.163831 | − | 0.0530823i | ||||
\(281\) | 6.23953 | 0.372219 | 0.186110 | − | 0.982529i | \(-0.440412\pi\) | ||||
0.186110 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(282\) | 1.99467 | + | 5.70289i | 0.118781 | + | 0.339602i | ||||
\(283\) | 7.82642 | 0.465232 | 0.232616 | − | 0.972569i | \(-0.425271\pi\) | ||||
0.232616 | + | 0.972569i | \(0.425271\pi\) | |||||||
\(284\) | − | 5.30287i | − | 0.314667i | ||||||
\(285\) | 10.8851 | − | 8.27142i | 0.644776 | − | 0.489956i | ||||
\(286\) | 13.7664i | 0.814023i | ||||||||
\(287\) | − | 16.3718i | − | 0.966398i | ||||||
\(288\) | −2.34600 | + | 1.86984i | −0.138239 | + | 0.110181i | ||||
\(289\) | −15.8547 | −0.932632 | ||||||||
\(290\) | 2.08935 | + | 6.44846i | 0.122691 | + | 0.378667i | ||||
\(291\) | −0.0153521 | − | 0.0438925i | −0.000899953 | − | 0.00257303i | ||||
\(292\) | 9.43385i | 0.552074i | ||||||||
\(293\) | − | 17.3337i | − | 1.01264i | −0.862345 | − | 0.506322i | \(-0.831005\pi\) | ||
0.862345 | − | 0.506322i | \(-0.168995\pi\) | |||||||
\(294\) | 3.05314 | + | 8.72912i | 0.178063 | + | 0.509093i | ||||
\(295\) | 8.80943 | + | 27.1890i | 0.512905 | + | 1.58301i | ||||
\(296\) | −8.69205 | −0.505215 | ||||||||
\(297\) | 19.9177 | + | 12.5263i | 1.15574 | + | 0.726849i | ||||
\(298\) | 12.8749 | 0.745824 | ||||||||
\(299\) | 0.401761 | − | 14.5745i | 0.0232344 | − | 0.842866i | ||||
\(300\) | −7.10993 | − | 4.94459i | −0.410492 | − | 0.285476i | ||||
\(301\) | 11.4059 | 0.657423 | ||||||||
\(302\) | −4.34447 | −0.249996 | ||||||||
\(303\) | −2.02492 | + | 0.708246i | −0.116329 | + | 0.0406876i | ||||
\(304\) | 3.52988i | 0.202453i | ||||||||
\(305\) | 2.09611 | + | 6.46933i | 0.120023 | + | 0.370432i | ||||
\(306\) | 10.7177 | + | 13.4470i | 0.612693 | + | 0.768715i | ||||
\(307\) | 14.6960i | 0.838745i | 0.907814 | + | 0.419373i | \(0.137750\pi\) | ||||
−0.907814 | + | 0.419373i | \(0.862250\pi\) | |||||||
\(308\) | 5.83567 | 0.332518 | ||||||||
\(309\) | 8.63011 | + | 24.6741i | 0.490950 | + | 1.40366i | ||||
\(310\) | −15.5478 | + | 5.03758i | −0.883054 | + | 0.286115i | ||||
\(311\) | 5.16495i | 0.292878i | 0.989220 | + | 0.146439i | \(0.0467811\pi\) | ||||
−0.989220 | + | 0.146439i | \(0.953219\pi\) | |||||||
\(312\) | 4.97044 | − | 1.73848i | 0.281396 | − | 0.0984222i | ||||
\(313\) | 14.4632 | 0.817509 | 0.408754 | − | 0.912644i | \(-0.365963\pi\) | ||||
0.408754 | + | 0.912644i | \(0.365963\pi\) | |||||||
\(314\) | −11.9565 | −0.674745 | ||||||||
\(315\) | −4.77048 | + | 7.20980i | −0.268786 | + | 0.406226i | ||||
\(316\) | 16.0456i | 0.902633i | ||||||||
\(317\) | −5.68991 | −0.319577 | −0.159789 | − | 0.987151i | \(-0.551081\pi\) | ||||
−0.159789 | + | 0.987151i | \(0.551081\pi\) | |||||||
\(318\) | −7.43248 | + | 2.59962i | −0.416793 | + | 0.145779i | ||||
\(319\) | 13.7269i | 0.768559i | ||||||||
\(320\) | 2.12720 | − | 0.689226i | 0.118914 | − | 0.0385289i | ||||
\(321\) | 27.0131 | − | 9.44824i | 1.50773 | − | 0.527349i | ||||
\(322\) | −6.17825 | − | 0.170309i | −0.344300 | − | 0.00949098i | ||||
\(323\) | 20.2330 | 1.12579 | ||||||||
\(324\) | 2.00739 | − | 8.77328i | 0.111522 | − | 0.487404i | ||||
\(325\) | 8.91446 | + | 12.3124i | 0.494485 | + | 0.682970i | ||||
\(326\) | 4.08030i | 0.225987i | ||||||||
\(327\) | −27.9531 | + | 9.77700i | −1.54581 | + | 0.540670i | ||||
\(328\) | − | 12.7037i | − | 0.701445i | ||||||
\(329\) | −4.49533 | −0.247836 | ||||||||
\(330\) | −10.6107 | − | 13.9635i | −0.584100 | − | 0.768667i | ||||
\(331\) | −12.3989 | −0.681506 | −0.340753 | − | 0.940153i | \(-0.610682\pi\) | ||||
−0.340753 | + | 0.940153i | \(0.610682\pi\) | |||||||
\(332\) | − | 8.09448i | − | 0.444242i | ||||||
\(333\) | 20.3915 | − | 16.2527i | 1.11745 | − | 0.890645i | ||||
\(334\) | 5.57148 | 0.304858 | ||||||||
\(335\) | 8.47624 | − | 2.74636i | 0.463106 | − | 0.150050i | ||||
\(336\) | −0.736956 | − | 2.10701i | −0.0402043 | − | 0.114947i | ||||
\(337\) | 13.5952 | 0.740575 | 0.370288 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370288 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(338\) | 3.75748 | 0.204380 | ||||||||
\(339\) | 28.2871 | − | 9.89383i | 1.53634 | − | 0.537359i | ||||
\(340\) | −3.95058 | − | 12.1929i | −0.214250 | − | 0.661252i | ||||
\(341\) | −33.0967 | −1.79229 | ||||||||
\(342\) | −6.60032 | − | 8.28109i | −0.356904 | − | 0.447790i | ||||
\(343\) | −15.9020 | −0.858627 | ||||||||
\(344\) | 8.85037 | 0.477180 | ||||||||
\(345\) | 10.8261 | + | 15.0929i | 0.582856 | + | 0.812575i | ||||
\(346\) | 11.6414 | 0.625848 | ||||||||
\(347\) | 6.55994 | 0.352156 | 0.176078 | − | 0.984376i | \(-0.443659\pi\) | ||||
0.176078 | + | 0.984376i | \(0.443659\pi\) | |||||||
\(348\) | 4.95619 | − | 1.73350i | 0.265679 | − | 0.0929253i | ||||
\(349\) | −28.1738 | −1.50811 | −0.754055 | − | 0.656811i | \(-0.771905\pi\) | ||||
−0.754055 | + | 0.656811i | \(0.771905\pi\) | |||||||
\(350\) | 5.21933 | − | 3.77891i | 0.278985 | − | 0.201991i | ||||
\(351\) | −8.40994 | + | 13.3724i | −0.448889 | + | 0.713766i | ||||
\(352\) | 4.52819 | 0.241353 | ||||||||
\(353\) | −5.76001 | −0.306574 | −0.153287 | − | 0.988182i | \(-0.548986\pi\) | ||||
−0.153287 | + | 0.988182i | \(0.548986\pi\) | |||||||
\(354\) | 20.8971 | − | 7.30905i | 1.11067 | − | 0.388472i | ||||
\(355\) | −3.65488 | − | 11.2802i | −0.193981 | − | 0.598693i | ||||
\(356\) | 6.63721 | 0.351772 | ||||||||
\(357\) | −12.0772 | + | 4.22416i | −0.639191 | + | 0.223566i | ||||
\(358\) | 6.37813i | 0.337095i | ||||||||
\(359\) | −6.40987 | −0.338300 | −0.169150 | − | 0.985590i | \(-0.554102\pi\) | ||||
−0.169150 | + | 0.985590i | \(0.554102\pi\) | |||||||
\(360\) | −3.70165 | + | 5.59444i | −0.195094 | + | 0.294853i | ||||
\(361\) | 6.53993 | 0.344207 | ||||||||
\(362\) | − | 7.84733i | − | 0.412447i | ||||||
\(363\) | −5.43506 | − | 15.5392i | −0.285267 | − | 0.815596i | ||||
\(364\) | 3.91797i | 0.205358i | ||||||||
\(365\) | 6.50206 | + | 20.0677i | 0.340333 | + | 1.05039i | ||||
\(366\) | 4.97222 | − | 1.73911i | 0.259902 | − | 0.0909046i | ||||
\(367\) | 26.8268 | 1.40035 | 0.700174 | − | 0.713972i | \(-0.253106\pi\) | ||||
0.700174 | + | 0.713972i | \(0.253106\pi\) | |||||||
\(368\) | −4.79401 | − | 0.132152i | −0.249905 | − | 0.00688888i | ||||
\(369\) | 23.7539 | + | 29.8029i | 1.23658 | + | 1.55148i | ||||
\(370\) | −18.4897 | + | 5.99079i | −0.961234 | + | 0.311446i | ||||
\(371\) | − | 5.85870i | − | 0.304168i | ||||||
\(372\) | 4.17961 | + | 11.9498i | 0.216702 | + | 0.619567i | ||||
\(373\) | −8.96103 | −0.463984 | −0.231992 | − | 0.972718i | \(-0.574524\pi\) | ||||
−0.231992 | + | 0.972718i | \(0.574524\pi\) | |||||||
\(374\) | − | 25.9552i | − | 1.34211i | ||||||
\(375\) | −18.5322 | − | 5.61776i | −0.956996 | − | 0.290100i | ||||
\(376\) | −3.48815 | −0.179888 | ||||||||
\(377\) | −9.21602 | −0.474649 | ||||||||
\(378\) | 5.66866 | + | 3.56504i | 0.291564 | + | 0.183366i | ||||
\(379\) | − | 4.30108i | − | 0.220931i | −0.993880 | − | 0.110466i | \(-0.964766\pi\) | ||
0.993880 | − | 0.110466i | \(-0.0352342\pi\) | |||||||
\(380\) | 2.43289 | + | 7.50876i | 0.124805 | + | 0.385191i | ||||
\(381\) | 11.2186 | − | 3.92388i | 0.574748 | − | 0.201026i | ||||
\(382\) | −6.06089 | −0.310102 | ||||||||
\(383\) | − | 10.2019i | − | 0.521291i | −0.965435 | − | 0.260646i | \(-0.916065\pi\) | ||
0.965435 | − | 0.260646i | \(-0.0839354\pi\) | |||||||
\(384\) | −0.571841 | − | 1.63493i | −0.0291816 | − | 0.0834322i | ||||
\(385\) | 12.4136 | − | 4.02210i | 0.632657 | − | 0.204985i | ||||
\(386\) | 4.83220i | 0.245952i | ||||||||
\(387\) | −20.7629 | + | 16.5488i | −1.05544 | + | 0.841222i | ||||
\(388\) | 0.0268467 | 0.00136294 | ||||||||
\(389\) | −10.3677 | −0.525664 | −0.262832 | − | 0.964842i | \(-0.584657\pi\) | ||||
−0.262832 | + | 0.964842i | \(0.584657\pi\) | |||||||
\(390\) | 9.37489 | − | 7.12385i | 0.474716 | − | 0.360730i | ||||
\(391\) | −0.757480 | + | 27.4788i | −0.0383074 | + | 1.38966i | ||||
\(392\) | −5.33914 | −0.269667 | ||||||||
\(393\) | 1.10397 | − | 0.386130i | 0.0556880 | − | 0.0194777i | ||||
\(394\) | −12.3455 | −0.621957 | ||||||||
\(395\) | 11.0590 | + | 34.1321i | 0.556440 | + | 1.71737i | ||||
\(396\) | −10.6231 | + | 8.46699i | −0.533832 | + | 0.425482i | ||||
\(397\) | − | 15.6662i | − | 0.786264i | −0.919482 | − | 0.393132i | \(-0.871392\pi\) | ||
0.919482 | − | 0.393132i | \(-0.128608\pi\) | |||||||
\(398\) | − | 4.31745i | − | 0.216414i | ||||||
\(399\) | 7.43748 | − | 2.60137i | 0.372340 | − | 0.130231i | ||||
\(400\) | 4.04993 | − | 2.93224i | 0.202497 | − | 0.146612i | ||||
\(401\) | 21.5559 | 1.07645 | 0.538224 | − | 0.842802i | \(-0.319095\pi\) | ||||
0.538224 | + | 0.842802i | \(0.319095\pi\) | |||||||
\(402\) | −2.27861 | − | 6.51470i | −0.113647 | − | 0.324924i | ||||
\(403\) | − | 22.2206i | − | 1.10689i | ||||||
\(404\) | − | 1.23854i | − | 0.0616195i | ||||||
\(405\) | −1.77665 | − | 20.0460i | −0.0882824 | − | 0.996095i | ||||
\(406\) | 3.90674i | 0.193888i | ||||||||
\(407\) | −39.3592 | −1.95096 | ||||||||
\(408\) | −9.37127 | + | 3.27774i | −0.463947 | + | 0.162272i | ||||
\(409\) | −32.7301 | −1.61840 | −0.809200 | − | 0.587533i | \(-0.800099\pi\) | ||||
−0.809200 | + | 0.587533i | \(0.800099\pi\) | |||||||
\(410\) | −8.75574 | − | 27.0233i | −0.432415 | − | 1.33459i | ||||
\(411\) | 10.0403 | − | 3.51174i | 0.495251 | − | 0.173221i | ||||
\(412\) | −15.0918 | −0.743520 | ||||||||
\(413\) | 16.4722i | 0.810545i | ||||||||
\(414\) | 11.4938 | − | 8.65401i | 0.564891 | − | 0.425321i | ||||
\(415\) | −5.57893 | − | 17.2185i | −0.273859 | − | 0.845225i | ||||
\(416\) | 3.04015i | 0.149056i | ||||||||
\(417\) | 7.93451 | + | 22.6853i | 0.388555 | + | 1.11090i | ||||
\(418\) | 15.9840i | 0.781802i | ||||||||
\(419\) | 3.77943 | 0.184637 | 0.0923186 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923186 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(420\) | −3.01986 | − | 3.97409i | −0.147354 | − | 0.193916i | ||||
\(421\) | 21.2423i | 1.03529i | 0.855597 | + | 0.517643i | \(0.173190\pi\) | ||||
−0.855597 | + | 0.517643i | \(0.826810\pi\) | |||||||
\(422\) | 21.0772 | 1.02602 | ||||||||
\(423\) | 8.18319 | − | 6.52229i | 0.397881 | − | 0.317125i | ||||
\(424\) | − | 4.54605i | − | 0.220776i | ||||||
\(425\) | −16.8073 | − | 23.2138i | −0.815275 | − | 1.12604i | ||||
\(426\) | −8.66982 | + | 3.03240i | −0.420054 | + | 0.146920i | ||||
\(427\) | 3.91938i | 0.189672i | ||||||||
\(428\) | 16.5225i | 0.798645i | ||||||||
\(429\) | 22.5071 | − | 7.87218i | 1.08665 | − | 0.380072i | ||||
\(430\) | 18.8265 | − | 6.09991i | 0.907893 | − | 0.294164i | ||||
\(431\) | −15.0460 | −0.724742 | −0.362371 | − | 0.932034i | \(-0.618033\pi\) | ||||
−0.362371 | + | 0.932034i | \(0.618033\pi\) | |||||||
\(432\) | 4.39860 | + | 2.76629i | 0.211628 | + | 0.133093i | ||||
\(433\) | −1.05773 | −0.0508313 | −0.0254157 | − | 0.999677i | \(-0.508091\pi\) | ||||
−0.0254157 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(434\) | −9.41947 | −0.452149 | ||||||||
\(435\) | 9.34801 | − | 7.10343i | 0.448203 | − | 0.340583i | ||||
\(436\) | − | 17.0974i | − | 0.818818i | ||||||
\(437\) | 0.466480 | − | 16.9223i | 0.0223147 | − | 0.809503i | ||||
\(438\) | 15.4237 | − | 5.39466i | 0.736973 | − | 0.257767i | ||||
\(439\) | 15.4166 | 0.735795 | 0.367897 | − | 0.929866i | \(-0.380078\pi\) | ||||
0.367897 | + | 0.929866i | \(0.380078\pi\) | |||||||
\(440\) | 9.63235 | − | 3.12095i | 0.459204 | − | 0.148785i | ||||
\(441\) | 12.5256 | − | 9.98334i | 0.596457 | − | 0.475397i | ||||
\(442\) | 17.4259 | 0.828864 | ||||||||
\(443\) | −19.2882 | −0.916410 | −0.458205 | − | 0.888847i | \(-0.651507\pi\) | ||||
−0.458205 | + | 0.888847i | \(0.651507\pi\) | |||||||
\(444\) | 4.97047 | + | 14.2109i | 0.235888 | + | 0.674419i | ||||
\(445\) | 14.1187 | − | 4.57454i | 0.669289 | − | 0.216854i | ||||
\(446\) | 20.9973i | 0.994251i | ||||||||
\(447\) | −7.36241 | − | 21.0496i | −0.348230 | − | 0.995612i | ||||
\(448\) | 1.28874 | 0.0608874 | ||||||||
\(449\) | − | 2.45364i | − | 0.115794i | −0.998323 | − | 0.0578972i | \(-0.981560\pi\) | ||
0.998323 | − | 0.0578972i | \(-0.0184395\pi\) | |||||||
\(450\) | −4.01831 | + | 14.4518i | −0.189425 | + | 0.681262i | ||||
\(451\) | − | 57.5248i | − | 2.70874i | ||||||
\(452\) | 17.3017i | 0.813804i | ||||||||
\(453\) | 2.48435 | + | 7.10291i | 0.116725 | + | 0.333724i | ||||
\(454\) | − | 5.88743i | − | 0.276311i | ||||||
\(455\) | 2.70037 | + | 8.33430i | 0.126595 | + | 0.390718i | ||||
\(456\) | 5.77111 | − | 2.01853i | 0.270257 | − | 0.0945264i | ||||
\(457\) | 31.5879 | 1.47762 | 0.738809 | − | 0.673915i | \(-0.235389\pi\) | ||||
0.738809 | + | 0.673915i | \(0.235389\pi\) | |||||||
\(458\) | − | 22.8454i | − | 1.06750i | ||||||
\(459\) | 15.8561 | − | 25.2123i | 0.740100 | − | 1.17681i | ||||
\(460\) | −10.2889 | + | 3.02305i | −0.479722 | + | 0.140950i | ||||
\(461\) | − | 30.5064i | − | 1.42082i | −0.703786 | − | 0.710412i | \(-0.748509\pi\) | ||
0.703786 | − | 0.710412i | \(-0.251491\pi\) | |||||||
\(462\) | −3.33708 | − | 9.54092i | −0.155255 | − | 0.443884i | ||||
\(463\) | − | 14.9598i | − | 0.695241i | −0.937635 | − | 0.347620i | \(-0.886990\pi\) | ||
0.937635 | − | 0.347620i | \(-0.113010\pi\) | |||||||
\(464\) | 3.03143i | 0.140731i | ||||||||
\(465\) | 17.1269 | + | 22.5388i | 0.794243 | + | 1.04521i | ||||
\(466\) | −1.99467 | −0.0924012 | ||||||||
\(467\) | − | 31.8778i | − | 1.47513i | −0.675277 | − | 0.737564i | \(-0.735976\pi\) | ||
0.675277 | − | 0.737564i | \(-0.264024\pi\) | |||||||
\(468\) | −5.68460 | − | 7.13218i | −0.262771 | − | 0.329685i | ||||
\(469\) | 5.13525 | 0.237124 | ||||||||
\(470\) | −7.41999 | + | 2.40413i | −0.342259 | + | 0.110894i | ||||
\(471\) | 6.83722 | + | 19.5481i | 0.315043 | + | 0.900728i | ||||
\(472\) | 12.7816i | 0.588322i | ||||||||
\(473\) | 40.0761 | 1.84270 | ||||||||
\(474\) | 26.2334 | − | 9.17551i | 1.20494 | − | 0.421445i | ||||
\(475\) | 10.3505 | + | 14.2958i | 0.474912 | + | 0.655936i | ||||
\(476\) | − | 7.38696i | − | 0.338581i | ||||||
\(477\) | 8.50039 | + | 10.6650i | 0.389206 | + | 0.488318i | ||||
\(478\) | − | 16.2137i | − | 0.741597i | ||||||
\(479\) | −16.8162 | −0.768351 | −0.384175 | − | 0.923260i | \(-0.625514\pi\) | ||||
−0.384175 | + | 0.923260i | \(0.625514\pi\) | |||||||
\(480\) | −2.34326 | − | 3.08369i | −0.106954 | − | 0.140751i | ||||
\(481\) | − | 26.4251i | − | 1.20488i | ||||||
\(482\) | − | 19.7040i | − | 0.897491i | ||||||
\(483\) | 3.25453 | + | 10.1984i | 0.148086 | + | 0.464043i | ||||
\(484\) | 9.50450 | 0.432023 | ||||||||
\(485\) | 0.0571083 | − | 0.0185035i | 0.00259315 | − | 0.000840199i | ||||
\(486\) | −15.4916 | + | 1.73497i | −0.702714 | + | 0.0786997i | ||||
\(487\) | − | 8.87949i | − | 0.402368i | −0.979553 | − | 0.201184i | \(-0.935521\pi\) | ||
0.979553 | − | 0.201184i | \(-0.0644789\pi\) | |||||||
\(488\) | 3.04124i | 0.137671i | ||||||||
\(489\) | 6.67101 | − | 2.33328i | 0.301673 | − | 0.105515i | ||||
\(490\) | −11.3574 | + | 3.67988i | −0.513075 | + | 0.166240i | ||||
\(491\) | 2.36576i | 0.106765i | 0.998574 | + | 0.0533827i | \(0.0170003\pi\) | ||||
−0.998574 | + | 0.0533827i | \(0.983000\pi\) | |||||||
\(492\) | −20.7697 | + | 7.26450i | −0.936370 | + | 0.327509i | ||||
\(493\) | 17.3759 | 0.782571 | ||||||||
\(494\) | −10.7314 | −0.482827 | ||||||||
\(495\) | −16.7618 | + | 25.3327i | −0.753386 | + | 1.13862i | ||||
\(496\) | −7.30904 | −0.328185 | ||||||||
\(497\) | − | 6.83404i | − | 0.306548i | ||||||
\(498\) | −13.2339 | + | 4.62875i | −0.593026 | + | 0.207419i | ||||
\(499\) | −15.7984 | −0.707234 | −0.353617 | − | 0.935390i | \(-0.615048\pi\) | ||||
−0.353617 | + | 0.935390i | \(0.615048\pi\) | |||||||
\(500\) | 6.59403 | − | 9.02878i | 0.294894 | − | 0.403779i | ||||
\(501\) | −3.18600 | − | 9.10898i | −0.142340 | − | 0.406959i | ||||
\(502\) | 5.44250 | 0.242910 | ||||||||
\(503\) | − | 14.9574i | − | 0.666916i | −0.942765 | − | 0.333458i | \(-0.891784\pi\) | ||
0.942765 | − | 0.333458i | \(-0.108216\pi\) | |||||||
\(504\) | −3.02339 | + | 2.40974i | −0.134672 | + | 0.107339i | ||||
\(505\) | −0.853632 | − | 2.63461i | −0.0379861 | − | 0.117239i | ||||
\(506\) | −21.7082 | − | 0.598407i | −0.965047 | − | 0.0266025i | ||||
\(507\) | −2.14868 | − | 6.14322i | −0.0954263 | − | 0.272830i | ||||
\(508\) | 6.86184i | 0.304445i | ||||||||
\(509\) | − | 5.36677i | − | 0.237878i | −0.992902 | − | 0.118939i | \(-0.962051\pi\) | ||
0.992902 | − | 0.118939i | \(-0.0379492\pi\) | |||||||
\(510\) | −17.6754 | + | 13.4313i | −0.782681 | + | 0.594749i | ||||
\(511\) | 12.1578i | 0.537830i | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.76468 | + | 15.5265i | −0.431121 | + | 0.685513i | ||||
\(514\) | −10.2937 | −0.454037 | ||||||||
\(515\) | −32.1033 | + | 10.4017i | −1.41464 | + | 0.458353i | ||||
\(516\) | −5.06100 | − | 14.4697i | −0.222798 | − | 0.636995i | ||||
\(517\) | −15.7950 | −0.694664 | ||||||||
\(518\) | −11.2018 | −0.492180 | ||||||||
\(519\) | −6.65705 | − | 19.0330i | −0.292212 | − | 0.835454i | ||||
\(520\) | 2.09535 | + | 6.46700i | 0.0918873 | + | 0.283597i | ||||
\(521\) | −32.7112 | −1.43310 | −0.716551 | − | 0.697535i | \(-0.754280\pi\) | ||||
−0.716551 | + | 0.697535i | \(0.754280\pi\) | |||||||
\(522\) | −5.66830 | − | 7.11173i | −0.248095 | − | 0.311272i | ||||
\(523\) | 13.9174 | 0.608567 | 0.304284 | − | 0.952582i | \(-0.401583\pi\) | ||||
0.304284 | + | 0.952582i | \(0.401583\pi\) | |||||||
\(524\) | 0.675240i | 0.0294980i | ||||||||
\(525\) | −9.16287 | − | 6.37230i | −0.399901 | − | 0.278110i | ||||
\(526\) | − | 18.0484i | − | 0.786948i | ||||||
\(527\) | 41.8947i | 1.82496i | ||||||||
\(528\) | −2.58940 | − | 7.40327i | −0.112689 | − | 0.322186i | ||||
\(529\) | 22.9651 | + | 1.26707i | 0.998481 | + | 0.0550901i | ||||
\(530\) | −3.13326 | − | 9.67035i | −0.136100 | − | 0.420053i | ||||
\(531\) | −23.8996 | − | 29.9856i | −1.03715 | − | 1.30127i | ||||
\(532\) | 4.54911i | 0.197229i | ||||||||
\(533\) | 38.6212 | 1.67287 | ||||||||
\(534\) | −3.79543 | − | 10.8514i | −0.164244 | − | 0.469585i | ||||
\(535\) | 11.3877 | + | 35.1466i | 0.492335 | + | 1.51952i | ||||
\(536\) | 3.98470 | 0.172113 | ||||||||
\(537\) | 10.4278 | − | 3.64727i | 0.449993 | − | 0.157392i | ||||
\(538\) | − | 5.62437i | − | 0.242484i | ||||||
\(539\) | −24.1766 | −1.04136 | ||||||||
\(540\) | 11.2633 | + | 2.85281i | 0.484694 | + | 0.122766i | ||||
\(541\) | 13.3952 | 0.575904 | 0.287952 | − | 0.957645i | \(-0.407026\pi\) | ||||
0.287952 | + | 0.957645i | \(0.407026\pi\) | |||||||
\(542\) | 19.4771 | 0.836614 | ||||||||
\(543\) | −12.8298 | + | 4.48742i | −0.550581 | + | 0.192574i | ||||
\(544\) | − | 5.73191i | − | 0.245753i | ||||||
\(545\) | −11.7840 | − | 36.3696i | −0.504771 | − | 1.55790i | ||||
\(546\) | 6.40562 | − | 2.24046i | 0.274135 | − | 0.0958828i | ||||
\(547\) | 39.1904i | 1.67566i | 0.545931 | + | 0.837830i | \(0.316176\pi\) | ||||
−0.545931 | + | 0.837830i | \(0.683824\pi\) | |||||||
\(548\) | 6.14111i | 0.262335i | ||||||||
\(549\) | −5.68664 | − | 7.13475i | −0.242700 | − | 0.304504i | ||||
\(550\) | 18.3389 | − | 13.2777i | 0.781972 | − | 0.566165i | ||||
\(551\) | −10.7006 | −0.455861 | ||||||||
\(552\) | 2.52535 | + | 7.91344i | 0.107486 | + | 0.336819i | ||||
\(553\) | 20.6786i | 0.879344i | ||||||||
\(554\) | − | 1.53636i | − | 0.0652738i | ||||||
\(555\) | 20.3677 | + | 26.8036i | 0.864560 | + | 1.13775i | ||||
\(556\) | −13.8754 | −0.588447 | ||||||||
\(557\) | 17.4131i | 0.737816i | 0.929466 | + | 0.368908i | \(0.120268\pi\) | ||||
−0.929466 | + | 0.368908i | \(0.879732\pi\) | |||||||
\(558\) | 17.1470 | − | 13.6667i | 0.725889 | − | 0.578559i | ||||
\(559\) | 26.9065i | 1.13802i | ||||||||
\(560\) | 2.74141 | − | 0.888236i | 0.115846 | − | 0.0375348i | ||||
\(561\) | −42.4349 | + | 14.8422i | −1.79160 | + | 0.626639i | ||||
\(562\) | 6.23953 | 0.263199 | ||||||||
\(563\) | 14.0445i | 0.591904i | 0.955203 | + | 0.295952i | \(0.0956369\pi\) | ||||
−0.955203 | + | 0.295952i | \(0.904363\pi\) | |||||||
\(564\) | 1.99467 | + | 5.70289i | 0.0839907 | + | 0.240135i | ||||
\(565\) | 11.9248 | + | 36.8042i | 0.501680 | + | 1.54836i | ||||
\(566\) | 7.82642 | 0.328969 | ||||||||
\(567\) | 2.58702 | − | 11.3065i | 0.108645 | − | 0.474828i | ||||
\(568\) | − | 5.30287i | − | 0.222503i | ||||||
\(569\) | −26.6443 | −1.11699 | −0.558493 | − | 0.829509i | \(-0.688620\pi\) | ||||
−0.558493 | + | 0.829509i | \(0.688620\pi\) | |||||||
\(570\) | 10.8851 | − | 8.27142i | 0.455925 | − | 0.346452i | ||||
\(571\) | 25.3537i | 1.06102i | 0.847679 | + | 0.530509i | \(0.177999\pi\) | ||||
−0.847679 | + | 0.530509i | \(0.822001\pi\) | |||||||
\(572\) | 13.7664i | 0.575601i | ||||||||
\(573\) | 3.46586 | + | 9.90913i | 0.144788 | + | 0.413960i | ||||
\(574\) | − | 16.3718i | − | 0.683347i | ||||||
\(575\) | −19.8029 | + | 13.5220i | −0.825839 | + | 0.563906i | ||||
\(576\) | −2.34600 | + | 1.86984i | −0.0977498 | + | 0.0779100i | ||||
\(577\) | − | 13.6359i | − | 0.567669i | −0.958873 | − | 0.283835i | \(-0.908393\pi\) | ||
0.958873 | − | 0.283835i | \(-0.0916067\pi\) | |||||||
\(578\) | −15.8547 | −0.659470 | ||||||||
\(579\) | 7.90030 | − | 2.76325i | 0.328325 | − | 0.114837i | ||||
\(580\) | 2.08935 | + | 6.44846i | 0.0867553 | + | 0.267758i | ||||
\(581\) | − | 10.4317i | − | 0.432780i | ||||||
\(582\) | −0.0153521 | − | 0.0438925i | −0.000636363 | − | 0.00181940i | ||||
\(583\) | − | 20.5854i | − | 0.852560i | ||||||
\(584\) | 9.43385i | 0.390376i | ||||||||
\(585\) | −17.0079 | − | 11.2536i | −0.703192 | − | 0.465278i | ||||
\(586\) | − | 17.3337i | − | 0.716047i | ||||||
\(587\) | −2.20981 | −0.0912086 | −0.0456043 | − | 0.998960i | \(-0.514521\pi\) | ||||
−0.0456043 | + | 0.998960i | \(0.514521\pi\) | |||||||
\(588\) | 3.05314 | + | 8.72912i | 0.125909 | + | 0.359983i | ||||
\(589\) | − | 25.8000i | − | 1.06307i | ||||||
\(590\) | 8.80943 | + | 27.1890i | 0.362678 | + | 1.11935i | ||||
\(591\) | 7.05966 | + | 20.1840i | 0.290396 | + | 0.830260i | ||||
\(592\) | −8.69205 | −0.357241 | ||||||||
\(593\) | −38.0686 | −1.56329 | −0.781646 | − | 0.623723i | \(-0.785619\pi\) | ||||
−0.781646 | + | 0.623723i | \(0.785619\pi\) | |||||||
\(594\) | 19.9177 | + | 12.5263i | 0.817232 | + | 0.513960i | ||||
\(595\) | −5.09129 | − | 15.7135i | −0.208722 | − | 0.644191i | ||||
\(596\) | 12.8749 | 0.527377 | ||||||||
\(597\) | −7.05873 | + | 2.46889i | −0.288895 | + | 0.101045i | ||||
\(598\) | 0.401761 | − | 14.5745i | 0.0164292 | − | 0.595996i | ||||
\(599\) | 11.0815i | 0.452780i | 0.974037 | + | 0.226390i | \(0.0726923\pi\) | ||||
−0.974037 | + | 0.226390i | \(0.927308\pi\) | |||||||
\(600\) | −7.10993 | − | 4.94459i | −0.290262 | − | 0.201862i | ||||
\(601\) | −17.3266 | −0.706767 | −0.353384 | − | 0.935479i | \(-0.614969\pi\) | ||||
−0.353384 | + | 0.935479i | \(0.614969\pi\) | |||||||
\(602\) | 11.4059 | 0.464868 | ||||||||
\(603\) | −9.34808 | + | 7.45075i | −0.380683 | + | 0.303418i | ||||
\(604\) | −4.34447 | −0.176774 | ||||||||
\(605\) | 20.2179 | − | 6.55075i | 0.821976 | − | 0.266326i | ||||
\(606\) | −2.02492 | + | 0.708246i | −0.0822568 | + | 0.0287705i | ||||
\(607\) | 19.9355i | 0.809157i | 0.914503 | + | 0.404578i | \(0.132582\pi\) | ||||
−0.914503 | + | 0.404578i | \(0.867418\pi\) | |||||||
\(608\) | 3.52988i | 0.143156i | ||||||||
\(609\) | 6.38725 | − | 2.23403i | 0.258824 | − | 0.0905277i | ||||
\(610\) | 2.09611 | + | 6.46933i | 0.0848689 | + | 0.261935i | ||||
\(611\) | − | 10.6045i | − | 0.429013i | ||||||
\(612\) | 10.7177 | + | 13.4470i | 0.433239 | + | 0.543564i | ||||
\(613\) | −21.9438 | −0.886301 | −0.443151 | − | 0.896447i | \(-0.646139\pi\) | ||||
−0.443151 | + | 0.896447i | \(0.646139\pi\) | |||||||
\(614\) | 14.6960i | 0.593083i | ||||||||
\(615\) | −39.1743 | + | 29.7680i | −1.57966 | + | 1.20036i | ||||
\(616\) | 5.83567 | 0.235126 | ||||||||
\(617\) | 32.9610i | 1.32696i | 0.748194 | + | 0.663480i | \(0.230921\pi\) | ||||
−0.748194 | + | 0.663480i | \(0.769079\pi\) | |||||||
\(618\) | 8.63011 | + | 24.6741i | 0.347154 | + | 0.992536i | ||||
\(619\) | − | 41.3766i | − | 1.66307i | −0.555475 | − | 0.831533i | \(-0.687463\pi\) | ||
0.555475 | − | 0.831533i | \(-0.312537\pi\) | |||||||
\(620\) | −15.5478 | + | 5.03758i | −0.624413 | + | 0.202314i | ||||
\(621\) | −20.7213 | − | 13.8429i | −0.831519 | − | 0.555497i | ||||
\(622\) | 5.16495i | 0.207096i | ||||||||
\(623\) | 8.55367 | 0.342695 | ||||||||
\(624\) | 4.97044 | − | 1.73848i | 0.198977 | − | 0.0695950i | ||||
\(625\) | 7.80393 | − | 23.7508i | 0.312157 | − | 0.950031i | ||||
\(626\) | 14.4632 | 0.578066 | ||||||||
\(627\) | 26.1327 | − | 9.14029i | 1.04364 | − | 0.365028i | ||||
\(628\) | −11.9565 | −0.477117 | ||||||||
\(629\) | 49.8220i | 1.98653i | ||||||||
\(630\) | −4.77048 | + | 7.20980i | −0.190060 | + | 0.287245i | ||||
\(631\) | 41.5867i | 1.65554i | 0.561068 | + | 0.827770i | \(0.310391\pi\) | ||||
−0.561068 | + | 0.827770i | \(0.689609\pi\) | |||||||
\(632\) | 16.0456i | 0.638258i | ||||||||
\(633\) | −12.0528 | − | 34.4598i | −0.479056 | − | 1.36965i | ||||
\(634\) | −5.68991 | −0.225975 | ||||||||
\(635\) | 4.72936 | + | 14.5965i | 0.187679 | + | 0.579244i | ||||
\(636\) | −7.43248 | + | 2.59962i | −0.294717 | + | 0.103082i | ||||
\(637\) | − | 16.2318i | − | 0.643127i | ||||||
\(638\) | 13.7269i | 0.543454i | ||||||||
\(639\) | 9.91552 | + | 12.4405i | 0.392252 | + | 0.492139i | ||||
\(640\) | 2.12720 | − | 0.689226i | 0.0840848 | − | 0.0272441i | ||||
\(641\) | 30.3693 | 1.19951 | 0.599757 | − | 0.800182i | \(-0.295264\pi\) | ||||
0.599757 | + | 0.800182i | \(0.295264\pi\) | |||||||
\(642\) | 27.0131 | − | 9.44824i | 1.06612 | − | 0.372892i | ||||
\(643\) | 24.8143 | 0.978582 | 0.489291 | − | 0.872121i | \(-0.337256\pi\) | ||||
0.489291 | + | 0.872121i | \(0.337256\pi\) | |||||||
\(644\) | −6.17825 | − | 0.170309i | −0.243457 | − | 0.00671113i | ||||
\(645\) | −20.7387 | − | 27.2918i | −0.816585 | − | 1.07461i | ||||
\(646\) | 20.2330 | 0.796055 | ||||||||
\(647\) | −4.31799 | −0.169758 | −0.0848788 | − | 0.996391i | \(-0.527050\pi\) | ||||
−0.0848788 | + | 0.996391i | \(0.527050\pi\) | |||||||
\(648\) | 2.00739 | − | 8.77328i | 0.0788579 | − | 0.344647i | ||||
\(649\) | 57.8776i | 2.27189i | ||||||||
\(650\) | 8.91446 | + | 12.3124i | 0.349654 | + | 0.482932i | ||||
\(651\) | 5.38644 | + | 15.4002i | 0.211111 | + | 0.603581i | ||||
\(652\) | 4.08030i | 0.159797i | ||||||||
\(653\) | 19.7040 | 0.771076 | 0.385538 | − | 0.922692i | \(-0.374016\pi\) | ||||
0.385538 | + | 0.922692i | \(0.374016\pi\) | |||||||
\(654\) | −27.9531 | + | 9.77700i | −1.09305 | + | 0.382311i | ||||
\(655\) | 0.465394 | + | 1.43637i | 0.0181844 | + | 0.0561236i | ||||
\(656\) | − | 12.7037i | − | 0.495997i | ||||||
\(657\) | −17.6398 | − | 22.1318i | −0.688194 | − | 0.863443i | ||||
\(658\) | −4.49533 | −0.175246 | ||||||||
\(659\) | −12.5928 | −0.490548 | −0.245274 | − | 0.969454i | \(-0.578878\pi\) | ||||
−0.245274 | + | 0.969454i | \(0.578878\pi\) | |||||||
\(660\) | −10.6107 | − | 13.9635i | −0.413021 | − | 0.543530i | ||||
\(661\) | 25.4148i | 0.988520i | 0.869314 | + | 0.494260i | \(0.164561\pi\) | ||||
−0.869314 | + | 0.494260i | \(0.835439\pi\) | |||||||
\(662\) | −12.3989 | −0.481898 | ||||||||
\(663\) | −9.96482 | − | 28.4901i | −0.387001 | − | 1.10646i | ||||
\(664\) | − | 8.09448i | − | 0.314127i | ||||||
\(665\) | 3.13537 | + | 9.67686i | 0.121584 | + | 0.375252i | ||||
\(666\) | 20.3915 | − | 16.2527i | 0.790155 | − | 0.629781i | ||||
\(667\) | 0.400609 | − | 14.5327i | 0.0155116 | − | 0.562710i | ||||
\(668\) | 5.57148 | 0.215567 | ||||||||
\(669\) | 34.3291 | − | 12.0071i | 1.32724 | − | 0.464222i | ||||
\(670\) | 8.47624 | − | 2.74636i | 0.327466 | − | 0.106101i | ||||
\(671\) | 13.7713i | 0.531636i | ||||||||
\(672\) | −0.736956 | − | 2.10701i | −0.0284287 | − | 0.0812795i | ||||
\(673\) | − | 9.43823i | − | 0.363817i | −0.983315 | − | 0.181908i | \(-0.941773\pi\) | ||
0.983315 | − | 0.181908i | \(-0.0582274\pi\) | |||||||
\(674\) | 13.5952 | 0.523666 | ||||||||
\(675\) | 25.9254 | − | 1.69445i | 0.997871 | − | 0.0652195i | ||||
\(676\) | 3.75748 | 0.144518 | ||||||||
\(677\) | 12.7665i | 0.490656i | 0.969440 | + | 0.245328i | \(0.0788957\pi\) | ||||
−0.969440 | + | 0.245328i | \(0.921104\pi\) | |||||||
\(678\) | 28.2871 | − | 9.89383i | 1.08636 | − | 0.379970i | ||||
\(679\) | 0.0345985 | 0.00132777 | ||||||||
\(680\) | −3.95058 | − | 12.1929i | −0.151498 | − | 0.467576i | ||||
\(681\) | −9.62554 | + | 3.36667i | −0.368851 | + | 0.129011i | ||||
\(682\) | −33.0967 | −1.26734 | ||||||||
\(683\) | 33.2408 | 1.27192 | 0.635962 | − | 0.771720i | \(-0.280603\pi\) | ||||
0.635962 | + | 0.771720i | \(0.280603\pi\) | |||||||
\(684\) | −6.60032 | − | 8.28109i | −0.252369 | − | 0.316635i | ||||
\(685\) | 4.23261 | + | 13.0633i | 0.161720 | + | 0.499125i | ||||
\(686\) | −15.9020 | −0.607141 | ||||||||
\(687\) | −37.3507 | + | 13.0639i | −1.42502 | + | 0.498420i | ||||
\(688\) | 8.85037 | 0.337417 | ||||||||
\(689\) | 13.8207 | 0.526526 | ||||||||
\(690\) | 10.8261 | + | 15.0929i | 0.412142 | + | 0.574577i | ||||
\(691\) | 16.1409 | 0.614028 | 0.307014 | − | 0.951705i | \(-0.400670\pi\) | ||||
0.307014 | + | 0.951705i | \(0.400670\pi\) | |||||||
\(692\) | 11.6414 | 0.442541 | ||||||||
\(693\) | −13.6905 | + | 10.9118i | −0.520058 | + | 0.414504i | ||||
\(694\) | 6.55994 | 0.249012 | ||||||||
\(695\) | −29.5157 | + | 9.56328i | −1.11959 | + | 0.362756i | ||||
\(696\) | 4.95619 | − | 1.73350i | 0.187864 | − | 0.0657081i | ||||
\(697\) | −72.8165 | −2.75812 | ||||||||
\(698\) | −28.1738 | −1.06639 | ||||||||
\(699\) | 1.14063 | + | 3.26114i | 0.0431427 | + | 0.123348i | ||||
\(700\) | 5.21933 | − | 3.77891i | 0.197272 | − | 0.142829i | ||||
\(701\) | −11.0988 | −0.419195 | −0.209598 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209598 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(702\) | −8.40994 | + | 13.3724i | −0.317413 | + | 0.504709i | ||||
\(703\) | − | 30.6819i | − | 1.15719i | ||||||
\(704\) | 4.52819 | 0.170663 | ||||||||
\(705\) | 8.17364 | + | 10.7564i | 0.307837 | + | 0.405109i | ||||
\(706\) | −5.76001 | −0.216781 | ||||||||
\(707\) | − | 1.59616i | − | 0.0600296i | ||||||
\(708\) | 20.8971 | − | 7.30905i | 0.785360 | − | 0.274691i | ||||
\(709\) | 27.1166i | 1.01839i | 0.860652 | + | 0.509193i | \(0.170056\pi\) | ||||
−0.860652 | + | 0.509193i | \(0.829944\pi\) | |||||||
\(710\) | −3.65488 | − | 11.2802i | −0.137165 | − | 0.423340i | ||||
\(711\) | −30.0026 | − | 37.6428i | −1.12519 | − | 1.41172i | ||||
\(712\) | 6.63721 | 0.248740 | ||||||||
\(713\) | 35.0396 | + | 0.965901i | 1.31224 | + | 0.0361733i | ||||
\(714\) | −12.0772 | + | 4.22416i | −0.451976 | + | 0.158085i | ||||
\(715\) | 9.48815 | + | 29.2838i | 0.354837 | + | 1.09515i | ||||
\(716\) | 6.37813i | 0.238362i | ||||||||
\(717\) | −26.5082 | + | 9.27165i | −0.989969 | + | 0.346256i | ||||
\(718\) | −6.40987 | −0.239214 | ||||||||
\(719\) | − | 48.4417i | − | 1.80657i | −0.429039 | − | 0.903286i | \(-0.641148\pi\) | ||
0.429039 | − | 0.903286i | \(-0.358852\pi\) | |||||||
\(720\) | −3.70165 | + | 5.59444i | −0.137952 | + | 0.208493i | ||||
\(721\) | −19.4495 | −0.724336 | ||||||||
\(722\) | 6.53993 | 0.243391 | ||||||||
\(723\) | −32.2146 | + | 11.2675i | −1.19807 | + | 0.419044i | ||||
\(724\) | − | 7.84733i | − | 0.291644i | ||||||
\(725\) | 8.88890 | + | 12.2771i | 0.330125 | + | 0.455960i | ||||
\(726\) | −5.43506 | − | 15.5392i | −0.201714 | − | 0.576713i | ||||
\(727\) | 34.0855 | 1.26416 | 0.632080 | − | 0.774903i | \(-0.282201\pi\) | ||||
0.632080 | + | 0.774903i | \(0.282201\pi\) | |||||||
\(728\) | 3.91797i | 0.145210i | ||||||||
\(729\) | 11.6953 | + | 24.3356i | 0.433159 | + | 0.901318i | ||||
\(730\) | 6.50206 | + | 20.0677i | 0.240652 | + | 0.742738i | ||||
\(731\) | − | 50.7295i | − | 1.87630i | ||||||
\(732\) | 4.97222 | − | 1.73911i | 0.183779 | − | 0.0642793i | ||||
\(733\) | 4.78843 | 0.176865 | 0.0884324 | − | 0.996082i | \(-0.471814\pi\) | ||||
0.0884324 | + | 0.996082i | \(0.471814\pi\) | |||||||
\(734\) | 26.8268 | 0.990196 | ||||||||
\(735\) | 12.5110 | + | 16.4643i | 0.461474 | + | 0.607293i | ||||
\(736\) | −4.79401 | − | 0.132152i | −0.176710 | − | 0.00487117i | ||||
\(737\) | 18.0435 | 0.664640 | ||||||||
\(738\) | 23.7539 | + | 29.8029i | 0.874394 | + | 1.09706i | ||||
\(739\) | −24.0111 | −0.883262 | −0.441631 | − | 0.897197i | \(-0.645600\pi\) | ||||
−0.441631 | + | 0.897197i | \(0.645600\pi\) | |||||||
\(740\) | −18.4897 | + | 5.99079i | −0.679695 | + | 0.220226i | ||||
\(741\) | 6.13664 | + | 17.5451i | 0.225435 | + | 0.644534i | ||||
\(742\) | − | 5.85870i | − | 0.215080i | ||||||
\(743\) | − | 5.51270i | − | 0.202242i | −0.994874 | − | 0.101121i | \(-0.967757\pi\) | ||
0.994874 | − | 0.101121i | \(-0.0322428\pi\) | |||||||
\(744\) | 4.17961 | + | 11.9498i | 0.153232 | + | 0.438100i | ||||
\(745\) | 27.3875 | − | 8.87374i | 1.00340 | − | 0.325109i | ||||
\(746\) | −8.96103 | −0.328086 | ||||||||
\(747\) | 15.1354 | + | 18.9896i | 0.553775 | + | 0.694794i | ||||
\(748\) | − | 25.9552i | − | 0.949014i | ||||||
\(749\) | 21.2933i | 0.778039i | ||||||||
\(750\) | −18.5322 | − | 5.61776i | −0.676699 | − | 0.205131i | ||||
\(751\) | − | 8.57209i | − | 0.312800i | −0.987694 | − | 0.156400i | \(-0.950011\pi\) | ||
0.987694 | − | 0.156400i | \(-0.0499889\pi\) | |||||||
\(752\) | −3.48815 | −0.127200 | ||||||||
\(753\) | −3.11224 | − | 8.89810i | −0.113416 | − | 0.324265i | ||||
\(754\) | −9.21602 | −0.335628 | ||||||||
\(755\) | −9.24155 | + | 2.99432i | −0.336334 | + | 0.108975i | ||||
\(756\) | 5.66866 | + | 3.56504i | 0.206167 | + | 0.129659i | ||||
\(757\) | −48.2632 | −1.75416 | −0.877078 | − | 0.480349i | \(-0.840510\pi\) | ||||
−0.877078 | + | 0.480349i | \(0.840510\pi\) | |||||||
\(758\) | − | 4.30108i | − | 0.156222i | ||||||
\(759\) | 11.4353 | + | 35.8336i | 0.415074 | + | 1.30068i | ||||
\(760\) | 2.43289 | + | 7.50876i | 0.0882501 | + | 0.272371i | ||||
\(761\) | 0.0297036i | 0.00107675i | 1.00000 | 0.000538377i | \(0.000171371\pi\) | |||||
−1.00000 | 0.000538377i | \(0.999829\pi\) | ||||||||
\(762\) | 11.2186 | − | 3.92388i | 0.406408 | − | 0.142147i | ||||
\(763\) | − | 22.0342i | − | 0.797691i | ||||||
\(764\) | −6.06089 | −0.219275 | ||||||||
\(765\) | 32.0668 | + | 21.2175i | 1.15938 | + | 0.767121i | ||||
\(766\) | − | 10.2019i | − | 0.368609i | ||||||
\(767\) | −38.8581 | −1.40308 | ||||||||
\(768\) | −0.571841 | − | 1.63493i | −0.0206345 | − | 0.0589955i | ||||
\(769\) | 32.7603i | 1.18137i | 0.806903 | + | 0.590684i | \(0.201142\pi\) | ||||
−0.806903 | + | 0.590684i | \(0.798858\pi\) | |||||||
\(770\) | 12.4136 | − | 4.02210i | 0.447356 | − | 0.144946i | ||||
\(771\) | 5.88637 | + | 16.8295i | 0.211993 | + | 0.606101i | ||||
\(772\) | 4.83220i | 0.173915i | ||||||||
\(773\) | − | 32.8434i | − | 1.18130i | −0.806929 | − | 0.590648i | \(-0.798872\pi\) | ||
0.806929 | − | 0.590648i | \(-0.201128\pi\) | |||||||
\(774\) | −20.7629 | + | 16.5488i | −0.746308 | + | 0.594834i | ||||
\(775\) | −29.6011 | + | 21.4319i | −1.06330 | + | 0.769855i | ||||
\(776\) | 0.0268467 | 0.000963741 | ||||||||
\(777\) | 6.40566 | + | 18.3142i | 0.229802 | + | 0.657018i | ||||
\(778\) | −10.3677 | −0.371701 | ||||||||
\(779\) | 44.8426 | 1.60665 | ||||||||
\(780\) | 9.37489 | − | 7.12385i | 0.335675 | − | 0.255075i | ||||
\(781\) | − | 24.0124i | − | 0.859231i | ||||||
\(782\) | −0.757480 | + | 27.4788i | −0.0270874 | + | 0.982640i | ||||
\(783\) | −8.38583 | + | 13.3341i | −0.299685 | + | 0.476520i | ||||
\(784\) | −5.33914 | −0.190684 | ||||||||
\(785\) | −25.4339 | + | 8.24075i | −0.907774 | + | 0.294125i | ||||
\(786\) | 1.10397 | − | 0.386130i | 0.0393774 | − | 0.0137728i | ||||
\(787\) | 28.7301 | 1.02412 | 0.512058 | − | 0.858951i | \(-0.328883\pi\) | ||||
0.512058 | + | 0.858951i | \(0.328883\pi\) | |||||||
\(788\) | −12.3455 | −0.439790 | ||||||||
\(789\) | −29.5079 | + | 10.3208i | −1.05051 | + | 0.367431i | ||||
\(790\) | 11.0590 | + | 34.1321i | 0.393463 | + | 1.21436i | ||||
\(791\) | 22.2975i | 0.792807i | ||||||||
\(792\) | −10.6231 | + | 8.46699i | −0.377476 | + | 0.300861i | ||||
\(793\) | −9.24584 | −0.328329 | ||||||||
\(794\) | − | 15.6662i | − | 0.555973i | ||||||
\(795\) | −14.0186 | + | 10.6526i | −0.497189 | + | 0.377808i | ||||
\(796\) | − | 4.31745i | − | 0.153028i | ||||||
\(797\) | − | 45.7409i | − | 1.62022i | −0.586275 | − | 0.810112i | \(-0.699406\pi\) | ||
0.586275 | − | 0.810112i | \(-0.300594\pi\) | |||||||
\(798\) | 7.43748 | − | 2.60137i | 0.263284 | − | 0.0920874i | ||||
\(799\) | 19.9938i | 0.707329i | ||||||||
\(800\) | 4.04993 | − | 2.93224i | 0.143187 | − | 0.103670i | ||||
\(801\) | −15.5709 | + | 12.4105i | −0.550170 | + | 0.438504i | ||||
\(802\) | 21.5559 | 0.761164 | ||||||||
\(803\) | 42.7183i | 1.50749i | ||||||||
\(804\) | −2.27861 | − | 6.51470i | −0.0803605 | − | 0.229756i | ||||
\(805\) | −13.2597 | + | 3.89593i | −0.467344 | + | 0.137314i | ||||
\(806\) | − | 22.2206i | − | 0.782687i | ||||||
\(807\) | −9.19546 | + | 3.21625i | −0.323695 | + | 0.113217i | ||||
\(808\) | − | 1.23854i | − | 0.0435715i | ||||||
\(809\) | − | 35.8505i | − | 1.26044i | −0.776419 | − | 0.630218i | \(-0.782966\pi\) | ||
0.776419 | − | 0.630218i | \(-0.217034\pi\) | |||||||
\(810\) | −1.77665 | − | 20.0460i | −0.0624251 | − | 0.704346i | ||||
\(811\) | 34.8564 | 1.22397 | 0.611987 | − | 0.790868i | \(-0.290370\pi\) | ||||
0.611987 | + | 0.790868i | \(0.290370\pi\) | |||||||
\(812\) | 3.90674i | 0.137100i | ||||||||
\(813\) | −11.1378 | − | 31.8437i | −0.390620 | − | 1.11681i | ||||
\(814\) | −39.3592 | −1.37954 | ||||||||
\(815\) | 2.81225 | + | 8.67960i | 0.0985088 | + | 0.304033i | ||||
\(816\) | −9.37127 | + | 3.27774i | −0.328060 | + | 0.114744i | ||||
\(817\) | 31.2408i | 1.09298i | ||||||||
\(818\) | −32.7301 | −1.14438 | ||||||||
\(819\) | −7.32599 | − | 9.19155i | −0.255991 | − | 0.321179i | ||||
\(820\) | −8.75574 | − | 27.0233i | −0.305764 | − | 0.943695i | ||||
\(821\) | 31.9229i | 1.11412i | 0.830474 | + | 0.557058i | \(0.188070\pi\) | ||||
−0.830474 | + | 0.557058i | \(0.811930\pi\) | |||||||
\(822\) | 10.0403 | − | 3.51174i | 0.350195 | − | 0.122486i | ||||
\(823\) | − | 46.3311i | − | 1.61500i | −0.589866 | − | 0.807501i | \(-0.700820\pi\) | ||
0.589866 | − | 0.807501i | \(-0.299180\pi\) | |||||||
\(824\) | −15.0918 | −0.525748 | ||||||||
\(825\) | −32.1951 | − | 22.3900i | −1.12089 | − | 0.779520i | ||||
\(826\) | 16.4722i | 0.573142i | ||||||||
\(827\) | − | 19.0668i | − | 0.663016i | −0.943452 | − | 0.331508i | \(-0.892443\pi\) | ||
0.943452 | − | 0.331508i | \(-0.107557\pi\) | |||||||
\(828\) | 11.4938 | − | 8.65401i | 0.399438 | − | 0.300748i | ||||
\(829\) | −52.5034 | −1.82352 | −0.911759 | − | 0.410727i | \(-0.865275\pi\) | ||||
−0.911759 | + | 0.410727i | \(0.865275\pi\) | |||||||
\(830\) | −5.57893 | − | 17.2185i | −0.193647 | − | 0.597665i | ||||
\(831\) | −2.51185 | + | 0.878555i | −0.0871350 | + | 0.0304767i | ||||
\(832\) | 3.04015i | 0.105398i | ||||||||
\(833\) | 30.6034i | 1.06035i | ||||||||
\(834\) | 7.93451 | + | 22.6853i | 0.274750 | + | 0.785527i | ||||
\(835\) | 11.8516 | − | 3.84001i | 0.410143 | − | 0.132889i | ||||
\(836\) | 15.9840i | 0.552817i | ||||||||
\(837\) | −32.1495 | − | 20.2189i | −1.11125 | − | 0.698868i | ||||
\(838\) | 3.77943 | 0.130558 | ||||||||
\(839\) | 15.3959 | 0.531525 | 0.265762 | − | 0.964039i | \(-0.414376\pi\) | ||||
0.265762 | + | 0.964039i | \(0.414376\pi\) | |||||||
\(840\) | −3.01986 | − | 3.97409i | −0.104195 | − | 0.137119i | ||||
\(841\) | 19.8104 | 0.683117 | ||||||||
\(842\) | 21.2423i | 0.732058i | ||||||||
\(843\) | −3.56802 | − | 10.2012i | −0.122889 | − | 0.351348i | ||||
\(844\) | 21.0772 | 0.725507 | ||||||||
\(845\) | 7.99290 | − | 2.58975i | 0.274964 | − | 0.0890903i | ||||
\(846\) | 8.18319 | − | 6.52229i | 0.281344 | − | 0.224241i | ||||
\(847\) | 12.2489 | 0.420876 | ||||||||
\(848\) | − | 4.54605i | − | 0.156112i | ||||||
\(849\) | −4.47547 | − | 12.7957i | −0.153598 | − | 0.439146i | ||||
\(850\) | −16.8073 | − | 23.2138i | −0.576487 | − | 0.796228i | ||||
\(851\) | 41.6698 | + | 1.14867i | 1.42842 | + | 0.0393758i | ||||
\(852\) | −8.66982 | + | 3.03240i | −0.297023 | + | 0.103888i | ||||
\(853\) | − | 22.8095i | − | 0.780982i | −0.920607 | − | 0.390491i | \(-0.872305\pi\) | ||
0.920607 | − | 0.390491i | \(-0.127695\pi\) | |||||||
\(854\) | 3.91938i | 0.134119i | ||||||||
\(855\) | −19.7477 | − | 13.0664i | −0.675358 | − | 0.446861i | ||||
\(856\) | 16.5225i | 0.564727i | ||||||||
\(857\) | 37.3502 | 1.27586 | 0.637930 | − | 0.770095i | \(-0.279791\pi\) | ||||
0.637930 | + | 0.770095i | \(0.279791\pi\) | |||||||
\(858\) | 22.5071 | − | 7.87218i | 0.768379 | − | 0.268752i | ||||
\(859\) | −2.26159 | −0.0771643 | −0.0385822 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385822 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(860\) | 18.8265 | − | 6.09991i | 0.641978 | − | 0.208005i | ||||
\(861\) | −26.7668 | + | 9.36208i | −0.912210 | + | 0.319059i | ||||
\(862\) | −15.0460 | −0.512470 | ||||||||
\(863\) | −44.0444 | −1.49929 | −0.749644 | − | 0.661842i | \(-0.769775\pi\) | ||||
−0.749644 | + | 0.661842i | \(0.769775\pi\) | |||||||
\(864\) | 4.39860 | + | 2.76629i | 0.149643 | + | 0.0941111i | ||||
\(865\) | 24.7636 | − | 8.02359i | 0.841989 | − | 0.272810i | ||||
\(866\) | −1.05773 | −0.0359432 | ||||||||
\(867\) | 9.06639 | + | 25.9214i | 0.307911 | + | 0.880337i | ||||
\(868\) | −9.41947 | −0.319718 | ||||||||
\(869\) | 72.6573i | 2.46473i | ||||||||
\(870\) | 9.34801 | − | 7.10343i | 0.316927 | − | 0.240829i | ||||
\(871\) | 12.1141i | 0.410470i | ||||||||
\(872\) | − | 17.0974i | − | 0.578992i | ||||||
\(873\) | −0.0629823 | + | 0.0501991i | −0.00213163 | + | 0.00169898i | ||||
\(874\) | 0.466480 | − | 16.9223i | 0.0157789 | − | 0.572405i | ||||
\(875\) | 8.49801 | − | 11.6358i | 0.287285 | − | 0.393361i | ||||
\(876\) | 15.4237 | − | 5.39466i | 0.521118 | − | 0.182269i | ||||
\(877\) | 40.4451i | 1.36573i | 0.730542 | + | 0.682867i | \(0.239267\pi\) | ||||
−0.730542 | + | 0.682867i | \(0.760733\pi\) | |||||||
\(878\) | 15.4166 | 0.520285 | ||||||||
\(879\) | −28.3393 | + | 9.91210i | −0.955862 | + | 0.334327i | ||||
\(880\) | 9.63235 | − | 3.12095i | 0.324706 | − | 0.105207i | ||||
\(881\) | −36.5778 | −1.23234 | −0.616168 | − | 0.787615i | \(-0.711316\pi\) | ||||
−0.616168 | + | 0.787615i | \(0.711316\pi\) | |||||||
\(882\) | 12.5256 | − | 9.98334i | 0.421759 | − | 0.336157i | ||||
\(883\) | − | 7.52943i | − | 0.253386i | −0.991942 | − | 0.126693i | \(-0.959564\pi\) | ||
0.991942 | − | 0.126693i | \(-0.0404362\pi\) | |||||||
\(884\) | 17.4259 | 0.586095 | ||||||||
\(885\) | 39.4146 | − | 29.9506i | 1.32491 | − | 1.00678i | ||||
\(886\) | −19.2882 | −0.648000 | ||||||||
\(887\) | 37.3052 | 1.25259 | 0.626293 | − | 0.779587i | \(-0.284571\pi\) | ||||
0.626293 | + | 0.779587i | \(0.284571\pi\) | |||||||
\(888\) | 4.97047 | + | 14.2109i | 0.166798 | + | 0.476886i | ||||
\(889\) | 8.84315i | 0.296590i | ||||||||
\(890\) | 14.1187 | − | 4.57454i | 0.473259 | − | 0.153339i | ||||
\(891\) | 9.08986 | − | 39.7271i | 0.304522 | − | 1.33091i | ||||
\(892\) | 20.9973i | 0.703042i | ||||||||
\(893\) | − | 12.3128i | − | 0.412031i | ||||||
\(894\) | −7.36241 | − | 21.0496i | −0.246236 | − | 0.704004i | ||||
\(895\) | 4.39598 | + | 13.5675i | 0.146941 | + | 0.453513i | ||||
\(896\) | 1.28874 | 0.0430539 | ||||||||
\(897\) | −24.0581 | + | 7.67745i | −0.803275 | + | 0.256343i | ||||
\(898\) | − | 2.45364i | − | 0.0818789i | ||||||
\(899\) | − | 22.1569i | − | 0.738973i | ||||||
\(900\) | −4.01831 | + | 14.4518i | −0.133944 | + | 0.481725i | ||||
\(901\) | −26.0575 | −0.868103 | ||||||||
\(902\) | − | 57.5248i | − | 1.91537i | ||||||
\(903\) | −6.52233 | − | 18.6478i | −0.217050 | − | 0.620559i | ||||
\(904\) | 17.3017i | 0.575447i | ||||||||
\(905\) | −5.40859 | − | 16.6928i | −0.179788 | − | 0.554888i | ||||
\(906\) | 2.48435 | + | 7.10291i | 0.0825369 | + | 0.235978i | ||||
\(907\) | 38.8447 | 1.28982 | 0.644909 | − | 0.764259i | \(-0.276895\pi\) | ||||
0.644909 | + | 0.764259i | \(0.276895\pi\) | |||||||
\(908\) | − | 5.88743i | − | 0.195381i | ||||||
\(909\) | 2.31586 | + | 2.90560i | 0.0768124 | + | 0.0963727i | ||||
\(910\) | 2.70037 | + | 8.33430i | 0.0895165 | + | 0.276279i | ||||
\(911\) | −2.59781 | −0.0860693 | −0.0430346 | − | 0.999074i | \(-0.513703\pi\) | ||||
−0.0430346 | + | 0.999074i | \(0.513703\pi\) | |||||||
\(912\) | 5.77111 | − | 2.01853i | 0.191101 | − | 0.0668402i | ||||
\(913\) | − | 36.6533i | − | 1.21305i | ||||||
\(914\) | 31.5879 | 1.04483 | ||||||||
\(915\) | 9.37826 | − | 7.12641i | 0.310036 | − | 0.235592i | ||||
\(916\) | − | 22.8454i | − | 0.754834i | ||||||
\(917\) | 0.870212i | 0.0287369i | ||||||||
\(918\) | 15.8561 | − | 25.2123i | 0.523330 | − | 0.832131i | ||||
\(919\) | − | 46.9542i | − | 1.54888i | −0.632650 | − | 0.774438i | \(-0.718033\pi\) | ||
0.632650 | − | 0.774438i | \(-0.281967\pi\) | |||||||
\(920\) | −10.2889 | + | 3.02305i | −0.339215 | + | 0.0996669i | ||||
\(921\) | 24.0270 | − | 8.40378i | 0.791715 | − | 0.276914i | ||||
\(922\) | − | 30.5064i | − | 1.00467i | ||||||
\(923\) | 16.1215 | 0.530646 | ||||||||
\(924\) | −3.33708 | − | 9.54092i | −0.109782 | − | 0.313873i | ||||
\(925\) | −35.2022 | + | 25.4872i | −1.15744 | + | 0.838013i | ||||
\(926\) | − | 14.9598i | − | 0.491609i | ||||||
\(927\) | 35.4053 | − | 28.2193i | 1.16286 | − | 0.926843i | ||||
\(928\) | 3.03143i | 0.0995117i | ||||||||
\(929\) | 37.5448i | 1.23181i | 0.787822 | + | 0.615903i | \(0.211209\pi\) | ||||
−0.787822 | + | 0.615903i | \(0.788791\pi\) | |||||||
\(930\) | 17.1269 | + | 22.5388i | 0.561615 | + | 0.739077i | ||||
\(931\) | − | 18.8465i | − | 0.617670i | ||||||
\(932\) | −1.99467 | −0.0653375 | ||||||||
\(933\) | 8.44434 | − | 2.95353i | 0.276455 | − | 0.0966943i | ||||
\(934\) | − | 31.8778i | − | 1.04307i | ||||||
\(935\) | −17.8890 | − | 55.2117i | −0.585032 | − | 1.80562i | ||||
\(936\) | −5.68460 | − | 7.13218i | −0.185807 | − | 0.233123i | ||||
\(937\) | 37.5203 | 1.22574 | 0.612868 | − | 0.790186i | \(-0.290016\pi\) | ||||
0.612868 | + | 0.790186i | \(0.290016\pi\) | |||||||
\(938\) | 5.13525 | 0.167672 | ||||||||
\(939\) | −8.27065 | − | 23.6463i | −0.269902 | − | 0.771669i | ||||
\(940\) | −7.41999 | + | 2.40413i | −0.242013 | + | 0.0784140i | ||||
\(941\) | 35.7322 | 1.16484 | 0.582418 | − | 0.812889i | \(-0.302107\pi\) | ||||
0.582418 | + | 0.812889i | \(0.302107\pi\) | |||||||
\(942\) | 6.83722 | + | 19.5481i | 0.222769 | + | 0.636911i | ||||
\(943\) | −1.67882 | + | 60.9017i | −0.0546698 | + | 1.98323i | ||||
\(944\) | 12.7816i | 0.416006i | ||||||||
\(945\) | 14.5155 | + | 3.67655i | 0.472188 | + | 0.119598i | ||||
\(946\) | 40.0761 | 1.30299 | ||||||||
\(947\) | −34.6296 | −1.12531 | −0.562656 | − | 0.826691i | \(-0.690220\pi\) | ||||
−0.562656 | + | 0.826691i | \(0.690220\pi\) | |||||||
\(948\) | 26.2334 | − | 9.17551i | 0.852021 | − | 0.298007i | ||||
\(949\) | −28.6803 | −0.931003 | ||||||||
\(950\) | 10.3505 | + | 14.2958i | 0.335813 | + | 0.463817i | ||||
\(951\) | 3.25372 | + | 9.30260i | 0.105509 | + | 0.301658i | ||||
\(952\) | − | 7.38696i | − | 0.239413i | ||||||
\(953\) | − | 16.1851i | − | 0.524287i | −0.965029 | − | 0.262144i | \(-0.915571\pi\) | ||
0.965029 | − | 0.262144i | \(-0.0844294\pi\) | |||||||
\(954\) | 8.50039 | + | 10.6650i | 0.275210 | + | 0.345293i | ||||
\(955\) | −12.8927 | + | 4.17732i | −0.417198 | + | 0.135175i | ||||
\(956\) | − | 16.2137i | − | 0.524388i | ||||||
\(957\) | 22.4425 | − | 7.84961i | 0.725464 | − | 0.253742i | ||||
\(958\) | −16.8162 | −0.543306 | ||||||||
\(959\) | 7.91431i | 0.255566i | ||||||||
\(960\) | −2.34326 | − | 3.08369i | −0.0756282 | − | 0.0995257i | ||||
\(961\) | 22.4220 | 0.723291 | ||||||||
\(962\) | − | 26.4251i | − | 0.851981i | ||||||
\(963\) | −30.8944 | − | 38.7617i | −0.995559 | − | 1.24908i | ||||
\(964\) | − | 19.7040i | − | 0.634622i | ||||||
\(965\) | 3.33048 | + | 10.2790i | 0.107212 | + | 0.330894i | ||||
\(966\) | 3.25453 | + | 10.1984i | 0.104713 | + | 0.328128i | ||||
\(967\) | − | 37.6064i | − | 1.20934i | −0.796476 | − | 0.604670i | \(-0.793305\pi\) | ||
0.796476 | − | 0.604670i | \(-0.206695\pi\) | |||||||
\(968\) | 9.50450 | 0.305486 | ||||||||
\(969\) | −11.5700 | − | 33.0795i | −0.371683 | − | 1.06267i | ||||
\(970\) | 0.0571083 | − | 0.0185035i | 0.00183364 | − | 0.000594111i | ||||
\(971\) | −12.0962 | −0.388187 | −0.194093 | − | 0.980983i | \(-0.562176\pi\) | ||||
−0.194093 | + | 0.980983i | \(0.562176\pi\) | |||||||
\(972\) | −15.4916 | + | 1.73497i | −0.496894 | + | 0.0556491i | ||||
\(973\) | −17.8818 | −0.573265 | ||||||||
\(974\) | − | 8.87949i | − | 0.284517i | ||||||
\(975\) | 15.0323 | − | 21.6153i | 0.481418 | − | 0.692242i | ||||
\(976\) | 3.04124i | 0.0973479i | ||||||||
\(977\) | − | 1.12241i | − | 0.0359092i | −0.999839 | − | 0.0179546i | \(-0.994285\pi\) | ||
0.999839 | − | 0.0179546i | \(-0.00571543\pi\) | |||||||
\(978\) | 6.67101 | − | 2.33328i | 0.213315 | − | 0.0746101i | ||||
\(979\) | 30.0546 | 0.960548 | ||||||||
\(980\) | −11.3574 | + | 3.67988i | −0.362799 | + | 0.117549i | ||||
\(981\) | 31.9694 | + | 40.1105i | 1.02071 | + | 1.28063i | ||||
\(982\) | 2.36576i | 0.0754946i | ||||||||
\(983\) | 33.1802i | 1.05828i | 0.848534 | + | 0.529141i | \(0.177486\pi\) | ||||
−0.848534 | + | 0.529141i | \(0.822514\pi\) | |||||||
\(984\) | −20.7697 | + | 7.26450i | −0.662114 | + | 0.231584i | ||||
\(985\) | −26.2613 | + | 8.50885i | −0.836755 | + | 0.271114i | ||||
\(986\) | 17.3759 | 0.553361 | ||||||||
\(987\) | 2.57062 | + | 7.34956i | 0.0818236 | + | 0.233939i | ||||
\(988\) | −10.7314 | −0.341411 | ||||||||
\(989\) | −42.4288 | − | 1.16959i | −1.34916 | − | 0.0371908i | ||||
\(990\) | −16.7618 | + | 25.3327i | −0.532724 | + | 0.805126i | ||||
\(991\) | −38.6528 | −1.22785 | −0.613924 | − | 0.789366i | \(-0.710410\pi\) | ||||
−0.613924 | + | 0.789366i | \(0.710410\pi\) | |||||||
\(992\) | −7.30904 | −0.232062 | ||||||||
\(993\) | 7.09021 | + | 20.2714i | 0.225001 | + | 0.643293i | ||||
\(994\) | − | 6.83404i | − | 0.216763i | ||||||
\(995\) | −2.97570 | − | 9.18406i | −0.0943360 | − | 0.291154i | ||||
\(996\) | −13.2339 | + | 4.62875i | −0.419332 | + | 0.146668i | ||||
\(997\) | − | 10.0084i | − | 0.316968i | −0.987362 | − | 0.158484i | \(-0.949339\pi\) | ||
0.987362 | − | 0.158484i | \(-0.0506606\pi\) | |||||||
\(998\) | −15.7984 | −0.500090 | ||||||||
\(999\) | −38.2328 | − | 24.0447i | −1.20963 | − | 0.760741i |
(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 | 690.2.h.b.689.10 | yes | 24 | |
3.2 | odd | 2 | 690.2.h.a.689.13 | ✓ | 24 | ||
5.4 | even | 2 | 690.2.h.a.689.16 | yes | 24 | ||
15.14 | odd | 2 | inner | 690.2.h.b.689.11 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.h.b.689.9 | yes | 24 | |
69.68 | even | 2 | 690.2.h.a.689.14 | yes | 24 | ||
115.114 | odd | 2 | 690.2.h.a.689.15 | yes | 24 | ||
345.344 | even | 2 | inner | 690.2.h.b.689.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.h.a.689.13 | ✓ | 24 | 3.2 | odd | 2 | ||
690.2.h.a.689.14 | yes | 24 | 69.68 | even | 2 | ||
690.2.h.a.689.15 | yes | 24 | 115.114 | odd | 2 | ||
690.2.h.a.689.16 | yes | 24 | 5.4 | even | 2 | ||
690.2.h.b.689.9 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.h.b.689.10 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.h.b.689.11 | yes | 24 | 15.14 | odd | 2 | inner | |
690.2.h.b.689.12 | yes | 24 | 345.344 | even | 2 | inner |