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 | 689.4 | ||
Character | \(\chi\) | \(=\) | 690.689 |
Dual form | 690.2.h.a.689.2 |
$q$-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 | ||||||||
\(3\) | −1.65921 | + | 0.497008i | −0.957946 | + | 0.286948i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.15459 | + | 1.91492i | 0.516347 | + | 0.856379i | ||||
\(6\) | 1.65921 | − | 0.497008i | 0.677370 | − | 0.202903i | ||||
\(7\) | 3.15825 | 1.19371 | 0.596853 | − | 0.802351i | \(-0.296418\pi\) | ||||
0.596853 | + | 0.802351i | \(0.296418\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.50597 | − | 1.64928i | 0.835322 | − | 0.549761i | ||||
\(10\) | −1.15459 | − | 1.91492i | −0.365113 | − | 0.605552i | ||||
\(11\) | 2.63765 | 0.795282 | 0.397641 | − | 0.917541i | \(-0.369829\pi\) | ||||
0.397641 | + | 0.917541i | \(0.369829\pi\) | |||||||
\(12\) | −1.65921 | + | 0.497008i | −0.478973 | + | 0.143474i | ||||
\(13\) | − | 3.37824i | − | 0.936955i | −0.883475 | − | 0.468477i | \(-0.844803\pi\) | ||
0.883475 | − | 0.468477i | \(-0.155197\pi\) | |||||||
\(14\) | −3.15825 | −0.844077 | ||||||||
\(15\) | −2.86744 | − | 2.60342i | −0.740369 | − | 0.672201i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.331367i | 0.0803682i | 0.999192 | + | 0.0401841i | \(0.0127944\pi\) | ||||
−0.999192 | + | 0.0401841i | \(0.987206\pi\) | |||||||
\(18\) | −2.50597 | + | 1.64928i | −0.590662 | + | 0.388740i | ||||
\(19\) | − | 2.06750i | − | 0.474316i | −0.971471 | − | 0.237158i | \(-0.923784\pi\) | ||
0.971471 | − | 0.237158i | \(-0.0762159\pi\) | |||||||
\(20\) | 1.15459 | + | 1.91492i | 0.258174 | + | 0.428190i | ||||
\(21\) | −5.24020 | + | 1.56967i | −1.14351 | + | 0.342531i | ||||
\(22\) | −2.63765 | −0.562349 | ||||||||
\(23\) | 2.19771 | − | 4.26263i | 0.458255 | − | 0.888821i | ||||
\(24\) | 1.65921 | − | 0.497008i | 0.338685 | − | 0.101451i | ||||
\(25\) | −2.33385 | + | 4.42189i | −0.466771 | + | 0.884378i | ||||
\(26\) | 3.37824i | 0.662527i | ||||||||
\(27\) | −3.33822 | + | 3.98199i | −0.642441 | + | 0.766335i | ||||
\(28\) | 3.15825 | 0.596853 | ||||||||
\(29\) | − | 6.73889i | − | 1.25138i | −0.780071 | − | 0.625691i | \(-0.784817\pi\) | ||
0.780071 | − | 0.625691i | \(-0.215183\pi\) | |||||||
\(30\) | 2.86744 | + | 2.60342i | 0.523520 | + | 0.475318i | ||||
\(31\) | 2.38669 | 0.428662 | 0.214331 | − | 0.976761i | \(-0.431243\pi\) | ||||
0.214331 | + | 0.976761i | \(0.431243\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.37642 | + | 1.31093i | −0.761837 | + | 0.228204i | ||||
\(34\) | − | 0.331367i | − | 0.0568289i | ||||||
\(35\) | 3.64647 | + | 6.04780i | 0.616367 | + | 1.02226i | ||||
\(36\) | 2.50597 | − | 1.64928i | 0.417661 | − | 0.274880i | ||||
\(37\) | −2.62847 | −0.432118 | −0.216059 | − | 0.976380i | \(-0.569320\pi\) | ||||
−0.216059 | + | 0.976380i | \(0.569320\pi\) | |||||||
\(38\) | 2.06750i | 0.335392i | ||||||||
\(39\) | 1.67901 | + | 5.60521i | 0.268857 | + | 0.897552i | ||||
\(40\) | −1.15459 | − | 1.91492i | −0.182556 | − | 0.302776i | ||||
\(41\) | 6.92322i | 1.08122i | 0.841272 | + | 0.540612i | \(0.181807\pi\) | ||||
−0.841272 | + | 0.540612i | \(0.818193\pi\) | |||||||
\(42\) | 5.24020 | − | 1.56967i | 0.808580 | − | 0.242206i | ||||
\(43\) | 7.19407 | 1.09709 | 0.548543 | − | 0.836122i | \(-0.315183\pi\) | ||||
0.548543 | + | 0.836122i | \(0.315183\pi\) | |||||||
\(44\) | 2.63765 | 0.397641 | ||||||||
\(45\) | 6.05161 | + | 2.89449i | 0.902120 | + | 0.431485i | ||||
\(46\) | −2.19771 | + | 4.26263i | −0.324035 | + | 0.628491i | ||||
\(47\) | 11.0631 | 1.61372 | 0.806862 | − | 0.590740i | \(-0.201164\pi\) | ||||
0.806862 | + | 0.590740i | \(0.201164\pi\) | |||||||
\(48\) | −1.65921 | + | 0.497008i | −0.239487 | + | 0.0717369i | ||||
\(49\) | 2.97452 | 0.424932 | ||||||||
\(50\) | 2.33385 | − | 4.42189i | 0.330057 | − | 0.625350i | ||||
\(51\) | −0.164692 | − | 0.549807i | −0.0230615 | − | 0.0769884i | ||||
\(52\) | − | 3.37824i | − | 0.468477i | ||||||
\(53\) | − | 13.7812i | − | 1.89300i | −0.322706 | − | 0.946499i | \(-0.604593\pi\) | ||
0.322706 | − | 0.946499i | \(-0.395407\pi\) | |||||||
\(54\) | 3.33822 | − | 3.98199i | 0.454275 | − | 0.541881i | ||||
\(55\) | 3.04540 | + | 5.05090i | 0.410642 | + | 0.681063i | ||||
\(56\) | −3.15825 | −0.422039 | ||||||||
\(57\) | 1.02756 | + | 3.43041i | 0.136104 | + | 0.454369i | ||||
\(58\) | 6.73889i | 0.884860i | ||||||||
\(59\) | 12.0898i | 1.57396i | 0.616978 | + | 0.786981i | \(0.288357\pi\) | ||||
−0.616978 | + | 0.786981i | \(0.711643\pi\) | |||||||
\(60\) | −2.86744 | − | 2.60342i | −0.370185 | − | 0.336100i | ||||
\(61\) | 0.685298i | 0.0877435i | 0.999037 | + | 0.0438717i | \(0.0139693\pi\) | ||||
−0.999037 | + | 0.0438717i | \(0.986031\pi\) | |||||||
\(62\) | −2.38669 | −0.303110 | ||||||||
\(63\) | 7.91446 | − | 5.20884i | 0.997128 | − | 0.656252i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.46906 | − | 3.90047i | 0.802389 | − | 0.483794i | ||||
\(66\) | 4.37642 | − | 1.31093i | 0.538700 | − | 0.161365i | ||||
\(67\) | −0.468752 | −0.0572672 | −0.0286336 | − | 0.999590i | \(-0.509116\pi\) | ||||
−0.0286336 | + | 0.999590i | \(0.509116\pi\) | |||||||
\(68\) | 0.331367i | 0.0401841i | ||||||||
\(69\) | −1.52791 | + | 8.16489i | −0.183939 | + | 0.982938i | ||||
\(70\) | −3.64647 | − | 6.04780i | −0.435837 | − | 0.722850i | ||||
\(71\) | 5.57976i | 0.662196i | 0.943596 | + | 0.331098i | \(0.107419\pi\) | ||||
−0.943596 | + | 0.331098i | \(0.892581\pi\) | |||||||
\(72\) | −2.50597 | + | 1.64928i | −0.295331 | + | 0.194370i | ||||
\(73\) | 7.91723i | 0.926642i | 0.886191 | + | 0.463321i | \(0.153342\pi\) | ||||
−0.886191 | + | 0.463321i | \(0.846658\pi\) | |||||||
\(74\) | 2.62847 | 0.305553 | ||||||||
\(75\) | 1.67464 | − | 8.49680i | 0.193371 | − | 0.981126i | ||||
\(76\) | − | 2.06750i | − | 0.237158i | ||||||
\(77\) | 8.33036 | 0.949332 | ||||||||
\(78\) | −1.67901 | − | 5.60521i | −0.190111 | − | 0.634665i | ||||
\(79\) | 6.81084i | 0.766280i | 0.923690 | + | 0.383140i | \(0.125157\pi\) | ||||
−0.923690 | + | 0.383140i | \(0.874843\pi\) | |||||||
\(80\) | 1.15459 | + | 1.91492i | 0.129087 | + | 0.214095i | ||||
\(81\) | 3.55974 | − | 8.26609i | 0.395526 | − | 0.918455i | ||||
\(82\) | − | 6.92322i | − | 0.764541i | ||||||
\(83\) | − | 4.16761i | − | 0.457455i | −0.973490 | − | 0.228728i | \(-0.926544\pi\) | ||
0.973490 | − | 0.228728i | \(-0.0734565\pi\) | |||||||
\(84\) | −5.24020 | + | 1.56967i | −0.571753 | + | 0.171265i | ||||
\(85\) | −0.634541 | + | 0.382592i | −0.0688257 | + | 0.0414979i | ||||
\(86\) | −7.19407 | −0.775757 | ||||||||
\(87\) | 3.34928 | + | 11.1813i | 0.359081 | + | 1.19876i | ||||
\(88\) | −2.63765 | −0.281175 | ||||||||
\(89\) | 7.02620 | 0.744775 | 0.372388 | − | 0.928077i | \(-0.378539\pi\) | ||||
0.372388 | + | 0.928077i | \(0.378539\pi\) | |||||||
\(90\) | −6.05161 | − | 2.89449i | −0.637895 | − | 0.305106i | ||||
\(91\) | − | 10.6693i | − | 1.11845i | ||||||
\(92\) | 2.19771 | − | 4.26263i | 0.229128 | − | 0.444410i | ||||
\(93\) | −3.96003 | + | 1.18620i | −0.410636 | + | 0.123004i | ||||
\(94\) | −11.0631 | −1.14108 | ||||||||
\(95\) | 3.95909 | − | 2.38711i | 0.406195 | − | 0.244912i | ||||
\(96\) | 1.65921 | − | 0.497008i | 0.169343 | − | 0.0507256i | ||||
\(97\) | −18.2042 | −1.84836 | −0.924181 | − | 0.381956i | \(-0.875251\pi\) | ||||
−0.924181 | + | 0.381956i | \(0.875251\pi\) | |||||||
\(98\) | −2.97452 | −0.300472 | ||||||||
\(99\) | 6.60987 | − | 4.35023i | 0.664317 | − | 0.437215i | ||||
\(100\) | −2.33385 | + | 4.42189i | −0.233385 | + | 0.442189i | ||||
\(101\) | 2.07347i | 0.206318i | 0.994665 | + | 0.103159i | \(0.0328951\pi\) | ||||
−0.994665 | + | 0.103159i | \(0.967105\pi\) | |||||||
\(102\) | 0.164692 | + | 0.549807i | 0.0163069 | + | 0.0544390i | ||||
\(103\) | −2.39866 | −0.236347 | −0.118174 | − | 0.992993i | \(-0.537704\pi\) | ||||
−0.118174 | + | 0.992993i | \(0.537704\pi\) | |||||||
\(104\) | 3.37824i | 0.331264i | ||||||||
\(105\) | −9.05607 | − | 8.22225i | −0.883782 | − | 0.802409i | ||||
\(106\) | 13.7812i | 1.33855i | ||||||||
\(107\) | 10.4463i | 1.00988i | 0.863154 | + | 0.504941i | \(0.168486\pi\) | ||||
−0.863154 | + | 0.504941i | \(0.831514\pi\) | |||||||
\(108\) | −3.33822 | + | 3.98199i | −0.321221 | + | 0.383167i | ||||
\(109\) | 3.63460i | 0.348132i | 0.984734 | + | 0.174066i | \(0.0556906\pi\) | ||||
−0.984734 | + | 0.174066i | \(0.944309\pi\) | |||||||
\(110\) | −3.04540 | − | 5.05090i | −0.290368 | − | 0.481584i | ||||
\(111\) | 4.36119 | − | 1.30637i | 0.413946 | − | 0.123995i | ||||
\(112\) | 3.15825 | 0.298426 | ||||||||
\(113\) | − | 0.586991i | − | 0.0552195i | −0.999619 | − | 0.0276097i | \(-0.991210\pi\) | ||
0.999619 | − | 0.0276097i | \(-0.00878957\pi\) | |||||||
\(114\) | −1.02756 | − | 3.43041i | −0.0962400 | − | 0.321288i | ||||
\(115\) | 10.7001 | − | 0.713133i | 0.997786 | − | 0.0665000i | ||||
\(116\) | − | 6.73889i | − | 0.625691i | ||||||
\(117\) | −5.57167 | − | 8.46575i | −0.515101 | − | 0.782659i | ||||
\(118\) | − | 12.0898i | − | 1.11296i | ||||||
\(119\) | 1.04654i | 0.0959359i | ||||||||
\(120\) | 2.86744 | + | 2.60342i | 0.261760 | + | 0.237659i | ||||
\(121\) | −4.04279 | −0.367527 | ||||||||
\(122\) | − | 0.685298i | − | 0.0620440i | ||||||
\(123\) | −3.44089 | − | 11.4871i | −0.310255 | − | 1.03576i | ||||
\(124\) | 2.38669 | 0.214331 | ||||||||
\(125\) | −11.1622 | + | 0.636316i | −0.998379 | + | 0.0569138i | ||||
\(126\) | −7.91446 | + | 5.20884i | −0.705076 | + | 0.464040i | ||||
\(127\) | 5.94678i | 0.527692i | 0.964565 | + | 0.263846i | \(0.0849910\pi\) | ||||
−0.964565 | + | 0.263846i | \(0.915009\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.9365 | + | 3.57551i | −1.05095 | + | 0.314806i | ||||
\(130\) | −6.46906 | + | 3.90047i | −0.567374 | + | 0.342094i | ||||
\(131\) | − | 6.85575i | − | 0.598990i | −0.954098 | − | 0.299495i | \(-0.903182\pi\) | ||
0.954098 | − | 0.299495i | \(-0.0968182\pi\) | |||||||
\(132\) | −4.37642 | + | 1.31093i | −0.380919 | + | 0.114102i | ||||
\(133\) | − | 6.52967i | − | 0.566194i | ||||||
\(134\) | 0.468752 | 0.0404940 | ||||||||
\(135\) | −11.4795 | − | 1.79487i | −0.987996 | − | 0.154478i | ||||
\(136\) | − | 0.331367i | − | 0.0284144i | ||||||
\(137\) | 14.8092i | 1.26523i | 0.774466 | + | 0.632616i | \(0.218019\pi\) | ||||
−0.774466 | + | 0.632616i | \(0.781981\pi\) | |||||||
\(138\) | 1.52791 | − | 8.16489i | 0.130064 | − | 0.695042i | ||||
\(139\) | 0.241417 | 0.0204767 | 0.0102384 | − | 0.999948i | \(-0.496741\pi\) | ||||
0.0102384 | + | 0.999948i | \(0.496741\pi\) | |||||||
\(140\) | 3.64647 | + | 6.04780i | 0.308183 | + | 0.511132i | ||||
\(141\) | −18.3561 | + | 5.49847i | −1.54586 | + | 0.463054i | ||||
\(142\) | − | 5.57976i | − | 0.468243i | ||||||
\(143\) | − | 8.91062i | − | 0.745143i | ||||||
\(144\) | 2.50597 | − | 1.64928i | 0.208831 | − | 0.137440i | ||||
\(145\) | 12.9045 | − | 7.78065i | 1.07166 | − | 0.646148i | ||||
\(146\) | − | 7.91723i | − | 0.655235i | ||||||
\(147\) | −4.93537 | + | 1.47836i | −0.407062 | + | 0.121933i | ||||
\(148\) | −2.62847 | −0.216059 | ||||||||
\(149\) | −21.2344 | −1.73959 | −0.869795 | − | 0.493412i | \(-0.835749\pi\) | ||||
−0.869795 | + | 0.493412i | \(0.835749\pi\) | |||||||
\(150\) | −1.67464 | + | 8.49680i | −0.136734 | + | 0.693761i | ||||
\(151\) | −16.3816 | −1.33311 | −0.666556 | − | 0.745455i | \(-0.732232\pi\) | ||||
−0.666556 | + | 0.745455i | \(0.732232\pi\) | |||||||
\(152\) | 2.06750i | 0.167696i | ||||||||
\(153\) | 0.546517 | + | 0.830394i | 0.0441833 | + | 0.0671333i | ||||
\(154\) | −8.33036 | −0.671279 | ||||||||
\(155\) | 2.75565 | + | 4.57033i | 0.221339 | + | 0.367098i | ||||
\(156\) | 1.67901 | + | 5.60521i | 0.134428 | + | 0.448776i | ||||
\(157\) | 9.20113 | 0.734330 | 0.367165 | − | 0.930156i | \(-0.380328\pi\) | ||||
0.367165 | + | 0.930156i | \(0.380328\pi\) | |||||||
\(158\) | − | 6.81084i | − | 0.541841i | ||||||
\(159\) | 6.84938 | + | 22.8660i | 0.543191 | + | 1.81339i | ||||
\(160\) | −1.15459 | − | 1.91492i | −0.0912782 | − | 0.151388i | ||||
\(161\) | 6.94093 | − | 13.4625i | 0.547022 | − | 1.06099i | ||||
\(162\) | −3.55974 | + | 8.26609i | −0.279679 | + | 0.649446i | ||||
\(163\) | − | 23.6263i | − | 1.85056i | −0.379288 | − | 0.925279i | \(-0.623831\pi\) | ||
0.379288 | − | 0.925279i | \(-0.376169\pi\) | |||||||
\(164\) | 6.92322i | 0.540612i | ||||||||
\(165\) | −7.56330 | − | 6.86692i | −0.588802 | − | 0.534589i | ||||
\(166\) | 4.16761i | 0.323470i | ||||||||
\(167\) | 9.99301 | 0.773282 | 0.386641 | − | 0.922230i | \(-0.373635\pi\) | ||||
0.386641 | + | 0.922230i | \(0.373635\pi\) | |||||||
\(168\) | 5.24020 | − | 1.56967i | 0.404290 | − | 0.121103i | ||||
\(169\) | 1.58751 | 0.122116 | ||||||||
\(170\) | 0.634541 | − | 0.382592i | 0.0486671 | − | 0.0293435i | ||||
\(171\) | −3.40989 | − | 5.18108i | −0.260760 | − | 0.396207i | ||||
\(172\) | 7.19407 | 0.548543 | ||||||||
\(173\) | −13.4215 | −1.02042 | −0.510208 | − | 0.860051i | \(-0.670432\pi\) | ||||
−0.510208 | + | 0.860051i | \(0.670432\pi\) | |||||||
\(174\) | −3.34928 | − | 11.1813i | −0.253909 | − | 0.847649i | ||||
\(175\) | −7.37089 | + | 13.9654i | −0.557187 | + | 1.05569i | ||||
\(176\) | 2.63765 | 0.198820 | ||||||||
\(177\) | −6.00874 | − | 20.0596i | −0.451644 | − | 1.50777i | ||||
\(178\) | −7.02620 | −0.526636 | ||||||||
\(179\) | − | 1.35729i | − | 0.101448i | −0.998713 | − | 0.0507242i | \(-0.983847\pi\) | ||
0.998713 | − | 0.0507242i | \(-0.0161530\pi\) | |||||||
\(180\) | 6.05161 | + | 2.89449i | 0.451060 | + | 0.215742i | ||||
\(181\) | − | 12.6059i | − | 0.936988i | −0.883467 | − | 0.468494i | \(-0.844797\pi\) | ||
0.883467 | − | 0.468494i | \(-0.155203\pi\) | |||||||
\(182\) | 10.6693i | 0.790862i | ||||||||
\(183\) | −0.340599 | − | 1.13705i | −0.0251778 | − | 0.0840535i | ||||
\(184\) | −2.19771 | + | 4.26263i | −0.162018 | + | 0.314246i | ||||
\(185\) | −3.03480 | − | 5.03332i | −0.223123 | − | 0.370057i | ||||
\(186\) | 3.96003 | − | 1.18620i | 0.290363 | − | 0.0869767i | ||||
\(187\) | 0.874030i | 0.0639154i | ||||||||
\(188\) | 11.0631 | 0.806862 | ||||||||
\(189\) | −10.5429 | + | 12.5761i | −0.766885 | + | 0.914778i | ||||
\(190\) | −3.95909 | + | 2.38711i | −0.287223 | + | 0.173179i | ||||
\(191\) | 23.4458 | 1.69648 | 0.848239 | − | 0.529614i | \(-0.177663\pi\) | ||||
0.848239 | + | 0.529614i | \(0.177663\pi\) | |||||||
\(192\) | −1.65921 | + | 0.497008i | −0.119743 | + | 0.0358684i | ||||
\(193\) | 18.6555i | 1.34286i | 0.741070 | + | 0.671428i | \(0.234319\pi\) | ||||
−0.741070 | + | 0.671428i | \(0.765681\pi\) | |||||||
\(194\) | 18.2042 | 1.30699 | ||||||||
\(195\) | −8.79498 | + | 9.68689i | −0.629822 | + | 0.693692i | ||||
\(196\) | 2.97452 | 0.212466 | ||||||||
\(197\) | 4.98294 | 0.355019 | 0.177510 | − | 0.984119i | \(-0.443196\pi\) | ||||
0.177510 | + | 0.984119i | \(0.443196\pi\) | |||||||
\(198\) | −6.60987 | + | 4.35023i | −0.469743 | + | 0.309158i | ||||
\(199\) | − | 14.6734i | − | 1.04017i | −0.854115 | − | 0.520084i | \(-0.825901\pi\) | ||
0.854115 | − | 0.520084i | \(-0.174099\pi\) | |||||||
\(200\) | 2.33385 | − | 4.42189i | 0.165028 | − | 0.312675i | ||||
\(201\) | 0.777759 | − | 0.232973i | 0.0548589 | − | 0.0164327i | ||||
\(202\) | − | 2.07347i | − | 0.145889i | ||||||
\(203\) | − | 21.2831i | − | 1.49378i | ||||||
\(204\) | −0.164692 | − | 0.549807i | −0.0115307 | − | 0.0384942i | ||||
\(205\) | −13.2574 | + | 7.99346i | −0.925938 | + | 0.558288i | ||||
\(206\) | 2.39866 | 0.167123 | ||||||||
\(207\) | −1.52289 | − | 14.3067i | −0.105848 | − | 0.994382i | ||||
\(208\) | − | 3.37824i | − | 0.234239i | ||||||
\(209\) | − | 5.45334i | − | 0.377215i | ||||||
\(210\) | 9.05607 | + | 8.22225i | 0.624929 | + | 0.567389i | ||||
\(211\) | 4.05994 | 0.279498 | 0.139749 | − | 0.990187i | \(-0.455370\pi\) | ||||
0.139749 | + | 0.990187i | \(0.455370\pi\) | |||||||
\(212\) | − | 13.7812i | − | 0.946499i | ||||||
\(213\) | −2.77319 | − | 9.25801i | −0.190016 | − | 0.634348i | ||||
\(214\) | − | 10.4463i | − | 0.714095i | ||||||
\(215\) | 8.30619 | + | 13.7761i | 0.566477 | + | 0.939521i | ||||
\(216\) | 3.33822 | − | 3.98199i | 0.227137 | − | 0.270940i | ||||
\(217\) | 7.53776 | 0.511697 | ||||||||
\(218\) | − | 3.63460i | − | 0.246166i | ||||||
\(219\) | −3.93493 | − | 13.1364i | −0.265898 | − | 0.887673i | ||||
\(220\) | 3.04540 | + | 5.05090i | 0.205321 | + | 0.340531i | ||||
\(221\) | 1.11944 | 0.0753014 | ||||||||
\(222\) | −4.36119 | + | 1.30637i | −0.292704 | + | 0.0876778i | ||||
\(223\) | 26.8510i | 1.79808i | 0.437871 | + | 0.899038i | \(0.355733\pi\) | ||||
−0.437871 | + | 0.899038i | \(0.644267\pi\) | |||||||
\(224\) | −3.15825 | −0.211019 | ||||||||
\(225\) | 1.44439 | + | 14.9303i | 0.0962927 | + | 0.995353i | ||||
\(226\) | 0.586991i | 0.0390461i | ||||||||
\(227\) | 16.3101i | 1.08254i | 0.840850 | + | 0.541268i | \(0.182056\pi\) | ||||
−0.840850 | + | 0.541268i | \(0.817944\pi\) | |||||||
\(228\) | 1.02756 | + | 3.43041i | 0.0680520 | + | 0.227185i | ||||
\(229\) | − | 13.0346i | − | 0.861349i | −0.902507 | − | 0.430675i | \(-0.858276\pi\) | ||
0.902507 | − | 0.430675i | \(-0.141724\pi\) | |||||||
\(230\) | −10.7001 | + | 0.713133i | −0.705542 | + | 0.0470226i | ||||
\(231\) | −13.8218 | + | 4.14025i | −0.909409 | + | 0.272409i | ||||
\(232\) | 6.73889i | 0.442430i | ||||||||
\(233\) | −18.3561 | −1.20255 | −0.601274 | − | 0.799043i | \(-0.705340\pi\) | ||||
−0.601274 | + | 0.799043i | \(0.705340\pi\) | |||||||
\(234\) | 5.57167 | + | 8.46575i | 0.364231 | + | 0.553424i | ||||
\(235\) | 12.7734 | + | 21.1850i | 0.833242 | + | 1.38196i | ||||
\(236\) | 12.0898i | 0.786981i | ||||||||
\(237\) | −3.38504 | − | 11.3006i | −0.219882 | − | 0.734055i | ||||
\(238\) | − | 1.04654i | − | 0.0678370i | ||||||
\(239\) | 7.83756i | 0.506970i | 0.967339 | + | 0.253485i | \(0.0815768\pi\) | ||||
−0.967339 | + | 0.253485i | \(0.918423\pi\) | |||||||
\(240\) | −2.86744 | − | 2.60342i | −0.185092 | − | 0.168050i | ||||
\(241\) | − | 16.8965i | − | 1.08840i | −0.838956 | − | 0.544199i | \(-0.816834\pi\) | ||
0.838956 | − | 0.544199i | \(-0.183166\pi\) | |||||||
\(242\) | 4.04279 | 0.259881 | ||||||||
\(243\) | −1.79804 | + | 15.4844i | −0.115344 | + | 0.993326i | ||||
\(244\) | 0.685298i | 0.0438717i | ||||||||
\(245\) | 3.43435 | + | 5.69598i | 0.219413 | + | 0.363903i | ||||
\(246\) | 3.44089 | + | 11.4871i | 0.219383 | + | 0.732390i | ||||
\(247\) | −6.98450 | −0.444413 | ||||||||
\(248\) | −2.38669 | −0.151555 | ||||||||
\(249\) | 2.07134 | + | 6.91495i | 0.131266 | + | 0.438217i | ||||
\(250\) | 11.1622 | − | 0.636316i | 0.705961 | − | 0.0402442i | ||||
\(251\) | −26.2859 | −1.65915 | −0.829577 | − | 0.558392i | \(-0.811418\pi\) | ||||
−0.829577 | + | 0.558392i | \(0.811418\pi\) | |||||||
\(252\) | 7.91446 | − | 5.20884i | 0.498564 | − | 0.328126i | ||||
\(253\) | 5.79681 | − | 11.2433i | 0.364442 | − | 0.706863i | ||||
\(254\) | − | 5.94678i | − | 0.373134i | ||||||
\(255\) | 0.862687 | − | 0.950173i | 0.0540236 | − | 0.0595021i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.32061 | 0.144756 | 0.0723780 | − | 0.997377i | \(-0.476941\pi\) | ||||
0.0723780 | + | 0.997377i | \(0.476941\pi\) | |||||||
\(258\) | 11.9365 | − | 3.57551i | 0.743133 | − | 0.222602i | ||||
\(259\) | −8.30136 | −0.515821 | ||||||||
\(260\) | 6.46906 | − | 3.90047i | 0.401194 | − | 0.241897i | ||||
\(261\) | −11.1143 | − | 16.8874i | −0.687960 | − | 1.04531i | ||||
\(262\) | 6.85575i | 0.423550i | ||||||||
\(263\) | − | 31.4516i | − | 1.93939i | −0.244327 | − | 0.969693i | \(-0.578567\pi\) | ||
0.244327 | − | 0.969693i | \(-0.421433\pi\) | |||||||
\(264\) | 4.37642 | − | 1.31093i | 0.269350 | − | 0.0806824i | ||||
\(265\) | 26.3900 | − | 15.9117i | 1.62112 | − | 0.977445i | ||||
\(266\) | 6.52967i | 0.400359i | ||||||||
\(267\) | −11.6579 | + | 3.49207i | −0.713455 | + | 0.213712i | ||||
\(268\) | −0.468752 | −0.0286336 | ||||||||
\(269\) | − | 10.7521i | − | 0.655570i | −0.944752 | − | 0.327785i | \(-0.893698\pi\) | ||
0.944752 | − | 0.327785i | \(-0.106302\pi\) | |||||||
\(270\) | 11.4795 | + | 1.79487i | 0.698619 | + | 0.109233i | ||||
\(271\) | 7.09113 | 0.430755 | 0.215378 | − | 0.976531i | \(-0.430902\pi\) | ||||
0.215378 | + | 0.976531i | \(0.430902\pi\) | |||||||
\(272\) | 0.331367i | 0.0200920i | ||||||||
\(273\) | 5.30273 | + | 17.7026i | 0.320936 | + | 1.07141i | ||||
\(274\) | − | 14.8092i | − | 0.894654i | ||||||
\(275\) | −6.15589 | + | 11.6634i | −0.371214 | + | 0.703330i | ||||
\(276\) | −1.52791 | + | 8.16489i | −0.0919695 | + | 0.491469i | ||||
\(277\) | − | 10.1872i | − | 0.612092i | −0.952017 | − | 0.306046i | \(-0.900994\pi\) | ||
0.952017 | − | 0.306046i | \(-0.0990061\pi\) | |||||||
\(278\) | −0.241417 | −0.0144792 | ||||||||
\(279\) | 5.98097 | − | 3.93633i | 0.358071 | − | 0.235662i | ||||
\(280\) | −3.64647 | − | 6.04780i | −0.217919 | − | 0.361425i | ||||
\(281\) | −16.0901 | −0.959853 | −0.479926 | − | 0.877309i | \(-0.659337\pi\) | ||||
−0.479926 | + | 0.877309i | \(0.659337\pi\) | |||||||
\(282\) | 18.3561 | − | 5.49847i | 1.09309 | − | 0.327429i | ||||
\(283\) | 28.1303 | 1.67217 | 0.836086 | − | 0.548598i | \(-0.184838\pi\) | ||||
0.836086 | + | 0.548598i | \(0.184838\pi\) | |||||||
\(284\) | 5.57976i | 0.331098i | ||||||||
\(285\) | −5.38257 | + | 5.92842i | −0.318836 | + | 0.351169i | ||||
\(286\) | 8.91062i | 0.526896i | ||||||||
\(287\) | 21.8652i | 1.29066i | ||||||||
\(288\) | −2.50597 | + | 1.64928i | −0.147665 | + | 0.0971849i | ||||
\(289\) | 16.8902 | 0.993541 | ||||||||
\(290\) | −12.9045 | + | 7.78065i | −0.757776 | + | 0.456895i | ||||
\(291\) | 30.2047 | − | 9.04765i | 1.77063 | − | 0.530383i | ||||
\(292\) | 7.91723i | 0.463321i | ||||||||
\(293\) | 10.7652i | 0.628910i | 0.949272 | + | 0.314455i | \(0.101822\pi\) | ||||
−0.949272 | + | 0.314455i | \(0.898178\pi\) | |||||||
\(294\) | 4.93537 | − | 1.47836i | 0.287836 | − | 0.0862198i | ||||
\(295\) | −23.1511 | + | 13.9588i | −1.34791 | + | 0.812711i | ||||
\(296\) | 2.62847 | 0.152777 | ||||||||
\(297\) | −8.80507 | + | 10.5031i | −0.510922 | + | 0.609452i | ||||
\(298\) | 21.2344 | 1.23008 | ||||||||
\(299\) | −14.4002 | − | 7.42440i | −0.832785 | − | 0.429364i | ||||
\(300\) | 1.67464 | − | 8.49680i | 0.0966855 | − | 0.490563i | ||||
\(301\) | 22.7207 | 1.30960 | ||||||||
\(302\) | 16.3816 | 0.942653 | ||||||||
\(303\) | −1.03053 | − | 3.44033i | −0.0592025 | − | 0.197642i | ||||
\(304\) | − | 2.06750i | − | 0.118579i | ||||||
\(305\) | −1.31229 | + | 0.791237i | −0.0751417 | + | 0.0453061i | ||||
\(306\) | −0.546517 | − | 0.830394i | −0.0312423 | − | 0.0474704i | ||||
\(307\) | 21.1061i | 1.20459i | 0.798274 | + | 0.602295i | \(0.205747\pi\) | ||||
−0.798274 | + | 0.602295i | \(0.794253\pi\) | |||||||
\(308\) | 8.33036 | 0.474666 | ||||||||
\(309\) | 3.97989 | − | 1.19215i | 0.226408 | − | 0.0678193i | ||||
\(310\) | −2.75565 | − | 4.57033i | −0.156510 | − | 0.259577i | ||||
\(311\) | 15.5206i | 0.880092i | 0.897975 | + | 0.440046i | \(0.145038\pi\) | ||||
−0.897975 | + | 0.440046i | \(0.854962\pi\) | |||||||
\(312\) | −1.67901 | − | 5.60521i | −0.0950553 | − | 0.317333i | ||||
\(313\) | −0.701429 | −0.0396471 | −0.0198236 | − | 0.999803i | \(-0.506310\pi\) | ||||
−0.0198236 | + | 0.999803i | \(0.506310\pi\) | |||||||
\(314\) | −9.20113 | −0.519250 | ||||||||
\(315\) | 19.1125 | + | 9.14151i | 1.07687 | + | 0.515066i | ||||
\(316\) | 6.81084i | 0.383140i | ||||||||
\(317\) | −26.6487 | −1.49674 | −0.748370 | − | 0.663281i | \(-0.769163\pi\) | ||||
−0.748370 | + | 0.663281i | \(0.769163\pi\) | |||||||
\(318\) | −6.84938 | − | 22.8660i | −0.384094 | − | 1.28226i | ||||
\(319\) | − | 17.7749i | − | 0.995201i | ||||||
\(320\) | 1.15459 | + | 1.91492i | 0.0645434 | + | 0.107047i | ||||
\(321\) | −5.19190 | − | 17.3326i | −0.289783 | − | 0.967413i | ||||
\(322\) | −6.94093 | + | 13.4625i | −0.386803 | + | 0.750233i | ||||
\(323\) | 0.685099 | 0.0381199 | ||||||||
\(324\) | 3.55974 | − | 8.26609i | 0.197763 | − | 0.459227i | ||||
\(325\) | 14.9382 | + | 7.88431i | 0.828623 | + | 0.437343i | ||||
\(326\) | 23.6263i | 1.30854i | ||||||||
\(327\) | −1.80643 | − | 6.03058i | −0.0998956 | − | 0.333492i | ||||
\(328\) | − | 6.92322i | − | 0.382271i | ||||||
\(329\) | 34.9401 | 1.92631 | ||||||||
\(330\) | 7.56330 | + | 6.86692i | 0.416346 | + | 0.378012i | ||||
\(331\) | −12.0090 | −0.660074 | −0.330037 | − | 0.943968i | \(-0.607061\pi\) | ||||
−0.330037 | + | 0.943968i | \(0.607061\pi\) | |||||||
\(332\) | − | 4.16761i | − | 0.228728i | ||||||
\(333\) | −6.58686 | + | 4.33509i | −0.360958 | + | 0.237561i | ||||
\(334\) | −9.99301 | −0.546793 | ||||||||
\(335\) | −0.541215 | − | 0.897624i | −0.0295698 | − | 0.0490424i | ||||
\(336\) | −5.24020 | + | 1.56967i | −0.285876 | + | 0.0856327i | ||||
\(337\) | 32.5953 | 1.77558 | 0.887789 | − | 0.460252i | \(-0.152241\pi\) | ||||
0.887789 | + | 0.460252i | \(0.152241\pi\) | |||||||
\(338\) | −1.58751 | −0.0863489 | ||||||||
\(339\) | 0.291739 | + | 0.973942i | 0.0158451 | + | 0.0528973i | ||||
\(340\) | −0.634541 | + | 0.382592i | −0.0344128 | + | 0.0207490i | ||||
\(341\) | 6.29526 | 0.340907 | ||||||||
\(342\) | 3.40989 | + | 5.18108i | 0.184385 | + | 0.280161i | ||||
\(343\) | −12.7134 | −0.686462 | ||||||||
\(344\) | −7.19407 | −0.387878 | ||||||||
\(345\) | −17.3992 | + | 6.50126i | −0.936744 | + | 0.350016i | ||||
\(346\) | 13.4215 | 0.721544 | ||||||||
\(347\) | 14.3932 | 0.772666 | 0.386333 | − | 0.922359i | \(-0.373742\pi\) | ||||
0.386333 | + | 0.922359i | \(0.373742\pi\) | |||||||
\(348\) | 3.34928 | + | 11.1813i | 0.179540 | + | 0.599378i | ||||
\(349\) | −0.672923 | −0.0360207 | −0.0180104 | − | 0.999838i | \(-0.505733\pi\) | ||||
−0.0180104 | + | 0.999838i | \(0.505733\pi\) | |||||||
\(350\) | 7.37089 | − | 13.9654i | 0.393990 | − | 0.746484i | ||||
\(351\) | 13.4521 | + | 11.2773i | 0.718021 | + | 0.601938i | ||||
\(352\) | −2.63765 | −0.140587 | ||||||||
\(353\) | −25.3608 | −1.34982 | −0.674909 | − | 0.737901i | \(-0.735817\pi\) | ||||
−0.674909 | + | 0.737901i | \(0.735817\pi\) | |||||||
\(354\) | 6.00874 | + | 20.0596i | 0.319361 | + | 1.06615i | ||||
\(355\) | −10.6848 | + | 6.44233i | −0.567091 | + | 0.341923i | ||||
\(356\) | 7.02620 | 0.372388 | ||||||||
\(357\) | −0.520137 | − | 1.73643i | −0.0275286 | − | 0.0919015i | ||||
\(358\) | 1.35729i | 0.0717349i | ||||||||
\(359\) | −18.0914 | −0.954827 | −0.477413 | − | 0.878679i | \(-0.658426\pi\) | ||||
−0.477413 | + | 0.878679i | \(0.658426\pi\) | |||||||
\(360\) | −6.05161 | − | 2.89449i | −0.318948 | − | 0.152553i | ||||
\(361\) | 14.7255 | 0.775024 | ||||||||
\(362\) | 12.6059i | 0.662550i | ||||||||
\(363\) | 6.70785 | − | 2.00930i | 0.352071 | − | 0.105461i | ||||
\(364\) | − | 10.6693i | − | 0.559224i | ||||||
\(365\) | −15.1609 | + | 9.14114i | −0.793557 | + | 0.478469i | ||||
\(366\) | 0.340599 | + | 1.13705i | 0.0178034 | + | 0.0594348i | ||||
\(367\) | 0.368267 | 0.0192234 | 0.00961170 | − | 0.999954i | \(-0.496940\pi\) | ||||
0.00961170 | + | 0.999954i | \(0.496940\pi\) | |||||||
\(368\) | 2.19771 | − | 4.26263i | 0.114564 | − | 0.222205i | ||||
\(369\) | 11.4183 | + | 17.3493i | 0.594415 | + | 0.903171i | ||||
\(370\) | 3.03480 | + | 5.03332i | 0.157772 | + | 0.261670i | ||||
\(371\) | − | 43.5246i | − | 2.25968i | ||||||
\(372\) | −3.96003 | + | 1.18620i | −0.205318 | + | 0.0615018i | ||||
\(373\) | −19.5200 | −1.01071 | −0.505353 | − | 0.862913i | \(-0.668638\pi\) | ||||
−0.505353 | + | 0.862913i | \(0.668638\pi\) | |||||||
\(374\) | − | 0.874030i | − | 0.0451950i | ||||||
\(375\) | 18.2042 | − | 6.60349i | 0.940062 | − | 0.341003i | ||||
\(376\) | −11.0631 | −0.570538 | ||||||||
\(377\) | −22.7656 | −1.17249 | ||||||||
\(378\) | 10.5429 | − | 12.5761i | 0.542270 | − | 0.646846i | ||||
\(379\) | − | 33.4418i | − | 1.71779i | −0.512153 | − | 0.858894i | \(-0.671152\pi\) | ||
0.512153 | − | 0.858894i | \(-0.328848\pi\) | |||||||
\(380\) | 3.95909 | − | 2.38711i | 0.203097 | − | 0.122456i | ||||
\(381\) | −2.95560 | − | 9.86697i | −0.151420 | − | 0.505500i | ||||
\(382\) | −23.4458 | −1.19959 | ||||||||
\(383\) | − | 17.0408i | − | 0.870745i | −0.900250 | − | 0.435373i | \(-0.856617\pi\) | ||
0.900250 | − | 0.435373i | \(-0.143383\pi\) | |||||||
\(384\) | 1.65921 | − | 0.497008i | 0.0846713 | − | 0.0253628i | ||||
\(385\) | 9.61813 | + | 15.9520i | 0.490185 | + | 0.812988i | ||||
\(386\) | − | 18.6555i | − | 0.949542i | ||||||
\(387\) | 18.0281 | − | 11.8651i | 0.916420 | − | 0.603135i | ||||
\(388\) | −18.2042 | −0.924181 | ||||||||
\(389\) | −0.355884 | −0.0180440 | −0.00902201 | − | 0.999959i | \(-0.502872\pi\) | ||||
−0.00902201 | + | 0.999959i | \(0.502872\pi\) | |||||||
\(390\) | 8.79498 | − | 9.68689i | 0.445351 | − | 0.490515i | ||||
\(391\) | 1.41249 | + | 0.728249i | 0.0714329 | + | 0.0368291i | ||||
\(392\) | −2.97452 | −0.150236 | ||||||||
\(393\) | 3.40736 | + | 11.3751i | 0.171879 | + | 0.573800i | ||||
\(394\) | −4.98294 | −0.251037 | ||||||||
\(395\) | −13.0422 | + | 7.86372i | −0.656226 | + | 0.395666i | ||||
\(396\) | 6.60987 | − | 4.35023i | 0.332158 | − | 0.218607i | ||||
\(397\) | 19.0771i | 0.957450i | 0.877965 | + | 0.478725i | \(0.158901\pi\) | ||||
−0.877965 | + | 0.478725i | \(0.841099\pi\) | |||||||
\(398\) | 14.6734i | 0.735510i | ||||||||
\(399\) | 3.24529 | + | 10.8341i | 0.162468 | + | 0.542383i | ||||
\(400\) | −2.33385 | + | 4.42189i | −0.116693 | + | 0.221095i | ||||
\(401\) | 29.7359 | 1.48494 | 0.742471 | − | 0.669879i | \(-0.233654\pi\) | ||||
0.742471 | + | 0.669879i | \(0.233654\pi\) | |||||||
\(402\) | −0.777759 | + | 0.232973i | −0.0387911 | + | 0.0116197i | ||||
\(403\) | − | 8.06281i | − | 0.401637i | ||||||
\(404\) | 2.07347i | 0.103159i | ||||||||
\(405\) | 19.9390 | − | 2.72731i | 0.990774 | − | 0.135521i | ||||
\(406\) | 21.2831i | 1.05626i | ||||||||
\(407\) | −6.93299 | −0.343656 | ||||||||
\(408\) | 0.164692 | + | 0.549807i | 0.00815346 | + | 0.0272195i | ||||
\(409\) | 14.1316 | 0.698763 | 0.349382 | − | 0.936981i | \(-0.386392\pi\) | ||||
0.349382 | + | 0.936981i | \(0.386392\pi\) | |||||||
\(410\) | 13.2574 | − | 7.99346i | 0.654737 | − | 0.394769i | ||||
\(411\) | −7.36027 | − | 24.5715i | −0.363055 | − | 1.21202i | ||||
\(412\) | −2.39866 | −0.118174 | ||||||||
\(413\) | 38.1827i | 1.87885i | ||||||||
\(414\) | 1.52289 | + | 14.3067i | 0.0748458 | + | 0.703134i | ||||
\(415\) | 7.98066 | − | 4.81188i | 0.391755 | − | 0.236206i | ||||
\(416\) | 3.37824i | 0.165632i | ||||||||
\(417\) | −0.400561 | + | 0.119986i | −0.0196156 | + | 0.00587574i | ||||
\(418\) | 5.45334i | 0.266731i | ||||||||
\(419\) | 16.0060 | 0.781943 | 0.390972 | − | 0.920403i | \(-0.372139\pi\) | ||||
0.390972 | + | 0.920403i | \(0.372139\pi\) | |||||||
\(420\) | −9.05607 | − | 8.22225i | −0.441891 | − | 0.401205i | ||||
\(421\) | − | 26.7513i | − | 1.30378i | −0.758315 | − | 0.651889i | \(-0.773977\pi\) | ||
0.758315 | − | 0.651889i | \(-0.226023\pi\) | |||||||
\(422\) | −4.05994 | −0.197635 | ||||||||
\(423\) | 27.7238 | − | 18.2462i | 1.34798 | − | 0.887162i | ||||
\(424\) | 13.7812i | 0.669276i | ||||||||
\(425\) | −1.46527 | − | 0.773361i | −0.0710759 | − | 0.0375135i | ||||
\(426\) | 2.77319 | + | 9.25801i | 0.134361 | + | 0.448552i | ||||
\(427\) | 2.16434i | 0.104740i | ||||||||
\(428\) | 10.4463i | 0.504941i | ||||||||
\(429\) | 4.42865 | + | 14.7846i | 0.213817 | + | 0.713807i | ||||
\(430\) | −8.30619 | − | 13.7761i | −0.400560 | − | 0.664342i | ||||
\(431\) | −1.45183 | −0.0699322 | −0.0349661 | − | 0.999388i | \(-0.511132\pi\) | ||||
−0.0349661 | + | 0.999388i | \(0.511132\pi\) | |||||||
\(432\) | −3.33822 | + | 3.98199i | −0.160610 | + | 0.191584i | ||||
\(433\) | 14.3432 | 0.689289 | 0.344645 | − | 0.938733i | \(-0.387999\pi\) | ||||
0.344645 | + | 0.938733i | \(0.387999\pi\) | |||||||
\(434\) | −7.53776 | −0.361824 | ||||||||
\(435\) | −17.5442 | + | 19.3234i | −0.841179 | + | 0.926484i | ||||
\(436\) | 3.63460i | 0.174066i | ||||||||
\(437\) | −8.81298 | − | 4.54377i | −0.421582 | − | 0.217358i | ||||
\(438\) | 3.93493 | + | 13.1364i | 0.188018 | + | 0.627680i | ||||
\(439\) | −31.5600 | −1.50628 | −0.753138 | − | 0.657863i | \(-0.771461\pi\) | ||||
−0.753138 | + | 0.657863i | \(0.771461\pi\) | |||||||
\(440\) | −3.04540 | − | 5.05090i | −0.145184 | − | 0.240792i | ||||
\(441\) | 7.45406 | − | 4.90583i | 0.354955 | − | 0.233611i | ||||
\(442\) | −1.11944 | −0.0532461 | ||||||||
\(443\) | −40.5298 | −1.92563 | −0.962815 | − | 0.270160i | \(-0.912923\pi\) | ||||
−0.962815 | + | 0.270160i | \(0.912923\pi\) | |||||||
\(444\) | 4.36119 | − | 1.30637i | 0.206973 | − | 0.0619976i | ||||
\(445\) | 8.11236 | + | 13.4546i | 0.384563 | + | 0.637810i | ||||
\(446\) | − | 26.8510i | − | 1.27143i | ||||||
\(447\) | 35.2324 | − | 10.5537i | 1.66643 | − | 0.499171i | ||||
\(448\) | 3.15825 | 0.149213 | ||||||||
\(449\) | − | 13.0425i | − | 0.615512i | −0.951465 | − | 0.307756i | \(-0.900422\pi\) | ||
0.951465 | − | 0.307756i | \(-0.0995780\pi\) | |||||||
\(450\) | −1.44439 | − | 14.9303i | −0.0680892 | − | 0.703821i | ||||
\(451\) | 18.2610i | 0.859879i | ||||||||
\(452\) | − | 0.586991i | − | 0.0276097i | ||||||
\(453\) | 27.1805 | − | 8.14176i | 1.27705 | − | 0.382533i | ||||
\(454\) | − | 16.3101i | − | 0.765469i | ||||||
\(455\) | 20.4309 | − | 12.3187i | 0.957815 | − | 0.577508i | ||||
\(456\) | −1.02756 | − | 3.43041i | −0.0481200 | − | 0.160644i | ||||
\(457\) | −32.9430 | −1.54101 | −0.770504 | − | 0.637435i | \(-0.779996\pi\) | ||||
−0.770504 | + | 0.637435i | \(0.779996\pi\) | |||||||
\(458\) | 13.0346i | 0.609066i | ||||||||
\(459\) | −1.31950 | − | 1.10618i | −0.0615890 | − | 0.0516318i | ||||
\(460\) | 10.7001 | − | 0.713133i | 0.498893 | − | 0.0332500i | ||||
\(461\) | 18.9180i | 0.881100i | 0.897728 | + | 0.440550i | \(0.145216\pi\) | ||||
−0.897728 | + | 0.440550i | \(0.854784\pi\) | |||||||
\(462\) | 13.8218 | − | 4.14025i | 0.643049 | − | 0.192622i | ||||
\(463\) | 1.43119i | 0.0665132i | 0.999447 | + | 0.0332566i | \(0.0105879\pi\) | ||||
−0.999447 | + | 0.0332566i | \(0.989412\pi\) | |||||||
\(464\) | − | 6.73889i | − | 0.312845i | ||||||
\(465\) | −6.84369 | − | 6.21356i | −0.317368 | − | 0.288147i | ||||
\(466\) | 18.3561 | 0.850329 | ||||||||
\(467\) | − | 36.8872i | − | 1.70694i | −0.521144 | − | 0.853469i | \(-0.674495\pi\) | ||
0.521144 | − | 0.853469i | \(-0.325505\pi\) | |||||||
\(468\) | −5.57167 | − | 8.46575i | −0.257550 | − | 0.391330i | ||||
\(469\) | −1.48043 | −0.0683601 | ||||||||
\(470\) | −12.7734 | − | 21.1850i | −0.589191 | − | 0.977193i | ||||
\(471\) | −15.2666 | + | 4.57303i | −0.703449 | + | 0.210714i | ||||
\(472\) | − | 12.0898i | − | 0.556479i | ||||||
\(473\) | 18.9755 | 0.872492 | ||||||||
\(474\) | 3.38504 | + | 11.3006i | 0.155480 | + | 0.519055i | ||||
\(475\) | 9.14225 | + | 4.82523i | 0.419475 | + | 0.221397i | ||||
\(476\) | 1.04654i | 0.0479680i | ||||||||
\(477\) | −22.7292 | − | 34.5353i | −1.04070 | − | 1.58126i | ||||
\(478\) | − | 7.83756i | − | 0.358482i | ||||||
\(479\) | 17.8352 | 0.814912 | 0.407456 | − | 0.913225i | \(-0.366416\pi\) | ||||
0.407456 | + | 0.913225i | \(0.366416\pi\) | |||||||
\(480\) | 2.86744 | + | 2.60342i | 0.130880 | + | 0.118829i | ||||
\(481\) | 8.87960i | 0.404875i | ||||||||
\(482\) | 16.8965i | 0.769613i | ||||||||
\(483\) | −4.82552 | + | 25.7868i | −0.219569 | + | 1.17334i | ||||
\(484\) | −4.04279 | −0.183763 | ||||||||
\(485\) | −21.0184 | − | 34.8597i | −0.954397 | − | 1.58290i | ||||
\(486\) | 1.79804 | − | 15.4844i | 0.0815609 | − | 0.702387i | ||||
\(487\) | − | 5.32528i | − | 0.241312i | −0.992694 | − | 0.120656i | \(-0.961500\pi\) | ||
0.992694 | − | 0.120656i | \(-0.0384997\pi\) | |||||||
\(488\) | − | 0.685298i | − | 0.0310220i | ||||||
\(489\) | 11.7425 | + | 39.2011i | 0.531013 | + | 1.77273i | ||||
\(490\) | −3.43435 | − | 5.69598i | −0.155148 | − | 0.257318i | ||||
\(491\) | 27.6023i | 1.24568i | 0.782351 | + | 0.622838i | \(0.214021\pi\) | ||||
−0.782351 | + | 0.622838i | \(0.785979\pi\) | |||||||
\(492\) | −3.44089 | − | 11.4871i | −0.155127 | − | 0.517878i | ||||
\(493\) | 2.23304 | 0.100571 | ||||||||
\(494\) | 6.98450 | 0.314247 | ||||||||
\(495\) | 15.9620 | + | 7.63465i | 0.717440 | + | 0.343152i | ||||
\(496\) | 2.38669 | 0.107166 | ||||||||
\(497\) | 17.6223i | 0.790467i | ||||||||
\(498\) | −2.07134 | − | 6.91495i | −0.0928188 | − | 0.309866i | ||||
\(499\) | −25.7722 | −1.15372 | −0.576861 | − | 0.816843i | \(-0.695722\pi\) | ||||
−0.576861 | + | 0.816843i | \(0.695722\pi\) | |||||||
\(500\) | −11.1622 | + | 0.636316i | −0.499190 | + | 0.0284569i | ||||
\(501\) | −16.5805 | + | 4.96660i | −0.740763 | + | 0.221891i | ||||
\(502\) | 26.2859 | 1.17320 | ||||||||
\(503\) | 36.2072i | 1.61440i | 0.590277 | + | 0.807201i | \(0.299018\pi\) | ||||
−0.590277 | + | 0.807201i | \(0.700982\pi\) | |||||||
\(504\) | −7.91446 | + | 5.20884i | −0.352538 | + | 0.232020i | ||||
\(505\) | −3.97054 | + | 2.39401i | −0.176687 | + | 0.106532i | ||||
\(506\) | −5.79681 | + | 11.2433i | −0.257699 | + | 0.499828i | ||||
\(507\) | −2.63401 | + | 0.789003i | −0.116980 | + | 0.0350408i | ||||
\(508\) | 5.94678i | 0.263846i | ||||||||
\(509\) | 9.39513i | 0.416432i | 0.978083 | + | 0.208216i | \(0.0667656\pi\) | ||||
−0.978083 | + | 0.208216i | \(0.933234\pi\) | |||||||
\(510\) | −0.862687 | + | 0.950173i | −0.0382004 | + | 0.0420744i | ||||
\(511\) | 25.0046i | 1.10614i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.23276 | + | 6.90176i | 0.363485 | + | 0.304720i | ||||
\(514\) | −2.32061 | −0.102358 | ||||||||
\(515\) | −2.76947 | − | 4.59325i | −0.122037 | − | 0.202403i | ||||
\(516\) | −11.9365 | + | 3.57551i | −0.525475 | + | 0.157403i | ||||
\(517\) | 29.1807 | 1.28337 | ||||||||
\(518\) | 8.30136 | 0.364741 | ||||||||
\(519\) | 22.2691 | − | 6.67058i | 0.977504 | − | 0.292806i | ||||
\(520\) | −6.46906 | + | 3.90047i | −0.283687 | + | 0.171047i | ||||
\(521\) | −21.5382 | −0.943606 | −0.471803 | − | 0.881704i | \(-0.656397\pi\) | ||||
−0.471803 | + | 0.881704i | \(0.656397\pi\) | |||||||
\(522\) | 11.1143 | + | 16.8874i | 0.486461 | + | 0.739143i | ||||
\(523\) | −12.2150 | −0.534126 | −0.267063 | − | 0.963679i | \(-0.586053\pi\) | ||||
−0.267063 | + | 0.963679i | \(0.586053\pi\) | |||||||
\(524\) | − | 6.85575i | − | 0.299495i | ||||||
\(525\) | 5.28893 | − | 26.8350i | 0.230828 | − | 1.17117i | ||||
\(526\) | 31.4516i | 1.37135i | ||||||||
\(527\) | 0.790870i | 0.0344508i | ||||||||
\(528\) | −4.37642 | + | 1.31093i | −0.190459 | + | 0.0570511i | ||||
\(529\) | −13.3401 | − | 18.7361i | −0.580004 | − | 0.814613i | ||||
\(530\) | −26.3900 | + | 15.9117i | −1.14631 | + | 0.691158i | ||||
\(531\) | 19.9395 | + | 30.2967i | 0.865302 | + | 1.31476i | ||||
\(532\) | − | 6.52967i | − | 0.283097i | ||||||
\(533\) | 23.3883 | 1.01306 | ||||||||
\(534\) | 11.6579 | − | 3.49207i | 0.504489 | − | 0.151117i | ||||
\(535\) | −20.0039 | + | 12.0612i | −0.864843 | + | 0.521450i | ||||
\(536\) | 0.468752 | 0.0202470 | ||||||||
\(537\) | 0.674582 | + | 2.25203i | 0.0291104 | + | 0.0971821i | ||||
\(538\) | 10.7521i | 0.463558i | ||||||||
\(539\) | 7.84576 | 0.337941 | ||||||||
\(540\) | −11.4795 | − | 1.79487i | −0.493998 | − | 0.0772391i | ||||
\(541\) | −15.9915 | −0.687529 | −0.343764 | − | 0.939056i | \(-0.611702\pi\) | ||||
−0.343764 | + | 0.939056i | \(0.611702\pi\) | |||||||
\(542\) | −7.09113 | −0.304590 | ||||||||
\(543\) | 6.26522 | + | 20.9158i | 0.268866 | + | 0.897584i | ||||
\(544\) | − | 0.331367i | − | 0.0142072i | ||||||
\(545\) | −6.95998 | + | 4.19647i | −0.298133 | + | 0.179757i | ||||
\(546\) | −5.30273 | − | 17.7026i | −0.226936 | − | 0.757603i | ||||
\(547\) | − | 42.8762i | − | 1.83325i | −0.399745 | − | 0.916627i | \(-0.630901\pi\) | ||
0.399745 | − | 0.916627i | \(-0.369099\pi\) | |||||||
\(548\) | 14.8092i | 0.632616i | ||||||||
\(549\) | 1.13025 | + | 1.71733i | 0.0482379 | + | 0.0732941i | ||||
\(550\) | 6.15589 | − | 11.6634i | 0.262488 | − | 0.497330i | ||||
\(551\) | −13.9326 | −0.593550 | ||||||||
\(552\) | 1.52791 | − | 8.16489i | 0.0650322 | − | 0.347521i | ||||
\(553\) | 21.5103i | 0.914712i | ||||||||
\(554\) | 10.1872i | 0.432814i | ||||||||
\(555\) | 7.53697 | + | 6.84302i | 0.319927 | + | 0.290470i | ||||
\(556\) | 0.241417 | 0.0102384 | ||||||||
\(557\) | − | 4.49189i | − | 0.190328i | −0.995462 | − | 0.0951638i | \(-0.969663\pi\) | ||
0.995462 | − | 0.0951638i | \(-0.0303375\pi\) | |||||||
\(558\) | −5.98097 | + | 3.93633i | −0.253195 | + | 0.166638i | ||||
\(559\) | − | 24.3033i | − | 1.02792i | ||||||
\(560\) | 3.64647 | + | 6.04780i | 0.154092 | + | 0.255566i | ||||
\(561\) | −0.434400 | − | 1.45020i | −0.0183404 | − | 0.0612275i | ||||
\(562\) | 16.0901 | 0.678718 | ||||||||
\(563\) | 18.8243i | 0.793348i | 0.917960 | + | 0.396674i | \(0.129836\pi\) | ||||
−0.917960 | + | 0.396674i | \(0.870164\pi\) | |||||||
\(564\) | −18.3561 | + | 5.49847i | −0.772931 | + | 0.231527i | ||||
\(565\) | 1.12404 | − | 0.677733i | 0.0472888 | − | 0.0285124i | ||||
\(566\) | −28.1303 | −1.18240 | ||||||||
\(567\) | 11.2425 | − | 26.1064i | 0.472142 | − | 1.09636i | ||||
\(568\) | − | 5.57976i | − | 0.234122i | ||||||
\(569\) | −34.8852 | −1.46246 | −0.731231 | − | 0.682130i | \(-0.761054\pi\) | ||||
−0.731231 | + | 0.682130i | \(0.761054\pi\) | |||||||
\(570\) | 5.38257 | − | 5.92842i | 0.225451 | − | 0.248314i | ||||
\(571\) | 28.9370i | 1.21097i | 0.795855 | + | 0.605487i | \(0.207022\pi\) | ||||
−0.795855 | + | 0.605487i | \(0.792978\pi\) | |||||||
\(572\) | − | 8.91062i | − | 0.372572i | ||||||
\(573\) | −38.9015 | + | 11.6527i | −1.62513 | + | 0.486800i | ||||
\(574\) | − | 21.8652i | − | 0.912637i | ||||||
\(575\) | 13.7198 | + | 19.6664i | 0.572154 | + | 0.820146i | ||||
\(576\) | 2.50597 | − | 1.64928i | 0.104415 | − | 0.0687201i | ||||
\(577\) | 28.8137i | 1.19953i | 0.800177 | + | 0.599764i | \(0.204739\pi\) | ||||
−0.800177 | + | 0.599764i | \(0.795261\pi\) | |||||||
\(578\) | −16.8902 | −0.702540 | ||||||||
\(579\) | −9.27195 | − | 30.9535i | −0.385329 | − | 1.28638i | ||||
\(580\) | 12.9045 | − | 7.78065i | 0.535828 | − | 0.323074i | ||||
\(581\) | − | 13.1624i | − | 0.546066i | ||||||
\(582\) | −30.2047 | + | 9.04765i | −1.25203 | + | 0.375037i | ||||
\(583\) | − | 36.3501i | − | 1.50547i | ||||||
\(584\) | − | 7.91723i | − | 0.327617i | ||||||
\(585\) | 9.77827 | − | 20.4438i | 0.404282 | − | 0.845246i | ||||
\(586\) | − | 10.7652i | − | 0.444707i | ||||||
\(587\) | −14.8097 | −0.611260 | −0.305630 | − | 0.952150i | \(-0.598867\pi\) | ||||
−0.305630 | + | 0.952150i | \(0.598867\pi\) | |||||||
\(588\) | −4.93537 | + | 1.47836i | −0.203531 | + | 0.0609666i | ||||
\(589\) | − | 4.93448i | − | 0.203322i | ||||||
\(590\) | 23.1511 | − | 13.9588i | 0.953115 | − | 0.574673i | ||||
\(591\) | −8.26774 | + | 2.47656i | −0.340090 | + | 0.101872i | ||||
\(592\) | −2.62847 | −0.108029 | ||||||||
\(593\) | 2.98454 | 0.122561 | 0.0612803 | − | 0.998121i | \(-0.480482\pi\) | ||||
0.0612803 | + | 0.998121i | \(0.480482\pi\) | |||||||
\(594\) | 8.80507 | − | 10.5031i | 0.361276 | − | 0.430948i | ||||
\(595\) | −2.00404 | + | 1.20832i | −0.0821575 | + | 0.0495363i | ||||
\(596\) | −21.2344 | −0.869795 | ||||||||
\(597\) | 7.29278 | + | 24.3462i | 0.298474 | + | 0.996425i | ||||
\(598\) | 14.4002 | + | 7.42440i | 0.588868 | + | 0.303606i | ||||
\(599\) | − | 5.47578i | − | 0.223734i | −0.993723 | − | 0.111867i | \(-0.964317\pi\) | ||
0.993723 | − | 0.111867i | \(-0.0356831\pi\) | |||||||
\(600\) | −1.67464 | + | 8.49680i | −0.0683670 | + | 0.346880i | ||||
\(601\) | 1.39688 | 0.0569799 | 0.0284900 | − | 0.999594i | \(-0.490930\pi\) | ||||
0.0284900 | + | 0.999594i | \(0.490930\pi\) | |||||||
\(602\) | −22.7207 | −0.926025 | ||||||||
\(603\) | −1.17468 | + | 0.773104i | −0.0478365 | + | 0.0314832i | ||||
\(604\) | −16.3816 | −0.666556 | ||||||||
\(605\) | −4.66776 | − | 7.74163i | −0.189771 | − | 0.314742i | ||||
\(606\) | 1.03053 | + | 3.44033i | 0.0418625 | + | 0.139754i | ||||
\(607\) | − | 32.7100i | − | 1.32766i | −0.747884 | − | 0.663830i | \(-0.768930\pi\) | ||
0.747884 | − | 0.663830i | \(-0.231070\pi\) | |||||||
\(608\) | 2.06750i | 0.0838481i | ||||||||
\(609\) | 10.5779 | + | 35.3132i | 0.428637 | + | 1.43096i | ||||
\(610\) | 1.31229 | − | 0.791237i | 0.0531332 | − | 0.0320363i | ||||
\(611\) | − | 37.3739i | − | 1.51199i | ||||||
\(612\) | 0.546517 | + | 0.830394i | 0.0220916 | + | 0.0335667i | ||||
\(613\) | −35.5819 | −1.43714 | −0.718569 | − | 0.695456i | \(-0.755202\pi\) | ||||
−0.718569 | + | 0.695456i | \(0.755202\pi\) | |||||||
\(614\) | − | 21.1061i | − | 0.851774i | ||||||
\(615\) | 18.0241 | − | 19.8519i | 0.726800 | − | 0.800505i | ||||
\(616\) | −8.33036 | −0.335640 | ||||||||
\(617\) | − | 36.0529i | − | 1.45144i | −0.687992 | − | 0.725718i | \(-0.741508\pi\) | ||
0.687992 | − | 0.725718i | \(-0.258492\pi\) | |||||||
\(618\) | −3.97989 | + | 1.19215i | −0.160095 | + | 0.0479555i | ||||
\(619\) | − | 2.79306i | − | 0.112263i | −0.998423 | − | 0.0561313i | \(-0.982123\pi\) | ||
0.998423 | − | 0.0561313i | \(-0.0178766\pi\) | |||||||
\(620\) | 2.75565 | + | 4.57033i | 0.110669 | + | 0.183549i | ||||
\(621\) | 9.63732 | + | 22.9809i | 0.386732 | + | 0.922192i | ||||
\(622\) | − | 15.5206i | − | 0.622319i | ||||||
\(623\) | 22.1905 | 0.889042 | ||||||||
\(624\) | 1.67901 | + | 5.60521i | 0.0672142 | + | 0.224388i | ||||
\(625\) | −14.1063 | − | 20.6401i | −0.564250 | − | 0.825604i | ||||
\(626\) | 0.701429 | 0.0280347 | ||||||||
\(627\) | 2.71035 | + | 9.04824i | 0.108241 | + | 0.361352i | ||||
\(628\) | 9.20113 | 0.367165 | ||||||||
\(629\) | − | 0.870987i | − | 0.0347285i | ||||||
\(630\) | −19.1125 | − | 9.14151i | −0.761459 | − | 0.364207i | ||||
\(631\) | 12.2810i | 0.488899i | 0.969662 | + | 0.244450i | \(0.0786073\pi\) | ||||
−0.969662 | + | 0.244450i | \(0.921393\pi\) | |||||||
\(632\) | − | 6.81084i | − | 0.270921i | ||||||
\(633\) | −6.73630 | + | 2.01782i | −0.267744 | + | 0.0802013i | ||||
\(634\) | 26.6487 | 1.05836 | ||||||||
\(635\) | −11.3876 | + | 6.86608i | −0.451904 | + | 0.272472i | ||||
\(636\) | 6.84938 | + | 22.8660i | 0.271596 | + | 0.906695i | ||||
\(637\) | − | 10.0487i | − | 0.398142i | ||||||
\(638\) | 17.7749i | 0.703713i | ||||||||
\(639\) | 9.20261 | + | 13.9827i | 0.364049 | + | 0.553147i | ||||
\(640\) | −1.15459 | − | 1.91492i | −0.0456391 | − | 0.0756939i | ||||
\(641\) | −13.5240 | −0.534164 | −0.267082 | − | 0.963674i | \(-0.586060\pi\) | ||||
−0.267082 | + | 0.963674i | \(0.586060\pi\) | |||||||
\(642\) | 5.19190 | + | 17.3326i | 0.204908 | + | 0.684065i | ||||
\(643\) | −22.1920 | −0.875167 | −0.437584 | − | 0.899178i | \(-0.644166\pi\) | ||||
−0.437584 | + | 0.899178i | \(0.644166\pi\) | |||||||
\(644\) | 6.94093 | − | 13.4625i | 0.273511 | − | 0.530495i | ||||
\(645\) | −20.6285 | − | 18.7292i | −0.812248 | − | 0.737462i | ||||
\(646\) | −0.685099 | −0.0269549 | ||||||||
\(647\) | −8.05146 | −0.316535 | −0.158268 | − | 0.987396i | \(-0.550591\pi\) | ||||
−0.158268 | + | 0.987396i | \(0.550591\pi\) | |||||||
\(648\) | −3.55974 | + | 8.26609i | −0.139840 | + | 0.324723i | ||||
\(649\) | 31.8888i | 1.25174i | ||||||||
\(650\) | −14.9382 | − | 7.88431i | −0.585925 | − | 0.309248i | ||||
\(651\) | −12.5067 | + | 3.74633i | −0.490178 | + | 0.146830i | ||||
\(652\) | − | 23.6263i | − | 0.925279i | ||||||
\(653\) | 36.1968 | 1.41649 | 0.708246 | − | 0.705966i | \(-0.249487\pi\) | ||||
0.708246 | + | 0.705966i | \(0.249487\pi\) | |||||||
\(654\) | 1.80643 | + | 6.03058i | 0.0706369 | + | 0.235814i | ||||
\(655\) | 13.1282 | − | 7.91557i | 0.512962 | − | 0.309287i | ||||
\(656\) | 6.92322i | 0.270306i | ||||||||
\(657\) | 13.0578 | + | 19.8403i | 0.509431 | + | 0.774045i | ||||
\(658\) | −34.9401 | −1.36211 | ||||||||
\(659\) | 27.2539 | 1.06166 | 0.530831 | − | 0.847478i | \(-0.321880\pi\) | ||||
0.530831 | + | 0.847478i | \(0.321880\pi\) | |||||||
\(660\) | −7.56330 | − | 6.86692i | −0.294401 | − | 0.267295i | ||||
\(661\) | 23.7666i | 0.924412i | 0.886773 | + | 0.462206i | \(0.152942\pi\) | ||||
−0.886773 | + | 0.462206i | \(0.847058\pi\) | |||||||
\(662\) | 12.0090 | 0.466743 | ||||||||
\(663\) | −1.85738 | + | 0.556368i | −0.0721347 | + | 0.0216075i | ||||
\(664\) | 4.16761i | 0.161735i | ||||||||
\(665\) | 12.5038 | − | 7.53907i | 0.484877 | − | 0.292353i | ||||
\(666\) | 6.58686 | − | 4.33509i | 0.255236 | − | 0.167981i | ||||
\(667\) | −28.7254 | − | 14.8102i | −1.11225 | − | 0.573452i | ||||
\(668\) | 9.99301 | 0.386641 | ||||||||
\(669\) | −13.3452 | − | 44.5515i | −0.515954 | − | 1.72246i | ||||
\(670\) | 0.541215 | + | 0.897624i | 0.0209090 | + | 0.0346782i | ||||
\(671\) | 1.80758i | 0.0697808i | ||||||||
\(672\) | 5.24020 | − | 1.56967i | 0.202145 | − | 0.0605515i | ||||
\(673\) | − | 14.3957i | − | 0.554912i | −0.960738 | − | 0.277456i | \(-0.910509\pi\) | ||
0.960738 | − | 0.277456i | \(-0.0894914\pi\) | |||||||
\(674\) | −32.5953 | −1.25552 | ||||||||
\(675\) | −9.81702 | − | 24.0546i | −0.377857 | − | 0.925864i | ||||
\(676\) | 1.58751 | 0.0610579 | ||||||||
\(677\) | − | 31.0852i | − | 1.19470i | −0.801981 | − | 0.597350i | \(-0.796220\pi\) | ||
0.801981 | − | 0.597350i | \(-0.203780\pi\) | |||||||
\(678\) | −0.291739 | − | 0.973942i | −0.0112042 | − | 0.0374040i | ||||
\(679\) | −57.4935 | −2.20640 | ||||||||
\(680\) | 0.634541 | − | 0.382592i | 0.0243335 | − | 0.0146717i | ||||
\(681\) | −8.10622 | − | 27.0618i | −0.310631 | − | 1.03701i | ||||
\(682\) | −6.29526 | −0.241058 | ||||||||
\(683\) | −3.72271 | −0.142446 | −0.0712228 | − | 0.997460i | \(-0.522690\pi\) | ||||
−0.0712228 | + | 0.997460i | \(0.522690\pi\) | |||||||
\(684\) | −3.40989 | − | 5.18108i | −0.130380 | − | 0.198103i | ||||
\(685\) | −28.3584 | + | 17.0985i | −1.08352 | + | 0.653299i | ||||
\(686\) | 12.7134 | 0.485402 | ||||||||
\(687\) | 6.47829 | + | 21.6271i | 0.247162 | + | 0.825126i | ||||
\(688\) | 7.19407 | 0.274271 | ||||||||
\(689\) | −46.5563 | −1.77365 | ||||||||
\(690\) | 17.3992 | − | 6.50126i | 0.662378 | − | 0.247499i | ||||
\(691\) | −37.6228 | −1.43124 | −0.715619 | − | 0.698491i | \(-0.753855\pi\) | ||||
−0.715619 | + | 0.698491i | \(0.753855\pi\) | |||||||
\(692\) | −13.4215 | −0.510208 | ||||||||
\(693\) | 20.8756 | − | 13.7391i | 0.792998 | − | 0.521906i | ||||
\(694\) | −14.3932 | −0.546357 | ||||||||
\(695\) | 0.278737 | + | 0.462294i | 0.0105731 | + | 0.0175358i | ||||
\(696\) | −3.34928 | − | 11.1813i | −0.126954 | − | 0.423824i | ||||
\(697\) | −2.29412 | −0.0868961 | ||||||||
\(698\) | 0.672923 | 0.0254705 | ||||||||
\(699\) | 30.4566 | − | 9.12312i | 1.15198 | − | 0.345068i | ||||
\(700\) | −7.37089 | + | 13.9654i | −0.278593 | + | 0.527844i | ||||
\(701\) | 12.0462 | 0.454979 | 0.227489 | − | 0.973781i | \(-0.426948\pi\) | ||||
0.227489 | + | 0.973781i | \(0.426948\pi\) | |||||||
\(702\) | −13.4521 | − | 11.2773i | −0.507718 | − | 0.425635i | ||||
\(703\) | 5.43435i | 0.204961i | ||||||||
\(704\) | 2.63765 | 0.0994102 | ||||||||
\(705\) | −31.7228 | − | 28.8020i | −1.19475 | − | 1.08475i | ||||
\(706\) | 25.3608 | 0.954465 | ||||||||
\(707\) | 6.54854i | 0.246283i | ||||||||
\(708\) | −6.00874 | − | 20.0596i | −0.225822 | − | 0.753885i | ||||
\(709\) | 49.3481i | 1.85331i | 0.375915 | + | 0.926654i | \(0.377328\pi\) | ||||
−0.375915 | + | 0.926654i | \(0.622672\pi\) | |||||||
\(710\) | 10.6848 | − | 6.44233i | 0.400994 | − | 0.241776i | ||||
\(711\) | 11.2330 | + | 17.0677i | 0.421270 | + | 0.640090i | ||||
\(712\) | −7.02620 | −0.263318 | ||||||||
\(713\) | 5.24527 | − | 10.1736i | 0.196437 | − | 0.381004i | ||||
\(714\) | 0.520137 | + | 1.73643i | 0.0194656 | + | 0.0649842i | ||||
\(715\) | 17.0631 | − | 10.2881i | 0.638125 | − | 0.384753i | ||||
\(716\) | − | 1.35729i | − | 0.0507242i | ||||||
\(717\) | −3.89533 | − | 13.0042i | −0.145474 | − | 0.485650i | ||||
\(718\) | 18.0914 | 0.675164 | ||||||||
\(719\) | − | 12.1521i | − | 0.453198i | −0.973988 | − | 0.226599i | \(-0.927239\pi\) | ||
0.973988 | − | 0.226599i | \(-0.0727608\pi\) | |||||||
\(720\) | 6.05161 | + | 2.89449i | 0.225530 | + | 0.107871i | ||||
\(721\) | −7.57557 | −0.282129 | ||||||||
\(722\) | −14.7255 | −0.548025 | ||||||||
\(723\) | 8.39768 | + | 28.0348i | 0.312313 | + | 1.04263i | ||||
\(724\) | − | 12.6059i | − | 0.468494i | ||||||
\(725\) | 29.7987 | + | 15.7276i | 1.10669 | + | 0.584108i | ||||
\(726\) | −6.70785 | + | 2.00930i | −0.248952 | + | 0.0745721i | ||||
\(727\) | 12.7421 | 0.472578 | 0.236289 | − | 0.971683i | \(-0.424069\pi\) | ||||
0.236289 | + | 0.971683i | \(0.424069\pi\) | |||||||
\(728\) | 10.6693i | 0.395431i | ||||||||
\(729\) | −4.71254 | − | 26.5856i | −0.174539 | − | 0.984650i | ||||
\(730\) | 15.1609 | − | 9.14114i | 0.561129 | − | 0.338329i | ||||
\(731\) | 2.38387i | 0.0881708i | ||||||||
\(732\) | −0.340599 | − | 1.13705i | −0.0125889 | − | 0.0420268i | ||||
\(733\) | 7.41403 | 0.273844 | 0.136922 | − | 0.990582i | \(-0.456279\pi\) | ||||
0.136922 | + | 0.990582i | \(0.456279\pi\) | |||||||
\(734\) | −0.368267 | −0.0135930 | ||||||||
\(735\) | −8.52926 | − | 7.74394i | −0.314607 | − | 0.285640i | ||||
\(736\) | −2.19771 | + | 4.26263i | −0.0810088 | + | 0.157123i | ||||
\(737\) | −1.23640 | −0.0455435 | ||||||||
\(738\) | −11.4183 | − | 17.3493i | −0.420315 | − | 0.638638i | ||||
\(739\) | −19.5512 | −0.719202 | −0.359601 | − | 0.933106i | \(-0.617087\pi\) | ||||
−0.359601 | + | 0.933106i | \(0.617087\pi\) | |||||||
\(740\) | −3.03480 | − | 5.03332i | −0.111561 | − | 0.185028i | ||||
\(741\) | 11.5888 | − | 3.47135i | 0.425724 | − | 0.127523i | ||||
\(742\) | 43.5246i | 1.59784i | ||||||||
\(743\) | − | 41.8808i | − | 1.53646i | −0.640176 | − | 0.768228i | \(-0.721139\pi\) | ||
0.640176 | − | 0.768228i | \(-0.278861\pi\) | |||||||
\(744\) | 3.96003 | − | 1.18620i | 0.145182 | − | 0.0434884i | ||||
\(745\) | −24.5170 | − | 40.6622i | −0.898233 | − | 1.48975i | ||||
\(746\) | 19.5200 | 0.714676 | ||||||||
\(747\) | −6.87357 | − | 10.4439i | −0.251491 | − | 0.382122i | ||||
\(748\) | 0.874030i | 0.0319577i | ||||||||
\(749\) | 32.9920i | 1.20550i | ||||||||
\(750\) | −18.2042 | + | 6.60349i | −0.664724 | + | 0.241125i | ||||
\(751\) | − | 19.1550i | − | 0.698975i | −0.936941 | − | 0.349488i | \(-0.886356\pi\) | ||
0.936941 | − | 0.349488i | \(-0.113644\pi\) | |||||||
\(752\) | 11.0631 | 0.403431 | ||||||||
\(753\) | 43.6139 | − | 13.0643i | 1.58938 | − | 0.476090i | ||||
\(754\) | 22.7656 | 0.829074 | ||||||||
\(755\) | −18.9140 | − | 31.3694i | −0.688349 | − | 1.14165i | ||||
\(756\) | −10.5429 | + | 12.5761i | −0.383443 | + | 0.457389i | ||||
\(757\) | 38.7480 | 1.40832 | 0.704160 | − | 0.710042i | \(-0.251324\pi\) | ||||
0.704160 | + | 0.710042i | \(0.251324\pi\) | |||||||
\(758\) | 33.4418i | 1.21466i | ||||||||
\(759\) | −4.03010 | + | 21.5361i | −0.146283 | + | 0.781713i | ||||
\(760\) | −3.95909 | + | 2.38711i | −0.143611 | + | 0.0865895i | ||||
\(761\) | 31.4000i | 1.13825i | 0.822252 | + | 0.569124i | \(0.192718\pi\) | ||||
−0.822252 | + | 0.569124i | \(0.807282\pi\) | |||||||
\(762\) | 2.95560 | + | 9.86697i | 0.107070 | + | 0.357443i | ||||
\(763\) | 11.4790i | 0.415567i | ||||||||
\(764\) | 23.4458 | 0.848239 | ||||||||
\(765\) | −0.959137 | + | 2.00530i | −0.0346777 | + | 0.0725018i | ||||
\(766\) | 17.0408i | 0.615710i | ||||||||
\(767\) | 40.8423 | 1.47473 | ||||||||
\(768\) | −1.65921 | + | 0.497008i | −0.0598716 | + | 0.0179342i | ||||
\(769\) | − | 44.1018i | − | 1.59035i | −0.606380 | − | 0.795175i | \(-0.707379\pi\) | ||
0.606380 | − | 0.795175i | \(-0.292621\pi\) | |||||||
\(770\) | −9.61813 | − | 15.9520i | −0.346613 | − | 0.574870i | ||||
\(771\) | −3.85039 | + | 1.15336i | −0.138668 | + | 0.0415374i | ||||
\(772\) | 18.6555i | 0.671428i | ||||||||
\(773\) | 38.2289i | 1.37500i | 0.726185 | + | 0.687499i | \(0.241292\pi\) | ||||
−0.726185 | + | 0.687499i | \(0.758708\pi\) | |||||||
\(774\) | −18.0281 | + | 11.8651i | −0.648007 | + | 0.426481i | ||||
\(775\) | −5.57019 | + | 10.5537i | −0.200087 | + | 0.379100i | ||||
\(776\) | 18.2042 | 0.653494 | ||||||||
\(777\) | 13.7737 | − | 4.12584i | 0.494129 | − | 0.148014i | ||||
\(778\) | 0.355884 | 0.0127591 | ||||||||
\(779\) | 14.3137 | 0.512842 | ||||||||
\(780\) | −8.79498 | + | 9.68689i | −0.314911 | + | 0.346846i | ||||
\(781\) | 14.7175i | 0.526633i | ||||||||
\(782\) | −1.41249 | − | 0.728249i | −0.0505107 | − | 0.0260421i | ||||
\(783\) | 26.8342 | + | 22.4959i | 0.958977 | + | 0.803939i | ||||
\(784\) | 2.97452 | 0.106233 | ||||||||
\(785\) | 10.6235 | + | 17.6194i | 0.379169 | + | 0.628865i | ||||
\(786\) | −3.40736 | − | 11.3751i | −0.121537 | − | 0.405738i | ||||
\(787\) | −41.9228 | −1.49439 | −0.747193 | − | 0.664607i | \(-0.768599\pi\) | ||||
−0.747193 | + | 0.664607i | \(0.768599\pi\) | |||||||
\(788\) | 4.98294 | 0.177510 | ||||||||
\(789\) | 15.6317 | + | 52.1848i | 0.556502 | + | 1.85783i | ||||
\(790\) | 13.0422 | − | 7.86372i | 0.464022 | − | 0.279778i | ||||
\(791\) | − | 1.85386i | − | 0.0659158i | ||||||
\(792\) | −6.60987 | + | 4.35023i | −0.234871 | + | 0.154579i | ||||
\(793\) | 2.31510 | 0.0822116 | ||||||||
\(794\) | − | 19.0771i | − | 0.677019i | ||||||
\(795\) | −35.8784 | + | 39.5168i | −1.27247 | + | 1.40152i | ||||
\(796\) | − | 14.6734i | − | 0.520084i | ||||||
\(797\) | 0.345464i | 0.0122370i | 0.999981 | + | 0.00611848i | \(0.00194758\pi\) | ||||
−0.999981 | + | 0.00611848i | \(0.998052\pi\) | |||||||
\(798\) | −3.24529 | − | 10.8341i | −0.114882 | − | 0.383523i | ||||
\(799\) | 3.66595i | 0.129692i | ||||||||
\(800\) | 2.33385 | − | 4.42189i | 0.0825142 | − | 0.156337i | ||||
\(801\) | 17.6074 | − | 11.5882i | 0.622127 | − | 0.409448i | ||||
\(802\) | −29.7359 | −1.05001 | ||||||||
\(803\) | 20.8829i | 0.736942i | ||||||||
\(804\) | 0.777759 | − | 0.232973i | 0.0274294 | − | 0.00821634i | ||||
\(805\) | 33.7935 | − | 2.25225i | 1.19106 | − | 0.0793814i | ||||
\(806\) | 8.06281i | 0.284000i | ||||||||
\(807\) | 5.34390 | + | 17.8401i | 0.188114 | + | 0.628000i | ||||
\(808\) | − | 2.07347i | − | 0.0729445i | ||||||
\(809\) | 39.9547i | 1.40473i | 0.711816 | + | 0.702366i | \(0.247873\pi\) | ||||
−0.711816 | + | 0.702366i | \(0.752127\pi\) | |||||||
\(810\) | −19.9390 | + | 2.72731i | −0.700583 | + | 0.0958280i | ||||
\(811\) | 30.4786 | 1.07025 | 0.535124 | − | 0.844774i | \(-0.320265\pi\) | ||||
0.535124 | + | 0.844774i | \(0.320265\pi\) | |||||||
\(812\) | − | 21.2831i | − | 0.746890i | ||||||
\(813\) | −11.7657 | + | 3.52435i | −0.412641 | + | 0.123604i | ||||
\(814\) | 6.93299 | 0.243001 | ||||||||
\(815\) | 45.2426 | − | 27.2787i | 1.58478 | − | 0.955531i | ||||
\(816\) | −0.164692 | − | 0.549807i | −0.00576537 | − | 0.0192471i | ||||
\(817\) | − | 14.8737i | − | 0.520365i | ||||||
\(818\) | −14.1316 | −0.494100 | ||||||||
\(819\) | −17.5967 | − | 26.7369i | −0.614879 | − | 0.934264i | ||||
\(820\) | −13.2574 | + | 7.99346i | −0.462969 | + | 0.279144i | ||||
\(821\) | − | 12.0374i | − | 0.420106i | −0.977690 | − | 0.210053i | \(-0.932636\pi\) | ||
0.977690 | − | 0.210053i | \(-0.0673637\pi\) | |||||||
\(822\) | 7.36027 | + | 24.5715i | 0.256719 | + | 0.857031i | ||||
\(823\) | 10.6364i | 0.370760i | 0.982667 | + | 0.185380i | \(0.0593516\pi\) | ||||
−0.982667 | + | 0.185380i | \(0.940648\pi\) | |||||||
\(824\) | 2.39866 | 0.0835614 | ||||||||
\(825\) | 4.41712 | − | 22.4116i | 0.153784 | − | 0.780272i | ||||
\(826\) | − | 38.1827i | − | 1.32854i | ||||||
\(827\) | 36.9079i | 1.28341i | 0.766950 | + | 0.641707i | \(0.221773\pi\) | ||||
−0.766950 | + | 0.641707i | \(0.778227\pi\) | |||||||
\(828\) | −1.52289 | − | 14.3067i | −0.0529240 | − | 0.497191i | ||||
\(829\) | 49.8365 | 1.73089 | 0.865446 | − | 0.501002i | \(-0.167035\pi\) | ||||
0.865446 | + | 0.501002i | \(0.167035\pi\) | |||||||
\(830\) | −7.98066 | + | 4.81188i | −0.277013 | + | 0.167023i | ||||
\(831\) | 5.06314 | + | 16.9028i | 0.175638 | + | 0.586351i | ||||
\(832\) | − | 3.37824i | − | 0.117119i | ||||||
\(833\) | 0.985658i | 0.0341510i | ||||||||
\(834\) | 0.400561 | − | 0.119986i | 0.0138703 | − | 0.00415478i | ||||
\(835\) | 11.5378 | + | 19.1358i | 0.399282 | + | 0.662223i | ||||
\(836\) | − | 5.45334i | − | 0.188608i | ||||||
\(837\) | −7.96731 | + | 9.50379i | −0.275390 | + | 0.328499i | ||||
\(838\) | −16.0060 | −0.552917 | ||||||||
\(839\) | −0.622041 | −0.0214752 | −0.0107376 | − | 0.999942i | \(-0.503418\pi\) | ||||
−0.0107376 | + | 0.999942i | \(0.503418\pi\) | |||||||
\(840\) | 9.05607 | + | 8.22225i | 0.312464 | + | 0.283695i | ||||
\(841\) | −16.4127 | −0.565955 | ||||||||
\(842\) | 26.7513i | 0.921910i | ||||||||
\(843\) | 26.6968 | − | 7.99689i | 0.919487 | − | 0.275427i | ||||
\(844\) | 4.05994 | 0.139749 | ||||||||
\(845\) | 1.83291 | + | 3.03995i | 0.0630542 | + | 0.104577i | ||||
\(846\) | −27.7238 | + | 18.2462i | −0.953166 | + | 0.627318i | ||||
\(847\) | −12.7681 | −0.438718 | ||||||||
\(848\) | − | 13.7812i | − | 0.473250i | ||||||
\(849\) | −46.6741 | + | 13.9810i | −1.60185 | + | 0.479826i | ||||
\(850\) | 1.46527 | + | 0.773361i | 0.0502582 | + | 0.0265261i | ||||
\(851\) | −5.77663 | + | 11.2042i | −0.198020 | + | 0.384075i | ||||
\(852\) | −2.77319 | − | 9.25801i | −0.0950078 | − | 0.317174i | ||||
\(853\) | 53.1589i | 1.82013i | 0.414468 | + | 0.910064i | \(0.363968\pi\) | ||||
−0.414468 | + | 0.910064i | \(0.636032\pi\) | |||||||
\(854\) | − | 2.16434i | − | 0.0740622i | ||||||
\(855\) | 5.98435 | − | 12.5117i | 0.204660 | − | 0.427890i | ||||
\(856\) | − | 10.4463i | − | 0.357047i | ||||||
\(857\) | 43.2814 | 1.47847 | 0.739233 | − | 0.673450i | \(-0.235188\pi\) | ||||
0.739233 | + | 0.673450i | \(0.235188\pi\) | |||||||
\(858\) | −4.42865 | − | 14.7846i | −0.151191 | − | 0.504738i | ||||
\(859\) | 14.1473 | 0.482701 | 0.241351 | − | 0.970438i | \(-0.422410\pi\) | ||||
0.241351 | + | 0.970438i | \(0.422410\pi\) | |||||||
\(860\) | 8.30619 | + | 13.7761i | 0.283239 | + | 0.469761i | ||||
\(861\) | −10.8672 | − | 36.2790i | −0.370353 | − | 1.23639i | ||||
\(862\) | 1.45183 | 0.0494496 | ||||||||
\(863\) | 13.3566 | 0.454664 | 0.227332 | − | 0.973817i | \(-0.427000\pi\) | ||||
0.227332 | + | 0.973817i | \(0.427000\pi\) | |||||||
\(864\) | 3.33822 | − | 3.98199i | 0.113569 | − | 0.135470i | ||||
\(865\) | −15.4963 | − | 25.7011i | −0.526890 | − | 0.873864i | ||||
\(866\) | −14.3432 | −0.487401 | ||||||||
\(867\) | −28.0244 | + | 8.39456i | −0.951759 | + | 0.285094i | ||||
\(868\) | 7.53776 | 0.255848 | ||||||||
\(869\) | 17.9646i | 0.609408i | ||||||||
\(870\) | 17.5442 | − | 19.3234i | 0.594804 | − | 0.655123i | ||||
\(871\) | 1.58356i | 0.0536567i | ||||||||
\(872\) | − | 3.63460i | − | 0.123083i | ||||||
\(873\) | −45.6192 | + | 30.0239i | −1.54398 | + | 1.01616i | ||||
\(874\) | 8.81298 | + | 4.54377i | 0.298104 | + | 0.153695i | ||||
\(875\) | −35.2530 | + | 2.00964i | −1.19177 | + | 0.0679383i | ||||
\(876\) | −3.93493 | − | 13.1364i | −0.132949 | − | 0.443837i | ||||
\(877\) | − | 6.59780i | − | 0.222792i | −0.993776 | − | 0.111396i | \(-0.964468\pi\) | ||
0.993776 | − | 0.111396i | \(-0.0355322\pi\) | |||||||
\(878\) | 31.5600 | 1.06510 | ||||||||
\(879\) | −5.35039 | − | 17.8618i | −0.180464 | − | 0.602462i | ||||
\(880\) | 3.04540 | + | 5.05090i | 0.102660 | + | 0.170266i | ||||
\(881\) | 22.5045 | 0.758196 | 0.379098 | − | 0.925357i | \(-0.376234\pi\) | ||||
0.379098 | + | 0.925357i | \(0.376234\pi\) | |||||||
\(882\) | −7.45406 | + | 4.90583i | −0.250991 | + | 0.165188i | ||||
\(883\) | − | 8.29422i | − | 0.279123i | −0.990213 | − | 0.139561i | \(-0.955431\pi\) | ||
0.990213 | − | 0.139561i | \(-0.0445692\pi\) | |||||||
\(884\) | 1.11944 | 0.0376507 | ||||||||
\(885\) | 31.4749 | − | 34.6668i | 1.05802 | − | 1.16531i | ||||
\(886\) | 40.5298 | 1.36163 | ||||||||
\(887\) | 48.1455 | 1.61657 | 0.808283 | − | 0.588794i | \(-0.200397\pi\) | ||||
0.808283 | + | 0.588794i | \(0.200397\pi\) | |||||||
\(888\) | −4.36119 | + | 1.30637i | −0.146352 | + | 0.0438389i | ||||
\(889\) | 18.7814i | 0.629908i | ||||||||
\(890\) | −8.11236 | − | 13.4546i | −0.271927 | − | 0.451000i | ||||
\(891\) | 9.38934 | − | 21.8031i | 0.314555 | − | 0.730430i | ||||
\(892\) | 26.8510i | 0.899038i | ||||||||
\(893\) | − | 22.8730i | − | 0.765416i | ||||||
\(894\) | −35.2324 | + | 10.5537i | −1.17835 | + | 0.352968i | ||||
\(895\) | 2.59910 | − | 1.56711i | 0.0868783 | − | 0.0523826i | ||||
\(896\) | −3.15825 | −0.105510 | ||||||||
\(897\) | 27.5830 | + | 5.16165i | 0.920968 | + | 0.172342i | ||||
\(898\) | 13.0425i | 0.435233i | ||||||||
\(899\) | − | 16.0837i | − | 0.536420i | ||||||
\(900\) | 1.44439 | + | 14.9303i | 0.0481463 | + | 0.497677i | ||||
\(901\) | 4.56664 | 0.152137 | ||||||||
\(902\) | − | 18.2610i | − | 0.608026i | ||||||
\(903\) | −37.6984 | + | 11.2923i | −1.25452 | + | 0.375786i | ||||
\(904\) | 0.586991i | 0.0195230i | ||||||||
\(905\) | 24.1393 | − | 14.5546i | 0.802417 | − | 0.483811i | ||||
\(906\) | −27.1805 | + | 8.14176i | −0.903011 | + | 0.270492i | ||||
\(907\) | 24.1181 | 0.800828 | 0.400414 | − | 0.916334i | \(-0.368866\pi\) | ||||
0.400414 | + | 0.916334i | \(0.368866\pi\) | |||||||
\(908\) | 16.3101i | 0.541268i | ||||||||
\(909\) | 3.41974 | + | 5.19605i | 0.113426 | + | 0.172342i | ||||
\(910\) | −20.4309 | + | 12.3187i | −0.677278 | + | 0.408360i | ||||
\(911\) | −5.60483 | −0.185696 | −0.0928481 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928481 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(912\) | 1.02756 | + | 3.43041i | 0.0340260 | + | 0.113592i | ||||
\(913\) | − | 10.9927i | − | 0.363806i | ||||||
\(914\) | 32.9430 | 1.08966 | ||||||||
\(915\) | 1.78412 | − | 1.96505i | 0.0589812 | − | 0.0649625i | ||||
\(916\) | − | 13.0346i | − | 0.430675i | ||||||
\(917\) | − | 21.6522i | − | 0.715017i | ||||||
\(918\) | 1.31950 | + | 1.10618i | 0.0435500 | + | 0.0365092i | ||||
\(919\) | 3.54435i | 0.116917i | 0.998290 | + | 0.0584587i | \(0.0186186\pi\) | ||||
−0.998290 | + | 0.0584587i | \(0.981381\pi\) | |||||||
\(920\) | −10.7001 | + | 0.713133i | −0.352771 | + | 0.0235113i | ||||
\(921\) | −10.4899 | − | 35.0195i | −0.345654 | − | 1.15393i | ||||
\(922\) | − | 18.9180i | − | 0.623032i | ||||||
\(923\) | 18.8498 | 0.620448 | ||||||||
\(924\) | −13.8218 | + | 4.14025i | −0.454705 | + | 0.136204i | ||||
\(925\) | 6.13446 | − | 11.6228i | 0.201700 | − | 0.382156i | ||||
\(926\) | − | 1.43119i | − | 0.0470319i | ||||||
\(927\) | −6.01097 | + | 3.95607i | −0.197426 | + | 0.129935i | ||||
\(928\) | 6.73889i | 0.221215i | ||||||||
\(929\) | 14.1130i | 0.463033i | 0.972831 | + | 0.231517i | \(0.0743688\pi\) | ||||
−0.972831 | + | 0.231517i | \(0.925631\pi\) | |||||||
\(930\) | 6.84369 | + | 6.21356i | 0.224413 | + | 0.203751i | ||||
\(931\) | − | 6.14982i | − | 0.201552i | ||||||
\(932\) | −18.3561 | −0.601274 | ||||||||
\(933\) | −7.71385 | − | 25.7519i | −0.252540 | − | 0.843081i | ||||
\(934\) | 36.8872i | 1.20699i | ||||||||
\(935\) | −1.67370 | + | 1.00914i | −0.0547358 | + | 0.0330025i | ||||
\(936\) | 5.57167 | + | 8.46575i | 0.182116 | + | 0.276712i | ||||
\(937\) | −0.752217 | −0.0245739 | −0.0122869 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122869 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(938\) | 1.48043 | 0.0483379 | ||||||||
\(939\) | 1.16382 | − | 0.348616i | 0.0379798 | − | 0.0113766i | ||||
\(940\) | 12.7734 | + | 21.1850i | 0.416621 | + | 0.690980i | ||||
\(941\) | 16.4726 | 0.536991 | 0.268495 | − | 0.963281i | \(-0.413474\pi\) | ||||
0.268495 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(942\) | 15.2666 | − | 4.57303i | 0.497413 | − | 0.148997i | ||||
\(943\) | 29.5111 | + | 15.2153i | 0.961015 | + | 0.495477i | ||||
\(944\) | 12.0898i | 0.393490i | ||||||||
\(945\) | −36.2550 | − | 5.66866i | −1.17938 | − | 0.184401i | ||||
\(946\) | −18.9755 | −0.616945 | ||||||||
\(947\) | −25.2263 | −0.819743 | −0.409872 | − | 0.912143i | \(-0.634427\pi\) | ||||
−0.409872 | + | 0.912143i | \(0.634427\pi\) | |||||||
\(948\) | −3.38504 | − | 11.3006i | −0.109941 | − | 0.367027i | ||||
\(949\) | 26.7463 | 0.868222 | ||||||||
\(950\) | −9.14225 | − | 4.82523i | −0.296614 | − | 0.156551i | ||||
\(951\) | 44.2158 | − | 13.2446i | 1.43380 | − | 0.429486i | ||||
\(952\) | − | 1.04654i | − | 0.0339185i | ||||||
\(953\) | − | 7.11142i | − | 0.230362i | −0.993345 | − | 0.115181i | \(-0.963255\pi\) | ||
0.993345 | − | 0.115181i | \(-0.0367447\pi\) | |||||||
\(954\) | 22.7292 | + | 34.5353i | 0.735883 | + | 1.11812i | ||||
\(955\) | 27.0702 | + | 44.8969i | 0.875972 | + | 1.45283i | ||||
\(956\) | 7.83756i | 0.253485i | ||||||||
\(957\) | 8.83424 | + | 29.4923i | 0.285571 | + | 0.953349i | ||||
\(958\) | −17.8352 | −0.576230 | ||||||||
\(959\) | 46.7710i | 1.51031i | ||||||||
\(960\) | −2.86744 | − | 2.60342i | −0.0925461 | − | 0.0840251i | ||||
\(961\) | −25.3037 | −0.816249 | ||||||||
\(962\) | − | 8.87960i | − | 0.286290i | ||||||
\(963\) | 17.2289 | + | 26.1781i | 0.555194 | + | 0.843577i | ||||
\(964\) | − | 16.8965i | − | 0.544199i | ||||||
\(965\) | −35.7239 | + | 21.5395i | −1.14999 | + | 0.693380i | ||||
\(966\) | 4.82552 | − | 25.7868i | 0.155259 | − | 0.829675i | ||||
\(967\) | 39.3623i | 1.26581i | 0.774231 | + | 0.632903i | \(0.218137\pi\) | ||||
−0.774231 | + | 0.632903i | \(0.781863\pi\) | |||||||
\(968\) | 4.04279 | 0.129940 | ||||||||
\(969\) | −1.13672 | + | 0.340500i | −0.0365169 | + | 0.0109384i | ||||
\(970\) | 21.0184 | + | 34.8597i | 0.674860 | + | 1.11928i | ||||
\(971\) | 13.1049 | 0.420555 | 0.210277 | − | 0.977642i | \(-0.432563\pi\) | ||||
0.210277 | + | 0.977642i | \(0.432563\pi\) | |||||||
\(972\) | −1.79804 | + | 15.4844i | −0.0576722 | + | 0.496663i | ||||
\(973\) | 0.762454 | 0.0244431 | ||||||||
\(974\) | 5.32528i | 0.170633i | ||||||||
\(975\) | −28.7042 | − | 5.65734i | −0.919270 | − | 0.181180i | ||||
\(976\) | 0.685298i | 0.0219359i | ||||||||
\(977\) | − | 2.33181i | − | 0.0746011i | −0.999304 | − | 0.0373006i | \(-0.988124\pi\) | ||
0.999304 | − | 0.0373006i | \(-0.0118759\pi\) | |||||||
\(978\) | −11.7425 | − | 39.2011i | −0.375483 | − | 1.25351i | ||||
\(979\) | 18.5327 | 0.592306 | ||||||||
\(980\) | 3.43435 | + | 5.69598i | 0.109706 | + | 0.181952i | ||||
\(981\) | 5.99449 | + | 9.10820i | 0.191389 | + | 0.290802i | ||||
\(982\) | − | 27.6023i | − | 0.880826i | ||||||
\(983\) | 5.68571i | 0.181346i | 0.995881 | + | 0.0906730i | \(0.0289018\pi\) | ||||
−0.995881 | + | 0.0906730i | \(0.971098\pi\) | |||||||
\(984\) | 3.44089 | + | 11.4871i | 0.109692 | + | 0.366195i | ||||
\(985\) | 5.75324 | + | 9.54193i | 0.183313 | + | 0.304031i | ||||
\(986\) | −2.23304 | −0.0711146 | ||||||||
\(987\) | −57.9731 | + | 17.3655i | −1.84530 | + | 0.552750i | ||||
\(988\) | −6.98450 | −0.222206 | ||||||||
\(989\) | 15.8105 | − | 30.6657i | 0.502745 | − | 0.975112i | ||||
\(990\) | −15.9620 | − | 7.63465i | −0.507307 | − | 0.242645i | ||||
\(991\) | 31.5258 | 1.00145 | 0.500724 | − | 0.865607i | \(-0.333067\pi\) | ||||
0.500724 | + | 0.865607i | \(0.333067\pi\) | |||||||
\(992\) | −2.38669 | −0.0757775 | ||||||||
\(993\) | 19.9255 | − | 5.96856i | 0.632315 | − | 0.189407i | ||||
\(994\) | − | 17.6223i | − | 0.558945i | ||||||
\(995\) | 28.0984 | − | 16.9417i | 0.890778 | − | 0.537088i | ||||
\(996\) | 2.07134 | + | 6.91495i | 0.0656328 | + | 0.219109i | ||||
\(997\) | 17.7313i | 0.561555i | 0.959773 | + | 0.280778i | \(0.0905924\pi\) | ||||
−0.959773 | + | 0.280778i | \(0.909408\pi\) | |||||||
\(998\) | 25.7722 | 0.815804 | ||||||||
\(999\) | 8.77442 | − | 10.4666i | 0.277610 | − | 0.331147i |
(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.a.689.4 | yes | 24 | |
3.2 | odd | 2 | 690.2.h.b.689.23 | yes | 24 | ||
5.4 | even | 2 | 690.2.h.b.689.22 | yes | 24 | ||
15.14 | odd | 2 | inner | 690.2.h.a.689.1 | ✓ | 24 | |
23.22 | odd | 2 | inner | 690.2.h.a.689.3 | yes | 24 | |
69.68 | even | 2 | 690.2.h.b.689.24 | yes | 24 | ||
115.114 | odd | 2 | 690.2.h.b.689.21 | yes | 24 | ||
345.344 | even | 2 | inner | 690.2.h.a.689.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.h.a.689.1 | ✓ | 24 | 15.14 | odd | 2 | inner | |
690.2.h.a.689.2 | yes | 24 | 345.344 | even | 2 | inner | |
690.2.h.a.689.3 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.h.a.689.4 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.h.b.689.21 | yes | 24 | 115.114 | odd | 2 | ||
690.2.h.b.689.22 | yes | 24 | 5.4 | even | 2 | ||
690.2.h.b.689.23 | yes | 24 | 3.2 | odd | 2 | ||
690.2.h.b.689.24 | yes | 24 | 69.68 | even | 2 |