Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(8,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.m (of order \(4\), degree \(2\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.3 | ||
Root | \(0.203482i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.8 |
Dual form | 315.2.m.b.197.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.876184 | − | 0.876184i | −0.619556 | − | 0.619556i | 0.325862 | − | 0.945417i | \(-0.394346\pi\) |
−0.945417 | + | 0.325862i | \(0.894346\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.464602i | − | 0.232301i | ||||||
\(5\) | −0.0251942 | + | 2.23593i | −0.0112672 | + | 0.999937i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −2.15945 | + | 2.15945i | −0.763479 | + | 0.763479i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.98116 | − | 1.93701i | 0.626497 | − | 0.612536i | ||||
\(11\) | 4.66231i | 1.40574i | 0.711319 | + | 0.702870i | \(0.248098\pi\) | ||||
−0.711319 | + | 0.702870i | \(0.751902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.54889 | + | 1.54889i | 0.429584 | + | 0.429584i | 0.888487 | − | 0.458903i | \(-0.151757\pi\) |
−0.458903 | + | 0.888487i | \(0.651757\pi\) | |||||||
\(14\) | 1.23911 | 0.331167 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.85494 | 0.713735 | ||||||||
\(17\) | −2.32993 | − | 2.32993i | −0.565091 | − | 0.565091i | 0.365658 | − | 0.930749i | \(-0.380844\pi\) |
−0.930749 | + | 0.365658i | \(0.880844\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.54791i | 0.813946i | 0.913440 | + | 0.406973i | \(0.133416\pi\) | ||||
−0.913440 | + | 0.406973i | \(0.866584\pi\) | |||||||
\(20\) | 1.03882 | + | 0.0117053i | 0.232286 | + | 0.00261738i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08504 | − | 4.08504i | 0.870934 | − | 0.870934i | ||||
\(23\) | −1.44259 | + | 1.44259i | −0.300802 | + | 0.300802i | −0.841327 | − | 0.540526i | \(-0.818225\pi\) |
0.540526 | + | 0.841327i | \(0.318225\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99873 | − | 0.112665i | −0.999746 | − | 0.0225330i | ||||
\(26\) | − | 2.71422i | − | 0.532303i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.328523 | + | 0.328523i | 0.0620851 | + | 0.0620851i | ||||
\(29\) | 7.58625 | 1.40873 | 0.704366 | − | 0.709837i | \(-0.251232\pi\) | ||||
0.704366 | + | 0.709837i | \(0.251232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.12691 | 1.45964 | 0.729818 | − | 0.683641i | \(-0.239605\pi\) | ||||
0.729818 | + | 0.683641i | \(0.239605\pi\) | |||||||
\(32\) | 1.81744 | + | 1.81744i | 0.321280 | + | 0.321280i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.08289i | 0.700211i | ||||||||
\(35\) | −1.56322 | − | 1.59885i | −0.264233 | − | 0.270256i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00046 | + | 6.00046i | −0.986470 | + | 0.986470i | −0.999910 | − | 0.0134395i | \(-0.995722\pi\) |
0.0134395 | + | 0.999910i | \(0.495722\pi\) | |||||||
\(38\) | 3.10862 | − | 3.10862i | 0.504285 | − | 0.504285i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.77396 | − | 4.88277i | −0.754829 | − | 0.772033i | ||||
\(41\) | − | 6.72475i | − | 1.05023i | −0.851032 | − | 0.525114i | \(-0.824023\pi\) | ||
0.851032 | − | 0.525114i | \(-0.175977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.46460 | + | 5.46460i | 0.833344 | + | 0.833344i | 0.987973 | − | 0.154629i | \(-0.0494181\pi\) |
−0.154629 | + | 0.987973i | \(0.549418\pi\) | |||||||
\(44\) | 2.16612 | 0.326555 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.52796 | 0.372727 | ||||||||
\(47\) | −5.16658 | − | 5.16658i | −0.753623 | − | 0.753623i | 0.221530 | − | 0.975154i | \(-0.428895\pi\) |
−0.975154 | + | 0.221530i | \(0.928895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 4.28109 | + | 4.47852i | 0.605438 | + | 0.633359i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.719616 | − | 0.719616i | 0.0997928 | − | 0.0997928i | ||||
\(53\) | −6.86452 | + | 6.86452i | −0.942915 | + | 0.942915i | −0.998456 | − | 0.0555419i | \(-0.982311\pi\) |
0.0555419 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.4246 | − | 0.117463i | −1.40565 | − | 0.0158387i | ||||
\(56\) | − | 3.05392i | − | 0.408097i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.64695 | − | 6.64695i | −0.872788 | − | 0.872788i | ||||
\(59\) | 6.40696 | 0.834116 | 0.417058 | − | 0.908880i | \(-0.363061\pi\) | ||||
0.417058 | + | 0.908880i | \(0.363061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6036 | −1.74176 | −0.870879 | − | 0.491498i | \(-0.836450\pi\) | ||||
−0.870879 | + | 0.491498i | \(0.836450\pi\) | |||||||
\(62\) | −7.12067 | − | 7.12067i | −0.904326 | − | 0.904326i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.89470i | − | 1.11184i | ||||||
\(65\) | −3.50222 | + | 3.42417i | −0.434397 | + | 0.424716i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.77125 | − | 2.77125i | 0.338562 | − | 0.338562i | −0.517264 | − | 0.855826i | \(-0.673049\pi\) |
0.855826 | + | 0.517264i | \(0.173049\pi\) | |||||||
\(68\) | −1.08249 | + | 1.08249i | −0.131271 | + | 0.131271i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0312185 | + | 2.77056i | −0.00373132 | + | 0.331146i | ||||
\(71\) | − | 0.576549i | − | 0.0684238i | −0.999415 | − | 0.0342119i | \(-0.989108\pi\) | ||
0.999415 | − | 0.0342119i | \(-0.0108921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.94384 | − | 4.94384i | −0.578632 | − | 0.578632i | 0.355894 | − | 0.934526i | \(-0.384176\pi\) |
−0.934526 | + | 0.355894i | \(0.884176\pi\) | |||||||
\(74\) | 10.5150 | 1.22235 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.64837 | 0.189081 | ||||||||
\(77\) | −3.29675 | − | 3.29675i | −0.375700 | − | 0.375700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50976i | 0.282370i | 0.989983 | + | 0.141185i | \(0.0450913\pi\) | ||||
−0.989983 | + | 0.141185i | \(0.954909\pi\) | |||||||
\(80\) | −0.0719280 | + | 6.38344i | −0.00804180 | + | 0.713690i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.89212 | + | 5.89212i | −0.650675 | + | 0.650675i | ||||
\(83\) | 3.99501 | − | 3.99501i | 0.438509 | − | 0.438509i | −0.453001 | − | 0.891510i | \(-0.649647\pi\) |
0.891510 | + | 0.453001i | \(0.149647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.26825 | − | 5.15085i | 0.571422 | − | 0.558688i | ||||
\(86\) | − | 9.57600i | − | 1.03261i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.0680 | − | 10.0680i | −1.07325 | − | 1.07325i | ||||
\(89\) | −6.86727 | −0.727929 | −0.363964 | − | 0.931413i | \(-0.618577\pi\) | ||||
−0.363964 | + | 0.931413i | \(0.618577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.19046 | −0.229622 | ||||||||
\(92\) | 0.670232 | + | 0.670232i | 0.0698765 | + | 0.0698765i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.05376i | 0.933824i | ||||||||
\(95\) | −7.93287 | − | 0.0893869i | −0.813895 | − | 0.00917090i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.43407 | − | 4.43407i | 0.450212 | − | 0.450212i | −0.445213 | − | 0.895425i | \(-0.646872\pi\) |
0.895425 | + | 0.445213i | \(0.146872\pi\) | |||||||
\(98\) | −0.876184 | + | 0.876184i | −0.0885080 | + | 0.0885080i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0523443 | + | 2.32242i | −0.00523443 | + | 0.232242i | ||||
\(101\) | 2.63552i | 0.262244i | 0.991366 | + | 0.131122i | \(0.0418579\pi\) | ||||
−0.991366 | + | 0.131122i | \(0.958142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.45961 | + | 7.45961i | 0.735017 | + | 0.735017i | 0.971609 | − | 0.236592i | \(-0.0760304\pi\) |
−0.236592 | + | 0.971609i | \(0.576030\pi\) | |||||||
\(104\) | −6.68947 | −0.655957 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0292 | 1.16838 | ||||||||
\(107\) | −4.48615 | − | 4.48615i | −0.433692 | − | 0.433692i | 0.456190 | − | 0.889882i | \(-0.349214\pi\) |
−0.889882 | + | 0.456190i | \(0.849214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.54504i | 0.722684i | 0.932433 | + | 0.361342i | \(0.117681\pi\) | ||||
−0.932433 | + | 0.361342i | \(0.882319\pi\) | |||||||
\(110\) | 9.03093 | + | 9.23677i | 0.861066 | + | 0.880692i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.01875 | + | 2.01875i | −0.190754 | + | 0.190754i | ||||
\(113\) | 1.80305 | − | 1.80305i | 0.169617 | − | 0.169617i | −0.617194 | − | 0.786811i | \(-0.711731\pi\) |
0.786811 | + | 0.617194i | \(0.211731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.18919 | − | 3.26188i | −0.297393 | − | 0.304172i | ||||
\(116\) | − | 3.52459i | − | 0.327250i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.61368 | − | 5.61368i | −0.516781 | − | 0.516781i | ||||
\(119\) | 3.29502 | 0.302054 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7371 | −0.976102 | ||||||||
\(122\) | 11.9192 | + | 11.9192i | 1.07912 | + | 1.07912i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3.77578i | − | 0.339075i | ||||||
\(125\) | 0.377849 | − | 11.1740i | 0.0337959 | − | 0.999429i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3511 | − | 14.3511i | 1.27346 | − | 1.27346i | 0.329195 | − | 0.944262i | \(-0.393223\pi\) |
0.944262 | − | 0.329195i | \(-0.106777\pi\) | |||||||
\(128\) | −4.15852 | + | 4.15852i | −0.367565 | + | 0.367565i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.06880 | + | 0.0683827i | 0.532269 | + | 0.00599756i | ||||
\(131\) | − | 3.22579i | − | 0.281839i | −0.990021 | − | 0.140919i | \(-0.954994\pi\) | ||
0.990021 | − | 0.140919i | \(-0.0450059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50875 | − | 2.50875i | −0.217536 | − | 0.217536i | ||||
\(134\) | −4.85626 | −0.419517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.0627 | 0.862870 | ||||||||
\(137\) | 1.36108 | + | 1.36108i | 0.116285 | + | 0.116285i | 0.762855 | − | 0.646570i | \(-0.223797\pi\) |
−0.646570 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.2867i | 1.89033i | 0.326589 | + | 0.945166i | \(0.394101\pi\) | ||||
−0.326589 | + | 0.945166i | \(0.605899\pi\) | |||||||
\(140\) | −0.742831 | + | 0.726277i | −0.0627806 | + | 0.0613816i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.505163 | + | 0.505163i | −0.0423923 | + | 0.0423923i | ||||
\(143\) | −7.22139 | + | 7.22139i | −0.603883 | + | 0.603883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.191130 | + | 16.9623i | −0.0158725 | + | 1.40864i | ||||
\(146\) | 8.66342i | 0.716990i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.78783 | + | 2.78783i | 0.229158 | + | 0.229158i | ||||
\(149\) | 23.4052 | 1.91743 | 0.958713 | − | 0.284376i | \(-0.0917865\pi\) | ||||
0.958713 | + | 0.284376i | \(0.0917865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9889 | 1.38254 | 0.691269 | − | 0.722597i | \(-0.257052\pi\) | ||||
0.691269 | + | 0.722597i | \(0.257052\pi\) | |||||||
\(152\) | −7.66152 | − | 7.66152i | −0.621431 | − | 0.621431i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.77712i | 0.465534i | ||||||||
\(155\) | −0.204751 | + | 18.1712i | −0.0164460 | + | 1.45954i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.07929 | − | 8.07929i | 0.644798 | − | 0.644798i | −0.306933 | − | 0.951731i | \(-0.599303\pi\) |
0.951731 | + | 0.306933i | \(0.0993028\pi\) | |||||||
\(158\) | 2.19901 | − | 2.19901i | 0.174944 | − | 0.174944i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.10944 | + | 4.01787i | −0.324880 | + | 0.317640i | ||||
\(161\) | − | 2.04014i | − | 0.160785i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.08622 | + | 9.08622i | 0.711688 | + | 0.711688i | 0.966888 | − | 0.255200i | \(-0.0821414\pi\) |
−0.255200 | + | 0.966888i | \(0.582141\pi\) | |||||||
\(164\) | −3.12433 | −0.243969 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.00073 | −0.543362 | ||||||||
\(167\) | 13.5425 | + | 13.5425i | 1.04795 | + | 1.04795i | 0.998791 | + | 0.0491596i | \(0.0156543\pi\) |
0.0491596 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.20190i | − | 0.630915i | ||||||
\(170\) | −9.12905 | − | 0.102865i | −0.700166 | − | 0.00788941i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.53887 | − | 2.53887i | 0.193587 | − | 0.193587i | ||||
\(173\) | 16.4883 | − | 16.4883i | 1.25358 | − | 1.25358i | 0.299483 | − | 0.954102i | \(-0.403186\pi\) |
0.954102 | − | 0.299483i | \(-0.0968141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61430 | − | 3.45497i | 0.273216 | − | 0.261171i | ||||
\(176\) | 13.3106i | 1.00333i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.01699 | + | 6.01699i | 0.450993 | + | 0.450993i | ||||
\(179\) | −7.15384 | −0.534703 | −0.267352 | − | 0.963599i | \(-0.586148\pi\) | ||||
−0.267352 | + | 0.963599i | \(0.586148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.86285 | −0.361453 | −0.180726 | − | 0.983533i | \(-0.557845\pi\) | ||||
−0.180726 | + | 0.983533i | \(0.557845\pi\) | |||||||
\(182\) | 1.91924 | + | 1.91924i | 0.142264 | + | 0.142264i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.23040i | − | 0.459312i | ||||||
\(185\) | −13.2654 | − | 13.5678i | −0.975293 | − | 0.997522i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8628 | − | 10.8628i | 0.794370 | − | 0.794370i | ||||
\(188\) | −2.40040 | + | 2.40040i | −0.175067 | + | 0.175067i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.87233 | + | 7.02897i | 0.498571 | + | 0.509935i | ||||
\(191\) | 0.990955i | 0.0717030i | 0.999357 | + | 0.0358515i | \(0.0114143\pi\) | ||||
−0.999357 | + | 0.0358515i | \(0.988586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.22384 | + | 8.22384i | 0.591965 | + | 0.591965i | 0.938162 | − | 0.346197i | \(-0.112527\pi\) |
−0.346197 | + | 0.938162i | \(0.612527\pi\) | |||||||
\(194\) | −7.77013 | −0.557863 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.464602 | −0.0331859 | ||||||||
\(197\) | 1.80305 | + | 1.80305i | 0.128462 | + | 0.128462i | 0.768414 | − | 0.639952i | \(-0.221046\pi\) |
−0.639952 | + | 0.768414i | \(0.721046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.0345i | − | 1.13666i | −0.822802 | − | 0.568328i | \(-0.807590\pi\) | ||
0.822802 | − | 0.568328i | \(-0.192410\pi\) | |||||||
\(200\) | 11.0378 | − | 10.5512i | 0.780489 | − | 0.746082i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.30920 | − | 2.30920i | 0.162475 | − | 0.162475i | ||||
\(203\) | −5.36429 | + | 5.36429i | −0.376499 | + | 0.376499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0360 | + | 0.169425i | 1.05016 | + | 0.0118331i | ||||
\(206\) | − | 13.0720i | − | 0.910769i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.42198 | + | 4.42198i | 0.306609 | + | 0.306609i | ||||
\(209\) | −16.5415 | −1.14420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.1632 | −1.52578 | −0.762890 | − | 0.646528i | \(-0.776220\pi\) | ||||
−0.762890 | + | 0.646528i | \(0.776220\pi\) | |||||||
\(212\) | 3.18927 | + | 3.18927i | 0.219040 | + | 0.219040i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.86138i | 0.537393i | ||||||||
\(215\) | −12.3561 | + | 12.0808i | −0.842681 | + | 0.823902i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.74659 | + | 5.74659i | −0.390104 | + | 0.390104i | ||||
\(218\) | 6.61085 | − | 6.61085i | 0.447743 | − | 0.447743i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0545737 | + | 4.84328i | −0.00367936 | + | 0.326534i | ||||
\(221\) | − | 7.21759i | − | 0.485508i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4515 | − | 13.4515i | −0.900781 | − | 0.900781i | 0.0947227 | − | 0.995504i | \(-0.469804\pi\) |
−0.995504 | + | 0.0947227i | \(0.969804\pi\) | |||||||
\(224\) | −2.57024 | −0.171732 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.15961 | −0.210174 | ||||||||
\(227\) | 8.57603 | + | 8.57603i | 0.569211 | + | 0.569211i | 0.931907 | − | 0.362696i | \(-0.118144\pi\) |
−0.362696 | + | 0.931907i | \(0.618144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.4314i | − | 1.48231i | −0.671335 | − | 0.741154i | \(-0.734279\pi\) | ||
0.671335 | − | 0.741154i | \(-0.265721\pi\) | |||||||
\(230\) | −0.0636899 | + | 5.65232i | −0.00419959 | + | 0.372703i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.3821 | + | 16.3821i | −1.07554 | + | 1.07554i | ||||
\(233\) | −3.98861 | + | 3.98861i | −0.261303 | + | 0.261303i | −0.825583 | − | 0.564281i | \(-0.809154\pi\) |
0.564281 | + | 0.825583i | \(0.309154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6823 | − | 11.4219i | 0.762067 | − | 0.745084i | ||||
\(236\) | − | 2.97669i | − | 0.193766i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.88704 | − | 2.88704i | −0.187139 | − | 0.187139i | ||||
\(239\) | 9.15757 | 0.592354 | 0.296177 | − | 0.955133i | \(-0.404288\pi\) | ||||
0.296177 | + | 0.955133i | \(0.404288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5613 | −0.873560 | −0.436780 | − | 0.899568i | \(-0.643881\pi\) | ||||
−0.436780 | + | 0.899568i | \(0.643881\pi\) | |||||||
\(242\) | 9.40770 | + | 9.40770i | 0.604750 | + | 0.604750i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.32024i | 0.404612i | ||||||||
\(245\) | 2.23593 | + | 0.0251942i | 0.142848 | + | 0.00160960i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.49531 | + | 5.49531i | −0.349658 | + | 0.349658i | ||||
\(248\) | −17.5496 | + | 17.5496i | −1.11440 | + | 1.11440i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.1215 | + | 9.45938i | −0.640140 | + | 0.598264i | ||||
\(251\) | 23.8741i | 1.50692i | 0.657494 | + | 0.753460i | \(0.271617\pi\) | ||||
−0.657494 | + | 0.753460i | \(0.728383\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.72582 | − | 6.72582i | −0.422848 | − | 0.422848i | ||||
\(254\) | −25.1485 | −1.57796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.5021 | −0.656383 | ||||||||
\(257\) | −12.0222 | − | 12.0222i | −0.749921 | − | 0.749921i | 0.224543 | − | 0.974464i | \(-0.427911\pi\) |
−0.974464 | + | 0.224543i | \(0.927911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.48594i | − | 0.527291i | ||||||
\(260\) | 1.59088 | + | 1.62714i | 0.0986621 | + | 0.100911i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.82639 | + | 2.82639i | −0.174615 | + | 0.174615i | ||||
\(263\) | 1.26198 | − | 1.26198i | 0.0778167 | − | 0.0778167i | −0.667127 | − | 0.744944i | \(-0.732476\pi\) |
0.744944 | + | 0.667127i | \(0.232476\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.1756 | − | 15.5215i | −0.932231 | − | 0.953479i | ||||
\(266\) | 4.39626i | 0.269552i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.28753 | − | 1.28753i | −0.0786484 | − | 0.0786484i | ||||
\(269\) | 3.41582 | 0.208266 | 0.104133 | − | 0.994563i | \(-0.466793\pi\) | ||||
0.104133 | + | 0.994563i | \(0.466793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.21326 | 0.498920 | 0.249460 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249460 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(272\) | −6.65181 | − | 6.65181i | −0.403325 | − | 0.403325i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 2.38511i | − | 0.144090i | ||||||
\(275\) | 0.525278 | − | 23.3056i | 0.0316755 | − | 1.40538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.57498 | + | 4.57498i | −0.274884 | + | 0.274884i | −0.831063 | − | 0.556179i | \(-0.812267\pi\) |
0.556179 | + | 0.831063i | \(0.312267\pi\) | |||||||
\(278\) | 19.5273 | − | 19.5273i | 1.17117 | − | 1.17117i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.82833 | + | 0.0769411i | 0.408071 | + | 0.00459811i | ||||
\(281\) | 11.0476i | 0.659042i | 0.944148 | + | 0.329521i | \(0.106887\pi\) | ||||
−0.944148 | + | 0.329521i | \(0.893113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.42604 | − | 4.42604i | −0.263101 | − | 0.263101i | 0.563212 | − | 0.826313i | \(-0.309566\pi\) |
−0.826313 | + | 0.563212i | \(0.809566\pi\) | |||||||
\(284\) | −0.267866 | −0.0158949 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.6545 | 0.748278 | ||||||||
\(287\) | 4.75511 | + | 4.75511i | 0.280685 | + | 0.280685i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.14286i | − | 0.361345i | ||||||
\(290\) | 15.0296 | − | 14.6946i | 0.882566 | − | 0.862899i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.29692 | + | 2.29692i | −0.134417 | + | 0.134417i | ||||
\(293\) | 22.3120 | − | 22.3120i | 1.30348 | − | 1.30348i | 0.377452 | − | 0.926029i | \(-0.376800\pi\) |
0.926029 | − | 0.377452i | \(-0.123200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.161419 | + | 14.3255i | −0.00939815 | + | 0.834063i | ||||
\(296\) | − | 25.9154i | − | 1.50630i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.5072 | − | 20.5072i | −1.18795 | − | 1.18795i | ||||
\(299\) | −4.46883 | −0.258439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.72811 | −0.445441 | ||||||||
\(302\) | −14.8854 | − | 14.8854i | −0.856560 | − | 0.856560i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.1291i | 0.580942i | ||||||||
\(305\) | 0.342731 | − | 30.4166i | 0.0196247 | − | 1.74165i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.65242 | − | 4.65242i | 0.265527 | − | 0.265527i | −0.561768 | − | 0.827295i | \(-0.689879\pi\) |
0.827295 | + | 0.561768i | \(0.189879\pi\) | |||||||
\(308\) | −1.53168 | + | 1.53168i | −0.0872754 | + | 0.0872754i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.1007 | − | 15.7419i | 0.914458 | − | 0.894080i | ||||
\(311\) | 12.7033i | 0.720337i | 0.932887 | + | 0.360169i | \(0.117281\pi\) | ||||
−0.932887 | + | 0.360169i | \(0.882719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.39195 | + | 9.39195i | 0.530864 | + | 0.530864i | 0.920830 | − | 0.389965i | \(-0.127513\pi\) |
−0.389965 | + | 0.920830i | \(0.627513\pi\) | |||||||
\(314\) | −14.1579 | −0.798977 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.16604 | 0.0655949 | ||||||||
\(317\) | 12.0566 | + | 12.0566i | 0.677166 | + | 0.677166i | 0.959358 | − | 0.282192i | \(-0.0910615\pi\) |
−0.282192 | + | 0.959358i | \(0.591061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.3694i | 1.98031i | ||||||||
\(320\) | 19.8879 | + | 0.224095i | 1.11177 | + | 0.0125273i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.78753 | + | 1.78753i | −0.0996154 | + | 0.0996154i | ||||
\(323\) | 8.26638 | − | 8.26638i | 0.459954 | − | 0.459954i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.56796 | − | 7.91697i | −0.419795 | − | 0.439155i | ||||
\(326\) | − | 15.9224i | − | 0.881861i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.5217 | + | 14.5217i | 0.801828 | + | 0.801828i | ||||
\(329\) | 7.30665 | 0.402829 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.841491 | −0.0462525 | −0.0231263 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231263 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(332\) | −1.85609 | − | 1.85609i | −0.101866 | − | 0.101866i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 23.7315i | − | 1.29853i | ||||||
\(335\) | 6.12650 | + | 6.26614i | 0.334726 | + | 0.342356i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1936 | + | 16.1936i | −0.882124 | + | 0.882124i | −0.993750 | − | 0.111626i | \(-0.964394\pi\) |
0.111626 | + | 0.993750i | \(0.464394\pi\) | |||||||
\(338\) | −7.18638 | + | 7.18638i | −0.390887 | + | 0.390887i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.39309 | − | 2.44764i | −0.129784 | − | 0.132742i | ||||
\(341\) | 37.8902i | 2.05187i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −23.6010 | −1.27248 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.8936 | −1.55333 | ||||||||
\(347\) | 6.72445 | + | 6.72445i | 0.360988 | + | 0.360988i | 0.864176 | − | 0.503189i | \(-0.167840\pi\) |
−0.503189 | + | 0.864176i | \(0.667840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.9697i | − | 1.39013i | −0.718949 | − | 0.695063i | \(-0.755376\pi\) | ||
0.718949 | − | 0.695063i | \(-0.244624\pi\) | |||||||
\(350\) | −6.19399 | − | 0.139604i | −0.331082 | − | 0.00746217i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.47345 | + | 8.47345i | −0.451637 | + | 0.451637i | ||||
\(353\) | 20.5943 | − | 20.5943i | 1.09612 | − | 1.09612i | 0.101264 | − | 0.994860i | \(-0.467711\pi\) |
0.994860 | − | 0.101264i | \(-0.0322885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.28912 | + | 0.0145257i | 0.0684194 | + | 0.000770944i | ||||
\(356\) | 3.19055i | 0.169099i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.26808 | + | 6.26808i | 0.331278 | + | 0.331278i | ||||
\(359\) | 29.4326 | 1.55339 | 0.776697 | − | 0.629874i | \(-0.216893\pi\) | ||||
0.776697 | + | 0.629874i | \(0.216893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.41233 | 0.337491 | ||||||||
\(362\) | 4.26075 | + | 4.26075i | 0.223940 | + | 0.223940i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.01769i | 0.0533415i | ||||||||
\(365\) | 11.1786 | − | 10.9295i | 0.585115 | − | 0.572076i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4205 | + | 13.4205i | −0.700544 | + | 0.700544i | −0.964527 | − | 0.263983i | \(-0.914964\pi\) |
0.263983 | + | 0.964527i | \(0.414964\pi\) | |||||||
\(368\) | −4.11852 | + | 4.11852i | −0.214693 | + | 0.214693i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.264918 | + | 23.5108i | −0.0137724 | + | 1.22227i | ||||
\(371\) | − | 9.70790i | − | 0.504009i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.38704 | + | 1.38704i | 0.0718184 | + | 0.0718184i | 0.742104 | − | 0.670285i | \(-0.233828\pi\) |
−0.670285 | + | 0.742104i | \(0.733828\pi\) | |||||||
\(374\) | −19.0357 | −0.984313 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.3139 | 1.15075 | ||||||||
\(377\) | 11.7502 | + | 11.7502i | 0.605168 | + | 0.605168i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.3851i | − | 1.30394i | −0.758243 | − | 0.651972i | \(-0.773942\pi\) | ||
0.758243 | − | 0.651972i | \(-0.226058\pi\) | |||||||
\(380\) | −0.0415293 | + | 3.68563i | −0.00213041 | + | 0.189069i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.868259 | − | 0.868259i | 0.0444240 | − | 0.0444240i | ||||
\(383\) | −3.12729 | + | 3.12729i | −0.159797 | + | 0.159797i | −0.782477 | − | 0.622680i | \(-0.786044\pi\) |
0.622680 | + | 0.782477i | \(0.286044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.45435 | − | 7.28823i | 0.379909 | − | 0.371443i | ||||
\(386\) | − | 14.4112i | − | 0.733511i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.06008 | − | 2.06008i | −0.104585 | − | 0.104585i | ||||
\(389\) | −10.5100 | −0.532876 | −0.266438 | − | 0.963852i | \(-0.585847\pi\) | ||||
−0.266438 | + | 0.963852i | \(0.585847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.72228 | 0.339960 | ||||||||
\(392\) | 2.15945 | + | 2.15945i | 0.109068 | + | 0.109068i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 3.15961i | − | 0.159179i | ||||||
\(395\) | −5.61164 | − | 0.0632315i | −0.282352 | − | 0.00318152i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.72909 | + | 3.72909i | −0.187158 | + | 0.187158i | −0.794466 | − | 0.607308i | \(-0.792249\pi\) |
0.607308 | + | 0.794466i | \(0.292249\pi\) | |||||||
\(398\) | −14.0492 | + | 14.0492i | −0.704222 | + | 0.704222i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.2711 | − | 0.321652i | −0.713554 | − | 0.0160826i | ||||
\(401\) | 17.8421i | 0.890994i | 0.895283 | + | 0.445497i | \(0.146973\pi\) | ||||
−0.895283 | + | 0.445497i | \(0.853027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5877 | + | 12.5877i | 0.627036 | + | 0.627036i | ||||
\(404\) | 1.22447 | 0.0609195 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.40021 | 0.466525 | ||||||||
\(407\) | −27.9760 | − | 27.9760i | −1.38672 | − | 1.38672i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9681i | 0.740127i | 0.929006 | + | 0.370064i | \(0.120664\pi\) | ||||
−0.929006 | + | 0.370064i | \(0.879336\pi\) | |||||||
\(410\) | −13.0259 | − | 13.3228i | −0.643303 | − | 0.657965i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.46575 | − | 3.46575i | 0.170745 | − | 0.170745i | ||||
\(413\) | −4.53041 | + | 4.53041i | −0.222927 | + | 0.222927i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.83189 | + | 9.03320i | 0.433541 | + | 0.443422i | ||||
\(416\) | 5.63001i | 0.276034i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.4934 | + | 14.4934i | 0.708894 | + | 0.708894i | ||||
\(419\) | −6.71408 | −0.328004 | −0.164002 | − | 0.986460i | \(-0.552440\pi\) | ||||
−0.164002 | + | 0.986460i | \(0.552440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.1593 | −1.46987 | −0.734937 | − | 0.678136i | \(-0.762788\pi\) | ||||
−0.734937 | + | 0.678136i | \(0.762788\pi\) | |||||||
\(422\) | 19.4191 | + | 19.4191i | 0.945307 | + | 0.945307i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 29.6471i | − | 1.43979i | ||||||
\(425\) | 11.3842 | + | 11.9092i | 0.552214 | + | 0.577680i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.61917 | − | 9.61917i | 0.465504 | − | 0.465504i | ||||
\(428\) | −2.08427 | + | 2.08427i | −0.100747 | + | 0.100747i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.4112 | + | 0.241260i | 1.03254 | + | 0.0116346i | ||||
\(431\) | 14.5595i | 0.701304i | 0.936506 | + | 0.350652i | \(0.114040\pi\) | ||||
−0.936506 | + | 0.350652i | \(0.885960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3159 | + | 14.3159i | 0.687976 | + | 0.687976i | 0.961784 | − | 0.273808i | \(-0.0882834\pi\) |
−0.273808 | + | 0.961784i | \(0.588283\pi\) | |||||||
\(434\) | 10.0702 | 0.483383 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50544 | 0.167880 | ||||||||
\(437\) | −5.11819 | − | 5.11819i | −0.244836 | − | 0.244836i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 23.7496i | − | 1.13351i | −0.823887 | − | 0.566754i | \(-0.808199\pi\) | ||
0.823887 | − | 0.566754i | \(-0.191801\pi\) | |||||||
\(440\) | 22.7650 | − | 22.2577i | 1.08528 | − | 1.06109i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.32394 | + | 6.32394i | −0.300799 | + | 0.300799i | ||||
\(443\) | −28.0781 | + | 28.0781i | −1.33403 | + | 1.33403i | −0.432299 | + | 0.901730i | \(0.642298\pi\) |
−0.901730 | + | 0.432299i | \(0.857702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.173015 | − | 15.3547i | 0.00820172 | − | 0.727883i | ||||
\(446\) | 23.5720i | 1.11617i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.28950 | + | 6.28950i | 0.297151 | + | 0.297151i | ||||
\(449\) | −23.1170 | −1.09096 | −0.545479 | − | 0.838125i | \(-0.683652\pi\) | ||||
−0.545479 | + | 0.838125i | \(0.683652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.3528 | 1.47635 | ||||||||
\(452\) | −0.837701 | − | 0.837701i | −0.0394021 | − | 0.0394021i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 15.0284i | − | 0.705316i | ||||||
\(455\) | 0.0551869 | − | 4.89770i | 0.00258720 | − | 0.229608i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.41339 | + | 2.41339i | −0.112893 | + | 0.112893i | −0.761297 | − | 0.648403i | \(-0.775437\pi\) |
0.648403 | + | 0.761297i | \(0.275437\pi\) | |||||||
\(458\) | −19.6540 | + | 19.6540i | −0.918373 | + | 0.918373i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.51547 | + | 1.48170i | −0.0706594 | + | 0.0690848i | ||||
\(461\) | 12.9836i | 0.604705i | 0.953196 | + | 0.302353i | \(0.0977720\pi\) | ||||
−0.953196 | + | 0.302353i | \(0.902228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5619 | + | 21.5619i | 1.00207 | + | 1.00207i | 0.999998 | + | 0.00206902i | \(0.000658591\pi\) |
0.00206902 | + | 0.999998i | \(0.499341\pi\) | |||||||
\(464\) | 21.6583 | 1.00546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.98952 | 0.323783 | ||||||||
\(467\) | −4.14681 | − | 4.14681i | −0.191891 | − | 0.191891i | 0.604622 | − | 0.796513i | \(-0.293324\pi\) |
−0.796513 | + | 0.604622i | \(0.793324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.91914i | 0.180969i | ||||||||
\(470\) | −20.2435 | − | 0.228102i | −0.933764 | − | 0.0105216i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.8355 | + | 13.8355i | −0.636830 | + | 0.636830i | ||||
\(473\) | −25.4777 | + | 25.4777i | −1.17146 | + | 1.17146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.399725 | − | 17.7350i | 0.0183406 | − | 0.813740i | ||||
\(476\) | − | 1.53087i | − | 0.0701674i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.02372 | − | 8.02372i | −0.366996 | − | 0.366996i | ||||
\(479\) | 11.3977 | 0.520774 | 0.260387 | − | 0.965504i | \(-0.416150\pi\) | ||||
0.260387 | + | 0.965504i | \(0.416150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5881 | −0.847544 | ||||||||
\(482\) | 11.8822 | + | 11.8822i | 0.541219 | + | 0.541219i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.98849i | 0.226750i | ||||||||
\(485\) | 9.80255 | + | 10.0260i | 0.445111 | + | 0.455256i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0942 | + | 11.0942i | −0.502727 | + | 0.502727i | −0.912284 | − | 0.409558i | \(-0.865683\pi\) |
0.409558 | + | 0.912284i | \(0.365683\pi\) | |||||||
\(488\) | 29.3762 | − | 29.3762i | 1.32980 | − | 1.32980i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.93701 | − | 1.98116i | −0.0875051 | − | 0.0894996i | ||||
\(491\) | − | 28.4593i | − | 1.28435i | −0.766559 | − | 0.642174i | \(-0.778033\pi\) | ||
0.766559 | − | 0.642174i | \(-0.221967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.6754 | − | 17.6754i | −0.796061 | − | 0.796061i | ||||
\(494\) | 9.62981 | 0.433266 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.2019 | 1.04179 | ||||||||
\(497\) | 0.407682 | + | 0.407682i | 0.0182870 | + | 0.0182870i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0081i | 0.582323i | 0.956674 | + | 0.291161i | \(0.0940417\pi\) | ||||
−0.956674 | + | 0.291161i | \(0.905958\pi\) | |||||||
\(500\) | −5.19144 | − | 0.175550i | −0.232168 | − | 0.00785082i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.9181 | − | 20.9181i | 0.933621 | − | 0.933621i | ||||
\(503\) | 19.6010 | − | 19.6010i | 0.873966 | − | 0.873966i | −0.118936 | − | 0.992902i | \(-0.537948\pi\) |
0.992902 | + | 0.118936i | \(0.0379482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.89282 | − | 0.0663999i | −0.262227 | − | 0.00295475i | ||||
\(506\) | 11.7861i | 0.523957i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.66756 | − | 6.66756i | −0.295825 | − | 0.295825i | ||||
\(509\) | −42.4087 | −1.87973 | −0.939866 | − | 0.341545i | \(-0.889050\pi\) | ||||
−0.939866 | + | 0.341545i | \(0.889050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.99164 | 0.309292 | ||||||||
\(512\) | 17.5189 | + | 17.5189i | 0.774231 | + | 0.774231i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.0672i | 0.929236i | ||||||||
\(515\) | −16.8671 | + | 16.4912i | −0.743252 | + | 0.726689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0882 | − | 24.0882i | 1.05940 | − | 1.05940i | ||||
\(518\) | −7.43525 | + | 7.43525i | −0.326686 | + | 0.326686i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.168536 | − | 14.9572i | 0.00739080 | − | 0.655915i | ||||
\(521\) | − | 13.9987i | − | 0.613296i | −0.951823 | − | 0.306648i | \(-0.900793\pi\) | ||
0.951823 | − | 0.306648i | \(-0.0992074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7665 | + | 15.7665i | 0.689421 | + | 0.689421i | 0.962104 | − | 0.272683i | \(-0.0879110\pi\) |
−0.272683 | + | 0.962104i | \(0.587911\pi\) | |||||||
\(524\) | −1.49871 | −0.0654715 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.21145 | −0.0964236 | ||||||||
\(527\) | −18.9351 | − | 18.9351i | −0.824827 | − | 0.824827i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8378i | 0.819037i | ||||||||
\(530\) | −0.303066 | + | 26.8963i | −0.0131643 | + | 1.16830i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.16557 | + | 1.16557i | −0.0505339 | + | 0.0505339i | ||||
\(533\) | 10.4159 | − | 10.4159i | 0.451161 | − | 0.451161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.1437 | − | 9.91767i | 0.438551 | − | 0.428778i | ||||
\(536\) | 11.9687i | 0.516971i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.99289 | − | 2.99289i | −0.129033 | − | 0.129033i | ||||
\(539\) | 4.66231 | 0.200820 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.1080 | 1.72438 | 0.862189 | − | 0.506587i | \(-0.169093\pi\) | ||||
0.862189 | + | 0.506587i | \(0.169093\pi\) | |||||||
\(542\) | −7.19633 | − | 7.19633i | −0.309109 | − | 0.309109i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 8.46900i | − | 0.363105i | ||||||
\(545\) | −16.8702 | − | 0.190092i | −0.722638 | − | 0.00814263i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.55083 | + | 8.55083i | −0.365607 | + | 0.365607i | −0.865872 | − | 0.500265i | \(-0.833236\pi\) |
0.500265 | + | 0.865872i | \(0.333236\pi\) | |||||||
\(548\) | 0.632361 | − | 0.632361i | 0.0270131 | − | 0.0270131i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.8803 | + | 19.9598i | −0.890337 | + | 0.851088i | ||||
\(551\) | 26.9153i | 1.14663i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.77467 | − | 1.77467i | −0.0754667 | − | 0.0754667i | ||||
\(554\) | 8.01704 | 0.340612 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3544 | 0.439126 | ||||||||
\(557\) | 15.5128 | + | 15.5128i | 0.657300 | + | 0.657300i | 0.954740 | − | 0.297441i | \(-0.0961330\pi\) |
−0.297441 | + | 0.954740i | \(0.596133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9281i | 0.715982i | ||||||||
\(560\) | −4.46291 | − | 4.56463i | −0.188592 | − | 0.192891i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.67970 | − | 9.67970i | 0.408313 | − | 0.408313i | ||||
\(563\) | 15.5187 | − | 15.5187i | 0.654036 | − | 0.654036i | −0.299926 | − | 0.953962i | \(-0.596962\pi\) |
0.953962 | + | 0.299926i | \(0.0969620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.98606 | + | 4.07691i | 0.167695 | + | 0.171517i | ||||
\(566\) | 7.75605i | 0.326011i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.24503 | + | 1.24503i | 0.0522401 | + | 0.0522401i | ||||
\(569\) | −31.6235 | −1.32573 | −0.662863 | − | 0.748741i | \(-0.730659\pi\) | ||||
−0.662863 | + | 0.748741i | \(0.730659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.0465 | −1.04816 | −0.524082 | − | 0.851668i | \(-0.675592\pi\) | ||||
−0.524082 | + | 0.851668i | \(0.675592\pi\) | |||||||
\(572\) | 3.35507 | + | 3.35507i | 0.140283 | + | 0.140283i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.33271i | − | 0.347801i | ||||||
\(575\) | 7.37367 | − | 7.04861i | 0.307503 | − | 0.293947i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.1909 | + | 20.1909i | −0.840557 | + | 0.840557i | −0.988931 | − | 0.148375i | \(-0.952596\pi\) |
0.148375 | + | 0.988931i | \(0.452596\pi\) | |||||||
\(578\) | −5.38228 | + | 5.38228i | −0.223873 | + | 0.223873i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.88072 | + | 0.0887993i | 0.327229 | + | 0.00368719i | ||||
\(581\) | 5.64980i | 0.234393i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.0045 | − | 32.0045i | −1.32549 | − | 1.32549i | ||||
\(584\) | 21.3519 | 0.883548 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.0989 | −1.61516 | ||||||||
\(587\) | −15.4569 | − | 15.4569i | −0.637976 | − | 0.637976i | 0.312080 | − | 0.950056i | \(-0.398974\pi\) |
−0.950056 | + | 0.312080i | \(0.898974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.8336i | 1.18807i | ||||||||
\(590\) | 12.6932 | − | 12.4103i | 0.522571 | − | 0.510926i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.1310 | + | 17.1310i | −0.704079 | + | 0.704079i | ||||
\(593\) | 2.50889 | − | 2.50889i | 0.103028 | − | 0.103028i | −0.653714 | − | 0.756742i | \(-0.726790\pi\) |
0.756742 | + | 0.653714i | \(0.226790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0830154 | + | 7.36741i | −0.00340330 | + | 0.302035i | ||||
\(596\) | − | 10.8741i | − | 0.445420i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.91552 | + | 3.91552i | 0.160117 | + | 0.160117i | ||||
\(599\) | 23.0111 | 0.940207 | 0.470104 | − | 0.882611i | \(-0.344217\pi\) | ||||
0.470104 | + | 0.882611i | \(0.344217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4097 | 0.465411 | 0.232706 | − | 0.972547i | \(-0.425242\pi\) | ||||
0.232706 | + | 0.972547i | \(0.425242\pi\) | |||||||
\(602\) | 6.77125 | + | 6.77125i | 0.275976 | + | 0.275976i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 7.89308i | − | 0.321165i | ||||||
\(605\) | 0.270514 | − | 24.0074i | 0.0109979 | − | 0.976040i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.7473 | − | 26.7473i | 1.08564 | − | 1.08564i | 0.0896663 | − | 0.995972i | \(-0.471420\pi\) |
0.995972 | − | 0.0896663i | \(-0.0285801\pi\) | |||||||
\(608\) | −6.44810 | + | 6.44810i | −0.261505 | + | 0.261505i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26.9508 | + | 26.3502i | −1.09121 | + | 1.06689i | ||||
\(611\) | − | 16.0049i | − | 0.647489i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.33197 | − | 9.33197i | −0.376915 | − | 0.376915i | 0.493073 | − | 0.869988i | \(-0.335874\pi\) |
−0.869988 | + | 0.493073i | \(0.835874\pi\) | |||||||
\(614\) | −8.15275 | −0.329018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.2383 | 0.573678 | ||||||||
\(617\) | −3.34333 | − | 3.34333i | −0.134597 | − | 0.134597i | 0.636598 | − | 0.771196i | \(-0.280341\pi\) |
−0.771196 | + | 0.636598i | \(0.780341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3147i | 0.615549i | 0.951459 | + | 0.307774i | \(0.0995842\pi\) | ||||
−0.951459 | + | 0.307774i | \(0.900416\pi\) | |||||||
\(620\) | 8.44236 | + | 0.0951278i | 0.339053 | + | 0.00382043i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.1304 | − | 11.1304i | 0.446289 | − | 0.446289i | ||||
\(623\) | 4.85589 | − | 4.85589i | 0.194547 | − | 0.194547i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9746 | + | 1.12636i | 0.998985 | + | 0.0450545i | ||||
\(626\) | − | 16.4582i | − | 0.657800i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.75366 | − | 3.75366i | −0.149787 | − | 0.149787i | ||||
\(629\) | 27.9613 | 1.11489 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4390 | −1.01271 | −0.506355 | − | 0.862325i | \(-0.669007\pi\) | ||||
−0.506355 | + | 0.862325i | \(0.669007\pi\) | |||||||
\(632\) | −5.41970 | − | 5.41970i | −0.215584 | − | 0.215584i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 21.1276i | − | 0.839085i | ||||||
\(635\) | 31.7265 | + | 32.4496i | 1.25903 | + | 1.28772i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.54889 | − | 1.54889i | 0.0613691 | − | 0.0613691i | ||||
\(638\) | 30.9902 | − | 30.9902i | 1.22691 | − | 1.22691i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.19338 | − | 9.40292i | −0.363400 | − | 0.371683i | ||||
\(641\) | − | 19.2081i | − | 0.758674i | −0.925259 | − | 0.379337i | \(-0.876152\pi\) | ||
0.925259 | − | 0.379337i | \(-0.123848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.50256 | − | 2.50256i | −0.0986915 | − | 0.0986915i | 0.656037 | − | 0.754729i | \(-0.272231\pi\) |
−0.754729 | + | 0.656037i | \(0.772231\pi\) | |||||||
\(644\) | −0.947851 | −0.0373506 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.4857 | −0.569934 | ||||||||
\(647\) | −10.7695 | − | 10.7695i | −0.423393 | − | 0.423393i | 0.462977 | − | 0.886370i | \(-0.346781\pi\) |
−0.886370 | + | 0.462977i | \(0.846781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.8712i | 1.17255i | ||||||||
\(650\) | −0.305797 | + | 13.5677i | −0.0119944 | + | 0.532167i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.22148 | − | 4.22148i | 0.165326 | − | 0.165326i | ||||
\(653\) | 26.4630 | − | 26.4630i | 1.03558 | − | 1.03558i | 0.0362330 | − | 0.999343i | \(-0.488464\pi\) |
0.999343 | − | 0.0362330i | \(-0.0115358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.21264 | + | 0.0812714i | 0.281821 | + | 0.00317554i | ||||
\(656\) | − | 19.1988i | − | 0.749585i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.40197 | − | 6.40197i | −0.249575 | − | 0.249575i | ||||
\(659\) | −8.78898 | −0.342370 | −0.171185 | − | 0.985239i | \(-0.554760\pi\) | ||||
−0.171185 | + | 0.985239i | \(0.554760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.11790 | −0.276854 | −0.138427 | − | 0.990373i | \(-0.544205\pi\) | ||||
−0.138427 | + | 0.990373i | \(0.544205\pi\) | |||||||
\(662\) | 0.737301 | + | 0.737301i | 0.0286560 | + | 0.0286560i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.2540i | 0.669586i | ||||||||
\(665\) | 5.67259 | − | 5.54618i | 0.219974 | − | 0.215072i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9439 | + | 10.9439i | −0.423749 | + | 0.423749i | ||||
\(668\) | 6.29188 | − | 6.29188i | 0.243440 | − | 0.243440i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.122350 | − | 10.8582i | 0.00472678 | − | 0.419490i | ||||
\(671\) | − | 63.4240i | − | 2.44846i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.822154 | + | 0.822154i | 0.0316917 | + | 0.0316917i | 0.722775 | − | 0.691083i | \(-0.242866\pi\) |
−0.691083 | + | 0.722775i | \(0.742866\pi\) | |||||||
\(674\) | 28.3772 | 1.09305 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.81062 | −0.146562 | ||||||||
\(677\) | −19.7788 | − | 19.7788i | −0.760162 | − | 0.760162i | 0.216189 | − | 0.976352i | \(-0.430637\pi\) |
−0.976352 | + | 0.216189i | \(0.930637\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.27073i | 0.240648i | ||||||||
\(680\) | −0.253522 | + | 22.4995i | −0.00972213 | + | 0.862815i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.1988 | − | 33.1988i | 1.27125 | − | 1.27125i | ||||
\(683\) | −22.2292 | + | 22.2292i | −0.850576 | + | 0.850576i | −0.990204 | − | 0.139628i | \(-0.955409\pi\) |
0.139628 | + | 0.990204i | \(0.455409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.07757 | + | 3.00898i | −0.117588 | + | 0.114967i | ||||
\(686\) | − | 1.23911i | − | 0.0473095i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.6011 | + | 15.6011i | 0.594787 | + | 0.594787i | ||||
\(689\) | −21.2647 | −0.810122 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5768 | 0.402361 | 0.201180 | − | 0.979554i | \(-0.435522\pi\) | ||||
0.201180 | + | 0.979554i | \(0.435522\pi\) | |||||||
\(692\) | −7.66051 | − | 7.66051i | −0.291209 | − | 0.291209i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 11.7837i | − | 0.447304i | ||||||
\(695\) | −49.8314 | − | 0.561496i | −1.89021 | − | 0.0212988i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.6682 | + | 15.6682i | −0.593475 | + | 0.593475i | ||||
\(698\) | −22.7542 | + | 22.7542i | −0.861261 | + | 0.861261i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.60519 | − | 1.67921i | −0.0606703 | − | 0.0634683i | ||||
\(701\) | 20.2841i | 0.766121i | 0.923723 | + | 0.383061i | \(0.125130\pi\) | ||||
−0.923723 | + | 0.383061i | \(0.874870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.2891 | − | 21.2891i | −0.802934 | − | 0.802934i | ||||
\(704\) | 41.4698 | 1.56295 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.0888 | −1.35822 | ||||||||
\(707\) | −1.86359 | − | 1.86359i | −0.0700876 | − | 0.0700876i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.7396i | − | 0.403333i | −0.979454 | − | 0.201666i | \(-0.935364\pi\) | ||
0.979454 | − | 0.201666i | \(-0.0646356\pi\) | |||||||
\(710\) | −1.11678 | − | 1.14223i | −0.0419120 | − | 0.0428673i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.8295 | − | 14.8295i | 0.555759 | − | 0.555759i | ||||
\(713\) | −11.7238 | + | 11.7238i | −0.439061 | + | 0.439061i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.9646 | − | 16.3284i | −0.597041 | − | 0.610649i | ||||
\(716\) | 3.32369i | 0.124212i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.7884 | − | 25.7884i | −0.962415 | − | 0.962415i | ||||
\(719\) | 24.5967 | 0.917302 | 0.458651 | − | 0.888616i | \(-0.348333\pi\) | ||||
0.458651 | + | 0.888616i | \(0.348333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5495 | −0.392883 | ||||||||
\(722\) | −5.61838 | − | 5.61838i | −0.209095 | − | 0.209095i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.25929i | 0.0839658i | ||||||||
\(725\) | −37.9216 | − | 0.854704i | −1.40837 | − | 0.0317429i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1032 | + | 22.1032i | −0.819763 | + | 0.819763i | −0.986073 | − | 0.166310i | \(-0.946815\pi\) |
0.166310 | + | 0.986073i | \(0.446815\pi\) | |||||||
\(728\) | 4.73017 | − | 4.73017i | 0.175312 | − | 0.175312i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.3708 | − | 0.218268i | −0.716945 | − | 0.00807847i | ||||
\(731\) | − | 25.4643i | − | 0.941830i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.38234 | + | 3.38234i | 0.124930 | + | 0.124930i | 0.766807 | − | 0.641878i | \(-0.221844\pi\) |
−0.641878 | + | 0.766807i | \(0.721844\pi\) | |||||||
\(734\) | 23.5177 | 0.868053 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.24365 | −0.193283 | ||||||||
\(737\) | 12.9204 | + | 12.9204i | 0.475930 | + | 0.475930i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0189i | 0.662838i | 0.943484 | + | 0.331419i | \(0.107527\pi\) | ||||
−0.943484 | + | 0.331419i | \(0.892473\pi\) | |||||||
\(740\) | −6.30361 | + | 6.16314i | −0.231725 | + | 0.226562i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.50591 | + | 8.50591i | −0.312262 | + | 0.312262i | ||||
\(743\) | −13.7680 | + | 13.7680i | −0.505099 | + | 0.505099i | −0.913018 | − | 0.407919i | \(-0.866255\pi\) |
0.407919 | + | 0.913018i | \(0.366255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.589675 | + | 52.3322i | −0.0216040 | + | 1.91730i | ||||
\(746\) | − | 2.43061i | − | 0.0889910i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.04690 | − | 5.04690i | −0.184533 | − | 0.184533i | ||||
\(749\) | 6.34437 | 0.231818 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7248 | −0.464336 | −0.232168 | − | 0.972676i | \(-0.574582\pi\) | ||||
−0.232168 | + | 0.972676i | \(0.574582\pi\) | |||||||
\(752\) | −14.7503 | − | 14.7503i | −0.537888 | − | 0.537888i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 20.5908i | − | 0.749871i | ||||||
\(755\) | −0.428023 | + | 37.9860i | −0.0155773 | + | 1.38245i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2644 | − | 31.2644i | 1.13633 | − | 1.13633i | 0.147222 | − | 0.989103i | \(-0.452967\pi\) |
0.989103 | − | 0.147222i | \(-0.0470332\pi\) | |||||||
\(758\) | −22.2420 | + | 22.2420i | −0.807866 | + | 0.807866i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.3236 | − | 16.9376i | 0.628394 | − | 0.614390i | ||||
\(761\) | − | 35.1072i | − | 1.27264i | −0.771427 | − | 0.636318i | \(-0.780457\pi\) | ||
0.771427 | − | 0.636318i | \(-0.219543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.33515 | − | 5.33515i | −0.193145 | − | 0.193145i | ||||
\(764\) | 0.460400 | 0.0166567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.48017 | 0.198006 | ||||||||
\(767\) | 9.92366 | + | 9.92366i | 0.358323 | + | 0.358323i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.2815i | − | 0.911673i | −0.890063 | − | 0.455837i | \(-0.849340\pi\) | ||
0.890063 | − | 0.455837i | \(-0.150660\pi\) | |||||||
\(770\) | −12.9172 | − | 0.145550i | −0.465504 | − | 0.00524526i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.82081 | − | 3.82081i | 0.137514 | − | 0.137514i | ||||
\(773\) | −15.4411 | + | 15.4411i | −0.555376 | + | 0.555376i | −0.927988 | − | 0.372611i | \(-0.878463\pi\) |
0.372611 | + | 0.927988i | \(0.378463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.6242 | − | 0.915617i | −1.45927 | − | 0.0328899i | ||||
\(776\) | 19.1503i | 0.687455i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.20867 | + | 9.20867i | 0.330147 | + | 0.330147i | ||||
\(779\) | 23.8588 | 0.854830 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.68805 | 0.0961859 | ||||||||
\(782\) | −5.88996 | − | 5.88996i | −0.210624 | − | 0.210624i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 2.85494i | − | 0.101962i | ||||||
\(785\) | 17.8612 | + | 18.2683i | 0.637492 | + | 0.652022i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7487 | − | 17.7487i | 0.632673 | − | 0.632673i | −0.316065 | − | 0.948738i | \(-0.602362\pi\) |
0.948738 | + | 0.316065i | \(0.102362\pi\) | |||||||
\(788\) | 0.837701 | − | 0.837701i | 0.0298419 | − | 0.0298419i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.86143 | + | 4.97224i | 0.172962 | + | 0.176904i | ||||
\(791\) | 2.54990i | 0.0906639i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.0704 | − | 21.0704i | −0.748231 | − | 0.748231i | ||||
\(794\) | 6.53474 | 0.231909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.44966 | −0.264046 | ||||||||
\(797\) | 17.3136 | + | 17.3136i | 0.613280 | + | 0.613280i | 0.943799 | − | 0.330520i | \(-0.107224\pi\) |
−0.330520 | + | 0.943799i | \(0.607224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0755i | 0.851731i | ||||||||
\(800\) | −8.88012 | − | 9.28964i | −0.313960 | − | 0.328438i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.6330 | − | 15.6330i | 0.552021 | − | 0.552021i | ||||
\(803\) | 23.0497 | − | 23.0497i | 0.813406 | − | 0.813406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.56159 | + | 0.0513996i | 0.160775 | + | 0.00181160i | ||||
\(806\) | − | 22.0582i | − | 0.776968i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.69126 | − | 5.69126i | −0.200218 | − | 0.200218i | ||||
\(809\) | −23.6436 | −0.831265 | −0.415632 | − | 0.909533i | \(-0.636440\pi\) | ||||
−0.415632 | + | 0.909533i | \(0.636440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9945 | −0.491412 | −0.245706 | − | 0.969344i | \(-0.579020\pi\) | ||||
−0.245706 | + | 0.969344i | \(0.579020\pi\) | |||||||
\(812\) | 2.49226 | + | 2.49226i | 0.0874612 | + | 0.0874612i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 49.0243i | 1.71830i | ||||||||
\(815\) | −20.5450 | + | 20.0872i | −0.719662 | + | 0.703624i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3879 | + | 19.3879i | −0.678297 | + | 0.678297i | ||||
\(818\) | 13.1149 | − | 13.1149i | 0.458550 | − | 0.458550i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0787151 | − | 6.98577i | 0.00274885 | − | 0.243954i | ||||
\(821\) | 32.7797i | 1.14402i | 0.820247 | + | 0.572010i | \(0.193836\pi\) | ||||
−0.820247 | + | 0.572010i | \(0.806164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.2743 | − | 15.2743i | −0.532430 | − | 0.532430i | 0.388865 | − | 0.921295i | \(-0.372867\pi\) |
−0.921295 | + | 0.388865i | \(0.872867\pi\) | |||||||
\(824\) | −32.2173 | −1.12234 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.93894 | 0.276231 | ||||||||
\(827\) | −19.3251 | − | 19.3251i | −0.672000 | − | 0.672000i | 0.286177 | − | 0.958177i | \(-0.407615\pi\) |
−0.958177 | + | 0.286177i | \(0.907615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.8148i | − | 1.62595i | −0.582302 | − | 0.812973i | \(-0.697848\pi\) | ||
0.582302 | − | 0.812973i | \(-0.302152\pi\) | |||||||
\(830\) | 0.176378 | − | 15.6531i | 0.00612217 | − | 0.543327i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.7769 | − | 13.7769i | 0.477628 | − | 0.477628i | ||||
\(833\) | −2.32993 | + | 2.32993i | −0.0807272 | + | 0.0807272i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.6212 | + | 29.9388i | −1.05969 | + | 1.03608i | ||||
\(836\) | 7.68519i | 0.265798i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.88277 | + | 5.88277i | 0.203217 | + | 0.203217i | ||||
\(839\) | −31.1400 | −1.07507 | −0.537535 | − | 0.843241i | \(-0.680645\pi\) | ||||
−0.537535 | + | 0.843241i | \(0.680645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5512 | 0.984524 | ||||||||
\(842\) | 26.4251 | + | 26.4251i | 0.910669 | + | 0.910669i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.2971i | 0.354440i | ||||||||
\(845\) | 18.3388 | + | 0.206641i | 0.630875 | + | 0.00710865i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.59229 | − | 7.59229i | 0.260874 | − | 0.260874i | ||||
\(848\) | −19.5978 | + | 19.5978i | −0.672991 | + | 0.672991i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.459999 | − | 20.4093i | 0.0157778 | − | 0.700033i | ||||
\(851\) | − | 17.3125i | − | 0.593464i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.5421 | + | 34.5421i | 1.18270 | + | 1.18270i | 0.979042 | + | 0.203657i | \(0.0652828\pi\) |
0.203657 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(854\) | −16.8563 | −0.576812 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.3752 | 0.662230 | ||||||||
\(857\) | 29.4941 | + | 29.4941i | 1.00750 | + | 1.00750i | 0.999972 | + | 0.00752899i | \(0.00239658\pi\) |
0.00752899 | + | 0.999972i | \(0.497603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.7748i | 1.49358i | 0.665061 | + | 0.746789i | \(0.268406\pi\) | ||||
−0.665061 | + | 0.746789i | \(0.731594\pi\) | |||||||
\(860\) | 5.61275 | + | 5.74068i | 0.191393 | + | 0.195756i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7568 | − | 12.7568i | 0.434497 | − | 0.434497i | ||||
\(863\) | −9.59074 | + | 9.59074i | −0.326472 | + | 0.326472i | −0.851243 | − | 0.524771i | \(-0.824151\pi\) |
0.524771 | + | 0.851243i | \(0.324151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.4513 | + | 37.2821i | 1.23938 | + | 1.26763i | ||||
\(866\) | − | 25.0867i | − | 0.852479i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.66988 | + | 2.66988i | 0.0906216 | + | 0.0906216i | ||||
\(869\) | −11.7013 | −0.396939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.58471 | 0.290882 | ||||||||
\(872\) | −16.2931 | − | 16.2931i | −0.551754 | − | 0.551754i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.96896i | 0.303380i | ||||||||
\(875\) | 7.63400 | + | 8.16836i | 0.258076 | + | 0.276141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.7983 | − | 38.7983i | 1.31013 | − | 1.31013i | 0.388809 | − | 0.921319i | \(-0.372887\pi\) |
0.921319 | − | 0.388809i | \(-0.127113\pi\) | |||||||
\(878\) | −20.8091 | + | 20.8091i | −0.702272 | + | 0.702272i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −29.7616 | − | 0.335351i | −1.00326 | − | 0.0113047i | ||||
\(881\) | − | 14.2447i | − | 0.479918i | −0.970783 | − | 0.239959i | \(-0.922866\pi\) | ||
0.970783 | − | 0.239959i | \(-0.0771339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0748 | − | 34.0748i | −1.14671 | − | 1.14671i | −0.987196 | − | 0.159511i | \(-0.949008\pi\) |
−0.159511 | − | 0.987196i | \(-0.550992\pi\) | |||||||
\(884\) | −3.35331 | −0.112784 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 49.2031 | 1.65301 | ||||||||
\(887\) | −0.895283 | − | 0.895283i | −0.0300607 | − | 0.0300607i | 0.691917 | − | 0.721977i | \(-0.256767\pi\) |
−0.721977 | + | 0.691917i | \(0.756767\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2956i | 0.680691i | ||||||||
\(890\) | −13.6051 | + | 13.3020i | −0.456045 | + | 0.445882i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.24961 | + | 6.24961i | −0.209252 | + | 0.209252i | ||||
\(893\) | 18.3306 | − | 18.3306i | 0.613409 | − | 0.613409i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.180235 | − | 15.9955i | 0.00602461 | − | 0.534669i | ||||
\(896\) | − | 5.88104i | − | 0.196472i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.2547 | + | 20.2547i | 0.675909 | + | 0.675909i | ||||
\(899\) | 61.6528 | 2.05624 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.9877 | 1.06566 | ||||||||
\(902\) | −27.4709 | − | 27.4709i | −0.914680 | − | 0.914680i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.78718i | 0.258998i | ||||||||
\(905\) | 0.122516 | − | 10.8730i | 0.00407256 | − | 0.361430i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4485 | − | 16.4485i | 0.546164 | − | 0.546164i | −0.379165 | − | 0.925329i | \(-0.623789\pi\) |
0.925329 | + | 0.379165i | \(0.123789\pi\) | |||||||
\(908\) | 3.98444 | − | 3.98444i | 0.132228 | − | 0.132228i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.33964 | + | 4.24293i | −0.143858 | + | 0.140652i | ||||
\(911\) | 19.8928i | 0.659078i | 0.944142 | + | 0.329539i | \(0.106893\pi\) | ||||
−0.944142 | + | 0.329539i | \(0.893107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.6260 | + | 18.6260i | 0.616430 | + | 0.616430i | ||||
\(914\) | 4.22914 | 0.139888 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.4217 | −0.344342 | ||||||||
\(917\) | 2.28098 | + | 2.28098i | 0.0753246 | + | 0.0753246i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3303i | 1.29739i | 0.761050 | + | 0.648693i | \(0.224684\pi\) | ||||
−0.761050 | + | 0.648693i | \(0.775316\pi\) | |||||||
\(920\) | 13.9307 | + | 0.156970i | 0.459282 | + | 0.00517516i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.3760 | − | 11.3760i | 0.374649 | − | 0.374649i | ||||
\(923\) | 0.893009 | − | 0.893009i | 0.0293937 | − | 0.0293937i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.6707 | − | 29.3187i | 1.00845 | − | 0.963992i | ||||
\(926\) | − | 37.7844i | − | 1.24167i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.7875 | + | 13.7875i | 0.452598 | + | 0.452598i | ||||
\(929\) | 26.3786 | 0.865455 | 0.432728 | − | 0.901525i | \(-0.357551\pi\) | ||||
0.432728 | + | 0.901525i | \(0.357551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.54791 | 0.116278 | ||||||||
\(932\) | 1.85312 | + | 1.85312i | 0.0607008 | + | 0.0607008i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.26673i | 0.237775i | ||||||||
\(935\) | 24.0148 | + | 24.5622i | 0.785369 | + | 0.803270i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.2937 | + | 37.2937i | −1.21833 | + | 1.21833i | −0.250118 | + | 0.968215i | \(0.580469\pi\) |
−0.968215 | + | 0.250118i | \(0.919531\pi\) | |||||||
\(938\) | 3.43389 | − | 3.43389i | 0.112121 | − | 0.112121i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.30665 | − | 5.42760i | −0.173084 | − | 0.177029i | ||||
\(941\) | 48.3991i | 1.57776i | 0.614544 | + | 0.788882i | \(0.289340\pi\) | ||||
−0.614544 | + | 0.788882i | \(0.710660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.70107 | + | 9.70107i | 0.315910 | + | 0.315910i | ||||
\(944\) | 18.2915 | 0.595338 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 44.6463 | 1.45158 | ||||||||
\(947\) | −27.4439 | − | 27.4439i | −0.891806 | − | 0.891806i | 0.102887 | − | 0.994693i | \(-0.467192\pi\) |
−0.994693 | + | 0.102887i | \(0.967192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.3149i | − | 0.497142i | ||||||
\(950\) | −15.8894 | + | 15.1889i | −0.515520 | + | 0.492794i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.11541 | + | 7.11541i | −0.230612 | + | 0.230612i | ||||
\(953\) | 7.74667 | − | 7.74667i | 0.250939 | − | 0.250939i | −0.570416 | − | 0.821356i | \(-0.693218\pi\) |
0.821356 | + | 0.570416i | \(0.193218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.21570 | − | 0.0249663i | −0.0716984 | − | 0.000807892i | ||||
\(956\) | − | 4.25463i | − | 0.137604i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.98648 | − | 9.98648i | −0.322648 | − | 0.322648i | ||||
\(959\) | −1.92486 | −0.0621569 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.0467 | 1.13054 | ||||||||
\(962\) | 16.2866 | + | 16.2866i | 0.525101 | + | 0.525101i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.30061i | 0.202929i | ||||||||
\(965\) | −18.5951 | + | 18.1807i | −0.598597 | + | 0.585258i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8257 | − | 12.8257i | 0.412448 | − | 0.412448i | −0.470143 | − | 0.882590i | \(-0.655797\pi\) |
0.882590 | + | 0.470143i | \(0.155797\pi\) | |||||||
\(968\) | 23.1862 | − | 23.1862i | 0.745234 | − | 0.745234i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.195762 | − | 17.3734i | 0.00628555 | − | 0.557828i | ||||
\(971\) | 30.4338i | 0.976666i | 0.872657 | + | 0.488333i | \(0.162395\pi\) | ||||
−0.872657 | + | 0.488333i | \(0.837605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.7591 | − | 15.7591i | −0.505213 | − | 0.505213i | ||||
\(974\) | 19.4412 | 0.622935 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.8374 | −1.24315 | ||||||||
\(977\) | −4.71670 | − | 4.71670i | −0.150901 | − | 0.150901i | 0.627620 | − | 0.778520i | \(-0.284029\pi\) |
−0.778520 | + | 0.627620i | \(0.784029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.0173i | − | 1.02328i | ||||||
\(980\) | 0.0117053 | − | 1.03882i | 0.000373912 | − | 0.0331838i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.9356 | + | 24.9356i | −0.795726 | + | 0.795726i | ||||
\(983\) | −28.6631 | + | 28.6631i | −0.914211 | + | 0.914211i | −0.996600 | − | 0.0823888i | \(-0.973745\pi\) |
0.0823888 | + | 0.996600i | \(0.473745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.07691 | + | 3.98606i | −0.129901 | + | 0.127006i | ||||
\(986\) | 30.9739i | 0.986409i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.55313 | + | 2.55313i | 0.0812260 | + | 0.0812260i | ||||
\(989\) | −15.7664 | −0.501342 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.6787 | 1.29220 | 0.646101 | − | 0.763252i | \(-0.276398\pi\) | ||||
0.646101 | + | 0.763252i | \(0.276398\pi\) | |||||||
\(992\) | 14.7701 | + | 14.7701i | 0.468953 | + | 0.468953i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 0.714408i | − | 0.0226597i | ||||||
\(995\) | 35.8520 | + | 0.403977i | 1.13658 | + | 0.0128069i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.6947 | + | 24.6947i | −0.782090 | + | 0.782090i | −0.980183 | − | 0.198094i | \(-0.936525\pi\) |
0.198094 | + | 0.980183i | \(0.436525\pi\) | |||||||
\(998\) | 11.3975 | − | 11.3975i | 0.360782 | − | 0.360782i | ||||
\(999\) | 0 | 0 |
(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 | 315.2.m.b.8.3 | yes | 12 | |
3.2 | odd | 2 | 315.2.m.a.8.4 | ✓ | 12 | ||
5.2 | odd | 4 | 315.2.m.a.197.4 | yes | 12 | ||
5.3 | odd | 4 | 1575.2.m.c.1457.3 | 12 | |||
5.4 | even | 2 | 1575.2.m.d.1268.4 | 12 | |||
15.2 | even | 4 | inner | 315.2.m.b.197.3 | yes | 12 | |
15.8 | even | 4 | 1575.2.m.d.1457.4 | 12 | |||
15.14 | odd | 2 | 1575.2.m.c.1268.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.m.a.8.4 | ✓ | 12 | 3.2 | odd | 2 | ||
315.2.m.a.197.4 | yes | 12 | 5.2 | odd | 4 | ||
315.2.m.b.8.3 | yes | 12 | 1.1 | even | 1 | trivial | |
315.2.m.b.197.3 | yes | 12 | 15.2 | even | 4 | inner | |
1575.2.m.c.1268.3 | 12 | 15.14 | odd | 2 | |||
1575.2.m.c.1457.3 | 12 | 5.3 | odd | 4 | |||
1575.2.m.d.1268.4 | 12 | 5.4 | even | 2 | |||
1575.2.m.d.1457.4 | 12 | 15.8 | even | 4 |