Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.1 | ||
Root | \(-2.78712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.e.1249.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.78712i | − 1.97079i | −0.170281 | − | 0.985395i | \(-0.554468\pi\) | ||||
0.170281 | − | 0.985395i | \(-0.445532\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −5.76803 | −2.88402 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.78712 | −1.13784 | ||||||||
\(7\) | 3.15000i | 1.19059i | 0.803508 | + | 0.595294i | \(0.202964\pi\) | ||||
−0.803508 | + | 0.595294i | \(0.797036\pi\) | |||||||
\(8\) | 10.5020i | 3.71300i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.94681 | 0.888496 | 0.444248 | − | 0.895904i | \(-0.353471\pi\) | ||||
0.444248 | + | 0.895904i | \(0.353471\pi\) | |||||||
\(12\) | 5.76803i | 1.66509i | ||||||||
\(13\) | 0.188171i | 0.0521891i | 0.999659 | + | 0.0260946i | \(0.00830710\pi\) | ||||
−0.999659 | + | 0.0260946i | \(0.991693\pi\) | |||||||
\(14\) | 8.77943 | 2.34640 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.7341 | 4.43354 | ||||||||
\(17\) | − 2.62743i | − 0.637246i | −0.947882 | − | 0.318623i | \(-0.896780\pi\) | ||||
0.947882 | − | 0.318623i | \(-0.103220\pi\) | |||||||
\(18\) | 2.78712i | 0.656930i | ||||||||
\(19\) | −1.94100 | −0.445296 | −0.222648 | − | 0.974899i | \(-0.571470\pi\) | ||||
−0.222648 | + | 0.974899i | \(0.571470\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.15000 | 0.687386 | ||||||||
\(22\) | − 8.21310i | − 1.75104i | ||||||||
\(23\) | − 1.30447i | − 0.272000i | −0.990709 | − | 0.136000i | \(-0.956575\pi\) | ||||
0.990709 | − | 0.136000i | \(-0.0434247\pi\) | |||||||
\(24\) | 10.5020 | 2.14370 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.524454 | 0.102854 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 18.1693i | − 3.43368i | ||||||||
\(29\) | −1.23197 | −0.228770 | −0.114385 | − | 0.993436i | \(-0.536490\pi\) | ||||
−0.114385 | + | 0.993436i | \(0.536490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65174 | 0.476266 | 0.238133 | − | 0.971233i | \(-0.423465\pi\) | ||||
0.238133 | + | 0.971233i | \(0.423465\pi\) | |||||||
\(32\) | − 28.4233i | − 5.02457i | ||||||||
\(33\) | − 2.94681i | − 0.512973i | ||||||||
\(34\) | −7.32297 | −1.25588 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.76803 | 0.961339 | ||||||||
\(37\) | − 10.1161i | − 1.66308i | −0.555466 | − | 0.831540i | \(-0.687460\pi\) | ||||
0.555466 | − | 0.831540i | \(-0.312540\pi\) | |||||||
\(38\) | 5.40980i | 0.877585i | ||||||||
\(39\) | 0.188171 | 0.0301314 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85940 | 0.602737 | 0.301368 | − | 0.953508i | \(-0.402557\pi\) | ||||
0.301368 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(42\) | − 8.77943i | − 1.35469i | ||||||||
\(43\) | − 9.63734i | − 1.46968i | −0.678240 | − | 0.734840i | \(-0.737257\pi\) | ||||
0.678240 | − | 0.734840i | \(-0.262743\pi\) | |||||||
\(44\) | −16.9973 | −2.56244 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.63570 | −0.536055 | ||||||||
\(47\) | 11.9846i | 1.74814i | 0.485804 | + | 0.874068i | \(0.338527\pi\) | ||||
−0.485804 | + | 0.874068i | \(0.661473\pi\) | |||||||
\(48\) | − 17.7341i | − 2.55970i | ||||||||
\(49\) | −2.92250 | −0.417500 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.62743 | −0.367914 | ||||||||
\(52\) | − 1.08537i | − 0.150514i | ||||||||
\(53\) | 0.369521i | 0.0507576i | 0.999678 | + | 0.0253788i | \(0.00807919\pi\) | ||||
−0.999678 | + | 0.0253788i | \(0.991921\pi\) | |||||||
\(54\) | 2.78712 | 0.379279 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −33.0812 | −4.42066 | ||||||||
\(57\) | 1.94100i | 0.257092i | ||||||||
\(58\) | 3.43364i | 0.450859i | ||||||||
\(59\) | 6.90864 | 0.899428 | 0.449714 | − | 0.893173i | \(-0.351526\pi\) | ||||
0.449714 | + | 0.893173i | \(0.351526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68643 | 0.728073 | 0.364037 | − | 0.931385i | \(-0.381398\pi\) | ||||
0.364037 | + | 0.931385i | \(0.381398\pi\) | |||||||
\(62\) | − 7.39071i | − 0.938621i | ||||||||
\(63\) | − 3.15000i | − 0.396863i | ||||||||
\(64\) | −43.7507 | −5.46884 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.21310 | −1.01096 | ||||||||
\(67\) | − 3.24188i | − 0.396058i | −0.980196 | − | 0.198029i | \(-0.936546\pi\) | ||||
0.980196 | − | 0.198029i | \(-0.0634541\pi\) | |||||||
\(68\) | 15.1551i | 1.83783i | ||||||||
\(69\) | −1.30447 | −0.157039 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.69982 | 0.795122 | 0.397561 | − | 0.917576i | \(-0.369857\pi\) | ||||
0.397561 | + | 0.917576i | \(0.369857\pi\) | |||||||
\(72\) | − 10.5020i | − 1.23767i | ||||||||
\(73\) | − 9.46938i | − 1.10831i | −0.832415 | − | 0.554153i | \(-0.813042\pi\) | ||||
0.832415 | − | 0.554153i | \(-0.186958\pi\) | |||||||
\(74\) | −28.1948 | −3.27758 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.1957 | 1.28424 | ||||||||
\(77\) | 9.28244i | 1.05783i | ||||||||
\(78\) | − 0.524454i | − 0.0593827i | ||||||||
\(79\) | −0.420137 | −0.0472691 | −0.0236345 | − | 0.999721i | \(-0.507524\pi\) | ||||
−0.0236345 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 10.7566i | − 1.18787i | ||||||||
\(83\) | − 12.1635i | − 1.33512i | −0.744557 | − | 0.667559i | \(-0.767339\pi\) | ||||
0.744557 | − | 0.667559i | \(-0.232661\pi\) | |||||||
\(84\) | −18.1693 | −1.98243 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −26.8604 | −2.89643 | ||||||||
\(87\) | 1.23197i | 0.132081i | ||||||||
\(88\) | 30.9473i | 3.29899i | ||||||||
\(89\) | 15.1828 | 1.60937 | 0.804687 | − | 0.593699i | \(-0.202333\pi\) | ||||
0.804687 | + | 0.593699i | \(0.202333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.592737 | −0.0621358 | ||||||||
\(92\) | 7.52421i | 0.784453i | ||||||||
\(93\) | − 2.65174i | − 0.274972i | ||||||||
\(94\) | 33.4025 | 3.44521 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −28.4233 | −2.90094 | ||||||||
\(97\) | − 13.9035i | − 1.41169i | −0.708367 | − | 0.705845i | \(-0.750568\pi\) | ||||
0.708367 | − | 0.705845i | \(-0.249432\pi\) | |||||||
\(98\) | 8.14536i | 0.822805i | ||||||||
\(99\) | −2.94681 | −0.296165 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.67188 | −0.962388 | −0.481194 | − | 0.876614i | \(-0.659797\pi\) | ||||
−0.481194 | + | 0.876614i | \(0.659797\pi\) | |||||||
\(102\) | 7.32297i | 0.725082i | ||||||||
\(103\) | 8.69434i | 0.856679i | 0.903618 | + | 0.428339i | \(0.140901\pi\) | ||||
−0.903618 | + | 0.428339i | \(0.859099\pi\) | |||||||
\(104\) | −1.97616 | −0.193778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.02990 | 0.100033 | ||||||||
\(107\) | 2.56585i | 0.248050i | 0.992279 | + | 0.124025i | \(0.0395804\pi\) | ||||
−0.992279 | + | 0.124025i | \(0.960420\pi\) | |||||||
\(108\) | − 5.76803i | − 0.555029i | ||||||||
\(109\) | 15.2352 | 1.45926 | 0.729632 | − | 0.683840i | \(-0.239691\pi\) | ||||
0.729632 | + | 0.683840i | \(0.239691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1161 | −0.960179 | ||||||||
\(112\) | 55.8626i | 5.27852i | ||||||||
\(113\) | 2.20391i | 0.207326i | 0.994612 | + | 0.103663i | \(0.0330564\pi\) | ||||
−0.994612 | + | 0.103663i | \(0.966944\pi\) | |||||||
\(114\) | 5.40980 | 0.506674 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.10602 | 0.659778 | ||||||||
\(117\) | − 0.188171i | − 0.0173964i | ||||||||
\(118\) | − 19.2552i | − 1.77258i | ||||||||
\(119\) | 8.27641 | 0.758697 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.31633 | −0.210575 | ||||||||
\(122\) | − 15.8488i | − 1.43488i | ||||||||
\(123\) | − 3.85940i | − 0.347990i | ||||||||
\(124\) | −15.2953 | −1.37356 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.77943 | −0.782133 | ||||||||
\(127\) | 14.9689i | 1.32827i | 0.747611 | + | 0.664136i | \(0.231201\pi\) | ||||
−0.747611 | + | 0.664136i | \(0.768799\pi\) | |||||||
\(128\) | 65.0920i | 5.75337i | ||||||||
\(129\) | −9.63734 | −0.848521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2957 | 0.986911 | 0.493456 | − | 0.869771i | \(-0.335734\pi\) | ||||
0.493456 | + | 0.869771i | \(0.335734\pi\) | |||||||
\(132\) | 16.9973i | 1.47942i | ||||||||
\(133\) | − 6.11415i | − 0.530164i | ||||||||
\(134\) | −9.03550 | −0.780548 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.5932 | 2.36610 | ||||||||
\(137\) | − 4.17877i | − 0.357017i | −0.983938 | − | 0.178508i | \(-0.942873\pi\) | ||||
0.983938 | − | 0.178508i | \(-0.0571271\pi\) | |||||||
\(138\) | 3.63570i | 0.309492i | ||||||||
\(139\) | 15.3552 | 1.30241 | 0.651207 | − | 0.758900i | \(-0.274263\pi\) | ||||
0.651207 | + | 0.758900i | \(0.274263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9846 | 1.00929 | ||||||||
\(142\) | − 18.6732i | − 1.56702i | ||||||||
\(143\) | 0.554502i | 0.0463698i | ||||||||
\(144\) | −17.7341 | −1.47785 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26.3923 | −2.18424 | ||||||||
\(147\) | 2.92250i | 0.241044i | ||||||||
\(148\) | 58.3501i | 4.79635i | ||||||||
\(149\) | −3.43364 | −0.281294 | −0.140647 | − | 0.990060i | \(-0.544918\pi\) | ||||
−0.140647 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7716 | 0.876581 | 0.438290 | − | 0.898833i | \(-0.355584\pi\) | ||||
0.438290 | + | 0.898833i | \(0.355584\pi\) | |||||||
\(152\) | − 20.3843i | − 1.65338i | ||||||||
\(153\) | 2.62743i | 0.212415i | ||||||||
\(154\) | 25.8713 | 2.08477 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.08537 | −0.0868995 | ||||||||
\(157\) | 13.4045i | 1.06980i | 0.844916 | + | 0.534900i | \(0.179651\pi\) | ||||
−0.844916 | + | 0.534900i | \(0.820349\pi\) | |||||||
\(158\) | 1.17097i | 0.0931574i | ||||||||
\(159\) | 0.369521 | 0.0293049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.10907 | 0.323840 | ||||||||
\(162\) | − 2.78712i | − 0.218977i | ||||||||
\(163\) | − 15.4178i | − 1.20762i | −0.797129 | − | 0.603808i | \(-0.793649\pi\) | ||||
0.797129 | − | 0.603808i | \(-0.206351\pi\) | |||||||
\(164\) | −22.2611 | −1.73830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.9011 | −2.63124 | ||||||||
\(167\) | − 17.4045i | − 1.34680i | −0.739276 | − | 0.673402i | \(-0.764832\pi\) | ||||
0.739276 | − | 0.673402i | \(-0.235168\pi\) | |||||||
\(168\) | 33.0812i | 2.55227i | ||||||||
\(169\) | 12.9646 | 0.997276 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.94100 | 0.148432 | ||||||||
\(172\) | 55.5885i | 4.23858i | ||||||||
\(173\) | − 19.2737i | − 1.46535i | −0.680578 | − | 0.732676i | \(-0.738271\pi\) | ||||
0.680578 | − | 0.732676i | \(-0.261729\pi\) | |||||||
\(174\) | 3.43364 | 0.260303 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 52.2591 | 3.93918 | ||||||||
\(177\) | − 6.90864i | − 0.519285i | ||||||||
\(178\) | − 42.3163i | − 3.17174i | ||||||||
\(179\) | −23.7940 | −1.77845 | −0.889223 | − | 0.457475i | \(-0.848754\pi\) | ||||
−0.889223 | + | 0.457475i | \(0.848754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6891 | −0.794516 | −0.397258 | − | 0.917707i | \(-0.630038\pi\) | ||||
−0.397258 | + | 0.917707i | \(0.630038\pi\) | |||||||
\(182\) | 1.65203i | 0.122457i | ||||||||
\(183\) | − 5.68643i | − 0.420353i | ||||||||
\(184\) | 13.6995 | 1.00994 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.39071 | −0.541913 | ||||||||
\(187\) | − 7.74253i | − 0.566190i | ||||||||
\(188\) | − 69.1277i | − 5.04165i | ||||||||
\(189\) | −3.15000 | −0.229129 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3581 | −1.03892 | −0.519458 | − | 0.854496i | \(-0.673866\pi\) | ||||
−0.519458 | + | 0.854496i | \(0.673866\pi\) | |||||||
\(192\) | 43.7507i | 3.15744i | ||||||||
\(193\) | 1.95508i | 0.140730i | 0.997521 | + | 0.0703648i | \(0.0224163\pi\) | ||||
−0.997521 | + | 0.0703648i | \(0.977584\pi\) | |||||||
\(194\) | −38.7508 | −2.78214 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.8571 | 1.20408 | ||||||||
\(197\) | 1.17958i | 0.0840417i | 0.999117 | + | 0.0420209i | \(0.0133796\pi\) | ||||
−0.999117 | + | 0.0420209i | \(0.986620\pi\) | |||||||
\(198\) | 8.21310i | 0.583680i | ||||||||
\(199\) | 6.55820 | 0.464899 | 0.232449 | − | 0.972608i | \(-0.425326\pi\) | ||||
0.232449 | + | 0.972608i | \(0.425326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.24188 | −0.228664 | ||||||||
\(202\) | 26.9567i | 1.89666i | ||||||||
\(203\) | − 3.88069i | − 0.272371i | ||||||||
\(204\) | 15.1551 | 1.06107 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 24.2322 | 1.68833 | ||||||||
\(207\) | 1.30447i | 0.0906667i | ||||||||
\(208\) | 3.33705i | 0.231382i | ||||||||
\(209\) | −5.71975 | −0.395643 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3573 | 0.850715 | 0.425357 | − | 0.905026i | \(-0.360148\pi\) | ||||
0.425357 | + | 0.905026i | \(0.360148\pi\) | |||||||
\(212\) | − 2.13141i | − 0.146386i | ||||||||
\(213\) | − 6.69982i | − 0.459064i | ||||||||
\(214\) | 7.15134 | 0.488856 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.5020 | −0.714568 | ||||||||
\(217\) | 8.35298i | 0.567037i | ||||||||
\(218\) | − 42.4622i | − 2.87591i | ||||||||
\(219\) | −9.46938 | −0.639881 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.494405 | 0.0332573 | ||||||||
\(222\) | 28.1948i | 1.89231i | ||||||||
\(223\) | − 7.30693i | − 0.489308i | −0.969610 | − | 0.244654i | \(-0.921326\pi\) | ||||
0.969610 | − | 0.244654i | \(-0.0786744\pi\) | |||||||
\(224\) | 89.5333 | 5.98219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.14256 | 0.408597 | ||||||||
\(227\) | 21.0202i | 1.39516i | 0.716508 | + | 0.697579i | \(0.245739\pi\) | ||||
−0.716508 | + | 0.697579i | \(0.754261\pi\) | |||||||
\(228\) | − 11.1957i | − 0.741457i | ||||||||
\(229\) | −19.5544 | −1.29219 | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.28244 | 0.610740 | ||||||||
\(232\) | − 12.9381i | − 0.849425i | ||||||||
\(233\) | 12.1472i | 0.795792i | 0.917430 | + | 0.397896i | \(0.130260\pi\) | ||||
−0.917430 | + | 0.397896i | \(0.869740\pi\) | |||||||
\(234\) | −0.524454 | −0.0342846 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −39.8493 | −2.59397 | ||||||||
\(237\) | 0.420137i | 0.0272908i | ||||||||
\(238\) | − 23.0673i | − 1.49523i | ||||||||
\(239\) | −13.4517 | −0.870119 | −0.435059 | − | 0.900402i | \(-0.643273\pi\) | ||||
−0.435059 | + | 0.900402i | \(0.643273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9370 | 1.28426 | 0.642129 | − | 0.766597i | \(-0.278051\pi\) | ||||
0.642129 | + | 0.766597i | \(0.278051\pi\) | |||||||
\(242\) | 6.45588i | 0.415000i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −32.7995 | −2.09978 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.7566 | −0.685816 | ||||||||
\(247\) | − 0.365239i | − 0.0232396i | ||||||||
\(248\) | 27.8485i | 1.76838i | ||||||||
\(249\) | −12.1635 | −0.770830 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.76013 | −0.174218 | −0.0871088 | − | 0.996199i | \(-0.527763\pi\) | ||||
−0.0871088 | + | 0.996199i | \(0.527763\pi\) | |||||||
\(252\) | 18.1693i | 1.14456i | ||||||||
\(253\) | − 3.84401i | − 0.241671i | ||||||||
\(254\) | 41.7200 | 2.61775 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 93.9177 | 5.86986 | ||||||||
\(257\) | 17.2848i | 1.07820i | 0.842243 | + | 0.539098i | \(0.181235\pi\) | ||||
−0.842243 | + | 0.539098i | \(0.818765\pi\) | |||||||
\(258\) | 26.8604i | 1.67226i | ||||||||
\(259\) | 31.8658 | 1.98004 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.23197 | 0.0762568 | ||||||||
\(262\) | − 31.4825i | − 1.94500i | ||||||||
\(263\) | − 3.96578i | − 0.244541i | −0.992497 | − | 0.122270i | \(-0.960983\pi\) | ||||
0.992497 | − | 0.122270i | \(-0.0390175\pi\) | |||||||
\(264\) | 30.9473 | 1.90467 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.0409 | −1.04484 | ||||||||
\(267\) | − 15.1828i | − 0.929173i | ||||||||
\(268\) | 18.6993i | 1.14224i | ||||||||
\(269\) | −1.19564 | −0.0728993 | −0.0364496 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364496 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.18295 | −0.132605 | −0.0663023 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663023 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(272\) | − 46.5953i | − 2.82525i | ||||||||
\(273\) | 0.592737i | 0.0358741i | ||||||||
\(274\) | −11.6467 | −0.703605 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.52421 | 0.452904 | ||||||||
\(277\) | − 1.95174i | − 0.117268i | −0.998280 | − | 0.0586342i | \(-0.981325\pi\) | ||||
0.998280 | − | 0.0586342i | \(-0.0186746\pi\) | |||||||
\(278\) | − 42.7969i | − 2.56679i | ||||||||
\(279\) | −2.65174 | −0.158755 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.30131 | 0.137284 | 0.0686422 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686422 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(282\) | − 33.4025i | − 1.98909i | ||||||||
\(283\) | − 10.6459i | − 0.632835i | −0.948620 | − | 0.316417i | \(-0.897520\pi\) | ||||
0.948620 | − | 0.316417i | \(-0.102480\pi\) | |||||||
\(284\) | −38.6448 | −2.29315 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54546 | 0.0913852 | ||||||||
\(287\) | 12.1571i | 0.717611i | ||||||||
\(288\) | 28.4233i | 1.67486i | ||||||||
\(289\) | 10.0966 | 0.593918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.9035 | −0.815039 | ||||||||
\(292\) | 54.6197i | 3.19638i | ||||||||
\(293\) | 14.9591i | 0.873921i | 0.899481 | + | 0.436960i | \(0.143945\pi\) | ||||
−0.899481 | + | 0.436960i | \(0.856055\pi\) | |||||||
\(294\) | 8.14536 | 0.475047 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 106.239 | 6.17502 | ||||||||
\(297\) | 2.94681i | 0.170991i | ||||||||
\(298\) | 9.56995i | 0.554373i | ||||||||
\(299\) | 0.245462 | 0.0141954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.3576 | 1.74978 | ||||||||
\(302\) | − 30.0217i | − 1.72756i | ||||||||
\(303\) | 9.67188i | 0.555635i | ||||||||
\(304\) | −34.4220 | −1.97424 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.32297 | 0.418626 | ||||||||
\(307\) | 3.07333i | 0.175404i | 0.996147 | + | 0.0877021i | \(0.0279524\pi\) | ||||
−0.996147 | + | 0.0877021i | \(0.972048\pi\) | |||||||
\(308\) | − 53.5414i | − 3.05081i | ||||||||
\(309\) | 8.69434 | 0.494604 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9095 | 1.41249 | 0.706244 | − | 0.707968i | \(-0.250388\pi\) | ||||
0.706244 | + | 0.707968i | \(0.250388\pi\) | |||||||
\(312\) | 1.97616i | 0.111878i | ||||||||
\(313\) | 9.28562i | 0.524854i | 0.964952 | + | 0.262427i | \(0.0845230\pi\) | ||||
−0.964952 | + | 0.262427i | \(0.915477\pi\) | |||||||
\(314\) | 37.3601 | 2.10835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.42336 | 0.136325 | ||||||||
\(317\) | − 20.7685i | − 1.16647i | −0.812302 | − | 0.583237i | \(-0.801786\pi\) | ||||
0.812302 | − | 0.583237i | \(-0.198214\pi\) | |||||||
\(318\) | − 1.02990i | − 0.0577538i | ||||||||
\(319\) | −3.63037 | −0.203261 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.56585 | 0.143212 | ||||||||
\(322\) | − 11.4525i | − 0.638221i | ||||||||
\(323\) | 5.09984i | 0.283763i | ||||||||
\(324\) | −5.76803 | −0.320446 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −42.9713 | −2.37996 | ||||||||
\(327\) | − 15.2352i | − 0.842507i | ||||||||
\(328\) | 40.5312i | 2.23796i | ||||||||
\(329\) | −37.7515 | −2.08131 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.9172 | −1.86426 | −0.932128 | − | 0.362129i | \(-0.882050\pi\) | ||||
−0.932128 | + | 0.362129i | \(0.882050\pi\) | |||||||
\(332\) | 70.1595i | 3.85050i | ||||||||
\(333\) | 10.1161i | 0.554360i | ||||||||
\(334\) | −48.5085 | −2.65427 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 55.8626 | 3.04755 | ||||||||
\(337\) | − 17.7792i | − 0.968494i | −0.874931 | − | 0.484247i | \(-0.839094\pi\) | ||||
0.874931 | − | 0.484247i | \(-0.160906\pi\) | |||||||
\(338\) | − 36.1339i | − 1.96542i | ||||||||
\(339\) | 2.20391 | 0.119700 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.81416 | 0.423161 | ||||||||
\(342\) | − 5.40980i | − 0.292528i | ||||||||
\(343\) | 12.8441i | 0.693518i | ||||||||
\(344\) | 101.211 | 5.45693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −53.7181 | −2.88790 | ||||||||
\(347\) | 12.2251i | 0.656277i | 0.944630 | + | 0.328138i | \(0.106421\pi\) | ||||
−0.944630 | + | 0.328138i | \(0.893579\pi\) | |||||||
\(348\) | − 7.10602i | − 0.380923i | ||||||||
\(349\) | −12.8425 | −0.687441 | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.188171 | −0.0100438 | ||||||||
\(352\) | − 83.7579i | − 4.46431i | ||||||||
\(353\) | 17.4163i | 0.926976i | 0.886103 | + | 0.463488i | \(0.153402\pi\) | ||||
−0.886103 | + | 0.463488i | \(0.846598\pi\) | |||||||
\(354\) | −19.2552 | −1.02340 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −87.5749 | −4.64146 | ||||||||
\(357\) | − 8.27641i | − 0.438034i | ||||||||
\(358\) | 66.3167i | 3.50494i | ||||||||
\(359\) | 3.82947 | 0.202111 | 0.101056 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101056 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2325 | −0.801712 | ||||||||
\(362\) | 29.7918i | 1.56582i | ||||||||
\(363\) | 2.31633i | 0.121576i | ||||||||
\(364\) | 3.41893 | 0.179201 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.8488 | −0.828428 | ||||||||
\(367\) | 29.6282i | 1.54658i | 0.634054 | + | 0.773289i | \(0.281390\pi\) | ||||
−0.634054 | + | 0.773289i | \(0.718610\pi\) | |||||||
\(368\) | − 23.1336i | − 1.20592i | ||||||||
\(369\) | −3.85940 | −0.200912 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.16399 | −0.0604314 | ||||||||
\(372\) | 15.2953i | 0.793025i | ||||||||
\(373\) | 11.4595i | 0.593350i | 0.954978 | + | 0.296675i | \(0.0958779\pi\) | ||||
−0.954978 | + | 0.296675i | \(0.904122\pi\) | |||||||
\(374\) | −21.5794 | −1.11584 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −125.862 | −6.49083 | ||||||||
\(377\) | − 0.231820i | − 0.0119393i | ||||||||
\(378\) | 8.77943i | 0.451565i | ||||||||
\(379\) | 2.19307 | 0.112650 | 0.0563251 | − | 0.998412i | \(-0.482062\pi\) | ||||
0.0563251 | + | 0.998412i | \(0.482062\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.9689 | 0.766879 | ||||||||
\(382\) | 40.0177i | 2.04749i | ||||||||
\(383\) | − 10.1997i | − 0.521181i | −0.965449 | − | 0.260591i | \(-0.916083\pi\) | ||||
0.965449 | − | 0.260591i | \(-0.0839173\pi\) | |||||||
\(384\) | 65.0920 | 3.32171 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.44904 | 0.277349 | ||||||||
\(387\) | 9.63734i | 0.489894i | ||||||||
\(388\) | 80.1960i | 4.07134i | ||||||||
\(389\) | −28.5482 | −1.44745 | −0.723726 | − | 0.690088i | \(-0.757572\pi\) | ||||
−0.723726 | + | 0.690088i | \(0.757572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.42740 | −0.173331 | ||||||||
\(392\) | − 30.6920i | − 1.55018i | ||||||||
\(393\) | − 11.2957i | − 0.569794i | ||||||||
\(394\) | 3.28764 | 0.165629 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.9973 | 0.854146 | ||||||||
\(397\) | − 37.1827i | − 1.86614i | −0.359688 | − | 0.933072i | \(-0.617117\pi\) | ||||
0.359688 | − | 0.933072i | \(-0.382883\pi\) | |||||||
\(398\) | − 18.2785i | − 0.916218i | ||||||||
\(399\) | −6.11415 | −0.306090 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.38648 | 0.368863 | 0.184432 | − | 0.982845i | \(-0.440956\pi\) | ||||
0.184432 | + | 0.982845i | \(0.440956\pi\) | |||||||
\(402\) | 9.03550i | 0.450650i | ||||||||
\(403\) | 0.498979i | 0.0248559i | ||||||||
\(404\) | 55.7877 | 2.77554 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8160 | −0.536787 | ||||||||
\(407\) | − 29.8102i | − 1.47764i | ||||||||
\(408\) | − 27.5932i | − 1.36607i | ||||||||
\(409\) | 5.19942 | 0.257095 | 0.128547 | − | 0.991703i | \(-0.458969\pi\) | ||||
0.128547 | + | 0.991703i | \(0.458969\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.17877 | −0.206124 | ||||||||
\(412\) | − 50.1492i | − 2.47068i | ||||||||
\(413\) | 21.7622i | 1.07085i | ||||||||
\(414\) | 3.63570 | 0.178685 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.34842 | 0.262228 | ||||||||
\(417\) | − 15.3552i | − 0.751949i | ||||||||
\(418\) | 15.9416i | 0.779730i | ||||||||
\(419\) | 14.9205 | 0.728914 | 0.364457 | − | 0.931220i | \(-0.381255\pi\) | ||||
0.364457 | + | 0.931220i | \(0.381255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0666925 | −0.00325039 | −0.00162520 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162520 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(422\) | − 34.4414i | − 1.67658i | ||||||||
\(423\) | − 11.9846i | − 0.582712i | ||||||||
\(424\) | −3.88069 | −0.188463 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.6732 | −0.904719 | ||||||||
\(427\) | 17.9123i | 0.866835i | ||||||||
\(428\) | − 14.7999i | − 0.715382i | ||||||||
\(429\) | 0.554502 | 0.0267716 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.6996 | 1.33424 | 0.667121 | − | 0.744950i | \(-0.267527\pi\) | ||||
0.667121 | + | 0.744950i | \(0.267527\pi\) | |||||||
\(432\) | 17.7341i | 0.853235i | ||||||||
\(433\) | − 30.5626i | − 1.46874i | −0.678748 | − | 0.734372i | \(-0.737477\pi\) | ||||
0.678748 | − | 0.734372i | \(-0.262523\pi\) | |||||||
\(434\) | 23.2807 | 1.11751 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −87.8770 | −4.20854 | ||||||||
\(437\) | 2.53197i | 0.121120i | ||||||||
\(438\) | 26.3923i | 1.26107i | ||||||||
\(439\) | −11.0968 | −0.529623 | −0.264812 | − | 0.964300i | \(-0.585310\pi\) | ||||
−0.264812 | + | 0.964300i | \(0.585310\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.92250 | 0.139167 | ||||||||
\(442\) | − 1.37797i | − 0.0655432i | ||||||||
\(443\) | − 9.82831i | − 0.466957i | −0.972362 | − | 0.233479i | \(-0.924989\pi\) | ||||
0.972362 | − | 0.233479i | \(-0.0750109\pi\) | |||||||
\(444\) | 58.3501 | 2.76917 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.3653 | −0.964324 | ||||||||
\(447\) | 3.43364i | 0.162405i | ||||||||
\(448\) | − 137.815i | − 6.51114i | ||||||||
\(449\) | 19.1301 | 0.902805 | 0.451402 | − | 0.892320i | \(-0.350924\pi\) | ||||
0.451402 | + | 0.892320i | \(0.350924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3729 | 0.535529 | ||||||||
\(452\) | − 12.7122i | − 0.597933i | ||||||||
\(453\) | − 10.7716i | − 0.506094i | ||||||||
\(454\) | 58.5858 | 2.74957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.3843 | −0.954582 | ||||||||
\(457\) | − 18.7578i | − 0.877452i | −0.898621 | − | 0.438726i | \(-0.855430\pi\) | ||||
0.898621 | − | 0.438726i | \(-0.144570\pi\) | |||||||
\(458\) | 54.5003i | 2.54663i | ||||||||
\(459\) | 2.62743 | 0.122638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.6208 | −1.75217 | −0.876087 | − | 0.482153i | \(-0.839855\pi\) | ||||
−0.876087 | + | 0.482153i | \(0.839855\pi\) | |||||||
\(462\) | − 25.8713i | − 1.20364i | ||||||||
\(463\) | − 19.9275i | − 0.926111i | −0.886329 | − | 0.463056i | \(-0.846753\pi\) | ||||
0.886329 | − | 0.463056i | \(-0.153247\pi\) | |||||||
\(464\) | −21.8479 | −1.01426 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.8558 | 1.56834 | ||||||||
\(467\) | − 27.3667i | − 1.26638i | −0.773997 | − | 0.633190i | \(-0.781745\pi\) | ||||
0.773997 | − | 0.633190i | \(-0.218255\pi\) | |||||||
\(468\) | 1.08537i | 0.0501714i | ||||||||
\(469\) | 10.2119 | 0.471542 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4045 | 0.617649 | ||||||||
\(472\) | 72.5542i | 3.33958i | ||||||||
\(473\) | − 28.3994i | − 1.30581i | ||||||||
\(474\) | 1.17097 | 0.0537845 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −47.7386 | −2.18810 | ||||||||
\(477\) | − 0.369521i | − 0.0169192i | ||||||||
\(478\) | 37.4915i | 1.71482i | ||||||||
\(479\) | 38.5742 | 1.76250 | 0.881250 | − | 0.472650i | \(-0.156703\pi\) | ||||
0.881250 | + | 0.472650i | \(0.156703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.90356 | 0.0867946 | ||||||||
\(482\) | − 55.5669i | − 2.53100i | ||||||||
\(483\) | − 4.10907i | − 0.186969i | ||||||||
\(484\) | 13.3607 | 0.607303 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.78712 | −0.126426 | ||||||||
\(487\) | 18.4995i | 0.838294i | 0.907918 | + | 0.419147i | \(0.137671\pi\) | ||||
−0.907918 | + | 0.419147i | \(0.862329\pi\) | |||||||
\(488\) | 59.7187i | 2.70334i | ||||||||
\(489\) | −15.4178 | −0.697218 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7211 | 0.890000 | 0.445000 | − | 0.895531i | \(-0.353204\pi\) | ||||
0.445000 | + | 0.895531i | \(0.353204\pi\) | |||||||
\(492\) | 22.2611i | 1.00361i | ||||||||
\(493\) | 3.23691i | 0.145783i | ||||||||
\(494\) | −1.01796 | −0.0458004 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.0263 | 2.11154 | ||||||||
\(497\) | 21.1044i | 0.946663i | ||||||||
\(498\) | 33.9011i | 1.51915i | ||||||||
\(499\) | 36.2906 | 1.62459 | 0.812296 | − | 0.583245i | \(-0.198217\pi\) | ||||
0.812296 | + | 0.583245i | \(0.198217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.4045 | −0.777578 | ||||||||
\(502\) | 7.69280i | 0.343347i | ||||||||
\(503\) | 2.66163i | 0.118676i | 0.998238 | + | 0.0593382i | \(0.0188990\pi\) | ||||
−0.998238 | + | 0.0593382i | \(0.981101\pi\) | |||||||
\(504\) | 33.0812 | 1.47355 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.7137 | −0.476283 | ||||||||
\(507\) | − 12.9646i | − 0.575778i | ||||||||
\(508\) | − 86.3410i | − 3.83076i | ||||||||
\(509\) | −22.8322 | −1.01202 | −0.506010 | − | 0.862528i | \(-0.668880\pi\) | ||||
−0.506010 | + | 0.862528i | \(0.668880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.8285 | 1.31954 | ||||||||
\(512\) | − 131.576i | − 5.81488i | ||||||||
\(513\) | − 1.94100i | − 0.0856972i | ||||||||
\(514\) | 48.1748 | 2.12490 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 55.5885 | 2.44715 | ||||||||
\(517\) | 35.3163i | 1.55321i | ||||||||
\(518\) | − 88.8137i | − 3.90225i | ||||||||
\(519\) | −19.2737 | −0.846021 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.3029 | −0.539001 | −0.269501 | − | 0.963000i | \(-0.586859\pi\) | ||||
−0.269501 | + | 0.963000i | \(0.586859\pi\) | |||||||
\(522\) | − 3.43364i | − 0.150286i | ||||||||
\(523\) | − 33.3902i | − 1.46005i | −0.683420 | − | 0.730025i | \(-0.739508\pi\) | ||||
0.683420 | − | 0.730025i | \(-0.260492\pi\) | |||||||
\(524\) | −65.1541 | −2.84627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0531 | −0.481939 | ||||||||
\(527\) | − 6.96726i | − 0.303499i | ||||||||
\(528\) | − 52.2591i | − 2.27429i | ||||||||
\(529\) | 21.2984 | 0.926016 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.90864 | −0.299809 | ||||||||
\(532\) | 35.2666i | 1.52900i | ||||||||
\(533\) | 0.726225i | 0.0314563i | ||||||||
\(534\) | −42.3163 | −1.83121 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.0461 | 1.47057 | ||||||||
\(537\) | 23.7940i | 1.02679i | ||||||||
\(538\) | 3.33238i | 0.143669i | ||||||||
\(539\) | −8.61204 | −0.370947 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.98673 | 0.257389 | 0.128695 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128695 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(542\) | 6.08413i | 0.261336i | ||||||||
\(543\) | 10.6891i | 0.458714i | ||||||||
\(544\) | −74.6802 | −3.20189 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.65203 | 0.0707003 | ||||||||
\(547\) | − 4.47889i | − 0.191503i | −0.995405 | − | 0.0957516i | \(-0.969475\pi\) | ||||
0.995405 | − | 0.0957516i | \(-0.0305255\pi\) | |||||||
\(548\) | 24.1033i | 1.02964i | ||||||||
\(549\) | −5.68643 | −0.242691 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.39124 | 0.101870 | ||||||||
\(552\) | − 13.6995i | − 0.583088i | ||||||||
\(553\) | − 1.32343i | − 0.0562780i | ||||||||
\(554\) | −5.43972 | −0.231112 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −88.5695 | −3.75618 | ||||||||
\(557\) | 14.4278i | 0.611326i | 0.952140 | + | 0.305663i | \(0.0988781\pi\) | ||||
−0.952140 | + | 0.305663i | \(0.901122\pi\) | |||||||
\(558\) | 7.39071i | 0.312874i | ||||||||
\(559\) | 1.81346 | 0.0767014 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.74253 | −0.326890 | ||||||||
\(562\) | − 6.41401i | − 0.270559i | ||||||||
\(563\) | 27.6973i | 1.16730i | 0.812004 | + | 0.583652i | \(0.198377\pi\) | ||||
−0.812004 | + | 0.583652i | \(0.801623\pi\) | |||||||
\(564\) | −69.1277 | −2.91080 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.6715 | −1.24719 | ||||||||
\(567\) | 3.15000i | 0.132288i | ||||||||
\(568\) | 70.3612i | 2.95229i | ||||||||
\(569\) | −35.6179 | −1.49318 | −0.746590 | − | 0.665285i | \(-0.768310\pi\) | ||||
−0.746590 | + | 0.665285i | \(0.768310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.85044 | 0.244833 | 0.122417 | − | 0.992479i | \(-0.460936\pi\) | ||||
0.122417 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(572\) | − 3.19839i | − 0.133731i | ||||||||
\(573\) | 14.3581i | 0.599818i | ||||||||
\(574\) | 33.8833 | 1.41426 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 43.7507 | 1.82295 | ||||||||
\(577\) | − 12.0524i | − 0.501746i | −0.968020 | − | 0.250873i | \(-0.919282\pi\) | ||||
0.968020 | − | 0.250873i | \(-0.0807177\pi\) | |||||||
\(578\) | − 28.1404i | − 1.17049i | ||||||||
\(579\) | 1.95508 | 0.0812503 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.3150 | 1.58958 | ||||||||
\(582\) | 38.7508i | 1.60627i | ||||||||
\(583\) | 1.08891i | 0.0450979i | ||||||||
\(584\) | 99.4470 | 4.11515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.6928 | 1.72232 | ||||||||
\(587\) | − 40.2350i | − 1.66068i | −0.557259 | − | 0.830339i | \(-0.688147\pi\) | ||||
0.557259 | − | 0.830339i | \(-0.311853\pi\) | |||||||
\(588\) | − 16.8571i | − 0.695174i | ||||||||
\(589\) | −5.14702 | −0.212079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17958 | 0.0485215 | ||||||||
\(592\) | − 179.401i | − 7.37332i | ||||||||
\(593\) | 33.4086i | 1.37193i | 0.727636 | + | 0.685964i | \(0.240619\pi\) | ||||
−0.727636 | + | 0.685964i | \(0.759381\pi\) | |||||||
\(594\) | 8.21310 | 0.336988 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8053 | 0.811258 | ||||||||
\(597\) | − 6.55820i | − 0.268409i | ||||||||
\(598\) | − 0.684132i | − 0.0279763i | ||||||||
\(599\) | 24.6421 | 1.00685 | 0.503424 | − | 0.864040i | \(-0.332073\pi\) | ||||
0.503424 | + | 0.864040i | \(0.332073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6327 | 0.678461 | 0.339230 | − | 0.940703i | \(-0.389833\pi\) | ||||
0.339230 | + | 0.940703i | \(0.389833\pi\) | |||||||
\(602\) | − 84.6103i | − 3.44846i | ||||||||
\(603\) | 3.24188i | 0.132019i | ||||||||
\(604\) | −62.1310 | −2.52807 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 26.9567 | 1.09504 | ||||||||
\(607\) | − 29.4057i | − 1.19354i | −0.802412 | − | 0.596770i | \(-0.796450\pi\) | ||||
0.802412 | − | 0.596770i | \(-0.203550\pi\) | |||||||
\(608\) | 55.1695i | 2.23742i | ||||||||
\(609\) | −3.88069 | −0.157254 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.25515 | −0.0912337 | ||||||||
\(612\) | − 15.1551i | − 0.612609i | ||||||||
\(613\) | 12.1702i | 0.491549i | 0.969327 | + | 0.245775i | \(0.0790423\pi\) | ||||
−0.969327 | + | 0.245775i | \(0.920958\pi\) | |||||||
\(614\) | 8.56574 | 0.345685 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −97.4838 | −3.92774 | ||||||||
\(617\) | 39.1024i | 1.57420i | 0.616823 | + | 0.787102i | \(0.288419\pi\) | ||||
−0.616823 | + | 0.787102i | \(0.711581\pi\) | |||||||
\(618\) | − 24.2322i | − 0.974761i | ||||||||
\(619\) | 4.72717 | 0.190001 | 0.0950006 | − | 0.995477i | \(-0.469715\pi\) | ||||
0.0950006 | + | 0.995477i | \(0.469715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.30447 | 0.0523464 | ||||||||
\(622\) | − 69.4258i | − 2.78372i | ||||||||
\(623\) | 47.8258i | 1.91610i | ||||||||
\(624\) | 3.33705 | 0.133589 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.8801 | 1.03438 | ||||||||
\(627\) | 5.71975i | 0.228425i | ||||||||
\(628\) | − 77.3179i | − 3.08532i | ||||||||
\(629\) | −26.5794 | −1.05979 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.8710 | −1.34838 | −0.674191 | − | 0.738557i | \(-0.735508\pi\) | ||||
−0.674191 | + | 0.738557i | \(0.735508\pi\) | |||||||
\(632\) | − 4.41226i | − 0.175510i | ||||||||
\(633\) | − 12.3573i | − 0.491160i | ||||||||
\(634\) | −57.8842 | −2.29888 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.13141 | −0.0845158 | ||||||||
\(637\) | − 0.549929i | − 0.0217890i | ||||||||
\(638\) | 10.1183i | 0.400586i | ||||||||
\(639\) | −6.69982 | −0.265041 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9571 | 0.630269 | 0.315135 | − | 0.949047i | \(-0.397950\pi\) | ||||
0.315135 | + | 0.949047i | \(0.397950\pi\) | |||||||
\(642\) | − 7.15134i | − 0.282241i | ||||||||
\(643\) | − 10.2436i | − 0.403968i | −0.979389 | − | 0.201984i | \(-0.935261\pi\) | ||||
0.979389 | − | 0.201984i | \(-0.0647389\pi\) | |||||||
\(644\) | −23.7013 | −0.933960 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.2139 | 0.559237 | ||||||||
\(647\) | 6.00244i | 0.235980i | 0.993015 | + | 0.117990i | \(0.0376451\pi\) | ||||
−0.993015 | + | 0.117990i | \(0.962355\pi\) | |||||||
\(648\) | 10.5020i | 0.412556i | ||||||||
\(649\) | 20.3584 | 0.799138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.35298 | 0.327379 | ||||||||
\(652\) | 88.9305i | 3.48279i | ||||||||
\(653\) | 33.1069i | 1.29557i | 0.761822 | + | 0.647787i | \(0.224305\pi\) | ||||
−0.761822 | + | 0.647787i | \(0.775695\pi\) | |||||||
\(654\) | −42.4622 | −1.66040 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 68.4431 | 2.67226 | ||||||||
\(657\) | 9.46938i | 0.369436i | ||||||||
\(658\) | 105.218i | 4.10183i | ||||||||
\(659\) | −19.5593 | −0.761922 | −0.380961 | − | 0.924591i | \(-0.624407\pi\) | ||||
−0.380961 | + | 0.924591i | \(0.624407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5290 | 1.18744 | 0.593721 | − | 0.804671i | \(-0.297658\pi\) | ||||
0.593721 | + | 0.804671i | \(0.297658\pi\) | |||||||
\(662\) | 94.5312i | 3.67406i | ||||||||
\(663\) | − 0.494405i | − 0.0192011i | ||||||||
\(664\) | 127.741 | 4.95730 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.1948 | 1.09253 | ||||||||
\(667\) | 1.60706i | 0.0622255i | ||||||||
\(668\) | 100.390i | 3.88421i | ||||||||
\(669\) | −7.30693 | −0.282502 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7568 | 0.646890 | ||||||||
\(672\) | − 89.5333i | − 3.45382i | ||||||||
\(673\) | 4.19687i | 0.161778i | 0.996723 | + | 0.0808888i | \(0.0257759\pi\) | ||||
−0.996723 | + | 0.0808888i | \(0.974224\pi\) | |||||||
\(674\) | −49.5527 | −1.90870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −74.7802 | −2.87616 | ||||||||
\(677\) | − 9.66481i | − 0.371449i | −0.982602 | − | 0.185724i | \(-0.940537\pi\) | ||||
0.982602 | − | 0.185724i | \(-0.0594632\pi\) | |||||||
\(678\) | − 6.14256i | − 0.235903i | ||||||||
\(679\) | 43.7961 | 1.68074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.0202 | 0.805495 | ||||||||
\(682\) | − 21.7790i | − 0.833961i | ||||||||
\(683\) | 9.03781i | 0.345822i | 0.984937 | + | 0.172911i | \(0.0553173\pi\) | ||||
−0.984937 | + | 0.172911i | \(0.944683\pi\) | |||||||
\(684\) | −11.1957 | −0.428080 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.7981 | 1.36678 | ||||||||
\(687\) | 19.5544i | 0.746045i | ||||||||
\(688\) | − 170.910i | − 6.51588i | ||||||||
\(689\) | −0.0695329 | −0.00264899 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1359 | −1.22251 | −0.611254 | − | 0.791435i | \(-0.709334\pi\) | ||||
−0.611254 | + | 0.791435i | \(0.709334\pi\) | |||||||
\(692\) | 111.171i | 4.22610i | ||||||||
\(693\) | − 9.28244i | − 0.352611i | ||||||||
\(694\) | 34.0728 | 1.29338 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.9381 | −0.490416 | ||||||||
\(697\) | − 10.1403i | − 0.384091i | ||||||||
\(698\) | 35.7935i | 1.35480i | ||||||||
\(699\) | 12.1472 | 0.459451 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.54116 | −0.322595 | −0.161298 | − | 0.986906i | \(-0.551568\pi\) | ||||
−0.161298 | + | 0.986906i | \(0.551568\pi\) | |||||||
\(702\) | 0.524454i | 0.0197942i | ||||||||
\(703\) | 19.6354i | 0.740562i | ||||||||
\(704\) | −128.925 | −4.85904 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.5413 | 1.82688 | ||||||||
\(707\) | − 30.4664i | − 1.14581i | ||||||||
\(708\) | 39.8493i | 1.49763i | ||||||||
\(709\) | −5.04613 | −0.189511 | −0.0947556 | − | 0.995501i | \(-0.530207\pi\) | ||||
−0.0947556 | + | 0.995501i | \(0.530207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.420137 | 0.0157564 | ||||||||
\(712\) | 159.449i | 5.97561i | ||||||||
\(713\) | − 3.45910i | − 0.129544i | ||||||||
\(714\) | −23.0673 | −0.863274 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 137.244 | 5.12907 | ||||||||
\(717\) | 13.4517i | 0.502363i | ||||||||
\(718\) | − 10.6732i | − 0.398319i | ||||||||
\(719\) | 19.5253 | 0.728170 | 0.364085 | − | 0.931366i | \(-0.381382\pi\) | ||||
0.364085 | + | 0.931366i | \(0.381382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.3872 | −1.01995 | ||||||||
\(722\) | 42.4549i | 1.58001i | ||||||||
\(723\) | − 19.9370i | − 0.741467i | ||||||||
\(724\) | 61.6552 | 2.29140 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.45588 | 0.239600 | ||||||||
\(727\) | − 40.4464i | − 1.50007i | −0.661395 | − | 0.750037i | \(-0.730035\pi\) | ||||
0.661395 | − | 0.750037i | \(-0.269965\pi\) | |||||||
\(728\) | − 6.22490i | − 0.230710i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3215 | −0.936548 | ||||||||
\(732\) | 32.7995i | 1.21231i | ||||||||
\(733\) | 29.3862i | 1.08540i | 0.839926 | + | 0.542702i | \(0.182599\pi\) | ||||
−0.839926 | + | 0.542702i | \(0.817401\pi\) | |||||||
\(734\) | 82.5772 | 3.04798 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.0772 | −1.36668 | ||||||||
\(737\) | − 9.55318i | − 0.351896i | ||||||||
\(738\) | 10.7566i | 0.395956i | ||||||||
\(739\) | 30.7254 | 1.13025 | 0.565126 | − | 0.825005i | \(-0.308828\pi\) | ||||
0.565126 | + | 0.825005i | \(0.308828\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.365239 | −0.0134174 | ||||||||
\(742\) | 3.24418i | 0.119098i | ||||||||
\(743\) | 41.4841i | 1.52190i | 0.648808 | + | 0.760952i | \(0.275268\pi\) | ||||
−0.648808 | + | 0.760952i | \(0.724732\pi\) | |||||||
\(744\) | 27.8485 | 1.02097 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.9390 | 1.16937 | ||||||||
\(747\) | 12.1635i | 0.445039i | ||||||||
\(748\) | 44.6592i | 1.63290i | ||||||||
\(749\) | −8.08244 | −0.295326 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6123 | 1.40898 | 0.704491 | − | 0.709713i | \(-0.251175\pi\) | ||||
0.704491 | + | 0.709713i | \(0.251175\pi\) | |||||||
\(752\) | 212.537i | 7.75042i | ||||||||
\(753\) | 2.76013i | 0.100585i | ||||||||
\(754\) | −0.646109 | −0.0235299 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.1693 | 0.660811 | ||||||||
\(757\) | 23.0860i | 0.839074i | 0.907738 | + | 0.419537i | \(0.137807\pi\) | ||||
−0.907738 | + | 0.419537i | \(0.862193\pi\) | |||||||
\(758\) | − 6.11234i | − 0.222010i | ||||||||
\(759\) | −3.84401 | −0.139529 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7092 | −1.14946 | −0.574728 | − | 0.818344i | \(-0.694892\pi\) | ||||
−0.574728 | + | 0.818344i | \(0.694892\pi\) | |||||||
\(762\) | − 41.7200i | − 1.51136i | ||||||||
\(763\) | 47.9908i | 1.73738i | ||||||||
\(764\) | 82.8180 | 2.99625 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.4278 | −1.02714 | ||||||||
\(767\) | 1.30000i | 0.0469404i | ||||||||
\(768\) | − 93.9177i | − 3.38896i | ||||||||
\(769\) | −38.6475 | −1.39366 | −0.696832 | − | 0.717235i | \(-0.745408\pi\) | ||||
−0.696832 | + | 0.717235i | \(0.745408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.2848 | 0.622497 | ||||||||
\(772\) | − 11.2770i | − 0.405867i | ||||||||
\(773\) | 38.9958i | 1.40258i | 0.712875 | + | 0.701291i | \(0.247393\pi\) | ||||
−0.712875 | + | 0.701291i | \(0.752607\pi\) | |||||||
\(774\) | 26.8604 | 0.965478 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 146.014 | 5.24161 | ||||||||
\(777\) | − 31.8658i | − 1.14318i | ||||||||
\(778\) | 79.5672i | 2.85262i | ||||||||
\(779\) | −7.49109 | −0.268396 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7431 | 0.706463 | ||||||||
\(782\) | 9.55256i | 0.341599i | ||||||||
\(783\) | − 1.23197i | − 0.0440269i | ||||||||
\(784\) | −51.8281 | −1.85100 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.4825 | −1.12294 | ||||||||
\(787\) | 8.11107i | 0.289128i | 0.989495 | + | 0.144564i | \(0.0461780\pi\) | ||||
−0.989495 | + | 0.144564i | \(0.953822\pi\) | |||||||
\(788\) | − 6.80387i | − 0.242378i | ||||||||
\(789\) | −3.96578 | −0.141186 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.94231 | −0.246840 | ||||||||
\(792\) | − 30.9473i | − 1.09966i | ||||||||
\(793\) | 1.07002i | 0.0379975i | ||||||||
\(794\) | −103.633 | −3.67778 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37.8279 | −1.34078 | ||||||||
\(797\) | 19.0152i | 0.673554i | 0.941584 | + | 0.336777i | \(0.109337\pi\) | ||||
−0.941584 | + | 0.336777i | \(0.890663\pi\) | |||||||
\(798\) | 17.0409i | 0.603240i | ||||||||
\(799\) | 31.4888 | 1.11399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1828 | −0.536458 | ||||||||
\(802\) | − 20.5870i | − 0.726952i | ||||||||
\(803\) | − 27.9044i | − 0.984726i | ||||||||
\(804\) | 18.6993 | 0.659472 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.39071 | 0.0489858 | ||||||||
\(807\) | 1.19564i | 0.0420884i | ||||||||
\(808\) | − 101.574i | − 3.57335i | ||||||||
\(809\) | −49.9078 | −1.75467 | −0.877333 | − | 0.479882i | \(-0.840679\pi\) | ||||
−0.877333 | + | 0.479882i | \(0.840679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.9727 | 1.08760 | 0.543799 | − | 0.839215i | \(-0.316985\pi\) | ||||
0.543799 | + | 0.839215i | \(0.316985\pi\) | |||||||
\(812\) | 22.3840i | 0.785523i | ||||||||
\(813\) | 2.18295i | 0.0765593i | ||||||||
\(814\) | −83.0847 | −2.91212 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −46.5953 | −1.63116 | ||||||||
\(817\) | 18.7061i | 0.654443i | ||||||||
\(818\) | − 14.4914i | − 0.506680i | ||||||||
\(819\) | 0.592737 | 0.0207119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9246 | 0.660473 | 0.330236 | − | 0.943898i | \(-0.392872\pi\) | ||||
0.330236 | + | 0.943898i | \(0.392872\pi\) | |||||||
\(822\) | 11.6467i | 0.406227i | ||||||||
\(823\) | − 9.31122i | − 0.324569i | −0.986744 | − | 0.162284i | \(-0.948114\pi\) | ||||
0.986744 | − | 0.162284i | \(-0.0518862\pi\) | |||||||
\(824\) | −91.3076 | −3.18085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 60.6539 | 2.11042 | ||||||||
\(827\) | − 23.7383i | − 0.825461i | −0.910853 | − | 0.412731i | \(-0.864575\pi\) | ||||
0.910853 | − | 0.412731i | \(-0.135425\pi\) | |||||||
\(828\) | − 7.52421i | − 0.261484i | ||||||||
\(829\) | −1.91351 | −0.0664590 | −0.0332295 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332295 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.95174 | −0.0677050 | ||||||||
\(832\) | − 8.23260i | − 0.285414i | ||||||||
\(833\) | 7.67867i | 0.266050i | ||||||||
\(834\) | −42.7969 | −1.48193 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.9917 | 1.14104 | ||||||||
\(837\) | 2.65174i | 0.0916575i | ||||||||
\(838\) | − 41.5852i | − 1.43654i | ||||||||
\(839\) | −40.5105 | −1.39858 | −0.699289 | − | 0.714839i | \(-0.746500\pi\) | ||||
−0.699289 | + | 0.714839i | \(0.746500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4823 | −0.947664 | ||||||||
\(842\) | 0.185880i | 0.00640584i | ||||||||
\(843\) | − 2.30131i | − 0.0792612i | ||||||||
\(844\) | −71.2776 | −2.45348 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −33.4025 | −1.14840 | ||||||||
\(847\) | − 7.29643i | − 0.250708i | ||||||||
\(848\) | 6.55314i | 0.225036i | ||||||||
\(849\) | −10.6459 | −0.365367 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1961 | −0.452358 | ||||||||
\(852\) | 38.6448i | 1.32395i | ||||||||
\(853\) | 18.7735i | 0.642792i | 0.946945 | + | 0.321396i | \(0.104152\pi\) | ||||
−0.946945 | + | 0.321396i | \(0.895848\pi\) | |||||||
\(854\) | 49.9236 | 1.70835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.9465 | −0.921012 | ||||||||
\(857\) | 10.0276i | 0.342536i | 0.985225 | + | 0.171268i | \(0.0547863\pi\) | ||||
−0.985225 | + | 0.171268i | \(0.945214\pi\) | |||||||
\(858\) | − 1.54546i | − 0.0527613i | ||||||||
\(859\) | 28.0443 | 0.956858 | 0.478429 | − | 0.878126i | \(-0.341206\pi\) | ||||
0.478429 | + | 0.878126i | \(0.341206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.1571 | 0.414313 | ||||||||
\(862\) | − 77.2020i | − 2.62951i | ||||||||
\(863\) | 9.84666i | 0.335184i | 0.985856 | + | 0.167592i | \(0.0535992\pi\) | ||||
−0.985856 | + | 0.167592i | \(0.946401\pi\) | |||||||
\(864\) | 28.4233 | 0.966979 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −85.1815 | −2.89459 | ||||||||
\(867\) | − 10.0966i | − 0.342899i | ||||||||
\(868\) | − 48.1802i | − 1.63534i | ||||||||
\(869\) | −1.23806 | −0.0419984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.610026 | 0.0206699 | ||||||||
\(872\) | 159.999i | 5.41826i | ||||||||
\(873\) | 13.9035i | 0.470563i | ||||||||
\(874\) | 7.05690 | 0.238703 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 54.6197 | 1.84543 | ||||||||
\(877\) | − 36.9671i | − 1.24829i | −0.781308 | − | 0.624146i | \(-0.785447\pi\) | ||||
0.781308 | − | 0.624146i | \(-0.214553\pi\) | |||||||
\(878\) | 30.9282i | 1.04378i | ||||||||
\(879\) | 14.9591 | 0.504558 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7137 | −0.697863 | −0.348932 | − | 0.937148i | \(-0.613455\pi\) | ||||
−0.348932 | + | 0.937148i | \(0.613455\pi\) | |||||||
\(882\) | − 8.14536i | − 0.274268i | ||||||||
\(883\) | 12.7254i | 0.428243i | 0.976807 | + | 0.214121i | \(0.0686888\pi\) | ||||
−0.976807 | + | 0.214121i | \(0.931311\pi\) | |||||||
\(884\) | −2.85175 | −0.0959146 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.3927 | −0.920275 | ||||||||
\(887\) | 21.6903i | 0.728287i | 0.931343 | + | 0.364144i | \(0.118638\pi\) | ||||
−0.931343 | + | 0.364144i | \(0.881362\pi\) | |||||||
\(888\) | − 106.239i | − 3.56515i | ||||||||
\(889\) | −47.1520 | −1.58143 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.94681 | 0.0987218 | ||||||||
\(892\) | 42.1466i | 1.41117i | ||||||||
\(893\) | − 23.2621i | − 0.778437i | ||||||||
\(894\) | 9.56995 | 0.320067 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −205.040 | −6.84990 | ||||||||
\(897\) | − 0.245462i | − 0.00819574i | ||||||||
\(898\) | − 53.3178i | − 1.77924i | ||||||||
\(899\) | −3.26685 | −0.108956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.970891 | 0.0323451 | ||||||||
\(902\) | − 31.6976i | − 1.05542i | ||||||||
\(903\) | − 30.3576i | − 1.01024i | ||||||||
\(904\) | −23.1454 | −0.769803 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −30.0217 | −0.997406 | ||||||||
\(907\) | 3.28462i | 0.109064i | 0.998512 | + | 0.0545320i | \(0.0173667\pi\) | ||||
−0.998512 | + | 0.0545320i | \(0.982633\pi\) | |||||||
\(908\) | − 121.245i | − 4.02366i | ||||||||
\(909\) | 9.67188 | 0.320796 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8264 | 0.955060 | 0.477530 | − | 0.878615i | \(-0.341532\pi\) | ||||
0.477530 | + | 0.878615i | \(0.341532\pi\) | |||||||
\(912\) | 34.4220i | 1.13983i | ||||||||
\(913\) | − 35.8435i | − 1.18625i | ||||||||
\(914\) | −52.2802 | −1.72927 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 112.790 | 3.72669 | ||||||||
\(917\) | 35.5815i | 1.17500i | ||||||||
\(918\) | − 7.32297i | − 0.241694i | ||||||||
\(919\) | 17.3985 | 0.573925 | 0.286962 | − | 0.957942i | \(-0.407355\pi\) | ||||
0.286962 | + | 0.957942i | \(0.407355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.07333 | 0.101270 | ||||||||
\(922\) | 104.854i | 3.45317i | ||||||||
\(923\) | 1.26071i | 0.0414967i | ||||||||
\(924\) | −53.5414 | −1.76138 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −55.5404 | −1.82517 | ||||||||
\(927\) | − 8.69434i | − 0.285560i | ||||||||
\(928\) | 35.0165i | 1.14947i | ||||||||
\(929\) | 24.3715 | 0.799603 | 0.399801 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399801 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.67257 | 0.185911 | ||||||||
\(932\) | − 70.0657i | − 2.29508i | ||||||||
\(933\) | − 24.9095i | − 0.815501i | ||||||||
\(934\) | −76.2742 | −2.49577 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.97616 | 0.0645928 | ||||||||
\(937\) | − 14.5784i | − 0.476257i | −0.971234 | − | 0.238129i | \(-0.923466\pi\) | ||||
0.971234 | − | 0.238129i | \(-0.0765339\pi\) | |||||||
\(938\) | − 28.4618i | − 0.929311i | ||||||||
\(939\) | 9.28562 | 0.303025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.19686 | −0.136814 | −0.0684068 | − | 0.997658i | \(-0.521792\pi\) | ||||
−0.0684068 | + | 0.997658i | \(0.521792\pi\) | |||||||
\(942\) | − 37.3601i | − 1.21726i | ||||||||
\(943\) | − 5.03445i | − 0.163944i | ||||||||
\(944\) | 122.519 | 3.98765 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −79.1525 | −2.57347 | ||||||||
\(947\) | 5.53251i | 0.179782i | 0.995952 | + | 0.0898912i | \(0.0286519\pi\) | ||||
−0.995952 | + | 0.0898912i | \(0.971348\pi\) | |||||||
\(948\) | − 2.42336i | − 0.0787071i | ||||||||
\(949\) | 1.78186 | 0.0578416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.7685 | −0.673464 | ||||||||
\(952\) | 86.9185i | 2.81705i | ||||||||
\(953\) | 50.4779i | 1.63514i | 0.575830 | + | 0.817570i | \(0.304679\pi\) | ||||
−0.575830 | + | 0.817570i | \(0.695321\pi\) | |||||||
\(954\) | −1.02990 | −0.0333442 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 77.5899 | 2.50944 | ||||||||
\(957\) | 3.63037i | 0.117353i | ||||||||
\(958\) | − 107.511i | − 3.47352i | ||||||||
\(959\) | 13.1631 | 0.425060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9683 | −0.773170 | ||||||||
\(962\) | − 5.30544i | − 0.171054i | ||||||||
\(963\) | − 2.56585i | − 0.0826835i | ||||||||
\(964\) | −114.998 | −3.70382 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.4525 | −0.368477 | ||||||||
\(967\) | 17.0340i | 0.547777i | 0.961761 | + | 0.273889i | \(0.0883100\pi\) | ||||
−0.961761 | + | 0.273889i | \(0.911690\pi\) | |||||||
\(968\) | − 24.3260i | − 0.781867i | ||||||||
\(969\) | 5.09984 | 0.163831 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4172 | 0.751494 | 0.375747 | − | 0.926722i | \(-0.377386\pi\) | ||||
0.375747 | + | 0.926722i | \(0.377386\pi\) | |||||||
\(972\) | 5.76803i | 0.185010i | ||||||||
\(973\) | 48.3690i | 1.55064i | ||||||||
\(974\) | 51.5604 | 1.65210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 100.844 | 3.22794 | ||||||||
\(977\) | 20.7626i | 0.664253i | 0.943235 | + | 0.332127i | \(0.107766\pi\) | ||||
−0.943235 | + | 0.332127i | \(0.892234\pi\) | |||||||
\(978\) | 42.9713i | 1.37407i | ||||||||
\(979\) | 44.7408 | 1.42992 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2352 | −0.486422 | ||||||||
\(982\) | − 54.9650i | − 1.75400i | ||||||||
\(983\) | 42.1977i | 1.34590i | 0.739690 | + | 0.672948i | \(0.234972\pi\) | ||||
−0.739690 | + | 0.672948i | \(0.765028\pi\) | |||||||
\(984\) | 40.5312 | 1.29209 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.02164 | 0.287308 | ||||||||
\(987\) | 37.7515i | 1.20164i | ||||||||
\(988\) | 2.10671i | 0.0670234i | ||||||||
\(989\) | −12.5716 | −0.399753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.83926 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(992\) | − 75.3711i | − 2.39303i | ||||||||
\(993\) | 33.9172i | 1.07633i | ||||||||
\(994\) | 58.8206 | 1.86567 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 70.1595 | 2.22309 | ||||||||
\(997\) | − 42.2091i | − 1.33678i | −0.743812 | − | 0.668389i | \(-0.766984\pi\) | ||||
0.743812 | − | 0.668389i | \(-0.233016\pi\) | |||||||
\(998\) | − 101.146i | − 3.20173i | ||||||||
\(999\) | 10.1161 | 0.320060 |
(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 | 1875.2.b.e.1249.1 | 12 | ||
5.2 | odd | 4 | 1875.2.a.l.1.6 | yes | 6 | ||
5.3 | odd | 4 | 1875.2.a.i.1.1 | ✓ | 6 | ||
5.4 | even | 2 | inner | 1875.2.b.e.1249.12 | 12 | ||
15.2 | even | 4 | 5625.2.a.o.1.1 | 6 | |||
15.8 | even | 4 | 5625.2.a.r.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.1 | ✓ | 6 | 5.3 | odd | 4 | ||
1875.2.a.l.1.6 | yes | 6 | 5.2 | odd | 4 | ||
1875.2.b.e.1249.1 | 12 | 1.1 | even | 1 | trivial | ||
1875.2.b.e.1249.12 | 12 | 5.4 | even | 2 | inner | ||
5625.2.a.o.1.1 | 6 | 15.2 | even | 4 | |||
5625.2.a.r.1.6 | 6 | 15.8 | even | 4 |