Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1369,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.5 | ||
Root | \(-1.75233 + 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1369 |
Dual form | 1710.2.d.d.1369.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.38900 | + | 1.75233i | −0.621181 | + | 0.783667i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.636672i | − | 0.240639i | −0.992735 | − | 0.120320i | \(-0.961608\pi\) | ||
0.992735 | − | 0.120320i | \(-0.0383920\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.75233 | − | 1.38900i | −0.554136 | − | 0.439242i | ||||
\(11\) | −3.50466 | −1.05670 | −0.528348 | − | 0.849028i | \(-0.677188\pi\) | ||||
−0.528348 | + | 0.849028i | \(0.677188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.141336i | − | 0.0391996i | −0.999808 | − | 0.0195998i | \(-0.993761\pi\) | ||
0.999808 | − | 0.0195998i | \(-0.00623921\pi\) | |||||||
\(14\) | 0.636672 | 0.170158 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.14134i | 0.519350i | 0.965696 | + | 0.259675i | \(0.0836155\pi\) | ||||
−0.965696 | + | 0.259675i | \(0.916385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.38900 | − | 1.75233i | 0.310591 | − | 0.391833i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.50466i | − | 0.747197i | ||||||
\(23\) | − | 4.91934i | − | 1.02575i | −0.858462 | − | 0.512877i | \(-0.828580\pi\) | ||
0.858462 | − | 0.512877i | \(-0.171420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.14134 | − | 4.86799i | −0.228267 | − | 0.973599i | ||||
\(26\) | 0.141336 | 0.0277183 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.636672i | 0.120320i | ||||||||
\(29\) | 7.15066 | 1.32785 | 0.663923 | − | 0.747801i | \(-0.268890\pi\) | ||||
0.663923 | + | 0.747801i | \(0.268890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.78734 | −1.39865 | −0.699323 | − | 0.714805i | \(-0.746515\pi\) | ||||
−0.699323 | + | 0.714805i | \(0.746515\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.14134 | −0.367236 | ||||||||
\(35\) | 1.11566 | + | 0.884340i | 0.188581 | + | 0.149481i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.27334i | − | 0.538134i | −0.963121 | − | 0.269067i | \(-0.913285\pi\) | ||
0.963121 | − | 0.269067i | \(-0.0867154\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.75233 | + | 1.38900i | 0.277068 | + | 0.219621i | ||||
\(41\) | 4.23132 | 0.660821 | 0.330411 | − | 0.943837i | \(-0.392813\pi\) | ||||
0.330411 | + | 0.943837i | \(0.392813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.49534i | 0.380535i | 0.981732 | + | 0.190268i | \(0.0609356\pi\) | ||||
−0.981732 | + | 0.190268i | \(0.939064\pi\) | |||||||
\(44\) | 3.50466 | 0.528348 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.91934 | 0.725318 | ||||||||
\(47\) | − | 10.2827i | − | 1.49988i | −0.661505 | − | 0.749941i | \(-0.730082\pi\) | ||
0.661505 | − | 0.749941i | \(-0.269918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59465 | 0.942093 | ||||||||
\(50\) | 4.86799 | − | 1.14134i | 0.688438 | − | 0.161409i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.141336i | 0.0195998i | ||||||||
\(53\) | − | 8.14134i | − | 1.11830i | −0.829067 | − | 0.559149i | \(-0.811128\pi\) | ||
0.829067 | − | 0.559149i | \(-0.188872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.86799 | − | 6.14134i | 0.656400 | − | 0.828098i | ||||
\(56\) | −0.636672 | −0.0850788 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.15066i | 0.938928i | ||||||||
\(59\) | −5.64600 | −0.735047 | −0.367523 | − | 0.930014i | \(-0.619794\pi\) | ||||
−0.367523 | + | 0.930014i | \(0.619794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.49534 | −0.831643 | −0.415821 | − | 0.909446i | \(-0.636506\pi\) | ||||
−0.415821 | + | 0.909446i | \(0.636506\pi\) | |||||||
\(62\) | − | 7.78734i | − | 0.988993i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.247668 | + | 0.196316i | 0.0307194 | + | 0.0243501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.37266i | − | 1.02288i | −0.859318 | − | 0.511441i | \(-0.829112\pi\) | ||
0.859318 | − | 0.511441i | \(-0.170888\pi\) | |||||||
\(68\) | − | 2.14134i | − | 0.259675i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.884340 | + | 1.11566i | −0.105699 | + | 0.133347i | ||||
\(71\) | 8.95798 | 1.06312 | 0.531558 | − | 0.847022i | \(-0.321607\pi\) | ||||
0.531558 | + | 0.847022i | \(0.321607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.69735i | − | 0.432742i | −0.976311 | − | 0.216371i | \(-0.930578\pi\) | ||
0.976311 | − | 0.216371i | \(-0.0694221\pi\) | |||||||
\(74\) | 3.27334 | 0.380518 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 2.23132i | 0.254283i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.17997 | 0.470283 | 0.235142 | − | 0.971961i | \(-0.424445\pi\) | ||||
0.235142 | + | 0.971961i | \(0.424445\pi\) | |||||||
\(80\) | −1.38900 | + | 1.75233i | −0.155295 | + | 0.195917i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.23132i | 0.467271i | ||||||||
\(83\) | 9.00933i | 0.988902i | 0.869205 | + | 0.494451i | \(0.164631\pi\) | ||||
−0.869205 | + | 0.494451i | \(0.835369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.75233 | − | 2.97432i | −0.406998 | − | 0.322611i | ||||
\(86\) | −2.49534 | −0.269079 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.50466i | 0.373598i | ||||||||
\(89\) | −6.77801 | −0.718467 | −0.359234 | − | 0.933248i | \(-0.616962\pi\) | ||||
−0.359234 | + | 0.933248i | \(0.616962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0899847 | −0.00943296 | ||||||||
\(92\) | 4.91934i | 0.512877i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2827 | 1.06058 | ||||||||
\(95\) | 1.38900 | − | 1.75233i | 0.142509 | − | 0.179785i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.5653i | − | 1.47889i | −0.673219 | − | 0.739443i | \(-0.735089\pi\) | ||
0.673219 | − | 0.739443i | \(-0.264911\pi\) | |||||||
\(98\) | 6.59465i | 0.666160i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.14134 | + | 4.86799i | 0.114134 | + | 0.486799i | ||||
\(101\) | 16.6167 | 1.65342 | 0.826712 | − | 0.562626i | \(-0.190209\pi\) | ||||
0.826712 | + | 0.562626i | \(0.190209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.06068i | 0.892775i | 0.894840 | + | 0.446388i | \(0.147290\pi\) | ||||
−0.894840 | + | 0.446388i | \(0.852710\pi\) | |||||||
\(104\) | −0.141336 | −0.0138591 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.14134 | 0.790756 | ||||||||
\(107\) | 0.0899847i | 0.00869915i | 0.999991 | + | 0.00434958i | \(0.00138452\pi\) | ||||
−0.999991 | + | 0.00434958i | \(0.998615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5946 | 1.30213 | 0.651066 | − | 0.759021i | \(-0.274322\pi\) | ||||
0.651066 | + | 0.759021i | \(0.274322\pi\) | |||||||
\(110\) | 6.14134 | + | 4.86799i | 0.585553 | + | 0.464145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 0.636672i | − | 0.0601598i | ||||||
\(113\) | − | 11.5233i | − | 1.08402i | −0.840371 | − | 0.542011i | \(-0.817663\pi\) | ||
0.840371 | − | 0.542011i | \(-0.182337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.62032 | + | 6.83299i | 0.803849 | + | 0.637179i | ||||
\(116\) | −7.15066 | −0.663923 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.64600i | − | 0.519756i | ||||||
\(119\) | 1.36333 | 0.124976 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28267 | 0.116607 | ||||||||
\(122\) | − | 6.49534i | − | 0.588060i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.78734 | 0.699323 | ||||||||
\(125\) | 10.1157 | + | 4.76166i | 0.904772 | + | 0.425896i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.29200i | 0.292118i | 0.989276 | + | 0.146059i | \(0.0466589\pi\) | ||||
−0.989276 | + | 0.146059i | \(0.953341\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.196316 | + | 0.247668i | −0.0172181 | + | 0.0217219i | ||||
\(131\) | −18.0187 | −1.57430 | −0.787149 | − | 0.616763i | \(-0.788444\pi\) | ||||
−0.787149 | + | 0.616763i | \(0.788444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.636672i | 0.0552064i | ||||||||
\(134\) | 8.37266 | 0.723287 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.14134 | 0.183618 | ||||||||
\(137\) | − | 14.4240i | − | 1.23233i | −0.787619 | − | 0.616163i | \(-0.788686\pi\) | ||
0.787619 | − | 0.616163i | \(-0.211314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4720 | −1.31232 | −0.656158 | − | 0.754624i | \(-0.727819\pi\) | ||||
−0.656158 | + | 0.754624i | \(0.727819\pi\) | |||||||
\(140\) | −1.11566 | − | 0.884340i | −0.0942905 | − | 0.0747403i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.95798i | 0.751737i | ||||||||
\(143\) | 0.495336i | 0.0414220i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.93230 | + | 12.5303i | −0.824833 | + | 1.04059i | ||||
\(146\) | 3.69735 | 0.305995 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.27334i | 0.269067i | ||||||||
\(149\) | −17.1893 | −1.40820 | −0.704101 | − | 0.710100i | \(-0.748650\pi\) | ||||
−0.704101 | + | 0.710100i | \(0.748650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.29200 | 0.267899 | 0.133950 | − | 0.990988i | \(-0.457234\pi\) | ||||
0.133950 | + | 0.990988i | \(0.457234\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.23132 | −0.179805 | ||||||||
\(155\) | 10.8166 | − | 13.6460i | 0.868814 | − | 1.09607i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.1893i | − | 1.21224i | −0.795374 | − | 0.606119i | \(-0.792726\pi\) | ||
0.795374 | − | 0.606119i | \(-0.207274\pi\) | |||||||
\(158\) | 4.17997i | 0.332541i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.75233 | − | 1.38900i | −0.138534 | − | 0.109810i | ||||
\(161\) | −3.13201 | −0.246837 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.0700i | − | 1.10205i | −0.834489 | − | 0.551024i | \(-0.814237\pi\) | ||
0.834489 | − | 0.551024i | \(-0.185763\pi\) | |||||||
\(164\) | −4.23132 | −0.330411 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00933 | −0.699260 | ||||||||
\(167\) | − | 14.7967i | − | 1.14500i | −0.819905 | − | 0.572500i | \(-0.805974\pi\) | ||
0.819905 | − | 0.572500i | \(-0.194026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9800 | 0.998463 | ||||||||
\(170\) | 2.97432 | − | 3.75233i | 0.228120 | − | 0.287791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.49534i | − | 0.190268i | ||||||
\(173\) | 17.2920i | 1.31469i | 0.753591 | + | 0.657343i | \(0.228320\pi\) | ||||
−0.753591 | + | 0.657343i | \(0.771680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.09931 | + | 0.726656i | −0.234286 | + | 0.0549301i | ||||
\(176\) | −3.50466 | −0.264174 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.77801i | − | 0.508033i | ||||||
\(179\) | 17.7360 | 1.32565 | 0.662825 | − | 0.748774i | \(-0.269357\pi\) | ||||
0.662825 | + | 0.748774i | \(0.269357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.17997 | 0.459354 | 0.229677 | − | 0.973267i | \(-0.426233\pi\) | ||||
0.229677 | + | 0.973267i | \(0.426233\pi\) | |||||||
\(182\) | − | 0.0899847i | − | 0.00667011i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.91934 | −0.362659 | ||||||||
\(185\) | 5.73599 | + | 4.54669i | 0.421718 | + | 0.334279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.50466i | − | 0.548795i | ||||||
\(188\) | 10.2827i | 0.749941i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.75233 | + | 1.38900i | 0.127128 | + | 0.100769i | ||||
\(191\) | −14.6367 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0187i | 1.44097i | 0.693468 | + | 0.720487i | \(0.256082\pi\) | ||||
−0.693468 | + | 0.720487i | \(0.743918\pi\) | |||||||
\(194\) | 14.5653 | 1.04573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.59465 | −0.471046 | ||||||||
\(197\) | − | 9.94865i | − | 0.708812i | −0.935092 | − | 0.354406i | \(-0.884683\pi\) | ||
0.935092 | − | 0.354406i | \(-0.115317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.74870 | −0.691067 | −0.345534 | − | 0.938406i | \(-0.612302\pi\) | ||||
−0.345534 | + | 0.938406i | \(0.612302\pi\) | |||||||
\(200\) | −4.86799 | + | 1.14134i | −0.344219 | + | 0.0807047i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.6167i | 1.16915i | ||||||||
\(203\) | − | 4.55263i | − | 0.319532i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.87732 | + | 7.41468i | −0.410490 | + | 0.517864i | ||||
\(206\) | −9.06068 | −0.631287 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 0.141336i | − | 0.00979990i | ||||||
\(209\) | 3.50466 | 0.242423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.7580 | −1.42904 | −0.714521 | − | 0.699614i | \(-0.753355\pi\) | ||||
−0.714521 | + | 0.699614i | \(0.753355\pi\) | |||||||
\(212\) | 8.14134i | 0.559149i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.0899847 | −0.00615123 | ||||||||
\(215\) | −4.37266 | − | 3.46603i | −0.298213 | − | 0.236381i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.95798i | 0.336569i | ||||||||
\(218\) | 13.5946i | 0.920746i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.86799 | + | 6.14134i | −0.328200 | + | 0.414049i | ||||
\(221\) | 0.302648 | 0.0203583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.7267i | − | 0.718310i | −0.933278 | − | 0.359155i | \(-0.883065\pi\) | ||
0.933278 | − | 0.359155i | \(-0.116935\pi\) | |||||||
\(224\) | 0.636672 | 0.0425394 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5233 | 0.766520 | ||||||||
\(227\) | 12.5526i | 0.833147i | 0.909102 | + | 0.416574i | \(0.136769\pi\) | ||||
−0.909102 | + | 0.416574i | \(0.863231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.4720 | −1.68324 | −0.841618 | − | 0.540074i | \(-0.818396\pi\) | ||||
−0.841618 | + | 0.540074i | \(0.818396\pi\) | |||||||
\(230\) | −6.83299 | + | 8.62032i | −0.450554 | + | 0.568407i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 7.15066i | − | 0.469464i | ||||||
\(233\) | 3.11203i | 0.203876i | 0.994791 | + | 0.101938i | \(0.0325043\pi\) | ||||
−0.994791 | + | 0.101938i | \(0.967496\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0187 | + | 14.2827i | 1.17541 | + | 0.931699i | ||||
\(236\) | 5.64600 | 0.367523 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.36333i | 0.0883714i | ||||||||
\(239\) | −1.54330 | −0.0998276 | −0.0499138 | − | 0.998754i | \(-0.515895\pi\) | ||||
−0.0499138 | + | 0.998754i | \(0.515895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2827 | 0.662365 | 0.331183 | − | 0.943567i | \(-0.392552\pi\) | ||||
0.331183 | + | 0.943567i | \(0.392552\pi\) | |||||||
\(242\) | 1.28267i | 0.0824533i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.49534 | 0.415821 | ||||||||
\(245\) | −9.15999 | + | 11.5560i | −0.585211 | + | 0.738287i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.141336i | 0.00899300i | ||||||||
\(248\) | 7.78734i | 0.494496i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.76166 | + | 10.1157i | −0.301154 | + | 0.639771i | ||||
\(251\) | 2.51399 | 0.158682 | 0.0793409 | − | 0.996848i | \(-0.474718\pi\) | ||||
0.0793409 | + | 0.996848i | \(0.474718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2406i | 1.08391i | ||||||||
\(254\) | −3.29200 | −0.206559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 24.7967i | − | 1.54677i | −0.633934 | − | 0.773387i | \(-0.718561\pi\) | ||
0.633934 | − | 0.773387i | \(-0.281439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.08405 | −0.129496 | ||||||||
\(260\) | −0.247668 | − | 0.196316i | −0.0153597 | − | 0.0121750i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 18.0187i | − | 1.11320i | ||||||
\(263\) | 22.5653i | 1.39144i | 0.718314 | + | 0.695719i | \(0.244914\pi\) | ||||
−0.718314 | + | 0.695719i | \(0.755086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.2663 | + | 11.3083i | 0.876373 | + | 0.694666i | ||||
\(266\) | −0.636672 | −0.0390369 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.37266i | 0.511441i | ||||||||
\(269\) | −26.5653 | −1.61972 | −0.809859 | − | 0.586625i | \(-0.800456\pi\) | ||||
−0.809859 | + | 0.586625i | \(0.800456\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.9380 | −1.51488 | −0.757438 | − | 0.652907i | \(-0.773549\pi\) | ||||
−0.757438 | + | 0.652907i | \(0.773549\pi\) | |||||||
\(272\) | 2.14134i | 0.129838i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.4240 | 0.871386 | ||||||||
\(275\) | 4.00000 | + | 17.0607i | 0.241209 | + | 1.02880i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.5467i | − | 1.11436i | −0.830391 | − | 0.557181i | \(-0.811883\pi\) | ||
0.830391 | − | 0.557181i | \(-0.188117\pi\) | |||||||
\(278\) | − | 15.4720i | − | 0.927947i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.884340 | − | 1.11566i | 0.0528494 | − | 0.0666735i | ||||
\(281\) | −24.7967 | −1.47925 | −0.739623 | − | 0.673022i | \(-0.764996\pi\) | ||||
−0.739623 | + | 0.673022i | \(0.764996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5747i | 0.806931i | 0.914995 | + | 0.403465i | \(0.132194\pi\) | ||||
−0.914995 | + | 0.403465i | \(0.867806\pi\) | |||||||
\(284\) | −8.95798 | −0.531558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.495336 | −0.0292898 | ||||||||
\(287\) | − | 2.69396i | − | 0.159020i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4147 | 0.730275 | ||||||||
\(290\) | −12.5303 | − | 9.93230i | −0.735807 | − | 0.583245i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.69735i | 0.216371i | ||||||||
\(293\) | 15.6133i | 0.912139i | 0.889944 | + | 0.456070i | \(0.150743\pi\) | ||||
−0.889944 | + | 0.456070i | \(0.849257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.84232 | − | 9.89367i | 0.456597 | − | 0.576032i | ||||
\(296\) | −3.27334 | −0.190259 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 17.1893i | − | 0.995749i | ||||||
\(299\) | −0.695281 | −0.0402091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58871 | 0.0915717 | ||||||||
\(302\) | 3.29200i | 0.189433i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 9.02205 | − | 11.3820i | 0.516601 | − | 0.651731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.0187i | − | 1.94155i | −0.239997 | − | 0.970774i | \(-0.577146\pi\) | ||
0.239997 | − | 0.970774i | \(-0.422854\pi\) | |||||||
\(308\) | − | 2.23132i | − | 0.127141i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.6460 | + | 10.8166i | 0.775041 | + | 0.614344i | ||||
\(311\) | −8.93800 | −0.506828 | −0.253414 | − | 0.967358i | \(-0.581553\pi\) | ||||
−0.253414 | + | 0.967358i | \(0.581553\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.4240i | − | 1.04139i | −0.853744 | − | 0.520693i | \(-0.825674\pi\) | ||
0.853744 | − | 0.520693i | \(-0.174326\pi\) | |||||||
\(314\) | 15.1893 | 0.857182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.17997 | −0.235142 | ||||||||
\(317\) | 33.5547i | 1.88462i | 0.334742 | + | 0.942310i | \(0.391351\pi\) | ||||
−0.334742 | + | 0.942310i | \(0.608649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.0607 | −1.40313 | ||||||||
\(320\) | 1.38900 | − | 1.75233i | 0.0776477 | − | 0.0979583i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 3.13201i | − | 0.174540i | ||||||
\(323\) | − | 2.14134i | − | 0.119147i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.688023 | + | 0.161312i | −0.0381647 | + | 0.00894798i | ||||
\(326\) | 14.0700 | 0.779266 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4.23132i | − | 0.233636i | ||||||
\(329\) | −6.54669 | −0.360931 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.25130 | 0.123742 | 0.0618712 | − | 0.998084i | \(-0.480293\pi\) | ||||
0.0618712 | + | 0.998084i | \(0.480293\pi\) | |||||||
\(332\) | − | 9.00933i | − | 0.494451i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7967 | 0.809638 | ||||||||
\(335\) | 14.6717 | + | 11.6297i | 0.801599 | + | 0.635396i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3620i | 1.16366i | 0.813309 | + | 0.581831i | \(0.197664\pi\) | ||||
−0.813309 | + | 0.581831i | \(0.802336\pi\) | |||||||
\(338\) | 12.9800i | 0.706020i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.75233 | + | 2.97432i | 0.203499 | + | 0.161305i | ||||
\(341\) | 27.2920 | 1.47794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.65533i | − | 0.467344i | ||||||
\(344\) | 2.49534 | 0.134539 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.2920 | −0.929624 | ||||||||
\(347\) | 11.5560i | 0.620359i | 0.950678 | + | 0.310180i | \(0.100389\pi\) | ||||
−0.950678 | + | 0.310180i | \(0.899611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1120 | 0.915986 | 0.457993 | − | 0.888956i | \(-0.348568\pi\) | ||||
0.457993 | + | 0.888956i | \(0.348568\pi\) | |||||||
\(350\) | −0.726656 | − | 3.09931i | −0.0388414 | − | 0.165665i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 3.50466i | − | 0.186799i | ||||||
\(353\) | − | 11.6974i | − | 0.622587i | −0.950314 | − | 0.311294i | \(-0.899238\pi\) | ||
0.950314 | − | 0.311294i | \(-0.100762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4427 | + | 15.6974i | −0.660388 | + | 0.833129i | ||||
\(356\) | 6.77801 | 0.359234 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.7360i | 0.937376i | ||||||||
\(359\) | −4.47536 | −0.236200 | −0.118100 | − | 0.993002i | \(-0.537680\pi\) | ||||
−0.118100 | + | 0.993002i | \(0.537680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.17997i | 0.324812i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0899847 | 0.00471648 | ||||||||
\(365\) | 6.47899 | + | 5.13564i | 0.339126 | + | 0.268811i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.7453i | − | 0.978497i | −0.872144 | − | 0.489249i | \(-0.837271\pi\) | ||
0.872144 | − | 0.489249i | \(-0.162729\pi\) | |||||||
\(368\) | − | 4.91934i | − | 0.256439i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.54669 | + | 5.73599i | −0.236371 | + | 0.298200i | ||||
\(371\) | −5.18336 | −0.269107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69735i | 0.0878855i | 0.999034 | + | 0.0439428i | \(0.0139919\pi\) | ||||
−0.999034 | + | 0.0439428i | \(0.986008\pi\) | |||||||
\(374\) | 7.50466 | 0.388057 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2827 | −0.530288 | ||||||||
\(377\) | − | 1.01065i | − | 0.0520510i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.63667 | −0.135437 | −0.0677184 | − | 0.997704i | \(-0.521572\pi\) | ||||
−0.0677184 | + | 0.997704i | \(0.521572\pi\) | |||||||
\(380\) | −1.38900 | + | 1.75233i | −0.0712544 | + | 0.0898927i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 14.6367i | − | 0.748877i | ||||||
\(383\) | − | 12.4953i | − | 0.638482i | −0.947674 | − | 0.319241i | \(-0.896572\pi\) | ||
0.947674 | − | 0.319241i | \(-0.103428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.91002 | − | 3.09931i | −0.199273 | − | 0.157956i | ||||
\(386\) | −20.0187 | −1.01892 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.5653i | 0.739443i | ||||||||
\(389\) | −4.51399 | −0.228869 | −0.114434 | − | 0.993431i | \(-0.536506\pi\) | ||||
−0.114434 | + | 0.993431i | \(0.536506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5340 | 0.532726 | ||||||||
\(392\) | − | 6.59465i | − | 0.333080i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.94865 | 0.501206 | ||||||||
\(395\) | −5.80599 | + | 7.32469i | −0.292131 | + | 0.368545i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.6774i | 1.79060i | 0.445468 | + | 0.895298i | \(0.353037\pi\) | ||||
−0.445468 | + | 0.895298i | \(0.646963\pi\) | |||||||
\(398\) | − | 9.74870i | − | 0.488658i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.14134 | − | 4.86799i | −0.0570668 | − | 0.243400i | ||||
\(401\) | −15.3434 | −0.766210 | −0.383105 | − | 0.923705i | \(-0.625145\pi\) | ||||
−0.383105 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10063i | 0.0548264i | ||||||||
\(404\) | −16.6167 | −0.826712 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.55263 | 0.225943 | ||||||||
\(407\) | 11.4720i | 0.568644i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3620 | −1.45186 | −0.725929 | − | 0.687770i | \(-0.758590\pi\) | ||||
−0.725929 | + | 0.687770i | \(0.758590\pi\) | |||||||
\(410\) | −7.41468 | − | 5.87732i | −0.366185 | − | 0.290260i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 9.06068i | − | 0.446388i | ||||||
\(413\) | 3.59465i | 0.176881i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.7873 | − | 12.5140i | −0.774970 | − | 0.614288i | ||||
\(416\) | 0.141336 | 0.00692957 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.50466i | 0.171419i | ||||||||
\(419\) | 25.1379 | 1.22807 | 0.614035 | − | 0.789279i | \(-0.289546\pi\) | ||||
0.614035 | + | 0.789279i | \(0.289546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5454 | 0.708898 | 0.354449 | − | 0.935075i | \(-0.384668\pi\) | ||||
0.354449 | + | 0.935075i | \(0.384668\pi\) | |||||||
\(422\) | − | 20.7580i | − | 1.01049i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.14134 | −0.395378 | ||||||||
\(425\) | 10.4240 | − | 2.44398i | 0.505639 | − | 0.118551i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.13540i | 0.200126i | ||||||||
\(428\) | − | 0.0899847i | − | 0.00434958i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46603 | − | 4.37266i | 0.167147 | − | 0.210868i | ||||
\(431\) | −19.4020 | −0.934560 | −0.467280 | − | 0.884109i | \(-0.654766\pi\) | ||||
−0.467280 | + | 0.884109i | \(0.654766\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.50466i | 0.264537i | 0.991214 | + | 0.132269i | \(0.0422262\pi\) | ||||
−0.991214 | + | 0.132269i | \(0.957774\pi\) | |||||||
\(434\) | −4.95798 | −0.237991 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.5946 | −0.651066 | ||||||||
\(437\) | 4.91934i | 0.235324i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2500 | −0.584660 | −0.292330 | − | 0.956318i | \(-0.594430\pi\) | ||||
−0.292330 | + | 0.956318i | \(0.594430\pi\) | |||||||
\(440\) | −6.14134 | − | 4.86799i | −0.292777 | − | 0.232072i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.302648i | 0.0143955i | ||||||||
\(443\) | − | 31.6006i | − | 1.50139i | −0.660649 | − | 0.750695i | \(-0.729719\pi\) | ||
0.660649 | − | 0.750695i | \(-0.270281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.41468 | − | 11.8773i | 0.446299 | − | 0.563039i | ||||
\(446\) | 10.7267 | 0.507922 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.636672i | 0.0300799i | ||||||||
\(449\) | −36.0187 | −1.69983 | −0.849913 | − | 0.526923i | \(-0.823345\pi\) | ||||
−0.849913 | + | 0.526923i | \(0.823345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8294 | −0.698287 | ||||||||
\(452\) | 11.5233i | 0.542011i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.5526 | −0.589124 | ||||||||
\(455\) | 0.124989 | − | 0.157683i | 0.00585958 | − | 0.00739230i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.1413i | − | 1.03573i | −0.855463 | − | 0.517864i | \(-0.826727\pi\) | ||
0.855463 | − | 0.517864i | \(-0.173273\pi\) | |||||||
\(458\) | − | 25.4720i | − | 1.19023i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.62032 | − | 6.83299i | −0.401925 | − | 0.318590i | ||||
\(461\) | 2.31537 | 0.107837 | 0.0539187 | − | 0.998545i | \(-0.482829\pi\) | ||||
0.0539187 | + | 0.998545i | \(0.482829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8387i | 0.736086i | 0.929809 | + | 0.368043i | \(0.119972\pi\) | ||||
−0.929809 | + | 0.368043i | \(0.880028\pi\) | |||||||
\(464\) | 7.15066 | 0.331961 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.11203 | −0.144162 | ||||||||
\(467\) | 23.1379i | 1.07070i | 0.844631 | + | 0.535348i | \(0.179820\pi\) | ||||
−0.844631 | + | 0.535348i | \(0.820180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.33063 | −0.246146 | ||||||||
\(470\) | −14.2827 | + | 18.0187i | −0.658811 | + | 0.831139i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.64600i | 0.259878i | ||||||||
\(473\) | − | 8.74531i | − | 0.402110i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.14134 | + | 4.86799i | 0.0523681 | + | 0.223359i | ||||
\(476\) | −1.36333 | −0.0624880 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 1.54330i | − | 0.0705888i | ||||||
\(479\) | −10.1214 | −0.462457 | −0.231228 | − | 0.972900i | \(-0.574274\pi\) | ||||
−0.231228 | + | 0.972900i | \(0.574274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.462642 | −0.0210946 | ||||||||
\(482\) | 10.2827i | 0.468363i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.28267 | −0.0583033 | ||||||||
\(485\) | 25.5233 | + | 20.2313i | 1.15895 | + | 0.918657i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.3854i | − | 0.923750i | −0.886945 | − | 0.461875i | \(-0.847177\pi\) | ||
0.886945 | − | 0.461875i | \(-0.152823\pi\) | |||||||
\(488\) | 6.49534i | 0.294030i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.5560 | − | 9.15999i | −0.522048 | − | 0.413806i | ||||
\(491\) | 7.78734 | 0.351438 | 0.175719 | − | 0.984440i | \(-0.443775\pi\) | ||||
0.175719 | + | 0.984440i | \(0.443775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.3120i | 0.689617i | ||||||||
\(494\) | −0.141336 | −0.00635901 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.78734 | −0.349662 | ||||||||
\(497\) | − | 5.70329i | − | 0.255828i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.31537 | −0.193182 | −0.0965912 | − | 0.995324i | \(-0.530794\pi\) | ||||
−0.0965912 | + | 0.995324i | \(0.530794\pi\) | |||||||
\(500\) | −10.1157 | − | 4.76166i | −0.452386 | − | 0.212948i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.51399i | 0.112205i | ||||||||
\(503\) | − | 18.5526i | − | 0.827221i | −0.910454 | − | 0.413610i | \(-0.864268\pi\) | ||
0.910454 | − | 0.413610i | \(-0.135732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.0807 | + | 29.1180i | −1.02708 | + | 1.29573i | ||||
\(506\) | −17.2406 | −0.766440 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 3.29200i | − | 0.146059i | ||||||
\(509\) | −7.73599 | −0.342892 | −0.171446 | − | 0.985194i | \(-0.554844\pi\) | ||||
−0.171446 | + | 0.985194i | \(0.554844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.35400 | −0.104135 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.7967 | 1.09373 | ||||||||
\(515\) | −15.8773 | − | 12.5853i | −0.699638 | − | 0.554575i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0373i | 1.58492i | ||||||||
\(518\) | − | 2.08405i | − | 0.0915677i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.196316 | − | 0.247668i | 0.00860904 | − | 0.0108610i | ||||
\(521\) | −15.2080 | −0.666273 | −0.333136 | − | 0.942879i | \(-0.608107\pi\) | ||||
−0.333136 | + | 0.942879i | \(0.608107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.2113i | − | 0.796327i | −0.917315 | − | 0.398163i | \(-0.869648\pi\) | ||
0.917315 | − | 0.398163i | \(-0.130352\pi\) | |||||||
\(524\) | 18.0187 | 0.787149 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.5653 | −0.983896 | ||||||||
\(527\) | − | 16.6753i | − | 0.726388i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.19995 | −0.0521715 | ||||||||
\(530\) | −11.3083 | + | 14.2663i | −0.491203 | + | 0.619690i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 0.636672i | − | 0.0276032i | ||||||
\(533\) | − | 0.598038i | − | 0.0259039i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.157683 | − | 0.124989i | −0.00681724 | − | 0.00540375i | ||||
\(536\) | −8.37266 | −0.361644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 26.5653i | − | 1.14531i | ||||||
\(539\) | −23.1120 | −0.995506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5140 | 0.709992 | 0.354996 | − | 0.934868i | \(-0.384482\pi\) | ||||
0.354996 | + | 0.934868i | \(0.384482\pi\) | |||||||
\(542\) | − | 24.9380i | − | 1.07118i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.14134 | −0.0918090 | ||||||||
\(545\) | −18.8830 | + | 23.8223i | −0.808860 | + | 1.02044i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.2827i | − | 0.696197i | −0.937458 | − | 0.348098i | \(-0.886828\pi\) | ||
0.937458 | − | 0.348098i | \(-0.113172\pi\) | |||||||
\(548\) | 14.4240i | 0.616163i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −17.0607 | + | 4.00000i | −0.727470 | + | 0.170561i | ||||
\(551\) | −7.15066 | −0.304629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.66127i | − | 0.113169i | ||||||
\(554\) | 18.5467 | 0.787973 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.4720 | 0.656158 | ||||||||
\(557\) | 37.4533i | 1.58695i | 0.608604 | + | 0.793474i | \(0.291730\pi\) | ||||
−0.608604 | + | 0.793474i | \(0.708270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.352681 | 0.0149168 | ||||||||
\(560\) | 1.11566 | + | 0.884340i | 0.0471453 | + | 0.0373702i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 24.7967i | − | 1.04598i | ||||||
\(563\) | 29.1307i | 1.22771i | 0.789418 | + | 0.613856i | \(0.210382\pi\) | ||||
−0.789418 | + | 0.613856i | \(0.789618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.1927 | + | 16.0059i | 0.849513 | + | 0.673375i | ||||
\(566\) | −13.5747 | −0.570586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8.95798i | − | 0.375868i | ||||||
\(569\) | 14.8480 | 0.622461 | 0.311231 | − | 0.950334i | \(-0.399259\pi\) | ||||
0.311231 | + | 0.950334i | \(0.399259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.9087 | 1.75382 | 0.876912 | − | 0.480651i | \(-0.159599\pi\) | ||||
0.876912 | + | 0.480651i | \(0.159599\pi\) | |||||||
\(572\) | − | 0.495336i | − | 0.0207110i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.69396 | 0.112444 | ||||||||
\(575\) | −23.9473 | + | 5.61462i | −0.998673 | + | 0.234146i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 16.4427i | − | 0.684517i | −0.939606 | − | 0.342259i | \(-0.888808\pi\) | ||
0.939606 | − | 0.342259i | \(-0.111192\pi\) | |||||||
\(578\) | 12.4147i | 0.516383i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.93230 | − | 12.5303i | 0.412416 | − | 0.520294i | ||||
\(581\) | 5.73599 | 0.237969 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.5327i | 1.18170i | ||||||||
\(584\) | −3.69735 | −0.152998 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.6133 | −0.644980 | ||||||||
\(587\) | − | 42.5327i | − | 1.75551i | −0.479109 | − | 0.877755i | \(-0.659040\pi\) | ||
0.479109 | − | 0.877755i | \(-0.340960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.78734 | 0.320872 | ||||||||
\(590\) | 9.89367 | + | 7.84232i | 0.407316 | + | 0.322863i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.27334i | − | 0.134534i | ||||||
\(593\) | − | 3.92273i | − | 0.161087i | −0.996751 | − | 0.0805437i | \(-0.974334\pi\) | ||
0.996751 | − | 0.0805437i | \(-0.0256656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.89367 | + | 2.38900i | −0.0776328 | + | 0.0979396i | ||||
\(596\) | 17.1893 | 0.704101 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 0.695281i | − | 0.0284322i | ||||||
\(599\) | −10.7594 | −0.439615 | −0.219808 | − | 0.975543i | \(-0.570543\pi\) | ||||
−0.219808 | + | 0.975543i | \(0.570543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2220 | 1.02883 | 0.514413 | − | 0.857542i | \(-0.328010\pi\) | ||||
0.514413 | + | 0.857542i | \(0.328010\pi\) | |||||||
\(602\) | 1.58871i | 0.0647510i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.29200 | −0.133950 | ||||||||
\(605\) | −1.78164 | + | 2.24767i | −0.0724338 | + | 0.0913807i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.2920i | − | 1.59481i | −0.603442 | − | 0.797407i | \(-0.706205\pi\) | ||
0.603442 | − | 0.797407i | \(-0.293795\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.3820 | + | 9.02205i | 0.460843 | + | 0.365292i | ||||
\(611\) | −1.45331 | −0.0587947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.80599i | 0.396060i | 0.980196 | + | 0.198030i | \(0.0634544\pi\) | ||||
−0.980196 | + | 0.198030i | \(0.936546\pi\) | |||||||
\(614\) | 34.0187 | 1.37288 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.23132 | 0.0899025 | ||||||||
\(617\) | − | 35.0093i | − | 1.40942i | −0.709494 | − | 0.704711i | \(-0.751077\pi\) | ||
0.709494 | − | 0.704711i | \(-0.248923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.4206 | −0.539420 | −0.269710 | − | 0.962942i | \(-0.586928\pi\) | ||||
−0.269710 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(620\) | −10.8166 | + | 13.6460i | −0.434407 | + | 0.548037i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.93800i | − | 0.358381i | ||||||
\(623\) | 4.31537i | 0.172891i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3947 | + | 11.1120i | −0.895788 | + | 0.444481i | ||||
\(626\) | 18.4240 | 0.736371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.1893i | 0.606119i | ||||||||
\(629\) | 7.00933 | 0.279480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.5254 | 1.61329 | 0.806645 | − | 0.591036i | \(-0.201281\pi\) | ||||
0.806645 | + | 0.591036i | \(0.201281\pi\) | |||||||
\(632\) | − | 4.17997i | − | 0.166270i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.5547 | −1.33263 | ||||||||
\(635\) | −5.76868 | − | 4.57260i | −0.228923 | − | 0.181458i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.932062i | − | 0.0369296i | ||||||
\(638\) | − | 25.0607i | − | 0.992162i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.75233 | + | 1.38900i | 0.0692670 | + | 0.0549052i | ||||
\(641\) | 26.0700 | 1.02970 | 0.514852 | − | 0.857279i | \(-0.327847\pi\) | ||||
0.514852 | + | 0.857279i | \(0.327847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1400i | 1.18861i | 0.804241 | + | 0.594303i | \(0.202572\pi\) | ||||
−0.804241 | + | 0.594303i | \(0.797428\pi\) | |||||||
\(644\) | 3.13201 | 0.123418 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.14134 | 0.0842497 | ||||||||
\(647\) | − | 20.1086i | − | 0.790552i | −0.918562 | − | 0.395276i | \(-0.870649\pi\) | ||
0.918562 | − | 0.395276i | \(-0.129351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.7873 | 0.776721 | ||||||||
\(650\) | −0.161312 | − | 0.688023i | −0.00632718 | − | 0.0269865i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.0700i | 0.551024i | ||||||||
\(653\) | 28.0373i | 1.09718i | 0.836090 | + | 0.548592i | \(0.184836\pi\) | ||||
−0.836090 | + | 0.548592i | \(0.815164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.0280 | − | 31.5747i | 0.977924 | − | 1.23372i | ||||
\(656\) | 4.23132 | 0.165205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 6.54669i | − | 0.255216i | ||||||
\(659\) | 4.90069 | 0.190904 | 0.0954518 | − | 0.995434i | \(-0.469570\pi\) | ||||
0.0954518 | + | 0.995434i | \(0.469570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.03863 | −0.312667 | −0.156333 | − | 0.987704i | \(-0.549967\pi\) | ||||
−0.156333 | + | 0.987704i | \(0.549967\pi\) | |||||||
\(662\) | 2.25130i | 0.0874991i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00933 | 0.349630 | ||||||||
\(665\) | −1.11566 | − | 0.884340i | −0.0432635 | − | 0.0342932i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 35.1766i | − | 1.36204i | ||||||
\(668\) | 14.7967i | 0.572500i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.6297 | + | 14.6717i | −0.449293 | + | 0.566816i | ||||
\(671\) | 22.7640 | 0.878793 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.82936i | − | 0.186158i | −0.995659 | − | 0.0930791i | \(-0.970329\pi\) | ||
0.995659 | − | 0.0930791i | \(-0.0296709\pi\) | |||||||
\(674\) | −21.3620 | −0.822834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9800 | −0.499232 | ||||||||
\(677\) | 12.8094i | 0.492305i | 0.969231 | + | 0.246152i | \(0.0791663\pi\) | ||||
−0.969231 | + | 0.246152i | \(0.920834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.27334 | −0.355878 | ||||||||
\(680\) | −2.97432 | + | 3.75233i | −0.114060 | + | 0.143895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.2920i | 1.04506i | ||||||||
\(683\) | − | 37.1307i | − | 1.42077i | −0.703815 | − | 0.710383i | \(-0.748522\pi\) | ||
0.703815 | − | 0.710383i | \(-0.251478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2757 | + | 20.0350i | 0.965733 | + | 0.765498i | ||||
\(686\) | 8.65533 | 0.330462 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.49534i | 0.0951338i | ||||||||
\(689\) | −1.15066 | −0.0438368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1986 | −0.692308 | −0.346154 | − | 0.938178i | \(-0.612513\pi\) | ||||
−0.346154 | + | 0.938178i | \(0.612513\pi\) | |||||||
\(692\) | − | 17.2920i | − | 0.657343i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.5560 | −0.438660 | ||||||||
\(695\) | 21.4906 | − | 27.1120i | 0.815186 | − | 1.02842i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.06068i | 0.343198i | ||||||||
\(698\) | 17.1120i | 0.647700i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.09931 | − | 0.726656i | 0.117143 | − | 0.0274650i | ||||
\(701\) | 26.2827 | 0.992683 | 0.496341 | − | 0.868127i | \(-0.334676\pi\) | ||||
0.496341 | + | 0.868127i | \(0.334676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.27334i | 0.123456i | ||||||||
\(704\) | 3.50466 | 0.132087 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.6974 | 0.440236 | ||||||||
\(707\) | − | 10.5794i | − | 0.397879i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9253 | 0.560531 | 0.280265 | − | 0.959923i | \(-0.409578\pi\) | ||||
0.280265 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(710\) | −15.6974 | − | 12.4427i | −0.589111 | − | 0.466965i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.77801i | 0.254017i | ||||||||
\(713\) | 38.3086i | 1.43467i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.867993 | − | 0.688023i | −0.0324611 | − | 0.0257306i | ||||
\(716\) | −17.7360 | −0.662825 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 4.47536i | − | 0.167019i | ||||||
\(719\) | 32.3327 | 1.20581 | 0.602903 | − | 0.797814i | \(-0.294011\pi\) | ||||
0.602903 | + | 0.797814i | \(0.294011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.76868 | 0.214837 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.17997 | −0.229677 | ||||||||
\(725\) | −8.16131 | − | 34.8094i | −0.303104 | − | 1.29279i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.0246i | 1.55861i | 0.626647 | + | 0.779303i | \(0.284427\pi\) | ||||
−0.626647 | + | 0.779303i | \(0.715573\pi\) | |||||||
\(728\) | 0.0899847i | 0.00333506i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.13564 | + | 6.47899i | −0.190078 | + | 0.239798i | ||||
\(731\) | −5.34335 | −0.197631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.5840i | 0.981903i | 0.871187 | + | 0.490951i | \(0.163351\pi\) | ||||
−0.871187 | + | 0.490951i | \(0.836649\pi\) | |||||||
\(734\) | 18.7453 | 0.691902 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.91934 | 0.181329 | ||||||||
\(737\) | 29.3434i | 1.08088i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.14728 | −0.299702 | −0.149851 | − | 0.988709i | \(-0.547879\pi\) | ||||
−0.149851 | + | 0.988709i | \(0.547879\pi\) | |||||||
\(740\) | −5.73599 | − | 4.54669i | −0.210859 | − | 0.167140i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 5.18336i | − | 0.190287i | ||||||
\(743\) | − | 35.8247i | − | 1.31428i | −0.753769 | − | 0.657139i | \(-0.771766\pi\) | ||
0.753769 | − | 0.657139i | \(-0.228234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8760 | − | 30.1214i | 0.874749 | − | 1.10356i | ||||
\(746\) | −1.69735 | −0.0621445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.50466i | 0.274398i | ||||||||
\(749\) | 0.0572907 | 0.00209336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.8994 | −0.543686 | −0.271843 | − | 0.962342i | \(-0.587633\pi\) | ||||
−0.271843 | + | 0.962342i | \(0.587633\pi\) | |||||||
\(752\) | − | 10.2827i | − | 0.374970i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.01065 | 0.0368056 | ||||||||
\(755\) | −4.57260 | + | 5.76868i | −0.166414 | + | 0.209944i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.7920i | 1.73703i | 0.495664 | + | 0.868514i | \(0.334925\pi\) | ||||
−0.495664 | + | 0.868514i | \(0.665075\pi\) | |||||||
\(758\) | − | 2.63667i | − | 0.0957682i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.75233 | − | 1.38900i | −0.0635638 | − | 0.0503845i | ||||
\(761\) | 38.9053 | 1.41032 | 0.705158 | − | 0.709050i | \(-0.250876\pi\) | ||||
0.705158 | + | 0.709050i | \(0.250876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.65533i | − | 0.313344i | ||||||
\(764\) | 14.6367 | 0.529536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.4953 | 0.451475 | ||||||||
\(767\) | 0.797984i | 0.0288135i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.74663 | −0.315412 | −0.157706 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157706 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(770\) | 3.09931 | − | 3.91002i | 0.111692 | − | 0.140907i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 20.0187i | − | 0.720487i | ||||||
\(773\) | 23.4707i | 0.844181i | 0.906554 | + | 0.422090i | \(0.138703\pi\) | ||||
−0.906554 | + | 0.422090i | \(0.861297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.88797 | + | 37.9087i | 0.319265 | + | 1.36172i | ||||
\(776\) | −14.5653 | −0.522865 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.51399i | − | 0.161834i | ||||||
\(779\) | −4.23132 | −0.151603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.3947 | −1.12339 | ||||||||
\(782\) | 10.5340i | 0.376694i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.59465 | 0.235523 | ||||||||
\(785\) | 26.6167 | + | 21.0980i | 0.949991 | + | 0.753020i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.26063i | − | 0.0449364i | −0.999748 | − | 0.0224682i | \(-0.992848\pi\) | ||
0.999748 | − | 0.0224682i | \(-0.00715246\pi\) | |||||||
\(788\) | 9.94865i | 0.354406i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.32469 | − | 5.80599i | −0.260601 | − | 0.206568i | ||||
\(791\) | −7.33657 | −0.260859 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918026i | 0.0326000i | ||||||||
\(794\) | −35.6774 | −1.26614 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.74870 | 0.345534 | ||||||||
\(797\) | − | 38.6481i | − | 1.36898i | −0.729020 | − | 0.684492i | \(-0.760024\pi\) | ||
0.729020 | − | 0.684492i | \(-0.239976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.0187 | 0.778964 | ||||||||
\(800\) | 4.86799 | − | 1.14134i | 0.172110 | − | 0.0403523i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 15.3434i | − | 0.541793i | ||||||
\(803\) | 12.9580i | 0.457277i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.35037 | − | 5.48832i | 0.153330 | − | 0.193438i | ||||
\(806\) | −1.10063 | −0.0387681 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 16.6167i | − | 0.584573i | ||||||
\(809\) | 51.6506 | 1.81594 | 0.907970 | − | 0.419036i | \(-0.137632\pi\) | ||||
0.907970 | + | 0.419036i | \(0.137632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.19269 | 0.287684 | 0.143842 | − | 0.989601i | \(-0.454054\pi\) | ||||
0.143842 | + | 0.989601i | \(0.454054\pi\) | |||||||
\(812\) | 4.55263i | 0.159766i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.4720 | −0.402092 | ||||||||
\(815\) | 24.6553 | + | 19.5433i | 0.863639 | + | 0.684572i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.49534i | − | 0.0873007i | ||||||
\(818\) | − | 29.3620i | − | 1.02662i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.87732 | − | 7.41468i | 0.205245 | − | 0.258932i | ||||
\(821\) | 49.9600 | 1.74362 | 0.871809 | − | 0.489846i | \(-0.162947\pi\) | ||||
0.871809 | + | 0.489846i | \(0.162947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 16.8421i | − | 0.587078i | −0.955947 | − | 0.293539i | \(-0.905167\pi\) | ||
0.955947 | − | 0.293539i | \(-0.0948330\pi\) | |||||||
\(824\) | 9.06068 | 0.315644 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.59465 | −0.125074 | ||||||||
\(827\) | − | 41.7487i | − | 1.45174i | −0.687829 | − | 0.725872i | \(-0.741436\pi\) | ||
0.687829 | − | 0.725872i | \(-0.258564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.98002 | 0.207695 | 0.103847 | − | 0.994593i | \(-0.466885\pi\) | ||||
0.103847 | + | 0.994593i | \(0.466885\pi\) | |||||||
\(830\) | 12.5140 | − | 15.7873i | 0.434367 | − | 0.547986i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.141336i | 0.00489995i | ||||||||
\(833\) | 14.1214i | 0.489276i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.9287 | + | 20.5526i | 0.897299 | + | 0.711253i | ||||
\(836\) | −3.50466 | −0.121211 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.1379i | 0.868376i | ||||||||
\(839\) | 32.0373 | 1.10605 | 0.553025 | − | 0.833164i | \(-0.313473\pi\) | ||||
0.553025 | + | 0.833164i | \(0.313473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1320 | 0.763173 | ||||||||
\(842\) | 14.5454i | 0.501267i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.7580 | 0.714521 | ||||||||
\(845\) | −18.0293 | + | 22.7453i | −0.620227 | + | 0.782463i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.816641i | − | 0.0280601i | ||||||
\(848\) | − | 8.14134i | − | 0.279575i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.44398 | + | 10.4240i | 0.0838280 | + | 0.357541i | ||||
\(851\) | −16.1027 | −0.551994 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.8480i | − | 1.39861i | −0.714824 | − | 0.699305i | \(-0.753493\pi\) | ||
0.714824 | − | 0.699305i | \(-0.246507\pi\) | |||||||
\(854\) | −4.13540 | −0.141510 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0899847 | 0.00307561 | ||||||||
\(857\) | 28.8667i | 0.986067i | 0.870010 | + | 0.493033i | \(0.164112\pi\) | ||||
−0.870010 | + | 0.493033i | \(0.835888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5047 | 0.392534 | 0.196267 | − | 0.980550i | \(-0.437118\pi\) | ||||
0.196267 | + | 0.980550i | \(0.437118\pi\) | |||||||
\(860\) | 4.37266 | + | 3.46603i | 0.149106 | + | 0.118191i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.4020i | − | 0.660833i | ||||||
\(863\) | 31.6074i | 1.07593i | 0.842968 | + | 0.537964i | \(0.180806\pi\) | ||||
−0.842968 | + | 0.537964i | \(0.819194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.3013 | − | 24.0187i | −1.03028 | − | 0.816659i | ||||
\(866\) | −5.50466 | −0.187056 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 4.95798i | − | 0.168285i | ||||||
\(869\) | −14.6494 | −0.496947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.18336 | −0.0400966 | ||||||||
\(872\) | − | 13.5946i | − | 0.460373i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.91934 | −0.166399 | ||||||||
\(875\) | 3.03162 | − | 6.44036i | 0.102487 | − | 0.217724i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 12.0641i | − | 0.407375i | −0.979036 | − | 0.203687i | \(-0.934707\pi\) | ||
0.979036 | − | 0.203687i | \(-0.0652926\pi\) | |||||||
\(878\) | − | 12.2500i | − | 0.413417i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.86799 | − | 6.14134i | 0.164100 | − | 0.207024i | ||||
\(881\) | 22.8480 | 0.769769 | 0.384885 | − | 0.922965i | \(-0.374241\pi\) | ||||
0.384885 | + | 0.922965i | \(0.374241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.1773i | − | 1.15016i | −0.818098 | − | 0.575079i | \(-0.804971\pi\) | ||
0.818098 | − | 0.575079i | \(-0.195029\pi\) | |||||||
\(884\) | −0.302648 | −0.0101792 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.6006 | 1.06164 | ||||||||
\(887\) | 26.6167i | 0.893701i | 0.894609 | + | 0.446851i | \(0.147454\pi\) | ||||
−0.894609 | + | 0.446851i | \(0.852546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.09592 | 0.0702950 | ||||||||
\(890\) | 11.8773 | + | 9.41468i | 0.398129 | + | 0.315581i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.7267i | 0.359155i | ||||||||
\(893\) | 10.2827i | 0.344097i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.6354 | + | 31.0793i | −0.823469 | + | 1.03887i | ||||
\(896\) | −0.636672 | −0.0212697 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 36.0187i | − | 1.20196i | ||||||
\(899\) | −55.6846 | −1.85719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4333 | 0.580789 | ||||||||
\(902\) | − | 14.8294i | − | 0.493764i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.5233 | −0.383260 | ||||||||
\(905\) | −8.58400 | + | 10.8294i | −0.285342 | + | 0.359980i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.1434i | − | 0.436420i | −0.975902 | − | 0.218210i | \(-0.929978\pi\) | ||
0.975902 | − | 0.218210i | \(-0.0700217\pi\) | |||||||
\(908\) | − | 12.5526i | − | 0.416574i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.157683 | + | 0.124989i | 0.00522714 | + | 0.00414335i | ||||
\(911\) | 32.9253 | 1.09086 | 0.545432 | − | 0.838155i | \(-0.316366\pi\) | ||||
0.545432 | + | 0.838155i | \(0.316366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.5747i | − | 1.04497i | ||||||
\(914\) | 22.1413 | 0.732370 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.4720 | 0.841618 | ||||||||
\(917\) | 11.4720i | 0.378838i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.1273 | 0.795886 | 0.397943 | − | 0.917410i | \(-0.369724\pi\) | ||||
0.397943 | + | 0.917410i | \(0.369724\pi\) | |||||||
\(920\) | 6.83299 | − | 8.62032i | 0.225277 | − | 0.284204i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.31537i | 0.0762525i | ||||||||
\(923\) | − | 1.26609i | − | 0.0416737i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9346 | + | 3.73599i | −0.523927 | + | 0.122838i | ||||
\(926\) | −15.8387 | −0.520492 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.15066i | 0.234732i | ||||||||
\(929\) | −15.9359 | −0.522841 | −0.261420 | − | 0.965225i | \(-0.584191\pi\) | ||||
−0.261420 | + | 0.965225i | \(0.584191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.59465 | −0.216131 | ||||||||
\(932\) | − | 3.11203i | − | 0.101938i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.1379 | −0.757097 | ||||||||
\(935\) | 13.1507 | + | 10.4240i | 0.430073 | + | 0.340902i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.5547i | − | 0.769498i | −0.923021 | − | 0.384749i | \(-0.874288\pi\) | ||
0.923021 | − | 0.384749i | \(-0.125712\pi\) | |||||||
\(938\) | − | 5.33063i | − | 0.174051i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0187 | − | 14.2827i | −0.587704 | − | 0.465849i | ||||
\(941\) | 25.6974 | 0.837710 | 0.418855 | − | 0.908053i | \(-0.362432\pi\) | ||||
0.418855 | + | 0.908053i | \(0.362432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20.8153i | − | 0.677840i | ||||||
\(944\) | −5.64600 | −0.183762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.74531 | 0.284335 | ||||||||
\(947\) | − | 16.3013i | − | 0.529722i | −0.964287 | − | 0.264861i | \(-0.914674\pi\) | ||
0.964287 | − | 0.264861i | \(-0.0853261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.522569 | −0.0169633 | ||||||||
\(950\) | −4.86799 | + | 1.14134i | −0.157939 | + | 0.0370298i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 1.36333i | − | 0.0441857i | ||||||
\(953\) | − | 10.2754i | − | 0.332853i | −0.986054 | − | 0.166427i | \(-0.946777\pi\) | ||
0.986054 | − | 0.166427i | \(-0.0532229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.3304 | − | 25.6483i | 0.657876 | − | 0.829960i | ||||
\(956\) | 1.54330 | 0.0499138 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 10.1214i | − | 0.327006i | ||||||
\(959\) | −9.18336 | −0.296546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6426 | 0.956213 | ||||||||
\(962\) | − | 0.462642i | − | 0.0149162i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.2827 | −0.331183 | ||||||||
\(965\) | −35.0793 | − | 27.8060i | −1.12924 | − | 0.895107i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.2920i | 1.71376i | 0.515520 | + | 0.856878i | \(0.327599\pi\) | ||||
−0.515520 | + | 0.856878i | \(0.672401\pi\) | |||||||
\(968\) | − | 1.28267i | − | 0.0412266i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.2313 | + | 25.5233i | −0.649589 | + | 0.819504i | ||||
\(971\) | −2.54669 | −0.0817271 | −0.0408635 | − | 0.999165i | \(-0.513011\pi\) | ||||
−0.0408635 | + | 0.999165i | \(0.513011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.85057i | 0.315795i | ||||||||
\(974\) | 20.3854 | 0.653190 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.49534 | −0.207911 | ||||||||
\(977\) | − | 49.2966i | − | 1.57714i | −0.614946 | − | 0.788569i | \(-0.710822\pi\) | ||
0.614946 | − | 0.788569i | \(-0.289178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.7546 | 0.759202 | ||||||||
\(980\) | 9.15999 | − | 11.5560i | 0.292605 | − | 0.369143i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.78734i | 0.248504i | ||||||||
\(983\) | 36.7453i | 1.17199i | 0.810313 | + | 0.585997i | \(0.199297\pi\) | ||||
−0.810313 | + | 0.585997i | \(0.800703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.4333 | + | 13.8187i | 0.555472 | + | 0.440301i | ||||
\(986\) | −15.3120 | −0.487633 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.141336i | − | 0.00449650i | ||||||
\(989\) | 12.2754 | 0.390335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.5674 | −1.12984 | −0.564918 | − | 0.825147i | \(-0.691092\pi\) | ||||
−0.564918 | + | 0.825147i | \(0.691092\pi\) | |||||||
\(992\) | − | 7.78734i | − | 0.247248i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.70329 | 0.180897 | ||||||||
\(995\) | 13.5410 | − | 17.0830i | 0.429278 | − | 0.541566i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.4299i | 1.53379i | 0.641771 | + | 0.766896i | \(0.278200\pi\) | ||||
−0.641771 | + | 0.766896i | \(0.721800\pi\) | |||||||
\(998\) | − | 4.31537i | − | 0.136601i | ||||||
\(999\) | 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 | 1710.2.d.d.1369.5 | 6 | ||
3.2 | odd | 2 | 190.2.b.b.39.2 | ✓ | 6 | ||
5.2 | odd | 4 | 8550.2.a.ck.1.2 | 3 | |||
5.3 | odd | 4 | 8550.2.a.cl.1.2 | 3 | |||
5.4 | even | 2 | inner | 1710.2.d.d.1369.2 | 6 | ||
12.11 | even | 2 | 1520.2.d.j.609.3 | 6 | |||
15.2 | even | 4 | 950.2.a.n.1.2 | 3 | |||
15.8 | even | 4 | 950.2.a.i.1.2 | 3 | |||
15.14 | odd | 2 | 190.2.b.b.39.5 | yes | 6 | ||
60.23 | odd | 4 | 7600.2.a.cd.1.2 | 3 | |||
60.47 | odd | 4 | 7600.2.a.bi.1.2 | 3 | |||
60.59 | even | 2 | 1520.2.d.j.609.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.2 | ✓ | 6 | 3.2 | odd | 2 | ||
190.2.b.b.39.5 | yes | 6 | 15.14 | odd | 2 | ||
950.2.a.i.1.2 | 3 | 15.8 | even | 4 | |||
950.2.a.n.1.2 | 3 | 15.2 | even | 4 | |||
1520.2.d.j.609.3 | 6 | 12.11 | even | 2 | |||
1520.2.d.j.609.4 | 6 | 60.59 | even | 2 | |||
1710.2.d.d.1369.2 | 6 | 5.4 | even | 2 | inner | ||
1710.2.d.d.1369.5 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bi.1.2 | 3 | 60.47 | odd | 4 | |||
7600.2.a.cd.1.2 | 3 | 60.23 | odd | 4 | |||
8550.2.a.ck.1.2 | 3 | 5.2 | odd | 4 | |||
8550.2.a.cl.1.2 | 3 | 5.3 | odd | 4 |