Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (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: | \(12.1372611072\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.3 | ||
Root | \(-1.75233 - 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.j.609.4 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.36333i | − | 0.787118i | −0.919299 | − | 0.393559i | \(-0.871244\pi\) | ||
0.919299 | − | 0.393559i | \(-0.128756\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38900 | − | 1.75233i | 0.621181 | − | 0.783667i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.636672i | 0.240639i | 0.992735 | + | 0.120320i | \(0.0383920\pi\) | ||||
−0.992735 | + | 0.120320i | \(0.961608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.14134 | 0.380445 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | 0 | ||||||||
\(15\) | −2.38900 | − | 1.89367i | −0.616838 | − | 0.488943i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.14134i | − | 0.519350i | −0.965696 | − | 0.259675i | \(-0.916385\pi\) | ||
0.965696 | − | 0.259675i | \(-0.0836155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.867993 | 0.189412 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 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 | 0 | ||||||||
\(27\) | − | 5.64600i | − | 1.08657i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.15066 | −1.32785 | −0.663923 | − | 0.747801i | \(-0.731110\pi\) | ||||
−0.663923 | + | 0.747801i | \(0.731110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.78734 | 1.39865 | 0.699323 | − | 0.714805i | \(-0.253485\pi\) | ||||
0.699323 | + | 0.714805i | \(0.253485\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.77801i | 0.831744i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 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 | \(-0.0867154\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.192688 | −0.0308547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.23132 | −0.660821 | −0.330411 | − | 0.943837i | \(-0.607187\pi\) | ||||
−0.330411 | + | 0.943837i | \(0.607187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.49534i | − | 0.380535i | −0.981732 | − | 0.190268i | \(-0.939064\pi\) | ||
0.981732 | − | 0.190268i | \(-0.0609356\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.58532 | − | 2.00000i | 0.236326 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.91934 | −0.408790 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.14134i | 1.11830i | 0.829067 | + | 0.559149i | \(0.188872\pi\) | ||||
−0.829067 | + | 0.559149i | \(0.811128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.86799 | + | 6.14134i | −0.656400 | + | 0.828098i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.36333i | − | 0.180577i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.636506\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.726656i | 0.0915501i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.247668 | − | 0.196316i | −0.0307194 | − | 0.0243501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.37266i | 1.02288i | 0.859318 | + | 0.511441i | \(0.170888\pi\) | ||||
−0.859318 | + | 0.511441i | \(0.829112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.70668 | −0.807389 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(-0.0694221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.63667 | + | 1.55602i | −0.766337 | + | 0.179673i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.23132i | − | 0.254283i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.17997 | −0.470283 | −0.235142 | − | 0.971961i | \(-0.575555\pi\) | ||||
−0.235142 | + | 0.971961i | \(0.575555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.27334 | −0.474816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.74870i | 1.04517i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.77801 | 0.718467 | 0.359234 | − | 0.933248i | \(-0.383038\pi\) | ||||
0.359234 | + | 0.933248i | \(0.383038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0899847 | 0.00943296 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.6167i | − | 1.10090i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 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 | \(-0.264911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.6167 | −1.65342 | −0.826712 | − | 0.562626i | \(-0.809791\pi\) | ||||
−0.826712 | + | 0.562626i | \(0.809791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.06068i | − | 0.892775i | −0.894840 | − | 0.446388i | \(-0.852710\pi\) | ||
0.894840 | − | 0.446388i | \(-0.147290\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20565 | − | 1.52101i | 0.117659 | − | 0.148436i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | \(0.274322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.46264 | −0.423575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5233i | 1.08402i | 0.840371 | + | 0.542011i | \(0.182337\pi\) | ||||
−0.840371 | + | 0.542011i | \(0.817663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.62032 | − | 6.83299i | −0.803849 | − | 0.637179i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.161312i | − | 0.0149133i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.36333 | 0.124976 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28267 | 0.116607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.76868i | 0.520144i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1157 | − | 4.76166i | −0.904772 | − | 0.425896i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.29200i | − | 0.292118i | −0.989276 | − | 0.146059i | \(-0.953341\pi\) | ||
0.989276 | − | 0.146059i | \(-0.0466589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.40196 | −0.299526 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.89367 | − | 7.84232i | −0.851511 | − | 0.674959i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4240i | 1.23233i | 0.787619 | + | 0.616163i | \(0.211314\pi\) | ||||
−0.787619 | + | 0.616163i | \(0.788686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4720 | 1.31232 | 0.656158 | − | 0.754624i | \(-0.272181\pi\) | ||||
0.656158 | + | 0.754624i | \(0.272181\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.0187 | −1.18058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.495336i | 0.0414220i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.93230 | + | 12.5303i | −0.824833 | + | 1.04059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 8.99067i | − | 0.741538i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.1893 | 1.40820 | 0.704101 | − | 0.710100i | \(-0.251350\pi\) | ||||
0.704101 | + | 0.710100i | \(0.251350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.29200 | −0.267899 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.44398i | − | 0.197584i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 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 | \(-0.207274\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.0993 | 0.880233 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.13201 | 0.246837 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0700i | 1.10205i | 0.834489 | + | 0.551024i | \(0.185763\pi\) | ||||
−0.834489 | + | 0.551024i | \(0.814237\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.37266 | + | 6.63667i | 0.651810 | + | 0.516664i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14134 | 0.0872802 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17.2920i | − | 1.31469i | −0.753591 | − | 0.657343i | \(-0.771680\pi\) | ||
0.753591 | − | 0.657343i | \(-0.228320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.09931 | − | 0.726656i | 0.234286 | − | 0.0549301i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.69735i | 0.578568i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | 0 | ||||||||
\(183\) | 8.85527i | 0.654601i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.73599 | − | 4.54669i | −0.421718 | − | 0.334279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50466i | 0.548795i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.59465 | 0.261472 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −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 | \(0.743918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.267644 | + | 0.337653i | −0.0191664 | + | 0.0241798i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.94865i | 0.708812i | 0.935092 | + | 0.354406i | \(0.115317\pi\) | ||||
−0.935092 | + | 0.354406i | \(0.884683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74870 | 0.691067 | 0.345534 | − | 0.938406i | \(-0.387698\pi\) | ||||
0.345534 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4147 | 0.805129 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.55263i | − | 0.319532i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.87732 | + | 7.41468i | −0.410490 | + | 0.517864i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.61462i | − | 0.390243i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.50466 | −0.242423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7580 | 1.42904 | 0.714521 | − | 0.699614i | \(-0.246645\pi\) | ||||
0.714521 | + | 0.699614i | \(0.246645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 12.2127i | − | 0.836798i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.37266 | − | 3.46603i | −0.298213 | − | 0.236381i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.95798i | 0.336569i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.04070 | −0.340619 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.302648 | −0.0203583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.7267i | 0.718310i | 0.933278 | + | 0.359155i | \(0.116935\pi\) | ||||
−0.933278 | + | 0.359155i | \(0.883065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.30265 | − | 5.55602i | −0.0868432 | − | 0.370401i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 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 | \(0.818396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.04202 | −0.200150 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.11203i | − | 0.203876i | −0.994791 | − | 0.101938i | \(-0.967496\pi\) | ||
0.994791 | − | 0.101938i | \(-0.0325043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0187 | − | 14.2827i | −1.17541 | − | 0.931699i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.69867i | 0.370168i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.392552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 11.1120i | − | 0.712837i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.15999 | − | 11.5560i | 0.585211 | − | 0.738287i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.141336i | − | 0.00899300i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.2827 | 0.778383 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.05498 | + | 5.11566i | −0.253933 | + | 0.320355i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.7967i | 1.54677i | 0.633934 | + | 0.773387i | \(0.281439\pi\) | ||||
−0.633934 | + | 0.773387i | \(0.718561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.08405 | 0.129496 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.16131 | −0.505173 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 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 | 0 | ||||||||
\(267\) | − | 9.24065i | − | 0.565519i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.5653 | 1.61972 | 0.809859 | − | 0.586625i | \(-0.199544\pi\) | ||||
0.809859 | + | 0.586625i | \(0.199544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.9380 | 1.51488 | 0.757438 | − | 0.652907i | \(-0.226451\pi\) | ||||
0.757438 | + | 0.652907i | \(0.226451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.122679i | − | 0.00742485i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 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 | \(-0.188117\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.88797 | 0.532109 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7967 | 1.47925 | 0.739623 | − | 0.673022i | \(-0.235004\pi\) | ||||
0.739623 | + | 0.673022i | \(0.235004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.5747i | − | 0.806931i | −0.914995 | − | 0.403465i | \(-0.867806\pi\) | ||
0.914995 | − | 0.403465i | \(-0.132194\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.38900 | − | 1.89367i | −0.141512 | − | 0.112171i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.69396i | − | 0.159020i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4147 | 0.730275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.8573 | −1.16406 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 15.6133i | − | 0.912139i | −0.889944 | − | 0.456070i | \(-0.849257\pi\) | ||
0.889944 | − | 0.456070i | \(-0.150743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.84232 | + | 9.89367i | −0.456597 | + | 0.576032i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.7873i | 1.14818i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.695281 | −0.0402091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58871 | 0.0915717 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.6540i | 1.30144i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.02205 | + | 11.3820i | −0.516601 | + | 0.651731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.0187i | 1.94155i | 0.239997 | + | 0.970774i | \(0.422854\pi\) | ||||
−0.239997 | + | 0.970774i | \(0.577146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.3527 | −0.702719 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(-0.174326\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.27334 | + | 1.00933i | 0.0717448 | + | 0.0568692i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 33.5547i | − | 1.88462i | −0.334742 | − | 0.942310i | \(-0.608649\pi\) | ||
0.334742 | − | 0.942310i | \(-0.391351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0607 | 1.40313 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.122679 | 0.00684726 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.14134i | − | 0.119147i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.688023 | + | 0.161312i | −0.0381647 | + | 0.00894798i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 18.5340i | − | 1.02493i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.54669 | 0.360931 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.25130 | −0.123742 | −0.0618712 | − | 0.998084i | \(-0.519707\pi\) | ||||
−0.0618712 | + | 0.998084i | \(0.519707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.73599i | − | 0.204731i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 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 | \(0.802336\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.7101 | 0.853254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.2920 | −1.47794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.65533i | 0.467344i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.31561 | + | 11.7523i | −0.501535 | + | 0.632724i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | 0 | ||||||||
\(351\) | −0.797984 | −0.0425932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6974i | 0.622587i | 0.950314 | + | 0.311294i | \(0.100762\pi\) | ||||
−0.950314 | + | 0.311294i | \(0.899238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4427 | − | 15.6974i | 0.660388 | − | 0.833129i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.85866i | − | 0.0983709i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.74870i | − | 0.0917831i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.47899 | − | 5.13564i | −0.339126 | − | 0.268811i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7453i | 0.978497i | 0.872144 | + | 0.489249i | \(0.162729\pi\) | ||||
−0.872144 | + | 0.489249i | \(0.837271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.82936 | −0.251406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.18336 | −0.269107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69735i | 0.0878855i | 0.999034 | + | 0.0439428i | \(0.0139919\pi\) | ||||
−0.999034 | + | 0.0439428i | \(0.986008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.49171 | + | 13.7910i | −0.335230 | + | 0.712162i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.01065i | 0.0520510i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.63667 | 0.135437 | 0.0677184 | − | 0.997704i | \(-0.478428\pi\) | ||||
0.0677184 | + | 0.997704i | \(0.478428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.48808 | −0.229931 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 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 | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.84802i | − | 0.144773i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.51399 | 0.228869 | 0.114434 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114434 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5340 | −0.532726 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.5653i | 1.23916i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −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 | \(0.646963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.867993 | 0.0434540 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.3434 | 0.766210 | 0.383105 | − | 0.923705i | \(-0.374855\pi\) | ||||
0.383105 | + | 0.923705i | \(0.374855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.10063i | − | 0.0548264i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.93569 | + | 7.48832i | −0.294947 | + | 0.372097i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.4720i | 0.568644i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3620 | −1.45186 | −0.725929 | − | 0.687770i | \(-0.758590\pi\) | ||||
−0.725929 | + | 0.687770i | \(0.758590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.6647 | 0.969986 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.59465i | − | 0.176881i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7873 | + | 12.5140i | 0.774970 | + | 0.614288i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 21.0934i | − | 1.03295i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.384668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 11.7360i | − | 0.570623i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.4240 | + | 2.44398i | −0.505639 | + | 0.118551i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.13540i | − | 0.200126i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.675305 | 0.0326040 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | \(0.957774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.0830 | + | 13.5410i | 0.819066 | + | 0.649241i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.91934i | − | 0.235324i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2500 | 0.584660 | 0.292330 | − | 0.956318i | \(-0.405570\pi\) | ||||
0.292330 | + | 0.956318i | \(0.405570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.52671 | 0.358415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 23.4347i | − | 1.10842i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.0187 | 1.69983 | 0.849913 | − | 0.526923i | \(-0.176655\pi\) | ||||
0.849913 | + | 0.526923i | \(0.176655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8294 | 0.698287 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.48808i | 0.210868i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 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 | \(-0.173273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.0900 | −0.564312 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.31537 | −0.107837 | −0.0539187 | − | 0.998545i | \(-0.517171\pi\) | ||||
−0.0539187 | + | 0.998545i | \(0.517171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.8387i | − | 0.736086i | −0.929809 | − | 0.368043i | \(-0.880028\pi\) | ||
0.929809 | − | 0.368043i | \(-0.119972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.6040 | − | 14.7466i | −0.862739 | − | 0.683859i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.7080 | −0.954174 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.74531i | 0.402110i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.14134 | − | 4.86799i | −0.0523681 | − | 0.223359i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.29200i | 0.425451i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.26995i | − | 0.194290i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.5233 | − | 20.2313i | −1.15895 | − | 0.918657i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3854i | 0.923750i | 0.886945 | + | 0.461875i | \(0.152823\pi\) | ||||
−0.886945 | + | 0.461875i | \(0.847177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.1820 | 0.867442 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | 0 | ||||||||
\(495\) | −5.55602 | + | 7.00933i | −0.249724 | + | 0.315046i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.70329i | 0.255828i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.31537 | 0.193182 | 0.0965912 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965912 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1727 | −0.901250 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 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 | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 17.6960i | − | 0.785908i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.73599 | 0.342892 | 0.171446 | − | 0.985194i | \(-0.445156\pi\) | ||||
0.171446 | + | 0.985194i | \(0.445156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.35400 | 0.104135 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.64600i | − | 0.249277i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8773 | − | 12.5853i | −0.699638 | − | 0.554575i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0373i | 1.58492i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.5747 | −1.03481 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2080 | 0.666273 | 0.333136 | − | 0.942879i | \(-0.391893\pi\) | ||||
0.333136 | + | 0.942879i | \(0.391893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2113i | 0.796327i | 0.917315 | + | 0.398163i | \(0.130352\pi\) | ||||
−0.917315 | + | 0.398163i | \(0.869648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.990671 | − | 4.22538i | −0.0432364 | − | 0.184411i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.6753i | − | 0.726388i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.19995 | −0.0521715 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.44398 | −0.279645 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.598038i | 0.0259039i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.157683 | + | 0.124989i | 0.00681724 | + | 0.00540375i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 24.1800i | − | 1.04344i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.1120 | −0.995506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5140 | 0.709992 | 0.354996 | − | 0.934868i | \(-0.384482\pi\) | ||||
0.354996 | + | 0.934868i | \(0.384482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.42533i | − | 0.361565i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.8830 | − | 23.8223i | 0.808860 | − | 1.02044i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2827i | 0.696197i | 0.937458 | + | 0.348098i | \(0.113172\pi\) | ||||
−0.937458 | + | 0.348098i | \(0.886828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.41336 | −0.316395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.15066 | −0.304629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.66127i | − | 0.113169i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.19863 | + | 7.82003i | −0.263117 | + | 0.331942i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 37.4533i | − | 1.58695i | −0.608604 | − | 0.793474i | \(-0.708270\pi\) | ||
0.608604 | − | 0.793474i | \(-0.291730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.352681 | −0.0149168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2313 | 0.431967 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.72072i | − | 0.114259i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.8480 | −0.622461 | −0.311231 | − | 0.950334i | \(-0.600741\pi\) | ||||
−0.311231 | + | 0.950334i | \(0.600741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.9087 | −1.75382 | −0.876912 | − | 0.480651i | \(-0.840401\pi\) | ||||
−0.876912 | + | 0.480651i | \(0.840401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9546i | 0.833615i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −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 | \(-0.111192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.2920 | 1.13422 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.73599 | −0.237969 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 28.5327i | − | 1.18170i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.282672 | − | 0.224063i | −0.0116871 | − | 0.00926387i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5633 | 0.557919 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.92273i | 0.161087i | 0.996751 | + | 0.0805437i | \(0.0256656\pi\) | ||||
−0.996751 | + | 0.0805437i | \(0.974334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89367 | − | 2.38900i | 0.0776328 | − | 0.0979396i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 13.2907i | − | 0.543951i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(0.328010\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.55602i | 0.389151i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.78164 | − | 2.24767i | 0.0724338 | − | 0.0913807i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2920i | 1.59481i | 0.603442 | + | 0.797407i | \(0.293795\pi\) | ||||
−0.603442 | + | 0.797407i | \(0.706205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.20672 | −0.251509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.45331 | −0.0587947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.80599i | 0.396060i | 0.980196 | + | 0.198030i | \(0.0634544\pi\) | ||||
−0.980196 | + | 0.198030i | \(0.936546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.1086 | + | 8.01272i | 0.407620 | + | 0.323104i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.0093i | 1.40942i | 0.709494 | + | 0.704711i | \(0.248923\pi\) | ||||
−0.709494 | + | 0.704711i | \(0.751077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.4206 | 0.539420 | 0.269710 | − | 0.962942i | \(-0.413072\pi\) | ||||
0.269710 | + | 0.962942i | \(0.413072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.7746 | −1.11456 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.31537i | 0.172891i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3947 | + | 11.1120i | −0.895788 | + | 0.444481i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.77801i | 0.190815i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.00933 | −0.279480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.5254 | −1.61329 | −0.806645 | − | 0.591036i | \(-0.798719\pi\) | ||||
−0.806645 | + | 0.591036i | \(0.798719\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 28.3000i | − | 1.12482i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.76868 | − | 4.57260i | −0.228923 | − | 0.181458i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.932062i | − | 0.0369296i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2241 | 0.404458 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0700 | −1.02970 | −0.514852 | − | 0.857279i | \(-0.672153\pi\) | ||||
−0.514852 | + | 0.857279i | \(0.672153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.1400i | − | 1.18861i | −0.804241 | − | 0.594303i | \(-0.797428\pi\) | ||
0.804241 | − | 0.594303i | \(-0.202572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.72534 | + | 5.96137i | −0.186060 | + | 0.234729i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 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 | 0 | ||||||||
\(651\) | 6.75935 | 0.264920 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 28.0373i | − | 1.09718i | −0.836090 | − | 0.548592i | \(-0.815164\pi\) | ||
0.836090 | − | 0.548592i | \(-0.184836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.0280 | + | 31.5747i | −0.977924 | + | 1.23372i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.21992i | − | 0.164635i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.549967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.412609i | 0.0160244i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11566 | + | 0.884340i | 0.0432635 | + | 0.0342932i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1766i | 1.36204i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.6240 | 0.565395 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.7640 | 0.878793 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.82936i | − | 0.186158i | −0.995659 | − | 0.0930791i | \(-0.970329\pi\) | ||
0.995659 | − | 0.0930791i | \(-0.0296709\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.4847 | + | 6.44398i | −1.05789 | + | 0.248029i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.8094i | − | 0.492305i | −0.969231 | − | 0.246152i | \(-0.920834\pi\) | ||
0.969231 | − | 0.246152i | \(-0.0791663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.27334 | 0.355878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1133 | 0.655785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 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 | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.7267i | 1.32490i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.15066 | 0.0438368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1986 | 0.692308 | 0.346154 | − | 0.938178i | \(-0.387487\pi\) | ||||
0.346154 | + | 0.938178i | \(0.387487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2.54669i | − | 0.0967406i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4906 | − | 27.1120i | 0.815186 | − | 1.02842i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.06068i | 0.343198i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.24272 | −0.160474 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.2827 | −0.992683 | −0.496341 | − | 0.868127i | \(-0.665324\pi\) | ||||
−0.496341 | + | 0.868127i | \(0.665324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.27334i | − | 0.123456i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.4720 | + | 24.5653i | −0.733357 | + | 0.925184i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 10.5794i | − | 0.397879i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9253 | 0.560531 | 0.280265 | − | 0.959923i | \(-0.409578\pi\) | ||||
0.280265 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.77075 | −0.178917 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 38.3086i | − | 1.43467i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.867993 | + | 0.688023i | 0.0324611 | + | 0.0257306i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.10402i | 0.0785761i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.0187i | − | 0.521359i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.16131 | + | 34.8094i | 0.303104 | + | 1.29279i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.0246i | − | 1.55861i | −0.626647 | − | 0.779303i | \(-0.715573\pi\) | ||
0.626647 | − | 0.779303i | \(-0.284427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.9694 | −1.03590 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.34335 | −0.197631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.5840i | 0.981903i | 0.871187 | + | 0.490951i | \(0.163351\pi\) | ||||
−0.871187 | + | 0.490951i | \(0.836649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.7546 | − | 12.4881i | −0.581119 | − | 0.460630i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 29.3434i | − | 1.08088i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.14728 | 0.299702 | 0.149851 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149851 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.192688 | −0.00707855 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 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 | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.2827i | 0.376223i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0572907 | −0.00209336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.8994 | 0.543686 | 0.271843 | − | 0.962342i | \(-0.412367\pi\) | ||||
0.271843 | + | 0.962342i | \(0.412367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 3.42740i | − | 0.124901i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −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 | \(0.665075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.5047 | 0.853165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.9053 | −1.41032 | −0.705158 | − | 0.709050i | \(-0.749124\pi\) | ||||
−0.705158 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.65533i | 0.313344i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.28267 | − | 3.39470i | −0.154840 | − | 0.122736i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.797984i | 0.0288135i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.74663 | −0.315412 | −0.157706 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157706 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.8060 | 1.21749 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 23.4707i | − | 0.844181i | −0.906554 | − | 0.422090i | \(-0.861297\pi\) | ||
0.906554 | − | 0.422090i | \(-0.138703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.88797 | − | 37.9087i | −0.319265 | − | 1.36172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.84124i | − | 0.101929i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.23132 | −0.151603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.3947 | −1.12339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.3727i | 1.44280i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.6167 | − | 21.0980i | −0.949991 | − | 0.753020i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.26063i | 0.0449364i | 0.999748 | + | 0.0224682i | \(0.00715246\pi\) | ||||
−0.999748 | + | 0.0224682i | \(0.992848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.7640 | 1.09523 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.33657 | −0.260859 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918026i | 0.0326000i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.4170 | − | 19.4497i | 0.546784 | − | 0.689809i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.6481i | 1.36898i | 0.729020 | + | 0.684492i | \(0.239976\pi\) | ||||
−0.729020 | + | 0.684492i | \(0.760024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.0187 | −0.778964 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.73599 | 0.273338 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.9580i | 0.457277i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.35037 | − | 5.48832i | 0.153330 | − | 0.193438i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 36.2173i | − | 1.27491i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.6506 | −1.81594 | −0.907970 | − | 0.419036i | \(-0.862368\pi\) | ||||
−0.907970 | + | 0.419036i | \(0.862368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.19269 | −0.287684 | −0.143842 | − | 0.989601i | \(-0.545946\pi\) | ||||
−0.143842 | + | 0.989601i | \(0.545946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 33.9987i | − | 1.19239i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.6553 | + | 19.5433i | 0.863639 | + | 0.684572i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.49534i | − | 0.0873007i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.102703 | 0.00358873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.9600 | −1.74362 | −0.871809 | − | 0.489846i | \(-0.837053\pi\) | ||||
−0.871809 | + | 0.489846i | \(0.837053\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.8421i | 0.587078i | 0.955947 | + | 0.293539i | \(0.0948330\pi\) | ||||
−0.955947 | + | 0.293539i | \(0.905167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.2593 | − | 5.45331i | 0.809785 | − | 0.189860i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | \(0.466885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.2852 | −0.877135 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14.1214i | − | 0.489276i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.9287 | − | 20.5526i | −0.897299 | − | 0.711253i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 43.9673i | − | 1.51973i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 33.8060i | − | 1.16434i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0293 | − | 22.7453i | 0.620227 | − | 0.782463i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.816641i | 0.0280601i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.5067 | −0.635150 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.1027 | −0.551994 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.8480i | − | 1.39861i | −0.714824 | − | 0.699305i | \(-0.753493\pi\) | ||
0.714824 | − | 0.699305i | \(-0.246507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.58532 | − | 2.00000i | 0.0542168 | − | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.8667i | − | 0.986067i | −0.870010 | − | 0.493033i | \(-0.835888\pi\) | ||
0.870010 | − | 0.493033i | \(-0.164112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5047 | −0.392534 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.67276 | −0.125167 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.9253i | − | 0.574813i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6494 | 0.496947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.18336 | 0.0400966 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 16.6240i | − | 0.562636i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 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 | \(-0.0652926\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.2861 | −0.717961 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.8480 | −0.769769 | −0.384885 | − | 0.922965i | \(-0.625759\pi\) | ||||
−0.384885 | + | 0.922965i | \(0.625759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.1773i | 1.15016i | 0.818098 | + | 0.575079i | \(0.195029\pi\) | ||||
−0.818098 | + | 0.575079i | \(0.804971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.4883 | + | 10.6917i | 0.453405 | + | 0.359396i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.9766 | 0.501736 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.2827i | − | 0.344097i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.6354 | − | 31.0793i | 0.823469 | − | 1.03887i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.947896i | 0.0316493i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.6846 | −1.85719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4333 | 0.580789 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.16593i | − | 0.0720777i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.58400 | − | 10.8294i | 0.285342 | − | 0.359980i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1434i | 0.436420i | 0.975902 | + | 0.218210i | \(0.0700217\pi\) | ||||
−0.975902 | + | 0.218210i | \(0.929978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.9652 | −0.629037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.5174 | + | 12.3000i | 0.512989 | + | 0.406626i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 11.4720i | − | 0.378838i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.1273 | −0.795886 | −0.397943 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.3786 | 1.52823 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.26609i | − | 0.0416737i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9346 | + | 3.73599i | −0.523927 | + | 0.122838i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 10.3413i | − | 0.339652i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.9359 | 0.522841 | 0.261420 | − | 0.965225i | \(-0.415809\pi\) | ||||
0.261420 | + | 0.965225i | \(0.415809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.59465 | 0.216131 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1854i | 0.398933i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | \(-0.125712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.1180 | −0.819694 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6974 | −0.837710 | −0.418855 | − | 0.908053i | \(-0.637568\pi\) | ||||
−0.418855 | + | 0.908053i | \(0.637568\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.8153i | 0.677840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.99298 | − | 6.29902i | 0.162422 | − | 0.204907i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.7461 | −1.48342 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.2754i | 0.332853i | 0.986054 | + | 0.166427i | \(0.0532229\pi\) | ||||
−0.986054 | + | 0.166427i | \(0.946777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.3304 | + | 25.6483i | −0.657876 | + | 0.829960i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 34.1659i | − | 1.10443i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.18336 | −0.296546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6426 | 0.956213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.102703i | 0.00330955i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.0793 | + | 27.8060i | 1.12924 | + | 0.895107i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.2920i | − | 1.71376i | −0.515520 | − | 0.856878i | \(-0.672401\pi\) | ||
0.515520 | − | 0.856878i | \(-0.327599\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.91934 | −0.0937828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.219921 | + | 0.938001i | 0.00704312 | + | 0.0300401i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.2966i | 1.57714i | 0.614946 | + | 0.788569i | \(0.289178\pi\) | ||||
−0.614946 | + | 0.788569i | \(0.710822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7546 | −0.759202 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5161 | 0.495390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 8.92528i | − | 0.284095i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.2754 | −0.390335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.5674 | 1.12984 | 0.564918 | − | 0.825147i | \(-0.308908\pi\) | ||||
0.564918 | + | 0.825147i | \(0.308908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.06926i | 0.0973999i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 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 | \(0.721800\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.4813 | −0.584722 |
(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 | 1520.2.d.j.609.3 | 6 | ||
4.3 | odd | 2 | 190.2.b.b.39.2 | ✓ | 6 | ||
5.2 | odd | 4 | 7600.2.a.bi.1.2 | 3 | |||
5.3 | odd | 4 | 7600.2.a.cd.1.2 | 3 | |||
5.4 | even | 2 | inner | 1520.2.d.j.609.4 | 6 | ||
12.11 | even | 2 | 1710.2.d.d.1369.5 | 6 | |||
20.3 | even | 4 | 950.2.a.i.1.2 | 3 | |||
20.7 | even | 4 | 950.2.a.n.1.2 | 3 | |||
20.19 | odd | 2 | 190.2.b.b.39.5 | yes | 6 | ||
60.23 | odd | 4 | 8550.2.a.cl.1.2 | 3 | |||
60.47 | odd | 4 | 8550.2.a.ck.1.2 | 3 | |||
60.59 | even | 2 | 1710.2.d.d.1369.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.2 | ✓ | 6 | 4.3 | odd | 2 | ||
190.2.b.b.39.5 | yes | 6 | 20.19 | odd | 2 | ||
950.2.a.i.1.2 | 3 | 20.3 | even | 4 | |||
950.2.a.n.1.2 | 3 | 20.7 | even | 4 | |||
1520.2.d.j.609.3 | 6 | 1.1 | even | 1 | trivial | ||
1520.2.d.j.609.4 | 6 | 5.4 | even | 2 | inner | ||
1710.2.d.d.1369.2 | 6 | 60.59 | even | 2 | |||
1710.2.d.d.1369.5 | 6 | 12.11 | even | 2 | |||
7600.2.a.bi.1.2 | 3 | 5.2 | odd | 4 | |||
7600.2.a.cd.1.2 | 3 | 5.3 | odd | 4 | |||
8550.2.a.ck.1.2 | 3 | 60.47 | odd | 4 | |||
8550.2.a.cl.1.2 | 3 | 60.23 | odd | 4 |