Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.39075800976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(0.851703 - 1.47519i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.p.577.4 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.59084 | − | 2.75542i | 0.918473 | − | 1.59084i | 0.116737 | − | 0.993163i | \(-0.462757\pi\) |
0.801736 | − | 0.597679i | \(-0.203910\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.28078 | + | 2.21837i | −0.572781 | + | 0.992085i | 0.423498 | + | 0.905897i | \(0.360802\pi\) |
−0.996279 | + | 0.0861882i | \(0.972531\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | − | 6.16879i | −1.18718 | − | 2.05626i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.96837 | −1.49802 | −0.749009 | − | 0.662559i | \(-0.769470\pi\) | ||||
−0.749009 | + | 0.662559i | \(0.769470\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.28078 | − | 3.95042i | −0.632574 | − | 1.09565i | −0.987024 | − | 0.160575i | \(-0.948665\pi\) |
0.354450 | − | 0.935075i | \(-0.384668\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.07502 | + | 7.05815i | 1.05217 | + | 1.82241i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.28078 | − | 3.95042i | 0.553170 | − | 0.958118i | −0.444874 | − | 0.895593i | \(-0.646752\pi\) |
0.998043 | − | 0.0625245i | \(-0.0199152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.697500 | + | 4.30273i | 0.160017 | + | 0.987114i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.893341 | + | 1.54731i | 0.186275 | + | 0.322637i | 0.944005 | − | 0.329930i | \(-0.107025\pi\) |
−0.757731 | + | 0.652567i | \(0.773692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.780776 | − | 1.35234i | −0.156155 | − | 0.270469i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.1184 | −2.52464 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.84233 | − | 6.65511i | −0.713503 | − | 1.23582i | −0.963534 | − | 0.267585i | \(-0.913774\pi\) |
0.250032 | − | 0.968238i | \(-0.419559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.36337 | −1.14289 | −0.571447 | − | 0.820639i | \(-0.693618\pi\) | ||||
−0.571447 | + | 0.820639i | \(0.693618\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.90388 | + | 13.6899i | −1.37589 | + | 2.38311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.12311 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.5134 | −2.32401 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.500000 | + | 0.866025i | −0.0780869 | + | 0.135250i | −0.902424 | − | 0.430848i | \(-0.858214\pi\) |
0.824338 | + | 0.566099i | \(0.191548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28834 | − | 3.96352i | 0.348969 | − | 0.604432i | −0.637098 | − | 0.770783i | \(-0.719865\pi\) |
0.986067 | + | 0.166351i | \(0.0531986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.2462 | 2.71998 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.07502 | + | 7.05815i | 0.594403 | + | 1.02954i | 0.993631 | + | 0.112685i | \(0.0359451\pi\) |
−0.399227 | + | 0.916852i | \(0.630722\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.25671 | − | 12.5690i | −1.01614 | − | 1.76001i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.28078 | + | 3.95042i | 0.313289 | + | 0.542632i | 0.979072 | − | 0.203513i | \(-0.0652359\pi\) |
−0.665784 | + | 0.746145i | \(0.731903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.36337 | − | 11.0217i | 0.858036 | − | 1.48616i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.9654 | + | 4.92306i | 1.71731 | + | 0.652075i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.59084 | + | 2.75542i | −0.207110 | + | 0.358725i | −0.950803 | − | 0.309796i | \(-0.899739\pi\) |
0.743693 | + | 0.668521i | \(0.233072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.28078 | − | 5.68247i | −0.420060 | − | 0.727566i | 0.575885 | − | 0.817531i | \(-0.304658\pi\) |
−0.995945 | + | 0.0899651i | \(0.971324\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.6847 | 1.44930 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.98584 | − | 5.17163i | −0.364779 | − | 0.631815i | 0.623962 | − | 0.781455i | \(-0.285522\pi\) |
−0.988741 | + | 0.149640i | \(0.952189\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.68466 | 0.684352 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.893341 | + | 1.54731i | −0.106020 | + | 0.183632i | −0.914155 | − | 0.405366i | \(-0.867144\pi\) |
0.808134 | + | 0.588998i | \(0.200477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.62311 | − | 13.2036i | 0.892217 | − | 1.54537i | 0.0550055 | − | 0.998486i | \(-0.482482\pi\) |
0.837212 | − | 0.546879i | \(-0.184184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.96837 | −0.573697 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.07502 | − | 7.05815i | 0.458476 | − | 0.794104i | −0.540405 | − | 0.841405i | \(-0.681729\pi\) |
0.998881 | + | 0.0473015i | \(0.0150621\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1847 | + | 17.6403i | −1.13163 | + | 1.96004i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.39500 | −0.153121 | −0.0765606 | − | 0.997065i | \(-0.524394\pi\) | ||||
−0.0765606 | + | 0.997065i | \(0.524394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.84233 | + | 10.1192i | 0.633690 | + | 1.09758i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.4501 | −2.62133 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.842329 | − | 1.45896i | −0.0892867 | − | 0.154649i | 0.817923 | − | 0.575328i | \(-0.195125\pi\) |
−0.907210 | + | 0.420678i | \(0.861792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.1231 | + | 17.5337i | −1.04972 | + | 1.81816i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.4384 | − | 3.96352i | −1.07096 | − | 0.406649i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.62311 | − | 4.54335i | 0.266336 | − | 0.461308i | −0.701577 | − | 0.712594i | \(-0.747520\pi\) |
0.967913 | + | 0.251286i | \(0.0808536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.6951 | + | 30.6488i | 1.77842 | + | 3.08032i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.40388 | + | 4.16365i | 0.239195 | + | 0.414298i | 0.960484 | − | 0.278337i | \(-0.0897831\pi\) |
−0.721288 | + | 0.692635i | \(0.756450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5167 | 1.52891 | 0.764454 | − | 0.644678i | \(-0.223008\pi\) | ||||
0.764454 | + | 0.644678i | \(0.223008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7267 | 1.23034 | 0.615170 | − | 0.788395i | \(-0.289087\pi\) | ||||
0.615170 | + | 0.788395i | \(0.289087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.40388 | − | 7.62775i | 0.421815 | − | 0.730606i | −0.574302 | − | 0.818644i | \(-0.694726\pi\) |
0.996117 | + | 0.0880380i | \(0.0280597\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3317 | + | 19.6271i | −1.07556 | + | 1.86293i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.43845 | −0.229390 | −0.114695 | − | 0.993401i | \(-0.536589\pi\) | ||||
−0.114695 | + | 0.993401i | \(0.536589\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.57668 | −0.426778 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.2462 | + | 28.1393i | −1.50196 | + | 2.60148i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.6847 | 1.24406 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.59084 | + | 2.75542i | 0.143441 | + | 0.248448i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.80776 | −0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.04339 | − | 15.6636i | −0.802471 | − | 1.38992i | −0.917985 | − | 0.396615i | \(-0.870185\pi\) |
0.115514 | − | 0.993306i | \(-0.463148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.28078 | − | 12.6107i | −0.641037 | − | 1.11031i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1359 | + | 19.2879i | −0.972947 | + | 1.68519i | −0.286398 | + | 0.958111i | \(0.592458\pi\) |
−0.686549 | + | 0.727083i | \(0.740875\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.8018 | − | 29.1015i | 1.44606 | − | 2.50466i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | + | 6.06218i | 0.299025 | + | 0.517927i | 0.975913 | − | 0.218159i | \(-0.0700052\pi\) |
−0.676888 | + | 0.736086i | \(0.736672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.195842 | + | 0.339207i | 0.0166111 | + | 0.0287712i | 0.874211 | − | 0.485545i | \(-0.161379\pi\) |
−0.857600 | + | 0.514317i | \(0.828046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.9309 | 2.18377 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3317 | + | 19.6271i | 0.947607 | + | 1.64130i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.6847 | 1.63472 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1359 | + | 19.2879i | −0.918473 | + | 1.59084i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.96543 | − | 17.2606i | 0.816400 | − | 1.41405i | −0.0919179 | − | 0.995767i | \(-0.529300\pi\) |
0.908318 | − | 0.418280i | \(-0.137367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.93673 | −0.808640 | −0.404320 | − | 0.914618i | \(-0.632492\pi\) | ||||
−0.404320 | + | 0.914618i | \(0.632492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32.4924 | −2.62686 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.15005 | − | 14.1163i | 0.654628 | − | 1.13385i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.403882 | + | 0.699544i | −0.0322333 | + | 0.0558297i | −0.881692 | − | 0.471825i | \(-0.843595\pi\) |
0.849459 | + | 0.527655i | \(0.176929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.5134 | 1.15099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.96837 | 0.389152 | 0.194576 | − | 0.980887i | \(-0.437667\pi\) | ||||
0.194576 | + | 0.980887i | \(0.437667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.2462 | − | 35.0675i | −1.57617 | − | 2.73000i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.86502 | + | 11.8906i | 0.531232 | + | 0.920120i | 0.999336 | + | 0.0364466i | \(0.0116039\pi\) |
−0.468104 | + | 0.883673i | \(0.655063\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.90388 | + | 6.76172i | −0.300299 | + | 0.520132i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.0585 | − | 19.6271i | 1.83980 | − | 1.50092i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.40388 | − | 12.8239i | 0.562907 | − | 0.974983i | −0.434334 | − | 0.900752i | \(-0.643016\pi\) |
0.997241 | − | 0.0742313i | \(-0.0236503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.06155 | + | 8.76687i | 0.380450 | + | 0.658958i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.8418 | 1.85677 | 0.928383 | − | 0.371625i | \(-0.121199\pi\) | ||||
0.928383 | + | 0.371625i | \(0.121199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.96543 | − | 6.86833i | −0.294748 | − | 0.510519i | 0.680178 | − | 0.733047i | \(-0.261903\pi\) |
−0.974926 | + | 0.222528i | \(0.928569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.8768 | −1.54326 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.12311 | − | 15.8017i | 0.670744 | − | 1.16176i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3317 | + | 19.6271i | −0.828658 | + | 1.43528i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.58000 | −0.403755 | −0.201877 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201877 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.40388 | + | 9.35980i | −0.388980 | + | 0.673733i | −0.992313 | − | 0.123757i | \(-0.960506\pi\) |
0.603333 | + | 0.797490i | \(0.293839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.5884 | − | 32.1961i | 1.33115 | − | 2.30561i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.36932 | −0.382548 | −0.191274 | − | 0.981537i | \(-0.561262\pi\) | ||||
−0.191274 | + | 0.981537i | \(0.561262\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8301 | − | 18.7582i | −0.767724 | − | 1.32974i | −0.938795 | − | 0.344477i | \(-0.888056\pi\) |
0.171071 | − | 0.985259i | \(-0.445277\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.0000 | −1.34016 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.28078 | − | 2.21837i | −0.0894533 | − | 0.154938i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.36337 | − | 11.0217i | 0.442284 | − | 0.766059i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46543 | − | 21.3775i | −0.239709 | − | 1.47872i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.28834 | + | 3.96352i | −0.157536 | + | 0.272860i | −0.933980 | − | 0.357327i | \(-0.883688\pi\) |
0.776444 | + | 0.630187i | \(0.217022\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.84233 | + | 4.92306i | 0.194753 | + | 0.337322i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.86171 | + | 10.1528i | 0.399765 | + | 0.692413i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.2543 | − | 42.0097i | −1.63895 | − | 2.83875i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8078 | −1.39968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8301 | − | 18.7582i | 0.725235 | − | 1.25614i | −0.233642 | − | 0.972323i | \(-0.575064\pi\) |
0.958877 | − | 0.283822i | \(-0.0916024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.56155 | + | 9.63289i | −0.370770 | + | 0.642193i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9051 | 0.989286 | 0.494643 | − | 0.869096i | \(-0.335299\pi\) | ||||
0.494643 | + | 0.869096i | \(0.335299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.2462 | 1.73440 | 0.867199 | − | 0.497961i | \(-0.165918\pi\) | ||||
0.867199 | + | 0.497961i | \(0.165918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.06155 | + | 10.4989i | −0.397106 | + | 0.687807i | −0.993367 | − | 0.114983i | \(-0.963319\pi\) |
0.596262 | + | 0.802790i | \(0.296652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.8768 | −1.36185 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9654 | − | 22.4568i | −0.842195 | − | 1.45873i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7201 | 0.693425 | 0.346713 | − | 0.937971i | \(-0.387298\pi\) | ||||
0.346713 | + | 0.937971i | \(0.387298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.74621 | − | 11.6848i | −0.434562 | − | 0.752683i | 0.562698 | − | 0.826662i | \(-0.309763\pi\) |
−0.997260 | + | 0.0739796i | \(0.976430\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7267 | + | 22.0433i | 0.816420 | + | 1.41408i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.96543 | − | 15.5286i | 0.572781 | − | 0.992085i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.4068 | − | 12.5690i | 0.980308 | − | 0.799745i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.21922 | + | 3.84381i | −0.140638 | + | 0.243591i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.98252 | − | 3.43383i | −0.125136 | − | 0.216742i | 0.796650 | − | 0.604441i | \(-0.206603\pi\) |
−0.921786 | + | 0.387699i | \(0.873270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.43845 | − | 7.68762i | −0.279043 | − | 0.483316i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.1769 | 2.32811 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.62311 | − | 4.54335i | −0.163625 | − | 0.283407i | 0.772541 | − | 0.634965i | \(-0.218985\pi\) |
−0.936166 | + | 0.351558i | \(0.885652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.3693 | + | 47.4050i | −1.69412 | + | 2.93430i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.86502 | + | 11.8906i | −0.423316 | + | 0.733204i | −0.996261 | − | 0.0863892i | \(-0.972467\pi\) |
0.572946 | + | 0.819593i | \(0.305800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6847 | −0.717783 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.36005 | −0.328030 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.71922 | + | 11.6380i | −0.409678 | + | 0.709584i | −0.994854 | − | 0.101323i | \(-0.967692\pi\) |
0.585175 | + | 0.810907i | \(0.301026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.07502 | + | 7.05815i | −0.247540 | + | 0.428752i | −0.962843 | − | 0.270063i | \(-0.912956\pi\) |
0.715303 | + | 0.698815i | \(0.246289\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.87918 | + | 6.71894i | 0.233924 | + | 0.405167i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.6635 | + | 39.2543i | 1.35683 | + | 2.35009i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5000 | − | 19.9186i | −0.686032 | − | 1.18824i | −0.973111 | − | 0.230336i | \(-0.926017\pi\) |
0.287079 | − | 0.957907i | \(-0.407316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.1359 | + | 19.2879i | −0.661960 | + | 1.14655i | 0.318140 | + | 0.948044i | \(0.396942\pi\) |
−0.980100 | + | 0.198505i | \(0.936392\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.5270 | + | 22.4568i | −1.63056 | + | 1.33023i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.90388 | − | 3.29762i | −0.111993 | − | 0.193978i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.34589 | − | 14.4555i | −0.489245 | − | 0.847397i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.07502 | − | 7.05815i | −0.237257 | − | 0.410941i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 65.1771 | 3.78196 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.07502 | − | 7.05815i | 0.235665 | − | 0.408183i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.2968 | 0.878777 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8078 | 0.962410 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.16752 | − | 10.6825i | 0.351999 | − | 0.609680i | −0.634600 | − | 0.772840i | \(-0.718835\pi\) |
0.986600 | + | 0.163160i | \(0.0521686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.6847 | − | 42.7551i | 1.40426 | − | 2.43225i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8168 | −1.80417 | −0.902083 | − | 0.431562i | \(-0.857963\pi\) | ||||
−0.902083 | + | 0.431562i | \(0.857963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.62311 | + | 4.54335i | 0.148267 | + | 0.256805i | 0.930587 | − | 0.366071i | \(-0.119297\pi\) |
−0.782320 | + | 0.622876i | \(0.785964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.08854 | + | 12.2777i | 0.398132 | + | 0.689585i | 0.993495 | − | 0.113872i | \(-0.0363252\pi\) |
−0.595363 | + | 0.803457i | \(0.702992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0901 | + | 33.0650i | 1.06884 | + | 1.85129i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2462 | − | 35.0675i | 1.13003 | − | 1.95728i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5884 | + | 7.05815i | 1.03429 | + | 0.392726i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.56155 | + | 6.16879i | −0.197559 | + | 0.342183i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0118 | − | 24.2691i | −0.774852 | − | 1.34208i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5484 | 0.579791 | 0.289895 | − | 0.957058i | \(-0.406380\pi\) | ||||
0.289895 | + | 0.957058i | \(0.406380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.3693 | + | 43.9409i | 1.39023 | + | 2.40795i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.2968 | 0.835752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06155 | − | 1.83866i | 0.0578265 | − | 0.100158i | −0.835663 | − | 0.549243i | \(-0.814916\pi\) |
0.893489 | + | 0.449084i | \(0.148250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.87918 | + | 6.71894i | −0.210688 | + | 0.364923i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.6155 | 1.71208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.28078 | + | 12.6107i | −0.391984 | + | 0.678936i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.1359 | − | 19.2879i | 0.597806 | − | 1.03543i | −0.395338 | − | 0.918536i | \(-0.629373\pi\) |
0.993144 | − | 0.116895i | \(-0.0372940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.9202 | + | 51.8233i | 1.59702 | + | 2.76612i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.19224 | −0.223130 | −0.111565 | − | 0.993757i | \(-0.535586\pi\) | ||||
−0.111565 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.28834 | − | 3.96352i | −0.121453 | − | 0.210362i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.893341 | − | 1.54731i | 0.0471488 | − | 0.0816640i | −0.841488 | − | 0.540276i | \(-0.818320\pi\) |
0.888637 | + | 0.458612i | \(0.151653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0270 | + | 6.00231i | −0.948789 | + | 0.315911i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.7701 | − | 37.7070i | 1.14264 | − | 1.97910i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.5270 | + | 33.8217i | 1.02209 | + | 1.77031i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8301 | − | 18.7582i | −0.565325 | − | 0.979172i | −0.997019 | − | 0.0771519i | \(-0.975417\pi\) |
0.431694 | − | 0.902020i | \(-0.357916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.12311 | 0.370814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6155 | 0.704985 | 0.352493 | − | 0.935815i | \(-0.385334\pi\) | ||||
0.352493 | + | 0.935815i | \(0.385334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.0118 | + | 24.2691i | −0.723564 | + | 1.25325i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.5270 | + | 30.3576i | −0.902686 | + | 1.56350i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.6002 | −1.67456 | −0.837280 | − | 0.546775i | \(-0.815855\pi\) | ||||
−0.837280 | + | 0.546775i | \(0.815855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −57.5464 | −2.94819 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.86171 | + | 10.1528i | −0.299519 | + | 0.518783i | −0.976026 | − | 0.217654i | \(-0.930160\pi\) |
0.676507 | + | 0.736436i | \(0.263493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.6002 | −1.65716 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6501 | − | 21.9106i | −0.641385 | − | 1.11091i | −0.985124 | − | 0.171846i | \(-0.945027\pi\) |
0.343739 | − | 0.939065i | \(-0.388307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.15005 | 0.412166 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.4309 | + | 61.3681i | 1.78725 | + | 3.09561i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.4384 | + | 18.0798i | 0.525212 | + | 0.909695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7192 | + | 20.2983i | −0.588171 | + | 1.01874i | 0.406301 | + | 0.913739i | \(0.366818\pi\) |
−0.994472 | + | 0.105003i | \(0.966515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.50000 | + | 14.7224i | −0.424470 | + | 0.735203i | −0.996371 | − | 0.0851195i | \(-0.972873\pi\) |
0.571901 | + | 0.820323i | \(0.306206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5134 | + | 25.1380i | 0.722965 | + | 1.25221i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.0885 | − | 45.1867i | −1.29635 | − | 2.24534i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.3902 | 1.75423 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.3078 | − | 19.5856i | −0.559133 | − | 0.968447i | −0.997569 | − | 0.0696843i | \(-0.977801\pi\) |
0.438436 | − | 0.898762i | \(-0.355533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.2718 | 1.09859 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.78668 | − | 3.09463i | 0.0877048 | − | 0.151909i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.24621 | 0.0610272 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.3067 | −0.894342 | −0.447171 | − | 0.894448i | \(-0.647569\pi\) | ||||
−0.447171 | + | 0.894448i | \(0.647569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.52699 | − | 4.37687i | 0.123158 | − | 0.213316i | −0.797854 | − | 0.602851i | \(-0.794031\pi\) |
0.921011 | + | 0.389536i | \(0.127365\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0268 | − | 50.2759i | 1.41133 | − | 2.44450i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.12311 | −0.345521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 72.1080 | 3.48140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.89666 | − | 3.28511i | −0.0913588 | − | 0.158238i | 0.816724 | − | 0.577028i | \(-0.195788\pi\) |
−0.908083 | + | 0.418790i | \(0.862454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.08854 | + | 12.2777i | 0.340654 | + | 0.590029i | 0.984554 | − | 0.175080i | \(-0.0560184\pi\) |
−0.643901 | + | 0.765109i | \(0.722685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.3152 | − | 54.2395i | 1.50145 | − | 2.60058i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.03457 | + | 4.92306i | −0.288672 | + | 0.235502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.893341 | + | 1.54731i | −0.0426369 | + | 0.0738492i | −0.886556 | − | 0.462621i | \(-0.846909\pi\) |
0.843919 | + | 0.536470i | \(0.180243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 24.9309 | + | 43.1815i | 1.18718 | + | 2.05626i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.77252 | − | 8.26625i | −0.226749 | − | 0.392742i | 0.730093 | − | 0.683347i | \(-0.239477\pi\) |
−0.956843 | + | 0.290606i | \(0.906143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.31534 | 0.204567 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.7069 | − | 54.9179i | −1.49968 | − | 2.59753i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.19224 | 0.197844 | 0.0989219 | − | 0.995095i | \(-0.468461\pi\) | ||||
0.0989219 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.48418 | − | 4.30273i | 0.116976 | − | 0.202608i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.8078 | + | 27.3799i | −0.742714 | + | 1.28642i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.4384 | −1.33029 | −0.665147 | − | 0.746712i | \(-0.731631\pi\) | ||||
−0.665147 | + | 0.746712i | \(0.731631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.9202 | + | 51.8233i | −1.39655 | + | 2.41890i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7192 | − | 20.2983i | 0.545819 | − | 0.945386i | −0.452736 | − | 0.891644i | \(-0.649552\pi\) |
0.998555 | − | 0.0537412i | \(-0.0171146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.5101 | −0.627867 | −0.313934 | − | 0.949445i | \(-0.601647\pi\) | ||||
−0.313934 | + | 0.949445i | \(0.601647\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.9309 | − | 44.9136i | −1.20252 | − | 2.08282i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.4851 | −0.947937 | −0.473969 | − | 0.880542i | \(-0.657179\pi\) | ||||
−0.473969 | + | 0.880542i | \(0.657179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.28502 | + | 2.22573i | 0.0592108 | + | 0.102556i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.3693 | + | 19.6922i | −0.522762 | + | 0.905450i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.27418 | − | 4.30273i | 0.241996 | − | 0.197423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.2462 | − | 28.1393i | 0.743863 | − | 1.28841i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8018 | + | 29.1015i | 0.767692 | + | 1.32968i | 0.938812 | + | 0.344431i | \(0.111928\pi\) |
−0.171120 | + | 0.985250i | \(0.554739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2462 | + | 28.1393i | 0.740763 | + | 1.28304i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.71922 | + | 11.6380i | 0.305104 | + | 0.528456i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.35673 | −0.197422 | −0.0987112 | − | 0.995116i | \(-0.531472\pi\) | ||||
−0.0987112 | + | 0.995116i | \(0.531472\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.90388 | − | 13.6899i | 0.357426 | − | 0.619080i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.07834 | + | 8.79594i | −0.229182 | + | 0.396955i | −0.957566 | − | 0.288214i | \(-0.906939\pi\) |
0.728384 | + | 0.685169i | \(0.240272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.0540 | −1.57875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −90.6539 | −4.07459 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5276 | + | 19.9663i | −0.516045 | + | 0.893816i | 0.483781 | + | 0.875189i | \(0.339263\pi\) |
−0.999826 | + | 0.0186274i | \(0.994070\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.6847 | 1.95169 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.89666 | − | 3.28511i | −0.0845678 | − | 0.146476i | 0.820639 | − | 0.571447i | \(-0.193618\pi\) |
−0.905207 | + | 0.424971i | \(0.860284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.3153 | −0.548026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.4209 | + | 21.5137i | 0.551632 | + | 0.955455i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.9654 | − | 25.9209i | −0.663331 | − | 1.14892i | −0.979735 | − | 0.200299i | \(-0.935809\pi\) |
0.316404 | − | 0.948625i | \(-0.397525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.15009 | − | 56.4450i | −0.403986 | − | 2.49211i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.8735 | + | 34.4218i | −0.875729 | + | 1.51681i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.2462 | − | 35.0675i | −0.890427 | − | 1.54227i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.5568 | − | 40.8016i | −1.03403 | − | 1.79099i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.4233 | −1.46430 | −0.732151 | − | 0.681143i | \(-0.761483\pi\) | ||||
−0.732151 | + | 0.681143i | \(0.761483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.86171 | + | 10.1528i | 0.256315 | + | 0.443950i | 0.965252 | − | 0.261322i | \(-0.0841584\pi\) |
−0.708937 | + | 0.705272i | \(0.750825\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.5134 | + | 25.1380i | −0.632214 | + | 1.09503i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.90388 | − | 17.1540i | 0.430604 | − | 0.745827i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.6635 | 0.983511 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.56155 | 0.197583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.3001 | + | 28.2326i | −0.704715 | + | 1.22060i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.5194 | − | 68.4496i | 1.70539 | − | 2.95382i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.7786 | 1.49802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6501 | + | 21.9106i | 0.543870 | + | 0.942010i | 0.998677 | + | 0.0514205i | \(0.0163749\pi\) |
−0.454807 | + | 0.890590i | \(0.650292\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.2335 | −1.08287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2808 | + | 19.5389i | 0.483215 | + | 0.836954i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.86171 | − | 10.1528i | −0.250629 | − | 0.434101i | 0.713071 | − | 0.701092i | \(-0.247304\pi\) |
−0.963699 | + | 0.266991i | \(0.913971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.3693 | + | 40.4768i | −0.997378 | + | 1.72751i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.9551 | − | 21.1744i | 1.10573 | − | 0.902062i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −29.0268 | − | 50.2759i | −1.23212 | − | 2.13409i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.28078 | − | 12.6107i | −0.308496 | − | 0.534331i | 0.669537 | − | 0.742778i | \(-0.266492\pi\) |
−0.978034 | + | 0.208447i | \(0.933159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.8768 | −0.882994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0540 | + | 62.4473i | 1.52220 | + | 2.63653i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.0018 | −1.51730 | −0.758648 | − | 0.651501i | \(-0.774140\pi\) | ||||
−0.758648 | + | 0.651501i | \(0.774140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.12311 | − | 5.40938i | 0.131390 | − | 0.227574i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.3693 | 1.06354 | 0.531769 | − | 0.846890i | \(-0.321528\pi\) | ||||
0.531769 | + | 0.846890i | \(0.321528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4851 | −0.857275 | −0.428637 | − | 0.903477i | \(-0.641006\pi\) | ||||
−0.428637 | + | 0.903477i | \(0.641006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.87689 | + | 15.3752i | −0.370838 | + | 0.642310i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.39500 | − | 2.41621i | 0.0581755 | − | 0.100763i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1771 | −0.881613 | −0.440807 | − | 0.897602i | \(-0.645308\pi\) | ||||
−0.440807 | + | 0.897602i | \(0.645308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.1934 | + | 29.7799i | 0.714535 | + | 1.23761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3317 | − | 19.6271i | −0.469312 | − | 0.812873i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −41.6155 | − | 72.0802i | −1.72059 | − | 2.98015i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.1618 | + | 38.3854i | −0.914716 | + | 1.58433i | −0.107398 | + | 0.994216i | \(0.534252\pi\) |
−0.807317 | + | 0.590118i | \(0.799081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.43845 | − | 27.3799i | −0.182883 | − | 1.12817i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.54173 | + | 14.7947i | −0.351360 | + | 0.608573i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.18466 | − | 2.05189i | −0.0486481 | − | 0.0842610i | 0.840676 | − | 0.541538i | \(-0.182158\pi\) |
−0.889324 | + | 0.457278i | \(0.848825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −68.9157 | −2.82053 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.8334 | − | 20.4960i | −0.483499 | − | 0.837445i | 0.516321 | − | 0.856395i | \(-0.327301\pi\) |
−0.999820 | + | 0.0189498i | \(0.993968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.4233 | −0.792293 | −0.396146 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396146 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.2685 | + | 36.8381i | −0.866119 | + | 1.50016i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.5270 | + | 30.3576i | −0.712573 | + | 1.23421i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2935 | −0.580154 | −0.290077 | − | 0.957003i | \(-0.593681\pi\) | ||||
−0.290077 | + | 0.957003i | \(0.593681\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5884 | − | 32.1961i | 0.752008 | − | 1.30252i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5961 | − | 21.8171i | 0.508752 | − | 0.881185i | −0.491196 | − | 0.871049i | \(-0.663440\pi\) |
0.999949 | − | 0.0101361i | \(-0.00322647\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.15005 | −0.328642 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.81534 | − | 6.60837i | −0.153600 | − | 0.266043i | 0.778948 | − | 0.627088i | \(-0.215753\pi\) |
−0.932548 | + | 0.361045i | \(0.882420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.14673 | 0.287251 | 0.143626 | − | 0.989632i | \(-0.454124\pi\) | ||||
0.143626 | + | 0.989632i | \(0.454124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7192 | − | 20.2983i | −0.470276 | − | 0.814542i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1847 | − | 26.3006i | 0.607386 | − | 1.05202i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −64.4170 | − | 24.4596i | −2.57257 | − | 0.976821i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.2462 | + | 28.1393i | −0.647779 | + | 1.12199i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0118 | + | 24.2691i | 0.557799 | + | 0.966137i | 0.997680 | + | 0.0680803i | \(0.0216874\pi\) |
−0.439881 | + | 0.898056i | \(0.644979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.28078 | + | 12.6107i | 0.289385 | + | 0.501229i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.3302 | 1.83856 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9654 | + | 27.6529i | 0.632574 | + | 1.09565i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7267 | 0.503462 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.18466 | − | 8.98009i | 0.204782 | − | 0.354692i | −0.745281 | − | 0.666750i | \(-0.767685\pi\) |
0.950063 | + | 0.312058i | \(0.101018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.1043 | − | 27.8934i | 0.635090 | − | 1.10001i | −0.351406 | − | 0.936223i | \(-0.614296\pi\) |
0.986496 | − | 0.163785i | \(-0.0523703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.3002 | 1.46869 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9702 | 1.61070 | 0.805352 | − | 0.592797i | \(-0.201976\pi\) | ||||
0.805352 | + | 0.592797i | \(0.201976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.90388 | − | 13.6899i | 0.310255 | − | 0.537377i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.50758 | 0.293794 | 0.146897 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146897 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.5252 | − | 49.4070i | −1.11457 | − | 1.93049i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −108.600 | −4.23690 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.86171 | + | 10.1528i | 0.228340 | + | 0.395496i | 0.957316 | − | 0.289043i | \(-0.0933370\pi\) |
−0.728976 | + | 0.684539i | \(0.760004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6501 | + | 42.6952i | 0.958778 | + | 1.66065i | 0.725477 | + | 0.688247i | \(0.241619\pi\) |
0.233301 | + | 0.972405i | \(0.425047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.1019 | + | 57.3341i | −1.28557 | + | 2.22667i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.86502 | − | 11.8906i | 0.265815 | − | 0.460405i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.4579 | − | 59.6828i | −1.33222 | − | 2.30747i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.3001 | + | 28.2326i | 0.629258 | + | 1.08991i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6155 | 0.601934 | 0.300967 | − | 0.953634i | \(-0.402691\pi\) | ||||
0.300967 | + | 0.953634i | \(0.402691\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2425 | + | 17.7406i | 0.394236 | + | 0.682837i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.12311 | 0.273763 | 0.136882 | − | 0.990587i | \(-0.456292\pi\) | ||||
0.136882 | + | 0.990587i | \(0.456292\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.7116 | − | 41.0698i | 0.908632 | − | 1.57380i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.4468 | 0.897168 | 0.448584 | − | 0.893741i | \(-0.351928\pi\) | ||||
0.448584 | + | 0.893741i | \(0.351928\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9309 | −0.685103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.7536 | − | 72.3193i | 1.59300 | − | 2.75915i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.4039 | − | 18.0201i | 0.396356 | − | 0.686509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.7602 | 1.66472 | 0.832358 | − | 0.554238i | \(-0.186990\pi\) | ||||
0.832358 | + | 0.554238i | \(0.186990\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.00332 | −0.0380580 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.28078 | + | 3.95042i | 0.0863906 | + | 0.149633i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.2859 | + | 33.4042i | 0.729461 | + | 1.26346i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7192 | + | 18.5662i | −0.404859 | + | 0.701237i | −0.994305 | − | 0.106571i | \(-0.966013\pi\) |
0.589446 | + | 0.807808i | \(0.299346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.96837 | − | 30.6488i | −0.187385 | − | 1.15594i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.2116 | + | 57.5243i | −1.25082 | + | 2.16649i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.59612 | − | 4.49661i | −0.0974993 | − | 0.168874i | 0.813150 | − | 0.582055i | \(-0.197751\pi\) |
−0.910649 | + | 0.413181i | \(0.864418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −58.0537 | −2.17718 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.68466 | − | 9.84612i | −0.212892 | − | 0.368740i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58.0537 | −2.17108 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.0540 | − | 29.5384i | 0.636892 | − | 1.10313i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.25339 | + | 10.8312i | −0.233212 | + | 0.403935i | −0.958752 | − | 0.284245i | \(-0.908257\pi\) |
0.725539 | + | 0.688181i | \(0.241590\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.9286 | −1.59653 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.28502 | + | 2.22573i | −0.0476589 | + | 0.0825477i | −0.888871 | − | 0.458158i | \(-0.848509\pi\) |
0.841212 | + | 0.540706i | \(0.181843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.8769 | 0.736181 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4384 | − | 18.0798i | −0.386078 | − | 0.668706i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.3693 | −0.789294 | −0.394647 | − | 0.918833i | \(-0.629133\pi\) | ||||
−0.394647 | + | 0.918833i | \(0.629133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.5252 | − | 49.4070i | −1.05217 | − | 1.82241i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.8348 | + | 25.6945i | 0.546445 | + | 0.946471i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1359 | − | 19.2879i | 0.409640 | − | 0.709518i | −0.585209 | − | 0.810882i | \(-0.698988\pi\) |
0.994849 | + | 0.101365i | \(0.0323209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1231 | − | 62.4473i | −0.371882 | − | 2.29406i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.89666 | + | 3.28511i | −0.0695816 | + | 0.120519i | −0.898717 | − | 0.438529i | \(-0.855500\pi\) |
0.829136 | + | 0.559048i | \(0.188833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.5270 | + | 44.2140i | 0.935236 | + | 1.61988i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.96837 | + | 8.60546i | 0.181783 | + | 0.314857i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.04007 | + | 13.9258i | 0.293386 | + | 0.508160i | 0.974608 | − | 0.223917i | \(-0.0718844\pi\) |
−0.681222 | + | 0.732077i | \(0.738551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.6155 | −0.459735 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.7267 | − | 22.0433i | 0.463173 | − | 0.802239i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8423 | + | 18.7795i | −0.394071 | + | 0.682551i | −0.992982 | − | 0.118264i | \(-0.962267\pi\) |
0.598911 | + | 0.800816i | \(0.295600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.2435 | −1.02517 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.93087 | 0.251244 | 0.125622 | − | 0.992078i | \(-0.459907\pi\) | ||||
0.125622 | + | 0.992078i | \(0.459907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.6155 | − | 72.0802i | 1.50461 | − | 2.60607i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.5134 | 0.524049 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.842329 | + | 1.45896i | 0.0303752 | + | 0.0526113i | 0.880813 | − | 0.473464i | \(-0.156996\pi\) |
−0.850438 | + | 0.526075i | \(0.823663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.6918 | −0.601140 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.15767 | − | 14.1295i | −0.293411 | − | 0.508203i | 0.681203 | − | 0.732095i | \(-0.261457\pi\) |
−0.974614 | + | 0.223892i | \(0.928124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.96837 | + | 8.60546i | 0.178469 | + | 0.309117i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.07502 | − | 1.54731i | −0.146003 | − | 0.0554382i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.43845 | − | 7.68762i | 0.158820 | − | 0.275085i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.4053 | + | 87.3045i | 1.80134 | + | 3.12001i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.03457 | − | 1.79192i | −0.0369252 | − | 0.0639563i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5484 | 0.376009 | 0.188004 | − | 0.982168i | \(-0.439798\pi\) | ||||
0.188004 | + | 0.982168i | \(0.439798\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.8423 | + | 37.8320i | 0.777608 | + | 1.34686i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.9654 | + | 25.9209i | −0.531438 | + | 0.920478i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.5884 | + | 32.1961i | −0.659264 | + | 1.14188i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.3693 | 1.32369 | 0.661845 | − | 0.749641i | \(-0.269774\pi\) | ||||
0.661845 | + | 0.749641i | \(0.269774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.1769 | 1.31522 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | + | 10.3923i | −0.212000 | + | 0.367194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.8744 | + | 65.6003i | −1.33656 | + | 2.31499i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.3784 | + | 37.0285i | 0.752557 | + | 1.30347i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.17708 | 0.182016 | 0.0910082 | − | 0.995850i | \(-0.470991\pi\) | ||||
0.0910082 | + | 0.995850i | \(0.470991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.50498 | + | 2.60669i | 0.0528468 | + | 0.0915334i | 0.891239 | − | 0.453535i | \(-0.149837\pi\) |
−0.838392 | + | 0.545068i | \(0.816504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9654 | + | 22.4568i | 0.454718 | + | 0.787594i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.36337 | + | 11.0217i | −0.222899 | + | 0.386072i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.6501 | + | 7.08156i | 0.652484 | + | 0.247752i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.2116 | + | 38.4717i | 0.775192 | + | 1.34267i | 0.934687 | + | 0.355473i | \(0.115680\pi\) |
−0.159495 | + | 0.987199i | \(0.550987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1901 | + | 28.0421i | 0.564352 | + | 0.977487i | 0.997110 | + | 0.0759762i | \(0.0242073\pi\) |
−0.432757 | + | 0.901510i | \(0.642459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.6847 | 0.859409 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.95421 | + | 13.7771i | 0.276595 | + | 0.479076i | 0.970536 | − | 0.240955i | \(-0.0774607\pi\) |
−0.693941 | + | 0.720032i | \(0.744127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.8769 | 0.794547 | 0.397274 | − | 0.917700i | \(-0.369956\pi\) | ||||
0.397274 | + | 0.917700i | \(0.369956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.36337 | − | 11.0217i | 0.220743 | − | 0.382338i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.9654 | + | 27.6529i | −0.553170 | + | 0.958118i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.1702 | −1.21712 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 83.4773 | 2.88540 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.0084 | − | 22.5313i | 0.449101 | − | 0.777866i | −0.549227 | − | 0.835673i | \(-0.685078\pi\) |
0.998328 | + | 0.0578074i | \(0.0184109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0270 | + | 26.0275i | −0.518172 | + | 0.897500i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −73.1787 | −2.52041 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0000 | − | 17.3205i | −0.344010 | − | 0.595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.4309 | + | 61.3681i | 1.21598 | + | 2.10615i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.36337 | − | 11.0217i | −0.218133 | − | 0.377818i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.280776 | − | 0.486319i | 0.00961360 | − | 0.0166512i | −0.861179 | − | 0.508303i | \(-0.830273\pi\) |
0.870792 | + | 0.491651i | \(0.163607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.7267 | + | 78.5085i | 0.435245 | + | 2.68494i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.1847 | − | 22.8365i | 0.450379 | − | 0.780080i | −0.548030 | − | 0.836459i | \(-0.684622\pi\) |
0.998409 | + | 0.0563787i | \(0.0179554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.16089 | + | 7.20687i | 0.141968 | + | 0.245895i | 0.928238 | − | 0.371988i | \(-0.121324\pi\) |
−0.786270 | + | 0.617883i | \(0.787990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.6701 | −0.839780 | −0.419890 | − | 0.907575i | \(-0.637931\pi\) | ||||
−0.419890 | + | 0.907575i | \(0.637931\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9654 | + | 32.8491i | 0.644844 | + | 1.11690i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.1151 | −0.411450 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.2462 | + | 35.0675i | −0.686806 | + | 1.18958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.6201 | + | 23.5907i | −0.461499 | + | 0.799339i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.3693 | −1.26476 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.8423 | + | 44.7602i | −0.872633 | + | 1.51145i | −0.0133709 | + | 0.999911i | \(0.504256\pi\) |
−0.859263 | + | 0.511535i | \(0.829077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.36337 | − | 11.0217i | 0.214631 | − | 0.371752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0540 | 0.877781 | 0.438890 | − | 0.898541i | \(-0.355372\pi\) | ||||
0.438890 | + | 0.898541i | \(0.355372\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9193 | − | 20.6448i | −0.401115 | − | 0.694751i | 0.592746 | − | 0.805390i | \(-0.298044\pi\) |
−0.993861 | + | 0.110638i | \(0.964711\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.9309 | −0.871657 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.86171 | − | 10.1528i | −0.196817 | − | 0.340897i | 0.750678 | − | 0.660669i | \(-0.229727\pi\) |
−0.947495 | + | 0.319772i | \(0.896394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.6011 | − | 87.6437i | 1.69520 | − | 2.93617i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.5270 | + | 22.4568i | −0.921156 | + | 0.751488i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.8168 | + | 55.1084i | −1.06352 | + | 1.84207i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.9654 | − | 22.4568i | −0.432903 | − | 0.749810i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.4501 | + | 42.3489i | 0.815458 | + | 1.41241i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.8078 | 0.693207 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.3153 | 0.675305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.8310 | − | 49.9367i | 0.957317 | − | 1.65812i | 0.228343 | − | 0.973581i | \(-0.426669\pi\) |
0.728974 | − | 0.684541i | \(-0.239997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.1231 | − | 29.6581i | 0.567938 | − | 0.983697i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.2637 | 1.83097 | 0.915483 | − | 0.402356i | \(-0.131809\pi\) | ||||
0.915483 | + | 0.402356i | \(0.131809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.93087 | 0.229378 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.7385 | − | 46.3124i | 0.883947 | − | 1.53104i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.22327 | −0.0403519 | −0.0201759 | − | 0.999796i | \(-0.506423\pi\) | ||||
−0.0201759 | + | 0.999796i | \(0.506423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.6231 | − | 33.9882i | −0.646603 | − | 1.11995i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.15005 | 0.268262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.56155 | + | 9.63289i | 0.182863 | + | 0.316728i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55.2637 | − | 95.7195i | −1.81510 | − | 3.14384i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.93845 | + | 3.35749i | −0.0635984 | + | 0.110156i | −0.896071 | − | 0.443910i | \(-0.853591\pi\) |
0.832473 | + | 0.554066i | \(0.186924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.88250 | − | 30.1191i | −0.160017 | − | 0.987114i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.6155 | + | 87.6687i | −1.65708 | + | 2.87014i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.0268 | − | 50.2759i | −0.949279 | − | 1.64420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.9924 | − | 20.7715i | −0.391775 | − | 0.678575i | 0.600908 | − | 0.799318i | \(-0.294806\pi\) |
−0.992684 | + | 0.120743i | \(0.961472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.6918 | 0.544716 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.71922 | − | 2.97778i | −0.0560451 | − | 0.0970729i | 0.836642 | − | 0.547751i | \(-0.184516\pi\) |
−0.892687 | + | 0.450678i | \(0.851182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.78668 | −0.0581824 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.85839 | + | 8.41498i | −0.157876 | + | 0.273450i | −0.934103 | − | 0.357004i | \(-0.883798\pi\) |
0.776226 | + | 0.630454i | \(0.217131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −69.5464 | −2.25757 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.1070 | 1.46269 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.69224 | + | 13.3233i | −0.249176 | + | 0.431585i | −0.963297 | − | 0.268436i | \(-0.913493\pi\) |
0.714121 | + | 0.700022i | \(0.246826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.14673 | − | 12.3785i | 0.231263 | − | 0.400559i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 121.477 | 3.92680 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.49242 | 0.306207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.3269 | − | 78.5085i | −1.46064 | − | 2.52990i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.8423 | − | 23.9756i | −0.445600 | − | 0.771802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.4101 | + | 28.4231i | −0.527712 | + | 0.914025i | 0.471766 | + | 0.881724i | \(0.343617\pi\) |
−0.999478 | + | 0.0323007i | \(0.989717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.0194 | − | 39.9905i | 1.57473 | − | 1.28468i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0410 | − | 45.1043i | 0.835695 | − | 1.44747i | −0.0577682 | − | 0.998330i | \(-0.518398\pi\) |
0.893463 | − | 0.449136i | \(-0.148268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.3317 | + | 19.6271i | 0.362906 | + | 0.628571i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.3002 | −0.521489 | −0.260745 | − | 0.965408i | \(-0.583968\pi\) | ||||
−0.260745 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.18500 | + | 7.24863i | 0.133753 | + | 0.231667i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −62.7386 | −2.00309 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4417 | + | 19.8176i | −0.364934 | + | 0.632084i | −0.988766 | − | 0.149475i | \(-0.952242\pi\) |
0.623832 | + | 0.781559i | \(0.285575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.87689 | − | 11.9111i | 0.219116 | − | 0.379520i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.17708 | 0.260016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5918 | − | 33.9339i | 0.622353 | − | 1.07795i | −0.366694 | − | 0.930342i | \(-0.619510\pi\) |
0.989046 | − | 0.147605i | \(-0.0471563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7808 | − | 29.0652i | 0.532522 | − | 0.922355i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.4836 | 1.75895 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.96543 | + | 5.13628i | 0.0939163 | + | 0.162668i | 0.909156 | − | 0.416456i | \(-0.136728\pi\) |
−0.815240 | + | 0.579124i | \(0.803395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 93.4439 | 2.95643 |
(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 | 1216.2.i.p.961.4 | 8 | ||
4.3 | odd | 2 | inner | 1216.2.i.p.961.1 | 8 | ||
8.3 | odd | 2 | 608.2.i.d.353.4 | yes | 8 | ||
8.5 | even | 2 | 608.2.i.d.353.1 | ✓ | 8 | ||
19.7 | even | 3 | inner | 1216.2.i.p.577.4 | 8 | ||
76.7 | odd | 6 | inner | 1216.2.i.p.577.1 | 8 | ||
152.45 | even | 6 | 608.2.i.d.577.1 | yes | 8 | ||
152.83 | odd | 6 | 608.2.i.d.577.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.d.353.1 | ✓ | 8 | 8.5 | even | 2 | ||
608.2.i.d.353.4 | yes | 8 | 8.3 | odd | 2 | ||
608.2.i.d.577.1 | yes | 8 | 152.45 | even | 6 | ||
608.2.i.d.577.4 | yes | 8 | 152.83 | odd | 6 | ||
1216.2.i.p.577.1 | 8 | 76.7 | odd | 6 | inner | ||
1216.2.i.p.577.4 | 8 | 19.7 | even | 3 | inner | ||
1216.2.i.p.961.1 | 8 | 4.3 | odd | 2 | inner | ||
1216.2.i.p.961.4 | 8 | 1.1 | even | 1 | trivial |