Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(80,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.80");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.bd (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.80274911095\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Root | \(-0.561693 + 0.561693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 351.215 |
Dual form | 351.2.bd.e.80.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.205594 | + | 0.767287i | 0.145377 | + | 0.542554i | 0.999738 | + | 0.0228747i | \(0.00728189\pi\) |
−0.854361 | + | 0.519679i | \(0.826051\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.18559 | − | 0.684501i | 0.592795 | − | 0.342250i | ||||
\(5\) | −2.75236 | + | 2.75236i | −1.23089 | + | 1.23089i | −0.267274 | + | 0.963620i | \(0.586123\pi\) |
−0.963620 | + | 0.267274i | \(0.913877\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.54508 | + | 0.414002i | 0.583984 | + | 0.156478i | 0.538702 | − | 0.842496i | \(-0.318915\pi\) |
0.0452816 | + | 0.998974i | \(0.485581\pi\) | |||||||
\(8\) | 1.89235 | + | 1.89235i | 0.669045 | + | 0.669045i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.67772 | − | 1.54598i | −0.846771 | − | 0.488883i | ||||
\(11\) | 1.42638 | − | 0.382196i | 0.430069 | − | 0.115237i | −0.0372897 | − | 0.999304i | \(-0.511872\pi\) |
0.467358 | + | 0.884068i | \(0.345206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55939 | + | 3.25089i | −0.432497 | + | 0.901635i | ||||
\(14\) | 1.27063i | 0.339591i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.306084 | − | 0.530153i | 0.0765210 | − | 0.132538i | ||||
\(17\) | −1.22700 | − | 2.12522i | −0.297591 | − | 0.515442i | 0.677993 | − | 0.735068i | \(-0.262850\pi\) |
−0.975584 | + | 0.219626i | \(0.929516\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.03606 | + | 7.59867i | −0.467104 | + | 1.74326i | 0.182715 | + | 0.983166i | \(0.441511\pi\) |
−0.649819 | + | 0.760089i | \(0.725155\pi\) | |||||||
\(20\) | −1.37918 | + | 5.14717i | −0.308394 | + | 1.15094i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.586509 | + | 1.01586i | 0.125044 | + | 0.216583i | ||||
\(23\) | 0.0635456 | − | 0.110064i | 0.0132502 | − | 0.0229500i | −0.859324 | − | 0.511431i | \(-0.829116\pi\) |
0.872574 | + | 0.488481i | \(0.162449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 10.1510i | − | 2.03020i | ||||||
\(26\) | −2.81497 | − | 0.528136i | −0.552061 | − | 0.103576i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.11521 | − | 0.566769i | 0.399737 | − | 0.107109i | ||||
\(29\) | 7.00921 | + | 4.04677i | 1.30158 | + | 0.751466i | 0.980675 | − | 0.195646i | \(-0.0626802\pi\) |
0.320903 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.87990 | + | 1.87990i | 0.337641 | + | 0.337641i | 0.855479 | − | 0.517838i | \(-0.173263\pi\) |
−0.517838 | + | 0.855479i | \(0.673263\pi\) | |||||||
\(32\) | 5.63969 | + | 1.51115i | 0.996966 | + | 0.267136i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.37839 | − | 1.37839i | 0.236393 | − | 0.236393i | ||||
\(35\) | −5.39210 | + | 3.11313i | −0.911431 | + | 0.526215i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.26053 | − | 4.70437i | −0.207230 | − | 0.773393i | −0.988758 | − | 0.149523i | \(-0.952226\pi\) |
0.781528 | − | 0.623870i | \(-0.214440\pi\) | |||||||
\(38\) | −6.24897 | −1.01372 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.4168 | −1.64705 | ||||||||
\(41\) | −1.07198 | − | 4.00068i | −0.167415 | − | 0.624801i | −0.997720 | − | 0.0674918i | \(-0.978500\pi\) |
0.830305 | − | 0.557309i | \(-0.188166\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.87623 | − | 5.70204i | 1.50611 | − | 0.869553i | 0.506136 | − | 0.862454i | \(-0.331074\pi\) |
0.999975 | − | 0.00709934i | \(-0.00225981\pi\) | |||||||
\(44\) | 1.42948 | − | 1.42948i | 0.215503 | − | 0.215503i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0975154 | + | 0.0261292i | 0.0143779 | + | 0.00385254i | ||||
\(47\) | −5.41270 | − | 5.41270i | −0.789523 | − | 0.789523i | 0.191892 | − | 0.981416i | \(-0.438538\pi\) |
−0.981416 | + | 0.191892i | \(0.938538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.84632 | − | 2.22067i | −0.549474 | − | 0.317239i | ||||
\(50\) | 7.78875 | − | 2.08699i | 1.10150 | − | 0.295145i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.376441 | + | 4.92163i | 0.0522030 | + | 0.682507i | ||||
\(53\) | − | 7.39660i | − | 1.01600i | −0.861357 | − | 0.508001i | \(-0.830385\pi\) | ||
0.861357 | − | 0.508001i | \(-0.169615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87396 | + | 4.97785i | −0.387525 | + | 0.671213i | ||||
\(56\) | 2.14038 | + | 3.70725i | 0.286021 | + | 0.495402i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.66398 | + | 6.21007i | −0.218492 | + | 0.815422i | ||||
\(59\) | −0.0877466 | + | 0.327475i | −0.0114236 | + | 0.0426336i | −0.971402 | − | 0.237439i | \(-0.923692\pi\) |
0.959979 | + | 0.280073i | \(0.0903586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.120262 | − | 0.208299i | −0.0153979 | − | 0.0266700i | 0.858224 | − | 0.513276i | \(-0.171568\pi\) |
−0.873622 | + | 0.486606i | \(0.838235\pi\) | |||||||
\(62\) | −1.05593 | + | 1.82892i | −0.134103 | + | 0.232274i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.41361i | 0.426701i | ||||||||
\(65\) | −4.65563 | − | 13.2397i | −0.577460 | − | 1.64218i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.41185 | + | 1.45010i | −0.661163 | + | 0.177158i | −0.573771 | − | 0.819016i | \(-0.694520\pi\) |
−0.0873923 | + | 0.996174i | \(0.527853\pi\) | |||||||
\(68\) | −2.90943 | − | 1.67976i | −0.352821 | − | 0.203701i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.49725 | − | 3.49725i | −0.418001 | − | 0.418001i | ||||
\(71\) | −0.902351 | − | 0.241784i | −0.107089 | − | 0.0286945i | 0.204876 | − | 0.978788i | \(-0.434321\pi\) |
−0.311966 | + | 0.950093i | \(0.600987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50619 | − | 4.50619i | 0.527409 | − | 0.527409i | −0.392390 | − | 0.919799i | \(-0.628352\pi\) |
0.919799 | + | 0.392390i | \(0.128352\pi\) | |||||||
\(74\) | 3.35044 | − | 1.93438i | 0.389481 | − | 0.224867i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.78737 | + | 10.4026i | 0.319733 | + | 1.19326i | ||||
\(77\) | 2.36209 | 0.269185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.351919 | −0.0395940 | −0.0197970 | − | 0.999804i | \(-0.506302\pi\) | ||||
−0.0197970 | + | 0.999804i | \(0.506302\pi\) | |||||||
\(80\) | 0.616719 | + | 2.30163i | 0.0689513 | + | 0.257330i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.84928 | − | 1.64503i | 0.314650 | − | 0.181663i | ||||
\(83\) | 10.6691 | − | 10.6691i | 1.17109 | − | 1.17109i | 0.189138 | − | 0.981951i | \(-0.439431\pi\) |
0.981951 | − | 0.189138i | \(-0.0605692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.22654 | + | 2.47224i | 1.00076 | + | 0.268152i | ||||
\(86\) | 6.40560 | + | 6.40560i | 0.690733 | + | 0.690733i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.42244 | + | 1.97595i | 0.364834 | + | 0.210637i | ||||
\(89\) | 13.1675 | − | 3.52822i | 1.39575 | − | 0.373990i | 0.518934 | − | 0.854814i | \(-0.326329\pi\) |
0.876817 | + | 0.480824i | \(0.159662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.75525 | + | 4.37729i | −0.393657 | + | 0.458864i | ||||
\(92\) | − | 0.173988i | − | 0.0181395i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.04028 | − | 5.26591i | 0.313581 | − | 0.543138i | ||||
\(95\) | −15.3103 | − | 26.5183i | −1.57081 | − | 2.72072i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.88713 | − | 10.7749i | 0.293143 | − | 1.09403i | −0.649537 | − | 0.760330i | \(-0.725037\pi\) |
0.942681 | − | 0.333697i | \(-0.108296\pi\) | |||||||
\(98\) | 0.913113 | − | 3.40779i | 0.0922384 | − | 0.344238i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.94838 | − | 12.0349i | −0.694838 | − | 1.20349i | ||||
\(101\) | −4.37119 | + | 7.57113i | −0.434950 | + | 0.753356i | −0.997292 | − | 0.0735496i | \(-0.976567\pi\) |
0.562342 | + | 0.826905i | \(0.309901\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.77354i | − | 0.568884i | −0.958693 | − | 0.284442i | \(-0.908192\pi\) | ||
0.958693 | − | 0.284442i | \(-0.0918083\pi\) | |||||||
\(104\) | −9.10272 | + | 3.20091i | −0.892595 | + | 0.313875i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.67532 | − | 1.52070i | 0.551236 | − | 0.147703i | ||||
\(107\) | −4.39109 | − | 2.53520i | −0.424503 | − | 0.245087i | 0.272499 | − | 0.962156i | \(-0.412150\pi\) |
−0.697002 | + | 0.717069i | \(0.745483\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.69280 | + | 9.69280i | 0.928402 | + | 0.928402i | 0.997603 | − | 0.0692012i | \(-0.0220450\pi\) |
−0.0692012 | + | 0.997603i | \(0.522045\pi\) | |||||||
\(110\) | −4.41031 | − | 1.18174i | −0.420507 | − | 0.112674i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.692407 | − | 0.692407i | 0.0654263 | − | 0.0654263i | ||||
\(113\) | −11.8168 | + | 6.82246i | −1.11164 | + | 0.641803i | −0.939253 | − | 0.343227i | \(-0.888480\pi\) |
−0.172383 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.128036 | + | 0.477837i | 0.0119394 | + | 0.0445586i | ||||
\(116\) | 11.0801 | 1.02876 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.269307 | −0.0247918 | ||||||||
\(119\) | −1.01596 | − | 3.79161i | −0.0931328 | − | 0.347576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.63780 | + | 4.40969i | −0.694346 | + | 0.400881i | ||||
\(122\) | 0.135100 | − | 0.135100i | 0.0122314 | − | 0.0122314i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.51559 | + | 0.942000i | 0.315709 | + | 0.0845941i | ||||
\(125\) | 14.1775 | + | 14.1775i | 1.26807 | + | 1.26807i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9255 | + | 7.46255i | 1.14695 | + | 0.662194i | 0.948143 | − | 0.317844i | \(-0.102959\pi\) |
0.198811 | + | 0.980038i | \(0.436292\pi\) | |||||||
\(128\) | 8.66016 | − | 2.32048i | 0.765458 | − | 0.205104i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.20145 | − | 6.29420i | 0.807020 | − | 0.552038i | ||||
\(131\) | 2.21920i | 0.193892i | 0.995290 | + | 0.0969461i | \(0.0309074\pi\) | ||||
−0.995290 | + | 0.0969461i | \(0.969093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.29173 | + | 10.8976i | −0.545562 | + | 0.944941i | ||||
\(134\) | −2.22529 | − | 3.85431i | −0.192236 | − | 0.332962i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.69975 | − | 6.34356i | 0.145753 | − | 0.543956i | ||||
\(137\) | −5.00500 | + | 18.6789i | −0.427606 | + | 1.59585i | 0.330558 | + | 0.943786i | \(0.392763\pi\) |
−0.758165 | + | 0.652063i | \(0.773904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.35562 | − | 7.54416i | −0.369439 | − | 0.639887i | 0.620039 | − | 0.784571i | \(-0.287117\pi\) |
−0.989478 | + | 0.144684i | \(0.953783\pi\) | |||||||
\(140\) | −4.26188 | + | 7.38179i | −0.360194 | + | 0.623875i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 0.742072i | − | 0.0622733i | ||||||
\(143\) | −0.981798 | + | 5.23299i | −0.0821021 | + | 0.437605i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.4301 | + | 8.15372i | −2.52708 | + | 0.677129i | ||||
\(146\) | 4.38399 | + | 2.53110i | 0.362821 | + | 0.209475i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.71461 | − | 4.71461i | −0.387539 | − | 0.387539i | ||||
\(149\) | 15.1274 | + | 4.05338i | 1.23929 | + | 0.332066i | 0.818188 | − | 0.574950i | \(-0.194979\pi\) |
0.421097 | + | 0.907016i | \(0.361645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2162 | + | 14.2162i | −1.15690 | + | 1.15690i | −0.171756 | + | 0.985139i | \(0.554944\pi\) |
−0.985139 | + | 0.171756i | \(0.945056\pi\) | |||||||
\(152\) | −18.2322 | + | 10.5264i | −1.47883 | + | 0.853803i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.485632 | + | 1.81240i | 0.0391333 | + | 0.146047i | ||||
\(155\) | −10.3484 | −0.831201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4197 | 0.831586 | 0.415793 | − | 0.909459i | \(-0.363504\pi\) | ||||
0.415793 | + | 0.909459i | \(0.363504\pi\) | |||||||
\(158\) | −0.0723524 | − | 0.270023i | −0.00575605 | − | 0.0214819i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.6817 | + | 11.3632i | −1.55598 | + | 0.898344i | ||||
\(161\) | 0.143750 | − | 0.143750i | 0.0113291 | − | 0.0113291i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1273 | − | 4.32129i | −1.26318 | − | 0.338469i | −0.435768 | − | 0.900059i | \(-0.643523\pi\) |
−0.827416 | + | 0.561590i | \(0.810190\pi\) | |||||||
\(164\) | −4.00940 | − | 4.00940i | −0.313081 | − | 0.313081i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3798 | + | 5.99277i | 0.805628 | + | 0.465129i | ||||
\(167\) | −2.28699 | + | 0.612796i | −0.176972 | + | 0.0474196i | −0.346217 | − | 0.938154i | \(-0.612534\pi\) |
0.169245 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.13660 | − | 10.1388i | −0.625893 | − | 0.779909i | ||||
\(170\) | 7.58768i | 0.581949i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.80610 | − | 13.5206i | 0.595210 | − | 1.03093i | ||||
\(173\) | 4.87703 | + | 8.44726i | 0.370793 | + | 0.642233i | 0.989688 | − | 0.143241i | \(-0.0457525\pi\) |
−0.618894 | + | 0.785474i | \(0.712419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.20254 | − | 15.6841i | 0.317682 | − | 1.18561i | ||||
\(176\) | 0.233968 | − | 0.873182i | 0.0176360 | − | 0.0658186i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.41431 | + | 9.37787i | 0.405820 | + | 0.702901i | ||||
\(179\) | 1.70298 | − | 2.94965i | 0.127287 | − | 0.220467i | −0.795338 | − | 0.606167i | \(-0.792706\pi\) |
0.922625 | + | 0.385699i | \(0.126040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3133i | 0.766584i | 0.923627 | + | 0.383292i | \(0.125210\pi\) | ||||
−0.923627 | + | 0.383292i | \(0.874790\pi\) | |||||||
\(182\) | −4.13069 | − | 1.98141i | −0.306187 | − | 0.146872i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.328530 | − | 0.0880293i | 0.0242195 | − | 0.00648960i | ||||
\(185\) | 16.4176 | + | 9.47869i | 1.20704 | + | 0.696887i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.56241 | − | 2.56241i | −0.187382 | − | 0.187382i | ||||
\(188\) | −10.1222 | − | 2.71225i | −0.738240 | − | 0.197811i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.1994 | − | 17.1994i | 1.24778 | − | 1.24778i | ||||
\(191\) | −8.60515 | + | 4.96819i | −0.622647 | + | 0.359485i | −0.777899 | − | 0.628389i | \(-0.783714\pi\) |
0.155252 | + | 0.987875i | \(0.450381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.370570 | − | 1.38299i | −0.0266742 | − | 0.0995495i | 0.951305 | − | 0.308250i | \(-0.0997433\pi\) |
−0.977980 | + | 0.208700i | \(0.933077\pi\) | |||||||
\(194\) | 8.86103 | 0.636185 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.08020 | −0.434300 | ||||||||
\(197\) | −4.60073 | − | 17.1702i | −0.327789 | − | 1.22332i | −0.911479 | − | 0.411348i | \(-0.865058\pi\) |
0.583690 | − | 0.811977i | \(-0.301608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.62946 | − | 5.55957i | 0.682615 | − | 0.394108i | −0.118225 | − | 0.992987i | \(-0.537720\pi\) |
0.800839 | + | 0.598879i | \(0.204387\pi\) | |||||||
\(200\) | 19.2092 | − | 19.2092i | 1.35830 | − | 1.35830i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.70792 | − | 1.79738i | −0.471968 | − | 0.126463i | ||||
\(203\) | 9.15439 | + | 9.15439i | 0.642512 | + | 0.642512i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9618 | + | 8.06085i | 0.975135 | + | 0.562994i | ||||
\(206\) | 4.42996 | − | 1.18701i | 0.308650 | − | 0.0827026i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.24617 | + | 1.82176i | 0.0864060 | + | 0.126316i | ||||
\(209\) | 11.6167i | 0.803547i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.05396 | − | 7.02166i | 0.279086 | − | 0.483391i | −0.692072 | − | 0.721829i | \(-0.743302\pi\) |
0.971158 | + | 0.238438i | \(0.0766353\pi\) | |||||||
\(212\) | −5.06298 | − | 8.76934i | −0.347727 | − | 0.602280i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.04244 | − | 3.89045i | 0.0712599 | − | 0.265946i | ||||
\(215\) | −11.4889 | + | 42.8771i | −0.783535 | + | 2.92419i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.12631 | + | 3.68288i | 0.144343 | + | 0.250010i | ||||
\(218\) | −5.44438 | + | 9.42994i | −0.368740 | + | 0.638676i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.86892i | 0.530523i | ||||||||
\(221\) | 8.82224 | − | 0.674787i | 0.593448 | − | 0.0453911i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.04625 | − | 0.816241i | 0.203992 | − | 0.0546595i | −0.155376 | − | 0.987855i | \(-0.549659\pi\) |
0.359368 | + | 0.933196i | \(0.382992\pi\) | |||||||
\(224\) | 8.08813 | + | 4.66969i | 0.540411 | + | 0.312006i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.66426 | − | 7.66426i | −0.509819 | − | 0.509819i | ||||
\(227\) | −23.5610 | − | 6.31315i | −1.56380 | − | 0.419018i | −0.629934 | − | 0.776648i | \(-0.716918\pi\) |
−0.933863 | + | 0.357630i | \(0.883585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.945623 | − | 0.945623i | 0.0624885 | − | 0.0624885i | −0.675172 | − | 0.737660i | \(-0.735931\pi\) |
0.737660 | + | 0.675172i | \(0.235931\pi\) | |||||||
\(230\) | −0.340315 | + | 0.196481i | −0.0224397 | + | 0.0129556i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.60596 | + | 20.9217i | 0.368049 | + | 1.37358i | ||||
\(233\) | −3.62616 | −0.237558 | −0.118779 | − | 0.992921i | \(-0.537898\pi\) | ||||
−0.118779 | + | 0.992921i | \(0.537898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.7954 | 1.94364 | ||||||||
\(236\) | 0.120125 | + | 0.448314i | 0.00781949 | + | 0.0291827i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.70038 | − | 1.55906i | 0.175040 | − | 0.101059i | ||||
\(239\) | −1.04328 | + | 1.04328i | −0.0674842 | + | 0.0674842i | −0.740043 | − | 0.672559i | \(-0.765195\pi\) |
0.672559 | + | 0.740043i | \(0.265195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.32118 | − | 1.69375i | −0.407183 | − | 0.109104i | 0.0494133 | − | 0.998778i | \(-0.484265\pi\) |
−0.456596 | + | 0.889674i | \(0.650932\pi\) | |||||||
\(242\) | −4.95378 | − | 4.95378i | −0.318441 | − | 0.318441i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.285162 | − | 0.164638i | −0.0182556 | − | 0.0105399i | ||||
\(245\) | 16.6986 | − | 4.47437i | 1.06683 | − | 0.285857i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.5275 | − | 18.4683i | −1.36976 | − | 1.17511i | ||||
\(248\) | 7.11486i | 0.451794i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.96340 | + | 13.7930i | −0.503649 | + | 0.872346i | ||||
\(251\) | −12.3112 | − | 21.3237i | −0.777079 | − | 1.34594i | −0.933619 | − | 0.358269i | \(-0.883367\pi\) |
0.156539 | − | 0.987672i | \(-0.449966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0485738 | − | 0.181280i | 0.00305381 | − | 0.0113970i | ||||
\(254\) | −3.06851 | + | 11.4518i | −0.192535 | + | 0.718552i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.97457 | + | 12.0803i | 0.435910 | + | 0.755019i | ||||
\(257\) | −6.23916 | + | 10.8066i | −0.389188 | + | 0.674094i | −0.992341 | − | 0.123532i | \(-0.960578\pi\) |
0.603152 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.79046i | − | 0.484076i | ||||||
\(260\) | −14.5822 | − | 12.5100i | −0.904351 | − | 0.775838i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.70276 | + | 0.456254i | −0.105197 | + | 0.0281874i | ||||
\(263\) | 19.4401 | + | 11.2238i | 1.19873 | + | 0.692087i | 0.960272 | − | 0.279066i | \(-0.0900248\pi\) |
0.238458 | + | 0.971153i | \(0.423358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.3581 | + | 20.3581i | 1.25059 | + | 1.25059i | ||||
\(266\) | −9.65513 | − | 2.58708i | −0.591994 | − | 0.158624i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.42364 | + | 5.42364i | −0.331302 | + | 0.331302i | ||||
\(269\) | 20.7591 | − | 11.9853i | 1.26571 | − | 0.730756i | 0.291534 | − | 0.956560i | \(-0.405834\pi\) |
0.974173 | + | 0.225804i | \(0.0725010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.714098 | − | 2.66505i | −0.0433783 | − | 0.161890i | 0.940839 | − | 0.338854i | \(-0.110039\pi\) |
−0.984217 | + | 0.176964i | \(0.943373\pi\) | |||||||
\(272\) | −1.50226 | −0.0910878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.3611 | −0.927998 | ||||||||
\(275\) | −3.87968 | − | 14.4792i | −0.233954 | − | 0.873127i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1680 | + | 8.75727i | −0.911359 | + | 0.526173i | −0.880868 | − | 0.473362i | \(-0.843040\pi\) |
−0.0304909 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(278\) | 4.89305 | − | 4.89305i | 0.293465 | − | 0.293465i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16.0948 | − | 4.31259i | −0.961849 | − | 0.257727i | ||||
\(281\) | 14.8429 | + | 14.8429i | 0.885454 | + | 0.885454i | 0.994082 | − | 0.108628i | \(-0.0346457\pi\) |
−0.108628 | + | 0.994082i | \(0.534646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.60392 | − | 3.23543i | −0.333119 | − | 0.192326i | 0.324106 | − | 0.946021i | \(-0.394936\pi\) |
−0.657225 | + | 0.753695i | \(0.728270\pi\) | |||||||
\(284\) | −1.23532 | + | 0.331003i | −0.0733028 | + | 0.0196414i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.21706 | + | 0.322550i | −0.249360 | + | 0.0190728i | ||||
\(287\) | − | 6.62516i | − | 0.391071i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.48895 | − | 9.50714i | 0.322879 | − | 0.559244i | ||||
\(290\) | −12.5125 | − | 21.6723i | −0.734759 | − | 1.27264i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.25800 | − | 8.42698i | 0.132140 | − | 0.493152i | ||||
\(293\) | 1.40538 | − | 5.24495i | 0.0821032 | − | 0.306413i | −0.912647 | − | 0.408749i | \(-0.865965\pi\) |
0.994750 | + | 0.102336i | \(0.0326317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.659819 | − | 1.14284i | −0.0384162 | − | 0.0665388i | ||||
\(296\) | 6.51692 | − | 11.2876i | 0.378789 | − | 0.656081i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4404i | 0.720654i | ||||||||
\(299\) | 0.258714 | + | 0.378213i | 0.0149618 | + | 0.0218726i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6202 | − | 4.72131i | 1.01561 | − | 0.272132i | ||||
\(302\) | −13.8306 | − | 7.98513i | −0.795864 | − | 0.459493i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.40525 | + | 3.40525i | 0.195305 | + | 0.195305i | ||||
\(305\) | 0.904318 | + | 0.242311i | 0.0517811 | + | 0.0138747i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.27550 | + | 7.27550i | −0.415235 | + | 0.415235i | −0.883558 | − | 0.468323i | \(-0.844859\pi\) |
0.468323 | + | 0.883558i | \(0.344859\pi\) | |||||||
\(308\) | 2.80047 | − | 1.61685i | 0.159572 | − | 0.0921287i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.12756 | − | 7.94017i | −0.120837 | − | 0.450971i | ||||
\(311\) | −4.40180 | −0.249603 | −0.124802 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124802 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.50602 | 0.198172 | 0.0990861 | − | 0.995079i | \(-0.468408\pi\) | ||||
0.0990861 | + | 0.995079i | \(0.468408\pi\) | |||||||
\(314\) | 2.14224 | + | 7.99494i | 0.120893 | + | 0.451180i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.417232 | + | 0.240889i | −0.0234711 | + | 0.0135511i | ||||
\(317\) | −8.78842 | + | 8.78842i | −0.493607 | + | 0.493607i | −0.909441 | − | 0.415834i | \(-0.863490\pi\) |
0.415834 | + | 0.909441i | \(0.363490\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5444 | + | 3.09332i | 0.646364 | + | 0.173193i | ||||
\(320\) | −9.39550 | − | 9.39550i | −0.525225 | − | 0.525225i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.139851 | + | 0.0807431i | 0.00779360 | + | 0.00449964i | ||||
\(323\) | 18.6471 | − | 4.99648i | 1.03755 | − | 0.278012i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.9999 | + | 15.8294i | 1.83050 | + | 0.878057i | ||||
\(326\) | − | 13.2627i | − | 0.734551i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.54211 | − | 9.59922i | 0.306012 | − | 0.530028i | ||||
\(329\) | −6.12216 | − | 10.6039i | −0.337526 | − | 0.584612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.41989 | + | 16.4952i | −0.242939 | + | 0.906661i | 0.731469 | + | 0.681875i | \(0.238835\pi\) |
−0.974408 | + | 0.224786i | \(0.927832\pi\) | |||||||
\(332\) | 5.34618 | − | 19.9522i | 0.293410 | − | 1.09502i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.940381 | − | 1.62879i | −0.0514554 | − | 0.0891233i | ||||
\(335\) | 10.9042 | − | 18.8866i | 0.595759 | − | 1.03189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.5394i | − | 1.06438i | −0.846625 | − | 0.532191i | \(-0.821369\pi\) | ||
0.846625 | − | 0.532191i | \(-0.178631\pi\) | |||||||
\(338\) | 6.10655 | − | 8.32759i | 0.332153 | − | 0.452961i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.6311 | − | 3.38450i | 0.685020 | − | 0.183551i | ||||
\(341\) | 3.39994 | + | 1.96296i | 0.184117 | + | 0.106300i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.9410 | − | 12.9410i | −0.698749 | − | 0.698749i | ||||
\(344\) | 29.4795 | + | 7.89900i | 1.58943 | + | 0.425885i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.47879 | + | 5.47879i | −0.294541 | + | 0.294541i | ||||
\(347\) | −14.5598 | + | 8.40611i | −0.781611 | + | 0.451263i | −0.837001 | − | 0.547201i | \(-0.815693\pi\) |
0.0553898 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.900657 | − | 3.36130i | −0.0482111 | − | 0.179926i | 0.937622 | − | 0.347657i | \(-0.113023\pi\) |
−0.985833 | + | 0.167731i | \(0.946356\pi\) | |||||||
\(350\) | 12.8982 | 0.689439 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.62188 | 0.459548 | ||||||||
\(353\) | −4.68448 | − | 17.4827i | −0.249330 | − | 0.930511i | −0.971158 | − | 0.238438i | \(-0.923365\pi\) |
0.721828 | − | 0.692072i | \(-0.243302\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.14908 | − | 1.81812i | 0.167136 | − | 0.0964959i | ||||
\(356\) | 13.1962 | − | 13.1962i | 0.699396 | − | 0.699396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.61335 | + | 0.700246i | 0.138120 | + | 0.0370091i | ||||
\(359\) | −14.4587 | − | 14.4587i | −0.763101 | − | 0.763101i | 0.213781 | − | 0.976882i | \(-0.431422\pi\) |
−0.976882 | + | 0.213781i | \(0.931422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.1398 | − | 21.4427i | −1.95473 | − | 1.12856i | ||||
\(362\) | −7.91329 | + | 2.12036i | −0.415913 | + | 0.111444i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.45593 | + | 7.76014i | −0.0763117 | + | 0.406742i | ||||
\(365\) | 24.8053i | 1.29837i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.8449 | − | 20.5160i | 0.618300 | − | 1.07093i | −0.371496 | − | 0.928434i | \(-0.621155\pi\) |
0.989796 | − | 0.142492i | \(-0.0455116\pi\) | |||||||
\(368\) | −0.0389006 | − | 0.0673777i | −0.00202783 | − | 0.00351231i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.89752 | + | 14.5458i | −0.202623 | + | 0.756198i | ||||
\(371\) | 3.06221 | − | 11.4283i | 0.158982 | − | 0.593328i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.993763 | + | 1.72125i | 0.0514551 | + | 0.0891228i | 0.890606 | − | 0.454776i | \(-0.150281\pi\) |
−0.839151 | + | 0.543899i | \(0.816947\pi\) | |||||||
\(374\) | 1.43929 | − | 2.49293i | 0.0744240 | − | 0.128906i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 20.4854i | − | 1.05645i | ||||||
\(377\) | −24.0857 | + | 16.4757i | −1.24048 | + | 0.848542i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.53547 | − | 1.75117i | 0.335704 | − | 0.0899517i | −0.0870291 | − | 0.996206i | \(-0.527737\pi\) |
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(380\) | −36.3036 | − | 20.9599i | −1.86233 | − | 1.07522i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.58120 | − | 5.58120i | −0.285559 | − | 0.285559i | ||||
\(383\) | 2.75402 | + | 0.737937i | 0.140724 | + | 0.0377068i | 0.328493 | − | 0.944506i | \(-0.393459\pi\) |
−0.187770 | + | 0.982213i | \(0.560126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.50133 | + | 6.50133i | −0.331339 | + | 0.331339i | ||||
\(386\) | 0.984960 | − | 0.568667i | 0.0501332 | − | 0.0289444i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.95248 | − | 14.7509i | −0.200657 | − | 0.748862i | ||||
\(389\) | 33.4065 | 1.69377 | 0.846887 | − | 0.531772i | \(-0.178474\pi\) | ||||
0.846887 | + | 0.531772i | \(0.178474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.311881 | −0.0157725 | ||||||||
\(392\) | −3.07628 | − | 11.4808i | −0.155376 | − | 0.579870i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.2286 | − | 7.06017i | 0.616067 | − | 0.355686i | ||||
\(395\) | 0.968609 | − | 0.968609i | 0.0487360 | − | 0.0487360i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.2479 | − | 4.62157i | −0.865650 | − | 0.231950i | −0.201444 | − | 0.979500i | \(-0.564563\pi\) |
−0.664206 | + | 0.747550i | \(0.731230\pi\) | |||||||
\(398\) | 6.24555 | + | 6.24555i | 0.313061 | + | 0.313061i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.38159 | − | 3.10706i | −0.269080 | − | 0.155353i | ||||
\(401\) | 15.5864 | − | 4.17636i | 0.778347 | − | 0.208557i | 0.152291 | − | 0.988336i | \(-0.451335\pi\) |
0.626056 | + | 0.779778i | \(0.284668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.04287 | + | 3.17986i | −0.450458 | + | 0.158400i | ||||
\(404\) | 11.9683i | 0.595447i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.14196 | + | 8.90614i | −0.255191 | + | 0.442004i | ||||
\(407\) | −3.59598 | − | 6.22843i | −0.178246 | − | 0.308732i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.31725 | + | 23.5763i | −0.312368 | + | 1.16577i | 0.614047 | + | 0.789269i | \(0.289540\pi\) |
−0.926415 | + | 0.376504i | \(0.877126\pi\) | |||||||
\(410\) | −3.31453 | + | 12.3700i | −0.163693 | + | 0.610910i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.95199 | − | 6.84505i | −0.194701 | − | 0.337232i | ||||
\(413\) | −0.271150 | + | 0.469646i | −0.0133424 | + | 0.0231098i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 58.7306i | 2.88297i | ||||||||
\(416\) | −13.7071 | + | 15.9776i | −0.672044 | + | 0.783364i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.91338 | + | 2.38833i | −0.435968 | + | 0.116817i | ||||
\(419\) | 31.3143 | + | 18.0793i | 1.52980 | + | 0.883231i | 0.999370 | + | 0.0355041i | \(0.0113037\pi\) |
0.530432 | + | 0.847727i | \(0.322030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.23855 | − | 5.23855i | −0.255311 | − | 0.255311i | 0.567833 | − | 0.823144i | \(-0.307782\pi\) |
−0.823144 | + | 0.567833i | \(0.807782\pi\) | |||||||
\(422\) | 6.22110 | + | 1.66694i | 0.302838 | + | 0.0811453i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.9969 | − | 13.9969i | 0.679751 | − | 0.679751i | ||||
\(425\) | −21.5732 | + | 12.4553i | −1.04645 | + | 0.604170i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0995770 | − | 0.371626i | −0.00481887 | − | 0.0179843i | ||||
\(428\) | −6.94138 | −0.335524 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.2611 | −1.70044 | ||||||||
\(431\) | 3.80867 | + | 14.2142i | 0.183457 | + | 0.684672i | 0.994956 | + | 0.100317i | \(0.0319857\pi\) |
−0.811498 | + | 0.584355i | \(0.801348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.9100 | − | 6.29888i | 0.524300 | − | 0.302705i | −0.214392 | − | 0.976748i | \(-0.568777\pi\) |
0.738692 | + | 0.674043i | \(0.235444\pi\) | |||||||
\(434\) | −2.38867 | + | 2.38867i | −0.114660 | + | 0.114660i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.1264 | + | 4.85696i | 0.868098 | + | 0.232606i | ||||
\(437\) | 0.706959 | + | 0.706959i | 0.0338184 | + | 0.0338184i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9172 | − | 12.0765i | −0.998322 | − | 0.576382i | −0.0905707 | − | 0.995890i | \(-0.528869\pi\) |
−0.907751 | + | 0.419508i | \(0.862202\pi\) | |||||||
\(440\) | −14.8583 | + | 3.98128i | −0.708344 | + | 0.189800i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.33156 | + | 6.63046i | 0.110901 | + | 0.315379i | ||||
\(443\) | − | 18.8052i | − | 0.893463i | −0.894668 | − | 0.446731i | \(-0.852588\pi\) | ||
0.894668 | − | 0.446731i | \(-0.147412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.5308 | + | 45.9527i | −1.25768 | + | 2.17837i | ||||
\(446\) | 1.25258 | + | 2.16954i | 0.0593115 | + | 0.102731i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.41324 | + | 5.27429i | −0.0667694 | + | 0.249187i | ||||
\(449\) | −5.23342 | + | 19.5314i | −0.246980 | + | 0.921743i | 0.725397 | + | 0.688330i | \(0.241656\pi\) |
−0.972378 | + | 0.233413i | \(0.925011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.05809 | − | 5.29677i | −0.144000 | − | 0.249415i | ||||
\(452\) | −9.33996 | + | 16.1773i | −0.439315 | + | 0.760915i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 19.3760i | − | 0.909360i | ||||||
\(455\) | −1.71206 | − | 22.3837i | −0.0802628 | − | 1.04936i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2298 | − | 7.83210i | 1.36731 | − | 0.366370i | 0.500815 | − | 0.865554i | \(-0.333034\pi\) |
0.866496 | + | 0.499184i | \(0.166367\pi\) | |||||||
\(458\) | 0.919979 | + | 0.531150i | 0.0429878 | + | 0.0248190i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.478878 | + | 0.478878i | 0.0223278 | + | 0.0223278i | ||||
\(461\) | −17.7596 | − | 4.75867i | −0.827148 | − | 0.221634i | −0.179679 | − | 0.983725i | \(-0.557506\pi\) |
−0.647469 | + | 0.762092i | \(0.724172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.86314 | + | 5.86314i | −0.272483 | + | 0.272483i | −0.830099 | − | 0.557616i | \(-0.811716\pi\) |
0.557616 | + | 0.830099i | \(0.311716\pi\) | |||||||
\(464\) | 4.29081 | − | 2.47730i | 0.199196 | − | 0.115006i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.745517 | − | 2.78231i | −0.0345354 | − | 0.128888i | ||||
\(467\) | −25.8432 | −1.19588 | −0.597939 | − | 0.801541i | \(-0.704014\pi\) | ||||
−0.597939 | + | 0.801541i | \(0.704014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.96207 | −0.413830 | ||||||||
\(470\) | 6.12576 | + | 22.8617i | 0.282560 | + | 1.05453i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.785742 | + | 0.453649i | −0.0361667 | + | 0.0208809i | ||||
\(473\) | 11.9079 | − | 11.9079i | 0.547527 | − | 0.547527i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 77.1343 | + | 20.6681i | 3.53916 | + | 0.948316i | ||||
\(476\) | −3.79987 | − | 3.79987i | −0.174167 | − | 0.174167i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.01499 | − | 0.586004i | −0.0464245 | − | 0.0268032i | ||||
\(479\) | −6.40241 | + | 1.71552i | −0.292534 | + | 0.0783841i | −0.402101 | − | 0.915595i | \(-0.631720\pi\) |
0.109568 | + | 0.993979i | \(0.465053\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2590 | + | 3.23809i | 0.786945 | + | 0.147644i | ||||
\(482\) | − | 5.19838i | − | 0.236780i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.03687 | + | 10.4562i | −0.274403 | + | 0.475280i | ||||
\(485\) | 21.7101 | + | 37.6029i | 0.985803 | + | 1.70746i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.89650 | + | 10.8099i | −0.131253 | + | 0.489843i | −0.999985 | − | 0.00543914i | \(-0.998269\pi\) |
0.868732 | + | 0.495282i | \(0.164935\pi\) | |||||||
\(488\) | 0.166597 | − | 0.621750i | 0.00754151 | − | 0.0281453i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.86625 | + | 11.8927i | 0.310185 | + | 0.537257i | ||||
\(491\) | −14.1823 | + | 24.5645i | −0.640038 | + | 1.10858i | 0.345386 | + | 0.938461i | \(0.387748\pi\) |
−0.985424 | + | 0.170118i | \(0.945585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 19.8615i | − | 0.894518i | ||||||
\(494\) | 9.74458 | − | 20.3147i | 0.438429 | − | 0.914002i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.57205 | − | 0.421228i | 0.0705869 | − | 0.0189137i | ||||
\(497\) | −1.29410 | − | 0.747150i | −0.0580484 | − | 0.0335143i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0922 | − | 25.0922i | −1.12328 | − | 1.12328i | −0.991245 | − | 0.132034i | \(-0.957849\pi\) |
−0.132034 | − | 0.991245i | \(-0.542151\pi\) | |||||||
\(500\) | 26.5132 | + | 7.10418i | 1.18571 | + | 0.317709i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.8303 | − | 13.8303i | 0.617276 | − | 0.617276i | ||||
\(503\) | 11.1968 | − | 6.46448i | 0.499241 | − | 0.288237i | −0.229159 | − | 0.973389i | \(-0.573598\pi\) |
0.728400 | + | 0.685152i | \(0.240264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.80739 | − | 32.8696i | −0.391924 | − | 1.46268i | ||||
\(506\) | 0.149080 | 0.00662742 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.4325 | 0.906544 | ||||||||
\(509\) | 5.21410 | + | 19.4593i | 0.231111 | + | 0.862517i | 0.979864 | + | 0.199668i | \(0.0639863\pi\) |
−0.748753 | + | 0.662849i | \(0.769347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.82797 | − | 5.09683i | 0.390527 | − | 0.225471i | ||||
\(512\) | 4.84423 | − | 4.84423i | 0.214087 | − | 0.214087i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.57446 | − | 2.56547i | −0.422311 | − | 0.113158i | ||||
\(515\) | 15.8909 | + | 15.8909i | 0.700236 | + | 0.700236i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.78926 | − | 5.65183i | −0.430531 | − | 0.248567i | ||||
\(518\) | 5.97752 | − | 1.60167i | 0.262637 | − | 0.0703734i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.2439 | − | 33.8641i | 0.712343 | − | 1.48504i | ||||
\(521\) | 2.32517i | 0.101868i | 0.998702 | + | 0.0509338i | \(0.0162197\pi\) | ||||
−0.998702 | + | 0.0509338i | \(0.983780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.10483 | − | 7.10977i | 0.179492 | − | 0.310888i | −0.762215 | − | 0.647324i | \(-0.775888\pi\) |
0.941706 | + | 0.336436i | \(0.109221\pi\) | |||||||
\(524\) | 1.51904 | + | 2.63106i | 0.0663597 | + | 0.114938i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.61508 | + | 17.2237i | −0.201227 | + | 0.750989i | ||||
\(527\) | 1.68858 | − | 6.30186i | 0.0735556 | − | 0.274513i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4919 | + | 19.9046i | 0.499649 | + | 0.865417i | ||||
\(530\) | −11.4350 | + | 19.8061i | −0.496706 | + | 0.860320i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.2268i | 0.746875i | ||||||||
\(533\) | 14.6774 | + | 2.75373i | 0.635749 | + | 0.119277i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.0637 | − | 5.10809i | 0.824194 | − | 0.220842i | ||||
\(536\) | −12.9852 | − | 7.49700i | −0.560875 | − | 0.323821i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.4641 | + | 13.4641i | 0.580479 | + | 0.580479i | ||||
\(539\) | −6.33503 | − | 1.69747i | −0.272869 | − | 0.0731150i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.7070 | − | 20.7070i | 0.890265 | − | 0.890265i | −0.104283 | − | 0.994548i | \(-0.533255\pi\) |
0.994548 | + | 0.104283i | \(0.0332547\pi\) | |||||||
\(542\) | 1.89804 | − | 1.09584i | 0.0815280 | − | 0.0470702i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.70836 | − | 13.8398i | −0.158995 | − | 0.593376i | ||||
\(545\) | −53.3562 | −2.28553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.8903 | −1.32078 | −0.660388 | − | 0.750925i | \(-0.729608\pi\) | ||||
−0.660388 | + | 0.750925i | \(0.729608\pi\) | |||||||
\(548\) | 6.85186 | + | 25.5715i | 0.292697 | + | 1.09236i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.3120 | − | 5.95366i | 0.439707 | − | 0.253865i | ||||
\(551\) | −45.0212 | + | 45.0212i | −1.91797 | + | 1.91797i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.543741 | − | 0.145695i | −0.0231222 | − | 0.00619559i | ||||
\(554\) | −9.83780 | − | 9.83780i | −0.417968 | − | 0.417968i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.3280 | − | 5.96285i | −0.438003 | − | 0.252881i | ||||
\(557\) | −4.49583 | + | 1.20465i | −0.190494 | + | 0.0510428i | −0.352805 | − | 0.935697i | \(-0.614772\pi\) |
0.162310 | + | 0.986740i | \(0.448105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.13584 | + | 40.9983i | 0.132632 | + | 1.73404i | ||||
\(560\) | 3.81151i | 0.161066i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.33717 | + | 14.4404i | −0.351682 | + | 0.609132i | ||||
\(563\) | 21.6843 | + | 37.5583i | 0.913885 | + | 1.58289i | 0.808526 | + | 0.588460i | \(0.200266\pi\) |
0.105359 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7464 | − | 51.3022i | 0.578314 | − | 2.15830i | ||||
\(566\) | 1.33037 | − | 4.96500i | 0.0559195 | − | 0.208695i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.25002 | − | 2.16510i | −0.0524497 | − | 0.0908456i | ||||
\(569\) | 18.6114 | − | 32.2359i | 0.780231 | − | 1.35140i | −0.151577 | − | 0.988445i | \(-0.548435\pi\) |
0.931807 | − | 0.362953i | \(-0.118232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1841i | 0.760980i | 0.924785 | + | 0.380490i | \(0.124245\pi\) | ||||
−0.924785 | + | 0.380490i | \(0.875755\pi\) | |||||||
\(572\) | 2.41798 | + | 6.87622i | 0.101101 | + | 0.287509i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.08340 | − | 1.36209i | 0.212177 | − | 0.0568526i | ||||
\(575\) | −1.11726 | − | 0.645052i | −0.0465931 | − | 0.0269005i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.4668 | + | 16.4668i | 0.685523 | + | 0.685523i | 0.961239 | − | 0.275716i | \(-0.0889149\pi\) |
−0.275716 | + | 0.961239i | \(0.588915\pi\) | |||||||
\(578\) | 8.42320 | + | 2.25699i | 0.350359 | + | 0.0938784i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −30.4964 | + | 30.4964i | −1.26629 | + | 1.26629i | ||||
\(581\) | 20.9016 | − | 12.0676i | 0.867146 | − | 0.500647i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82695 | − | 10.5503i | −0.117080 | − | 0.436950i | ||||
\(584\) | 17.0545 | 0.705721 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.31332 | 0.178182 | ||||||||
\(587\) | −0.333222 | − | 1.24360i | −0.0137536 | − | 0.0513290i | 0.958708 | − | 0.284392i | \(-0.0917918\pi\) |
−0.972462 | + | 0.233063i | \(0.925125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.1124 | + | 10.4572i | −0.746307 | + | 0.430881i | ||||
\(590\) | 0.741232 | − | 0.741232i | 0.0305160 | − | 0.0305160i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.87986 | − | 0.771656i | −0.118362 | − | 0.0317149i | ||||
\(593\) | 7.64836 | + | 7.64836i | 0.314080 | + | 0.314080i | 0.846488 | − | 0.532408i | \(-0.178713\pi\) |
−0.532408 | + | 0.846488i | \(0.678713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.2322 | + | 7.63961i | 0.542467 | + | 0.313193i | ||||
\(596\) | 20.7094 | − | 5.54908i | 0.848292 | − | 0.227299i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.237008 | + | 0.276267i | −0.00969197 | + | 0.0112974i | ||||
\(599\) | − | 44.2262i | − | 1.80704i | −0.428551 | − | 0.903518i | \(-0.640976\pi\) | ||
0.428551 | − | 0.903518i | \(-0.359024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6644 | − | 21.9353i | 0.516590 | − | 0.894761i | −0.483224 | − | 0.875497i | \(-0.660534\pi\) |
0.999814 | − | 0.0192641i | \(-0.00613233\pi\) | |||||||
\(602\) | 7.24520 | + | 12.5491i | 0.295292 | + | 0.511462i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.12357 | + | 26.5855i | −0.289854 | + | 1.08175i | ||||
\(605\) | 8.88495 | − | 33.1591i | 0.361225 | − | 1.34811i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.46383 | − | 4.26749i | −0.100004 | − | 0.173212i | 0.811682 | − | 0.584099i | \(-0.198552\pi\) |
−0.911686 | + | 0.410888i | \(0.865219\pi\) | |||||||
\(608\) | −22.9655 | + | 39.7774i | −0.931373 | + | 1.61319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.743690i | 0.0301111i | ||||||||
\(611\) | 26.0366 | − | 9.15560i | 1.05333 | − | 0.370396i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4249 | + | 2.79334i | −0.421057 | + | 0.112822i | −0.463125 | − | 0.886293i | \(-0.653272\pi\) |
0.0420682 | + | 0.999115i | \(0.486605\pi\) | |||||||
\(614\) | −7.07820 | − | 4.08660i | −0.285653 | − | 0.164922i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.46989 | + | 4.46989i | 0.180097 | + | 0.180097i | ||||
\(617\) | −33.9359 | − | 9.09310i | −1.36621 | − | 0.366074i | −0.500116 | − | 0.865958i | \(-0.666709\pi\) |
−0.866092 | + | 0.499884i | \(0.833376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.2332 | + | 27.2332i | −1.09459 | + | 1.09459i | −0.0995626 | + | 0.995031i | \(0.531744\pi\) |
−0.995031 | + | 0.0995626i | \(0.968256\pi\) | |||||||
\(620\) | −12.2689 | + | 7.08346i | −0.492732 | + | 0.284479i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.904983 | − | 3.37744i | −0.0362865 | − | 0.135423i | ||||
\(623\) | 21.8055 | 0.873617 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2881 | −1.09152 | ||||||||
\(626\) | 0.720817 | + | 2.69013i | 0.0288097 | + | 0.107519i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.3535 | − | 7.13232i | 0.492960 | − | 0.284611i | ||||
\(629\) | −8.45116 | + | 8.45116i | −0.336970 | + | 0.336970i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3657 | − | 9.47620i | −1.40788 | − | 0.377242i | −0.526715 | − | 0.850042i | \(-0.676577\pi\) |
−0.881170 | + | 0.472800i | \(0.843243\pi\) | |||||||
\(632\) | −0.665952 | − | 0.665952i | −0.0264902 | − | 0.0264902i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.55009 | − | 4.93640i | −0.339567 | − | 0.196049i | ||||
\(635\) | −56.1154 | + | 15.0361i | −2.22687 | + | 0.596688i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2171 | − | 9.04107i | 0.523679 | − | 0.358220i | ||||
\(638\) | 9.49387i | 0.375866i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.4491 | + | 30.2227i | −0.689737 | + | 1.19466i | ||||
\(641\) | −18.7159 | − | 32.4169i | −0.739234 | − | 1.28039i | −0.952840 | − | 0.303472i | \(-0.901854\pi\) |
0.213606 | − | 0.976920i | \(-0.431479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.10595 | + | 4.12746i | −0.0436144 | + | 0.162771i | −0.984298 | − | 0.176513i | \(-0.943518\pi\) |
0.940684 | + | 0.339284i | \(0.110185\pi\) | |||||||
\(644\) | 0.0720314 | − | 0.268825i | 0.00283843 | − | 0.0105932i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.66747 | + | 13.2804i | 0.301673 | + | 0.522512i | ||||
\(647\) | 19.9930 | − | 34.6289i | 0.786007 | − | 1.36140i | −0.142388 | − | 0.989811i | \(-0.545478\pi\) |
0.928396 | − | 0.371593i | \(-0.121188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.500639i | 0.0196518i | ||||||||
\(650\) | −5.36112 | + | 28.5748i | −0.210280 | + | 1.12080i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.0782 | + | 5.91585i | −0.864651 | + | 0.231682i | ||||
\(653\) | 11.7612 | + | 6.79035i | 0.460253 | + | 0.265727i | 0.712151 | − | 0.702027i | \(-0.247721\pi\) |
−0.251898 | + | 0.967754i | \(0.581055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.10804 | − | 6.10804i | −0.238661 | − | 0.238661i | ||||
\(656\) | −2.44909 | − | 0.656231i | −0.0956208 | − | 0.0256215i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.87756 | − | 6.87756i | 0.268115 | − | 0.268115i | ||||
\(659\) | −28.8666 | + | 16.6661i | −1.12448 | + | 0.649220i | −0.942541 | − | 0.334089i | \(-0.891571\pi\) |
−0.181941 | + | 0.983309i | \(0.558238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.02088 | + | 7.54201i | 0.0786029 | + | 0.293350i | 0.994026 | − | 0.109143i | \(-0.0348105\pi\) |
−0.915423 | + | 0.402493i | \(0.868144\pi\) | |||||||
\(662\) | −13.5653 | −0.527230 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40.3793 | 1.56702 | ||||||||
\(665\) | −12.6770 | − | 47.3113i | −0.491594 | − | 1.83465i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.890809 | − | 0.514309i | 0.0344923 | − | 0.0199141i | ||||
\(668\) | −2.29197 | + | 2.29197i | −0.0886789 | + | 0.0886789i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.7333 | + | 4.48367i | 0.646463 | + | 0.173219i | ||||
\(671\) | −0.251149 | − | 0.251149i | −0.00969551 | − | 0.00969551i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.8114 | − | 13.1702i | −0.879316 | − | 0.507673i | −0.00888322 | − | 0.999961i | \(-0.502828\pi\) |
−0.870433 | + | 0.492287i | \(0.836161\pi\) | |||||||
\(674\) | 14.9924 | − | 4.01719i | 0.577484 | − | 0.154736i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5867 | − | 6.45097i | −0.637950 | − | 0.248114i | ||||
\(677\) | 5.45329i | 0.209587i | 0.994494 | + | 0.104793i | \(0.0334181\pi\) | ||||
−0.994494 | + | 0.104793i | \(0.966582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.92167 | − | 15.4528i | 0.342382 | − | 0.593023i | ||||
\(680\) | 12.7815 | + | 22.1381i | 0.490146 | + | 0.848959i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.807145 | + | 3.01231i | −0.0309072 | + | 0.115347i | ||||
\(683\) | −0.462889 | + | 1.72753i | −0.0177120 | + | 0.0661019i | −0.974216 | − | 0.225617i | \(-0.927560\pi\) |
0.956504 | + | 0.291718i | \(0.0942270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.6356 | − | 65.1868i | −1.43798 | − | 2.49066i | ||||
\(686\) | 7.26888 | − | 12.5901i | 0.277527 | − | 0.480691i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 6.98121i | − | 0.266156i | ||||||
\(689\) | 24.0456 | + | 11.5342i | 0.916063 | + | 0.439418i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.03133 | − | 0.812242i | 0.115317 | − | 0.0308991i | −0.200699 | − | 0.979653i | \(-0.564321\pi\) |
0.316016 | + | 0.948754i | \(0.397655\pi\) | |||||||
\(692\) | 11.5643 | + | 6.67666i | 0.439609 | + | 0.253808i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.44331 | − | 9.44331i | −0.358463 | − | 0.358463i | ||||
\(695\) | 32.7525 | + | 8.77601i | 1.24237 | + | 0.332893i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.18702 | + | 7.18702i | −0.272228 | + | 0.272228i | ||||
\(698\) | 2.39391 | − | 1.38212i | 0.0906109 | − | 0.0523142i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.75328 | − | 21.4715i | −0.217454 | − | 0.811548i | ||||
\(701\) | −23.3688 | −0.882629 | −0.441315 | − | 0.897352i | \(-0.645488\pi\) | ||||
−0.441315 | + | 0.897352i | \(0.645488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.3134 | 1.44502 | ||||||||
\(704\) | 1.30467 | + | 4.86910i | 0.0491716 | + | 0.183511i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.4512 | − | 7.18868i | 0.468606 | − | 0.270550i | ||||
\(707\) | −9.88829 | + | 9.88829i | −0.371887 | + | 0.371887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.62430 | − | 1.77498i | −0.248781 | − | 0.0666606i | 0.132274 | − | 0.991213i | \(-0.457772\pi\) |
−0.381054 | + | 0.924553i | \(0.624439\pi\) | |||||||
\(710\) | 2.04245 | + | 2.04245i | 0.0766519 | + | 0.0766519i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.5940 | + | 18.2408i | 1.18404 | + | 0.683604i | ||||
\(713\) | 0.326370 | − | 0.0874505i | 0.0122226 | − | 0.00327505i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.7008 | − | 17.1054i | −0.437586 | − | 0.639704i | ||||
\(716\) | − | 4.66277i | − | 0.174256i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.12135 | − | 14.0666i | 0.303086 | − | 0.524961i | ||||
\(719\) | 2.72338 | + | 4.71703i | 0.101565 | + | 0.175916i | 0.912330 | − | 0.409457i | \(-0.134282\pi\) |
−0.810765 | + | 0.585372i | \(0.800948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39026 | − | 8.92056i | 0.0890178 | − | 0.332219i | ||||
\(722\) | 8.81697 | − | 32.9054i | 0.328134 | − | 1.22461i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.05949 | + | 12.2274i | 0.262364 | + | 0.454427i | ||||
\(725\) | 41.0788 | − | 71.1506i | 1.52563 | − | 2.64247i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8286i | 0.698316i | 0.937064 | + | 0.349158i | \(0.113532\pi\) | ||||
−0.937064 | + | 0.349158i | \(0.886468\pi\) | |||||||
\(728\) | −15.3896 | + | 1.17710i | −0.570375 | + | 0.0436263i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.0328 | + | 5.09983i | −0.704436 | + | 0.188753i | ||||
\(731\) | −24.2362 | − | 13.9928i | −0.896409 | − | 0.517542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0612 | + | 13.0612i | 0.482427 | + | 0.482427i | 0.905906 | − | 0.423479i | \(-0.139191\pi\) |
−0.423479 | + | 0.905906i | \(0.639191\pi\) | |||||||
\(734\) | 18.1769 | + | 4.87049i | 0.670922 | + | 0.179773i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.524701 | − | 0.524701i | 0.0193407 | − | 0.0193407i | ||||
\(737\) | −7.16512 | + | 4.13678i | −0.263931 | + | 0.152380i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.11762 | + | 22.8313i | 0.225040 | + | 0.839862i | 0.982388 | + | 0.186851i | \(0.0598280\pi\) |
−0.757348 | + | 0.653012i | \(0.773505\pi\) | |||||||
\(740\) | 25.9527 | 0.954039 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.39837 | 0.345025 | ||||||||
\(743\) | −5.89718 | − | 22.0086i | −0.216347 | − | 0.807417i | −0.985688 | − | 0.168579i | \(-0.946082\pi\) |
0.769342 | − | 0.638838i | \(-0.220584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.7925 | + | 30.4798i | −1.93417 | + | 1.11669i | ||||
\(746\) | −1.11638 | + | 1.11638i | −0.0408736 | + | 0.0408736i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.79195 | − | 1.28400i | −0.175211 | − | 0.0469476i | ||||
\(749\) | −5.73499 | − | 5.73499i | −0.209552 | − | 0.209552i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7803 | + | 13.1522i | 0.831266 | + | 0.479931i | 0.854286 | − | 0.519804i | \(-0.173995\pi\) |
−0.0230202 | + | 0.999735i | \(0.507328\pi\) | |||||||
\(752\) | −4.52630 | + | 1.21282i | −0.165057 | + | 0.0442269i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.5935 | − | 15.0934i | −0.640716 | − | 0.549668i | ||||
\(755\) | − | 78.2562i | − | 2.84803i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.61207 | − | 9.72038i | 0.203974 | − | 0.353293i | −0.745831 | − | 0.666135i | \(-0.767948\pi\) |
0.949805 | + | 0.312842i | \(0.101281\pi\) | |||||||
\(758\) | 2.68731 | + | 4.65455i | 0.0976073 | + | 0.169061i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 21.2093 | − | 79.1542i | 0.769342 | − | 2.87123i | ||||
\(761\) | 2.36137 | − | 8.81276i | 0.0855997 | − | 0.319462i | −0.909827 | − | 0.414987i | \(-0.863786\pi\) |
0.995427 | + | 0.0955245i | \(0.0304528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9633 | + | 18.9889i | 0.396897 | + | 0.687446i | ||||
\(764\) | −6.80146 | + | 11.7805i | −0.246068 | + | 0.426202i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.26484i | 0.0818319i | ||||||||
\(767\) | −0.927754 | − | 0.795916i | −0.0334993 | − | 0.0287389i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.2388 | − | 13.1935i | 1.77560 | − | 0.475770i | 0.785828 | − | 0.618445i | \(-0.212237\pi\) |
0.989770 | + | 0.142675i | \(0.0455703\pi\) | |||||||
\(770\) | −6.32502 | − | 3.65175i | −0.227938 | − | 0.131600i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.38600 | − | 1.38600i | −0.0498832 | − | 0.0498832i | ||||
\(773\) | −15.3153 | − | 4.10372i | −0.550852 | − | 0.147600i | −0.0273518 | − | 0.999626i | \(-0.508707\pi\) |
−0.523500 | + | 0.852025i | \(0.675374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.0829 | − | 19.0829i | 0.685480 | − | 0.685480i | ||||
\(776\) | 25.8533 | − | 14.9264i | 0.928079 | − | 0.535827i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.86817 | + | 25.6324i | 0.246236 | + | 0.918964i | ||||
\(779\) | 32.5825 | 1.16739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.37950 | −0.0493625 | ||||||||
\(782\) | −0.0641209 | − | 0.239303i | −0.00229296 | − | 0.00855744i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.35459 | + | 1.35942i | −0.0840925 | + | 0.0485508i | ||||
\(785\) | −28.6789 | + | 28.6789i | −1.02359 | + | 1.02359i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.9551 | − | 7.75850i | −1.03214 | − | 0.276561i | −0.297286 | − | 0.954788i | \(-0.596082\pi\) |
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(788\) | −17.2076 | − | 17.2076i | −0.612995 | − | 0.612995i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.942342 | + | 0.544061i | 0.0335270 | + | 0.0193568i | ||||
\(791\) | −21.0824 | + | 5.64902i | −0.749605 | + | 0.200856i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.864692 | − | 0.0661378i | 0.0307061 | − | 0.00234862i | ||||
\(794\) | − | 14.1843i | − | 0.503382i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.61106 | − | 13.1827i | 0.269767 | − | 0.467250i | ||||
\(797\) | 1.19542 | + | 2.07053i | 0.0423439 | + | 0.0733418i | 0.886421 | − | 0.462881i | \(-0.153184\pi\) |
−0.844077 | + | 0.536222i | \(0.819851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.86182 | + | 18.1446i | −0.171999 | + | 0.641909i | ||||
\(800\) | 15.3397 | − | 57.2486i | 0.542341 | − | 2.02404i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.40894 | + | 11.1006i | 0.226307 | + | 0.391976i | ||||
\(803\) | 4.70527 | − | 8.14977i | 0.166045 | − | 0.287599i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.791302i | 0.0278897i | ||||||||
\(806\) | −4.29903 | − | 6.28472i | −0.151427 | − | 0.221370i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22.5990 | + | 6.05538i | −0.795030 | + | 0.213028i | ||||
\(809\) | −27.2960 | − | 15.7594i | −0.959678 | − | 0.554070i | −0.0636037 | − | 0.997975i | \(-0.520259\pi\) |
−0.896074 | + | 0.443905i | \(0.853593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2928 | − | 17.2928i | −0.607232 | − | 0.607232i | 0.334990 | − | 0.942222i | \(-0.391267\pi\) |
−0.942222 | + | 0.334990i | \(0.891267\pi\) | |||||||
\(812\) | 17.1195 | + | 4.58717i | 0.600778 | + | 0.160978i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.03968 | − | 4.03968i | 0.141591 | − | 0.141591i | ||||
\(815\) | 56.2818 | − | 32.4943i | 1.97147 | − | 1.13823i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.2194 | + | 86.6559i | 0.812343 | + | 3.03171i | ||||
\(818\) | −19.3886 | −0.677906 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.0706 | 0.770740 | ||||||||
\(821\) | 1.10028 | + | 4.10629i | 0.0383999 | + | 0.143310i | 0.982464 | − | 0.186451i | \(-0.0596985\pi\) |
−0.944064 | + | 0.329761i | \(0.893032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7990 | + | 16.6271i | −1.00387 | + | 0.579585i | −0.909391 | − | 0.415942i | \(-0.863452\pi\) |
−0.0944794 | + | 0.995527i | \(0.530119\pi\) | |||||||
\(824\) | 10.9255 | − | 10.9255i | 0.380609 | − | 0.380609i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.416100 | − | 0.111494i | −0.0144780 | − | 0.00387936i | ||||
\(827\) | −17.6567 | − | 17.6567i | −0.613984 | − | 0.613984i | 0.329997 | − | 0.943982i | \(-0.392952\pi\) |
−0.943982 | + | 0.329997i | \(0.892952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.19452 | + | 2.99906i | 0.180413 | + | 0.104162i | 0.587487 | − | 0.809234i | \(-0.300117\pi\) |
−0.407074 | + | 0.913395i | \(0.633451\pi\) | |||||||
\(830\) | −45.0633 | + | 12.0747i | −1.56417 | + | 0.419118i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.0973 | − | 5.32315i | −0.384729 | − | 0.184547i | ||||
\(833\) | 10.8990i | 0.377629i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.60798 | − | 7.98126i | 0.159466 | − | 0.276203i | ||||
\(836\) | 7.95167 | + | 13.7727i | 0.275014 | + | 0.476339i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.43399 | + | 27.7440i | −0.256803 | + | 0.958401i | ||||
\(839\) | −3.75035 | + | 13.9965i | −0.129477 | + | 0.483213i | −0.999960 | − | 0.00898522i | \(-0.997140\pi\) |
0.870483 | + | 0.492198i | \(0.163807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.2527 | + | 31.6146i | 0.629403 | + | 1.09016i | ||||
\(842\) | 2.94246 | − | 5.09649i | 0.101404 | − | 0.175637i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 11.0997i | − | 0.382069i | ||||||
\(845\) | 50.3006 | + | 5.51082i | 1.73039 | + | 0.189578i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6266 | + | 3.65124i | −0.468216 | + | 0.125458i | ||||
\(848\) | −3.92133 | − | 2.26398i | −0.134659 | − | 0.0777454i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.9921 | − | 13.9921i | −0.479925 | − | 0.479925i | ||||
\(851\) | −0.597883 | − | 0.160202i | −0.0204952 | − | 0.00549167i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.04887 | + | 6.04887i | −0.207110 | + | 0.207110i | −0.803038 | − | 0.595928i | \(-0.796784\pi\) |
0.595928 | + | 0.803038i | \(0.296784\pi\) | |||||||
\(854\) | 0.264672 | − | 0.152808i | 0.00905688 | − | 0.00522899i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.51199 | − | 13.1069i | −0.120037 | − | 0.447985i | ||||
\(857\) | −26.6863 | −0.911588 | −0.455794 | − | 0.890085i | \(-0.650645\pi\) | ||||
−0.455794 | + | 0.890085i | \(0.650645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.3033 | −0.488022 | −0.244011 | − | 0.969773i | \(-0.578463\pi\) | ||||
−0.244011 | + | 0.969773i | \(0.578463\pi\) | |||||||
\(860\) | 15.7283 | + | 58.6988i | 0.536330 | + | 2.00161i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1233 | + | 5.84469i | −0.344801 | + | 0.199071i | ||||
\(863\) | −1.53000 | + | 1.53000i | −0.0520819 | + | 0.0520819i | −0.732668 | − | 0.680586i | \(-0.761725\pi\) |
0.680586 | + | 0.732668i | \(0.261725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.6733 | − | 9.82658i | −1.24693 | − | 0.334114i | ||||
\(866\) | 7.07608 | + | 7.07608i | 0.240455 | + | 0.240455i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.04187 | + | 2.91092i | 0.171132 | + | 0.0988032i | ||||
\(869\) | −0.501969 | + | 0.134502i | −0.0170281 | + | 0.00456267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72507 | − | 19.8546i | 0.126219 | − | 0.672749i | ||||
\(872\) | 36.6842i | 1.24228i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.397094 | + | 0.687787i | −0.0134319 | + | 0.0232648i | ||||
\(875\) | 16.0358 | + | 27.7748i | 0.542108 | + | 0.938959i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.83843 | − | 14.3252i | 0.129614 | − | 0.483728i | −0.870348 | − | 0.492438i | \(-0.836106\pi\) |
0.999962 | + | 0.00871020i | \(0.00277258\pi\) | |||||||
\(878\) | 4.96573 | − | 18.5323i | 0.167585 | − | 0.625436i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.75935 | + | 3.04728i | 0.0593076 | + | 0.102724i | ||||
\(881\) | −16.0129 | + | 27.7351i | −0.539488 | + | 0.934420i | 0.459444 | + | 0.888207i | \(0.348049\pi\) |
−0.998932 | + | 0.0462131i | \(0.985285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.05381i | 0.102769i | 0.998679 | + | 0.0513844i | \(0.0163634\pi\) | ||||
−0.998679 | + | 0.0513844i | \(0.983637\pi\) | |||||||
\(884\) | 9.99767 | − | 6.83885i | 0.336258 | − | 0.230015i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.4290 | − | 3.86624i | 0.484752 | − | 0.129889i | ||||
\(887\) | −7.75681 | − | 4.47840i | −0.260448 | − | 0.150370i | 0.364091 | − | 0.931363i | \(-0.381380\pi\) |
−0.624539 | + | 0.780994i | \(0.714713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8814 | + | 16.8814i | 0.566184 | + | 0.566184i | ||||
\(890\) | −40.7135 | − | 10.9091i | −1.36472 | − | 0.365675i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.05289 | − | 3.05289i | 0.102218 | − | 0.102218i | ||||
\(893\) | 52.1499 | − | 30.1088i | 1.74513 | − | 1.00755i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.43129 | + | 12.8057i | 0.114695 | + | 0.428049i | ||||
\(896\) | 14.3413 | 0.479109 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0621 | −0.536001 | ||||||||
\(899\) | 5.56911 | + | 20.7842i | 0.185740 | + | 0.693192i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.7194 | + | 9.07562i | −0.523690 | + | 0.302353i | ||||
\(902\) | 3.43542 | − | 3.43542i | 0.114387 | − | 0.114387i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −35.2720 | − | 9.45111i | −1.17313 | − | 0.314339i | ||||
\(905\) | −28.3861 | − | 28.3861i | −0.943584 | − | 0.943584i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.7841 | + | 18.3506i | 1.05537 | + | 0.609320i | 0.924149 | − | 0.382033i | \(-0.124776\pi\) |
0.131224 | + | 0.991353i | \(0.458109\pi\) | |||||||
\(908\) | −32.2550 | + | 8.64271i | −1.07042 | + | 0.286818i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.8227 | − | 5.91560i | 0.557668 | − | 0.196100i | ||||
\(911\) | 40.1992i | 1.33186i | 0.746014 | + | 0.665930i | \(0.231965\pi\) | ||||
−0.746014 | + | 0.665930i | \(0.768035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1405 | − | 19.2959i | 0.368696 | − | 0.638601i | ||||
\(914\) | 12.0189 | + | 20.8174i | 0.397551 | + | 0.688579i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.473842 | − | 1.76840i | 0.0156562 | − | 0.0584296i | ||||
\(917\) | −0.918752 | + | 3.42883i | −0.0303399 | + | 0.113230i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.46542 | + | 7.73433i | 0.147301 | + | 0.255132i | 0.930229 | − | 0.366980i | \(-0.119608\pi\) |
−0.782928 | + | 0.622112i | \(0.786275\pi\) | |||||||
\(920\) | −0.661945 | + | 1.14652i | −0.0218237 | + | 0.0377997i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 14.6051i | − | 0.480993i | ||||||
\(923\) | 2.19313 | − | 2.55641i | 0.0721878 | − | 0.0841453i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.7541 | + | 12.7957i | −1.57015 | + | 0.420719i | ||||
\(926\) | −5.70414 | − | 3.29328i | −0.187450 | − | 0.108224i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.4145 | + | 33.4145i | 1.09689 | + | 1.09689i | ||||
\(929\) | −34.3628 | − | 9.20749i | −1.12741 | − | 0.302088i | −0.353530 | − | 0.935423i | \(-0.615019\pi\) |
−0.773877 | + | 0.633335i | \(0.781685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.7055 | − | 24.7055i | 0.809689 | − | 0.809689i | ||||
\(932\) | −4.29914 | + | 2.48211i | −0.140823 | + | 0.0813043i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.31320 | − | 19.8291i | −0.173853 | − | 0.648829i | ||||
\(935\) | 14.1054 | 0.461296 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.6097 | 1.65335 | 0.826673 | − | 0.562682i | \(-0.190231\pi\) | ||||
0.826673 | + | 0.562682i | \(0.190231\pi\) | |||||||
\(938\) | −1.84255 | − | 6.87648i | −0.0601613 | − | 0.224525i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 35.3252 | − | 20.3950i | 1.15218 | − | 0.665212i | ||||
\(941\) | −9.82184 | + | 9.82184i | −0.320183 | + | 0.320183i | −0.848837 | − | 0.528654i | \(-0.822697\pi\) |
0.528654 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.508451 | − | 0.136239i | −0.0165574 | − | 0.00443655i | ||||
\(944\) | 0.146754 | + | 0.146754i | 0.00477643 | + | 0.00477643i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5850 | + | 6.68860i | 0.376661 | + | 0.217465i | ||||
\(947\) | −11.4112 | + | 3.05763i | −0.370815 | + | 0.0993597i | −0.439414 | − | 0.898285i | \(-0.644814\pi\) |
0.0685986 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.62223 | + | 21.6760i | 0.247428 | + | 0.703634i | ||||
\(950\) | 63.4334i | 2.05805i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.25249 | − | 9.09758i | 0.170234 | − | 0.294854i | ||||
\(953\) | 3.32064 | + | 5.75152i | 0.107566 | + | 0.186310i | 0.914784 | − | 0.403944i | \(-0.132361\pi\) |
−0.807218 | + | 0.590254i | \(0.799028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0103 | − | 37.3588i | 0.323924 | − | 1.20890i | ||||
\(956\) | −0.522777 | + | 1.95103i | −0.0169078 | + | 0.0631008i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.63259 | − | 4.55979i | −0.0850553 | − | 0.147320i | ||||
\(959\) | −15.4662 | + | 26.7883i | −0.499430 | + | 0.865039i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 23.9319i | − | 0.771997i | ||||||
\(962\) | 1.06381 | + | 13.9084i | 0.0342986 | + | 0.448424i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.65370 | + | 2.31875i | −0.278717 | + | 0.0746820i | ||||
\(965\) | 4.82642 | + | 2.78654i | 0.155368 | + | 0.0897018i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.4796 | − | 12.4796i | −0.401318 | − | 0.401318i | 0.477380 | − | 0.878697i | \(-0.341587\pi\) |
−0.878697 | + | 0.477380i | \(0.841587\pi\) | |||||||
\(968\) | −22.7980 | − | 6.10871i | −0.732756 | − | 0.196341i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.3888 | + | 24.3888i | −0.783076 | + | 0.783076i | ||||
\(971\) | 28.4284 | − | 16.4132i | 0.912312 | − | 0.526724i | 0.0311377 | − | 0.999515i | \(-0.490087\pi\) |
0.881174 | + | 0.472792i | \(0.156754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.60647 | − | 13.4595i | −0.115618 | − | 0.431493i | ||||
\(974\) | −8.88980 | −0.284847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.147240 | −0.00471305 | ||||||||
\(977\) | −1.29137 | − | 4.81947i | −0.0413147 | − | 0.154189i | 0.942187 | − | 0.335088i | \(-0.108766\pi\) |
−0.983502 | + | 0.180899i | \(0.942099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4333 | − | 10.0651i | 0.557172 | − | 0.321683i | ||||
\(980\) | 16.7349 | − | 16.7349i | 0.534578 | − | 0.534578i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.7638 | − | 5.83159i | −0.694510 | − | 0.186094i | ||||
\(983\) | −33.3284 | − | 33.3284i | −1.06301 | − | 1.06301i | −0.997877 | − | 0.0651332i | \(-0.979253\pi\) |
−0.0651332 | − | 0.997877i | \(-0.520747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.9215 | + | 34.5957i | 1.90926 | + | 1.10231i | ||||
\(986\) | 15.2395 | − | 4.08341i | 0.485324 | − | 0.130042i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.1643 | − | 7.16027i | −1.21417 | − | 0.227799i | ||||
\(989\) | − | 1.44936i | − | 0.0460869i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.1712 | − | 47.0620i | 0.863123 | − | 1.49497i | −0.00577642 | − | 0.999983i | \(-0.501839\pi\) |
0.868899 | − | 0.494989i | \(-0.164828\pi\) | |||||||
\(992\) | 7.76126 | + | 13.4429i | 0.246420 | + | 0.426813i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.307219 | − | 1.14656i | 0.00974440 | − | 0.0363666i | ||||
\(995\) | −11.2018 | + | 41.8058i | −0.355122 | + | 1.32533i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.900561 | + | 1.55982i | 0.0285211 | + | 0.0493999i | 0.879934 | − | 0.475097i | \(-0.157587\pi\) |
−0.851413 | + | 0.524497i | \(0.824254\pi\) | |||||||
\(998\) | 14.0941 | − | 24.4117i | 0.446141 | − | 0.772739i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 351.2.bd.e.215.3 | yes | 20 | |
3.2 | odd | 2 | 351.2.bd.d.215.3 | yes | 20 | ||
13.2 | odd | 12 | 351.2.bd.d.80.3 | ✓ | 20 | ||
39.2 | even | 12 | inner | 351.2.bd.e.80.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
351.2.bd.d.80.3 | ✓ | 20 | 13.2 | odd | 12 | ||
351.2.bd.d.215.3 | yes | 20 | 3.2 | odd | 2 | ||
351.2.bd.e.80.3 | yes | 20 | 39.2 | even | 12 | inner | |
351.2.bd.e.215.3 | yes | 20 | 1.1 | even | 1 | trivial |