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.d.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 | \(-0.992718\pi\) |
0.854361 | − | 0.519679i | \(-0.173949\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.18559 | − | 0.684501i | 0.592795 | − | 0.342250i | ||||
\(5\) | 2.75236 | − | 2.75236i | 1.23089 | − | 1.23089i | 0.267274 | − | 0.963620i | \(-0.413877\pi\) |
0.963620 | − | 0.267274i | \(-0.0861230\pi\) | |||||||
\(6\) | 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 | −0.467358 | − | 0.884068i | \(-0.654794\pi\) |
0.0372897 | + | 0.999304i | \(0.488128\pi\) | |||||||
\(12\) | 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 | 0.975584 | − | 0.219626i | \(-0.0704836\pi\) |
−0.677993 | + | 0.735068i | \(0.737150\pi\) | |||||||
\(18\) | 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 | −0.872574 | − | 0.488481i | \(-0.837551\pi\) |
0.859324 | + | 0.511431i | \(0.170884\pi\) | |||||||
\(24\) | 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 | −0.320903 | − | 0.947112i | \(-0.603986\pi\) |
−0.980675 | + | 0.195646i | \(0.937320\pi\) | |||||||
\(30\) | 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 | \(0.0214996\pi\) |
−0.830305 | + | 0.557309i | \(0.811834\pi\) | |||||||
\(42\) | 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 | 0.981416 | − | 0.191892i | \(-0.0614625\pi\) |
−0.191892 | + | 0.981416i | \(0.561462\pi\) | |||||||
\(48\) | 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 | \(0.169615\pi\) | ||||
−0.861357 | + | 0.508001i | \(0.830385\pi\) | |||||||
\(54\) | 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 | −0.959979 | − | 0.280073i | \(-0.909641\pi\) |
0.971402 | + | 0.237439i | \(0.0763081\pi\) | |||||||
\(60\) | 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 | 0.311966 | − | 0.950093i | \(-0.399013\pi\) |
−0.204876 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(72\) | 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 | \(0.560569\pi\) |
−0.981951 | + | 0.189138i | \(0.939431\pi\) | |||||||
\(84\) | 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 | −0.876817 | − | 0.480824i | \(-0.840338\pi\) |
−0.518934 | + | 0.854814i | \(0.673671\pi\) | |||||||
\(90\) | 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 | −0.562342 | − | 0.826905i | \(-0.690099\pi\) |
0.997292 | + | 0.0735496i | \(0.0234327\pi\) | |||||||
\(102\) | 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 | 0.697002 | − | 0.717069i | \(-0.254517\pi\) |
−0.272499 | + | 0.962156i | \(0.587850\pi\) | |||||||
\(108\) | 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 | 0.172383 | − | 0.985030i | \(-0.444853\pi\) |
0.939253 | + | 0.343227i | \(0.111520\pi\) | |||||||
\(114\) | 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 | \(-0.969093\pi\) | ||
0.995290 | − | 0.0969461i | \(-0.0309074\pi\) | |||||||
\(132\) | 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 | \(-0.607237\pi\) |
0.758165 | − | 0.652063i | \(-0.226096\pi\) | |||||||
\(138\) | 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 | −0.421097 | − | 0.907016i | \(-0.638355\pi\) |
−0.818188 | + | 0.574950i | \(0.805021\pi\) | |||||||
\(150\) | 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 | −0.169245 | − | 0.985574i | \(-0.554133\pi\) |
0.346217 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(168\) | 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 | 0.618894 | − | 0.785474i | \(-0.287581\pi\) |
−0.989688 | + | 0.143241i | \(0.954248\pi\) | |||||||
\(174\) | 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 | −0.922625 | − | 0.385699i | \(-0.873960\pi\) |
0.795338 | + | 0.606167i | \(0.207294\pi\) | |||||||
\(180\) | 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 | −0.155252 | − | 0.987875i | \(-0.549619\pi\) |
0.777899 | + | 0.628389i | \(0.216286\pi\) | |||||||
\(192\) | 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 | \(0.134942\pi\) |
−0.583690 | + | 0.811977i | \(0.698392\pi\) | |||||||
\(198\) | 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 | 0.933863 | − | 0.357630i | \(-0.116415\pi\) |
0.629934 | + | 0.776648i | \(0.283082\pi\) | |||||||
\(228\) | 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 | \(-0.462102\pi\) | ||||
0.118779 | + | 0.992921i | \(0.462102\pi\) | |||||||
\(234\) | 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 | −0.672559 | − | 0.740043i | \(-0.734805\pi\) |
0.740043 | + | 0.672559i | \(0.234805\pi\) | |||||||
\(240\) | 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 | \(0.116633\pi\) |
−0.156539 | + | 0.987672i | \(0.550034\pi\) | |||||||
\(252\) | 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 | −0.603152 | − | 0.797626i | \(-0.706089\pi\) |
0.992341 | + | 0.123532i | \(0.0394222\pi\) | |||||||
\(258\) | 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 | −0.238458 | − | 0.971153i | \(-0.576642\pi\) |
−0.960272 | + | 0.279066i | \(0.909975\pi\) | |||||||
\(264\) | 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 | −0.974173 | − | 0.225804i | \(-0.927499\pi\) |
−0.291534 | + | 0.956560i | \(0.594166\pi\) | |||||||
\(270\) | 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 | 0.108628 | − | 0.994082i | \(-0.465354\pi\) |
−0.994082 | + | 0.108628i | \(0.965354\pi\) | |||||||
\(282\) | 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 | −0.994750 | − | 0.102336i | \(-0.967368\pi\) |
0.912647 | + | 0.408749i | \(0.134035\pi\) | |||||||
\(294\) | 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 | \(-0.460171\pi\) | ||||
0.124802 | + | 0.992182i | \(0.460171\pi\) | |||||||
\(312\) | 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 | −0.415834 | − | 0.909441i | \(-0.636510\pi\) |
0.909441 | + | 0.415834i | \(0.136510\pi\) | |||||||
\(318\) | 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 | −0.0553898 | − | 0.998465i | \(-0.517640\pi\) |
0.837001 | + | 0.547201i | \(0.184307\pi\) | |||||||
\(348\) | 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 | \(0.0766355\pi\) |
−0.721828 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(354\) | 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 | 0.976882 | − | 0.213781i | \(-0.0685778\pi\) |
−0.213781 | + | 0.976882i | \(0.568578\pi\) | |||||||
\(360\) | 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 | 0.187770 | − | 0.982213i | \(-0.439874\pi\) |
−0.328493 | + | 0.944506i | \(0.606541\pi\) | |||||||
\(384\) | 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 | \(-0.821526\pi\) | ||||
−0.846887 | + | 0.531772i | \(0.821526\pi\) | |||||||
\(390\) | 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 | −0.626056 | − | 0.779778i | \(-0.715332\pi\) |
−0.152291 | + | 0.988336i | \(0.548665\pi\) | |||||||
\(402\) | 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 | \(-0.988696\pi\) |
−0.530432 | − | 0.847727i | \(-0.677970\pi\) | |||||||
\(420\) | 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 | \(-0.968014\pi\) |
0.811498 | − | 0.584355i | \(-0.198652\pi\) | |||||||
\(432\) | 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 | \(0.147412\pi\) | ||||
−0.894668 | + | 0.446731i | \(0.852588\pi\) | |||||||
\(444\) | 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 | \(-0.758344\pi\) |
0.972378 | − | 0.233413i | \(-0.0749894\pi\) | |||||||
\(450\) | 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 | 0.647469 | − | 0.762092i | \(-0.275828\pi\) |
0.179679 | + | 0.983725i | \(0.442494\pi\) | |||||||
\(462\) | 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 | \(-0.295986\pi\) | ||||
0.597939 | + | 0.801541i | \(0.295986\pi\) | |||||||
\(468\) | 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 | −0.109568 | − | 0.993979i | \(-0.534947\pi\) |
0.402101 | + | 0.915595i | \(0.368280\pi\) | |||||||
\(480\) | 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 | \(-0.612252\pi\) |
0.985424 | − | 0.170118i | \(-0.0544148\pi\) | |||||||
\(492\) | 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 | −0.728400 | − | 0.685152i | \(-0.759736\pi\) |
0.229159 | + | 0.973389i | \(0.426402\pi\) | |||||||
\(504\) | 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 | \(-0.936014\pi\) |
0.748753 | − | 0.662849i | \(-0.230653\pi\) | |||||||
\(510\) | 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 | \(-0.983780\pi\) | ||
0.998702 | − | 0.0509338i | \(-0.0162197\pi\) | |||||||
\(522\) | 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 | −0.162310 | − | 0.986740i | \(-0.551895\pi\) |
0.352805 | + | 0.935697i | \(0.385228\pi\) | |||||||
\(558\) | 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 | \(-0.799734\pi\) |
−0.105359 | − | 0.994434i | \(-0.533599\pi\) | |||||||
\(564\) | 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 | \(0.451565\pi\) |
−0.931807 | + | 0.362953i | \(0.881768\pi\) | |||||||
\(570\) | 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 | 0.972462 | − | 0.233063i | \(-0.0748749\pi\) |
−0.958708 | + | 0.284392i | \(0.908208\pi\) | |||||||
\(588\) | 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 | 0.532408 | − | 0.846488i | \(-0.321287\pi\) |
−0.846488 | + | 0.532408i | \(0.821287\pi\) | |||||||
\(594\) | 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 | \(0.359024\pi\) | ||||
−0.428551 | + | 0.903518i | \(0.640976\pi\) | |||||||
\(600\) | 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 | 0.866092 | − | 0.499884i | \(-0.166624\pi\) |
0.500116 | + | 0.865958i | \(0.333291\pi\) | |||||||
\(618\) | 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 | \(0.0981458\pi\) |
−0.213606 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(642\) | 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 | \(0.454522\pi\) |
−0.928396 | + | 0.371593i | \(0.878812\pi\) | |||||||
\(648\) | 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 | 0.251898 | − | 0.967754i | \(-0.418945\pi\) |
−0.712151 | + | 0.702027i | \(0.752279\pi\) | |||||||
\(654\) | 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 | 0.181941 | − | 0.983309i | \(-0.441762\pi\) |
0.942541 | + | 0.334089i | \(0.108429\pi\) | |||||||
\(660\) | 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 | \(-0.966582\pi\) | ||
0.994494 | − | 0.104793i | \(-0.0334181\pi\) | |||||||
\(678\) | 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 | −0.956504 | − | 0.291718i | \(-0.905773\pi\) |
0.974216 | + | 0.225617i | \(0.0724396\pi\) | |||||||
\(684\) | 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 | \(-0.354512\pi\) | ||||
0.441315 | + | 0.897352i | \(0.354512\pi\) | |||||||
\(702\) | 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 | 0.810765 | − | 0.585372i | \(-0.199052\pi\) |
−0.912330 | + | 0.409457i | \(0.865718\pi\) | |||||||
\(720\) | 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 | \(0.0539178\pi\) |
−0.769342 | + | 0.638838i | \(0.779416\pi\) | |||||||
\(744\) | 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 | −0.995427 | − | 0.0955245i | \(-0.969547\pi\) |
0.909827 | + | 0.414987i | \(0.136214\pi\) | |||||||
\(762\) | 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 | 0.523500 | − | 0.852025i | \(-0.324626\pi\) |
0.0273518 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(774\) | 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 | 0.844077 | − | 0.536222i | \(-0.180149\pi\) |
−0.886421 | + | 0.462881i | \(0.846816\pi\) | |||||||
\(798\) | 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 | 0.896074 | − | 0.443905i | \(-0.146407\pi\) |
0.0636037 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(810\) | 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 | 0.944064 | − | 0.329761i | \(-0.106968\pi\) |
−0.982464 | + | 0.186451i | \(0.940302\pi\) | |||||||
\(822\) | 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 | 0.943982 | − | 0.329997i | \(-0.107048\pi\) |
−0.329997 | + | 0.943982i | \(0.607048\pi\) | |||||||
\(828\) | 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 | −0.870483 | − | 0.492198i | \(-0.836193\pi\) |
0.999960 | + | 0.00898522i | \(0.00286012\pi\) | |||||||
\(840\) | 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 | \(-0.349355\pi\) | ||||
0.455794 | + | 0.890085i | \(0.349355\pi\) | |||||||
\(858\) | 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 | −0.680586 | − | 0.732668i | \(-0.738275\pi\) |
0.732668 | + | 0.680586i | \(0.238275\pi\) | |||||||
\(864\) | 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 | \(-0.651951\pi\) |
0.998932 | − | 0.0462131i | \(-0.0147153\pi\) | |||||||
\(882\) | 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 | 0.624539 | − | 0.780994i | \(-0.285287\pi\) |
−0.364091 | + | 0.931363i | \(0.618620\pi\) | |||||||
\(888\) | 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 | \(-0.768035\pi\) | ||
0.746014 | − | 0.665930i | \(-0.231965\pi\) | |||||||
\(912\) | 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 | 0.773877 | − | 0.633335i | \(-0.218315\pi\) |
0.353530 | + | 0.935423i | \(0.384981\pi\) | |||||||
\(930\) | 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 | −0.528654 | − | 0.848837i | \(-0.677303\pi\) |
0.848837 | + | 0.528654i | \(0.177303\pi\) | |||||||
\(942\) | 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 | −0.0685986 | − | 0.997644i | \(-0.521853\pi\) |
0.439414 | + | 0.898285i | \(0.355186\pi\) | |||||||
\(948\) | 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 | 0.807218 | − | 0.590254i | \(-0.200972\pi\) |
−0.914784 | + | 0.403944i | \(0.867639\pi\) | |||||||
\(954\) | 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 | −0.881174 | − | 0.472792i | \(-0.843246\pi\) |
−0.0311377 | + | 0.999515i | \(0.509913\pi\) | |||||||
\(972\) | 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 | 0.983502 | − | 0.180899i | \(-0.0579007\pi\) |
−0.942187 | + | 0.335088i | \(0.891234\pi\) | |||||||
\(978\) | 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 | \(0.0207472\pi\) |
0.0651332 | + | 0.997877i | \(0.479253\pi\) | |||||||
\(984\) | 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.d.215.3 | yes | 20 | |
3.2 | odd | 2 | 351.2.bd.e.215.3 | yes | 20 | ||
13.2 | odd | 12 | 351.2.bd.e.80.3 | yes | 20 | ||
39.2 | even | 12 | inner | 351.2.bd.d.80.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
351.2.bd.d.80.3 | ✓ | 20 | 39.2 | even | 12 | inner | |
351.2.bd.d.215.3 | yes | 20 | 1.1 | even | 1 | trivial | |
351.2.bd.e.80.3 | yes | 20 | 13.2 | odd | 12 | ||
351.2.bd.e.215.3 | yes | 20 | 3.2 | odd | 2 |