Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(527,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.527");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 527.11 | ||
Character | \(\chi\) | \(=\) | 1232.527 |
Dual form | 1232.2.bi.b.879.11 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.31308 | − | 0.758109i | 0.758109 | − | 0.437694i | −0.0705073 | − | 0.997511i | \(-0.522462\pi\) |
0.828616 | + | 0.559817i | \(0.189128\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.222329 | + | 0.385085i | −0.0994286 | + | 0.172215i | −0.911448 | − | 0.411415i | \(-0.865035\pi\) |
0.812020 | + | 0.583630i | \(0.198368\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.33979 | + | 1.23506i | −0.884358 | + | 0.466810i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.350541 | + | 0.607155i | −0.116847 | + | 0.202385i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.28850 | − | 0.430977i | −0.991521 | − | 0.129944i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.68613i | − | 1.02235i | −0.859477 | − | 0.511175i | \(-0.829211\pi\) | ||
0.859477 | − | 0.511175i | \(-0.170789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.674199i | 0.174077i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.86739 | + | 1.07814i | −0.452909 | + | 0.261487i | −0.709058 | − | 0.705150i | \(-0.750880\pi\) |
0.256149 | + | 0.966637i | \(0.417546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.83947 | + | 4.91811i | −0.651419 | + | 1.12829i | 0.331360 | + | 0.943505i | \(0.392493\pi\) |
−0.982779 | + | 0.184787i | \(0.940841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.13603 | + | 3.39556i | −0.466120 | + | 0.740971i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.10168 | + | 4.10016i | 1.48080 | + | 0.854942i | 0.999763 | − | 0.0217573i | \(-0.00692610\pi\) |
0.481039 | + | 0.876699i | \(0.340259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.40114 | + | 4.15890i | 0.480228 | + | 0.831779i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61165i | 1.07996i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.09291i | 0.760035i | 0.924979 | + | 0.380018i | \(0.124082\pi\) | ||||
−0.924979 | + | 0.380018i | \(0.875918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.31121 | + | 1.91173i | −0.594710 | + | 0.343356i | −0.766958 | − | 0.641698i | \(-0.778230\pi\) |
0.172248 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.64481 | + | 1.92714i | −0.808557 | + | 0.335471i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0445993 | − | 1.17561i | 0.00753866 | − | 0.198714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.522119 | − | 0.904337i | 0.0858358 | − | 0.148672i | −0.819911 | − | 0.572491i | \(-0.805977\pi\) |
0.905747 | + | 0.423819i | \(0.139311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.79449 | − | 4.84020i | −0.447477 | − | 0.775052i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.32406i | 0.362957i | 0.983395 | + | 0.181479i | \(0.0580884\pi\) | ||||
−0.983395 | + | 0.181479i | \(0.941912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4945 | −1.75290 | −0.876450 | − | 0.481493i | \(-0.840095\pi\) | ||||
−0.876450 | + | 0.481493i | \(0.840095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.155871 | − | 0.269977i | −0.0232359 | − | 0.0402457i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.79602 | − | 1.03693i | −0.261976 | − | 0.151252i | 0.363259 | − | 0.931688i | \(-0.381664\pi\) |
−0.625236 | + | 0.780436i | \(0.714997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94924 | − | 5.77957i | 0.564178 | − | 0.825653i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.63469 | + | 2.83137i | −0.228903 | + | 0.396471i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.30025 | − | 9.18031i | −0.728046 | − | 1.26101i | −0.957708 | − | 0.287742i | \(-0.907095\pi\) |
0.229662 | − | 0.973270i | \(-0.426238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.897093 | − | 1.17054i | 0.120964 | − | 0.157835i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.61051i | 1.14049i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4146 | + | 6.59023i | −1.48606 | + | 0.857974i | −0.999874 | − | 0.0158836i | \(-0.994944\pi\) |
−0.486181 | + | 0.873858i | \(0.661611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3396 | + | 5.96955i | 1.32384 | + | 0.764322i | 0.984340 | − | 0.176282i | \(-0.0564071\pi\) |
0.339505 | + | 0.940604i | \(0.389740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0703188 | − | 1.85356i | 0.00885933 | − | 0.233526i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41948 | + | 0.819534i | 0.176064 | + | 0.101651i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50977 | − | 0.871668i | 0.184448 | − | 0.106491i | −0.404933 | − | 0.914346i | \(-0.632705\pi\) |
0.589381 | + | 0.807855i | \(0.299372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.4335 | 1.49681 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.53120i | − | 0.300398i | −0.988656 | − | 0.150199i | \(-0.952009\pi\) | ||
0.988656 | − | 0.150199i | \(-0.0479915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.15659 | + | 4.13186i | −0.837615 | + | 0.483597i | −0.856453 | − | 0.516225i | \(-0.827337\pi\) |
0.0188377 | + | 0.999823i | \(0.494003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.30579 | + | 3.64065i | 0.728130 | + | 0.420386i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.22669 | − | 3.05311i | 0.937519 | − | 0.347934i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.17540 | − | 3.76790i | 0.244751 | − | 0.423921i | −0.717310 | − | 0.696754i | \(-0.754627\pi\) |
0.962062 | + | 0.272832i | \(0.0879604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.20262 | + | 5.54710i | 0.355846 | + | 0.616344i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8881 | −1.63418 | −0.817092 | − | 0.576507i | \(-0.804415\pi\) | ||||
−0.817092 | + | 0.576507i | \(0.804415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.958806i | − | 0.103997i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.10288 | + | 5.37434i | 0.332663 | + | 0.576190i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.62144 | − | 4.54047i | 0.277872 | − | 0.481289i | −0.692983 | − | 0.720954i | \(-0.743704\pi\) |
0.970856 | + | 0.239664i | \(0.0770374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.55260 | + | 8.62478i | 0.477242 | + | 0.904123i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.89859 | + | 5.02051i | −0.300570 | + | 0.520603i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.26259 | − | 2.18688i | −0.129539 | − | 0.224369i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2783 | 1.24667 | 0.623335 | − | 0.781955i | \(-0.285777\pi\) | ||||
0.623335 | + | 0.781955i | \(0.285777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41443 | − | 1.84556i | 0.142155 | − | 0.185486i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.3051 | − | 8.25906i | 1.42341 | − | 0.821807i | 0.426822 | − | 0.904335i | \(-0.359633\pi\) |
0.996589 | + | 0.0825286i | \(0.0262996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.01188 | − | 0.584209i | −0.0997035 | − | 0.0575638i | 0.449319 | − | 0.893371i | \(-0.351667\pi\) |
−0.549023 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.832677 | − | 1.57748i | −0.0812610 | − | 0.153947i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.58515 | − | 14.8699i | 0.829958 | − | 1.43753i | −0.0681122 | − | 0.997678i | \(-0.521698\pi\) |
0.898070 | − | 0.439852i | \(-0.144969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.14649 | + | 1.23928i | −0.205597 | + | 0.118701i | −0.599263 | − | 0.800552i | \(-0.704540\pi\) |
0.393667 | + | 0.919253i | \(0.371206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.58329i | − | 0.150279i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0680 | −1.51155 | −0.755775 | − | 0.654831i | \(-0.772740\pi\) | ||||
−0.755775 | + | 0.654831i | \(0.772740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.15782 | + | 1.82317i | −0.294468 | + | 0.170011i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.23805 | + | 1.29214i | 0.206908 | + | 0.119459i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.03774 | − | 4.82896i | 0.278469 | − | 0.442670i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6285 | + | 2.83454i | 0.966229 | + | 0.257685i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.76189 | + | 3.05169i | 0.158864 | + | 0.275161i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.35866 | −0.389851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5441 | −1.37932 | −0.689659 | − | 0.724134i | \(-0.742240\pi\) | ||||
−0.689659 | + | 0.724134i | \(0.742240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.0933 | + | 8.71411i | −1.32889 | + | 0.767235i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.826984 | − | 1.43238i | 0.0722539 | − | 0.125147i | −0.827635 | − | 0.561267i | \(-0.810314\pi\) |
0.899889 | + | 0.436119i | \(0.143647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.569599 | − | 15.0143i | 0.0493905 | − | 1.30190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.16096 | − | 1.24763i | −0.185986 | − | 0.107379i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.88353 | + | 13.6547i | 0.673536 | + | 1.16660i | 0.976895 | + | 0.213722i | \(0.0685586\pi\) |
−0.303359 | + | 0.952876i | \(0.598108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0641939 | −0.00544485 | −0.00272243 | − | 0.999996i | \(-0.500867\pi\) | ||||
−0.00272243 | + | 0.999996i | \(0.500867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.14443 | −0.264809 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.58864 | + | 12.1219i | −0.132848 | + | 1.01368i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.57612 | − | 0.909974i | −0.130890 | − | 0.0755692i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.804138 | − | 10.5830i | 0.0663242 | − | 0.872873i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.11909 | + | 4.11021i | 0.583219 | + | 0.336722i | 0.762412 | − | 0.647092i | \(-0.224015\pi\) |
−0.179193 | + | 0.983814i | \(0.557349\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5612 | + | 18.2926i | 0.859461 | + | 1.48863i | 0.872443 | + | 0.488715i | \(0.162534\pi\) |
−0.0129820 | + | 0.999916i | \(0.504132\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.51173i | − | 0.122216i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1.70013i | − | 0.136558i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.85762 | − | 15.3418i | −0.706915 | − | 1.22441i | −0.965996 | − | 0.258557i | \(-0.916753\pi\) |
0.259081 | − | 0.965855i | \(-0.416580\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.9193 | − | 8.03634i | −1.10388 | − | 0.637323i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.6804 | − | 0.822494i | −1.70865 | − | 0.0648216i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8719 | + | 8.00895i | 1.08653 | + | 0.627309i | 0.932651 | − | 0.360780i | \(-0.117489\pi\) |
0.153881 | + | 0.988089i | \(0.450823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.290564 | − | 2.21711i | 0.0226204 | − | 0.172601i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.07459 | 0.702213 | 0.351106 | − | 0.936336i | \(-0.385806\pi\) | ||||
0.351106 | + | 0.936336i | \(0.385806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.587572 | −0.0451978 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.99070 | − | 3.44800i | −0.152233 | − | 0.263675i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.87165 | − | 3.39000i | −0.446413 | − | 0.257737i | 0.259901 | − | 0.965635i | \(-0.416310\pi\) |
−0.706314 | + | 0.707899i | \(0.749643\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7547 | − | 6.76539i | −0.812976 | − | 0.511415i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.99222 | + | 17.3070i | −0.751061 | + | 1.30088i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.43639 | − | 1.40665i | 0.182105 | − | 0.105138i | −0.406176 | − | 0.913795i | \(-0.633138\pi\) |
0.588281 | + | 0.808656i | \(0.299805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2247 | −0.834323 | −0.417161 | − | 0.908832i | \(-0.636975\pi\) | ||||
−0.417161 | + | 0.908832i | \(0.636975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1023 | 1.33816 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.232164 | + | 0.402121i | 0.0170691 | + | 0.0295645i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.60557 | − | 2.74066i | 0.483047 | − | 0.200417i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.93073 | − | 13.1301i | −0.504137 | − | 0.955073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.40235 | + | 3.69640i | 0.463258 | + | 0.267462i | 0.713413 | − | 0.700744i | \(-0.247148\pi\) |
−0.250155 | + | 0.968206i | \(0.580482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8092 | − | 10.2822i | 1.28194 | − | 0.740126i | 0.304734 | − | 0.952438i | \(-0.401432\pi\) |
0.977202 | + | 0.212311i | \(0.0680991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.48519 | 0.177968 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.46118i | 0.104105i | 0.998644 | + | 0.0520524i | \(0.0165763\pi\) | ||||
−0.998644 | + | 0.0520524i | \(0.983424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.35358 | − | 1.35884i | 0.166841 | − | 0.0963258i | −0.414254 | − | 0.910161i | \(-0.635958\pi\) |
0.581096 | + | 0.813835i | \(0.302624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.32164 | − | 2.28915i | 0.0932212 | − | 0.161464i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.05500 | − | 9.57656i | −0.354792 | − | 0.672143i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.894962 | − | 0.516706i | −0.0625068 | − | 0.0360883i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.97886 | + | 2.87455i | −0.346055 | + | 0.199795i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.4572 | − | 14.9495i | 0.792511 | − | 1.03408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1309 | 1.11050 | 0.555248 | − | 0.831685i | \(-0.312623\pi\) | ||||
0.555248 | + | 0.831685i | \(0.312623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.91893 | − | 3.32368i | −0.131483 | − | 0.227735i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.55557 | − | 4.42638i | 0.174288 | − | 0.301876i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.38643 | − | 8.56258i | 0.365655 | − | 0.581266i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.26480 | + | 10.8509i | −0.423336 | + | 0.733239i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.97416 | + | 6.88345i | 0.267331 | + | 0.463031i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.69783i | − | 0.247625i | −0.992306 | − | 0.123812i | \(-0.960488\pi\) | ||
0.992306 | − | 0.123812i | \(-0.0395121\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.36679 | −0.224453 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4176 | + | 18.0438i | 0.691439 | + | 1.19761i | 0.971366 | + | 0.237586i | \(0.0763563\pi\) |
−0.279927 | + | 0.960021i | \(0.590310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.73473 | + | 13.3969i | −0.511125 | + | 0.885295i | 0.488792 | + | 0.872401i | \(0.337438\pi\) |
−0.999917 | + | 0.0128943i | \(0.995896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.48775 | − | 10.2457i | 0.558453 | − | 0.674119i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.43672 | − | 3.13889i | −0.356172 | − | 0.205636i | 0.311229 | − | 0.950335i | \(-0.399260\pi\) |
−0.667400 | + | 0.744699i | \(0.732593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.798615 | − | 0.461080i | 0.0520959 | − | 0.0300776i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.59675i | − | 0.428505i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.14626 | 0.203515 | 0.101757 | − | 0.994809i | \(-0.467553\pi\) | ||||
0.101757 | + | 0.994809i | \(0.467553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.9004 | + | 10.3348i | −1.15306 | + | 0.665722i | −0.949632 | − | 0.313367i | \(-0.898543\pi\) |
−0.203432 | + | 0.979089i | \(0.565210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.16888 | − | 3.56161i | −0.395734 | − | 0.228477i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.34760 | + | 2.80576i | 0.0860948 | + | 0.179254i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1288 | + | 10.4667i | 1.15351 | + | 0.665978i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.5494 | + | 11.2868i | −1.23889 | + | 0.715274i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 30.1273i | − | 1.90162i | −0.309779 | − | 0.950809i | \(-0.600255\pi\) | ||
0.309779 | − | 0.950809i | \(-0.399745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.5868 | − | 16.5440i | −1.35715 | − | 1.04011i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.726880 | − | 1.25899i | −0.0455190 | − | 0.0788412i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8381 | + | 18.7721i | −0.676062 | + | 1.17097i | 0.300096 | + | 0.953909i | \(0.402981\pi\) |
−0.976157 | + | 0.217064i | \(0.930352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.104737 | + | 2.76081i | −0.00650806 | + | 0.171548i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.48503 | − | 1.43474i | −0.153820 | − | 0.0888079i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.84367 | − | 6.65744i | −0.237011 | − | 0.410515i | 0.722844 | − | 0.691011i | \(-0.242834\pi\) |
−0.959855 | + | 0.280496i | \(0.909501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.71360 | 0.289554 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.94936i | − | 0.486493i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.02034 | − | 12.1596i | −0.428038 | − | 0.741383i | 0.568661 | − | 0.822572i | \(-0.307462\pi\) |
−0.996699 | + | 0.0811891i | \(0.974128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9634 | + | 18.9892i | −0.665982 | + | 1.15351i | 0.313036 | + | 0.949741i | \(0.398654\pi\) |
−0.979018 | + | 0.203773i | \(0.934680\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.5165 | + | 7.87369i | 0.757531 | + | 0.476537i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.10377 | − | 14.7114i | −0.368071 | − | 0.887130i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.9931 | − | 15.5844i | 1.62186 | − | 0.936379i | 0.635432 | − | 0.772157i | \(-0.280822\pi\) |
0.986423 | − | 0.164222i | \(-0.0525112\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.68055i | − | 0.160481i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.6275i | 0.753293i | 0.926357 | + | 0.376646i | \(0.122923\pi\) | ||||
−0.926357 | + | 0.376646i | \(0.877077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5556 | + | 20.0149i | 0.686910 | + | 1.18976i | 0.972832 | + | 0.231510i | \(0.0743667\pi\) |
−0.285922 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.31578 | − | 1.91437i | −0.196410 | − | 0.113397i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.87036 | − | 5.43782i | −0.169432 | − | 0.320984i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.17523 | + | 10.6958i | −0.363249 | + | 0.629166i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1224 | − | 9.30827i | 0.945112 | − | 0.545661i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.4853i | − | 0.612555i | −0.951942 | − | 0.306278i | \(-0.900916\pi\) | ||
0.951942 | − | 0.306278i | \(-0.0990836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.86079i | − | 0.341229i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.41849 | − | 18.4539i | 0.140335 | − | 1.07081i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1137 | − | 26.1777i | 0.874049 | − | 1.51390i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8948 | − | 14.1965i | 1.55019 | − | 0.818271i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.5225 | − | 21.6897i | 0.719401 | − | 1.24604i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.59757 | + | 2.65441i | −0.263256 | + | 0.151991i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.97370 | 0.512156 | 0.256078 | − | 0.966656i | \(-0.417570\pi\) | ||||
0.256078 | + | 0.966656i | \(0.417570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.77158 | −0.100782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.8641 | + | 9.73650i | −0.956276 | + | 0.552106i | −0.895025 | − | 0.446016i | \(-0.852842\pi\) |
−0.0612509 | + | 0.998122i | \(0.519509\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.15640 | − | 8.93115i | 0.291457 | − | 0.504818i | −0.682698 | − | 0.730701i | \(-0.739193\pi\) |
0.974154 | + | 0.225883i | \(0.0725267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.698143 | + | 0.439178i | 0.0393359 | + | 0.0247449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.69923 | + | 9.87136i | −0.320101 | + | 0.554431i | −0.980509 | − | 0.196476i | \(-0.937050\pi\) |
0.660408 | + | 0.750907i | \(0.270383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.76395 | − | 13.4596i | 0.0987623 | − | 0.753591i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 26.0339i | − | 1.45307i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.2454i | − | 0.681351i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.3302 | − | 8.85092i | 0.850369 | − | 0.490961i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.87902 | + | 3.25455i | −0.103910 | + | 0.179977i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.48299 | + | 0.208009i | 0.302287 | + | 0.0114679i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0115 | − | 5.78015i | −0.550283 | − | 0.317706i | 0.198953 | − | 0.980009i | \(-0.436246\pi\) |
−0.749236 | + | 0.662303i | \(0.769579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.366048 | + | 0.634015i | 0.0200593 | + | 0.0347438i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.775188i | 0.0423531i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.3252i | 1.65192i | 0.563731 | + | 0.825959i | \(0.309366\pi\) | ||||
−0.563731 | + | 0.825959i | \(0.690634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.0986 | + | 12.1813i | −1.14592 | + | 0.661597i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7128 | − | 4.85967i | 0.634285 | − | 0.263166i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.10227 | + | 18.4006i | −0.113512 | + | 0.993537i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.76432 | + | 4.78794i | −0.148826 | + | 0.257774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.19003 | − | 14.1856i | −0.439664 | − | 0.761521i | 0.557999 | − | 0.829841i | \(-0.311569\pi\) |
−0.997663 | + | 0.0683209i | \(0.978236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5196i | 0.670160i | 0.942190 | + | 0.335080i | \(0.108763\pi\) | ||||
−0.942190 | + | 0.335080i | \(0.891237\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.6853 | 1.10410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4965 | − | 19.9126i | −0.611899 | − | 1.05984i | −0.990920 | − | 0.134452i | \(-0.957073\pi\) |
0.379021 | − | 0.925388i | \(-0.376261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.974728 | + | 0.562759i | 0.0517332 | + | 0.0298682i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.327920 | − | 8.64377i | 0.0173554 | − | 0.457477i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.25828 | + | 5.64352i | −0.171966 | + | 0.297853i | −0.939107 | − | 0.343625i | \(-0.888345\pi\) |
0.767141 | + | 0.641478i | \(0.221678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.62518 | − | 11.4752i | −0.348694 | − | 0.603955i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.1050 | − | 4.33559i | 0.845294 | − | 0.227560i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.67453i | − | 0.192334i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.8110 | − | 9.12851i | 0.825330 | − | 0.476505i | −0.0269210 | − | 0.999638i | \(-0.508570\pi\) |
0.852251 | + | 0.523133i | \(0.175237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.41107 | − | 0.814680i | −0.0734572 | − | 0.0424105i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.7397 | + | 14.9339i | 1.23251 | + | 0.775327i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1887 | + | 12.2333i | 1.09711 | + | 0.633416i | 0.935460 | − | 0.353432i | \(-0.114985\pi\) |
0.161649 | + | 0.986848i | \(0.448319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.72329 | + | 3.30434i | −0.295549 | + | 0.170635i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.0870 | 0.777021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.9742i | 0.923274i | 0.887069 | + | 0.461637i | \(0.152738\pi\) | ||||
−0.887069 | + | 0.461637i | \(0.847262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.4107 | + | 11.7841i | −1.04567 | + | 0.603720i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9906 | + | 6.34544i | 0.561595 | + | 0.324237i | 0.753785 | − | 0.657121i | \(-0.228226\pi\) |
−0.192191 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.653325 | + | 3.84677i | −0.0332965 | + | 0.196050i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.02931 | − | 6.97897i | 0.204821 | − | 0.354761i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0005 | − | 17.3213i | −0.507043 | − | 0.878225i | −0.999967 | − | 0.00815194i | \(-0.997405\pi\) |
0.492924 | − | 0.870073i | \(-0.335928\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6821 | −0.894225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.50778i | − | 0.126501i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.967307 | + | 1.67543i | 0.0486705 | + | 0.0842998i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.65096 | + | 6.32365i | −0.183237 | + | 0.317375i | −0.942981 | − | 0.332847i | \(-0.891991\pi\) |
0.759744 | + | 0.650222i | \(0.225324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6345 | − | 20.1468i | −0.532392 | − | 1.00860i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.687115 | + | 1.19012i | −0.0343129 | + | 0.0594317i | −0.882672 | − | 0.469990i | \(-0.844258\pi\) |
0.848359 | + | 0.529421i | \(0.177591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.04687 | + | 12.2055i | 0.351030 | + | 0.608001i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.84814 | −0.141525 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.10674 | + | 2.74889i | −0.104427 | + | 0.136258i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3944 | + | 10.0426i | −0.860095 | + | 0.496576i | −0.864044 | − | 0.503416i | \(-0.832076\pi\) |
0.00394883 | + | 0.999992i | \(0.498743\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.7035 | + | 11.9532i | 1.02123 | + | 0.589606i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.5685 | − | 29.5175i | 0.913694 | − | 1.45246i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.31006 | − | 5.73320i | 0.162485 | − | 0.281432i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0842919 | + | 0.0486660i | −0.00412779 | + | 0.00238318i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.428111i | 0.0209146i | 0.999945 | + | 0.0104573i | \(0.00332872\pi\) | ||||
−0.999945 | + | 0.0104573i | \(0.996671\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.15342 | 0.348636 | 0.174318 | − | 0.984689i | \(-0.444228\pi\) | ||||
0.174318 | + | 0.984689i | \(0.444228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.25916 | − | 0.726975i | 0.0612224 | − | 0.0353468i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.96773 | − | 5.17752i | −0.434999 | − | 0.251147i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5652 | − | 1.19749i | −1.52755 | − | 0.0579508i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.10368 | + | 17.1214i | 0.342969 | + | 0.826628i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.54908 | − | 4.41514i | −0.122785 | − | 0.212670i | 0.798080 | − | 0.602551i | \(-0.205849\pi\) |
−0.920865 | + | 0.389882i | \(0.872516\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.544832 | −0.0261830 | −0.0130915 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130915 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.75944 | −0.132305 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.3300 | + | 23.2845i | −1.92925 | + | 1.11385i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.06575 | − | 1.84593i | 0.0508653 | − | 0.0881012i | −0.839472 | − | 0.543403i | \(-0.817135\pi\) |
0.890337 | + | 0.455302i | \(0.150469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.12473 | + | 4.42378i | 0.101177 | + | 0.210656i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.89496 | + | 2.82611i | 0.232567 | + | 0.134272i | 0.611756 | − | 0.791047i | \(-0.290464\pi\) |
−0.379189 | + | 0.925319i | \(0.623797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.16565 | + | 2.01896i | 0.0552569 | + | 0.0957078i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4639 | 0.589525 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.23955 | −0.388848 | −0.194424 | − | 0.980918i | \(-0.562284\pi\) | ||||
−0.194424 | + | 0.980918i | \(0.562284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00162 | − | 7.64269i | 0.0471643 | − | 0.359880i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.7356 | + | 16.0131i | 1.30313 | + | 0.752363i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.33345 | − | 0.164399i | −0.203155 | − | 0.00770715i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4987 | + | 10.1029i | 0.818554 | + | 0.472592i | 0.849917 | − | 0.526916i | \(-0.176652\pi\) |
−0.0313638 | + | 0.999508i | \(0.509985\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.05013 | − | 10.4791i | −0.282396 | − | 0.489124i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.4160i | − | 0.624848i | −0.949943 | − | 0.312424i | \(-0.898859\pi\) | ||
0.949943 | − | 0.312424i | \(-0.101141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.6735i | 1.47199i | 0.676986 | + | 0.735996i | \(0.263286\pi\) | ||||
−0.676986 | + | 0.735996i | \(0.736714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.28888 | − | 2.23241i | −0.0597705 | − | 0.103526i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.27799 | + | 1.31520i | 0.105413 | + | 0.0608602i | 0.551780 | − | 0.833990i | \(-0.313949\pi\) |
−0.446367 | + | 0.894850i | \(0.647282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.45599 | + | 3.90418i | −0.113407 | + | 0.180278i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.2616 | − | 13.4301i | −1.07184 | − | 0.618825i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.7998 | + | 4.95388i | 1.73804 | + | 0.227779i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.2719 | −1.25132 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.43183 | 0.340280 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4995 | − | 25.1139i | −0.662500 | − | 1.14748i | −0.979957 | − | 0.199211i | \(-0.936162\pi\) |
0.317457 | − | 0.948273i | \(-0.397171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.33350 | − | 1.92460i | −0.151995 | − | 0.0877542i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.0917 | + | 15.3561i | −1.32372 | + | 0.698727i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.72982 | + | 4.72818i | −0.123955 | + | 0.214696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.4060 | − | 15.8229i | 1.24189 | − | 0.717003i | 0.272408 | − | 0.962182i | \(-0.412180\pi\) |
0.969478 | + | 0.245179i | \(0.0788466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2866 | 1.09828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.790237 | 0.0356629 | 0.0178314 | − | 0.999841i | \(-0.494324\pi\) | ||||
0.0178314 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.41273 | − | 7.64307i | −0.198739 | − | 0.344227i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.396229 | + | 0.954996i | 0.0178092 | + | 0.0429239i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.12619 | + | 5.92248i | 0.140229 | + | 0.265660i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7657 | + | 8.52496i | 0.661002 | + | 0.381630i | 0.792659 | − | 0.609666i | \(-0.208696\pi\) |
−0.131657 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9157 | − | 6.87953i | 0.532354 | − | 0.307355i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.2695 | −0.814597 | −0.407299 | − | 0.913295i | \(-0.633529\pi\) | ||||
−0.407299 | + | 0.913295i | \(0.633529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.34491i | 0.326844i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.771531 | + | 0.445443i | −0.0342649 | + | 0.0197828i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.836386 | + | 1.44866i | −0.0370722 | + | 0.0642109i | −0.883966 | − | 0.467551i | \(-0.845136\pi\) |
0.846894 | + | 0.531762i | \(0.178470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6418 | − | 18.5065i | 0.515004 | − | 0.818680i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.5987 | − | 15.9341i | −1.21851 | − | 0.703508i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.449941 | − | 0.259773i | 0.0198268 | − | 0.0114470i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.45933 | + | 4.18400i | 0.240101 | + | 0.184012i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.2799 | −0.451240 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.4684 | − | 21.5958i | −0.546249 | − | 0.946131i | −0.998527 | − | 0.0542543i | \(-0.982722\pi\) |
0.452278 | − | 0.891877i | \(-0.350611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0685 | + | 20.9033i | −0.527720 | + | 0.914038i | 0.471758 | + | 0.881728i | \(0.343620\pi\) |
−0.999478 | + | 0.0323095i | \(0.989714\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.2507 | − | 0.730317i | −0.840168 | − | 0.0318736i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.12221 | − | 7.13988i | 0.179566 | − | 0.311018i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1226 | + | 38.3174i | 0.961851 | + | 1.66597i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.24058i | − | 0.401007i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.56680 | 0.371069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.81746 | + | 6.61203i | 0.165043 | + | 0.285863i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.13279 | − | 3.69410i | 0.0920368 | − | 0.159412i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.4780 | + | 17.3041i | −0.666683 | + | 0.745341i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9721 | + | 11.5309i | 0.858666 | + | 0.495751i | 0.863565 | − | 0.504237i | \(-0.168226\pi\) |
−0.00489930 | + | 0.999988i | \(0.501560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.7389 | + | 8.50952i | −0.632507 | + | 0.365178i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.10211i | − | 0.0472092i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.71106 | −0.0731596 | −0.0365798 | − | 0.999331i | \(-0.511646\pi\) | ||||
−0.0365798 | + | 0.999331i | \(0.511646\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.24888 | + | 4.18514i | −0.309375 | + | 0.178618i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.1294 | − | 11.6217i | −0.857541 | − | 0.495101i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.436386 | + | 11.5028i | −0.0185570 | + | 0.489150i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.609702 | + | 0.352012i | 0.0258804 | + | 0.0149421i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.4941 | + | 17.0284i | −1.24971 | + | 0.721518i | −0.971051 | − | 0.238873i | \(-0.923222\pi\) |
−0.278655 | + | 0.960391i | \(0.589889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.3704i | 1.79208i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.59595 | − | 8.60646i | 0.278481 | − | 0.363365i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.72091 | − | 6.44480i | −0.156817 | − | 0.271616i | 0.776902 | − | 0.629622i | \(-0.216790\pi\) |
−0.933719 | + | 0.358006i | \(0.883457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.57238 | − | 6.18755i | 0.150291 | − | 0.260312i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.3445 | − | 9.02361i | −0.602411 | − | 0.378956i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.34931 | − | 2.51108i | −0.182333 | − | 0.105270i | 0.406055 | − | 0.913848i | \(-0.366904\pi\) |
−0.588388 | + | 0.808579i | \(0.700237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.28733 | + | 7.42587i | 0.179419 | + | 0.310763i | 0.941682 | − | 0.336505i | \(-0.109245\pi\) |
−0.762263 | + | 0.647268i | \(0.775911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.2091 | 0.468266 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.3802i | 1.64227i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.36472 | − | 11.0240i | −0.264967 | − | 0.458936i | 0.702588 | − | 0.711597i | \(-0.252028\pi\) |
−0.967555 | + | 0.252661i | \(0.918694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.5900 | − | 27.0027i | 0.647898 | − | 1.12219i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.8351 | − | 18.3878i | 1.44520 | − | 0.762853i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4734 | + | 32.4738i | 0.558012 | + | 1.34493i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.995169 | + | 0.574561i | −0.0411452 | + | 0.0237552i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.65362i | 0.0682520i | 0.999418 | + | 0.0341260i | \(0.0108648\pi\) | ||||
−0.999418 | + | 0.0341260i | \(0.989135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.7132i | − | 0.894675i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.10773 | + | 1.91865i | 0.0455661 | + | 0.0789228i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.4070 | − | 9.47258i | −0.673754 | − | 0.388992i | 0.123743 | − | 0.992314i | \(-0.460510\pi\) |
−0.797498 | + | 0.603322i | \(0.793843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.18419 | + | 2.24341i | 0.0485469 | + | 0.0919707i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.06030 | − | 3.56855i | 0.0843225 | − | 0.146051i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.9830 | + | 17.3107i | −1.22507 | + | 0.707296i | −0.965995 | − | 0.258561i | \(-0.916752\pi\) |
−0.259077 | + | 0.965857i | \(0.583418\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5339i | 1.69420i | 0.531431 | + | 0.847102i | \(0.321655\pi\) | ||||
−0.531431 | + | 0.847102i | \(0.678345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.22222i | 0.0497727i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.45457 | + | 3.46269i | −0.140448 | + | 0.140778i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7473 | + | 23.8111i | −0.557987 | + | 0.966462i | 0.439677 | + | 0.898156i | \(0.355093\pi\) |
−0.997664 | + | 0.0683062i | \(0.978241\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.8977 | − | 8.74258i | −0.563164 | − | 0.354267i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.82227 | + | 6.62037i | −0.154633 | + | 0.267831i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1804 | + | 15.1153i | −1.05742 | + | 0.610500i | −0.924717 | − | 0.380656i | \(-0.875698\pi\) |
−0.132701 | + | 0.991156i | \(0.542365\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.56688 | −0.0631827 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.81946 | −0.194024 | −0.0970122 | − | 0.995283i | \(-0.530929\pi\) | ||||
−0.0970122 | + | 0.995283i | \(0.530929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.44195 | + | 4.29661i | −0.299117 | + | 0.172695i | −0.642046 | − | 0.766666i | \(-0.721914\pi\) |
0.342929 | + | 0.939361i | \(0.388581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.0086 | + | 39.8521i | −0.923305 | + | 1.59921i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.525863 | + | 13.8614i | −0.0210683 | + | 0.555345i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0366 | + | 19.1160i | −0.441466 | + | 0.764641i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.71093 | − | 28.3157i | 0.148200 | − | 1.13082i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.25167i | 0.0897798i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1184i | 0.920327i | 0.887834 | + | 0.460164i | \(0.152209\pi\) | ||||
−0.887834 | + | 0.460164i | \(0.847791\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.1812 | − | 12.2290i | 0.841877 | − | 0.486058i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.45591 | − | 5.98581i | 0.137144 | − | 0.237540i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.3043 | − | 14.5574i | −0.844106 | − | 0.576786i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.53683 | + | 0.887290i | 0.0607961 | + | 0.0351007i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1069 | + | 26.1659i | 0.596685 | + | 1.03349i | 0.993307 | + | 0.115507i | \(0.0368492\pi\) |
−0.396621 | + | 0.917982i | \(0.629817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.4763i | − | 0.413145i | −0.978431 | − | 0.206572i | \(-0.933769\pi\) | ||
0.978431 | − | 0.206572i | \(-0.0662309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.74960i | − | 0.305140i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7841 | − | 15.4638i | 1.05299 | − | 0.607944i | 0.129506 | − | 0.991579i | \(-0.458661\pi\) |
0.923485 | + | 0.383634i | \(0.125328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.3772 | − | 16.7526i | 1.58494 | − | 0.657595i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.581459 | − | 15.3269i | 0.0227892 | − | 0.600708i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7611 | + | 22.1029i | −0.499381 | + | 0.864954i | −1.00000 | 0.000714266i | \(-0.999773\pi\) | |
0.500618 | + | 0.865668i | \(0.333106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.367725 | + | 0.636918i | 0.0143682 | + | 0.0248865i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.79355i | − | 0.226028i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.28212 | −0.361580 | −0.180790 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180790 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8440 | − | 22.2465i | −0.499575 | − | 0.865289i | 0.500425 | − | 0.865780i | \(-0.333177\pi\) |
−1.00000 | 0.000491031i | \(0.999844\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4368 | + | 6.02570i | 0.405332 | + | 0.234019i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.65513 | + | 3.55745i | 0.219297 | + | 0.137952i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.7816 | + | 29.0666i | −0.649786 | + | 1.12546i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.80336 | − | 4.85556i | −0.108384 | − | 0.187727i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.4289 | − | 24.0870i | −1.21330 | − | 0.929868i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.9138i | − | 0.574886i | −0.957798 | − | 0.287443i | \(-0.907195\pi\) | ||
0.957798 | − | 0.287443i | \(-0.0928053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.3383 | + | 13.4744i | −0.898290 | + | 0.518628i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0008 | + | 12.1248i | 0.807127 | + | 0.465995i | 0.845957 | − | 0.533251i | \(-0.179030\pi\) |
−0.0388304 | + | 0.999246i | \(0.512363\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.7286 | + | 15.1644i | −1.10250 | + | 0.581957i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.3583 | + | 15.7953i | 1.04837 | + | 0.605278i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.76035 | − | 2.74839i | 0.182150 | − | 0.105164i | −0.406153 | − | 0.913805i | \(-0.633130\pi\) |
0.588302 | + | 0.808641i | \(0.299797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.01095 | −0.267875 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.4551i | 0.894867i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.8398 | + | 19.5374i | −1.28919 | + | 0.744317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7407 | + | 24.0990i | 1.58789 | + | 0.916770i | 0.993654 | + | 0.112481i | \(0.0358797\pi\) |
0.594238 | + | 0.804289i | \(0.297454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.03008 | + | 6.06512i | −0.0391296 | + | 0.230395i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0142722 | − | 0.0247201i | 0.000541374 | − | 0.000937687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.50566 | − | 4.33993i | −0.0949087 | − | 0.164387i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.51849 | −0.360022 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.1877i | 1.48010i | 0.672553 | + | 0.740049i | \(0.265198\pi\) | ||||
−0.672553 | + | 0.740049i | \(0.734802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.96508 | + | 5.13567i | 0.111830 | + | 0.193696i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.699099 | − | 1.21087i | 0.0263296 | − | 0.0456042i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.2705 | + | 36.9922i | −0.875178 | + | 1.39123i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.52544 | + | 9.57035i | −0.207512 | + | 0.359422i | −0.950930 | − | 0.309405i | \(-0.899870\pi\) |
0.743418 | + | 0.668827i | \(0.233203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.52513 | + | 2.64161i | 0.0571969 | + | 0.0990680i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.3535 | −1.17420 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.31475 | − | 3.30680i | −0.161362 | − | 0.123667i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.13130 | − | 2.38521i | 0.154286 | − | 0.0890772i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6902 | − | 9.05875i | −0.585146 | − | 0.337834i | 0.178030 | − | 0.984025i | \(-0.443028\pi\) |
−0.763176 | + | 0.646191i | \(0.776361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.08912 | + | 0.117193i | 0.115045 | + | 0.00436448i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.6698 | + | 27.1409i | −0.582766 | + | 1.00938i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.0220 | + | 9.82766i | −0.632181 | + | 0.364990i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.5442i | − | 1.24408i | −0.782984 | − | 0.622042i | \(-0.786303\pi\) | ||
0.782984 | − | 0.622042i | \(-0.213697\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0160 | −1.11171 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4648 | − | 12.3927i | 0.793904 | − | 0.458361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.5991 | − | 17.0891i | −1.09327 | − | 0.631199i | −0.158824 | − | 0.987307i | \(-0.550770\pi\) |
−0.934445 | + | 0.356108i | \(0.884104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.89658 | + | 2.66257i | 0.143728 | + | 0.0982105i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.34056 | + | 2.21581i | −0.196722 | + | 0.0816203i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8587 | − | 29.2002i | −0.620159 | − | 1.07415i | −0.989456 | − | 0.144835i | \(-0.953735\pi\) |
0.369297 | − | 0.929311i | \(-0.379598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.7395 | 1.16598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.4286 | 1.70330 | 0.851650 | − | 0.524112i | \(-0.175603\pi\) | ||||
0.851650 | + | 0.524112i | \(0.175603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.16556 | + | 1.82764i | −0.115977 | + | 0.0669595i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.21890 | − | 9.03941i | 0.190950 | − | 0.330735i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.72219 | + | 45.3957i | −0.0629273 | + | 1.65872i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6089 | + | 8.43447i | 0.533088 | + | 0.307778i | 0.742273 | − | 0.670098i | \(-0.233748\pi\) |
−0.209185 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.8398 | − | 39.5596i | −0.832327 | − | 1.44163i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.39228 | −0.341820 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.2078 | 1.53407 | 0.767035 | − | 0.641605i | \(-0.221731\pi\) | ||||
0.767035 | + | 0.641605i | \(0.221731\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −40.8875 | − | 5.35853i | −1.48412 | − | 0.194502i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.35266 | − | 3.09036i | −0.194034 | − | 0.112026i | 0.399836 | − | 0.916587i | \(-0.369067\pi\) |
−0.593870 | + | 0.804561i | \(0.702401\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.49176 | − | 5.55071i | 0.126410 | − | 0.200949i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.582144 | + | 0.336101i | 0.0210475 | + | 0.0121518i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.2924 | + | 42.0757i | 0.877149 | + | 1.51927i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.19742i | − | 0.151363i | −0.997132 | − | 0.0756815i | \(-0.975887\pi\) | ||
0.997132 | − | 0.0756815i | \(-0.0241132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.8658i | 1.18363i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.20163 | − | 3.81334i | −0.0791873 | − | 0.137156i | 0.823712 | − | 0.567008i | \(-0.191899\pi\) |
−0.902900 | + | 0.429852i | \(0.858566\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.9013 | − | 9.18064i | −0.571193 | − | 0.329778i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.95546 | + | 3.70457i | 0.0701519 | + | 0.132901i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4300 | − | 6.59910i | −0.409522 | − | 0.236437i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.09089 | + | 8.32386i | −0.0390350 | + | 0.297851i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.9680 | −0.820809 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.87722 | 0.281150 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.14558 | − | 3.71626i | −0.0764818 | − | 0.132470i | 0.825248 | − | 0.564771i | \(-0.191035\pi\) |
−0.901730 | + | 0.432300i | \(0.857702\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0941 | − | 5.82785i | −0.359360 | − | 0.207477i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.5958 | − | 19.8450i | 1.33675 | − | 0.705606i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0045 | − | 38.1130i | 0.781404 | − | 1.35343i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.18935 | − | 3.57342i | 0.219514 | − | 0.126736i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.2668 | 1.21379 | 0.606896 | − | 0.794781i | \(-0.292415\pi\) | ||||
0.606896 | + | 0.794781i | \(0.292415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.47183 | 0.158202 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.83785 | + | 3.18325i | 0.0649372 | + | 0.112474i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.3152 | − | 10.5033i | 0.893354 | − | 0.370654i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.13691 | − | 8.16593i | 0.181052 | − | 0.287811i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.4366 | − | 10.6444i | −0.648998 | − | 0.374699i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.0755 | − | 16.7868i | 1.02224 | − | 0.590192i | 0.107489 | − | 0.994206i | \(-0.465719\pi\) |
0.914753 | + | 0.404015i | \(0.132386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.00928 | −0.316359 | −0.158179 | − | 0.987410i | \(-0.550562\pi\) | ||||
−0.158179 | + | 0.987410i | \(0.550562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.2459i | 1.16599i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.16826 | + | 3.56124i | −0.216065 | + | 0.124745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.6384 | − | 56.5314i | 1.14187 | − | 1.97778i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.83246 | − | 0.259204i | −0.238745 | − | 0.00905733i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.5864 | + | 24.5873i | 1.48627 | + | 0.858101i | 0.999878 | − | 0.0156370i | \(-0.00497762\pi\) |
0.486397 | + | 0.873738i | \(0.338311\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.73756 | − | 2.73523i | 0.165141 | − | 0.0953442i | −0.415152 | − | 0.909752i | \(-0.636272\pi\) |
0.580293 | + | 0.814408i | \(0.302938\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.1676 | − | 14.6899i | −0.667330 | − | 0.511438i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.4857 | −0.990544 | −0.495272 | − | 0.868738i | \(-0.664932\pi\) | ||||
−0.495272 | + | 0.868738i | \(0.664932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5693 | + | 23.5027i | 0.471281 | + | 0.816283i | 0.999460 | − | 0.0328498i | \(-0.0104583\pi\) |
−0.528179 | + | 0.849133i | \(0.677125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.6294 | − | 40.9274i | 0.819695 | − | 1.41975i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.14360 | + | 15.0506i | −0.0396233 | + | 0.521471i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.01754 | + | 3.49449i | −0.0698200 | + | 0.120932i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.7279 | − | 18.5813i | −0.370812 | − | 0.642264i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.95474i | − | 0.274628i | −0.990528 | − | 0.137314i | \(-0.956153\pi\) | ||
0.990528 | − | 0.137314i | \(-0.0438469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2481 | 0.422347 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.57301 | + | 16.5809i | 0.329712 | + | 0.571078i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.130634 | − | 0.226265i | 0.00449396 | − | 0.00778376i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.3693 | + | 6.49466i | −0.974782 | + | 0.223159i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.3470 | + | 17.5208i | 1.04151 | + | 0.601313i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.41584 | − | 4.28154i | 0.254212 | − | 0.146769i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.6690i | − | 0.947370i | −0.880694 | − | 0.473685i | \(-0.842923\pi\) | ||
0.880694 | − | 0.473685i | \(-0.157077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.77036 | 0.0605452 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.2087 | − | 12.2449i | 0.724477 | − | 0.418277i | −0.0919213 | − | 0.995766i | \(-0.529301\pi\) |
0.816398 | + | 0.577489i | \(0.195967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3365 | + | 14.6280i | 0.864470 | + | 0.499102i | 0.865507 | − | 0.500897i | \(-0.166997\pi\) |
−0.00103656 | + | 0.999999i | \(0.500330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.89148 | − | 4.96426i | −0.268941 | − | 0.169182i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.89963 | − | 1.67410i | −0.0987046 | − | 0.0569871i | 0.449835 | − | 0.893112i | \(-0.351483\pi\) |
−0.548540 | + | 0.836124i | \(0.684816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.61087 | − | 1.50739i | 0.0887724 | − | 0.0512528i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.7260i | 0.635968i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.77767 | + | 11.4532i | −0.297762 | + | 0.388523i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.21308 | − | 5.56522i | −0.108871 | − | 0.188570i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.30404 | + | 7.45482i | −0.145670 | + | 0.252307i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.1984 | − | 5.38322i | 0.344767 | − | 0.181986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.9223 | − | 13.2342i | −0.774031 | − | 0.446887i | 0.0602800 | − | 0.998182i | \(-0.480801\pi\) |
−0.834311 | + | 0.551295i | \(0.814134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.94897 | − | 13.7680i | −0.268112 | − | 0.464384i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.7302 | 0.361509 | 0.180754 | − | 0.983528i | \(-0.442146\pi\) | ||||
0.180754 | + | 0.983528i | \(0.442146\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.7266i | − | 1.30325i | −0.758540 | − | 0.651626i | \(-0.774087\pi\) | ||
0.758540 | − | 0.651626i | \(-0.225913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.44312 | − | 7.69571i | −0.149354 | − | 0.258689i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.35475 | + | 14.4709i | −0.280525 | + | 0.485884i | −0.971514 | − | 0.236982i | \(-0.923842\pi\) |
0.690989 | + | 0.722865i | \(0.257175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.3700 | − | 19.1980i | 1.21981 | − | 0.643879i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.14115 | − | 19.6219i | −0.272739 | − | 0.657358i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1995 | − | 5.88868i | 0.341313 | − | 0.197057i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.25096i | 0.0418149i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 45.8314i | − | 1.53027i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.82453 | − | 13.5525i | −0.260963 | − | 0.452001i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7953 | + | 11.4288i | 0.659477 | + | 0.380749i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.5527 | − | 39.0303i | 0.817061 | − | 1.29885i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.49557 | − | 4.32245i | 0.0829555 | − | 0.143683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.3082 | + | 23.2719i | −1.33841 | + | 0.772732i | −0.986572 | − | 0.163328i | \(-0.947777\pi\) |
−0.351840 | + | 0.936060i | \(0.614444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.5806i | 0.384103i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.8951i | − | 1.52057i | −0.649589 | − | 0.760286i | \(-0.725059\pi\) | ||
0.649589 | − | 0.760286i | \(-0.274941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.9597 | + | 6.41644i | 1.62033 | + | 0.212353i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.02466 | + | 6.97092i | −0.133051 | + | 0.230451i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.165893 | + | 4.37284i | −0.00547828 | + | 0.144404i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.2681 | − | 33.3733i | 0.635596 | − | 1.10088i | −0.350793 | − | 0.936453i | \(-0.614088\pi\) |
0.986389 | − | 0.164431i | \(-0.0525789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7832 | − | 6.80304i | 0.388270 | − | 0.224168i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.33034 | −0.307112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.01472 | 0.164883 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.709411 | − | 0.409579i | 0.0233001 | − | 0.0134523i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.1911 | + | 41.9003i | −0.793686 | + | 1.37470i | 0.129984 | + | 0.991516i | \(0.458507\pi\) |
−0.923670 | + | 0.383188i | \(0.874826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.2108 | + | 35.8337i | 0.564061 | + | 1.17440i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.7627 | + | 25.5697i | −0.483308 | + | 0.837113i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.413223 | + | 3.15304i | −0.0135138 | + | 0.103115i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0707i | 1.21105i | 0.795827 | + | 0.605523i | \(0.207036\pi\) | ||||
−0.795827 | + | 0.605523i | \(0.792964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 15.6365i | − | 0.510276i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4067 | + | 10.0498i | −0.567443 | + | 0.327613i | −0.756127 | − | 0.654424i | \(-0.772911\pi\) |
0.188684 | + | 0.982038i | \(0.439578\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.52902 | + | 16.5047i | −0.310307 | + | 0.537468i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.59710 | + | 0.250276i | 0.214604 | + | 0.00814147i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.52964 | + | 4.92459i | 0.277176 | + | 0.160028i | 0.632144 | − | 0.774851i | \(-0.282175\pi\) |
−0.354968 | + | 0.934878i | \(0.615508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.2306 | + | 26.3801i | 0.494405 | + | 0.856335i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.2826i | 0.560425i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.43881i | 0.305753i | 0.988245 | + | 0.152877i | \(0.0488537\pi\) | ||||
−0.988245 | + | 0.152877i | \(0.951146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.84686 | + | 1.64363i | −0.0921221 | + | 0.0531867i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.88761 | − | 19.0108i | −0.254970 | − | 0.614532i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.3102 | − | 22.2124i | −1.14023 | − | 0.717277i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.19061 | + | 14.1866i | −0.264213 | + | 0.457631i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.01890 | + | 10.4250i | 0.193956 | + | 0.335942i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.14409i | 0.294359i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.2470 | 1.10131 | 0.550655 | − | 0.834733i | \(-0.314378\pi\) | ||||
0.550655 | + | 0.834733i | \(0.314378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.28333 | − | 16.0792i | −0.298223 | − | 0.516538i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.1644 | − | 9.33252i | −0.518740 | − | 0.299495i | 0.217679 | − | 0.976020i | \(-0.430151\pi\) |
−0.736419 | + | 0.676526i | \(0.763485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.150200 | − | 0.0792834i | 0.00481520 | − | 0.00254171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.4199 | − | 23.2440i | 0.429781 | − | 0.744403i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.6425 | − | 25.3615i | −0.468455 | − | 0.811387i | 0.530895 | − | 0.847437i | \(-0.321856\pi\) |
−0.999350 | + | 0.0360501i | \(0.988522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5775 | + | 13.8016i | −0.338057 | + | 0.441100i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.73767i | − | 0.0554797i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.4161 | − | 24.4889i | 1.35286 | − | 0.781076i | 0.364213 | − | 0.931315i | \(-0.381338\pi\) |
0.988650 | + | 0.150240i | \(0.0480045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.562679 | − | 0.324863i | −0.0179285 | − | 0.0103510i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.35731 | − | 3.88357i | 0.234186 | − | 0.123615i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.6305 | − | 47.1294i | −2.59570 | − | 1.49863i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.5251 | − | 9.54080i | 0.524938 | − | 0.303073i | −0.214014 | − | 0.976831i | \(-0.568654\pi\) |
0.738953 | + | 0.673757i | \(0.235321\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.5279 | −0.556233 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.20844i | 0.0383101i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.9673 | + | 12.1055i | −0.664042 | + | 0.383385i | −0.793815 | − | 0.608159i | \(-0.791908\pi\) |
0.129774 | + | 0.991544i | \(0.458575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.07482 | + | 2.92995i | 0.160560 | + | 0.0926995i |
(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 | 1232.2.bi.b.527.11 | yes | 32 | |
4.3 | odd | 2 | 1232.2.bi.a.527.6 | yes | 32 | ||
7.4 | even | 3 | 1232.2.bi.a.879.5 | yes | 32 | ||
11.10 | odd | 2 | inner | 1232.2.bi.b.527.12 | yes | 32 | |
28.11 | odd | 6 | inner | 1232.2.bi.b.879.12 | yes | 32 | |
44.43 | even | 2 | 1232.2.bi.a.527.5 | ✓ | 32 | ||
77.32 | odd | 6 | 1232.2.bi.a.879.6 | yes | 32 | ||
308.263 | even | 6 | inner | 1232.2.bi.b.879.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1232.2.bi.a.527.5 | ✓ | 32 | 44.43 | even | 2 | ||
1232.2.bi.a.527.6 | yes | 32 | 4.3 | odd | 2 | ||
1232.2.bi.a.879.5 | yes | 32 | 7.4 | even | 3 | ||
1232.2.bi.a.879.6 | yes | 32 | 77.32 | odd | 6 | ||
1232.2.bi.b.527.11 | yes | 32 | 1.1 | even | 1 | trivial | |
1232.2.bi.b.527.12 | yes | 32 | 11.10 | odd | 2 | inner | |
1232.2.bi.b.879.11 | yes | 32 | 308.263 | even | 6 | inner | |
1232.2.bi.b.879.12 | yes | 32 | 28.11 | odd | 6 | inner |