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 | 879.12 | ||
Character | \(\chi\) | \(=\) | 1232.879 |
Dual form | 1232.2.bi.b.527.12 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
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 | 0.828616 | − | 0.559817i | \(-0.189128\pi\) |
−0.0705073 | + | 0.997511i | \(0.522462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.222329 | − | 0.385085i | −0.0994286 | − | 0.172215i | 0.812020 | − | 0.583630i | \(-0.198368\pi\) |
−0.911448 | + | 0.411415i | \(0.865035\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −1.27102 | − | 3.06342i | −0.383226 | − | 0.923655i | ||||
\(12\) | 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 | \(-0.249120\pi\) |
−0.256149 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.83947 | + | 4.91811i | 0.651419 | + | 1.12829i | 0.982779 | + | 0.184787i | \(0.0591594\pi\) |
−0.331360 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.13603 | + | 3.39556i | 0.466120 | + | 0.740971i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.10168 | − | 4.10016i | 1.48080 | − | 0.854942i | 0.481039 | − | 0.876699i | \(-0.340259\pi\) |
0.999763 | + | 0.0217573i | \(0.00692610\pi\) | |||||||
\(24\) | 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 | 0.172248 | − | 0.985054i | \(-0.444897\pi\) |
−0.766958 | + | 0.641698i | \(0.778230\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.653455 | − | 4.98609i | 0.113752 | − | 0.867967i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0445993 | − | 1.17561i | −0.00753866 | − | 0.198714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.522119 | + | 0.904337i | 0.0858358 | + | 0.148672i | 0.905747 | − | 0.423819i | \(-0.139311\pi\) |
−0.819911 | + | 0.572491i | \(0.805977\pi\) | |||||||
\(38\) | 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 | \(-0.159905\pi\) | ||||
0.876450 | + | 0.481493i | \(0.159905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.155871 | + | 0.269977i | −0.0232359 | + | 0.0402457i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.79602 | + | 1.03693i | −0.261976 | + | 0.151252i | −0.625236 | − | 0.780436i | \(-0.714997\pi\) |
0.363259 | + | 0.931688i | \(0.381664\pi\) | |||||||
\(48\) | 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 | 0.229662 | + | 0.973270i | \(0.426238\pi\) |
−0.957708 | + | 0.287742i | \(0.907095\pi\) | |||||||
\(54\) | 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 | −0.486181 | − | 0.873858i | \(-0.661611\pi\) |
−0.999874 | + | 0.0158836i | \(0.994944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3396 | + | 5.96955i | −1.32384 | + | 0.764322i | −0.984340 | − | 0.176282i | \(-0.943593\pi\) |
−0.339505 | + | 0.940604i | \(0.610260\pi\) | |||||||
\(62\) | 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 | 0.589381 | − | 0.807855i | \(-0.299372\pi\) |
−0.404933 | + | 0.914346i | \(0.632705\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.4335 | 1.49681 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53120i | 0.300398i | 0.988656 | + | 0.150199i | \(0.0479915\pi\) | ||||
−0.988656 | + | 0.150199i | \(0.952009\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.15659 | + | 4.13186i | 0.837615 | + | 0.483597i | 0.856453 | − | 0.516225i | \(-0.172663\pi\) |
−0.0188377 | + | 0.999823i | \(0.505997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.30579 | − | 3.64065i | 0.728130 | − | 0.420386i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.809599 | − | 8.73754i | 0.0922624 | − | 0.995735i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.17540 | − | 3.76790i | −0.244751 | − | 0.423921i | 0.717310 | − | 0.696754i | \(-0.245373\pi\) |
−0.962062 | + | 0.272832i | \(0.912040\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.20262 | − | 5.54710i | 0.355846 | − | 0.616344i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.8881 | 1.63418 | 0.817092 | − | 0.576507i | \(-0.195585\pi\) | ||||
0.817092 | + | 0.576507i | \(0.195585\pi\) | |||||||
\(84\) | 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 | 0.970856 | − | 0.239664i | \(-0.0770374\pi\) |
−0.692983 | + | 0.720954i | \(0.743704\pi\) | |||||||
\(90\) | 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 | \(-0.640367\pi\) |
−0.996589 | + | 0.0825286i | \(0.973700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.01188 | + | 0.584209i | −0.0997035 | + | 0.0575638i | −0.549023 | − | 0.835807i | \(-0.685000\pi\) |
0.449319 | + | 0.893371i | \(0.351667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.832677 | − | 1.57748i | 0.0812610 | − | 0.153947i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.58515 | − | 14.8699i | −0.829958 | − | 1.43753i | −0.898070 | − | 0.439852i | \(-0.855031\pi\) |
0.0681122 | − | 0.997678i | \(-0.478302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.14649 | + | 1.23928i | 0.205597 | + | 0.118701i | 0.599263 | − | 0.800552i | \(-0.295460\pi\) |
−0.393667 | + | 0.919253i | \(0.628794\pi\) | |||||||
\(110\) | 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 | ||||||||
\(121\) | −7.76904 | + | 7.78730i | −0.706276 | + | 0.707936i | ||||
\(122\) | 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 | \(-0.257760\pi\) | ||||
0.689659 | + | 0.724134i | \(0.257760\pi\) | |||||||
\(128\) | 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 | \(-0.189686\pi\) |
−0.899889 | + | 0.436119i | \(0.856353\pi\) | |||||||
\(132\) | 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 | −0.303359 | − | 0.952876i | \(-0.598108\pi\) |
0.976895 | − | 0.213722i | \(-0.0685586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0641939 | 0.00544485 | 0.00272243 | − | 0.999996i | \(-0.499133\pi\) | ||||
0.00272243 | + | 0.999996i | \(0.499133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.14443 | −0.264809 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.2922 | + | 4.68513i | −0.944298 | + | 0.391790i | ||||
\(144\) | 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 | \(-0.775985\pi\) |
0.179193 | + | 0.983814i | \(0.442651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5612 | + | 18.2926i | −0.859461 | + | 1.48863i | 0.0129820 | + | 0.999916i | \(0.495868\pi\) |
−0.872443 | + | 0.488715i | \(0.837466\pi\) | |||||||
\(152\) | 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 | 0.259081 | + | 0.965855i | \(0.416580\pi\) |
−0.965996 | + | 0.258557i | \(0.916753\pi\) | |||||||
\(158\) | 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 | 0.153881 | − | 0.988089i | \(-0.450823\pi\) |
0.932651 | + | 0.360780i | \(0.117489\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.06535 | + | 0.856917i | −0.160787 | + | 0.0667109i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.07459 | −0.702213 | −0.351106 | − | 0.936336i | \(-0.614194\pi\) | ||||
−0.351106 | + | 0.936336i | \(0.614194\pi\) | |||||||
\(168\) | 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 | \(-0.583690\pi\) |
0.706314 | + | 0.707899i | \(0.250357\pi\) | |||||||
\(174\) | 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 | 0.588281 | − | 0.808656i | \(-0.299805\pi\) |
−0.406176 | + | 0.913795i | \(0.633138\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | 0.929305 | − | 7.09093i | 0.0679575 | − | 0.518540i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.93073 | − | 13.1301i | 0.504137 | − | 0.955073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.40235 | − | 3.69640i | 0.463258 | − | 0.267462i | −0.250155 | − | 0.968206i | \(-0.580482\pi\) |
0.713413 | + | 0.700744i | \(0.247148\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8092 | − | 10.2822i | −1.28194 | − | 0.740126i | −0.304734 | − | 0.952438i | \(-0.598568\pi\) |
−0.977202 | + | 0.212311i | \(0.931901\pi\) | |||||||
\(194\) | 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 | 0.581096 | − | 0.813835i | \(-0.302624\pi\) |
−0.414254 | + | 0.910161i | \(0.635958\pi\) | |||||||
\(200\) | 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 | \(-0.687377\pi\) | ||||
−0.555248 | + | 0.831685i | \(0.687377\pi\) | |||||||
\(212\) | 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 | \(0.0395121\pi\) | ||||
−0.992306 | + | 0.123812i | \(0.960488\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.36679 | −0.224453 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.4176 | + | 18.0438i | −0.691439 | + | 1.19761i | 0.279927 | + | 0.960021i | \(0.409690\pi\) |
−0.971366 | + | 0.237586i | \(0.923644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.73473 | − | 13.3969i | −0.511125 | − | 0.885295i | −0.999917 | − | 0.0128943i | \(-0.995896\pi\) |
0.488792 | − | 0.872401i | \(-0.337438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.68708 | − | 10.8594i | 0.505773 | − | 0.714493i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.43672 | − | 3.13889i | 0.356172 | − | 0.205636i | −0.311229 | − | 0.950335i | \(-0.600740\pi\) |
0.667400 | + | 0.744699i | \(0.267407\pi\) | |||||||
\(234\) | 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 | \(-0.532447\pi\) | ||||
−0.101757 | + | 0.994809i | \(0.532447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9004 | + | 10.3348i | 1.15306 | + | 0.665722i | 0.949632 | − | 0.313367i | \(-0.101457\pi\) |
0.203432 | + | 0.979089i | \(0.434790\pi\) | |||||||
\(242\) | 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 | \(0.399745\pi\) | ||||
−0.309779 | + | 0.950809i | \(0.600255\pi\) | |||||||
\(252\) | 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 | −0.976157 | − | 0.217064i | \(-0.930352\pi\) |
0.300096 | − | 0.953909i | \(-0.402981\pi\) | |||||||
\(258\) | 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 | \(-0.757166\pi\) |
0.959855 | + | 0.280496i | \(0.0904989\pi\) | |||||||
\(264\) | 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 | −0.996699 | − | 0.0811891i | \(-0.974128\pi\) |
0.568661 | + | 0.822572i | \(0.307462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9634 | + | 18.9892i | 0.665982 | + | 1.15351i | 0.979018 | + | 0.203773i | \(0.0653205\pi\) |
−0.313036 | + | 0.949741i | \(0.601346\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.5165 | − | 7.87369i | 0.757531 | − | 0.476537i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.7923 | − | 2.06967i | −0.952312 | − | 0.124806i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.9931 | − | 15.5844i | −1.62186 | − | 0.936379i | −0.986423 | − | 0.164222i | \(-0.947489\pi\) |
−0.635432 | − | 0.772157i | \(-0.719178\pi\) | |||||||
\(278\) | 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 | 0.285922 | + | 0.958253i | \(0.407700\pi\) |
−0.972832 | + | 0.231510i | \(0.925633\pi\) | |||||||
\(284\) | 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 | ||||||||
\(297\) | −17.1908 | + | 7.13249i | −0.997512 | + | 0.413869i | ||||
\(298\) | 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 | \(-0.582430\pi\) | ||||
−0.256078 | + | 0.966656i | \(0.582430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.77158 | −0.100782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.8641 | − | 9.73650i | −0.956276 | − | 0.552106i | −0.0612509 | − | 0.998122i | \(-0.519509\pi\) |
−0.895025 | + | 0.446016i | \(0.852842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.15640 | + | 8.93115i | 0.291457 | + | 0.504818i | 0.974154 | − | 0.225883i | \(-0.0725267\pi\) |
−0.682698 | + | 0.730701i | \(0.739193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.698143 | + | 0.439178i | −0.0393359 | + | 0.0247449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.69923 | − | 9.87136i | −0.320101 | − | 0.554431i | 0.660408 | − | 0.750907i | \(-0.270383\pi\) |
−0.980509 | + | 0.196476i | \(0.937050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5383 | − | 5.20216i | 0.702010 | − | 0.291265i | ||||
\(320\) | 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 | −0.749236 | − | 0.662303i | \(-0.769579\pi\) |
0.198953 | + | 0.980009i | \(0.436246\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | −1.64782 | + | 12.5734i | −0.0892343 | + | 0.680890i | ||||
\(342\) | 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 | \(-0.688431\pi\) |
0.997663 | + | 0.0683209i | \(0.0217642\pi\) | |||||||
\(348\) | 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 | 0.379021 | + | 0.925388i | \(0.376261\pi\) |
−0.990920 | + | 0.134452i | \(0.957073\pi\) | |||||||
\(354\) | 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 | \(-0.111655\pi\) |
−0.767141 | + | 0.641478i | \(0.778322\pi\) | |||||||
\(360\) | 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 | 0.852251 | − | 0.523133i | \(-0.175237\pi\) |
−0.0269210 | + | 0.999638i | \(0.508570\pi\) | |||||||
\(368\) | 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 | \(-0.885015\pi\) |
−0.161649 | + | 0.986848i | \(0.551681\pi\) | |||||||
\(374\) | 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 | \(-0.847262\pi\) | ||
0.887069 | − | 0.461637i | \(-0.152738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4107 | + | 11.7841i | 1.04567 | + | 0.603720i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9906 | − | 6.34544i | 0.561595 | − | 0.324237i | −0.192191 | − | 0.981358i | \(-0.561559\pi\) |
0.753785 | + | 0.657121i | \(0.228226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54469 | + | 1.63084i | −0.180654 | + | 0.0831155i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.02931 | − | 6.97897i | −0.204821 | − | 0.354761i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0005 | + | 17.3213i | −0.507043 | + | 0.878225i | 0.492924 | + | 0.870073i | \(0.335928\pi\) |
−0.999967 | + | 0.00815194i | \(0.997405\pi\) | |||||||
\(390\) | 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 | 0.759744 | − | 0.650222i | \(-0.225324\pi\) |
−0.942981 | + | 0.332847i | \(0.891991\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6345 | + | 20.1468i | −0.532392 | + | 1.00860i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.687115 | − | 1.19012i | −0.0343129 | − | 0.0594317i | 0.848359 | − | 0.529421i | \(-0.177591\pi\) |
−0.882672 | + | 0.469990i | \(0.844258\pi\) | |||||||
\(402\) | 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 | \(-0.167924\pi\) |
−0.00394883 | + | 0.999992i | \(0.501257\pi\) | |||||||
\(410\) | 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 | \(-0.996671\pi\) | ||
0.999945 | − | 0.0104573i | \(-0.00332872\pi\) | |||||||
\(420\) | 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 | ||||||||
\(429\) | −18.3794 | − | 2.40872i | −0.887365 | − | 0.116294i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.54908 | − | 4.41514i | 0.122785 | − | 0.212670i | −0.798080 | − | 0.602551i | \(-0.794151\pi\) |
0.920865 | + | 0.389882i | \(0.127484\pi\) | |||||||
\(432\) | 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 | \(-0.182865\pi\) |
−0.890337 | + | 0.455302i | \(0.849531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.12473 | − | 4.42378i | 0.101177 | − | 0.210656i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.89496 | − | 2.82611i | 0.232567 | − | 0.134272i | −0.379189 | − | 0.925319i | \(-0.623797\pi\) |
0.611756 | + | 0.791047i | \(0.290464\pi\) | |||||||
\(444\) | 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 | ||||||||
\(451\) | 7.11957 | − | 2.95392i | 0.335247 | − | 0.139095i | ||||
\(452\) | 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 | \(-0.823348\pi\) |
0.0313638 | + | 0.999508i | \(0.490015\pi\) | |||||||
\(458\) | 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 | \(-0.736714\pi\) | ||
0.676986 | − | 0.735996i | \(-0.263286\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.28888 | + | 2.23241i | −0.0597705 | + | 0.103526i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.27799 | − | 1.31520i | 0.105413 | − | 0.0608602i | −0.446367 | − | 0.894850i | \(-0.647282\pi\) |
0.551780 | + | 0.833990i | \(0.313949\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −14.6097 | − | 35.2126i | −0.671756 | − | 1.61907i | ||||
\(474\) | 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 | −0.317457 | − | 0.948273i | \(-0.602829\pi\) |
0.979957 | − | 0.199211i | \(-0.0638378\pi\) | |||||||
\(480\) | 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 | 0.969478 | − | 0.245179i | \(-0.0788466\pi\) |
0.272408 | + | 0.962182i | \(0.412180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2866 | 1.09828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.790237 | −0.0356629 | −0.0178314 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178314 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.41273 | + | 7.64307i | −0.198739 | + | 0.344227i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.02516 | + | 0.134354i | 0.0460777 | + | 0.00603874i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.12619 | + | 5.92248i | −0.140229 | + | 0.265660i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7657 | − | 8.52496i | 0.661002 | − | 0.381630i | −0.131657 | − | 0.991295i | \(-0.542030\pi\) |
0.792659 | + | 0.609666i | \(0.208696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.9157 | − | 6.87953i | −0.532354 | − | 0.307355i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.2695 | 0.814597 | 0.407299 | − | 0.913295i | \(-0.366471\pi\) | ||||
0.407299 | + | 0.913295i | \(0.366471\pi\) | |||||||
\(504\) | 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 | 0.846894 | − | 0.531762i | \(-0.178470\pi\) |
−0.883966 | + | 0.467551i | \(0.845136\pi\) | |||||||
\(510\) | 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 | 0.452278 | + | 0.891877i | \(0.350611\pi\) |
−0.998527 | + | 0.0542543i | \(0.982722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0685 | + | 20.9033i | 0.527720 | + | 0.914038i | 0.999478 | + | 0.0323095i | \(0.0102862\pi\) |
−0.471758 | + | 0.881728i | \(0.656380\pi\) | |||||||
\(524\) | 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 | ||||||||
\(539\) | 12.6857 | − | 19.4441i | 0.546412 | − | 0.837517i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.9721 | + | 11.5309i | −0.858666 | + | 0.495751i | −0.863565 | − | 0.504237i | \(-0.831774\pi\) |
0.00489930 | + | 0.999988i | \(0.498440\pi\) | |||||||
\(542\) | 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 | \(-0.488354\pi\) | ||||
0.0365798 | + | 0.999331i | \(0.488354\pi\) | |||||||
\(548\) | 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 | \(-0.0767781\pi\) |
0.278655 | + | 0.960391i | \(0.410111\pi\) | |||||||
\(558\) | 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 | \(-0.783210\pi\) |
0.933719 | + | 0.358006i | \(0.116543\pi\) | |||||||
\(564\) | 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 | \(-0.633096\pi\) |
0.588388 | + | 0.808579i | \(0.299763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.28733 | + | 7.42587i | −0.179419 | + | 0.310763i | −0.941682 | − | 0.336505i | \(-0.890755\pi\) |
0.762263 | + | 0.647268i | \(0.224089\pi\) | |||||||
\(572\) | 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 | −0.967555 | − | 0.252661i | \(-0.918694\pi\) |
0.702588 | + | 0.711597i | \(0.252028\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 34.8598 | + | 4.56857i | 1.44375 | + | 0.189211i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.995169 | + | 0.574561i | 0.0411452 | + | 0.0237552i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.65362i | − | 0.0682520i | −0.999418 | − | 0.0341260i | \(-0.989135\pi\) | ||
0.999418 | − | 0.0341260i | \(-0.0108648\pi\) | |||||||
\(588\) | 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 | \(-0.539490\pi\) |
0.797498 | + | 0.603322i | \(0.206157\pi\) | |||||||
\(594\) | 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 | −0.259077 | − | 0.965857i | \(-0.583418\pi\) |
−0.965995 | + | 0.258561i | \(0.916752\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 4.72606 | + | 1.26040i | 0.192142 | + | 0.0512425i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.7473 | + | 23.8111i | 0.557987 | + | 0.966462i | 0.997664 | + | 0.0683062i | \(0.0217595\pi\) |
−0.439677 | + | 0.898156i | \(0.644907\pi\) | |||||||
\(608\) | 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 | \(-0.124302\pi\) |
0.132701 | + | 0.991156i | \(0.457635\pi\) | |||||||
\(614\) | 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 | 0.342929 | − | 0.939361i | \(-0.388581\pi\) |
−0.642046 | + | 0.766666i | \(0.721914\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | 26.3776 | − | 10.9441i | 1.05342 | − | 0.437065i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.25167i | 0.0897798i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 23.1184i | − | 0.920327i | −0.887834 | − | 0.460164i | \(-0.847791\pi\) | ||
0.887834 | − | 0.460164i | \(-0.152209\pi\) | |||||||
\(632\) | 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 | −0.396621 | − | 0.917982i | \(-0.629817\pi\) |
0.993307 | − | 0.115507i | \(-0.0368492\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4763i | 0.413145i | 0.978431 | + | 0.206572i | \(0.0662309\pi\) | ||||
−0.978431 | + | 0.206572i | \(0.933769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.74960i | − | 0.305140i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7841 | + | 15.4638i | 1.05299 | + | 0.607944i | 0.923485 | − | 0.383634i | \(-0.125328\pi\) |
0.129506 | + | 0.991579i | \(0.458661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.68047 | + | 43.3440i | −0.222978 | + | 1.70140i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.581459 | − | 15.3269i | −0.0227892 | − | 0.600708i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7611 | − | 22.1029i | −0.499381 | − | 0.864954i | 0.500618 | − | 0.865668i | \(-0.333106\pi\) |
−1.00000 | 0.000714266i | \(0.999773\pi\) | ||||||||
\(654\) | 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 | \(-0.442135\pi\) | ||||
0.180790 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8440 | + | 22.2465i | −0.499575 | + | 0.865289i | −1.00000 | 0.000491031i | \(-0.999844\pi\) | |
0.500425 | + | 0.865780i | \(0.333177\pi\) | |||||||
\(662\) | 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 | \(-0.820970\pi\) |
0.0388304 | + | 0.999246i | \(0.487637\pi\) | |||||||
\(678\) | 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 | 0.588302 | − | 0.808641i | \(-0.299797\pi\) |
−0.406153 | + | 0.913805i | \(0.633130\pi\) | |||||||
\(684\) | 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 | 0.594238 | − | 0.804289i | \(-0.297454\pi\) |
0.993654 | − | 0.112481i | \(-0.0358797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.58884 | + | 2.57131i | −0.212302 | + | 0.0976762i | ||||
\(694\) | 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 | 0.743418 | − | 0.668827i | \(-0.233203\pi\) |
−0.950930 | + | 0.309405i | \(0.899870\pi\) | |||||||
\(710\) | 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 | −0.763176 | − | 0.646191i | \(-0.776361\pi\) |
0.178030 | + | 0.984025i | \(0.443028\pi\) | |||||||
\(720\) | 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 | \(0.213697\pi\) | ||||
−0.782984 | + | 0.622042i | \(0.786303\pi\) | |||||||
\(728\) | 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 | \(-0.449230\pi\) |
0.934445 | + | 0.356108i | \(0.115896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.89658 | − | 2.66257i | 0.143728 | − | 0.0982105i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.751337 | − | 5.73297i | 0.0276759 | − | 0.211177i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8587 | − | 29.2002i | 0.620159 | − | 1.07415i | −0.369297 | − | 0.929311i | \(-0.620402\pi\) |
0.989456 | − | 0.144835i | \(-0.0462651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.7395 | 1.16598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.4286 | −1.70330 | −0.851650 | − | 0.524112i | \(-0.824397\pi\) | ||||
−0.851650 | + | 0.524112i | \(0.824397\pi\) | |||||||
\(744\) | 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 | −0.209185 | − | 0.977876i | \(-0.567081\pi\) |
0.742273 | + | 0.670098i | \(0.233748\pi\) | |||||||
\(752\) | 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 | ||||||||
\(759\) | −15.8031 | − | 38.0889i | −0.573617 | − | 1.38254i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.35266 | − | 3.09036i | 0.194034 | − | 0.112026i | −0.399836 | − | 0.916587i | \(-0.630933\pi\) |
0.593870 | + | 0.804561i | \(0.297599\pi\) | |||||||
\(762\) | 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 | −0.902900 | − | 0.429852i | \(-0.858566\pi\) |
0.823712 | + | 0.567008i | \(0.191899\pi\) | |||||||
\(774\) | 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 | ||||||||
\(781\) | 7.75412 | − | 3.21719i | 0.277464 | − | 0.115120i | ||||
\(782\) | 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 | \(-0.808965\pi\) |
0.901730 | + | 0.432300i | \(0.142298\pi\) | |||||||
\(788\) | 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 | ||||||||
\(803\) | 3.56147 | − | 27.1753i | 0.125681 | − | 0.958994i | ||||
\(804\) | 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 | \(-0.534281\pi\) |
−0.914753 | + | 0.404015i | \(0.867614\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00928 | 0.316359 | 0.158179 | − | 0.987410i | \(-0.449438\pi\) | ||||
0.158179 | + | 0.987410i | \(0.449438\pi\) | |||||||
\(812\) | 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 | \(-0.995022\pi\) |
−0.486397 | + | 0.873738i | \(0.661689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.73756 | + | 2.73523i | 0.165141 | + | 0.0953442i | 0.580293 | − | 0.814408i | \(-0.302938\pi\) |
−0.415152 | + | 0.909752i | \(0.636272\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.1676 | − | 14.6899i | −0.667330 | − | 0.511438i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.4857 | 0.990544 | 0.495272 | − | 0.868738i | \(-0.335068\pi\) | ||||
0.495272 | + | 0.868738i | \(0.335068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5693 | − | 23.5027i | 0.471281 | − | 0.816283i | −0.528179 | − | 0.849133i | \(-0.677125\pi\) |
0.999460 | + | 0.0328498i | \(0.0104583\pi\) | |||||||
\(830\) | 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 | \(0.0438469\pi\) | ||||
−0.990528 | + | 0.137314i | \(0.956153\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | −27.7957 | + | 8.62540i | −0.955072 | + | 0.296372i | ||||
\(848\) | 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 | \(-0.470699\pi\) |
−0.816398 | + | 0.577489i | \(0.804033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3365 | − | 14.6280i | 0.864470 | − | 0.499102i | −0.00103656 | − | 0.999999i | \(-0.500330\pi\) |
0.865507 | + | 0.500897i | \(0.166997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.89148 | + | 4.96426i | −0.268941 | + | 0.169182i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.89963 | + | 1.67410i | −0.0987046 | + | 0.0569871i | −0.548540 | − | 0.836124i | \(-0.684816\pi\) |
0.449835 | + | 0.893112i | \(0.351483\pi\) | |||||||
\(864\) | 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 | \(-0.519199\pi\) |
0.834311 | + | 0.551295i | \(0.185866\pi\) | |||||||
\(878\) | 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 | \(0.225913\pi\) | ||||
−0.758540 | + | 0.651626i | \(0.774087\pi\) | |||||||
\(884\) | 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 | \(-0.0761581\pi\) |
−0.690989 | + | 0.722865i | \(0.742825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.3700 | + | 19.1980i | 1.21981 | + | 0.643879i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0636 | − | 2.76051i | −0.705659 | − | 0.0924805i | ||||
\(892\) | 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 | −0.351840 | − | 0.936060i | \(-0.614444\pi\) |
−0.986572 | + | 0.163328i | \(0.947777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.5806i | 0.384103i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.8951i | 1.52057i | 0.649589 | + | 0.760286i | \(0.274941\pi\) | ||||
−0.649589 | + | 0.760286i | \(0.725059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.9230 | − | 45.6085i | −0.626261 | − | 1.50942i | ||||
\(914\) | 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 | −0.986389 | − | 0.164431i | \(-0.947421\pi\) |
0.350793 | − | 0.936453i | \(-0.385912\pi\) | |||||||
\(920\) | 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 | −0.923670 | − | 0.383188i | \(-0.874826\pi\) |
0.129984 | − | 0.991516i | \(-0.458507\pi\) | |||||||
\(930\) | 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 | ||||||||
\(935\) | −2.93722 | + | 1.21866i | −0.0960574 | + | 0.0398544i | ||||
\(936\) | 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 | \(-0.227089\pi\) |
−0.188684 | + | 0.982038i | \(0.560422\pi\) | |||||||
\(942\) | 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 | −0.354968 | − | 0.934878i | \(-0.615508\pi\) |
0.632144 | + | 0.774851i | \(0.282175\pi\) | |||||||
\(948\) | 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 | ||||||||
\(957\) | 20.4076 | + | 2.67453i | 0.659685 | + | 0.0864554i | ||||
\(958\) | 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 | \(-0.685622\pi\) | ||||
−0.550655 | + | 0.834733i | \(0.685622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.28333 | + | 16.0792i | −0.298223 | + | 0.516538i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.1644 | + | 9.33252i | −0.518740 | + | 0.299495i | −0.736419 | − | 0.676526i | \(-0.763485\pi\) |
0.217679 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(972\) | 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 | −0.999350 | − | 0.0360501i | \(-0.988522\pi\) |
0.530895 | + | 0.847437i | \(0.321856\pi\) | |||||||
\(978\) | 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 | 0.988650 | − | 0.150240i | \(-0.0480045\pi\) |
0.364213 | + | 0.931315i | \(0.381338\pi\) | |||||||
\(984\) | 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 | 0.738953 | − | 0.673757i | \(-0.235321\pi\) |
−0.214014 | + | 0.976831i | \(0.568654\pi\) | |||||||
\(992\) | 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 | \(-0.208092\pi\) |
−0.129774 | + | 0.991544i | \(0.541425\pi\) | |||||||
\(998\) | 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.879.12 | yes | 32 | |
4.3 | odd | 2 | 1232.2.bi.a.879.5 | yes | 32 | ||
7.2 | even | 3 | 1232.2.bi.a.527.6 | yes | 32 | ||
11.10 | odd | 2 | inner | 1232.2.bi.b.879.11 | yes | 32 | |
28.23 | odd | 6 | inner | 1232.2.bi.b.527.11 | yes | 32 | |
44.43 | even | 2 | 1232.2.bi.a.879.6 | yes | 32 | ||
77.65 | odd | 6 | 1232.2.bi.a.527.5 | ✓ | 32 | ||
308.219 | even | 6 | inner | 1232.2.bi.b.527.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1232.2.bi.a.527.5 | ✓ | 32 | 77.65 | odd | 6 | ||
1232.2.bi.a.527.6 | yes | 32 | 7.2 | even | 3 | ||
1232.2.bi.a.879.5 | yes | 32 | 4.3 | odd | 2 | ||
1232.2.bi.a.879.6 | yes | 32 | 44.43 | even | 2 | ||
1232.2.bi.b.527.11 | yes | 32 | 28.23 | odd | 6 | inner | |
1232.2.bi.b.527.12 | yes | 32 | 308.219 | even | 6 | inner | |
1232.2.bi.b.879.11 | yes | 32 | 11.10 | odd | 2 | inner | |
1232.2.bi.b.879.12 | yes | 32 | 1.1 | even | 1 | trivial |