Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1839,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1839");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.m (of order \(2\), degree \(1\), 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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1839.6 | ||
Character | \(\chi\) | \(=\) | 1840.1839 |
Dual form | 1840.2.m.g.1839.7 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.49894 | −1.44276 | −0.721381 | − | 0.692539i | \(-0.756492\pi\) | ||||
−0.721381 | + | 0.692539i | \(0.756492\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19676 | + | 0.417445i | 0.982419 | + | 0.186687i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.04922i | − | 1.15250i | −0.817275 | − | 0.576248i | \(-0.804516\pi\) | ||
0.817275 | − | 0.576248i | \(-0.195484\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.24468 | 1.08156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.87962 | 1.77277 | 0.886386 | − | 0.462948i | \(-0.153208\pi\) | ||||
0.886386 | + | 0.462948i | \(0.153208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00311i | 1.66496i | 0.554052 | + | 0.832482i | \(0.313081\pi\) | ||||
−0.554052 | + | 0.832482i | \(0.686919\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.48956 | − | 1.04317i | −1.41740 | − | 0.269345i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.968611 | 0.234923 | 0.117461 | − | 0.993077i | \(-0.462524\pi\) | ||||
0.117461 | + | 0.993077i | \(0.462524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72585 | 0.395937 | 0.197969 | − | 0.980208i | \(-0.436566\pi\) | ||||
0.197969 | + | 0.980208i | \(0.436566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.61980i | 1.66278i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.79127 | − | 2.93705i | −0.790535 | − | 0.612417i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65148 | + | 1.83405i | 0.930296 | + | 0.366810i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.611451 | −0.117674 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.89743 | −0.723734 | −0.361867 | − | 0.932230i | \(-0.617861\pi\) | ||||
−0.361867 | + | 0.932230i | \(0.617861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.01605i | 1.61933i | 0.586892 | + | 0.809665i | \(0.300351\pi\) | ||||
−0.586892 | + | 0.809665i | \(0.699649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.6928 | −2.55769 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.27288 | − | 6.69839i | 0.215156 | − | 1.13223i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.15559 | −0.354377 | −0.177189 | − | 0.984177i | \(-0.556700\pi\) | ||||
−0.177189 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 15.0014i | − | 2.40215i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.17642 | 0.964595 | 0.482297 | − | 0.876008i | \(-0.339802\pi\) | ||||
0.482297 | + | 0.876008i | \(0.339802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.08209i | − | 1.38501i | −0.721415 | − | 0.692503i | \(-0.756508\pi\) | ||
0.721415 | − | 0.692503i | \(-0.243492\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.12778 | + | 1.35448i | 1.06255 | + | 0.201914i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.73942 | −1.42064 | −0.710320 | − | 0.703879i | \(-0.751450\pi\) | ||||
−0.710320 | + | 0.703879i | \(0.751450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.29773 | −0.328247 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.42050 | −0.338937 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.18153 | 1.26118 | 0.630590 | − | 0.776116i | \(-0.282813\pi\) | ||||
0.630590 | + | 0.776116i | \(0.282813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.9161 | + | 2.45442i | 1.74161 | + | 0.330953i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.31279 | −0.571243 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.17122i | − | 0.152480i | −0.997089 | − | 0.0762401i | \(-0.975708\pi\) | ||
0.997089 | − | 0.0762401i | \(-0.0242916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.951354i | − | 0.121808i | −0.998144 | − | 0.0609042i | \(-0.980602\pi\) | ||
0.998144 | − | 0.0609042i | \(-0.0193984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 9.89375i | − | 1.24650i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.50597 | + | 13.1874i | −0.310827 | + | 1.63569i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.83203i | 1.20117i | 0.799559 | + | 0.600587i | \(0.205066\pi\) | ||||
−0.799559 | + | 0.600587i | \(0.794934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.47415 | + | 7.33950i | 1.14055 | + | 0.883572i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.99828i | 1.06790i | 0.845516 | + | 0.533949i | \(0.179293\pi\) | ||||
−0.845516 | + | 0.533949i | \(0.820707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.53105i | − | 0.998483i | −0.866463 | − | 0.499242i | \(-0.833612\pi\) | ||
0.866463 | − | 0.499242i | \(-0.166388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.6238 | − | 4.58317i | −1.34220 | − | 0.529219i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 17.9282i | − | 2.04311i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.59242 | 0.629196 | 0.314598 | − | 0.949225i | \(-0.398130\pi\) | ||||
0.314598 | + | 0.949225i | \(0.398130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.20608 | −0.911786 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.97096i | 0.655397i | 0.944782 | + | 0.327699i | \(0.106273\pi\) | ||||
−0.944782 | + | 0.327699i | \(0.893727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.12780 | + | 0.404342i | 0.230793 | + | 0.0438570i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.73942 | 1.04418 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.22303i | 0.765640i | 0.923823 | + | 0.382820i | \(0.125047\pi\) | ||||
−0.923823 | + | 0.382820i | \(0.874953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.3048 | 1.91886 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 22.5305i | − | 2.33631i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.79127 | + | 0.720447i | 0.388976 | + | 0.0739163i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.51772 | 0.763309 | 0.381654 | − | 0.924305i | \(-0.375354\pi\) | ||||
0.381654 | + | 0.924305i | \(0.375354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.0775 | 1.91736 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8797 | 1.28158 | 0.640788 | − | 0.767718i | \(-0.278608\pi\) | ||||
0.640788 | + | 0.767718i | \(0.278608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2773i | 1.60385i | 0.597427 | + | 0.801923i | \(0.296190\pi\) | ||||
−0.597427 | + | 0.801923i | \(0.703810\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.18085 | + | 16.7389i | −0.310419 | + | 1.63354i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.07686i | − | 0.297452i | −0.988878 | − | 0.148726i | \(-0.952483\pi\) | ||
0.988878 | − | 0.148726i | \(-0.0475172\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.89197i | − | 0.468566i | −0.972168 | − | 0.234283i | \(-0.924726\pi\) | ||
0.972168 | − | 0.234283i | \(-0.0752742\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.38669 | 0.511282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.92574 | 0.181158 | 0.0905791 | − | 0.995889i | \(-0.471128\pi\) | ||||
0.0905791 | + | 0.995889i | \(0.471128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.10245 | − | 8.03463i | −0.662307 | − | 0.749233i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.4782i | 1.80076i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.95350i | − | 0.270747i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5699 | 2.14272 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4345 | −1.39168 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.45255 | + | 5.97070i | 0.845462 | + | 0.534035i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5081 | 1.19865 | 0.599324 | − | 0.800506i | \(-0.295436\pi\) | ||||
0.599324 | + | 0.800506i | \(0.295436\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.6956i | 1.99823i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50575i | 0.306299i | 0.988203 | + | 0.153149i | \(0.0489416\pi\) | ||||
−0.988203 | + | 0.153149i | \(0.951058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.26249i | − | 0.456316i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.34321 | − | 0.255247i | −0.115605 | − | 0.0219682i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.570160 | 0.0487121 | 0.0243560 | − | 0.999703i | \(-0.492246\pi\) | ||||
0.0243560 | + | 0.999703i | \(0.492246\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.54130i | − | 0.300369i | −0.988658 | − | 0.150185i | \(-0.952013\pi\) | ||
0.988658 | − | 0.150185i | \(-0.0479868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.3382 | 2.04965 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.2960i | 2.95160i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.56170 | − | 1.62696i | −0.711010 | − | 0.135112i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.74188 | 0.473583 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.0365i | − | 1.47761i | −0.673919 | − | 0.738805i | \(-0.735390\pi\) | ||
0.673919 | − | 0.738805i | \(-0.264610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.5790i | − | 0.860909i | −0.902612 | − | 0.430454i | \(-0.858353\pi\) | ||
0.902612 | − | 0.430454i | \(-0.141647\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.14284 | 0.254083 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.76371 | + | 19.8061i | −0.302308 | + | 1.59086i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3320 | 1.30344 | 0.651719 | − | 0.758460i | \(-0.274048\pi\) | ||||
0.651719 | + | 0.758460i | \(0.274048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.9441 | −1.81958 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.95570 | + | 11.5604i | −0.705808 | + | 0.911089i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1664 | 1.10959 | 0.554797 | − | 0.831985i | \(-0.312796\pi\) | ||||
0.554797 | + | 0.831985i | \(0.312796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −32.2765 | − | 6.13343i | −2.51272 | − | 0.477487i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.54576 | −0.196997 | −0.0984985 | − | 0.995137i | \(-0.531404\pi\) | ||||
−0.0984985 | + | 0.995137i | \(0.531404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0374 | −1.77210 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.59984 | 0.428230 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.52121i | − | 0.343741i | −0.985120 | − | 0.171870i | \(-0.945019\pi\) | ||
0.985120 | − | 0.171870i | \(-0.0549810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.59242 | − | 14.1834i | 0.422747 | − | 1.07216i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.92681i | 0.219993i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 20.1473i | − | 1.50588i | −0.658088 | − | 0.752941i | \(-0.728635\pi\) | ||
0.658088 | − | 0.752941i | \(-0.271365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.1244i | − | 1.04986i | −0.851146 | − | 0.524930i | \(-0.824092\pi\) | ||
0.851146 | − | 0.524930i | \(-0.175908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.37737i | 0.175741i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.73532 | − | 0.899842i | −0.348147 | − | 0.0661577i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.69506 | 0.416464 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.86445i | 0.135619i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.52741 | 0.544664 | 0.272332 | − | 0.962203i | \(-0.412205\pi\) | ||||
0.272332 | + | 0.962203i | \(0.412205\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0605i | 1.15606i | 0.816016 | + | 0.578030i | \(0.196178\pi\) | ||||
−0.816016 | + | 0.578030i | \(0.803822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.26226 | − | 32.9544i | 0.448450 | − | 2.35992i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6707i | 1.68647i | 0.537546 | + | 0.843234i | \(0.319351\pi\) | ||||
−0.537546 | + | 0.843234i | \(0.680649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5976 | −1.46013 | −0.730064 | − | 0.683379i | \(-0.760510\pi\) | ||||
−0.730064 | + | 0.683379i | \(0.760510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 24.5696i | − | 1.73301i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8841i | 0.834100i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5681 | + | 2.57832i | 0.947636 | + | 0.180077i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.3015 | − | 9.52979i | −0.855012 | − | 0.662367i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.1473 | 0.701906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.254864i | 0.0175456i | 0.999962 | + | 0.00877279i | \(0.00279250\pi\) | ||||
−0.999962 | + | 0.00877279i | \(0.997207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 22.4861i | − | 1.54072i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.79127 | − | 19.9511i | 0.258563 | − | 1.36066i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.4919 | 1.86627 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.3185i | 1.44057i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.81468i | 0.391138i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.90122 | −0.261245 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0926 | + | 5.95091i | 1.00617 | + | 0.396728i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 17.6776i | − | 1.17331i | −0.809839 | − | 0.586653i | \(-0.800445\pi\) | ||
0.809839 | − | 0.586653i | \(-0.199555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.1981i | 1.73122i | 0.500722 | + | 0.865608i | \(0.333068\pi\) | ||||
−0.500722 | + | 0.865608i | \(0.666932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.8015i | 2.94772i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.2589i | − | 0.868618i | −0.900764 | − | 0.434309i | \(-0.856993\pi\) | ||
0.900764 | − | 0.434309i | \(-0.143007\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.3951 | − | 4.06567i | −1.39566 | − | 0.265215i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9751 | −0.907780 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.29573i | 0.536606i | 0.963335 | + | 0.268303i | \(0.0864629\pi\) | ||||
−0.963335 | + | 0.268303i | \(0.913537\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.9949i | − | 1.61006i | −0.593232 | − | 0.805031i | \(-0.702148\pi\) | ||
0.593232 | − | 0.805031i | \(-0.297852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3408 | 1.43316 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.04756 | − | 0.959176i | −0.322477 | − | 0.0612795i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3605i | 0.659221i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.9210i | − | 0.945582i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5642 | 0.666809 | 0.333405 | − | 0.942784i | \(-0.391803\pi\) | ||||
0.333405 | + | 0.942784i | \(0.391803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.2912 | − | 17.2687i | −1.40144 | − | 1.08568i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.31724 | − | 1.01042i | −0.332979 | − | 0.0632752i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9404i | 0.807202i | 0.914935 | + | 0.403601i | \(0.132242\pi\) | ||||
−0.914935 | + | 0.403601i | \(0.867758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.57288i | 0.408419i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6459 | −0.782763 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.5116i | − | 1.38813i | −0.719914 | − | 0.694063i | \(-0.755819\pi\) | ||
0.719914 | − | 0.694063i | \(-0.244181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.1696 | + | 3.83279i | 1.23901 | + | 0.235446i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 18.0499i | − | 1.10464i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.1013 | 1.65240 | 0.826199 | − | 0.563379i | \(-0.190499\pi\) | ||||
0.826199 | + | 0.563379i | \(0.190499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.3787i | − | 1.11643i | −0.829697 | − | 0.558214i | \(-0.811487\pi\) | ||
0.829697 | − | 0.558214i | \(-0.188513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −45.7425 | −2.76846 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.3489 | + | 10.7835i | 1.64920 | + | 0.650270i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.28386i | − | 0.257392i | −0.991684 | − | 0.128696i | \(-0.958921\pi\) | ||
0.991684 | − | 0.128696i | \(-0.0410792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.2542i | 1.75141i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.2609i | − | 1.20866i | −0.796733 | − | 0.604332i | \(-0.793440\pi\) | ||
0.796733 | − | 0.604332i | \(-0.206560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.40056i | 0.439918i | 0.975509 | + | 0.219959i | \(0.0705923\pi\) | ||||
−0.975509 | + | 0.219959i | \(0.929408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.47415 | − | 1.80035i | −0.561200 | − | 0.106644i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 18.8332i | − | 1.11169i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0618 | −0.944811 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.7863 | −1.10127 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.0574 | −1.46387 | −0.731933 | − | 0.681376i | \(-0.761382\pi\) | ||||
−0.731933 | + | 0.681376i | \(0.761382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.488921 | − | 2.57289i | 0.0284661 | − | 0.149800i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.59510 | −0.208609 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.6314 | − | 22.7594i | 1.01965 | − | 1.31621i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.6933 | −1.59621 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.1855 | −1.84901 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.397138 | − | 2.08989i | 0.0227401 | − | 0.119667i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.46339 | −0.483031 | −0.241515 | − | 0.970397i | \(-0.577644\pi\) | ||||
−0.241515 | + | 0.970397i | \(0.577644\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 40.6759i | − | 2.31397i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5882i | 1.22416i | 0.790798 | + | 0.612078i | \(0.209666\pi\) | ||||
−0.790798 | + | 0.612078i | \(0.790334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7441 | 0.720338 | 0.360169 | − | 0.932887i | \(-0.382719\pi\) | ||||
0.360169 | + | 0.932887i | \(0.382719\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.13010 | − | 21.7342i | 0.232705 | − | 1.22458i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.3313i | 1.14192i | 0.820978 | + | 0.570960i | \(0.193429\pi\) | ||||
−0.820978 | + | 0.570960i | \(0.806571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.9154 | −1.28301 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.68889i | 0.429152i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.67168 | 0.0930146 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0100 | + | 27.9234i | −0.610725 | + | 1.54891i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.2247i | 0.676029i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.6976i | 1.63728i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.989723i | 0.0544001i | 0.999630 | + | 0.0272000i | \(0.00865911\pi\) | ||||
−0.999630 | + | 0.0272000i | \(0.991341\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.99422 | −0.383281 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.10433 | + | 21.5986i | −0.224244 | + | 1.18006i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4823 | −1.38811 | −0.694056 | − | 0.719921i | \(-0.744178\pi\) | ||||
−0.694056 | + | 0.719921i | \(0.744178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.81230 | −0.261368 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.0109i | 2.87070i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.3382i | − | 0.774192i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.7486 | + | 20.0780i | 0.955551 | + | 1.08096i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.9535 | 1.07116 | 0.535579 | − | 0.844485i | \(-0.320093\pi\) | ||||
0.535579 | + | 0.844485i | \(0.320093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9641 | −1.22924 | −0.614620 | − | 0.788823i | \(-0.710691\pi\) | ||||
−0.614620 | + | 0.788823i | \(0.710691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.67061i | − | 0.195923i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.0078i | − | 0.692337i | −0.938172 | − | 0.346168i | \(-0.887483\pi\) | ||
0.938172 | − | 0.346168i | \(-0.112517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.75628 | + | 19.7670i | −0.199363 | + | 1.04912i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.38062i | 0.390624i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2551 | −1.28013 | −0.640066 | − | 0.768320i | \(-0.721093\pi\) | ||||
−0.640066 | + | 0.768320i | \(0.721093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0214 | −0.843234 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −58.8997 | −3.09143 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.56124 | − | 18.7406i | 0.186404 | − | 0.980929i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0126i | 1.30565i | 0.757511 | + | 0.652823i | \(0.226415\pi\) | ||||
−0.757511 | + | 0.652823i | \(0.773585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.0405 | 1.04327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 27.9965i | − | 1.45351i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.79181 | 0.299889 | 0.149944 | − | 0.988694i | \(-0.452091\pi\) | ||||
0.149944 | + | 0.988694i | \(0.452091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.6213 | − | 14.9204i | −1.21980 | − | 0.770486i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.3967i | − | 1.20499i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.1025 | −1.90583 | −0.952914 | − | 0.303240i | \(-0.901932\pi\) | ||||
−0.952914 | + | 0.303240i | \(0.901932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.7558 | −1.72936 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.75029i | 0.498216i | 0.968476 | + | 0.249108i | \(0.0801375\pi\) | ||||
−0.968476 | + | 0.249108i | \(0.919863\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.48405 | − | 39.3840i | 0.381423 | − | 2.00719i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 29.4685i | − | 1.49797i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3075i | 0.624014i | 0.950080 | + | 0.312007i | \(0.101001\pi\) | ||||
−0.950080 | + | 0.312007i | \(0.898999\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.67227 | − | 2.84486i | −0.185715 | − | 0.143871i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.76065i | − | 0.441916i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.2852 | + | 2.33453i | 0.618135 | + | 0.117463i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.73767i | − | 0.438531i | −0.975665 | − | 0.219266i | \(-0.929634\pi\) | ||
0.975665 | − | 0.219266i | \(-0.0703661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.1506i | 0.658355i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.58414i | 0.0791083i | 0.999217 | + | 0.0395541i | \(0.0125938\pi\) | ||||
−0.999217 | + | 0.0395541i | \(0.987406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −54.1244 | −2.69613 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0268 | − | 3.42559i | −0.895757 | − | 0.170219i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.6741 | −0.628230 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0682 | −0.992306 | −0.496153 | − | 0.868235i | \(-0.665255\pi\) | ||||
−0.496153 | + | 0.868235i | \(0.665255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.42479 | −0.0702799 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.57131 | −0.175733 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.49255 | + | 13.1167i | −0.122354 | + | 0.643875i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.84949i | 0.433361i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4700 | 1.09773 | 0.548865 | − | 0.835911i | \(-0.315060\pi\) | ||||
0.548865 | + | 0.835911i | \(0.315060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10.3190i | − | 0.502917i | −0.967868 | − | 0.251458i | \(-0.919090\pi\) | ||
0.967868 | − | 0.251458i | \(-0.0809102\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.6013 | −1.53651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.50547 | + | 1.77648i | 0.218548 | + | 0.0861719i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.90089 | −0.140384 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 88.2025i | − | 4.25846i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.5506 | −1.32707 | −0.663534 | − | 0.748146i | \(-0.730944\pi\) | ||||
−0.663534 | + | 0.748146i | \(0.730944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.84191 | −0.472972 | −0.236486 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236486 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.3951 | + | 4.06567i | 1.02582 | + | 0.194934i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.54317 | − | 5.06890i | −0.313002 | − | 0.242479i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5128i | 1.07448i | 0.843431 | + | 0.537238i | \(0.180532\pi\) | ||||
−0.843431 | + | 0.537238i | \(0.819468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.45541 | −0.355020 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.0216 | 1.47388 | 0.736941 | − | 0.675957i | \(-0.236270\pi\) | ||||
0.736941 | + | 0.675957i | \(0.236270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.01522 | + | 15.8672i | −0.142935 | + | 0.752180i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 45.0721i | 2.13184i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.2768 | −1.05131 | −0.525654 | − | 0.850698i | \(-0.676179\pi\) | ||||
−0.525654 | + | 0.850698i | \(0.676179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.3150 | 1.71001 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.4363i | 1.24209i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 40.2112 | + | 7.64125i | 1.88513 | + | 0.358227i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0377 | 0.750210 | 0.375105 | − | 0.926982i | \(-0.377607\pi\) | ||||
0.375105 | + | 0.926982i | \(0.377607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.592258 | −0.0276442 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.8075 | 0.596507 | 0.298253 | − | 0.954487i | \(-0.403596\pi\) | ||||
0.298253 | + | 0.954487i | \(0.403596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0225 | 0.558735 | 0.279368 | − | 0.960184i | \(-0.409875\pi\) | ||||
0.279368 | + | 0.960184i | \(0.409875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.40526 | − | 49.4941i | 0.436159 | − | 2.29523i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 0.645389i | − | 0.0298650i | −0.999889 | − | 0.0149325i | \(-0.995247\pi\) | ||
0.999889 | − | 0.0149325i | \(-0.00475334\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.9800 | 1.38435 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.8127 | −1.88055 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 53.3992i | − | 2.45530i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.02776 | + | 3.16530i | 0.368339 | + | 0.145234i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.7912 | 1.36404 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.9225 | 1.50427 | 0.752134 | − | 0.659011i | \(-0.229025\pi\) | ||||
0.752134 | + | 0.659011i | \(0.229025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 12.9403i | − | 0.590026i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.3797 | − | 28.8888i | 1.01831 | − | 1.31448i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5146 | + | 3.13823i | 0.749889 | + | 0.142500i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.57008 | 0.207090 | 0.103545 | − | 0.994625i | \(-0.466981\pi\) | ||||
0.103545 | + | 0.994625i | \(0.466981\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.4008 | −1.60088 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5326i | 1.19740i | 0.800974 | + | 0.598700i | \(0.204316\pi\) | ||||
−0.800974 | + | 0.598700i | \(0.795684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.77509 | −0.170021 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 41.9086 | + | 7.96381i | 1.88365 | + | 0.357947i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.4377 | 1.23075 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.30379i | 0.192664i | 0.995349 | + | 0.0963322i | \(0.0307111\pi\) | ||||
−0.995349 | + | 0.0963322i | \(0.969289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.36170 | 0.284220 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.17002i | − | 0.141344i | −0.997500 | − | 0.0706720i | \(-0.977486\pi\) | ||
0.997500 | − | 0.0706720i | \(-0.0225144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.2935 | + | 5.37656i | 1.25905 | + | 0.239254i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 57.5689 | 2.55673 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0671 | 1.15540 | 0.577702 | − | 0.816248i | \(-0.303950\pi\) | ||||
0.577702 | + | 0.816248i | \(0.303950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.0130 | −1.15075 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.05527 | −0.0465914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.79486 | + | 35.7572i | −0.299417 | + | 1.57565i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.2641 | −2.51847 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.2982i | 0.495936i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.7148i | − | 0.907532i | −0.891121 | − | 0.453766i | \(-0.850080\pi\) | ||
0.891121 | − | 0.453766i | \(-0.149920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.82308i | − | 0.123445i | −0.998093 | − | 0.0617223i | \(-0.980341\pi\) | ||
0.998093 | − | 0.0617223i | \(-0.0196593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.9751 | + | 35.4434i | −0.609923 | + | 1.54687i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.73304i | 0.380417i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.74750 | + | 22.2703i | 0.249891 | + | 0.968274i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 3.80025i | − | 0.164917i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.0777i | 1.60602i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.28442 | − | 6.75912i | 0.0555304 | − | 0.292222i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.3469i | 2.17263i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5098 | −0.581907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.8743 | −1.15542 | −0.577709 | − | 0.816243i | \(-0.696053\pi\) | ||||
−0.577709 | + | 0.816243i | \(0.696053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.2960i | 1.51470i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.04213 | − | 10.7465i | 0.0874751 | − | 0.460328i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.62485 | −0.0694737 | −0.0347368 | − | 0.999396i | \(-0.511059\pi\) | ||||
−0.0347368 | + | 0.999396i | \(0.511059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.08684i | − | 0.131743i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.72637 | −0.286553 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.0525i | − | 0.725146i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.8333 | + | 2.24865i | 0.502294 | + | 0.0954498i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.8048 | 0.500186 | 0.250093 | − | 0.968222i | \(-0.419539\pi\) | ||||
0.250093 | + | 0.968222i | \(0.419539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.5208 | 2.30598 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.2316 | −0.600858 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7.58816i | − | 0.319803i | −0.987133 | − | 0.159901i | \(-0.948882\pi\) | ||
0.987133 | − | 0.159901i | \(-0.0511176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.23038 | + | 0.803889i | 0.177973 | + | 0.0338199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.0221i | 1.05083i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.86024i | − | 0.203752i | −0.994797 | − | 0.101876i | \(-0.967516\pi\) | ||
0.994797 | − | 0.101876i | \(-0.0324844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.68775 | 0.238025 | 0.119012 | − | 0.992893i | \(-0.462027\pi\) | ||||
0.119012 | + | 0.992893i | \(0.462027\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.8105 | −0.785821 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.2483 | − | 20.6150i | −0.510791 | − | 0.859705i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.1269i | − | 1.83703i | −0.395391 | − | 0.918513i | \(-0.629391\pi\) | ||
0.395391 | − | 0.918513i | \(-0.370609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 40.1341i | − | 1.66792i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.2067 | 0.755343 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.9839 | 2.23578 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.13108 | + | 42.7889i | −0.336179 | + | 1.76910i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.8106 | −0.487474 | −0.243737 | − | 0.969841i | \(-0.578373\pi\) | ||||
−0.243737 | + | 0.969841i | \(0.578373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.5604i | 0.641153i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 59.1516i | − | 2.43317i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19.7606i | − | 0.811472i | −0.913990 | − | 0.405736i | \(-0.867015\pi\) | ||
0.913990 | − | 0.405736i | \(-0.132985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.23293 | − | 6.48813i | 0.0505450 | − | 0.265987i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 51.4722 | 2.10662 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 22.0799i | − | 0.902160i | −0.892483 | − | 0.451080i | \(-0.851039\pi\) | ||
0.892483 | − | 0.451080i | \(-0.148961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.2764 | −0.867883 | −0.433941 | − | 0.900941i | \(-0.642877\pi\) | ||||
−0.433941 | + | 0.900941i | \(0.642877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.9019i | 1.29914i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 51.7773 | + | 9.83914i | 2.10505 | + | 0.400018i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.66921 | 0.230106 | 0.115053 | − | 0.993359i | \(-0.463296\pi\) | ||||
0.115053 | + | 0.993359i | \(0.463296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 29.6976i | − | 1.20341i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 58.4668i | − | 2.36532i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4953 | −0.504678 | −0.252339 | − | 0.967639i | \(-0.581200\pi\) | ||||
−0.252339 | + | 0.967639i | \(0.581200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.9058 | − | 6.44305i | −1.36721 | − | 0.259809i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4637 | −0.582286 | −0.291143 | − | 0.956680i | \(-0.594035\pi\) | ||||
−0.291143 | + | 0.956680i | \(0.594035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0292 | 0.644270 | 0.322135 | − | 0.946694i | \(-0.395600\pi\) | ||||
0.322135 | + | 0.946694i | \(0.395600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.31818 | + | 1.79586i | 0.0930253 | + | 0.0720654i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.0246 | 0.882397 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.2725 | + | 17.0621i | 0.730901 | + | 0.682484i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.3576 | −1.01268 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.08793 | −0.0832513 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9112 | −0.713034 | −0.356517 | − | 0.934289i | \(-0.616036\pi\) | ||||
−0.356517 | + | 0.934289i | \(0.616036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.636889i | − | 0.0253141i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.6740 | + | 5.63888i | 1.17758 | + | 0.223772i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 13.7935i | − | 0.546520i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.1966i | 1.15500i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2324i | 0.483150i | 0.970382 | + | 0.241575i | \(0.0776639\pi\) | ||||
−0.970382 | + | 0.241575i | \(0.922336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.2616i | 1.58776i | 0.608072 | + | 0.793882i | \(0.291943\pi\) | ||||
−0.608072 | + | 0.793882i | \(0.708057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.47415 | + | 49.8566i | −0.373044 | + | 1.96310i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.217415 | 0.00854748 | 0.00427374 | − | 0.999991i | \(-0.498640\pi\) | ||||
0.00427374 | + | 0.999991i | \(0.498640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.88634i | − | 0.270313i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −68.7005 | −2.69259 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.08204i | − | 0.0423434i | −0.999776 | − | 0.0211717i | \(-0.993260\pi\) | ||
0.999776 | − | 0.0211717i | \(-0.00673966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.46346 | + | 7.70128i | −0.0571820 | + | 0.300914i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 27.6806i | − | 1.07992i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.7166 | −0.417460 | −0.208730 | − | 0.977973i | \(-0.566933\pi\) | ||||
−0.208730 | + | 0.977973i | \(0.566933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 46.7678i | − | 1.81905i | −0.415644 | − | 0.909527i | \(-0.636444\pi\) | ||
0.415644 | − | 0.909527i | \(-0.363556\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 14.5305i | − | 0.564318i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.19680 | − | 11.5604i | 0.0851883 | − | 0.448294i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.7762 | + | 11.4469i | 0.572137 | + | 0.443227i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.74891 | 0.376915 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.59360i | − | 0.215938i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4945i | 0.867100i | 0.901129 | + | 0.433550i | \(0.142739\pi\) | ||||
−0.901129 | + | 0.433550i | \(0.857261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.84415 | − | 1.12143i | −0.109471 | − | 0.0431639i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.4298 | −0.823614 | −0.411807 | − | 0.911271i | \(-0.635102\pi\) | ||||
−0.411807 | + | 0.911271i | \(0.635102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.9232i | − | 0.879710i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44.1753i | 1.69280i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.7273 | −0.907899 | −0.453949 | − | 0.891027i | \(-0.649985\pi\) | ||||
−0.453949 | + | 0.891027i | \(0.649985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.25250 | + | 0.238011i | 0.0478557 | + | 0.00909392i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 65.4673i | − | 2.49773i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 55.1178i | 2.09982i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.4839i | − | 0.512952i | −0.966551 | − | 0.256476i | \(-0.917439\pi\) | ||
0.966551 | − | 0.256476i | \(-0.0825615\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 58.1715i | − | 2.20975i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.47830 | − | 7.77938i | 0.0560751 | − | 0.295089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.98255 | 0.226605 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.1331i | 1.25321i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.04107i | 0.190399i | 0.995458 | + | 0.0951993i | \(0.0303489\pi\) | ||||
−0.995458 | + | 0.0951993i | \(0.969651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.72023 | −0.140311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 53.4651 | + | 10.1599i | 2.01361 | + | 0.382642i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 39.2730i | − | 1.47701i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 20.7675i | − | 0.779938i | −0.920828 | − | 0.389969i | \(-0.872486\pi\) | ||
0.920828 | − | 0.389969i | \(-0.127514\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.1456 | 0.680514 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.4806 | − | 34.1823i | 0.991705 | − | 1.28014i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7341 | + | 77.5367i | −0.551026 | + | 2.89971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 20.7305i | − | 0.774195i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 39.1171i | − | 1.45882i | −0.684077 | − | 0.729410i | \(-0.739795\pi\) | ||
0.684077 | − | 0.729410i | \(-0.260205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.6329 | 1.84843 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 62.4607i | 2.32294i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1288 | − | 7.14807i | −0.673287 | − | 0.265473i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8782i | 0.663065i | 0.943444 | + | 0.331533i | \(0.107566\pi\) | ||||
−0.943444 | + | 0.331533i | \(0.892434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.2101 | −1.15593 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.79701i | − | 0.325369i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7920 | 0.472482 | 0.236241 | − | 0.971694i | \(-0.424084\pi\) | ||||
0.236241 | + | 0.971694i | \(0.424084\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.6135 | + | 2.39692i | 0.465257 | + | 0.0884118i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.8086i | 2.12941i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.81963i | 0.214079i | 0.994255 | + | 0.107039i | \(0.0341371\pi\) | ||||
−0.994255 | + | 0.107039i | \(0.965863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 25.8902i | − | 0.951099i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.0511796i | − | 0.00187760i | −1.00000 | 0.000938799i | \(-0.999701\pi\) | |||
1.00000 | 0.000938799i | \(-0.000298829\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.52926 | − | 39.6219i | 0.275851 | − | 1.45163i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.3739i | 0.708853i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.38203 | −0.342812 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.4547 | 1.29376 | 0.646881 | − | 0.762591i | \(-0.276073\pi\) | ||||
0.646881 | + | 0.762591i | \(0.276073\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.3994 | −0.962047 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.41616 | − | 23.2395i | 0.160721 | − | 0.845773i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.5666 | −1.72884 | −0.864418 | − | 0.502773i | \(-0.832313\pi\) | ||||
−0.864418 | + | 0.502773i | \(0.832313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55.7044 | + | 43.1534i | 2.02194 | + | 1.56637i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.2647 | 0.662095 | 0.331047 | − | 0.943614i | \(-0.392598\pi\) | ||||
0.331047 | + | 0.943614i | \(0.392598\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9167 | −0.540020 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.90405 | + | 1.31196i | 0.249616 | + | 0.0474340i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.03098 | 0.253874 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.5027i | − | 1.13602i | −0.823022 | − | 0.568009i | \(-0.807714\pi\) | ||
0.823022 | − | 0.568009i | \(-0.192286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 32.3373i | − | 1.16460i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.3913 | −0.589554 | −0.294777 | − | 0.955566i | \(-0.595245\pi\) | ||||
−0.294777 | + | 0.955566i | \(0.595245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.5359 | + | 41.9380i | −0.593987 | + | 1.50646i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 16.4252i | − | 0.589251i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.6596 | 0.381919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.9064i | 1.89314i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.38309 | 0.0851645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.8775 | + | 6.81773i | 1.28052 | + | 0.243335i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.6427i | 1.37746i | 0.725017 | + | 0.688731i | \(0.241832\pi\) | ||||
−0.725017 | + | 0.688731i | \(0.758168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 56.2551i | 2.00273i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.87199i | − | 0.208784i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.71109 | 0.202807 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −50.4025 | − | 9.57789i | −1.78759 | − | 0.339693i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.5892 | 1.68569 | 0.842847 | − | 0.538153i | \(-0.180878\pi\) | ||||
0.842847 | + | 0.538153i | \(0.180878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.43371 | −0.333741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.4365i | 0.828087i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 50.1593i | − | 1.77008i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.4993 | + | 21.6569i | −0.863488 | + | 0.763306i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −67.7245 | −2.38402 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.89661 | 0.207314 | 0.103657 | − | 0.994613i | \(-0.466946\pi\) | ||||
0.103657 | + | 0.994613i | \(0.466946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5295i | 1.52853i | 0.644904 | + | 0.764264i | \(0.276897\pi\) | ||||
−0.644904 | + | 0.764264i | \(0.723103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.9272i | 1.61074i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.1200 | + | 5.91368i | 1.09009 | + | 0.207147i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.6743i | − | 0.548375i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 59.3933 | 2.07537 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.03114 | −0.140688 | −0.0703439 | − | 0.997523i | \(-0.522410\pi\) | ||||
−0.0703439 | + | 0.997523i | \(0.522410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.1442 | −0.597609 | −0.298804 | − | 0.954314i | \(-0.596588\pi\) | ||||
−0.298804 | + | 0.954314i | \(0.596588\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −68.3432 | − | 26.9473i | −2.37941 | − | 0.938185i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.2312i | − | 0.668735i | −0.942443 | − | 0.334368i | \(-0.891477\pi\) | ||
0.942443 | − | 0.334368i | \(-0.108523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.83105 | −0.0983263 | −0.0491632 | − | 0.998791i | \(-0.515655\pi\) | ||||
−0.0491632 | + | 0.998791i | \(0.515655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7051i | 0.371356i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.22561 | −0.0771127 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.59242 | − | 1.06272i | −0.193534 | − | 0.0367768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.51287i | − | 0.190553i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.6216 | −1.81670 | −0.908349 | − | 0.418212i | \(-0.862657\pi\) | ||||
−0.908349 | + | 0.418212i | \(0.862657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.8101 | −0.476209 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.6307i | 1.74381i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.6075 | − | 9.61683i | −1.74095 | − | 0.330829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 71.8698i | − | 2.46947i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 18.4935i | − | 0.634696i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.17244 | + | 6.33108i | 0.280148 | + | 0.217027i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32.4984i | − | 1.11272i | −0.830940 | − | 0.556362i | \(-0.812197\pi\) | ||
0.830940 | − | 0.556362i | \(-0.187803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.3015 | + | 2.33762i | 0.420702 | + | 0.0799451i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6503i | 1.45691i | 0.685096 | + | 0.728453i | \(0.259760\pi\) | ||||
−0.685096 | + | 0.728453i | \(0.740240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.4645i | − | 0.664122i | −0.943258 | − | 0.332061i | \(-0.892256\pi\) | ||
0.943258 | − | 0.332061i | \(-0.107744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 47.0631i | 1.60391i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6963 | −0.670468 | −0.335234 | − | 0.942135i | \(-0.608815\pi\) | ||||
−0.335234 | + | 0.942135i | \(0.608815\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.88735 | − | 9.93199i | 0.0641720 | − | 0.337698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.1374 | 1.36314 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.8813 | 1.11542 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.0228 | −1.99991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.3926 | 0.825565 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.2060 | − | 28.8229i | 0.615474 | − | 0.974392i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.4682i | 0.995070i | 0.867444 | + | 0.497535i | \(0.165761\pi\) | ||||
−0.867444 | + | 0.497535i | \(0.834239\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 62.6168 | 2.11201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.8258i | 1.61129i | 0.592397 | + | 0.805646i | \(0.298182\pi\) | ||||
−0.592397 | + | 0.805646i | \(0.701818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.36009 | −0.214034 | −0.107017 | − | 0.994257i | \(-0.534130\pi\) | ||||
−0.107017 | + | 0.994257i | \(0.534130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.22178 | + | 6.42949i | −0.0410698 | + | 0.216125i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −58.2351 | −1.95534 | −0.977672 | − | 0.210138i | \(-0.932609\pi\) | ||||
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 41.1891i | − | 1.38144i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48.2486 | −1.61639 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.8088 | −0.562484 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.41040 | − | 44.2588i | 0.281129 | − | 1.47941i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.0598 | + | 56.8744i | −1.47111 | + | 1.89898i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 35.1394i | − | 1.17196i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.89333 | 0.296280 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 69.2037 | 2.30296 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.89616 | − | 31.0279i | 0.195995 | − | 1.03140i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 29.7495i | − | 0.987816i | −0.869514 | − | 0.493908i | \(-0.835568\pi\) | ||
0.869514 | − | 0.493908i | \(-0.164432\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.7905 | 1.38610 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.21507 | 0.305309 | 0.152654 | − | 0.988280i | \(-0.451218\pi\) | ||||
0.152654 | + | 0.988280i | \(0.451218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.1069i | 1.16187i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.992423 | + | 5.22251i | −0.0328085 | + | 0.172651i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.6898 | 0.353008 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.6543 | −0.648337 | −0.324168 | − | 0.945999i | \(-0.605084\pi\) | ||||
−0.324168 | + | 0.945999i | \(0.605084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1495 | 0.696899 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.0177 | −1.77801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0267 | − | 3.95347i | −0.329676 | − | 0.129989i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.8146i | 1.73466i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.30520 | 0.141249 | 0.0706245 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706245 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.96554 | −0.129965 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 53.9476i | − | 1.76616i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.5107 | + | 2.37737i | 0.409142 | + | 0.0777484i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.4172 | −0.961018 | −0.480509 | − | 0.876990i | \(-0.659548\pi\) | ||||
−0.480509 | + | 0.876990i | \(0.659548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.8467 | −1.03928 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.6435i | 1.84653i | 0.384169 | + | 0.923263i | \(0.374488\pi\) | ||||
−0.384169 | + | 0.923263i | \(0.625512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.4165 | − | 18.1404i | −0.762546 | − | 0.590734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.778304 | + | 4.09574i | −0.0253182 | + | 0.133234i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.9839 | 1.42928 | 0.714642 | − | 0.699490i | \(-0.246590\pi\) | ||||
0.714642 | + | 0.699490i | \(0.246590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.2128 | 1.66244 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 50.8067i | − | 1.64752i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.1773 | 1.78737 | 0.893685 | − | 0.448696i | \(-0.148111\pi\) | ||||
0.893685 | + | 0.448696i | \(0.148111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.5359 | + | 3.14228i | 0.535089 | + | 0.101682i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 57.2641 | 1.85108 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.73854i | − | 0.0561405i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.2892 | −1.62223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 9.98346i | − | 0.321712i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.70437 | + | 35.2810i | −0.215821 | + | 1.13574i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.7346 | −1.79230 | −0.896151 | − | 0.443749i | \(-0.853648\pi\) | ||||
−0.896151 | + | 0.443749i | \(0.853648\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.17741 | −0.134198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0223 | 0.610454 | 0.305227 | − | 0.952280i | \(-0.401268\pi\) | ||||
0.305227 | + | 0.952280i | \(0.401268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7982 | −0.346175 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.5133 | − | 69.7787i | 0.881131 | − | 2.23471i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.17270 | −0.133496 | −0.0667482 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667482 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.4687i | 1.35730i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 15.8729i | − | 0.506783i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.3376i | 1.12710i | 0.826084 | + | 0.563548i | \(0.190564\pi\) | ||||
−0.826084 | + | 0.563548i | \(0.809436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.88122 | + | 51.9988i | −0.314842 | + | 1.65682i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 74.2125i | − | 2.36221i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.6745 | + | 34.4327i | −0.848201 | + | 1.09490i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 56.0708i | − | 1.78115i | −0.454839 | − | 0.890574i | \(-0.650303\pi\) | ||
0.454839 | − | 0.890574i | \(-0.349697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.47325i | − | 0.0784863i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.2480 | − | 8.59838i | −1.43446 | − | 0.272587i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.80102i | − | 0.0570389i | −0.999593 | − | 0.0285195i | \(-0.990921\pi\) | ||
0.999593 | − | 0.0285195i | \(-0.00907926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.31804 | 0.0417009 |
(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 | 1840.2.m.g.1839.6 | yes | 40 | |
4.3 | odd | 2 | inner | 1840.2.m.g.1839.35 | yes | 40 | |
5.4 | even | 2 | inner | 1840.2.m.g.1839.36 | yes | 40 | |
20.19 | odd | 2 | inner | 1840.2.m.g.1839.5 | ✓ | 40 | |
23.22 | odd | 2 | inner | 1840.2.m.g.1839.8 | yes | 40 | |
92.91 | even | 2 | inner | 1840.2.m.g.1839.33 | yes | 40 | |
115.114 | odd | 2 | inner | 1840.2.m.g.1839.34 | yes | 40 | |
460.459 | even | 2 | inner | 1840.2.m.g.1839.7 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.m.g.1839.5 | ✓ | 40 | 20.19 | odd | 2 | inner | |
1840.2.m.g.1839.6 | yes | 40 | 1.1 | even | 1 | trivial | |
1840.2.m.g.1839.7 | yes | 40 | 460.459 | even | 2 | inner | |
1840.2.m.g.1839.8 | yes | 40 | 23.22 | odd | 2 | inner | |
1840.2.m.g.1839.33 | yes | 40 | 92.91 | even | 2 | inner | |
1840.2.m.g.1839.34 | yes | 40 | 115.114 | odd | 2 | inner | |
1840.2.m.g.1839.35 | yes | 40 | 4.3 | odd | 2 | inner | |
1840.2.m.g.1839.36 | yes | 40 | 5.4 | even | 2 | inner |