Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.f (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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.1 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.a.626.2 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71965 | −1.92308 | −0.961541 | − | 0.274663i | \(-0.911434\pi\) | ||||
−0.961541 | + | 0.274663i | \(0.911434\pi\) | |||||||
\(3\) | − | 2.28311i | − | 1.31815i | −0.752076 | − | 0.659077i | \(-0.770947\pi\) | ||
0.752076 | − | 0.659077i | \(-0.229053\pi\) | |||||||
\(4\) | 5.39648 | 2.69824 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 6.20925i | 2.53492i | ||||||||
\(7\) | 2.59337i | 0.980201i | 0.871666 | + | 0.490100i | \(0.163040\pi\) | ||||
−0.871666 | + | 0.490100i | \(0.836960\pi\) | |||||||
\(8\) | −9.23723 | −3.26585 | ||||||||
\(9\) | −2.21259 | −0.737529 | ||||||||
\(10\) | 2.71965 | 0.860028 | ||||||||
\(11\) | −2.91614 | − | 1.57992i | −0.879248 | − | 0.476365i | ||||
\(12\) | − | 12.3208i | − | 3.55670i | ||||||
\(13\) | −3.84876 | −1.06745 | −0.533727 | − | 0.845657i | \(-0.679209\pi\) | ||||
−0.533727 | + | 0.845657i | \(0.679209\pi\) | |||||||
\(14\) | − | 7.05304i | − | 1.88501i | ||||||
\(15\) | 2.28311i | 0.589496i | ||||||||
\(16\) | 14.3290 | 3.58226 | ||||||||
\(17\) | − | 1.32421i | − | 0.321167i | −0.987022 | − | 0.160584i | \(-0.948662\pi\) | ||
0.987022 | − | 0.160584i | \(-0.0513376\pi\) | |||||||
\(18\) | 6.01746 | 1.41833 | ||||||||
\(19\) | 1.51223 | − | 4.08817i | 0.346929 | − | 0.937891i | ||||
\(20\) | −5.39648 | −1.20669 | ||||||||
\(21\) | 5.92094 | 1.29206 | ||||||||
\(22\) | 7.93086 | + | 4.29683i | 1.69086 | + | 0.916088i | ||||
\(23\) | −4.75248 | −0.990960 | −0.495480 | − | 0.868619i | \(-0.665008\pi\) | ||||
−0.495480 | + | 0.868619i | \(0.665008\pi\) | |||||||
\(24\) | 21.0896i | 4.30490i | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 10.4673 | 2.05280 | ||||||||
\(27\) | − | 1.79775i | − | 0.345977i | ||||||
\(28\) | 13.9951i | 2.64482i | ||||||||
\(29\) | 5.07960 | 0.943258 | 0.471629 | − | 0.881797i | \(-0.343666\pi\) | ||||
0.471629 | + | 0.881797i | \(0.343666\pi\) | |||||||
\(30\) | − | 6.20925i | − | 1.13365i | ||||||
\(31\) | 5.94228i | 1.06726i | 0.845717 | + | 0.533632i | \(0.179173\pi\) | ||||
−0.845717 | + | 0.533632i | \(0.820827\pi\) | |||||||
\(32\) | −20.4955 | −3.62313 | ||||||||
\(33\) | −3.60714 | + | 6.65785i | −0.627922 | + | 1.15898i | ||||
\(34\) | 3.60137i | 0.617631i | ||||||||
\(35\) | − | 2.59337i | − | 0.438359i | ||||||
\(36\) | −11.9402 | −1.99003 | ||||||||
\(37\) | 0.538972i | 0.0886064i | 0.999018 | + | 0.0443032i | \(0.0141068\pi\) | ||||
−0.999018 | + | 0.0443032i | \(0.985893\pi\) | |||||||
\(38\) | −4.11273 | + | 11.1184i | −0.667172 | + | 1.80364i | ||||
\(39\) | 8.78715i | 1.40707i | ||||||||
\(40\) | 9.23723 | 1.46053 | ||||||||
\(41\) | −6.13890 | −0.958735 | −0.479367 | − | 0.877614i | \(-0.659134\pi\) | ||||
−0.479367 | + | 0.877614i | \(0.659134\pi\) | |||||||
\(42\) | −16.1029 | −2.48473 | ||||||||
\(43\) | 10.0967i | 1.53973i | 0.638206 | + | 0.769866i | \(0.279677\pi\) | ||||
−0.638206 | + | 0.769866i | \(0.720323\pi\) | |||||||
\(44\) | −15.7369 | − | 8.52602i | −2.37242 | − | 1.28535i | ||||
\(45\) | 2.21259 | 0.329833 | ||||||||
\(46\) | 12.9251 | 1.90570 | ||||||||
\(47\) | 9.19886 | 1.34179 | 0.670896 | − | 0.741552i | \(-0.265910\pi\) | ||||
0.670896 | + | 0.741552i | \(0.265910\pi\) | |||||||
\(48\) | − | 32.7148i | − | 4.72197i | ||||||
\(49\) | 0.274446 | 0.0392066 | ||||||||
\(50\) | −2.71965 | −0.384616 | ||||||||
\(51\) | −3.02331 | −0.423348 | ||||||||
\(52\) | −20.7698 | −2.88025 | ||||||||
\(53\) | − | 1.16719i | − | 0.160326i | −0.996782 | − | 0.0801632i | \(-0.974456\pi\) | ||
0.996782 | − | 0.0801632i | \(-0.0255441\pi\) | |||||||
\(54\) | 4.88924i | 0.665342i | ||||||||
\(55\) | 2.91614 | + | 1.57992i | 0.393212 | + | 0.213037i | ||||
\(56\) | − | 23.9555i | − | 3.20119i | ||||||
\(57\) | −9.33375 | − | 3.45258i | −1.23629 | − | 0.457306i | ||||
\(58\) | −13.8147 | −1.81396 | ||||||||
\(59\) | 12.3841i | 1.61228i | 0.591728 | + | 0.806138i | \(0.298446\pi\) | ||||
−0.591728 | + | 0.806138i | \(0.701554\pi\) | |||||||
\(60\) | 12.3208i | 1.59060i | ||||||||
\(61\) | − | 6.07026i | − | 0.777218i | −0.921403 | − | 0.388609i | \(-0.872956\pi\) | ||
0.921403 | − | 0.388609i | \(-0.127044\pi\) | |||||||
\(62\) | − | 16.1609i | − | 2.05244i | ||||||
\(63\) | − | 5.73805i | − | 0.722927i | ||||||
\(64\) | 27.0824 | 3.38530 | ||||||||
\(65\) | 3.84876 | 0.477380 | ||||||||
\(66\) | 9.81014 | − | 18.1070i | 1.20754 | − | 2.22882i | ||||
\(67\) | − | 5.71516i | − | 0.698217i | −0.937082 | − | 0.349109i | \(-0.886484\pi\) | ||
0.937082 | − | 0.349109i | \(-0.113516\pi\) | |||||||
\(68\) | − | 7.14606i | − | 0.866586i | ||||||
\(69\) | 10.8504i | 1.30624i | ||||||||
\(70\) | 7.05304i | 0.843000i | ||||||||
\(71\) | 11.0687i | 1.31361i | 0.754061 | + | 0.656805i | \(0.228093\pi\) | ||||
−0.754061 | + | 0.656805i | \(0.771907\pi\) | |||||||
\(72\) | 20.4382 | 2.40866 | ||||||||
\(73\) | 15.5827i | 1.82382i | 0.410394 | + | 0.911908i | \(0.365391\pi\) | ||||
−0.410394 | + | 0.911908i | \(0.634609\pi\) | |||||||
\(74\) | − | 1.46581i | − | 0.170397i | ||||||
\(75\) | − | 2.28311i | − | 0.263631i | ||||||
\(76\) | 8.16071 | − | 22.0618i | 0.936097 | − | 2.53066i | ||||
\(77\) | 4.09732 | − | 7.56261i | 0.466933 | − | 0.861839i | ||||
\(78\) | − | 23.8979i | − | 2.70591i | ||||||
\(79\) | 11.4547 | 1.28876 | 0.644379 | − | 0.764706i | \(-0.277116\pi\) | ||||
0.644379 | + | 0.764706i | \(0.277116\pi\) | |||||||
\(80\) | −14.3290 | −1.60204 | ||||||||
\(81\) | −10.7422 | −1.19358 | ||||||||
\(82\) | 16.6956 | 1.84372 | ||||||||
\(83\) | − | 7.45980i | − | 0.818819i | −0.912351 | − | 0.409410i | \(-0.865735\pi\) | ||
0.912351 | − | 0.409410i | \(-0.134265\pi\) | |||||||
\(84\) | 31.9522 | 3.48628 | ||||||||
\(85\) | 1.32421i | 0.143630i | ||||||||
\(86\) | − | 27.4594i | − | 2.96103i | ||||||
\(87\) | − | 11.5973i | − | 1.24336i | ||||||
\(88\) | 26.9370 | + | 14.5941i | 2.87150 | + | 1.55574i | ||||
\(89\) | 8.00568i | 0.848600i | 0.905522 | + | 0.424300i | \(0.139480\pi\) | ||||
−0.905522 | + | 0.424300i | \(0.860520\pi\) | |||||||
\(90\) | −6.01746 | −0.634296 | ||||||||
\(91\) | − | 9.98126i | − | 1.04632i | ||||||
\(92\) | −25.6466 | −2.67385 | ||||||||
\(93\) | 13.5669 | 1.40682 | ||||||||
\(94\) | −25.0177 | −2.58037 | ||||||||
\(95\) | −1.51223 | + | 4.08817i | −0.155151 | + | 0.419438i | ||||
\(96\) | 46.7934i | 4.77584i | ||||||||
\(97\) | 17.6549i | 1.79259i | 0.443462 | + | 0.896293i | \(0.353750\pi\) | ||||
−0.443462 | + | 0.896293i | \(0.646250\pi\) | |||||||
\(98\) | −0.746397 | −0.0753975 | ||||||||
\(99\) | 6.45220 | + | 3.49572i | 0.648471 | + | 0.351333i | ||||
\(100\) | 5.39648 | 0.539648 | ||||||||
\(101\) | 12.0320i | 1.19723i | 0.801037 | + | 0.598615i | \(0.204282\pi\) | ||||
−0.801037 | + | 0.598615i | \(0.795718\pi\) | |||||||
\(102\) | 8.22233 | 0.814132 | ||||||||
\(103\) | − | 2.53280i | − | 0.249565i | −0.992184 | − | 0.124782i | \(-0.960177\pi\) | ||
0.992184 | − | 0.124782i | \(-0.0398232\pi\) | |||||||
\(104\) | 35.5519 | 3.48615 | ||||||||
\(105\) | −5.92094 | −0.577825 | ||||||||
\(106\) | 3.17435i | 0.308321i | ||||||||
\(107\) | 4.40937 | 0.426270 | 0.213135 | − | 0.977023i | \(-0.431633\pi\) | ||||
0.213135 | + | 0.977023i | \(0.431633\pi\) | |||||||
\(108\) | − | 9.70152i | − | 0.933529i | ||||||
\(109\) | −10.1230 | −0.969607 | −0.484804 | − | 0.874623i | \(-0.661109\pi\) | ||||
−0.484804 | + | 0.874623i | \(0.661109\pi\) | |||||||
\(110\) | −7.93086 | − | 4.29683i | −0.756178 | − | 0.409687i | ||||
\(111\) | 1.23053 | 0.116797 | ||||||||
\(112\) | 37.1605i | 3.51134i | ||||||||
\(113\) | 5.82809i | 0.548261i | 0.961693 | + | 0.274130i | \(0.0883900\pi\) | ||||
−0.961693 | + | 0.274130i | \(0.911610\pi\) | |||||||
\(114\) | 25.3845 | + | 9.38980i | 2.37748 | + | 0.879436i | ||||
\(115\) | 4.75248 | 0.443171 | ||||||||
\(116\) | 27.4120 | 2.54514 | ||||||||
\(117\) | 8.51572 | 0.787279 | ||||||||
\(118\) | − | 33.6804i | − | 3.10054i | ||||||
\(119\) | 3.43415 | 0.314808 | ||||||||
\(120\) | − | 21.0896i | − | 1.92521i | ||||||
\(121\) | 6.00769 | + | 9.21454i | 0.546154 | + | 0.837685i | ||||
\(122\) | 16.5090i | 1.49465i | ||||||||
\(123\) | 14.0158i | 1.26376i | ||||||||
\(124\) | 32.0674i | 2.87974i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 15.6055i | 1.39025i | ||||||||
\(127\) | 0.196466 | 0.0174335 | 0.00871677 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871677 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(128\) | −32.6636 | −2.88708 | ||||||||
\(129\) | 23.0519 | 2.02960 | ||||||||
\(130\) | −10.4673 | −0.918041 | ||||||||
\(131\) | 9.10643i | 0.795632i | 0.917465 | + | 0.397816i | \(0.130232\pi\) | ||||
−0.917465 | + | 0.397816i | \(0.869768\pi\) | |||||||
\(132\) | −19.4658 | + | 35.9290i | −1.69428 | + | 3.12722i | ||||
\(133\) | 10.6021 | + | 3.92176i | 0.919322 | + | 0.340060i | ||||
\(134\) | 15.5432i | 1.34273i | ||||||||
\(135\) | 1.79775i | 0.154726i | ||||||||
\(136\) | 12.2320i | 1.04889i | ||||||||
\(137\) | −3.76731 | −0.321863 | −0.160932 | − | 0.986966i | \(-0.551450\pi\) | ||||
−0.160932 | + | 0.986966i | \(0.551450\pi\) | |||||||
\(138\) | − | 29.5093i | − | 2.51200i | ||||||
\(139\) | − | 3.48063i | − | 0.295223i | −0.989045 | − | 0.147612i | \(-0.952841\pi\) | ||
0.989045 | − | 0.147612i | \(-0.0471586\pi\) | |||||||
\(140\) | − | 13.9951i | − | 1.18280i | ||||||
\(141\) | − | 21.0020i | − | 1.76869i | ||||||
\(142\) | − | 30.1029i | − | 2.52618i | ||||||
\(143\) | 11.2235 | + | 6.08075i | 0.938557 | + | 0.508498i | ||||
\(144\) | −31.7043 | −2.64202 | ||||||||
\(145\) | −5.07960 | −0.421838 | ||||||||
\(146\) | − | 42.3794i | − | 3.50735i | ||||||
\(147\) | − | 0.626591i | − | 0.0516803i | ||||||
\(148\) | 2.90855i | 0.239082i | ||||||||
\(149\) | 3.22238i | 0.263987i | 0.991251 | + | 0.131994i | \(0.0421378\pi\) | ||||
−0.991251 | + | 0.131994i | \(0.957862\pi\) | |||||||
\(150\) | 6.20925i | 0.506983i | ||||||||
\(151\) | 0.819171 | 0.0666632 | 0.0333316 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333316 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(152\) | −13.9688 | + | 37.7634i | −1.13302 | + | 3.06302i | ||||
\(153\) | 2.92992i | 0.236870i | ||||||||
\(154\) | −11.1433 | + | 20.5676i | −0.897950 | + | 1.65739i | ||||
\(155\) | − | 5.94228i | − | 0.477295i | ||||||
\(156\) | 47.4197i | 3.79661i | ||||||||
\(157\) | 19.6930 | 1.57167 | 0.785835 | − | 0.618436i | \(-0.212234\pi\) | ||||
0.785835 | + | 0.618436i | \(0.212234\pi\) | |||||||
\(158\) | −31.1528 | −2.47839 | ||||||||
\(159\) | −2.66483 | −0.211335 | ||||||||
\(160\) | 20.4955 | 1.62031 | ||||||||
\(161\) | − | 12.3249i | − | 0.971339i | ||||||
\(162\) | 29.2150 | 2.29535 | ||||||||
\(163\) | −13.4915 | −1.05673 | −0.528367 | − | 0.849016i | \(-0.677195\pi\) | ||||
−0.528367 | + | 0.849016i | \(0.677195\pi\) | |||||||
\(164\) | −33.1284 | −2.58690 | ||||||||
\(165\) | 3.60714 | − | 6.65785i | 0.280815 | − | 0.518313i | ||||
\(166\) | 20.2880i | 1.57466i | ||||||||
\(167\) | 19.6312 | 1.51911 | 0.759554 | − | 0.650444i | \(-0.225417\pi\) | ||||
0.759554 | + | 0.650444i | \(0.225417\pi\) | |||||||
\(168\) | −54.6931 | −4.21966 | ||||||||
\(169\) | 1.81298 | 0.139460 | ||||||||
\(170\) | − | 3.60137i | − | 0.276213i | ||||||
\(171\) | −3.34594 | + | 9.04544i | −0.255870 | + | 0.691722i | ||||
\(172\) | 54.4866i | 4.15457i | ||||||||
\(173\) | −4.76420 | −0.362215 | −0.181108 | − | 0.983463i | \(-0.557968\pi\) | ||||
−0.181108 | + | 0.983463i | \(0.557968\pi\) | |||||||
\(174\) | 31.5405i | 2.39108i | ||||||||
\(175\) | 2.59337i | 0.196040i | ||||||||
\(176\) | −41.7854 | − | 22.6388i | −3.14970 | − | 1.70646i | ||||
\(177\) | 28.2743 | 2.12523 | ||||||||
\(178\) | − | 21.7726i | − | 1.63193i | ||||||
\(179\) | − | 17.4461i | − | 1.30399i | −0.758225 | − | 0.651993i | \(-0.773933\pi\) | ||
0.758225 | − | 0.651993i | \(-0.226067\pi\) | |||||||
\(180\) | 11.9402 | 0.889969 | ||||||||
\(181\) | − | 12.2191i | − | 0.908237i | −0.890941 | − | 0.454118i | \(-0.849954\pi\) | ||
0.890941 | − | 0.454118i | \(-0.150046\pi\) | |||||||
\(182\) | 27.1455i | 2.01216i | ||||||||
\(183\) | −13.8591 | −1.02449 | ||||||||
\(184\) | 43.8997 | 3.23633 | ||||||||
\(185\) | − | 0.538972i | − | 0.0396260i | ||||||
\(186\) | −36.8971 | −2.70543 | ||||||||
\(187\) | −2.09214 | + | 3.86156i | −0.152993 | + | 0.282386i | ||||
\(188\) | 49.6415 | 3.62048 | ||||||||
\(189\) | 4.66222 | 0.339127 | ||||||||
\(190\) | 4.11273 | − | 11.1184i | 0.298369 | − | 0.806613i | ||||
\(191\) | −3.86569 | −0.279711 | −0.139856 | − | 0.990172i | \(-0.544664\pi\) | ||||
−0.139856 | + | 0.990172i | \(0.544664\pi\) | |||||||
\(192\) | − | 61.8321i | − | 4.46235i | ||||||
\(193\) | 11.6387 | 0.837773 | 0.418887 | − | 0.908038i | \(-0.362420\pi\) | ||||
0.418887 | + | 0.908038i | \(0.362420\pi\) | |||||||
\(194\) | − | 48.0152i | − | 3.44729i | ||||||
\(195\) | − | 8.78715i | − | 0.629261i | ||||||
\(196\) | 1.48104 | 0.105789 | ||||||||
\(197\) | − | 14.4045i | − | 1.02627i | −0.858306 | − | 0.513137i | \(-0.828483\pi\) | ||
0.858306 | − | 0.513137i | \(-0.171517\pi\) | |||||||
\(198\) | −17.5477 | − | 9.50712i | −1.24706 | − | 0.675641i | ||||
\(199\) | −10.2338 | −0.725453 | −0.362727 | − | 0.931896i | \(-0.618154\pi\) | ||||
−0.362727 | + | 0.931896i | \(0.618154\pi\) | |||||||
\(200\) | −9.23723 | −0.653171 | ||||||||
\(201\) | −13.0483 | −0.920358 | ||||||||
\(202\) | − | 32.7228i | − | 2.30237i | ||||||
\(203\) | 13.1733i | 0.924582i | ||||||||
\(204\) | −16.3152 | −1.14229 | ||||||||
\(205\) | 6.13890 | 0.428759 | ||||||||
\(206\) | 6.88833i | 0.479933i | ||||||||
\(207\) | 10.5153 | 0.730862 | ||||||||
\(208\) | −55.1491 | −3.82390 | ||||||||
\(209\) | −10.8689 | + | 9.53247i | −0.751815 | + | 0.659374i | ||||
\(210\) | 16.1029 | 1.11120 | ||||||||
\(211\) | 5.84312 | 0.402257 | 0.201129 | − | 0.979565i | \(-0.435539\pi\) | ||||
0.201129 | + | 0.979565i | \(0.435539\pi\) | |||||||
\(212\) | − | 6.29874i | − | 0.432599i | ||||||
\(213\) | 25.2710 | 1.73154 | ||||||||
\(214\) | −11.9919 | −0.819752 | ||||||||
\(215\) | − | 10.0967i | − | 0.688589i | ||||||
\(216\) | 16.6062i | 1.12991i | ||||||||
\(217\) | −15.4105 | −1.04613 | ||||||||
\(218\) | 27.5310 | 1.86463 | ||||||||
\(219\) | 35.5770 | 2.40407 | ||||||||
\(220\) | 15.7369 | + | 8.52602i | 1.06098 | + | 0.574824i | ||||
\(221\) | 5.09656i | 0.342832i | ||||||||
\(222\) | −3.34661 | −0.224610 | ||||||||
\(223\) | − | 28.8841i | − | 1.93422i | −0.254357 | − | 0.967110i | \(-0.581864\pi\) | ||
0.254357 | − | 0.967110i | \(-0.418136\pi\) | |||||||
\(224\) | − | 53.1523i | − | 3.55139i | ||||||
\(225\) | −2.21259 | −0.147506 | ||||||||
\(226\) | − | 15.8504i | − | 1.05435i | ||||||
\(227\) | 17.0489 | 1.13158 | 0.565788 | − | 0.824551i | \(-0.308572\pi\) | ||||
0.565788 | + | 0.824551i | \(0.308572\pi\) | |||||||
\(228\) | −50.3694 | − | 18.6318i | −3.33579 | − | 1.23392i | ||||
\(229\) | −16.6298 | −1.09893 | −0.549463 | − | 0.835518i | \(-0.685168\pi\) | ||||
−0.549463 | + | 0.835518i | \(0.685168\pi\) | |||||||
\(230\) | −12.9251 | −0.852253 | ||||||||
\(231\) | −17.2663 | − | 9.35463i | −1.13604 | − | 0.615489i | ||||
\(232\) | −46.9215 | −3.08054 | ||||||||
\(233\) | 15.5584i | 1.01926i | 0.860393 | + | 0.509632i | \(0.170218\pi\) | ||||
−0.860393 | + | 0.509632i | \(0.829782\pi\) | |||||||
\(234\) | −23.1598 | −1.51400 | ||||||||
\(235\) | −9.19886 | −0.600067 | ||||||||
\(236\) | 66.8307i | 4.35031i | ||||||||
\(237\) | − | 26.1524i | − | 1.69878i | ||||||
\(238\) | −9.33969 | −0.605402 | ||||||||
\(239\) | − | 4.36882i | − | 0.282595i | −0.989967 | − | 0.141298i | \(-0.954873\pi\) | ||
0.989967 | − | 0.141298i | \(-0.0451274\pi\) | |||||||
\(240\) | 32.7148i | 2.11173i | ||||||||
\(241\) | −27.0174 | −1.74035 | −0.870173 | − | 0.492746i | \(-0.835993\pi\) | ||||
−0.870173 | + | 0.492746i | \(0.835993\pi\) | |||||||
\(242\) | −16.3388 | − | 25.0603i | −1.05030 | − | 1.61094i | ||||
\(243\) | 19.1324i | 1.22734i | ||||||||
\(244\) | − | 32.7581i | − | 2.09712i | ||||||
\(245\) | −0.274446 | −0.0175337 | ||||||||
\(246\) | − | 38.1180i | − | 2.43031i | ||||||
\(247\) | −5.82021 | + | 15.7344i | −0.370331 | + | 1.00116i | ||||
\(248\) | − | 54.8902i | − | 3.48553i | ||||||
\(249\) | −17.0315 | −1.07933 | ||||||||
\(250\) | 2.71965 | 0.172006 | ||||||||
\(251\) | −29.3382 | −1.85181 | −0.925907 | − | 0.377752i | \(-0.876697\pi\) | ||||
−0.925907 | + | 0.377752i | \(0.876697\pi\) | |||||||
\(252\) | − | 30.9653i | − | 1.95063i | ||||||
\(253\) | 13.8589 | + | 7.50854i | 0.871299 | + | 0.472058i | ||||
\(254\) | −0.534318 | −0.0335261 | ||||||||
\(255\) | 3.02331 | 0.189327 | ||||||||
\(256\) | 34.6687 | 2.16680 | ||||||||
\(257\) | 20.4152i | 1.27347i | 0.771084 | + | 0.636734i | \(0.219715\pi\) | ||||
−0.771084 | + | 0.636734i | \(0.780285\pi\) | |||||||
\(258\) | −62.6929 | −3.90309 | ||||||||
\(259\) | −1.39775 | −0.0868521 | ||||||||
\(260\) | 20.7698 | 1.28809 | ||||||||
\(261\) | −11.2391 | −0.695680 | ||||||||
\(262\) | − | 24.7663i | − | 1.53007i | ||||||
\(263\) | − | 1.95755i | − | 0.120708i | −0.998177 | − | 0.0603538i | \(-0.980777\pi\) | ||
0.998177 | − | 0.0603538i | \(-0.0192229\pi\) | |||||||
\(264\) | 33.3199 | − | 61.5001i | 2.05070 | − | 3.78507i | ||||
\(265\) | 1.16719i | 0.0717001i | ||||||||
\(266\) | −28.8341 | − | 10.6658i | −1.76793 | − | 0.653963i | ||||
\(267\) | 18.2778 | 1.11859 | ||||||||
\(268\) | − | 30.8417i | − | 1.88396i | ||||||
\(269\) | − | 8.82051i | − | 0.537796i | −0.963169 | − | 0.268898i | \(-0.913341\pi\) | ||
0.963169 | − | 0.268898i | \(-0.0866594\pi\) | |||||||
\(270\) | − | 4.88924i | − | 0.297550i | ||||||
\(271\) | 1.56326i | 0.0949611i | 0.998872 | + | 0.0474806i | \(0.0151192\pi\) | ||||
−0.998872 | + | 0.0474806i | \(0.984881\pi\) | |||||||
\(272\) | − | 18.9746i | − | 1.15051i | ||||||
\(273\) | −22.7883 | −1.37921 | ||||||||
\(274\) | 10.2458 | 0.618969 | ||||||||
\(275\) | −2.91614 | − | 1.57992i | −0.175850 | − | 0.0952729i | ||||
\(276\) | 58.5541i | 3.52454i | ||||||||
\(277\) | 0.228901i | 0.0137533i | 0.999976 | + | 0.00687667i | \(0.00218893\pi\) | ||||
−0.999976 | + | 0.00687667i | \(0.997811\pi\) | |||||||
\(278\) | 9.46609i | 0.567738i | ||||||||
\(279\) | − | 13.1478i | − | 0.787139i | ||||||
\(280\) | 23.9555i | 1.43162i | ||||||||
\(281\) | −7.93845 | −0.473568 | −0.236784 | − | 0.971562i | \(-0.576093\pi\) | ||||
−0.236784 | + | 0.971562i | \(0.576093\pi\) | |||||||
\(282\) | 57.1180i | 3.40133i | ||||||||
\(283\) | 7.72636i | 0.459285i | 0.973275 | + | 0.229642i | \(0.0737556\pi\) | ||||
−0.973275 | + | 0.229642i | \(0.926244\pi\) | |||||||
\(284\) | 59.7319i | 3.54444i | ||||||||
\(285\) | 9.33375 | + | 3.45258i | 0.552883 | + | 0.204513i | ||||
\(286\) | −30.5240 | − | 16.5375i | −1.80492 | − | 0.977882i | ||||
\(287\) | − | 15.9204i | − | 0.939753i | ||||||
\(288\) | 45.3481 | 2.67216 | ||||||||
\(289\) | 15.2465 | 0.896852 | ||||||||
\(290\) | 13.8147 | 0.811229 | ||||||||
\(291\) | 40.3081 | 2.36290 | ||||||||
\(292\) | 84.0917i | 4.92110i | ||||||||
\(293\) | −22.2268 | −1.29850 | −0.649252 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649252 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(294\) | 1.70411i | 0.0993855i | ||||||||
\(295\) | − | 12.3841i | − | 0.721032i | ||||||
\(296\) | − | 4.97861i | − | 0.289376i | ||||||
\(297\) | −2.84030 | + | 5.24248i | −0.164811 | + | 0.304199i | ||||
\(298\) | − | 8.76372i | − | 0.507669i | ||||||
\(299\) | 18.2912 | 1.05780 | ||||||||
\(300\) | − | 12.3208i | − | 0.711339i | ||||||
\(301\) | −26.1844 | −1.50925 | ||||||||
\(302\) | −2.22786 | −0.128199 | ||||||||
\(303\) | 27.4704 | 1.57813 | ||||||||
\(304\) | 21.6688 | − | 58.5796i | 1.24279 | − | 3.35977i | ||||
\(305\) | 6.07026i | 0.347582i | ||||||||
\(306\) | − | 7.96836i | − | 0.455521i | ||||||
\(307\) | −1.70905 | −0.0975404 | −0.0487702 | − | 0.998810i | \(-0.515530\pi\) | ||||
−0.0487702 | + | 0.998810i | \(0.515530\pi\) | |||||||
\(308\) | 22.1111 | − | 40.8115i | 1.25990 | − | 2.32545i | ||||
\(309\) | −5.78267 | −0.328964 | ||||||||
\(310\) | 16.1609i | 0.917877i | ||||||||
\(311\) | 32.7579 | 1.85753 | 0.928766 | − | 0.370667i | \(-0.120871\pi\) | ||||
0.928766 | + | 0.370667i | \(0.120871\pi\) | |||||||
\(312\) | − | 81.1689i | − | 4.59528i | ||||||
\(313\) | 3.61072 | 0.204090 | 0.102045 | − | 0.994780i | \(-0.467461\pi\) | ||||
0.102045 | + | 0.994780i | \(0.467461\pi\) | |||||||
\(314\) | −53.5579 | −3.02245 | ||||||||
\(315\) | 5.73805i | 0.323303i | ||||||||
\(316\) | 61.8152 | 3.47738 | ||||||||
\(317\) | 13.3609i | 0.750421i | 0.926940 | + | 0.375211i | \(0.122430\pi\) | ||||
−0.926940 | + | 0.375211i | \(0.877570\pi\) | |||||||
\(318\) | 7.24740 | 0.406414 | ||||||||
\(319\) | −14.8128 | − | 8.02538i | −0.829358 | − | 0.449335i | ||||
\(320\) | −27.0824 | −1.51395 | ||||||||
\(321\) | − | 10.0671i | − | 0.561890i | ||||||
\(322\) | 33.5194i | 1.86796i | ||||||||
\(323\) | −5.41359 | − | 2.00250i | −0.301220 | − | 0.111422i | ||||
\(324\) | −57.9702 | −3.22057 | ||||||||
\(325\) | −3.84876 | −0.213491 | ||||||||
\(326\) | 36.6920 | 2.03218 | ||||||||
\(327\) | 23.1119i | 1.27809i | ||||||||
\(328\) | 56.7064 | 3.13109 | ||||||||
\(329\) | 23.8560i | 1.31523i | ||||||||
\(330\) | −9.81014 | + | 18.1070i | −0.540030 | + | 0.996758i | ||||
\(331\) | 18.0012i | 0.989437i | 0.869053 | + | 0.494718i | \(0.164729\pi\) | ||||
−0.869053 | + | 0.494718i | \(0.835271\pi\) | |||||||
\(332\) | − | 40.2567i | − | 2.20937i | ||||||
\(333\) | − | 1.19252i | − | 0.0653498i | ||||||
\(334\) | −53.3900 | −2.92137 | ||||||||
\(335\) | 5.71516i | 0.312252i | ||||||||
\(336\) | 84.8414 | 4.62848 | ||||||||
\(337\) | −17.8934 | −0.974717 | −0.487359 | − | 0.873202i | \(-0.662040\pi\) | ||||
−0.487359 | + | 0.873202i | \(0.662040\pi\) | |||||||
\(338\) | −4.93066 | −0.268192 | ||||||||
\(339\) | 13.3062 | 0.722692 | ||||||||
\(340\) | 7.14606i | 0.387549i | ||||||||
\(341\) | 9.38834 | − | 17.3285i | 0.508407 | − | 0.938390i | ||||
\(342\) | 9.09977 | − | 24.6004i | 0.492059 | − | 1.33024i | ||||
\(343\) | 18.8653i | 1.01863i | ||||||||
\(344\) | − | 93.2655i | − | 5.02854i | ||||||
\(345\) | − | 10.8504i | − | 0.584167i | ||||||
\(346\) | 12.9569 | 0.696569 | ||||||||
\(347\) | 31.5547i | 1.69395i | 0.531635 | + | 0.846974i | \(0.321578\pi\) | ||||
−0.531635 | + | 0.846974i | \(0.678422\pi\) | |||||||
\(348\) | − | 62.5845i | − | 3.35488i | ||||||
\(349\) | 10.5028i | 0.562205i | 0.959678 | + | 0.281102i | \(0.0907000\pi\) | ||||
−0.959678 | + | 0.281102i | \(0.909300\pi\) | |||||||
\(350\) | − | 7.05304i | − | 0.377001i | ||||||
\(351\) | 6.91911i | 0.369315i | ||||||||
\(352\) | 59.7676 | + | 32.3813i | 3.18563 | + | 1.72593i | ||||
\(353\) | −23.9603 | −1.27528 | −0.637640 | − | 0.770335i | \(-0.720089\pi\) | ||||
−0.637640 | + | 0.770335i | \(0.720089\pi\) | |||||||
\(354\) | −76.8961 | −4.08698 | ||||||||
\(355\) | − | 11.0687i | − | 0.587464i | ||||||
\(356\) | 43.2025i | 2.28973i | ||||||||
\(357\) | − | 7.84055i | − | 0.414966i | ||||||
\(358\) | 47.4473i | 2.50767i | ||||||||
\(359\) | − | 10.5701i | − | 0.557868i | −0.960310 | − | 0.278934i | \(-0.910019\pi\) | ||
0.960310 | − | 0.278934i | \(-0.0899810\pi\) | |||||||
\(360\) | −20.4382 | −1.07719 | ||||||||
\(361\) | −14.4263 | − | 12.3645i | −0.759281 | − | 0.650763i | ||||
\(362\) | 33.2316i | 1.74661i | ||||||||
\(363\) | 21.0378 | − | 13.7162i | 1.10420 | − | 0.719914i | ||||
\(364\) | − | 53.8637i | − | 2.82322i | ||||||
\(365\) | − | 15.5827i | − | 0.815635i | ||||||
\(366\) | 37.6918 | 1.97018 | ||||||||
\(367\) | −27.3093 | −1.42553 | −0.712766 | − | 0.701402i | \(-0.752558\pi\) | ||||
−0.712766 | + | 0.701402i | \(0.752558\pi\) | |||||||
\(368\) | −68.0984 | −3.54988 | ||||||||
\(369\) | 13.5828 | 0.707095 | ||||||||
\(370\) | 1.46581i | 0.0762040i | ||||||||
\(371\) | 3.02696 | 0.157152 | ||||||||
\(372\) | 73.2134 | 3.79594 | ||||||||
\(373\) | 27.9735 | 1.44841 | 0.724206 | − | 0.689583i | \(-0.242206\pi\) | ||||
0.724206 | + | 0.689583i | \(0.242206\pi\) | |||||||
\(374\) | 5.68989 | − | 10.5021i | 0.294217 | − | 0.543050i | ||||
\(375\) | 2.28311i | 0.117899i | ||||||||
\(376\) | −84.9720 | −4.38210 | ||||||||
\(377\) | −19.5502 | −1.00689 | ||||||||
\(378\) | −12.6796 | −0.652168 | ||||||||
\(379\) | 3.00076i | 0.154138i | 0.997026 | + | 0.0770692i | \(0.0245562\pi\) | ||||
−0.997026 | + | 0.0770692i | \(0.975444\pi\) | |||||||
\(380\) | −8.16071 | + | 22.0618i | −0.418636 | + | 1.13174i | ||||
\(381\) | − | 0.448553i | − | 0.0229801i | ||||||
\(382\) | 10.5133 | 0.537908 | ||||||||
\(383\) | 12.2086i | 0.623828i | 0.950110 | + | 0.311914i | \(0.100970\pi\) | ||||
−0.950110 | + | 0.311914i | \(0.899030\pi\) | |||||||
\(384\) | 74.5746i | 3.80562i | ||||||||
\(385\) | −4.09732 | + | 7.56261i | −0.208819 | + | 0.385426i | ||||
\(386\) | −31.6532 | −1.61111 | ||||||||
\(387\) | − | 22.3398i | − | 1.13560i | ||||||
\(388\) | 95.2745i | 4.83683i | ||||||||
\(389\) | −32.4838 | −1.64700 | −0.823498 | − | 0.567320i | \(-0.807980\pi\) | ||||
−0.823498 | + | 0.567320i | \(0.807980\pi\) | |||||||
\(390\) | 23.8979i | 1.21012i | ||||||||
\(391\) | 6.29326i | 0.318264i | ||||||||
\(392\) | −2.53512 | −0.128043 | ||||||||
\(393\) | 20.7910 | 1.04877 | ||||||||
\(394\) | 39.1750i | 1.97361i | ||||||||
\(395\) | −11.4547 | −0.576350 | ||||||||
\(396\) | 34.8192 | + | 18.8646i | 1.74973 | + | 0.947980i | ||||
\(397\) | −21.7253 | −1.09036 | −0.545180 | − | 0.838319i | \(-0.683539\pi\) | ||||
−0.545180 | + | 0.838319i | \(0.683539\pi\) | |||||||
\(398\) | 27.8323 | 1.39511 | ||||||||
\(399\) | 8.95381 | − | 24.2058i | 0.448251 | − | 1.21181i | ||||
\(400\) | 14.3290 | 0.716452 | ||||||||
\(401\) | 7.68637i | 0.383839i | 0.981411 | + | 0.191919i | \(0.0614712\pi\) | ||||
−0.981411 | + | 0.191919i | \(0.938529\pi\) | |||||||
\(402\) | 35.4868 | 1.76992 | ||||||||
\(403\) | − | 22.8704i | − | 1.13926i | ||||||
\(404\) | 64.9305i | 3.23041i | ||||||||
\(405\) | 10.7422 | 0.533785 | ||||||||
\(406\) | − | 35.8267i | − | 1.77805i | ||||||
\(407\) | 0.851534 | − | 1.57172i | 0.0422090 | − | 0.0779070i | ||||
\(408\) | 27.9270 | 1.38259 | ||||||||
\(409\) | −1.84466 | −0.0912123 | −0.0456062 | − | 0.998959i | \(-0.514522\pi\) | ||||
−0.0456062 | + | 0.998959i | \(0.514522\pi\) | |||||||
\(410\) | −16.6956 | −0.824539 | ||||||||
\(411\) | 8.60119i | 0.424265i | ||||||||
\(412\) | − | 13.6682i | − | 0.673385i | ||||||
\(413\) | −32.1166 | −1.58035 | ||||||||
\(414\) | −28.5978 | −1.40551 | ||||||||
\(415\) | 7.45980i | 0.366187i | ||||||||
\(416\) | 78.8823 | 3.86752 | ||||||||
\(417\) | −7.94666 | −0.389150 | ||||||||
\(418\) | 29.5595 | − | 25.9249i | 1.44580 | − | 1.26803i | ||||
\(419\) | 5.98752 | 0.292509 | 0.146255 | − | 0.989247i | \(-0.453278\pi\) | ||||
0.146255 | + | 0.989247i | \(0.453278\pi\) | |||||||
\(420\) | −31.9522 | −1.55911 | ||||||||
\(421\) | − | 23.1954i | − | 1.13047i | −0.824929 | − | 0.565237i | \(-0.808785\pi\) | ||
0.824929 | − | 0.565237i | \(-0.191215\pi\) | |||||||
\(422\) | −15.8912 | −0.773573 | ||||||||
\(423\) | −20.3533 | −0.989610 | ||||||||
\(424\) | 10.7816i | 0.523603i | ||||||||
\(425\) | − | 1.32421i | − | 0.0642334i | ||||||
\(426\) | −68.7282 | −3.32989 | ||||||||
\(427\) | 15.7424 | 0.761829 | ||||||||
\(428\) | 23.7951 | 1.15018 | ||||||||
\(429\) | 13.8830 | − | 25.6245i | 0.670278 | − | 1.23716i | ||||
\(430\) | 27.4594i | 1.32421i | ||||||||
\(431\) | 24.4251 | 1.17651 | 0.588257 | − | 0.808674i | \(-0.299814\pi\) | ||||
0.588257 | + | 0.808674i | \(0.299814\pi\) | |||||||
\(432\) | − | 25.7600i | − | 1.23938i | ||||||
\(433\) | − | 20.2267i | − | 0.972032i | −0.873950 | − | 0.486016i | \(-0.838450\pi\) | ||
0.873950 | − | 0.486016i | \(-0.161550\pi\) | |||||||
\(434\) | 41.9111 | 2.01180 | ||||||||
\(435\) | 11.5973i | 0.556047i | ||||||||
\(436\) | −54.6286 | −2.61623 | ||||||||
\(437\) | −7.18682 | + | 19.4289i | −0.343792 | + | 0.929413i | ||||
\(438\) | −96.7569 | −4.62322 | ||||||||
\(439\) | −6.92575 | −0.330548 | −0.165274 | − | 0.986248i | \(-0.552851\pi\) | ||||
−0.165274 | + | 0.986248i | \(0.552851\pi\) | |||||||
\(440\) | −26.9370 | − | 14.5941i | −1.28417 | − | 0.695747i | ||||
\(441\) | −0.607236 | −0.0289160 | ||||||||
\(442\) | − | 13.8608i | − | 0.659293i | ||||||
\(443\) | −6.46044 | −0.306945 | −0.153472 | − | 0.988153i | \(-0.549046\pi\) | ||||
−0.153472 | + | 0.988153i | \(0.549046\pi\) | |||||||
\(444\) | 6.64054 | 0.315146 | ||||||||
\(445\) | − | 8.00568i | − | 0.379506i | ||||||
\(446\) | 78.5545i | 3.71966i | ||||||||
\(447\) | 7.35703 | 0.347976 | ||||||||
\(448\) | 70.2347i | 3.31828i | ||||||||
\(449\) | 0.954419i | 0.0450418i | 0.999746 | + | 0.0225209i | \(0.00716924\pi\) | ||||
−0.999746 | + | 0.0225209i | \(0.992831\pi\) | |||||||
\(450\) | 6.01746 | 0.283666 | ||||||||
\(451\) | 17.9019 | + | 9.69898i | 0.842966 | + | 0.456707i | ||||
\(452\) | 31.4512i | 1.47934i | ||||||||
\(453\) | − | 1.87026i | − | 0.0878723i | ||||||
\(454\) | −46.3670 | −2.17611 | ||||||||
\(455\) | 9.98126i | 0.467929i | ||||||||
\(456\) | 86.2180 | + | 31.8923i | 4.03753 | + | 1.49349i | ||||
\(457\) | − | 27.5121i | − | 1.28696i | −0.765462 | − | 0.643481i | \(-0.777490\pi\) | ||
0.765462 | − | 0.643481i | \(-0.222510\pi\) | |||||||
\(458\) | 45.2271 | 2.11332 | ||||||||
\(459\) | −2.38059 | −0.111116 | ||||||||
\(460\) | 25.6466 | 1.19578 | ||||||||
\(461\) | 42.9295i | 1.99943i | 0.0239396 | + | 0.999713i | \(0.492379\pi\) | ||||
−0.0239396 | + | 0.999713i | \(0.507621\pi\) | |||||||
\(462\) | 46.9581 | + | 25.4413i | 2.18469 | + | 1.18364i | ||||
\(463\) | 27.5331 | 1.27957 | 0.639787 | − | 0.768553i | \(-0.279023\pi\) | ||||
0.639787 | + | 0.768553i | \(0.279023\pi\) | |||||||
\(464\) | 72.7859 | 3.37900 | ||||||||
\(465\) | −13.5669 | −0.629149 | ||||||||
\(466\) | − | 42.3133i | − | 1.96013i | ||||||
\(467\) | 7.91119 | 0.366086 | 0.183043 | − | 0.983105i | \(-0.441405\pi\) | ||||
0.183043 | + | 0.983105i | \(0.441405\pi\) | |||||||
\(468\) | 45.9549 | 2.12427 | ||||||||
\(469\) | 14.8215 | 0.684393 | ||||||||
\(470\) | 25.0177 | 1.15398 | ||||||||
\(471\) | − | 44.9612i | − | 2.07170i | ||||||
\(472\) | − | 114.395i | − | 5.26546i | ||||||
\(473\) | 15.9520 | − | 29.4433i | 0.733474 | − | 1.35381i | ||||
\(474\) | 71.1253i | 3.26689i | ||||||||
\(475\) | 1.51223 | − | 4.08817i | 0.0693858 | − | 0.187578i | ||||
\(476\) | 18.5323 | 0.849429 | ||||||||
\(477\) | 2.58252i | 0.118245i | ||||||||
\(478\) | 11.8816i | 0.543453i | ||||||||
\(479\) | 8.70174i | 0.397593i | 0.980041 | + | 0.198796i | \(0.0637032\pi\) | ||||
−0.980041 | + | 0.198796i | \(0.936297\pi\) | |||||||
\(480\) | − | 46.7934i | − | 2.13582i | ||||||
\(481\) | − | 2.07438i | − | 0.0945834i | ||||||
\(482\) | 73.4779 | 3.34683 | ||||||||
\(483\) | −28.1391 | −1.28037 | ||||||||
\(484\) | 32.4204 | + | 49.7261i | 1.47365 | + | 2.26028i | ||||
\(485\) | − | 17.6549i | − | 0.801669i | ||||||
\(486\) | − | 52.0334i | − | 2.36028i | ||||||
\(487\) | 12.0708i | 0.546980i | 0.961875 | + | 0.273490i | \(0.0881780\pi\) | ||||
−0.961875 | + | 0.273490i | \(0.911822\pi\) | |||||||
\(488\) | 56.0724i | 2.53828i | ||||||||
\(489\) | 30.8025i | 1.39294i | ||||||||
\(490\) | 0.746397 | 0.0337188 | ||||||||
\(491\) | 24.0982i | 1.08754i | 0.839235 | + | 0.543769i | \(0.183003\pi\) | ||||
−0.839235 | + | 0.543769i | \(0.816997\pi\) | |||||||
\(492\) | 75.6359i | 3.40993i | ||||||||
\(493\) | − | 6.72644i | − | 0.302944i | ||||||
\(494\) | 15.8289 | − | 42.7921i | 0.712176 | − | 1.92531i | ||||
\(495\) | −6.45220 | − | 3.49572i | −0.290005 | − | 0.157121i | ||||
\(496\) | 85.1472i | 3.82322i | ||||||||
\(497\) | −28.7051 | −1.28760 | ||||||||
\(498\) | 46.3198 | 2.07564 | ||||||||
\(499\) | 29.7475 | 1.33168 | 0.665840 | − | 0.746095i | \(-0.268073\pi\) | ||||
0.665840 | + | 0.746095i | \(0.268073\pi\) | |||||||
\(500\) | −5.39648 | −0.241338 | ||||||||
\(501\) | − | 44.8202i | − | 2.00242i | ||||||
\(502\) | 79.7897 | 3.56119 | ||||||||
\(503\) | − | 3.52627i | − | 0.157229i | −0.996905 | − | 0.0786144i | \(-0.974950\pi\) | ||
0.996905 | − | 0.0786144i | \(-0.0250496\pi\) | |||||||
\(504\) | 53.0037i | 2.36097i | ||||||||
\(505\) | − | 12.0320i | − | 0.535417i | ||||||
\(506\) | −37.6912 | − | 20.4206i | −1.67558 | − | 0.907806i | ||||
\(507\) | − | 4.13922i | − | 0.183829i | ||||||
\(508\) | 1.06022 | 0.0470399 | ||||||||
\(509\) | 26.4681i | 1.17318i | 0.809885 | + | 0.586588i | \(0.199529\pi\) | ||||
−0.809885 | + | 0.586588i | \(0.800471\pi\) | |||||||
\(510\) | −8.22233 | −0.364091 | ||||||||
\(511\) | −40.4116 | −1.78771 | ||||||||
\(512\) | −28.9594 | −1.27984 | ||||||||
\(513\) | −7.34951 | − | 2.71861i | −0.324489 | − | 0.120029i | ||||
\(514\) | − | 55.5223i | − | 2.44898i | ||||||
\(515\) | 2.53280i | 0.111609i | ||||||||
\(516\) | 124.399 | 5.47636 | ||||||||
\(517\) | −26.8251 | − | 14.5335i | −1.17977 | − | 0.639182i | ||||
\(518\) | 3.80139 | 0.167024 | ||||||||
\(519\) | 10.8772i | 0.477455i | ||||||||
\(520\) | −35.5519 | −1.55905 | ||||||||
\(521\) | 8.09065i | 0.354458i | 0.984170 | + | 0.177229i | \(0.0567133\pi\) | ||||
−0.984170 | + | 0.177229i | \(0.943287\pi\) | |||||||
\(522\) | 30.5663 | 1.33785 | ||||||||
\(523\) | −4.77075 | −0.208611 | −0.104305 | − | 0.994545i | \(-0.533262\pi\) | ||||
−0.104305 | + | 0.994545i | \(0.533262\pi\) | |||||||
\(524\) | 49.1427i | 2.14681i | ||||||||
\(525\) | 5.92094 | 0.258411 | ||||||||
\(526\) | 5.32384i | 0.232130i | ||||||||
\(527\) | 7.86880 | 0.342770 | ||||||||
\(528\) | −51.6868 | + | 95.4007i | −2.24938 | + | 4.15178i | ||||
\(529\) | −0.413980 | −0.0179991 | ||||||||
\(530\) | − | 3.17435i | − | 0.137885i | ||||||
\(531\) | − | 27.4010i | − | 1.18910i | ||||||
\(532\) | 57.2142 | + | 21.1637i | 2.48055 | + | 0.917563i | ||||
\(533\) | 23.6272 | 1.02341 | ||||||||
\(534\) | −49.7093 | −2.15113 | ||||||||
\(535\) | −4.40937 | −0.190634 | ||||||||
\(536\) | 52.7922i | 2.28028i | ||||||||
\(537\) | −39.8314 | −1.71885 | ||||||||
\(538\) | 23.9887i | 1.03422i | ||||||||
\(539\) | −0.800322 | − | 0.433604i | −0.0344723 | − | 0.0186766i | ||||
\(540\) | 9.70152i | 0.417487i | ||||||||
\(541\) | − | 34.6340i | − | 1.48903i | −0.667605 | − | 0.744516i | \(-0.732680\pi\) | ||
0.667605 | − | 0.744516i | \(-0.267320\pi\) | |||||||
\(542\) | − | 4.25151i | − | 0.182618i | ||||||
\(543\) | −27.8975 | −1.19720 | ||||||||
\(544\) | 27.1403i | 1.16363i | ||||||||
\(545\) | 10.1230 | 0.433622 | ||||||||
\(546\) | 61.9761 | 2.65233 | ||||||||
\(547\) | −7.85791 | −0.335980 | −0.167990 | − | 0.985789i | \(-0.553728\pi\) | ||||
−0.167990 | + | 0.985789i | \(0.553728\pi\) | |||||||
\(548\) | −20.3302 | −0.868465 | ||||||||
\(549\) | 13.4310i | 0.573221i | ||||||||
\(550\) | 7.93086 | + | 4.29683i | 0.338173 | + | 0.183218i | ||||
\(551\) | 7.68151 | − | 20.7663i | 0.327244 | − | 0.884674i | ||||
\(552\) | − | 100.228i | − | 4.26598i | ||||||
\(553\) | 29.7063i | 1.26324i | ||||||||
\(554\) | − | 0.622531i | − | 0.0264488i | ||||||
\(555\) | −1.23053 | −0.0522332 | ||||||||
\(556\) | − | 18.7832i | − | 0.796584i | ||||||
\(557\) | 4.67243i | 0.197977i | 0.995089 | + | 0.0989886i | \(0.0315607\pi\) | ||||
−0.995089 | + | 0.0989886i | \(0.968439\pi\) | |||||||
\(558\) | 35.7574i | 1.51373i | ||||||||
\(559\) | − | 38.8598i | − | 1.64359i | ||||||
\(560\) | − | 37.1605i | − | 1.57032i | ||||||
\(561\) | 8.81637 | + | 4.77659i | 0.372228 | + | 0.201668i | ||||
\(562\) | 21.5898 | 0.910710 | ||||||||
\(563\) | −36.5088 | −1.53866 | −0.769331 | − | 0.638850i | \(-0.779410\pi\) | ||||
−0.769331 | + | 0.638850i | \(0.779410\pi\) | |||||||
\(564\) | − | 113.337i | − | 4.77234i | ||||||
\(565\) | − | 5.82809i | − | 0.245190i | ||||||
\(566\) | − | 21.0130i | − | 0.883242i | ||||||
\(567\) | − | 27.8585i | − | 1.16995i | ||||||
\(568\) | − | 102.244i | − | 4.29006i | ||||||
\(569\) | −35.9943 | −1.50896 | −0.754480 | − | 0.656323i | \(-0.772111\pi\) | ||||
−0.754480 | + | 0.656323i | \(0.772111\pi\) | |||||||
\(570\) | −25.3845 | − | 9.38980i | −1.06324 | − | 0.393296i | ||||
\(571\) | 18.0377i | 0.754856i | 0.926039 | + | 0.377428i | \(0.123191\pi\) | ||||
−0.926039 | + | 0.377428i | \(0.876809\pi\) | |||||||
\(572\) | 60.5675 | + | 32.8146i | 2.53245 | + | 1.37205i | ||||
\(573\) | 8.82579i | 0.368703i | ||||||||
\(574\) | 43.2979i | 1.80722i | ||||||||
\(575\) | −4.75248 | −0.198192 | ||||||||
\(576\) | −59.9222 | −2.49676 | ||||||||
\(577\) | −29.0808 | −1.21065 | −0.605325 | − | 0.795978i | \(-0.706957\pi\) | ||||
−0.605325 | + | 0.795978i | \(0.706957\pi\) | |||||||
\(578\) | −41.4650 | −1.72472 | ||||||||
\(579\) | − | 26.5725i | − | 1.10431i | ||||||
\(580\) | −27.4120 | −1.13822 | ||||||||
\(581\) | 19.3460 | 0.802607 | ||||||||
\(582\) | −109.624 | −4.54406 | ||||||||
\(583\) | −1.84408 | + | 3.40369i | −0.0763738 | + | 0.140967i | ||||
\(584\) | − | 143.941i | − | 5.95632i | ||||||
\(585\) | −8.51572 | −0.352082 | ||||||||
\(586\) | 60.4491 | 2.49713 | ||||||||
\(587\) | −0.497758 | −0.0205447 | −0.0102723 | − | 0.999947i | \(-0.503270\pi\) | ||||
−0.0102723 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(588\) | − | 3.38139i | − | 0.139446i | ||||||
\(589\) | 24.2931 | + | 8.98608i | 1.00098 | + | 0.370265i | ||||
\(590\) | 33.6804i | 1.38660i | ||||||||
\(591\) | −32.8869 | −1.35279 | ||||||||
\(592\) | 7.72296i | 0.317411i | ||||||||
\(593\) | 12.3964i | 0.509058i | 0.967065 | + | 0.254529i | \(0.0819205\pi\) | ||||
−0.967065 | + | 0.254529i | \(0.918080\pi\) | |||||||
\(594\) | 7.72463 | − | 14.2577i | 0.316945 | − | 0.585000i | ||||
\(595\) | −3.43415 | −0.140787 | ||||||||
\(596\) | 17.3895i | 0.712301i | ||||||||
\(597\) | 23.3648i | 0.956259i | ||||||||
\(598\) | −49.7455 | −2.03424 | ||||||||
\(599\) | 26.9617i | 1.10162i | 0.834630 | + | 0.550812i | \(0.185682\pi\) | ||||
−0.834630 | + | 0.550812i | \(0.814318\pi\) | |||||||
\(600\) | 21.0896i | 0.860980i | ||||||||
\(601\) | −47.9125 | −1.95439 | −0.977197 | − | 0.212337i | \(-0.931893\pi\) | ||||
−0.977197 | + | 0.212337i | \(0.931893\pi\) | |||||||
\(602\) | 71.2124 | 2.90240 | ||||||||
\(603\) | 12.6453i | 0.514956i | ||||||||
\(604\) | 4.42064 | 0.179873 | ||||||||
\(605\) | −6.00769 | − | 9.21454i | −0.244247 | − | 0.374624i | ||||
\(606\) | −74.7097 | −3.03488 | ||||||||
\(607\) | 17.5422 | 0.712017 | 0.356009 | − | 0.934483i | \(-0.384137\pi\) | ||||
0.356009 | + | 0.934483i | \(0.384137\pi\) | |||||||
\(608\) | −30.9939 | + | 83.7891i | −1.25697 | + | 3.39810i | ||||
\(609\) | 30.0760 | 1.21874 | ||||||||
\(610\) | − | 16.5090i | − | 0.668429i | ||||||
\(611\) | −35.4042 | −1.43230 | ||||||||
\(612\) | 15.8113i | 0.639133i | ||||||||
\(613\) | 6.93942i | 0.280281i | 0.990132 | + | 0.140140i | \(0.0447553\pi\) | ||||
−0.990132 | + | 0.140140i | \(0.955245\pi\) | |||||||
\(614\) | 4.64800 | 0.187578 | ||||||||
\(615\) | − | 14.0158i | − | 0.565171i | ||||||
\(616\) | −37.8479 | + | 69.8576i | −1.52493 | + | 2.81464i | ||||
\(617\) | −4.52330 | −0.182101 | −0.0910506 | − | 0.995846i | \(-0.529023\pi\) | ||||
−0.0910506 | + | 0.995846i | \(0.529023\pi\) | |||||||
\(618\) | 15.7268 | 0.632625 | ||||||||
\(619\) | 25.7607 | 1.03541 | 0.517705 | − | 0.855559i | \(-0.326787\pi\) | ||||
0.517705 | + | 0.855559i | \(0.326787\pi\) | |||||||
\(620\) | − | 32.0674i | − | 1.28786i | ||||||
\(621\) | 8.54376i | 0.342849i | ||||||||
\(622\) | −89.0900 | −3.57218 | ||||||||
\(623\) | −20.7617 | −0.831799 | ||||||||
\(624\) | 125.911i | 5.04049i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.81988 | −0.392481 | ||||||||
\(627\) | 21.7637 | + | 24.8148i | 0.869157 | + | 0.991007i | ||||
\(628\) | 106.273 | 4.24074 | ||||||||
\(629\) | 0.713710 | 0.0284575 | ||||||||
\(630\) | − | 15.6055i | − | 0.621737i | ||||||
\(631\) | −7.45186 | −0.296654 | −0.148327 | − | 0.988938i | \(-0.547389\pi\) | ||||
−0.148327 | + | 0.988938i | \(0.547389\pi\) | |||||||
\(632\) | −105.810 | −4.20889 | ||||||||
\(633\) | − | 13.3405i | − | 0.530237i | ||||||
\(634\) | − | 36.3369i | − | 1.44312i | ||||||
\(635\) | −0.196466 | −0.00779651 | ||||||||
\(636\) | −14.3807 | −0.570232 | ||||||||
\(637\) | −1.05628 | −0.0418513 | ||||||||
\(638\) | 40.2856 | + | 21.8262i | 1.59492 | + | 0.864107i | ||||
\(639\) | − | 24.4904i | − | 0.968826i | ||||||
\(640\) | 32.6636 | 1.29114 | ||||||||
\(641\) | − | 46.1595i | − | 1.82319i | −0.411091 | − | 0.911594i | \(-0.634852\pi\) | ||
0.411091 | − | 0.911594i | \(-0.365148\pi\) | |||||||
\(642\) | 27.3789i | 1.08056i | ||||||||
\(643\) | 29.2285 | 1.15266 | 0.576331 | − | 0.817217i | \(-0.304484\pi\) | ||||
0.576331 | + | 0.817217i | \(0.304484\pi\) | |||||||
\(644\) | − | 66.5112i | − | 2.62091i | ||||||
\(645\) | −23.0519 | −0.907666 | ||||||||
\(646\) | 14.7230 | + | 5.44610i | 0.579270 | + | 0.214274i | ||||
\(647\) | 11.3553 | 0.446423 | 0.223211 | − | 0.974770i | \(-0.428346\pi\) | ||||
0.223211 | + | 0.974770i | \(0.428346\pi\) | |||||||
\(648\) | 99.2284 | 3.89806 | ||||||||
\(649\) | 19.5660 | − | 36.1138i | 0.768031 | − | 1.41759i | ||||
\(650\) | 10.4673 | 0.410560 | ||||||||
\(651\) | 35.1839i | 1.37896i | ||||||||
\(652\) | −72.8064 | −2.85132 | ||||||||
\(653\) | 19.4499 | 0.761135 | 0.380568 | − | 0.924753i | \(-0.375729\pi\) | ||||
0.380568 | + | 0.924753i | \(0.375729\pi\) | |||||||
\(654\) | − | 62.8562i | − | 2.45787i | ||||||
\(655\) | − | 9.10643i | − | 0.355817i | ||||||
\(656\) | −87.9646 | −3.43444 | ||||||||
\(657\) | − | 34.4781i | − | 1.34512i | ||||||
\(658\) | − | 64.8800i | − | 2.52928i | ||||||
\(659\) | 25.6726 | 1.00006 | 0.500031 | − | 0.866008i | \(-0.333322\pi\) | ||||
0.500031 | + | 0.866008i | \(0.333322\pi\) | |||||||
\(660\) | 19.4658 | − | 35.9290i | 0.757707 | − | 1.39853i | ||||
\(661\) | 24.8328i | 0.965882i | 0.875653 | + | 0.482941i | \(0.160432\pi\) | ||||
−0.875653 | + | 0.482941i | \(0.839568\pi\) | |||||||
\(662\) | − | 48.9570i | − | 1.90277i | ||||||
\(663\) | 11.6360 | 0.451905 | ||||||||
\(664\) | 68.9079i | 2.67415i | ||||||||
\(665\) | −10.6021 | − | 3.92176i | −0.411133 | − | 0.152079i | ||||
\(666\) | 3.24324i | 0.125673i | ||||||||
\(667\) | −24.1407 | −0.934731 | ||||||||
\(668\) | 105.939 | 4.09892 | ||||||||
\(669\) | −65.9455 | −2.54960 | ||||||||
\(670\) | − | 15.5432i | − | 0.600487i | ||||||
\(671\) | −9.59055 | + | 17.7017i | −0.370239 | + | 0.683367i | ||||
\(672\) | −121.353 | −4.68128 | ||||||||
\(673\) | −27.2501 | −1.05042 | −0.525208 | − | 0.850974i | \(-0.676012\pi\) | ||||
−0.525208 | + | 0.850974i | \(0.676012\pi\) | |||||||
\(674\) | 48.6638 | 1.87446 | ||||||||
\(675\) | − | 1.79775i | − | 0.0691954i | ||||||
\(676\) | 9.78370 | 0.376296 | ||||||||
\(677\) | 32.2614 | 1.23991 | 0.619953 | − | 0.784639i | \(-0.287152\pi\) | ||||
0.619953 | + | 0.784639i | \(0.287152\pi\) | |||||||
\(678\) | −36.1881 | −1.38980 | ||||||||
\(679\) | −45.7857 | −1.75709 | ||||||||
\(680\) | − | 12.2320i | − | 0.469076i | ||||||
\(681\) | − | 38.9245i | − | 1.49159i | ||||||
\(682\) | −25.5330 | + | 47.1274i | −0.977708 | + | 1.80460i | ||||
\(683\) | − | 28.1759i | − | 1.07812i | −0.842268 | − | 0.539060i | \(-0.818780\pi\) | ||
0.842268 | − | 0.539060i | \(-0.181220\pi\) | |||||||
\(684\) | −18.0563 | + | 48.8136i | −0.690399 | + | 1.86643i | ||||
\(685\) | 3.76731 | 0.143942 | ||||||||
\(686\) | − | 51.3070i | − | 1.95891i | ||||||
\(687\) | 37.9675i | 1.44855i | ||||||||
\(688\) | 144.676i | 5.51572i | ||||||||
\(689\) | 4.49225i | 0.171141i | ||||||||
\(690\) | 29.5093i | 1.12340i | ||||||||
\(691\) | −15.2544 | −0.580306 | −0.290153 | − | 0.956980i | \(-0.593706\pi\) | ||||
−0.290153 | + | 0.956980i | \(0.593706\pi\) | |||||||
\(692\) | −25.7099 | −0.977344 | ||||||||
\(693\) | −9.06568 | + | 16.7329i | −0.344377 | + | 0.635632i | ||||
\(694\) | − | 85.8178i | − | 3.25760i | ||||||
\(695\) | 3.48063i | 0.132028i | ||||||||
\(696\) | 107.127i | 4.06063i | ||||||||
\(697\) | 8.12917i | 0.307914i | ||||||||
\(698\) | − | 28.5640i | − | 1.08116i | ||||||
\(699\) | 35.5215 | 1.34355 | ||||||||
\(700\) | 13.9951i | 0.528963i | ||||||||
\(701\) | − | 10.7433i | − | 0.405767i | −0.979203 | − | 0.202884i | \(-0.934969\pi\) | ||
0.979203 | − | 0.202884i | \(-0.0650313\pi\) | |||||||
\(702\) | − | 18.8175i | − | 0.710222i | ||||||
\(703\) | 2.20341 | + | 0.815048i | 0.0831032 | + | 0.0307401i | ||||
\(704\) | −78.9760 | − | 42.7881i | −2.97652 | − | 1.61264i | ||||
\(705\) | 21.0020i | 0.790981i | ||||||||
\(706\) | 65.1636 | 2.45247 | ||||||||
\(707\) | −31.2034 | −1.17352 | ||||||||
\(708\) | 152.582 | 5.73437 | ||||||||
\(709\) | 38.5054 | 1.44610 | 0.723050 | − | 0.690796i | \(-0.242740\pi\) | ||||
0.723050 | + | 0.690796i | \(0.242740\pi\) | |||||||
\(710\) | 30.1029i | 1.12974i | ||||||||
\(711\) | −25.3446 | −0.950496 | ||||||||
\(712\) | − | 73.9503i | − | 2.77141i | ||||||
\(713\) | − | 28.2405i | − | 1.05762i | ||||||
\(714\) | 21.3235i | 0.798013i | ||||||||
\(715\) | −11.2235 | − | 6.08075i | −0.419736 | − | 0.227407i | ||||
\(716\) | − | 94.1478i | − | 3.51847i | ||||||
\(717\) | −9.97448 | −0.372504 | ||||||||
\(718\) | 28.7469i | 1.07282i | ||||||||
\(719\) | 45.5394 | 1.69833 | 0.849167 | − | 0.528125i | \(-0.177105\pi\) | ||||
0.849167 | + | 0.528125i | \(0.177105\pi\) | |||||||
\(720\) | 31.7043 | 1.18155 | ||||||||
\(721\) | 6.56849 | 0.244623 | ||||||||
\(722\) | 39.2345 | + | 33.6271i | 1.46016 | + | 1.25147i | ||||
\(723\) | 61.6838i | 2.29404i | ||||||||
\(724\) | − | 65.9400i | − | 2.45064i | ||||||
\(725\) | 5.07960 | 0.188652 | ||||||||
\(726\) | −57.2154 | + | 37.3032i | −2.12346 | + | 1.38445i | ||||
\(727\) | −3.29804 | −0.122317 | −0.0611587 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611587 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(728\) | 92.1992i | 3.41713i | ||||||||
\(729\) | 11.4547 | 0.424249 | ||||||||
\(730\) | 42.3794i | 1.56853i | ||||||||
\(731\) | 13.3701 | 0.494511 | ||||||||
\(732\) | −74.7902 | −2.76433 | ||||||||
\(733\) | − | 18.4626i | − | 0.681930i | −0.940076 | − | 0.340965i | \(-0.889246\pi\) | ||
0.940076 | − | 0.340965i | \(-0.110754\pi\) | |||||||
\(734\) | 74.2716 | 2.74141 | ||||||||
\(735\) | 0.626591i | 0.0231121i | ||||||||
\(736\) | 97.4043 | 3.59037 | ||||||||
\(737\) | −9.02951 | + | 16.6662i | −0.332606 | + | 0.613906i | ||||
\(738\) | −36.9406 | −1.35980 | ||||||||
\(739\) | 24.7991i | 0.912248i | 0.889916 | + | 0.456124i | \(0.150763\pi\) | ||||
−0.889916 | + | 0.456124i | \(0.849237\pi\) | |||||||
\(740\) | − | 2.90855i | − | 0.106921i | ||||||
\(741\) | 35.9234 | + | 13.2882i | 1.31968 | + | 0.488153i | ||||
\(742\) | −8.23227 | −0.302216 | ||||||||
\(743\) | 4.35764 | 0.159866 | 0.0799331 | − | 0.996800i | \(-0.474529\pi\) | ||||
0.0799331 | + | 0.996800i | \(0.474529\pi\) | |||||||
\(744\) | −125.320 | −4.59447 | ||||||||
\(745\) | − | 3.22238i | − | 0.118059i | ||||||
\(746\) | −76.0780 | −2.78541 | ||||||||
\(747\) | 16.5055i | 0.603903i | ||||||||
\(748\) | −11.2902 | + | 20.8389i | −0.412811 | + | 0.761944i | ||||
\(749\) | 11.4351i | 0.417830i | ||||||||
\(750\) | − | 6.20925i | − | 0.226730i | ||||||
\(751\) | − | 28.4909i | − | 1.03965i | −0.854273 | − | 0.519824i | \(-0.825998\pi\) | ||
0.854273 | − | 0.519824i | \(-0.174002\pi\) | |||||||
\(752\) | 131.811 | 4.80665 | ||||||||
\(753\) | 66.9824i | 2.44098i | ||||||||
\(754\) | 53.1696 | 1.93632 | ||||||||
\(755\) | −0.819171 | −0.0298127 | ||||||||
\(756\) | 25.1596 | 0.915046 | ||||||||
\(757\) | −16.1577 | −0.587262 | −0.293631 | − | 0.955919i | \(-0.594864\pi\) | ||||
−0.293631 | + | 0.955919i | \(0.594864\pi\) | |||||||
\(758\) | − | 8.16100i | − | 0.296421i | ||||||
\(759\) | 17.1428 | − | 31.6413i | 0.622245 | − | 1.14851i | ||||
\(760\) | 13.9688 | − | 37.7634i | 0.506702 | − | 1.36982i | ||||
\(761\) | − | 40.0708i | − | 1.45257i | −0.687396 | − | 0.726283i | \(-0.741246\pi\) | ||
0.687396 | − | 0.726283i | \(-0.258754\pi\) | |||||||
\(762\) | 1.21991i | 0.0441926i | ||||||||
\(763\) | − | 26.2526i | − | 0.950410i | ||||||
\(764\) | −20.8611 | −0.754729 | ||||||||
\(765\) | − | 2.92992i | − | 0.105932i | ||||||
\(766\) | − | 33.2030i | − | 1.19967i | ||||||
\(767\) | − | 47.6636i | − | 1.72103i | ||||||
\(768\) | − | 79.1525i | − | 2.85617i | ||||||
\(769\) | 42.8114i | 1.54382i | 0.635732 | + | 0.771910i | \(0.280698\pi\) | ||||
−0.635732 | + | 0.771910i | \(0.719302\pi\) | |||||||
\(770\) | 11.1433 | − | 20.5676i | 0.401575 | − | 0.741206i | ||||
\(771\) | 46.6102 | 1.67863 | ||||||||
\(772\) | 62.8081 | 2.26051 | ||||||||
\(773\) | − | 35.6628i | − | 1.28270i | −0.767248 | − | 0.641351i | \(-0.778374\pi\) | ||
0.767248 | − | 0.641351i | \(-0.221626\pi\) | |||||||
\(774\) | 60.7564i | 2.18384i | ||||||||
\(775\) | 5.94228i | 0.213453i | ||||||||
\(776\) | − | 163.083i | − | 5.85433i | ||||||
\(777\) | 3.19122i | 0.114484i | ||||||||
\(778\) | 88.3445 | 3.16731 | ||||||||
\(779\) | −9.28341 | + | 25.0969i | −0.332613 | + | 0.899189i | ||||
\(780\) | − | 47.4197i | − | 1.69790i | ||||||
\(781\) | 17.4876 | − | 32.2777i | 0.625757 | − | 1.15499i | ||||
\(782\) | − | 17.1154i | − | 0.612047i | ||||||
\(783\) | − | 9.13185i | − | 0.326346i | ||||||
\(784\) | 3.93255 | 0.140448 | ||||||||
\(785\) | −19.6930 | −0.702872 | ||||||||
\(786\) | −56.5441 | −2.01686 | ||||||||
\(787\) | 10.6336 | 0.379046 | 0.189523 | − | 0.981876i | \(-0.439306\pi\) | ||||
0.189523 | + | 0.981876i | \(0.439306\pi\) | |||||||
\(788\) | − | 77.7334i | − | 2.76914i | ||||||
\(789\) | −4.46929 | −0.159111 | ||||||||
\(790\) | 31.1528 | 1.10837 | ||||||||
\(791\) | −15.1144 | −0.537406 | ||||||||
\(792\) | −59.6005 | − | 32.2907i | −2.11781 | − | 1.14740i | ||||
\(793\) | 23.3630i | 0.829645i | ||||||||
\(794\) | 59.0851 | 2.09685 | ||||||||
\(795\) | 2.66483 | 0.0945118 | ||||||||
\(796\) | −55.2264 | −1.95745 | ||||||||
\(797\) | 50.8767i | 1.80215i | 0.433668 | + | 0.901073i | \(0.357219\pi\) | ||||
−0.433668 | + | 0.901073i | \(0.642781\pi\) | |||||||
\(798\) | −24.3512 | + | 65.8313i | −0.862023 | + | 2.33040i | ||||
\(799\) | − | 12.1812i | − | 0.430940i | ||||||
\(800\) | −20.4955 | −0.724625 | ||||||||
\(801\) | − | 17.7133i | − | 0.625868i | ||||||
\(802\) | − | 20.9042i | − | 0.738153i | ||||||
\(803\) | 24.6195 | − | 45.4412i | 0.868802 | − | 1.60359i | ||||
\(804\) | −70.4150 | −2.48335 | ||||||||
\(805\) | 12.3249i | 0.434396i | ||||||||
\(806\) | 62.1995i | 2.19088i | ||||||||
\(807\) | −20.1382 | −0.708897 | ||||||||
\(808\) | − | 111.142i | − | 3.90998i | ||||||
\(809\) | − | 43.5683i | − | 1.53178i | −0.642973 | − | 0.765889i | \(-0.722299\pi\) | ||
0.642973 | − | 0.765889i | \(-0.277701\pi\) | |||||||
\(810\) | −29.2150 | −1.02651 | ||||||||
\(811\) | −7.19373 | −0.252606 | −0.126303 | − | 0.991992i | \(-0.540311\pi\) | ||||
−0.126303 | + | 0.991992i | \(0.540311\pi\) | |||||||
\(812\) | 71.0893i | 2.49475i | ||||||||
\(813\) | 3.56909 | 0.125173 | ||||||||
\(814\) | −2.31587 | + | 4.27451i | −0.0811713 | + | 0.149822i | ||||
\(815\) | 13.4915 | 0.472585 | ||||||||
\(816\) | −43.3211 | −1.51654 | ||||||||
\(817\) | 41.2770 | + | 15.2685i | 1.44410 | + | 0.534177i | ||||
\(818\) | 5.01681 | 0.175409 | ||||||||
\(819\) | 22.0844i | 0.771691i | ||||||||
\(820\) | 33.1284 | 1.15690 | ||||||||
\(821\) | − | 15.0312i | − | 0.524593i | −0.964987 | − | 0.262297i | \(-0.915520\pi\) | ||
0.964987 | − | 0.262297i | \(-0.0844798\pi\) | |||||||
\(822\) | − | 23.3922i | − | 0.815897i | ||||||
\(823\) | 44.3453 | 1.54578 | 0.772889 | − | 0.634541i | \(-0.218811\pi\) | ||||
0.772889 | + | 0.634541i | \(0.218811\pi\) | |||||||
\(824\) | 23.3961i | 0.815041i | ||||||||
\(825\) | −3.60714 | + | 6.65785i | −0.125584 | + | 0.231797i | ||||
\(826\) | 87.3458 | 3.03915 | ||||||||
\(827\) | −2.11368 | −0.0735000 | −0.0367500 | − | 0.999324i | \(-0.511701\pi\) | ||||
−0.0367500 | + | 0.999324i | \(0.511701\pi\) | |||||||
\(828\) | 56.7454 | 1.97204 | ||||||||
\(829\) | 42.8233i | 1.48731i | 0.668562 | + | 0.743657i | \(0.266910\pi\) | ||||
−0.668562 | + | 0.743657i | \(0.733090\pi\) | |||||||
\(830\) | − | 20.2880i | − | 0.704208i | ||||||
\(831\) | 0.522607 | 0.0181290 | ||||||||
\(832\) | −104.234 | −3.61366 | ||||||||
\(833\) | − | 0.363423i | − | 0.0125919i | ||||||
\(834\) | 21.6121 | 0.748366 | ||||||||
\(835\) | −19.6312 | −0.679366 | ||||||||
\(836\) | −58.6536 | + | 51.4418i | −2.02858 | + | 1.77915i | ||||
\(837\) | 10.6827 | 0.369249 | ||||||||
\(838\) | −16.2839 | −0.562519 | ||||||||
\(839\) | 54.5334i | 1.88270i | 0.337427 | + | 0.941352i | \(0.390443\pi\) | ||||
−0.337427 | + | 0.941352i | \(0.609557\pi\) | |||||||
\(840\) | 54.6931 | 1.88709 | ||||||||
\(841\) | −3.19765 | −0.110264 | ||||||||
\(842\) | 63.0833i | 2.17399i | ||||||||
\(843\) | 18.1243i | 0.624236i | ||||||||
\(844\) | 31.5323 | 1.08539 | ||||||||
\(845\) | −1.81298 | −0.0623683 | ||||||||
\(846\) | 55.3537 | 1.90310 | ||||||||
\(847\) | −23.8967 | + | 15.5801i | −0.821100 | + | 0.535340i | ||||
\(848\) | − | 16.7248i | − | 0.574331i | ||||||
\(849\) | 17.6401 | 0.605408 | ||||||||
\(850\) | 3.60137i | 0.123526i | ||||||||
\(851\) | − | 2.56145i | − | 0.0878054i | ||||||
\(852\) | 136.374 | 4.67211 | ||||||||
\(853\) | 17.3880i | 0.595354i | 0.954667 | + | 0.297677i | \(0.0962118\pi\) | ||||
−0.954667 | + | 0.297677i | \(0.903788\pi\) | |||||||
\(854\) | −42.8138 | −1.46506 | ||||||||
\(855\) | 3.34594 | − | 9.04544i | 0.114429 | − | 0.309348i | ||||
\(856\) | −40.7304 | −1.39214 | ||||||||
\(857\) | 38.1650 | 1.30369 | 0.651845 | − | 0.758352i | \(-0.273995\pi\) | ||||
0.651845 | + | 0.758352i | \(0.273995\pi\) | |||||||
\(858\) | −37.7569 | + | 69.6896i | −1.28900 | + | 2.37916i | ||||
\(859\) | 3.54926 | 0.121099 | 0.0605495 | − | 0.998165i | \(-0.480715\pi\) | ||||
0.0605495 | + | 0.998165i | \(0.480715\pi\) | |||||||
\(860\) | − | 54.4866i | − | 1.85798i | ||||||
\(861\) | −36.3481 | −1.23874 | ||||||||
\(862\) | −66.4275 | −2.26253 | ||||||||
\(863\) | 12.1644i | 0.414081i | 0.978332 | + | 0.207040i | \(0.0663832\pi\) | ||||
−0.978332 | + | 0.207040i | \(0.933617\pi\) | |||||||
\(864\) | 36.8458i | 1.25352i | ||||||||
\(865\) | 4.76420 | 0.161988 | ||||||||
\(866\) | 55.0094i | 1.86930i | ||||||||
\(867\) | − | 34.8094i | − | 1.18219i | ||||||
\(868\) | −83.1625 | −2.82272 | ||||||||
\(869\) | −33.4035 | − | 18.0976i | −1.13314 | − | 0.613918i | ||||
\(870\) | − | 31.5405i | − | 1.06932i | ||||||
\(871\) | 21.9963i | 0.745316i | ||||||||
\(872\) | 93.5085 | 3.16660 | ||||||||
\(873\) | − | 39.0631i | − | 1.32208i | ||||||
\(874\) | 19.5456 | − | 52.8399i | 0.661141 | − | 1.78734i | ||||
\(875\) | − | 2.59337i | − | 0.0876718i | ||||||
\(876\) | 191.991 | 6.48676 | ||||||||
\(877\) | −14.3803 | −0.485589 | −0.242794 | − | 0.970078i | \(-0.578064\pi\) | ||||
−0.242794 | + | 0.970078i | \(0.578064\pi\) | |||||||
\(878\) | 18.8356 | 0.635671 | ||||||||
\(879\) | 50.7462i | 1.71163i | ||||||||
\(880\) | 41.7854 | + | 22.6388i | 1.40859 | + | 0.763153i | ||||
\(881\) | −27.8657 | −0.938820 | −0.469410 | − | 0.882980i | \(-0.655533\pi\) | ||||
−0.469410 | + | 0.882980i | \(0.655533\pi\) | |||||||
\(882\) | 1.65147 | 0.0556078 | ||||||||
\(883\) | −54.7948 | −1.84399 | −0.921995 | − | 0.387201i | \(-0.873442\pi\) | ||||
−0.921995 | + | 0.387201i | \(0.873442\pi\) | |||||||
\(884\) | 27.5035i | 0.925042i | ||||||||
\(885\) | −28.2743 | −0.950430 | ||||||||
\(886\) | 17.5701 | 0.590280 | ||||||||
\(887\) | −15.7314 | −0.528210 | −0.264105 | − | 0.964494i | \(-0.585077\pi\) | ||||
−0.264105 | + | 0.964494i | \(0.585077\pi\) | |||||||
\(888\) | −11.3667 | −0.381442 | ||||||||
\(889\) | 0.509508i | 0.0170884i | ||||||||
\(890\) | 21.7726i | 0.729820i | ||||||||
\(891\) | 31.3258 | + | 16.9719i | 1.04945 | + | 0.568579i | ||||
\(892\) | − | 155.872i | − | 5.21899i | ||||||
\(893\) | 13.9108 | − | 37.6065i | 0.465506 | − | 1.25845i | ||||
\(894\) | −20.0085 | −0.669186 | ||||||||
\(895\) | 17.4461i | 0.583160i | ||||||||
\(896\) | − | 84.7088i | − | 2.82992i | ||||||
\(897\) | − | 41.7607i | − | 1.39435i | ||||||
\(898\) | − | 2.59568i | − | 0.0866191i | ||||||
\(899\) | 30.1844i | 1.00671i | ||||||||
\(900\) | −11.9402 | −0.398006 | ||||||||
\(901\) | −1.54561 | −0.0514916 | ||||||||
\(902\) | −48.6867 | − | 26.3778i | −1.62109 | − | 0.878285i | ||||
\(903\) | 59.7819i | 1.98942i | ||||||||
\(904\) | − | 53.8354i | − | 1.79054i | ||||||
\(905\) | 12.2191i | 0.406176i | ||||||||
\(906\) | 5.08644i | 0.168986i | ||||||||
\(907\) | − | 7.02813i | − | 0.233365i | −0.993169 | − | 0.116683i | \(-0.962774\pi\) | ||
0.993169 | − | 0.116683i | \(-0.0372261\pi\) | |||||||
\(908\) | 92.0041 | 3.05326 | ||||||||
\(909\) | − | 26.6219i | − | 0.882991i | ||||||
\(910\) | − | 27.1455i | − | 0.899864i | ||||||
\(911\) | 2.08325i | 0.0690213i | 0.999404 | + | 0.0345106i | \(0.0109873\pi\) | ||||
−0.999404 | + | 0.0345106i | \(0.989013\pi\) | |||||||
\(912\) | −133.744 | − | 49.4722i | −4.42870 | − | 1.63819i | ||||
\(913\) | −11.7859 | + | 21.7538i | −0.390057 | + | 0.719945i | ||||
\(914\) | 74.8232i | 2.47493i | ||||||||
\(915\) | 13.8591 | 0.458167 | ||||||||
\(916\) | −89.7422 | −2.96516 | ||||||||
\(917\) | −23.6163 | −0.779879 | ||||||||
\(918\) | 6.47437 | 0.213686 | ||||||||
\(919\) | − | 14.5525i | − | 0.480042i | −0.970768 | − | 0.240021i | \(-0.922846\pi\) | ||
0.970768 | − | 0.240021i | \(-0.0771544\pi\) | |||||||
\(920\) | −43.8997 | −1.44733 | ||||||||
\(921\) | 3.90194i | 0.128573i | ||||||||
\(922\) | − | 116.753i | − | 3.84506i | ||||||
\(923\) | − | 42.6007i | − | 1.40222i | ||||||
\(924\) | −93.1771 | − | 50.4821i | −3.06530 | − | 1.66074i | ||||
\(925\) | 0.538972i | 0.0177213i | ||||||||
\(926\) | −74.8804 | −2.46072 | ||||||||
\(927\) | 5.60405i | 0.184061i | ||||||||
\(928\) | −104.109 | −3.41754 | ||||||||
\(929\) | 26.1795 | 0.858923 | 0.429461 | − | 0.903085i | \(-0.358703\pi\) | ||||
0.429461 | + | 0.903085i | \(0.358703\pi\) | |||||||
\(930\) | 36.8971 | 1.20990 | ||||||||
\(931\) | 0.415025 | − | 1.12198i | 0.0136019 | − | 0.0367715i | ||||
\(932\) | 83.9606i | 2.75022i | ||||||||
\(933\) | − | 74.7899i | − | 2.44851i | ||||||
\(934\) | −21.5156 | −0.704013 | ||||||||
\(935\) | 2.09214 | − | 3.86156i | 0.0684204 | − | 0.126287i | ||||
\(936\) | −78.6617 | −2.57114 | ||||||||
\(937\) | − | 6.03224i | − | 0.197065i | −0.995134 | − | 0.0985323i | \(-0.968585\pi\) | ||
0.995134 | − | 0.0985323i | \(-0.0314148\pi\) | |||||||
\(938\) | −40.3092 | −1.31614 | ||||||||
\(939\) | − | 8.24366i | − | 0.269022i | ||||||
\(940\) | −49.6415 | −1.61913 | ||||||||
\(941\) | 18.2697 | 0.595575 | 0.297787 | − | 0.954632i | \(-0.403751\pi\) | ||||
0.297787 | + | 0.954632i | \(0.403751\pi\) | |||||||
\(942\) | 122.279i | 3.98405i | ||||||||
\(943\) | 29.1750 | 0.950067 | ||||||||
\(944\) | 177.453i | 5.77559i | ||||||||
\(945\) | −4.66222 | −0.151662 | ||||||||
\(946\) | −43.3838 | + | 80.0755i | −1.41053 | + | 2.60348i | ||||
\(947\) | 35.9840 | 1.16932 | 0.584662 | − | 0.811277i | \(-0.301227\pi\) | ||||
0.584662 | + | 0.811277i | \(0.301227\pi\) | |||||||
\(948\) | − | 141.131i | − | 4.58372i | ||||||
\(949\) | − | 59.9741i | − | 1.94684i | ||||||
\(950\) | −4.11273 | + | 11.1184i | −0.133434 | + | 0.360728i | ||||
\(951\) | 30.5043 | 0.989171 | ||||||||
\(952\) | −31.7221 | −1.02812 | ||||||||
\(953\) | 3.75257 | 0.121558 | 0.0607788 | − | 0.998151i | \(-0.480642\pi\) | ||||
0.0607788 | + | 0.998151i | \(0.480642\pi\) | |||||||
\(954\) | − | 7.02354i | − | 0.227395i | ||||||
\(955\) | 3.86569 | 0.125091 | ||||||||
\(956\) | − | 23.5762i | − | 0.762510i | ||||||
\(957\) | −18.3228 | + | 33.8192i | −0.592292 | + | 1.09322i | ||||
\(958\) | − | 23.6657i | − | 0.764603i | ||||||
\(959\) | − | 9.77003i | − | 0.315491i | ||||||
\(960\) | 61.8321i | 1.99562i | ||||||||
\(961\) | −4.31067 | −0.139054 | ||||||||
\(962\) | 5.64157i | 0.181892i | ||||||||
\(963\) | −9.75612 | −0.314387 | ||||||||
\(964\) | −145.799 | −4.69587 | ||||||||
\(965\) | −11.6387 | −0.374664 | ||||||||
\(966\) | 76.5285 | 2.46226 | ||||||||
\(967\) | − | 10.7161i | − | 0.344605i | −0.985044 | − | 0.172303i | \(-0.944879\pi\) | ||
0.985044 | − | 0.172303i | \(-0.0551207\pi\) | |||||||
\(968\) | −55.4944 | − | 85.1168i | −1.78366 | − | 2.73576i | ||||
\(969\) | −4.57193 | + | 12.3598i | −0.146872 | + | 0.397054i | ||||
\(970\) | 48.0152i | 1.54167i | ||||||||
\(971\) | 0.656184i | 0.0210579i | 0.999945 | + | 0.0105290i | \(0.00335154\pi\) | ||||
−0.999945 | + | 0.0105290i | \(0.996648\pi\) | |||||||
\(972\) | 103.248i | 3.31167i | ||||||||
\(973\) | 9.02656 | 0.289378 | ||||||||
\(974\) | − | 32.8283i | − | 1.05189i | ||||||
\(975\) | 8.78715i | 0.281414i | ||||||||
\(976\) | − | 86.9811i | − | 2.78420i | ||||||
\(977\) | 21.7556i | 0.696024i | 0.937490 | + | 0.348012i | \(0.113143\pi\) | ||||
−0.937490 | + | 0.348012i | \(0.886857\pi\) | |||||||
\(978\) | − | 83.7719i | − | 2.67873i | ||||||
\(979\) | 12.6484 | − | 23.3456i | 0.404243 | − | 0.746130i | ||||
\(980\) | −1.48104 | −0.0473102 | ||||||||
\(981\) | 22.3980 | 0.715114 | ||||||||
\(982\) | − | 65.5387i | − | 2.09142i | ||||||
\(983\) | 50.6245i | 1.61467i | 0.590093 | + | 0.807336i | \(0.299091\pi\) | ||||
−0.590093 | + | 0.807336i | \(0.700909\pi\) | |||||||
\(984\) | − | 129.467i | − | 4.12726i | ||||||
\(985\) | 14.4045i | 0.458964i | ||||||||
\(986\) | 18.2935i | 0.582585i | ||||||||
\(987\) | 54.4659 | 1.73367 | ||||||||
\(988\) | −31.4086 | + | 84.9105i | −0.999242 | + | 2.70136i | ||||
\(989\) | − | 47.9843i | − | 1.52581i | ||||||
\(990\) | 17.5477 | + | 9.50712i | 0.557703 | + | 0.302156i | ||||
\(991\) | 31.9998i | 1.01651i | 0.861208 | + | 0.508253i | \(0.169709\pi\) | ||||
−0.861208 | + | 0.508253i | \(0.830291\pi\) | |||||||
\(992\) | − | 121.790i | − | 3.86683i | ||||||
\(993\) | 41.0988 | 1.30423 | ||||||||
\(994\) | 78.0678 | 2.47616 | ||||||||
\(995\) | 10.2338 | 0.324433 | ||||||||
\(996\) | −91.9104 | −2.91229 | ||||||||
\(997\) | − | 2.80146i | − | 0.0887230i | −0.999016 | − | 0.0443615i | \(-0.985875\pi\) | ||
0.999016 | − | 0.0443615i | \(-0.0141253\pi\) | |||||||
\(998\) | −80.9026 | −2.56093 | ||||||||
\(999\) | 0.968936 | 0.0306558 |
(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 | 1045.2.f.a.626.1 | ✓ | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.a.626.39 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.a.626.40 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.a.626.2 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.a.626.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.a.626.2 | yes | 40 | 209.208 | even | 2 | inner | |
1045.2.f.a.626.39 | yes | 40 | 11.10 | odd | 2 | inner | |
1045.2.f.a.626.40 | yes | 40 | 19.18 | odd | 2 | inner |