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 | 626.15 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.b.626.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.863466 | −0.610562 | −0.305281 | − | 0.952262i | \(-0.598750\pi\) | ||||
−0.305281 | + | 0.952262i | \(0.598750\pi\) | |||||||
\(3\) | − | 0.924425i | − | 0.533717i | −0.963736 | − | 0.266859i | \(-0.914014\pi\) | ||
0.963736 | − | 0.266859i | \(-0.0859857\pi\) | |||||||
\(4\) | −1.25443 | −0.627214 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.798209i | 0.325868i | ||||||||
\(7\) | − | 0.285490i | − | 0.107905i | −0.998544 | − | 0.0539525i | \(-0.982818\pi\) | ||
0.998544 | − | 0.0539525i | \(-0.0171819\pi\) | |||||||
\(8\) | 2.81009 | 0.993515 | ||||||||
\(9\) | 2.14544 | 0.715146 | ||||||||
\(10\) | −0.863466 | −0.273052 | ||||||||
\(11\) | 0.818744 | − | 3.21398i | 0.246860 | − | 0.969051i | ||||
\(12\) | 1.15962i | 0.334755i | ||||||||
\(13\) | −0.419046 | −0.116223 | −0.0581113 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581113 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(14\) | 0.246510i | 0.0658827i | ||||||||
\(15\) | − | 0.924425i | − | 0.238686i | ||||||
\(16\) | 0.0824425 | 0.0206106 | ||||||||
\(17\) | 2.73616i | 0.663616i | 0.943347 | + | 0.331808i | \(0.107659\pi\) | ||||
−0.943347 | + | 0.331808i | \(0.892341\pi\) | |||||||
\(18\) | −1.85251 | −0.436641 | ||||||||
\(19\) | −2.97108 | + | 3.18946i | −0.681613 | + | 0.731713i | ||||
\(20\) | −1.25443 | −0.280498 | ||||||||
\(21\) | −0.263914 | −0.0575907 | ||||||||
\(22\) | −0.706957 | + | 2.77516i | −0.150724 | + | 0.591666i | ||||
\(23\) | 7.54111 | 1.57243 | 0.786215 | − | 0.617953i | \(-0.212038\pi\) | ||||
0.786215 | + | 0.617953i | \(0.212038\pi\) | |||||||
\(24\) | − | 2.59771i | − | 0.530256i | ||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.361832 | 0.0709611 | ||||||||
\(27\) | − | 4.75657i | − | 0.915403i | ||||||
\(28\) | 0.358126i | 0.0676794i | ||||||||
\(29\) | −2.67264 | −0.496297 | −0.248148 | − | 0.968722i | \(-0.579822\pi\) | ||||
−0.248148 | + | 0.968722i | \(0.579822\pi\) | |||||||
\(30\) | 0.798209i | 0.145732i | ||||||||
\(31\) | 3.45730i | 0.620950i | 0.950582 | + | 0.310475i | \(0.100488\pi\) | ||||
−0.950582 | + | 0.310475i | \(0.899512\pi\) | |||||||
\(32\) | −5.69136 | −1.00610 | ||||||||
\(33\) | −2.97108 | − | 0.756867i | −0.517199 | − | 0.131754i | ||||
\(34\) | − | 2.36258i | − | 0.405179i | ||||||
\(35\) | − | 0.285490i | − | 0.0482566i | ||||||
\(36\) | −2.69130 | −0.448549 | ||||||||
\(37\) | − | 1.21456i | − | 0.199672i | −0.995004 | − | 0.0998359i | \(-0.968168\pi\) | ||
0.995004 | − | 0.0998359i | \(-0.0318318\pi\) | |||||||
\(38\) | 2.56543 | − | 2.75399i | 0.416167 | − | 0.446756i | ||||
\(39\) | 0.387377i | 0.0620300i | ||||||||
\(40\) | 2.81009 | 0.444314 | ||||||||
\(41\) | 9.74248 | 1.52152 | 0.760760 | − | 0.649033i | \(-0.224826\pi\) | ||||
0.760760 | + | 0.649033i | \(0.224826\pi\) | |||||||
\(42\) | 0.227880 | 0.0351627 | ||||||||
\(43\) | − | 0.0617565i | − | 0.00941777i | −0.999989 | − | 0.00470889i | \(-0.998501\pi\) | ||
0.999989 | − | 0.00470889i | \(-0.00149889\pi\) | |||||||
\(44\) | −1.02705 | + | 4.03170i | −0.154834 | + | 0.607802i | ||||
\(45\) | 2.14544 | 0.319823 | ||||||||
\(46\) | −6.51149 | −0.960066 | ||||||||
\(47\) | 2.51294 | 0.366550 | 0.183275 | − | 0.983062i | \(-0.441330\pi\) | ||||
0.183275 | + | 0.983062i | \(0.441330\pi\) | |||||||
\(48\) | − | 0.0762119i | − | 0.0110002i | ||||||
\(49\) | 6.91850 | 0.988357 | ||||||||
\(50\) | −0.863466 | −0.122112 | ||||||||
\(51\) | 2.52937 | 0.354183 | ||||||||
\(52\) | 0.525663 | 0.0728964 | ||||||||
\(53\) | − | 10.1781i | − | 1.39807i | −0.715088 | − | 0.699034i | \(-0.753614\pi\) | ||
0.715088 | − | 0.699034i | \(-0.246386\pi\) | |||||||
\(54\) | 4.10714i | 0.558910i | ||||||||
\(55\) | 0.818744 | − | 3.21398i | 0.110399 | − | 0.433373i | ||||
\(56\) | − | 0.802250i | − | 0.107205i | ||||||
\(57\) | 2.94842 | + | 2.74654i | 0.390528 | + | 0.363789i | ||||
\(58\) | 2.30773 | 0.303020 | ||||||||
\(59\) | − | 8.40673i | − | 1.09446i | −0.836981 | − | 0.547232i | \(-0.815682\pi\) | ||
0.836981 | − | 0.547232i | \(-0.184318\pi\) | |||||||
\(60\) | 1.15962i | 0.149707i | ||||||||
\(61\) | − | 2.63798i | − | 0.337758i | −0.985637 | − | 0.168879i | \(-0.945985\pi\) | ||
0.985637 | − | 0.168879i | \(-0.0540147\pi\) | |||||||
\(62\) | − | 2.98526i | − | 0.379128i | ||||||
\(63\) | − | 0.612500i | − | 0.0771678i | ||||||
\(64\) | 4.74941 | 0.593676 | ||||||||
\(65\) | −0.419046 | −0.0519763 | ||||||||
\(66\) | 2.56543 | + | 0.653529i | 0.315782 | + | 0.0804438i | ||||
\(67\) | − | 11.1802i | − | 1.36587i | −0.730477 | − | 0.682937i | \(-0.760702\pi\) | ||
0.730477 | − | 0.682937i | \(-0.239298\pi\) | |||||||
\(68\) | − | 3.43231i | − | 0.416229i | ||||||
\(69\) | − | 6.97119i | − | 0.839233i | ||||||
\(70\) | 0.246510i | 0.0294636i | ||||||||
\(71\) | 2.61887i | 0.310803i | 0.987851 | + | 0.155401i | \(0.0496671\pi\) | ||||
−0.987851 | + | 0.155401i | \(0.950333\pi\) | |||||||
\(72\) | 6.02886 | 0.710509 | ||||||||
\(73\) | − | 7.15415i | − | 0.837330i | −0.908141 | − | 0.418665i | \(-0.862498\pi\) | ||
0.908141 | − | 0.418665i | \(-0.137502\pi\) | |||||||
\(74\) | 1.04873i | 0.121912i | ||||||||
\(75\) | − | 0.924425i | − | 0.106743i | ||||||
\(76\) | 3.72701 | − | 4.00095i | 0.427517 | − | 0.458940i | ||||
\(77\) | −0.917557 | − | 0.233743i | −0.104565 | − | 0.0266375i | ||||
\(78\) | − | 0.334487i | − | 0.0378732i | ||||||
\(79\) | −10.9113 | −1.22762 | −0.613811 | − | 0.789453i | \(-0.710364\pi\) | ||||
−0.613811 | + | 0.789453i | \(0.710364\pi\) | |||||||
\(80\) | 0.0824425 | 0.00921735 | ||||||||
\(81\) | 2.03922 | 0.226580 | ||||||||
\(82\) | −8.41230 | −0.928983 | ||||||||
\(83\) | − | 14.5167i | − | 1.59342i | −0.604363 | − | 0.796709i | \(-0.706572\pi\) | ||
0.604363 | − | 0.796709i | \(-0.293428\pi\) | |||||||
\(84\) | 0.331061 | 0.0361217 | ||||||||
\(85\) | 2.73616i | 0.296778i | ||||||||
\(86\) | 0.0533246i | 0.00575014i | ||||||||
\(87\) | 2.47066i | 0.264882i | ||||||||
\(88\) | 2.30074 | − | 9.03156i | 0.245260 | − | 0.962767i | ||||
\(89\) | 13.9172i | 1.47522i | 0.675226 | + | 0.737611i | \(0.264046\pi\) | ||||
−0.675226 | + | 0.737611i | \(0.735954\pi\) | |||||||
\(90\) | −1.85251 | −0.195272 | ||||||||
\(91\) | 0.119633i | 0.0125410i | ||||||||
\(92\) | −9.45977 | −0.986249 | ||||||||
\(93\) | 3.19602 | 0.331411 | ||||||||
\(94\) | −2.16984 | −0.223802 | ||||||||
\(95\) | −2.97108 | + | 3.18946i | −0.304827 | + | 0.327232i | ||||
\(96\) | 5.26123i | 0.536973i | ||||||||
\(97\) | 19.2960i | 1.95922i | 0.200920 | + | 0.979608i | \(0.435607\pi\) | ||||
−0.200920 | + | 0.979608i | \(0.564393\pi\) | |||||||
\(98\) | −5.97388 | −0.603453 | ||||||||
\(99\) | 1.75656 | − | 6.89539i | 0.176541 | − | 0.693013i | ||||
\(100\) | −1.25443 | −0.125443 | ||||||||
\(101\) | − | 6.27231i | − | 0.624119i | −0.950063 | − | 0.312059i | \(-0.898981\pi\) | ||
0.950063 | − | 0.312059i | \(-0.101019\pi\) | |||||||
\(102\) | −2.18403 | −0.216251 | ||||||||
\(103\) | − | 13.7149i | − | 1.35137i | −0.737191 | − | 0.675684i | \(-0.763848\pi\) | ||
0.737191 | − | 0.675684i | \(-0.236152\pi\) | |||||||
\(104\) | −1.17756 | −0.115469 | ||||||||
\(105\) | −0.263914 | −0.0257553 | ||||||||
\(106\) | 8.78843i | 0.853608i | ||||||||
\(107\) | −3.57005 | −0.345130 | −0.172565 | − | 0.984998i | \(-0.555205\pi\) | ||||
−0.172565 | + | 0.984998i | \(0.555205\pi\) | |||||||
\(108\) | 5.96677i | 0.574153i | ||||||||
\(109\) | 9.85614 | 0.944047 | 0.472024 | − | 0.881586i | \(-0.343524\pi\) | ||||
0.472024 | + | 0.881586i | \(0.343524\pi\) | |||||||
\(110\) | −0.706957 | + | 2.77516i | −0.0674057 | + | 0.264601i | ||||
\(111\) | −1.12277 | −0.106568 | ||||||||
\(112\) | − | 0.0235365i | − | 0.00222399i | ||||||
\(113\) | − | 4.11217i | − | 0.386840i | −0.981116 | − | 0.193420i | \(-0.938042\pi\) | ||
0.981116 | − | 0.193420i | \(-0.0619580\pi\) | |||||||
\(114\) | −2.54586 | − | 2.37155i | −0.238441 | − | 0.222116i | ||||
\(115\) | 7.54111 | 0.703212 | ||||||||
\(116\) | 3.35263 | 0.311284 | ||||||||
\(117\) | −0.899038 | −0.0831161 | ||||||||
\(118\) | 7.25892i | 0.668238i | ||||||||
\(119\) | 0.781144 | 0.0716074 | ||||||||
\(120\) | − | 2.59771i | − | 0.237138i | ||||||
\(121\) | −9.65932 | − | 5.26285i | −0.878120 | − | 0.478441i | ||||
\(122\) | 2.27780i | 0.206222i | ||||||||
\(123\) | − | 9.00620i | − | 0.812061i | ||||||
\(124\) | − | 4.33693i | − | 0.389468i | ||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.528873i | 0.0471157i | ||||||||
\(127\) | 18.2607 | 1.62037 | 0.810187 | − | 0.586171i | \(-0.199365\pi\) | ||||
0.810187 | + | 0.586171i | \(0.199365\pi\) | |||||||
\(128\) | 7.28177 | 0.643623 | ||||||||
\(129\) | −0.0570892 | −0.00502643 | ||||||||
\(130\) | 0.361832 | 0.0317348 | ||||||||
\(131\) | 11.0127i | 0.962180i | 0.876671 | + | 0.481090i | \(0.159759\pi\) | ||||
−0.876671 | + | 0.481090i | \(0.840241\pi\) | |||||||
\(132\) | 3.72701 | + | 0.949435i | 0.324394 | + | 0.0826377i | ||||
\(133\) | 0.910558 | + | 0.848213i | 0.0789554 | + | 0.0735494i | ||||
\(134\) | 9.65369i | 0.833951i | ||||||||
\(135\) | − | 4.75657i | − | 0.409381i | ||||||
\(136\) | 7.68884i | 0.659312i | ||||||||
\(137\) | 0.163904 | 0.0140033 | 0.00700164 | − | 0.999975i | \(-0.497771\pi\) | ||||
0.00700164 | + | 0.999975i | \(0.497771\pi\) | |||||||
\(138\) | 6.01938i | 0.512404i | ||||||||
\(139\) | − | 16.5377i | − | 1.40271i | −0.712812 | − | 0.701355i | \(-0.752579\pi\) | ||
0.712812 | − | 0.701355i | \(-0.247421\pi\) | |||||||
\(140\) | 0.358126i | 0.0302672i | ||||||||
\(141\) | − | 2.32303i | − | 0.195634i | ||||||
\(142\) | − | 2.26131i | − | 0.189765i | ||||||
\(143\) | −0.343091 | + | 1.34681i | −0.0286908 | + | 0.112626i | ||||
\(144\) | 0.176875 | 0.0147396 | ||||||||
\(145\) | −2.67264 | −0.221951 | ||||||||
\(146\) | 6.17736i | 0.511242i | ||||||||
\(147\) | − | 6.39563i | − | 0.527503i | ||||||
\(148\) | 1.52357i | 0.125237i | ||||||||
\(149\) | 17.8869i | 1.46535i | 0.680577 | + | 0.732676i | \(0.261729\pi\) | ||||
−0.680577 | + | 0.732676i | \(0.738271\pi\) | |||||||
\(150\) | 0.798209i | 0.0651735i | ||||||||
\(151\) | 3.24652 | 0.264198 | 0.132099 | − | 0.991237i | \(-0.457828\pi\) | ||||
0.132099 | + | 0.991237i | \(0.457828\pi\) | |||||||
\(152\) | −8.34900 | + | 8.96266i | −0.677193 | + | 0.726968i | ||||
\(153\) | 5.87025i | 0.474582i | ||||||||
\(154\) | 0.792279 | + | 0.201829i | 0.0638437 | + | 0.0162638i | ||||
\(155\) | 3.45730i | 0.277697i | ||||||||
\(156\) | − | 0.485936i | − | 0.0389060i | ||||||
\(157\) | −15.5202 | −1.23865 | −0.619323 | − | 0.785136i | \(-0.712593\pi\) | ||||
−0.619323 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(158\) | 9.42156 | 0.749539 | ||||||||
\(159\) | −9.40888 | −0.746173 | ||||||||
\(160\) | −5.69136 | −0.449941 | ||||||||
\(161\) | − | 2.15291i | − | 0.169673i | ||||||
\(162\) | −1.76079 | −0.138341 | ||||||||
\(163\) | 20.4847 | 1.60448 | 0.802241 | − | 0.597000i | \(-0.203641\pi\) | ||||
0.802241 | + | 0.597000i | \(0.203641\pi\) | |||||||
\(164\) | −12.2212 | −0.954318 | ||||||||
\(165\) | −2.97108 | − | 0.756867i | −0.231299 | − | 0.0589220i | ||||
\(166\) | 12.5347i | 0.972881i | ||||||||
\(167\) | −8.05481 | −0.623300 | −0.311650 | − | 0.950197i | \(-0.600882\pi\) | ||||
−0.311650 | + | 0.950197i | \(0.600882\pi\) | |||||||
\(168\) | −0.741620 | −0.0572173 | ||||||||
\(169\) | −12.8244 | −0.986492 | ||||||||
\(170\) | − | 2.36258i | − | 0.181201i | ||||||
\(171\) | −6.37427 | + | 6.84279i | −0.487453 | + | 0.523281i | ||||
\(172\) | 0.0774690i | 0.00590696i | ||||||||
\(173\) | 13.5272 | 1.02846 | 0.514228 | − | 0.857653i | \(-0.328078\pi\) | ||||
0.514228 | + | 0.857653i | \(0.328078\pi\) | |||||||
\(174\) | − | 2.13333i | − | 0.161727i | ||||||
\(175\) | − | 0.285490i | − | 0.0215810i | ||||||
\(176\) | 0.0674993 | − | 0.264968i | 0.00508795 | − | 0.0199727i | ||||
\(177\) | −7.77140 | −0.584134 | ||||||||
\(178\) | − | 12.0170i | − | 0.900715i | ||||||
\(179\) | 15.9692i | 1.19360i | 0.802391 | + | 0.596799i | \(0.203561\pi\) | ||||
−0.802391 | + | 0.596799i | \(0.796439\pi\) | |||||||
\(180\) | −2.69130 | −0.200597 | ||||||||
\(181\) | 21.9473i | 1.63133i | 0.578523 | + | 0.815666i | \(0.303629\pi\) | ||||
−0.578523 | + | 0.815666i | \(0.696371\pi\) | |||||||
\(182\) | − | 0.103299i | − | 0.00765705i | ||||||
\(183\) | −2.43861 | −0.180267 | ||||||||
\(184\) | 21.1912 | 1.56223 | ||||||||
\(185\) | − | 1.21456i | − | 0.0892960i | ||||||
\(186\) | −2.75965 | −0.202347 | ||||||||
\(187\) | 8.79395 | + | 2.24021i | 0.643077 | + | 0.163820i | ||||
\(188\) | −3.15230 | −0.229905 | ||||||||
\(189\) | −1.35795 | −0.0987765 | ||||||||
\(190\) | 2.56543 | − | 2.75399i | 0.186116 | − | 0.199795i | ||||
\(191\) | −14.9039 | −1.07841 | −0.539205 | − | 0.842174i | \(-0.681275\pi\) | ||||
−0.539205 | + | 0.842174i | \(0.681275\pi\) | |||||||
\(192\) | − | 4.39047i | − | 0.316855i | ||||||
\(193\) | 14.3290 | 1.03142 | 0.515710 | − | 0.856763i | \(-0.327528\pi\) | ||||
0.515710 | + | 0.856763i | \(0.327528\pi\) | |||||||
\(194\) | − | 16.6615i | − | 1.19622i | ||||||
\(195\) | 0.387377i | 0.0277406i | ||||||||
\(196\) | −8.67875 | −0.619911 | ||||||||
\(197\) | − | 21.3998i | − | 1.52467i | −0.647182 | − | 0.762336i | \(-0.724053\pi\) | ||
0.647182 | − | 0.762336i | \(-0.275947\pi\) | |||||||
\(198\) | −1.51673 | + | 5.95393i | −0.107789 | + | 0.423128i | ||||
\(199\) | 5.35992 | 0.379955 | 0.189977 | − | 0.981788i | \(-0.439159\pi\) | ||||
0.189977 | + | 0.981788i | \(0.439159\pi\) | |||||||
\(200\) | 2.81009 | 0.198703 | ||||||||
\(201\) | −10.3352 | −0.728991 | ||||||||
\(202\) | 5.41593i | 0.381063i | ||||||||
\(203\) | 0.763011i | 0.0535529i | ||||||||
\(204\) | −3.17291 | −0.222148 | ||||||||
\(205\) | 9.74248 | 0.680444 | ||||||||
\(206\) | 11.8423i | 0.825095i | ||||||||
\(207\) | 16.1790 | 1.12452 | ||||||||
\(208\) | −0.0345472 | −0.00239542 | ||||||||
\(209\) | 7.81831 | + | 12.1603i | 0.540804 | + | 0.841149i | ||||
\(210\) | 0.227880 | 0.0157252 | ||||||||
\(211\) | 16.0790 | 1.10692 | 0.553462 | − | 0.832875i | \(-0.313307\pi\) | ||||
0.553462 | + | 0.832875i | \(0.313307\pi\) | |||||||
\(212\) | 12.7677i | 0.876888i | ||||||||
\(213\) | 2.42095 | 0.165881 | ||||||||
\(214\) | 3.08262 | 0.210723 | ||||||||
\(215\) | − | 0.0617565i | − | 0.00421176i | ||||||
\(216\) | − | 13.3664i | − | 0.909467i | ||||||
\(217\) | 0.987023 | 0.0670035 | ||||||||
\(218\) | −8.51044 | −0.576400 | ||||||||
\(219\) | −6.61348 | −0.446898 | ||||||||
\(220\) | −1.02705 | + | 4.03170i | −0.0692440 | + | 0.271817i | ||||
\(221\) | − | 1.14658i | − | 0.0771271i | ||||||
\(222\) | 0.969470 | 0.0650666 | ||||||||
\(223\) | − | 23.7630i | − | 1.59129i | −0.605765 | − | 0.795644i | \(-0.707133\pi\) | ||
0.605765 | − | 0.795644i | \(-0.292867\pi\) | |||||||
\(224\) | 1.62482i | 0.108563i | ||||||||
\(225\) | 2.14544 | 0.143029 | ||||||||
\(226\) | 3.55071i | 0.236190i | ||||||||
\(227\) | −3.25234 | −0.215865 | −0.107933 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107933 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(228\) | −3.69858 | − | 3.44534i | −0.244944 | − | 0.228173i | ||||
\(229\) | −14.7762 | −0.976439 | −0.488219 | − | 0.872721i | \(-0.662353\pi\) | ||||
−0.488219 | + | 0.872721i | \(0.662353\pi\) | |||||||
\(230\) | −6.51149 | −0.429355 | ||||||||
\(231\) | −0.216078 | + | 0.848213i | −0.0142169 | + | 0.0558083i | ||||
\(232\) | −7.51035 | −0.493078 | ||||||||
\(233\) | 25.4229i | 1.66551i | 0.553644 | + | 0.832753i | \(0.313237\pi\) | ||||
−0.553644 | + | 0.832753i | \(0.686763\pi\) | |||||||
\(234\) | 0.776288 | 0.0507475 | ||||||||
\(235\) | 2.51294 | 0.163926 | ||||||||
\(236\) | 10.5456i | 0.686462i | ||||||||
\(237\) | 10.0867i | 0.655202i | ||||||||
\(238\) | −0.674491 | −0.0437208 | ||||||||
\(239\) | 27.3076i | 1.76638i | 0.469011 | + | 0.883192i | \(0.344610\pi\) | ||||
−0.469011 | + | 0.883192i | \(0.655390\pi\) | |||||||
\(240\) | − | 0.0762119i | − | 0.00491946i | ||||||
\(241\) | −25.9387 | −1.67086 | −0.835429 | − | 0.549598i | \(-0.814781\pi\) | ||||
−0.835429 | + | 0.549598i | \(0.814781\pi\) | |||||||
\(242\) | 8.34049 | + | 4.54429i | 0.536147 | + | 0.292118i | ||||
\(243\) | − | 16.1548i | − | 1.03633i | ||||||
\(244\) | 3.30915i | 0.211847i | ||||||||
\(245\) | 6.91850 | 0.442006 | ||||||||
\(246\) | 7.77654i | 0.495814i | ||||||||
\(247\) | 1.24502 | − | 1.33653i | 0.0792188 | − | 0.0850415i | ||||
\(248\) | 9.71531i | 0.616923i | ||||||||
\(249\) | −13.4196 | −0.850435 | ||||||||
\(250\) | −0.863466 | −0.0546104 | ||||||||
\(251\) | −25.4969 | −1.60935 | −0.804676 | − | 0.593715i | \(-0.797661\pi\) | ||||
−0.804676 | + | 0.593715i | \(0.797661\pi\) | |||||||
\(252\) | 0.768337i | 0.0484007i | ||||||||
\(253\) | 6.17423 | − | 24.2370i | 0.388171 | − | 1.52376i | ||||
\(254\) | −15.7675 | −0.989339 | ||||||||
\(255\) | 2.52937 | 0.158395 | ||||||||
\(256\) | −15.7864 | −0.986648 | ||||||||
\(257\) | 2.63088i | 0.164110i | 0.996628 | + | 0.0820549i | \(0.0261483\pi\) | ||||
−0.996628 | + | 0.0820549i | \(0.973852\pi\) | |||||||
\(258\) | 0.0492946 | 0.00306895 | ||||||||
\(259\) | −0.346743 | −0.0215456 | ||||||||
\(260\) | 0.525663 | 0.0326002 | ||||||||
\(261\) | −5.73398 | −0.354925 | ||||||||
\(262\) | − | 9.50905i | − | 0.587471i | ||||||
\(263\) | − | 11.6130i | − | 0.716088i | −0.933705 | − | 0.358044i | \(-0.883444\pi\) | ||
0.933705 | − | 0.358044i | \(-0.116556\pi\) | |||||||
\(264\) | −8.34900 | − | 2.12686i | −0.513845 | − | 0.130899i | ||||
\(265\) | − | 10.1781i | − | 0.625235i | ||||||
\(266\) | −0.786236 | − | 0.732403i | −0.0482072 | − | 0.0449065i | ||||
\(267\) | 12.8654 | 0.787351 | ||||||||
\(268\) | 14.0247i | 0.856695i | ||||||||
\(269\) | 22.7940i | 1.38978i | 0.719118 | + | 0.694888i | \(0.244546\pi\) | ||||
−0.719118 | + | 0.694888i | \(0.755454\pi\) | |||||||
\(270\) | 4.10714i | 0.249952i | ||||||||
\(271\) | − | 9.35459i | − | 0.568251i | −0.958787 | − | 0.284125i | \(-0.908297\pi\) | ||
0.958787 | − | 0.284125i | \(-0.0917032\pi\) | |||||||
\(272\) | 0.225576i | 0.0136775i | ||||||||
\(273\) | 0.110592 | 0.00669334 | ||||||||
\(274\) | −0.141526 | −0.00854988 | ||||||||
\(275\) | 0.818744 | − | 3.21398i | 0.0493721 | − | 0.193810i | ||||
\(276\) | 8.74485i | 0.526378i | ||||||||
\(277\) | 9.57982i | 0.575595i | 0.957691 | + | 0.287798i | \(0.0929231\pi\) | ||||
−0.957691 | + | 0.287798i | \(0.907077\pi\) | |||||||
\(278\) | 14.2797i | 0.856442i | ||||||||
\(279\) | 7.41742i | 0.444070i | ||||||||
\(280\) | − | 0.802250i | − | 0.0479436i | ||||||
\(281\) | 23.3350 | 1.39205 | 0.696026 | − | 0.718017i | \(-0.254950\pi\) | ||||
0.696026 | + | 0.718017i | \(0.254950\pi\) | |||||||
\(282\) | 2.00585i | 0.119447i | ||||||||
\(283\) | 32.5616i | 1.93559i | 0.251749 | + | 0.967793i | \(0.418994\pi\) | ||||
−0.251749 | + | 0.967793i | \(0.581006\pi\) | |||||||
\(284\) | − | 3.28519i | − | 0.194940i | ||||||
\(285\) | 2.94842 | + | 2.74654i | 0.174649 | + | 0.162691i | ||||
\(286\) | 0.296248 | − | 1.16292i | 0.0175175 | − | 0.0687649i | ||||
\(287\) | − | 2.78138i | − | 0.164179i | ||||||
\(288\) | −12.2105 | −0.719508 | ||||||||
\(289\) | 9.51345 | 0.559614 | ||||||||
\(290\) | 2.30773 | 0.135515 | ||||||||
\(291\) | 17.8377 | 1.04567 | ||||||||
\(292\) | 8.97437i | 0.525185i | ||||||||
\(293\) | −21.8725 | −1.27781 | −0.638904 | − | 0.769286i | \(-0.720612\pi\) | ||||
−0.638904 | + | 0.769286i | \(0.720612\pi\) | |||||||
\(294\) | 5.52241i | 0.322073i | ||||||||
\(295\) | − | 8.40673i | − | 0.489459i | ||||||
\(296\) | − | 3.41301i | − | 0.198377i | ||||||
\(297\) | −15.2875 | − | 3.89441i | −0.887072 | − | 0.225977i | ||||
\(298\) | − | 15.4447i | − | 0.894689i | ||||||
\(299\) | −3.16007 | −0.182752 | ||||||||
\(300\) | 1.15962i | 0.0669509i | ||||||||
\(301\) | −0.0176308 | −0.00101622 | ||||||||
\(302\) | −2.80326 | −0.161309 | ||||||||
\(303\) | −5.79829 | −0.333103 | ||||||||
\(304\) | −0.244944 | + | 0.262947i | −0.0140485 | + | 0.0150811i | ||||
\(305\) | − | 2.63798i | − | 0.151050i | ||||||
\(306\) | − | 5.06876i | − | 0.289762i | ||||||
\(307\) | −13.1466 | −0.750317 | −0.375158 | − | 0.926961i | \(-0.622412\pi\) | ||||
−0.375158 | + | 0.926961i | \(0.622412\pi\) | |||||||
\(308\) | 1.15101 | + | 0.293213i | 0.0655848 | + | 0.0167074i | ||||
\(309\) | −12.6784 | −0.721249 | ||||||||
\(310\) | − | 2.98526i | − | 0.169551i | ||||||
\(311\) | −19.4254 | −1.10151 | −0.550756 | − | 0.834666i | \(-0.685661\pi\) | ||||
−0.550756 | + | 0.834666i | \(0.685661\pi\) | |||||||
\(312\) | 1.08856i | 0.0616277i | ||||||||
\(313\) | 15.7237 | 0.888757 | 0.444379 | − | 0.895839i | \(-0.353425\pi\) | ||||
0.444379 | + | 0.895839i | \(0.353425\pi\) | |||||||
\(314\) | 13.4011 | 0.756271 | ||||||||
\(315\) | − | 0.612500i | − | 0.0345105i | ||||||
\(316\) | 13.6875 | 0.769981 | ||||||||
\(317\) | 2.48262i | 0.139438i | 0.997567 | + | 0.0697189i | \(0.0222102\pi\) | ||||
−0.997567 | + | 0.0697189i | \(0.977790\pi\) | |||||||
\(318\) | 8.12425 | 0.455585 | ||||||||
\(319\) | −2.18821 | + | 8.58981i | −0.122516 | + | 0.480937i | ||||
\(320\) | 4.74941 | 0.265500 | ||||||||
\(321\) | 3.30025i | 0.184202i | ||||||||
\(322\) | 1.85896i | 0.103596i | ||||||||
\(323\) | −8.72687 | − | 8.12935i | −0.485576 | − | 0.452329i | ||||
\(324\) | −2.55805 | −0.142114 | ||||||||
\(325\) | −0.419046 | −0.0232445 | ||||||||
\(326\) | −17.6878 | −0.979637 | ||||||||
\(327\) | − | 9.11127i | − | 0.503854i | ||||||
\(328\) | 27.3772 | 1.51165 | ||||||||
\(329\) | − | 0.717419i | − | 0.0395526i | ||||||
\(330\) | 2.56543 | + | 0.653529i | 0.141222 | + | 0.0359756i | ||||
\(331\) | − | 10.3625i | − | 0.569575i | −0.958591 | − | 0.284787i | \(-0.908077\pi\) | ||
0.958591 | − | 0.284787i | \(-0.0919230\pi\) | |||||||
\(332\) | 18.2102i | 0.999414i | ||||||||
\(333\) | − | 2.60576i | − | 0.142795i | ||||||
\(334\) | 6.95505 | 0.380563 | ||||||||
\(335\) | − | 11.1802i | − | 0.610838i | ||||||
\(336\) | −0.0217577 | −0.00118698 | ||||||||
\(337\) | −7.00099 | −0.381368 | −0.190684 | − | 0.981651i | \(-0.561071\pi\) | ||||
−0.190684 | + | 0.981651i | \(0.561071\pi\) | |||||||
\(338\) | 11.0734 | 0.602315 | ||||||||
\(339\) | −3.80139 | −0.206463 | ||||||||
\(340\) | − | 3.43231i | − | 0.186143i | ||||||
\(341\) | 11.1117 | + | 2.83064i | 0.601732 | + | 0.153288i | ||||
\(342\) | 5.50397 | − | 5.90851i | 0.297620 | − | 0.319496i | ||||
\(343\) | − | 3.97359i | − | 0.214553i | ||||||
\(344\) | − | 0.173541i | − | 0.00935670i | ||||||
\(345\) | − | 6.97119i | − | 0.375316i | ||||||
\(346\) | −11.6803 | −0.627937 | ||||||||
\(347\) | 8.33222i | 0.447297i | 0.974670 | + | 0.223648i | \(0.0717968\pi\) | ||||
−0.974670 | + | 0.223648i | \(0.928203\pi\) | |||||||
\(348\) | − | 3.09926i | − | 0.166138i | ||||||
\(349\) | − | 11.1985i | − | 0.599444i | −0.954027 | − | 0.299722i | \(-0.903106\pi\) | ||
0.954027 | − | 0.299722i | \(-0.0968940\pi\) | |||||||
\(350\) | 0.246510i | 0.0131765i | ||||||||
\(351\) | 1.99322i | 0.106390i | ||||||||
\(352\) | −4.65976 | + | 18.2919i | −0.248366 | + | 0.974962i | ||||
\(353\) | −25.8509 | −1.37590 | −0.687952 | − | 0.725756i | \(-0.741490\pi\) | ||||
−0.687952 | + | 0.725756i | \(0.741490\pi\) | |||||||
\(354\) | 6.71033 | 0.356650 | ||||||||
\(355\) | 2.61887i | 0.138995i | ||||||||
\(356\) | − | 17.4581i | − | 0.925279i | ||||||
\(357\) | − | 0.722110i | − | 0.0382181i | ||||||
\(358\) | − | 13.7889i | − | 0.728765i | ||||||
\(359\) | 12.0184i | 0.634308i | 0.948374 | + | 0.317154i | \(0.102727\pi\) | ||||
−0.948374 | + | 0.317154i | \(0.897273\pi\) | |||||||
\(360\) | 6.02886 | 0.317749 | ||||||||
\(361\) | −1.34533 | − | 18.9523i | −0.0708069 | − | 0.997490i | ||||
\(362\) | − | 18.9508i | − | 0.996030i | ||||||
\(363\) | −4.86511 | + | 8.92932i | −0.255352 | + | 0.468668i | ||||
\(364\) | − | 0.150071i | − | 0.00786588i | ||||||
\(365\) | − | 7.15415i | − | 0.374465i | ||||||
\(366\) | 2.10566 | 0.110064 | ||||||||
\(367\) | 3.31693 | 0.173142 | 0.0865710 | − | 0.996246i | \(-0.472409\pi\) | ||||
0.0865710 | + | 0.996246i | \(0.472409\pi\) | |||||||
\(368\) | 0.621708 | 0.0324088 | ||||||||
\(369\) | 20.9019 | 1.08811 | ||||||||
\(370\) | 1.04873i | 0.0545207i | ||||||||
\(371\) | −2.90574 | −0.150858 | ||||||||
\(372\) | −4.00917 | −0.207866 | ||||||||
\(373\) | −18.9618 | −0.981803 | −0.490902 | − | 0.871215i | \(-0.663333\pi\) | ||||
−0.490902 | + | 0.871215i | \(0.663333\pi\) | |||||||
\(374\) | −7.59327 | − | 1.93434i | −0.392639 | − | 0.100023i | ||||
\(375\) | − | 0.924425i | − | 0.0477371i | ||||||
\(376\) | 7.06158 | 0.364173 | ||||||||
\(377\) | 1.11996 | 0.0576809 | ||||||||
\(378\) | 1.17254 | 0.0603092 | ||||||||
\(379\) | − | 16.8155i | − | 0.863753i | −0.901933 | − | 0.431876i | \(-0.857852\pi\) | ||
0.901933 | − | 0.431876i | \(-0.142148\pi\) | |||||||
\(380\) | 3.72701 | − | 4.00095i | 0.191191 | − | 0.205244i | ||||
\(381\) | − | 16.8806i | − | 0.864822i | ||||||
\(382\) | 12.8690 | 0.658437 | ||||||||
\(383\) | 23.4062i | 1.19600i | 0.801496 | + | 0.598000i | \(0.204038\pi\) | ||||
−0.801496 | + | 0.598000i | \(0.795962\pi\) | |||||||
\(384\) | − | 6.73145i | − | 0.343513i | ||||||
\(385\) | −0.917557 | − | 0.233743i | −0.0467631 | − | 0.0119126i | ||||
\(386\) | −12.3726 | −0.629747 | ||||||||
\(387\) | − | 0.132495i | − | 0.00673508i | ||||||
\(388\) | − | 24.2055i | − | 1.22885i | ||||||
\(389\) | −10.9278 | −0.554061 | −0.277030 | − | 0.960861i | \(-0.589350\pi\) | ||||
−0.277030 | + | 0.960861i | \(0.589350\pi\) | |||||||
\(390\) | − | 0.334487i | − | 0.0169374i | ||||||
\(391\) | 20.6337i | 1.04349i | ||||||||
\(392\) | 19.4416 | 0.981947 | ||||||||
\(393\) | 10.1804 | 0.513532 | ||||||||
\(394\) | 18.4780i | 0.930907i | ||||||||
\(395\) | −10.9113 | −0.549009 | ||||||||
\(396\) | −2.20348 | + | 8.64977i | −0.110729 | + | 0.434667i | ||||
\(397\) | 11.3605 | 0.570168 | 0.285084 | − | 0.958503i | \(-0.407979\pi\) | ||||
0.285084 | + | 0.958503i | \(0.407979\pi\) | |||||||
\(398\) | −4.62811 | −0.231986 | ||||||||
\(399\) | 0.784110 | − | 0.841743i | 0.0392546 | − | 0.0421399i | ||||
\(400\) | 0.0824425 | 0.00412213 | ||||||||
\(401\) | 35.4498i | 1.77028i | 0.465325 | + | 0.885140i | \(0.345937\pi\) | ||||
−0.465325 | + | 0.885140i | \(0.654063\pi\) | |||||||
\(402\) | 8.92411 | 0.445094 | ||||||||
\(403\) | − | 1.44877i | − | 0.0721683i | ||||||
\(404\) | 7.86816i | 0.391456i | ||||||||
\(405\) | 2.03922 | 0.101330 | ||||||||
\(406\) | − | 0.658834i | − | 0.0326974i | ||||||
\(407\) | −3.90356 | − | 0.994410i | −0.193492 | − | 0.0492911i | ||||
\(408\) | 7.10775 | 0.351886 | ||||||||
\(409\) | 15.0326 | 0.743313 | 0.371657 | − | 0.928370i | \(-0.378790\pi\) | ||||
0.371657 | + | 0.928370i | \(0.378790\pi\) | |||||||
\(410\) | −8.41230 | −0.415454 | ||||||||
\(411\) | − | 0.151517i | − | 0.00747380i | ||||||
\(412\) | 17.2043i | 0.847597i | ||||||||
\(413\) | −2.40003 | −0.118098 | ||||||||
\(414\) | −13.9700 | −0.686588 | ||||||||
\(415\) | − | 14.5167i | − | 0.712598i | ||||||
\(416\) | 2.38494 | 0.116931 | ||||||||
\(417\) | −15.2879 | −0.748651 | ||||||||
\(418\) | −6.75084 | − | 10.5000i | −0.330194 | − | 0.513574i | ||||
\(419\) | −0.962258 | −0.0470094 | −0.0235047 | − | 0.999724i | \(-0.507482\pi\) | ||||
−0.0235047 | + | 0.999724i | \(0.507482\pi\) | |||||||
\(420\) | 0.331061 | 0.0161541 | ||||||||
\(421\) | − | 8.70537i | − | 0.424274i | −0.977240 | − | 0.212137i | \(-0.931958\pi\) | ||
0.977240 | − | 0.212137i | \(-0.0680423\pi\) | |||||||
\(422\) | −13.8837 | −0.675846 | ||||||||
\(423\) | 5.39136 | 0.262137 | ||||||||
\(424\) | − | 28.6013i | − | 1.38900i | ||||||
\(425\) | 2.73616i | 0.132723i | ||||||||
\(426\) | −2.09041 | −0.101281 | ||||||||
\(427\) | −0.753115 | −0.0364458 | ||||||||
\(428\) | 4.47837 | 0.216470 | ||||||||
\(429\) | 1.24502 | + | 0.317162i | 0.0601102 | + | 0.0153127i | ||||
\(430\) | 0.0533246i | 0.00257154i | ||||||||
\(431\) | 23.7218 | 1.14264 | 0.571320 | − | 0.820728i | \(-0.306432\pi\) | ||||
0.571320 | + | 0.820728i | \(0.306432\pi\) | |||||||
\(432\) | − | 0.392144i | − | 0.0188670i | ||||||
\(433\) | 7.71823i | 0.370914i | 0.982652 | + | 0.185457i | \(0.0593766\pi\) | ||||
−0.982652 | + | 0.185457i | \(0.940623\pi\) | |||||||
\(434\) | −0.852261 | −0.0409098 | ||||||||
\(435\) | 2.47066i | 0.118459i | ||||||||
\(436\) | −12.3638 | −0.592119 | ||||||||
\(437\) | −22.4053 | + | 24.0521i | −1.07179 | + | 1.15057i | ||||
\(438\) | 5.71051 | 0.272859 | ||||||||
\(439\) | 16.4495 | 0.785090 | 0.392545 | − | 0.919733i | \(-0.371595\pi\) | ||||
0.392545 | + | 0.919733i | \(0.371595\pi\) | |||||||
\(440\) | 2.30074 | − | 9.03156i | 0.109683 | − | 0.430563i | ||||
\(441\) | 14.8432 | 0.706819 | ||||||||
\(442\) | 0.990029i | 0.0470909i | ||||||||
\(443\) | −8.78802 | −0.417531 | −0.208766 | − | 0.977966i | \(-0.566945\pi\) | ||||
−0.208766 | + | 0.977966i | \(0.566945\pi\) | |||||||
\(444\) | 1.40843 | 0.0668411 | ||||||||
\(445\) | 13.9172i | 0.659739i | ||||||||
\(446\) | 20.5185i | 0.971580i | ||||||||
\(447\) | 16.5351 | 0.782084 | ||||||||
\(448\) | − | 1.35591i | − | 0.0640605i | ||||||
\(449\) | − | 21.1724i | − | 0.999188i | −0.866260 | − | 0.499594i | \(-0.833483\pi\) | ||
0.866260 | − | 0.499594i | \(-0.166517\pi\) | |||||||
\(450\) | −1.85251 | −0.0873282 | ||||||||
\(451\) | 7.97659 | − | 31.3121i | 0.375603 | − | 1.47443i | ||||
\(452\) | 5.15842i | 0.242631i | ||||||||
\(453\) | − | 3.00116i | − | 0.141007i | ||||||
\(454\) | 2.80828 | 0.131799 | ||||||||
\(455\) | 0.119633i | 0.00560850i | ||||||||
\(456\) | 8.28531 | + | 7.71802i | 0.387995 | + | 0.361430i | ||||
\(457\) | − | 17.5917i | − | 0.822905i | −0.911431 | − | 0.411453i | \(-0.865022\pi\) | ||
0.911431 | − | 0.411453i | \(-0.134978\pi\) | |||||||
\(458\) | 12.7587 | 0.596177 | ||||||||
\(459\) | 13.0147 | 0.607476 | ||||||||
\(460\) | −9.45977 | −0.441064 | ||||||||
\(461\) | − | 8.96166i | − | 0.417386i | −0.977981 | − | 0.208693i | \(-0.933079\pi\) | ||
0.977981 | − | 0.208693i | \(-0.0669209\pi\) | |||||||
\(462\) | 0.186576 | − | 0.732403i | 0.00868029 | − | 0.0340745i | ||||
\(463\) | 8.21384 | 0.381729 | 0.190865 | − | 0.981616i | \(-0.438871\pi\) | ||||
0.190865 | + | 0.981616i | \(0.438871\pi\) | |||||||
\(464\) | −0.220339 | −0.0102290 | ||||||||
\(465\) | 3.19602 | 0.148212 | ||||||||
\(466\) | − | 21.9518i | − | 1.01690i | ||||||
\(467\) | 2.60310 | 0.120457 | 0.0602285 | − | 0.998185i | \(-0.480817\pi\) | ||||
0.0602285 | + | 0.998185i | \(0.480817\pi\) | |||||||
\(468\) | 1.12778 | 0.0521315 | ||||||||
\(469\) | −3.19182 | −0.147385 | ||||||||
\(470\) | −2.16984 | −0.100087 | ||||||||
\(471\) | 14.3473i | 0.661087i | ||||||||
\(472\) | − | 23.6236i | − | 1.08737i | ||||||
\(473\) | −0.198484 | − | 0.0505627i | −0.00912630 | − | 0.00232488i | ||||
\(474\) | − | 8.70953i | − | 0.400042i | ||||||
\(475\) | −2.97108 | + | 3.18946i | −0.136323 | + | 0.146343i | ||||
\(476\) | −0.979889 | −0.0449131 | ||||||||
\(477\) | − | 21.8365i | − | 0.999823i | ||||||
\(478\) | − | 23.5792i | − | 1.07849i | ||||||
\(479\) | − | 5.42770i | − | 0.247998i | −0.992282 | − | 0.123999i | \(-0.960428\pi\) | ||
0.992282 | − | 0.123999i | \(-0.0395720\pi\) | |||||||
\(480\) | 5.26123i | 0.240141i | ||||||||
\(481\) | 0.508955i | 0.0232064i | ||||||||
\(482\) | 22.3972 | 1.02016 | ||||||||
\(483\) | −1.99020 | −0.0905573 | ||||||||
\(484\) | 12.1169 | + | 6.60186i | 0.550769 | + | 0.300085i | ||||
\(485\) | 19.2960i | 0.876188i | ||||||||
\(486\) | 13.9491i | 0.632745i | ||||||||
\(487\) | − | 18.0629i | − | 0.818508i | −0.912420 | − | 0.409254i | \(-0.865789\pi\) | ||
0.912420 | − | 0.409254i | \(-0.134211\pi\) | |||||||
\(488\) | − | 7.41294i | − | 0.335568i | ||||||
\(489\) | − | 18.9365i | − | 0.856340i | ||||||
\(490\) | −5.97388 | −0.269872 | ||||||||
\(491\) | − | 3.41626i | − | 0.154174i | −0.997024 | − | 0.0770869i | \(-0.975438\pi\) | ||
0.997024 | − | 0.0770869i | \(-0.0245619\pi\) | |||||||
\(492\) | 11.2976i | 0.509336i | ||||||||
\(493\) | − | 7.31276i | − | 0.329350i | ||||||
\(494\) | −1.07503 | + | 1.15405i | −0.0483680 | + | 0.0519231i | ||||
\(495\) | 1.75656 | − | 6.89539i | 0.0789517 | − | 0.309925i | ||||
\(496\) | 0.285029i | 0.0127982i | ||||||||
\(497\) | 0.747661 | 0.0335372 | ||||||||
\(498\) | 11.5874 | 0.519243 | ||||||||
\(499\) | 24.8994 | 1.11465 | 0.557325 | − | 0.830294i | \(-0.311828\pi\) | ||||
0.557325 | + | 0.830294i | \(0.311828\pi\) | |||||||
\(500\) | −1.25443 | −0.0560997 | ||||||||
\(501\) | 7.44607i | 0.332666i | ||||||||
\(502\) | 22.0157 | 0.982609 | ||||||||
\(503\) | 3.76317i | 0.167792i | 0.996475 | + | 0.0838958i | \(0.0267363\pi\) | ||||
−0.996475 | + | 0.0838958i | \(0.973264\pi\) | |||||||
\(504\) | − | 1.72118i | − | 0.0766674i | ||||||
\(505\) | − | 6.27231i | − | 0.279114i | ||||||
\(506\) | −5.33124 | + | 20.9278i | −0.237002 | + | 0.930353i | ||||
\(507\) | 11.8552i | 0.526508i | ||||||||
\(508\) | −22.9067 | −1.01632 | ||||||||
\(509\) | 20.6837i | 0.916787i | 0.888749 | + | 0.458394i | \(0.151575\pi\) | ||||
−0.888749 | + | 0.458394i | \(0.848425\pi\) | |||||||
\(510\) | −2.18403 | −0.0967103 | ||||||||
\(511\) | −2.04244 | −0.0903521 | ||||||||
\(512\) | −0.932551 | −0.0412133 | ||||||||
\(513\) | 15.1709 | + | 14.1322i | 0.669812 | + | 0.623951i | ||||
\(514\) | − | 2.27168i | − | 0.100199i | ||||||
\(515\) | − | 13.7149i | − | 0.604350i | ||||||
\(516\) | 0.0716143 | 0.00315264 | ||||||||
\(517\) | 2.05745 | − | 8.07654i | 0.0904868 | − | 0.355206i | ||||
\(518\) | 0.299401 | 0.0131549 | ||||||||
\(519\) | − | 12.5049i | − | 0.548905i | ||||||
\(520\) | −1.17756 | −0.0516392 | ||||||||
\(521\) | 33.3317i | 1.46029i | 0.683293 | + | 0.730144i | \(0.260547\pi\) | ||||
−0.683293 | + | 0.730144i | \(0.739453\pi\) | |||||||
\(522\) | 4.95110 | 0.216704 | ||||||||
\(523\) | −36.8461 | −1.61117 | −0.805584 | − | 0.592482i | \(-0.798148\pi\) | ||||
−0.805584 | + | 0.592482i | \(0.798148\pi\) | |||||||
\(524\) | − | 13.8146i | − | 0.603492i | ||||||
\(525\) | −0.263914 | −0.0115181 | ||||||||
\(526\) | 10.0274i | 0.437216i | ||||||||
\(527\) | −9.45972 | −0.412072 | ||||||||
\(528\) | −0.244944 | − | 0.0623980i | −0.0106598 | − | 0.00271553i | ||||
\(529\) | 33.8683 | 1.47253 | ||||||||
\(530\) | 8.78843i | 0.381745i | ||||||||
\(531\) | − | 18.0361i | − | 0.782701i | ||||||
\(532\) | −1.14223 | − | 1.06402i | −0.0495219 | − | 0.0461312i | ||||
\(533\) | −4.08255 | −0.176835 | ||||||||
\(534\) | −11.1088 | −0.480727 | ||||||||
\(535\) | −3.57005 | −0.154347 | ||||||||
\(536\) | − | 31.4172i | − | 1.35702i | ||||||
\(537\) | 14.7624 | 0.637043 | ||||||||
\(538\) | − | 19.6819i | − | 0.848545i | ||||||
\(539\) | 5.66447 | − | 22.2359i | 0.243986 | − | 0.957768i | ||||
\(540\) | 5.96677i | 0.256769i | ||||||||
\(541\) | 33.6821i | 1.44811i | 0.689743 | + | 0.724054i | \(0.257723\pi\) | ||||
−0.689743 | + | 0.724054i | \(0.742277\pi\) | |||||||
\(542\) | 8.07736i | 0.346952i | ||||||||
\(543\) | 20.2887 | 0.870670 | ||||||||
\(544\) | − | 15.5724i | − | 0.667663i | ||||||
\(545\) | 9.85614 | 0.422191 | ||||||||
\(546\) | −0.0954925 | −0.00408670 | ||||||||
\(547\) | 21.0334 | 0.899323 | 0.449662 | − | 0.893199i | \(-0.351545\pi\) | ||||
0.449662 | + | 0.893199i | \(0.351545\pi\) | |||||||
\(548\) | −0.205606 | −0.00878305 | ||||||||
\(549\) | − | 5.65961i | − | 0.241546i | ||||||
\(550\) | −0.706957 | + | 2.77516i | −0.0301447 | + | 0.118333i | ||||
\(551\) | 7.94064 | − | 8.52428i | 0.338282 | − | 0.363147i | ||||
\(552\) | − | 19.5896i | − | 0.833791i | ||||||
\(553\) | 3.11507i | 0.132466i | ||||||||
\(554\) | − | 8.27184i | − | 0.351437i | ||||||
\(555\) | −1.12277 | −0.0476588 | ||||||||
\(556\) | 20.7454i | 0.879799i | ||||||||
\(557\) | 16.2882i | 0.690152i | 0.938575 | + | 0.345076i | \(0.112147\pi\) | ||||
−0.938575 | + | 0.345076i | \(0.887853\pi\) | |||||||
\(558\) | − | 6.40469i | − | 0.271132i | ||||||
\(559\) | 0.0258788i | 0.00109456i | ||||||||
\(560\) | − | 0.0235365i | − | 0.000994598i | ||||||
\(561\) | 2.07091 | − | 8.12935i | 0.0874338 | − | 0.343221i | ||||
\(562\) | −20.1490 | −0.849934 | ||||||||
\(563\) | 9.87561 | 0.416207 | 0.208104 | − | 0.978107i | \(-0.433271\pi\) | ||||
0.208104 | + | 0.978107i | \(0.433271\pi\) | |||||||
\(564\) | 2.91407i | 0.122704i | ||||||||
\(565\) | − | 4.11217i | − | 0.173000i | ||||||
\(566\) | − | 28.1158i | − | 1.18180i | ||||||
\(567\) | − | 0.582175i | − | 0.0244491i | ||||||
\(568\) | 7.35926i | 0.308788i | ||||||||
\(569\) | 34.7858 | 1.45830 | 0.729149 | − | 0.684355i | \(-0.239916\pi\) | ||||
0.729149 | + | 0.684355i | \(0.239916\pi\) | |||||||
\(570\) | −2.54586 | − | 2.37155i | −0.106634 | − | 0.0993331i | ||||
\(571\) | − | 20.2405i | − | 0.847037i | −0.905888 | − | 0.423518i | \(-0.860795\pi\) | ||
0.905888 | − | 0.423518i | \(-0.139205\pi\) | |||||||
\(572\) | 0.430383 | − | 1.68947i | 0.0179952 | − | 0.0706403i | ||||
\(573\) | 13.7776i | 0.575566i | ||||||||
\(574\) | 2.40162i | 0.100242i | ||||||||
\(575\) | 7.54111 | 0.314486 | ||||||||
\(576\) | 10.1896 | 0.424565 | ||||||||
\(577\) | 0.308647 | 0.0128491 | 0.00642456 | − | 0.999979i | \(-0.497955\pi\) | ||||
0.00642456 | + | 0.999979i | \(0.497955\pi\) | |||||||
\(578\) | −8.21453 | −0.341679 | ||||||||
\(579\) | − | 13.2461i | − | 0.550487i | ||||||
\(580\) | 3.35263 | 0.139210 | ||||||||
\(581\) | −4.14438 | −0.171938 | ||||||||
\(582\) | −15.4023 | −0.638445 | ||||||||
\(583\) | −32.7122 | − | 8.33325i | −1.35480 | − | 0.345128i | ||||
\(584\) | − | 20.1038i | − | 0.831900i | ||||||
\(585\) | −0.899038 | −0.0371706 | ||||||||
\(586\) | 18.8862 | 0.780181 | ||||||||
\(587\) | 22.4405 | 0.926218 | 0.463109 | − | 0.886301i | \(-0.346734\pi\) | ||||
0.463109 | + | 0.886301i | \(0.346734\pi\) | |||||||
\(588\) | 8.02286i | 0.330857i | ||||||||
\(589\) | −11.0269 | − | 10.2719i | −0.454357 | − | 0.423247i | ||||
\(590\) | 7.25892i | 0.298845i | ||||||||
\(591\) | −19.7825 | −0.813743 | ||||||||
\(592\) | − | 0.100131i | − | 0.00411536i | ||||||
\(593\) | − | 9.46067i | − | 0.388503i | −0.980952 | − | 0.194252i | \(-0.937772\pi\) | ||
0.980952 | − | 0.194252i | \(-0.0622278\pi\) | |||||||
\(594\) | 13.2002 | + | 3.36269i | 0.541613 | + | 0.137973i | ||||
\(595\) | 0.781144 | 0.0320238 | ||||||||
\(596\) | − | 22.4378i | − | 0.919089i | ||||||
\(597\) | − | 4.95485i | − | 0.202788i | ||||||
\(598\) | 2.72861 | 0.111581 | ||||||||
\(599\) | 1.87763i | 0.0767181i | 0.999264 | + | 0.0383590i | \(0.0122131\pi\) | ||||
−0.999264 | + | 0.0383590i | \(0.987787\pi\) | |||||||
\(600\) | − | 2.59771i | − | 0.106051i | ||||||
\(601\) | −40.6076 | −1.65642 | −0.828210 | − | 0.560418i | \(-0.810640\pi\) | ||||
−0.828210 | + | 0.560418i | \(0.810640\pi\) | |||||||
\(602\) | 0.0152236 | 0.000620468 | ||||||||
\(603\) | − | 23.9863i | − | 0.976800i | ||||||
\(604\) | −4.07252 | −0.165709 | ||||||||
\(605\) | −9.65932 | − | 5.26285i | −0.392707 | − | 0.213965i | ||||
\(606\) | 5.00662 | 0.203380 | ||||||||
\(607\) | 12.7418 | 0.517172 | 0.258586 | − | 0.965988i | \(-0.416743\pi\) | ||||
0.258586 | + | 0.965988i | \(0.416743\pi\) | |||||||
\(608\) | 16.9095 | − | 18.1524i | 0.685771 | − | 0.736176i | ||||
\(609\) | 0.705347 | 0.0285821 | ||||||||
\(610\) | 2.27780i | 0.0922255i | ||||||||
\(611\) | −1.05304 | −0.0426014 | ||||||||
\(612\) | − | 7.36381i | − | 0.297664i | ||||||
\(613\) | 36.8280i | 1.48747i | 0.668475 | + | 0.743734i | \(0.266947\pi\) | ||||
−0.668475 | + | 0.743734i | \(0.733053\pi\) | |||||||
\(614\) | 11.3516 | 0.458115 | ||||||||
\(615\) | − | 9.00620i | − | 0.363165i | ||||||
\(616\) | −2.57842 | − | 0.656837i | −0.103887 | − | 0.0264647i | ||||
\(617\) | −9.39927 | −0.378400 | −0.189200 | − | 0.981939i | \(-0.560590\pi\) | ||||
−0.189200 | + | 0.981939i | \(0.560590\pi\) | |||||||
\(618\) | 10.9474 | 0.440367 | ||||||||
\(619\) | 10.0687 | 0.404695 | 0.202347 | − | 0.979314i | \(-0.435143\pi\) | ||||
0.202347 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(620\) | − | 4.33693i | − | 0.174175i | ||||||
\(621\) | − | 35.8698i | − | 1.43941i | ||||||
\(622\) | 16.7731 | 0.672542 | ||||||||
\(623\) | 3.97322 | 0.159184 | ||||||||
\(624\) | 0.0319363i | 0.00127848i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.5769 | −0.542642 | ||||||||
\(627\) | 11.2413 | − | 7.22744i | 0.448936 | − | 0.288636i | ||||
\(628\) | 19.4689 | 0.776896 | ||||||||
\(629\) | 3.32322 | 0.132505 | ||||||||
\(630\) | 0.528873i | 0.0210708i | ||||||||
\(631\) | −1.63533 | −0.0651013 | −0.0325506 | − | 0.999470i | \(-0.510363\pi\) | ||||
−0.0325506 | + | 0.999470i | \(0.510363\pi\) | |||||||
\(632\) | −30.6618 | −1.21966 | ||||||||
\(633\) | − | 14.8638i | − | 0.590784i | ||||||
\(634\) | − | 2.14366i | − | 0.0851355i | ||||||
\(635\) | 18.2607 | 0.724653 | ||||||||
\(636\) | 11.8028 | 0.468010 | ||||||||
\(637\) | −2.89917 | −0.114869 | ||||||||
\(638\) | 1.88944 | − | 7.41700i | 0.0748037 | − | 0.293642i | ||||
\(639\) | 5.61863i | 0.222270i | ||||||||
\(640\) | 7.28177 | 0.287837 | ||||||||
\(641\) | − | 28.3914i | − | 1.12139i | −0.828022 | − | 0.560696i | \(-0.810534\pi\) | ||
0.828022 | − | 0.560696i | \(-0.189466\pi\) | |||||||
\(642\) | − | 2.84965i | − | 0.112467i | ||||||
\(643\) | 11.0504 | 0.435785 | 0.217892 | − | 0.975973i | \(-0.430082\pi\) | ||||
0.217892 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(644\) | 2.70067i | 0.106421i | ||||||||
\(645\) | −0.0570892 | −0.00224789 | ||||||||
\(646\) | 7.53535 | + | 7.01941i | 0.296474 | + | 0.276175i | ||||
\(647\) | −0.304025 | −0.0119525 | −0.00597623 | − | 0.999982i | \(-0.501902\pi\) | ||||
−0.00597623 | + | 0.999982i | \(0.501902\pi\) | |||||||
\(648\) | 5.73038 | 0.225110 | ||||||||
\(649\) | −27.0191 | − | 6.88296i | −1.06059 | − | 0.270180i | ||||
\(650\) | 0.361832 | 0.0141922 | ||||||||
\(651\) | − | 0.912429i | − | 0.0357609i | ||||||
\(652\) | −25.6965 | −1.00635 | ||||||||
\(653\) | −33.1227 | −1.29619 | −0.648096 | − | 0.761559i | \(-0.724434\pi\) | ||||
−0.648096 | + | 0.761559i | \(0.724434\pi\) | |||||||
\(654\) | 7.86726i | 0.307634i | ||||||||
\(655\) | 11.0127i | 0.430300i | ||||||||
\(656\) | 0.803195 | 0.0313595 | ||||||||
\(657\) | − | 15.3488i | − | 0.598813i | ||||||
\(658\) | 0.619466i | 0.0241493i | ||||||||
\(659\) | 7.22187 | 0.281324 | 0.140662 | − | 0.990058i | \(-0.455077\pi\) | ||||
0.140662 | + | 0.990058i | \(0.455077\pi\) | |||||||
\(660\) | 3.72701 | + | 0.949435i | 0.145074 | + | 0.0369567i | ||||
\(661\) | 33.4062i | 1.29935i | 0.760213 | + | 0.649674i | \(0.225095\pi\) | ||||
−0.760213 | + | 0.649674i | \(0.774905\pi\) | |||||||
\(662\) | 8.94766i | 0.347761i | ||||||||
\(663\) | −1.05992 | −0.0411640 | ||||||||
\(664\) | − | 40.7933i | − | 1.58309i | ||||||
\(665\) | 0.910558 | + | 0.848213i | 0.0353099 | + | 0.0328923i | ||||
\(666\) | 2.24998i | 0.0871849i | ||||||||
\(667\) | −20.1547 | −0.780392 | ||||||||
\(668\) | 10.1042 | 0.390942 | ||||||||
\(669\) | −21.9671 | −0.849298 | ||||||||
\(670\) | 9.65369i | 0.372954i | ||||||||
\(671\) | −8.47840 | − | 2.15983i | −0.327305 | − | 0.0833791i | ||||
\(672\) | 1.50203 | 0.0579420 | ||||||||
\(673\) | 18.7855 | 0.724129 | 0.362064 | − | 0.932153i | \(-0.382072\pi\) | ||||
0.362064 | + | 0.932153i | \(0.382072\pi\) | |||||||
\(674\) | 6.04512 | 0.232849 | ||||||||
\(675\) | − | 4.75657i | − | 0.183081i | ||||||
\(676\) | 16.0873 | 0.618741 | ||||||||
\(677\) | 36.0219 | 1.38444 | 0.692218 | − | 0.721689i | \(-0.256634\pi\) | ||||
0.692218 | + | 0.721689i | \(0.256634\pi\) | |||||||
\(678\) | 3.28237 | 0.126059 | ||||||||
\(679\) | 5.50882 | 0.211409 | ||||||||
\(680\) | 7.68884i | 0.294853i | ||||||||
\(681\) | 3.00655i | 0.115211i | ||||||||
\(682\) | −9.59456 | − | 2.44416i | −0.367395 | − | 0.0935918i | ||||
\(683\) | 22.1505i | 0.847564i | 0.905764 | + | 0.423782i | \(0.139298\pi\) | ||||
−0.905764 | + | 0.423782i | \(0.860702\pi\) | |||||||
\(684\) | 7.99606 | − | 8.58379i | 0.305737 | − | 0.328209i | ||||
\(685\) | 0.163904 | 0.00626246 | ||||||||
\(686\) | 3.43105i | 0.130998i | ||||||||
\(687\) | 13.6595i | 0.521142i | ||||||||
\(688\) | − | 0.00509136i | − | 0.000194106i | ||||||
\(689\) | 4.26509i | 0.162487i | ||||||||
\(690\) | 6.01938i | 0.229154i | ||||||||
\(691\) | 46.9200 | 1.78492 | 0.892460 | − | 0.451126i | \(-0.148978\pi\) | ||||
0.892460 | + | 0.451126i | \(0.148978\pi\) | |||||||
\(692\) | −16.9689 | −0.645062 | ||||||||
\(693\) | −1.96856 | − | 0.501481i | −0.0747795 | − | 0.0190497i | ||||
\(694\) | − | 7.19458i | − | 0.273103i | ||||||
\(695\) | − | 16.5377i | − | 0.627311i | ||||||
\(696\) | 6.94276i | 0.263164i | ||||||||
\(697\) | 26.6570i | 1.00970i | ||||||||
\(698\) | 9.66956i | 0.365998i | ||||||||
\(699\) | 23.5015 | 0.888909 | ||||||||
\(700\) | 0.358126i | 0.0135359i | ||||||||
\(701\) | 0.369565i | 0.0139583i | 0.999976 | + | 0.00697914i | \(0.00222155\pi\) | ||||
−0.999976 | + | 0.00697914i | \(0.997778\pi\) | |||||||
\(702\) | − | 1.72108i | − | 0.0649580i | ||||||
\(703\) | 3.87378 | + | 3.60855i | 0.146102 | + | 0.136099i | ||||
\(704\) | 3.88855 | − | 15.2645i | 0.146555 | − | 0.575302i | ||||
\(705\) | − | 2.32303i | − | 0.0874902i | ||||||
\(706\) | 22.3214 | 0.840076 | ||||||||
\(707\) | −1.79068 | −0.0673455 | ||||||||
\(708\) | 9.74865 | 0.366377 | ||||||||
\(709\) | −24.3967 | −0.916238 | −0.458119 | − | 0.888891i | \(-0.651477\pi\) | ||||
−0.458119 | + | 0.888891i | \(0.651477\pi\) | |||||||
\(710\) | − | 2.26131i | − | 0.0848653i | ||||||
\(711\) | −23.4096 | −0.877928 | ||||||||
\(712\) | 39.1086i | 1.46566i | ||||||||
\(713\) | 26.0719i | 0.976399i | ||||||||
\(714\) | 0.623517i | 0.0233345i | ||||||||
\(715\) | −0.343091 | + | 1.34681i | −0.0128309 | + | 0.0503677i | ||||
\(716\) | − | 20.0323i | − | 0.748640i | ||||||
\(717\) | 25.2439 | 0.942750 | ||||||||
\(718\) | − | 10.3775i | − | 0.387284i | ||||||
\(719\) | −47.3952 | −1.76754 | −0.883771 | − | 0.467920i | \(-0.845004\pi\) | ||||
−0.883771 | + | 0.467920i | \(0.845004\pi\) | |||||||
\(720\) | 0.176875 | 0.00659175 | ||||||||
\(721\) | −3.91546 | −0.145819 | ||||||||
\(722\) | 1.16165 | + | 16.3647i | 0.0432320 | + | 0.609030i | ||||
\(723\) | 23.9784i | 0.891766i | ||||||||
\(724\) | − | 27.5313i | − | 1.02319i | ||||||
\(725\) | −2.67264 | −0.0992594 | ||||||||
\(726\) | 4.20086 | − | 7.71016i | 0.155908 | − | 0.286151i | ||||
\(727\) | −7.90775 | −0.293282 | −0.146641 | − | 0.989190i | \(-0.546846\pi\) | ||||
−0.146641 | + | 0.989190i | \(0.546846\pi\) | |||||||
\(728\) | 0.336180i | 0.0124597i | ||||||||
\(729\) | −8.81627 | −0.326529 | ||||||||
\(730\) | 6.17736i | 0.228635i | ||||||||
\(731\) | 0.168975 | 0.00624978 | ||||||||
\(732\) | 3.05906 | 0.113066 | ||||||||
\(733\) | 32.5236i | 1.20129i | 0.799518 | + | 0.600643i | \(0.205089\pi\) | ||||
−0.799518 | + | 0.600643i | \(0.794911\pi\) | |||||||
\(734\) | −2.86405 | −0.105714 | ||||||||
\(735\) | − | 6.39563i | − | 0.235906i | ||||||
\(736\) | −42.9191 | −1.58202 | ||||||||
\(737\) | −35.9328 | − | 9.15369i | −1.32360 | − | 0.337180i | ||||
\(738\) | −18.0481 | −0.664358 | ||||||||
\(739\) | 46.6996i | 1.71787i | 0.512082 | + | 0.858937i | \(0.328875\pi\) | ||||
−0.512082 | + | 0.858937i | \(0.671125\pi\) | |||||||
\(740\) | 1.52357i | 0.0560076i | ||||||||
\(741\) | −1.23552 | − | 1.15093i | −0.0453881 | − | 0.0422804i | ||||
\(742\) | 2.50901 | 0.0921085 | ||||||||
\(743\) | −5.69888 | −0.209072 | −0.104536 | − | 0.994521i | \(-0.533336\pi\) | ||||
−0.104536 | + | 0.994521i | \(0.533336\pi\) | |||||||
\(744\) | 8.98108 | 0.329262 | ||||||||
\(745\) | 17.8869i | 0.655326i | ||||||||
\(746\) | 16.3728 | 0.599452 | ||||||||
\(747\) | − | 31.1447i | − | 1.13953i | ||||||
\(748\) | −11.0314 | − | 2.81018i | −0.403347 | − | 0.102750i | ||||
\(749\) | 1.01921i | 0.0372412i | ||||||||
\(750\) | 0.798209i | 0.0291465i | ||||||||
\(751\) | 33.8150i | 1.23393i | 0.786992 | + | 0.616964i | \(0.211638\pi\) | ||||
−0.786992 | + | 0.616964i | \(0.788362\pi\) | |||||||
\(752\) | 0.207173 | 0.00755483 | ||||||||
\(753\) | 23.5700i | 0.858938i | ||||||||
\(754\) | −0.967047 | −0.0352178 | ||||||||
\(755\) | 3.24652 | 0.118153 | ||||||||
\(756\) | 1.70345 | 0.0619540 | ||||||||
\(757\) | −16.9966 | −0.617753 | −0.308876 | − | 0.951102i | \(-0.599953\pi\) | ||||
−0.308876 | + | 0.951102i | \(0.599953\pi\) | |||||||
\(758\) | 14.5196i | 0.527375i | ||||||||
\(759\) | −22.4053 | − | 5.70762i | −0.813259 | − | 0.207173i | ||||
\(760\) | −8.34900 | + | 8.96266i | −0.302850 | + | 0.325110i | ||||
\(761\) | − | 9.58612i | − | 0.347497i | −0.984790 | − | 0.173748i | \(-0.944412\pi\) | ||
0.984790 | − | 0.173748i | \(-0.0555879\pi\) | |||||||
\(762\) | 14.5759i | 0.528027i | ||||||||
\(763\) | − | 2.81383i | − | 0.101867i | ||||||
\(764\) | 18.6959 | 0.676394 | ||||||||
\(765\) | 5.87025i | 0.212240i | ||||||||
\(766\) | − | 20.2104i | − | 0.730233i | ||||||
\(767\) | 3.52281i | 0.127201i | ||||||||
\(768\) | 14.5933i | 0.526591i | ||||||||
\(769\) | − | 1.36265i | − | 0.0491385i | −0.999698 | − | 0.0245692i | \(-0.992179\pi\) | ||
0.999698 | − | 0.0245692i | \(-0.00782141\pi\) | |||||||
\(770\) | 0.792279 | + | 0.201829i | 0.0285518 | + | 0.00727341i | ||||
\(771\) | 2.43205 | 0.0875883 | ||||||||
\(772\) | −17.9746 | −0.646921 | ||||||||
\(773\) | 20.3558i | 0.732148i | 0.930586 | + | 0.366074i | \(0.119298\pi\) | ||||
−0.930586 | + | 0.366074i | \(0.880702\pi\) | |||||||
\(774\) | 0.114405i | 0.00411219i | ||||||||
\(775\) | 3.45730i | 0.124190i | ||||||||
\(776\) | 54.2235i | 1.94651i | ||||||||
\(777\) | 0.320538i | 0.0114992i | ||||||||
\(778\) | 9.43577 | 0.338289 | ||||||||
\(779\) | −28.9457 | + | 31.0733i | −1.03709 | + | 1.11332i | ||||
\(780\) | − | 0.485936i | − | 0.0173993i | ||||||
\(781\) | 8.41700 | + | 2.14419i | 0.301184 | + | 0.0767250i | ||||
\(782\) | − | 17.8164i | − | 0.637115i | ||||||
\(783\) | 12.7126i | 0.454312i | ||||||||
\(784\) | 0.570378 | 0.0203706 | ||||||||
\(785\) | −15.5202 | −0.553939 | ||||||||
\(786\) | −8.79040 | −0.313543 | ||||||||
\(787\) | −21.6286 | −0.770975 | −0.385487 | − | 0.922713i | \(-0.625967\pi\) | ||||
−0.385487 | + | 0.922713i | \(0.625967\pi\) | |||||||
\(788\) | 26.8445i | 0.956295i | ||||||||
\(789\) | −10.7353 | −0.382189 | ||||||||
\(790\) | 9.42156 | 0.335204 | ||||||||
\(791\) | −1.17398 | −0.0417420 | ||||||||
\(792\) | 4.93609 | − | 19.3766i | 0.175396 | − | 0.688519i | ||||
\(793\) | 1.10543i | 0.0392551i | ||||||||
\(794\) | −9.80941 | −0.348123 | ||||||||
\(795\) | −9.40888 | −0.333699 | ||||||||
\(796\) | −6.72363 | −0.238313 | ||||||||
\(797\) | − | 16.9815i | − | 0.601516i | −0.953700 | − | 0.300758i | \(-0.902760\pi\) | ||
0.953700 | − | 0.300758i | \(-0.0972396\pi\) | |||||||
\(798\) | −0.677052 | + | 0.726816i | −0.0239674 | + | 0.0257290i | ||||
\(799\) | 6.87580i | 0.243248i | ||||||||
\(800\) | −5.69136 | −0.201220 | ||||||||
\(801\) | 29.8585i | 1.05500i | ||||||||
\(802\) | − | 30.6097i | − | 1.08087i | ||||||
\(803\) | −22.9933 | − | 5.85742i | −0.811416 | − | 0.206704i | ||||
\(804\) | 12.9648 | 0.457233 | ||||||||
\(805\) | − | 2.15291i | − | 0.0758800i | ||||||
\(806\) | 1.25096i | 0.0440633i | ||||||||
\(807\) | 21.0714 | 0.741748 | ||||||||
\(808\) | − | 17.6257i | − | 0.620071i | ||||||
\(809\) | 27.8406i | 0.978825i | 0.872052 | + | 0.489412i | \(0.162789\pi\) | ||||
−0.872052 | + | 0.489412i | \(0.837211\pi\) | |||||||
\(810\) | −1.76079 | −0.0618680 | ||||||||
\(811\) | 7.67428 | 0.269481 | 0.134740 | − | 0.990881i | \(-0.456980\pi\) | ||||
0.134740 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(812\) | − | 0.957142i | − | 0.0335891i | ||||||
\(813\) | −8.64762 | −0.303285 | ||||||||
\(814\) | 3.37059 | + | 0.858639i | 0.118139 | + | 0.0300953i | ||||
\(815\) | 20.4847 | 0.717546 | ||||||||
\(816\) | 0.208528 | 0.00729993 | ||||||||
\(817\) | 0.196970 | + | 0.183484i | 0.00689110 | + | 0.00641928i | ||||
\(818\) | −12.9801 | −0.453839 | ||||||||
\(819\) | 0.256666i | 0.00896863i | ||||||||
\(820\) | −12.2212 | −0.426784 | ||||||||
\(821\) | − | 43.8616i | − | 1.53078i | −0.643565 | − | 0.765391i | \(-0.722546\pi\) | ||
0.643565 | − | 0.765391i | \(-0.277454\pi\) | |||||||
\(822\) | 0.130830i | 0.00456322i | ||||||||
\(823\) | −20.6693 | −0.720487 | −0.360243 | − | 0.932858i | \(-0.617306\pi\) | ||||
−0.360243 | + | 0.932858i | \(0.617306\pi\) | |||||||
\(824\) | − | 38.5400i | − | 1.34261i | ||||||
\(825\) | −2.97108 | − | 0.756867i | −0.103440 | − | 0.0263507i | ||||
\(826\) | 2.07235 | 0.0721062 | ||||||||
\(827\) | −46.7287 | −1.62492 | −0.812458 | − | 0.583020i | \(-0.801871\pi\) | ||||
−0.812458 | + | 0.583020i | \(0.801871\pi\) | |||||||
\(828\) | −20.2954 | −0.705312 | ||||||||
\(829\) | 3.18720i | 0.110696i | 0.998467 | + | 0.0553480i | \(0.0176268\pi\) | ||||
−0.998467 | + | 0.0553480i | \(0.982373\pi\) | |||||||
\(830\) | 12.5347i | 0.435086i | ||||||||
\(831\) | 8.85583 | 0.307205 | ||||||||
\(832\) | −1.99022 | −0.0689985 | ||||||||
\(833\) | 18.9301i | 0.655889i | ||||||||
\(834\) | 13.2006 | 0.457098 | ||||||||
\(835\) | −8.05481 | −0.278748 | ||||||||
\(836\) | −9.80750 | − | 15.2543i | −0.339199 | − | 0.527580i | ||||
\(837\) | 16.4449 | 0.568419 | ||||||||
\(838\) | 0.830877 | 0.0287022 | ||||||||
\(839\) | 26.5411i | 0.916301i | 0.888875 | + | 0.458151i | \(0.151488\pi\) | ||||
−0.888875 | + | 0.458151i | \(0.848512\pi\) | |||||||
\(840\) | −0.741620 | −0.0255883 | ||||||||
\(841\) | −21.8570 | −0.753689 | ||||||||
\(842\) | 7.51679i | 0.259046i | ||||||||
\(843\) | − | 21.5715i | − | 0.742962i | ||||||
\(844\) | −20.1699 | −0.694277 | ||||||||
\(845\) | −12.8244 | −0.441173 | ||||||||
\(846\) | −4.65525 | −0.160051 | ||||||||
\(847\) | −1.50249 | + | 2.75763i | −0.0516261 | + | 0.0947535i | ||||
\(848\) | − | 0.839107i | − | 0.0288151i | ||||||
\(849\) | 30.1008 | 1.03306 | ||||||||
\(850\) | − | 2.36258i | − | 0.0810357i | ||||||
\(851\) | − | 9.15910i | − | 0.313970i | ||||||
\(852\) | −3.03691 | −0.104043 | ||||||||
\(853\) | − | 9.53476i | − | 0.326464i | −0.986588 | − | 0.163232i | \(-0.947808\pi\) | ||
0.986588 | − | 0.163232i | \(-0.0521919\pi\) | |||||||
\(854\) | 0.650288 | 0.0222524 | ||||||||
\(855\) | −6.37427 | + | 6.84279i | −0.217996 | + | 0.234019i | ||||
\(856\) | −10.0322 | −0.342892 | ||||||||
\(857\) | 48.2839 | 1.64934 | 0.824672 | − | 0.565611i | \(-0.191359\pi\) | ||||
0.824672 | + | 0.565611i | \(0.191359\pi\) | |||||||
\(858\) | −1.07503 | − | 0.273859i | −0.0367010 | − | 0.00934939i | ||||
\(859\) | 3.97883 | 0.135756 | 0.0678780 | − | 0.997694i | \(-0.478377\pi\) | ||||
0.0678780 | + | 0.997694i | \(0.478377\pi\) | |||||||
\(860\) | 0.0774690i | 0.00264167i | ||||||||
\(861\) | −2.57118 | −0.0876254 | ||||||||
\(862\) | −20.4830 | −0.697653 | ||||||||
\(863\) | − | 13.3069i | − | 0.452973i | −0.974014 | − | 0.226486i | \(-0.927276\pi\) | ||
0.974014 | − | 0.226486i | \(-0.0727239\pi\) | |||||||
\(864\) | 27.0714i | 0.920986i | ||||||||
\(865\) | 13.5272 | 0.459940 | ||||||||
\(866\) | − | 6.66442i | − | 0.226466i | ||||||
\(867\) | − | 8.79447i | − | 0.298676i | ||||||
\(868\) | −1.23815 | −0.0420255 | ||||||||
\(869\) | −8.93359 | + | 35.0688i | −0.303051 | + | 1.18963i | ||||
\(870\) | − | 2.13333i | − | 0.0723265i | ||||||
\(871\) | 4.68501i | 0.158745i | ||||||||
\(872\) | 27.6966 | 0.937925 | ||||||||
\(873\) | 41.3984i | 1.40112i | ||||||||
\(874\) | 19.3462 | − | 20.7681i | 0.654394 | − | 0.702493i | ||||
\(875\) | − | 0.285490i | − | 0.00965131i | ||||||
\(876\) | 8.29613 | 0.280300 | ||||||||
\(877\) | −2.91229 | −0.0983411 | −0.0491706 | − | 0.998790i | \(-0.515658\pi\) | ||||
−0.0491706 | + | 0.998790i | \(0.515658\pi\) | |||||||
\(878\) | −14.2035 | −0.479346 | ||||||||
\(879\) | 20.2195i | 0.681988i | ||||||||
\(880\) | 0.0674993 | − | 0.264968i | 0.00227540 | − | 0.00893209i | ||||
\(881\) | −4.59051 | −0.154658 | −0.0773291 | − | 0.997006i | \(-0.524639\pi\) | ||||
−0.0773291 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(882\) | −12.8166 | −0.431557 | ||||||||
\(883\) | −3.09847 | −0.104272 | −0.0521360 | − | 0.998640i | \(-0.516603\pi\) | ||||
−0.0521360 | + | 0.998640i | \(0.516603\pi\) | |||||||
\(884\) | 1.43830i | 0.0483752i | ||||||||
\(885\) | −7.77140 | −0.261233 | ||||||||
\(886\) | 7.58815 | 0.254929 | ||||||||
\(887\) | −53.9299 | −1.81079 | −0.905395 | − | 0.424571i | \(-0.860425\pi\) | ||||
−0.905395 | + | 0.424571i | \(0.860425\pi\) | |||||||
\(888\) | −3.15507 | −0.105877 | ||||||||
\(889\) | − | 5.21324i | − | 0.174846i | ||||||
\(890\) | − | 12.0170i | − | 0.402812i | ||||||
\(891\) | 1.66960 | − | 6.55400i | 0.0559336 | − | 0.219567i | ||||
\(892\) | 29.8089i | 0.998077i | ||||||||
\(893\) | −7.46616 | + | 8.01493i | −0.249845 | + | 0.268209i | ||||
\(894\) | −14.2775 | −0.477511 | ||||||||
\(895\) | 15.9692i | 0.533793i | ||||||||
\(896\) | − | 2.07887i | − | 0.0694501i | ||||||
\(897\) | 2.92125i | 0.0975377i | ||||||||
\(898\) | 18.2816i | 0.610066i | ||||||||
\(899\) | − | 9.24012i | − | 0.308175i | ||||||
\(900\) | −2.69130 | −0.0897099 | ||||||||
\(901\) | 27.8489 | 0.927780 | ||||||||
\(902\) | −6.88751 | + | 27.0369i | −0.229329 | + | 0.900232i | ||||
\(903\) | 0.0162984i | 0.000542376i | ||||||||
\(904\) | − | 11.5555i | − | 0.384332i | ||||||
\(905\) | 21.9473i | 0.729554i | ||||||||
\(906\) | 2.59140i | 0.0860936i | ||||||||
\(907\) | 2.40179i | 0.0797502i | 0.999205 | + | 0.0398751i | \(0.0126960\pi\) | ||||
−0.999205 | + | 0.0398751i | \(0.987304\pi\) | |||||||
\(908\) | 4.07982 | 0.135394 | ||||||||
\(909\) | − | 13.4569i | − | 0.446336i | ||||||
\(910\) | − | 0.103299i | − | 0.00342434i | ||||||
\(911\) | 5.69493i | 0.188681i | 0.995540 | + | 0.0943407i | \(0.0300743\pi\) | ||||
−0.995540 | + | 0.0943407i | \(0.969926\pi\) | |||||||
\(912\) | 0.243075 | + | 0.226432i | 0.00804902 | + | 0.00749791i | ||||
\(913\) | −46.6565 | − | 11.8855i | −1.54410 | − | 0.393352i | ||||
\(914\) | 15.1898i | 0.502435i | ||||||||
\(915\) | −2.43861 | −0.0806180 | ||||||||
\(916\) | 18.5357 | 0.612436 | ||||||||
\(917\) | 3.14400 | 0.103824 | ||||||||
\(918\) | −11.2378 | −0.370902 | ||||||||
\(919\) | − | 41.7750i | − | 1.37803i | −0.724747 | − | 0.689015i | \(-0.758044\pi\) | ||
0.724747 | − | 0.689015i | \(-0.241956\pi\) | |||||||
\(920\) | 21.1912 | 0.698652 | ||||||||
\(921\) | 12.1531i | 0.400457i | ||||||||
\(922\) | 7.73808i | 0.254840i | ||||||||
\(923\) | − | 1.09743i | − | 0.0361223i | ||||||
\(924\) | 0.271054 | − | 1.06402i | 0.00891702 | − | 0.0350038i | ||||
\(925\) | − | 1.21456i | − | 0.0399344i | ||||||
\(926\) | −7.09237 | −0.233070 | ||||||||
\(927\) | − | 29.4245i | − | 0.966426i | ||||||
\(928\) | 15.2110 | 0.499324 | ||||||||
\(929\) | −40.9476 | −1.34345 | −0.671723 | − | 0.740802i | \(-0.734446\pi\) | ||||
−0.671723 | + | 0.740802i | \(0.734446\pi\) | |||||||
\(930\) | −2.75965 | −0.0904925 | ||||||||
\(931\) | −20.5554 | + | 22.0663i | −0.673677 | + | 0.723193i | ||||
\(932\) | − | 31.8911i | − | 1.04463i | ||||||
\(933\) | 17.9573i | 0.587896i | ||||||||
\(934\) | −2.24769 | −0.0735466 | ||||||||
\(935\) | 8.79395 | + | 2.24021i | 0.287593 | + | 0.0732627i | ||||
\(936\) | −2.52637 | −0.0825771 | ||||||||
\(937\) | 11.8360i | 0.386666i | 0.981133 | + | 0.193333i | \(0.0619298\pi\) | ||||
−0.981133 | + | 0.193333i | \(0.938070\pi\) | |||||||
\(938\) | 2.75603 | 0.0899875 | ||||||||
\(939\) | − | 14.5354i | − | 0.474345i | ||||||
\(940\) | −3.15230 | −0.102817 | ||||||||
\(941\) | 8.40698 | 0.274060 | 0.137030 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137030 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(942\) | − | 12.3884i | − | 0.403635i | ||||||
\(943\) | 73.4691 | 2.39248 | ||||||||
\(944\) | − | 0.693072i | − | 0.0225576i | ||||||
\(945\) | −1.35795 | −0.0441742 | ||||||||
\(946\) | 0.171384 | + | 0.0436592i | 0.00557218 | + | 0.00141948i | ||||
\(947\) | 12.2038 | 0.396569 | 0.198285 | − | 0.980144i | \(-0.436463\pi\) | ||||
0.198285 | + | 0.980144i | \(0.436463\pi\) | |||||||
\(948\) | − | 12.6530i | − | 0.410952i | ||||||
\(949\) | 2.99792i | 0.0973166i | ||||||||
\(950\) | 2.56543 | − | 2.75399i | 0.0832335 | − | 0.0893512i | ||||
\(951\) | 2.29500 | 0.0744204 | ||||||||
\(952\) | 2.19508 | 0.0711430 | ||||||||
\(953\) | 37.8910 | 1.22741 | 0.613706 | − | 0.789535i | \(-0.289678\pi\) | ||||
0.613706 | + | 0.789535i | \(0.289678\pi\) | |||||||
\(954\) | 18.8550i | 0.610454i | ||||||||
\(955\) | −14.9039 | −0.482280 | ||||||||
\(956\) | − | 34.2554i | − | 1.10790i | ||||||
\(957\) | 7.94064 | + | 2.02283i | 0.256684 | + | 0.0653889i | ||||
\(958\) | 4.68663i | 0.151418i | ||||||||
\(959\) | − | 0.0467930i | − | 0.00151102i | ||||||
\(960\) | − | 4.39047i | − | 0.141702i | ||||||
\(961\) | 19.0471 | 0.614422 | ||||||||
\(962\) | − | 0.439465i | − | 0.0141689i | ||||||
\(963\) | −7.65933 | −0.246818 | ||||||||
\(964\) | 32.5382 | 1.04799 | ||||||||
\(965\) | 14.3290 | 0.461265 | ||||||||
\(966\) | 1.71847 | 0.0552909 | ||||||||
\(967\) | 14.2006i | 0.456660i | 0.973584 | + | 0.228330i | \(0.0733264\pi\) | ||||
−0.973584 | + | 0.228330i | \(0.926674\pi\) | |||||||
\(968\) | −27.1435 | − | 14.7891i | −0.872425 | − | 0.475338i | ||||
\(969\) | −7.51498 | + | 8.06734i | −0.241416 | + | 0.259160i | ||||
\(970\) | − | 16.6615i | − | 0.534967i | ||||||
\(971\) | 16.5201i | 0.530155i | 0.964227 | + | 0.265077i | \(0.0853975\pi\) | ||||
−0.964227 | + | 0.265077i | \(0.914602\pi\) | |||||||
\(972\) | 20.2651i | 0.650002i | ||||||||
\(973\) | −4.72134 | −0.151359 | ||||||||
\(974\) | 15.5967i | 0.499750i | ||||||||
\(975\) | 0.387377i | 0.0124060i | ||||||||
\(976\) | − | 0.217481i | − | 0.00696141i | ||||||
\(977\) | − | 50.8851i | − | 1.62796i | −0.580893 | − | 0.813980i | \(-0.697297\pi\) | ||
0.580893 | − | 0.813980i | \(-0.302703\pi\) | |||||||
\(978\) | 16.3511i | 0.522849i | ||||||||
\(979\) | 44.7296 | + | 11.3946i | 1.42956 | + | 0.364174i | ||||
\(980\) | −8.67875 | −0.277232 | ||||||||
\(981\) | 21.1457 | 0.675132 | ||||||||
\(982\) | 2.94983i | 0.0941327i | ||||||||
\(983\) | 49.9366i | 1.59273i | 0.604817 | + | 0.796365i | \(0.293246\pi\) | ||||
−0.604817 | + | 0.796365i | \(0.706754\pi\) | |||||||
\(984\) | − | 25.3082i | − | 0.806795i | ||||||
\(985\) | − | 21.3998i | − | 0.681854i | ||||||
\(986\) | 6.31432i | 0.201089i | ||||||||
\(987\) | −0.663200 | −0.0211099 | ||||||||
\(988\) | −1.56179 | + | 1.67658i | −0.0496871 | + | 0.0533392i | ||||
\(989\) | − | 0.465712i | − | 0.0148088i | ||||||
\(990\) | −1.51673 | + | 5.95393i | −0.0482049 | + | 0.189228i | ||||
\(991\) | − | 40.8792i | − | 1.29857i | −0.760545 | − | 0.649285i | \(-0.775068\pi\) | ||
0.760545 | − | 0.649285i | \(-0.224932\pi\) | |||||||
\(992\) | − | 19.6767i | − | 0.624737i | ||||||
\(993\) | −9.57936 | −0.303992 | ||||||||
\(994\) | −0.645579 | −0.0204765 | ||||||||
\(995\) | 5.35992 | 0.169921 | ||||||||
\(996\) | 16.8340 | 0.533404 | ||||||||
\(997\) | 31.0466i | 0.983257i | 0.870805 | + | 0.491629i | \(0.163598\pi\) | ||||
−0.870805 | + | 0.491629i | \(0.836402\pi\) | |||||||
\(998\) | −21.4998 | −0.680564 | ||||||||
\(999\) | −5.77713 | −0.182780 |
(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.b.626.15 | ✓ | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.b.626.25 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.b.626.26 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.b.626.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.b.626.15 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.b.626.16 | yes | 40 | 209.208 | even | 2 | inner | |
1045.2.f.b.626.25 | yes | 40 | 11.10 | odd | 2 | inner | |
1045.2.f.b.626.26 | yes | 40 | 19.18 | odd | 2 | inner |