Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.8 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.a.367.8 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.57090 | − | 1.59131i | −0.702527 | − | 0.711657i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.37926 | − | 1.37926i | −0.521312 | − | 0.521312i | 0.396656 | − | 0.917967i | \(-0.370171\pi\) |
−0.917967 | + | 0.396656i | \(0.870171\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −2.23602 | − | 0.0144369i | −0.707092 | − | 0.00456536i | ||||
\(11\) | − | 0.0288739i | − | 0.00870580i | −0.999991 | − | 0.00435290i | \(-0.998614\pi\) | ||
0.999991 | − | 0.00435290i | \(-0.00138558\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 0.711585 | + | 0.711585i | 0.197358 | + | 0.197358i | 0.798866 | − | 0.601508i | \(-0.205433\pi\) |
−0.601508 | + | 0.798866i | \(0.705433\pi\) | |||||||
\(14\) | −1.95057 | −0.521312 | ||||||||
\(15\) | −0.0144369 | + | 2.23602i | −0.00372760 | + | 0.577338i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.438634 | − | 0.438634i | −0.106384 | − | 0.106384i | 0.651911 | − | 0.758295i | \(-0.273968\pi\) |
−0.758295 | + | 0.651911i | \(0.773968\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | −7.23057 | −1.65881 | −0.829403 | − | 0.558651i | \(-0.811319\pi\) | ||||
−0.829403 | + | 0.558651i | \(0.811319\pi\) | |||||||
\(20\) | −1.59131 | + | 1.57090i | −0.355829 | + | 0.351263i | ||||
\(21\) | 1.95057i | 0.425649i | ||||||||
\(22\) | −0.0204169 | − | 0.0204169i | −0.00435290 | − | 0.00435290i | ||||
\(23\) | 3.06679 | + | 3.68711i | 0.639470 | + | 0.768816i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −0.0645626 | + | 4.99958i | −0.0129125 | + | 0.999917i | ||||
\(26\) | 1.00633 | 0.197358 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −1.37926 | + | 1.37926i | −0.260656 | + | 0.260656i | ||||
\(29\) | − | 3.97284i | − | 0.737738i | −0.929481 | − | 0.368869i | \(-0.879745\pi\) | ||
0.929481 | − | 0.368869i | \(-0.120255\pi\) | |||||||
\(30\) | 1.57090 | + | 1.59131i | 0.286805 | + | 0.290533i | ||||
\(31\) | −5.20915 | −0.935591 | −0.467795 | − | 0.883837i | \(-0.654952\pi\) | ||||
−0.467795 | + | 0.883837i | \(0.654952\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −0.0204169 | + | 0.0204169i | −0.00355413 | + | 0.00355413i | ||||
\(34\) | −0.620322 | −0.106384 | ||||||||
\(35\) | −0.0281603 | + | 4.36152i | −0.00475995 | + | 0.737231i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.46265 | + | 1.46265i | 0.240457 | + | 0.240457i | 0.817039 | − | 0.576582i | \(-0.195614\pi\) |
−0.576582 | + | 0.817039i | \(0.695614\pi\) | |||||||
\(38\) | −5.11278 | + | 5.11278i | −0.829403 | + | 0.829403i | ||||
\(39\) | − | 1.00633i | − | 0.161142i | ||||||
\(40\) | −0.0144369 | + | 2.23602i | −0.00228268 | + | 0.353546i | ||||
\(41\) | −7.17074 | −1.11988 | −0.559941 | − | 0.828533i | \(-0.689176\pi\) | ||||
−0.559941 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(42\) | 1.37926 | + | 1.37926i | 0.212825 | + | 0.212825i | ||||
\(43\) | −5.83089 | + | 5.83089i | −0.889202 | + | 0.889202i | −0.994446 | − | 0.105244i | \(-0.966438\pi\) |
0.105244 | + | 0.994446i | \(0.466438\pi\) | |||||||
\(44\) | −0.0288739 | −0.00435290 | ||||||||
\(45\) | 1.59131 | − | 1.57090i | 0.237219 | − | 0.234176i | ||||
\(46\) | 4.77573 | + | 0.438634i | 0.704143 | + | 0.0646731i | ||||
\(47\) | 6.90153 | − | 6.90153i | 1.00669 | − | 1.00669i | 0.00671393 | − | 0.999977i | \(-0.497863\pi\) |
0.999977 | − | 0.00671393i | \(-0.00213713\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 3.19528i | − | 0.456468i | ||||||
\(50\) | 3.48959 | + | 3.58089i | 0.493502 | + | 0.506415i | ||||
\(51\) | 0.620322i | 0.0868625i | ||||||||
\(52\) | 0.711585 | − | 0.711585i | 0.0986790 | − | 0.0986790i | ||||
\(53\) | 2.73811 | − | 2.73811i | 0.376108 | − | 0.376108i | −0.493588 | − | 0.869696i | \(-0.664315\pi\) |
0.869696 | + | 0.493588i | \(0.164315\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | −0.0459474 | + | 0.0453579i | −0.00619555 | + | 0.00611606i | ||||
\(56\) | 1.95057i | 0.260656i | ||||||||
\(57\) | 5.11278 | + | 5.11278i | 0.677205 | + | 0.677205i | ||||
\(58\) | −2.80922 | − | 2.80922i | −0.368869 | − | 0.368869i | ||||
\(59\) | − | 5.73861i | − | 0.747104i | −0.927609 | − | 0.373552i | \(-0.878140\pi\) | ||
0.927609 | − | 0.373552i | \(-0.121860\pi\) | |||||||
\(60\) | 2.23602 | + | 0.0144369i | 0.288669 | + | 0.00186380i | ||||
\(61\) | − | 5.09237i | − | 0.652011i | −0.945368 | − | 0.326005i | \(-0.894297\pi\) | ||
0.945368 | − | 0.326005i | \(-0.105703\pi\) | |||||||
\(62\) | −3.68342 | + | 3.68342i | −0.467795 | + | 0.467795i | ||||
\(63\) | 1.37926 | − | 1.37926i | 0.173771 | − | 0.173771i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.0145284 | − | 2.25018i | 0.00180202 | − | 0.279101i | ||||
\(66\) | 0.0288739i | 0.00355413i | ||||||||
\(67\) | −4.63966 | − | 4.63966i | −0.566825 | − | 0.566825i | 0.364413 | − | 0.931238i | \(-0.381270\pi\) |
−0.931238 | + | 0.364413i | \(0.881270\pi\) | |||||||
\(68\) | −0.438634 | + | 0.438634i | −0.0531922 | + | 0.0531922i | ||||
\(69\) | 0.438634 | − | 4.77573i | 0.0528053 | − | 0.574930i | ||||
\(70\) | 3.06415 | + | 3.10397i | 0.366235 | + | 0.370995i | ||||
\(71\) | −5.47777 | −0.650092 | −0.325046 | − | 0.945698i | \(-0.605380\pi\) | ||||
−0.325046 | + | 0.945698i | \(0.605380\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −0.908695 | − | 0.908695i | −0.106355 | − | 0.106355i | 0.651927 | − | 0.758282i | \(-0.273961\pi\) |
−0.758282 | + | 0.651927i | \(0.773961\pi\) | |||||||
\(74\) | 2.06849 | 0.240457 | ||||||||
\(75\) | 3.58089 | − | 3.48959i | 0.413486 | − | 0.402943i | ||||
\(76\) | 7.23057i | 0.829403i | ||||||||
\(77\) | −0.0398246 | + | 0.0398246i | −0.00453844 | + | 0.00453844i | ||||
\(78\) | −0.711585 | − | 0.711585i | −0.0805711 | − | 0.0805711i | ||||
\(79\) | −5.20235 | −0.585310 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(80\) | 1.57090 | + | 1.59131i | 0.175632 | + | 0.177914i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −5.07048 | + | 5.07048i | −0.559941 | + | 0.559941i | ||||
\(83\) | 9.95414 | − | 9.95414i | 1.09261 | − | 1.09261i | 0.0973599 | − | 0.995249i | \(-0.468960\pi\) |
0.995249 | − | 0.0973599i | \(-0.0310398\pi\) | |||||||
\(84\) | 1.95057 | 0.212825 | ||||||||
\(85\) | −0.00895556 | + | 1.38705i | −0.000971366 | + | 0.150447i | ||||
\(86\) | 8.24612i | 0.889202i | ||||||||
\(87\) | −2.80922 | + | 2.80922i | −0.301180 | + | 0.301180i | ||||
\(88\) | −0.0204169 | + | 0.0204169i | −0.00217645 | + | 0.00217645i | ||||
\(89\) | 10.5118 | 1.11425 | 0.557123 | − | 0.830430i | \(-0.311905\pi\) | ||||
0.557123 | + | 0.830430i | \(0.311905\pi\) | |||||||
\(90\) | 0.0144369 | − | 2.23602i | 0.00152179 | − | 0.235697i | ||||
\(91\) | − | 1.96292i | − | 0.205770i | ||||||
\(92\) | 3.68711 | − | 3.06679i | 0.384408 | − | 0.319735i | ||||
\(93\) | 3.68342 | + | 3.68342i | 0.381953 | + | 0.381953i | ||||
\(94\) | − | 9.76024i | − | 1.00669i | ||||||
\(95\) | 11.3585 | + | 11.5061i | 1.16536 | + | 1.18050i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.850780 | − | 0.850780i | −0.0863836 | − | 0.0863836i | 0.662595 | − | 0.748978i | \(-0.269455\pi\) |
−0.748978 | + | 0.662595i | \(0.769455\pi\) | |||||||
\(98\) | −2.25940 | − | 2.25940i | −0.228234 | − | 0.228234i | ||||
\(99\) | 0.0288739 | 0.00290193 | ||||||||
\(100\) | 4.99958 | + | 0.0645626i | 0.499958 | + | 0.00645626i | ||||
\(101\) | −15.2097 | −1.51342 | −0.756712 | − | 0.653748i | \(-0.773196\pi\) | ||||
−0.756712 | + | 0.653748i | \(0.773196\pi\) | |||||||
\(102\) | 0.438634 | + | 0.438634i | 0.0434313 | + | 0.0434313i | ||||
\(103\) | −2.54161 | + | 2.54161i | −0.250432 | + | 0.250432i | −0.821148 | − | 0.570715i | \(-0.806666\pi\) |
0.570715 | + | 0.821148i | \(0.306666\pi\) | |||||||
\(104\) | − | 1.00633i | − | 0.0986790i | ||||||
\(105\) | 3.10397 | − | 3.06415i | 0.302916 | − | 0.299030i | ||||
\(106\) | − | 3.87227i | − | 0.376108i | ||||||
\(107\) | −7.38286 | − | 7.38286i | −0.713728 | − | 0.713728i | 0.253585 | − | 0.967313i | \(-0.418390\pi\) |
−0.967313 | + | 0.253585i | \(0.918390\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.23206 | 0.118010 | 0.0590049 | − | 0.998258i | \(-0.481207\pi\) | ||||
0.0590049 | + | 0.998258i | \(0.481207\pi\) | |||||||
\(110\) | −0.000416850 | 0.0645626i | −3.97451e−5 | 0.00615580i | ||||||
\(111\) | − | 2.06849i | − | 0.196333i | ||||||
\(112\) | 1.37926 | + | 1.37926i | 0.130328 | + | 0.130328i | ||||
\(113\) | 10.6065 | − | 10.6065i | 0.997771 | − | 0.997771i | −0.00222660 | − | 0.999998i | \(-0.500709\pi\) |
0.999998 | + | 0.00222660i | \(0.000708750\pi\) | |||||||
\(114\) | 7.23057 | 0.677205 | ||||||||
\(115\) | 1.04974 | − | 10.6723i | 0.0978890 | − | 0.995197i | ||||
\(116\) | −3.97284 | −0.368869 | ||||||||
\(117\) | −0.711585 | + | 0.711585i | −0.0657860 | + | 0.0657860i | ||||
\(118\) | −4.05781 | − | 4.05781i | −0.373552 | − | 0.373552i | ||||
\(119\) | 1.20998i | 0.110919i | ||||||||
\(120\) | 1.59131 | − | 1.57090i | 0.145266 | − | 0.143403i | ||||
\(121\) | 10.9992 | 0.999924 | ||||||||
\(122\) | −3.60085 | − | 3.60085i | −0.326005 | − | 0.326005i | ||||
\(123\) | 5.07048 | + | 5.07048i | 0.457190 | + | 0.457190i | ||||
\(124\) | 5.20915i | 0.467795i | ||||||||
\(125\) | 8.05733 | − | 7.75109i | 0.720669 | − | 0.693279i | ||||
\(126\) | − | 1.95057i | − | 0.173771i | ||||||
\(127\) | −6.45653 | + | 6.45653i | −0.572925 | + | 0.572925i | −0.932945 | − | 0.360020i | \(-0.882770\pi\) |
0.360020 | + | 0.932945i | \(0.382770\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.24612 | 0.726030 | ||||||||
\(130\) | −1.58085 | − | 1.60139i | −0.138649 | − | 0.140451i | ||||
\(131\) | −14.1312 | −1.23465 | −0.617323 | − | 0.786710i | \(-0.711783\pi\) | ||||
−0.617323 | + | 0.786710i | \(0.711783\pi\) | |||||||
\(132\) | 0.0204169 | + | 0.0204169i | 0.00177706 | + | 0.00177706i | ||||
\(133\) | 9.97284 | + | 9.97284i | 0.864755 | + | 0.864755i | ||||
\(134\) | −6.56147 | −0.566825 | ||||||||
\(135\) | −2.23602 | − | 0.0144369i | −0.192446 | − | 0.00124253i | ||||
\(136\) | 0.620322i | 0.0531922i | ||||||||
\(137\) | 9.99147 | + | 9.99147i | 0.853629 | + | 0.853629i | 0.990578 | − | 0.136949i | \(-0.0437296\pi\) |
−0.136949 | + | 0.990578i | \(0.543730\pi\) | |||||||
\(138\) | −3.06679 | − | 3.68711i | −0.261063 | − | 0.313868i | ||||
\(139\) | − | 11.0483i | − | 0.937102i | −0.883436 | − | 0.468551i | \(-0.844776\pi\) | ||
0.883436 | − | 0.468551i | \(-0.155224\pi\) | |||||||
\(140\) | 4.36152 | + | 0.0281603i | 0.368615 | + | 0.00237998i | ||||
\(141\) | −9.76024 | −0.821960 | ||||||||
\(142\) | −3.87337 | + | 3.87337i | −0.325046 | + | 0.325046i | ||||
\(143\) | 0.0205462 | − | 0.0205462i | 0.00171816 | − | 0.00171816i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −6.32204 | + | 6.24092i | −0.525017 | + | 0.518281i | ||||
\(146\) | −1.28509 | −0.106355 | ||||||||
\(147\) | −2.25940 | + | 2.25940i | −0.186352 | + | 0.186352i | ||||
\(148\) | 1.46265 | − | 1.46265i | 0.120229 | − | 0.120229i | ||||
\(149\) | 13.0448 | 1.06867 | 0.534336 | − | 0.845272i | \(-0.320562\pi\) | ||||
0.534336 | + | 0.845272i | \(0.320562\pi\) | |||||||
\(150\) | 0.0645626 | − | 4.99958i | 0.00527152 | − | 0.408214i | ||||
\(151\) | 2.16088 | 0.175850 | 0.0879250 | − | 0.996127i | \(-0.471976\pi\) | ||||
0.0879250 | + | 0.996127i | \(0.471976\pi\) | |||||||
\(152\) | 5.11278 | + | 5.11278i | 0.414701 | + | 0.414701i | ||||
\(153\) | 0.438634 | − | 0.438634i | 0.0354615 | − | 0.0354615i | ||||
\(154\) | 0.0563205i | 0.00453844i | ||||||||
\(155\) | 8.18304 | + | 8.28939i | 0.657277 | + | 0.665820i | ||||
\(156\) | −1.00633 | −0.0805711 | ||||||||
\(157\) | −13.4623 | − | 13.4623i | −1.07441 | − | 1.07441i | −0.996999 | − | 0.0774088i | \(-0.975335\pi\) |
−0.0774088 | − | 0.996999i | \(-0.524665\pi\) | |||||||
\(158\) | −3.67862 | + | 3.67862i | −0.292655 | + | 0.292655i | ||||
\(159\) | −3.87227 | −0.307091 | ||||||||
\(160\) | 2.23602 | + | 0.0144369i | 0.176773 | + | 0.00114134i | ||||
\(161\) | 0.855587 | − | 9.31540i | 0.0674297 | − | 0.734156i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −0.576831 | − | 0.576831i | −0.0451809 | − | 0.0451809i | 0.684155 | − | 0.729336i | \(-0.260171\pi\) |
−0.729336 | + | 0.684155i | \(0.760171\pi\) | |||||||
\(164\) | 7.17074i | 0.559941i | ||||||||
\(165\) | 0.0645626 | 0.000416850i | 0.00502619 | 3.24518e-5i | ||||||
\(166\) | − | 14.0773i | − | 1.09261i | ||||||
\(167\) | 4.06044 | − | 4.06044i | 0.314206 | − | 0.314206i | −0.532331 | − | 0.846537i | \(-0.678684\pi\) |
0.846537 | + | 0.532331i | \(0.178684\pi\) | |||||||
\(168\) | 1.37926 | − | 1.37926i | 0.106412 | − | 0.106412i | ||||
\(169\) | − | 11.9873i | − | 0.922100i | ||||||
\(170\) | 0.974463 | + | 0.987128i | 0.0747379 | + | 0.0757092i | ||||
\(171\) | − | 7.23057i | − | 0.552935i | ||||||
\(172\) | 5.83089 | + | 5.83089i | 0.444601 | + | 0.444601i | ||||
\(173\) | 12.1320 | + | 12.1320i | 0.922379 | + | 0.922379i | 0.997197 | − | 0.0748182i | \(-0.0238377\pi\) |
−0.0748182 | + | 0.997197i | \(0.523838\pi\) | |||||||
\(174\) | 3.97284i | 0.301180i | ||||||||
\(175\) | 6.98478 | − | 6.80668i | 0.528000 | − | 0.514537i | ||||
\(176\) | 0.0288739i | 0.00217645i | ||||||||
\(177\) | −4.05781 | + | 4.05781i | −0.305004 | + | 0.305004i | ||||
\(178\) | 7.43295 | − | 7.43295i | 0.557123 | − | 0.557123i | ||||
\(179\) | − | 16.6646i | − | 1.24557i | −0.782393 | − | 0.622785i | \(-0.786001\pi\) | ||
0.782393 | − | 0.622785i | \(-0.213999\pi\) | |||||||
\(180\) | −1.57090 | − | 1.59131i | −0.117088 | − | 0.118610i | ||||
\(181\) | 6.69613i | 0.497719i | 0.968540 | + | 0.248860i | \(0.0800558\pi\) | ||||
−0.968540 | + | 0.248860i | \(0.919944\pi\) | |||||||
\(182\) | −1.38800 | − | 1.38800i | −0.102885 | − | 0.102885i | ||||
\(183\) | −3.60085 | + | 3.60085i | −0.266182 | + | 0.266182i | ||||
\(184\) | 0.438634 | − | 4.77573i | 0.0323365 | − | 0.352072i | ||||
\(185\) | 0.0298627 | − | 4.62519i | 0.00219555 | − | 0.340051i | ||||
\(186\) | 5.20915 | 0.381953 | ||||||||
\(187\) | −0.0126651 | + | 0.0126651i | −0.000926162 | + | 0.000926162i | ||||
\(188\) | −6.90153 | − | 6.90153i | −0.503346 | − | 0.503346i | ||||
\(189\) | −1.95057 | −0.141883 | ||||||||
\(190\) | 16.1677 | + | 0.104387i | 1.17293 | + | 0.00757305i | ||||
\(191\) | 7.32933i | 0.530332i | 0.964203 | + | 0.265166i | \(0.0854267\pi\) | ||||
−0.964203 | + | 0.265166i | \(0.914573\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −5.03982 | − | 5.03982i | −0.362775 | − | 0.362775i | 0.502059 | − | 0.864833i | \(-0.332576\pi\) |
−0.864833 | + | 0.502059i | \(0.832576\pi\) | |||||||
\(194\) | −1.20318 | −0.0863836 | ||||||||
\(195\) | −1.60139 | + | 1.58085i | −0.114678 | + | 0.113207i | ||||
\(196\) | −3.19528 | −0.228234 | ||||||||
\(197\) | 6.17707 | − | 6.17707i | 0.440098 | − | 0.440098i | −0.451947 | − | 0.892045i | \(-0.649270\pi\) |
0.892045 | + | 0.451947i | \(0.149270\pi\) | |||||||
\(198\) | 0.0204169 | − | 0.0204169i | 0.00145097 | − | 0.00145097i | ||||
\(199\) | −20.6272 | −1.46222 | −0.731111 | − | 0.682258i | \(-0.760998\pi\) | ||||
−0.731111 | + | 0.682258i | \(0.760998\pi\) | |||||||
\(200\) | 3.58089 | − | 3.48959i | 0.253207 | − | 0.246751i | ||||
\(201\) | 6.56147i | 0.462811i | ||||||||
\(202\) | −10.7549 | + | 10.7549i | −0.756712 | + | 0.756712i | ||||
\(203\) | −5.47959 | + | 5.47959i | −0.384592 | + | 0.384592i | ||||
\(204\) | 0.620322 | 0.0434313 | ||||||||
\(205\) | 11.2645 | + | 11.4109i | 0.786747 | + | 0.796972i | ||||
\(206\) | 3.59438i | 0.250432i | ||||||||
\(207\) | −3.68711 | + | 3.06679i | −0.256272 | + | 0.213157i | ||||
\(208\) | −0.711585 | − | 0.711585i | −0.0493395 | − | 0.0493395i | ||||
\(209\) | 0.208774i | 0.0144412i | ||||||||
\(210\) | 0.0281603 | − | 4.36152i | 0.00194324 | − | 0.300973i | ||||
\(211\) | −25.2880 | −1.74090 | −0.870448 | − | 0.492261i | \(-0.836171\pi\) | ||||
−0.870448 | + | 0.492261i | \(0.836171\pi\) | |||||||
\(212\) | −2.73811 | − | 2.73811i | −0.188054 | − | 0.188054i | ||||
\(213\) | 3.87337 | + | 3.87337i | 0.265399 | + | 0.265399i | ||||
\(214\) | −10.4409 | −0.713728 | ||||||||
\(215\) | 18.4385 | + | 0.119049i | 1.25750 | + | 0.00811906i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 7.18478 | + | 7.18478i | 0.487735 | + | 0.487735i | ||||
\(218\) | 0.871197 | − | 0.871197i | 0.0590049 | − | 0.0590049i | ||||
\(219\) | 1.28509i | 0.0868382i | ||||||||
\(220\) | 0.0453579 | + | 0.0459474i | 0.00305803 | + | 0.00309777i | ||||
\(221\) | − | 0.624251i | − | 0.0419916i | ||||||
\(222\) | −1.46265 | − | 1.46265i | −0.0981663 | − | 0.0981663i | ||||
\(223\) | 6.36523 | + | 6.36523i | 0.426247 | + | 0.426247i | 0.887348 | − | 0.461101i | \(-0.152545\pi\) |
−0.461101 | + | 0.887348i | \(0.652545\pi\) | |||||||
\(224\) | 1.95057 | 0.130328 | ||||||||
\(225\) | −4.99958 | − | 0.0645626i | −0.333306 | − | 0.00430417i | ||||
\(226\) | − | 14.9998i | − | 0.997771i | ||||||
\(227\) | 12.2183 | + | 12.2183i | 0.810956 | + | 0.810956i | 0.984777 | − | 0.173822i | \(-0.0556116\pi\) |
−0.173822 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(228\) | 5.11278 | − | 5.11278i | 0.338602 | − | 0.338602i | ||||
\(229\) | 20.2222 | 1.33632 | 0.668162 | − | 0.744016i | \(-0.267081\pi\) | ||||
0.668162 | + | 0.744016i | \(0.267081\pi\) | |||||||
\(230\) | −6.80418 | − | 8.28874i | −0.448654 | − | 0.546543i | ||||
\(231\) | 0.0563205 | 0.00370562 | ||||||||
\(232\) | −2.80922 | + | 2.80922i | −0.184434 | + | 0.184434i | ||||
\(233\) | −2.91503 | − | 2.91503i | −0.190970 | − | 0.190970i | 0.605145 | − | 0.796115i | \(-0.293115\pi\) |
−0.796115 | + | 0.605145i | \(0.793115\pi\) | |||||||
\(234\) | 1.00633i | 0.0657860i | ||||||||
\(235\) | −21.8241 | − | 0.140908i | −1.42365 | − | 0.00919182i | ||||
\(236\) | −5.73861 | −0.373552 | ||||||||
\(237\) | 3.67862 | + | 3.67862i | 0.238952 | + | 0.238952i | ||||
\(238\) | 0.855587 | + | 0.855587i | 0.0554594 | + | 0.0554594i | ||||
\(239\) | 8.30821i | 0.537413i | 0.963222 | + | 0.268707i | \(0.0865962\pi\) | ||||
−0.963222 | + | 0.268707i | \(0.913404\pi\) | |||||||
\(240\) | 0.0144369 | − | 2.23602i | 0.000931900 | − | 0.144335i | ||||
\(241\) | 14.5130i | 0.934862i | 0.884030 | + | 0.467431i | \(0.154820\pi\) | ||||
−0.884030 | + | 0.467431i | \(0.845180\pi\) | |||||||
\(242\) | 7.77759 | − | 7.77759i | 0.499962 | − | 0.499962i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −5.09237 | −0.326005 | ||||||||
\(245\) | −5.08469 | + | 5.01945i | −0.324849 | + | 0.320681i | ||||
\(246\) | 7.17074 | 0.457190 | ||||||||
\(247\) | −5.14516 | − | 5.14516i | −0.327379 | − | 0.327379i | ||||
\(248\) | 3.68342 | + | 3.68342i | 0.233898 | + | 0.233898i | ||||
\(249\) | −14.0773 | −0.892112 | ||||||||
\(250\) | 0.216542 | − | 11.1782i | 0.0136953 | − | 0.706974i | ||||
\(251\) | − | 14.3863i | − | 0.908054i | −0.890988 | − | 0.454027i | \(-0.849987\pi\) | ||
0.890988 | − | 0.454027i | \(-0.150013\pi\) | |||||||
\(252\) | −1.37926 | − | 1.37926i | −0.0868853 | − | 0.0868853i | ||||
\(253\) | 0.106461 | − | 0.0885501i | 0.00669316 | − | 0.00556710i | ||||
\(254\) | 9.13091i | 0.572925i | ||||||||
\(255\) | 0.987128 | − | 0.974463i | 0.0618163 | − | 0.0610232i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.82209 | − | 3.82209i | 0.238416 | − | 0.238416i | −0.577778 | − | 0.816194i | \(-0.696080\pi\) |
0.816194 | + | 0.577778i | \(0.196080\pi\) | |||||||
\(258\) | 5.83089 | − | 5.83089i | 0.363015 | − | 0.363015i | ||||
\(259\) | − | 4.03474i | − | 0.250707i | ||||||
\(260\) | −2.25018 | − | 0.0145284i | −0.139550 | − | 0.000901011i | ||||
\(261\) | 3.97284 | 0.245913 | ||||||||
\(262\) | −9.99224 | + | 9.99224i | −0.617323 | + | 0.617323i | ||||
\(263\) | −19.6268 | + | 19.6268i | −1.21024 | + | 1.21024i | −0.239296 | + | 0.970947i | \(0.576917\pi\) |
−0.970947 | + | 0.239296i | \(0.923083\pi\) | |||||||
\(264\) | 0.0288739 | 0.00177706 | ||||||||
\(265\) | −8.65847 | − | 0.0559037i | −0.531886 | − | 0.00343414i | ||||
\(266\) | 14.1037 | 0.864755 | ||||||||
\(267\) | −7.43295 | − | 7.43295i | −0.454889 | − | 0.454889i | ||||
\(268\) | −4.63966 | + | 4.63966i | −0.283413 | + | 0.283413i | ||||
\(269\) | − | 1.94226i | − | 0.118422i | −0.998245 | − | 0.0592110i | \(-0.981142\pi\) | ||
0.998245 | − | 0.0592110i | \(-0.0188585\pi\) | |||||||
\(270\) | −1.59131 | + | 1.57090i | −0.0968443 | + | 0.0956018i | ||||
\(271\) | 5.65568 | 0.343558 | 0.171779 | − | 0.985136i | \(-0.445049\pi\) | ||||
0.171779 | + | 0.985136i | \(0.445049\pi\) | |||||||
\(272\) | 0.438634 | + | 0.438634i | 0.0265961 | + | 0.0265961i | ||||
\(273\) | −1.38800 | + | 1.38800i | −0.0840053 | + | 0.0840053i | ||||
\(274\) | 14.1301 | 0.853629 | ||||||||
\(275\) | 0.144357 | + | 0.00186417i | 0.00870508 | + | 0.000112414i | ||||
\(276\) | −4.77573 | − | 0.438634i | −0.287465 | − | 0.0264027i | ||||
\(277\) | −6.03861 | + | 6.03861i | −0.362825 | + | 0.362825i | −0.864852 | − | 0.502027i | \(-0.832588\pi\) |
0.502027 | + | 0.864852i | \(0.332588\pi\) | |||||||
\(278\) | −7.81231 | − | 7.81231i | −0.468551 | − | 0.468551i | ||||
\(279\) | − | 5.20915i | − | 0.311864i | ||||||
\(280\) | 3.10397 | − | 3.06415i | 0.185498 | − | 0.183118i | ||||
\(281\) | 19.0527i | 1.13659i | 0.822825 | + | 0.568294i | \(0.192396\pi\) | ||||
−0.822825 | + | 0.568294i | \(0.807604\pi\) | |||||||
\(282\) | −6.90153 | + | 6.90153i | −0.410980 | + | 0.410980i | ||||
\(283\) | 3.82033 | − | 3.82033i | 0.227095 | − | 0.227095i | −0.584383 | − | 0.811478i | \(-0.698663\pi\) |
0.811478 | + | 0.584383i | \(0.198663\pi\) | |||||||
\(284\) | 5.47777i | 0.325046i | ||||||||
\(285\) | 0.104387 | − | 16.1677i | 0.00618337 | − | 0.957692i | ||||
\(286\) | − | 0.0290567i | − | 0.00171816i | ||||||
\(287\) | 9.89032 | + | 9.89032i | 0.583807 | + | 0.583807i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 16.6152i | − | 0.977365i | ||||||
\(290\) | −0.0573557 | + | 8.88336i | −0.00336804 | + | 0.521649i | ||||
\(291\) | 1.20318i | 0.0705319i | ||||||||
\(292\) | −0.908695 | + | 0.908695i | −0.0531773 | + | 0.0531773i | ||||
\(293\) | 2.20441 | − | 2.20441i | 0.128783 | − | 0.128783i | −0.639777 | − | 0.768560i | \(-0.720973\pi\) |
0.768560 | + | 0.639777i | \(0.220973\pi\) | |||||||
\(294\) | 3.19528i | 0.186352i | ||||||||
\(295\) | −9.13194 | + | 9.01477i | −0.531682 | + | 0.524860i | ||||
\(296\) | − | 2.06849i | − | 0.120229i | ||||||
\(297\) | −0.0204169 | − | 0.0204169i | −0.00118471 | − | 0.00118471i | ||||
\(298\) | 9.22408 | − | 9.22408i | 0.534336 | − | 0.534336i | ||||
\(299\) | −0.441412 | + | 4.80597i | −0.0255275 | + | 0.277937i | ||||
\(300\) | −3.48959 | − | 3.58089i | −0.201471 | − | 0.206743i | ||||
\(301\) | 16.0846 | 0.927103 | ||||||||
\(302\) | 1.52797 | − | 1.52797i | 0.0879250 | − | 0.0879250i | ||||
\(303\) | 10.7549 | + | 10.7549i | 0.617853 | + | 0.617853i | ||||
\(304\) | 7.23057 | 0.414701 | ||||||||
\(305\) | −8.10355 | + | 7.99958i | −0.464008 | + | 0.458055i | ||||
\(306\) | − | 0.620322i | − | 0.0354615i | ||||||
\(307\) | −13.5388 | + | 13.5388i | −0.772700 | + | 0.772700i | −0.978578 | − | 0.205878i | \(-0.933995\pi\) |
0.205878 | + | 0.978578i | \(0.433995\pi\) | |||||||
\(308\) | 0.0398246 | + | 0.0398246i | 0.00226922 | + | 0.00226922i | ||||
\(309\) | 3.59438 | 0.204477 | ||||||||
\(310\) | 11.6478 | + | 0.0752042i | 0.661549 | + | 0.00427131i | ||||
\(311\) | −32.1959 | −1.82566 | −0.912831 | − | 0.408337i | \(-0.866109\pi\) | ||||
−0.912831 | + | 0.408337i | \(0.866109\pi\) | |||||||
\(312\) | −0.711585 | + | 0.711585i | −0.0402855 | + | 0.0402855i | ||||
\(313\) | 19.4438 | − | 19.4438i | 1.09903 | − | 1.09903i | 0.104502 | − | 0.994525i | \(-0.466675\pi\) |
0.994525 | − | 0.104502i | \(-0.0333247\pi\) | |||||||
\(314\) | −19.0386 | −1.07441 | ||||||||
\(315\) | −4.36152 | − | 0.0281603i | −0.245744 | − | 0.00158665i | ||||
\(316\) | 5.20235i | 0.292655i | ||||||||
\(317\) | −1.40155 | + | 1.40155i | −0.0787188 | + | 0.0787188i | −0.745370 | − | 0.666651i | \(-0.767727\pi\) |
0.666651 | + | 0.745370i | \(0.267727\pi\) | |||||||
\(318\) | −2.73811 | + | 2.73811i | −0.153545 | + | 0.153545i | ||||
\(319\) | −0.114711 | −0.00642260 | ||||||||
\(320\) | 1.59131 | − | 1.57090i | 0.0889572 | − | 0.0878158i | ||||
\(321\) | 10.4409i | 0.582756i | ||||||||
\(322\) | −5.98199 | − | 7.19197i | −0.333363 | − | 0.400793i | ||||
\(323\) | 3.17157 | + | 3.17157i | 0.176471 | + | 0.176471i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −3.60357 | + | 3.51168i | −0.199890 | + | 0.194793i | ||||
\(326\) | −0.815762 | −0.0451809 | ||||||||
\(327\) | −0.871197 | − | 0.871197i | −0.0481773 | − | 0.0481773i | ||||
\(328\) | 5.07048 | + | 5.07048i | 0.279970 | + | 0.279970i | ||||
\(329\) | −19.0380 | −1.04960 | ||||||||
\(330\) | 0.0459474 | − | 0.0453579i | 0.00252932 | − | 0.00249687i | ||||
\(331\) | 29.9547 | 1.64646 | 0.823229 | − | 0.567709i | \(-0.192170\pi\) | ||||
0.823229 | + | 0.567709i | \(0.192170\pi\) | |||||||
\(332\) | −9.95414 | − | 9.95414i | −0.546305 | − | 0.546305i | ||||
\(333\) | −1.46265 | + | 1.46265i | −0.0801525 | + | 0.0801525i | ||||
\(334\) | − | 5.74232i | − | 0.314206i | ||||||
\(335\) | −0.0947276 | + | 14.6716i | −0.00517552 | + | 0.801595i | ||||
\(336\) | − | 1.95057i | − | 0.106412i | ||||||
\(337\) | 9.66919 | + | 9.66919i | 0.526714 | + | 0.526714i | 0.919591 | − | 0.392877i | \(-0.128520\pi\) |
−0.392877 | + | 0.919591i | \(0.628520\pi\) | |||||||
\(338\) | −8.47630 | − | 8.47630i | −0.461050 | − | 0.461050i | ||||
\(339\) | −14.9998 | −0.814677 | ||||||||
\(340\) | 1.38705 | + | 0.00895556i | 0.0752236 | + | 0.000485683i | ||||
\(341\) | 0.150408i | 0.00814507i | ||||||||
\(342\) | −5.11278 | − | 5.11278i | −0.276468 | − | 0.276468i | ||||
\(343\) | −14.0620 | + | 14.0620i | −0.759274 | + | 0.759274i | ||||
\(344\) | 8.24612 | 0.444601 | ||||||||
\(345\) | −8.28874 | + | 6.80418i | −0.446251 | + | 0.366325i | ||||
\(346\) | 17.1572 | 0.922379 | ||||||||
\(347\) | 5.75653 | − | 5.75653i | 0.309026 | − | 0.309026i | −0.535505 | − | 0.844532i | \(-0.679879\pi\) |
0.844532 | + | 0.535505i | \(0.179879\pi\) | |||||||
\(348\) | 2.80922 | + | 2.80922i | 0.150590 | + | 0.150590i | ||||
\(349\) | 15.4579i | 0.827443i | 0.910404 | + | 0.413721i | \(0.135771\pi\) | ||||
−0.910404 | + | 0.413721i | \(0.864229\pi\) | |||||||
\(350\) | 0.125934 | − | 9.75204i | 0.00673145 | − | 0.521268i | ||||
\(351\) | 1.00633 | 0.0537141 | ||||||||
\(352\) | 0.0204169 | + | 0.0204169i | 0.00108823 | + | 0.00108823i | ||||
\(353\) | 0.0222101 | + | 0.0222101i | 0.00118213 | + | 0.00118213i | 0.707698 | − | 0.706515i | \(-0.249734\pi\) |
−0.706515 | + | 0.707698i | \(0.749734\pi\) | |||||||
\(354\) | 5.73861i | 0.305004i | ||||||||
\(355\) | 8.60501 | + | 8.71685i | 0.456707 | + | 0.462643i | ||||
\(356\) | − | 10.5118i | − | 0.557123i | ||||||
\(357\) | 0.855587 | − | 0.855587i | 0.0452824 | − | 0.0452824i | ||||
\(358\) | −11.7837 | − | 11.7837i | −0.622785 | − | 0.622785i | ||||
\(359\) | 32.6259 | 1.72193 | 0.860964 | − | 0.508666i | \(-0.169861\pi\) | ||||
0.860964 | + | 0.508666i | \(0.169861\pi\) | |||||||
\(360\) | −2.23602 | − | 0.0144369i | −0.117849 | − | 0.000760894i | ||||
\(361\) | 33.2811 | 1.75164 | ||||||||
\(362\) | 4.73488 | + | 4.73488i | 0.248860 | + | 0.248860i | ||||
\(363\) | −7.77759 | − | 7.77759i | −0.408217 | − | 0.408217i | ||||
\(364\) | −1.96292 | −0.102885 | ||||||||
\(365\) | −0.0185527 | + | 2.87348i | −0.000971095 | + | 0.150405i | ||||
\(366\) | 5.09237i | 0.266182i | ||||||||
\(367\) | 15.1093 | + | 15.1093i | 0.788701 | + | 0.788701i | 0.981281 | − | 0.192580i | \(-0.0616854\pi\) |
−0.192580 | + | 0.981281i | \(0.561685\pi\) | |||||||
\(368\) | −3.06679 | − | 3.68711i | −0.159867 | − | 0.192204i | ||||
\(369\) | − | 7.17074i | − | 0.373294i | ||||||
\(370\) | −3.24939 | − | 3.29162i | −0.168928 | − | 0.171123i | ||||
\(371\) | −7.55313 | −0.392139 | ||||||||
\(372\) | 3.68342 | − | 3.68342i | 0.190977 | − | 0.190977i | ||||
\(373\) | −9.38306 | + | 9.38306i | −0.485836 | + | 0.485836i | −0.906990 | − | 0.421153i | \(-0.861625\pi\) |
0.421153 | + | 0.906990i | \(0.361625\pi\) | |||||||
\(374\) | 0.0179111i | 0.000926162i | ||||||||
\(375\) | −11.1782 | − | 0.216542i | −0.577242 | − | 0.0111822i | ||||
\(376\) | −9.76024 | −0.503346 | ||||||||
\(377\) | 2.82701 | − | 2.82701i | 0.145599 | − | 0.145599i | ||||
\(378\) | −1.37926 | + | 1.37926i | −0.0709416 | + | 0.0709416i | ||||
\(379\) | 14.3962 | 0.739483 | 0.369741 | − | 0.929135i | \(-0.379446\pi\) | ||||
0.369741 | + | 0.929135i | \(0.379446\pi\) | |||||||
\(380\) | 11.5061 | − | 11.3585i | 0.590251 | − | 0.582678i | ||||
\(381\) | 9.13091 | 0.467791 | ||||||||
\(382\) | 5.18262 | + | 5.18262i | 0.265166 | + | 0.265166i | ||||
\(383\) | −6.21540 | + | 6.21540i | −0.317592 | + | 0.317592i | −0.847842 | − | 0.530249i | \(-0.822098\pi\) |
0.530249 | + | 0.847842i | \(0.322098\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0.125934 | 0.000813096i | 0.00641819 | 4.14392e-5i | ||||||
\(386\) | −7.12739 | −0.362775 | ||||||||
\(387\) | −5.83089 | − | 5.83089i | −0.296401 | − | 0.296401i | ||||
\(388\) | −0.850780 | + | 0.850780i | −0.0431918 | + | 0.0431918i | ||||
\(389\) | −23.6231 | −1.19774 | −0.598869 | − | 0.800847i | \(-0.704383\pi\) | ||||
−0.598869 | + | 0.800847i | \(0.704383\pi\) | |||||||
\(390\) | −0.0145284 | + | 2.25018i | −0.000735672 | + | 0.113942i | ||||
\(391\) | 0.272095 | − | 2.96249i | 0.0137604 | − | 0.149820i | ||||
\(392\) | −2.25940 | + | 2.25940i | −0.114117 | + | 0.114117i | ||||
\(393\) | 9.99224 | + | 9.99224i | 0.504042 | + | 0.504042i | ||||
\(394\) | − | 8.73570i | − | 0.440098i | ||||||
\(395\) | 8.17236 | + | 8.27858i | 0.411196 | + | 0.416540i | ||||
\(396\) | − | 0.0288739i | − | 0.00145097i | ||||||
\(397\) | −4.91069 | + | 4.91069i | −0.246461 | + | 0.246461i | −0.819516 | − | 0.573056i | \(-0.805758\pi\) |
0.573056 | + | 0.819516i | \(0.305758\pi\) | |||||||
\(398\) | −14.5856 | + | 14.5856i | −0.731111 | + | 0.731111i | ||||
\(399\) | − | 14.1037i | − | 0.706069i | ||||||
\(400\) | 0.0645626 | − | 4.99958i | 0.00322813 | − | 0.249979i | ||||
\(401\) | − | 14.4696i | − | 0.722575i | −0.932454 | − | 0.361288i | \(-0.882337\pi\) | ||
0.932454 | − | 0.361288i | \(-0.117663\pi\) | |||||||
\(402\) | 4.63966 | + | 4.63966i | 0.231405 | + | 0.231405i | ||||
\(403\) | −3.70675 | − | 3.70675i | −0.184646 | − | 0.184646i | ||||
\(404\) | 15.2097i | 0.756712i | ||||||||
\(405\) | 1.57090 | + | 1.59131i | 0.0780585 | + | 0.0790730i | ||||
\(406\) | 7.74930i | 0.384592i | ||||||||
\(407\) | 0.0422322 | − | 0.0422322i | 0.00209337 | − | 0.00209337i | ||||
\(408\) | 0.438634 | − | 0.438634i | 0.0217156 | − | 0.0217156i | ||||
\(409\) | − | 22.5518i | − | 1.11512i | −0.830138 | − | 0.557558i | \(-0.811738\pi\) | ||
0.830138 | − | 0.557558i | \(-0.188262\pi\) | |||||||
\(410\) | 16.0339 | + | 0.103524i | 0.791859 | + | 0.00511266i | ||||
\(411\) | − | 14.1301i | − | 0.696985i | ||||||
\(412\) | 2.54161 | + | 2.54161i | 0.125216 | + | 0.125216i | ||||
\(413\) | −7.91505 | + | 7.91505i | −0.389474 | + | 0.389474i | ||||
\(414\) | −0.438634 | + | 4.77573i | −0.0215577 | + | 0.234714i | ||||
\(415\) | −31.4771 | − | 0.203233i | −1.54515 | − | 0.00997631i | ||||
\(416\) | −1.00633 | −0.0493395 | ||||||||
\(417\) | −7.81231 | + | 7.81231i | −0.382570 | + | 0.382570i | ||||
\(418\) | 0.147626 | + | 0.147626i | 0.00722062 | + | 0.00722062i | ||||
\(419\) | −30.0512 | −1.46810 | −0.734049 | − | 0.679097i | \(-0.762372\pi\) | ||||
−0.734049 | + | 0.679097i | \(0.762372\pi\) | |||||||
\(420\) | −3.06415 | − | 3.10397i | −0.149515 | − | 0.151458i | ||||
\(421\) | 21.5409i | 1.04984i | 0.851152 | + | 0.524919i | \(0.175905\pi\) | ||||
−0.851152 | + | 0.524919i | \(0.824095\pi\) | |||||||
\(422\) | −17.8813 | + | 17.8813i | −0.870448 | + | 0.870448i | ||||
\(423\) | 6.90153 | + | 6.90153i | 0.335564 | + | 0.335564i | ||||
\(424\) | −3.87227 | −0.188054 | ||||||||
\(425\) | 2.22131 | − | 2.16467i | 0.107749 | − | 0.105002i | ||||
\(426\) | 5.47777 | 0.265399 | ||||||||
\(427\) | −7.02370 | + | 7.02370i | −0.339901 | + | 0.339901i | ||||
\(428\) | −7.38286 | + | 7.38286i | −0.356864 | + | 0.356864i | ||||
\(429\) | −0.0290567 | −0.00140287 | ||||||||
\(430\) | 13.1222 | − | 12.9538i | 0.632807 | − | 0.624688i | ||||
\(431\) | 15.6022i | 0.751529i | 0.926715 | + | 0.375765i | \(0.122620\pi\) | ||||
−0.926715 | + | 0.375765i | \(0.877380\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −11.2969 | + | 11.2969i | −0.542893 | + | 0.542893i | −0.924376 | − | 0.381483i | \(-0.875414\pi\) |
0.381483 | + | 0.924376i | \(0.375414\pi\) | |||||||
\(434\) | 10.1608 | 0.487735 | ||||||||
\(435\) | 8.88336 | + | 0.0573557i | 0.425924 | + | 0.00274999i | ||||
\(436\) | − | 1.23206i | − | 0.0590049i | ||||||
\(437\) | −22.1746 | − | 26.6599i | −1.06076 | − | 1.27532i | ||||
\(438\) | 0.908695 | + | 0.908695i | 0.0434191 | + | 0.0434191i | ||||
\(439\) | − | 3.20333i | − | 0.152887i | −0.997074 | − | 0.0764433i | \(-0.975644\pi\) | ||
0.997074 | − | 0.0764433i | \(-0.0243564\pi\) | |||||||
\(440\) | 0.0645626 | 0.000416850i | 0.00307790 | 1.98726e-5i | ||||||
\(441\) | 3.19528 | 0.152156 | ||||||||
\(442\) | −0.441412 | − | 0.441412i | −0.0209958 | − | 0.0209958i | ||||
\(443\) | −15.6087 | − | 15.6087i | −0.741590 | − | 0.741590i | 0.231294 | − | 0.972884i | \(-0.425704\pi\) |
−0.972884 | + | 0.231294i | \(0.925704\pi\) | |||||||
\(444\) | −2.06849 | −0.0981663 | ||||||||
\(445\) | −16.5129 | − | 16.7275i | −0.782788 | − | 0.792961i | ||||
\(446\) | 9.00179 | 0.426247 | ||||||||
\(447\) | −9.22408 | − | 9.22408i | −0.436284 | − | 0.436284i | ||||
\(448\) | 1.37926 | − | 1.37926i | 0.0651640 | − | 0.0651640i | ||||
\(449\) | 11.2112i | 0.529087i | 0.964374 | + | 0.264543i | \(0.0852213\pi\) | ||||
−0.964374 | + | 0.264543i | \(0.914779\pi\) | |||||||
\(450\) | −3.58089 | + | 3.48959i | −0.168805 | + | 0.164501i | ||||
\(451\) | 0.207047i | 0.00974947i | ||||||||
\(452\) | −10.6065 | − | 10.6065i | −0.498885 | − | 0.498885i | ||||
\(453\) | −1.52797 | − | 1.52797i | −0.0717904 | − | 0.0717904i | ||||
\(454\) | 17.2793 | 0.810956 | ||||||||
\(455\) | −3.12363 | + | 3.08355i | −0.146438 | + | 0.144559i | ||||
\(456\) | − | 7.23057i | − | 0.338602i | ||||||
\(457\) | 17.6613 | + | 17.6613i | 0.826163 | + | 0.826163i | 0.986984 | − | 0.160821i | \(-0.0514141\pi\) |
−0.160821 | + | 0.986984i | \(0.551414\pi\) | |||||||
\(458\) | 14.2993 | − | 14.2993i | 0.668162 | − | 0.668162i | ||||
\(459\) | −0.620322 | −0.0289542 | ||||||||
\(460\) | −10.6723 | − | 1.04974i | −0.497599 | − | 0.0489445i | ||||
\(461\) | 19.3119 | 0.899444 | 0.449722 | − | 0.893169i | \(-0.351523\pi\) | ||||
0.449722 | + | 0.893169i | \(0.351523\pi\) | |||||||
\(462\) | 0.0398246 | − | 0.0398246i | 0.00185281 | − | 0.00185281i | ||||
\(463\) | 12.6411 | + | 12.6411i | 0.587484 | + | 0.587484i | 0.936949 | − | 0.349465i | \(-0.113637\pi\) |
−0.349465 | + | 0.936949i | \(0.613637\pi\) | |||||||
\(464\) | 3.97284i | 0.184434i | ||||||||
\(465\) | 0.0752042 | − | 11.6478i | 0.00348751 | − | 0.540152i | ||||
\(466\) | −4.12247 | −0.190970 | ||||||||
\(467\) | −27.3483 | − | 27.3483i | −1.26553 | − | 1.26553i | −0.948373 | − | 0.317157i | \(-0.897272\pi\) |
−0.317157 | − | 0.948373i | \(-0.602728\pi\) | |||||||
\(468\) | 0.711585 | + | 0.711585i | 0.0328930 | + | 0.0328930i | ||||
\(469\) | 12.7986i | 0.590985i | ||||||||
\(470\) | −15.5316 | + | 15.3323i | −0.716419 | + | 0.707228i | ||||
\(471\) | 19.0386i | 0.877251i | ||||||||
\(472\) | −4.05781 | + | 4.05781i | −0.186776 | + | 0.186776i | ||||
\(473\) | 0.168360 | + | 0.168360i | 0.00774122 | + | 0.00774122i | ||||
\(474\) | 5.20235 | 0.238952 | ||||||||
\(475\) | 0.466824 | − | 36.1498i | 0.0214194 | − | 1.65867i | ||||
\(476\) | 1.20998 | 0.0554594 | ||||||||
\(477\) | 2.73811 | + | 2.73811i | 0.125369 | + | 0.125369i | ||||
\(478\) | 5.87479 | + | 5.87479i | 0.268707 | + | 0.268707i | ||||
\(479\) | −26.9547 | −1.23159 | −0.615796 | − | 0.787906i | \(-0.711165\pi\) | ||||
−0.615796 | + | 0.787906i | \(0.711165\pi\) | |||||||
\(480\) | −1.57090 | − | 1.59131i | −0.0717013 | − | 0.0726332i | ||||
\(481\) | 2.08159i | 0.0949124i | ||||||||
\(482\) | 10.2622 | + | 10.2622i | 0.467431 | + | 0.467431i | ||||
\(483\) | −7.19197 | + | 5.98199i | −0.327246 | + | 0.272190i | ||||
\(484\) | − | 10.9992i | − | 0.499962i | ||||||
\(485\) | −0.0173703 | + | 2.69035i | −0.000788745 | + | 0.122162i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 28.7208 | − | 28.7208i | 1.30146 | − | 1.30146i | 0.374058 | − | 0.927405i | \(-0.377966\pi\) |
0.927405 | − | 0.374058i | \(-0.122034\pi\) | |||||||
\(488\) | −3.60085 | + | 3.60085i | −0.163003 | + | 0.163003i | ||||
\(489\) | 0.815762i | 0.0368900i | ||||||||
\(490\) | −0.0461300 | + | 7.14470i | −0.00208394 | + | 0.322765i | ||||
\(491\) | 2.65360 | 0.119755 | 0.0598777 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598777 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(492\) | 5.07048 | − | 5.07048i | 0.228595 | − | 0.228595i | ||||
\(493\) | −1.74262 | + | 1.74262i | −0.0784838 | + | 0.0784838i | ||||
\(494\) | −7.27635 | −0.327379 | ||||||||
\(495\) | −0.0453579 | − | 0.0459474i | −0.00203869 | − | 0.00206518i | ||||
\(496\) | 5.20915 | 0.233898 | ||||||||
\(497\) | 7.55528 | + | 7.55528i | 0.338900 | + | 0.338900i | ||||
\(498\) | −9.95414 | + | 9.95414i | −0.446056 | + | 0.446056i | ||||
\(499\) | 9.11525i | 0.408055i | 0.978965 | + | 0.204027i | \(0.0654032\pi\) | ||||
−0.978965 | + | 0.204027i | \(0.934597\pi\) | |||||||
\(500\) | −7.75109 | − | 8.05733i | −0.346639 | − | 0.360335i | ||||
\(501\) | −5.74232 | −0.256548 | ||||||||
\(502\) | −10.1726 | − | 10.1726i | −0.454027 | − | 0.454027i | ||||
\(503\) | 17.5461 | − | 17.5461i | 0.782343 | − | 0.782343i | −0.197883 | − | 0.980226i | \(-0.563407\pi\) |
0.980226 | + | 0.197883i | \(0.0634065\pi\) | |||||||
\(504\) | −1.95057 | −0.0868853 | ||||||||
\(505\) | 23.8929 | + | 24.2035i | 1.06322 | + | 1.07704i | ||||
\(506\) | 0.0126651 | − | 0.137894i | 0.000563031 | − | 0.00613013i | ||||
\(507\) | −8.47630 | + | 8.47630i | −0.376446 | + | 0.376446i | ||||
\(508\) | 6.45653 | + | 6.45653i | 0.286462 | + | 0.286462i | ||||
\(509\) | − | 23.7897i | − | 1.05446i | −0.849722 | − | 0.527231i | \(-0.823230\pi\) | ||
0.849722 | − | 0.527231i | \(-0.176770\pi\) | |||||||
\(510\) | 0.00895556 | − | 1.38705i | 0.000396559 | − | 0.0614198i | ||||
\(511\) | 2.50666i | 0.110888i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.11278 | + | 5.11278i | −0.225735 | + | 0.225735i | ||||
\(514\) | − | 5.40526i | − | 0.238416i | ||||||
\(515\) | 8.03712 | + | 0.0518919i | 0.354158 | + | 0.00228663i | ||||
\(516\) | − | 8.24612i | − | 0.363015i | ||||||
\(517\) | −0.199274 | − | 0.199274i | −0.00876406 | − | 0.00876406i | ||||
\(518\) | −2.85299 | − | 2.85299i | −0.125353 | − | 0.125353i | ||||
\(519\) | − | 17.1572i | − | 0.753119i | ||||||
\(520\) | −1.60139 | + | 1.58085i | −0.0702257 | + | 0.0693246i | ||||
\(521\) | − | 34.3911i | − | 1.50670i | −0.657619 | − | 0.753351i | \(-0.728436\pi\) | ||
0.657619 | − | 0.753351i | \(-0.271564\pi\) | |||||||
\(522\) | 2.80922 | − | 2.80922i | 0.122956 | − | 0.122956i | ||||
\(523\) | 7.14069 | − | 7.14069i | 0.312240 | − | 0.312240i | −0.533537 | − | 0.845777i | \(-0.679137\pi\) |
0.845777 | + | 0.533537i | \(0.179137\pi\) | |||||||
\(524\) | 14.1312i | 0.617323i | ||||||||
\(525\) | −9.75204 | − | 0.125934i | −0.425614 | − | 0.00549621i | ||||
\(526\) | 27.7565i | 1.21024i | ||||||||
\(527\) | 2.28491 | + | 2.28491i | 0.0995323 | + | 0.0995323i | ||||
\(528\) | 0.0204169 | − | 0.0204169i | 0.000888532 | − | 0.000888532i | ||||
\(529\) | −4.18960 | + | 22.6152i | −0.182156 | + | 0.983270i | ||||
\(530\) | −6.16199 | + | 6.08293i | −0.267660 | + | 0.264226i | ||||
\(531\) | 5.73861 | 0.249035 | ||||||||
\(532\) | 9.97284 | − | 9.97284i | 0.432377 | − | 0.432377i | ||||
\(533\) | −5.10259 | − | 5.10259i | −0.221018 | − | 0.221018i | ||||
\(534\) | −10.5118 | −0.454889 | ||||||||
\(535\) | −0.150735 | + | 23.3462i | −0.00651685 | + | 1.00934i | ||||
\(536\) | 6.56147i | 0.283413i | ||||||||
\(537\) | −11.7837 | + | 11.7837i | −0.508502 | + | 0.508502i | ||||
\(538\) | −1.37339 | − | 1.37339i | −0.0592110 | − | 0.0592110i | ||||
\(539\) | −0.0922600 | −0.00397392 | ||||||||
\(540\) | −0.0144369 | + | 2.23602i | −0.000621267 | + | 0.0962230i | ||||
\(541\) | 8.24675 | 0.354555 | 0.177278 | − | 0.984161i | \(-0.443271\pi\) | ||||
0.177278 | + | 0.984161i | \(0.443271\pi\) | |||||||
\(542\) | 3.99917 | − | 3.99917i | 0.171779 | − | 0.171779i | ||||
\(543\) | 4.73488 | − | 4.73488i | 0.203193 | − | 0.203193i | ||||
\(544\) | 0.620322 | 0.0265961 | ||||||||
\(545\) | −1.93544 | − | 1.96059i | −0.0829050 | − | 0.0839825i | ||||
\(546\) | 1.96292i | 0.0840053i | ||||||||
\(547\) | 11.4282 | − | 11.4282i | 0.488633 | − | 0.488633i | −0.419242 | − | 0.907875i | \(-0.637704\pi\) |
0.907875 | + | 0.419242i | \(0.137704\pi\) | |||||||
\(548\) | 9.99147 | − | 9.99147i | 0.426815 | − | 0.426815i | ||||
\(549\) | 5.09237 | 0.217337 | ||||||||
\(550\) | 0.103394 | − | 0.100758i | 0.00440875 | − | 0.00429633i | ||||
\(551\) | 28.7259i | 1.22376i | ||||||||
\(552\) | −3.68711 | + | 3.06679i | −0.156934 | + | 0.130531i | ||||
\(553\) | 7.17540 | + | 7.17540i | 0.305129 | + | 0.305129i | ||||
\(554\) | 8.53988i | 0.362825i | ||||||||
\(555\) | −3.29162 | + | 3.24939i | −0.139722 | + | 0.137929i | ||||
\(556\) | −11.0483 | −0.468551 | ||||||||
\(557\) | −28.6684 | − | 28.6684i | −1.21472 | − | 1.21472i | −0.969456 | − | 0.245264i | \(-0.921125\pi\) |
−0.245264 | − | 0.969456i | \(-0.578875\pi\) | |||||||
\(558\) | −3.68342 | − | 3.68342i | −0.155932 | − | 0.155932i | ||||
\(559\) | −8.29834 | −0.350982 | ||||||||
\(560\) | 0.0281603 | − | 4.36152i | 0.00118999 | − | 0.184308i | ||||
\(561\) | 0.0179111 | 0.000756208 | ||||||||
\(562\) | 13.4723 | + | 13.4723i | 0.568294 | + | 0.568294i | ||||
\(563\) | 6.96259 | − | 6.96259i | 0.293438 | − | 0.293438i | −0.544999 | − | 0.838437i | \(-0.683470\pi\) |
0.838437 | + | 0.544999i | \(0.183470\pi\) | |||||||
\(564\) | 9.76024i | 0.410980i | ||||||||
\(565\) | −33.5398 | − | 0.216551i | −1.41103 | − | 0.00911037i | ||||
\(566\) | − | 5.40276i | − | 0.227095i | ||||||
\(567\) | 1.37926 | + | 1.37926i | 0.0579235 | + | 0.0579235i | ||||
\(568\) | 3.87337 | + | 3.87337i | 0.162523 | + | 0.162523i | ||||
\(569\) | 14.2217 | 0.596204 | 0.298102 | − | 0.954534i | \(-0.403647\pi\) | ||||
0.298102 | + | 0.954534i | \(0.403647\pi\) | |||||||
\(570\) | −11.3585 | − | 11.5061i | −0.475754 | − | 0.481938i | ||||
\(571\) | − | 35.8009i | − | 1.49822i | −0.662444 | − | 0.749111i | \(-0.730481\pi\) | ||
0.662444 | − | 0.749111i | \(-0.269519\pi\) | |||||||
\(572\) | −0.0205462 | − | 0.0205462i | −0.000859080 | − | 0.000859080i | ||||
\(573\) | 5.18262 | − | 5.18262i | 0.216507 | − | 0.216507i | ||||
\(574\) | 13.9870 | 0.583807 | ||||||||
\(575\) | −18.6320 | + | 15.0946i | −0.777009 | + | 0.629489i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −27.3402 | + | 27.3402i | −1.13819 | + | 1.13819i | −0.149414 | + | 0.988775i | \(0.547739\pi\) |
−0.988775 | + | 0.149414i | \(0.952261\pi\) | |||||||
\(578\) | −11.7487 | − | 11.7487i | −0.488682 | − | 0.488682i | ||||
\(579\) | 7.12739i | 0.296204i | ||||||||
\(580\) | 6.24092 | + | 6.32204i | 0.259140 | + | 0.262508i | ||||
\(581\) | −27.4587 | −1.13918 | ||||||||
\(582\) | 0.850780 | + | 0.850780i | 0.0352660 | + | 0.0352660i | ||||
\(583\) | −0.0790597 | − | 0.0790597i | −0.00327432 | − | 0.00327432i | ||||
\(584\) | 1.28509i | 0.0531773i | ||||||||
\(585\) | 2.25018 | + | 0.0145284i | 0.0930335 | + | 0.000600674i | ||||
\(586\) | − | 3.11750i | − | 0.128783i | ||||||
\(587\) | 20.3799 | − | 20.3799i | 0.841168 | − | 0.841168i | −0.147843 | − | 0.989011i | \(-0.547233\pi\) |
0.989011 | + | 0.147843i | \(0.0472330\pi\) | |||||||
\(588\) | 2.25940 | + | 2.25940i | 0.0931761 | + | 0.0931761i | ||||
\(589\) | 37.6651 | 1.55196 | ||||||||
\(590\) | −0.0828480 | + | 12.8317i | −0.00341080 | + | 0.528271i | ||||
\(591\) | −8.73570 | −0.359339 | ||||||||
\(592\) | −1.46265 | − | 1.46265i | −0.0601144 | − | 0.0601144i | ||||
\(593\) | 25.3498 | + | 25.3498i | 1.04099 | + | 1.04099i | 0.999123 | + | 0.0418694i | \(0.0133313\pi\) |
0.0418694 | + | 0.999123i | \(0.486669\pi\) | |||||||
\(594\) | −0.0288739 | −0.00118471 | ||||||||
\(595\) | 1.92546 | − | 1.90076i | 0.0789363 | − | 0.0779235i | ||||
\(596\) | − | 13.0448i | − | 0.534336i | ||||||
\(597\) | 14.5856 | + | 14.5856i | 0.596950 | + | 0.596950i | ||||
\(598\) | 3.08621 | + | 3.71046i | 0.126205 | + | 0.151732i | ||||
\(599\) | 10.3371i | 0.422363i | 0.977447 | + | 0.211182i | \(0.0677311\pi\) | ||||
−0.977447 | + | 0.211182i | \(0.932269\pi\) | |||||||
\(600\) | −4.99958 | − | 0.0645626i | −0.204107 | − | 0.00263576i | ||||
\(601\) | −4.83569 | −0.197252 | −0.0986259 | − | 0.995125i | \(-0.531445\pi\) | ||||
−0.0986259 | + | 0.995125i | \(0.531445\pi\) | |||||||
\(602\) | 11.3736 | − | 11.3736i | 0.463552 | − | 0.463552i | ||||
\(603\) | 4.63966 | − | 4.63966i | 0.188942 | − | 0.188942i | ||||
\(604\) | − | 2.16088i | − | 0.0879250i | ||||||
\(605\) | −17.2786 | − | 17.5031i | −0.702473 | − | 0.711603i | ||||
\(606\) | 15.2097 | 0.617853 | ||||||||
\(607\) | 25.7553 | − | 25.7553i | 1.04538 | − | 1.04538i | 0.0464558 | − | 0.998920i | \(-0.485207\pi\) |
0.998920 | − | 0.0464558i | \(-0.0147927\pi\) | |||||||
\(608\) | 5.11278 | − | 5.11278i | 0.207351 | − | 0.207351i | ||||
\(609\) | 7.74930 | 0.314018 | ||||||||
\(610\) | −0.0735182 | + | 11.3866i | −0.00297666 | + | 0.461031i | ||||
\(611\) | 9.82204 | 0.397357 | ||||||||
\(612\) | −0.438634 | − | 0.438634i | −0.0177307 | − | 0.0177307i | ||||
\(613\) | 16.7564 | − | 16.7564i | 0.676784 | − | 0.676784i | −0.282487 | − | 0.959271i | \(-0.591159\pi\) |
0.959271 | + | 0.282487i | \(0.0911593\pi\) | |||||||
\(614\) | 19.1467i | 0.772700i | ||||||||
\(615\) | 0.103524 | − | 16.0339i | 0.00417447 | − | 0.646550i | ||||
\(616\) | 0.0563205 | 0.00226922 | ||||||||
\(617\) | 3.44309 | + | 3.44309i | 0.138614 | + | 0.138614i | 0.773009 | − | 0.634395i | \(-0.218751\pi\) |
−0.634395 | + | 0.773009i | \(0.718751\pi\) | |||||||
\(618\) | 2.54161 | − | 2.54161i | 0.102239 | − | 0.102239i | ||||
\(619\) | 41.6136 | 1.67259 | 0.836296 | − | 0.548278i | \(-0.184716\pi\) | ||||
0.836296 | + | 0.548278i | \(0.184716\pi\) | |||||||
\(620\) | 8.28939 | − | 8.18304i | 0.332910 | − | 0.328639i | ||||
\(621\) | 4.77573 | + | 0.438634i | 0.191643 | + | 0.0176018i | ||||
\(622\) | −22.7659 | + | 22.7659i | −0.912831 | + | 0.912831i | ||||
\(623\) | −14.4985 | − | 14.4985i | −0.580870 | − | 0.580870i | ||||
\(624\) | 1.00633i | 0.0402855i | ||||||||
\(625\) | −24.9917 | − | 0.645572i | −0.999667 | − | 0.0258229i | ||||
\(626\) | − | 27.4976i | − | 1.09903i | ||||||
\(627\) | 0.147626 | − | 0.147626i | 0.00589561 | − | 0.00589561i | ||||
\(628\) | −13.4623 | + | 13.4623i | −0.537204 | + | 0.537204i | ||||
\(629\) | − | 1.28313i | − | 0.0511618i | ||||||
\(630\) | −3.10397 | + | 3.06415i | −0.123665 | + | 0.122078i | ||||
\(631\) | 6.27086i | 0.249639i | 0.992179 | + | 0.124820i | \(0.0398352\pi\) | ||||
−0.992179 | + | 0.124820i | \(0.960165\pi\) | |||||||
\(632\) | 3.67862 | + | 3.67862i | 0.146328 | + | 0.146328i | ||||
\(633\) | 17.8813 | + | 17.8813i | 0.710718 | + | 0.710718i | ||||
\(634\) | 1.98209i | 0.0787188i | ||||||||
\(635\) | 20.4169 | + | 0.131822i | 0.810221 | + | 0.00523121i | ||||
\(636\) | 3.87227i | 0.153545i | ||||||||
\(637\) | 2.27371 | − | 2.27371i | 0.0900876 | − | 0.0900876i | ||||
\(638\) | −0.0811132 | + | 0.0811132i | −0.00321130 | + | 0.00321130i | ||||
\(639\) | − | 5.47777i | − | 0.216697i | ||||||
\(640\) | 0.0144369 | − | 2.23602i | 0.000570670 | − | 0.0883865i | ||||
\(641\) | 21.1913i | 0.837007i | 0.908215 | + | 0.418504i | \(0.137445\pi\) | ||||
−0.908215 | + | 0.418504i | \(0.862555\pi\) | |||||||
\(642\) | 7.38286 | + | 7.38286i | 0.291378 | + | 0.291378i | ||||
\(643\) | 25.8131 | − | 25.8131i | 1.01797 | − | 1.01797i | 0.0181324 | − | 0.999836i | \(-0.494228\pi\) |
0.999836 | − | 0.0181324i | \(-0.00577205\pi\) | |||||||
\(644\) | −9.31540 | − | 0.855587i | −0.367078 | − | 0.0337148i | ||||
\(645\) | −12.9538 | − | 13.1222i | −0.510056 | − | 0.516685i | ||||
\(646\) | 4.48528 | 0.176471 | ||||||||
\(647\) | 33.5677 | − | 33.5677i | 1.31968 | − | 1.31968i | 0.405654 | − | 0.914027i | \(-0.367044\pi\) |
0.914027 | − | 0.405654i | \(-0.132956\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −0.165696 | −0.00650414 | ||||||||
\(650\) | −0.0649715 | + | 5.03124i | −0.00254839 | + | 0.197342i | ||||
\(651\) | − | 10.1608i | − | 0.398234i | ||||||
\(652\) | −0.576831 | + | 0.576831i | −0.0225904 | + | 0.0225904i | ||||
\(653\) | −13.1083 | − | 13.1083i | −0.512967 | − | 0.512967i | 0.402467 | − | 0.915434i | \(-0.368153\pi\) |
−0.915434 | + | 0.402467i | \(0.868153\pi\) | |||||||
\(654\) | −1.23206 | −0.0481773 | ||||||||
\(655\) | 22.1986 | + | 22.4871i | 0.867372 | + | 0.878645i | ||||
\(656\) | 7.17074 | 0.279970 | ||||||||
\(657\) | 0.908695 | − | 0.908695i | 0.0354516 | − | 0.0354516i | ||||
\(658\) | −13.4619 | + | 13.4619i | −0.524800 | + | 0.524800i | ||||
\(659\) | 13.3409 | 0.519688 | 0.259844 | − | 0.965651i | \(-0.416329\pi\) | ||||
0.259844 | + | 0.965651i | \(0.416329\pi\) | |||||||
\(660\) | 0.000416850 | − | 0.0645626i | 1.62259e−5 | − | 0.00251310i | ||||
\(661\) | − | 42.1609i | − | 1.63987i | −0.572459 | − | 0.819934i | \(-0.694010\pi\) | ||
0.572459 | − | 0.819934i | \(-0.305990\pi\) | |||||||
\(662\) | 21.1812 | − | 21.1812i | 0.823229 | − | 0.823229i | ||||
\(663\) | −0.441412 | + | 0.441412i | −0.0171430 | + | 0.0171430i | ||||
\(664\) | −14.0773 | −0.546305 | ||||||||
\(665\) | 0.203615 | − | 31.5362i | 0.00789584 | − | 1.22292i | ||||
\(666\) | 2.06849i | 0.0801525i | ||||||||
\(667\) | 14.6483 | − | 12.1839i | 0.567185 | − | 0.471761i | ||||
\(668\) | −4.06044 | − | 4.06044i | −0.157103 | − | 0.157103i | ||||
\(669\) | − | 9.00179i | − | 0.348029i | ||||||
\(670\) | 10.3074 | + | 10.4414i | 0.398210 | + | 0.403385i | ||||
\(671\) | −0.147036 | −0.00567627 | ||||||||
\(672\) | −1.37926 | − | 1.37926i | −0.0532062 | − | 0.0532062i | ||||
\(673\) | −8.80148 | − | 8.80148i | −0.339272 | − | 0.339272i | 0.516821 | − | 0.856093i | \(-0.327115\pi\) |
−0.856093 | + | 0.516821i | \(0.827115\pi\) | |||||||
\(674\) | 13.6743 | 0.526714 | ||||||||
\(675\) | 3.48959 | + | 3.58089i | 0.134314 | + | 0.137829i | ||||
\(676\) | −11.9873 | −0.461050 | ||||||||
\(677\) | 1.46521 | + | 1.46521i | 0.0563127 | + | 0.0563127i | 0.734702 | − | 0.678390i | \(-0.237322\pi\) |
−0.678390 | + | 0.734702i | \(0.737322\pi\) | |||||||
\(678\) | −10.6065 | + | 10.6065i | −0.407338 | + | 0.407338i | ||||
\(679\) | 2.34690i | 0.0900656i | ||||||||
\(680\) | 0.987128 | − | 0.974463i | 0.0378546 | − | 0.0373689i | ||||
\(681\) | − | 17.2793i | − | 0.662142i | ||||||
\(682\) | 0.106355 | + | 0.106355i | 0.00407253 | + | 0.00407253i | ||||
\(683\) | −8.63814 | − | 8.63814i | −0.330529 | − | 0.330529i | 0.522258 | − | 0.852787i | \(-0.325090\pi\) |
−0.852787 | + | 0.522258i | \(0.825090\pi\) | |||||||
\(684\) | −7.23057 | −0.276468 | ||||||||
\(685\) | 0.203995 | − | 31.5952i | 0.00779425 | − | 1.20719i | ||||
\(686\) | 19.8866i | 0.759274i | ||||||||
\(687\) | −14.2993 | − | 14.2993i | −0.545552 | − | 0.545552i | ||||
\(688\) | 5.83089 | − | 5.83089i | 0.222300 | − | 0.222300i | ||||
\(689\) | 3.89679 | 0.148456 | ||||||||
\(690\) | −1.04974 | + | 10.6723i | −0.0399630 | + | 0.406288i | ||||
\(691\) | −3.45873 | −0.131576 | −0.0657882 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657882 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(692\) | 12.1320 | − | 12.1320i | 0.461189 | − | 0.461189i | ||||
\(693\) | −0.0398246 | − | 0.0398246i | −0.00151281 | − | 0.00151281i | ||||
\(694\) | − | 8.14096i | − | 0.309026i | ||||||
\(695\) | −17.5813 | + | 17.3557i | −0.666895 | + | 0.658339i | ||||
\(696\) | 3.97284 | 0.150590 | ||||||||
\(697\) | 3.14533 | + | 3.14533i | 0.119138 | + | 0.119138i | ||||
\(698\) | 10.9304 | + | 10.9304i | 0.413721 | + | 0.413721i | ||||
\(699\) | 4.12247i | 0.155926i | ||||||||
\(700\) | −6.80668 | − | 6.98478i | −0.257268 | − | 0.264000i | ||||
\(701\) | − | 27.3257i | − | 1.03208i | −0.856565 | − | 0.516039i | \(-0.827406\pi\) | ||
0.856565 | − | 0.516039i | \(-0.172594\pi\) | |||||||
\(702\) | 0.711585 | − | 0.711585i | 0.0268570 | − | 0.0268570i | ||||
\(703\) | −10.5758 | − | 10.5758i | −0.398872 | − | 0.398872i | ||||
\(704\) | 0.0288739 | 0.00108823 | ||||||||
\(705\) | 15.3323 | + | 15.5316i | 0.577449 | + | 0.584954i | ||||
\(706\) | 0.0314099 | 0.00118213 | ||||||||
\(707\) | 20.9782 | + | 20.9782i | 0.788966 | + | 0.788966i | ||||
\(708\) | 4.05781 | + | 4.05781i | 0.152502 | + | 0.152502i | ||||
\(709\) | −16.0144 | −0.601435 | −0.300717 | − | 0.953713i | \(-0.597226\pi\) | ||||
−0.300717 | + | 0.953713i | \(0.597226\pi\) | |||||||
\(710\) | 12.2484 | + | 0.0790822i | 0.459675 | + | 0.00296790i | ||||
\(711\) | − | 5.20235i | − | 0.195103i | ||||||
\(712\) | −7.43295 | − | 7.43295i | −0.278562 | − | 0.278562i | ||||
\(713\) | −15.9754 | − | 19.2067i | −0.598282 | − | 0.719297i | ||||
\(714\) | − | 1.20998i | − | 0.0452824i | ||||||
\(715\) | −0.0649715 | 0.000419490i | −0.00242979 | 1.56880e-5i | ||||||
\(716\) | −16.6646 | −0.622785 | ||||||||
\(717\) | 5.87479 | − | 5.87479i | 0.219398 | − | 0.219398i | ||||
\(718\) | 23.0700 | − | 23.0700i | 0.860964 | − | 0.860964i | ||||
\(719\) | 19.1306i | 0.713451i | 0.934209 | + | 0.356726i | \(0.116107\pi\) | ||||
−0.934209 | + | 0.356726i | \(0.883893\pi\) | |||||||
\(720\) | −1.59131 | + | 1.57090i | −0.0593048 | + | 0.0585439i | ||||
\(721\) | 7.01110 | 0.261107 | ||||||||
\(722\) | 23.5333 | − | 23.5333i | 0.875818 | − | 0.875818i | ||||
\(723\) | 10.2622 | − | 10.2622i | 0.381656 | − | 0.381656i | ||||
\(724\) | 6.69613 | 0.248860 | ||||||||
\(725\) | 19.8625 | + | 0.256497i | 0.737676 | + | 0.00952606i | ||||
\(726\) | −10.9992 | −0.408217 | ||||||||
\(727\) | 19.9934 | + | 19.9934i | 0.741513 | + | 0.741513i | 0.972869 | − | 0.231356i | \(-0.0743162\pi\) |
−0.231356 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(728\) | −1.38800 | + | 1.38800i | −0.0514425 | + | 0.0514425i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 2.01874 | + | 2.04498i | 0.0747170 | + | 0.0756881i | ||||
\(731\) | 5.11525 | 0.189194 | ||||||||
\(732\) | 3.60085 | + | 3.60085i | 0.133091 | + | 0.133091i | ||||
\(733\) | 24.0119 | − | 24.0119i | 0.886899 | − | 0.886899i | −0.107325 | − | 0.994224i | \(-0.534229\pi\) |
0.994224 | + | 0.107325i | \(0.0342286\pi\) | |||||||
\(734\) | 21.3678 | 0.788701 | ||||||||
\(735\) | 7.14470 | + | 0.0461300i | 0.263536 | + | 0.00170153i | ||||
\(736\) | −4.77573 | − | 0.438634i | −0.176036 | − | 0.0161683i | ||||
\(737\) | −0.133965 | + | 0.133965i | −0.00493467 | + | 0.00493467i | ||||
\(738\) | −5.07048 | − | 5.07048i | −0.186647 | − | 0.186647i | ||||
\(739\) | 34.2178i | 1.25872i | 0.777114 | + | 0.629360i | \(0.216683\pi\) | ||||
−0.777114 | + | 0.629360i | \(0.783317\pi\) | |||||||
\(740\) | −4.62519 | − | 0.0298627i | −0.170026 | − | 0.00109777i | ||||
\(741\) | 7.27635i | 0.267304i | ||||||||
\(742\) | −5.34087 | + | 5.34087i | −0.196069 | + | 0.196069i | ||||
\(743\) | 4.18125 | − | 4.18125i | 0.153395 | − | 0.153395i | −0.626237 | − | 0.779633i | \(-0.715406\pi\) |
0.779633 | + | 0.626237i | \(0.215406\pi\) | |||||||
\(744\) | − | 5.20915i | − | 0.190977i | ||||||
\(745\) | −20.4921 | − | 20.7584i | −0.750771 | − | 0.760529i | ||||
\(746\) | 13.2696i | 0.485836i | ||||||||
\(747\) | 9.95414 | + | 9.95414i | 0.364203 | + | 0.364203i | ||||
\(748\) | 0.0126651 | + | 0.0126651i | 0.000463081 | + | 0.000463081i | ||||
\(749\) | 20.3658i | 0.744150i | ||||||||
\(750\) | −8.05733 | + | 7.75109i | −0.294212 | + | 0.283030i | ||||
\(751\) | − | 27.8901i | − | 1.01772i | −0.860848 | − | 0.508861i | \(-0.830067\pi\) | ||
0.860848 | − | 0.508861i | \(-0.169933\pi\) | |||||||
\(752\) | −6.90153 | + | 6.90153i | −0.251673 | + | 0.251673i | ||||
\(753\) | −10.1726 | + | 10.1726i | −0.370712 | + | 0.370712i | ||||
\(754\) | − | 3.99800i | − | 0.145599i | ||||||
\(755\) | −3.39452 | − | 3.43864i | −0.123539 | − | 0.125145i | ||||
\(756\) | 1.95057i | 0.0709416i | ||||||||
\(757\) | 24.9495 | + | 24.9495i | 0.906806 | + | 0.906806i | 0.996013 | − | 0.0892070i | \(-0.0284333\pi\) |
−0.0892070 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(758\) | 10.1796 | − | 10.1796i | 0.369741 | − | 0.369741i | ||||
\(759\) | −0.137894 | − | 0.0126651i | −0.00500523 | − | 0.000459713i | ||||
\(760\) | 0.104387 | − | 16.1677i | 0.00378652 | − | 0.586464i | ||||
\(761\) | 13.0514 | 0.473115 | 0.236557 | − | 0.971618i | \(-0.423981\pi\) | ||||
0.236557 | + | 0.971618i | \(0.423981\pi\) | |||||||
\(762\) | 6.45653 | − | 6.45653i | 0.233895 | − | 0.233895i | ||||
\(763\) | −1.69933 | − | 1.69933i | −0.0615199 | − | 0.0615199i | ||||
\(764\) | 7.32933 | 0.265166 | ||||||||
\(765\) | −1.38705 | − | 0.00895556i | −0.0501490 | − | 0.000323789i | ||||
\(766\) | 8.78991i | 0.317592i | ||||||||
\(767\) | 4.08351 | − | 4.08351i | 0.147447 | − | 0.147447i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | −50.0583 | −1.80515 | −0.902574 | − | 0.430536i | \(-0.858325\pi\) | ||||
−0.902574 | + | 0.430536i | \(0.858325\pi\) | |||||||
\(770\) | 0.0896237 | − | 0.0884738i | 0.00322981 | − | 0.00318837i | ||||
\(771\) | −5.40526 | −0.194666 | ||||||||
\(772\) | −5.03982 | + | 5.03982i | −0.181387 | + | 0.181387i | ||||
\(773\) | 4.59947 | − | 4.59947i | 0.165431 | − | 0.165431i | −0.619537 | − | 0.784968i | \(-0.712679\pi\) |
0.784968 | + | 0.619537i | \(0.212679\pi\) | |||||||
\(774\) | −8.24612 | −0.296401 | ||||||||
\(775\) | 0.336316 | − | 26.0436i | 0.0120808 | − | 0.935513i | ||||
\(776\) | 1.20318i | 0.0431918i | ||||||||
\(777\) | −2.85299 | + | 2.85299i | −0.102351 | + | 0.102351i | ||||
\(778\) | −16.7040 | + | 16.7040i | −0.598869 | + | 0.598869i | ||||
\(779\) | 51.8485 | 1.85767 | ||||||||
\(780\) | 1.58085 | + | 1.60139i | 0.0566033 | + | 0.0573390i | ||||
\(781\) | 0.158164i | 0.00565957i | ||||||||
\(782\) | −1.90240 | − | 2.28720i | −0.0680296 | − | 0.0817900i | ||||
\(783\) | −2.80922 | − | 2.80922i | −0.100393 | − | 0.100393i | ||||
\(784\) | 3.19528i | 0.114117i | ||||||||
\(785\) | −0.274859 | + | 42.5706i | −0.00981012 | + | 1.51941i | ||||
\(786\) | 14.1312 | 0.504042 | ||||||||
\(787\) | −34.0252 | − | 34.0252i | −1.21287 | − | 1.21287i | −0.970080 | − | 0.242787i | \(-0.921938\pi\) |
−0.242787 | − | 0.970080i | \(-0.578062\pi\) | |||||||
\(788\) | −6.17707 | − | 6.17707i | −0.220049 | − | 0.220049i | ||||
\(789\) | 27.7565 | 0.988159 | ||||||||
\(790\) | 11.6326 | + | 0.0751060i | 0.413868 | + | 0.00267215i | ||||
\(791\) | −29.2581 | −1.04030 | ||||||||
\(792\) | −0.0204169 | − | 0.0204169i | −0.000725484 | − | 0.000725484i | ||||
\(793\) | 3.62365 | − | 3.62365i | 0.128680 | − | 0.128680i | ||||
\(794\) | 6.94477i | 0.246461i | ||||||||
\(795\) | 6.08293 | + | 6.16199i | 0.215739 | + | 0.218543i | ||||
\(796\) | 20.6272i | 0.731111i | ||||||||
\(797\) | −1.37656 | − | 1.37656i | −0.0487602 | − | 0.0487602i | 0.682306 | − | 0.731066i | \(-0.260977\pi\) |
−0.731066 | + | 0.682306i | \(0.760977\pi\) | |||||||
\(798\) | −9.97284 | − | 9.97284i | −0.353035 | − | 0.353035i | ||||
\(799\) | −6.05449 | −0.214193 | ||||||||
\(800\) | −3.48959 | − | 3.58089i | −0.123376 | − | 0.126604i | ||||
\(801\) | 10.5118i | 0.371415i | ||||||||
\(802\) | −10.2315 | − | 10.2315i | −0.361288 | − | 0.361288i | ||||
\(803\) | −0.0262375 | + | 0.0262375i | −0.000925903 | + | 0.000925903i | ||||
\(804\) | 6.56147 | 0.231405 | ||||||||
\(805\) | −16.1678 | + | 13.2720i | −0.569839 | + | 0.467777i | ||||
\(806\) | −5.24214 | −0.184646 | ||||||||
\(807\) | −1.37339 | + | 1.37339i | −0.0483456 | + | 0.0483456i | ||||
\(808\) | 10.7549 | + | 10.7549i | 0.378356 | + | 0.378356i | ||||
\(809\) | 22.8770i | 0.804313i | 0.915571 | + | 0.402156i | \(0.131739\pi\) | ||||
−0.915571 | + | 0.402156i | \(0.868261\pi\) | |||||||
\(810\) | 2.23602 | + | 0.0144369i | 0.0785658 | + | 0.000507262i | ||||
\(811\) | 13.7863 | 0.484103 | 0.242052 | − | 0.970263i | \(-0.422180\pi\) | ||||
0.242052 | + | 0.970263i | \(0.422180\pi\) | |||||||
\(812\) | 5.47959 | + | 5.47959i | 0.192296 | + | 0.192296i | ||||
\(813\) | −3.99917 | − | 3.99917i | −0.140257 | − | 0.140257i | ||||
\(814\) | − | 0.0597254i | − | 0.00209337i | ||||||
\(815\) | −0.0117771 | + | 1.82406i | −0.000412534 | + | 0.0638941i | ||||
\(816\) | − | 0.620322i | − | 0.0217156i | ||||||
\(817\) | 42.1606 | − | 42.1606i | 1.47501 | − | 1.47501i | ||||
\(818\) | −15.9466 | − | 15.9466i | −0.557558 | − | 0.557558i | ||||
\(819\) | 1.96292 | 0.0685901 | ||||||||
\(820\) | 11.4109 | − | 11.2645i | 0.398486 | − | 0.393373i | ||||
\(821\) | 22.3491 | 0.779988 | 0.389994 | − | 0.920817i | \(-0.372477\pi\) | ||||
0.389994 | + | 0.920817i | \(0.372477\pi\) | |||||||
\(822\) | −9.99147 | − | 9.99147i | −0.348493 | − | 0.348493i | ||||
\(823\) | 26.7332 | + | 26.7332i | 0.931861 | + | 0.931861i | 0.997822 | − | 0.0659610i | \(-0.0210113\pi\) |
−0.0659610 | + | 0.997822i | \(0.521011\pi\) | |||||||
\(824\) | 3.59438 | 0.125216 | ||||||||
\(825\) | −0.100758 | − | 0.103394i | −0.00350794 | − | 0.00359973i | ||||
\(826\) | 11.1936i | 0.389474i | ||||||||
\(827\) | 15.5121 | + | 15.5121i | 0.539409 | + | 0.539409i | 0.923355 | − | 0.383947i | \(-0.125435\pi\) |
−0.383947 | + | 0.923355i | \(0.625435\pi\) | |||||||
\(828\) | 3.06679 | + | 3.68711i | 0.106578 | + | 0.128136i | ||||
\(829\) | 32.8637i | 1.14140i | 0.821157 | + | 0.570702i | \(0.193329\pi\) | ||||
−0.821157 | + | 0.570702i | \(0.806671\pi\) | |||||||
\(830\) | −22.4014 | + | 22.1140i | −0.777563 | + | 0.767587i | ||||
\(831\) | 8.53988 | 0.296245 | ||||||||
\(832\) | −0.711585 | + | 0.711585i | −0.0246698 | + | 0.0246698i | ||||
\(833\) | −1.40156 | + | 1.40156i | −0.0485611 | + | 0.0485611i | ||||
\(834\) | 11.0483i | 0.382570i | ||||||||
\(835\) | −12.8400 | − | 0.0829016i | −0.444345 | − | 0.00286893i | ||||
\(836\) | 0.208774 | 0.00722062 | ||||||||
\(837\) | −3.68342 | + | 3.68342i | −0.127318 | + | 0.127318i | ||||
\(838\) | −21.2494 | + | 21.2494i | −0.734049 | + | 0.734049i | ||||
\(839\) | −1.16009 | −0.0400506 | −0.0200253 | − | 0.999799i | \(-0.506375\pi\) | ||||
−0.0200253 | + | 0.999799i | \(0.506375\pi\) | |||||||
\(840\) | −4.36152 | − | 0.0281603i | −0.150487 | − | 0.000971621i | ||||
\(841\) | 13.2165 | 0.455743 | ||||||||
\(842\) | 15.2317 | + | 15.2317i | 0.524919 | + | 0.524919i | ||||
\(843\) | 13.4723 | − | 13.4723i | 0.464010 | − | 0.464010i | ||||
\(844\) | 25.2880i | 0.870448i | ||||||||
\(845\) | −19.0756 | + | 18.8308i | −0.656219 | + | 0.647800i | ||||
\(846\) | 9.76024 | 0.335564 | ||||||||
\(847\) | −15.1707 | − | 15.1707i | −0.521272 | − | 0.521272i | ||||
\(848\) | −2.73811 | + | 2.73811i | −0.0940269 | + | 0.0940269i | ||||
\(849\) | −5.40276 | −0.185422 | ||||||||
\(850\) | 0.0400496 | − | 3.10135i | 0.00137369 | − | 0.106376i | ||||
\(851\) | −0.907312 | + | 9.87856i | −0.0311022 | + | 0.338633i | ||||
\(852\) | 3.87337 | − | 3.87337i | 0.132699 | − | 0.132699i | ||||
\(853\) | −23.7980 | − | 23.7980i | −0.814828 | − | 0.814828i | 0.170525 | − | 0.985353i | \(-0.445454\pi\) |
−0.985353 | + | 0.170525i | \(0.945454\pi\) | |||||||
\(854\) | 9.93302i | 0.339901i | ||||||||
\(855\) | −11.5061 | + | 11.3585i | −0.393500 | + | 0.388452i | ||||
\(856\) | 10.4409i | 0.356864i | ||||||||
\(857\) | −5.14887 | + | 5.14887i | −0.175882 | + | 0.175882i | −0.789558 | − | 0.613676i | \(-0.789690\pi\) |
0.613676 | + | 0.789558i | \(0.289690\pi\) | |||||||
\(858\) | −0.0205462 | + | 0.0205462i | −0.000701436 | + | 0.000701436i | ||||
\(859\) | 45.5119i | 1.55285i | 0.630212 | + | 0.776423i | \(0.282968\pi\) | ||||
−0.630212 | + | 0.776423i | \(0.717032\pi\) | |||||||
\(860\) | 0.119049 | − | 18.4385i | 0.00405953 | − | 0.628748i | ||||
\(861\) | − | 13.9870i | − | 0.476677i | ||||||
\(862\) | 11.0324 | + | 11.0324i | 0.375765 | + | 0.375765i | ||||
\(863\) | −17.4151 | − | 17.4151i | −0.592816 | − | 0.592816i | 0.345575 | − | 0.938391i | \(-0.387684\pi\) |
−0.938391 | + | 0.345575i | \(0.887684\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 0.247698 | − | 38.3640i | 0.00842199 | − | 1.30441i | ||||
\(866\) | 15.9762i | 0.542893i | ||||||||
\(867\) | −11.7487 | + | 11.7487i | −0.399007 | + | 0.399007i | ||||
\(868\) | 7.18478 | − | 7.18478i | 0.243867 | − | 0.243867i | ||||
\(869\) | 0.150212i | 0.00509560i | ||||||||
\(870\) | 6.32204 | − | 6.24092i | 0.214337 | − | 0.211587i | ||||
\(871\) | − | 6.60302i | − | 0.223735i | ||||||
\(872\) | −0.871197 | − | 0.871197i | −0.0295024 | − | 0.0295024i | ||||
\(873\) | 0.850780 | − | 0.850780i | 0.0287945 | − | 0.0287945i | ||||
\(874\) | −34.5312 | − | 3.17157i | −1.16804 | − | 0.107280i | ||||
\(875\) | −21.8039 | − | 0.422381i | −0.737108 | − | 0.0142791i | ||||
\(876\) | 1.28509 | 0.0434191 | ||||||||
\(877\) | 3.53043 | − | 3.53043i | 0.119214 | − | 0.119214i | −0.644983 | − | 0.764197i | \(-0.723136\pi\) |
0.764197 | + | 0.644983i | \(0.223136\pi\) | |||||||
\(878\) | −2.26510 | − | 2.26510i | −0.0764433 | − | 0.0764433i | ||||
\(879\) | −3.11750 | −0.105151 | ||||||||
\(880\) | 0.0459474 | − | 0.0453579i | 0.00154889 | − | 0.00152901i | ||||
\(881\) | − | 47.1248i | − | 1.58768i | −0.608130 | − | 0.793838i | \(-0.708080\pi\) | ||
0.608130 | − | 0.793838i | \(-0.291920\pi\) | |||||||
\(882\) | 2.25940 | − | 2.25940i | 0.0760780 | − | 0.0760780i | ||||
\(883\) | −4.17195 | − | 4.17195i | −0.140397 | − | 0.140397i | 0.633415 | − | 0.773812i | \(-0.281653\pi\) |
−0.773812 | + | 0.633415i | \(0.781653\pi\) | |||||||
\(884\) | −0.624251 | −0.0209958 | ||||||||
\(885\) | 12.8317 | + | 0.0828480i | 0.431332 | + | 0.00278491i | ||||
\(886\) | −22.0740 | −0.741590 | ||||||||
\(887\) | −28.7906 | + | 28.7906i | −0.966694 | + | 0.966694i | −0.999463 | − | 0.0327690i | \(-0.989567\pi\) |
0.0327690 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(888\) | −1.46265 | + | 1.46265i | −0.0490832 | + | 0.0490832i | ||||
\(889\) | 17.8105 | 0.597345 | ||||||||
\(890\) | −23.5046 | − | 0.151758i | −0.787874 | − | 0.00508694i | ||||
\(891\) | 0.0288739i | 0.000967311i | ||||||||
\(892\) | 6.36523 | − | 6.36523i | 0.213124 | − | 0.213124i | ||||
\(893\) | −49.9020 | + | 49.9020i | −1.66991 | + | 1.66991i | ||||
\(894\) | −13.0448 | −0.436284 | ||||||||
\(895\) | −26.5186 | + | 26.1784i | −0.886420 | + | 0.875047i | ||||
\(896\) | − | 1.95057i | − | 0.0651640i | ||||||
\(897\) | 3.71046 | − | 3.08621i | 0.123889 | − | 0.103046i | ||||
\(898\) | 7.92748 | + | 7.92748i | 0.264543 | + | 0.264543i | ||||
\(899\) | 20.6951i | 0.690221i | ||||||||
\(900\) | −0.0645626 | + | 4.99958i | −0.00215209 | + | 0.166653i | ||||
\(901\) | −2.40205 | −0.0800240 | ||||||||
\(902\) | 0.146404 | + | 0.146404i | 0.00487473 | + | 0.00487473i | ||||
\(903\) | −11.3736 | − | 11.3736i | −0.378488 | − | 0.378488i | ||||
\(904\) | −14.9998 | −0.498885 | ||||||||
\(905\) | 10.6556 | − | 10.5189i | 0.354206 | − | 0.349661i | ||||
\(906\) | −2.16088 | −0.0717904 | ||||||||
\(907\) | −25.5309 | − | 25.5309i | −0.847738 | − | 0.847738i | 0.142112 | − | 0.989851i | \(-0.454611\pi\) |
−0.989851 | + | 0.142112i | \(0.954611\pi\) | |||||||
\(908\) | 12.2183 | − | 12.2183i | 0.405478 | − | 0.405478i | ||||
\(909\) | − | 15.2097i | − | 0.504475i | ||||||
\(910\) | −0.0283386 | + | 4.38914i | −0.000939415 | + | 0.145498i | ||||
\(911\) | 60.0473i | 1.98946i | 0.102548 | + | 0.994728i | \(0.467300\pi\) | ||||
−0.102548 | + | 0.994728i | \(0.532700\pi\) | |||||||
\(912\) | −5.11278 | − | 5.11278i | −0.169301 | − | 0.169301i | ||||
\(913\) | −0.287415 | − | 0.287415i | −0.00951204 | − | 0.00951204i | ||||
\(914\) | 24.9769 | 0.826163 | ||||||||
\(915\) | 11.3866 | + | 0.0735182i | 0.376431 | + | 0.00243044i | ||||
\(916\) | − | 20.2222i | − | 0.668162i | ||||||
\(917\) | 19.4906 | + | 19.4906i | 0.643635 | + | 0.643635i | ||||
\(918\) | −0.438634 | + | 0.438634i | −0.0144771 | + | 0.0144771i | ||||
\(919\) | 12.2350 | 0.403596 | 0.201798 | − | 0.979427i | \(-0.435322\pi\) | ||||
0.201798 | + | 0.979427i | \(0.435322\pi\) | |||||||
\(920\) | −8.28874 | + | 6.80418i | −0.273272 | + | 0.224327i | ||||
\(921\) | 19.1467 | 0.630907 | ||||||||
\(922\) | 13.6556 | − | 13.6556i | 0.449722 | − | 0.449722i | ||||
\(923\) | −3.89790 | − | 3.89790i | −0.128301 | − | 0.128301i | ||||
\(924\) | − | 0.0563205i | − | 0.00185281i | ||||||
\(925\) | −7.40705 | + | 7.21818i | −0.243542 | + | 0.237332i | ||||
\(926\) | 17.8773 | 0.587484 | ||||||||
\(927\) | −2.54161 | − | 2.54161i | −0.0834775 | − | 0.0834775i | ||||
\(928\) | 2.80922 | + | 2.80922i | 0.0922172 | + | 0.0922172i | ||||
\(929\) | 48.6994i | 1.59777i | 0.601481 | + | 0.798887i | \(0.294578\pi\) | ||||
−0.601481 | + | 0.798887i | \(0.705422\pi\) | |||||||
\(930\) | −8.18304 | − | 8.28939i | −0.268332 | − | 0.271820i | ||||
\(931\) | 23.1037i | 0.757192i | ||||||||
\(932\) | −2.91503 | + | 2.91503i | −0.0954849 | + | 0.0954849i | ||||
\(933\) | 22.7659 | + | 22.7659i | 0.745323 | + | 0.745323i | ||||
\(934\) | −38.6764 | −1.26553 | ||||||||
\(935\) | 0.0400496 | 0.000258582i | 0.00130976 | 8.45652e-6i | ||||||
\(936\) | 1.00633 | 0.0328930 | ||||||||
\(937\) | −40.3568 | − | 40.3568i | −1.31840 | − | 1.31840i | −0.915042 | − | 0.403359i | \(-0.867843\pi\) |
−0.403359 | − | 0.915042i | \(-0.632157\pi\) | |||||||
\(938\) | 9.04999 | + | 9.04999i | 0.295493 | + | 0.295493i | ||||
\(939\) | −27.4976 | −0.897351 | ||||||||
\(940\) | −0.140908 | + | 21.8241i | −0.00459591 | + | 0.711823i | ||||
\(941\) | 1.28193i | 0.0417897i | 0.999782 | + | 0.0208949i | \(0.00665152\pi\) | ||||
−0.999782 | + | 0.0208949i | \(0.993348\pi\) | |||||||
\(942\) | 13.4623 | + | 13.4623i | 0.438625 | + | 0.438625i | ||||
\(943\) | −21.9912 | − | 26.4393i | −0.716130 | − | 0.860983i | ||||
\(944\) | 5.73861i | 0.186776i | ||||||||
\(945\) | 3.06415 | + | 3.10397i | 0.0996767 | + | 0.100972i | ||||
\(946\) | 0.238097 | 0.00774122 | ||||||||
\(947\) | 24.0315 | − | 24.0315i | 0.780919 | − | 0.780919i | −0.199067 | − | 0.979986i | \(-0.563791\pi\) |
0.979986 | + | 0.199067i | \(0.0637912\pi\) | |||||||
\(948\) | 3.67862 | − | 3.67862i | 0.119476 | − | 0.119476i | ||||
\(949\) | − | 1.29323i | − | 0.0419799i | ||||||
\(950\) | −25.2317 | − | 25.8919i | −0.818624 | − | 0.840043i | ||||
\(951\) | 1.98209 | 0.0642736 | ||||||||
\(952\) | 0.855587 | − | 0.855587i | 0.0277297 | − | 0.0277297i | ||||
\(953\) | 1.28685 | − | 1.28685i | 0.0416850 | − | 0.0416850i | −0.685957 | − | 0.727642i | \(-0.740616\pi\) |
0.727642 | + | 0.685957i | \(0.240616\pi\) | |||||||
\(954\) | 3.87227 | 0.125369 | ||||||||
\(955\) | 11.6633 | − | 11.5136i | 0.377414 | − | 0.372572i | ||||
\(956\) | 8.30821 | 0.268707 | ||||||||
\(957\) | 0.0811132 | + | 0.0811132i | 0.00262202 | + | 0.00262202i | ||||
\(958\) | −19.0598 | + | 19.0598i | −0.615796 | + | 0.615796i | ||||
\(959\) | − | 27.5617i | − | 0.890014i | ||||||
\(960\) | −2.23602 | − | 0.0144369i | −0.0721673 | − | 0.000465950i | ||||
\(961\) | −3.86477 | −0.124670 | ||||||||
\(962\) | 1.47191 | + | 1.47191i | 0.0474562 | + | 0.0474562i | ||||
\(963\) | 7.38286 | − | 7.38286i | 0.237909 | − | 0.237909i | ||||
\(964\) | 14.5130 | 0.467431 | ||||||||
\(965\) | −0.102898 | + | 15.9370i | −0.00331239 | + | 0.513030i | ||||
\(966\) | −0.855587 | + | 9.31540i | −0.0275281 | + | 0.299718i | ||||
\(967\) | 34.5037 | − | 34.5037i | 1.10956 | − | 1.10956i | 0.116356 | − | 0.993208i | \(-0.462879\pi\) |
0.993208 | − | 0.116356i | \(-0.0371214\pi\) | |||||||
\(968\) | −7.77759 | − | 7.77759i | −0.249981 | − | 0.249981i | ||||
\(969\) | − | 4.48528i | − | 0.144088i | ||||||
\(970\) | 1.89008 | + | 1.91464i | 0.0606868 | + | 0.0614755i | ||||
\(971\) | 14.6826i | 0.471188i | 0.971852 | + | 0.235594i | \(0.0757035\pi\) | ||||
−0.971852 | + | 0.235594i | \(0.924297\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −15.2385 | + | 15.2385i | −0.488522 | + | 0.488522i | ||||
\(974\) | − | 40.6173i | − | 1.30146i | ||||||
\(975\) | 5.03124 | + | 0.0649715i | 0.161129 | + | 0.00208075i | ||||
\(976\) | 5.09237i | 0.163003i | ||||||||
\(977\) | −40.9702 | − | 40.9702i | −1.31075 | − | 1.31075i | −0.920859 | − | 0.389895i | \(-0.872511\pi\) |
−0.389895 | − | 0.920859i | \(-0.627489\pi\) | |||||||
\(978\) | 0.576831 | + | 0.576831i | 0.0184450 | + | 0.0184450i | ||||
\(979\) | − | 0.303516i | − | 0.00970041i | ||||||
\(980\) | 5.01945 | + | 5.08469i | 0.160340 | + | 0.162424i | ||||
\(981\) | 1.23206i | 0.0393366i | ||||||||
\(982\) | 1.87638 | − | 1.87638i | 0.0598777 | − | 0.0598777i | ||||
\(983\) | −30.5500 | + | 30.5500i | −0.974393 | + | 0.974393i | −0.999680 | − | 0.0252874i | \(-0.991950\pi\) |
0.0252874 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(984\) | − | 7.17074i | − | 0.228595i | ||||||
\(985\) | −19.5332 | − | 0.126117i | −0.622380 | − | 0.00401841i | ||||
\(986\) | 2.46444i | 0.0784838i | ||||||||
\(987\) | 13.4619 | + | 13.4619i | 0.428498 | + | 0.428498i | ||||
\(988\) | −5.14516 | + | 5.14516i | −0.163689 | + | 0.163689i | ||||
\(989\) | −39.3812 | − | 3.61703i | −1.25225 | − | 0.115015i | ||||
\(990\) | −0.0645626 | 0.000416850i | −0.00205193 | 1.32484e-5i | ||||||
\(991\) | −33.7746 | −1.07289 | −0.536443 | − | 0.843936i | \(-0.680232\pi\) | ||||
−0.536443 | + | 0.843936i | \(0.680232\pi\) | |||||||
\(992\) | 3.68342 | − | 3.68342i | 0.116949 | − | 0.116949i | ||||
\(993\) | −21.1812 | − | 21.1812i | −0.672164 | − | 0.672164i | ||||
\(994\) | 10.6848 | 0.338900 | ||||||||
\(995\) | 32.4032 | + | 32.8243i | 1.02725 | + | 1.04060i | ||||
\(996\) | 14.0773i | 0.446056i | ||||||||
\(997\) | 2.06252 | − | 2.06252i | 0.0653208 | − | 0.0653208i | −0.673692 | − | 0.739012i | \(-0.735292\pi\) |
0.739012 | + | 0.673692i | \(0.235292\pi\) | |||||||
\(998\) | 6.44546 | + | 6.44546i | 0.204027 | + | 0.204027i | ||||
\(999\) | 2.06849 | 0.0654442 |
(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 | 690.2.j.a.643.8 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.a.367.11 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.a.643.11 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.a.367.8 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.a.367.8 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.a.367.11 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.a.643.8 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.a.643.11 | yes | 24 | 23.22 | odd | 2 | inner |