Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.u.991.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.20711 | − | 2.09077i | 0.539835 | − | 0.935021i | −0.459078 | − | 0.888396i | \(-0.651820\pi\) |
0.998912 | − | 0.0466249i | \(-0.0148465\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.20711 | − | 2.09077i | −0.381721 | − | 0.661160i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82843 | −1.89386 | −0.946932 | − | 0.321433i | \(-0.895836\pi\) | ||||
−0.946932 | + | 0.321433i | \(0.895836\pi\) | |||||||
\(14\) | 2.62132 | − | 0.358719i | 0.700577 | − | 0.0958718i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.91421 | − | 6.77962i | −0.949336 | − | 1.64430i | −0.746827 | − | 0.665018i | \(-0.768424\pi\) |
−0.202509 | − | 0.979280i | \(-0.564910\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41421 | − | 4.18154i | 0.553859 | − | 0.959311i | −0.444133 | − | 0.895961i | \(-0.646488\pi\) |
0.997991 | − | 0.0633502i | \(-0.0201785\pi\) | |||||||
\(20\) | −2.41421 | −0.539835 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.62132 | − | 4.54026i | 0.546583 | − | 0.946710i | −0.451922 | − | 0.892057i | \(-0.649262\pi\) |
0.998505 | − | 0.0546524i | \(-0.0174051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.414214 | − | 0.717439i | −0.0828427 | − | 0.143488i | ||||
\(26\) | −3.41421 | + | 5.91359i | −0.669582 | + | 1.15975i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.24264 | − | 9.08052i | −0.941606 | − | 1.63091i | −0.762408 | − | 0.647097i | \(-0.775983\pi\) |
−0.179198 | − | 0.983813i | \(-0.557350\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.82843 | −1.34256 | ||||||||
\(35\) | 6.32843 | − | 0.866025i | 1.06970 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.828427 | − | 1.43488i | 0.136193 | − | 0.235892i | −0.789860 | − | 0.613287i | \(-0.789847\pi\) |
0.926052 | + | 0.377395i | \(0.123180\pi\) | |||||||
\(38\) | −2.41421 | − | 4.18154i | −0.391637 | − | 0.678335i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.20711 | + | 2.09077i | −0.190860 | + | 0.330580i | ||||
\(41\) | 6.65685 | 1.03963 | 0.519813 | − | 0.854280i | \(-0.326002\pi\) | ||||
0.519813 | + | 0.854280i | \(0.326002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843 | 0.431331 | 0.215666 | − | 0.976467i | \(-0.430808\pi\) | ||||
0.215666 | + | 0.976467i | \(0.430808\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62132 | − | 4.54026i | −0.386493 | − | 0.669425i | ||||
\(47\) | −0.378680 | + | 0.655892i | −0.0552361 | + | 0.0956717i | −0.892321 | − | 0.451401i | \(-0.850924\pi\) |
0.837085 | + | 0.547073i | \(0.184258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | −0.828427 | −0.117157 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.41421 | + | 5.91359i | 0.473466 | + | 0.820068i | ||||
\(53\) | −5.41421 | − | 9.37769i | −0.743699 | − | 1.28813i | −0.950800 | − | 0.309806i | \(-0.899736\pi\) |
0.207101 | − | 0.978320i | \(-0.433597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.41421 | 0.325532 | ||||||||
\(56\) | −1.62132 | − | 2.09077i | −0.216658 | − | 0.279391i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41421 | − | 2.44949i | 0.185695 | − | 0.321634i | ||||
\(59\) | 3.82843 | + | 6.63103i | 0.498419 | + | 0.863287i | 0.999998 | − | 0.00182490i | \(-0.000580884\pi\) |
−0.501580 | + | 0.865112i | \(0.667248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.20711 | − | 3.82282i | 0.282591 | − | 0.489462i | −0.689431 | − | 0.724351i | \(-0.742139\pi\) |
0.972022 | + | 0.234889i | \(0.0754727\pi\) | |||||||
\(62\) | −10.4853 | −1.33163 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.24264 | + | 14.2767i | −1.02237 | + | 1.77080i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.74264 | − | 3.01834i | −0.212897 | − | 0.368749i | 0.739723 | − | 0.672912i | \(-0.234957\pi\) |
−0.952620 | + | 0.304163i | \(0.901623\pi\) | |||||||
\(68\) | −3.91421 | + | 6.77962i | −0.474668 | + | 0.822149i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.41421 | − | 5.91359i | 0.288554 | − | 0.706809i | ||||
\(71\) | 9.31371 | 1.10533 | 0.552667 | − | 0.833402i | \(-0.313610\pi\) | ||||
0.552667 | + | 0.833402i | \(0.313610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.414214 | − | 0.717439i | −0.0484800 | − | 0.0839699i | 0.840767 | − | 0.541397i | \(-0.182104\pi\) |
−0.889247 | + | 0.457427i | \(0.848771\pi\) | |||||||
\(74\) | −0.828427 | − | 1.43488i | −0.0963027 | − | 0.166801i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.82843 | −0.553859 | ||||||||
\(77\) | −1.00000 | + | 2.44949i | −0.113961 | + | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.62132 | + | 11.4685i | −0.744957 | + | 1.29030i | 0.205258 | + | 0.978708i | \(0.434197\pi\) |
−0.950215 | + | 0.311595i | \(0.899137\pi\) | |||||||
\(80\) | 1.20711 | + | 2.09077i | 0.134959 | + | 0.233755i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.32843 | − | 5.76500i | 0.367563 | − | 0.636638i | ||||
\(83\) | 4.17157 | 0.457890 | 0.228945 | − | 0.973439i | \(-0.426472\pi\) | ||||
0.228945 | + | 0.973439i | \(0.426472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.8995 | −2.04994 | ||||||||
\(86\) | 1.41421 | − | 2.44949i | 0.152499 | − | 0.264135i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −2.24264 | + | 3.88437i | −0.237719 | + | 0.411742i | −0.960060 | − | 0.279796i | \(-0.909733\pi\) |
0.722340 | + | 0.691538i | \(0.243067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0711 | − | 14.2767i | −1.16056 | − | 1.49660i | ||||
\(92\) | −5.24264 | −0.546583 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.378680 | + | 0.655892i | 0.0390578 | + | 0.0676501i | ||||
\(95\) | −5.82843 | − | 10.0951i | −0.597984 | − | 1.03574i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.8284 | −1.60713 | −0.803567 | − | 0.595215i | \(-0.797067\pi\) | ||||
−0.803567 | + | 0.595215i | \(0.797067\pi\) | |||||||
\(98\) | 5.00000 | + | 4.89898i | 0.505076 | + | 0.494872i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.414214 | + | 0.717439i | −0.0414214 | + | 0.0717439i | ||||
\(101\) | 7.07107 | + | 12.2474i | 0.703598 | + | 1.21867i | 0.967195 | + | 0.254034i | \(0.0817575\pi\) |
−0.263598 | + | 0.964633i | \(0.584909\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.41421 | − | 12.8418i | 0.730544 | − | 1.26534i | −0.226107 | − | 0.974103i | \(-0.572600\pi\) |
0.956651 | − | 0.291237i | \(-0.0940669\pi\) | |||||||
\(104\) | 6.82843 | 0.669582 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.8284 | −1.05175 | ||||||||
\(107\) | −2.67157 | + | 4.62730i | −0.258271 | + | 0.447338i | −0.965779 | − | 0.259367i | \(-0.916486\pi\) |
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.62132 | + | 4.54026i | 0.251077 | + | 0.434878i | 0.963823 | − | 0.266545i | \(-0.0858819\pi\) |
−0.712746 | + | 0.701423i | \(0.752549\pi\) | |||||||
\(110\) | 1.20711 | − | 2.09077i | 0.115093 | − | 0.199347i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.62132 | + | 0.358719i | −0.247691 | + | 0.0338958i | ||||
\(113\) | 7.65685 | 0.720296 | 0.360148 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360148 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.32843 | − | 10.9612i | −0.590129 | − | 1.02213i | ||||
\(116\) | −1.41421 | − | 2.44949i | −0.131306 | − | 0.227429i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.65685 | 0.704871 | ||||||||
\(119\) | 7.82843 | − | 19.1757i | 0.717631 | − | 1.75783i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −2.20711 | − | 3.82282i | −0.199822 | − | 0.346102i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.24264 | + | 9.08052i | −0.470803 | + | 0.815455i | ||||
\(125\) | 10.0711 | 0.900784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.24264 | −0.642680 | −0.321340 | − | 0.946964i | \(-0.604133\pi\) | ||||
−0.321340 | + | 0.946964i | \(0.604133\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.24264 | + | 14.2767i | 0.722927 | + | 1.25215i | ||||
\(131\) | −3.65685 | + | 6.33386i | −0.319501 | + | 0.553392i | −0.980384 | − | 0.197097i | \(-0.936849\pi\) |
0.660883 | + | 0.750489i | \(0.270182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.6569 | − | 1.73205i | 1.09749 | − | 0.150188i | ||||
\(134\) | −3.48528 | −0.301082 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.91421 | + | 6.77962i | 0.335641 | + | 0.581347i | ||||
\(137\) | 0.414214 | + | 0.717439i | 0.0353887 | + | 0.0612949i | 0.883177 | − | 0.469039i | \(-0.155400\pi\) |
−0.847789 | + | 0.530334i | \(0.822066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | −0.508913 | −0.254457 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254457 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(140\) | −3.91421 | − | 5.04757i | −0.330811 | − | 0.426597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.65685 | − | 8.06591i | 0.390795 | − | 0.676876i | ||||
\(143\) | −3.41421 | − | 5.91359i | −0.285511 | − | 0.494519i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.41421 | − | 5.91359i | 0.283535 | − | 0.491097i | ||||
\(146\) | −0.828427 | −0.0685611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.65685 | −0.136193 | ||||||||
\(149\) | −5.65685 | + | 9.79796i | −0.463428 | + | 0.802680i | −0.999129 | − | 0.0417274i | \(-0.986714\pi\) |
0.535701 | + | 0.844407i | \(0.320047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.62132 | + | 6.27231i | 0.294699 | + | 0.510433i | 0.974915 | − | 0.222578i | \(-0.0714473\pi\) |
−0.680216 | + | 0.733012i | \(0.738114\pi\) | |||||||
\(152\) | −2.41421 | + | 4.18154i | −0.195819 | + | 0.339168i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.62132 | + | 2.09077i | 0.130650 | + | 0.168479i | ||||
\(155\) | −25.3137 | −2.03325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.41421 | + | 12.8418i | 0.591719 | + | 1.02489i | 0.994001 | + | 0.109371i | \(0.0348837\pi\) |
−0.402282 | + | 0.915516i | \(0.631783\pi\) | |||||||
\(158\) | 6.62132 | + | 11.4685i | 0.526764 | + | 0.912382i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.41421 | 0.190860 | ||||||||
\(161\) | 13.7426 | − | 1.88064i | 1.08307 | − | 0.148215i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.50000 | + | 2.59808i | −0.117489 | + | 0.203497i | −0.918772 | − | 0.394789i | \(-0.870818\pi\) |
0.801283 | + | 0.598286i | \(0.204151\pi\) | |||||||
\(164\) | −3.32843 | − | 5.76500i | −0.259906 | − | 0.450171i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.08579 | − | 3.61269i | 0.161888 | − | 0.280399i | ||||
\(167\) | −0.485281 | −0.0375522 | −0.0187761 | − | 0.999824i | \(-0.505977\pi\) | ||||
−0.0187761 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | −9.44975 | + | 16.3674i | −0.724763 | + | 1.25533i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.41421 | − | 2.44949i | −0.107833 | − | 0.186772i | ||||
\(173\) | 8.07107 | − | 13.9795i | 0.613632 | − | 1.06284i | −0.376991 | − | 0.926217i | \(-0.623041\pi\) |
0.990623 | − | 0.136625i | \(-0.0436254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.828427 | − | 2.02922i | 0.0626232 | − | 0.153395i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.24264 | + | 3.88437i | 0.168093 | + | 0.291146i | ||||
\(179\) | −4.41421 | − | 7.64564i | −0.329934 | − | 0.571462i | 0.652565 | − | 0.757733i | \(-0.273693\pi\) |
−0.982498 | + | 0.186271i | \(0.940360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6569 | −1.01511 | −0.507553 | − | 0.861621i | \(-0.669450\pi\) | ||||
−0.507553 | + | 0.861621i | \(0.669450\pi\) | |||||||
\(182\) | −17.8995 | + | 2.44949i | −1.32680 | + | 0.181568i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.62132 | + | 4.54026i | −0.193246 | + | 0.334712i | ||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.91421 | − | 6.77962i | 0.286236 | − | 0.495775i | ||||
\(188\) | 0.757359 | 0.0552361 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.6569 | −0.845677 | ||||||||
\(191\) | 6.65685 | − | 11.5300i | 0.481673 | − | 0.834282i | −0.518106 | − | 0.855317i | \(-0.673363\pi\) |
0.999779 | + | 0.0210344i | \(0.00669595\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.41421 | + | 12.8418i | 0.533687 | + | 0.924373i | 0.999226 | + | 0.0393452i | \(0.0125272\pi\) |
−0.465539 | + | 0.885027i | \(0.654139\pi\) | |||||||
\(194\) | −7.91421 | + | 13.7078i | −0.568207 | + | 0.984164i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.74264 | − | 1.88064i | 0.481617 | − | 0.134331i | ||||
\(197\) | 20.4853 | 1.45952 | 0.729758 | − | 0.683706i | \(-0.239633\pi\) | ||||
0.729758 | + | 0.683706i | \(0.239633\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.82843 | + | 17.0233i | 0.696719 | + | 1.20675i | 0.969598 | + | 0.244704i | \(0.0786908\pi\) |
−0.272879 | + | 0.962048i | \(0.587976\pi\) | |||||||
\(200\) | 0.414214 | + | 0.717439i | 0.0292893 | + | 0.0507306i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.1421 | 0.995037 | ||||||||
\(203\) | 4.58579 | + | 5.91359i | 0.321859 | + | 0.415053i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.03553 | − | 13.9180i | 0.561226 | − | 0.972072i | ||||
\(206\) | −7.41421 | − | 12.8418i | −0.516573 | − | 0.894730i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.41421 | − | 5.91359i | 0.236733 | − | 0.410034i | ||||
\(209\) | 4.82843 | 0.333989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.17157 | 0.631397 | 0.315699 | − | 0.948860i | \(-0.397761\pi\) | ||||
0.315699 | + | 0.948860i | \(0.397761\pi\) | |||||||
\(212\) | −5.41421 | + | 9.37769i | −0.371850 | + | 0.644063i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.67157 | + | 4.62730i | 0.182625 | + | 0.316316i | ||||
\(215\) | 3.41421 | − | 5.91359i | 0.232847 | − | 0.403304i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4853 | − | 25.6836i | 0.711787 | − | 1.74352i | ||||
\(218\) | 5.24264 | 0.355076 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.20711 | − | 2.09077i | −0.0813831 | − | 0.140960i | ||||
\(221\) | 26.7279 | + | 46.2941i | 1.79791 | + | 3.11408i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.31371 | 0.623692 | 0.311846 | − | 0.950133i | \(-0.399053\pi\) | ||||
0.311846 | + | 0.950133i | \(0.399053\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.82843 | − | 6.63103i | 0.254663 | − | 0.441090i | ||||
\(227\) | −5.15685 | − | 8.93193i | −0.342272 | − | 0.592833i | 0.642582 | − | 0.766217i | \(-0.277863\pi\) |
−0.984854 | + | 0.173384i | \(0.944530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.65685 | + | 9.79796i | −0.373815 | + | 0.647467i | −0.990149 | − | 0.140018i | \(-0.955284\pi\) |
0.616334 | + | 0.787485i | \(0.288617\pi\) | |||||||
\(230\) | −12.6569 | −0.834568 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.82843 | −0.185695 | ||||||||
\(233\) | −7.15685 | + | 12.3960i | −0.468861 | + | 0.812091i | −0.999366 | − | 0.0355903i | \(-0.988669\pi\) |
0.530505 | + | 0.847682i | \(0.322002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.914214 | + | 1.58346i | 0.0596367 | + | 0.103294i | ||||
\(236\) | 3.82843 | − | 6.63103i | 0.249209 | − | 0.431643i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.6924 | − | 16.3674i | −0.822725 | − | 1.06094i | ||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.48528 | + | 7.76874i | 0.288922 | + | 0.500428i | 0.973553 | − | 0.228462i | \(-0.0733697\pi\) |
−0.684630 | + | 0.728890i | \(0.740036\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.41421 | −0.282591 | ||||||||
\(245\) | 12.0711 | + | 11.8272i | 0.771192 | + | 0.755611i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4853 | + | 28.5533i | −1.04893 | + | 1.81681i | ||||
\(248\) | 5.24264 | + | 9.08052i | 0.332908 | + | 0.576614i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.03553 | − | 8.72180i | 0.318475 | − | 0.551615i | ||||
\(251\) | 2.14214 | 0.135210 | 0.0676052 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676052 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.24264 | 0.329602 | ||||||||
\(254\) | −3.62132 | + | 6.27231i | −0.227222 | + | 0.393560i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.4142 | − | 26.6982i | 0.961512 | − | 1.66539i | 0.242805 | − | 0.970075i | \(-0.421932\pi\) |
0.718707 | − | 0.695313i | \(-0.244734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.34315 | − | 0.594346i | 0.269870 | − | 0.0369309i | ||||
\(260\) | 16.4853 | 1.02237 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.65685 | + | 6.33386i | 0.225921 | + | 0.391307i | ||||
\(263\) | −6.65685 | − | 11.5300i | −0.410479 | − | 0.710971i | 0.584463 | − | 0.811420i | \(-0.301305\pi\) |
−0.994942 | + | 0.100450i | \(0.967972\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.1421 | −1.60590 | ||||||||
\(266\) | 4.82843 | − | 11.8272i | 0.296050 | − | 0.725171i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.74264 | + | 3.01834i | −0.106449 | + | 0.184375i | ||||
\(269\) | 3.03553 | + | 5.25770i | 0.185080 | + | 0.320568i | 0.943603 | − | 0.331078i | \(-0.107412\pi\) |
−0.758524 | + | 0.651646i | \(0.774079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.65685 | + | 8.06591i | −0.282884 | + | 0.489969i | −0.972094 | − | 0.234593i | \(-0.924624\pi\) |
0.689210 | + | 0.724562i | \(0.257958\pi\) | |||||||
\(272\) | 7.82843 | 0.474668 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.828427 | 0.0500471 | ||||||||
\(275\) | 0.414214 | − | 0.717439i | 0.0249780 | − | 0.0432632i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.585786 | + | 1.01461i | 0.0351965 | + | 0.0609621i | 0.883087 | − | 0.469209i | \(-0.155461\pi\) |
−0.847891 | + | 0.530171i | \(0.822128\pi\) | |||||||
\(278\) | −3.00000 | + | 5.19615i | −0.179928 | + | 0.311645i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.32843 | + | 0.866025i | −0.378196 | + | 0.0517549i | ||||
\(281\) | −19.4853 | −1.16239 | −0.581197 | − | 0.813763i | \(-0.697416\pi\) | ||||
−0.581197 | + | 0.813763i | \(0.697416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0711 | + | 26.1039i | 0.895882 | + | 1.55171i | 0.832709 | + | 0.553711i | \(0.186789\pi\) |
0.0631728 | + | 0.998003i | \(0.479878\pi\) | |||||||
\(284\) | −4.65685 | − | 8.06591i | −0.276333 | − | 0.478624i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.82843 | −0.403773 | ||||||||
\(287\) | 10.7929 | + | 13.9180i | 0.637084 | + | 0.821551i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.1421 | + | 38.3513i | −1.30248 | + | 2.25596i | ||||
\(290\) | −3.41421 | − | 5.91359i | −0.200490 | − | 0.347258i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.414214 | + | 0.717439i | −0.0242400 | + | 0.0419849i | ||||
\(293\) | −7.17157 | −0.418968 | −0.209484 | − | 0.977812i | \(-0.567178\pi\) | ||||
−0.209484 | + | 0.977812i | \(0.567178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.4853 | 1.07625 | ||||||||
\(296\) | −0.828427 | + | 1.43488i | −0.0481513 | + | 0.0834006i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.65685 | + | 9.79796i | 0.327693 | + | 0.567581i | ||||
\(299\) | −17.8995 | + | 31.0028i | −1.03515 | + | 1.79294i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.58579 | + | 5.91359i | 0.264320 | + | 0.340854i | ||||
\(302\) | 7.24264 | 0.416767 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.41421 | + | 4.18154i | 0.138465 | + | 0.239828i | ||||
\(305\) | −5.32843 | − | 9.22911i | −0.305105 | − | 0.528457i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6274 | 0.606539 | 0.303269 | − | 0.952905i | \(-0.401922\pi\) | ||||
0.303269 | + | 0.952905i | \(0.401922\pi\) | |||||||
\(308\) | 2.62132 | − | 0.358719i | 0.149364 | − | 0.0204399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.6569 | + | 21.9223i | −0.718861 | + | 1.24510i | ||||
\(311\) | −16.1066 | − | 27.8975i | −0.913322 | − | 1.58192i | −0.809340 | − | 0.587340i | \(-0.800175\pi\) |
−0.103981 | − | 0.994579i | \(-0.533158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.34315 | − | 5.79050i | 0.188966 | − | 0.327298i | −0.755940 | − | 0.654641i | \(-0.772820\pi\) |
0.944906 | + | 0.327343i | \(0.106153\pi\) | |||||||
\(314\) | 14.8284 | 0.836817 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.2426 | 0.744957 | ||||||||
\(317\) | 9.93503 | − | 17.2080i | 0.558007 | − | 0.966496i | −0.439656 | − | 0.898166i | \(-0.644900\pi\) |
0.997663 | − | 0.0683299i | \(-0.0217670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.41421 | + | 2.44949i | 0.0791808 | + | 0.137145i | ||||
\(320\) | 1.20711 | − | 2.09077i | 0.0674793 | − | 0.116878i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.24264 | − | 12.8418i | 0.292161 | − | 0.715645i | ||||
\(323\) | −37.7990 | −2.10319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.82843 | + | 4.89898i | 0.156893 | + | 0.271746i | ||||
\(326\) | 1.50000 | + | 2.59808i | 0.0830773 | + | 0.143894i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.65685 | −0.367563 | ||||||||
\(329\) | −1.98528 | + | 0.271680i | −0.109452 | + | 0.0149782i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.15685 | − | 14.1281i | 0.448341 | − | 0.776550i | −0.549937 | − | 0.835206i | \(-0.685348\pi\) |
0.998278 | + | 0.0586563i | \(0.0186816\pi\) | |||||||
\(332\) | −2.08579 | − | 3.61269i | −0.114472 | − | 0.198272i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.242641 | + | 0.420266i | −0.0132767 | + | 0.0229959i | ||||
\(335\) | −8.41421 | −0.459718 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4853 | 1.44275 | 0.721373 | − | 0.692547i | \(-0.243512\pi\) | ||||
0.721373 | + | 0.692547i | \(0.243512\pi\) | |||||||
\(338\) | 16.8137 | − | 29.1222i | 0.914545 | − | 1.58404i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.44975 | + | 16.3674i | 0.512485 | + | 0.887649i | ||||
\(341\) | 5.24264 | − | 9.08052i | 0.283905 | − | 0.491738i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | −2.82843 | −0.152499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.07107 | − | 13.9795i | −0.433903 | − | 0.751543i | ||||
\(347\) | 16.5711 | + | 28.7019i | 0.889582 | + | 1.54080i | 0.840371 | + | 0.542012i | \(0.182337\pi\) |
0.0492108 | + | 0.998788i | \(0.484329\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.72792 | 0.520724 | 0.260362 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260362 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(350\) | −1.34315 | − | 1.73205i | −0.0717942 | − | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −5.58579 | − | 9.67487i | −0.297301 | − | 0.514941i | 0.678216 | − | 0.734862i | \(-0.262753\pi\) |
−0.975518 | + | 0.219921i | \(0.929420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2426 | − | 19.4728i | 0.596697 | − | 1.03351i | ||||
\(356\) | 4.48528 | 0.237719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.82843 | −0.466597 | ||||||||
\(359\) | 4.24264 | − | 7.34847i | 0.223918 | − | 0.387837i | −0.732076 | − | 0.681223i | \(-0.761449\pi\) |
0.955994 | + | 0.293385i | \(0.0947819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.15685 | − | 3.73578i | −0.113519 | − | 0.196620i | ||||
\(362\) | −6.82843 | + | 11.8272i | −0.358894 | + | 0.621623i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.82843 | + | 16.7262i | −0.357907 | + | 0.876689i | ||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2426 | − | 19.4728i | −0.586861 | − | 1.01647i | −0.994641 | − | 0.103393i | \(-0.967030\pi\) |
0.407780 | − | 0.913080i | \(-0.366303\pi\) | |||||||
\(368\) | 2.62132 | + | 4.54026i | 0.136646 | + | 0.236677i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 10.8284 | − | 26.5241i | 0.562184 | − | 1.37706i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.86396 | + | 8.42463i | −0.251846 | + | 0.436211i | −0.964034 | − | 0.265778i | \(-0.914371\pi\) |
0.712188 | + | 0.701989i | \(0.247704\pi\) | |||||||
\(374\) | −3.91421 | − | 6.77962i | −0.202399 | − | 0.350566i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.378680 | − | 0.655892i | 0.0195289 | − | 0.0338251i | ||||
\(377\) | −19.3137 | −0.994707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6569 | 1.57474 | 0.787368 | − | 0.616483i | \(-0.211443\pi\) | ||||
0.787368 | + | 0.616483i | \(0.211443\pi\) | |||||||
\(380\) | −5.82843 | + | 10.0951i | −0.298992 | + | 0.517869i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.65685 | − | 11.5300i | −0.340594 | − | 0.589927i | ||||
\(383\) | 11.1421 | − | 19.2987i | 0.569337 | − | 0.986120i | −0.427295 | − | 0.904112i | \(-0.640533\pi\) |
0.996632 | − | 0.0820076i | \(-0.0261332\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.91421 | + | 5.04757i | 0.199487 | + | 0.257248i | ||||
\(386\) | 14.8284 | 0.754747 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.91421 | + | 13.7078i | 0.401783 | + | 0.695909i | ||||
\(389\) | 11.8640 | + | 20.5490i | 0.601527 | + | 1.04187i | 0.992590 | + | 0.121511i | \(0.0387740\pi\) |
−0.391063 | + | 0.920364i | \(0.627893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.0416 | −2.07556 | ||||||||
\(392\) | 1.74264 | − | 6.77962i | 0.0880166 | − | 0.342422i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.2426 | − | 17.7408i | 0.516017 | − | 0.893767i | ||||
\(395\) | 15.9853 | + | 27.6873i | 0.804307 | + | 1.39310i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.24264 | − | 3.88437i | 0.112555 | − | 0.194951i | −0.804245 | − | 0.594298i | \(-0.797430\pi\) |
0.916800 | + | 0.399347i | \(0.130763\pi\) | |||||||
\(398\) | 19.6569 | 0.985309 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.828427 | 0.0414214 | ||||||||
\(401\) | 11.8995 | − | 20.6105i | 0.594232 | − | 1.02924i | −0.399422 | − | 0.916767i | \(-0.630789\pi\) |
0.993655 | − | 0.112474i | \(-0.0358774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.7990 | + | 62.0057i | 1.78327 | + | 3.08872i | ||||
\(404\) | 7.07107 | − | 12.2474i | 0.351799 | − | 0.609333i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.41421 | − | 1.01461i | 0.367961 | − | 0.0503543i | ||||
\(407\) | 1.65685 | 0.0821272 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7279 | − | 34.1698i | −0.975483 | − | 1.68959i | −0.678332 | − | 0.734756i | \(-0.737297\pi\) |
−0.297151 | − | 0.954831i | \(-0.596036\pi\) | |||||||
\(410\) | −8.03553 | − | 13.9180i | −0.396847 | − | 0.687359i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.8284 | −0.730544 | ||||||||
\(413\) | −7.65685 | + | 18.7554i | −0.376769 | + | 0.922892i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.03553 | − | 8.72180i | 0.247185 | − | 0.428136i | ||||
\(416\) | −3.41421 | − | 5.91359i | −0.167396 | − | 0.289938i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.41421 | − | 4.18154i | 0.118083 | − | 0.204526i | ||||
\(419\) | −13.7990 | −0.674125 | −0.337062 | − | 0.941482i | \(-0.609433\pi\) | ||||
−0.337062 | + | 0.941482i | \(0.609433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.17157 | 0.446995 | 0.223498 | − | 0.974704i | \(-0.428253\pi\) | ||||
0.223498 | + | 0.974704i | \(0.428253\pi\) | |||||||
\(422\) | 4.58579 | − | 7.94282i | 0.223233 | − | 0.386650i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.41421 | + | 9.37769i | 0.262937 | + | 0.455421i | ||||
\(425\) | −3.24264 | + | 5.61642i | −0.157291 | + | 0.272436i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.5711 | − | 1.58346i | 0.559963 | − | 0.0766292i | ||||
\(428\) | 5.34315 | 0.258271 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.41421 | − | 5.91359i | −0.164648 | − | 0.285179i | ||||
\(431\) | −12.4142 | − | 21.5020i | −0.597972 | − | 1.03572i | −0.993120 | − | 0.117100i | \(-0.962640\pi\) |
0.395149 | − | 0.918617i | \(-0.370693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3431 | −0.737345 | −0.368672 | − | 0.929559i | \(-0.620188\pi\) | ||||
−0.368672 | + | 0.929559i | \(0.620188\pi\) | |||||||
\(434\) | −17.0000 | − | 21.9223i | −0.816026 | − | 1.05230i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.62132 | − | 4.54026i | 0.125538 | − | 0.217439i | ||||
\(437\) | −12.6569 | − | 21.9223i | −0.605459 | − | 1.04869i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.6924 | − | 28.9121i | 0.796684 | − | 1.37990i | −0.125080 | − | 0.992147i | \(-0.539919\pi\) |
0.921764 | − | 0.387751i | \(-0.126748\pi\) | |||||||
\(440\) | −2.41421 | −0.115093 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 53.4558 | 2.54264 | ||||||||
\(443\) | 12.8284 | − | 22.2195i | 0.609497 | − | 1.05568i | −0.381826 | − | 0.924234i | \(-0.624705\pi\) |
0.991323 | − | 0.131446i | \(-0.0419619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.41421 | + | 9.37769i | 0.256658 | + | 0.444545i | ||||
\(446\) | 4.65685 | − | 8.06591i | 0.220508 | − | 0.381932i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.62132 | + | 2.09077i | 0.0766002 | + | 0.0987796i | ||||
\(449\) | 39.1127 | 1.84584 | 0.922921 | − | 0.384989i | \(-0.125795\pi\) | ||||
0.922921 | + | 0.384989i | \(0.125795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.32843 | + | 5.76500i | 0.156730 | + | 0.271463i | ||||
\(452\) | −3.82843 | − | 6.63103i | −0.180074 | − | 0.311897i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.3137 | −0.484046 | ||||||||
\(455\) | −43.2132 | + | 5.91359i | −2.02587 | + | 0.277233i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.31371 | − | 9.20361i | 0.248565 | − | 0.430527i | −0.714563 | − | 0.699571i | \(-0.753374\pi\) |
0.963128 | + | 0.269044i | \(0.0867078\pi\) | |||||||
\(458\) | 5.65685 | + | 9.79796i | 0.264327 | + | 0.457829i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.32843 | + | 10.9612i | −0.295064 | + | 0.511067i | ||||
\(461\) | 12.3431 | 0.574878 | 0.287439 | − | 0.957799i | \(-0.407196\pi\) | ||||
0.287439 | + | 0.957799i | \(0.407196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1127 | −1.81772 | −0.908861 | − | 0.417100i | \(-0.863046\pi\) | ||||
−0.908861 | + | 0.417100i | \(0.863046\pi\) | |||||||
\(464\) | −1.41421 | + | 2.44949i | −0.0656532 | + | 0.113715i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.15685 | + | 12.3960i | 0.331535 | + | 0.574235i | ||||
\(467\) | 15.4853 | − | 26.8213i | 0.716573 | − | 1.24114i | −0.245776 | − | 0.969327i | \(-0.579043\pi\) |
0.962350 | − | 0.271815i | \(-0.0876238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48528 | − | 8.53716i | 0.160935 | − | 0.394209i | ||||
\(470\) | 1.82843 | 0.0843391 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.82843 | − | 6.63103i | −0.176218 | − | 0.305218i | ||||
\(473\) | 1.41421 | + | 2.44949i | 0.0650256 | + | 0.112628i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | −20.5208 | + | 2.80821i | −0.940570 | + | 0.128714i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.0000 | + | 17.3205i | −0.457389 | + | 0.792222i | ||||
\(479\) | 5.41421 | + | 9.37769i | 0.247382 | + | 0.428478i | 0.962799 | − | 0.270220i | \(-0.0870965\pi\) |
−0.715417 | + | 0.698698i | \(0.753763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65685 | + | 9.79796i | −0.257930 | + | 0.446748i | ||||
\(482\) | 8.97056 | 0.408598 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −19.1066 | + | 33.0936i | −0.867586 | + | 1.50270i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.656854 | − | 1.13770i | −0.0297649 | − | 0.0515543i | 0.850759 | − | 0.525556i | \(-0.176143\pi\) |
−0.880524 | + | 0.474001i | \(0.842809\pi\) | |||||||
\(488\) | −2.20711 | + | 3.82282i | −0.0999110 | + | 0.173051i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.2782 | − | 4.54026i | 0.735373 | − | 0.205108i | ||||
\(491\) | −29.6274 | −1.33707 | −0.668533 | − | 0.743682i | \(-0.733078\pi\) | ||||
−0.668533 | + | 0.743682i | \(0.733078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0711 | − | 19.1757i | −0.498616 | − | 0.863628i | ||||
\(494\) | 16.4853 | + | 28.5533i | 0.741708 | + | 1.28468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.4853 | 0.470803 | ||||||||
\(497\) | 15.1005 | + | 19.4728i | 0.677350 | + | 0.873476i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8284 | + | 22.2195i | −0.574279 | + | 0.994681i | 0.421840 | + | 0.906670i | \(0.361384\pi\) |
−0.996120 | + | 0.0880107i | \(0.971949\pi\) | |||||||
\(500\) | −5.03553 | − | 8.72180i | −0.225196 | − | 0.390051i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.07107 | − | 1.85514i | 0.0478041 | − | 0.0827991i | ||||
\(503\) | 24.9706 | 1.11338 | 0.556691 | − | 0.830720i | \(-0.312071\pi\) | ||||
0.556691 | + | 0.830720i | \(0.312071\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.1421 | 1.51931 | ||||||||
\(506\) | 2.62132 | − | 4.54026i | 0.116532 | − | 0.201839i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.62132 | + | 6.27231i | 0.160670 | + | 0.278289i | ||||
\(509\) | 15.4142 | − | 26.6982i | 0.683223 | − | 1.18338i | −0.290769 | − | 0.956793i | \(-0.593911\pi\) |
0.973992 | − | 0.226584i | \(-0.0727556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.828427 | − | 2.02922i | 0.0366475 | − | 0.0897676i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.4142 | − | 26.6982i | −0.679892 | − | 1.17761i | ||||
\(515\) | −17.8995 | − | 31.0028i | −0.788746 | − | 1.36615i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.757359 | −0.0333086 | ||||||||
\(518\) | 1.65685 | − | 4.05845i | 0.0727980 | − | 0.178318i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.24264 | − | 14.2767i | 0.361464 | − | 0.626074i | ||||
\(521\) | 3.34315 | + | 5.79050i | 0.146466 | + | 0.253686i | 0.929919 | − | 0.367765i | \(-0.119877\pi\) |
−0.783453 | + | 0.621451i | \(0.786543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.72792 | + | 16.8493i | −0.425372 | + | 0.736766i | −0.996455 | − | 0.0841260i | \(-0.973190\pi\) |
0.571083 | + | 0.820892i | \(0.306524\pi\) | |||||||
\(524\) | 7.31371 | 0.319501 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.3137 | −0.580505 | ||||||||
\(527\) | −41.0416 | + | 71.0862i | −1.78780 | + | 3.09656i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.24264 | − | 3.88437i | −0.0975061 | − | 0.168886i | ||||
\(530\) | −13.0711 | + | 22.6398i | −0.567771 | + | 0.983408i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.82843 | − | 10.0951i | −0.339405 | − | 0.437679i | ||||
\(533\) | −45.4558 | −1.96891 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.44975 | + | 11.1713i | 0.278847 | + | 0.482977i | ||||
\(536\) | 1.74264 | + | 3.01834i | 0.0752706 | + | 0.130373i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.07107 | 0.261742 | ||||||||
\(539\) | −6.74264 | + | 1.88064i | −0.290426 | + | 0.0810048i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2782 | − | 31.6587i | 0.785840 | − | 1.36111i | −0.142656 | − | 0.989772i | \(-0.545564\pi\) |
0.928496 | − | 0.371343i | \(-0.121102\pi\) | |||||||
\(542\) | 4.65685 | + | 8.06591i | 0.200029 | + | 0.346460i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.91421 | − | 6.77962i | 0.167821 | − | 0.290674i | ||||
\(545\) | 12.6569 | 0.542160 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.85786 | −0.335978 | −0.167989 | − | 0.985789i | \(-0.553727\pi\) | ||||
−0.167989 | + | 0.985789i | \(0.553727\pi\) | |||||||
\(548\) | 0.414214 | − | 0.717439i | 0.0176943 | − | 0.0306475i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.414214 | − | 0.717439i | −0.0176621 | − | 0.0305917i | ||||
\(551\) | 6.82843 | − | 11.8272i | 0.290901 | − | 0.503855i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.7132 | + | 4.75039i | −1.47616 | + | 0.202007i | ||||
\(554\) | 1.17157 | 0.0497754 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.00000 | + | 5.19615i | 0.127228 | + | 0.220366i | ||||
\(557\) | 6.24264 | + | 10.8126i | 0.264509 | + | 0.458143i | 0.967435 | − | 0.253120i | \(-0.0814567\pi\) |
−0.702926 | + | 0.711263i | \(0.748123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3137 | −0.816883 | ||||||||
\(560\) | −2.41421 | + | 5.91359i | −0.102019 | + | 0.249895i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.74264 | + | 16.8747i | −0.410968 | + | 0.711818i | ||||
\(563\) | 7.17157 | + | 12.4215i | 0.302246 | + | 0.523505i | 0.976644 | − | 0.214863i | \(-0.0689303\pi\) |
−0.674399 | + | 0.738368i | \(0.735597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.24264 | − | 16.0087i | 0.388841 | − | 0.673492i | ||||
\(566\) | 30.1421 | 1.26697 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.31371 | −0.390795 | ||||||||
\(569\) | −11.0000 | + | 19.0526i | −0.461144 | + | 0.798725i | −0.999018 | − | 0.0443003i | \(-0.985894\pi\) |
0.537874 | + | 0.843025i | \(0.319228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.17157 | + | 8.95743i | 0.216424 | + | 0.374857i | 0.953712 | − | 0.300721i | \(-0.0972274\pi\) |
−0.737288 | + | 0.675578i | \(0.763894\pi\) | |||||||
\(572\) | −3.41421 | + | 5.91359i | −0.142755 | + | 0.247260i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.4497 | − | 2.38794i | 0.728338 | − | 0.0996708i | ||||
\(575\) | −4.34315 | −0.181122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5711 | + | 20.0417i | 0.481710 | + | 0.834346i | 0.999780 | − | 0.0209924i | \(-0.00668258\pi\) |
−0.518070 | + | 0.855338i | \(0.673349\pi\) | |||||||
\(578\) | 22.1421 | + | 38.3513i | 0.920991 | + | 1.59520i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.82843 | −0.283535 | ||||||||
\(581\) | 6.76346 | + | 8.72180i | 0.280595 | + | 0.361841i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.41421 | − | 9.37769i | 0.224234 | − | 0.388384i | ||||
\(584\) | 0.414214 | + | 0.717439i | 0.0171403 | + | 0.0296878i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.58579 | + | 6.21076i | −0.148127 | + | 0.256564i | ||||
\(587\) | −0.142136 | −0.00586657 | −0.00293328 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293328 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.6274 | −2.08607 | ||||||||
\(590\) | 9.24264 | − | 16.0087i | 0.380513 | − | 0.659069i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.828427 | + | 1.43488i | 0.0340481 | + | 0.0589731i | ||||
\(593\) | −13.9706 | + | 24.1977i | −0.573702 | + | 0.993681i | 0.422479 | + | 0.906373i | \(0.361160\pi\) |
−0.996181 | + | 0.0873088i | \(0.972173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.6421 | − | 39.5145i | −1.25621 | − | 1.61994i | ||||
\(596\) | 11.3137 | 0.463428 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.8995 | + | 31.0028i | 0.731965 | + | 1.26780i | ||||
\(599\) | −9.52082 | − | 16.4905i | −0.389010 | − | 0.673785i | 0.603307 | − | 0.797509i | \(-0.293850\pi\) |
−0.992317 | + | 0.123724i | \(0.960516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0000 | −0.815817 | −0.407909 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407909 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(602\) | 7.41421 | − | 1.01461i | 0.302181 | − | 0.0413525i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.62132 | − | 6.27231i | 0.147349 | − | 0.255217i | ||||
\(605\) | 1.20711 | + | 2.09077i | 0.0490759 | + | 0.0850019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.89340 | + | 3.27946i | −0.0768507 | + | 0.133109i | −0.901890 | − | 0.431967i | \(-0.857820\pi\) |
0.825039 | + | 0.565076i | \(0.191153\pi\) | |||||||
\(608\) | 4.82843 | 0.195819 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.6569 | −0.431483 | ||||||||
\(611\) | 2.58579 | − | 4.47871i | 0.104610 | − | 0.181189i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.55025 | + | 9.61332i | 0.224173 | + | 0.388278i | 0.956071 | − | 0.293136i | \(-0.0946987\pi\) |
−0.731898 | + | 0.681414i | \(0.761365\pi\) | |||||||
\(614\) | 5.31371 | − | 9.20361i | 0.214444 | − | 0.371428i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | − | 2.44949i | 0.0402911 | − | 0.0986928i | ||||
\(617\) | 7.51472 | 0.302531 | 0.151266 | − | 0.988493i | \(-0.451665\pi\) | ||||
0.151266 | + | 0.988493i | \(0.451665\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.74264 | − | 15.1427i | −0.351396 | − | 0.608636i | 0.635098 | − | 0.772432i | \(-0.280960\pi\) |
−0.986494 | + | 0.163795i | \(0.947626\pi\) | |||||||
\(620\) | 12.6569 | + | 21.9223i | 0.508311 | + | 0.880421i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.2132 | −1.29163 | ||||||||
\(623\) | −11.7574 | + | 1.60896i | −0.471049 | + | 0.0644615i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.2279 | − | 24.6435i | 0.569117 | − | 0.985739i | ||||
\(626\) | −3.34315 | − | 5.79050i | −0.133619 | − | 0.231435i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.41421 | − | 12.8418i | 0.295859 | − | 0.512443i | ||||
\(629\) | −12.9706 | −0.517170 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9706 | −1.39216 | −0.696078 | − | 0.717966i | \(-0.745073\pi\) | ||||
−0.696078 | + | 0.717966i | \(0.745073\pi\) | |||||||
\(632\) | 6.62132 | − | 11.4685i | 0.263382 | − | 0.456191i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.93503 | − | 17.2080i | −0.394570 | − | 0.683416i | ||||
\(635\) | −8.74264 | + | 15.1427i | −0.346941 | + | 0.600920i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.8995 | − | 46.2941i | 0.471475 | − | 1.83424i | ||||
\(638\) | 2.82843 | 0.111979 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.20711 | − | 2.09077i | −0.0477151 | − | 0.0826450i | ||||
\(641\) | −2.34315 | − | 4.05845i | −0.0925487 | − | 0.160299i | 0.816034 | − | 0.578004i | \(-0.196168\pi\) |
−0.908583 | + | 0.417705i | \(0.862835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.34315 | 0.250149 | 0.125075 | − | 0.992147i | \(-0.460083\pi\) | ||||
0.125075 | + | 0.992147i | \(0.460083\pi\) | |||||||
\(644\) | −8.50000 | − | 10.9612i | −0.334947 | − | 0.431930i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.8995 | + | 32.7349i | −0.743591 | + | 1.28794i | ||||
\(647\) | −8.34924 | − | 14.4613i | −0.328243 | − | 0.568533i | 0.653921 | − | 0.756563i | \(-0.273123\pi\) |
−0.982163 | + | 0.188030i | \(0.939790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.82843 | + | 6.63103i | −0.150279 | + | 0.260291i | ||||
\(650\) | 5.65685 | 0.221880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00000 | 0.117489 | ||||||||
\(653\) | −13.1777 | + | 22.8244i | −0.515682 | + | 0.893188i | 0.484152 | + | 0.874984i | \(0.339128\pi\) |
−0.999834 | + | 0.0182037i | \(0.994205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.82843 | + | 15.2913i | 0.344955 | + | 0.597480i | ||||
\(656\) | −3.32843 | + | 5.76500i | −0.129953 | + | 0.225086i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.757359 | + | 1.85514i | −0.0295249 | + | 0.0723210i | ||||
\(659\) | −30.9411 | −1.20530 | −0.602648 | − | 0.798007i | \(-0.705888\pi\) | ||||
−0.602648 | + | 0.798007i | \(0.705888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.51472 | + | 4.35562i | 0.0978112 | + | 0.169414i | 0.910778 | − | 0.412895i | \(-0.135483\pi\) |
−0.812967 | + | 0.582309i | \(0.802149\pi\) | |||||||
\(662\) | −8.15685 | − | 14.1281i | −0.317025 | − | 0.549104i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.17157 | −0.161888 | ||||||||
\(665\) | 11.6569 | − | 28.5533i | 0.452033 | − | 1.10725i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.41421 | − | 12.8418i | 0.287079 | − | 0.497236i | ||||
\(668\) | 0.242641 | + | 0.420266i | 0.00938805 | + | 0.0162606i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.20711 | + | 7.28692i | −0.162535 | + | 0.281518i | ||||
\(671\) | 4.41421 | 0.170409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6274 | −0.795128 | −0.397564 | − | 0.917574i | \(-0.630144\pi\) | ||||
−0.397564 | + | 0.917574i | \(0.630144\pi\) | |||||||
\(674\) | 13.2426 | − | 22.9369i | 0.510087 | − | 0.883497i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.8137 | − | 29.1222i | −0.646681 | − | 1.12008i | ||||
\(677\) | −15.3848 | + | 26.6472i | −0.591285 | + | 1.02414i | 0.402775 | + | 0.915299i | \(0.368046\pi\) |
−0.994060 | + | 0.108836i | \(0.965288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.6630 | − | 33.0936i | −0.984854 | − | 1.27002i | ||||
\(680\) | 18.8995 | 0.724763 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.24264 | − | 9.08052i | −0.200751 | − | 0.347711i | ||||
\(683\) | 3.17157 | + | 5.49333i | 0.121357 | + | 0.210196i | 0.920303 | − | 0.391206i | \(-0.127942\pi\) |
−0.798946 | + | 0.601403i | \(0.794609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | −2.13604 | + | 18.3967i | −0.0815543 | + | 0.702388i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.41421 | + | 2.44949i | −0.0539164 | + | 0.0933859i | ||||
\(689\) | 36.9706 | + | 64.0349i | 1.40847 | + | 2.43954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.428932 | + | 0.742932i | −0.0163173 | + | 0.0282625i | −0.874069 | − | 0.485802i | \(-0.838528\pi\) |
0.857751 | + | 0.514065i | \(0.171861\pi\) | |||||||
\(692\) | −16.1421 | −0.613632 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.1421 | 1.25806 | ||||||||
\(695\) | −7.24264 | + | 12.5446i | −0.274729 | + | 0.475845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.0563 | − | 45.1309i | −0.986955 | − | 1.70946i | ||||
\(698\) | 4.86396 | − | 8.42463i | 0.184104 | − | 0.318877i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.17157 | + | 0.297173i | −0.0820777 | + | 0.0112321i | ||||
\(701\) | 0.142136 | 0.00536839 | 0.00268419 | − | 0.999996i | \(-0.499146\pi\) | ||||
0.00268419 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | − | 6.92820i | −0.150863 | − | 0.261302i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.1716 | −0.420448 | ||||||||
\(707\) | −14.1421 | + | 34.6410i | −0.531870 | + | 1.30281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0711 | + | 27.8359i | −0.603562 | + | 1.04540i | 0.388715 | + | 0.921358i | \(0.372919\pi\) |
−0.992277 | + | 0.124042i | \(0.960414\pi\) | |||||||
\(710\) | −11.2426 | − | 19.4728i | −0.421929 | − | 0.730802i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.24264 | − | 3.88437i | 0.0840465 | − | 0.145573i | ||||
\(713\) | −54.9706 | −2.05866 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4853 | −0.616515 | ||||||||
\(716\) | −4.41421 | + | 7.64564i | −0.164967 | + | 0.285731i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.24264 | − | 7.34847i | −0.158334 | − | 0.274242i | ||||
\(719\) | 13.1066 | − | 22.7013i | 0.488794 | − | 0.846616i | −0.511123 | − | 0.859508i | \(-0.670770\pi\) |
0.999917 | + | 0.0128919i | \(0.00410372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.8701 | − | 5.31925i | 1.44760 | − | 0.198099i | ||||
\(722\) | −4.31371 | −0.160540 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.82843 | + | 11.8272i | 0.253776 | + | 0.439554i | ||||
\(725\) | −1.17157 | − | 2.02922i | −0.0435111 | − | 0.0753635i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.5147 | −0.575409 | −0.287705 | − | 0.957719i | \(-0.592892\pi\) | ||||
−0.287705 | + | 0.957719i | \(0.592892\pi\) | |||||||
\(728\) | 11.0711 | + | 14.2767i | 0.410321 | + | 0.529129i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | −11.0711 | − | 19.1757i | −0.409478 | − | 0.709237i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.6213 | − | 20.1287i | 0.429243 | − | 0.743471i | −0.567563 | − | 0.823330i | \(-0.692114\pi\) |
0.996806 | + | 0.0798589i | \(0.0254470\pi\) | |||||||
\(734\) | −22.4853 | −0.829947 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.24264 | 0.193246 | ||||||||
\(737\) | 1.74264 | − | 3.01834i | 0.0641910 | − | 0.111182i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0000 | + | 29.4449i | 0.625355 | + | 1.08315i | 0.988472 | + | 0.151403i | \(0.0483792\pi\) |
−0.363117 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(740\) | −2.00000 | + | 3.46410i | −0.0735215 | + | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.5563 | − | 22.6398i | −0.644514 | − | 0.831132i | ||||
\(743\) | 2.34315 | 0.0859617 | 0.0429808 | − | 0.999076i | \(-0.486315\pi\) | ||||
0.0429808 | + | 0.999076i | \(0.486315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6569 | + | 23.6544i | 0.500348 | + | 0.866629i | ||||
\(746\) | 4.86396 | + | 8.42463i | 0.178082 | + | 0.308448i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.82843 | −0.286236 | ||||||||
\(749\) | −14.0061 | + | 1.91669i | −0.511772 | + | 0.0700343i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.89949 | − | 8.48617i | 0.178785 | − | 0.309665i | −0.762680 | − | 0.646777i | \(-0.776117\pi\) |
0.941465 | + | 0.337112i | \(0.109450\pi\) | |||||||
\(752\) | −0.378680 | − | 0.655892i | −0.0138090 | − | 0.0239179i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.65685 | + | 16.7262i | −0.351682 | + | 0.609131i | ||||
\(755\) | 17.4853 | 0.636355 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.34315 | 0.303237 | 0.151618 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151618 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(758\) | 15.3284 | − | 26.5496i | 0.556754 | − | 0.964325i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.82843 | + | 10.0951i | 0.211419 | + | 0.366189i | ||||
\(761\) | −13.2279 | + | 22.9114i | −0.479512 | + | 0.830539i | −0.999724 | − | 0.0234983i | \(-0.992520\pi\) |
0.520212 | + | 0.854037i | \(0.325853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.24264 | + | 12.8418i | −0.189796 | + | 0.464904i | ||||
\(764\) | −13.3137 | −0.481673 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.1421 | − | 19.2987i | −0.402582 | − | 0.697292i | ||||
\(767\) | −26.1421 | − | 45.2795i | −0.943938 | − | 1.63495i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.51472 | 0.343110 | 0.171555 | − | 0.985175i | \(-0.445121\pi\) | ||||
0.171555 | + | 0.985175i | \(0.445121\pi\) | |||||||
\(770\) | 6.32843 | − | 0.866025i | 0.228061 | − | 0.0312094i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.41421 | − | 12.8418i | 0.266843 | − | 0.462186i | ||||
\(773\) | 11.3787 | + | 19.7085i | 0.409263 | + | 0.708864i | 0.994807 | − | 0.101776i | \(-0.0324526\pi\) |
−0.585545 | + | 0.810640i | \(0.699119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.34315 | + | 7.52255i | −0.156010 | + | 0.270218i | ||||
\(776\) | 15.8284 | 0.568207 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.7279 | 0.850687 | ||||||||
\(779\) | 16.0711 | − | 27.8359i | 0.575806 | − | 0.997325i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.65685 | + | 8.06591i | 0.166635 | + | 0.288621i | ||||
\(782\) | −20.5208 | + | 35.5431i | −0.733823 | + | 1.27102i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | 35.7990 | 1.27772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3848 | − | 30.1113i | −0.619700 | − | 1.07335i | −0.989540 | − | 0.144257i | \(-0.953921\pi\) |
0.369840 | − | 0.929095i | \(-0.379413\pi\) | |||||||
\(788\) | −10.2426 | − | 17.7408i | −0.364879 | − | 0.631989i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 31.9706 | 1.13746 | ||||||||
\(791\) | 12.4142 | + | 16.0087i | 0.441399 | + | 0.569205i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.0711 | + | 26.1039i | −0.535189 | + | 0.926975i | ||||
\(794\) | −2.24264 | − | 3.88437i | −0.0795883 | − | 0.137851i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.82843 | − | 17.0233i | 0.348359 | − | 0.603376i | ||||
\(797\) | −33.1005 | −1.17248 | −0.586240 | − | 0.810137i | \(-0.699392\pi\) | ||||
−0.586240 | + | 0.810137i | \(0.699392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.92893 | 0.209751 | ||||||||
\(800\) | 0.414214 | − | 0.717439i | 0.0146447 | − | 0.0253653i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.8995 | − | 20.6105i | −0.420186 | − | 0.727783i | ||||
\(803\) | 0.414214 | − | 0.717439i | 0.0146173 | − | 0.0253179i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6569 | − | 31.0028i | 0.446095 | − | 1.09271i | ||||
\(806\) | 71.5980 | 2.52193 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.07107 | − | 12.2474i | −0.248759 | − | 0.430864i | ||||
\(809\) | −10.3284 | − | 17.8894i | −0.363128 | − | 0.628956i | 0.625346 | − | 0.780348i | \(-0.284958\pi\) |
−0.988474 | + | 0.151391i | \(0.951625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.65685 | 0.128410 | 0.0642048 | − | 0.997937i | \(-0.479549\pi\) | ||||
0.0642048 | + | 0.997937i | \(0.479549\pi\) | |||||||
\(812\) | 2.82843 | − | 6.92820i | 0.0992583 | − | 0.243132i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.828427 | − | 1.43488i | 0.0290364 | − | 0.0502924i | ||||
\(815\) | 3.62132 | + | 6.27231i | 0.126849 | + | 0.219709i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.82843 | − | 11.8272i | 0.238896 | − | 0.413781i | ||||
\(818\) | −39.4558 | −1.37954 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.0711 | −0.561226 | ||||||||
\(821\) | 19.2426 | − | 33.3292i | 0.671573 | − | 1.16320i | −0.305885 | − | 0.952068i | \(-0.598952\pi\) |
0.977458 | − | 0.211130i | \(-0.0677143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.2426 | + | 33.3292i | 0.670756 | + | 1.16178i | 0.977690 | + | 0.210053i | \(0.0673637\pi\) |
−0.306934 | + | 0.951731i | \(0.599303\pi\) | |||||||
\(824\) | −7.41421 | + | 12.8418i | −0.258286 | + | 0.447365i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.4142 | + | 16.0087i | 0.431946 | + | 0.557015i | ||||
\(827\) | −7.82843 | −0.272221 | −0.136111 | − | 0.990694i | \(-0.543460\pi\) | ||||
−0.136111 | + | 0.990694i | \(0.543460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | + | 24.2487i | 0.486240 | + | 0.842193i | 0.999875 | − | 0.0158163i | \(-0.00503471\pi\) |
−0.513635 | + | 0.858009i | \(0.671701\pi\) | |||||||
\(830\) | −5.03553 | − | 8.72180i | −0.174786 | − | 0.302738i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.82843 | −0.236733 | ||||||||
\(833\) | 52.7843 | − | 14.7224i | 1.82887 | − | 0.510102i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.585786 | + | 1.01461i | −0.0202720 | + | 0.0351121i | ||||
\(836\) | −2.41421 | − | 4.18154i | −0.0834973 | − | 0.144622i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.89949 | + | 11.9503i | −0.238339 | + | 0.412815i | ||||
\(839\) | 34.2132 | 1.18117 | 0.590585 | − | 0.806975i | \(-0.298897\pi\) | ||||
0.590585 | + | 0.806975i | \(0.298897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 4.58579 | − | 7.94282i | 0.158037 | − | 0.273727i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.58579 | − | 7.94282i | −0.157849 | − | 0.273403i | ||||
\(845\) | 40.5919 | − | 70.3072i | 1.39640 | − | 2.41864i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.62132 | + | 0.358719i | −0.0900696 | + | 0.0123257i | ||||
\(848\) | 10.8284 | 0.371850 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.24264 | + | 5.61642i | 0.111222 | + | 0.192642i | ||||
\(851\) | −4.34315 | − | 7.52255i | −0.148881 | − | 0.257870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.7574 | −0.505282 | −0.252641 | − | 0.967560i | \(-0.581299\pi\) | ||||
−0.252641 | + | 0.967560i | \(0.581299\pi\) | |||||||
\(854\) | 4.41421 | − | 10.8126i | 0.151051 | − | 0.369999i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.67157 | − | 4.62730i | 0.0913125 | − | 0.158158i | ||||
\(857\) | 22.1569 | + | 38.3768i | 0.756864 | + | 1.31093i | 0.944442 | + | 0.328677i | \(0.106603\pi\) |
−0.187579 | + | 0.982250i | \(0.560064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.47056 | + | 14.6714i | −0.289012 | + | 0.500583i | −0.973574 | − | 0.228371i | \(-0.926660\pi\) |
0.684562 | + | 0.728954i | \(0.259993\pi\) | |||||||
\(860\) | −6.82843 | −0.232847 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.8284 | −0.845660 | ||||||||
\(863\) | 18.5919 | − | 32.2021i | 0.632875 | − | 1.09617i | −0.354086 | − | 0.935213i | \(-0.615208\pi\) |
0.986961 | − | 0.160959i | \(-0.0514587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.4853 | − | 33.7495i | −0.662519 | − | 1.14752i | ||||
\(866\) | −7.67157 | + | 13.2876i | −0.260691 | + | 0.451529i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −27.4853 | + | 3.76127i | −0.932911 | + | 0.127666i | ||||
\(869\) | −13.2426 | −0.449226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8995 | + | 20.6105i | 0.403199 | + | 0.698361i | ||||
\(872\) | −2.62132 | − | 4.54026i | −0.0887691 | − | 0.153753i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25.3137 | −0.856249 | ||||||||
\(875\) | 16.3284 | + | 21.0563i | 0.552002 | + | 0.711832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.27817 | − | 5.67796i | 0.110696 | − | 0.191731i | −0.805355 | − | 0.592793i | \(-0.798025\pi\) |
0.916051 | + | 0.401062i | \(0.131359\pi\) | |||||||
\(878\) | −16.6924 | − | 28.9121i | −0.563341 | − | 0.975735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.20711 | + | 2.09077i | −0.0406916 | + | 0.0704799i | ||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.4853 | 0.588427 | 0.294213 | − | 0.955740i | \(-0.404942\pi\) | ||||
0.294213 | + | 0.955740i | \(0.404942\pi\) | |||||||
\(884\) | 26.7279 | − | 46.2941i | 0.898957 | − | 1.55704i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.8284 | − | 22.2195i | −0.430979 | − | 0.746478i | ||||
\(887\) | 9.82843 | − | 17.0233i | 0.330006 | − | 0.571588i | −0.652506 | − | 0.757783i | \(-0.726282\pi\) |
0.982513 | + | 0.186196i | \(0.0596158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.7426 | − | 15.1427i | −0.393836 | − | 0.507870i | ||||
\(890\) | 10.8284 | 0.362970 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.65685 | − | 8.06591i | −0.155923 | − | 0.270067i | ||||
\(893\) | 1.82843 | + | 3.16693i | 0.0611860 | + | 0.105977i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.3137 | −0.712439 | ||||||||
\(896\) | 2.62132 | − | 0.358719i | 0.0875722 | − | 0.0119840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5563 | − | 33.8726i | 0.652604 | − | 1.13034i | ||||
\(899\) | −14.8284 | − | 25.6836i | −0.494556 | − | 0.856596i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.3848 | + | 73.4126i | −1.41204 | + | 2.44573i | ||||
\(902\) | 6.65685 | 0.221649 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.65685 | −0.254663 | ||||||||
\(905\) | −16.4853 | + | 28.5533i | −0.547989 | + | 0.949145i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5711 | − | 33.8981i | −0.649847 | − | 1.12557i | −0.983159 | − | 0.182751i | \(-0.941500\pi\) |
0.333313 | − | 0.942816i | \(-0.391834\pi\) | |||||||
\(908\) | −5.15685 | + | 8.93193i | −0.171136 | + | 0.296417i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.4853 | + | 40.3805i | −0.546482 | + | 1.33860i | ||||
\(911\) | −7.78680 | −0.257988 | −0.128994 | − | 0.991645i | \(-0.541175\pi\) | ||||
−0.128994 | + | 0.991645i | \(0.541175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.08579 | + | 3.61269i | 0.0690295 | + | 0.119563i | ||||
\(914\) | −5.31371 | − | 9.20361i | −0.175762 | − | 0.304428i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.3137 | 0.373815 | ||||||||
\(917\) | −19.1716 | + | 2.62357i | −0.633101 | + | 0.0866379i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.55025 | − | 2.68512i | 0.0511381 | − | 0.0885738i | −0.839323 | − | 0.543633i | \(-0.817048\pi\) |
0.890461 | + | 0.455059i | \(0.150382\pi\) | |||||||
\(920\) | 6.32843 | + | 10.9612i | 0.208642 | + | 0.361379i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.17157 | − | 10.6895i | 0.203250 | − | 0.352039i | ||||
\(923\) | −63.5980 | −2.09335 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.37258 | −0.0451303 | ||||||||
\(926\) | −19.5563 | + | 33.8726i | −0.642662 | + | 1.11312i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.41421 | + | 2.44949i | 0.0464238 | + | 0.0804084i | ||||
\(929\) | −21.7279 | + | 37.6339i | −0.712870 | + | 1.23473i | 0.250905 | + | 0.968012i | \(0.419272\pi\) |
−0.963775 | + | 0.266715i | \(0.914062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1421 | + | 23.6544i | 0.791227 | + | 0.775241i | ||||
\(932\) | 14.3137 | 0.468861 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.4853 | − | 26.8213i | −0.506694 | − | 0.877620i | ||||
\(935\) | −9.44975 | − | 16.3674i | −0.309040 | − | 0.535273i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.343146 | 0.0112101 | 0.00560504 | − | 0.999984i | \(-0.498216\pi\) | ||||
0.00560504 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(938\) | −5.65076 | − | 7.28692i | −0.184504 | − | 0.237926i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.914214 | − | 1.58346i | 0.0298184 | − | 0.0516469i | ||||
\(941\) | 28.3137 | + | 49.0408i | 0.923001 | + | 1.59868i | 0.794746 | + | 0.606943i | \(0.207604\pi\) |
0.128255 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4497 | − | 30.2238i | 0.568242 | − | 0.984224i | ||||
\(944\) | −7.65685 | −0.249209 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.82843 | 0.0919601 | ||||||||
\(947\) | −16.3137 | + | 28.2562i | −0.530124 | + | 0.918202i | 0.469258 | + | 0.883061i | \(0.344521\pi\) |
−0.999382 | + | 0.0351411i | \(0.988812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.82843 | + | 4.89898i | 0.0918146 | + | 0.159028i | ||||
\(950\) | −2.00000 | + | 3.46410i | −0.0648886 | + | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.82843 | + | 19.1757i | −0.253721 | + | 0.621486i | ||||
\(953\) | −16.3137 | −0.528453 | −0.264226 | − | 0.964461i | \(-0.585117\pi\) | ||||
−0.264226 | + | 0.964461i | \(0.585117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.0711 | − | 27.8359i | −0.520048 | − | 0.900749i | ||||
\(956\) | 10.0000 | + | 17.3205i | 0.323423 | + | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.8284 | 0.349851 | ||||||||
\(959\) | −0.828427 | + | 2.02922i | −0.0267513 | + | 0.0655271i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.4706 | + | 68.3650i | −1.27324 | + | 2.20532i | ||||
\(962\) | 5.65685 | + | 9.79796i | 0.182384 | + | 0.315899i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.48528 | − | 7.76874i | 0.144461 | − | 0.250214i | ||||
\(965\) | 35.7990 | 1.15241 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8995 | 0.736398 | 0.368199 | − | 0.929747i | \(-0.379974\pi\) | ||||
0.368199 | + | 0.929747i | \(0.379974\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.1066 | + | 33.0936i | 0.613476 | + | 1.06257i | ||||
\(971\) | −5.00000 | + | 8.66025i | −0.160458 | + | 0.277921i | −0.935033 | − | 0.354561i | \(-0.884630\pi\) |
0.774575 | + | 0.632482i | \(0.217964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.72792 | − | 12.5446i | −0.311863 | − | 0.402162i | ||||
\(974\) | −1.31371 | −0.0420939 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.20711 | + | 3.82282i | 0.0706478 | + | 0.122366i | ||||
\(977\) | −17.9706 | − | 31.1259i | −0.574929 | − | 0.995807i | −0.996049 | − | 0.0888018i | \(-0.971696\pi\) |
0.421120 | − | 0.907005i | \(-0.361637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.48528 | −0.143350 | ||||||||
\(980\) | 4.20711 | − | 16.3674i | 0.134391 | − | 0.522839i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.8137 | + | 25.6581i | −0.472724 | + | 0.818783i | ||||
\(983\) | 22.6213 | + | 39.1813i | 0.721508 | + | 1.24969i | 0.960395 | + | 0.278641i | \(0.0898841\pi\) |
−0.238887 | + | 0.971047i | \(0.576783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.7279 | − | 42.8300i | 0.787897 | − | 1.36468i | ||||
\(986\) | −22.1421 | −0.705149 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.9706 | 1.04893 | ||||||||
\(989\) | 7.41421 | − | 12.8418i | 0.235758 | − | 0.408345i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.8284 | − | 29.1477i | −0.534573 | − | 0.925907i | −0.999184 | − | 0.0403922i | \(-0.987139\pi\) |
0.464611 | − | 0.885515i | \(-0.346194\pi\) | |||||||
\(992\) | 5.24264 | − | 9.08052i | 0.166454 | − | 0.288307i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.4142 | − | 3.34101i | 0.774372 | − | 0.105970i | ||||
\(995\) | 47.4558 | 1.50445 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.10051 | − | 7.10228i | −0.129864 | − | 0.224932i | 0.793760 | − | 0.608232i | \(-0.208121\pi\) |
−0.923624 | + | 0.383300i | \(0.874788\pi\) | |||||||
\(998\) | 12.8284 | + | 22.2195i | 0.406077 | + | 0.703346i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.k.u.793.2 | yes | 4 | |
3.2 | odd | 2 | 1386.2.k.q.793.1 | ✓ | 4 | ||
7.2 | even | 3 | 9702.2.a.cj.1.1 | 2 | |||
7.4 | even | 3 | inner | 1386.2.k.u.991.2 | yes | 4 | |
7.5 | odd | 6 | 9702.2.a.cv.1.2 | 2 | |||
21.2 | odd | 6 | 9702.2.a.ds.1.2 | 2 | |||
21.5 | even | 6 | 9702.2.a.da.1.1 | 2 | |||
21.11 | odd | 6 | 1386.2.k.q.991.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.q.793.1 | ✓ | 4 | 3.2 | odd | 2 | ||
1386.2.k.q.991.1 | yes | 4 | 21.11 | odd | 6 | ||
1386.2.k.u.793.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1386.2.k.u.991.2 | yes | 4 | 7.4 | even | 3 | inner | |
9702.2.a.cj.1.1 | 2 | 7.2 | even | 3 | |||
9702.2.a.cv.1.2 | 2 | 7.5 | odd | 6 | |||
9702.2.a.da.1.1 | 2 | 21.5 | even | 6 | |||
9702.2.a.ds.1.2 | 2 | 21.2 | odd | 6 |