Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [686,2,Mod(361,686)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(686, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("686.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 686 = 2 \cdot 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 686.c (of order \(3\), degree \(2\), not 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: | \(5.47773757866\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(-0.623490 - 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 686.667 |
Dual form | 686.2.c.d.361.1 |
$q$-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 \(\left(\mathbb{Z}/686\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(3\) | −0.623490 | − | 1.07992i | −0.359972 | − | 0.623490i | 0.627984 | − | 0.778226i | \(-0.283880\pi\) |
−0.987956 | + | 0.154737i | \(0.950547\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.678448 | − | 1.17511i | 0.303411 | − | 0.525524i | −0.673495 | − | 0.739192i | \(-0.735208\pi\) |
0.976906 | + | 0.213668i | \(0.0685411\pi\) | |||||||
\(6\) | −1.24698 | −0.509077 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.722521 | − | 1.25144i | 0.240840 | − | 0.417148i | ||||
\(10\) | −0.678448 | − | 1.17511i | −0.214544 | − | 0.371601i | ||||
\(11\) | 0.167563 | + | 0.290227i | 0.0505221 | + | 0.0875068i | 0.890180 | − | 0.455608i | \(-0.150578\pi\) |
−0.839658 | + | 0.543115i | \(0.817245\pi\) | |||||||
\(12\) | −0.623490 | + | 1.07992i | −0.179986 | + | 0.311745i | ||||
\(13\) | −6.38404 | −1.77061 | −0.885307 | − | 0.465006i | \(-0.846052\pi\) | ||||
−0.885307 | + | 0.465006i | \(0.846052\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.69202 | −0.436878 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.48039 | − | 2.56410i | −0.359046 | − | 0.621886i | 0.628755 | − | 0.777603i | \(-0.283565\pi\) |
−0.987802 | + | 0.155717i | \(0.950231\pi\) | |||||||
\(18\) | −0.722521 | − | 1.25144i | −0.170300 | − | 0.294968i | ||||
\(19\) | 2.05496 | − | 3.55929i | 0.471440 | − | 0.816558i | −0.528026 | − | 0.849228i | \(-0.677068\pi\) |
0.999466 | + | 0.0326704i | \(0.0104011\pi\) | |||||||
\(20\) | −1.35690 | −0.303411 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.335126 | 0.0714490 | ||||||||
\(23\) | 1.82640 | − | 3.16341i | 0.380830 | − | 0.659617i | −0.610351 | − | 0.792131i | \(-0.708972\pi\) |
0.991181 | + | 0.132514i | \(0.0423050\pi\) | |||||||
\(24\) | 0.623490 | + | 1.07992i | 0.127269 | + | 0.220437i | ||||
\(25\) | 1.57942 | + | 2.73563i | 0.315883 | + | 0.547126i | ||||
\(26\) | −3.19202 | + | 5.52874i | −0.626007 | + | 1.08428i | ||||
\(27\) | −5.54288 | −1.06673 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.04892 | 0.751865 | 0.375933 | − | 0.926647i | \(-0.377322\pi\) | ||||
0.375933 | + | 0.926647i | \(0.377322\pi\) | |||||||
\(30\) | −0.846011 | + | 1.46533i | −0.154460 | + | 0.267532i | ||||
\(31\) | 0.352052 | + | 0.609771i | 0.0632303 | + | 0.109518i | 0.895908 | − | 0.444240i | \(-0.146526\pi\) |
−0.832677 | + | 0.553759i | \(0.813193\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.208947 | − | 0.361908i | 0.0363731 | − | 0.0630000i | ||||
\(34\) | −2.96077 | −0.507768 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.44504 | −0.240840 | ||||||||
\(37\) | −3.37047 | + | 5.83782i | −0.554102 | + | 0.959732i | 0.443871 | + | 0.896091i | \(0.353605\pi\) |
−0.997973 | + | 0.0636417i | \(0.979729\pi\) | |||||||
\(38\) | −2.05496 | − | 3.55929i | −0.333358 | − | 0.577393i | ||||
\(39\) | 3.98039 | + | 6.89423i | 0.637372 | + | 1.10396i | ||||
\(40\) | −0.678448 | + | 1.17511i | −0.107272 | + | 0.185801i | ||||
\(41\) | −6.60388 | −1.03135 | −0.515676 | − | 0.856784i | \(-0.672459\pi\) | ||||
−0.515676 | + | 0.856784i | \(0.672459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.91185 | −0.749051 | −0.374525 | − | 0.927217i | \(-0.622194\pi\) | ||||
−0.374525 | + | 0.927217i | \(0.622194\pi\) | |||||||
\(44\) | 0.167563 | − | 0.290227i | 0.0252610 | − | 0.0437534i | ||||
\(45\) | −0.980386 | − | 1.69808i | −0.146147 | − | 0.253134i | ||||
\(46\) | −1.82640 | − | 3.16341i | −0.269287 | − | 0.466420i | ||||
\(47\) | −0.431468 | + | 0.747325i | −0.0629361 | + | 0.109009i | −0.895777 | − | 0.444504i | \(-0.853380\pi\) |
0.832840 | + | 0.553513i | \(0.186713\pi\) | |||||||
\(48\) | 1.24698 | 0.179986 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.15883 | 0.446727 | ||||||||
\(51\) | −1.84601 | + | 3.19738i | −0.258493 | + | 0.447723i | ||||
\(52\) | 3.19202 | + | 5.52874i | 0.442654 | + | 0.766699i | ||||
\(53\) | −6.44385 | − | 11.1611i | −0.885130 | − | 1.53309i | −0.845564 | − | 0.533874i | \(-0.820736\pi\) |
−0.0395659 | − | 0.999217i | \(-0.512598\pi\) | |||||||
\(54\) | −2.77144 | + | 4.80027i | −0.377145 | + | 0.653234i | ||||
\(55\) | 0.454731 | 0.0613159 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.12498 | −0.678820 | ||||||||
\(58\) | 2.02446 | − | 3.50647i | 0.265824 | − | 0.460421i | ||||
\(59\) | 4.52930 | + | 7.84498i | 0.589665 | + | 1.02133i | 0.994276 | + | 0.106841i | \(0.0340736\pi\) |
−0.404611 | + | 0.914489i | \(0.632593\pi\) | |||||||
\(60\) | 0.846011 | + | 1.46533i | 0.109220 | + | 0.189174i | ||||
\(61\) | 6.57942 | − | 11.3959i | 0.842408 | − | 1.45909i | −0.0454453 | − | 0.998967i | \(-0.514471\pi\) |
0.887853 | − | 0.460127i | \(-0.152196\pi\) | |||||||
\(62\) | 0.704103 | 0.0894212 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.33124 | + | 7.50193i | −0.537224 | + | 0.930500i | ||||
\(66\) | −0.208947 | − | 0.361908i | −0.0257196 | − | 0.0445477i | ||||
\(67\) | −1.57457 | − | 2.72724i | −0.192365 | − | 0.333185i | 0.753669 | − | 0.657254i | \(-0.228282\pi\) |
−0.946033 | + | 0.324069i | \(0.894949\pi\) | |||||||
\(68\) | −1.48039 | + | 2.56410i | −0.179523 | + | 0.310943i | ||||
\(69\) | −4.55496 | −0.548353 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5700 | 1.25443 | 0.627216 | − | 0.778846i | \(-0.284195\pi\) | ||||
0.627216 | + | 0.778846i | \(0.284195\pi\) | |||||||
\(72\) | −0.722521 | + | 1.25144i | −0.0851499 | + | 0.147484i | ||||
\(73\) | 5.01089 | + | 8.67911i | 0.586480 | + | 1.01581i | 0.994689 | + | 0.102924i | \(0.0328200\pi\) |
−0.408209 | + | 0.912888i | \(0.633847\pi\) | |||||||
\(74\) | 3.37047 | + | 5.83782i | 0.391809 | + | 0.678633i | ||||
\(75\) | 1.96950 | − | 3.41127i | 0.227418 | − | 0.393900i | ||||
\(76\) | −4.10992 | −0.471440 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.96077 | 0.901380 | ||||||||
\(79\) | 4.43147 | − | 7.67553i | 0.498579 | − | 0.863564i | −0.501420 | − | 0.865204i | \(-0.667189\pi\) |
0.999999 | + | 0.00163989i | \(0.000521994\pi\) | |||||||
\(80\) | 0.678448 | + | 1.17511i | 0.0758528 | + | 0.131381i | ||||
\(81\) | 1.28836 | + | 2.23151i | 0.143152 | + | 0.247946i | ||||
\(82\) | −3.30194 | + | 5.71912i | −0.364638 | + | 0.631572i | ||||
\(83\) | 17.4426 | 1.91458 | 0.957290 | − | 0.289130i | \(-0.0933661\pi\) | ||||
0.957290 | + | 0.289130i | \(0.0933661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.01746 | −0.435755 | ||||||||
\(86\) | −2.45593 | + | 4.25379i | −0.264829 | + | 0.458698i | ||||
\(87\) | −2.52446 | − | 4.37249i | −0.270650 | − | 0.468780i | ||||
\(88\) | −0.167563 | − | 0.290227i | −0.0178623 | − | 0.0309383i | ||||
\(89\) | −0.312823 | + | 0.541825i | −0.0331592 | + | 0.0574333i | −0.882129 | − | 0.471008i | \(-0.843890\pi\) |
0.848970 | + | 0.528442i | \(0.177223\pi\) | |||||||
\(90\) | −1.96077 | −0.206683 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.65279 | −0.380830 | ||||||||
\(93\) | 0.439001 | − | 0.760372i | 0.0455223 | − | 0.0788469i | ||||
\(94\) | 0.431468 | + | 0.747325i | 0.0445026 | + | 0.0770807i | ||||
\(95\) | −2.78836 | − | 4.82959i | −0.286080 | − | 0.495505i | ||||
\(96\) | 0.623490 | − | 1.07992i | 0.0636347 | − | 0.110218i | ||||
\(97\) | −3.24698 | −0.329681 | −0.164840 | − | 0.986320i | \(-0.552711\pi\) | ||||
−0.164840 | + | 0.986320i | \(0.552711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.484271 | 0.0486710 | ||||||||
\(100\) | 1.57942 | − | 2.73563i | 0.157942 | − | 0.273563i | ||||
\(101\) | 0.887395 | + | 1.53701i | 0.0882991 | + | 0.152939i | 0.906792 | − | 0.421578i | \(-0.138524\pi\) |
−0.818493 | + | 0.574516i | \(0.805190\pi\) | |||||||
\(102\) | 1.84601 | + | 3.19738i | 0.182782 | + | 0.316588i | ||||
\(103\) | 7.85839 | − | 13.6111i | 0.774310 | − | 1.34114i | −0.160872 | − | 0.986975i | \(-0.551430\pi\) |
0.935181 | − | 0.354169i | \(-0.115236\pi\) | |||||||
\(104\) | 6.38404 | 0.626007 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.8877 | −1.25176 | ||||||||
\(107\) | 8.71528 | − | 15.0953i | 0.842538 | − | 1.45932i | −0.0452037 | − | 0.998978i | \(-0.514394\pi\) |
0.887742 | − | 0.460341i | \(-0.152273\pi\) | |||||||
\(108\) | 2.77144 | + | 4.80027i | 0.266682 | + | 0.461906i | ||||
\(109\) | −3.54623 | − | 6.14225i | −0.339667 | − | 0.588321i | 0.644703 | − | 0.764433i | \(-0.276981\pi\) |
−0.984370 | + | 0.176112i | \(0.943648\pi\) | |||||||
\(110\) | 0.227365 | − | 0.393808i | 0.0216784 | − | 0.0375481i | ||||
\(111\) | 8.40581 | 0.797844 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9433 | −1.21760 | −0.608802 | − | 0.793322i | \(-0.708350\pi\) | ||||
−0.608802 | + | 0.793322i | \(0.708350\pi\) | |||||||
\(114\) | −2.56249 | + | 4.43836i | −0.239999 | + | 0.415691i | ||||
\(115\) | −2.47823 | − | 4.29242i | −0.231096 | − | 0.400270i | ||||
\(116\) | −2.02446 | − | 3.50647i | −0.187966 | − | 0.325567i | ||||
\(117\) | −4.61260 | + | 7.98927i | −0.426435 | + | 0.738608i | ||||
\(118\) | 9.05861 | 0.833912 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.69202 | 0.154460 | ||||||||
\(121\) | 5.44385 | − | 9.42902i | 0.494895 | − | 0.857183i | ||||
\(122\) | −6.57942 | − | 11.3959i | −0.595672 | − | 1.03173i | ||||
\(123\) | 4.11745 | + | 7.13163i | 0.371258 | + | 0.643038i | ||||
\(124\) | 0.352052 | − | 0.609771i | 0.0316152 | − | 0.0547591i | ||||
\(125\) | 11.0707 | 0.990192 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9487 | 0.971539 | 0.485770 | − | 0.874087i | \(-0.338539\pi\) | ||||
0.485770 | + | 0.874087i | \(0.338539\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.06249 | + | 5.30439i | 0.269637 | + | 0.467025i | ||||
\(130\) | 4.33124 | + | 7.50193i | 0.379875 | + | 0.657963i | ||||
\(131\) | −2.21983 | + | 3.84486i | −0.193948 | + | 0.335927i | −0.946555 | − | 0.322542i | \(-0.895463\pi\) |
0.752607 | + | 0.658470i | \(0.228796\pi\) | |||||||
\(132\) | −0.417895 | −0.0363731 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.14914 | −0.272045 | ||||||||
\(135\) | −3.76055 | + | 6.51347i | −0.323657 | + | 0.560590i | ||||
\(136\) | 1.48039 | + | 2.56410i | 0.126942 | + | 0.219870i | ||||
\(137\) | 7.88135 | + | 13.6509i | 0.673350 | + | 1.16628i | 0.976948 | + | 0.213476i | \(0.0684784\pi\) |
−0.303599 | + | 0.952800i | \(0.598188\pi\) | |||||||
\(138\) | −2.27748 | + | 3.94471i | −0.193872 | + | 0.335796i | ||||
\(139\) | 17.9584 | 1.52321 | 0.761605 | − | 0.648042i | \(-0.224412\pi\) | ||||
0.761605 | + | 0.648042i | \(0.224412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.07606 | 0.0906210 | ||||||||
\(142\) | 5.28501 | − | 9.15391i | 0.443508 | − | 0.768179i | ||||
\(143\) | −1.06973 | − | 1.85282i | −0.0894552 | − | 0.154941i | ||||
\(144\) | 0.722521 | + | 1.25144i | 0.0602101 | + | 0.104287i | ||||
\(145\) | 2.74698 | − | 4.75791i | 0.228124 | − | 0.395123i | ||||
\(146\) | 10.0218 | 0.829408 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.74094 | 0.554102 | ||||||||
\(149\) | −7.04556 | + | 12.2033i | −0.577195 | + | 0.999731i | 0.418604 | + | 0.908169i | \(0.362519\pi\) |
−0.995799 | + | 0.0915626i | \(0.970814\pi\) | |||||||
\(150\) | −1.96950 | − | 3.41127i | −0.160809 | − | 0.278529i | ||||
\(151\) | −6.12833 | − | 10.6146i | −0.498717 | − | 0.863803i | 0.501282 | − | 0.865284i | \(-0.332862\pi\) |
−0.999999 | + | 0.00148113i | \(0.999529\pi\) | |||||||
\(152\) | −2.05496 | + | 3.55929i | −0.166679 | + | 0.288697i | ||||
\(153\) | −4.27844 | −0.345891 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.955395 | 0.0767391 | ||||||||
\(156\) | 3.98039 | − | 6.89423i | 0.318686 | − | 0.551980i | ||||
\(157\) | −10.6027 | − | 18.3644i | −0.846186 | − | 1.46564i | −0.884587 | − | 0.466375i | \(-0.845560\pi\) |
0.0384014 | − | 0.999262i | \(-0.487773\pi\) | |||||||
\(158\) | −4.43147 | − | 7.67553i | −0.352549 | − | 0.610632i | ||||
\(159\) | −8.03534 | + | 13.9176i | −0.637244 | + | 1.10374i | ||||
\(160\) | 1.35690 | 0.107272 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.57673 | 0.202447 | ||||||||
\(163\) | −9.24309 | + | 16.0095i | −0.723975 | + | 1.25396i | 0.235419 | + | 0.971894i | \(0.424354\pi\) |
−0.959394 | + | 0.282068i | \(0.908980\pi\) | |||||||
\(164\) | 3.30194 | + | 5.71912i | 0.257838 | + | 0.446589i | ||||
\(165\) | −0.283520 | − | 0.491071i | −0.0220720 | − | 0.0382298i | ||||
\(166\) | 8.72132 | − | 15.1058i | 0.676906 | − | 1.17244i | ||||
\(167\) | 20.2741 | 1.56886 | 0.784430 | − | 0.620218i | \(-0.212956\pi\) | ||||
0.784430 | + | 0.620218i | \(0.212956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.7560 | 2.13508 | ||||||||
\(170\) | −2.00873 | + | 3.47922i | −0.154062 | + | 0.266844i | ||||
\(171\) | −2.96950 | − | 5.14333i | −0.227083 | − | 0.393320i | ||||
\(172\) | 2.45593 | + | 4.25379i | 0.187263 | + | 0.324348i | ||||
\(173\) | −3.17845 | + | 5.50523i | −0.241653 | + | 0.418555i | −0.961185 | − | 0.275904i | \(-0.911023\pi\) |
0.719532 | + | 0.694459i | \(0.244356\pi\) | |||||||
\(174\) | −5.04892 | −0.382757 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.335126 | −0.0252610 | ||||||||
\(177\) | 5.64795 | − | 9.78253i | 0.424526 | − | 0.735300i | ||||
\(178\) | 0.312823 | + | 0.541825i | 0.0234471 | + | 0.0406115i | ||||
\(179\) | −1.73005 | − | 2.99654i | −0.129310 | − | 0.223972i | 0.794099 | − | 0.607788i | \(-0.207943\pi\) |
−0.923410 | + | 0.383816i | \(0.874610\pi\) | |||||||
\(180\) | −0.980386 | + | 1.69808i | −0.0730736 | + | 0.126567i | ||||
\(181\) | −13.7071 | −1.01884 | −0.509420 | − | 0.860518i | \(-0.670140\pi\) | ||||
−0.509420 | + | 0.860518i | \(0.670140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.4088 | −1.21297 | ||||||||
\(184\) | −1.82640 | + | 3.16341i | −0.134644 | + | 0.233210i | ||||
\(185\) | 4.57338 | + | 7.92132i | 0.336241 | + | 0.582387i | ||||
\(186\) | −0.439001 | − | 0.760372i | −0.0321891 | − | 0.0557532i | ||||
\(187\) | 0.496115 | − | 0.859297i | 0.0362795 | − | 0.0628380i | ||||
\(188\) | 0.862937 | 0.0629361 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.57673 | −0.404578 | ||||||||
\(191\) | 3.46466 | − | 6.00096i | 0.250694 | − | 0.434214i | −0.713023 | − | 0.701140i | \(-0.752675\pi\) |
0.963717 | + | 0.266926i | \(0.0860080\pi\) | |||||||
\(192\) | −0.623490 | − | 1.07992i | −0.0449965 | − | 0.0779362i | ||||
\(193\) | 0.358092 | + | 0.620234i | 0.0257760 | + | 0.0446454i | 0.878626 | − | 0.477511i | \(-0.158461\pi\) |
−0.852850 | + | 0.522157i | \(0.825128\pi\) | |||||||
\(194\) | −1.62349 | + | 2.81197i | −0.116560 | + | 0.201887i | ||||
\(195\) | 10.8019 | 0.773543 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.06100 | 0.146840 | 0.0734200 | − | 0.997301i | \(-0.476609\pi\) | ||||
0.0734200 | + | 0.997301i | \(0.476609\pi\) | |||||||
\(198\) | 0.242135 | − | 0.419391i | 0.0172078 | − | 0.0298048i | ||||
\(199\) | 0.0108851 | + | 0.0188536i | 0.000771627 | + | 0.00133650i | 0.866411 | − | 0.499332i | \(-0.166421\pi\) |
−0.865639 | + | 0.500668i | \(0.833088\pi\) | |||||||
\(200\) | −1.57942 | − | 2.73563i | −0.111682 | − | 0.193438i | ||||
\(201\) | −1.96346 | + | 3.40081i | −0.138492 | + | 0.239875i | ||||
\(202\) | 1.77479 | 0.124874 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.69202 | 0.258493 | ||||||||
\(205\) | −4.48039 | + | 7.76026i | −0.312924 | + | 0.542000i | ||||
\(206\) | −7.85839 | − | 13.6111i | −0.547520 | − | 0.948332i | ||||
\(207\) | −2.63922 | − | 4.57126i | −0.183438 | − | 0.317725i | ||||
\(208\) | 3.19202 | − | 5.52874i | 0.221327 | − | 0.383349i | ||||
\(209\) | 1.37734 | 0.0952725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.7875 | −1.91297 | −0.956484 | − | 0.291785i | \(-0.905751\pi\) | ||||
−0.956484 | + | 0.291785i | \(0.905751\pi\) | |||||||
\(212\) | −6.44385 | + | 11.1611i | −0.442565 | + | 0.766545i | ||||
\(213\) | −6.59030 | − | 11.4147i | −0.451560 | − | 0.782125i | ||||
\(214\) | −8.71528 | − | 15.0953i | −0.595765 | − | 1.03189i | ||||
\(215\) | −3.33244 | + | 5.77195i | −0.227270 | + | 0.393644i | ||||
\(216\) | 5.54288 | 0.377145 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.09246 | −0.480362 | ||||||||
\(219\) | 6.24847 | − | 10.8227i | 0.422233 | − | 0.731328i | ||||
\(220\) | −0.227365 | − | 0.393808i | −0.0153290 | − | 0.0265505i | ||||
\(221\) | 9.45085 | + | 16.3693i | 0.635733 | + | 1.10112i | ||||
\(222\) | 4.20291 | − | 7.27965i | 0.282081 | − | 0.488578i | ||||
\(223\) | 12.7017 | 0.850569 | 0.425285 | − | 0.905060i | \(-0.360174\pi\) | ||||
0.425285 | + | 0.905060i | \(0.360174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.56465 | 0.304310 | ||||||||
\(226\) | −6.47166 | + | 11.2092i | −0.430488 | + | 0.745627i | ||||
\(227\) | −3.24818 | − | 5.62601i | −0.215589 | − | 0.373411i | 0.737866 | − | 0.674948i | \(-0.235834\pi\) |
−0.953455 | + | 0.301537i | \(0.902500\pi\) | |||||||
\(228\) | 2.56249 | + | 4.43836i | 0.169705 | + | 0.293938i | ||||
\(229\) | 4.85086 | − | 8.40193i | 0.320554 | − | 0.555215i | −0.660049 | − | 0.751223i | \(-0.729464\pi\) |
0.980602 | + | 0.196008i | \(0.0627978\pi\) | |||||||
\(230\) | −4.95646 | −0.326819 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.04892 | −0.265824 | ||||||||
\(233\) | −0.909698 | + | 1.57564i | −0.0595963 | + | 0.103224i | −0.894284 | − | 0.447499i | \(-0.852315\pi\) |
0.834688 | + | 0.550723i | \(0.185648\pi\) | |||||||
\(234\) | 4.61260 | + | 7.98927i | 0.301535 | + | 0.522275i | ||||
\(235\) | 0.585458 | + | 1.01404i | 0.0381910 | + | 0.0661488i | ||||
\(236\) | 4.52930 | − | 7.84498i | 0.294833 | − | 0.510665i | ||||
\(237\) | −11.0519 | −0.717898 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.19567 | 0.530134 | 0.265067 | − | 0.964230i | \(-0.414606\pi\) | ||||
0.265067 | + | 0.964230i | \(0.414606\pi\) | |||||||
\(240\) | 0.846011 | − | 1.46533i | 0.0546098 | − | 0.0945869i | ||||
\(241\) | 2.61865 | + | 4.53563i | 0.168682 | + | 0.292165i | 0.937957 | − | 0.346753i | \(-0.112716\pi\) |
−0.769275 | + | 0.638918i | \(0.779382\pi\) | |||||||
\(242\) | −5.44385 | − | 9.42902i | −0.349944 | − | 0.606120i | ||||
\(243\) | −6.70775 | + | 11.6182i | −0.430302 | + | 0.745306i | ||||
\(244\) | −13.1588 | −0.842408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.23490 | 0.525038 | ||||||||
\(247\) | −13.1189 | + | 22.7227i | −0.834738 | + | 1.44581i | ||||
\(248\) | −0.352052 | − | 0.609771i | −0.0223553 | − | 0.0387205i | ||||
\(249\) | −10.8753 | − | 18.8366i | −0.689195 | − | 1.19372i | ||||
\(250\) | 5.53534 | − | 9.58750i | 0.350086 | − | 0.606367i | ||||
\(251\) | −0.972853 | −0.0614059 | −0.0307030 | − | 0.999529i | \(-0.509775\pi\) | ||||
−0.0307030 | + | 0.999529i | \(0.509775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.22414 | 0.0769613 | ||||||||
\(254\) | 5.47434 | − | 9.48184i | 0.343491 | − | 0.594944i | ||||
\(255\) | 2.50484 | + | 4.33852i | 0.156859 | + | 0.271689i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.85839 | + | 13.6111i | −0.490193 | + | 0.849039i | −0.999936 | − | 0.0112876i | \(-0.996407\pi\) |
0.509744 | + | 0.860326i | \(0.329740\pi\) | |||||||
\(258\) | 6.12498 | 0.381325 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.66248 | 0.537224 | ||||||||
\(261\) | 2.92543 | − | 5.06699i | 0.181079 | − | 0.313639i | ||||
\(262\) | 2.21983 | + | 3.84486i | 0.137142 | + | 0.237536i | ||||
\(263\) | 9.28113 | + | 16.0754i | 0.572299 | + | 0.991251i | 0.996329 | + | 0.0856027i | \(0.0272816\pi\) |
−0.424031 | + | 0.905648i | \(0.639385\pi\) | |||||||
\(264\) | −0.208947 | + | 0.361908i | −0.0128598 | + | 0.0222739i | ||||
\(265\) | −17.4873 | −1.07423 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.780167 | 0.0477455 | ||||||||
\(268\) | −1.57457 | + | 2.72724i | −0.0961823 | + | 0.166593i | ||||
\(269\) | 5.56518 | + | 9.63917i | 0.339315 | + | 0.587711i | 0.984304 | − | 0.176481i | \(-0.0564714\pi\) |
−0.644989 | + | 0.764192i | \(0.723138\pi\) | |||||||
\(270\) | 3.76055 | + | 6.51347i | 0.228860 | + | 0.396397i | ||||
\(271\) | 10.0625 | − | 17.4287i | 0.611253 | − | 1.05872i | −0.379777 | − | 0.925078i | \(-0.623999\pi\) |
0.991030 | − | 0.133643i | \(-0.0426675\pi\) | |||||||
\(272\) | 2.96077 | 0.179523 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7627 | 0.952260 | ||||||||
\(275\) | −0.529303 | + | 0.916780i | −0.0319182 | + | 0.0552839i | ||||
\(276\) | 2.27748 | + | 3.94471i | 0.137088 | + | 0.237444i | ||||
\(277\) | 12.9242 | + | 22.3854i | 0.776542 | + | 1.34501i | 0.933924 | + | 0.357472i | \(0.116361\pi\) |
−0.157382 | + | 0.987538i | \(0.550305\pi\) | |||||||
\(278\) | 8.97919 | − | 15.5524i | 0.538536 | − | 0.932772i | ||||
\(279\) | 1.01746 | 0.0609136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0737 | −0.779910 | −0.389955 | − | 0.920834i | \(-0.627509\pi\) | ||||
−0.389955 | + | 0.920834i | \(0.627509\pi\) | |||||||
\(282\) | 0.538032 | − | 0.931899i | 0.0320394 | − | 0.0554938i | ||||
\(283\) | 2.88859 | + | 5.00319i | 0.171709 | + | 0.297409i | 0.939017 | − | 0.343870i | \(-0.111738\pi\) |
−0.767308 | + | 0.641278i | \(0.778404\pi\) | |||||||
\(284\) | −5.28501 | − | 9.15391i | −0.313608 | − | 0.543185i | ||||
\(285\) | −3.47703 | + | 6.02240i | −0.205962 | + | 0.356736i | ||||
\(286\) | −2.13946 | −0.126509 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.44504 | 0.0851499 | ||||||||
\(289\) | 4.11692 | − | 7.13071i | 0.242172 | − | 0.419453i | ||||
\(290\) | −2.74698 | − | 4.75791i | −0.161308 | − | 0.279394i | ||||
\(291\) | 2.02446 | + | 3.50647i | 0.118676 | + | 0.205553i | ||||
\(292\) | 5.01089 | − | 8.67911i | 0.293240 | − | 0.507906i | ||||
\(293\) | −20.5200 | −1.19879 | −0.599397 | − | 0.800452i | \(-0.704593\pi\) | ||||
−0.599397 | + | 0.800452i | \(0.704593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2916 | 0.715644 | ||||||||
\(296\) | 3.37047 | − | 5.83782i | 0.195905 | − | 0.339317i | ||||
\(297\) | −0.928780 | − | 1.60869i | −0.0538933 | − | 0.0933459i | ||||
\(298\) | 7.04556 | + | 12.2033i | 0.408139 | + | 0.706917i | ||||
\(299\) | −11.6598 | + | 20.1954i | −0.674303 | + | 1.16793i | ||||
\(300\) | −3.93900 | −0.227418 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.2567 | −0.705292 | ||||||||
\(303\) | 1.10656 | − | 1.91662i | 0.0635704 | − | 0.110107i | ||||
\(304\) | 2.05496 | + | 3.55929i | 0.117860 | + | 0.204139i | ||||
\(305\) | −8.92758 | − | 15.4630i | −0.511192 | − | 0.885410i | ||||
\(306\) | −2.13922 | + | 3.70524i | −0.122291 | + | 0.211814i | ||||
\(307\) | −10.2446 | −0.584689 | −0.292345 | − | 0.956313i | \(-0.594435\pi\) | ||||
−0.292345 | + | 0.956313i | \(0.594435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.5985 | −1.11492 | ||||||||
\(310\) | 0.477697 | − | 0.827396i | 0.0271314 | − | 0.0469929i | ||||
\(311\) | 17.3339 | + | 30.0232i | 0.982917 | + | 1.70246i | 0.650850 | + | 0.759206i | \(0.274413\pi\) |
0.332067 | + | 0.943256i | \(0.392254\pi\) | |||||||
\(312\) | −3.98039 | − | 6.89423i | −0.225345 | − | 0.390309i | ||||
\(313\) | −5.84966 | + | 10.1319i | −0.330642 | + | 0.572689i | −0.982638 | − | 0.185533i | \(-0.940599\pi\) |
0.651996 | + | 0.758223i | \(0.273932\pi\) | |||||||
\(314\) | −21.2054 | −1.19669 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.86294 | −0.498579 | ||||||||
\(317\) | 3.41454 | − | 5.91416i | 0.191780 | − | 0.332172i | −0.754060 | − | 0.656805i | \(-0.771907\pi\) |
0.945840 | + | 0.324633i | \(0.105241\pi\) | |||||||
\(318\) | 8.03534 | + | 13.9176i | 0.450600 | + | 0.780462i | ||||
\(319\) | 0.678448 | + | 1.17511i | 0.0379858 | + | 0.0657933i | ||||
\(320\) | 0.678448 | − | 1.17511i | 0.0379264 | − | 0.0656904i | ||||
\(321\) | −21.7356 | −1.21316 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1685 | −0.677075 | ||||||||
\(324\) | 1.28836 | − | 2.23151i | 0.0715758 | − | 0.123973i | ||||
\(325\) | −10.0831 | − | 17.4644i | −0.559308 | − | 0.968750i | ||||
\(326\) | 9.24309 | + | 16.0095i | 0.511928 | + | 0.886685i | ||||
\(327\) | −4.42208 | + | 7.65926i | −0.244541 | + | 0.423558i | ||||
\(328\) | 6.60388 | 0.364638 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.567040 | −0.0312145 | ||||||||
\(331\) | 7.63318 | − | 13.2211i | 0.419557 | − | 0.726695i | −0.576337 | − | 0.817212i | \(-0.695519\pi\) |
0.995895 | + | 0.0905170i | \(0.0288519\pi\) | |||||||
\(332\) | −8.72132 | − | 15.1058i | −0.478645 | − | 0.829037i | ||||
\(333\) | 4.87047 | + | 8.43590i | 0.266900 | + | 0.462284i | ||||
\(334\) | 10.1371 | − | 17.5579i | 0.554675 | − | 0.960726i | ||||
\(335\) | −4.27306 | −0.233462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0163935 | −0.000893008 | −0.000446504 | − | 1.00000i | \(-0.500142\pi\) | ||||
−0.000446504 | 1.00000i | \(0.500142\pi\) | ||||||||
\(338\) | 13.8780 | − | 24.0374i | 0.754864 | − | 1.30746i | ||||
\(339\) | 8.07002 | + | 13.9777i | 0.438304 | + | 0.759164i | ||||
\(340\) | 2.00873 | + | 3.47922i | 0.108939 | + | 0.188687i | ||||
\(341\) | −0.117981 | + | 0.204350i | −0.00638906 | + | 0.0110662i | ||||
\(342\) | −5.93900 | −0.321144 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.91185 | 0.264829 | ||||||||
\(345\) | −3.09030 | + | 5.35256i | −0.166376 | + | 0.288172i | ||||
\(346\) | 3.17845 | + | 5.50523i | 0.170874 | + | 0.295963i | ||||
\(347\) | −9.75667 | − | 16.8990i | −0.523765 | − | 0.907188i | −0.999617 | − | 0.0276629i | \(-0.991194\pi\) |
0.475852 | − | 0.879525i | \(-0.342140\pi\) | |||||||
\(348\) | −2.52446 | + | 4.37249i | −0.135325 | + | 0.234390i | ||||
\(349\) | −11.7778 | −0.630450 | −0.315225 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315225 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.3860 | 1.88876 | ||||||||
\(352\) | −0.167563 | + | 0.290227i | −0.00893113 | + | 0.0154692i | ||||
\(353\) | 17.0836 | + | 29.5897i | 0.909268 | + | 1.57490i | 0.815083 | + | 0.579344i | \(0.196691\pi\) |
0.0941849 | + | 0.995555i | \(0.469976\pi\) | |||||||
\(354\) | −5.64795 | − | 9.78253i | −0.300185 | − | 0.519936i | ||||
\(355\) | 7.17121 | − | 12.4209i | 0.380608 | − | 0.659233i | ||||
\(356\) | 0.625646 | 0.0331592 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.46011 | −0.182872 | ||||||||
\(359\) | −5.32789 | + | 9.22817i | −0.281195 | + | 0.487044i | −0.971679 | − | 0.236303i | \(-0.924064\pi\) |
0.690484 | + | 0.723347i | \(0.257398\pi\) | |||||||
\(360\) | 0.980386 | + | 1.69808i | 0.0516709 | + | 0.0894966i | ||||
\(361\) | 1.05429 | + | 1.82609i | 0.0554892 | + | 0.0961101i | ||||
\(362\) | −6.85354 | + | 11.8707i | −0.360214 | + | 0.623909i | ||||
\(363\) | −13.5767 | −0.712593 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5985 | 0.711778 | ||||||||
\(366\) | −8.20440 | + | 14.2104i | −0.428851 | + | 0.742791i | ||||
\(367\) | −16.5489 | − | 28.6636i | −0.863846 | − | 1.49623i | −0.868188 | − | 0.496235i | \(-0.834715\pi\) |
0.00434158 | − | 0.999991i | \(-0.498618\pi\) | |||||||
\(368\) | 1.82640 | + | 3.16341i | 0.0952075 | + | 0.164904i | ||||
\(369\) | −4.77144 | + | 8.26437i | −0.248391 | + | 0.430226i | ||||
\(370\) | 9.14675 | 0.475517 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.878002 | −0.0455223 | ||||||||
\(373\) | 9.28770 | − | 16.0868i | 0.480899 | − | 0.832941i | −0.518861 | − | 0.854859i | \(-0.673644\pi\) |
0.999760 | + | 0.0219174i | \(0.00697708\pi\) | |||||||
\(374\) | −0.496115 | − | 0.859297i | −0.0256535 | − | 0.0444332i | ||||
\(375\) | −6.90246 | − | 11.9554i | −0.356442 | − | 0.617375i | ||||
\(376\) | 0.431468 | − | 0.747325i | 0.0222513 | − | 0.0385403i | ||||
\(377\) | −25.8485 | −1.33126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.85517 | 0.454859 | 0.227430 | − | 0.973795i | \(-0.426968\pi\) | ||||
0.227430 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(380\) | −2.78836 | + | 4.82959i | −0.143040 | + | 0.247753i | ||||
\(381\) | −6.82640 | − | 11.8237i | −0.349727 | − | 0.605745i | ||||
\(382\) | −3.46466 | − | 6.00096i | −0.177267 | − | 0.307036i | ||||
\(383\) | −15.3485 | + | 26.5843i | −0.784270 | + | 1.35840i | 0.145165 | + | 0.989408i | \(0.453629\pi\) |
−0.929434 | + | 0.368988i | \(0.879704\pi\) | |||||||
\(384\) | −1.24698 | −0.0636347 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.716185 | 0.0364528 | ||||||||
\(387\) | −3.54892 | + | 6.14691i | −0.180402 | + | 0.312465i | ||||
\(388\) | 1.62349 | + | 2.81197i | 0.0824202 | + | 0.142756i | ||||
\(389\) | 0.631023 | + | 1.09296i | 0.0319941 | + | 0.0554154i | 0.881579 | − | 0.472036i | \(-0.156481\pi\) |
−0.849585 | + | 0.527452i | \(0.823148\pi\) | |||||||
\(390\) | 5.40097 | − | 9.35475i | 0.273489 | − | 0.473696i | ||||
\(391\) | −10.8151 | −0.546942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.53617 | 0.279263 | ||||||||
\(394\) | 1.03050 | − | 1.78488i | 0.0519158 | − | 0.0899208i | ||||
\(395\) | −6.01304 | − | 10.4149i | −0.302549 | − | 0.524030i | ||||
\(396\) | −0.242135 | − | 0.419391i | −0.0121678 | − | 0.0210752i | ||||
\(397\) | −6.22790 | + | 10.7870i | −0.312569 | + | 0.541386i | −0.978918 | − | 0.204255i | \(-0.934523\pi\) |
0.666349 | + | 0.745640i | \(0.267856\pi\) | |||||||
\(398\) | 0.0217703 | 0.00109124 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.15883 | −0.157942 | ||||||||
\(401\) | 5.91335 | − | 10.2422i | 0.295298 | − | 0.511472i | −0.679756 | − | 0.733438i | \(-0.737914\pi\) |
0.975054 | + | 0.221967i | \(0.0712476\pi\) | |||||||
\(402\) | 1.96346 | + | 3.40081i | 0.0979285 | + | 0.169617i | ||||
\(403\) | −2.24751 | − | 3.89281i | −0.111957 | − | 0.193914i | ||||
\(404\) | 0.887395 | − | 1.53701i | 0.0441496 | − | 0.0764693i | ||||
\(405\) | 3.49635 | 0.173735 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.25906 | −0.111978 | ||||||||
\(408\) | 1.84601 | − | 3.19738i | 0.0913911 | − | 0.158294i | ||||
\(409\) | 9.20291 | + | 15.9399i | 0.455054 | + | 0.788177i | 0.998691 | − | 0.0511431i | \(-0.0162865\pi\) |
−0.543637 | + | 0.839321i | \(0.682953\pi\) | |||||||
\(410\) | 4.48039 | + | 7.76026i | 0.221270 | + | 0.383252i | ||||
\(411\) | 9.82789 | − | 17.0224i | 0.484774 | − | 0.839653i | ||||
\(412\) | −15.7168 | −0.774310 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.27844 | −0.259421 | ||||||||
\(415\) | 11.8339 | − | 20.4970i | 0.580905 | − | 1.00616i | ||||
\(416\) | −3.19202 | − | 5.52874i | −0.156502 | − | 0.271069i | ||||
\(417\) | −11.1969 | − | 19.3935i | −0.548313 | − | 0.949706i | ||||
\(418\) | 0.688669 | − | 1.19281i | 0.0336839 | − | 0.0583422i | ||||
\(419\) | 5.12067 | 0.250161 | 0.125081 | − | 0.992147i | \(-0.460081\pi\) | ||||
0.125081 | + | 0.992147i | \(0.460081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4034 | −0.799454 | −0.399727 | − | 0.916634i | \(-0.630895\pi\) | ||||
−0.399727 | + | 0.916634i | \(0.630895\pi\) | |||||||
\(422\) | −13.8937 | + | 24.0646i | −0.676336 | + | 1.17145i | ||||
\(423\) | 0.623490 | + | 1.07992i | 0.0303151 | + | 0.0525073i | ||||
\(424\) | 6.44385 | + | 11.1611i | 0.312941 | + | 0.542029i | ||||
\(425\) | 4.67629 | − | 8.09958i | 0.226833 | − | 0.392887i | ||||
\(426\) | −13.1806 | −0.638602 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.4306 | −0.842538 | ||||||||
\(429\) | −1.33393 | + | 2.31043i | −0.0644027 | + | 0.111549i | ||||
\(430\) | 3.33244 | + | 5.77195i | 0.160704 | + | 0.278348i | ||||
\(431\) | 0.165407 | + | 0.286493i | 0.00796737 | + | 0.0137999i | 0.869982 | − | 0.493084i | \(-0.164131\pi\) |
−0.862014 | + | 0.506884i | \(0.830797\pi\) | |||||||
\(432\) | 2.77144 | − | 4.80027i | 0.133341 | − | 0.230953i | ||||
\(433\) | 2.45042 | 0.117760 | 0.0588798 | − | 0.998265i | \(-0.481247\pi\) | ||||
0.0588798 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.85086 | −0.328473 | ||||||||
\(436\) | −3.54623 | + | 6.14225i | −0.169834 | + | 0.294160i | ||||
\(437\) | −7.50634 | − | 13.0014i | −0.359077 | − | 0.621939i | ||||
\(438\) | −6.24847 | − | 10.8227i | −0.298564 | − | 0.517127i | ||||
\(439\) | 1.34601 | − | 2.33136i | 0.0642416 | − | 0.111270i | −0.832116 | − | 0.554602i | \(-0.812871\pi\) |
0.896357 | + | 0.443332i | \(0.146204\pi\) | |||||||
\(440\) | −0.454731 | −0.0216784 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.9017 | 0.899062 | ||||||||
\(443\) | −18.2763 | + | 31.6555i | −0.868332 | + | 1.50400i | −0.00463256 | + | 0.999989i | \(0.501475\pi\) |
−0.863700 | + | 0.504007i | \(0.831859\pi\) | |||||||
\(444\) | −4.20291 | − | 7.27965i | −0.199461 | − | 0.345477i | ||||
\(445\) | 0.424468 | + | 0.735200i | 0.0201217 | + | 0.0348518i | ||||
\(446\) | 6.35086 | − | 11.0000i | 0.300722 | − | 0.520865i | ||||
\(447\) | 17.5714 | 0.831096 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.48427 | −0.164433 | −0.0822164 | − | 0.996614i | \(-0.526200\pi\) | ||||
−0.0822164 | + | 0.996614i | \(0.526200\pi\) | |||||||
\(450\) | 2.28232 | − | 3.95310i | 0.107590 | − | 0.186351i | ||||
\(451\) | −1.10656 | − | 1.91662i | −0.0521061 | − | 0.0902503i | ||||
\(452\) | 6.47166 | + | 11.2092i | 0.304401 | + | 0.527238i | ||||
\(453\) | −7.64191 | + | 13.2362i | −0.359048 | + | 0.621890i | ||||
\(454\) | −6.49635 | −0.304889 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.12498 | 0.239999 | ||||||||
\(457\) | 11.5591 | − | 20.0210i | 0.540714 | − | 0.936544i | −0.458150 | − | 0.888875i | \(-0.651488\pi\) |
0.998863 | − | 0.0476684i | \(-0.0151791\pi\) | |||||||
\(458\) | −4.85086 | − | 8.40193i | −0.226666 | − | 0.392596i | ||||
\(459\) | 8.20560 | + | 14.2125i | 0.383004 | + | 0.663383i | ||||
\(460\) | −2.47823 | + | 4.29242i | −0.115548 | + | 0.200135i | ||||
\(461\) | −9.69501 | −0.451541 | −0.225771 | − | 0.974180i | \(-0.572490\pi\) | ||||
−0.225771 | + | 0.974180i | \(0.572490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.84654 | −0.271712 | −0.135856 | − | 0.990729i | \(-0.543378\pi\) | ||||
−0.135856 | + | 0.990729i | \(0.543378\pi\) | |||||||
\(464\) | −2.02446 | + | 3.50647i | −0.0939831 | + | 0.162784i | ||||
\(465\) | −0.595679 | − | 1.03175i | −0.0276239 | − | 0.0478461i | ||||
\(466\) | 0.909698 | + | 1.57564i | 0.0421409 | + | 0.0729903i | ||||
\(467\) | −12.8916 | + | 22.3289i | −0.596551 | + | 1.03326i | 0.396775 | + | 0.917916i | \(0.370129\pi\) |
−0.993326 | + | 0.115341i | \(0.963204\pi\) | |||||||
\(468\) | 9.22521 | 0.426435 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.17092 | 0.0540103 | ||||||||
\(471\) | −13.2213 | + | 22.9000i | −0.609206 | + | 1.05518i | ||||
\(472\) | −4.52930 | − | 7.84498i | −0.208478 | − | 0.361095i | ||||
\(473\) | −0.823044 | − | 1.42555i | −0.0378436 | − | 0.0655470i | ||||
\(474\) | −5.52595 | + | 9.57123i | −0.253815 | + | 0.439621i | ||||
\(475\) | 12.9825 | 0.595680 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.6233 | −0.852700 | ||||||||
\(478\) | 4.09783 | − | 7.09766i | 0.187431 | − | 0.324639i | ||||
\(479\) | 10.4400 | + | 18.0825i | 0.477014 | + | 0.826212i | 0.999653 | − | 0.0263416i | \(-0.00838577\pi\) |
−0.522639 | + | 0.852554i | \(0.675052\pi\) | |||||||
\(480\) | −0.846011 | − | 1.46533i | −0.0386149 | − | 0.0668830i | ||||
\(481\) | 21.5172 | − | 37.2689i | 0.981101 | − | 1.69932i | ||||
\(482\) | 5.23729 | 0.238552 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8877 | −0.494895 | ||||||||
\(485\) | −2.20291 | + | 3.81555i | −0.100029 | + | 0.173255i | ||||
\(486\) | 6.70775 | + | 11.6182i | 0.304270 | + | 0.527011i | ||||
\(487\) | 0.314979 | + | 0.545559i | 0.0142731 | + | 0.0247217i | 0.873074 | − | 0.487588i | \(-0.162123\pi\) |
−0.858801 | + | 0.512310i | \(0.828790\pi\) | |||||||
\(488\) | −6.57942 | + | 11.3959i | −0.297836 | + | 0.515867i | ||||
\(489\) | 23.0519 | 1.04244 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.19269 | −0.324601 | −0.162301 | − | 0.986741i | \(-0.551891\pi\) | ||||
−0.162301 | + | 0.986741i | \(0.551891\pi\) | |||||||
\(492\) | 4.11745 | − | 7.13163i | 0.185629 | − | 0.321519i | ||||
\(493\) | −5.99396 | − | 10.3818i | −0.269954 | − | 0.467575i | ||||
\(494\) | 13.1189 | + | 22.7227i | 0.590249 | + | 1.02234i | ||||
\(495\) | 0.328552 | − | 0.569069i | 0.0147673 | − | 0.0255778i | ||||
\(496\) | −0.704103 | −0.0316152 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −21.7506 | −0.974669 | ||||||||
\(499\) | −10.6283 | + | 18.4088i | −0.475790 | + | 0.824092i | −0.999615 | − | 0.0277337i | \(-0.991171\pi\) |
0.523826 | + | 0.851825i | \(0.324504\pi\) | |||||||
\(500\) | −5.53534 | − | 9.58750i | −0.247548 | − | 0.428766i | ||||
\(501\) | −12.6407 | − | 21.8944i | −0.564745 | − | 0.978168i | ||||
\(502\) | −0.486426 | + | 0.842515i | −0.0217103 | + | 0.0376033i | ||||
\(503\) | −25.7614 | −1.14864 | −0.574322 | − | 0.818630i | \(-0.694734\pi\) | ||||
−0.574322 | + | 0.818630i | \(0.694734\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.40821 | 0.107164 | ||||||||
\(506\) | 0.612072 | − | 1.06014i | 0.0272099 | − | 0.0471290i | ||||
\(507\) | −17.3056 | − | 29.9742i | −0.768568 | − | 1.33120i | ||||
\(508\) | −5.47434 | − | 9.48184i | −0.242885 | − | 0.420689i | ||||
\(509\) | 8.59837 | − | 14.8928i | 0.381116 | − | 0.660112i | −0.610106 | − | 0.792320i | \(-0.708873\pi\) |
0.991222 | + | 0.132208i | \(0.0422065\pi\) | |||||||
\(510\) | 5.00969 | 0.221833 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −11.3904 | + | 19.7287i | −0.502898 | + | 0.871044i | ||||
\(514\) | 7.85839 | + | 13.6111i | 0.346619 | + | 0.600361i | ||||
\(515\) | −10.6630 | − | 18.4689i | −0.469869 | − | 0.813836i | ||||
\(516\) | 3.06249 | − | 5.30439i | 0.134819 | − | 0.233513i | ||||
\(517\) | −0.289192 | −0.0127187 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.92692 | 0.347953 | ||||||||
\(520\) | 4.33124 | − | 7.50193i | 0.189937 | − | 0.328981i | ||||
\(521\) | −0.216480 | − | 0.374955i | −0.00948417 | − | 0.0164271i | 0.861244 | − | 0.508191i | \(-0.169686\pi\) |
−0.870729 | + | 0.491764i | \(0.836352\pi\) | |||||||
\(522\) | −2.92543 | − | 5.06699i | −0.128042 | − | 0.221776i | ||||
\(523\) | 16.4535 | − | 28.4984i | 0.719463 | − | 1.24615i | −0.241750 | − | 0.970339i | \(-0.577721\pi\) |
0.961213 | − | 0.275808i | \(-0.0889453\pi\) | |||||||
\(524\) | 4.43967 | 0.193948 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.5623 | 0.809353 | ||||||||
\(527\) | 1.04234 | − | 1.80539i | 0.0454052 | − | 0.0786441i | ||||
\(528\) | 0.208947 | + | 0.361908i | 0.00909327 | + | 0.0157500i | ||||
\(529\) | 4.82855 | + | 8.36330i | 0.209937 | + | 0.363622i | ||||
\(530\) | −8.74363 | + | 15.1444i | −0.379799 | + | 0.657831i | ||||
\(531\) | 13.0901 | 0.568060 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.1594 | 1.82613 | ||||||||
\(534\) | 0.390084 | − | 0.675645i | 0.0168806 | − | 0.0292380i | ||||
\(535\) | −11.8257 | − | 20.4828i | −0.511271 | − | 0.885547i | ||||
\(536\) | 1.57457 | + | 2.72724i | 0.0680112 | + | 0.117799i | ||||
\(537\) | −2.15734 | + | 3.73663i | −0.0930962 | + | 0.161247i | ||||
\(538\) | 11.1304 | 0.479864 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.52111 | 0.323657 | ||||||||
\(541\) | −5.15279 | + | 8.92490i | −0.221536 | + | 0.383711i | −0.955275 | − | 0.295720i | \(-0.904440\pi\) |
0.733739 | + | 0.679432i | \(0.237774\pi\) | |||||||
\(542\) | −10.0625 | − | 17.4287i | −0.432221 | − | 0.748629i | ||||
\(543\) | 8.54623 | + | 14.8025i | 0.366754 | + | 0.635236i | ||||
\(544\) | 1.48039 | − | 2.56410i | 0.0634710 | − | 0.109935i | ||||
\(545\) | −9.62373 | −0.412235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.55363 | 0.194699 | 0.0973496 | − | 0.995250i | \(-0.468964\pi\) | ||||
0.0973496 | + | 0.995250i | \(0.468964\pi\) | |||||||
\(548\) | 7.88135 | − | 13.6509i | 0.336675 | − | 0.583138i | ||||
\(549\) | −9.50753 | − | 16.4675i | −0.405772 | − | 0.702817i | ||||
\(550\) | 0.529303 | + | 0.916780i | 0.0225696 | + | 0.0390916i | ||||
\(551\) | 8.32036 | − | 14.4113i | 0.354459 | − | 0.613941i | ||||
\(552\) | 4.55496 | 0.193872 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.8485 | 1.09820 | ||||||||
\(555\) | 5.70291 | − | 9.87772i | 0.242075 | − | 0.419286i | ||||
\(556\) | −8.97919 | − | 15.5524i | −0.380802 | − | 0.659569i | ||||
\(557\) | 14.1456 | + | 24.5008i | 0.599366 | + | 1.03813i | 0.992915 | + | 0.118829i | \(0.0379141\pi\) |
−0.393548 | + | 0.919304i | \(0.628753\pi\) | |||||||
\(558\) | 0.508729 | − | 0.881145i | 0.0215362 | − | 0.0373018i | ||||
\(559\) | 31.3575 | 1.32628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23729 | −0.0522385 | ||||||||
\(562\) | −6.53684 | + | 11.3221i | −0.275740 | + | 0.477595i | ||||
\(563\) | 13.0531 | + | 22.6086i | 0.550122 | + | 0.952840i | 0.998265 | + | 0.0588781i | \(0.0187523\pi\) |
−0.448143 | + | 0.893962i | \(0.647914\pi\) | |||||||
\(564\) | −0.538032 | − | 0.931899i | −0.0226552 | − | 0.0392400i | ||||
\(565\) | −8.78136 | + | 15.2098i | −0.369435 | + | 0.639880i | ||||
\(566\) | 5.77718 | 0.242833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.5700 | −0.443508 | ||||||||
\(569\) | 4.83124 | − | 8.36795i | 0.202536 | − | 0.350803i | −0.746809 | − | 0.665039i | \(-0.768415\pi\) |
0.949345 | + | 0.314236i | \(0.101748\pi\) | |||||||
\(570\) | 3.47703 | + | 6.02240i | 0.145637 | + | 0.252251i | ||||
\(571\) | 8.77077 | + | 15.1914i | 0.367045 | + | 0.635741i | 0.989102 | − | 0.147231i | \(-0.0470360\pi\) |
−0.622057 | + | 0.782972i | \(0.713703\pi\) | |||||||
\(572\) | −1.06973 | + | 1.85282i | −0.0447276 | + | 0.0774704i | ||||
\(573\) | −8.64071 | −0.360971 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.5386 | 0.481191 | ||||||||
\(576\) | 0.722521 | − | 1.25144i | 0.0301050 | − | 0.0521435i | ||||
\(577\) | −2.52297 | − | 4.36991i | −0.105032 | − | 0.181922i | 0.808719 | − | 0.588195i | \(-0.200161\pi\) |
−0.913751 | + | 0.406274i | \(0.866828\pi\) | |||||||
\(578\) | −4.11692 | − | 7.13071i | −0.171241 | − | 0.296598i | ||||
\(579\) | 0.446534 | − | 0.773419i | 0.0185573 | − | 0.0321422i | ||||
\(580\) | −5.49396 | −0.228124 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.04892 | 0.167833 | ||||||||
\(583\) | 2.15950 | − | 3.74036i | 0.0894373 | − | 0.154910i | ||||
\(584\) | −5.01089 | − | 8.67911i | −0.207352 | − | 0.359144i | ||||
\(585\) | 6.25882 | + | 10.8406i | 0.258771 | + | 0.448204i | ||||
\(586\) | −10.2600 | + | 17.7709i | −0.423838 | + | 0.734108i | ||||
\(587\) | 23.3787 | 0.964941 | 0.482470 | − | 0.875912i | \(-0.339740\pi\) | ||||
0.482470 | + | 0.875912i | \(0.339740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.89380 | 0.119237 | ||||||||
\(590\) | 6.14579 | − | 10.6448i | 0.253018 | − | 0.438241i | ||||
\(591\) | −1.28501 | − | 2.22571i | −0.0528583 | − | 0.0915533i | ||||
\(592\) | −3.37047 | − | 5.83782i | −0.138525 | − | 0.239933i | ||||
\(593\) | 10.7165 | − | 18.5615i | 0.440073 | − | 0.762229i | −0.557621 | − | 0.830095i | \(-0.688286\pi\) |
0.997694 | + | 0.0678665i | \(0.0216192\pi\) | |||||||
\(594\) | −1.85756 | −0.0762166 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0911 | 0.577195 | ||||||||
\(597\) | 0.0135735 | − | 0.0235101i | 0.000555528 | − | 0.000962203i | ||||
\(598\) | 11.6598 | + | 20.1954i | 0.476804 | + | 0.825849i | ||||
\(599\) | 16.9085 | + | 29.2864i | 0.690863 | + | 1.19661i | 0.971556 | + | 0.236812i | \(0.0761024\pi\) |
−0.280693 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(600\) | −1.96950 | + | 3.41127i | −0.0804045 | + | 0.139265i | ||||
\(601\) | 44.4161 | 1.81177 | 0.905885 | − | 0.423524i | \(-0.139207\pi\) | ||||
0.905885 | + | 0.423524i | \(0.139207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.55065 | −0.185317 | ||||||||
\(604\) | −6.12833 | + | 10.6146i | −0.249358 | + | 0.431901i | ||||
\(605\) | −7.38673 | − | 12.7942i | −0.300313 | − | 0.520158i | ||||
\(606\) | −1.10656 | − | 1.91662i | −0.0449511 | − | 0.0778576i | ||||
\(607\) | 2.87263 | − | 4.97553i | 0.116596 | − | 0.201951i | −0.801820 | − | 0.597565i | \(-0.796135\pi\) |
0.918417 | + | 0.395614i | \(0.129468\pi\) | |||||||
\(608\) | 4.10992 | 0.166679 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.8552 | −0.722935 | ||||||||
\(611\) | 2.75451 | − | 4.77096i | 0.111436 | − | 0.193012i | ||||
\(612\) | 2.13922 | + | 3.70524i | 0.0864728 | + | 0.149775i | ||||
\(613\) | −20.2371 | − | 35.0516i | −0.817367 | − | 1.41572i | −0.907616 | − | 0.419802i | \(-0.862100\pi\) |
0.0902489 | − | 0.995919i | \(-0.471234\pi\) | |||||||
\(614\) | −5.12229 | + | 8.87207i | −0.206719 | + | 0.358048i | ||||
\(615\) | 11.1739 | 0.450575 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.3706 | −1.42397 | −0.711984 | − | 0.702196i | \(-0.752203\pi\) | ||||
−0.711984 | + | 0.702196i | \(0.752203\pi\) | |||||||
\(618\) | −9.79925 | + | 16.9728i | −0.394184 | + | 0.682746i | ||||
\(619\) | 13.5641 | + | 23.4937i | 0.545188 | + | 0.944293i | 0.998595 | + | 0.0529895i | \(0.0168750\pi\) |
−0.453407 | + | 0.891303i | \(0.649792\pi\) | |||||||
\(620\) | −0.477697 | − | 0.827396i | −0.0191848 | − | 0.0332290i | ||||
\(621\) | −10.1235 | + | 17.5344i | −0.406242 | + | 0.703631i | ||||
\(622\) | 34.6679 | 1.39005 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.96077 | −0.318686 | ||||||||
\(625\) | −0.386199 | + | 0.668916i | −0.0154480 | + | 0.0267566i | ||||
\(626\) | 5.84966 | + | 10.1319i | 0.233799 | + | 0.404952i | ||||
\(627\) | −0.858756 | − | 1.48741i | −0.0342954 | − | 0.0594014i | ||||
\(628\) | −10.6027 | + | 18.3644i | −0.423093 | + | 0.732818i | ||||
\(629\) | 19.9584 | 0.795793 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.8418 | −1.74531 | −0.872656 | − | 0.488335i | \(-0.837605\pi\) | ||||
−0.872656 | + | 0.488335i | \(0.837605\pi\) | |||||||
\(632\) | −4.43147 | + | 7.67553i | −0.176274 | + | 0.305316i | ||||
\(633\) | 17.3252 | + | 30.0081i | 0.688615 | + | 1.19272i | ||||
\(634\) | −3.41454 | − | 5.91416i | −0.135609 | − | 0.234881i | ||||
\(635\) | 7.42812 | − | 12.8659i | 0.294776 | − | 0.510567i | ||||
\(636\) | 16.0707 | 0.637244 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.35690 | 0.0537200 | ||||||||
\(639\) | 7.63706 | − | 13.2278i | 0.302118 | − | 0.523283i | ||||
\(640\) | −0.678448 | − | 1.17511i | −0.0268180 | − | 0.0464502i | ||||
\(641\) | −12.7383 | − | 22.0633i | −0.503131 | − | 0.871448i | −0.999993 | − | 0.00361873i | \(-0.998848\pi\) |
0.496863 | − | 0.867829i | \(-0.334485\pi\) | |||||||
\(642\) | −10.8678 | + | 18.8235i | −0.428917 | + | 0.742906i | ||||
\(643\) | 4.20344 | 0.165767 | 0.0828837 | − | 0.996559i | \(-0.473587\pi\) | ||||
0.0828837 | + | 0.996559i | \(0.473587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.31096 | 0.327244 | ||||||||
\(646\) | −6.08426 | + | 10.5382i | −0.239382 | + | 0.414622i | ||||
\(647\) | −18.2141 | − | 31.5477i | −0.716070 | − | 1.24027i | −0.962546 | − | 0.271120i | \(-0.912606\pi\) |
0.246476 | − | 0.969149i | \(-0.420727\pi\) | |||||||
\(648\) | −1.28836 | − | 2.23151i | −0.0506117 | − | 0.0876621i | ||||
\(649\) | −1.51789 | + | 2.62905i | −0.0595822 | + | 0.103199i | ||||
\(650\) | −20.1661 | −0.790981 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.4862 | 0.723975 | ||||||||
\(653\) | 18.0269 | − | 31.2235i | 0.705448 | − | 1.22187i | −0.261082 | − | 0.965317i | \(-0.584079\pi\) |
0.966530 | − | 0.256554i | \(-0.0825873\pi\) | |||||||
\(654\) | 4.42208 | + | 7.65926i | 0.172917 | + | 0.299501i | ||||
\(655\) | 3.01208 | + | 5.21708i | 0.117692 | + | 0.203848i | ||||
\(656\) | 3.30194 | − | 5.71912i | 0.128919 | − | 0.223294i | ||||
\(657\) | 14.4819 | 0.564992 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.5881 | −1.15259 | −0.576294 | − | 0.817243i | \(-0.695502\pi\) | ||||
−0.576294 | + | 0.817243i | \(0.695502\pi\) | |||||||
\(660\) | −0.283520 | + | 0.491071i | −0.0110360 | + | 0.0191149i | ||||
\(661\) | −6.67025 | − | 11.5532i | −0.259443 | − | 0.449368i | 0.706650 | − | 0.707563i | \(-0.250206\pi\) |
−0.966093 | + | 0.258195i | \(0.916872\pi\) | |||||||
\(662\) | −7.63318 | − | 13.2211i | −0.296672 | − | 0.513851i | ||||
\(663\) | 11.7850 | − | 20.4122i | 0.457692 | − | 0.792746i | ||||
\(664\) | −17.4426 | −0.676906 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.74094 | 0.377454 | ||||||||
\(667\) | 7.39493 | − | 12.8084i | 0.286333 | − | 0.495943i | ||||
\(668\) | −10.1371 | − | 17.5579i | −0.392215 | − | 0.679336i | ||||
\(669\) | −7.91939 | − | 13.7168i | −0.306181 | − | 0.530321i | ||||
\(670\) | −2.13653 | + | 3.70058i | −0.0825414 | + | 0.142966i | ||||
\(671\) | 4.40986 | 0.170241 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.5332 | 0.868591 | 0.434295 | − | 0.900771i | \(-0.356997\pi\) | ||||
0.434295 | + | 0.900771i | \(0.356997\pi\) | |||||||
\(674\) | −0.00819673 | + | 0.0141971i | −0.000315726 | + | 0.000546854i | ||||
\(675\) | −8.75451 | − | 15.1633i | −0.336961 | − | 0.583634i | ||||
\(676\) | −13.8780 | − | 24.0374i | −0.533769 | − | 0.924516i | ||||
\(677\) | 12.7962 | − | 22.1637i | 0.491798 | − | 0.851818i | −0.508158 | − | 0.861264i | \(-0.669673\pi\) |
0.999955 | + | 0.00944553i | \(0.00300665\pi\) | |||||||
\(678\) | 16.1400 | 0.619855 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.01746 | 0.154062 | ||||||||
\(681\) | −4.05041 | + | 7.01551i | −0.155212 | + | 0.268835i | ||||
\(682\) | 0.117981 | + | 0.204350i | 0.00451774 | + | 0.00782496i | ||||
\(683\) | 1.08695 | + | 1.88265i | 0.0415910 | + | 0.0720377i | 0.886072 | − | 0.463549i | \(-0.153424\pi\) |
−0.844481 | + | 0.535586i | \(0.820091\pi\) | |||||||
\(684\) | −2.96950 | + | 5.14333i | −0.113542 | + | 0.196660i | ||||
\(685\) | 21.3884 | 0.817207 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.0978 | −0.461561 | ||||||||
\(688\) | 2.45593 | − | 4.25379i | 0.0936313 | − | 0.162174i | ||||
\(689\) | 41.1378 | + | 71.2527i | 1.56722 | + | 2.71451i | ||||
\(690\) | 3.09030 | + | 5.35256i | 0.117646 | + | 0.203768i | ||||
\(691\) | −10.2758 | + | 17.7981i | −0.390908 | + | 0.677072i | −0.992570 | − | 0.121679i | \(-0.961172\pi\) |
0.601662 | + | 0.798751i | \(0.294506\pi\) | |||||||
\(692\) | 6.35690 | 0.241653 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.5133 | −0.740716 | ||||||||
\(695\) | 12.1838 | − | 21.1030i | 0.462159 | − | 0.800483i | ||||
\(696\) | 2.52446 | + | 4.37249i | 0.0956894 | + | 0.165739i | ||||
\(697\) | 9.77628 | + | 16.9330i | 0.370303 | + | 0.641384i | ||||
\(698\) | −5.88889 | + | 10.1999i | −0.222898 | + | 0.386070i | ||||
\(699\) | 2.26875 | 0.0858120 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8170 | 0.786247 | 0.393124 | − | 0.919486i | \(-0.371394\pi\) | ||||
0.393124 | + | 0.919486i | \(0.371394\pi\) | |||||||
\(702\) | 17.6930 | − | 30.6451i | 0.667779 | − | 1.15663i | ||||
\(703\) | 13.8523 | + | 23.9930i | 0.522451 | + | 0.904912i | ||||
\(704\) | 0.167563 | + | 0.290227i | 0.00631526 | + | 0.0109384i | ||||
\(705\) | 0.730054 | − | 1.26449i | 0.0274954 | − | 0.0476235i | ||||
\(706\) | 34.1672 | 1.28590 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.2959 | −0.424526 | ||||||||
\(709\) | −4.33340 | + | 7.50566i | −0.162744 | + | 0.281881i | −0.935852 | − | 0.352394i | \(-0.885368\pi\) |
0.773108 | + | 0.634275i | \(0.218701\pi\) | |||||||
\(710\) | −7.17121 | − | 12.4209i | −0.269131 | − | 0.466148i | ||||
\(711\) | −6.40366 | − | 11.0915i | −0.240156 | − | 0.415962i | ||||
\(712\) | 0.312823 | − | 0.541825i | 0.0117235 | − | 0.0203058i | ||||
\(713\) | 2.57194 | 0.0963200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.90302 | −0.108567 | ||||||||
\(716\) | −1.73005 | + | 2.99654i | −0.0646551 | + | 0.111986i | ||||
\(717\) | −5.10992 | − | 8.85063i | −0.190833 | − | 0.330533i | ||||
\(718\) | 5.32789 | + | 9.22817i | 0.198835 | + | 0.344392i | ||||
\(719\) | −13.1773 | + | 22.8237i | −0.491429 | + | 0.851179i | −0.999951 | − | 0.00986933i | \(-0.996858\pi\) |
0.508523 | + | 0.861049i | \(0.330192\pi\) | |||||||
\(720\) | 1.96077 | 0.0730736 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.10859 | 0.0784735 | ||||||||
\(723\) | 3.26540 | − | 5.65583i | 0.121441 | − | 0.210343i | ||||
\(724\) | 6.85354 | + | 11.8707i | 0.254710 | + | 0.441171i | ||||
\(725\) | 6.39493 | + | 11.0763i | 0.237502 | + | 0.411365i | ||||
\(726\) | −6.78836 | + | 11.7578i | −0.251940 | + | 0.436373i | ||||
\(727\) | −16.8931 | −0.626529 | −0.313265 | − | 0.949666i | \(-0.601423\pi\) | ||||
−0.313265 | + | 0.949666i | \(0.601423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4590 | 0.905890 | ||||||||
\(730\) | 6.79925 | − | 11.7766i | 0.251652 | − | 0.435873i | ||||
\(731\) | 7.27144 | + | 12.5945i | 0.268944 | + | 0.465824i | ||||
\(732\) | 8.20440 | + | 14.2104i | 0.303243 | + | 0.525233i | ||||
\(733\) | 8.52930 | − | 14.7732i | 0.315037 | − | 0.545660i | −0.664408 | − | 0.747370i | \(-0.731316\pi\) |
0.979445 | + | 0.201710i | \(0.0646497\pi\) | |||||||
\(734\) | −33.0978 | −1.22166 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.65279 | 0.134644 | ||||||||
\(737\) | 0.527680 | − | 0.913968i | 0.0194373 | − | 0.0336664i | ||||
\(738\) | 4.77144 | + | 8.26437i | 0.175639 | + | 0.304216i | ||||
\(739\) | 18.1722 | + | 31.4751i | 0.668474 | + | 1.15783i | 0.978331 | + | 0.207048i | \(0.0663856\pi\) |
−0.309857 | + | 0.950783i | \(0.600281\pi\) | |||||||
\(740\) | 4.57338 | − | 7.92132i | 0.168121 | − | 0.291194i | ||||
\(741\) | 32.7181 | 1.20193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1890 | 1.25427 | 0.627136 | − | 0.778910i | \(-0.284227\pi\) | ||||
0.627136 | + | 0.778910i | \(0.284227\pi\) | |||||||
\(744\) | −0.439001 | + | 0.760372i | −0.0160946 | + | 0.0278766i | ||||
\(745\) | 9.56010 | + | 16.5586i | 0.350255 | + | 0.606659i | ||||
\(746\) | −9.28770 | − | 16.0868i | −0.340047 | − | 0.588978i | ||||
\(747\) | 12.6027 | − | 21.8285i | 0.461108 | − | 0.798662i | ||||
\(748\) | −0.992230 | −0.0362795 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.8049 | −0.504084 | ||||||||
\(751\) | 4.83273 | − | 8.37054i | 0.176349 | − | 0.305445i | −0.764278 | − | 0.644887i | \(-0.776905\pi\) |
0.940627 | + | 0.339441i | \(0.110238\pi\) | |||||||
\(752\) | −0.431468 | − | 0.747325i | −0.0157340 | − | 0.0272521i | ||||
\(753\) | 0.606564 | + | 1.05060i | 0.0221044 | + | 0.0382860i | ||||
\(754\) | −12.9242 | + | 22.3854i | −0.470673 | + | 0.815229i | ||||
\(755\) | −16.6310 | −0.605265 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.97584 | 0.108159 | 0.0540793 | − | 0.998537i | \(-0.482778\pi\) | ||||
0.0540793 | + | 0.998537i | \(0.482778\pi\) | |||||||
\(758\) | 4.42758 | − | 7.66880i | 0.160817 | − | 0.278543i | ||||
\(759\) | −0.763242 | − | 1.32197i | −0.0277039 | − | 0.0479846i | ||||
\(760\) | 2.78836 | + | 4.82959i | 0.101145 | + | 0.175188i | ||||
\(761\) | 11.0942 | − | 19.2157i | 0.402164 | − | 0.696568i | −0.591823 | − | 0.806068i | \(-0.701592\pi\) |
0.993987 | + | 0.109500i | \(0.0349248\pi\) | |||||||
\(762\) | −13.6528 | −0.494588 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.92931 | −0.250694 | ||||||||
\(765\) | −2.90270 | + | 5.02762i | −0.104947 | + | 0.181774i | ||||
\(766\) | 15.3485 | + | 26.5843i | 0.554562 | + | 0.960530i | ||||
\(767\) | −28.9153 | − | 50.0827i | −1.04407 | − | 1.80838i | ||||
\(768\) | −0.623490 | + | 1.07992i | −0.0224983 | + | 0.0389681i | ||||
\(769\) | 27.5803 | 0.994571 | 0.497286 | − | 0.867587i | \(-0.334330\pi\) | ||||
0.497286 | + | 0.867587i | \(0.334330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5985 | 0.705823 | ||||||||
\(772\) | 0.358092 | − | 0.620234i | 0.0128880 | − | 0.0223227i | ||||
\(773\) | −18.2664 | − | 31.6383i | −0.656995 | − | 1.13795i | −0.981390 | − | 0.192027i | \(-0.938494\pi\) |
0.324394 | − | 0.945922i | \(-0.394839\pi\) | |||||||
\(774\) | 3.54892 | + | 6.14691i | 0.127563 | + | 0.220946i | ||||
\(775\) | −1.11207 | + | 1.92617i | −0.0399468 | + | 0.0691899i | ||||
\(776\) | 3.24698 | 0.116560 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.26205 | 0.0452465 | ||||||||
\(779\) | −13.5707 | + | 23.5051i | −0.486220 | + | 0.842158i | ||||
\(780\) | −5.40097 | − | 9.35475i | −0.193386 | − | 0.334954i | ||||
\(781\) | 1.77114 | + | 3.06771i | 0.0633765 | + | 0.109771i | ||||
\(782\) | −5.40754 | + | 9.36614i | −0.193373 | + | 0.334932i | ||||
\(783\) | −22.4426 | −0.802035 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.7735 | −1.02697 | ||||||||
\(786\) | 2.76809 | − | 4.79447i | 0.0987344 | − | 0.171013i | ||||
\(787\) | −7.19351 | − | 12.4595i | −0.256421 | − | 0.444134i | 0.708859 | − | 0.705350i | \(-0.249210\pi\) |
−0.965281 | + | 0.261215i | \(0.915877\pi\) | |||||||
\(788\) | −1.03050 | − | 1.78488i | −0.0367100 | − | 0.0635836i | ||||
\(789\) | 11.5734 | − | 20.0457i | 0.412023 | − | 0.713645i | ||||
\(790\) | −12.0261 | −0.427869 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.484271 | −0.0172078 | ||||||||
\(793\) | −42.0033 | + | 72.7518i | −1.49158 | + | 2.58349i | ||||
\(794\) | 6.22790 | + | 10.7870i | 0.221020 | + | 0.382818i | ||||
\(795\) | 10.9031 | + | 18.8848i | 0.386694 | + | 0.669774i | ||||
\(796\) | 0.0108851 | − | 0.0188536i | 0.000385813 | − | 0.000668248i | ||||
\(797\) | 19.1564 | 0.678556 | 0.339278 | − | 0.940686i | \(-0.389817\pi\) | ||||
0.339278 | + | 0.940686i | \(0.389817\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.55496 | 0.0903879 | ||||||||
\(800\) | −1.57942 | + | 2.73563i | −0.0558408 | + | 0.0967191i | ||||
\(801\) | 0.452042 | + | 0.782960i | 0.0159721 | + | 0.0276645i | ||||
\(802\) | −5.91335 | − | 10.2422i | −0.208808 | − | 0.361665i | ||||
\(803\) | −1.67928 | + | 2.90859i | −0.0592604 | + | 0.102642i | ||||
\(804\) | 3.92692 | 0.138492 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.49502 | −0.158330 | ||||||||
\(807\) | 6.93967 | − | 12.0199i | 0.244288 | − | 0.423119i | ||||
\(808\) | −0.887395 | − | 1.53701i | −0.0312185 | − | 0.0540720i | ||||
\(809\) | 23.6386 | + | 40.9432i | 0.831087 | + | 1.43949i | 0.897177 | + | 0.441672i | \(0.145614\pi\) |
−0.0660893 | + | 0.997814i | \(0.521052\pi\) | |||||||
\(810\) | 1.74818 | − | 3.02793i | 0.0614246 | − | 0.106391i | ||||
\(811\) | −35.9691 | −1.26305 | −0.631524 | − | 0.775357i | \(-0.717570\pi\) | ||||
−0.631524 | + | 0.775357i | \(0.717570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.0954 | −0.880136 | ||||||||
\(814\) | −1.12953 | + | 1.95640i | −0.0395900 | + | 0.0685719i | ||||
\(815\) | 12.5419 | + | 21.7232i | 0.439324 | + | 0.760932i | ||||
\(816\) | −1.84601 | − | 3.19738i | −0.0646233 | − | 0.111931i | ||||
\(817\) | −10.0937 | + | 17.4827i | −0.353132 | + | 0.611643i | ||||
\(818\) | 18.4058 | 0.643544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.96077 | 0.312924 | ||||||||
\(821\) | 7.97770 | − | 13.8178i | 0.278424 | − | 0.482244i | −0.692570 | − | 0.721351i | \(-0.743521\pi\) |
0.970993 | + | 0.239107i | \(0.0768548\pi\) | |||||||
\(822\) | −9.82789 | − | 17.0224i | −0.342787 | − | 0.593724i | ||||
\(823\) | −16.2905 | − | 28.2160i | −0.567852 | − | 0.983548i | −0.996778 | − | 0.0802087i | \(-0.974441\pi\) |
0.428926 | − | 0.903340i | \(-0.358892\pi\) | |||||||
\(824\) | −7.85839 | + | 13.6111i | −0.273760 | + | 0.474166i | ||||
\(825\) | 1.32006 | 0.0459586 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.6300 | 0.647827 | 0.323914 | − | 0.946087i | \(-0.395001\pi\) | ||||
0.323914 | + | 0.946087i | \(0.395001\pi\) | |||||||
\(828\) | −2.63922 | + | 4.57126i | −0.0917192 | + | 0.158862i | ||||
\(829\) | −8.48307 | − | 14.6931i | −0.294629 | − | 0.510313i | 0.680269 | − | 0.732962i | \(-0.261863\pi\) |
−0.974899 | + | 0.222649i | \(0.928530\pi\) | |||||||
\(830\) | −11.8339 | − | 20.4970i | −0.410762 | − | 0.711460i | ||||
\(831\) | 16.1163 | − | 27.9142i | 0.559067 | − | 0.968332i | ||||
\(832\) | −6.38404 | −0.221327 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −22.3937 | −0.775432 | ||||||||
\(835\) | 13.7549 | − | 23.8243i | 0.476009 | − | 0.824472i | ||||
\(836\) | −0.688669 | − | 1.19281i | −0.0238181 | − | 0.0412542i | ||||
\(837\) | −1.95138 | − | 3.37989i | −0.0674495 | − | 0.116826i | ||||
\(838\) | 2.56033 | − | 4.43463i | 0.0884453 | − | 0.153192i | ||||
\(839\) | 9.12365 | 0.314984 | 0.157492 | − | 0.987520i | \(-0.449659\pi\) | ||||
0.157492 | + | 0.987520i | \(0.449659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6063 | −0.434699 | ||||||||
\(842\) | −8.20171 | + | 14.2058i | −0.282650 | + | 0.489563i | ||||
\(843\) | 8.15130 | + | 14.1185i | 0.280746 | + | 0.486266i | ||||
\(844\) | 13.8937 | + | 24.0646i | 0.478242 | + | 0.828339i | ||||
\(845\) | 18.8310 | − | 32.6163i | 0.647806 | − | 1.12203i | ||||
\(846\) | 1.24698 | 0.0428720 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.8877 | 0.442565 | ||||||||
\(849\) | 3.60202 | − | 6.23887i | 0.123621 | − | 0.214118i | ||||
\(850\) | −4.67629 | − | 8.09958i | −0.160395 | − | 0.277813i | ||||
\(851\) | 12.3116 | + | 21.3244i | 0.422037 | + | 0.730990i | ||||
\(852\) | −6.59030 | + | 11.4147i | −0.225780 | + | 0.391062i | ||||
\(853\) | 10.2620 | 0.351366 | 0.175683 | − | 0.984447i | \(-0.443787\pi\) | ||||
0.175683 | + | 0.984447i | \(0.443787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.05861 | −0.275599 | ||||||||
\(856\) | −8.71528 | + | 15.0953i | −0.297882 | + | 0.515947i | ||||
\(857\) | 5.64161 | + | 9.77156i | 0.192714 | + | 0.333790i | 0.946149 | − | 0.323732i | \(-0.104938\pi\) |
−0.753435 | + | 0.657523i | \(0.771604\pi\) | |||||||
\(858\) | 1.33393 | + | 2.31043i | 0.0455396 | + | 0.0788769i | ||||
\(859\) | 10.0121 | − | 17.3414i | 0.341608 | − | 0.591682i | −0.643124 | − | 0.765762i | \(-0.722362\pi\) |
0.984731 | + | 0.174080i | \(0.0556952\pi\) | |||||||
\(860\) | 6.66487 | 0.227270 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.330814 | 0.0112676 | ||||||||
\(863\) | −20.7298 | + | 35.9051i | −0.705651 | + | 1.22222i | 0.260805 | + | 0.965392i | \(0.416012\pi\) |
−0.966456 | + | 0.256832i | \(0.917321\pi\) | |||||||
\(864\) | −2.77144 | − | 4.80027i | −0.0942862 | − | 0.163309i | ||||
\(865\) | 4.31282 | + | 7.47003i | 0.146640 | + | 0.253989i | ||||
\(866\) | 1.22521 | − | 2.12212i | 0.0416343 | − | 0.0721127i | ||||
\(867\) | −10.2674 | −0.348700 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.97020 | 0.100757 | ||||||||
\(870\) | −3.42543 | + | 5.93301i | −0.116133 | + | 0.201148i | ||||
\(871\) | 10.0521 | + | 17.4108i | 0.340604 | + | 0.589943i | ||||
\(872\) | 3.54623 | + | 6.14225i | 0.120090 | + | 0.208003i | ||||
\(873\) | −2.34601 | + | 4.06341i | −0.0794004 | + | 0.137526i | ||||
\(874\) | −15.0127 | −0.507811 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4969 | −0.422233 | ||||||||
\(877\) | −12.1017 | + | 20.9608i | −0.408646 | + | 0.707796i | −0.994738 | − | 0.102449i | \(-0.967332\pi\) |
0.586092 | + | 0.810244i | \(0.300666\pi\) | |||||||
\(878\) | −1.34601 | − | 2.33136i | −0.0454257 | − | 0.0786796i | ||||
\(879\) | 12.7940 | + | 22.1599i | 0.431532 | + | 0.747436i | ||||
\(880\) | −0.227365 | + | 0.393808i | −0.00766448 | + | 0.0132753i | ||||
\(881\) | −37.3793 | −1.25934 | −0.629670 | − | 0.776863i | \(-0.716810\pi\) | ||||
−0.629670 | + | 0.776863i | \(0.716810\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.550172 | 0.0185148 | 0.00925739 | − | 0.999957i | \(-0.497053\pi\) | ||||
0.00925739 | + | 0.999957i | \(0.497053\pi\) | |||||||
\(884\) | 9.45085 | − | 16.3693i | 0.317866 | − | 0.550561i | ||||
\(885\) | −7.66368 | − | 13.2739i | −0.257612 | − | 0.446197i | ||||
\(886\) | 18.2763 | + | 31.6555i | 0.614004 | + | 1.06349i | ||||
\(887\) | 12.6761 | − | 21.9556i | 0.425620 | − | 0.737196i | −0.570858 | − | 0.821049i | \(-0.693389\pi\) |
0.996478 | + | 0.0838530i | \(0.0267226\pi\) | |||||||
\(888\) | −8.40581 | −0.282081 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.848936 | 0.0284564 | ||||||||
\(891\) | −0.431764 | + | 0.747837i | −0.0144646 | + | 0.0250535i | ||||
\(892\) | −6.35086 | − | 11.0000i | −0.212642 | − | 0.368307i | ||||
\(893\) | 1.77330 | + | 3.07144i | 0.0593412 | + | 0.102782i | ||||
\(894\) | 8.78568 | − | 15.2172i | 0.293837 | − | 0.508941i | ||||
\(895\) | −4.69501 | −0.156937 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.0790 | 0.970921 | ||||||||
\(898\) | −1.74214 | + | 3.01747i | −0.0581358 | + | 0.100694i | ||||
\(899\) | 1.42543 | + | 2.46891i | 0.0475407 | + | 0.0823429i | ||||
\(900\) | −2.28232 | − | 3.95310i | −0.0760774 | − | 0.131770i | ||||
\(901\) | −19.0788 | + | 33.0454i | −0.635605 | + | 1.10090i | ||||
\(902\) | −2.21313 | −0.0736891 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.9433 | 0.430488 | ||||||||
\(905\) | −9.29954 | + | 16.1073i | −0.309127 | + | 0.535424i | ||||
\(906\) | 7.64191 | + | 13.2362i | 0.253885 | + | 0.439742i | ||||
\(907\) | −26.9756 | − | 46.7231i | −0.895710 | − | 1.55142i | −0.832923 | − | 0.553388i | \(-0.813335\pi\) |
−0.0627868 | − | 0.998027i | \(-0.519999\pi\) | |||||||
\(908\) | −3.24818 | + | 5.62601i | −0.107795 | + | 0.186706i | ||||
\(909\) | 2.56465 | 0.0850640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2433 | 0.438769 | 0.219384 | − | 0.975639i | \(-0.429595\pi\) | ||||
0.219384 | + | 0.975639i | \(0.429595\pi\) | |||||||
\(912\) | 2.56249 | − | 4.43836i | 0.0848526 | − | 0.146969i | ||||
\(913\) | 2.92274 | + | 5.06233i | 0.0967285 | + | 0.167539i | ||||
\(914\) | −11.5591 | − | 20.0210i | −0.382342 | − | 0.662236i | ||||
\(915\) | −11.1325 | + | 19.2821i | −0.368030 | + | 0.637446i | ||||
\(916\) | −9.70171 | −0.320554 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 16.4112 | 0.541650 | ||||||||
\(919\) | 12.1195 | − | 20.9915i | 0.399785 | − | 0.692447i | −0.593915 | − | 0.804528i | \(-0.702418\pi\) |
0.993699 | + | 0.112081i | \(0.0357516\pi\) | |||||||
\(920\) | 2.47823 | + | 4.29242i | 0.0817048 | + | 0.141517i | ||||
\(921\) | 6.38740 | + | 11.0633i | 0.210472 | + | 0.364548i | ||||
\(922\) | −4.84750 | + | 8.39612i | −0.159644 | + | 0.276512i | ||||
\(923\) | −67.4795 | −2.22111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.2935 | −0.700126 | ||||||||
\(926\) | −2.92327 | + | 5.06325i | −0.0960647 | + | 0.166389i | ||||
\(927\) | −11.3557 | − | 19.6686i | −0.372970 | − | 0.646003i | ||||
\(928\) | 2.02446 | + | 3.50647i | 0.0664561 | + | 0.115105i | ||||
\(929\) | −6.21475 | + | 10.7643i | −0.203899 | + | 0.353164i | −0.949782 | − | 0.312914i | \(-0.898695\pi\) |
0.745882 | + | 0.666078i | \(0.232028\pi\) | |||||||
\(930\) | −1.19136 | −0.0390662 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.81940 | 0.0595963 | ||||||||
\(933\) | 21.6151 | − | 37.4384i | 0.707645 | − | 1.22568i | ||||
\(934\) | 12.8916 | + | 22.3289i | 0.421825 | + | 0.730623i | ||||
\(935\) | −0.673177 | − | 1.16598i | −0.0220152 | − | 0.0381315i | ||||
\(936\) | 4.61260 | − | 7.98927i | 0.150768 | − | 0.261137i | ||||
\(937\) | −25.0672 | −0.818911 | −0.409455 | − | 0.912330i | \(-0.634281\pi\) | ||||
−0.409455 | + | 0.912330i | \(0.634281\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5888 | 0.476088 | ||||||||
\(940\) | 0.585458 | − | 1.01404i | 0.0190955 | − | 0.0330744i | ||||
\(941\) | −20.9480 | − | 36.2830i | −0.682886 | − | 1.18279i | −0.974096 | − | 0.226134i | \(-0.927391\pi\) |
0.291210 | − | 0.956659i | \(-0.405942\pi\) | |||||||
\(942\) | 13.2213 | + | 22.9000i | 0.430774 | + | 0.746123i | ||||
\(943\) | −12.0613 | + | 20.8908i | −0.392770 | + | 0.680297i | ||||
\(944\) | −9.05861 | −0.294833 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.64609 | −0.0535189 | ||||||||
\(947\) | −6.98941 | + | 12.1060i | −0.227125 | + | 0.393393i | −0.956955 | − | 0.290236i | \(-0.906266\pi\) |
0.729830 | + | 0.683629i | \(0.239599\pi\) | |||||||
\(948\) | 5.52595 | + | 9.57123i | 0.179475 | + | 0.310859i | ||||
\(949\) | −31.9897 | − | 55.4078i | −1.03843 | − | 1.79861i | ||||
\(950\) | 6.49127 | − | 11.2432i | 0.210605 | − | 0.364778i | ||||
\(951\) | −8.51573 | −0.276141 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.9038 | −0.482782 | −0.241391 | − | 0.970428i | \(-0.577604\pi\) | ||||
−0.241391 | + | 0.970428i | \(0.577604\pi\) | |||||||
\(954\) | −9.31163 | + | 16.1282i | −0.301475 | + | 0.522170i | ||||
\(955\) | −4.70118 | − | 8.14268i | −0.152127 | − | 0.263491i | ||||
\(956\) | −4.09783 | − | 7.09766i | −0.132533 | − | 0.229555i | ||||
\(957\) | 0.846011 | − | 1.46533i | 0.0273476 | − | 0.0473675i | ||||
\(958\) | 20.8799 | 0.674600 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.69202 | −0.0546098 | ||||||||
\(961\) | 15.2521 | − | 26.4174i | 0.492004 | − | 0.852176i | ||||
\(962\) | −21.5172 | − | 37.2689i | −0.693743 | − | 1.20160i | ||||
\(963\) | −12.5939 | − | 21.8134i | −0.405834 | − | 0.702926i | ||||
\(964\) | 2.61865 | − | 4.53563i | 0.0843409 | − | 0.146083i | ||||
\(965\) | 0.971788 | 0.0312830 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.6469 | 1.37143 | 0.685717 | − | 0.727869i | \(-0.259489\pi\) | ||||
0.685717 | + | 0.727869i | \(0.259489\pi\) | |||||||
\(968\) | −5.44385 | + | 9.42902i | −0.174972 | + | 0.303060i | ||||
\(969\) | 7.58695 | + | 13.1410i | 0.243728 | + | 0.422149i | ||||
\(970\) | 2.20291 | + | 3.81555i | 0.0707311 | + | 0.122510i | ||||
\(971\) | −1.51895 | + | 2.63090i | −0.0487454 | + | 0.0844296i | −0.889369 | − | 0.457191i | \(-0.848856\pi\) |
0.840623 | + | 0.541620i | \(0.182189\pi\) | |||||||
\(972\) | 13.4155 | 0.430302 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.629958 | 0.0201851 | ||||||||
\(975\) | −12.5734 | + | 21.7777i | −0.402670 | + | 0.697445i | ||||
\(976\) | 6.57942 | + | 11.3959i | 0.210602 | + | 0.364773i | ||||
\(977\) | −2.80045 | − | 4.85051i | −0.0895942 | − | 0.155182i | 0.817745 | − | 0.575580i | \(-0.195224\pi\) |
−0.907340 | + | 0.420398i | \(0.861890\pi\) | |||||||
\(978\) | 11.5260 | − | 19.9635i | 0.368559 | − | 0.638363i | ||||
\(979\) | −0.209670 | −0.00670108 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.2489 | −0.327222 | ||||||||
\(982\) | −3.59634 | + | 6.22905i | −0.114764 | + | 0.198777i | ||||
\(983\) | −4.06800 | − | 7.04598i | −0.129749 | − | 0.224732i | 0.793830 | − | 0.608139i | \(-0.208084\pi\) |
−0.923579 | + | 0.383407i | \(0.874750\pi\) | |||||||
\(984\) | −4.11745 | − | 7.13163i | −0.131259 | − | 0.227348i | ||||
\(985\) | 1.39828 | − | 2.42189i | 0.0445529 | − | 0.0771679i | ||||
\(986\) | −11.9879 | −0.381773 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.2379 | 0.834738 | ||||||||
\(989\) | −8.97099 | + | 15.5382i | −0.285261 | + | 0.494086i | ||||
\(990\) | −0.328552 | − | 0.569069i | −0.0104421 | − | 0.0180862i | ||||
\(991\) | 8.08187 | + | 13.9982i | 0.256729 | + | 0.444668i | 0.965364 | − | 0.260908i | \(-0.0840219\pi\) |
−0.708635 | + | 0.705576i | \(0.750689\pi\) | |||||||
\(992\) | −0.352052 | + | 0.609771i | −0.0111776 | + | 0.0193603i | ||||
\(993\) | −19.0368 | −0.604116 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0295400 | 0.000936480 | ||||||||
\(996\) | −10.8753 | + | 18.8366i | −0.344598 | + | 0.596860i | ||||
\(997\) | −15.8307 | − | 27.4196i | −0.501364 | − | 0.868387i | −0.999999 | − | 0.00157522i | \(-0.999499\pi\) |
0.498635 | − | 0.866812i | \(-0.333835\pi\) | |||||||
\(998\) | 10.6283 | + | 18.4088i | 0.336434 | + | 0.582721i | ||||
\(999\) | 18.6821 | − | 32.3583i | 0.591075 | − | 1.02377i |
(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 | 686.2.c.d.667.1 | 6 | ||
7.2 | even | 3 | 686.2.a.a.1.3 | ✓ | 3 | ||
7.3 | odd | 6 | 686.2.c.c.361.3 | 6 | |||
7.4 | even | 3 | inner | 686.2.c.d.361.1 | 6 | ||
7.5 | odd | 6 | 686.2.a.b.1.1 | yes | 3 | ||
7.6 | odd | 2 | 686.2.c.c.667.3 | 6 | |||
21.2 | odd | 6 | 6174.2.a.k.1.2 | 3 | |||
21.5 | even | 6 | 6174.2.a.l.1.2 | 3 | |||
28.19 | even | 6 | 5488.2.a.b.1.3 | 3 | |||
28.23 | odd | 6 | 5488.2.a.e.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
686.2.a.a.1.3 | ✓ | 3 | 7.2 | even | 3 | ||
686.2.a.b.1.1 | yes | 3 | 7.5 | odd | 6 | ||
686.2.c.c.361.3 | 6 | 7.3 | odd | 6 | |||
686.2.c.c.667.3 | 6 | 7.6 | odd | 2 | |||
686.2.c.d.361.1 | 6 | 7.4 | even | 3 | inner | ||
686.2.c.d.667.1 | 6 | 1.1 | even | 1 | trivial | ||
5488.2.a.b.1.3 | 3 | 28.19 | even | 6 | |||
5488.2.a.e.1.1 | 3 | 28.23 | odd | 6 | |||
6174.2.a.k.1.2 | 3 | 21.2 | odd | 6 | |||
6174.2.a.l.1.2 | 3 | 21.5 | even | 6 |