Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.10 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.f.47.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.01467 | + | 1.40373i | −0.585819 | + | 0.810442i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.22721 | − | 0.198845i | −0.996038 | − | 0.0889264i | ||||
\(6\) | −1.71006 | + | 0.275105i | −0.698130 | + | 0.112311i | ||||
\(7\) | 0.787190 | − | 0.787190i | 0.297530 | − | 0.297530i | −0.542516 | − | 0.840046i | \(-0.682528\pi\) |
0.840046 | + | 0.542516i | \(0.182528\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −0.940895 | − | 2.84863i | −0.313632 | − | 0.949545i | ||||
\(10\) | −1.43427 | − | 1.71548i | −0.453556 | − | 0.542482i | ||||
\(11\) | − | 0.307245i | − | 0.0926378i | −0.998927 | − | 0.0463189i | \(-0.985251\pi\) | ||
0.998927 | − | 0.0463189i | \(-0.0147490\pi\) | |||||||
\(12\) | −1.40373 | − | 1.01467i | −0.405221 | − | 0.292910i | ||||
\(13\) | −4.92204 | − | 4.92204i | −1.36513 | − | 1.36513i | −0.867243 | − | 0.497885i | \(-0.834110\pi\) |
−0.497885 | − | 0.867243i | \(-0.665890\pi\) | |||||||
\(14\) | 1.11326 | 0.297530 | ||||||||
\(15\) | 2.53900 | − | 2.92463i | 0.655568 | − | 0.755136i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.790416 | − | 0.790416i | −0.191704 | − | 0.191704i | 0.604728 | − | 0.796432i | \(-0.293282\pi\) |
−0.796432 | + | 0.604728i | \(0.793282\pi\) | |||||||
\(18\) | 1.34897 | − | 2.67960i | 0.317956 | − | 0.631588i | ||||
\(19\) | 0.691928i | 0.158739i | 0.996845 | + | 0.0793696i | \(0.0252907\pi\) | ||||
−0.996845 | + | 0.0793696i | \(0.974709\pi\) | |||||||
\(20\) | 0.198845 | − | 2.22721i | 0.0444632 | − | 0.498019i | ||||
\(21\) | 0.306263 | + | 1.90374i | 0.0668320 | + | 0.415430i | ||||
\(22\) | 0.217255 | − | 0.217255i | 0.0463189 | − | 0.0463189i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | −0.275105 | − | 1.71006i | −0.0561557 | − | 0.349065i | ||||
\(25\) | 4.92092 | + | 0.885741i | 0.984184 | + | 0.177148i | ||||
\(26\) | − | 6.96081i | − | 1.36513i | ||||||
\(27\) | 4.95340 | + | 1.56966i | 0.953282 | + | 0.302081i | ||||
\(28\) | 0.787190 | + | 0.787190i | 0.148765 | + | 0.148765i | ||||
\(29\) | −6.67517 | −1.23955 | −0.619774 | − | 0.784780i | \(-0.712776\pi\) | ||||
−0.619774 | + | 0.784780i | \(0.712776\pi\) | |||||||
\(30\) | 3.86337 | − | 0.272679i | 0.705352 | − | 0.0497841i | ||||
\(31\) | 4.52557 | 0.812817 | 0.406408 | − | 0.913692i | \(-0.366781\pi\) | ||||
0.406408 | + | 0.913692i | \(0.366781\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0.431287 | + | 0.311752i | 0.0750775 | + | 0.0542690i | ||||
\(34\) | − | 1.11782i | − | 0.191704i | ||||||
\(35\) | −1.90977 | + | 1.59671i | −0.322810 | + | 0.269893i | ||||
\(36\) | 2.84863 | − | 0.940895i | 0.474772 | − | 0.156816i | ||||
\(37\) | 1.77676 | − | 1.77676i | 0.292098 | − | 0.292098i | −0.545811 | − | 0.837909i | \(-0.683778\pi\) |
0.837909 | + | 0.545811i | \(0.183778\pi\) | |||||||
\(38\) | −0.489267 | + | 0.489267i | −0.0793696 | + | 0.0793696i | ||||
\(39\) | 11.9034 | − | 1.91496i | 1.90607 | − | 0.306639i | ||||
\(40\) | 1.71548 | − | 1.43427i | 0.271241 | − | 0.226778i | ||||
\(41\) | − | 0.596103i | − | 0.0930956i | −0.998916 | − | 0.0465478i | \(-0.985178\pi\) | ||
0.998916 | − | 0.0465478i | \(-0.0148220\pi\) | |||||||
\(42\) | −1.12959 | + | 1.56271i | −0.174299 | + | 0.241131i | ||||
\(43\) | −6.70489 | − | 6.70489i | −1.02249 | − | 1.02249i | −0.999741 | − | 0.0227444i | \(-0.992760\pi\) |
−0.0227444 | − | 0.999741i | \(-0.507240\pi\) | |||||||
\(44\) | 0.307245 | 0.0463189 | ||||||||
\(45\) | 1.52913 | + | 6.53160i | 0.227950 | + | 0.973673i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −6.88967 | − | 6.88967i | −1.00496 | − | 1.00496i | −0.999988 | − | 0.00497448i | \(-0.998417\pi\) |
−0.00497448 | − | 0.999988i | \(-0.501583\pi\) | |||||||
\(48\) | 1.01467 | − | 1.40373i | 0.146455 | − | 0.202610i | ||||
\(49\) | 5.76066i | 0.822952i | ||||||||
\(50\) | 2.85330 | + | 4.10593i | 0.403518 | + | 0.580666i | ||||
\(51\) | 1.91154 | − | 0.307518i | 0.267669 | − | 0.0430611i | ||||
\(52\) | 4.92204 | − | 4.92204i | 0.682564 | − | 0.682564i | ||||
\(53\) | 5.94467 | − | 5.94467i | 0.816563 | − | 0.816563i | −0.169045 | − | 0.985608i | \(-0.554068\pi\) |
0.985608 | + | 0.169045i | \(0.0540683\pi\) | |||||||
\(54\) | 2.39267 | + | 4.61250i | 0.325601 | + | 0.627682i | ||||
\(55\) | −0.0610942 | + | 0.684298i | −0.00823794 | + | 0.0922707i | ||||
\(56\) | 1.11326i | 0.148765i | ||||||||
\(57\) | −0.971277 | − | 0.702077i | −0.128649 | − | 0.0929924i | ||||
\(58\) | −4.72006 | − | 4.72006i | −0.619774 | − | 0.619774i | ||||
\(59\) | −6.38319 | −0.831021 | −0.415510 | − | 0.909588i | \(-0.636397\pi\) | ||||
−0.415510 | + | 0.909588i | \(0.636397\pi\) | |||||||
\(60\) | 2.92463 | + | 2.53900i | 0.377568 | + | 0.327784i | ||||
\(61\) | −9.95861 | −1.27507 | −0.637535 | − | 0.770422i | \(-0.720046\pi\) | ||||
−0.637535 | + | 0.770422i | \(0.720046\pi\) | |||||||
\(62\) | 3.20006 | + | 3.20006i | 0.406408 | + | 0.406408i | ||||
\(63\) | −2.98308 | − | 1.50175i | −0.375833 | − | 0.189203i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 9.98368 | + | 11.9411i | 1.23832 | + | 1.48112i | ||||
\(66\) | 0.0845247 | + | 0.525408i | 0.0104043 | + | 0.0646732i | ||||
\(67\) | 2.19342 | − | 2.19342i | 0.267969 | − | 0.267969i | −0.560312 | − | 0.828281i | \(-0.689319\pi\) |
0.828281 | + | 0.560312i | \(0.189319\pi\) | |||||||
\(68\) | 0.790416 | − | 0.790416i | 0.0958521 | − | 0.0958521i | ||||
\(69\) | 0.275105 | + | 1.71006i | 0.0331188 | + | 0.205867i | ||||
\(70\) | −2.47945 | − | 0.221366i | −0.296351 | − | 0.0264583i | ||||
\(71\) | − | 4.55564i | − | 0.540655i | −0.962768 | − | 0.270327i | \(-0.912868\pi\) | ||
0.962768 | − | 0.270327i | \(-0.0871320\pi\) | |||||||
\(72\) | 2.67960 | + | 1.34897i | 0.315794 | + | 0.158978i | ||||
\(73\) | −4.90914 | − | 4.90914i | −0.574571 | − | 0.574571i | 0.358831 | − | 0.933403i | \(-0.383175\pi\) |
−0.933403 | + | 0.358831i | \(0.883175\pi\) | |||||||
\(74\) | 2.51272 | 0.292098 | ||||||||
\(75\) | −6.23644 | + | 6.00889i | −0.720122 | + | 0.693847i | ||||
\(76\) | −0.691928 | −0.0793696 | ||||||||
\(77\) | −0.241860 | − | 0.241860i | −0.0275625 | − | 0.0275625i | ||||
\(78\) | 9.77108 | + | 7.06292i | 1.10636 | + | 0.799718i | ||||
\(79\) | 15.7352i | 1.77035i | 0.465255 | + | 0.885177i | \(0.345963\pi\) | ||||
−0.465255 | + | 0.885177i | \(0.654037\pi\) | |||||||
\(80\) | 2.22721 | + | 0.198845i | 0.249010 | + | 0.0222316i | ||||
\(81\) | −7.22943 | + | 5.36053i | −0.803270 | + | 0.595615i | ||||
\(82\) | 0.421508 | − | 0.421508i | 0.0465478 | − | 0.0465478i | ||||
\(83\) | −6.65861 | + | 6.65861i | −0.730878 | + | 0.730878i | −0.970794 | − | 0.239916i | \(-0.922880\pi\) |
0.239916 | + | 0.970794i | \(0.422880\pi\) | |||||||
\(84\) | −1.90374 | + | 0.306263i | −0.207715 | + | 0.0334160i | ||||
\(85\) | 1.60325 | + | 1.91759i | 0.173897 | + | 0.207992i | ||||
\(86\) | − | 9.48214i | − | 1.02249i | ||||||
\(87\) | 6.77309 | − | 9.37012i | 0.726151 | − | 1.00458i | ||||
\(88\) | 0.217255 | + | 0.217255i | 0.0231594 | + | 0.0231594i | ||||
\(89\) | 11.5425 | 1.22351 | 0.611753 | − | 0.791049i | \(-0.290465\pi\) | ||||
0.611753 | + | 0.791049i | \(0.290465\pi\) | |||||||
\(90\) | −3.53728 | + | 5.69980i | −0.372862 | + | 0.600811i | ||||
\(91\) | −7.74916 | −0.812333 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −4.59195 | + | 6.35266i | −0.476163 | + | 0.658740i | ||||
\(94\) | − | 9.74347i | − | 1.00496i | ||||||
\(95\) | 0.137587 | − | 1.54107i | 0.0141161 | − | 0.158110i | ||||
\(96\) | 1.71006 | − | 0.275105i | 0.174533 | − | 0.0280778i | ||||
\(97\) | −12.8277 | + | 12.8277i | −1.30246 | + | 1.30246i | −0.375726 | + | 0.926731i | \(0.622606\pi\) |
−0.926731 | + | 0.375726i | \(0.877394\pi\) | |||||||
\(98\) | −4.07340 | + | 4.07340i | −0.411476 | + | 0.411476i | ||||
\(99\) | −0.875228 | + | 0.289085i | −0.0879637 | + | 0.0290541i | ||||
\(100\) | −0.885741 | + | 4.92092i | −0.0885741 | + | 0.492092i | ||||
\(101\) | 0.435698i | 0.0433536i | 0.999765 | + | 0.0216768i | \(0.00690048\pi\) | ||||
−0.999765 | + | 0.0216768i | \(0.993100\pi\) | |||||||
\(102\) | 1.56911 | + | 1.13421i | 0.155365 | + | 0.112304i | ||||
\(103\) | −2.47087 | − | 2.47087i | −0.243463 | − | 0.243463i | 0.574818 | − | 0.818281i | \(-0.305073\pi\) |
−0.818281 | + | 0.574818i | \(0.805073\pi\) | |||||||
\(104\) | 6.96081 | 0.682564 | ||||||||
\(105\) | −0.303561 | − | 4.30092i | −0.0296245 | − | 0.419727i | ||||
\(106\) | 8.40703 | 0.816563 | ||||||||
\(107\) | −9.00580 | − | 9.00580i | −0.870623 | − | 0.870623i | 0.121917 | − | 0.992540i | \(-0.461096\pi\) |
−0.992540 | + | 0.121917i | \(0.961096\pi\) | |||||||
\(108\) | −1.56966 | + | 4.95340i | −0.151041 | + | 0.476641i | ||||
\(109\) | − | 4.71540i | − | 0.451654i | −0.974167 | − | 0.225827i | \(-0.927492\pi\) | ||
0.974167 | − | 0.225827i | \(-0.0725084\pi\) | |||||||
\(110\) | −0.527072 | + | 0.440672i | −0.0502543 | + | 0.0420164i | ||||
\(111\) | 0.691264 | + | 4.29692i | 0.0656118 | + | 0.407845i | ||||
\(112\) | −0.787190 | + | 0.787190i | −0.0743825 | + | 0.0743825i | ||||
\(113\) | −9.74177 | + | 9.74177i | −0.916428 | + | 0.916428i | −0.996768 | − | 0.0803391i | \(-0.974400\pi\) |
0.0803391 | + | 0.996768i | \(0.474400\pi\) | |||||||
\(114\) | −0.190353 | − | 1.18324i | −0.0178282 | − | 0.110821i | ||||
\(115\) | −1.71548 | + | 1.43427i | −0.159969 | + | 0.133746i | ||||
\(116\) | − | 6.67517i | − | 0.619774i | ||||||
\(117\) | −9.38996 | + | 18.6522i | −0.868102 | + | 1.72440i | ||||
\(118\) | −4.51360 | − | 4.51360i | −0.415510 | − | 0.415510i | ||||
\(119\) | −1.24442 | −0.114075 | ||||||||
\(120\) | 0.272679 | + | 3.86337i | 0.0248921 | + | 0.352676i | ||||
\(121\) | 10.9056 | 0.991418 | ||||||||
\(122\) | −7.04180 | − | 7.04180i | −0.637535 | − | 0.637535i | ||||
\(123\) | 0.836765 | + | 0.604847i | 0.0754486 | + | 0.0545372i | ||||
\(124\) | 4.52557i | 0.406408i | ||||||||
\(125\) | −10.7838 | − | 2.95123i | −0.964532 | − | 0.263966i | ||||
\(126\) | −1.04746 | − | 3.17126i | −0.0933149 | − | 0.282518i | ||||
\(127\) | 13.7618 | − | 13.7618i | 1.22116 | − | 1.22116i | 0.253945 | − | 0.967219i | \(-0.418272\pi\) |
0.967219 | − | 0.253945i | \(-0.0817282\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 16.2151 | − | 2.60859i | 1.42766 | − | 0.229673i | ||||
\(130\) | −1.38413 | + | 15.5032i | −0.121396 | + | 1.35972i | ||||
\(131\) | − | 9.08484i | − | 0.793746i | −0.917874 | − | 0.396873i | \(-0.870095\pi\) | ||
0.917874 | − | 0.396873i | \(-0.129905\pi\) | |||||||
\(132\) | −0.311752 | + | 0.431287i | −0.0271345 | + | 0.0375388i | ||||
\(133\) | 0.544679 | + | 0.544679i | 0.0472297 | + | 0.0472297i | ||||
\(134\) | 3.10197 | 0.267969 | ||||||||
\(135\) | −10.7201 | − | 4.48092i | −0.922643 | − | 0.385656i | ||||
\(136\) | 1.11782 | 0.0958521 | ||||||||
\(137\) | −6.12207 | − | 6.12207i | −0.523044 | − | 0.523044i | 0.395445 | − | 0.918489i | \(-0.370590\pi\) |
−0.918489 | + | 0.395445i | \(0.870590\pi\) | |||||||
\(138\) | −1.01467 | + | 1.40373i | −0.0863743 | + | 0.119493i | ||||
\(139\) | 1.70991i | 0.145033i | 0.997367 | + | 0.0725164i | \(0.0231030\pi\) | ||||
−0.997367 | + | 0.0725164i | \(0.976897\pi\) | |||||||
\(140\) | −1.59671 | − | 1.90977i | −0.134946 | − | 0.161405i | ||||
\(141\) | 16.6620 | − | 2.68048i | 1.40319 | − | 0.225737i | ||||
\(142\) | 3.22132 | − | 3.22132i | 0.270327 | − | 0.270327i | ||||
\(143\) | −1.51227 | + | 1.51227i | −0.126462 | + | 0.126462i | ||||
\(144\) | 0.940895 | + | 2.84863i | 0.0784080 | + | 0.237386i | ||||
\(145\) | 14.8670 | + | 1.32733i | 1.23464 | + | 0.110229i | ||||
\(146\) | − | 6.94257i | − | 0.574571i | ||||||
\(147\) | −8.08639 | − | 5.84516i | −0.666955 | − | 0.482101i | ||||
\(148\) | 1.77676 | + | 1.77676i | 0.146049 | + | 0.146049i | ||||
\(149\) | 4.44032 | 0.363765 | 0.181883 | − | 0.983320i | \(-0.441781\pi\) | ||||
0.181883 | + | 0.983320i | \(0.441781\pi\) | |||||||
\(150\) | −8.65876 | − | 0.160901i | −0.706985 | − | 0.0131375i | ||||
\(151\) | −18.8511 | −1.53408 | −0.767040 | − | 0.641599i | \(-0.778271\pi\) | ||||
−0.767040 | + | 0.641599i | \(0.778271\pi\) | |||||||
\(152\) | −0.489267 | − | 0.489267i | −0.0396848 | − | 0.0396848i | ||||
\(153\) | −1.50791 | + | 2.99531i | −0.121907 | + | 0.242156i | ||||
\(154\) | − | 0.342042i | − | 0.0275625i | ||||||
\(155\) | −10.0794 | − | 0.899889i | −0.809596 | − | 0.0722808i | ||||
\(156\) | 1.91496 | + | 11.9034i | 0.153319 | + | 0.953037i | ||||
\(157\) | −9.78600 | + | 9.78600i | −0.781007 | + | 0.781007i | −0.980001 | − | 0.198993i | \(-0.936233\pi\) |
0.198993 | + | 0.980001i | \(0.436233\pi\) | |||||||
\(158\) | −11.1265 | + | 11.1265i | −0.885177 | + | 0.885177i | ||||
\(159\) | 2.31282 | + | 14.3766i | 0.183419 | + | 1.14014i | ||||
\(160\) | 1.43427 | + | 1.71548i | 0.113389 | + | 0.135621i | ||||
\(161\) | − | 1.11326i | − | 0.0877368i | ||||||
\(162\) | −8.90245 | − | 1.32151i | −0.699443 | − | 0.103828i | ||||
\(163\) | 9.24359 | + | 9.24359i | 0.724014 | + | 0.724014i | 0.969420 | − | 0.245406i | \(-0.0789214\pi\) |
−0.245406 | + | 0.969420i | \(0.578921\pi\) | |||||||
\(164\) | 0.596103 | 0.0465478 | ||||||||
\(165\) | −0.898577 | − | 0.780095i | −0.0699541 | − | 0.0607303i | ||||
\(166\) | −9.41670 | −0.730878 | ||||||||
\(167\) | −7.44173 | − | 7.44173i | −0.575858 | − | 0.575858i | 0.357901 | − | 0.933759i | \(-0.383492\pi\) |
−0.933759 | + | 0.357901i | \(0.883492\pi\) | |||||||
\(168\) | −1.56271 | − | 1.12959i | −0.120565 | − | 0.0871494i | ||||
\(169\) | 35.4529i | 2.72715i | ||||||||
\(170\) | −0.222273 | + | 2.48961i | −0.0170476 | + | 0.190945i | ||||
\(171\) | 1.97105 | − | 0.651032i | 0.150730 | − | 0.0497856i | ||||
\(172\) | 6.70489 | − | 6.70489i | 0.511243 | − | 0.511243i | ||||
\(173\) | 9.04703 | − | 9.04703i | 0.687833 | − | 0.687833i | −0.273920 | − | 0.961753i | \(-0.588320\pi\) |
0.961753 | + | 0.273920i | \(0.0883202\pi\) | |||||||
\(174\) | 11.4150 | − | 1.83638i | 0.865367 | − | 0.139215i | ||||
\(175\) | 4.57095 | − | 3.17646i | 0.345531 | − | 0.240117i | ||||
\(176\) | 0.307245i | 0.0231594i | ||||||||
\(177\) | 6.47682 | − | 8.96025i | 0.486828 | − | 0.673494i | ||||
\(178\) | 8.16181 | + | 8.16181i | 0.611753 | + | 0.611753i | ||||
\(179\) | 11.2260 | 0.839068 | 0.419534 | − | 0.907740i | \(-0.362193\pi\) | ||||
0.419534 | + | 0.907740i | \(0.362193\pi\) | |||||||
\(180\) | −6.53160 | + | 1.52913i | −0.486836 | + | 0.113975i | ||||
\(181\) | −8.65815 | −0.643555 | −0.321778 | − | 0.946815i | \(-0.604280\pi\) | ||||
−0.321778 | + | 0.946815i | \(0.604280\pi\) | |||||||
\(182\) | −5.47949 | − | 5.47949i | −0.406167 | − | 0.406167i | ||||
\(183\) | 10.1047 | − | 13.9792i | 0.746960 | − | 1.03337i | ||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | −4.31053 | + | 3.60392i | −0.316916 | + | 0.264966i | ||||
\(186\) | −7.73901 | + | 1.24501i | −0.567452 | + | 0.0912885i | ||||
\(187\) | −0.242851 | + | 0.242851i | −0.0177590 | + | 0.0177590i | ||||
\(188\) | 6.88967 | − | 6.88967i | 0.502481 | − | 0.502481i | ||||
\(189\) | 5.13489 | − | 2.66365i | 0.373508 | − | 0.193752i | ||||
\(190\) | 1.18699 | − | 0.992411i | 0.0861132 | − | 0.0719971i | ||||
\(191\) | − | 18.1677i | − | 1.31457i | −0.753643 | − | 0.657284i | \(-0.771705\pi\) | ||
0.753643 | − | 0.657284i | \(-0.228295\pi\) | |||||||
\(192\) | 1.40373 | + | 1.01467i | 0.101305 | + | 0.0732274i | ||||
\(193\) | 6.41622 | + | 6.41622i | 0.461850 | + | 0.461850i | 0.899261 | − | 0.437412i | \(-0.144105\pi\) |
−0.437412 | + | 0.899261i | \(0.644105\pi\) | |||||||
\(194\) | −18.1411 | −1.30246 | ||||||||
\(195\) | −26.8922 | + | 1.89807i | −1.92579 | + | 0.135923i | ||||
\(196\) | −5.76066 | −0.411476 | ||||||||
\(197\) | 14.6739 | + | 14.6739i | 1.04547 | + | 1.04547i | 0.998916 | + | 0.0465587i | \(0.0148255\pi\) |
0.0465587 | + | 0.998916i | \(0.485175\pi\) | |||||||
\(198\) | −0.823293 | − | 0.414465i | −0.0585089 | − | 0.0294548i | ||||
\(199\) | 2.60795i | 0.184873i | 0.995719 | + | 0.0924363i | \(0.0294655\pi\) | ||||
−0.995719 | + | 0.0924363i | \(0.970535\pi\) | |||||||
\(200\) | −4.10593 | + | 2.85330i | −0.290333 | + | 0.201759i | ||||
\(201\) | 0.853368 | + | 5.30456i | 0.0601919 | + | 0.374155i | ||||
\(202\) | −0.308085 | + | 0.308085i | −0.0216768 | + | 0.0216768i | ||||
\(203\) | −5.25463 | + | 5.25463i | −0.368803 | + | 0.368803i | ||||
\(204\) | 0.307518 | + | 1.91154i | 0.0215305 | + | 0.133834i | ||||
\(205\) | −0.118532 | + | 1.32765i | −0.00827865 | + | 0.0927268i | ||||
\(206\) | − | 3.49434i | − | 0.243463i | ||||||
\(207\) | −2.67960 | − | 1.34897i | −0.186245 | − | 0.0937602i | ||||
\(208\) | 4.92204 | + | 4.92204i | 0.341282 | + | 0.341282i | ||||
\(209\) | 0.212591 | 0.0147052 | ||||||||
\(210\) | 2.82656 | − | 3.25586i | 0.195051 | − | 0.224676i | ||||
\(211\) | 24.9846 | 1.72001 | 0.860004 | − | 0.510287i | \(-0.170461\pi\) | ||||
0.860004 | + | 0.510287i | \(0.170461\pi\) | |||||||
\(212\) | 5.94467 | + | 5.94467i | 0.408282 | + | 0.408282i | ||||
\(213\) | 6.39487 | + | 4.62246i | 0.438169 | + | 0.316726i | ||||
\(214\) | − | 12.7361i | − | 0.870623i | ||||||
\(215\) | 13.5999 | + | 16.2664i | 0.927509 | + | 1.10936i | ||||
\(216\) | −4.61250 | + | 2.39267i | −0.313841 | + | 0.162800i | ||||
\(217\) | 3.56249 | − | 3.56249i | 0.241837 | − | 0.241837i | ||||
\(218\) | 3.33429 | − | 3.33429i | 0.225827 | − | 0.225827i | ||||
\(219\) | 11.8722 | − | 1.90994i | 0.802252 | − | 0.129062i | ||||
\(220\) | −0.684298 | − | 0.0610942i | −0.0461354 | − | 0.00411897i | ||||
\(221\) | 7.78092i | 0.523401i | ||||||||
\(222\) | −2.54958 | + | 3.52718i | −0.171117 | + | 0.236729i | ||||
\(223\) | 2.06860 | + | 2.06860i | 0.138524 | + | 0.138524i | 0.772968 | − | 0.634444i | \(-0.218771\pi\) |
−0.634444 | + | 0.772968i | \(0.718771\pi\) | |||||||
\(224\) | −1.11326 | −0.0743825 | ||||||||
\(225\) | −2.10692 | − | 14.8513i | −0.140461 | − | 0.990086i | ||||
\(226\) | −13.7769 | −0.916428 | ||||||||
\(227\) | −14.8927 | − | 14.8927i | −0.988463 | − | 0.988463i | 0.0114717 | − | 0.999934i | \(-0.496348\pi\) |
−0.999934 | + | 0.0114717i | \(0.996348\pi\) | |||||||
\(228\) | 0.702077 | − | 0.971277i | 0.0464962 | − | 0.0643244i | ||||
\(229\) | − | 4.61161i | − | 0.304743i | −0.988323 | − | 0.152372i | \(-0.951309\pi\) | ||
0.988323 | − | 0.152372i | \(-0.0486911\pi\) | |||||||
\(230\) | −2.22721 | − | 0.198845i | −0.146858 | − | 0.0131115i | ||||
\(231\) | 0.584913 | − | 0.0940976i | 0.0384845 | − | 0.00619116i | ||||
\(232\) | 4.72006 | − | 4.72006i | 0.309887 | − | 0.309887i | ||||
\(233\) | −3.47172 | + | 3.47172i | −0.227440 | + | 0.227440i | −0.811622 | − | 0.584182i | \(-0.801415\pi\) |
0.584182 | + | 0.811622i | \(0.301415\pi\) | |||||||
\(234\) | −19.8288 | + | 6.54940i | −1.29625 | + | 0.428148i | ||||
\(235\) | 13.9748 | + | 16.7147i | 0.911613 | + | 1.09035i | ||||
\(236\) | − | 6.38319i | − | 0.415510i | ||||||
\(237\) | −22.0880 | − | 15.9661i | −1.43477 | − | 1.03711i | ||||
\(238\) | −0.879935 | − | 0.879935i | −0.0570377 | − | 0.0570377i | ||||
\(239\) | 20.2807 | 1.31185 | 0.655924 | − | 0.754827i | \(-0.272279\pi\) | ||||
0.655924 | + | 0.754827i | \(0.272279\pi\) | |||||||
\(240\) | −2.53900 | + | 2.92463i | −0.163892 | + | 0.188784i | ||||
\(241\) | 6.16685 | 0.397242 | 0.198621 | − | 0.980076i | \(-0.436354\pi\) | ||||
0.198621 | + | 0.980076i | \(0.436354\pi\) | |||||||
\(242\) | 7.71142 | + | 7.71142i | 0.495709 | + | 0.495709i | ||||
\(243\) | −0.189246 | − | 15.5873i | −0.0121401 | − | 0.999926i | ||||
\(244\) | − | 9.95861i | − | 0.637535i | ||||||
\(245\) | 1.14548 | − | 12.8302i | 0.0731821 | − | 0.819691i | ||||
\(246\) | 0.163991 | + | 1.01937i | 0.0104557 | + | 0.0649929i | ||||
\(247\) | 3.40570 | − | 3.40570i | 0.216699 | − | 0.216699i | ||||
\(248\) | −3.20006 | + | 3.20006i | −0.203204 | + | 0.203204i | ||||
\(249\) | −2.59059 | − | 16.1032i | −0.164172 | − | 1.02050i | ||||
\(250\) | −5.53846 | − | 9.71213i | −0.350283 | − | 0.614249i | ||||
\(251\) | 6.43760i | 0.406338i | 0.979144 | + | 0.203169i | \(0.0651240\pi\) | ||||
−0.979144 | + | 0.203169i | \(0.934876\pi\) | |||||||
\(252\) | 1.50175 | − | 2.98308i | 0.0946016 | − | 0.187916i | ||||
\(253\) | −0.217255 | − | 0.217255i | −0.0136587 | − | 0.0136587i | ||||
\(254\) | 19.4621 | 1.22116 | ||||||||
\(255\) | −4.31855 | + | 0.304805i | −0.270438 | + | 0.0190876i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.53147 | + | 8.53147i | 0.532178 | + | 0.532178i | 0.921220 | − | 0.389042i | \(-0.127194\pi\) |
−0.389042 | + | 0.921220i | \(0.627194\pi\) | |||||||
\(258\) | 13.3103 | + | 9.62123i | 0.828665 | + | 0.598992i | ||||
\(259\) | − | 2.79730i | − | 0.173816i | ||||||
\(260\) | −11.9411 | + | 9.98368i | −0.740558 | + | 0.619162i | ||||
\(261\) | 6.28064 | + | 19.0151i | 0.388762 | + | 1.17701i | ||||
\(262\) | 6.42395 | − | 6.42395i | 0.396873 | − | 0.396873i | ||||
\(263\) | 4.18176 | − | 4.18176i | 0.257858 | − | 0.257858i | −0.566324 | − | 0.824183i | \(-0.691635\pi\) |
0.824183 | + | 0.566324i | \(0.191635\pi\) | |||||||
\(264\) | −0.525408 | + | 0.0845247i | −0.0323366 | + | 0.00520213i | ||||
\(265\) | −14.4221 | + | 12.0580i | −0.885942 | + | 0.740714i | ||||
\(266\) | 0.770292i | 0.0472297i | ||||||||
\(267\) | −11.7118 | + | 16.2026i | −0.716754 | + | 0.991581i | ||||
\(268\) | 2.19342 | + | 2.19342i | 0.133985 | + | 0.133985i | ||||
\(269\) | −4.70169 | −0.286667 | −0.143334 | − | 0.989674i | \(-0.545782\pi\) | ||||
−0.143334 | + | 0.989674i | \(0.545782\pi\) | |||||||
\(270\) | −4.41179 | − | 10.7488i | −0.268493 | − | 0.654149i | ||||
\(271\) | 2.81014 | 0.170704 | 0.0853521 | − | 0.996351i | \(-0.472799\pi\) | ||||
0.0853521 | + | 0.996351i | \(0.472799\pi\) | |||||||
\(272\) | 0.790416 | + | 0.790416i | 0.0479260 | + | 0.0479260i | ||||
\(273\) | 7.86283 | − | 10.8777i | 0.475880 | − | 0.658349i | ||||
\(274\) | − | 8.65792i | − | 0.523044i | ||||||
\(275\) | 0.272139 | − | 1.51193i | 0.0164106 | − | 0.0911726i | ||||
\(276\) | −1.71006 | + | 0.275105i | −0.102934 | + | 0.0165594i | ||||
\(277\) | −7.56846 | + | 7.56846i | −0.454744 | + | 0.454744i | −0.896926 | − | 0.442181i | \(-0.854205\pi\) |
0.442181 | + | 0.896926i | \(0.354205\pi\) | |||||||
\(278\) | −1.20909 | + | 1.20909i | −0.0725164 | + | 0.0725164i | ||||
\(279\) | −4.25809 | − | 12.8917i | −0.254925 | − | 0.771806i | ||||
\(280\) | 0.221366 | − | 2.47945i | 0.0132291 | − | 0.148176i | ||||
\(281\) | 6.92797i | 0.413288i | 0.978416 | + | 0.206644i | \(0.0662542\pi\) | ||||
−0.978416 | + | 0.206644i | \(0.933746\pi\) | |||||||
\(282\) | 13.6772 | + | 9.88639i | 0.814463 | + | 0.588726i | ||||
\(283\) | −12.5993 | − | 12.5993i | −0.748951 | − | 0.748951i | 0.225331 | − | 0.974282i | \(-0.427654\pi\) |
−0.974282 | + | 0.225331i | \(0.927654\pi\) | |||||||
\(284\) | 4.55564 | 0.270327 | ||||||||
\(285\) | 2.02363 | + | 1.75681i | 0.119870 | + | 0.104064i | ||||
\(286\) | −2.13867 | −0.126462 | ||||||||
\(287\) | −0.469246 | − | 0.469246i | −0.0276987 | − | 0.0276987i | ||||
\(288\) | −1.34897 | + | 2.67960i | −0.0794891 | + | 0.157897i | ||||
\(289\) | − | 15.7505i | − | 0.926499i | ||||||
\(290\) | 9.57400 | + | 11.4511i | 0.562205 | + | 0.672433i | ||||
\(291\) | −4.99072 | − | 31.0225i | −0.292561 | − | 1.81857i | ||||
\(292\) | 4.90914 | − | 4.90914i | 0.287286 | − | 0.287286i | ||||
\(293\) | 4.71078 | − | 4.71078i | 0.275207 | − | 0.275207i | −0.555985 | − | 0.831192i | \(-0.687659\pi\) |
0.831192 | + | 0.555985i | \(0.187659\pi\) | |||||||
\(294\) | −1.58479 | − | 9.85110i | −0.0924268 | − | 0.574528i | ||||
\(295\) | 14.2167 | + | 1.26927i | 0.827728 | + | 0.0738997i | ||||
\(296\) | 2.51272i | 0.146049i | ||||||||
\(297\) | 0.482270 | − | 1.52191i | 0.0279841 | − | 0.0883099i | ||||
\(298\) | 3.13978 | + | 3.13978i | 0.181883 | + | 0.181883i | ||||
\(299\) | −6.96081 | −0.402554 | ||||||||
\(300\) | −6.00889 | − | 6.23644i | −0.346924 | − | 0.360061i | ||||
\(301\) | −10.5560 | −0.608440 | ||||||||
\(302\) | −13.3297 | − | 13.3297i | −0.767040 | − | 0.767040i | ||||
\(303\) | −0.611601 | − | 0.442089i | −0.0351356 | − | 0.0253974i | ||||
\(304\) | − | 0.691928i | − | 0.0396848i | ||||||
\(305\) | 22.1799 | + | 1.98022i | 1.27002 | + | 0.113387i | ||||
\(306\) | −3.18425 | + | 1.05175i | −0.182032 | + | 0.0601245i | ||||
\(307\) | 6.16188 | − | 6.16188i | 0.351677 | − | 0.351677i | −0.509056 | − | 0.860733i | \(-0.670006\pi\) |
0.860733 | + | 0.509056i | \(0.170006\pi\) | |||||||
\(308\) | 0.241860 | − | 0.241860i | 0.0137813 | − | 0.0137813i | ||||
\(309\) | 5.97555 | − | 0.961313i | 0.339937 | − | 0.0546872i | ||||
\(310\) | −6.49089 | − | 7.76352i | −0.368658 | − | 0.440939i | ||||
\(311\) | − | 6.56745i | − | 0.372406i | −0.982511 | − | 0.186203i | \(-0.940382\pi\) | ||
0.982511 | − | 0.186203i | \(-0.0596182\pi\) | |||||||
\(312\) | −7.06292 | + | 9.77108i | −0.399859 | + | 0.553178i | ||||
\(313\) | 5.15434 | + | 5.15434i | 0.291341 | + | 0.291341i | 0.837610 | − | 0.546269i | \(-0.183952\pi\) |
−0.546269 | + | 0.837610i | \(0.683952\pi\) | |||||||
\(314\) | −13.8395 | −0.781007 | ||||||||
\(315\) | 6.34533 | + | 3.93789i | 0.357519 | + | 0.221875i | ||||
\(316\) | −15.7352 | −0.885177 | ||||||||
\(317\) | 18.9615 | + | 18.9615i | 1.06498 | + | 1.06498i | 0.997736 | + | 0.0672456i | \(0.0214211\pi\) |
0.0672456 | + | 0.997736i | \(0.478579\pi\) | |||||||
\(318\) | −8.53035 | + | 11.8012i | −0.478358 | + | 0.661777i | ||||
\(319\) | 2.05091i | 0.114829i | ||||||||
\(320\) | −0.198845 | + | 2.22721i | −0.0111158 | + | 0.124505i | ||||
\(321\) | 21.7796 | − | 3.50378i | 1.21562 | − | 0.195562i | ||||
\(322\) | 0.787190 | − | 0.787190i | 0.0438684 | − | 0.0438684i | ||||
\(323\) | 0.546911 | − | 0.546911i | 0.0304309 | − | 0.0304309i | ||||
\(324\) | −5.36053 | − | 7.22943i | −0.297807 | − | 0.401635i | ||||
\(325\) | −19.8613 | − | 28.5806i | −1.10171 | − | 1.58537i | ||||
\(326\) | 13.0724i | 0.724014i | ||||||||
\(327\) | 6.61914 | + | 4.78457i | 0.366039 | + | 0.264587i | ||||
\(328\) | 0.421508 | + | 0.421508i | 0.0232739 | + | 0.0232739i | ||||
\(329\) | −10.8470 | −0.598013 | ||||||||
\(330\) | −0.0837792 | − | 1.18700i | −0.00461189 | − | 0.0653422i | ||||
\(331\) | −0.116417 | −0.00639884 | −0.00319942 | − | 0.999995i | \(-0.501018\pi\) | ||||
−0.00319942 | + | 0.999995i | \(0.501018\pi\) | |||||||
\(332\) | −6.65861 | − | 6.65861i | −0.365439 | − | 0.365439i | ||||
\(333\) | −6.73310 | − | 3.38960i | −0.368971 | − | 0.185749i | ||||
\(334\) | − | 10.5242i | − | 0.575858i | ||||||
\(335\) | −5.32136 | + | 4.44906i | −0.290737 | + | 0.243078i | ||||
\(336\) | −0.306263 | − | 1.90374i | −0.0167080 | − | 0.103857i | ||||
\(337\) | 8.19544 | − | 8.19544i | 0.446434 | − | 0.446434i | −0.447733 | − | 0.894167i | \(-0.647769\pi\) |
0.894167 | + | 0.447733i | \(0.147769\pi\) | |||||||
\(338\) | −25.0690 | + | 25.0690i | −1.36357 | + | 1.36357i | ||||
\(339\) | −3.79011 | − | 23.5594i | −0.205851 | − | 1.27957i | ||||
\(340\) | −1.91759 | + | 1.60325i | −0.103996 | + | 0.0869485i | ||||
\(341\) | − | 1.39046i | − | 0.0752975i | ||||||
\(342\) | 1.85409 | + | 0.933393i | 0.100258 | + | 0.0504721i | ||||
\(343\) | 10.0451 | + | 10.0451i | 0.542383 | + | 0.542383i | ||||
\(344\) | 9.48214 | 0.511243 | ||||||||
\(345\) | −0.272679 | − | 3.86337i | −0.0146805 | − | 0.207997i | ||||
\(346\) | 12.7944 | 0.687833 | ||||||||
\(347\) | 4.19660 | + | 4.19660i | 0.225285 | + | 0.225285i | 0.810720 | − | 0.585435i | \(-0.199076\pi\) |
−0.585435 | + | 0.810720i | \(0.699076\pi\) | |||||||
\(348\) | 9.37012 | + | 6.77309i | 0.502291 | + | 0.363076i | ||||
\(349\) | 5.51143i | 0.295020i | 0.989061 | + | 0.147510i | \(0.0471259\pi\) | ||||
−0.989061 | + | 0.147510i | \(0.952874\pi\) | |||||||
\(350\) | 5.47824 | + | 0.986056i | 0.292824 | + | 0.0527069i | ||||
\(351\) | −16.6549 | − | 32.1067i | −0.888973 | − | 1.71373i | ||||
\(352\) | −0.217255 | + | 0.217255i | −0.0115797 | + | 0.0115797i | ||||
\(353\) | −2.34200 | + | 2.34200i | −0.124652 | + | 0.124652i | −0.766681 | − | 0.642029i | \(-0.778093\pi\) |
0.642029 | + | 0.766681i | \(0.278093\pi\) | |||||||
\(354\) | 10.9157 | − | 1.75605i | 0.580161 | − | 0.0933330i | ||||
\(355\) | −0.905868 | + | 10.1464i | −0.0480785 | + | 0.538513i | ||||
\(356\) | 11.5425i | 0.611753i | ||||||||
\(357\) | 1.26267 | − | 1.74682i | 0.0668276 | − | 0.0924515i | ||||
\(358\) | 7.93796 | + | 7.93796i | 0.419534 | + | 0.419534i | ||||
\(359\) | −12.4668 | −0.657974 | −0.328987 | − | 0.944334i | \(-0.606707\pi\) | ||||
−0.328987 | + | 0.944334i | \(0.606707\pi\) | |||||||
\(360\) | −5.69980 | − | 3.53728i | −0.300406 | − | 0.186431i | ||||
\(361\) | 18.5212 | 0.974802 | ||||||||
\(362\) | −6.12224 | − | 6.12224i | −0.321778 | − | 0.321778i | ||||
\(363\) | −11.0656 | + | 15.3085i | −0.580792 | + | 0.803487i | ||||
\(364\) | − | 7.74916i | − | 0.406167i | ||||||
\(365\) | 9.95752 | + | 11.9098i | 0.521201 | + | 0.623390i | ||||
\(366\) | 17.0299 | − | 2.73967i | 0.890165 | − | 0.143205i | ||||
\(367\) | 3.53418 | − | 3.53418i | 0.184483 | − | 0.184483i | −0.608823 | − | 0.793306i | \(-0.708358\pi\) |
0.793306 | + | 0.608823i | \(0.208358\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | −1.69808 | + | 0.560870i | −0.0883984 | + | 0.0291977i | ||||
\(370\) | −5.59636 | − | 0.499644i | −0.290941 | − | 0.0259752i | ||||
\(371\) | − | 9.35918i | − | 0.485904i | ||||||
\(372\) | −6.35266 | − | 4.59195i | −0.329370 | − | 0.238082i | ||||
\(373\) | −17.4340 | − | 17.4340i | −0.902700 | − | 0.902700i | 0.0929686 | − | 0.995669i | \(-0.470364\pi\) |
−0.995669 | + | 0.0929686i | \(0.970364\pi\) | |||||||
\(374\) | −0.343444 | −0.0177590 | ||||||||
\(375\) | 15.0847 | − | 12.1430i | 0.778971 | − | 0.627060i | ||||
\(376\) | 9.74347 | 0.502481 | ||||||||
\(377\) | 32.8555 | + | 32.8555i | 1.69214 | + | 1.69214i | ||||
\(378\) | 5.51440 | + | 1.74743i | 0.283630 | + | 0.0898782i | ||||
\(379\) | 27.9253i | 1.43443i | 0.696853 | + | 0.717214i | \(0.254583\pi\) | ||||
−0.696853 | + | 0.717214i | \(0.745417\pi\) | |||||||
\(380\) | 1.54107 | + | 0.137587i | 0.0790551 | + | 0.00705805i | ||||
\(381\) | 5.35414 | + | 33.2815i | 0.274301 | + | 1.70506i | ||||
\(382\) | 12.8465 | − | 12.8465i | 0.657284 | − | 0.657284i | ||||
\(383\) | −10.0383 | + | 10.0383i | −0.512932 | + | 0.512932i | −0.915424 | − | 0.402492i | \(-0.868144\pi\) |
0.402492 | + | 0.915424i | \(0.368144\pi\) | |||||||
\(384\) | 0.275105 | + | 1.71006i | 0.0140389 | + | 0.0872663i | ||||
\(385\) | 0.490580 | + | 0.586766i | 0.0250023 | + | 0.0299044i | ||||
\(386\) | 9.07391i | 0.461850i | ||||||||
\(387\) | −12.7912 | + | 25.4084i | −0.650212 | + | 1.29158i | ||||
\(388\) | −12.8277 | − | 12.8277i | −0.651228 | − | 0.651228i | ||||
\(389\) | 20.3937 | 1.03400 | 0.517000 | − | 0.855985i | \(-0.327049\pi\) | ||||
0.517000 | + | 0.855985i | \(0.327049\pi\) | |||||||
\(390\) | −20.3578 | − | 17.6735i | −1.03086 | − | 0.894934i | ||||
\(391\) | −1.11782 | −0.0565305 | ||||||||
\(392\) | −4.07340 | − | 4.07340i | −0.205738 | − | 0.205738i | ||||
\(393\) | 12.7526 | + | 9.21810i | 0.643285 | + | 0.464992i | ||||
\(394\) | 20.7521i | 1.04547i | ||||||||
\(395\) | 3.12888 | − | 35.0457i | 0.157431 | − | 1.76334i | ||||
\(396\) | −0.289085 | − | 0.875228i | −0.0145271 | − | 0.0439818i | ||||
\(397\) | 11.8044 | − | 11.8044i | 0.592447 | − | 0.592447i | −0.345845 | − | 0.938292i | \(-0.612408\pi\) |
0.938292 | + | 0.345845i | \(0.112408\pi\) | |||||||
\(398\) | −1.84410 | + | 1.84410i | −0.0924363 | + | 0.0924363i | ||||
\(399\) | −1.31725 | + | 0.211912i | −0.0659449 | + | 0.0106089i | ||||
\(400\) | −4.92092 | − | 0.885741i | −0.246046 | − | 0.0442870i | ||||
\(401\) | 8.66485i | 0.432702i | 0.976316 | + | 0.216351i | \(0.0694156\pi\) | ||||
−0.976316 | + | 0.216351i | \(0.930584\pi\) | |||||||
\(402\) | −3.14747 | + | 4.35431i | −0.156981 | + | 0.217173i | ||||
\(403\) | −22.2750 | − | 22.2750i | −1.10960 | − | 1.10960i | ||||
\(404\) | −0.435698 | −0.0216768 | ||||||||
\(405\) | 17.1674 | − | 10.5015i | 0.853054 | − | 0.521823i | ||||
\(406\) | −7.43117 | −0.368803 | ||||||||
\(407\) | −0.545901 | − | 0.545901i | −0.0270593 | − | 0.0270593i | ||||
\(408\) | −1.13421 | + | 1.56911i | −0.0561520 | + | 0.0776825i | ||||
\(409\) | − | 22.5197i | − | 1.11353i | −0.830670 | − | 0.556765i | \(-0.812043\pi\) | ||
0.830670 | − | 0.556765i | \(-0.187957\pi\) | |||||||
\(410\) | −1.02260 | + | 0.854972i | −0.0505027 | + | 0.0422241i | ||||
\(411\) | 14.8056 | − | 2.38184i | 0.730306 | − | 0.117488i | ||||
\(412\) | 2.47087 | − | 2.47087i | 0.121731 | − | 0.121731i | ||||
\(413\) | −5.02479 | + | 5.02479i | −0.247254 | + | 0.247254i | ||||
\(414\) | −0.940895 | − | 2.84863i | −0.0462425 | − | 0.140003i | ||||
\(415\) | 16.1542 | − | 13.5061i | 0.792977 | − | 0.662988i | ||||
\(416\) | 6.96081i | 0.341282i | ||||||||
\(417\) | −2.40025 | − | 1.73499i | −0.117541 | − | 0.0849630i | ||||
\(418\) | 0.150325 | + | 0.150325i | 0.00735262 | + | 0.00735262i | ||||
\(419\) | −19.7745 | −0.966048 | −0.483024 | − | 0.875607i | \(-0.660462\pi\) | ||||
−0.483024 | + | 0.875607i | \(0.660462\pi\) | |||||||
\(420\) | 4.30092 | − | 0.303561i | 0.209863 | − | 0.0148123i | ||||
\(421\) | −3.54002 | −0.172530 | −0.0862649 | − | 0.996272i | \(-0.527493\pi\) | ||||
−0.0862649 | + | 0.996272i | \(0.527493\pi\) | |||||||
\(422\) | 17.6667 | + | 17.6667i | 0.860004 | + | 0.860004i | ||||
\(423\) | −13.1437 | + | 26.1086i | −0.639068 | + | 1.26944i | ||||
\(424\) | 8.40703i | 0.408282i | ||||||||
\(425\) | −3.18947 | − | 4.58968i | −0.154712 | − | 0.222632i | ||||
\(426\) | 1.25328 | + | 7.79043i | 0.0607217 | + | 0.377448i | ||||
\(427\) | −7.83932 | + | 7.83932i | −0.379371 | + | 0.379371i | ||||
\(428\) | 9.00580 | − | 9.00580i | 0.435312 | − | 0.435312i | ||||
\(429\) | −0.588361 | − | 3.65727i | −0.0284063 | − | 0.176574i | ||||
\(430\) | −1.88548 | + | 21.1187i | −0.0909260 | + | 1.01843i | ||||
\(431\) | 6.98806i | 0.336603i | 0.985736 | + | 0.168302i | \(0.0538282\pi\) | ||||
−0.985736 | + | 0.168302i | \(0.946172\pi\) | |||||||
\(432\) | −4.95340 | − | 1.56966i | −0.238321 | − | 0.0755203i | ||||
\(433\) | −22.0257 | − | 22.0257i | −1.05849 | − | 1.05849i | −0.998180 | − | 0.0603055i | \(-0.980793\pi\) |
−0.0603055 | − | 0.998180i | \(-0.519207\pi\) | |||||||
\(434\) | 5.03812 | 0.241837 | ||||||||
\(435\) | −16.9483 | + | 19.5224i | −0.812608 | + | 0.936028i | ||||
\(436\) | 4.71540 | 0.225827 | ||||||||
\(437\) | 0.489267 | + | 0.489267i | 0.0234048 | + | 0.0234048i | ||||
\(438\) | 9.74547 | + | 7.04441i | 0.465657 | + | 0.336595i | ||||
\(439\) | − | 12.4962i | − | 0.596410i | −0.954502 | − | 0.298205i | \(-0.903612\pi\) | ||
0.954502 | − | 0.298205i | \(-0.0963879\pi\) | |||||||
\(440\) | −0.440672 | − | 0.527072i | −0.0210082 | − | 0.0251272i | ||||
\(441\) | 16.4100 | − | 5.42018i | 0.781429 | − | 0.258104i | ||||
\(442\) | −5.50194 | + | 5.50194i | −0.261701 | + | 0.261701i | ||||
\(443\) | −3.45517 | + | 3.45517i | −0.164160 | + | 0.164160i | −0.784407 | − | 0.620247i | \(-0.787033\pi\) |
0.620247 | + | 0.784407i | \(0.287033\pi\) | |||||||
\(444\) | −4.29692 | + | 0.691264i | −0.203923 | + | 0.0328059i | ||||
\(445\) | −25.7076 | − | 2.29518i | −1.21866 | − | 0.108802i | ||||
\(446\) | 2.92545i | 0.138524i | ||||||||
\(447\) | −4.50546 | + | 6.23300i | −0.213101 | + | 0.294811i | ||||
\(448\) | −0.787190 | − | 0.787190i | −0.0371913 | − | 0.0371913i | ||||
\(449\) | −5.44836 | −0.257124 | −0.128562 | − | 0.991701i | \(-0.541036\pi\) | ||||
−0.128562 | + | 0.991701i | \(0.541036\pi\) | |||||||
\(450\) | 9.01163 | − | 11.9913i | 0.424812 | − | 0.565274i | ||||
\(451\) | −0.183149 | −0.00862417 | ||||||||
\(452\) | −9.74177 | − | 9.74177i | −0.458214 | − | 0.458214i | ||||
\(453\) | 19.1276 | − | 26.4618i | 0.898694 | − | 1.24328i | ||||
\(454\) | − | 21.0614i | − | 0.988463i | ||||||
\(455\) | 17.2590 | + | 1.54089i | 0.809115 | + | 0.0722378i | ||||
\(456\) | 1.18324 | − | 0.190353i | 0.0554103 | − | 0.00891410i | ||||
\(457\) | −9.46760 | + | 9.46760i | −0.442876 | + | 0.442876i | −0.892977 | − | 0.450102i | \(-0.851388\pi\) |
0.450102 | + | 0.892977i | \(0.351388\pi\) | |||||||
\(458\) | 3.26090 | − | 3.26090i | 0.152372 | − | 0.152372i | ||||
\(459\) | −2.67456 | − | 5.15593i | −0.124838 | − | 0.240658i | ||||
\(460\) | −1.43427 | − | 1.71548i | −0.0668732 | − | 0.0799847i | ||||
\(461\) | − | 29.8517i | − | 1.39033i | −0.718849 | − | 0.695166i | \(-0.755331\pi\) | ||
0.718849 | − | 0.695166i | \(-0.244669\pi\) | |||||||
\(462\) | 0.480133 | + | 0.347059i | 0.0223378 | + | 0.0161466i | ||||
\(463\) | −17.9865 | − | 17.9865i | −0.835905 | − | 0.835905i | 0.152412 | − | 0.988317i | \(-0.451296\pi\) |
−0.988317 | + | 0.152412i | \(0.951296\pi\) | |||||||
\(464\) | 6.67517 | 0.309887 | ||||||||
\(465\) | 11.4904 | − | 13.2356i | 0.532856 | − | 0.613787i | ||||
\(466\) | −4.90975 | −0.227440 | ||||||||
\(467\) | 3.58351 | + | 3.58351i | 0.165825 | + | 0.165825i | 0.785141 | − | 0.619317i | \(-0.212590\pi\) |
−0.619317 | + | 0.785141i | \(0.712590\pi\) | |||||||
\(468\) | −18.6522 | − | 9.38996i | −0.862199 | − | 0.434051i | ||||
\(469\) | − | 3.45328i | − | 0.159458i | ||||||
\(470\) | −1.93744 | + | 21.7007i | −0.0893677 | + | 1.00098i | ||||
\(471\) | −3.80732 | − | 23.6664i | −0.175432 | − | 1.09049i | ||||
\(472\) | 4.51360 | − | 4.51360i | 0.207755 | − | 0.207755i | ||||
\(473\) | −2.06004 | + | 2.06004i | −0.0947208 | + | 0.0947208i | ||||
\(474\) | −4.32885 | − | 26.9083i | −0.198831 | − | 1.23594i | ||||
\(475\) | −0.612869 | + | 3.40492i | −0.0281203 | + | 0.156229i | ||||
\(476\) | − | 1.24442i | − | 0.0570377i | ||||||
\(477\) | −22.5275 | − | 11.3409i | −1.03146 | − | 0.519263i | ||||
\(478\) | 14.3406 | + | 14.3406i | 0.655924 | + | 0.655924i | ||||
\(479\) | 39.2172 | 1.79188 | 0.895939 | − | 0.444177i | \(-0.146504\pi\) | ||||
0.895939 | + | 0.444177i | \(0.146504\pi\) | |||||||
\(480\) | −3.86337 | + | 0.272679i | −0.176338 | + | 0.0124460i | ||||
\(481\) | −17.4906 | −0.797503 | ||||||||
\(482\) | 4.36062 | + | 4.36062i | 0.198621 | + | 0.198621i | ||||
\(483\) | 1.56271 | + | 1.12959i | 0.0711056 | + | 0.0513979i | ||||
\(484\) | 10.9056i | 0.495709i | ||||||||
\(485\) | 31.1207 | − | 26.0193i | 1.41312 | − | 1.18147i | ||||
\(486\) | 10.8881 | − | 11.1557i | 0.493893 | − | 0.506033i | ||||
\(487\) | 18.9608 | − | 18.9608i | 0.859194 | − | 0.859194i | −0.132049 | − | 0.991243i | \(-0.542156\pi\) |
0.991243 | + | 0.132049i | \(0.0421556\pi\) | |||||||
\(488\) | 7.04180 | − | 7.04180i | 0.318767 | − | 0.318767i | ||||
\(489\) | −22.3547 | + | 3.59629i | −1.01091 | + | 0.162630i | ||||
\(490\) | 9.88230 | − | 8.26234i | 0.446437 | − | 0.373255i | ||||
\(491\) | 14.7080i | 0.663761i | 0.943321 | + | 0.331880i | \(0.107683\pi\) | ||||
−0.943321 | + | 0.331880i | \(0.892317\pi\) | |||||||
\(492\) | −0.604847 | + | 0.836765i | −0.0272686 | + | 0.0377243i | ||||
\(493\) | 5.27617 | + | 5.27617i | 0.237627 | + | 0.237627i | ||||
\(494\) | 4.81638 | 0.216699 | ||||||||
\(495\) | 2.00680 | − | 0.469818i | 0.0901989 | − | 0.0211167i | ||||
\(496\) | −4.52557 | −0.203204 | ||||||||
\(497\) | −3.58616 | − | 3.58616i | −0.160861 | − | 0.160861i | ||||
\(498\) | 9.55483 | − | 13.2185i | 0.428162 | − | 0.592334i | ||||
\(499\) | − | 12.6459i | − | 0.566109i | −0.959104 | − | 0.283055i | \(-0.908652\pi\) | ||
0.959104 | − | 0.283055i | \(-0.0913477\pi\) | |||||||
\(500\) | 2.95123 | − | 10.7838i | 0.131983 | − | 0.482266i | ||||
\(501\) | 17.9970 | − | 2.89526i | 0.804048 | − | 0.129351i | ||||
\(502\) | −4.55207 | + | 4.55207i | −0.203169 | + | 0.203169i | ||||
\(503\) | 29.2502 | − | 29.2502i | 1.30420 | − | 1.30420i | 0.378668 | − | 0.925532i | \(-0.376382\pi\) |
0.925532 | − | 0.378668i | \(-0.123618\pi\) | |||||||
\(504\) | 3.17126 | − | 1.04746i | 0.141259 | − | 0.0466574i | ||||
\(505\) | 0.0866366 | − | 0.970391i | 0.00385528 | − | 0.0431818i | ||||
\(506\) | − | 0.307245i | − | 0.0136587i | ||||||
\(507\) | −49.7662 | − | 35.9730i | −2.21019 | − | 1.59762i | ||||
\(508\) | 13.7618 | + | 13.7618i | 0.610582 | + | 0.610582i | ||||
\(509\) | −17.2813 | −0.765978 | −0.382989 | − | 0.923753i | \(-0.625105\pi\) | ||||
−0.382989 | + | 0.923753i | \(0.625105\pi\) | |||||||
\(510\) | −3.26920 | − | 2.83814i | −0.144763 | − | 0.125675i | ||||
\(511\) | −7.72886 | −0.341904 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −1.08609 | + | 3.42740i | −0.0479521 | + | 0.151323i | ||||
\(514\) | 12.0653i | 0.532178i | ||||||||
\(515\) | 5.01183 | + | 5.99448i | 0.220848 | + | 0.264148i | ||||
\(516\) | 2.60859 | + | 16.2151i | 0.114837 | + | 0.713828i | ||||
\(517\) | −2.11682 | + | 2.11682i | −0.0930974 | + | 0.0930974i | ||||
\(518\) | 1.97799 | − | 1.97799i | 0.0869080 | − | 0.0869080i | ||||
\(519\) | 3.51982 | + | 21.8793i | 0.154503 | + | 0.960394i | ||||
\(520\) | −15.5032 | − | 1.38413i | −0.679860 | − | 0.0606980i | ||||
\(521\) | − | 34.5203i | − | 1.51236i | −0.654363 | − | 0.756181i | \(-0.727063\pi\) | ||
0.654363 | − | 0.756181i | \(-0.272937\pi\) | |||||||
\(522\) | −9.00464 | + | 17.8868i | −0.394123 | + | 0.782884i | ||||
\(523\) | 29.4556 | + | 29.4556i | 1.28800 | + | 1.28800i | 0.935998 | + | 0.352005i | \(0.114500\pi\) |
0.352005 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(524\) | 9.08484 | 0.396873 | ||||||||
\(525\) | −0.179124 | + | 9.63941i | −0.00781761 | + | 0.420698i | ||||
\(526\) | 5.91390 | 0.257858 | ||||||||
\(527\) | −3.57709 | − | 3.57709i | −0.155820 | − | 0.155820i | ||||
\(528\) | −0.431287 | − | 0.311752i | −0.0187694 | − | 0.0135672i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −18.7242 | − | 1.67170i | −0.813328 | − | 0.0726140i | ||||
\(531\) | 6.00591 | + | 18.1834i | 0.260634 | + | 0.789091i | ||||
\(532\) | −0.544679 | + | 0.544679i | −0.0236148 | + | 0.0236148i | ||||
\(533\) | −2.93404 | + | 2.93404i | −0.127087 | + | 0.127087i | ||||
\(534\) | −19.7385 | + | 3.17541i | −0.854167 | + | 0.137414i | ||||
\(535\) | 18.2670 | + | 21.8486i | 0.789753 | + | 0.944595i | ||||
\(536\) | 3.10197i | 0.133985i | ||||||||
\(537\) | −11.3906 | + | 15.7582i | −0.491542 | + | 0.680016i | ||||
\(538\) | −3.32460 | − | 3.32460i | −0.143334 | − | 0.143334i | ||||
\(539\) | 1.76993 | 0.0762364 | ||||||||
\(540\) | 4.48092 | − | 10.7201i | 0.192828 | − | 0.461321i | ||||
\(541\) | −22.6506 | −0.973824 | −0.486912 | − | 0.873451i | \(-0.661877\pi\) | ||||
−0.486912 | + | 0.873451i | \(0.661877\pi\) | |||||||
\(542\) | 1.98707 | + | 1.98707i | 0.0853521 | + | 0.0853521i | ||||
\(543\) | 8.78515 | − | 12.1537i | 0.377007 | − | 0.521564i | ||||
\(544\) | 1.11782i | 0.0479260i | ||||||||
\(545\) | −0.937637 | + | 10.5022i | −0.0401639 | + | 0.449864i | ||||
\(546\) | 13.2516 | − | 2.13184i | 0.567114 | − | 0.0912342i | ||||
\(547\) | 0.166563 | − | 0.166563i | 0.00712170 | − | 0.00712170i | −0.703537 | − | 0.710659i | \(-0.748397\pi\) |
0.710659 | + | 0.703537i | \(0.248397\pi\) | |||||||
\(548\) | 6.12207 | − | 6.12207i | 0.261522 | − | 0.261522i | ||||
\(549\) | 9.37001 | + | 28.3684i | 0.399902 | + | 1.21074i | ||||
\(550\) | 1.26153 | − | 0.876662i | 0.0537916 | − | 0.0373810i | ||||
\(551\) | − | 4.61874i | − | 0.196765i | ||||||
\(552\) | −1.40373 | − | 1.01467i | −0.0597466 | − | 0.0431872i | ||||
\(553\) | 12.3866 | + | 12.3866i | 0.526733 | + | 0.526733i | ||||
\(554\) | −10.7034 | −0.454744 | ||||||||
\(555\) | −0.685167 | − | 9.70758i | −0.0290837 | − | 0.412064i | ||||
\(556\) | −1.70991 | −0.0725164 | ||||||||
\(557\) | −22.4801 | − | 22.4801i | −0.952511 | − | 0.952511i | 0.0464113 | − | 0.998922i | \(-0.485222\pi\) |
−0.998922 | + | 0.0464113i | \(0.985222\pi\) | |||||||
\(558\) | 6.10488 | − | 12.1267i | 0.258440 | − | 0.513365i | ||||
\(559\) | 66.0034i | 2.79165i | ||||||||
\(560\) | 1.90977 | − | 1.59671i | 0.0807024 | − | 0.0674732i | ||||
\(561\) | −0.0944832 | − | 0.587310i | −0.00398908 | − | 0.0247963i | ||||
\(562\) | −4.89882 | + | 4.89882i | −0.206644 | + | 0.206644i | ||||
\(563\) | −24.7485 | + | 24.7485i | −1.04302 | + | 1.04302i | −0.0439915 | + | 0.999032i | \(0.514007\pi\) |
−0.999032 | + | 0.0439915i | \(0.985993\pi\) | |||||||
\(564\) | 2.68048 | + | 16.6620i | 0.112869 | + | 0.701595i | ||||
\(565\) | 23.6341 | − | 19.7598i | 0.994292 | − | 0.831303i | ||||
\(566\) | − | 17.8181i | − | 0.748951i | ||||||
\(567\) | −1.47118 | + | 9.91070i | −0.0617837 | + | 0.416210i | ||||
\(568\) | 3.22132 | + | 3.22132i | 0.135164 | + | 0.135164i | ||||
\(569\) | −41.8001 | −1.75235 | −0.876176 | − | 0.481991i | \(-0.839914\pi\) | ||||
−0.876176 | + | 0.481991i | \(0.839914\pi\) | |||||||
\(570\) | 0.188674 | + | 2.67317i | 0.00790269 | + | 0.111967i | ||||
\(571\) | −6.16454 | −0.257978 | −0.128989 | − | 0.991646i | \(-0.541173\pi\) | ||||
−0.128989 | + | 0.991646i | \(0.541173\pi\) | |||||||
\(572\) | −1.51227 | − | 1.51227i | −0.0632312 | − | 0.0632312i | ||||
\(573\) | 25.5025 | + | 18.4342i | 1.06538 | + | 0.770099i | ||||
\(574\) | − | 0.663614i | − | 0.0276987i | ||||||
\(575\) | 4.10593 | − | 2.85330i | 0.171229 | − | 0.118991i | ||||
\(576\) | −2.84863 | + | 0.940895i | −0.118693 | + | 0.0392040i | ||||
\(577\) | −32.6610 | + | 32.6610i | −1.35970 | + | 1.35970i | −0.485410 | + | 0.874287i | \(0.661330\pi\) |
−0.874287 | + | 0.485410i | \(0.838670\pi\) | |||||||
\(578\) | 11.1373 | − | 11.1373i | 0.463250 | − | 0.463250i | ||||
\(579\) | −15.5170 | + | 2.49628i | −0.644863 | + | 0.103742i | ||||
\(580\) | −1.32733 | + | 14.8670i | −0.0551143 | + | 0.617319i | ||||
\(581\) | 10.4832i | 0.434916i | ||||||||
\(582\) | 18.4072 | − | 25.4652i | 0.763004 | − | 1.05557i | ||||
\(583\) | −1.82647 | − | 1.82647i | −0.0756446 | − | 0.0756446i | ||||
\(584\) | 6.94257 | 0.287286 | ||||||||
\(585\) | 24.6223 | − | 39.6752i | 1.01801 | − | 1.64037i | ||||
\(586\) | 6.66204 | 0.275207 | ||||||||
\(587\) | 22.6013 | + | 22.6013i | 0.932856 | + | 0.932856i | 0.997883 | − | 0.0650272i | \(-0.0207134\pi\) |
−0.0650272 | + | 0.997883i | \(0.520713\pi\) | |||||||
\(588\) | 5.84516 | − | 8.08639i | 0.241050 | − | 0.333477i | ||||
\(589\) | 3.13137i | 0.129026i | ||||||||
\(590\) | 9.15522 | + | 10.9502i | 0.376914 | + | 0.450814i | ||||
\(591\) | −35.4874 | + | 5.70901i | −1.45975 | + | 0.234837i | ||||
\(592\) | −1.77676 | + | 1.77676i | −0.0730245 | + | 0.0730245i | ||||
\(593\) | 16.9395 | − | 16.9395i | 0.695621 | − | 0.695621i | −0.267842 | − | 0.963463i | \(-0.586311\pi\) |
0.963463 | + | 0.267842i | \(0.0863106\pi\) | |||||||
\(594\) | 1.41717 | − | 0.735134i | 0.0581470 | − | 0.0301629i | ||||
\(595\) | 2.77158 | + | 0.247447i | 0.113624 | + | 0.0101443i | ||||
\(596\) | 4.44032i | 0.181883i | ||||||||
\(597\) | −3.66085 | − | 2.64620i | −0.149828 | − | 0.108302i | ||||
\(598\) | −4.92204 | − | 4.92204i | −0.201277 | − | 0.201277i | ||||
\(599\) | −35.0050 | −1.43027 | −0.715133 | − | 0.698988i | \(-0.753634\pi\) | ||||
−0.715133 | + | 0.698988i | \(0.753634\pi\) | |||||||
\(600\) | 0.160901 | − | 8.65876i | 0.00656876 | − | 0.353492i | ||||
\(601\) | −2.10282 | −0.0857759 | −0.0428880 | − | 0.999080i | \(-0.513656\pi\) | ||||
−0.0428880 | + | 0.999080i | \(0.513656\pi\) | |||||||
\(602\) | −7.46425 | − | 7.46425i | −0.304220 | − | 0.304220i | ||||
\(603\) | −8.31203 | − | 4.18447i | −0.338492 | − | 0.170405i | ||||
\(604\) | − | 18.8511i | − | 0.767040i | ||||||
\(605\) | −24.2891 | − | 2.16853i | −0.987490 | − | 0.0881633i | ||||
\(606\) | −0.119863 | − | 0.745072i | −0.00486910 | − | 0.0302665i | ||||
\(607\) | 3.54626 | − | 3.54626i | 0.143938 | − | 0.143938i | −0.631466 | − | 0.775404i | \(-0.717546\pi\) |
0.775404 | + | 0.631466i | \(0.217546\pi\) | |||||||
\(608\) | 0.489267 | − | 0.489267i | 0.0198424 | − | 0.0198424i | ||||
\(609\) | −2.04436 | − | 12.7078i | −0.0828415 | − | 0.514945i | ||||
\(610\) | 14.2833 | + | 17.0838i | 0.578315 | + | 0.691703i | ||||
\(611\) | 67.8225i | 2.74380i | ||||||||
\(612\) | −2.99531 | − | 1.50791i | −0.121078 | − | 0.0609536i | ||||
\(613\) | −29.6529 | − | 29.6529i | −1.19767 | − | 1.19767i | −0.974862 | − | 0.222808i | \(-0.928478\pi\) |
−0.222808 | − | 0.974862i | \(-0.571522\pi\) | |||||||
\(614\) | 8.71421 | 0.351677 | ||||||||
\(615\) | −1.74338 | − | 1.51351i | −0.0702998 | − | 0.0610305i | ||||
\(616\) | 0.342042 | 0.0137813 | ||||||||
\(617\) | 32.2270 | + | 32.2270i | 1.29741 | + | 1.29741i | 0.930098 | + | 0.367311i | \(0.119721\pi\) |
0.367311 | + | 0.930098i | \(0.380279\pi\) | |||||||
\(618\) | 4.90510 | + | 3.54560i | 0.197312 | + | 0.142625i | ||||
\(619\) | 17.9166i | 0.720130i | 0.932927 | + | 0.360065i | \(0.117245\pi\) | ||||
−0.932927 | + | 0.360065i | \(0.882755\pi\) | |||||||
\(620\) | 0.899889 | − | 10.0794i | 0.0361404 | − | 0.404798i | ||||
\(621\) | 4.61250 | − | 2.39267i | 0.185093 | − | 0.0960144i | ||||
\(622\) | 4.64389 | − | 4.64389i | 0.186203 | − | 0.186203i | ||||
\(623\) | 9.08617 | − | 9.08617i | 0.364030 | − | 0.364030i | ||||
\(624\) | −11.9034 | + | 1.91496i | −0.476519 | + | 0.0766597i | ||||
\(625\) | 23.4309 | + | 8.71732i | 0.937237 | + | 0.348693i | ||||
\(626\) | 7.28934i | 0.291341i | ||||||||
\(627\) | −0.215710 | + | 0.298420i | −0.00861461 | + | 0.0119177i | ||||
\(628\) | −9.78600 | − | 9.78600i | −0.390504 | − | 0.390504i | ||||
\(629\) | −2.80877 | −0.111993 | ||||||||
\(630\) | 1.70232 | + | 7.27133i | 0.0678219 | + | 0.289697i | ||||
\(631\) | −7.91640 | −0.315147 | −0.157573 | − | 0.987507i | \(-0.550367\pi\) | ||||
−0.157573 | + | 0.987507i | \(0.550367\pi\) | |||||||
\(632\) | −11.1265 | − | 11.1265i | −0.442588 | − | 0.442588i | ||||
\(633\) | −25.3510 | + | 35.0715i | −1.00761 | + | 1.39397i | ||||
\(634\) | 26.8156i | 1.06498i | ||||||||
\(635\) | −33.3869 | + | 27.9140i | −1.32492 | + | 1.10773i | ||||
\(636\) | −14.3766 | + | 2.31282i | −0.570068 | + | 0.0917093i | ||||
\(637\) | 28.3542 | − | 28.3542i | 1.12343 | − | 1.12343i | ||||
\(638\) | −1.45021 | + | 1.45021i | −0.0574145 | + | 0.0574145i | ||||
\(639\) | −12.9773 | + | 4.28638i | −0.513376 | + | 0.169567i | ||||
\(640\) | −1.71548 | + | 1.43427i | −0.0678103 | + | 0.0566945i | ||||
\(641\) | 27.3529i | 1.08037i | 0.841545 | + | 0.540187i | \(0.181646\pi\) | ||||
−0.841545 | + | 0.540187i | \(0.818354\pi\) | |||||||
\(642\) | 17.8780 | + | 12.9229i | 0.705589 | + | 0.510028i | ||||
\(643\) | −9.00024 | − | 9.00024i | −0.354935 | − | 0.354935i | 0.507007 | − | 0.861942i | \(-0.330752\pi\) |
−0.861942 | + | 0.507007i | \(0.830752\pi\) | |||||||
\(644\) | 1.11326 | 0.0438684 | ||||||||
\(645\) | −36.6330 | + | 2.58558i | −1.44242 | + | 0.101807i | ||||
\(646\) | 0.773449 | 0.0304309 | ||||||||
\(647\) | −15.7372 | − | 15.7372i | −0.618691 | − | 0.618691i | 0.326504 | − | 0.945196i | \(-0.394129\pi\) |
−0.945196 | + | 0.326504i | \(0.894129\pi\) | |||||||
\(648\) | 1.32151 | − | 8.90245i | 0.0519138 | − | 0.349721i | ||||
\(649\) | 1.96120i | 0.0769839i | ||||||||
\(650\) | 6.16548 | − | 34.2536i | 0.241830 | − | 1.34354i | ||||
\(651\) | 1.38601 | + | 8.61550i | 0.0543221 | + | 0.337668i | ||||
\(652\) | −9.24359 | + | 9.24359i | −0.362007 | + | 0.362007i | ||||
\(653\) | −9.00813 | + | 9.00813i | −0.352515 | + | 0.352515i | −0.861045 | − | 0.508529i | \(-0.830189\pi\) |
0.508529 | + | 0.861045i | \(0.330189\pi\) | |||||||
\(654\) | 1.29723 | + | 8.06364i | 0.0507258 | + | 0.315313i | ||||
\(655\) | −1.80648 | + | 20.2338i | −0.0705850 | + | 0.790601i | ||||
\(656\) | 0.596103i | 0.0232739i | ||||||||
\(657\) | −9.36536 | + | 18.6033i | −0.365377 | + | 0.725785i | ||||
\(658\) | −7.66997 | − | 7.66997i | −0.299006 | − | 0.299006i | ||||
\(659\) | −0.859802 | −0.0334931 | −0.0167466 | − | 0.999860i | \(-0.505331\pi\) | ||||
−0.0167466 | + | 0.999860i | \(0.505331\pi\) | |||||||
\(660\) | 0.780095 | − | 0.898577i | 0.0303652 | − | 0.0349771i | ||||
\(661\) | −2.50289 | −0.0973513 | −0.0486757 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486757 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(662\) | −0.0823190 | − | 0.0823190i | −0.00319942 | − | 0.00319942i | ||||
\(663\) | −10.9223 | − | 7.89505i | −0.424186 | − | 0.306619i | ||||
\(664\) | − | 9.41670i | − | 0.365439i | ||||||
\(665\) | −1.10481 | − | 1.32142i | −0.0428426 | − | 0.0512425i | ||||
\(666\) | −2.36421 | − | 7.15783i | −0.0916113 | − | 0.277360i | ||||
\(667\) | −4.72006 | + | 4.72006i | −0.182762 | + | 0.182762i | ||||
\(668\) | 7.44173 | − | 7.44173i | 0.287929 | − | 0.287929i | ||||
\(669\) | −5.00270 | + | 0.804807i | −0.193416 | + | 0.0311156i | ||||
\(670\) | −6.90873 | − | 0.616812i | −0.266907 | − | 0.0238295i | ||||
\(671\) | 3.05973i | 0.118120i | ||||||||
\(672\) | 1.12959 | − | 1.56271i | 0.0435747 | − | 0.0602827i | ||||
\(673\) | −22.4457 | − | 22.4457i | −0.865220 | − | 0.865220i | 0.126719 | − | 0.991939i | \(-0.459555\pi\) |
−0.991939 | + | 0.126719i | \(0.959555\pi\) | |||||||
\(674\) | 11.5901 | 0.446434 | ||||||||
\(675\) | 22.9850 | + | 12.1116i | 0.884692 | + | 0.466176i | ||||
\(676\) | −35.4529 | −1.36357 | ||||||||
\(677\) | 28.5893 | + | 28.5893i | 1.09878 | + | 1.09878i | 0.994554 | + | 0.104222i | \(0.0332354\pi\) |
0.104222 | + | 0.994554i | \(0.466765\pi\) | |||||||
\(678\) | 13.9790 | − | 19.3391i | 0.536861 | − | 0.742712i | ||||
\(679\) | 20.1957i | 0.775040i | ||||||||
\(680\) | −2.48961 | − | 0.222273i | −0.0954723 | − | 0.00852378i | ||||
\(681\) | 36.0164 | − | 5.79412i | 1.38015 | − | 0.222031i | ||||
\(682\) | 0.983202 | − | 0.983202i | 0.0376488 | − | 0.0376488i | ||||
\(683\) | 14.6754 | − | 14.6754i | 0.561537 | − | 0.561537i | −0.368207 | − | 0.929744i | \(-0.620028\pi\) |
0.929744 | + | 0.368207i | \(0.120028\pi\) | |||||||
\(684\) | 0.651032 | + | 1.97105i | 0.0248928 | + | 0.0753650i | ||||
\(685\) | 12.4178 | + | 14.8525i | 0.474459 | + | 0.567484i | ||||
\(686\) | 14.2059i | 0.542383i | ||||||||
\(687\) | 6.47343 | + | 4.67925i | 0.246977 | + | 0.178525i | ||||
\(688\) | 6.70489 | + | 6.70489i | 0.255621 | + | 0.255621i | ||||
\(689\) | −58.5198 | −2.22943 | ||||||||
\(690\) | 2.53900 | − | 2.92463i | 0.0966582 | − | 0.111339i | ||||
\(691\) | 41.2032 | 1.56744 | 0.783721 | − | 0.621113i | \(-0.213319\pi\) | ||||
0.783721 | + | 0.621113i | \(0.213319\pi\) | |||||||
\(692\) | 9.04703 | + | 9.04703i | 0.343916 | + | 0.343916i | ||||
\(693\) | −0.461406 | + | 0.916536i | −0.0175274 | + | 0.0348163i | ||||
\(694\) | 5.93489i | 0.225285i | ||||||||
\(695\) | 0.340008 | − | 3.80833i | 0.0128972 | − | 0.144458i | ||||
\(696\) | 1.83638 | + | 11.4150i | 0.0696077 | + | 0.432683i | ||||
\(697\) | −0.471169 | + | 0.471169i | −0.0178468 | + | 0.0178468i | ||||
\(698\) | −3.89717 | + | 3.89717i | −0.147510 | + | 0.147510i | ||||
\(699\) | −1.35070 | − | 8.39599i | −0.0510882 | − | 0.317566i | ||||
\(700\) | 3.17646 | + | 4.57095i | 0.120059 | + | 0.172766i | ||||
\(701\) | 15.0725i | 0.569281i | 0.958634 | + | 0.284641i | \(0.0918743\pi\) | ||||
−0.958634 | + | 0.284641i | \(0.908126\pi\) | |||||||
\(702\) | 10.9261 | − | 34.4797i | 0.412379 | − | 1.30135i | ||||
\(703\) | 1.22939 | + | 1.22939i | 0.0463674 | + | 0.0463674i | ||||
\(704\) | −0.307245 | −0.0115797 | ||||||||
\(705\) | −37.6426 | + | 2.65684i | −1.41770 | + | 0.100062i | ||||
\(706\) | −3.31208 | −0.124652 | ||||||||
\(707\) | 0.342978 | + | 0.342978i | 0.0128990 | + | 0.0128990i | ||||
\(708\) | 8.96025 | + | 6.47682i | 0.336747 | + | 0.243414i | ||||
\(709\) | 18.9496i | 0.711666i | 0.934550 | + | 0.355833i | \(0.115803\pi\) | ||||
−0.934550 | + | 0.355833i | \(0.884197\pi\) | |||||||
\(710\) | −7.81511 | + | 6.53402i | −0.293296 | + | 0.245217i | ||||
\(711\) | 44.8240 | − | 14.8052i | 1.68103 | − | 0.555239i | ||||
\(712\) | −8.16181 | + | 8.16181i | −0.305877 | + | 0.305877i | ||||
\(713\) | 3.20006 | − | 3.20006i | 0.119843 | − | 0.119843i | ||||
\(714\) | 2.12803 | − | 0.342346i | 0.0796396 | − | 0.0128120i | ||||
\(715\) | 3.66885 | − | 3.06743i | 0.137207 | − | 0.114716i | ||||
\(716\) | 11.2260i | 0.419534i | ||||||||
\(717\) | −20.5782 | + | 28.4685i | −0.768506 | + | 1.06318i | ||||
\(718\) | −8.81537 | − | 8.81537i | −0.328987 | − | 0.328987i | ||||
\(719\) | −32.0644 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(720\) | −1.52913 | − | 6.53160i | −0.0569874 | − | 0.243418i | ||||
\(721\) | −3.89010 | −0.144875 | ||||||||
\(722\) | 13.0965 | + | 13.0965i | 0.487401 | + | 0.487401i | ||||
\(723\) | −6.25731 | + | 8.65657i | −0.232712 | + | 0.321941i | ||||
\(724\) | − | 8.65815i | − | 0.321778i | ||||||
\(725\) | −32.8480 | − | 5.91248i | −1.21994 | − | 0.219584i | ||||
\(726\) | −18.6493 | + | 3.00019i | −0.692139 | + | 0.111347i | ||||
\(727\) | −24.2721 | + | 24.2721i | −0.900201 | + | 0.900201i | −0.995453 | − | 0.0952521i | \(-0.969634\pi\) |
0.0952521 | + | 0.995453i | \(0.469634\pi\) | |||||||
\(728\) | 5.47949 | − | 5.47949i | 0.203083 | − | 0.203083i | ||||
\(729\) | 22.0723 | + | 15.5503i | 0.817494 | + | 0.575937i | ||||
\(730\) | −1.38050 | + | 15.4626i | −0.0510946 | + | 0.572295i | ||||
\(731\) | 10.5993i | 0.392029i | ||||||||
\(732\) | 13.9792 | + | 10.1047i | 0.516685 | + | 0.373480i | ||||
\(733\) | 26.6081 | + | 26.6081i | 0.982793 | + | 0.982793i | 0.999854 | − | 0.0170616i | \(-0.00543113\pi\) |
−0.0170616 | + | 0.999854i | \(0.505431\pi\) | |||||||
\(734\) | 4.99809 | 0.184483 | ||||||||
\(735\) | 16.8478 | + | 14.6263i | 0.621441 | + | 0.539501i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −0.673917 | − | 0.673917i | −0.0248240 | − | 0.0248240i | ||||
\(738\) | −1.59732 | − | 0.804127i | −0.0587981 | − | 0.0296003i | ||||
\(739\) | − | 38.0885i | − | 1.40111i | −0.713599 | − | 0.700554i | \(-0.752936\pi\) | ||
0.713599 | − | 0.700554i | \(-0.247064\pi\) | |||||||
\(740\) | −3.60392 | − | 4.31053i | −0.132483 | − | 0.158458i | ||||
\(741\) | 1.32501 | + | 8.23632i | 0.0486756 | + | 0.302569i | ||||
\(742\) | 6.61794 | − | 6.61794i | 0.242952 | − | 0.242952i | ||||
\(743\) | 27.8032 | − | 27.8032i | 1.02000 | − | 1.02000i | 0.0202029 | − | 0.999796i | \(-0.493569\pi\) |
0.999796 | − | 0.0202029i | \(-0.00643121\pi\) | |||||||
\(744\) | −1.24501 | − | 7.73901i | −0.0456442 | − | 0.283726i | ||||
\(745\) | −9.88953 | − | 0.882938i | −0.362324 | − | 0.0323484i | ||||
\(746\) | − | 24.6555i | − | 0.902700i | ||||||
\(747\) | 25.2330 | + | 12.7029i | 0.923228 | + | 0.464775i | ||||
\(748\) | −0.242851 | − | 0.242851i | −0.00887952 | − | 0.00887952i | ||||
\(749\) | −14.1786 | −0.518073 | ||||||||
\(750\) | 19.2529 | + | 2.08012i | 0.703016 | + | 0.0759551i | ||||
\(751\) | 11.8305 | 0.431701 | 0.215850 | − | 0.976426i | \(-0.430748\pi\) | ||||
0.215850 | + | 0.976426i | \(0.430748\pi\) | |||||||
\(752\) | 6.88967 | + | 6.88967i | 0.251241 | + | 0.251241i | ||||
\(753\) | −9.03663 | − | 6.53203i | −0.329313 | − | 0.238040i | ||||
\(754\) | 46.4646i | 1.69214i | ||||||||
\(755\) | 41.9853 | + | 3.74846i | 1.52800 | + | 0.136420i | ||||
\(756\) | 2.66365 | + | 5.13489i | 0.0968759 | + | 0.186754i | ||||
\(757\) | −9.09388 | + | 9.09388i | −0.330523 | + | 0.330523i | −0.852785 | − | 0.522262i | \(-0.825088\pi\) |
0.522262 | + | 0.852785i | \(0.325088\pi\) | |||||||
\(758\) | −19.7462 | + | 19.7462i | −0.717214 | + | 0.717214i | ||||
\(759\) | 0.525408 | − | 0.0845247i | 0.0190711 | − | 0.00306805i | ||||
\(760\) | 0.992411 | + | 1.18699i | 0.0359985 | + | 0.0430566i | ||||
\(761\) | 41.4873i | 1.50391i | 0.659213 | + | 0.751956i | \(0.270889\pi\) | ||||
−0.659213 | + | 0.751956i | \(0.729111\pi\) | |||||||
\(762\) | −19.7476 | + | 27.3195i | −0.715381 | + | 0.989682i | ||||
\(763\) | −3.71192 | − | 3.71192i | −0.134381 | − | 0.134381i | ||||
\(764\) | 18.1677 | 0.657284 | ||||||||
\(765\) | 3.95403 | − | 6.37133i | 0.142958 | − | 0.230356i | ||||
\(766\) | −14.1963 | −0.512932 | ||||||||
\(767\) | 31.4183 | + | 31.4183i | 1.13445 | + | 1.13445i | ||||
\(768\) | −1.01467 | + | 1.40373i | −0.0366137 | + | 0.0506526i | ||||
\(769\) | − | 45.6787i | − | 1.64722i | −0.567159 | − | 0.823608i | \(-0.691958\pi\) | ||
0.567159 | − | 0.823608i | \(-0.308042\pi\) | |||||||
\(770\) | −0.0680135 | + | 0.761799i | −0.00245104 | + | 0.0274533i | ||||
\(771\) | −20.6325 | + | 3.31923i | −0.743060 | + | 0.119539i | ||||
\(772\) | −6.41622 | + | 6.41622i | −0.230925 | + | 0.230925i | ||||
\(773\) | −29.1634 | + | 29.1634i | −1.04894 | + | 1.04894i | −0.0501962 | + | 0.998739i | \(0.515985\pi\) |
−0.998739 | + | 0.0501962i | \(0.984015\pi\) | |||||||
\(774\) | −27.0112 | + | 8.92170i | −0.970896 | + | 0.320684i | ||||
\(775\) | 22.2700 | + | 4.00848i | 0.799961 | + | 0.143989i | ||||
\(776\) | − | 18.1411i | − | 0.651228i | ||||||
\(777\) | 3.92665 | + | 2.83833i | 0.140868 | + | 0.101825i | ||||
\(778\) | 14.4205 | + | 14.4205i | 0.517000 | + | 0.517000i | ||||
\(779\) | 0.412460 | 0.0147779 | ||||||||
\(780\) | −1.89807 | − | 26.8922i | −0.0679617 | − | 0.962896i | ||||
\(781\) | −1.39970 | −0.0500851 | ||||||||
\(782\) | −0.790416 | − | 0.790416i | −0.0282652 | − | 0.0282652i | ||||
\(783\) | −33.0648 | − | 10.4778i | −1.18164 | − | 0.374444i | ||||
\(784\) | − | 5.76066i | − | 0.205738i | ||||||
\(785\) | 23.7414 | − | 19.8496i | 0.847365 | − | 0.708461i | ||||
\(786\) | 2.49929 | + | 15.5356i | 0.0891467 | + | 0.554138i | ||||
\(787\) | 24.6107 | − | 24.6107i | 0.877277 | − | 0.877277i | −0.115975 | − | 0.993252i | \(-0.536999\pi\) |
0.993252 | + | 0.115975i | \(0.0369993\pi\) | |||||||
\(788\) | −14.6739 | + | 14.6739i | −0.522737 | + | 0.522737i | ||||
\(789\) | 1.62695 | + | 10.1132i | 0.0579209 | + | 0.360038i | ||||
\(790\) | 26.9935 | − | 22.5686i | 0.960386 | − | 0.802954i | ||||
\(791\) | 15.3373i | 0.545330i | ||||||||
\(792\) | 0.414465 | − | 0.823293i | 0.0147274 | − | 0.0292545i | ||||
\(793\) | 49.0167 | + | 49.0167i | 1.74063 | + | 1.74063i | ||||
\(794\) | 16.6940 | 0.592447 | ||||||||
\(795\) | −2.29242 | − | 32.4795i | −0.0813038 | − | 1.15193i | ||||
\(796\) | −2.60795 | −0.0924363 | ||||||||
\(797\) | −25.2336 | − | 25.2336i | −0.893820 | − | 0.893820i | 0.101060 | − | 0.994880i | \(-0.467777\pi\) |
−0.994880 | + | 0.101060i | \(0.967777\pi\) | |||||||
\(798\) | −1.08128 | − | 0.781591i | −0.0382769 | − | 0.0276680i | ||||
\(799\) | 10.8914i | 0.385311i | ||||||||
\(800\) | −2.85330 | − | 4.10593i | −0.100880 | − | 0.145167i | ||||
\(801\) | −10.8603 | − | 32.8805i | −0.383731 | − | 1.16177i | ||||
\(802\) | −6.12698 | + | 6.12698i | −0.216351 | + | 0.216351i | ||||
\(803\) | −1.50831 | + | 1.50831i | −0.0532270 | + | 0.0532270i | ||||
\(804\) | −5.30456 | + | 0.853368i | −0.187077 | + | 0.0300960i | ||||
\(805\) | −0.221366 | + | 2.47945i | −0.00780212 | + | 0.0873892i | ||||
\(806\) | − | 31.5017i | − | 1.10960i | ||||||
\(807\) | 4.77066 | − | 6.59989i | 0.167935 | − | 0.232327i | ||||
\(808\) | −0.308085 | − | 0.308085i | −0.0108384 | − | 0.0108384i | ||||
\(809\) | −2.69190 | −0.0946422 | −0.0473211 | − | 0.998880i | \(-0.515068\pi\) | ||||
−0.0473211 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(810\) | 19.5648 | + | 4.71349i | 0.687438 | + | 0.165615i | ||||
\(811\) | −40.9585 | −1.43825 | −0.719124 | − | 0.694881i | \(-0.755457\pi\) | ||||
−0.719124 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(812\) | −5.25463 | − | 5.25463i | −0.184401 | − | 0.184401i | ||||
\(813\) | −2.85137 | + | 3.94467i | −0.100002 | + | 0.138346i | ||||
\(814\) | − | 0.772021i | − | 0.0270593i | ||||||
\(815\) | −18.7494 | − | 22.4255i | −0.656762 | − | 0.785529i | ||||
\(816\) | −1.91154 | + | 0.307518i | −0.0669172 | + | 0.0107653i | ||||
\(817\) | 4.63930 | − | 4.63930i | 0.162308 | − | 0.162308i | ||||
\(818\) | 15.9239 | − | 15.9239i | 0.556765 | − | 0.556765i | ||||
\(819\) | 7.29115 | + | 22.0745i | 0.254773 | + | 0.771346i | ||||
\(820\) | −1.32765 | − | 0.118532i | −0.0463634 | − | 0.00413933i | ||||
\(821\) | 43.8765i | 1.53130i | 0.643257 | + | 0.765651i | \(0.277583\pi\) | ||||
−0.643257 | + | 0.765651i | \(0.722417\pi\) | |||||||
\(822\) | 12.1534 | + | 8.78492i | 0.423897 | + | 0.306409i | ||||
\(823\) | −26.3103 | − | 26.3103i | −0.917118 | − | 0.917118i | 0.0797004 | − | 0.996819i | \(-0.474604\pi\) |
−0.996819 | + | 0.0797004i | \(0.974604\pi\) | |||||||
\(824\) | 3.49434 | 0.121731 | ||||||||
\(825\) | 1.84620 | + | 1.91611i | 0.0642765 | + | 0.0667105i | ||||
\(826\) | −7.10612 | −0.247254 | ||||||||
\(827\) | −19.6739 | − | 19.6739i | −0.684130 | − | 0.684130i | 0.276798 | − | 0.960928i | \(-0.410727\pi\) |
−0.960928 | + | 0.276798i | \(0.910727\pi\) | |||||||
\(828\) | 1.34897 | − | 2.67960i | 0.0468801 | − | 0.0931226i | ||||
\(829\) | − | 46.9364i | − | 1.63017i | −0.579343 | − | 0.815084i | \(-0.696691\pi\) | ||
0.579343 | − | 0.815084i | \(-0.303309\pi\) | |||||||
\(830\) | 20.9730 | + | 1.87247i | 0.727982 | + | 0.0649943i | ||||
\(831\) | −2.94457 | − | 18.3035i | −0.102146 | − | 0.634942i | ||||
\(832\) | −4.92204 | + | 4.92204i | −0.170641 | + | 0.170641i | ||||
\(833\) | 4.55332 | − | 4.55332i | 0.157763 | − | 0.157763i | ||||
\(834\) | −0.470406 | − | 2.92406i | −0.0162888 | − | 0.101252i | ||||
\(835\) | 15.0945 | + | 18.0540i | 0.522368 | + | 0.624786i | ||||
\(836\) | 0.212591i | 0.00735262i | ||||||||
\(837\) | 22.4170 | + | 7.10361i | 0.774844 | + | 0.245537i | ||||
\(838\) | −13.9827 | − | 13.9827i | −0.483024 | − | 0.483024i | ||||
\(839\) | 27.6624 | 0.955013 | 0.477507 | − | 0.878628i | \(-0.341541\pi\) | ||||
0.477507 | + | 0.878628i | \(0.341541\pi\) | |||||||
\(840\) | 3.25586 | + | 2.82656i | 0.112338 | + | 0.0975256i | ||||
\(841\) | 15.5580 | 0.536481 | ||||||||
\(842\) | −2.50317 | − | 2.50317i | −0.0862649 | − | 0.0862649i | ||||
\(843\) | −9.72498 | − | 7.02960i | −0.334946 | − | 0.242112i | ||||
\(844\) | 24.9846i | 0.860004i | ||||||||
\(845\) | 7.04965 | − | 78.9611i | 0.242515 | − | 2.71634i | ||||
\(846\) | −27.7556 | + | 9.16759i | −0.954256 | + | 0.315188i | ||||
\(847\) | 8.58478 | − | 8.58478i | 0.294977 | − | 0.294977i | ||||
\(848\) | −5.94467 | + | 5.94467i | −0.204141 | + | 0.204141i | ||||
\(849\) | 30.4701 | − | 4.90186i | 1.04573 | − | 0.168231i | ||||
\(850\) | 0.990097 | − | 5.50069i | 0.0339600 | − | 0.188672i | ||||
\(851\) | − | 2.51272i | − | 0.0861350i | ||||||
\(852\) | −4.62246 | + | 6.39487i | −0.158363 | + | 0.219085i | ||||
\(853\) | −11.6144 | − | 11.6144i | −0.397671 | − | 0.397671i | 0.479740 | − | 0.877411i | \(-0.340731\pi\) |
−0.877411 | + | 0.479740i | \(0.840731\pi\) | |||||||
\(854\) | −11.0865 | −0.379371 | ||||||||
\(855\) | −4.51939 | + | 1.05805i | −0.154560 | + | 0.0361845i | ||||
\(856\) | 12.7361 | 0.435312 | ||||||||
\(857\) | 2.96243 | + | 2.96243i | 0.101195 | + | 0.101195i | 0.755892 | − | 0.654697i | \(-0.227204\pi\) |
−0.654697 | + | 0.755892i | \(0.727204\pi\) | |||||||
\(858\) | 2.17004 | − | 3.00211i | 0.0740841 | − | 0.102490i | ||||
\(859\) | − | 54.1769i | − | 1.84849i | −0.381797 | − | 0.924246i | \(-0.624695\pi\) | ||
0.381797 | − | 0.924246i | \(-0.375305\pi\) | |||||||
\(860\) | −16.2664 | + | 13.5999i | −0.554680 | + | 0.463754i | ||||
\(861\) | 1.13482 | − | 0.182564i | 0.0386747 | − | 0.00622176i | ||||
\(862\) | −4.94131 | + | 4.94131i | −0.168302 | + | 0.168302i | ||||
\(863\) | 23.6935 | − | 23.6935i | 0.806536 | − | 0.806536i | −0.177572 | − | 0.984108i | \(-0.556824\pi\) |
0.984108 | + | 0.177572i | \(0.0568242\pi\) | |||||||
\(864\) | −2.39267 | − | 4.61250i | −0.0814001 | − | 0.156920i | ||||
\(865\) | −21.9486 | + | 18.3507i | −0.746274 | + | 0.623941i | ||||
\(866\) | − | 31.1490i | − | 1.05849i | ||||||
\(867\) | 22.1094 | + | 15.9815i | 0.750874 | + | 0.542761i | ||||
\(868\) | 3.56249 | + | 3.56249i | 0.120919 | + | 0.120919i | ||||
\(869\) | 4.83457 | 0.164002 | ||||||||
\(870\) | −25.7887 | + | 1.82018i | −0.874318 | + | 0.0617099i | ||||
\(871\) | −21.5922 | −0.731624 | ||||||||
\(872\) | 3.33429 | + | 3.33429i | 0.112913 | + | 0.112913i | ||||
\(873\) | 48.6110 | + | 24.4719i | 1.64523 | + | 0.828249i | ||||
\(874\) | 0.691928i | 0.0234048i | ||||||||
\(875\) | −10.8121 | + | 6.16572i | −0.365515 | + | 0.208439i | ||||
\(876\) | 1.90994 | + | 11.8722i | 0.0645309 | + | 0.401126i | ||||
\(877\) | −17.6838 | + | 17.6838i | −0.597140 | + | 0.597140i | −0.939551 | − | 0.342410i | \(-0.888757\pi\) |
0.342410 | + | 0.939551i | \(0.388757\pi\) | |||||||
\(878\) | 8.83613 | − | 8.83613i | 0.298205 | − | 0.298205i | ||||
\(879\) | 1.83276 | + | 11.3925i | 0.0618176 | + | 0.384260i | ||||
\(880\) | 0.0610942 | − | 0.684298i | 0.00205949 | − | 0.0230677i | ||||
\(881\) | − | 41.8174i | − | 1.40886i | −0.709772 | − | 0.704432i | \(-0.751202\pi\) | ||
0.709772 | − | 0.704432i | \(-0.248798\pi\) | |||||||
\(882\) | 15.4363 | + | 7.77099i | 0.519767 | + | 0.261663i | ||||
\(883\) | −15.8834 | − | 15.8834i | −0.534520 | − | 0.534520i | 0.387394 | − | 0.921914i | \(-0.373375\pi\) |
−0.921914 | + | 0.387394i | \(0.873375\pi\) | |||||||
\(884\) | −7.78092 | −0.261701 | ||||||||
\(885\) | −16.2069 | + | 18.6685i | −0.544790 | + | 0.627534i | ||||
\(886\) | −4.88635 | −0.164160 | ||||||||
\(887\) | 26.4613 | + | 26.4613i | 0.888484 | + | 0.888484i | 0.994378 | − | 0.105893i | \(-0.0337701\pi\) |
−0.105893 | + | 0.994378i | \(0.533770\pi\) | |||||||
\(888\) | −3.52718 | − | 2.54958i | −0.118364 | − | 0.0855583i | ||||
\(889\) | − | 21.6663i | − | 0.726666i | ||||||
\(890\) | −16.5551 | − | 19.8010i | −0.554929 | − | 0.663731i | ||||
\(891\) | 1.64700 | + | 2.22120i | 0.0551764 | + | 0.0744131i | ||||
\(892\) | −2.06860 | + | 2.06860i | −0.0692620 | + | 0.0692620i | ||||
\(893\) | 4.76716 | − | 4.76716i | 0.159527 | − | 0.159527i | ||||
\(894\) | −7.59323 | + | 1.22156i | −0.253956 | + | 0.0408550i | ||||
\(895\) | −25.0026 | − | 2.23223i | −0.835744 | − | 0.0746153i | ||||
\(896\) | − | 1.11326i | − | 0.0371913i | ||||||
\(897\) | 7.06292 | − | 9.77108i | 0.235824 | − | 0.326247i | ||||
\(898\) | −3.85257 | − | 3.85257i | −0.128562 | − | 0.128562i | ||||
\(899\) | −30.2090 | −1.00753 | ||||||||
\(900\) | 14.8513 | − | 2.10692i | 0.495043 | − | 0.0702307i | ||||
\(901\) | −9.39753 | −0.313077 | ||||||||
\(902\) | −0.129506 | − | 0.129506i | −0.00431208 | − | 0.00431208i | ||||
\(903\) | 10.7109 | − | 14.8178i | 0.356436 | − | 0.493106i | ||||
\(904\) | − | 13.7769i | − | 0.458214i | ||||||
\(905\) | 19.2835 | + | 1.72163i | 0.641006 | + | 0.0572290i | ||||
\(906\) | 32.2366 | − | 5.18604i | 1.07099 | − | 0.172295i | ||||
\(907\) | 36.4729 | − | 36.4729i | 1.21106 | − | 1.21106i | 0.240387 | − | 0.970677i | \(-0.422726\pi\) |
0.970677 | − | 0.240387i | \(-0.0772743\pi\) | |||||||
\(908\) | 14.8927 | − | 14.8927i | 0.494231 | − | 0.494231i | ||||
\(909\) | 1.24115 | − | 0.409947i | 0.0411662 | − | 0.0135971i | ||||
\(910\) | 11.1144 | + | 13.2935i | 0.368438 | + | 0.440676i | ||||
\(911\) | − | 41.2639i | − | 1.36713i | −0.729888 | − | 0.683567i | \(-0.760428\pi\) | ||
0.729888 | − | 0.683567i | \(-0.239572\pi\) | |||||||
\(912\) | 0.971277 | + | 0.702077i | 0.0321622 | + | 0.0232481i | ||||
\(913\) | 2.04582 | + | 2.04582i | 0.0677069 | + | 0.0677069i | ||||
\(914\) | −13.3892 | −0.442876 | ||||||||
\(915\) | −25.2849 | + | 29.1252i | −0.835895 | + | 0.962851i | ||||
\(916\) | 4.61161 | 0.152372 | ||||||||
\(917\) | −7.15150 | − | 7.15150i | −0.236163 | − | 0.236163i | ||||
\(918\) | 1.75459 | − | 5.53700i | 0.0579102 | − | 0.182748i | ||||
\(919\) | − | 9.49797i | − | 0.313309i | −0.987653 | − | 0.156655i | \(-0.949929\pi\) | ||
0.987653 | − | 0.156655i | \(-0.0500710\pi\) | |||||||
\(920\) | 0.198845 | − | 2.22721i | 0.00655574 | − | 0.0734289i | ||||
\(921\) | 2.39733 | + | 14.9018i | 0.0789946 | + | 0.491033i | ||||
\(922\) | 21.1083 | − | 21.1083i | 0.695166 | − | 0.695166i | ||||
\(923\) | −22.4230 | + | 22.4230i | −0.738063 | + | 0.738063i | ||||
\(924\) | 0.0940976 | + | 0.584913i | 0.00309558 | + | 0.0192422i | ||||
\(925\) | 10.3171 | − | 7.16956i | 0.339223 | − | 0.235734i | ||||
\(926\) | − | 25.4368i | − | 0.835905i | ||||||
\(927\) | −4.71378 | + | 9.36345i | −0.154821 | + | 0.307536i | ||||
\(928\) | 4.72006 | + | 4.72006i | 0.154944 | + | 0.154944i | ||||
\(929\) | −54.3893 | −1.78446 | −0.892228 | − | 0.451585i | \(-0.850859\pi\) | ||||
−0.892228 | + | 0.451585i | \(0.850859\pi\) | |||||||
\(930\) | 17.4840 | − | 1.23403i | 0.573322 | − | 0.0404654i | ||||
\(931\) | −3.98596 | −0.130635 | ||||||||
\(932\) | −3.47172 | − | 3.47172i | −0.113720 | − | 0.113720i | ||||
\(933\) | 9.21890 | + | 6.66378i | 0.301813 | + | 0.218162i | ||||
\(934\) | 5.06784i | 0.165825i | ||||||||
\(935\) | 0.589170 | − | 0.492591i | 0.0192679 | − | 0.0161094i | ||||
\(936\) | −6.54940 | − | 19.8288i | −0.214074 | − | 0.648125i | ||||
\(937\) | −1.83354 | + | 1.83354i | −0.0598992 | + | 0.0598992i | −0.736422 | − | 0.676523i | \(-0.763486\pi\) |
0.676523 | + | 0.736422i | \(0.263486\pi\) | |||||||
\(938\) | 2.44184 | − | 2.44184i | 0.0797288 | − | 0.0797288i | ||||
\(939\) | −12.4652 | + | 2.00534i | −0.406788 | + | 0.0654417i | ||||
\(940\) | −16.7147 | + | 13.9748i | −0.545174 | + | 0.455806i | ||||
\(941\) | 24.0075i | 0.782621i | 0.920259 | + | 0.391310i | \(0.127978\pi\) | ||||
−0.920259 | + | 0.391310i | \(0.872022\pi\) | |||||||
\(942\) | 14.0425 | − | 19.4269i | 0.457529 | − | 0.632961i | ||||
\(943\) | −0.421508 | − | 0.421508i | −0.0137262 | − | 0.0137262i | ||||
\(944\) | 6.38319 | 0.207755 | ||||||||
\(945\) | −11.9661 | + | 4.91145i | −0.389258 | + | 0.159770i | ||||
\(946\) | −2.91334 | −0.0947208 | ||||||||
\(947\) | −4.17084 | − | 4.17084i | −0.135534 | − | 0.135534i | 0.636085 | − | 0.771619i | \(-0.280553\pi\) |
−0.771619 | + | 0.636085i | \(0.780553\pi\) | |||||||
\(948\) | 15.9661 | − | 22.0880i | 0.518554 | − | 0.717384i | ||||
\(949\) | 48.3260i | 1.56873i | ||||||||
\(950\) | −2.84101 | + | 1.97428i | −0.0921744 | + | 0.0640541i | ||||
\(951\) | −45.8563 | + | 7.37711i | −1.48699 | + | 0.239219i | ||||
\(952\) | 0.879935 | − | 0.879935i | 0.0285189 | − | 0.0285189i | ||||
\(953\) | −4.40507 | + | 4.40507i | −0.142694 | + | 0.142694i | −0.774845 | − | 0.632151i | \(-0.782172\pi\) |
0.632151 | + | 0.774845i | \(0.282172\pi\) | |||||||
\(954\) | −7.91014 | − | 23.9486i | −0.256100 | − | 0.775363i | ||||
\(955\) | −3.61256 | + | 40.4632i | −0.116900 | + | 1.30936i | ||||
\(956\) | 20.2807i | 0.655924i | ||||||||
\(957\) | −2.87892 | − | 2.08100i | −0.0930622 | − | 0.0672690i | ||||
\(958\) | 27.7307 | + | 27.7307i | 0.895939 | + | 0.895939i | ||||
\(959\) | −9.63848 | −0.311243 | ||||||||
\(960\) | −2.92463 | − | 2.53900i | −0.0943920 | − | 0.0819460i | ||||
\(961\) | −10.5192 | −0.339329 | ||||||||
\(962\) | −12.3677 | − | 12.3677i | −0.398751 | − | 0.398751i | ||||
\(963\) | −17.1807 | + | 34.1277i | −0.553640 | + | 1.09975i | ||||
\(964\) | 6.16685i | 0.198621i | ||||||||
\(965\) | −13.0144 | − | 15.5661i | −0.418949 | − | 0.501091i | ||||
\(966\) | 0.306263 | + | 1.90374i | 0.00985384 | + | 0.0612517i | ||||
\(967\) | 30.9294 | − | 30.9294i | 0.994624 | − | 0.994624i | −0.00536164 | − | 0.999986i | \(-0.501707\pi\) |
0.999986 | + | 0.00536164i | \(0.00170667\pi\) | |||||||
\(968\) | −7.71142 | + | 7.71142i | −0.247855 | + | 0.247855i | ||||
\(969\) | 0.212780 | + | 1.32265i | 0.00683548 | + | 0.0424895i | ||||
\(970\) | 40.4041 | + | 3.60728i | 1.29730 | + | 0.115823i | ||||
\(971\) | 57.5128i | 1.84568i | 0.385189 | + | 0.922838i | \(0.374136\pi\) | ||||
−0.385189 | + | 0.922838i | \(0.625864\pi\) | |||||||
\(972\) | 15.5873 | − | 0.189246i | 0.499963 | − | 0.00607006i | ||||
\(973\) | 1.34603 | + | 1.34603i | 0.0431516 | + | 0.0431516i | ||||
\(974\) | 26.8146 | 0.859194 | ||||||||
\(975\) | 60.2720 | + | 1.12000i | 1.93025 | + | 0.0358688i | ||||
\(976\) | 9.95861 | 0.318767 | ||||||||
\(977\) | −36.8392 | − | 36.8392i | −1.17859 | − | 1.17859i | −0.980103 | − | 0.198487i | \(-0.936397\pi\) |
−0.198487 | − | 0.980103i | \(-0.563603\pi\) | |||||||
\(978\) | −18.3501 | − | 13.2642i | −0.586771 | − | 0.424141i | ||||
\(979\) | − | 3.54638i | − | 0.113343i | ||||||
\(980\) | 12.8302 | + | 1.14548i | 0.409846 | + | 0.0365911i | ||||
\(981\) | −13.4325 | + | 4.43670i | −0.428865 | + | 0.141653i | ||||
\(982\) | −10.4001 | + | 10.4001i | −0.331880 | + | 0.331880i | ||||
\(983\) | 36.6462 | − | 36.6462i | 1.16883 | − | 1.16883i | 0.186349 | − | 0.982484i | \(-0.440334\pi\) |
0.982484 | − | 0.186349i | \(-0.0596657\pi\) | |||||||
\(984\) | −1.01937 | + | 0.163991i | −0.0324964 | + | 0.00522784i | ||||
\(985\) | −29.7641 | − | 35.5998i | −0.948362 | − | 1.13430i | ||||
\(986\) | 7.46163i | 0.237627i | ||||||||
\(987\) | 11.0061 | − | 15.2262i | 0.350327 | − | 0.484655i | ||||
\(988\) | 3.40570 | + | 3.40570i | 0.108350 | + | 0.108350i | ||||
\(989\) | −9.48214 | −0.301515 | ||||||||
\(990\) | 1.75123 | + | 1.08681i | 0.0556578 | + | 0.0345411i | ||||
\(991\) | 18.6888 | 0.593669 | 0.296834 | − | 0.954929i | \(-0.404069\pi\) | ||||
0.296834 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(992\) | −3.20006 | − | 3.20006i | −0.101602 | − | 0.101602i | ||||
\(993\) | 0.118124 | − | 0.163417i | 0.00374856 | − | 0.00518588i | ||||
\(994\) | − | 5.07159i | − | 0.160861i | ||||||
\(995\) | 0.518579 | − | 5.80845i | 0.0164401 | − | 0.184140i | ||||
\(996\) | 16.1032 | − | 2.59059i | 0.510248 | − | 0.0820859i | ||||
\(997\) | 6.75334 | − | 6.75334i | 0.213881 | − | 0.213881i | −0.592033 | − | 0.805914i | \(-0.701675\pi\) |
0.805914 | + | 0.592033i | \(0.201675\pi\) | |||||||
\(998\) | 8.94201 | − | 8.94201i | 0.283055 | − | 0.283055i | ||||
\(999\) | 11.5899 | − | 6.01211i | 0.366689 | − | 0.190215i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.2.i.f.323.10 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.323.8 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.f.47.8 | ✓ | 32 | |
15.2 | even | 4 | inner | 690.2.i.f.47.10 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.8 | ✓ | 32 | 5.2 | odd | 4 | inner | |
690.2.i.f.47.10 | yes | 32 | 15.2 | even | 4 | inner | |
690.2.i.f.323.8 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.10 | yes | 32 | 1.1 | even | 1 | trivial |