Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.26873856000000000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(0.294032 + 1.38331i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.161 |
Dual form | 363.2.f.h.239.3 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.98168 | + | 1.43977i | 1.40126 | + | 1.01807i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(3\) | −1.28716 | + | 1.15897i | −0.743145 | + | 0.669131i | ||||
\(4\) | 1.23607 | + | 3.80423i | 0.618034 | + | 1.90211i | ||||
\(5\) | 1.01807 | + | 1.40126i | 0.455296 | + | 0.626662i | 0.973525 | − | 0.228580i | \(-0.0734083\pi\) |
−0.518229 | + | 0.855242i | \(0.673408\pi\) | |||||||
\(6\) | −4.21940 | + | 0.443477i | −1.72256 | + | 0.181049i | ||||
\(7\) | −1.34500 | + | 0.437016i | −0.508361 | + | 0.165177i | −0.551957 | − | 0.833873i | \(-0.686119\pi\) |
0.0435957 | + | 0.999049i | \(0.486119\pi\) | |||||||
\(8\) | −1.51387 | + | 4.65921i | −0.535233 | + | 1.64728i | ||||
\(9\) | 0.313585 | − | 2.98357i | 0.104528 | − | 0.994522i | ||||
\(10\) | 4.24264i | 1.34164i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −6.00000 | − | 3.46410i | −1.73205 | − | 1.00000i | ||||
\(13\) | 1.66251 | − | 2.28825i | 0.461097 | − | 0.634645i | −0.513639 | − | 0.858006i | \(-0.671703\pi\) |
0.974736 | + | 0.223361i | \(0.0717029\pi\) | |||||||
\(14\) | −3.29456 | − | 1.07047i | −0.880507 | − | 0.286094i | ||||
\(15\) | −2.93444 | − | 0.623735i | −0.757670 | − | 0.161048i | ||||
\(16\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(17\) | 1.98168 | − | 1.43977i | 0.480628 | − | 0.349196i | −0.320941 | − | 0.947099i | \(-0.603999\pi\) |
0.801569 | + | 0.597903i | \(0.203999\pi\) | |||||||
\(18\) | 4.91709 | − | 5.46098i | 1.15897 | − | 1.28716i | ||||
\(19\) | −2.68999 | − | 0.874032i | −0.617127 | − | 0.200517i | −0.0162627 | − | 0.999868i | \(-0.505177\pi\) |
−0.600864 | + | 0.799351i | \(0.705177\pi\) | |||||||
\(20\) | −4.07230 | + | 5.60503i | −0.910593 | + | 1.25332i | ||||
\(21\) | 1.22474 | − | 2.12132i | 0.267261 | − | 0.462910i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.66025i | 1.80579i | 0.429863 | + | 0.902894i | \(0.358562\pi\) | ||||
−0.429863 | + | 0.902894i | \(0.641438\pi\) | |||||||
\(24\) | −3.45127 | − | 7.75169i | −0.704489 | − | 1.58231i | ||||
\(25\) | 0.618034 | − | 1.90211i | 0.123607 | − | 0.380423i | ||||
\(26\) | 6.58911 | − | 2.14093i | 1.29223 | − | 0.419871i | ||||
\(27\) | 3.05422 | + | 4.20378i | 0.587785 | + | 0.809017i | ||||
\(28\) | −3.32502 | − | 4.57649i | −0.628369 | − | 0.864876i | ||||
\(29\) | 1.51387 | + | 4.65921i | 0.281118 | + | 0.865193i | 0.987535 | + | 0.157397i | \(0.0503103\pi\) |
−0.706417 | + | 0.707796i | \(0.749690\pi\) | |||||||
\(30\) | −4.91709 | − | 5.46098i | −0.897733 | − | 0.997033i | ||||
\(31\) | −2.42705 | − | 1.76336i | −0.435911 | − | 0.316708i | 0.348097 | − | 0.937459i | \(-0.386828\pi\) |
−0.784008 | + | 0.620750i | \(0.786828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −1.98168 | − | 1.43977i | −0.334965 | − | 0.243366i | ||||
\(36\) | 11.7378 | − | 2.49494i | 1.95630 | − | 0.415823i | ||||
\(37\) | 0.927051 | + | 2.85317i | 0.152406 | + | 0.469058i | 0.997889 | − | 0.0649448i | \(-0.0206871\pi\) |
−0.845483 | + | 0.534003i | \(0.820687\pi\) | |||||||
\(38\) | −4.07230 | − | 5.60503i | −0.660614 | − | 0.909257i | ||||
\(39\) | 0.512083 | + | 4.87214i | 0.0819989 | + | 0.780167i | ||||
\(40\) | −8.06998 | + | 2.62210i | −1.27598 | + | 0.414590i | ||||
\(41\) | 3.02774 | − | 9.31841i | 0.472853 | − | 1.45529i | −0.375979 | − | 0.926628i | \(-0.622693\pi\) |
0.848832 | − | 0.528663i | \(-0.177307\pi\) | |||||||
\(42\) | 5.48127 | − | 2.44042i | 0.845779 | − | 0.376565i | ||||
\(43\) | − | 9.89949i | − | 1.50966i | −0.655921 | − | 0.754829i | \(-0.727720\pi\) | ||
0.655921 | − | 0.754829i | \(-0.272280\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.50000 | − | 2.59808i | 0.670820 | − | 0.387298i | ||||
\(46\) | −12.4688 | + | 17.1618i | −1.83843 | + | 2.53038i | ||||
\(47\) | 6.58911 | + | 2.14093i | 0.961121 | + | 0.312287i | 0.747226 | − | 0.664570i | \(-0.231385\pi\) |
0.213895 | + | 0.976857i | \(0.431385\pi\) | |||||||
\(48\) | 1.44045 | − | 6.77681i | 0.207912 | − | 0.978148i | ||||
\(49\) | −4.04508 | + | 2.93893i | −0.577869 | + | 0.419847i | ||||
\(50\) | 3.96336 | − | 2.87955i | 0.560503 | − | 0.407230i | ||||
\(51\) | −0.882095 | + | 4.14993i | −0.123518 | + | 0.581106i | ||||
\(52\) | 10.7600 | + | 3.49613i | 1.49214 | + | 0.484826i | ||||
\(53\) | −2.03615 | + | 2.80252i | −0.279686 | + | 0.384955i | −0.925630 | − | 0.378430i | \(-0.876464\pi\) |
0.645944 | + | 0.763385i | \(0.276464\pi\) | |||||||
\(54\) | 12.7279i | 1.73205i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 6.92820i | − | 0.925820i | ||||||
\(57\) | 4.47544 | − | 1.99259i | 0.592787 | − | 0.263926i | ||||
\(58\) | −3.70820 | + | 11.4127i | −0.486911 | + | 1.49856i | ||||
\(59\) | 1.64728 | − | 0.535233i | 0.214457 | − | 0.0696814i | −0.199818 | − | 0.979833i | \(-0.564035\pi\) |
0.414275 | + | 0.910152i | \(0.364035\pi\) | |||||||
\(60\) | −1.25434 | − | 11.9343i | −0.161935 | − | 1.54071i | ||||
\(61\) | −1.66251 | − | 2.28825i | −0.212862 | − | 0.292980i | 0.689213 | − | 0.724559i | \(-0.257957\pi\) |
−0.902075 | + | 0.431579i | \(0.857957\pi\) | |||||||
\(62\) | −2.27080 | − | 6.98881i | −0.288392 | − | 0.887580i | ||||
\(63\) | 0.882095 | + | 4.14993i | 0.111133 | + | 0.522842i | ||||
\(64\) | 6.47214 | + | 4.70228i | 0.809017 | + | 0.587785i | ||||
\(65\) | 4.89898 | 0.607644 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | −0.366508 | −0.183254 | − | 0.983066i | \(-0.558663\pi\) | ||||
−0.183254 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(68\) | 7.92672 | + | 5.75910i | 0.961255 | + | 0.698393i | ||||
\(69\) | −10.0370 | − | 11.1472i | −1.20831 | − | 1.34196i | ||||
\(70\) | −1.85410 | − | 5.70634i | −0.221608 | − | 0.682038i | ||||
\(71\) | 1.01807 | + | 1.40126i | 0.120823 | + | 0.166299i | 0.865144 | − | 0.501523i | \(-0.167227\pi\) |
−0.744321 | + | 0.667822i | \(0.767227\pi\) | |||||||
\(72\) | 13.4263 | + | 5.97778i | 1.58231 | + | 0.704489i | ||||
\(73\) | 5.37999 | − | 1.74806i | 0.629680 | − | 0.204595i | 0.0232466 | − | 0.999730i | \(-0.492600\pi\) |
0.606433 | + | 0.795134i | \(0.292600\pi\) | |||||||
\(74\) | −2.27080 | + | 6.98881i | −0.263975 | + | 0.812433i | ||||
\(75\) | 1.40898 | + | 3.16461i | 0.162695 | + | 0.365418i | ||||
\(76\) | − | 11.3137i | − | 1.29777i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | + | 10.3923i | −0.679366 | + | 1.17670i | ||||
\(79\) | 5.81878 | − | 8.00886i | 0.654664 | − | 0.901067i | −0.344627 | − | 0.938740i | \(-0.611994\pi\) |
0.999290 | + | 0.0376728i | \(0.0119944\pi\) | |||||||
\(80\) | −6.58911 | − | 2.14093i | −0.736685 | − | 0.239364i | ||||
\(81\) | −8.80333 | − | 1.87121i | −0.978148 | − | 0.207912i | ||||
\(82\) | 19.4164 | − | 14.1068i | 2.14418 | − | 1.55784i | ||||
\(83\) | −1.98168 | + | 1.43977i | −0.217518 | + | 0.158036i | −0.691208 | − | 0.722655i | \(-0.742921\pi\) |
0.473691 | + | 0.880691i | \(0.342921\pi\) | |||||||
\(84\) | 9.58385 | + | 2.03711i | 1.04568 | + | 0.222267i | ||||
\(85\) | 4.03499 | + | 1.31105i | 0.437656 | + | 0.142203i | ||||
\(86\) | 14.2530 | − | 19.6176i | 1.53694 | − | 2.11542i | ||||
\(87\) | −7.34847 | − | 4.24264i | −0.787839 | − | 0.454859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.66025i | − | 0.917985i | −0.888440 | − | 0.458993i | \(-0.848210\pi\) | ||
0.888440 | − | 0.458993i | \(-0.151790\pi\) | |||||||
\(90\) | 12.6582 | + | 1.33043i | 1.33429 | + | 0.140240i | ||||
\(91\) | −1.23607 | + | 3.80423i | −0.129575 | + | 0.398791i | ||||
\(92\) | −32.9456 | + | 10.7047i | −3.43481 | + | 1.11604i | ||||
\(93\) | 5.16769 | − | 0.543146i | 0.535864 | − | 0.0563216i | ||||
\(94\) | 9.97505 | + | 13.7295i | 1.02885 | + | 1.41609i | ||||
\(95\) | −1.51387 | − | 4.65921i | −0.155320 | − | 0.478024i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5172 | − | 7.64121i | −1.06786 | − | 0.775847i | −0.0923353 | − | 0.995728i | \(-0.529433\pi\) |
−0.975527 | + | 0.219881i | \(0.929433\pi\) | |||||||
\(98\) | −12.2474 | −1.23718 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000 | 0.800000 | ||||||||
\(101\) | −9.90839 | − | 7.19887i | −0.985922 | − | 0.716314i | −0.0268978 | − | 0.999638i | \(-0.508563\pi\) |
−0.959024 | + | 0.283324i | \(0.908563\pi\) | |||||||
\(102\) | −7.72299 | + | 6.95381i | −0.764690 | + | 0.688530i | ||||
\(103\) | −0.618034 | − | 1.90211i | −0.0608967 | − | 0.187421i | 0.915980 | − | 0.401224i | \(-0.131415\pi\) |
−0.976877 | + | 0.213803i | \(0.931415\pi\) | |||||||
\(104\) | 8.14459 | + | 11.2101i | 0.798643 | + | 1.09924i | ||||
\(105\) | 4.21940 | − | 0.443477i | 0.411771 | − | 0.0432789i | ||||
\(106\) | −8.06998 | + | 2.62210i | −0.783826 | + | 0.254680i | ||||
\(107\) | 0.756934 | − | 2.32960i | 0.0731756 | − | 0.225211i | −0.907779 | − | 0.419449i | \(-0.862223\pi\) |
0.980954 | + | 0.194238i | \(0.0622233\pi\) | |||||||
\(108\) | −12.2169 | + | 16.8151i | −1.17557 | + | 1.61803i | ||||
\(109\) | 18.3848i | 1.76094i | 0.474100 | + | 0.880471i | \(0.342774\pi\) | ||||
−0.474100 | + | 0.880471i | \(0.657226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | − | 2.59808i | −0.427121 | − | 0.246598i | ||||
\(112\) | 3.32502 | − | 4.57649i | 0.314184 | − | 0.432438i | ||||
\(113\) | −1.64728 | − | 0.535233i | −0.154963 | − | 0.0503505i | 0.230508 | − | 0.973070i | \(-0.425961\pi\) |
−0.385471 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(114\) | 11.7378 | + | 2.49494i | 1.09934 | + | 0.233673i | ||||
\(115\) | −12.1353 | + | 8.81678i | −1.13162 | + | 0.822169i | ||||
\(116\) | −15.8534 | + | 11.5182i | −1.47195 | + | 1.06944i | ||||
\(117\) | −6.30579 | − | 5.67776i | −0.582971 | − | 0.524909i | ||||
\(118\) | 4.03499 | + | 1.31105i | 0.371451 | + | 0.120692i | ||||
\(119\) | −2.03615 | + | 2.80252i | −0.186653 | + | 0.256906i | ||||
\(120\) | 7.34847 | − | 12.7279i | 0.670820 | − | 1.16190i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 6.92820i | − | 0.627250i | ||||||
\(123\) | 6.90255 | + | 15.5034i | 0.622382 | + | 1.39789i | ||||
\(124\) | 3.70820 | − | 11.4127i | 0.333007 | − | 1.02489i | ||||
\(125\) | 11.5309 | − | 3.74663i | 1.03136 | − | 0.335109i | ||||
\(126\) | −4.22693 | + | 9.49384i | −0.376565 | + | 0.845779i | ||||
\(127\) | −1.66251 | − | 2.28825i | −0.147524 | − | 0.203049i | 0.728860 | − | 0.684663i | \(-0.240051\pi\) |
−0.876383 | + | 0.481614i | \(0.840051\pi\) | |||||||
\(128\) | 6.05547 | + | 18.6368i | 0.535233 | + | 1.64728i | ||||
\(129\) | 11.4732 | + | 12.7423i | 1.01016 | + | 1.12190i | ||||
\(130\) | 9.70820 | + | 7.05342i | 0.851466 | + | 0.618626i | ||||
\(131\) | −12.2474 | −1.07006 | −0.535032 | − | 0.844832i | \(-0.679701\pi\) | ||||
−0.535032 | + | 0.844832i | \(0.679701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | −5.94504 | − | 4.31932i | −0.513573 | − | 0.373133i | ||||
\(135\) | −2.78115 | + | 8.55951i | −0.239364 | + | 0.736685i | ||||
\(136\) | 3.70820 | + | 11.4127i | 0.317976 | + | 0.978629i | ||||
\(137\) | −9.16267 | − | 12.6113i | −0.782819 | − | 1.07746i | −0.994965 | − | 0.100220i | \(-0.968045\pi\) |
0.212146 | − | 0.977238i | \(-0.431955\pi\) | |||||||
\(138\) | −3.84062 | − | 36.5411i | −0.326935 | − | 3.11058i | ||||
\(139\) | −14.7950 | + | 4.80718i | −1.25489 | + | 0.407739i | −0.859672 | − | 0.510847i | \(-0.829332\pi\) |
−0.395221 | + | 0.918586i | \(0.629332\pi\) | |||||||
\(140\) | 3.02774 | − | 9.31841i | 0.255890 | − | 0.787550i | ||||
\(141\) | −10.9625 | + | 4.88084i | −0.923213 | + | 0.411041i | ||||
\(142\) | 4.24264i | 0.356034i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(145\) | −4.98752 | + | 6.86474i | −0.414191 | + | 0.570085i | ||||
\(146\) | 13.1782 | + | 4.28187i | 1.09064 | + | 0.354370i | ||||
\(147\) | 1.80057 | − | 8.47101i | 0.148508 | − | 0.698677i | ||||
\(148\) | −9.70820 | + | 7.05342i | −0.798009 | + | 0.579788i | ||||
\(149\) | 1.98168 | − | 1.43977i | 0.162345 | − | 0.117951i | −0.503646 | − | 0.863910i | \(-0.668009\pi\) |
0.665992 | + | 0.745959i | \(0.268009\pi\) | |||||||
\(150\) | −1.76419 | + | 8.29986i | −0.144045 | + | 0.677681i | ||||
\(151\) | −9.41498 | − | 3.05911i | −0.766180 | − | 0.248947i | −0.100251 | − | 0.994962i | \(-0.531965\pi\) |
−0.665929 | + | 0.746015i | \(0.731965\pi\) | |||||||
\(152\) | 8.14459 | − | 11.2101i | 0.660614 | − | 0.909257i | ||||
\(153\) | −3.67423 | − | 6.36396i | −0.297044 | − | 0.514496i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.19615i | − | 0.417365i | ||||||
\(156\) | −17.9018 | + | 7.97038i | −1.43329 | + | 0.638141i | ||||
\(157\) | 4.63525 | − | 14.2658i | 0.369934 | − | 1.13854i | −0.576900 | − | 0.816815i | \(-0.695738\pi\) |
0.946834 | − | 0.321724i | \(-0.104262\pi\) | |||||||
\(158\) | 23.0619 | − | 7.49326i | 1.83471 | − | 0.596132i | ||||
\(159\) | −0.627171 | − | 5.96713i | −0.0497379 | − | 0.473224i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.78467 | − | 11.6480i | −0.298274 | − | 0.917992i | ||||
\(162\) | −14.7513 | − | 16.3829i | −1.15897 | − | 1.28716i | ||||
\(163\) | 8.09017 | + | 5.87785i | 0.633671 | + | 0.460389i | 0.857670 | − | 0.514200i | \(-0.171911\pi\) |
−0.223999 | + | 0.974589i | \(0.571911\pi\) | |||||||
\(164\) | 39.1918 | 3.06037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −15.8534 | − | 11.5182i | −1.22678 | − | 0.891304i | −0.230131 | − | 0.973160i | \(-0.573915\pi\) |
−0.996644 | + | 0.0818552i | \(0.973915\pi\) | |||||||
\(168\) | 8.02957 | + | 8.91774i | 0.619495 | + | 0.688018i | ||||
\(169\) | 1.54508 | + | 4.75528i | 0.118853 | + | 0.365791i | ||||
\(170\) | 6.10844 | + | 8.40755i | 0.468496 | + | 0.644830i | ||||
\(171\) | −3.45127 | + | 7.75169i | −0.263926 | + | 0.592787i | ||||
\(172\) | 37.6599 | − | 12.2364i | 2.87154 | − | 0.933020i | ||||
\(173\) | −0.756934 | + | 2.32960i | −0.0575486 | + | 0.177116i | −0.975699 | − | 0.219116i | \(-0.929683\pi\) |
0.918150 | + | 0.396233i | \(0.129683\pi\) | |||||||
\(174\) | −8.45386 | − | 18.9877i | −0.640886 | − | 1.43945i | ||||
\(175\) | 2.82843i | 0.213809i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | 12.4688 | − | 17.1618i | 0.934577 | − | 1.28633i | ||||
\(179\) | 14.8255 | + | 4.81710i | 1.10811 | + | 0.360047i | 0.805219 | − | 0.592978i | \(-0.202048\pi\) |
0.302892 | + | 0.953025i | \(0.402048\pi\) | |||||||
\(180\) | 15.4460 | + | 13.9076i | 1.15128 | + | 1.03661i | ||||
\(181\) | 4.04508 | − | 2.93893i | 0.300669 | − | 0.218449i | −0.427213 | − | 0.904151i | \(-0.640505\pi\) |
0.727882 | + | 0.685702i | \(0.240505\pi\) | |||||||
\(182\) | −7.92672 | + | 5.75910i | −0.587567 | + | 0.426893i | ||||
\(183\) | 4.79193 | + | 1.01856i | 0.354229 | + | 0.0752938i | ||||
\(184\) | −40.3499 | − | 13.1105i | −2.97463 | − | 0.966517i | ||||
\(185\) | −3.05422 | + | 4.20378i | −0.224551 | + | 0.309068i | ||||
\(186\) | 11.0227 | + | 6.36396i | 0.808224 | + | 0.466628i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 27.7128i | 2.02116i | ||||||||
\(189\) | −5.94504 | − | 4.31932i | −0.432438 | − | 0.314184i | ||||
\(190\) | 3.70820 | − | 11.4127i | 0.269021 | − | 0.827963i | ||||
\(191\) | −4.94183 | + | 1.60570i | −0.357579 | + | 0.116184i | −0.482297 | − | 0.876008i | \(-0.660197\pi\) |
0.124718 | + | 0.992192i | \(0.460197\pi\) | |||||||
\(192\) | −13.7805 | + | 1.44839i | −0.994522 | + | 0.104528i | ||||
\(193\) | −8.31254 | − | 11.4412i | −0.598350 | − | 0.823558i | 0.397206 | − | 0.917729i | \(-0.369980\pi\) |
−0.995556 | + | 0.0941717i | \(0.969980\pi\) | |||||||
\(194\) | −9.84014 | − | 30.2848i | −0.706481 | − | 2.17432i | ||||
\(195\) | −6.30579 | + | 5.67776i | −0.451567 | + | 0.406593i | ||||
\(196\) | −16.1803 | − | 11.7557i | −1.15574 | − | 0.839693i | ||||
\(197\) | 7.34847 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 7.92672 | + | 5.75910i | 0.560503 | + | 0.407230i | ||||
\(201\) | 3.86149 | − | 3.47690i | 0.272369 | − | 0.245242i | ||||
\(202\) | −9.27051 | − | 28.5317i | −0.652271 | − | 2.00748i | ||||
\(203\) | −4.07230 | − | 5.60503i | −0.285819 | − | 0.393396i | ||||
\(204\) | −16.8776 | + | 1.77391i | −1.18167 | + | 0.124198i | ||||
\(205\) | 16.1400 | − | 5.24419i | 1.12726 | − | 0.366270i | ||||
\(206\) | 1.51387 | − | 4.65921i | 0.105476 | − | 0.324622i | ||||
\(207\) | 25.8384 | + | 2.71573i | 1.79590 | + | 0.188756i | ||||
\(208\) | 11.3137i | 0.784465i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.00000 | + | 5.19615i | 0.621059 | + | 0.358569i | ||||
\(211\) | 3.32502 | − | 4.57649i | 0.228904 | − | 0.315059i | −0.679080 | − | 0.734064i | \(-0.737621\pi\) |
0.907984 | + | 0.419005i | \(0.137621\pi\) | |||||||
\(212\) | −13.1782 | − | 4.28187i | −0.905084 | − | 0.294080i | ||||
\(213\) | −2.93444 | − | 0.623735i | −0.201065 | − | 0.0427376i | ||||
\(214\) | 4.85410 | − | 3.52671i | 0.331820 | − | 0.241081i | ||||
\(215\) | 13.8718 | − | 10.0784i | 0.946046 | − | 0.687342i | ||||
\(216\) | −24.2099 | + | 7.86629i | −1.64728 | + | 0.535233i | ||||
\(217\) | 4.03499 | + | 1.31105i | 0.273913 | + | 0.0889997i | ||||
\(218\) | −26.4699 | + | 36.4327i | −1.79277 | + | 2.46754i | ||||
\(219\) | −4.89898 | + | 8.48528i | −0.331042 | + | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.92820i | − | 0.466041i | ||||||
\(222\) | −5.17691 | − | 11.6275i | −0.347452 | − | 0.780389i | ||||
\(223\) | −3.39919 | + | 10.4616i | −0.227626 | + | 0.700562i | 0.770388 | + | 0.637575i | \(0.220063\pi\) |
−0.998014 | + | 0.0629866i | \(0.979937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.48127 | − | 2.44042i | −0.365418 | − | 0.162695i | ||||
\(226\) | −2.49376 | − | 3.43237i | −0.165883 | − | 0.228318i | ||||
\(227\) | 6.81241 | + | 20.9664i | 0.452155 | + | 1.39159i | 0.874443 | + | 0.485129i | \(0.161227\pi\) |
−0.422287 | + | 0.906462i | \(0.638773\pi\) | |||||||
\(228\) | 13.1122 | + | 14.5626i | 0.868379 | + | 0.964432i | ||||
\(229\) | 7.28115 | + | 5.29007i | 0.481152 | + | 0.349577i | 0.801772 | − | 0.597631i | \(-0.203891\pi\) |
−0.320619 | + | 0.947208i | \(0.603891\pi\) | |||||||
\(230\) | −36.7423 | −2.42272 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.0000 | −1.57568 | ||||||||
\(233\) | 19.8168 | + | 14.3977i | 1.29824 | + | 0.943227i | 0.999937 | − | 0.0112436i | \(-0.00357902\pi\) |
0.298304 | + | 0.954471i | \(0.403579\pi\) | |||||||
\(234\) | −4.32136 | − | 20.3304i | −0.282496 | − | 1.32904i | ||||
\(235\) | 3.70820 | + | 11.4127i | 0.241897 | + | 0.744481i | ||||
\(236\) | 4.07230 | + | 5.60503i | 0.265084 | + | 0.364857i | ||||
\(237\) | 1.79229 | + | 17.0525i | 0.116422 | + | 1.10768i | ||||
\(238\) | −8.06998 | + | 2.62210i | −0.523099 | + | 0.169965i | ||||
\(239\) | −6.81241 | + | 20.9664i | −0.440658 | + | 1.35621i | 0.446518 | + | 0.894775i | \(0.352664\pi\) |
−0.887176 | + | 0.461431i | \(0.847336\pi\) | |||||||
\(240\) | 10.9625 | − | 4.88084i | 0.707629 | − | 0.315057i | ||||
\(241\) | − | 2.82843i | − | 0.182195i | −0.995842 | − | 0.0910975i | \(-0.970963\pi\) | ||
0.995842 | − | 0.0910975i | \(-0.0290375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 6.65003 | − | 9.15298i | 0.425725 | − | 0.585960i | ||||
\(245\) | −8.23639 | − | 2.67617i | −0.526204 | − | 0.170974i | ||||
\(246\) | −8.64273 | + | 40.6608i | −0.551040 | + | 2.59244i | ||||
\(247\) | −6.47214 | + | 4.70228i | −0.411812 | + | 0.299199i | ||||
\(248\) | 11.8901 | − | 8.63864i | 0.755020 | − | 0.548554i | ||||
\(249\) | 0.882095 | − | 4.14993i | 0.0559005 | − | 0.262991i | ||||
\(250\) | 28.2449 | + | 9.17734i | 1.78637 | + | 0.580426i | ||||
\(251\) | 9.16267 | − | 12.6113i | 0.578342 | − | 0.796020i | −0.415170 | − | 0.909744i | \(-0.636278\pi\) |
0.993512 | + | 0.113724i | \(0.0362779\pi\) | |||||||
\(252\) | −14.6969 | + | 8.48528i | −0.925820 | + | 0.534522i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 6.92820i | − | 0.434714i | ||||||
\(255\) | −6.71316 | + | 2.98889i | −0.420394 | + | 0.187172i | ||||
\(256\) | −9.88854 | + | 30.4338i | −0.618034 | + | 1.90211i | ||||
\(257\) | 9.88367 | − | 3.21140i | 0.616526 | − | 0.200322i | 0.0159289 | − | 0.999873i | \(-0.494929\pi\) |
0.600597 | + | 0.799552i | \(0.294929\pi\) | |||||||
\(258\) | 4.39020 | + | 41.7699i | 0.273322 | + | 2.60048i | ||||
\(259\) | −2.49376 | − | 3.43237i | −0.154955 | − | 0.213277i | ||||
\(260\) | 6.05547 | + | 18.6368i | 0.375544 | + | 1.15581i | ||||
\(261\) | 14.3758 | − | 3.05567i | 0.889838 | − | 0.189141i | ||||
\(262\) | −24.2705 | − | 17.6336i | −1.49944 | − | 1.08940i | ||||
\(263\) | 12.2474 | 0.755210 | 0.377605 | − | 0.925967i | \(-0.376748\pi\) | ||||
0.377605 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 7.92672 | + | 5.75910i | 0.486018 | + | 0.353113i | ||||
\(267\) | 10.0370 | + | 11.1472i | 0.614252 | + | 0.682196i | ||||
\(268\) | −3.70820 | − | 11.4127i | −0.226515 | − | 0.697140i | ||||
\(269\) | 10.1807 | + | 14.0126i | 0.620731 | + | 0.854362i | 0.997406 | − | 0.0719830i | \(-0.0229327\pi\) |
−0.376675 | + | 0.926345i | \(0.622933\pi\) | |||||||
\(270\) | −17.8351 | + | 12.9580i | −1.08541 | + | 0.788597i | ||||
\(271\) | −5.37999 | + | 1.74806i | −0.326811 | + | 0.106187i | −0.467827 | − | 0.883820i | \(-0.654963\pi\) |
0.141016 | + | 0.990007i | \(0.454963\pi\) | |||||||
\(272\) | −3.02774 | + | 9.31841i | −0.183583 | + | 0.565012i | ||||
\(273\) | −2.81795 | − | 6.32923i | −0.170550 | − | 0.383062i | ||||
\(274\) | − | 38.1838i | − | 2.30677i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 30.0000 | − | 51.9615i | 1.80579 | − | 3.12772i | ||||
\(277\) | −10.8063 | + | 14.8736i | −0.649288 | + | 0.893668i | −0.999068 | − | 0.0431639i | \(-0.986256\pi\) |
0.349780 | + | 0.936832i | \(0.386256\pi\) | |||||||
\(278\) | −36.2401 | − | 11.7751i | −2.17354 | − | 0.706225i | ||||
\(279\) | −6.02218 | + | 6.68830i | −0.360538 | + | 0.400418i | ||||
\(280\) | 9.70820 | − | 7.05342i | 0.580176 | − | 0.421523i | ||||
\(281\) | −17.8351 | + | 12.9580i | −1.06395 | + | 0.773007i | −0.974816 | − | 0.223012i | \(-0.928411\pi\) |
−0.0891377 | + | 0.996019i | \(0.528411\pi\) | |||||||
\(282\) | −28.7516 | − | 6.11133i | −1.71213 | − | 0.363924i | ||||
\(283\) | −18.8300 | − | 6.11822i | −1.11932 | − | 0.363691i | −0.309815 | − | 0.950797i | \(-0.600267\pi\) |
−0.809510 | + | 0.587106i | \(0.800267\pi\) | |||||||
\(284\) | −4.07230 | + | 5.60503i | −0.241646 | + | 0.332598i | ||||
\(285\) | 7.34847 | + | 4.24264i | 0.435286 | + | 0.251312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.8564i | 0.817918i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.39919 | + | 10.4616i | −0.199952 | + | 0.615390i | ||||
\(290\) | −19.7673 | + | 6.42280i | −1.16078 | + | 0.377160i | ||||
\(291\) | 22.3933 | − | 2.35363i | 1.31272 | − | 0.137972i | ||||
\(292\) | 13.3001 | + | 18.3060i | 0.778327 | + | 1.07128i | ||||
\(293\) | 1.51387 | + | 4.65921i | 0.0884411 | + | 0.272194i | 0.985489 | − | 0.169740i | \(-0.0542927\pi\) |
−0.897048 | + | 0.441934i | \(0.854293\pi\) | |||||||
\(294\) | 15.7645 | − | 14.1944i | 0.919403 | − | 0.827834i | ||||
\(295\) | 2.42705 | + | 1.76336i | 0.141308 | + | 0.102667i | ||||
\(296\) | −14.6969 | −0.854242 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 19.8168 | + | 14.3977i | 1.14603 | + | 0.832643i | ||||
\(300\) | −10.2973 | + | 9.27175i | −0.594516 | + | 0.535304i | ||||
\(301\) | 4.32624 | + | 13.3148i | 0.249360 | + | 0.767452i | ||||
\(302\) | −14.2530 | − | 19.6176i | −0.820170 | − | 1.12887i | ||||
\(303\) | 21.0970 | − | 2.21738i | 1.21199 | − | 0.127385i | ||||
\(304\) | 10.7600 | − | 3.49613i | 0.617127 | − | 0.200517i | ||||
\(305\) | 1.51387 | − | 4.65921i | 0.0866838 | − | 0.266785i | ||||
\(306\) | 1.88151 | − | 17.9014i | 0.107559 | − | 1.02335i | ||||
\(307\) | − | 2.82843i | − | 0.161427i | −0.996737 | − | 0.0807134i | \(-0.974280\pi\) | ||
0.996737 | − | 0.0807134i | \(-0.0257199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.00000 | + | 1.73205i | 0.170664 | + | 0.0985329i | ||||
\(310\) | 7.48128 | − | 10.2971i | 0.424908 | − | 0.584836i | ||||
\(311\) | −16.4728 | − | 5.35233i | −0.934086 | − | 0.303503i | −0.197853 | − | 0.980232i | \(-0.563397\pi\) |
−0.736232 | + | 0.676729i | \(0.763397\pi\) | |||||||
\(312\) | −23.4755 | − | 4.98988i | −1.32904 | − | 0.282496i | ||||
\(313\) | 26.6976 | − | 19.3969i | 1.50904 | − | 1.09638i | 0.542432 | − | 0.840099i | \(-0.317503\pi\) |
0.966603 | − | 0.256279i | \(-0.0824966\pi\) | |||||||
\(314\) | 29.7252 | − | 21.5966i | 1.67749 | − | 1.21877i | ||||
\(315\) | −4.91709 | + | 5.46098i | −0.277046 | + | 0.307691i | ||||
\(316\) | 37.6599 | + | 12.2364i | 2.11854 | + | 0.688354i | ||||
\(317\) | −1.01807 | + | 1.40126i | −0.0571807 | + | 0.0787025i | −0.836650 | − | 0.547738i | \(-0.815489\pi\) |
0.779469 | + | 0.626441i | \(0.215489\pi\) | |||||||
\(318\) | 7.34847 | − | 12.7279i | 0.412082 | − | 0.713746i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.8564i | 0.774597i | ||||||||
\(321\) | 1.72564 | + | 3.87585i | 0.0963157 | + | 0.216329i | ||||
\(322\) | 9.27051 | − | 28.5317i | 0.516625 | − | 1.59001i | ||||
\(323\) | −6.58911 | + | 2.14093i | −0.366628 | + | 0.119125i | ||||
\(324\) | −3.76302 | − | 35.8028i | −0.209057 | − | 1.98904i | ||||
\(325\) | −3.32502 | − | 4.57649i | −0.184439 | − | 0.253858i | ||||
\(326\) | 7.56934 | + | 23.2960i | 0.419227 | + | 1.29025i | ||||
\(327\) | −21.3074 | − | 23.6642i | −1.17830 | − | 1.30864i | ||||
\(328\) | 38.8328 | + | 28.2137i | 2.14418 | + | 1.55784i | ||||
\(329\) | −9.79796 | −0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | −7.92672 | − | 5.75910i | −0.435035 | − | 0.316071i | ||||
\(333\) | 8.80333 | − | 1.87121i | 0.482419 | − | 0.102541i | ||||
\(334\) | −14.8328 | − | 45.6507i | −0.811616 | − | 2.49790i | ||||
\(335\) | −3.05422 | − | 4.20378i | −0.166870 | − | 0.229677i | ||||
\(336\) | 1.02417 | + | 9.74428i | 0.0558728 | + | 0.531594i | ||||
\(337\) | 22.8649 | − | 7.42927i | 1.24553 | − | 0.404698i | 0.389215 | − | 0.921147i | \(-0.372746\pi\) |
0.856318 | + | 0.516449i | \(0.172746\pi\) | |||||||
\(338\) | −3.78467 | + | 11.6480i | −0.205859 | + | 0.633569i | ||||
\(339\) | 2.74064 | − | 1.22021i | 0.148851 | − | 0.0662727i | ||||
\(340\) | 16.9706i | 0.920358i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −18.0000 | + | 10.3923i | −0.973329 | + | 0.561951i | ||||
\(343\) | 9.97505 | − | 13.7295i | 0.538602 | − | 0.741322i | ||||
\(344\) | 46.1238 | + | 14.9865i | 2.48683 | + | 0.808019i | ||||
\(345\) | 5.40170 | − | 25.4130i | 0.290818 | − | 1.36819i | ||||
\(346\) | −4.85410 | + | 3.52671i | −0.260958 | + | 0.189597i | ||||
\(347\) | 7.92672 | − | 5.75910i | 0.425528 | − | 0.309164i | −0.354330 | − | 0.935120i | \(-0.615291\pi\) |
0.779858 | + | 0.625956i | \(0.215291\pi\) | |||||||
\(348\) | 7.05676 | − | 33.1994i | 0.378282 | − | 1.77968i | ||||
\(349\) | −9.41498 | − | 3.05911i | −0.503972 | − | 0.163751i | 0.0459869 | − | 0.998942i | \(-0.485357\pi\) |
−0.549959 | + | 0.835192i | \(0.685357\pi\) | |||||||
\(350\) | −4.07230 | + | 5.60503i | −0.217673 | + | 0.299602i | ||||
\(351\) | 14.6969 | 0.784465 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9808i | 1.38282i | 0.722464 | + | 0.691408i | \(0.243009\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(354\) | −6.71316 | + | 2.98889i | −0.356800 | + | 0.158858i | ||||
\(355\) | −0.927051 | + | 2.85317i | −0.0492028 | + | 0.151431i | ||||
\(356\) | 32.9456 | − | 10.7047i | 1.74611 | − | 0.567346i | ||||
\(357\) | −0.627171 | − | 5.96713i | −0.0331934 | − | 0.315814i | ||||
\(358\) | 22.4439 | + | 30.8913i | 1.18619 | + | 1.63266i | ||||
\(359\) | −7.56934 | − | 23.2960i | −0.399494 | − | 1.22952i | −0.925406 | − | 0.378978i | \(-0.876276\pi\) |
0.525911 | − | 0.850539i | \(-0.323724\pi\) | |||||||
\(360\) | 5.29257 | + | 24.8996i | 0.278943 | + | 1.31232i | ||||
\(361\) | −8.89919 | − | 6.46564i | −0.468378 | − | 0.340297i | ||||
\(362\) | 12.2474 | 0.643712 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.0000 | −0.838628 | ||||||||
\(365\) | 7.92672 | + | 5.75910i | 0.414903 | + | 0.301445i | ||||
\(366\) | 8.02957 | + | 8.91774i | 0.419712 | + | 0.466138i | ||||
\(367\) | −2.16312 | − | 6.65740i | −0.112914 | − | 0.347513i | 0.878592 | − | 0.477573i | \(-0.158483\pi\) |
−0.991506 | + | 0.130059i | \(0.958483\pi\) | |||||||
\(368\) | −20.3615 | − | 28.0252i | −1.06142 | − | 1.46091i | ||||
\(369\) | −26.8526 | − | 11.9556i | −1.39789 | − | 0.622382i | ||||
\(370\) | −12.1050 | + | 3.93314i | −0.629308 | + | 0.204474i | ||||
\(371\) | 1.51387 | − | 4.65921i | 0.0785961 | − | 0.241894i | ||||
\(372\) | 8.45386 | + | 18.9877i | 0.438312 | + | 0.984466i | ||||
\(373\) | 32.5269i | 1.68418i | 0.539337 | + | 0.842090i | \(0.318675\pi\) | ||||
−0.539337 | + | 0.842090i | \(0.681325\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5000 | + | 18.1865i | −0.542218 | + | 0.939149i | ||||
\(376\) | −19.9501 | + | 27.4589i | −1.02885 | + | 1.41609i | ||||
\(377\) | 13.1782 | + | 4.28187i | 0.678713 | + | 0.220527i | ||||
\(378\) | −5.56231 | − | 17.1190i | −0.286094 | − | 0.880507i | ||||
\(379\) | −13.7533 | + | 9.99235i | −0.706459 | + | 0.513273i | −0.882029 | − | 0.471194i | \(-0.843823\pi\) |
0.175570 | + | 0.984467i | \(0.443823\pi\) | |||||||
\(380\) | 15.8534 | − | 11.5182i | 0.813264 | − | 0.590871i | ||||
\(381\) | 4.79193 | + | 1.01856i | 0.245498 | + | 0.0521822i | ||||
\(382\) | −12.1050 | − | 3.93314i | −0.619344 | − | 0.201237i | ||||
\(383\) | 13.2350 | − | 18.2164i | 0.676275 | − | 0.930813i | −0.323607 | − | 0.946192i | \(-0.604896\pi\) |
0.999882 | + | 0.0153791i | \(0.00489551\pi\) | |||||||
\(384\) | −29.3939 | − | 16.9706i | −1.50000 | − | 0.866025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 34.6410i | − | 1.76318i | ||||||
\(387\) | −29.5358 | − | 3.10434i | −1.50139 | − | 0.157802i | ||||
\(388\) | 16.0689 | − | 49.4549i | 0.815774 | − | 2.51069i | ||||
\(389\) | −21.4146 | + | 6.95803i | −1.08576 | + | 0.352786i | −0.796608 | − | 0.604496i | \(-0.793375\pi\) |
−0.289156 | + | 0.957282i | \(0.593375\pi\) | |||||||
\(390\) | −20.6707 | + | 2.17258i | −1.04670 | + | 0.110013i | ||||
\(391\) | 12.4688 | + | 17.1618i | 0.630575 | + | 0.867912i | ||||
\(392\) | −7.56934 | − | 23.2960i | −0.382309 | − | 1.17663i | ||||
\(393\) | 15.7645 | − | 14.1944i | 0.795213 | − | 0.716013i | ||||
\(394\) | 14.5623 | + | 10.5801i | 0.733638 | + | 0.533019i | ||||
\(395\) | 17.1464 | 0.862730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0000 | 1.60603 | 0.803017 | − | 0.595956i | \(-0.203227\pi\) | ||||
0.803017 | + | 0.595956i | \(0.203227\pi\) | |||||||
\(398\) | −35.6702 | − | 25.9159i | −1.78799 | − | 1.29905i | ||||
\(399\) | −5.14866 | + | 4.63587i | −0.257755 | + | 0.232084i | ||||
\(400\) | 2.47214 | + | 7.60845i | 0.123607 | + | 0.380423i | ||||
\(401\) | 6.10844 | + | 8.40755i | 0.305041 | + | 0.419853i | 0.933827 | − | 0.357726i | \(-0.116448\pi\) |
−0.628786 | + | 0.777579i | \(0.716448\pi\) | |||||||
\(402\) | 12.6582 | − | 1.33043i | 0.631333 | − | 0.0663558i | ||||
\(403\) | −8.06998 | + | 2.62210i | −0.401994 | + | 0.130616i | ||||
\(404\) | 15.1387 | − | 46.5921i | 0.753177 | − | 2.31804i | ||||
\(405\) | −6.34040 | − | 14.2408i | −0.315057 | − | 0.707629i | ||||
\(406\) | − | 16.9706i | − | 0.842235i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.0000 | − | 10.3923i | −0.891133 | − | 0.514496i | ||||
\(409\) | −10.8063 | + | 14.8736i | −0.534337 | + | 0.735452i | −0.987784 | − | 0.155831i | \(-0.950194\pi\) |
0.453446 | + | 0.891284i | \(0.350194\pi\) | |||||||
\(410\) | 39.5347 | + | 12.8456i | 1.95248 | + | 0.634399i | ||||
\(411\) | 26.4100 | + | 5.61362i | 1.30271 | + | 0.276899i | ||||
\(412\) | 6.47214 | − | 4.70228i | 0.318859 | − | 0.231665i | ||||
\(413\) | −1.98168 | + | 1.43977i | −0.0975120 | + | 0.0708466i | ||||
\(414\) | 47.2934 | + | 42.5832i | 2.32435 | + | 2.09285i | ||||
\(415\) | −4.03499 | − | 1.31105i | −0.198070 | − | 0.0643568i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4722 | − | 23.3345i | 0.659736 | − | 1.14270i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.92820i | − | 0.338465i | −0.985576 | − | 0.169232i | \(-0.945871\pi\) | ||
0.985576 | − | 0.169232i | \(-0.0541289\pi\) | |||||||
\(420\) | 6.90255 | + | 15.5034i | 0.336810 | + | 0.756488i | ||||
\(421\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(422\) | 13.1782 | − | 4.28187i | 0.641506 | − | 0.208438i | ||||
\(423\) | 8.45386 | − | 18.9877i | 0.411041 | − | 0.923213i | ||||
\(424\) | −9.97505 | − | 13.7295i | −0.484431 | − | 0.666762i | ||||
\(425\) | −1.51387 | − | 4.65921i | −0.0734334 | − | 0.226005i | ||||
\(426\) | −4.91709 | − | 5.46098i | −0.238234 | − | 0.264585i | ||||
\(427\) | 3.23607 | + | 2.35114i | 0.156604 | + | 0.113780i | ||||
\(428\) | 9.79796 | 0.473602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 42.0000 | 2.02542 | ||||||||
\(431\) | 5.94504 | + | 4.31932i | 0.286362 | + | 0.208054i | 0.721688 | − | 0.692219i | \(-0.243367\pi\) |
−0.435325 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(432\) | −19.7673 | − | 6.42280i | −0.951057 | − | 0.309017i | ||||
\(433\) | 1.54508 | + | 4.75528i | 0.0742520 | + | 0.228524i | 0.981294 | − | 0.192517i | \(-0.0616649\pi\) |
−0.907042 | + | 0.421041i | \(0.861665\pi\) | |||||||
\(434\) | 6.10844 | + | 8.40755i | 0.293215 | + | 0.403575i | ||||
\(435\) | −1.53625 | − | 14.6164i | −0.0736575 | − | 0.700804i | ||||
\(436\) | −69.9398 | + | 22.7248i | −3.34951 | + | 1.08832i | ||||
\(437\) | 7.56934 | − | 23.2960i | 0.362091 | − | 1.11440i | ||||
\(438\) | −21.9251 | + | 9.76168i | −1.04762 | + | 0.466431i | ||||
\(439\) | − | 5.65685i | − | 0.269987i | −0.990846 | − | 0.134993i | \(-0.956899\pi\) | ||
0.990846 | − | 0.134993i | \(-0.0431013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.50000 | + | 12.9904i | 0.357143 | + | 0.618590i | ||||
\(442\) | 9.97505 | − | 13.7295i | 0.474465 | − | 0.653044i | ||||
\(443\) | −24.7092 | − | 8.02850i | −1.17397 | − | 0.381445i | −0.343846 | − | 0.939026i | \(-0.611730\pi\) |
−0.830123 | + | 0.557581i | \(0.811730\pi\) | |||||||
\(444\) | 4.32136 | − | 20.3304i | 0.205083 | − | 0.964839i | ||||
\(445\) | 12.1353 | − | 8.81678i | 0.575266 | − | 0.417955i | ||||
\(446\) | −21.7985 | + | 15.8375i | −1.03219 | + | 0.749928i | ||||
\(447\) | −0.882095 | + | 4.14993i | −0.0417216 | + | 0.196285i | ||||
\(448\) | −10.7600 | − | 3.49613i | −0.508361 | − | 0.165177i | ||||
\(449\) | −7.12652 | + | 9.80881i | −0.336321 | + | 0.462906i | −0.943362 | − | 0.331764i | \(-0.892356\pi\) |
0.607041 | + | 0.794670i | \(0.292356\pi\) | |||||||
\(450\) | −7.34847 | − | 12.7279i | −0.346410 | − | 0.600000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.92820i | − | 0.325875i | ||||||
\(453\) | 15.6640 | − | 6.97408i | 0.735961 | − | 0.327671i | ||||
\(454\) | −16.6869 | + | 51.3571i | −0.783156 | + | 2.41031i | ||||
\(455\) | −6.58911 | + | 2.14093i | −0.308902 | + | 0.100368i | ||||
\(456\) | 2.50868 | + | 23.8685i | 0.117480 | + | 1.11775i | ||||
\(457\) | −18.2876 | − | 25.1707i | −0.855457 | − | 1.17744i | −0.982634 | − | 0.185556i | \(-0.940591\pi\) |
0.127177 | − | 0.991880i | \(-0.459409\pi\) | |||||||
\(458\) | 6.81241 | + | 20.9664i | 0.318323 | + | 0.979697i | ||||
\(459\) | 12.1050 | + | 3.93314i | 0.565012 | + | 0.183583i | ||||
\(460\) | −48.5410 | − | 35.2671i | −2.26324 | − | 1.64434i | ||||
\(461\) | −4.89898 | −0.228168 | −0.114084 | − | 0.993471i | \(-0.536393\pi\) | ||||
−0.114084 | + | 0.993471i | \(0.536393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0000 | 0.883005 | 0.441502 | − | 0.897260i | \(-0.354446\pi\) | ||||
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(464\) | −15.8534 | − | 11.5182i | −0.735977 | − | 0.534719i | ||||
\(465\) | 6.02218 | + | 6.68830i | 0.279272 | + | 0.310163i | ||||
\(466\) | 18.5410 | + | 57.0634i | 0.858896 | + | 2.64341i | ||||
\(467\) | 15.2711 | + | 21.0189i | 0.706663 | + | 0.972638i | 0.999862 | + | 0.0165865i | \(0.00527989\pi\) |
−0.293200 | + | 0.956051i | \(0.594720\pi\) | |||||||
\(468\) | 13.8051 | − | 31.0068i | 0.638141 | − | 1.43329i | ||||
\(469\) | 4.03499 | − | 1.31105i | 0.186319 | − | 0.0605386i | ||||
\(470\) | −9.08321 | + | 27.9552i | −0.418977 | + | 1.28948i | ||||
\(471\) | 10.5673 | + | 23.7346i | 0.486917 | + | 1.09363i | ||||
\(472\) | 8.48528i | 0.390567i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −21.0000 | + | 36.3731i | −0.964562 | + | 1.67067i | ||||
\(475\) | −3.32502 | + | 4.57649i | −0.152562 | + | 0.209984i | ||||
\(476\) | −13.1782 | − | 4.28187i | −0.604023 | − | 0.196259i | ||||
\(477\) | 7.72299 | + | 6.95381i | 0.353611 | + | 0.318393i | ||||
\(478\) | −43.6869 | + | 31.7404i | −1.99819 | + | 1.45177i | ||||
\(479\) | −23.7801 | + | 17.2773i | −1.08654 | + | 0.789419i | −0.978812 | − | 0.204761i | \(-0.934358\pi\) |
−0.107731 | + | 0.994180i | \(0.534358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.06998 | + | 2.62210i | 0.367960 | + | 0.119557i | ||||
\(482\) | 4.07230 | − | 5.60503i | 0.185488 | − | 0.255302i | ||||
\(483\) | 18.3712 | + | 10.6066i | 0.835917 | + | 0.482617i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 22.5167i | − | 1.02243i | ||||||
\(486\) | 37.9746 | + | 3.99129i | 1.72256 | + | 0.181049i | ||||
\(487\) | 8.34346 | − | 25.6785i | 0.378078 | − | 1.16361i | −0.563300 | − | 0.826252i | \(-0.690469\pi\) |
0.941378 | − | 0.337353i | \(-0.109531\pi\) | |||||||
\(488\) | 13.1782 | − | 4.28187i | 0.596550 | − | 0.193831i | ||||
\(489\) | −17.2256 | + | 1.81049i | −0.778970 | + | 0.0818730i | ||||
\(490\) | −12.4688 | − | 17.1618i | −0.563283 | − | 0.775293i | ||||
\(491\) | 7.56934 | + | 23.2960i | 0.341600 | + | 1.05134i | 0.963379 | + | 0.268143i | \(0.0864100\pi\) |
−0.621780 | + | 0.783192i | \(0.713590\pi\) | |||||||
\(492\) | −50.4463 | + | 45.4221i | −2.27430 | + | 2.04779i | ||||
\(493\) | 9.70820 | + | 7.05342i | 0.437236 | + | 0.317670i | ||||
\(494\) | −19.5959 | −0.881662 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | −1.98168 | − | 1.43977i | −0.0888904 | − | 0.0645827i | ||||
\(498\) | 7.72299 | − | 6.95381i | 0.346075 | − | 0.311608i | ||||
\(499\) | 1.85410 | + | 5.70634i | 0.0830010 | + | 0.255451i | 0.983941 | − | 0.178492i | \(-0.0571219\pi\) |
−0.900940 | + | 0.433943i | \(0.857122\pi\) | |||||||
\(500\) | 28.5061 | + | 39.2352i | 1.27483 | + | 1.75465i | ||||
\(501\) | 33.7552 | − | 3.54781i | 1.50807 | − | 0.158505i | ||||
\(502\) | 36.3149 | − | 11.7994i | 1.62081 | − | 0.526634i | ||||
\(503\) | −6.81241 | + | 20.9664i | −0.303750 | + | 0.934847i | 0.676390 | + | 0.736543i | \(0.263543\pi\) |
−0.980141 | + | 0.198304i | \(0.936457\pi\) | |||||||
\(504\) | −20.6707 | − | 2.17258i | −0.920748 | − | 0.0967746i | ||||
\(505\) | − | 21.2132i | − | 0.943975i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.50000 | − | 4.33013i | −0.333087 | − | 0.192308i | ||||
\(508\) | 6.65003 | − | 9.15298i | 0.295047 | − | 0.406098i | ||||
\(509\) | −28.0037 | − | 9.09896i | −1.24124 | − | 0.403304i | −0.386468 | − | 0.922303i | \(-0.626305\pi\) |
−0.854775 | + | 0.518998i | \(0.826305\pi\) | |||||||
\(510\) | −17.6067 | − | 3.74241i | −0.779636 | − | 0.165717i | ||||
\(511\) | −6.47214 | + | 4.70228i | −0.286310 | + | 0.208017i | ||||
\(512\) | −31.7069 | + | 23.0364i | −1.40126 | + | 1.01807i | ||||
\(513\) | −4.54160 | − | 13.9776i | −0.200517 | − | 0.617127i | ||||
\(514\) | 24.2099 | + | 7.86629i | 1.06785 | + | 0.346967i | ||||
\(515\) | 2.03615 | − | 2.80252i | 0.0897234 | − | 0.123494i | ||||
\(516\) | −34.2929 | + | 59.3970i | −1.50966 | + | 2.61481i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 10.3923i | − | 0.456612i | ||||||
\(519\) | −1.72564 | − | 3.87585i | −0.0757471 | − | 0.170131i | ||||
\(520\) | −7.41641 | + | 22.8254i | −0.325231 | + | 1.00096i | ||||
\(521\) | −37.8874 | + | 12.3104i | −1.65988 | + | 0.539327i | −0.980846 | − | 0.194783i | \(-0.937600\pi\) |
−0.679031 | + | 0.734110i | \(0.737600\pi\) | |||||||
\(522\) | 32.8876 | + | 14.6425i | 1.43945 | + | 0.640886i | ||||
\(523\) | 16.6251 | + | 22.8825i | 0.726964 | + | 1.00058i | 0.999264 | + | 0.0383675i | \(0.0122157\pi\) |
−0.272300 | + | 0.962212i | \(0.587784\pi\) | |||||||
\(524\) | −15.1387 | − | 46.5921i | −0.661336 | − | 2.03538i | ||||
\(525\) | −3.27806 | − | 3.64065i | −0.143066 | − | 0.158891i | ||||
\(526\) | 24.2705 | + | 17.6336i | 1.05824 | + | 0.768860i | ||||
\(527\) | −7.34847 | −0.320104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.0000 | −2.26087 | ||||||||
\(530\) | −11.8901 | − | 8.63864i | −0.516472 | − | 0.375239i | ||||
\(531\) | −1.08034 | − | 5.08260i | −0.0468828 | − | 0.220566i | ||||
\(532\) | 4.94427 | + | 15.2169i | 0.214361 | + | 0.659736i | ||||
\(533\) | −16.2892 | − | 22.4201i | −0.705563 | − | 0.971124i | ||||
\(534\) | 3.84062 | + | 36.5411i | 0.166200 | + | 1.58129i | ||||
\(535\) | 4.03499 | − | 1.31105i | 0.174448 | − | 0.0566816i | ||||
\(536\) | 4.54160 | − | 13.9776i | 0.196167 | − | 0.603741i | ||||
\(537\) | −24.6657 | + | 10.9819i | −1.06440 | + | 0.473904i | ||||
\(538\) | 42.4264i | 1.82913i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −36.0000 | −1.54919 | ||||||||
\(541\) | 8.31254 | − | 11.4412i | 0.357384 | − | 0.491897i | −0.592034 | − | 0.805913i | \(-0.701675\pi\) |
0.949418 | + | 0.314016i | \(0.101675\pi\) | |||||||
\(542\) | −13.1782 | − | 4.28187i | −0.566053 | − | 0.183922i | ||||
\(543\) | −1.80057 | + | 8.47101i | −0.0772698 | + | 0.363526i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.7618 | + | 18.7171i | −1.10352 | + | 0.801751i | ||||
\(546\) | 3.52838 | − | 16.5997i | 0.151001 | − | 0.710402i | ||||
\(547\) | 13.4500 | + | 4.37016i | 0.575079 | + | 0.186855i | 0.582095 | − | 0.813121i | \(-0.302233\pi\) |
−0.00701574 | + | 0.999975i | \(0.502233\pi\) | |||||||
\(548\) | 36.6507 | − | 50.4453i | 1.56564 | − | 2.15492i | ||||
\(549\) | −7.34847 | + | 4.24264i | −0.313625 | + | 0.181071i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8564i | − | 0.590303i | ||||||
\(552\) | 67.1316 | − | 29.8889i | 2.85731 | − | 1.27216i | ||||
\(553\) | −4.32624 | + | 13.3148i | −0.183970 | + | 0.566203i | ||||
\(554\) | −42.8292 | + | 13.9161i | −1.81964 | + | 0.591237i | ||||
\(555\) | −0.940756 | − | 8.95070i | −0.0399329 | − | 0.379936i | ||||
\(556\) | −36.5752 | − | 50.3414i | −1.55113 | − | 2.13495i | ||||
\(557\) | −9.84014 | − | 30.2848i | −0.416940 | − | 1.28321i | −0.910504 | − | 0.413500i | \(-0.864306\pi\) |
0.493564 | − | 0.869710i | \(-0.335694\pi\) | |||||||
\(558\) | −21.5637 | + | 4.58350i | −0.912863 | + | 0.194035i | ||||
\(559\) | −22.6525 | − | 16.4580i | −0.958098 | − | 0.696099i | ||||
\(560\) | 9.79796 | 0.414039 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.0000 | −2.27785 | ||||||||
\(563\) | 3.96336 | + | 2.87955i | 0.167036 | + | 0.121358i | 0.668163 | − | 0.744015i | \(-0.267081\pi\) |
−0.501127 | + | 0.865374i | \(0.667081\pi\) | |||||||
\(564\) | −32.1183 | − | 35.6710i | −1.35242 | − | 1.50202i | ||||
\(565\) | −0.927051 | − | 2.85317i | −0.0390013 | − | 0.120034i | ||||
\(566\) | −28.5061 | − | 39.2352i | −1.19820 | − | 1.64918i | ||||
\(567\) | 12.6582 | − | 1.33043i | 0.531594 | − | 0.0558728i | ||||
\(568\) | −8.06998 | + | 2.62210i | −0.338609 | + | 0.110021i | ||||
\(569\) | −9.08321 | + | 27.9552i | −0.380788 | + | 1.17194i | 0.558702 | + | 0.829368i | \(0.311299\pi\) |
−0.939490 | + | 0.342576i | \(0.888701\pi\) | |||||||
\(570\) | 8.45386 | + | 18.9877i | 0.354093 | + | 0.795307i | ||||
\(571\) | − | 19.7990i | − | 0.828562i | −0.910149 | − | 0.414281i | \(-0.864033\pi\) | ||
0.910149 | − | 0.414281i | \(-0.135967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.50000 | − | 7.79423i | 0.187990 | − | 0.325609i | ||||
\(574\) | −19.9501 | + | 27.4589i | −0.832701 | + | 1.14611i | ||||
\(575\) | 16.4728 | + | 5.35233i | 0.686963 | + | 0.223208i | ||||
\(576\) | 16.0591 | − | 17.8355i | 0.669131 | − | 0.743145i | ||||
\(577\) | −2.42705 | + | 1.76336i | −0.101039 | + | 0.0734095i | −0.637158 | − | 0.770733i | \(-0.719890\pi\) |
0.536118 | + | 0.844143i | \(0.319890\pi\) | |||||||
\(578\) | −21.7985 | + | 15.8375i | −0.906697 | + | 0.658754i | ||||
\(579\) | 23.9596 | + | 5.09278i | 0.995728 | + | 0.211649i | ||||
\(580\) | −32.2799 | − | 10.4884i | −1.34035 | − | 0.435506i | ||||
\(581\) | 2.03615 | − | 2.80252i | 0.0844736 | − | 0.116268i | ||||
\(582\) | 47.7650 | + | 27.5772i | 1.97993 | + | 1.14311i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 27.7128i | 1.14676i | ||||||||
\(585\) | 1.53625 | − | 14.6164i | 0.0635161 | − | 0.604315i | ||||
\(586\) | −3.70820 | + | 11.4127i | −0.153184 | + | 0.471453i | ||||
\(587\) | 26.3565 | − | 8.56373i | 1.08785 | − | 0.353463i | 0.290433 | − | 0.956895i | \(-0.406201\pi\) |
0.797414 | + | 0.603432i | \(0.206201\pi\) | |||||||
\(588\) | 34.4512 | − | 3.62097i | 1.42075 | − | 0.149326i | ||||
\(589\) | 4.98752 | + | 6.86474i | 0.205507 | + | 0.282857i | ||||
\(590\) | 2.27080 | + | 6.98881i | 0.0934874 | + | 0.287725i | ||||
\(591\) | −9.45869 | + | 8.51664i | −0.389078 | + | 0.350328i | ||||
\(592\) | −9.70820 | − | 7.05342i | −0.399005 | − | 0.289894i | ||||
\(593\) | −19.5959 | −0.804708 | −0.402354 | − | 0.915484i | \(-0.631808\pi\) | ||||
−0.402354 | + | 0.915484i | \(0.631808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 7.92672 | + | 5.75910i | 0.324691 | + | 0.235902i | ||||
\(597\) | 23.1690 | − | 20.8614i | 0.948243 | − | 0.853801i | ||||
\(598\) | 18.5410 | + | 57.0634i | 0.758199 | + | 2.33350i | ||||
\(599\) | 12.2169 | + | 16.8151i | 0.499168 | + | 0.687046i | 0.982046 | − | 0.188641i | \(-0.0604084\pi\) |
−0.482878 | + | 0.875688i | \(0.660408\pi\) | |||||||
\(600\) | −16.8776 | + | 1.77391i | −0.689025 | + | 0.0724194i | ||||
\(601\) | 1.34500 | − | 0.437016i | 0.0548636 | − | 0.0178263i | −0.281457 | − | 0.959574i | \(-0.590818\pi\) |
0.336320 | + | 0.941748i | \(0.390818\pi\) | |||||||
\(602\) | −10.5971 | + | 32.6144i | −0.431905 | + | 1.32927i | ||||
\(603\) | −0.940756 | + | 8.95070i | −0.0383106 | + | 0.364501i | ||||
\(604\) | − | 39.5980i | − | 1.61122i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 45.0000 | + | 25.9808i | 1.82800 | + | 1.05540i | ||||
\(607\) | 5.81878 | − | 8.00886i | 0.236177 | − | 0.325070i | −0.674433 | − | 0.738336i | \(-0.735612\pi\) |
0.910610 | + | 0.413266i | \(0.135612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.7378 | + | 2.49494i | 0.475638 | + | 0.101100i | ||||
\(610\) | 9.70820 | − | 7.05342i | 0.393074 | − | 0.285585i | ||||
\(611\) | 15.8534 | − | 11.5182i | 0.641361 | − | 0.465976i | ||||
\(612\) | 19.6683 | − | 21.8439i | 0.795046 | − | 0.882988i | ||||
\(613\) | 10.7600 | + | 3.49613i | 0.434591 | + | 0.141207i | 0.518139 | − | 0.855297i | \(-0.326625\pi\) |
−0.0835475 | + | 0.996504i | \(0.526625\pi\) | |||||||
\(614\) | 4.07230 | − | 5.60503i | 0.164344 | − | 0.226201i | ||||
\(615\) | −14.6969 | + | 25.4558i | −0.592638 | + | 1.02648i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3923i | 0.418378i | 0.977875 | + | 0.209189i | \(0.0670825\pi\) | ||||
−0.977875 | + | 0.209189i | \(0.932918\pi\) | |||||||
\(618\) | 3.45127 | + | 7.75169i | 0.138831 | + | 0.311819i | ||||
\(619\) | −7.72542 | + | 23.7764i | −0.310511 | + | 0.955655i | 0.667052 | + | 0.745011i | \(0.267556\pi\) |
−0.977563 | + | 0.210643i | \(0.932444\pi\) | |||||||
\(620\) | 19.7673 | − | 6.42280i | 0.793875 | − | 0.257946i | ||||
\(621\) | −36.4058 | + | 26.4503i | −1.46091 | + | 1.06142i | ||||
\(622\) | −24.9376 | − | 34.3237i | −0.999907 | − | 1.37625i | ||||
\(623\) | 3.78467 | + | 11.6480i | 0.151630 | + | 0.466668i | ||||
\(624\) | −13.1122 | − | 14.5626i | −0.524909 | − | 0.582971i | ||||
\(625\) | 8.89919 | + | 6.46564i | 0.355967 | + | 0.258626i | ||||
\(626\) | 80.8332 | 3.23074 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 60.0000 | 2.39426 | ||||||||
\(629\) | 5.94504 | + | 4.31932i | 0.237044 | + | 0.172223i | ||||
\(630\) | −17.6067 | + | 3.74241i | −0.701466 | + | 0.149101i | ||||
\(631\) | −12.0517 | − | 37.0912i | −0.479769 | − | 1.47658i | −0.839416 | − | 0.543489i | \(-0.817103\pi\) |
0.359647 | − | 0.933088i | \(-0.382897\pi\) | |||||||
\(632\) | 28.5061 | + | 39.2352i | 1.13391 | + | 1.56069i | ||||
\(633\) | 1.02417 | + | 9.74428i | 0.0407069 | + | 0.387301i | ||||
\(634\) | −4.03499 | + | 1.31105i | −0.160250 | + | 0.0520684i | ||||
\(635\) | 1.51387 | − | 4.65921i | 0.0600760 | − | 0.184895i | ||||
\(636\) | 21.9251 | − | 9.76168i | 0.869386 | − | 0.387076i | ||||
\(637\) | 14.1421i | 0.560332i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.50000 | − | 2.59808i | 0.178017 | − | 0.102778i | ||||
\(640\) | −19.9501 | + | 27.4589i | −0.788597 | + | 1.08541i | ||||
\(641\) | 8.23639 | + | 2.67617i | 0.325318 | + | 0.105702i | 0.467123 | − | 0.884192i | \(-0.345291\pi\) |
−0.141805 | + | 0.989895i | \(0.545291\pi\) | |||||||
\(642\) | −2.16068 | + | 10.1652i | −0.0852753 | + | 0.401189i | ||||
\(643\) | −5.66312 | + | 4.11450i | −0.223332 | + | 0.162260i | −0.693825 | − | 0.720144i | \(-0.744076\pi\) |
0.470493 | + | 0.882403i | \(0.344076\pi\) | |||||||
\(644\) | 39.6336 | − | 28.7955i | 1.56178 | − | 1.13470i | ||||
\(645\) | −6.17466 | + | 29.0495i | −0.243127 | + | 1.14382i | ||||
\(646\) | −16.1400 | − | 5.24419i | −0.635018 | − | 0.206330i | ||||
\(647\) | −17.3073 | + | 23.8214i | −0.680418 | + | 0.936516i | −0.999939 | − | 0.0110637i | \(-0.996478\pi\) |
0.319520 | + | 0.947579i | \(0.396478\pi\) | |||||||
\(648\) | 22.0454 | − | 38.1838i | 0.866025 | − | 1.50000i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 13.8564i | − | 0.543493i | ||||||
\(651\) | −6.71316 | + | 2.98889i | −0.263110 | + | 0.117144i | ||||
\(652\) | −12.3607 | + | 38.0423i | −0.484082 | + | 1.48985i | ||||
\(653\) | 1.64728 | − | 0.535233i | 0.0644630 | − | 0.0209453i | −0.276608 | − | 0.960983i | \(-0.589210\pi\) |
0.341071 | + | 0.940038i | \(0.389210\pi\) | |||||||
\(654\) | −8.15322 | − | 77.5727i | −0.318816 | − | 3.03333i | ||||
\(655\) | −12.4688 | − | 17.1618i | −0.487197 | − | 0.670569i | ||||
\(656\) | 12.1109 | + | 37.2737i | 0.472853 | + | 1.45529i | ||||
\(657\) | −3.52838 | − | 16.5997i | −0.137655 | − | 0.647617i | ||||
\(658\) | −19.4164 | − | 14.1068i | −0.756930 | − | 0.549942i | ||||
\(659\) | −36.7423 | −1.43128 | −0.715639 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715639 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0000 | 0.583432 | 0.291716 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291716 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(662\) | 9.90839 | + | 7.19887i | 0.385101 | + | 0.279792i | ||||
\(663\) | 8.02957 | + | 8.91774i | 0.311843 | + | 0.346336i | ||||
\(664\) | −3.70820 | − | 11.4127i | −0.143906 | − | 0.442898i | ||||
\(665\) | 4.07230 | + | 5.60503i | 0.157917 | + | 0.217354i | ||||
\(666\) | 20.1395 | + | 8.96668i | 0.780389 | + | 0.347452i | ||||
\(667\) | −40.3499 | + | 13.1105i | −1.56235 | + | 0.507640i | ||||
\(668\) | 24.2219 | − | 74.5473i | 0.937173 | − | 2.88432i | ||||
\(669\) | −7.74937 | − | 17.4054i | −0.299608 | − | 0.672931i | ||||
\(670\) | − | 12.7279i | − | 0.491723i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.1188 | + | 26.3148i | −0.736977 | + | 1.01436i | 0.261810 | + | 0.965119i | \(0.415681\pi\) |
−0.998787 | + | 0.0492424i | \(0.984319\pi\) | |||||||
\(674\) | 56.0075 | + | 18.1979i | 2.15733 | + | 0.700958i | ||||
\(675\) | 9.88367 | − | 3.21140i | 0.380423 | − | 0.123607i | ||||
\(676\) | −16.1803 | + | 11.7557i | −0.622321 | + | 0.452143i | ||||
\(677\) | 33.6885 | − | 24.4762i | 1.29476 | − | 0.940695i | 0.294866 | − | 0.955539i | \(-0.404725\pi\) |
0.999890 | + | 0.0148435i | \(0.00472501\pi\) | |||||||
\(678\) | 7.18789 | + | 1.52783i | 0.276049 | + | 0.0586761i | ||||
\(679\) | 17.4850 | + | 5.68121i | 0.671011 | + | 0.218025i | ||||
\(680\) | −12.2169 | + | 16.8151i | −0.468496 | + | 0.644830i | ||||
\(681\) | −33.0681 | − | 19.0919i | −1.26717 | − | 0.731603i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 45.0333i | − | 1.72315i | −0.507628 | − | 0.861576i | \(-0.669478\pi\) | ||
0.507628 | − | 0.861576i | \(-0.330522\pi\) | |||||||
\(684\) | −33.7552 | − | 3.54781i | −1.29066 | − | 0.135654i | ||||
\(685\) | 8.34346 | − | 25.6785i | 0.318787 | − | 0.981126i | ||||
\(686\) | 39.5347 | − | 12.8456i | 1.50944 | − | 0.490447i | ||||
\(687\) | −15.5031 | + | 1.62944i | −0.591479 | + | 0.0621669i | ||||
\(688\) | 23.2751 | + | 32.0354i | 0.887355 | + | 1.22134i | ||||
\(689\) | 3.02774 | + | 9.31841i | 0.115348 | + | 0.355003i | ||||
\(690\) | 47.2934 | − | 42.5832i | 1.80043 | − | 1.62112i | ||||
\(691\) | −4.04508 | − | 2.93893i | −0.153882 | − | 0.111802i | 0.508180 | − | 0.861251i | \(-0.330319\pi\) |
−0.662062 | + | 0.749449i | \(0.730319\pi\) | |||||||
\(692\) | −9.79796 | −0.372463 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −21.7985 | − | 15.8375i | −0.826863 | − | 0.600751i | ||||
\(696\) | 30.8920 | − | 27.8152i | 1.17096 | − | 1.05433i | ||||
\(697\) | −7.41641 | − | 22.8254i | −0.280916 | − | 0.864572i | ||||
\(698\) | −14.2530 | − | 19.6176i | −0.539485 | − | 0.742538i | ||||
\(699\) | −42.1940 | + | 4.43477i | −1.59592 | + | 0.167738i | ||||
\(700\) | −10.7600 | + | 3.49613i | −0.406689 | + | 0.132141i | ||||
\(701\) | −8.32627 | + | 25.6256i | −0.314479 | + | 0.967867i | 0.661489 | + | 0.749955i | \(0.269925\pi\) |
−0.975968 | + | 0.217912i | \(0.930075\pi\) | |||||||
\(702\) | 29.1246 | + | 21.1603i | 1.09924 | + | 0.798643i | ||||
\(703\) | − | 8.48528i | − | 0.320028i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.0000 | − | 10.3923i | −0.677919 | − | 0.391397i | ||||
\(706\) | −37.4064 | + | 51.4855i | −1.40781 | + | 1.93768i | ||||
\(707\) | 16.4728 | + | 5.35233i | 0.619523 | + | 0.201295i | ||||
\(708\) | −11.7378 | − | 2.49494i | −0.441132 | − | 0.0937656i | ||||
\(709\) | −2.42705 | + | 1.76336i | −0.0911498 | + | 0.0662242i | −0.632427 | − | 0.774620i | \(-0.717941\pi\) |
0.541277 | + | 0.840844i | \(0.317941\pi\) | |||||||
\(710\) | −5.94504 | + | 4.31932i | −0.223113 | + | 0.162101i | ||||
\(711\) | −22.0703 | − | 19.8722i | −0.827700 | − | 0.745264i | ||||
\(712\) | 40.3499 | + | 13.1105i | 1.51218 | + | 0.491336i | ||||
\(713\) | 15.2711 | − | 21.0189i | 0.571908 | − | 0.787163i | ||||
\(714\) | 7.34847 | − | 12.7279i | 0.275010 | − | 0.476331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 62.3538i | 2.33027i | ||||||||
\(717\) | −15.5307 | − | 34.8826i | −0.580006 | − | 1.30271i | ||||
\(718\) | 18.5410 | − | 57.0634i | 0.691945 | − | 2.12959i | ||||
\(719\) | 11.5309 | − | 3.74663i | 0.430032 | − | 0.139726i | −0.0860002 | − | 0.996295i | \(-0.527409\pi\) |
0.516032 | + | 0.856569i | \(0.327409\pi\) | |||||||
\(720\) | −8.45386 | + | 18.9877i | −0.315057 | + | 0.707629i | ||||
\(721\) | 1.66251 | + | 2.28825i | 0.0619150 | + | 0.0852187i | ||||
\(722\) | −8.32627 | − | 25.6256i | −0.309872 | − | 0.953687i | ||||
\(723\) | 3.27806 | + | 3.64065i | 0.121912 | + | 0.135397i | ||||
\(724\) | 16.1803 | + | 11.7557i | 0.601338 | + | 0.436897i | ||||
\(725\) | 9.79796 | 0.363887 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.00000 | −0.111264 | −0.0556319 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556319 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(728\) | −15.8534 | − | 11.5182i | −0.587567 | − | 0.426893i | ||||
\(729\) | −8.34346 | + | 25.6785i | −0.309017 | + | 0.951057i | ||||
\(730\) | 7.41641 | + | 22.8254i | 0.274494 | + | 0.844804i | ||||
\(731\) | −14.2530 | − | 19.6176i | −0.527168 | − | 0.725584i | ||||
\(732\) | 2.04833 | + | 19.4886i | 0.0757085 | + | 0.720318i | ||||
\(733\) | −34.9699 | + | 11.3624i | −1.29164 | + | 0.419680i | −0.872667 | − | 0.488316i | \(-0.837611\pi\) |
−0.418977 | + | 0.907997i | \(0.637611\pi\) | |||||||
\(734\) | 5.29854 | − | 16.3072i | 0.195573 | − | 0.601911i | ||||
\(735\) | 13.7032 | − | 6.10105i | 0.505449 | − | 0.225041i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −36.0000 | − | 62.3538i | −1.32518 | − | 2.29528i | ||||
\(739\) | 30.7564 | − | 42.3325i | 1.13139 | − | 1.55723i | 0.345994 | − | 0.938237i | \(-0.387542\pi\) |
0.785398 | − | 0.618991i | \(-0.212458\pi\) | |||||||
\(740\) | −19.7673 | − | 6.42280i | −0.726662 | − | 0.236107i | ||||
\(741\) | 2.88091 | − | 13.5536i | 0.105833 | − | 0.497904i | ||||
\(742\) | 9.70820 | − | 7.05342i | 0.356399 | − | 0.258939i | ||||
\(743\) | −11.8901 | + | 8.63864i | −0.436204 | + | 0.316921i | −0.784125 | − | 0.620603i | \(-0.786888\pi\) |
0.347921 | + | 0.937524i | \(0.386888\pi\) | |||||||
\(744\) | −5.29257 | + | 24.8996i | −0.194035 | + | 0.912863i | ||||
\(745\) | 4.03499 | + | 1.31105i | 0.147831 | + | 0.0480331i | ||||
\(746\) | −46.8314 | + | 64.4579i | −1.71462 | + | 2.35997i | ||||
\(747\) | 3.67423 | + | 6.36396i | 0.134433 | + | 0.232845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.46410i | 0.126576i | ||||||||
\(750\) | −46.9921 | + | 20.9222i | −1.71591 | + | 0.763972i | ||||
\(751\) | 8.34346 | − | 25.6785i | 0.304457 | − | 0.937023i | −0.675422 | − | 0.737431i | \(-0.736039\pi\) |
0.979879 | − | 0.199591i | \(-0.0639615\pi\) | |||||||
\(752\) | −26.3565 | + | 8.56373i | −0.961121 | + | 0.312287i | ||||
\(753\) | 2.82227 | + | 26.8521i | 0.102849 | + | 0.978545i | ||||
\(754\) | 19.9501 | + | 27.4589i | 0.726540 | + | 0.999996i | ||||
\(755\) | −5.29854 | − | 16.3072i | −0.192834 | − | 0.593481i | ||||
\(756\) | 9.08321 | − | 27.9552i | 0.330353 | − | 1.01672i | ||||
\(757\) | 24.2705 | + | 17.6336i | 0.882127 | + | 0.640903i | 0.933813 | − | 0.357761i | \(-0.116460\pi\) |
−0.0516866 | + | 0.998663i | \(0.516460\pi\) | |||||||
\(758\) | −41.6413 | −1.51248 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.0000 | 0.870572 | ||||||||
\(761\) | −19.8168 | − | 14.3977i | −0.718358 | − | 0.521918i | 0.167501 | − | 0.985872i | \(-0.446430\pi\) |
−0.885859 | + | 0.463954i | \(0.846430\pi\) | |||||||
\(762\) | 8.02957 | + | 8.91774i | 0.290881 | + | 0.323056i | ||||
\(763\) | −8.03444 | − | 24.7275i | −0.290866 | − | 0.895194i | ||||
\(764\) | −12.2169 | − | 16.8151i | −0.441991 | − | 0.608349i | ||||
\(765\) | 5.17691 | − | 11.6275i | 0.187172 | − | 0.420394i | ||||
\(766\) | 52.4549 | − | 17.0436i | 1.89527 | − | 0.615811i | ||||
\(767\) | 1.51387 | − | 4.65921i | 0.0546626 | − | 0.168234i | ||||
\(768\) | −22.5436 | − | 50.6338i | −0.813473 | − | 1.82709i | ||||
\(769\) | 14.1421i | 0.509978i | 0.966944 | + | 0.254989i | \(0.0820719\pi\) | ||||
−0.966944 | + | 0.254989i | \(0.917928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | + | 15.5885i | −0.324127 | + | 0.561405i | ||||
\(772\) | 33.2502 | − | 45.7649i | 1.19670 | − | 1.64712i | ||||
\(773\) | −3.29456 | − | 1.07047i | −0.118497 | − | 0.0385020i | 0.249168 | − | 0.968460i | \(-0.419843\pi\) |
−0.367665 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(774\) | −54.0609 | − | 48.6767i | −1.94318 | − | 1.74965i | ||||
\(775\) | −4.85410 | + | 3.52671i | −0.174364 | + | 0.126683i | ||||
\(776\) | 51.5236 | − | 37.4341i | 1.84959 | − | 1.34381i | ||||
\(777\) | 7.18789 | + | 1.52783i | 0.257864 | + | 0.0548107i | ||||
\(778\) | −52.4549 | − | 17.0436i | −1.88060 | − | 0.611044i | ||||
\(779\) | −16.2892 | + | 22.4201i | −0.583621 | + | 0.803285i | ||||
\(780\) | −29.3939 | − | 16.9706i | −1.05247 | − | 0.607644i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 51.9615i | 1.85814i | ||||||||
\(783\) | −14.9626 | + | 20.5942i | −0.534719 | + | 0.735977i | ||||
\(784\) | 6.18034 | − | 19.0211i | 0.220726 | − | 0.679326i | ||||
\(785\) | 24.7092 | − | 8.02850i | 0.881908 | − | 0.286549i | ||||
\(786\) | 51.6769 | − | 5.43146i | 1.84325 | − | 0.193734i | ||||
\(787\) | 16.6251 | + | 22.8825i | 0.592620 | + | 0.815671i | 0.995008 | − | 0.0997979i | \(-0.0318196\pi\) |
−0.402388 | + | 0.915469i | \(0.631820\pi\) | |||||||
\(788\) | 9.08321 | + | 27.9552i | 0.323576 | + | 0.995864i | ||||
\(789\) | −15.7645 | + | 14.1944i | −0.561230 | + | 0.505334i | ||||
\(790\) | 33.9787 | + | 24.6870i | 1.20891 | + | 0.878323i | ||||
\(791\) | 2.44949 | 0.0870938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | 63.4137 | + | 46.0728i | 2.25047 | + | 1.63506i | ||||
\(795\) | 7.72299 | − | 6.95381i | 0.273906 | − | 0.246626i | ||||
\(796\) | −22.2492 | − | 68.4761i | −0.788603 | − | 2.42707i | ||||
\(797\) | −19.3434 | − | 26.6239i | −0.685179 | − | 0.943067i | 0.314803 | − | 0.949157i | \(-0.398062\pi\) |
−0.999981 | + | 0.00608970i | \(0.998062\pi\) | |||||||
\(798\) | −16.8776 | + | 1.77391i | −0.597460 | + | 0.0627956i | ||||
\(799\) | 16.1400 | − | 5.24419i | 0.570991 | − | 0.185526i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.8384 | − | 2.71573i | −0.912956 | − | 0.0959556i | ||||
\(802\) | 25.4558i | 0.898877i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 18.0000 | + | 10.3923i | 0.634811 | + | 0.366508i | ||||
\(805\) | 12.4688 | − | 17.1618i | 0.439468 | − | 0.604875i | ||||
\(806\) | −19.7673 | − | 6.42280i | −0.696275 | − | 0.226233i | ||||
\(807\) | −29.3444 | − | 6.23735i | −1.03297 | − | 0.219565i | ||||
\(808\) | 48.5410 | − | 35.2671i | 1.70767 | − | 1.24069i | ||||
\(809\) | 39.6336 | − | 28.7955i | 1.39344 | − | 1.01240i | 0.397965 | − | 0.917401i | \(-0.369717\pi\) |
0.995478 | − | 0.0949943i | \(-0.0302833\pi\) | |||||||
\(810\) | 7.93885 | − | 37.3494i | 0.278943 | − | 1.31232i | ||||
\(811\) | 14.7950 | + | 4.80718i | 0.519522 | + | 0.168803i | 0.557028 | − | 0.830494i | \(-0.311942\pi\) |
−0.0375066 | + | 0.999296i | \(0.511942\pi\) | |||||||
\(812\) | 16.2892 | − | 22.4201i | 0.571638 | − | 0.786793i | ||||
\(813\) | 4.89898 | − | 8.48528i | 0.171815 | − | 0.297592i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.3205i | 0.606711i | ||||||||
\(816\) | −6.90255 | − | 15.5034i | −0.241638 | − | 0.542727i | ||||
\(817\) | −8.65248 | + | 26.6296i | −0.302712 | + | 0.931651i | ||||
\(818\) | −42.8292 | + | 13.9161i | −1.49749 | + | 0.486564i | ||||
\(819\) | 10.9625 | + | 4.88084i | 0.383062 | + | 0.170550i | ||||
\(820\) | 39.9002 | + | 54.9179i | 1.39337 | + | 1.91782i | ||||
\(821\) | 9.84014 | + | 30.2848i | 0.343423 | + | 1.05695i | 0.962422 | + | 0.271557i | \(0.0875384\pi\) |
−0.618999 | + | 0.785392i | \(0.712462\pi\) | |||||||
\(822\) | 44.2538 | + | 49.1488i | 1.54353 | + | 1.71426i | ||||
\(823\) | −25.0795 | − | 18.2213i | −0.874217 | − | 0.635156i | 0.0574979 | − | 0.998346i | \(-0.481688\pi\) |
−0.931715 | + | 0.363190i | \(0.881688\pi\) | |||||||
\(824\) | 9.79796 | 0.341328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 3.96336 | + | 2.87955i | 0.137819 | + | 0.100132i | 0.654559 | − | 0.756011i | \(-0.272854\pi\) |
−0.516739 | + | 0.856143i | \(0.672854\pi\) | |||||||
\(828\) | 21.6068 | + | 101.652i | 0.750889 | + | 3.53265i | ||||
\(829\) | 9.57953 | + | 29.4828i | 0.332711 | + | 1.02398i | 0.967839 | + | 0.251571i | \(0.0809473\pi\) |
−0.635128 | + | 0.772407i | \(0.719053\pi\) | |||||||
\(830\) | −6.10844 | − | 8.40755i | −0.212027 | − | 0.291830i | ||||
\(831\) | −3.32854 | − | 31.6689i | −0.115466 | − | 1.09858i | ||||
\(832\) | 21.5200 | − | 6.99226i | 0.746070 | − | 0.242413i | ||||
\(833\) | −3.78467 | + | 11.6480i | −0.131131 | + | 0.403580i | ||||
\(834\) | 60.2940 | − | 26.8446i | 2.08781 | − | 0.929553i | ||||
\(835\) | − | 33.9411i | − | 1.17458i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 15.5885i | − | 0.538816i | ||||||
\(838\) | 9.97505 | − | 13.7295i | 0.344582 | − | 0.474277i | ||||
\(839\) | −44.4765 | − | 14.4513i | −1.53550 | − | 0.498914i | −0.585369 | − | 0.810767i | \(-0.699050\pi\) |
−0.950130 | + | 0.311853i | \(0.899050\pi\) | |||||||
\(840\) | −4.32136 | + | 20.3304i | −0.149101 | + | 0.701466i | ||||
\(841\) | 4.04508 | − | 2.93893i | 0.139486 | − | 0.101342i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.93885 | − | 37.3494i | 0.273429 | − | 1.28638i | ||||
\(844\) | 21.5200 | + | 6.99226i | 0.740747 | + | 0.240683i | ||||
\(845\) | −5.09037 | + | 7.00629i | −0.175114 | + | 0.241024i | ||||
\(846\) | 44.0908 | − | 25.4558i | 1.51587 | − | 0.875190i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 13.8564i | − | 0.475831i | ||||||
\(849\) | 31.3281 | − | 13.9482i | 1.07518 | − | 0.478700i | ||||
\(850\) | 3.70820 | − | 11.4127i | 0.127190 | − | 0.391452i | ||||
\(851\) | −24.7092 | + | 8.02850i | −0.847020 | + | 0.275213i | ||||
\(852\) | −1.25434 | − | 11.9343i | −0.0429730 | − | 0.408861i | ||||
\(853\) | 34.0814 | + | 46.9090i | 1.16693 | + | 1.60613i | 0.681398 | + | 0.731913i | \(0.261372\pi\) |
0.485528 | + | 0.874221i | \(0.338628\pi\) | |||||||
\(854\) | 3.02774 | + | 9.31841i | 0.103607 | + | 0.318870i | ||||
\(855\) | −14.3758 | + | 3.05567i | −0.491641 | + | 0.104502i | ||||
\(856\) | 9.70820 | + | 7.05342i | 0.331820 | + | 0.241081i | ||||
\(857\) | −19.5959 | −0.669384 | −0.334692 | − | 0.942328i | \(-0.608632\pi\) | ||||
−0.334692 | + | 0.942328i | \(0.608632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0000 | 0.852989 | 0.426494 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426494 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(860\) | 55.4870 | + | 40.3137i | 1.89209 | + | 1.37468i | ||||
\(861\) | −16.0591 | − | 17.8355i | −0.547294 | − | 0.607831i | ||||
\(862\) | 5.56231 | + | 17.1190i | 0.189453 | + | 0.583076i | ||||
\(863\) | 12.2169 | + | 16.8151i | 0.415868 | + | 0.572393i | 0.964637 | − | 0.263581i | \(-0.0849036\pi\) |
−0.548770 | + | 0.835974i | \(0.684904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.03499 | + | 1.31105i | −0.137194 | + | 0.0445770i | ||||
\(866\) | −3.78467 | + | 11.6480i | −0.128608 | + | 0.395816i | ||||
\(867\) | −7.74937 | − | 17.4054i | −0.263183 | − | 0.591118i | ||||
\(868\) | 16.9706i | 0.576018i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | − | 31.1769i | 0.610257 | − | 1.05700i | ||||
\(871\) | −4.98752 | + | 6.86474i | −0.168996 | + | 0.232603i | ||||
\(872\) | −85.6585 | − | 27.8321i | −2.90076 | − | 0.942515i | ||||
\(873\) | −26.0961 | + | 28.9826i | −0.883219 | + | 0.980914i | ||||
\(874\) | 48.5410 | − | 35.2671i | 1.64192 | − | 1.19293i | ||||
\(875\) | −13.8718 | + | 10.0784i | −0.468951 | + | 0.340713i | ||||
\(876\) | −38.3354 | − | 8.14844i | −1.29523 | − | 0.275310i | ||||
\(877\) | −26.8999 | − | 8.74032i | −0.908346 | − | 0.295140i | −0.182669 | − | 0.983175i | \(-0.558474\pi\) |
−0.725678 | + | 0.688035i | \(0.758474\pi\) | |||||||
\(878\) | 8.14459 | − | 11.2101i | 0.274867 | − | 0.378321i | ||||
\(879\) | −7.34847 | − | 4.24264i | −0.247858 | − | 0.143101i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.73205i | 0.0583543i | 0.999574 | + | 0.0291771i | \(0.00928869\pi\) | ||||
−0.999574 | + | 0.0291771i | \(0.990711\pi\) | |||||||
\(882\) | −3.84062 | + | 36.5411i | −0.129320 | + | 1.23040i | ||||
\(883\) | 1.85410 | − | 5.70634i | 0.0623955 | − | 0.192034i | −0.915000 | − | 0.403455i | \(-0.867809\pi\) |
0.977395 | + | 0.211421i | \(0.0678092\pi\) | |||||||
\(884\) | 26.3565 | − | 8.56373i | 0.886463 | − | 0.288029i | ||||
\(885\) | −5.16769 | + | 0.543146i | −0.173710 | + | 0.0182576i | ||||
\(886\) | −37.4064 | − | 51.4855i | −1.25669 | − | 1.72969i | ||||
\(887\) | 6.81241 | + | 20.9664i | 0.228738 | + | 0.703984i | 0.997891 | + | 0.0649184i | \(0.0206787\pi\) |
−0.769152 | + | 0.639065i | \(0.779321\pi\) | |||||||
\(888\) | 18.9174 | − | 17.0333i | 0.634826 | − | 0.571600i | ||||
\(889\) | 3.23607 | + | 2.35114i | 0.108534 | + | 0.0788547i | ||||
\(890\) | 36.7423 | 1.23161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −44.0000 | −1.47323 | ||||||||
\(893\) | −15.8534 | − | 11.5182i | −0.530515 | − | 0.385442i | ||||
\(894\) | −7.72299 | + | 6.95381i | −0.258295 | + | 0.232570i | ||||
\(895\) | 8.34346 | + | 25.6785i | 0.278891 | + | 0.858338i | ||||
\(896\) | −16.2892 | − | 22.4201i | −0.544183 | − | 0.749004i | ||||
\(897\) | −42.1940 | + | 4.43477i | −1.40882 | + | 0.148073i | ||||
\(898\) | −28.2449 | + | 9.17734i | −0.942546 | + | 0.306252i | ||||
\(899\) | 4.54160 | − | 13.9776i | 0.151471 | − | 0.466180i | ||||
\(900\) | 2.50868 | − | 23.8685i | 0.0836228 | − | 0.795618i | ||||
\(901\) | 8.48528i | 0.282686i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.0000 | − | 12.1244i | −0.698836 | − | 0.403473i | ||||
\(904\) | 4.98752 | − | 6.86474i | 0.165883 | − | 0.228318i | ||||
\(905\) | 8.23639 | + | 2.67617i | 0.273787 | + | 0.0889588i | ||||
\(906\) | 41.0822 | + | 8.73229i | 1.36486 | + | 0.290111i | ||||
\(907\) | −17.7984 | + | 12.9313i | −0.590985 | + | 0.429376i | −0.842668 | − | 0.538434i | \(-0.819016\pi\) |
0.251682 | + | 0.967810i | \(0.419016\pi\) | |||||||
\(908\) | −71.3404 | + | 51.8319i | −2.36752 | + | 1.72010i | ||||
\(909\) | −24.5854 | + | 27.3049i | −0.815447 | + | 0.905646i | ||||
\(910\) | −16.1400 | − | 5.24419i | −0.535035 | − | 0.173843i | ||||
\(911\) | 2.03615 | − | 2.80252i | 0.0674606 | − | 0.0928515i | −0.773954 | − | 0.633242i | \(-0.781724\pi\) |
0.841414 | + | 0.540391i | \(0.181724\pi\) | |||||||
\(912\) | −9.79796 | + | 16.9706i | −0.324443 | + | 0.561951i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 76.2102i | − | 2.52081i | ||||||
\(915\) | 3.45127 | + | 7.75169i | 0.114096 | + | 0.256263i | ||||
\(916\) | −11.1246 | + | 34.2380i | −0.367568 | + | 1.13126i | ||||
\(917\) | 16.4728 | − | 5.35233i | 0.543979 | − | 0.176750i | ||||
\(918\) | 18.3253 | + | 25.2227i | 0.604826 | + | 0.832472i | ||||
\(919\) | −4.15627 | − | 5.72061i | −0.137103 | − | 0.188706i | 0.734945 | − | 0.678127i | \(-0.237208\pi\) |
−0.872047 | + | 0.489421i | \(0.837208\pi\) | |||||||
\(920\) | −22.7080 | − | 69.8881i | −0.748661 | − | 2.30414i | ||||
\(921\) | 3.27806 | + | 3.64065i | 0.108016 | + | 0.119964i | ||||
\(922\) | −9.70820 | − | 7.05342i | −0.319723 | − | 0.232292i | ||||
\(923\) | 4.89898 | 0.161252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 37.6519 | + | 27.3557i | 1.23732 | + | 0.898964i | ||||
\(927\) | −5.86889 | + | 1.24747i | −0.192759 | + | 0.0409723i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.4699 | + | 36.4327i | 0.868450 | + | 1.19532i | 0.979488 | + | 0.201503i | \(0.0645825\pi\) |
−0.111038 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(930\) | 2.30437 | + | 21.9246i | 0.0755634 | + | 0.718937i | ||||
\(931\) | 13.4500 | − | 4.37016i | 0.440805 | − | 0.143226i | ||||
\(932\) | −30.2774 | + | 93.1841i | −0.991768 | + | 3.05235i | ||||
\(933\) | 27.4064 | − | 12.2021i | 0.897244 | − | 0.399479i | ||||
\(934\) | 63.6396i | 2.08235i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 36.0000 | − | 20.7846i | 1.17670 | − | 0.679366i | ||||
\(937\) | −33.2502 | + | 45.7649i | −1.08624 | + | 1.49507i | −0.233769 | + | 0.972292i | \(0.575106\pi\) |
−0.852466 | + | 0.522782i | \(0.824894\pi\) | |||||||
\(938\) | 9.88367 | + | 3.21140i | 0.322713 | + | 0.104856i | ||||
\(939\) | −11.8837 | + | 55.9086i | −0.387811 | + | 1.82451i | ||||
\(940\) | −38.8328 | + | 28.2137i | −1.26659 | + | 0.920229i | ||||
\(941\) | −5.94504 | + | 4.31932i | −0.193803 | + | 0.140806i | −0.680455 | − | 0.732790i | \(-0.738218\pi\) |
0.486652 | + | 0.873596i | \(0.338218\pi\) | |||||||
\(942\) | −13.2314 | + | 62.2489i | −0.431103 | + | 2.02818i | ||||
\(943\) | 80.6998 | + | 26.2210i | 2.62795 | + | 0.853872i | ||||
\(944\) | −4.07230 | + | 5.60503i | −0.132542 | + | 0.182428i | ||||
\(945\) | − | 12.7279i | − | 0.414039i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.2295i | 1.63224i | 0.577883 | + | 0.816119i | \(0.303879\pi\) | ||||
−0.577883 | + | 0.816119i | \(0.696121\pi\) | |||||||
\(948\) | −62.6562 | + | 27.8963i | −2.03498 | + | 0.906030i | ||||
\(949\) | 4.94427 | − | 15.2169i | 0.160498 | − | 0.493962i | ||||
\(950\) | −13.1782 | + | 4.28187i | −0.427558 | + | 0.138922i | ||||
\(951\) | −0.313585 | − | 2.98357i | −0.0101687 | − | 0.0967487i | ||||
\(952\) | −9.97505 | − | 13.7295i | −0.323293 | − | 0.444975i | ||||
\(953\) | −2.27080 | − | 6.98881i | −0.0735585 | − | 0.226390i | 0.907517 | − | 0.420015i | \(-0.137975\pi\) |
−0.981075 | + | 0.193626i | \(0.937975\pi\) | |||||||
\(954\) | 5.29257 | + | 24.8996i | 0.171353 | + | 0.806153i | ||||
\(955\) | −7.28115 | − | 5.29007i | −0.235613 | − | 0.171183i | ||||
\(956\) | −88.1816 | −2.85200 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −72.0000 | −2.32621 | ||||||||
\(959\) | 17.8351 | + | 12.9580i | 0.575926 | + | 0.418435i | ||||
\(960\) | −16.0591 | − | 17.8355i | −0.518306 | − | 0.575638i | ||||
\(961\) | −6.79837 | − | 20.9232i | −0.219302 | − | 0.674943i | ||||
\(962\) | 12.2169 | + | 16.8151i | 0.393888 | + | 0.542141i | ||||
\(963\) | −6.71316 | − | 2.98889i | −0.216329 | − | 0.0963157i | ||||
\(964\) | 10.7600 | − | 3.49613i | 0.346555 | − | 0.112603i | ||||
\(965\) | 7.56934 | − | 23.2960i | 0.243666 | − | 0.749926i | ||||
\(966\) | 21.1347 | + | 47.4692i | 0.679996 | + | 1.52730i | ||||
\(967\) | − | 31.1127i | − | 1.00052i | −0.865876 | − | 0.500258i | \(-0.833238\pi\) | ||
0.865876 | − | 0.500258i | \(-0.166762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | 32.4189 | − | 44.6208i | 1.04091 | − | 1.43269i | ||||
\(971\) | 37.8874 | + | 12.3104i | 1.21586 | + | 0.395058i | 0.845574 | − | 0.533858i | \(-0.179258\pi\) |
0.370290 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(972\) | 46.3379 | + | 41.7229i | 1.48629 | + | 1.33826i | ||||
\(973\) | 17.7984 | − | 12.9313i | 0.570590 | − | 0.414558i | ||||
\(974\) | 53.5053 | − | 38.8739i | 1.71442 | − | 1.24560i | ||||
\(975\) | 9.58385 | + | 2.03711i | 0.306929 | + | 0.0652397i | ||||
\(976\) | 10.7600 | + | 3.49613i | 0.344418 | + | 0.111908i | ||||
\(977\) | −21.3796 | + | 29.4264i | −0.683992 | + | 0.941435i | −0.999973 | − | 0.00733075i | \(-0.997667\pi\) |
0.315981 | + | 0.948766i | \(0.397667\pi\) | |||||||
\(978\) | −36.7423 | − | 21.2132i | −1.17489 | − | 0.678323i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 34.6410i | − | 1.10657i | ||||||
\(981\) | 54.8522 | + | 5.76520i | 1.75130 | + | 0.184069i | ||||
\(982\) | −18.5410 | + | 57.0634i | −0.591668 | + | 1.82097i | ||||
\(983\) | 1.64728 | − | 0.535233i | 0.0525400 | − | 0.0170713i | −0.282629 | − | 0.959229i | \(-0.591207\pi\) |
0.335169 | + | 0.942158i | \(0.391207\pi\) | |||||||
\(984\) | −82.6830 | + | 8.69033i | −2.63584 | + | 0.277038i | ||||
\(985\) | 7.48128 | + | 10.2971i | 0.238374 | + | 0.328093i | ||||
\(986\) | 9.08321 | + | 27.9552i | 0.289268 | + | 0.890276i | ||||
\(987\) | 12.6116 | − | 11.3555i | 0.401431 | − | 0.361450i | ||||
\(988\) | −25.8885 | − | 18.8091i | −0.823624 | − | 0.598398i | ||||
\(989\) | 85.7321 | 2.72612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000 | 0.571789 | 0.285894 | − | 0.958261i | \(-0.407709\pi\) | ||||
0.285894 | + | 0.958261i | \(0.407709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.43582 | + | 5.79484i | −0.204235 | + | 0.183894i | ||||
\(994\) | −1.85410 | − | 5.70634i | −0.0588085 | − | 0.180994i | ||||
\(995\) | −18.3253 | − | 25.2227i | −0.580952 | − | 0.799612i | ||||
\(996\) | 16.8776 | − | 1.77391i | 0.534787 | − | 0.0562084i | ||||
\(997\) | 1.34500 | − | 0.437016i | 0.0425965 | − | 0.0138404i | −0.287641 | − | 0.957738i | \(-0.592871\pi\) |
0.330238 | + | 0.943898i | \(0.392871\pi\) | |||||||
\(998\) | −4.54160 | + | 13.9776i | −0.143762 | + | 0.442454i | ||||
\(999\) | −9.16267 | + | 12.6113i | −0.289894 | + | 0.399005i |
(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 | 363.2.f.h.161.3 | 16 | ||
3.2 | odd | 2 | inner | 363.2.f.h.161.2 | 16 | ||
11.2 | odd | 10 | inner | 363.2.f.h.215.3 | 16 | ||
11.3 | even | 5 | inner | 363.2.f.h.239.4 | 16 | ||
11.4 | even | 5 | inner | 363.2.f.h.233.2 | 16 | ||
11.5 | even | 5 | 363.2.d.c.362.1 | ✓ | 4 | ||
11.6 | odd | 10 | 363.2.d.c.362.3 | yes | 4 | ||
11.7 | odd | 10 | inner | 363.2.f.h.233.4 | 16 | ||
11.8 | odd | 10 | inner | 363.2.f.h.239.2 | 16 | ||
11.9 | even | 5 | inner | 363.2.f.h.215.1 | 16 | ||
11.10 | odd | 2 | inner | 363.2.f.h.161.1 | 16 | ||
33.2 | even | 10 | inner | 363.2.f.h.215.2 | 16 | ||
33.5 | odd | 10 | 363.2.d.c.362.4 | yes | 4 | ||
33.8 | even | 10 | inner | 363.2.f.h.239.3 | 16 | ||
33.14 | odd | 10 | inner | 363.2.f.h.239.1 | 16 | ||
33.17 | even | 10 | 363.2.d.c.362.2 | yes | 4 | ||
33.20 | odd | 10 | inner | 363.2.f.h.215.4 | 16 | ||
33.26 | odd | 10 | inner | 363.2.f.h.233.3 | 16 | ||
33.29 | even | 10 | inner | 363.2.f.h.233.1 | 16 | ||
33.32 | even | 2 | inner | 363.2.f.h.161.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.c.362.1 | ✓ | 4 | 11.5 | even | 5 | ||
363.2.d.c.362.2 | yes | 4 | 33.17 | even | 10 | ||
363.2.d.c.362.3 | yes | 4 | 11.6 | odd | 10 | ||
363.2.d.c.362.4 | yes | 4 | 33.5 | odd | 10 | ||
363.2.f.h.161.1 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.h.161.2 | 16 | 3.2 | odd | 2 | inner | ||
363.2.f.h.161.3 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.h.161.4 | 16 | 33.32 | even | 2 | inner | ||
363.2.f.h.215.1 | 16 | 11.9 | even | 5 | inner | ||
363.2.f.h.215.2 | 16 | 33.2 | even | 10 | inner | ||
363.2.f.h.215.3 | 16 | 11.2 | odd | 10 | inner | ||
363.2.f.h.215.4 | 16 | 33.20 | odd | 10 | inner | ||
363.2.f.h.233.1 | 16 | 33.29 | even | 10 | inner | ||
363.2.f.h.233.2 | 16 | 11.4 | even | 5 | inner | ||
363.2.f.h.233.3 | 16 | 33.26 | odd | 10 | inner | ||
363.2.f.h.233.4 | 16 | 11.7 | odd | 10 | inner | ||
363.2.f.h.239.1 | 16 | 33.14 | odd | 10 | inner | ||
363.2.f.h.239.2 | 16 | 11.8 | odd | 10 | inner | ||
363.2.f.h.239.3 | 16 | 33.8 | even | 10 | inner | ||
363.2.f.h.239.4 | 16 | 11.3 | even | 5 | inner |