Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(121,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.bg (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.38363328.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.247423 + 2.63416i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 840.121 |
Dual form | 840.2.bg.i.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40496 | − | 1.10280i | −0.908989 | − | 0.416821i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.90496 | − | 3.29948i | −0.574366 | − | 0.994832i | −0.996110 | − | 0.0881168i | \(-0.971915\pi\) |
0.421744 | − | 0.906715i | \(-0.361418\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.31507 | 1.19679 | 0.598393 | − | 0.801203i | \(-0.295806\pi\) | ||||
0.598393 | + | 0.801203i | \(0.295806\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.657535 | + | 1.13888i | 0.159476 | + | 0.276220i | 0.934680 | − | 0.355491i | \(-0.115686\pi\) |
−0.775204 | + | 0.631711i | \(0.782353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.81507 | + | 6.60790i | −0.875237 | + | 1.51596i | −0.0187273 | + | 0.999825i | \(0.505961\pi\) |
−0.856510 | + | 0.516131i | \(0.827372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.247423 | + | 2.63416i | 0.0539921 | + | 0.574820i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.41011 | + | 5.90649i | −0.711058 | + | 1.23159i | 0.253403 | + | 0.967361i | \(0.418450\pi\) |
−0.964461 | + | 0.264227i | \(0.914883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.30476 | −0.799374 | −0.399687 | − | 0.916652i | \(-0.630881\pi\) | ||||
−0.399687 | + | 0.916652i | \(0.630881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.747423 | − | 1.29457i | −0.134241 | − | 0.232512i | 0.791066 | − | 0.611731i | \(-0.209526\pi\) |
−0.925307 | + | 0.379218i | \(0.876193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.90496 | + | 3.29948i | −0.331611 | + | 0.574366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.15754 | − | 1.53135i | 0.364690 | − | 0.258846i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.65238 | + | 8.05816i | −0.764847 | + | 1.32475i | 0.175481 | + | 0.984483i | \(0.443852\pi\) |
−0.940328 | + | 0.340271i | \(0.889481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.15754 | − | 3.73696i | −0.345482 | − | 0.598393i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.4401 | −1.63046 | −0.815231 | − | 0.579135i | \(-0.803390\pi\) | ||||
−0.815231 | + | 0.579135i | \(0.803390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.80992 | −0.733505 | −0.366753 | − | 0.930318i | \(-0.619530\pi\) | ||||
−0.366753 | + | 0.930318i | \(0.619530\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.75258 | − | 3.03555i | 0.255640 | − | 0.442781i | −0.709429 | − | 0.704776i | \(-0.751047\pi\) |
0.965069 | + | 0.261996i | \(0.0843806\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.56765 | + | 5.30439i | 0.652521 | + | 0.757771i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.657535 | − | 1.13888i | 0.0920733 | − | 0.159476i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.06765 | + | 7.04537i | 0.558734 | + | 0.967756i | 0.997602 | + | 0.0692048i | \(0.0220462\pi\) |
−0.438868 | + | 0.898551i | \(0.644620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.80992 | 0.513729 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.63014 | 1.01064 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.15238 | − | 7.19214i | −0.540594 | − | 0.936336i | −0.998870 | − | 0.0475263i | \(-0.984866\pi\) |
0.458276 | − | 0.888810i | \(-0.348467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.31507 | − | 5.74187i | 0.424451 | − | 0.735171i | −0.571918 | − | 0.820311i | \(-0.693800\pi\) |
0.996369 | + | 0.0851398i | \(0.0271337\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.15754 | − | 1.53135i | 0.271824 | − | 0.192932i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.15754 | + | 3.73696i | −0.267609 | + | 0.463513i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72003 | + | 13.3715i | 0.943152 | + | 1.63359i | 0.759410 | + | 0.650612i | \(0.225487\pi\) |
0.183741 | + | 0.982975i | \(0.441179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.82022 | 0.821059 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.32538 | −0.513328 | −0.256664 | − | 0.966501i | \(-0.582623\pi\) | ||||
−0.256664 | + | 0.966501i | \(0.582623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.91011 | − | 3.30841i | −0.223562 | − | 0.387220i | 0.732325 | − | 0.680955i | \(-0.238435\pi\) |
−0.955887 | + | 0.293735i | \(0.905102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.942661 | + | 10.0359i | 0.107426 | + | 1.14370i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06249 | − | 1.84029i | 0.119540 | − | 0.207049i | −0.800046 | − | 0.599939i | \(-0.795191\pi\) |
0.919585 | + | 0.392890i | \(0.128525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9349 | −1.20026 | −0.600131 | − | 0.799902i | \(-0.704885\pi\) | ||||
−0.600131 | + | 0.799902i | \(0.704885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31507 | −0.142639 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.15238 | + | 3.72803i | 0.230759 | + | 0.399687i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.65754 | + | 9.79914i | −0.599698 | + | 1.03871i | 0.393168 | + | 0.919467i | \(0.371379\pi\) |
−0.992865 | + | 0.119240i | \(0.961954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3776 | − | 4.75868i | −1.08786 | − | 0.498845i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.747423 | + | 1.29457i | −0.0775041 | + | 0.134241i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.81507 | − | 6.60790i | −0.391418 | − | 0.677956i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6301 | 1.07933 | 0.539664 | − | 0.841881i | \(-0.318551\pi\) | ||||
0.539664 | + | 0.841881i | \(0.318551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.80992 | 0.382911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.34246 | − | 9.25342i | −0.531595 | − | 0.920750i | −0.999320 | − | 0.0368756i | \(-0.988259\pi\) |
0.467725 | − | 0.883874i | \(-0.345074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.72003 | − | 16.8356i | 0.957743 | − | 1.65886i | 0.229780 | − | 0.973243i | \(-0.426199\pi\) |
0.727963 | − | 0.685617i | \(-0.240467\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.40496 | − | 1.10280i | −0.234700 | − | 0.107623i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.15238 | + | 8.92419i | −0.498099 | + | 0.862734i | −0.999998 | − | 0.00219314i | \(-0.999302\pi\) |
0.501898 | + | 0.864927i | \(0.332635\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.55734 | + | 6.16149i | 0.340731 | + | 0.590164i | 0.984569 | − | 0.174998i | \(-0.0559920\pi\) |
−0.643837 | + | 0.765162i | \(0.722659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.30476 | 0.883169 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41011 | − | 5.90649i | −0.317995 | − | 0.550783i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.15754 | + | 3.73696i | −0.199464 | + | 0.345482i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.325379 | − | 3.46410i | −0.0298274 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.75773 | + | 3.04448i | −0.159794 | + | 0.276771i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.22003 | + | 9.04135i | 0.470674 | + | 0.815231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9452 | 1.50364 | 0.751822 | − | 0.659366i | \(-0.229175\pi\) | ||||
0.751822 | + | 0.659366i | \(0.229175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40496 | + | 4.16551i | 0.211745 | + | 0.366753i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.55219 | − | 11.3487i | 0.572467 | − | 0.991542i | −0.423845 | − | 0.905735i | \(-0.639320\pi\) |
0.996312 | − | 0.0858072i | \(-0.0273469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4623 | − | 11.6844i | 1.42746 | − | 1.01317i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.46745 | − | 11.2020i | −0.552552 | − | 0.957048i | −0.998090 | − | 0.0617845i | \(-0.980321\pi\) |
0.445538 | − | 0.895263i | \(-0.353012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7448 | −0.996183 | −0.498091 | − | 0.867125i | \(-0.665966\pi\) | ||||
−0.498091 | + | 0.867125i | \(0.665966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.50515 | −0.295187 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.22003 | − | 14.2375i | −0.687393 | − | 1.19060i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.15238 | − | 3.72803i | 0.178746 | − | 0.309596i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.30992 | − | 6.60790i | 0.190519 | − | 0.545010i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | − | 3.46410i | 0.163846 | − | 0.283790i | −0.772399 | − | 0.635138i | \(-0.780943\pi\) |
0.936245 | + | 0.351348i | \(0.114277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.315070 | − | 0.545718i | −0.0256401 | − | 0.0444099i | 0.852921 | − | 0.522041i | \(-0.174829\pi\) |
−0.878561 | + | 0.477631i | \(0.841496\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.31507 | −0.106317 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.49485 | 0.120069 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.43751 | − | 7.68599i | −0.354152 | − | 0.613409i | 0.632821 | − | 0.774298i | \(-0.281897\pi\) |
−0.986972 | + | 0.160890i | \(0.948564\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.06765 | − | 7.04537i | 0.322585 | − | 0.558734i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.7149 | − | 10.4442i | 1.15969 | − | 0.823116i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | + | 13.8564i | −0.626608 | + | 1.08532i | 0.361619 | + | 0.932326i | \(0.382224\pi\) |
−0.988227 | + | 0.152992i | \(0.951109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.90496 | − | 3.29948i | −0.148301 | − | 0.256865i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0599 | 0.933222 | 0.466611 | − | 0.884463i | \(-0.345475\pi\) | ||||
0.466611 | + | 0.884463i | \(0.345475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.61983 | 0.432295 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.81507 | − | 6.60790i | −0.291746 | − | 0.505318i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.56249 | + | 14.8307i | −0.650994 | + | 1.12756i | 0.331888 | + | 0.943319i | \(0.392315\pi\) |
−0.982882 | + | 0.184236i | \(0.941019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.247423 | + | 2.63416i | 0.0187034 | + | 0.199124i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.15238 | + | 7.19214i | −0.312112 | + | 0.540594i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.75258 | + | 9.96376i | 0.429968 | + | 0.744726i | 0.996870 | − | 0.0790591i | \(-0.0251916\pi\) |
−0.566902 | + | 0.823785i | \(0.691858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.48454 | 0.481992 | 0.240996 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240996 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.63014 | −0.490114 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.65238 | − | 8.05816i | −0.342050 | − | 0.592448i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.50515 | − | 4.33905i | 0.183195 | − | 0.317303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.40496 | − | 1.10280i | −0.174935 | − | 0.0802172i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.61983 | − | 11.4659i | 0.478994 | − | 0.829642i | −0.520716 | − | 0.853730i | \(-0.674335\pi\) |
0.999710 | + | 0.0240878i | \(0.00766813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.73034 | − | 13.3893i | −0.556442 | − | 0.963785i | −0.997790 | − | 0.0664495i | \(-0.978833\pi\) |
0.441348 | − | 0.897336i | \(-0.354500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.31507 | 0.309009 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.4401 | −1.02881 | −0.514406 | − | 0.857547i | \(-0.671987\pi\) | ||||
−0.514406 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.19008 | − | 2.06129i | −0.0843628 | − | 0.146121i | 0.820757 | − | 0.571278i | \(-0.193552\pi\) |
−0.905120 | + | 0.425157i | \(0.860219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.72003 | − | 13.3715i | 0.544529 | − | 0.943152i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3528 | + | 4.74731i | 0.726622 | + | 0.333196i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.22003 | − | 9.04135i | 0.364583 | − | 0.631476i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.41011 | − | 5.90649i | −0.237019 | − | 0.410529i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.0702 | 2.01083 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1147 | −1.10938 | −0.554690 | − | 0.832057i | \(-0.687163\pi\) | ||||
−0.554690 | + | 0.832057i | \(0.687163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.16269 | + | 3.74589i | 0.148185 | + | 0.256664i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.40496 | − | 4.16551i | 0.164017 | − | 0.284085i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.369859 | + | 3.93766i | 0.0251077 | + | 0.267306i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.91011 | + | 3.30841i | −0.129073 | + | 0.223562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.83731 | + | 4.91437i | 0.190858 | + | 0.330576i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6095 | 0.844396 | 0.422198 | − | 0.906504i | \(-0.361259\pi\) | ||||
0.422198 | + | 0.906504i | \(0.361259\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.46745 | + | 2.54170i | 0.0973982 | + | 0.168699i | 0.910607 | − | 0.413273i | \(-0.135615\pi\) |
−0.813209 | + | 0.581972i | \(0.802281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24227 | + | 10.8119i | −0.412501 | + | 0.714472i | −0.995163 | − | 0.0982425i | \(-0.968678\pi\) |
0.582662 | + | 0.812715i | \(0.302011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.22003 | − | 5.83433i | 0.540838 | − | 0.383871i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3151 | − | 21.3303i | 0.806787 | − | 1.39740i | −0.108291 | − | 0.994119i | \(-0.534538\pi\) |
0.915078 | − | 0.403277i | \(-0.132129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.75258 | + | 3.03555i | 0.114326 | + | 0.198018i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.12499 | −0.138033 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.87756 | − | 13.6443i | −0.507438 | − | 0.878909i | −0.999963 | − | 0.00861063i | \(-0.997259\pi\) |
0.492524 | − | 0.870299i | \(-0.336074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.87756 | + | 1.30350i | −0.439391 | + | 0.0832777i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4623 | + | 28.5135i | −1.04747 | + | 1.81427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.46745 | + | 9.46990i | 0.346486 | + | 0.600131i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.82022 | −0.556728 | −0.278364 | − | 0.960476i | \(-0.589792\pi\) | ||||
−0.278364 | + | 0.960476i | \(0.589792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.9845 | 1.63363 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.657535 | + | 1.13888i | 0.0411765 | + | 0.0713197i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.46745 | + | 12.9340i | −0.465807 | + | 0.806801i | −0.999238 | − | 0.0390427i | \(-0.987569\pi\) |
0.533431 | + | 0.845844i | \(0.320903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0754 | − | 14.2489i | 1.24742 | − | 0.885382i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.15238 | − | 3.72803i | 0.133229 | − | 0.230759i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.31507 | − | 2.27777i | −0.0810907 | − | 0.140453i | 0.822628 | − | 0.568580i | \(-0.192507\pi\) |
−0.903719 | + | 0.428127i | \(0.859174\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.13529 | −0.499747 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3151 | 0.692471 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.82022 | − | 17.0091i | −0.598750 | − | 1.03706i | −0.993006 | − | 0.118064i | \(-0.962331\pi\) |
0.394256 | − | 0.919001i | \(-0.371002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.44006 | + | 12.8866i | −0.451951 | + | 0.782803i | −0.998507 | − | 0.0546200i | \(-0.982605\pi\) |
0.546556 | + | 0.837423i | \(0.315939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.06765 | + | 11.3666i | 0.0646170 | + | 0.687936i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.90496 | + | 3.29948i | −0.114873 | + | 0.198966i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.41527 | + | 4.18336i | 0.145119 | + | 0.251354i | 0.929417 | − | 0.369030i | \(-0.120310\pi\) |
−0.784298 | + | 0.620384i | \(0.786977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.49485 | 0.0894941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50515 | −0.567030 | −0.283515 | − | 0.958968i | \(-0.591501\pi\) | ||||
−0.283515 | + | 0.958968i | \(0.591501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8553 | + | 23.9981i | 0.823613 | + | 1.42654i | 0.902974 | + | 0.429694i | \(0.141379\pi\) |
−0.0793609 | + | 0.996846i | \(0.525288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.81507 | + | 6.60790i | −0.225985 | + | 0.391418i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.1079 | + | 11.5133i | 1.48207 | + | 0.679611i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.63529 | − | 13.2247i | 0.449135 | − | 0.777925i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.31507 | − | 9.20597i | −0.311575 | − | 0.539664i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.49485 | −0.145750 | −0.0728752 | − | 0.997341i | \(-0.523217\pi\) | ||||
−0.0728752 | + | 0.997341i | \(0.523217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.30476 | 0.483522 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.90496 | − | 3.29948i | −0.110537 | − | 0.191455i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.7149 | + | 25.4869i | −0.850983 | + | 1.47395i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5676 | + | 5.30439i | 0.666748 | + | 0.305740i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.34246 | + | 9.25342i | −0.306917 | + | 0.531595i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.31507 | + | 5.74187i | 0.189820 | + | 0.328779i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.21070 | 0.0690983 | 0.0345492 | − | 0.999403i | \(-0.489000\pi\) | ||||
0.0345492 | + | 0.999403i | \(0.489000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.4401 | −1.10591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6027 | − | 25.2927i | −0.828046 | − | 1.43422i | −0.899569 | − | 0.436778i | \(-0.856119\pi\) |
0.0715233 | − | 0.997439i | \(-0.477214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.404958 | − | 0.701408i | 0.0228896 | − | 0.0396459i | −0.854354 | − | 0.519692i | \(-0.826047\pi\) |
0.877243 | + | 0.480046i | \(0.159380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.247423 | + | 2.63416i | 0.0139407 | + | 0.148418i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.14207 | − | 7.17428i | 0.232642 | − | 0.402948i | −0.725943 | − | 0.687755i | \(-0.758596\pi\) |
0.958585 | + | 0.284807i | \(0.0919296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.20039 | + | 14.2035i | 0.459134 | + | 0.795243i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3048 | 0.575156 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0342 | −0.558316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15754 | − | 3.73696i | −0.119679 | − | 0.207289i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.55734 | − | 6.16149i | 0.196721 | − | 0.340731i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.56249 | + | 5.36763i | −0.416934 | + | 0.295927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9401 | + | 22.4128i | −0.711250 | + | 1.23192i | 0.253138 | + | 0.967430i | \(0.418537\pi\) |
−0.964388 | + | 0.264491i | \(0.914796\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.65238 | − | 8.05816i | −0.254949 | − | 0.441584i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.4401 | −0.843580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.6797 | −1.67123 | −0.835615 | − | 0.549315i | \(-0.814889\pi\) | ||||
−0.835615 | + | 0.549315i | \(0.814889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.84762 | + | 4.93222i | −0.154207 | + | 0.267095i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.13529 | − | 17.7941i | −0.277280 | − | 0.960789i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.41011 | + | 5.90649i | −0.183594 | + | 0.317995i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1250 | + | 26.1972i | 0.811952 | + | 1.40634i | 0.911496 | + | 0.411309i | \(0.134928\pi\) |
−0.0995443 | + | 0.995033i | \(0.531738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.9897 | 1.44473 | 0.722363 | − | 0.691515i | \(-0.243056\pi\) | ||||
0.722363 | + | 0.691515i | \(0.243056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.31507 | 0.230321 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.46745 | + | 12.9340i | 0.397452 | + | 0.688408i | 0.993411 | − | 0.114608i | \(-0.0365611\pi\) |
−0.595959 | + | 0.803015i | \(0.703228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.16269 | − | 3.74589i | 0.114784 | − | 0.198811i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.83731 | + | 2.01384i | −0.150166 | + | 0.106584i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.84762 | − | 13.5925i | 0.414181 | − | 0.717383i | −0.581161 | − | 0.813789i | \(-0.697401\pi\) |
0.995342 | + | 0.0964055i | \(0.0307345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.6095 | − | 33.9647i | −1.03208 | − | 1.78762i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.51546 | 0.184514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.82022 | 0.199960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1575 | − | 17.5934i | −0.530219 | − | 0.918366i | −0.999378 | − | 0.0352528i | \(-0.988776\pi\) |
0.469159 | − | 0.883113i | \(-0.344557\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.22003 | − | 9.04135i | 0.271744 | − | 0.470674i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.01286 | − | 21.4296i | −0.104502 | − | 1.11257i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.40496 | − | 5.89756i | 0.176302 | − | 0.305364i | −0.764309 | − | 0.644850i | \(-0.776920\pi\) |
0.940611 | + | 0.339486i | \(0.110253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.5754 | −0.956679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.2397 | −1.55331 | −0.776654 | − | 0.629928i | \(-0.783084\pi\) | ||||
−0.776654 | + | 0.629928i | \(0.783084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.47261 | − | 14.6750i | −0.434065 | − | 0.751822i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.06765 | + | 7.04537i | −0.207847 | + | 0.360002i | −0.951036 | − | 0.309080i | \(-0.899979\pi\) |
0.743189 | + | 0.669082i | \(0.233312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.16269 | − | 4.20159i | −0.466974 | − | 0.214133i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.40496 | − | 4.16551i | 0.122251 | − | 0.211745i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4675 | + | 25.0584i | 0.733529 | + | 1.27051i | 0.955366 | + | 0.295426i | \(0.0954614\pi\) |
−0.221837 | + | 0.975084i | \(0.571205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.96908 | −0.453586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1044 | −0.661028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.06249 | + | 1.84029i | 0.0534598 | + | 0.0925952i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.214874 | − | 0.372173i | 0.0107842 | − | 0.0186789i | −0.860583 | − | 0.509310i | \(-0.829901\pi\) |
0.871367 | + | 0.490631i | \(0.163234\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.3502 | − | 8.41455i | −0.918658 | − | 0.421254i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.55219 | + | 2.68846i | −0.0775124 | + | 0.134255i | −0.902176 | − | 0.431368i | \(-0.858031\pi\) |
0.824664 | + | 0.565623i | \(0.191364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.22518 | − | 5.58618i | −0.160658 | − | 0.278267i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.4504 | 1.75721 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.75773 | + | 9.97268i | 0.284701 | + | 0.493117i | 0.972537 | − | 0.232749i | \(-0.0747722\pi\) |
−0.687835 | + | 0.725867i | \(0.741439\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.46745 | + | 11.2020i | −0.319016 | + | 0.552552i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.05479 | + | 21.8760i | 0.101110 | + | 1.07645i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.46745 | − | 9.46990i | 0.268387 | − | 0.464859i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.87241 | + | 10.1713i | 0.287573 | + | 0.498091i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.86471 | −0.481922 | −0.240961 | − | 0.970535i | \(-0.577463\pi\) | ||||
−0.240961 | + | 0.970535i | \(0.577463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1353 | −1.03007 | −0.515036 | − | 0.857169i | \(-0.672221\pi\) | ||||
−0.515036 | + | 0.857169i | \(0.672221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.75258 | + | 3.03555i | 0.0852132 | + | 0.147594i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.657535 | − | 1.13888i | 0.0318951 | − | 0.0552440i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3048 | + | 10.1531i | −0.692256 | + | 0.491342i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.22003 | + | 14.2375i | −0.396867 | + | 0.687393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.0599 | + | 33.0127i | 0.918083 | + | 1.59017i | 0.802324 | + | 0.596888i | \(0.203596\pi\) |
0.115758 | + | 0.993277i | \(0.463070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.8099 | 0.807833 | 0.403917 | − | 0.914796i | \(-0.367649\pi\) | ||||
0.403917 | + | 0.914796i | \(0.367649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.30476 | −0.206398 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.0196 | − | 45.0673i | −1.24469 | − | 2.15586i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50515 | + | 7.80316i | −0.215019 | + | 0.372424i | −0.953279 | − | 0.302093i | \(-0.902315\pi\) |
0.738259 | + | 0.674517i | \(0.235648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.87756 | + | 1.30350i | −0.327503 | + | 0.0620715i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.30476 | + | 10.9202i | −0.299548 | + | 0.518833i | −0.976033 | − | 0.217624i | \(-0.930169\pi\) |
0.676484 | + | 0.736457i | \(0.263503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.65754 | − | 9.79914i | −0.268193 | − | 0.464524i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.00000 | −0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.74482 | 0.318308 | 0.159154 | − | 0.987254i | \(-0.449123\pi\) | ||||
0.159154 | + | 0.987254i | \(0.449123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.8879 | + | 34.4468i | 0.936483 | + | 1.62204i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.315070 | + | 0.545718i | −0.0148033 | + | 0.0256401i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.30992 | − | 6.60790i | 0.436456 | − | 0.309783i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0454 | + | 29.5235i | −0.797351 | + | 1.38105i | 0.123985 | + | 0.992284i | \(0.460432\pi\) |
−0.921336 | + | 0.388768i | \(0.872901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.657535 | + | 1.13888i | 0.0306911 | + | 0.0531586i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5857 | 1.47109 | 0.735545 | − | 0.677475i | \(-0.236926\pi\) | ||||
0.735545 | + | 0.677475i | \(0.236926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5857 | −1.42144 | −0.710718 | − | 0.703477i | \(-0.751630\pi\) | ||||
−0.710718 | + | 0.703477i | \(0.751630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.747423 | − | 1.29457i | −0.0346609 | − | 0.0600345i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.51546 | − | 6.08896i | 0.162676 | − | 0.281763i | −0.773151 | − | 0.634221i | \(-0.781321\pi\) |
0.935828 | + | 0.352458i | \(0.114654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.82022 | − | 40.6715i | −0.176402 | − | 1.87804i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.43751 | + | 7.68599i | −0.204470 | + | 0.354152i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.16269 | + | 15.8702i | 0.421301 | + | 0.729715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.63014 | 0.350095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.13529 | −0.372490 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.7551 | + | 27.2887i | 0.719870 | + | 1.24685i | 0.961051 | + | 0.276371i | \(0.0891320\pi\) |
−0.241181 | + | 0.970480i | \(0.577535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0754 | + | 34.7715i | −0.915357 | + | 1.58545i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.4024 | − | 7.52137i | −0.746333 | − | 0.342234i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.31507 | + | 9.20597i | −0.241345 | + | 0.418022i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0248 | + | 17.3634i | 0.454267 | + | 0.786813i | 0.998646 | − | 0.0520264i | \(-0.0165680\pi\) |
−0.544379 | + | 0.838839i | \(0.683235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.60952 | 0.208025 | 0.104012 | − | 0.994576i | \(-0.466832\pi\) | ||||
0.104012 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.83053 | − | 4.90263i | −0.127481 | − | 0.220803i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.90496 | + | 3.29948i | −0.0856215 | + | 0.148301i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.4024 | + | 4.77004i | 0.466609 | + | 0.213966i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1327 | + | 36.6029i | −0.946029 | + | 1.63857i | −0.192352 | + | 0.981326i | \(0.561611\pi\) |
−0.753677 | + | 0.657245i | \(0.771722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.02994 | − | 10.4442i | −0.269398 | − | 0.466611i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.61983 | 0.250576 | 0.125288 | − | 0.992120i | \(-0.460015\pi\) | ||||
0.125288 | + | 0.992120i | \(0.460015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.6849 | 0.475473 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.80992 | − | 4.86692i | −0.124793 | − | 0.216147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5650 | − | 25.2274i | 0.645584 | − | 1.11818i | −0.338582 | − | 0.940937i | \(-0.609947\pi\) |
0.984166 | − | 0.177248i | \(-0.0567194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.945211 | + | 10.0631i | 0.0418137 | + | 0.445164i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.81507 | + | 6.60790i | −0.168439 | + | 0.291746i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.72003 | + | 16.8356i | 0.428316 | + | 0.741864i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.3543 | −0.587323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1250 | 0.751703 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.68748 | + | 13.3151i | 0.336795 | + | 0.583345i | 0.983828 | − | 0.179116i | \(-0.0573239\pi\) |
−0.647033 | + | 0.762462i | \(0.723991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.59504 | − | 4.49474i | 0.113473 | − | 0.196541i | −0.803695 | − | 0.595041i | \(-0.797136\pi\) |
0.917168 | + | 0.398500i | \(0.130469\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.15754 | − | 1.53135i | 0.0941626 | − | 0.0668337i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.982914 | − | 1.70246i | 0.0428164 | − | 0.0741602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7577 | − | 20.3650i | −0.511206 | − | 0.885434i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.30476 | 0.360396 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.0496 | −1.95131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.15238 | − | 8.92419i | −0.222757 | − | 0.385826i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.75258 | − | 9.96376i | 0.248242 | − | 0.429968i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.80059 | − | 25.1755i | 0.379068 | − | 1.08439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24227 | + | 3.88372i | −0.0964027 | + | 0.166974i | −0.910193 | − | 0.414184i | \(-0.864067\pi\) |
0.813790 | + | 0.581158i | \(0.197400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.24227 | − | 5.61577i | −0.139139 | − | 0.240996i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.11468 | −0.304759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.650757 | −0.0278244 | −0.0139122 | − | 0.999903i | \(-0.504429\pi\) | ||||
−0.0139122 | + | 0.999903i | \(0.504429\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.31507 | + | 5.74187i | 0.141484 | + | 0.245057i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4230 | − | 28.4454i | 0.699642 | − | 1.21182i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.58473 | + | 3.25410i | −0.194963 | + | 0.138379i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.65238 | + | 8.05816i | −0.197483 | + | 0.342050i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5077 | − | 30.3242i | −0.741825 | − | 1.28488i | −0.951663 | − | 0.307143i | \(-0.900627\pi\) |
0.209838 | − | 0.977736i | \(-0.432706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.7551 | −0.877848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.01031 | −0.211535 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6301 | + | 27.0722i | 0.658732 | + | 1.14096i | 0.980944 | + | 0.194290i | \(0.0622402\pi\) |
−0.322212 | + | 0.946667i | \(0.604426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.247423 | + | 2.63416i | 0.0103908 | + | 0.110624i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.779971 | − | 1.35095i | 0.0326981 | − | 0.0566348i | −0.849213 | − | 0.528050i | \(-0.822923\pi\) |
0.881911 | + | 0.471415i | \(0.156257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.57796 | + | 7.92925i | 0.191581 | + | 0.331829i | 0.945775 | − | 0.324824i | \(-0.105305\pi\) |
−0.754193 | + | 0.656653i | \(0.771972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.2397 | −0.553095 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.82022 | 0.284423 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.415266 | + | 0.719262i | 0.0172878 | + | 0.0299433i | 0.874540 | − | 0.484954i | \(-0.161164\pi\) |
−0.857252 | + | 0.514897i | \(0.827830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.73034 | + | 13.3893i | −0.321262 | + | 0.556442i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.2980 | + | 12.0591i | 1.09102 | + | 0.500294i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.4974 | − | 26.8423i | 0.641837 | − | 1.11169i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.15754 | − | 3.73696i | −0.0892031 | − | 0.154504i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.0651 | −0.951998 | −0.475999 | − | 0.879446i | \(-0.657913\pi\) | ||||
−0.475999 | + | 0.879446i | \(0.657913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4059 | 0.469971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.22003 | + | 12.5055i | 0.296992 | + | 0.514406i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7928 | − | 20.4258i | 0.484273 | − | 0.838786i | −0.515563 | − | 0.856851i | \(-0.672417\pi\) |
0.999837 | + | 0.0180652i | \(0.00575064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.16269 | + | 1.45026i | 0.129658 | + | 0.0594551i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.19008 | + | 2.06129i | −0.0487069 | + | 0.0843628i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.190084 | + | 0.329235i | 0.00776661 | + | 0.0134522i | 0.869883 | − | 0.493259i | \(-0.164194\pi\) |
−0.862116 | + | 0.506711i | \(0.830861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.10437 | −0.249002 | −0.124501 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124501 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4401 | −0.628768 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.75773 | − | 3.04448i | −0.0714619 | − | 0.123776i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.71748 | − | 8.17091i | 0.191477 | − | 0.331647i | −0.754263 | − | 0.656572i | \(-0.772006\pi\) |
0.945740 | + | 0.324925i | \(0.105339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.06510 | − | 11.3394i | −0.0431599 | − | 0.459496i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.56249 | − | 13.0986i | 0.305946 | − | 0.529914i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0676 | − | 20.9018i | −0.487408 | − | 0.844215i | 0.512487 | − | 0.858695i | \(-0.328724\pi\) |
−0.999895 | + | 0.0144798i | \(0.995391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.4401 | −0.420984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.8595 | 1.48391 | 0.741954 | − | 0.670451i | \(-0.233899\pi\) | ||||
0.741954 | + | 0.670451i | \(0.233899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0650 | − | 27.8255i | −0.645709 | − | 1.11840i | −0.984137 | − | 0.177408i | \(-0.943229\pi\) |
0.338429 | − | 0.940992i | \(-0.390105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.41011 | + | 5.90649i | −0.136843 | + | 0.237019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.4127 | − | 17.3274i | 0.978073 | − | 0.694206i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.5351 | − | 25.1755i | −0.580476 | − | 1.00541i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2364 | −0.487898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2912 | 0.887399 | 0.443699 | − | 0.896176i | \(-0.353666\pi\) | ||||
0.443699 | + | 0.896176i | \(0.353666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.05734 | + | 13.9557i | 0.320250 | + | 0.554690i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.47261 | + | 14.6750i | −0.336225 | + | 0.582359i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7097 | + | 22.8888i | 0.780928 | + | 0.906889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.16269 | − | 3.74589i | 0.0855547 | − | 0.148185i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0196 | + | 29.4789i | 0.672235 | + | 1.16435i | 0.977269 | + | 0.212004i | \(0.0679990\pi\) |
−0.305034 | + | 0.952342i | \(0.598668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.4297 | 1.43665 | 0.718325 | − | 0.695708i | \(-0.244909\pi\) | ||||
0.718325 | + | 0.695708i | \(0.244909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.80992 | −0.189390 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0196 | + | 19.0866i | 0.433227 | + | 0.750371i | 0.997149 | − | 0.0754573i | \(-0.0240416\pi\) |
−0.563922 | + | 0.825828i | \(0.690708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.8202 | + | 27.4014i | −0.620998 | + | 1.07560i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.22518 | − | 2.28914i | 0.126405 | − | 0.0897183i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.79028 | − | 8.29701i | 0.187458 | − | 0.324687i | −0.756944 | − | 0.653480i | \(-0.773308\pi\) |
0.944402 | + | 0.328793i | \(0.106642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.55219 | + | 11.3487i | 0.256015 | + | 0.443431i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.82022 | 0.149041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2603 | −0.984001 | −0.492000 | − | 0.870595i | \(-0.663734\pi\) | ||||
−0.492000 | + | 0.870595i | \(0.663734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8827 | + | 22.3135i | 0.501080 | + | 0.867895i | 0.999999 | + | 0.00124712i | \(0.000396971\pi\) |
−0.498920 | + | 0.866648i | \(0.666270\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.83731 | − | 4.91437i | 0.110192 | − | 0.190858i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.88787 | + | 20.0990i | 0.0732085 | + | 0.779405i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6797 | − | 25.4260i | 0.568401 | − | 0.984500i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.30476 | − | 10.9202i | −0.243756 | − | 0.422198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.2603 | −0.975162 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.82022 | −0.224353 | −0.112177 | − | 0.993688i | \(-0.535782\pi\) | ||||
−0.112177 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.05056 | + | 15.6760i | −0.347841 | + | 0.602479i | −0.985866 | − | 0.167537i | \(-0.946419\pi\) |
0.638024 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.5650 | − | 11.7230i | −0.981096 | − | 0.449886i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.46745 | − | 2.54170i | 0.0562329 | − | 0.0973982i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.65754 | + | 8.06709i | 0.178216 | + | 0.308679i | 0.941269 | − | 0.337656i | \(-0.109634\pi\) |
−0.763054 | + | 0.646335i | \(0.776301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9349 | 0.494217 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4845 | 0.476315 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.5522 | + | 30.4013i | 0.668685 | + | 1.15820i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1875 | − | 33.2337i | 0.729926 | − | 1.26427i | −0.226988 | − | 0.973898i | \(-0.572888\pi\) |
0.956914 | − | 0.290372i | \(-0.0937789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.16269 | − | 4.20159i | −0.348062 | − | 0.159605i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.87241 | − | 10.1713i | 0.222753 | − | 0.385820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.86471 | − | 11.8900i | −0.260019 | − | 0.450367i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.6301 | −0.931597 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.575352 | 0.0217307 | 0.0108654 | − | 0.999941i | \(-0.496541\pi\) | ||||
0.0108654 | + | 0.999941i | \(0.496541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.4983 | − | 61.4849i | −1.33884 | − | 2.31895i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.75258 | − | 3.03555i | 0.0660059 | − | 0.114326i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.64370 | + | 28.1458i | 0.0994265 | + | 1.05853i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3151 | + | 19.5983i | −0.424946 | + | 0.736029i | −0.996415 | − | 0.0845949i | \(-0.973040\pi\) |
0.571469 | + | 0.820624i | \(0.306374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06249 | + | 1.84029i | 0.0398466 | + | 0.0690164i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1952 | 0.381813 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4401 | 0.614823 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.3151 | + | 17.8662i | −0.384687 | + | 0.666298i | −0.991726 | − | 0.128375i | \(-0.959024\pi\) |
0.607039 | + | 0.794672i | \(0.292357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.9426 | + | 29.7696i | −1.56202 | + | 1.10868i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.87756 | + | 13.6443i | −0.292970 | + | 0.507438i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.15238 | + | 3.72803i | 0.0799374 | + | 0.138456i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.27384 | 0.232684 | 0.116342 | − | 0.993209i | \(-0.462883\pi\) | ||||
0.116342 | + | 0.993209i | \(0.462883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.16269 | − | 5.47794i | −0.116976 | − | 0.202609i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.33731 | + | 5.78039i | −0.123266 | + | 0.213504i | −0.921054 | − | 0.389435i | \(-0.872670\pi\) |
0.797788 | + | 0.602939i | \(0.206004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.56765 | + | 5.30439i | 0.168480 | + | 0.195656i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.4127 | − | 50.9442i | 1.08343 | − | 1.87655i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.13014 | − | 8.88566i | −0.188715 | − | 0.326864i | 0.756107 | − | 0.654448i | \(-0.227099\pi\) |
−0.944822 | + | 0.327584i | \(0.893766\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.9246 | 1.20952 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.85115 | −0.0679121 | −0.0339560 | − | 0.999423i | \(-0.510811\pi\) | ||||
−0.0339560 | + | 0.999423i | \(0.510811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | + | 3.46410i | 0.0732743 | + | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.46745 | − | 9.46990i | 0.200044 | − | 0.346486i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.2329 | − | 15.7802i | 0.812372 | − | 0.576597i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.68233 | + | 13.3062i | −0.280332 | + | 0.485549i | −0.971466 | − | 0.237177i | \(-0.923778\pi\) |
0.691134 | + | 0.722726i | \(0.257111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.41011 | + | 7.63854i | 0.160713 | + | 0.278364i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.630141 | 0.0229332 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0206 | 1.16381 | 0.581905 | − | 0.813257i | \(-0.302308\pi\) | ||||
0.581905 | + | 0.813257i | \(0.302308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.9922 | − | 22.5032i | −0.471589 | − | 0.816815i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.70457 | + | 13.3447i | −0.279290 | + | 0.483745i | −0.971209 | − | 0.238231i | \(-0.923433\pi\) |
0.691918 | + | 0.721976i | \(0.256766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.76033 | − | 18.7412i | −0.0637284 | − | 0.678476i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.657535 | − | 1.13888i | 0.0237732 | − | 0.0411765i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.9178 | − | 31.0346i | −0.646975 | − | 1.12059i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.2500 | 1.41539 | 0.707695 | − | 0.706518i | \(-0.249735\pi\) | ||||
0.707695 | + | 0.706518i | \(0.249735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.9349 | 0.537867 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0196 | − | 19.0866i | −0.396349 | − | 0.686496i | 0.596924 | − | 0.802298i | \(-0.296390\pi\) |
−0.993272 | + | 0.115802i | \(0.963056\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.747423 | + | 1.29457i | −0.0268482 | + | 0.0465025i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.3776 | − | 10.2613i | −0.802791 | − | 0.368123i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.8296 | − | 68.9868i | 1.42704 | − | 2.47171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.23967 | + | 14.2715i | 0.294838 | + | 0.510675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.30476 | −0.153840 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.87501 | 0.316763 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.4401 | − | 42.3314i | −0.871194 | − | 1.50895i | −0.860763 | − | 0.509007i | \(-0.830013\pi\) |
−0.0104313 | − | 0.999946i | \(-0.503320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.31507 | + | 2.27777i | −0.0468177 | + | 0.0810907i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.4297 | + | 6.61682i | 0.513063 | + | 0.235267i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.3048 | − | 24.7766i | 0.507977 | − | 0.879842i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.06765 | + | 7.04537i | 0.144265 | + | 0.249874i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.1746 | 0.997994 | 0.498997 | − | 0.866604i | \(-0.333702\pi\) | ||||
0.498997 | + | 0.866604i | \(0.333702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.60952 | 0.163073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.65754 | − | 9.79914i | −0.199899 | − | 0.346236i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.27737 | + | 12.6048i | −0.256813 | + | 0.444813i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.68748 | + | 17.9655i | 0.0594759 | + | 0.633202i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.82022 | + | 17.0091i | −0.345688 | + | 0.598750i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.1275 | − | 46.9863i | −0.953753 | − | 1.65195i | −0.737195 | − | 0.675680i | \(-0.763850\pi\) |
−0.216558 | − | 0.976270i | \(-0.569483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5258 | −0.474954 | −0.237477 | − | 0.971393i | \(-0.576320\pi\) | ||||
−0.237477 | + | 0.971393i | \(0.576320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8801 | 0.521868 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | − | 13.8564i | −0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.3502 | − | 31.7834i | 0.641991 | − | 1.11196i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.30992 | − | 6.60790i | 0.325315 | − | 0.230899i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.85793 | − | 10.1462i | 0.204443 | − | 0.354106i | −0.745512 | − | 0.666492i | \(-0.767795\pi\) |
0.949955 | + | 0.312386i | \(0.101128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.50515 | + | 14.7314i | 0.296471 | + | 0.513503i | 0.975326 | − | 0.220769i | \(-0.0708568\pi\) |
−0.678855 | + | 0.734272i | \(0.737524\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.80992 | 0.132644 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3905 | 0.882913 | 0.441457 | − | 0.897283i | \(-0.354462\pi\) | ||||
0.441457 | + | 0.897283i | \(0.354462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6275 | + | 46.1202i | 0.924813 | + | 1.60182i | 0.791862 | + | 0.610700i | \(0.209112\pi\) |
0.132950 | + | 0.991123i | \(0.457555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.41527 | − | 4.18336i | 0.0837847 | − | 0.145119i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.03770 | + | 8.68985i | −0.105250 | + | 0.301085i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.02994 | + | 10.4442i | −0.208675 | + | 0.361435i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.747423 | − | 1.29457i | −0.0258347 | − | 0.0447470i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.6952 | −0.818050 | −0.409025 | − | 0.912523i | \(-0.634131\pi\) | ||||
−0.409025 | + | 0.912523i | \(0.634131\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.4690 | −0.361001 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.75258 | + | 8.23170i | 0.163687 | + | 0.283515i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.80992 | + | 4.86692i | −0.0966641 | + | 0.167427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.58473 | − | 5.38341i | 0.260615 | − | 0.184976i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.8553 | − | 23.9981i | 0.475513 | − | 0.823613i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.7303 | − | 54.9585i | −1.08770 | − | 1.88395i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5238 | 0.771201 | 0.385600 | − | 0.922666i | \(-0.373994\pi\) | ||||
0.385600 | + | 0.922666i | \(0.373994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.63014 | 0.260945 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.7380 | − | 39.3834i | −0.776717 | − | 1.34531i | −0.933825 | − | 0.357731i | \(-0.883550\pi\) |
0.157108 | − | 0.987581i | \(-0.449783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7345 | − | 35.9132i | 0.707452 | − | 1.22534i | −0.258347 | − | 0.966052i | \(-0.583178\pi\) |
0.965799 | − | 0.259291i | \(-0.0834890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.58311 | − | 27.5007i | −0.0880321 | − | 0.937223i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8331 | + | 37.8160i | −0.743207 | + | 1.28727i | 0.207821 | + | 0.978167i | \(0.433363\pi\) |
−0.951028 | + | 0.309105i | \(0.899971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.56249 | − | 14.8307i | −0.291134 | − | 0.504258i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.2706 | −0.518616 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.09602 | −0.274639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3125 | + | 57.6989i | 1.12875 | + | 1.95505i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.31507 | + | 9.20597i | −0.179888 | + | 0.311575i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.40496 | − | 1.10280i | −0.0813024 | − | 0.0372816i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7423 | + | 35.9267i | −0.700417 | + | 1.21316i | 0.267904 | + | 0.963446i | \(0.413669\pi\) |
−0.968320 | + | 0.249712i | \(0.919664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.24742 | + | 2.16060i | 0.0420745 | + | 0.0728752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0154 | 0.438500 | 0.219250 | − | 0.975669i | \(-0.429639\pi\) | ||||
0.219250 | + | 0.975669i | \(0.429639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2996 | 0.750440 | 0.375220 | − | 0.926936i | \(-0.377567\pi\) | ||||
0.375220 | + | 0.926936i | \(0.377567\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.15238 | − | 7.19214i | −0.139581 | − | 0.241761i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7722 | − | 23.8542i | 0.462426 | − | 0.800945i | −0.536656 | − | 0.843801i | \(-0.680313\pi\) |
0.999081 | + | 0.0428566i | \(0.0136459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.7525 | − | 18.6872i | −1.36680 | − | 0.626750i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.90496 | + | 3.29948i | −0.0638185 | + | 0.110537i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.3724 | + | 23.1617i | 0.447491 | + | 0.775077i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5052 | −0.384575 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.4297 | 0.982631 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.21748 | + | 5.57284i | 0.107309 | + | 0.185864i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.34924 | + | 9.26516i | −0.178209 | + | 0.308667i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.19008 | − | 12.6701i | −0.0396035 | − | 0.421634i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.24227 | + | 5.61577i | −0.107777 | + | 0.186675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1601 | − | 27.9901i | −0.536587 | − | 0.929396i | −0.999085 | − | 0.0427753i | \(-0.986380\pi\) |
0.462498 | − | 0.886620i | \(-0.346953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6849 | 0.354397 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.55474 | −0.0846422 | −0.0423211 | − | 0.999104i | \(-0.513475\pi\) | ||||
−0.0423211 | + | 0.999104i | \(0.513475\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.8305 | + | 36.0795i | 0.689390 | + | 1.19406i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.31507 | − | 5.74187i | 0.109593 | − | 0.189820i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.2731 | + | 20.0674i | −0.933661 | + | 0.662684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5573 | − | 35.6064i | 0.678124 | − | 1.17455i | −0.297421 | − | 0.954746i | \(-0.596127\pi\) |
0.975545 | − | 0.219799i | \(-0.0705401\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.605350 | − | 1.04850i | −0.0199470 | − | 0.0345492i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.6643 | −0.614343 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.30476 | 0.305939 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.72003 | + | 16.8356i | 0.319248 | + | 0.552953i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.10535 | − | 1.91452i | 0.0362654 | − | 0.0628134i | −0.847323 | − | 0.531078i | \(-0.821787\pi\) |
0.883588 | + | 0.468264i | \(0.155121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.4768 | + | 9.94590i | −1.71986 | + | 0.325964i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6027 | + | 25.2927i | −0.478072 | + | 0.828046i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.50515 | + | 4.33905i | 0.0819273 | + | 0.141902i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.7003 | −1.59097 | −0.795485 | − | 0.605973i | \(-0.792784\pi\) | ||||
−0.795485 | + | 0.605973i | \(0.792784\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.809916 | −0.0264306 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.9075 | + | 24.0885i | 0.453372 | + | 0.785263i | 0.998593 | − | 0.0530292i | \(-0.0168876\pi\) |
−0.545221 | + | 0.838292i | \(0.683554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.6018 | − | 61.6641i | 1.15935 | − | 2.00806i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.15754 | − | 1.53135i | 0.0701846 | − | 0.0498149i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.9520 | − | 32.8258i | 0.615857 | − | 1.06670i | −0.374377 | − | 0.927277i | \(-0.622143\pi\) |
0.990234 | − | 0.139419i | \(-0.0445234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.24227 | − | 14.2760i | −0.267555 | − | 0.463419i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.28415 | −0.268632 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9110 | −0.450623 | −0.225311 | − | 0.974287i | \(-0.572340\pi\) | ||||
−0.225311 | + | 0.974287i | \(0.572340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61983 | + | 11.4659i | 0.214213 | + | 0.371027i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.20039 | − | 14.2035i | 0.265081 | − | 0.459134i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.20039 | + | 34.0726i | 0.103346 | + | 1.10026i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3827 | − | 24.9116i | 0.463959 | − | 0.803600i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.15238 | − | 8.92419i | −0.166033 | − | 0.287578i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4607 | 0.497697 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.80992 | 0.154676 | 0.0773382 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773382 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.01709 | + | 8.68985i | 0.161172 | + | 0.279158i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.25773 | + | 3.91051i | −0.0724540 | + | 0.125494i | −0.899976 | − | 0.435939i | \(-0.856416\pi\) |
0.827522 | + | 0.561433i | \(0.189750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.2458 | + | 12.9522i | 0.905519 | + | 0.415229i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.15754 | + | 3.73696i | −0.0690964 | + | 0.119679i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.5480 | + | 37.3222i | 0.689380 | + | 1.19404i | 0.972039 | + | 0.234821i | \(0.0754504\pi\) |
−0.282658 | + | 0.959221i | \(0.591216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.1095 | 1.37778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.11468 | −0.227154 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.57958 | − | 13.1282i | −0.241751 | − | 0.418725i | 0.719462 | − | 0.694532i | \(-0.244388\pi\) |
−0.961213 | + | 0.275807i | \(0.911055\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.22003 | − | 12.5055i | 0.230049 | − | 0.398457i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.42975 | + | 3.86550i | 0.268322 | + | 0.123040i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.4024 | − | 28.4097i | 0.521565 | − | 0.903376i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.68233 | + | 13.3062i | 0.244037 | + | 0.422685i | 0.961860 | − | 0.273541i | \(-0.0881948\pi\) |
−0.717823 | + | 0.696225i | \(0.754861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.8801 | 0.821281 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.38017 | 0.0754564 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.4153 | − | 38.8244i | −0.709899 | − | 1.22958i | −0.964894 | − | 0.262638i | \(-0.915407\pi\) |
0.254996 | − | 0.966942i | \(-0.417926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.65238 | + | 8.05816i | −0.147195 | + | 0.254949i |
(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 | 840.2.bg.i.121.1 | ✓ | 6 | |
3.2 | odd | 2 | 2520.2.bi.o.1801.1 | 6 | |||
4.3 | odd | 2 | 1680.2.bg.u.961.3 | 6 | |||
7.2 | even | 3 | 5880.2.a.bw.1.3 | 3 | |||
7.4 | even | 3 | inner | 840.2.bg.i.361.1 | yes | 6 | |
7.5 | odd | 6 | 5880.2.a.bt.1.3 | 3 | |||
21.11 | odd | 6 | 2520.2.bi.o.361.1 | 6 | |||
28.11 | odd | 6 | 1680.2.bg.u.1201.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.i.121.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
840.2.bg.i.361.1 | yes | 6 | 7.4 | even | 3 | inner | |
1680.2.bg.u.961.3 | 6 | 4.3 | odd | 2 | |||
1680.2.bg.u.1201.3 | 6 | 28.11 | odd | 6 | |||
2520.2.bi.o.361.1 | 6 | 21.11 | odd | 6 | |||
2520.2.bi.o.1801.1 | 6 | 3.2 | odd | 2 | |||
5880.2.a.bt.1.3 | 3 | 7.5 | odd | 6 | |||
5880.2.a.bw.1.3 | 3 | 7.2 | even | 3 |