Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(449,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.f (of order \(2\), degree \(1\), 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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4337012736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 8x^{6} + 4x^{5} + 12x^{4} - 40x^{3} + 72x^{2} + 24x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.7 | ||
Root | \(2.25296 + 2.25296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.449 |
Dual form | 525.3.f.a.449.8 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.50592 | 1.75296 | 0.876481 | − | 0.481436i | \(-0.159885\pi\) | ||||
0.876481 | + | 0.481436i | \(0.159885\pi\) | |||||||
\(3\) | 2.88494 | − | 0.822876i | 0.961646 | − | 0.274292i | ||||
\(4\) | 8.29150 | 2.07288 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.1144 | − | 2.88494i | 1.68573 | − | 0.480823i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 15.0457 | 1.88071 | ||||||||
\(9\) | 7.64575 | − | 4.74789i | 0.849528 | − | 0.527544i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.01185i | − | 0.637441i | −0.947849 | − | 0.318720i | \(-0.896747\pi\) | ||
0.947849 | − | 0.318720i | \(-0.103253\pi\) | |||||||
\(12\) | 23.9205 | − | 6.82288i | 1.99337 | − | 0.568573i | ||||
\(13\) | 11.6458i | 0.895827i | 0.894077 | + | 0.447914i | \(0.147833\pi\) | ||||
−0.894077 | + | 0.447914i | \(0.852167\pi\) | |||||||
\(14\) | 9.27580i | 0.662557i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.5830 | 1.22394 | ||||||||
\(17\) | −4.52791 | −0.266348 | −0.133174 | − | 0.991093i | \(-0.542517\pi\) | ||||
−0.133174 | + | 0.991093i | \(0.542517\pi\) | |||||||
\(18\) | 26.8054 | − | 16.6458i | 1.48919 | − | 0.924764i | ||||
\(19\) | −16.2288 | −0.854145 | −0.427073 | − | 0.904217i | \(-0.640455\pi\) | ||||
−0.427073 | + | 0.904217i | \(0.640455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17712 | + | 7.63283i | 0.103673 | + | 0.363468i | ||||
\(22\) | − | 24.5830i | − | 1.11741i | ||||||
\(23\) | −25.5635 | −1.11145 | −0.555727 | − | 0.831365i | \(-0.687560\pi\) | ||||
−0.555727 | + | 0.831365i | \(0.687560\pi\) | |||||||
\(24\) | 43.4059 | − | 12.3807i | 1.80858 | − | 0.515864i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 40.8291i | 1.57035i | ||||||||
\(27\) | 18.1506 | − | 19.9889i | 0.672245 | − | 0.740329i | ||||
\(28\) | 21.9373i | 0.783473i | ||||||||
\(29\) | − | 9.49579i | − | 0.327441i | −0.986507 | − | 0.163720i | \(-0.947650\pi\) | ||
0.986507 | − | 0.163720i | \(-0.0523495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.7085 | 0.926081 | 0.463040 | − | 0.886337i | \(-0.346759\pi\) | ||||
0.463040 | + | 0.886337i | \(0.346759\pi\) | |||||||
\(32\) | 8.47380 | 0.264806 | ||||||||
\(33\) | −5.76988 | − | 20.2288i | −0.174845 | − | 0.612993i | ||||
\(34\) | −15.8745 | −0.466897 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 63.3948 | − | 39.3672i | 1.76097 | − | 1.09353i | ||||
\(37\) | − | 33.0405i | − | 0.892987i | −0.894787 | − | 0.446493i | \(-0.852673\pi\) | ||
0.894787 | − | 0.446493i | \(-0.147327\pi\) | |||||||
\(38\) | −56.8968 | −1.49728 | ||||||||
\(39\) | 9.58301 | + | 33.5973i | 0.245718 | + | 0.861469i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 67.1946i | 1.63889i | 0.573156 | + | 0.819446i | \(0.305719\pi\) | ||||
−0.573156 | + | 0.819446i | \(0.694281\pi\) | |||||||
\(42\) | 7.63283 | + | 26.7601i | 0.181734 | + | 0.637146i | ||||
\(43\) | 24.1255i | 0.561058i | 0.959846 | + | 0.280529i | \(0.0905099\pi\) | ||||
−0.959846 | + | 0.280529i | \(0.909490\pi\) | |||||||
\(44\) | − | 58.1388i | − | 1.32134i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −89.6235 | −1.94834 | ||||||||
\(47\) | 33.0153 | 0.702452 | 0.351226 | − | 0.936291i | \(-0.385765\pi\) | ||||
0.351226 | + | 0.936291i | \(0.385765\pi\) | |||||||
\(48\) | 56.4958 | − | 16.1144i | 1.17700 | − | 0.335716i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0627 | + | 3.72591i | −0.256132 | + | 0.0730570i | ||||
\(52\) | 96.5608i | 1.85694i | ||||||||
\(53\) | −15.1877 | −0.286561 | −0.143281 | − | 0.989682i | \(-0.545765\pi\) | ||||
−0.143281 | + | 0.989682i | \(0.545765\pi\) | |||||||
\(54\) | 63.6346 | − | 70.0795i | 1.17842 | − | 1.29777i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 39.8071i | 0.710842i | ||||||||
\(57\) | −46.8190 | + | 13.3542i | −0.821386 | + | 0.234285i | ||||
\(58\) | − | 33.2915i | − | 0.573991i | ||||||
\(59\) | − | 92.3960i | − | 1.56603i | −0.622000 | − | 0.783017i | \(-0.713680\pi\) | ||
0.622000 | − | 0.783017i | \(-0.286320\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.5203 | −0.942955 | −0.471478 | − | 0.881878i | \(-0.656279\pi\) | ||||
−0.471478 | + | 0.881878i | \(0.656279\pi\) | |||||||
\(62\) | 100.650 | 1.62338 | ||||||||
\(63\) | 12.5617 | + | 20.2288i | 0.199393 | + | 0.321091i | ||||
\(64\) | −48.6235 | −0.759743 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.2288 | − | 70.9205i | −0.306496 | − | 1.07455i | ||||
\(67\) | 15.1660i | 0.226358i | 0.993575 | + | 0.113179i | \(0.0361034\pi\) | ||||
−0.993575 | + | 0.113179i | \(0.963897\pi\) | |||||||
\(68\) | −37.5432 | −0.552106 | ||||||||
\(69\) | −73.7490 | + | 21.0355i | −1.06883 | + | 0.304863i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 70.5584i | − | 0.993781i | −0.867813 | − | 0.496890i | \(-0.834475\pi\) | ||
0.867813 | − | 0.496890i | \(-0.165525\pi\) | |||||||
\(72\) | 115.036 | − | 71.4353i | 1.59772 | − | 0.992157i | ||||
\(73\) | 76.7895i | 1.05191i | 0.850512 | + | 0.525956i | \(0.176292\pi\) | ||||
−0.850512 | + | 0.525956i | \(0.823708\pi\) | |||||||
\(74\) | − | 115.838i | − | 1.56537i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −134.561 | −1.77054 | ||||||||
\(77\) | 18.5516 | 0.240930 | ||||||||
\(78\) | 33.5973 | + | 117.790i | 0.430734 | + | 1.51012i | ||||
\(79\) | −127.247 | −1.61072 | −0.805361 | − | 0.592785i | \(-0.798029\pi\) | ||||
−0.805361 | + | 0.592785i | \(0.798029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9150 | − | 72.6024i | 0.443395 | − | 0.896326i | ||||
\(82\) | 235.579i | 2.87292i | ||||||||
\(83\) | 74.2844 | 0.894992 | 0.447496 | − | 0.894286i | \(-0.352316\pi\) | ||||
0.447496 | + | 0.894286i | \(0.352316\pi\) | |||||||
\(84\) | 18.0516 | + | 63.2876i | 0.214900 | + | 0.753424i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 84.5821i | 0.983513i | ||||||||
\(87\) | −7.81385 | − | 27.3948i | −0.0898144 | − | 0.314882i | ||||
\(88\) | − | 105.498i | − | 1.19884i | ||||||
\(89\) | 127.377i | 1.43121i | 0.698507 | + | 0.715603i | \(0.253848\pi\) | ||||
−0.698507 | + | 0.715603i | \(0.746152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.8118 | −0.338591 | ||||||||
\(92\) | −211.959 | −2.30391 | ||||||||
\(93\) | 82.8223 | − | 23.6235i | 0.890562 | − | 0.254016i | ||||
\(94\) | 115.749 | 1.23137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 24.4464 | − | 6.97288i | 0.254650 | − | 0.0726342i | ||||
\(97\) | − | 23.1660i | − | 0.238825i | −0.992845 | − | 0.119412i | \(-0.961899\pi\) | ||
0.992845 | − | 0.119412i | \(-0.0381011\pi\) | |||||||
\(98\) | −24.5415 | −0.250423 | ||||||||
\(99\) | −33.2915 | − | 53.6108i | −0.336278 | − | 0.541524i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 134.907i | − | 1.33571i | −0.744290 | − | 0.667857i | \(-0.767212\pi\) | ||
0.744290 | − | 0.667857i | \(-0.232788\pi\) | |||||||
\(102\) | −45.7970 | + | 13.0627i | −0.448990 | + | 0.128066i | ||||
\(103\) | 119.749i | 1.16261i | 0.813685 | + | 0.581306i | \(0.197458\pi\) | ||||
−0.813685 | + | 0.581306i | \(0.802542\pi\) | |||||||
\(104\) | 175.218i | 1.68479i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −53.2470 | −0.502331 | ||||||||
\(107\) | 77.8544 | 0.727611 | 0.363806 | − | 0.931475i | \(-0.381477\pi\) | ||||
0.363806 | + | 0.931475i | \(0.381477\pi\) | |||||||
\(108\) | 150.496 | − | 165.738i | 1.39348 | − | 1.53461i | ||||
\(109\) | 36.5385 | 0.335216 | 0.167608 | − | 0.985854i | \(-0.446396\pi\) | ||||
0.167608 | + | 0.985854i | \(0.446396\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.1882 | − | 95.3199i | −0.244939 | − | 0.858738i | ||||
\(112\) | 51.8118i | 0.462605i | ||||||||
\(113\) | 21.7596 | 0.192563 | 0.0962815 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962815 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(114\) | −164.144 | + | 46.8190i | −1.43986 | + | 0.410693i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 78.7343i | − | 0.678744i | ||||||
\(117\) | 55.2928 | + | 89.0405i | 0.472588 | + | 0.761030i | ||||
\(118\) | − | 323.933i | − | 2.74520i | ||||||
\(119\) | − | 11.9797i | − | 0.100670i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 71.8340 | 0.593669 | ||||||||
\(122\) | −201.662 | −1.65296 | ||||||||
\(123\) | 55.2928 | + | 193.852i | 0.449535 | + | 1.57603i | ||||
\(124\) | 238.037 | 1.91965 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 44.0405 | + | 70.9205i | 0.349528 | + | 0.562861i | ||||
\(127\) | − | 15.4170i | − | 0.121394i | −0.998156 | − | 0.0606968i | \(-0.980668\pi\) | ||
0.998156 | − | 0.0606968i | \(-0.0193323\pi\) | |||||||
\(128\) | −204.366 | −1.59661 | ||||||||
\(129\) | 19.8523 | + | 69.6006i | 0.153894 | + | 0.539539i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 183.110i | 1.39779i | 0.715226 | + | 0.698893i | \(0.246324\pi\) | ||||
−0.715226 | + | 0.698893i | \(0.753676\pi\) | |||||||
\(132\) | −47.8410 | − | 167.727i | −0.362432 | − | 1.27066i | ||||
\(133\) | − | 42.9373i | − | 0.322836i | ||||||
\(134\) | 53.1709i | 0.396798i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −68.1255 | −0.500923 | ||||||||
\(137\) | −33.0153 | −0.240987 | −0.120494 | − | 0.992714i | \(-0.538448\pi\) | ||||
−0.120494 | + | 0.992714i | \(0.538448\pi\) | |||||||
\(138\) | −258.558 | + | 73.7490i | −1.87361 | + | 0.534413i | ||||
\(139\) | −64.6418 | −0.465049 | −0.232525 | − | 0.972591i | \(-0.574699\pi\) | ||||
−0.232525 | + | 0.972591i | \(0.574699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 95.2470 | − | 27.1675i | 0.675511 | − | 0.192677i | ||||
\(142\) | − | 247.373i | − | 1.74206i | ||||||
\(143\) | 81.6582 | 0.571037 | ||||||||
\(144\) | 149.727 | − | 92.9780i | 1.03977 | − | 0.645681i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 269.218i | 1.84396i | ||||||||
\(147\) | −20.1946 | + | 5.76013i | −0.137378 | + | 0.0391846i | ||||
\(148\) | − | 273.956i | − | 1.85105i | ||||||
\(149\) | − | 195.736i | − | 1.31366i | −0.754037 | − | 0.656832i | \(-0.771896\pi\) | ||
0.754037 | − | 0.656832i | \(-0.228104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 102.251 | 0.677159 | 0.338579 | − | 0.940938i | \(-0.390054\pi\) | ||||
0.338579 | + | 0.940938i | \(0.390054\pi\) | |||||||
\(152\) | −244.173 | −1.60640 | ||||||||
\(153\) | −34.6193 | + | 21.4980i | −0.226270 | + | 0.140510i | ||||
\(154\) | 65.0405 | 0.422341 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 79.4575 | + | 278.572i | 0.509343 | + | 1.78572i | ||||
\(157\) | 104.723i | 0.667025i | 0.942746 | + | 0.333512i | \(0.108234\pi\) | ||||
−0.942746 | + | 0.333512i | \(0.891766\pi\) | |||||||
\(158\) | −446.118 | −2.82353 | ||||||||
\(159\) | −43.8157 | + | 12.4976i | −0.275570 | + | 0.0786014i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 67.6345i | − | 0.420090i | ||||||
\(162\) | 125.915 | − | 254.539i | 0.777255 | − | 1.57123i | ||||
\(163\) | 70.9595i | 0.435334i | 0.976023 | + | 0.217667i | \(0.0698447\pi\) | ||||
−0.976023 | + | 0.217667i | \(0.930155\pi\) | |||||||
\(164\) | 557.144i | 3.39722i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 260.435 | 1.56889 | ||||||||
\(167\) | 206.992 | 1.23947 | 0.619735 | − | 0.784811i | \(-0.287240\pi\) | ||||
0.619735 | + | 0.784811i | \(0.287240\pi\) | |||||||
\(168\) | 32.7563 | + | 114.841i | 0.194978 | + | 0.683578i | ||||
\(169\) | 33.3765 | 0.197494 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −124.081 | + | 77.0524i | −0.725620 | + | 0.450599i | ||||
\(172\) | 200.037i | 1.16300i | ||||||||
\(173\) | 108.464 | 0.626958 | 0.313479 | − | 0.949595i | \(-0.398506\pi\) | ||||
0.313479 | + | 0.949595i | \(0.398506\pi\) | |||||||
\(174\) | −27.3948 | − | 96.0440i | −0.157441 | − | 0.551977i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 137.313i | − | 0.780188i | ||||||
\(177\) | −76.0304 | − | 266.557i | −0.429550 | − | 1.50597i | ||||
\(178\) | 446.575i | 2.50885i | ||||||||
\(179\) | − | 159.357i | − | 0.890261i | −0.895466 | − | 0.445131i | \(-0.853157\pi\) | ||
0.895466 | − | 0.445131i | \(-0.146843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −233.889 | −1.29220 | −0.646102 | − | 0.763251i | \(-0.723602\pi\) | ||||
−0.646102 | + | 0.763251i | \(0.723602\pi\) | |||||||
\(182\) | −108.024 | −0.593537 | ||||||||
\(183\) | −165.942 | + | 47.3320i | −0.906789 | + | 0.258645i | ||||
\(184\) | −384.620 | −2.09032 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 290.369 | − | 82.8223i | 1.56112 | − | 0.445281i | ||||
\(187\) | 31.7490i | 0.169781i | ||||||||
\(188\) | 273.746 | 1.45610 | ||||||||
\(189\) | 52.8856 | + | 48.0220i | 0.279818 | + | 0.254085i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 288.210i | − | 1.50895i | −0.656328 | − | 0.754476i | \(-0.727891\pi\) | ||
0.656328 | − | 0.754476i | \(-0.272109\pi\) | |||||||
\(192\) | −140.276 | + | 40.0111i | −0.730604 | + | 0.208391i | ||||
\(193\) | − | 77.1216i | − | 0.399594i | −0.979837 | − | 0.199797i | \(-0.935972\pi\) | ||
0.979837 | − | 0.199797i | \(-0.0640282\pi\) | |||||||
\(194\) | − | 81.2183i | − | 0.418651i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −58.0405 | −0.296125 | ||||||||
\(197\) | 136.433 | 0.692554 | 0.346277 | − | 0.938132i | \(-0.387446\pi\) | ||||
0.346277 | + | 0.938132i | \(0.387446\pi\) | |||||||
\(198\) | −116.717 | − | 187.956i | −0.589482 | − | 0.949270i | ||||
\(199\) | −86.5830 | −0.435090 | −0.217545 | − | 0.976050i | \(-0.569805\pi\) | ||||
−0.217545 | + | 0.976050i | \(0.569805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4797 | + | 43.7530i | 0.0620883 | + | 0.217677i | ||||
\(202\) | − | 472.974i | − | 2.34145i | ||||||
\(203\) | 25.1235 | 0.123761 | ||||||||
\(204\) | −108.310 | + | 30.8934i | −0.530930 | + | 0.151438i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 419.831i | 2.03801i | ||||||||
\(207\) | −195.452 | + | 121.373i | −0.944212 | + | 0.586341i | ||||
\(208\) | 228.059i | 1.09644i | ||||||||
\(209\) | 113.794i | 0.544467i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4170 | 0.0920237 | 0.0460118 | − | 0.998941i | \(-0.485349\pi\) | ||||
0.0460118 | + | 0.998941i | \(0.485349\pi\) | |||||||
\(212\) | −125.929 | −0.594005 | ||||||||
\(213\) | −58.0608 | − | 203.557i | −0.272586 | − | 0.955666i | ||||
\(214\) | 272.952 | 1.27547 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 273.088 | − | 300.746i | 1.26430 | − | 1.39234i | ||||
\(217\) | 75.9555i | 0.350026i | ||||||||
\(218\) | 128.101 | 0.587621 | ||||||||
\(219\) | 63.1882 | + | 221.533i | 0.288531 | + | 1.01157i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 52.7309i | − | 0.238601i | ||||||
\(222\) | −95.3199 | − | 334.184i | −0.429369 | − | 1.50533i | ||||
\(223\) | − | 175.041i | − | 0.784935i | −0.919766 | − | 0.392468i | \(-0.871622\pi\) | ||
0.919766 | − | 0.392468i | \(-0.128378\pi\) | |||||||
\(224\) | 22.4196i | 0.100087i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 76.2876 | 0.337556 | ||||||||
\(227\) | 177.574 | 0.782264 | 0.391132 | − | 0.920335i | \(-0.372084\pi\) | ||||
0.391132 | + | 0.920335i | \(0.372084\pi\) | |||||||
\(228\) | −388.200 | + | 110.727i | −1.70263 | + | 0.485644i | ||||
\(229\) | −40.8118 | −0.178217 | −0.0891087 | − | 0.996022i | \(-0.528402\pi\) | ||||
−0.0891087 | + | 0.996022i | \(0.528402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 53.5203 | − | 15.2657i | 0.231689 | − | 0.0660851i | ||||
\(232\) | − | 142.871i | − | 0.615821i | ||||||
\(233\) | 387.696 | 1.66393 | 0.831965 | − | 0.554828i | \(-0.187216\pi\) | ||||
0.831965 | + | 0.554828i | \(0.187216\pi\) | |||||||
\(234\) | 193.852 | + | 312.169i | 0.828429 | + | 1.33406i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 766.102i | − | 3.24619i | ||||||
\(237\) | −367.100 | + | 104.708i | −1.54895 | + | 0.441808i | ||||
\(238\) | − | 42.0000i | − | 0.176471i | ||||||
\(239\) | 49.5229i | 0.207209i | 0.994619 | + | 0.103604i | \(0.0330376\pi\) | ||||
−0.994619 | + | 0.103604i | \(0.966962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 325.247 | 1.34957 | 0.674786 | − | 0.738013i | \(-0.264236\pi\) | ||||
0.674786 | + | 0.738013i | \(0.264236\pi\) | |||||||
\(242\) | 251.845 | 1.04068 | ||||||||
\(243\) | 43.8699 | − | 239.007i | 0.180535 | − | 0.983569i | ||||
\(244\) | −476.929 | −1.95463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 193.852 | + | 679.631i | 0.788017 | + | 2.76273i | ||||
\(247\) | − | 188.996i | − | 0.765166i | ||||||
\(248\) | 431.939 | 1.74169 | ||||||||
\(249\) | 214.306 | − | 61.1268i | 0.860666 | − | 0.245489i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 263.732i | − | 1.05073i | −0.850878 | − | 0.525364i | \(-0.823929\pi\) | ||
0.850878 | − | 0.525364i | \(-0.176071\pi\) | |||||||
\(252\) | 104.156 | + | 167.727i | 0.413316 | + | 0.665582i | ||||
\(253\) | 179.247i | 0.708486i | ||||||||
\(254\) | − | 54.0508i | − | 0.212798i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −521.996 | −2.03905 | ||||||||
\(257\) | 151.181 | 0.588252 | 0.294126 | − | 0.955767i | \(-0.404971\pi\) | ||||
0.294126 | + | 0.955767i | \(0.404971\pi\) | |||||||
\(258\) | 69.6006 | + | 244.014i | 0.269770 | + | 0.945792i | ||||
\(259\) | 87.4170 | 0.337517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −45.0850 | − | 72.6024i | −0.172739 | − | 0.278170i | ||||
\(262\) | 641.970i | 2.45027i | ||||||||
\(263\) | 114.389 | 0.434941 | 0.217470 | − | 0.976067i | \(-0.430219\pi\) | ||||
0.217470 | + | 0.976067i | \(0.430219\pi\) | |||||||
\(264\) | −86.8118 | − | 304.355i | −0.328832 | − | 1.15286i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 150.535i | − | 0.565920i | ||||||
\(267\) | 104.816 | + | 367.476i | 0.392568 | + | 1.37631i | ||||
\(268\) | 125.749i | 0.469213i | ||||||||
\(269\) | − | 4.76170i | − | 0.0177015i | −0.999961 | − | 0.00885074i | \(-0.997183\pi\) | ||
0.999961 | − | 0.00885074i | \(-0.00281731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −518.701 | −1.91402 | −0.957012 | − | 0.290048i | \(-0.906329\pi\) | ||||
−0.957012 | + | 0.290048i | \(0.906329\pi\) | |||||||
\(272\) | −88.6701 | −0.325993 | ||||||||
\(273\) | −88.8901 | + | 25.3542i | −0.325605 | + | 0.0928727i | ||||
\(274\) | −115.749 | −0.422442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −611.490 | + | 174.416i | −2.21554 | + | 0.631943i | ||||
\(277\) | − | 121.085i | − | 0.437130i | −0.975822 | − | 0.218565i | \(-0.929862\pi\) | ||
0.975822 | − | 0.218565i | \(-0.0701375\pi\) | |||||||
\(278\) | −226.629 | −0.815213 | ||||||||
\(279\) | 219.498 | − | 136.305i | 0.786731 | − | 0.488548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 407.255i | 1.44931i | 0.689113 | + | 0.724654i | \(0.258000\pi\) | ||||
−0.689113 | + | 0.724654i | \(0.742000\pi\) | |||||||
\(282\) | 333.929 | − | 95.2470i | 1.18415 | − | 0.337755i | ||||
\(283\) | 398.634i | 1.40860i | 0.709902 | + | 0.704300i | \(0.248739\pi\) | ||||
−0.709902 | + | 0.704300i | \(0.751261\pi\) | |||||||
\(284\) | − | 585.036i | − | 2.05998i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 286.288 | 1.00101 | ||||||||
\(287\) | −177.780 | −0.619443 | ||||||||
\(288\) | 64.7886 | − | 40.2327i | 0.224960 | − | 0.139697i | ||||
\(289\) | −268.498 | −0.929059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.0627 | − | 66.8325i | −0.0655077 | − | 0.229665i | ||||
\(292\) | 636.701i | 2.18048i | ||||||||
\(293\) | 2.53426 | 0.00864935 | 0.00432468 | − | 0.999991i | \(-0.498623\pi\) | ||||
0.00432468 | + | 0.999991i | \(0.498623\pi\) | |||||||
\(294\) | −70.8006 | + | 20.1946i | −0.240819 | + | 0.0686890i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 497.117i | − | 1.67945i | ||||||
\(297\) | −140.159 | − | 127.269i | −0.471916 | − | 0.428516i | ||||
\(298\) | − | 686.235i | − | 2.30280i | ||||||
\(299\) | − | 297.706i | − | 0.995671i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −63.8301 | −0.212060 | ||||||||
\(302\) | 358.484 | 1.18703 | ||||||||
\(303\) | −111.012 | − | 389.199i | −0.366375 | − | 1.28448i | ||||
\(304\) | −317.808 | −1.04542 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −121.373 | + | 75.3705i | −0.396642 | + | 0.246309i | ||||
\(307\) | 86.2366i | 0.280901i | 0.990088 | + | 0.140451i | \(0.0448551\pi\) | ||||
−0.990088 | + | 0.140451i | \(0.955145\pi\) | |||||||
\(308\) | 153.821 | 0.499418 | ||||||||
\(309\) | 98.5385 | + | 345.469i | 0.318895 | + | 1.11802i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 151.777i | 0.488028i | 0.969772 | + | 0.244014i | \(0.0784643\pi\) | ||||
−0.969772 | + | 0.244014i | \(0.921536\pi\) | |||||||
\(312\) | 144.183 | + | 505.494i | 0.462125 | + | 1.62017i | ||||
\(313\) | − | 318.118i | − | 1.01635i | −0.861254 | − | 0.508175i | \(-0.830320\pi\) | ||
0.861254 | − | 0.508175i | \(-0.169680\pi\) | |||||||
\(314\) | 367.150i | 1.16927i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1055.07 | −3.33883 | ||||||||
\(317\) | −364.020 | −1.14833 | −0.574164 | − | 0.818740i | \(-0.694673\pi\) | ||||
−0.574164 | + | 0.818740i | \(0.694673\pi\) | |||||||
\(318\) | −153.615 | + | 43.8157i | −0.483064 | + | 0.137785i | ||||
\(319\) | −66.5830 | −0.208724 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 224.605 | − | 64.0645i | 0.699705 | − | 0.199578i | ||||
\(322\) | − | 237.122i | − | 0.736402i | ||||||
\(323\) | 73.4823 | 0.227500 | ||||||||
\(324\) | 297.790 | − | 601.983i | 0.919104 | − | 1.85797i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 248.779i | 0.763124i | ||||||||
\(327\) | 105.412 | − | 30.0667i | 0.322359 | − | 0.0919470i | ||||
\(328\) | 1010.99i | 3.08228i | ||||||||
\(329\) | 87.3502i | 0.265502i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 154.369 | 0.466370 | 0.233185 | − | 0.972432i | \(-0.425085\pi\) | ||||
0.233185 | + | 0.972432i | \(0.425085\pi\) | |||||||
\(332\) | 615.929 | 1.85521 | ||||||||
\(333\) | −156.873 | − | 252.620i | −0.471090 | − | 0.758617i | ||||
\(334\) | 725.697 | 2.17274 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 42.6346 | + | 149.474i | 0.126889 | + | 0.444862i | ||||
\(337\) | 403.041i | 1.19597i | 0.801509 | + | 0.597983i | \(0.204031\pi\) | ||||
−0.801509 | + | 0.597983i | \(0.795969\pi\) | |||||||
\(338\) | 117.015 | 0.346199 | ||||||||
\(339\) | 62.7752 | − | 17.9055i | 0.185178 | − | 0.0528185i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 201.300i | − | 0.590321i | ||||||
\(342\) | −435.019 | + | 270.140i | −1.27198 | + | 0.789883i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | 362.984i | 1.05519i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 380.265 | 1.09903 | ||||||||
\(347\) | 471.242 | 1.35805 | 0.679023 | − | 0.734117i | \(-0.262404\pi\) | ||||
0.679023 | + | 0.734117i | \(0.262404\pi\) | |||||||
\(348\) | −64.7886 | − | 227.144i | −0.186174 | − | 0.652712i | ||||
\(349\) | 364.516 | 1.04446 | 0.522230 | − | 0.852805i | \(-0.325100\pi\) | ||||
0.522230 | + | 0.852805i | \(0.325100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 232.786 | + | 211.377i | 0.663207 | + | 0.602215i | ||||
\(352\) | − | 59.4170i | − | 0.168798i | ||||||
\(353\) | −86.3420 | −0.244595 | −0.122297 | − | 0.992493i | \(-0.539026\pi\) | ||||
−0.122297 | + | 0.992493i | \(0.539026\pi\) | |||||||
\(354\) | −266.557 | − | 934.528i | −0.752985 | − | 2.63991i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1056.15i | 2.96671i | ||||||||
\(357\) | −9.85782 | − | 34.5608i | −0.0276129 | − | 0.0968089i | ||||
\(358\) | − | 558.693i | − | 1.56059i | ||||||
\(359\) | − | 372.068i | − | 1.03640i | −0.855259 | − | 0.518200i | \(-0.826602\pi\) | ||
0.855259 | − | 0.518200i | \(-0.173398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −97.6275 | −0.270436 | ||||||||
\(362\) | −819.997 | −2.26518 | ||||||||
\(363\) | 207.237 | − | 59.1104i | 0.570900 | − | 0.162839i | ||||
\(364\) | −255.476 | −0.701857 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −581.782 | + | 165.942i | −1.58957 | + | 0.453395i | ||||
\(367\) | − | 161.786i | − | 0.440833i | −0.975406 | − | 0.220416i | \(-0.929258\pi\) | ||
0.975406 | − | 0.220416i | \(-0.0707416\pi\) | |||||||
\(368\) | −500.609 | −1.36035 | ||||||||
\(369\) | 319.033 | + | 513.753i | 0.864587 | + | 1.39228i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 40.1830i | − | 0.108310i | ||||||
\(372\) | 686.721 | − | 195.875i | 1.84602 | − | 0.526544i | ||||
\(373\) | − | 378.251i | − | 1.01408i | −0.861923 | − | 0.507039i | \(-0.830740\pi\) | ||
0.861923 | − | 0.507039i | \(-0.169260\pi\) | |||||||
\(374\) | 111.310i | 0.297619i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 496.737 | 1.32111 | ||||||||
\(377\) | 110.586 | 0.293330 | ||||||||
\(378\) | 185.413 | + | 168.361i | 0.490510 | + | 0.445401i | ||||
\(379\) | 50.7974 | 0.134030 | 0.0670151 | − | 0.997752i | \(-0.478652\pi\) | ||||
0.0670151 | + | 0.997752i | \(0.478652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6863 | − | 44.4771i | −0.0332973 | − | 0.116738i | ||||
\(382\) | − | 1010.44i | − | 2.64514i | ||||||
\(383\) | 113.381 | 0.296034 | 0.148017 | − | 0.988985i | \(-0.452711\pi\) | ||||
0.148017 | + | 0.988985i | \(0.452711\pi\) | |||||||
\(384\) | −589.582 | + | 168.167i | −1.53537 | + | 0.437936i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 270.382i | − | 0.700472i | ||||||
\(387\) | 114.545 | + | 184.458i | 0.295983 | + | 0.476634i | ||||
\(388\) | − | 192.081i | − | 0.495054i | ||||||
\(389\) | 725.584i | 1.86526i | 0.360841 | + | 0.932628i | \(0.382490\pi\) | ||||
−0.360841 | + | 0.932628i | \(0.617510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 115.749 | 0.296033 | ||||||||
\(392\) | −105.320 | −0.268673 | ||||||||
\(393\) | 150.677 | + | 528.261i | 0.383402 | + | 1.34418i | ||||
\(394\) | 478.324 | 1.21402 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −276.037 | − | 444.514i | −0.697062 | − | 1.12251i | ||||
\(397\) | − | 94.3464i | − | 0.237648i | −0.992915 | − | 0.118824i | \(-0.962088\pi\) | ||
0.992915 | − | 0.118824i | \(-0.0379125\pi\) | |||||||
\(398\) | −303.553 | −0.762697 | ||||||||
\(399\) | −35.3320 | − | 123.871i | −0.0885514 | − | 0.310455i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 677.665i | − | 1.68994i | −0.534815 | − | 0.844969i | \(-0.679619\pi\) | ||
0.534815 | − | 0.844969i | \(-0.320381\pi\) | |||||||
\(402\) | 43.7530 | + | 153.395i | 0.108838 | + | 0.381579i | ||||
\(403\) | 334.332i | 0.829608i | ||||||||
\(404\) | − | 1118.58i | − | 2.76877i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 88.0810 | 0.216948 | ||||||||
\(407\) | −231.675 | −0.569226 | ||||||||
\(408\) | −196.538 | + | 56.0588i | −0.481711 | + | 0.137399i | ||||
\(409\) | −17.3647 | −0.0424564 | −0.0212282 | − | 0.999775i | \(-0.506758\pi\) | ||||
−0.0212282 | + | 0.999775i | \(0.506758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −95.2470 | + | 27.1675i | −0.231745 | + | 0.0661009i | ||||
\(412\) | 992.899i | 2.40995i | ||||||||
\(413\) | 244.457 | 0.591905 | ||||||||
\(414\) | −685.239 | + | 425.523i | −1.65517 | + | 1.02783i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 98.6838i | 0.237221i | ||||||||
\(417\) | −186.488 | + | 53.1922i | −0.447213 | + | 0.127559i | ||||
\(418\) | 398.952i | 0.954430i | ||||||||
\(419\) | − | 136.071i | − | 0.324752i | −0.986729 | − | 0.162376i | \(-0.948084\pi\) | ||
0.986729 | − | 0.162376i | \(-0.0519157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 423.992 | 1.00711 | 0.503554 | − | 0.863964i | \(-0.332026\pi\) | ||||
0.503554 | + | 0.863964i | \(0.332026\pi\) | |||||||
\(422\) | 68.0745 | 0.161314 | ||||||||
\(423\) | 252.427 | − | 156.753i | 0.596753 | − | 0.370574i | ||||
\(424\) | −228.510 | −0.538938 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −203.557 | − | 713.655i | −0.477833 | − | 1.67525i | ||||
\(427\) | − | 152.184i | − | 0.356404i | ||||||
\(428\) | 645.530 | 1.50825 | ||||||||
\(429\) | 235.579 | − | 67.1946i | 0.549135 | − | 0.156631i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 340.244i | 0.789430i | 0.918804 | + | 0.394715i | \(0.129157\pi\) | ||||
−0.918804 | + | 0.394715i | \(0.870843\pi\) | |||||||
\(432\) | 355.443 | − | 391.442i | 0.822786 | − | 0.906117i | ||||
\(433\) | − | 159.166i | − | 0.367589i | −0.982965 | − | 0.183794i | \(-0.941162\pi\) | ||
0.982965 | − | 0.183794i | \(-0.0588381\pi\) | |||||||
\(434\) | 266.294i | 0.613581i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 302.959 | 0.694861 | ||||||||
\(437\) | 414.863 | 0.949343 | ||||||||
\(438\) | 221.533 | + | 776.678i | 0.505783 | + | 1.77324i | ||||
\(439\) | −128.073 | −0.291738 | −0.145869 | − | 0.989304i | \(-0.546598\pi\) | ||||
−0.145869 | + | 0.989304i | \(0.546598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.5203 | + | 33.2353i | −0.121361 | + | 0.0753634i | ||||
\(442\) | − | 184.871i | − | 0.418259i | ||||||
\(443\) | −197.340 | −0.445463 | −0.222731 | − | 0.974880i | \(-0.571497\pi\) | ||||
−0.222731 | + | 0.974880i | \(0.571497\pi\) | |||||||
\(444\) | −225.431 | − | 790.345i | −0.507728 | − | 1.78006i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 613.679i | − | 1.37596i | ||||||
\(447\) | −161.066 | − | 564.686i | −0.360327 | − | 1.26328i | ||||
\(448\) | − | 128.646i | − | 0.287156i | ||||||
\(449\) | − | 148.101i | − | 0.329847i | −0.986306 | − | 0.164923i | \(-0.947262\pi\) | ||
0.986306 | − | 0.164923i | \(-0.0527377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 471.158 | 1.04470 | ||||||||
\(452\) | 180.420 | 0.399159 | ||||||||
\(453\) | 294.988 | − | 84.1398i | 0.651187 | − | 0.185739i | ||||
\(454\) | 622.561 | 1.37128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −704.423 | + | 200.924i | −1.54479 | + | 0.440622i | ||||
\(457\) | − | 122.214i | − | 0.267428i | −0.991020 | − | 0.133714i | \(-0.957310\pi\) | ||
0.991020 | − | 0.133714i | \(-0.0426903\pi\) | |||||||
\(458\) | −143.083 | −0.312408 | ||||||||
\(459\) | −82.1843 | + | 90.5079i | −0.179051 | + | 0.197185i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 602.089i | 1.30605i | 0.757337 | + | 0.653025i | \(0.226500\pi\) | ||||
−0.757337 | + | 0.653025i | \(0.773500\pi\) | |||||||
\(462\) | 187.638 | − | 53.5203i | 0.406143 | − | 0.115845i | ||||
\(463\) | 637.061i | 1.37594i | 0.725738 | + | 0.687971i | \(0.241498\pi\) | ||||
−0.725738 | + | 0.687971i | \(0.758502\pi\) | |||||||
\(464\) | − | 185.956i | − | 0.400767i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1359.23 | 2.91681 | ||||||||
\(467\) | 767.706 | 1.64391 | 0.821955 | − | 0.569553i | \(-0.192884\pi\) | ||||
0.821955 | + | 0.569553i | \(0.192884\pi\) | |||||||
\(468\) | 458.460 | + | 738.280i | 0.979616 | + | 1.57752i | ||||
\(469\) | −40.1255 | −0.0855554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 86.1739 | + | 302.119i | 0.182959 | + | 0.641442i | ||||
\(472\) | − | 1390.16i | − | 2.94526i | ||||||
\(473\) | 169.164 | 0.357641 | ||||||||
\(474\) | −1287.02 | + | 367.100i | −2.71524 | + | 0.774473i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 99.3299i | − | 0.208676i | ||||||
\(477\) | −116.122 | + | 72.1097i | −0.243442 | + | 0.151173i | ||||
\(478\) | 173.624i | 0.363229i | ||||||||
\(479\) | − | 393.855i | − | 0.822245i | −0.911580 | − | 0.411122i | \(-0.865137\pi\) | ||
0.911580 | − | 0.411122i | \(-0.134863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 384.782 | 0.799962 | ||||||||
\(482\) | 1140.29 | 2.36575 | ||||||||
\(483\) | −55.6548 | − | 195.122i | −0.115227 | − | 0.403978i | ||||
\(484\) | 595.612 | 1.23060 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 153.805 | − | 837.941i | 0.316470 | − | 1.72416i | ||||
\(487\) | 573.409i | 1.17743i | 0.808340 | + | 0.588716i | \(0.200366\pi\) | ||||
−0.808340 | + | 0.588716i | \(0.799634\pi\) | |||||||
\(488\) | −865.432 | −1.77343 | ||||||||
\(489\) | 58.3908 | + | 204.714i | 0.119409 | + | 0.418638i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 170.796i | − | 0.347853i | −0.984759 | − | 0.173927i | \(-0.944354\pi\) | ||
0.984759 | − | 0.173927i | \(-0.0556455\pi\) | |||||||
\(492\) | 458.460 | + | 1607.33i | 0.931830 | + | 3.26692i | ||||
\(493\) | 42.9961i | 0.0872131i | ||||||||
\(494\) | − | 662.606i | − | 1.34131i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 562.199 | 1.13347 | ||||||||
\(497\) | 186.680 | 0.375614 | ||||||||
\(498\) | 751.340 | − | 214.306i | 1.50871 | − | 0.430333i | ||||
\(499\) | 847.814 | 1.69903 | 0.849513 | − | 0.527567i | \(-0.176896\pi\) | ||||
0.849513 | + | 0.527567i | \(0.176896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 597.158 | − | 170.328i | 1.19193 | − | 0.339977i | ||||
\(502\) | − | 924.626i | − | 1.84188i | ||||||
\(503\) | 197.624 | 0.392891 | 0.196445 | − | 0.980515i | \(-0.437060\pi\) | ||||
0.196445 | + | 0.980515i | \(0.437060\pi\) | |||||||
\(504\) | 189.000 | + | 304.355i | 0.375000 | + | 0.603880i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 628.427i | 1.24195i | ||||||||
\(507\) | 96.2891 | − | 27.4647i | 0.189919 | − | 0.0541710i | ||||
\(508\) | − | 127.830i | − | 0.251634i | ||||||
\(509\) | − | 491.448i | − | 0.965516i | −0.875754 | − | 0.482758i | \(-0.839635\pi\) | ||
0.875754 | − | 0.482758i | \(-0.160365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −203.166 | −0.397585 | ||||||||
\(512\) | −1012.62 | −1.97777 | ||||||||
\(513\) | −294.562 | + | 324.395i | −0.574194 | + | 0.632348i | ||||
\(514\) | 530.029 | 1.03118 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 164.605 | + | 577.093i | 0.319002 | + | 1.11840i | ||||
\(517\) | − | 231.498i | − | 0.447772i | ||||||
\(518\) | 306.477 | 0.591655 | ||||||||
\(519\) | 312.911 | − | 89.2521i | 0.602912 | − | 0.171969i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 870.010i | 1.66988i | 0.550338 | + | 0.834942i | \(0.314499\pi\) | ||||
−0.550338 | + | 0.834942i | \(0.685501\pi\) | |||||||
\(522\) | −158.064 | − | 254.539i | −0.302806 | − | 0.487622i | ||||
\(523\) | − | 798.707i | − | 1.52716i | −0.645710 | − | 0.763582i | \(-0.723439\pi\) | ||
0.645710 | − | 0.763582i | \(-0.276561\pi\) | |||||||
\(524\) | 1518.26i | 2.89744i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 401.041 | 0.762434 | ||||||||
\(527\) | −129.989 | −0.246659 | ||||||||
\(528\) | −112.992 | − | 396.140i | −0.213999 | − | 0.750265i | ||||
\(529\) | 124.490 | 0.235331 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −438.686 | − | 706.437i | −0.826151 | − | 1.33039i | ||||
\(532\) | − | 356.014i | − | 0.669200i | ||||||
\(533\) | −782.531 | −1.46816 | ||||||||
\(534\) | 367.476 | + | 1288.34i | 0.688157 | + | 2.41263i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 228.183i | 0.425714i | ||||||||
\(537\) | −131.131 | − | 459.735i | −0.244191 | − | 0.856117i | ||||
\(538\) | − | 16.6941i | − | 0.0310300i | ||||||
\(539\) | 49.0829i | 0.0910630i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −736.243 | −1.36089 | −0.680446 | − | 0.732798i | \(-0.738214\pi\) | ||||
−0.680446 | + | 0.732798i | \(0.738214\pi\) | |||||||
\(542\) | −1818.52 | −3.35521 | ||||||||
\(543\) | −674.755 | + | 192.461i | −1.24264 | + | 0.354441i | ||||
\(544\) | −38.3686 | −0.0705305 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −311.642 | + | 88.8901i | −0.570773 | + | 0.162802i | ||||
\(547\) | − | 228.952i | − | 0.418559i | −0.977856 | − | 0.209279i | \(-0.932888\pi\) | ||
0.977856 | − | 0.209279i | \(-0.0671118\pi\) | |||||||
\(548\) | −273.746 | −0.499537 | ||||||||
\(549\) | −439.786 | + | 273.100i | −0.801067 | + | 0.497450i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 154.105i | 0.279682i | ||||||||
\(552\) | −1109.60 | + | 316.494i | −2.01015 | + | 0.573359i | ||||
\(553\) | − | 336.664i | − | 0.608796i | ||||||
\(554\) | − | 424.515i | − | 0.766272i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −535.978 | −0.963989 | ||||||||
\(557\) | −906.288 | −1.62709 | −0.813544 | − | 0.581503i | \(-0.802465\pi\) | ||||
−0.813544 | + | 0.581503i | \(0.802465\pi\) | |||||||
\(558\) | 769.543 | − | 477.875i | 1.37911 | − | 0.856406i | ||||
\(559\) | −280.959 | −0.502611 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.1255 | + | 91.5940i | 0.0465695 | + | 0.163269i | ||||
\(562\) | 1427.81i | 2.54058i | ||||||||
\(563\) | −458.616 | −0.814593 | −0.407297 | − | 0.913296i | \(-0.633529\pi\) | ||||
−0.407297 | + | 0.913296i | \(0.633529\pi\) | |||||||
\(564\) | 789.741 | − | 225.259i | 1.40025 | − | 0.399396i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1397.58i | 2.46922i | ||||||||
\(567\) | 192.088 | + | 95.0222i | 0.338779 | + | 0.167588i | ||||
\(568\) | − | 1061.60i | − | 1.86901i | ||||||
\(569\) | 577.428i | 1.01481i | 0.861707 | + | 0.507406i | \(0.169395\pi\) | ||||
−0.861707 | + | 0.507406i | \(0.830605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −103.122 | −0.180598 | −0.0902991 | − | 0.995915i | \(-0.528782\pi\) | ||||
−0.0902991 | + | 0.995915i | \(0.528782\pi\) | |||||||
\(572\) | 677.069 | 1.18369 | ||||||||
\(573\) | −237.161 | − | 831.468i | −0.413893 | − | 1.45108i | ||||
\(574\) | −623.284 | −1.08586 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −371.763 | + | 230.859i | −0.645423 | + | 0.400797i | ||||
\(577\) | − | 676.583i | − | 1.17259i | −0.810099 | − | 0.586294i | \(-0.800586\pi\) | ||
0.810099 | − | 0.586294i | \(-0.199414\pi\) | |||||||
\(578\) | −941.334 | −1.62860 | ||||||||
\(579\) | −63.4615 | − | 222.491i | −0.109605 | − | 0.384268i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 196.538i | 0.338275i | ||||||||
\(582\) | −66.8325 | − | 234.310i | −0.114833 | − | 0.402594i | ||||
\(583\) | 106.494i | 0.182666i | ||||||||
\(584\) | 1155.35i | 1.97834i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.88492 | 0.0151620 | ||||||||
\(587\) | −158.683 | −0.270329 | −0.135164 | − | 0.990823i | \(-0.543156\pi\) | ||||
−0.135164 | + | 0.990823i | \(0.543156\pi\) | |||||||
\(588\) | −167.443 | + | 47.7601i | −0.284768 | + | 0.0812247i | ||||
\(589\) | −465.903 | −0.791007 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 393.601 | − | 112.267i | 0.665992 | − | 0.189962i | ||||
\(592\) | − | 647.033i | − | 1.09296i | ||||||
\(593\) | −935.371 | −1.57735 | −0.788677 | − | 0.614807i | \(-0.789234\pi\) | ||||
−0.788677 | + | 0.614807i | \(0.789234\pi\) | |||||||
\(594\) | −491.387 | − | 446.196i | −0.827251 | − | 0.751172i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1622.94i | − | 2.72306i | ||||||
\(597\) | −249.787 | + | 71.2470i | −0.418403 | + | 0.119342i | ||||
\(598\) | − | 1043.73i | − | 1.74537i | ||||||
\(599\) | − | 73.7665i | − | 0.123149i | −0.998102 | − | 0.0615747i | \(-0.980388\pi\) | ||
0.998102 | − | 0.0615747i | \(-0.0196122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −934.280 | −1.55454 | −0.777271 | − | 0.629166i | \(-0.783397\pi\) | ||||
−0.777271 | + | 0.629166i | \(0.783397\pi\) | |||||||
\(602\) | −223.783 | −0.371733 | ||||||||
\(603\) | 72.0066 | + | 115.956i | 0.119414 | + | 0.192298i | ||||
\(604\) | 847.814 | 1.40367 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −389.199 | − | 1364.50i | −0.642242 | − | 2.25165i | ||||
\(607\) | − | 181.608i | − | 0.299189i | −0.988747 | − | 0.149595i | \(-0.952203\pi\) | ||
0.988747 | − | 0.149595i | \(-0.0477968\pi\) | |||||||
\(608\) | −137.519 | −0.226183 | ||||||||
\(609\) | 72.4797 | − | 20.6735i | 0.119014 | − | 0.0339466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 384.488i | 0.629276i | ||||||||
\(612\) | −287.046 | + | 178.251i | −0.469029 | + | 0.291260i | ||||
\(613\) | 897.940i | 1.46483i | 0.680859 | + | 0.732414i | \(0.261606\pi\) | ||||
−0.680859 | + | 0.732414i | \(0.738394\pi\) | |||||||
\(614\) | 302.339i | 0.492409i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 279.122 | 0.453119 | ||||||||
\(617\) | −1169.69 | −1.89576 | −0.947882 | − | 0.318622i | \(-0.896780\pi\) | ||||
−0.947882 | + | 0.318622i | \(0.896780\pi\) | |||||||
\(618\) | 345.469 | + | 1211.19i | 0.559011 | + | 1.95985i | ||||
\(619\) | −1208.97 | −1.95310 | −0.976548 | − | 0.215301i | \(-0.930927\pi\) | ||||
−0.976548 | + | 0.215301i | \(0.930927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −463.992 | + | 510.985i | −0.747169 | + | 0.822842i | ||||
\(622\) | 532.118i | 0.855495i | ||||||||
\(623\) | −337.009 | −0.540945 | ||||||||
\(624\) | 187.664 | + | 657.936i | 0.300744 | + | 1.05438i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1115.30i | − | 1.78162i | ||||||
\(627\) | 93.6380 | + | 328.288i | 0.149343 | + | 0.523585i | ||||
\(628\) | 868.310i | 1.38266i | ||||||||
\(629\) | 149.604i | 0.237845i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 901.223 | 1.42825 | 0.714123 | − | 0.700020i | \(-0.246826\pi\) | ||||
0.714123 | + | 0.700020i | \(0.246826\pi\) | |||||||
\(632\) | −1914.52 | −3.02930 | ||||||||
\(633\) | 56.0169 | − | 15.9778i | 0.0884942 | − | 0.0252413i | ||||
\(634\) | −1276.23 | −2.01298 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −363.298 | + | 103.624i | −0.571223 | + | 0.162931i | ||||
\(637\) | − | 81.5203i | − | 0.127975i | ||||||
\(638\) | −233.435 | −0.365886 | ||||||||
\(639\) | −335.004 | − | 539.472i | −0.524263 | − | 0.844245i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 528.629i | 0.824694i | 0.911027 | + | 0.412347i | \(0.135291\pi\) | ||||
−0.911027 | + | 0.412347i | \(0.864709\pi\) | |||||||
\(642\) | 787.449 | − | 224.605i | 1.22656 | − | 0.349852i | ||||
\(643\) | − | 33.4392i | − | 0.0520050i | −0.999662 | − | 0.0260025i | \(-0.991722\pi\) | ||
0.999662 | − | 0.0260025i | \(-0.00827779\pi\) | |||||||
\(644\) | − | 560.792i | − | 0.870795i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 257.624 | 0.398798 | ||||||||
\(647\) | 786.308 | 1.21531 | 0.607657 | − | 0.794200i | \(-0.292110\pi\) | ||||
0.607657 | + | 0.794200i | \(0.292110\pi\) | |||||||
\(648\) | 540.366 | − | 1092.35i | 0.833898 | − | 1.68573i | ||||
\(649\) | −647.867 | −0.998254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 62.5020 | + | 219.127i | 0.0960092 | + | 0.336601i | ||||
\(652\) | 588.361i | 0.902394i | ||||||||
\(653\) | −385.807 | −0.590823 | −0.295412 | − | 0.955370i | \(-0.595457\pi\) | ||||
−0.295412 | + | 0.955370i | \(0.595457\pi\) | |||||||
\(654\) | 369.565 | − | 105.412i | 0.565084 | − | 0.161180i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1315.87i | 2.00590i | ||||||||
\(657\) | 364.588 | + | 587.114i | 0.554929 | + | 0.893628i | ||||
\(658\) | 306.243i | 0.465415i | ||||||||
\(659\) | 97.2583i | 0.147585i | 0.997274 | + | 0.0737924i | \(0.0235102\pi\) | ||||
−0.997274 | + | 0.0737924i | \(0.976490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −961.505 | −1.45462 | −0.727311 | − | 0.686309i | \(-0.759230\pi\) | ||||
−0.727311 | + | 0.686309i | \(0.759230\pi\) | |||||||
\(662\) | 541.205 | 0.817530 | ||||||||
\(663\) | −43.3910 | − | 152.125i | −0.0654464 | − | 0.229450i | ||||
\(664\) | 1117.66 | 1.68322 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −549.984 | − | 885.665i | −0.825802 | − | 1.32983i | ||||
\(667\) | 242.745i | 0.363936i | ||||||||
\(668\) | 1716.27 | 2.56927 | ||||||||
\(669\) | −144.037 | − | 504.981i | −0.215301 | − | 0.754830i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 403.323i | 0.601078i | ||||||||
\(672\) | 18.4485 | + | 64.6791i | 0.0274531 | + | 0.0962487i | ||||
\(673\) | 1089.81i | 1.61933i | 0.586895 | + | 0.809663i | \(0.300350\pi\) | ||||
−0.586895 | + | 0.809663i | \(0.699650\pi\) | |||||||
\(674\) | 1413.03i | 2.09648i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 276.741 | 0.409380 | ||||||||
\(677\) | −1252.56 | −1.85016 | −0.925080 | − | 0.379771i | \(-0.876003\pi\) | ||||
−0.925080 | + | 0.379771i | \(0.876003\pi\) | |||||||
\(678\) | 220.085 | − | 62.7752i | 0.324609 | − | 0.0925888i | ||||
\(679\) | 61.2915 | 0.0902673 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 512.290 | − | 146.121i | 0.752262 | − | 0.214569i | ||||
\(682\) | − | 705.741i | − | 1.03481i | ||||||
\(683\) | 341.097 | 0.499409 | 0.249705 | − | 0.968322i | \(-0.419666\pi\) | ||||
0.249705 | + | 0.968322i | \(0.419666\pi\) | |||||||
\(684\) | −1028.82 | + | 638.880i | −1.50412 | + | 0.934035i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 64.9306i | − | 0.0946510i | ||||||
\(687\) | −117.739 | + | 33.5830i | −0.171382 | + | 0.0488836i | ||||
\(688\) | 472.450i | 0.686700i | ||||||||
\(689\) | − | 176.873i | − | 0.256709i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −783.667 | −1.13411 | −0.567053 | − | 0.823682i | \(-0.691916\pi\) | ||||
−0.567053 | + | 0.823682i | \(0.691916\pi\) | |||||||
\(692\) | 899.327 | 1.29961 | ||||||||
\(693\) | 141.841 | − | 88.0810i | 0.204677 | − | 0.127101i | ||||
\(694\) | 1652.14 | 2.38060 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −117.565 | − | 412.173i | −0.168915 | − | 0.592203i | ||||
\(697\) | − | 304.251i | − | 0.436515i | ||||||
\(698\) | 1277.97 | 1.83090 | ||||||||
\(699\) | 1118.48 | − | 319.025i | 1.60011 | − | 0.456402i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1331.76i | − | 1.89979i | −0.312562 | − | 0.949897i | \(-0.601187\pi\) | ||
0.312562 | − | 0.949897i | \(-0.398813\pi\) | |||||||
\(702\) | 816.129 | + | 741.073i | 1.16258 | + | 1.05566i | ||||
\(703\) | 536.207i | 0.762740i | ||||||||
\(704\) | 340.941i | 0.484291i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −302.708 | −0.428766 | ||||||||
\(707\) | 356.930 | 0.504852 | ||||||||
\(708\) | −630.406 | − | 2210.16i | −0.890404 | − | 3.12169i | ||||
\(709\) | −763.963 | −1.07752 | −0.538761 | − | 0.842459i | \(-0.681107\pi\) | ||||
−0.538761 | + | 0.842459i | \(0.681107\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −972.899 | + | 604.155i | −1.36835 | + | 0.849726i | ||||
\(712\) | 1916.48i | 2.69168i | ||||||||
\(713\) | −733.888 | −1.02930 | ||||||||
\(714\) | −34.5608 | − | 121.167i | −0.0484045 | − | 0.169702i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1321.31i | − | 1.84540i | ||||||
\(717\) | 40.7512 | + | 142.871i | 0.0568357 | + | 0.199262i | ||||
\(718\) | − | 1304.44i | − | 1.81677i | ||||||
\(719\) | 623.715i | 0.867476i | 0.901039 | + | 0.433738i | \(0.142806\pi\) | ||||
−0.901039 | + | 0.433738i | \(0.857194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −316.826 | −0.439426 | ||||||||
\(722\) | −342.274 | −0.474064 | ||||||||
\(723\) | 938.318 | − | 267.638i | 1.29781 | − | 0.370177i | ||||
\(724\) | −1939.29 | −2.67858 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 726.556 | − | 207.237i | 1.00077 | − | 0.285450i | ||||
\(727\) | 678.494i | 0.933279i | 0.884448 | + | 0.466640i | \(0.154536\pi\) | ||||
−0.884448 | + | 0.466640i | \(0.845464\pi\) | |||||||
\(728\) | −463.584 | −0.636791 | ||||||||
\(729\) | −70.1111 | − | 725.621i | −0.0961744 | − | 0.995364i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 109.238i | − | 0.149436i | ||||||
\(732\) | −1375.91 | + | 392.454i | −1.87966 | + | 0.536139i | ||||
\(733\) | 394.966i | 0.538835i | 0.963023 | + | 0.269417i | \(0.0868311\pi\) | ||||
−0.963023 | + | 0.269417i | \(0.913169\pi\) | |||||||
\(734\) | − | 567.208i | − | 0.772763i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −216.620 | −0.294320 | ||||||||
\(737\) | 106.342 | 0.144290 | ||||||||
\(738\) | 1118.50 | + | 1801.18i | 1.51559 | + | 2.44062i | ||||
\(739\) | −292.199 | −0.395397 | −0.197699 | − | 0.980263i | \(-0.563347\pi\) | ||||
−0.197699 | + | 0.980263i | \(0.563347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −155.520 | − | 545.242i | −0.209879 | − | 0.735819i | ||||
\(742\) | − | 140.878i | − | 0.189863i | ||||||
\(743\) | 383.452 | 0.516086 | 0.258043 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258043 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(744\) | 1246.12 | − | 355.432i | 1.67489 | − | 0.477731i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 1326.12i | − | 1.77764i | ||||||
\(747\) | 567.960 | − | 352.694i | 0.760321 | − | 0.472147i | ||||
\(748\) | 263.247i | 0.351935i | ||||||||
\(749\) | 205.983i | 0.275011i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −696.332 | −0.927206 | −0.463603 | − | 0.886043i | \(-0.653444\pi\) | ||||
−0.463603 | + | 0.886043i | \(0.653444\pi\) | |||||||
\(752\) | 646.538 | 0.859758 | ||||||||
\(753\) | −217.019 | − | 760.852i | −0.288206 | − | 1.01043i | ||||
\(754\) | 387.705 | 0.514197 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 438.501 | + | 398.174i | 0.580028 | + | 0.526686i | ||||
\(757\) | 967.357i | 1.27788i | 0.769256 | + | 0.638941i | \(0.220627\pi\) | ||||
−0.769256 | + | 0.638941i | \(0.779373\pi\) | |||||||
\(758\) | 178.092 | 0.234950 | ||||||||
\(759\) | 147.498 | + | 517.117i | 0.194332 | + | 0.681313i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 89.7059i | 0.117879i | 0.998262 | + | 0.0589395i | \(0.0187719\pi\) | ||||
−0.998262 | + | 0.0589395i | \(0.981228\pi\) | |||||||
\(762\) | −44.4771 | − | 155.933i | −0.0583689 | − | 0.204637i | ||||
\(763\) | 96.6719i | 0.126700i | ||||||||
\(764\) | − | 2389.69i | − | 3.12787i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 397.506 | 0.518937 | ||||||||
\(767\) | 1076.02 | 1.40290 | ||||||||
\(768\) | −1505.93 | + | 429.538i | −1.96084 | + | 0.559294i | ||||
\(769\) | −926.219 | −1.20445 | −0.602223 | − | 0.798328i | \(-0.705718\pi\) | ||||
−0.602223 | + | 0.798328i | \(0.705718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 436.148 | − | 124.403i | 0.565691 | − | 0.161353i | ||||
\(772\) | − | 639.454i | − | 0.828308i | ||||||
\(773\) | −424.125 | −0.548674 | −0.274337 | − | 0.961634i | \(-0.588458\pi\) | ||||
−0.274337 | + | 0.961634i | \(0.588458\pi\) | |||||||
\(774\) | 401.587 | + | 646.694i | 0.518846 | + | 0.835522i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 348.548i | − | 0.449160i | ||||||
\(777\) | 252.193 | − | 71.9333i | 0.324572 | − | 0.0925783i | ||||
\(778\) | 2543.84i | 3.26972i | ||||||||
\(779\) | − | 1090.48i | − | 1.39985i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −494.745 | −0.633476 | ||||||||
\(782\) | 405.807 | 0.518935 | ||||||||
\(783\) | −189.810 | − | 172.354i | −0.242414 | − | 0.220120i | ||||
\(784\) | −137.081 | −0.174848 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 528.261 | + | 1852.04i | 0.672088 | + | 2.35629i | ||||
\(787\) | − | 155.889i | − | 0.198080i | −0.995083 | − | 0.0990399i | \(-0.968423\pi\) | ||
0.995083 | − | 0.0990399i | \(-0.0315772\pi\) | |||||||
\(788\) | 1131.24 | 1.43558 | ||||||||
\(789\) | 330.006 | − | 94.1282i | 0.418259 | − | 0.119301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.5705i | 0.0727820i | ||||||||
\(792\) | −500.893 | − | 806.612i | −0.632441 | − | 1.01845i | ||||
\(793\) | − | 669.867i | − | 0.844725i | ||||||
\(794\) | − | 330.771i | − | 0.416588i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −717.903 | −0.901888 | ||||||||
\(797\) | −719.191 | −0.902373 | −0.451186 | − | 0.892430i | \(-0.648999\pi\) | ||||
−0.451186 | + | 0.892430i | \(0.648999\pi\) | |||||||
\(798\) | −123.871 | − | 434.284i | −0.155227 | − | 0.544215i | ||||
\(799\) | −149.490 | −0.187097 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 604.774 | + | 973.895i | 0.755023 | + | 1.21585i | ||||
\(802\) | − | 2375.84i | − | 2.96240i | ||||||
\(803\) | 538.437 | 0.670531 | ||||||||
\(804\) | 103.476 | + | 362.778i | 0.128701 | + | 0.451217i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1172.14i | 1.45427i | ||||||||
\(807\) | −3.91828 | − | 13.7372i | −0.00485537 | − | 0.0170226i | ||||
\(808\) | − | 2029.77i | − | 2.51209i | ||||||
\(809\) | − | 212.244i | − | 0.262353i | −0.991359 | − | 0.131176i | \(-0.958125\pi\) | ||
0.991359 | − | 0.131176i | \(-0.0418755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1058.66 | 1.30538 | 0.652690 | − | 0.757625i | \(-0.273641\pi\) | ||||
0.652690 | + | 0.757625i | \(0.273641\pi\) | |||||||
\(812\) | 208.311 | 0.256541 | ||||||||
\(813\) | −1496.42 | + | 426.826i | −1.84061 | + | 0.525001i | ||||
\(814\) | −812.235 | −0.997832 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −255.808 | + | 72.9645i | −0.313490 | + | 0.0894172i | ||||
\(817\) | − | 391.527i | − | 0.479225i | ||||||
\(818\) | −60.8792 | −0.0744244 | ||||||||
\(819\) | −235.579 | + | 146.291i | −0.287642 | + | 0.178621i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 818.571i | − | 0.997042i | −0.866878 | − | 0.498521i | \(-0.833877\pi\) | ||
0.866878 | − | 0.498521i | \(-0.166123\pi\) | |||||||
\(822\) | −333.929 | + | 95.2470i | −0.406240 | + | 0.115872i | ||||
\(823\) | − | 206.850i | − | 0.251336i | −0.992072 | − | 0.125668i | \(-0.959893\pi\) | ||
0.992072 | − | 0.125668i | \(-0.0401074\pi\) | |||||||
\(824\) | 1801.71i | 2.18654i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 857.047 | 1.03759 | ||||||||
\(827\) | −438.639 | −0.530398 | −0.265199 | − | 0.964194i | \(-0.585438\pi\) | ||||
−0.265199 | + | 0.964194i | \(0.585438\pi\) | |||||||
\(828\) | −1620.59 | + | 1006.36i | −1.95723 | + | 1.21541i | ||||
\(829\) | −654.804 | −0.789872 | −0.394936 | − | 0.918709i | \(-0.629233\pi\) | ||||
−0.394936 | + | 0.918709i | \(0.629233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −99.6379 | − | 349.323i | −0.119901 | − | 0.420364i | ||||
\(832\) | − | 566.257i | − | 0.680598i | ||||||
\(833\) | 31.6954 | 0.0380497 | ||||||||
\(834\) | −653.812 | + | 186.488i | −0.783947 | + | 0.223606i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 943.520i | 1.12861i | ||||||||
\(837\) | 521.077 | − | 573.851i | 0.622553 | − | 0.685604i | ||||
\(838\) | − | 477.055i | − | 0.569278i | ||||||
\(839\) | 50.9710i | 0.0607521i | 0.999539 | + | 0.0303761i | \(0.00967049\pi\) | ||||
−0.999539 | + | 0.0303761i | \(0.990330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 750.830 | 0.892782 | ||||||||
\(842\) | 1486.48 | 1.76542 | ||||||||
\(843\) | 335.121 | + | 1174.91i | 0.397533 | + | 1.39372i | ||||
\(844\) | 160.996 | 0.190754 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 884.988 | − | 549.564i | 1.04609 | − | 0.649603i | ||||
\(847\) | 190.055i | 0.224386i | ||||||||
\(848\) | −297.422 | −0.350733 | ||||||||
\(849\) | 328.026 | + | 1150.03i | 0.386368 | + | 1.35458i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 844.630i | 0.992514i | ||||||||
\(852\) | −481.411 | − | 1687.79i | −0.565037 | − | 1.98098i | ||||
\(853\) | 883.941i | 1.03627i | 0.855298 | + | 0.518137i | \(0.173374\pi\) | ||||
−0.855298 | + | 0.518137i | \(0.826626\pi\) | |||||||
\(854\) | − | 533.547i | − | 0.624762i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1171.37 | 1.36843 | ||||||||
\(857\) | −556.521 | −0.649382 | −0.324691 | − | 0.945820i | \(-0.605260\pi\) | ||||
−0.324691 | + | 0.945820i | \(0.605260\pi\) | |||||||
\(858\) | 825.922 | − | 235.579i | 0.962613 | − | 0.274568i | ||||
\(859\) | 643.078 | 0.748636 | 0.374318 | − | 0.927300i | \(-0.377877\pi\) | ||||
0.374318 | + | 0.927300i | \(0.377877\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −512.885 | + | 146.291i | −0.595685 | + | 0.169908i | ||||
\(862\) | 1192.87i | 1.38384i | ||||||||
\(863\) | 204.892 | 0.237419 | 0.118709 | − | 0.992929i | \(-0.462124\pi\) | ||||
0.118709 | + | 0.992929i | \(0.462124\pi\) | |||||||
\(864\) | 153.805 | − | 169.382i | 0.178015 | − | 0.196044i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 558.024i | − | 0.644369i | ||||||
\(867\) | −774.601 | + | 220.940i | −0.893426 | + | 0.254833i | ||||
\(868\) | 629.786i | 0.725559i | ||||||||
\(869\) | 892.237i | 1.02674i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −176.620 | −0.202778 | ||||||||
\(872\) | 549.747 | 0.630444 | ||||||||
\(873\) | −109.990 | − | 177.122i | −0.125991 | − | 0.202888i | ||||
\(874\) | 1454.48 | 1.66416 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 523.925 | + | 1836.84i | 0.598088 | + | 2.09685i | ||||
\(877\) | − | 207.210i | − | 0.236272i | −0.992997 | − | 0.118136i | \(-0.962308\pi\) | ||
0.992997 | − | 0.118136i | \(-0.0376919\pi\) | |||||||
\(878\) | −449.015 | −0.511406 | ||||||||
\(879\) | 7.31119 | − | 2.08538i | 0.00831762 | − | 0.00237245i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1391.37i | − | 1.57931i | −0.613552 | − | 0.789654i | \(-0.710260\pi\) | ||
0.613552 | − | 0.789654i | \(-0.289740\pi\) | |||||||
\(882\) | −187.638 | + | 116.520i | −0.212741 | + | 0.132109i | ||||
\(883\) | 1091.99i | 1.23668i | 0.785909 | + | 0.618342i | \(0.212195\pi\) | ||||
−0.785909 | + | 0.618342i | \(0.787805\pi\) | |||||||
\(884\) | − | 437.219i | − | 0.494591i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −691.859 | −0.780879 | ||||||||
\(887\) | −149.449 | −0.168488 | −0.0842439 | − | 0.996445i | \(-0.526847\pi\) | ||||
−0.0842439 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(888\) | −409.066 | − | 1434.15i | −0.460659 | − | 1.61504i | ||||
\(889\) | 40.7895 | 0.0458825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −509.077 | − | 251.831i | −0.571355 | − | 0.282638i | ||||
\(892\) | − | 1451.35i | − | 1.62707i | ||||||
\(893\) | −535.797 | −0.599996 | ||||||||
\(894\) | −564.686 | − | 1979.75i | −0.631640 | − | 2.21448i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 540.700i | − | 0.603460i | ||||||
\(897\) | −244.975 | − | 858.863i | −0.273104 | − | 0.957483i | ||||
\(898\) | − | 519.231i | − | 0.578209i | ||||||
\(899\) | − | 272.610i | − | 0.303237i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68.7687 | 0.0763249 | ||||||||
\(902\) | 1651.84 | 1.83131 | ||||||||
\(903\) | −184.146 | + | 52.5242i | −0.203927 | + | 0.0581663i | ||||
\(904\) | 327.388 | 0.362155 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1034.21 | − | 294.988i | 1.14151 | − | 0.325594i | ||||
\(907\) | 593.718i | 0.654595i | 0.944921 | + | 0.327297i | \(0.106138\pi\) | ||||
−0.944921 | + | 0.327297i | \(0.893862\pi\) | |||||||
\(908\) | 1472.35 | 1.62154 | ||||||||
\(909\) | −640.524 | − | 1031.47i | −0.704647 | − | 1.13473i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1133.75i | 1.24451i | 0.782815 | + | 0.622254i | \(0.213783\pi\) | ||||
−0.782815 | + | 0.622254i | \(0.786217\pi\) | |||||||
\(912\) | −916.856 | + | 261.516i | −1.00532 | + | 0.286750i | ||||
\(913\) | − | 520.871i | − | 0.570504i | ||||||
\(914\) | − | 428.474i | − | 0.468790i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −338.391 | −0.369422 | ||||||||
\(917\) | −484.464 | −0.528314 | ||||||||
\(918\) | −288.132 | + | 317.314i | −0.313869 | + | 0.345658i | ||||
\(919\) | 684.988 | 0.745363 | 0.372681 | − | 0.927959i | \(-0.378438\pi\) | ||||
0.372681 | + | 0.927959i | \(0.378438\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 70.9620 | + | 248.787i | 0.0770489 | + | 0.270128i | ||||
\(922\) | 2110.88i | 2.28945i | ||||||||
\(923\) | 821.706 | 0.890256 | ||||||||
\(924\) | 443.763 | − | 126.575i | 0.480263 | − | 0.136986i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2233.49i | 2.41197i | ||||||||
\(927\) | 568.556 | + | 915.571i | 0.613328 | + | 0.987671i | ||||
\(928\) | − | 80.4654i | − | 0.0867084i | ||||||
\(929\) | 192.317i | 0.207015i | 0.994629 | + | 0.103507i | \(0.0330066\pi\) | ||||
−0.994629 | + | 0.103507i | \(0.966993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 113.601 | 0.122021 | ||||||||
\(932\) | 3214.58 | 3.44912 | ||||||||
\(933\) | 124.893 | + | 437.867i | 0.133862 | + | 0.469310i | ||||
\(934\) | 2691.52 | 2.88171 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 831.918 | + | 1339.68i | 0.888801 | + | 1.43128i | ||||
\(937\) | − | 1270.28i | − | 1.35569i | −0.735206 | − | 0.677844i | \(-0.762914\pi\) | ||
0.735206 | − | 0.677844i | \(-0.237086\pi\) | |||||||
\(938\) | −140.677 | −0.149975 | ||||||||
\(939\) | −261.771 | − | 917.750i | −0.278777 | − | 0.977370i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 156.951i | 0.166791i | 0.996517 | + | 0.0833957i | \(0.0265766\pi\) | ||||
−0.996517 | + | 0.0833957i | \(0.973423\pi\) | |||||||
\(942\) | 302.119 | + | 1059.21i | 0.320721 | + | 1.12442i | ||||
\(943\) | − | 1717.73i | − | 1.82155i | ||||||
\(944\) | − | 1809.39i | − | 1.91673i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 593.077 | 0.626931 | ||||||||
\(947\) | −879.945 | −0.929193 | −0.464596 | − | 0.885523i | \(-0.653801\pi\) | ||||
−0.464596 | + | 0.885523i | \(0.653801\pi\) | |||||||
\(948\) | −3043.81 | + | 868.191i | −3.21077 | + | 0.915813i | ||||
\(949\) | −894.272 | −0.942331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1050.18 | + | 299.543i | −1.10429 | + | 0.314977i | ||||
\(952\) | − | 180.243i | − | 0.189331i | ||||||
\(953\) | 563.276 | 0.591056 | 0.295528 | − | 0.955334i | \(-0.404505\pi\) | ||||
0.295528 | + | 0.955334i | \(0.404505\pi\) | |||||||
\(954\) | −407.114 | + | 252.811i | −0.426744 | + | 0.265001i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 410.619i | 0.429518i | ||||||||
\(957\) | −192.088 | + | 54.7895i | −0.200719 | + | 0.0572513i | ||||
\(958\) | − | 1380.83i | − | 1.44136i | ||||||
\(959\) | − | 87.3502i | − | 0.0910847i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −136.822 | −0.142375 | ||||||||
\(962\) | 1349.02 | 1.40230 | ||||||||
\(963\) | 595.255 | − | 369.644i | 0.618126 | − | 0.383847i | ||||
\(964\) | 2696.79 | 2.79750 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −195.122 | − | 684.081i | −0.201989 | − | 0.708159i | ||||
\(967\) | 237.676i | 0.245787i | 0.992420 | + | 0.122893i | \(0.0392173\pi\) | ||||
−0.992420 | + | 0.122893i | \(0.960783\pi\) | |||||||
\(968\) | 1080.79 | 1.11652 | ||||||||
\(969\) | 211.992 | − | 60.4668i | 0.218774 | − | 0.0624013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1355.00i | − | 1.39546i | −0.716359 | − | 0.697732i | \(-0.754192\pi\) | ||
0.716359 | − | 0.697732i | \(-0.245808\pi\) | |||||||
\(972\) | 363.748 | − | 1981.73i | 0.374226 | − | 2.03882i | ||||
\(973\) | − | 171.026i | − | 0.175772i | ||||||
\(974\) | 2010.33i | 2.06399i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1126.42 | −1.15412 | ||||||||
\(977\) | 493.726 | 0.505349 | 0.252674 | − | 0.967551i | \(-0.418690\pi\) | ||||
0.252674 | + | 0.967551i | \(0.418690\pi\) | |||||||
\(978\) | 204.714 | + | 717.711i | 0.209319 | + | 0.733856i | ||||
\(979\) | 893.150 | 0.912309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 279.365 | − | 173.481i | 0.284775 | − | 0.176841i | ||||
\(982\) | − | 598.797i | − | 0.609773i | ||||||
\(983\) | −1538.05 | −1.56465 | −0.782325 | − | 0.622870i | \(-0.785966\pi\) | ||||
−0.782325 | + | 0.622870i | \(0.785966\pi\) | |||||||
\(984\) | 831.918 | + | 2916.64i | 0.845445 | + | 2.96406i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 150.741i | 0.152881i | ||||||||
\(987\) | 71.8783 | + | 252.000i | 0.0728251 | + | 0.255319i | ||||
\(988\) | − | 1567.06i | − | 1.58609i | ||||||
\(989\) | − | 616.731i | − | 0.623590i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1514.73 | 1.52849 | 0.764243 | − | 0.644929i | \(-0.223113\pi\) | ||||
0.764243 | + | 0.644929i | \(0.223113\pi\) | |||||||
\(992\) | 243.270 | 0.245232 | ||||||||
\(993\) | 445.344 | − | 127.026i | 0.448483 | − | 0.127922i | ||||
\(994\) | 654.486 | 0.658437 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1776.92 | − | 506.833i | 1.78405 | − | 0.508868i | ||||
\(997\) | 1826.43i | 1.83193i | 0.401260 | + | 0.915964i | \(0.368572\pi\) | ||||
−0.401260 | + | 0.915964i | \(0.631428\pi\) | |||||||
\(998\) | 2972.37 | 2.97833 | ||||||||
\(999\) | −660.443 | − | 599.705i | −0.661104 | − | 0.600306i |
(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 | 525.3.f.a.449.7 | 8 | ||
3.2 | odd | 2 | inner | 525.3.f.a.449.1 | 8 | ||
5.2 | odd | 4 | 525.3.c.a.176.4 | 4 | |||
5.3 | odd | 4 | 21.3.b.a.8.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 525.3.f.a.449.2 | 8 | ||
15.2 | even | 4 | 525.3.c.a.176.1 | 4 | |||
15.8 | even | 4 | 21.3.b.a.8.4 | yes | 4 | ||
15.14 | odd | 2 | inner | 525.3.f.a.449.8 | 8 | ||
20.3 | even | 4 | 336.3.d.c.113.1 | 4 | |||
35.3 | even | 12 | 147.3.h.c.128.4 | 8 | |||
35.13 | even | 4 | 147.3.b.f.50.1 | 4 | |||
35.18 | odd | 12 | 147.3.h.e.128.4 | 8 | |||
35.23 | odd | 12 | 147.3.h.e.116.1 | 8 | |||
35.33 | even | 12 | 147.3.h.c.116.1 | 8 | |||
40.3 | even | 4 | 1344.3.d.b.449.4 | 4 | |||
40.13 | odd | 4 | 1344.3.d.f.449.1 | 4 | |||
45.13 | odd | 12 | 567.3.r.c.512.4 | 8 | |||
45.23 | even | 12 | 567.3.r.c.512.1 | 8 | |||
45.38 | even | 12 | 567.3.r.c.134.4 | 8 | |||
45.43 | odd | 12 | 567.3.r.c.134.1 | 8 | |||
60.23 | odd | 4 | 336.3.d.c.113.2 | 4 | |||
105.23 | even | 12 | 147.3.h.e.116.4 | 8 | |||
105.38 | odd | 12 | 147.3.h.c.128.1 | 8 | |||
105.53 | even | 12 | 147.3.h.e.128.1 | 8 | |||
105.68 | odd | 12 | 147.3.h.c.116.4 | 8 | |||
105.83 | odd | 4 | 147.3.b.f.50.4 | 4 | |||
120.53 | even | 4 | 1344.3.d.f.449.2 | 4 | |||
120.83 | odd | 4 | 1344.3.d.b.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.1 | ✓ | 4 | 5.3 | odd | 4 | ||
21.3.b.a.8.4 | yes | 4 | 15.8 | even | 4 | ||
147.3.b.f.50.1 | 4 | 35.13 | even | 4 | |||
147.3.b.f.50.4 | 4 | 105.83 | odd | 4 | |||
147.3.h.c.116.1 | 8 | 35.33 | even | 12 | |||
147.3.h.c.116.4 | 8 | 105.68 | odd | 12 | |||
147.3.h.c.128.1 | 8 | 105.38 | odd | 12 | |||
147.3.h.c.128.4 | 8 | 35.3 | even | 12 | |||
147.3.h.e.116.1 | 8 | 35.23 | odd | 12 | |||
147.3.h.e.116.4 | 8 | 105.23 | even | 12 | |||
147.3.h.e.128.1 | 8 | 105.53 | even | 12 | |||
147.3.h.e.128.4 | 8 | 35.18 | odd | 12 | |||
336.3.d.c.113.1 | 4 | 20.3 | even | 4 | |||
336.3.d.c.113.2 | 4 | 60.23 | odd | 4 | |||
525.3.c.a.176.1 | 4 | 15.2 | even | 4 | |||
525.3.c.a.176.4 | 4 | 5.2 | odd | 4 | |||
525.3.f.a.449.1 | 8 | 3.2 | odd | 2 | inner | ||
525.3.f.a.449.2 | 8 | 5.4 | even | 2 | inner | ||
525.3.f.a.449.7 | 8 | 1.1 | even | 1 | trivial | ||
525.3.f.a.449.8 | 8 | 15.14 | odd | 2 | inner | ||
567.3.r.c.134.1 | 8 | 45.43 | odd | 12 | |||
567.3.r.c.134.4 | 8 | 45.38 | even | 12 | |||
567.3.r.c.512.1 | 8 | 45.23 | even | 12 | |||
567.3.r.c.512.4 | 8 | 45.13 | odd | 12 | |||
1344.3.d.b.449.3 | 4 | 120.83 | odd | 4 | |||
1344.3.d.b.449.4 | 4 | 40.3 | even | 4 | |||
1344.3.d.f.449.1 | 4 | 40.13 | odd | 4 | |||
1344.3.d.f.449.2 | 4 | 120.53 | even | 4 |