Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(251,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.12 | ||
Root | \(1.07046 - 0.924187i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.251 |
Dual form | 280.2.h.b.251.11 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07046 | + | 0.924187i | 0.756928 | + | 0.653499i | ||||
\(3\) | − | 2.99734i | − | 1.73052i | −0.501328 | − | 0.865258i | \(-0.667155\pi\) | ||
0.501328 | − | 0.865258i | \(-0.332845\pi\) | |||||||
\(4\) | 0.291758 | + | 1.97860i | 0.145879 | + | 0.989302i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.77010 | − | 3.20852i | 1.13089 | − | 1.30987i | ||||
\(7\) | 0.183359 | − | 2.63939i | 0.0693031 | − | 0.997596i | ||||
\(8\) | −1.51629 | + | 2.38765i | −0.536088 | + | 0.844162i | ||||
\(9\) | −5.98405 | −1.99468 | ||||||||
\(10\) | 1.07046 | + | 0.924187i | 0.338508 | + | 0.292253i | ||||
\(11\) | 4.87706 | 1.47049 | 0.735244 | − | 0.677803i | \(-0.237068\pi\) | ||||
0.735244 | + | 0.677803i | \(0.237068\pi\) | |||||||
\(12\) | 5.93055 | − | 0.874498i | 1.71200 | − | 0.252446i | ||||
\(13\) | −2.42800 | −0.673406 | −0.336703 | − | 0.941611i | \(-0.609312\pi\) | ||||
−0.336703 | + | 0.941611i | \(0.609312\pi\) | |||||||
\(14\) | 2.63557 | − | 2.65590i | 0.704385 | − | 0.709818i | ||||
\(15\) | − | 2.99734i | − | 0.773910i | ||||||
\(16\) | −3.82975 | + | 1.15455i | −0.957439 | + | 0.288637i | ||||
\(17\) | − | 3.92955i | − | 0.953057i | −0.879159 | − | 0.476528i | \(-0.841895\pi\) | ||
0.879159 | − | 0.476528i | \(-0.158105\pi\) | |||||||
\(18\) | −6.40567 | − | 5.53038i | −1.50983 | − | 1.30352i | ||||
\(19\) | 5.24043i | 1.20224i | 0.799160 | + | 0.601118i | \(0.205278\pi\) | ||||
−0.799160 | + | 0.601118i | \(0.794722\pi\) | |||||||
\(20\) | 0.291758 | + | 1.97860i | 0.0652391 | + | 0.442430i | ||||
\(21\) | −7.91115 | − | 0.549588i | −1.72635 | − | 0.119930i | ||||
\(22\) | 5.22068 | + | 4.50731i | 1.11305 | + | 0.960962i | ||||
\(23\) | 0.114122i | 0.0237961i | 0.999929 | + | 0.0118981i | \(0.00378736\pi\) | ||||
−0.999929 | + | 0.0118981i | \(0.996213\pi\) | |||||||
\(24\) | 7.15660 | + | 4.54482i | 1.46084 | + | 0.927708i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.59907 | − | 2.24393i | −0.509720 | − | 0.440070i | ||||
\(27\) | 8.94421i | 1.72131i | ||||||||
\(28\) | 5.27581 | − | 0.407269i | 0.997034 | − | 0.0769665i | ||||
\(29\) | 3.60881i | 0.670139i | 0.942193 | + | 0.335069i | \(0.108760\pi\) | ||||
−0.942193 | + | 0.335069i | \(0.891240\pi\) | |||||||
\(30\) | 2.77010 | − | 3.20852i | 0.505749 | − | 0.585794i | ||||
\(31\) | 4.62694 | 0.831023 | 0.415511 | − | 0.909588i | \(-0.363603\pi\) | ||||
0.415511 | + | 0.909588i | \(0.363603\pi\) | |||||||
\(32\) | −5.16661 | − | 2.30351i | −0.913336 | − | 0.407208i | ||||
\(33\) | − | 14.6182i | − | 2.54470i | ||||||
\(34\) | 3.63164 | − | 4.20642i | 0.622821 | − | 0.721395i | ||||
\(35\) | 0.183359 | − | 2.63939i | 0.0309933 | − | 0.446138i | ||||
\(36\) | −1.74589 | − | 11.8401i | −0.290982 | − | 1.97334i | ||||
\(37\) | 7.83800i | 1.28856i | 0.764790 | + | 0.644279i | \(0.222843\pi\) | ||||
−0.764790 | + | 0.644279i | \(0.777157\pi\) | |||||||
\(38\) | −4.84313 | + | 5.60965i | −0.785660 | + | 0.910006i | ||||
\(39\) | 7.27754i | 1.16534i | ||||||||
\(40\) | −1.51629 | + | 2.38765i | −0.239746 | + | 0.377521i | ||||
\(41\) | 10.4815i | 1.63694i | 0.574552 | + | 0.818468i | \(0.305176\pi\) | ||||
−0.574552 | + | 0.818468i | \(0.694824\pi\) | |||||||
\(42\) | −7.96063 | − | 7.89969i | −1.22835 | − | 1.21895i | ||||
\(43\) | 2.76350 | 0.421430 | 0.210715 | − | 0.977548i | \(-0.432421\pi\) | ||||
0.210715 | + | 0.977548i | \(0.432421\pi\) | |||||||
\(44\) | 1.42292 | + | 9.64977i | 0.214513 | + | 1.45476i | ||||
\(45\) | −5.98405 | −0.892049 | ||||||||
\(46\) | −0.105470 | + | 0.122163i | −0.0155507 | + | 0.0180119i | ||||
\(47\) | −12.0817 | −1.76229 | −0.881145 | − | 0.472846i | \(-0.843227\pi\) | ||||
−0.881145 | + | 0.472846i | \(0.843227\pi\) | |||||||
\(48\) | 3.46057 | + | 11.4791i | 0.499490 | + | 1.65686i | ||||
\(49\) | −6.93276 | − | 0.967910i | −0.990394 | − | 0.138273i | ||||
\(50\) | 1.07046 | + | 0.924187i | 0.151386 | + | 0.130700i | ||||
\(51\) | −11.7782 | −1.64928 | ||||||||
\(52\) | −0.708388 | − | 4.80405i | −0.0982358 | − | 0.666202i | ||||
\(53\) | − | 0.668088i | − | 0.0917689i | −0.998947 | − | 0.0458845i | \(-0.985389\pi\) | ||
0.998947 | − | 0.0458845i | \(-0.0146106\pi\) | |||||||
\(54\) | −8.26612 | + | 9.57439i | −1.12488 | + | 1.30291i | ||||
\(55\) | 4.87706 | 0.657622 | ||||||||
\(56\) | 6.02392 | + | 4.43987i | 0.804980 | + | 0.593302i | ||||
\(57\) | 15.7073 | 2.08049 | ||||||||
\(58\) | −3.33521 | + | 3.86307i | −0.437935 | + | 0.507246i | ||||
\(59\) | 1.37541i | 0.179063i | 0.995984 | + | 0.0895314i | \(0.0285369\pi\) | ||||
−0.995984 | + | 0.0895314i | \(0.971463\pi\) | |||||||
\(60\) | 5.93055 | − | 0.874498i | 0.765631 | − | 0.112897i | ||||
\(61\) | −1.17808 | −0.150837 | −0.0754186 | − | 0.997152i | \(-0.524029\pi\) | ||||
−0.0754186 | + | 0.997152i | \(0.524029\pi\) | |||||||
\(62\) | 4.95294 | + | 4.27615i | 0.629024 | + | 0.543072i | ||||
\(63\) | −1.09723 | + | 15.7942i | −0.138238 | + | 1.98989i | ||||
\(64\) | −3.40175 | − | 7.24072i | −0.425219 | − | 0.905090i | ||||
\(65\) | −2.42800 | −0.301156 | ||||||||
\(66\) | 13.5099 | − | 15.6482i | 1.66296 | − | 1.92615i | ||||
\(67\) | 2.57766 | 0.314911 | 0.157456 | − | 0.987526i | \(-0.449671\pi\) | ||||
0.157456 | + | 0.987526i | \(0.449671\pi\) | |||||||
\(68\) | 7.77504 | − | 1.14648i | 0.942862 | − | 0.139031i | ||||
\(69\) | 0.342063 | 0.0411795 | ||||||||
\(70\) | 2.63557 | − | 2.65590i | 0.315010 | − | 0.317440i | ||||
\(71\) | − | 9.43699i | − | 1.11996i | −0.828505 | − | 0.559982i | \(-0.810808\pi\) | ||
0.828505 | − | 0.559982i | \(-0.189192\pi\) | |||||||
\(72\) | 9.07353 | − | 14.2878i | 1.06933 | − | 1.68384i | ||||
\(73\) | 5.62623i | 0.658500i | 0.944243 | + | 0.329250i | \(0.106796\pi\) | ||||
−0.944243 | + | 0.329250i | \(0.893204\pi\) | |||||||
\(74\) | −7.24377 | + | 8.39024i | −0.842072 | + | 0.975346i | ||||
\(75\) | − | 2.99734i | − | 0.346103i | ||||||
\(76\) | −10.3687 | + | 1.52894i | −1.18938 | + | 0.175381i | ||||
\(77\) | 0.894251 | − | 12.8725i | 0.101909 | − | 1.46695i | ||||
\(78\) | −6.72581 | + | 7.79030i | −0.761548 | + | 0.882078i | ||||
\(79\) | − | 11.8804i | − | 1.33665i | −0.743872 | − | 0.668323i | \(-0.767013\pi\) | ||
0.743872 | − | 0.668323i | \(-0.232987\pi\) | |||||||
\(80\) | −3.82975 | + | 1.15455i | −0.428180 | + | 0.129082i | ||||
\(81\) | 8.85669 | 0.984077 | ||||||||
\(82\) | −9.68687 | + | 11.2200i | −1.06974 | + | 1.23904i | ||||
\(83\) | 5.52348i | 0.606280i | 0.952946 | + | 0.303140i | \(0.0980350\pi\) | ||||
−0.952946 | + | 0.303140i | \(0.901965\pi\) | |||||||
\(84\) | −1.22072 | − | 15.8134i | −0.133192 | − | 1.72538i | ||||
\(85\) | − | 3.92955i | − | 0.426220i | ||||||
\(86\) | 2.95821 | + | 2.55399i | 0.318992 | + | 0.275404i | ||||
\(87\) | 10.8168 | 1.15969 | ||||||||
\(88\) | −7.39501 | + | 11.6447i | −0.788311 | + | 1.24133i | ||||
\(89\) | − | 6.21826i | − | 0.659135i | −0.944132 | − | 0.329567i | \(-0.893097\pi\) | ||
0.944132 | − | 0.329567i | \(-0.106903\pi\) | |||||||
\(90\) | −6.40567 | − | 5.53038i | −0.675217 | − | 0.582953i | ||||
\(91\) | −0.445195 | + | 6.40844i | −0.0466691 | + | 0.671787i | ||||
\(92\) | −0.225803 | + | 0.0332961i | −0.0235416 | + | 0.00347135i | ||||
\(93\) | − | 13.8685i | − | 1.43810i | ||||||
\(94\) | −12.9329 | − | 11.1657i | −1.33393 | − | 1.15165i | ||||
\(95\) | 5.24043i | 0.537657i | ||||||||
\(96\) | −6.90442 | + | 15.4861i | −0.704679 | + | 1.58054i | ||||
\(97\) | − | 7.85094i | − | 0.797142i | −0.917137 | − | 0.398571i | \(-0.869506\pi\) | ||
0.917137 | − | 0.398571i | \(-0.130494\pi\) | |||||||
\(98\) | −6.52669 | − | 7.44327i | −0.659296 | − | 0.751884i | ||||
\(99\) | −29.1845 | −2.93316 | ||||||||
\(100\) | 0.291758 | + | 1.97860i | 0.0291758 | + | 0.197860i | ||||
\(101\) | −10.9057 | −1.08516 | −0.542580 | − | 0.840004i | \(-0.682552\pi\) | ||||
−0.542580 | + | 0.840004i | \(0.682552\pi\) | |||||||
\(102\) | −12.6081 | − | 10.8853i | −1.24839 | − | 1.07780i | ||||
\(103\) | 15.8202 | 1.55881 | 0.779403 | − | 0.626523i | \(-0.215523\pi\) | ||||
0.779403 | + | 0.626523i | \(0.215523\pi\) | |||||||
\(104\) | 3.68154 | − | 5.79722i | 0.361005 | − | 0.568464i | ||||
\(105\) | −7.91115 | − | 0.549588i | −0.772049 | − | 0.0536343i | ||||
\(106\) | 0.617438 | − | 0.715160i | 0.0599709 | − | 0.0694624i | ||||
\(107\) | 6.53444 | 0.631708 | 0.315854 | − | 0.948808i | \(-0.397709\pi\) | ||||
0.315854 | + | 0.948808i | \(0.397709\pi\) | |||||||
\(108\) | −17.6971 | + | 2.60954i | −1.70290 | + | 0.251103i | ||||
\(109\) | − | 10.9309i | − | 1.04699i | −0.852028 | − | 0.523496i | \(-0.824628\pi\) | ||
0.852028 | − | 0.523496i | \(-0.175372\pi\) | |||||||
\(110\) | 5.22068 | + | 4.50731i | 0.497772 | + | 0.429755i | ||||
\(111\) | 23.4931 | 2.22987 | ||||||||
\(112\) | 2.34508 | + | 10.3199i | 0.221589 | + | 0.975140i | ||||
\(113\) | 3.72004 | 0.349951 | 0.174976 | − | 0.984573i | \(-0.444015\pi\) | ||||
0.174976 | + | 0.984573i | \(0.444015\pi\) | |||||||
\(114\) | 16.8140 | + | 14.5165i | 1.57478 | + | 1.35960i | ||||
\(115\) | 0.114122i | 0.0106419i | ||||||||
\(116\) | −7.14040 | + | 1.05290i | −0.662970 | + | 0.0977591i | ||||
\(117\) | 14.5293 | 1.34323 | ||||||||
\(118\) | −1.27113 | + | 1.47232i | −0.117017 | + | 0.135538i | ||||
\(119\) | −10.3716 | − | 0.720518i | −0.950766 | − | 0.0660498i | ||||
\(120\) | 7.15660 | + | 4.54482i | 0.653305 | + | 0.414884i | ||||
\(121\) | 12.7857 | 1.16233 | ||||||||
\(122\) | −1.26108 | − | 1.08876i | −0.114173 | − | 0.0985719i | ||||
\(123\) | 31.4166 | 2.83274 | ||||||||
\(124\) | 1.34995 | + | 9.15488i | 0.121229 | + | 0.822133i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −15.7714 | + | 15.8930i | −1.40502 | + | 1.41586i | ||||
\(127\) | − | 3.80326i | − | 0.337485i | −0.985660 | − | 0.168742i | \(-0.946029\pi\) | ||
0.985660 | − | 0.168742i | \(-0.0539706\pi\) | |||||||
\(128\) | 3.05035 | − | 10.8947i | 0.269615 | − | 0.962968i | ||||
\(129\) | − | 8.28315i | − | 0.729291i | ||||||
\(130\) | −2.59907 | − | 2.24393i | −0.227954 | − | 0.196805i | ||||
\(131\) | − | 7.68109i | − | 0.671100i | −0.942022 | − | 0.335550i | \(-0.891078\pi\) | ||
0.942022 | − | 0.335550i | \(-0.108922\pi\) | |||||||
\(132\) | 28.9236 | − | 4.26497i | 2.51748 | − | 0.371218i | ||||
\(133\) | 13.8315 | + | 0.960878i | 1.19935 | + | 0.0833187i | ||||
\(134\) | 2.75927 | + | 2.38224i | 0.238365 | + | 0.205794i | ||||
\(135\) | 8.94421i | 0.769795i | ||||||||
\(136\) | 9.38241 | + | 5.95833i | 0.804535 | + | 0.510922i | ||||
\(137\) | −16.9739 | −1.45018 | −0.725090 | − | 0.688655i | \(-0.758202\pi\) | ||||
−0.725090 | + | 0.688655i | \(0.758202\pi\) | |||||||
\(138\) | 0.366164 | + | 0.316130i | 0.0311699 | + | 0.0269108i | ||||
\(139\) | − | 2.54598i | − | 0.215947i | −0.994154 | − | 0.107973i | \(-0.965564\pi\) | ||
0.994154 | − | 0.107973i | \(-0.0344362\pi\) | |||||||
\(140\) | 5.27581 | − | 0.407269i | 0.445887 | − | 0.0344205i | ||||
\(141\) | 36.2128i | 3.04967i | ||||||||
\(142\) | 8.72154 | − | 10.1019i | 0.731895 | − | 0.847732i | ||||
\(143\) | −11.8415 | −0.990235 | ||||||||
\(144\) | 22.9174 | − | 6.90887i | 1.90979 | − | 0.575739i | ||||
\(145\) | 3.60881i | 0.299695i | ||||||||
\(146\) | −5.19969 | + | 6.02264i | −0.430329 | + | 0.498437i | ||||
\(147\) | −2.90116 | + | 20.7798i | −0.239283 | + | 1.71389i | ||||
\(148\) | −15.5083 | + | 2.28680i | −1.27477 | + | 0.187974i | ||||
\(149\) | 13.7925i | 1.12992i | 0.825118 | + | 0.564961i | \(0.191109\pi\) | ||||
−0.825118 | + | 0.564961i | \(0.808891\pi\) | |||||||
\(150\) | 2.77010 | − | 3.20852i | 0.226178 | − | 0.261975i | ||||
\(151\) | − | 0.128374i | − | 0.0104469i | −0.999986 | − | 0.00522347i | \(-0.998337\pi\) | ||
0.999986 | − | 0.00522347i | \(-0.00166269\pi\) | |||||||
\(152\) | −12.5123 | − | 7.94599i | −1.01488 | − | 0.644505i | ||||
\(153\) | 23.5146i | 1.90105i | ||||||||
\(154\) | 12.8538 | − | 12.9530i | 1.03579 | − | 1.04378i | ||||
\(155\) | 4.62694 | 0.371645 | ||||||||
\(156\) | −14.3994 | + | 2.12328i | −1.15287 | + | 0.169999i | ||||
\(157\) | 13.1585 | 1.05017 | 0.525083 | − | 0.851051i | \(-0.324034\pi\) | ||||
0.525083 | + | 0.851051i | \(0.324034\pi\) | |||||||
\(158\) | 10.9797 | − | 12.7174i | 0.873496 | − | 1.01174i | ||||
\(159\) | −2.00249 | −0.158808 | ||||||||
\(160\) | −5.16661 | − | 2.30351i | −0.408456 | − | 0.182109i | ||||
\(161\) | 0.301213 | + | 0.0209253i | 0.0237389 | + | 0.00164914i | ||||
\(162\) | 9.48071 | + | 8.18523i | 0.744875 | + | 0.643093i | ||||
\(163\) | 0.158264 | 0.0123962 | 0.00619809 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619809 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(164\) | −20.7388 | + | 3.05806i | −1.61943 | + | 0.238795i | ||||
\(165\) | − | 14.6182i | − | 1.13802i | ||||||
\(166\) | −5.10472 | + | 5.91264i | −0.396203 | + | 0.458910i | ||||
\(167\) | −16.7105 | −1.29310 | −0.646550 | − | 0.762871i | \(-0.723789\pi\) | ||||
−0.646550 | + | 0.762871i | \(0.723789\pi\) | |||||||
\(168\) | 13.3078 | − | 18.0557i | 1.02672 | − | 1.39303i | ||||
\(169\) | −7.10482 | −0.546524 | ||||||||
\(170\) | 3.63164 | − | 4.20642i | 0.278534 | − | 0.322618i | ||||
\(171\) | − | 31.3590i | − | 2.39808i | ||||||
\(172\) | 0.806274 | + | 5.46788i | 0.0614778 | + | 0.416922i | ||||
\(173\) | 5.19433 | 0.394918 | 0.197459 | − | 0.980311i | \(-0.436731\pi\) | ||||
0.197459 | + | 0.980311i | \(0.436731\pi\) | |||||||
\(174\) | 11.5789 | + | 9.99676i | 0.877798 | + | 0.757853i | ||||
\(175\) | 0.183359 | − | 2.63939i | 0.0138606 | − | 0.199519i | ||||
\(176\) | −18.6779 | + | 5.63079i | −1.40790 | + | 0.424437i | ||||
\(177\) | 4.12256 | 0.309871 | ||||||||
\(178\) | 5.74684 | − | 6.65639i | 0.430744 | − | 0.498917i | ||||
\(179\) | −17.3274 | −1.29511 | −0.647555 | − | 0.762019i | \(-0.724208\pi\) | ||||
−0.647555 | + | 0.762019i | \(0.724208\pi\) | |||||||
\(180\) | −1.74589 | − | 11.8401i | −0.130131 | − | 0.882507i | ||||
\(181\) | 21.0585 | 1.56526 | 0.782631 | − | 0.622485i | \(-0.213877\pi\) | ||||
0.782631 | + | 0.622485i | \(0.213877\pi\) | |||||||
\(182\) | −6.39916 | + | 6.44852i | −0.474337 | + | 0.477996i | ||||
\(183\) | 3.53110i | 0.261026i | ||||||||
\(184\) | −0.272484 | − | 0.173042i | −0.0200878 | − | 0.0127568i | ||||
\(185\) | 7.83800i | 0.576261i | ||||||||
\(186\) | 12.8171 | − | 14.8456i | 0.939795 | − | 1.08854i | ||||
\(187\) | − | 19.1647i | − | 1.40146i | ||||||
\(188\) | −3.52492 | − | 23.9048i | −0.257081 | − | 1.74344i | ||||
\(189\) | 23.6073 | + | 1.64000i | 1.71718 | + | 0.119292i | ||||
\(190\) | −4.84313 | + | 5.60965i | −0.351358 | + | 0.406967i | ||||
\(191\) | − | 8.43465i | − | 0.610310i | −0.952303 | − | 0.305155i | \(-0.901292\pi\) | ||
0.952303 | − | 0.305155i | \(-0.0987083\pi\) | |||||||
\(192\) | −21.7029 | + | 10.1962i | −1.56627 | + | 0.735849i | ||||
\(193\) | −25.6337 | −1.84516 | −0.922578 | − | 0.385811i | \(-0.873922\pi\) | ||||
−0.922578 | + | 0.385811i | \(0.873922\pi\) | |||||||
\(194\) | 7.25573 | − | 8.40410i | 0.520931 | − | 0.603379i | ||||
\(195\) | 7.27754i | 0.521156i | ||||||||
\(196\) | −0.107576 | − | 13.9996i | −0.00768397 | − | 0.999970i | ||||
\(197\) | 1.78729i | 0.127339i | 0.997971 | + | 0.0636697i | \(0.0202804\pi\) | ||||
−0.997971 | + | 0.0636697i | \(0.979720\pi\) | |||||||
\(198\) | −31.2408 | − | 26.9720i | −2.22019 | − | 1.91681i | ||||
\(199\) | 22.3178 | 1.58206 | 0.791032 | − | 0.611774i | \(-0.209544\pi\) | ||||
0.791032 | + | 0.611774i | \(0.209544\pi\) | |||||||
\(200\) | −1.51629 | + | 2.38765i | −0.107218 | + | 0.168832i | ||||
\(201\) | − | 7.72612i | − | 0.544958i | ||||||
\(202\) | −11.6741 | − | 10.0789i | −0.821388 | − | 0.709151i | ||||
\(203\) | 9.52505 | + | 0.661706i | 0.668527 | + | 0.0464427i | ||||
\(204\) | −3.43639 | − | 23.3044i | −0.240595 | − | 1.63164i | ||||
\(205\) | 10.4815i | 0.732060i | ||||||||
\(206\) | 16.9348 | + | 14.6208i | 1.17990 | + | 1.01868i | ||||
\(207\) | − | 0.682913i | − | 0.0474657i | ||||||
\(208\) | 9.29864 | − | 2.80324i | 0.644745 | − | 0.194370i | ||||
\(209\) | 25.5579i | 1.76787i | ||||||||
\(210\) | −7.96063 | − | 7.89969i | −0.549335 | − | 0.545130i | ||||
\(211\) | 8.58471 | 0.590996 | 0.295498 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295498 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(212\) | 1.32188 | − | 0.194920i | 0.0907872 | − | 0.0133872i | ||||
\(213\) | −28.2859 | −1.93812 | ||||||||
\(214\) | 6.99484 | + | 6.03904i | 0.478157 | + | 0.412820i | ||||
\(215\) | 2.76350 | 0.188469 | ||||||||
\(216\) | −21.3556 | − | 13.5620i | −1.45307 | − | 0.922776i | ||||
\(217\) | 0.848389 | − | 12.2123i | 0.0575924 | − | 0.829024i | ||||
\(218\) | 10.1022 | − | 11.7011i | 0.684207 | − | 0.792497i | ||||
\(219\) | 16.8637 | 1.13954 | ||||||||
\(220\) | 1.42292 | + | 9.64977i | 0.0959332 | + | 0.650587i | ||||
\(221\) | 9.54096i | 0.641794i | ||||||||
\(222\) | 25.1484 | + | 21.7121i | 1.68785 | + | 1.45722i | ||||
\(223\) | −14.0359 | −0.939916 | −0.469958 | − | 0.882689i | \(-0.655731\pi\) | ||||
−0.469958 | + | 0.882689i | \(0.655731\pi\) | |||||||
\(224\) | −7.02721 | + | 13.2143i | −0.469526 | + | 0.882919i | ||||
\(225\) | −5.98405 | −0.398937 | ||||||||
\(226\) | 3.98214 | + | 3.43801i | 0.264888 | + | 0.228693i | ||||
\(227\) | − | 29.9063i | − | 1.98495i | −0.122442 | − | 0.992476i | \(-0.539073\pi\) | ||
0.122442 | − | 0.992476i | \(-0.460927\pi\) | |||||||
\(228\) | 4.58274 | + | 31.0786i | 0.303500 | + | 2.05823i | ||||
\(229\) | −8.92103 | −0.589518 | −0.294759 | − | 0.955572i | \(-0.595239\pi\) | ||||
−0.294759 | + | 0.955572i | \(0.595239\pi\) | |||||||
\(230\) | −0.105470 | + | 0.122163i | −0.00695450 | + | 0.00805518i | ||||
\(231\) | −38.5831 | − | 2.68037i | −2.53858 | − | 0.176356i | ||||
\(232\) | −8.61657 | − | 5.47198i | −0.565706 | − | 0.359253i | ||||
\(233\) | 0.565155 | 0.0370245 | 0.0185123 | − | 0.999829i | \(-0.494107\pi\) | ||||
0.0185123 | + | 0.999829i | \(0.494107\pi\) | |||||||
\(234\) | 15.5530 | + | 13.4278i | 1.01673 | + | 0.877800i | ||||
\(235\) | −12.0817 | −0.788120 | ||||||||
\(236\) | −2.72139 | + | 0.401286i | −0.177147 | + | 0.0261215i | ||||
\(237\) | −35.6095 | −2.31309 | ||||||||
\(238\) | −10.4365 | − | 10.3566i | −0.676497 | − | 0.671319i | ||||
\(239\) | − | 8.51136i | − | 0.550554i | −0.961365 | − | 0.275277i | \(-0.911230\pi\) | ||
0.961365 | − | 0.275277i | \(-0.0887695\pi\) | |||||||
\(240\) | 3.46057 | + | 11.4791i | 0.223379 | + | 0.740971i | ||||
\(241\) | − | 2.17523i | − | 0.140119i | −0.997543 | − | 0.0700595i | \(-0.977681\pi\) | ||
0.997543 | − | 0.0700595i | \(-0.0223189\pi\) | |||||||
\(242\) | 13.6865 | + | 11.8163i | 0.879803 | + | 0.759584i | ||||
\(243\) | 0.286112i | 0.0183541i | ||||||||
\(244\) | −0.343713 | − | 2.33095i | −0.0220040 | − | 0.149224i | ||||
\(245\) | −6.93276 | − | 0.967910i | −0.442918 | − | 0.0618375i | ||||
\(246\) | 33.6302 | + | 29.0348i | 2.14418 | + | 1.85119i | ||||
\(247\) | − | 12.7238i | − | 0.809593i | ||||||
\(248\) | −7.01576 | + | 11.0475i | −0.445501 | + | 0.701518i | ||||
\(249\) | 16.5557 | 1.04918 | ||||||||
\(250\) | 1.07046 | + | 0.924187i | 0.0677017 | + | 0.0584507i | ||||
\(251\) | 9.41690i | 0.594390i | 0.954817 | + | 0.297195i | \(0.0960511\pi\) | ||||
−0.954817 | + | 0.297195i | \(0.903949\pi\) | |||||||
\(252\) | −31.5707 | + | 2.43712i | −1.98877 | + | 0.153524i | ||||
\(253\) | 0.556580i | 0.0349919i | ||||||||
\(254\) | 3.51492 | − | 4.07123i | 0.220546 | − | 0.255452i | ||||
\(255\) | −11.7782 | −0.737580 | ||||||||
\(256\) | 13.3340 | − | 8.84327i | 0.833378 | − | 0.552704i | ||||
\(257\) | 4.44138i | 0.277045i | 0.990359 | + | 0.138523i | \(0.0442354\pi\) | ||||
−0.990359 | + | 0.138523i | \(0.955765\pi\) | |||||||
\(258\) | 7.65518 | − | 8.86676i | 0.476591 | − | 0.552021i | ||||
\(259\) | 20.6875 | + | 1.43717i | 1.28546 | + | 0.0893011i | ||||
\(260\) | −0.708388 | − | 4.80405i | −0.0439324 | − | 0.297935i | ||||
\(261\) | − | 21.5953i | − | 1.33671i | ||||||
\(262\) | 7.09876 | − | 8.22228i | 0.438563 | − | 0.507974i | ||||
\(263\) | − | 13.6247i | − | 0.840132i | −0.907493 | − | 0.420066i | \(-0.862007\pi\) | ||
0.907493 | − | 0.420066i | \(-0.137993\pi\) | |||||||
\(264\) | 34.9031 | + | 22.1654i | 2.14814 | + | 1.36418i | ||||
\(265\) | − | 0.668088i | − | 0.0410403i | ||||||
\(266\) | 13.9180 | + | 13.8115i | 0.853370 | + | 0.846837i | ||||
\(267\) | −18.6383 | −1.14064 | ||||||||
\(268\) | 0.752052 | + | 5.10017i | 0.0459389 | + | 0.311542i | ||||
\(269\) | −10.2713 | −0.626253 | −0.313127 | − | 0.949711i | \(-0.601376\pi\) | ||||
−0.313127 | + | 0.949711i | \(0.601376\pi\) | |||||||
\(270\) | −8.26612 | + | 9.57439i | −0.503060 | + | 0.582679i | ||||
\(271\) | −2.67264 | −0.162352 | −0.0811758 | − | 0.996700i | \(-0.525868\pi\) | ||||
−0.0811758 | + | 0.996700i | \(0.525868\pi\) | |||||||
\(272\) | 4.53686 | + | 15.0492i | 0.275087 | + | 0.912494i | ||||
\(273\) | 19.2083 | + | 1.33440i | 1.16254 | + | 0.0807616i | ||||
\(274\) | −18.1698 | − | 15.6871i | −1.09768 | − | 0.947690i | ||||
\(275\) | 4.87706 | 0.294098 | ||||||||
\(276\) | 0.0997996 | + | 0.676807i | 0.00600723 | + | 0.0407390i | ||||
\(277\) | 28.1383i | 1.69067i | 0.534239 | + | 0.845333i | \(0.320598\pi\) | ||||
−0.534239 | + | 0.845333i | \(0.679402\pi\) | |||||||
\(278\) | 2.35296 | − | 2.72536i | 0.141121 | − | 0.163456i | ||||
\(279\) | −27.6878 | −1.65763 | ||||||||
\(280\) | 6.02392 | + | 4.43987i | 0.359998 | + | 0.265333i | ||||
\(281\) | 0.466842 | 0.0278494 | 0.0139247 | − | 0.999903i | \(-0.495567\pi\) | ||||
0.0139247 | + | 0.999903i | \(0.495567\pi\) | |||||||
\(282\) | −33.4674 | + | 38.7643i | −1.99295 | + | 2.30838i | ||||
\(283\) | 10.8004i | 0.642019i | 0.947076 | + | 0.321009i | \(0.104022\pi\) | ||||
−0.947076 | + | 0.321009i | \(0.895978\pi\) | |||||||
\(284\) | 18.6721 | − | 2.75332i | 1.10798 | − | 0.163379i | ||||
\(285\) | 15.7073 | 0.930423 | ||||||||
\(286\) | −12.6758 | − | 10.9437i | −0.749536 | − | 0.647117i | ||||
\(287\) | 27.6648 | + | 1.92188i | 1.63300 | + | 0.113445i | ||||
\(288\) | 30.9172 | + | 13.7843i | 1.82181 | + | 0.812250i | ||||
\(289\) | 1.55860 | 0.0916824 | ||||||||
\(290\) | −3.33521 | + | 3.86307i | −0.195850 | + | 0.226848i | ||||
\(291\) | −23.5319 | −1.37947 | ||||||||
\(292\) | −11.1321 | + | 1.64150i | −0.651456 | + | 0.0960613i | ||||
\(293\) | 7.34532 | 0.429118 | 0.214559 | − | 0.976711i | \(-0.431169\pi\) | ||||
0.214559 | + | 0.976711i | \(0.431169\pi\) | |||||||
\(294\) | −22.3100 | + | 19.5627i | −1.30115 | + | 1.14092i | ||||
\(295\) | 1.37541i | 0.0800793i | ||||||||
\(296\) | −18.7144 | − | 11.8846i | −1.08775 | − | 0.690781i | ||||
\(297\) | 43.6214i | 2.53117i | ||||||||
\(298\) | −12.7468 | + | 14.7642i | −0.738402 | + | 0.855269i | ||||
\(299\) | − | 0.277089i | − | 0.0160244i | ||||||
\(300\) | 5.93055 | − | 0.874498i | 0.342401 | − | 0.0504892i | ||||
\(301\) | 0.506712 | − | 7.29396i | 0.0292064 | − | 0.420417i | ||||
\(302\) | 0.118642 | − | 0.137419i | 0.00682706 | − | 0.00790758i | ||||
\(303\) | 32.6882i | 1.87789i | ||||||||
\(304\) | −6.05032 | − | 20.0696i | −0.347010 | − | 1.15107i | ||||
\(305\) | −1.17808 | −0.0674564 | ||||||||
\(306\) | −21.7319 | + | 25.1714i | −1.24233 | + | 1.43895i | ||||
\(307\) | 5.08078i | 0.289975i | 0.989433 | + | 0.144988i | \(0.0463142\pi\) | ||||
−0.989433 | + | 0.144988i | \(0.953686\pi\) | |||||||
\(308\) | 25.7304 | − | 1.98627i | 1.46613 | − | 0.113178i | ||||
\(309\) | − | 47.4184i | − | 2.69754i | ||||||
\(310\) | 4.95294 | + | 4.27615i | 0.281308 | + | 0.242869i | ||||
\(311\) | −17.8319 | −1.01116 | −0.505578 | − | 0.862781i | \(-0.668721\pi\) | ||||
−0.505578 | + | 0.862781i | \(0.668721\pi\) | |||||||
\(312\) | −17.3762 | − | 11.0348i | −0.983735 | − | 0.624724i | ||||
\(313\) | − | 3.54008i | − | 0.200097i | −0.994983 | − | 0.100049i | \(-0.968100\pi\) | ||
0.994983 | − | 0.100049i | \(-0.0318998\pi\) | |||||||
\(314\) | 14.0857 | + | 12.1610i | 0.794900 | + | 0.686282i | ||||
\(315\) | −1.09723 | + | 15.7942i | −0.0618218 | + | 0.889904i | ||||
\(316\) | 23.5065 | − | 3.46619i | 1.32235 | − | 0.194988i | ||||
\(317\) | − | 4.86360i | − | 0.273167i | −0.990629 | − | 0.136583i | \(-0.956388\pi\) | ||
0.990629 | − | 0.136583i | \(-0.0436122\pi\) | |||||||
\(318\) | −2.14358 | − | 1.85067i | −0.120206 | − | 0.103781i | ||||
\(319\) | 17.6004i | 0.985431i | ||||||||
\(320\) | −3.40175 | − | 7.24072i | −0.190164 | − | 0.404769i | ||||
\(321\) | − | 19.5859i | − | 1.09318i | ||||||
\(322\) | 0.303097 | + | 0.300777i | 0.0168909 | + | 0.0167616i | ||||
\(323\) | 20.5925 | 1.14580 | ||||||||
\(324\) | 2.58401 | + | 17.5239i | 0.143556 | + | 0.973549i | ||||
\(325\) | −2.42800 | −0.134681 | ||||||||
\(326\) | 0.169415 | + | 0.146265i | 0.00938301 | + | 0.00810088i | ||||
\(327\) | −32.7637 | −1.81183 | ||||||||
\(328\) | −25.0262 | − | 15.8930i | −1.38184 | − | 0.877542i | ||||
\(329\) | −2.21528 | + | 31.8882i | −0.122132 | + | 1.75805i | ||||
\(330\) | 13.5099 | − | 15.6482i | 0.743698 | − | 0.861403i | ||||
\(331\) | −9.38870 | −0.516050 | −0.258025 | − | 0.966138i | \(-0.583072\pi\) | ||||
−0.258025 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(332\) | −10.9288 | + | 1.61152i | −0.599794 | + | 0.0884435i | ||||
\(333\) | − | 46.9030i | − | 2.57027i | ||||||
\(334\) | −17.8879 | − | 15.4437i | −0.978784 | − | 0.845040i | ||||
\(335\) | 2.57766 | 0.140832 | ||||||||
\(336\) | 30.9323 | − | 7.02901i | 1.68749 | − | 0.383464i | ||||
\(337\) | 19.7551 | 1.07613 | 0.538064 | − | 0.842904i | \(-0.319156\pi\) | ||||
0.538064 | + | 0.842904i | \(0.319156\pi\) | |||||||
\(338\) | −7.60540 | − | 6.56618i | −0.413679 | − | 0.357153i | ||||
\(339\) | − | 11.1502i | − | 0.605596i | ||||||
\(340\) | 7.77504 | − | 1.14648i | 0.421661 | − | 0.0621765i | ||||
\(341\) | 22.5658 | 1.22201 | ||||||||
\(342\) | 28.9815 | − | 33.5684i | 1.56714 | − | 1.81517i | ||||
\(343\) | −3.82587 | + | 18.1208i | −0.206578 | + | 0.978430i | ||||
\(344\) | −4.19026 | + | 6.59828i | −0.225924 | + | 0.355755i | ||||
\(345\) | 0.342063 | 0.0184161 | ||||||||
\(346\) | 5.56031 | + | 4.80053i | 0.298924 | + | 0.258078i | ||||
\(347\) | −29.8093 | −1.60025 | −0.800124 | − | 0.599835i | \(-0.795233\pi\) | ||||
−0.800124 | + | 0.599835i | \(0.795233\pi\) | |||||||
\(348\) | 3.15589 | + | 21.4022i | 0.169174 | + | 1.14728i | ||||
\(349\) | −15.6993 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(350\) | 2.63557 | − | 2.65590i | 0.140877 | − | 0.141964i | ||||
\(351\) | − | 21.7165i | − | 1.15914i | ||||||
\(352\) | −25.1978 | − | 11.2344i | −1.34305 | − | 0.598794i | ||||
\(353\) | 10.2186i | 0.543879i | 0.962314 | + | 0.271939i | \(0.0876651\pi\) | ||||
−0.962314 | + | 0.271939i | \(0.912335\pi\) | |||||||
\(354\) | 4.41303 | + | 3.81002i | 0.234550 | + | 0.202500i | ||||
\(355\) | − | 9.43699i | − | 0.500863i | ||||||
\(356\) | 12.3035 | − | 1.81423i | 0.652084 | − | 0.0961539i | ||||
\(357\) | −2.15964 | + | 31.0873i | −0.114300 | + | 1.64531i | ||||
\(358\) | −18.5482 | − | 16.0137i | −0.980304 | − | 0.846352i | ||||
\(359\) | 23.4758i | 1.23900i | 0.784995 | + | 0.619502i | \(0.212666\pi\) | ||||
−0.784995 | + | 0.619502i | \(0.787334\pi\) | |||||||
\(360\) | 9.07353 | − | 14.2878i | 0.478217 | − | 0.753034i | ||||
\(361\) | −8.46208 | −0.445373 | ||||||||
\(362\) | 22.5422 | + | 19.4619i | 1.18479 | + | 1.02290i | ||||
\(363\) | − | 38.3230i | − | 2.01144i | ||||||
\(364\) | −12.8097 | + | 0.988848i | −0.671408 | + | 0.0518297i | ||||
\(365\) | 5.62623i | 0.294490i | ||||||||
\(366\) | −3.26339 | + | 3.77989i | −0.170580 | + | 0.197578i | ||||
\(367\) | 21.5002 | 1.12230 | 0.561151 | − | 0.827714i | \(-0.310359\pi\) | ||||
0.561151 | + | 0.827714i | \(0.310359\pi\) | |||||||
\(368\) | −0.131759 | − | 0.437060i | −0.00686844 | − | 0.0227833i | ||||
\(369\) | − | 62.7218i | − | 3.26517i | ||||||
\(370\) | −7.24377 | + | 8.39024i | −0.376586 | + | 0.436188i | ||||
\(371\) | −1.76334 | − | 0.122500i | −0.0915483 | − | 0.00635987i | ||||
\(372\) | 27.4403 | − | 4.04625i | 1.42271 | − | 0.209788i | ||||
\(373\) | − | 0.781051i | − | 0.0404413i | −0.999796 | − | 0.0202206i | \(-0.993563\pi\) | ||
0.999796 | − | 0.0202206i | \(-0.00643687\pi\) | |||||||
\(374\) | 17.7117 | − | 20.5149i | 0.915851 | − | 1.06080i | ||||
\(375\) | − | 2.99734i | − | 0.154782i | ||||||
\(376\) | 18.3192 | − | 28.8468i | 0.944742 | − | 1.48766i | ||||
\(377\) | − | 8.76218i | − | 0.451275i | ||||||
\(378\) | 23.7549 | + | 23.5731i | 1.22182 | + | 1.21247i | ||||
\(379\) | 4.53381 | 0.232886 | 0.116443 | − | 0.993197i | \(-0.462851\pi\) | ||||
0.116443 | + | 0.993197i | \(0.462851\pi\) | |||||||
\(380\) | −10.3687 | + | 1.52894i | −0.531905 | + | 0.0784328i | ||||
\(381\) | −11.3997 | −0.584023 | ||||||||
\(382\) | 7.79519 | − | 9.02893i | 0.398837 | − | 0.461960i | ||||
\(383\) | −36.0555 | −1.84235 | −0.921176 | − | 0.389147i | \(-0.872770\pi\) | ||||
−0.921176 | + | 0.389147i | \(0.872770\pi\) | |||||||
\(384\) | −32.6552 | − | 9.14293i | −1.66643 | − | 0.466573i | ||||
\(385\) | 0.894251 | − | 12.8725i | 0.0455752 | − | 0.656041i | ||||
\(386\) | −27.4398 | − | 23.6903i | −1.39665 | − | 1.20581i | ||||
\(387\) | −16.5369 | −0.840619 | ||||||||
\(388\) | 15.5339 | − | 2.29057i | 0.788615 | − | 0.116286i | ||||
\(389\) | 21.1691i | 1.07332i | 0.843800 | + | 0.536658i | \(0.180313\pi\) | ||||
−0.843800 | + | 0.536658i | \(0.819687\pi\) | |||||||
\(390\) | −6.72581 | + | 7.79030i | −0.340574 | + | 0.394477i | ||||
\(391\) | 0.448449 | 0.0226791 | ||||||||
\(392\) | 12.8231 | − | 15.0854i | 0.647663 | − | 0.761927i | ||||
\(393\) | −23.0228 | −1.16135 | ||||||||
\(394\) | −1.65179 | + | 1.91322i | −0.0832161 | + | 0.0963867i | ||||
\(395\) | − | 11.8804i | − | 0.597766i | ||||||
\(396\) | −8.51482 | − | 57.7447i | −0.427886 | − | 2.90178i | ||||
\(397\) | 14.1445 | 0.709891 | 0.354946 | − | 0.934887i | \(-0.384499\pi\) | ||||
0.354946 | + | 0.934887i | \(0.384499\pi\) | |||||||
\(398\) | 23.8902 | + | 20.6258i | 1.19751 | + | 1.03388i | ||||
\(399\) | 2.88008 | − | 41.4578i | 0.144184 | − | 2.07549i | ||||
\(400\) | −3.82975 | + | 1.15455i | −0.191488 | + | 0.0577274i | ||||
\(401\) | 17.8168 | 0.889729 | 0.444865 | − | 0.895598i | \(-0.353252\pi\) | ||||
0.444865 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(402\) | 7.14037 | − | 8.27048i | 0.356130 | − | 0.412494i | ||||
\(403\) | −11.2342 | −0.559616 | ||||||||
\(404\) | −3.18183 | − | 21.5781i | −0.158302 | − | 1.07355i | ||||
\(405\) | 8.85669 | 0.440092 | ||||||||
\(406\) | 9.58462 | + | 9.51125i | 0.475677 | + | 0.472035i | ||||
\(407\) | 38.2264i | 1.89481i | ||||||||
\(408\) | 17.8591 | − | 28.1223i | 0.884159 | − | 1.39226i | ||||
\(409\) | 32.5292i | 1.60846i | 0.594315 | + | 0.804232i | \(0.297423\pi\) | ||||
−0.594315 | + | 0.804232i | \(0.702577\pi\) | |||||||
\(410\) | −9.68687 | + | 11.2200i | −0.478400 | + | 0.554117i | ||||
\(411\) | 50.8766i | 2.50956i | ||||||||
\(412\) | 4.61566 | + | 31.3018i | 0.227397 | + | 1.54213i | ||||
\(413\) | 3.63024 | + | 0.252193i | 0.178632 | + | 0.0124096i | ||||
\(414\) | 0.631139 | − | 0.731029i | 0.0310188 | − | 0.0359281i | ||||
\(415\) | 5.52348i | 0.271137i | ||||||||
\(416\) | 12.5445 | + | 5.59293i | 0.615046 | + | 0.274216i | ||||
\(417\) | −7.63116 | −0.373699 | ||||||||
\(418\) | −23.6202 | + | 27.3586i | −1.15530 | + | 1.33815i | ||||
\(419\) | − | 34.4793i | − | 1.68443i | −0.539146 | − | 0.842213i | \(-0.681253\pi\) | ||
0.539146 | − | 0.842213i | \(-0.318747\pi\) | |||||||
\(420\) | −1.22072 | − | 15.8134i | −0.0595652 | − | 0.771614i | ||||
\(421\) | − | 12.2635i | − | 0.597688i | −0.954302 | − | 0.298844i | \(-0.903399\pi\) | ||
0.954302 | − | 0.298844i | \(-0.0966010\pi\) | |||||||
\(422\) | 9.18957 | + | 7.93388i | 0.447341 | + | 0.386215i | ||||
\(423\) | 72.2972 | 3.51521 | ||||||||
\(424\) | 1.59516 | + | 1.01301i | 0.0774679 | + | 0.0491962i | ||||
\(425\) | − | 3.92955i | − | 0.190611i | ||||||
\(426\) | −30.2788 | − | 26.1414i | −1.46701 | − | 1.26656i | ||||
\(427\) | −0.216011 | + | 3.10940i | −0.0104535 | + | 0.150475i | ||||
\(428\) | 1.90647 | + | 12.9291i | 0.0921529 | + | 0.624950i | ||||
\(429\) | 35.4930i | 1.71362i | ||||||||
\(430\) | 2.95821 | + | 2.55399i | 0.142658 | + | 0.123164i | ||||
\(431\) | 21.7718i | 1.04871i | 0.851499 | + | 0.524357i | \(0.175694\pi\) | ||||
−0.851499 | + | 0.524357i | \(0.824306\pi\) | |||||||
\(432\) | −10.3265 | − | 34.2541i | −0.496835 | − | 1.64805i | ||||
\(433\) | − | 26.1597i | − | 1.25715i | −0.777747 | − | 0.628577i | \(-0.783638\pi\) | ||
0.777747 | − | 0.628577i | \(-0.216362\pi\) | |||||||
\(434\) | 12.1946 | − | 12.2887i | 0.585360 | − | 0.589875i | ||||
\(435\) | 10.8168 | 0.518627 | ||||||||
\(436\) | 21.6279 | − | 3.18918i | 1.03579 | − | 0.152734i | ||||
\(437\) | −0.598049 | −0.0286086 | ||||||||
\(438\) | 18.0519 | + | 15.5852i | 0.862553 | + | 0.744691i | ||||
\(439\) | 29.5333 | 1.40955 | 0.704775 | − | 0.709431i | \(-0.251048\pi\) | ||||
0.704775 | + | 0.709431i | \(0.251048\pi\) | |||||||
\(440\) | −7.39501 | + | 11.6447i | −0.352543 | + | 0.555140i | ||||
\(441\) | 41.4860 | + | 5.79202i | 1.97552 | + | 0.275811i | ||||
\(442\) | −8.81763 | + | 10.2132i | −0.419412 | + | 0.485792i | ||||
\(443\) | −21.7915 | −1.03535 | −0.517673 | − | 0.855579i | \(-0.673202\pi\) | ||||
−0.517673 | + | 0.855579i | \(0.673202\pi\) | |||||||
\(444\) | 6.85431 | + | 46.4837i | 0.325291 | + | 2.20602i | ||||
\(445\) | − | 6.21826i | − | 0.294774i | ||||||
\(446\) | −15.0249 | − | 12.9718i | −0.711449 | − | 0.614234i | ||||
\(447\) | 41.3407 | 1.95535 | ||||||||
\(448\) | −19.7348 | + | 7.65091i | −0.932383 | + | 0.361471i | ||||
\(449\) | −1.75711 | −0.0829231 | −0.0414615 | − | 0.999140i | \(-0.513201\pi\) | ||||
−0.0414615 | + | 0.999140i | \(0.513201\pi\) | |||||||
\(450\) | −6.40567 | − | 5.53038i | −0.301966 | − | 0.260705i | ||||
\(451\) | 51.1189i | 2.40709i | ||||||||
\(452\) | 1.08535 | + | 7.36048i | 0.0510506 | + | 0.346208i | ||||
\(453\) | −0.384781 | −0.0180786 | ||||||||
\(454\) | 27.6390 | − | 32.0134i | 1.29716 | − | 1.50246i | ||||
\(455\) | −0.445195 | + | 6.40844i | −0.0208711 | + | 0.300432i | ||||
\(456\) | −23.8168 | + | 37.5037i | −1.11532 | + | 1.75627i | ||||
\(457\) | 3.78856 | 0.177221 | 0.0886106 | − | 0.996066i | \(-0.471757\pi\) | ||||
0.0886106 | + | 0.996066i | \(0.471757\pi\) | |||||||
\(458\) | −9.54958 | − | 8.24470i | −0.446223 | − | 0.385249i | ||||
\(459\) | 35.1468 | 1.64051 | ||||||||
\(460\) | −0.225803 | + | 0.0332961i | −0.0105281 | + | 0.00155244i | ||||
\(461\) | 32.3541 | 1.50688 | 0.753439 | − | 0.657517i | \(-0.228393\pi\) | ||||
0.753439 | + | 0.657517i | \(0.228393\pi\) | |||||||
\(462\) | −38.8244 | − | 38.5272i | −1.80628 | − | 1.79245i | ||||
\(463\) | 31.2530i | 1.45245i | 0.687456 | + | 0.726226i | \(0.258727\pi\) | ||||
−0.687456 | + | 0.726226i | \(0.741273\pi\) | |||||||
\(464\) | −4.16654 | − | 13.8208i | −0.193427 | − | 0.641617i | ||||
\(465\) | − | 13.8685i | − | 0.643137i | ||||||
\(466\) | 0.604974 | + | 0.522309i | 0.0280249 | + | 0.0241955i | ||||
\(467\) | − | 22.6800i | − | 1.04950i | −0.851255 | − | 0.524752i | \(-0.824158\pi\) | ||
0.851255 | − | 0.524752i | \(-0.175842\pi\) | |||||||
\(468\) | 4.23903 | + | 28.7477i | 0.195949 | + | 1.32886i | ||||
\(469\) | 0.472636 | − | 6.80344i | 0.0218243 | − | 0.314154i | ||||
\(470\) | −12.9329 | − | 11.1657i | −0.596550 | − | 0.515035i | ||||
\(471\) | − | 39.4406i | − | 1.81733i | ||||||
\(472\) | −3.28399 | − | 2.08551i | −0.151158 | − | 0.0959934i | ||||
\(473\) | 13.4777 | 0.619708 | ||||||||
\(474\) | −38.1184 | − | 32.9098i | −1.75084 | − | 1.51160i | ||||
\(475\) | 5.24043i | 0.240447i | ||||||||
\(476\) | −1.60038 | − | 20.7316i | −0.0733535 | − | 0.950230i | ||||
\(477\) | 3.99787i | 0.183050i | ||||||||
\(478\) | 7.86608 | − | 9.11104i | 0.359786 | − | 0.416729i | ||||
\(479\) | 12.8639 | 0.587765 | 0.293883 | − | 0.955842i | \(-0.405053\pi\) | ||||
0.293883 | + | 0.955842i | \(0.405053\pi\) | |||||||
\(480\) | −6.90442 | + | 15.4861i | −0.315142 | + | 0.706839i | ||||
\(481\) | − | 19.0307i | − | 0.867723i | ||||||
\(482\) | 2.01032 | − | 2.32849i | 0.0915675 | − | 0.106060i | ||||
\(483\) | 0.0627202 | − | 0.902838i | 0.00285387 | − | 0.0410805i | ||||
\(484\) | 3.73032 | + | 25.2978i | 0.169560 | + | 1.14990i | ||||
\(485\) | − | 7.85094i | − | 0.356493i | ||||||
\(486\) | −0.264421 | + | 0.306271i | −0.0119944 | + | 0.0138927i | ||||
\(487\) | − | 20.3133i | − | 0.920483i | −0.887794 | − | 0.460241i | \(-0.847763\pi\) | ||
0.887794 | − | 0.460241i | \(-0.152237\pi\) | |||||||
\(488\) | 1.78630 | − | 2.81283i | 0.0808620 | − | 0.127331i | ||||
\(489\) | − | 0.474370i | − | 0.0214518i | ||||||
\(490\) | −6.52669 | − | 7.44327i | −0.294846 | − | 0.336253i | ||||
\(491\) | 16.4582 | 0.742746 | 0.371373 | − | 0.928484i | \(-0.378887\pi\) | ||||
0.371373 | + | 0.928484i | \(0.378887\pi\) | |||||||
\(492\) | 9.16606 | + | 62.1611i | 0.413238 | + | 2.80244i | ||||
\(493\) | 14.1810 | 0.638680 | ||||||||
\(494\) | 11.7591 | − | 13.6202i | 0.529068 | − | 0.612804i | ||||
\(495\) | −29.1845 | −1.31175 | ||||||||
\(496\) | −17.7200 | + | 5.34202i | −0.795653 | + | 0.239864i | ||||
\(497\) | −24.9079 | − | 1.73035i | −1.11727 | − | 0.0776170i | ||||
\(498\) | 17.7222 | + | 15.3006i | 0.794151 | + | 0.685636i | ||||
\(499\) | 18.7483 | 0.839291 | 0.419645 | − | 0.907688i | \(-0.362154\pi\) | ||||
0.419645 | + | 0.907688i | \(0.362154\pi\) | |||||||
\(500\) | 0.291758 | + | 1.97860i | 0.0130478 | + | 0.0884859i | ||||
\(501\) | 50.0872i | 2.23773i | ||||||||
\(502\) | −8.70298 | + | 10.0804i | −0.388433 | + | 0.449910i | ||||
\(503\) | 19.5629 | 0.872269 | 0.436134 | − | 0.899882i | \(-0.356347\pi\) | ||||
0.436134 | + | 0.899882i | \(0.356347\pi\) | |||||||
\(504\) | −36.0474 | − | 26.5684i | −1.60568 | − | 1.18345i | ||||
\(505\) | −10.9057 | −0.485298 | ||||||||
\(506\) | −0.514384 | + | 0.595795i | −0.0228672 | + | 0.0264863i | ||||
\(507\) | 21.2956i | 0.945769i | ||||||||
\(508\) | 7.52515 | − | 1.10963i | 0.333875 | − | 0.0492320i | ||||
\(509\) | −19.9845 | −0.885797 | −0.442898 | − | 0.896572i | \(-0.646050\pi\) | ||||
−0.442898 | + | 0.896572i | \(0.646050\pi\) | |||||||
\(510\) | −12.6081 | − | 10.8853i | −0.558295 | − | 0.482008i | ||||
\(511\) | 14.8498 | + | 1.03162i | 0.656917 | + | 0.0456361i | ||||
\(512\) | 22.4464 | + | 2.85680i | 0.991998 | + | 0.126254i | ||||
\(513\) | −46.8715 | −2.06943 | ||||||||
\(514\) | −4.10466 | + | 4.75430i | −0.181049 | + | 0.209703i | ||||
\(515\) | 15.8202 | 0.697119 | ||||||||
\(516\) | 16.3891 | − | 2.41668i | 0.721489 | − | 0.106388i | ||||
\(517\) | −58.9229 | −2.59143 | ||||||||
\(518\) | 20.8169 | + | 20.6576i | 0.914643 | + | 0.907641i | ||||
\(519\) | − | 15.5692i | − | 0.683411i | ||||||
\(520\) | 3.68154 | − | 5.79722i | 0.161446 | − | 0.254225i | ||||
\(521\) | 1.35111i | 0.0591932i | 0.999562 | + | 0.0295966i | \(0.00942226\pi\) | ||||
−0.999562 | + | 0.0295966i | \(0.990578\pi\) | |||||||
\(522\) | 19.9581 | − | 23.1168i | 0.873541 | − | 1.01180i | ||||
\(523\) | 28.1452i | 1.23071i | 0.788252 | + | 0.615353i | \(0.210986\pi\) | ||||
−0.788252 | + | 0.615353i | \(0.789014\pi\) | |||||||
\(524\) | 15.1978 | − | 2.24102i | 0.663921 | − | 0.0978994i | ||||
\(525\) | −7.91115 | − | 0.549588i | −0.345271 | − | 0.0239860i | ||||
\(526\) | 12.5917 | − | 14.5846i | 0.549025 | − | 0.635919i | ||||
\(527\) | − | 18.1818i | − | 0.792012i | ||||||
\(528\) | 16.8774 | + | 55.9841i | 0.734495 | + | 2.43640i | ||||
\(529\) | 22.9870 | 0.999434 | ||||||||
\(530\) | 0.617438 | − | 0.715160i | 0.0268198 | − | 0.0310645i | ||||
\(531\) | − | 8.23051i | − | 0.357174i | ||||||
\(532\) | 2.13426 | + | 27.6475i | 0.0925320 | + | 1.19867i | ||||
\(533\) | − | 25.4491i | − | 1.10232i | ||||||
\(534\) | −19.9515 | − | 17.2252i | −0.863384 | − | 0.745408i | ||||
\(535\) | 6.53444 | 0.282508 | ||||||||
\(536\) | −3.90847 | + | 6.15455i | −0.168820 | + | 0.265836i | ||||
\(537\) | 51.9360i | 2.24121i | ||||||||
\(538\) | −10.9950 | − | 9.49262i | −0.474028 | − | 0.409256i | ||||
\(539\) | −33.8115 | − | 4.72055i | −1.45636 | − | 0.203329i | ||||
\(540\) | −17.6971 | + | 2.60954i | −0.761560 | + | 0.112297i | ||||
\(541\) | 0.0636523i | 0.00273663i | 0.999999 | + | 0.00136831i | \(0.000435548\pi\) | ||||
−0.999999 | + | 0.00136831i | \(0.999564\pi\) | |||||||
\(542\) | −2.86095 | − | 2.47002i | −0.122888 | − | 0.106096i | ||||
\(543\) | − | 63.1194i | − | 2.70871i | ||||||
\(544\) | −9.05179 | + | 20.3025i | −0.388092 | + | 0.870461i | ||||
\(545\) | − | 10.9309i | − | 0.468229i | ||||||
\(546\) | 19.3284 | + | 19.1804i | 0.827179 | + | 0.820847i | ||||
\(547\) | 26.6632 | 1.14004 | 0.570018 | − | 0.821632i | \(-0.306936\pi\) | ||||
0.570018 | + | 0.821632i | \(0.306936\pi\) | |||||||
\(548\) | −4.95227 | − | 33.5847i | −0.211551 | − | 1.43467i | ||||
\(549\) | 7.04966 | 0.300872 | ||||||||
\(550\) | 5.22068 | + | 4.50731i | 0.222611 | + | 0.192192i | ||||
\(551\) | −18.9117 | −0.805665 | ||||||||
\(552\) | −0.518665 | + | 0.816727i | −0.0220759 | + | 0.0347622i | ||||
\(553\) | −31.3569 | − | 2.17837i | −1.33343 | − | 0.0926336i | ||||
\(554\) | −26.0050 | + | 30.1208i | −1.10485 | + | 1.27971i | ||||
\(555\) | 23.4931 | 0.997228 | ||||||||
\(556\) | 5.03748 | − | 0.742809i | 0.213637 | − | 0.0315021i | ||||
\(557\) | − | 9.81678i | − | 0.415950i | −0.978134 | − | 0.207975i | \(-0.933313\pi\) | ||
0.978134 | − | 0.207975i | \(-0.0666873\pi\) | |||||||
\(558\) | −29.6386 | − | 25.5887i | −1.25470 | − | 1.08326i | ||||
\(559\) | −6.70978 | −0.283794 | ||||||||
\(560\) | 2.34508 | + | 10.3199i | 0.0990978 | + | 0.436096i | ||||
\(561\) | −57.4430 | −2.42525 | ||||||||
\(562\) | 0.499734 | + | 0.431449i | 0.0210800 | + | 0.0181996i | ||||
\(563\) | − | 30.8680i | − | 1.30093i | −0.759535 | − | 0.650466i | \(-0.774574\pi\) | ||
0.759535 | − | 0.650466i | \(-0.225426\pi\) | |||||||
\(564\) | −71.6509 | + | 10.5654i | −3.01705 | + | 0.444883i | ||||
\(565\) | 3.72004 | 0.156503 | ||||||||
\(566\) | −9.98161 | + | 11.5614i | −0.419558 | + | 0.485962i | ||||
\(567\) | 1.62395 | − | 23.3763i | 0.0681995 | − | 0.981711i | ||||
\(568\) | 22.5322 | + | 14.3092i | 0.945432 | + | 0.600400i | ||||
\(569\) | 30.9000 | 1.29540 | 0.647698 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647698 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(570\) | 16.8140 | + | 14.5165i | 0.704263 | + | 0.608030i | ||||
\(571\) | −37.5033 | −1.56946 | −0.784732 | − | 0.619835i | \(-0.787199\pi\) | ||||
−0.784732 | + | 0.619835i | \(0.787199\pi\) | |||||||
\(572\) | −3.45485 | − | 23.4296i | −0.144455 | − | 0.979642i | ||||
\(573\) | −25.2815 | −1.05615 | ||||||||
\(574\) | 27.8378 | + | 27.6247i | 1.16193 | + | 1.15303i | ||||
\(575\) | 0.114122i | 0.00475922i | ||||||||
\(576\) | 20.3563 | + | 43.3288i | 0.848178 | + | 1.80537i | ||||
\(577\) | − | 17.4216i | − | 0.725272i | −0.931931 | − | 0.362636i | \(-0.881877\pi\) | ||
0.931931 | − | 0.362636i | \(-0.118123\pi\) | |||||||
\(578\) | 1.66842 | + | 1.44044i | 0.0693969 | + | 0.0599143i | ||||
\(579\) | 76.8330i | 3.19307i | ||||||||
\(580\) | −7.14040 | + | 1.05290i | −0.296489 | + | 0.0437192i | ||||
\(581\) | 14.5786 | + | 1.01278i | 0.604822 | + | 0.0420171i | ||||
\(582\) | −25.1899 | − | 21.7479i | −1.04416 | − | 0.901479i | ||||
\(583\) | − | 3.25830i | − | 0.134945i | ||||||
\(584\) | −13.4335 | − | 8.53097i | −0.555881 | − | 0.353014i | ||||
\(585\) | 14.5293 | 0.600711 | ||||||||
\(586\) | 7.86286 | + | 6.78845i | 0.324812 | + | 0.280428i | ||||
\(587\) | 12.4270i | 0.512918i | 0.966555 | + | 0.256459i | \(0.0825558\pi\) | ||||
−0.966555 | + | 0.256459i | \(0.917444\pi\) | |||||||
\(588\) | −41.9615 | + | 0.322441i | −1.73046 | + | 0.0132972i | ||||
\(589\) | 24.2471i | 0.999086i | ||||||||
\(590\) | −1.27113 | + | 1.47232i | −0.0523317 | + | 0.0606143i | ||||
\(591\) | 5.35713 | 0.220363 | ||||||||
\(592\) | −9.04934 | − | 30.0176i | −0.371926 | − | 1.23372i | ||||
\(593\) | − | 13.7257i | − | 0.563646i | −0.959466 | − | 0.281823i | \(-0.909061\pi\) | ||
0.959466 | − | 0.281823i | \(-0.0909391\pi\) | |||||||
\(594\) | −40.3143 | + | 46.6948i | −1.65412 | + | 1.91591i | ||||
\(595\) | −10.3716 | − | 0.720518i | −0.425195 | − | 0.0295384i | ||||
\(596\) | −27.2898 | + | 4.02406i | −1.11783 | + | 0.164832i | ||||
\(597\) | − | 66.8940i | − | 2.73779i | ||||||
\(598\) | 0.256082 | − | 0.296612i | 0.0104720 | − | 0.0121293i | ||||
\(599\) | − | 27.7947i | − | 1.13566i | −0.823146 | − | 0.567829i | \(-0.807783\pi\) | ||
0.823146 | − | 0.567829i | \(-0.192217\pi\) | |||||||
\(600\) | 7.15660 | + | 4.54482i | 0.292167 | + | 0.185542i | ||||
\(601\) | 38.9855i | 1.59025i | 0.606443 | + | 0.795127i | \(0.292596\pi\) | ||||
−0.606443 | + | 0.795127i | \(0.707404\pi\) | |||||||
\(602\) | 7.28339 | − | 7.33957i | 0.296849 | − | 0.299139i | ||||
\(603\) | −15.4248 | −0.628148 | ||||||||
\(604\) | 0.254002 | − | 0.0374542i | 0.0103352 | − | 0.00152399i | ||||
\(605\) | 12.7857 | 0.519811 | ||||||||
\(606\) | −30.2100 | + | 34.9913i | −1.22720 | + | 1.42142i | ||||
\(607\) | −11.7981 | −0.478872 | −0.239436 | − | 0.970912i | \(-0.576962\pi\) | ||||
−0.239436 | + | 0.970912i | \(0.576962\pi\) | |||||||
\(608\) | 12.0714 | − | 27.0752i | 0.489560 | − | 1.09805i | ||||
\(609\) | 1.98336 | − | 28.5498i | 0.0803697 | − | 1.15690i | ||||
\(610\) | −1.26108 | − | 1.08876i | −0.0510597 | − | 0.0440827i | ||||
\(611\) | 29.3342 | 1.18674 | ||||||||
\(612\) | −46.5262 | + | 6.86058i | −1.88071 | + | 0.277323i | ||||
\(613\) | 13.4628i | 0.543756i | 0.962332 | + | 0.271878i | \(0.0876447\pi\) | ||||
−0.962332 | + | 0.271878i | \(0.912355\pi\) | |||||||
\(614\) | −4.69559 | + | 5.43876i | −0.189498 | + | 0.219490i | ||||
\(615\) | 31.4166 | 1.26684 | ||||||||
\(616\) | 29.3790 | + | 21.6535i | 1.18371 | + | 0.872443i | ||||
\(617\) | −15.2924 | −0.615650 | −0.307825 | − | 0.951443i | \(-0.599601\pi\) | ||||
−0.307825 | + | 0.951443i | \(0.599601\pi\) | |||||||
\(618\) | 43.8234 | − | 50.7594i | 1.76284 | − | 2.04184i | ||||
\(619\) | − | 3.76548i | − | 0.151347i | −0.997133 | − | 0.0756736i | \(-0.975889\pi\) | ||
0.997133 | − | 0.0756736i | \(-0.0241107\pi\) | |||||||
\(620\) | 1.34995 | + | 9.15488i | 0.0542151 | + | 0.367669i | ||||
\(621\) | −1.02073 | −0.0409606 | ||||||||
\(622\) | −19.0883 | − | 16.4800i | −0.765372 | − | 0.660789i | ||||
\(623\) | −16.4124 | − | 1.14017i | −0.657550 | − | 0.0456801i | ||||
\(624\) | −8.40227 | − | 27.8712i | −0.336360 | − | 1.11574i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.27169 | − | 3.78950i | 0.130763 | − | 0.151459i | ||||
\(627\) | 76.6056 | 3.05933 | ||||||||
\(628\) | 3.83911 | + | 26.0356i | 0.153197 | + | 1.03893i | ||||
\(629\) | 30.7998 | 1.22807 | ||||||||
\(630\) | −15.7714 | + | 15.8930i | −0.628346 | + | 0.633193i | ||||
\(631\) | 21.1777i | 0.843070i | 0.906812 | + | 0.421535i | \(0.138508\pi\) | ||||
−0.906812 | + | 0.421535i | \(0.861492\pi\) | |||||||
\(632\) | 28.3662 | + | 18.0140i | 1.12835 | + | 0.716560i | ||||
\(633\) | − | 25.7313i | − | 1.02273i | ||||||
\(634\) | 4.49487 | − | 5.20627i | 0.178514 | − | 0.206768i | ||||
\(635\) | − | 3.80326i | − | 0.150928i | ||||||
\(636\) | −0.584241 | − | 3.96213i | −0.0231667 | − | 0.157109i | ||||
\(637\) | 16.8327 | + | 2.35009i | 0.666937 | + | 0.0931138i | ||||
\(638\) | −16.2660 | + | 18.8404i | −0.643978 | + | 0.745900i | ||||
\(639\) | 56.4714i | 2.23397i | ||||||||
\(640\) | 3.05035 | − | 10.8947i | 0.120576 | − | 0.430652i | ||||
\(641\) | 29.5569 | 1.16743 | 0.583713 | − | 0.811960i | \(-0.301599\pi\) | ||||
0.583713 | + | 0.811960i | \(0.301599\pi\) | |||||||
\(642\) | 18.1011 | − | 20.9659i | 0.714392 | − | 0.827458i | ||||
\(643\) | 19.8063i | 0.781085i | 0.920585 | + | 0.390543i | \(0.127713\pi\) | ||||
−0.920585 | + | 0.390543i | \(0.872287\pi\) | |||||||
\(644\) | 0.0464784 | + | 0.602086i | 0.00183150 | + | 0.0237255i | ||||
\(645\) | − | 8.28315i | − | 0.326149i | ||||||
\(646\) | 22.0434 | + | 19.0314i | 0.867288 | + | 0.748779i | ||||
\(647\) | 12.4755 | 0.490461 | 0.245231 | − | 0.969465i | \(-0.421136\pi\) | ||||
0.245231 | + | 0.969465i | \(0.421136\pi\) | |||||||
\(648\) | −13.4293 | + | 21.1467i | −0.527552 | + | 0.830720i | ||||
\(649\) | 6.70794i | 0.263310i | ||||||||
\(650\) | −2.59907 | − | 2.24393i | −0.101944 | − | 0.0880140i | ||||
\(651\) | −36.6044 | − | 2.54291i | −1.43464 | − | 0.0996646i | ||||
\(652\) | 0.0461747 | + | 0.313141i | 0.00180834 | + | 0.0122636i | ||||
\(653\) | 9.99757i | 0.391235i | 0.980680 | + | 0.195618i | \(0.0626712\pi\) | ||||
−0.980680 | + | 0.195618i | \(0.937329\pi\) | |||||||
\(654\) | −35.0721 | − | 30.2797i | −1.37143 | − | 1.18403i | ||||
\(655\) | − | 7.68109i | − | 0.300125i | ||||||
\(656\) | −12.1014 | − | 40.1416i | −0.472480 | − | 1.56727i | ||||
\(657\) | − | 33.6676i | − | 1.31350i | ||||||
\(658\) | −31.8420 | + | 32.0876i | −1.24133 | + | 1.25091i | ||||
\(659\) | 27.2870 | 1.06295 | 0.531475 | − | 0.847074i | \(-0.321638\pi\) | ||||
0.531475 | + | 0.847074i | \(0.321638\pi\) | |||||||
\(660\) | 28.9236 | − | 4.26497i | 1.12585 | − | 0.166014i | ||||
\(661\) | −38.2384 | −1.48730 | −0.743650 | − | 0.668569i | \(-0.766907\pi\) | ||||
−0.743650 | + | 0.668569i | \(0.766907\pi\) | |||||||
\(662\) | −10.0502 | − | 8.67691i | −0.390612 | − | 0.337238i | ||||
\(663\) | 28.5975 | 1.11063 | ||||||||
\(664\) | −13.1881 | − | 8.37517i | −0.511799 | − | 0.325020i | ||||
\(665\) | 13.8315 | + | 0.960878i | 0.536364 | + | 0.0372613i | ||||
\(666\) | 43.3471 | − | 50.2076i | 1.67967 | − | 1.94551i | ||||
\(667\) | −0.411845 | −0.0159467 | ||||||||
\(668\) | −4.87543 | − | 33.0636i | −0.188636 | − | 1.27927i | ||||
\(669\) | 42.0705i | 1.62654i | ||||||||
\(670\) | 2.75927 | + | 2.38224i | 0.106600 | + | 0.0920338i | ||||
\(671\) | −5.74554 | −0.221804 | ||||||||
\(672\) | 39.6078 | + | 21.0630i | 1.52790 | + | 0.812521i | ||||
\(673\) | 8.47579 | 0.326718 | 0.163359 | − | 0.986567i | \(-0.447767\pi\) | ||||
0.163359 | + | 0.986567i | \(0.447767\pi\) | |||||||
\(674\) | 21.1470 | + | 18.2574i | 0.814552 | + | 0.703249i | ||||
\(675\) | 8.94421i | 0.344263i | ||||||||
\(676\) | −2.07289 | − | 14.0576i | −0.0797264 | − | 0.540678i | ||||
\(677\) | 23.2065 | 0.891897 | 0.445948 | − | 0.895059i | \(-0.352866\pi\) | ||||
0.445948 | + | 0.895059i | \(0.352866\pi\) | |||||||
\(678\) | 10.3049 | − | 11.9358i | 0.395756 | − | 0.458393i | ||||
\(679\) | −20.7217 | − | 1.43954i | −0.795225 | − | 0.0552444i | ||||
\(680\) | 9.38241 | + | 5.95833i | 0.359799 | + | 0.228491i | ||||
\(681\) | −89.6394 | −3.43499 | ||||||||
\(682\) | 24.1558 | + | 20.8550i | 0.924972 | + | 0.798581i | ||||
\(683\) | −25.7680 | −0.985986 | −0.492993 | − | 0.870033i | \(-0.664097\pi\) | ||||
−0.492993 | + | 0.870033i | \(0.664097\pi\) | |||||||
\(684\) | 62.0470 | − | 9.14923i | 2.37243 | − | 0.349830i | ||||
\(685\) | −16.9739 | −0.648540 | ||||||||
\(686\) | −20.8424 | + | 15.8617i | −0.795767 | + | 0.605603i | ||||
\(687\) | 26.7394i | 1.02017i | ||||||||
\(688\) | −10.5835 | + | 3.19059i | −0.403493 | + | 0.121640i | ||||
\(689\) | 1.62212i | 0.0617978i | ||||||||
\(690\) | 0.366164 | + | 0.316130i | 0.0139396 | + | 0.0120349i | ||||
\(691\) | − | 24.5498i | − | 0.933917i | −0.884279 | − | 0.466958i | \(-0.845350\pi\) | ||
0.884279 | − | 0.466958i | \(-0.154650\pi\) | |||||||
\(692\) | 1.51549 | + | 10.2775i | 0.0576102 | + | 0.390693i | ||||
\(693\) | −5.35124 | + | 77.0294i | −0.203277 | + | 2.92610i | ||||
\(694\) | −31.9096 | − | 27.5494i | −1.21127 | − | 1.04576i | ||||
\(695\) | − | 2.54598i | − | 0.0965744i | ||||||
\(696\) | −16.4014 | + | 25.8268i | −0.621693 | + | 0.978962i | ||||
\(697\) | 41.1877 | 1.56009 | ||||||||
\(698\) | −16.8054 | − | 14.5091i | −0.636095 | − | 0.549177i | ||||
\(699\) | − | 1.69396i | − | 0.0640715i | ||||||
\(700\) | 5.27581 | − | 0.407269i | 0.199407 | − | 0.0153933i | ||||
\(701\) | 2.33837i | 0.0883188i | 0.999024 | + | 0.0441594i | \(0.0140610\pi\) | ||||
−0.999024 | + | 0.0441594i | \(0.985939\pi\) | |||||||
\(702\) | 20.0701 | − | 23.2466i | 0.757498 | − | 0.877387i | ||||
\(703\) | −41.0745 | −1.54915 | ||||||||
\(704\) | −16.5905 | − | 35.3134i | −0.625280 | − | 1.33092i | ||||
\(705\) | 36.2128i | 1.36385i | ||||||||
\(706\) | −9.44386 | + | 10.9385i | −0.355424 | + | 0.411677i | ||||
\(707\) | −1.99966 | + | 28.7845i | −0.0752049 | + | 1.08255i | ||||
\(708\) | 1.20279 | + | 8.15693i | 0.0452037 | + | 0.306556i | ||||
\(709\) | − | 36.8318i | − | 1.38325i | −0.722257 | − | 0.691624i | \(-0.756895\pi\) | ||
0.722257 | − | 0.691624i | \(-0.243105\pi\) | |||||||
\(710\) | 8.72154 | − | 10.1019i | 0.327314 | − | 0.379117i | ||||
\(711\) | 71.0927i | 2.66618i | ||||||||
\(712\) | 14.8470 | + | 9.42867i | 0.556417 | + | 0.353354i | ||||
\(713\) | 0.528036i | 0.0197751i | ||||||||
\(714\) | −31.0423 | + | 31.2817i | −1.16173 | + | 1.17069i | ||||
\(715\) | −11.8415 | −0.442847 | ||||||||
\(716\) | −5.05540 | − | 34.2840i | −0.188929 | − | 1.28125i | ||||
\(717\) | −25.5114 | −0.952742 | ||||||||
\(718\) | −21.6960 | + | 25.1298i | −0.809688 | + | 0.937837i | ||||
\(719\) | 33.8925 | 1.26398 | 0.631989 | − | 0.774978i | \(-0.282239\pi\) | ||||
0.631989 | + | 0.774978i | \(0.282239\pi\) | |||||||
\(720\) | 22.9174 | − | 6.90887i | 0.854082 | − | 0.257478i | ||||
\(721\) | 2.90076 | − | 41.7556i | 0.108030 | − | 1.55506i | ||||
\(722\) | −9.05830 | − | 7.82055i | −0.337115 | − | 0.291051i | ||||
\(723\) | −6.51991 | −0.242478 | ||||||||
\(724\) | 6.14397 | + | 41.6664i | 0.228339 | + | 1.54852i | ||||
\(725\) | 3.60881i | 0.134028i | ||||||||
\(726\) | 35.4176 | − | 41.0231i | 1.31447 | − | 1.52251i | ||||
\(727\) | −4.28102 | −0.158774 | −0.0793871 | − | 0.996844i | \(-0.525296\pi\) | ||||
−0.0793871 | + | 0.996844i | \(0.525296\pi\) | |||||||
\(728\) | −14.6261 | − | 10.7800i | −0.542078 | − | 0.399533i | ||||
\(729\) | 27.4276 | 1.01584 | ||||||||
\(730\) | −5.19969 | + | 6.02264i | −0.192449 | + | 0.222908i | ||||
\(731\) | − | 10.8593i | − | 0.401647i | ||||||
\(732\) | −6.98664 | + | 1.03023i | −0.258234 | + | 0.0380782i | ||||
\(733\) | −38.0426 | −1.40513 | −0.702567 | − | 0.711618i | \(-0.747963\pi\) | ||||
−0.702567 | + | 0.711618i | \(0.747963\pi\) | |||||||
\(734\) | 23.0151 | + | 19.8702i | 0.849501 | + | 0.733422i | ||||
\(735\) | −2.90116 | + | 20.7798i | −0.107011 | + | 0.766476i | ||||
\(736\) | 0.262882 | − | 0.589624i | 0.00968996 | − | 0.0217338i | ||||
\(737\) | 12.5714 | 0.463073 | ||||||||
\(738\) | 57.9667 | − | 67.1411i | 2.13378 | − | 2.47150i | ||||
\(739\) | 9.93398 | 0.365427 | 0.182714 | − | 0.983166i | \(-0.441512\pi\) | ||||
0.182714 | + | 0.983166i | \(0.441512\pi\) | |||||||
\(740\) | −15.5083 | + | 2.28680i | −0.570096 | + | 0.0840644i | ||||
\(741\) | −38.1374 | −1.40101 | ||||||||
\(742\) | −1.77437 | − | 1.76079i | −0.0651393 | − | 0.0646406i | ||||
\(743\) | 1.68905i | 0.0619651i | 0.999520 | + | 0.0309826i | \(0.00986363\pi\) | ||||
−0.999520 | + | 0.0309826i | \(0.990136\pi\) | |||||||
\(744\) | 33.1132 | + | 21.0286i | 1.21399 | + | 0.770947i | ||||
\(745\) | 13.7925i | 0.505316i | ||||||||
\(746\) | 0.721837 | − | 0.836082i | 0.0264283 | − | 0.0306111i | ||||
\(747\) | − | 33.0527i | − | 1.20934i | ||||||
\(748\) | 37.9193 | − | 5.59144i | 1.38647 | − | 0.204443i | ||||
\(749\) | 1.19815 | − | 17.2469i | 0.0437793 | − | 0.630189i | ||||
\(750\) | 2.77010 | − | 3.20852i | 0.101150 | − | 0.117159i | ||||
\(751\) | − | 36.9451i | − | 1.34815i | −0.738664 | − | 0.674073i | \(-0.764543\pi\) | ||
0.738664 | − | 0.674073i | \(-0.235457\pi\) | |||||||
\(752\) | 46.2698 | − | 13.9488i | 1.68728 | − | 0.508662i | ||||
\(753\) | 28.2257 | 1.02860 | ||||||||
\(754\) | 8.09789 | − | 9.37954i | 0.294908 | − | 0.341583i | ||||
\(755\) | − | 0.128374i | − | 0.00467202i | ||||||
\(756\) | 3.64270 | + | 47.1879i | 0.132484 | + | 1.71621i | ||||
\(757\) | − | 45.8391i | − | 1.66605i | −0.553235 | − | 0.833025i | \(-0.686607\pi\) | ||
0.553235 | − | 0.833025i | \(-0.313393\pi\) | |||||||
\(758\) | 4.85325 | + | 4.19009i | 0.176278 | + | 0.152191i | ||||
\(759\) | 1.66826 | 0.0605540 | ||||||||
\(760\) | −12.5123 | − | 7.94599i | −0.453869 | − | 0.288231i | ||||
\(761\) | − | 19.9588i | − | 0.723506i | −0.932274 | − | 0.361753i | \(-0.882178\pi\) | ||
0.932274 | − | 0.361753i | \(-0.117822\pi\) | |||||||
\(762\) | −12.2029 | − | 10.5354i | −0.442063 | − | 0.381658i | ||||
\(763\) | −28.8509 | − | 2.00428i | −1.04447 | − | 0.0725597i | ||||
\(764\) | 16.6888 | − | 2.46088i | 0.603781 | − | 0.0890314i | ||||
\(765\) | 23.5146i | 0.850174i | ||||||||
\(766\) | −38.5959 | − | 33.3220i | −1.39453 | − | 1.20397i | ||||
\(767\) | − | 3.33949i | − | 0.120582i | ||||||
\(768\) | −26.5063 | − | 39.9667i | −0.956463 | − | 1.44217i | ||||
\(769\) | 13.9529i | 0.503153i | 0.967837 | + | 0.251576i | \(0.0809490\pi\) | ||||
−0.967837 | + | 0.251576i | \(0.919051\pi\) | |||||||
\(770\) | 12.8538 | − | 12.9530i | 0.463219 | − | 0.466792i | ||||
\(771\) | 13.3123 | 0.479431 | ||||||||
\(772\) | −7.47884 | − | 50.7190i | −0.269169 | − | 1.82542i | ||||
\(773\) | 33.8775 | 1.21849 | 0.609245 | − | 0.792982i | \(-0.291473\pi\) | ||||
0.609245 | + | 0.792982i | \(0.291473\pi\) | |||||||
\(774\) | −17.7021 | − | 15.2832i | −0.636288 | − | 0.549344i | ||||
\(775\) | 4.62694 | 0.166205 | ||||||||
\(776\) | 18.7453 | + | 11.9043i | 0.672917 | + | 0.427338i | ||||
\(777\) | 4.30767 | − | 62.0076i | 0.154537 | − | 2.22451i | ||||
\(778\) | −19.5642 | + | 22.6606i | −0.701410 | + | 0.812422i | ||||
\(779\) | −54.9276 | −1.96798 | ||||||||
\(780\) | −14.3994 | + | 2.12328i | −0.515581 | + | 0.0760256i | ||||
\(781\) | − | 46.0247i | − | 1.64689i | ||||||
\(782\) | 0.480046 | + | 0.414451i | 0.0171664 | + | 0.0148207i | ||||
\(783\) | −32.2779 | −1.15352 | ||||||||
\(784\) | 27.6683 | − | 4.29734i | 0.988152 | − | 0.153476i | ||||
\(785\) | 13.1585 | 0.469649 | ||||||||
\(786\) | −24.6450 | − | 21.2774i | −0.879057 | − | 0.758940i | ||||
\(787\) | 8.07748i | 0.287931i | 0.989583 | + | 0.143965i | \(0.0459854\pi\) | ||||
−0.989583 | + | 0.143965i | \(0.954015\pi\) | |||||||
\(788\) | −3.53635 | + | 0.521457i | −0.125977 | + | 0.0185761i | ||||
\(789\) | −40.8377 | −1.45386 | ||||||||
\(790\) | 10.9797 | − | 12.7174i | 0.390639 | − | 0.452466i | ||||
\(791\) | 0.682101 | − | 9.81862i | 0.0242527 | − | 0.349110i | ||||
\(792\) | 44.2521 | − | 69.6825i | 1.57243 | − | 2.47606i | ||||
\(793\) | 2.86037 | 0.101575 | ||||||||
\(794\) | 15.1411 | + | 13.0721i | 0.537337 | + | 0.463913i | ||||
\(795\) | −2.00249 | −0.0710209 | ||||||||
\(796\) | 6.51139 | + | 44.1580i | 0.230790 | + | 1.56514i | ||||
\(797\) | 30.9873 | 1.09763 | 0.548813 | − | 0.835945i | \(-0.315080\pi\) | ||||
0.548813 | + | 0.835945i | \(0.315080\pi\) | |||||||
\(798\) | 41.3978 | − | 41.7171i | 1.46546 | − | 1.47677i | ||||
\(799\) | 47.4755i | 1.67956i | ||||||||
\(800\) | −5.16661 | − | 2.30351i | −0.182667 | − | 0.0814415i | ||||
\(801\) | 37.2104i | 1.31476i | ||||||||
\(802\) | 19.0721 | + | 16.4661i | 0.673461 | + | 0.581437i | ||||
\(803\) | 27.4394i | 0.968316i | ||||||||
\(804\) | 15.2869 | − | 2.25416i | 0.539129 | − | 0.0794980i | ||||
\(805\) | 0.301213 | + | 0.0209253i | 0.0106164 | + | 0.000737520i | ||||
\(806\) | −12.0257 | − | 10.3825i | −0.423588 | − | 0.365708i | ||||
\(807\) | 30.7866i | 1.08374i | ||||||||
\(808\) | 16.5362 | − | 26.0391i | 0.581741 | − | 0.916051i | ||||
\(809\) | −52.5895 | −1.84895 | −0.924474 | − | 0.381245i | \(-0.875495\pi\) | ||||
−0.924474 | + | 0.381245i | \(0.875495\pi\) | |||||||
\(810\) | 9.48071 | + | 8.18523i | 0.333118 | + | 0.287600i | ||||
\(811\) | − | 37.3872i | − | 1.31284i | −0.754395 | − | 0.656421i | \(-0.772069\pi\) | ||
0.754395 | − | 0.656421i | \(-0.227931\pi\) | |||||||
\(812\) | 1.46975 | + | 19.0394i | 0.0515782 | + | 0.668151i | ||||
\(813\) | 8.01082i | 0.280952i | ||||||||
\(814\) | −35.3283 | + | 40.9197i | −1.23826 | + | 1.43423i | ||||
\(815\) | 0.158264 | 0.00554374 | ||||||||
\(816\) | 45.1077 | − | 13.5985i | 1.57908 | − | 0.476043i | ||||
\(817\) | 14.4819i | 0.506659i | ||||||||
\(818\) | −30.0630 | + | 34.8211i | −1.05113 | + | 1.21749i | ||||
\(819\) | 2.66407 | − | 38.3484i | 0.0930901 | − | 1.34000i | ||||
\(820\) | −20.7388 | + | 3.05806i | −0.724229 | + | 0.106792i | ||||
\(821\) | 23.1500i | 0.807941i | 0.914772 | + | 0.403970i | \(0.132370\pi\) | ||||
−0.914772 | + | 0.403970i | \(0.867630\pi\) | |||||||
\(822\) | −47.0195 | + | 54.4612i | −1.63999 | + | 1.89955i | ||||
\(823\) | 10.1543i | 0.353957i | 0.984215 | + | 0.176979i | \(0.0566323\pi\) | ||||
−0.984215 | + | 0.176979i | \(0.943368\pi\) | |||||||
\(824\) | −23.9879 | + | 37.7730i | −0.835657 | + | 1.31588i | ||||
\(825\) | − | 14.6182i | − | 0.508940i | ||||||
\(826\) | 3.65294 | + | 3.62498i | 0.127102 | + | 0.126129i | ||||
\(827\) | −25.7346 | −0.894881 | −0.447440 | − | 0.894314i | \(-0.647664\pi\) | ||||
−0.447440 | + | 0.894314i | \(0.647664\pi\) | |||||||
\(828\) | 1.35121 | − | 0.199245i | 0.0469579 | − | 0.00692425i | ||||
\(829\) | −29.2920 | −1.01735 | −0.508677 | − | 0.860958i | \(-0.669865\pi\) | ||||
−0.508677 | + | 0.860958i | \(0.669865\pi\) | |||||||
\(830\) | −5.10472 | + | 5.91264i | −0.177187 | + | 0.205231i | ||||
\(831\) | 84.3400 | 2.92572 | ||||||||
\(832\) | 8.25946 | + | 17.5805i | 0.286345 | + | 0.609493i | ||||
\(833\) | −3.80346 | + | 27.2427i | −0.131782 | + | 0.943902i | ||||
\(834\) | −8.16883 | − | 7.05261i | −0.282863 | − | 0.244212i | ||||
\(835\) | −16.7105 | −0.578292 | ||||||||
\(836\) | −50.5689 | + | 7.45671i | −1.74896 | + | 0.257896i | ||||
\(837\) | 41.3843i | 1.43045i | ||||||||
\(838\) | 31.8653 | − | 36.9086i | 1.10077 | − | 1.27499i | ||||
\(839\) | −11.5479 | −0.398676 | −0.199338 | − | 0.979931i | \(-0.563879\pi\) | ||||
−0.199338 | + | 0.979931i | \(0.563879\pi\) | |||||||
\(840\) | 13.3078 | − | 18.0557i | 0.459162 | − | 0.622982i | ||||
\(841\) | 15.9765 | 0.550914 | ||||||||
\(842\) | 11.3338 | − | 13.1276i | 0.390588 | − | 0.452407i | ||||
\(843\) | − | 1.39928i | − | 0.0481939i | ||||||
\(844\) | 2.50466 | + | 16.9858i | 0.0862139 | + | 0.584674i | ||||
\(845\) | −7.10482 | −0.244413 | ||||||||
\(846\) | 77.3911 | + | 66.8161i | 2.66076 | + | 2.29718i | ||||
\(847\) | 2.34436 | − | 33.7464i | 0.0805533 | − | 1.15954i | ||||
\(848\) | 0.771339 | + | 2.55861i | 0.0264879 | + | 0.0878631i | ||||
\(849\) | 32.3726 | 1.11102 | ||||||||
\(850\) | 3.63164 | − | 4.20642i | 0.124564 | − | 0.144279i | ||||
\(851\) | −0.894489 | −0.0306627 | ||||||||
\(852\) | −8.25263 | − | 55.9666i | −0.282730 | − | 1.91738i | ||||
\(853\) | 35.5827 | 1.21833 | 0.609164 | − | 0.793045i | \(-0.291505\pi\) | ||||
0.609164 | + | 0.793045i | \(0.291505\pi\) | |||||||
\(854\) | −3.10490 | + | 3.12885i | −0.106247 | + | 0.107067i | ||||
\(855\) | − | 31.3590i | − | 1.07245i | ||||||
\(856\) | −9.90808 | + | 15.6020i | −0.338651 | + | 0.533264i | ||||
\(857\) | 1.71368i | 0.0585383i | 0.999572 | + | 0.0292691i | \(0.00931799\pi\) | ||||
−0.999572 | + | 0.0292691i | \(0.990682\pi\) | |||||||
\(858\) | −32.8021 | + | 37.9937i | −1.11985 | + | 1.29708i | ||||
\(859\) | 14.7176i | 0.502158i | 0.967967 | + | 0.251079i | \(0.0807855\pi\) | ||||
−0.967967 | + | 0.251079i | \(0.919215\pi\) | |||||||
\(860\) | 0.806274 | + | 5.46788i | 0.0274937 | + | 0.186453i | ||||
\(861\) | 5.76052 | − | 82.9208i | 0.196318 | − | 2.82593i | ||||
\(862\) | −20.1213 | + | 23.3058i | −0.685333 | + | 0.793800i | ||||
\(863\) | − | 37.4241i | − | 1.27393i | −0.770892 | − | 0.636966i | \(-0.780189\pi\) | ||
0.770892 | − | 0.636966i | \(-0.219811\pi\) | |||||||
\(864\) | 20.6031 | − | 46.2112i | 0.700932 | − | 1.57214i | ||||
\(865\) | 5.19433 | 0.176612 | ||||||||
\(866\) | 24.1764 | − | 28.0028i | 0.821549 | − | 0.951575i | ||||
\(867\) | − | 4.67166i | − | 0.158658i | ||||||
\(868\) | 24.4108 | − | 1.88441i | 0.828557 | − | 0.0639609i | ||||
\(869\) | − | 57.9412i | − | 1.96552i | ||||||
\(870\) | 11.5789 | + | 9.99676i | 0.392563 | + | 0.338922i | ||||
\(871\) | −6.25855 | −0.212063 | ||||||||
\(872\) | 26.0992 | + | 16.5744i | 0.883830 | + | 0.561279i | ||||
\(873\) | 46.9804i | 1.59005i | ||||||||
\(874\) | −0.640186 | − | 0.552709i | −0.0216546 | − | 0.0186957i | ||||
\(875\) | 0.183359 | − | 2.63939i | 0.00619866 | − | 0.0892277i | ||||
\(876\) | 4.92013 | + | 33.3666i | 0.166236 | + | 1.12735i | ||||
\(877\) | 24.9933i | 0.843965i | 0.906604 | + | 0.421982i | \(0.138666\pi\) | ||||
−0.906604 | + | 0.421982i | \(0.861334\pi\) | |||||||
\(878\) | 31.6142 | + | 27.2943i | 1.06693 | + | 0.921139i | ||||
\(879\) | − | 22.0164i | − | 0.742596i | ||||||
\(880\) | −18.6779 | + | 5.63079i | −0.629633 | + | 0.189814i | ||||
\(881\) | − | 27.7020i | − | 0.933303i | −0.884441 | − | 0.466651i | \(-0.845460\pi\) | ||
0.884441 | − | 0.466651i | \(-0.154540\pi\) | |||||||
\(882\) | 39.0560 | + | 44.5409i | 1.31509 | + | 1.49977i | ||||
\(883\) | 3.66299 | 0.123269 | 0.0616347 | − | 0.998099i | \(-0.480369\pi\) | ||||
0.0616347 | + | 0.998099i | \(0.480369\pi\) | |||||||
\(884\) | −18.8778 | + | 2.78365i | −0.634929 | + | 0.0936243i | ||||
\(885\) | 4.12256 | 0.138579 | ||||||||
\(886\) | −23.3269 | − | 20.1394i | −0.783682 | − | 0.676597i | ||||
\(887\) | −40.0849 | −1.34592 | −0.672960 | − | 0.739679i | \(-0.734978\pi\) | ||||
−0.672960 | + | 0.739679i | \(0.734978\pi\) | |||||||
\(888\) | −35.6223 | + | 56.0934i | −1.19541 | + | 1.88237i | ||||
\(889\) | −10.0383 | − | 0.697361i | −0.336674 | − | 0.0233887i | ||||
\(890\) | 5.74684 | − | 6.65639i | 0.192634 | − | 0.223123i | ||||
\(891\) | 43.1946 | 1.44707 | ||||||||
\(892\) | −4.09510 | − | 27.7716i | −0.137114 | − | 0.929862i | ||||
\(893\) | − | 63.3130i | − | 2.11869i | ||||||
\(894\) | 44.2534 | + | 38.2065i | 1.48006 | + | 1.27782i | ||||
\(895\) | −17.3274 | −0.579190 | ||||||||
\(896\) | −28.1962 | − | 10.0487i | −0.941968 | − | 0.335703i | ||||
\(897\) | −0.830529 | −0.0277306 | ||||||||
\(898\) | −1.88091 | − | 1.62390i | −0.0627668 | − | 0.0541901i | ||||
\(899\) | 16.6977i | 0.556900i | ||||||||
\(900\) | −1.74589 | − | 11.8401i | −0.0581965 | − | 0.394669i | ||||
\(901\) | −2.62529 | −0.0874610 | ||||||||
\(902\) | −47.2434 | + | 54.7206i | −1.57303 | + | 1.82200i | ||||
\(903\) | −21.8625 | − | 1.51879i | −0.727538 | − | 0.0505421i | ||||
\(904\) | −5.64064 | + | 8.88215i | −0.187605 | + | 0.295416i | ||||
\(905\) | 21.0585 | 0.700007 | ||||||||
\(906\) | −0.411892 | − | 0.355610i | −0.0136842 | − | 0.0118143i | ||||
\(907\) | −33.0878 | −1.09866 | −0.549331 | − | 0.835605i | \(-0.685117\pi\) | ||||
−0.549331 | + | 0.835605i | \(0.685117\pi\) | |||||||
\(908\) | 59.1728 | − | 8.72540i | 1.96372 | − | 0.289563i | ||||
\(909\) | 65.2604 | 2.16455 | ||||||||
\(910\) | −6.39916 | + | 6.44852i | −0.212130 | + | 0.213766i | ||||
\(911\) | 41.4259i | 1.37250i | 0.727365 | + | 0.686250i | \(0.240745\pi\) | ||||
−0.727365 | + | 0.686250i | \(0.759255\pi\) | |||||||
\(912\) | −60.1553 | + | 18.1349i | −1.99194 | + | 0.600506i | ||||
\(913\) | 26.9383i | 0.891527i | ||||||||
\(914\) | 4.05549 | + | 3.50133i | 0.134144 | + | 0.115814i | ||||
\(915\) | 3.53110i | 0.116734i | ||||||||
\(916\) | −2.60278 | − | 17.6512i | −0.0859983 | − | 0.583212i | ||||
\(917\) | −20.2734 | − | 1.40840i | −0.669487 | − | 0.0465093i | ||||
\(918\) | 37.6231 | + | 32.4822i | 1.24175 | + | 1.07207i | ||||
\(919\) | − | 2.61219i | − | 0.0861682i | −0.999071 | − | 0.0430841i | \(-0.986282\pi\) | ||
0.999071 | − | 0.0430841i | \(-0.0137183\pi\) | |||||||
\(920\) | −0.272484 | − | 0.173042i | −0.00898353 | − | 0.00570502i | ||||
\(921\) | 15.2288 | 0.501807 | ||||||||
\(922\) | 34.6336 | + | 29.9012i | 1.14060 | + | 0.984743i | ||||
\(923\) | 22.9130i | 0.754191i | ||||||||
\(924\) | −5.95353 | − | 77.1228i | −0.195857 | − | 2.53715i | ||||
\(925\) | 7.83800i | 0.257712i | ||||||||
\(926\) | −28.8836 | + | 33.4551i | −0.949176 | + | 1.09940i | ||||
\(927\) | −94.6686 | −3.10932 | ||||||||
\(928\) | 8.31294 | − | 18.6453i | 0.272886 | − | 0.612061i | ||||
\(929\) | 29.7850i | 0.977213i | 0.872504 | + | 0.488606i | \(0.162495\pi\) | ||||
−0.872504 | + | 0.488606i | \(0.837505\pi\) | |||||||
\(930\) | 12.8171 | − | 14.8456i | 0.420289 | − | 0.486808i | ||||
\(931\) | 5.07226 | − | 36.3306i | 0.166237 | − | 1.19069i | ||||
\(932\) | 0.164888 | + | 1.11822i | 0.00540110 | + | 0.0366285i | ||||
\(933\) | 53.4484i | 1.74982i | ||||||||
\(934\) | 20.9605 | − | 24.2780i | 0.685850 | − | 0.794399i | ||||
\(935\) | − | 19.1647i | − | 0.626751i | ||||||
\(936\) | −22.0305 | + | 34.6908i | −0.720090 | + | 1.13391i | ||||
\(937\) | − | 20.9620i | − | 0.684800i | −0.939554 | − | 0.342400i | \(-0.888760\pi\) | ||
0.939554 | − | 0.342400i | \(-0.111240\pi\) | |||||||
\(938\) | 6.79359 | − | 6.84599i | 0.221819 | − | 0.223530i | ||||
\(939\) | −10.6108 | −0.346271 | ||||||||
\(940\) | −3.52492 | − | 23.9048i | −0.114970 | − | 0.779689i | ||||
\(941\) | −21.3589 | −0.696280 | −0.348140 | − | 0.937443i | \(-0.613187\pi\) | ||||
−0.348140 | + | 0.937443i | \(0.613187\pi\) | |||||||
\(942\) | 36.4505 | − | 42.2195i | 1.18762 | − | 1.37559i | ||||
\(943\) | −1.19617 | −0.0389527 | ||||||||
\(944\) | −1.58797 | − | 5.26747i | −0.0516841 | − | 0.171442i | ||||
\(945\) | 23.6073 | + | 1.64000i | 0.767944 | + | 0.0533492i | ||||
\(946\) | 14.4274 | + | 12.4560i | 0.469074 | + | 0.404978i | ||||
\(947\) | −54.2008 | −1.76129 | −0.880645 | − | 0.473777i | \(-0.842890\pi\) | ||||
−0.880645 | + | 0.473777i | \(0.842890\pi\) | |||||||
\(948\) | −10.3894 | − | 70.4571i | −0.337430 | − | 2.28834i | ||||
\(949\) | − | 13.6605i | − | 0.443438i | ||||||
\(950\) | −4.84313 | + | 5.60965i | −0.157132 | + | 0.182001i | ||||
\(951\) | −14.5779 | −0.472719 | ||||||||
\(952\) | 17.4467 | − | 23.6713i | 0.565451 | − | 0.767192i | ||||
\(953\) | 26.3943 | 0.854994 | 0.427497 | − | 0.904017i | \(-0.359395\pi\) | ||||
0.427497 | + | 0.904017i | \(0.359395\pi\) | |||||||
\(954\) | −3.69478 | + | 4.27955i | −0.119623 | + | 0.138556i | ||||
\(955\) | − | 8.43465i | − | 0.272939i | ||||||
\(956\) | 16.8406 | − | 2.48326i | 0.544664 | − | 0.0803142i | ||||
\(957\) | 52.7542 | 1.70530 | ||||||||
\(958\) | 13.7702 | + | 11.8886i | 0.444896 | + | 0.384104i | ||||
\(959\) | −3.11231 | + | 44.8008i | −0.100502 | + | 1.44669i | ||||
\(960\) | −21.7029 | + | 10.1962i | −0.700458 | + | 0.329081i | ||||
\(961\) | −9.59145 | −0.309402 | ||||||||
\(962\) | 17.5879 | − | 20.3715i | 0.567056 | − | 0.656804i | ||||
\(963\) | −39.1024 | −1.26006 | ||||||||
\(964\) | 4.30392 | − | 0.634641i | 0.138620 | − | 0.0204404i | ||||
\(965\) | −25.6337 | −0.825179 | ||||||||
\(966\) | 0.901530 | − | 0.908484i | 0.0290062 | − | 0.0292300i | ||||
\(967\) | − | 32.9216i | − | 1.05869i | −0.848408 | − | 0.529343i | \(-0.822438\pi\) | ||
0.848408 | − | 0.529343i | \(-0.177562\pi\) | |||||||
\(968\) | −19.3867 | + | 30.5277i | −0.623113 | + | 0.981198i | ||||
\(969\) | − | 61.7229i | − | 1.98282i | ||||||
\(970\) | 7.25573 | − | 8.40410i | 0.232968 | − | 0.269839i | ||||
\(971\) | − | 32.2598i | − | 1.03527i | −0.855603 | − | 0.517633i | \(-0.826813\pi\) | ||
0.855603 | − | 0.517633i | \(-0.173187\pi\) | |||||||
\(972\) | −0.566103 | + | 0.0834756i | −0.0181578 | + | 0.00267748i | ||||
\(973\) | −6.71982 | − | 0.466827i | −0.215428 | − | 0.0149658i | ||||
\(974\) | 18.7733 | − | 21.7445i | 0.601534 | − | 0.696739i | ||||
\(975\) | 7.27754i | 0.233068i | ||||||||
\(976\) | 4.51174 | − | 1.36014i | 0.144417 | − | 0.0435372i | ||||
\(977\) | −21.3881 | −0.684265 | −0.342132 | − | 0.939652i | \(-0.611149\pi\) | ||||
−0.342132 | + | 0.939652i | \(0.611149\pi\) | |||||||
\(978\) | 0.438407 | − | 0.507793i | 0.0140187 | − | 0.0162374i | ||||
\(979\) | − | 30.3268i | − | 0.969249i | ||||||
\(980\) | −0.107576 | − | 13.9996i | −0.00343638 | − | 0.447200i | ||||
\(981\) | 65.4111i | 2.08842i | ||||||||
\(982\) | 17.6178 | + | 15.2104i | 0.562205 | + | 0.485384i | ||||
\(983\) | 18.6503 | 0.594852 | 0.297426 | − | 0.954745i | \(-0.403872\pi\) | ||||
0.297426 | + | 0.954745i | \(0.403872\pi\) | |||||||
\(984\) | −47.6366 | + | 75.0120i | −1.51860 | + | 2.39129i | ||||
\(985\) | 1.78729i | 0.0569479i | ||||||||
\(986\) | 15.1802 | + | 13.1059i | 0.483435 | + | 0.417377i | ||||
\(987\) | 95.5798 | + | 6.63994i | 3.04234 | + | 0.211351i | ||||
\(988\) | 25.1753 | − | 3.71226i | 0.800933 | − | 0.118103i | ||||
\(989\) | 0.315377i | 0.0100284i | ||||||||
\(990\) | −31.2408 | − | 26.9720i | −0.992898 | − | 0.857225i | ||||
\(991\) | − | 13.5821i | − | 0.431448i | −0.976454 | − | 0.215724i | \(-0.930789\pi\) | ||
0.976454 | − | 0.215724i | \(-0.0692112\pi\) | |||||||
\(992\) | −23.9056 | − | 10.6582i | −0.759002 | − | 0.338399i | ||||
\(993\) | 28.1411i | 0.893032i | ||||||||
\(994\) | −25.0637 | − | 24.8718i | −0.794971 | − | 0.788886i | ||||
\(995\) | 22.3178 | 0.707521 | ||||||||
\(996\) | 4.83027 | + | 32.7573i | 0.153053 | + | 1.03795i | ||||
\(997\) | 25.3616 | 0.803210 | 0.401605 | − | 0.915813i | \(-0.368452\pi\) | ||||
0.401605 | + | 0.915813i | \(0.368452\pi\) | |||||||
\(998\) | 20.0693 | + | 17.3270i | 0.635282 | + | 0.548475i | ||||
\(999\) | −70.1047 | −2.21801 |
(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 | 280.2.h.b.251.12 | yes | 16 | |
4.3 | odd | 2 | 1120.2.h.b.111.15 | 16 | |||
7.6 | odd | 2 | 280.2.h.a.251.12 | yes | 16 | ||
8.3 | odd | 2 | 280.2.h.a.251.11 | ✓ | 16 | ||
8.5 | even | 2 | 1120.2.h.a.111.15 | 16 | |||
28.27 | even | 2 | 1120.2.h.a.111.2 | 16 | |||
56.13 | odd | 2 | 1120.2.h.b.111.2 | 16 | |||
56.27 | even | 2 | inner | 280.2.h.b.251.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.11 | ✓ | 16 | 8.3 | odd | 2 | ||
280.2.h.a.251.12 | yes | 16 | 7.6 | odd | 2 | ||
280.2.h.b.251.11 | yes | 16 | 56.27 | even | 2 | inner | |
280.2.h.b.251.12 | yes | 16 | 1.1 | even | 1 | trivial | |
1120.2.h.a.111.2 | 16 | 28.27 | even | 2 | |||
1120.2.h.a.111.15 | 16 | 8.5 | even | 2 | |||
1120.2.h.b.111.2 | 16 | 56.13 | odd | 2 | |||
1120.2.h.b.111.15 | 16 | 4.3 | odd | 2 |