Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.11 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.11 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.94131 | − | 0.763816i | −0.988263 | − | 0.152763i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 8.62845 | + | 8.62845i | 1.23264 | + | 1.23264i | 0.962948 | + | 0.269688i | \(0.0869205\pi\) |
0.269688 | + | 0.962948i | \(0.413080\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 4.17750 | + | 5.70513i | 0.417750 | + | 0.570513i | ||||
\(11\) | −9.96233 | −0.905667 | −0.452833 | − | 0.891595i | \(-0.649587\pi\) | ||||
−0.452833 | + | 0.891595i | \(0.649587\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | −1.36926 | + | 1.36926i | −0.105328 | + | 0.105328i | −0.757807 | − | 0.652479i | \(-0.773729\pi\) |
0.652479 | + | 0.757807i | \(0.273729\pi\) | |||||||
\(14\) | − | 17.2569i | − | 1.23264i | ||||||
\(15\) | 6.98733 | − | 5.11637i | 0.465822 | − | 0.341091i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 12.8665 | + | 12.8665i | 0.756853 | + | 0.756853i | 0.975748 | − | 0.218895i | \(-0.0702452\pi\) |
−0.218895 | + | 0.975748i | \(0.570245\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | 21.6135i | 1.13755i | 0.822493 | + | 0.568776i | \(0.192583\pi\) | ||||
−0.822493 | + | 0.568776i | \(0.807417\pi\) | |||||||
\(20\) | 1.52763 | − | 9.88263i | 0.0763816 | − | 0.494131i | ||||
\(21\) | −21.1353 | −1.00644 | ||||||||
\(22\) | 9.96233 | + | 9.96233i | 0.452833 | + | 0.452833i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 23.8332 | + | 7.54851i | 0.953327 | + | 0.301940i | ||||
\(26\) | 2.73852 | 0.105328 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −17.2569 | + | 17.2569i | −0.616318 | + | 0.616318i | ||||
\(29\) | − | 41.0639i | − | 1.41600i | −0.706214 | − | 0.707998i | \(-0.749598\pi\) | ||
0.706214 | − | 0.707998i | \(-0.250402\pi\) | |||||||
\(30\) | −12.1037 | − | 1.87096i | −0.403457 | − | 0.0623653i | ||||
\(31\) | 39.6561 | 1.27923 | 0.639614 | − | 0.768696i | \(-0.279094\pi\) | ||||
0.639614 | + | 0.768696i | \(0.279094\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 12.2013 | − | 12.2013i | 0.369737 | − | 0.369737i | ||||
\(34\) | − | 25.7330i | − | 0.756853i | ||||||
\(35\) | −36.0453 | − | 49.2264i | −1.02987 | − | 1.40647i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −47.8886 | − | 47.8886i | −1.29429 | − | 1.29429i | −0.932109 | − | 0.362178i | \(-0.882033\pi\) |
−0.362178 | − | 0.932109i | \(-0.617967\pi\) | |||||||
\(38\) | 21.6135 | − | 21.6135i | 0.568776 | − | 0.568776i | ||||
\(39\) | − | 3.35399i | − | 0.0859997i | ||||||
\(40\) | −11.4103 | + | 8.35500i | −0.285257 | + | 0.208875i | ||||
\(41\) | −46.0597 | −1.12341 | −0.561704 | − | 0.827338i | \(-0.689854\pi\) | ||||
−0.561704 | + | 0.827338i | \(0.689854\pi\) | |||||||
\(42\) | 21.1353 | + | 21.1353i | 0.503221 | + | 0.503221i | ||||
\(43\) | −42.5076 | + | 42.5076i | −0.988550 | + | 0.988550i | −0.999935 | − | 0.0113855i | \(-0.996376\pi\) |
0.0113855 | + | 0.999935i | \(0.496376\pi\) | |||||||
\(44\) | − | 19.9247i | − | 0.452833i | ||||||
\(45\) | −2.29145 | + | 14.8239i | −0.0509211 | + | 0.329421i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 4.44905 | + | 4.44905i | 0.0946607 | + | 0.0946607i | 0.752851 | − | 0.658191i | \(-0.228678\pi\) |
−0.658191 | + | 0.752851i | \(0.728678\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 99.9003i | 2.03878i | ||||||||
\(50\) | −16.2847 | − | 31.3817i | −0.325693 | − | 0.627634i | ||||
\(51\) | −31.5164 | −0.617968 | ||||||||
\(52\) | −2.73852 | − | 2.73852i | −0.0526638 | − | 0.0526638i | ||||
\(53\) | −10.1671 | + | 10.1671i | −0.191832 | + | 0.191832i | −0.796487 | − | 0.604655i | \(-0.793311\pi\) |
0.604655 | + | 0.796487i | \(0.293311\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 49.2270 | + | 7.60939i | 0.895037 | + | 0.138353i | ||||
\(56\) | 34.5138 | 0.616318 | ||||||||
\(57\) | −26.4710 | − | 26.4710i | −0.464403 | − | 0.464403i | ||||
\(58\) | −41.0639 | + | 41.0639i | −0.707998 | + | 0.707998i | ||||
\(59\) | 83.8782i | 1.42166i | 0.703362 | + | 0.710832i | \(0.251681\pi\) | ||||
−0.703362 | + | 0.710832i | \(0.748319\pi\) | |||||||
\(60\) | 10.2327 | + | 13.9747i | 0.170546 | + | 0.232911i | ||||
\(61\) | −94.9681 | −1.55685 | −0.778427 | − | 0.627735i | \(-0.783982\pi\) | ||||
−0.778427 | + | 0.627735i | \(0.783982\pi\) | |||||||
\(62\) | −39.6561 | − | 39.6561i | −0.639614 | − | 0.639614i | ||||
\(63\) | 25.8853 | − | 25.8853i | 0.410879 | − | 0.410879i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 7.81181 | − | 5.72008i | 0.120182 | − | 0.0880013i | ||||
\(66\) | −24.4026 | −0.369737 | ||||||||
\(67\) | −24.0838 | − | 24.0838i | −0.359460 | − | 0.359460i | 0.504154 | − | 0.863614i | \(-0.331804\pi\) |
−0.863614 | + | 0.504154i | \(0.831804\pi\) | |||||||
\(68\) | −25.7330 | + | 25.7330i | −0.378427 | + | 0.378427i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −13.1811 | + | 85.2718i | −0.188301 | + | 1.21817i | ||||
\(71\) | −127.966 | −1.80234 | −0.901171 | − | 0.433464i | \(-0.857291\pi\) | ||||
−0.901171 | + | 0.433464i | \(0.857291\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 59.6158 | − | 59.6158i | 0.816655 | − | 0.816655i | −0.168967 | − | 0.985622i | \(-0.554043\pi\) |
0.985622 | + | 0.168967i | \(0.0540432\pi\) | |||||||
\(74\) | 95.7772i | 1.29429i | ||||||||
\(75\) | −38.4346 | + | 19.9446i | −0.512461 | + | 0.265927i | ||||
\(76\) | −43.2269 | −0.568776 | ||||||||
\(77\) | −85.9595 | − | 85.9595i | −1.11636 | − | 1.11636i | ||||
\(78\) | −3.35399 | + | 3.35399i | −0.0429999 | + | 0.0429999i | ||||
\(79\) | 27.1346i | 0.343476i | 0.985143 | + | 0.171738i | \(0.0549383\pi\) | ||||
−0.985143 | + | 0.171738i | \(0.945062\pi\) | |||||||
\(80\) | 19.7653 | + | 3.05526i | 0.247066 | + | 0.0381908i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 46.0597 | + | 46.0597i | 0.561704 | + | 0.561704i | ||||
\(83\) | −61.0630 | + | 61.0630i | −0.735698 | + | 0.735698i | −0.971742 | − | 0.236044i | \(-0.924149\pi\) |
0.236044 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(84\) | − | 42.2706i | − | 0.503221i | ||||||
\(85\) | −53.7498 | − | 73.4051i | −0.632351 | − | 0.863589i | ||||
\(86\) | 85.0153 | 0.988550 | ||||||||
\(87\) | 50.2928 | + | 50.2928i | 0.578078 | + | 0.578078i | ||||
\(88\) | −19.9247 | + | 19.9247i | −0.226417 | + | 0.226417i | ||||
\(89\) | 84.3721i | 0.948001i | 0.880524 | + | 0.474001i | \(0.157191\pi\) | ||||
−0.880524 | + | 0.474001i | \(0.842809\pi\) | |||||||
\(90\) | 17.1154 | − | 12.5325i | 0.190171 | − | 0.139250i | ||||
\(91\) | −23.6292 | −0.259661 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −48.5686 | + | 48.5686i | −0.522243 | + | 0.522243i | ||||
\(94\) | − | 8.89810i | − | 0.0946607i | ||||||
\(95\) | 16.5087 | − | 106.799i | 0.173776 | − | 1.12420i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −111.709 | − | 111.709i | −1.15164 | − | 1.15164i | −0.986223 | − | 0.165418i | \(-0.947103\pi\) |
−0.165418 | − | 0.986223i | \(-0.552897\pi\) | |||||||
\(98\) | 99.9003 | − | 99.9003i | 1.01939 | − | 1.01939i | ||||
\(99\) | 29.8870i | 0.301889i | ||||||||
\(100\) | −15.0970 | + | 47.6663i | −0.150970 | + | 0.476663i | ||||
\(101\) | 77.7181 | 0.769486 | 0.384743 | − | 0.923024i | \(-0.374290\pi\) | ||||
0.384743 | + | 0.923024i | \(0.374290\pi\) | |||||||
\(102\) | 31.5164 | + | 31.5164i | 0.308984 | + | 0.308984i | ||||
\(103\) | 42.3360 | − | 42.3360i | 0.411029 | − | 0.411029i | −0.471068 | − | 0.882097i | \(-0.656131\pi\) |
0.882097 | + | 0.471068i | \(0.156131\pi\) | |||||||
\(104\) | 5.47704i | 0.0526638i | ||||||||
\(105\) | 104.436 | + | 16.1435i | 0.994630 | + | 0.153747i | ||||
\(106\) | 20.3342 | 0.191832 | ||||||||
\(107\) | −106.967 | − | 106.967i | −0.999693 | − | 0.999693i | 0.000307102 | − | 1.00000i | \(-0.499902\pi\) |
−1.00000 | 0.000307102i | \(0.999902\pi\) | ||||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 36.5144i | 0.334994i | 0.985873 | + | 0.167497i | \(0.0535685\pi\) | ||||
−0.985873 | + | 0.167497i | \(0.946432\pi\) | |||||||
\(110\) | −41.6176 | − | 56.8364i | −0.378342 | − | 0.516695i | ||||
\(111\) | 117.303 | 1.05678 | ||||||||
\(112\) | −34.5138 | − | 34.5138i | −0.308159 | − | 0.308159i | ||||
\(113\) | −10.6656 | + | 10.6656i | −0.0943859 | + | 0.0943859i | −0.752723 | − | 0.658337i | \(-0.771260\pi\) |
0.658337 | + | 0.752723i | \(0.271260\pi\) | |||||||
\(114\) | 52.9420i | 0.464403i | ||||||||
\(115\) | −19.3470 | + | 14.1666i | −0.168235 | + | 0.123188i | ||||
\(116\) | 82.1278 | 0.707998 | ||||||||
\(117\) | 4.10778 | + | 4.10778i | 0.0351092 | + | 0.0351092i | ||||
\(118\) | 83.8782 | − | 83.8782i | 0.710832 | − | 0.710832i | ||||
\(119\) | 222.036i | 1.86585i | ||||||||
\(120\) | 3.74192 | − | 24.2074i | 0.0311827 | − | 0.201728i | ||||
\(121\) | −21.7519 | −0.179768 | ||||||||
\(122\) | 94.9681 | + | 94.9681i | 0.778427 | + | 0.778427i | ||||
\(123\) | 56.4114 | − | 56.4114i | 0.458629 | − | 0.458629i | ||||
\(124\) | 79.3121i | 0.639614i | ||||||||
\(125\) | −112.002 | − | 55.5037i | −0.896012 | − | 0.444030i | ||||
\(126\) | −51.7707 | −0.410879 | ||||||||
\(127\) | 121.366 | + | 121.366i | 0.955634 | + | 0.955634i | 0.999057 | − | 0.0434223i | \(-0.0138261\pi\) |
−0.0434223 | + | 0.999057i | \(0.513826\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 104.122i | − | 0.807147i | ||||||
\(130\) | −13.5319 | − | 2.09173i | −0.104091 | − | 0.0160902i | ||||
\(131\) | 188.546 | 1.43928 | 0.719642 | − | 0.694345i | \(-0.244306\pi\) | ||||
0.719642 | + | 0.694345i | \(0.244306\pi\) | |||||||
\(132\) | 24.4026 | + | 24.4026i | 0.184868 | + | 0.184868i | ||||
\(133\) | −186.491 | + | 186.491i | −1.40219 | + | 1.40219i | ||||
\(134\) | 48.1676i | 0.359460i | ||||||||
\(135\) | −15.3491 | − | 20.9620i | −0.113697 | − | 0.155274i | ||||
\(136\) | 51.4660 | 0.378427 | ||||||||
\(137\) | −86.1083 | − | 86.1083i | −0.628528 | − | 0.628528i | 0.319170 | − | 0.947698i | \(-0.396596\pi\) |
−0.947698 | + | 0.319170i | \(0.896596\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | 145.443i | 1.04636i | 0.852224 | + | 0.523178i | \(0.175254\pi\) | ||||
−0.852224 | + | 0.523178i | \(0.824746\pi\) | |||||||
\(140\) | 98.4528 | − | 72.0907i | 0.703235 | − | 0.514933i | ||||
\(141\) | −10.8979 | −0.0772901 | ||||||||
\(142\) | 127.966 | + | 127.966i | 0.901171 | + | 0.901171i | ||||
\(143\) | 13.6410 | − | 13.6410i | 0.0953918 | − | 0.0953918i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −31.3653 | + | 202.910i | −0.216312 | + | 1.39938i | ||||
\(146\) | −119.232 | −0.816655 | ||||||||
\(147\) | −122.352 | − | 122.352i | −0.832329 | − | 0.832329i | ||||
\(148\) | 95.7772 | − | 95.7772i | 0.647144 | − | 0.647144i | ||||
\(149\) | − | 135.574i | − | 0.909889i | −0.890520 | − | 0.454945i | \(-0.849659\pi\) | ||
0.890520 | − | 0.454945i | \(-0.150341\pi\) | |||||||
\(150\) | 58.3791 | + | 18.4900i | 0.389194 | + | 0.123267i | ||||
\(151\) | −222.424 | −1.47300 | −0.736502 | − | 0.676435i | \(-0.763524\pi\) | ||||
−0.736502 | + | 0.676435i | \(0.763524\pi\) | |||||||
\(152\) | 43.2269 | + | 43.2269i | 0.284388 | + | 0.284388i | ||||
\(153\) | 38.5995 | − | 38.5995i | 0.252284 | − | 0.252284i | ||||
\(154\) | 171.919i | 1.11636i | ||||||||
\(155\) | −195.953 | − | 30.2899i | −1.26421 | − | 0.195419i | ||||
\(156\) | 6.70798 | 0.0429999 | ||||||||
\(157\) | −164.277 | − | 164.277i | −1.04635 | − | 1.04635i | −0.998872 | − | 0.0474752i | \(-0.984882\pi\) |
−0.0474752 | − | 0.998872i | \(-0.515118\pi\) | |||||||
\(158\) | 27.1346 | − | 27.1346i | 0.171738 | − | 0.171738i | ||||
\(159\) | − | 24.9042i | − | 0.156630i | ||||||
\(160\) | −16.7100 | − | 22.8205i | −0.104437 | − | 0.142628i | ||||
\(161\) | 58.5210 | 0.363484 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 50.5955 | − | 50.5955i | 0.310402 | − | 0.310402i | −0.534663 | − | 0.845065i | \(-0.679562\pi\) |
0.845065 | + | 0.534663i | \(0.179562\pi\) | |||||||
\(164\) | − | 92.1194i | − | 0.561704i | ||||||
\(165\) | −69.6101 | + | 50.9710i | −0.421879 | + | 0.308915i | ||||
\(166\) | 122.126 | 0.735698 | ||||||||
\(167\) | −129.032 | − | 129.032i | −0.772645 | − | 0.772645i | 0.205923 | − | 0.978568i | \(-0.433980\pi\) |
−0.978568 | + | 0.205923i | \(0.933980\pi\) | |||||||
\(168\) | −42.2706 | + | 42.2706i | −0.251611 | + | 0.251611i | ||||
\(169\) | 165.250i | 0.977812i | ||||||||
\(170\) | −19.6553 | + | 127.155i | −0.115619 | + | 0.747970i | ||||
\(171\) | 64.8404 | 0.379184 | ||||||||
\(172\) | −85.0153 | − | 85.0153i | −0.494275 | − | 0.494275i | ||||
\(173\) | 31.0922 | − | 31.0922i | 0.179724 | − | 0.179724i | −0.611512 | − | 0.791235i | \(-0.709438\pi\) |
0.791235 | + | 0.611512i | \(0.209438\pi\) | |||||||
\(174\) | − | 100.586i | − | 0.578078i | ||||||
\(175\) | 140.511 | + | 270.775i | 0.802922 | + | 1.54729i | ||||
\(176\) | 39.8493 | 0.226417 | ||||||||
\(177\) | −102.729 | − | 102.729i | −0.580392 | − | 0.580392i | ||||
\(178\) | 84.3721 | − | 84.3721i | 0.474001 | − | 0.474001i | ||||
\(179\) | − | 66.4446i | − | 0.371199i | −0.982625 | − | 0.185599i | \(-0.940577\pi\) | ||
0.982625 | − | 0.185599i | \(-0.0594227\pi\) | |||||||
\(180\) | −29.6479 | − | 4.58290i | −0.164710 | − | 0.0254605i | ||||
\(181\) | 57.8597 | 0.319667 | 0.159833 | − | 0.987144i | \(-0.448904\pi\) | ||||
0.159833 | + | 0.987144i | \(0.448904\pi\) | |||||||
\(182\) | 23.6292 | + | 23.6292i | 0.129831 | + | 0.129831i | ||||
\(183\) | 116.312 | − | 116.312i | 0.635583 | − | 0.635583i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 200.055 | + | 273.211i | 1.08138 | + | 1.47682i | ||||
\(186\) | 97.1371 | 0.522243 | ||||||||
\(187\) | −128.180 | − | 128.180i | −0.685457 | − | 0.685457i | ||||
\(188\) | −8.89810 | + | 8.89810i | −0.0473303 | + | 0.0473303i | ||||
\(189\) | 63.4059i | 0.335481i | ||||||||
\(190\) | −123.308 | + | 90.2903i | −0.648988 | + | 0.475212i | ||||
\(191\) | 5.50354 | 0.0288143 | 0.0144072 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144072 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 179.960 | − | 179.960i | 0.932434 | − | 0.932434i | −0.0654238 | − | 0.997858i | \(-0.520840\pi\) |
0.997858 | + | 0.0654238i | \(0.0208399\pi\) | |||||||
\(194\) | 223.419i | 1.15164i | ||||||||
\(195\) | −2.56183 | + | 16.5731i | −0.0131376 | + | 0.0849903i | ||||
\(196\) | −199.801 | −1.01939 | ||||||||
\(197\) | 145.865 | + | 145.865i | 0.740432 | + | 0.740432i | 0.972661 | − | 0.232229i | \(-0.0746019\pi\) |
−0.232229 | + | 0.972661i | \(0.574602\pi\) | |||||||
\(198\) | 29.8870 | − | 29.8870i | 0.150944 | − | 0.150944i | ||||
\(199\) | − | 94.1556i | − | 0.473144i | −0.971614 | − | 0.236572i | \(-0.923976\pi\) | ||
0.971614 | − | 0.236572i | \(-0.0760239\pi\) | |||||||
\(200\) | 62.7634 | − | 32.5693i | 0.313817 | − | 0.162847i | ||||
\(201\) | 58.9930 | 0.293498 | ||||||||
\(202\) | −77.7181 | − | 77.7181i | −0.384743 | − | 0.384743i | ||||
\(203\) | 354.318 | − | 354.318i | 1.74541 | − | 1.74541i | ||||
\(204\) | − | 63.0328i | − | 0.308984i | ||||||
\(205\) | 227.596 | + | 35.1811i | 1.11022 | + | 0.171615i | ||||
\(206\) | −84.6721 | −0.411029 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | 5.47704 | − | 5.47704i | 0.0263319 | − | 0.0263319i | ||||
\(209\) | − | 215.321i | − | 1.03024i | ||||||
\(210\) | −88.2927 | − | 120.580i | −0.420441 | − | 0.574189i | ||||
\(211\) | −36.0474 | −0.170841 | −0.0854204 | − | 0.996345i | \(-0.527223\pi\) | ||||
−0.0854204 | + | 0.996345i | \(0.527223\pi\) | |||||||
\(212\) | −20.3342 | − | 20.3342i | −0.0959159 | − | 0.0959159i | ||||
\(213\) | 156.726 | − | 156.726i | 0.735803 | − | 0.735803i | ||||
\(214\) | 213.934i | 0.999693i | ||||||||
\(215\) | 242.512 | − | 177.576i | 1.12796 | − | 0.825933i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 342.170 | + | 342.170i | 1.57682 | + | 1.57682i | ||||
\(218\) | 36.5144 | − | 36.5144i | 0.167497 | − | 0.167497i | ||||
\(219\) | 146.028i | 0.666796i | ||||||||
\(220\) | −15.2188 | + | 98.4540i | −0.0691763 | + | 0.447518i | ||||
\(221\) | −35.2352 | −0.159435 | ||||||||
\(222\) | −117.303 | − | 117.303i | −0.528391 | − | 0.528391i | ||||
\(223\) | 68.4373 | − | 68.4373i | 0.306894 | − | 0.306894i | −0.536810 | − | 0.843703i | \(-0.680371\pi\) |
0.843703 | + | 0.536810i | \(0.180371\pi\) | |||||||
\(224\) | 69.0276i | 0.308159i | ||||||||
\(225\) | 22.6455 | − | 71.4995i | 0.100647 | − | 0.317776i | ||||
\(226\) | 21.3312 | 0.0943859 | ||||||||
\(227\) | −157.931 | − | 157.931i | −0.695732 | − | 0.695732i | 0.267755 | − | 0.963487i | \(-0.413718\pi\) |
−0.963487 | + | 0.267755i | \(0.913718\pi\) | |||||||
\(228\) | 52.9420 | − | 52.9420i | 0.232202 | − | 0.232202i | ||||
\(229\) | 278.744i | 1.21722i | 0.793468 | + | 0.608612i | \(0.208274\pi\) | ||||
−0.793468 | + | 0.608612i | \(0.791726\pi\) | |||||||
\(230\) | 33.5136 | + | 5.18045i | 0.145711 | + | 0.0225237i | ||||
\(231\) | 210.557 | 0.911502 | ||||||||
\(232\) | −82.1278 | − | 82.1278i | −0.353999 | − | 0.353999i | ||||
\(233\) | −263.213 | + | 263.213i | −1.12967 | + | 1.12967i | −0.139438 | + | 0.990231i | \(0.544530\pi\) |
−0.990231 | + | 0.139438i | \(0.955470\pi\) | |||||||
\(234\) | − | 8.21556i | − | 0.0351092i | ||||||
\(235\) | −18.5859 | − | 25.3824i | −0.0790889 | − | 0.108010i | ||||
\(236\) | −167.756 | −0.710832 | ||||||||
\(237\) | −33.2330 | − | 33.2330i | −0.140224 | − | 0.140224i | ||||
\(238\) | 222.036 | − | 222.036i | 0.932924 | − | 0.932924i | ||||
\(239\) | − | 47.8510i | − | 0.200214i | −0.994977 | − | 0.100107i | \(-0.968082\pi\) | ||
0.994977 | − | 0.100107i | \(-0.0319184\pi\) | |||||||
\(240\) | −27.9493 | + | 20.4655i | −0.116455 | + | 0.0852728i | ||||
\(241\) | −91.5567 | −0.379903 | −0.189952 | − | 0.981793i | \(-0.560833\pi\) | ||||
−0.189952 | + | 0.981793i | \(0.560833\pi\) | |||||||
\(242\) | 21.7519 | + | 21.7519i | 0.0898839 | + | 0.0898839i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 189.936i | − | 0.778427i | ||||||
\(245\) | 76.3054 | − | 493.639i | 0.311451 | − | 2.01485i | ||||
\(246\) | −112.823 | −0.458629 | ||||||||
\(247\) | −29.5945 | − | 29.5945i | −0.119816 | − | 0.119816i | ||||
\(248\) | 79.3121 | − | 79.3121i | 0.319807 | − | 0.319807i | ||||
\(249\) | − | 149.573i | − | 0.600695i | ||||||
\(250\) | 56.4978 | + | 167.505i | 0.225991 | + | 0.670021i | ||||
\(251\) | 358.473 | 1.42818 | 0.714090 | − | 0.700054i | \(-0.246841\pi\) | ||||
0.714090 | + | 0.700054i | \(0.246841\pi\) | |||||||
\(252\) | 51.7707 | + | 51.7707i | 0.205439 | + | 0.205439i | ||||
\(253\) | −33.7839 | + | 33.7839i | −0.133533 | + | 0.133533i | ||||
\(254\) | − | 242.731i | − | 0.955634i | ||||||
\(255\) | 155.732 | + | 24.0727i | 0.610715 | + | 0.0944028i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 45.2189 | + | 45.2189i | 0.175949 | + | 0.175949i | 0.789587 | − | 0.613638i | \(-0.210295\pi\) |
−0.613638 | + | 0.789587i | \(0.710295\pi\) | |||||||
\(258\) | −104.122 | + | 104.122i | −0.403574 | + | 0.403574i | ||||
\(259\) | − | 826.409i | − | 3.19077i | ||||||
\(260\) | 11.4402 | + | 15.6236i | 0.0440006 | + | 0.0600908i | ||||
\(261\) | −123.192 | −0.471999 | ||||||||
\(262\) | −188.546 | − | 188.546i | −0.719642 | − | 0.719642i | ||||
\(263\) | 7.35905 | − | 7.35905i | 0.0279812 | − | 0.0279812i | −0.692978 | − | 0.720959i | \(-0.743702\pi\) |
0.720959 | + | 0.692978i | \(0.243702\pi\) | |||||||
\(264\) | − | 48.8053i | − | 0.184868i | ||||||
\(265\) | 58.0046 | − | 42.4730i | 0.218885 | − | 0.160275i | ||||
\(266\) | 372.982 | 1.40219 | ||||||||
\(267\) | −103.334 | − | 103.334i | −0.387020 | − | 0.387020i | ||||
\(268\) | 48.1676 | − | 48.1676i | 0.179730 | − | 0.179730i | ||||
\(269\) | 159.878i | 0.594341i | 0.954824 | + | 0.297171i | \(0.0960430\pi\) | ||||
−0.954824 | + | 0.297171i | \(0.903957\pi\) | |||||||
\(270\) | −5.61288 | + | 36.3111i | −0.0207884 | + | 0.134486i | ||||
\(271\) | 211.259 | 0.779554 | 0.389777 | − | 0.920909i | \(-0.372552\pi\) | ||||
0.389777 | + | 0.920909i | \(0.372552\pi\) | |||||||
\(272\) | −51.4660 | − | 51.4660i | −0.189213 | − | 0.189213i | ||||
\(273\) | 28.9397 | − | 28.9397i | 0.106006 | − | 0.106006i | ||||
\(274\) | 172.217i | 0.628528i | ||||||||
\(275\) | −237.434 | − | 75.2008i | −0.863396 | − | 0.273457i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 219.374 | + | 219.374i | 0.791962 | + | 0.791962i | 0.981813 | − | 0.189851i | \(-0.0608004\pi\) |
−0.189851 | + | 0.981813i | \(0.560800\pi\) | |||||||
\(278\) | 145.443 | − | 145.443i | 0.523178 | − | 0.523178i | ||||
\(279\) | − | 118.968i | − | 0.426409i | ||||||
\(280\) | −170.544 | − | 26.3622i | −0.609084 | − | 0.0941507i | ||||
\(281\) | 168.520 | 0.599714 | 0.299857 | − | 0.953984i | \(-0.403061\pi\) | ||||
0.299857 | + | 0.953984i | \(0.403061\pi\) | |||||||
\(282\) | 10.8979 | + | 10.8979i | 0.0386450 | + | 0.0386450i | ||||
\(283\) | 154.756 | − | 154.756i | 0.546843 | − | 0.546843i | −0.378684 | − | 0.925526i | \(-0.623623\pi\) |
0.925526 | + | 0.378684i | \(0.123623\pi\) | |||||||
\(284\) | − | 255.933i | − | 0.901171i | ||||||
\(285\) | 110.583 | + | 151.020i | 0.388009 | + | 0.529896i | ||||
\(286\) | −27.2821 | −0.0953918 | ||||||||
\(287\) | −397.424 | − | 397.424i | −1.38475 | − | 1.38475i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 42.0941i | 0.145654i | ||||||||
\(290\) | 234.275 | − | 171.544i | 0.807844 | − | 0.591532i | ||||
\(291\) | 273.631 | 0.940312 | ||||||||
\(292\) | 119.232 | + | 119.232i | 0.408327 | + | 0.408327i | ||||
\(293\) | −312.900 | + | 312.900i | −1.06792 | + | 1.06792i | −0.0703988 | + | 0.997519i | \(0.522427\pi\) |
−0.997519 | + | 0.0703988i | \(0.977573\pi\) | |||||||
\(294\) | 244.705i | 0.832329i | ||||||||
\(295\) | 64.0675 | − | 414.469i | 0.217178 | − | 1.40498i | ||||
\(296\) | −191.554 | −0.647144 | ||||||||
\(297\) | −36.6040 | − | 36.6040i | −0.123246 | − | 0.123246i | ||||
\(298\) | −135.574 | + | 135.574i | −0.454945 | + | 0.454945i | ||||
\(299\) | 9.28677i | 0.0310594i | ||||||||
\(300\) | −39.8891 | − | 76.8691i | −0.132964 | − | 0.256230i | ||||
\(301\) | −733.550 | −2.43704 | ||||||||
\(302\) | 222.424 | + | 222.424i | 0.736502 | + | 0.736502i | ||||
\(303\) | −95.1848 | + | 95.1848i | −0.314141 | + | 0.314141i | ||||
\(304\) | − | 86.4539i | − | 0.284388i | ||||||
\(305\) | 469.267 | + | 72.5381i | 1.53858 | + | 0.237830i | ||||
\(306\) | −77.1991 | −0.252284 | ||||||||
\(307\) | 66.0310 | + | 66.0310i | 0.215085 | + | 0.215085i | 0.806423 | − | 0.591339i | \(-0.201400\pi\) |
−0.591339 | + | 0.806423i | \(0.701400\pi\) | |||||||
\(308\) | 171.919 | − | 171.919i | 0.558179 | − | 0.558179i | ||||
\(309\) | 103.702i | 0.335604i | ||||||||
\(310\) | 165.663 | + | 226.243i | 0.534397 | + | 0.729816i | ||||
\(311\) | −47.7193 | −0.153438 | −0.0767191 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767191 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(312\) | −6.70798 | − | 6.70798i | −0.0214999 | − | 0.0214999i | ||||
\(313\) | −342.502 | + | 342.502i | −1.09425 | + | 1.09425i | −0.0991860 | + | 0.995069i | \(0.531624\pi\) |
−0.995069 | + | 0.0991860i | \(0.968376\pi\) | |||||||
\(314\) | 328.553i | 1.04635i | ||||||||
\(315\) | −147.679 | + | 108.136i | −0.468823 | + | 0.343289i | ||||
\(316\) | −54.2693 | −0.171738 | ||||||||
\(317\) | 265.894 | + | 265.894i | 0.838783 | + | 0.838783i | 0.988699 | − | 0.149916i | \(-0.0479002\pi\) |
−0.149916 | + | 0.988699i | \(0.547900\pi\) | |||||||
\(318\) | −24.9042 | + | 24.9042i | −0.0783150 | + | 0.0783150i | ||||
\(319\) | 409.092i | 1.28242i | ||||||||
\(320\) | −6.11053 | + | 39.5305i | −0.0190954 | + | 0.123533i | ||||
\(321\) | 262.015 | 0.816246 | ||||||||
\(322\) | −58.5210 | − | 58.5210i | −0.181742 | − | 0.181742i | ||||
\(323\) | −278.090 | + | 278.090i | −0.860960 | + | 0.860960i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −42.9697 | + | 22.2979i | −0.132214 | + | 0.0686090i | ||||
\(326\) | −101.191 | −0.310402 | ||||||||
\(327\) | −44.7208 | − | 44.7208i | −0.136761 | − | 0.136761i | ||||
\(328\) | −92.1194 | + | 92.1194i | −0.280852 | + | 0.280852i | ||||
\(329\) | 76.7768i | 0.233364i | ||||||||
\(330\) | 120.581 | + | 18.6391i | 0.365397 | + | 0.0564822i | ||||
\(331\) | −49.2824 | −0.148889 | −0.0744447 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744447 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(332\) | −122.126 | − | 122.126i | −0.367849 | − | 0.367849i | ||||
\(333\) | −143.666 | + | 143.666i | −0.431429 | + | 0.431429i | ||||
\(334\) | 258.064i | 0.772645i | ||||||||
\(335\) | 100.610 | + | 137.401i | 0.300328 | + | 0.410153i | ||||
\(336\) | 84.5412 | 0.251611 | ||||||||
\(337\) | 196.678 | + | 196.678i | 0.583614 | + | 0.583614i | 0.935894 | − | 0.352281i | \(-0.114594\pi\) |
−0.352281 | + | 0.935894i | \(0.614594\pi\) | |||||||
\(338\) | 165.250 | − | 165.250i | 0.488906 | − | 0.488906i | ||||
\(339\) | − | 26.1253i | − | 0.0770658i | ||||||
\(340\) | 146.810 | − | 107.500i | 0.431795 | − | 0.316175i | ||||
\(341\) | −395.067 | −1.15855 | ||||||||
\(342\) | −64.8404 | − | 64.8404i | −0.189592 | − | 0.189592i | ||||
\(343\) | −439.190 | + | 439.190i | −1.28044 | + | 1.28044i | ||||
\(344\) | 170.031i | 0.494275i | ||||||||
\(345\) | 6.34473 | − | 41.0456i | 0.0183905 | − | 0.118973i | ||||
\(346\) | −62.1844 | −0.179724 | ||||||||
\(347\) | 161.562 | + | 161.562i | 0.465596 | + | 0.465596i | 0.900484 | − | 0.434888i | \(-0.143212\pi\) |
−0.434888 | + | 0.900484i | \(0.643212\pi\) | |||||||
\(348\) | −100.586 | + | 100.586i | −0.289039 | + | 0.289039i | ||||
\(349\) | 69.2537i | 0.198435i | 0.995066 | + | 0.0992173i | \(0.0316339\pi\) | ||||
−0.995066 | + | 0.0992173i | \(0.968366\pi\) | |||||||
\(350\) | 130.264 | − | 411.287i | 0.372182 | − | 1.17510i | ||||
\(351\) | −10.0620 | −0.0286666 | ||||||||
\(352\) | −39.8493 | − | 39.8493i | −0.113208 | − | 0.113208i | ||||
\(353\) | 187.924 | − | 187.924i | 0.532363 | − | 0.532363i | −0.388912 | − | 0.921275i | \(-0.627149\pi\) |
0.921275 | + | 0.388912i | \(0.127149\pi\) | |||||||
\(354\) | 205.459i | 0.580392i | ||||||||
\(355\) | 632.322 | + | 97.7427i | 1.78119 | + | 0.275331i | ||||
\(356\) | −168.744 | −0.474001 | ||||||||
\(357\) | −271.937 | − | 271.937i | −0.761730 | − | 0.761730i | ||||
\(358\) | −66.4446 | + | 66.4446i | −0.185599 | + | 0.185599i | ||||
\(359\) | 327.086i | 0.911103i | 0.890209 | + | 0.455551i | \(0.150558\pi\) | ||||
−0.890209 | + | 0.455551i | \(0.849442\pi\) | |||||||
\(360\) | 25.0650 | + | 34.2308i | 0.0696250 | + | 0.0950855i | ||||
\(361\) | −106.142 | −0.294023 | ||||||||
\(362\) | −57.8597 | − | 57.8597i | −0.159833 | − | 0.159833i | ||||
\(363\) | 26.6405 | − | 26.6405i | 0.0733899 | − | 0.0733899i | ||||
\(364\) | − | 47.2584i | − | 0.129831i | ||||||
\(365\) | −340.116 | + | 249.045i | −0.931824 | + | 0.682315i | ||||
\(366\) | −232.623 | −0.635583 | ||||||||
\(367\) | −490.806 | − | 490.806i | −1.33735 | − | 1.33735i | −0.898622 | − | 0.438724i | \(-0.855431\pi\) |
−0.438724 | − | 0.898622i | \(-0.644569\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 138.179i | 0.374469i | ||||||||
\(370\) | 73.1562 | − | 473.265i | 0.197719 | − | 1.27910i | ||||
\(371\) | −175.452 | −0.472917 | ||||||||
\(372\) | −97.1371 | − | 97.1371i | −0.261121 | − | 0.261121i | ||||
\(373\) | −21.0158 | + | 21.0158i | −0.0563427 | + | 0.0563427i | −0.734717 | − | 0.678374i | \(-0.762685\pi\) |
0.678374 | + | 0.734717i | \(0.262685\pi\) | |||||||
\(374\) | 256.361i | 0.685457i | ||||||||
\(375\) | 205.151 | − | 69.1954i | 0.547070 | − | 0.184521i | ||||
\(376\) | 17.7962 | 0.0473303 | ||||||||
\(377\) | 56.2272 | + | 56.2272i | 0.149144 | + | 0.149144i | ||||
\(378\) | 63.4059 | − | 63.4059i | 0.167740 | − | 0.167740i | ||||
\(379\) | − | 310.295i | − | 0.818720i | −0.912373 | − | 0.409360i | \(-0.865752\pi\) | ||
0.912373 | − | 0.409360i | \(-0.134248\pi\) | |||||||
\(380\) | 213.598 | + | 33.0174i | 0.562100 | + | 0.0868880i | ||||
\(381\) | −297.284 | −0.780272 | ||||||||
\(382\) | −5.50354 | − | 5.50354i | −0.0144072 | − | 0.0144072i | ||||
\(383\) | 246.947 | − | 246.947i | 0.644769 | − | 0.644769i | −0.306955 | − | 0.951724i | \(-0.599310\pi\) |
0.951724 | + | 0.306955i | \(0.0993101\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 359.096 | + | 490.410i | 0.932716 | + | 1.27379i | ||||
\(386\) | −359.919 | −0.932434 | ||||||||
\(387\) | 127.523 | + | 127.523i | 0.329517 | + | 0.329517i | ||||
\(388\) | 223.419 | − | 223.419i | 0.575821 | − | 0.575821i | ||||
\(389\) | 467.057i | 1.20066i | 0.799752 | + | 0.600330i | \(0.204964\pi\) | ||||
−0.799752 | + | 0.600330i | \(0.795036\pi\) | |||||||
\(390\) | 19.1349 | − | 14.0113i | 0.0490639 | − | 0.0359264i | ||||
\(391\) | 87.2649 | 0.223184 | ||||||||
\(392\) | 199.801 | + | 199.801i | 0.509695 | + | 0.509695i | ||||
\(393\) | −230.921 | + | 230.921i | −0.587586 | + | 0.587586i | ||||
\(394\) | − | 291.730i | − | 0.740432i | ||||||
\(395\) | 20.7259 | − | 134.081i | 0.0524705 | − | 0.339445i | ||||
\(396\) | −59.7740 | −0.150944 | ||||||||
\(397\) | 387.028 | + | 387.028i | 0.974882 | + | 0.974882i | 0.999692 | − | 0.0248106i | \(-0.00789828\pi\) |
−0.0248106 | + | 0.999692i | \(0.507898\pi\) | |||||||
\(398\) | −94.1556 | + | 94.1556i | −0.236572 | + | 0.236572i | ||||
\(399\) | − | 456.807i | − | 1.14488i | ||||||
\(400\) | −95.3327 | − | 30.1940i | −0.238332 | − | 0.0754851i | ||||
\(401\) | −448.866 | −1.11937 | −0.559684 | − | 0.828706i | \(-0.689077\pi\) | ||||
−0.559684 | + | 0.828706i | \(0.689077\pi\) | |||||||
\(402\) | −58.9930 | − | 58.9930i | −0.146749 | − | 0.146749i | ||||
\(403\) | −54.2995 | + | 54.2995i | −0.134738 | + | 0.134738i | ||||
\(404\) | 155.436i | 0.384743i | ||||||||
\(405\) | 44.4718 | + | 6.87434i | 0.109807 | + | 0.0169737i | ||||
\(406\) | −708.635 | −1.74541 | ||||||||
\(407\) | 477.082 | + | 477.082i | 1.17219 | + | 1.17219i | ||||
\(408\) | −63.0328 | + | 63.0328i | −0.154492 | + | 0.154492i | ||||
\(409\) | 335.091i | 0.819293i | 0.912244 | + | 0.409647i | \(0.134348\pi\) | ||||
−0.912244 | + | 0.409647i | \(0.865652\pi\) | |||||||
\(410\) | −192.414 | − | 262.777i | −0.469303 | − | 0.640919i | ||||
\(411\) | 210.921 | 0.513191 | ||||||||
\(412\) | 84.6721 | + | 84.6721i | 0.205515 | + | 0.205515i | ||||
\(413\) | −723.739 | + | 723.739i | −1.75239 | + | 1.75239i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 348.372 | − | 255.090i | 0.839451 | − | 0.614676i | ||||
\(416\) | −10.9541 | −0.0263319 | ||||||||
\(417\) | −178.131 | − | 178.131i | −0.427173 | − | 0.427173i | ||||
\(418\) | −215.321 | + | 215.321i | −0.515121 | + | 0.515121i | ||||
\(419\) | 235.423i | 0.561869i | 0.959727 | + | 0.280934i | \(0.0906444\pi\) | ||||
−0.959727 | + | 0.280934i | \(0.909356\pi\) | |||||||
\(420\) | −32.2870 | + | 208.872i | −0.0768737 | + | 0.497315i | ||||
\(421\) | −326.446 | −0.775406 | −0.387703 | − | 0.921784i | \(-0.626731\pi\) | ||||
−0.387703 | + | 0.921784i | \(0.626731\pi\) | |||||||
\(422\) | 36.0474 | + | 36.0474i | 0.0854204 | + | 0.0854204i | ||||
\(423\) | 13.3472 | − | 13.3472i | 0.0315536 | − | 0.0315536i | ||||
\(424\) | 40.6683i | 0.0959159i | ||||||||
\(425\) | 209.527 | + | 403.773i | 0.493004 | + | 0.950053i | ||||
\(426\) | −313.452 | −0.735803 | ||||||||
\(427\) | −819.427 | − | 819.427i | −1.91903 | − | 1.91903i | ||||
\(428\) | 213.934 | − | 213.934i | 0.499846 | − | 0.499846i | ||||
\(429\) | 33.4136i | 0.0778871i | ||||||||
\(430\) | −420.087 | − | 64.9360i | −0.976947 | − | 0.151014i | ||||
\(431\) | −307.959 | −0.714523 | −0.357262 | − | 0.934004i | \(-0.616290\pi\) | ||||
−0.357262 | + | 0.934004i | \(0.616290\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 393.236 | − | 393.236i | 0.908166 | − | 0.908166i | −0.0879578 | − | 0.996124i | \(-0.528034\pi\) |
0.996124 | + | 0.0879578i | \(0.0280341\pi\) | |||||||
\(434\) | − | 684.341i | − | 1.57682i | ||||||
\(435\) | −210.098 | − | 286.927i | −0.482984 | − | 0.659602i | ||||
\(436\) | −73.0287 | −0.167497 | ||||||||
\(437\) | 73.2949 | + | 73.2949i | 0.167723 | + | 0.167723i | ||||
\(438\) | 146.028 | − | 146.028i | 0.333398 | − | 0.333398i | ||||
\(439\) | − | 330.522i | − | 0.752897i | −0.926438 | − | 0.376448i | \(-0.877145\pi\) | ||
0.926438 | − | 0.376448i | \(-0.122855\pi\) | |||||||
\(440\) | 113.673 | − | 83.2353i | 0.258347 | − | 0.189171i | ||||
\(441\) | 299.701 | 0.679594 | ||||||||
\(442\) | 35.2352 | + | 35.2352i | 0.0797176 | + | 0.0797176i | ||||
\(443\) | −116.455 | + | 116.455i | −0.262879 | + | 0.262879i | −0.826223 | − | 0.563344i | \(-0.809515\pi\) |
0.563344 | + | 0.826223i | \(0.309515\pi\) | |||||||
\(444\) | 234.605i | 0.528391i | ||||||||
\(445\) | 64.4448 | − | 416.909i | 0.144820 | − | 0.936874i | ||||
\(446\) | −136.875 | −0.306894 | ||||||||
\(447\) | 166.043 | + | 166.043i | 0.371461 | + | 0.371461i | ||||
\(448\) | 69.0276 | − | 69.0276i | 0.154079 | − | 0.154079i | ||||
\(449\) | − | 149.486i | − | 0.332930i | −0.986047 | − | 0.166465i | \(-0.946765\pi\) | ||
0.986047 | − | 0.166465i | \(-0.0532354\pi\) | |||||||
\(450\) | −94.1450 | + | 48.8540i | −0.209211 | + | 0.108564i | ||||
\(451\) | 458.862 | 1.01743 | ||||||||
\(452\) | −21.3312 | − | 21.3312i | −0.0471929 | − | 0.0471929i | ||||
\(453\) | 272.412 | − | 272.412i | 0.601351 | − | 0.601351i | ||||
\(454\) | 315.862i | 0.695732i | ||||||||
\(455\) | 116.759 | + | 18.0483i | 0.256614 | + | 0.0396667i | ||||
\(456\) | −105.884 | −0.232202 | ||||||||
\(457\) | 259.178 | + | 259.178i | 0.567130 | + | 0.567130i | 0.931323 | − | 0.364193i | \(-0.118655\pi\) |
−0.364193 | + | 0.931323i | \(0.618655\pi\) | |||||||
\(458\) | 278.744 | − | 278.744i | 0.608612 | − | 0.608612i | ||||
\(459\) | 94.5491i | 0.205989i | ||||||||
\(460\) | −28.3332 | − | 38.6941i | −0.0615939 | − | 0.0841176i | ||||
\(461\) | −804.421 | −1.74495 | −0.872474 | − | 0.488661i | \(-0.837486\pi\) | ||||
−0.872474 | + | 0.488661i | \(0.837486\pi\) | |||||||
\(462\) | −210.557 | − | 210.557i | −0.455751 | − | 0.455751i | ||||
\(463\) | 284.414 | − | 284.414i | 0.614284 | − | 0.614284i | −0.329775 | − | 0.944059i | \(-0.606973\pi\) |
0.944059 | + | 0.329775i | \(0.106973\pi\) | |||||||
\(464\) | 164.256i | 0.353999i | ||||||||
\(465\) | 277.090 | − | 202.895i | 0.595892 | − | 0.436333i | ||||
\(466\) | 526.426 | 1.12967 | ||||||||
\(467\) | 542.008 | + | 542.008i | 1.16062 | + | 1.16062i | 0.984341 | + | 0.176276i | \(0.0564050\pi\) |
0.176276 | + | 0.984341i | \(0.443595\pi\) | |||||||
\(468\) | −8.21556 | + | 8.21556i | −0.0175546 | + | 0.0175546i | ||||
\(469\) | − | 415.612i | − | 0.886165i | ||||||
\(470\) | −6.79651 | + | 43.9683i | −0.0144607 | + | 0.0935496i | ||||
\(471\) | 402.394 | 0.854339 | ||||||||
\(472\) | 167.756 | + | 167.756i | 0.355416 | + | 0.355416i | ||||
\(473\) | 423.475 | − | 423.475i | 0.895297 | − | 0.895297i | ||||
\(474\) | 66.4660i | 0.140224i | ||||||||
\(475\) | −163.149 | + | 515.118i | −0.343473 | + | 1.08446i | ||||
\(476\) | −444.072 | −0.932924 | ||||||||
\(477\) | 30.5013 | + | 30.5013i | 0.0639439 | + | 0.0639439i | ||||
\(478\) | −47.8510 | + | 47.8510i | −0.100107 | + | 0.100107i | ||||
\(479\) | 419.970i | 0.876764i | 0.898789 | + | 0.438382i | \(0.144448\pi\) | ||||
−0.898789 | + | 0.438382i | \(0.855552\pi\) | |||||||
\(480\) | 48.4148 | + | 7.48384i | 0.100864 | + | 0.0155913i | ||||
\(481\) | 131.144 | 0.272649 | ||||||||
\(482\) | 91.5567 | + | 91.5567i | 0.189952 | + | 0.189952i | ||||
\(483\) | −71.6733 | + | 71.6733i | −0.148392 | + | 0.148392i | ||||
\(484\) | − | 43.5038i | − | 0.0898839i | ||||||
\(485\) | 466.665 | + | 637.316i | 0.962196 | + | 1.31405i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −463.650 | − | 463.650i | −0.952054 | − | 0.952054i | 0.0468485 | − | 0.998902i | \(-0.485082\pi\) |
−0.998902 | + | 0.0468485i | \(0.985082\pi\) | |||||||
\(488\) | −189.936 | + | 189.936i | −0.389213 | + | 0.389213i | ||||
\(489\) | 123.933i | 0.253442i | ||||||||
\(490\) | −569.944 | + | 417.333i | −1.16315 | + | 0.851700i | ||||
\(491\) | −81.2134 | −0.165404 | −0.0827021 | − | 0.996574i | \(-0.526355\pi\) | ||||
−0.0827021 | + | 0.996574i | \(0.526355\pi\) | |||||||
\(492\) | 112.823 | + | 112.823i | 0.229315 | + | 0.229315i | ||||
\(493\) | 528.349 | − | 528.349i | 1.07170 | − | 1.07170i | ||||
\(494\) | 59.1889i | 0.119816i | ||||||||
\(495\) | 22.8282 | − | 147.681i | 0.0461175 | − | 0.298346i | ||||
\(496\) | −158.624 | −0.319807 | ||||||||
\(497\) | −1104.15 | − | 1104.15i | −2.22163 | − | 2.22163i | ||||
\(498\) | −149.573 | + | 149.573i | −0.300348 | + | 0.300348i | ||||
\(499\) | 486.389i | 0.974727i | 0.873199 | + | 0.487364i | \(0.162041\pi\) | ||||
−0.873199 | + | 0.487364i | \(0.837959\pi\) | |||||||
\(500\) | 111.007 | − | 224.003i | 0.222015 | − | 0.448006i | ||||
\(501\) | 316.062 | 0.630862 | ||||||||
\(502\) | −358.473 | − | 358.473i | −0.714090 | − | 0.714090i | ||||
\(503\) | −243.288 | + | 243.288i | −0.483674 | + | 0.483674i | −0.906303 | − | 0.422629i | \(-0.861107\pi\) |
0.422629 | + | 0.906303i | \(0.361107\pi\) | |||||||
\(504\) | − | 103.541i | − | 0.205439i | ||||||
\(505\) | −384.029 | − | 59.3623i | −0.760454 | − | 0.117549i | ||||
\(506\) | 67.5678 | 0.133533 | ||||||||
\(507\) | −202.389 | − | 202.389i | −0.399190 | − | 0.399190i | ||||
\(508\) | −242.731 | + | 242.731i | −0.477817 | + | 0.477817i | ||||
\(509\) | − | 224.497i | − | 0.441056i | −0.975381 | − | 0.220528i | \(-0.929222\pi\) | ||
0.975381 | − | 0.220528i | \(-0.0707780\pi\) | |||||||
\(510\) | −131.660 | − | 179.805i | −0.258156 | − | 0.352559i | ||||
\(511\) | 1028.78 | 2.01327 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −79.4130 | + | 79.4130i | −0.154801 | + | 0.154801i | ||||
\(514\) | − | 90.4377i | − | 0.175949i | ||||||
\(515\) | −241.533 | + | 176.859i | −0.468995 | + | 0.343415i | ||||
\(516\) | 208.244 | 0.403574 | ||||||||
\(517\) | −44.3229 | − | 44.3229i | −0.0857310 | − | 0.0857310i | ||||
\(518\) | −826.409 | + | 826.409i | −1.59538 | + | 1.59538i | ||||
\(519\) | 76.1600i | 0.146744i | ||||||||
\(520\) | 4.18345 | − | 27.0638i | 0.00804510 | − | 0.0520457i | ||||
\(521\) | −581.302 | −1.11574 | −0.557872 | − | 0.829927i | \(-0.688382\pi\) | ||||
−0.557872 | + | 0.829927i | \(0.688382\pi\) | |||||||
\(522\) | 123.192 | + | 123.192i | 0.235999 | + | 0.235999i | ||||
\(523\) | −573.621 | + | 573.621i | −1.09679 | + | 1.09679i | −0.102005 | + | 0.994784i | \(0.532526\pi\) |
−0.994784 | + | 0.102005i | \(0.967474\pi\) | |||||||
\(524\) | 377.093i | 0.719642i | ||||||||
\(525\) | −503.721 | − | 159.540i | −0.959469 | − | 0.303886i | ||||
\(526\) | −14.7181 | −0.0279812 | ||||||||
\(527\) | 510.235 | + | 510.235i | 0.968188 | + | 0.968188i | ||||
\(528\) | −48.8053 | + | 48.8053i | −0.0924342 | + | 0.0924342i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −100.478 | − | 15.5316i | −0.189580 | − | 0.0293048i | ||||
\(531\) | 251.635 | 0.473888 | ||||||||
\(532\) | −372.982 | − | 372.982i | −0.701093 | − | 0.701093i | ||||
\(533\) | 63.0677 | − | 63.0677i | 0.118326 | − | 0.118326i | ||||
\(534\) | 206.669i | 0.387020i | ||||||||
\(535\) | 446.855 | + | 610.261i | 0.835243 | + | 1.14068i | ||||
\(536\) | −96.3352 | −0.179730 | ||||||||
\(537\) | 81.3777 | + | 81.3777i | 0.151541 | + | 0.151541i | ||||
\(538\) | 159.878 | − | 159.878i | 0.297171 | − | 0.297171i | ||||
\(539\) | − | 995.240i | − | 1.84646i | ||||||
\(540\) | 41.9240 | − | 30.6982i | 0.0776370 | − | 0.0568486i | ||||
\(541\) | 582.198 | 1.07615 | 0.538075 | − | 0.842897i | \(-0.319152\pi\) | ||||
0.538075 | + | 0.842897i | \(0.319152\pi\) | |||||||
\(542\) | −211.259 | − | 211.259i | −0.389777 | − | 0.389777i | ||||
\(543\) | −70.8634 | + | 70.8634i | −0.130503 | + | 0.130503i | ||||
\(544\) | 102.932i | 0.189213i | ||||||||
\(545\) | 27.8902 | − | 180.429i | 0.0511748 | − | 0.331062i | ||||
\(546\) | −57.8794 | −0.106006 | ||||||||
\(547\) | −242.902 | − | 242.902i | −0.444063 | − | 0.444063i | 0.449312 | − | 0.893375i | \(-0.351669\pi\) |
−0.893375 | + | 0.449312i | \(0.851669\pi\) | |||||||
\(548\) | 172.217 | − | 172.217i | 0.314264 | − | 0.314264i | ||||
\(549\) | 284.904i | 0.518951i | ||||||||
\(550\) | 162.233 | + | 312.635i | 0.294970 | + | 0.568427i | ||||
\(551\) | 887.533 | 1.61077 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | −234.130 | + | 234.130i | −0.423381 | + | 0.423381i | ||||
\(554\) | − | 438.747i | − | 0.791962i | ||||||
\(555\) | −579.629 | − | 89.5977i | −1.04438 | − | 0.161437i | ||||
\(556\) | −290.887 | −0.523178 | ||||||||
\(557\) | 269.139 | + | 269.139i | 0.483194 | + | 0.483194i | 0.906150 | − | 0.422956i | \(-0.139007\pi\) |
−0.422956 | + | 0.906150i | \(0.639007\pi\) | |||||||
\(558\) | −118.968 | + | 118.968i | −0.213205 | + | 0.213205i | ||||
\(559\) | − | 116.408i | − | 0.208243i | ||||||
\(560\) | 144.181 | + | 196.906i | 0.257467 | + | 0.351617i | ||||
\(561\) | 313.977 | 0.559673 | ||||||||
\(562\) | −168.520 | − | 168.520i | −0.299857 | − | 0.299857i | ||||
\(563\) | −695.370 | + | 695.370i | −1.23511 | + | 1.23511i | −0.273141 | + | 0.961974i | \(0.588062\pi\) |
−0.961974 | + | 0.273141i | \(0.911938\pi\) | |||||||
\(564\) | − | 21.7958i | − | 0.0386450i | ||||||
\(565\) | 60.8487 | − | 44.5555i | 0.107697 | − | 0.0788594i | ||||
\(566\) | −309.513 | −0.546843 | ||||||||
\(567\) | −77.6560 | − | 77.6560i | −0.136960 | − | 0.136960i | ||||
\(568\) | −255.933 | + | 255.933i | −0.450585 | + | 0.450585i | ||||
\(569\) | − | 132.973i | − | 0.233696i | −0.993150 | − | 0.116848i | \(-0.962721\pi\) | ||
0.993150 | − | 0.116848i | \(-0.0372790\pi\) | |||||||
\(570\) | 40.4379 | − | 261.603i | 0.0709437 | − | 0.458953i | ||||
\(571\) | 331.378 | 0.580347 | 0.290174 | − | 0.956974i | \(-0.406287\pi\) | ||||
0.290174 | + | 0.956974i | \(0.406287\pi\) | |||||||
\(572\) | 27.2821 | + | 27.2821i | 0.0476959 | + | 0.0476959i | ||||
\(573\) | −6.74043 | + | 6.74043i | −0.0117634 | + | 0.0117634i | ||||
\(574\) | 794.848i | 1.38475i | ||||||||
\(575\) | 106.420 | − | 55.2240i | 0.185079 | − | 0.0960417i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 342.624 | + | 342.624i | 0.593803 | + | 0.593803i | 0.938656 | − | 0.344854i | \(-0.112072\pi\) |
−0.344854 | + | 0.938656i | \(0.612072\pi\) | |||||||
\(578\) | 42.0941 | − | 42.0941i | 0.0728271 | − | 0.0728271i | ||||
\(579\) | 440.809i | 0.761329i | ||||||||
\(580\) | −405.819 | − | 62.7305i | −0.699688 | − | 0.108156i | ||||
\(581\) | −1053.76 | −1.81370 | ||||||||
\(582\) | −273.631 | − | 273.631i | −0.470156 | − | 0.470156i | ||||
\(583\) | 101.288 | − | 101.288i | 0.173736 | − | 0.173736i | ||||
\(584\) | − | 238.463i | − | 0.408327i | ||||||
\(585\) | −17.1602 | − | 23.4354i | −0.0293338 | − | 0.0400605i | ||||
\(586\) | 625.800 | 1.06792 | ||||||||
\(587\) | −761.501 | − | 761.501i | −1.29728 | − | 1.29728i | −0.930185 | − | 0.367091i | \(-0.880354\pi\) |
−0.367091 | − | 0.930185i | \(-0.619646\pi\) | |||||||
\(588\) | 244.705 | − | 244.705i | 0.416164 | − | 0.416164i | ||||
\(589\) | 857.105i | 1.45519i | ||||||||
\(590\) | −478.536 | + | 350.401i | −0.811078 | + | 0.593900i | ||||
\(591\) | −357.295 | −0.604560 | ||||||||
\(592\) | 191.554 | + | 191.554i | 0.323572 | + | 0.323572i | ||||
\(593\) | 9.06060 | − | 9.06060i | 0.0152793 | − | 0.0152793i | −0.699426 | − | 0.714705i | \(-0.746561\pi\) |
0.714705 | + | 0.699426i | \(0.246561\pi\) | |||||||
\(594\) | 73.2079i | 0.123246i | ||||||||
\(595\) | 169.595 | − | 1097.15i | 0.285033 | − | 1.84395i | ||||
\(596\) | 271.147 | 0.454945 | ||||||||
\(597\) | 115.317 | + | 115.317i | 0.193160 | + | 0.193160i | ||||
\(598\) | 9.28677 | − | 9.28677i | 0.0155297 | − | 0.0155297i | ||||
\(599\) | 730.067i | 1.21881i | 0.792859 | + | 0.609405i | \(0.208592\pi\) | ||||
−0.792859 | + | 0.609405i | \(0.791408\pi\) | |||||||
\(600\) | −36.9800 | + | 116.758i | −0.0616333 | + | 0.194597i | ||||
\(601\) | −1150.36 | −1.91407 | −0.957036 | − | 0.289969i | \(-0.906355\pi\) | ||||
−0.957036 | + | 0.289969i | \(0.906355\pi\) | |||||||
\(602\) | 733.550 | + | 733.550i | 1.21852 | + | 1.21852i | ||||
\(603\) | −72.2514 | + | 72.2514i | −0.119820 | + | 0.119820i | ||||
\(604\) | − | 444.847i | − | 0.736502i | ||||||
\(605\) | 107.483 | + | 16.6144i | 0.177658 | + | 0.0274619i | ||||
\(606\) | 190.370 | 0.314141 | ||||||||
\(607\) | −121.692 | − | 121.692i | −0.200481 | − | 0.200481i | 0.599725 | − | 0.800206i | \(-0.295277\pi\) |
−0.800206 | + | 0.599725i | \(0.795277\pi\) | |||||||
\(608\) | −86.4539 | + | 86.4539i | −0.142194 | + | 0.142194i | ||||
\(609\) | 867.898i | 1.42512i | ||||||||
\(610\) | −396.729 | − | 541.805i | −0.650375 | − | 0.888205i | ||||
\(611\) | −12.1838 | −0.0199408 | ||||||||
\(612\) | 77.1991 | + | 77.1991i | 0.126142 | + | 0.126142i | ||||
\(613\) | 624.795 | − | 624.795i | 1.01924 | − | 1.01924i | 0.0194306 | − | 0.999811i | \(-0.493815\pi\) |
0.999811 | − | 0.0194306i | \(-0.00618533\pi\) | |||||||
\(614\) | − | 132.062i | − | 0.215085i | ||||||
\(615\) | −321.834 | + | 235.659i | −0.523308 | + | 0.383185i | ||||
\(616\) | −343.838 | −0.558179 | ||||||||
\(617\) | −136.943 | − | 136.943i | −0.221951 | − | 0.221951i | 0.587369 | − | 0.809319i | \(-0.300164\pi\) |
−0.809319 | + | 0.587369i | \(0.800164\pi\) | |||||||
\(618\) | 103.702 | − | 103.702i | 0.167802 | − | 0.167802i | ||||
\(619\) | − | 57.3312i | − | 0.0926191i | −0.998927 | − | 0.0463095i | \(-0.985254\pi\) | ||
0.998927 | − | 0.0463095i | \(-0.0147461\pi\) | |||||||
\(620\) | 60.5799 | − | 391.906i | 0.0977094 | − | 0.632107i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 47.7193 | + | 47.7193i | 0.0767191 | + | 0.0767191i | ||||
\(623\) | −728.000 | + | 728.000i | −1.16854 | + | 1.16854i | ||||
\(624\) | 13.4160i | 0.0214999i | ||||||||
\(625\) | 511.040 | + | 359.810i | 0.817664 | + | 0.575696i | ||||
\(626\) | 685.004 | 1.09425 | ||||||||
\(627\) | 263.713 | + | 263.713i | 0.420595 | + | 0.420595i | ||||
\(628\) | 328.553 | − | 328.553i | 0.523174 | − | 0.523174i | ||||
\(629\) | − | 1232.32i | − | 1.95917i | ||||||
\(630\) | 255.815 | + | 39.5433i | 0.406056 | + | 0.0627671i | ||||
\(631\) | −148.750 | −0.235737 | −0.117868 | − | 0.993029i | \(-0.537606\pi\) | ||||
−0.117868 | + | 0.993029i | \(0.537606\pi\) | |||||||
\(632\) | 54.2693 | + | 54.2693i | 0.0858691 | + | 0.0858691i | ||||
\(633\) | 44.1489 | − | 44.1489i | 0.0697454 | − | 0.0697454i | ||||
\(634\) | − | 531.789i | − | 0.838783i | ||||||
\(635\) | −507.004 | − | 692.406i | −0.798432 | − | 1.09040i | ||||
\(636\) | 49.8083 | 0.0783150 | ||||||||
\(637\) | −136.789 | − | 136.789i | −0.214740 | − | 0.214740i | ||||
\(638\) | 409.092 | − | 409.092i | 0.641210 | − | 0.641210i | ||||
\(639\) | 383.899i | 0.600781i | ||||||||
\(640\) | 45.6410 | − | 33.4200i | 0.0713141 | − | 0.0522187i | ||||
\(641\) | −891.369 | −1.39059 | −0.695296 | − | 0.718724i | \(-0.744727\pi\) | ||||
−0.695296 | + | 0.718724i | \(0.744727\pi\) | |||||||
\(642\) | −262.015 | − | 262.015i | −0.408123 | − | 0.408123i | ||||
\(643\) | 518.375 | − | 518.375i | 0.806182 | − | 0.806182i | −0.177872 | − | 0.984054i | \(-0.556921\pi\) |
0.984054 | + | 0.177872i | \(0.0569213\pi\) | |||||||
\(644\) | 117.042i | 0.181742i | ||||||||
\(645\) | −79.5301 | + | 514.500i | −0.123302 | + | 0.797674i | ||||
\(646\) | 556.180 | 0.860960 | ||||||||
\(647\) | 716.167 | + | 716.167i | 1.10690 | + | 1.10690i | 0.993555 | + | 0.113349i | \(0.0361579\pi\) |
0.113349 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 835.623i | − | 1.28755i | ||||||
\(650\) | 65.2676 | + | 20.6717i | 0.100412 | + | 0.0318027i | ||||
\(651\) | −838.143 | −1.28747 | ||||||||
\(652\) | 101.191 | + | 101.191i | 0.155201 | + | 0.155201i | ||||
\(653\) | 3.21608 | − | 3.21608i | 0.00492509 | − | 0.00492509i | −0.704640 | − | 0.709565i | \(-0.748891\pi\) |
0.709565 | + | 0.704640i | \(0.248891\pi\) | |||||||
\(654\) | 89.4415i | 0.136761i | ||||||||
\(655\) | −931.667 | − | 144.015i | −1.42239 | − | 0.219870i | ||||
\(656\) | 184.239 | 0.280852 | ||||||||
\(657\) | −178.847 | − | 178.847i | −0.272218 | − | 0.272218i | ||||
\(658\) | 76.7768 | − | 76.7768i | 0.116682 | − | 0.116682i | ||||
\(659\) | − | 197.407i | − | 0.299555i | −0.988720 | − | 0.149778i | \(-0.952144\pi\) | ||
0.988720 | − | 0.149778i | \(-0.0478558\pi\) | |||||||
\(660\) | −101.942 | − | 139.220i | −0.154458 | − | 0.210940i | ||||
\(661\) | 560.346 | 0.847725 | 0.423862 | − | 0.905727i | \(-0.360674\pi\) | ||||
0.423862 | + | 0.905727i | \(0.360674\pi\) | |||||||
\(662\) | 49.2824 | + | 49.2824i | 0.0744447 | + | 0.0744447i | ||||
\(663\) | 43.1541 | − | 43.1541i | 0.0650892 | − | 0.0650892i | ||||
\(664\) | 244.252i | 0.367849i | ||||||||
\(665\) | 1063.95 | − | 779.065i | 1.59993 | − | 1.17153i | ||||
\(666\) | 287.332 | 0.431429 | ||||||||
\(667\) | −139.254 | − | 139.254i | −0.208777 | − | 0.208777i | ||||
\(668\) | 258.064 | − | 258.064i | 0.386323 | − | 0.386323i | ||||
\(669\) | 167.637i | 0.250578i | ||||||||
\(670\) | 36.7912 | − | 238.011i | 0.0549122 | − | 0.355241i | ||||
\(671\) | 946.104 | 1.40999 | ||||||||
\(672\) | −84.5412 | − | 84.5412i | −0.125805 | − | 0.125805i | ||||
\(673\) | −947.596 | + | 947.596i | −1.40802 | + | 1.40802i | −0.637889 | + | 0.770129i | \(0.720192\pi\) |
−0.770129 | + | 0.637889i | \(0.779808\pi\) | |||||||
\(674\) | − | 393.356i | − | 0.583614i | ||||||
\(675\) | 59.8337 | + | 115.304i | 0.0886425 | + | 0.170820i | ||||
\(676\) | −330.501 | −0.488906 | ||||||||
\(677\) | −121.113 | − | 121.113i | −0.178896 | − | 0.178896i | 0.611978 | − | 0.790874i | \(-0.290374\pi\) |
−0.790874 | + | 0.611978i | \(0.790374\pi\) | |||||||
\(678\) | −26.1253 | + | 26.1253i | −0.0385329 | + | 0.0385329i | ||||
\(679\) | − | 1927.76i | − | 2.83911i | ||||||
\(680\) | −254.310 | − | 39.3106i | −0.373985 | − | 0.0578097i | ||||
\(681\) | 386.851 | 0.568063 | ||||||||
\(682\) | 395.067 | + | 395.067i | 0.579277 | + | 0.579277i | ||||
\(683\) | 446.080 | − | 446.080i | 0.653119 | − | 0.653119i | −0.300624 | − | 0.953743i | \(-0.597195\pi\) |
0.953743 | + | 0.300624i | \(0.0971948\pi\) | |||||||
\(684\) | 129.681i | 0.189592i | ||||||||
\(685\) | 359.717 | + | 491.259i | 0.525135 | + | 0.717167i | ||||
\(686\) | 878.380 | 1.28044 | ||||||||
\(687\) | −341.391 | − | 341.391i | −0.496930 | − | 0.496930i | ||||
\(688\) | 170.031 | − | 170.031i | 0.247137 | − | 0.247137i | ||||
\(689\) | − | 27.8428i | − | 0.0404104i | ||||||
\(690\) | −47.3904 | + | 34.7009i | −0.0686817 | + | 0.0502912i | ||||
\(691\) | −885.496 | −1.28147 | −0.640735 | − | 0.767762i | \(-0.721370\pi\) | ||||
−0.640735 | + | 0.767762i | \(0.721370\pi\) | |||||||
\(692\) | 62.1844 | + | 62.1844i | 0.0898619 | + | 0.0898619i | ||||
\(693\) | −257.878 | + | 257.878i | −0.372119 | + | 0.372119i | ||||
\(694\) | − | 323.124i | − | 0.465596i | ||||||
\(695\) | 111.092 | − | 718.682i | 0.159845 | − | 1.03407i | ||||
\(696\) | 201.171 | 0.289039 | ||||||||
\(697\) | −592.628 | − | 592.628i | −0.850255 | − | 0.850255i | ||||
\(698\) | 69.2537 | − | 69.2537i | 0.0992173 | − | 0.0992173i | ||||
\(699\) | − | 644.737i | − | 0.922371i | ||||||
\(700\) | −541.550 | + | 281.023i | −0.773643 | + | 0.401461i | ||||
\(701\) | 1097.97 | 1.56628 | 0.783142 | − | 0.621843i | \(-0.213616\pi\) | ||||
0.783142 | + | 0.621843i | \(0.213616\pi\) | |||||||
\(702\) | 10.0620 | + | 10.0620i | 0.0143333 | + | 0.0143333i | ||||
\(703\) | 1035.04 | − | 1035.04i | 1.47232 | − | 1.47232i | ||||
\(704\) | 79.6987i | 0.113208i | ||||||||
\(705\) | 53.8500 | + | 8.32399i | 0.0763829 | + | 0.0118071i | ||||
\(706\) | −375.848 | −0.532363 | ||||||||
\(707\) | 670.586 | + | 670.586i | 0.948496 | + | 0.948496i | ||||
\(708\) | 205.459 | − | 205.459i | 0.290196 | − | 0.290196i | ||||
\(709\) | − | 567.023i | − | 0.799750i | −0.916570 | − | 0.399875i | \(-0.869054\pi\) | ||
0.916570 | − | 0.399875i | \(-0.130946\pi\) | |||||||
\(710\) | −534.579 | − | 730.064i | −0.752928 | − | 1.02826i | ||||
\(711\) | 81.4039 | 0.114492 | ||||||||
\(712\) | 168.744 | + | 168.744i | 0.237000 | + | 0.237000i | ||||
\(713\) | 134.480 | − | 134.480i | 0.188612 | − | 0.188612i | ||||
\(714\) | 543.875i | 0.761730i | ||||||||
\(715\) | −77.8238 | + | 56.9854i | −0.108845 | + | 0.0796998i | ||||
\(716\) | 132.889 | 0.185599 | ||||||||
\(717\) | 58.6053 | + | 58.6053i | 0.0817368 | + | 0.0817368i | ||||
\(718\) | 327.086 | − | 327.086i | 0.455551 | − | 0.455551i | ||||
\(719\) | 1190.36i | 1.65557i | 0.561045 | + | 0.827785i | \(0.310399\pi\) | ||||
−0.561045 | + | 0.827785i | \(0.689601\pi\) | |||||||
\(720\) | 9.16579 | − | 59.2958i | 0.0127303 | − | 0.0823552i | ||||
\(721\) | 730.589 | 1.01330 | ||||||||
\(722\) | 106.142 | + | 106.142i | 0.147011 | + | 0.147011i | ||||
\(723\) | 112.134 | − | 112.134i | 0.155095 | − | 0.155095i | ||||
\(724\) | 115.719i | 0.159833i | ||||||||
\(725\) | 309.971 | − | 978.683i | 0.427546 | − | 1.34991i | ||||
\(726\) | −53.2810 | −0.0733899 | ||||||||
\(727\) | 100.239 | + | 100.239i | 0.137881 | + | 0.137881i | 0.772678 | − | 0.634798i | \(-0.218917\pi\) |
−0.634798 | + | 0.772678i | \(0.718917\pi\) | |||||||
\(728\) | −47.2584 | + | 47.2584i | −0.0649153 | + | 0.0649153i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 589.161 | + | 91.0710i | 0.807069 | + | 0.124755i | ||||
\(731\) | −1093.85 | −1.49637 | ||||||||
\(732\) | 232.623 | + | 232.623i | 0.317791 | + | 0.317791i | ||||
\(733\) | 272.933 | − | 272.933i | 0.372350 | − | 0.372350i | −0.495982 | − | 0.868333i | \(-0.665192\pi\) |
0.868333 | + | 0.495982i | \(0.165192\pi\) | |||||||
\(734\) | 981.612i | 1.33735i | ||||||||
\(735\) | 511.127 | + | 698.036i | 0.695410 | + | 0.949709i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 239.931 | + | 239.931i | 0.325551 | + | 0.325551i | ||||
\(738\) | 138.179 | − | 138.179i | 0.187235 | − | 0.187235i | ||||
\(739\) | 1375.85i | 1.86177i | 0.365313 | + | 0.930885i | \(0.380962\pi\) | ||||
−0.365313 | + | 0.930885i | \(0.619038\pi\) | |||||||
\(740\) | −546.422 | + | 400.109i | −0.738408 | + | 0.540688i | ||||
\(741\) | 72.4913 | 0.0978291 | ||||||||
\(742\) | 175.452 | + | 175.452i | 0.236459 | + | 0.236459i | ||||
\(743\) | −200.083 | + | 200.083i | −0.269291 | + | 0.269291i | −0.828814 | − | 0.559524i | \(-0.810984\pi\) |
0.559524 | + | 0.828814i | \(0.310984\pi\) | |||||||
\(744\) | 194.274i | 0.261121i | ||||||||
\(745\) | −103.553 | + | 669.911i | −0.138998 | + | 0.899210i | ||||
\(746\) | 42.0317 | 0.0563427 | ||||||||
\(747\) | 183.189 | + | 183.189i | 0.245233 | + | 0.245233i | ||||
\(748\) | 256.361 | − | 256.361i | 0.342729 | − | 0.342729i | ||||
\(749\) | − | 1845.92i | − | 2.46451i | ||||||
\(750\) | −274.347 | − | 135.956i | −0.365795 | − | 0.181274i | ||||
\(751\) | 46.1912 | 0.0615063 | 0.0307531 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307531 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(752\) | −17.7962 | − | 17.7962i | −0.0236652 | − | 0.0236652i | ||||
\(753\) | −439.038 | + | 439.038i | −0.583052 | + | 0.583052i | ||||
\(754\) | − | 112.454i | − | 0.149144i | ||||||
\(755\) | 1099.06 | + | 169.891i | 1.45571 | + | 0.225021i | ||||
\(756\) | −126.812 | −0.167740 | ||||||||
\(757\) | −379.305 | − | 379.305i | −0.501063 | − | 0.501063i | 0.410705 | − | 0.911768i | \(-0.365283\pi\) |
−0.911768 | + | 0.410705i | \(0.865283\pi\) | |||||||
\(758\) | −310.295 | + | 310.295i | −0.409360 | + | 0.409360i | ||||
\(759\) | − | 82.7534i | − | 0.109029i | ||||||
\(760\) | −180.581 | − | 246.615i | −0.237606 | − | 0.324494i | ||||
\(761\) | −496.235 | −0.652083 | −0.326042 | − | 0.945355i | \(-0.605715\pi\) | ||||
−0.326042 | + | 0.945355i | \(0.605715\pi\) | |||||||
\(762\) | 297.284 | + | 297.284i | 0.390136 | + | 0.390136i | ||||
\(763\) | −315.062 | + | 315.062i | −0.412926 | + | 0.412926i | ||||
\(764\) | 11.0071i | 0.0144072i | ||||||||
\(765\) | −220.215 | + | 161.249i | −0.287863 | + | 0.210784i | ||||
\(766\) | −493.893 | −0.644769 | ||||||||
\(767\) | −114.851 | − | 114.851i | −0.149741 | − | 0.149741i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 128.084i | − | 0.166560i | −0.996526 | − | 0.0832798i | \(-0.973460\pi\) | ||
0.996526 | − | 0.0832798i | \(-0.0265395\pi\) | |||||||
\(770\) | 131.314 | − | 849.506i | 0.170538 | − | 1.10325i | ||||
\(771\) | −110.763 | −0.143662 | ||||||||
\(772\) | 359.919 | + | 359.919i | 0.466217 | + | 0.466217i | ||||
\(773\) | −52.1777 | + | 52.1777i | −0.0675003 | + | 0.0675003i | −0.740051 | − | 0.672551i | \(-0.765199\pi\) |
0.672551 | + | 0.740051i | \(0.265199\pi\) | |||||||
\(774\) | − | 255.046i | − | 0.329517i | ||||||
\(775\) | 945.130 | + | 299.344i | 1.21952 | + | 0.386250i | ||||
\(776\) | −446.837 | −0.575821 | ||||||||
\(777\) | 1012.14 | + | 1012.14i | 1.30263 | + | 1.30263i | ||||
\(778\) | 467.057 | − | 467.057i | 0.600330 | − | 0.600330i | ||||
\(779\) | − | 995.510i | − | 1.27793i | ||||||
\(780\) | −33.1462 | − | 5.12366i | −0.0424952 | − | 0.00656879i | ||||
\(781\) | 1274.84 | 1.63232 | ||||||||
\(782\) | −87.2649 | − | 87.2649i | −0.111592 | − | 0.111592i | ||||
\(783\) | 150.878 | − | 150.878i | 0.192693 | − | 0.192693i | ||||
\(784\) | − | 399.601i | − | 0.509695i | ||||||
\(785\) | 686.265 | + | 937.219i | 0.874223 | + | 1.19391i | ||||
\(786\) | 461.842 | 0.587586 | ||||||||
\(787\) | 433.630 | + | 433.630i | 0.550991 | + | 0.550991i | 0.926727 | − | 0.375736i | \(-0.122610\pi\) |
−0.375736 | + | 0.926727i | \(0.622610\pi\) | |||||||
\(788\) | −291.730 | + | 291.730i | −0.370216 | + | 0.370216i | ||||
\(789\) | 18.0259i | 0.0228465i | ||||||||
\(790\) | −154.807 | + | 113.355i | −0.195958 | + | 0.143487i | ||||
\(791\) | −184.055 | −0.232687 | ||||||||
\(792\) | 59.7740 | + | 59.7740i | 0.0754722 | + | 0.0754722i | ||||
\(793\) | 130.036 | − | 130.036i | 0.163980 | − | 0.163980i | ||||
\(794\) | − | 774.056i | − | 0.974882i | ||||||
\(795\) | −19.0222 | + | 123.059i | −0.0239273 | + | 0.154792i | ||||
\(796\) | 188.311 | 0.236572 | ||||||||
\(797\) | −209.327 | − | 209.327i | −0.262643 | − | 0.262643i | 0.563484 | − | 0.826127i | \(-0.309461\pi\) |
−0.826127 | + | 0.563484i | \(0.809461\pi\) | |||||||
\(798\) | −456.807 | + | 456.807i | −0.572440 | + | 0.572440i | ||||
\(799\) | 114.487i | 0.143288i | ||||||||
\(800\) | 65.1386 | + | 125.527i | 0.0814233 | + | 0.156908i | ||||
\(801\) | 253.116 | 0.316000 | ||||||||
\(802\) | 448.866 | + | 448.866i | 0.559684 | + | 0.559684i | ||||
\(803\) | −593.912 | + | 593.912i | −0.739617 | + | 0.739617i | ||||
\(804\) | 117.986i | 0.146749i | ||||||||
\(805\) | −289.171 | − | 44.6993i | −0.359218 | − | 0.0555270i | ||||
\(806\) | 108.599 | 0.134738 | ||||||||
\(807\) | −195.810 | − | 195.810i | −0.242639 | − | 0.242639i | ||||
\(808\) | 155.436 | − | 155.436i | 0.192371 | − | 0.192371i | ||||
\(809\) | 1559.05i | 1.92713i | 0.267469 | + | 0.963566i | \(0.413813\pi\) | ||||
−0.267469 | + | 0.963566i | \(0.586187\pi\) | |||||||
\(810\) | −37.5975 | − | 51.3462i | −0.0464166 | − | 0.0633903i | ||||
\(811\) | −203.515 | −0.250943 | −0.125471 | − | 0.992097i | \(-0.540044\pi\) | ||||
−0.125471 | + | 0.992097i | \(0.540044\pi\) | |||||||
\(812\) | 708.635 | + | 708.635i | 0.872704 | + | 0.872704i | ||||
\(813\) | −258.738 | + | 258.738i | −0.318251 | + | 0.318251i | ||||
\(814\) | − | 954.165i | − | 1.17219i | ||||||
\(815\) | −288.654 | + | 211.362i | −0.354176 | + | 0.259340i | ||||
\(816\) | 126.066 | 0.154492 | ||||||||
\(817\) | −918.738 | − | 918.738i | −1.12453 | − | 1.12453i | ||||
\(818\) | 335.091 | − | 335.091i | 0.409647 | − | 0.409647i | ||||
\(819\) | 70.8875i | 0.0865538i | ||||||||
\(820\) | −70.3623 | + | 455.191i | −0.0858077 | + | 0.555111i | ||||
\(821\) | 245.802 | 0.299393 | 0.149697 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149697 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(822\) | −210.921 | − | 210.921i | −0.256595 | − | 0.256595i | ||||
\(823\) | 725.015 | − | 725.015i | 0.880942 | − | 0.880942i | −0.112688 | − | 0.993630i | \(-0.535946\pi\) |
0.993630 | + | 0.112688i | \(0.0359462\pi\) | |||||||
\(824\) | − | 169.344i | − | 0.205515i | ||||||
\(825\) | 382.898 | − | 198.694i | 0.464119 | − | 0.240842i | ||||
\(826\) | 1447.48 | 1.75239 | ||||||||
\(827\) | 40.3403 | + | 40.3403i | 0.0487791 | + | 0.0487791i | 0.731076 | − | 0.682296i | \(-0.239019\pi\) |
−0.682296 | + | 0.731076i | \(0.739019\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | − | 112.945i | − | 0.136243i | −0.997677 | − | 0.0681213i | \(-0.978300\pi\) | ||
0.997677 | − | 0.0681213i | \(-0.0217005\pi\) | |||||||
\(830\) | −603.462 | − | 93.2817i | −0.727063 | − | 0.112388i | ||||
\(831\) | −537.353 | −0.646635 | ||||||||
\(832\) | 10.9541 | + | 10.9541i | 0.0131660 | + | 0.0131660i | ||||
\(833\) | −1285.37 | + | 1285.37i | −1.54306 | + | 1.54306i | ||||
\(834\) | 356.262i | 0.427173i | ||||||||
\(835\) | 539.030 | + | 736.143i | 0.645545 | + | 0.881608i | ||||
\(836\) | 430.641 | 0.515121 | ||||||||
\(837\) | 145.706 | + | 145.706i | 0.174081 | + | 0.174081i | ||||
\(838\) | 235.423 | − | 235.423i | 0.280934 | − | 0.280934i | ||||
\(839\) | − | 1114.62i | − | 1.32851i | −0.747508 | − | 0.664253i | \(-0.768750\pi\) | ||
0.747508 | − | 0.664253i | \(-0.231250\pi\) | |||||||
\(840\) | 241.159 | − | 176.585i | 0.287094 | − | 0.210221i | ||||
\(841\) | −845.243 | −1.00505 | ||||||||
\(842\) | 326.446 | + | 326.446i | 0.387703 | + | 0.387703i | ||||
\(843\) | −206.393 | + | 206.393i | −0.244832 | + | 0.244832i | ||||
\(844\) | − | 72.0948i | − | 0.0854204i | ||||||
\(845\) | 126.221 | − | 816.553i | 0.149374 | − | 0.966335i | ||||
\(846\) | −26.6943 | −0.0315536 | ||||||||
\(847\) | −187.685 | − | 187.685i | −0.221588 | − | 0.221588i | ||||
\(848\) | 40.6683 | − | 40.6683i | 0.0479580 | − | 0.0479580i | ||||
\(849\) | 379.074i | 0.446495i | ||||||||
\(850\) | 194.246 | − | 613.299i | 0.228525 | − | 0.721529i | ||||
\(851\) | −324.796 | −0.381664 | ||||||||
\(852\) | 313.452 | + | 313.452i | 0.367902 | + | 0.367902i | ||||
\(853\) | 968.069 | − | 968.069i | 1.13490 | − | 1.13490i | 0.145547 | − | 0.989351i | \(-0.453506\pi\) |
0.989351 | − | 0.145547i | \(-0.0464943\pi\) | |||||||
\(854\) | 1638.85i | 1.91903i | ||||||||
\(855\) | −320.397 | − | 49.5261i | −0.374733 | − | 0.0579253i | ||||
\(856\) | −427.869 | −0.499846 | ||||||||
\(857\) | −226.450 | − | 226.450i | −0.264235 | − | 0.264235i | 0.562537 | − | 0.826772i | \(-0.309825\pi\) |
−0.826772 | + | 0.562537i | \(0.809825\pi\) | |||||||
\(858\) | 33.4136 | − | 33.4136i | 0.0389435 | − | 0.0389435i | ||||
\(859\) | − | 130.650i | − | 0.152096i | −0.997104 | − | 0.0760478i | \(-0.975770\pi\) | ||
0.997104 | − | 0.0760478i | \(-0.0242301\pi\) | |||||||
\(860\) | 355.151 | + | 485.023i | 0.412966 | + | 0.563980i | ||||
\(861\) | 973.486 | 1.13065 | ||||||||
\(862\) | 307.959 | + | 307.959i | 0.357262 | + | 0.357262i | ||||
\(863\) | −433.283 | + | 433.283i | −0.502066 | + | 0.502066i | −0.912079 | − | 0.410014i | \(-0.865524\pi\) |
0.410014 | + | 0.912079i | \(0.365524\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −177.385 | + | 129.888i | −0.205069 | + | 0.150159i | ||||
\(866\) | −786.472 | −0.908166 | ||||||||
\(867\) | −51.5545 | − | 51.5545i | −0.0594631 | − | 0.0594631i | ||||
\(868\) | −684.341 | + | 684.341i | −0.788411 | + | 0.788411i | ||||
\(869\) | − | 270.324i | − | 0.311075i | ||||||
\(870\) | −76.8289 | + | 497.025i | −0.0883090 | + | 0.571293i | ||||
\(871\) | 65.9540 | 0.0757221 | ||||||||
\(872\) | 73.0287 | + | 73.0287i | 0.0837485 | + | 0.0837485i | ||||
\(873\) | −335.128 | + | 335.128i | −0.383881 | + | 0.383881i | ||||
\(874\) | − | 146.590i | − | 0.167723i | ||||||
\(875\) | −487.488 | − | 1445.31i | −0.557130 | − | 1.65178i | ||||
\(876\) | −292.057 | −0.333398 | ||||||||
\(877\) | 1098.13 | + | 1098.13i | 1.25215 | + | 1.25215i | 0.954755 | + | 0.297392i | \(0.0961170\pi\) |
0.297392 | + | 0.954755i | \(0.403883\pi\) | |||||||
\(878\) | −330.522 | + | 330.522i | −0.376448 | + | 0.376448i | ||||
\(879\) | − | 766.445i | − | 0.871951i | ||||||
\(880\) | −196.908 | − | 30.4376i | −0.223759 | − | 0.0345881i | ||||
\(881\) | −0.176371 | −0.000200194 | −0.000100097 | − | 1.00000i | \(-0.500032\pi\) | ||||
−0.000100097 | 1.00000i | \(0.500032\pi\) | ||||||||
\(882\) | −299.701 | − | 299.701i | −0.339797 | − | 0.339797i | ||||
\(883\) | 896.020 | − | 896.020i | 1.01475 | − | 1.01475i | 0.0148558 | − | 0.999890i | \(-0.495271\pi\) |
0.999890 | − | 0.0148558i | \(-0.00472891\pi\) | |||||||
\(884\) | − | 70.4704i | − | 0.0797176i | ||||||
\(885\) | 429.152 | + | 586.085i | 0.484917 | + | 0.662242i | ||||
\(886\) | 232.911 | 0.262879 | ||||||||
\(887\) | 358.656 | + | 358.656i | 0.404348 | + | 0.404348i | 0.879762 | − | 0.475414i | \(-0.157702\pi\) |
−0.475414 | + | 0.879762i | \(0.657702\pi\) | |||||||
\(888\) | 234.605 | − | 234.605i | 0.264195 | − | 0.264195i | ||||
\(889\) | 2094.39i | 2.35590i | ||||||||
\(890\) | −481.354 | + | 352.464i | −0.540847 | + | 0.396027i | ||||
\(891\) | 89.6610 | 0.100630 | ||||||||
\(892\) | 136.875 | + | 136.875i | 0.153447 | + | 0.153447i | ||||
\(893\) | −96.1594 | + | 96.1594i | −0.107681 | + | 0.107681i | ||||
\(894\) | − | 332.086i | − | 0.371461i | ||||||
\(895\) | −50.7514 | + | 328.324i | −0.0567055 | + | 0.366842i | ||||
\(896\) | −138.055 | −0.154079 | ||||||||
\(897\) | −11.3739 | − | 11.3739i | −0.0126800 | − | 0.0126800i | ||||
\(898\) | −149.486 | + | 149.486i | −0.166465 | + | 0.166465i | ||||
\(899\) | − | 1628.43i | − | 1.81138i | ||||||
\(900\) | 142.999 | + | 45.2911i | 0.158888 | + | 0.0503234i | ||||
\(901\) | −261.630 | −0.290377 | ||||||||
\(902\) | −458.862 | − | 458.862i | −0.508716 | − | 0.508716i | ||||
\(903\) | 898.412 | − | 898.412i | 0.994919 | − | 0.994919i | ||||
\(904\) | 42.6624i | 0.0471929i | ||||||||
\(905\) | −285.903 | − | 44.1942i | −0.315915 | − | 0.0488333i | ||||
\(906\) | −544.824 | −0.601351 | ||||||||
\(907\) | −81.2671 | − | 81.2671i | −0.0895999 | − | 0.0895999i | 0.660886 | − | 0.750486i | \(-0.270181\pi\) |
−0.750486 | + | 0.660886i | \(0.770181\pi\) | |||||||
\(908\) | 315.862 | − | 315.862i | 0.347866 | − | 0.347866i | ||||
\(909\) | − | 233.154i | − | 0.256495i | ||||||
\(910\) | −98.7109 | − | 134.808i | −0.108473 | − | 0.148140i | ||||
\(911\) | 678.197 | 0.744453 | 0.372227 | − | 0.928142i | \(-0.378594\pi\) | ||||
0.372227 | + | 0.928142i | \(0.378594\pi\) | |||||||
\(912\) | 105.884 | + | 105.884i | 0.116101 | + | 0.116101i | ||||
\(913\) | 608.330 | − | 608.330i | 0.666297 | − | 0.666297i | ||||
\(914\) | − | 518.357i | − | 0.567130i | ||||||
\(915\) | −663.573 | + | 485.892i | −0.725217 | + | 0.531029i | ||||
\(916\) | −557.489 | −0.608612 | ||||||||
\(917\) | 1626.86 | + | 1626.86i | 1.77411 | + | 1.77411i | ||||
\(918\) | 94.5491 | − | 94.5491i | 0.102995 | − | 0.102995i | ||||
\(919\) | 1004.97i | 1.09355i | 0.837281 | + | 0.546773i | \(0.184144\pi\) | ||||
−0.837281 | + | 0.546773i | \(0.815856\pi\) | |||||||
\(920\) | −10.3609 | + | 67.0272i | −0.0112619 | + | 0.0728557i | ||||
\(921\) | −161.742 | −0.175616 | ||||||||
\(922\) | 804.421 | + | 804.421i | 0.872474 | + | 0.872474i | ||||
\(923\) | 175.219 | − | 175.219i | 0.189837 | − | 0.189837i | ||||
\(924\) | 421.114i | 0.455751i | ||||||||
\(925\) | −779.850 | − | 1502.83i | −0.843081 | − | 1.62468i | ||||
\(926\) | −568.827 | −0.614284 | ||||||||
\(927\) | −127.008 | − | 127.008i | −0.137010 | − | 0.137010i | ||||
\(928\) | 164.256 | − | 164.256i | 0.177000 | − | 0.177000i | ||||
\(929\) | − | 719.296i | − | 0.774269i | −0.922023 | − | 0.387134i | \(-0.873465\pi\) | ||
0.922023 | − | 0.387134i | \(-0.126535\pi\) | |||||||
\(930\) | −479.985 | − | 74.1949i | −0.516113 | − | 0.0797794i | ||||
\(931\) | −2159.19 | −2.31922 | ||||||||
\(932\) | −526.426 | − | 526.426i | −0.564834 | − | 0.564834i | ||||
\(933\) | 58.4440 | − | 58.4440i | 0.0626409 | − | 0.0626409i | ||||
\(934\) | − | 1084.02i | − | 1.16062i | ||||||
\(935\) | 535.474 | + | 731.286i | 0.572699 | + | 0.782124i | ||||
\(936\) | 16.4311 | 0.0175546 | ||||||||
\(937\) | −73.5570 | − | 73.5570i | −0.0785027 | − | 0.0785027i | 0.666765 | − | 0.745268i | \(-0.267678\pi\) |
−0.745268 | + | 0.666765i | \(0.767678\pi\) | |||||||
\(938\) | −415.612 | + | 415.612i | −0.443083 | + | 0.443083i | ||||
\(939\) | − | 838.955i | − | 0.893455i | ||||||
\(940\) | 50.7648 | − | 37.1718i | 0.0540051 | − | 0.0395445i | ||||
\(941\) | 647.565 | 0.688167 | 0.344084 | − | 0.938939i | \(-0.388190\pi\) | ||||
0.344084 | + | 0.938939i | \(0.388190\pi\) | |||||||
\(942\) | −402.394 | − | 402.394i | −0.427170 | − | 0.427170i | ||||
\(943\) | −156.196 | + | 156.196i | −0.165637 | + | 0.165637i | ||||
\(944\) | − | 335.513i | − | 0.355416i | ||||||
\(945\) | 48.4304 | − | 313.308i | 0.0512491 | − | 0.331543i | ||||
\(946\) | −846.951 | −0.895297 | ||||||||
\(947\) | 331.454 | + | 331.454i | 0.350004 | + | 0.350004i | 0.860111 | − | 0.510107i | \(-0.170394\pi\) |
−0.510107 | + | 0.860111i | \(0.670394\pi\) | |||||||
\(948\) | 66.4660 | − | 66.4660i | 0.0701118 | − | 0.0701118i | ||||
\(949\) | 163.259i | 0.172033i | ||||||||
\(950\) | 678.267 | − | 351.968i | 0.713965 | − | 0.370493i | ||||
\(951\) | −651.305 | −0.684864 | ||||||||
\(952\) | 444.072 | + | 444.072i | 0.466462 | + | 0.466462i | ||||
\(953\) | 169.575 | − | 169.575i | 0.177938 | − | 0.177938i | −0.612518 | − | 0.790457i | \(-0.709843\pi\) |
0.790457 | + | 0.612518i | \(0.209843\pi\) | |||||||
\(954\) | − | 61.0025i | − | 0.0639439i | ||||||
\(955\) | −27.1947 | − | 4.20369i | −0.0284761 | − | 0.00440177i | ||||
\(956\) | 95.7021 | 0.100107 | ||||||||
\(957\) | −501.034 | − | 501.034i | −0.523546 | − | 0.523546i | ||||
\(958\) | 419.970 | − | 419.970i | 0.438382 | − | 0.438382i | ||||
\(959\) | − | 1485.96i | − | 1.54949i | ||||||
\(960\) | −40.9310 | − | 55.8986i | −0.0426364 | − | 0.0582277i | ||||
\(961\) | 611.603 | 0.636424 | ||||||||
\(962\) | −131.144 | − | 131.144i | −0.136324 | − | 0.136324i | ||||
\(963\) | −320.901 | + | 320.901i | −0.333231 | + | 0.333231i | ||||
\(964\) | − | 183.113i | − | 0.189952i | ||||||
\(965\) | −1026.69 | + | 751.781i | −1.06393 | + | 0.779048i | ||||
\(966\) | 143.347 | 0.148392 | ||||||||
\(967\) | −330.701 | − | 330.701i | −0.341986 | − | 0.341986i | 0.515127 | − | 0.857114i | \(-0.327745\pi\) |
−0.857114 | + | 0.515127i | \(0.827745\pi\) | |||||||
\(968\) | −43.5038 | + | 43.5038i | −0.0449419 | + | 0.0449419i | ||||
\(969\) | − | 681.178i | − | 0.702971i | ||||||
\(970\) | 170.651 | − | 1103.98i | 0.175928 | − | 1.13812i | ||||
\(971\) | 1031.02 | 1.06181 | 0.530904 | − | 0.847432i | \(-0.321853\pi\) | ||||
0.530904 | + | 0.847432i | \(0.321853\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −1254.95 | + | 1254.95i | −1.28978 | + | 1.28978i | ||||
\(974\) | 927.300i | 0.952054i | ||||||||
\(975\) | 25.3176 | − | 79.9362i | 0.0259668 | − | 0.0819858i | ||||
\(976\) | 379.872 | 0.389213 | ||||||||
\(977\) | 348.065 | + | 348.065i | 0.356259 | + | 0.356259i | 0.862432 | − | 0.506173i | \(-0.168940\pi\) |
−0.506173 | + | 0.862432i | \(0.668940\pi\) | |||||||
\(978\) | 123.933 | − | 123.933i | 0.126721 | − | 0.126721i | ||||
\(979\) | − | 840.543i | − | 0.858573i | ||||||
\(980\) | 987.277 | + | 152.611i | 1.00743 | + | 0.155725i | ||||
\(981\) | 109.543 | 0.111665 | ||||||||
\(982\) | 81.2134 | + | 81.2134i | 0.0827021 | + | 0.0827021i | ||||
\(983\) | −358.451 | + | 358.451i | −0.364650 | + | 0.364650i | −0.865522 | − | 0.500872i | \(-0.833013\pi\) |
0.500872 | + | 0.865522i | \(0.333013\pi\) | |||||||
\(984\) | − | 225.646i | − | 0.229315i | ||||||
\(985\) | −609.351 | − | 832.179i | −0.618631 | − | 0.844852i | ||||
\(986\) | −1056.70 | −1.07170 | ||||||||
\(987\) | −94.0320 | − | 94.0320i | −0.0952705 | − | 0.0952705i | ||||
\(988\) | 59.1889 | − | 59.1889i | 0.0599078 | − | 0.0599078i | ||||
\(989\) | 288.301i | 0.291507i | ||||||||
\(990\) | −170.509 | + | 124.853i | −0.172232 | + | 0.126114i | ||||
\(991\) | 1743.30 | 1.75913 | 0.879565 | − | 0.475779i | \(-0.157834\pi\) | ||||
0.879565 | + | 0.475779i | \(0.157834\pi\) | |||||||
\(992\) | 158.624 | + | 158.624i | 0.159903 | + | 0.159903i | ||||
\(993\) | 60.3584 | − | 60.3584i | 0.0607838 | − | 0.0607838i | ||||
\(994\) | 2208.30i | 2.22163i | ||||||||
\(995\) | −71.9175 | + | 465.252i | −0.0722789 | + | 0.467590i | ||||
\(996\) | 299.146 | 0.300348 | ||||||||
\(997\) | 1281.65 | + | 1281.65i | 1.28551 | + | 1.28551i | 0.937487 | + | 0.348021i | \(0.113146\pi\) |
0.348021 | + | 0.937487i | \(0.386854\pi\) | |||||||
\(998\) | 486.389 | − | 486.389i | 0.487364 | − | 0.487364i | ||||
\(999\) | − | 351.908i | − | 0.352260i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.3.k.b.277.11 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.11 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.11 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.11 | yes | 48 | 5.3 | odd | 4 | inner |