Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(459,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.g (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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 459.17 | ||
Character | \(\chi\) | \(=\) | 460.459 |
Dual form | 460.2.g.c.459.19 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.627129 | − | 1.26756i | −0.443447 | − | 0.896301i | ||||
\(3\) | −3.03928 | −1.75473 | −0.877363 | − | 0.479827i | \(-0.840700\pi\) | ||||
−0.877363 | + | 0.479827i | \(0.840700\pi\) | |||||||
\(4\) | −1.21342 | + | 1.58985i | −0.606710 | + | 0.794924i | ||||
\(5\) | −0.951754 | + | 2.02340i | −0.425637 | + | 0.904894i | ||||
\(6\) | 1.90602 | + | 3.85247i | 0.778128 | + | 1.57276i | ||||
\(7\) | 1.96560i | 0.742926i | 0.928448 | + | 0.371463i | \(0.121144\pi\) | ||||
−0.928448 | + | 0.371463i | \(0.878856\pi\) | |||||||
\(8\) | 2.77620 | + | 0.541043i | 0.981534 | + | 0.191288i | ||||
\(9\) | 6.23720 | 2.07907 | ||||||||
\(10\) | 3.16166 | − | 0.0625285i | 0.999804 | − | 0.0197733i | ||||
\(11\) | −5.30588 | −1.59978 | −0.799891 | − | 0.600145i | \(-0.795109\pi\) | ||||
−0.799891 | + | 0.600145i | \(0.795109\pi\) | |||||||
\(12\) | 3.68792 | − | 4.83198i | 1.06461 | − | 1.39487i | ||||
\(13\) | 0.315328i | 0.0874562i | 0.999043 | + | 0.0437281i | \(0.0139235\pi\) | ||||
−0.999043 | + | 0.0437281i | \(0.986076\pi\) | |||||||
\(14\) | 2.49151 | − | 1.23268i | 0.665885 | − | 0.329448i | ||||
\(15\) | 2.89264 | − | 6.14968i | 0.746877 | − | 1.58784i | ||||
\(16\) | −1.05523 | − | 3.85830i | −0.263807 | − | 0.964575i | ||||
\(17\) | −1.43205 | −0.347323 | −0.173662 | − | 0.984805i | \(-0.555560\pi\) | ||||
−0.173662 | + | 0.984805i | \(0.555560\pi\) | |||||||
\(18\) | −3.91152 | − | 7.90602i | −0.921955 | − | 1.86347i | ||||
\(19\) | 4.48278 | 1.02842 | 0.514210 | − | 0.857664i | \(-0.328085\pi\) | ||||
0.514210 | + | 0.857664i | \(0.328085\pi\) | |||||||
\(20\) | −2.06203 | − | 3.96838i | −0.461083 | − | 0.887357i | ||||
\(21\) | − | 5.97399i | − | 1.30363i | ||||||
\(22\) | 3.32747 | + | 6.72552i | 0.709419 | + | 1.43389i | ||||
\(23\) | 0.916686 | + | 4.70741i | 0.191142 | + | 0.981562i | ||||
\(24\) | −8.43763 | − | 1.64438i | −1.72232 | − | 0.335658i | ||||
\(25\) | −3.18833 | − | 3.85157i | −0.637665 | − | 0.770313i | ||||
\(26\) | 0.399697 | − | 0.197751i | 0.0783870 | − | 0.0387822i | ||||
\(27\) | −9.83873 | −1.89346 | ||||||||
\(28\) | −3.12500 | − | 2.38509i | −0.590569 | − | 0.450740i | ||||
\(29\) | −6.11341 | −1.13523 | −0.567616 | − | 0.823294i | \(-0.692134\pi\) | ||||
−0.567616 | + | 0.823294i | \(0.692134\pi\) | |||||||
\(30\) | −9.60915 | + | 0.190041i | −1.75438 | + | 0.0346967i | ||||
\(31\) | − | 7.40223i | − | 1.32948i | −0.747075 | − | 0.664740i | \(-0.768542\pi\) | ||
0.747075 | − | 0.664740i | \(-0.231458\pi\) | |||||||
\(32\) | −4.22887 | + | 3.75722i | −0.747565 | + | 0.664188i | ||||
\(33\) | 16.1260 | 2.80718 | ||||||||
\(34\) | 0.898081 | + | 1.81521i | 0.154020 | + | 0.311306i | ||||
\(35\) | −3.97720 | − | 1.87077i | −0.672269 | − | 0.316217i | ||||
\(36\) | −7.56833 | + | 9.91619i | −1.26139 | + | 1.65270i | ||||
\(37\) | −6.56660 | −1.07954 | −0.539771 | − | 0.841812i | \(-0.681489\pi\) | ||||
−0.539771 | + | 0.841812i | \(0.681489\pi\) | |||||||
\(38\) | −2.81128 | − | 5.68219i | −0.456050 | − | 0.921774i | ||||
\(39\) | − | 0.958368i | − | 0.153462i | ||||||
\(40\) | −3.73701 | + | 5.10243i | −0.590873 | + | 0.806765i | ||||
\(41\) | −0.152099 | −0.0237538 | −0.0118769 | − | 0.999929i | \(-0.503781\pi\) | ||||
−0.0118769 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(42\) | −7.57239 | + | 3.74646i | −1.16845 | + | 0.578092i | ||||
\(43\) | − | 8.98786i | − | 1.37064i | −0.728244 | − | 0.685318i | \(-0.759663\pi\) | ||
0.728244 | − | 0.685318i | \(-0.240337\pi\) | |||||||
\(44\) | 6.43825 | − | 8.43553i | 0.970603 | − | 1.27170i | ||||
\(45\) | −5.93628 | + | 12.6204i | −0.884928 | + | 1.88133i | ||||
\(46\) | 5.39204 | − | 4.11411i | 0.795013 | − | 0.606592i | ||||
\(47\) | 1.31095 | 0.191221 | 0.0956107 | − | 0.995419i | \(-0.469520\pi\) | ||||
0.0956107 | + | 0.995419i | \(0.469520\pi\) | |||||||
\(48\) | 3.20713 | + | 11.7264i | 0.462909 | + | 1.69257i | ||||
\(49\) | 3.13643 | 0.448061 | ||||||||
\(50\) | −2.88260 | + | 6.45683i | −0.407662 | + | 0.913133i | ||||
\(51\) | 4.35240 | 0.609458 | ||||||||
\(52\) | −0.501323 | − | 0.382625i | −0.0695210 | − | 0.0530605i | ||||
\(53\) | 10.8030 | 1.48390 | 0.741952 | − | 0.670453i | \(-0.233900\pi\) | ||||
0.741952 | + | 0.670453i | \(0.233900\pi\) | |||||||
\(54\) | 6.17015 | + | 12.4712i | 0.839651 | + | 1.69711i | ||||
\(55\) | 5.04989 | − | 10.7359i | 0.680927 | − | 1.44763i | ||||
\(56\) | −1.06347 | + | 5.45689i | −0.142113 | + | 0.729207i | ||||
\(57\) | −13.6244 | −1.80460 | ||||||||
\(58\) | 3.83389 | + | 7.74911i | 0.503415 | + | 1.01751i | ||||
\(59\) | − | 7.22568i | − | 0.940703i | −0.882479 | − | 0.470352i | \(-0.844127\pi\) | ||
0.882479 | − | 0.470352i | \(-0.155873\pi\) | |||||||
\(60\) | 6.26707 | + | 12.0610i | 0.809075 | + | 1.55707i | ||||
\(61\) | 4.20106i | 0.537891i | 0.963155 | + | 0.268945i | \(0.0866751\pi\) | ||||
−0.963155 | + | 0.268945i | \(0.913325\pi\) | |||||||
\(62\) | −9.38278 | + | 4.64215i | −1.19161 | + | 0.589554i | ||||
\(63\) | 12.2598i | 1.54459i | ||||||||
\(64\) | 7.41454 | + | 3.00409i | 0.926818 | + | 0.375511i | ||||
\(65\) | −0.638035 | − | 0.300115i | −0.0791385 | − | 0.0372246i | ||||
\(66\) | −10.1131 | − | 20.4407i | −1.24484 | − | 2.51608i | ||||
\(67\) | − | 3.99252i | − | 0.487764i | −0.969805 | − | 0.243882i | \(-0.921579\pi\) | ||
0.969805 | − | 0.243882i | \(-0.0784210\pi\) | |||||||
\(68\) | 1.73768 | − | 2.27674i | 0.210724 | − | 0.276096i | ||||
\(69\) | −2.78606 | − | 14.3071i | −0.335402 | − | 1.72237i | ||||
\(70\) | 0.122906 | + | 6.21455i | 0.0146901 | + | 0.742781i | ||||
\(71\) | − | 0.608318i | − | 0.0721940i | −0.999348 | − | 0.0360970i | \(-0.988507\pi\) | ||
0.999348 | − | 0.0360970i | \(-0.0114925\pi\) | |||||||
\(72\) | 17.3157 | + | 3.37459i | 2.04067 | + | 0.397700i | ||||
\(73\) | − | 14.2324i | − | 1.66577i | −0.553443 | − | 0.832887i | \(-0.686686\pi\) | ||
0.553443 | − | 0.832887i | \(-0.313314\pi\) | |||||||
\(74\) | 4.11810 | + | 8.32356i | 0.478720 | + | 0.967595i | ||||
\(75\) | 9.69021 | + | 11.7060i | 1.11893 | + | 1.35169i | ||||
\(76\) | −5.43949 | + | 7.12693i | −0.623952 | + | 0.817515i | ||||
\(77\) | − | 10.4292i | − | 1.18852i | ||||||
\(78\) | −1.21479 | + | 0.601020i | −0.137548 | + | 0.0680521i | ||||
\(79\) | 4.74332 | 0.533666 | 0.266833 | − | 0.963743i | \(-0.414023\pi\) | ||||
0.266833 | + | 0.963743i | \(0.414023\pi\) | |||||||
\(80\) | 8.81122 | + | 1.53700i | 0.985124 | + | 0.171842i | ||||
\(81\) | 11.1910 | 1.24345 | ||||||||
\(82\) | 0.0953854 | + | 0.192794i | 0.0105336 | + | 0.0212906i | ||||
\(83\) | − | 5.33199i | − | 0.585262i | −0.956225 | − | 0.292631i | \(-0.905469\pi\) | ||
0.956225 | − | 0.292631i | \(-0.0945307\pi\) | |||||||
\(84\) | 9.49773 | + | 7.24895i | 1.03629 | + | 0.790926i | ||||
\(85\) | 1.36296 | − | 2.89762i | 0.147834 | − | 0.314291i | ||||
\(86\) | −11.3927 | + | 5.63654i | −1.22850 | + | 0.607804i | ||||
\(87\) | 18.5803 | 1.99202 | ||||||||
\(88\) | −14.7302 | − | 2.87071i | −1.57024 | − | 0.306019i | ||||
\(89\) | − | 10.5110i | − | 1.11416i | −0.830459 | − | 0.557080i | \(-0.811922\pi\) | ||
0.830459 | − | 0.557080i | \(-0.188078\pi\) | |||||||
\(90\) | 19.7199 | − | 0.390003i | 2.07866 | − | 0.0411099i | ||||
\(91\) | −0.619807 | −0.0649734 | ||||||||
\(92\) | −8.59638 | − | 4.25467i | −0.896235 | − | 0.443580i | ||||
\(93\) | 22.4974i | 2.33287i | ||||||||
\(94\) | −0.822133 | − | 1.66170i | −0.0847965 | − | 0.171392i | ||||
\(95\) | −4.26650 | + | 9.07047i | −0.437734 | + | 0.930611i | ||||
\(96\) | 12.8527 | − | 11.4192i | 1.31177 | − | 1.16547i | ||||
\(97\) | 6.27182 | 0.636806 | 0.318403 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318403 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(98\) | −1.96694 | − | 3.97561i | −0.198691 | − | 0.401598i | ||||
\(99\) | −33.0938 | −3.32605 | ||||||||
\(100\) | 9.99218 | − | 0.395388i | 0.999218 | − | 0.0395388i | ||||
\(101\) | −17.2761 | −1.71904 | −0.859519 | − | 0.511103i | \(-0.829237\pi\) | ||||
−0.859519 | + | 0.511103i | \(0.829237\pi\) | |||||||
\(102\) | −2.72951 | − | 5.51693i | −0.270262 | − | 0.546257i | ||||
\(103\) | 10.8970i | 1.07372i | 0.843673 | + | 0.536858i | \(0.180389\pi\) | ||||
−0.843673 | + | 0.536858i | \(0.819611\pi\) | |||||||
\(104\) | −0.170606 | + | 0.875412i | −0.0167293 | + | 0.0858412i | ||||
\(105\) | 12.0878 | + | 5.68577i | 1.17965 | + | 0.554875i | ||||
\(106\) | −6.77486 | − | 13.6934i | −0.658033 | − | 1.33002i | ||||
\(107\) | 10.6102i | 1.02573i | 0.858470 | + | 0.512863i | \(0.171415\pi\) | ||||
−0.858470 | + | 0.512863i | \(0.828585\pi\) | |||||||
\(108\) | 11.9385 | − | 15.6421i | 1.14878 | − | 1.50516i | ||||
\(109\) | 11.5772i | 1.10889i | 0.832219 | + | 0.554447i | \(0.187070\pi\) | ||||
−0.832219 | + | 0.554447i | \(0.812930\pi\) | |||||||
\(110\) | −16.7754 | + | 0.331769i | −1.59947 | + | 0.0316329i | ||||
\(111\) | 19.9577 | 1.89430 | ||||||||
\(112\) | 7.58387 | − | 2.07415i | 0.716608 | − | 0.195989i | ||||
\(113\) | −3.56369 | −0.335244 | −0.167622 | − | 0.985851i | \(-0.553609\pi\) | ||||
−0.167622 | + | 0.985851i | \(0.553609\pi\) | |||||||
\(114\) | 8.54425 | + | 17.2698i | 0.800243 | + | 1.61746i | ||||
\(115\) | −10.3974 | − | 2.62547i | −0.969567 | − | 0.244826i | ||||
\(116\) | 7.41813 | − | 9.71938i | 0.688756 | − | 0.902422i | ||||
\(117\) | 1.96676i | 0.181827i | ||||||||
\(118\) | −9.15898 | + | 4.53143i | −0.843153 | + | 0.417152i | ||||
\(119\) | − | 2.81484i | − | 0.258036i | ||||||
\(120\) | 11.3578 | − | 15.5077i | 1.03682 | − | 1.41565i | ||||
\(121\) | 17.1523 | 1.55930 | ||||||||
\(122\) | 5.32510 | − | 2.63461i | 0.482112 | − | 0.238526i | ||||
\(123\) | 0.462270 | 0.0416815 | ||||||||
\(124\) | 11.7684 | + | 8.98201i | 1.05684 | + | 0.806608i | ||||
\(125\) | 10.8278 | − | 2.78553i | 0.968466 | − | 0.249145i | ||||
\(126\) | 15.5401 | − | 7.68848i | 1.38442 | − | 0.684944i | ||||
\(127\) | −1.35452 | −0.120194 | −0.0600971 | − | 0.998193i | \(-0.519141\pi\) | ||||
−0.0600971 | + | 0.998193i | \(0.519141\pi\) | |||||||
\(128\) | −0.842013 | − | 11.2823i | −0.0744242 | − | 0.997227i | ||||
\(129\) | 27.3166i | 2.40509i | ||||||||
\(130\) | 0.0197170 | + | 0.996959i | 0.00172929 | + | 0.0874391i | ||||
\(131\) | 8.96892i | 0.783618i | 0.920047 | + | 0.391809i | \(0.128151\pi\) | ||||
−0.920047 | + | 0.391809i | \(0.871849\pi\) | |||||||
\(132\) | −19.5676 | + | 25.6379i | −1.70314 | + | 2.23149i | ||||
\(133\) | 8.81134i | 0.764040i | ||||||||
\(134\) | −5.06076 | + | 2.50382i | −0.437183 | + | 0.216298i | ||||
\(135\) | 9.36406 | − | 19.9077i | 0.805930 | − | 1.71338i | ||||
\(136\) | −3.97566 | − | 0.774802i | −0.340910 | − | 0.0664387i | ||||
\(137\) | −20.3624 | −1.73968 | −0.869839 | − | 0.493336i | \(-0.835777\pi\) | ||||
−0.869839 | + | 0.493336i | \(0.835777\pi\) | |||||||
\(138\) | −16.3879 | + | 12.5039i | −1.39503 | + | 1.06440i | ||||
\(139\) | − | 16.2845i | − | 1.38123i | −0.723222 | − | 0.690616i | \(-0.757340\pi\) | ||
0.723222 | − | 0.690616i | \(-0.242660\pi\) | |||||||
\(140\) | 7.80024 | − | 4.05311i | 0.659240 | − | 0.342551i | ||||
\(141\) | −3.98433 | −0.335541 | ||||||||
\(142\) | −0.771080 | + | 0.381494i | −0.0647076 | + | 0.0320142i | ||||
\(143\) | − | 1.67309i | − | 0.139911i | ||||||
\(144\) | −6.58166 | − | 24.0650i | −0.548472 | − | 2.00542i | ||||
\(145\) | 5.81846 | − | 12.3699i | 0.483197 | − | 1.02726i | ||||
\(146\) | −18.0404 | + | 8.92554i | −1.49303 | + | 0.738683i | ||||
\(147\) | −9.53247 | −0.786225 | ||||||||
\(148\) | 7.96804 | − | 10.4399i | 0.654969 | − | 0.858154i | ||||
\(149\) | − | 12.8748i | − | 1.05475i | −0.849634 | − | 0.527373i | \(-0.823177\pi\) | ||
0.849634 | − | 0.527373i | \(-0.176823\pi\) | |||||||
\(150\) | 8.76102 | − | 19.6241i | 0.715335 | − | 1.60230i | ||||
\(151\) | 7.83400i | 0.637522i | 0.947835 | + | 0.318761i | \(0.103267\pi\) | ||||
−0.947835 | + | 0.318761i | \(0.896733\pi\) | |||||||
\(152\) | 12.4451 | + | 2.42538i | 1.00943 | + | 0.196724i | ||||
\(153\) | −8.93199 | −0.722108 | ||||||||
\(154\) | −13.2197 | + | 6.54046i | −1.06527 | + | 0.527045i | ||||
\(155\) | 14.9777 | + | 7.04511i | 1.20304 | + | 0.565877i | ||||
\(156\) | 1.52366 | + | 1.16290i | 0.121990 | + | 0.0931067i | ||||
\(157\) | 5.46720 | 0.436330 | 0.218165 | − | 0.975912i | \(-0.429993\pi\) | ||||
0.218165 | + | 0.975912i | \(0.429993\pi\) | |||||||
\(158\) | −2.97467 | − | 6.01245i | −0.236652 | − | 0.478325i | ||||
\(159\) | −32.8333 | −2.60385 | ||||||||
\(160\) | −3.57753 | − | 12.1327i | −0.282828 | − | 0.959171i | ||||
\(161\) | −9.25287 | + | 1.80184i | −0.729228 | + | 0.142005i | ||||
\(162\) | −7.01821 | − | 14.1853i | −0.551403 | − | 1.11450i | ||||
\(163\) | 5.70232 | 0.446641 | 0.223320 | − | 0.974745i | \(-0.428310\pi\) | ||||
0.223320 | + | 0.974745i | \(0.428310\pi\) | |||||||
\(164\) | 0.184559 | − | 0.241814i | 0.0144117 | − | 0.0188825i | ||||
\(165\) | −15.3480 | + | 32.6295i | −1.19484 | + | 2.54020i | ||||
\(166\) | −6.75862 | + | 3.34384i | −0.524571 | + | 0.259533i | ||||
\(167\) | −10.1090 | −0.782257 | −0.391129 | − | 0.920336i | \(-0.627915\pi\) | ||||
−0.391129 | + | 0.920336i | \(0.627915\pi\) | |||||||
\(168\) | 3.23219 | − | 16.5850i | 0.249369 | − | 1.27956i | ||||
\(169\) | 12.9006 | 0.992351 | ||||||||
\(170\) | −4.52766 | + | 0.0895441i | −0.347256 | + | 0.00686772i | ||||
\(171\) | 27.9600 | 2.13815 | ||||||||
\(172\) | 14.2893 | + | 10.9060i | 1.08955 | + | 0.831578i | ||||
\(173\) | − | 6.64716i | − | 0.505375i | −0.967548 | − | 0.252687i | \(-0.918686\pi\) | ||
0.967548 | − | 0.252687i | \(-0.0813144\pi\) | |||||||
\(174\) | −11.6523 | − | 23.5517i | −0.883356 | − | 1.78545i | ||||
\(175\) | 7.57063 | − | 6.26697i | 0.572286 | − | 0.473738i | ||||
\(176\) | 5.59891 | + | 20.4717i | 0.422034 | + | 1.54311i | ||||
\(177\) | 21.9608i | 1.65068i | ||||||||
\(178\) | −13.3233 | + | 6.59173i | −0.998622 | + | 0.494071i | ||||
\(179\) | 18.0713i | 1.35071i | 0.737491 | + | 0.675357i | \(0.236011\pi\) | ||||
−0.737491 | + | 0.675357i | \(0.763989\pi\) | |||||||
\(180\) | −12.8613 | − | 24.7516i | −0.958622 | − | 1.84487i | ||||
\(181\) | 8.00130i | 0.594732i | 0.954764 | + | 0.297366i | \(0.0961081\pi\) | ||||
−0.954764 | + | 0.297366i | \(0.903892\pi\) | |||||||
\(182\) | 0.388699 | + | 0.785643i | 0.0288123 | + | 0.0582357i | ||||
\(183\) | − | 12.7682i | − | 0.943851i | ||||||
\(184\) | −0.00200930 | + | 13.5647i | −0.000148128 | + | 1.00000i | ||||
\(185\) | 6.24979 | − | 13.2869i | 0.459494 | − | 0.976871i | ||||
\(186\) | 28.5168 | − | 14.1088i | 2.09096 | − | 1.03451i | ||||
\(187\) | 7.59829 | 0.555642 | ||||||||
\(188\) | −1.59073 | + | 2.08421i | −0.116016 | + | 0.152006i | ||||
\(189\) | − | 19.3390i | − | 1.40670i | ||||||
\(190\) | 14.1730 | − | 0.280302i | 1.02822 | − | 0.0203352i | ||||
\(191\) | −11.2451 | −0.813670 | −0.406835 | − | 0.913502i | \(-0.633368\pi\) | ||||
−0.406835 | + | 0.913502i | \(0.633368\pi\) | |||||||
\(192\) | −22.5348 | − | 9.13024i | −1.62631 | − | 0.658919i | ||||
\(193\) | 12.0682i | 0.868689i | 0.900747 | + | 0.434344i | \(0.143020\pi\) | ||||
−0.900747 | + | 0.434344i | \(0.856980\pi\) | |||||||
\(194\) | −3.93324 | − | 7.94990i | −0.282390 | − | 0.570770i | ||||
\(195\) | 1.93917 | + | 0.912131i | 0.138867 | + | 0.0653190i | ||||
\(196\) | −3.80580 | + | 4.98644i | −0.271843 | + | 0.356174i | ||||
\(197\) | − | 6.58115i | − | 0.468888i | −0.972130 | − | 0.234444i | \(-0.924673\pi\) | ||
0.972130 | − | 0.234444i | \(-0.0753269\pi\) | |||||||
\(198\) | 20.7541 | + | 41.9484i | 1.47493 | + | 2.98114i | ||||
\(199\) | −22.8257 | −1.61807 | −0.809037 | − | 0.587758i | \(-0.800011\pi\) | ||||
−0.809037 | + | 0.587758i | \(0.800011\pi\) | |||||||
\(200\) | −6.76756 | − | 12.4177i | −0.478539 | − | 0.878066i | ||||
\(201\) | 12.1344i | 0.855893i | ||||||||
\(202\) | 10.8344 | + | 21.8985i | 0.762302 | + | 1.54078i | ||||
\(203\) | − | 12.0165i | − | 0.843393i | ||||||
\(204\) | −5.28128 | + | 6.91965i | −0.369764 | + | 0.484472i | ||||
\(205\) | 0.144761 | − | 0.307757i | 0.0101105 | − | 0.0214947i | ||||
\(206\) | 13.8126 | − | 6.83384i | 0.962372 | − | 0.476136i | ||||
\(207\) | 5.71755 | + | 29.3610i | 0.397397 | + | 2.04073i | ||||
\(208\) | 1.21663 | − | 0.332743i | 0.0843581 | − | 0.0230716i | ||||
\(209\) | −23.7851 | −1.64525 | ||||||||
\(210\) | −0.373545 | − | 18.8877i | −0.0257771 | − | 1.30338i | ||||
\(211\) | 9.60875i | 0.661494i | 0.943720 | + | 0.330747i | \(0.107301\pi\) | ||||
−0.943720 | + | 0.330747i | \(0.892699\pi\) | |||||||
\(212\) | −13.1086 | + | 17.1751i | −0.900299 | + | 1.17959i | ||||
\(213\) | 1.84885i | 0.126681i | ||||||||
\(214\) | 13.4491 | − | 6.65396i | 0.919359 | − | 0.454855i | ||||
\(215\) | 18.1861 | + | 8.55423i | 1.24028 | + | 0.583394i | ||||
\(216\) | −27.3143 | − | 5.32318i | −1.85850 | − | 0.362196i | ||||
\(217\) | 14.5498 | 0.987705 | ||||||||
\(218\) | 14.6748 | − | 7.26039i | 0.993902 | − | 0.491735i | ||||
\(219\) | 43.2561i | 2.92298i | ||||||||
\(220\) | 10.9409 | + | 21.0557i | 0.737633 | + | 1.41958i | ||||
\(221\) | − | 0.451565i | − | 0.0303756i | ||||||
\(222\) | −12.5161 | − | 25.2976i | −0.840022 | − | 1.69786i | ||||
\(223\) | −6.16459 | −0.412812 | −0.206406 | − | 0.978466i | \(-0.566177\pi\) | ||||
−0.206406 | + | 0.978466i | \(0.566177\pi\) | |||||||
\(224\) | −7.38518 | − | 8.31225i | −0.493443 | − | 0.555385i | ||||
\(225\) | −19.8862 | − | 24.0230i | −1.32575 | − | 1.60153i | ||||
\(226\) | 2.23489 | + | 4.51720i | 0.148663 | + | 0.300479i | ||||
\(227\) | − | 21.9012i | − | 1.45364i | −0.686830 | − | 0.726818i | \(-0.740998\pi\) | ||
0.686830 | − | 0.726818i | \(-0.259002\pi\) | |||||||
\(228\) | 16.5321 | − | 21.6607i | 1.09487 | − | 1.43452i | ||||
\(229\) | − | 13.8844i | − | 0.917510i | −0.888563 | − | 0.458755i | \(-0.848296\pi\) | ||
0.888563 | − | 0.458755i | \(-0.151704\pi\) | |||||||
\(230\) | 3.19260 | + | 14.8259i | 0.210514 | + | 0.977591i | ||||
\(231\) | 31.6973i | 2.08553i | ||||||||
\(232\) | −16.9720 | − | 3.30762i | −1.11427 | − | 0.217156i | ||||
\(233\) | − | 17.3917i | − | 1.13937i | −0.821864 | − | 0.569684i | \(-0.807065\pi\) | ||
0.821864 | − | 0.569684i | \(-0.192935\pi\) | |||||||
\(234\) | 2.49299 | − | 1.23341i | 0.162972 | − | 0.0806307i | ||||
\(235\) | −1.24770 | + | 2.65258i | −0.0813910 | + | 0.173035i | ||||
\(236\) | 11.4877 | + | 8.76778i | 0.747787 | + | 0.570734i | ||||
\(237\) | −14.4163 | −0.936437 | ||||||||
\(238\) | −3.56797 | + | 1.76526i | −0.231277 | + | 0.114425i | ||||
\(239\) | 18.0859i | 1.16988i | 0.811076 | + | 0.584941i | \(0.198882\pi\) | ||||
−0.811076 | + | 0.584941i | \(0.801118\pi\) | |||||||
\(240\) | −26.7797 | − | 4.67138i | −1.72862 | − | 0.301536i | ||||
\(241\) | − | 6.55414i | − | 0.422189i | −0.977466 | − | 0.211095i | \(-0.932297\pi\) | ||
0.977466 | − | 0.211095i | \(-0.0677028\pi\) | |||||||
\(242\) | −10.7567 | − | 21.7416i | −0.691468 | − | 1.39760i | ||||
\(243\) | −4.49642 | −0.288446 | ||||||||
\(244\) | −6.67904 | − | 5.09765i | −0.427582 | − | 0.326343i | ||||
\(245\) | −2.98511 | + | 6.34626i | −0.190712 | + | 0.405448i | ||||
\(246\) | −0.289903 | − | 0.585955i | −0.0184835 | − | 0.0373591i | ||||
\(247\) | 1.41354i | 0.0899417i | ||||||||
\(248\) | 4.00493 | − | 20.5501i | 0.254313 | − | 1.30493i | ||||
\(249\) | 16.2054i | 1.02697i | ||||||||
\(250\) | −10.3212 | − | 11.9780i | −0.652772 | − | 0.757554i | ||||
\(251\) | −23.1792 | −1.46306 | −0.731530 | − | 0.681809i | \(-0.761193\pi\) | ||||
−0.731530 | + | 0.681809i | \(0.761193\pi\) | |||||||
\(252\) | −19.4912 | − | 14.8763i | −1.22783 | − | 0.937118i | ||||
\(253\) | −4.86382 | − | 24.9769i | −0.305786 | − | 1.57029i | ||||
\(254\) | 0.849459 | + | 1.71694i | 0.0532998 | + | 0.107730i | ||||
\(255\) | −4.14241 | + | 8.80666i | −0.259408 | + | 0.551495i | ||||
\(256\) | −13.7730 | + | 8.14278i | −0.860812 | + | 0.508924i | ||||
\(257\) | − | 17.8689i | − | 1.11463i | −0.830300 | − | 0.557317i | \(-0.811831\pi\) | ||
0.830300 | − | 0.557317i | \(-0.188169\pi\) | |||||||
\(258\) | 34.6254 | − | 17.1310i | 2.15568 | − | 1.06653i | ||||
\(259\) | − | 12.9073i | − | 0.802020i | ||||||
\(260\) | 1.25134 | − | 0.650214i | 0.0776048 | − | 0.0403246i | ||||
\(261\) | −38.1305 | −2.36022 | ||||||||
\(262\) | 11.3686 | − | 5.62467i | 0.702357 | − | 0.347493i | ||||
\(263\) | − | 2.81172i | − | 0.173378i | −0.996235 | − | 0.0866891i | \(-0.972371\pi\) | ||
0.996235 | − | 0.0866891i | \(-0.0276287\pi\) | |||||||
\(264\) | 44.7690 | + | 8.72488i | 2.75534 | + | 0.536979i | ||||
\(265\) | −10.2818 | + | 21.8588i | −0.631605 | + | 1.34278i | ||||
\(266\) | 11.1689 | − | 5.52584i | 0.684809 | − | 0.338811i | ||||
\(267\) | 31.9457i | 1.95505i | ||||||||
\(268\) | 6.34750 | + | 4.84460i | 0.387735 | + | 0.295931i | ||||
\(269\) | 21.7129 | 1.32386 | 0.661930 | − | 0.749566i | \(-0.269738\pi\) | ||||
0.661930 | + | 0.749566i | \(0.269738\pi\) | |||||||
\(270\) | −31.1067 | + | 0.615202i | −1.89309 | + | 0.0374400i | ||||
\(271\) | − | 26.6902i | − | 1.62131i | −0.585521 | − | 0.810657i | \(-0.699110\pi\) | ||
0.585521 | − | 0.810657i | \(-0.300890\pi\) | |||||||
\(272\) | 1.51114 | + | 5.52529i | 0.0916264 | + | 0.335020i | ||||
\(273\) | 1.88376 | 0.114011 | ||||||||
\(274\) | 12.7699 | + | 25.8106i | 0.771455 | + | 1.55927i | ||||
\(275\) | 16.9169 | + | 20.4359i | 1.02013 | + | 1.23233i | ||||
\(276\) | 26.1268 | + | 12.9311i | 1.57265 | + | 0.778361i | ||||
\(277\) | − | 14.3237i | − | 0.860628i | −0.902679 | − | 0.430314i | \(-0.858403\pi\) | ||
0.902679 | − | 0.430314i | \(-0.141597\pi\) | |||||||
\(278\) | −20.6416 | + | 10.2125i | −1.23800 | + | 0.612503i | ||||
\(279\) | − | 46.1692i | − | 2.76408i | ||||||
\(280\) | −10.0293 | − | 7.34545i | −0.599366 | − | 0.438975i | ||||
\(281\) | 7.07446i | 0.422027i | 0.977483 | + | 0.211013i | \(0.0676763\pi\) | ||||
−0.977483 | + | 0.211013i | \(0.932324\pi\) | |||||||
\(282\) | 2.49869 | + | 5.05038i | 0.148795 | + | 0.300746i | ||||
\(283\) | − | 7.08249i | − | 0.421010i | −0.977593 | − | 0.210505i | \(-0.932489\pi\) | ||
0.977593 | − | 0.210505i | \(-0.0675108\pi\) | |||||||
\(284\) | 0.967132 | + | 0.738144i | 0.0573887 | + | 0.0438008i | ||||
\(285\) | 12.9671 | − | 27.5677i | 0.768104 | − | 1.63297i | ||||
\(286\) | −2.12074 | + | 1.04924i | −0.125402 | + | 0.0620430i | ||||
\(287\) | − | 0.298965i | − | 0.0176473i | ||||||
\(288\) | −26.3763 | + | 23.4345i | −1.55424 | + | 1.38089i | ||||
\(289\) | −14.9492 | −0.879366 | ||||||||
\(290\) | −19.3285 | + | 0.382263i | −1.13501 | + | 0.0224472i | ||||
\(291\) | −19.0618 | −1.11742 | ||||||||
\(292\) | 22.6273 | + | 17.2698i | 1.32416 | + | 1.01064i | ||||
\(293\) | 4.07886 | 0.238289 | 0.119145 | − | 0.992877i | \(-0.461985\pi\) | ||||
0.119145 | + | 0.992877i | \(0.461985\pi\) | |||||||
\(294\) | 5.97809 | + | 12.0830i | 0.348649 | + | 0.704694i | ||||
\(295\) | 14.6205 | + | 6.87707i | 0.851236 | + | 0.400399i | ||||
\(296\) | −18.2302 | − | 3.55281i | −1.05961 | − | 0.206503i | ||||
\(297\) | 52.2031 | 3.02913 | ||||||||
\(298\) | −16.3196 | + | 8.07417i | −0.945370 | + | 0.467724i | ||||
\(299\) | −1.48438 | + | 0.289057i | −0.0858437 | + | 0.0167166i | ||||
\(300\) | −30.3690 | + | 1.20169i | −1.75335 | + | 0.0693798i | ||||
\(301\) | 17.6665 | 1.01828 | ||||||||
\(302\) | 9.93006 | − | 4.91292i | 0.571411 | − | 0.282707i | ||||
\(303\) | 52.5069 | 3.01644 | ||||||||
\(304\) | −4.73036 | − | 17.2959i | −0.271304 | − | 0.991989i | ||||
\(305\) | −8.50044 | − | 3.99838i | −0.486734 | − | 0.228946i | ||||
\(306\) | 5.60150 | + | 11.3218i | 0.320217 | + | 0.647226i | ||||
\(307\) | −12.1381 | −0.692758 | −0.346379 | − | 0.938095i | \(-0.612589\pi\) | ||||
−0.346379 | + | 0.938095i | \(0.612589\pi\) | |||||||
\(308\) | 16.5809 | + | 12.6550i | 0.944782 | + | 0.721086i | ||||
\(309\) | − | 33.1191i | − | 1.88408i | ||||||
\(310\) | −0.462851 | − | 23.4033i | −0.0262882 | − | 1.32922i | ||||
\(311\) | − | 23.4935i | − | 1.33219i | −0.745865 | − | 0.666097i | \(-0.767964\pi\) | ||
0.745865 | − | 0.666097i | \(-0.232036\pi\) | |||||||
\(312\) | 0.518518 | − | 2.66062i | 0.0293553 | − | 0.150628i | ||||
\(313\) | −1.95042 | −0.110244 | −0.0551220 | − | 0.998480i | \(-0.517555\pi\) | ||||
−0.0551220 | + | 0.998480i | \(0.517555\pi\) | |||||||
\(314\) | −3.42864 | − | 6.93001i | −0.193489 | − | 0.391083i | ||||
\(315\) | −24.8066 | − | 11.6683i | −1.39769 | − | 0.657436i | ||||
\(316\) | −5.75564 | + | 7.54116i | −0.323780 | + | 0.424223i | ||||
\(317\) | − | 0.290018i | − | 0.0162890i | −0.999967 | − | 0.00814452i | \(-0.997407\pi\) | ||
0.999967 | − | 0.00814452i | \(-0.00259251\pi\) | |||||||
\(318\) | 20.5907 | + | 41.6181i | 1.15467 | + | 2.33383i | ||||
\(319\) | 32.4370 | 1.81612 | ||||||||
\(320\) | −13.1353 | + | 12.1435i | −0.734286 | + | 0.678840i | ||||
\(321\) | − | 32.2473i | − | 1.79987i | ||||||
\(322\) | 8.08667 | + | 10.5986i | 0.450653 | + | 0.590636i | ||||
\(323\) | −6.41957 | −0.357194 | ||||||||
\(324\) | −13.5794 | + | 17.7920i | −0.754411 | + | 0.988446i | ||||
\(325\) | 1.21451 | − | 1.00537i | 0.0673687 | − | 0.0557678i | ||||
\(326\) | −3.57609 | − | 7.22804i | −0.198061 | − | 0.400324i | ||||
\(327\) | − | 35.1863i | − | 1.94580i | ||||||
\(328\) | −0.422256 | − | 0.0822919i | −0.0233152 | − | 0.00454381i | ||||
\(329\) | 2.57679i | 0.142063i | ||||||||
\(330\) | 50.9850 | − | 1.00834i | 2.80663 | − | 0.0555071i | ||||
\(331\) | − | 11.4185i | − | 0.627619i | −0.949486 | − | 0.313810i | \(-0.898395\pi\) | ||
0.949486 | − | 0.313810i | \(-0.101605\pi\) | |||||||
\(332\) | 8.47705 | + | 6.46994i | 0.465239 | + | 0.355084i | ||||
\(333\) | −40.9572 | −2.24444 | ||||||||
\(334\) | 6.33964 | + | 12.8138i | 0.346890 | + | 0.701138i | ||||
\(335\) | 8.07848 | + | 3.79990i | 0.441375 | + | 0.207611i | ||||
\(336\) | −23.0495 | + | 6.30392i | −1.25745 | + | 0.343907i | ||||
\(337\) | −17.7990 | −0.969572 | −0.484786 | − | 0.874633i | \(-0.661102\pi\) | ||||
−0.484786 | + | 0.874633i | \(0.661102\pi\) | |||||||
\(338\) | −8.09032 | − | 16.3523i | −0.440055 | − | 0.889445i | ||||
\(339\) | 10.8310 | 0.588262 | ||||||||
\(340\) | 2.95293 | + | 5.68293i | 0.160145 | + | 0.308200i | ||||
\(341\) | 39.2753i | 2.12688i | ||||||||
\(342\) | −17.5345 | − | 35.4410i | −0.948157 | − | 1.91643i | ||||
\(343\) | 19.9241i | 1.07580i | ||||||||
\(344\) | 4.86282 | − | 24.9521i | 0.262186 | − | 1.34533i | ||||
\(345\) | 31.6007 | + | 7.97952i | 1.70132 | + | 0.429603i | ||||
\(346\) | −8.42568 | + | 4.16863i | −0.452968 | + | 0.224107i | ||||
\(347\) | 6.82029 | 0.366132 | 0.183066 | − | 0.983101i | \(-0.441398\pi\) | ||||
0.183066 | + | 0.983101i | \(0.441398\pi\) | |||||||
\(348\) | −22.5457 | + | 29.5399i | −1.20858 | + | 1.58350i | ||||
\(349\) | 11.8293 | 0.633208 | 0.316604 | − | 0.948558i | \(-0.397457\pi\) | ||||
0.316604 | + | 0.948558i | \(0.397457\pi\) | |||||||
\(350\) | −12.6915 | − | 5.66604i | −0.678390 | − | 0.302862i | ||||
\(351\) | − | 3.10242i | − | 0.165595i | ||||||
\(352\) | 22.4379 | − | 19.9353i | 1.19594 | − | 1.06256i | ||||
\(353\) | 21.7201i | 1.15604i | 0.816022 | + | 0.578021i | \(0.196175\pi\) | ||||
−0.816022 | + | 0.578021i | \(0.803825\pi\) | |||||||
\(354\) | 27.8367 | − | 13.7723i | 1.47950 | − | 0.731988i | ||||
\(355\) | 1.23087 | + | 0.578969i | 0.0653279 | + | 0.0307285i | ||||
\(356\) | 16.7108 | + | 12.7542i | 0.885672 | + | 0.675972i | ||||
\(357\) | 8.55506i | 0.452782i | ||||||||
\(358\) | 22.9065 | − | 11.3331i | 1.21065 | − | 0.598970i | ||||
\(359\) | −4.50420 | −0.237723 | −0.118861 | − | 0.992911i | \(-0.537924\pi\) | ||||
−0.118861 | + | 0.992911i | \(0.537924\pi\) | |||||||
\(360\) | −23.3084 | + | 31.8248i | −1.22846 | + | 1.67732i | ||||
\(361\) | 1.09531 | 0.0576480 | ||||||||
\(362\) | 10.1421 | − | 5.01784i | 0.533058 | − | 0.263732i | ||||
\(363\) | −52.1307 | −2.73615 | ||||||||
\(364\) | 0.752086 | − | 0.985399i | 0.0394200 | − | 0.0516489i | ||||
\(365\) | 28.7979 | + | 13.5457i | 1.50735 | + | 0.709016i | ||||
\(366\) | −16.1844 | + | 8.00729i | −0.845974 | + | 0.418548i | ||||
\(367\) | − | 11.8186i | − | 0.616927i | −0.951236 | − | 0.308464i | \(-0.900185\pi\) | ||
0.951236 | − | 0.308464i | \(-0.0998148\pi\) | |||||||
\(368\) | 17.1953 | − | 8.50424i | 0.896366 | − | 0.443314i | ||||
\(369\) | −0.948669 | −0.0493857 | ||||||||
\(370\) | −20.7614 | + | 0.410600i | −1.07933 | + | 0.0213461i | ||||
\(371\) | 21.2343i | 1.10243i | ||||||||
\(372\) | −35.7675 | − | 27.2988i | −1.85446 | − | 1.41538i | ||||
\(373\) | −28.6637 | −1.48415 | −0.742075 | − | 0.670317i | \(-0.766158\pi\) | ||||
−0.742075 | + | 0.670317i | \(0.766158\pi\) | |||||||
\(374\) | −4.76511 | − | 9.63129i | −0.246398 | − | 0.498022i | ||||
\(375\) | −32.9086 | + | 8.46599i | −1.69939 | + | 0.437182i | ||||
\(376\) | 3.63945 | + | 0.709279i | 0.187690 | + | 0.0365783i | ||||
\(377\) | − | 1.92773i | − | 0.0992830i | ||||||
\(378\) | −24.5133 | + | 12.1280i | −1.26083 | + | 0.623799i | ||||
\(379\) | −30.0386 | −1.54298 | −0.771489 | − | 0.636243i | \(-0.780488\pi\) | ||||
−0.771489 | + | 0.636243i | \(0.780488\pi\) | |||||||
\(380\) | −9.24361 | − | 17.7894i | −0.474187 | − | 0.912576i | ||||
\(381\) | 4.11676 | 0.210908 | ||||||||
\(382\) | 7.05215 | + | 14.2539i | 0.360819 | + | 0.729293i | ||||
\(383\) | − | 5.76649i | − | 0.294654i | −0.989088 | − | 0.147327i | \(-0.952933\pi\) | ||
0.989088 | − | 0.147327i | \(-0.0470669\pi\) | |||||||
\(384\) | 2.55911 | + | 34.2901i | 0.130594 | + | 1.74986i | ||||
\(385\) | 21.1025 | + | 9.92605i | 1.07548 | + | 0.505878i | ||||
\(386\) | 15.2972 | − | 7.56832i | 0.778606 | − | 0.385217i | ||||
\(387\) | − | 56.0590i | − | 2.84964i | ||||||
\(388\) | −7.61034 | + | 9.97123i | −0.386356 | + | 0.506212i | ||||
\(389\) | − | 23.6265i | − | 1.19791i | −0.800782 | − | 0.598956i | \(-0.795582\pi\) | ||
0.800782 | − | 0.598956i | \(-0.204418\pi\) | |||||||
\(390\) | −0.0599253 | − | 3.03003i | −0.00303444 | − | 0.153432i | ||||
\(391\) | −1.31274 | − | 6.74125i | −0.0663882 | − | 0.340920i | ||||
\(392\) | 8.70734 | + | 1.69694i | 0.439787 | + | 0.0857086i | ||||
\(393\) | − | 27.2590i | − | 1.37504i | ||||||
\(394\) | −8.34201 | + | 4.12723i | −0.420264 | + | 0.207927i | ||||
\(395\) | −4.51448 | + | 9.59766i | −0.227148 | + | 0.482911i | ||||
\(396\) | 40.1566 | − | 52.6141i | 2.01795 | − | 2.64396i | ||||
\(397\) | 12.8794i | 0.646400i | 0.946331 | + | 0.323200i | \(0.104759\pi\) | ||||
−0.946331 | + | 0.323200i | \(0.895241\pi\) | |||||||
\(398\) | 14.3147 | + | 28.9330i | 0.717530 | + | 1.45028i | ||||
\(399\) | − | 26.7801i | − | 1.34068i | ||||||
\(400\) | −11.4961 | + | 16.3658i | −0.574805 | + | 0.818291i | ||||
\(401\) | 0.810438i | 0.0404713i | 0.999795 | + | 0.0202357i | \(0.00644165\pi\) | ||||
−0.999795 | + | 0.0202357i | \(0.993558\pi\) | |||||||
\(402\) | 15.3811 | − | 7.60981i | 0.767137 | − | 0.379543i | ||||
\(403\) | 2.33413 | 0.116271 | ||||||||
\(404\) | 20.9632 | − | 27.4664i | 1.04296 | − | 1.36650i | ||||
\(405\) | −10.6511 | + | 22.6440i | −0.529258 | + | 1.12519i | ||||
\(406\) | −15.2316 | + | 7.53589i | −0.755933 | + | 0.374000i | ||||
\(407\) | 34.8416 | 1.72703 | ||||||||
\(408\) | 12.0831 | + | 2.35484i | 0.598204 | + | 0.116582i | ||||
\(409\) | −2.68630 | −0.132829 | −0.0664145 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664145 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(410\) | −0.480884 | + | 0.00951051i | −0.0237492 | + | 0.000469690i | ||||
\(411\) | 61.8870 | 3.05266 | ||||||||
\(412\) | −17.3246 | − | 13.2227i | −0.853522 | − | 0.651433i | ||||
\(413\) | 14.2028 | 0.698873 | ||||||||
\(414\) | 33.6312 | − | 25.6605i | 1.65288 | − | 1.26114i | ||||
\(415\) | 10.7888 | + | 5.07474i | 0.529600 | + | 0.249109i | ||||
\(416\) | −1.18475 | − | 1.33348i | −0.0580874 | − | 0.0653792i | ||||
\(417\) | 49.4930i | 2.42368i | ||||||||
\(418\) | 14.9163 | + | 30.1490i | 0.729580 | + | 1.47464i | ||||
\(419\) | 15.3053 | 0.747715 | 0.373857 | − | 0.927486i | \(-0.378035\pi\) | ||||
0.373857 | + | 0.927486i | \(0.378035\pi\) | |||||||
\(420\) | −23.7071 | + | 12.3185i | −1.15679 | + | 0.601083i | ||||
\(421\) | 34.1894i | 1.66629i | 0.553056 | + | 0.833144i | \(0.313461\pi\) | ||||
−0.553056 | + | 0.833144i | \(0.686539\pi\) | |||||||
\(422\) | 12.1797 | − | 6.02592i | 0.592897 | − | 0.293337i | ||||
\(423\) | 8.17663 | 0.397562 | ||||||||
\(424\) | 29.9912 | + | 5.84488i | 1.45650 | + | 0.283853i | ||||
\(425\) | 4.56585 | + | 5.51564i | 0.221476 | + | 0.267548i | ||||
\(426\) | 2.34352 | − | 1.15946i | 0.113544 | − | 0.0561762i | ||||
\(427\) | −8.25759 | −0.399613 | ||||||||
\(428\) | −16.8686 | − | 12.8746i | −0.815374 | − | 0.622318i | ||||
\(429\) | 5.08498i | 0.245505i | ||||||||
\(430\) | −0.561998 | − | 28.4165i | −0.0271019 | − | 1.37037i | ||||
\(431\) | 7.29598 | 0.351435 | 0.175718 | − | 0.984441i | \(-0.443775\pi\) | ||||
0.175718 | + | 0.984441i | \(0.443775\pi\) | |||||||
\(432\) | 10.3821 | + | 37.9608i | 0.499509 | + | 1.82639i | ||||
\(433\) | −28.2265 | −1.35648 | −0.678239 | − | 0.734841i | \(-0.737257\pi\) | ||||
−0.678239 | + | 0.734841i | \(0.737257\pi\) | |||||||
\(434\) | −9.12460 | − | 18.4428i | −0.437995 | − | 0.885281i | ||||
\(435\) | −17.6839 | + | 37.5955i | −0.847879 | + | 1.80257i | ||||
\(436\) | −18.4060 | − | 14.0480i | −0.881485 | − | 0.672776i | ||||
\(437\) | 4.10930 | + | 21.1023i | 0.196575 | + | 1.00946i | ||||
\(438\) | 54.8298 | − | 27.1272i | 2.61987 | − | 1.29619i | ||||
\(439\) | 5.24795i | 0.250471i | 0.992127 | + | 0.125235i | \(0.0399686\pi\) | ||||
−0.992127 | + | 0.125235i | \(0.960031\pi\) | |||||||
\(440\) | 19.8281 | − | 27.0729i | 0.945268 | − | 1.29065i | ||||
\(441\) | 19.5625 | 0.931549 | ||||||||
\(442\) | −0.572387 | + | 0.283190i | −0.0272257 | + | 0.0134700i | ||||
\(443\) | −23.6676 | −1.12448 | −0.562242 | − | 0.826973i | \(-0.690061\pi\) | ||||
−0.562242 | + | 0.826973i | \(0.690061\pi\) | |||||||
\(444\) | −24.2171 | + | 31.7297i | −1.14929 | + | 1.50583i | ||||
\(445\) | 21.2679 | + | 10.0039i | 1.00820 | + | 0.474228i | ||||
\(446\) | 3.86599 | + | 7.81400i | 0.183060 | + | 0.370003i | ||||
\(447\) | 39.1301i | 1.85079i | ||||||||
\(448\) | −5.90482 | + | 14.5740i | −0.278977 | + | 0.688557i | ||||
\(449\) | 7.63135 | 0.360146 | 0.180073 | − | 0.983653i | \(-0.442367\pi\) | ||||
0.180073 | + | 0.983653i | \(0.442367\pi\) | |||||||
\(450\) | −17.9794 | + | 40.2725i | −0.847555 | + | 1.89846i | ||||
\(451\) | 0.807017 | 0.0380009 | ||||||||
\(452\) | 4.32425 | − | 5.66573i | 0.203396 | − | 0.266493i | ||||
\(453\) | − | 23.8097i | − | 1.11868i | ||||||
\(454\) | −27.7611 | + | 13.7349i | −1.30289 | + | 0.644610i | ||||
\(455\) | 0.589904 | − | 1.25412i | 0.0276551 | − | 0.0587941i | ||||
\(456\) | −37.8240 | − | 7.37139i | −1.77127 | − | 0.345197i | ||||
\(457\) | 4.49342 | 0.210193 | 0.105097 | − | 0.994462i | \(-0.466485\pi\) | ||||
0.105097 | + | 0.994462i | \(0.466485\pi\) | |||||||
\(458\) | −17.5994 | + | 8.70734i | −0.822365 | + | 0.406867i | ||||
\(459\) | 14.0896 | 0.657645 | ||||||||
\(460\) | 16.7906 | − | 13.3446i | 0.782864 | − | 0.622193i | ||||
\(461\) | 18.8701 | 0.878867 | 0.439433 | − | 0.898275i | \(-0.355179\pi\) | ||||
0.439433 | + | 0.898275i | \(0.355179\pi\) | |||||||
\(462\) | 40.1782 | − | 19.8783i | 1.86926 | − | 0.924821i | ||||
\(463\) | 17.9468 | 0.834057 | 0.417028 | − | 0.908893i | \(-0.363072\pi\) | ||||
0.417028 | + | 0.908893i | \(0.363072\pi\) | |||||||
\(464\) | 6.45104 | + | 23.5874i | 0.299482 | + | 1.09502i | ||||
\(465\) | −45.5214 | − | 21.4120i | −2.11100 | − | 0.992959i | ||||
\(466\) | −22.0450 | + | 10.9068i | −1.02122 | + | 0.505250i | ||||
\(467\) | − | 8.94489i | − | 0.413920i | −0.978349 | − | 0.206960i | \(-0.933643\pi\) | ||
0.978349 | − | 0.206960i | \(-0.0663571\pi\) | |||||||
\(468\) | −3.12685 | − | 2.38651i | −0.144539 | − | 0.110316i | ||||
\(469\) | 7.84769 | 0.362373 | ||||||||
\(470\) | 4.14477 | − | 0.0819716i | 0.191184 | − | 0.00378107i | ||||
\(471\) | −16.6163 | −0.765640 | ||||||||
\(472\) | 3.90940 | − | 20.0599i | 0.179945 | − | 0.923332i | ||||
\(473\) | 47.6885i | 2.19272i | ||||||||
\(474\) | 9.04086 | + | 18.2735i | 0.415260 | + | 0.839329i | ||||
\(475\) | −14.2926 | − | 17.2657i | −0.655788 | − | 0.792206i | ||||
\(476\) | 4.47516 | + | 3.41558i | 0.205119 | + | 0.156553i | ||||
\(477\) | 67.3803 | 3.08513 | ||||||||
\(478\) | 22.9250 | − | 11.3422i | 1.04857 | − | 0.518780i | ||||
\(479\) | 2.65650 | 0.121379 | 0.0606894 | − | 0.998157i | \(-0.480670\pi\) | ||||
0.0606894 | + | 0.998157i | \(0.480670\pi\) | |||||||
\(480\) | 10.8731 | + | 36.8745i | 0.496286 | + | 1.68308i | ||||
\(481\) | − | 2.07063i | − | 0.0944126i | ||||||
\(482\) | −8.30777 | + | 4.11029i | −0.378408 | + | 0.187218i | ||||
\(483\) | 28.1220 | − | 5.47627i | 1.27960 | − | 0.249179i | ||||
\(484\) | −20.8130 | + | 27.2696i | −0.946044 | + | 1.23953i | ||||
\(485\) | −5.96923 | + | 12.6904i | −0.271049 | + | 0.576242i | ||||
\(486\) | 2.81983 | + | 5.69949i | 0.127910 | + | 0.258534i | ||||
\(487\) | −31.3103 | −1.41880 | −0.709402 | − | 0.704804i | \(-0.751035\pi\) | ||||
−0.709402 | + | 0.704804i | \(0.751035\pi\) | |||||||
\(488\) | −2.27296 | + | 11.6630i | −0.102892 | + | 0.527958i | ||||
\(489\) | −17.3309 | −0.783732 | ||||||||
\(490\) | 9.91632 | − | 0.196116i | 0.447974 | − | 0.00885963i | ||||
\(491\) | 15.8572i | 0.715626i | 0.933793 | + | 0.357813i | \(0.116477\pi\) | ||||
−0.933793 | + | 0.357813i | \(0.883523\pi\) | |||||||
\(492\) | −0.560927 | + | 0.734938i | −0.0252885 | + | 0.0331336i | ||||
\(493\) | 8.75471 | 0.394292 | ||||||||
\(494\) | 1.79175 | − | 0.886474i | 0.0806148 | − | 0.0398844i | ||||
\(495\) | 31.4972 | − | 66.9621i | 1.41569 | − | 3.00972i | ||||
\(496\) | −28.5601 | + | 7.81105i | −1.28238 | + | 0.350726i | ||||
\(497\) | 1.19571 | 0.0536348 | ||||||||
\(498\) | 20.5413 | − | 10.1629i | 0.920478 | − | 0.455409i | ||||
\(499\) | − | 11.1197i | − | 0.497786i | −0.968531 | − | 0.248893i | \(-0.919933\pi\) | ||
0.968531 | − | 0.248893i | \(-0.0800667\pi\) | |||||||
\(500\) | −8.71007 | + | 20.5945i | −0.389526 | + | 0.921015i | ||||
\(501\) | 30.7240 | 1.37265 | ||||||||
\(502\) | 14.5364 | + | 29.3811i | 0.648790 | + | 1.31134i | ||||
\(503\) | − | 22.9162i | − | 1.02178i | −0.859646 | − | 0.510891i | \(-0.829316\pi\) | ||
0.859646 | − | 0.510891i | \(-0.170684\pi\) | |||||||
\(504\) | −6.63309 | + | 34.0357i | −0.295461 | + | 1.51607i | ||||
\(505\) | 16.4426 | − | 34.9566i | 0.731687 | − | 1.55555i | ||||
\(506\) | −28.6095 | + | 21.8289i | −1.27185 | + | 0.970415i | ||||
\(507\) | −39.2084 | −1.74131 | ||||||||
\(508\) | 1.64360 | − | 2.15348i | 0.0729230 | − | 0.0955452i | ||||
\(509\) | 33.8034 | 1.49831 | 0.749154 | − | 0.662396i | \(-0.230460\pi\) | ||||
0.749154 | + | 0.662396i | \(0.230460\pi\) | |||||||
\(510\) | 13.7608 | − | 0.272149i | 0.609339 | − | 0.0120510i | ||||
\(511\) | 27.9751 | 1.23755 | ||||||||
\(512\) | 18.9589 | + | 12.3515i | 0.837873 | + | 0.545865i | ||||
\(513\) | −44.1049 | −1.94728 | ||||||||
\(514\) | −22.6499 | + | 11.2061i | −0.999046 | + | 0.494281i | ||||
\(515\) | −22.0491 | − | 10.3713i | −0.971598 | − | 0.457014i | ||||
\(516\) | −43.4292 | − | 33.1465i | −1.91186 | − | 1.45919i | ||||
\(517\) | −6.95573 | −0.305912 | ||||||||
\(518\) | −16.3608 | + | 8.09453i | −0.718851 | + | 0.355653i | ||||
\(519\) | 20.2026i | 0.886794i | ||||||||
\(520\) | −1.60894 | − | 1.17838i | −0.0705566 | − | 0.0516755i | ||||
\(521\) | − | 37.4724i | − | 1.64170i | −0.571147 | − | 0.820848i | \(-0.693501\pi\) | ||
0.571147 | − | 0.820848i | \(-0.306499\pi\) | |||||||
\(522\) | 23.9127 | + | 48.3327i | 1.04663 | + | 2.11547i | ||||
\(523\) | 25.5681i | 1.11802i | 0.829162 | + | 0.559008i | \(0.188818\pi\) | ||||
−0.829162 | + | 0.559008i | \(0.811182\pi\) | |||||||
\(524\) | −14.2592 | − | 10.8831i | −0.622917 | − | 0.475429i | ||||
\(525\) | −23.0092 | + | 19.0470i | −1.00420 | + | 0.831281i | ||||
\(526\) | −3.56403 | + | 1.76331i | −0.155399 | + | 0.0768840i | ||||
\(527\) | 10.6004i | 0.461760i | ||||||||
\(528\) | −17.0166 | − | 62.2191i | −0.740554 | − | 2.70774i | ||||
\(529\) | −21.3194 | + | 8.63043i | −0.926929 | + | 0.375236i | ||||
\(530\) | 34.1554 | − | 0.675495i | 1.48361 | − | 0.0293416i | ||||
\(531\) | − | 45.0680i | − | 1.95578i | ||||||
\(532\) | −14.0087 | − | 10.6918i | −0.607353 | − | 0.463550i | ||||
\(533\) | − | 0.0479609i | − | 0.00207742i | ||||||
\(534\) | 40.4931 | − | 20.0341i | 1.75231 | − | 0.866959i | ||||
\(535\) | −21.4687 | − | 10.0983i | −0.928173 | − | 0.436588i | ||||
\(536\) | 2.16013 | − | 11.0840i | 0.0933033 | − | 0.478757i | ||||
\(537\) | − | 54.9238i | − | 2.37014i | ||||||
\(538\) | −13.6168 | − | 27.5224i | −0.587062 | − | 1.18658i | ||||
\(539\) | −16.6415 | −0.716800 | ||||||||
\(540\) | 20.2877 | + | 39.0438i | 0.873044 | + | 1.68018i | ||||
\(541\) | 6.58911 | 0.283288 | 0.141644 | − | 0.989918i | \(-0.454761\pi\) | ||||
0.141644 | + | 0.989918i | \(0.454761\pi\) | |||||||
\(542\) | −33.8314 | + | 16.7382i | −1.45318 | + | 0.718967i | ||||
\(543\) | − | 24.3181i | − | 1.04359i | ||||||
\(544\) | 6.05596 | − | 5.38053i | 0.259647 | − | 0.230688i | ||||
\(545\) | −23.4253 | − | 11.0186i | −1.00343 | − | 0.471987i | ||||
\(546\) | −1.18136 | − | 2.38779i | −0.0505577 | − | 0.102188i | ||||
\(547\) | 12.3733 | 0.529043 | 0.264522 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264522 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(548\) | 24.7081 | − | 32.3731i | 1.05548 | − | 1.38291i | ||||
\(549\) | 26.2028i | 1.11831i | ||||||||
\(550\) | 15.2947 | − | 34.2591i | 0.652170 | − | 1.46081i | ||||
\(551\) | −27.4051 | −1.16749 | ||||||||
\(552\) | 0.00610683 | − | 41.2267i | 0.000259924 | − | 1.75473i | ||||
\(553\) | 9.32346i | 0.396474i | ||||||||
\(554\) | −18.1562 | + | 8.98281i | −0.771381 | + | 0.381643i | ||||
\(555\) | −18.9948 | + | 40.3825i | −0.806286 | + | 1.71414i | ||||
\(556\) | 25.8898 | + | 19.7599i | 1.09797 | + | 0.838006i | ||||
\(557\) | −36.0239 | −1.52638 | −0.763190 | − | 0.646174i | \(-0.776368\pi\) | ||||
−0.763190 | + | 0.646174i | \(0.776368\pi\) | |||||||
\(558\) | −58.5222 | + | 28.9540i | −2.47744 | + | 1.22572i | ||||
\(559\) | 2.83412 | 0.119871 | ||||||||
\(560\) | −3.02113 | + | 17.3193i | −0.127666 | + | 0.731874i | ||||
\(561\) | −23.0933 | −0.975000 | ||||||||
\(562\) | 8.96730 | − | 4.43659i | 0.378263 | − | 0.187146i | ||||
\(563\) | 20.0892i | 0.846660i | 0.905976 | + | 0.423330i | \(0.139139\pi\) | ||||
−0.905976 | + | 0.423330i | \(0.860861\pi\) | |||||||
\(564\) | 4.83466 | − | 6.33448i | 0.203576 | − | 0.266730i | ||||
\(565\) | 3.39176 | − | 7.21079i | 0.142692 | − | 0.303360i | ||||
\(566\) | −8.97748 | + | 4.44163i | −0.377352 | + | 0.186696i | ||||
\(567\) | 21.9970i | 0.923789i | ||||||||
\(568\) | 0.329126 | − | 1.68881i | 0.0138098 | − | 0.0708609i | ||||
\(569\) | − | 1.67886i | − | 0.0703814i | −0.999381 | − | 0.0351907i | \(-0.988796\pi\) | ||
0.999381 | − | 0.0351907i | \(-0.0112039\pi\) | |||||||
\(570\) | −43.0757 | + | 0.851914i | −1.80424 | + | 0.0356828i | ||||
\(571\) | −22.8810 | −0.957541 | −0.478771 | − | 0.877940i | \(-0.658917\pi\) | ||||
−0.478771 | + | 0.877940i | \(0.658917\pi\) | |||||||
\(572\) | 2.65996 | + | 2.03016i | 0.111218 | + | 0.0848852i | ||||
\(573\) | 34.1771 | 1.42777 | ||||||||
\(574\) | −0.378956 | + | 0.187489i | −0.0158173 | + | 0.00782565i | ||||
\(575\) | 15.2082 | − | 18.5394i | 0.634226 | − | 0.773148i | ||||
\(576\) | 46.2460 | + | 18.7371i | 1.92692 | + | 0.780711i | ||||
\(577\) | 19.2083i | 0.799651i | 0.916591 | + | 0.399826i | \(0.130929\pi\) | ||||
−0.916591 | + | 0.399826i | \(0.869071\pi\) | |||||||
\(578\) | 9.37509 | + | 18.9491i | 0.389952 | + | 0.788177i | ||||
\(579\) | − | 36.6786i | − | 1.52431i | ||||||
\(580\) | 12.6060 | + | 24.2603i | 0.523436 | + | 1.00736i | ||||
\(581\) | 10.4805 | 0.434806 | ||||||||
\(582\) | 11.9542 | + | 24.1620i | 0.495517 | + | 1.00155i | ||||
\(583\) | −57.3193 | −2.37392 | ||||||||
\(584\) | 7.70034 | − | 39.5119i | 0.318642 | − | 1.63501i | ||||
\(585\) | −3.97955 | − | 1.87187i | −0.164534 | − | 0.0773924i | ||||
\(586\) | −2.55797 | − | 5.17020i | −0.105669 | − | 0.213579i | ||||
\(587\) | −31.4892 | −1.29970 | −0.649849 | − | 0.760064i | \(-0.725168\pi\) | ||||
−0.649849 | + | 0.760064i | \(0.725168\pi\) | |||||||
\(588\) | 11.5669 | − | 15.1552i | 0.477010 | − | 0.624989i | ||||
\(589\) | − | 33.1826i | − | 1.36726i | ||||||
\(590\) | −0.451811 | − | 22.8451i | −0.0186008 | − | 0.940519i | ||||
\(591\) | 20.0019i | 0.822770i | ||||||||
\(592\) | 6.92926 | + | 25.3359i | 0.284791 | + | 1.04130i | ||||
\(593\) | 35.6962i | 1.46587i | 0.680301 | + | 0.732933i | \(0.261849\pi\) | ||||
−0.680301 | + | 0.732933i | \(0.738151\pi\) | |||||||
\(594\) | −32.7381 | − | 66.1706i | −1.34326 | − | 2.71501i | ||||
\(595\) | 5.69555 | + | 2.67903i | 0.233495 | + | 0.109830i | ||||
\(596\) | 20.4690 | + | 15.6226i | 0.838443 | + | 0.639925i | ||||
\(597\) | 69.3737 | 2.83928 | ||||||||
\(598\) | 1.29729 | + | 1.70026i | 0.0530502 | + | 0.0695288i | ||||
\(599\) | − | 1.31702i | − | 0.0538120i | −0.999638 | − | 0.0269060i | \(-0.991435\pi\) | ||
0.999638 | − | 0.0269060i | \(-0.00856549\pi\) | |||||||
\(600\) | 20.5685 | + | 37.7409i | 0.839705 | + | 1.54077i | ||||
\(601\) | −45.1682 | −1.84245 | −0.921225 | − | 0.389030i | \(-0.872810\pi\) | ||||
−0.921225 | + | 0.389030i | \(0.872810\pi\) | |||||||
\(602\) | −11.0792 | − | 22.3934i | −0.451553 | − | 0.912686i | ||||
\(603\) | − | 24.9021i | − | 1.01409i | ||||||
\(604\) | −12.4549 | − | 9.50592i | −0.506781 | − | 0.386790i | ||||
\(605\) | −16.3248 | + | 34.7061i | −0.663698 | + | 1.41100i | ||||
\(606\) | −32.9286 | − | 66.5557i | −1.33763 | − | 2.70364i | ||||
\(607\) | 29.5404 | 1.19901 | 0.599505 | − | 0.800371i | \(-0.295364\pi\) | ||||
0.599505 | + | 0.800371i | \(0.295364\pi\) | |||||||
\(608\) | −18.9571 | + | 16.8428i | −0.768811 | + | 0.683065i | ||||
\(609\) | 36.5214i | 1.47992i | ||||||||
\(610\) | 0.262686 | + | 13.2823i | 0.0106359 | + | 0.537786i | ||||
\(611\) | 0.413378i | 0.0167235i | ||||||||
\(612\) | 10.8382 | − | 14.2005i | 0.438110 | − | 0.574021i | ||||
\(613\) | 21.6214 | 0.873280 | 0.436640 | − | 0.899636i | \(-0.356168\pi\) | ||||
0.436640 | + | 0.899636i | \(0.356168\pi\) | |||||||
\(614\) | 7.61215 | + | 15.3858i | 0.307201 | + | 0.620919i | ||||
\(615\) | −0.439967 | + | 0.935358i | −0.0177412 | + | 0.0377173i | ||||
\(616\) | 5.64266 | − | 28.9536i | 0.227349 | − | 1.16657i | ||||
\(617\) | −17.0808 | −0.687645 | −0.343823 | − | 0.939035i | \(-0.611722\pi\) | ||||
−0.343823 | + | 0.939035i | \(0.611722\pi\) | |||||||
\(618\) | −41.9804 | + | 20.7699i | −1.68870 | + | 0.835488i | ||||
\(619\) | 25.0506 | 1.00687 | 0.503434 | − | 0.864034i | \(-0.332070\pi\) | ||||
0.503434 | + | 0.864034i | \(0.332070\pi\) | |||||||
\(620\) | −29.3749 | + | 15.2636i | −1.17972 | + | 0.613001i | ||||
\(621\) | −9.01903 | − | 46.3149i | −0.361921 | − | 1.85855i | ||||
\(622\) | −29.7794 | + | 14.7335i | −1.19405 | + | 0.590758i | ||||
\(623\) | 20.6603 | 0.827738 | ||||||||
\(624\) | −3.69767 | + | 1.01130i | −0.148025 | + | 0.0404843i | ||||
\(625\) | −4.66914 | + | 24.5601i | −0.186766 | + | 0.982405i | ||||
\(626\) | 1.22316 | + | 2.47227i | 0.0488874 | + | 0.0988119i | ||||
\(627\) | 72.2894 | 2.88696 | ||||||||
\(628\) | −6.63401 | + | 8.69202i | −0.264726 | + | 0.346849i | ||||
\(629\) | 9.40371 | 0.374950 | ||||||||
\(630\) | 0.766588 | + | 38.7614i | 0.0305416 | + | 1.54429i | ||||
\(631\) | 15.7315 | 0.626261 | 0.313131 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313131 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(632\) | 13.1684 | + | 2.56634i | 0.523811 | + | 0.102084i | ||||
\(633\) | − | 29.2036i | − | 1.16074i | ||||||
\(634\) | −0.367616 | + | 0.181879i | −0.0145999 | + | 0.00722333i | ||||
\(635\) | 1.28917 | − | 2.74074i | 0.0511592 | − | 0.108763i | ||||
\(636\) | 39.8405 | − | 52.1999i | 1.57978 | − | 2.06986i | ||||
\(637\) | 0.989003i | 0.0391857i | ||||||||
\(638\) | −20.3422 | − | 41.1159i | −0.805354 | − | 1.62779i | ||||
\(639\) | − | 3.79420i | − | 0.150096i | ||||||
\(640\) | 23.6301 | + | 9.03428i | 0.934062 | + | 0.357111i | ||||
\(641\) | − | 30.3401i | − | 1.19836i | −0.800614 | − | 0.599181i | \(-0.795493\pi\) | ||
0.800614 | − | 0.599181i | \(-0.204507\pi\) | |||||||
\(642\) | −40.8754 | + | 20.2232i | −1.61322 | + | 0.798147i | ||||
\(643\) | 25.1755i | 0.992823i | 0.868087 | + | 0.496411i | \(0.165349\pi\) | ||||
−0.868087 | + | 0.496411i | \(0.834651\pi\) | |||||||
\(644\) | 8.36296 | − | 16.8970i | 0.329547 | − | 0.665836i | ||||
\(645\) | −55.2725 | − | 25.9987i | −2.17635 | − | 1.02370i | ||||
\(646\) | 4.02590 | + | 8.13719i | 0.158397 | + | 0.320154i | ||||
\(647\) | 0.617495 | 0.0242762 | 0.0121381 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121381 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(648\) | 31.0685 | + | 6.05483i | 1.22049 | + | 0.237856i | ||||
\(649\) | 38.3386i | 1.50492i | ||||||||
\(650\) | −2.03602 | − | 0.908964i | −0.0798591 | − | 0.0356525i | ||||
\(651\) | −44.2209 | −1.73315 | ||||||||
\(652\) | −6.91931 | + | 9.06582i | −0.270981 | + | 0.355045i | ||||
\(653\) | − | 9.46066i | − | 0.370224i | −0.982717 | − | 0.185112i | \(-0.940735\pi\) | ||
0.982717 | − | 0.185112i | \(-0.0592648\pi\) | |||||||
\(654\) | −44.6007 | + | 22.0663i | −1.74403 | + | 0.862861i | ||||
\(655\) | −18.1477 | − | 8.53621i | −0.709091 | − | 0.333537i | ||||
\(656\) | 0.160499 | + | 0.586842i | 0.00626642 | + | 0.0229123i | ||||
\(657\) | − | 88.7702i | − | 3.46325i | ||||||
\(658\) | 3.26624 | − | 1.61598i | 0.127331 | − | 0.0629975i | ||||
\(659\) | 5.61344 | 0.218668 | 0.109334 | − | 0.994005i | \(-0.465128\pi\) | ||||
0.109334 | + | 0.994005i | \(0.465128\pi\) | |||||||
\(660\) | −33.2523 | − | 63.9942i | −1.29434 | − | 2.49097i | ||||
\(661\) | − | 18.4372i | − | 0.717124i | −0.933506 | − | 0.358562i | \(-0.883267\pi\) | ||
0.933506 | − | 0.358562i | \(-0.116733\pi\) | |||||||
\(662\) | −14.4737 | + | 7.16089i | −0.562535 | + | 0.278316i | ||||
\(663\) | 1.37243i | 0.0533008i | ||||||||
\(664\) | 2.88484 | − | 14.8027i | 0.111953 | − | 0.574454i | ||||
\(665\) | −17.8289 | − | 8.38623i | −0.691375 | − | 0.325204i | ||||
\(666\) | 25.6854 | + | 51.9157i | 0.995290 | + | 2.01169i | ||||
\(667\) | −5.60408 | − | 28.7783i | −0.216991 | − | 1.11430i | ||||
\(668\) | 12.2664 | − | 16.0718i | 0.474603 | − | 0.621835i | ||||
\(669\) | 18.7359 | 0.724372 | ||||||||
\(670\) | −0.249647 | − | 12.6230i | −0.00964469 | − | 0.487669i | ||||
\(671\) | − | 22.2903i | − | 0.860508i | ||||||
\(672\) | 22.4456 | + | 25.2632i | 0.865857 | + | 0.974550i | ||||
\(673\) | − | 16.1011i | − | 0.620652i | −0.950630 | − | 0.310326i | \(-0.899562\pi\) | ||
0.950630 | − | 0.310326i | \(-0.100438\pi\) | |||||||
\(674\) | 11.1622 | + | 22.5613i | 0.429954 | + | 0.869028i | ||||
\(675\) | 31.3691 | + | 37.8945i | 1.20740 | + | 1.45856i | ||||
\(676\) | −15.6538 | + | 20.5099i | −0.602069 | + | 0.788844i | ||||
\(677\) | −24.6759 | −0.948371 | −0.474186 | − | 0.880425i | \(-0.657257\pi\) | ||||
−0.474186 | + | 0.880425i | \(0.657257\pi\) | |||||||
\(678\) | −6.79246 | − | 13.7290i | −0.260863 | − | 0.527259i | ||||
\(679\) | 12.3279i | 0.473100i | ||||||||
\(680\) | 5.35159 | − | 7.30694i | 0.205224 | − | 0.280208i | ||||
\(681\) | 66.5639i | 2.55073i | ||||||||
\(682\) | 49.7839 | − | 24.6307i | 1.90632 | − | 0.943158i | ||||
\(683\) | 9.43088 | 0.360862 | 0.180431 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180431 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(684\) | −33.9272 | + | 44.4521i | −1.29724 | + | 1.69967i | ||||
\(685\) | 19.3800 | − | 41.2014i | 0.740472 | − | 1.57422i | ||||
\(686\) | 25.2550 | − | 12.4950i | 0.964242 | − | 0.477061i | ||||
\(687\) | 42.1987i | 1.60998i | ||||||||
\(688\) | −34.6779 | + | 9.48424i | −1.32208 | + | 0.361583i | ||||
\(689\) | 3.40648i | 0.129777i | ||||||||
\(690\) | −9.70318 | − | 45.0600i | −0.369394 | − | 1.71540i | ||||
\(691\) | − | 37.5697i | − | 1.42922i | −0.699524 | − | 0.714610i | \(-0.746604\pi\) | ||
0.699524 | − | 0.714610i | \(-0.253396\pi\) | |||||||
\(692\) | 10.5680 | + | 8.06580i | 0.401734 | + | 0.306616i | ||||
\(693\) | − | 65.0491i | − | 2.47101i | ||||||
\(694\) | −4.27720 | − | 8.64513i | −0.162360 | − | 0.328165i | ||||
\(695\) | 32.9501 | + | 15.4988i | 1.24987 | + | 0.587904i | ||||
\(696\) | 51.5827 | + | 10.0528i | 1.95524 | + | 0.381049i | ||||
\(697\) | 0.217813 | 0.00825026 | ||||||||
\(698\) | −7.41850 | − | 14.9944i | −0.280794 | − | 0.567545i | ||||
\(699\) | 52.8582i | 1.99928i | ||||||||
\(700\) | 0.777173 | + | 19.6406i | 0.0293744 | + | 0.742345i | ||||
\(701\) | − | 31.0741i | − | 1.17365i | −0.809713 | − | 0.586826i | \(-0.800377\pi\) | ||
0.809713 | − | 0.586826i | \(-0.199623\pi\) | |||||||
\(702\) | −3.93251 | + | 1.94562i | −0.148423 | + | 0.0734327i | ||||
\(703\) | −29.4366 | −1.11022 | ||||||||
\(704\) | −39.3407 | − | 15.9393i | −1.48271 | − | 0.600735i | ||||
\(705\) | 3.79210 | − | 8.06191i | 0.142819 | − | 0.303629i | ||||
\(706\) | 27.5315 | − | 13.6213i | 1.03616 | − | 0.512643i | ||||
\(707\) | − | 33.9579i | − | 1.27712i | ||||||
\(708\) | −34.9144 | − | 26.6477i | −1.31216 | − | 1.00148i | ||||
\(709\) | 2.26915i | 0.0852196i | 0.999092 | + | 0.0426098i | \(0.0135672\pi\) | ||||
−0.999092 | + | 0.0426098i | \(0.986433\pi\) | |||||||
\(710\) | −0.0380372 | − | 1.92329i | −0.00142751 | − | 0.0721799i | ||||
\(711\) | 29.5850 | 1.10953 | ||||||||
\(712\) | 5.68689 | − | 29.1805i | 0.213125 | − | 1.09359i | ||||
\(713\) | 34.8453 | − | 6.78553i | 1.30497 | − | 0.254120i | ||||
\(714\) | 10.8441 | − | 5.36513i | 0.405829 | − | 0.200785i | ||||
\(715\) | 3.38534 | + | 1.59237i | 0.126604 | + | 0.0595513i | ||||
\(716\) | −28.7307 | − | 21.9281i | −1.07372 | − | 0.819492i | ||||
\(717\) | − | 54.9681i | − | 2.05282i | ||||||
\(718\) | 2.82471 | + | 5.70935i | 0.105417 | + | 0.213071i | ||||
\(719\) | − | 1.64576i | − | 0.0613764i | −0.999529 | − | 0.0306882i | \(-0.990230\pi\) | ||
0.999529 | − | 0.0306882i | \(-0.00976989\pi\) | |||||||
\(720\) | 54.9573 | + | 9.58659i | 2.04814 | + | 0.357271i | ||||
\(721\) | −21.4192 | −0.797691 | ||||||||
\(722\) | −0.686901 | − | 1.38837i | −0.0255638 | − | 0.0516699i | ||||
\(723\) | 19.9198i | 0.740826i | ||||||||
\(724\) | −12.7208 | − | 9.70893i | −0.472766 | − | 0.360829i | ||||
\(725\) | 19.4915 | + | 23.5462i | 0.723898 | + | 0.874484i | ||||
\(726\) | 32.6926 | + | 66.0788i | 1.21334 | + | 2.45241i | ||||
\(727\) | − | 35.3467i | − | 1.31094i | −0.755222 | − | 0.655469i | \(-0.772471\pi\) | ||
0.755222 | − | 0.655469i | \(-0.227529\pi\) | |||||||
\(728\) | −1.72071 | − | 0.335342i | −0.0637736 | − | 0.0124286i | ||||
\(729\) | −19.9072 | −0.737304 | ||||||||
\(730\) | −0.889930 | − | 44.9979i | −0.0329378 | − | 1.66545i | ||||
\(731\) | 12.8711i | 0.476054i | ||||||||
\(732\) | 20.2995 | + | 15.4932i | 0.750290 | + | 0.572643i | ||||
\(733\) | −3.58076 | −0.132258 | −0.0661292 | − | 0.997811i | \(-0.521065\pi\) | ||||
−0.0661292 | + | 0.997811i | \(0.521065\pi\) | |||||||
\(734\) | −14.9808 | + | 7.41180i | −0.552952 | + | 0.273575i | ||||
\(735\) | 9.07257 | − | 19.2880i | 0.334647 | − | 0.711450i | ||||
\(736\) | −21.5633 | − | 16.4628i | −0.794834 | − | 0.606827i | ||||
\(737\) | 21.1838i | 0.780316i | ||||||||
\(738\) | 0.594938 | + | 1.20250i | 0.0219000 | + | 0.0442645i | ||||
\(739\) | − | 42.9433i | − | 1.57969i | −0.613303 | − | 0.789847i | \(-0.710160\pi\) | ||
0.613303 | − | 0.789847i | \(-0.289840\pi\) | |||||||
\(740\) | 13.5405 | + | 26.0588i | 0.497759 | + | 0.957940i | ||||
\(741\) | − | 4.29615i | − | 0.157823i | ||||||
\(742\) | 26.9158 | − | 13.3167i | 0.988109 | − | 0.488870i | ||||
\(743\) | 24.4266i | 0.896125i | 0.894002 | + | 0.448062i | \(0.147886\pi\) | ||||
−0.894002 | + | 0.448062i | \(0.852114\pi\) | |||||||
\(744\) | −12.1721 | + | 62.4573i | −0.446250 | + | 2.28980i | ||||
\(745\) | 26.0510 | + | 12.2537i | 0.954434 | + | 0.448940i | ||||
\(746\) | 17.9758 | + | 36.3329i | 0.658141 | + | 1.33024i | ||||
\(747\) | − | 33.2567i | − | 1.21680i | ||||||
\(748\) | −9.21991 | + | 12.0801i | −0.337113 | + | 0.441693i | ||||
\(749\) | −20.8554 | −0.762039 | ||||||||
\(750\) | 31.3691 | + | 36.4044i | 1.14544 | + | 1.32930i | ||||
\(751\) | −31.2187 | −1.13919 | −0.569594 | − | 0.821927i | \(-0.692899\pi\) | ||||
−0.569594 | + | 0.821927i | \(0.692899\pi\) | |||||||
\(752\) | −1.38335 | − | 5.05803i | −0.0504455 | − | 0.184447i | ||||
\(753\) | 70.4481 | 2.56727 | ||||||||
\(754\) | −2.44351 | + | 1.20893i | −0.0889874 | + | 0.0440267i | ||||
\(755\) | −15.8513 | − | 7.45604i | −0.576889 | − | 0.271353i | ||||
\(756\) | 30.7460 | + | 23.4663i | 1.11822 | + | 0.853461i | ||||
\(757\) | −50.3322 | −1.82935 | −0.914677 | − | 0.404185i | \(-0.867555\pi\) | ||||
−0.914677 | + | 0.404185i | \(0.867555\pi\) | |||||||
\(758\) | 18.8380 | + | 38.0757i | 0.684229 | + | 1.38297i | ||||
\(759\) | 14.7825 | + | 75.9118i | 0.536571 | + | 2.75542i | ||||
\(760\) | −16.7522 | + | 22.8731i | −0.607665 | + | 0.829693i | ||||
\(761\) | 18.0523 | 0.654396 | 0.327198 | − | 0.944956i | \(-0.393896\pi\) | ||||
0.327198 | + | 0.944956i | \(0.393896\pi\) | |||||||
\(762\) | −2.58174 | − | 5.21824i | −0.0935265 | − | 0.189037i | ||||
\(763\) | −22.7561 | −0.823825 | ||||||||
\(764\) | 13.6451 | − | 17.8781i | 0.493661 | − | 0.646805i | ||||
\(765\) | 8.50106 | − | 18.0730i | 0.307356 | − | 0.653431i | ||||
\(766\) | −7.30937 | + | 3.61633i | −0.264098 | + | 0.130663i | ||||
\(767\) | 2.27846 | 0.0822703 | ||||||||
\(768\) | 41.8599 | − | 24.7481i | 1.51049 | − | 0.893022i | ||||
\(769\) | 52.1627i | 1.88103i | 0.339746 | + | 0.940517i | \(0.389659\pi\) | ||||
−0.339746 | + | 0.940517i | \(0.610341\pi\) | |||||||
\(770\) | −0.652124 | − | 32.9736i | −0.0235009 | − | 1.18829i | ||||
\(771\) | 54.3086i | 1.95588i | ||||||||
\(772\) | −19.1866 | − | 14.6438i | −0.690541 | − | 0.527042i | ||||
\(773\) | 3.28678 | 0.118217 | 0.0591086 | − | 0.998252i | \(-0.481174\pi\) | ||||
0.0591086 | + | 0.998252i | \(0.481174\pi\) | |||||||
\(774\) | −71.0582 | + | 35.1562i | −2.55414 | + | 1.26366i | ||||
\(775\) | −28.5102 | + | 23.6007i | −1.02412 | + | 0.847764i | ||||
\(776\) | 17.4118 | + | 3.39332i | 0.625047 | + | 0.121813i | ||||
\(777\) | 39.2288i | 1.40733i | ||||||||
\(778\) | −29.9481 | + | 14.8169i | −1.07369 | + | 0.531211i | ||||
\(779\) | −0.681825 | −0.0244289 | ||||||||
\(780\) | −3.80317 | + | 1.97618i | −0.136175 | + | 0.0707586i | ||||
\(781\) | 3.22766i | 0.115495i | ||||||||
\(782\) | −7.72168 | + | 5.89161i | −0.276127 | + | 0.210684i | ||||
\(783\) | 60.1482 | 2.14952 | ||||||||
\(784\) | −3.30965 | − | 12.1013i | −0.118202 | − | 0.432189i | ||||
\(785\) | −5.20343 | + | 11.0624i | −0.185718 | + | 0.394832i | ||||
\(786\) | −34.5525 | + | 17.0949i | −1.23245 | + | 0.609755i | ||||
\(787\) | − | 36.8898i | − | 1.31498i | −0.753463 | − | 0.657490i | \(-0.771618\pi\) | ||
0.753463 | − | 0.657490i | \(-0.228382\pi\) | |||||||
\(788\) | 10.4630 | + | 7.98570i | 0.372730 | + | 0.284479i | ||||
\(789\) | 8.54559i | 0.304231i | ||||||||
\(790\) | 14.9968 | − | 0.296593i | 0.533561 | − | 0.0105523i | ||||
\(791\) | − | 7.00478i | − | 0.249061i | ||||||
\(792\) | −91.8749 | − | 17.9052i | −3.26463 | − | 0.636233i | ||||
\(793\) | −1.32471 | −0.0470419 | ||||||||
\(794\) | 16.3255 | − | 8.07706i | 0.579369 | − | 0.286644i | ||||
\(795\) | 31.2492 | − | 66.4349i | 1.10829 | − | 2.35620i | ||||
\(796\) | 27.6972 | − | 36.2894i | 0.981700 | − | 1.28624i | ||||
\(797\) | 25.1170 | 0.889689 | 0.444844 | − | 0.895608i | \(-0.353259\pi\) | ||||
0.444844 | + | 0.895608i | \(0.353259\pi\) | |||||||
\(798\) | −33.9454 | + | 16.7946i | −1.20165 | + | 0.594521i | ||||
\(799\) | −1.87734 | −0.0664156 | ||||||||
\(800\) | 27.9542 | + | 4.30853i | 0.988330 | + | 0.152329i | ||||
\(801\) | − | 65.5590i | − | 2.31641i | ||||||
\(802\) | 1.02728 | − | 0.508249i | 0.0362745 | − | 0.0179469i | ||||
\(803\) | 75.5153i | 2.66488i | ||||||||
\(804\) | −19.2918 | − | 14.7241i | −0.680369 | − | 0.519278i | ||||
\(805\) | 5.16061 | − | 20.4372i | 0.181888 | − | 0.720316i | ||||
\(806\) | −1.46380 | − | 2.95865i | −0.0515601 | − | 0.104214i | ||||
\(807\) | −65.9915 | −2.32301 | ||||||||
\(808\) | −47.9619 | − | 9.34713i | −1.68729 | − | 0.328831i | ||||
\(809\) | 8.04409 | 0.282815 | 0.141408 | − | 0.989951i | \(-0.454837\pi\) | ||||
0.141408 | + | 0.989951i | \(0.454837\pi\) | |||||||
\(810\) | 35.3822 | − | 0.699759i | 1.24320 | − | 0.0245870i | ||||
\(811\) | 28.5641i | 1.00302i | 0.865152 | + | 0.501510i | \(0.167222\pi\) | ||||
−0.865152 | + | 0.501510i | \(0.832778\pi\) | |||||||
\(812\) | 19.1044 | + | 14.5810i | 0.670433 | + | 0.511694i | ||||
\(813\) | 81.1189i | 2.84496i | ||||||||
\(814\) | −21.8502 | − | 44.1638i | −0.765848 | − | 1.54794i | ||||
\(815\) | −5.42721 | + | 11.5381i | −0.190107 | + | 0.404162i | ||||
\(816\) | −4.59277 | − | 16.7929i | −0.160779 | − | 0.587868i | ||||
\(817\) | − | 40.2906i | − | 1.40959i | ||||||
\(818\) | 1.68466 | + | 3.40505i | 0.0589027 | + | 0.119055i | ||||
\(819\) | −3.86586 | −0.135084 | ||||||||
\(820\) | 0.313631 | + | 0.603585i | 0.0109525 | + | 0.0210781i | ||||
\(821\) | 0.711372 | 0.0248271 | 0.0124135 | − | 0.999923i | \(-0.496049\pi\) | ||||
0.0124135 | + | 0.999923i | \(0.496049\pi\) | |||||||
\(822\) | −38.8111 | − | 78.4455i | −1.35369 | − | 2.73610i | ||||
\(823\) | 4.70445 | 0.163987 | 0.0819934 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819934 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(824\) | −5.89576 | + | 30.2523i | −0.205389 | + | 1.05389i | ||||
\(825\) | −51.4150 | − | 62.1105i | −1.79004 | − | 2.16241i | ||||
\(826\) | −8.90697 | − | 18.0029i | −0.309913 | − | 0.626400i | ||||
\(827\) | 12.4128i | 0.431637i | 0.976433 | + | 0.215819i | \(0.0692420\pi\) | ||||
−0.976433 | + | 0.215819i | \(0.930758\pi\) | |||||||
\(828\) | −53.6173 | − | 26.5372i | −1.86333 | − | 0.922231i | ||||
\(829\) | 12.0648 | 0.419029 | 0.209514 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209514 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(830\) | −0.333402 | − | 16.8579i | −0.0115725 | − | 0.585148i | ||||
\(831\) | 43.5337i | 1.51017i | ||||||||
\(832\) | −0.947271 | + | 2.33801i | −0.0328407 | + | 0.0810560i | ||||
\(833\) | −4.49153 | −0.155622 | ||||||||
\(834\) | 62.7354 | − | 31.0385i | 2.17235 | − | 1.07478i | ||||
\(835\) | 9.62128 | − | 20.4546i | 0.332958 | − | 0.707860i | ||||
\(836\) | 28.8613 | − | 37.8146i | 0.998188 | − | 1.30785i | ||||
\(837\) | 72.8286i | 2.51732i | ||||||||
\(838\) | −9.59842 | − | 19.4004i | −0.331572 | − | 0.670177i | ||||
\(839\) | 13.2758 | 0.458331 | 0.229165 | − | 0.973388i | \(-0.426400\pi\) | ||||
0.229165 | + | 0.973388i | \(0.426400\pi\) | |||||||
\(840\) | 30.4819 | + | 22.3248i | 1.05172 | + | 0.770280i | ||||
\(841\) | 8.37376 | 0.288750 | ||||||||
\(842\) | 43.3371 | − | 21.4411i | 1.49349 | − | 0.738910i | ||||
\(843\) | − | 21.5012i | − | 0.740541i | ||||||
\(844\) | −15.2764 | − | 11.6594i | −0.525837 | − | 0.401335i | ||||
\(845\) | −12.2782 | + | 26.1031i | −0.422382 | + | 0.897973i | ||||
\(846\) | −5.12780 | − | 10.3644i | −0.176297 | − | 0.356335i | ||||
\(847\) | 33.7146i | 1.15845i | ||||||||
\(848\) | −11.3996 | − | 41.6812i | −0.391464 | − | 1.43134i | ||||
\(849\) | 21.5256i | 0.738758i | ||||||||
\(850\) | 4.12804 | − | 9.24651i | 0.141590 | − | 0.317153i | ||||
\(851\) | −6.01951 | − | 30.9117i | −0.206346 | − | 1.05964i | ||||
\(852\) | −2.93938 | − | 2.24342i | −0.100702 | − | 0.0768584i | ||||
\(853\) | 5.60642i | 0.191960i | 0.995383 | + | 0.0959801i | \(0.0305985\pi\) | ||||
−0.995383 | + | 0.0959801i | \(0.969401\pi\) | |||||||
\(854\) | 5.17857 | + | 10.4670i | 0.177207 | + | 0.358173i | ||||
\(855\) | −26.6110 | + | 56.5743i | −0.910078 | + | 1.93480i | ||||
\(856\) | −5.74058 | + | 29.4560i | −0.196209 | + | 1.00679i | ||||
\(857\) | 48.7034i | 1.66368i | 0.555017 | + | 0.831839i | \(0.312712\pi\) | ||||
−0.555017 | + | 0.831839i | \(0.687288\pi\) | |||||||
\(858\) | 6.44552 | − | 3.18894i | 0.220047 | − | 0.108869i | ||||
\(859\) | − | 18.4565i | − | 0.629729i | −0.949137 | − | 0.314865i | \(-0.898041\pi\) | ||
0.949137 | − | 0.314865i | \(-0.101959\pi\) | |||||||
\(860\) | −35.6673 | + | 18.5332i | −1.21624 | + | 0.631977i | ||||
\(861\) | 0.908636i | 0.0309662i | ||||||||
\(862\) | −4.57552 | − | 9.24810i | −0.155843 | − | 0.314992i | ||||
\(863\) | 10.6497 | 0.362520 | 0.181260 | − | 0.983435i | \(-0.441982\pi\) | ||||
0.181260 | + | 0.983435i | \(0.441982\pi\) | |||||||
\(864\) | 41.6067 | − | 36.9663i | 1.41549 | − | 1.25762i | ||||
\(865\) | 13.4499 | + | 6.32647i | 0.457310 | + | 0.215106i | ||||
\(866\) | 17.7016 | + | 35.7788i | 0.601526 | + | 1.21581i | ||||
\(867\) | 45.4348 | 1.54305 | ||||||||
\(868\) | −17.6550 | + | 23.1320i | −0.599250 | + | 0.785150i | ||||
\(869\) | −25.1675 | −0.853749 | ||||||||
\(870\) | 58.7447 | − | 1.16180i | 1.99163 | − | 0.0393887i | ||||
\(871\) | 1.25895 | 0.0426580 | ||||||||
\(872\) | −6.26376 | + | 32.1406i | −0.212118 | + | 1.08842i | ||||
\(873\) | 39.1185 | 1.32396 | ||||||||
\(874\) | 24.1713 | − | 18.4426i | 0.817608 | − | 0.623831i | ||||
\(875\) | 5.47523 | + | 21.2831i | 0.185096 | + | 0.719499i | ||||
\(876\) | −68.7706 | − | 52.4878i | −2.32354 | − | 1.77340i | ||||
\(877\) | 42.0887i | 1.42123i | 0.703579 | + | 0.710617i | \(0.251584\pi\) | ||||
−0.703579 | + | 0.710617i | \(0.748416\pi\) | |||||||
\(878\) | 6.65209 | − | 3.29114i | 0.224497 | − | 0.111071i | ||||
\(879\) | −12.3968 | −0.418133 | ||||||||
\(880\) | −46.7513 | − | 8.15515i | −1.57598 | − | 0.274910i | ||||
\(881\) | 8.00319i | 0.269634i | 0.990870 | + | 0.134817i | \(0.0430447\pi\) | ||||
−0.990870 | + | 0.134817i | \(0.956955\pi\) | |||||||
\(882\) | −12.2682 | − | 24.7967i | −0.413092 | − | 0.834948i | ||||
\(883\) | 25.1885 | 0.847660 | 0.423830 | − | 0.905742i | \(-0.360685\pi\) | ||||
0.423830 | + | 0.905742i | \(0.360685\pi\) | |||||||
\(884\) | 0.717920 | + | 0.547938i | 0.0241463 | + | 0.0184292i | ||||
\(885\) | −44.4356 | − | 20.9013i | −1.49369 | − | 0.702590i | ||||
\(886\) | 14.8427 | + | 30.0002i | 0.498649 | + | 1.00788i | ||||
\(887\) | 0.951905 | 0.0319618 | 0.0159809 | − | 0.999872i | \(-0.494913\pi\) | ||||
0.0159809 | + | 0.999872i | \(0.494913\pi\) | |||||||
\(888\) | 55.4065 | + | 10.7980i | 1.85932 | + | 0.362357i | ||||
\(889\) | − | 2.66244i | − | 0.0892954i | ||||||
\(890\) | −0.657235 | − | 33.2321i | −0.0220306 | − | 1.11394i | ||||
\(891\) | −59.3782 | −1.98925 | ||||||||
\(892\) | 7.48024 | − | 9.80076i | 0.250457 | − | 0.328154i | ||||
\(893\) | 5.87669 | 0.196656 | ||||||||
\(894\) | 49.5998 | − | 24.5396i | 1.65887 | − | 0.820728i | ||||
\(895\) | −36.5656 | − | 17.1995i | −1.22225 | − | 0.574915i | ||||
\(896\) | 22.1765 | − | 1.65506i | 0.740865 | − | 0.0552916i | ||||
\(897\) | 4.51143 | − | 0.878522i | 0.150632 | − | 0.0293330i | ||||
\(898\) | −4.78584 | − | 9.67320i | −0.159705 | − | 0.322799i | ||||
\(899\) | 45.2529i | 1.50927i | ||||||||
\(900\) | 62.3232 | − | 2.46611i | 2.07744 | − | 0.0822037i | ||||
\(901\) | −15.4704 | −0.515395 | ||||||||
\(902\) | −0.506103 | − | 1.02294i | −0.0168514 | − | 0.0340603i | ||||
\(903\) | −53.6934 | −1.78680 | ||||||||
\(904\) | −9.89352 | − | 1.92811i | −0.329053 | − | 0.0641281i | ||||
\(905\) | −16.1899 | − | 7.61527i | −0.538169 | − | 0.253140i | ||||
\(906\) | −30.1802 | + | 14.9317i | −1.00267 | + | 0.496073i | ||||
\(907\) | − | 22.9903i | − | 0.763381i | −0.924290 | − | 0.381690i | \(-0.875342\pi\) | ||
0.924290 | − | 0.381690i | \(-0.124658\pi\) | |||||||
\(908\) | 34.8196 | + | 26.5754i | 1.15553 | + | 0.881935i | ||||
\(909\) | −107.755 | −3.57399 | ||||||||
\(910\) | −1.95962 | + | 0.0387556i | −0.0649607 | + | 0.00128474i | ||||
\(911\) | −35.5666 | −1.17838 | −0.589188 | − | 0.807996i | \(-0.700552\pi\) | ||||
−0.589188 | + | 0.807996i | \(0.700552\pi\) | |||||||
\(912\) | 14.3769 | + | 52.5671i | 0.476065 | + | 1.74067i | ||||
\(913\) | 28.2909i | 0.936292i | ||||||||
\(914\) | −2.81795 | − | 5.69568i | −0.0932095 | − | 0.188396i | ||||
\(915\) | 25.8352 | + | 12.1522i | 0.854085 | + | 0.401738i | ||||
\(916\) | 22.0742 | + | 16.8477i | 0.729351 | + | 0.556662i | ||||
\(917\) | −17.6293 | −0.582170 | ||||||||
\(918\) | −8.83597 | − | 17.8594i | −0.291631 | − | 0.589447i | ||||
\(919\) | 20.0233 | 0.660507 | 0.330253 | − | 0.943892i | \(-0.392866\pi\) | ||||
0.330253 | + | 0.943892i | \(0.392866\pi\) | |||||||
\(920\) | −27.4449 | − | 12.9143i | −0.904831 | − | 0.425772i | ||||
\(921\) | 36.8910 | 1.21560 | ||||||||
\(922\) | −11.8340 | − | 23.9190i | −0.389731 | − | 0.787729i | ||||
\(923\) | 0.191819 | 0.00631381 | ||||||||
\(924\) | −50.3938 | − | 38.4621i | −1.65783 | − | 1.26531i | ||||
\(925\) | 20.9365 | + | 25.2917i | 0.688387 | + | 0.831586i | ||||
\(926\) | −11.2549 | − | 22.7486i | −0.369860 | − | 0.747566i | ||||
\(927\) | 67.9669i | 2.23232i | ||||||||
\(928\) | 25.8528 | − | 22.9694i | 0.848659 | − | 0.754008i | ||||
\(929\) | −48.4534 | −1.58970 | −0.794852 | − | 0.606803i | \(-0.792452\pi\) | ||||
−0.794852 | + | 0.606803i | \(0.792452\pi\) | |||||||
\(930\) | 1.40673 | + | 71.1292i | 0.0461285 | + | 2.33242i | ||||
\(931\) | 14.0599 | 0.460795 | ||||||||
\(932\) | 27.6502 | + | 21.1034i | 0.905711 | + | 0.691266i | ||||
\(933\) | 71.4032i | 2.33764i | ||||||||
\(934\) | −11.3382 | + | 5.60960i | −0.370997 | + | 0.183552i | ||||
\(935\) | −7.23171 | + | 15.3744i | −0.236502 | + | 0.502797i | ||||
\(936\) | −1.06410 | + | 5.46012i | −0.0347813 | + | 0.178469i | ||||
\(937\) | −5.53983 | −0.180978 | −0.0904892 | − | 0.995897i | \(-0.528843\pi\) | ||||
−0.0904892 | + | 0.995897i | \(0.528843\pi\) | |||||||
\(938\) | −4.92151 | − | 9.94742i | −0.160693 | − | 0.324795i | ||||
\(939\) | 5.92786 | 0.193448 | ||||||||
\(940\) | −2.70321 | − | 5.20234i | −0.0881689 | − | 0.169682i | ||||
\(941\) | 21.9834i | 0.716640i | 0.933599 | + | 0.358320i | \(0.116650\pi\) | ||||
−0.933599 | + | 0.358320i | \(0.883350\pi\) | |||||||
\(942\) | 10.4206 | + | 21.0622i | 0.339521 | + | 0.686244i | ||||
\(943\) | −0.139427 | − | 0.715990i | −0.00454036 | − | 0.0233159i | ||||
\(944\) | −27.8788 | + | 7.62474i | −0.907379 | + | 0.248164i | ||||
\(945\) | 39.1306 | + | 18.4060i | 1.27292 | + | 0.598746i | ||||
\(946\) | 60.4480 | − | 29.9068i | 1.96534 | − | 0.972354i | ||||
\(947\) | 2.09657 | 0.0681295 | 0.0340647 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340647 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(948\) | 17.4930 | − | 22.9197i | 0.568145 | − | 0.744396i | ||||
\(949\) | 4.48786 | 0.145682 | ||||||||
\(950\) | −12.9221 | + | 28.9445i | −0.419247 | + | 0.939084i | ||||
\(951\) | 0.881445i | 0.0285828i | ||||||||
\(952\) | 1.52295 | − | 7.81454i | 0.0493590 | − | 0.253271i | ||||
\(953\) | 14.5951 | 0.472781 | 0.236391 | − | 0.971658i | \(-0.424036\pi\) | ||||
0.236391 | + | 0.971658i | \(0.424036\pi\) | |||||||
\(954\) | −42.2562 | − | 85.4087i | −1.36809 | − | 2.76521i | ||||
\(955\) | 10.7026 | − | 22.7535i | 0.346328 | − | 0.736285i | ||||
\(956\) | −28.7539 | − | 21.9458i | −0.929966 | − | 0.709778i | ||||
\(957\) | −98.5850 | −3.18680 | ||||||||
\(958\) | −1.66597 | − | 3.36728i | −0.0538250 | − | 0.108792i | ||||
\(959\) | − | 40.0243i | − | 1.29245i | ||||||
\(960\) | 39.9218 | − | 36.9073i | 1.28847 | − | 1.19118i | ||||
\(961\) | −23.7931 | −0.767518 | ||||||||
\(962\) | −2.62465 | + | 1.29855i | −0.0846221 | + | 0.0418670i | ||||
\(963\) | 66.1779i | 2.13255i | ||||||||
\(964\) | 10.4201 | + | 7.95292i | 0.335608 | + | 0.256146i | ||||
\(965\) | −24.4189 | − | 11.4860i | −0.786071 | − | 0.369747i | ||||
\(966\) | −24.5776 | − | 32.2120i | −0.790772 | − | 1.03640i | ||||
\(967\) | 7.59575 | 0.244263 | 0.122131 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122131 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(968\) | 47.6183 | + | 9.28016i | 1.53051 | + | 0.298275i | ||||
\(969\) | 19.5108 | 0.626779 | ||||||||
\(970\) | 19.8293 | − | 0.392167i | 0.636682 | − | 0.0125917i | ||||
\(971\) | 5.38902 | 0.172942 | 0.0864710 | − | 0.996254i | \(-0.472441\pi\) | ||||
0.0864710 | + | 0.996254i | \(0.472441\pi\) | |||||||
\(972\) | 5.45604 | − | 7.14862i | 0.175003 | − | 0.229292i | ||||
\(973\) | 32.0087 | 1.02615 | ||||||||
\(974\) | 19.6356 | + | 39.6877i | 0.629165 | + | 1.27168i | ||||
\(975\) | −3.69122 | + | 3.05559i | −0.118214 | + | 0.0978572i | ||||
\(976\) | 16.2090 | − | 4.43308i | 0.518836 | − | 0.141899i | ||||
\(977\) | −36.9313 | −1.18154 | −0.590768 | − | 0.806841i | \(-0.701175\pi\) | ||||
−0.590768 | + | 0.806841i | \(0.701175\pi\) | |||||||
\(978\) | 10.8687 | + | 21.9680i | 0.347544 | + | 0.702459i | ||||
\(979\) | 55.7699i | 1.78241i | ||||||||
\(980\) | −6.46740 | − | 12.4465i | −0.206593 | − | 0.397590i | ||||
\(981\) | 72.2092i | 2.30546i | ||||||||
\(982\) | 20.1000 | − | 9.94451i | 0.641416 | − | 0.317342i | ||||
\(983\) | − | 39.8734i | − | 1.27176i | −0.771786 | − | 0.635882i | \(-0.780637\pi\) | ||
0.771786 | − | 0.635882i | \(-0.219363\pi\) | |||||||
\(984\) | 1.28335 | + | 0.250108i | 0.0409118 | + | 0.00797315i | ||||
\(985\) | 13.3163 | + | 6.26364i | 0.424294 | + | 0.199576i | ||||
\(986\) | −5.49033 | − | 11.0971i | −0.174848 | − | 0.353405i | ||||
\(987\) | − | 7.83159i | − | 0.249282i | ||||||
\(988\) | −2.24732 | − | 1.71522i | −0.0714968 | − | 0.0545685i | ||||
\(989\) | 42.3095 | − | 8.23905i | 1.34536 | − | 0.261986i | ||||
\(990\) | −104.631 | + | 2.06931i | −3.32540 | + | 0.0657669i | ||||
\(991\) | 2.38830i | 0.0758667i | 0.999280 | + | 0.0379334i | \(0.0120775\pi\) | ||||
−0.999280 | + | 0.0379334i | \(0.987923\pi\) | |||||||
\(992\) | 27.8118 | + | 31.3031i | 0.883026 | + | 0.993873i | ||||
\(993\) | 34.7041i | 1.10130i | ||||||||
\(994\) | −0.749863 | − | 1.51563i | −0.0237842 | − | 0.0480729i | ||||
\(995\) | 21.7245 | − | 46.1857i | 0.688713 | − | 1.46418i | ||||
\(996\) | −25.7641 | − | 19.6639i | −0.816366 | − | 0.623075i | ||||
\(997\) | − | 3.56721i | − | 0.112975i | −0.998403 | − | 0.0564873i | \(-0.982010\pi\) | ||
0.998403 | − | 0.0564873i | \(-0.0179900\pi\) | |||||||
\(998\) | −14.0949 | + | 6.97348i | −0.446166 | + | 0.220742i | ||||
\(999\) | 64.6070 | 2.04408 |
(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 | 460.2.g.c.459.17 | ✓ | 56 | |
4.3 | odd | 2 | inner | 460.2.g.c.459.37 | yes | 56 | |
5.4 | even | 2 | inner | 460.2.g.c.459.40 | yes | 56 | |
20.19 | odd | 2 | inner | 460.2.g.c.459.20 | yes | 56 | |
23.22 | odd | 2 | inner | 460.2.g.c.459.18 | yes | 56 | |
92.91 | even | 2 | inner | 460.2.g.c.459.38 | yes | 56 | |
115.114 | odd | 2 | inner | 460.2.g.c.459.39 | yes | 56 | |
460.459 | even | 2 | inner | 460.2.g.c.459.19 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.g.c.459.17 | ✓ | 56 | 1.1 | even | 1 | trivial | |
460.2.g.c.459.18 | yes | 56 | 23.22 | odd | 2 | inner | |
460.2.g.c.459.19 | yes | 56 | 460.459 | even | 2 | inner | |
460.2.g.c.459.20 | yes | 56 | 20.19 | odd | 2 | inner | |
460.2.g.c.459.37 | yes | 56 | 4.3 | odd | 2 | inner | |
460.2.g.c.459.38 | yes | 56 | 92.91 | even | 2 | inner | |
460.2.g.c.459.39 | yes | 56 | 115.114 | odd | 2 | inner | |
460.2.g.c.459.40 | yes | 56 | 5.4 | even | 2 | inner |