Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(107,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("400.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.s (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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 243.9 | ||
Root | \(-0.480367 + 1.33013i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.243 |
Dual form | 400.2.s.d.107.9 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38031 | − | 0.307817i | 0.976025 | − | 0.217659i | ||||
\(3\) | −2.85601 | −1.64892 | −0.824458 | − | 0.565923i | \(-0.808520\pi\) | ||||
−0.824458 | + | 0.565923i | \(0.808520\pi\) | |||||||
\(4\) | 1.81050 | − | 0.849763i | 0.905249 | − | 0.424882i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.94217 | + | 0.879127i | −1.60938 | + | 0.358902i | ||||
\(7\) | 0.458895 | − | 0.458895i | 0.173446 | − | 0.173446i | −0.615046 | − | 0.788491i | \(-0.710862\pi\) |
0.788491 | + | 0.615046i | \(0.210862\pi\) | |||||||
\(8\) | 2.23747 | − | 1.73024i | 0.791066 | − | 0.611731i | ||||
\(9\) | 5.15678 | 1.71893 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.492763 | − | 0.492763i | −0.148574 | − | 0.148574i | 0.628907 | − | 0.777481i | \(-0.283503\pi\) |
−0.777481 | + | 0.628907i | \(0.783503\pi\) | |||||||
\(12\) | −5.17080 | + | 2.42693i | −1.49268 | + | 0.700594i | ||||
\(13\) | − | 4.52109i | − | 1.25393i | −0.779049 | − | 0.626963i | \(-0.784298\pi\) | ||
0.779049 | − | 0.626963i | \(-0.215702\pi\) | |||||||
\(14\) | 0.492160 | − | 0.774671i | 0.131535 | − | 0.207040i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.55581 | − | 3.07699i | 0.638951 | − | 0.769247i | ||||
\(17\) | 3.12823 | − | 3.12823i | 0.758708 | − | 0.758708i | −0.217379 | − | 0.976087i | \(-0.569751\pi\) |
0.976087 | + | 0.217379i | \(0.0697508\pi\) | |||||||
\(18\) | 7.11794 | − | 1.58734i | 1.67772 | − | 0.374140i | ||||
\(19\) | −4.04508 | − | 4.04508i | −0.928005 | − | 0.928005i | 0.0695721 | − | 0.997577i | \(-0.477837\pi\) |
−0.997577 | + | 0.0695721i | \(0.977837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.31061 | + | 1.31061i | −0.285998 | + | 0.285998i | ||||
\(22\) | −0.831845 | − | 0.528484i | −0.177350 | − | 0.112673i | ||||
\(23\) | 1.80660 | + | 1.80660i | 0.376701 | + | 0.376701i | 0.869911 | − | 0.493209i | \(-0.164176\pi\) |
−0.493209 | + | 0.869911i | \(0.664176\pi\) | |||||||
\(24\) | −6.39024 | + | 4.94157i | −1.30440 | + | 1.00869i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.39167 | − | 6.24050i | −0.272928 | − | 1.22386i | ||||
\(27\) | −6.15978 | −1.18545 | ||||||||
\(28\) | 0.440876 | − | 1.22078i | 0.0833177 | − | 0.230706i | ||||
\(29\) | 3.83926 | − | 3.83926i | 0.712932 | − | 0.712932i | −0.254215 | − | 0.967148i | \(-0.581817\pi\) |
0.967148 | + | 0.254215i | \(0.0818172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.139949i | 0.0251356i | 0.999921 | + | 0.0125678i | \(0.00400057\pi\) | ||||
−0.999921 | + | 0.0125678i | \(0.995999\pi\) | |||||||
\(32\) | 2.58065 | − | 5.03391i | 0.456199 | − | 0.889878i | ||||
\(33\) | 1.40733 | + | 1.40733i | 0.244985 | + | 0.244985i | ||||
\(34\) | 3.35500 | − | 5.28085i | 0.575378 | − | 0.905658i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.33634 | − | 4.38204i | 1.55606 | − | 0.730340i | ||||
\(37\) | 5.84330i | 0.960633i | 0.877095 | + | 0.480317i | \(0.159478\pi\) | ||||
−0.877095 | + | 0.480317i | \(0.840522\pi\) | |||||||
\(38\) | −6.82860 | − | 4.33831i | −1.10774 | − | 0.703767i | ||||
\(39\) | 12.9123i | 2.06762i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.55648i | 0.711602i | 0.934562 | + | 0.355801i | \(0.115792\pi\) | ||||
−0.934562 | + | 0.355801i | \(0.884208\pi\) | |||||||
\(42\) | −1.40561 | + | 2.21247i | −0.216891 | + | 0.341391i | ||||
\(43\) | 7.49928i | 1.14363i | 0.820383 | + | 0.571815i | \(0.193760\pi\) | ||||
−0.820383 | + | 0.571815i | \(0.806240\pi\) | |||||||
\(44\) | −1.31088 | − | 0.473414i | −0.197622 | − | 0.0713699i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.04976 | + | 1.93756i | 0.449662 | + | 0.285677i | ||||
\(47\) | −4.14073 | − | 4.14073i | −0.603987 | − | 0.603987i | 0.337381 | − | 0.941368i | \(-0.390459\pi\) |
−0.941368 | + | 0.337381i | \(0.890459\pi\) | |||||||
\(48\) | −7.29940 | + | 8.78790i | −1.05358 | + | 1.26842i | ||||
\(49\) | 6.57883i | 0.939833i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.93426 | + | 8.93426i | −1.25105 | + | 1.25105i | ||||
\(52\) | −3.84186 | − | 8.18543i | −0.532770 | − | 1.13511i | ||||
\(53\) | −2.75773 | −0.378803 | −0.189402 | − | 0.981900i | \(-0.560655\pi\) | ||||
−0.189402 | + | 0.981900i | \(0.560655\pi\) | |||||||
\(54\) | −8.50239 | + | 1.89608i | −1.15703 | + | 0.258024i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.232768 | − | 1.82076i | 0.0311050 | − | 0.243309i | ||||
\(57\) | 11.5528 | + | 11.5528i | 1.53020 | + | 1.53020i | ||||
\(58\) | 4.11757 | − | 6.48115i | 0.540663 | − | 0.851016i | ||||
\(59\) | 3.62521 | − | 3.62521i | 0.471962 | − | 0.471962i | −0.430587 | − | 0.902549i | \(-0.641694\pi\) |
0.902549 | + | 0.430587i | \(0.141694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.72781 | + | 3.72781i | 0.477298 | + | 0.477298i | 0.904266 | − | 0.426969i | \(-0.140419\pi\) |
−0.426969 | + | 0.904266i | \(0.640419\pi\) | |||||||
\(62\) | 0.0430787 | + | 0.193173i | 0.00547100 | + | 0.0245330i | ||||
\(63\) | 2.36642 | − | 2.36642i | 0.298141 | − | 0.298141i | ||||
\(64\) | 2.01257 | − | 7.74271i | 0.251571 | − | 0.967839i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.37576 | + | 1.50935i | 0.292435 | + | 0.185789i | ||||
\(67\) | 3.32677i | 0.406430i | 0.979134 | + | 0.203215i | \(0.0651390\pi\) | ||||
−0.979134 | + | 0.203215i | \(0.934861\pi\) | |||||||
\(68\) | 3.00540 | − | 8.32192i | 0.364459 | − | 1.00918i | ||||
\(69\) | −5.15965 | − | 5.15965i | −0.621149 | − | 0.621149i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.37056 | 0.162655 | 0.0813275 | − | 0.996687i | \(-0.474084\pi\) | ||||
0.0813275 | + | 0.996687i | \(0.474084\pi\) | |||||||
\(72\) | 11.5382 | − | 8.92244i | 1.35978 | − | 1.05152i | ||||
\(73\) | −2.55028 | + | 2.55028i | −0.298488 | + | 0.298488i | −0.840422 | − | 0.541933i | \(-0.817693\pi\) |
0.541933 | + | 0.840422i | \(0.317693\pi\) | |||||||
\(74\) | 1.79867 | + | 8.06556i | 0.209091 | + | 0.937602i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.7610 | − | 3.88625i | −1.23437 | − | 0.445783i | ||||
\(77\) | −0.452252 | −0.0515389 | ||||||||
\(78\) | 3.97461 | + | 17.8229i | 0.450036 | + | 2.01805i | ||||
\(79\) | 3.86426 | 0.434763 | 0.217382 | − | 0.976087i | \(-0.430248\pi\) | ||||
0.217382 | + | 0.976087i | \(0.430248\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.12204 | 0.235782 | ||||||||
\(82\) | 1.40256 | + | 6.28934i | 0.154887 | + | 0.694541i | ||||
\(83\) | −14.4698 | −1.58827 | −0.794133 | − | 0.607744i | \(-0.792075\pi\) | ||||
−0.794133 | + | 0.607744i | \(0.792075\pi\) | |||||||
\(84\) | −1.25915 | + | 3.48655i | −0.137384 | + | 0.380414i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.30840 | + | 10.3513i | 0.248922 | + | 1.11621i | ||||
\(87\) | −10.9650 | + | 10.9650i | −1.17557 | + | 1.17557i | ||||
\(88\) | −1.95514 | − | 0.249948i | −0.208419 | − | 0.0266445i | ||||
\(89\) | 3.35011 | 0.355111 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07470 | − | 2.07470i | −0.217488 | − | 0.217488i | ||||
\(92\) | 4.80602 | + | 1.73566i | 0.501062 | + | 0.180955i | ||||
\(93\) | − | 0.399696i | − | 0.0414466i | ||||||
\(94\) | −6.99006 | − | 4.44089i | −0.720970 | − | 0.458043i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.37035 | + | 14.3769i | −0.752234 | + | 1.46733i | ||||
\(97\) | 4.95582 | − | 4.95582i | 0.503187 | − | 0.503187i | −0.409240 | − | 0.912427i | \(-0.634206\pi\) |
0.912427 | + | 0.409240i | \(0.134206\pi\) | |||||||
\(98\) | 2.02507 | + | 9.08081i | 0.204563 | + | 0.917300i | ||||
\(99\) | −2.54107 | − | 2.54107i | −0.255387 | − | 0.255387i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.84536 | + | 1.84536i | −0.183621 | + | 0.183621i | −0.792931 | − | 0.609311i | \(-0.791446\pi\) |
0.609311 | + | 0.792931i | \(0.291446\pi\) | |||||||
\(102\) | −9.58191 | + | 15.0821i | −0.948751 | + | 1.49335i | ||||
\(103\) | 11.6655 | + | 11.6655i | 1.14944 | + | 1.14944i | 0.986664 | + | 0.162773i | \(0.0520437\pi\) |
0.162773 | + | 0.986664i | \(0.447956\pi\) | |||||||
\(104\) | −7.82256 | − | 10.1158i | −0.767065 | − | 0.991938i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.80651 | + | 0.848874i | −0.369721 | + | 0.0824500i | ||||
\(107\) | 15.3106 | 1.48013 | 0.740067 | − | 0.672534i | \(-0.234794\pi\) | ||||
0.740067 | + | 0.672534i | \(0.234794\pi\) | |||||||
\(108\) | −11.1523 | + | 5.23435i | −1.07313 | + | 0.503676i | ||||
\(109\) | −12.4798 | + | 12.4798i | −1.19535 | + | 1.19535i | −0.219803 | + | 0.975544i | \(0.570542\pi\) |
−0.975544 | + | 0.219803i | \(0.929458\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 16.6885i | − | 1.58400i | ||||||
\(112\) | −0.239168 | − | 2.58486i | −0.0225993 | − | 0.244246i | ||||
\(113\) | −2.53557 | − | 2.53557i | −0.238526 | − | 0.238526i | 0.577713 | − | 0.816240i | \(-0.303945\pi\) |
−0.816240 | + | 0.577713i | \(0.803945\pi\) | |||||||
\(114\) | 19.5025 | + | 12.3903i | 1.82658 | + | 1.16045i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.68851 | − | 10.2134i | 0.342470 | − | 0.948293i | ||||
\(117\) | − | 23.3143i | − | 2.15541i | ||||||
\(118\) | 3.88800 | − | 6.11980i | 0.357919 | − | 0.563373i | ||||
\(119\) | − | 2.87106i | − | 0.263189i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.5144i | − | 0.955852i | ||||||
\(122\) | 6.29301 | + | 3.99805i | 0.569743 | + | 0.361966i | ||||
\(123\) | − | 13.0133i | − | 1.17337i | ||||||
\(124\) | 0.118924 | + | 0.253378i | 0.0106797 | + | 0.0227540i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.53796 | − | 3.99481i | 0.226100 | − | 0.355886i | ||||
\(127\) | −0.615790 | − | 0.615790i | −0.0546426 | − | 0.0546426i | 0.679257 | − | 0.733900i | \(-0.262302\pi\) |
−0.733900 | + | 0.679257i | \(0.762302\pi\) | |||||||
\(128\) | 0.394630 | − | 11.3068i | 0.0348807 | − | 0.999391i | ||||
\(129\) | − | 21.4180i | − | 1.88575i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.55413 | − | 9.55413i | 0.834748 | − | 0.834748i | −0.153414 | − | 0.988162i | \(-0.549027\pi\) |
0.988162 | + | 0.153414i | \(0.0490268\pi\) | |||||||
\(132\) | 3.74388 | + | 1.35208i | 0.325863 | + | 0.117683i | ||||
\(133\) | −3.71253 | −0.321917 | ||||||||
\(134\) | 1.02404 | + | 4.59197i | 0.0884632 | + | 0.396686i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.58676 | − | 12.4119i | 0.136063 | − | 1.06431i | ||||
\(137\) | −3.70277 | − | 3.70277i | −0.316349 | − | 0.316349i | 0.531014 | − | 0.847363i | \(-0.321811\pi\) |
−0.847363 | + | 0.531014i | \(0.821811\pi\) | |||||||
\(138\) | −8.71013 | − | 5.53368i | −0.741456 | − | 0.471058i | ||||
\(139\) | −5.46761 | + | 5.46761i | −0.463756 | + | 0.463756i | −0.899885 | − | 0.436128i | \(-0.856349\pi\) |
0.436128 | + | 0.899885i | \(0.356349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8260 | + | 11.8260i | 0.995925 | + | 0.995925i | ||||
\(142\) | 1.89179 | − | 0.421880i | 0.158755 | − | 0.0354034i | ||||
\(143\) | −2.22783 | + | 2.22783i | −0.186300 | + | 0.186300i | ||||
\(144\) | 13.1797 | − | 15.8674i | 1.09831 | − | 1.32228i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.73516 | + | 4.30520i | −0.226363 | + | 0.356301i | ||||
\(147\) | − | 18.7892i | − | 1.54971i | ||||||
\(148\) | 4.96542 | + | 10.5793i | 0.408155 | + | 0.869612i | ||||
\(149\) | −4.21561 | − | 4.21561i | −0.345356 | − | 0.345356i | 0.513021 | − | 0.858376i | \(-0.328526\pi\) |
−0.858376 | + | 0.513021i | \(0.828526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4417 | 1.01249 | 0.506244 | − | 0.862390i | \(-0.331034\pi\) | ||||
0.506244 | + | 0.862390i | \(0.331034\pi\) | |||||||
\(152\) | −16.0497 | − | 2.05181i | −1.30180 | − | 0.166424i | ||||
\(153\) | 16.1316 | − | 16.1316i | 1.30416 | − | 1.30416i | ||||
\(154\) | −0.624247 | + | 0.139211i | −0.0503033 | + | 0.0112179i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.9724 | + | 23.3777i | 0.878493 | + | 1.87171i | ||||
\(157\) | −7.50500 | −0.598964 | −0.299482 | − | 0.954102i | \(-0.596814\pi\) | ||||
−0.299482 | + | 0.954102i | \(0.596814\pi\) | |||||||
\(158\) | 5.33387 | − | 1.18948i | 0.424340 | − | 0.0946302i | ||||
\(159\) | 7.87609 | 0.624615 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.65807 | 0.130675 | ||||||||
\(162\) | 2.92907 | − | 0.653199i | 0.230129 | − | 0.0513202i | ||||
\(163\) | 23.7284 | 1.85855 | 0.929277 | − | 0.369383i | \(-0.120431\pi\) | ||||
0.929277 | + | 0.369383i | \(0.120431\pi\) | |||||||
\(164\) | 3.87193 | + | 8.24949i | 0.302347 | + | 0.644177i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.9728 | + | 4.45404i | −1.55019 | + | 0.345701i | ||||
\(167\) | 0.402976 | − | 0.402976i | 0.0311832 | − | 0.0311832i | −0.691343 | − | 0.722526i | \(-0.742981\pi\) |
0.722526 | + | 0.691343i | \(0.242981\pi\) | |||||||
\(168\) | −0.664788 | + | 5.20010i | −0.0512895 | + | 0.401197i | ||||
\(169\) | −7.44028 | −0.572330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.8596 | − | 20.8596i | −1.59517 | − | 1.59517i | ||||
\(172\) | 6.37261 | + | 13.5774i | 0.485907 | + | 1.03527i | ||||
\(173\) | 15.4500i | 1.17464i | 0.809355 | + | 0.587320i | \(0.199817\pi\) | ||||
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(174\) | −11.7598 | + | 18.5102i | −0.891509 | + | 1.40325i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.77563 | + | 0.256820i | −0.209221 | + | 0.0193585i | ||||
\(177\) | −10.3536 | + | 10.3536i | −0.778225 | + | 0.778225i | ||||
\(178\) | 4.62419 | − | 1.03122i | 0.346597 | − | 0.0772932i | ||||
\(179\) | −5.20444 | − | 5.20444i | −0.388998 | − | 0.388998i | 0.485332 | − | 0.874330i | \(-0.338699\pi\) |
−0.874330 | + | 0.485332i | \(0.838699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.08925 | + | 9.08925i | −0.675599 | + | 0.675599i | −0.959001 | − | 0.283402i | \(-0.908537\pi\) |
0.283402 | + | 0.959001i | \(0.408537\pi\) | |||||||
\(182\) | −3.50236 | − | 2.22510i | −0.259612 | − | 0.164936i | ||||
\(183\) | −10.6467 | − | 10.6467i | −0.787024 | − | 0.787024i | ||||
\(184\) | 7.16804 | + | 0.916372i | 0.528435 | + | 0.0675559i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.123033 | − | 0.551704i | −0.00902123 | − | 0.0404529i | ||||
\(187\) | −3.08295 | −0.225448 | ||||||||
\(188\) | −11.0154 | − | 3.97814i | −0.803382 | − | 0.290136i | ||||
\(189\) | −2.82669 | + | 2.82669i | −0.205611 | + | 0.205611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1075i | 1.09314i | 0.837413 | + | 0.546571i | \(0.184067\pi\) | ||||
−0.837413 | + | 0.546571i | \(0.815933\pi\) | |||||||
\(192\) | −5.74791 | + | 22.1132i | −0.414820 | + | 1.59589i | ||||
\(193\) | −4.19166 | − | 4.19166i | −0.301722 | − | 0.301722i | 0.539965 | − | 0.841687i | \(-0.318437\pi\) |
−0.841687 | + | 0.539965i | \(0.818437\pi\) | |||||||
\(194\) | 5.31507 | − | 8.36604i | 0.381600 | − | 0.600647i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.59045 | + | 11.9110i | 0.399318 | + | 0.850783i | ||||
\(197\) | − | 4.03184i | − | 0.287256i | −0.989632 | − | 0.143628i | \(-0.954123\pi\) | ||
0.989632 | − | 0.143628i | \(-0.0458769\pi\) | |||||||
\(198\) | −4.28964 | − | 2.72527i | −0.304852 | − | 0.193677i | ||||
\(199\) | 5.43055i | 0.384961i | 0.981301 | + | 0.192481i | \(0.0616533\pi\) | ||||
−0.981301 | + | 0.192481i | \(0.938347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.50129i | − | 0.670169i | ||||||
\(202\) | −1.97914 | + | 3.11520i | −0.139252 | + | 0.219185i | ||||
\(203\) | − | 3.52363i | − | 0.247310i | ||||||
\(204\) | −8.58345 | + | 23.7675i | −0.600962 | + | 1.66405i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.6928 | + | 12.5111i | 1.37206 | + | 0.871693i | ||||
\(207\) | 9.31622 | + | 9.31622i | 0.647522 | + | 0.647522i | ||||
\(208\) | −13.9114 | − | 11.5550i | −0.964579 | − | 0.801197i | ||||
\(209\) | 3.98653i | 0.275754i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.23020 | − | 3.23020i | 0.222376 | − | 0.222376i | −0.587122 | − | 0.809498i | \(-0.699739\pi\) |
0.809498 | + | 0.587122i | \(0.199739\pi\) | |||||||
\(212\) | −4.99286 | + | 2.34342i | −0.342911 | + | 0.160946i | ||||
\(213\) | −3.91432 | −0.268205 | ||||||||
\(214\) | 21.1334 | − | 4.71286i | 1.44465 | − | 0.322165i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −13.7823 | + | 10.6579i | −0.937770 | + | 0.725176i | ||||
\(217\) | 0.0642220 | + | 0.0642220i | 0.00435967 | + | 0.00435967i | ||||
\(218\) | −13.3845 | + | 21.0674i | −0.906511 | + | 1.42687i | ||||
\(219\) | 7.28363 | − | 7.28363i | 0.492182 | − | 0.492182i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.1430 | − | 14.1430i | −0.951363 | − | 0.951363i | ||||
\(222\) | −5.13700 | − | 23.0353i | −0.344773 | − | 1.54603i | ||||
\(223\) | −8.17319 | + | 8.17319i | −0.547317 | + | 0.547317i | −0.925664 | − | 0.378347i | \(-0.876493\pi\) |
0.378347 | + | 0.925664i | \(0.376493\pi\) | |||||||
\(224\) | −1.12579 | − | 3.49428i | −0.0752199 | − | 0.233471i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.28035 | − | 2.71937i | −0.284725 | − | 0.180890i | ||||
\(227\) | − | 1.54068i | − | 0.102258i | −0.998692 | − | 0.0511292i | \(-0.983718\pi\) | ||
0.998692 | − | 0.0511292i | \(-0.0162820\pi\) | |||||||
\(228\) | 30.7334 | + | 11.0992i | 2.03537 | + | 0.735060i | ||||
\(229\) | 17.5646 | + | 17.5646i | 1.16070 | + | 1.16070i | 0.984322 | + | 0.176378i | \(0.0564382\pi\) |
0.176378 | + | 0.984322i | \(0.443562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.29164 | 0.0849834 | ||||||||
\(232\) | 1.94741 | − | 15.2331i | 0.127854 | − | 1.00010i | ||||
\(233\) | 9.99018 | − | 9.99018i | 0.654479 | − | 0.654479i | −0.299590 | − | 0.954068i | \(-0.596850\pi\) |
0.954068 | + | 0.299590i | \(0.0968498\pi\) | |||||||
\(234\) | −7.17652 | − | 32.1809i | −0.469144 | − | 2.10373i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.48286 | − | 9.64399i | 0.226715 | − | 0.627771i | ||||
\(237\) | −11.0364 | −0.716889 | ||||||||
\(238\) | −0.883759 | − | 3.96294i | −0.0572856 | − | 0.256879i | ||||
\(239\) | −26.2762 | −1.69967 | −0.849833 | − | 0.527052i | \(-0.823297\pi\) | ||||
−0.849833 | + | 0.527052i | \(0.823297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.113242 | −0.00729456 | −0.00364728 | − | 0.999993i | \(-0.501161\pi\) | ||||
−0.00364728 | + | 0.999993i | \(0.501161\pi\) | |||||||
\(242\) | −3.23650 | − | 14.5131i | −0.208050 | − | 0.932935i | ||||
\(243\) | 12.4188 | 0.796665 | ||||||||
\(244\) | 9.91696 | + | 3.58144i | 0.634868 | + | 0.229278i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.00572 | − | 17.9624i | −0.255395 | − | 1.14524i | ||||
\(247\) | −18.2882 | + | 18.2882i | −1.16365 | + | 1.16365i | ||||
\(248\) | 0.242145 | + | 0.313133i | 0.0153762 | + | 0.0198840i | ||||
\(249\) | 41.3258 | 2.61892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2220 | + | 19.2220i | 1.21328 | + | 1.21328i | 0.969941 | + | 0.243339i | \(0.0782427\pi\) |
0.243339 | + | 0.969941i | \(0.421757\pi\) | |||||||
\(252\) | 2.27350 | − | 6.29529i | 0.143217 | − | 0.396566i | ||||
\(253\) | − | 1.78045i | − | 0.111936i | ||||||
\(254\) | −1.03953 | − | 0.660430i | −0.0652260 | − | 0.0414390i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.93572 | − | 15.7284i | −0.183482 | − | 0.983023i | ||||
\(257\) | 0.757800 | − | 0.757800i | 0.0472703 | − | 0.0472703i | −0.683077 | − | 0.730347i | \(-0.739358\pi\) |
0.730347 | + | 0.683077i | \(0.239358\pi\) | |||||||
\(258\) | −6.59282 | − | 29.5634i | −0.410451 | − | 1.84054i | ||||
\(259\) | 2.68146 | + | 2.68146i | 0.166618 | + | 0.166618i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.7982 | − | 19.7982i | 1.22548 | − | 1.22548i | ||||
\(262\) | 10.2467 | − | 16.1286i | 0.633044 | − | 0.996425i | ||||
\(263\) | −5.73017 | − | 5.73017i | −0.353338 | − | 0.353338i | 0.508012 | − | 0.861350i | \(-0.330380\pi\) |
−0.861350 | + | 0.508012i | \(0.830380\pi\) | |||||||
\(264\) | 5.58389 | + | 0.713852i | 0.343665 | + | 0.0439346i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.12443 | + | 1.14278i | −0.314199 | + | 0.0700682i | ||||
\(267\) | −9.56795 | −0.585549 | ||||||||
\(268\) | 2.82697 | + | 6.02311i | 0.172685 | + | 0.367920i | ||||
\(269\) | −9.78879 | + | 9.78879i | −0.596833 | + | 0.596833i | −0.939468 | − | 0.342635i | \(-0.888680\pi\) |
0.342635 | + | 0.939468i | \(0.388680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.10159i | 0.249154i | 0.992210 | + | 0.124577i | \(0.0397574\pi\) | ||||
−0.992210 | + | 0.124577i | \(0.960243\pi\) | |||||||
\(272\) | −1.63038 | − | 17.6207i | −0.0988565 | − | 1.06841i | ||||
\(273\) | 5.92537 | + | 5.92537i | 0.358620 | + | 0.358620i | ||||
\(274\) | −6.25074 | − | 3.97119i | −0.377621 | − | 0.239908i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.7260 | − | 4.95706i | −0.826209 | − | 0.298380i | ||||
\(277\) | 24.6755i | 1.48261i | 0.671169 | + | 0.741305i | \(0.265793\pi\) | ||||
−0.671169 | + | 0.741305i | \(0.734207\pi\) | |||||||
\(278\) | −5.86396 | + | 9.23000i | −0.351697 | + | 0.553578i | ||||
\(279\) | 0.721688i | 0.0432063i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.6688i | − | 1.41196i | −0.708230 | − | 0.705981i | \(-0.750506\pi\) | ||
0.708230 | − | 0.705981i | \(-0.249494\pi\) | |||||||
\(282\) | 19.9637 | + | 12.6832i | 1.18882 | + | 0.755275i | ||||
\(283\) | − | 13.0492i | − | 0.775694i | −0.921724 | − | 0.387847i | \(-0.873219\pi\) | ||
0.921724 | − | 0.387847i | \(-0.126781\pi\) | |||||||
\(284\) | 2.48139 | − | 1.16465i | 0.147243 | − | 0.0691091i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.38932 | + | 3.76085i | −0.141284 | + | 0.222384i | ||||
\(287\) | 2.09094 | + | 2.09094i | 0.123424 | + | 0.123424i | ||||
\(288\) | 13.3078 | − | 25.9588i | 0.784172 | − | 1.52963i | ||||
\(289\) | − | 2.57168i | − | 0.151275i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1539 | + | 14.1539i | −0.829714 | + | 0.829714i | ||||
\(292\) | −2.45015 | + | 6.78442i | −0.143384 | + | 0.397028i | ||||
\(293\) | 31.6731 | 1.85036 | 0.925181 | − | 0.379526i | \(-0.123913\pi\) | ||||
0.925181 | + | 0.379526i | \(0.123913\pi\) | |||||||
\(294\) | −5.78363 | − | 25.9349i | −0.337308 | − | 1.51255i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.1103 | + | 13.0742i | 0.587649 | + | 0.759924i | ||||
\(297\) | 3.03531 | + | 3.03531i | 0.176127 | + | 0.176127i | ||||
\(298\) | −7.11646 | − | 4.52120i | −0.412246 | − | 0.261906i | ||||
\(299\) | 8.16779 | − | 8.16779i | 0.472355 | − | 0.472355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.44138 | + | 3.44138i | 0.198358 | + | 0.198358i | ||||
\(302\) | 17.1733 | − | 3.82975i | 0.988213 | − | 0.220377i | ||||
\(303\) | 5.27037 | − | 5.27037i | 0.302775 | − | 0.302775i | ||||
\(304\) | −22.7851 | + | 2.10823i | −1.30682 | + | 0.120915i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.3010 | − | 27.2322i | 0.989033 | − | 1.55676i | ||||
\(307\) | − | 27.3597i | − | 1.56150i | −0.624843 | − | 0.780751i | \(-0.714837\pi\) | ||
0.624843 | − | 0.780751i | \(-0.285163\pi\) | |||||||
\(308\) | −0.818802 | + | 0.384307i | −0.0466556 | + | 0.0218979i | ||||
\(309\) | −33.3168 | − | 33.3168i | −1.89532 | − | 1.89532i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.8076 | −0.896368 | −0.448184 | − | 0.893941i | \(-0.647929\pi\) | ||||
−0.448184 | + | 0.893941i | \(0.647929\pi\) | |||||||
\(312\) | 22.3413 | + | 28.8909i | 1.26483 | + | 1.63562i | ||||
\(313\) | −13.8388 | + | 13.8388i | −0.782217 | + | 0.782217i | −0.980205 | − | 0.197988i | \(-0.936559\pi\) |
0.197988 | + | 0.980205i | \(0.436559\pi\) | |||||||
\(314\) | −10.3592 | + | 2.31016i | −0.584604 | + | 0.130370i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.99624 | − | 3.28371i | 0.393569 | − | 0.184723i | ||||
\(317\) | 35.0092 | 1.96631 | 0.983156 | − | 0.182766i | \(-0.0585051\pi\) | ||||
0.983156 | + | 0.182766i | \(0.0585051\pi\) | |||||||
\(318\) | 10.8714 | − | 2.42439i | 0.609639 | − | 0.135953i | ||||
\(319\) | −3.78369 | −0.211846 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −43.7272 | −2.44062 | ||||||||
\(322\) | 2.28865 | − | 0.510383i | 0.127542 | − | 0.0284425i | ||||
\(323\) | −25.3079 | −1.40817 | ||||||||
\(324\) | 3.84195 | − | 1.80323i | 0.213442 | − | 0.100180i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.7525 | − | 7.30401i | 1.81400 | − | 0.404532i | ||||
\(327\) | 35.6424 | − | 35.6424i | 1.97103 | − | 1.97103i | ||||
\(328\) | 7.88378 | + | 10.1950i | 0.435309 | + | 0.562924i | ||||
\(329\) | −3.80032 | −0.209518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8212 | + | 16.8212i | 0.924578 | + | 0.924578i | 0.997349 | − | 0.0727709i | \(-0.0231842\pi\) |
−0.0727709 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(332\) | −26.1975 | + | 12.2959i | −1.43778 | + | 0.674825i | ||||
\(333\) | 30.1326i | 1.65126i | ||||||||
\(334\) | 0.432188 | − | 0.680273i | 0.0236483 | − | 0.0372229i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.683066 | + | 7.38238i | 0.0372643 | + | 0.402742i | ||||
\(337\) | −14.4984 | + | 14.4984i | −0.789777 | + | 0.789777i | −0.981457 | − | 0.191680i | \(-0.938606\pi\) |
0.191680 | + | 0.981457i | \(0.438606\pi\) | |||||||
\(338\) | −10.2699 | + | 2.29024i | −0.558608 | + | 0.124573i | ||||
\(339\) | 7.24160 | + | 7.24160i | 0.393310 | + | 0.393310i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0689618 | − | 0.0689618i | 0.00373449 | − | 0.00373449i | ||||
\(342\) | −35.2136 | − | 22.3717i | −1.90413 | − | 1.20972i | ||||
\(343\) | 6.23125 | + | 6.23125i | 0.336456 | + | 0.336456i | ||||
\(344\) | 12.9755 | + | 16.7794i | 0.699593 | + | 0.904687i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.75576 | + | 21.3257i | 0.255671 | + | 1.14648i | ||||
\(347\) | 16.7705 | 0.900286 | 0.450143 | − | 0.892956i | \(-0.351373\pi\) | ||||
0.450143 | + | 0.892956i | \(0.351373\pi\) | |||||||
\(348\) | −10.5344 | + | 29.1696i | −0.564704 | + | 1.56366i | ||||
\(349\) | −1.86337 | + | 1.86337i | −0.0997439 | + | 0.0997439i | −0.755218 | − | 0.655474i | \(-0.772469\pi\) |
0.655474 | + | 0.755218i | \(0.272469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.8489i | 1.48647i | ||||||||
\(352\) | −3.75217 | + | 1.20888i | −0.199991 | + | 0.0644333i | ||||
\(353\) | −24.1362 | − | 24.1362i | −1.28464 | − | 1.28464i | −0.937998 | − | 0.346642i | \(-0.887322\pi\) |
−0.346642 | − | 0.937998i | \(-0.612678\pi\) | |||||||
\(354\) | −11.1042 | + | 17.4782i | −0.590179 | + | 0.928955i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.06537 | − | 2.84680i | 0.321464 | − | 0.150880i | ||||
\(357\) | 8.19976i | 0.433978i | ||||||||
\(358\) | −8.78574 | − | 5.58171i | −0.464341 | − | 0.295003i | ||||
\(359\) | − | 12.2500i | − | 0.646532i | −0.946308 | − | 0.323266i | \(-0.895219\pi\) | ||
0.946308 | − | 0.323266i | \(-0.104781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7253i | 0.722386i | ||||||||
\(362\) | −9.74814 | + | 15.3438i | −0.512351 | + | 0.806451i | ||||
\(363\) | 30.0291i | 1.57612i | ||||||||
\(364\) | −5.51926 | − | 1.99324i | −0.289288 | − | 0.104474i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.9729 | − | 11.4185i | −0.939458 | − | 0.596852i | ||||
\(367\) | 2.71307 | + | 2.71307i | 0.141621 | + | 0.141621i | 0.774363 | − | 0.632742i | \(-0.218071\pi\) |
−0.632742 | + | 0.774363i | \(0.718071\pi\) | |||||||
\(368\) | 10.1762 | − | 0.941567i | 0.530470 | − | 0.0490826i | ||||
\(369\) | 23.4967i | 1.22319i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26551 | + | 1.26551i | −0.0657018 | + | 0.0657018i | ||||
\(372\) | −0.339647 | − | 0.723649i | −0.0176099 | − | 0.0375195i | ||||
\(373\) | −16.4846 | −0.853541 | −0.426771 | − | 0.904360i | \(-0.640349\pi\) | ||||
−0.426771 | + | 0.904360i | \(0.640349\pi\) | |||||||
\(374\) | −4.25542 | + | 0.948984i | −0.220043 | + | 0.0490708i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.4292 | − | 2.10033i | −0.847272 | − | 0.108316i | ||||
\(377\) | −17.3576 | − | 17.3576i | −0.893964 | − | 0.893964i | ||||
\(378\) | −3.03160 | + | 4.77180i | −0.155929 | + | 0.245435i | ||||
\(379\) | 13.7716 | − | 13.7716i | 0.707401 | − | 0.707401i | −0.258587 | − | 0.965988i | \(-0.583257\pi\) |
0.965988 | + | 0.258587i | \(0.0832568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.75870 | + | 1.75870i | 0.0901011 | + | 0.0901011i | ||||
\(382\) | 4.65034 | + | 20.8530i | 0.237932 | + | 1.06693i | ||||
\(383\) | 11.5530 | − | 11.5530i | 0.590332 | − | 0.590332i | −0.347389 | − | 0.937721i | \(-0.612932\pi\) |
0.937721 | + | 0.347389i | \(0.112932\pi\) | |||||||
\(384\) | −1.12707 | + | 32.2924i | −0.0575153 | + | 1.64791i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.07604 | − | 4.49552i | −0.360161 | − | 0.228816i | ||||
\(387\) | 38.6722i | 1.96582i | ||||||||
\(388\) | 4.76123 | − | 13.1838i | 0.241715 | − | 0.669305i | ||||
\(389\) | 15.7728 | + | 15.7728i | 0.799712 | + | 0.799712i | 0.983050 | − | 0.183338i | \(-0.0586903\pi\) |
−0.183338 | + | 0.983050i | \(0.558690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3029 | 0.571612 | ||||||||
\(392\) | 11.3829 | + | 14.7200i | 0.574925 | + | 0.743470i | ||||
\(393\) | −27.2867 | + | 27.2867i | −1.37643 | + | 1.37643i | ||||
\(394\) | −1.24107 | − | 5.56517i | −0.0625240 | − | 0.280369i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.75991 | − | 2.44129i | −0.339698 | − | 0.122680i | ||||
\(397\) | −29.9558 | −1.50344 | −0.751720 | − | 0.659483i | \(-0.770775\pi\) | ||||
−0.751720 | + | 0.659483i | \(0.770775\pi\) | |||||||
\(398\) | 1.67161 | + | 7.49583i | 0.0837904 | + | 0.375732i | ||||
\(399\) | 10.6030 | 0.530815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9241 | 0.994963 | 0.497481 | − | 0.867475i | \(-0.334258\pi\) | ||||
0.497481 | + | 0.867475i | \(0.334258\pi\) | |||||||
\(402\) | −2.92465 | − | 13.1147i | −0.145868 | − | 0.654102i | ||||
\(403\) | 0.632724 | 0.0315182 | ||||||||
\(404\) | −1.77291 | + | 4.90915i | −0.0882054 | + | 0.244239i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.08463 | − | 4.86369i | −0.0538294 | − | 0.241381i | ||||
\(407\) | 2.87936 | − | 2.87936i | 0.142725 | − | 0.142725i | ||||
\(408\) | −4.53179 | + | 35.4485i | −0.224357 | + | 1.75496i | ||||
\(409\) | −5.89856 | −0.291665 | −0.145832 | − | 0.989309i | \(-0.546586\pi\) | ||||
−0.145832 | + | 0.989309i | \(0.546586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5751 | + | 10.5751i | 0.521634 | + | 0.521634i | ||||
\(412\) | 31.0333 | + | 11.2075i | 1.52890 | + | 0.552152i | ||||
\(413\) | − | 3.32717i | − | 0.163720i | ||||||
\(414\) | 15.7269 | + | 9.99156i | 0.772936 | + | 0.491058i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.7588 | − | 11.6674i | −1.11584 | − | 0.572039i | ||||
\(417\) | 15.6155 | − | 15.6155i | 0.764696 | − | 0.764696i | ||||
\(418\) | 1.22712 | + | 5.50264i | 0.0600204 | + | 0.269143i | ||||
\(419\) | −8.24430 | − | 8.24430i | −0.402760 | − | 0.402760i | 0.476444 | − | 0.879205i | \(-0.341925\pi\) |
−0.879205 | + | 0.476444i | \(0.841925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1776 | + | 17.1776i | −0.837184 | + | 0.837184i | −0.988487 | − | 0.151304i | \(-0.951653\pi\) |
0.151304 | + | 0.988487i | \(0.451653\pi\) | |||||||
\(422\) | 3.46436 | − | 5.45297i | 0.168642 | − | 0.265447i | ||||
\(423\) | −21.3528 | − | 21.3528i | −1.03821 | − | 1.03821i | ||||
\(424\) | −6.17034 | + | 4.77152i | −0.299658 | + | 0.231725i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.40296 | + | 1.20489i | −0.261774 | + | 0.0583772i | ||||
\(427\) | 3.42135 | 0.165571 | ||||||||
\(428\) | 27.7198 | − | 13.0104i | 1.33989 | − | 0.628881i | ||||
\(429\) | 6.36269 | − | 6.36269i | 0.307194 | − | 0.307194i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.1769i | − | 1.54990i | −0.632020 | − | 0.774952i | \(-0.717774\pi\) | ||
0.632020 | − | 0.774952i | \(-0.282226\pi\) | |||||||
\(432\) | −15.7432 | + | 18.9536i | −0.757445 | + | 0.911904i | ||||
\(433\) | 20.3383 | + | 20.3383i | 0.977396 | + | 0.977396i | 0.999750 | − | 0.0223540i | \(-0.00711609\pi\) |
−0.0223540 | + | 0.999750i | \(0.507116\pi\) | |||||||
\(434\) | 0.108415 | + | 0.0688775i | 0.00520407 | + | 0.00330623i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.9898 | + | 33.1995i | −0.574206 | + | 1.58997i | ||||
\(437\) | − | 14.6156i | − | 0.699161i | ||||||
\(438\) | 7.81163 | − | 12.2957i | 0.373254 | − | 0.587510i | ||||
\(439\) | 35.4180i | 1.69041i | 0.534444 | + | 0.845204i | \(0.320521\pi\) | ||||
−0.534444 | + | 0.845204i | \(0.679479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.9256i | 1.61550i | ||||||||
\(442\) | −23.8752 | − | 15.1683i | −1.13563 | − | 0.721481i | ||||
\(443\) | 3.03787i | 0.144333i | 0.997393 | + | 0.0721667i | \(0.0229913\pi\) | ||||
−0.997393 | + | 0.0721667i | \(0.977009\pi\) | |||||||
\(444\) | −14.1813 | − | 30.2145i | −0.673014 | − | 1.43392i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.76567 | + | 13.7974i | −0.415067 | + | 0.653324i | ||||
\(447\) | 12.0398 | + | 12.0398i | 0.569463 | + | 0.569463i | ||||
\(448\) | −2.62953 | − | 4.47664i | −0.124234 | − | 0.211502i | ||||
\(449\) | 8.65559i | 0.408483i | 0.978921 | + | 0.204241i | \(0.0654727\pi\) | ||||
−0.978921 | + | 0.204241i | \(0.934527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24526 | − | 2.24526i | 0.105725 | − | 0.105725i | ||||
\(452\) | −6.74527 | − | 2.43601i | −0.317271 | − | 0.114580i | ||||
\(453\) | −35.5335 | −1.66951 | ||||||||
\(454\) | −0.474247 | − | 2.12661i | −0.0222575 | − | 0.0998068i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 45.8381 | + | 5.86000i | 2.14656 | + | 0.274420i | ||||
\(457\) | −13.5575 | − | 13.5575i | −0.634193 | − | 0.634193i | 0.314924 | − | 0.949117i | \(-0.398021\pi\) |
−0.949117 | + | 0.314924i | \(0.898021\pi\) | |||||||
\(458\) | 29.6512 | + | 18.8379i | 1.38551 | + | 0.880236i | ||||
\(459\) | −19.2692 | + | 19.2692i | −0.899411 | + | 0.899411i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.19682 | − | 1.19682i | −0.0557416 | − | 0.0557416i | 0.678687 | − | 0.734428i | \(-0.262550\pi\) |
−0.734428 | + | 0.678687i | \(0.762550\pi\) | |||||||
\(462\) | 1.78286 | − | 0.397587i | 0.0829459 | − | 0.0184974i | ||||
\(463\) | −21.1815 | + | 21.1815i | −0.984390 | + | 0.984390i | −0.999880 | − | 0.0154904i | \(-0.995069\pi\) |
0.0154904 | + | 0.999880i | \(0.495069\pi\) | |||||||
\(464\) | −2.00096 | − | 21.6258i | −0.0928921 | − | 1.00395i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7144 | − | 16.8647i | 0.496334 | − | 0.781241i | ||||
\(467\) | 24.8448i | 1.14968i | 0.818266 | + | 0.574840i | \(0.194936\pi\) | ||||
−0.818266 | + | 0.574840i | \(0.805064\pi\) | |||||||
\(468\) | −19.8116 | − | 42.2105i | −0.915792 | − | 1.95118i | ||||
\(469\) | 1.52664 | + | 1.52664i | 0.0704936 | + | 0.0704936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.4343 | 0.987642 | ||||||||
\(472\) | 1.83884 | − | 14.3838i | 0.0846394 | − | 0.662066i | ||||
\(473\) | 3.69537 | − | 3.69537i | 0.169913 | − | 0.169913i | ||||
\(474\) | −15.2336 | + | 3.39717i | −0.699701 | + | 0.156037i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.43972 | − | 5.19804i | −0.111824 | − | 0.238252i | ||||
\(477\) | −14.2210 | −0.651135 | ||||||||
\(478\) | −36.2692 | + | 8.08825i | −1.65892 | + | 0.369948i | ||||
\(479\) | 23.5766 | 1.07724 | 0.538621 | − | 0.842548i | \(-0.318946\pi\) | ||||
0.538621 | + | 0.842548i | \(0.318946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4181 | 1.20456 | ||||||||
\(482\) | −0.156309 | + | 0.0348578i | −0.00711967 | + | 0.00158773i | ||||
\(483\) | −4.73547 | −0.215471 | ||||||||
\(484\) | −8.93472 | − | 19.0362i | −0.406124 | − | 0.865284i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 17.1417 | − | 3.82271i | 0.777565 | − | 0.173401i | ||||
\(487\) | 2.63011 | − | 2.63011i | 0.119182 | − | 0.119182i | −0.645001 | − | 0.764182i | \(-0.723143\pi\) |
0.764182 | + | 0.645001i | \(0.223143\pi\) | |||||||
\(488\) | 14.7909 | + | 1.89089i | 0.669552 | + | 0.0855964i | ||||
\(489\) | −67.7686 | −3.06460 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6899 | − | 18.6899i | −0.843465 | − | 0.843465i | 0.145843 | − | 0.989308i | \(-0.453411\pi\) |
−0.989308 | + | 0.145843i | \(0.953411\pi\) | |||||||
\(492\) | −11.0582 | − | 23.5606i | −0.498544 | − | 1.06219i | ||||
\(493\) | − | 24.0202i | − | 1.08182i | ||||||
\(494\) | −19.6139 | + | 30.8727i | −0.882472 | + | 1.38903i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.430623 | + | 0.357683i | 0.0193355 | + | 0.0160605i | ||||
\(497\) | 0.628940 | − | 0.628940i | 0.0282118 | − | 0.0282118i | ||||
\(498\) | 57.0424 | − | 12.7208i | 2.55613 | − | 0.570032i | ||||
\(499\) | 9.69342 | + | 9.69342i | 0.433937 | + | 0.433937i | 0.889965 | − | 0.456028i | \(-0.150728\pi\) |
−0.456028 | + | 0.889965i | \(0.650728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.15090 | + | 1.15090i | −0.0514185 | + | 0.0514185i | ||||
\(502\) | 32.4491 | + | 20.6154i | 1.44827 | + | 0.920110i | ||||
\(503\) | 13.0434 | + | 13.0434i | 0.581577 | + | 0.581577i | 0.935336 | − | 0.353759i | \(-0.115097\pi\) |
−0.353759 | + | 0.935336i | \(0.615097\pi\) | |||||||
\(504\) | 1.20034 | − | 9.38926i | 0.0534672 | − | 0.418231i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.548051 | − | 2.45756i | −0.0243638 | − | 0.109252i | ||||
\(507\) | 21.2495 | 0.943724 | ||||||||
\(508\) | −1.63816 | − | 0.591611i | −0.0726817 | − | 0.0262485i | ||||
\(509\) | 25.8539 | − | 25.8539i | 1.14595 | − | 1.14595i | 0.158611 | − | 0.987341i | \(-0.449298\pi\) |
0.987341 | − | 0.158611i | \(-0.0507016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.34062i | 0.103543i | ||||||||
\(512\) | −8.89365 | − | 20.8063i | −0.393047 | − | 0.919518i | ||||
\(513\) | 24.9168 | + | 24.9168i | 1.10010 | + | 1.10010i | ||||
\(514\) | 0.812734 | − | 1.27926i | 0.0358481 | − | 0.0564258i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −18.2002 | − | 38.7773i | −0.801221 | − | 1.70707i | ||||
\(517\) | 4.08080i | 0.179473i | ||||||||
\(518\) | 4.52664 | + | 2.87584i | 0.198889 | + | 0.126357i | ||||
\(519\) | − | 44.1252i | − | 1.93688i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.0528i | 1.09758i | 0.835959 | + | 0.548792i | \(0.184912\pi\) | ||||
−0.835959 | + | 0.548792i | \(0.815088\pi\) | |||||||
\(522\) | 21.2334 | − | 33.4218i | 0.929361 | − | 1.46283i | ||||
\(523\) | − | 40.3434i | − | 1.76410i | −0.471160 | − | 0.882048i | \(-0.656165\pi\) | ||
0.471160 | − | 0.882048i | \(-0.343835\pi\) | |||||||
\(524\) | 9.17898 | − | 25.4165i | 0.400986 | − | 1.11032i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.67325 | − | 6.14556i | −0.421774 | − | 0.267959i | ||||
\(527\) | 0.437794 | + | 0.437794i | 0.0190706 | + | 0.0190706i | ||||
\(528\) | 7.92723 | − | 0.733479i | 0.344988 | − | 0.0319206i | ||||
\(529\) | − | 16.4724i | − | 0.716192i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.6944 | − | 18.6944i | 0.811267 | − | 0.811267i | ||||
\(532\) | −6.72153 | + | 3.15477i | −0.291415 | + | 0.136777i | ||||
\(533\) | 20.6003 | 0.892296 | ||||||||
\(534\) | −13.2067 | + | 2.94517i | −0.571510 | + | 0.127450i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.75610 | + | 7.44356i | 0.248626 | + | 0.321513i | ||||
\(537\) | 14.8639 | + | 14.8639i | 0.641425 | + | 0.641425i | ||||
\(538\) | −10.4984 | + | 16.5247i | −0.452618 | + | 0.712430i | ||||
\(539\) | 3.24180 | − | 3.24180i | 0.139634 | − | 0.139634i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7446 | − | 24.7446i | −1.06385 | − | 1.06385i | −0.997817 | − | 0.0660360i | \(-0.978965\pi\) |
−0.0660360 | − | 0.997817i | \(-0.521035\pi\) | |||||||
\(542\) | 1.26254 | + | 5.66146i | 0.0542307 | + | 0.243181i | ||||
\(543\) | 25.9590 | − | 25.9590i | 1.11401 | − | 1.11401i | ||||
\(544\) | −7.67437 | − | 23.8201i | −0.329036 | − | 1.02128i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0028 | + | 6.35491i | 0.428079 | + | 0.271965i | ||||
\(547\) | 19.0254i | 0.813465i | 0.913547 | + | 0.406733i | \(0.133332\pi\) | ||||
−0.913547 | + | 0.406733i | \(0.866668\pi\) | |||||||
\(548\) | −9.85034 | − | 3.55738i | −0.420786 | − | 0.151964i | ||||
\(549\) | 19.2235 | + | 19.2235i | 0.820440 | + | 0.820440i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.0602 | −1.32321 | ||||||||
\(552\) | −20.4720 | − | 2.61717i | −0.871346 | − | 0.111394i | ||||
\(553\) | 1.77329 | − | 1.77329i | 0.0754079 | − | 0.0754079i | ||||
\(554\) | 7.59554 | + | 34.0598i | 0.322704 | + | 1.44706i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.25292 | + | 14.5453i | −0.222773 | + | 0.616856i | ||||
\(557\) | −30.9517 | −1.31146 | −0.655732 | − | 0.754993i | \(-0.727640\pi\) | ||||
−0.655732 | + | 0.754993i | \(0.727640\pi\) | |||||||
\(558\) | 0.222148 | + | 0.996151i | 0.00940425 | + | 0.0421704i | ||||
\(559\) | 33.9050 | 1.43403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.80494 | 0.371745 | ||||||||
\(562\) | −7.28565 | − | 32.6702i | −0.307327 | − | 1.37811i | ||||
\(563\) | −3.50238 | −0.147608 | −0.0738039 | − | 0.997273i | \(-0.523514\pi\) | ||||
−0.0738039 | + | 0.997273i | \(0.523514\pi\) | |||||||
\(564\) | 31.4601 | + | 11.3616i | 1.32471 | + | 0.478410i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.01676 | − | 18.0119i | −0.168837 | − | 0.757097i | ||||
\(567\) | 0.973793 | − | 0.973793i | 0.0408955 | − | 0.0408955i | ||||
\(568\) | 3.06658 | − | 2.37138i | 0.128671 | − | 0.0995011i | ||||
\(569\) | 0.525780 | 0.0220418 | 0.0110209 | − | 0.999939i | \(-0.496492\pi\) | ||||
0.0110209 | + | 0.999939i | \(0.496492\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2487 | − | 11.2487i | −0.470743 | − | 0.470743i | 0.431412 | − | 0.902155i | \(-0.358016\pi\) |
−0.902155 | + | 0.431412i | \(0.858016\pi\) | |||||||
\(572\) | −2.14035 | + | 5.92660i | −0.0894926 | + | 0.247804i | ||||
\(573\) | − | 43.1472i | − | 1.80250i | ||||||
\(574\) | 3.52977 | + | 2.24252i | 0.147330 | + | 0.0936008i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.3784 | − | 39.9275i | 0.432432 | − | 1.66364i | ||||
\(577\) | 2.92884 | − | 2.92884i | 0.121929 | − | 0.121929i | −0.643509 | − | 0.765438i | \(-0.722522\pi\) |
0.765438 | + | 0.643509i | \(0.222522\pi\) | |||||||
\(578\) | −0.791607 | − | 3.54971i | −0.0329265 | − | 0.147649i | ||||
\(579\) | 11.9714 | + | 11.9714i | 0.497515 | + | 0.497515i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.64011 | + | 6.64011i | −0.275478 | + | 0.275478i | ||||
\(582\) | −15.1799 | + | 23.8935i | −0.629227 | + | 0.990416i | ||||
\(583\) | 1.35891 | + | 1.35891i | 0.0562801 | + | 0.0562801i | ||||
\(584\) | −1.29360 | + | 10.1188i | −0.0535295 | + | 0.418718i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.7186 | − | 9.74951i | 1.80600 | − | 0.402748i | ||||
\(587\) | −23.1574 | −0.955809 | −0.477905 | − | 0.878412i | \(-0.658604\pi\) | ||||
−0.477905 | + | 0.878412i | \(0.658604\pi\) | |||||||
\(588\) | −15.9664 | − | 34.0178i | −0.658442 | − | 1.40287i | ||||
\(589\) | 0.566106 | − | 0.566106i | 0.0233260 | − | 0.0233260i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5150i | 0.473662i | ||||||||
\(592\) | 17.9798 | + | 14.9343i | 0.738964 | + | 0.613798i | ||||
\(593\) | 13.9325 | + | 13.9325i | 0.572141 | + | 0.572141i | 0.932726 | − | 0.360585i | \(-0.117423\pi\) |
−0.360585 | + | 0.932726i | \(0.617423\pi\) | |||||||
\(594\) | 5.12398 | + | 3.25534i | 0.210240 | + | 0.133568i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.2146 | − | 4.05008i | −0.459368 | − | 0.165898i | ||||
\(597\) | − | 15.5097i | − | 0.634769i | ||||||
\(598\) | 8.75988 | − | 13.7882i | 0.358218 | − | 0.563843i | ||||
\(599\) | − | 33.5311i | − | 1.37004i | −0.728523 | − | 0.685021i | \(-0.759793\pi\) | ||
0.728523 | − | 0.685021i | \(-0.240207\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.4164i | − | 0.792011i | −0.918248 | − | 0.396005i | \(-0.870396\pi\) | ||
0.918248 | − | 0.396005i | \(-0.129604\pi\) | |||||||
\(602\) | 5.80948 | + | 3.69085i | 0.236777 | + | 0.150428i | ||||
\(603\) | 17.1554i | 0.698623i | ||||||||
\(604\) | 22.5256 | − | 10.5725i | 0.916554 | − | 0.430187i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.65243 | − | 8.89705i | 0.229614 | − | 0.361418i | ||||
\(607\) | −9.51495 | − | 9.51495i | −0.386200 | − | 0.386200i | 0.487130 | − | 0.873330i | \(-0.338044\pi\) |
−0.873330 | + | 0.487130i | \(0.838044\pi\) | |||||||
\(608\) | −30.8015 | + | 9.92363i | −1.24917 | + | 0.402456i | ||||
\(609\) | 10.0635i | 0.407794i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.7206 | + | 18.7206i | −0.757355 | + | 0.757355i | ||||
\(612\) | 15.4982 | − | 42.9143i | 0.626478 | − | 1.73471i | ||||
\(613\) | 9.37947 | 0.378833 | 0.189417 | − | 0.981897i | \(-0.439340\pi\) | ||||
0.189417 | + | 0.981897i | \(0.439340\pi\) | |||||||
\(614\) | −8.42177 | − | 37.7648i | −0.339875 | − | 1.52406i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.01190 | + | 0.782503i | −0.0407707 | + | 0.0315280i | ||||
\(617\) | −3.54768 | − | 3.54768i | −0.142824 | − | 0.142824i | 0.632079 | − | 0.774904i | \(-0.282202\pi\) |
−0.774904 | + | 0.632079i | \(0.782202\pi\) | |||||||
\(618\) | −56.2428 | − | 35.7319i | −2.26242 | − | 1.43735i | ||||
\(619\) | −24.6158 | + | 24.6158i | −0.989392 | + | 0.989392i | −0.999944 | − | 0.0105527i | \(-0.996641\pi\) |
0.0105527 | + | 0.999944i | \(0.496641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.1282 | − | 11.1282i | −0.446561 | − | 0.446561i | ||||
\(622\) | −21.8194 | + | 4.86585i | −0.874877 | + | 0.195103i | ||||
\(623\) | 1.53735 | − | 1.53735i | 0.0615926 | − | 0.0615926i | ||||
\(624\) | 39.7309 | + | 33.0013i | 1.59051 | + | 1.32111i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.8420 | + | 23.3617i | −0.593206 | + | 0.933720i | ||||
\(627\) | − | 11.3856i | − | 0.454695i | ||||||
\(628\) | −13.5878 | + | 6.37747i | −0.542211 | + | 0.254489i | ||||
\(629\) | 18.2792 | + | 18.2792i | 0.728840 | + | 0.728840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8921 | −1.15018 | −0.575088 | − | 0.818092i | \(-0.695032\pi\) | ||||
−0.575088 | + | 0.818092i | \(0.695032\pi\) | |||||||
\(632\) | 8.64618 | − | 6.68608i | 0.343927 | − | 0.265958i | ||||
\(633\) | −9.22547 | + | 9.22547i | −0.366679 | + | 0.366679i | ||||
\(634\) | 48.3235 | − | 10.7764i | 1.91917 | − | 0.427986i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.2596 | − | 6.69281i | 0.565432 | − | 0.265387i | ||||
\(637\) | 29.7435 | 1.17848 | ||||||||
\(638\) | −5.22265 | + | 1.16468i | −0.206767 | + | 0.0461102i | ||||
\(639\) | 7.06765 | 0.279592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.6914 | −0.659271 | −0.329636 | − | 0.944108i | \(-0.606926\pi\) | ||||
−0.329636 | + | 0.944108i | \(0.606926\pi\) | |||||||
\(642\) | −60.3570 | + | 13.4600i | −2.38210 | + | 0.531223i | ||||
\(643\) | 5.22468 | 0.206041 | 0.103021 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103021 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(644\) | 3.00194 | − | 1.40897i | 0.118293 | − | 0.0555212i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −34.9327 | + | 7.79019i | −1.37441 | + | 0.306501i | ||||
\(647\) | −21.6797 | + | 21.6797i | −0.852318 | + | 0.852318i | −0.990418 | − | 0.138100i | \(-0.955900\pi\) |
0.138100 | + | 0.990418i | \(0.455900\pi\) | |||||||
\(648\) | 4.74801 | − | 3.67163i | 0.186519 | − | 0.144235i | ||||
\(649\) | −3.57273 | −0.140242 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.183418 | − | 0.183418i | −0.00718874 | − | 0.00718874i | ||||
\(652\) | 42.9603 | − | 20.1636i | 1.68245 | − | 0.789666i | ||||
\(653\) | − | 22.7642i | − | 0.890833i | −0.895323 | − | 0.445417i | \(-0.853056\pi\) | ||
0.895323 | − | 0.445417i | \(-0.146944\pi\) | |||||||
\(654\) | 38.2261 | − | 60.1688i | 1.49476 | − | 2.35279i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.0202 | + | 11.6455i | 0.547398 | + | 0.454679i | ||||
\(657\) | −13.1513 | + | 13.1513i | −0.513079 | + | 0.513079i | ||||
\(658\) | −5.24560 | + | 1.16980i | −0.204495 | + | 0.0456036i | ||||
\(659\) | 1.66201 | + | 1.66201i | 0.0647427 | + | 0.0647427i | 0.738737 | − | 0.673994i | \(-0.235423\pi\) |
−0.673994 | + | 0.738737i | \(0.735423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.62818 | + | 5.62818i | −0.218911 | + | 0.218911i | −0.808039 | − | 0.589129i | \(-0.799471\pi\) |
0.589129 | + | 0.808039i | \(0.299471\pi\) | |||||||
\(662\) | 28.3963 | + | 18.0406i | 1.10365 | + | 0.701168i | ||||
\(663\) | 40.3926 | + | 40.3926i | 1.56872 | + | 1.56872i | ||||
\(664\) | −32.3758 | + | 25.0362i | −1.25642 | + | 0.971591i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.27532 | + | 41.5923i | 0.359411 | + | 1.61167i | ||||
\(667\) | 13.8720 | 0.537125 | ||||||||
\(668\) | 0.387153 | − | 1.07202i | 0.0149794 | − | 0.0414777i | ||||
\(669\) | 23.3427 | − | 23.3427i | 0.902481 | − | 0.902481i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.67386i | − | 0.141828i | ||||||
\(672\) | 3.21526 | + | 9.97969i | 0.124031 | + | 0.384975i | ||||
\(673\) | −0.278251 | − | 0.278251i | −0.0107258 | − | 0.0107258i | 0.701724 | − | 0.712449i | \(-0.252414\pi\) |
−0.712449 | + | 0.701724i | \(0.752414\pi\) | |||||||
\(674\) | −15.5494 | + | 24.4751i | −0.598940 | + | 0.942744i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.4706 | + | 6.32248i | −0.518101 | + | 0.243172i | ||||
\(677\) | 26.3591i | 1.01306i | 0.862222 | + | 0.506531i | \(0.169072\pi\) | ||||
−0.862222 | + | 0.506531i | \(0.830928\pi\) | |||||||
\(678\) | 12.2247 | + | 7.76655i | 0.469488 | + | 0.298273i | ||||
\(679\) | − | 4.54840i | − | 0.174551i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.40019i | 0.168616i | ||||||||
\(682\) | 0.0739609 | − | 0.116416i | 0.00283211 | − | 0.00445780i | ||||
\(683\) | 2.83023i | 0.108296i | 0.998533 | + | 0.0541479i | \(0.0172442\pi\) | ||||
−0.998533 | + | 0.0541479i | \(0.982756\pi\) | |||||||
\(684\) | −55.4919 | − | 20.0405i | −2.12179 | − | 0.766269i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.5191 | + | 6.68296i | 0.401622 | + | 0.255157i | ||||
\(687\) | −50.1646 | − | 50.1646i | −1.91390 | − | 1.91390i | ||||
\(688\) | 23.0752 | + | 19.1667i | 0.879734 | + | 0.730724i | ||||
\(689\) | 12.4679i | 0.474991i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.1815 | − | 22.1815i | 0.843825 | − | 0.843825i | −0.145529 | − | 0.989354i | \(-0.546488\pi\) |
0.989354 | + | 0.145529i | \(0.0464884\pi\) | |||||||
\(692\) | 13.1288 | + | 27.9721i | 0.499083 | + | 1.06334i | ||||
\(693\) | −2.33217 | −0.0885917 | ||||||||
\(694\) | 23.1484 | − | 5.16223i | 0.878702 | − | 0.195956i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.56183 | + | 43.5057i | −0.210821 | + | 1.64908i | ||||
\(697\) | 14.2537 | + | 14.2537i | 0.539898 | + | 0.539898i | ||||
\(698\) | −1.99845 | + | 3.14560i | −0.0756423 | + | 0.119063i | ||||
\(699\) | −28.5320 | + | 28.5320i | −1.07918 | + | 1.07918i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.2264 | + | 16.2264i | 0.612864 | + | 0.612864i | 0.943691 | − | 0.330828i | \(-0.107328\pi\) |
−0.330828 | + | 0.943691i | \(0.607328\pi\) | |||||||
\(702\) | 8.57237 | + | 38.4401i | 0.323543 | + | 1.45083i | ||||
\(703\) | 23.6366 | − | 23.6366i | 0.891472 | − | 0.891472i | ||||
\(704\) | −4.80704 | + | 2.82360i | −0.181172 | + | 0.106418i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.7449 | − | 25.8858i | −1.53345 | − | 0.974226i | ||||
\(707\) | 1.69365i | 0.0636965i | ||||||||
\(708\) | −9.94708 | + | 27.5433i | −0.373834 | + | 1.03514i | ||||
\(709\) | −25.3577 | − | 25.3577i | −0.952329 | − | 0.952329i | 0.0465856 | − | 0.998914i | \(-0.485166\pi\) |
−0.998914 | + | 0.0465856i | \(0.985166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.9271 | 0.747326 | ||||||||
\(712\) | 7.49579 | − | 5.79648i | 0.280916 | − | 0.217232i | ||||
\(713\) | −0.252832 | + | 0.252832i | −0.00946863 | + | 0.00946863i | ||||
\(714\) | 2.52402 | + | 11.3182i | 0.0944592 | + | 0.423573i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.8452 | − | 5.00009i | −0.517418 | − | 0.186862i | ||||
\(717\) | 75.0450 | 2.80261 | ||||||||
\(718\) | −3.77076 | − | 16.9088i | −0.140724 | − | 0.631031i | ||||
\(719\) | −41.3374 | −1.54163 | −0.770813 | − | 0.637061i | \(-0.780150\pi\) | ||||
−0.770813 | + | 0.637061i | \(0.780150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7065 | 0.398730 | ||||||||
\(722\) | 4.22489 | + | 18.9452i | 0.157234 | + | 0.705067i | ||||
\(723\) | 0.323420 | 0.0120281 | ||||||||
\(724\) | −8.73236 | + | 24.1798i | −0.324536 | + | 0.898635i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.24346 | + | 41.4494i | 0.343057 | + | 1.53833i | ||||
\(727\) | 23.4630 | − | 23.4630i | 0.870193 | − | 0.870193i | −0.122300 | − | 0.992493i | \(-0.539027\pi\) |
0.992493 | + | 0.122300i | \(0.0390271\pi\) | |||||||
\(728\) | −8.23182 | − | 1.05237i | −0.305092 | − | 0.0390033i | ||||
\(729\) | −41.8342 | −1.54942 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.4595 | + | 23.4595i | 0.867681 | + | 0.867681i | ||||
\(732\) | −28.3229 | − | 10.2286i | −1.04684 | − | 0.378061i | ||||
\(733\) | 15.1628i | 0.560051i | 0.959993 | + | 0.280025i | \(0.0903429\pi\) | ||||
−0.959993 | + | 0.280025i | \(0.909657\pi\) | |||||||
\(734\) | 4.58000 | + | 2.90975i | 0.169051 | + | 0.107401i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.7564 | − | 4.43205i | 0.507069 | − | 0.163368i | ||||
\(737\) | 1.63931 | − | 1.63931i | 0.0603848 | − | 0.0603848i | ||||
\(738\) | 7.23269 | + | 32.4327i | 0.266239 | + | 1.19387i | ||||
\(739\) | 0.974343 | + | 0.974343i | 0.0358418 | + | 0.0358418i | 0.724801 | − | 0.688959i | \(-0.241932\pi\) |
−0.688959 | + | 0.724801i | \(0.741932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 52.2312 | − | 52.2312i | 1.91876 | − | 1.91876i | ||||
\(742\) | −1.35724 | + | 2.13633i | −0.0498260 | + | 0.0784272i | ||||
\(743\) | −29.0897 | − | 29.0897i | −1.06720 | − | 1.06720i | −0.997573 | − | 0.0696259i | \(-0.977819\pi\) |
−0.0696259 | − | 0.997573i | \(-0.522181\pi\) | |||||||
\(744\) | −0.691569 | − | 0.894310i | −0.0253541 | − | 0.0327870i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.7538 | + | 5.07424i | −0.833078 | + | 0.185781i | ||||
\(747\) | −74.6176 | −2.73011 | ||||||||
\(748\) | −5.58168 | + | 2.61978i | −0.204087 | + | 0.0957887i | ||||
\(749\) | 7.02596 | − | 7.02596i | 0.256723 | − | 0.256723i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 7.77705i | − | 0.283789i | −0.989882 | − | 0.141894i | \(-0.954681\pi\) | ||
0.989882 | − | 0.141894i | \(-0.0453193\pi\) | |||||||
\(752\) | −23.3239 | + | 2.15808i | −0.850534 | + | 0.0786970i | ||||
\(753\) | −54.8981 | − | 54.8981i | −2.00060 | − | 2.00060i | ||||
\(754\) | −29.3019 | − | 18.6159i | −1.06711 | − | 0.677952i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.71570 | + | 7.51973i | −0.0987690 | + | 0.273490i | ||||
\(757\) | 1.42073i | 0.0516372i | 0.999667 | + | 0.0258186i | \(0.00821923\pi\) | ||||
−0.999667 | + | 0.0258186i | \(0.991781\pi\) | |||||||
\(758\) | 14.7699 | − | 23.2482i | 0.536469 | − | 0.844413i | ||||
\(759\) | 5.08497i | 0.184573i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.6737i | − | 0.966921i | −0.875366 | − | 0.483460i | \(-0.839380\pi\) | ||
0.875366 | − | 0.483460i | \(-0.160620\pi\) | |||||||
\(762\) | 2.96891 | + | 1.88619i | 0.107552 | + | 0.0683295i | ||||
\(763\) | 11.4538i | 0.414656i | ||||||||
\(764\) | 12.8378 | + | 27.3521i | 0.464456 | + | 0.989565i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.3905 | − | 19.5029i | 0.447687 | − | 0.704669i | ||||
\(767\) | −16.3899 | − | 16.3899i | −0.591805 | − | 0.591805i | ||||
\(768\) | 8.38443 | + | 44.9203i | 0.302547 | + | 1.62092i | ||||
\(769\) | − | 45.8210i | − | 1.65235i | −0.563415 | − | 0.826174i | \(-0.690513\pi\) | ||
0.563415 | − | 0.826174i | \(-0.309487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.16428 | + | 2.16428i | −0.0779447 | + | 0.0779447i | ||||
\(772\) | −11.1509 | − | 4.02707i | −0.401330 | − | 0.144937i | ||||
\(773\) | 18.5473 | 0.667101 | 0.333550 | − | 0.942732i | \(-0.391753\pi\) | ||||
0.333550 | + | 0.942732i | \(0.391753\pi\) | |||||||
\(774\) | 11.9039 | + | 53.3795i | 0.427878 | + | 1.91869i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.51378 | − | 19.6633i | 0.0902393 | − | 0.705870i | ||||
\(777\) | −7.65827 | − | 7.65827i | −0.274739 | − | 0.274739i | ||||
\(778\) | 26.6264 | + | 16.9162i | 0.954603 | + | 0.606474i | ||||
\(779\) | 18.4313 | − | 18.4313i | 0.660370 | − | 0.660370i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.675359 | − | 0.675359i | −0.0241662 | − | 0.0241662i | ||||
\(782\) | 15.6015 | − | 3.47922i | 0.557908 | − | 0.124417i | ||||
\(783\) | −23.6490 | + | 23.6490i | −0.845146 | + | 0.845146i | ||||
\(784\) | 20.2430 | + | 16.8142i | 0.722964 | + | 0.600508i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.2647 | + | 46.0633i | −1.04384 | + | 1.64302i | ||||
\(787\) | − | 21.3016i | − | 0.759319i | −0.925126 | − | 0.379659i | \(-0.876041\pi\) | ||
0.925126 | − | 0.379659i | \(-0.123959\pi\) | |||||||
\(788\) | −3.42610 | − | 7.29963i | −0.122050 | − | 0.260039i | ||||
\(789\) | 16.3654 | + | 16.3654i | 0.582624 | + | 0.582624i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.32712 | −0.0827427 | ||||||||
\(792\) | −10.0822 | − | 1.28892i | −0.358256 | − | 0.0458000i | ||||
\(793\) | 16.8538 | − | 16.8538i | 0.598496 | − | 0.598496i | ||||
\(794\) | −41.3482 | + | 9.22090i | −1.46739 | + | 0.327237i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.61468 | + | 9.83200i | 0.163563 | + | 0.348486i | ||||
\(797\) | 2.35457 | 0.0834033 | 0.0417016 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417016 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(798\) | 14.6354 | − | 3.26378i | 0.518088 | − | 0.115537i | ||||
\(799\) | −25.9063 | −0.916500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.2758 | 0.610410 | ||||||||
\(802\) | 27.5014 | − | 6.13297i | 0.971108 | − | 0.216563i | ||||
\(803\) | 2.51337 | 0.0886949 | ||||||||
\(804\) | −8.07384 | − | 17.2021i | −0.284742 | − | 0.606670i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.873354 | − | 0.194763i | 0.0307626 | − | 0.00686023i | ||||
\(807\) | 27.9569 | − | 27.9569i | 0.984128 | − | 0.984128i | ||||
\(808\) | −0.936037 | + | 7.32187i | −0.0329297 | + | 0.257582i | ||||
\(809\) | 23.9476 | 0.841952 | 0.420976 | − | 0.907072i | \(-0.361688\pi\) | ||||
0.420976 | + | 0.907072i | \(0.361688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.33006 | − | 1.33006i | −0.0467048 | − | 0.0467048i | 0.683369 | − | 0.730073i | \(-0.260514\pi\) |
−0.730073 | + | 0.683369i | \(0.760514\pi\) | |||||||
\(812\) | −2.99425 | − | 6.37952i | −0.105078 | − | 0.223877i | ||||
\(813\) | − | 11.7142i | − | 0.410834i | ||||||
\(814\) | 3.08809 | − | 4.86072i | 0.108238 | − | 0.170368i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.65638 | + | 50.3248i | 0.163006 | + | 1.76172i | ||||
\(817\) | 30.3352 | − | 30.3352i | 1.06129 | − | 1.06129i | ||||
\(818\) | −8.14182 | + | 1.81567i | −0.284672 | + | 0.0634836i | ||||
\(819\) | −10.6988 | − | 10.6988i | −0.373846 | − | 0.373846i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.4676 | − | 36.4676i | 1.27273 | − | 1.27273i | 0.328076 | − | 0.944651i | \(-0.393600\pi\) |
0.944651 | − | 0.328076i | \(-0.106400\pi\) | |||||||
\(822\) | 17.8522 | + | 11.3417i | 0.622666 | + | 0.395589i | ||||
\(823\) | −26.3978 | − | 26.3978i | −0.920170 | − | 0.920170i | 0.0768712 | − | 0.997041i | \(-0.475507\pi\) |
−0.997041 | + | 0.0768712i | \(0.975507\pi\) | |||||||
\(824\) | 46.2853 | + | 5.91718i | 1.61243 | + | 0.206135i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.02416 | − | 4.59252i | −0.0356351 | − | 0.159794i | ||||
\(827\) | 1.99830 | 0.0694878 | 0.0347439 | − | 0.999396i | \(-0.488938\pi\) | ||||
0.0347439 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(828\) | 24.7836 | + | 8.95041i | 0.861288 | + | 0.311048i | ||||
\(829\) | 13.0376 | − | 13.0376i | 0.452813 | − | 0.452813i | −0.443474 | − | 0.896287i | \(-0.646254\pi\) |
0.896287 | + | 0.443474i | \(0.146254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 70.4735i | − | 2.44470i | ||||||
\(832\) | −35.0055 | − | 9.09901i | −1.21360 | − | 0.315451i | ||||
\(833\) | 20.5801 | + | 20.5801i | 0.713059 | + | 0.713059i | ||||
\(834\) | 16.7475 | − | 26.3609i | 0.579919 | − | 0.912805i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.38761 | + | 7.21760i | 0.117163 | + | 0.249626i | ||||
\(837\) | − | 0.862057i | − | 0.0297971i | ||||||
\(838\) | −13.9174 | − | 8.84194i | −0.480769 | − | 0.305440i | ||||
\(839\) | 15.4102i | 0.532018i | 0.963971 | + | 0.266009i | \(0.0857050\pi\) | ||||
−0.963971 | + | 0.266009i | \(0.914295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 0.479815i | − | 0.0165453i | ||||||
\(842\) | −18.4228 | + | 28.9979i | −0.634891 | + | 0.999333i | ||||
\(843\) | 67.5983i | 2.32821i | ||||||||
\(844\) | 3.10336 | − | 8.59317i | 0.106822 | − | 0.295789i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −36.0462 | − | 22.9007i | −1.23929 | − | 0.787343i | ||||
\(847\) | −4.82499 | − | 4.82499i | −0.165789 | − | 0.165789i | ||||
\(848\) | −7.04822 | + | 8.48550i | −0.242037 | + | 0.291393i | ||||
\(849\) | 37.2686i | 1.27906i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5565 | + | 10.5565i | −0.361872 | + | 0.361872i | ||||
\(852\) | −7.08686 | + | 3.32624i | −0.242792 | + | 0.113955i | ||||
\(853\) | −7.96419 | −0.272689 | −0.136344 | − | 0.990662i | \(-0.543535\pi\) | ||||
−0.136344 | + | 0.990662i | \(0.543535\pi\) | |||||||
\(854\) | 4.72251 | − | 1.05315i | 0.161601 | − | 0.0360380i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34.2571 | − | 26.4910i | 1.17088 | − | 0.905443i | ||||
\(857\) | 5.35407 | + | 5.35407i | 0.182891 | + | 0.182891i | 0.792615 | − | 0.609723i | \(-0.208719\pi\) |
−0.609723 | + | 0.792615i | \(0.708719\pi\) | |||||||
\(858\) | 6.82393 | − | 10.7410i | 0.232965 | − | 0.366692i | ||||
\(859\) | −35.0058 | + | 35.0058i | −1.19438 | + | 1.19438i | −0.218559 | + | 0.975824i | \(0.570136\pi\) |
−0.975824 | + | 0.218559i | \(0.929864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.97175 | − | 5.97175i | −0.203517 | − | 0.203517i | ||||
\(862\) | −9.90457 | − | 44.4140i | −0.337351 | − | 1.51275i | ||||
\(863\) | −36.7138 | + | 36.7138i | −1.24975 | + | 1.24975i | −0.293923 | + | 0.955829i | \(0.594961\pi\) |
−0.955829 | + | 0.293923i | \(0.905039\pi\) | |||||||
\(864\) | −15.8962 | + | 31.0078i | −0.540801 | + | 1.05491i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.3336 | + | 21.8126i | 1.16670 | + | 0.741224i | ||||
\(867\) | 7.34475i | 0.249441i | ||||||||
\(868\) | 0.170847 | + | 0.0617003i | 0.00579893 | + | 0.00209424i | ||||
\(869\) | −1.90416 | − | 1.90416i | −0.0645943 | − | 0.0645943i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.0406 | 0.509633 | ||||||||
\(872\) | −6.33022 | + | 49.5162i | −0.214368 | + | 1.67683i | ||||
\(873\) | 25.5561 | − | 25.5561i | 0.864942 | − | 0.864942i | ||||
\(874\) | −4.49894 | − | 20.1741i | −0.152179 | − | 0.682399i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.99764 | − | 19.3764i | 0.236428 | − | 0.654667i | ||||
\(877\) | 14.3410 | 0.484262 | 0.242131 | − | 0.970244i | \(-0.422154\pi\) | ||||
0.242131 | + | 0.970244i | \(0.422154\pi\) | |||||||
\(878\) | 10.9022 | + | 48.8877i | 0.367933 | + | 1.64988i | ||||
\(879\) | −90.4586 | −3.05109 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6397 | −0.459533 | −0.229767 | − | 0.973246i | \(-0.573796\pi\) | ||||
−0.229767 | + | 0.973246i | \(0.573796\pi\) | |||||||
\(882\) | 10.4429 | + | 46.8277i | 0.351629 | + | 1.57677i | ||||
\(883\) | −6.12563 | −0.206144 | −0.103072 | − | 0.994674i | \(-0.532867\pi\) | ||||
−0.103072 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(884\) | −37.6242 | − | 13.5877i | −1.26544 | − | 0.457004i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.935105 | + | 4.19319i | 0.0314155 | + | 0.140873i | ||||
\(887\) | −25.5187 | + | 25.5187i | −0.856834 | + | 0.856834i | −0.990964 | − | 0.134130i | \(-0.957176\pi\) |
0.134130 | + | 0.990964i | \(0.457176\pi\) | |||||||
\(888\) | −28.8751 | − | 37.3401i | −0.968984 | − | 1.25305i | ||||
\(889\) | −0.565166 | −0.0189551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.04566 | − | 1.04566i | −0.0350310 | − | 0.0350310i | ||||
\(892\) | −7.85227 | + | 21.7428i | −0.262913 | + | 0.728003i | ||||
\(893\) | 33.4992i | 1.12101i | ||||||||
\(894\) | 20.3247 | + | 12.9126i | 0.679759 | + | 0.431861i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.00755 | − | 5.36973i | −0.167290 | − | 0.179390i | ||||
\(897\) | −23.3273 | + | 23.3273i | −0.778875 | + | 0.778875i | ||||
\(898\) | 2.66433 | + | 11.9474i | 0.0889100 | + | 0.398689i | ||||
\(899\) | 0.537302 | + | 0.537302i | 0.0179200 | + | 0.0179200i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.62682 | + | 8.62682i | −0.287401 | + | 0.287401i | ||||
\(902\) | 2.40802 | − | 3.79028i | 0.0801784 | − | 0.126203i | ||||
\(903\) | −9.82861 | − | 9.82861i | −0.327076 | − | 0.327076i | ||||
\(904\) | −10.0604 | − | 1.28613i | −0.334604 | − | 0.0427762i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −49.0471 | + | 10.9378i | −1.62948 | + | 0.363384i | ||||
\(907\) | −32.1815 | −1.06857 | −0.534284 | − | 0.845305i | \(-0.679419\pi\) | ||||
−0.534284 | + | 0.845305i | \(0.679419\pi\) | |||||||
\(908\) | −1.30921 | − | 2.78940i | −0.0434477 | − | 0.0925694i | ||||
\(909\) | −9.51614 | + | 9.51614i | −0.315630 | + | 0.315630i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6282i | 1.27981i | 0.768455 | + | 0.639904i | \(0.221026\pi\) | ||||
−0.768455 | + | 0.639904i | \(0.778974\pi\) | |||||||
\(912\) | 65.0744 | − | 6.02111i | 2.15483 | − | 0.199379i | ||||
\(913\) | 7.13018 | + | 7.13018i | 0.235974 | + | 0.235974i | ||||
\(914\) | −22.8868 | − | 14.5403i | −0.757027 | − | 0.480950i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.7264 | + | 16.8749i | 1.54388 | + | 0.557563i | ||||
\(917\) | − | 8.76867i | − | 0.289567i | ||||||
\(918\) | −20.6661 | + | 32.5289i | −0.682082 | + | 1.07361i | ||||
\(919\) | − | 19.1924i | − | 0.633099i | −0.948576 | − | 0.316550i | \(-0.897476\pi\) | ||
0.948576 | − | 0.316550i | \(-0.102524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 78.1395i | 2.57479i | ||||||||
\(922\) | −2.02038 | − | 1.28358i | −0.0665378 | − | 0.0422725i | ||||
\(923\) | − | 6.19641i | − | 0.203957i | ||||||
\(924\) | 2.33850 | − | 1.09758i | 0.0769312 | − | 0.0361079i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.7170 | + | 35.7571i | −0.746527 | + | 1.17505i | ||||
\(927\) | 60.1564 | + | 60.1564i | 1.97580 | + | 1.97580i | ||||
\(928\) | −9.41870 | − | 29.2343i | −0.309184 | − | 0.959662i | ||||
\(929\) | 16.8576i | 0.553081i | 0.961002 | + | 0.276541i | \(0.0891880\pi\) | ||||
−0.961002 | + | 0.276541i | \(0.910812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.6119 | − | 26.6119i | 0.872170 | − | 0.872170i | ||||
\(932\) | 9.59792 | − | 26.5765i | 0.314390 | − | 0.870542i | ||||
\(933\) | 45.1467 | 1.47804 | ||||||||
\(934\) | 7.64764 | + | 34.2935i | 0.250239 | + | 1.12212i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −40.3392 | − | 52.1651i | −1.31853 | − | 1.70507i | ||||
\(937\) | −23.9511 | − | 23.9511i | −0.782449 | − | 0.782449i | 0.197795 | − | 0.980243i | \(-0.436622\pi\) |
−0.980243 | + | 0.197795i | \(0.936622\pi\) | |||||||
\(938\) | 2.57715 | + | 1.63730i | 0.0841470 | + | 0.0534599i | ||||
\(939\) | 39.5238 | − | 39.5238i | 1.28981 | − | 1.28981i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2496 | + | 14.2496i | 0.464525 | + | 0.464525i | 0.900135 | − | 0.435610i | \(-0.143467\pi\) |
−0.435610 | + | 0.900135i | \(0.643467\pi\) | |||||||
\(942\) | 29.5860 | − | 6.59784i | 0.963963 | − | 0.214969i | ||||
\(943\) | −8.23171 | + | 8.23171i | −0.268061 | + | 0.268061i | ||||
\(944\) | −1.88940 | − | 20.4200i | −0.0614946 | − | 0.664616i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.96325 | − | 6.23824i | 0.128856 | − | 0.202823i | ||||
\(947\) | 20.2943i | 0.659477i | 0.944072 | + | 0.329738i | \(0.106961\pi\) | ||||
−0.944072 | + | 0.329738i | \(0.893039\pi\) | |||||||
\(948\) | −19.9813 | + | 9.37829i | −0.648963 | + | 0.304593i | ||||
\(949\) | 11.5301 | + | 11.5301i | 0.374282 | + | 0.374282i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −99.9866 | −3.24229 | ||||||||
\(952\) | −4.96761 | − | 6.42391i | −0.161001 | − | 0.208200i | ||||
\(953\) | −10.9257 | + | 10.9257i | −0.353919 | + | 0.353919i | −0.861565 | − | 0.507647i | \(-0.830516\pi\) |
0.507647 | + | 0.861565i | \(0.330516\pi\) | |||||||
\(954\) | −19.6293 | + | 4.37746i | −0.635524 | + | 0.141725i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −47.5730 | + | 22.3285i | −1.53862 | + | 0.722157i | ||||
\(957\) | 10.8062 | 0.349316 | ||||||||
\(958\) | 32.5429 | − | 7.25726i | 1.05141 | − | 0.234471i | ||||
\(959\) | −3.39836 | −0.109739 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9804 | 0.999368 | ||||||||
\(962\) | 36.4651 | − | 8.13193i | 1.17568 | − | 0.262184i | ||||
\(963\) | 78.9535 | 2.54424 | ||||||||
\(964\) | −0.205024 | + | 0.0962289i | −0.00660339 | + | 0.00309932i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.53641 | + | 1.45766i | −0.210305 | + | 0.0468993i | ||||
\(967\) | −10.7569 | + | 10.7569i | −0.345918 | + | 0.345918i | −0.858586 | − | 0.512669i | \(-0.828657\pi\) |
0.512669 | + | 0.858586i | \(0.328657\pi\) | |||||||
\(968\) | −18.1923 | − | 23.5256i | −0.584724 | − | 0.756142i | ||||
\(969\) | 72.2796 | 2.32195 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7456 | − | 18.7456i | −0.601574 | − | 0.601574i | 0.339156 | − | 0.940730i | \(-0.389858\pi\) |
−0.940730 | + | 0.339156i | \(0.889858\pi\) | |||||||
\(972\) | 22.4842 | − | 10.5530i | 0.721180 | − | 0.338488i | ||||
\(973\) | 5.01811i | 0.160873i | ||||||||
\(974\) | 2.82077 | − | 4.43995i | 0.0903832 | − | 0.142265i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.9980 | − | 1.94287i | 0.672130 | − | 0.0621899i | ||||
\(977\) | 26.3906 | − | 26.3906i | 0.844309 | − | 0.844309i | −0.145107 | − | 0.989416i | \(-0.546353\pi\) |
0.989416 | + | 0.145107i | \(0.0463526\pi\) | |||||||
\(978\) | −93.5415 | + | 20.8603i | −2.99113 | + | 0.667039i | ||||
\(979\) | −1.65081 | − | 1.65081i | −0.0527602 | − | 0.0527602i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −64.3556 | + | 64.3556i | −2.05472 | + | 2.05472i | ||||
\(982\) | −31.5509 | − | 20.0448i | −1.00683 | − | 0.639655i | ||||
\(983\) | 4.87875 | + | 4.87875i | 0.155608 | + | 0.155608i | 0.780617 | − | 0.625009i | \(-0.214905\pi\) |
−0.625009 | + | 0.780617i | \(0.714905\pi\) | |||||||
\(984\) | −22.5161 | − | 29.1170i | −0.717788 | − | 0.928215i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.39381 | − | 33.1553i | −0.235467 | − | 1.05588i | ||||
\(987\) | 10.8537 | 0.345478 | ||||||||
\(988\) | −17.5701 | + | 48.6513i | −0.558979 | + | 1.54781i | ||||
\(989\) | −13.5482 | + | 13.5482i | −0.430807 | + | 0.430807i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.2103i | 1.94441i | 0.234130 | + | 0.972205i | \(0.424776\pi\) | ||||
−0.234130 | + | 0.972205i | \(0.575224\pi\) | |||||||
\(992\) | 0.704492 | + | 0.361160i | 0.0223677 | + | 0.0114668i | ||||
\(993\) | −48.0415 | − | 48.0415i | −1.52455 | − | 1.52455i | ||||
\(994\) | 0.674533 | − | 1.06173i | 0.0213949 | − | 0.0336760i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 74.8204 | − | 35.1172i | 2.37077 | − | 1.11273i | ||||
\(997\) | 39.1082i | 1.23857i | 0.785167 | + | 0.619284i | \(0.212577\pi\) | ||||
−0.785167 | + | 0.619284i | \(0.787423\pi\) | |||||||
\(998\) | 16.3637 | + | 10.3961i | 0.517984 | + | 0.329083i | ||||
\(999\) | − | 35.9935i | − | 1.13878i |
(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 | 400.2.s.d.243.9 | 18 | ||
4.3 | odd | 2 | 1600.2.s.d.943.9 | 18 | |||
5.2 | odd | 4 | 400.2.j.d.307.5 | 18 | |||
5.3 | odd | 4 | 80.2.j.b.67.5 | yes | 18 | ||
5.4 | even | 2 | 80.2.s.b.3.1 | yes | 18 | ||
15.8 | even | 4 | 720.2.bd.g.307.5 | 18 | |||
15.14 | odd | 2 | 720.2.z.g.163.9 | 18 | |||
16.5 | even | 4 | 1600.2.j.d.143.9 | 18 | |||
16.11 | odd | 4 | 400.2.j.d.43.5 | 18 | |||
20.3 | even | 4 | 320.2.j.b.47.9 | 18 | |||
20.7 | even | 4 | 1600.2.j.d.1007.1 | 18 | |||
20.19 | odd | 2 | 320.2.s.b.303.1 | 18 | |||
40.3 | even | 4 | 640.2.j.c.607.1 | 18 | |||
40.13 | odd | 4 | 640.2.j.d.607.9 | 18 | |||
40.19 | odd | 2 | 640.2.s.c.223.9 | 18 | |||
40.29 | even | 2 | 640.2.s.d.223.1 | 18 | |||
80.3 | even | 4 | 640.2.s.d.287.1 | 18 | |||
80.13 | odd | 4 | 640.2.s.c.287.9 | 18 | |||
80.19 | odd | 4 | 640.2.j.d.543.1 | 18 | |||
80.27 | even | 4 | inner | 400.2.s.d.107.9 | 18 | ||
80.29 | even | 4 | 640.2.j.c.543.9 | 18 | |||
80.37 | odd | 4 | 1600.2.s.d.207.9 | 18 | |||
80.43 | even | 4 | 80.2.s.b.27.1 | yes | 18 | ||
80.53 | odd | 4 | 320.2.s.b.207.1 | 18 | |||
80.59 | odd | 4 | 80.2.j.b.43.5 | ✓ | 18 | ||
80.69 | even | 4 | 320.2.j.b.143.1 | 18 | |||
240.59 | even | 4 | 720.2.bd.g.523.5 | 18 | |||
240.203 | odd | 4 | 720.2.z.g.667.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.5 | ✓ | 18 | 80.59 | odd | 4 | ||
80.2.j.b.67.5 | yes | 18 | 5.3 | odd | 4 | ||
80.2.s.b.3.1 | yes | 18 | 5.4 | even | 2 | ||
80.2.s.b.27.1 | yes | 18 | 80.43 | even | 4 | ||
320.2.j.b.47.9 | 18 | 20.3 | even | 4 | |||
320.2.j.b.143.1 | 18 | 80.69 | even | 4 | |||
320.2.s.b.207.1 | 18 | 80.53 | odd | 4 | |||
320.2.s.b.303.1 | 18 | 20.19 | odd | 2 | |||
400.2.j.d.43.5 | 18 | 16.11 | odd | 4 | |||
400.2.j.d.307.5 | 18 | 5.2 | odd | 4 | |||
400.2.s.d.107.9 | 18 | 80.27 | even | 4 | inner | ||
400.2.s.d.243.9 | 18 | 1.1 | even | 1 | trivial | ||
640.2.j.c.543.9 | 18 | 80.29 | even | 4 | |||
640.2.j.c.607.1 | 18 | 40.3 | even | 4 | |||
640.2.j.d.543.1 | 18 | 80.19 | odd | 4 | |||
640.2.j.d.607.9 | 18 | 40.13 | odd | 4 | |||
640.2.s.c.223.9 | 18 | 40.19 | odd | 2 | |||
640.2.s.c.287.9 | 18 | 80.13 | odd | 4 | |||
640.2.s.d.223.1 | 18 | 40.29 | even | 2 | |||
640.2.s.d.287.1 | 18 | 80.3 | even | 4 | |||
720.2.z.g.163.9 | 18 | 15.14 | odd | 2 | |||
720.2.z.g.667.9 | 18 | 240.203 | odd | 4 | |||
720.2.bd.g.307.5 | 18 | 15.8 | even | 4 | |||
720.2.bd.g.523.5 | 18 | 240.59 | even | 4 | |||
1600.2.j.d.143.9 | 18 | 16.5 | even | 4 | |||
1600.2.j.d.1007.1 | 18 | 20.7 | even | 4 | |||
1600.2.s.d.207.9 | 18 | 80.37 | odd | 4 | |||
1600.2.s.d.943.9 | 18 | 4.3 | odd | 2 |