Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 29.8 | ||
Root | \(1.28499 + 1.53258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.29 |
Dual form | 48.3.i.b.5.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28499 | − | 1.53258i | 0.642495 | − | 0.766290i | ||||
\(3\) | −2.17774 | − | 2.06336i | −0.725914 | − | 0.687785i | ||||
\(4\) | −0.697601 | − | 3.93870i | −0.174400 | − | 0.984675i | ||||
\(5\) | 3.17955 | + | 3.17955i | 0.635909 | + | 0.635909i | 0.949544 | − | 0.313634i | \(-0.101547\pi\) |
−0.313634 | + | 0.949544i | \(0.601547\pi\) | |||||||
\(6\) | −5.96063 | + | 0.686173i | −0.993439 | + | 0.114362i | ||||
\(7\) | − | 6.03979i | − | 0.862827i | −0.902154 | − | 0.431414i | \(-0.858015\pi\) | ||
0.902154 | − | 0.431414i | \(-0.141985\pi\) | |||||||
\(8\) | −6.93278 | − | 3.99206i | −0.866598 | − | 0.499008i | ||||
\(9\) | 0.485128 | + | 8.98692i | 0.0539031 | + | 0.998546i | ||||
\(10\) | 8.95859 | − | 0.787223i | 0.895859 | − | 0.0787223i | ||||
\(11\) | 13.0097 | + | 13.0097i | 1.18270 | + | 1.18270i | 0.979042 | + | 0.203657i | \(0.0652828\pi\) |
0.203657 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(12\) | −6.60774 | + | 10.0169i | −0.550645 | + | 0.834739i | ||||
\(13\) | 6.39520 | + | 6.39520i | 0.491939 | + | 0.491939i | 0.908917 | − | 0.416978i | \(-0.136911\pi\) |
−0.416978 | + | 0.908917i | \(0.636911\pi\) | |||||||
\(14\) | −9.25646 | − | 7.76107i | −0.661176 | − | 0.554362i | ||||
\(15\) | −0.363700 | − | 13.4848i | −0.0242466 | − | 0.898985i | ||||
\(16\) | −15.0267 | + | 5.49528i | −0.939169 | + | 0.343455i | ||||
\(17\) | − | 4.39848i | − | 0.258734i | −0.991597 | − | 0.129367i | \(-0.958705\pi\) | ||
0.991597 | − | 0.129367i | \(-0.0412945\pi\) | |||||||
\(18\) | 14.3965 | + | 10.8046i | 0.799808 | + | 0.600256i | ||||
\(19\) | −3.21075 | − | 3.21075i | −0.168987 | − | 0.168987i | 0.617547 | − | 0.786534i | \(-0.288126\pi\) |
−0.786534 | + | 0.617547i | \(0.788126\pi\) | |||||||
\(20\) | 10.3052 | − | 14.7413i | 0.515261 | − | 0.737067i | ||||
\(21\) | −12.4622 | + | 13.1531i | −0.593440 | + | 0.626339i | ||||
\(22\) | 36.6557 | − | 3.22107i | 1.66617 | − | 0.146412i | ||||
\(23\) | −34.0396 | −1.47998 | −0.739992 | − | 0.672616i | \(-0.765171\pi\) | ||||
−0.739992 | + | 0.672616i | \(0.765171\pi\) | |||||||
\(24\) | 6.86077 | + | 22.9985i | 0.285866 | + | 0.958270i | ||||
\(25\) | − | 4.78097i | − | 0.191239i | ||||||
\(26\) | 18.0189 | − | 1.58339i | 0.693036 | − | 0.0608994i | ||||
\(27\) | 17.4867 | − | 20.5722i | 0.647656 | − | 0.761933i | ||||
\(28\) | −23.7889 | + | 4.21336i | −0.849604 | + | 0.150477i | ||||
\(29\) | −27.9597 | + | 27.9597i | −0.964128 | + | 0.964128i | −0.999378 | − | 0.0352510i | \(-0.988777\pi\) |
0.0352510 | + | 0.999378i | \(0.488777\pi\) | |||||||
\(30\) | −21.1338 | − | 16.7704i | −0.704461 | − | 0.559013i | ||||
\(31\) | −7.90993 | −0.255159 | −0.127580 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127580 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(32\) | −10.8872 | + | 30.0910i | −0.340225 | + | 0.940344i | ||||
\(33\) | −1.48814 | − | 55.1754i | −0.0450952 | − | 1.67198i | ||||
\(34\) | −6.74102 | − | 5.65200i | −0.198265 | − | 0.166235i | ||||
\(35\) | 19.2038 | − | 19.2038i | 0.548680 | − | 0.548680i | ||||
\(36\) | 35.0583 | − | 8.18005i | 0.973843 | − | 0.227224i | ||||
\(37\) | 20.0443 | − | 20.0443i | 0.541736 | − | 0.541736i | −0.382301 | − | 0.924038i | \(-0.624868\pi\) |
0.924038 | + | 0.382301i | \(0.124868\pi\) | |||||||
\(38\) | −9.04650 | + | 0.794947i | −0.238066 | + | 0.0209197i | ||||
\(39\) | −0.731530 | − | 27.1227i | −0.0187572 | − | 0.695453i | ||||
\(40\) | −9.35016 | − | 34.7360i | −0.233754 | − | 0.868401i | ||||
\(41\) | 45.1067 | 1.10016 | 0.550081 | − | 0.835111i | \(-0.314597\pi\) | ||||
0.550081 | + | 0.835111i | \(0.314597\pi\) | |||||||
\(42\) | 4.14434 | + | 36.0010i | 0.0986748 | + | 0.857166i | ||||
\(43\) | −36.0095 | + | 36.0095i | −0.837431 | + | 0.837431i | −0.988520 | − | 0.151089i | \(-0.951722\pi\) |
0.151089 | + | 0.988520i | \(0.451722\pi\) | |||||||
\(44\) | 42.1657 | − | 60.3168i | 0.958311 | − | 1.37084i | ||||
\(45\) | −27.0318 | + | 30.1168i | −0.600707 | + | 0.669262i | ||||
\(46\) | −43.7406 | + | 52.1684i | −0.950882 | + | 1.13410i | ||||
\(47\) | 5.08935i | 0.108284i | 0.998533 | + | 0.0541421i | \(0.0172424\pi\) | ||||
−0.998533 | + | 0.0541421i | \(0.982758\pi\) | |||||||
\(48\) | 44.0630 | + | 19.0381i | 0.917980 | + | 0.396628i | ||||
\(49\) | 12.5209 | 0.255529 | ||||||||
\(50\) | −7.32721 | − | 6.14349i | −0.146544 | − | 0.122870i | ||||
\(51\) | −9.07563 | + | 9.57876i | −0.177953 | + | 0.187819i | ||||
\(52\) | 20.7275 | − | 29.6501i | 0.398605 | − | 0.570194i | ||||
\(53\) | −20.7687 | − | 20.7687i | −0.391863 | − | 0.391863i | 0.483488 | − | 0.875351i | \(-0.339370\pi\) |
−0.875351 | + | 0.483488i | \(0.839370\pi\) | |||||||
\(54\) | −9.05825 | − | 53.2348i | −0.167745 | − | 0.985830i | ||||
\(55\) | 82.7299i | 1.50418i | ||||||||
\(56\) | −24.1112 | + | 41.8725i | −0.430557 | + | 0.747724i | ||||
\(57\) | 0.367268 | + | 13.6171i | 0.00644331 | + | 0.238896i | ||||
\(58\) | 6.92253 | + | 78.7784i | 0.119354 | + | 1.35825i | ||||
\(59\) | 39.0656 | + | 39.0656i | 0.662129 | + | 0.662129i | 0.955881 | − | 0.293753i | \(-0.0949043\pi\) |
−0.293753 | + | 0.955881i | \(0.594904\pi\) | |||||||
\(60\) | −52.8587 | + | 10.8395i | −0.880979 | + | 0.180658i | ||||
\(61\) | −49.8322 | − | 49.8322i | −0.816921 | − | 0.816921i | 0.168739 | − | 0.985661i | \(-0.446030\pi\) |
−0.985661 | + | 0.168739i | \(0.946030\pi\) | |||||||
\(62\) | −10.1642 | + | 12.1226i | −0.163938 | + | 0.195526i | ||||
\(63\) | 54.2791 | − | 2.93007i | 0.861573 | − | 0.0465090i | ||||
\(64\) | 32.1269 | + | 55.3522i | 0.501983 | + | 0.864878i | ||||
\(65\) | 40.6677i | 0.625657i | ||||||||
\(66\) | −86.4729 | − | 68.6191i | −1.31020 | − | 1.03968i | ||||
\(67\) | 44.9162 | + | 44.9162i | 0.670390 | + | 0.670390i | 0.957806 | − | 0.287416i | \(-0.0927961\pi\) |
−0.287416 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(68\) | −17.3243 | + | 3.06838i | −0.254769 | + | 0.0451233i | ||||
\(69\) | 74.1295 | + | 70.2358i | 1.07434 | + | 1.01791i | ||||
\(70\) | −4.75466 | − | 54.1080i | −0.0679237 | − | 0.772972i | ||||
\(71\) | −46.6947 | −0.657672 | −0.328836 | − | 0.944387i | \(-0.606656\pi\) | ||||
−0.328836 | + | 0.944387i | \(0.606656\pi\) | |||||||
\(72\) | 32.5130 | − | 64.2410i | 0.451570 | − | 0.892236i | ||||
\(73\) | − | 97.3523i | − | 1.33359i | −0.745240 | − | 0.666797i | \(-0.767665\pi\) | ||
0.745240 | − | 0.666797i | \(-0.232335\pi\) | |||||||
\(74\) | −4.96275 | − | 56.4761i | −0.0670642 | − | 0.763190i | ||||
\(75\) | −9.86483 | + | 10.4117i | −0.131531 | + | 0.138823i | ||||
\(76\) | −10.4063 | + | 14.8860i | −0.136926 | + | 0.195868i | ||||
\(77\) | 78.5758 | − | 78.5758i | 1.02047 | − | 1.02047i | ||||
\(78\) | −42.5077 | − | 33.7312i | −0.544970 | − | 0.432452i | ||||
\(79\) | −40.1637 | −0.508402 | −0.254201 | − | 0.967151i | \(-0.581812\pi\) | ||||
−0.254201 | + | 0.967151i | \(0.581812\pi\) | |||||||
\(80\) | −65.2506 | − | 30.3056i | −0.815633 | − | 0.378820i | ||||
\(81\) | −80.5293 | + | 8.71960i | −0.994189 | + | 0.107649i | ||||
\(82\) | 57.9616 | − | 69.1296i | 0.706849 | − | 0.843043i | ||||
\(83\) | 35.5451 | − | 35.5451i | 0.428254 | − | 0.428254i | −0.459779 | − | 0.888033i | \(-0.652071\pi\) |
0.888033 | + | 0.459779i | \(0.152071\pi\) | |||||||
\(84\) | 60.4998 | + | 39.9094i | 0.720236 | + | 0.475112i | ||||
\(85\) | 13.9852 | − | 13.9852i | 0.164531 | − | 0.164531i | ||||
\(86\) | 8.91558 | + | 101.459i | 0.103670 | + | 1.17976i | ||||
\(87\) | 118.580 | − | 3.19823i | 1.36299 | − | 0.0367613i | ||||
\(88\) | −38.2579 | − | 142.129i | −0.434749 | − | 1.61510i | ||||
\(89\) | −69.6795 | −0.782916 | −0.391458 | − | 0.920196i | \(-0.628029\pi\) | ||||
−0.391458 | + | 0.920196i | \(0.628029\pi\) | |||||||
\(90\) | 11.4208 | + | 80.1282i | 0.126897 | + | 0.890314i | ||||
\(91\) | 38.6257 | − | 38.6257i | 0.424458 | − | 0.424458i | ||||
\(92\) | 23.7461 | + | 134.072i | 0.258109 | + | 1.45730i | ||||
\(93\) | 17.2258 | + | 16.3210i | 0.185224 | + | 0.175495i | ||||
\(94\) | 7.79984 | + | 6.53977i | 0.0829770 | + | 0.0695720i | ||||
\(95\) | − | 20.4174i | − | 0.214920i | ||||||
\(96\) | 85.7980 | − | 43.0663i | 0.893729 | − | 0.448607i | ||||
\(97\) | 61.0939 | 0.629834 | 0.314917 | − | 0.949119i | \(-0.398023\pi\) | ||||
0.314917 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(98\) | 16.0893 | − | 19.1893i | 0.164176 | − | 0.195809i | ||||
\(99\) | −110.606 | + | 123.228i | −1.11723 | + | 1.24473i | ||||
\(100\) | −18.8308 | + | 3.33521i | −0.188308 | + | 0.0333521i | ||||
\(101\) | −104.036 | − | 104.036i | −1.03006 | − | 1.03006i | −0.999534 | − | 0.0305280i | \(-0.990281\pi\) |
−0.0305280 | − | 0.999534i | \(-0.509719\pi\) | |||||||
\(102\) | 3.01812 | + | 26.2177i | 0.0295894 | + | 0.257037i | ||||
\(103\) | − | 57.2961i | − | 0.556272i | −0.960542 | − | 0.278136i | \(-0.910283\pi\) | ||
0.960542 | − | 0.278136i | \(-0.0897167\pi\) | |||||||
\(104\) | −18.8065 | − | 69.8666i | −0.180832 | − | 0.671794i | ||||
\(105\) | −81.4452 | + | 2.19667i | −0.775668 | + | 0.0209207i | ||||
\(106\) | −58.5173 | + | 5.14212i | −0.552050 | + | 0.0485105i | ||||
\(107\) | −92.4468 | − | 92.4468i | −0.863989 | − | 0.863989i | 0.127810 | − | 0.991799i | \(-0.459205\pi\) |
−0.991799 | + | 0.127810i | \(0.959205\pi\) | |||||||
\(108\) | −93.2264 | − | 54.5238i | −0.863207 | − | 0.504850i | ||||
\(109\) | 75.3749 | + | 75.3749i | 0.691513 | + | 0.691513i | 0.962565 | − | 0.271052i | \(-0.0873714\pi\) |
−0.271052 | + | 0.962565i | \(0.587371\pi\) | |||||||
\(110\) | 126.790 | + | 106.307i | 1.15264 | + | 0.966428i | ||||
\(111\) | −85.0096 | + | 2.29281i | −0.765853 | + | 0.0206559i | ||||
\(112\) | 33.1903 | + | 90.7581i | 0.296342 | + | 0.810341i | ||||
\(113\) | 112.254i | 0.993401i | 0.867922 | + | 0.496701i | \(0.165455\pi\) | ||||
−0.867922 | + | 0.496701i | \(0.834545\pi\) | |||||||
\(114\) | 21.3412 | + | 16.9350i | 0.187204 | + | 0.148552i | ||||
\(115\) | −108.231 | − | 108.231i | −0.941135 | − | 0.941135i | ||||
\(116\) | 129.630 | + | 90.6201i | 1.11750 | + | 0.781208i | ||||
\(117\) | −54.3707 | + | 60.5756i | −0.464706 | + | 0.517740i | ||||
\(118\) | 110.070 | − | 9.67223i | 0.932797 | − | 0.0819681i | ||||
\(119\) | −26.5659 | −0.223243 | ||||||||
\(120\) | −51.3106 | + | 94.9389i | −0.427588 | + | 0.791157i | ||||
\(121\) | 217.504i | 1.79756i | ||||||||
\(122\) | −140.406 | + | 12.3379i | −1.15087 | + | 0.101131i | ||||
\(123\) | −98.2307 | − | 93.0711i | −0.798624 | − | 0.756676i | ||||
\(124\) | 5.51798 | + | 31.1548i | 0.0444998 | + | 0.251249i | ||||
\(125\) | 94.6900 | − | 94.6900i | 0.757520 | − | 0.757520i | ||||
\(126\) | 65.2575 | − | 86.9521i | 0.517917 | − | 0.690096i | ||||
\(127\) | 93.6335 | 0.737272 | 0.368636 | − | 0.929574i | \(-0.379825\pi\) | ||||
0.368636 | + | 0.929574i | \(0.379825\pi\) | |||||||
\(128\) | 126.114 | + | 21.8899i | 0.985268 | + | 0.171015i | ||||
\(129\) | 152.720 | − | 4.11903i | 1.18388 | − | 0.0319305i | ||||
\(130\) | 62.3265 | + | 52.2576i | 0.479434 | + | 0.401981i | ||||
\(131\) | 81.5208 | − | 81.5208i | 0.622296 | − | 0.622296i | −0.323822 | − | 0.946118i | \(-0.604968\pi\) |
0.946118 | + | 0.323822i | \(0.104968\pi\) | |||||||
\(132\) | −216.281 | + | 44.3518i | −1.63849 | + | 0.335998i | ||||
\(133\) | −19.3922 | + | 19.3922i | −0.145806 | + | 0.145806i | ||||
\(134\) | 126.554 | − | 11.1208i | 0.944436 | − | 0.0829909i | ||||
\(135\) | 121.010 | − | 9.81037i | 0.896371 | − | 0.0726694i | ||||
\(136\) | −17.5590 | + | 30.4937i | −0.129110 | + | 0.224218i | ||||
\(137\) | 24.5510 | 0.179205 | 0.0896023 | − | 0.995978i | \(-0.471440\pi\) | ||||
0.0896023 | + | 0.995978i | \(0.471440\pi\) | |||||||
\(138\) | 202.898 | − | 23.3571i | 1.47027 | − | 0.169254i | ||||
\(139\) | 3.06917 | − | 3.06917i | 0.0220804 | − | 0.0220804i | −0.695980 | − | 0.718061i | \(-0.745030\pi\) |
0.718061 | + | 0.695980i | \(0.245030\pi\) | |||||||
\(140\) | −89.0346 | − | 62.2414i | −0.635961 | − | 0.444581i | ||||
\(141\) | 10.5011 | − | 11.0833i | 0.0744762 | − | 0.0786050i | ||||
\(142\) | −60.0022 | + | 71.5633i | −0.422551 | + | 0.503967i | ||||
\(143\) | 166.399i | 1.16363i | ||||||||
\(144\) | −56.6755 | − | 132.378i | −0.393580 | − | 0.919290i | ||||
\(145\) | −177.798 | −1.22620 | ||||||||
\(146\) | −149.200 | − | 125.097i | −1.02192 | − | 0.856827i | ||||
\(147\) | −27.2674 | − | 25.8351i | −0.185492 | − | 0.175749i | ||||
\(148\) | −92.9312 | − | 64.9654i | −0.627913 | − | 0.438955i | ||||
\(149\) | −5.86344 | − | 5.86344i | −0.0393519 | − | 0.0393519i | 0.687157 | − | 0.726509i | \(-0.258858\pi\) |
−0.726509 | + | 0.687157i | \(0.758858\pi\) | |||||||
\(150\) | 3.28057 | + | 28.4976i | 0.0218705 | + | 0.189984i | ||||
\(151\) | − | 179.561i | − | 1.18914i | −0.804043 | − | 0.594571i | \(-0.797322\pi\) | ||
0.804043 | − | 0.594571i | \(-0.202678\pi\) | |||||||
\(152\) | 9.44191 | + | 35.0769i | 0.0621178 | + | 0.230769i | ||||
\(153\) | 39.5288 | − | 2.13382i | 0.258358 | − | 0.0139466i | ||||
\(154\) | −19.4546 | − | 221.393i | −0.126328 | − | 1.43762i | ||||
\(155\) | −25.1500 | − | 25.1500i | −0.162258 | − | 0.162258i | ||||
\(156\) | −106.318 | + | 21.8021i | −0.681524 | + | 0.139757i | ||||
\(157\) | −14.8689 | − | 14.8689i | −0.0947067 | − | 0.0947067i | 0.658166 | − | 0.752873i | \(-0.271332\pi\) |
−0.752873 | + | 0.658166i | \(0.771332\pi\) | |||||||
\(158\) | −51.6100 | + | 61.5541i | −0.326646 | + | 0.389583i | ||||
\(159\) | 2.37568 | + | 88.0822i | 0.0149414 | + | 0.553976i | ||||
\(160\) | −130.292 | + | 61.0594i | −0.814326 | + | 0.381621i | ||||
\(161\) | 205.592i | 1.27697i | ||||||||
\(162\) | −90.1159 | + | 134.622i | −0.556271 | + | 0.831001i | ||||
\(163\) | 66.1190 | + | 66.1190i | 0.405638 | + | 0.405638i | 0.880214 | − | 0.474577i | \(-0.157399\pi\) |
−0.474577 | + | 0.880214i | \(0.657399\pi\) | |||||||
\(164\) | −31.4665 | − | 177.662i | −0.191869 | − | 1.08330i | ||||
\(165\) | 170.701 | − | 180.164i | 1.03455 | − | 1.09191i | ||||
\(166\) | −8.80060 | − | 100.151i | −0.0530156 | − | 0.603318i | ||||
\(167\) | 158.709 | 0.950353 | 0.475176 | − | 0.879891i | \(-0.342384\pi\) | ||||
0.475176 | + | 0.879891i | \(0.342384\pi\) | |||||||
\(168\) | 138.906 | − | 41.4376i | 0.826821 | − | 0.246653i | ||||
\(169\) | − | 87.2028i | − | 0.515993i | ||||||
\(170\) | −3.46258 | − | 39.4042i | −0.0203681 | − | 0.231789i | ||||
\(171\) | 27.2971 | − | 30.4123i | 0.159632 | − | 0.177850i | ||||
\(172\) | 166.951 | + | 116.710i | 0.970645 | + | 0.678549i | ||||
\(173\) | −76.9955 | + | 76.9955i | −0.445061 | + | 0.445061i | −0.893709 | − | 0.448648i | \(-0.851906\pi\) |
0.448648 | + | 0.893709i | \(0.351906\pi\) | |||||||
\(174\) | 147.472 | − | 185.843i | 0.847542 | − | 1.06806i | ||||
\(175\) | −28.8760 | −0.165006 | ||||||||
\(176\) | −266.985 | − | 124.001i | −1.51696 | − | 0.704551i | ||||
\(177\) | −4.46861 | − | 165.681i | −0.0252464 | − | 0.936051i | ||||
\(178\) | −89.5375 | + | 106.789i | −0.503020 | + | 0.599941i | ||||
\(179\) | −101.360 | + | 101.360i | −0.566257 | + | 0.566257i | −0.931078 | − | 0.364821i | \(-0.881130\pi\) |
0.364821 | + | 0.931078i | \(0.381130\pi\) | |||||||
\(180\) | 137.478 | + | 85.4607i | 0.763769 | + | 0.474782i | ||||
\(181\) | −212.373 | + | 212.373i | −1.17333 | + | 1.17333i | −0.191920 | + | 0.981411i | \(0.561471\pi\) |
−0.981411 | + | 0.191920i | \(0.938529\pi\) | |||||||
\(182\) | −9.56332 | − | 108.831i | −0.0525457 | − | 0.597970i | ||||
\(183\) | 5.70017 | + | 211.343i | 0.0311485 | + | 1.15488i | ||||
\(184\) | 235.989 | + | 135.888i | 1.28255 | + | 0.738523i | ||||
\(185\) | 127.463 | 0.688991 | ||||||||
\(186\) | 47.1482 | − | 5.42758i | 0.253485 | − | 0.0291805i | ||||
\(187\) | 57.2229 | − | 57.2229i | 0.306005 | − | 0.306005i | ||||
\(188\) | 20.0454 | − | 3.55034i | 0.106625 | − | 0.0188848i | ||||
\(189\) | −124.252 | − | 105.616i | −0.657416 | − | 0.558815i | ||||
\(190\) | −31.2913 | − | 26.2362i | −0.164691 | − | 0.138085i | ||||
\(191\) | 36.3314i | 0.190217i | 0.995467 | + | 0.0951083i | \(0.0303197\pi\) | ||||
−0.995467 | + | 0.0951083i | \(0.969680\pi\) | |||||||
\(192\) | 44.2471 | − | 186.832i | 0.230453 | − | 0.973083i | ||||
\(193\) | 47.1090 | 0.244088 | 0.122044 | − | 0.992525i | \(-0.461055\pi\) | ||||
0.122044 | + | 0.992525i | \(0.461055\pi\) | |||||||
\(194\) | 78.5050 | − | 93.6313i | 0.404665 | − | 0.482635i | ||||
\(195\) | 83.9119 | − | 88.5638i | 0.430317 | − | 0.454173i | ||||
\(196\) | −8.73462 | − | 49.3162i | −0.0445644 | − | 0.251613i | ||||
\(197\) | 32.2783 | + | 32.2783i | 0.163849 | + | 0.163849i | 0.784269 | − | 0.620420i | \(-0.213038\pi\) |
−0.620420 | + | 0.784269i | \(0.713038\pi\) | |||||||
\(198\) | 46.7301 | + | 327.859i | 0.236011 | + | 1.65585i | ||||
\(199\) | 118.181i | 0.593874i | 0.954897 | + | 0.296937i | \(0.0959651\pi\) | ||||
−0.954897 | + | 0.296937i | \(0.904035\pi\) | |||||||
\(200\) | −19.0859 | + | 33.1454i | −0.0954295 | + | 0.165727i | ||||
\(201\) | −5.13784 | − | 190.494i | −0.0255614 | − | 0.947731i | ||||
\(202\) | −293.129 | + | 25.7583i | −1.45114 | + | 0.127516i | ||||
\(203\) | 168.871 | + | 168.871i | 0.831875 | + | 0.831875i | ||||
\(204\) | 44.0590 | + | 29.0640i | 0.215976 | + | 0.142471i | ||||
\(205\) | 143.419 | + | 143.419i | 0.699604 | + | 0.699604i | ||||
\(206\) | −87.8108 | − | 73.6249i | −0.426266 | − | 0.357402i | ||||
\(207\) | −16.5136 | − | 305.911i | −0.0797756 | − | 1.47783i | ||||
\(208\) | −131.242 | − | 60.9554i | −0.630972 | − | 0.293055i | ||||
\(209\) | − | 83.5416i | − | 0.399721i | ||||||
\(210\) | −101.290 | + | 127.644i | −0.482332 | + | 0.607828i | ||||
\(211\) | 63.8884 | + | 63.8884i | 0.302789 | + | 0.302789i | 0.842104 | − | 0.539315i | \(-0.181317\pi\) |
−0.539315 | + | 0.842104i | \(0.681317\pi\) | |||||||
\(212\) | −67.3134 | + | 96.2900i | −0.317516 | + | 0.454198i | ||||
\(213\) | 101.689 | + | 96.3478i | 0.477413 | + | 0.452337i | ||||
\(214\) | −260.475 | + | 22.8889i | −1.21717 | + | 0.106957i | ||||
\(215\) | −228.988 | −1.06506 | ||||||||
\(216\) | −203.357 | + | 72.8144i | −0.941468 | + | 0.337104i | ||||
\(217\) | 47.7743i | 0.220158i | ||||||||
\(218\) | 212.374 | − | 18.6621i | 0.974193 | − | 0.0856057i | ||||
\(219\) | −200.872 | + | 212.008i | −0.917226 | + | 0.968075i | ||||
\(220\) | 325.848 | − | 57.7124i | 1.48113 | − | 0.262329i | ||||
\(221\) | 28.1292 | − | 28.1292i | 0.127281 | − | 0.127281i | ||||
\(222\) | −105.723 | + | 133.230i | −0.476228 | + | 0.600136i | ||||
\(223\) | −42.8886 | −0.192326 | −0.0961628 | − | 0.995366i | \(-0.530657\pi\) | ||||
−0.0961628 | + | 0.995366i | \(0.530657\pi\) | |||||||
\(224\) | 181.743 | + | 65.7565i | 0.811354 | + | 0.293556i | ||||
\(225\) | 42.9661 | − | 2.31938i | 0.190961 | − | 0.0103084i | ||||
\(226\) | 172.039 | + | 144.246i | 0.761233 | + | 0.638255i | ||||
\(227\) | −23.0035 | + | 23.0035i | −0.101337 | + | 0.101337i | −0.755958 | − | 0.654621i | \(-0.772828\pi\) |
0.654621 | + | 0.755958i | \(0.272828\pi\) | |||||||
\(228\) | 53.3774 | − | 10.9459i | 0.234111 | − | 0.0480081i | ||||
\(229\) | 241.282 | − | 241.282i | 1.05363 | − | 1.05363i | 0.0551571 | − | 0.998478i | \(-0.482434\pi\) |
0.998478 | − | 0.0551571i | \(-0.0175660\pi\) | |||||||
\(230\) | −304.947 | + | 26.7968i | −1.32586 | + | 0.116508i | ||||
\(231\) | −333.248 | + | 8.98807i | −1.44263 | + | 0.0389094i | ||||
\(232\) | 305.455 | − | 82.2217i | 1.31662 | − | 0.354404i | ||||
\(233\) | −240.310 | −1.03137 | −0.515687 | − | 0.856777i | \(-0.672463\pi\) | ||||
−0.515687 | + | 0.856777i | \(0.672463\pi\) | |||||||
\(234\) | 22.9712 | + | 161.166i | 0.0981677 | + | 0.688745i | ||||
\(235\) | −16.1818 | + | 16.1818i | −0.0688589 | + | 0.0688589i | ||||
\(236\) | 126.615 | − | 181.120i | 0.536506 | − | 0.767457i | ||||
\(237\) | 87.4663 | + | 82.8721i | 0.369056 | + | 0.349671i | ||||
\(238\) | −34.1369 | + | 40.7143i | −0.143432 | + | 0.171069i | ||||
\(239\) | − | 218.171i | − | 0.912851i | −0.889762 | − | 0.456425i | \(-0.849130\pi\) | ||
0.889762 | − | 0.456425i | \(-0.150870\pi\) | |||||||
\(240\) | 79.5678 | + | 200.633i | 0.331533 | + | 0.835971i | ||||
\(241\) | −88.9611 | −0.369133 | −0.184567 | − | 0.982820i | \(-0.559088\pi\) | ||||
−0.184567 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(242\) | 333.343 | + | 279.491i | 1.37745 | + | 1.15492i | ||||
\(243\) | 193.364 | + | 147.172i | 0.795736 | + | 0.605644i | ||||
\(244\) | −161.511 | + | 231.037i | −0.661931 | + | 0.946873i | ||||
\(245\) | 39.8109 | + | 39.8109i | 0.162493 | + | 0.162493i | ||||
\(246\) | −268.864 | + | 30.9510i | −1.09294 | + | 0.125817i | ||||
\(247\) | − | 41.0667i | − | 0.166262i | ||||||
\(248\) | 54.8378 | + | 31.5769i | 0.221120 | + | 0.127326i | ||||
\(249\) | −150.750 | + | 4.06591i | −0.605423 | + | 0.0163289i | ||||
\(250\) | −23.4443 | − | 266.796i | −0.0937770 | − | 1.06718i | ||||
\(251\) | 169.225 | + | 169.225i | 0.674205 | + | 0.674205i | 0.958683 | − | 0.284478i | \(-0.0918201\pi\) |
−0.284478 | + | 0.958683i | \(0.591820\pi\) | |||||||
\(252\) | −49.4058 | − | 211.745i | −0.196055 | − | 0.840258i | ||||
\(253\) | −442.845 | − | 442.845i | −1.75038 | − | 1.75038i | ||||
\(254\) | 120.318 | − | 143.501i | 0.473693 | − | 0.564964i | ||||
\(255\) | −59.3125 | + | 1.59973i | −0.232598 | + | 0.00627343i | ||||
\(256\) | 195.604 | − | 165.152i | 0.764077 | − | 0.645125i | ||||
\(257\) | − | 393.109i | − | 1.52961i | −0.644262 | − | 0.764804i | \(-0.722836\pi\) | ||
0.644262 | − | 0.764804i | \(-0.277164\pi\) | |||||||
\(258\) | 189.931 | − | 239.348i | 0.736166 | − | 0.927707i | ||||
\(259\) | −121.063 | − | 121.063i | −0.467425 | − | 0.467425i | ||||
\(260\) | 160.178 | − | 28.3698i | 0.616068 | − | 0.109115i | ||||
\(261\) | −264.835 | − | 237.707i | −1.01470 | − | 0.910756i | ||||
\(262\) | −20.1837 | − | 229.690i | −0.0770370 | − | 0.876681i | ||||
\(263\) | −179.865 | −0.683897 | −0.341948 | − | 0.939719i | \(-0.611087\pi\) | ||||
−0.341948 | + | 0.939719i | \(0.611087\pi\) | |||||||
\(264\) | −209.947 | + | 388.460i | −0.795252 | + | 1.47144i | ||||
\(265\) | − | 132.070i | − | 0.498378i | ||||||
\(266\) | 4.80131 | + | 54.6390i | 0.0180501 | + | 0.205410i | ||||
\(267\) | 151.744 | + | 143.774i | 0.568330 | + | 0.538478i | ||||
\(268\) | 145.578 | − | 208.245i | 0.543200 | − | 0.777033i | ||||
\(269\) | −290.530 | + | 290.530i | −1.08004 | + | 1.08004i | −0.0835324 | + | 0.996505i | \(0.526620\pi\) |
−0.996505 | + | 0.0835324i | \(0.973380\pi\) | |||||||
\(270\) | 140.462 | − | 198.064i | 0.520228 | − | 0.733570i | ||||
\(271\) | 496.550 | 1.83229 | 0.916144 | − | 0.400849i | \(-0.131285\pi\) | ||||
0.916144 | + | 0.400849i | \(0.131285\pi\) | |||||||
\(272\) | 24.1709 | + | 66.0947i | 0.0888635 | + | 0.242995i | ||||
\(273\) | −163.815 | + | 4.41829i | −0.600056 | + | 0.0161842i | ||||
\(274\) | 31.5478 | − | 37.6264i | 0.115138 | − | 0.137323i | ||||
\(275\) | 62.1989 | − | 62.1989i | 0.226178 | − | 0.226178i | ||||
\(276\) | 224.925 | − | 340.970i | 0.814946 | − | 1.23540i | ||||
\(277\) | −93.0101 | + | 93.0101i | −0.335776 | + | 0.335776i | −0.854775 | − | 0.518999i | \(-0.826305\pi\) |
0.518999 | + | 0.854775i | \(0.326305\pi\) | |||||||
\(278\) | −0.759895 | − | 8.64760i | −0.00273343 | − | 0.0311065i | ||||
\(279\) | −3.83733 | − | 71.0859i | −0.0137539 | − | 0.254788i | ||||
\(280\) | −209.798 | + | 56.4730i | −0.749280 | + | 0.201689i | ||||
\(281\) | 300.875 | 1.07073 | 0.535365 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535365 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(282\) | −3.49218 | − | 30.3358i | −0.0123836 | − | 0.107574i | ||||
\(283\) | 101.469 | − | 101.469i | 0.358549 | − | 0.358549i | −0.504729 | − | 0.863278i | \(-0.668408\pi\) |
0.863278 | + | 0.504729i | \(0.168408\pi\) | |||||||
\(284\) | 32.5743 | + | 183.916i | 0.114698 | + | 0.647593i | ||||
\(285\) | −42.1284 | + | 44.4639i | −0.147819 | + | 0.156014i | ||||
\(286\) | 255.020 | + | 213.821i | 0.891679 | + | 0.747627i | ||||
\(287\) | − | 272.435i | − | 0.949250i | ||||||
\(288\) | −275.707 | − | 83.2445i | −0.957316 | − | 0.289043i | ||||
\(289\) | 269.653 | 0.933057 | ||||||||
\(290\) | −228.469 | + | 272.490i | −0.787824 | + | 0.939621i | ||||
\(291\) | −133.047 | − | 126.058i | −0.457205 | − | 0.433190i | ||||
\(292\) | −383.442 | + | 67.9131i | −1.31316 | + | 0.232579i | ||||
\(293\) | 321.104 | + | 321.104i | 1.09592 | + | 1.09592i | 0.994883 | + | 0.101037i | \(0.0322160\pi\) |
0.101037 | + | 0.994883i | \(0.467784\pi\) | |||||||
\(294\) | −74.6327 | + | 8.59153i | −0.253853 | + | 0.0292229i | ||||
\(295\) | 248.422i | 0.842107i | ||||||||
\(296\) | −218.980 | + | 58.9445i | −0.739798 | + | 0.199137i | ||||
\(297\) | 495.135 | − | 40.1409i | 1.66712 | − | 0.135155i | ||||
\(298\) | −16.5206 | + | 1.45173i | −0.0554384 | + | 0.00487156i | ||||
\(299\) | −217.690 | − | 217.690i | −0.728061 | − | 0.728061i | ||||
\(300\) | 47.8903 | + | 31.5914i | 0.159634 | + | 0.105305i | ||||
\(301\) | 217.490 | + | 217.490i | 0.722558 | + | 0.722558i | ||||
\(302\) | −275.191 | − | 230.733i | −0.911228 | − | 0.764018i | ||||
\(303\) | 11.9004 | + | 441.228i | 0.0392753 | + | 1.45620i | ||||
\(304\) | 65.8909 | + | 30.6030i | 0.216746 | + | 0.100668i | ||||
\(305\) | − | 316.888i | − | 1.03898i | ||||||
\(306\) | 47.5238 | − | 63.3229i | 0.155307 | − | 0.206938i | ||||
\(307\) | 94.2282 | + | 94.2282i | 0.306932 | + | 0.306932i | 0.843718 | − | 0.536786i | \(-0.180362\pi\) |
−0.536786 | + | 0.843718i | \(0.680362\pi\) | |||||||
\(308\) | −364.301 | − | 254.672i | −1.18280 | − | 0.826857i | ||||
\(309\) | −118.222 | + | 124.776i | −0.382596 | + | 0.403806i | ||||
\(310\) | −70.8619 | + | 6.22688i | −0.228587 | + | 0.0200867i | ||||
\(311\) | 245.712 | 0.790070 | 0.395035 | − | 0.918666i | \(-0.370732\pi\) | ||||
0.395035 | + | 0.918666i | \(0.370732\pi\) | |||||||
\(312\) | −103.204 | + | 190.956i | −0.330782 | + | 0.612038i | ||||
\(313\) | 353.841i | 1.13048i | 0.824925 | + | 0.565242i | \(0.191217\pi\) | ||||
−0.824925 | + | 0.565242i | \(0.808783\pi\) | |||||||
\(314\) | −41.8943 | + | 3.68140i | −0.133421 | + | 0.0117242i | ||||
\(315\) | 181.899 | + | 163.267i | 0.577458 | + | 0.518307i | ||||
\(316\) | 28.0183 | + | 158.193i | 0.0886654 | + | 0.500610i | ||||
\(317\) | −234.024 | + | 234.024i | −0.738245 | + | 0.738245i | −0.972238 | − | 0.233994i | \(-0.924821\pi\) |
0.233994 | + | 0.972238i | \(0.424821\pi\) | |||||||
\(318\) | 138.046 | + | 109.544i | 0.434106 | + | 0.344477i | ||||
\(319\) | −727.494 | −2.28055 | ||||||||
\(320\) | −73.8458 | + | 278.144i | −0.230768 | + | 0.869199i | ||||
\(321\) | 10.5747 | + | 392.076i | 0.0329431 | + | 1.22142i | ||||
\(322\) | 315.086 | + | 264.184i | 0.978529 | + | 0.820447i | ||||
\(323\) | −14.1224 | + | 14.1224i | −0.0437226 | + | 0.0437226i | ||||
\(324\) | 90.5212 | + | 311.098i | 0.279386 | + | 0.960179i | ||||
\(325\) | 30.5752 | − | 30.5752i | 0.0940777 | − | 0.0940777i | ||||
\(326\) | 186.295 | − | 16.3704i | 0.571456 | − | 0.0502158i | ||||
\(327\) | −8.62193 | − | 319.673i | −0.0263668 | − | 0.977592i | ||||
\(328\) | −312.715 | − | 180.069i | −0.953398 | − | 0.548989i | ||||
\(329\) | 30.7386 | 0.0934305 | ||||||||
\(330\) | −56.7670 | − | 493.122i | −0.172021 | − | 1.49431i | ||||
\(331\) | −32.5392 | + | 32.5392i | −0.0983058 | + | 0.0983058i | −0.754549 | − | 0.656243i | \(-0.772144\pi\) |
0.656243 | + | 0.754549i | \(0.272144\pi\) | |||||||
\(332\) | −164.798 | − | 115.205i | −0.496379 | − | 0.347004i | ||||
\(333\) | 189.860 | + | 170.412i | 0.570150 | + | 0.511748i | ||||
\(334\) | 203.939 | − | 243.234i | 0.610597 | − | 0.728246i | ||||
\(335\) | 285.626i | 0.852615i | ||||||||
\(336\) | 114.986 | − | 266.131i | 0.342221 | − | 0.792058i | ||||
\(337\) | −185.573 | −0.550660 | −0.275330 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275330 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(338\) | −133.645 | − | 112.055i | −0.395400 | − | 0.331523i | ||||
\(339\) | 231.621 | − | 244.461i | 0.683247 | − | 0.721124i | ||||
\(340\) | −64.8395 | − | 45.3273i | −0.190704 | − | 0.133316i | ||||
\(341\) | −102.906 | − | 102.906i | −0.301776 | − | 0.301776i | ||||
\(342\) | −11.5328 | − | 80.9145i | −0.0337217 | − | 0.236592i | ||||
\(343\) | − | 371.574i | − | 1.08330i | ||||||
\(344\) | 393.398 | − | 105.894i | 1.14360 | − | 0.307831i | ||||
\(345\) | 12.3802 | + | 459.016i | 0.0358846 | + | 1.33048i | ||||
\(346\) | 19.0633 | + | 216.940i | 0.0550962 | + | 0.626995i | ||||
\(347\) | −51.9585 | − | 51.9585i | −0.149736 | − | 0.149736i | 0.628264 | − | 0.778000i | \(-0.283766\pi\) |
−0.778000 | + | 0.628264i | \(0.783766\pi\) | |||||||
\(348\) | −95.3183 | − | 464.819i | −0.273903 | − | 1.33569i | ||||
\(349\) | 378.719 | + | 378.719i | 1.08515 | + | 1.08515i | 0.996020 | + | 0.0891344i | \(0.0284101\pi\) |
0.0891344 | + | 0.996020i | \(0.471590\pi\) | |||||||
\(350\) | −37.1054 | + | 44.2548i | −0.106015 | + | 0.126442i | ||||
\(351\) | 243.394 | − | 19.7322i | 0.693431 | − | 0.0562170i | ||||
\(352\) | −533.114 | + | 249.835i | −1.51453 | + | 0.709760i | ||||
\(353\) | − | 326.435i | − | 0.924744i | −0.886686 | − | 0.462372i | \(-0.846998\pi\) | ||
0.886686 | − | 0.462372i | \(-0.153002\pi\) | |||||||
\(354\) | −259.661 | − | 206.050i | −0.733507 | − | 0.582062i | ||||
\(355\) | −148.468 | − | 148.468i | −0.418220 | − | 0.418220i | ||||
\(356\) | 48.6085 | + | 274.447i | 0.136541 | + | 0.770918i | ||||
\(357\) | 57.8537 | + | 54.8149i | 0.162055 | + | 0.153543i | ||||
\(358\) | 25.0957 | + | 285.589i | 0.0700997 | + | 0.797734i | ||||
\(359\) | 254.927 | 0.710103 | 0.355051 | − | 0.934847i | \(-0.384463\pi\) | ||||
0.355051 | + | 0.934847i | \(0.384463\pi\) | |||||||
\(360\) | 307.634 | − | 100.880i | 0.854539 | − | 0.280224i | ||||
\(361\) | − | 340.382i | − | 0.942887i | ||||||
\(362\) | 52.5813 | + | 598.375i | 0.145252 | + | 1.65297i | ||||
\(363\) | 448.789 | − | 473.668i | 1.23633 | − | 1.30487i | ||||
\(364\) | −179.080 | − | 125.190i | −0.491979 | − | 0.343928i | ||||
\(365\) | 309.536 | − | 309.536i | 0.848045 | − | 0.848045i | ||||
\(366\) | 331.225 | + | 262.838i | 0.904986 | + | 0.718137i | ||||
\(367\) | −124.247 | −0.338548 | −0.169274 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169274 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(368\) | 511.503 | − | 187.057i | 1.38995 | − | 0.508308i | ||||
\(369\) | 21.8825 | + | 405.370i | 0.0593021 | + | 1.09856i | ||||
\(370\) | 163.789 | − | 195.348i | 0.442673 | − | 0.527966i | ||||
\(371\) | −125.439 | + | 125.439i | −0.338110 | + | 0.338110i | ||||
\(372\) | 52.2668 | − | 79.2328i | 0.140502 | − | 0.212991i | ||||
\(373\) | −201.674 | + | 201.674i | −0.540680 | + | 0.540680i | −0.923728 | − | 0.383048i | \(-0.874874\pi\) |
0.383048 | + | 0.923728i | \(0.374874\pi\) | |||||||
\(374\) | −14.1678 | − | 161.229i | −0.0378818 | − | 0.431095i | ||||
\(375\) | −401.589 | + | 10.8313i | −1.07091 | + | 0.0288835i | ||||
\(376\) | 20.3170 | − | 35.2834i | 0.0540346 | − | 0.0938388i | ||||
\(377\) | −357.616 | −0.948583 | ||||||||
\(378\) | −321.527 | + | 54.7099i | −0.850601 | + | 0.144735i | ||||
\(379\) | −227.541 | + | 227.541i | −0.600372 | + | 0.600372i | −0.940411 | − | 0.340040i | \(-0.889560\pi\) |
0.340040 | + | 0.940411i | \(0.389560\pi\) | |||||||
\(380\) | −80.4181 | + | 14.2432i | −0.211627 | + | 0.0374822i | ||||
\(381\) | −203.910 | − | 193.199i | −0.535196 | − | 0.507084i | ||||
\(382\) | 55.6807 | + | 46.6854i | 0.145761 | + | 0.122213i | ||||
\(383\) | − | 128.933i | − | 0.336641i | −0.985732 | − | 0.168320i | \(-0.946166\pi\) | ||
0.985732 | − | 0.168320i | \(-0.0538343\pi\) | |||||||
\(384\) | −229.478 | − | 307.889i | −0.597599 | − | 0.801795i | ||||
\(385\) | 499.671 | 1.29785 | ||||||||
\(386\) | 60.5346 | − | 72.1982i | 0.156825 | − | 0.187042i | ||||
\(387\) | −341.084 | − | 306.145i | −0.881353 | − | 0.791073i | ||||
\(388\) | −42.6192 | − | 240.630i | −0.109843 | − | 0.620182i | ||||
\(389\) | −107.474 | − | 107.474i | −0.276283 | − | 0.276283i | 0.555340 | − | 0.831623i | \(-0.312588\pi\) |
−0.831623 | + | 0.555340i | \(0.812588\pi\) | |||||||
\(390\) | −27.9051 | − | 242.405i | −0.0715515 | − | 0.621552i | ||||
\(391\) | 149.723i | 0.382922i | ||||||||
\(392\) | −86.8049 | − | 49.9843i | −0.221441 | − | 0.127511i | ||||
\(393\) | −345.738 | + | 9.32494i | −0.879739 | + | 0.0237276i | ||||
\(394\) | 90.9463 | − | 7.99176i | 0.230828 | − | 0.0202837i | ||||
\(395\) | −127.702 | − | 127.702i | −0.323297 | − | 0.323297i | ||||
\(396\) | 562.518 | + | 349.678i | 1.42050 | + | 0.883026i | ||||
\(397\) | −259.306 | − | 259.306i | −0.653163 | − | 0.653163i | 0.300591 | − | 0.953753i | \(-0.402816\pi\) |
−0.953753 | + | 0.300591i | \(0.902816\pi\) | |||||||
\(398\) | 181.122 | + | 151.861i | 0.455080 | + | 0.381561i | ||||
\(399\) | 82.2444 | − | 2.21822i | 0.206126 | − | 0.00555946i | ||||
\(400\) | 26.2728 | + | 71.8422i | 0.0656819 | + | 0.179605i | ||||
\(401\) | 335.810i | 0.837431i | 0.908117 | + | 0.418716i | \(0.137520\pi\) | ||||
−0.908117 | + | 0.418716i | \(0.862480\pi\) | |||||||
\(402\) | −298.549 | − | 236.909i | −0.742659 | − | 0.589325i | ||||
\(403\) | −50.5856 | − | 50.5856i | −0.125523 | − | 0.125523i | ||||
\(404\) | −337.192 | + | 482.343i | −0.834633 | + | 1.19392i | ||||
\(405\) | −283.771 | − | 228.322i | −0.700669 | − | 0.563759i | ||||
\(406\) | 475.805 | − | 41.8106i | 1.17193 | − | 0.102982i | ||||
\(407\) | 521.539 | 1.28142 | ||||||||
\(408\) | 101.158 | − | 30.1770i | 0.247937 | − | 0.0739632i | ||||
\(409\) | − | 66.3618i | − | 0.162254i | −0.996704 | − | 0.0811269i | \(-0.974148\pi\) | ||
0.996704 | − | 0.0811269i | \(-0.0258519\pi\) | |||||||
\(410\) | 404.092 | − | 35.5090i | 0.985591 | − | 0.0866073i | ||||
\(411\) | −53.4658 | − | 50.6575i | −0.130087 | − | 0.123254i | ||||
\(412\) | −225.672 | + | 39.9698i | −0.547747 | + | 0.0970140i | ||||
\(413\) | 235.948 | − | 235.948i | 0.571303 | − | 0.571303i | ||||
\(414\) | −490.053 | − | 367.784i | −1.18370 | − | 0.888368i | ||||
\(415\) | 226.035 | 0.544662 | ||||||||
\(416\) | −262.064 | + | 122.812i | −0.629961 | + | 0.295222i | ||||
\(417\) | −13.0167 | + | 0.351074i | −0.0312150 | + | 0.000841904i | ||||
\(418\) | −128.034 | − | 107.350i | −0.306302 | − | 0.256819i | ||||
\(419\) | −371.566 | + | 371.566i | −0.886792 | + | 0.886792i | −0.994214 | − | 0.107422i | \(-0.965740\pi\) |
0.107422 | + | 0.994214i | \(0.465740\pi\) | |||||||
\(420\) | 65.4683 | + | 319.256i | 0.155877 | + | 0.760133i | ||||
\(421\) | 487.629 | − | 487.629i | 1.15826 | − | 1.15826i | 0.173416 | − | 0.984849i | \(-0.444519\pi\) |
0.984849 | − | 0.173416i | \(-0.0554806\pi\) | |||||||
\(422\) | 180.010 | − | 15.8181i | 0.426564 | − | 0.0374837i | ||||
\(423\) | −45.7376 | + | 2.46899i | −0.108127 | + | 0.00583685i | ||||
\(424\) | 61.0750 | + | 226.895i | 0.144045 | + | 0.535129i | ||||
\(425\) | −21.0290 | −0.0494800 | ||||||||
\(426\) | 278.330 | − | 32.0406i | 0.653357 | − | 0.0752128i | ||||
\(427\) | −300.976 | + | 300.976i | −0.704862 | + | 0.704862i | ||||
\(428\) | −299.629 | + | 428.611i | −0.700068 | + | 1.00143i | ||||
\(429\) | 343.341 | − | 362.375i | 0.800328 | − | 0.844696i | ||||
\(430\) | −294.247 | + | 350.942i | −0.684296 | + | 0.816145i | ||||
\(431\) | − | 505.901i | − | 1.17378i | −0.809665 | − | 0.586892i | \(-0.800351\pi\) | ||
0.809665 | − | 0.586892i | \(-0.199649\pi\) | |||||||
\(432\) | −149.718 | + | 405.227i | −0.346569 | + | 0.938024i | ||||
\(433\) | −758.226 | −1.75110 | −0.875550 | − | 0.483128i | \(-0.839500\pi\) | ||||
−0.875550 | + | 0.483128i | \(0.839500\pi\) | |||||||
\(434\) | 73.2180 | + | 61.3895i | 0.168705 | + | 0.141451i | ||||
\(435\) | 387.199 | + | 366.861i | 0.890113 | + | 0.843359i | ||||
\(436\) | 244.298 | − | 349.461i | 0.560316 | − | 0.801516i | ||||
\(437\) | 109.293 | + | 109.293i | 0.250097 | + | 0.250097i | ||||
\(438\) | 66.8005 | + | 580.282i | 0.152513 | + | 1.32484i | ||||
\(439\) | 145.760i | 0.332026i | 0.986124 | + | 0.166013i | \(0.0530895\pi\) | ||||
−0.986124 | + | 0.166013i | \(0.946911\pi\) | |||||||
\(440\) | 330.263 | − | 573.548i | 0.750597 | − | 1.30352i | ||||
\(441\) | 6.07425 | + | 112.525i | 0.0137738 | + | 0.255158i | ||||
\(442\) | −6.96449 | − | 79.2559i | −0.0157568 | − | 0.179312i | ||||
\(443\) | −607.046 | − | 607.046i | −1.37031 | − | 1.37031i | −0.859983 | − | 0.510323i | \(-0.829526\pi\) |
−0.510323 | − | 0.859983i | \(-0.670474\pi\) | |||||||
\(444\) | 68.3335 | + | 333.228i | 0.153904 | + | 0.750513i | ||||
\(445\) | −221.549 | − | 221.549i | −0.497864 | − | 0.497864i | ||||
\(446\) | −55.1114 | + | 65.7302i | −0.123568 | + | 0.147377i | ||||
\(447\) | 0.670702 | + | 24.8674i | 0.00150045 | + | 0.0556318i | ||||
\(448\) | 334.315 | − | 194.040i | 0.746240 | − | 0.433124i | ||||
\(449\) | 190.654i | 0.424620i | 0.977202 | + | 0.212310i | \(0.0680986\pi\) | ||||
−0.977202 | + | 0.212310i | \(0.931901\pi\) | |||||||
\(450\) | 51.6564 | − | 68.8294i | 0.114792 | − | 0.152954i | ||||
\(451\) | 586.824 | + | 586.824i | 1.30116 | + | 1.30116i | ||||
\(452\) | 442.136 | − | 78.3087i | 0.978177 | − | 0.173249i | ||||
\(453\) | −370.497 | + | 391.037i | −0.817875 | + | 0.863216i | ||||
\(454\) | 5.69542 | + | 64.8139i | 0.0125450 | + | 0.142762i | ||||
\(455\) | 245.624 | 0.539834 | ||||||||
\(456\) | 51.8141 | − | 95.8705i | 0.113627 | − | 0.210242i | ||||
\(457\) | − | 128.091i | − | 0.280287i | −0.990131 | − | 0.140143i | \(-0.955244\pi\) | ||
0.990131 | − | 0.140143i | \(-0.0447563\pi\) | |||||||
\(458\) | −59.7390 | − | 679.830i | −0.130435 | − | 1.48434i | ||||
\(459\) | −90.4863 | − | 76.9150i | −0.197138 | − | 0.167571i | ||||
\(460\) | −350.786 | + | 501.789i | −0.762578 | + | 1.09085i | ||||
\(461\) | 74.2060 | − | 74.2060i | 0.160968 | − | 0.160968i | −0.622028 | − | 0.782995i | \(-0.713691\pi\) |
0.782995 | + | 0.622028i | \(0.213691\pi\) | |||||||
\(462\) | −414.445 | + | 522.278i | −0.897067 | + | 1.13047i | ||||
\(463\) | 620.192 | 1.33951 | 0.669753 | − | 0.742584i | \(-0.266400\pi\) | ||||
0.669753 | + | 0.742584i | \(0.266400\pi\) | |||||||
\(464\) | 266.496 | − | 573.789i | 0.574344 | − | 1.23661i | ||||
\(465\) | 2.87684 | + | 106.664i | 0.00618675 | + | 0.229384i | ||||
\(466\) | −308.796 | + | 368.294i | −0.662653 | + | 0.790331i | ||||
\(467\) | −331.708 | + | 331.708i | −0.710296 | + | 0.710296i | −0.966597 | − | 0.256301i | \(-0.917496\pi\) |
0.256301 | + | 0.966597i | \(0.417496\pi\) | |||||||
\(468\) | 276.518 | + | 171.892i | 0.590851 | + | 0.367291i | ||||
\(469\) | 271.284 | − | 271.284i | 0.578431 | − | 0.578431i | ||||
\(470\) | 4.00646 | + | 45.5935i | 0.00852437 | + | 0.0970074i | ||||
\(471\) | 1.70082 | + | 63.0607i | 0.00361108 | + | 0.133887i | ||||
\(472\) | −114.881 | − | 426.785i | −0.243392 | − | 0.904206i | ||||
\(473\) | −936.946 | −1.98086 | ||||||||
\(474\) | 239.401 | − | 27.5593i | 0.505066 | − | 0.0581419i | ||||
\(475\) | −15.3505 | + | 15.3505i | −0.0323168 | + | 0.0323168i | ||||
\(476\) | 18.5324 | + | 104.635i | 0.0389336 | + | 0.219822i | ||||
\(477\) | 176.571 | − | 196.722i | 0.370170 | − | 0.412415i | ||||
\(478\) | −334.365 | − | 280.348i | −0.699508 | − | 0.586502i | ||||
\(479\) | 867.941i | 1.81198i | 0.423294 | + | 0.905992i | \(0.360874\pi\) | ||||
−0.423294 | + | 0.905992i | \(0.639126\pi\) | |||||||
\(480\) | 409.730 | + | 135.867i | 0.853604 | + | 0.283057i | ||||
\(481\) | 256.374 | 0.533002 | ||||||||
\(482\) | −114.314 | + | 136.340i | −0.237166 | + | 0.282863i | ||||
\(483\) | 424.210 | − | 447.727i | 0.878281 | − | 0.926970i | ||||
\(484\) | 856.684 | − | 151.731i | 1.77001 | − | 0.313494i | ||||
\(485\) | 194.251 | + | 194.251i | 0.400517 | + | 0.400517i | ||||
\(486\) | 474.023 | − | 107.231i | 0.975355 | − | 0.220641i | ||||
\(487\) | 815.778i | 1.67511i | 0.546354 | + | 0.837554i | \(0.316015\pi\) | ||||
−0.546354 | + | 0.837554i | \(0.683985\pi\) | |||||||
\(488\) | 146.543 | + | 544.409i | 0.300292 | + | 1.11559i | ||||
\(489\) | −7.56317 | − | 280.417i | −0.0154666 | − | 0.573450i | ||||
\(490\) | 112.170 | − | 9.85676i | 0.228918 | − | 0.0201158i | ||||
\(491\) | 337.746 | + | 337.746i | 0.687874 | + | 0.687874i | 0.961762 | − | 0.273888i | \(-0.0883098\pi\) |
−0.273888 | + | 0.961762i | \(0.588310\pi\) | |||||||
\(492\) | −298.053 | + | 451.828i | −0.605799 | + | 0.918349i | ||||
\(493\) | 122.980 | + | 122.980i | 0.249453 | + | 0.249453i | ||||
\(494\) | −62.9380 | − | 52.7703i | −0.127405 | − | 0.106823i | ||||
\(495\) | −743.486 | + | 40.1345i | −1.50199 | + | 0.0810799i | ||||
\(496\) | 118.860 | − | 43.4673i | 0.239637 | − | 0.0876357i | ||||
\(497\) | 282.026i | 0.567457i | ||||||||
\(498\) | −187.481 | + | 236.261i | −0.376468 | + | 0.474421i | ||||
\(499\) | −515.289 | − | 515.289i | −1.03264 | − | 1.03264i | −0.999449 | − | 0.0331940i | \(-0.989432\pi\) |
−0.0331940 | − | 0.999449i | \(-0.510568\pi\) | |||||||
\(500\) | −439.011 | − | 306.900i | −0.878022 | − | 0.613799i | ||||
\(501\) | −345.627 | − | 327.473i | −0.689875 | − | 0.653639i | ||||
\(502\) | 476.805 | − | 41.8985i | 0.949810 | − | 0.0834631i | ||||
\(503\) | 196.781 | 0.391215 | 0.195607 | − | 0.980682i | \(-0.437332\pi\) | ||||
0.195607 | + | 0.980682i | \(0.437332\pi\) | |||||||
\(504\) | −388.002 | − | 196.372i | −0.769845 | − | 0.389627i | ||||
\(505\) | − | 661.576i | − | 1.31005i | ||||||
\(506\) | −1247.75 | + | 109.644i | −2.46590 | + | 0.216687i | ||||
\(507\) | −179.930 | + | 189.905i | −0.354892 | + | 0.374567i | ||||
\(508\) | −65.3188 | − | 368.794i | −0.128580 | − | 0.725973i | ||||
\(509\) | −29.3054 | + | 29.3054i | −0.0575744 | + | 0.0575744i | −0.735308 | − | 0.677733i | \(-0.762962\pi\) |
0.677733 | + | 0.735308i | \(0.262962\pi\) | |||||||
\(510\) | −73.7642 | + | 92.9567i | −0.144636 | + | 0.182268i | ||||
\(511\) | −587.988 | −1.15066 | ||||||||
\(512\) | −1.75962 | − | 511.997i | −0.00343675 | − | 0.999994i | ||||
\(513\) | −122.197 | + | 9.90664i | −0.238202 | + | 0.0193112i | ||||
\(514\) | −602.472 | − | 505.142i | −1.17212 | − | 0.982766i | ||||
\(515\) | 182.175 | − | 182.175i | 0.353739 | − | 0.353739i | ||||
\(516\) | −122.761 | − | 598.644i | −0.237909 | − | 1.16016i | ||||
\(517\) | −66.2109 | + | 66.2109i | −0.128068 | + | 0.128068i | ||||
\(518\) | −341.104 | + | 29.9740i | −0.658501 | + | 0.0578648i | ||||
\(519\) | 326.546 | − | 8.80731i | 0.629182 | − | 0.0169698i | ||||
\(520\) | 162.348 | − | 281.940i | 0.312207 | − | 0.542193i | ||||
\(521\) | 770.641 | 1.47916 | 0.739578 | − | 0.673071i | \(-0.235025\pi\) | ||||
0.739578 | + | 0.673071i | \(0.235025\pi\) | |||||||
\(522\) | −704.617 | + | 100.430i | −1.34984 | + | 0.192394i | ||||
\(523\) | 258.725 | − | 258.725i | 0.494694 | − | 0.494694i | −0.415087 | − | 0.909782i | \(-0.636249\pi\) |
0.909782 | + | 0.415087i | \(0.136249\pi\) | |||||||
\(524\) | −377.955 | − | 264.217i | −0.721288 | − | 0.504231i | ||||
\(525\) | 62.8846 | + | 59.5815i | 0.119780 | + | 0.113489i | ||||
\(526\) | −231.125 | + | 275.657i | −0.439400 | + | 0.524063i | ||||
\(527\) | 34.7917i | 0.0660183i | ||||||||
\(528\) | 325.566 | + | 820.927i | 0.616603 | + | 1.55479i | ||||
\(529\) | 629.695 | 1.19035 | ||||||||
\(530\) | −202.408 | − | 169.709i | −0.381902 | − | 0.320205i | ||||
\(531\) | −332.127 | + | 370.031i | −0.625475 | + | 0.696857i | ||||
\(532\) | 89.9082 | + | 62.8521i | 0.169000 | + | 0.118143i | ||||
\(533\) | 288.466 | + | 288.466i | 0.541212 | + | 0.541212i | ||||
\(534\) | 415.334 | − | 47.8122i | 0.777780 | − | 0.0895360i | ||||
\(535\) | − | 587.878i | − | 1.09884i | ||||||
\(536\) | −132.086 | − | 490.702i | −0.246429 | − | 0.915489i | ||||
\(537\) | 429.878 | − | 11.5943i | 0.800517 | − | 0.0215909i | ||||
\(538\) | 71.9322 | + | 818.589i | 0.133703 | + | 1.52154i | ||||
\(539\) | 162.894 | + | 162.894i | 0.302214 | + | 0.302214i | ||||
\(540\) | −123.057 | − | 469.778i | −0.227883 | − | 0.869960i | ||||
\(541\) | −122.667 | − | 122.667i | −0.226742 | − | 0.226742i | 0.584588 | − | 0.811330i | \(-0.301256\pi\) |
−0.811330 | + | 0.584588i | \(0.801256\pi\) | |||||||
\(542\) | 638.062 | − | 761.003i | 1.17724 | − | 1.40406i | ||||
\(543\) | 900.694 | − | 24.2927i | 1.65874 | − | 0.0447380i | ||||
\(544\) | 132.355 | + | 47.8872i | 0.243299 | + | 0.0880279i | ||||
\(545\) | 479.316i | 0.879479i | ||||||||
\(546\) | −203.730 | + | 256.737i | −0.373131 | + | 0.470215i | ||||
\(547\) | 334.075 | + | 334.075i | 0.610740 | + | 0.610740i | 0.943139 | − | 0.332399i | \(-0.107858\pi\) |
−0.332399 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(548\) | −17.1268 | − | 96.6991i | −0.0312533 | − | 0.176458i | ||||
\(549\) | 423.663 | − | 472.013i | 0.771699 | − | 0.859768i | ||||
\(550\) | −15.3998 | − | 175.250i | −0.0279996 | − | 0.318636i | ||||
\(551\) | 179.543 | 0.325849 | ||||||||
\(552\) | −233.538 | − | 782.859i | −0.423076 | − | 1.41822i | ||||
\(553\) | 242.581i | 0.438663i | ||||||||
\(554\) | 23.0283 | + | 262.062i | 0.0415674 | + | 0.473037i | ||||
\(555\) | −277.582 | − | 263.002i | −0.500148 | − | 0.473878i | ||||
\(556\) | −14.2296 | − | 9.94748i | −0.0255928 | − | 0.0178912i | ||||
\(557\) | −159.480 | + | 159.480i | −0.286320 | + | 0.286320i | −0.835623 | − | 0.549303i | \(-0.814893\pi\) |
0.549303 | + | 0.835623i | \(0.314893\pi\) | |||||||
\(558\) | −113.876 | − | 85.4636i | −0.204078 | − | 0.153161i | ||||
\(559\) | −460.576 | −0.823929 | ||||||||
\(560\) | −183.040 | + | 394.100i | −0.326856 | + | 0.703750i | ||||
\(561\) | −242.688 | + | 6.54557i | −0.432599 | + | 0.0116677i | ||||
\(562\) | 386.621 | − | 461.115i | 0.687938 | − | 0.820489i | ||||
\(563\) | 341.226 | − | 341.226i | 0.606086 | − | 0.606086i | −0.335835 | − | 0.941921i | \(-0.609018\pi\) |
0.941921 | + | 0.335835i | \(0.109018\pi\) | |||||||
\(564\) | −50.9794 | − | 33.6291i | −0.0903890 | − | 0.0596261i | ||||
\(565\) | −356.918 | + | 356.918i | −0.631713 | + | 0.631713i | ||||
\(566\) | −25.1227 | − | 285.897i | −0.0443865 | − | 0.505118i | ||||
\(567\) | 52.6646 | + | 486.380i | 0.0928828 | + | 0.857813i | ||||
\(568\) | 323.724 | + | 186.408i | 0.569937 | + | 0.328183i | ||||
\(569\) | 882.975 | 1.55180 | 0.775901 | − | 0.630855i | \(-0.217296\pi\) | ||||
0.775901 | + | 0.630855i | \(0.217296\pi\) | |||||||
\(570\) | 14.0099 | + | 121.701i | 0.0245788 | + | 0.213510i | ||||
\(571\) | 370.112 | − | 370.112i | 0.648181 | − | 0.648181i | −0.304372 | − | 0.952553i | \(-0.598447\pi\) |
0.952553 | + | 0.304372i | \(0.0984466\pi\) | |||||||
\(572\) | 655.397 | − | 116.080i | 1.14580 | − | 0.202938i | ||||
\(573\) | 74.9645 | − | 79.1204i | 0.130828 | − | 0.138081i | ||||
\(574\) | −417.528 | − | 350.076i | −0.727401 | − | 0.609889i | ||||
\(575\) | 162.742i | 0.283030i | ||||||||
\(576\) | −481.860 | + | 315.575i | −0.836562 | + | 0.547873i | ||||
\(577\) | −698.607 | −1.21076 | −0.605378 | − | 0.795938i | \(-0.706978\pi\) | ||||
−0.605378 | + | 0.795938i | \(0.706978\pi\) | |||||||
\(578\) | 346.502 | − | 413.265i | 0.599484 | − | 0.714992i | ||||
\(579\) | −102.591 | − | 97.2025i | −0.177187 | − | 0.167880i | ||||
\(580\) | 124.032 | + | 700.294i | 0.213849 | + | 1.20740i | ||||
\(581\) | −214.685 | − | 214.685i | −0.369509 | − | 0.369509i | ||||
\(582\) | −364.158 | + | 41.9210i | −0.625702 | + | 0.0720292i | ||||
\(583\) | − | 540.389i | − | 0.926911i | ||||||
\(584\) | −388.636 | + | 674.922i | −0.665473 | + | 1.15569i | ||||
\(585\) | −365.477 | + | 19.7290i | −0.624747 | + | 0.0337248i | ||||
\(586\) | 904.734 | − | 79.5021i | 1.54392 | − | 0.135669i | ||||
\(587\) | −196.072 | − | 196.072i | −0.334024 | − | 0.334024i | 0.520088 | − | 0.854112i | \(-0.325899\pi\) |
−0.854112 | + | 0.520088i | \(0.825899\pi\) | |||||||
\(588\) | −82.7351 | + | 125.421i | −0.140706 | + | 0.213300i | ||||
\(589\) | 25.3968 | + | 25.3968i | 0.0431185 | + | 0.0431185i | ||||
\(590\) | 380.726 | + | 319.219i | 0.645298 | + | 0.541050i | ||||
\(591\) | −3.69222 | − | 136.895i | −0.00624742 | − | 0.231633i | ||||
\(592\) | −191.050 | + | 411.348i | −0.322720 | + | 0.694844i | ||||
\(593\) | − | 774.011i | − | 1.30525i | −0.757683 | − | 0.652623i | \(-0.773669\pi\) | ||
0.757683 | − | 0.652623i | \(-0.226331\pi\) | |||||||
\(594\) | 574.724 | − | 810.414i | 0.967549 | − | 1.36433i | ||||
\(595\) | −84.4675 | − | 84.4675i | −0.141962 | − | 0.141962i | ||||
\(596\) | −19.0040 | + | 27.1847i | −0.0318859 | + | 0.0456118i | ||||
\(597\) | 243.849 | − | 257.368i | 0.408458 | − | 0.431102i | ||||
\(598\) | −613.357 | + | 53.8978i | −1.02568 | + | 0.0901301i | ||||
\(599\) | −783.533 | −1.30807 | −0.654034 | − | 0.756465i | \(-0.726925\pi\) | ||||
−0.654034 | + | 0.756465i | \(0.726925\pi\) | |||||||
\(600\) | 109.955 | − | 32.8011i | 0.183258 | − | 0.0546685i | ||||
\(601\) | 797.210i | 1.32647i | 0.748410 | + | 0.663236i | \(0.230818\pi\) | ||||
−0.748410 | + | 0.663236i | \(0.769182\pi\) | |||||||
\(602\) | 612.793 | − | 53.8482i | 1.01793 | − | 0.0894489i | ||||
\(603\) | −381.868 | + | 425.448i | −0.633280 | + | 0.705552i | ||||
\(604\) | −707.235 | + | 125.262i | −1.17092 | + | 0.207387i | ||||
\(605\) | −691.565 | + | 691.565i | −1.14308 | + | 1.14308i | ||||
\(606\) | 691.509 | + | 548.735i | 1.14110 | + | 0.905504i | ||||
\(607\) | 433.576 | 0.714293 | 0.357146 | − | 0.934048i | \(-0.383750\pi\) | ||||
0.357146 | + | 0.934048i | \(0.383750\pi\) | |||||||
\(608\) | 131.571 | − | 61.6585i | 0.216399 | − | 0.101412i | ||||
\(609\) | −19.3167 | − | 716.197i | −0.0317186 | − | 1.17602i | ||||
\(610\) | −485.656 | − | 407.197i | −0.796157 | − | 0.667537i | ||||
\(611\) | −32.5475 | + | 32.5475i | −0.0532692 | + | 0.0532692i | ||||
\(612\) | −35.9798 | − | 154.203i | −0.0587905 | − | 0.251966i | ||||
\(613\) | −493.642 | + | 493.642i | −0.805289 | + | 0.805289i | −0.983917 | − | 0.178628i | \(-0.942834\pi\) |
0.178628 | + | 0.983917i | \(0.442834\pi\) | |||||||
\(614\) | 265.494 | − | 23.3299i | 0.432401 | − | 0.0379966i | ||||
\(615\) | −16.4053 | − | 608.253i | −0.0266752 | − | 0.989029i | ||||
\(616\) | −858.428 | + | 231.070i | −1.39355 | + | 0.375113i | ||||
\(617\) | −685.069 | −1.11032 | −0.555161 | − | 0.831743i | \(-0.687343\pi\) | ||||
−0.555161 | + | 0.831743i | \(0.687343\pi\) | |||||||
\(618\) | 39.3150 | + | 341.521i | 0.0636165 | + | 0.552623i | ||||
\(619\) | −379.995 | + | 379.995i | −0.613885 | + | 0.613885i | −0.943956 | − | 0.330071i | \(-0.892927\pi\) |
0.330071 | + | 0.943956i | \(0.392927\pi\) | |||||||
\(620\) | −81.5136 | + | 116.603i | −0.131474 | + | 0.188069i | ||||
\(621\) | −595.241 | + | 700.269i | −0.958520 | + | 1.12765i | ||||
\(622\) | 315.737 | − | 376.573i | 0.507616 | − | 0.605422i | ||||
\(623\) | 420.850i | 0.675521i | ||||||||
\(624\) | 160.039 | + | 403.545i | 0.256473 | + | 0.646706i | ||||
\(625\) | 482.618 | 0.772189 | ||||||||
\(626\) | 542.290 | + | 454.683i | 0.866278 | + | 0.726330i | ||||
\(627\) | −172.376 | + | 181.932i | −0.274922 | + | 0.290163i | ||||
\(628\) | −48.1917 | + | 68.9369i | −0.0767384 | + | 0.109772i | ||||
\(629\) | −88.1642 | − | 88.1642i | −0.140166 | − | 0.140166i | ||||
\(630\) | 483.958 | − | 68.9790i | 0.768187 | − | 0.109491i | ||||
\(631\) | 489.285i | 0.775412i | 0.921783 | + | 0.387706i | \(0.126732\pi\) | ||||
−0.921783 | + | 0.387706i | \(0.873268\pi\) | |||||||
\(632\) | 278.446 | + | 160.336i | 0.440580 | + | 0.253696i | ||||
\(633\) | −7.30802 | − | 270.957i | −0.0115451 | − | 0.428052i | ||||
\(634\) | 57.9418 | + | 659.378i | 0.0913908 | + | 1.04003i | ||||
\(635\) | 297.712 | + | 297.712i | 0.468838 | + | 0.468838i | ||||
\(636\) | 345.272 | − | 70.8033i | 0.542880 | − | 0.111326i | ||||
\(637\) | 80.0739 | + | 80.0739i | 0.125705 | + | 0.125705i | ||||
\(638\) | −934.823 | + | 1114.94i | −1.46524 | + | 1.74756i | ||||
\(639\) | −22.6529 | − | 419.641i | −0.0354505 | − | 0.656716i | ||||
\(640\) | 331.386 | + | 470.587i | 0.517791 | + | 0.735291i | ||||
\(641\) | − | 492.158i | − | 0.767797i | −0.923375 | − | 0.383898i | \(-0.874581\pi\) | ||
0.923375 | − | 0.383898i | \(-0.125419\pi\) | |||||||
\(642\) | 614.476 | + | 487.607i | 0.957128 | + | 0.759513i | ||||
\(643\) | −169.985 | − | 169.985i | −0.264362 | − | 0.264362i | 0.562462 | − | 0.826823i | \(-0.309854\pi\) |
−0.826823 | + | 0.562462i | \(0.809854\pi\) | |||||||
\(644\) | 809.766 | − | 143.421i | 1.25740 | − | 0.222704i | ||||
\(645\) | 498.677 | + | 472.483i | 0.773142 | + | 0.732532i | ||||
\(646\) | 3.49656 | + | 39.7908i | 0.00541263 | + | 0.0615957i | ||||
\(647\) | −1003.50 | −1.55101 | −0.775503 | − | 0.631343i | \(-0.782504\pi\) | ||||
−0.775503 | + | 0.631343i | \(0.782504\pi\) | |||||||
\(648\) | 593.101 | + | 261.027i | 0.915280 | + | 0.402819i | ||||
\(649\) | 1016.46i | 1.56620i | ||||||||
\(650\) | −7.57011 | − | 86.1479i | −0.0116463 | − | 0.132535i | ||||
\(651\) | 98.5754 | − | 104.040i | 0.151422 | − | 0.159816i | ||||
\(652\) | 214.298 | − | 306.547i | 0.328678 | − | 0.470165i | ||||
\(653\) | 407.090 | − | 407.090i | 0.623415 | − | 0.623415i | −0.322988 | − | 0.946403i | \(-0.604687\pi\) |
0.946403 | + | 0.322988i | \(0.104687\pi\) | |||||||
\(654\) | −501.003 | − | 397.562i | −0.766059 | − | 0.607893i | ||||
\(655\) | 518.398 | 0.791448 | ||||||||
\(656\) | −677.805 | + | 247.874i | −1.03324 | + | 0.377856i | ||||
\(657\) | 874.897 | − | 47.2283i | 1.33165 | − | 0.0718848i | ||||
\(658\) | 39.4988 | − | 47.1094i | 0.0600286 | − | 0.0715948i | ||||
\(659\) | 635.355 | − | 635.355i | 0.964119 | − | 0.964119i | −0.0352587 | − | 0.999378i | \(-0.511226\pi\) |
0.999378 | + | 0.0352587i | \(0.0112255\pi\) | |||||||
\(660\) | −828.694 | − | 546.658i | −1.25560 | − | 0.828269i | ||||
\(661\) | −196.325 | + | 196.325i | −0.297013 | + | 0.297013i | −0.839843 | − | 0.542830i | \(-0.817353\pi\) |
0.542830 | + | 0.839843i | \(0.317353\pi\) | |||||||
\(662\) | 8.05637 | + | 91.6815i | 0.0121697 | + | 0.138492i | ||||
\(663\) | −119.299 | + | 3.21762i | −0.179937 | + | 0.00485312i | ||||
\(664\) | −388.325 | + | 104.528i | −0.584826 | + | 0.157422i | ||||
\(665\) | −123.317 | −0.185439 | ||||||||
\(666\) | 505.138 | − | 71.9979i | 0.758466 | − | 0.108105i | ||||
\(667\) | 951.737 | − | 951.737i | 1.42689 | − | 1.42689i | ||||
\(668\) | −110.715 | − | 625.107i | −0.165742 | − | 0.935788i | ||||
\(669\) | 93.4003 | + | 88.4944i | 0.139612 | + | 0.132279i | ||||
\(670\) | 437.745 | + | 367.027i | 0.653350 | + | 0.547801i | ||||
\(671\) | − | 1296.60i | − | 1.93234i | ||||||
\(672\) | −260.111 | − | 518.202i | −0.387070 | − | 0.771134i | ||||
\(673\) | −489.653 | −0.727568 | −0.363784 | − | 0.931483i | \(-0.618515\pi\) | ||||
−0.363784 | + | 0.931483i | \(0.618515\pi\) | |||||||
\(674\) | −238.459 | + | 284.405i | −0.353797 | + | 0.421966i | ||||
\(675\) | −98.3549 | − | 83.6034i | −0.145711 | − | 0.123857i | ||||
\(676\) | −343.466 | + | 60.8327i | −0.508085 | + | 0.0899893i | ||||
\(677\) | −832.940 | − | 832.940i | −1.23034 | − | 1.23034i | −0.963833 | − | 0.266507i | \(-0.914131\pi\) |
−0.266507 | − | 0.963833i | \(-0.585869\pi\) | |||||||
\(678\) | −77.0259 | − | 669.107i | −0.113608 | − | 0.986884i | ||||
\(679\) | − | 368.994i | − | 0.543438i | ||||||
\(680\) | −152.786 | + | 41.1265i | −0.224685 | + | 0.0604801i | ||||
\(681\) | 97.5600 | − | 2.63131i | 0.143260 | − | 0.00386388i | ||||
\(682\) | −289.944 | + | 25.4784i | −0.425138 | + | 0.0373584i | ||||
\(683\) | 773.804 | + | 773.804i | 1.13295 | + | 1.13295i | 0.989684 | + | 0.143264i | \(0.0457599\pi\) |
0.143264 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(684\) | −138.827 | − | 86.2993i | −0.202964 | − | 0.126169i | ||||
\(685\) | 78.0611 | + | 78.0611i | 0.113958 | + | 0.113958i | ||||
\(686\) | −569.466 | − | 477.468i | −0.830125 | − | 0.696018i | ||||
\(687\) | −1023.30 | + | 27.5996i | −1.48952 | + | 0.0401741i | ||||
\(688\) | 343.222 | − | 738.987i | 0.498869 | − | 1.07411i | ||||
\(689\) | − | 265.640i | − | 0.385545i | ||||||
\(690\) | 719.388 | + | 570.858i | 1.04259 | + | 0.827330i | ||||
\(691\) | −840.306 | − | 840.306i | −1.21607 | − | 1.21607i | −0.968996 | − | 0.247077i | \(-0.920530\pi\) |
−0.247077 | − | 0.968996i | \(-0.579470\pi\) | |||||||
\(692\) | 356.974 | + | 249.550i | 0.515859 | + | 0.360622i | ||||
\(693\) | 744.274 | + | 668.035i | 1.07399 | + | 0.963975i | ||||
\(694\) | −146.397 | + | 12.8644i | −0.210946 | + | 0.0185366i | ||||
\(695\) | 19.5171 | 0.0280822 | ||||||||
\(696\) | −834.856 | − | 451.205i | −1.19951 | − | 0.648283i | ||||
\(697\) | − | 198.401i | − | 0.284650i | ||||||
\(698\) | 1067.07 | − | 93.7668i | 1.52875 | − | 0.134336i | ||||
\(699\) | 523.334 | + | 495.845i | 0.748689 | + | 0.709364i | ||||
\(700\) | 20.1440 | + | 113.734i | 0.0287771 | + | 0.162477i | ||||
\(701\) | 529.432 | − | 529.432i | 0.755253 | − | 0.755253i | −0.220201 | − | 0.975454i | \(-0.570671\pi\) |
0.975454 | + | 0.220201i | \(0.0706715\pi\) | |||||||
\(702\) | 282.518 | − | 398.377i | 0.402448 | − | 0.567488i | ||||
\(703\) | −128.714 | −0.183092 | ||||||||
\(704\) | −302.153 | + | 1138.08i | −0.429195 | + | 1.61659i | ||||
\(705\) | 68.6288 | − | 1.85100i | 0.0973458 | − | 0.00262553i | ||||
\(706\) | −500.287 | − | 419.465i | −0.708622 | − | 0.594144i | ||||
\(707\) | −628.357 | + | 628.357i | −0.888765 | + | 0.888765i | ||||
\(708\) | −649.450 | + | 133.180i | −0.917303 | + | 0.188107i | ||||
\(709\) | −56.2182 | + | 56.2182i | −0.0792923 | + | 0.0792923i | −0.745641 | − | 0.666348i | \(-0.767856\pi\) |
0.666348 | + | 0.745641i | \(0.267856\pi\) | |||||||
\(710\) | −418.319 | + | 36.7591i | −0.589181 | + | 0.0517734i | ||||
\(711\) | −19.4845 | − | 360.948i | −0.0274044 | − | 0.507663i | ||||
\(712\) | 483.073 | + | 278.165i | 0.678473 | + | 0.390681i | ||||
\(713\) | 269.251 | 0.377631 | ||||||||
\(714\) | 158.350 | − | 18.2288i | 0.221778 | − | 0.0255305i | ||||
\(715\) | −529.074 | + | 529.074i | −0.739964 | + | 0.739964i | ||||
\(716\) | 469.936 | + | 328.518i | 0.656335 | + | 0.458824i | ||||
\(717\) | −450.165 | + | 475.121i | −0.627845 | + | 0.662651i | ||||
\(718\) | 327.578 | − | 390.696i | 0.456237 | − | 0.544144i | ||||
\(719\) | − | 966.944i | − | 1.34485i | −0.740167 | − | 0.672423i | \(-0.765254\pi\) | ||
0.740167 | − | 0.672423i | \(-0.234746\pi\) | |||||||
\(720\) | 240.699 | − | 601.104i | 0.334304 | − | 0.834866i | ||||
\(721\) | −346.056 | −0.479967 | ||||||||
\(722\) | −521.663 | − | 437.388i | −0.722525 | − | 0.605800i | ||||
\(723\) | 193.734 | + | 183.558i | 0.267959 | + | 0.253884i | ||||
\(724\) | 984.624 | + | 688.321i | 1.35998 | + | 0.950720i | ||||
\(725\) | 133.674 | + | 133.674i | 0.184378 | + | 0.184378i | ||||
\(726\) | −149.246 | − | 1296.46i | −0.205572 | − | 1.78576i | ||||
\(727\) | − | 1338.18i | − | 1.84069i | −0.391110 | − | 0.920344i | \(-0.627909\pi\) | ||
0.391110 | − | 0.920344i | \(-0.372091\pi\) | |||||||
\(728\) | −421.979 | + | 113.587i | −0.579642 | + | 0.156027i | ||||
\(729\) | −117.429 | − | 719.480i | −0.161083 | − | 0.986941i | ||||
\(730\) | −76.6380 | − | 872.140i | −0.104984 | − | 1.19471i | ||||
\(731\) | 158.387 | + | 158.387i | 0.216672 | + | 0.216672i | ||||
\(732\) | 828.441 | − | 169.885i | 1.13175 | − | 0.232083i | ||||
\(733\) | 757.046 | + | 757.046i | 1.03280 | + | 1.03280i | 0.999443 | + | 0.0333615i | \(0.0106213\pi\) |
0.0333615 | + | 0.999443i | \(0.489379\pi\) | |||||||
\(734\) | −159.656 | + | 190.418i | −0.217515 | + | 0.259426i | ||||
\(735\) | −4.55386 | − | 168.842i | −0.00619573 | − | 0.229717i | ||||
\(736\) | 370.596 | − | 1024.29i | 0.503528 | − | 1.39169i | ||||
\(737\) | 1168.69i | 1.58574i | ||||||||
\(738\) | 649.380 | + | 487.360i | 0.879919 | + | 0.660379i | ||||
\(739\) | 495.335 | + | 495.335i | 0.670278 | + | 0.670278i | 0.957780 | − | 0.287502i | \(-0.0928249\pi\) |
−0.287502 | + | 0.957780i | \(0.592825\pi\) | |||||||
\(740\) | −88.9185 | − | 502.039i | −0.120160 | − | 0.678432i | ||||
\(741\) | −84.7353 | + | 89.4328i | −0.114353 | + | 0.120692i | ||||
\(742\) | 31.0573 | + | 353.432i | 0.0418562 | + | 0.476324i | ||||
\(743\) | −1421.01 | −1.91253 | −0.956266 | − | 0.292500i | \(-0.905513\pi\) | ||||
−0.956266 | + | 0.292500i | \(0.905513\pi\) | |||||||
\(744\) | −54.2682 | − | 181.916i | −0.0729412 | − | 0.244511i | ||||
\(745\) | − | 37.2861i | − | 0.0500485i | ||||||
\(746\) | 49.9323 | + | 568.230i | 0.0669334 | + | 0.761702i | ||||
\(747\) | 336.685 | + | 302.197i | 0.450716 | + | 0.404547i | ||||
\(748\) | −265.302 | − | 185.465i | −0.354682 | − | 0.247948i | ||||
\(749\) | −558.359 | + | 558.359i | −0.745473 | + | 0.745473i | ||||
\(750\) | −499.439 | + | 629.386i | −0.665918 | + | 0.839181i | ||||
\(751\) | −143.509 | −0.191090 | −0.0955452 | − | 0.995425i | \(-0.530459\pi\) | ||||
−0.0955452 | + | 0.995425i | \(0.530459\pi\) | |||||||
\(752\) | −27.9674 | − | 76.4762i | −0.0371907 | − | 0.101697i | ||||
\(753\) | −19.3572 | − | 717.702i | −0.0257068 | − | 0.953123i | ||||
\(754\) | −459.533 | + | 548.075i | −0.609460 | + | 0.726890i | ||||
\(755\) | 570.921 | − | 570.921i | 0.756187 | − | 0.756187i | ||||
\(756\) | −329.312 | + | 563.068i | −0.435598 | + | 0.744799i | ||||
\(757\) | 651.883 | − | 651.883i | 0.861140 | − | 0.861140i | −0.130331 | − | 0.991471i | \(-0.541604\pi\) |
0.991471 | + | 0.130331i | \(0.0416040\pi\) | |||||||
\(758\) | 56.3367 | + | 641.112i | 0.0743229 | + | 0.845794i | ||||
\(759\) | 50.6558 | + | 1878.15i | 0.0667402 | + | 2.47450i | ||||
\(760\) | −81.5076 | + | 141.550i | −0.107247 | + | 0.186249i | ||||
\(761\) | 434.623 | 0.571122 | 0.285561 | − | 0.958361i | \(-0.407820\pi\) | ||||
0.285561 | + | 0.958361i | \(0.407820\pi\) | |||||||
\(762\) | −558.115 | + | 64.2488i | −0.732434 | + | 0.0843160i | ||||
\(763\) | 455.249 | − | 455.249i | 0.596656 | − | 0.596656i | ||||
\(764\) | 143.098 | − | 25.3448i | 0.187301 | − | 0.0331738i | ||||
\(765\) | 132.468 | + | 118.899i | 0.173161 | + | 0.155423i | ||||
\(766\) | −197.601 | − | 165.678i | −0.257964 | − | 0.216290i | ||||
\(767\) | 499.665i | 0.651453i | ||||||||
\(768\) | −766.742 | − | 43.9417i | −0.998362 | − | 0.0572157i | ||||
\(769\) | 17.1894 | 0.0223529 | 0.0111764 | − | 0.999938i | \(-0.496442\pi\) | ||||
0.0111764 | + | 0.999938i | \(0.496442\pi\) | |||||||
\(770\) | 642.072 | − | 765.786i | 0.833860 | − | 0.994527i | ||||
\(771\) | −811.125 | + | 856.091i | −1.05204 | + | 1.11036i | ||||
\(772\) | −32.8633 | − | 185.548i | −0.0425690 | − | 0.240347i | ||||
\(773\) | 553.125 | + | 553.125i | 0.715557 | + | 0.715557i | 0.967692 | − | 0.252135i | \(-0.0811328\pi\) |
−0.252135 | + | 0.967692i | \(0.581133\pi\) | |||||||
\(774\) | −907.481 | + | 129.344i | −1.17246 | + | 0.167112i | ||||
\(775\) | 37.8171i | 0.0487963i | ||||||||
\(776\) | −423.551 | − | 243.891i | −0.545813 | − | 0.314292i | ||||
\(777\) | 13.8481 | + | 513.440i | 0.0178225 | + | 0.660798i | ||||
\(778\) | −302.815 | + | 26.6094i | −0.389223 | + | 0.0342024i | ||||
\(779\) | −144.826 | − | 144.826i | −0.185913 | − | 0.185913i | ||||
\(780\) | −407.363 | − | 268.722i | −0.522260 | − | 0.344515i | ||||
\(781\) | −607.484 | − | 607.484i | −0.777828 | − | 0.777828i | ||||
\(782\) | 229.462 | + | 192.392i | 0.293429 | + | 0.246026i | ||||
\(783\) | 86.2686 | + | 1064.12i | 0.110177 | + | 1.35902i | ||||
\(784\) | −188.148 | + | 68.8061i | −0.239985 | + | 0.0877628i | ||||
\(785\) | − | 94.5530i | − | 0.120450i | ||||||
\(786\) | −429.978 | + | 541.853i | −0.547046 | + | 0.689380i | ||||
\(787\) | 274.851 | + | 274.851i | 0.349239 | + | 0.349239i | 0.859826 | − | 0.510587i | \(-0.170572\pi\) |
−0.510587 | + | 0.859826i | \(0.670572\pi\) | |||||||
\(788\) | 104.617 | − | 149.652i | 0.132763 | − | 0.189913i | ||||
\(789\) | 391.699 | + | 371.125i | 0.496450 | + | 0.470374i | ||||
\(790\) | −359.811 | + | 31.6178i | −0.455457 | + | 0.0400225i | ||||
\(791\) | 677.993 | 0.857134 | ||||||||
\(792\) | 1258.74 | − | 412.771i | 1.58932 | − | 0.521175i | ||||
\(793\) | − | 637.374i | − | 0.803750i | ||||||
\(794\) | −730.612 | + | 64.2014i | −0.920166 | + | 0.0808582i | ||||
\(795\) | −272.508 | + | 287.615i | −0.342777 | + | 0.361780i | ||||
\(796\) | 465.479 | − | 82.4431i | 0.584773 | − | 0.103572i | ||||
\(797\) | 165.770 | − | 165.770i | 0.207993 | − | 0.207993i | −0.595421 | − | 0.803414i | \(-0.703015\pi\) |
0.803414 | + | 0.595421i | \(0.203015\pi\) | |||||||
\(798\) | 102.284 | − | 128.896i | 0.128175 | − | 0.161524i | ||||
\(799\) | 22.3854 | 0.0280168 | ||||||||
\(800\) | 143.864 | + | 52.0514i | 0.179830 | + | 0.0650642i | ||||
\(801\) | −33.8035 | − | 626.204i | −0.0422016 | − | 0.781778i | ||||
\(802\) | 514.656 | + | 431.513i | 0.641715 | + | 0.538046i | ||||
\(803\) | 1266.52 | − | 1266.52i | 1.57724 | − | 1.57724i | ||||
\(804\) | −746.714 | + | 153.125i | −0.928749 | + | 0.190454i | ||||
\(805\) | −653.690 | + | 653.690i | −0.812037 | + | 0.812037i | ||||
\(806\) | −142.528 | + | 12.5245i | −0.176834 | + | 0.0155390i | ||||
\(807\) | 1232.17 | − | 33.2329i | 1.52685 | − | 0.0411808i | ||||
\(808\) | 305.942 | + | 1136.58i | 0.378641 | + | 1.40666i | ||||
\(809\) | 184.708 | 0.228316 | 0.114158 | − | 0.993463i | \(-0.463583\pi\) | ||||
0.114158 | + | 0.993463i | \(0.463583\pi\) | |||||||
\(810\) | −714.565 | + | 141.510i | −0.882179 | + | 0.174704i | ||||
\(811\) | −585.531 | + | 585.531i | −0.721986 | + | 0.721986i | −0.969010 | − | 0.247023i | \(-0.920548\pi\) |
0.247023 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(812\) | 547.327 | − | 782.935i | 0.674048 | − | 0.964206i | ||||
\(813\) | −1081.36 | − | 1024.56i | −1.33008 | − | 1.26022i | ||||
\(814\) | 670.173 | − | 799.300i | 0.823308 | − | 0.981941i | ||||
\(815\) | 420.457i | 0.515898i | ||||||||
\(816\) | 83.7388 | − | 193.810i | 0.102621 | − | 0.237513i | ||||
\(817\) | 231.235 | 0.283029 | ||||||||
\(818\) | −101.705 | − | 85.2742i | −0.124333 | − | 0.104247i | ||||
\(819\) | 365.864 | + | 328.387i | 0.446720 | + | 0.400961i | ||||
\(820\) | 464.834 | − | 664.932i | 0.566871 | − | 0.810893i | ||||
\(821\) | −659.299 | − | 659.299i | −0.803044 | − | 0.803044i | 0.180526 | − | 0.983570i | \(-0.442220\pi\) |
−0.983570 | + | 0.180526i | \(0.942220\pi\) | |||||||
\(822\) | −146.340 | + | 16.8462i | −0.178029 | + | 0.0204942i | ||||
\(823\) | 1397.61i | 1.69819i | 0.528237 | + | 0.849097i | \(0.322853\pi\) | ||||
−0.528237 | + | 0.849097i | \(0.677147\pi\) | |||||||
\(824\) | −228.729 | + | 397.221i | −0.277584 | + | 0.482064i | ||||
\(825\) | −263.792 | + | 7.11476i | −0.319748 | + | 0.00862395i | ||||
\(826\) | −58.4183 | − | 664.800i | −0.0707243 | − | 0.804842i | ||||
\(827\) | 78.1971 | + | 78.1971i | 0.0945551 | + | 0.0945551i | 0.752802 | − | 0.658247i | \(-0.228702\pi\) |
−0.658247 | + | 0.752802i | \(0.728702\pi\) | |||||||
\(828\) | −1193.37 | + | 278.446i | −1.44127 | + | 0.336287i | ||||
\(829\) | −30.4254 | − | 30.4254i | −0.0367014 | − | 0.0367014i | 0.688518 | − | 0.725219i | \(-0.258262\pi\) |
−0.725219 | + | 0.688518i | \(0.758262\pi\) | |||||||
\(830\) | 290.452 | − | 346.416i | 0.349942 | − | 0.417369i | ||||
\(831\) | 394.465 | − | 10.6392i | 0.474687 | − | 0.0128028i | ||||
\(832\) | −148.530 | + | 559.446i | −0.178522 | + | 0.672411i | ||||
\(833\) | − | 55.0731i | − | 0.0661141i | ||||||
\(834\) | −16.1882 | + | 20.4002i | −0.0194103 | + | 0.0244607i | ||||
\(835\) | 504.622 | + | 504.622i | 0.604338 | + | 0.604338i | ||||
\(836\) | −329.045 | + | 58.2787i | −0.393595 | + | 0.0697114i | ||||
\(837\) | −138.319 | + | 162.725i | −0.165255 | + | 0.194414i | ||||
\(838\) | 91.9958 | + | 1046.91i | 0.109780 | + | 1.24930i | ||||
\(839\) | 694.526 | 0.827802 | 0.413901 | − | 0.910322i | \(-0.364166\pi\) | ||||
0.413901 | + | 0.910322i | \(0.364166\pi\) | |||||||
\(840\) | 573.411 | + | 309.905i | 0.682632 | + | 0.368935i | ||||
\(841\) | − | 722.489i | − | 0.859084i | ||||||
\(842\) | −120.732 | − | 1373.93i | −0.143387 | − | 1.63175i | ||||
\(843\) | −655.228 | − | 620.812i | −0.777258 | − | 0.736432i | ||||
\(844\) | 207.069 | − | 296.206i | 0.245342 | − | 0.350955i | ||||
\(845\) | 277.265 | − | 277.265i | 0.328125 | − | 0.328125i | ||||
\(846\) | −54.9884 | + | 73.2691i | −0.0649982 | + | 0.0866065i | ||||
\(847\) | 1313.68 | 1.55098 | ||||||||
\(848\) | 426.215 | + | 197.955i | 0.502612 | + | 0.233438i | ||||
\(849\) | −430.341 | + | 11.6068i | −0.506880 | + | 0.0136711i | ||||
\(850\) | −27.0220 | + | 32.2286i | −0.0317906 | + | 0.0379160i | ||||
\(851\) | −682.298 | + | 682.298i | −0.801761 | + | 0.801761i | ||||
\(852\) | 308.546 | − | 467.735i | 0.362144 | − | 0.548985i | ||||
\(853\) | 727.489 | − | 727.489i | 0.852860 | − | 0.852860i | −0.137625 | − | 0.990484i | \(-0.543947\pi\) |
0.990484 | + | 0.137625i | \(0.0439468\pi\) | |||||||
\(854\) | 74.5185 | + | 848.021i | 0.0872582 | + | 0.992999i | ||||
\(855\) | 183.490 | − | 9.90506i | 0.214608 | − | 0.0115849i | ||||
\(856\) | 271.860 | + | 1009.97i | 0.317594 | + | 1.17987i | ||||
\(857\) | 1275.44 | 1.48826 | 0.744128 | − | 0.668037i | \(-0.232865\pi\) | ||||
0.744128 | + | 0.668037i | \(0.232865\pi\) | |||||||
\(858\) | −114.179 | − | 991.845i | −0.133075 | − | 1.15600i | ||||
\(859\) | 2.20191 | − | 2.20191i | 0.00256334 | − | 0.00256334i | −0.705824 | − | 0.708387i | \(-0.749423\pi\) |
0.708387 | + | 0.705824i | \(0.249423\pi\) | |||||||
\(860\) | 159.742 | + | 901.914i | 0.185747 | + | 1.04874i | ||||
\(861\) | −562.130 | + | 593.293i | −0.652880 | + | 0.689074i | ||||
\(862\) | −775.334 | − | 650.078i | −0.899459 | − | 0.754151i | ||||
\(863\) | 1311.55i | 1.51976i | 0.650063 | + | 0.759880i | \(0.274742\pi\) | ||||
−0.650063 | + | 0.759880i | \(0.725258\pi\) | |||||||
\(864\) | 428.656 | + | 750.167i | 0.496130 | + | 0.868248i | ||||
\(865\) | −489.622 | −0.566037 | ||||||||
\(866\) | −974.313 | + | 1162.04i | −1.12507 | + | 1.34185i | ||||
\(867\) | −587.236 | − | 556.391i | −0.677319 | − | 0.641743i | ||||
\(868\) | 188.169 | − | 33.3274i | 0.216784 | − | 0.0383956i | ||||
\(869\) | −522.518 | − | 522.518i | −0.601287 | − | 0.601287i | ||||
\(870\) | 1059.79 | − | 122.000i | 1.21815 | − | 0.140230i | ||||
\(871\) | 574.496i | 0.659582i | ||||||||
\(872\) | −221.657 | − | 823.459i | −0.254193 | − | 0.944334i | ||||
\(873\) | 29.6383 | + | 549.046i | 0.0339500 | + | 0.628918i | ||||
\(874\) | 307.939 | − | 27.0597i | 0.352333 | − | 0.0309608i | ||||
\(875\) | −571.908 | − | 571.908i | −0.653609 | − | 0.653609i | ||||
\(876\) | 975.166 | + | 643.279i | 1.11320 | + | 0.734337i | ||||
\(877\) | −449.158 | − | 449.158i | −0.512152 | − | 0.512152i | 0.403033 | − | 0.915185i | \(-0.367956\pi\) |
−0.915185 | + | 0.403033i | \(0.867956\pi\) | |||||||
\(878\) | 223.388 | + | 187.300i | 0.254429 | + | 0.213325i | ||||
\(879\) | −36.7303 | − | 1361.84i | −0.0417864 | − | 1.54930i | ||||
\(880\) | −454.624 | − | 1243.16i | −0.516618 | − | 1.41268i | ||||
\(881\) | 982.786i | 1.11553i | 0.829998 | + | 0.557767i | \(0.188342\pi\) | ||||
−0.829998 | + | 0.557767i | \(0.811658\pi\) | |||||||
\(882\) | 180.258 | + | 135.284i | 0.204374 | + | 0.153383i | ||||
\(883\) | 233.961 | + | 233.961i | 0.264962 | + | 0.264962i | 0.827066 | − | 0.562104i | \(-0.190008\pi\) |
−0.562104 | + | 0.827066i | \(0.690008\pi\) | |||||||
\(884\) | −130.415 | − | 91.1694i | −0.147529 | − | 0.103133i | ||||
\(885\) | 512.582 | − | 540.999i | 0.579189 | − | 0.611298i | ||||
\(886\) | −1710.39 | + | 150.298i | −1.93047 | + | 0.169637i | ||||
\(887\) | −1421.57 | −1.60267 | −0.801334 | − | 0.598217i | \(-0.795876\pi\) | ||||
−0.801334 | + | 0.598217i | \(0.795876\pi\) | |||||||
\(888\) | 598.506 | + | 323.468i | 0.673994 | + | 0.364266i | ||||
\(889\) | − | 565.527i | − | 0.636138i | ||||||
\(890\) | −624.231 | + | 54.8533i | −0.701383 | + | 0.0616329i | ||||
\(891\) | −1161.10 | − | 934.222i | −1.30314 | − | 1.04851i | ||||
\(892\) | 29.9191 | + | 168.925i | 0.0335416 | + | 0.189378i | ||||
\(893\) | 16.3406 | − | 16.3406i | 0.0182986 | − | 0.0182986i | ||||
\(894\) | 38.9731 | + | 30.9265i | 0.0435941 | + | 0.0345934i | ||||
\(895\) | −644.558 | −0.720176 | ||||||||
\(896\) | 132.211 | − | 761.704i | 0.147557 | − | 0.850116i | ||||
\(897\) | 24.9010 | + | 923.246i | 0.0277603 | + | 1.02926i | ||||
\(898\) | 292.193 | + | 244.989i | 0.325382 | + | 0.272816i | ||||
\(899\) | 221.159 | − | 221.159i | 0.246006 | − | 0.246006i | ||||
\(900\) | −39.1086 | − | 167.613i | −0.0434540 | − | 0.186236i | ||||
\(901\) | −91.3508 | + | 91.3508i | −0.101388 | + | 0.101388i | ||||
\(902\) | 1653.42 | − | 145.292i | 1.83306 | − | 0.161077i | ||||
\(903\) | −24.8781 | − | 922.396i | −0.0275505 | − | 1.02148i | ||||
\(904\) | 448.126 | − | 778.235i | 0.495715 | − | 0.860879i | ||||
\(905\) | −1350.50 | −1.49226 | ||||||||
\(906\) | 123.210 | + | 1070.29i | 0.135993 | + | 1.18134i | ||||
\(907\) | −358.736 | + | 358.736i | −0.395519 | + | 0.395519i | −0.876649 | − | 0.481130i | \(-0.840226\pi\) |
0.481130 | + | 0.876649i | \(0.340226\pi\) | |||||||
\(908\) | 106.651 | + | 74.5565i | 0.117457 | + | 0.0821107i | ||||
\(909\) | 884.494 | − | 985.436i | 0.973041 | − | 1.08409i | ||||
\(910\) | 315.625 | − | 376.439i | 0.346840 | − | 0.413669i | ||||
\(911\) | 353.455i | 0.387986i | 0.981003 | + | 0.193993i | \(0.0621439\pi\) | ||||
−0.981003 | + | 0.193993i | \(0.937856\pi\) | |||||||
\(912\) | −80.3486 | − | 202.602i | −0.0881015 | − | 0.222151i | ||||
\(913\) | 924.862 | 1.01299 | ||||||||
\(914\) | −196.310 | − | 164.596i | −0.214781 | − | 0.180083i | ||||
\(915\) | −653.852 | + | 690.100i | −0.714592 | + | 0.754207i | ||||
\(916\) | −1118.66 | − | 782.020i | −1.22124 | − | 0.853734i | ||||
\(917\) | −492.368 | − | 492.368i | −0.536934 | − | 0.536934i | ||||
\(918\) | −234.152 | + | 39.8425i | −0.255068 | + | 0.0434014i | ||||
\(919\) | − | 1519.58i | − | 1.65351i | −0.562560 | − | 0.826757i | \(-0.690183\pi\) | ||
0.562560 | − | 0.826757i | \(-0.309817\pi\) | |||||||
\(920\) | 318.276 | + | 1182.40i | 0.345952 | + | 1.28522i | ||||
\(921\) | −10.7785 | − | 399.631i | −0.0117030 | − | 0.433910i | ||||
\(922\) | −18.3726 | − | 209.081i | −0.0199269 | − | 0.226769i | ||||
\(923\) | −298.622 | − | 298.622i | −0.323534 | − | 0.323534i | ||||
\(924\) | 267.875 | + | 1306.29i | 0.289908 | + | 1.41374i | ||||
\(925\) | −95.8309 | − | 95.8309i | −0.103601 | − | 0.103601i | ||||
\(926\) | 796.940 | − | 950.493i | 0.860626 | − | 1.02645i | ||||
\(927\) | 514.915 | − | 27.7959i | 0.555464 | − | 0.0299848i | ||||
\(928\) | −536.932 | − | 1145.74i | −0.578591 | − | 1.23463i | ||||
\(929\) | − | 95.2916i | − | 0.102574i | −0.998684 | − | 0.0512872i | \(-0.983668\pi\) | ||
0.998684 | − | 0.0512872i | \(-0.0163324\pi\) | |||||||
\(930\) | 167.167 | + | 132.653i | 0.179750 | + | 0.142637i | ||||
\(931\) | −40.2015 | − | 40.2015i | −0.0431810 | − | 0.0431810i | ||||
\(932\) | 167.641 | + | 946.509i | 0.179872 | + | 1.01557i | ||||
\(933\) | −535.097 | − | 506.991i | −0.573523 | − | 0.543398i | ||||
\(934\) | 82.1275 | + | 934.611i | 0.0879309 | + | 1.00065i | ||||
\(935\) | 363.886 | 0.389182 | ||||||||
\(936\) | 618.761 | − | 202.907i | 0.661070 | − | 0.216781i | ||||
\(937\) | 701.772i | 0.748956i | 0.927236 | + | 0.374478i | \(0.122178\pi\) | ||||
−0.927236 | + | 0.374478i | \(0.877822\pi\) | |||||||
\(938\) | −67.1671 | − | 764.362i | −0.0716068 | − | 0.814885i | ||||
\(939\) | 730.101 | − | 770.576i | 0.777530 | − | 0.820634i | ||||
\(940\) | 75.0239 | + | 52.4469i | 0.0798126 | + | 0.0557946i | ||||
\(941\) | 88.8345 | − | 88.8345i | 0.0944044 | − | 0.0944044i | −0.658327 | − | 0.752732i | \(-0.728736\pi\) |
0.752732 | + | 0.658327i | \(0.228736\pi\) | |||||||
\(942\) | 98.8310 | + | 78.4257i | 0.104916 | + | 0.0832545i | ||||
\(943\) | −1535.41 | −1.62822 | ||||||||
\(944\) | −801.703 | − | 372.351i | −0.849262 | − | 0.394439i | ||||
\(945\) | −59.2526 | − | 730.875i | −0.0627012 | − | 0.773413i | ||||
\(946\) | −1203.97 | + | 1435.94i | −1.27269 | + | 1.51791i | ||||
\(947\) | −345.769 | + | 345.769i | −0.365120 | + | 0.365120i | −0.865694 | − | 0.500574i | \(-0.833122\pi\) |
0.500574 | + | 0.865694i | \(0.333122\pi\) | |||||||
\(948\) | 265.392 | − | 402.315i | 0.279949 | − | 0.424383i | ||||
\(949\) | 622.588 | − | 622.588i | 0.656046 | − | 0.656046i | ||||
\(950\) | 3.80062 | + | 43.2510i | 0.00400065 | + | 0.0455274i | ||||
\(951\) | 992.517 | − | 26.7693i | 1.04366 | − | 0.0281486i | ||||
\(952\) | 184.176 | + | 106.053i | 0.193462 | + | 0.111400i | ||||
\(953\) | −1627.75 | −1.70803 | −0.854013 | − | 0.520251i | \(-0.825838\pi\) | ||||
−0.854013 | + | 0.520251i | \(0.825838\pi\) | |||||||
\(954\) | −74.6001 | − | 523.395i | −0.0781972 | − | 0.548633i | ||||
\(955\) | −115.517 | + | 115.517i | −0.120961 | + | 0.120961i | ||||
\(956\) | −859.311 | + | 152.197i | −0.898861 | + | 0.159201i | ||||
\(957\) | 1584.30 | + | 1501.08i | 1.65548 | + | 1.56853i | ||||
\(958\) | 1330.19 | + | 1115.30i | 1.38851 | + | 1.16419i | ||||
\(959\) | − | 148.283i | − | 0.154623i | ||||||
\(960\) | 734.727 | − | 453.355i | 0.765340 | − | 0.472245i | ||||
\(961\) | −898.433 | −0.934894 | ||||||||
\(962\) | 329.438 | − | 392.914i | 0.342451 | − | 0.408434i | ||||
\(963\) | 785.963 | − | 875.660i | 0.816161 | − | 0.909304i | ||||
\(964\) | 62.0594 | + | 350.391i | 0.0643770 | + | 0.363476i | ||||
\(965\) | 149.785 | + | 149.785i | 0.155218 | + | 0.155218i | ||||
\(966\) | −141.072 | − | 1225.46i | −0.146037 | − | 1.26859i | ||||
\(967\) | 1444.31i | 1.49360i | 0.665049 | + | 0.746799i | \(0.268410\pi\) | ||||
−0.665049 | + | 0.746799i | \(0.731590\pi\) | |||||||
\(968\) | 868.290 | − | 1507.91i | 0.896994 | − | 1.55776i | ||||
\(969\) | 59.8945 | − | 1.61542i | 0.0618106 | − | 0.00166710i | ||||
\(970\) | 547.315 | − | 48.0945i | 0.564243 | − | 0.0495820i | ||||
\(971\) | 165.972 | + | 165.972i | 0.170929 | + | 0.170929i | 0.787388 | − | 0.616458i | \(-0.211433\pi\) |
−0.616458 | + | 0.787388i | \(0.711433\pi\) | |||||||
\(972\) | 444.774 | − | 864.269i | 0.457586 | − | 0.889165i | ||||
\(973\) | −18.5371 | − | 18.5371i | −0.0190515 | − | 0.0190515i | ||||
\(974\) | 1250.24 | + | 1048.27i | 1.28362 | + | 1.07625i | ||||
\(975\) | −129.673 | + | 3.49742i | −0.132998 | + | 0.00358710i | ||||
\(976\) | 1022.66 | + | 474.972i | 1.04780 | + | 0.486651i | ||||
\(977\) | 1708.09i | 1.74830i | 0.485658 | + | 0.874149i | \(0.338580\pi\) | ||||
−0.485658 | + | 0.874149i | \(0.661420\pi\) | |||||||
\(978\) | −439.480 | − | 348.742i | −0.449366 | − | 0.356587i | ||||
\(979\) | −906.510 | − | 906.510i | −0.925955 | − | 0.925955i | ||||
\(980\) | 129.031 | − | 184.575i | 0.131664 | − | 0.188342i | ||||
\(981\) | −640.822 | + | 713.955i | −0.653233 | + | 0.727783i | ||||
\(982\) | 951.623 | − | 83.6224i | 0.969066 | − | 0.0851552i | ||||
\(983\) | 285.345 | 0.290279 | 0.145140 | − | 0.989411i | \(-0.453637\pi\) | ||||
0.145140 | + | 0.989411i | \(0.453637\pi\) | |||||||
\(984\) | 309.467 | + | 1037.38i | 0.314499 | + | 1.05425i | ||||
\(985\) | 205.261i | 0.208386i | ||||||||
\(986\) | 346.505 | − | 30.4486i | 0.351425 | − | 0.0308809i | ||||
\(987\) | −66.9408 | − | 63.4247i | −0.0678225 | − | 0.0642601i | ||||
\(988\) | −161.750 | + | 28.6482i | −0.163714 | + | 0.0289961i | ||||
\(989\) | 1225.75 | − | 1225.75i | 1.23938 | − | 1.23938i | ||||
\(990\) | −893.863 | + | 1191.02i | −0.902892 | + | 1.20305i | ||||
\(991\) | −437.191 | −0.441162 | −0.220581 | − | 0.975369i | \(-0.570795\pi\) | ||||
−0.220581 | + | 0.975369i | \(0.570795\pi\) | |||||||
\(992\) | 86.1171 | − | 238.018i | 0.0868116 | − | 0.239937i | ||||
\(993\) | 138.002 | − | 3.72207i | 0.138975 | − | 0.00374831i | ||||
\(994\) | 432.228 | + | 362.401i | 0.434837 | + | 0.364588i | ||||
\(995\) | −375.762 | + | 375.762i | −0.377650 | + | 0.377650i | ||||
\(996\) | 121.178 | + | 590.924i | 0.121665 | + | 0.593297i | ||||
\(997\) | −1029.10 | + | 1029.10i | −1.03220 | + | 1.03220i | −0.0327341 | + | 0.999464i | \(0.510421\pi\) |
−0.999464 | + | 0.0327341i | \(0.989579\pi\) | |||||||
\(998\) | −1451.86 | + | 127.580i | −1.45477 | + | 0.127836i | ||||
\(999\) | −61.8458 | − | 762.862i | −0.0619077 | − | 0.763626i |
(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 | 48.3.i.b.29.8 | yes | 20 | |
3.2 | odd | 2 | inner | 48.3.i.b.29.3 | yes | 20 | |
4.3 | odd | 2 | 192.3.i.b.17.8 | 20 | |||
8.3 | odd | 2 | 384.3.i.c.161.3 | 20 | |||
8.5 | even | 2 | 384.3.i.d.161.8 | 20 | |||
12.11 | even | 2 | 192.3.i.b.17.7 | 20 | |||
16.3 | odd | 4 | 384.3.i.c.353.4 | 20 | |||
16.5 | even | 4 | inner | 48.3.i.b.5.3 | ✓ | 20 | |
16.11 | odd | 4 | 192.3.i.b.113.7 | 20 | |||
16.13 | even | 4 | 384.3.i.d.353.7 | 20 | |||
24.5 | odd | 2 | 384.3.i.d.161.7 | 20 | |||
24.11 | even | 2 | 384.3.i.c.161.4 | 20 | |||
48.5 | odd | 4 | inner | 48.3.i.b.5.8 | yes | 20 | |
48.11 | even | 4 | 192.3.i.b.113.8 | 20 | |||
48.29 | odd | 4 | 384.3.i.d.353.8 | 20 | |||
48.35 | even | 4 | 384.3.i.c.353.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.3 | ✓ | 20 | 16.5 | even | 4 | inner | |
48.3.i.b.5.8 | yes | 20 | 48.5 | odd | 4 | inner | |
48.3.i.b.29.3 | yes | 20 | 3.2 | odd | 2 | inner | |
48.3.i.b.29.8 | yes | 20 | 1.1 | even | 1 | trivial | |
192.3.i.b.17.7 | 20 | 12.11 | even | 2 | |||
192.3.i.b.17.8 | 20 | 4.3 | odd | 2 | |||
192.3.i.b.113.7 | 20 | 16.11 | odd | 4 | |||
192.3.i.b.113.8 | 20 | 48.11 | even | 4 | |||
384.3.i.c.161.3 | 20 | 8.3 | odd | 2 | |||
384.3.i.c.161.4 | 20 | 24.11 | even | 2 | |||
384.3.i.c.353.3 | 20 | 48.35 | even | 4 | |||
384.3.i.c.353.4 | 20 | 16.3 | odd | 4 | |||
384.3.i.d.161.7 | 20 | 24.5 | odd | 2 | |||
384.3.i.d.161.8 | 20 | 8.5 | even | 2 | |||
384.3.i.d.353.7 | 20 | 16.13 | even | 4 | |||
384.3.i.d.353.8 | 20 | 48.29 | odd | 4 |