Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(267,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.267");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 267.10 | ||
Character | \(\chi\) | \(=\) | 380.267 |
Dual form | 380.2.k.c.343.10 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.600761 | + | 1.28027i | −0.424802 | + | 0.905286i | ||||
\(3\) | 1.93295 | + | 1.93295i | 1.11599 | + | 1.11599i | 0.992324 | + | 0.123663i | \(0.0394642\pi\) |
0.123663 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(4\) | −1.27817 | − | 1.53827i | −0.639086 | − | 0.769135i | ||||
\(5\) | 2.18132 | + | 0.491792i | 0.975514 | + | 0.219936i | ||||
\(6\) | −3.63593 | + | 1.31345i | −1.48436 | + | 0.536214i | ||||
\(7\) | −3.06024 | + | 3.06024i | −1.15666 | + | 1.15666i | −0.171472 | + | 0.985189i | \(0.554852\pi\) |
−0.985189 | + | 0.171472i | \(0.945148\pi\) | |||||||
\(8\) | 2.73727 | − | 0.712271i | 0.967773 | − | 0.251826i | ||||
\(9\) | 4.47257i | 1.49086i | ||||||||
\(10\) | −1.94007 | + | 2.49722i | −0.613506 | + | 0.789690i | ||||
\(11\) | − | 4.14335i | − | 1.24927i | −0.780918 | − | 0.624633i | \(-0.785249\pi\) | ||
0.780918 | − | 0.624633i | \(-0.214751\pi\) | |||||||
\(12\) | 0.502754 | − | 5.44403i | 0.145133 | − | 1.57156i | ||||
\(13\) | −2.07701 | + | 2.07701i | −0.576059 | + | 0.576059i | −0.933815 | − | 0.357756i | \(-0.883542\pi\) |
0.357756 | + | 0.933815i | \(0.383542\pi\) | |||||||
\(14\) | −2.07945 | − | 5.75640i | −0.555757 | − | 1.53846i | ||||
\(15\) | 3.26576 | + | 5.16698i | 0.843216 | + | 1.33411i | ||||
\(16\) | −0.732549 | + | 3.93235i | −0.183137 | + | 0.983087i | ||||
\(17\) | −0.314830 | − | 0.314830i | −0.0763576 | − | 0.0763576i | 0.667897 | − | 0.744254i | \(-0.267195\pi\) |
−0.744254 | + | 0.667897i | \(0.767195\pi\) | |||||||
\(18\) | −5.72608 | − | 2.68694i | −1.34965 | − | 0.633319i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.03159 | − | 3.98405i | −0.454277 | − | 0.890860i | ||||
\(21\) | −11.8306 | −2.58164 | ||||||||
\(22\) | 5.30459 | + | 2.48916i | 1.13094 | + | 0.530691i | ||||
\(23\) | 5.43304 | + | 5.43304i | 1.13287 | + | 1.13287i | 0.989698 | + | 0.143169i | \(0.0457294\pi\) |
0.143169 | + | 0.989698i | \(0.454271\pi\) | |||||||
\(24\) | 6.66779 | + | 3.91422i | 1.36106 | + | 0.798987i | ||||
\(25\) | 4.51628 | + | 2.14551i | 0.903256 | + | 0.429101i | ||||
\(26\) | −1.41134 | − | 3.90691i | −0.276787 | − | 0.766209i | ||||
\(27\) | −2.84639 | + | 2.84639i | −0.547789 | + | 0.547789i | ||||
\(28\) | 8.61899 | + | 0.795960i | 1.62884 | + | 0.150422i | ||||
\(29\) | − | 0.106253i | − | 0.0197306i | −0.999951 | − | 0.00986532i | \(-0.996860\pi\) | ||
0.999951 | − | 0.00986532i | \(-0.00314028\pi\) | |||||||
\(30\) | −8.57706 | + | 1.07693i | −1.56595 | + | 0.196620i | ||||
\(31\) | − | 8.35227i | − | 1.50011i | −0.661374 | − | 0.750056i | \(-0.730026\pi\) | ||
0.661374 | − | 0.750056i | \(-0.269974\pi\) | |||||||
\(32\) | −4.59437 | − | 3.30026i | −0.812178 | − | 0.583409i | ||||
\(33\) | 8.00887 | − | 8.00887i | 1.39416 | − | 1.39416i | ||||
\(34\) | 0.592205 | − | 0.213930i | 0.101562 | − | 0.0366886i | ||||
\(35\) | −8.18035 | + | 5.17035i | −1.38273 | + | 0.873948i | ||||
\(36\) | 6.88001 | − | 5.71671i | 1.14667 | − | 0.952785i | ||||
\(37\) | 3.26782 | + | 3.26782i | 0.537227 | + | 0.537227i | 0.922713 | − | 0.385487i | \(-0.125966\pi\) |
−0.385487 | + | 0.922713i | \(0.625966\pi\) | |||||||
\(38\) | −0.600761 | + | 1.28027i | −0.0974563 | + | 0.207687i | ||||
\(39\) | −8.02949 | −1.28575 | ||||||||
\(40\) | 6.32115 | − | 0.207520i | 0.999462 | − | 0.0328118i | ||||
\(41\) | −3.02173 | −0.471915 | −0.235957 | − | 0.971763i | \(-0.575823\pi\) | ||||
−0.235957 | + | 0.971763i | \(0.575823\pi\) | |||||||
\(42\) | 7.10733 | − | 15.1463i | 1.09669 | − | 2.33712i | ||||
\(43\) | −7.14446 | − | 7.14446i | −1.08952 | − | 1.08952i | −0.995578 | − | 0.0939420i | \(-0.970053\pi\) |
−0.0939420 | − | 0.995578i | \(-0.529947\pi\) | |||||||
\(44\) | −6.37359 | + | 5.29591i | −0.960854 | + | 0.798389i | ||||
\(45\) | −2.19957 | + | 9.75608i | −0.327893 | + | 1.45435i | ||||
\(46\) | −10.2197 | + | 3.69179i | −1.50681 | + | 0.544325i | ||||
\(47\) | 3.91723 | − | 3.91723i | 0.571387 | − | 0.571387i | −0.361129 | − | 0.932516i | \(-0.617609\pi\) |
0.932516 | + | 0.361129i | \(0.117609\pi\) | |||||||
\(48\) | −9.01700 | + | 6.18504i | −1.30149 | + | 0.892734i | ||||
\(49\) | − | 11.7301i | − | 1.67573i | ||||||
\(50\) | −5.46003 | + | 4.49311i | −0.772165 | + | 0.635422i | ||||
\(51\) | − | 1.21710i | − | 0.170428i | ||||||
\(52\) | 5.84978 | + | 0.540224i | 0.811218 | + | 0.0749156i | ||||
\(53\) | 0.521892 | − | 0.521892i | 0.0716873 | − | 0.0716873i | −0.670354 | − | 0.742041i | \(-0.733858\pi\) |
0.742041 | + | 0.670354i | \(0.233858\pi\) | |||||||
\(54\) | −1.93414 | − | 5.35415i | −0.263204 | − | 0.728607i | ||||
\(55\) | 2.03766 | − | 9.03795i | 0.274759 | − | 1.21868i | ||||
\(56\) | −6.19699 | + | 10.5564i | −0.828108 | + | 1.41066i | ||||
\(57\) | 1.93295 | + | 1.93295i | 0.256025 | + | 0.256025i | ||||
\(58\) | 0.136032 | + | 0.0638325i | 0.0178619 | + | 0.00838161i | ||||
\(59\) | 7.27666 | 0.947340 | 0.473670 | − | 0.880702i | \(-0.342929\pi\) | ||||
0.473670 | + | 0.880702i | \(0.342929\pi\) | |||||||
\(60\) | 3.77400 | − | 11.6279i | 0.487221 | − | 1.50116i | ||||
\(61\) | 9.20099 | 1.17807 | 0.589033 | − | 0.808109i | \(-0.299509\pi\) | ||||
0.589033 | + | 0.808109i | \(0.299509\pi\) | |||||||
\(62\) | 10.6931 | + | 5.01772i | 1.35803 | + | 0.637251i | ||||
\(63\) | −13.6871 | − | 13.6871i | −1.72441 | − | 1.72441i | ||||
\(64\) | 6.98534 | − | 3.89936i | 0.873167 | − | 0.487420i | ||||
\(65\) | −5.55207 | + | 3.50916i | −0.688649 | + | 0.435257i | ||||
\(66\) | 5.44208 | + | 15.0649i | 0.669874 | + | 1.85436i | ||||
\(67\) | −4.78675 | + | 4.78675i | −0.584794 | + | 0.584794i | −0.936217 | − | 0.351423i | \(-0.885698\pi\) |
0.351423 | + | 0.936217i | \(0.385698\pi\) | |||||||
\(68\) | −0.0818865 | + | 0.886702i | −0.00993020 | + | 0.107528i | ||||
\(69\) | 21.0036i | 2.52853i | ||||||||
\(70\) | −1.70500 | − | 13.5792i | −0.203786 | − | 1.62302i | ||||
\(71\) | 10.2743i | 1.21933i | 0.792659 | + | 0.609665i | \(0.208696\pi\) | ||||
−0.792659 | + | 0.609665i | \(0.791304\pi\) | |||||||
\(72\) | 3.18568 | + | 12.2426i | 0.375436 | + | 1.44281i | ||||
\(73\) | 4.65123 | − | 4.65123i | 0.544386 | − | 0.544386i | −0.380426 | − | 0.924811i | \(-0.624223\pi\) |
0.924811 | + | 0.380426i | \(0.124223\pi\) | |||||||
\(74\) | −6.14687 | + | 2.22051i | −0.714559 | + | 0.258129i | ||||
\(75\) | 4.58258 | + | 12.8769i | 0.529151 | + | 1.48689i | ||||
\(76\) | −1.27817 | − | 1.53827i | −0.146616 | − | 0.176452i | ||||
\(77\) | 12.6796 | + | 12.6796i | 1.44498 | + | 1.44498i | ||||
\(78\) | 4.82381 | − | 10.2799i | 0.546188 | − | 1.16397i | ||||
\(79\) | 2.41405 | 0.271601 | 0.135801 | − | 0.990736i | \(-0.456639\pi\) | ||||
0.135801 | + | 0.990736i | \(0.456639\pi\) | |||||||
\(80\) | −3.53182 | + | 8.21744i | −0.394869 | + | 0.918737i | ||||
\(81\) | 2.41385 | 0.268205 | ||||||||
\(82\) | 1.81534 | − | 3.86862i | 0.200470 | − | 0.427218i | ||||
\(83\) | −8.80850 | − | 8.80850i | −0.966858 | − | 0.966858i | 0.0326101 | − | 0.999468i | \(-0.489618\pi\) |
−0.999468 | + | 0.0326101i | \(0.989618\pi\) | |||||||
\(84\) | 15.1215 | + | 18.1986i | 1.64989 | + | 1.98563i | ||||
\(85\) | −0.531914 | − | 0.841576i | −0.0576941 | − | 0.0912817i | ||||
\(86\) | 13.4389 | − | 4.85471i | 1.44916 | − | 0.523497i | ||||
\(87\) | 0.205381 | − | 0.205381i | 0.0220191 | − | 0.0220191i | ||||
\(88\) | −2.95119 | − | 11.3415i | −0.314598 | − | 1.20901i | ||||
\(89\) | 1.25042i | 0.132544i | 0.997802 | + | 0.0662721i | \(0.0211105\pi\) | ||||
−0.997802 | + | 0.0662721i | \(0.978889\pi\) | |||||||
\(90\) | −11.1690 | − | 8.67711i | −1.17731 | − | 0.914648i | ||||
\(91\) | − | 12.7123i | − | 1.33261i | ||||||
\(92\) | 1.41312 | − | 15.3019i | 0.147328 | − | 1.59533i | ||||
\(93\) | 16.1445 | − | 16.1445i | 1.67411 | − | 1.67411i | ||||
\(94\) | 2.66179 | + | 7.36843i | 0.274542 | + | 0.759995i | ||||
\(95\) | 2.18132 | + | 0.491792i | 0.223798 | + | 0.0504568i | ||||
\(96\) | −2.50145 | − | 15.2599i | −0.255303 | − | 1.55746i | ||||
\(97\) | −2.87685 | − | 2.87685i | −0.292100 | − | 0.292100i | 0.545810 | − | 0.837909i | \(-0.316222\pi\) |
−0.837909 | + | 0.545810i | \(0.816222\pi\) | |||||||
\(98\) | 15.0177 | + | 7.04699i | 1.51702 | + | 0.711854i | ||||
\(99\) | 18.5314 | 1.86247 | ||||||||
\(100\) | −2.47222 | − | 9.68959i | −0.247222 | − | 0.968959i | ||||
\(101\) | −3.29590 | −0.327954 | −0.163977 | − | 0.986464i | \(-0.552432\pi\) | ||||
−0.163977 | + | 0.986464i | \(0.552432\pi\) | |||||||
\(102\) | 1.55822 | + | 0.731187i | 0.154286 | + | 0.0723983i | ||||
\(103\) | 8.36336 | + | 8.36336i | 0.824066 | + | 0.824066i | 0.986688 | − | 0.162622i | \(-0.0519951\pi\) |
−0.162622 | + | 0.986688i | \(0.551995\pi\) | |||||||
\(104\) | −4.20595 | + | 7.16474i | −0.412427 | + | 0.702560i | ||||
\(105\) | −25.8062 | − | 5.81817i | −2.51843 | − | 0.567795i | ||||
\(106\) | 0.354629 | + | 0.981693i | 0.0344446 | + | 0.0953505i | ||||
\(107\) | 0.887437 | − | 0.887437i | 0.0857918 | − | 0.0857918i | −0.662909 | − | 0.748700i | \(-0.730678\pi\) |
0.748700 | + | 0.662909i | \(0.230678\pi\) | |||||||
\(108\) | 8.01670 | + | 0.740339i | 0.771407 | + | 0.0712392i | ||||
\(109\) | − | 1.36449i | − | 0.130694i | −0.997863 | − | 0.0653470i | \(-0.979185\pi\) | ||
0.997863 | − | 0.0653470i | \(-0.0208154\pi\) | |||||||
\(110\) | 10.3468 | + | 8.03840i | 0.986533 | + | 0.766432i | ||||
\(111\) | 12.6330i | 1.19908i | ||||||||
\(112\) | −9.79215 | − | 14.2757i | −0.925271 | − | 1.34893i | ||||
\(113\) | −1.40611 | + | 1.40611i | −0.132276 | + | 0.132276i | −0.770145 | − | 0.637869i | \(-0.779816\pi\) |
0.637869 | + | 0.770145i | \(0.279816\pi\) | |||||||
\(114\) | −3.63593 | + | 1.31345i | −0.340536 | + | 0.123016i | ||||
\(115\) | 9.17926 | + | 14.5231i | 0.855970 | + | 1.35429i | ||||
\(116\) | −0.163445 | + | 0.135809i | −0.0151755 | + | 0.0126096i | ||||
\(117\) | −9.28956 | − | 9.28956i | −0.858820 | − | 0.858820i | ||||
\(118\) | −4.37153 | + | 9.31607i | −0.402432 | + | 0.857614i | ||||
\(119\) | 1.92691 | 0.176640 | ||||||||
\(120\) | 12.6196 | + | 11.8173i | 1.15200 | + | 1.07877i | ||||
\(121\) | −6.16732 | −0.560665 | ||||||||
\(122\) | −5.52759 | + | 11.7797i | −0.500445 | + | 1.06649i | ||||
\(123\) | −5.84084 | − | 5.84084i | −0.526651 | − | 0.526651i | ||||
\(124\) | −12.8480 | + | 10.6756i | −1.15379 | + | 0.958701i | ||||
\(125\) | 8.79630 | + | 6.90110i | 0.786765 | + | 0.617253i | ||||
\(126\) | 25.7459 | − | 9.30050i | 2.29362 | − | 0.828554i | ||||
\(127\) | −4.26882 | + | 4.26882i | −0.378797 | + | 0.378797i | −0.870668 | − | 0.491871i | \(-0.836313\pi\) |
0.491871 | + | 0.870668i | \(0.336313\pi\) | |||||||
\(128\) | 0.795712 | + | 11.2857i | 0.0703317 | + | 0.997524i | ||||
\(129\) | − | 27.6197i | − | 2.43178i | ||||||
\(130\) | −1.15720 | − | 9.21630i | −0.101493 | − | 0.808323i | ||||
\(131\) | − | 4.06634i | − | 0.355278i | −0.984096 | − | 0.177639i | \(-0.943154\pi\) | ||
0.984096 | − | 0.177639i | \(-0.0568460\pi\) | |||||||
\(132\) | −22.5565 | − | 2.08308i | −1.96329 | − | 0.181309i | ||||
\(133\) | −3.06024 | + | 3.06024i | −0.265356 | + | 0.265356i | ||||
\(134\) | −3.25263 | − | 9.00401i | −0.280984 | − | 0.777828i | ||||
\(135\) | −7.60872 | + | 4.80905i | −0.654854 | + | 0.413897i | ||||
\(136\) | −1.08602 | − | 0.637533i | −0.0931256 | − | 0.0546680i | ||||
\(137\) | −4.18040 | − | 4.18040i | −0.357156 | − | 0.357156i | 0.505608 | − | 0.862764i | \(-0.331268\pi\) |
−0.862764 | + | 0.505608i | \(0.831268\pi\) | |||||||
\(138\) | −26.8902 | − | 12.6181i | −2.28905 | − | 1.07413i | ||||
\(139\) | 20.2237 | 1.71535 | 0.857674 | − | 0.514193i | \(-0.171909\pi\) | ||||
0.857674 | + | 0.514193i | \(0.171909\pi\) | |||||||
\(140\) | 18.4093 | + | 5.97499i | 1.55587 | + | 0.504978i | ||||
\(141\) | 15.1436 | 1.27532 | ||||||||
\(142\) | −13.1538 | − | 6.17237i | −1.10384 | − | 0.517974i | ||||
\(143\) | 8.60577 | + | 8.60577i | 0.719650 | + | 0.719650i | ||||
\(144\) | −17.5877 | − | 3.27637i | −1.46564 | − | 0.273031i | ||||
\(145\) | 0.0522542 | − | 0.231771i | 0.00433948 | − | 0.0192475i | ||||
\(146\) | 3.16055 | + | 8.74910i | 0.261569 | + | 0.724081i | ||||
\(147\) | 22.6737 | − | 22.6737i | 1.87009 | − | 1.87009i | ||||
\(148\) | 0.849951 | − | 9.20363i | 0.0698656 | − | 0.756534i | ||||
\(149\) | 6.18976i | 0.507085i | 0.967324 | + | 0.253542i | \(0.0815957\pi\) | ||||
−0.967324 | + | 0.253542i | \(0.918404\pi\) | |||||||
\(150\) | −19.2389 | − | 1.86900i | −1.57085 | − | 0.152603i | ||||
\(151\) | − | 0.852809i | − | 0.0694006i | −0.999398 | − | 0.0347003i | \(-0.988952\pi\) | ||
0.999398 | − | 0.0347003i | \(-0.0110477\pi\) | |||||||
\(152\) | 2.73727 | − | 0.712271i | 0.222022 | − | 0.0577728i | ||||
\(153\) | 1.40810 | − | 1.40810i | 0.113838 | − | 0.113838i | ||||
\(154\) | −23.8507 | + | 8.61590i | −1.92195 | + | 0.694289i | ||||
\(155\) | 4.10758 | − | 18.2189i | 0.329929 | − | 1.46338i | ||||
\(156\) | 10.2631 | + | 12.3515i | 0.821704 | + | 0.988914i | ||||
\(157\) | −15.3133 | − | 15.3133i | −1.22213 | − | 1.22213i | −0.966873 | − | 0.255257i | \(-0.917840\pi\) |
−0.255257 | − | 0.966873i | \(-0.582160\pi\) | |||||||
\(158\) | −1.45026 | + | 3.09063i | −0.115377 | + | 0.245877i | ||||
\(159\) | 2.01758 | 0.160004 | ||||||||
\(160\) | −8.39874 | − | 9.45839i | −0.663979 | − | 0.747751i | ||||
\(161\) | −33.2528 | −2.62069 | ||||||||
\(162\) | −1.45015 | + | 3.09037i | −0.113934 | + | 0.242803i | ||||
\(163\) | −7.61959 | − | 7.61959i | −0.596812 | − | 0.596812i | 0.342651 | − | 0.939463i | \(-0.388675\pi\) |
−0.939463 | + | 0.342651i | \(0.888675\pi\) | |||||||
\(164\) | 3.86229 | + | 4.64823i | 0.301594 | + | 0.362966i | ||||
\(165\) | 21.4086 | − | 13.5312i | 1.66665 | − | 1.05340i | ||||
\(166\) | 16.5690 | − | 5.98544i | 1.28601 | − | 0.464560i | ||||
\(167\) | 9.87017 | − | 9.87017i | 0.763776 | − | 0.763776i | −0.213226 | − | 0.977003i | \(-0.568397\pi\) |
0.977003 | + | 0.213226i | \(0.0683972\pi\) | |||||||
\(168\) | −32.3835 | + | 8.42656i | −2.49844 | + | 0.650124i | ||||
\(169\) | 4.37207i | 0.336313i | ||||||||
\(170\) | 1.39700 | − | 0.175406i | 0.107145 | − | 0.0134531i | ||||
\(171\) | 4.47257i | 0.342026i | ||||||||
\(172\) | −1.85825 | + | 20.1220i | −0.141691 | + | 1.53428i | ||||
\(173\) | −11.9281 | + | 11.9281i | −0.906874 | + | 0.906874i | −0.996019 | − | 0.0891449i | \(-0.971587\pi\) |
0.0891449 | + | 0.996019i | \(0.471587\pi\) | |||||||
\(174\) | 0.139558 | + | 0.386327i | 0.0105798 | + | 0.0292874i | ||||
\(175\) | −20.3867 | + | 7.25513i | −1.54109 | + | 0.548437i | ||||
\(176\) | 16.2931 | + | 3.03520i | 1.22814 | + | 0.228787i | ||||
\(177\) | 14.0654 | + | 14.0654i | 1.05722 | + | 1.05722i | ||||
\(178\) | −1.60087 | − | 0.751203i | −0.119990 | − | 0.0563051i | ||||
\(179\) | −15.5820 | −1.16465 | −0.582326 | − | 0.812956i | \(-0.697857\pi\) | ||||
−0.582326 | + | 0.812956i | \(0.697857\pi\) | |||||||
\(180\) | 17.8189 | − | 9.08642i | 1.32814 | − | 0.677262i | ||||
\(181\) | −12.0911 | −0.898727 | −0.449363 | − | 0.893349i | \(-0.648349\pi\) | ||||
−0.449363 | + | 0.893349i | \(0.648349\pi\) | |||||||
\(182\) | 16.2751 | + | 7.63704i | 1.20639 | + | 0.566095i | ||||
\(183\) | 17.7850 | + | 17.7850i | 1.31471 | + | 1.31471i | ||||
\(184\) | 18.7415 | + | 11.0019i | 1.38164 | + | 0.811073i | ||||
\(185\) | 5.52106 | + | 8.73524i | 0.405917 | + | 0.642228i | ||||
\(186\) | 10.9703 | + | 30.3683i | 0.804382 | + | 2.22671i | ||||
\(187\) | −1.30445 | + | 1.30445i | −0.0953909 | + | 0.0953909i | ||||
\(188\) | −11.0327 | − | 1.01886i | −0.804640 | − | 0.0743081i | ||||
\(189\) | − | 17.4213i | − | 1.26721i | ||||||
\(190\) | −1.94007 | + | 2.49722i | −0.140748 | + | 0.181167i | ||||
\(191\) | − | 12.0103i | − | 0.869036i | −0.900663 | − | 0.434518i | \(-0.856919\pi\) | ||
0.900663 | − | 0.434518i | \(-0.143081\pi\) | |||||||
\(192\) | 21.0396 | + | 5.96503i | 1.51840 | + | 0.430489i | ||||
\(193\) | 16.9937 | − | 16.9937i | 1.22323 | − | 1.22323i | 0.256754 | − | 0.966477i | \(-0.417347\pi\) |
0.966477 | − | 0.256754i | \(-0.0826530\pi\) | |||||||
\(194\) | 5.41143 | − | 1.95484i | 0.388518 | − | 0.140349i | ||||
\(195\) | −17.5149 | − | 3.94884i | −1.25427 | − | 0.282782i | ||||
\(196\) | −18.0441 | + | 14.9931i | −1.28886 | + | 1.07094i | ||||
\(197\) | −10.1361 | − | 10.1361i | −0.722166 | − | 0.722166i | 0.246880 | − | 0.969046i | \(-0.420595\pi\) |
−0.969046 | + | 0.246880i | \(0.920595\pi\) | |||||||
\(198\) | −11.1329 | + | 23.7251i | −0.791183 | + | 1.68607i | ||||
\(199\) | −18.9801 | −1.34547 | −0.672733 | − | 0.739886i | \(-0.734880\pi\) | ||||
−0.672733 | + | 0.739886i | \(0.734880\pi\) | |||||||
\(200\) | 13.8905 | + | 2.65602i | 0.982206 | + | 0.187809i | ||||
\(201\) | −18.5051 | −1.30525 | ||||||||
\(202\) | 1.98005 | − | 4.21963i | 0.139316 | − | 0.296892i | ||||
\(203\) | 0.325159 | + | 0.325159i | 0.0228217 | + | 0.0228217i | ||||
\(204\) | −1.87223 | + | 1.55567i | −0.131082 | + | 0.108918i | ||||
\(205\) | −6.59135 | − | 1.48606i | −0.460360 | − | 0.103791i | ||||
\(206\) | −15.7317 | + | 5.68296i | −1.09608 | + | 0.395951i | ||||
\(207\) | −24.2996 | + | 24.2996i | −1.68894 | + | 1.68894i | ||||
\(208\) | −6.64601 | − | 9.68903i | −0.460818 | − | 0.671814i | ||||
\(209\) | − | 4.14335i | − | 0.286601i | ||||||
\(210\) | 22.9522 | − | 29.5435i | 1.58385 | − | 2.03870i | ||||
\(211\) | − | 1.07044i | − | 0.0736923i | −0.999321 | − | 0.0368462i | \(-0.988269\pi\) | ||
0.999321 | − | 0.0368462i | \(-0.0117312\pi\) | |||||||
\(212\) | −1.46988 | − | 0.135743i | −0.100952 | − | 0.00932284i | ||||
\(213\) | −19.8596 | + | 19.8596i | −1.36076 | + | 1.36076i | ||||
\(214\) | 0.603020 | + | 1.66930i | 0.0412216 | + | 0.114111i | ||||
\(215\) | −12.0707 | − | 19.0979i | −0.823217 | − | 1.30247i | ||||
\(216\) | −5.76395 | + | 9.81876i | −0.392187 | + | 0.668082i | ||||
\(217\) | 25.5599 | + | 25.5599i | 1.73512 | + | 1.73512i | ||||
\(218\) | 1.74691 | + | 0.819730i | 0.118316 | + | 0.0555191i | ||||
\(219\) | 17.9812 | 1.21505 | ||||||||
\(220\) | −16.5073 | + | 8.41758i | −1.11292 | + | 0.567513i | ||||
\(221\) | 1.30781 | 0.0879729 | ||||||||
\(222\) | −16.1737 | − | 7.58944i | −1.08551 | − | 0.509370i | ||||
\(223\) | −10.7260 | − | 10.7260i | −0.718268 | − | 0.718268i | 0.249982 | − | 0.968250i | \(-0.419575\pi\) |
−0.968250 | + | 0.249982i | \(0.919575\pi\) | |||||||
\(224\) | 24.1595 | − | 3.96030i | 1.61422 | − | 0.264608i | ||||
\(225\) | −9.59592 | + | 20.1994i | −0.639728 | + | 1.34662i | ||||
\(226\) | −0.955461 | − | 2.64493i | −0.0635563 | − | 0.175938i | ||||
\(227\) | −8.16413 | + | 8.16413i | −0.541872 | + | 0.541872i | −0.924077 | − | 0.382205i | \(-0.875165\pi\) |
0.382205 | + | 0.924077i | \(0.375165\pi\) | |||||||
\(228\) | 0.502754 | − | 5.44403i | 0.0332957 | − | 0.360540i | ||||
\(229\) | − | 2.80772i | − | 0.185539i | −0.995688 | − | 0.0927696i | \(-0.970428\pi\) | ||
0.995688 | − | 0.0927696i | \(-0.0295720\pi\) | |||||||
\(230\) | −24.1080 | + | 3.02699i | −1.58964 | + | 0.199594i | ||||
\(231\) | 49.0181i | 3.22515i | ||||||||
\(232\) | −0.0756807 | − | 0.290843i | −0.00496868 | − | 0.0190948i | ||||
\(233\) | −13.6889 | + | 13.6889i | −0.896789 | + | 0.896789i | −0.995151 | − | 0.0983615i | \(-0.968640\pi\) |
0.0983615 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(234\) | 17.4739 | − | 6.31232i | 1.14231 | − | 0.412649i | ||||
\(235\) | 10.4712 | − | 6.61826i | 0.683065 | − | 0.431728i | ||||
\(236\) | −9.30082 | − | 11.1935i | −0.605432 | − | 0.728632i | ||||
\(237\) | 4.66622 | + | 4.66622i | 0.303104 | + | 0.303104i | ||||
\(238\) | −1.15761 | + | 2.46696i | −0.0750369 | + | 0.159910i | ||||
\(239\) | −22.3794 | −1.44760 | −0.723800 | − | 0.690009i | \(-0.757606\pi\) | ||||
−0.723800 | + | 0.690009i | \(0.757606\pi\) | |||||||
\(240\) | −22.7107 | + | 9.05705i | −1.46597 | + | 0.584630i | ||||
\(241\) | −8.23988 | −0.530777 | −0.265389 | − | 0.964142i | \(-0.585500\pi\) | ||||
−0.265389 | + | 0.964142i | \(0.585500\pi\) | |||||||
\(242\) | 3.70508 | − | 7.89582i | 0.238172 | − | 0.507563i | ||||
\(243\) | 13.2050 | + | 13.2050i | 0.847102 | + | 0.847102i | ||||
\(244\) | −11.7604 | − | 14.1536i | −0.752886 | − | 0.906091i | ||||
\(245\) | 5.76877 | − | 25.5871i | 0.368553 | − | 1.63470i | ||||
\(246\) | 10.9868 | − | 3.96889i | 0.700492 | − | 0.253047i | ||||
\(247\) | −2.07701 | + | 2.07701i | −0.132157 | + | 0.132157i | ||||
\(248\) | −5.94908 | − | 22.8625i | −0.377767 | − | 1.45177i | ||||
\(249\) | − | 34.0527i | − | 2.15800i | ||||||
\(250\) | −14.1197 | + | 7.11571i | −0.893010 | + | 0.450037i | ||||
\(251\) | − | 1.80566i | − | 0.113972i | −0.998375 | − | 0.0569861i | \(-0.981851\pi\) | ||
0.998375 | − | 0.0569861i | \(-0.0181491\pi\) | |||||||
\(252\) | −3.55998 | + | 38.5490i | −0.224258 | + | 2.42836i | ||||
\(253\) | 22.5110 | − | 22.5110i | 1.41525 | − | 1.41525i | ||||
\(254\) | −2.90070 | − | 8.02978i | −0.182006 | − | 0.503833i | ||||
\(255\) | 0.598560 | − | 2.65488i | 0.0374833 | − | 0.166255i | ||||
\(256\) | −14.9267 | − | 5.76128i | −0.932921 | − | 0.360080i | ||||
\(257\) | −5.48793 | − | 5.48793i | −0.342328 | − | 0.342328i | 0.514914 | − | 0.857242i | \(-0.327824\pi\) |
−0.857242 | + | 0.514914i | \(0.827824\pi\) | |||||||
\(258\) | 35.3606 | + | 16.5928i | 2.20146 | + | 1.03303i | ||||
\(259\) | −20.0006 | −1.24278 | ||||||||
\(260\) | 12.4945 | + | 4.05527i | 0.774878 | + | 0.251497i | ||||
\(261\) | 0.475222 | 0.0294155 | ||||||||
\(262\) | 5.20601 | + | 2.44290i | 0.321628 | + | 0.150923i | ||||
\(263\) | 10.0969 | + | 10.0969i | 0.622602 | + | 0.622602i | 0.946196 | − | 0.323594i | \(-0.104891\pi\) |
−0.323594 | + | 0.946196i | \(0.604891\pi\) | |||||||
\(264\) | 16.2180 | − | 27.6270i | 0.998148 | − | 1.70032i | ||||
\(265\) | 1.39507 | − | 0.881749i | 0.0856986 | − | 0.0541654i | ||||
\(266\) | −2.07945 | − | 5.75640i | −0.127499 | − | 0.352947i | ||||
\(267\) | −2.41699 | + | 2.41699i | −0.147918 | + | 0.147918i | ||||
\(268\) | 13.4816 | + | 1.24502i | 0.823520 | + | 0.0760517i | ||||
\(269\) | − | 0.438106i | − | 0.0267118i | −0.999911 | − | 0.0133559i | \(-0.995749\pi\) | ||
0.999911 | − | 0.0133559i | \(-0.00425144\pi\) | |||||||
\(270\) | −1.58585 | − | 12.6303i | −0.0965120 | − | 0.768655i | ||||
\(271\) | − | 8.49434i | − | 0.515994i | −0.966146 | − | 0.257997i | \(-0.916937\pi\) | ||
0.966146 | − | 0.257997i | \(-0.0830625\pi\) | |||||||
\(272\) | 1.46865 | − | 1.00739i | 0.0890501 | − | 0.0610823i | ||||
\(273\) | 24.5722 | − | 24.5722i | 1.48718 | − | 1.48718i | ||||
\(274\) | 7.86346 | − | 2.84061i | 0.475049 | − | 0.171608i | ||||
\(275\) | 8.88958 | − | 18.7125i | 0.536062 | − | 1.12841i | ||||
\(276\) | 32.3092 | − | 26.8462i | 1.94478 | − | 1.61595i | ||||
\(277\) | −10.0130 | − | 10.0130i | −0.601622 | − | 0.601622i | 0.339121 | − | 0.940743i | \(-0.389870\pi\) |
−0.940743 | + | 0.339121i | \(0.889870\pi\) | |||||||
\(278\) | −12.1496 | + | 25.8917i | −0.728684 | + | 1.55288i | ||||
\(279\) | 37.3561 | 2.23645 | ||||||||
\(280\) | −18.7092 | + | 19.9793i | −1.11809 | + | 1.19399i | ||||
\(281\) | −7.39792 | −0.441323 | −0.220661 | − | 0.975350i | \(-0.570822\pi\) | ||||
−0.220661 | + | 0.975350i | \(0.570822\pi\) | |||||||
\(282\) | −9.09769 | + | 19.3879i | −0.541759 | + | 1.15453i | ||||
\(283\) | 14.5566 | + | 14.5566i | 0.865298 | + | 0.865298i | 0.991948 | − | 0.126649i | \(-0.0404222\pi\) |
−0.126649 | + | 0.991948i | \(0.540422\pi\) | |||||||
\(284\) | 15.8046 | − | 13.1323i | 0.937830 | − | 0.779257i | ||||
\(285\) | 3.26576 | + | 5.16698i | 0.193447 | + | 0.306065i | ||||
\(286\) | −16.1877 | + | 5.84768i | −0.957199 | + | 0.345781i | ||||
\(287\) | 9.24721 | − | 9.24721i | 0.545845 | − | 0.545845i | ||||
\(288\) | 14.7606 | − | 20.5486i | 0.869779 | − | 1.21084i | ||||
\(289\) | − | 16.8018i | − | 0.988339i | ||||||
\(290\) | 0.265336 | + | 0.206138i | 0.0155811 | + | 0.0121049i | ||||
\(291\) | − | 11.1216i | − | 0.651959i | ||||||
\(292\) | −13.0999 | − | 1.20977i | −0.766615 | − | 0.0707966i | ||||
\(293\) | −1.15451 | + | 1.15451i | −0.0674471 | + | 0.0674471i | −0.740026 | − | 0.672579i | \(-0.765187\pi\) |
0.672579 | + | 0.740026i | \(0.265187\pi\) | |||||||
\(294\) | 15.4069 | + | 42.6499i | 0.898551 | + | 2.48739i | ||||
\(295\) | 15.8727 | + | 3.57860i | 0.924144 | + | 0.208354i | ||||
\(296\) | 11.2725 | + | 6.61735i | 0.655201 | + | 0.384626i | ||||
\(297\) | 11.7936 | + | 11.7936i | 0.684334 | + | 0.684334i | ||||
\(298\) | −7.92455 | − | 3.71856i | −0.459057 | − | 0.215411i | ||||
\(299\) | −22.5690 | −1.30520 | ||||||||
\(300\) | 13.9508 | − | 23.5081i | 0.805449 | − | 1.35724i | ||||
\(301\) | 43.7275 | 2.52041 | ||||||||
\(302\) | 1.09182 | + | 0.512334i | 0.0628274 | + | 0.0294815i | ||||
\(303\) | −6.37079 | − | 6.37079i | −0.365993 | − | 0.365993i | ||||
\(304\) | −0.732549 | + | 3.93235i | −0.0420146 | + | 0.225536i | ||||
\(305\) | 20.0703 | + | 4.52497i | 1.14922 | + | 0.259099i | ||||
\(306\) | 0.956814 | + | 2.64868i | 0.0546974 | + | 0.151415i | ||||
\(307\) | 17.1688 | − | 17.1688i | 0.979878 | − | 0.979878i | −0.0199236 | − | 0.999802i | \(-0.506342\pi\) |
0.999802 | + | 0.0199236i | \(0.00634229\pi\) | |||||||
\(308\) | 3.29794 | − | 35.7114i | 0.187917 | − | 2.03485i | ||||
\(309\) | 32.3319i | 1.83930i | ||||||||
\(310\) | 20.8575 | + | 16.2040i | 1.18462 | + | 0.920327i | ||||
\(311\) | 8.36370i | 0.474262i | 0.971478 | + | 0.237131i | \(0.0762070\pi\) | ||||
−0.971478 | + | 0.237131i | \(0.923793\pi\) | |||||||
\(312\) | −21.9789 | + | 5.71918i | −1.24431 | + | 0.323785i | ||||
\(313\) | −8.96217 | + | 8.96217i | −0.506572 | + | 0.506572i | −0.913472 | − | 0.406901i | \(-0.866610\pi\) |
0.406901 | + | 0.913472i | \(0.366610\pi\) | |||||||
\(314\) | 28.8047 | − | 10.4055i | 1.62554 | − | 0.587214i | ||||
\(315\) | −23.1247 | − | 36.5871i | −1.30293 | − | 2.06145i | ||||
\(316\) | −3.08557 | − | 3.71346i | −0.173577 | − | 0.208898i | ||||
\(317\) | 0.158606 | + | 0.158606i | 0.00890818 | + | 0.00890818i | 0.711547 | − | 0.702639i | \(-0.247995\pi\) |
−0.702639 | + | 0.711547i | \(0.747995\pi\) | |||||||
\(318\) | −1.21208 | + | 2.58304i | −0.0679702 | + | 0.144850i | ||||
\(319\) | −0.440242 | −0.0246488 | ||||||||
\(320\) | 17.1549 | − | 5.07041i | 0.958989 | − | 0.283445i | ||||
\(321\) | 3.43074 | 0.191485 | ||||||||
\(322\) | 19.9770 | − | 42.5725i | 1.11327 | − | 2.37247i | ||||
\(323\) | −0.314830 | − | 0.314830i | −0.0175176 | − | 0.0175176i | ||||
\(324\) | −3.08532 | − | 3.71315i | −0.171406 | − | 0.206286i | ||||
\(325\) | −13.8366 | + | 4.92412i | −0.767516 | + | 0.273141i | ||||
\(326\) | 14.3327 | − | 5.17756i | 0.793813 | − | 0.286759i | ||||
\(327\) | 2.63748 | − | 2.63748i | 0.145853 | − | 0.145853i | ||||
\(328\) | −8.27130 | + | 2.15229i | −0.456706 | + | 0.118840i | ||||
\(329\) | 23.9753i | 1.32180i | ||||||||
\(330\) | 4.46210 | + | 35.5377i | 0.245631 | + | 1.95629i | ||||
\(331\) | − | 30.6880i | − | 1.68677i | −0.537312 | − | 0.843384i | \(-0.680560\pi\) | ||
0.537312 | − | 0.843384i | \(-0.319440\pi\) | |||||||
\(332\) | −2.29107 | + | 24.8086i | −0.125739 | + | 1.36155i | ||||
\(333\) | −14.6155 | + | 14.6155i | −0.800927 | + | 0.800927i | ||||
\(334\) | 6.70685 | + | 18.5661i | 0.366982 | + | 1.01589i | ||||
\(335\) | −12.7955 | + | 8.08733i | −0.699093 | + | 0.441858i | ||||
\(336\) | 8.66646 | − | 46.5219i | 0.472794 | − | 2.53798i | ||||
\(337\) | 13.0981 | + | 13.0981i | 0.713502 | + | 0.713502i | 0.967266 | − | 0.253765i | \(-0.0816688\pi\) |
−0.253765 | + | 0.967266i | \(0.581669\pi\) | |||||||
\(338\) | −5.59742 | − | 2.62657i | −0.304460 | − | 0.142867i | ||||
\(339\) | −5.43587 | −0.295236 | ||||||||
\(340\) | −0.614693 | + | 1.89391i | −0.0333364 | + | 0.102711i | ||||
\(341\) | −34.6064 | −1.87404 | ||||||||
\(342\) | −5.72608 | − | 2.68694i | −0.309631 | − | 0.145293i | ||||
\(343\) | 14.4753 | + | 14.4753i | 0.781592 | + | 0.781592i | ||||
\(344\) | −24.6451 | − | 14.4675i | −1.32878 | − | 0.780038i | ||||
\(345\) | −10.3294 | + | 45.8154i | −0.556115 | + | 2.46662i | ||||
\(346\) | −8.10520 | − | 22.4370i | −0.435738 | − | 1.20622i | ||||
\(347\) | 1.64722 | − | 1.64722i | 0.0884272 | − | 0.0884272i | −0.661510 | − | 0.749937i | \(-0.730084\pi\) |
0.749937 | + | 0.661510i | \(0.230084\pi\) | |||||||
\(348\) | −0.578443 | − | 0.0534190i | −0.0310078 | − | 0.00286356i | ||||
\(349\) | − | 10.2088i | − | 0.546466i | −0.961948 | − | 0.273233i | \(-0.911907\pi\) | ||
0.961948 | − | 0.273233i | \(-0.0880929\pi\) | |||||||
\(350\) | 2.95899 | − | 30.4590i | 0.158165 | − | 1.62810i | ||||
\(351\) | − | 11.8240i | − | 0.631117i | ||||||
\(352\) | −13.6741 | + | 19.0361i | −0.728833 | + | 1.01463i | ||||
\(353\) | −7.07367 | + | 7.07367i | −0.376493 | + | 0.376493i | −0.869835 | − | 0.493342i | \(-0.835775\pi\) |
0.493342 | + | 0.869835i | \(0.335775\pi\) | |||||||
\(354\) | −26.4574 | + | 9.55753i | −1.40620 | + | 0.507977i | ||||
\(355\) | −5.05280 | + | 22.4114i | −0.268175 | + | 1.18947i | ||||
\(356\) | 1.92348 | − | 1.59825i | 0.101944 | − | 0.0847072i | ||||
\(357\) | 3.72462 | + | 3.72462i | 0.197128 | + | 0.197128i | ||||
\(358\) | 9.36104 | − | 19.9491i | 0.494746 | − | 1.05434i | ||||
\(359\) | 13.0121 | 0.686753 | 0.343377 | − | 0.939198i | \(-0.388429\pi\) | ||||
0.343377 | + | 0.939198i | \(0.388429\pi\) | |||||||
\(360\) | 0.928147 | + | 28.2718i | 0.0489176 | + | 1.49005i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 7.26388 | − | 15.4799i | 0.381781 | − | 0.813605i | ||||
\(363\) | −11.9211 | − | 11.9211i | −0.625695 | − | 0.625695i | ||||
\(364\) | −19.5549 | + | 16.2485i | −1.02496 | + | 0.851652i | ||||
\(365\) | 12.4332 | − | 7.85837i | 0.650786 | − | 0.411326i | ||||
\(366\) | −33.4541 | + | 12.0850i | −1.74868 | + | 0.631696i | ||||
\(367\) | −22.6401 | + | 22.6401i | −1.18180 | + | 1.18180i | −0.202528 | + | 0.979277i | \(0.564916\pi\) |
−0.979277 | + | 0.202528i | \(0.935084\pi\) | |||||||
\(368\) | −25.3446 | + | 17.3847i | −1.32118 | + | 0.906238i | ||||
\(369\) | − | 13.5149i | − | 0.703557i | ||||||
\(370\) | −14.5003 | + | 1.82065i | −0.753834 | + | 0.0946512i | ||||
\(371\) | 3.19423i | 0.165836i | ||||||||
\(372\) | −45.4701 | − | 4.19914i | −2.35751 | − | 0.217715i | ||||
\(373\) | 5.75270 | − | 5.75270i | 0.297864 | − | 0.297864i | −0.542313 | − | 0.840177i | \(-0.682451\pi\) |
0.840177 | + | 0.542313i | \(0.182451\pi\) | |||||||
\(374\) | −0.886384 | − | 2.45371i | −0.0458338 | − | 0.126878i | ||||
\(375\) | 3.66331 | + | 30.3422i | 0.189173 | + | 1.56687i | ||||
\(376\) | 7.93241 | − | 13.5127i | 0.409083 | − | 0.696863i | ||||
\(377\) | 0.220688 | + | 0.220688i | 0.0113660 | + | 0.0113660i | ||||
\(378\) | 22.3039 | + | 10.4660i | 1.14719 | + | 0.538314i | ||||
\(379\) | 1.86322 | 0.0957072 | 0.0478536 | − | 0.998854i | \(-0.484762\pi\) | ||||
0.0478536 | + | 0.998854i | \(0.484762\pi\) | |||||||
\(380\) | −2.03159 | − | 3.98405i | −0.104218 | − | 0.204377i | ||||
\(381\) | −16.5028 | −0.845465 | ||||||||
\(382\) | 15.3764 | + | 7.21533i | 0.786727 | + | 0.369169i | ||||
\(383\) | 22.4289 | + | 22.4289i | 1.14606 | + | 1.14606i | 0.987320 | + | 0.158745i | \(0.0507448\pi\) |
0.158745 | + | 0.987320i | \(0.449255\pi\) | |||||||
\(384\) | −20.2766 | + | 23.3527i | −1.03473 | + | 1.19171i | ||||
\(385\) | 21.4225 | + | 33.8940i | 1.09179 | + | 1.72740i | ||||
\(386\) | 11.5473 | + | 31.9656i | 0.587743 | + | 1.62700i | ||||
\(387\) | 31.9541 | − | 31.9541i | 1.62432 | − | 1.62432i | ||||
\(388\) | −0.748260 | + | 8.10248i | −0.0379872 | + | 0.411341i | ||||
\(389\) | − | 20.0422i | − | 1.01618i | −0.861305 | − | 0.508089i | \(-0.830352\pi\) | ||
0.861305 | − | 0.508089i | \(-0.169648\pi\) | |||||||
\(390\) | 15.5778 | − | 20.0514i | 0.788814 | − | 1.01534i | ||||
\(391\) | − | 3.42097i | − | 0.173006i | ||||||
\(392\) | −8.35502 | − | 32.1085i | −0.421992 | − | 1.62173i | ||||
\(393\) | 7.86003 | − | 7.86003i | 0.396486 | − | 0.396486i | ||||
\(394\) | 19.0663 | − | 6.88754i | 0.960544 | − | 0.346989i | ||||
\(395\) | 5.26580 | + | 1.18721i | 0.264951 | + | 0.0597349i | ||||
\(396\) | −23.6863 | − | 28.5063i | −1.19028 | − | 1.43249i | ||||
\(397\) | 2.30242 | + | 2.30242i | 0.115555 | + | 0.115555i | 0.762520 | − | 0.646965i | \(-0.223962\pi\) |
−0.646965 | + | 0.762520i | \(0.723962\pi\) | |||||||
\(398\) | 11.4025 | − | 24.2996i | 0.571556 | − | 1.21803i | ||||
\(399\) | −11.8306 | −0.592269 | ||||||||
\(400\) | −11.7453 | + | 16.1879i | −0.587264 | + | 0.809395i | ||||
\(401\) | 6.80995 | 0.340073 | 0.170036 | − | 0.985438i | \(-0.445612\pi\) | ||||
0.170036 | + | 0.985438i | \(0.445612\pi\) | |||||||
\(402\) | 11.1171 | − | 23.6914i | 0.554471 | − | 1.18162i | ||||
\(403\) | 17.3477 | + | 17.3477i | 0.864153 | + | 0.864153i | ||||
\(404\) | 4.21273 | + | 5.06998i | 0.209591 | + | 0.252241i | ||||
\(405\) | 5.26537 | + | 1.18711i | 0.261638 | + | 0.0589880i | ||||
\(406\) | −0.611633 | + | 0.220948i | −0.0303548 | + | 0.0109654i | ||||
\(407\) | 13.5397 | − | 13.5397i | 0.671139 | − | 0.671139i | ||||
\(408\) | −0.866906 | − | 3.33154i | −0.0429182 | − | 0.164936i | ||||
\(409\) | 17.2472i | 0.852821i | 0.904530 | + | 0.426410i | \(0.140222\pi\) | ||||
−0.904530 | + | 0.426410i | \(0.859778\pi\) | |||||||
\(410\) | 5.86238 | − | 7.54592i | 0.289522 | − | 0.372667i | ||||
\(411\) | − | 16.1610i | − | 0.797163i | ||||||
\(412\) | 2.17529 | − | 23.5549i | 0.107169 | − | 1.16047i | ||||
\(413\) | −22.2683 | + | 22.2683i | −1.09575 | + | 1.09575i | ||||
\(414\) | −16.5118 | − | 45.7083i | −0.811510 | − | 2.24644i | ||||
\(415\) | −14.8822 | − | 23.5461i | −0.730537 | − | 1.15583i | ||||
\(416\) | 16.3972 | − | 2.68789i | 0.803940 | − | 0.131784i | ||||
\(417\) | 39.0913 | + | 39.0913i | 1.91431 | + | 1.91431i | ||||
\(418\) | 5.30459 | + | 2.48916i | 0.259456 | + | 0.121749i | ||||
\(419\) | −6.11638 | −0.298805 | −0.149402 | − | 0.988776i | \(-0.547735\pi\) | ||||
−0.149402 | + | 0.988776i | \(0.547735\pi\) | |||||||
\(420\) | 24.0348 | + | 47.1335i | 1.17278 | + | 2.29988i | ||||
\(421\) | 3.01067 | 0.146731 | 0.0733655 | − | 0.997305i | \(-0.476626\pi\) | ||||
0.0733655 | + | 0.997305i | \(0.476626\pi\) | |||||||
\(422\) | 1.37045 | + | 0.643080i | 0.0667126 | + | 0.0313046i | ||||
\(423\) | 17.5201 | + | 17.5201i | 0.851856 | + | 0.851856i | ||||
\(424\) | 1.05683 | − | 1.80029i | 0.0513243 | − | 0.0874298i | ||||
\(425\) | −0.746392 | − | 2.09733i | −0.0362053 | − | 0.101736i | ||||
\(426\) | −13.4947 | − | 37.3565i | −0.653822 | − | 1.80993i | ||||
\(427\) | −28.1572 | + | 28.1572i | −1.36262 | + | 1.36262i | ||||
\(428\) | −2.49942 | − | 0.230820i | −0.120814 | − | 0.0111571i | ||||
\(429\) | 33.2690i | 1.60624i | ||||||||
\(430\) | 31.7021 | − | 3.98050i | 1.52881 | − | 0.191957i | ||||
\(431\) | 39.0994i | 1.88335i | 0.336518 | + | 0.941677i | \(0.390751\pi\) | ||||
−0.336518 | + | 0.941677i | \(0.609249\pi\) | |||||||
\(432\) | −9.10789 | − | 13.2781i | −0.438203 | − | 0.638844i | ||||
\(433\) | 4.66253 | − | 4.66253i | 0.224067 | − | 0.224067i | −0.586142 | − | 0.810209i | \(-0.699354\pi\) |
0.810209 | + | 0.586142i | \(0.199354\pi\) | |||||||
\(434\) | −48.0790 | + | 17.3682i | −2.30787 | + | 0.833699i | ||||
\(435\) | 0.549005 | − | 0.346996i | 0.0263228 | − | 0.0166372i | ||||
\(436\) | −2.09895 | + | 1.74405i | −0.100521 | + | 0.0835248i | ||||
\(437\) | 5.43304 | + | 5.43304i | 0.259898 | + | 0.259898i | ||||
\(438\) | −10.8024 | + | 23.0207i | −0.516158 | + | 1.09997i | ||||
\(439\) | −31.4437 | −1.50072 | −0.750362 | − | 0.661027i | \(-0.770121\pi\) | ||||
−0.750362 | + | 0.661027i | \(0.770121\pi\) | |||||||
\(440\) | −0.859827 | − | 26.1907i | −0.0409906 | − | 1.24859i | ||||
\(441\) | 52.4637 | 2.49827 | ||||||||
\(442\) | −0.785682 | + | 1.67435i | −0.0373711 | + | 0.0796407i | ||||
\(443\) | 6.74152 | + | 6.74152i | 0.320300 | + | 0.320300i | 0.848882 | − | 0.528582i | \(-0.177276\pi\) |
−0.528582 | + | 0.848882i | \(0.677276\pi\) | |||||||
\(444\) | 19.4330 | − | 16.1472i | 0.922251 | − | 0.766313i | ||||
\(445\) | −0.614946 | + | 2.72756i | −0.0291512 | + | 0.129299i | ||||
\(446\) | 20.1760 | − | 7.28841i | 0.955360 | − | 0.345116i | ||||
\(447\) | −11.9645 | + | 11.9645i | −0.565900 | + | 0.565900i | ||||
\(448\) | −9.44382 | + | 33.3098i | −0.446179 | + | 1.57374i | ||||
\(449\) | 2.27550i | 0.107387i | 0.998557 | + | 0.0536937i | \(0.0170995\pi\) | ||||
−0.998557 | + | 0.0536937i | \(0.982901\pi\) | |||||||
\(450\) | −20.0958 | − | 24.4203i | −0.947323 | − | 1.15119i | ||||
\(451\) | 12.5201i | 0.589547i | ||||||||
\(452\) | 3.96023 | + | 0.365725i | 0.186273 | + | 0.0172023i | ||||
\(453\) | 1.64843 | − | 1.64843i | 0.0774502 | − | 0.0774502i | ||||
\(454\) | −5.54758 | − | 15.3570i | −0.260361 | − | 0.720738i | ||||
\(455\) | 6.25180 | − | 27.7295i | 0.293089 | − | 1.29998i | ||||
\(456\) | 6.66779 | + | 3.91422i | 0.312248 | + | 0.183300i | ||||
\(457\) | −21.1563 | − | 21.1563i | −0.989651 | − | 0.989651i | 0.0102955 | − | 0.999947i | \(-0.496723\pi\) |
−0.999947 | + | 0.0102955i | \(0.996723\pi\) | |||||||
\(458\) | 3.59463 | + | 1.68677i | 0.167966 | + | 0.0788174i | ||||
\(459\) | 1.79226 | 0.0836556 | ||||||||
\(460\) | 10.6078 | − | 32.6832i | 0.494591 | − | 1.52386i | ||||
\(461\) | −38.9174 | −1.81256 | −0.906282 | − | 0.422673i | \(-0.861092\pi\) | ||||
−0.906282 | + | 0.422673i | \(0.861092\pi\) | |||||||
\(462\) | −62.7563 | − | 29.4481i | −2.91969 | − | 1.37005i | ||||
\(463\) | −1.04918 | − | 1.04918i | −0.0487597 | − | 0.0487597i | 0.682307 | − | 0.731066i | \(-0.260977\pi\) |
−0.731066 | + | 0.682307i | \(0.760977\pi\) | |||||||
\(464\) | 0.417823 | + | 0.0778353i | 0.0193969 | + | 0.00361341i | ||||
\(465\) | 43.1560 | − | 27.2765i | 2.00131 | − | 1.26492i | ||||
\(466\) | −9.30170 | − | 25.7492i | −0.430893 | − | 1.19281i | ||||
\(467\) | 0.388425 | − | 0.388425i | 0.0179742 | − | 0.0179742i | −0.698063 | − | 0.716037i | \(-0.745954\pi\) |
0.716037 | + | 0.698063i | \(0.245954\pi\) | |||||||
\(468\) | −2.41619 | + | 26.1635i | −0.111688 | + | 1.20941i | ||||
\(469\) | − | 29.2972i | − | 1.35282i | ||||||
\(470\) | 2.18247 | + | 17.3819i | 0.100670 | + | 0.801768i | ||||
\(471\) | − | 59.1994i | − | 2.72776i | ||||||
\(472\) | 19.9182 | − | 5.18295i | 0.916810 | − | 0.238565i | ||||
\(473\) | −29.6020 | + | 29.6020i | −1.36110 | + | 1.36110i | ||||
\(474\) | −8.77730 | + | 3.17073i | −0.403155 | + | 0.145637i | ||||
\(475\) | 4.51628 | + | 2.14551i | 0.207221 | + | 0.0984426i | ||||
\(476\) | −2.46293 | − | 2.96411i | −0.112888 | − | 0.135860i | ||||
\(477\) | 2.33419 | + | 2.33419i | 0.106875 | + | 0.106875i | ||||
\(478\) | 13.4446 | − | 28.6516i | 0.614944 | − | 1.31049i | ||||
\(479\) | 6.97897 | 0.318877 | 0.159439 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159439 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(480\) | 2.04824 | − | 34.5169i | 0.0934889 | − | 1.57547i | ||||
\(481\) | −13.5746 | −0.618948 | ||||||||
\(482\) | 4.95020 | − | 10.5493i | 0.225475 | − | 0.480505i | ||||
\(483\) | −64.2759 | − | 64.2759i | −2.92465 | − | 2.92465i | ||||
\(484\) | 7.88290 | + | 9.48700i | 0.358314 | + | 0.431227i | ||||
\(485\) | −4.86051 | − | 7.69013i | −0.220704 | − | 0.349191i | ||||
\(486\) | −24.8390 | + | 8.97291i | −1.12672 | + | 0.407019i | ||||
\(487\) | 0.386963 | − | 0.386963i | 0.0175350 | − | 0.0175350i | −0.698285 | − | 0.715820i | \(-0.746053\pi\) |
0.715820 | + | 0.698285i | \(0.246053\pi\) | |||||||
\(488\) | 25.1856 | − | 6.55360i | 1.14010 | − | 0.296667i | ||||
\(489\) | − | 29.4565i | − | 1.33207i | ||||||
\(490\) | 29.2927 | + | 22.7573i | 1.32331 | + | 1.02807i | ||||
\(491\) | − | 16.1542i | − | 0.729028i | −0.931198 | − | 0.364514i | \(-0.881235\pi\) | ||
0.931198 | − | 0.364514i | \(-0.118765\pi\) | |||||||
\(492\) | −1.51919 | + | 16.4504i | −0.0684902 | + | 0.741641i | ||||
\(493\) | −0.0334516 | + | 0.0334516i | −0.00150658 | + | 0.00150658i | ||||
\(494\) | −1.41134 | − | 3.90691i | −0.0634993 | − | 0.175780i | ||||
\(495\) | 40.4228 | + | 9.11359i | 1.81687 | + | 0.409625i | ||||
\(496\) | 32.8441 | + | 6.11845i | 1.47474 | + | 0.274726i | ||||
\(497\) | −31.4417 | − | 31.4417i | −1.41035 | − | 1.41035i | ||||
\(498\) | 43.5966 | + | 20.4575i | 1.95361 | + | 0.916724i | ||||
\(499\) | 33.8383 | 1.51481 | 0.757405 | − | 0.652945i | \(-0.226467\pi\) | ||||
0.757405 | + | 0.652945i | \(0.226467\pi\) | |||||||
\(500\) | −0.627431 | − | 22.3519i | −0.0280596 | − | 0.999606i | ||||
\(501\) | 38.1570 | 1.70473 | ||||||||
\(502\) | 2.31173 | + | 1.08477i | 0.103177 | + | 0.0484156i | ||||
\(503\) | −7.57074 | − | 7.57074i | −0.337563 | − | 0.337563i | 0.517887 | − | 0.855449i | \(-0.326719\pi\) |
−0.855449 | + | 0.517887i | \(0.826719\pi\) | |||||||
\(504\) | −47.2143 | − | 27.7165i | −2.10309 | − | 1.23459i | ||||
\(505\) | −7.18939 | − | 1.62090i | −0.319924 | − | 0.0721289i | ||||
\(506\) | 15.2964 | + | 42.3438i | 0.680007 | + | 1.88241i | ||||
\(507\) | −8.45098 | + | 8.45098i | −0.375321 | + | 0.375321i | ||||
\(508\) | 12.0229 | + | 1.11031i | 0.533430 | + | 0.0492620i | ||||
\(509\) | 24.3847i | 1.08083i | 0.841398 | + | 0.540416i | \(0.181733\pi\) | ||||
−0.841398 | + | 0.540416i | \(0.818267\pi\) | |||||||
\(510\) | 3.03937 | + | 2.36127i | 0.134586 | + | 0.104559i | ||||
\(511\) | 28.4678i | 1.25934i | ||||||||
\(512\) | 16.3434 | − | 15.6491i | 0.722282 | − | 0.691598i | ||||
\(513\) | −2.84639 | + | 2.84639i | −0.125671 | + | 0.125671i | ||||
\(514\) | 10.3230 | − | 3.72909i | 0.455326 | − | 0.164483i | ||||
\(515\) | 14.1301 | + | 22.3562i | 0.622647 | + | 0.985130i | ||||
\(516\) | −42.4866 | + | 35.3028i | −1.87037 | + | 1.55412i | ||||
\(517\) | −16.2305 | − | 16.2305i | −0.713814 | − | 0.713814i | ||||
\(518\) | 12.0156 | − | 25.6062i | 0.527935 | − | 1.12507i | ||||
\(519\) | −46.1126 | −2.02412 | ||||||||
\(520\) | −12.6981 | + | 13.5601i | −0.556847 | + | 0.594650i | ||||
\(521\) | 24.4994 | 1.07334 | 0.536670 | − | 0.843792i | \(-0.319682\pi\) | ||||
0.536670 | + | 0.843792i | \(0.319682\pi\) | |||||||
\(522\) | −0.285495 | + | 0.608412i | −0.0124958 | + | 0.0266295i | ||||
\(523\) | −4.42412 | − | 4.42412i | −0.193453 | − | 0.193453i | 0.603733 | − | 0.797186i | \(-0.293679\pi\) |
−0.797186 | + | 0.603733i | \(0.793679\pi\) | |||||||
\(524\) | −6.25513 | + | 5.19749i | −0.273257 | + | 0.227053i | ||||
\(525\) | −53.4301 | − | 25.3825i | −2.33188 | − | 1.10778i | ||||
\(526\) | −18.9926 | + | 6.86092i | −0.828116 | + | 0.299150i | ||||
\(527\) | −2.62955 | + | 2.62955i | −0.114545 | + | 0.114545i | ||||
\(528\) | 25.6268 | + | 37.3606i | 1.11526 | + | 1.62591i | ||||
\(529\) | 36.0359i | 1.56678i | ||||||||
\(530\) | 0.290770 | + | 2.31579i | 0.0126302 | + | 0.100591i | ||||
\(531\) | 32.5453i | 1.41235i | ||||||||
\(532\) | 8.61899 | + | 0.795960i | 0.373680 | + | 0.0345092i | ||||
\(533\) | 6.27616 | − | 6.27616i | 0.271851 | − | 0.271851i | ||||
\(534\) | −1.64237 | − | 4.54644i | −0.0710721 | − | 0.196744i | ||||
\(535\) | 2.37222 | − | 1.49935i | 0.102560 | − | 0.0648224i | ||||
\(536\) | −9.69318 | + | 16.5121i | −0.418682 | + | 0.713214i | ||||
\(537\) | −30.1191 | − | 30.1191i | −1.29974 | − | 1.29974i | ||||
\(538\) | 0.560893 | + | 0.263197i | 0.0241818 | + | 0.0113472i | ||||
\(539\) | −48.6019 | −2.09343 | ||||||||
\(540\) | 17.1229 | + | 5.55746i | 0.736851 | + | 0.239155i | ||||
\(541\) | 41.5657 | 1.78705 | 0.893525 | − | 0.449013i | \(-0.148224\pi\) | ||||
0.893525 | + | 0.449013i | \(0.148224\pi\) | |||||||
\(542\) | 10.8750 | + | 5.10307i | 0.467123 | + | 0.219195i | ||||
\(543\) | −23.3715 | − | 23.3715i | −1.00297 | − | 1.00297i | ||||
\(544\) | 0.407426 | + | 2.48547i | 0.0174683 | + | 0.106564i | ||||
\(545\) | 0.671043 | − | 2.97637i | 0.0287443 | − | 0.127494i | ||||
\(546\) | 16.6970 | + | 46.2210i | 0.714564 | + | 1.97807i | ||||
\(547\) | −10.6371 | + | 10.6371i | −0.454809 | + | 0.454809i | −0.896947 | − | 0.442138i | \(-0.854220\pi\) |
0.442138 | + | 0.896947i | \(0.354220\pi\) | |||||||
\(548\) | −1.08731 | + | 11.7739i | −0.0464476 | + | 0.502955i | ||||
\(549\) | 41.1520i | 1.75633i | ||||||||
\(550\) | 18.6165 | + | 22.6228i | 0.793811 | + | 0.964639i | ||||
\(551\) | − | 0.106253i | − | 0.00452652i | ||||||
\(552\) | 14.9602 | + | 57.4925i | 0.636750 | + | 2.44704i | ||||
\(553\) | −7.38756 | + | 7.38756i | −0.314151 | + | 0.314151i | ||||
\(554\) | 18.8347 | − | 6.80390i | 0.800211 | − | 0.289070i | ||||
\(555\) | −6.21283 | + | 27.5567i | −0.263720 | + | 1.16972i | ||||
\(556\) | −25.8493 | − | 31.1095i | −1.09626 | − | 1.31933i | ||||
\(557\) | −24.4145 | − | 24.4145i | −1.03447 | − | 1.03447i | −0.999384 | − | 0.0350905i | \(-0.988828\pi\) |
−0.0350905 | − | 0.999384i | \(-0.511172\pi\) | |||||||
\(558\) | −22.4421 | + | 47.8258i | −0.950049 | + | 2.02463i | ||||
\(559\) | 29.6782 | 1.25525 | ||||||||
\(560\) | −14.3391 | − | 35.9555i | −0.605938 | − | 1.51940i | ||||
\(561\) | −5.04287 | −0.212910 | ||||||||
\(562\) | 4.44438 | − | 9.47132i | 0.187475 | − | 0.399524i | ||||
\(563\) | 22.7286 | + | 22.7286i | 0.957898 | + | 0.957898i | 0.999149 | − | 0.0412505i | \(-0.0131342\pi\) |
−0.0412505 | + | 0.999149i | \(0.513134\pi\) | |||||||
\(564\) | −19.3561 | − | 23.2950i | −0.815041 | − | 0.980894i | ||||
\(565\) | −3.75868 | + | 2.37566i | −0.158129 | + | 0.0999446i | ||||
\(566\) | −27.3813 | + | 9.89130i | −1.15092 | + | 0.415762i | ||||
\(567\) | −7.38695 | + | 7.38695i | −0.310223 | + | 0.310223i | ||||
\(568\) | 7.31806 | + | 28.1235i | 0.307059 | + | 1.18003i | ||||
\(569\) | 23.5108i | 0.985623i | 0.870136 | + | 0.492811i | \(0.164031\pi\) | ||||
−0.870136 | + | 0.492811i | \(0.835969\pi\) | |||||||
\(570\) | −8.57706 | + | 1.07693i | −0.359253 | + | 0.0451077i | ||||
\(571\) | 11.2223i | 0.469640i | 0.972039 | + | 0.234820i | \(0.0754501\pi\) | ||||
−0.972039 | + | 0.234820i | \(0.924550\pi\) | |||||||
\(572\) | 2.23834 | − | 24.2376i | 0.0935895 | − | 1.01343i | ||||
\(573\) | 23.2153 | − | 23.2153i | 0.969834 | − | 0.969834i | ||||
\(574\) | 6.28354 | + | 17.3943i | 0.262270 | + | 0.726023i | ||||
\(575\) | 12.8805 | + | 36.1938i | 0.537155 | + | 1.50938i | ||||
\(576\) | 17.4402 | + | 31.2424i | 0.726673 | + | 1.30177i | ||||
\(577\) | 11.7453 | + | 11.7453i | 0.488965 | + | 0.488965i | 0.907979 | − | 0.419015i | \(-0.137624\pi\) |
−0.419015 | + | 0.907979i | \(0.637624\pi\) | |||||||
\(578\) | 21.5108 | + | 10.0938i | 0.894730 | + | 0.419848i | ||||
\(579\) | 65.6957 | 2.73022 | ||||||||
\(580\) | −0.423316 | + | 0.215862i | −0.0175772 | + | 0.00896318i | ||||
\(581\) | 53.9122 | 2.23665 | ||||||||
\(582\) | 14.2386 | + | 6.68142i | 0.590210 | + | 0.276954i | ||||
\(583\) | −2.16238 | − | 2.16238i | −0.0895565 | − | 0.0895565i | ||||
\(584\) | 9.41876 | − | 16.0446i | 0.389751 | − | 0.663932i | ||||
\(585\) | −15.6949 | − | 24.8320i | −0.648906 | − | 1.02668i | ||||
\(586\) | −0.784497 | − | 2.17166i | −0.0324073 | − | 0.0897106i | ||||
\(587\) | 22.7792 | − | 22.7792i | 0.940200 | − | 0.940200i | −0.0581101 | − | 0.998310i | \(-0.518507\pi\) |
0.998310 | + | 0.0581101i | \(0.0185074\pi\) | |||||||
\(588\) | −63.8591 | − | 5.89736i | −2.63351 | − | 0.243203i | ||||
\(589\) | − | 8.35227i | − | 0.344149i | ||||||
\(590\) | −14.1173 | + | 18.1714i | −0.581198 | + | 0.748105i | ||||
\(591\) | − | 39.1850i | − | 1.61186i | ||||||
\(592\) | −15.2441 | + | 10.4564i | −0.626527 | + | 0.429754i | ||||
\(593\) | 2.63023 | − | 2.63023i | 0.108010 | − | 0.108010i | −0.651036 | − | 0.759047i | \(-0.725665\pi\) |
0.759047 | + | 0.651036i | \(0.225665\pi\) | |||||||
\(594\) | −22.1841 | + | 8.01383i | −0.910224 | + | 0.328811i | ||||
\(595\) | 4.20321 | + | 0.947640i | 0.172315 | + | 0.0388494i | ||||
\(596\) | 9.52152 | − | 7.91158i | 0.390017 | − | 0.324071i | ||||
\(597\) | −36.6876 | − | 36.6876i | −1.50152 | − | 1.50152i | ||||
\(598\) | 13.5585 | − | 28.8943i | 0.554450 | − | 1.18158i | ||||
\(599\) | −36.8676 | −1.50637 | −0.753186 | − | 0.657808i | \(-0.771484\pi\) | ||||
−0.753186 | + | 0.657808i | \(0.771484\pi\) | |||||||
\(600\) | 21.7156 | + | 31.9835i | 0.886536 | + | 1.30572i | ||||
\(601\) | −21.6992 | −0.885130 | −0.442565 | − | 0.896736i | \(-0.645931\pi\) | ||||
−0.442565 | + | 0.896736i | \(0.645931\pi\) | |||||||
\(602\) | −26.2698 | + | 55.9829i | −1.07068 | + | 2.28169i | ||||
\(603\) | −21.4091 | − | 21.4091i | −0.871844 | − | 0.871844i | ||||
\(604\) | −1.31185 | + | 1.09004i | −0.0533784 | + | 0.0443530i | ||||
\(605\) | −13.4529 | − | 3.03304i | −0.546937 | − | 0.123310i | ||||
\(606\) | 11.9836 | − | 4.32900i | 0.486802 | − | 0.175854i | ||||
\(607\) | −22.4916 | + | 22.4916i | −0.912904 | + | 0.912904i | −0.996500 | − | 0.0835953i | \(-0.973360\pi\) |
0.0835953 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(608\) | −4.59437 | − | 3.30026i | −0.186326 | − | 0.133843i | ||||
\(609\) | 1.25703i | 0.0509374i | ||||||||
\(610\) | −17.8506 | + | 22.9769i | −0.722750 | + | 0.930307i | ||||
\(611\) | 16.2723i | 0.658305i | ||||||||
\(612\) | −3.96583 | − | 0.366243i | −0.160309 | − | 0.0148045i | ||||
\(613\) | −20.2852 | + | 20.2852i | −0.819313 | + | 0.819313i | −0.986008 | − | 0.166695i | \(-0.946690\pi\) |
0.166695 | + | 0.986008i | \(0.446690\pi\) | |||||||
\(614\) | 11.6664 | + | 32.2951i | 0.470816 | + | 1.30332i | ||||
\(615\) | −9.86824 | − | 15.6132i | −0.397926 | − | 0.629585i | ||||
\(616\) | 43.7389 | + | 25.6763i | 1.76229 | + | 1.03453i | ||||
\(617\) | −28.8210 | − | 28.8210i | −1.16029 | − | 1.16029i | −0.984412 | − | 0.175876i | \(-0.943724\pi\) |
−0.175876 | − | 0.984412i | \(-0.556276\pi\) | |||||||
\(618\) | −41.3934 | − | 19.4237i | −1.66509 | − | 0.781336i | ||||
\(619\) | 10.0305 | 0.403159 | 0.201580 | − | 0.979472i | \(-0.435393\pi\) | ||||
0.201580 | + | 0.979472i | \(0.435393\pi\) | |||||||
\(620\) | −33.2759 | + | 16.9684i | −1.33639 | + | 0.681467i | ||||
\(621\) | −30.9291 | −1.24114 | ||||||||
\(622\) | −10.7078 | − | 5.02458i | −0.429343 | − | 0.201467i | ||||
\(623\) | −3.82658 | − | 3.82658i | −0.153309 | − | 0.153309i | ||||
\(624\) | 5.88200 | − | 31.5748i | 0.235468 | − | 1.26400i | ||||
\(625\) | 15.7936 | + | 19.3794i | 0.631744 | + | 0.775177i | ||||
\(626\) | −6.08986 | − | 16.8581i | −0.243400 | − | 0.673785i | ||||
\(627\) | 8.00887 | − | 8.00887i | 0.319843 | − | 0.319843i | ||||
\(628\) | −3.98293 | + | 43.1289i | −0.158936 | + | 1.72103i | ||||
\(629\) | − | 2.05762i | − | 0.0820427i | ||||||
\(630\) | 60.7338 | − | 7.62572i | 2.41969 | − | 0.303816i | ||||
\(631\) | − | 45.8155i | − | 1.82389i | −0.410318 | − | 0.911943i | \(-0.634582\pi\) | ||
0.410318 | − | 0.911943i | \(-0.365418\pi\) | |||||||
\(632\) | 6.60791 | − | 1.71946i | 0.262848 | − | 0.0683963i | ||||
\(633\) | 2.06911 | − | 2.06911i | 0.0822397 | − | 0.0822397i | ||||
\(634\) | −0.298342 | + | 0.107774i | −0.0118487 | + | 0.00428024i | ||||
\(635\) | −11.4110 | + | 7.21228i | −0.452833 | + | 0.286211i | ||||
\(636\) | −2.57881 | − | 3.10358i | −0.102257 | − | 0.123065i | ||||
\(637\) | 24.3636 | + | 24.3636i | 0.965319 | + | 0.965319i | ||||
\(638\) | 0.264480 | − | 0.563627i | 0.0104709 | − | 0.0223142i | ||||
\(639\) | −45.9523 | −1.81785 | ||||||||
\(640\) | −3.81451 | + | 25.0090i | −0.150782 | + | 0.988567i | ||||
\(641\) | 29.3805 | 1.16046 | 0.580231 | − | 0.814452i | \(-0.302962\pi\) | ||||
0.580231 | + | 0.814452i | \(0.302962\pi\) | |||||||
\(642\) | −2.06105 | + | 4.39226i | −0.0813433 | + | 0.173349i | ||||
\(643\) | 33.1165 | + | 33.1165i | 1.30599 | + | 1.30599i | 0.924286 | + | 0.381700i | \(0.124661\pi\) |
0.381700 | + | 0.924286i | \(0.375339\pi\) | |||||||
\(644\) | 42.5028 | + | 51.1518i | 1.67485 | + | 2.01566i | ||||
\(645\) | 13.5831 | − | 60.2473i | 0.534836 | − | 2.37224i | ||||
\(646\) | 0.592205 | − | 0.213930i | 0.0233000 | − | 0.00841695i | ||||
\(647\) | −7.26261 | + | 7.26261i | −0.285523 | + | 0.285523i | −0.835307 | − | 0.549784i | \(-0.814710\pi\) |
0.549784 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(648\) | 6.60737 | − | 1.71931i | 0.259562 | − | 0.0675411i | ||||
\(649\) | − | 30.1497i | − | 1.18348i | ||||||
\(650\) | 2.00829 | − | 20.6728i | 0.0787716 | − | 0.810853i | ||||
\(651\) | 98.8120i | 3.87275i | ||||||||
\(652\) | −1.98183 | + | 21.4601i | −0.0776146 | + | 0.840444i | ||||
\(653\) | 26.0447 | − | 26.0447i | 1.01921 | − | 1.01921i | 0.0193970 | − | 0.999812i | \(-0.493825\pi\) |
0.999812 | − | 0.0193970i | \(-0.00617465\pi\) | |||||||
\(654\) | 1.79219 | + | 4.96117i | 0.0700800 | + | 0.193997i | ||||
\(655\) | 1.99979 | − | 8.86998i | 0.0781384 | − | 0.346579i | ||||
\(656\) | 2.21356 | − | 11.8825i | 0.0864252 | − | 0.463933i | ||||
\(657\) | 20.8029 | + | 20.8029i | 0.811600 | + | 0.811600i | ||||
\(658\) | −30.6949 | − | 14.4034i | −1.19661 | − | 0.561505i | ||||
\(659\) | 23.0974 | 0.899746 | 0.449873 | − | 0.893093i | \(-0.351469\pi\) | ||||
0.449873 | + | 0.893093i | \(0.351469\pi\) | |||||||
\(660\) | −48.1785 | − | 15.6370i | −1.87534 | − | 0.608669i | ||||
\(661\) | 6.43437 | 0.250268 | 0.125134 | − | 0.992140i | \(-0.460064\pi\) | ||||
0.125134 | + | 0.992140i | \(0.460064\pi\) | |||||||
\(662\) | 39.2889 | + | 18.4362i | 1.52701 | + | 0.716542i | ||||
\(663\) | 2.52793 | + | 2.52793i | 0.0981766 | + | 0.0981766i | ||||
\(664\) | −30.3853 | − | 17.8372i | −1.17918 | − | 0.692219i | ||||
\(665\) | −8.18035 | + | 5.17035i | −0.317220 | + | 0.200497i | ||||
\(666\) | −9.93137 | − | 27.4923i | −0.384833 | − | 1.06530i | ||||
\(667\) | 0.577275 | − | 0.577275i | 0.0223522 | − | 0.0223522i | ||||
\(668\) | −27.7988 | − | 2.56720i | −1.07557 | − | 0.0993281i | ||||
\(669\) | − | 41.4657i | − | 1.60316i | ||||||
\(670\) | −2.66692 | − | 21.2402i | −0.103032 | − | 0.820581i | ||||
\(671\) | − | 38.1229i | − | 1.47172i | ||||||
\(672\) | 54.3540 | + | 39.0439i | 2.09675 | + | 1.50615i | ||||
\(673\) | −19.4454 | + | 19.4454i | −0.749564 | + | 0.749564i | −0.974397 | − | 0.224833i | \(-0.927816\pi\) |
0.224833 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(674\) | −24.6380 | + | 8.90028i | −0.949020 | + | 0.342826i | ||||
\(675\) | −18.9621 | + | 6.74816i | −0.729850 | + | 0.259737i | ||||
\(676\) | 6.72542 | − | 5.58826i | 0.258670 | − | 0.214933i | ||||
\(677\) | 32.4800 | + | 32.4800i | 1.24831 | + | 1.24831i | 0.956467 | + | 0.291839i | \(0.0942671\pi\) |
0.291839 | + | 0.956467i | \(0.405733\pi\) | |||||||
\(678\) | 3.26566 | − | 6.95937i | 0.125417 | − | 0.267273i | ||||
\(679\) | 17.6077 | 0.675721 | ||||||||
\(680\) | −2.05542 | − | 1.92476i | −0.0788219 | − | 0.0738111i | ||||
\(681\) | −31.5617 | −1.20945 | ||||||||
\(682\) | 20.7901 | − | 44.3054i | 0.796096 | − | 1.69654i | ||||
\(683\) | −15.3564 | − | 15.3564i | −0.587598 | − | 0.587598i | 0.349383 | − | 0.936980i | \(-0.386391\pi\) |
−0.936980 | + | 0.349383i | \(0.886391\pi\) | |||||||
\(684\) | 6.88001 | − | 5.71671i | 0.263064 | − | 0.218584i | ||||
\(685\) | −7.06289 | − | 11.1747i | −0.269859 | − | 0.426962i | ||||
\(686\) | −27.2284 | + | 9.83606i | −1.03959 | + | 0.375542i | ||||
\(687\) | 5.42717 | − | 5.42717i | 0.207059 | − | 0.207059i | ||||
\(688\) | 33.3282 | − | 22.8608i | 1.27062 | − | 0.871561i | ||||
\(689\) | 2.16795i | 0.0825922i | ||||||||
\(690\) | −52.4505 | − | 40.7485i | −1.99676 | − | 1.55127i | ||||
\(691\) | − | 42.2379i | − | 1.60681i | −0.595436 | − | 0.803403i | \(-0.703021\pi\) | ||
0.595436 | − | 0.803403i | \(-0.296979\pi\) | |||||||
\(692\) | 33.5947 | + | 3.10246i | 1.27708 | + | 0.117938i | ||||
\(693\) | −56.7105 | + | 56.7105i | −2.15425 | + | 2.15425i | ||||
\(694\) | 1.11930 | + | 3.09846i | 0.0424879 | + | 0.117616i | ||||
\(695\) | 44.1142 | + | 9.94583i | 1.67335 | + | 0.377267i | ||||
\(696\) | 0.415897 | − | 0.708470i | 0.0157645 | − | 0.0268545i | ||||
\(697\) | 0.951332 | + | 0.951332i | 0.0360343 | + | 0.0360343i | ||||
\(698\) | 13.0700 | + | 6.13306i | 0.494708 | + | 0.232140i | ||||
\(699\) | −52.9198 | −2.00161 | ||||||||
\(700\) | 37.2180 | + | 22.0869i | 1.40671 | + | 0.834805i | ||||
\(701\) | −2.93471 | −0.110843 | −0.0554213 | − | 0.998463i | \(-0.517650\pi\) | ||||
−0.0554213 | + | 0.998463i | \(0.517650\pi\) | |||||||
\(702\) | 15.1378 | + | 7.10338i | 0.571341 | + | 0.268100i | ||||
\(703\) | 3.26782 | + | 3.26782i | 0.123248 | + | 0.123248i | ||||
\(704\) | −16.1564 | − | 28.9427i | −0.608918 | − | 1.09082i | ||||
\(705\) | 33.0330 | + | 7.44750i | 1.24409 | + | 0.280489i | ||||
\(706\) | −4.80661 | − | 13.3058i | −0.180899 | − | 0.500769i | ||||
\(707\) | 10.0862 | − | 10.0862i | 0.379332 | − | 0.379332i | ||||
\(708\) | 3.65837 | − | 39.6144i | 0.137490 | − | 1.48880i | ||||
\(709\) | 25.4554i | 0.955996i | 0.878361 | + | 0.477998i | \(0.158637\pi\) | ||||
−0.878361 | + | 0.477998i | \(0.841363\pi\) | |||||||
\(710\) | −25.6571 | − | 19.9328i | −0.962893 | − | 0.748066i | ||||
\(711\) | 10.7970i | 0.404919i | ||||||||
\(712\) | 0.890638 | + | 3.42274i | 0.0333781 | + | 0.128273i | ||||
\(713\) | 45.3782 | − | 45.3782i | 1.69943 | − | 1.69943i | ||||
\(714\) | −7.00612 | + | 2.53091i | −0.262197 | + | 0.0947168i | ||||
\(715\) | 14.5397 | + | 23.0041i | 0.543752 | + | 0.860306i | ||||
\(716\) | 19.9165 | + | 23.9693i | 0.744313 | + | 0.895774i | ||||
\(717\) | −43.2581 | − | 43.2581i | −1.61550 | − | 1.61550i | ||||
\(718\) | −7.81717 | + | 16.6590i | −0.291734 | + | 0.621708i | ||||
\(719\) | 6.31560 | 0.235532 | 0.117766 | − | 0.993041i | \(-0.462427\pi\) | ||||
0.117766 | + | 0.993041i | \(0.462427\pi\) | |||||||
\(720\) | −36.7530 | − | 15.7963i | −1.36970 | − | 0.588693i | ||||
\(721\) | −51.1877 | −1.90633 | ||||||||
\(722\) | −0.600761 | + | 1.28027i | −0.0223580 | + | 0.0476466i | ||||
\(723\) | −15.9272 | − | 15.9272i | −0.592341 | − | 0.592341i | ||||
\(724\) | 15.4546 | + | 18.5994i | 0.574364 | + | 0.691242i | ||||
\(725\) | 0.227966 | − | 0.479867i | 0.00846644 | − | 0.0178218i | ||||
\(726\) | 22.4239 | − | 8.10047i | 0.832230 | − | 0.300637i | ||||
\(727\) | −22.0719 | + | 22.0719i | −0.818600 | + | 0.818600i | −0.985905 | − | 0.167305i | \(-0.946493\pi\) |
0.167305 | + | 0.985905i | \(0.446493\pi\) | |||||||
\(728\) | −9.05459 | − | 34.7970i | −0.335586 | − | 1.28966i | ||||
\(729\) | 43.8077i | 1.62251i | ||||||||
\(730\) | 2.59141 | + | 20.6389i | 0.0959125 | + | 0.763880i | ||||
\(731\) | 4.49859i | 0.166386i | ||||||||
\(732\) | 4.62583 | − | 50.0905i | 0.170976 | − | 1.85140i | ||||
\(733\) | 24.9523 | − | 24.9523i | 0.921635 | − | 0.921635i | −0.0755102 | − | 0.997145i | \(-0.524059\pi\) |
0.997145 | + | 0.0755102i | \(0.0240585\pi\) | |||||||
\(734\) | −15.3841 | − | 42.5867i | −0.567838 | − | 1.57190i | ||||
\(735\) | 60.6092 | − | 38.3078i | 2.23560 | − | 1.41300i | ||||
\(736\) | −7.03097 | − | 42.8919i | −0.259165 | − | 1.58102i | ||||
\(737\) | 19.8332 | + | 19.8332i | 0.730564 | + | 0.730564i | ||||
\(738\) | 17.3027 | + | 8.11921i | 0.636920 | + | 0.298872i | ||||
\(739\) | 24.8524 | 0.914209 | 0.457104 | − | 0.889413i | \(-0.348887\pi\) | ||||
0.457104 | + | 0.889413i | \(0.348887\pi\) | |||||||
\(740\) | 6.38028 | − | 19.6580i | 0.234544 | − | 0.722644i | ||||
\(741\) | −8.02949 | −0.294971 | ||||||||
\(742\) | −4.08946 | − | 1.91897i | −0.150129 | − | 0.0704474i | ||||
\(743\) | −15.8488 | − | 15.8488i | −0.581435 | − | 0.581435i | 0.353862 | − | 0.935298i | \(-0.384868\pi\) |
−0.935298 | + | 0.353862i | \(0.884868\pi\) | |||||||
\(744\) | 32.6927 | − | 55.6912i | 1.19857 | − | 2.04174i | ||||
\(745\) | −3.04407 | + | 13.5018i | −0.111526 | + | 0.494668i | ||||
\(746\) | 3.90900 | + | 10.8210i | 0.143119 | + | 0.396185i | ||||
\(747\) | 39.3966 | − | 39.3966i | 1.44145 | − | 1.44145i | ||||
\(748\) | 3.67391 | + | 0.339284i | 0.134332 | + | 0.0124055i | ||||
\(749\) | 5.43154i | 0.198464i | ||||||||
\(750\) | −41.0470 | − | 13.5384i | −1.49882 | − | 0.494353i | ||||
\(751\) | 36.4483i | 1.33002i | 0.746836 | + | 0.665009i | \(0.231572\pi\) | ||||
−0.746836 | + | 0.665009i | \(0.768428\pi\) | |||||||
\(752\) | 12.5344 | + | 18.2735i | 0.457081 | + | 0.666366i | ||||
\(753\) | 3.49024 | − | 3.49024i | 0.127192 | − | 0.127192i | ||||
\(754\) | −0.415120 | + | 0.149959i | −0.0151178 | + | 0.00546118i | ||||
\(755\) | 0.419404 | − | 1.86025i | 0.0152637 | − | 0.0677013i | ||||
\(756\) | −26.7986 | + | 22.2674i | −0.974657 | + | 0.809858i | ||||
\(757\) | −31.2540 | − | 31.2540i | −1.13595 | − | 1.13595i | −0.989170 | − | 0.146776i | \(-0.953110\pi\) |
−0.146776 | − | 0.989170i | \(-0.546890\pi\) | |||||||
\(758\) | −1.11935 | + | 2.38542i | −0.0406566 | + | 0.0866424i | ||||
\(759\) | 87.0250 | 3.15881 | ||||||||
\(760\) | 6.32115 | − | 0.207520i | 0.229292 | − | 0.00752754i | ||||
\(761\) | −13.1619 | −0.477120 | −0.238560 | − | 0.971128i | \(-0.576675\pi\) | ||||
−0.238560 | + | 0.971128i | \(0.576675\pi\) | |||||||
\(762\) | 9.91424 | − | 21.1280i | 0.359155 | − | 0.765388i | ||||
\(763\) | 4.17565 | + | 4.17565i | 0.151169 | + | 0.151169i | ||||
\(764\) | −18.4751 | + | 15.3513i | −0.668406 | + | 0.555389i | ||||
\(765\) | 3.76400 | − | 2.37902i | 0.136088 | − | 0.0860136i | ||||
\(766\) | −42.1895 | + | 15.2406i | −1.52437 | + | 0.550666i | ||||
\(767\) | −15.1137 | + | 15.1137i | −0.545723 | + | 0.545723i | ||||
\(768\) | −17.7164 | − | 39.9888i | −0.639284 | − | 1.44297i | ||||
\(769\) | − | 0.433837i | − | 0.0156445i | −0.999969 | − | 0.00782227i | \(-0.997510\pi\) | ||
0.999969 | − | 0.00782227i | \(-0.00248993\pi\) | |||||||
\(770\) | −56.2632 | + | 7.06440i | −2.02759 | + | 0.254583i | ||||
\(771\) | − | 21.2158i | − | 0.764067i | ||||||
\(772\) | −47.8617 | − | 4.42001i | −1.72258 | − | 0.159079i | ||||
\(773\) | −23.0588 | + | 23.0588i | −0.829368 | + | 0.829368i | −0.987429 | − | 0.158061i | \(-0.949476\pi\) |
0.158061 | + | 0.987429i | \(0.449476\pi\) | |||||||
\(774\) | 21.7130 | + | 60.1065i | 0.780458 | + | 2.16048i | ||||
\(775\) | 17.9199 | − | 37.7212i | 0.643700 | − | 1.35499i | ||||
\(776\) | −9.92382 | − | 5.82563i | −0.356244 | − | 0.209128i | ||||
\(777\) | −38.6601 | − | 38.6601i | −1.38692 | − | 1.38692i | ||||
\(778\) | 25.6593 | + | 12.0405i | 0.919932 | + | 0.431674i | ||||
\(779\) | −3.02173 | −0.108265 | ||||||||
\(780\) | 16.3126 | + | 31.9899i | 0.584086 | + | 1.14542i | ||||
\(781\) | 42.5698 | 1.52327 | ||||||||
\(782\) | 4.37976 | + | 2.05519i | 0.156620 | + | 0.0734934i | ||||
\(783\) | 0.302437 | + | 0.302437i | 0.0108082 | + | 0.0108082i | ||||
\(784\) | 46.1269 | + | 8.59289i | 1.64739 | + | 0.306889i | ||||
\(785\) | −25.8721 | − | 40.9340i | −0.923415 | − | 1.46100i | ||||
\(786\) | 5.34094 | + | 14.7849i | 0.190505 | + | 0.527361i | ||||
\(787\) | −20.2252 | + | 20.2252i | −0.720952 | + | 0.720952i | −0.968799 | − | 0.247847i | \(-0.920277\pi\) |
0.247847 | + | 0.968799i | \(0.420277\pi\) | |||||||
\(788\) | −2.63637 | + | 28.5477i | −0.0939167 | + | 1.01697i | ||||
\(789\) | 39.0336i | 1.38963i | ||||||||
\(790\) | −4.68343 | + | 6.02841i | −0.166629 | + | 0.214481i | ||||
\(791\) | − | 8.60606i | − | 0.305996i | ||||||
\(792\) | 50.7255 | − | 13.1994i | 1.80245 | − | 0.469019i | ||||
\(793\) | −19.1105 | + | 19.1105i | −0.678635 | + | 0.678635i | ||||
\(794\) | −4.33093 | + | 1.56451i | −0.153699 | + | 0.0555225i | ||||
\(795\) | 4.40097 | + | 0.992228i | 0.156086 | + | 0.0351907i | ||||
\(796\) | 24.2599 | + | 29.1966i | 0.859868 | + | 1.03484i | ||||
\(797\) | 39.3739 | + | 39.3739i | 1.39469 | + | 1.39469i | 0.814426 | + | 0.580268i | \(0.197052\pi\) |
0.580268 | + | 0.814426i | \(0.302948\pi\) | |||||||
\(798\) | 7.10733 | − | 15.1463i | 0.251597 | − | 0.536173i | ||||
\(799\) | −2.46653 | −0.0872595 | ||||||||
\(800\) | −13.6688 | − | 24.7622i | −0.483264 | − | 0.875475i | ||||
\(801\) | −5.59259 | −0.197604 | ||||||||
\(802\) | −4.09115 | + | 8.71856i | −0.144464 | + | 0.307863i | ||||
\(803\) | −19.2717 | − | 19.2717i | −0.680082 | − | 0.680082i | ||||
\(804\) | 23.6527 | + | 28.4658i | 0.834165 | + | 1.00391i | ||||
\(805\) | −72.5349 | − | 16.3535i | −2.55652 | − | 0.576384i | ||||
\(806\) | −32.6316 | + | 11.7879i | −1.14940 | + | 0.415212i | ||||
\(807\) | 0.846835 | − | 0.846835i | 0.0298100 | − | 0.0298100i | ||||
\(808\) | −9.02177 | + | 2.34757i | −0.317385 | + | 0.0825873i | ||||
\(809\) | − | 42.5366i | − | 1.49551i | −0.663976 | − | 0.747754i | \(-0.731132\pi\) | ||
0.663976 | − | 0.747754i | \(-0.268868\pi\) | |||||||
\(810\) | −4.68305 | + | 6.02791i | −0.164546 | + | 0.211799i | ||||
\(811\) | 15.4836i | 0.543701i | 0.962339 | + | 0.271851i | \(0.0876357\pi\) | ||||
−0.962339 | + | 0.271851i | \(0.912364\pi\) | |||||||
\(812\) | 0.0845729 | − | 0.915791i | 0.00296793 | − | 0.0321379i | ||||
\(813\) | 16.4191 | − | 16.4191i | 0.575843 | − | 0.575843i | ||||
\(814\) | 9.20033 | + | 25.4686i | 0.322472 | + | 0.892674i | ||||
\(815\) | −12.8735 | − | 20.3680i | −0.450938 | − | 0.713459i | ||||
\(816\) | 4.78607 | + | 0.891586i | 0.167546 | + | 0.0312118i | ||||
\(817\) | −7.14446 | − | 7.14446i | −0.249953 | − | 0.249953i | ||||
\(818\) | −22.0811 | − | 10.3615i | −0.772047 | − | 0.362280i | ||||
\(819\) | 56.8565 | 1.98673 | ||||||||
\(820\) | 6.13891 | + | 12.0387i | 0.214380 | + | 0.420410i | ||||
\(821\) | 29.2299 | 1.02013 | 0.510066 | − | 0.860135i | \(-0.329621\pi\) | ||||
0.510066 | + | 0.860135i | \(0.329621\pi\) | |||||||
\(822\) | 20.6904 | + | 9.70889i | 0.721661 | + | 0.338637i | ||||
\(823\) | −0.713219 | − | 0.713219i | −0.0248613 | − | 0.0248613i | 0.694567 | − | 0.719428i | \(-0.255596\pi\) |
−0.719428 | + | 0.694567i | \(0.755596\pi\) | |||||||
\(824\) | 28.8498 | + | 16.9358i | 1.00503 | + | 0.589988i | ||||
\(825\) | 53.3534 | − | 18.9872i | 1.85753 | − | 0.661050i | ||||
\(826\) | −15.1315 | − | 41.8873i | −0.526491 | − | 1.45745i | ||||
\(827\) | 15.3053 | − | 15.3053i | 0.532219 | − | 0.532219i | −0.389013 | − | 0.921232i | \(-0.627184\pi\) |
0.921232 | + | 0.389013i | \(0.127184\pi\) | |||||||
\(828\) | 68.4386 | + | 6.32027i | 2.37840 | + | 0.219645i | ||||
\(829\) | − | 51.9914i | − | 1.80574i | −0.429918 | − | 0.902868i | \(-0.641458\pi\) | ||
0.429918 | − | 0.902868i | \(-0.358542\pi\) | |||||||
\(830\) | 39.0859 | − | 4.90761i | 1.35669 | − | 0.170346i | ||||
\(831\) | − | 38.7091i | − | 1.34281i | ||||||
\(832\) | −6.40960 | + | 22.6076i | −0.222213 | + | 0.783778i | ||||
\(833\) | −3.69300 | + | 3.69300i | −0.127955 | + | 0.127955i | ||||
\(834\) | −73.5318 | + | 26.5628i | −2.54620 | + | 0.919794i | ||||
\(835\) | 26.3840 | − | 16.6759i | 0.913057 | − | 0.577093i | ||||
\(836\) | −6.37359 | + | 5.29591i | −0.220435 | + | 0.183163i | ||||
\(837\) | 23.7738 | + | 23.7738i | 0.821744 | + | 0.821744i | ||||
\(838\) | 3.67448 | − | 7.83060i | 0.126933 | − | 0.270504i | ||||
\(839\) | −27.3498 | −0.944221 | −0.472110 | − | 0.881539i | \(-0.656508\pi\) | ||||
−0.472110 | + | 0.881539i | \(0.656508\pi\) | |||||||
\(840\) | −74.7827 | + | 2.45508i | −2.58025 | + | 0.0847082i | ||||
\(841\) | 28.9887 | 0.999611 | ||||||||
\(842\) | −1.80869 | + | 3.85446i | −0.0623316 | + | 0.132834i | ||||
\(843\) | −14.2998 | − | 14.2998i | −0.492511 | − | 0.492511i | ||||
\(844\) | −1.64663 | + | 1.36821i | −0.0566793 | + | 0.0470957i | ||||
\(845\) | −2.15015 | + | 9.53687i | −0.0739673 | + | 0.328078i | ||||
\(846\) | −32.9558 | + | 11.9050i | −1.13304 | + | 0.409303i | ||||
\(847\) | 18.8735 | − | 18.8735i | 0.648500 | − | 0.648500i | ||||
\(848\) | 1.66995 | + | 2.43457i | 0.0573463 | + | 0.0836035i | ||||
\(849\) | 56.2742i | 1.93132i | ||||||||
\(850\) | 3.13355 | + | 0.304414i | 0.107480 | + | 0.0104413i | ||||
\(851\) | 35.5084i | 1.21721i | ||||||||
\(852\) | 55.9334 | + | 5.16543i | 1.91625 | + | 0.176965i | ||||
\(853\) | 12.2962 | − | 12.2962i | 0.421013 | − | 0.421013i | −0.464539 | − | 0.885553i | \(-0.653780\pi\) |
0.885553 | + | 0.464539i | \(0.153780\pi\) | |||||||
\(854\) | −19.1330 | − | 52.9645i | −0.654719 | − | 1.81241i | ||||
\(855\) | −2.19957 | + | 9.75608i | −0.0752238 | + | 0.333651i | ||||
\(856\) | 1.79706 | − | 3.06125i | 0.0614223 | − | 0.104632i | ||||
\(857\) | 24.1129 | + | 24.1129i | 0.823681 | + | 0.823681i | 0.986634 | − | 0.162953i | \(-0.0521018\pi\) |
−0.162953 | + | 0.986634i | \(0.552102\pi\) | |||||||
\(858\) | −42.5932 | − | 19.9867i | −1.45411 | − | 0.682335i | ||||
\(859\) | −10.5761 | −0.360853 | −0.180426 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180426 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(860\) | −13.9493 | + | 42.9785i | −0.475666 | + | 1.46555i | ||||
\(861\) | 35.7487 | 1.21831 | ||||||||
\(862\) | −50.0578 | − | 23.4894i | −1.70497 | − | 0.800053i | ||||
\(863\) | 5.45347 | + | 5.45347i | 0.185638 | + | 0.185638i | 0.793807 | − | 0.608169i | \(-0.208096\pi\) |
−0.608169 | + | 0.793807i | \(0.708096\pi\) | |||||||
\(864\) | 22.4712 | − | 3.68356i | 0.764487 | − | 0.125317i | ||||
\(865\) | −31.8850 | + | 20.1528i | −1.08412 | + | 0.685214i | ||||
\(866\) | 3.16822 | + | 8.77036i | 0.107661 | + | 0.298029i | ||||
\(867\) | 32.4769 | − | 32.4769i | 1.10297 | − | 1.10297i | ||||
\(868\) | 6.64807 | − | 71.9881i | 0.225650 | − | 2.44344i | ||||
\(869\) | − | 10.0022i | − | 0.339302i | ||||||
\(870\) | 0.114427 | + | 0.911335i | 0.00387944 | + | 0.0308972i | ||||
\(871\) | − | 19.8842i | − | 0.673752i | ||||||
\(872\) | −0.971884 | − | 3.73497i | −0.0329121 | − | 0.126482i | ||||
\(873\) | 12.8669 | − | 12.8669i | 0.435478 | − | 0.435478i | ||||
\(874\) | −10.2197 | + | 3.69179i | −0.345687 | + | 0.124877i | ||||
\(875\) | −48.0378 | + | 5.79975i | −1.62397 | + | 0.196067i | ||||
\(876\) | −22.9830 | − | 27.6599i | −0.776525 | − | 0.934541i | ||||
\(877\) | 29.9399 | + | 29.9399i | 1.01100 | + | 1.01100i | 0.999939 | + | 0.0110592i | \(0.00352032\pi\) |
0.0110592 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(878\) | 18.8901 | − | 40.2563i | 0.637511 | − | 1.35859i | ||||
\(879\) | −4.46321 | −0.150540 | ||||||||
\(880\) | 34.0477 | + | 14.6335i | 1.14775 | + | 0.493297i | ||||
\(881\) | −8.25200 | −0.278017 | −0.139008 | − | 0.990291i | \(-0.544392\pi\) | ||||
−0.139008 | + | 0.990291i | \(0.544392\pi\) | |||||||
\(882\) | −31.5182 | + | 67.1676i | −1.06127 | + | 2.26165i | ||||
\(883\) | −14.8130 | − | 14.8130i | −0.498497 | − | 0.498497i | 0.412473 | − | 0.910970i | \(-0.364665\pi\) |
−0.910970 | + | 0.412473i | \(0.864665\pi\) | |||||||
\(884\) | −1.67161 | − | 2.01177i | −0.0562223 | − | 0.0676630i | ||||
\(885\) | 23.7638 | + | 37.5983i | 0.798812 | + | 1.26385i | ||||
\(886\) | −12.6810 | + | 4.58091i | −0.426027 | + | 0.153899i | ||||
\(887\) | −38.0665 | + | 38.0665i | −1.27815 | + | 1.27815i | −0.336443 | + | 0.941704i | \(0.609224\pi\) |
−0.941704 | + | 0.336443i | \(0.890776\pi\) | |||||||
\(888\) | 8.99816 | + | 34.5801i | 0.301958 | + | 1.16043i | ||||
\(889\) | − | 26.1272i | − | 0.876279i | ||||||
\(890\) | −3.12257 | − | 2.42591i | −0.104669 | − | 0.0813166i | ||||
\(891\) | − | 10.0014i | − | 0.335060i | ||||||
\(892\) | −2.78981 | + | 30.2092i | −0.0934098 | + | 1.01148i | ||||
\(893\) | 3.91723 | − | 3.91723i | 0.131085 | − | 0.131085i | ||||
\(894\) | −8.12994 | − | 22.5055i | −0.271906 | − | 0.752697i | ||||
\(895\) | −33.9892 | − | 7.66309i | −1.13613 | − | 0.256149i | ||||
\(896\) | −36.9720 | − | 32.1018i | −1.23515 | − | 1.07245i | ||||
\(897\) | −43.6246 | − | 43.6246i | −1.45658 | − | 1.45658i | ||||
\(898\) | −2.91325 | − | 1.36703i | −0.0972163 | − | 0.0456184i | ||||
\(899\) | −0.887452 | −0.0295982 | ||||||||
\(900\) | 43.3373 | − | 11.0572i | 1.44458 | − | 0.368572i | ||||
\(901\) | −0.328615 | −0.0109477 | ||||||||
\(902\) | −16.0290 | − | 7.52157i | −0.533709 | − | 0.250441i | ||||
\(903\) | 84.5229 | + | 84.5229i | 2.81275 | + | 2.81275i | ||||
\(904\) | −2.84737 | + | 4.85044i | −0.0947023 | + | 0.161323i | ||||
\(905\) | −26.3746 | − | 5.94632i | −0.876721 | − | 0.197662i | ||||
\(906\) | 1.12012 | + | 3.10075i | 0.0372136 | + | 0.103016i | ||||
\(907\) | 28.7677 | − | 28.7677i | 0.955217 | − | 0.955217i | −0.0438222 | − | 0.999039i | \(-0.513954\pi\) |
0.999039 | + | 0.0438222i | \(0.0139535\pi\) | |||||||
\(908\) | 22.9938 | + | 2.12347i | 0.763076 | + | 0.0704698i | ||||
\(909\) | − | 14.7411i | − | 0.488932i | ||||||
\(910\) | 31.7454 | + | 24.6628i | 1.05235 | + | 0.817563i | ||||
\(911\) | − | 20.5412i | − | 0.680562i | −0.940324 | − | 0.340281i | \(-0.889478\pi\) | ||
0.940324 | − | 0.340281i | \(-0.110522\pi\) | |||||||
\(912\) | −9.01700 | + | 6.18504i | −0.298583 | + | 0.204807i | ||||
\(913\) | −36.4966 | + | 36.4966i | −1.20786 | + | 1.20786i | ||||
\(914\) | 39.7957 | − | 14.3759i | 1.31632 | − | 0.475512i | ||||
\(915\) | 30.0482 | + | 47.5413i | 0.993364 | + | 1.57167i | ||||
\(916\) | −4.31903 | + | 3.58875i | −0.142705 | + | 0.118576i | ||||
\(917\) | 12.4440 | + | 12.4440i | 0.410936 | + | 0.410936i | ||||
\(918\) | −1.07672 | + | 2.29458i | −0.0355371 | + | 0.0757323i | ||||
\(919\) | −11.2507 | −0.371126 | −0.185563 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185563 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(920\) | 35.4705 | + | 33.2156i | 1.16943 | + | 1.09509i | ||||
\(921\) | 66.3729 | 2.18706 | ||||||||
\(922\) | 23.3801 | − | 49.8247i | 0.769981 | − | 1.64089i | ||||
\(923\) | −21.3397 | − | 21.3397i | −0.702406 | − | 0.702406i | ||||
\(924\) | 75.4031 | − | 62.6536i | 2.48058 | − | 2.06115i | ||||
\(925\) | 7.74727 | + | 21.7695i | 0.254729 | + | 0.715778i | ||||
\(926\) | 1.97355 | − | 0.712928i | 0.0648547 | − | 0.0234283i | ||||
\(927\) | −37.4057 | + | 37.4057i | −1.22856 | + | 1.22856i | ||||
\(928\) | −0.350662 | + | 0.488165i | −0.0115110 | + | 0.0160248i | ||||
\(929\) | 8.66599i | 0.284322i | 0.989844 | + | 0.142161i | \(0.0454051\pi\) | ||||
−0.989844 | + | 0.142161i | \(0.954595\pi\) | |||||||
\(930\) | 8.99483 | + | 71.6379i | 0.294952 | + | 2.34910i | ||||
\(931\) | − | 11.7301i | − | 0.384439i | ||||||
\(932\) | 38.5540 | + | 3.56044i | 1.26288 | + | 0.116626i | ||||
\(933\) | −16.1666 | + | 16.1666i | −0.529270 | + | 0.529270i | ||||
\(934\) | 0.263937 | + | 0.730638i | 0.00863630 | + | 0.0239072i | ||||
\(935\) | −3.48694 | + | 2.20390i | −0.114035 | + | 0.0720753i | ||||
\(936\) | −32.0448 | − | 18.8114i | −1.04742 | − | 0.614869i | ||||
\(937\) | 15.8631 | + | 15.8631i | 0.518226 | + | 0.518226i | 0.917034 | − | 0.398808i | \(-0.130576\pi\) |
−0.398808 | + | 0.917034i | \(0.630576\pi\) | |||||||
\(938\) | 37.5082 | + | 17.6006i | 1.22469 | + | 0.574680i | ||||
\(939\) | −34.6468 | −1.13066 | ||||||||
\(940\) | −23.5647 | − | 7.64823i | −0.768594 | − | 0.249458i | ||||
\(941\) | 40.9080 | 1.33356 | 0.666781 | − | 0.745254i | \(-0.267672\pi\) | ||||
0.666781 | + | 0.745254i | \(0.267672\pi\) | |||||||
\(942\) | 75.7911 | + | 35.5647i | 2.46941 | + | 1.15876i | ||||
\(943\) | −16.4172 | − | 16.4172i | −0.534617 | − | 0.534617i | ||||
\(944\) | −5.33051 | + | 28.6144i | −0.173493 | + | 0.931318i | ||||
\(945\) | 8.56764 | − | 38.0013i | 0.278705 | − | 1.23618i | ||||
\(946\) | −20.1147 | − | 55.6822i | −0.653987 | − | 1.81038i | ||||
\(947\) | −28.1988 | + | 28.1988i | −0.916339 | + | 0.916339i | −0.996761 | − | 0.0804218i | \(-0.974373\pi\) |
0.0804218 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(948\) | 1.21367 | − | 13.1422i | 0.0394182 | − | 0.426837i | ||||
\(949\) | 19.3213i | 0.627196i | ||||||||
\(950\) | −5.46003 | + | 4.49311i | −0.177147 | + | 0.145776i | ||||
\(951\) | 0.613153i | 0.0198828i | ||||||||
\(952\) | 5.27449 | − | 1.37248i | 0.170947 | − | 0.0444825i | ||||
\(953\) | 2.49156 | − | 2.49156i | 0.0807097 | − | 0.0807097i | −0.665599 | − | 0.746309i | \(-0.731824\pi\) |
0.746309 | + | 0.665599i | \(0.231824\pi\) | |||||||
\(954\) | −4.39069 | + | 1.58610i | −0.142154 | + | 0.0513520i | ||||
\(955\) | 5.90658 | − | 26.1983i | 0.191132 | − | 0.847758i | ||||
\(956\) | 28.6047 | + | 34.4255i | 0.925142 | + | 1.11340i | ||||
\(957\) | −0.850964 | − | 0.850964i | −0.0275078 | − | 0.0275078i | ||||
\(958\) | −4.19269 | + | 8.93495i | −0.135460 | + | 0.288675i | ||||
\(959\) | 25.5861 | 0.826217 | ||||||||
\(960\) | 42.9604 | + | 23.3587i | 1.38654 | + | 0.753898i | ||||
\(961\) | −38.7605 | −1.25034 | ||||||||
\(962\) | 8.15508 | − | 17.3791i | 0.262930 | − | 0.560325i | ||||
\(963\) | 3.96912 | + | 3.96912i | 0.127903 | + | 0.127903i | ||||
\(964\) | 10.5320 | + | 12.6752i | 0.339212 | + | 0.408239i | ||||
\(965\) | 45.4259 | − | 28.7112i | 1.46231 | − | 0.924247i | ||||
\(966\) | 120.905 | − | 43.6759i | 3.89005 | − | 1.40525i | ||||
\(967\) | 11.1962 | − | 11.1962i | 0.360044 | − | 0.360044i | −0.503785 | − | 0.863829i | \(-0.668060\pi\) |
0.863829 | + | 0.503785i | \(0.168060\pi\) | |||||||
\(968\) | −16.8816 | + | 4.39280i | −0.542597 | + | 0.141190i | ||||
\(969\) | − | 1.21710i | − | 0.0390989i | ||||||
\(970\) | 12.7654 | − | 1.60282i | 0.409873 | − | 0.0514635i | ||||
\(971\) | 47.4336i | 1.52222i | 0.648625 | + | 0.761108i | \(0.275344\pi\) | ||||
−0.648625 | + | 0.761108i | \(0.724656\pi\) | |||||||
\(972\) | 3.43459 | − | 37.1912i | 0.110165 | − | 1.19291i | ||||
\(973\) | −61.8892 | + | 61.8892i | −1.98408 | + | 1.98408i | ||||
\(974\) | 0.262944 | + | 0.727889i | 0.00842527 | + | 0.0233231i | ||||
\(975\) | −36.2635 | − | 17.2273i | −1.16136 | − | 0.551716i | ||||
\(976\) | −6.74017 | + | 36.1815i | −0.215748 | + | 1.15814i | ||||
\(977\) | −37.1356 | − | 37.1356i | −1.18807 | − | 1.18807i | −0.977600 | − | 0.210473i | \(-0.932500\pi\) |
−0.210473 | − | 0.977600i | \(-0.567500\pi\) | |||||||
\(978\) | 37.7122 | + | 17.6963i | 1.20590 | + | 0.565866i | ||||
\(979\) | 5.18092 | 0.165583 | ||||||||
\(980\) | −46.7333 | + | 23.8308i | −1.49284 | + | 0.761247i | ||||
\(981\) | 6.10275 | 0.194846 | ||||||||
\(982\) | 20.6817 | + | 9.70480i | 0.659979 | + | 0.309693i | ||||
\(983\) | 27.4641 | + | 27.4641i | 0.875970 | + | 0.875970i | 0.993115 | − | 0.117145i | \(-0.0373742\pi\) |
−0.117145 | + | 0.993115i | \(0.537374\pi\) | |||||||
\(984\) | −20.1482 | − | 11.8277i | −0.642303 | − | 0.377054i | ||||
\(985\) | −17.1252 | − | 27.0948i | −0.545653 | − | 0.863313i | ||||
\(986\) | −0.0227306 | − | 0.0629234i | −0.000723890 | − | 0.00200389i | ||||
\(987\) | −46.3430 | + | 46.3430i | −1.47512 | + | 1.47512i | ||||
\(988\) | 5.84978 | + | 0.540224i | 0.186106 | + | 0.0171868i | ||||
\(989\) | − | 77.6323i | − | 2.46856i | ||||||
\(990\) | −35.9523 | + | 46.2770i | −1.14264 | + | 1.47078i | ||||
\(991\) | 36.3848i | 1.15580i | 0.816107 | + | 0.577901i | \(0.196128\pi\) | ||||
−0.816107 | + | 0.577901i | \(0.803872\pi\) | |||||||
\(992\) | −27.5647 | + | 38.3735i | −0.875179 | + | 1.21836i | ||||
\(993\) | 59.3184 | − | 59.3184i | 1.88241 | − | 1.88241i | ||||
\(994\) | 59.1427 | − | 21.3648i | 1.87589 | − | 0.677652i | ||||
\(995\) | −41.4016 | − | 9.33427i | −1.31252 | − | 0.295916i | ||||
\(996\) | −52.3823 | + | 43.5252i | −1.65980 | + | 1.37915i | ||||
\(997\) | 30.7644 | + | 30.7644i | 0.974320 | + | 0.974320i | 0.999678 | − | 0.0253586i | \(-0.00807276\pi\) |
−0.0253586 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(998\) | −20.3287 | + | 43.3221i | −0.643495 | + | 1.37134i | ||||
\(999\) | −18.6030 | −0.588573 |
(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 | 380.2.k.c.267.10 | ✓ | 52 | |
4.3 | odd | 2 | 380.2.k.d.267.23 | yes | 52 | ||
5.3 | odd | 4 | 380.2.k.d.343.23 | yes | 52 | ||
20.3 | even | 4 | inner | 380.2.k.c.343.10 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.10 | ✓ | 52 | 1.1 | even | 1 | trivial | |
380.2.k.c.343.10 | yes | 52 | 20.3 | even | 4 | inner | |
380.2.k.d.267.23 | yes | 52 | 4.3 | odd | 2 | ||
380.2.k.d.343.23 | yes | 52 | 5.3 | odd | 4 |