Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(376,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.376");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.o (of order \(6\), 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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.523596960000.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 376.4 | ||
Root | \(-1.26021 + 2.18275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.376 |
Dual form | 525.3.o.l.451.4 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26021 | − | 2.18275i | 0.630107 | − | 1.09138i | −0.357423 | − | 0.933943i | \(-0.616344\pi\) |
0.987529 | − | 0.157434i | \(-0.0503223\pi\) | |||||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.17628 | − | 2.03737i | −0.294069 | − | 0.509343i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 4.36551i | − | 0.727585i | ||||||
\(7\) | 6.18050 | + | 3.28656i | 0.882928 | + | 0.469508i | ||||
\(8\) | 4.15226 | 0.519033 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.36036 | + | 7.55236i | 0.396396 | + | 0.686579i | 0.993278 | − | 0.115750i | \(-0.0369273\pi\) |
−0.596882 | + | 0.802329i | \(0.703594\pi\) | |||||||
\(12\) | −3.52883 | − | 2.03737i | −0.294069 | − | 0.169781i | ||||
\(13\) | 21.5286i | 1.65605i | 0.560693 | + | 0.828024i | \(0.310535\pi\) | ||||
−0.560693 | + | 0.828024i | \(0.689465\pi\) | |||||||
\(14\) | 14.9625 | − | 9.34874i | 1.06875 | − | 0.667767i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.93785 | − | 17.2129i | 0.621116 | − | 1.07580i | ||||
\(17\) | 18.7862 | − | 10.8462i | 1.10507 | − | 0.638013i | 0.167523 | − | 0.985868i | \(-0.446423\pi\) |
0.937548 | + | 0.347855i | \(0.113090\pi\) | |||||||
\(18\) | −3.78064 | − | 6.54826i | −0.210036 | − | 0.363792i | ||||
\(19\) | −2.71590 | − | 1.56803i | −0.142942 | − | 0.0825276i | 0.426823 | − | 0.904335i | \(-0.359633\pi\) |
−0.569765 | + | 0.821807i | \(0.692966\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.1170 | − | 0.422628i | 0.576999 | − | 0.0201251i | ||||
\(22\) | 21.9799 | 0.999088 | ||||||||
\(23\) | 2.05421 | − | 3.55799i | 0.0893134 | − | 0.154695i | −0.817908 | − | 0.575349i | \(-0.804866\pi\) |
0.907221 | + | 0.420654i | \(0.138199\pi\) | |||||||
\(24\) | 6.22840 | − | 3.59597i | 0.259517 | − | 0.149832i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 46.9917 | + | 27.1307i | 1.80737 | + | 1.04349i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −0.574033 | − | 16.4579i | −0.0205012 | − | 0.587781i | ||||
\(29\) | −50.8583 | −1.75373 | −0.876867 | − | 0.480732i | \(-0.840371\pi\) | ||||
−0.876867 | + | 0.480732i | \(0.840371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.9213 | + | 19.5845i | −1.09424 | + | 0.631758i | −0.934701 | − | 0.355434i | \(-0.884333\pi\) |
−0.159536 | + | 0.987192i | \(0.551000\pi\) | |||||||
\(32\) | −16.7431 | − | 28.9999i | −0.523222 | − | 0.906247i | ||||
\(33\) | 13.0811 | + | 7.55236i | 0.396396 | + | 0.228860i | ||||
\(34\) | − | 54.6743i | − | 1.60807i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.05767 | −0.196046 | ||||||||
\(37\) | 26.4906 | − | 45.8831i | 0.715962 | − | 1.24008i | −0.246625 | − | 0.969111i | \(-0.579322\pi\) |
0.962587 | − | 0.270972i | \(-0.0873451\pi\) | |||||||
\(38\) | −6.84523 | + | 3.95209i | −0.180138 | + | 0.104002i | ||||
\(39\) | 18.6443 | + | 32.2929i | 0.478060 | + | 0.828024i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 36.8122i | − | 0.897857i | −0.893568 | − | 0.448929i | \(-0.851806\pi\) | ||
0.893568 | − | 0.448929i | \(-0.148194\pi\) | |||||||
\(42\) | 14.3475 | − | 26.9810i | 0.341607 | − | 0.642405i | ||||
\(43\) | −17.6504 | −0.410475 | −0.205238 | − | 0.978712i | \(-0.565797\pi\) | ||||
−0.205238 | + | 0.978712i | \(0.565797\pi\) | |||||||
\(44\) | 10.2580 | − | 17.7674i | 0.233136 | − | 0.403804i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.17748 | − | 8.96766i | −0.112554 | − | 0.194949i | ||||
\(47\) | 3.49804 | + | 2.01959i | 0.0744263 | + | 0.0429701i | 0.536751 | − | 0.843740i | \(-0.319651\pi\) |
−0.462325 | + | 0.886711i | \(0.652985\pi\) | |||||||
\(48\) | − | 34.4257i | − | 0.717203i | ||||||
\(49\) | 27.3971 | + | 40.6251i | 0.559124 | + | 0.829084i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.7862 | − | 32.5387i | 0.368357 | − | 0.638013i | ||||
\(52\) | 43.8618 | − | 25.3236i | 0.843496 | − | 0.486993i | ||||
\(53\) | 2.22593 | + | 3.85542i | 0.0419986 | + | 0.0727438i | 0.886261 | − | 0.463187i | \(-0.153294\pi\) |
−0.844262 | + | 0.535931i | \(0.819961\pi\) | |||||||
\(54\) | −11.3419 | − | 6.54826i | −0.210036 | − | 0.121264i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 25.6631 | + | 13.6467i | 0.458269 | + | 0.243690i | ||||
\(57\) | −5.43180 | −0.0952947 | ||||||||
\(58\) | −64.0923 | + | 111.011i | −1.10504 | + | 1.91399i | ||||
\(59\) | 81.5032 | − | 47.0559i | 1.38141 | − | 0.797558i | 0.389084 | − | 0.921202i | \(-0.372792\pi\) |
0.992327 | + | 0.123644i | \(0.0394582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −63.3781 | − | 36.5913i | −1.03898 | − | 0.599858i | −0.119439 | − | 0.992842i | \(-0.538110\pi\) |
−0.919546 | + | 0.392984i | \(0.871443\pi\) | |||||||
\(62\) | 98.7226i | 1.59230i | ||||||||
\(63\) | 17.8095 | − | 11.1276i | 0.282690 | − | 0.176628i | ||||
\(64\) | −4.89677 | −0.0765121 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 32.9699 | − | 19.0352i | 0.499544 | − | 0.288412i | ||||
\(67\) | −50.2661 | − | 87.0635i | −0.750241 | − | 1.29946i | −0.947706 | − | 0.319145i | \(-0.896604\pi\) |
0.197465 | − | 0.980310i | \(-0.436729\pi\) | |||||||
\(68\) | −44.1956 | − | 25.5164i | −0.649936 | − | 0.375241i | ||||
\(69\) | − | 7.11598i | − | 0.103130i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56.6975 | −0.798557 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(72\) | 6.22840 | − | 10.7879i | 0.0865055 | − | 0.149832i | ||||
\(73\) | −64.8042 | + | 37.4147i | −0.887729 | + | 0.512531i | −0.873199 | − | 0.487364i | \(-0.837959\pi\) |
−0.0145299 | + | 0.999894i | \(0.504625\pi\) | |||||||
\(74\) | −66.7676 | − | 115.645i | −0.902266 | − | 1.56277i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.37773i | 0.0970754i | ||||||||
\(77\) | 2.12789 | + | 61.0079i | 0.0276350 | + | 0.792311i | ||||
\(78\) | 93.9833 | 1.20491 | ||||||||
\(79\) | −14.4903 | + | 25.0980i | −0.183422 | + | 0.317696i | −0.943044 | − | 0.332669i | \(-0.892051\pi\) |
0.759622 | + | 0.650365i | \(0.225384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −80.3519 | − | 46.3912i | −0.979901 | − | 0.565746i | ||||
\(83\) | 21.1116i | 0.254357i | 0.991880 | + | 0.127179i | \(0.0405921\pi\) | ||||
−0.991880 | + | 0.127179i | \(0.959408\pi\) | |||||||
\(84\) | −15.1140 | − | 24.1897i | −0.179928 | − | 0.287973i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22.2433 | + | 38.5266i | −0.258643 | + | 0.447983i | ||||
\(87\) | −76.2875 | + | 44.0446i | −0.876867 | + | 0.506260i | ||||
\(88\) | 18.1054 | + | 31.3594i | 0.205743 | + | 0.356357i | ||||
\(89\) | 63.1066 | + | 36.4346i | 0.709063 | + | 0.409378i | 0.810714 | − | 0.585442i | \(-0.199079\pi\) |
−0.101651 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −70.7551 | + | 133.057i | −0.777528 | + | 1.46217i | ||||
\(92\) | −9.66528 | −0.105057 | ||||||||
\(93\) | −33.9213 | + | 58.7535i | −0.364746 | + | 0.631758i | ||||
\(94\) | 8.81655 | − | 5.09024i | 0.0937931 | − | 0.0541515i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −50.2293 | − | 28.9999i | −0.523222 | − | 0.302082i | ||||
\(97\) | 73.7985i | 0.760809i | 0.924820 | + | 0.380405i | \(0.124215\pi\) | ||||
−0.924820 | + | 0.380405i | \(0.875785\pi\) | |||||||
\(98\) | 123.201 | − | 8.60469i | 1.25715 | − | 0.0878030i | ||||
\(99\) | 26.1622 | 0.264264 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −92.6245 | + | 53.4768i | −0.917075 | + | 0.529473i | −0.882701 | − | 0.469936i | \(-0.844277\pi\) |
−0.0343741 | + | 0.999409i | \(0.510944\pi\) | |||||||
\(102\) | −47.3493 | − | 82.0114i | −0.464209 | − | 0.804033i | ||||
\(103\) | −18.6535 | − | 10.7696i | −0.181102 | − | 0.104559i | 0.406708 | − | 0.913558i | \(-0.366677\pi\) |
−0.587810 | + | 0.808999i | \(0.700010\pi\) | |||||||
\(104\) | 89.3925i | 0.859543i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2206 | 0.105855 | ||||||||
\(107\) | 44.8184 | − | 77.6277i | 0.418863 | − | 0.725492i | −0.576962 | − | 0.816771i | \(-0.695762\pi\) |
0.995825 | + | 0.0912785i | \(0.0290953\pi\) | |||||||
\(108\) | −10.5865 | + | 6.11212i | −0.0980232 | + | 0.0565937i | ||||
\(109\) | −13.6751 | − | 23.6859i | −0.125459 | − | 0.217302i | 0.796453 | − | 0.604700i | \(-0.206707\pi\) |
−0.921912 | + | 0.387398i | \(0.873374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 91.7661i | − | 0.826722i | ||||||
\(112\) | 117.992 | − | 73.7227i | 1.05350 | − | 0.658238i | ||||
\(113\) | 92.3372 | 0.817144 | 0.408572 | − | 0.912726i | \(-0.366027\pi\) | ||||
0.408572 | + | 0.912726i | \(0.366027\pi\) | |||||||
\(114\) | −6.84523 | + | 11.8563i | −0.0600459 | + | 0.104002i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 59.8235 | + | 103.617i | 0.515720 | + | 0.893253i | ||||
\(117\) | 55.9330 | + | 32.2929i | 0.478060 | + | 0.276008i | ||||
\(118\) | − | 237.202i | − | 2.01019i | ||||||
\(119\) | 151.755 | − | 5.29305i | 1.27525 | − | 0.0444794i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.4745 | − | 38.9270i | 0.185740 | − | 0.321711i | ||||
\(122\) | −159.740 | + | 92.2258i | −1.30934 | + | 0.755949i | ||||
\(123\) | −31.8803 | − | 55.2182i | −0.259189 | − | 0.448929i | ||||
\(124\) | 79.8019 | + | 46.0736i | 0.643563 | + | 0.371562i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.84498 | − | 52.8968i | −0.0146427 | − | 0.419816i | ||||
\(127\) | −191.591 | −1.50859 | −0.754297 | − | 0.656534i | \(-0.772022\pi\) | ||||
−0.754297 | + | 0.656534i | \(0.772022\pi\) | |||||||
\(128\) | 60.8015 | − | 105.311i | 0.475011 | − | 0.822744i | ||||
\(129\) | −26.4757 | + | 15.2857i | −0.205238 | + | 0.118494i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50.9329 | + | 29.4062i | 0.388801 | + | 0.224474i | 0.681641 | − | 0.731687i | \(-0.261267\pi\) |
−0.292839 | + | 0.956162i | \(0.594600\pi\) | |||||||
\(132\) | − | 35.5347i | − | 0.269202i | ||||||
\(133\) | −11.6322 | − | 18.6171i | −0.0874601 | − | 0.139978i | ||||
\(134\) | −253.384 | −1.89093 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 78.0054 | − | 45.0364i | 0.573569 | − | 0.331150i | ||||
\(137\) | 82.9571 | + | 143.686i | 0.605526 | + | 1.04880i | 0.991968 | + | 0.126488i | \(0.0403706\pi\) |
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(138\) | −15.5324 | − | 8.96766i | −0.112554 | − | 0.0649831i | ||||
\(139\) | 139.625i | 1.00449i | 0.864724 | + | 0.502247i | \(0.167493\pi\) | ||||
−0.864724 | + | 0.502247i | \(0.832507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.99607 | 0.0496176 | ||||||||
\(142\) | −71.4510 | + | 123.757i | −0.503176 | + | 0.871527i | ||||
\(143\) | −162.592 | + | 93.8725i | −1.13701 | + | 0.656451i | ||||
\(144\) | −29.8136 | − | 51.6386i | −0.207039 | − | 0.358601i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 188.602i | 1.29180i | ||||||||
\(147\) | 76.2780 | + | 37.2111i | 0.518898 | + | 0.253137i | ||||
\(148\) | −124.641 | −0.842171 | ||||||||
\(149\) | 7.16861 | − | 12.4164i | 0.0481115 | − | 0.0833315i | −0.840967 | − | 0.541087i | \(-0.818013\pi\) |
0.889078 | + | 0.457755i | \(0.151346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −106.187 | − | 183.922i | −0.703226 | − | 1.21802i | −0.967328 | − | 0.253529i | \(-0.918409\pi\) |
0.264102 | − | 0.964495i | \(-0.414925\pi\) | |||||||
\(152\) | −11.2771 | − | 6.51085i | −0.0741917 | − | 0.0428346i | ||||
\(153\) | − | 65.0774i | − | 0.425342i | ||||||
\(154\) | 135.847 | + | 72.2384i | 0.882123 | + | 0.469080i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 43.8618 | − | 75.9709i | 0.281165 | − | 0.486993i | ||||
\(157\) | 210.373 | − | 121.459i | 1.33996 | − | 0.773624i | 0.353156 | − | 0.935565i | \(-0.385109\pi\) |
0.986801 | + | 0.161941i | \(0.0517753\pi\) | |||||||
\(158\) | 36.5218 | + | 63.2577i | 0.231151 | + | 0.400365i | ||||
\(159\) | 6.67778 | + | 3.85542i | 0.0419986 | + | 0.0242479i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.3896 | − | 15.2389i | 0.151488 | − | 0.0946514i | ||||
\(162\) | −22.6838 | −0.140024 | ||||||||
\(163\) | 6.61728 | − | 11.4615i | 0.0405968 | − | 0.0703157i | −0.845013 | − | 0.534746i | \(-0.820407\pi\) |
0.885610 | + | 0.464430i | \(0.153741\pi\) | |||||||
\(164\) | −75.0001 | + | 43.3013i | −0.457318 | + | 0.264032i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 46.0815 | + | 26.6052i | 0.277600 | + | 0.160272i | ||||
\(167\) | 212.616i | 1.27315i | 0.771216 | + | 0.636574i | \(0.219649\pi\) | ||||
−0.771216 | + | 0.636574i | \(0.780351\pi\) | |||||||
\(168\) | 50.3129 | − | 1.75486i | 0.299482 | − | 0.0104456i | ||||
\(169\) | −294.481 | −1.74249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.14770 | + | 4.70408i | −0.0476474 | + | 0.0275092i | ||||
\(172\) | 20.7618 | + | 35.9605i | 0.120708 | + | 0.209073i | ||||
\(173\) | 215.456 | + | 124.393i | 1.24541 | + | 0.719037i | 0.970190 | − | 0.242345i | \(-0.0779164\pi\) |
0.275219 | + | 0.961382i | \(0.411250\pi\) | |||||||
\(174\) | 222.022i | 1.27599i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 173.330 | 0.984832 | ||||||||
\(177\) | 81.5032 | − | 141.168i | 0.460470 | − | 0.797558i | ||||
\(178\) | 159.056 | − | 91.8308i | 0.893571 | − | 0.515903i | ||||
\(179\) | −27.6352 | − | 47.8655i | −0.154386 | − | 0.267405i | 0.778449 | − | 0.627708i | \(-0.216007\pi\) |
−0.932835 | + | 0.360303i | \(0.882673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 46.9001i | − | 0.259117i | −0.991572 | − | 0.129558i | \(-0.958644\pi\) | ||
0.991572 | − | 0.129558i | \(-0.0413559\pi\) | |||||||
\(182\) | 201.265 | + | 322.122i | 1.10585 | + | 1.76990i | ||||
\(183\) | −126.756 | −0.692656 | ||||||||
\(184\) | 8.52961 | − | 14.7737i | 0.0463566 | − | 0.0802920i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 85.4963 | + | 148.084i | 0.459658 | + | 0.796150i | ||||
\(187\) | 163.829 | + | 94.5869i | 0.876093 | + | 0.505812i | ||||
\(188\) | − | 9.50241i | − | 0.0505447i | ||||||
\(189\) | 17.0775 | − | 32.1148i | 0.0903569 | − | 0.169920i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0561 | − | 17.4177i | 0.0526499 | − | 0.0911923i | −0.838499 | − | 0.544903i | \(-0.816567\pi\) |
0.891149 | + | 0.453710i | \(0.149900\pi\) | |||||||
\(192\) | −7.34516 | + | 4.24073i | −0.0382560 | + | 0.0220871i | ||||
\(193\) | 14.3516 | + | 24.8578i | 0.0743609 | + | 0.128797i | 0.900808 | − | 0.434217i | \(-0.142975\pi\) |
−0.826447 | + | 0.563014i | \(0.809642\pi\) | |||||||
\(194\) | 161.084 | + | 93.0019i | 0.830330 | + | 0.479391i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 50.5420 | − | 103.604i | 0.257867 | − | 0.528594i | ||||
\(197\) | −224.436 | −1.13927 | −0.569636 | − | 0.821897i | \(-0.692916\pi\) | ||||
−0.569636 | + | 0.821897i | \(0.692916\pi\) | |||||||
\(198\) | 32.9699 | − | 57.1056i | 0.166515 | − | 0.288412i | ||||
\(199\) | −275.447 | + | 159.030i | −1.38416 | + | 0.799144i | −0.992649 | − | 0.121030i | \(-0.961380\pi\) |
−0.391509 | + | 0.920174i | \(0.628047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −150.798 | − | 87.0635i | −0.750241 | − | 0.433152i | ||||
\(202\) | 269.569i | 1.33450i | ||||||||
\(203\) | −314.330 | − | 167.149i | −1.54842 | − | 0.823393i | ||||
\(204\) | −88.3913 | −0.433290 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −47.0148 | + | 27.1440i | −0.228227 | + | 0.131767i | ||||
\(207\) | −6.16262 | − | 10.6740i | −0.0297711 | − | 0.0515651i | ||||
\(208\) | 370.569 | + | 213.948i | 1.78158 | + | 1.02860i | ||||
\(209\) | − | 27.3486i | − | 0.130855i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 285.317 | 1.35221 | 0.676107 | − | 0.736804i | \(-0.263666\pi\) | ||||
0.676107 | + | 0.736804i | \(0.263666\pi\) | |||||||
\(212\) | 5.23662 | − | 9.07009i | 0.0247010 | − | 0.0427835i | ||||
\(213\) | −85.0463 | + | 49.1015i | −0.399278 | + | 0.230523i | ||||
\(214\) | −112.961 | − | 195.655i | −0.527857 | − | 0.914276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 21.5758i | − | 0.0998880i | ||||||
\(217\) | −274.016 | + | 9.55740i | −1.26275 | + | 0.0440433i | ||||
\(218\) | −68.9341 | −0.316211 | ||||||||
\(219\) | −64.8042 | + | 112.244i | −0.295910 | + | 0.512531i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 233.504 | + | 404.441i | 1.05658 | + | 1.83005i | ||||
\(222\) | −200.303 | − | 115.645i | −0.902266 | − | 0.520923i | ||||
\(223\) | 57.0977i | 0.256044i | 0.991771 | + | 0.128022i | \(0.0408627\pi\) | ||||
−0.991771 | + | 0.128022i | \(0.959137\pi\) | |||||||
\(224\) | −8.17078 | − | 234.261i | −0.0364767 | − | 1.04581i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 116.365 | − | 201.549i | 0.514888 | − | 0.891812i | ||||
\(227\) | 158.185 | − | 91.3279i | 0.696848 | − | 0.402325i | −0.109324 | − | 0.994006i | \(-0.534869\pi\) |
0.806172 | + | 0.591681i | \(0.201535\pi\) | |||||||
\(228\) | 6.38930 | + | 11.0666i | 0.0280233 | + | 0.0485377i | ||||
\(229\) | −14.5347 | − | 8.39159i | −0.0634702 | − | 0.0366445i | 0.467929 | − | 0.883766i | \(-0.345000\pi\) |
−0.531399 | + | 0.847121i | \(0.678334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 56.0263 | + | 89.6691i | 0.242538 | + | 0.388178i | ||||
\(232\) | −211.177 | −0.910246 | ||||||||
\(233\) | −133.203 | + | 230.715i | −0.571688 | + | 0.990193i | 0.424704 | + | 0.905332i | \(0.360378\pi\) |
−0.996393 | + | 0.0848612i | \(0.972955\pi\) | |||||||
\(234\) | 140.975 | − | 81.3920i | 0.602457 | − | 0.347829i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −191.741 | − | 110.702i | −0.812461 | − | 0.469075i | ||||
\(237\) | 50.1960i | 0.211797i | ||||||||
\(238\) | 179.690 | − | 337.914i | 0.755001 | − | 1.41981i | ||||
\(239\) | −39.7012 | −0.166114 | −0.0830568 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830568 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 72.1896 | − | 41.6787i | 0.299542 | − | 0.172941i | −0.342695 | − | 0.939447i | \(-0.611340\pi\) |
0.642237 | + | 0.766506i | \(0.278006\pi\) | |||||||
\(242\) | −56.6454 | − | 98.1128i | −0.234072 | − | 0.405425i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 172.166i | 0.705600i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −160.704 | −0.653267 | ||||||||
\(247\) | 33.7574 | − | 58.4695i | 0.136670 | − | 0.236719i | ||||
\(248\) | −140.850 | + | 81.3200i | −0.567945 | + | 0.327903i | ||||
\(249\) | 18.2832 | + | 31.6675i | 0.0734266 | + | 0.127179i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 111.464i | 0.444079i | 0.975038 | + | 0.222039i | \(0.0712713\pi\) | ||||
−0.975038 | + | 0.222039i | \(0.928729\pi\) | |||||||
\(252\) | −43.6199 | − | 23.1954i | −0.173095 | − | 0.0920454i | ||||
\(253\) | 35.8283 | 0.141614 | ||||||||
\(254\) | −241.446 | + | 418.197i | −0.950575 | + | 1.64644i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −163.039 | − | 282.392i | −0.636872 | − | 1.10309i | ||||
\(257\) | 193.043 | + | 111.454i | 0.751141 | + | 0.433672i | 0.826106 | − | 0.563515i | \(-0.190551\pi\) |
−0.0749649 | + | 0.997186i | \(0.523884\pi\) | |||||||
\(258\) | 77.0531i | 0.298656i | ||||||||
\(259\) | 314.522 | − | 196.517i | 1.21437 | − | 0.758754i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −76.2875 | + | 132.134i | −0.292289 | + | 0.506260i | ||||
\(262\) | 128.373 | − | 74.1161i | 0.489973 | − | 0.282886i | ||||
\(263\) | −213.250 | − | 369.360i | −0.810837 | − | 1.40441i | −0.912279 | − | 0.409569i | \(-0.865679\pi\) |
0.101442 | − | 0.994841i | \(-0.467654\pi\) | |||||||
\(264\) | 54.3161 | + | 31.3594i | 0.205743 | + | 0.118786i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −55.2957 | + | 1.92865i | −0.207879 | + | 0.00725058i | ||||
\(267\) | 126.213 | 0.472709 | ||||||||
\(268\) | −118.254 | + | 204.822i | −0.441246 | + | 0.764260i | ||||
\(269\) | −51.5210 | + | 29.7457i | −0.191528 | + | 0.110579i | −0.592698 | − | 0.805425i | \(-0.701937\pi\) |
0.401170 | + | 0.916004i | \(0.368604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −47.1819 | − | 27.2405i | −0.174103 | − | 0.100518i | 0.410416 | − | 0.911898i | \(-0.365383\pi\) |
−0.584519 | + | 0.811380i | \(0.698717\pi\) | |||||||
\(272\) | − | 431.153i | − | 1.58512i | ||||||
\(273\) | 9.09858 | + | 260.862i | 0.0333281 | + | 0.955538i | ||||
\(274\) | 418.175 | 1.52618 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.4979 | + | 8.37037i | −0.0525287 | + | 0.0303274i | ||||
\(277\) | −236.189 | − | 409.092i | −0.852669 | − | 1.47687i | −0.878791 | − | 0.477207i | \(-0.841649\pi\) |
0.0261222 | − | 0.999659i | \(-0.491684\pi\) | |||||||
\(278\) | 304.766 | + | 175.957i | 1.09628 | + | 0.632939i | ||||
\(279\) | 117.507i | 0.421172i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −534.544 | −1.90229 | −0.951146 | − | 0.308743i | \(-0.900092\pi\) | ||||
−0.951146 | + | 0.308743i | \(0.900092\pi\) | |||||||
\(282\) | 8.81655 | − | 15.2707i | 0.0312644 | − | 0.0541515i | ||||
\(283\) | 387.352 | − | 223.638i | 1.36873 | − | 0.790239i | 0.377967 | − | 0.925819i | \(-0.376623\pi\) |
0.990766 | + | 0.135580i | \(0.0432899\pi\) | |||||||
\(284\) | 66.6921 | + | 115.514i | 0.234831 | + | 0.406740i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 473.198i | 1.65454i | ||||||||
\(287\) | 120.985 | − | 227.517i | 0.421552 | − | 0.792743i | ||||
\(288\) | −100.459 | −0.348815 | ||||||||
\(289\) | 90.7814 | − | 157.238i | 0.314122 | − | 0.544076i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 63.9114 | + | 110.698i | 0.219627 | + | 0.380405i | ||||
\(292\) | 152.456 | + | 88.0202i | 0.522108 | + | 0.301439i | ||||
\(293\) | − | 504.200i | − | 1.72082i | −0.509604 | − | 0.860409i | \(-0.670208\pi\) | ||
0.509604 | − | 0.860409i | \(-0.329792\pi\) | |||||||
\(294\) | 177.349 | − | 119.602i | 0.603229 | − | 0.406810i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 109.996 | − | 190.519i | 0.371608 | − | 0.643644i | ||||
\(297\) | 39.2432 | − | 22.6571i | 0.132132 | − | 0.0762865i | ||||
\(298\) | −18.0680 | − | 31.2946i | −0.0606308 | − | 0.105016i | ||||
\(299\) | 76.5986 | + | 44.2242i | 0.256183 | + | 0.147907i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −109.088 | − | 58.0092i | −0.362420 | − | 0.192722i | ||||
\(302\) | −535.274 | −1.77243 | ||||||||
\(303\) | −92.6245 | + | 160.430i | −0.305692 | + | 0.529473i | ||||
\(304\) | −53.9804 | + | 31.1656i | −0.177567 | + | 0.102518i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −142.048 | − | 82.0114i | −0.464209 | − | 0.268011i | ||||
\(307\) | 398.792i | 1.29900i | 0.760363 | + | 0.649499i | \(0.225021\pi\) | ||||
−0.760363 | + | 0.649499i | \(0.774979\pi\) | |||||||
\(308\) | 121.793 | − | 76.0976i | 0.395432 | − | 0.247070i | ||||
\(309\) | −37.3070 | −0.120735 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −207.085 | + | 119.561i | −0.665869 | + | 0.384440i | −0.794510 | − | 0.607252i | \(-0.792272\pi\) |
0.128640 | + | 0.991691i | \(0.458939\pi\) | |||||||
\(312\) | 77.4162 | + | 134.089i | 0.248129 | + | 0.429772i | ||||
\(313\) | −193.296 | − | 111.599i | −0.617559 | − | 0.356548i | 0.158359 | − | 0.987382i | \(-0.449380\pi\) |
−0.775918 | + | 0.630834i | \(0.782713\pi\) | |||||||
\(314\) | − | 612.257i | − | 1.94986i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 68.1786 | 0.215755 | ||||||||
\(317\) | −143.007 | + | 247.695i | −0.451126 | + | 0.781373i | −0.998456 | − | 0.0555434i | \(-0.982311\pi\) |
0.547330 | + | 0.836917i | \(0.315644\pi\) | |||||||
\(318\) | 16.8309 | − | 9.71731i | 0.0529273 | − | 0.0305576i | ||||
\(319\) | −221.761 | − | 384.100i | −0.695174 | − | 1.20408i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 155.255i | − | 0.483662i | ||||||
\(322\) | −2.52665 | − | 72.4407i | −0.00784675 | − | 0.224971i | ||||
\(323\) | −68.0286 | −0.210615 | ||||||||
\(324\) | −10.5865 | + | 18.3364i | −0.0326744 | + | 0.0565937i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.6784 | − | 28.8878i | −0.0511607 | − | 0.0886129i | ||||
\(327\) | −41.0252 | − | 23.6859i | −0.125459 | − | 0.0724340i | ||||
\(328\) | − | 152.854i | − | 0.466018i | ||||||
\(329\) | 14.9821 | + | 23.9786i | 0.0455383 | + | 0.0728833i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −269.512 | + | 466.809i | −0.814236 | + | 1.41030i | 0.0956391 | + | 0.995416i | \(0.469511\pi\) |
−0.909875 | + | 0.414882i | \(0.863823\pi\) | |||||||
\(332\) | 43.0123 | − | 24.8332i | 0.129555 | − | 0.0747987i | ||||
\(333\) | −79.4718 | − | 137.649i | −0.238654 | − | 0.413361i | ||||
\(334\) | 464.088 | + | 267.941i | 1.38948 | + | 0.802219i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 113.142 | − | 212.768i | 0.336733 | − | 0.633238i | ||||
\(337\) | −68.2484 | −0.202518 | −0.101259 | − | 0.994860i | \(-0.532287\pi\) | ||||
−0.101259 | + | 0.994860i | \(0.532287\pi\) | |||||||
\(338\) | −371.109 | + | 642.780i | −1.09796 | + | 1.90172i | ||||
\(339\) | 138.506 | − | 79.9664i | 0.408572 | − | 0.235889i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −295.819 | − | 170.791i | −0.867503 | − | 0.500853i | ||||
\(342\) | 23.7126i | 0.0693350i | ||||||||
\(343\) | 35.8105 | + | 341.126i | 0.104404 | + | 0.994535i | ||||
\(344\) | −73.2893 | −0.213050 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 543.041 | − | 313.525i | 1.56948 | − | 0.906141i | ||||
\(347\) | 190.947 | + | 330.731i | 0.550281 | + | 0.953114i | 0.998254 | + | 0.0590672i | \(0.0188126\pi\) |
−0.447973 | + | 0.894047i | \(0.647854\pi\) | |||||||
\(348\) | 179.470 | + | 103.617i | 0.515720 | + | 0.297751i | ||||
\(349\) | − | 301.869i | − | 0.864953i | −0.901645 | − | 0.432477i | \(-0.857640\pi\) | ||
0.901645 | − | 0.432477i | \(-0.142360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 111.866 | 0.318706 | ||||||||
\(352\) | 146.012 | − | 252.900i | 0.414807 | − | 0.718466i | ||||
\(353\) | −110.891 | + | 64.0227i | −0.314138 | + | 0.181367i | −0.648776 | − | 0.760979i | \(-0.724719\pi\) |
0.334639 | + | 0.942346i | \(0.391386\pi\) | |||||||
\(354\) | −205.423 | − | 355.803i | −0.580291 | − | 1.00509i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 171.429i | − | 0.481542i | ||||||
\(357\) | 223.048 | − | 139.363i | 0.624786 | − | 0.390373i | ||||
\(358\) | −139.305 | −0.389120 | ||||||||
\(359\) | 262.113 | − | 453.993i | 0.730119 | − | 1.26460i | −0.226713 | − | 0.973962i | \(-0.572798\pi\) |
0.956832 | − | 0.290642i | \(-0.0938688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −175.583 | − | 304.118i | −0.486378 | − | 0.842432i | ||||
\(362\) | −102.371 | − | 59.1041i | −0.282794 | − | 0.163271i | ||||
\(363\) | − | 77.8541i | − | 0.214474i | ||||||
\(364\) | 354.315 | − | 12.3581i | 0.973394 | − | 0.0339509i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −159.740 | + | 276.677i | −0.436448 | + | 0.755949i | ||||
\(367\) | −30.8202 | + | 17.7941i | −0.0839789 | + | 0.0484852i | −0.541401 | − | 0.840764i | \(-0.682106\pi\) |
0.457423 | + | 0.889249i | \(0.348773\pi\) | |||||||
\(368\) | −40.8288 | − | 70.7176i | −0.110948 | − | 0.192167i | ||||
\(369\) | −95.6408 | − | 55.2182i | −0.259189 | − | 0.149643i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.08627 | + | 31.1441i | 0.00292796 | + | 0.0839462i | ||||
\(372\) | 159.604 | 0.429042 | ||||||||
\(373\) | −133.546 | + | 231.308i | −0.358031 | + | 0.620128i | −0.987632 | − | 0.156791i | \(-0.949885\pi\) |
0.629601 | + | 0.776919i | \(0.283219\pi\) | |||||||
\(374\) | 412.920 | − | 238.399i | 1.10406 | − | 0.637432i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.5248 | + | 8.38588i | 0.0386297 | + | 0.0223029i | ||||
\(377\) | − | 1094.91i | − | 2.90427i | ||||||
\(378\) | −48.5775 | − | 77.7474i | −0.128512 | − | 0.205681i | ||||
\(379\) | −125.687 | −0.331627 | −0.165813 | − | 0.986157i | \(-0.553025\pi\) | ||||
−0.165813 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −287.387 | + | 165.923i | −0.754297 | + | 0.435493i | ||||
\(382\) | −25.3457 | − | 43.9001i | −0.0663501 | − | 0.114922i | ||||
\(383\) | 308.755 | + | 178.260i | 0.806149 | + | 0.465430i | 0.845617 | − | 0.533790i | \(-0.179233\pi\) |
−0.0394677 | + | 0.999221i | \(0.512566\pi\) | |||||||
\(384\) | − | 210.622i | − | 0.548496i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 72.3446 | 0.187421 | ||||||||
\(387\) | −26.4757 | + | 45.8572i | −0.0684126 | + | 0.118494i | ||||
\(388\) | 150.355 | − | 86.8076i | 0.387513 | − | 0.223731i | ||||
\(389\) | −223.316 | − | 386.795i | −0.574078 | − | 0.994332i | −0.996141 | − | 0.0877654i | \(-0.972027\pi\) |
0.422064 | − | 0.906566i | \(-0.361306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 89.1216i | − | 0.227933i | ||||||
\(392\) | 113.760 | + | 168.686i | 0.290204 | + | 0.430322i | ||||
\(393\) | 101.866 | 0.259201 | ||||||||
\(394\) | −282.838 | + | 489.890i | −0.717863 | + | 1.24337i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −30.7740 | − | 53.3021i | −0.0777120 | − | 0.134601i | ||||
\(397\) | −525.089 | − | 303.160i | −1.32264 | − | 0.763627i | −0.338492 | − | 0.940969i | \(-0.609917\pi\) |
−0.984149 | + | 0.177342i | \(0.943250\pi\) | |||||||
\(398\) | 801.645i | 2.01418i | ||||||||
\(399\) | −33.5712 | − | 17.8519i | −0.0841384 | − | 0.0447417i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 364.402 | − | 631.163i | 0.908734 | − | 1.57397i | 0.0929080 | − | 0.995675i | \(-0.470384\pi\) |
0.815826 | − | 0.578298i | \(-0.196283\pi\) | |||||||
\(402\) | −380.076 | + | 219.437i | −0.945464 | + | 0.545864i | ||||
\(403\) | −421.627 | − | 730.280i | −1.04622 | − | 1.81211i | ||||
\(404\) | 217.904 | + | 125.807i | 0.539367 | + | 0.311404i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −760.967 | + | 475.461i | −1.87430 | + | 1.17109i | ||||
\(407\) | 462.034 | 1.13522 | ||||||||
\(408\) | 78.0054 | − | 135.109i | 0.191190 | − | 0.331150i | ||||
\(409\) | −459.563 | + | 265.329i | −1.12363 | + | 0.648725i | −0.942324 | − | 0.334702i | \(-0.891364\pi\) |
−0.181301 | + | 0.983428i | \(0.558031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 248.871 | + | 143.686i | 0.605526 | + | 0.349601i | ||||
\(412\) | 50.6722i | 0.122991i | ||||||||
\(413\) | 658.382 | − | 22.9637i | 1.59415 | − | 0.0556021i | ||||
\(414\) | −31.0649 | −0.0750360 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 624.328 | − | 360.456i | 1.50079 | − | 0.866481i | ||||
\(417\) | 120.919 | + | 209.437i | 0.289973 | + | 0.502247i | ||||
\(418\) | −59.6953 | − | 34.4651i | −0.142812 | − | 0.0824524i | ||||
\(419\) | 282.637i | 0.674552i | 0.941406 | + | 0.337276i | \(0.109506\pi\) | ||||
−0.941406 | + | 0.337276i | \(0.890494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 440.590 | 1.04653 | 0.523267 | − | 0.852169i | \(-0.324713\pi\) | ||||
0.523267 | + | 0.852169i | \(0.324713\pi\) | |||||||
\(422\) | 359.560 | − | 622.777i | 0.852039 | − | 1.47577i | ||||
\(423\) | 10.4941 | − | 6.05878i | 0.0248088 | − | 0.0143234i | ||||
\(424\) | 9.24264 | + | 16.0087i | 0.0217987 | + | 0.0377564i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 247.514i | 0.581018i | ||||||||
\(427\) | −271.448 | − | 434.448i | −0.635710 | − | 1.01744i | ||||
\(428\) | −210.875 | −0.492700 | ||||||||
\(429\) | −162.592 | + | 281.617i | −0.379002 | + | 0.656451i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 63.7174 | + | 110.362i | 0.147836 | + | 0.256060i | 0.930427 | − | 0.366476i | \(-0.119436\pi\) |
−0.782591 | + | 0.622536i | \(0.786103\pi\) | |||||||
\(432\) | −89.4407 | − | 51.6386i | −0.207039 | − | 0.119534i | ||||
\(433\) | 433.284i | 1.00066i | 0.865836 | + | 0.500328i | \(0.166787\pi\) | ||||
−0.865836 | + | 0.500328i | \(0.833213\pi\) | |||||||
\(434\) | −324.458 | + | 610.155i | −0.747599 | + | 1.40589i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.1714 | + | 55.7225i | −0.0737876 | + | 0.127804i | ||||
\(437\) | −11.1580 | + | 6.44210i | −0.0255333 | + | 0.0147416i | ||||
\(438\) | 163.334 | + | 282.903i | 0.372909 | + | 0.645898i | ||||
\(439\) | −54.7578 | − | 31.6144i | −0.124733 | − | 0.0720146i | 0.436335 | − | 0.899784i | \(-0.356276\pi\) |
−0.561068 | + | 0.827770i | \(0.689609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 146.643 | − | 10.2419i | 0.332523 | − | 0.0232244i | ||||
\(442\) | 1177.06 | 2.66303 | ||||||||
\(443\) | 219.190 | − | 379.648i | 0.494785 | − | 0.856992i | −0.505197 | − | 0.863004i | \(-0.668580\pi\) |
0.999982 | + | 0.00601155i | \(0.00191355\pi\) | |||||||
\(444\) | −186.962 | + | 107.942i | −0.421085 | + | 0.243114i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 124.630 | + | 71.9553i | 0.279440 | + | 0.161335i | ||||
\(447\) | − | 24.8328i | − | 0.0555544i | ||||||
\(448\) | −30.2645 | − | 16.0935i | −0.0675547 | − | 0.0359231i | ||||
\(449\) | 214.986 | 0.478810 | 0.239405 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239405 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 278.019 | − | 160.514i | 0.616450 | − | 0.355907i | ||||
\(452\) | −108.614 | − | 188.125i | −0.240297 | − | 0.416207i | ||||
\(453\) | −318.561 | − | 183.922i | −0.703226 | − | 0.406008i | ||||
\(454\) | − | 460.371i | − | 1.01403i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.5543 | −0.0494611 | ||||||||
\(457\) | −120.600 | + | 208.885i | −0.263894 | + | 0.457078i | −0.967273 | − | 0.253737i | \(-0.918340\pi\) |
0.703379 | + | 0.710815i | \(0.251674\pi\) | |||||||
\(458\) | −36.6336 | + | 21.1504i | −0.0799860 | + | 0.0461799i | ||||
\(459\) | −56.3587 | − | 97.6161i | −0.122786 | − | 0.212671i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 343.383i | − | 0.744865i | −0.928059 | − | 0.372432i | \(-0.878524\pi\) | ||
0.928059 | − | 0.372432i | \(-0.121476\pi\) | |||||||
\(462\) | 266.331 | − | 9.28933i | 0.576473 | − | 0.0201068i | ||||
\(463\) | −74.7714 | −0.161493 | −0.0807467 | − | 0.996735i | \(-0.525730\pi\) | ||||
−0.0807467 | + | 0.996735i | \(0.525730\pi\) | |||||||
\(464\) | −505.422 | + | 875.417i | −1.08927 | + | 1.88667i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 335.730 | + | 581.501i | 0.720450 | + | 1.24786i | ||||
\(467\) | 308.470 | + | 178.095i | 0.660535 | + | 0.381360i | 0.792481 | − | 0.609897i | \(-0.208789\pi\) |
−0.131946 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(468\) | − | 151.942i | − | 0.324662i | ||||||
\(469\) | −24.5303 | − | 703.298i | −0.0523034 | − | 1.49957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 210.373 | − | 364.377i | 0.446652 | − | 0.773624i | ||||
\(472\) | 338.423 | − | 195.389i | 0.716998 | − | 0.413959i | ||||
\(473\) | −76.9623 | − | 133.303i | −0.162711 | − | 0.281824i | ||||
\(474\) | 109.565 | + | 63.2577i | 0.231151 | + | 0.133455i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −189.290 | − | 302.955i | −0.397668 | − | 0.636461i | ||||
\(477\) | 13.3556 | 0.0279991 | ||||||||
\(478\) | −50.0319 | + | 86.6579i | −0.104669 | + | 0.181293i | ||||
\(479\) | 323.678 | − | 186.876i | 0.675737 | − | 0.390137i | −0.122510 | − | 0.992467i | \(-0.539094\pi\) |
0.798247 | + | 0.602330i | \(0.205761\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 987.799 | + | 570.306i | 2.05364 | + | 1.18567i | ||||
\(482\) | − | 210.096i | − | 0.435884i | ||||||
\(483\) | 23.3871 | − | 43.9803i | 0.0484205 | − | 0.0910565i | ||||
\(484\) | −105.745 | −0.218482 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.0258 | + | 19.6448i | −0.0700119 | + | 0.0404214i | ||||
\(487\) | 388.781 | + | 673.389i | 0.798319 | + | 1.38273i | 0.920710 | + | 0.390247i | \(0.127610\pi\) |
−0.122391 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(488\) | −263.162 | − | 151.937i | −0.539267 | − | 0.311346i | ||||
\(489\) | − | 22.9229i | − | 0.0468772i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 458.794 | 0.934407 | 0.467203 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467203 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(492\) | −75.0001 | + | 129.904i | −0.152439 | + | 0.264032i | ||||
\(493\) | −955.435 | + | 551.621i | −1.93800 | + | 1.11891i | ||||
\(494\) | −85.0831 | − | 147.368i | −0.172233 | − | 0.298316i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 778.511i | 1.56958i | ||||||||
\(497\) | −350.419 | − | 186.340i | −0.705068 | − | 0.374929i | ||||
\(498\) | 92.1631 | 0.185066 | ||||||||
\(499\) | −317.772 | + | 550.396i | −0.636817 | + | 1.10300i | 0.349310 | + | 0.937007i | \(0.386416\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 184.131 | + | 318.924i | 0.367526 | + | 0.636574i | ||||
\(502\) | 243.298 | + | 140.468i | 0.484657 | + | 0.279817i | ||||
\(503\) | − | 10.6561i | − | 0.0211852i | −0.999944 | − | 0.0105926i | \(-0.996628\pi\) | ||
0.999944 | − | 0.0105926i | \(-0.00337179\pi\) | |||||||
\(504\) | 73.9496 | − | 46.2046i | 0.146725 | − | 0.0916757i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 45.1514 | − | 78.2045i | 0.0892319 | − | 0.154554i | ||||
\(507\) | −441.722 | + | 255.028i | −0.871246 | + | 0.503014i | ||||
\(508\) | 225.365 | + | 390.343i | 0.443631 | + | 0.768392i | ||||
\(509\) | 706.084 | + | 407.658i | 1.38720 | + | 0.800899i | 0.992999 | − | 0.118126i | \(-0.0376885\pi\) |
0.394200 | + | 0.919025i | \(0.371022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −523.488 | + | 18.2587i | −1.02444 | + | 0.0357313i | ||||
\(512\) | −335.445 | −0.655167 | ||||||||
\(513\) | −8.14770 | + | 14.1122i | −0.0158825 | + | 0.0275092i | ||||
\(514\) | 486.552 | − | 280.911i | 0.946599 | − | 0.546519i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 62.2855 | + | 35.9605i | 0.120708 | + | 0.0696909i | ||||
\(517\) | 35.2246i | 0.0681327i | ||||||||
\(518\) | −32.5832 | − | 934.179i | −0.0629019 | − | 1.80343i | ||||
\(519\) | 430.911 | 0.830273 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −383.930 | + | 221.662i | −0.736911 | + | 0.425456i | −0.820945 | − | 0.571007i | \(-0.806553\pi\) |
0.0840344 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(522\) | 192.277 | + | 333.034i | 0.368347 | + | 0.637995i | ||||
\(523\) | 549.148 | + | 317.051i | 1.05000 | + | 0.606216i | 0.922648 | − | 0.385642i | \(-0.126020\pi\) |
0.127348 | + | 0.991858i | \(0.459354\pi\) | |||||||
\(524\) | − | 138.359i | − | 0.264044i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1074.96 | −2.04366 | ||||||||
\(527\) | −424.836 | + | 735.837i | −0.806140 | + | 1.39628i | ||||
\(528\) | 259.996 | − | 150.109i | 0.492416 | − | 0.284297i | ||||
\(529\) | 256.060 | + | 443.510i | 0.484046 | + | 0.838393i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 282.335i | − | 0.531705i | ||||||
\(532\) | −24.2474 | + | 45.5980i | −0.0455777 | + | 0.0857106i | ||||
\(533\) | 792.515 | 1.48689 | ||||||||
\(534\) | 159.056 | − | 275.492i | 0.297857 | − | 0.515903i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −208.718 | − | 361.511i | −0.389400 | − | 0.674460i | ||||
\(537\) | −82.9055 | − | 47.8655i | −0.154386 | − | 0.0891351i | ||||
\(538\) | 149.944i | 0.278706i | ||||||||
\(539\) | −187.355 | + | 384.053i | −0.347597 | + | 0.712528i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 87.5750 | − | 151.684i | 0.161876 | − | 0.280378i | −0.773665 | − | 0.633594i | \(-0.781579\pi\) |
0.935542 | + | 0.353217i | \(0.114912\pi\) | |||||||
\(542\) | −118.919 | + | 68.6577i | −0.219407 | + | 0.126675i | ||||
\(543\) | −40.6167 | − | 70.3501i | −0.0748005 | − | 0.129558i | ||||
\(544\) | −629.079 | − | 363.199i | −1.15640 | − | 0.667646i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 580.864 | + | 308.882i | 1.06385 | + | 0.565718i | ||||
\(547\) | 773.543 | 1.41416 | 0.707078 | − | 0.707136i | \(-0.250013\pi\) | ||||
0.707078 | + | 0.707136i | \(0.250013\pi\) | |||||||
\(548\) | 195.161 | − | 338.029i | 0.356133 | − | 0.616841i | ||||
\(549\) | −190.134 | + | 109.774i | −0.346328 | + | 0.199953i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 138.126 | + | 79.7471i | 0.250682 | + | 0.144732i | ||||
\(552\) | − | 29.5474i | − | 0.0535280i | ||||||
\(553\) | −172.043 | + | 107.495i | −0.311109 | + | 0.194385i | ||||
\(554\) | −1190.60 | −2.14909 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 284.468 | − | 164.237i | 0.511632 | − | 0.295391i | ||||
\(557\) | −378.264 | − | 655.173i | −0.679110 | − | 1.17625i | −0.975249 | − | 0.221108i | \(-0.929033\pi\) |
0.296140 | − | 0.955145i | \(-0.404301\pi\) | |||||||
\(558\) | 256.489 | + | 148.084i | 0.459658 | + | 0.265383i | ||||
\(559\) | − | 379.989i | − | 0.679766i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 327.659 | 0.584062 | ||||||||
\(562\) | −673.639 | + | 1166.78i | −1.19865 | + | 2.07612i | ||||
\(563\) | 451.185 | − | 260.492i | 0.801394 | − | 0.462685i | −0.0425646 | − | 0.999094i | \(-0.513553\pi\) |
0.843958 | + | 0.536409i | \(0.180219\pi\) | |||||||
\(564\) | −8.22933 | − | 14.2536i | −0.0145910 | − | 0.0252724i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1127.32i | − | 1.99174i | ||||||
\(567\) | −2.19604 | − | 62.9617i | −0.00387308 | − | 0.111044i | ||||
\(568\) | −235.423 | −0.414477 | ||||||||
\(569\) | 91.5332 | − | 158.540i | 0.160867 | − | 0.278629i | −0.774313 | − | 0.632803i | \(-0.781904\pi\) |
0.935180 | + | 0.354173i | \(0.115238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −498.800 | − | 863.947i | −0.873555 | − | 1.51304i | −0.858294 | − | 0.513159i | \(-0.828475\pi\) |
−0.0152618 | − | 0.999884i | \(-0.504858\pi\) | |||||||
\(572\) | 382.507 | + | 220.840i | 0.668718 | + | 0.386084i | ||||
\(573\) | − | 34.8355i | − | 0.0607949i | ||||||
\(574\) | −344.147 | − | 550.802i | −0.599560 | − | 0.959585i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.34516 | + | 12.7222i | −0.0127520 | + | 0.0220871i | ||||
\(577\) | −279.135 | + | 161.158i | −0.483769 | + | 0.279304i | −0.721986 | − | 0.691908i | \(-0.756770\pi\) |
0.238217 | + | 0.971212i | \(0.423437\pi\) | |||||||
\(578\) | −228.808 | − | 396.307i | −0.395861 | − | 0.685652i | ||||
\(579\) | 43.0549 | + | 24.8578i | 0.0743609 | + | 0.0429323i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −69.3847 | + | 130.480i | −0.119423 | + | 0.224579i | ||||
\(582\) | 322.168 | 0.553553 | ||||||||
\(583\) | −19.4117 | + | 33.6220i | −0.0332962 | + | 0.0576707i | ||||
\(584\) | −269.084 | + | 155.356i | −0.460761 | + | 0.266020i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1100.54 | − | 635.400i | −1.87806 | − | 1.08430i | ||||
\(587\) | − | 406.391i | − | 0.692318i | −0.938176 | − | 0.346159i | \(-0.887486\pi\) | ||
0.938176 | − | 0.346159i | \(-0.112514\pi\) | |||||||
\(588\) | −13.9111 | − | 199.177i | −0.0236583 | − | 0.338737i | ||||
\(589\) | 122.836 | 0.208550 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −336.655 | + | 194.368i | −0.569636 | + | 0.328879i | ||||
\(592\) | −526.519 | − | 911.958i | −0.889391 | − | 1.54047i | ||||
\(593\) | −333.688 | − | 192.655i | −0.562711 | − | 0.324881i | 0.191522 | − | 0.981488i | \(-0.438658\pi\) |
−0.754233 | + | 0.656607i | \(0.771991\pi\) | |||||||
\(594\) | − | 114.211i | − | 0.192275i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.7291 | −0.0565925 | ||||||||
\(597\) | −275.447 | + | 477.089i | −0.461386 | + | 0.799144i | ||||
\(598\) | 193.061 | − | 111.464i | 0.322845 | − | 0.186395i | ||||
\(599\) | 448.272 | + | 776.430i | 0.748367 | + | 1.29621i | 0.948605 | + | 0.316463i | \(0.102495\pi\) |
−0.200238 | + | 0.979747i | \(0.564171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 599.296i | 0.997166i | 0.866842 | + | 0.498583i | \(0.166146\pi\) | ||||
−0.866842 | + | 0.498583i | \(0.833854\pi\) | |||||||
\(602\) | −264.095 | + | 165.009i | −0.438695 | + | 0.274102i | ||||
\(603\) | −301.597 | −0.500161 | ||||||||
\(604\) | −249.811 | + | 432.686i | −0.413595 | + | 0.716367i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 233.453 | + | 404.353i | 0.385237 | + | 0.667250i | ||||
\(607\) | 426.925 | + | 246.485i | 0.703336 | + | 0.406071i | 0.808589 | − | 0.588374i | \(-0.200232\pi\) |
−0.105253 | + | 0.994445i | \(0.533565\pi\) | |||||||
\(608\) | 105.014i | 0.172721i | ||||||||
\(609\) | −616.249 | + | 21.4941i | −1.01190 | + | 0.0352941i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.4790 | + | 75.3079i | −0.0711604 | + | 0.123253i | ||||
\(612\) | −132.587 | + | 76.5491i | −0.216645 | + | 0.125080i | ||||
\(613\) | −70.4822 | − | 122.079i | −0.114979 | − | 0.199150i | 0.802792 | − | 0.596259i | \(-0.203347\pi\) |
−0.917771 | + | 0.397109i | \(0.870013\pi\) | |||||||
\(614\) | 870.465 | + | 502.563i | 1.41770 | + | 0.818507i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.83557 | + | 253.321i | 0.0143435 | + | 0.411236i | ||||
\(617\) | −61.9853 | −0.100462 | −0.0502312 | − | 0.998738i | \(-0.515996\pi\) | ||||
−0.0502312 | + | 0.998738i | \(0.515996\pi\) | |||||||
\(618\) | −47.0148 | + | 81.4321i | −0.0760758 | + | 0.131767i | ||||
\(619\) | −549.456 | + | 317.228i | −0.887651 | + | 0.512485i | −0.873173 | − | 0.487410i | \(-0.837942\pi\) |
−0.0144774 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4879 | − | 10.6740i | −0.0297711 | − | 0.0171884i | ||||
\(622\) | 602.689i | 0.968953i | ||||||||
\(623\) | 270.286 | + | 432.588i | 0.433845 | + | 0.694362i | ||||
\(624\) | 741.138 | 1.18772 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −487.188 | + | 281.278i | −0.778256 | + | 0.449326i | ||||
\(627\) | −23.6846 | − | 41.0229i | −0.0377745 | − | 0.0654273i | ||||
\(628\) | −494.914 | − | 285.739i | −0.788080 | − | 0.454998i | ||||
\(629\) | − | 1149.29i | − | 1.82717i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 93.3216 | 0.147895 | 0.0739474 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739474 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(632\) | −60.1677 | + | 104.213i | −0.0952020 | + | 0.164895i | ||||
\(633\) | 427.976 | − | 247.092i | 0.676107 | − | 0.390350i | ||||
\(634\) | 360.439 | + | 624.298i | 0.568515 | + | 0.984698i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 18.1402i | − | 0.0285223i | ||||||
\(637\) | −874.603 | + | 589.821i | −1.37300 | + | 0.925935i | ||||
\(638\) | −1117.86 | −1.75214 | ||||||||
\(639\) | −85.0463 | + | 147.305i | −0.133093 | + | 0.230523i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −153.961 | − | 266.668i | −0.240188 | − | 0.416018i | 0.720579 | − | 0.693372i | \(-0.243876\pi\) |
−0.960768 | + | 0.277354i | \(0.910543\pi\) | |||||||
\(642\) | −338.884 | − | 195.655i | −0.527857 | − | 0.304759i | ||||
\(643\) | 296.519i | 0.461150i | 0.973055 | + | 0.230575i | \(0.0740607\pi\) | ||||
−0.973055 | + | 0.230575i | \(0.925939\pi\) | |||||||
\(644\) | −59.7362 | − | 31.7655i | −0.0927581 | − | 0.0493253i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −85.7306 | + | 148.490i | −0.132710 | + | 0.229860i | ||||
\(647\) | −203.727 | + | 117.622i | −0.314880 | + | 0.181796i | −0.649108 | − | 0.760696i | \(-0.724858\pi\) |
0.334228 | + | 0.942492i | \(0.391524\pi\) | |||||||
\(648\) | −18.6852 | − | 32.3637i | −0.0288352 | − | 0.0499440i | ||||
\(649\) | 710.767 | + | 410.361i | 1.09517 | + | 0.632298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −402.748 | + | 251.641i | −0.618660 | + | 0.386546i | ||||
\(652\) | −31.1350 | −0.0477531 | ||||||||
\(653\) | 148.823 | − | 257.769i | 0.227906 | − | 0.394746i | −0.729281 | − | 0.684214i | \(-0.760145\pi\) |
0.957187 | + | 0.289469i | \(0.0934786\pi\) | |||||||
\(654\) | −103.401 | + | 59.6987i | −0.158106 | + | 0.0912823i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −633.643 | − | 365.834i | −0.965919 | − | 0.557673i | ||||
\(657\) | 224.488i | 0.341687i | ||||||||
\(658\) | 71.2200 | − | 2.48408i | 0.108237 | − | 0.00377519i | ||||
\(659\) | −127.740 | −0.193839 | −0.0969197 | − | 0.995292i | \(-0.530899\pi\) | ||||
−0.0969197 | + | 0.995292i | \(0.530899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −823.610 | + | 475.512i | −1.24601 | + | 0.719382i | −0.970311 | − | 0.241863i | \(-0.922242\pi\) |
−0.275696 | + | 0.961245i | \(0.588908\pi\) | |||||||
\(662\) | 679.286 | + | 1176.56i | 1.02611 | + | 1.77728i | ||||
\(663\) | 700.513 | + | 404.441i | 1.05658 | + | 0.610017i | ||||
\(664\) | 87.6611i | 0.132020i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −400.606 | −0.601510 | ||||||||
\(667\) | −104.474 | + | 180.953i | −0.156632 | + | 0.271295i | ||||
\(668\) | 433.178 | − | 250.095i | 0.648469 | − | 0.374394i | ||||
\(669\) | 49.4481 | + | 85.6466i | 0.0739134 | + | 0.128022i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 638.206i | − | 0.951126i | ||||||
\(672\) | −215.132 | − | 344.316i | −0.320137 | − | 0.512374i | ||||
\(673\) | 1003.39 | 1.49092 | 0.745460 | − | 0.666550i | \(-0.232230\pi\) | ||||
0.745460 | + | 0.666550i | \(0.232230\pi\) | |||||||
\(674\) | −86.0076 | + | 148.970i | −0.127608 | + | 0.221023i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 346.392 | + | 599.968i | 0.512414 | + | 0.887526i | ||||
\(677\) | −408.603 | − | 235.907i | −0.603550 | − | 0.348460i | 0.166887 | − | 0.985976i | \(-0.446629\pi\) |
−0.770437 | + | 0.637516i | \(0.779962\pi\) | |||||||
\(678\) | − | 403.099i | − | 0.594541i | ||||||
\(679\) | −242.543 | + | 456.111i | −0.357206 | + | 0.671740i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 158.185 | − | 273.984i | 0.232283 | − | 0.402325i | ||||
\(682\) | −745.589 | + | 430.466i | −1.09324 | + | 0.631182i | ||||
\(683\) | 208.614 | + | 361.330i | 0.305438 | + | 0.529034i | 0.977359 | − | 0.211589i | \(-0.0678638\pi\) |
−0.671921 | + | 0.740623i | \(0.734530\pi\) | |||||||
\(684\) | 19.1679 | + | 11.0666i | 0.0280233 | + | 0.0161792i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 789.722 | + | 351.726i | 1.15120 | + | 0.512719i | ||||
\(687\) | −29.0693 | −0.0423134 | ||||||||
\(688\) | −175.407 | + | 303.815i | −0.254953 | + | 0.441591i | ||||
\(689\) | −83.0019 | + | 47.9211i | −0.120467 | + | 0.0695517i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 160.907 | + | 92.8995i | 0.232860 | + | 0.134442i | 0.611891 | − | 0.790942i | \(-0.290409\pi\) |
−0.379030 | + | 0.925384i | \(0.623742\pi\) | |||||||
\(692\) | − | 585.285i | − | 0.845787i | ||||||
\(693\) | 161.695 | + | 85.9835i | 0.233326 | + | 0.124074i | ||||
\(694\) | 962.538 | 1.38694 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −316.766 | + | 182.885i | −0.455123 | + | 0.262765i | ||||
\(697\) | −399.273 | − | 691.561i | −0.572845 | − | 0.992197i | ||||
\(698\) | −658.905 | − | 380.419i | −0.943990 | − | 0.545013i | ||||
\(699\) | 461.430i | 0.660129i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1034.80 | 1.47618 | 0.738089 | − | 0.674704i | \(-0.235729\pi\) | ||||
0.738089 | + | 0.674704i | \(0.235729\pi\) | |||||||
\(702\) | 140.975 | − | 244.176i | 0.200819 | − | 0.347829i | ||||
\(703\) | −143.892 | + | 83.0759i | −0.204682 | + | 0.118173i | ||||
\(704\) | −21.3517 | − | 36.9822i | −0.0303291 | − | 0.0525316i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 322.729i | 0.457123i | ||||||||
\(707\) | −748.220 | + | 26.0971i | −1.05830 | + | 0.0369125i | ||||
\(708\) | −383.482 | −0.541641 | ||||||||
\(709\) | 108.321 | − | 187.618i | 0.152780 | − | 0.264623i | −0.779468 | − | 0.626442i | \(-0.784511\pi\) |
0.932248 | + | 0.361819i | \(0.117844\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.4710 | + | 75.2940i | 0.0611406 | + | 0.105899i | ||||
\(712\) | 262.035 | + | 151.286i | 0.368027 | + | 0.212481i | ||||
\(713\) | 160.923i | 0.225698i | ||||||||
\(714\) | −23.1069 | − | 662.487i | −0.0323625 | − | 0.927854i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −65.0133 | + | 112.606i | −0.0908007 | + | 0.157271i | ||||
\(717\) | −59.5517 | + | 34.3822i | −0.0830568 | + | 0.0479529i | ||||
\(718\) | −660.636 | − | 1144.26i | −0.920106 | − | 1.59367i | ||||
\(719\) | 0.325449 | + | 0.187898i | 0.000452641 | + | 0.000261332i | 0.500226 | − | 0.865895i | \(-0.333250\pi\) |
−0.499774 | + | 0.866156i | \(0.666583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −79.8930 | − | 127.867i | −0.110809 | − | 0.177347i | ||||
\(722\) | −885.086 | −1.22588 | ||||||||
\(723\) | 72.1896 | − | 125.036i | 0.0998473 | − | 0.172941i | ||||
\(724\) | −95.5530 | + | 55.1675i | −0.131979 | + | 0.0761983i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −169.936 | − | 98.1128i | −0.234072 | − | 0.135142i | ||||
\(727\) | − | 174.857i | − | 0.240518i | −0.992743 | − | 0.120259i | \(-0.961627\pi\) | ||
0.992743 | − | 0.120259i | \(-0.0383726\pi\) | |||||||
\(728\) | −293.794 | + | 552.490i | −0.403563 | + | 0.758915i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −331.585 | + | 191.441i | −0.453605 | + | 0.261889i | ||||
\(732\) | 149.100 | + | 258.249i | 0.203689 | + | 0.352800i | ||||
\(733\) | 738.210 | + | 426.206i | 1.00711 | + | 0.581454i | 0.910344 | − | 0.413853i | \(-0.135817\pi\) |
0.0967645 | + | 0.995307i | \(0.469151\pi\) | |||||||
\(734\) | 89.6973i | 0.122203i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −137.575 | −0.186923 | ||||||||
\(737\) | 438.357 | − | 759.256i | 0.594785 | − | 1.03020i | ||||
\(738\) | −241.056 | + | 139.174i | −0.326634 | + | 0.188582i | ||||
\(739\) | 584.126 | + | 1011.74i | 0.790428 | + | 1.36906i | 0.925702 | + | 0.378253i | \(0.123475\pi\) |
−0.135275 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 116.939i | − | 0.157813i | ||||||
\(742\) | 69.3488 | + | 36.8771i | 0.0934619 | + | 0.0496996i | ||||
\(743\) | 558.877 | 0.752190 | 0.376095 | − | 0.926581i | \(-0.377267\pi\) | ||||
0.376095 | + | 0.926581i | \(0.377267\pi\) | |||||||
\(744\) | −140.850 | + | 243.960i | −0.189315 | + | 0.327903i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 336.592 | + | 582.995i | 0.451196 | + | 0.781494i | ||||
\(747\) | 54.8497 | + | 31.6675i | 0.0734266 | + | 0.0423929i | ||||
\(748\) | − | 445.042i | − | 0.594976i | ||||||
\(749\) | 532.128 | − | 332.479i | 0.710451 | − | 0.443898i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −630.654 | + | 1092.32i | −0.839752 | + | 1.45449i | 0.0503493 | + | 0.998732i | \(0.483967\pi\) |
−0.890102 | + | 0.455762i | \(0.849367\pi\) | |||||||
\(752\) | 69.5260 | − | 40.1408i | 0.0924547 | − | 0.0533788i | ||||
\(753\) | 96.5304 | + | 167.196i | 0.128194 | + | 0.222039i | ||||
\(754\) | −2389.92 | − | 1379.82i | −3.16965 | − | 1.83000i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −85.5177 | + | 2.98276i | −0.113119 | + | 0.00394546i | ||||
\(757\) | 1269.13 | 1.67652 | 0.838262 | − | 0.545268i | \(-0.183572\pi\) | ||||
0.838262 | + | 0.545268i | \(0.183572\pi\) | |||||||
\(758\) | −158.392 | + | 274.343i | −0.208960 | + | 0.361930i | ||||
\(759\) | 53.7425 | − | 31.0282i | 0.0708070 | − | 0.0408804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −157.718 | − | 91.0585i | −0.207251 | − | 0.119656i | 0.392782 | − | 0.919632i | \(-0.371513\pi\) |
−0.600033 | + | 0.799975i | \(0.704846\pi\) | |||||||
\(762\) | 836.394i | 1.09763i | ||||||||
\(763\) | −6.67355 | − | 191.335i | −0.00874646 | − | 0.250766i | ||||
\(764\) | −47.3152 | −0.0619309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 778.195 | − | 449.291i | 1.01592 | − | 0.586542i | ||||
\(767\) | 1013.05 | + | 1754.65i | 1.32079 | + | 2.28768i | ||||
\(768\) | −489.118 | − | 282.392i | −0.636872 | − | 0.367698i | ||||
\(769\) | 810.237i | 1.05362i | 0.849982 | + | 0.526812i | \(0.176613\pi\) | ||||
−0.849982 | + | 0.526812i | \(0.823387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 386.087 | 0.500761 | ||||||||
\(772\) | 33.7630 | − | 58.4793i | 0.0437345 | − | 0.0757504i | ||||
\(773\) | −212.492 | + | 122.682i | −0.274893 | + | 0.158709i | −0.631109 | − | 0.775694i | \(-0.717400\pi\) |
0.356216 | + | 0.934404i | \(0.384067\pi\) | |||||||
\(774\) | 66.7300 | + | 115.580i | 0.0862144 | + | 0.149328i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 306.431i | 0.394885i | ||||||||
\(777\) | 301.595 | − | 567.160i | 0.388153 | − | 0.729936i | ||||
\(778\) | −1125.70 | −1.44692 | ||||||||
\(779\) | −57.7224 | + | 99.9781i | −0.0740981 | + | 0.128342i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −247.222 | − | 428.200i | −0.316545 | − | 0.548272i | ||||
\(782\) | −194.531 | − | 112.312i | −0.248760 | − | 0.143622i | ||||
\(783\) | 264.268i | 0.337506i | ||||||||
\(784\) | 971.543 | − | 67.8553i | 1.23921 | − | 0.0865501i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 128.373 | − | 222.348i | 0.163324 | − | 0.282886i | ||||
\(787\) | 373.020 | − | 215.363i | 0.473977 | − | 0.273651i | −0.243926 | − | 0.969794i | \(-0.578435\pi\) |
0.717903 | + | 0.696143i | \(0.245102\pi\) | |||||||
\(788\) | 264.000 | + | 457.261i | 0.335025 | + | 0.580280i | ||||
\(789\) | −639.750 | − | 369.360i | −0.810837 | − | 0.468137i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 570.690 | + | 303.472i | 0.721479 | + | 0.383656i | ||||
\(792\) | 108.632 | 0.137162 | ||||||||
\(793\) | 787.761 | − | 1364.44i | 0.993393 | − | 1.72061i | ||||
\(794\) | −1323.45 | + | 764.093i | −1.66681 | + | 0.962334i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 648.005 | + | 374.126i | 0.814077 | + | 0.470008i | ||||
\(797\) | − | 1137.61i | − | 1.42737i | −0.700468 | − | 0.713684i | \(-0.747025\pi\) | ||
0.700468 | − | 0.713684i | \(-0.252975\pi\) | |||||||
\(798\) | −81.2733 | + | 50.7805i | −0.101846 | + | 0.0636347i | ||||
\(799\) | 87.6199 | 0.109662 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 189.320 | − | 109.304i | 0.236354 | − | 0.136459i | ||||
\(802\) | −918.449 | − | 1590.80i | −1.14520 | − | 1.98354i | ||||
\(803\) | −565.139 | − | 326.283i | −0.703785 | − | 0.406330i | ||||
\(804\) | 409.643i | 0.509507i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2125.36 | −2.63692 | ||||||||
\(807\) | −51.5210 | + | 89.2370i | −0.0638426 | + | 0.110579i | ||||
\(808\) | −384.602 | + | 222.050i | −0.475992 | + | 0.274814i | ||||
\(809\) | −455.336 | − | 788.665i | −0.562838 | − | 0.974864i | −0.997247 | − | 0.0741482i | \(-0.976376\pi\) |
0.434409 | − | 0.900716i | \(-0.356957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 546.361i | − | 0.673688i | −0.941560 | − | 0.336844i | \(-0.890640\pi\) | ||
0.941560 | − | 0.336844i | \(-0.109360\pi\) | |||||||
\(812\) | 29.1944 | + | 837.020i | 0.0359537 | + | 1.03081i | ||||
\(813\) | −94.3638 | −0.116069 | ||||||||
\(814\) | 582.262 | − | 1008.51i | 0.715309 | − | 1.23895i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −373.389 | − | 646.729i | −0.457585 | − | 0.792560i | ||||
\(817\) | 47.9368 | + | 27.6763i | 0.0586742 | + | 0.0338756i | ||||
\(818\) | 1337.48i | 1.63507i | ||||||||
\(819\) | 239.561 | + | 383.413i | 0.292504 | + | 0.468148i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −322.150 | + | 557.980i | −0.392388 | + | 0.679635i | −0.992764 | − | 0.120082i | \(-0.961684\pi\) |
0.600376 | + | 0.799718i | \(0.295017\pi\) | |||||||
\(822\) | 627.262 | − | 362.150i | 0.763092 | − | 0.440572i | ||||
\(823\) | 384.661 | + | 666.252i | 0.467388 | + | 0.809540i | 0.999306 | − | 0.0372559i | \(-0.0118617\pi\) |
−0.531917 | + | 0.846796i | \(0.678528\pi\) | |||||||
\(824\) | −77.4543 | − | 44.7183i | −0.0939980 | − | 0.0542697i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 779.579 | − | 1466.03i | 0.943800 | − | 1.77485i | ||||
\(827\) | −715.404 | −0.865060 | −0.432530 | − | 0.901620i | \(-0.642379\pi\) | ||||
−0.432530 | + | 0.901620i | \(0.642379\pi\) | |||||||
\(828\) | −14.4979 | + | 25.1111i | −0.0175096 | + | 0.0303274i | ||||
\(829\) | 68.2973 | − | 39.4315i | 0.0823852 | − | 0.0475651i | −0.458241 | − | 0.888828i | \(-0.651521\pi\) |
0.540627 | + | 0.841263i | \(0.318187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −708.568 | − | 409.092i | −0.852669 | − | 0.492289i | ||||
\(832\) | − | 105.421i | − | 0.126708i | ||||||
\(833\) | 955.317 | + | 466.038i | 1.14684 | + | 0.559469i | ||||
\(834\) | 609.533 | 0.730855 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −55.7193 | + | 32.1696i | −0.0666499 | + | 0.0384803i | ||||
\(837\) | 101.764 | + | 176.261i | 0.121582 | + | 0.210586i | ||||
\(838\) | 616.928 | + | 356.184i | 0.736191 | + | 0.425040i | ||||
\(839\) | 165.698i | 0.197494i | 0.995113 | + | 0.0987471i | \(0.0314835\pi\) | ||||
−0.995113 | + | 0.0987471i | \(0.968517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1745.57 | 2.07559 | ||||||||
\(842\) | 555.238 | − | 961.701i | 0.659428 | − | 1.14216i | ||||
\(843\) | −801.816 | + | 462.929i | −0.951146 | + | 0.549144i | ||||
\(844\) | −335.612 | − | 581.297i | −0.397645 | − | 0.688741i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 30.5414i | − | 0.0361010i | ||||||
\(847\) | 266.840 | − | 166.724i | 0.315041 | − | 0.196841i | ||||
\(848\) | 88.4838 | 0.104344 | ||||||||
\(849\) | 387.352 | − | 670.913i | 0.456245 | − | 0.790239i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −108.834 | − | 188.507i | −0.127890 | − | 0.221512i | ||||
\(852\) | 200.076 | + | 115.514i | 0.234831 | + | 0.135580i | ||||
\(853\) | − | 1066.17i | − | 1.24991i | −0.780661 | − | 0.624955i | \(-0.785117\pi\) | ||
0.780661 | − | 0.624955i | \(-0.214883\pi\) | |||||||
\(854\) | −1290.38 | + | 45.0070i | −1.51098 | + | 0.0527014i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 186.098 | − | 322.331i | 0.217404 | − | 0.376555i | ||||
\(857\) | −192.821 | + | 111.325i | −0.224995 | + | 0.129901i | −0.608261 | − | 0.793737i | \(-0.708133\pi\) |
0.383266 | + | 0.923638i | \(0.374799\pi\) | |||||||
\(858\) | 409.801 | + | 709.796i | 0.477624 | + | 0.827269i | ||||
\(859\) | 1313.46 | + | 758.329i | 1.52906 | + | 0.882805i | 0.999401 | + | 0.0345956i | \(0.0110143\pi\) |
0.529661 | + | 0.848209i | \(0.322319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.5578 | − | 446.052i | −0.0180695 | − | 0.518063i | ||||
\(862\) | 321.190 | 0.372610 | ||||||||
\(863\) | 69.0180 | − | 119.543i | 0.0799745 | − | 0.138520i | −0.823264 | − | 0.567658i | \(-0.807849\pi\) |
0.903239 | + | 0.429139i | \(0.141183\pi\) | |||||||
\(864\) | −150.688 | + | 86.9997i | −0.174407 | + | 0.100694i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 945.752 | + | 546.030i | 1.09209 | + | 0.630520i | ||||
\(867\) | − | 314.476i | − | 0.362717i | ||||||
\(868\) | 341.791 | + | 547.031i | 0.393769 | + | 0.630221i | ||||
\(869\) | −252.732 | −0.290831 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1874.36 | − | 1082.16i | 2.15196 | − | 1.24243i | ||||
\(872\) | −56.7825 | − | 98.3502i | −0.0651176 | − | 0.112787i | ||||
\(873\) | 191.734 | + | 110.698i | 0.219627 | + | 0.126802i | ||||
\(874\) | 32.4737i | 0.0371552i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 304.911 | 0.348072 | ||||||||
\(877\) | −308.810 | + | 534.875i | −0.352121 | + | 0.609892i | −0.986621 | − | 0.163031i | \(-0.947873\pi\) |
0.634500 | + | 0.772923i | \(0.281206\pi\) | |||||||
\(878\) | −138.013 | + | 79.6818i | −0.157190 | + | 0.0907538i | ||||
\(879\) | −436.650 | − | 756.300i | −0.496757 | − | 0.860409i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 425.629i | − | 0.483120i | −0.970386 | − | 0.241560i | \(-0.922341\pi\) | ||
0.970386 | − | 0.241560i | \(-0.0776591\pi\) | |||||||
\(882\) | 162.446 | − | 332.992i | 0.184179 | − | 0.377542i | ||||
\(883\) | −295.270 | −0.334394 | −0.167197 | − | 0.985923i | \(-0.553472\pi\) | ||||
−0.167197 | + | 0.985923i | \(0.553472\pi\) | |||||||
\(884\) | 549.332 | − | 951.471i | 0.621416 | − | 1.07632i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −552.452 | − | 956.874i | −0.623535 | − | 1.07999i | ||||
\(887\) | 1463.38 | + | 844.884i | 1.64981 | + | 0.952519i | 0.977146 | + | 0.212571i | \(0.0681838\pi\) |
0.672665 | + | 0.739947i | \(0.265150\pi\) | |||||||
\(888\) | − | 381.037i | − | 0.429096i | ||||||
\(889\) | −1184.13 | − | 629.676i | −1.33198 | − | 0.708297i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.2432 | − | 67.9713i | 0.0440440 | − | 0.0762865i | ||||
\(892\) | 116.329 | − | 67.1628i | 0.130414 | − | 0.0752946i | ||||
\(893\) | −6.33354 | − | 10.9700i | −0.00709244 | − | 0.0122845i | ||||
\(894\) | −54.2039 | − | 31.2946i | −0.0606308 | − | 0.0350052i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 721.895 | − | 451.048i | 0.805686 | − | 0.503402i | ||||
\(897\) | 153.197 | 0.170788 | ||||||||
\(898\) | 270.928 | − | 469.261i | 0.301702 | − | 0.522563i | ||||
\(899\) | 1725.18 | − | 996.035i | 1.91900 | − | 1.10794i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.6336 | + | 48.2859i | 0.0928230 | + | 0.0535914i | ||||
\(902\) | − | 809.129i | − | 0.897039i | ||||||
\(903\) | −213.870 | + | 7.45956i | −0.236844 | + | 0.00826087i | ||||
\(904\) | 383.409 | 0.424124 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −802.911 | + | 463.561i | −0.886215 | + | 0.511657i | ||||
\(907\) | 221.038 | + | 382.848i | 0.243702 | + | 0.422104i | 0.961766 | − | 0.273873i | \(-0.0883048\pi\) |
−0.718064 | + | 0.695977i | \(0.754972\pi\) | |||||||
\(908\) | −372.138 | − | 214.854i | −0.409843 | − | 0.236623i | ||||
\(909\) | 320.861i | 0.352982i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 998.378 | 1.09591 | 0.547957 | − | 0.836507i | \(-0.315406\pi\) | ||||
0.547957 | + | 0.836507i | \(0.315406\pi\) | |||||||
\(912\) | −53.9804 | + | 93.4968i | −0.0591890 | + | 0.102518i | ||||
\(913\) | −159.443 | + | 92.0544i | −0.174636 | + | 0.100826i | ||||
\(914\) | 303.963 | + | 526.479i | 0.332563 | + | 0.576016i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.4834i | 0.0431041i | ||||||||
\(917\) | 218.146 | + | 349.139i | 0.237891 | + | 0.380740i | ||||
\(918\) | −284.096 | −0.309473 | ||||||||
\(919\) | −154.797 | + | 268.116i | −0.168441 | + | 0.291748i | −0.937872 | − | 0.346982i | \(-0.887206\pi\) |
0.769431 | + | 0.638730i | \(0.220540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 345.364 | + | 598.188i | 0.374988 | + | 0.649499i | ||||
\(922\) | −749.520 | − | 432.736i | −0.812928 | − | 0.469344i | ||||
\(923\) | − | 1220.62i | − | 1.32245i | ||||||
\(924\) | 116.787 | − | 219.622i | 0.126393 | − | 0.237686i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −94.2280 | + | 163.208i | −0.101758 | + | 0.176250i | ||||
\(927\) | −55.9605 | + | 32.3088i | −0.0603674 | + | 0.0348531i | ||||
\(928\) | 851.526 | + | 1474.89i | 0.917593 | + | 1.58932i | ||||
\(929\) | −443.269 | − | 255.921i | −0.477146 | − | 0.275480i | 0.242080 | − | 0.970256i | \(-0.422170\pi\) |
−0.719226 | + | 0.694776i | \(0.755504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.7064 | − | 153.293i | −0.0114999 | − | 0.164654i | ||||
\(932\) | 626.737 | 0.672464 | ||||||||
\(933\) | −207.085 | + | 358.682i | −0.221956 | + | 0.384440i | ||||
\(934\) | 777.476 | − | 448.876i | 0.832415 | − | 0.480595i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 232.248 | + | 134.089i | 0.248129 | + | 0.143257i | ||||
\(937\) | − | 592.935i | − | 0.632801i | −0.948626 | − | 0.316401i | \(-0.897526\pi\) | ||
0.948626 | − | 0.316401i | \(-0.102474\pi\) | |||||||
\(938\) | −1566.04 | − | 832.762i | −1.66955 | − | 0.887807i | ||||
\(939\) | −386.592 | −0.411706 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −549.458 | + | 317.230i | −0.583909 | + | 0.337120i | −0.762685 | − | 0.646770i | \(-0.776119\pi\) |
0.178777 | + | 0.983890i | \(0.442786\pi\) | |||||||
\(942\) | −530.230 | − | 918.386i | −0.562877 | − | 0.974932i | ||||
\(943\) | −130.977 | − | 75.6198i | −0.138894 | − | 0.0801907i | ||||
\(944\) | − | 1870.54i | − | 1.98150i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −387.956 | −0.410101 | ||||||||
\(947\) | 329.805 | − | 571.239i | 0.348263 | − | 0.603209i | −0.637678 | − | 0.770303i | \(-0.720105\pi\) |
0.985941 | + | 0.167094i | \(0.0534384\pi\) | |||||||
\(948\) | 102.268 | − | 59.0444i | 0.107878 | − | 0.0622831i | ||||
\(949\) | −805.487 | − | 1395.14i | −0.848775 | − | 1.47012i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 495.391i | 0.520916i | ||||||||
\(952\) | 630.127 | − | 21.9781i | 0.661898 | − | 0.0230863i | ||||
\(953\) | 615.571 | 0.645930 | 0.322965 | − | 0.946411i | \(-0.395320\pi\) | ||||
0.322965 | + | 0.946411i | \(0.395320\pi\) | |||||||
\(954\) | 16.8309 | − | 29.1519i | 0.0176424 | − | 0.0305576i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 46.6996 | + | 80.8861i | 0.0488489 | + | 0.0846088i | ||||
\(957\) | −665.282 | − | 384.100i | −0.695174 | − | 0.401359i | ||||
\(958\) | − | 942.013i | − | 0.983312i | ||||||
\(959\) | 40.4837 | + | 1160.69i | 0.0422145 | + | 1.21032i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 286.605 | − | 496.415i | 0.298237 | − | 0.516561i | ||||
\(962\) | 2489.68 | − | 1437.41i | 2.58802 | − | 1.49419i | ||||
\(963\) | −134.455 | − | 232.883i | −0.139621 | − | 0.241831i | ||||
\(964\) | −169.830 | − | 98.0515i | −0.176172 | − | 0.101713i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −66.5255 | − | 106.473i | −0.0688669 | − | 0.110220i | ||||
\(967\) | −386.702 | −0.399899 | −0.199949 | − | 0.979806i | \(-0.564078\pi\) | ||||
−0.199949 | + | 0.979806i | \(0.564078\pi\) | |||||||
\(968\) | 93.3202 | − | 161.635i | 0.0964052 | − | 0.166979i | ||||
\(969\) | −102.043 | + | 58.9145i | −0.105307 | + | 0.0607993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 487.138 | + | 281.249i | 0.501687 | + | 0.289649i | 0.729410 | − | 0.684077i | \(-0.239795\pi\) |
−0.227723 | + | 0.973726i | \(0.573128\pi\) | |||||||
\(972\) | 36.6727i | 0.0377291i | ||||||||
\(973\) | −458.885 | + | 862.950i | −0.471619 | + | 0.886896i | ||||
\(974\) | 1959.79 | 2.01211 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1259.68 | + | 727.279i | −1.29066 | + | 0.745163i | ||||
\(977\) | 356.041 | + | 616.682i | 0.364423 | + | 0.631199i | 0.988683 | − | 0.150017i | \(-0.0479329\pi\) |
−0.624260 | + | 0.781216i | \(0.714600\pi\) | |||||||
\(978\) | −50.0351 | − | 28.8878i | −0.0511607 | − | 0.0295376i | ||||
\(979\) | 635.472i | 0.649103i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −82.0504 | −0.0836396 | ||||||||
\(982\) | 578.178 | − | 1001.43i | 0.588776 | − | 1.01979i | ||||
\(983\) | −1064.18 | + | 614.407i | −1.08259 | + | 0.625032i | −0.931593 | − | 0.363502i | \(-0.881581\pi\) |
−0.150995 | + | 0.988535i | \(0.548248\pi\) | |||||||
\(984\) | −132.375 | − | 229.281i | −0.134528 | − | 0.233009i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2780.64i | 2.82012i | ||||||||
\(987\) | 43.2392 | + | 22.9930i | 0.0438087 | + | 0.0232959i | ||||
\(988\) | −158.832 | −0.160761 | ||||||||
\(989\) | −36.2577 | + | 62.8001i | −0.0366609 | + | 0.0634986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 621.249 | + | 1076.04i | 0.626892 | + | 1.08581i | 0.988172 | + | 0.153351i | \(0.0490064\pi\) |
−0.361280 | + | 0.932457i | \(0.617660\pi\) | |||||||
\(992\) | 1135.90 | + | 655.811i | 1.14506 | + | 0.661100i | ||||
\(993\) | 933.617i | 0.940199i | ||||||||
\(994\) | −848.337 | + | 530.050i | −0.853457 | + | 0.533250i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 43.0123 | − | 74.4995i | 0.0431850 | − | 0.0747987i | ||||
\(997\) | 694.350 | − | 400.883i | 0.696439 | − | 0.402089i | −0.109581 | − | 0.993978i | \(-0.534951\pi\) |
0.806020 | + | 0.591889i | \(0.201618\pi\) | |||||||
\(998\) | 800.920 | + | 1387.23i | 0.802525 | + | 1.39001i | ||||
\(999\) | −238.415 | − | 137.649i | −0.238654 | − | 0.137787i |
(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 | 525.3.o.l.376.4 | 8 | ||
5.2 | odd | 4 | 525.3.s.h.124.7 | 16 | |||
5.3 | odd | 4 | 525.3.s.h.124.2 | 16 | |||
5.4 | even | 2 | 105.3.n.a.61.1 | yes | 8 | ||
7.3 | odd | 6 | inner | 525.3.o.l.451.4 | 8 | ||
15.14 | odd | 2 | 315.3.w.a.271.4 | 8 | |||
35.3 | even | 12 | 525.3.s.h.199.7 | 16 | |||
35.9 | even | 6 | 735.3.h.a.391.7 | 8 | |||
35.17 | even | 12 | 525.3.s.h.199.2 | 16 | |||
35.19 | odd | 6 | 735.3.h.a.391.8 | 8 | |||
35.24 | odd | 6 | 105.3.n.a.31.1 | ✓ | 8 | ||
105.59 | even | 6 | 315.3.w.a.136.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.n.a.31.1 | ✓ | 8 | 35.24 | odd | 6 | ||
105.3.n.a.61.1 | yes | 8 | 5.4 | even | 2 | ||
315.3.w.a.136.4 | 8 | 105.59 | even | 6 | |||
315.3.w.a.271.4 | 8 | 15.14 | odd | 2 | |||
525.3.o.l.376.4 | 8 | 1.1 | even | 1 | trivial | ||
525.3.o.l.451.4 | 8 | 7.3 | odd | 6 | inner | ||
525.3.s.h.124.2 | 16 | 5.3 | odd | 4 | |||
525.3.s.h.124.7 | 16 | 5.2 | odd | 4 | |||
525.3.s.h.199.2 | 16 | 35.17 | even | 12 | |||
525.3.s.h.199.7 | 16 | 35.3 | even | 12 | |||
735.3.h.a.391.7 | 8 | 35.9 | even | 6 | |||
735.3.h.a.391.8 | 8 | 35.19 | odd | 6 |