Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} - 18375 x^{3} + 60975 x^{2} + 2000 x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(-0.0163000 - 0.0118427i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.481 |
Dual form | 930.2.n.e.901.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.302791 | + | 0.931895i | −0.114444 | + | 0.352223i | −0.991831 | − | 0.127561i | \(-0.959285\pi\) |
0.877386 | + | 0.479784i | \(0.159285\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0.809017 | − | 0.587785i | 0.255834 | − | 0.185874i | ||||
\(11\) | 0.197209 | − | 0.606947i | 0.0594608 | − | 0.183001i | −0.916914 | − | 0.399084i | \(-0.869328\pi\) |
0.976375 | + | 0.216083i | \(0.0693281\pi\) | |||||||
\(12\) | −0.809017 | + | 0.587785i | −0.233543 | + | 0.169679i | ||||
\(13\) | −5.66279 | − | 4.11426i | −1.57058 | − | 1.14109i | −0.926603 | − | 0.376041i | \(-0.877285\pi\) |
−0.643973 | − | 0.765049i | \(-0.722715\pi\) | |||||||
\(14\) | 0.302791 | + | 0.931895i | 0.0809243 | + | 0.249059i | ||||
\(15\) | −0.809017 | − | 0.587785i | −0.208887 | − | 0.151765i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.21877 | − | 3.75099i | −0.295595 | − | 0.909748i | −0.983021 | − | 0.183493i | \(-0.941259\pi\) |
0.687426 | − | 0.726255i | \(-0.258741\pi\) | |||||||
\(18\) | 0.809017 | + | 0.587785i | 0.190687 | + | 0.138542i | ||||
\(19\) | 5.17909 | − | 3.76283i | 1.18816 | − | 0.863252i | 0.195096 | − | 0.980784i | \(-0.437498\pi\) |
0.993069 | + | 0.117532i | \(0.0374982\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | 0.792717 | − | 0.575943i | 0.172985 | − | 0.125681i | ||||
\(22\) | −0.197209 | − | 0.606947i | −0.0420451 | − | 0.129402i | ||||
\(23\) | −0.319091 | − | 0.982061i | −0.0665351 | − | 0.204774i | 0.912262 | − | 0.409608i | \(-0.134335\pi\) |
−0.978797 | + | 0.204834i | \(0.934335\pi\) | |||||||
\(24\) | −0.309017 | + | 0.951057i | −0.0630778 | + | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.99959 | −1.37273 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 0.792717 | + | 0.575943i | 0.149809 | + | 0.108843i | ||||
\(29\) | 1.97201 | − | 1.43275i | 0.366193 | − | 0.266055i | −0.389437 | − | 0.921053i | \(-0.627331\pi\) |
0.755631 | + | 0.654998i | \(0.227331\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 0.409753 | − | 5.55267i | 0.0735937 | − | 0.997288i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.516300 | + | 0.375114i | −0.0898763 | + | 0.0652990i | ||||
\(34\) | −3.19078 | − | 2.31824i | −0.547214 | − | 0.397574i | ||||
\(35\) | −0.302791 | + | 0.931895i | −0.0511810 | + | 0.157519i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.93157 | 0.317548 | 0.158774 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158774 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(38\) | 1.97824 | − | 6.08839i | 0.320912 | − | 0.987667i | ||||
\(39\) | 2.16299 | + | 6.65701i | 0.346356 | + | 1.06597i | ||||
\(40\) | −0.309017 | − | 0.951057i | −0.0488599 | − | 0.150375i | ||||
\(41\) | 0.827931 | − | 0.601527i | 0.129301 | − | 0.0939427i | −0.521255 | − | 0.853401i | \(-0.674536\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(42\) | 0.302791 | − | 0.931895i | 0.0467217 | − | 0.143794i | ||||
\(43\) | −4.17286 | + | 3.03176i | −0.636356 | + | 0.462340i | −0.858596 | − | 0.512652i | \(-0.828663\pi\) |
0.222240 | + | 0.974992i | \(0.428663\pi\) | |||||||
\(44\) | −0.516300 | − | 0.375114i | −0.0778352 | − | 0.0565506i | ||||
\(45\) | 0.309017 | + | 0.951057i | 0.0460655 | + | 0.141775i | ||||
\(46\) | −0.835391 | − | 0.606947i | −0.123172 | − | 0.0894895i | ||||
\(47\) | −5.48188 | − | 3.98282i | −0.799615 | − | 0.580954i | 0.111186 | − | 0.993800i | \(-0.464535\pi\) |
−0.910801 | + | 0.412846i | \(0.864535\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | 4.88637 | + | 3.55016i | 0.698053 | + | 0.507165i | ||||
\(50\) | 0.809017 | − | 0.587785i | 0.114412 | − | 0.0831254i | ||||
\(51\) | −1.21877 | + | 3.75099i | −0.170662 | + | 0.525243i | ||||
\(52\) | −5.66279 | + | 4.11426i | −0.785288 | + | 0.570545i | ||||
\(53\) | 0.824351 | + | 2.53709i | 0.113233 | + | 0.348496i | 0.991574 | − | 0.129538i | \(-0.0413494\pi\) |
−0.878341 | + | 0.478034i | \(0.841349\pi\) | |||||||
\(54\) | −0.309017 | − | 0.951057i | −0.0420519 | − | 0.129422i | ||||
\(55\) | 0.197209 | − | 0.606947i | 0.0265917 | − | 0.0818407i | ||||
\(56\) | 0.979852 | 0.130938 | ||||||||
\(57\) | −6.40171 | −0.847927 | ||||||||
\(58\) | 0.753241 | − | 2.31824i | 0.0989054 | − | 0.304399i | ||||
\(59\) | −4.13019 | − | 3.00076i | −0.537705 | − | 0.390666i | 0.285527 | − | 0.958371i | \(-0.407831\pi\) |
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(60\) | −0.809017 | + | 0.587785i | −0.104444 | + | 0.0758827i | ||||
\(61\) | −8.93157 | −1.14357 | −0.571785 | − | 0.820403i | \(-0.693749\pi\) | ||||
−0.571785 | + | 0.820403i | \(0.693749\pi\) | |||||||
\(62\) | −2.93228 | − | 4.73305i | −0.372400 | − | 0.601098i | ||||
\(63\) | −0.979852 | −0.123450 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −5.66279 | − | 4.11426i | −0.702383 | − | 0.510311i | ||||
\(66\) | −0.197209 | + | 0.606947i | −0.0242748 | + | 0.0747100i | ||||
\(67\) | 8.74062 | 1.06784 | 0.533918 | − | 0.845536i | \(-0.320719\pi\) | ||||
0.533918 | + | 0.845536i | \(0.320719\pi\) | |||||||
\(68\) | −3.94402 | −0.478283 | ||||||||
\(69\) | −0.319091 | + | 0.982061i | −0.0384140 | + | 0.118226i | ||||
\(70\) | 0.302791 | + | 0.931895i | 0.0361904 | + | 0.111383i | ||||
\(71\) | −3.07287 | − | 9.45733i | −0.364683 | − | 1.12238i | −0.950179 | − | 0.311703i | \(-0.899100\pi\) |
0.585497 | − | 0.810675i | \(-0.300900\pi\) | |||||||
\(72\) | 0.809017 | − | 0.587785i | 0.0953436 | − | 0.0692712i | ||||
\(73\) | −3.76611 | + | 11.5909i | −0.440790 | + | 1.35661i | 0.446246 | + | 0.894910i | \(0.352761\pi\) |
−0.887036 | + | 0.461700i | \(0.847239\pi\) | |||||||
\(74\) | 1.56267 | − | 1.13535i | 0.181657 | − | 0.131981i | ||||
\(75\) | −0.809017 | − | 0.587785i | −0.0934172 | − | 0.0678716i | ||||
\(76\) | −1.97824 | − | 6.08839i | −0.226919 | − | 0.698386i | ||||
\(77\) | 0.505898 | + | 0.367556i | 0.0576524 | + | 0.0418869i | ||||
\(78\) | 5.66279 | + | 4.11426i | 0.641185 | + | 0.465848i | ||||
\(79\) | 0.0759239 | + | 0.233670i | 0.00854211 | + | 0.0262899i | 0.955237 | − | 0.295843i | \(-0.0956004\pi\) |
−0.946695 | + | 0.322132i | \(0.895600\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0.316241 | − | 0.973291i | 0.0349230 | − | 0.107482i | ||||
\(83\) | 12.0607 | − | 8.76258i | 1.32383 | − | 0.961818i | 0.323952 | − | 0.946073i | \(-0.394988\pi\) |
0.999876 | − | 0.0157442i | \(-0.00501175\pi\) | |||||||
\(84\) | −0.302791 | − | 0.931895i | −0.0330372 | − | 0.101678i | ||||
\(85\) | −1.21877 | − | 3.75099i | −0.132194 | − | 0.406852i | ||||
\(86\) | −1.59389 | + | 4.90550i | −0.171874 | + | 0.528973i | ||||
\(87\) | −2.43754 | −0.261332 | ||||||||
\(88\) | −0.638182 | −0.0680304 | ||||||||
\(89\) | −4.06590 | + | 12.5136i | −0.430985 | + | 1.32643i | 0.466161 | + | 0.884700i | \(0.345637\pi\) |
−0.897146 | + | 0.441735i | \(0.854363\pi\) | |||||||
\(90\) | 0.809017 | + | 0.587785i | 0.0852779 | + | 0.0619580i | ||||
\(91\) | 5.54870 | − | 4.03136i | 0.581662 | − | 0.422602i | ||||
\(92\) | −1.03260 | −0.107656 | ||||||||
\(93\) | −3.59527 | + | 4.25135i | −0.372812 | + | 0.440845i | ||||
\(94\) | −6.77598 | −0.698889 | ||||||||
\(95\) | 5.17909 | − | 3.76283i | 0.531363 | − | 0.386058i | ||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | −3.54708 | + | 10.9168i | −0.360152 | + | 1.10843i | 0.592810 | + | 0.805342i | \(0.298018\pi\) |
−0.952962 | + | 0.303090i | \(0.901982\pi\) | |||||||
\(98\) | 6.03989 | 0.610121 | ||||||||
\(99\) | 0.638182 | 0.0641397 | ||||||||
\(100\) | 0.309017 | − | 0.951057i | 0.0309017 | − | 0.0951057i | ||||
\(101\) | 2.01817 | + | 6.21129i | 0.200816 | + | 0.618047i | 0.999859 | + | 0.0167739i | \(0.00533954\pi\) |
−0.799044 | + | 0.601273i | \(0.794660\pi\) | |||||||
\(102\) | 1.21877 | + | 3.75099i | 0.120676 | + | 0.371403i | ||||
\(103\) | 10.8739 | − | 7.90035i | 1.07144 | − | 0.778444i | 0.0952669 | − | 0.995452i | \(-0.469630\pi\) |
0.976170 | + | 0.217007i | \(0.0696295\pi\) | |||||||
\(104\) | −2.16299 | + | 6.65701i | −0.212099 | + | 0.652773i | ||||
\(105\) | 0.792717 | − | 0.575943i | 0.0773613 | − | 0.0562062i | ||||
\(106\) | 2.15818 | + | 1.56801i | 0.209621 | + | 0.152299i | ||||
\(107\) | 2.99072 | + | 9.20449i | 0.289124 | + | 0.889832i | 0.985132 | + | 0.171798i | \(0.0549577\pi\) |
−0.696008 | + | 0.718034i | \(0.745042\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 13.0042 | + | 9.44807i | 1.24557 | + | 0.904961i | 0.997956 | − | 0.0638975i | \(-0.0203531\pi\) |
0.247615 | + | 0.968858i | \(0.420353\pi\) | |||||||
\(110\) | −0.197209 | − | 0.606947i | −0.0188031 | − | 0.0578701i | ||||
\(111\) | −1.56267 | − | 1.13535i | −0.148322 | − | 0.107762i | ||||
\(112\) | 0.792717 | − | 0.575943i | 0.0749047 | − | 0.0544215i | ||||
\(113\) | 1.41598 | − | 4.35793i | 0.133204 | − | 0.409960i | −0.862102 | − | 0.506734i | \(-0.830853\pi\) |
0.995306 | + | 0.0967744i | \(0.0308525\pi\) | |||||||
\(114\) | −5.17909 | + | 3.76283i | −0.485066 | + | 0.352421i | ||||
\(115\) | −0.319091 | − | 0.982061i | −0.0297554 | − | 0.0915777i | ||||
\(116\) | −0.753241 | − | 2.31824i | −0.0699367 | − | 0.215243i | ||||
\(117\) | 2.16299 | − | 6.65701i | 0.199969 | − | 0.615441i | ||||
\(118\) | −5.10520 | −0.469971 | ||||||||
\(119\) | 3.86456 | 0.354263 | ||||||||
\(120\) | −0.309017 | + | 0.951057i | −0.0282093 | + | 0.0868192i | ||||
\(121\) | 8.56969 | + | 6.22625i | 0.779063 | + | 0.566022i | ||||
\(122\) | −7.22579 | + | 5.24984i | −0.654192 | + | 0.475299i | ||||
\(123\) | −1.02338 | −0.0922750 | ||||||||
\(124\) | −5.15428 | − | 2.10557i | −0.462868 | − | 0.189085i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.792717 | + | 0.575943i | −0.0706208 | + | 0.0513090i | ||||
\(127\) | −5.14188 | − | 3.73579i | −0.456268 | − | 0.331498i | 0.335797 | − | 0.941934i | \(-0.390994\pi\) |
−0.792066 | + | 0.610436i | \(0.790994\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 5.15794 | 0.454132 | ||||||||
\(130\) | −6.99959 | −0.613905 | ||||||||
\(131\) | 5.75020 | − | 17.6973i | 0.502397 | − | 1.54622i | −0.302705 | − | 0.953084i | \(-0.597890\pi\) |
0.805102 | − | 0.593136i | \(-0.202110\pi\) | |||||||
\(132\) | 0.197209 | + | 0.606947i | 0.0171648 | + | 0.0528280i | ||||
\(133\) | 1.93838 | + | 5.96572i | 0.168079 | + | 0.517293i | ||||
\(134\) | 7.07131 | − | 5.13761i | 0.610868 | − | 0.443822i | ||||
\(135\) | 0.309017 | − | 0.951057i | 0.0265959 | − | 0.0818539i | ||||
\(136\) | −3.19078 | + | 2.31824i | −0.273607 | + | 0.198787i | ||||
\(137\) | −8.99175 | − | 6.53289i | −0.768217 | − | 0.558143i | 0.133202 | − | 0.991089i | \(-0.457474\pi\) |
−0.901420 | + | 0.432946i | \(0.857474\pi\) | |||||||
\(138\) | 0.319091 | + | 0.982061i | 0.0271628 | + | 0.0835986i | ||||
\(139\) | 8.97798 | + | 6.52288i | 0.761502 | + | 0.553264i | 0.899371 | − | 0.437187i | \(-0.144025\pi\) |
−0.137868 | + | 0.990451i | \(0.544025\pi\) | |||||||
\(140\) | 0.792717 | + | 0.575943i | 0.0669968 | + | 0.0486760i | ||||
\(141\) | 2.09389 | + | 6.44434i | 0.176338 | + | 0.542711i | ||||
\(142\) | −8.04488 | − | 5.84495i | −0.675112 | − | 0.490497i | ||||
\(143\) | −3.61389 | + | 2.62565i | −0.302209 | + | 0.219567i | ||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | 1.97201 | − | 1.43275i | 0.163767 | − | 0.118983i | ||||
\(146\) | 3.76611 | + | 11.5909i | 0.311685 | + | 0.959269i | ||||
\(147\) | −1.86643 | − | 5.74428i | −0.153940 | − | 0.473780i | ||||
\(148\) | 0.596888 | − | 1.83703i | 0.0490639 | − | 0.151003i | ||||
\(149\) | 13.5520 | 1.11022 | 0.555110 | − | 0.831777i | \(-0.312676\pi\) | ||||
0.555110 | + | 0.831777i | \(0.312676\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 1.54597 | − | 4.75801i | 0.125809 | − | 0.387201i | −0.868238 | − | 0.496147i | \(-0.834748\pi\) |
0.994048 | + | 0.108946i | \(0.0347476\pi\) | |||||||
\(152\) | −5.17909 | − | 3.76283i | −0.420080 | − | 0.305206i | ||||
\(153\) | 3.19078 | − | 2.31824i | 0.257959 | − | 0.187418i | ||||
\(154\) | 0.625324 | 0.0503900 | ||||||||
\(155\) | 0.409753 | − | 5.55267i | 0.0329121 | − | 0.446001i | ||||
\(156\) | 6.99959 | 0.560416 | ||||||||
\(157\) | 1.35410 | − | 0.983813i | 0.108069 | − | 0.0785168i | −0.532438 | − | 0.846469i | \(-0.678724\pi\) |
0.640507 | + | 0.767952i | \(0.278724\pi\) | |||||||
\(158\) | 0.198771 | + | 0.144416i | 0.0158134 | + | 0.0114891i | ||||
\(159\) | 0.824351 | − | 2.53709i | 0.0653753 | − | 0.201205i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.01180 | 0.0797406 | ||||||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | 2.70006 | + | 8.30993i | 0.211485 | + | 0.650884i | 0.999385 | + | 0.0350799i | \(0.0111686\pi\) |
−0.787900 | + | 0.615804i | \(0.788831\pi\) | |||||||
\(164\) | −0.316241 | − | 0.973291i | −0.0246943 | − | 0.0760013i | ||||
\(165\) | −0.516300 | + | 0.375114i | −0.0401939 | + | 0.0292026i | ||||
\(166\) | 4.60676 | − | 14.1781i | 0.357554 | − | 1.10044i | ||||
\(167\) | −1.52103 | + | 1.10509i | −0.117701 | + | 0.0855146i | −0.645078 | − | 0.764116i | \(-0.723175\pi\) |
0.527378 | + | 0.849631i | \(0.323175\pi\) | |||||||
\(168\) | −0.792717 | − | 0.575943i | −0.0611594 | − | 0.0444349i | ||||
\(169\) | 11.1229 | + | 34.2326i | 0.855604 | + | 2.63328i | ||||
\(170\) | −3.19078 | − | 2.31824i | −0.244722 | − | 0.177801i | ||||
\(171\) | 5.17909 | + | 3.76283i | 0.396055 | + | 0.287751i | ||||
\(172\) | 1.59389 | + | 4.90550i | 0.121533 | + | 0.374041i | ||||
\(173\) | −11.1506 | − | 8.10136i | −0.847762 | − | 0.615935i | 0.0767660 | − | 0.997049i | \(-0.475541\pi\) |
−0.924528 | + | 0.381114i | \(0.875541\pi\) | |||||||
\(174\) | −1.97201 | + | 1.43275i | −0.149498 | + | 0.108616i | ||||
\(175\) | −0.302791 | + | 0.931895i | −0.0228888 | + | 0.0704446i | ||||
\(176\) | −0.516300 | + | 0.375114i | −0.0389176 | + | 0.0282753i | ||||
\(177\) | 1.57759 | + | 4.85533i | 0.118579 | + | 0.364949i | ||||
\(178\) | 4.06590 | + | 12.5136i | 0.304752 | + | 0.937931i | ||||
\(179\) | −2.48546 | + | 7.64946i | −0.185772 | + | 0.571748i | −0.999961 | − | 0.00885262i | \(-0.997182\pi\) |
0.814189 | + | 0.580600i | \(0.197182\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 2.35377 | 0.174954 | 0.0874770 | − | 0.996167i | \(-0.472120\pi\) | ||||
0.0874770 | + | 0.996167i | \(0.472120\pi\) | |||||||
\(182\) | 2.11941 | − | 6.52288i | 0.157101 | − | 0.483508i | ||||
\(183\) | 7.22579 | + | 5.24984i | 0.534146 | + | 0.388080i | ||||
\(184\) | −0.835391 | + | 0.606947i | −0.0615858 | + | 0.0447447i | ||||
\(185\) | 1.93157 | 0.142012 | ||||||||
\(186\) | −0.409753 | + | 5.55267i | −0.0300445 | + | 0.407141i | ||||
\(187\) | −2.51700 | −0.184061 | ||||||||
\(188\) | −5.48188 | + | 3.98282i | −0.399807 | + | 0.290477i | ||||
\(189\) | 0.792717 | + | 0.575943i | 0.0576617 | + | 0.0418937i | ||||
\(190\) | 1.97824 | − | 6.08839i | 0.143516 | − | 0.441698i | ||||
\(191\) | −9.44364 | −0.683317 | −0.341659 | − | 0.939824i | \(-0.610989\pi\) | ||||
−0.341659 | + | 0.939824i | \(0.610989\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −5.46861 | + | 16.8307i | −0.393639 | + | 1.21150i | 0.536377 | + | 0.843979i | \(0.319793\pi\) |
−0.930016 | + | 0.367519i | \(0.880207\pi\) | |||||||
\(194\) | 3.54708 | + | 10.9168i | 0.254666 | + | 0.783780i | ||||
\(195\) | 2.16299 | + | 6.65701i | 0.154895 | + | 0.476718i | ||||
\(196\) | 4.88637 | − | 3.55016i | 0.349027 | − | 0.253583i | ||||
\(197\) | 4.72540 | − | 14.5433i | 0.336671 | − | 1.03617i | −0.629223 | − | 0.777225i | \(-0.716627\pi\) |
0.965893 | − | 0.258941i | \(-0.0833734\pi\) | |||||||
\(198\) | 0.516300 | − | 0.375114i | 0.0366918 | − | 0.0266582i | ||||
\(199\) | 21.6590 | + | 15.7361i | 1.53536 | + | 1.11551i | 0.953162 | + | 0.302461i | \(0.0978081\pi\) |
0.582200 | + | 0.813045i | \(0.302192\pi\) | |||||||
\(200\) | −0.309017 | − | 0.951057i | −0.0218508 | − | 0.0672499i | ||||
\(201\) | −7.07131 | − | 5.13761i | −0.498772 | − | 0.362379i | ||||
\(202\) | 5.28364 | + | 3.83879i | 0.371756 | + | 0.270096i | ||||
\(203\) | 0.738065 | + | 2.27153i | 0.0518020 | + | 0.159430i | ||||
\(204\) | 3.19078 | + | 2.31824i | 0.223399 | + | 0.162309i | ||||
\(205\) | 0.827931 | − | 0.601527i | 0.0578252 | − | 0.0420125i | ||||
\(206\) | 4.15346 | − | 12.7830i | 0.289385 | − | 0.890636i | ||||
\(207\) | 0.835391 | − | 0.606947i | 0.0580637 | − | 0.0421857i | ||||
\(208\) | 2.16299 | + | 6.65701i | 0.149977 | + | 0.461581i | ||||
\(209\) | −1.26247 | − | 3.88550i | −0.0873272 | − | 0.268766i | ||||
\(210\) | 0.302791 | − | 0.931895i | 0.0208946 | − | 0.0643068i | ||||
\(211\) | −3.59124 | −0.247231 | −0.123616 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123616 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(212\) | 2.66766 | 0.183215 | ||||||||
\(213\) | −3.07287 | + | 9.45733i | −0.210550 | + | 0.648005i | ||||
\(214\) | 7.82981 | + | 5.68869i | 0.535235 | + | 0.388871i | ||||
\(215\) | −4.17286 | + | 3.03176i | −0.284587 | + | 0.206765i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.05043 | + | 2.06314i | 0.342846 | + | 0.140055i | ||||
\(218\) | 16.0740 | 1.08867 | ||||||||
\(219\) | 9.85980 | − | 7.16356i | 0.666263 | − | 0.484069i | ||||
\(220\) | −0.516300 | − | 0.375114i | −0.0348089 | − | 0.0252902i | ||||
\(221\) | −8.53089 | + | 26.2554i | −0.573850 | + | 1.76613i | ||||
\(222\) | −1.93157 | −0.129638 | ||||||||
\(223\) | 0.357890 | 0.0239661 | 0.0119830 | − | 0.999928i | \(-0.496186\pi\) | ||||
0.0119830 | + | 0.999928i | \(0.496186\pi\) | |||||||
\(224\) | 0.302791 | − | 0.931895i | 0.0202311 | − | 0.0622648i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | −1.41598 | − | 4.35793i | −0.0941895 | − | 0.289885i | ||||
\(227\) | 11.8878 | − | 8.63701i | 0.789023 | − | 0.573259i | −0.118651 | − | 0.992936i | \(-0.537857\pi\) |
0.907673 | + | 0.419678i | \(0.137857\pi\) | |||||||
\(228\) | −1.97824 | + | 6.08839i | −0.131012 | + | 0.403213i | ||||
\(229\) | 3.83947 | − | 2.78954i | 0.253719 | − | 0.184338i | −0.453654 | − | 0.891178i | \(-0.649880\pi\) |
0.707374 | + | 0.706840i | \(0.249880\pi\) | |||||||
\(230\) | −0.835391 | − | 0.606947i | −0.0550840 | − | 0.0400209i | ||||
\(231\) | −0.193236 | − | 0.594718i | −0.0127140 | − | 0.0391296i | ||||
\(232\) | −1.97201 | − | 1.43275i | −0.129469 | − | 0.0940646i | ||||
\(233\) | −6.78059 | − | 4.92639i | −0.444211 | − | 0.322738i | 0.343095 | − | 0.939301i | \(-0.388525\pi\) |
−0.787306 | + | 0.616562i | \(0.788525\pi\) | |||||||
\(234\) | −2.16299 | − | 6.65701i | −0.141399 | − | 0.435182i | ||||
\(235\) | −5.48188 | − | 3.98282i | −0.357599 | − | 0.259811i | ||||
\(236\) | −4.13019 | + | 3.00076i | −0.268853 | + | 0.195333i | ||||
\(237\) | 0.0759239 | − | 0.233670i | 0.00493179 | − | 0.0151785i | ||||
\(238\) | 3.12649 | − | 2.27153i | 0.202660 | − | 0.147241i | ||||
\(239\) | −6.93759 | − | 21.3517i | −0.448756 | − | 1.38113i | −0.878312 | − | 0.478088i | \(-0.841330\pi\) |
0.429557 | − | 0.903040i | \(-0.358670\pi\) | |||||||
\(240\) | 0.309017 | + | 0.951057i | 0.0199470 | + | 0.0613904i | ||||
\(241\) | 6.37005 | − | 19.6050i | 0.410331 | − | 1.26287i | −0.506030 | − | 0.862516i | \(-0.668887\pi\) |
0.916361 | − | 0.400353i | \(-0.131113\pi\) | |||||||
\(242\) | 10.5927 | 0.680926 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.76001 | + | 8.49443i | −0.176691 | + | 0.543800i | ||||
\(245\) | 4.88637 | + | 3.55016i | 0.312179 | + | 0.226811i | ||||
\(246\) | −0.827931 | + | 0.601527i | −0.0527869 | + | 0.0383520i | ||||
\(247\) | −44.8094 | −2.85115 | ||||||||
\(248\) | −5.40752 | + | 1.32617i | −0.343378 | + | 0.0842119i | ||||
\(249\) | −14.9078 | −0.944742 | ||||||||
\(250\) | 0.809017 | − | 0.587785i | 0.0511667 | − | 0.0371748i | ||||
\(251\) | 13.3163 | + | 9.67486i | 0.840518 | + | 0.610672i | 0.922515 | − | 0.385961i | \(-0.126130\pi\) |
−0.0819976 | + | 0.996633i | \(0.526130\pi\) | |||||||
\(252\) | −0.302791 | + | 0.931895i | −0.0190740 | + | 0.0587038i | ||||
\(253\) | −0.658987 | −0.0414301 | ||||||||
\(254\) | −6.35571 | −0.398793 | ||||||||
\(255\) | −1.21877 | + | 3.75099i | −0.0763223 | + | 0.234896i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −6.66380 | − | 20.5091i | −0.415677 | − | 1.27932i | −0.911644 | − | 0.410980i | \(-0.865187\pi\) |
0.495968 | − | 0.868341i | \(-0.334813\pi\) | |||||||
\(258\) | 4.17286 | − | 3.03176i | 0.259791 | − | 0.188749i | ||||
\(259\) | −0.584862 | + | 1.80002i | −0.0363415 | + | 0.111848i | ||||
\(260\) | −5.66279 | + | 4.11426i | −0.351191 | + | 0.255155i | ||||
\(261\) | 1.97201 | + | 1.43275i | 0.122064 | + | 0.0886850i | ||||
\(262\) | −5.75020 | − | 17.6973i | −0.355249 | − | 1.09334i | ||||
\(263\) | 8.84843 | + | 6.42876i | 0.545617 | + | 0.396414i | 0.826167 | − | 0.563425i | \(-0.190517\pi\) |
−0.280550 | + | 0.959840i | \(0.590517\pi\) | |||||||
\(264\) | 0.516300 | + | 0.375114i | 0.0317761 | + | 0.0230867i | ||||
\(265\) | 0.824351 | + | 2.53709i | 0.0506395 | + | 0.155852i | ||||
\(266\) | 5.07474 | + | 3.68702i | 0.311152 | + | 0.226065i | ||||
\(267\) | 10.6447 | − | 7.73381i | 0.651443 | − | 0.473301i | ||||
\(268\) | 2.70100 | − | 8.31282i | 0.164990 | − | 0.507786i | ||||
\(269\) | 14.6594 | − | 10.6507i | 0.893800 | − | 0.649384i | −0.0430660 | − | 0.999072i | \(-0.513713\pi\) |
0.936866 | + | 0.349689i | \(0.113713\pi\) | |||||||
\(270\) | −0.309017 | − | 0.951057i | −0.0188062 | − | 0.0578795i | ||||
\(271\) | −1.11363 | − | 3.42739i | −0.0676480 | − | 0.208199i | 0.911518 | − | 0.411260i | \(-0.134911\pi\) |
−0.979166 | + | 0.203061i | \(0.934911\pi\) | |||||||
\(272\) | −1.21877 | + | 3.75099i | −0.0738988 | + | 0.227437i | ||||
\(273\) | −6.85857 | −0.415099 | ||||||||
\(274\) | −11.1144 | −0.671447 | ||||||||
\(275\) | 0.197209 | − | 0.606947i | 0.0118922 | − | 0.0366003i | ||||
\(276\) | 0.835391 | + | 0.606947i | 0.0502846 | + | 0.0365339i | ||||
\(277\) | 2.62840 | − | 1.90964i | 0.157925 | − | 0.114739i | −0.506016 | − | 0.862524i | \(-0.668882\pi\) |
0.663941 | + | 0.747785i | \(0.268882\pi\) | |||||||
\(278\) | 11.0974 | 0.665577 | ||||||||
\(279\) | 5.40752 | − | 1.32617i | 0.323740 | − | 0.0793957i | ||||
\(280\) | 0.979852 | 0.0585574 | ||||||||
\(281\) | −20.0327 | + | 14.5546i | −1.19505 | + | 0.868253i | −0.993789 | − | 0.111284i | \(-0.964504\pi\) |
−0.201260 | + | 0.979538i | \(0.564504\pi\) | |||||||
\(282\) | 5.48188 | + | 3.98282i | 0.326441 | + | 0.237173i | ||||
\(283\) | −8.47201 | + | 26.0742i | −0.503609 | + | 1.54995i | 0.299488 | + | 0.954100i | \(0.403184\pi\) |
−0.803097 | + | 0.595848i | \(0.796816\pi\) | |||||||
\(284\) | −9.94402 | −0.590069 | ||||||||
\(285\) | −6.40171 | −0.379204 | ||||||||
\(286\) | −1.38038 | + | 4.24838i | −0.0816238 | + | 0.251212i | ||||
\(287\) | 0.309870 | + | 0.953681i | 0.0182910 | + | 0.0562940i | ||||
\(288\) | −0.309017 | − | 0.951057i | −0.0182090 | − | 0.0560415i | ||||
\(289\) | 1.16879 | − | 0.849172i | 0.0687521 | − | 0.0499513i | ||||
\(290\) | 0.753241 | − | 2.31824i | 0.0442318 | − | 0.136132i | ||||
\(291\) | 9.28638 | − | 6.74695i | 0.544377 | − | 0.395513i | ||||
\(292\) | 9.85980 | + | 7.16356i | 0.577001 | + | 0.419216i | ||||
\(293\) | −2.16525 | − | 6.66394i | −0.126495 | − | 0.389312i | 0.867675 | − | 0.497131i | \(-0.165613\pi\) |
−0.994171 | + | 0.107819i | \(0.965613\pi\) | |||||||
\(294\) | −4.88637 | − | 3.55016i | −0.284979 | − | 0.207049i | ||||
\(295\) | −4.13019 | − | 3.00076i | −0.240469 | − | 0.174711i | ||||
\(296\) | −0.596888 | − | 1.83703i | −0.0346934 | − | 0.106775i | ||||
\(297\) | −0.516300 | − | 0.375114i | −0.0299588 | − | 0.0217663i | ||||
\(298\) | 10.9638 | − | 7.96564i | 0.635114 | − | 0.461437i | ||||
\(299\) | −2.23351 | + | 6.87403i | −0.129167 | + | 0.397535i | ||||
\(300\) | −0.809017 | + | 0.587785i | −0.0467086 | + | 0.0339358i | ||||
\(301\) | −1.56178 | − | 4.80666i | −0.0900194 | − | 0.277051i | ||||
\(302\) | −1.54597 | − | 4.75801i | −0.0889606 | − | 0.273793i | ||||
\(303\) | 2.01817 | − | 6.21129i | 0.115941 | − | 0.356829i | ||||
\(304\) | −6.40171 | −0.367163 | ||||||||
\(305\) | −8.93157 | −0.511420 | ||||||||
\(306\) | 1.21877 | − | 3.75099i | 0.0696724 | − | 0.214430i | ||||
\(307\) | −2.35759 | − | 1.71289i | −0.134555 | − | 0.0977597i | 0.518472 | − | 0.855095i | \(-0.326501\pi\) |
−0.653027 | + | 0.757335i | \(0.726501\pi\) | |||||||
\(308\) | 0.505898 | − | 0.367556i | 0.0288262 | − | 0.0209435i | ||||
\(309\) | −13.4409 | −0.764625 | ||||||||
\(310\) | −2.93228 | − | 4.73305i | −0.166542 | − | 0.268819i | ||||
\(311\) | 24.8497 | 1.40910 | 0.704550 | − | 0.709655i | \(-0.251149\pi\) | ||||
0.704550 | + | 0.709655i | \(0.251149\pi\) | |||||||
\(312\) | 5.66279 | − | 4.11426i | 0.320592 | − | 0.232924i | ||||
\(313\) | −8.91612 | − | 6.47794i | −0.503969 | − | 0.366155i | 0.306562 | − | 0.951851i | \(-0.400821\pi\) |
−0.810531 | + | 0.585696i | \(0.800821\pi\) | |||||||
\(314\) | 0.517221 | − | 1.59184i | 0.0291885 | − | 0.0898329i | ||||
\(315\) | −0.979852 | −0.0552084 | ||||||||
\(316\) | 0.245695 | 0.0138214 | ||||||||
\(317\) | −7.36015 | + | 22.6522i | −0.413387 | + | 1.27227i | 0.500299 | + | 0.865853i | \(0.333223\pi\) |
−0.913686 | + | 0.406421i | \(0.866777\pi\) | |||||||
\(318\) | −0.824351 | − | 2.53709i | −0.0462273 | − | 0.142273i | ||||
\(319\) | −0.480705 | − | 1.47946i | −0.0269143 | − | 0.0828337i | ||||
\(320\) | −0.809017 | + | 0.587785i | −0.0452254 | + | 0.0328582i | ||||
\(321\) | 2.99072 | − | 9.20449i | 0.166926 | − | 0.513745i | ||||
\(322\) | 0.818560 | − | 0.594718i | 0.0456165 | − | 0.0331424i | ||||
\(323\) | −20.4264 | − | 14.8407i | −1.13656 | − | 0.825757i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | −5.66279 | − | 4.11426i | −0.314115 | − | 0.228218i | ||||
\(326\) | 7.06884 | + | 5.13582i | 0.391507 | + | 0.284447i | ||||
\(327\) | −4.96714 | − | 15.2873i | −0.274684 | − | 0.845389i | ||||
\(328\) | −0.827931 | − | 0.601527i | −0.0457148 | − | 0.0332138i | ||||
\(329\) | 5.37143 | − | 3.90257i | 0.296137 | − | 0.215156i | ||||
\(330\) | −0.197209 | + | 0.606947i | −0.0108560 | + | 0.0334113i | ||||
\(331\) | −11.8804 | + | 8.63159i | −0.653004 | + | 0.474435i | −0.864293 | − | 0.502989i | \(-0.832234\pi\) |
0.211289 | + | 0.977424i | \(0.432234\pi\) | |||||||
\(332\) | −4.60676 | − | 14.1781i | −0.252829 | − | 0.778127i | ||||
\(333\) | 0.596888 | + | 1.83703i | 0.0327092 | + | 0.100669i | ||||
\(334\) | −0.580981 | + | 1.78808i | −0.0317899 | + | 0.0978392i | ||||
\(335\) | 8.74062 | 0.477551 | ||||||||
\(336\) | −0.979852 | −0.0534553 | ||||||||
\(337\) | 0.212982 | − | 0.655491i | 0.0116019 | − | 0.0357069i | −0.945088 | − | 0.326816i | \(-0.894024\pi\) |
0.956690 | + | 0.291109i | \(0.0940243\pi\) | |||||||
\(338\) | 29.1200 | + | 21.1569i | 1.58392 | + | 1.15079i | ||||
\(339\) | −3.70708 | + | 2.69335i | −0.201341 | + | 0.146283i | ||||
\(340\) | −3.94402 | −0.213895 | ||||||||
\(341\) | −3.28937 | − | 1.34373i | −0.178129 | − | 0.0727673i | ||||
\(342\) | 6.40171 | 0.346165 | ||||||||
\(343\) | −10.3369 | + | 7.51023i | −0.558142 | + | 0.405514i | ||||
\(344\) | 4.17286 | + | 3.03176i | 0.224986 | + | 0.163462i | ||||
\(345\) | −0.319091 | + | 0.982061i | −0.0171793 | + | 0.0528724i | ||||
\(346\) | −13.7829 | −0.740971 | ||||||||
\(347\) | −5.75848 | −0.309132 | −0.154566 | − | 0.987982i | \(-0.549398\pi\) | ||||
−0.154566 | + | 0.987982i | \(0.549398\pi\) | |||||||
\(348\) | −0.753241 | + | 2.31824i | −0.0403780 | + | 0.124271i | ||||
\(349\) | −3.85018 | − | 11.8496i | −0.206095 | − | 0.634297i | −0.999667 | − | 0.0258192i | \(-0.991781\pi\) |
0.793571 | − | 0.608477i | \(-0.208219\pi\) | |||||||
\(350\) | 0.302791 | + | 0.931895i | 0.0161849 | + | 0.0498119i | ||||
\(351\) | −5.66279 | + | 4.11426i | −0.302257 | + | 0.219603i | ||||
\(352\) | −0.197209 | + | 0.606947i | −0.0105113 | + | 0.0323504i | ||||
\(353\) | 20.1464 | − | 14.6372i | 1.07229 | − | 0.779062i | 0.0959652 | − | 0.995385i | \(-0.469406\pi\) |
0.976322 | + | 0.216323i | \(0.0694063\pi\) | |||||||
\(354\) | 4.13019 | + | 3.00076i | 0.219517 | + | 0.159489i | ||||
\(355\) | −3.07287 | − | 9.45733i | −0.163091 | − | 0.501943i | ||||
\(356\) | 10.6447 | + | 7.73381i | 0.564166 | + | 0.409891i | ||||
\(357\) | −3.12649 | − | 2.27153i | −0.165472 | − | 0.120222i | ||||
\(358\) | 2.48546 | + | 7.64946i | 0.131361 | + | 0.404287i | ||||
\(359\) | −0.737163 | − | 0.535580i | −0.0389060 | − | 0.0282669i | 0.568162 | − | 0.822917i | \(-0.307655\pi\) |
−0.607068 | + | 0.794650i | \(0.707655\pi\) | |||||||
\(360\) | 0.809017 | − | 0.587785i | 0.0426389 | − | 0.0309790i | ||||
\(361\) | 6.79277 | − | 20.9060i | 0.357514 | − | 1.10032i | ||||
\(362\) | 1.90424 | − | 1.38351i | 0.100084 | − | 0.0727156i | ||||
\(363\) | −3.27333 | − | 10.0743i | −0.171805 | − | 0.528763i | ||||
\(364\) | −2.11941 | − | 6.52288i | −0.111087 | − | 0.341892i | ||||
\(365\) | −3.76611 | + | 11.5909i | −0.197127 | + | 0.606695i | ||||
\(366\) | 8.93157 | 0.466861 | ||||||||
\(367\) | 20.6237 | 1.07655 | 0.538274 | − | 0.842770i | \(-0.319077\pi\) | ||||
0.538274 | + | 0.842770i | \(0.319077\pi\) | |||||||
\(368\) | −0.319091 | + | 0.982061i | −0.0166338 | + | 0.0511935i | ||||
\(369\) | 0.827931 | + | 0.601527i | 0.0431004 | + | 0.0313142i | ||||
\(370\) | 1.56267 | − | 1.13535i | 0.0812395 | − | 0.0590239i | ||||
\(371\) | −2.61391 | −0.135707 | ||||||||
\(372\) | 2.93228 | + | 4.73305i | 0.152032 | + | 0.245397i | ||||
\(373\) | 18.2982 | 0.947443 | 0.473722 | − | 0.880675i | \(-0.342910\pi\) | ||||
0.473722 | + | 0.880675i | \(0.342910\pi\) | |||||||
\(374\) | −2.03630 | + | 1.47946i | −0.105294 | + | 0.0765009i | ||||
\(375\) | −0.809017 | − | 0.587785i | −0.0417775 | − | 0.0303531i | ||||
\(376\) | −2.09389 | + | 6.44434i | −0.107984 | + | 0.332341i | ||||
\(377\) | −17.0618 | −0.878727 | ||||||||
\(378\) | 0.979852 | 0.0503982 | ||||||||
\(379\) | −0.279156 | + | 0.859154i | −0.0143393 | + | 0.0441318i | −0.957970 | − | 0.286868i | \(-0.907386\pi\) |
0.943631 | + | 0.331000i | \(0.107386\pi\) | |||||||
\(380\) | −1.97824 | − | 6.08839i | −0.101481 | − | 0.312328i | ||||
\(381\) | 1.96402 | + | 6.04464i | 0.100620 | + | 0.309676i | ||||
\(382\) | −7.64006 | + | 5.55083i | −0.390900 | + | 0.284005i | ||||
\(383\) | 2.03137 | − | 6.25190i | 0.103798 | − | 0.319457i | −0.885648 | − | 0.464356i | \(-0.846286\pi\) |
0.989446 | + | 0.144899i | \(0.0462857\pi\) | |||||||
\(384\) | 0.809017 | − | 0.587785i | 0.0412850 | − | 0.0299953i | ||||
\(385\) | 0.505898 | + | 0.367556i | 0.0257829 | + | 0.0187324i | ||||
\(386\) | 5.46861 | + | 16.8307i | 0.278345 | + | 0.856658i | ||||
\(387\) | −4.17286 | − | 3.03176i | −0.212119 | − | 0.154113i | ||||
\(388\) | 9.28638 | + | 6.74695i | 0.471445 | + | 0.342525i | ||||
\(389\) | 4.23173 | + | 13.0239i | 0.214557 | + | 0.660340i | 0.999185 | + | 0.0403721i | \(0.0128543\pi\) |
−0.784627 | + | 0.619968i | \(0.787146\pi\) | |||||||
\(390\) | 5.66279 | + | 4.11426i | 0.286747 | + | 0.208334i | ||||
\(391\) | −3.29480 | + | 2.39381i | −0.166625 | + | 0.121060i | ||||
\(392\) | 1.86643 | − | 5.74428i | 0.0942689 | − | 0.290130i | ||||
\(393\) | −15.0542 | + | 10.9375i | −0.759385 | + | 0.551726i | ||||
\(394\) | −4.72540 | − | 14.5433i | −0.238062 | − | 0.732680i | ||||
\(395\) | 0.0759239 | + | 0.233670i | 0.00382015 | + | 0.0117572i | ||||
\(396\) | 0.197209 | − | 0.606947i | 0.00991013 | − | 0.0305002i | ||||
\(397\) | −3.69480 | −0.185437 | −0.0927184 | − | 0.995692i | \(-0.529556\pi\) | ||||
−0.0927184 | + | 0.995692i | \(0.529556\pi\) | |||||||
\(398\) | 26.7719 | 1.34196 | ||||||||
\(399\) | 1.93838 | − | 5.96572i | 0.0970403 | − | 0.298659i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | −14.4921 | + | 10.5292i | −0.723703 | + | 0.525801i | −0.887565 | − | 0.460682i | \(-0.847605\pi\) |
0.163862 | + | 0.986483i | \(0.447605\pi\) | |||||||
\(402\) | −8.74062 | −0.435942 | ||||||||
\(403\) | −25.1654 | + | 29.7578i | −1.25358 | + | 1.48234i | ||||
\(404\) | 6.53094 | 0.324926 | ||||||||
\(405\) | −0.809017 | + | 0.587785i | −0.0402004 | + | 0.0292073i | ||||
\(406\) | 1.93228 | + | 1.40388i | 0.0958974 | + | 0.0696735i | ||||
\(407\) | 0.380923 | − | 1.17236i | 0.0188816 | − | 0.0581117i | ||||
\(408\) | 3.94402 | 0.195258 | ||||||||
\(409\) | −20.2226 | −0.999946 | −0.499973 | − | 0.866041i | \(-0.666657\pi\) | ||||
−0.499973 | + | 0.866041i | \(0.666657\pi\) | |||||||
\(410\) | 0.316241 | − | 0.973291i | 0.0156181 | − | 0.0480674i | ||||
\(411\) | 3.43454 | + | 10.5704i | 0.169414 | + | 0.521401i | ||||
\(412\) | −4.15346 | − | 12.7830i | −0.204626 | − | 0.629775i | ||||
\(413\) | 4.04698 | − | 2.94030i | 0.199139 | − | 0.144683i | ||||
\(414\) | 0.319091 | − | 0.982061i | 0.0156825 | − | 0.0482657i | ||||
\(415\) | 12.0607 | − | 8.76258i | 0.592034 | − | 0.430138i | ||||
\(416\) | 5.66279 | + | 4.11426i | 0.277641 | + | 0.201718i | ||||
\(417\) | −3.42928 | − | 10.5542i | −0.167933 | − | 0.516844i | ||||
\(418\) | −3.30520 | − | 2.40137i | −0.161663 | − | 0.117455i | ||||
\(419\) | 2.30793 | + | 1.67681i | 0.112750 | + | 0.0819176i | 0.642731 | − | 0.766092i | \(-0.277801\pi\) |
−0.529981 | + | 0.848009i | \(0.677801\pi\) | |||||||
\(420\) | −0.302791 | − | 0.931895i | −0.0147747 | − | 0.0454718i | ||||
\(421\) | 19.1149 | + | 13.8878i | 0.931601 | + | 0.676848i | 0.946384 | − | 0.323043i | \(-0.104706\pi\) |
−0.0147829 | + | 0.999891i | \(0.504706\pi\) | |||||||
\(422\) | −2.90537 | + | 2.11088i | −0.141431 | + | 0.102756i | ||||
\(423\) | 2.09389 | − | 6.44434i | 0.101809 | − | 0.313334i | ||||
\(424\) | 2.15818 | − | 1.56801i | 0.104810 | − | 0.0761493i | ||||
\(425\) | −1.21877 | − | 3.75099i | −0.0591190 | − | 0.181950i | ||||
\(426\) | 3.07287 | + | 9.45733i | 0.148881 | + | 0.458209i | ||||
\(427\) | 2.70440 | − | 8.32328i | 0.130875 | − | 0.402792i | ||||
\(428\) | 9.67818 | 0.467812 | ||||||||
\(429\) | 4.46701 | 0.215669 | ||||||||
\(430\) | −1.59389 | + | 4.90550i | −0.0768643 | + | 0.236564i | ||||
\(431\) | −27.0843 | − | 19.6779i | −1.30460 | − | 0.947851i | −0.304616 | − | 0.952475i | \(-0.598528\pi\) |
−0.999989 | + | 0.00462440i | \(0.998528\pi\) | |||||||
\(432\) | −0.809017 | + | 0.587785i | −0.0389238 | + | 0.0282798i | ||||
\(433\) | −0.904025 | −0.0434447 | −0.0217223 | − | 0.999764i | \(-0.506915\pi\) | ||||
−0.0217223 | + | 0.999764i | \(0.506915\pi\) | |||||||
\(434\) | 5.29857 | − | 1.29945i | 0.254339 | − | 0.0623756i | ||||
\(435\) | −2.43754 | −0.116871 | ||||||||
\(436\) | 13.0042 | − | 9.44807i | 0.622786 | − | 0.452480i | ||||
\(437\) | −5.34793 | − | 3.88550i | −0.255826 | − | 0.185869i | ||||
\(438\) | 3.76611 | − | 11.5909i | 0.179952 | − | 0.553834i | ||||
\(439\) | −28.6944 | −1.36951 | −0.684755 | − | 0.728773i | \(-0.740091\pi\) | ||||
−0.684755 | + | 0.728773i | \(0.740091\pi\) | |||||||
\(440\) | −0.638182 | −0.0304241 | ||||||||
\(441\) | −1.86643 | + | 5.74428i | −0.0888776 | + | 0.273537i | ||||
\(442\) | 8.53089 | + | 26.2554i | 0.405773 | + | 1.24884i | ||||
\(443\) | −10.1569 | − | 31.2598i | −0.482571 | − | 1.48520i | −0.835469 | − | 0.549538i | \(-0.814804\pi\) |
0.352898 | − | 0.935662i | \(-0.385196\pi\) | |||||||
\(444\) | −1.56267 | + | 1.13535i | −0.0741611 | + | 0.0538812i | ||||
\(445\) | −4.06590 | + | 12.5136i | −0.192742 | + | 0.593200i | ||||
\(446\) | 0.289539 | − | 0.210362i | 0.0137101 | − | 0.00996095i | ||||
\(447\) | −10.9638 | − | 7.96564i | −0.518568 | − | 0.376762i | ||||
\(448\) | −0.302791 | − | 0.931895i | −0.0143055 | − | 0.0440279i | ||||
\(449\) | −22.9007 | − | 16.6383i | −1.08075 | − | 0.785212i | −0.102938 | − | 0.994688i | \(-0.532824\pi\) |
−0.977814 | + | 0.209476i | \(0.932824\pi\) | |||||||
\(450\) | 0.809017 | + | 0.587785i | 0.0381374 | + | 0.0277085i | ||||
\(451\) | −0.201820 | − | 0.621137i | −0.00950331 | − | 0.0292482i | ||||
\(452\) | −3.70708 | − | 2.69335i | −0.174366 | − | 0.126685i | ||||
\(453\) | −4.04740 | + | 2.94061i | −0.190164 | + | 0.138162i | ||||
\(454\) | 4.54075 | − | 13.9750i | 0.213108 | − | 0.655878i | ||||
\(455\) | 5.54870 | − | 4.03136i | 0.260127 | − | 0.188993i | ||||
\(456\) | 1.97824 | + | 6.08839i | 0.0926394 | + | 0.285115i | ||||
\(457\) | 9.07320 | + | 27.9245i | 0.424427 | + | 1.30625i | 0.903542 | + | 0.428499i | \(0.140957\pi\) |
−0.479116 | + | 0.877752i | \(0.659043\pi\) | |||||||
\(458\) | 1.46655 | − | 4.51357i | 0.0685272 | − | 0.210905i | ||||
\(459\) | −3.94402 | −0.184091 | ||||||||
\(460\) | −1.03260 | −0.0481452 | ||||||||
\(461\) | −10.8555 | + | 33.4099i | −0.505592 | + | 1.55605i | 0.294180 | + | 0.955750i | \(0.404953\pi\) |
−0.799773 | + | 0.600303i | \(0.795047\pi\) | |||||||
\(462\) | −0.505898 | − | 0.367556i | −0.0235365 | − | 0.0171003i | ||||
\(463\) | 14.6761 | − | 10.6628i | 0.682056 | − | 0.495543i | −0.191983 | − | 0.981398i | \(-0.561492\pi\) |
0.874039 | + | 0.485855i | \(0.161492\pi\) | |||||||
\(464\) | −2.43754 | −0.113160 | ||||||||
\(465\) | −3.59527 | + | 4.25135i | −0.166727 | + | 0.197152i | ||||
\(466\) | −8.38127 | −0.388255 | ||||||||
\(467\) | 12.4867 | − | 9.07212i | 0.577816 | − | 0.419808i | −0.260120 | − | 0.965576i | \(-0.583762\pi\) |
0.837936 | + | 0.545769i | \(0.183762\pi\) | |||||||
\(468\) | −5.66279 | − | 4.11426i | −0.261763 | − | 0.190182i | ||||
\(469\) | −2.64658 | + | 8.14534i | −0.122208 | + | 0.376117i | ||||
\(470\) | −6.77598 | −0.312553 | ||||||||
\(471\) | −1.67376 | −0.0771229 | ||||||||
\(472\) | −1.57759 | + | 4.85533i | −0.0726146 | + | 0.223485i | ||||
\(473\) | 1.01719 | + | 3.13060i | 0.0467706 | + | 0.143945i | ||||
\(474\) | −0.0759239 | − | 0.233670i | −0.00348730 | − | 0.0107328i | ||||
\(475\) | 5.17909 | − | 3.76283i | 0.237633 | − | 0.172650i | ||||
\(476\) | 1.19421 | − | 3.67541i | 0.0547367 | − | 0.168462i | ||||
\(477\) | −2.15818 | + | 1.56801i | −0.0988163 | + | 0.0717942i | ||||
\(478\) | −18.1629 | − | 13.1961i | −0.830749 | − | 0.603575i | ||||
\(479\) | 7.62482 | + | 23.4668i | 0.348387 | + | 1.07222i | 0.959746 | + | 0.280871i | \(0.0906233\pi\) |
−0.611359 | + | 0.791354i | \(0.709377\pi\) | |||||||
\(480\) | 0.809017 | + | 0.587785i | 0.0369264 | + | 0.0268286i | ||||
\(481\) | −10.9381 | − | 7.94697i | −0.498733 | − | 0.362351i | ||||
\(482\) | −6.37005 | − | 19.6050i | −0.290148 | − | 0.892984i | ||||
\(483\) | −0.818560 | − | 0.594718i | −0.0372458 | − | 0.0270606i | ||||
\(484\) | 8.56969 | − | 6.22625i | 0.389532 | − | 0.283011i | ||||
\(485\) | −3.54708 | + | 10.9168i | −0.161065 | + | 0.495706i | ||||
\(486\) | 0.809017 | − | 0.587785i | 0.0366978 | − | 0.0266625i | ||||
\(487\) | −0.368282 | − | 1.13346i | −0.0166885 | − | 0.0513618i | 0.942365 | − | 0.334585i | \(-0.108596\pi\) |
−0.959054 | + | 0.283223i | \(0.908596\pi\) | |||||||
\(488\) | 2.76001 | + | 8.49443i | 0.124940 | + | 0.384525i | ||||
\(489\) | 2.70006 | − | 8.30993i | 0.122101 | − | 0.375788i | ||||
\(490\) | 6.03989 | 0.272854 | ||||||||
\(491\) | 20.3648 | 0.919049 | 0.459525 | − | 0.888165i | \(-0.348020\pi\) | ||||
0.459525 | + | 0.888165i | \(0.348020\pi\) | |||||||
\(492\) | −0.316241 | + | 0.973291i | −0.0142573 | + | 0.0438794i | ||||
\(493\) | −7.77765 | − | 5.65079i | −0.350288 | − | 0.254499i | ||||
\(494\) | −36.2515 | + | 26.3383i | −1.63103 | + | 1.18502i | ||||
\(495\) | 0.638182 | 0.0286841 | ||||||||
\(496\) | −3.59527 | + | 4.25135i | −0.161432 | + | 0.190891i | ||||
\(497\) | 9.74367 | 0.437063 | ||||||||
\(498\) | −12.0607 | + | 8.76258i | −0.540451 | + | 0.392660i | ||||
\(499\) | 22.8881 | + | 16.6292i | 1.02461 | + | 0.744425i | 0.967223 | − | 0.253927i | \(-0.0817224\pi\) |
0.0573893 | + | 0.998352i | \(0.481722\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | 1.88010 | 0.0839965 | ||||||||
\(502\) | 16.4599 | 0.734639 | ||||||||
\(503\) | −7.07307 | + | 21.7687i | −0.315373 | + | 0.970617i | 0.660228 | + | 0.751065i | \(0.270460\pi\) |
−0.975601 | + | 0.219552i | \(0.929540\pi\) | |||||||
\(504\) | 0.302791 | + | 0.931895i | 0.0134874 | + | 0.0415099i | ||||
\(505\) | 2.01817 | + | 6.21129i | 0.0898075 | + | 0.276399i | ||||
\(506\) | −0.533131 | + | 0.387343i | −0.0237006 | + | 0.0172195i | ||||
\(507\) | 11.1229 | − | 34.2326i | 0.493983 | − | 1.52032i | ||||
\(508\) | −5.14188 | + | 3.73579i | −0.228134 | + | 0.165749i | ||||
\(509\) | 12.1129 | + | 8.80051i | 0.536893 | + | 0.390076i | 0.822930 | − | 0.568143i | \(-0.192338\pi\) |
−0.286037 | + | 0.958219i | \(0.592338\pi\) | |||||||
\(510\) | 1.21877 | + | 3.75099i | 0.0539680 | + | 0.166096i | ||||
\(511\) | −9.66114 | − | 7.01923i | −0.427384 | − | 0.310512i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −1.97824 | − | 6.08839i | −0.0873413 | − | 0.268809i | ||||
\(514\) | −17.4461 | − | 12.6753i | −0.769513 | − | 0.559084i | ||||
\(515\) | 10.8739 | − | 7.90035i | 0.479161 | − | 0.348131i | ||||
\(516\) | 1.59389 | − | 4.90550i | 0.0701672 | − | 0.215952i | ||||
\(517\) | −3.49844 | + | 2.54176i | −0.153861 | + | 0.111787i | ||||
\(518\) | 0.584862 | + | 1.80002i | 0.0256973 | + | 0.0790883i | ||||
\(519\) | 4.25914 | + | 13.1083i | 0.186955 | + | 0.575390i | ||||
\(520\) | −2.16299 | + | 6.65701i | −0.0948535 | + | 0.291929i | ||||
\(521\) | −33.5284 | −1.46890 | −0.734452 | − | 0.678661i | \(-0.762561\pi\) | ||||
−0.734452 | + | 0.678661i | \(0.762561\pi\) | |||||||
\(522\) | 2.43754 | 0.106688 | ||||||||
\(523\) | 12.0001 | − | 36.9325i | 0.524728 | − | 1.61495i | −0.240125 | − | 0.970742i | \(-0.577188\pi\) |
0.764853 | − | 0.644205i | \(-0.222812\pi\) | |||||||
\(524\) | −15.0542 | − | 10.9375i | −0.657647 | − | 0.477808i | ||||
\(525\) | 0.792717 | − | 0.575943i | 0.0345970 | − | 0.0251362i | ||||
\(526\) | 10.9373 | 0.476887 | ||||||||
\(527\) | −21.3274 | + | 5.23044i | −0.929035 | + | 0.227842i | ||||
\(528\) | 0.638182 | 0.0277733 | ||||||||
\(529\) | 17.7448 | − | 12.8923i | 0.771512 | − | 0.560536i | ||||
\(530\) | 2.15818 | + | 1.56801i | 0.0937453 | + | 0.0681100i | ||||
\(531\) | 1.57759 | − | 4.85533i | 0.0684617 | − | 0.210703i | ||||
\(532\) | 6.27273 | 0.271957 | ||||||||
\(533\) | −7.16324 | −0.310274 | ||||||||
\(534\) | 4.06590 | − | 12.5136i | 0.175949 | − | 0.541515i | ||||
\(535\) | 2.99072 | + | 9.20449i | 0.129300 | + | 0.397945i | ||||
\(536\) | −2.70100 | − | 8.31282i | −0.116665 | − | 0.359059i | ||||
\(537\) | 6.50702 | − | 4.72763i | 0.280799 | − | 0.204012i | ||||
\(538\) | 5.59940 | − | 17.2332i | 0.241407 | − | 0.742975i | ||||
\(539\) | 3.11840 | − | 2.26565i | 0.134319 | − | 0.0975883i | ||||
\(540\) | −0.809017 | − | 0.587785i | −0.0348145 | − | 0.0252942i | ||||
\(541\) | −10.6491 | − | 32.7747i | −0.457842 | − | 1.40909i | −0.867766 | − | 0.496973i | \(-0.834445\pi\) |
0.409924 | − | 0.912120i | \(-0.365555\pi\) | |||||||
\(542\) | −2.91551 | − | 2.11824i | −0.125232 | − | 0.0909863i | ||||
\(543\) | −1.90424 | − | 1.38351i | −0.0817186 | − | 0.0593720i | ||||
\(544\) | 1.21877 | + | 3.75099i | 0.0522543 | + | 0.160822i | ||||
\(545\) | 13.0042 | + | 9.44807i | 0.557037 | + | 0.404711i | ||||
\(546\) | −5.54870 | + | 4.03136i | −0.237462 | + | 0.172526i | ||||
\(547\) | −8.29020 | + | 25.5146i | −0.354464 | + | 1.09093i | 0.601856 | + | 0.798604i | \(0.294428\pi\) |
−0.956320 | + | 0.292322i | \(0.905572\pi\) | |||||||
\(548\) | −8.99175 | + | 6.53289i | −0.384109 | + | 0.279071i | ||||
\(549\) | −2.76001 | − | 8.49443i | −0.117794 | − | 0.362533i | ||||
\(550\) | −0.197209 | − | 0.606947i | −0.00840902 | − | 0.0258803i | ||||
\(551\) | 4.82203 | − | 14.8407i | 0.205425 | − | 0.632234i | ||||
\(552\) | 1.03260 | 0.0439504 | ||||||||
\(553\) | −0.240745 | −0.0102375 | ||||||||
\(554\) | 1.00396 | − | 3.08987i | 0.0426541 | − | 0.131276i | ||||
\(555\) | −1.56267 | − | 1.13535i | −0.0663317 | − | 0.0481928i | ||||
\(556\) | 8.97798 | − | 6.52288i | 0.380751 | − | 0.276632i | ||||
\(557\) | −3.99121 | −0.169113 | −0.0845566 | − | 0.996419i | \(-0.526947\pi\) | ||||
−0.0845566 | + | 0.996419i | \(0.526947\pi\) | |||||||
\(558\) | 3.59527 | − | 4.25135i | 0.152200 | − | 0.179974i | ||||
\(559\) | 36.1035 | 1.52702 | ||||||||
\(560\) | 0.792717 | − | 0.575943i | 0.0334984 | − | 0.0243380i | ||||
\(561\) | 2.03630 | + | 1.47946i | 0.0859726 | + | 0.0624627i | ||||
\(562\) | −7.65180 | + | 23.5498i | −0.322772 | + | 0.993389i | ||||
\(563\) | −34.4435 | −1.45162 | −0.725811 | − | 0.687894i | \(-0.758535\pi\) | ||||
−0.725811 | + | 0.687894i | \(0.758535\pi\) | |||||||
\(564\) | 6.77598 | 0.285320 | ||||||||
\(565\) | 1.41598 | − | 4.35793i | 0.0595707 | − | 0.183340i | ||||
\(566\) | 8.47201 | + | 26.0742i | 0.356105 | + | 1.09598i | ||||
\(567\) | −0.302791 | − | 0.931895i | −0.0127160 | − | 0.0391359i | ||||
\(568\) | −8.04488 | + | 5.84495i | −0.337556 | + | 0.245249i | ||||
\(569\) | 6.58102 | − | 20.2543i | 0.275891 | − | 0.849104i | −0.713092 | − | 0.701071i | \(-0.752706\pi\) |
0.988982 | − | 0.148033i | \(-0.0472943\pi\) | |||||||
\(570\) | −5.17909 | + | 3.76283i | −0.216928 | + | 0.157608i | ||||
\(571\) | −18.7063 | − | 13.5910i | −0.782836 | − | 0.568764i | 0.122993 | − | 0.992408i | \(-0.460751\pi\) |
−0.905829 | + | 0.423644i | \(0.860751\pi\) | |||||||
\(572\) | 1.38038 | + | 4.24838i | 0.0577167 | + | 0.177634i | ||||
\(573\) | 7.64006 | + | 5.55083i | 0.319168 | + | 0.231889i | ||||
\(574\) | 0.811250 | + | 0.589408i | 0.0338609 | + | 0.0246014i | ||||
\(575\) | −0.319091 | − | 0.982061i | −0.0133070 | − | 0.0409548i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | 1.92827 | − | 1.40097i | 0.0802750 | − | 0.0583232i | −0.546924 | − | 0.837182i | \(-0.684201\pi\) |
0.627199 | + | 0.778859i | \(0.284201\pi\) | |||||||
\(578\) | 0.446436 | − | 1.37399i | 0.0185693 | − | 0.0571504i | ||||
\(579\) | 14.3170 | − | 10.4019i | 0.594995 | − | 0.432289i | ||||
\(580\) | −0.753241 | − | 2.31824i | −0.0312766 | − | 0.0962596i | ||||
\(581\) | 4.51394 | + | 13.8925i | 0.187270 | + | 0.576357i | ||||
\(582\) | 3.54708 | − | 10.9168i | 0.147031 | − | 0.452516i | ||||
\(583\) | 1.70245 | 0.0705083 | ||||||||
\(584\) | 12.1874 | 0.504317 | ||||||||
\(585\) | 2.16299 | − | 6.65701i | 0.0894288 | − | 0.275233i | ||||
\(586\) | −5.66869 | − | 4.11854i | −0.234171 | − | 0.170135i | ||||
\(587\) | −19.2256 | + | 13.9682i | −0.793527 | + | 0.576531i | −0.909008 | − | 0.416779i | \(-0.863159\pi\) |
0.115481 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(588\) | −6.03989 | −0.249081 | ||||||||
\(589\) | −18.7716 | − | 30.2996i | −0.773470 | − | 1.24847i | ||||
\(590\) | −5.10520 | −0.210178 | ||||||||
\(591\) | −12.3713 | + | 8.98824i | −0.508885 | + | 0.369727i | ||||
\(592\) | −1.56267 | − | 1.13535i | −0.0642254 | − | 0.0466625i | ||||
\(593\) | −9.25331 | + | 28.4787i | −0.379988 | + | 1.16948i | 0.560064 | + | 0.828450i | \(0.310777\pi\) |
−0.940051 | + | 0.341033i | \(0.889223\pi\) | |||||||
\(594\) | −0.638182 | −0.0261849 | ||||||||
\(595\) | 3.86456 | 0.158431 | ||||||||
\(596\) | 4.18778 | − | 12.8887i | 0.171538 | − | 0.527941i | ||||
\(597\) | −8.27298 | − | 25.4616i | −0.338591 | − | 1.04207i | ||||
\(598\) | 2.23351 | + | 6.87403i | 0.0913349 | + | 0.281100i | ||||
\(599\) | 14.1071 | − | 10.2494i | 0.576400 | − | 0.418779i | −0.261025 | − | 0.965332i | \(-0.584060\pi\) |
0.837424 | + | 0.546553i | \(0.184060\pi\) | |||||||
\(600\) | −0.309017 | + | 0.951057i | −0.0126156 | + | 0.0388267i | ||||
\(601\) | 0.741681 | − | 0.538863i | 0.0302538 | − | 0.0219807i | −0.572556 | − | 0.819866i | \(-0.694048\pi\) |
0.602809 | + | 0.797885i | \(0.294048\pi\) | |||||||
\(602\) | −4.08879 | − | 2.97068i | −0.166647 | − | 0.121076i | ||||
\(603\) | 2.70100 | + | 8.31282i | 0.109993 | + | 0.338524i | ||||
\(604\) | −4.04740 | − | 2.94061i | −0.164686 | − | 0.119652i | ||||
\(605\) | 8.56969 | + | 6.22625i | 0.348408 | + | 0.253133i | ||||
\(606\) | −2.01817 | − | 6.21129i | −0.0819826 | − | 0.252317i | ||||
\(607\) | −2.28505 | − | 1.66019i | −0.0927475 | − | 0.0673850i | 0.540445 | − | 0.841379i | \(-0.318256\pi\) |
−0.633193 | + | 0.773994i | \(0.718256\pi\) | |||||||
\(608\) | −5.17909 | + | 3.76283i | −0.210040 | + | 0.152603i | ||||
\(609\) | 0.738065 | − | 2.27153i | 0.0299079 | − | 0.0920470i | ||||
\(610\) | −7.22579 | + | 5.24984i | −0.292564 | + | 0.212560i | ||||
\(611\) | 14.6564 | + | 45.1078i | 0.592934 | + | 1.82486i | ||||
\(612\) | −1.21877 | − | 3.75099i | −0.0492658 | − | 0.151625i | ||||
\(613\) | 12.8093 | − | 39.4229i | 0.517361 | − | 1.59227i | −0.261583 | − | 0.965181i | \(-0.584244\pi\) |
0.778944 | − | 0.627093i | \(-0.215756\pi\) | |||||||
\(614\) | −2.91414 | −0.117605 | ||||||||
\(615\) | −1.02338 | −0.0412666 | ||||||||
\(616\) | 0.193236 | − | 0.594718i | 0.00778569 | − | 0.0239619i | ||||
\(617\) | 36.3494 | + | 26.4094i | 1.46337 | + | 1.06320i | 0.982469 | + | 0.186426i | \(0.0596903\pi\) |
0.480901 | + | 0.876775i | \(0.340310\pi\) | |||||||
\(618\) | −10.8739 | + | 7.90035i | −0.437412 | + | 0.317799i | ||||
\(619\) | −43.1962 | −1.73620 | −0.868100 | − | 0.496389i | \(-0.834659\pi\) | ||||
−0.868100 | + | 0.496389i | \(0.834659\pi\) | |||||||
\(620\) | −5.15428 | − | 2.10557i | −0.207001 | − | 0.0845616i | ||||
\(621\) | −1.03260 | −0.0414368 | ||||||||
\(622\) | 20.1039 | − | 14.6063i | 0.806092 | − | 0.585660i | ||||
\(623\) | −10.4302 | − | 7.57799i | −0.417877 | − | 0.303606i | ||||
\(624\) | 2.16299 | − | 6.65701i | 0.0865890 | − | 0.266494i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.0209 | −0.440485 | ||||||||
\(627\) | −1.26247 | + | 3.88550i | −0.0504184 | + | 0.155172i | ||||
\(628\) | −0.517221 | − | 1.59184i | −0.0206394 | − | 0.0635214i | ||||
\(629\) | −2.35414 | − | 7.24529i | −0.0938656 | − | 0.288889i | ||||
\(630\) | −0.792717 | + | 0.575943i | −0.0315826 | + | 0.0229461i | ||||
\(631\) | 1.64000 | − | 5.04740i | 0.0652874 | − | 0.200934i | −0.913091 | − | 0.407755i | \(-0.866312\pi\) |
0.978379 | + | 0.206821i | \(0.0663118\pi\) | |||||||
\(632\) | 0.198771 | − | 0.144416i | 0.00790670 | − | 0.00574456i | ||||
\(633\) | 2.90537 | + | 2.11088i | 0.115478 | + | 0.0838998i | ||||
\(634\) | 7.36015 | + | 22.6522i | 0.292309 | + | 0.899634i | ||||
\(635\) | −5.14188 | − | 3.73579i | −0.204049 | − | 0.148250i | ||||
\(636\) | −2.15818 | − | 1.56801i | −0.0855774 | − | 0.0621756i | ||||
\(637\) | −13.0642 | − | 40.2076i | −0.517624 | − | 1.59308i | ||||
\(638\) | −1.25850 | − | 0.914355i | −0.0498245 | − | 0.0361997i | ||||
\(639\) | 8.04488 | − | 5.84495i | 0.318251 | − | 0.231223i | ||||
\(640\) | −0.309017 | + | 0.951057i | −0.0122150 | + | 0.0375938i | ||||
\(641\) | −31.9810 | + | 23.2356i | −1.26318 | + | 0.917751i | −0.998909 | − | 0.0466992i | \(-0.985130\pi\) |
−0.264266 | + | 0.964450i | \(0.585130\pi\) | |||||||
\(642\) | −2.99072 | − | 9.20449i | −0.118034 | − | 0.363272i | ||||
\(643\) | −2.72004 | − | 8.37144i | −0.107268 | − | 0.330137i | 0.882988 | − | 0.469396i | \(-0.155528\pi\) |
−0.990256 | + | 0.139258i | \(0.955528\pi\) | |||||||
\(644\) | 0.312662 | − | 0.962274i | 0.0123206 | − | 0.0379189i | ||||
\(645\) | 5.15794 | 0.203094 | ||||||||
\(646\) | −25.2485 | −0.993388 | ||||||||
\(647\) | 10.0392 | − | 30.8975i | 0.394681 | − | 1.21470i | −0.534528 | − | 0.845151i | \(-0.679511\pi\) |
0.929209 | − | 0.369554i | \(-0.120489\pi\) | |||||||
\(648\) | 0.809017 | + | 0.587785i | 0.0317812 | + | 0.0230904i | ||||
\(649\) | −2.63581 | + | 1.91503i | −0.103465 | + | 0.0751715i | ||||
\(650\) | −6.99959 | −0.274547 | ||||||||
\(651\) | −2.87320 | − | 4.63769i | −0.112610 | − | 0.181765i | ||||
\(652\) | 8.73757 | 0.342190 | ||||||||
\(653\) | 1.77801 | − | 1.29180i | 0.0695788 | − | 0.0505520i | −0.552452 | − | 0.833545i | \(-0.686308\pi\) |
0.622031 | + | 0.782993i | \(0.286308\pi\) | |||||||
\(654\) | −13.0042 | − | 9.44807i | −0.508503 | − | 0.369449i | ||||
\(655\) | 5.75020 | − | 17.6973i | 0.224679 | − | 0.691491i | ||||
\(656\) | −1.02338 | −0.0399562 | ||||||||
\(657\) | −12.1874 | −0.475475 | ||||||||
\(658\) | 2.05170 | − | 6.31450i | 0.0799838 | − | 0.246165i | ||||
\(659\) | 13.9322 | + | 42.8790i | 0.542722 | + | 1.67033i | 0.726345 | + | 0.687331i | \(0.241218\pi\) |
−0.183622 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(660\) | 0.197209 | + | 0.606947i | 0.00767635 | + | 0.0236254i | ||||
\(661\) | 3.68403 | − | 2.67660i | 0.143292 | − | 0.104108i | −0.513830 | − | 0.857892i | \(-0.671774\pi\) |
0.657122 | + | 0.753784i | \(0.271774\pi\) | |||||||
\(662\) | −4.53789 | + | 13.9662i | −0.176370 | + | 0.542812i | ||||
\(663\) | 22.3342 | − | 16.2267i | 0.867387 | − | 0.630194i | ||||
\(664\) | −12.0607 | − | 8.76258i | −0.468044 | − | 0.340054i | ||||
\(665\) | 1.93838 | + | 5.96572i | 0.0751671 | + | 0.231341i | ||||
\(666\) | 1.56267 | + | 1.13535i | 0.0605523 | + | 0.0439938i | ||||
\(667\) | −2.03630 | − | 1.47946i | −0.0788458 | − | 0.0572848i | ||||
\(668\) | 0.580981 | + | 1.78808i | 0.0224788 | + | 0.0691828i | ||||
\(669\) | −0.289539 | − | 0.210362i | −0.0111942 | − | 0.00813308i | ||||
\(670\) | 7.07131 | − | 5.13761i | 0.273189 | − | 0.198483i | ||||
\(671\) | −1.76139 | + | 5.42099i | −0.0679976 | + | 0.209275i | ||||
\(672\) | −0.792717 | + | 0.575943i | −0.0305797 | + | 0.0222175i | ||||
\(673\) | −13.9706 | − | 42.9970i | −0.538527 | − | 1.65741i | −0.735903 | − | 0.677087i | \(-0.763242\pi\) |
0.197377 | − | 0.980328i | \(-0.436758\pi\) | |||||||
\(674\) | −0.212982 | − | 0.655491i | −0.00820376 | − | 0.0252486i | ||||
\(675\) | 0.309017 | − | 0.951057i | 0.0118941 | − | 0.0366062i | ||||
\(676\) | 35.9943 | 1.38440 | ||||||||
\(677\) | −8.39375 | −0.322598 | −0.161299 | − | 0.986906i | \(-0.551568\pi\) | ||||
−0.161299 | + | 0.986906i | \(0.551568\pi\) | |||||||
\(678\) | −1.41598 | + | 4.35793i | −0.0543803 | + | 0.167365i | ||||
\(679\) | −9.09928 | − | 6.61101i | −0.349198 | − | 0.253707i | ||||
\(680\) | −3.19078 | + | 2.31824i | −0.122361 | + | 0.0889003i | ||||
\(681\) | −14.6942 | −0.563081 | ||||||||
\(682\) | −3.45098 | + | 0.846338i | −0.132145 | + | 0.0324080i | ||||
\(683\) | 44.9622 | 1.72043 | 0.860215 | − | 0.509932i | \(-0.170329\pi\) | ||||
0.860215 | + | 0.509932i | \(0.170329\pi\) | |||||||
\(684\) | 5.17909 | − | 3.76283i | 0.198027 | − | 0.143875i | ||||
\(685\) | −8.99175 | − | 6.53289i | −0.343557 | − | 0.249609i | ||||
\(686\) | −3.94836 | + | 12.1518i | −0.150749 | + | 0.463958i | ||||
\(687\) | −4.74585 | −0.181065 | ||||||||
\(688\) | 5.15794 | 0.196645 | ||||||||
\(689\) | 5.77013 | − | 17.7586i | 0.219824 | − | 0.676550i | ||||
\(690\) | 0.319091 | + | 0.982061i | 0.0121476 | + | 0.0373864i | ||||
\(691\) | −6.90265 | − | 21.2442i | −0.262589 | − | 0.808167i | −0.992239 | − | 0.124346i | \(-0.960317\pi\) |
0.729650 | − | 0.683821i | \(-0.239683\pi\) | |||||||
\(692\) | −11.1506 | + | 8.10136i | −0.423881 | + | 0.307968i | ||||
\(693\) | −0.193236 | + | 0.594718i | −0.00734042 | + | 0.0225915i | ||||
\(694\) | −4.65871 | + | 3.38475i | −0.176842 | + | 0.128483i | ||||
\(695\) | 8.97798 | + | 6.52288i | 0.340554 | + | 0.247427i | ||||
\(696\) | 0.753241 | + | 2.31824i | 0.0285515 | + | 0.0878726i | ||||
\(697\) | −3.26538 | − | 2.37244i | −0.123685 | − | 0.0898624i | ||||
\(698\) | −10.0799 | − | 7.32348i | −0.381530 | − | 0.277198i | ||||
\(699\) | 2.58995 | + | 7.97106i | 0.0979611 | + | 0.301493i | ||||
\(700\) | 0.792717 | + | 0.575943i | 0.0299619 | + | 0.0217686i | ||||
\(701\) | −4.78463 | + | 3.47623i | −0.180713 | + | 0.131296i | −0.674464 | − | 0.738308i | \(-0.735625\pi\) |
0.493751 | + | 0.869603i | \(0.335625\pi\) | |||||||
\(702\) | −2.16299 | + | 6.65701i | −0.0816369 | + | 0.251253i | ||||
\(703\) | 10.0038 | − | 7.26816i | 0.377299 | − | 0.274124i | ||||
\(704\) | 0.197209 | + | 0.606947i | 0.00743260 | + | 0.0228752i | ||||
\(705\) | 2.09389 | + | 6.44434i | 0.0788606 | + | 0.242708i | ||||
\(706\) | 7.69526 | − | 23.6836i | 0.289615 | − | 0.891343i | ||||
\(707\) | −6.39936 | −0.240673 | ||||||||
\(708\) | 5.10520 | 0.191865 | ||||||||
\(709\) | −12.8558 | + | 39.5660i | −0.482809 | + | 1.48593i | 0.352320 | + | 0.935880i | \(0.385393\pi\) |
−0.835129 | + | 0.550054i | \(0.814607\pi\) | |||||||
\(710\) | −8.04488 | − | 5.84495i | −0.301919 | − | 0.219357i | ||||
\(711\) | −0.198771 | + | 0.144416i | −0.00745451 | + | 0.00541602i | ||||
\(712\) | 13.1575 | 0.493100 | ||||||||
\(713\) | −5.58381 | + | 1.36940i | −0.209115 | + | 0.0512846i | ||||
\(714\) | −3.86456 | −0.144627 | ||||||||
\(715\) | −3.61389 | + | 2.62565i | −0.135152 | + | 0.0981936i | ||||
\(716\) | 6.50702 | + | 4.72763i | 0.243179 | + | 0.176680i | ||||
\(717\) | −6.93759 | + | 21.3517i | −0.259089 | + | 0.797394i | ||||
\(718\) | −0.911184 | −0.0340051 | ||||||||
\(719\) | −2.88043 | −0.107422 | −0.0537109 | − | 0.998557i | \(-0.517105\pi\) | ||||
−0.0537109 | + | 0.998557i | \(0.517105\pi\) | |||||||
\(720\) | 0.309017 | − | 0.951057i | 0.0115164 | − | 0.0354438i | ||||
\(721\) | 4.06978 | + | 12.5255i | 0.151566 | + | 0.466473i | ||||
\(722\) | −6.79277 | − | 20.9060i | −0.252801 | − | 0.778041i | ||||
\(723\) | −16.6770 | + | 12.1166i | −0.620225 | + | 0.450620i | ||||
\(724\) | 0.727353 | − | 2.23856i | 0.0270319 | − | 0.0831956i | ||||
\(725\) | 1.97201 | − | 1.43275i | 0.0732386 | − | 0.0532110i | ||||
\(726\) | −8.56969 | − | 6.22625i | −0.318051 | − | 0.231078i | ||||
\(727\) | 0.277581 | + | 0.854307i | 0.0102949 | + | 0.0316845i | 0.956072 | − | 0.293132i | \(-0.0946975\pi\) |
−0.945777 | + | 0.324816i | \(0.894698\pi\) | |||||||
\(728\) | −5.54870 | − | 4.03136i | −0.205648 | − | 0.149412i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 3.76611 | + | 11.5909i | 0.139390 | + | 0.428998i | ||||
\(731\) | 16.4579 | + | 11.9573i | 0.608716 | + | 0.442258i | ||||
\(732\) | 7.22579 | − | 5.24984i | 0.267073 | − | 0.194040i | ||||
\(733\) | 0.952102 | − | 2.93027i | 0.0351667 | − | 0.108232i | −0.931932 | − | 0.362632i | \(-0.881878\pi\) |
0.967099 | + | 0.254400i | \(0.0818781\pi\) | |||||||
\(734\) | 16.6849 | − | 12.1223i | 0.615851 | − | 0.447442i | ||||
\(735\) | −1.86643 | − | 5.74428i | −0.0688443 | − | 0.211881i | ||||
\(736\) | 0.319091 | + | 0.982061i | 0.0117618 | + | 0.0361992i | ||||
\(737\) | 1.72373 | − | 5.30509i | 0.0634944 | − | 0.195416i | ||||
\(738\) | 1.02338 | 0.0376711 | ||||||||
\(739\) | −12.2372 | −0.450153 | −0.225077 | − | 0.974341i | \(-0.572263\pi\) | ||||
−0.225077 | + | 0.974341i | \(0.572263\pi\) | |||||||
\(740\) | 0.596888 | − | 1.83703i | 0.0219420 | − | 0.0675306i | ||||
\(741\) | 36.2515 | + | 26.3383i | 1.33173 | + | 0.967561i | ||||
\(742\) | −2.11470 | + | 1.53642i | −0.0776330 | + | 0.0564037i | ||||
\(743\) | −4.77574 | −0.175205 | −0.0876025 | − | 0.996156i | \(-0.527921\pi\) | ||||
−0.0876025 | + | 0.996156i | \(0.527921\pi\) | |||||||
\(744\) | 5.15428 | + | 2.10557i | 0.188965 | + | 0.0771938i | ||||
\(745\) | 13.5520 | 0.496505 | ||||||||
\(746\) | 14.8035 | − | 10.7554i | 0.541996 | − | 0.393783i | ||||
\(747\) | 12.0607 | + | 8.76258i | 0.441276 | + | 0.320606i | ||||
\(748\) | −0.777797 | + | 2.39381i | −0.0284391 | + | 0.0875264i | ||||
\(749\) | −9.48318 | −0.346508 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 10.9925 | − | 33.8313i | 0.401121 | − | 1.23452i | −0.522971 | − | 0.852351i | \(-0.675176\pi\) |
0.924091 | − | 0.382172i | \(-0.124824\pi\) | |||||||
\(752\) | 2.09389 | + | 6.44434i | 0.0763564 | + | 0.235001i | ||||
\(753\) | −5.08637 | − | 15.6543i | −0.185358 | − | 0.570473i | ||||
\(754\) | −13.8033 | + | 10.0287i | −0.502686 | + | 0.365222i | ||||
\(755\) | 1.54597 | − | 4.75801i | 0.0562636 | − | 0.173162i | ||||
\(756\) | 0.792717 | − | 0.575943i | 0.0288308 | − | 0.0209468i | ||||
\(757\) | 43.8291 | + | 31.8437i | 1.59300 | + | 1.15738i | 0.899500 | + | 0.436920i | \(0.143931\pi\) |
0.693496 | + | 0.720460i | \(0.256069\pi\) | |||||||
\(758\) | 0.279156 | + | 0.859154i | 0.0101394 | + | 0.0312059i | ||||
\(759\) | 0.533131 | + | 0.387343i | 0.0193514 | + | 0.0140596i | ||||
\(760\) | −5.17909 | − | 3.76283i | −0.187865 | − | 0.136492i | ||||
\(761\) | 4.32086 | + | 13.2983i | 0.156631 | + | 0.482061i | 0.998323 | − | 0.0578977i | \(-0.0184397\pi\) |
−0.841691 | + | 0.539959i | \(0.818440\pi\) | |||||||
\(762\) | 5.14188 | + | 3.73579i | 0.186271 | + | 0.135334i | ||||
\(763\) | −12.7421 | + | 9.25771i | −0.461297 | + | 0.335152i | ||||
\(764\) | −2.91824 | + | 8.98143i | −0.105578 | + | 0.324937i | ||||
\(765\) | 3.19078 | − | 2.31824i | 0.115363 | − | 0.0838160i | ||||
\(766\) | −2.03137 | − | 6.25190i | −0.0733962 | − | 0.225890i | ||||
\(767\) | 11.0425 | + | 33.9853i | 0.398722 | + | 1.22714i | ||||
\(768\) | 0.309017 | − | 0.951057i | 0.0111507 | − | 0.0343183i | ||||
\(769\) | 39.2991 | 1.41716 | 0.708581 | − | 0.705630i | \(-0.249336\pi\) | ||||
0.708581 | + | 0.705630i | \(0.249336\pi\) | |||||||
\(770\) | 0.625324 | 0.0225351 | ||||||||
\(771\) | −6.66380 | + | 20.5091i | −0.239991 | + | 0.738616i | ||||
\(772\) | 14.3170 | + | 10.4019i | 0.515281 | + | 0.374373i | ||||
\(773\) | 11.8276 | − | 8.59323i | 0.425408 | − | 0.309077i | −0.354402 | − | 0.935093i | \(-0.615316\pi\) |
0.779810 | + | 0.626016i | \(0.215316\pi\) | |||||||
\(774\) | −5.15794 | −0.185398 | ||||||||
\(775\) | 0.409753 | − | 5.55267i | 0.0147187 | − | 0.199458i | ||||
\(776\) | 11.4786 | 0.412058 | ||||||||
\(777\) | 1.53119 | − | 1.11247i | 0.0549310 | − | 0.0399097i | ||||
\(778\) | 11.0788 | + | 8.04924i | 0.397195 | + | 0.288579i | ||||
\(779\) | 2.02449 | − | 6.23073i | 0.0725347 | − | 0.223239i | ||||
\(780\) | 6.99959 | 0.250626 | ||||||||
\(781\) | −6.34609 | −0.227081 | ||||||||
\(782\) | −1.25850 | + | 3.87327i | −0.0450039 | + | 0.138508i | ||||
\(783\) | −0.753241 | − | 2.31824i | −0.0269186 | − | 0.0828470i | ||||
\(784\) | −1.86643 | − | 5.74428i | −0.0666582 | − | 0.205153i | ||||
\(785\) | 1.35410 | − | 0.983813i | 0.0483300 | − | 0.0351138i | ||||
\(786\) | −5.75020 | + | 17.6973i | −0.205103 | + | 0.631242i | ||||
\(787\) | 14.4303 | − | 10.4842i | 0.514384 | − | 0.373722i | −0.300100 | − | 0.953908i | \(-0.597020\pi\) |
0.814484 | + | 0.580186i | \(0.197020\pi\) | |||||||
\(788\) | −12.3713 | − | 8.98824i | −0.440708 | − | 0.320193i | ||||
\(789\) | −3.37980 | − | 10.4020i | −0.120324 | − | 0.370319i | ||||
\(790\) | 0.198771 | + | 0.144416i | 0.00707197 | + | 0.00513809i | ||||
\(791\) | 3.63239 | + | 2.63909i | 0.129153 | + | 0.0938351i | ||||
\(792\) | −0.197209 | − | 0.606947i | −0.00700752 | − | 0.0215669i | ||||
\(793\) | 50.5776 | + | 36.7468i | 1.79606 | + | 1.30492i | ||||
\(794\) | −2.98916 | + | 2.17175i | −0.106081 | + | 0.0770726i | ||||
\(795\) | 0.824351 | − | 2.53709i | 0.0292367 | − | 0.0899814i | ||||
\(796\) | 21.6590 | − | 15.7361i | 0.767681 | − | 0.557753i | ||||
\(797\) | 10.2174 | + | 31.4460i | 0.361920 | + | 1.11387i | 0.951888 | + | 0.306448i | \(0.0991404\pi\) |
−0.589968 | + | 0.807427i | \(0.700860\pi\) | |||||||
\(798\) | −1.93838 | − | 5.96572i | −0.0686179 | − | 0.211184i | ||||
\(799\) | −8.25836 | + | 25.4166i | −0.292160 | + | 0.899175i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −13.1575 | −0.464899 | ||||||||
\(802\) | −5.53550 | + | 17.0365i | −0.195465 | + | 0.601581i | ||||
\(803\) | 6.29234 | + | 4.57166i | 0.222052 | + | 0.161330i | ||||
\(804\) | −7.07131 | + | 5.13761i | −0.249386 | + | 0.181189i | ||||
\(805\) | 1.01180 | 0.0356611 | ||||||||
\(806\) | −2.86810 | + | 38.8664i | −0.101025 | + | 1.36901i | ||||
\(807\) | −18.1200 | −0.637855 | ||||||||
\(808\) | 5.28364 | − | 3.83879i | 0.185878 | − | 0.135048i | ||||
\(809\) | −40.5983 | − | 29.4964i | −1.42736 | − | 1.03704i | −0.990500 | − | 0.137510i | \(-0.956090\pi\) |
−0.436861 | − | 0.899529i | \(-0.643910\pi\) | |||||||
\(810\) | −0.309017 | + | 0.951057i | −0.0108578 | + | 0.0334167i | ||||
\(811\) | 51.8830 | 1.82186 | 0.910930 | − | 0.412561i | \(-0.135366\pi\) | ||||
0.910930 | + | 0.412561i | \(0.135366\pi\) | |||||||
\(812\) | 2.38843 | 0.0838174 | ||||||||
\(813\) | −1.11363 | + | 3.42739i | −0.0390566 | + | 0.120204i | ||||
\(814\) | −0.380923 | − | 1.17236i | −0.0133513 | − | 0.0410912i | ||||
\(815\) | 2.70006 | + | 8.30993i | 0.0945789 | + | 0.291084i | ||||
\(816\) | 3.19078 | − | 2.31824i | 0.111700 | − | 0.0811545i | ||||
\(817\) | −10.2036 | + | 31.4036i | −0.356980 | + | 1.09867i | ||||
\(818\) | −16.3605 | + | 11.8866i | −0.572030 | + | 0.415604i | ||||
\(819\) | 5.54870 | + | 4.03136i | 0.193887 | + | 0.140867i | ||||
\(820\) | −0.316241 | − | 0.973291i | −0.0110436 | − | 0.0339888i | ||||
\(821\) | −17.3634 | − | 12.6153i | −0.605988 | − | 0.440276i | 0.242011 | − | 0.970273i | \(-0.422193\pi\) |
−0.847999 | + | 0.529997i | \(0.822193\pi\) | |||||||
\(822\) | 8.99175 | + | 6.53289i | 0.313623 | + | 0.227861i | ||||
\(823\) | 4.09944 | + | 12.6168i | 0.142898 | + | 0.439793i | 0.996735 | − | 0.0807469i | \(-0.0257306\pi\) |
−0.853837 | + | 0.520540i | \(0.825731\pi\) | |||||||
\(824\) | −10.8739 | − | 7.90035i | −0.378810 | − | 0.275222i | ||||
\(825\) | −0.516300 | + | 0.375114i | −0.0179753 | + | 0.0130598i | ||||
\(826\) | 1.54581 | − | 4.75751i | 0.0537855 | − | 0.165535i | ||||
\(827\) | −2.31191 | + | 1.67970i | −0.0803929 | + | 0.0584088i | −0.627256 | − | 0.778813i | \(-0.715822\pi\) |
0.546863 | + | 0.837222i | \(0.315822\pi\) | |||||||
\(828\) | −0.319091 | − | 0.982061i | −0.0110892 | − | 0.0341290i | ||||
\(829\) | −15.7715 | − | 48.5397i | −0.547767 | − | 1.68585i | −0.714319 | − | 0.699820i | \(-0.753263\pi\) |
0.166552 | − | 0.986033i | \(-0.446737\pi\) | |||||||
\(830\) | 4.60676 | − | 14.1781i | 0.159903 | − | 0.492131i | ||||
\(831\) | −3.24888 | −0.112702 | ||||||||
\(832\) | 6.99959 | 0.242667 | ||||||||
\(833\) | 7.36123 | − | 22.6555i | 0.255052 | − | 0.784968i | ||||
\(834\) | −8.97798 | − | 6.52288i | −0.310882 | − | 0.225869i | ||||
\(835\) | −1.52103 | + | 1.10509i | −0.0526374 | + | 0.0382433i | ||||
\(836\) | −4.08545 | −0.141298 | ||||||||
\(837\) | −5.15428 | − | 2.10557i | −0.178158 | − | 0.0727790i | ||||
\(838\) | 2.85276 | 0.0985470 | ||||||||
\(839\) | 6.65926 | − | 4.83824i | 0.229903 | − | 0.167035i | −0.466870 | − | 0.884326i | \(-0.654618\pi\) |
0.696773 | + | 0.717291i | \(0.254618\pi\) | |||||||
\(840\) | −0.792717 | − | 0.575943i | −0.0273513 | − | 0.0198719i | ||||
\(841\) | −7.12544 | + | 21.9298i | −0.245705 | + | 0.756202i | ||||
\(842\) | 23.6273 | 0.814250 | ||||||||
\(843\) | 24.7617 | 0.852839 | ||||||||
\(844\) | −1.10975 | + | 3.41547i | −0.0381993 | + | 0.117565i | ||||
\(845\) | 11.1229 | + | 34.2326i | 0.382638 | + | 1.17764i | ||||
\(846\) | −2.09389 | − | 6.44434i | −0.0719895 | − | 0.221561i | ||||
\(847\) | −8.39703 | + | 6.10080i | −0.288525 | + | 0.209626i | ||||
\(848\) | 0.824351 | − | 2.53709i | 0.0283083 | − | 0.0871241i | ||||
\(849\) | 22.1800 | − | 16.1147i | 0.761216 | − | 0.553056i | ||||
\(850\) | −3.19078 | − | 2.31824i | −0.109443 | − | 0.0795149i | ||||
\(851\) | −0.616346 | − | 1.89692i | −0.0211281 | − | 0.0650255i | ||||
\(852\) | 8.04488 | + | 5.84495i | 0.275613 | + | 0.200245i | ||||
\(853\) | −3.93766 | − | 2.86088i | −0.134823 | − | 0.0979547i | 0.518330 | − | 0.855181i | \(-0.326554\pi\) |
−0.653153 | + | 0.757226i | \(0.726554\pi\) | |||||||
\(854\) | −2.70440 | − | 8.32328i | −0.0925426 | − | 0.284817i | ||||
\(855\) | 5.17909 | + | 3.76283i | 0.177121 | + | 0.128686i | ||||
\(856\) | 7.82981 | − | 5.68869i | 0.267617 | − | 0.194435i | ||||
\(857\) | 2.51469 | − | 7.73943i | 0.0859003 | − | 0.264374i | −0.898875 | − | 0.438205i | \(-0.855615\pi\) |
0.984776 | + | 0.173831i | \(0.0556146\pi\) | |||||||
\(858\) | 3.61389 | − | 2.62565i | 0.123376 | − | 0.0896380i | ||||
\(859\) | 12.6809 | + | 39.0277i | 0.432666 | + | 1.33161i | 0.895460 | + | 0.445142i | \(0.146847\pi\) |
−0.462794 | + | 0.886466i | \(0.653153\pi\) | |||||||
\(860\) | 1.59389 | + | 4.90550i | 0.0543513 | + | 0.167276i | ||||
\(861\) | 0.309870 | − | 0.953681i | 0.0105603 | − | 0.0325014i | ||||
\(862\) | −33.4780 | −1.14027 | ||||||||
\(863\) | −11.6267 | −0.395778 | −0.197889 | − | 0.980224i | \(-0.563409\pi\) | ||||
−0.197889 | + | 0.980224i | \(0.563409\pi\) | |||||||
\(864\) | −0.309017 | + | 0.951057i | −0.0105130 | + | 0.0323556i | ||||
\(865\) | −11.1506 | − | 8.10136i | −0.379131 | − | 0.275455i | ||||
\(866\) | −0.731372 | + | 0.531373i | −0.0248530 | + | 0.0180568i | ||||
\(867\) | −1.44470 | −0.0490645 | ||||||||
\(868\) | 3.52283 | − | 4.16570i | 0.119573 | − | 0.141393i | ||||
\(869\) | 0.156798 | 0.00531901 | ||||||||
\(870\) | −1.97201 | + | 1.43275i | −0.0668574 | + | 0.0485748i | ||||
\(871\) | −49.4963 | − | 35.9612i | −1.67712 | − | 1.21850i | ||||
\(872\) | 4.96714 | − | 15.2873i | 0.168209 | − | 0.517693i | ||||
\(873\) | −11.4786 | −0.388492 | ||||||||
\(874\) | −6.61040 | −0.223600 | ||||||||
\(875\) | −0.302791 | + | 0.931895i | −0.0102362 | + | 0.0315038i | ||||
\(876\) | −3.76611 | − | 11.5909i | −0.127245 | − | 0.391620i | ||||
\(877\) | 5.14874 | + | 15.8462i | 0.173860 | + | 0.535087i | 0.999580 | − | 0.0289940i | \(-0.00923039\pi\) |
−0.825719 | + | 0.564081i | \(0.809230\pi\) | |||||||
\(878\) | −23.2143 | + | 16.8662i | −0.783444 | + | 0.569205i | ||||
\(879\) | −2.16525 | + | 6.66394i | −0.0730319 | + | 0.224769i | ||||
\(880\) | −0.516300 | + | 0.375114i | −0.0174045 | + | 0.0126451i | ||||
\(881\) | 24.6217 | + | 17.8887i | 0.829526 | + | 0.602686i | 0.919425 | − | 0.393265i | \(-0.128655\pi\) |
−0.0898994 | + | 0.995951i | \(0.528655\pi\) | |||||||
\(882\) | 1.86643 | + | 5.74428i | 0.0628459 | + | 0.193420i | ||||
\(883\) | 8.54741 | + | 6.21006i | 0.287643 | + | 0.208985i | 0.722244 | − | 0.691638i | \(-0.243111\pi\) |
−0.434601 | + | 0.900623i | \(0.643111\pi\) | |||||||
\(884\) | 22.3342 | + | 16.2267i | 0.751179 | + | 0.545764i | ||||
\(885\) | 1.57759 | + | 4.85533i | 0.0530302 | + | 0.163210i | ||||
\(886\) | −26.5912 | − | 19.3196i | −0.893349 | − | 0.649056i | ||||
\(887\) | 37.0235 | − | 26.8992i | 1.24313 | − | 0.903185i | 0.245325 | − | 0.969441i | \(-0.421105\pi\) |
0.997803 | + | 0.0662557i | \(0.0211053\pi\) | |||||||
\(888\) | −0.596888 | + | 1.83703i | −0.0200302 | + | 0.0616467i | ||||
\(889\) | 5.03828 | − | 3.66053i | 0.168979 | − | 0.122770i | ||||
\(890\) | 4.06590 | + | 12.5136i | 0.136289 | + | 0.419456i | ||||
\(891\) | 0.197209 | + | 0.606947i | 0.00660675 | + | 0.0203335i | ||||
\(892\) | 0.110594 | − | 0.340374i | 0.00370296 | − | 0.0113966i | ||||
\(893\) | −43.3778 | −1.45158 | ||||||||
\(894\) | −13.5520 | −0.453245 | ||||||||
\(895\) | −2.48546 | + | 7.64946i | −0.0830798 | + | 0.255693i | ||||
\(896\) | −0.792717 | − | 0.575943i | −0.0264828 | − | 0.0192409i | ||||
\(897\) | 5.84740 | − | 4.24838i | 0.195239 | − | 0.141849i | ||||
\(898\) | −28.3068 | −0.944611 | ||||||||
\(899\) | −7.14754 | − | 11.5370i | −0.238384 | − | 0.384780i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 8.51191 | − | 6.18426i | 0.283573 | − | 0.206028i | ||||
\(902\) | −0.528371 | − | 0.383884i | −0.0175928 | − | 0.0127819i | ||||
\(903\) | −1.56178 | + | 4.80666i | −0.0519727 | + | 0.159956i | ||||
\(904\) | −4.58220 | −0.152402 | ||||||||
\(905\) | 2.35377 | 0.0782418 | ||||||||
\(906\) | −1.54597 | + | 4.75801i | −0.0513614 | + | 0.158074i | ||||
\(907\) | 13.8311 | + | 42.5676i | 0.459253 | + | 1.41344i | 0.866069 | + | 0.499925i | \(0.166639\pi\) |
−0.406816 | + | 0.913510i | \(0.633361\pi\) | |||||||
\(908\) | −4.54075 | − | 13.9750i | −0.150690 | − | 0.463776i | ||||
\(909\) | −5.28364 | + | 3.83879i | −0.175247 | + | 0.127325i | ||||
\(910\) | 2.11941 | − | 6.52288i | 0.0702579 | − | 0.216232i | ||||
\(911\) | 23.6796 | − | 17.2042i | 0.784539 | − | 0.570001i | −0.121799 | − | 0.992555i | \(-0.538866\pi\) |
0.906338 | + | 0.422554i | \(0.138866\pi\) | |||||||
\(912\) | 5.17909 | + | 3.76283i | 0.171497 | + | 0.124600i | ||||
\(913\) | −2.93995 | − | 9.04824i | −0.0972981 | − | 0.299453i | ||||
\(914\) | 23.7540 | + | 17.2583i | 0.785711 | + | 0.570853i | ||||
\(915\) | 7.22579 | + | 5.24984i | 0.238877 | + | 0.173555i | ||||
\(916\) | −1.46655 | − | 4.51357i | −0.0484561 | − | 0.149132i | ||||
\(917\) | 14.7509 | + | 10.7172i | 0.487118 | + | 0.353912i | ||||
\(918\) | −3.19078 | + | 2.31824i | −0.105311 | + | 0.0765132i | ||||
\(919\) | −0.166982 | + | 0.513918i | −0.00550823 | + | 0.0169526i | −0.953773 | − | 0.300528i | \(-0.902837\pi\) |
0.948265 | + | 0.317481i | \(0.102837\pi\) | |||||||
\(920\) | −0.835391 | + | 0.606947i | −0.0275420 | + | 0.0200105i | ||||
\(921\) | 0.900519 | + | 2.77151i | 0.0296731 | + | 0.0913244i | ||||
\(922\) | 10.8555 | + | 33.4099i | 0.357508 | + | 1.10030i | ||||
\(923\) | −21.5089 | + | 66.1974i | −0.707973 | + | 2.17892i | ||||
\(924\) | −0.625324 | −0.0205716 | ||||||||
\(925\) | 1.93157 | 0.0635096 | ||||||||
\(926\) | 5.60577 | − | 17.2528i | 0.184217 | − | 0.566962i | ||||
\(927\) | 10.8739 | + | 7.90035i | 0.357146 | + | 0.259481i | ||||
\(928\) | −1.97201 | + | 1.43275i | −0.0647344 | + | 0.0470323i | ||||
\(929\) | −10.7530 | −0.352794 | −0.176397 | − | 0.984319i | \(-0.556444\pi\) | ||||
−0.176397 | + | 0.984319i | \(0.556444\pi\) | |||||||
\(930\) | −0.409753 | + | 5.55267i | −0.0134363 | + | 0.182079i | ||||
\(931\) | 38.6656 | 1.26721 | ||||||||
\(932\) | −6.78059 | + | 4.92639i | −0.222106 | + | 0.161369i | ||||
\(933\) | −20.1039 | − | 14.6063i | −0.658171 | − | 0.478189i | ||||
\(934\) | 4.76950 | − | 14.6790i | 0.156063 | − | 0.480312i | ||||
\(935\) | −2.51700 | −0.0823148 | ||||||||
\(936\) | −6.99959 | −0.228789 | ||||||||
\(937\) | 7.78738 | − | 23.9671i | 0.254403 | − | 0.782971i | −0.739544 | − | 0.673108i | \(-0.764959\pi\) |
0.993947 | − | 0.109863i | \(-0.0350412\pi\) | |||||||
\(938\) | 2.64658 | + | 8.14534i | 0.0864139 | + | 0.265955i | ||||
\(939\) | 3.40566 | + | 10.4815i | 0.111139 | + | 0.342052i | ||||
\(940\) | −5.48188 | + | 3.98282i | −0.178799 | + | 0.129905i | ||||
\(941\) | 2.31264 | − | 7.11759i | 0.0753901 | − | 0.232027i | −0.906259 | − | 0.422723i | \(-0.861074\pi\) |
0.981649 | + | 0.190696i | \(0.0610744\pi\) | |||||||
\(942\) | −1.35410 | + | 0.983813i | −0.0441190 | + | 0.0320543i | ||||
\(943\) | −0.854922 | − | 0.621137i | −0.0278401 | − | 0.0202270i | ||||
\(944\) | 1.57759 | + | 4.85533i | 0.0513463 | + | 0.158028i | ||||
\(945\) | 0.792717 | + | 0.575943i | 0.0257871 | + | 0.0187354i | ||||
\(946\) | 2.66305 | + | 1.93482i | 0.0865831 | + | 0.0629063i | ||||
\(947\) | 18.5469 | + | 57.0815i | 0.602693 | + | 1.85490i | 0.511933 | + | 0.859025i | \(0.328930\pi\) |
0.0907601 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(948\) | −0.198771 | − | 0.144416i | −0.00645580 | − | 0.00469041i | ||||
\(949\) | 69.0146 | − | 50.1420i | 2.24031 | − | 1.62768i | ||||
\(950\) | 1.97824 | − | 6.08839i | 0.0641825 | − | 0.197533i | ||||
\(951\) | 19.2691 | − | 13.9998i | 0.624844 | − | 0.453976i | ||||
\(952\) | −1.19421 | − | 3.67541i | −0.0387047 | − | 0.119121i | ||||
\(953\) | 4.15440 | + | 12.7859i | 0.134574 | + | 0.414177i | 0.995524 | − | 0.0945138i | \(-0.0301296\pi\) |
−0.860949 | + | 0.508691i | \(0.830130\pi\) | |||||||
\(954\) | −0.824351 | + | 2.53709i | −0.0266894 | + | 0.0821414i | ||||
\(955\) | −9.44364 | −0.305589 | ||||||||
\(956\) | −22.4505 | −0.726102 | ||||||||
\(957\) | −0.480705 | + | 1.47946i | −0.0155390 | + | 0.0478241i | ||||
\(958\) | 19.9620 | + | 14.5033i | 0.644944 | + | 0.468579i | ||||
\(959\) | 8.81059 | − | 6.40127i | 0.284509 | − | 0.206708i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −30.6642 | − | 4.55044i | −0.989168 | − | 0.146788i | ||||
\(962\) | −13.5202 | −0.435909 | ||||||||
\(963\) | −7.82981 | + | 5.68869i | −0.252312 | + | 0.183315i | ||||
\(964\) | −16.6770 | − | 12.1166i | −0.537131 | − | 0.390248i | ||||
\(965\) | −5.46861 | + | 16.8307i | −0.176041 | + | 0.541798i | ||||
\(966\) | −1.01180 | −0.0325540 | ||||||||
\(967\) | −22.3871 | −0.719920 | −0.359960 | − | 0.932968i | \(-0.617210\pi\) | ||||
−0.359960 | + | 0.932968i | \(0.617210\pi\) | |||||||
\(968\) | 3.27333 | − | 10.0743i | 0.105209 | − | 0.323800i | ||||
\(969\) | 7.80221 | + | 24.0127i | 0.250643 | + | 0.771400i | ||||
\(970\) | 3.54708 | + | 10.9168i | 0.113890 | + | 0.350517i | ||||
\(971\) | 10.8334 | − | 7.87089i | 0.347659 | − | 0.252589i | −0.400227 | − | 0.916416i | \(-0.631069\pi\) |
0.747886 | + | 0.663827i | \(0.231069\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | −8.79709 | + | 6.39146i | −0.282022 | + | 0.204901i | ||||
\(974\) | −0.964176 | − | 0.700515i | −0.0308942 | − | 0.0224459i | ||||
\(975\) | 2.16299 | + | 6.65701i | 0.0692712 | + | 0.213195i | ||||
\(976\) | 7.22579 | + | 5.24984i | 0.231292 | + | 0.168043i | ||||
\(977\) | 40.2823 | + | 29.2668i | 1.28875 | + | 0.936329i | 0.999779 | − | 0.0210102i | \(-0.00668823\pi\) |
0.288967 | + | 0.957339i | \(0.406688\pi\) | |||||||
\(978\) | −2.70006 | − | 8.30993i | −0.0863384 | − | 0.265722i | ||||
\(979\) | 6.79324 | + | 4.93558i | 0.217113 | + | 0.157742i | ||||
\(980\) | 4.88637 | − | 3.55016i | 0.156089 | − | 0.113406i | ||||
\(981\) | −4.96714 | + | 15.2873i | −0.158589 | + | 0.488086i | ||||
\(982\) | 16.4754 | − | 11.9701i | 0.525753 | − | 0.381982i | ||||
\(983\) | −1.74381 | − | 5.36690i | −0.0556190 | − | 0.171178i | 0.919388 | − | 0.393352i | \(-0.128685\pi\) |
−0.975007 | + | 0.222174i | \(0.928685\pi\) | |||||||
\(984\) | 0.316241 | + | 0.973291i | 0.0100814 | + | 0.0310274i | ||||
\(985\) | 4.72540 | − | 14.5433i | 0.150564 | − | 0.463387i | ||||
\(986\) | −9.61371 | −0.306163 | ||||||||
\(987\) | −6.63946 | −0.211336 | ||||||||
\(988\) | −13.8469 | + | 42.6162i | −0.440527 | + | 1.35580i | ||||
\(989\) | 4.30890 | + | 3.13060i | 0.137015 | + | 0.0995473i | ||||
\(990\) | 0.516300 | − | 0.375114i | 0.0164091 | − | 0.0119219i | ||||
\(991\) | −36.9061 | −1.17236 | −0.586181 | − | 0.810180i | \(-0.699369\pi\) | ||||
−0.586181 | + | 0.810180i | \(0.699369\pi\) | |||||||
\(992\) | −0.409753 | + | 5.55267i | −0.0130097 | + | 0.176297i | ||||
\(993\) | 14.6849 | 0.466012 | ||||||||
\(994\) | 7.88279 | − | 5.72719i | 0.250027 | − | 0.181655i | ||||
\(995\) | 21.6590 | + | 15.7361i | 0.686635 | + | 0.498869i | ||||
\(996\) | −4.60676 | + | 14.1781i | −0.145971 | + | 0.449252i | ||||
\(997\) | 16.9472 | 0.536725 | 0.268362 | − | 0.963318i | \(-0.413518\pi\) | ||||
0.268362 | + | 0.963318i | \(0.413518\pi\) | |||||||
\(998\) | 28.2913 | 0.895544 | ||||||||
\(999\) | 0.596888 | − | 1.83703i | 0.0188847 | − | 0.0581211i |
(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 | 930.2.n.e.481.2 | ✓ | 12 | |
31.2 | even | 5 | inner | 930.2.n.e.901.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.e.481.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
930.2.n.e.901.2 | yes | 12 | 31.2 | even | 5 | inner |