Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 751.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.751 |
Dual form | 825.2.n.b.301.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.363271i | −0.353553 | + | 0.256872i | −0.750358 | − | 0.661031i | \(-0.770119\pi\) |
0.396805 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | −0.500000 | + | 1.53884i | −0.250000 | + | 0.769421i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | + | 0.363271i | 0.204124 | + | 0.148305i | ||||
\(7\) | −0.236068 | + | 0.726543i | −0.0892253 | + | 0.274607i | −0.985706 | − | 0.168476i | \(-0.946115\pi\) |
0.896480 | + | 0.443083i | \(0.146115\pi\) | |||||||
\(8\) | −0.690983 | − | 2.12663i | −0.244299 | − | 0.751876i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | + | 0.726543i | 0.975711 | + | 0.219061i | ||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 1.00000 | − | 0.726543i | 0.277350 | − | 0.201507i | −0.440411 | − | 0.897796i | \(-0.645167\pi\) |
0.717761 | + | 0.696290i | \(0.245167\pi\) | |||||||
\(14\) | −0.145898 | − | 0.449028i | −0.0389929 | − | 0.120008i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 1.08981i | −0.375000 | − | 0.272453i | ||||
\(17\) | −1.61803 | − | 1.17557i | −0.392431 | − | 0.285118i | 0.374020 | − | 0.927421i | \(-0.377979\pi\) |
−0.766451 | + | 0.642303i | \(0.777979\pi\) | |||||||
\(18\) | 0.190983 | − | 0.587785i | 0.0450151 | − | 0.138542i | ||||
\(19\) | 1.54508 | + | 4.75528i | 0.354467 | + | 1.09094i | 0.956318 | + | 0.292328i | \(0.0944300\pi\) |
−0.601851 | + | 0.798608i | \(0.705570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.763932 | 0.166704 | ||||||||
\(22\) | −1.88197 | + | 0.812299i | −0.401237 | + | 0.173183i | ||||
\(23\) | 2.38197 | 0.496674 | 0.248337 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248337 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(24\) | −1.80902 | + | 1.31433i | −0.369264 | + | 0.268286i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.236068 | + | 0.726543i | −0.0462967 | + | 0.142487i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −1.00000 | − | 0.726543i | −0.188982 | − | 0.137304i | ||||
\(29\) | −1.80902 | + | 5.56758i | −0.335926 | + | 1.03387i | 0.630338 | + | 0.776321i | \(0.282916\pi\) |
−0.966264 | + | 0.257553i | \(0.917084\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.66312 | + | 4.11450i | −1.01713 | + | 0.738985i | −0.965692 | − | 0.259691i | \(-0.916379\pi\) |
−0.0514344 | + | 0.998676i | \(0.516379\pi\) | |||||||
\(32\) | 5.61803 | 0.993137 | ||||||||
\(33\) | −0.309017 | − | 3.30220i | −0.0537930 | − | 0.574839i | ||||
\(34\) | 1.23607 | 0.211984 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 1.53884i | −0.0833333 | − | 0.256474i | ||||
\(37\) | −2.30902 | + | 7.10642i | −0.379600 | + | 1.16829i | 0.560722 | + | 0.828004i | \(0.310524\pi\) |
−0.940322 | + | 0.340285i | \(0.889476\pi\) | |||||||
\(38\) | −2.50000 | − | 1.81636i | −0.405554 | − | 0.294652i | ||||
\(39\) | −1.00000 | − | 0.726543i | −0.160128 | − | 0.116340i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.781153 | + | 2.40414i | 0.121996 | + | 0.375464i | 0.993342 | − | 0.115205i | \(-0.0367525\pi\) |
−0.871346 | + | 0.490669i | \(0.836752\pi\) | |||||||
\(42\) | −0.381966 | + | 0.277515i | −0.0589386 | + | 0.0428214i | ||||
\(43\) | −2.09017 | −0.318748 | −0.159374 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159374 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(44\) | −2.73607 | + | 4.61653i | −0.412478 | + | 0.695967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.19098 | + | 0.865300i | −0.175601 | + | 0.127581i | ||||
\(47\) | 1.57295 | + | 4.84104i | 0.229438 | + | 0.706138i | 0.997811 | + | 0.0661352i | \(0.0210669\pi\) |
−0.768372 | + | 0.640003i | \(0.778933\pi\) | |||||||
\(48\) | −0.572949 | + | 1.76336i | −0.0826981 | + | 0.254518i | ||||
\(49\) | 5.19098 | + | 3.77147i | 0.741569 | + | 0.538781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.618034 | + | 1.90211i | −0.0865421 | + | 0.266349i | ||||
\(52\) | 0.618034 | + | 1.90211i | 0.0857059 | + | 0.263776i | ||||
\(53\) | 6.16312 | − | 4.47777i | 0.846569 | − | 0.615069i | −0.0776285 | − | 0.996982i | \(-0.524735\pi\) |
0.924198 | + | 0.381914i | \(0.124735\pi\) | |||||||
\(54\) | −0.618034 | −0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.70820 | 0.228268 | ||||||||
\(57\) | 4.04508 | − | 2.93893i | 0.535785 | − | 0.389270i | ||||
\(58\) | −1.11803 | − | 3.44095i | −0.146805 | − | 0.451820i | ||||
\(59\) | −2.07295 | + | 6.37988i | −0.269875 | + | 0.830590i | 0.720655 | + | 0.693294i | \(0.243841\pi\) |
−0.990530 | + | 0.137296i | \(0.956159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.66312 | − | 4.11450i | −0.725088 | − | 0.526807i | 0.162918 | − | 0.986640i | \(-0.447910\pi\) |
−0.888006 | + | 0.459832i | \(0.847910\pi\) | |||||||
\(62\) | 1.33688 | − | 4.11450i | 0.169784 | − | 0.522542i | ||||
\(63\) | −0.236068 | − | 0.726543i | −0.0297418 | − | 0.0915358i | ||||
\(64\) | 0.190983 | − | 0.138757i | 0.0238729 | − | 0.0173447i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.35410 | + | 1.53884i | 0.166678 | + | 0.189418i | ||||
\(67\) | −9.38197 | −1.14619 | −0.573095 | − | 0.819489i | \(-0.694257\pi\) | ||||
−0.573095 | + | 0.819489i | \(0.694257\pi\) | |||||||
\(68\) | 2.61803 | − | 1.90211i | 0.317483 | − | 0.230665i | ||||
\(69\) | −0.736068 | − | 2.26538i | −0.0886122 | − | 0.272720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47214 | + | 4.70228i | 0.768101 | + | 0.558058i | 0.901384 | − | 0.433020i | \(-0.142552\pi\) |
−0.133283 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(72\) | 1.80902 | + | 1.31433i | 0.213195 | + | 0.154895i | ||||
\(73\) | −4.16312 | + | 12.8128i | −0.487256 | + | 1.49962i | 0.341430 | + | 0.939907i | \(0.389089\pi\) |
−0.828686 | + | 0.559713i | \(0.810911\pi\) | |||||||
\(74\) | −1.42705 | − | 4.39201i | −0.165891 | − | 0.510561i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.09017 | −0.928006 | ||||||||
\(77\) | −1.29180 | + | 2.17963i | −0.147214 | + | 0.248392i | ||||
\(78\) | 0.763932 | 0.0864983 | ||||||||
\(79\) | 6.54508 | − | 4.75528i | 0.736380 | − | 0.535011i | −0.155196 | − | 0.987884i | \(-0.549601\pi\) |
0.891575 | + | 0.452873i | \(0.149601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −1.26393 | − | 0.918300i | −0.139578 | − | 0.101409i | ||||
\(83\) | 4.61803 | + | 3.35520i | 0.506895 | + | 0.368281i | 0.811644 | − | 0.584152i | \(-0.198573\pi\) |
−0.304749 | + | 0.952433i | \(0.598573\pi\) | |||||||
\(84\) | −0.381966 | + | 1.17557i | −0.0416759 | + | 0.128265i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.04508 | − | 0.759299i | 0.112694 | − | 0.0818773i | ||||
\(87\) | 5.85410 | 0.627626 | ||||||||
\(88\) | −0.690983 | − | 7.38394i | −0.0736590 | − | 0.787130i | ||||
\(89\) | 10.8541 | 1.15053 | 0.575266 | − | 0.817966i | \(-0.304898\pi\) | ||||
0.575266 | + | 0.817966i | \(0.304898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.291796 | + | 0.898056i | 0.0305885 | + | 0.0941418i | ||||
\(92\) | −1.19098 | + | 3.66547i | −0.124169 | + | 0.382152i | ||||
\(93\) | 5.66312 | + | 4.11450i | 0.587238 | + | 0.426653i | ||||
\(94\) | −2.54508 | − | 1.84911i | −0.262505 | − | 0.190721i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.73607 | − | 5.34307i | −0.177187 | − | 0.545325i | ||||
\(97\) | −9.28115 | + | 6.74315i | −0.942358 | + | 0.684663i | −0.948987 | − | 0.315315i | \(-0.897890\pi\) |
0.00662888 | + | 0.999978i | \(0.497890\pi\) | |||||||
\(98\) | −3.96556 | −0.400582 | ||||||||
\(99\) | −3.04508 | + | 1.31433i | −0.306043 | + | 0.132095i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.454915 | − | 0.330515i | 0.0452657 | − | 0.0328875i | −0.564922 | − | 0.825144i | \(-0.691094\pi\) |
0.610188 | + | 0.792257i | \(0.291094\pi\) | |||||||
\(102\) | −0.381966 | − | 1.17557i | −0.0378203 | − | 0.116399i | ||||
\(103\) | 0.736068 | − | 2.26538i | 0.0725269 | − | 0.223215i | −0.908222 | − | 0.418489i | \(-0.862560\pi\) |
0.980749 | + | 0.195274i | \(0.0625597\pi\) | |||||||
\(104\) | −2.23607 | − | 1.62460i | −0.219265 | − | 0.159305i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.45492 | + | 4.47777i | −0.141314 | + | 0.434919i | ||||
\(107\) | 0.881966 | + | 2.71441i | 0.0852629 | + | 0.262412i | 0.984594 | − | 0.174856i | \(-0.0559460\pi\) |
−0.899331 | + | 0.437268i | \(0.855946\pi\) | |||||||
\(108\) | −1.30902 | + | 0.951057i | −0.125960 | + | 0.0915155i | ||||
\(109\) | 4.14590 | 0.397105 | 0.198553 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198553 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.47214 | 0.709224 | ||||||||
\(112\) | 1.14590 | − | 0.832544i | 0.108277 | − | 0.0786680i | ||||
\(113\) | 1.69098 | + | 5.20431i | 0.159074 | + | 0.489580i | 0.998551 | − | 0.0538155i | \(-0.0171383\pi\) |
−0.839477 | + | 0.543396i | \(0.817138\pi\) | |||||||
\(114\) | −0.954915 | + | 2.93893i | −0.0894360 | + | 0.275256i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.66312 | − | 5.56758i | −0.711503 | − | 0.516937i | ||||
\(117\) | −0.381966 | + | 1.17557i | −0.0353128 | + | 0.108682i | ||||
\(118\) | −1.28115 | − | 3.94298i | −0.117940 | − | 0.362981i | ||||
\(119\) | 1.23607 | − | 0.898056i | 0.113310 | − | 0.0823247i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | 4.32624 | 0.391679 | ||||||||
\(123\) | 2.04508 | − | 1.48584i | 0.184399 | − | 0.133974i | ||||
\(124\) | −3.50000 | − | 10.7719i | −0.314309 | − | 0.967344i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | + | 0.277515i | 0.0340282 | + | 0.0247230i | ||||
\(127\) | −12.8992 | − | 9.37181i | −1.14462 | − | 0.831613i | −0.156862 | − | 0.987621i | \(-0.550138\pi\) |
−0.987756 | + | 0.156007i | \(0.950138\pi\) | |||||||
\(128\) | −3.51722 | + | 10.8249i | −0.310881 | + | 0.956794i | ||||
\(129\) | 0.645898 | + | 1.98787i | 0.0568682 | + | 0.175022i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1803 | 1.15157 | 0.575786 | − | 0.817601i | \(-0.304696\pi\) | ||||
0.575786 | + | 0.817601i | \(0.304696\pi\) | |||||||
\(132\) | 5.23607 | + | 1.17557i | 0.455741 | + | 0.102320i | ||||
\(133\) | −3.81966 | −0.331207 | ||||||||
\(134\) | 4.69098 | − | 3.40820i | 0.405239 | − | 0.294424i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.38197 | + | 4.25325i | −0.118503 | + | 0.364714i | ||||
\(137\) | −15.1353 | − | 10.9964i | −1.29309 | − | 0.939486i | −0.293229 | − | 0.956042i | \(-0.594730\pi\) |
−0.999863 | + | 0.0165558i | \(0.994730\pi\) | |||||||
\(138\) | 1.19098 | + | 0.865300i | 0.101383 | + | 0.0736592i | ||||
\(139\) | 6.54508 | − | 20.1437i | 0.555147 | − | 1.70857i | −0.140408 | − | 0.990094i | \(-0.544842\pi\) |
0.695555 | − | 0.718473i | \(-0.255158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.11803 | − | 2.99193i | 0.346801 | − | 0.251966i | ||||
\(142\) | −4.94427 | −0.414914 | ||||||||
\(143\) | 3.76393 | − | 1.62460i | 0.314756 | − | 0.135856i | ||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.57295 | − | 7.91872i | −0.212939 | − | 0.655358i | ||||
\(147\) | 1.98278 | − | 6.10237i | 0.163537 | − | 0.503315i | ||||
\(148\) | −9.78115 | − | 7.10642i | −0.804006 | − | 0.584144i | ||||
\(149\) | −16.2812 | − | 11.8290i | −1.33380 | − | 0.969065i | −0.999648 | − | 0.0265477i | \(-0.991549\pi\) |
−0.334156 | − | 0.942518i | \(-0.608451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.32624 | − | 10.2371i | −0.270685 | − | 0.833084i | −0.990329 | − | 0.138740i | \(-0.955695\pi\) |
0.719643 | − | 0.694344i | \(-0.244305\pi\) | |||||||
\(152\) | 9.04508 | − | 6.57164i | 0.733653 | − | 0.533030i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | −0.145898 | − | 1.55909i | −0.0117568 | − | 0.125635i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.61803 | − | 1.17557i | 0.129546 | − | 0.0941210i | ||||
\(157\) | −1.02786 | − | 3.16344i | −0.0820325 | − | 0.252470i | 0.901625 | − | 0.432518i | \(-0.142375\pi\) |
−0.983658 | + | 0.180048i | \(0.942375\pi\) | |||||||
\(158\) | −1.54508 | + | 4.75528i | −0.122920 | + | 0.378310i | ||||
\(159\) | −6.16312 | − | 4.47777i | −0.488767 | − | 0.355110i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.562306 | + | 1.73060i | −0.0443159 | + | 0.136390i | ||||
\(162\) | 0.190983 | + | 0.587785i | 0.0150050 | + | 0.0461808i | ||||
\(163\) | −10.9721 | + | 7.97172i | −0.859404 | + | 0.624394i | −0.927723 | − | 0.373270i | \(-0.878237\pi\) |
0.0683187 | + | 0.997664i | \(0.478237\pi\) | |||||||
\(164\) | −4.09017 | −0.319389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.52786 | −0.273815 | ||||||||
\(167\) | 16.2082 | − | 11.7759i | 1.25423 | − | 0.911250i | 0.255769 | − | 0.966738i | \(-0.417671\pi\) |
0.998459 | + | 0.0554876i | \(0.0176713\pi\) | |||||||
\(168\) | −0.527864 | − | 1.62460i | −0.0407256 | − | 0.125340i | ||||
\(169\) | −3.54508 | + | 10.9106i | −0.272699 | + | 0.839281i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.04508 | − | 2.93893i | −0.309335 | − | 0.224745i | ||||
\(172\) | 1.04508 | − | 3.21644i | 0.0796870 | − | 0.245251i | ||||
\(173\) | 1.10081 | + | 3.38795i | 0.0836933 | + | 0.257581i | 0.984142 | − | 0.177380i | \(-0.0567621\pi\) |
−0.900449 | + | 0.434961i | \(0.856762\pi\) | |||||||
\(174\) | −2.92705 | + | 2.12663i | −0.221899 | + | 0.161219i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.06231 | − | 4.61653i | −0.306208 | − | 0.347984i | ||||
\(177\) | 6.70820 | 0.504219 | ||||||||
\(178\) | −5.42705 | + | 3.94298i | −0.406775 | + | 0.295539i | ||||
\(179\) | −6.01722 | − | 18.5191i | −0.449748 | − | 1.38418i | −0.877192 | − | 0.480141i | \(-0.840586\pi\) |
0.427443 | − | 0.904042i | \(-0.359414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.23607 | + | 3.07768i | 0.314864 | + | 0.228762i | 0.733981 | − | 0.679170i | \(-0.237660\pi\) |
−0.419117 | + | 0.907932i | \(0.637660\pi\) | |||||||
\(182\) | −0.472136 | − | 0.343027i | −0.0349970 | − | 0.0254268i | ||||
\(183\) | −2.16312 | + | 6.65740i | −0.159902 | + | 0.492129i | ||||
\(184\) | −1.64590 | − | 5.06555i | −0.121337 | − | 0.373438i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.32624 | −0.317215 | ||||||||
\(187\) | −4.38197 | − | 4.97980i | −0.320441 | − | 0.364159i | ||||
\(188\) | −8.23607 | −0.600677 | ||||||||
\(189\) | −0.618034 | + | 0.449028i | −0.0449554 | + | 0.0326620i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.21885 | − | 9.90659i | 0.232908 | − | 0.716816i | −0.764484 | − | 0.644642i | \(-0.777006\pi\) |
0.997392 | − | 0.0721737i | \(-0.0229936\pi\) | |||||||
\(192\) | −0.190983 | − | 0.138757i | −0.0137830 | − | 0.0100139i | ||||
\(193\) | 17.0172 | + | 12.3637i | 1.22493 | + | 0.889961i | 0.996499 | − | 0.0836000i | \(-0.0266418\pi\) |
0.228427 | + | 0.973561i | \(0.426642\pi\) | |||||||
\(194\) | 2.19098 | − | 6.74315i | 0.157303 | − | 0.484130i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.39919 | + | 6.10237i | −0.599942 | + | 0.435883i | ||||
\(197\) | 14.2361 | 1.01428 | 0.507139 | − | 0.861864i | \(-0.330703\pi\) | ||||
0.507139 | + | 0.861864i | \(0.330703\pi\) | |||||||
\(198\) | 1.04508 | − | 1.76336i | 0.0742710 | − | 0.125316i | ||||
\(199\) | 19.7984 | 1.40347 | 0.701735 | − | 0.712438i | \(-0.252409\pi\) | ||||
0.701735 | + | 0.712438i | \(0.252409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.89919 | + | 8.92278i | 0.204493 | + | 0.629364i | ||||
\(202\) | −0.107391 | + | 0.330515i | −0.00755600 | + | 0.0232550i | ||||
\(203\) | −3.61803 | − | 2.62866i | −0.253936 | − | 0.184495i | ||||
\(204\) | −2.61803 | − | 1.90211i | −0.183299 | − | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.454915 | + | 1.40008i | 0.0316954 | + | 0.0975485i | ||||
\(207\) | −1.92705 | + | 1.40008i | −0.133939 | + | 0.0973126i | ||||
\(208\) | −2.29180 | −0.158907 | ||||||||
\(209\) | 1.54508 | + | 16.5110i | 0.106876 | + | 1.14209i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.11803 | − | 2.26538i | 0.214654 | − | 0.155955i | −0.475263 | − | 0.879844i | \(-0.657647\pi\) |
0.689917 | + | 0.723888i | \(0.257647\pi\) | |||||||
\(212\) | 3.80902 | + | 11.7229i | 0.261604 | + | 0.805135i | ||||
\(213\) | 2.47214 | − | 7.60845i | 0.169388 | − | 0.521323i | ||||
\(214\) | −1.42705 | − | 1.03681i | −0.0975512 | − | 0.0708751i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.690983 | − | 2.12663i | 0.0470154 | − | 0.144699i | ||||
\(217\) | −1.65248 | − | 5.08580i | −0.112177 | − | 0.345246i | ||||
\(218\) | −2.07295 | + | 1.50609i | −0.140398 | + | 0.102005i | ||||
\(219\) | 13.4721 | 0.910363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | −3.73607 | + | 2.71441i | −0.250748 | + | 0.182179i | ||||
\(223\) | 2.48278 | + | 7.64121i | 0.166259 | + | 0.511693i | 0.999127 | − | 0.0417790i | \(-0.0133025\pi\) |
−0.832868 | + | 0.553472i | \(0.813303\pi\) | |||||||
\(224\) | −1.32624 | + | 4.08174i | −0.0886130 | + | 0.272723i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.73607 | − | 1.98787i | −0.182001 | − | 0.132231i | ||||
\(227\) | 8.01722 | − | 24.6745i | 0.532122 | − | 1.63770i | −0.217666 | − | 0.976023i | \(-0.569844\pi\) |
0.749788 | − | 0.661679i | \(-0.230156\pi\) | |||||||
\(228\) | 2.50000 | + | 7.69421i | 0.165567 | + | 0.509561i | ||||
\(229\) | −14.6353 | + | 10.6331i | −0.967125 | + | 0.702657i | −0.954795 | − | 0.297267i | \(-0.903925\pi\) |
−0.0123304 | + | 0.999924i | \(0.503925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.47214 | + | 0.555029i | 0.162655 | + | 0.0365182i | ||||
\(232\) | 13.0902 | 0.859412 | ||||||||
\(233\) | 18.8262 | − | 13.6781i | 1.23335 | − | 0.896080i | 0.236211 | − | 0.971702i | \(-0.424094\pi\) |
0.997137 | + | 0.0756220i | \(0.0240942\pi\) | |||||||
\(234\) | −0.236068 | − | 0.726543i | −0.0154322 | − | 0.0474956i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.78115 | − | 6.37988i | −0.571604 | − | 0.415295i | ||||
\(237\) | −6.54508 | − | 4.75528i | −0.425149 | − | 0.308889i | ||||
\(238\) | −0.291796 | + | 0.898056i | −0.0189143 | + | 0.0582123i | ||||
\(239\) | −2.17376 | − | 6.69015i | −0.140609 | − | 0.432750i | 0.855811 | − | 0.517288i | \(-0.173058\pi\) |
−0.996420 | + | 0.0845383i | \(0.973058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.61803 | −0.104227 | −0.0521134 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521134 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(242\) | −6.68034 | + | 1.26133i | −0.429429 | + | 0.0810812i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.16312 | − | 6.65740i | 0.586609 | − | 0.426196i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.482779 | + | 1.48584i | −0.0307809 | + | 0.0947338i | ||||
\(247\) | 5.00000 | + | 3.63271i | 0.318142 | + | 0.231144i | ||||
\(248\) | 12.6631 | + | 9.20029i | 0.804109 | + | 0.584219i | ||||
\(249\) | 1.76393 | − | 5.42882i | 0.111785 | − | 0.344038i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.09017 | + | 4.42477i | −0.384408 | + | 0.279289i | −0.763160 | − | 0.646209i | \(-0.776353\pi\) |
0.378752 | + | 0.925498i | \(0.376353\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | 7.70820 | + | 1.73060i | 0.484611 | + | 0.108802i | ||||
\(254\) | 9.85410 | 0.618301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.02786 | − | 6.24112i | −0.126742 | − | 0.390070i | ||||
\(257\) | −3.26393 | + | 10.0453i | −0.203598 | + | 0.626612i | 0.796170 | + | 0.605074i | \(0.206856\pi\) |
−0.999768 | + | 0.0215381i | \(0.993144\pi\) | |||||||
\(258\) | −1.04508 | − | 0.759299i | −0.0650641 | − | 0.0472719i | ||||
\(259\) | −4.61803 | − | 3.35520i | −0.286951 | − | 0.208482i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.80902 | − | 5.56758i | −0.111975 | − | 0.344625i | ||||
\(262\) | −6.59017 | + | 4.78804i | −0.407142 | + | 0.295806i | ||||
\(263\) | −27.2148 | −1.67814 | −0.839068 | − | 0.544027i | \(-0.816899\pi\) | ||||
−0.839068 | + | 0.544027i | \(0.816899\pi\) | |||||||
\(264\) | −6.80902 | + | 2.93893i | −0.419066 | + | 0.180878i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.90983 | − | 1.38757i | 0.117099 | − | 0.0850775i | ||||
\(267\) | −3.35410 | − | 10.3229i | −0.205268 | − | 0.631749i | ||||
\(268\) | 4.69098 | − | 14.4374i | 0.286547 | − | 0.881902i | ||||
\(269\) | 4.73607 | + | 3.44095i | 0.288763 | + | 0.209799i | 0.722731 | − | 0.691130i | \(-0.242887\pi\) |
−0.433967 | + | 0.900929i | \(0.642887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.37132 | − | 19.6089i | 0.387030 | − | 1.19116i | −0.547966 | − | 0.836500i | \(-0.684598\pi\) |
0.934997 | − | 0.354656i | \(-0.115402\pi\) | |||||||
\(272\) | 1.14590 | + | 3.52671i | 0.0694803 | + | 0.213838i | ||||
\(273\) | 0.763932 | − | 0.555029i | 0.0462353 | − | 0.0335919i | ||||
\(274\) | 11.5623 | 0.698504 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.85410 | 0.231990 | ||||||||
\(277\) | 7.00000 | − | 5.08580i | 0.420589 | − | 0.305576i | −0.357286 | − | 0.933995i | \(-0.616298\pi\) |
0.777875 | + | 0.628419i | \(0.216298\pi\) | |||||||
\(278\) | 4.04508 | + | 12.4495i | 0.242608 | + | 0.746671i | ||||
\(279\) | 2.16312 | − | 6.65740i | 0.129503 | − | 0.398568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.16312 | − | 5.93085i | −0.486971 | − | 0.353805i | 0.317047 | − | 0.948410i | \(-0.397309\pi\) |
−0.804018 | + | 0.594605i | \(0.797309\pi\) | |||||||
\(282\) | −0.972136 | + | 2.99193i | −0.0578899 | + | 0.178167i | ||||
\(283\) | 4.02786 | + | 12.3965i | 0.239432 | + | 0.736895i | 0.996503 | + | 0.0835622i | \(0.0266297\pi\) |
−0.757071 | + | 0.653333i | \(0.773370\pi\) | |||||||
\(284\) | −10.4721 | + | 7.60845i | −0.621407 | + | 0.451479i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.29180 | + | 2.17963i | −0.0763855 | + | 0.128884i | ||||
\(287\) | −1.93112 | −0.113990 | ||||||||
\(288\) | −4.54508 | + | 3.30220i | −0.267822 | + | 0.194584i | ||||
\(289\) | −4.01722 | − | 12.3637i | −0.236307 | − | 0.727279i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.28115 | + | 6.74315i | 0.544071 | + | 0.395291i | ||||
\(292\) | −17.6353 | − | 12.8128i | −1.03203 | − | 0.749810i | ||||
\(293\) | 5.10739 | − | 15.7189i | 0.298377 | − | 0.918310i | −0.683689 | − | 0.729773i | \(-0.739626\pi\) |
0.982066 | − | 0.188537i | \(-0.0603744\pi\) | |||||||
\(294\) | 1.22542 | + | 3.77147i | 0.0714682 | + | 0.219957i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.7082 | 0.971145 | ||||||||
\(297\) | 2.19098 | + | 2.48990i | 0.127134 | + | 0.144479i | ||||
\(298\) | 12.4377 | 0.720496 | ||||||||
\(299\) | 2.38197 | − | 1.73060i | 0.137753 | − | 0.100083i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.493422 | − | 1.51860i | 0.0284404 | − | 0.0875305i | ||||
\(302\) | 5.38197 | + | 3.91023i | 0.309697 | + | 0.225008i | ||||
\(303\) | −0.454915 | − | 0.330515i | −0.0261342 | − | 0.0189876i | ||||
\(304\) | 2.86475 | − | 8.81678i | 0.164304 | − | 0.505677i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | + | 0.726543i | −0.0571662 | + | 0.0415337i | ||||
\(307\) | 12.1246 | 0.691988 | 0.345994 | − | 0.938237i | \(-0.387542\pi\) | ||||
0.345994 | + | 0.938237i | \(0.387542\pi\) | |||||||
\(308\) | −2.70820 | − | 3.07768i | −0.154314 | − | 0.175367i | ||||
\(309\) | −2.38197 | −0.135505 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.63525 | + | 20.4212i | 0.376251 | + | 1.15798i | 0.942631 | + | 0.333837i | \(0.108343\pi\) |
−0.566380 | + | 0.824144i | \(0.691657\pi\) | |||||||
\(312\) | −0.854102 | + | 2.62866i | −0.0483540 | + | 0.148818i | ||||
\(313\) | −0.381966 | − | 0.277515i | −0.0215900 | − | 0.0156860i | 0.576938 | − | 0.816788i | \(-0.304247\pi\) |
−0.598528 | + | 0.801102i | \(0.704247\pi\) | |||||||
\(314\) | 1.66312 | + | 1.20833i | 0.0938552 | + | 0.0681898i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04508 | + | 12.4495i | 0.227554 | + | 0.700339i | ||||
\(317\) | −24.6074 | + | 17.8783i | −1.38209 | + | 1.00415i | −0.385407 | + | 0.922747i | \(0.625939\pi\) |
−0.996682 | + | 0.0813997i | \(0.974061\pi\) | |||||||
\(318\) | 4.70820 | 0.264023 | ||||||||
\(319\) | −9.89919 | + | 16.7027i | −0.554248 | + | 0.935174i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.30902 | − | 1.67760i | 0.128877 | − | 0.0936344i | ||||
\(322\) | −0.347524 | − | 1.06957i | −0.0193668 | − | 0.0596048i | ||||
\(323\) | 3.09017 | − | 9.51057i | 0.171942 | − | 0.529182i | ||||
\(324\) | 1.30902 | + | 0.951057i | 0.0727232 | + | 0.0528365i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.59017 | − | 7.97172i | 0.143456 | − | 0.441513i | ||||
\(327\) | −1.28115 | − | 3.94298i | −0.0708479 | − | 0.218047i | ||||
\(328\) | 4.57295 | − | 3.32244i | 0.252499 | − | 0.183451i | ||||
\(329\) | −3.88854 | −0.214382 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5967 | 1.18706 | 0.593532 | − | 0.804810i | \(-0.297733\pi\) | ||||
0.593532 | + | 0.804810i | \(0.297733\pi\) | |||||||
\(332\) | −7.47214 | + | 5.42882i | −0.410087 | + | 0.297945i | ||||
\(333\) | −2.30902 | − | 7.10642i | −0.126533 | − | 0.389430i | ||||
\(334\) | −3.82624 | + | 11.7759i | −0.209362 | + | 0.644351i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14590 | − | 0.832544i | −0.0625139 | − | 0.0454190i | ||||
\(337\) | −6.84346 | + | 21.0620i | −0.372787 | + | 1.14732i | 0.572173 | + | 0.820133i | \(0.306101\pi\) |
−0.944960 | + | 0.327187i | \(0.893899\pi\) | |||||||
\(338\) | −2.19098 | − | 6.74315i | −0.119174 | − | 0.366779i | ||||
\(339\) | 4.42705 | − | 3.21644i | 0.240444 | − | 0.174693i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.3156 | + | 9.20029i | −1.15430 | + | 0.498224i | ||||
\(342\) | 3.09017 | 0.167097 | ||||||||
\(343\) | −8.29180 | + | 6.02434i | −0.447715 | + | 0.325284i | ||||
\(344\) | 1.44427 | + | 4.44501i | 0.0778699 | + | 0.239659i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.78115 | − | 1.29408i | −0.0957554 | − | 0.0695704i | ||||
\(347\) | −4.70820 | − | 3.42071i | −0.252750 | − | 0.183633i | 0.454195 | − | 0.890902i | \(-0.349927\pi\) |
−0.706945 | + | 0.707269i | \(0.749927\pi\) | |||||||
\(348\) | −2.92705 | + | 9.00854i | −0.156906 | + | 0.482908i | ||||
\(349\) | 8.57953 | + | 26.4051i | 0.459252 | + | 1.41343i | 0.866070 | + | 0.499922i | \(0.166638\pi\) |
−0.406819 | + | 0.913509i | \(0.633362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23607 | 0.0659764 | ||||||||
\(352\) | 18.1803 | + | 4.08174i | 0.969015 | + | 0.217558i | ||||
\(353\) | −35.8328 | −1.90719 | −0.953594 | − | 0.301095i | \(-0.902648\pi\) | ||||
−0.953594 | + | 0.301095i | \(0.902648\pi\) | |||||||
\(354\) | −3.35410 | + | 2.43690i | −0.178269 | + | 0.129520i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.42705 | + | 16.7027i | −0.287633 | + | 0.885244i | ||||
\(357\) | −1.23607 | − | 0.898056i | −0.0654197 | − | 0.0475302i | ||||
\(358\) | 9.73607 | + | 7.07367i | 0.514567 | + | 0.373855i | ||||
\(359\) | 5.16312 | − | 15.8904i | 0.272499 | − | 0.838666i | −0.717371 | − | 0.696691i | \(-0.754655\pi\) |
0.989870 | − | 0.141975i | \(-0.0453451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.85410 | + | 3.52671i | −0.255479 | + | 0.185616i | ||||
\(362\) | −3.23607 | −0.170084 | ||||||||
\(363\) | 1.39919 | − | 10.9106i | 0.0734383 | − | 0.572661i | ||||
\(364\) | −1.52786 | −0.0800818 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.33688 | − | 4.11450i | −0.0698799 | − | 0.215068i | ||||
\(367\) | −5.60081 | + | 17.2375i | −0.292360 | + | 0.899792i | 0.691735 | + | 0.722151i | \(0.256846\pi\) |
−0.984095 | + | 0.177641i | \(0.943154\pi\) | |||||||
\(368\) | −3.57295 | − | 2.59590i | −0.186253 | − | 0.135321i | ||||
\(369\) | −2.04508 | − | 1.48584i | −0.106463 | − | 0.0773498i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79837 | + | 5.53483i | 0.0933669 | + | 0.287354i | ||||
\(372\) | −9.16312 | + | 6.65740i | −0.475086 | + | 0.345170i | ||||
\(373\) | 9.74265 | 0.504455 | 0.252228 | − | 0.967668i | \(-0.418837\pi\) | ||||
0.252228 | + | 0.967668i | \(0.418837\pi\) | |||||||
\(374\) | 4.00000 | + | 0.898056i | 0.206835 | + | 0.0464374i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.20820 | − | 6.69015i | 0.474877 | − | 0.345018i | ||||
\(377\) | 2.23607 | + | 6.88191i | 0.115163 | + | 0.354436i | ||||
\(378\) | 0.145898 | − | 0.449028i | 0.00750419 | − | 0.0230955i | ||||
\(379\) | 4.04508 | + | 2.93893i | 0.207782 | + | 0.150963i | 0.686810 | − | 0.726837i | \(-0.259011\pi\) |
−0.479028 | + | 0.877800i | \(0.659011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.92705 | + | 15.1639i | −0.252420 | + | 0.776870i | ||||
\(382\) | 1.98936 | + | 6.12261i | 0.101784 | + | 0.313260i | ||||
\(383\) | 25.3713 | − | 18.4333i | 1.29641 | − | 0.941900i | 0.296500 | − | 0.955033i | \(-0.404180\pi\) |
0.999914 | + | 0.0131328i | \(0.00418043\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | 1.69098 | − | 1.22857i | 0.0859575 | − | 0.0624518i | ||||
\(388\) | −5.73607 | − | 17.6538i | −0.291205 | − | 0.896236i | ||||
\(389\) | −12.0344 | + | 37.0382i | −0.610170 | + | 1.87791i | −0.153855 | + | 0.988093i | \(0.549169\pi\) |
−0.456316 | + | 0.889818i | \(0.650831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.85410 | − | 2.80017i | −0.194910 | − | 0.141611i | ||||
\(392\) | 4.43363 | − | 13.6453i | 0.223932 | − | 0.689192i | ||||
\(393\) | −4.07295 | − | 12.5352i | −0.205453 | − | 0.632320i | ||||
\(394\) | −7.11803 | + | 5.17155i | −0.358601 | + | 0.260539i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | − | 5.34307i | −0.0251259 | − | 0.268499i | ||||
\(397\) | 36.2705 | 1.82036 | 0.910182 | − | 0.414208i | \(-0.135941\pi\) | ||||
0.910182 | + | 0.414208i | \(0.135941\pi\) | |||||||
\(398\) | −9.89919 | + | 7.19218i | −0.496201 | + | 0.360511i | ||||
\(399\) | 1.18034 | + | 3.63271i | 0.0590909 | + | 0.181863i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.95492 | − | 2.87341i | −0.197499 | − | 0.143491i | 0.484641 | − | 0.874713i | \(-0.338950\pi\) |
−0.682140 | + | 0.731222i | \(0.738950\pi\) | |||||||
\(402\) | −4.69098 | − | 3.40820i | −0.233965 | − | 0.169985i | ||||
\(403\) | −2.67376 | + | 8.22899i | −0.133190 | + | 0.409915i | ||||
\(404\) | 0.281153 | + | 0.865300i | 0.0139879 | + | 0.0430503i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.76393 | 0.137172 | ||||||||
\(407\) | −12.6353 | + | 21.3193i | −0.626306 | + | 1.05676i | ||||
\(408\) | 4.47214 | 0.221404 | ||||||||
\(409\) | −29.3713 | + | 21.3395i | −1.45232 | + | 1.05517i | −0.467036 | + | 0.884238i | \(0.654678\pi\) |
−0.985283 | + | 0.170933i | \(0.945322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.78115 | + | 17.7926i | −0.285163 | + | 0.877642i | ||||
\(412\) | 3.11803 | + | 2.26538i | 0.153615 | + | 0.111607i | ||||
\(413\) | −4.14590 | − | 3.01217i | −0.204006 | − | 0.148219i | ||||
\(414\) | 0.454915 | − | 1.40008i | 0.0223579 | − | 0.0688104i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.61803 | − | 4.08174i | 0.275447 | − | 0.200124i | ||||
\(417\) | −21.1803 | −1.03721 | ||||||||
\(418\) | −6.77051 | − | 7.69421i | −0.331156 | − | 0.376336i | ||||
\(419\) | 24.5967 | 1.20163 | 0.600815 | − | 0.799388i | \(-0.294843\pi\) | ||||
0.600815 | + | 0.799388i | \(0.294843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.881966 | + | 2.71441i | 0.0429844 | + | 0.132292i | 0.970246 | − | 0.242123i | \(-0.0778436\pi\) |
−0.927261 | + | 0.374415i | \(0.877844\pi\) | |||||||
\(422\) | −0.736068 | + | 2.26538i | −0.0358312 | + | 0.110277i | ||||
\(423\) | −4.11803 | − | 2.99193i | −0.200226 | − | 0.145472i | ||||
\(424\) | −13.7812 | − | 10.0126i | −0.669272 | − | 0.486255i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.52786 | + | 4.70228i | 0.0740253 | + | 0.227826i | ||||
\(427\) | 4.32624 | − | 3.14320i | 0.209361 | − | 0.152110i | ||||
\(428\) | −4.61803 | −0.223221 | ||||||||
\(429\) | −2.70820 | − | 3.07768i | −0.130753 | − | 0.148592i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0902 | + | 11.6902i | −0.775036 | + | 0.563097i | −0.903485 | − | 0.428619i | \(-0.859000\pi\) |
0.128449 | + | 0.991716i | \(0.459000\pi\) | |||||||
\(432\) | −0.572949 | − | 1.76336i | −0.0275660 | − | 0.0848395i | ||||
\(433\) | 8.66312 | − | 26.6623i | 0.416323 | − | 1.28131i | −0.494739 | − | 0.869041i | \(-0.664736\pi\) |
0.911062 | − | 0.412269i | \(-0.135264\pi\) | |||||||
\(434\) | 2.67376 | + | 1.94260i | 0.128345 | + | 0.0932479i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.07295 | + | 6.37988i | −0.0992763 | + | 0.305541i | ||||
\(437\) | 3.68034 | + | 11.3269i | 0.176055 | + | 0.541840i | ||||
\(438\) | −6.73607 | + | 4.89404i | −0.321862 | + | 0.233846i | ||||
\(439\) | 9.67376 | 0.461703 | 0.230852 | − | 0.972989i | \(-0.425849\pi\) | ||||
0.230852 | + | 0.972989i | \(0.425849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.41641 | −0.305543 | ||||||||
\(442\) | 1.23607 | − | 0.898056i | 0.0587938 | − | 0.0427162i | ||||
\(443\) | 7.80902 | + | 24.0337i | 0.371018 | + | 1.14187i | 0.946126 | + | 0.323798i | \(0.104960\pi\) |
−0.575109 | + | 0.818077i | \(0.695040\pi\) | |||||||
\(444\) | −3.73607 | + | 11.4984i | −0.177306 | + | 0.545692i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.01722 | − | 2.91868i | −0.190221 | − | 0.138204i | ||||
\(447\) | −6.21885 | + | 19.1396i | −0.294141 | + | 0.905274i | ||||
\(448\) | 0.0557281 | + | 0.171513i | 0.00263290 | + | 0.00810325i | ||||
\(449\) | 0.590170 | − | 0.428784i | 0.0278518 | − | 0.0202355i | −0.573772 | − | 0.819015i | \(-0.694521\pi\) |
0.601624 | + | 0.798779i | \(0.294521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.781153 | + | 8.34751i | 0.0367831 | + | 0.393069i | ||||
\(452\) | −8.85410 | −0.416462 | ||||||||
\(453\) | −8.70820 | + | 6.32688i | −0.409147 | + | 0.297263i | ||||
\(454\) | 4.95492 | + | 15.2497i | 0.232546 | + | 0.715702i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.04508 | − | 6.57164i | −0.423575 | − | 0.307745i | ||||
\(457\) | −1.19098 | − | 0.865300i | −0.0557118 | − | 0.0404770i | 0.559581 | − | 0.828776i | \(-0.310962\pi\) |
−0.615293 | + | 0.788299i | \(0.710962\pi\) | |||||||
\(458\) | 3.45492 | − | 10.6331i | 0.161438 | − | 0.496854i | ||||
\(459\) | −0.618034 | − | 1.90211i | −0.0288474 | − | 0.0887830i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.9443 | 1.20835 | 0.604173 | − | 0.796853i | \(-0.293504\pi\) | ||||
0.604173 | + | 0.796853i | \(0.293504\pi\) | |||||||
\(462\) | −1.43769 | + | 0.620541i | −0.0668876 | + | 0.0288702i | ||||
\(463\) | −33.2705 | −1.54621 | −0.773106 | − | 0.634277i | \(-0.781298\pi\) | ||||
−0.773106 | + | 0.634277i | \(0.781298\pi\) | |||||||
\(464\) | 8.78115 | − | 6.37988i | 0.407655 | − | 0.296179i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.44427 | + | 13.6781i | −0.205877 | + | 0.633624i | ||||
\(467\) | −3.95492 | − | 2.87341i | −0.183012 | − | 0.132966i | 0.492507 | − | 0.870308i | \(-0.336080\pi\) |
−0.675519 | + | 0.737342i | \(0.736080\pi\) | |||||||
\(468\) | −1.61803 | − | 1.17557i | −0.0747936 | − | 0.0543408i | ||||
\(469\) | 2.21478 | − | 6.81640i | 0.102269 | − | 0.314752i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.69098 | + | 1.95511i | −0.123994 | + | 0.0900869i | ||||
\(472\) | 15.0000 | 0.690431 | ||||||||
\(473\) | −6.76393 | − | 1.51860i | −0.311006 | − | 0.0698252i | ||||
\(474\) | 5.00000 | 0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.763932 | + | 2.35114i | 0.0350148 | + | 0.107764i | ||||
\(477\) | −2.35410 | + | 7.24518i | −0.107787 | + | 0.331734i | ||||
\(478\) | 3.51722 | + | 2.55541i | 0.160874 | + | 0.116882i | ||||
\(479\) | −27.0344 | − | 19.6417i | −1.23524 | − | 0.897451i | −0.237964 | − | 0.971274i | \(-0.576480\pi\) |
−0.997271 | + | 0.0738231i | \(0.976480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.85410 | + | 8.78402i | 0.130136 | + | 0.400517i | ||||
\(482\) | 0.809017 | − | 0.587785i | 0.0368497 | − | 0.0267729i | ||||
\(483\) | 1.81966 | 0.0827974 | ||||||||
\(484\) | −12.2082 | + | 12.9515i | −0.554918 | + | 0.588705i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | − | 0.363271i | 0.0226805 | − | 0.0164783i | ||||
\(487\) | −4.38197 | − | 13.4863i | −0.198566 | − | 0.611123i | −0.999916 | − | 0.0129278i | \(-0.995885\pi\) |
0.801351 | − | 0.598195i | \(-0.204115\pi\) | |||||||
\(488\) | −4.83688 | + | 14.8864i | −0.218955 | + | 0.673875i | ||||
\(489\) | 10.9721 | + | 7.97172i | 0.496177 | + | 0.360494i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.82624 | − | 30.2421i | 0.443452 | − | 1.36480i | −0.440721 | − | 0.897644i | \(-0.645277\pi\) |
0.884173 | − | 0.467160i | \(-0.154723\pi\) | |||||||
\(492\) | 1.26393 | + | 3.88998i | 0.0569825 | + | 0.175374i | ||||
\(493\) | 9.47214 | − | 6.88191i | 0.426604 | − | 0.309946i | ||||
\(494\) | −3.81966 | −0.171855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.9787 | 0.582761 | ||||||||
\(497\) | −4.94427 | + | 3.59222i | −0.221781 | + | 0.161133i | ||||
\(498\) | 1.09017 | + | 3.35520i | 0.0488517 | + | 0.150350i | ||||
\(499\) | −3.45492 | + | 10.6331i | −0.154663 | + | 0.476005i | −0.998127 | − | 0.0611822i | \(-0.980513\pi\) |
0.843463 | + | 0.537187i | \(0.180513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.2082 | − | 11.7759i | −0.724129 | − | 0.526111i | ||||
\(502\) | 1.43769 | − | 4.42477i | 0.0641674 | − | 0.197487i | ||||
\(503\) | −6.76393 | − | 20.8172i | −0.301589 | − | 0.928195i | −0.980928 | − | 0.194371i | \(-0.937734\pi\) |
0.679339 | − | 0.733824i | \(-0.262266\pi\) | |||||||
\(504\) | −1.38197 | + | 1.00406i | −0.0615577 | + | 0.0447243i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.48278 | + | 1.93487i | −0.199284 | + | 0.0860154i | ||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | 20.8713 | − | 15.1639i | 0.926015 | − | 0.672789i | ||||
\(509\) | 0.163119 | + | 0.502029i | 0.00723012 | + | 0.0222520i | 0.954606 | − | 0.297870i | \(-0.0962761\pi\) |
−0.947376 | + | 0.320122i | \(0.896276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.32624 | − | 6.04937i | −0.368331 | − | 0.267608i | ||||
\(512\) | −15.1353 | − | 10.9964i | −0.668890 | − | 0.485977i | ||||
\(513\) | −1.54508 | + | 4.75528i | −0.0682172 | + | 0.209951i | ||||
\(514\) | −2.01722 | − | 6.20837i | −0.0889758 | − | 0.273839i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.38197 | −0.148883 | ||||||||
\(517\) | 1.57295 | + | 16.8087i | 0.0691782 | + | 0.739248i | ||||
\(518\) | 3.52786 | 0.155005 | ||||||||
\(519\) | 2.88197 | − | 2.09387i | 0.126504 | − | 0.0919107i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.74671 | + | 14.6089i | −0.207957 | + | 0.640026i | 0.791622 | + | 0.611011i | \(0.209237\pi\) |
−0.999579 | + | 0.0290150i | \(0.990763\pi\) | |||||||
\(522\) | 2.92705 | + | 2.12663i | 0.128114 | + | 0.0930799i | ||||
\(523\) | −6.66312 | − | 4.84104i | −0.291358 | − | 0.211684i | 0.432498 | − | 0.901635i | \(-0.357632\pi\) |
−0.723856 | + | 0.689951i | \(0.757632\pi\) | |||||||
\(524\) | −6.59017 | + | 20.2825i | −0.287893 | + | 0.886043i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.6074 | − | 9.88635i | 0.593310 | − | 0.431065i | ||||
\(527\) | 14.0000 | 0.609850 | ||||||||
\(528\) | −3.13525 | + | 5.29007i | −0.136444 | + | 0.230221i | ||||
\(529\) | −17.3262 | −0.753315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.07295 | − | 6.37988i | −0.0899583 | − | 0.276863i | ||||
\(532\) | 1.90983 | − | 5.87785i | 0.0828016 | − | 0.254837i | ||||
\(533\) | 2.52786 | + | 1.83660i | 0.109494 | + | 0.0795520i | ||||
\(534\) | 5.42705 | + | 3.94298i | 0.234851 | + | 0.170630i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.48278 | + | 19.9519i | 0.280013 | + | 0.861793i | ||||
\(537\) | −15.7533 | + | 11.4454i | −0.679805 | + | 0.493907i | ||||
\(538\) | −3.61803 | −0.155985 | ||||||||
\(539\) | 14.0582 | + | 15.9762i | 0.605531 | + | 0.688144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.500000 | + | 0.363271i | −0.0214967 | + | 0.0156183i | −0.598482 | − | 0.801136i | \(-0.704229\pi\) |
0.576985 | + | 0.816755i | \(0.304229\pi\) | |||||||
\(542\) | 3.93769 | + | 12.1190i | 0.169138 | + | 0.520555i | ||||
\(543\) | 1.61803 | − | 4.97980i | 0.0694365 | − | 0.213704i | ||||
\(544\) | −9.09017 | − | 6.60440i | −0.389738 | − | 0.283161i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.180340 | + | 0.555029i | −0.00771783 | + | 0.0237531i | ||||
\(547\) | −7.83688 | − | 24.1194i | −0.335081 | − | 1.03127i | −0.966682 | − | 0.255979i | \(-0.917602\pi\) |
0.631601 | − | 0.775293i | \(-0.282398\pi\) | |||||||
\(548\) | 24.4894 | − | 17.7926i | 1.04613 | − | 0.760060i | ||||
\(549\) | 7.00000 | 0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.2705 | −1.24697 | ||||||||
\(552\) | −4.30902 | + | 3.13068i | −0.183404 | + | 0.133251i | ||||
\(553\) | 1.90983 | + | 5.87785i | 0.0812142 | + | 0.249952i | ||||
\(554\) | −1.65248 | + | 5.08580i | −0.0702070 | + | 0.216075i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.7254 | + | 20.1437i | 1.17582 | + | 0.854283i | ||||
\(557\) | 9.70163 | − | 29.8585i | 0.411071 | − | 1.26515i | −0.504647 | − | 0.863326i | \(-0.668377\pi\) |
0.915718 | − | 0.401821i | \(-0.131623\pi\) | |||||||
\(558\) | 1.33688 | + | 4.11450i | 0.0565947 | + | 0.174181i | ||||
\(559\) | −2.09017 | + | 1.51860i | −0.0884048 | + | 0.0642298i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.38197 | + | 5.70634i | −0.142787 | + | 0.240922i | ||||
\(562\) | 6.23607 | 0.263053 | ||||||||
\(563\) | −29.3885 | + | 21.3520i | −1.23858 | + | 0.899881i | −0.997503 | − | 0.0706255i | \(-0.977500\pi\) |
−0.241077 | + | 0.970506i | \(0.577500\pi\) | |||||||
\(564\) | 2.54508 | + | 7.83297i | 0.107167 | + | 0.329827i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.51722 | − | 4.73504i | −0.273939 | − | 0.199028i | ||||
\(567\) | 0.618034 | + | 0.449028i | 0.0259550 | + | 0.0188574i | ||||
\(568\) | 5.52786 | − | 17.0130i | 0.231944 | − | 0.713850i | ||||
\(569\) | −0.753289 | − | 2.31838i | −0.0315795 | − | 0.0971917i | 0.934024 | − | 0.357209i | \(-0.116272\pi\) |
−0.965604 | + | 0.260017i | \(0.916272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0901699 | 0.00377349 | 0.00188675 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188675 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(572\) | 0.618034 | + | 6.60440i | 0.0258413 | + | 0.276144i | ||||
\(573\) | −10.4164 | −0.435152 | ||||||||
\(574\) | 0.965558 | − | 0.701519i | 0.0403016 | − | 0.0292808i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0729490 | + | 0.224514i | −0.00303954 | + | 0.00935475i | ||||
\(577\) | 37.2254 | + | 27.0459i | 1.54971 | + | 1.12593i | 0.943854 | + | 0.330363i | \(0.107171\pi\) |
0.605861 | + | 0.795571i | \(0.292829\pi\) | |||||||
\(578\) | 6.50000 | + | 4.72253i | 0.270364 | + | 0.196431i | ||||
\(579\) | 6.50000 | − | 20.0049i | 0.270131 | − | 0.831377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.52786 | + | 2.56314i | −0.146360 | + | 0.106337i | ||||
\(582\) | −7.09017 | −0.293897 | ||||||||
\(583\) | 23.1976 | − | 10.0126i | 0.960745 | − | 0.414679i | ||||
\(584\) | 30.1246 | 1.24657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.15654 | + | 9.71483i | 0.130396 | + | 0.401316i | ||||
\(587\) | −5.98936 | + | 18.4333i | −0.247207 | + | 0.760826i | 0.748058 | + | 0.663633i | \(0.230986\pi\) |
−0.995266 | + | 0.0971926i | \(0.969014\pi\) | |||||||
\(588\) | 8.39919 | + | 6.10237i | 0.346377 | + | 0.251657i | ||||
\(589\) | −28.3156 | − | 20.5725i | −1.16672 | − | 0.847674i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.39919 | − | 13.5393i | −0.180958 | − | 0.556933i | ||||
\(592\) | 11.2082 | − | 8.14324i | 0.460654 | − | 0.334685i | ||||
\(593\) | 38.8885 | 1.59696 | 0.798481 | − | 0.602021i | \(-0.205638\pi\) | ||||
0.798481 | + | 0.602021i | \(0.205638\pi\) | |||||||
\(594\) | −2.00000 | − | 0.449028i | −0.0820610 | − | 0.0184238i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.3435 | − | 19.1396i | 1.07907 | − | 0.783990i | ||||
\(597\) | −6.11803 | − | 18.8294i | −0.250394 | − | 0.770635i | ||||
\(598\) | −0.562306 | + | 1.73060i | −0.0229944 | + | 0.0707695i | ||||
\(599\) | 17.9894 | + | 13.0700i | 0.735025 | + | 0.534027i | 0.891149 | − | 0.453710i | \(-0.149900\pi\) |
−0.156124 | + | 0.987737i | \(0.549900\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6180 | − | 32.6789i | 0.433119 | − | 1.33300i | −0.461884 | − | 0.886941i | \(-0.652826\pi\) |
0.895002 | − | 0.446062i | \(-0.147174\pi\) | |||||||
\(602\) | 0.304952 | + | 0.938545i | 0.0124289 | + | 0.0382522i | ||||
\(603\) | 7.59017 | − | 5.51458i | 0.309096 | − | 0.224571i | ||||
\(604\) | 17.4164 | 0.708664 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.347524 | 0.0141172 | ||||||||
\(607\) | 26.6976 | − | 19.3969i | 1.08362 | − | 0.787296i | 0.105310 | − | 0.994439i | \(-0.466417\pi\) |
0.978311 | + | 0.207143i | \(0.0664165\pi\) | |||||||
\(608\) | 8.68034 | + | 26.7153i | 0.352034 | + | 1.08345i | ||||
\(609\) | −1.38197 | + | 4.25325i | −0.0560001 | + | 0.172351i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.09017 | + | 3.69822i | 0.205926 | + | 0.149614i | ||||
\(612\) | −1.00000 | + | 3.07768i | −0.0404226 | + | 0.124408i | ||||
\(613\) | 2.54508 | + | 7.83297i | 0.102795 | + | 0.316371i | 0.989207 | − | 0.146527i | \(-0.0468096\pi\) |
−0.886412 | + | 0.462898i | \(0.846810\pi\) | |||||||
\(614\) | −6.06231 | + | 4.40452i | −0.244655 | + | 0.177752i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.52786 | + | 1.24108i | 0.222724 | + | 0.0500047i | ||||
\(617\) | −38.2492 | −1.53986 | −0.769928 | − | 0.638131i | \(-0.779708\pi\) | ||||
−0.769928 | + | 0.638131i | \(0.779708\pi\) | |||||||
\(618\) | 1.19098 | − | 0.865300i | 0.0479084 | − | 0.0348075i | ||||
\(619\) | 2.19756 | + | 6.76340i | 0.0883274 | + | 0.271844i | 0.985457 | − | 0.169923i | \(-0.0543519\pi\) |
−0.897130 | + | 0.441767i | \(0.854352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92705 | + | 1.40008i | 0.0773299 | + | 0.0561835i | ||||
\(622\) | −10.7361 | − | 7.80021i | −0.430477 | − | 0.312760i | ||||
\(623\) | −2.56231 | + | 7.88597i | −0.102657 | + | 0.315945i | ||||
\(624\) | 0.708204 | + | 2.17963i | 0.0283508 | + | 0.0872549i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.291796 | 0.0116625 | ||||||||
\(627\) | 15.2254 | − | 6.57164i | 0.608045 | − | 0.262446i | ||||
\(628\) | 5.38197 | 0.214764 | ||||||||
\(629\) | 12.0902 | − | 8.78402i | 0.482067 | − | 0.350242i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9377 | − | 36.7404i | 0.475232 | − | 1.46261i | −0.370412 | − | 0.928867i | \(-0.620784\pi\) |
0.845644 | − | 0.533747i | \(-0.179216\pi\) | |||||||
\(632\) | −14.6353 | − | 10.6331i | −0.582159 | − | 0.422963i | ||||
\(633\) | −3.11803 | − | 2.26538i | −0.123931 | − | 0.0900409i | ||||
\(634\) | 5.80902 | − | 17.8783i | 0.230706 | − | 0.710039i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.97214 | − | 7.24518i | 0.395421 | − | 0.287290i | ||||
\(637\) | 7.93112 | 0.314242 | ||||||||
\(638\) | −1.11803 | − | 11.9475i | −0.0442634 | − | 0.473005i | ||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0729490 | − | 0.224514i | −0.00288131 | − | 0.00886777i | 0.949606 | − | 0.313448i | \(-0.101484\pi\) |
−0.952487 | + | 0.304580i | \(0.901484\pi\) | |||||||
\(642\) | −0.545085 | + | 1.67760i | −0.0215128 | + | 0.0662096i | ||||
\(643\) | 23.7254 | + | 17.2375i | 0.935639 | + | 0.679782i | 0.947367 | − | 0.320149i | \(-0.103733\pi\) |
−0.0117276 | + | 0.999931i | \(0.503733\pi\) | |||||||
\(644\) | −2.38197 | − | 1.73060i | −0.0938626 | − | 0.0681952i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.90983 | + | 5.87785i | 0.0751413 | + | 0.231261i | ||||
\(647\) | 14.2361 | − | 10.3431i | 0.559678 | − | 0.406630i | −0.271663 | − | 0.962392i | \(-0.587574\pi\) |
0.831341 | + | 0.555763i | \(0.187574\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | −11.3435 | + | 19.1396i | −0.445270 | + | 0.751297i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.32624 | + | 3.14320i | −0.169559 | + | 0.123192i | ||||
\(652\) | −6.78115 | − | 20.8702i | −0.265570 | − | 0.817342i | ||||
\(653\) | 7.24265 | − | 22.2906i | 0.283427 | − | 0.872297i | −0.703439 | − | 0.710755i | \(-0.748353\pi\) |
0.986866 | − | 0.161542i | \(-0.0516467\pi\) | |||||||
\(654\) | 2.07295 | + | 1.50609i | 0.0810587 | + | 0.0588926i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.44834 | − | 4.45752i | 0.0565481 | − | 0.174037i | ||||
\(657\) | −4.16312 | − | 12.8128i | −0.162419 | − | 0.499873i | ||||
\(658\) | 1.94427 | − | 1.41260i | 0.0757956 | − | 0.0550687i | ||||
\(659\) | 12.9656 | 0.505066 | 0.252533 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252533 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.90983 | 0.152075 | 0.0760374 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760374 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(662\) | −10.7984 | + | 7.84548i | −0.419691 | + | 0.304923i | ||||
\(663\) | 0.763932 | + | 2.35114i | 0.0296687 | + | 0.0913108i | ||||
\(664\) | 3.94427 | − | 12.1392i | 0.153067 | − | 0.471093i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.73607 | + | 2.71441i | 0.144770 | + | 0.105181i | ||||
\(667\) | −4.30902 | + | 13.2618i | −0.166846 | + | 0.513499i | ||||
\(668\) | 10.0172 | + | 30.8298i | 0.387578 | + | 1.19284i | ||||
\(669\) | 6.50000 | − | 4.72253i | 0.251305 | − | 0.182583i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.3369 | − | 17.4293i | −0.592074 | − | 0.672850i | ||||
\(672\) | 4.29180 | 0.165560 | ||||||||
\(673\) | −22.0902 | + | 16.0494i | −0.851513 | + | 0.618661i | −0.925563 | − | 0.378594i | \(-0.876408\pi\) |
0.0740494 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(674\) | −4.22949 | − | 13.0170i | −0.162914 | − | 0.501397i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.0172 | − | 10.9106i | −0.577585 | − | 0.419640i | ||||
\(677\) | 9.66312 | + | 7.02067i | 0.371384 | + | 0.269826i | 0.757785 | − | 0.652505i | \(-0.226282\pi\) |
−0.386401 | + | 0.922331i | \(0.626282\pi\) | |||||||
\(678\) | −1.04508 | + | 3.21644i | −0.0401362 | + | 0.123527i | ||||
\(679\) | −2.70820 | − | 8.33499i | −0.103931 | − | 0.319868i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.9443 | −0.994187 | ||||||||
\(682\) | 7.31559 | − | 12.3435i | 0.280129 | − | 0.472657i | ||||
\(683\) | −2.29180 | −0.0876931 | −0.0438466 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438466 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(684\) | 6.54508 | − | 4.75528i | 0.250258 | − | 0.181823i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.95743 | − | 6.02434i | 0.0747349 | − | 0.230010i | ||||
\(687\) | 14.6353 | + | 10.6331i | 0.558370 | + | 0.405679i | ||||
\(688\) | 3.13525 | + | 2.27790i | 0.119530 | + | 0.0868440i | ||||
\(689\) | 2.90983 | − | 8.95554i | 0.110856 | − | 0.341179i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9443 | + | 19.5762i | −1.02501 | + | 0.744712i | −0.967304 | − | 0.253621i | \(-0.918378\pi\) |
−0.0577049 | + | 0.998334i | \(0.518378\pi\) | |||||||
\(692\) | −5.76393 | −0.219112 | ||||||||
\(693\) | −0.236068 | − | 2.52265i | −0.00896748 | − | 0.0958277i | ||||
\(694\) | 3.59675 | 0.136531 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.04508 | − | 12.4495i | −0.153329 | − | 0.471897i | ||||
\(697\) | 1.56231 | − | 4.80828i | 0.0591766 | − | 0.182127i | ||||
\(698\) | −13.8820 | − | 10.0858i | −0.525440 | − | 0.381755i | ||||
\(699\) | −18.8262 | − | 13.6781i | −0.712074 | − | 0.517352i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.19756 | + | 12.9188i | 0.158540 | + | 0.487935i | 0.998502 | − | 0.0547093i | \(-0.0174232\pi\) |
−0.839963 | + | 0.542644i | \(0.817423\pi\) | |||||||
\(702\) | −0.618034 | + | 0.449028i | −0.0233262 | + | 0.0169475i | ||||
\(703\) | −37.3607 | −1.40908 | ||||||||
\(704\) | 0.718847 | − | 0.310271i | 0.0270926 | − | 0.0116938i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9164 | − | 13.0170i | 0.674293 | − | 0.489902i | ||||
\(707\) | 0.132742 | + | 0.408539i | 0.00499229 | + | 0.0153647i | ||||
\(708\) | −3.35410 | + | 10.3229i | −0.126055 | + | 0.387957i | ||||
\(709\) | −33.3156 | − | 24.2052i | −1.25119 | − | 0.909045i | −0.252903 | − | 0.967492i | \(-0.581385\pi\) |
−0.998291 | + | 0.0584464i | \(0.981385\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | + | 7.69421i | −0.0937573 | + | 0.288555i | ||||
\(712\) | −7.50000 | − | 23.0826i | −0.281074 | − | 0.865058i | ||||
\(713\) | −13.4894 | + | 9.80059i | −0.505180 | + | 0.367035i | ||||
\(714\) | 0.944272 | 0.0353385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.5066 | 1.17746 | ||||||||
\(717\) | −5.69098 | + | 4.13474i | −0.212534 | + | 0.154415i | ||||
\(718\) | 3.19098 | + | 9.82084i | 0.119086 | + | 0.366510i | ||||
\(719\) | 11.7705 | − | 36.2259i | 0.438966 | − | 1.35100i | −0.450001 | − | 0.893028i | \(-0.648577\pi\) |
0.888967 | − | 0.457970i | \(-0.151423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.47214 | + | 1.06957i | 0.0548252 | + | 0.0398328i | ||||
\(722\) | 1.14590 | − | 3.52671i | 0.0426459 | − | 0.131251i | ||||
\(723\) | 0.500000 | + | 1.53884i | 0.0185952 | + | 0.0572301i | ||||
\(724\) | −6.85410 | + | 4.97980i | −0.254731 | + | 0.185073i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.26393 | + | 5.96361i | 0.121136 | + | 0.221330i | ||||
\(727\) | 37.3262 | 1.38435 | 0.692177 | − | 0.721728i | \(-0.256652\pi\) | ||||
0.692177 | + | 0.721728i | \(0.256652\pi\) | |||||||
\(728\) | 1.70820 | − | 1.24108i | 0.0633102 | − | 0.0459976i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.38197 | + | 2.45714i | 0.125087 | + | 0.0908807i | ||||
\(732\) | −9.16312 | − | 6.65740i | −0.338679 | − | 0.246064i | ||||
\(733\) | 0.572949 | − | 1.76336i | 0.0211624 | − | 0.0651310i | −0.939918 | − | 0.341401i | \(-0.889098\pi\) |
0.961080 | + | 0.276270i | \(0.0890985\pi\) | |||||||
\(734\) | −3.46149 | − | 10.6534i | −0.127766 | − | 0.393223i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3820 | 0.493266 | ||||||||
\(737\) | −30.3607 | − | 6.81640i | −1.11835 | − | 0.251085i | ||||
\(738\) | 1.56231 | 0.0575093 | ||||||||
\(739\) | 16.1803 | − | 11.7557i | 0.595203 | − | 0.432441i | −0.248970 | − | 0.968511i | \(-0.580092\pi\) |
0.844173 | + | 0.536071i | \(0.180092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.90983 | − | 5.87785i | 0.0701594 | − | 0.215928i | ||||
\(742\) | −2.90983 | − | 2.11412i | −0.106823 | − | 0.0776116i | ||||
\(743\) | −0.281153 | − | 0.204270i | −0.0103145 | − | 0.00749392i | 0.582616 | − | 0.812748i | \(-0.302029\pi\) |
−0.592931 | + | 0.805254i | \(0.702029\pi\) | |||||||
\(744\) | 4.83688 | − | 14.8864i | 0.177329 | − | 0.545762i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.87132 | + | 3.53922i | −0.178352 | + | 0.129580i | ||||
\(747\) | −5.70820 | −0.208852 | ||||||||
\(748\) | 9.85410 | − | 4.25325i | 0.360302 | − | 0.155514i | ||||
\(749\) | −2.18034 | −0.0796679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1803 | − | 43.6426i | −0.517448 | − | 1.59254i | −0.778783 | − | 0.627293i | \(-0.784163\pi\) |
0.261335 | − | 0.965248i | \(-0.415837\pi\) | |||||||
\(752\) | 2.91641 | − | 8.97578i | 0.106350 | − | 0.327313i | ||||
\(753\) | 6.09017 | + | 4.42477i | 0.221938 | + | 0.161247i | ||||
\(754\) | −3.61803 | − | 2.62866i | −0.131761 | − | 0.0957300i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.381966 | − | 1.17557i | −0.0138920 | − | 0.0427551i | ||||
\(757\) | 19.5623 | − | 14.2128i | 0.711004 | − | 0.516575i | −0.172493 | − | 0.985011i | \(-0.555182\pi\) |
0.883497 | + | 0.468436i | \(0.155182\pi\) | |||||||
\(758\) | −3.09017 | −0.112240 | ||||||||
\(759\) | −0.736068 | − | 7.86572i | −0.0267176 | − | 0.285508i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5795 | + | 22.9439i | −1.14476 | + | 0.831715i | −0.987775 | − | 0.155887i | \(-0.950176\pi\) |
−0.156982 | + | 0.987601i | \(0.550176\pi\) | |||||||
\(762\) | −3.04508 | − | 9.37181i | −0.110312 | − | 0.339505i | ||||
\(763\) | −0.978714 | + | 3.01217i | −0.0354318 | + | 0.109048i | ||||
\(764\) | 13.6353 | + | 9.90659i | 0.493306 | + | 0.358408i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.98936 | + | 18.4333i | −0.216404 | + | 0.666024i | ||||
\(767\) | 2.56231 | + | 7.88597i | 0.0925195 | + | 0.284746i | ||||
\(768\) | −5.30902 | + | 3.85723i | −0.191573 | + | 0.139186i | ||||
\(769\) | 12.7639 | 0.460279 | 0.230140 | − | 0.973158i | \(-0.426082\pi\) | ||||
0.230140 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5623 | 0.380392 | ||||||||
\(772\) | −27.5344 | + | 20.0049i | −0.990986 | + | 0.719994i | ||||
\(773\) | −3.24671 | − | 9.99235i | −0.116776 | − | 0.359400i | 0.875537 | − | 0.483151i | \(-0.160508\pi\) |
−0.992313 | + | 0.123751i | \(0.960508\pi\) | |||||||
\(774\) | −0.399187 | + | 1.22857i | −0.0143485 | + | 0.0441601i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.7533 | + | 15.0781i | 0.745000 | + | 0.541274i | ||||
\(777\) | −1.76393 | + | 5.42882i | −0.0632807 | + | 0.194758i | ||||
\(778\) | −7.43769 | − | 22.8909i | −0.266654 | − | 0.820677i | ||||
\(779\) | −10.2254 | + | 7.42921i | −0.366364 | + | 0.266179i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5279 | + | 19.9192i | 0.627196 | + | 0.712765i | ||||
\(782\) | 2.94427 | 0.105287 | ||||||||
\(783\) | −4.73607 | + | 3.44095i | −0.169253 | + | 0.122970i | ||||
\(784\) | −3.67627 | − | 11.3144i | −0.131296 | − | 0.404086i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.59017 | + | 4.78804i | 0.235064 | + | 0.170784i | ||||
\(787\) | 6.63525 | + | 4.82079i | 0.236521 | + | 0.171843i | 0.699732 | − | 0.714405i | \(-0.253303\pi\) |
−0.463211 | + | 0.886248i | \(0.653303\pi\) | |||||||
\(788\) | −7.11803 | + | 21.9071i | −0.253569 | + | 0.780407i | ||||
\(789\) | 8.40983 | + | 25.8828i | 0.299398 | + | 0.921452i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.18034 | −0.148636 | ||||||||
\(792\) | 4.89919 | + | 5.56758i | 0.174085 | + | 0.197835i | ||||
\(793\) | −8.65248 | −0.307258 | ||||||||
\(794\) | −18.1353 | + | 13.1760i | −0.643596 | + | 0.467600i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.89919 | + | 30.4666i | −0.350867 | + | 1.07986i | ||||
\(797\) | −23.2254 | − | 16.8743i | −0.822687 | − | 0.597717i | 0.0947941 | − | 0.995497i | \(-0.469781\pi\) |
−0.917481 | + | 0.397780i | \(0.869781\pi\) | |||||||
\(798\) | −1.90983 | − | 1.38757i | −0.0676073 | − | 0.0491195i | ||||
\(799\) | 3.14590 | − | 9.68208i | 0.111294 | − | 0.342527i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.78115 | + | 6.37988i | −0.310267 | + | 0.225422i | ||||
\(802\) | 3.02129 | 0.106685 | ||||||||
\(803\) | −22.7812 | + | 38.4383i | −0.803929 | + | 1.35646i | ||||
\(804\) | −15.1803 | −0.535369 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.65248 | − | 5.08580i | −0.0582060 | − | 0.179140i | ||||
\(807\) | 1.80902 | − | 5.56758i | 0.0636804 | − | 0.195988i | ||||
\(808\) | −1.01722 | − | 0.739054i | −0.0357857 | − | 0.0259998i | ||||
\(809\) | −36.6697 | − | 26.6421i | −1.28924 | − | 0.936686i | −0.289448 | − | 0.957194i | \(-0.593472\pi\) |
−0.999790 | + | 0.0205075i | \(0.993472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7016 | − | 32.9362i | −0.375785 | − | 1.15655i | −0.942948 | − | 0.332941i | \(-0.891959\pi\) |
0.567163 | − | 0.823606i | \(-0.308041\pi\) | |||||||
\(812\) | 5.85410 | − | 4.25325i | 0.205439 | − | 0.149260i | ||||
\(813\) | −20.6180 | −0.723106 | ||||||||
\(814\) | −1.42705 | − | 15.2497i | −0.0500181 | − | 0.534500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 2.17963i | 0.105021 | − | 0.0763022i | ||||
\(817\) | −3.22949 | − | 9.93935i | −0.112986 | − | 0.347734i | ||||
\(818\) | 6.93363 | − | 21.3395i | 0.242429 | − | 0.746119i | ||||
\(819\) | −0.763932 | − | 0.555029i | −0.0266939 | − | 0.0193943i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3435 | − | 41.0669i | 0.465690 | − | 1.43325i | −0.392423 | − | 0.919785i | \(-0.628363\pi\) |
0.858113 | − | 0.513461i | \(-0.171637\pi\) | |||||||
\(822\) | −3.57295 | − | 10.9964i | −0.124621 | − | 0.383544i | ||||
\(823\) | −20.6074 | + | 14.9721i | −0.718328 | + | 0.521896i | −0.885850 | − | 0.463972i | \(-0.846424\pi\) |
0.167521 | + | 0.985868i | \(0.446424\pi\) | |||||||
\(824\) | −5.32624 | −0.185548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.16718 | 0.110200 | ||||||||
\(827\) | 19.8885 | − | 14.4499i | 0.691592 | − | 0.502471i | −0.185591 | − | 0.982627i | \(-0.559420\pi\) |
0.877183 | + | 0.480156i | \(0.159420\pi\) | |||||||
\(828\) | −1.19098 | − | 3.66547i | −0.0413895 | − | 0.127384i | ||||
\(829\) | 0.892609 | − | 2.74717i | 0.0310016 | − | 0.0954131i | −0.934358 | − | 0.356335i | \(-0.884026\pi\) |
0.965360 | + | 0.260921i | \(0.0840264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.00000 | − | 5.08580i | −0.242827 | − | 0.176424i | ||||
\(832\) | 0.0901699 | − | 0.277515i | 0.00312608 | − | 0.00962109i | ||||
\(833\) | −3.96556 | − | 12.2047i | −0.137398 | − | 0.422869i | ||||
\(834\) | 10.5902 | − | 7.69421i | 0.366708 | − | 0.266429i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.1803 | − | 5.87785i | −0.905466 | − | 0.203290i | ||||
\(837\) | −7.00000 | −0.241955 | ||||||||
\(838\) | −12.2984 | + | 8.93529i | −0.424840 | + | 0.308665i | ||||
\(839\) | −8.12868 | − | 25.0175i | −0.280633 | − | 0.863700i | −0.987674 | − | 0.156527i | \(-0.949970\pi\) |
0.707041 | − | 0.707173i | \(-0.250030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.26393 | − | 3.09793i | −0.147032 | − | 0.106825i | ||||
\(842\) | −1.42705 | − | 1.03681i | −0.0491794 | − | 0.0357309i | ||||
\(843\) | −3.11803 | + | 9.59632i | −0.107391 | + | 0.330515i | ||||
\(844\) | 1.92705 | + | 5.93085i | 0.0663318 | + | 0.204148i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.14590 | 0.108158 | ||||||||
\(847\) | −5.76393 | + | 6.11488i | −0.198051 | + | 0.210110i | ||||
\(848\) | −14.1246 | −0.485041 | ||||||||
\(849\) | 10.5451 | − | 7.66145i | 0.361906 | − | 0.262940i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.50000 | + | 16.9273i | −0.188538 | + | 0.580259i | ||||
\(852\) | 10.4721 | + | 7.60845i | 0.358769 | + | 0.260661i | ||||
\(853\) | 17.2812 | + | 12.5555i | 0.591695 | + | 0.429892i | 0.842922 | − | 0.538037i | \(-0.180834\pi\) |
−0.251226 | + | 0.967928i | \(0.580834\pi\) | |||||||
\(854\) | −1.02129 | + | 3.14320i | −0.0349477 | + | 0.107558i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.16312 | − | 3.75123i | 0.176472 | − | 0.128214i | ||||
\(857\) | 35.0132 | 1.19603 | 0.598013 | − | 0.801486i | \(-0.295957\pi\) | ||||
0.598013 | + | 0.801486i | \(0.295957\pi\) | |||||||
\(858\) | 2.47214 | + | 0.555029i | 0.0843973 | + | 0.0189484i | ||||
\(859\) | −5.72949 | −0.195488 | −0.0977438 | − | 0.995212i | \(-0.531163\pi\) | ||||
−0.0977438 | + | 0.995212i | \(0.531163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.596748 | + | 1.83660i | 0.0203371 | + | 0.0625912i | ||||
\(862\) | 3.79837 | − | 11.6902i | 0.129373 | − | 0.398170i | ||||
\(863\) | 4.88197 | + | 3.54696i | 0.166184 | + | 0.120740i | 0.667769 | − | 0.744369i | \(-0.267249\pi\) |
−0.501585 | + | 0.865108i | \(0.667249\pi\) | |||||||
\(864\) | 4.54508 | + | 3.30220i | 0.154627 | + | 0.112343i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.35410 | + | 16.4782i | 0.181940 | + | 0.559953i | ||||
\(867\) | −10.5172 | + | 7.64121i | −0.357184 | + | 0.259509i | ||||
\(868\) | 8.65248 | 0.293684 | ||||||||
\(869\) | 24.6353 | − | 10.6331i | 0.835694 | − | 0.360704i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38197 | + | 6.81640i | −0.317896 | + | 0.230965i | ||||
\(872\) | −2.86475 | − | 8.81678i | −0.0970125 | − | 0.298574i | ||||
\(873\) | 3.54508 | − | 10.9106i | 0.119983 | − | 0.369270i | ||||
\(874\) | −5.95492 | − | 4.32650i | −0.201428 | − | 0.146346i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.73607 | + | 20.7315i | −0.227591 | + | 0.700452i | ||||
\(877\) | 5.09017 | + | 15.6659i | 0.171883 | + | 0.529001i | 0.999477 | − | 0.0323254i | \(-0.0102913\pi\) |
−0.827595 | + | 0.561326i | \(0.810291\pi\) | |||||||
\(878\) | −4.83688 | + | 3.51420i | −0.163237 | + | 0.118598i | ||||
\(879\) | −16.5279 | −0.557471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.8541 | −0.803665 | −0.401833 | − | 0.915713i | \(-0.631627\pi\) | ||||
−0.401833 | + | 0.915713i | \(0.631627\pi\) | |||||||
\(882\) | 3.20820 | − | 2.33090i | 0.108026 | − | 0.0784854i | ||||
\(883\) | 5.79837 | + | 17.8456i | 0.195131 | + | 0.600551i | 0.999975 | + | 0.00706479i | \(0.00224881\pi\) |
−0.804844 | + | 0.593486i | \(0.797751\pi\) | |||||||
\(884\) | 1.23607 | − | 3.80423i | 0.0415735 | − | 0.127950i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.6353 | − | 9.18005i | −0.424490 | − | 0.308410i | ||||
\(887\) | 16.6353 | − | 51.1981i | 0.558557 | − | 1.71906i | −0.127802 | − | 0.991800i | \(-0.540792\pi\) |
0.686359 | − | 0.727263i | \(-0.259208\pi\) | |||||||
\(888\) | −5.16312 | − | 15.8904i | −0.173263 | − | 0.533248i | ||||
\(889\) | 9.85410 | − | 7.15942i | 0.330496 | − | 0.240119i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.69098 | − | 2.85317i | 0.0566501 | − | 0.0955848i | ||||
\(892\) | −13.0000 | −0.435272 | ||||||||
\(893\) | −20.5902 | + | 14.9596i | −0.689024 | + | 0.500605i | ||||
\(894\) | −3.84346 | − | 11.8290i | −0.128544 | − | 0.395619i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.03444 | − | 5.11082i | −0.235004 | − | 0.170741i | ||||
\(897\) | −2.38197 | − | 1.73060i | −0.0795315 | − | 0.0577830i | ||||
\(898\) | −0.139320 | + | 0.428784i | −0.00464918 | + | 0.0143087i | ||||
\(899\) | −12.6631 | − | 38.9731i | −0.422339 | − | 1.29982i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.2361 | −0.507587 | ||||||||
\(902\) | −3.42299 | − | 3.88998i | −0.113973 | − | 0.129522i | ||||
\(903\) | −1.59675 | −0.0531364 | ||||||||
\(904\) | 9.89919 | − | 7.19218i | 0.329242 | − | 0.239208i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.05573 | − | 6.32688i | 0.0682970 | − | 0.210197i | ||||
\(907\) | −7.37132 | − | 5.35558i | −0.244761 | − | 0.177829i | 0.458641 | − | 0.888622i | \(-0.348336\pi\) |
−0.703402 | + | 0.710793i | \(0.748336\pi\) | |||||||
\(908\) | 33.9615 | + | 24.6745i | 1.12705 | + | 0.818851i | ||||
\(909\) | −0.173762 | + | 0.534785i | −0.00576332 | + | 0.0177377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6525 | − | 34.6216i | 1.57880 | − | 1.14706i | 0.660740 | − | 0.750615i | \(-0.270243\pi\) |
0.918057 | − | 0.396448i | \(-0.129757\pi\) | |||||||
\(912\) | −9.27051 | −0.306977 | ||||||||
\(913\) | 12.5066 | + | 14.2128i | 0.413907 | + | 0.470377i | ||||
\(914\) | 0.909830 | 0.0300945 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.04508 | − | 27.8379i | −0.298858 | − | 0.919790i | ||||
\(917\) | −3.11146 | + | 9.57608i | −0.102749 | + | 0.316230i | ||||
\(918\) | 1.00000 | + | 0.726543i | 0.0330049 | + | 0.0239795i | ||||
\(919\) | 14.3713 | + | 10.4414i | 0.474066 | + | 0.344429i | 0.799024 | − | 0.601299i | \(-0.205350\pi\) |
−0.324958 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.74671 | − | 11.5312i | −0.123458 | − | 0.379966i | ||||
\(922\) | −12.9721 | + | 9.42481i | −0.427215 | + | 0.310390i | ||||
\(923\) | 9.88854 | 0.325485 | ||||||||
\(924\) | −2.09017 | + | 3.52671i | −0.0687615 | + | 0.116020i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.6353 | − | 12.0862i | 0.546668 | − | 0.397178i | ||||
\(927\) | 0.736068 | + | 2.26538i | 0.0241756 | + | 0.0744050i | ||||
\(928\) | −10.1631 | + | 31.2789i | −0.333621 | + | 1.02678i | ||||
\(929\) | 3.35410 | + | 2.43690i | 0.110045 | + | 0.0799520i | 0.641447 | − | 0.767168i | \(-0.278335\pi\) |
−0.531402 | + | 0.847120i | \(0.678335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.91390 | + | 30.5118i | −0.324915 | + | 0.999985i | ||||
\(932\) | 11.6353 | + | 35.8096i | 0.381125 | + | 1.17298i | ||||
\(933\) | 17.3713 | − | 12.6210i | 0.568712 | − | 0.413193i | ||||
\(934\) | 3.02129 | 0.0988595 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.76393 | 0.0903419 | ||||||||
\(937\) | −33.8156 | + | 24.5685i | −1.10471 | + | 0.802617i | −0.981822 | − | 0.189804i | \(-0.939215\pi\) |
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(938\) | 1.36881 | + | 4.21277i | 0.0446932 | + | 0.137552i | ||||
\(939\) | −0.145898 | + | 0.449028i | −0.00476120 | + | 0.0146535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | − | 2.17963i | −0.0977972 | − | 0.0710538i | 0.537812 | − | 0.843065i | \(-0.319251\pi\) |
−0.635609 | + | 0.772011i | \(0.719251\pi\) | |||||||
\(942\) | 0.635255 | − | 1.95511i | 0.0206977 | − | 0.0637010i | ||||
\(943\) | 1.86068 | + | 5.72658i | 0.0605921 | + | 0.186483i | ||||
\(944\) | 10.0623 | − | 7.31069i | 0.327500 | − | 0.237943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.93363 | − | 1.69784i | 0.127893 | − | 0.0552017i | ||||
\(947\) | −15.5623 | −0.505707 | −0.252853 | − | 0.967505i | \(-0.581369\pi\) | ||||
−0.252853 | + | 0.967505i | \(0.581369\pi\) | |||||||
\(948\) | 10.5902 | − | 7.69421i | 0.343953 | − | 0.249896i | ||||
\(949\) | 5.14590 | + | 15.8374i | 0.167043 | + | 0.514105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.6074 | + | 17.8783i | 0.797949 | + | 0.579744i | ||||
\(952\) | −2.76393 | − | 2.00811i | −0.0895796 | − | 0.0650834i | ||||
\(953\) | 11.7148 | − | 36.0544i | 0.379479 | − | 1.16792i | −0.560928 | − | 0.827865i | \(-0.689555\pi\) |
0.940407 | − | 0.340052i | \(-0.110445\pi\) | |||||||
\(954\) | −1.45492 | − | 4.47777i | −0.0471046 | − | 0.144973i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.3820 | 0.368119 | ||||||||
\(957\) | 18.9443 | + | 4.25325i | 0.612381 | + | 0.137488i | ||||
\(958\) | 20.6525 | 0.667251 | ||||||||
\(959\) | 11.5623 | − | 8.40051i | 0.373366 | − | 0.271267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.56231 | − | 17.1190i | 0.179429 | − | 0.552226i | ||||
\(962\) | −4.61803 | − | 3.35520i | −0.148891 | − | 0.108176i | ||||
\(963\) | −2.30902 | − | 1.67760i | −0.0744070 | − | 0.0540599i | ||||
\(964\) | 0.809017 | − | 2.48990i | 0.0260567 | − | 0.0801942i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.909830 | + | 0.661030i | −0.0292733 | + | 0.0212683i | ||||
\(967\) | −48.3262 | −1.55407 | −0.777034 | − | 0.629459i | \(-0.783276\pi\) | ||||
−0.777034 | + | 0.629459i | \(0.783276\pi\) | |||||||
\(968\) | 3.12868 | − | 24.3970i | 0.100559 | − | 0.784148i | ||||
\(969\) | −10.0000 | −0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.9828 | + | 33.8015i | 0.352454 | + | 1.08474i | 0.957471 | + | 0.288530i | \(0.0931664\pi\) |
−0.605017 | + | 0.796213i | \(0.706834\pi\) | |||||||
\(972\) | 0.500000 | − | 1.53884i | 0.0160375 | − | 0.0493584i | ||||
\(973\) | 13.0902 | + | 9.51057i | 0.419652 | + | 0.304895i | ||||
\(974\) | 7.09017 | + | 5.15131i | 0.227184 | + | 0.165059i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.01064 | + | 12.3435i | 0.128378 | + | 0.395105i | ||||
\(977\) | 28.2426 | − | 20.5195i | 0.903562 | − | 0.656476i | −0.0358162 | − | 0.999358i | \(-0.511403\pi\) |
0.939378 | + | 0.342882i | \(0.111403\pi\) | |||||||
\(978\) | −8.38197 | −0.268026 | ||||||||
\(979\) | 35.1246 | + | 7.88597i | 1.12259 | + | 0.252037i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.35410 | + | 2.43690i | −0.107088 | + | 0.0778042i | ||||
\(982\) | 6.07295 | + | 18.6906i | 0.193796 | + | 0.596441i | ||||
\(983\) | −5.87132 | + | 18.0701i | −0.187266 | + | 0.576346i | −0.999980 | − | 0.00631707i | \(-0.997989\pi\) |
0.812714 | + | 0.582663i | \(0.197989\pi\) | |||||||
\(984\) | −4.57295 | − | 3.32244i | −0.145780 | − | 0.105916i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.23607 | + | 6.88191i | −0.0712109 | + | 0.219165i | ||||
\(987\) | 1.20163 | + | 3.69822i | 0.0382482 | + | 0.117716i | ||||
\(988\) | −8.09017 | + | 5.87785i | −0.257383 | + | 0.186999i | ||||
\(989\) | −4.97871 | −0.158314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −31.8156 | + | 23.1154i | −1.01015 | + | 0.733914i | ||||
\(993\) | −6.67376 | − | 20.5397i | −0.211785 | − | 0.651809i | ||||
\(994\) | 1.16718 | − | 3.59222i | 0.0370208 | − | 0.113938i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.47214 | + | 5.42882i | 0.236764 | + | 0.172019i | ||||
\(997\) | −7.63525 | + | 23.4989i | −0.241811 | + | 0.744218i | 0.754334 | + | 0.656491i | \(0.227960\pi\) |
−0.996145 | + | 0.0877264i | \(0.972040\pi\) | |||||||
\(998\) | −2.13525 | − | 6.57164i | −0.0675903 | − | 0.208022i | ||||
\(999\) | −6.04508 | + | 4.39201i | −0.191258 | + | 0.138957i |
(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 | 825.2.n.b.751.1 | yes | 4 | |
5.2 | odd | 4 | 825.2.bx.c.124.1 | 8 | |||
5.3 | odd | 4 | 825.2.bx.c.124.2 | 8 | |||
5.4 | even | 2 | 825.2.n.d.751.1 | yes | 4 | ||
11.2 | odd | 10 | 9075.2.a.bt.1.1 | 2 | |||
11.4 | even | 5 | inner | 825.2.n.b.301.1 | ✓ | 4 | |
11.9 | even | 5 | 9075.2.a.z.1.2 | 2 | |||
55.4 | even | 10 | 825.2.n.d.301.1 | yes | 4 | ||
55.9 | even | 10 | 9075.2.a.by.1.1 | 2 | |||
55.24 | odd | 10 | 9075.2.a.bc.1.2 | 2 | |||
55.37 | odd | 20 | 825.2.bx.c.499.2 | 8 | |||
55.48 | odd | 20 | 825.2.bx.c.499.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.301.1 | ✓ | 4 | 11.4 | even | 5 | inner | |
825.2.n.b.751.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.n.d.301.1 | yes | 4 | 55.4 | even | 10 | ||
825.2.n.d.751.1 | yes | 4 | 5.4 | even | 2 | ||
825.2.bx.c.124.1 | 8 | 5.2 | odd | 4 | |||
825.2.bx.c.124.2 | 8 | 5.3 | odd | 4 | |||
825.2.bx.c.499.1 | 8 | 55.48 | odd | 20 | |||
825.2.bx.c.499.2 | 8 | 55.37 | odd | 20 | |||
9075.2.a.z.1.2 | 2 | 11.9 | even | 5 | |||
9075.2.a.bc.1.2 | 2 | 55.24 | odd | 10 | |||
9075.2.a.bt.1.1 | 2 | 11.2 | odd | 10 | |||
9075.2.a.by.1.1 | 2 | 55.9 | even | 10 |