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.d.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 | −0.396805 | − | 0.917903i | \(-0.629881\pi\) |
0.750358 | + | 0.661031i | \(0.229881\pi\) | |||||||
\(3\) | 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 | −0.896480 | − | 0.443083i | \(-0.853885\pi\) |
0.985706 | + | 0.168476i | \(0.0538846\pi\) | |||||||
\(8\) | 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 | −0.717761 | − | 0.696290i | \(-0.754833\pi\) |
0.440411 | + | 0.897796i | \(0.354833\pi\) | |||||||
\(14\) | −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 | 0.766451 | − | 0.642303i | \(-0.222021\pi\) |
−0.374020 | + | 0.927421i | \(0.622021\pi\) | |||||||
\(18\) | −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 | \(-0.579884\pi\) | ||||
−0.248337 | + | 0.968674i | \(0.579884\pi\) | |||||||
\(24\) | −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 | \(-0.689476\pi\) |
0.940322 | − | 0.340285i | \(-0.110524\pi\) | |||||||
\(38\) | 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 | \(-0.449052\pi\) | ||||
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(44\) | −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 | \(-0.978933\pi\) |
0.768372 | − | 0.640003i | \(-0.221067\pi\) | |||||||
\(48\) | 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 | −0.924198 | − | 0.381914i | \(-0.875265\pi\) |
0.0776285 | + | 0.996982i | \(0.475265\pi\) | |||||||
\(54\) | −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 | \(-0.305743\pi\) | ||||
0.573095 | + | 0.819489i | \(0.305743\pi\) | |||||||
\(68\) | −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 | \(-0.610911\pi\) |
0.828686 | − | 0.559713i | \(-0.189089\pi\) | |||||||
\(74\) | −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 | 0.304749 | − | 0.952433i | \(-0.401427\pi\) |
−0.811644 | + | 0.584152i | \(0.801427\pi\) | |||||||
\(84\) | −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 | −0.00662888 | − | 0.999978i | \(-0.502110\pi\) |
0.948987 | + | 0.315315i | \(0.102110\pi\) | |||||||
\(98\) | 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 | −0.980749 | − | 0.195274i | \(-0.937440\pi\) |
0.908222 | + | 0.418489i | \(0.137440\pi\) | |||||||
\(104\) | −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 | 0.899331 | − | 0.437268i | \(-0.144054\pi\) |
−0.984594 | + | 0.174856i | \(0.944054\pi\) | |||||||
\(108\) | 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 | 0.839477 | − | 0.543396i | \(-0.182862\pi\) |
−0.998551 | + | 0.0538155i | \(0.982862\pi\) | |||||||
\(114\) | −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 | 0.987756 | − | 0.156007i | \(-0.0498623\pi\) |
0.156862 | + | 0.987621i | \(0.449862\pi\) | |||||||
\(128\) | 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 | 0.999863 | − | 0.0165558i | \(-0.00527011\pi\) |
0.293229 | + | 0.956042i | \(0.405270\pi\) | |||||||
\(138\) | −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 | 0.983658 | − | 0.180048i | \(-0.0576253\pi\) |
−0.901625 | + | 0.432518i | \(0.857625\pi\) | |||||||
\(158\) | 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 | −0.0683187 | − | 0.997664i | \(-0.521763\pi\) |
0.927723 | + | 0.373270i | \(0.121763\pi\) | |||||||
\(164\) | −4.09017 | −0.319389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.52786 | −0.273815 | ||||||||
\(167\) | −16.2082 | + | 11.7759i | −1.25423 | + | 0.911250i | −0.998459 | − | 0.0554876i | \(-0.982329\pi\) |
−0.255769 | + | 0.966738i | \(0.582329\pi\) | |||||||
\(168\) | 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 | 0.900449 | − | 0.434961i | \(-0.143238\pi\) |
−0.984142 | + | 0.177380i | \(0.943238\pi\) | |||||||
\(174\) | −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 | −0.228427 | − | 0.973561i | \(-0.573358\pi\) |
−0.996499 | + | 0.0836000i | \(0.973358\pi\) | |||||||
\(194\) | 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 | \(-0.669297\pi\) | ||||
−0.507139 | + | 0.861864i | \(0.669297\pi\) | |||||||
\(198\) | −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 | 0.832868 | − | 0.553472i | \(-0.186697\pi\) |
−0.999127 | + | 0.0417790i | \(0.986697\pi\) | |||||||
\(224\) | −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 | \(0.430156\pi\) |
−0.749788 | + | 0.661679i | \(0.769844\pi\) | |||||||
\(228\) | −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 | −0.997137 | − | 0.0756220i | \(-0.975906\pi\) |
−0.236211 | + | 0.971702i | \(0.575906\pi\) | |||||||
\(234\) | −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 | \(-0.793144\pi\) |
0.999768 | − | 0.0215381i | \(-0.00685632\pi\) | |||||||
\(258\) | 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 | \(-0.183101\pi\) | ||||
0.839068 | + | 0.544027i | \(0.183101\pi\) | |||||||
\(264\) | −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 | −0.777875 | − | 0.628419i | \(-0.783702\pi\) |
0.357286 | + | 0.933995i | \(0.383702\pi\) | |||||||
\(278\) | −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 | \(-0.973370\pi\) |
0.757071 | − | 0.653333i | \(-0.226630\pi\) | |||||||
\(284\) | −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 | \(0.260374\pi\) |
−0.982066 | + | 0.188537i | \(0.939626\pi\) | |||||||
\(294\) | 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 | \(-0.612458\pi\) | ||||
−0.345994 | + | 0.938237i | \(0.612458\pi\) | |||||||
\(308\) | 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 | 0.598528 | − | 0.801102i | \(-0.295753\pi\) |
−0.576938 | + | 0.816788i | \(0.695753\pi\) | |||||||
\(314\) | 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 | \(-0.374061\pi\) |
0.996682 | − | 0.0813997i | \(-0.0259390\pi\) | |||||||
\(318\) | −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 | \(-0.693899\pi\) |
0.944960 | − | 0.327187i | \(-0.106101\pi\) | |||||||
\(338\) | 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 | 0.706945 | − | 0.707269i | \(-0.250073\pi\) |
−0.454195 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(348\) | 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 | \(-0.0973521\pi\) | ||||
0.953594 | + | 0.301095i | \(0.0973521\pi\) | |||||||
\(354\) | −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 | \(-0.743154\pi\) |
0.984095 | − | 0.177641i | \(-0.0568465\pi\) | |||||||
\(368\) | 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 | \(-0.581163\pi\) | ||||
−0.252228 | + | 0.967668i | \(0.581163\pi\) | |||||||
\(374\) | 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 | −0.999914 | − | 0.0131328i | \(-0.995820\pi\) |
−0.296500 | + | 0.955033i | \(0.595820\pi\) | |||||||
\(384\) | 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 | \(-0.864059\pi\) | ||||
−0.910182 | + | 0.414208i | \(0.864059\pi\) | |||||||
\(398\) | 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 | \(0.335264\pi\) |
−0.911062 | + | 0.412269i | \(0.864736\pi\) | |||||||
\(434\) | 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 | \(-0.895040\pi\) |
0.575109 | − | 0.818077i | \(-0.304960\pi\) | |||||||
\(444\) | −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 | 0.615293 | − | 0.788299i | \(-0.289038\pi\) |
−0.559581 | + | 0.828776i | \(0.689038\pi\) | |||||||
\(458\) | −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 | \(-0.218702\pi\) | ||||
0.773106 | + | 0.634277i | \(0.218702\pi\) | |||||||
\(464\) | 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 | 0.675519 | − | 0.737342i | \(-0.263920\pi\) |
−0.492507 | + | 0.870308i | \(0.663920\pi\) | |||||||
\(468\) | 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 | \(0.00411517\pi\) |
−0.801351 | + | 0.598195i | \(0.795885\pi\) | |||||||
\(488\) | 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 | \(0.0622665\pi\) |
−0.679339 | + | 0.733824i | \(0.737734\pi\) | |||||||
\(504\) | −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 | 0.723856 | − | 0.689951i | \(-0.242368\pi\) |
−0.432498 | + | 0.901635i | \(0.642368\pi\) | |||||||
\(524\) | −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 | \(0.0823980\pi\) |
−0.631601 | + | 0.775293i | \(0.717602\pi\) | |||||||
\(548\) | −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 | \(0.331623\pi\) |
−0.915718 | + | 0.401821i | \(0.868377\pi\) | |||||||
\(558\) | −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 | 0.241077 | − | 0.970506i | \(-0.422500\pi\) |
0.997503 | + | 0.0706255i | \(0.0224995\pi\) | |||||||
\(564\) | 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 | \(-0.892829\pi\) |
−0.605861 | − | 0.795571i | \(-0.707171\pi\) | |||||||
\(578\) | −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 | \(-0.769014\pi\) |
0.995266 | − | 0.0971926i | \(-0.0309863\pi\) | |||||||
\(588\) | −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 | \(-0.794362\pi\) | ||||
−0.798481 | + | 0.602021i | \(0.794362\pi\) | |||||||
\(594\) | −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 | −0.978311 | − | 0.207143i | \(-0.933583\pi\) |
−0.105310 | + | 0.994439i | \(0.533583\pi\) | |||||||
\(608\) | −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 | 0.886412 | − | 0.462898i | \(-0.153190\pi\) |
−0.989207 | + | 0.146527i | \(0.953190\pi\) | |||||||
\(614\) | −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 | \(-0.220292\pi\) | ||||
0.769928 | + | 0.638131i | \(0.220292\pi\) | |||||||
\(618\) | −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 | 0.0117276 | − | 0.999931i | \(-0.496267\pi\) |
−0.947367 | + | 0.320149i | \(0.896267\pi\) | |||||||
\(644\) | −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 | −0.831341 | − | 0.555763i | \(-0.812426\pi\) |
0.271663 | + | 0.962392i | \(0.412426\pi\) | |||||||
\(648\) | 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 | \(0.251647\pi\) |
−0.986866 | + | 0.161542i | \(0.948353\pi\) | |||||||
\(654\) | 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 | −0.0740494 | − | 0.997255i | \(-0.523592\pi\) |
0.925563 | + | 0.378594i | \(0.123592\pi\) | |||||||
\(674\) | −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 | 0.386401 | − | 0.922331i | \(-0.373718\pi\) |
−0.757785 | + | 0.652505i | \(0.773718\pi\) | |||||||
\(678\) | 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 | \(-0.486039\pi\) | ||||
0.0438466 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(684\) | 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 | \(-0.743348\pi\) | ||||
−0.692177 | + | 0.721728i | \(0.743348\pi\) | |||||||
\(728\) | −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 | −0.961080 | − | 0.276270i | \(-0.910902\pi\) |
0.939918 | + | 0.341401i | \(0.110902\pi\) | |||||||
\(734\) | −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 | 0.592931 | − | 0.805254i | \(-0.297971\pi\) |
−0.582616 | + | 0.812748i | \(0.697971\pi\) | |||||||
\(744\) | 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 | −0.883497 | − | 0.468436i | \(-0.844818\pi\) |
0.172493 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(758\) | 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 | 0.992313 | − | 0.123751i | \(-0.0394923\pi\) |
−0.875537 | + | 0.483151i | \(0.839492\pi\) | |||||||
\(774\) | −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 | 0.463211 | − | 0.886248i | \(-0.346697\pi\) |
−0.699732 | + | 0.714405i | \(0.746697\pi\) | |||||||
\(788\) | 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 | 0.917481 | − | 0.397780i | \(-0.130219\pi\) |
−0.0947941 | + | 0.995497i | \(0.530219\pi\) | |||||||
\(798\) | 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 | −0.167521 | − | 0.985868i | \(-0.553576\pi\) |
0.885850 | + | 0.463972i | \(0.153576\pi\) | |||||||
\(824\) | −5.32624 | −0.185548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.16718 | 0.110200 | ||||||||
\(827\) | −19.8885 | + | 14.4499i | −0.691592 | + | 0.502471i | −0.877183 | − | 0.480156i | \(-0.840580\pi\) |
0.185591 | + | 0.982627i | \(0.440580\pi\) | |||||||
\(828\) | 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 | 0.251226 | − | 0.967928i | \(-0.419166\pi\) |
−0.842922 | + | 0.538037i | \(0.819166\pi\) | |||||||
\(854\) | −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 | \(-0.704043\pi\) | ||||
−0.598013 | + | 0.801486i | \(0.704043\pi\) | |||||||
\(858\) | −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 | 0.501585 | − | 0.865108i | \(-0.332751\pi\) |
−0.667769 | + | 0.744369i | \(0.732751\pi\) | |||||||
\(864\) | 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 | 0.827595 | − | 0.561326i | \(-0.189709\pi\) |
−0.999477 | + | 0.0323254i | \(0.989709\pi\) | |||||||
\(878\) | 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 | \(-0.997751\pi\) |
0.804844 | − | 0.593486i | \(-0.202249\pi\) | |||||||
\(884\) | 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 | \(0.459208\pi\) |
−0.686359 | + | 0.727263i | \(0.740792\pi\) | |||||||
\(888\) | 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 | 0.703402 | − | 0.710793i | \(-0.251664\pi\) |
−0.458641 | + | 0.888622i | \(0.651664\pi\) | |||||||
\(908\) | −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 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) |
0.981822 | + | 0.189804i | \(0.0607853\pi\) | |||||||
\(938\) | −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 | \(-0.418631\pi\) | ||||
0.252853 | + | 0.967505i | \(0.418631\pi\) | |||||||
\(948\) | −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 | \(0.310445\pi\) |
−0.940407 | + | 0.340052i | \(0.889555\pi\) | |||||||
\(954\) | −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 | \(-0.216724\pi\) | ||||
0.777034 | + | 0.629459i | \(0.216724\pi\) | |||||||
\(968\) | −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 | −0.939378 | − | 0.342882i | \(-0.888597\pi\) |
0.0358162 | + | 0.999358i | \(0.488597\pi\) | |||||||
\(978\) | 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 | −0.812714 | − | 0.582663i | \(-0.802011\pi\) |
0.999980 | + | 0.00631707i | \(0.00201080\pi\) | |||||||
\(984\) | −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 | \(-0.772040\pi\) |
0.996145 | − | 0.0877264i | \(-0.0279601\pi\) | |||||||
\(998\) | 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.d.751.1 | yes | 4 | |
5.2 | odd | 4 | 825.2.bx.c.124.2 | 8 | |||
5.3 | odd | 4 | 825.2.bx.c.124.1 | 8 | |||
5.4 | even | 2 | 825.2.n.b.751.1 | yes | 4 | ||
11.2 | odd | 10 | 9075.2.a.bc.1.2 | 2 | |||
11.4 | even | 5 | inner | 825.2.n.d.301.1 | yes | 4 | |
11.9 | even | 5 | 9075.2.a.by.1.1 | 2 | |||
55.4 | even | 10 | 825.2.n.b.301.1 | ✓ | 4 | ||
55.9 | even | 10 | 9075.2.a.z.1.2 | 2 | |||
55.24 | odd | 10 | 9075.2.a.bt.1.1 | 2 | |||
55.37 | odd | 20 | 825.2.bx.c.499.1 | 8 | |||
55.48 | odd | 20 | 825.2.bx.c.499.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.301.1 | ✓ | 4 | 55.4 | even | 10 | ||
825.2.n.b.751.1 | yes | 4 | 5.4 | even | 2 | ||
825.2.n.d.301.1 | yes | 4 | 11.4 | even | 5 | inner | |
825.2.n.d.751.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.bx.c.124.1 | 8 | 5.3 | odd | 4 | |||
825.2.bx.c.124.2 | 8 | 5.2 | odd | 4 | |||
825.2.bx.c.499.1 | 8 | 55.37 | odd | 20 | |||
825.2.bx.c.499.2 | 8 | 55.48 | odd | 20 | |||
9075.2.a.z.1.2 | 2 | 55.9 | even | 10 | |||
9075.2.a.bc.1.2 | 2 | 11.2 | odd | 10 | |||
9075.2.a.bt.1.1 | 2 | 55.24 | odd | 10 | |||
9075.2.a.by.1.1 | 2 | 11.9 | even | 5 |