Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
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, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not 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: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.499 |
Dual form | 825.2.bx.c.124.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.363271 | + | 0.500000i | −0.256872 | + | 0.353553i | −0.917903 | − | 0.396805i | \(-0.870119\pi\) |
0.661031 | + | 0.750358i | \(0.270119\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | 0.500000 | + | 1.53884i | 0.250000 | + | 0.769421i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 0.363271i | 0.204124 | − | 0.148305i | ||||
\(7\) | −0.726543 | + | 0.236068i | −0.274607 | + | 0.0892253i | −0.443083 | − | 0.896480i | \(-0.646115\pi\) |
0.168476 | + | 0.985706i | \(0.446115\pi\) | |||||||
\(8\) | −2.12663 | − | 0.690983i | −0.751876 | − | 0.244299i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | − | 0.726543i | 0.975711 | − | 0.219061i | ||||
\(12\) | − | 1.61803i | − | 0.467086i | ||||||
\(13\) | −0.726543 | + | 1.00000i | −0.201507 | + | 0.277350i | −0.897796 | − | 0.440411i | \(-0.854833\pi\) |
0.696290 | + | 0.717761i | \(0.254833\pi\) | |||||||
\(14\) | 0.145898 | − | 0.449028i | 0.0389929 | − | 0.120008i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 1.08981i | −0.375000 | + | 0.272453i | ||||
\(17\) | 1.17557 | + | 1.61803i | 0.285118 | + | 0.392431i | 0.927421 | − | 0.374020i | \(-0.122021\pi\) |
−0.642303 | + | 0.766451i | \(0.722021\pi\) | |||||||
\(18\) | −0.587785 | + | 0.190983i | −0.138542 | + | 0.0450151i | ||||
\(19\) | −1.54508 | + | 4.75528i | −0.354467 | + | 1.09094i | 0.601851 | + | 0.798608i | \(0.294430\pi\) |
−0.956318 | + | 0.292328i | \(0.905570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.763932 | 0.166704 | ||||||||
\(22\) | −0.812299 | + | 1.88197i | −0.173183 | + | 0.401237i | ||||
\(23\) | 2.38197i | 0.496674i | 0.968674 | + | 0.248337i | \(0.0798841\pi\) | ||||
−0.968674 | + | 0.248337i | \(0.920116\pi\) | |||||||
\(24\) | 1.80902 | + | 1.31433i | 0.369264 | + | 0.268286i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.236068 | − | 0.726543i | −0.0462967 | − | 0.142487i | ||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | −0.726543 | − | 1.00000i | −0.137304 | − | 0.188982i | ||||
\(29\) | 1.80902 | + | 5.56758i | 0.335926 | + | 1.03387i | 0.966264 | + | 0.257553i | \(0.0829163\pi\) |
−0.630338 | + | 0.776321i | \(0.717084\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.66312 | − | 4.11450i | −1.01713 | − | 0.738985i | −0.0514344 | − | 0.998676i | \(-0.516379\pi\) |
−0.965692 | + | 0.259691i | \(0.916379\pi\) | |||||||
\(32\) | − | 5.61803i | − | 0.993137i | ||||||
\(33\) | −3.30220 | − | 0.309017i | −0.574839 | − | 0.0537930i | ||||
\(34\) | −1.23607 | −0.211984 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 1.53884i | −0.0833333 | + | 0.256474i | ||||
\(37\) | −7.10642 | + | 2.30902i | −1.16829 | + | 0.379600i | −0.828004 | − | 0.560722i | \(-0.810524\pi\) |
−0.340285 | + | 0.940322i | \(0.610524\pi\) | |||||||
\(38\) | −1.81636 | − | 2.50000i | −0.294652 | − | 0.405554i | ||||
\(39\) | 1.00000 | − | 0.726543i | 0.160128 | − | 0.116340i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.781153 | − | 2.40414i | 0.121996 | − | 0.375464i | −0.871346 | − | 0.490669i | \(-0.836752\pi\) |
0.993342 | + | 0.115205i | \(0.0367525\pi\) | |||||||
\(42\) | −0.277515 | + | 0.381966i | −0.0428214 | + | 0.0589386i | ||||
\(43\) | − | 2.09017i | − | 0.318748i | −0.987218 | − | 0.159374i | \(-0.949052\pi\) | ||
0.987218 | − | 0.159374i | \(-0.0509476\pi\) | |||||||
\(44\) | 2.73607 | + | 4.61653i | 0.412478 | + | 0.695967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.19098 | − | 0.865300i | −0.175601 | − | 0.127581i | ||||
\(47\) | −4.84104 | − | 1.57295i | −0.706138 | − | 0.229438i | −0.0661352 | − | 0.997811i | \(-0.521067\pi\) |
−0.640003 | + | 0.768372i | \(0.721067\pi\) | |||||||
\(48\) | 1.76336 | − | 0.572949i | 0.254518 | − | 0.0826981i | ||||
\(49\) | −5.19098 | + | 3.77147i | −0.741569 | + | 0.538781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.618034 | − | 1.90211i | −0.0865421 | − | 0.266349i | ||||
\(52\) | −1.90211 | − | 0.618034i | −0.263776 | − | 0.0857059i | ||||
\(53\) | −4.47777 | + | 6.16312i | −0.615069 | + | 0.846569i | −0.996982 | − | 0.0776285i | \(-0.975265\pi\) |
0.381914 | + | 0.924198i | \(0.375265\pi\) | |||||||
\(54\) | 0.618034 | 0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.70820 | 0.228268 | ||||||||
\(57\) | 2.93893 | − | 4.04508i | 0.389270 | − | 0.535785i | ||||
\(58\) | −3.44095 | − | 1.11803i | −0.451820 | − | 0.146805i | ||||
\(59\) | 2.07295 | + | 6.37988i | 0.269875 | + | 0.830590i | 0.990530 | + | 0.137296i | \(0.0438412\pi\) |
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.66312 | + | 4.11450i | −0.725088 | + | 0.526807i | −0.888006 | − | 0.459832i | \(-0.847910\pi\) |
0.162918 | + | 0.986640i | \(0.447910\pi\) | |||||||
\(62\) | 4.11450 | − | 1.33688i | 0.522542 | − | 0.169784i | ||||
\(63\) | −0.726543 | − | 0.236068i | −0.0915358 | − | 0.0297418i | ||||
\(64\) | −0.190983 | − | 0.138757i | −0.0238729 | − | 0.0173447i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.35410 | − | 1.53884i | 0.166678 | − | 0.189418i | ||||
\(67\) | 9.38197i | 1.14619i | 0.819489 | + | 0.573095i | \(0.194257\pi\) | ||||
−0.819489 | + | 0.573095i | \(0.805743\pi\) | |||||||
\(68\) | −1.90211 | + | 2.61803i | −0.230665 | + | 0.317483i | ||||
\(69\) | 0.736068 | − | 2.26538i | 0.0886122 | − | 0.272720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47214 | − | 4.70228i | 0.768101 | − | 0.558058i | −0.133283 | − | 0.991078i | \(-0.542552\pi\) |
0.901384 | + | 0.433020i | \(0.142552\pi\) | |||||||
\(72\) | −1.31433 | − | 1.80902i | −0.154895 | − | 0.213195i | ||||
\(73\) | 12.8128 | − | 4.16312i | 1.49962 | − | 0.487256i | 0.559713 | − | 0.828686i | \(-0.310911\pi\) |
0.939907 | + | 0.341430i | \(0.110911\pi\) | |||||||
\(74\) | 1.42705 | − | 4.39201i | 0.165891 | − | 0.510561i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.09017 | −0.928006 | ||||||||
\(77\) | −2.17963 | + | 1.29180i | −0.248392 | + | 0.147214i | ||||
\(78\) | 0.763932i | 0.0864983i | ||||||||
\(79\) | −6.54508 | − | 4.75528i | −0.736380 | − | 0.535011i | 0.155196 | − | 0.987884i | \(-0.450399\pi\) |
−0.891575 | + | 0.452873i | \(0.850399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0.918300 | + | 1.26393i | 0.101409 | + | 0.139578i | ||||
\(83\) | 3.35520 | + | 4.61803i | 0.368281 | + | 0.506895i | 0.952433 | − | 0.304749i | \(-0.0985727\pi\) |
−0.584152 | + | 0.811644i | \(0.698573\pi\) | |||||||
\(84\) | 0.381966 | + | 1.17557i | 0.0416759 | + | 0.128265i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.04508 | + | 0.759299i | 0.112694 | + | 0.0818773i | ||||
\(87\) | − | 5.85410i | − | 0.627626i | ||||||
\(88\) | −7.38394 | − | 0.690983i | −0.787130 | − | 0.0736590i | ||||
\(89\) | −10.8541 | −1.15053 | −0.575266 | − | 0.817966i | \(-0.695102\pi\) | ||||
−0.575266 | + | 0.817966i | \(0.695102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.291796 | − | 0.898056i | 0.0305885 | − | 0.0941418i | ||||
\(92\) | −3.66547 | + | 1.19098i | −0.382152 | + | 0.124169i | ||||
\(93\) | 4.11450 | + | 5.66312i | 0.426653 | + | 0.587238i | ||||
\(94\) | 2.54508 | − | 1.84911i | 0.262505 | − | 0.190721i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.73607 | + | 5.34307i | −0.177187 | + | 0.545325i | ||||
\(97\) | −6.74315 | + | 9.28115i | −0.684663 | + | 0.942358i | −0.999978 | − | 0.00662888i | \(-0.997890\pi\) |
0.315315 | + | 0.948987i | \(0.397890\pi\) | |||||||
\(98\) | − | 3.96556i | − | 0.400582i | ||||||
\(99\) | 3.04508 | + | 1.31433i | 0.306043 | + | 0.132095i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.454915 | + | 0.330515i | 0.0452657 | + | 0.0328875i | 0.610188 | − | 0.792257i | \(-0.291094\pi\) |
−0.564922 | + | 0.825144i | \(0.691094\pi\) | |||||||
\(102\) | 1.17557 | + | 0.381966i | 0.116399 | + | 0.0378203i | ||||
\(103\) | −2.26538 | + | 0.736068i | −0.223215 | + | 0.0725269i | −0.418489 | − | 0.908222i | \(-0.637440\pi\) |
0.195274 | + | 0.980749i | \(0.437440\pi\) | |||||||
\(104\) | 2.23607 | − | 1.62460i | 0.219265 | − | 0.159305i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.45492 | − | 4.47777i | −0.141314 | − | 0.434919i | ||||
\(107\) | −2.71441 | − | 0.881966i | −0.262412 | − | 0.0852629i | 0.174856 | − | 0.984594i | \(-0.444054\pi\) |
−0.437268 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(108\) | 0.951057 | − | 1.30902i | 0.0915155 | − | 0.125960i | ||||
\(109\) | −4.14590 | −0.397105 | −0.198553 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198553 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.47214 | 0.709224 | ||||||||
\(112\) | 0.832544 | − | 1.14590i | 0.0786680 | − | 0.108277i | ||||
\(113\) | 5.20431 | + | 1.69098i | 0.489580 | + | 0.159074i | 0.543396 | − | 0.839477i | \(-0.317138\pi\) |
−0.0538155 | + | 0.998551i | \(0.517138\pi\) | |||||||
\(114\) | 0.954915 | + | 2.93893i | 0.0894360 | + | 0.275256i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.66312 | + | 5.56758i | −0.711503 | + | 0.516937i | ||||
\(117\) | −1.17557 | + | 0.381966i | −0.108682 | + | 0.0353128i | ||||
\(118\) | −3.94298 | − | 1.28115i | −0.362981 | − | 0.117940i | ||||
\(119\) | −1.23607 | − | 0.898056i | −0.113310 | − | 0.0823247i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | − | 4.70228i | 0.904025 | − | 0.427480i | ||||
\(122\) | − | 4.32624i | − | 0.391679i | ||||||
\(123\) | −1.48584 | + | 2.04508i | −0.133974 | + | 0.184399i | ||||
\(124\) | 3.50000 | − | 10.7719i | 0.314309 | − | 0.967344i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | − | 0.277515i | 0.0340282 | − | 0.0247230i | ||||
\(127\) | 9.37181 | + | 12.8992i | 0.831613 | + | 1.14462i | 0.987621 | + | 0.156862i | \(0.0501377\pi\) |
−0.156007 | + | 0.987756i | \(0.549862\pi\) | |||||||
\(128\) | 10.8249 | − | 3.51722i | 0.956794 | − | 0.310881i | ||||
\(129\) | −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 | \(0.304696\pi\) | |||||||
\(132\) | −1.17557 | − | 5.23607i | −0.102320 | − | 0.455741i | ||||
\(133\) | − | 3.81966i | − | 0.331207i | ||||||
\(134\) | −4.69098 | − | 3.40820i | −0.405239 | − | 0.294424i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.38197 | − | 4.25325i | −0.118503 | − | 0.364714i | ||||
\(137\) | 10.9964 | + | 15.1353i | 0.939486 | + | 1.29309i | 0.956042 | + | 0.293229i | \(0.0947299\pi\) |
−0.0165558 | + | 0.999863i | \(0.505270\pi\) | |||||||
\(138\) | 0.865300 | + | 1.19098i | 0.0736592 | + | 0.101383i | ||||
\(139\) | −6.54508 | − | 20.1437i | −0.555147 | − | 1.70857i | −0.695555 | − | 0.718473i | \(-0.744842\pi\) |
0.140408 | − | 0.990094i | \(-0.455158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.11803 | + | 2.99193i | 0.346801 | + | 0.251966i | ||||
\(142\) | 4.94427i | 0.414914i | ||||||||
\(143\) | −1.62460 | + | 3.76393i | −0.135856 | + | 0.314756i | ||||
\(144\) | −1.85410 | −0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.57295 | + | 7.91872i | −0.212939 | + | 0.655358i | ||||
\(147\) | 6.10237 | − | 1.98278i | 0.503315 | − | 0.163537i | ||||
\(148\) | −7.10642 | − | 9.78115i | −0.584144 | − | 0.804006i | ||||
\(149\) | 16.2812 | − | 11.8290i | 1.33380 | − | 0.969065i | 0.334156 | − | 0.942518i | \(-0.391549\pi\) |
0.999648 | − | 0.0265477i | \(-0.00845140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.32624 | + | 10.2371i | −0.270685 | + | 0.833084i | 0.719643 | + | 0.694344i | \(0.244305\pi\) |
−0.990329 | + | 0.138740i | \(0.955695\pi\) | |||||||
\(152\) | 6.57164 | − | 9.04508i | 0.533030 | − | 0.733653i | ||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0.145898 | − | 1.55909i | 0.0117568 | − | 0.125635i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.61803 | + | 1.17557i | 0.129546 | + | 0.0941210i | ||||
\(157\) | 3.16344 | + | 1.02786i | 0.252470 | + | 0.0820325i | 0.432518 | − | 0.901625i | \(-0.357625\pi\) |
−0.180048 | + | 0.983658i | \(0.557625\pi\) | |||||||
\(158\) | 4.75528 | − | 1.54508i | 0.378310 | − | 0.122920i | ||||
\(159\) | 6.16312 | − | 4.47777i | 0.488767 | − | 0.355110i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.562306 | − | 1.73060i | −0.0443159 | − | 0.136390i | ||||
\(162\) | −0.587785 | − | 0.190983i | −0.0461808 | − | 0.0150050i | ||||
\(163\) | 7.97172 | − | 10.9721i | 0.624394 | − | 0.859404i | −0.373270 | − | 0.927723i | \(-0.621763\pi\) |
0.997664 | + | 0.0683187i | \(0.0217635\pi\) | |||||||
\(164\) | 4.09017 | 0.319389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.52786 | −0.273815 | ||||||||
\(167\) | 11.7759 | − | 16.2082i | 0.911250 | − | 1.25423i | −0.0554876 | − | 0.998459i | \(-0.517671\pi\) |
0.966738 | − | 0.255769i | \(-0.0823287\pi\) | |||||||
\(168\) | −1.62460 | − | 0.527864i | −0.125340 | − | 0.0407256i | ||||
\(169\) | 3.54508 | + | 10.9106i | 0.272699 | + | 0.839281i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.04508 | + | 2.93893i | −0.309335 | + | 0.224745i | ||||
\(172\) | 3.21644 | − | 1.04508i | 0.245251 | − | 0.0796870i | ||||
\(173\) | 3.38795 | + | 1.10081i | 0.257581 | + | 0.0836933i | 0.434961 | − | 0.900449i | \(-0.356762\pi\) |
−0.177380 | + | 0.984142i | \(0.556762\pi\) | |||||||
\(174\) | 2.92705 | + | 2.12663i | 0.221899 | + | 0.161219i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.06231 | + | 4.61653i | −0.306208 | + | 0.347984i | ||||
\(177\) | − | 6.70820i | − | 0.504219i | ||||||
\(178\) | 3.94298 | − | 5.42705i | 0.295539 | − | 0.406775i | ||||
\(179\) | 6.01722 | − | 18.5191i | 0.449748 | − | 1.38418i | −0.427443 | − | 0.904042i | \(-0.640586\pi\) |
0.877192 | − | 0.480141i | \(-0.159414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.23607 | − | 3.07768i | 0.314864 | − | 0.228762i | −0.419117 | − | 0.907932i | \(-0.637660\pi\) |
0.733981 | + | 0.679170i | \(0.237660\pi\) | |||||||
\(182\) | 0.343027 | + | 0.472136i | 0.0254268 | + | 0.0349970i | ||||
\(183\) | 6.65740 | − | 2.16312i | 0.492129 | − | 0.159902i | ||||
\(184\) | 1.64590 | − | 5.06555i | 0.121337 | − | 0.373438i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.32624 | −0.317215 | ||||||||
\(187\) | 4.97980 | + | 4.38197i | 0.364159 | + | 0.320441i | ||||
\(188\) | − | 8.23607i | − | 0.600677i | ||||||
\(189\) | 0.618034 | + | 0.449028i | 0.0449554 | + | 0.0326620i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.21885 | + | 9.90659i | 0.232908 | + | 0.716816i | 0.997392 | + | 0.0721737i | \(0.0229936\pi\) |
−0.764484 | + | 0.644642i | \(0.777006\pi\) | |||||||
\(192\) | 0.138757 | + | 0.190983i | 0.0100139 | + | 0.0137830i | ||||
\(193\) | 12.3637 | + | 17.0172i | 0.889961 | + | 1.22493i | 0.973561 | + | 0.228427i | \(0.0733582\pi\) |
−0.0836000 | + | 0.996499i | \(0.526642\pi\) | |||||||
\(194\) | −2.19098 | − | 6.74315i | −0.157303 | − | 0.484130i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.39919 | − | 6.10237i | −0.599942 | − | 0.435883i | ||||
\(197\) | − | 14.2361i | − | 1.01428i | −0.861864 | − | 0.507139i | \(-0.830703\pi\) | ||
0.861864 | − | 0.507139i | \(-0.169297\pi\) | |||||||
\(198\) | −1.76336 | + | 1.04508i | −0.125316 | + | 0.0742710i | ||||
\(199\) | −19.7984 | −1.40347 | −0.701735 | − | 0.712438i | \(-0.747591\pi\) | ||||
−0.701735 | + | 0.712438i | \(0.747591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.89919 | − | 8.92278i | 0.204493 | − | 0.629364i | ||||
\(202\) | −0.330515 | + | 0.107391i | −0.0232550 | + | 0.00755600i | ||||
\(203\) | −2.62866 | − | 3.61803i | −0.184495 | − | 0.253936i | ||||
\(204\) | 2.61803 | − | 1.90211i | 0.183299 | − | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.454915 | − | 1.40008i | 0.0316954 | − | 0.0975485i | ||||
\(207\) | −1.40008 | + | 1.92705i | −0.0973126 | + | 0.133939i | ||||
\(208\) | − | 2.29180i | − | 0.158907i | ||||||
\(209\) | −1.54508 | + | 16.5110i | −0.106876 | + | 1.14209i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.11803 | + | 2.26538i | 0.214654 | + | 0.155955i | 0.689917 | − | 0.723888i | \(-0.257647\pi\) |
−0.475263 | + | 0.879844i | \(0.657647\pi\) | |||||||
\(212\) | −11.7229 | − | 3.80902i | −0.805135 | − | 0.261604i | ||||
\(213\) | −7.60845 | + | 2.47214i | −0.521323 | + | 0.169388i | ||||
\(214\) | 1.42705 | − | 1.03681i | 0.0975512 | − | 0.0708751i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.690983 | + | 2.12663i | 0.0470154 | + | 0.144699i | ||||
\(217\) | 5.08580 | + | 1.65248i | 0.345246 | + | 0.112177i | ||||
\(218\) | 1.50609 | − | 2.07295i | 0.102005 | − | 0.140398i | ||||
\(219\) | −13.4721 | −0.910363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | −2.71441 | + | 3.73607i | −0.182179 | + | 0.250748i | ||||
\(223\) | 7.64121 | + | 2.48278i | 0.511693 | + | 0.166259i | 0.553472 | − | 0.832868i | \(-0.313303\pi\) |
−0.0417790 | + | 0.999127i | \(0.513303\pi\) | |||||||
\(224\) | 1.32624 | + | 4.08174i | 0.0886130 | + | 0.272723i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.73607 | + | 1.98787i | −0.182001 | + | 0.132231i | ||||
\(227\) | 24.6745 | − | 8.01722i | 1.63770 | − | 0.532122i | 0.661679 | − | 0.749788i | \(-0.269844\pi\) |
0.976023 | + | 0.217666i | \(0.0698443\pi\) | |||||||
\(228\) | 7.69421 | + | 2.50000i | 0.509561 | + | 0.165567i | ||||
\(229\) | 14.6353 | + | 10.6331i | 0.967125 | + | 0.702657i | 0.954795 | − | 0.297267i | \(-0.0960750\pi\) |
0.0123304 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.47214 | − | 0.555029i | 0.162655 | − | 0.0365182i | ||||
\(232\) | − | 13.0902i | − | 0.859412i | ||||||
\(233\) | −13.6781 | + | 18.8262i | −0.896080 | + | 1.23335i | 0.0756220 | + | 0.997137i | \(0.475906\pi\) |
−0.971702 | + | 0.236211i | \(0.924094\pi\) | |||||||
\(234\) | 0.236068 | − | 0.726543i | 0.0154322 | − | 0.0474956i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.78115 | + | 6.37988i | −0.571604 | + | 0.415295i | ||||
\(237\) | 4.75528 | + | 6.54508i | 0.308889 | + | 0.425149i | ||||
\(238\) | 0.898056 | − | 0.291796i | 0.0582123 | − | 0.0189143i | ||||
\(239\) | 2.17376 | − | 6.69015i | 0.140609 | − | 0.432750i | −0.855811 | − | 0.517288i | \(-0.826942\pi\) |
0.996420 | + | 0.0845383i | \(0.0269415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.61803 | −0.104227 | −0.0521134 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521134 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(242\) | −1.26133 | + | 6.68034i | −0.0810812 | + | 0.429429i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −9.16312 | − | 6.65740i | −0.586609 | − | 0.426196i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.482779 | − | 1.48584i | −0.0307809 | − | 0.0947338i | ||||
\(247\) | −3.63271 | − | 5.00000i | −0.231144 | − | 0.318142i | ||||
\(248\) | 9.20029 | + | 12.6631i | 0.584219 | + | 0.804109i | ||||
\(249\) | −1.76393 | − | 5.42882i | −0.111785 | − | 0.344038i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.09017 | − | 4.42477i | −0.384408 | − | 0.279289i | 0.378752 | − | 0.925498i | \(-0.376353\pi\) |
−0.763160 | + | 0.646209i | \(0.776353\pi\) | |||||||
\(252\) | − | 1.23607i | − | 0.0778650i | ||||||
\(253\) | 1.73060 | + | 7.70820i | 0.108802 | + | 0.484611i | ||||
\(254\) | −9.85410 | −0.618301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.02786 | + | 6.24112i | −0.126742 | + | 0.390070i | ||||
\(257\) | −10.0453 | + | 3.26393i | −0.626612 | + | 0.203598i | −0.605074 | − | 0.796170i | \(-0.706856\pi\) |
−0.0215381 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(258\) | −0.759299 | − | 1.04508i | −0.0472719 | − | 0.0650641i | ||||
\(259\) | 4.61803 | − | 3.35520i | 0.286951 | − | 0.208482i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.80902 | + | 5.56758i | −0.111975 | + | 0.344625i | ||||
\(262\) | −4.78804 | + | 6.59017i | −0.295806 | + | 0.407142i | ||||
\(263\) | − | 27.2148i | − | 1.67814i | −0.544027 | − | 0.839068i | \(-0.683101\pi\) | ||
0.544027 | − | 0.839068i | \(-0.316899\pi\) | |||||||
\(264\) | 6.80902 | + | 2.93893i | 0.419066 | + | 0.180878i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.90983 | + | 1.38757i | 0.117099 | + | 0.0850775i | ||||
\(267\) | 10.3229 | + | 3.35410i | 0.631749 | + | 0.205268i | ||||
\(268\) | −14.4374 | + | 4.69098i | −0.881902 | + | 0.286547i | ||||
\(269\) | −4.73607 | + | 3.44095i | −0.288763 | + | 0.209799i | −0.722731 | − | 0.691130i | \(-0.757113\pi\) |
0.433967 | + | 0.900929i | \(0.357113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.37132 | + | 19.6089i | 0.387030 | + | 1.19116i | 0.934997 | + | 0.354656i | \(0.115402\pi\) |
−0.547966 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(272\) | −3.52671 | − | 1.14590i | −0.213838 | − | 0.0694803i | ||||
\(273\) | −0.555029 | + | 0.763932i | −0.0335919 | + | 0.0462353i | ||||
\(274\) | −11.5623 | −0.698504 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.85410 | 0.231990 | ||||||||
\(277\) | 5.08580 | − | 7.00000i | 0.305576 | − | 0.420589i | −0.628419 | − | 0.777875i | \(-0.716298\pi\) |
0.933995 | + | 0.357286i | \(0.116298\pi\) | |||||||
\(278\) | 12.4495 | + | 4.04508i | 0.746671 | + | 0.242608i | ||||
\(279\) | −2.16312 | − | 6.65740i | −0.129503 | − | 0.398568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.16312 | + | 5.93085i | −0.486971 | + | 0.353805i | −0.804018 | − | 0.594605i | \(-0.797309\pi\) |
0.317047 | + | 0.948410i | \(0.397309\pi\) | |||||||
\(282\) | −2.99193 | + | 0.972136i | −0.178167 | + | 0.0578899i | ||||
\(283\) | 12.3965 | + | 4.02786i | 0.736895 | + | 0.239432i | 0.653333 | − | 0.757071i | \(-0.273370\pi\) |
0.0835622 | + | 0.996503i | \(0.473370\pi\) | |||||||
\(284\) | 10.4721 | + | 7.60845i | 0.621407 | + | 0.451479i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.29180 | − | 2.17963i | −0.0763855 | − | 0.128884i | ||||
\(287\) | 1.93112i | 0.113990i | ||||||||
\(288\) | 3.30220 | − | 4.54508i | 0.194584 | − | 0.267822i | ||||
\(289\) | 4.01722 | − | 12.3637i | 0.236307 | − | 0.727279i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.28115 | − | 6.74315i | 0.544071 | − | 0.395291i | ||||
\(292\) | 12.8128 | + | 17.6353i | 0.749810 | + | 1.03203i | ||||
\(293\) | −15.7189 | + | 5.10739i | −0.918310 | + | 0.298377i | −0.729773 | − | 0.683689i | \(-0.760374\pi\) |
−0.188537 | + | 0.982066i | \(0.560374\pi\) | |||||||
\(294\) | −1.22542 | + | 3.77147i | −0.0714682 | + | 0.219957i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.7082 | 0.971145 | ||||||||
\(297\) | −2.48990 | − | 2.19098i | −0.144479 | − | 0.127134i | ||||
\(298\) | 12.4377i | 0.720496i | ||||||||
\(299\) | −2.38197 | − | 1.73060i | −0.137753 | − | 0.100083i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.493422 | + | 1.51860i | 0.0284404 | + | 0.0875305i | ||||
\(302\) | −3.91023 | − | 5.38197i | −0.225008 | − | 0.309697i | ||||
\(303\) | −0.330515 | − | 0.454915i | −0.0189876 | − | 0.0261342i | ||||
\(304\) | −2.86475 | − | 8.81678i | −0.164304 | − | 0.505677i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | − | 0.726543i | −0.0571662 | − | 0.0415337i | ||||
\(307\) | − | 12.1246i | − | 0.691988i | −0.938237 | − | 0.345994i | \(-0.887542\pi\) | ||
0.938237 | − | 0.345994i | \(-0.112458\pi\) | |||||||
\(308\) | −3.07768 | − | 2.70820i | −0.175367 | − | 0.154314i | ||||
\(309\) | 2.38197 | 0.135505 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.63525 | − | 20.4212i | 0.376251 | − | 1.15798i | −0.566380 | − | 0.824144i | \(-0.691657\pi\) |
0.942631 | − | 0.333837i | \(-0.108343\pi\) | |||||||
\(312\) | −2.62866 | + | 0.854102i | −0.148818 | + | 0.0483540i | ||||
\(313\) | −0.277515 | − | 0.381966i | −0.0156860 | − | 0.0215900i | 0.801102 | − | 0.598528i | \(-0.204247\pi\) |
−0.816788 | + | 0.576938i | \(0.804247\pi\) | |||||||
\(314\) | −1.66312 | + | 1.20833i | −0.0938552 | + | 0.0681898i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04508 | − | 12.4495i | 0.227554 | − | 0.700339i | ||||
\(317\) | −17.8783 | + | 24.6074i | −1.00415 | + | 1.38209i | −0.0813997 | + | 0.996682i | \(0.525939\pi\) |
−0.922747 | + | 0.385407i | \(0.874061\pi\) | |||||||
\(318\) | 4.70820i | 0.264023i | ||||||||
\(319\) | 9.89919 | + | 16.7027i | 0.554248 | + | 0.935174i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.30902 | + | 1.67760i | 0.128877 | + | 0.0936344i | ||||
\(322\) | 1.06957 | + | 0.347524i | 0.0596048 | + | 0.0193668i | ||||
\(323\) | −9.51057 | + | 3.09017i | −0.529182 | + | 0.171942i | ||||
\(324\) | −1.30902 | + | 0.951057i | −0.0727232 | + | 0.0528365i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.59017 | + | 7.97172i | 0.143456 | + | 0.441513i | ||||
\(327\) | 3.94298 | + | 1.28115i | 0.218047 | + | 0.0708479i | ||||
\(328\) | −3.32244 | + | 4.57295i | −0.183451 | + | 0.252499i | ||||
\(329\) | 3.88854 | 0.214382 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5967 | 1.18706 | 0.593532 | − | 0.804810i | \(-0.297733\pi\) | ||||
0.593532 | + | 0.804810i | \(0.297733\pi\) | |||||||
\(332\) | −5.42882 | + | 7.47214i | −0.297945 | + | 0.410087i | ||||
\(333\) | −7.10642 | − | 2.30902i | −0.389430 | − | 0.126533i | ||||
\(334\) | 3.82624 | + | 11.7759i | 0.209362 | + | 0.644351i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14590 | + | 0.832544i | −0.0625139 | + | 0.0454190i | ||||
\(337\) | −21.0620 | + | 6.84346i | −1.14732 | + | 0.372787i | −0.820133 | − | 0.572173i | \(-0.806101\pi\) |
−0.327187 | + | 0.944960i | \(0.606101\pi\) | |||||||
\(338\) | −6.74315 | − | 2.19098i | −0.366779 | − | 0.119174i | ||||
\(339\) | −4.42705 | − | 3.21644i | −0.240444 | − | 0.174693i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.3156 | − | 9.20029i | −1.15430 | − | 0.498224i | ||||
\(342\) | − | 3.09017i | − | 0.167097i | ||||||
\(343\) | 6.02434 | − | 8.29180i | 0.325284 | − | 0.447715i | ||||
\(344\) | −1.44427 | + | 4.44501i | −0.0778699 | + | 0.239659i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.78115 | + | 1.29408i | −0.0957554 | + | 0.0695704i | ||||
\(347\) | 3.42071 | + | 4.70820i | 0.183633 | + | 0.252750i | 0.890902 | − | 0.454195i | \(-0.150073\pi\) |
−0.707269 | + | 0.706945i | \(0.750073\pi\) | |||||||
\(348\) | 9.00854 | − | 2.92705i | 0.482908 | − | 0.156906i | ||||
\(349\) | −8.57953 | + | 26.4051i | −0.459252 | + | 1.41343i | 0.406819 | + | 0.913509i | \(0.366638\pi\) |
−0.866070 | + | 0.499922i | \(0.833362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23607 | 0.0659764 | ||||||||
\(352\) | −4.08174 | − | 18.1803i | −0.217558 | − | 0.969015i | ||||
\(353\) | − | 35.8328i | − | 1.90719i | −0.301095 | − | 0.953594i | \(-0.597352\pi\) | ||
0.301095 | − | 0.953594i | \(-0.402648\pi\) | |||||||
\(354\) | 3.35410 | + | 2.43690i | 0.178269 | + | 0.129520i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.42705 | − | 16.7027i | −0.287633 | − | 0.885244i | ||||
\(357\) | 0.898056 | + | 1.23607i | 0.0475302 | + | 0.0654197i | ||||
\(358\) | 7.07367 | + | 9.73607i | 0.373855 | + | 0.514567i | ||||
\(359\) | −5.16312 | − | 15.8904i | −0.272499 | − | 0.838666i | −0.989870 | − | 0.141975i | \(-0.954655\pi\) |
0.717371 | − | 0.696691i | \(-0.245345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.85410 | − | 3.52671i | −0.255479 | − | 0.185616i | ||||
\(362\) | 3.23607i | 0.170084i | ||||||||
\(363\) | −10.9106 | + | 1.39919i | −0.572661 | + | 0.0734383i | ||||
\(364\) | 1.52786 | 0.0800818 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.33688 | + | 4.11450i | −0.0698799 | + | 0.215068i | ||||
\(367\) | −17.2375 | + | 5.60081i | −0.899792 | + | 0.292360i | −0.722151 | − | 0.691735i | \(-0.756846\pi\) |
−0.177641 | + | 0.984095i | \(0.556846\pi\) | |||||||
\(368\) | −2.59590 | − | 3.57295i | −0.135321 | − | 0.186253i | ||||
\(369\) | 2.04508 | − | 1.48584i | 0.106463 | − | 0.0773498i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79837 | − | 5.53483i | 0.0933669 | − | 0.287354i | ||||
\(372\) | −6.65740 | + | 9.16312i | −0.345170 | + | 0.475086i | ||||
\(373\) | 9.74265i | 0.504455i | 0.967668 | + | 0.252228i | \(0.0811631\pi\) | ||||
−0.967668 | + | 0.252228i | \(0.918837\pi\) | |||||||
\(374\) | −4.00000 | + | 0.898056i | −0.206835 | + | 0.0464374i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.20820 | + | 6.69015i | 0.474877 | + | 0.345018i | ||||
\(377\) | −6.88191 | − | 2.23607i | −0.354436 | − | 0.115163i | ||||
\(378\) | −0.449028 | + | 0.145898i | −0.0230955 | + | 0.00750419i | ||||
\(379\) | −4.04508 | + | 2.93893i | −0.207782 | + | 0.150963i | −0.686810 | − | 0.726837i | \(-0.740989\pi\) |
0.479028 | + | 0.877800i | \(0.340989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.92705 | − | 15.1639i | −0.252420 | − | 0.776870i | ||||
\(382\) | −6.12261 | − | 1.98936i | −0.313260 | − | 0.101784i | ||||
\(383\) | −18.4333 | + | 25.3713i | −0.941900 | + | 1.29641i | 0.0131328 | + | 0.999914i | \(0.495820\pi\) |
−0.955033 | + | 0.296500i | \(0.904180\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | 1.22857 | − | 1.69098i | 0.0624518 | − | 0.0859575i | ||||
\(388\) | −17.6538 | − | 5.73607i | −0.896236 | − | 0.291205i | ||||
\(389\) | 12.0344 | + | 37.0382i | 0.610170 | + | 1.87791i | 0.456316 | + | 0.889818i | \(0.349169\pi\) |
0.153855 | + | 0.988093i | \(0.450831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.85410 | + | 2.80017i | −0.194910 | + | 0.141611i | ||||
\(392\) | 13.6453 | − | 4.43363i | 0.689192 | − | 0.223932i | ||||
\(393\) | −12.5352 | − | 4.07295i | −0.632320 | − | 0.205453i | ||||
\(394\) | 7.11803 | + | 5.17155i | 0.358601 | + | 0.260539i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | + | 5.34307i | −0.0251259 | + | 0.268499i | ||||
\(397\) | − | 36.2705i | − | 1.82036i | −0.414208 | − | 0.910182i | \(-0.635941\pi\) | ||
0.414208 | − | 0.910182i | \(-0.364059\pi\) | |||||||
\(398\) | 7.19218 | − | 9.89919i | 0.360511 | − | 0.496201i | ||||
\(399\) | −1.18034 | + | 3.63271i | −0.0590909 | + | 0.181863i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.95492 | + | 2.87341i | −0.197499 | + | 0.143491i | −0.682140 | − | 0.731222i | \(-0.738950\pi\) |
0.484641 | + | 0.874713i | \(0.338950\pi\) | |||||||
\(402\) | 3.40820 | + | 4.69098i | 0.169985 | + | 0.233965i | ||||
\(403\) | 8.22899 | − | 2.67376i | 0.409915 | − | 0.133190i | ||||
\(404\) | −0.281153 | + | 0.865300i | −0.0139879 | + | 0.0430503i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.76393 | 0.137172 | ||||||||
\(407\) | −21.3193 | + | 12.6353i | −1.05676 | + | 0.626306i | ||||
\(408\) | 4.47214i | 0.221404i | ||||||||
\(409\) | 29.3713 | + | 21.3395i | 1.45232 | + | 1.05517i | 0.985283 | + | 0.170933i | \(0.0546781\pi\) |
0.467036 | + | 0.884238i | \(0.345322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.78115 | − | 17.7926i | −0.285163 | − | 0.877642i | ||||
\(412\) | −2.26538 | − | 3.11803i | −0.111607 | − | 0.153615i | ||||
\(413\) | −3.01217 | − | 4.14590i | −0.148219 | − | 0.204006i | ||||
\(414\) | −0.454915 | − | 1.40008i | −0.0223579 | − | 0.0688104i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.61803 | + | 4.08174i | 0.275447 | + | 0.200124i | ||||
\(417\) | 21.1803i | 1.03721i | ||||||||
\(418\) | −7.69421 | − | 6.77051i | −0.376336 | − | 0.331156i | ||||
\(419\) | −24.5967 | −1.20163 | −0.600815 | − | 0.799388i | \(-0.705157\pi\) | ||||
−0.600815 | + | 0.799388i | \(0.705157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.881966 | − | 2.71441i | 0.0429844 | − | 0.132292i | −0.927261 | − | 0.374415i | \(-0.877844\pi\) |
0.970246 | + | 0.242123i | \(0.0778436\pi\) | |||||||
\(422\) | −2.26538 | + | 0.736068i | −0.110277 | + | 0.0358312i | ||||
\(423\) | −2.99193 | − | 4.11803i | −0.145472 | − | 0.200226i | ||||
\(424\) | 13.7812 | − | 10.0126i | 0.669272 | − | 0.486255i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.52786 | − | 4.70228i | 0.0740253 | − | 0.227826i | ||||
\(427\) | 3.14320 | − | 4.32624i | 0.152110 | − | 0.209361i | ||||
\(428\) | − | 4.61803i | − | 0.223221i | ||||||
\(429\) | 2.70820 | − | 3.07768i | 0.130753 | − | 0.148592i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0902 | − | 11.6902i | −0.775036 | − | 0.563097i | 0.128449 | − | 0.991716i | \(-0.459000\pi\) |
−0.903485 | + | 0.428619i | \(0.859000\pi\) | |||||||
\(432\) | 1.76336 | + | 0.572949i | 0.0848395 | + | 0.0275660i | ||||
\(433\) | −26.6623 | + | 8.66312i | −1.28131 | + | 0.416323i | −0.869041 | − | 0.494739i | \(-0.835264\pi\) |
−0.412269 | + | 0.911062i | \(0.635264\pi\) | |||||||
\(434\) | −2.67376 | + | 1.94260i | −0.128345 | + | 0.0932479i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.07295 | − | 6.37988i | −0.0992763 | − | 0.305541i | ||||
\(437\) | −11.3269 | − | 3.68034i | −0.541840 | − | 0.176055i | ||||
\(438\) | 4.89404 | − | 6.73607i | 0.233846 | − | 0.321862i | ||||
\(439\) | −9.67376 | −0.461703 | −0.230852 | − | 0.972989i | \(-0.574151\pi\) | ||||
−0.230852 | + | 0.972989i | \(0.574151\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.41641 | −0.305543 | ||||||||
\(442\) | 0.898056 | − | 1.23607i | 0.0427162 | − | 0.0587938i | ||||
\(443\) | 24.0337 | + | 7.80902i | 1.14187 | + | 0.371018i | 0.818077 | − | 0.575109i | \(-0.195040\pi\) |
0.323798 | + | 0.946126i | \(0.395040\pi\) | |||||||
\(444\) | 3.73607 | + | 11.4984i | 0.177306 | + | 0.545692i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.01722 | + | 2.91868i | −0.190221 | + | 0.138204i | ||||
\(447\) | −19.1396 | + | 6.21885i | −0.905274 | + | 0.294141i | ||||
\(448\) | 0.171513 | + | 0.0557281i | 0.00810325 | + | 0.00263290i | ||||
\(449\) | −0.590170 | − | 0.428784i | −0.0278518 | − | 0.0202355i | 0.573772 | − | 0.819015i | \(-0.305479\pi\) |
−0.601624 | + | 0.798779i | \(0.705479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.781153 | − | 8.34751i | 0.0367831 | − | 0.393069i | ||||
\(452\) | 8.85410i | 0.416462i | ||||||||
\(453\) | 6.32688 | − | 8.70820i | 0.297263 | − | 0.409147i | ||||
\(454\) | −4.95492 | + | 15.2497i | −0.232546 | + | 0.715702i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.04508 | + | 6.57164i | −0.423575 | + | 0.307745i | ||||
\(457\) | 0.865300 | + | 1.19098i | 0.0404770 | + | 0.0557118i | 0.828776 | − | 0.559581i | \(-0.189038\pi\) |
−0.788299 | + | 0.615293i | \(0.789038\pi\) | |||||||
\(458\) | −10.6331 | + | 3.45492i | −0.496854 | + | 0.161438i | ||||
\(459\) | 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 | \(0.293504\pi\) | |||||||
\(462\) | −0.620541 | + | 1.43769i | −0.0288702 | + | 0.0668876i | ||||
\(463\) | − | 33.2705i | − | 1.54621i | −0.634277 | − | 0.773106i | \(-0.718702\pi\) | ||
0.634277 | − | 0.773106i | \(-0.281298\pi\) | |||||||
\(464\) | −8.78115 | − | 6.37988i | −0.407655 | − | 0.296179i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.44427 | − | 13.6781i | −0.205877 | − | 0.633624i | ||||
\(467\) | 2.87341 | + | 3.95492i | 0.132966 | + | 0.183012i | 0.870308 | − | 0.492507i | \(-0.163920\pi\) |
−0.737342 | + | 0.675519i | \(0.763920\pi\) | |||||||
\(468\) | −1.17557 | − | 1.61803i | −0.0543408 | − | 0.0747936i | ||||
\(469\) | −2.21478 | − | 6.81640i | −0.102269 | − | 0.314752i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.69098 | − | 1.95511i | −0.123994 | − | 0.0900869i | ||||
\(472\) | − | 15.0000i | − | 0.690431i | ||||||
\(473\) | −1.51860 | − | 6.76393i | −0.0698252 | − | 0.311006i | ||||
\(474\) | −5.00000 | −0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.763932 | − | 2.35114i | 0.0350148 | − | 0.107764i | ||||
\(477\) | −7.24518 | + | 2.35410i | −0.331734 | + | 0.107787i | ||||
\(478\) | 2.55541 | + | 3.51722i | 0.116882 | + | 0.160874i | ||||
\(479\) | 27.0344 | − | 19.6417i | 1.23524 | − | 0.897451i | 0.237964 | − | 0.971274i | \(-0.423520\pi\) |
0.997271 | + | 0.0738231i | \(0.0235200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.85410 | − | 8.78402i | 0.130136 | − | 0.400517i | ||||
\(482\) | 0.587785 | − | 0.809017i | 0.0267729 | − | 0.0368497i | ||||
\(483\) | 1.81966i | 0.0827974i | ||||||||
\(484\) | 12.2082 | + | 12.9515i | 0.554918 | + | 0.588705i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.363271i | 0.0226805 | + | 0.0164783i | ||||
\(487\) | 13.4863 | + | 4.38197i | 0.611123 | + | 0.198566i | 0.598195 | − | 0.801351i | \(-0.295885\pi\) |
0.0129278 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(488\) | 14.8864 | − | 4.83688i | 0.673875 | − | 0.218955i | ||||
\(489\) | −10.9721 | + | 7.97172i | −0.496177 | + | 0.360494i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.82624 | + | 30.2421i | 0.443452 | + | 1.36480i | 0.884173 | + | 0.467160i | \(0.154723\pi\) |
−0.440721 | + | 0.897644i | \(0.645277\pi\) | |||||||
\(492\) | −3.88998 | − | 1.26393i | −0.175374 | − | 0.0569825i | ||||
\(493\) | −6.88191 | + | 9.47214i | −0.309946 | + | 0.426604i | ||||
\(494\) | 3.81966 | 0.171855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.9787 | 0.582761 | ||||||||
\(497\) | −3.59222 | + | 4.94427i | −0.161133 | + | 0.221781i | ||||
\(498\) | 3.35520 | + | 1.09017i | 0.150350 | + | 0.0488517i | ||||
\(499\) | 3.45492 | + | 10.6331i | 0.154663 | + | 0.476005i | 0.998127 | − | 0.0611822i | \(-0.0194871\pi\) |
−0.843463 | + | 0.537187i | \(0.819487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.2082 | + | 11.7759i | −0.724129 | + | 0.526111i | ||||
\(502\) | 4.42477 | − | 1.43769i | 0.197487 | − | 0.0641674i | ||||
\(503\) | −20.8172 | − | 6.76393i | −0.928195 | − | 0.301589i | −0.194371 | − | 0.980928i | \(-0.562266\pi\) |
−0.733824 | + | 0.679339i | \(0.762266\pi\) | |||||||
\(504\) | 1.38197 | + | 1.00406i | 0.0615577 | + | 0.0447243i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.48278 | − | 1.93487i | −0.199284 | − | 0.0860154i | ||||
\(507\) | − | 11.4721i | − | 0.509495i | ||||||
\(508\) | −15.1639 | + | 20.8713i | −0.672789 | + | 0.926015i | ||||
\(509\) | −0.163119 | + | 0.502029i | −0.00723012 | + | 0.0222520i | −0.954606 | − | 0.297870i | \(-0.903724\pi\) |
0.947376 | + | 0.320122i | \(0.103724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.32624 | + | 6.04937i | −0.368331 | + | 0.267608i | ||||
\(512\) | 10.9964 | + | 15.1353i | 0.485977 | + | 0.668890i | ||||
\(513\) | 4.75528 | − | 1.54508i | 0.209951 | − | 0.0682172i | ||||
\(514\) | 2.01722 | − | 6.20837i | 0.0889758 | − | 0.273839i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.38197 | −0.148883 | ||||||||
\(517\) | −16.8087 | − | 1.57295i | −0.739248 | − | 0.0691782i | ||||
\(518\) | 3.52786i | 0.155005i | ||||||||
\(519\) | −2.88197 | − | 2.09387i | −0.126504 | − | 0.0919107i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.74671 | − | 14.6089i | −0.207957 | − | 0.640026i | −0.999579 | − | 0.0290150i | \(-0.990763\pi\) |
0.791622 | − | 0.611011i | \(-0.209237\pi\) | |||||||
\(522\) | −2.12663 | − | 2.92705i | −0.0930799 | − | 0.128114i | ||||
\(523\) | −4.84104 | − | 6.66312i | −0.211684 | − | 0.291358i | 0.689951 | − | 0.723856i | \(-0.257632\pi\) |
−0.901635 | + | 0.432498i | \(0.857632\pi\) | |||||||
\(524\) | 6.59017 | + | 20.2825i | 0.287893 | + | 0.886043i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.6074 | + | 9.88635i | 0.593310 | + | 0.431065i | ||||
\(527\) | − | 14.0000i | − | 0.609850i | ||||||
\(528\) | 5.29007 | − | 3.13525i | 0.230221 | − | 0.136444i | ||||
\(529\) | 17.3262 | 0.753315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.07295 | + | 6.37988i | −0.0899583 | + | 0.276863i | ||||
\(532\) | 5.87785 | − | 1.90983i | 0.254837 | − | 0.0828016i | ||||
\(533\) | 1.83660 | + | 2.52786i | 0.0795520 | + | 0.109494i | ||||
\(534\) | −5.42705 | + | 3.94298i | −0.234851 | + | 0.170630i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.48278 | − | 19.9519i | 0.280013 | − | 0.861793i | ||||
\(537\) | −11.4454 | + | 15.7533i | −0.493907 | + | 0.679805i | ||||
\(538\) | − | 3.61803i | − | 0.155985i | ||||||
\(539\) | −14.0582 | + | 15.9762i | −0.605531 | + | 0.688144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.500000 | − | 0.363271i | −0.0214967 | − | 0.0156183i | 0.576985 | − | 0.816755i | \(-0.304229\pi\) |
−0.598482 | + | 0.801136i | \(0.704229\pi\) | |||||||
\(542\) | −12.1190 | − | 3.93769i | −0.520555 | − | 0.169138i | ||||
\(543\) | −4.97980 | + | 1.61803i | −0.213704 | + | 0.0694365i | ||||
\(544\) | 9.09017 | − | 6.60440i | 0.389738 | − | 0.283161i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.180340 | − | 0.555029i | −0.00771783 | − | 0.0237531i | ||||
\(547\) | 24.1194 | + | 7.83688i | 1.03127 | + | 0.335081i | 0.775293 | − | 0.631601i | \(-0.217602\pi\) |
0.255979 | + | 0.966682i | \(0.417602\pi\) | |||||||
\(548\) | −17.7926 | + | 24.4894i | −0.760060 | + | 1.04613i | ||||
\(549\) | −7.00000 | −0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.2705 | −1.24697 | ||||||||
\(552\) | −3.13068 | + | 4.30902i | −0.133251 | + | 0.183404i | ||||
\(553\) | 5.87785 | + | 1.90983i | 0.249952 | + | 0.0812142i | ||||
\(554\) | 1.65248 | + | 5.08580i | 0.0702070 | + | 0.216075i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.7254 | − | 20.1437i | 1.17582 | − | 0.854283i | ||||
\(557\) | 29.8585 | − | 9.70163i | 1.26515 | − | 0.411071i | 0.401821 | − | 0.915718i | \(-0.368377\pi\) |
0.863326 | + | 0.504647i | \(0.168377\pi\) | |||||||
\(558\) | 4.11450 | + | 1.33688i | 0.174181 | + | 0.0565947i | ||||
\(559\) | 2.09017 | + | 1.51860i | 0.0884048 | + | 0.0642298i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.38197 | − | 5.70634i | −0.142787 | − | 0.240922i | ||||
\(562\) | − | 6.23607i | − | 0.263053i | ||||||
\(563\) | 21.3520 | − | 29.3885i | 0.899881 | − | 1.23858i | −0.0706255 | − | 0.997503i | \(-0.522500\pi\) |
0.970506 | − | 0.241077i | \(-0.0775005\pi\) | |||||||
\(564\) | −2.54508 | + | 7.83297i | −0.107167 | + | 0.329827i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.51722 | + | 4.73504i | −0.273939 | + | 0.199028i | ||||
\(567\) | −0.449028 | − | 0.618034i | −0.0188574 | − | 0.0259550i | ||||
\(568\) | −17.0130 | + | 5.52786i | −0.713850 | + | 0.231944i | ||||
\(569\) | 0.753289 | − | 2.31838i | 0.0315795 | − | 0.0971917i | −0.934024 | − | 0.357209i | \(-0.883728\pi\) |
0.965604 | + | 0.260017i | \(0.0837283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0901699 | 0.00377349 | 0.00188675 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188675 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(572\) | −6.60440 | − | 0.618034i | −0.276144 | − | 0.0258413i | ||||
\(573\) | − | 10.4164i | − | 0.435152i | ||||||
\(574\) | −0.965558 | − | 0.701519i | −0.0403016 | − | 0.0292808i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0729490 | − | 0.224514i | −0.00303954 | − | 0.00935475i | ||||
\(577\) | −27.0459 | − | 37.2254i | −1.12593 | − | 1.54971i | −0.795571 | − | 0.605861i | \(-0.792829\pi\) |
−0.330363 | − | 0.943854i | \(-0.607171\pi\) | |||||||
\(578\) | 4.72253 | + | 6.50000i | 0.196431 | + | 0.270364i | ||||
\(579\) | −6.50000 | − | 20.0049i | −0.270131 | − | 0.831377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.52786 | − | 2.56314i | −0.146360 | − | 0.106337i | ||||
\(582\) | 7.09017i | 0.293897i | ||||||||
\(583\) | −10.0126 | + | 23.1976i | −0.414679 | + | 0.960745i | ||||
\(584\) | −30.1246 | −1.24657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.15654 | − | 9.71483i | 0.130396 | − | 0.401316i | ||||
\(587\) | −18.4333 | + | 5.98936i | −0.760826 | + | 0.247207i | −0.663633 | − | 0.748058i | \(-0.730986\pi\) |
−0.0971926 | + | 0.995266i | \(0.530986\pi\) | |||||||
\(588\) | 6.10237 | + | 8.39919i | 0.251657 | + | 0.346377i | ||||
\(589\) | 28.3156 | − | 20.5725i | 1.16672 | − | 0.847674i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.39919 | + | 13.5393i | −0.180958 | + | 0.556933i | ||||
\(592\) | 8.14324 | − | 11.2082i | 0.334685 | − | 0.460654i | ||||
\(593\) | 38.8885i | 1.59696i | 0.602021 | + | 0.798481i | \(0.294362\pi\) | ||||
−0.602021 | + | 0.798481i | \(0.705638\pi\) | |||||||
\(594\) | 2.00000 | − | 0.449028i | 0.0820610 | − | 0.0184238i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.3435 | + | 19.1396i | 1.07907 | + | 0.783990i | ||||
\(597\) | 18.8294 | + | 6.11803i | 0.770635 | + | 0.250394i | ||||
\(598\) | 1.73060 | − | 0.562306i | 0.0707695 | − | 0.0229944i | ||||
\(599\) | −17.9894 | + | 13.0700i | −0.735025 | + | 0.534027i | −0.891149 | − | 0.453710i | \(-0.850100\pi\) |
0.156124 | + | 0.987737i | \(0.450100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6180 | + | 32.6789i | 0.433119 | + | 1.33300i | 0.895002 | + | 0.446062i | \(0.147174\pi\) |
−0.461884 | + | 0.886941i | \(0.652826\pi\) | |||||||
\(602\) | −0.938545 | − | 0.304952i | −0.0382522 | − | 0.0124289i | ||||
\(603\) | −5.51458 | + | 7.59017i | −0.224571 | + | 0.309096i | ||||
\(604\) | −17.4164 | −0.708664 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.347524 | 0.0141172 | ||||||||
\(607\) | 19.3969 | − | 26.6976i | 0.787296 | − | 1.08362i | −0.207143 | − | 0.978311i | \(-0.566417\pi\) |
0.994439 | − | 0.105310i | \(-0.0335835\pi\) | |||||||
\(608\) | 26.7153 | + | 8.68034i | 1.08345 | + | 0.352034i | ||||
\(609\) | 1.38197 | + | 4.25325i | 0.0560001 | + | 0.172351i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.09017 | − | 3.69822i | 0.205926 | − | 0.149614i | ||||
\(612\) | −3.07768 | + | 1.00000i | −0.124408 | + | 0.0404226i | ||||
\(613\) | 7.83297 | + | 2.54508i | 0.316371 | + | 0.102795i | 0.462898 | − | 0.886412i | \(-0.346810\pi\) |
−0.146527 | + | 0.989207i | \(0.546810\pi\) | |||||||
\(614\) | 6.06231 | + | 4.40452i | 0.244655 | + | 0.177752i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.52786 | − | 1.24108i | 0.222724 | − | 0.0500047i | ||||
\(617\) | 38.2492i | 1.53986i | 0.638131 | + | 0.769928i | \(0.279708\pi\) | ||||
−0.638131 | + | 0.769928i | \(0.720292\pi\) | |||||||
\(618\) | −0.865300 | + | 1.19098i | −0.0348075 | + | 0.0479084i | ||||
\(619\) | −2.19756 | + | 6.76340i | −0.0883274 | + | 0.271844i | −0.985457 | − | 0.169923i | \(-0.945648\pi\) |
0.897130 | + | 0.441767i | \(0.145648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92705 | − | 1.40008i | 0.0773299 | − | 0.0561835i | ||||
\(622\) | 7.80021 | + | 10.7361i | 0.312760 | + | 0.430477i | ||||
\(623\) | 7.88597 | − | 2.56231i | 0.315945 | − | 0.102657i | ||||
\(624\) | −0.708204 | + | 2.17963i | −0.0283508 | + | 0.0872549i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.291796 | 0.0116625 | ||||||||
\(627\) | 6.57164 | − | 15.2254i | 0.262446 | − | 0.608045i | ||||
\(628\) | 5.38197i | 0.214764i | ||||||||
\(629\) | −12.0902 | − | 8.78402i | −0.482067 | − | 0.350242i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9377 | + | 36.7404i | 0.475232 | + | 1.46261i | 0.845644 | + | 0.533747i | \(0.179216\pi\) |
−0.370412 | + | 0.928867i | \(0.620784\pi\) | |||||||
\(632\) | 10.6331 | + | 14.6353i | 0.422963 | + | 0.582159i | ||||
\(633\) | −2.26538 | − | 3.11803i | −0.0900409 | − | 0.123931i | ||||
\(634\) | −5.80902 | − | 17.8783i | −0.230706 | − | 0.710039i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.97214 | + | 7.24518i | 0.395421 | + | 0.287290i | ||||
\(637\) | − | 7.93112i | − | 0.314242i | ||||||
\(638\) | −11.9475 | − | 1.11803i | −0.473005 | − | 0.0442634i | ||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0729490 | + | 0.224514i | −0.00288131 | + | 0.00886777i | −0.952487 | − | 0.304580i | \(-0.901484\pi\) |
0.949606 | + | 0.313448i | \(0.101484\pi\) | |||||||
\(642\) | −1.67760 | + | 0.545085i | −0.0662096 | + | 0.0215128i | ||||
\(643\) | 17.2375 | + | 23.7254i | 0.679782 | + | 0.935639i | 0.999931 | − | 0.0117276i | \(-0.00373311\pi\) |
−0.320149 | + | 0.947367i | \(0.603733\pi\) | |||||||
\(644\) | 2.38197 | − | 1.73060i | 0.0938626 | − | 0.0681952i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.90983 | − | 5.87785i | 0.0751413 | − | 0.231261i | ||||
\(647\) | 10.3431 | − | 14.2361i | 0.406630 | − | 0.559678i | −0.555763 | − | 0.831341i | \(-0.687574\pi\) |
0.962392 | + | 0.271663i | \(0.0875737\pi\) | |||||||
\(648\) | − | 2.23607i | − | 0.0878410i | ||||||
\(649\) | 11.3435 | + | 19.1396i | 0.445270 | + | 0.751297i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.32624 | − | 3.14320i | −0.169559 | − | 0.123192i | ||||
\(652\) | 20.8702 | + | 6.78115i | 0.817342 | + | 0.265570i | ||||
\(653\) | −22.2906 | + | 7.24265i | −0.872297 | + | 0.283427i | −0.710755 | − | 0.703439i | \(-0.751647\pi\) |
−0.161542 | + | 0.986866i | \(0.551647\pi\) | |||||||
\(654\) | −2.07295 | + | 1.50609i | −0.0810587 | + | 0.0588926i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.44834 | + | 4.45752i | 0.0565481 | + | 0.174037i | ||||
\(657\) | 12.8128 | + | 4.16312i | 0.499873 | + | 0.162419i | ||||
\(658\) | −1.41260 | + | 1.94427i | −0.0550687 | + | 0.0757956i | ||||
\(659\) | −12.9656 | −0.505066 | −0.252533 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252533 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.90983 | 0.152075 | 0.0760374 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760374 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(662\) | −7.84548 | + | 10.7984i | −0.304923 | + | 0.419691i | ||||
\(663\) | 2.35114 | + | 0.763932i | 0.0913108 | + | 0.0296687i | ||||
\(664\) | −3.94427 | − | 12.1392i | −0.153067 | − | 0.471093i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.73607 | − | 2.71441i | 0.144770 | − | 0.105181i | ||||
\(667\) | −13.2618 | + | 4.30902i | −0.513499 | + | 0.166846i | ||||
\(668\) | 30.8298 | + | 10.0172i | 1.19284 | + | 0.387578i | ||||
\(669\) | −6.50000 | − | 4.72253i | −0.251305 | − | 0.182583i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.3369 | + | 17.4293i | −0.592074 | + | 0.672850i | ||||
\(672\) | − | 4.29180i | − | 0.165560i | ||||||
\(673\) | 16.0494 | − | 22.0902i | 0.618661 | − | 0.851513i | −0.378594 | − | 0.925563i | \(-0.623592\pi\) |
0.997255 | + | 0.0740494i | \(0.0235923\pi\) | |||||||
\(674\) | 4.22949 | − | 13.0170i | 0.162914 | − | 0.501397i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.0172 | + | 10.9106i | −0.577585 | + | 0.419640i | ||||
\(677\) | −7.02067 | − | 9.66312i | −0.269826 | − | 0.371384i | 0.652505 | − | 0.757785i | \(-0.273718\pi\) |
−0.922331 | + | 0.386401i | \(0.873718\pi\) | |||||||
\(678\) | 3.21644 | − | 1.04508i | 0.123527 | − | 0.0401362i | ||||
\(679\) | 2.70820 | − | 8.33499i | 0.103931 | − | 0.319868i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.9443 | −0.994187 | ||||||||
\(682\) | 12.3435 | − | 7.31559i | 0.472657 | − | 0.280129i | ||||
\(683\) | − | 2.29180i | − | 0.0876931i | −0.999038 | − | 0.0438466i | \(-0.986039\pi\) | ||
0.999038 | − | 0.0438466i | \(-0.0139613\pi\) | |||||||
\(684\) | −6.54508 | − | 4.75528i | −0.250258 | − | 0.181823i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.95743 | + | 6.02434i | 0.0747349 | + | 0.230010i | ||||
\(687\) | −10.6331 | − | 14.6353i | −0.405679 | − | 0.558370i | ||||
\(688\) | 2.27790 | + | 3.13525i | 0.0868440 | + | 0.119530i | ||||
\(689\) | −2.90983 | − | 8.95554i | −0.110856 | − | 0.341179i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9443 | − | 19.5762i | −1.02501 | − | 0.744712i | −0.0577049 | − | 0.998334i | \(-0.518378\pi\) |
−0.967304 | + | 0.253621i | \(0.918378\pi\) | |||||||
\(692\) | 5.76393i | 0.219112i | ||||||||
\(693\) | −2.52265 | − | 0.236068i | −0.0958277 | − | 0.00896748i | ||||
\(694\) | −3.59675 | −0.136531 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.04508 | + | 12.4495i | −0.153329 | + | 0.471897i | ||||
\(697\) | 4.80828 | − | 1.56231i | 0.182127 | − | 0.0591766i | ||||
\(698\) | −10.0858 | − | 13.8820i | −0.381755 | − | 0.525440i | ||||
\(699\) | 18.8262 | − | 13.6781i | 0.712074 | − | 0.517352i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.19756 | − | 12.9188i | 0.158540 | − | 0.487935i | −0.839963 | − | 0.542644i | \(-0.817423\pi\) |
0.998502 | + | 0.0547093i | \(0.0174232\pi\) | |||||||
\(702\) | −0.449028 | + | 0.618034i | −0.0169475 | + | 0.0233262i | ||||
\(703\) | − | 37.3607i | − | 1.40908i | ||||||
\(704\) | −0.718847 | − | 0.310271i | −0.0270926 | − | 0.0116938i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9164 | + | 13.0170i | 0.674293 | + | 0.489902i | ||||
\(707\) | −0.408539 | − | 0.132742i | −0.0153647 | − | 0.00499229i | ||||
\(708\) | 10.3229 | − | 3.35410i | 0.387957 | − | 0.126055i | ||||
\(709\) | 33.3156 | − | 24.2052i | 1.25119 | − | 0.909045i | 0.252903 | − | 0.967492i | \(-0.418615\pi\) |
0.998291 | + | 0.0584464i | \(0.0186147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 7.69421i | −0.0937573 | − | 0.288555i | ||||
\(712\) | 23.0826 | + | 7.50000i | 0.865058 | + | 0.281074i | ||||
\(713\) | 9.80059 | − | 13.4894i | 0.367035 | − | 0.505180i | ||||
\(714\) | −0.944272 | −0.0353385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.5066 | 1.17746 | ||||||||
\(717\) | −4.13474 | + | 5.69098i | −0.154415 | + | 0.212534i | ||||
\(718\) | 9.82084 | + | 3.19098i | 0.366510 | + | 0.119086i | ||||
\(719\) | −11.7705 | − | 36.2259i | −0.438966 | − | 1.35100i | −0.888967 | − | 0.457970i | \(-0.848577\pi\) |
0.450001 | − | 0.893028i | \(-0.351423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.47214 | − | 1.06957i | 0.0548252 | − | 0.0398328i | ||||
\(722\) | 3.52671 | − | 1.14590i | 0.131251 | − | 0.0426459i | ||||
\(723\) | 1.53884 | + | 0.500000i | 0.0572301 | + | 0.0185952i | ||||
\(724\) | 6.85410 | + | 4.97980i | 0.254731 | + | 0.185073i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.26393 | − | 5.96361i | 0.121136 | − | 0.221330i | ||||
\(727\) | − | 37.3262i | − | 1.38435i | −0.721728 | − | 0.692177i | \(-0.756652\pi\) | ||
0.721728 | − | 0.692177i | \(-0.243348\pi\) | |||||||
\(728\) | −1.24108 | + | 1.70820i | −0.0459976 | + | 0.0633102i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.38197 | − | 2.45714i | 0.125087 | − | 0.0908807i | ||||
\(732\) | 6.65740 | + | 9.16312i | 0.246064 | + | 0.338679i | ||||
\(733\) | −1.76336 | + | 0.572949i | −0.0651310 | + | 0.0211624i | −0.341401 | − | 0.939918i | \(-0.610902\pi\) |
0.276270 | + | 0.961080i | \(0.410902\pi\) | |||||||
\(734\) | 3.46149 | − | 10.6534i | 0.127766 | − | 0.393223i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3820 | 0.493266 | ||||||||
\(737\) | 6.81640 | + | 30.3607i | 0.251085 | + | 1.11835i | ||||
\(738\) | 1.56231i | 0.0575093i | ||||||||
\(739\) | −16.1803 | − | 11.7557i | −0.595203 | − | 0.432441i | 0.248970 | − | 0.968511i | \(-0.419908\pi\) |
−0.844173 | + | 0.536071i | \(0.819908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.90983 | + | 5.87785i | 0.0701594 | + | 0.215928i | ||||
\(742\) | 2.11412 | + | 2.90983i | 0.0776116 | + | 0.106823i | ||||
\(743\) | −0.204270 | − | 0.281153i | −0.00749392 | − | 0.0103145i | 0.805254 | − | 0.592931i | \(-0.202029\pi\) |
−0.812748 | + | 0.582616i | \(0.802029\pi\) | |||||||
\(744\) | −4.83688 | − | 14.8864i | −0.177329 | − | 0.545762i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.87132 | − | 3.53922i | −0.178352 | − | 0.129580i | ||||
\(747\) | 5.70820i | 0.208852i | ||||||||
\(748\) | −4.25325 | + | 9.85410i | −0.155514 | + | 0.360302i | ||||
\(749\) | 2.18034 | 0.0796679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1803 | + | 43.6426i | −0.517448 | + | 1.59254i | 0.261335 | + | 0.965248i | \(0.415837\pi\) |
−0.778783 | + | 0.627293i | \(0.784163\pi\) | |||||||
\(752\) | 8.97578 | − | 2.91641i | 0.327313 | − | 0.106350i | ||||
\(753\) | 4.42477 | + | 6.09017i | 0.161247 | + | 0.221938i | ||||
\(754\) | 3.61803 | − | 2.62866i | 0.131761 | − | 0.0957300i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.381966 | + | 1.17557i | −0.0138920 | + | 0.0427551i | ||||
\(757\) | 14.2128 | − | 19.5623i | 0.516575 | − | 0.711004i | −0.468436 | − | 0.883497i | \(-0.655182\pi\) |
0.985011 | + | 0.172493i | \(0.0551823\pi\) | |||||||
\(758\) | − | 3.09017i | − | 0.112240i | ||||||
\(759\) | 0.736068 | − | 7.86572i | 0.0267176 | − | 0.285508i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5795 | − | 22.9439i | −1.14476 | − | 0.831715i | −0.156982 | − | 0.987601i | \(-0.550176\pi\) |
−0.987775 | + | 0.155887i | \(0.950176\pi\) | |||||||
\(762\) | 9.37181 | + | 3.04508i | 0.339505 | + | 0.110312i | ||||
\(763\) | 3.01217 | − | 0.978714i | 0.109048 | − | 0.0354318i | ||||
\(764\) | −13.6353 | + | 9.90659i | −0.493306 | + | 0.358408i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.98936 | − | 18.4333i | −0.216404 | − | 0.666024i | ||||
\(767\) | −7.88597 | − | 2.56231i | −0.284746 | − | 0.0925195i | ||||
\(768\) | 3.85723 | − | 5.30902i | 0.139186 | − | 0.191573i | ||||
\(769\) | −12.7639 | −0.460279 | −0.230140 | − | 0.973158i | \(-0.573918\pi\) | ||||
−0.230140 | + | 0.973158i | \(0.573918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5623 | 0.380392 | ||||||||
\(772\) | −20.0049 | + | 27.5344i | −0.719994 | + | 0.990986i | ||||
\(773\) | −9.99235 | − | 3.24671i | −0.359400 | − | 0.116776i | 0.123751 | − | 0.992313i | \(-0.460508\pi\) |
−0.483151 | + | 0.875537i | \(0.660508\pi\) | |||||||
\(774\) | 0.399187 | + | 1.22857i | 0.0143485 | + | 0.0441601i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.7533 | − | 15.0781i | 0.745000 | − | 0.541274i | ||||
\(777\) | −5.42882 | + | 1.76393i | −0.194758 | + | 0.0632807i | ||||
\(778\) | −22.8909 | − | 7.43769i | −0.820677 | − | 0.266654i | ||||
\(779\) | 10.2254 | + | 7.42921i | 0.366364 | + | 0.266179i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5279 | − | 19.9192i | 0.627196 | − | 0.712765i | ||||
\(782\) | − | 2.94427i | − | 0.105287i | ||||||
\(783\) | 3.44095 | − | 4.73607i | 0.122970 | − | 0.169253i | ||||
\(784\) | 3.67627 | − | 11.3144i | 0.131296 | − | 0.404086i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.59017 | − | 4.78804i | 0.235064 | − | 0.170784i | ||||
\(787\) | −4.82079 | − | 6.63525i | −0.171843 | − | 0.236521i | 0.714405 | − | 0.699732i | \(-0.246697\pi\) |
−0.886248 | + | 0.463211i | \(0.846697\pi\) | |||||||
\(788\) | 21.9071 | − | 7.11803i | 0.780407 | − | 0.253569i | ||||
\(789\) | −8.40983 | + | 25.8828i | −0.299398 | + | 0.921452i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.18034 | −0.148636 | ||||||||
\(792\) | −5.56758 | − | 4.89919i | −0.197835 | − | 0.174085i | ||||
\(793\) | − | 8.65248i | − | 0.307258i | ||||||
\(794\) | 18.1353 | + | 13.1760i | 0.643596 | + | 0.467600i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.89919 | − | 30.4666i | −0.350867 | − | 1.07986i | ||||
\(797\) | 16.8743 | + | 23.2254i | 0.597717 | + | 0.822687i | 0.995497 | − | 0.0947941i | \(-0.0302193\pi\) |
−0.397780 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(798\) | −1.38757 | − | 1.90983i | −0.0491195 | − | 0.0676073i | ||||
\(799\) | −3.14590 | − | 9.68208i | −0.111294 | − | 0.342527i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.78115 | − | 6.37988i | −0.310267 | − | 0.225422i | ||||
\(802\) | − | 3.02129i | − | 0.106685i | ||||||
\(803\) | 38.4383 | − | 22.7812i | 1.35646 | − | 0.803929i | ||||
\(804\) | 15.1803 | 0.535369 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.65248 | + | 5.08580i | −0.0582060 | + | 0.179140i | ||||
\(807\) | 5.56758 | − | 1.80902i | 0.195988 | − | 0.0636804i | ||||
\(808\) | −0.739054 | − | 1.01722i | −0.0259998 | − | 0.0357857i | ||||
\(809\) | 36.6697 | − | 26.6421i | 1.28924 | − | 0.936686i | 0.289448 | − | 0.957194i | \(-0.406528\pi\) |
0.999790 | + | 0.0205075i | \(0.00652821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7016 | + | 32.9362i | −0.375785 | + | 1.15655i | 0.567163 | + | 0.823606i | \(0.308041\pi\) |
−0.942948 | + | 0.332941i | \(0.891959\pi\) | |||||||
\(812\) | 4.25325 | − | 5.85410i | 0.149260 | − | 0.205439i | ||||
\(813\) | − | 20.6180i | − | 0.723106i | ||||||
\(814\) | 1.42705 | − | 15.2497i | 0.0500181 | − | 0.534500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | + | 2.17963i | 0.105021 | + | 0.0763022i | ||||
\(817\) | 9.93935 | + | 3.22949i | 0.347734 | + | 0.112986i | ||||
\(818\) | −21.3395 | + | 6.93363i | −0.746119 | + | 0.242429i | ||||
\(819\) | 0.763932 | − | 0.555029i | 0.0266939 | − | 0.0193943i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3435 | + | 41.0669i | 0.465690 | + | 1.43325i | 0.858113 | + | 0.513461i | \(0.171637\pi\) |
−0.392423 | + | 0.919785i | \(0.628363\pi\) | |||||||
\(822\) | 10.9964 | + | 3.57295i | 0.383544 | + | 0.124621i | ||||
\(823\) | 14.9721 | − | 20.6074i | 0.521896 | − | 0.718328i | −0.463972 | − | 0.885850i | \(-0.653576\pi\) |
0.985868 | + | 0.167521i | \(0.0535763\pi\) | |||||||
\(824\) | 5.32624 | 0.185548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.16718 | 0.110200 | ||||||||
\(827\) | 14.4499 | − | 19.8885i | 0.502471 | − | 0.691592i | −0.480156 | − | 0.877183i | \(-0.659420\pi\) |
0.982627 | + | 0.185591i | \(0.0594199\pi\) | |||||||
\(828\) | −3.66547 | − | 1.19098i | −0.127384 | − | 0.0413895i | ||||
\(829\) | −0.892609 | − | 2.74717i | −0.0310016 | − | 0.0954131i | 0.934358 | − | 0.356335i | \(-0.115974\pi\) |
−0.965360 | + | 0.260921i | \(0.915974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.00000 | + | 5.08580i | −0.242827 | + | 0.176424i | ||||
\(832\) | 0.277515 | − | 0.0901699i | 0.00962109 | − | 0.00312608i | ||||
\(833\) | −12.2047 | − | 3.96556i | −0.422869 | − | 0.137398i | ||||
\(834\) | −10.5902 | − | 7.69421i | −0.366708 | − | 0.266429i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.1803 | + | 5.87785i | −0.905466 | + | 0.203290i | ||||
\(837\) | 7.00000i | 0.241955i | ||||||||
\(838\) | 8.93529 | − | 12.2984i | 0.308665 | − | 0.424840i | ||||
\(839\) | 8.12868 | − | 25.0175i | 0.280633 | − | 0.863700i | −0.707041 | − | 0.707173i | \(-0.749970\pi\) |
0.987674 | − | 0.156527i | \(-0.0500298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.26393 | + | 3.09793i | −0.147032 | + | 0.106825i | ||||
\(842\) | 1.03681 | + | 1.42705i | 0.0357309 | + | 0.0491794i | ||||
\(843\) | 9.59632 | − | 3.11803i | 0.330515 | − | 0.107391i | ||||
\(844\) | −1.92705 | + | 5.93085i | −0.0663318 | + | 0.204148i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.14590 | 0.108158 | ||||||||
\(847\) | −6.11488 | + | 5.76393i | −0.210110 | + | 0.198051i | ||||
\(848\) | − | 14.1246i | − | 0.485041i | ||||||
\(849\) | −10.5451 | − | 7.66145i | −0.361906 | − | 0.262940i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.50000 | − | 16.9273i | −0.188538 | − | 0.580259i | ||||
\(852\) | −7.60845 | − | 10.4721i | −0.260661 | − | 0.358769i | ||||
\(853\) | 12.5555 | + | 17.2812i | 0.429892 | + | 0.591695i | 0.967928 | − | 0.251226i | \(-0.0808338\pi\) |
−0.538037 | + | 0.842922i | \(0.680834\pi\) | |||||||
\(854\) | 1.02129 | + | 3.14320i | 0.0349477 | + | 0.107558i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.16312 | + | 3.75123i | 0.176472 | + | 0.128214i | ||||
\(857\) | − | 35.0132i | − | 1.19603i | −0.801486 | − | 0.598013i | \(-0.795957\pi\) | ||
0.801486 | − | 0.598013i | \(-0.204043\pi\) | |||||||
\(858\) | 0.555029 | + | 2.47214i | 0.0189484 | + | 0.0843973i | ||||
\(859\) | 5.72949 | 0.195488 | 0.0977438 | − | 0.995212i | \(-0.468837\pi\) | ||||
0.0977438 | + | 0.995212i | \(0.468837\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.596748 | − | 1.83660i | 0.0203371 | − | 0.0625912i | ||||
\(862\) | 11.6902 | − | 3.79837i | 0.398170 | − | 0.129373i | ||||
\(863\) | 3.54696 | + | 4.88197i | 0.120740 | + | 0.166184i | 0.865108 | − | 0.501585i | \(-0.167249\pi\) |
−0.744369 | + | 0.667769i | \(0.767249\pi\) | |||||||
\(864\) | −4.54508 | + | 3.30220i | −0.154627 | + | 0.112343i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.35410 | − | 16.4782i | 0.181940 | − | 0.559953i | ||||
\(867\) | −7.64121 | + | 10.5172i | −0.259509 | + | 0.357184i | ||||
\(868\) | 8.65248i | 0.293684i | ||||||||
\(869\) | −24.6353 | − | 10.6331i | −0.835694 | − | 0.360704i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38197 | − | 6.81640i | −0.317896 | − | 0.230965i | ||||
\(872\) | 8.81678 | + | 2.86475i | 0.298574 | + | 0.0970125i | ||||
\(873\) | −10.9106 | + | 3.54508i | −0.369270 | + | 0.119983i | ||||
\(874\) | 5.95492 | − | 4.32650i | 0.201428 | − | 0.146346i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.73607 | − | 20.7315i | −0.227591 | − | 0.700452i | ||||
\(877\) | −15.6659 | − | 5.09017i | −0.529001 | − | 0.171883i | 0.0323254 | − | 0.999477i | \(-0.489709\pi\) |
−0.561326 | + | 0.827595i | \(0.689709\pi\) | |||||||
\(878\) | 3.51420 | − | 4.83688i | 0.118598 | − | 0.163237i | ||||
\(879\) | 16.5279 | 0.557471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.8541 | −0.803665 | −0.401833 | − | 0.915713i | \(-0.631627\pi\) | ||||
−0.401833 | + | 0.915713i | \(0.631627\pi\) | |||||||
\(882\) | 2.33090 | − | 3.20820i | 0.0784854 | − | 0.108026i | ||||
\(883\) | 17.8456 | + | 5.79837i | 0.600551 | + | 0.195131i | 0.593486 | − | 0.804844i | \(-0.297751\pi\) |
0.00706479 | + | 0.999975i | \(0.497751\pi\) | |||||||
\(884\) | −1.23607 | − | 3.80423i | −0.0415735 | − | 0.127950i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.6353 | + | 9.18005i | −0.424490 | + | 0.308410i | ||||
\(887\) | 51.1981 | − | 16.6353i | 1.71906 | − | 0.558557i | 0.727263 | − | 0.686359i | \(-0.240792\pi\) |
0.991800 | + | 0.127802i | \(0.0407922\pi\) | |||||||
\(888\) | −15.8904 | − | 5.16312i | −0.533248 | − | 0.173263i | ||||
\(889\) | −9.85410 | − | 7.15942i | −0.330496 | − | 0.240119i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.69098 | + | 2.85317i | 0.0566501 | + | 0.0955848i | ||||
\(892\) | 13.0000i | 0.435272i | ||||||||
\(893\) | 14.9596 | − | 20.5902i | 0.500605 | − | 0.689024i | ||||
\(894\) | 3.84346 | − | 11.8290i | 0.128544 | − | 0.395619i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.03444 | + | 5.11082i | −0.235004 | + | 0.170741i | ||||
\(897\) | 1.73060 | + | 2.38197i | 0.0577830 | + | 0.0795315i | ||||
\(898\) | 0.428784 | − | 0.139320i | 0.0143087 | − | 0.00464918i | ||||
\(899\) | 12.6631 | − | 38.9731i | 0.422339 | − | 1.29982i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.2361 | −0.507587 | ||||||||
\(902\) | 3.88998 | + | 3.42299i | 0.129522 | + | 0.113973i | ||||
\(903\) | − | 1.59675i | − | 0.0531364i | ||||||
\(904\) | −9.89919 | − | 7.19218i | −0.329242 | − | 0.239208i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.05573 | + | 6.32688i | 0.0682970 | + | 0.210197i | ||||
\(907\) | 5.35558 | + | 7.37132i | 0.177829 | + | 0.244761i | 0.888622 | − | 0.458641i | \(-0.151664\pi\) |
−0.710793 | + | 0.703402i | \(0.751664\pi\) | |||||||
\(908\) | 24.6745 | + | 33.9615i | 0.818851 | + | 1.12705i | ||||
\(909\) | 0.173762 | + | 0.534785i | 0.00576332 | + | 0.0177377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6525 | + | 34.6216i | 1.57880 | + | 1.14706i | 0.918057 | + | 0.396448i | \(0.129757\pi\) |
0.660740 | + | 0.750615i | \(0.270243\pi\) | |||||||
\(912\) | 9.27051i | 0.306977i | ||||||||
\(913\) | 14.2128 | + | 12.5066i | 0.470377 | + | 0.413907i | ||||
\(914\) | −0.909830 | −0.0300945 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.04508 | + | 27.8379i | −0.298858 | + | 0.919790i | ||||
\(917\) | −9.57608 | + | 3.11146i | −0.316230 | + | 0.102749i | ||||
\(918\) | 0.726543 | + | 1.00000i | 0.0239795 | + | 0.0330049i | ||||
\(919\) | −14.3713 | + | 10.4414i | −0.474066 | + | 0.344429i | −0.799024 | − | 0.601299i | \(-0.794650\pi\) |
0.324958 | + | 0.945729i | \(0.394650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.74671 | + | 11.5312i | −0.123458 | + | 0.379966i | ||||
\(922\) | −9.42481 | + | 12.9721i | −0.310390 | + | 0.427215i | ||||
\(923\) | 9.88854i | 0.325485i | ||||||||
\(924\) | 2.09017 | + | 3.52671i | 0.0687615 | + | 0.116020i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.6353 | + | 12.0862i | 0.546668 | + | 0.397178i | ||||
\(927\) | −2.26538 | − | 0.736068i | −0.0744050 | − | 0.0241756i | ||||
\(928\) | 31.2789 | − | 10.1631i | 1.02678 | − | 0.333621i | ||||
\(929\) | −3.35410 | + | 2.43690i | −0.110045 | + | 0.0799520i | −0.641447 | − | 0.767168i | \(-0.721665\pi\) |
0.531402 | + | 0.847120i | \(0.321665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.91390 | − | 30.5118i | −0.324915 | − | 0.999985i | ||||
\(932\) | −35.8096 | − | 11.6353i | −1.17298 | − | 0.381125i | ||||
\(933\) | −12.6210 | + | 17.3713i | −0.413193 | + | 0.568712i | ||||
\(934\) | −3.02129 | −0.0988595 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.76393 | 0.0903419 | ||||||||
\(937\) | −24.5685 | + | 33.8156i | −0.802617 | + | 1.10471i | 0.189804 | + | 0.981822i | \(0.439215\pi\) |
−0.992421 | + | 0.122885i | \(0.960785\pi\) | |||||||
\(938\) | 4.21277 | + | 1.36881i | 0.137552 | + | 0.0446932i | ||||
\(939\) | 0.145898 | + | 0.449028i | 0.00476120 | + | 0.0146535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 2.17963i | −0.0977972 | + | 0.0710538i | −0.635609 | − | 0.772011i | \(-0.719251\pi\) |
0.537812 | + | 0.843065i | \(0.319251\pi\) | |||||||
\(942\) | 1.95511 | − | 0.635255i | 0.0637010 | − | 0.0206977i | ||||
\(943\) | 5.72658 | + | 1.86068i | 0.186483 | + | 0.0605921i | ||||
\(944\) | −10.0623 | − | 7.31069i | −0.327500 | − | 0.237943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.93363 | + | 1.69784i | 0.127893 | + | 0.0552017i | ||||
\(947\) | 15.5623i | 0.505707i | 0.967505 | + | 0.252853i | \(0.0813691\pi\) | ||||
−0.967505 | + | 0.252853i | \(0.918631\pi\) | |||||||
\(948\) | −7.69421 | + | 10.5902i | −0.249896 | + | 0.343953i | ||||
\(949\) | −5.14590 | + | 15.8374i | −0.167043 | + | 0.514105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.6074 | − | 17.8783i | 0.797949 | − | 0.579744i | ||||
\(952\) | 2.00811 | + | 2.76393i | 0.0650834 | + | 0.0895796i | ||||
\(953\) | −36.0544 | + | 11.7148i | −1.16792 | + | 0.379479i | −0.827865 | − | 0.560928i | \(-0.810445\pi\) |
−0.340052 | + | 0.940407i | \(0.610445\pi\) | |||||||
\(954\) | 1.45492 | − | 4.47777i | 0.0471046 | − | 0.144973i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.3820 | 0.368119 | ||||||||
\(957\) | −4.25325 | − | 18.9443i | −0.137488 | − | 0.612381i | ||||
\(958\) | 20.6525i | 0.667251i | ||||||||
\(959\) | −11.5623 | − | 8.40051i | −0.373366 | − | 0.271267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.56231 | + | 17.1190i | 0.179429 | + | 0.552226i | ||||
\(962\) | 3.35520 | + | 4.61803i | 0.108176 | + | 0.148891i | ||||
\(963\) | −1.67760 | − | 2.30902i | −0.0540599 | − | 0.0744070i | ||||
\(964\) | −0.809017 | − | 2.48990i | −0.0260567 | − | 0.0801942i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.909830 | − | 0.661030i | −0.0292733 | − | 0.0212683i | ||||
\(967\) | 48.3262i | 1.55407i | 0.629459 | + | 0.777034i | \(0.283276\pi\) | ||||
−0.629459 | + | 0.777034i | \(0.716724\pi\) | |||||||
\(968\) | −24.3970 | + | 3.12868i | −0.784148 | + | 0.100559i | ||||
\(969\) | 10.0000 | 0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.9828 | − | 33.8015i | 0.352454 | − | 1.08474i | −0.605017 | − | 0.796213i | \(-0.706834\pi\) |
0.957471 | − | 0.288530i | \(-0.0931664\pi\) | |||||||
\(972\) | 1.53884 | − | 0.500000i | 0.0493584 | − | 0.0160375i | ||||
\(973\) | 9.51057 | + | 13.0902i | 0.304895 | + | 0.419652i | ||||
\(974\) | −7.09017 | + | 5.15131i | −0.227184 | + | 0.165059i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.01064 | − | 12.3435i | 0.128378 | − | 0.395105i | ||||
\(977\) | 20.5195 | − | 28.2426i | 0.656476 | − | 0.903562i | −0.342882 | − | 0.939378i | \(-0.611403\pi\) |
0.999358 | + | 0.0358162i | \(0.0114031\pi\) | |||||||
\(978\) | − | 8.38197i | − | 0.268026i | ||||||
\(979\) | −35.1246 | + | 7.88597i | −1.12259 | + | 0.252037i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.35410 | − | 2.43690i | −0.107088 | − | 0.0778042i | ||||
\(982\) | −18.6906 | − | 6.07295i | −0.596441 | − | 0.193796i | ||||
\(983\) | 18.0701 | − | 5.87132i | 0.576346 | − | 0.187266i | −0.00631707 | − | 0.999980i | \(-0.502011\pi\) |
0.582663 | + | 0.812714i | \(0.302011\pi\) | |||||||
\(984\) | 4.57295 | − | 3.32244i | 0.145780 | − | 0.105916i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.23607 | − | 6.88191i | −0.0712109 | − | 0.219165i | ||||
\(987\) | −3.69822 | − | 1.20163i | −0.117716 | − | 0.0382482i | ||||
\(988\) | 5.87785 | − | 8.09017i | 0.186999 | − | 0.257383i | ||||
\(989\) | 4.97871 | 0.158314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −23.1154 | + | 31.8156i | −0.733914 | + | 1.01015i | ||||
\(993\) | −20.5397 | − | 6.67376i | −0.651809 | − | 0.211785i | ||||
\(994\) | −1.16718 | − | 3.59222i | −0.0370208 | − | 0.113938i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.47214 | − | 5.42882i | 0.236764 | − | 0.172019i | ||||
\(997\) | −23.4989 | + | 7.63525i | −0.744218 | + | 0.241811i | −0.656491 | − | 0.754334i | \(-0.727960\pi\) |
−0.0877264 | + | 0.996145i | \(0.527960\pi\) | |||||||
\(998\) | −6.57164 | − | 2.13525i | −0.208022 | − | 0.0675903i | ||||
\(999\) | 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.bx.c.499.1 | 8 | ||
5.2 | odd | 4 | 825.2.n.b.301.1 | ✓ | 4 | ||
5.3 | odd | 4 | 825.2.n.d.301.1 | yes | 4 | ||
5.4 | even | 2 | inner | 825.2.bx.c.499.2 | 8 | ||
11.3 | even | 5 | inner | 825.2.bx.c.124.2 | 8 | ||
55.3 | odd | 20 | 825.2.n.d.751.1 | yes | 4 | ||
55.14 | even | 10 | inner | 825.2.bx.c.124.1 | 8 | ||
55.17 | even | 20 | 9075.2.a.bt.1.1 | 2 | |||
55.27 | odd | 20 | 9075.2.a.z.1.2 | 2 | |||
55.28 | even | 20 | 9075.2.a.bc.1.2 | 2 | |||
55.38 | odd | 20 | 9075.2.a.by.1.1 | 2 | |||
55.47 | odd | 20 | 825.2.n.b.751.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.301.1 | ✓ | 4 | 5.2 | odd | 4 | ||
825.2.n.b.751.1 | yes | 4 | 55.47 | odd | 20 | ||
825.2.n.d.301.1 | yes | 4 | 5.3 | odd | 4 | ||
825.2.n.d.751.1 | yes | 4 | 55.3 | odd | 20 | ||
825.2.bx.c.124.1 | 8 | 55.14 | even | 10 | inner | ||
825.2.bx.c.124.2 | 8 | 11.3 | even | 5 | inner | ||
825.2.bx.c.499.1 | 8 | 1.1 | even | 1 | trivial | ||
825.2.bx.c.499.2 | 8 | 5.4 | even | 2 | inner | ||
9075.2.a.z.1.2 | 2 | 55.27 | odd | 20 | |||
9075.2.a.bc.1.2 | 2 | 55.28 | even | 20 | |||
9075.2.a.bt.1.1 | 2 | 55.17 | even | 20 | |||
9075.2.a.by.1.1 | 2 | 55.38 | odd | 20 |