Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(64,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.j (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: | \(1.84454428669\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.169 |
Dual form | 231.2.j.a.190.1 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11803 | − | 1.53884i | −1.49768 | − | 1.08813i | −0.971295 | − | 0.237877i | \(-0.923549\pi\) |
−0.526381 | − | 0.850249i | \(-0.676451\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 1.50000 | + | 4.61653i | 0.750000 | + | 2.30826i | ||||
\(5\) | −1.30902 | + | 0.951057i | −0.585410 | + | 0.425325i | −0.840670 | − | 0.541547i | \(-0.817839\pi\) |
0.255260 | + | 0.966872i | \(0.417839\pi\) | |||||||
\(6\) | 2.11803 | − | 1.53884i | 0.864684 | − | 0.628230i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 2.30902 | − | 7.10642i | 0.816361 | − | 2.51250i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 4.23607 | 1.33956 | ||||||||
\(11\) | −2.54508 | − | 2.12663i | −0.767372 | − | 0.641202i | ||||
\(12\) | −4.85410 | −1.40126 | ||||||||
\(13\) | −4.42705 | − | 3.21644i | −1.22784 | − | 0.892080i | −0.231116 | − | 0.972926i | \(-0.574238\pi\) |
−0.996727 | + | 0.0808459i | \(0.974238\pi\) | |||||||
\(14\) | 0.809017 | − | 2.48990i | 0.216219 | − | 0.665453i | ||||
\(15\) | −0.500000 | − | 1.53884i | −0.129099 | − | 0.397327i | ||||
\(16\) | −7.97214 | + | 5.79210i | −1.99303 | + | 1.44802i | ||||
\(17\) | 2.42705 | − | 1.76336i | 0.588646 | − | 0.427677i | −0.253185 | − | 0.967418i | \(-0.581478\pi\) |
0.841831 | + | 0.539741i | \(0.181478\pi\) | |||||||
\(18\) | 0.809017 | + | 2.48990i | 0.190687 | + | 0.586875i | ||||
\(19\) | 1.23607 | − | 3.80423i | 0.283573 | − | 0.872749i | −0.703249 | − | 0.710943i | \(-0.748268\pi\) |
0.986823 | − | 0.161806i | \(-0.0517318\pi\) | |||||||
\(20\) | −6.35410 | − | 4.61653i | −1.42082 | − | 1.03229i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.11803 | + | 8.42075i | 0.451566 | + | 1.79531i | ||||
\(23\) | −7.23607 | −1.50882 | −0.754412 | − | 0.656401i | \(-0.772078\pi\) | ||||
−0.754412 | + | 0.656401i | \(0.772078\pi\) | |||||||
\(24\) | 6.04508 | + | 4.39201i | 1.23395 | + | 0.896516i | ||||
\(25\) | −0.736068 | + | 2.26538i | −0.147214 | + | 0.453077i | ||||
\(26\) | 4.42705 | + | 13.6251i | 0.868216 | + | 2.67209i | ||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | −3.92705 | + | 2.85317i | −0.742143 | + | 0.539198i | ||||
\(29\) | 0.927051 | + | 2.85317i | 0.172149 | + | 0.529820i | 0.999492 | − | 0.0318771i | \(-0.0101485\pi\) |
−0.827343 | + | 0.561697i | \(0.810149\pi\) | |||||||
\(30\) | −1.30902 | + | 4.02874i | −0.238993 | + | 0.735544i | ||||
\(31\) | −0.190983 | − | 0.138757i | −0.0343016 | − | 0.0249215i | 0.570502 | − | 0.821296i | \(-0.306749\pi\) |
−0.604804 | + | 0.796374i | \(0.706749\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | 2.80902 | − | 1.76336i | 0.488987 | − | 0.306961i | ||||
\(34\) | −7.85410 | −1.34697 | ||||||||
\(35\) | −1.30902 | − | 0.951057i | −0.221264 | − | 0.160758i | ||||
\(36\) | 1.50000 | − | 4.61653i | 0.250000 | − | 0.769421i | ||||
\(37\) | −2.61803 | − | 8.05748i | −0.430402 | − | 1.32464i | −0.897726 | − | 0.440555i | \(-0.854782\pi\) |
0.467323 | − | 0.884086i | \(-0.345218\pi\) | |||||||
\(38\) | −8.47214 | + | 6.15537i | −1.37436 | + | 0.998532i | ||||
\(39\) | 4.42705 | − | 3.21644i | 0.708896 | − | 0.515043i | ||||
\(40\) | 3.73607 | + | 11.4984i | 0.590724 | + | 1.81806i | ||||
\(41\) | −0.954915 | + | 2.93893i | −0.149133 | + | 0.458983i | −0.997519 | − | 0.0703940i | \(-0.977574\pi\) |
0.848387 | + | 0.529377i | \(0.177574\pi\) | |||||||
\(42\) | 2.11803 | + | 1.53884i | 0.326820 | + | 0.237448i | ||||
\(43\) | −9.00000 | −1.37249 | −0.686244 | − | 0.727372i | \(-0.740742\pi\) | ||||
−0.686244 | + | 0.727372i | \(0.740742\pi\) | |||||||
\(44\) | 6.00000 | − | 14.9394i | 0.904534 | − | 2.25220i | ||||
\(45\) | 1.61803 | 0.241202 | ||||||||
\(46\) | 15.3262 | + | 11.1352i | 2.25973 | + | 1.64179i | ||||
\(47\) | 3.11803 | − | 9.59632i | 0.454812 | − | 1.39977i | −0.416544 | − | 0.909116i | \(-0.636759\pi\) |
0.871356 | − | 0.490652i | \(-0.163241\pi\) | |||||||
\(48\) | −3.04508 | − | 9.37181i | −0.439520 | − | 1.35270i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 5.04508 | − | 3.66547i | 0.713483 | − | 0.518376i | ||||
\(51\) | 0.927051 | + | 2.85317i | 0.129813 | + | 0.399524i | ||||
\(52\) | 8.20820 | − | 25.2623i | 1.13827 | − | 3.50324i | ||||
\(53\) | −3.30902 | − | 2.40414i | −0.454528 | − | 0.330234i | 0.336853 | − | 0.941557i | \(-0.390638\pi\) |
−0.791381 | + | 0.611323i | \(0.790638\pi\) | |||||||
\(54\) | −2.61803 | −0.356269 | ||||||||
\(55\) | 5.35410 | + | 0.363271i | 0.721947 | + | 0.0489835i | ||||
\(56\) | 7.47214 | 0.998506 | ||||||||
\(57\) | 3.23607 | + | 2.35114i | 0.428628 | + | 0.311416i | ||||
\(58\) | 2.42705 | − | 7.46969i | 0.318687 | − | 0.980819i | ||||
\(59\) | 3.89919 | + | 12.0005i | 0.507631 | + | 1.56233i | 0.796302 | + | 0.604899i | \(0.206787\pi\) |
−0.288671 | + | 0.957428i | \(0.593213\pi\) | |||||||
\(60\) | 6.35410 | − | 4.61653i | 0.820311 | − | 0.595991i | ||||
\(61\) | 5.42705 | − | 3.94298i | 0.694863 | − | 0.504847i | −0.183392 | − | 0.983040i | \(-0.558708\pi\) |
0.878255 | + | 0.478193i | \(0.158708\pi\) | |||||||
\(62\) | 0.190983 | + | 0.587785i | 0.0242549 | + | 0.0746488i | ||||
\(63\) | 0.309017 | − | 0.951057i | 0.0389325 | − | 0.119822i | ||||
\(64\) | −7.04508 | − | 5.11855i | −0.880636 | − | 0.639819i | ||||
\(65\) | 8.85410 | 1.09822 | ||||||||
\(66\) | −8.66312 | − | 0.587785i | −1.06636 | − | 0.0723514i | ||||
\(67\) | −3.70820 | −0.453029 | −0.226515 | − | 0.974008i | \(-0.572733\pi\) | ||||
−0.226515 | + | 0.974008i | \(0.572733\pi\) | |||||||
\(68\) | 11.7812 | + | 8.55951i | 1.42867 | + | 1.03799i | ||||
\(69\) | 2.23607 | − | 6.88191i | 0.269191 | − | 0.828485i | ||||
\(70\) | 1.30902 | + | 4.02874i | 0.156457 | + | 0.481527i | ||||
\(71\) | −9.89919 | + | 7.19218i | −1.17482 | + | 0.853555i | −0.991578 | − | 0.129513i | \(-0.958658\pi\) |
−0.183240 | + | 0.983068i | \(0.558658\pi\) | |||||||
\(72\) | −6.04508 | + | 4.39201i | −0.712420 | + | 0.517603i | ||||
\(73\) | −1.19098 | − | 3.66547i | −0.139394 | − | 0.429011i | 0.856854 | − | 0.515560i | \(-0.172416\pi\) |
−0.996248 | + | 0.0865492i | \(0.972416\pi\) | |||||||
\(74\) | −6.85410 | + | 21.0948i | −0.796773 | + | 2.45222i | ||||
\(75\) | −1.92705 | − | 1.40008i | −0.222517 | − | 0.161668i | ||||
\(76\) | 19.4164 | 2.22721 | ||||||||
\(77\) | 1.23607 | − | 3.07768i | 0.140863 | − | 0.350735i | ||||
\(78\) | −14.3262 | −1.62213 | ||||||||
\(79\) | −5.54508 | − | 4.02874i | −0.623871 | − | 0.453269i | 0.230401 | − | 0.973096i | \(-0.425996\pi\) |
−0.854271 | + | 0.519827i | \(0.825996\pi\) | |||||||
\(80\) | 4.92705 | − | 15.1639i | 0.550861 | − | 1.69538i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 6.54508 | − | 4.75528i | 0.722784 | − | 0.525133i | ||||
\(83\) | −2.38197 | + | 1.73060i | −0.261455 | + | 0.189958i | −0.710788 | − | 0.703406i | \(-0.751662\pi\) |
0.449333 | + | 0.893364i | \(0.351662\pi\) | |||||||
\(84\) | −1.50000 | − | 4.61653i | −0.163663 | − | 0.503704i | ||||
\(85\) | −1.50000 | + | 4.61653i | −0.162698 | + | 0.500732i | ||||
\(86\) | 19.0623 | + | 13.8496i | 2.05554 | + | 1.49344i | ||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | −20.9894 | + | 13.1760i | −2.23747 | + | 1.40457i | ||||
\(89\) | 2.67376 | 0.283418 | 0.141709 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141709 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(90\) | −3.42705 | − | 2.48990i | −0.361243 | − | 0.262458i | ||||
\(91\) | 1.69098 | − | 5.20431i | 0.177263 | − | 0.545560i | ||||
\(92\) | −10.8541 | − | 33.4055i | −1.13162 | − | 3.48276i | ||||
\(93\) | 0.190983 | − | 0.138757i | 0.0198040 | − | 0.0143885i | ||||
\(94\) | −21.3713 | + | 15.5272i | −2.20428 | + | 1.60151i | ||||
\(95\) | 2.00000 | + | 6.15537i | 0.205196 | + | 0.631527i | ||||
\(96\) | −3.35410 | + | 10.3229i | −0.342327 | + | 1.05357i | ||||
\(97\) | 13.2812 | + | 9.64932i | 1.34850 | + | 0.979740i | 0.999085 | + | 0.0427710i | \(0.0136186\pi\) |
0.349412 | + | 0.936969i | \(0.386381\pi\) | |||||||
\(98\) | 2.61803 | 0.264461 | ||||||||
\(99\) | 0.809017 | + | 3.21644i | 0.0813093 | + | 0.323264i | ||||
\(100\) | −11.5623 | −1.15623 | ||||||||
\(101\) | −2.61803 | − | 1.90211i | −0.260504 | − | 0.189267i | 0.449865 | − | 0.893096i | \(-0.351472\pi\) |
−0.710369 | + | 0.703829i | \(0.751472\pi\) | |||||||
\(102\) | 2.42705 | − | 7.46969i | 0.240314 | − | 0.739610i | ||||
\(103\) | 3.78115 | + | 11.6372i | 0.372568 | + | 1.14665i | 0.945105 | + | 0.326768i | \(0.105959\pi\) |
−0.572537 | + | 0.819879i | \(0.694041\pi\) | |||||||
\(104\) | −33.0795 | + | 24.0337i | −3.24371 | + | 2.35670i | ||||
\(105\) | 1.30902 | − | 0.951057i | 0.127747 | − | 0.0928136i | ||||
\(106\) | 3.30902 | + | 10.1841i | 0.321400 | + | 0.989168i | ||||
\(107\) | −4.92705 | + | 15.1639i | −0.476316 | + | 1.46595i | 0.367859 | + | 0.929882i | \(0.380091\pi\) |
−0.844175 | + | 0.536068i | \(0.819909\pi\) | |||||||
\(108\) | 3.92705 | + | 2.85317i | 0.377881 | + | 0.274546i | ||||
\(109\) | 0.437694 | 0.0419235 | 0.0209617 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209617 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(110\) | −10.7812 | − | 9.00854i | −1.02794 | − | 0.858930i | ||||
\(111\) | 8.47214 | 0.804140 | ||||||||
\(112\) | −7.97214 | − | 5.79210i | −0.753296 | − | 0.547302i | ||||
\(113\) | −0.454915 | + | 1.40008i | −0.0427948 | + | 0.131709i | −0.970171 | − | 0.242421i | \(-0.922059\pi\) |
0.927376 | + | 0.374130i | \(0.122059\pi\) | |||||||
\(114\) | −3.23607 | − | 9.95959i | −0.303086 | − | 0.932801i | ||||
\(115\) | 9.47214 | − | 6.88191i | 0.883281 | − | 0.641741i | ||||
\(116\) | −11.7812 | + | 8.55951i | −1.09385 | + | 0.794730i | ||||
\(117\) | 1.69098 | + | 5.20431i | 0.156331 | + | 0.481139i | ||||
\(118\) | 10.2082 | − | 31.4176i | 0.939741 | − | 2.89223i | ||||
\(119\) | 2.42705 | + | 1.76336i | 0.222487 | + | 0.161647i | ||||
\(120\) | −12.0902 | −1.10368 | ||||||||
\(121\) | 1.95492 | + | 10.8249i | 0.177720 | + | 0.984081i | ||||
\(122\) | −17.5623 | −1.59002 | ||||||||
\(123\) | −2.50000 | − | 1.81636i | −0.225417 | − | 0.163775i | ||||
\(124\) | 0.354102 | − | 1.08981i | 0.0317993 | − | 0.0978682i | ||||
\(125\) | −3.69098 | − | 11.3597i | −0.330132 | − | 1.01604i | ||||
\(126\) | −2.11803 | + | 1.53884i | −0.188689 | + | 0.137091i | ||||
\(127\) | −5.30902 | + | 3.85723i | −0.471099 | + | 0.342274i | −0.797869 | − | 0.602830i | \(-0.794040\pi\) |
0.326770 | + | 0.945104i | \(0.394040\pi\) | |||||||
\(128\) | 0.336881 | + | 1.03681i | 0.0297764 | + | 0.0916422i | ||||
\(129\) | 2.78115 | − | 8.55951i | 0.244867 | − | 0.753623i | ||||
\(130\) | −18.7533 | − | 13.6251i | −1.64477 | − | 1.19500i | ||||
\(131\) | −1.32624 | −0.115874 | −0.0579370 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579370 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(132\) | 12.3541 | + | 10.3229i | 1.07529 | + | 0.898490i | ||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 7.85410 | + | 5.70634i | 0.678491 | + | 0.492953i | ||||
\(135\) | −0.500000 | + | 1.53884i | −0.0430331 | + | 0.132442i | ||||
\(136\) | −6.92705 | − | 21.3193i | −0.593990 | − | 1.82811i | ||||
\(137\) | 8.47214 | − | 6.15537i | 0.723823 | − | 0.525888i | −0.163780 | − | 0.986497i | \(-0.552369\pi\) |
0.887603 | + | 0.460608i | \(0.152369\pi\) | |||||||
\(138\) | −15.3262 | + | 11.1352i | −1.30466 | + | 0.947888i | ||||
\(139\) | −5.42705 | − | 16.7027i | −0.460316 | − | 1.41671i | −0.864778 | − | 0.502154i | \(-0.832541\pi\) |
0.404462 | − | 0.914555i | \(-0.367459\pi\) | |||||||
\(140\) | 2.42705 | − | 7.46969i | 0.205123 | − | 0.631304i | ||||
\(141\) | 8.16312 | + | 5.93085i | 0.687459 | + | 0.499468i | ||||
\(142\) | 32.0344 | 2.68827 | ||||||||
\(143\) | 4.42705 | + | 17.6008i | 0.370209 | + | 1.47185i | ||||
\(144\) | 9.85410 | 0.821175 | ||||||||
\(145\) | −3.92705 | − | 2.85317i | −0.326124 | − | 0.236943i | ||||
\(146\) | −3.11803 | + | 9.59632i | −0.258050 | + | 0.794197i | ||||
\(147\) | −0.309017 | − | 0.951057i | −0.0254873 | − | 0.0784418i | ||||
\(148\) | 33.2705 | − | 24.1724i | 2.73482 | − | 1.98696i | ||||
\(149\) | 16.4443 | − | 11.9475i | 1.34717 | − | 0.978774i | 0.348020 | − | 0.937487i | \(-0.386854\pi\) |
0.999147 | − | 0.0412872i | \(-0.0131458\pi\) | |||||||
\(150\) | 1.92705 | + | 5.93085i | 0.157343 | + | 0.484252i | ||||
\(151\) | −3.28115 | + | 10.0984i | −0.267016 | + | 0.821792i | 0.724206 | + | 0.689584i | \(0.242207\pi\) |
−0.991222 | + | 0.132208i | \(0.957793\pi\) | |||||||
\(152\) | −24.1803 | − | 17.5680i | −1.96128 | − | 1.42496i | ||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | −7.35410 | + | 4.61653i | −0.592610 | + | 0.372010i | ||||
\(155\) | 0.381966 | 0.0306802 | ||||||||
\(156\) | 21.4894 | + | 15.6129i | 1.72053 | + | 1.25003i | ||||
\(157\) | −4.98936 | + | 15.3557i | −0.398194 | + | 1.22552i | 0.528252 | + | 0.849088i | \(0.322848\pi\) |
−0.926446 | + | 0.376428i | \(0.877152\pi\) | |||||||
\(158\) | 5.54508 | + | 17.0660i | 0.441143 | + | 1.35770i | ||||
\(159\) | 3.30902 | − | 2.40414i | 0.262422 | − | 0.190661i | ||||
\(160\) | −14.2082 | + | 10.3229i | −1.12326 | + | 0.816094i | ||||
\(161\) | −2.23607 | − | 6.88191i | −0.176227 | − | 0.542370i | ||||
\(162\) | 0.809017 | − | 2.48990i | 0.0635624 | − | 0.195625i | ||||
\(163\) | −9.82624 | − | 7.13918i | −0.769650 | − | 0.559184i | 0.132205 | − | 0.991222i | \(-0.457794\pi\) |
−0.901855 | + | 0.432039i | \(0.857794\pi\) | |||||||
\(164\) | −15.0000 | −1.17130 | ||||||||
\(165\) | −2.00000 | + | 4.97980i | −0.155700 | + | 0.387677i | ||||
\(166\) | 7.70820 | 0.598273 | ||||||||
\(167\) | −12.2082 | − | 8.86978i | −0.944699 | − | 0.686364i | 0.00484803 | − | 0.999988i | \(-0.498457\pi\) |
−0.949547 | + | 0.313624i | \(0.898457\pi\) | |||||||
\(168\) | −2.30902 | + | 7.10642i | −0.178145 | + | 0.548272i | ||||
\(169\) | 5.23607 | + | 16.1150i | 0.402774 | + | 1.23961i | ||||
\(170\) | 10.2812 | − | 7.46969i | 0.788528 | − | 0.572899i | ||||
\(171\) | −3.23607 | + | 2.35114i | −0.247468 | + | 0.179796i | ||||
\(172\) | −13.5000 | − | 41.5487i | −1.02937 | − | 3.16806i | ||||
\(173\) | 3.89919 | − | 12.0005i | 0.296450 | − | 0.912378i | −0.686281 | − | 0.727337i | \(-0.740758\pi\) |
0.982731 | − | 0.185042i | \(-0.0592421\pi\) | |||||||
\(174\) | 6.35410 | + | 4.61653i | 0.481703 | + | 0.349978i | ||||
\(175\) | −2.38197 | −0.180060 | ||||||||
\(176\) | 32.6074 | + | 2.21238i | 2.45787 | + | 0.166765i | ||||
\(177\) | −12.6180 | −0.948430 | ||||||||
\(178\) | −5.66312 | − | 4.11450i | −0.424469 | − | 0.308395i | ||||
\(179\) | 3.87132 | − | 11.9147i | 0.289356 | − | 0.890547i | −0.695703 | − | 0.718330i | \(-0.744907\pi\) |
0.985059 | − | 0.172217i | \(-0.0550931\pi\) | |||||||
\(180\) | 2.42705 | + | 7.46969i | 0.180902 | + | 0.556758i | ||||
\(181\) | −6.28115 | + | 4.56352i | −0.466874 | + | 0.339204i | −0.796222 | − | 0.605005i | \(-0.793171\pi\) |
0.329348 | + | 0.944209i | \(0.393171\pi\) | |||||||
\(182\) | −11.5902 | + | 8.42075i | −0.859121 | + | 0.624188i | ||||
\(183\) | 2.07295 | + | 6.37988i | 0.153237 | + | 0.471614i | ||||
\(184\) | −16.7082 | + | 51.4226i | −1.23175 | + | 3.79092i | ||||
\(185\) | 11.0902 | + | 8.05748i | 0.815366 | + | 0.592398i | ||||
\(186\) | −0.618034 | −0.0453165 | ||||||||
\(187\) | −9.92705 | − | 0.673542i | −0.725938 | − | 0.0492543i | ||||
\(188\) | 48.9787 | 3.57214 | ||||||||
\(189\) | 0.809017 | + | 0.587785i | 0.0588473 | + | 0.0427551i | ||||
\(190\) | 5.23607 | − | 16.1150i | 0.379864 | − | 1.16910i | ||||
\(191\) | 5.10739 | + | 15.7189i | 0.369558 | + | 1.13738i | 0.947077 | + | 0.321005i | \(0.104021\pi\) |
−0.577520 | + | 0.816377i | \(0.695979\pi\) | |||||||
\(192\) | 7.04508 | − | 5.11855i | 0.508435 | − | 0.369400i | ||||
\(193\) | 17.3262 | − | 12.5882i | 1.24717 | − | 0.906122i | 0.249116 | − | 0.968474i | \(-0.419860\pi\) |
0.998054 | + | 0.0623518i | \(0.0198601\pi\) | |||||||
\(194\) | −13.2812 | − | 40.8752i | −0.953531 | − | 2.93467i | ||||
\(195\) | −2.73607 | + | 8.42075i | −0.195934 | + | 0.603023i | ||||
\(196\) | −3.92705 | − | 2.85317i | −0.280504 | − | 0.203798i | ||||
\(197\) | −2.18034 | −0.155343 | −0.0776714 | − | 0.996979i | \(-0.524748\pi\) | ||||
−0.0776714 | + | 0.996979i | \(0.524748\pi\) | |||||||
\(198\) | 3.23607 | − | 8.05748i | 0.229977 | − | 0.572620i | ||||
\(199\) | −11.5623 | −0.819630 | −0.409815 | − | 0.912169i | \(-0.634407\pi\) | ||||
−0.409815 | + | 0.912169i | \(0.634407\pi\) | |||||||
\(200\) | 14.3992 | + | 10.4616i | 1.01818 | + | 0.739748i | ||||
\(201\) | 1.14590 | − | 3.52671i | 0.0808254 | − | 0.248755i | ||||
\(202\) | 2.61803 | + | 8.05748i | 0.184204 | + | 0.566922i | ||||
\(203\) | −2.42705 | + | 1.76336i | −0.170346 | + | 0.123763i | ||||
\(204\) | −11.7812 | + | 8.55951i | −0.824846 | + | 0.599285i | ||||
\(205\) | −1.54508 | − | 4.75528i | −0.107913 | − | 0.332123i | ||||
\(206\) | 9.89919 | − | 30.4666i | 0.689709 | − | 2.12271i | ||||
\(207\) | 5.85410 | + | 4.25325i | 0.406888 | + | 0.295622i | ||||
\(208\) | 53.9230 | 3.73889 | ||||||||
\(209\) | −11.2361 | + | 7.05342i | −0.777215 | + | 0.487895i | ||||
\(210\) | −4.23607 | −0.292316 | ||||||||
\(211\) | −11.0451 | − | 8.02472i | −0.760375 | − | 0.552445i | 0.138650 | − | 0.990341i | \(-0.455724\pi\) |
−0.899025 | + | 0.437897i | \(0.855724\pi\) | |||||||
\(212\) | 6.13525 | − | 18.8824i | 0.421371 | − | 1.29685i | ||||
\(213\) | −3.78115 | − | 11.6372i | −0.259080 | − | 0.797367i | ||||
\(214\) | 33.7705 | − | 24.5357i | 2.30850 | − | 1.67723i | ||||
\(215\) | 11.7812 | − | 8.55951i | 0.803468 | − | 0.583754i | ||||
\(216\) | −2.30902 | − | 7.10642i | −0.157109 | − | 0.483531i | ||||
\(217\) | 0.0729490 | − | 0.224514i | 0.00495210 | − | 0.0152410i | ||||
\(218\) | −0.927051 | − | 0.673542i | −0.0627878 | − | 0.0456180i | ||||
\(219\) | 3.85410 | 0.260436 | ||||||||
\(220\) | 6.35410 | + | 25.2623i | 0.428393 | + | 1.70318i | ||||
\(221\) | −16.4164 | −1.10429 | ||||||||
\(222\) | −17.9443 | − | 13.0373i | −1.20434 | − | 0.875005i | ||||
\(223\) | −4.69098 | + | 14.4374i | −0.314131 | + | 0.966797i | 0.661979 | + | 0.749522i | \(0.269717\pi\) |
−0.976110 | + | 0.217275i | \(0.930283\pi\) | |||||||
\(224\) | 3.35410 | + | 10.3229i | 0.224105 | + | 0.689725i | ||||
\(225\) | 1.92705 | − | 1.40008i | 0.128470 | − | 0.0933390i | ||||
\(226\) | 3.11803 | − | 2.26538i | 0.207409 | − | 0.150691i | ||||
\(227\) | −0.190983 | − | 0.587785i | −0.0126760 | − | 0.0390127i | 0.944518 | − | 0.328458i | \(-0.106529\pi\) |
−0.957194 | + | 0.289446i | \(0.906529\pi\) | |||||||
\(228\) | −6.00000 | + | 18.4661i | −0.397360 | + | 1.22295i | ||||
\(229\) | −22.7082 | − | 16.4985i | −1.50060 | − | 1.09025i | −0.970142 | − | 0.242539i | \(-0.922020\pi\) |
−0.530459 | − | 0.847711i | \(-0.677980\pi\) | |||||||
\(230\) | −30.6525 | −2.02116 | ||||||||
\(231\) | 2.54508 | + | 2.12663i | 0.167454 | + | 0.139922i | ||||
\(232\) | 22.4164 | 1.47171 | ||||||||
\(233\) | −3.57295 | − | 2.59590i | −0.234072 | − | 0.170063i | 0.464566 | − | 0.885538i | \(-0.346210\pi\) |
−0.698638 | + | 0.715475i | \(0.746210\pi\) | |||||||
\(234\) | 4.42705 | − | 13.6251i | 0.289405 | − | 0.890698i | ||||
\(235\) | 5.04508 | + | 15.5272i | 0.329105 | + | 1.01288i | ||||
\(236\) | −49.5517 | + | 36.0014i | −3.22554 | + | 2.34349i | ||||
\(237\) | 5.54508 | − | 4.02874i | 0.360192 | − | 0.261695i | ||||
\(238\) | −2.42705 | − | 7.46969i | −0.157322 | − | 0.484188i | ||||
\(239\) | −0.118034 | + | 0.363271i | −0.00763498 | + | 0.0234981i | −0.954801 | − | 0.297244i | \(-0.903932\pi\) |
0.947166 | + | 0.320742i | \(0.103932\pi\) | |||||||
\(240\) | 12.8992 | + | 9.37181i | 0.832639 | + | 0.604948i | ||||
\(241\) | −0.708204 | −0.0456194 | −0.0228097 | − | 0.999740i | \(-0.507261\pi\) | ||||
−0.0228097 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(242\) | 12.5172 | − | 25.9358i | 0.804637 | − | 1.66722i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 26.3435 | + | 19.1396i | 1.68647 | + | 1.22529i | ||||
\(245\) | 0.500000 | − | 1.53884i | 0.0319438 | − | 0.0983130i | ||||
\(246\) | 2.50000 | + | 7.69421i | 0.159394 | + | 0.490565i | ||||
\(247\) | −17.7082 | + | 12.8658i | −1.12675 | + | 0.818629i | ||||
\(248\) | −1.42705 | + | 1.03681i | −0.0906178 | + | 0.0658377i | ||||
\(249\) | −0.909830 | − | 2.80017i | −0.0576581 | − | 0.177453i | ||||
\(250\) | −9.66312 | + | 29.7400i | −0.611149 | + | 1.88092i | ||||
\(251\) | 8.42705 | + | 6.12261i | 0.531911 | + | 0.386456i | 0.821072 | − | 0.570825i | \(-0.193376\pi\) |
−0.289161 | + | 0.957280i | \(0.593376\pi\) | |||||||
\(252\) | 4.85410 | 0.305780 | ||||||||
\(253\) | 18.4164 | + | 15.3884i | 1.15783 | + | 0.967462i | ||||
\(254\) | 17.1803 | 1.07799 | ||||||||
\(255\) | −3.92705 | − | 2.85317i | −0.245921 | − | 0.178672i | ||||
\(256\) | −4.50000 | + | 13.8496i | −0.281250 | + | 0.865598i | ||||
\(257\) | −0.145898 | − | 0.449028i | −0.00910087 | − | 0.0280096i | 0.946403 | − | 0.322988i | \(-0.104687\pi\) |
−0.955504 | + | 0.294979i | \(0.904687\pi\) | |||||||
\(258\) | −19.0623 | + | 13.8496i | −1.18677 | + | 0.862237i | ||||
\(259\) | 6.85410 | − | 4.97980i | 0.425893 | − | 0.309430i | ||||
\(260\) | 13.2812 | + | 40.8752i | 0.823662 | + | 2.53497i | ||||
\(261\) | 0.927051 | − | 2.85317i | 0.0573830 | − | 0.176607i | ||||
\(262\) | 2.80902 | + | 2.04087i | 0.173542 | + | 0.126085i | ||||
\(263\) | −15.0000 | −0.924940 | −0.462470 | − | 0.886635i | \(-0.653037\pi\) | ||||
−0.462470 | + | 0.886635i | \(0.653037\pi\) | |||||||
\(264\) | −6.04508 | − | 24.0337i | −0.372049 | − | 1.47917i | ||||
\(265\) | 6.61803 | 0.406543 | ||||||||
\(266\) | −8.47214 | − | 6.15537i | −0.519460 | − | 0.377410i | ||||
\(267\) | −0.826238 | + | 2.54290i | −0.0505649 | + | 0.155623i | ||||
\(268\) | −5.56231 | − | 17.1190i | −0.339772 | − | 1.04571i | ||||
\(269\) | 16.2812 | − | 11.8290i | 0.992679 | − | 0.721224i | 0.0321732 | − | 0.999482i | \(-0.489757\pi\) |
0.960506 | + | 0.278258i | \(0.0897572\pi\) | |||||||
\(270\) | 3.42705 | − | 2.48990i | 0.208564 | − | 0.151530i | ||||
\(271\) | −5.21885 | − | 16.0620i | −0.317022 | − | 0.975695i | −0.974914 | − | 0.222582i | \(-0.928552\pi\) |
0.657892 | − | 0.753113i | \(-0.271448\pi\) | |||||||
\(272\) | −9.13525 | + | 28.1154i | −0.553906 | + | 1.70475i | ||||
\(273\) | 4.42705 | + | 3.21644i | 0.267937 | + | 0.194668i | ||||
\(274\) | −27.4164 | −1.65629 | ||||||||
\(275\) | 6.69098 | − | 4.20025i | 0.403481 | − | 0.253285i | ||||
\(276\) | 35.1246 | 2.11425 | ||||||||
\(277\) | 10.0902 | + | 7.33094i | 0.606260 | + | 0.440473i | 0.848095 | − | 0.529844i | \(-0.177749\pi\) |
−0.241836 | + | 0.970317i | \(0.577749\pi\) | |||||||
\(278\) | −14.2082 | + | 43.7284i | −0.852151 | + | 2.62265i | ||||
\(279\) | 0.0729490 | + | 0.224514i | 0.00436734 | + | 0.0134413i | ||||
\(280\) | −9.78115 | + | 7.10642i | −0.584536 | + | 0.424690i | ||||
\(281\) | −9.30902 | + | 6.76340i | −0.555329 | + | 0.403470i | −0.829747 | − | 0.558140i | \(-0.811515\pi\) |
0.274417 | + | 0.961611i | \(0.411515\pi\) | |||||||
\(282\) | −8.16312 | − | 25.1235i | −0.486107 | − | 1.49608i | ||||
\(283\) | −6.39919 | + | 19.6947i | −0.380392 | + | 1.17073i | 0.559376 | + | 0.828914i | \(0.311041\pi\) |
−0.939768 | + | 0.341813i | \(0.888959\pi\) | |||||||
\(284\) | −48.0517 | − | 34.9116i | −2.85134 | − | 2.07162i | ||||
\(285\) | −6.47214 | −0.383376 | ||||||||
\(286\) | 17.7082 | − | 44.0916i | 1.04711 | − | 2.60719i | ||||
\(287\) | −3.09017 | −0.182407 | ||||||||
\(288\) | −8.78115 | − | 6.37988i | −0.517434 | − | 0.375938i | ||||
\(289\) | −2.47214 | + | 7.60845i | −0.145420 | + | 0.447556i | ||||
\(290\) | 3.92705 | + | 12.0862i | 0.230604 | + | 0.709727i | ||||
\(291\) | −13.2812 | + | 9.64932i | −0.778555 | + | 0.565653i | ||||
\(292\) | 15.1353 | − | 10.9964i | 0.885724 | − | 0.643516i | ||||
\(293\) | 0.201626 | + | 0.620541i | 0.0117791 | + | 0.0362524i | 0.956773 | − | 0.290835i | \(-0.0939330\pi\) |
−0.944994 | + | 0.327087i | \(0.893933\pi\) | |||||||
\(294\) | −0.809017 | + | 2.48990i | −0.0471828 | + | 0.145214i | ||||
\(295\) | −16.5172 | − | 12.0005i | −0.961670 | − | 0.698694i | ||||
\(296\) | −63.3050 | −3.67953 | ||||||||
\(297\) | −3.30902 | − | 0.224514i | −0.192009 | − | 0.0130276i | ||||
\(298\) | −53.2148 | −3.08265 | ||||||||
\(299\) | 32.0344 | + | 23.2744i | 1.85260 | + | 1.34599i | ||||
\(300\) | 3.57295 | − | 10.9964i | 0.206284 | − | 0.634878i | ||||
\(301\) | −2.78115 | − | 8.55951i | −0.160303 | − | 0.493362i | ||||
\(302\) | 22.4894 | − | 16.3395i | 1.29412 | − | 0.940231i | ||||
\(303\) | 2.61803 | − | 1.90211i | 0.150402 | − | 0.109274i | ||||
\(304\) | 12.1803 | + | 37.4872i | 0.698590 | + | 2.15004i | ||||
\(305\) | −3.35410 | + | 10.3229i | −0.192055 | + | 0.591085i | ||||
\(306\) | 6.35410 | + | 4.61653i | 0.363240 | + | 0.263909i | ||||
\(307\) | −6.70820 | −0.382857 | −0.191429 | − | 0.981507i | \(-0.561312\pi\) | ||||
−0.191429 | + | 0.981507i | \(0.561312\pi\) | |||||||
\(308\) | 16.0623 | + | 1.08981i | 0.915235 | + | 0.0620979i | ||||
\(309\) | −12.2361 | −0.696086 | ||||||||
\(310\) | −0.809017 | − | 0.587785i | −0.0459491 | − | 0.0333840i | ||||
\(311\) | 7.42705 | − | 22.8581i | 0.421149 | − | 1.29616i | −0.485484 | − | 0.874246i | \(-0.661357\pi\) |
0.906633 | − | 0.421919i | \(-0.138643\pi\) | |||||||
\(312\) | −12.6353 | − | 38.8873i | −0.715330 | − | 2.20156i | ||||
\(313\) | 1.07295 | − | 0.779543i | 0.0606467 | − | 0.0440624i | −0.557049 | − | 0.830480i | \(-0.688066\pi\) |
0.617696 | + | 0.786417i | \(0.288066\pi\) | |||||||
\(314\) | 34.1976 | − | 24.8460i | 1.92988 | − | 1.40214i | ||||
\(315\) | 0.500000 | + | 1.53884i | 0.0281718 | + | 0.0867039i | ||||
\(316\) | 10.2812 | − | 31.6421i | 0.578360 | − | 1.78001i | ||||
\(317\) | −11.5172 | − | 8.36775i | −0.646872 | − | 0.469980i | 0.215333 | − | 0.976541i | \(-0.430916\pi\) |
−0.862204 | + | 0.506561i | \(0.830916\pi\) | |||||||
\(318\) | −10.7082 | −0.600486 | ||||||||
\(319\) | 3.70820 | − | 9.23305i | 0.207620 | − | 0.516952i | ||||
\(320\) | 14.0902 | 0.787664 | ||||||||
\(321\) | −12.8992 | − | 9.37181i | −0.719962 | − | 0.523083i | ||||
\(322\) | −5.85410 | + | 18.0171i | −0.326236 | + | 1.00405i | ||||
\(323\) | −3.70820 | − | 11.4127i | −0.206330 | − | 0.635018i | ||||
\(324\) | −3.92705 | + | 2.85317i | −0.218169 | + | 0.158509i | ||||
\(325\) | 10.5451 | − | 7.66145i | 0.584936 | − | 0.424981i | ||||
\(326\) | 9.82624 | + | 30.2421i | 0.544225 | + | 1.67495i | ||||
\(327\) | −0.135255 | + | 0.416272i | −0.00747961 | + | 0.0230199i | ||||
\(328\) | 18.6803 | + | 13.5721i | 1.03145 | + | 0.749392i | ||||
\(329\) | 10.0902 | 0.556289 | ||||||||
\(330\) | 11.8992 | − | 7.46969i | 0.655029 | − | 0.411193i | ||||
\(331\) | 31.5410 | 1.73365 | 0.866826 | − | 0.498611i | \(-0.166157\pi\) | ||||
0.866826 | + | 0.498611i | \(0.166157\pi\) | |||||||
\(332\) | −11.5623 | − | 8.40051i | −0.634564 | − | 0.461038i | ||||
\(333\) | −2.61803 | + | 8.05748i | −0.143467 | + | 0.441547i | ||||
\(334\) | 12.2082 | + | 37.5730i | 0.668003 | + | 2.05590i | ||||
\(335\) | 4.85410 | − | 3.52671i | 0.265208 | − | 0.192685i | ||||
\(336\) | 7.97214 | − | 5.79210i | 0.434916 | − | 0.315985i | ||||
\(337\) | −0.0729490 | − | 0.224514i | −0.00397379 | − | 0.0122301i | 0.949050 | − | 0.315126i | \(-0.102047\pi\) |
−0.953024 | + | 0.302896i | \(0.902047\pi\) | |||||||
\(338\) | 13.7082 | − | 42.1895i | 0.745628 | − | 2.29481i | ||||
\(339\) | −1.19098 | − | 0.865300i | −0.0646853 | − | 0.0469966i | ||||
\(340\) | −23.5623 | −1.27785 | ||||||||
\(341\) | 0.190983 | + | 0.759299i | 0.0103423 | + | 0.0411183i | ||||
\(342\) | 10.4721 | 0.566268 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | −20.7812 | + | 63.9578i | −1.12044 | + | 3.44837i | ||||
\(345\) | 3.61803 | + | 11.1352i | 0.194788 | + | 0.599497i | ||||
\(346\) | −26.7254 | + | 19.4172i | −1.43677 | + | 1.04387i | ||||
\(347\) | 19.3262 | − | 14.0413i | 1.03749 | − | 0.753778i | 0.0676934 | − | 0.997706i | \(-0.478436\pi\) |
0.969793 | + | 0.243928i | \(0.0784360\pi\) | |||||||
\(348\) | −4.50000 | − | 13.8496i | −0.241225 | − | 0.742415i | ||||
\(349\) | 0.791796 | − | 2.43690i | 0.0423839 | − | 0.130444i | −0.927626 | − | 0.373512i | \(-0.878154\pi\) |
0.970009 | + | 0.243067i | \(0.0781536\pi\) | |||||||
\(350\) | 5.04508 | + | 3.66547i | 0.269671 | + | 0.195928i | ||||
\(351\) | −5.47214 | −0.292081 | ||||||||
\(352\) | −27.6246 | − | 23.0826i | −1.47240 | − | 1.23031i | ||||
\(353\) | 24.7082 | 1.31509 | 0.657543 | − | 0.753417i | \(-0.271596\pi\) | ||||
0.657543 | + | 0.753417i | \(0.271596\pi\) | |||||||
\(354\) | 26.7254 | + | 19.4172i | 1.42044 | + | 1.03201i | ||||
\(355\) | 6.11803 | − | 18.8294i | 0.324712 | − | 0.999359i | ||||
\(356\) | 4.01064 | + | 12.3435i | 0.212564 | + | 0.654204i | ||||
\(357\) | −2.42705 | + | 1.76336i | −0.128453 | + | 0.0933267i | ||||
\(358\) | −26.5344 | + | 19.2784i | −1.40239 | + | 1.01890i | ||||
\(359\) | 4.93769 | + | 15.1967i | 0.260602 | + | 0.802049i | 0.992674 | + | 0.120822i | \(0.0385532\pi\) |
−0.732073 | + | 0.681227i | \(0.761447\pi\) | |||||||
\(360\) | 3.73607 | − | 11.4984i | 0.196908 | − | 0.606021i | ||||
\(361\) | 2.42705 | + | 1.76336i | 0.127740 | + | 0.0928082i | ||||
\(362\) | 20.3262 | 1.06832 | ||||||||
\(363\) | −10.8992 | − | 1.48584i | −0.572059 | − | 0.0779864i | ||||
\(364\) | 26.5623 | 1.39224 | ||||||||
\(365\) | 5.04508 | + | 3.66547i | 0.264072 | + | 0.191859i | ||||
\(366\) | 5.42705 | − | 16.7027i | 0.283676 | − | 0.873066i | ||||
\(367\) | −7.63525 | − | 23.4989i | −0.398557 | − | 1.22663i | −0.926157 | − | 0.377139i | \(-0.876908\pi\) |
0.527599 | − | 0.849493i | \(-0.323092\pi\) | |||||||
\(368\) | 57.6869 | − | 41.9120i | 3.00714 | − | 2.18481i | ||||
\(369\) | 2.50000 | − | 1.81636i | 0.130145 | − | 0.0945557i | ||||
\(370\) | −11.0902 | − | 34.1320i | −0.576550 | − | 1.77444i | ||||
\(371\) | 1.26393 | − | 3.88998i | 0.0656201 | − | 0.201958i | ||||
\(372\) | 0.927051 | + | 0.673542i | 0.0480654 | + | 0.0349215i | ||||
\(373\) | −34.1803 | −1.76979 | −0.884895 | − | 0.465790i | \(-0.845770\pi\) | ||||
−0.884895 | + | 0.465790i | \(0.845770\pi\) | |||||||
\(374\) | 19.9894 | + | 16.7027i | 1.03363 | + | 0.863678i | ||||
\(375\) | 11.9443 | 0.616800 | ||||||||
\(376\) | −60.9959 | − | 44.3161i | −3.14563 | − | 2.28543i | ||||
\(377\) | 5.07295 | − | 15.6129i | 0.261270 | − | 0.804107i | ||||
\(378\) | −0.809017 | − | 2.48990i | −0.0416113 | − | 0.128067i | ||||
\(379\) | 9.54508 | − | 6.93491i | 0.490298 | − | 0.356222i | −0.315001 | − | 0.949091i | \(-0.602005\pi\) |
0.805299 | + | 0.592869i | \(0.202005\pi\) | |||||||
\(380\) | −25.4164 | + | 18.4661i | −1.30383 | + | 0.947291i | ||||
\(381\) | −2.02786 | − | 6.24112i | −0.103891 | − | 0.319742i | ||||
\(382\) | 13.3713 | − | 41.1527i | 0.684136 | − | 2.10556i | ||||
\(383\) | 5.07295 | + | 3.68571i | 0.259216 | + | 0.188331i | 0.709801 | − | 0.704402i | \(-0.248785\pi\) |
−0.450586 | + | 0.892733i | \(0.648785\pi\) | |||||||
\(384\) | −1.09017 | −0.0556325 | ||||||||
\(385\) | 1.30902 | + | 5.20431i | 0.0667137 | + | 0.265236i | ||||
\(386\) | −56.0689 | −2.85383 | ||||||||
\(387\) | 7.28115 | + | 5.29007i | 0.370122 | + | 0.268909i | ||||
\(388\) | −24.6246 | + | 75.7868i | −1.25013 | + | 3.84749i | ||||
\(389\) | −8.67376 | − | 26.6951i | −0.439777 | − | 1.35350i | −0.888111 | − | 0.459629i | \(-0.847982\pi\) |
0.448334 | − | 0.893866i | \(-0.352018\pi\) | |||||||
\(390\) | 18.7533 | − | 13.6251i | 0.949610 | − | 0.689932i | ||||
\(391\) | −17.5623 | + | 12.7598i | −0.888164 | + | 0.645289i | ||||
\(392\) | 2.30902 | + | 7.10642i | 0.116623 | + | 0.358929i | ||||
\(393\) | 0.409830 | − | 1.26133i | 0.0206732 | − | 0.0636255i | ||||
\(394\) | 4.61803 | + | 3.35520i | 0.232653 | + | 0.169032i | ||||
\(395\) | 11.0902 | 0.558007 | ||||||||
\(396\) | −13.6353 | + | 8.55951i | −0.685197 | + | 0.430131i | ||||
\(397\) | 18.2705 | 0.916971 | 0.458485 | − | 0.888702i | \(-0.348392\pi\) | ||||
0.458485 | + | 0.888702i | \(0.348392\pi\) | |||||||
\(398\) | 24.4894 | + | 17.7926i | 1.22754 | + | 0.891860i | ||||
\(399\) | −1.23607 | + | 3.80423i | −0.0618808 | + | 0.190450i | ||||
\(400\) | −7.25329 | − | 22.3233i | −0.362664 | − | 1.11617i | ||||
\(401\) | −2.64590 | + | 1.92236i | −0.132130 | + | 0.0959979i | −0.651887 | − | 0.758316i | \(-0.726022\pi\) |
0.519757 | + | 0.854314i | \(0.326022\pi\) | |||||||
\(402\) | −7.85410 | + | 5.70634i | −0.391727 | + | 0.284606i | ||||
\(403\) | 0.399187 | + | 1.22857i | 0.0198849 | + | 0.0611995i | ||||
\(404\) | 4.85410 | − | 14.9394i | 0.241501 | − | 0.743262i | ||||
\(405\) | −1.30902 | − | 0.951057i | −0.0650456 | − | 0.0472584i | ||||
\(406\) | 7.85410 | 0.389793 | ||||||||
\(407\) | −10.4721 | + | 26.0746i | −0.519085 | + | 1.29247i | ||||
\(408\) | 22.4164 | 1.10978 | ||||||||
\(409\) | −7.78115 | − | 5.65334i | −0.384753 | − | 0.279540i | 0.378549 | − | 0.925581i | \(-0.376423\pi\) |
−0.763302 | + | 0.646042i | \(0.776423\pi\) | |||||||
\(410\) | −4.04508 | + | 12.4495i | −0.199773 | + | 0.614837i | ||||
\(411\) | 3.23607 | + | 9.95959i | 0.159623 | + | 0.491271i | ||||
\(412\) | −48.0517 | + | 34.9116i | −2.36734 | + | 1.71997i | ||||
\(413\) | −10.2082 | + | 7.41669i | −0.502313 | + | 0.364952i | ||||
\(414\) | −5.85410 | − | 18.0171i | −0.287713 | − | 0.885491i | ||||
\(415\) | 1.47214 | − | 4.53077i | 0.0722643 | − | 0.222407i | ||||
\(416\) | −48.0517 | − | 34.9116i | −2.35593 | − | 1.71168i | ||||
\(417\) | 17.5623 | 0.860030 | ||||||||
\(418\) | 34.6525 | + | 2.35114i | 1.69491 | + | 0.114998i | ||||
\(419\) | −13.3262 | −0.651029 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(420\) | 6.35410 | + | 4.61653i | 0.310048 | + | 0.225263i | ||||
\(421\) | 1.42705 | − | 4.39201i | 0.0695502 | − | 0.214054i | −0.910240 | − | 0.414081i | \(-0.864103\pi\) |
0.979790 | + | 0.200027i | \(0.0641031\pi\) | |||||||
\(422\) | 11.0451 | + | 33.9933i | 0.537666 | + | 1.65477i | ||||
\(423\) | −8.16312 | + | 5.93085i | −0.396904 | + | 0.288368i | ||||
\(424\) | −24.7254 | + | 17.9641i | −1.20077 | + | 0.872412i | ||||
\(425\) | 2.20820 | + | 6.79615i | 0.107114 | + | 0.329662i | ||||
\(426\) | −9.89919 | + | 30.4666i | −0.479617 | + | 1.47611i | ||||
\(427\) | 5.42705 | + | 3.94298i | 0.262633 | + | 0.190814i | ||||
\(428\) | −77.3951 | −3.74103 | ||||||||
\(429\) | −18.1074 | − | 1.22857i | −0.874233 | − | 0.0593160i | ||||
\(430\) | −38.1246 | −1.83853 | ||||||||
\(431\) | −15.8713 | − | 11.5312i | −0.764495 | − | 0.555438i | 0.135791 | − | 0.990738i | \(-0.456642\pi\) |
−0.900286 | + | 0.435300i | \(0.856642\pi\) | |||||||
\(432\) | −3.04508 | + | 9.37181i | −0.146507 | + | 0.450901i | ||||
\(433\) | 5.85410 | + | 18.0171i | 0.281330 | + | 0.865845i | 0.987475 | + | 0.157778i | \(0.0504329\pi\) |
−0.706144 | + | 0.708068i | \(0.749567\pi\) | |||||||
\(434\) | −0.500000 | + | 0.363271i | −0.0240008 | + | 0.0174376i | ||||
\(435\) | 3.92705 | − | 2.85317i | 0.188288 | − | 0.136799i | ||||
\(436\) | 0.656541 | + | 2.02063i | 0.0314426 | + | 0.0967704i | ||||
\(437\) | −8.94427 | + | 27.5276i | −0.427863 | + | 1.31683i | ||||
\(438\) | −8.16312 | − | 5.93085i | −0.390049 | − | 0.283387i | ||||
\(439\) | 29.8328 | 1.42384 | 0.711921 | − | 0.702259i | \(-0.247825\pi\) | ||||
0.711921 | + | 0.702259i | \(0.247825\pi\) | |||||||
\(440\) | 14.9443 | − | 37.2097i | 0.712440 | − | 1.77390i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 34.7705 | + | 25.2623i | 1.65386 | + | 1.20160i | ||||
\(443\) | 2.27051 | − | 6.98791i | 0.107875 | − | 0.332006i | −0.882519 | − | 0.470276i | \(-0.844154\pi\) |
0.990395 | + | 0.138270i | \(0.0441543\pi\) | |||||||
\(444\) | 12.7082 | + | 39.1118i | 0.603105 | + | 1.85617i | ||||
\(445\) | −3.50000 | + | 2.54290i | −0.165916 | + | 0.120545i | ||||
\(446\) | 32.1525 | − | 23.3601i | 1.52246 | − | 1.10613i | ||||
\(447\) | 6.28115 | + | 19.3314i | 0.297088 | + | 0.914344i | ||||
\(448\) | 2.69098 | − | 8.28199i | 0.127137 | − | 0.391287i | ||||
\(449\) | −10.8992 | − | 7.91872i | −0.514364 | − | 0.373708i | 0.300112 | − | 0.953904i | \(-0.402976\pi\) |
−0.814477 | + | 0.580196i | \(0.802976\pi\) | |||||||
\(450\) | −6.23607 | −0.293971 | ||||||||
\(451\) | 8.68034 | − | 5.44907i | 0.408741 | − | 0.256587i | ||||
\(452\) | −7.14590 | −0.336115 | ||||||||
\(453\) | −8.59017 | − | 6.24112i | −0.403601 | − | 0.293234i | ||||
\(454\) | −0.500000 | + | 1.53884i | −0.0234662 | + | 0.0722214i | ||||
\(455\) | 2.73607 | + | 8.42075i | 0.128269 | + | 0.394771i | ||||
\(456\) | 24.1803 | − | 17.5680i | 1.13235 | − | 0.822699i | ||||
\(457\) | 9.01722 | − | 6.55139i | 0.421808 | − | 0.306461i | −0.356557 | − | 0.934274i | \(-0.616049\pi\) |
0.778365 | + | 0.627812i | \(0.216049\pi\) | |||||||
\(458\) | 22.7082 | + | 69.8887i | 1.06108 | + | 3.26568i | ||||
\(459\) | 0.927051 | − | 2.85317i | 0.0432710 | − | 0.133175i | ||||
\(460\) | 45.9787 | + | 33.4055i | 2.14377 | + | 1.55754i | ||||
\(461\) | 4.41641 | 0.205693 | 0.102846 | − | 0.994697i | \(-0.467205\pi\) | ||||
0.102846 | + | 0.994697i | \(0.467205\pi\) | |||||||
\(462\) | −2.11803 | − | 8.42075i | −0.0985399 | − | 0.391769i | ||||
\(463\) | 30.6869 | 1.42614 | 0.713071 | − | 0.701092i | \(-0.247304\pi\) | ||||
0.713071 | + | 0.701092i | \(0.247304\pi\) | |||||||
\(464\) | −23.9164 | − | 17.3763i | −1.11029 | − | 0.806674i | ||||
\(465\) | −0.118034 | + | 0.363271i | −0.00547370 | + | 0.0168463i | ||||
\(466\) | 3.57295 | + | 10.9964i | 0.165514 | + | 0.509399i | ||||
\(467\) | −22.3713 | + | 16.2537i | −1.03522 | + | 0.752132i | −0.969347 | − | 0.245696i | \(-0.920984\pi\) |
−0.0658743 | + | 0.997828i | \(0.520984\pi\) | |||||||
\(468\) | −21.4894 | + | 15.6129i | −0.993346 | + | 0.721708i | ||||
\(469\) | −1.14590 | − | 3.52671i | −0.0529127 | − | 0.162848i | ||||
\(470\) | 13.2082 | − | 40.6507i | 0.609249 | − | 1.87508i | ||||
\(471\) | −13.0623 | − | 9.49032i | −0.601879 | − | 0.437291i | ||||
\(472\) | 94.2837 | 4.33976 | ||||||||
\(473\) | 22.9058 | + | 19.1396i | 1.05321 | + | 0.880042i | ||||
\(474\) | −17.9443 | −0.824208 | ||||||||
\(475\) | 7.70820 | + | 5.60034i | 0.353677 | + | 0.256961i | ||||
\(476\) | −4.50000 | + | 13.8496i | −0.206257 | + | 0.634794i | ||||
\(477\) | 1.26393 | + | 3.88998i | 0.0578715 | + | 0.178110i | ||||
\(478\) | 0.809017 | − | 0.587785i | 0.0370036 | − | 0.0268847i | ||||
\(479\) | −3.78115 | + | 2.74717i | −0.172765 | + | 0.125521i | −0.670808 | − | 0.741631i | \(-0.734052\pi\) |
0.498042 | + | 0.867153i | \(0.334052\pi\) | |||||||
\(480\) | −5.42705 | − | 16.7027i | −0.247710 | − | 0.762373i | ||||
\(481\) | −14.3262 | + | 44.0916i | −0.653220 | + | 2.01041i | ||||
\(482\) | 1.50000 | + | 1.08981i | 0.0683231 | + | 0.0496397i | ||||
\(483\) | 7.23607 | 0.329252 | ||||||||
\(484\) | −47.0410 | + | 25.2623i | −2.13823 | + | 1.14828i | ||||
\(485\) | −26.5623 | −1.20613 | ||||||||
\(486\) | 2.11803 | + | 1.53884i | 0.0960760 | + | 0.0698033i | ||||
\(487\) | −6.57295 | + | 20.2295i | −0.297849 | + | 0.916684i | 0.684401 | + | 0.729106i | \(0.260064\pi\) |
−0.982250 | + | 0.187578i | \(0.939936\pi\) | |||||||
\(488\) | −15.4894 | − | 47.6713i | −0.701170 | − | 2.15798i | ||||
\(489\) | 9.82624 | − | 7.13918i | 0.444358 | − | 0.322845i | ||||
\(490\) | −3.42705 | + | 2.48990i | −0.154818 | + | 0.112482i | ||||
\(491\) | −12.5623 | − | 38.6628i | −0.566929 | − | 1.74483i | −0.662150 | − | 0.749372i | \(-0.730356\pi\) |
0.0952207 | − | 0.995456i | \(-0.469644\pi\) | |||||||
\(492\) | 4.63525 | − | 14.2658i | 0.208973 | − | 0.643154i | ||||
\(493\) | 7.28115 | + | 5.29007i | 0.327927 | + | 0.238253i | ||||
\(494\) | 57.3050 | 2.57827 | ||||||||
\(495\) | −4.11803 | − | 3.44095i | −0.185092 | − | 0.154659i | ||||
\(496\) | 2.32624 | 0.104451 | ||||||||
\(497\) | −9.89919 | − | 7.19218i | −0.444039 | − | 0.322613i | ||||
\(498\) | −2.38197 | + | 7.33094i | −0.106738 | + | 0.328507i | ||||
\(499\) | −1.54508 | − | 4.75528i | −0.0691675 | − | 0.212876i | 0.910498 | − | 0.413514i | \(-0.135699\pi\) |
−0.979665 | + | 0.200638i | \(0.935699\pi\) | |||||||
\(500\) | 46.9058 | − | 34.0790i | 2.09769 | − | 1.52406i | ||||
\(501\) | 12.2082 | − | 8.86978i | 0.545422 | − | 0.396273i | ||||
\(502\) | −8.42705 | − | 25.9358i | −0.376118 | − | 1.15757i | ||||
\(503\) | 7.34346 | − | 22.6008i | 0.327429 | − | 1.00772i | −0.642904 | − | 0.765947i | \(-0.722270\pi\) |
0.970332 | − | 0.241775i | \(-0.0777295\pi\) | |||||||
\(504\) | −6.04508 | − | 4.39201i | −0.269269 | − | 0.195636i | ||||
\(505\) | 5.23607 | 0.233002 | ||||||||
\(506\) | −15.3262 | − | 60.9331i | −0.681334 | − | 2.70881i | ||||
\(507\) | −16.9443 | −0.752522 | ||||||||
\(508\) | −25.7705 | − | 18.7234i | −1.14338 | − | 0.830715i | ||||
\(509\) | 1.48936 | − | 4.58377i | 0.0660146 | − | 0.203172i | −0.912608 | − | 0.408835i | \(-0.865935\pi\) |
0.978623 | + | 0.205663i | \(0.0659351\pi\) | |||||||
\(510\) | 3.92705 | + | 12.0862i | 0.173893 | + | 0.535187i | ||||
\(511\) | 3.11803 | − | 2.26538i | 0.137934 | − | 0.100215i | ||||
\(512\) | 32.6074 | − | 23.6907i | 1.44106 | − | 1.04699i | ||||
\(513\) | −1.23607 | − | 3.80423i | −0.0545737 | − | 0.167961i | ||||
\(514\) | −0.381966 | + | 1.17557i | −0.0168478 | + | 0.0518522i | ||||
\(515\) | −16.0172 | − | 11.6372i | −0.705803 | − | 0.512796i | ||||
\(516\) | 43.6869 | 1.92321 | ||||||||
\(517\) | −28.3435 | + | 17.7926i | −1.24654 | + | 0.782516i | ||||
\(518\) | −22.1803 | −0.974548 | ||||||||
\(519\) | 10.2082 | + | 7.41669i | 0.448090 | + | 0.325557i | ||||
\(520\) | 20.4443 | − | 62.9210i | 0.896541 | − | 2.75927i | ||||
\(521\) | −7.83688 | − | 24.1194i | −0.343340 | − | 1.05669i | −0.962466 | − | 0.271401i | \(-0.912513\pi\) |
0.619126 | − | 0.785291i | \(-0.287487\pi\) | |||||||
\(522\) | −6.35410 | + | 4.61653i | −0.278111 | + | 0.202060i | ||||
\(523\) | −6.13525 | + | 4.45752i | −0.268276 | + | 0.194914i | −0.713788 | − | 0.700362i | \(-0.753022\pi\) |
0.445512 | + | 0.895276i | \(0.353022\pi\) | |||||||
\(524\) | −1.98936 | − | 6.12261i | −0.0869055 | − | 0.267468i | ||||
\(525\) | 0.736068 | − | 2.26538i | 0.0321246 | − | 0.0988695i | ||||
\(526\) | 31.7705 | + | 23.0826i | 1.38526 | + | 1.00645i | ||||
\(527\) | −0.708204 | −0.0308498 | ||||||||
\(528\) | −12.1803 | + | 30.3278i | −0.530081 | + | 1.31985i | ||||
\(529\) | 29.3607 | 1.27655 | ||||||||
\(530\) | −14.0172 | − | 10.1841i | −0.608869 | − | 0.442369i | ||||
\(531\) | 3.89919 | − | 12.0005i | 0.169210 | − | 0.520776i | ||||
\(532\) | 6.00000 | + | 18.4661i | 0.260133 | + | 0.800607i | ||||
\(533\) | 13.6803 | − | 9.93935i | 0.592561 | − | 0.430521i | ||||
\(534\) | 5.66312 | − | 4.11450i | 0.245067 | − | 0.178052i | ||||
\(535\) | −7.97214 | − | 24.5357i | −0.344665 | − | 1.06077i | ||||
\(536\) | −8.56231 | + | 26.3521i | −0.369835 | + | 1.13824i | ||||
\(537\) | 10.1353 | + | 7.36369i | 0.437369 | + | 0.317767i | ||||
\(538\) | −52.6869 | −2.27149 | ||||||||
\(539\) | 3.30902 | + | 0.224514i | 0.142529 | + | 0.00967050i | ||||
\(540\) | −7.85410 | −0.337987 | ||||||||
\(541\) | −13.3090 | − | 9.66957i | −0.572199 | − | 0.415727i | 0.263704 | − | 0.964604i | \(-0.415056\pi\) |
−0.835903 | + | 0.548876i | \(0.815056\pi\) | |||||||
\(542\) | −13.6631 | + | 42.0508i | −0.586881 | + | 1.80623i | ||||
\(543\) | −2.39919 | − | 7.38394i | −0.102959 | − | 0.316875i | ||||
\(544\) | 26.3435 | − | 19.1396i | 1.12947 | − | 0.820605i | ||||
\(545\) | −0.572949 | + | 0.416272i | −0.0245424 | + | 0.0178311i | ||||
\(546\) | −4.42705 | − | 13.6251i | −0.189460 | − | 0.583099i | ||||
\(547\) | 6.98278 | − | 21.4908i | 0.298562 | − | 0.918880i | −0.683440 | − | 0.730007i | \(-0.739517\pi\) |
0.982002 | − | 0.188872i | \(-0.0604833\pi\) | |||||||
\(548\) | 41.1246 | + | 29.8788i | 1.75676 | + | 1.27636i | ||||
\(549\) | −6.70820 | −0.286299 | ||||||||
\(550\) | −20.6353 | − | 1.40008i | −0.879890 | − | 0.0596998i | ||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | −43.7426 | − | 31.7809i | −1.86181 | − | 1.35268i | ||||
\(553\) | 2.11803 | − | 6.51864i | 0.0900680 | − | 0.277201i | ||||
\(554\) | −10.0902 | − | 31.0543i | −0.428690 | − | 1.31937i | ||||
\(555\) | −11.0902 | + | 8.05748i | −0.470751 | + | 0.342021i | ||||
\(556\) | 68.9681 | − | 50.1082i | 2.92490 | − | 2.12506i | ||||
\(557\) | 2.52786 | + | 7.77997i | 0.107109 | + | 0.329648i | 0.990220 | − | 0.139517i | \(-0.0445550\pi\) |
−0.883111 | + | 0.469165i | \(0.844555\pi\) | |||||||
\(558\) | 0.190983 | − | 0.587785i | 0.00808496 | − | 0.0248829i | ||||
\(559\) | 39.8435 | + | 28.9480i | 1.68520 | + | 1.22437i | ||||
\(560\) | 15.9443 | 0.673768 | ||||||||
\(561\) | 3.70820 | − | 9.23305i | 0.156560 | − | 0.389820i | ||||
\(562\) | 30.1246 | 1.27073 | ||||||||
\(563\) | 14.8090 | + | 10.7594i | 0.624126 | + | 0.453454i | 0.854360 | − | 0.519681i | \(-0.173949\pi\) |
−0.230235 | + | 0.973135i | \(0.573949\pi\) | |||||||
\(564\) | −15.1353 | + | 46.5815i | −0.637309 | + | 1.96144i | ||||
\(565\) | −0.736068 | − | 2.26538i | −0.0309666 | − | 0.0953054i | ||||
\(566\) | 43.8607 | − | 31.8666i | 1.84360 | − | 1.33946i | ||||
\(567\) | −0.809017 | + | 0.587785i | −0.0339755 | + | 0.0246847i | ||||
\(568\) | 28.2533 | + | 86.9547i | 1.18548 | + | 3.64854i | ||||
\(569\) | −3.54508 | + | 10.9106i | −0.148618 | + | 0.457398i | −0.997458 | − | 0.0712504i | \(-0.977301\pi\) |
0.848841 | + | 0.528649i | \(0.177301\pi\) | |||||||
\(570\) | 13.7082 | + | 9.95959i | 0.574173 | + | 0.417161i | ||||
\(571\) | −22.8885 | −0.957856 | −0.478928 | − | 0.877854i | \(-0.658974\pi\) | ||||
−0.478928 | + | 0.877854i | \(0.658974\pi\) | |||||||
\(572\) | −74.6140 | + | 46.8388i | −3.11977 | + | 1.95843i | ||||
\(573\) | −16.5279 | −0.690461 | ||||||||
\(574\) | 6.54508 | + | 4.75528i | 0.273187 | + | 0.198482i | ||||
\(575\) | 5.32624 | − | 16.3925i | 0.222119 | − | 0.683613i | ||||
\(576\) | 2.69098 | + | 8.28199i | 0.112124 | + | 0.345083i | ||||
\(577\) | 20.1074 | − | 14.6089i | 0.837082 | − | 0.608175i | −0.0844723 | − | 0.996426i | \(-0.526920\pi\) |
0.921554 | + | 0.388250i | \(0.126920\pi\) | |||||||
\(578\) | 16.9443 | − | 12.3107i | 0.704789 | − | 0.512059i | ||||
\(579\) | 6.61803 | + | 20.3682i | 0.275036 | + | 0.846474i | ||||
\(580\) | 7.28115 | − | 22.4091i | 0.302333 | − | 0.930487i | ||||
\(581\) | −2.38197 | − | 1.73060i | −0.0988206 | − | 0.0717974i | ||||
\(582\) | 42.9787 | 1.78153 | ||||||||
\(583\) | 3.30902 | + | 13.1558i | 0.137045 | + | 0.544857i | ||||
\(584\) | −28.7984 | −1.19169 | ||||||||
\(585\) | −7.16312 | − | 5.20431i | −0.296159 | − | 0.215172i | ||||
\(586\) | 0.527864 | − | 1.62460i | 0.0218059 | − | 0.0671115i | ||||
\(587\) | 1.85410 | + | 5.70634i | 0.0765270 | + | 0.235526i | 0.982001 | − | 0.188876i | \(-0.0604844\pi\) |
−0.905474 | + | 0.424402i | \(0.860484\pi\) | |||||||
\(588\) | 3.92705 | − | 2.85317i | 0.161949 | − | 0.117663i | ||||
\(589\) | −0.763932 | + | 0.555029i | −0.0314773 | + | 0.0228696i | ||||
\(590\) | 16.5172 | + | 50.8348i | 0.680003 | + | 2.09283i | ||||
\(591\) | 0.673762 | − | 2.07363i | 0.0277149 | − | 0.0852976i | ||||
\(592\) | 67.5410 | + | 49.0714i | 2.77592 | + | 2.01682i | ||||
\(593\) | −26.3607 | −1.08250 | −0.541252 | − | 0.840861i | \(-0.682049\pi\) | ||||
−0.541252 | + | 0.840861i | \(0.682049\pi\) | |||||||
\(594\) | 6.66312 | + | 5.56758i | 0.273391 | + | 0.228441i | ||||
\(595\) | −4.85410 | −0.198999 | ||||||||
\(596\) | 79.8222 | + | 57.9942i | 3.26964 | + | 2.37554i | ||||
\(597\) | 3.57295 | − | 10.9964i | 0.146231 | − | 0.450053i | ||||
\(598\) | −32.0344 | − | 98.5919i | −1.30999 | − | 4.03172i | ||||
\(599\) | −13.1074 | + | 9.52308i | −0.535553 | + | 0.389102i | −0.822431 | − | 0.568865i | \(-0.807383\pi\) |
0.286878 | + | 0.957967i | \(0.407383\pi\) | |||||||
\(600\) | −14.3992 | + | 10.4616i | −0.587844 | + | 0.427094i | ||||
\(601\) | 4.29180 | + | 13.2088i | 0.175066 | + | 0.538798i | 0.999636 | − | 0.0269615i | \(-0.00858315\pi\) |
−0.824570 | + | 0.565759i | \(0.808583\pi\) | |||||||
\(602\) | −7.28115 | + | 22.4091i | −0.296758 | + | 0.913326i | ||||
\(603\) | 3.00000 | + | 2.17963i | 0.122169 | + | 0.0887613i | ||||
\(604\) | −51.5410 | −2.09717 | ||||||||
\(605\) | −12.8541 | − | 12.3107i | −0.522594 | − | 0.500503i | ||||
\(606\) | −8.47214 | −0.344157 | ||||||||
\(607\) | −29.0066 | − | 21.0745i | −1.17734 | − | 0.855388i | −0.185471 | − | 0.982650i | \(-0.559381\pi\) |
−0.991869 | + | 0.127262i | \(0.959381\pi\) | |||||||
\(608\) | 13.4164 | − | 41.2915i | 0.544107 | − | 1.67459i | ||||
\(609\) | −0.927051 | − | 2.85317i | −0.0375660 | − | 0.115616i | ||||
\(610\) | 22.9894 | − | 16.7027i | 0.930812 | − | 0.676274i | ||||
\(611\) | −44.6697 | + | 32.4544i | −1.80714 | + | 1.31297i | ||||
\(612\) | −4.50000 | − | 13.8496i | −0.181902 | − | 0.559836i | ||||
\(613\) | 4.93769 | − | 15.1967i | 0.199432 | − | 0.613787i | −0.800465 | − | 0.599380i | \(-0.795414\pi\) |
0.999896 | − | 0.0144073i | \(-0.00458615\pi\) | |||||||
\(614\) | 14.2082 | + | 10.3229i | 0.573396 | + | 0.416597i | ||||
\(615\) | 5.00000 | 0.201619 | ||||||||
\(616\) | −19.0172 | − | 15.8904i | −0.766226 | − | 0.640244i | ||||
\(617\) | 13.7984 | 0.555502 | 0.277751 | − | 0.960653i | \(-0.410411\pi\) | ||||
0.277751 | + | 0.960653i | \(0.410411\pi\) | |||||||
\(618\) | 25.9164 | + | 18.8294i | 1.04251 | + | 0.757428i | ||||
\(619\) | 9.79837 | − | 30.1563i | 0.393830 | − | 1.21208i | −0.536039 | − | 0.844193i | \(-0.680080\pi\) |
0.929869 | − | 0.367891i | \(-0.119920\pi\) | |||||||
\(620\) | 0.572949 | + | 1.76336i | 0.0230102 | + | 0.0708181i | ||||
\(621\) | −5.85410 | + | 4.25325i | −0.234917 | + | 0.170677i | ||||
\(622\) | −50.9058 | + | 36.9852i | −2.04114 | + | 1.48297i | ||||
\(623\) | 0.826238 | + | 2.54290i | 0.0331025 | + | 0.101879i | ||||
\(624\) | −16.6631 | + | 51.2838i | −0.667059 | + | 2.05300i | ||||
\(625\) | 6.00000 | + | 4.35926i | 0.240000 | + | 0.174370i | ||||
\(626\) | −3.47214 | −0.138774 | ||||||||
\(627\) | −3.23607 | − | 12.8658i | −0.129236 | − | 0.513809i | ||||
\(628\) | −78.3738 | −3.12746 | ||||||||
\(629\) | −20.5623 | − | 14.9394i | −0.819873 | − | 0.595672i | ||||
\(630\) | 1.30902 | − | 4.02874i | 0.0521525 | − | 0.160509i | ||||
\(631\) | −7.30902 | − | 22.4948i | −0.290967 | − | 0.895505i | −0.984546 | − | 0.175125i | \(-0.943967\pi\) |
0.693579 | − | 0.720381i | \(-0.256033\pi\) | |||||||
\(632\) | −41.4336 | + | 30.1033i | −1.64814 | + | 1.19744i | ||||
\(633\) | 11.0451 | − | 8.02472i | 0.439003 | − | 0.318954i | ||||
\(634\) | 11.5172 | + | 35.4464i | 0.457407 | + | 1.40775i | ||||
\(635\) | 3.28115 | − | 10.0984i | 0.130209 | − | 0.400741i | ||||
\(636\) | 16.0623 | + | 11.6699i | 0.636912 | + | 0.462744i | ||||
\(637\) | 5.47214 | 0.216814 | ||||||||
\(638\) | −22.0623 | + | 13.8496i | −0.873455 | + | 0.548310i | ||||
\(639\) | 12.2361 | 0.484051 | ||||||||
\(640\) | −1.42705 | − | 1.03681i | −0.0564091 | − | 0.0409836i | ||||
\(641\) | −0.152476 | + | 0.469272i | −0.00602243 | + | 0.0185351i | −0.954023 | − | 0.299735i | \(-0.903102\pi\) |
0.948000 | + | 0.318270i | \(0.103102\pi\) | |||||||
\(642\) | 12.8992 | + | 39.6996i | 0.509090 | + | 1.56682i | ||||
\(643\) | 25.8885 | − | 18.8091i | 1.02094 | − | 0.741760i | 0.0544682 | − | 0.998516i | \(-0.482654\pi\) |
0.966476 | + | 0.256756i | \(0.0826536\pi\) | |||||||
\(644\) | 28.4164 | − | 20.6457i | 1.11976 | − | 0.813556i | ||||
\(645\) | 4.50000 | + | 13.8496i | 0.177187 | + | 0.545327i | ||||
\(646\) | −9.70820 | + | 29.8788i | −0.381964 | + | 1.17556i | ||||
\(647\) | 3.28115 | + | 2.38390i | 0.128995 | + | 0.0937207i | 0.650412 | − | 0.759582i | \(-0.274596\pi\) |
−0.521417 | + | 0.853302i | \(0.674596\pi\) | |||||||
\(648\) | 7.47214 | 0.293533 | ||||||||
\(649\) | 15.5967 | − | 38.8343i | 0.612226 | − | 1.52438i | ||||
\(650\) | −34.1246 | −1.33848 | ||||||||
\(651\) | 0.190983 | + | 0.138757i | 0.00748521 | + | 0.00543833i | ||||
\(652\) | 18.2188 | − | 56.0718i | 0.713505 | − | 2.19594i | ||||
\(653\) | 9.72542 | + | 29.9318i | 0.380585 | + | 1.17132i | 0.939633 | + | 0.342185i | \(0.111167\pi\) |
−0.559047 | + | 0.829136i | \(0.688833\pi\) | |||||||
\(654\) | 0.927051 | − | 0.673542i | 0.0362506 | − | 0.0263376i | ||||
\(655\) | 1.73607 | − | 1.26133i | 0.0678338 | − | 0.0492841i | ||||
\(656\) | −9.40983 | − | 28.9605i | −0.367392 | − | 1.13072i | ||||
\(657\) | −1.19098 | + | 3.66547i | −0.0464647 | + | 0.143004i | ||||
\(658\) | −21.3713 | − | 15.5272i | −0.833141 | − | 0.605312i | ||||
\(659\) | −8.12461 | −0.316490 | −0.158245 | − | 0.987400i | \(-0.550584\pi\) | ||||
−0.158245 | + | 0.987400i | \(0.550584\pi\) | |||||||
\(660\) | −25.9894 | − | 1.76336i | −1.01163 | − | 0.0686385i | ||||
\(661\) | −18.4164 | −0.716315 | −0.358158 | − | 0.933661i | \(-0.616595\pi\) | ||||
−0.358158 | + | 0.933661i | \(0.616595\pi\) | |||||||
\(662\) | −66.8050 | − | 48.5366i | −2.59645 | − | 1.88643i | ||||
\(663\) | 5.07295 | − | 15.6129i | 0.197017 | − | 0.606356i | ||||
\(664\) | 6.79837 | + | 20.9232i | 0.263828 | + | 0.811979i | ||||
\(665\) | −5.23607 | + | 3.80423i | −0.203046 | + | 0.147522i | ||||
\(666\) | 17.9443 | − | 13.0373i | 0.695326 | − | 0.505184i | ||||
\(667\) | −6.70820 | − | 20.6457i | −0.259743 | − | 0.799406i | ||||
\(668\) | 22.6353 | − | 69.6642i | 0.875784 | − | 2.69539i | ||||
\(669\) | −12.2812 | − | 8.92278i | −0.474817 | − | 0.344975i | ||||
\(670\) | −15.7082 | −0.606861 | ||||||||
\(671\) | −22.1976 | − | 1.50609i | −0.856927 | − | 0.0581418i | ||||
\(672\) | −10.8541 | −0.418706 | ||||||||
\(673\) | 8.42705 | + | 6.12261i | 0.324839 | + | 0.236009i | 0.738238 | − | 0.674541i | \(-0.235658\pi\) |
−0.413399 | + | 0.910550i | \(0.635658\pi\) | |||||||
\(674\) | −0.190983 | + | 0.587785i | −0.00735639 | + | 0.0226406i | ||||
\(675\) | 0.736068 | + | 2.26538i | 0.0283313 | + | 0.0871947i | ||||
\(676\) | −66.5410 | + | 48.3449i | −2.55927 | + | 1.85942i | ||||
\(677\) | −18.5344 | + | 13.4661i | −0.712336 | + | 0.517543i | −0.883927 | − | 0.467626i | \(-0.845110\pi\) |
0.171590 | + | 0.985168i | \(0.445110\pi\) | |||||||
\(678\) | 1.19098 | + | 3.66547i | 0.0457394 | + | 0.140771i | ||||
\(679\) | −5.07295 | + | 15.6129i | −0.194682 | + | 0.599169i | ||||
\(680\) | 29.3435 | + | 21.3193i | 1.12527 | + | 0.817557i | ||||
\(681\) | 0.618034 | 0.0236831 | ||||||||
\(682\) | 0.763932 | − | 1.90211i | 0.0292525 | − | 0.0728357i | ||||
\(683\) | 0.347524 | 0.0132976 | 0.00664882 | − | 0.999978i | \(-0.497884\pi\) | ||||
0.00664882 | + | 0.999978i | \(0.497884\pi\) | |||||||
\(684\) | −15.7082 | − | 11.4127i | −0.600618 | − | 0.436375i | ||||
\(685\) | −5.23607 | + | 16.1150i | −0.200060 | + | 0.615721i | ||||
\(686\) | 0.809017 | + | 2.48990i | 0.0308884 | + | 0.0950648i | ||||
\(687\) | 22.7082 | − | 16.4985i | 0.866372 | − | 0.629456i | ||||
\(688\) | 71.7492 | − | 52.1289i | 2.73541 | − | 1.98739i | ||||
\(689\) | 6.91641 | + | 21.2865i | 0.263494 | + | 0.810952i | ||||
\(690\) | 9.47214 | − | 29.1522i | 0.360598 | − | 1.10981i | ||||
\(691\) | −3.78115 | − | 2.74717i | −0.143842 | − | 0.104507i | 0.513537 | − | 0.858067i | \(-0.328335\pi\) |
−0.657379 | + | 0.753560i | \(0.728335\pi\) | |||||||
\(692\) | 61.2492 | 2.32835 | ||||||||
\(693\) | −2.80902 | + | 1.76336i | −0.106706 | + | 0.0669843i | ||||
\(694\) | −62.5410 | −2.37402 | ||||||||
\(695\) | 22.9894 | + | 16.7027i | 0.872036 | + | 0.633571i | ||||
\(696\) | −6.92705 | + | 21.3193i | −0.262569 | + | 0.808105i | ||||
\(697\) | 2.86475 | + | 8.81678i | 0.108510 | + | 0.333959i | ||||
\(698\) | −5.42705 | + | 3.94298i | −0.205417 | + | 0.149244i | ||||
\(699\) | 3.57295 | − | 2.59590i | 0.135141 | − | 0.0981859i | ||||
\(700\) | −3.57295 | − | 10.9964i | −0.135045 | − | 0.415625i | ||||
\(701\) | −3.45492 | + | 10.6331i | −0.130490 | + | 0.401608i | −0.994861 | − | 0.101247i | \(-0.967717\pi\) |
0.864371 | + | 0.502855i | \(0.167717\pi\) | |||||||
\(702\) | 11.5902 | + | 8.42075i | 0.437443 | + | 0.317821i | ||||
\(703\) | −33.8885 | −1.27813 | ||||||||
\(704\) | 7.04508 | + | 28.0094i | 0.265522 | + | 1.05564i | ||||
\(705\) | −16.3262 | −0.614882 | ||||||||
\(706\) | −52.3328 | − | 38.0220i | −1.96957 | − | 1.43098i | ||||
\(707\) | 1.00000 | − | 3.07768i | 0.0376089 | − | 0.115748i | ||||
\(708\) | −18.9271 | − | 58.2515i | −0.711322 | − | 2.18922i | ||||
\(709\) | −3.38197 | + | 2.45714i | −0.127012 | + | 0.0922799i | −0.649478 | − | 0.760381i | \(-0.725012\pi\) |
0.522465 | + | 0.852661i | \(0.325012\pi\) | |||||||
\(710\) | −41.9336 | + | 30.4666i | −1.57374 | + | 1.14339i | ||||
\(711\) | 2.11803 | + | 6.51864i | 0.0794325 | + | 0.244468i | ||||
\(712\) | 6.17376 | − | 19.0009i | 0.231372 | − | 0.712088i | ||||
\(713\) | 1.38197 | + | 1.00406i | 0.0517550 | + | 0.0376022i | ||||
\(714\) | 7.85410 | 0.293932 | ||||||||
\(715\) | −22.5344 | − | 18.8294i | −0.842740 | − | 0.704179i | ||||
\(716\) | 60.8115 | 2.27263 | ||||||||
\(717\) | −0.309017 | − | 0.224514i | −0.0115405 | − | 0.00838463i | ||||
\(718\) | 12.9271 | − | 39.7854i | 0.482433 | − | 1.48478i | ||||
\(719\) | −2.13525 | − | 6.57164i | −0.0796316 | − | 0.245081i | 0.903313 | − | 0.428982i | \(-0.141127\pi\) |
−0.982945 | + | 0.183901i | \(0.941127\pi\) | |||||||
\(720\) | −12.8992 | + | 9.37181i | −0.480724 | + | 0.349267i | ||||
\(721\) | −9.89919 | + | 7.19218i | −0.368665 | + | 0.267851i | ||||
\(722\) | −2.42705 | − | 7.46969i | −0.0903255 | − | 0.277993i | ||||
\(723\) | 0.218847 | − | 0.673542i | 0.00813901 | − | 0.0250493i | ||||
\(724\) | −30.4894 | − | 22.1518i | −1.13313 | − | 0.823266i | ||||
\(725\) | −7.14590 | −0.265392 | ||||||||
\(726\) | 20.7984 | + | 19.9192i | 0.771900 | + | 0.739270i | ||||
\(727\) | 36.3951 | 1.34982 | 0.674910 | − | 0.737900i | \(-0.264182\pi\) | ||||
0.674910 | + | 0.737900i | \(0.264182\pi\) | |||||||
\(728\) | −33.0795 | − | 24.0337i | −1.22601 | − | 0.890748i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −5.04508 | − | 15.5272i | −0.186727 | − | 0.574687i | ||||
\(731\) | −21.8435 | + | 15.8702i | −0.807910 | + | 0.586981i | ||||
\(732\) | −26.3435 | + | 19.1396i | −0.973682 | + | 0.707422i | ||||
\(733\) | 7.74671 | + | 23.8419i | 0.286131 | + | 0.880622i | 0.986057 | + | 0.166406i | \(0.0532163\pi\) |
−0.699926 | + | 0.714215i | \(0.746784\pi\) | |||||||
\(734\) | −19.9894 | + | 61.5209i | −0.737821 | + | 2.27078i | ||||
\(735\) | 1.30902 | + | 0.951057i | 0.0482838 | + | 0.0350802i | ||||
\(736\) | −78.5410 | −2.89506 | ||||||||
\(737\) | 9.43769 | + | 7.88597i | 0.347642 | + | 0.290483i | ||||
\(738\) | −8.09017 | −0.297803 | ||||||||
\(739\) | 9.35410 | + | 6.79615i | 0.344096 | + | 0.250001i | 0.746388 | − | 0.665511i | \(-0.231786\pi\) |
−0.402292 | + | 0.915511i | \(0.631786\pi\) | |||||||
\(740\) | −20.5623 | + | 63.2843i | −0.755885 | + | 2.32638i | ||||
\(741\) | −6.76393 | − | 20.8172i | −0.248479 | − | 0.764741i | ||||
\(742\) | −8.66312 | + | 6.29412i | −0.318033 | + | 0.231065i | ||||
\(743\) | −3.16312 | + | 2.29814i | −0.116044 | + | 0.0843106i | −0.644293 | − | 0.764778i | \(-0.722848\pi\) |
0.528250 | + | 0.849089i | \(0.322848\pi\) | |||||||
\(744\) | −0.545085 | − | 1.67760i | −0.0199838 | − | 0.0615038i | ||||
\(745\) | −10.1631 | + | 31.2789i | −0.372348 | + | 1.14597i | ||||
\(746\) | 72.3951 | + | 52.5981i | 2.65057 | + | 1.92575i | ||||
\(747\) | 2.94427 | 0.107725 | ||||||||
\(748\) | −11.7812 | − | 46.8388i | −0.430762 | − | 1.71260i | ||||
\(749\) | −15.9443 | −0.582591 | ||||||||
\(750\) | −25.2984 | − | 18.3803i | −0.923766 | − | 0.671155i | ||||
\(751\) | 8.20820 | − | 25.2623i | 0.299522 | − | 0.921833i | −0.682143 | − | 0.731218i | \(-0.738952\pi\) |
0.981665 | − | 0.190614i | \(-0.0610480\pi\) | |||||||
\(752\) | 30.7254 | + | 94.5631i | 1.12044 | + | 3.44836i | ||||
\(753\) | −8.42705 | + | 6.12261i | −0.307099 | + | 0.223120i | ||||
\(754\) | −34.7705 | + | 25.2623i | −1.26627 | + | 0.919997i | ||||
\(755\) | −5.30902 | − | 16.3395i | −0.193215 | − | 0.594654i | ||||
\(756\) | −1.50000 | + | 4.61653i | −0.0545545 | + | 0.167901i | ||||
\(757\) | 12.2361 | + | 8.89002i | 0.444727 | + | 0.323113i | 0.787511 | − | 0.616301i | \(-0.211370\pi\) |
−0.342783 | + | 0.939415i | \(0.611370\pi\) | |||||||
\(758\) | −30.8885 | −1.12192 | ||||||||
\(759\) | −20.3262 | + | 12.7598i | −0.737796 | + | 0.463150i | ||||
\(760\) | 48.3607 | 1.75423 | ||||||||
\(761\) | 30.4894 | + | 22.1518i | 1.10524 | + | 0.803003i | 0.981907 | − | 0.189363i | \(-0.0606423\pi\) |
0.123331 | + | 0.992366i | \(0.460642\pi\) | |||||||
\(762\) | −5.30902 | + | 16.3395i | −0.192325 | + | 0.591917i | ||||
\(763\) | 0.135255 | + | 0.416272i | 0.00489656 | + | 0.0150701i | ||||
\(764\) | −64.9058 | + | 47.1568i | −2.34821 | + | 1.70607i | ||||
\(765\) | 3.92705 | − | 2.85317i | 0.141983 | − | 0.103157i | ||||
\(766\) | −5.07295 | − | 15.6129i | −0.183293 | − | 0.564118i | ||||
\(767\) | 21.3369 | − | 65.6682i | 0.770430 | − | 2.37114i | ||||
\(768\) | −11.7812 | − | 8.55951i | −0.425116 | − | 0.308865i | ||||
\(769\) | 23.5279 | 0.848436 | 0.424218 | − | 0.905560i | \(-0.360549\pi\) | ||||
0.424218 | + | 0.905560i | \(0.360549\pi\) | |||||||
\(770\) | 5.23607 | − | 13.0373i | 0.188695 | − | 0.469831i | ||||
\(771\) | 0.472136 | 0.0170036 | ||||||||
\(772\) | 84.1033 | + | 61.1046i | 3.02694 | + | 2.19920i | ||||
\(773\) | 5.85410 | − | 18.0171i | 0.210557 | − | 0.648029i | −0.788882 | − | 0.614545i | \(-0.789340\pi\) |
0.999439 | − | 0.0334842i | \(-0.0106603\pi\) | |||||||
\(774\) | −7.28115 | − | 22.4091i | −0.261716 | − | 0.805478i | ||||
\(775\) | 0.454915 | − | 0.330515i | 0.0163410 | − | 0.0118725i | ||||
\(776\) | 99.2386 | − | 72.1010i | 3.56246 | − | 2.58828i | ||||
\(777\) | 2.61803 | + | 8.05748i | 0.0939214 | + | 0.289060i | ||||
\(778\) | −22.7082 | + | 69.8887i | −0.814129 | + | 2.50563i | ||||
\(779\) | 10.0000 | + | 7.26543i | 0.358287 | + | 0.260311i | ||||
\(780\) | −42.9787 | −1.53888 | ||||||||
\(781\) | 40.4894 | + | 2.74717i | 1.44882 | + | 0.0983014i | ||||
\(782\) | 56.8328 | 2.03234 | ||||||||
\(783\) | 2.42705 | + | 1.76336i | 0.0867357 | + | 0.0630172i | ||||
\(784\) | 3.04508 | − | 9.37181i | 0.108753 | − | 0.334707i | ||||
\(785\) | −8.07295 | − | 24.8460i | −0.288136 | − | 0.886791i | ||||
\(786\) | −2.80902 | + | 2.04087i | −0.100194 | + | 0.0727954i | ||||
\(787\) | 15.9271 | − | 11.5717i | 0.567738 | − | 0.412486i | −0.266545 | − | 0.963823i | \(-0.585882\pi\) |
0.834283 | + | 0.551337i | \(0.185882\pi\) | |||||||
\(788\) | −3.27051 | − | 10.0656i | −0.116507 | − | 0.358572i | ||||
\(789\) | 4.63525 | − | 14.2658i | 0.165019 | − | 0.507878i | ||||
\(790\) | −23.4894 | − | 17.0660i | −0.835714 | − | 0.607182i | ||||
\(791\) | −1.47214 | −0.0523431 | ||||||||
\(792\) | 24.7254 | + | 1.67760i | 0.878580 | + | 0.0596109i | ||||
\(793\) | −36.7082 | −1.30355 | ||||||||
\(794\) | −38.6976 | − | 28.1154i | −1.37333 | − | 0.997779i | ||||
\(795\) | −2.04508 | + | 6.29412i | −0.0725317 | + | 0.223230i | ||||
\(796\) | −17.3435 | − | 53.3777i | −0.614723 | − | 1.89192i | ||||
\(797\) | −37.9058 | + | 27.5402i | −1.34269 | + | 0.975522i | −0.343351 | + | 0.939207i | \(0.611562\pi\) |
−0.999340 | + | 0.0363149i | \(0.988438\pi\) | |||||||
\(798\) | 8.47214 | − | 6.15537i | 0.299910 | − | 0.217898i | ||||
\(799\) | −9.35410 | − | 28.7890i | −0.330924 | − | 1.01848i | ||||
\(800\) | −7.98936 | + | 24.5887i | −0.282466 | + | 0.869342i | ||||
\(801\) | −2.16312 | − | 1.57160i | −0.0764301 | − | 0.0555297i | ||||
\(802\) | 8.56231 | 0.302346 | ||||||||
\(803\) | −4.76393 | + | 11.8617i | −0.168116 | + | 0.418591i | ||||
\(804\) | 18.0000 | 0.634811 | ||||||||
\(805\) | 9.47214 | + | 6.88191i | 0.333849 | + | 0.242555i | ||||
\(806\) | 1.04508 | − | 3.21644i | 0.0368115 | − | 0.113294i | ||||
\(807\) | 6.21885 | + | 19.1396i | 0.218914 | + | 0.673747i | ||||
\(808\) | −19.5623 | + | 14.2128i | −0.688200 | + | 0.500006i | ||||
\(809\) | −12.7361 | + | 9.25330i | −0.447776 | + | 0.325329i | −0.788717 | − | 0.614756i | \(-0.789254\pi\) |
0.340941 | + | 0.940085i | \(0.389254\pi\) | |||||||
\(810\) | 1.30902 | + | 4.02874i | 0.0459942 | + | 0.141555i | ||||
\(811\) | −11.0344 | + | 33.9605i | −0.387472 | + | 1.19252i | 0.547200 | + | 0.837002i | \(0.315694\pi\) |
−0.934671 | + | 0.355513i | \(0.884306\pi\) | |||||||
\(812\) | −11.7812 | − | 8.55951i | −0.413437 | − | 0.300380i | ||||
\(813\) | 16.8885 | 0.592307 | ||||||||
\(814\) | 62.3050 | − | 39.1118i | 2.18379 | − | 1.37087i | ||||
\(815\) | 19.6525 | 0.688396 | ||||||||
\(816\) | −23.9164 | − | 17.3763i | −0.837242 | − | 0.608292i | ||||
\(817\) | −11.1246 | + | 34.2380i | −0.389201 | + | 1.19784i | ||||
\(818\) | 7.78115 | + | 23.9479i | 0.272062 | + | 0.837320i | ||||
\(819\) | −4.42705 | + | 3.21644i | −0.154694 | + | 0.112392i | ||||
\(820\) | 19.6353 | − | 14.2658i | 0.685693 | − | 0.498185i | ||||
\(821\) | 3.72949 | + | 11.4782i | 0.130160 | + | 0.400592i | 0.994806 | − | 0.101790i | \(-0.0324571\pi\) |
−0.864646 | + | 0.502382i | \(0.832457\pi\) | |||||||
\(822\) | 8.47214 | − | 26.0746i | 0.295500 | − | 0.909454i | ||||
\(823\) | −37.8885 | − | 27.5276i | −1.32071 | − | 0.959553i | −0.999923 | − | 0.0124023i | \(-0.996052\pi\) |
−0.320789 | − | 0.947151i | \(-0.603948\pi\) | |||||||
\(824\) | 91.4296 | 3.18510 | ||||||||
\(825\) | 1.92705 | + | 7.66145i | 0.0670913 | + | 0.266738i | ||||
\(826\) | 33.0344 | 1.14942 | ||||||||
\(827\) | −31.1353 | − | 22.6211i | −1.08268 | − | 0.786612i | −0.104531 | − | 0.994522i | \(-0.533334\pi\) |
−0.978148 | + | 0.207909i | \(0.933334\pi\) | |||||||
\(828\) | −10.8541 | + | 33.4055i | −0.377206 | + | 1.16092i | ||||
\(829\) | 2.29837 | + | 7.07367i | 0.0798258 | + | 0.245679i | 0.983003 | − | 0.183589i | \(-0.0587716\pi\) |
−0.903177 | + | 0.429268i | \(0.858772\pi\) | |||||||
\(830\) | −10.0902 | + | 7.33094i | −0.350235 | + | 0.254461i | ||||
\(831\) | −10.0902 | + | 7.33094i | −0.350024 | + | 0.254307i | ||||
\(832\) | 14.7254 | + | 45.3202i | 0.510512 | + | 1.57120i | ||||
\(833\) | −0.927051 | + | 2.85317i | −0.0321204 | + | 0.0988565i | ||||
\(834\) | −37.1976 | − | 27.0256i | −1.28805 | − | 0.935820i | ||||
\(835\) | 24.4164 | 0.844965 | ||||||||
\(836\) | −49.4164 | − | 41.2915i | −1.70910 | − | 1.42809i | ||||
\(837\) | −0.236068 | −0.00815970 | ||||||||
\(838\) | 28.2254 | + | 20.5070i | 0.975031 | + | 0.708402i | ||||
\(839\) | −4.63525 | + | 14.2658i | −0.160027 | + | 0.492512i | −0.998635 | − | 0.0522225i | \(-0.983369\pi\) |
0.838609 | + | 0.544734i | \(0.183369\pi\) | |||||||
\(840\) | −3.73607 | − | 11.4984i | −0.128907 | − | 0.396734i | ||||
\(841\) | 16.1803 | − | 11.7557i | 0.557943 | − | 0.405369i | ||||
\(842\) | −9.78115 | + | 7.10642i | −0.337081 | + | 0.244904i | ||||
\(843\) | −3.55573 | − | 10.9434i | −0.122466 | − | 0.376911i | ||||
\(844\) | 20.4787 | − | 63.0270i | 0.704906 | − | 2.16948i | ||||
\(845\) | −22.1803 | − | 16.1150i | −0.763027 | − | 0.554371i | ||||
\(846\) | 26.4164 | 0.908215 | ||||||||
\(847\) | −9.69098 | + | 5.20431i | −0.332986 | + | 0.178822i | ||||
\(848\) | 40.3050 | 1.38408 | ||||||||
\(849\) | −16.7533 | − | 12.1720i | −0.574971 | − | 0.417741i | ||||
\(850\) | 5.78115 | − | 17.7926i | 0.198292 | − | 0.610280i | ||||
\(851\) | 18.9443 | + | 58.3045i | 0.649401 | + | 1.99865i | ||||
\(852\) | 48.0517 | − | 34.9116i | 1.64622 | − | 1.19605i | ||||
\(853\) | −5.44427 | + | 3.95550i | −0.186408 | + | 0.135434i | −0.677076 | − | 0.735913i | \(-0.736753\pi\) |
0.490667 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(854\) | −5.42705 | − | 16.7027i | −0.185710 | − | 0.571556i | ||||
\(855\) | 2.00000 | − | 6.15537i | 0.0683986 | − | 0.210509i | ||||
\(856\) | 96.3845 | + | 70.0274i | 3.29435 | + | 2.39349i | ||||
\(857\) | 23.9443 | 0.817921 | 0.408960 | − | 0.912552i | \(-0.365891\pi\) | ||||
0.408960 | + | 0.912552i | \(0.365891\pi\) | |||||||
\(858\) | 36.4615 | + | 30.4666i | 1.24477 | + | 1.04011i | ||||
\(859\) | 40.4164 | 1.37899 | 0.689495 | − | 0.724290i | \(-0.257833\pi\) | ||||
0.689495 | + | 0.724290i | \(0.257833\pi\) | |||||||
\(860\) | 57.1869 | + | 41.5487i | 1.95006 | + | 1.41680i | ||||
\(861\) | 0.954915 | − | 2.93893i | 0.0325434 | − | 0.100158i | ||||
\(862\) | 15.8713 | + | 48.8469i | 0.540579 | + | 1.66373i | ||||
\(863\) | 1.80902 | − | 1.31433i | 0.0615797 | − | 0.0447402i | −0.556570 | − | 0.830801i | \(-0.687883\pi\) |
0.618149 | + | 0.786061i | \(0.287883\pi\) | |||||||
\(864\) | 8.78115 | − | 6.37988i | 0.298741 | − | 0.217048i | ||||
\(865\) | 6.30902 | + | 19.4172i | 0.214513 | + | 0.660203i | ||||
\(866\) | 15.3262 | − | 47.1693i | 0.520807 | − | 1.60288i | ||||
\(867\) | −6.47214 | − | 4.70228i | −0.219805 | − | 0.159698i | ||||
\(868\) | 1.14590 | 0.0388943 | ||||||||
\(869\) | 5.54508 | + | 22.0458i | 0.188104 | + | 0.747853i | ||||
\(870\) | −12.7082 | −0.430848 | ||||||||
\(871\) | 16.4164 | + | 11.9272i | 0.556249 | + | 0.404138i | ||||
\(872\) | 1.01064 | − | 3.11044i | 0.0342247 | − | 0.105333i | ||||
\(873\) | −5.07295 | − | 15.6129i | −0.171693 | − | 0.528418i | ||||
\(874\) | 61.3050 | − | 44.5407i | 2.07367 | − | 1.50661i | ||||
\(875\) | 9.66312 | − | 7.02067i | 0.326673 | − | 0.237342i | ||||
\(876\) | 5.78115 | + | 17.7926i | 0.195327 | + | 0.601155i | ||||
\(877\) | −2.92047 | + | 8.98829i | −0.0986174 | + | 0.303513i | −0.988180 | − | 0.153301i | \(-0.951010\pi\) |
0.889562 | + | 0.456814i | \(0.151010\pi\) | |||||||
\(878\) | −63.1869 | − | 45.9080i | −2.13246 | − | 1.54932i | ||||
\(879\) | −0.652476 | −0.0220075 | ||||||||
\(880\) | −44.7877 | + | 28.1154i | −1.50979 | + | 0.947771i | ||||
\(881\) | 1.06888 | 0.0360116 | 0.0180058 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180058 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(882\) | −2.11803 | − | 1.53884i | −0.0713179 | − | 0.0518155i | ||||
\(883\) | −1.37539 | + | 4.23301i | −0.0462855 | + | 0.142452i | −0.971528 | − | 0.236923i | \(-0.923861\pi\) |
0.925243 | + | 0.379375i | \(0.123861\pi\) | |||||||
\(884\) | −24.6246 | − | 75.7868i | −0.828215 | − | 2.54898i | ||||
\(885\) | 16.5172 | − | 12.0005i | 0.555220 | − | 0.403391i | ||||
\(886\) | −15.5623 | + | 11.3067i | −0.522826 | + | 0.379855i | ||||
\(887\) | 9.52380 | + | 29.3112i | 0.319778 | + | 0.984175i | 0.973743 | + | 0.227650i | \(0.0731043\pi\) |
−0.653965 | + | 0.756525i | \(0.726896\pi\) | |||||||
\(888\) | 19.5623 | − | 60.2066i | 0.656468 | − | 2.02040i | ||||
\(889\) | −5.30902 | − | 3.85723i | −0.178059 | − | 0.129367i | ||||
\(890\) | 11.3262 | 0.379656 | ||||||||
\(891\) | 1.23607 | − | 3.07768i | 0.0414098 | − | 0.103106i | ||||
\(892\) | −73.6869 | −2.46722 | ||||||||
\(893\) | −32.6525 | − | 23.7234i | −1.09267 | − | 0.793874i | ||||
\(894\) | 16.4443 | − | 50.6103i | 0.549979 | − | 1.69266i | ||||
\(895\) | 6.26393 | + | 19.2784i | 0.209380 | + | 0.644406i | ||||
\(896\) | −0.881966 | + | 0.640786i | −0.0294644 | + | 0.0214072i | ||||
\(897\) | −32.0344 | + | 23.2744i | −1.06960 | + | 0.777109i | ||||
\(898\) | 10.8992 | + | 33.5442i | 0.363711 | + | 1.11939i | ||||
\(899\) | 0.218847 | − | 0.673542i | 0.00729896 | − | 0.0224639i | ||||
\(900\) | 9.35410 | + | 6.79615i | 0.311803 | + | 0.226538i | ||||
\(901\) | −12.2705 | −0.408790 | ||||||||
\(902\) | −26.7705 | − | 1.81636i | −0.891360 | − | 0.0604781i | ||||
\(903\) | 9.00000 | 0.299501 | ||||||||
\(904\) | 8.89919 | + | 6.46564i | 0.295983 | + | 0.215044i | ||||
\(905\) | 3.88197 | − | 11.9475i | 0.129041 | − | 0.397147i | ||||
\(906\) | 8.59017 | + | 26.4378i | 0.285389 | + | 0.878338i | ||||
\(907\) | 2.17376 | − | 1.57933i | 0.0721786 | − | 0.0524408i | −0.551111 | − | 0.834432i | \(-0.685796\pi\) |
0.623289 | + | 0.781991i | \(0.285796\pi\) | |||||||
\(908\) | 2.42705 | − | 1.76336i | 0.0805445 | − | 0.0585190i | ||||
\(909\) | 1.00000 | + | 3.07768i | 0.0331679 | + | 0.102080i | ||||
\(910\) | 7.16312 | − | 22.0458i | 0.237455 | − | 0.730812i | ||||
\(911\) | −18.7812 | − | 13.6453i | −0.622247 | − | 0.452089i | 0.231458 | − | 0.972845i | \(-0.425650\pi\) |
−0.853706 | + | 0.520756i | \(0.825650\pi\) | |||||||
\(912\) | −39.4164 | −1.30521 | ||||||||
\(913\) | 9.74265 | + | 0.661030i | 0.322435 | + | 0.0218769i | ||||
\(914\) | −29.1803 | −0.965200 | ||||||||
\(915\) | −8.78115 | − | 6.37988i | −0.290296 | − | 0.210912i | ||||
\(916\) | 42.1033 | − | 129.581i | 1.39113 | − | 4.28147i | ||||
\(917\) | −0.409830 | − | 1.26133i | −0.0135338 | − | 0.0416527i | ||||
\(918\) | −6.35410 | + | 4.61653i | −0.209717 | + | 0.152368i | ||||
\(919\) | 17.4164 | − | 12.6538i | 0.574514 | − | 0.417409i | −0.262228 | − | 0.965006i | \(-0.584457\pi\) |
0.836742 | + | 0.547597i | \(0.184457\pi\) | |||||||
\(920\) | −27.0344 | − | 83.2035i | −0.891299 | − | 2.74314i | ||||
\(921\) | 2.07295 | − | 6.37988i | 0.0683060 | − | 0.210224i | ||||
\(922\) | −9.35410 | − | 6.79615i | −0.308061 | − | 0.223819i | ||||
\(923\) | 66.9574 | 2.20393 | ||||||||
\(924\) | −6.00000 | + | 14.9394i | −0.197386 | + | 0.491470i | ||||
\(925\) | 20.1803 | 0.663525 | ||||||||
\(926\) | −64.9959 | − | 47.2223i | −2.13590 | − | 1.55182i | ||||
\(927\) | 3.78115 | − | 11.6372i | 0.124189 | − | 0.382216i | ||||
\(928\) | 10.0623 | + | 30.9686i | 0.330311 | + | 1.01659i | ||||
\(929\) | −29.1246 | + | 21.1603i | −0.955548 | + | 0.694246i | −0.952112 | − | 0.305748i | \(-0.901093\pi\) |
−0.00343511 | + | 0.999994i | \(0.501093\pi\) | |||||||
\(930\) | 0.809017 | − | 0.587785i | 0.0265287 | − | 0.0192742i | ||||
\(931\) | 1.23607 | + | 3.80423i | 0.0405105 | + | 0.124678i | ||||
\(932\) | 6.62461 | − | 20.3885i | 0.216996 | − | 0.667846i | ||||
\(933\) | 19.4443 | + | 14.1271i | 0.636577 | + | 0.462500i | ||||
\(934\) | 72.3951 | 2.36884 | ||||||||
\(935\) | 13.6353 | − | 8.55951i | 0.445921 | − | 0.279926i | ||||
\(936\) | 40.8885 | 1.33648 | ||||||||
\(937\) | 16.6074 | + | 12.0660i | 0.542540 | + | 0.394178i | 0.825027 | − | 0.565093i | \(-0.191160\pi\) |
−0.282488 | + | 0.959271i | \(0.591160\pi\) | |||||||
\(938\) | −3.00000 | + | 9.23305i | −0.0979535 | + | 0.301470i | ||||
\(939\) | 0.409830 | + | 1.26133i | 0.0133743 | + | 0.0411619i | ||||
\(940\) | −64.1140 | + | 46.5815i | −2.09117 | + | 1.51932i | ||||
\(941\) | −13.7639 | + | 10.0001i | −0.448691 | + | 0.325993i | −0.789079 | − | 0.614292i | \(-0.789442\pi\) |
0.340388 | + | 0.940285i | \(0.389442\pi\) | |||||||
\(942\) | 13.0623 | + | 40.2016i | 0.425593 | + | 1.30984i | ||||
\(943\) | 6.90983 | − | 21.2663i | 0.225015 | − | 0.692525i | ||||
\(944\) | −100.593 | − | 73.0849i | −3.27401 | − | 2.37871i | ||||
\(945\) | −1.61803 | −0.0526346 | ||||||||
\(946\) | −19.0623 | − | 75.7868i | −0.619769 | − | 2.46404i | ||||
\(947\) | 11.5623 | 0.375724 | 0.187862 | − | 0.982195i | \(-0.439844\pi\) | ||||
0.187862 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(948\) | 26.9164 | + | 19.5559i | 0.874204 | + | 0.635147i | ||||
\(949\) | −6.51722 | + | 20.0579i | −0.211558 | + | 0.651108i | ||||
\(950\) | −7.70820 | − | 23.7234i | −0.250087 | − | 0.769689i | ||||
\(951\) | 11.5172 | − | 8.36775i | 0.373471 | − | 0.271343i | ||||
\(952\) | 18.1353 | − | 13.1760i | 0.587767 | − | 0.427038i | ||||
\(953\) | 12.1697 | + | 37.4545i | 0.394215 | + | 1.21327i | 0.929571 | + | 0.368643i | \(0.120177\pi\) |
−0.535356 | + | 0.844627i | \(0.679823\pi\) | |||||||
\(954\) | 3.30902 | − | 10.1841i | 0.107133 | − | 0.329723i | ||||
\(955\) | −21.6353 | − | 15.7189i | −0.700100 | − | 0.508653i | ||||
\(956\) | −1.85410 | −0.0599659 | ||||||||
\(957\) | 7.63525 | + | 6.37988i | 0.246813 | + | 0.206232i | ||||
\(958\) | 12.2361 | 0.395329 | ||||||||
\(959\) | 8.47214 | + | 6.15537i | 0.273580 | + | 0.198767i | ||||
\(960\) | −4.35410 | + | 13.4005i | −0.140528 | + | 0.432501i | ||||
\(961\) | −9.56231 | − | 29.4298i | −0.308461 | − | 0.949347i | ||||
\(962\) | 98.1935 | − | 71.3418i | 3.16589 | − | 2.30015i | ||||
\(963\) | 12.8992 | − | 9.37181i | 0.415670 | − | 0.302002i | ||||
\(964\) | −1.06231 | − | 3.26944i | −0.0342146 | − | 0.105302i | ||||
\(965\) | −10.7082 | + | 32.9565i | −0.344709 | + | 1.06091i | ||||
\(966\) | −15.3262 | − | 11.1352i | −0.493114 | − | 0.358268i | ||||
\(967\) | −32.6525 | −1.05003 | −0.525016 | − | 0.851092i | \(-0.675941\pi\) | ||||
−0.525016 | + | 0.851092i | \(0.675941\pi\) | |||||||
\(968\) | 81.4402 | + | 11.1024i | 2.61759 | + | 0.356845i | ||||
\(969\) | 12.0000 | 0.385496 | ||||||||
\(970\) | 56.2599 | + | 40.8752i | 1.80640 | + | 1.31242i | ||||
\(971\) | −12.4894 | + | 38.4383i | −0.400803 | + | 1.23354i | 0.523547 | + | 0.851997i | \(0.324608\pi\) |
−0.924350 | + | 0.381547i | \(0.875392\pi\) | |||||||
\(972\) | −1.50000 | − | 4.61653i | −0.0481125 | − | 0.148075i | ||||
\(973\) | 14.2082 | − | 10.3229i | 0.455494 | − | 0.330936i | ||||
\(974\) | 45.0517 | − | 32.7319i | 1.44355 | − | 1.04880i | ||||
\(975\) | 4.02786 | + | 12.3965i | 0.128995 | + | 0.397005i | ||||
\(976\) | −20.4271 | + | 62.8680i | −0.653854 | + | 2.01236i | ||||
\(977\) | −44.1697 | − | 32.0912i | −1.41311 | − | 1.02669i | −0.992861 | − | 0.119280i | \(-0.961941\pi\) |
−0.420253 | − | 0.907407i | \(-0.638059\pi\) | |||||||
\(978\) | −31.7984 | −1.01680 | ||||||||
\(979\) | −6.80495 | − | 5.68609i | −0.217487 | − | 0.181728i | ||||
\(980\) | 7.85410 | 0.250890 | ||||||||
\(981\) | −0.354102 | − | 0.257270i | −0.0113056 | − | 0.00821400i | ||||
\(982\) | −32.8885 | + | 101.221i | −1.04952 | + | 3.23008i | ||||
\(983\) | 14.3647 | + | 44.2101i | 0.458164 | + | 1.41008i | 0.867380 | + | 0.497647i | \(0.165802\pi\) |
−0.409216 | + | 0.912438i | \(0.634198\pi\) | |||||||
\(984\) | −18.6803 | + | 13.5721i | −0.595507 | + | 0.432662i | ||||
\(985\) | 2.85410 | − | 2.07363i | 0.0909393 | − | 0.0660712i | ||||
\(986\) | −7.28115 | − | 22.4091i | −0.231879 | − | 0.713651i | ||||
\(987\) | −3.11803 | + | 9.59632i | −0.0992481 | + | 0.305454i | ||||
\(988\) | −85.9574 | − | 62.4517i | −2.73467 | − | 1.98685i | ||||
\(989\) | 65.1246 | 2.07084 | ||||||||
\(990\) | 3.42705 | + | 13.6251i | 0.108919 | + | 0.433033i | ||||
\(991\) | 42.7984 | 1.35954 | 0.679768 | − | 0.733428i | \(-0.262081\pi\) | ||||
0.679768 | + | 0.733428i | \(0.262081\pi\) | |||||||
\(992\) | −2.07295 | − | 1.50609i | −0.0658162 | − | 0.0478183i | ||||
\(993\) | −9.74671 | + | 29.9973i | −0.309303 | + | 0.951935i | ||||
\(994\) | 9.89919 | + | 30.4666i | 0.313983 | + | 0.966341i | ||||
\(995\) | 15.1353 | − | 10.9964i | 0.479820 | − | 0.348610i | ||||
\(996\) | 11.5623 | − | 8.40051i | 0.366366 | − | 0.266180i | ||||
\(997\) | 11.4508 | + | 35.2421i | 0.362652 | + | 1.11613i | 0.951438 | + | 0.307839i | \(0.0996060\pi\) |
−0.588786 | + | 0.808289i | \(0.700394\pi\) | |||||||
\(998\) | −4.04508 | + | 12.4495i | −0.128045 | + | 0.394082i | ||||
\(999\) | −6.85410 | − | 4.97980i | −0.216854 | − | 0.157554i |
(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 | 231.2.j.a.169.1 | ✓ | 4 | |
3.2 | odd | 2 | 693.2.m.e.631.1 | 4 | |||
11.3 | even | 5 | inner | 231.2.j.a.190.1 | yes | 4 | |
11.5 | even | 5 | 2541.2.a.bf.1.2 | 2 | |||
11.6 | odd | 10 | 2541.2.a.m.1.1 | 2 | |||
33.5 | odd | 10 | 7623.2.a.u.1.1 | 2 | |||
33.14 | odd | 10 | 693.2.m.e.190.1 | 4 | |||
33.17 | even | 10 | 7623.2.a.by.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.a.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
231.2.j.a.190.1 | yes | 4 | 11.3 | even | 5 | inner | |
693.2.m.e.190.1 | 4 | 33.14 | odd | 10 | |||
693.2.m.e.631.1 | 4 | 3.2 | odd | 2 | |||
2541.2.a.m.1.1 | 2 | 11.6 | odd | 10 | |||
2541.2.a.bf.1.2 | 2 | 11.5 | even | 5 | |||
7623.2.a.u.1.1 | 2 | 33.5 | odd | 10 | |||
7623.2.a.by.1.2 | 2 | 33.17 | even | 10 |