Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(15,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.15");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.f (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: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.113 |
Dual form | 154.2.f.c.15.1 |
$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | −0.500000 | − | 1.53884i | −0.288675 | − | 0.888451i | −0.985273 | − | 0.170989i | \(-0.945304\pi\) |
0.696598 | − | 0.717462i | \(-0.254696\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −1.61803 | − | 1.17557i | −0.723607 | − | 0.525731i | 0.163928 | − | 0.986472i | \(-0.447584\pi\) |
−0.887535 | + | 0.460741i | \(0.847584\pi\) | |||||||
\(6\) | −1.30902 | − | 0.951057i | −0.534404 | − | 0.388267i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.224514i | 0.103006 | − | 0.0748380i | ||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | 2.54508 | − | 2.12663i | 0.767372 | − | 0.641202i | ||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −2.61803 | + | 1.90211i | −0.726112 | + | 0.527551i | −0.888331 | − | 0.459204i | \(-0.848135\pi\) |
0.162219 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | −1.00000 | + | 3.07768i | −0.258199 | + | 0.794654i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 4.73607 | + | 3.44095i | 1.14867 | + | 0.834554i | 0.988303 | − | 0.152504i | \(-0.0487337\pi\) |
0.160362 | + | 0.987058i | \(0.448734\pi\) | |||||||
\(18\) | 0.118034 | − | 0.363271i | 0.0278209 | − | 0.0856239i | ||||
\(19\) | −0.0450850 | − | 0.138757i | −0.0103432 | − | 0.0318331i | 0.945752 | − | 0.324890i | \(-0.105327\pi\) |
−0.956095 | + | 0.293057i | \(0.905327\pi\) | |||||||
\(20\) | −1.61803 | + | 1.17557i | −0.361803 | + | 0.262866i | ||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0.809017 | − | 3.21644i | 0.172483 | − | 0.685747i | ||||
\(23\) | 8.47214 | 1.76656 | 0.883281 | − | 0.468844i | \(-0.155329\pi\) | ||||
0.883281 | + | 0.468844i | \(0.155329\pi\) | |||||||
\(24\) | −1.30902 | + | 0.951057i | −0.267202 | + | 0.194134i | ||||
\(25\) | −0.309017 | − | 0.951057i | −0.0618034 | − | 0.190211i | ||||
\(26\) | −1.00000 | + | 3.07768i | −0.196116 | + | 0.603583i | ||||
\(27\) | −4.42705 | − | 3.21644i | −0.851986 | − | 0.619004i | ||||
\(28\) | 0.809017 | + | 0.587785i | 0.152890 | + | 0.111081i | ||||
\(29\) | −2.47214 | + | 7.60845i | −0.459064 | + | 1.41285i | 0.407233 | + | 0.913324i | \(0.366494\pi\) |
−0.866297 | + | 0.499530i | \(0.833506\pi\) | |||||||
\(30\) | 1.00000 | + | 3.07768i | 0.182574 | + | 0.561906i | ||||
\(31\) | 3.61803 | − | 2.62866i | 0.649818 | − | 0.472120i | −0.213391 | − | 0.976967i | \(-0.568451\pi\) |
0.863209 | + | 0.504846i | \(0.168451\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.54508 | − | 2.85317i | −0.791198 | − | 0.496673i | ||||
\(34\) | 5.85410 | 1.00397 | ||||||||
\(35\) | 1.61803 | − | 1.17557i | 0.273498 | − | 0.198708i | ||||
\(36\) | −0.118034 | − | 0.363271i | −0.0196723 | − | 0.0605452i | ||||
\(37\) | −2.38197 | + | 7.33094i | −0.391593 | + | 1.20520i | 0.539991 | + | 0.841671i | \(0.318428\pi\) |
−0.931583 | + | 0.363528i | \(0.881572\pi\) | |||||||
\(38\) | −0.118034 | − | 0.0857567i | −0.0191476 | − | 0.0139116i | ||||
\(39\) | 4.23607 | + | 3.07768i | 0.678314 | + | 0.492824i | ||||
\(40\) | −0.618034 | + | 1.90211i | −0.0977198 | + | 0.300750i | ||||
\(41\) | 0.263932 | + | 0.812299i | 0.0412193 | + | 0.126860i | 0.969549 | − | 0.244899i | \(-0.0787548\pi\) |
−0.928329 | + | 0.371759i | \(0.878755\pi\) | |||||||
\(42\) | 1.30902 | − | 0.951057i | 0.201986 | − | 0.146751i | ||||
\(43\) | −4.85410 | −0.740244 | −0.370122 | − | 0.928983i | \(-0.620684\pi\) | ||||
−0.370122 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(44\) | −1.23607 | − | 3.07768i | −0.186344 | − | 0.463978i | ||||
\(45\) | −0.763932 | −0.113880 | ||||||||
\(46\) | 6.85410 | − | 4.97980i | 1.01058 | − | 0.734231i | ||||
\(47\) | 0.527864 | + | 1.62460i | 0.0769969 | + | 0.236972i | 0.982145 | − | 0.188123i | \(-0.0602405\pi\) |
−0.905149 | + | 0.425096i | \(0.860241\pi\) | |||||||
\(48\) | −0.500000 | + | 1.53884i | −0.0721688 | + | 0.222113i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −0.809017 | − | 0.587785i | −0.114412 | − | 0.0831254i | ||||
\(51\) | 2.92705 | − | 9.00854i | 0.409869 | − | 1.26145i | ||||
\(52\) | 1.00000 | + | 3.07768i | 0.138675 | + | 0.426798i | ||||
\(53\) | −4.00000 | + | 2.90617i | −0.549442 | + | 0.399193i | −0.827580 | − | 0.561348i | \(-0.810283\pi\) |
0.278138 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | −6.61803 | + | 0.449028i | −0.892376 | + | 0.0605469i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −0.190983 | + | 0.138757i | −0.0252963 | + | 0.0183789i | ||||
\(58\) | 2.47214 | + | 7.60845i | 0.324607 | + | 0.999039i | ||||
\(59\) | 1.28115 | − | 3.94298i | 0.166792 | − | 0.513333i | −0.832372 | − | 0.554217i | \(-0.813018\pi\) |
0.999164 | + | 0.0408847i | \(0.0130176\pi\) | |||||||
\(60\) | 2.61803 | + | 1.90211i | 0.337987 | + | 0.245562i | ||||
\(61\) | −5.23607 | − | 3.80423i | −0.670410 | − | 0.487081i | 0.199753 | − | 0.979846i | \(-0.435986\pi\) |
−0.870162 | + | 0.492765i | \(0.835986\pi\) | |||||||
\(62\) | 1.38197 | − | 4.25325i | 0.175510 | − | 0.540164i | ||||
\(63\) | 0.118034 | + | 0.363271i | 0.0148709 | + | 0.0457679i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 6.47214 | 0.802770 | ||||||||
\(66\) | −5.35410 | + | 0.363271i | −0.659044 | + | 0.0447156i | ||||
\(67\) | 1.09017 | 0.133185 | 0.0665927 | − | 0.997780i | \(-0.478787\pi\) | ||||
0.0665927 | + | 0.997780i | \(0.478787\pi\) | |||||||
\(68\) | 4.73607 | − | 3.44095i | 0.574333 | − | 0.417277i | ||||
\(69\) | −4.23607 | − | 13.0373i | −0.509963 | − | 1.56950i | ||||
\(70\) | 0.618034 | − | 1.90211i | 0.0738692 | − | 0.227346i | ||||
\(71\) | −8.47214 | − | 6.15537i | −1.00546 | − | 0.730508i | −0.0422061 | − | 0.999109i | \(-0.513439\pi\) |
−0.963251 | + | 0.268601i | \(0.913439\pi\) | |||||||
\(72\) | −0.309017 | − | 0.224514i | −0.0364180 | − | 0.0264592i | ||||
\(73\) | −0.736068 | + | 2.26538i | −0.0861502 | + | 0.265143i | −0.984846 | − | 0.173428i | \(-0.944515\pi\) |
0.898696 | + | 0.438572i | \(0.144515\pi\) | |||||||
\(74\) | 2.38197 | + | 7.33094i | 0.276898 | + | 0.852204i | ||||
\(75\) | −1.30902 | + | 0.951057i | −0.151152 | + | 0.109819i | ||||
\(76\) | −0.145898 | −0.0167357 | ||||||||
\(77\) | 1.23607 | + | 3.07768i | 0.140863 | + | 0.350735i | ||||
\(78\) | 5.23607 | 0.592868 | ||||||||
\(79\) | 1.00000 | − | 0.726543i | 0.112509 | − | 0.0817424i | −0.530108 | − | 0.847930i | \(-0.677849\pi\) |
0.642617 | + | 0.766188i | \(0.277849\pi\) | |||||||
\(80\) | 0.618034 | + | 1.90211i | 0.0690983 | + | 0.212663i | ||||
\(81\) | −2.38197 | + | 7.33094i | −0.264663 | + | 0.814549i | ||||
\(82\) | 0.690983 | + | 0.502029i | 0.0763063 | + | 0.0554398i | ||||
\(83\) | 10.5451 | + | 7.66145i | 1.15747 | + | 0.840954i | 0.989456 | − | 0.144830i | \(-0.0462637\pi\) |
0.168017 | + | 0.985784i | \(0.446264\pi\) | |||||||
\(84\) | 0.500000 | − | 1.53884i | 0.0545545 | − | 0.167901i | ||||
\(85\) | −3.61803 | − | 11.1352i | −0.392431 | − | 1.20778i | ||||
\(86\) | −3.92705 | + | 2.85317i | −0.423465 | + | 0.307665i | ||||
\(87\) | 12.9443 | 1.38777 | ||||||||
\(88\) | −2.80902 | − | 1.76336i | −0.299442 | − | 0.187974i | ||||
\(89\) | −15.3262 | −1.62458 | −0.812289 | − | 0.583255i | \(-0.801779\pi\) | ||||
−0.812289 | + | 0.583255i | \(0.801779\pi\) | |||||||
\(90\) | −0.618034 | + | 0.449028i | −0.0651465 | + | 0.0473317i | ||||
\(91\) | −1.00000 | − | 3.07768i | −0.104828 | − | 0.322629i | ||||
\(92\) | 2.61803 | − | 8.05748i | 0.272949 | − | 0.840050i | ||||
\(93\) | −5.85410 | − | 4.25325i | −0.607042 | − | 0.441042i | ||||
\(94\) | 1.38197 | + | 1.00406i | 0.142539 | + | 0.103561i | ||||
\(95\) | −0.0901699 | + | 0.277515i | −0.00925124 | + | 0.0284724i | ||||
\(96\) | 0.500000 | + | 1.53884i | 0.0510310 | + | 0.157057i | ||||
\(97\) | 2.54508 | − | 1.84911i | 0.258414 | − | 0.187749i | −0.451033 | − | 0.892507i | \(-0.648944\pi\) |
0.709448 | + | 0.704758i | \(0.248944\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.309017 | − | 1.22857i | 0.0310574 | − | 0.123476i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 15.0902 | − | 10.9637i | 1.50153 | − | 1.09092i | 0.531760 | − | 0.846895i | \(-0.321531\pi\) |
0.969768 | − | 0.244029i | \(-0.0784692\pi\) | |||||||
\(102\) | −2.92705 | − | 9.00854i | −0.289821 | − | 0.891978i | ||||
\(103\) | −3.00000 | + | 9.23305i | −0.295599 | + | 0.909760i | 0.687421 | + | 0.726259i | \(0.258743\pi\) |
−0.983020 | + | 0.183500i | \(0.941257\pi\) | |||||||
\(104\) | 2.61803 | + | 1.90211i | 0.256719 | + | 0.186518i | ||||
\(105\) | −2.61803 | − | 1.90211i | −0.255494 | − | 0.185627i | ||||
\(106\) | −1.52786 | + | 4.70228i | −0.148399 | + | 0.456726i | ||||
\(107\) | −2.26393 | − | 6.96767i | −0.218863 | − | 0.673590i | −0.998857 | − | 0.0478030i | \(-0.984778\pi\) |
0.779994 | − | 0.625787i | \(-0.215222\pi\) | |||||||
\(108\) | −4.42705 | + | 3.21644i | −0.425993 | + | 0.309502i | ||||
\(109\) | −10.1803 | −0.975100 | −0.487550 | − | 0.873095i | \(-0.662109\pi\) | ||||
−0.487550 | + | 0.873095i | \(0.662109\pi\) | |||||||
\(110\) | −5.09017 | + | 4.25325i | −0.485329 | + | 0.405532i | ||||
\(111\) | 12.4721 | 1.18380 | ||||||||
\(112\) | 0.809017 | − | 0.587785i | 0.0764449 | − | 0.0555405i | ||||
\(113\) | 1.42705 | + | 4.39201i | 0.134246 | + | 0.413166i | 0.995472 | − | 0.0950561i | \(-0.0303030\pi\) |
−0.861226 | + | 0.508222i | \(0.830303\pi\) | |||||||
\(114\) | −0.0729490 | + | 0.224514i | −0.00683230 | + | 0.0210277i | ||||
\(115\) | −13.7082 | − | 9.95959i | −1.27830 | − | 0.928737i | ||||
\(116\) | 6.47214 | + | 4.70228i | 0.600923 | + | 0.436596i | ||||
\(117\) | −0.381966 | + | 1.17557i | −0.0353128 | + | 0.108682i | ||||
\(118\) | −1.28115 | − | 3.94298i | −0.117940 | − | 0.362981i | ||||
\(119\) | −4.73607 | + | 3.44095i | −0.434155 | + | 0.315432i | ||||
\(120\) | 3.23607 | 0.295411 | ||||||||
\(121\) | 1.95492 | − | 10.8249i | 0.177720 | − | 0.984081i | ||||
\(122\) | −6.47214 | −0.585960 | ||||||||
\(123\) | 1.11803 | − | 0.812299i | 0.100810 | − | 0.0732426i | ||||
\(124\) | −1.38197 | − | 4.25325i | −0.124104 | − | 0.381953i | ||||
\(125\) | −3.70820 | + | 11.4127i | −0.331672 | + | 1.02078i | ||||
\(126\) | 0.309017 | + | 0.224514i | 0.0275294 | + | 0.0200013i | ||||
\(127\) | 7.09017 | + | 5.15131i | 0.629151 | + | 0.457105i | 0.856106 | − | 0.516800i | \(-0.172877\pi\) |
−0.226955 | + | 0.973905i | \(0.572877\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 2.42705 | + | 7.46969i | 0.213690 | + | 0.657670i | ||||
\(130\) | 5.23607 | − | 3.80423i | 0.459234 | − | 0.333653i | ||||
\(131\) | 15.5623 | 1.35968 | 0.679842 | − | 0.733358i | \(-0.262048\pi\) | ||||
0.679842 | + | 0.733358i | \(0.262048\pi\) | |||||||
\(132\) | −4.11803 | + | 3.44095i | −0.358429 | + | 0.299497i | ||||
\(133\) | 0.145898 | 0.0126510 | ||||||||
\(134\) | 0.881966 | − | 0.640786i | 0.0761903 | − | 0.0553555i | ||||
\(135\) | 3.38197 | + | 10.4086i | 0.291073 | + | 0.895831i | ||||
\(136\) | 1.80902 | − | 5.56758i | 0.155122 | − | 0.477416i | ||||
\(137\) | 15.6353 | + | 11.3597i | 1.33581 | + | 0.970523i | 0.999587 | + | 0.0287404i | \(0.00914961\pi\) |
0.336223 | + | 0.941782i | \(0.390850\pi\) | |||||||
\(138\) | −11.0902 | − | 8.05748i | −0.944058 | − | 0.685898i | ||||
\(139\) | −4.47214 | + | 13.7638i | −0.379322 | + | 1.16743i | 0.561195 | + | 0.827684i | \(0.310342\pi\) |
−0.940516 | + | 0.339748i | \(0.889658\pi\) | |||||||
\(140\) | −0.618034 | − | 1.90211i | −0.0522334 | − | 0.160758i | ||||
\(141\) | 2.23607 | − | 1.62460i | 0.188311 | − | 0.136816i | ||||
\(142\) | −10.4721 | −0.878802 | ||||||||
\(143\) | −2.61803 | + | 10.4086i | −0.218931 | + | 0.870413i | ||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 12.9443 | − | 9.40456i | 1.07496 | − | 0.781007i | ||||
\(146\) | 0.736068 | + | 2.26538i | 0.0609174 | + | 0.187485i | ||||
\(147\) | −0.500000 | + | 1.53884i | −0.0412393 | + | 0.126922i | ||||
\(148\) | 6.23607 | + | 4.53077i | 0.512602 | + | 0.372427i | ||||
\(149\) | 8.70820 | + | 6.32688i | 0.713404 | + | 0.518318i | 0.884270 | − | 0.466976i | \(-0.154657\pi\) |
−0.170866 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(150\) | −0.500000 | + | 1.53884i | −0.0408248 | + | 0.125646i | ||||
\(151\) | −0.708204 | − | 2.17963i | −0.0576328 | − | 0.177376i | 0.918096 | − | 0.396358i | \(-0.129726\pi\) |
−0.975729 | + | 0.218983i | \(0.929726\pi\) | |||||||
\(152\) | −0.118034 | + | 0.0857567i | −0.00957382 | + | 0.00695579i | ||||
\(153\) | 2.23607 | 0.180775 | ||||||||
\(154\) | 2.80902 | + | 1.76336i | 0.226357 | + | 0.142095i | ||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | 4.23607 | − | 3.07768i | 0.339157 | − | 0.246412i | ||||
\(157\) | −0.854102 | − | 2.62866i | −0.0681648 | − | 0.209790i | 0.911172 | − | 0.412026i | \(-0.135179\pi\) |
−0.979337 | + | 0.202237i | \(0.935179\pi\) | |||||||
\(158\) | 0.381966 | − | 1.17557i | 0.0303876 | − | 0.0935234i | ||||
\(159\) | 6.47214 | + | 4.70228i | 0.513274 | + | 0.372915i | ||||
\(160\) | 1.61803 | + | 1.17557i | 0.127917 | + | 0.0929370i | ||||
\(161\) | −2.61803 | + | 8.05748i | −0.206330 | + | 0.635018i | ||||
\(162\) | 2.38197 | + | 7.33094i | 0.187145 | + | 0.575973i | ||||
\(163\) | −18.8262 | + | 13.6781i | −1.47458 | + | 1.07135i | −0.495333 | + | 0.868703i | \(0.664954\pi\) |
−0.979252 | + | 0.202645i | \(0.935046\pi\) | |||||||
\(164\) | 0.854102 | 0.0666942 | ||||||||
\(165\) | 4.00000 | + | 9.95959i | 0.311400 | + | 0.775353i | ||||
\(166\) | 13.0344 | 1.01167 | ||||||||
\(167\) | −13.3262 | + | 9.68208i | −1.03122 | + | 0.749222i | −0.968552 | − | 0.248813i | \(-0.919960\pi\) |
−0.0626637 | + | 0.998035i | \(0.519960\pi\) | |||||||
\(168\) | −0.500000 | − | 1.53884i | −0.0385758 | − | 0.118724i | ||||
\(169\) | −0.781153 | + | 2.40414i | −0.0600887 | + | 0.184934i | ||||
\(170\) | −9.47214 | − | 6.88191i | −0.726480 | − | 0.527818i | ||||
\(171\) | −0.0450850 | − | 0.0327561i | −0.00344773 | − | 0.00250493i | ||||
\(172\) | −1.50000 | + | 4.61653i | −0.114374 | + | 0.352007i | ||||
\(173\) | 0.708204 | + | 2.17963i | 0.0538437 | + | 0.165714i | 0.974362 | − | 0.224985i | \(-0.0722333\pi\) |
−0.920518 | + | 0.390699i | \(0.872233\pi\) | |||||||
\(174\) | 10.4721 | − | 7.60845i | 0.793891 | − | 0.576795i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −3.30902 | + | 0.224514i | −0.249427 | + | 0.0169234i | ||||
\(177\) | −6.70820 | −0.504219 | ||||||||
\(178\) | −12.3992 | + | 9.00854i | −0.929358 | + | 0.675218i | ||||
\(179\) | −7.57295 | − | 23.3071i | −0.566029 | − | 1.74206i | −0.664875 | − | 0.746955i | \(-0.731515\pi\) |
0.0988461 | − | 0.995103i | \(-0.468485\pi\) | |||||||
\(180\) | −0.236068 | + | 0.726543i | −0.0175955 | + | 0.0541533i | ||||
\(181\) | 15.1803 | + | 11.0292i | 1.12835 | + | 0.819791i | 0.985453 | − | 0.169947i | \(-0.0543597\pi\) |
0.142893 | + | 0.989738i | \(0.454360\pi\) | |||||||
\(182\) | −2.61803 | − | 1.90211i | −0.194062 | − | 0.140994i | ||||
\(183\) | −3.23607 | + | 9.95959i | −0.239217 | + | 0.736234i | ||||
\(184\) | −2.61803 | − | 8.05748i | −0.193004 | − | 0.594005i | ||||
\(185\) | 12.4721 | − | 9.06154i | 0.916970 | − | 0.666217i | ||||
\(186\) | −7.23607 | −0.530574 | ||||||||
\(187\) | 19.3713 | − | 1.31433i | 1.41657 | − | 0.0961132i | ||||
\(188\) | 1.70820 | 0.124584 | ||||||||
\(189\) | 4.42705 | − | 3.21644i | 0.322021 | − | 0.233962i | ||||
\(190\) | 0.0901699 | + | 0.277515i | 0.00654162 | + | 0.0201330i | ||||
\(191\) | 3.85410 | − | 11.8617i | 0.278873 | − | 0.858283i | −0.709296 | − | 0.704911i | \(-0.750987\pi\) |
0.988169 | − | 0.153372i | \(-0.0490132\pi\) | |||||||
\(192\) | 1.30902 | + | 0.951057i | 0.0944702 | + | 0.0686366i | ||||
\(193\) | −14.0902 | − | 10.2371i | −1.01423 | − | 0.736883i | −0.0491400 | − | 0.998792i | \(-0.515648\pi\) |
−0.965093 | + | 0.261909i | \(0.915648\pi\) | |||||||
\(194\) | 0.972136 | − | 2.99193i | 0.0697953 | − | 0.214808i | ||||
\(195\) | −3.23607 | − | 9.95959i | −0.231740 | − | 0.713221i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | −3.52786 | −0.251350 | −0.125675 | − | 0.992071i | \(-0.540110\pi\) | ||||
−0.125675 | + | 0.992071i | \(0.540110\pi\) | |||||||
\(198\) | −0.472136 | − | 1.17557i | −0.0335532 | − | 0.0835442i | ||||
\(199\) | −20.1803 | −1.43055 | −0.715273 | − | 0.698845i | \(-0.753698\pi\) | ||||
−0.715273 | + | 0.698845i | \(0.753698\pi\) | |||||||
\(200\) | −0.809017 | + | 0.587785i | −0.0572061 | + | 0.0415627i | ||||
\(201\) | −0.545085 | − | 1.67760i | −0.0384473 | − | 0.118329i | ||||
\(202\) | 5.76393 | − | 17.7396i | 0.405549 | − | 1.24815i | ||||
\(203\) | −6.47214 | − | 4.70228i | −0.454255 | − | 0.330035i | ||||
\(204\) | −7.66312 | − | 5.56758i | −0.536526 | − | 0.389809i | ||||
\(205\) | 0.527864 | − | 1.62460i | 0.0368676 | − | 0.113467i | ||||
\(206\) | 3.00000 | + | 9.23305i | 0.209020 | + | 0.643297i | ||||
\(207\) | 2.61803 | − | 1.90211i | 0.181966 | − | 0.132206i | ||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | −0.409830 | − | 0.257270i | −0.0283485 | − | 0.0177957i | ||||
\(210\) | −3.23607 | −0.223310 | ||||||||
\(211\) | 12.8713 | − | 9.35156i | 0.886098 | − | 0.643788i | −0.0487594 | − | 0.998811i | \(-0.515527\pi\) |
0.934858 | + | 0.355022i | \(0.115527\pi\) | |||||||
\(212\) | 1.52786 | + | 4.70228i | 0.104934 | + | 0.322954i | ||||
\(213\) | −5.23607 | + | 16.1150i | −0.358769 | + | 1.10418i | ||||
\(214\) | −5.92705 | − | 4.30625i | −0.405165 | − | 0.294370i | ||||
\(215\) | 7.85410 | + | 5.70634i | 0.535645 | + | 0.389169i | ||||
\(216\) | −1.69098 | + | 5.20431i | −0.115057 | + | 0.354108i | ||||
\(217\) | 1.38197 | + | 4.25325i | 0.0938140 | + | 0.288730i | ||||
\(218\) | −8.23607 | + | 5.98385i | −0.557817 | + | 0.405278i | ||||
\(219\) | 3.85410 | 0.260436 | ||||||||
\(220\) | −1.61803 | + | 6.43288i | −0.109088 | + | 0.433705i | ||||
\(221\) | −18.9443 | −1.27433 | ||||||||
\(222\) | 10.0902 | − | 7.33094i | 0.677208 | − | 0.492020i | ||||
\(223\) | −5.38197 | − | 16.5640i | −0.360403 | − | 1.10921i | −0.952810 | − | 0.303568i | \(-0.901822\pi\) |
0.592407 | − | 0.805639i | \(-0.298178\pi\) | |||||||
\(224\) | 0.309017 | − | 0.951057i | 0.0206471 | − | 0.0635451i | ||||
\(225\) | −0.309017 | − | 0.224514i | −0.0206011 | − | 0.0149676i | ||||
\(226\) | 3.73607 | + | 2.71441i | 0.248520 | + | 0.180560i | ||||
\(227\) | 8.42705 | − | 25.9358i | 0.559323 | − | 1.72142i | −0.124922 | − | 0.992167i | \(-0.539868\pi\) |
0.684245 | − | 0.729253i | \(-0.260132\pi\) | |||||||
\(228\) | 0.0729490 | + | 0.224514i | 0.00483117 | + | 0.0148688i | ||||
\(229\) | 18.4164 | − | 13.3803i | 1.21699 | − | 0.884195i | 0.221144 | − | 0.975241i | \(-0.429021\pi\) |
0.995847 | + | 0.0910459i | \(0.0290210\pi\) | |||||||
\(230\) | −16.9443 | −1.11727 | ||||||||
\(231\) | 4.11803 | − | 3.44095i | 0.270947 | − | 0.226398i | ||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −6.39919 | + | 4.64928i | −0.419225 | + | 0.304585i | −0.777326 | − | 0.629098i | \(-0.783424\pi\) |
0.358101 | + | 0.933683i | \(0.383424\pi\) | |||||||
\(234\) | 0.381966 | + | 1.17557i | 0.0249699 | + | 0.0768494i | ||||
\(235\) | 1.05573 | − | 3.24920i | 0.0688681 | − | 0.211954i | ||||
\(236\) | −3.35410 | − | 2.43690i | −0.218333 | − | 0.158629i | ||||
\(237\) | −1.61803 | − | 1.17557i | −0.105103 | − | 0.0763615i | ||||
\(238\) | −1.80902 | + | 5.56758i | −0.117261 | + | 0.360893i | ||||
\(239\) | 0.0901699 | + | 0.277515i | 0.00583261 | + | 0.0179509i | 0.953930 | − | 0.300028i | \(-0.0969960\pi\) |
−0.948098 | + | 0.317979i | \(0.896996\pi\) | |||||||
\(240\) | 2.61803 | − | 1.90211i | 0.168993 | − | 0.122781i | ||||
\(241\) | −6.79837 | −0.437922 | −0.218961 | − | 0.975734i | \(-0.570267\pi\) | ||||
−0.218961 | + | 0.975734i | \(0.570267\pi\) | |||||||
\(242\) | −4.78115 | − | 9.90659i | −0.307344 | − | 0.636820i | ||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −5.23607 | + | 3.80423i | −0.335205 | + | 0.243541i | ||||
\(245\) | 0.618034 | + | 1.90211i | 0.0394847 | + | 0.121522i | ||||
\(246\) | 0.427051 | − | 1.31433i | 0.0272278 | − | 0.0837985i | ||||
\(247\) | 0.381966 | + | 0.277515i | 0.0243039 | + | 0.0176578i | ||||
\(248\) | −3.61803 | − | 2.62866i | −0.229745 | − | 0.166920i | ||||
\(249\) | 6.51722 | − | 20.0579i | 0.413012 | − | 1.27112i | ||||
\(250\) | 3.70820 | + | 11.4127i | 0.234527 | + | 0.721801i | ||||
\(251\) | 4.00000 | − | 2.90617i | 0.252478 | − | 0.183436i | −0.454346 | − | 0.890825i | \(-0.650127\pi\) |
0.706824 | + | 0.707389i | \(0.250127\pi\) | |||||||
\(252\) | 0.381966 | 0.0240616 | ||||||||
\(253\) | 21.5623 | − | 18.0171i | 1.35561 | − | 1.13272i | ||||
\(254\) | 8.76393 | 0.549898 | ||||||||
\(255\) | −15.3262 | + | 11.1352i | −0.959766 | + | 0.697311i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 7.91641 | − | 24.3642i | 0.493812 | − | 1.51980i | −0.324988 | − | 0.945718i | \(-0.605360\pi\) |
0.818800 | − | 0.574079i | \(-0.194640\pi\) | |||||||
\(258\) | 6.35410 | + | 4.61653i | 0.395589 | + | 0.287412i | ||||
\(259\) | −6.23607 | − | 4.53077i | −0.387490 | − | 0.281528i | ||||
\(260\) | 2.00000 | − | 6.15537i | 0.124035 | − | 0.381740i | ||||
\(261\) | 0.944272 | + | 2.90617i | 0.0584490 | + | 0.179887i | ||||
\(262\) | 12.5902 | − | 9.14729i | 0.777823 | − | 0.565122i | ||||
\(263\) | −12.9443 | −0.798178 | −0.399089 | − | 0.916912i | \(-0.630674\pi\) | ||||
−0.399089 | + | 0.916912i | \(0.630674\pi\) | |||||||
\(264\) | −1.30902 | + | 5.20431i | −0.0805644 | + | 0.320303i | ||||
\(265\) | 9.88854 | 0.607448 | ||||||||
\(266\) | 0.118034 | − | 0.0857567i | 0.00723713 | − | 0.00525808i | ||||
\(267\) | 7.66312 | + | 23.5847i | 0.468975 | + | 1.44336i | ||||
\(268\) | 0.336881 | − | 1.03681i | 0.0205783 | − | 0.0633334i | ||||
\(269\) | 2.09017 | + | 1.51860i | 0.127440 | + | 0.0925905i | 0.649679 | − | 0.760208i | \(-0.274903\pi\) |
−0.522239 | + | 0.852799i | \(0.674903\pi\) | |||||||
\(270\) | 8.85410 | + | 6.43288i | 0.538843 | + | 0.391493i | ||||
\(271\) | −5.76393 | + | 17.7396i | −0.350134 | + | 1.07760i | 0.608644 | + | 0.793444i | \(0.291714\pi\) |
−0.958778 | + | 0.284158i | \(0.908286\pi\) | |||||||
\(272\) | −1.80902 | − | 5.56758i | −0.109688 | − | 0.337584i | ||||
\(273\) | −4.23607 | + | 3.07768i | −0.256378 | + | 0.186270i | ||||
\(274\) | 19.3262 | 1.16754 | ||||||||
\(275\) | −2.80902 | − | 1.76336i | −0.169390 | − | 0.106334i | ||||
\(276\) | −13.7082 | −0.825137 | ||||||||
\(277\) | −18.7984 | + | 13.6578i | −1.12948 | + | 0.820619i | −0.985620 | − | 0.168979i | \(-0.945953\pi\) |
−0.143865 | + | 0.989597i | \(0.545953\pi\) | |||||||
\(278\) | 4.47214 | + | 13.7638i | 0.268221 | + | 0.825499i | ||||
\(279\) | 0.527864 | − | 1.62460i | 0.0316024 | − | 0.0972622i | ||||
\(280\) | −1.61803 | − | 1.17557i | −0.0966960 | − | 0.0702538i | ||||
\(281\) | −7.92705 | − | 5.75934i | −0.472888 | − | 0.343573i | 0.325678 | − | 0.945481i | \(-0.394408\pi\) |
−0.798566 | + | 0.601907i | \(0.794408\pi\) | |||||||
\(282\) | 0.854102 | − | 2.62866i | 0.0508610 | − | 0.156534i | ||||
\(283\) | 3.41641 | + | 10.5146i | 0.203084 | + | 0.625029i | 0.999787 | + | 0.0206574i | \(0.00657592\pi\) |
−0.796702 | + | 0.604372i | \(0.793424\pi\) | |||||||
\(284\) | −8.47214 | + | 6.15537i | −0.502729 | + | 0.365254i | ||||
\(285\) | 0.472136 | 0.0279669 | ||||||||
\(286\) | 4.00000 | + | 9.95959i | 0.236525 | + | 0.588923i | ||||
\(287\) | −0.854102 | −0.0504160 | ||||||||
\(288\) | −0.309017 | + | 0.224514i | −0.0182090 | + | 0.0132296i | ||||
\(289\) | 5.33688 | + | 16.4252i | 0.313934 | + | 0.966190i | ||||
\(290\) | 4.94427 | − | 15.2169i | 0.290338 | − | 0.893567i | ||||
\(291\) | −4.11803 | − | 2.99193i | −0.241403 | − | 0.175390i | ||||
\(292\) | 1.92705 | + | 1.40008i | 0.112772 | + | 0.0819337i | ||||
\(293\) | 8.09017 | − | 24.8990i | 0.472633 | − | 1.45461i | −0.376491 | − | 0.926420i | \(-0.622869\pi\) |
0.849124 | − | 0.528194i | \(-0.177131\pi\) | |||||||
\(294\) | 0.500000 | + | 1.53884i | 0.0291606 | + | 0.0897471i | ||||
\(295\) | −6.70820 | + | 4.87380i | −0.390567 | + | 0.283763i | ||||
\(296\) | 7.70820 | 0.448030 | ||||||||
\(297\) | −18.1074 | + | 1.22857i | −1.05070 | + | 0.0712889i | ||||
\(298\) | 10.7639 | 0.623538 | ||||||||
\(299\) | −22.1803 | + | 16.1150i | −1.28272 | + | 0.931952i | ||||
\(300\) | 0.500000 | + | 1.53884i | 0.0288675 | + | 0.0888451i | ||||
\(301\) | 1.50000 | − | 4.61653i | 0.0864586 | − | 0.266092i | ||||
\(302\) | −1.85410 | − | 1.34708i | −0.106692 | − | 0.0775160i | ||||
\(303\) | −24.4164 | − | 17.7396i | −1.40269 | − | 1.01911i | ||||
\(304\) | −0.0450850 | + | 0.138757i | −0.00258580 | + | 0.00795828i | ||||
\(305\) | 4.00000 | + | 12.3107i | 0.229039 | + | 0.704911i | ||||
\(306\) | 1.80902 | − | 1.31433i | 0.103415 | − | 0.0751351i | ||||
\(307\) | −17.6180 | −1.00551 | −0.502757 | − | 0.864428i | \(-0.667681\pi\) | ||||
−0.502757 | + | 0.864428i | \(0.667681\pi\) | |||||||
\(308\) | 3.30902 | − | 0.224514i | 0.188549 | − | 0.0127929i | ||||
\(309\) | 15.7082 | 0.893609 | ||||||||
\(310\) | −7.23607 | + | 5.25731i | −0.410981 | + | 0.298595i | ||||
\(311\) | −1.32624 | − | 4.08174i | −0.0752041 | − | 0.231454i | 0.906387 | − | 0.422448i | \(-0.138829\pi\) |
−0.981591 | + | 0.190994i | \(0.938829\pi\) | |||||||
\(312\) | 1.61803 | − | 4.97980i | 0.0916031 | − | 0.281925i | ||||
\(313\) | 8.73607 | + | 6.34712i | 0.493792 | + | 0.358761i | 0.806641 | − | 0.591042i | \(-0.201283\pi\) |
−0.312849 | + | 0.949803i | \(0.601283\pi\) | |||||||
\(314\) | −2.23607 | − | 1.62460i | −0.126189 | − | 0.0916814i | ||||
\(315\) | 0.236068 | − | 0.726543i | 0.0133009 | − | 0.0409360i | ||||
\(316\) | −0.381966 | − | 1.17557i | −0.0214873 | − | 0.0661310i | ||||
\(317\) | −9.70820 | + | 7.05342i | −0.545267 | + | 0.396160i | −0.826037 | − | 0.563615i | \(-0.809410\pi\) |
0.280770 | + | 0.959775i | \(0.409410\pi\) | |||||||
\(318\) | 8.00000 | 0.448618 | ||||||||
\(319\) | 9.88854 | + | 24.6215i | 0.553652 | + | 1.37854i | ||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | −9.59017 | + | 6.96767i | −0.535271 | + | 0.388897i | ||||
\(322\) | 2.61803 | + | 8.05748i | 0.145897 | + | 0.449026i | ||||
\(323\) | 0.263932 | − | 0.812299i | 0.0146856 | − | 0.0451975i | ||||
\(324\) | 6.23607 | + | 4.53077i | 0.346448 | + | 0.251709i | ||||
\(325\) | 2.61803 | + | 1.90211i | 0.145222 | + | 0.105510i | ||||
\(326\) | −7.19098 | + | 22.1316i | −0.398272 | + | 1.22575i | ||||
\(327\) | 5.09017 | + | 15.6659i | 0.281487 | + | 0.866328i | ||||
\(328\) | 0.690983 | − | 0.502029i | 0.0381532 | − | 0.0277199i | ||||
\(329\) | −1.70820 | −0.0941763 | ||||||||
\(330\) | 9.09017 | + | 5.70634i | 0.500397 | + | 0.314124i | ||||
\(331\) | −4.27051 | −0.234728 | −0.117364 | − | 0.993089i | \(-0.537444\pi\) | ||||
−0.117364 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(332\) | 10.5451 | − | 7.66145i | 0.578737 | − | 0.420477i | ||||
\(333\) | 0.909830 | + | 2.80017i | 0.0498584 | + | 0.153448i | ||||
\(334\) | −5.09017 | + | 15.6659i | −0.278522 | + | 0.857202i | ||||
\(335\) | −1.76393 | − | 1.28157i | −0.0963739 | − | 0.0700197i | ||||
\(336\) | −1.30902 | − | 0.951057i | −0.0714127 | − | 0.0518844i | ||||
\(337\) | 0.371323 | − | 1.14281i | 0.0202272 | − | 0.0622531i | −0.940433 | − | 0.339978i | \(-0.889580\pi\) |
0.960661 | + | 0.277725i | \(0.0895804\pi\) | |||||||
\(338\) | 0.781153 | + | 2.40414i | 0.0424891 | + | 0.130768i | ||||
\(339\) | 6.04508 | − | 4.39201i | 0.328324 | − | 0.238541i | ||||
\(340\) | −11.7082 | −0.634967 | ||||||||
\(341\) | 3.61803 | − | 14.3844i | 0.195928 | − | 0.778957i | ||||
\(342\) | −0.0557281 | −0.00301343 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | 1.50000 | + | 4.61653i | 0.0808746 | + | 0.248906i | ||||
\(345\) | −8.47214 | + | 26.0746i | −0.456124 | + | 1.40381i | ||||
\(346\) | 1.85410 | + | 1.34708i | 0.0996771 | + | 0.0724197i | ||||
\(347\) | −9.82624 | − | 7.13918i | −0.527500 | − | 0.383251i | 0.291922 | − | 0.956442i | \(-0.405705\pi\) |
−0.819422 | + | 0.573191i | \(0.805705\pi\) | |||||||
\(348\) | 4.00000 | − | 12.3107i | 0.214423 | − | 0.659925i | ||||
\(349\) | −1.41641 | − | 4.35926i | −0.0758186 | − | 0.233346i | 0.905964 | − | 0.423356i | \(-0.139148\pi\) |
−0.981782 | + | 0.190010i | \(0.939148\pi\) | |||||||
\(350\) | 0.809017 | − | 0.587785i | 0.0432438 | − | 0.0314184i | ||||
\(351\) | 17.7082 | 0.945194 | ||||||||
\(352\) | −2.54508 | + | 2.12663i | −0.135653 | + | 0.113350i | ||||
\(353\) | 1.27051 | 0.0676224 | 0.0338112 | − | 0.999428i | \(-0.489236\pi\) | ||||
0.0338112 | + | 0.999428i | \(0.489236\pi\) | |||||||
\(354\) | −5.42705 | + | 3.94298i | −0.288445 | + | 0.209567i | ||||
\(355\) | 6.47214 | + | 19.9192i | 0.343505 | + | 1.05720i | ||||
\(356\) | −4.73607 | + | 14.5761i | −0.251011 | + | 0.772533i | ||||
\(357\) | 7.66312 | + | 5.56758i | 0.405575 | + | 0.294668i | ||||
\(358\) | −19.8262 | − | 14.4046i | −1.04785 | − | 0.761307i | ||||
\(359\) | 5.32624 | − | 16.3925i | 0.281108 | − | 0.865162i | −0.706430 | − | 0.707783i | \(-0.749696\pi\) |
0.987538 | − | 0.157379i | \(-0.0503044\pi\) | |||||||
\(360\) | 0.236068 | + | 0.726543i | 0.0124419 | + | 0.0382922i | ||||
\(361\) | 15.3541 | − | 11.1554i | 0.808111 | − | 0.587127i | ||||
\(362\) | 18.7639 | 0.986210 | ||||||||
\(363\) | −17.6353 | + | 2.40414i | −0.925611 | + | 0.126185i | ||||
\(364\) | −3.23607 | −0.169616 | ||||||||
\(365\) | 3.85410 | − | 2.80017i | 0.201733 | − | 0.146568i | ||||
\(366\) | 3.23607 | + | 9.95959i | 0.169152 | + | 0.520596i | ||||
\(367\) | −3.70820 | + | 11.4127i | −0.193567 | + | 0.595737i | 0.806424 | + | 0.591338i | \(0.201400\pi\) |
−0.999990 | + | 0.00439874i | \(0.998600\pi\) | |||||||
\(368\) | −6.85410 | − | 4.97980i | −0.357295 | − | 0.259590i | ||||
\(369\) | 0.263932 | + | 0.191758i | 0.0137398 | + | 0.00998251i | ||||
\(370\) | 4.76393 | − | 14.6619i | 0.247665 | − | 0.762235i | ||||
\(371\) | −1.52786 | − | 4.70228i | −0.0793227 | − | 0.244130i | ||||
\(372\) | −5.85410 | + | 4.25325i | −0.303521 | + | 0.220521i | ||||
\(373\) | 30.4721 | 1.57779 | 0.788894 | − | 0.614530i | \(-0.210654\pi\) | ||||
0.788894 | + | 0.614530i | \(0.210654\pi\) | |||||||
\(374\) | 14.8992 | − | 12.4495i | 0.770419 | − | 0.643748i | ||||
\(375\) | 19.4164 | 1.00266 | ||||||||
\(376\) | 1.38197 | − | 1.00406i | 0.0712695 | − | 0.0517803i | ||||
\(377\) | −8.00000 | − | 24.6215i | −0.412021 | − | 1.26807i | ||||
\(378\) | 1.69098 | − | 5.20431i | 0.0869748 | − | 0.267681i | ||||
\(379\) | 10.3992 | + | 7.55545i | 0.534170 | + | 0.388097i | 0.821915 | − | 0.569610i | \(-0.192906\pi\) |
−0.287745 | + | 0.957707i | \(0.592906\pi\) | |||||||
\(380\) | 0.236068 | + | 0.171513i | 0.0121100 | + | 0.00879845i | ||||
\(381\) | 4.38197 | − | 13.4863i | 0.224495 | − | 0.690924i | ||||
\(382\) | −3.85410 | − | 11.8617i | −0.197193 | − | 0.606898i | ||||
\(383\) | −2.70820 | + | 1.96763i | −0.138383 | + | 0.100541i | −0.654823 | − | 0.755782i | \(-0.727257\pi\) |
0.516440 | + | 0.856323i | \(0.327257\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | 1.61803 | − | 6.43288i | 0.0824626 | − | 0.327850i | ||||
\(386\) | −17.4164 | −0.886472 | ||||||||
\(387\) | −1.50000 | + | 1.08981i | −0.0762493 | + | 0.0553983i | ||||
\(388\) | −0.972136 | − | 2.99193i | −0.0493527 | − | 0.151892i | ||||
\(389\) | 2.00000 | − | 6.15537i | 0.101404 | − | 0.312089i | −0.887466 | − | 0.460874i | \(-0.847536\pi\) |
0.988870 | + | 0.148784i | \(0.0475360\pi\) | |||||||
\(390\) | −8.47214 | − | 6.15537i | −0.429003 | − | 0.311689i | ||||
\(391\) | 40.1246 | + | 29.1522i | 2.02919 | + | 1.47429i | ||||
\(392\) | −0.309017 | + | 0.951057i | −0.0156077 | + | 0.0480356i | ||||
\(393\) | −7.78115 | − | 23.9479i | −0.392507 | − | 1.20801i | ||||
\(394\) | −2.85410 | + | 2.07363i | −0.143788 | + | 0.104468i | ||||
\(395\) | −2.47214 | −0.124387 | ||||||||
\(396\) | −1.07295 | − | 0.673542i | −0.0539177 | − | 0.0338468i | ||||
\(397\) | −31.5967 | −1.58580 | −0.792898 | − | 0.609355i | \(-0.791429\pi\) | ||||
−0.792898 | + | 0.609355i | \(0.791429\pi\) | |||||||
\(398\) | −16.3262 | + | 11.8617i | −0.818360 | + | 0.594574i | ||||
\(399\) | −0.0729490 | − | 0.224514i | −0.00365202 | − | 0.0112398i | ||||
\(400\) | −0.309017 | + | 0.951057i | −0.0154508 | + | 0.0475528i | ||||
\(401\) | −3.78115 | − | 2.74717i | −0.188822 | − | 0.137187i | 0.489358 | − | 0.872083i | \(-0.337231\pi\) |
−0.678180 | + | 0.734896i | \(0.737231\pi\) | |||||||
\(402\) | −1.42705 | − | 1.03681i | −0.0711748 | − | 0.0517115i | ||||
\(403\) | −4.47214 | + | 13.7638i | −0.222773 | + | 0.685625i | ||||
\(404\) | −5.76393 | − | 17.7396i | −0.286766 | − | 0.882576i | ||||
\(405\) | 12.4721 | − | 9.06154i | 0.619745 | − | 0.450271i | ||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 9.52786 | + | 23.7234i | 0.472279 | + | 1.17593i | ||||
\(408\) | −9.47214 | −0.468941 | ||||||||
\(409\) | −14.8541 | + | 10.7921i | −0.734488 | + | 0.533637i | −0.890980 | − | 0.454042i | \(-0.849981\pi\) |
0.156492 | + | 0.987679i | \(0.449981\pi\) | |||||||
\(410\) | −0.527864 | − | 1.62460i | −0.0260693 | − | 0.0802332i | ||||
\(411\) | 9.66312 | − | 29.7400i | 0.476647 | − | 1.46697i | ||||
\(412\) | 7.85410 | + | 5.70634i | 0.386944 | + | 0.281131i | ||||
\(413\) | 3.35410 | + | 2.43690i | 0.165045 | + | 0.119912i | ||||
\(414\) | 1.00000 | − | 3.07768i | 0.0491473 | − | 0.151260i | ||||
\(415\) | −8.05573 | − | 24.7930i | −0.395440 | − | 1.21704i | ||||
\(416\) | 2.61803 | − | 1.90211i | 0.128360 | − | 0.0932588i | ||||
\(417\) | 23.4164 | 1.14671 | ||||||||
\(418\) | −0.482779 | + | 0.0327561i | −0.0236135 | + | 0.00160216i | ||||
\(419\) | 11.5066 | 0.562133 | 0.281067 | − | 0.959688i | \(-0.409312\pi\) | ||||
0.281067 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(420\) | −2.61803 | + | 1.90211i | −0.127747 | + | 0.0928136i | ||||
\(421\) | −1.38197 | − | 4.25325i | −0.0673529 | − | 0.207291i | 0.911716 | − | 0.410822i | \(-0.134758\pi\) |
−0.979068 | + | 0.203531i | \(0.934758\pi\) | |||||||
\(422\) | 4.91641 | − | 15.1311i | 0.239327 | − | 0.736573i | ||||
\(423\) | 0.527864 | + | 0.383516i | 0.0256656 | + | 0.0186472i | ||||
\(424\) | 4.00000 | + | 2.90617i | 0.194257 | + | 0.141136i | ||||
\(425\) | 1.80902 | − | 5.56758i | 0.0877502 | − | 0.270067i | ||||
\(426\) | 5.23607 | + | 16.1150i | 0.253688 | + | 0.780772i | ||||
\(427\) | 5.23607 | − | 3.80423i | 0.253391 | − | 0.184099i | ||||
\(428\) | −7.32624 | −0.354127 | ||||||||
\(429\) | 17.3262 | − | 1.17557i | 0.836519 | − | 0.0567571i | ||||
\(430\) | 9.70820 | 0.468171 | ||||||||
\(431\) | −19.9443 | + | 14.4904i | −0.960682 | + | 0.697976i | −0.953309 | − | 0.301997i | \(-0.902347\pi\) |
−0.00737279 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(432\) | 1.69098 | + | 5.20431i | 0.0813575 | + | 0.250393i | ||||
\(433\) | 2.01064 | − | 6.18812i | 0.0966253 | − | 0.297382i | −0.891049 | − | 0.453908i | \(-0.850029\pi\) |
0.987674 | + | 0.156526i | \(0.0500294\pi\) | |||||||
\(434\) | 3.61803 | + | 2.62866i | 0.173671 | + | 0.126180i | ||||
\(435\) | −20.9443 | − | 15.2169i | −1.00420 | − | 0.729595i | ||||
\(436\) | −3.14590 | + | 9.68208i | −0.150661 | + | 0.463687i | ||||
\(437\) | −0.381966 | − | 1.17557i | −0.0182719 | − | 0.0562352i | ||||
\(438\) | 3.11803 | − | 2.26538i | 0.148985 | − | 0.108244i | ||||
\(439\) | −16.9443 | −0.808706 | −0.404353 | − | 0.914603i | \(-0.632503\pi\) | ||||
−0.404353 | + | 0.914603i | \(0.632503\pi\) | |||||||
\(440\) | 2.47214 | + | 6.15537i | 0.117854 | + | 0.293446i | ||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −15.3262 | + | 11.1352i | −0.728995 | + | 0.529646i | ||||
\(443\) | 9.91641 | + | 30.5196i | 0.471143 | + | 1.45003i | 0.851090 | + | 0.525020i | \(0.175942\pi\) |
−0.379947 | + | 0.925008i | \(0.624058\pi\) | |||||||
\(444\) | 3.85410 | − | 11.8617i | 0.182908 | − | 0.562932i | ||||
\(445\) | 24.7984 | + | 18.0171i | 1.17556 | + | 0.854091i | ||||
\(446\) | −14.0902 | − | 10.2371i | −0.667189 | − | 0.484741i | ||||
\(447\) | 5.38197 | − | 16.5640i | 0.254558 | − | 0.783450i | ||||
\(448\) | −0.309017 | − | 0.951057i | −0.0145997 | − | 0.0449332i | ||||
\(449\) | −15.9721 | + | 11.6044i | −0.753772 | + | 0.547647i | −0.896994 | − | 0.442043i | \(-0.854254\pi\) |
0.143222 | + | 0.989691i | \(0.454254\pi\) | |||||||
\(450\) | −0.381966 | −0.0180061 | ||||||||
\(451\) | 2.39919 | + | 1.50609i | 0.112973 | + | 0.0709188i | ||||
\(452\) | 4.61803 | 0.217214 | ||||||||
\(453\) | −3.00000 | + | 2.17963i | −0.140952 | + | 0.102408i | ||||
\(454\) | −8.42705 | − | 25.9358i | −0.395501 | − | 1.21723i | ||||
\(455\) | −2.00000 | + | 6.15537i | −0.0937614 | + | 0.288568i | ||||
\(456\) | 0.190983 | + | 0.138757i | 0.00894360 | + | 0.00649790i | ||||
\(457\) | −30.7254 | − | 22.3233i | −1.43727 | − | 1.04424i | −0.988603 | − | 0.150544i | \(-0.951897\pi\) |
−0.448672 | − | 0.893697i | \(-0.648103\pi\) | |||||||
\(458\) | 7.03444 | − | 21.6498i | 0.328698 | − | 1.01163i | ||||
\(459\) | −9.89919 | − | 30.4666i | −0.462054 | − | 1.42206i | ||||
\(460\) | −13.7082 | + | 9.95959i | −0.639148 | + | 0.464368i | ||||
\(461\) | −41.0132 | −1.91017 | −0.955087 | − | 0.296327i | \(-0.904238\pi\) | ||||
−0.955087 | + | 0.296327i | \(0.904238\pi\) | |||||||
\(462\) | 1.30902 | − | 5.20431i | 0.0609010 | − | 0.242126i | ||||
\(463\) | 24.7639 | 1.15088 | 0.575439 | − | 0.817845i | \(-0.304831\pi\) | ||||
0.575439 | + | 0.817845i | \(0.304831\pi\) | |||||||
\(464\) | 6.47214 | − | 4.70228i | 0.300461 | − | 0.218298i | ||||
\(465\) | 4.47214 | + | 13.7638i | 0.207390 | + | 0.638282i | ||||
\(466\) | −2.44427 | + | 7.52270i | −0.113229 | + | 0.348482i | ||||
\(467\) | −17.7082 | − | 12.8658i | −0.819438 | − | 0.595357i | 0.0971135 | − | 0.995273i | \(-0.469039\pi\) |
−0.916551 | + | 0.399917i | \(0.869039\pi\) | |||||||
\(468\) | 1.00000 | + | 0.726543i | 0.0462250 | + | 0.0335844i | ||||
\(469\) | −0.336881 | + | 1.03681i | −0.0155557 | + | 0.0478756i | ||||
\(470\) | −1.05573 | − | 3.24920i | −0.0486971 | − | 0.149874i | ||||
\(471\) | −3.61803 | + | 2.62866i | −0.166710 | + | 0.121122i | ||||
\(472\) | −4.14590 | −0.190830 | ||||||||
\(473\) | −12.3541 | + | 10.3229i | −0.568042 | + | 0.474646i | ||||
\(474\) | −2.00000 | −0.0918630 | ||||||||
\(475\) | −0.118034 | + | 0.0857567i | −0.00541577 | + | 0.00393479i | ||||
\(476\) | 1.80902 | + | 5.56758i | 0.0829162 | + | 0.255190i | ||||
\(477\) | −0.583592 | + | 1.79611i | −0.0267208 | + | 0.0822383i | ||||
\(478\) | 0.236068 | + | 0.171513i | 0.0107975 | + | 0.00784484i | ||||
\(479\) | 7.00000 | + | 5.08580i | 0.319838 | + | 0.232376i | 0.736106 | − | 0.676866i | \(-0.236662\pi\) |
−0.416268 | + | 0.909242i | \(0.636662\pi\) | |||||||
\(480\) | 1.00000 | − | 3.07768i | 0.0456435 | − | 0.140476i | ||||
\(481\) | −7.70820 | − | 23.7234i | −0.351464 | − | 1.08169i | ||||
\(482\) | −5.50000 | + | 3.99598i | −0.250518 | + | 0.182012i | ||||
\(483\) | 13.7082 | 0.623745 | ||||||||
\(484\) | −9.69098 | − | 5.20431i | −0.440499 | − | 0.236560i | ||||
\(485\) | −6.29180 | −0.285696 | ||||||||
\(486\) | −3.19098 | + | 2.31838i | −0.144746 | + | 0.105164i | ||||
\(487\) | −5.96556 | − | 18.3601i | −0.270325 | − | 0.831976i | −0.990419 | − | 0.138098i | \(-0.955901\pi\) |
0.720093 | − | 0.693877i | \(-0.244099\pi\) | |||||||
\(488\) | −2.00000 | + | 6.15537i | −0.0905357 | + | 0.278640i | ||||
\(489\) | 30.4615 | + | 22.1316i | 1.37752 | + | 1.00082i | ||||
\(490\) | 1.61803 | + | 1.17557i | 0.0730953 | + | 0.0531069i | ||||
\(491\) | −5.50000 | + | 16.9273i | −0.248212 | + | 0.763917i | 0.746880 | + | 0.664959i | \(0.231551\pi\) |
−0.995092 | + | 0.0989578i | \(0.968449\pi\) | |||||||
\(492\) | −0.427051 | − | 1.31433i | −0.0192529 | − | 0.0592545i | ||||
\(493\) | −37.8885 | + | 27.5276i | −1.70641 | + | 1.23978i | ||||
\(494\) | 0.472136 | 0.0212424 | ||||||||
\(495\) | −1.94427 | + | 1.62460i | −0.0873885 | + | 0.0730203i | ||||
\(496\) | −4.47214 | −0.200805 | ||||||||
\(497\) | 8.47214 | − | 6.15537i | 0.380027 | − | 0.276106i | ||||
\(498\) | −6.51722 | − | 20.0579i | −0.292044 | − | 0.898818i | ||||
\(499\) | 8.73607 | − | 26.8869i | 0.391080 | − | 1.20362i | −0.540892 | − | 0.841092i | \(-0.681913\pi\) |
0.931972 | − | 0.362529i | \(-0.118087\pi\) | |||||||
\(500\) | 9.70820 | + | 7.05342i | 0.434164 | + | 0.315439i | ||||
\(501\) | 21.5623 | + | 15.6659i | 0.963333 | + | 0.699902i | ||||
\(502\) | 1.52786 | − | 4.70228i | 0.0681919 | − | 0.209873i | ||||
\(503\) | 6.67376 | + | 20.5397i | 0.297568 | + | 0.915821i | 0.982347 | + | 0.187070i | \(0.0598990\pi\) |
−0.684778 | + | 0.728751i | \(0.740101\pi\) | |||||||
\(504\) | 0.309017 | − | 0.224514i | 0.0137647 | − | 0.0100006i | ||||
\(505\) | −37.3050 | −1.66005 | ||||||||
\(506\) | 6.85410 | − | 27.2501i | 0.304702 | − | 1.21142i | ||||
\(507\) | 4.09017 | 0.181651 | ||||||||
\(508\) | 7.09017 | − | 5.15131i | 0.314575 | − | 0.228552i | ||||
\(509\) | 6.09017 | + | 18.7436i | 0.269942 | + | 0.830796i | 0.990513 | + | 0.137415i | \(0.0438795\pi\) |
−0.720571 | + | 0.693381i | \(0.756120\pi\) | |||||||
\(510\) | −5.85410 | + | 18.0171i | −0.259224 | + | 0.797809i | ||||
\(511\) | −1.92705 | − | 1.40008i | −0.0852477 | − | 0.0619361i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −0.246711 | + | 0.759299i | −0.0108926 | + | 0.0335239i | ||||
\(514\) | −7.91641 | − | 24.3642i | −0.349178 | − | 1.07466i | ||||
\(515\) | 15.7082 | − | 11.4127i | 0.692186 | − | 0.502903i | ||||
\(516\) | 7.85410 | 0.345758 | ||||||||
\(517\) | 4.79837 | + | 3.01217i | 0.211032 | + | 0.132475i | ||||
\(518\) | −7.70820 | −0.338679 | ||||||||
\(519\) | 3.00000 | − | 2.17963i | 0.131685 | − | 0.0956750i | ||||
\(520\) | −2.00000 | − | 6.15537i | −0.0877058 | − | 0.269931i | ||||
\(521\) | −1.04508 | + | 3.21644i | −0.0457860 | + | 0.140915i | −0.971336 | − | 0.237710i | \(-0.923603\pi\) |
0.925550 | + | 0.378625i | \(0.123603\pi\) | |||||||
\(522\) | 2.47214 | + | 1.79611i | 0.108202 | + | 0.0786137i | ||||
\(523\) | −7.88197 | − | 5.72658i | −0.344654 | − | 0.250406i | 0.401969 | − | 0.915653i | \(-0.368326\pi\) |
−0.746623 | + | 0.665247i | \(0.768326\pi\) | |||||||
\(524\) | 4.80902 | − | 14.8006i | 0.210083 | − | 0.646569i | ||||
\(525\) | −0.500000 | − | 1.53884i | −0.0218218 | − | 0.0671606i | ||||
\(526\) | −10.4721 | + | 7.60845i | −0.456607 | + | 0.331744i | ||||
\(527\) | 26.1803 | 1.14043 | ||||||||
\(528\) | 2.00000 | + | 4.97980i | 0.0870388 | + | 0.216718i | ||||
\(529\) | 48.7771 | 2.12074 | ||||||||
\(530\) | 8.00000 | − | 5.81234i | 0.347498 | − | 0.252472i | ||||
\(531\) | −0.489357 | − | 1.50609i | −0.0212363 | − | 0.0653585i | ||||
\(532\) | 0.0450850 | − | 0.138757i | 0.00195468 | − | 0.00601589i | ||||
\(533\) | −2.23607 | − | 1.62460i | −0.0968549 | − | 0.0703692i | ||||
\(534\) | 20.0623 | + | 14.5761i | 0.868181 | + | 0.630770i | ||||
\(535\) | −4.52786 | + | 13.9353i | −0.195757 | + | 0.602477i | ||||
\(536\) | −0.336881 | − | 1.03681i | −0.0145510 | − | 0.0447835i | ||||
\(537\) | −32.0795 | + | 23.3071i | −1.38433 | + | 1.00578i | ||||
\(538\) | 2.58359 | 0.111387 | ||||||||
\(539\) | −3.30902 | + | 0.224514i | −0.142529 | + | 0.00967050i | ||||
\(540\) | 10.9443 | 0.470966 | ||||||||
\(541\) | 23.6525 | − | 17.1845i | 1.01690 | − | 0.738821i | 0.0512544 | − | 0.998686i | \(-0.483678\pi\) |
0.965645 | + | 0.259865i | \(0.0836781\pi\) | |||||||
\(542\) | 5.76393 | + | 17.7396i | 0.247582 | + | 0.761979i | ||||
\(543\) | 9.38197 | − | 28.8747i | 0.402619 | − | 1.23913i | ||||
\(544\) | −4.73607 | − | 3.44095i | −0.203057 | − | 0.147530i | ||||
\(545\) | 16.4721 | + | 11.9677i | 0.705589 | + | 0.512640i | ||||
\(546\) | −1.61803 | + | 4.97980i | −0.0692455 | + | 0.213116i | ||||
\(547\) | 2.71885 | + | 8.36775i | 0.116250 | + | 0.357779i | 0.992206 | − | 0.124612i | \(-0.0397685\pi\) |
−0.875956 | + | 0.482391i | \(0.839769\pi\) | |||||||
\(548\) | 15.6353 | − | 11.3597i | 0.667905 | − | 0.485261i | ||||
\(549\) | −2.47214 | −0.105508 | ||||||||
\(550\) | −3.30902 | + | 0.224514i | −0.141097 | + | 0.00957331i | ||||
\(551\) | 1.16718 | 0.0497237 | ||||||||
\(552\) | −11.0902 | + | 8.05748i | −0.472029 | + | 0.342949i | ||||
\(553\) | 0.381966 | + | 1.17557i | 0.0162428 | + | 0.0499903i | ||||
\(554\) | −7.18034 | + | 22.0988i | −0.305063 | + | 0.938889i | ||||
\(555\) | −20.1803 | − | 14.6619i | −0.856608 | − | 0.622362i | ||||
\(556\) | 11.7082 | + | 8.50651i | 0.496538 | + | 0.360756i | ||||
\(557\) | 5.52786 | − | 17.0130i | 0.234223 | − | 0.720865i | −0.763000 | − | 0.646398i | \(-0.776275\pi\) |
0.997224 | − | 0.0744666i | \(-0.0237254\pi\) | |||||||
\(558\) | −0.527864 | − | 1.62460i | −0.0223463 | − | 0.0687747i | ||||
\(559\) | 12.7082 | − | 9.23305i | 0.537500 | − | 0.390516i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | −11.7082 | − | 29.1522i | −0.494321 | − | 1.23081i | ||||
\(562\) | −9.79837 | −0.413319 | ||||||||
\(563\) | 18.5451 | − | 13.4738i | 0.781582 | − | 0.567853i | −0.123871 | − | 0.992298i | \(-0.539531\pi\) |
0.905453 | + | 0.424446i | \(0.139531\pi\) | |||||||
\(564\) | −0.854102 | − | 2.62866i | −0.0359642 | − | 0.110686i | ||||
\(565\) | 2.85410 | − | 8.78402i | 0.120073 | − | 0.369547i | ||||
\(566\) | 8.94427 | + | 6.49839i | 0.375956 | + | 0.273148i | ||||
\(567\) | −6.23607 | − | 4.53077i | −0.261890 | − | 0.190274i | ||||
\(568\) | −3.23607 | + | 9.95959i | −0.135782 | + | 0.417895i | ||||
\(569\) | 13.0451 | + | 40.1486i | 0.546878 | + | 1.68312i | 0.716481 | + | 0.697606i | \(0.245751\pi\) |
−0.169603 | + | 0.985512i | \(0.554249\pi\) | |||||||
\(570\) | 0.381966 | − | 0.277515i | 0.0159988 | − | 0.0116238i | ||||
\(571\) | 18.8328 | 0.788129 | 0.394064 | − | 0.919083i | \(-0.371069\pi\) | ||||
0.394064 | + | 0.919083i | \(0.371069\pi\) | |||||||
\(572\) | 9.09017 | + | 5.70634i | 0.380079 | + | 0.238594i | ||||
\(573\) | −20.1803 | −0.843046 | ||||||||
\(574\) | −0.690983 | + | 0.502029i | −0.0288411 | + | 0.0209543i | ||||
\(575\) | −2.61803 | − | 8.05748i | −0.109180 | − | 0.336020i | ||||
\(576\) | −0.118034 | + | 0.363271i | −0.00491808 | + | 0.0151363i | ||||
\(577\) | 33.9164 | + | 24.6417i | 1.41196 | + | 1.02585i | 0.993034 | + | 0.117827i | \(0.0375928\pi\) |
0.418924 | + | 0.908021i | \(0.362407\pi\) | |||||||
\(578\) | 13.9721 | + | 10.1514i | 0.581164 | + | 0.422241i | ||||
\(579\) | −8.70820 | + | 26.8011i | −0.361901 | + | 1.11382i | ||||
\(580\) | −4.94427 | − | 15.2169i | −0.205300 | − | 0.631848i | ||||
\(581\) | −10.5451 | + | 7.66145i | −0.437484 | + | 0.317851i | ||||
\(582\) | −5.09017 | −0.210994 | ||||||||
\(583\) | −4.00000 | + | 15.9030i | −0.165663 | + | 0.658633i | ||||
\(584\) | 2.38197 | 0.0985665 | ||||||||
\(585\) | 2.00000 | − | 1.45309i | 0.0826898 | − | 0.0600777i | ||||
\(586\) | −8.09017 | − | 24.8990i | −0.334202 | − | 1.02857i | ||||
\(587\) | 5.66312 | − | 17.4293i | 0.233742 | − | 0.719384i | −0.763544 | − | 0.645756i | \(-0.776542\pi\) |
0.997286 | − | 0.0736277i | \(-0.0234577\pi\) | |||||||
\(588\) | 1.30902 | + | 0.951057i | 0.0539830 | + | 0.0392209i | ||||
\(589\) | −0.527864 | − | 0.383516i | −0.0217503 | − | 0.0158025i | ||||
\(590\) | −2.56231 | + | 7.88597i | −0.105488 | + | 0.324660i | ||||
\(591\) | 1.76393 | + | 5.42882i | 0.0725585 | + | 0.223312i | ||||
\(592\) | 6.23607 | − | 4.53077i | 0.256301 | − | 0.186213i | ||||
\(593\) | −11.0902 | −0.455419 | −0.227709 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227709 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(594\) | −13.9271 | + | 11.6372i | −0.571434 | + | 0.477480i | ||||
\(595\) | 11.7082 | 0.479990 | ||||||||
\(596\) | 8.70820 | − | 6.32688i | 0.356702 | − | 0.259159i | ||||
\(597\) | 10.0902 | + | 31.0543i | 0.412963 | + | 1.27097i | ||||
\(598\) | −8.47214 | + | 26.0746i | −0.346451 | + | 1.06627i | ||||
\(599\) | −2.00000 | − | 1.45309i | −0.0817178 | − | 0.0593714i | 0.546176 | − | 0.837670i | \(-0.316083\pi\) |
−0.627894 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(600\) | 1.30902 | + | 0.951057i | 0.0534404 | + | 0.0388267i | ||||
\(601\) | −9.79180 | + | 30.1360i | −0.399416 | + | 1.22928i | 0.526053 | + | 0.850452i | \(0.323671\pi\) |
−0.925469 | + | 0.378823i | \(0.876329\pi\) | |||||||
\(602\) | −1.50000 | − | 4.61653i | −0.0611354 | − | 0.188156i | ||||
\(603\) | 0.336881 | − | 0.244758i | 0.0137189 | − | 0.00996733i | ||||
\(604\) | −2.29180 | −0.0932519 | ||||||||
\(605\) | −15.8885 | + | 15.2169i | −0.645961 | + | 0.618655i | ||||
\(606\) | −30.1803 | −1.22599 | ||||||||
\(607\) | −12.0902 | + | 8.78402i | −0.490725 | + | 0.356532i | −0.805463 | − | 0.592646i | \(-0.798083\pi\) |
0.314738 | + | 0.949179i | \(0.398083\pi\) | |||||||
\(608\) | 0.0450850 | + | 0.138757i | 0.00182844 | + | 0.00562735i | ||||
\(609\) | −4.00000 | + | 12.3107i | −0.162088 | + | 0.498856i | ||||
\(610\) | 10.4721 | + | 7.60845i | 0.424004 | + | 0.308057i | ||||
\(611\) | −4.47214 | − | 3.24920i | −0.180923 | − | 0.131448i | ||||
\(612\) | 0.690983 | − | 2.12663i | 0.0279313 | − | 0.0859638i | ||||
\(613\) | −4.38197 | − | 13.4863i | −0.176986 | − | 0.544707i | 0.822733 | − | 0.568429i | \(-0.192448\pi\) |
−0.999719 | + | 0.0237218i | \(0.992448\pi\) | |||||||
\(614\) | −14.2533 | + | 10.3556i | −0.575216 | + | 0.417919i | ||||
\(615\) | −2.76393 | −0.111452 | ||||||||
\(616\) | 2.54508 | − | 2.12663i | 0.102544 | − | 0.0856842i | ||||
\(617\) | −39.1591 | −1.57648 | −0.788242 | − | 0.615365i | \(-0.789009\pi\) | ||||
−0.788242 | + | 0.615365i | \(0.789009\pi\) | |||||||
\(618\) | 12.7082 | − | 9.23305i | 0.511199 | − | 0.371408i | ||||
\(619\) | −4.33688 | − | 13.3475i | −0.174314 | − | 0.536483i | 0.825287 | − | 0.564713i | \(-0.191013\pi\) |
−0.999601 | + | 0.0282296i | \(0.991013\pi\) | |||||||
\(620\) | −2.76393 | + | 8.50651i | −0.111002 | + | 0.341630i | ||||
\(621\) | −37.5066 | − | 27.2501i | −1.50509 | − | 1.09351i | ||||
\(622\) | −3.47214 | − | 2.52265i | −0.139220 | − | 0.101149i | ||||
\(623\) | 4.73607 | − | 14.5761i | 0.189747 | − | 0.583980i | ||||
\(624\) | −1.61803 | − | 4.97980i | −0.0647732 | − | 0.199351i | ||||
\(625\) | 15.3713 | − | 11.1679i | 0.614853 | − | 0.446717i | ||||
\(626\) | 10.7984 | 0.431590 | ||||||||
\(627\) | −0.190983 | + | 0.759299i | −0.00762713 | + | 0.0303235i | ||||
\(628\) | −2.76393 | −0.110293 | ||||||||
\(629\) | −36.5066 | + | 26.5236i | −1.45561 | + | 1.05756i | ||||
\(630\) | −0.236068 | − | 0.726543i | −0.00940517 | − | 0.0289461i | ||||
\(631\) | 10.8885 | − | 33.5115i | 0.433466 | − | 1.33407i | −0.461184 | − | 0.887304i | \(-0.652575\pi\) |
0.894650 | − | 0.446767i | \(-0.147425\pi\) | |||||||
\(632\) | −1.00000 | − | 0.726543i | −0.0397779 | − | 0.0289003i | ||||
\(633\) | −20.8262 | − | 15.1311i | −0.827769 | − | 0.601409i | ||||
\(634\) | −3.70820 | + | 11.4127i | −0.147272 | + | 0.453255i | ||||
\(635\) | −5.41641 | − | 16.6700i | −0.214944 | − | 0.661528i | ||||
\(636\) | 6.47214 | − | 4.70228i | 0.256637 | − | 0.186458i | ||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 22.4721 | + | 14.1068i | 0.889680 | + | 0.558495i | ||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 1.61803 | − | 1.17557i | 0.0639584 | − | 0.0464685i | ||||
\(641\) | 7.26393 | + | 22.3561i | 0.286908 | + | 0.883012i | 0.985820 | + | 0.167805i | \(0.0536678\pi\) |
−0.698912 | + | 0.715207i | \(0.746332\pi\) | |||||||
\(642\) | −3.66312 | + | 11.2739i | −0.144572 | + | 0.444946i | ||||
\(643\) | 11.6353 | + | 8.45351i | 0.458850 | + | 0.333374i | 0.793080 | − | 0.609118i | \(-0.208476\pi\) |
−0.334230 | + | 0.942491i | \(0.608476\pi\) | |||||||
\(644\) | 6.85410 | + | 4.97980i | 0.270089 | + | 0.196231i | ||||
\(645\) | 4.85410 | − | 14.9394i | 0.191130 | − | 0.588238i | ||||
\(646\) | −0.263932 | − | 0.812299i | −0.0103843 | − | 0.0319595i | ||||
\(647\) | 30.2705 | − | 21.9928i | 1.19006 | − | 0.864627i | 0.196786 | − | 0.980446i | \(-0.436949\pi\) |
0.993270 | + | 0.115820i | \(0.0369495\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | −5.12461 | − | 12.7598i | −0.201159 | − | 0.500864i | ||||
\(650\) | 3.23607 | 0.126929 | ||||||||
\(651\) | 5.85410 | − | 4.25325i | 0.229440 | − | 0.166698i | ||||
\(652\) | 7.19098 | + | 22.1316i | 0.281621 | + | 0.866739i | ||||
\(653\) | −1.96556 | + | 6.04937i | −0.0769182 | + | 0.236730i | −0.982121 | − | 0.188249i | \(-0.939719\pi\) |
0.905203 | + | 0.424979i | \(0.139719\pi\) | |||||||
\(654\) | 13.3262 | + | 9.68208i | 0.521097 | + | 0.378599i | ||||
\(655\) | −25.1803 | − | 18.2946i | −0.983877 | − | 0.714829i | ||||
\(656\) | 0.263932 | − | 0.812299i | 0.0103048 | − | 0.0317150i | ||||
\(657\) | 0.281153 | + | 0.865300i | 0.0109688 | + | 0.0337586i | ||||
\(658\) | −1.38197 | + | 1.00406i | −0.0538746 | + | 0.0391422i | ||||
\(659\) | 16.5066 | 0.643005 | 0.321502 | − | 0.946909i | \(-0.395812\pi\) | ||||
0.321502 | + | 0.946909i | \(0.395812\pi\) | |||||||
\(660\) | 10.7082 | − | 0.726543i | 0.416816 | − | 0.0282806i | ||||
\(661\) | 16.4721 | 0.640692 | 0.320346 | − | 0.947301i | \(-0.396201\pi\) | ||||
0.320346 | + | 0.947301i | \(0.396201\pi\) | |||||||
\(662\) | −3.45492 | + | 2.51014i | −0.134279 | + | 0.0975595i | ||||
\(663\) | 9.47214 | + | 29.1522i | 0.367867 | + | 1.13218i | ||||
\(664\) | 4.02786 | − | 12.3965i | 0.156311 | − | 0.481077i | ||||
\(665\) | −0.236068 | − | 0.171513i | −0.00915432 | − | 0.00665101i | ||||
\(666\) | 2.38197 | + | 1.73060i | 0.0922993 | + | 0.0670594i | ||||
\(667\) | −20.9443 | + | 64.4598i | −0.810965 | + | 2.49590i | ||||
\(668\) | 5.09017 | + | 15.6659i | 0.196945 | + | 0.606133i | ||||
\(669\) | −22.7984 | + | 16.5640i | −0.881436 | + | 0.640401i | ||||
\(670\) | −2.18034 | −0.0842339 | ||||||||
\(671\) | −21.4164 | + | 1.45309i | −0.826771 | + | 0.0560957i | ||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | 37.6246 | − | 27.3359i | 1.45032 | − | 1.05372i | 0.464566 | − | 0.885538i | \(-0.346210\pi\) |
0.985756 | − | 0.168182i | \(-0.0537898\pi\) | |||||||
\(674\) | −0.371323 | − | 1.14281i | −0.0143028 | − | 0.0440196i | ||||
\(675\) | −1.69098 | + | 5.20431i | −0.0650860 | + | 0.200314i | ||||
\(676\) | 2.04508 | + | 1.48584i | 0.0786571 | + | 0.0571477i | ||||
\(677\) | 29.0344 | + | 21.0948i | 1.11588 | + | 0.810737i | 0.983580 | − | 0.180472i | \(-0.0577625\pi\) |
0.132304 | + | 0.991209i | \(0.457762\pi\) | |||||||
\(678\) | 2.30902 | − | 7.10642i | 0.0886773 | − | 0.272921i | ||||
\(679\) | 0.972136 | + | 2.99193i | 0.0373072 | + | 0.114820i | ||||
\(680\) | −9.47214 | + | 6.88191i | −0.363240 | + | 0.263909i | ||||
\(681\) | −44.1246 | −1.69086 | ||||||||
\(682\) | −5.52786 | − | 13.7638i | −0.211673 | − | 0.527044i | ||||
\(683\) | 24.3607 | 0.932136 | 0.466068 | − | 0.884749i | \(-0.345670\pi\) | ||||
0.466068 | + | 0.884749i | \(0.345670\pi\) | |||||||
\(684\) | −0.0450850 | + | 0.0327561i | −0.00172387 | + | 0.00125246i | ||||
\(685\) | −11.9443 | − | 36.7607i | −0.456367 | − | 1.40455i | ||||
\(686\) | 0.309017 | − | 0.951057i | 0.0117983 | − | 0.0363115i | ||||
\(687\) | −29.7984 | − | 21.6498i | −1.13688 | − | 0.825991i | ||||
\(688\) | 3.92705 | + | 2.85317i | 0.149717 | + | 0.108776i | ||||
\(689\) | 4.94427 | − | 15.2169i | 0.188362 | − | 0.579718i | ||||
\(690\) | 8.47214 | + | 26.0746i | 0.322529 | + | 0.992641i | ||||
\(691\) | −1.88197 | + | 1.36733i | −0.0715934 | + | 0.0520156i | −0.623006 | − | 0.782217i | \(-0.714089\pi\) |
0.551413 | + | 0.834232i | \(0.314089\pi\) | |||||||
\(692\) | 2.29180 | 0.0871210 | ||||||||
\(693\) | 1.07295 | + | 0.673542i | 0.0407580 | + | 0.0255857i | ||||
\(694\) | −12.1459 | −0.461052 | ||||||||
\(695\) | 23.4164 | − | 17.0130i | 0.888235 | − | 0.645340i | ||||
\(696\) | −4.00000 | − | 12.3107i | −0.151620 | − | 0.466637i | ||||
\(697\) | −1.54508 | + | 4.75528i | −0.0585243 | + | 0.180119i | ||||
\(698\) | −3.70820 | − | 2.69417i | −0.140358 | − | 0.101976i | ||||
\(699\) | 10.3541 | + | 7.52270i | 0.391628 | + | 0.284534i | ||||
\(700\) | 0.309017 | − | 0.951057i | 0.0116797 | − | 0.0359466i | ||||
\(701\) | 15.1803 | + | 46.7203i | 0.573354 | + | 1.76460i | 0.641718 | + | 0.766940i | \(0.278222\pi\) |
−0.0683649 | + | 0.997660i | \(0.521778\pi\) | |||||||
\(702\) | 14.3262 | − | 10.4086i | 0.540709 | − | 0.392848i | ||||
\(703\) | 1.12461 | 0.0424155 | ||||||||
\(704\) | −0.809017 | + | 3.21644i | −0.0304910 | + | 0.121224i | ||||
\(705\) | −5.52786 | −0.208191 | ||||||||
\(706\) | 1.02786 | − | 0.746787i | 0.0386842 | − | 0.0281057i | ||||
\(707\) | 5.76393 | + | 17.7396i | 0.216775 | + | 0.667165i | ||||
\(708\) | −2.07295 | + | 6.37988i | −0.0779062 | + | 0.239771i | ||||
\(709\) | −7.56231 | − | 5.49434i | −0.284008 | − | 0.206344i | 0.436656 | − | 0.899629i | \(-0.356163\pi\) |
−0.720664 | + | 0.693285i | \(0.756163\pi\) | |||||||
\(710\) | 16.9443 | + | 12.3107i | 0.635907 | + | 0.462014i | ||||
\(711\) | 0.145898 | − | 0.449028i | 0.00547160 | − | 0.0168399i | ||||
\(712\) | 4.73607 | + | 14.5761i | 0.177492 | + | 0.546263i | ||||
\(713\) | 30.6525 | − | 22.2703i | 1.14794 | − | 0.834030i | ||||
\(714\) | 9.47214 | 0.354486 | ||||||||
\(715\) | 16.4721 | − | 13.7638i | 0.616023 | − | 0.514738i | ||||
\(716\) | −24.5066 | −0.915854 | ||||||||
\(717\) | 0.381966 | − | 0.277515i | 0.0142648 | − | 0.0103640i | ||||
\(718\) | −5.32624 | − | 16.3925i | −0.198773 | − | 0.611762i | ||||
\(719\) | 1.85410 | − | 5.70634i | 0.0691463 | − | 0.212811i | −0.910512 | − | 0.413482i | \(-0.864312\pi\) |
0.979659 | + | 0.200672i | \(0.0643124\pi\) | |||||||
\(720\) | 0.618034 | + | 0.449028i | 0.0230328 | + | 0.0167343i | ||||
\(721\) | −7.85410 | − | 5.70634i | −0.292502 | − | 0.212515i | ||||
\(722\) | 5.86475 | − | 18.0498i | 0.218263 | − | 0.671745i | ||||
\(723\) | 3.39919 | + | 10.4616i | 0.126417 | + | 0.389072i | ||||
\(724\) | 15.1803 | − | 11.0292i | 0.564173 | − | 0.409896i | ||||
\(725\) | 8.00000 | 0.297113 | ||||||||
\(726\) | −12.8541 | + | 12.3107i | −0.477060 | + | 0.456894i | ||||
\(727\) | −29.5279 | −1.09513 | −0.547564 | − | 0.836764i | \(-0.684445\pi\) | ||||
−0.547564 | + | 0.836764i | \(0.684445\pi\) | |||||||
\(728\) | −2.61803 | + | 1.90211i | −0.0970308 | + | 0.0704970i | ||||
\(729\) | 9.11803 | + | 28.0624i | 0.337705 | + | 1.03935i | ||||
\(730\) | 1.47214 | − | 4.53077i | 0.0544862 | − | 0.167691i | ||||
\(731\) | −22.9894 | − | 16.7027i | −0.850292 | − | 0.617773i | ||||
\(732\) | 8.47214 | + | 6.15537i | 0.313139 | + | 0.227509i | ||||
\(733\) | 7.00000 | − | 21.5438i | 0.258551 | − | 0.795738i | −0.734558 | − | 0.678546i | \(-0.762611\pi\) |
0.993109 | − | 0.117192i | \(-0.0373894\pi\) | |||||||
\(734\) | 3.70820 | + | 11.4127i | 0.136872 | + | 0.421250i | ||||
\(735\) | 2.61803 | − | 1.90211i | 0.0965676 | − | 0.0701605i | ||||
\(736\) | −8.47214 | −0.312287 | ||||||||
\(737\) | 2.77458 | − | 2.31838i | 0.102203 | − | 0.0853988i | ||||
\(738\) | 0.326238 | 0.0120090 | ||||||||
\(739\) | −0.354102 | + | 0.257270i | −0.0130259 | + | 0.00946383i | −0.594279 | − | 0.804259i | \(-0.702563\pi\) |
0.581253 | + | 0.813723i | \(0.302563\pi\) | |||||||
\(740\) | −4.76393 | − | 14.6619i | −0.175126 | − | 0.538981i | ||||
\(741\) | 0.236068 | − | 0.726543i | 0.00867217 | − | 0.0266902i | ||||
\(742\) | −4.00000 | − | 2.90617i | −0.146845 | − | 0.106689i | ||||
\(743\) | 2.38197 | + | 1.73060i | 0.0873859 | + | 0.0634895i | 0.630620 | − | 0.776091i | \(-0.282801\pi\) |
−0.543234 | + | 0.839581i | \(0.682801\pi\) | |||||||
\(744\) | −2.23607 | + | 6.88191i | −0.0819782 | + | 0.252303i | ||||
\(745\) | −6.65248 | − | 20.4742i | −0.243728 | − | 0.750117i | ||||
\(746\) | 24.6525 | − | 17.9111i | 0.902591 | − | 0.655771i | ||||
\(747\) | 4.97871 | 0.182162 | ||||||||
\(748\) | 4.73607 | − | 18.8294i | 0.173168 | − | 0.688470i | ||||
\(749\) | 7.32624 | 0.267695 | ||||||||
\(750\) | 15.7082 | − | 11.4127i | 0.573583 | − | 0.416732i | ||||
\(751\) | −15.2016 | − | 46.7858i | −0.554715 | − | 1.70724i | −0.696694 | − | 0.717368i | \(-0.745347\pi\) |
0.141979 | − | 0.989870i | \(-0.454653\pi\) | |||||||
\(752\) | 0.527864 | − | 1.62460i | 0.0192492 | − | 0.0592430i | ||||
\(753\) | −6.47214 | − | 4.70228i | −0.235858 | − | 0.171361i | ||||
\(754\) | −20.9443 | − | 15.2169i | −0.762745 | − | 0.554167i | ||||
\(755\) | −1.41641 | + | 4.35926i | −0.0515484 | + | 0.158650i | ||||
\(756\) | −1.69098 | − | 5.20431i | −0.0615005 | − | 0.189279i | ||||
\(757\) | −11.3820 | + | 8.26948i | −0.413685 | + | 0.300559i | −0.775092 | − | 0.631849i | \(-0.782296\pi\) |
0.361407 | + | 0.932408i | \(0.382296\pi\) | |||||||
\(758\) | 12.8541 | 0.466882 | ||||||||
\(759\) | −38.5066 | − | 24.1724i | −1.39770 | − | 0.877404i | ||||
\(760\) | 0.291796 | 0.0105846 | ||||||||
\(761\) | 11.6803 | − | 8.48626i | 0.423412 | − | 0.307627i | −0.355597 | − | 0.934639i | \(-0.615723\pi\) |
0.779009 | + | 0.627012i | \(0.215723\pi\) | |||||||
\(762\) | −4.38197 | − | 13.4863i | −0.158742 | − | 0.488557i | ||||
\(763\) | 3.14590 | − | 9.68208i | 0.113889 | − | 0.350515i | ||||
\(764\) | −10.0902 | − | 7.33094i | −0.365050 | − | 0.265224i | ||||
\(765\) | −3.61803 | − | 2.62866i | −0.130810 | − | 0.0950392i | ||||
\(766\) | −1.03444 | + | 3.18368i | −0.0373759 | + | 0.115031i | ||||
\(767\) | 4.14590 | + | 12.7598i | 0.149700 | + | 0.460728i | ||||
\(768\) | 1.30902 | − | 0.951057i | 0.0472351 | − | 0.0343183i | ||||
\(769\) | −22.5836 | −0.814385 | −0.407193 | − | 0.913342i | \(-0.633492\pi\) | ||||
−0.407193 | + | 0.913342i | \(0.633492\pi\) | |||||||
\(770\) | −2.47214 | − | 6.15537i | −0.0890896 | − | 0.221824i | ||||
\(771\) | −41.4508 | −1.49282 | ||||||||
\(772\) | −14.0902 | + | 10.2371i | −0.507116 | + | 0.368442i | ||||
\(773\) | −9.52786 | − | 29.3238i | −0.342693 | − | 1.05470i | −0.962807 | − | 0.270190i | \(-0.912913\pi\) |
0.620114 | − | 0.784512i | \(-0.287087\pi\) | |||||||
\(774\) | −0.572949 | + | 1.76336i | −0.0205942 | + | 0.0633825i | ||||
\(775\) | −3.61803 | − | 2.62866i | −0.129964 | − | 0.0944241i | ||||
\(776\) | −2.54508 | − | 1.84911i | −0.0913632 | − | 0.0663793i | ||||
\(777\) | −3.85410 | + | 11.8617i | −0.138265 | + | 0.425536i | ||||
\(778\) | −2.00000 | − | 6.15537i | −0.0717035 | − | 0.220681i | ||||
\(779\) | 0.100813 | − | 0.0732450i | 0.00361200 | − | 0.00262427i | ||||
\(780\) | −10.4721 | −0.374963 | ||||||||
\(781\) | −34.6525 | + | 2.35114i | −1.23996 | + | 0.0841304i | ||||
\(782\) | 49.5967 | 1.77358 | ||||||||
\(783\) | 35.4164 | − | 25.7315i | 1.26568 | − | 0.919570i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | −1.70820 | + | 5.25731i | −0.0609684 | + | 0.187641i | ||||
\(786\) | −20.3713 | − | 14.8006i | −0.726621 | − | 0.527921i | ||||
\(787\) | −3.35410 | − | 2.43690i | −0.119561 | − | 0.0868660i | 0.526398 | − | 0.850238i | \(-0.323542\pi\) |
−0.645959 | + | 0.763372i | \(0.723542\pi\) | |||||||
\(788\) | −1.09017 | + | 3.35520i | −0.0388357 | + | 0.119524i | ||||
\(789\) | 6.47214 | + | 19.9192i | 0.230414 | + | 0.709142i | ||||
\(790\) | −2.00000 | + | 1.45309i | −0.0711568 | + | 0.0516984i | ||||
\(791\) | −4.61803 | −0.164198 | ||||||||
\(792\) | −1.26393 | + | 0.0857567i | −0.0449119 | + | 0.00304723i | ||||
\(793\) | 20.9443 | 0.743753 | ||||||||
\(794\) | −25.5623 | + | 18.5721i | −0.907172 | + | 0.659099i | ||||
\(795\) | −4.94427 | − | 15.2169i | −0.175355 | − | 0.539688i | ||||
\(796\) | −6.23607 | + | 19.1926i | −0.221032 | + | 0.680265i | ||||
\(797\) | −34.6525 | − | 25.1765i | −1.22745 | − | 0.891797i | −0.230757 | − | 0.973011i | \(-0.574120\pi\) |
−0.996697 | + | 0.0812141i | \(0.974120\pi\) | |||||||
\(798\) | −0.190983 | − | 0.138757i | −0.00676073 | − | 0.00491195i | ||||
\(799\) | −3.09017 | + | 9.51057i | −0.109322 | + | 0.336460i | ||||
\(800\) | 0.309017 | + | 0.951057i | 0.0109254 | + | 0.0336249i | ||||
\(801\) | −4.73607 | + | 3.44095i | −0.167341 | + | 0.121580i | ||||
\(802\) | −4.67376 | −0.165036 | ||||||||
\(803\) | 2.94427 | + | 7.33094i | 0.103901 | + | 0.258703i | ||||
\(804\) | −1.76393 | −0.0622091 | ||||||||
\(805\) | 13.7082 | − | 9.95959i | 0.483151 | − | 0.351030i | ||||
\(806\) | 4.47214 | + | 13.7638i | 0.157524 | + | 0.484810i | ||||
\(807\) | 1.29180 | − | 3.97574i | 0.0454734 | − | 0.139953i | ||||
\(808\) | −15.0902 | − | 10.9637i | −0.530870 | − | 0.385700i | ||||
\(809\) | −0.444272 | − | 0.322782i | −0.0156198 | − | 0.0113484i | 0.579948 | − | 0.814654i | \(-0.303073\pi\) |
−0.595568 | + | 0.803305i | \(0.703073\pi\) | |||||||
\(810\) | 4.76393 | − | 14.6619i | 0.167388 | − | 0.515166i | ||||
\(811\) | 9.61146 | + | 29.5810i | 0.337504 | + | 1.03873i | 0.965475 | + | 0.260494i | \(0.0838854\pi\) |
−0.627972 | + | 0.778236i | \(0.716115\pi\) | |||||||
\(812\) | −6.47214 | + | 4.70228i | −0.227127 | + | 0.165018i | ||||
\(813\) | 30.1803 | 1.05847 | ||||||||
\(814\) | 21.6525 | + | 13.5923i | 0.758919 | + | 0.476410i | ||||
\(815\) | 46.5410 | 1.63026 | ||||||||
\(816\) | −7.66312 | + | 5.56758i | −0.268263 | + | 0.194904i | ||||
\(817\) | 0.218847 | + | 0.673542i | 0.00765649 | + | 0.0235643i | ||||
\(818\) | −5.67376 | + | 17.4620i | −0.198378 | + | 0.610546i | ||||
\(819\) | −1.00000 | − | 0.726543i | −0.0349428 | − | 0.0253875i | ||||
\(820\) | −1.38197 | − | 1.00406i | −0.0482603 | − | 0.0350632i | ||||
\(821\) | 5.00000 | − | 15.3884i | 0.174501 | − | 0.537059i | −0.825109 | − | 0.564973i | \(-0.808886\pi\) |
0.999610 | + | 0.0279139i | \(0.00888643\pi\) | |||||||
\(822\) | −9.66312 | − | 29.7400i | −0.337040 | − | 1.03730i | ||||
\(823\) | −7.00000 | + | 5.08580i | −0.244005 | + | 0.177280i | −0.703066 | − | 0.711125i | \(-0.748186\pi\) |
0.459061 | + | 0.888405i | \(0.348186\pi\) | |||||||
\(824\) | 9.70820 | 0.338201 | ||||||||
\(825\) | −1.30902 | + | 5.20431i | −0.0455741 | + | 0.181191i | ||||
\(826\) | 4.14590 | 0.144254 | ||||||||
\(827\) | −5.59017 | + | 4.06150i | −0.194389 | + | 0.141232i | −0.680723 | − | 0.732541i | \(-0.738334\pi\) |
0.486333 | + | 0.873773i | \(0.338334\pi\) | |||||||
\(828\) | −1.00000 | − | 3.07768i | −0.0347524 | − | 0.106957i | ||||
\(829\) | 1.20163 | − | 3.69822i | 0.0417342 | − | 0.128445i | −0.928019 | − | 0.372534i | \(-0.878489\pi\) |
0.969753 | + | 0.244089i | \(0.0784890\pi\) | |||||||
\(830\) | −21.0902 | − | 15.3229i | −0.732050 | − | 0.531866i | ||||
\(831\) | 30.4164 | + | 22.0988i | 1.05513 | + | 0.766599i | ||||
\(832\) | 1.00000 | − | 3.07768i | 0.0346688 | − | 0.106699i | ||||
\(833\) | −1.80902 | − | 5.56758i | −0.0626787 | − | 0.192905i | ||||
\(834\) | 18.9443 | − | 13.7638i | 0.655986 | − | 0.476602i | ||||
\(835\) | 32.9443 | 1.14008 | ||||||||
\(836\) | −0.371323 | + | 0.310271i | −0.0128425 | + | 0.0107309i | ||||
\(837\) | −24.4721 | −0.845881 | ||||||||
\(838\) | 9.30902 | − | 6.76340i | 0.321575 | − | 0.233638i | ||||
\(839\) | −15.0000 | − | 46.1653i | −0.517858 | − | 1.59380i | −0.778022 | − | 0.628237i | \(-0.783777\pi\) |
0.260164 | − | 0.965564i | \(-0.416223\pi\) | |||||||
\(840\) | −1.00000 | + | 3.07768i | −0.0345033 | + | 0.106190i | ||||
\(841\) | −28.3156 | − | 20.5725i | −0.976400 | − | 0.709396i | ||||
\(842\) | −3.61803 | − | 2.62866i | −0.124686 | − | 0.0905895i | ||||
\(843\) | −4.89919 | + | 15.0781i | −0.168737 | + | 0.519319i | ||||
\(844\) | −4.91641 | − | 15.1311i | −0.169230 | − | 0.520836i | ||||
\(845\) | 4.09017 | − | 2.97168i | 0.140706 | − | 0.102229i | ||||
\(846\) | 0.652476 | 0.0224326 | ||||||||
\(847\) | 9.69098 | + | 5.20431i | 0.332986 | + | 0.178822i | ||||
\(848\) | 4.94427 | 0.169787 | ||||||||
\(849\) | 14.4721 | − | 10.5146i | 0.496682 | − | 0.360861i | ||||
\(850\) | −1.80902 | − | 5.56758i | −0.0620488 | − | 0.190966i | ||||
\(851\) | −20.1803 | + | 62.1087i | −0.691773 | + | 2.12906i | ||||
\(852\) | 13.7082 | + | 9.95959i | 0.469635 | + | 0.341210i | ||||
\(853\) | −22.7082 | − | 16.4985i | −0.777514 | − | 0.564897i | 0.126718 | − | 0.991939i | \(-0.459556\pi\) |
−0.904232 | + | 0.427042i | \(0.859556\pi\) | |||||||
\(854\) | 2.00000 | − | 6.15537i | 0.0684386 | − | 0.210632i | ||||
\(855\) | 0.0344419 | + | 0.106001i | 0.00117789 | + | 0.00362516i | ||||
\(856\) | −5.92705 | + | 4.30625i | −0.202582 | + | 0.147185i | ||||
\(857\) | −16.0902 | −0.549630 | −0.274815 | − | 0.961497i | \(-0.588617\pi\) | ||||
−0.274815 | + | 0.961497i | \(0.588617\pi\) | |||||||
\(858\) | 13.3262 | − | 11.1352i | 0.454950 | − | 0.380148i | ||||
\(859\) | 25.3820 | 0.866022 | 0.433011 | − | 0.901389i | \(-0.357451\pi\) | ||||
0.433011 | + | 0.901389i | \(0.357451\pi\) | |||||||
\(860\) | 7.85410 | − | 5.70634i | 0.267823 | − | 0.194585i | ||||
\(861\) | 0.427051 | + | 1.31433i | 0.0145539 | + | 0.0447922i | ||||
\(862\) | −7.61803 | + | 23.4459i | −0.259471 | + | 0.798570i | ||||
\(863\) | 32.5623 | + | 23.6579i | 1.10843 | + | 0.805324i | 0.982416 | − | 0.186704i | \(-0.0597804\pi\) |
0.126018 | + | 0.992028i | \(0.459780\pi\) | |||||||
\(864\) | 4.42705 | + | 3.21644i | 0.150611 | + | 0.109426i | ||||
\(865\) | 1.41641 | − | 4.35926i | 0.0481593 | − | 0.148219i | ||||
\(866\) | −2.01064 | − | 6.18812i | −0.0683244 | − | 0.210281i | ||||
\(867\) | 22.6074 | − | 16.4252i | 0.767787 | − | 0.557830i | ||||
\(868\) | 4.47214 | 0.151794 | ||||||||
\(869\) | 1.00000 | − | 3.97574i | 0.0339227 | − | 0.134868i | ||||
\(870\) | −25.8885 | −0.877704 | ||||||||
\(871\) | −2.85410 | + | 2.07363i | −0.0967076 | + | 0.0702622i | ||||
\(872\) | 3.14590 | + | 9.68208i | 0.106534 | + | 0.327877i | ||||
\(873\) | 0.371323 | − | 1.14281i | 0.0125674 | − | 0.0386784i | ||||
\(874\) | −1.00000 | − | 0.726543i | −0.0338255 | − | 0.0245757i | ||||
\(875\) | −9.70820 | − | 7.05342i | −0.328197 | − | 0.238449i | ||||
\(876\) | 1.19098 | − | 3.66547i | 0.0402396 | − | 0.123845i | ||||
\(877\) | 11.2918 | + | 34.7526i | 0.381297 | + | 1.17351i | 0.939131 | + | 0.343559i | \(0.111632\pi\) |
−0.557834 | + | 0.829952i | \(0.688368\pi\) | |||||||
\(878\) | −13.7082 | + | 9.95959i | −0.462629 | + | 0.336120i | ||||
\(879\) | −42.3607 | −1.42879 | ||||||||
\(880\) | 5.61803 | + | 3.52671i | 0.189384 | + | 0.118885i | ||||
\(881\) | 42.9230 | 1.44611 | 0.723056 | − | 0.690789i | \(-0.242737\pi\) | ||||
0.723056 | + | 0.690789i | \(0.242737\pi\) | |||||||
\(882\) | −0.309017 | + | 0.224514i | −0.0104051 | + | 0.00755978i | ||||
\(883\) | 7.97214 | + | 24.5357i | 0.268284 | + | 0.825692i | 0.990919 | + | 0.134463i | \(0.0429308\pi\) |
−0.722635 | + | 0.691230i | \(0.757069\pi\) | |||||||
\(884\) | −5.85410 | + | 18.0171i | −0.196895 | + | 0.605980i | ||||
\(885\) | 10.8541 | + | 7.88597i | 0.364857 | + | 0.265084i | ||||
\(886\) | 25.9615 | + | 18.8621i | 0.872193 | + | 0.633686i | ||||
\(887\) | −3.85410 | + | 11.8617i | −0.129408 | + | 0.398277i | −0.994678 | − | 0.103028i | \(-0.967147\pi\) |
0.865270 | + | 0.501306i | \(0.167147\pi\) | |||||||
\(888\) | −3.85410 | − | 11.8617i | −0.129335 | − | 0.398053i | ||||
\(889\) | −7.09017 | + | 5.15131i | −0.237797 | + | 0.172769i | ||||
\(890\) | 30.6525 | 1.02747 | ||||||||
\(891\) | 9.52786 | + | 23.7234i | 0.319195 | + | 0.794764i | ||||
\(892\) | −17.4164 | −0.583144 | ||||||||
\(893\) | 0.201626 | − | 0.146490i | 0.00674716 | − | 0.00490210i | ||||
\(894\) | −5.38197 | − | 16.5640i | −0.180000 | − | 0.553983i | ||||
\(895\) | −15.1459 | + | 46.6143i | −0.506272 | + | 1.55814i | ||||
\(896\) | −0.809017 | − | 0.587785i | −0.0270274 | − | 0.0196365i | ||||
\(897\) | 35.8885 | + | 26.0746i | 1.19828 | + | 0.870604i | ||||
\(898\) | −6.10081 | + | 18.7764i | −0.203587 | + | 0.626576i | ||||
\(899\) | 11.0557 | + | 34.0260i | 0.368729 | + | 1.13483i | ||||
\(900\) | −0.309017 | + | 0.224514i | −0.0103006 | + | 0.00748380i | ||||
\(901\) | −28.9443 | −0.964274 | ||||||||
\(902\) | 2.82624 | − | 0.191758i | 0.0941034 | − | 0.00638484i | ||||
\(903\) | −7.85410 | −0.261368 | ||||||||
\(904\) | 3.73607 | − | 2.71441i | 0.124260 | − | 0.0902800i | ||||
\(905\) | −11.5967 | − | 35.6911i | −0.385489 | − | 1.18641i | ||||
\(906\) | −1.14590 | + | 3.52671i | −0.0380699 | + | 0.117167i | ||||
\(907\) | 2.40983 | + | 1.75084i | 0.0800171 | + | 0.0581358i | 0.627075 | − | 0.778959i | \(-0.284252\pi\) |
−0.547058 | + | 0.837095i | \(0.684252\pi\) | |||||||
\(908\) | −22.0623 | − | 16.0292i | −0.732163 | − | 0.531948i | ||||
\(909\) | 2.20163 | − | 6.77591i | 0.0730233 | − | 0.224743i | ||||
\(910\) | 2.00000 | + | 6.15537i | 0.0662994 | + | 0.204048i | ||||
\(911\) | 20.7984 | − | 15.1109i | 0.689081 | − | 0.500647i | −0.187277 | − | 0.982307i | \(-0.559966\pi\) |
0.876358 | + | 0.481661i | \(0.159966\pi\) | |||||||
\(912\) | 0.236068 | 0.00781699 | ||||||||
\(913\) | 43.1312 | − | 2.92641i | 1.42743 | − | 0.0968502i | ||||
\(914\) | −37.9787 | −1.25622 | ||||||||
\(915\) | 16.9443 | − | 12.3107i | 0.560160 | − | 0.406980i | ||||
\(916\) | −7.03444 | − | 21.6498i | −0.232425 | − | 0.715329i | ||||
\(917\) | −4.80902 | + | 14.8006i | −0.158808 | + | 0.488760i | ||||
\(918\) | −25.9164 | − | 18.8294i | −0.855369 | − | 0.621462i | ||||
\(919\) | −22.7082 | − | 16.4985i | −0.749075 | − | 0.544235i | 0.146465 | − | 0.989216i | \(-0.453210\pi\) |
−0.895540 | + | 0.444981i | \(0.853210\pi\) | |||||||
\(920\) | −5.23607 | + | 16.1150i | −0.172628 | + | 0.531295i | ||||
\(921\) | 8.80902 | + | 27.1114i | 0.290267 | + | 0.893350i | ||||
\(922\) | −33.1803 | + | 24.1069i | −1.09274 | + | 0.793919i | ||||
\(923\) | 33.8885 | 1.11546 | ||||||||
\(924\) | −2.00000 | − | 4.97980i | −0.0657952 | − | 0.163823i | ||||
\(925\) | 7.70820 | 0.253444 | ||||||||
\(926\) | 20.0344 | − | 14.5559i | 0.658373 | − | 0.478336i | ||||
\(927\) | 1.14590 | + | 3.52671i | 0.0376362 | + | 0.115832i | ||||
\(928\) | 2.47214 | − | 7.60845i | 0.0811518 | − | 0.249760i | ||||
\(929\) | 32.6246 | + | 23.7032i | 1.07038 | + | 0.777676i | 0.975980 | − | 0.217859i | \(-0.0699072\pi\) |
0.0943985 | + | 0.995534i | \(0.469907\pi\) | |||||||
\(930\) | 11.7082 | + | 8.50651i | 0.383927 | + | 0.278939i | ||||
\(931\) | −0.0450850 | + | 0.138757i | −0.00147760 | + | 0.00454759i | ||||
\(932\) | 2.44427 | + | 7.52270i | 0.0800648 | + | 0.246414i | ||||
\(933\) | −5.61803 | + | 4.08174i | −0.183926 | + | 0.133630i | ||||
\(934\) | −21.8885 | −0.716215 | ||||||||
\(935\) | −32.8885 | − | 20.6457i | −1.07557 | − | 0.675188i | ||||
\(936\) | 1.23607 | 0.0404021 | ||||||||
\(937\) | 21.1525 | − | 15.3682i | 0.691021 | − | 0.502056i | −0.185974 | − | 0.982555i | \(-0.559544\pi\) |
0.876996 | + | 0.480498i | \(0.159544\pi\) | |||||||
\(938\) | 0.336881 | + | 1.03681i | 0.0109996 | + | 0.0338532i | ||||
\(939\) | 5.39919 | − | 16.6170i | 0.176196 | − | 0.542275i | ||||
\(940\) | −2.76393 | − | 2.00811i | −0.0901495 | − | 0.0654975i | ||||
\(941\) | 17.0344 | + | 12.3762i | 0.555307 | + | 0.403454i | 0.829738 | − | 0.558153i | \(-0.188490\pi\) |
−0.274431 | + | 0.961607i | \(0.588490\pi\) | |||||||
\(942\) | −1.38197 | + | 4.25325i | −0.0450269 | + | 0.138579i | ||||
\(943\) | 2.23607 | + | 6.88191i | 0.0728164 | + | 0.224106i | ||||
\(944\) | −3.35410 | + | 2.43690i | −0.109167 | + | 0.0793143i | ||||
\(945\) | −10.9443 | −0.356017 | ||||||||
\(946\) | −3.92705 | + | 15.6129i | −0.127679 | + | 0.507620i | ||||
\(947\) | −27.2705 | −0.886172 | −0.443086 | − | 0.896479i | \(-0.646116\pi\) | ||||
−0.443086 | + | 0.896479i | \(0.646116\pi\) | |||||||
\(948\) | −1.61803 | + | 1.17557i | −0.0525513 | + | 0.0381808i | ||||
\(949\) | −2.38197 | − | 7.33094i | −0.0773219 | − | 0.237972i | ||||
\(950\) | −0.0450850 | + | 0.138757i | −0.00146275 | + | 0.00450188i | ||||
\(951\) | 15.7082 | + | 11.4127i | 0.509373 | + | 0.370081i | ||||
\(952\) | 4.73607 | + | 3.44095i | 0.153497 | + | 0.111522i | ||||
\(953\) | −12.4443 | + | 38.2995i | −0.403110 | + | 1.24064i | 0.519354 | + | 0.854559i | \(0.326173\pi\) |
−0.922464 | + | 0.386084i | \(0.873827\pi\) | |||||||
\(954\) | 0.583592 | + | 1.79611i | 0.0188945 | + | 0.0581513i | ||||
\(955\) | −20.1803 | + | 14.6619i | −0.653020 | + | 0.474447i | ||||
\(956\) | 0.291796 | 0.00943736 | ||||||||
\(957\) | 32.9443 | − | 27.5276i | 1.06494 | − | 0.889842i | ||||
\(958\) | 8.65248 | 0.279549 | ||||||||
\(959\) | −15.6353 | + | 11.3597i | −0.504889 | + | 0.366823i | ||||
\(960\) | −1.00000 | − | 3.07768i | −0.0322749 | − | 0.0993318i | ||||
\(961\) | −3.39919 | + | 10.4616i | −0.109651 | + | 0.337472i | ||||
\(962\) | −20.1803 | − | 14.6619i | −0.650640 | − | 0.472718i | ||||
\(963\) | −2.26393 | − | 1.64484i | −0.0729542 | − | 0.0530043i | ||||
\(964\) | −2.10081 | + | 6.46564i | −0.0676626 | + | 0.208244i | ||||
\(965\) | 10.7639 | + | 33.1280i | 0.346503 | + | 1.06643i | ||||
\(966\) | 11.0902 | − | 8.05748i | 0.356820 | − | 0.259245i | ||||
\(967\) | 0.472136 | 0.0151829 | 0.00759143 | − | 0.999971i | \(-0.497584\pi\) | ||||
0.00759143 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(968\) | −10.8992 | + | 1.48584i | −0.350313 | + | 0.0477567i | ||||
\(969\) | −1.38197 | −0.0443951 | ||||||||
\(970\) | −5.09017 | + | 3.69822i | −0.163436 | + | 0.118743i | ||||
\(971\) | 7.88854 | + | 24.2784i | 0.253155 | + | 0.779132i | 0.994187 | + | 0.107663i | \(0.0343366\pi\) |
−0.741032 | + | 0.671470i | \(0.765663\pi\) | |||||||
\(972\) | −1.21885 | + | 3.75123i | −0.0390945 | + | 0.120321i | ||||
\(973\) | −11.7082 | − | 8.50651i | −0.375348 | − | 0.272706i | ||||
\(974\) | −15.6180 | − | 11.3472i | −0.500434 | − | 0.363587i | ||||
\(975\) | 1.61803 | − | 4.97980i | 0.0518186 | − | 0.159481i | ||||
\(976\) | 2.00000 | + | 6.15537i | 0.0640184 | + | 0.197028i | ||||
\(977\) | 22.2705 | − | 16.1805i | 0.712497 | − | 0.517659i | −0.171481 | − | 0.985187i | \(-0.554855\pi\) |
0.883978 | + | 0.467528i | \(0.154855\pi\) | |||||||
\(978\) | 37.6525 | 1.20399 | ||||||||
\(979\) | −39.0066 | + | 32.5932i | −1.24666 | + | 1.04168i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | −3.14590 | + | 2.28563i | −0.100441 | + | 0.0729745i | ||||
\(982\) | 5.50000 | + | 16.9273i | 0.175512 | + | 0.540171i | ||||
\(983\) | −0.708204 | + | 2.17963i | −0.0225882 | + | 0.0695193i | −0.961715 | − | 0.274051i | \(-0.911636\pi\) |
0.939127 | + | 0.343570i | \(0.111636\pi\) | |||||||
\(984\) | −1.11803 | − | 0.812299i | −0.0356416 | − | 0.0258952i | ||||
\(985\) | 5.70820 | + | 4.14725i | 0.181879 | + | 0.132142i | ||||
\(986\) | −14.4721 | + | 44.5407i | −0.460887 | + | 1.41846i | ||||
\(987\) | 0.854102 | + | 2.62866i | 0.0271864 | + | 0.0836710i | ||||
\(988\) | 0.381966 | − | 0.277515i | 0.0121520 | − | 0.00882891i | ||||
\(989\) | −41.1246 | −1.30769 | ||||||||
\(990\) | −0.618034 | + | 2.45714i | −0.0196424 | + | 0.0780931i | ||||
\(991\) | 33.2361 | 1.05578 | 0.527889 | − | 0.849313i | \(-0.322984\pi\) | ||||
0.527889 | + | 0.849313i | \(0.322984\pi\) | |||||||
\(992\) | −3.61803 | + | 2.62866i | −0.114873 | + | 0.0834599i | ||||
\(993\) | 2.13525 | + | 6.57164i | 0.0677603 | + | 0.208545i | ||||
\(994\) | 3.23607 | − | 9.95959i | 0.102642 | − | 0.315899i | ||||
\(995\) | 32.6525 | + | 23.7234i | 1.03515 | + | 0.752083i | ||||
\(996\) | −17.0623 | − | 12.3965i | −0.540640 | − | 0.392798i | ||||
\(997\) | −4.85410 | + | 14.9394i | −0.153731 | + | 0.473135i | −0.998030 | − | 0.0627369i | \(-0.980017\pi\) |
0.844299 | + | 0.535872i | \(0.180017\pi\) | |||||||
\(998\) | −8.73607 | − | 26.8869i | −0.276535 | − | 0.851088i | ||||
\(999\) | 34.1246 | − | 24.7930i | 1.07965 | − | 0.784415i |
(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 | 154.2.f.c.113.1 | yes | 4 | |
11.2 | odd | 10 | 1694.2.a.r.1.1 | 2 | |||
11.4 | even | 5 | inner | 154.2.f.c.15.1 | ✓ | 4 | |
11.9 | even | 5 | 1694.2.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.f.c.15.1 | ✓ | 4 | 11.4 | even | 5 | inner | |
154.2.f.c.113.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1694.2.a.m.1.1 | 2 | 11.9 | even | 5 | |||
1694.2.a.r.1.1 | 2 | 11.2 | odd | 10 |