Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.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: | \(3.33774680449\) |
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 | 115.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.115 |
Dual form | 418.2.f.c.229.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | 0.796305 | − | 0.604896i | \(-0.206785\pi\) |
−0.329218 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.809017 | + | 2.48990i | −0.361803 | + | 1.11352i | 0.590155 | + | 0.807290i | \(0.299067\pi\) |
−0.951959 | + | 0.306227i | \(0.900933\pi\) | |||||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | −1.30902 | + | 0.951057i | −0.494762 | + | 0.359466i | −0.807013 | − | 0.590534i | \(-0.798917\pi\) |
0.312251 | + | 0.950000i | \(0.398917\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | −0.618034 | − | 1.90211i | −0.206011 | − | 0.634038i | ||||
\(10\) | −2.61803 | −0.827895 | ||||||||
\(11\) | −3.30902 | + | 0.224514i | −0.997706 | + | 0.0676935i | ||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.50000 | + | 4.61653i | 0.416025 | + | 1.28039i | 0.911331 | + | 0.411675i | \(0.135056\pi\) |
−0.495306 | + | 0.868719i | \(0.664944\pi\) | |||||||
\(14\) | −1.30902 | − | 0.951057i | −0.349850 | − | 0.254181i | ||||
\(15\) | −2.11803 | + | 1.53884i | −0.546874 | + | 0.397327i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 0.0729490 | − | 0.224514i | 0.0176927 | − | 0.0544526i | −0.941820 | − | 0.336117i | \(-0.890886\pi\) |
0.959513 | + | 0.281664i | \(0.0908864\pi\) | |||||||
\(18\) | 1.61803 | − | 1.17557i | 0.381374 | − | 0.277085i | ||||
\(19\) | 0.809017 | + | 0.587785i | 0.185601 | + | 0.134847i | ||||
\(20\) | −0.809017 | − | 2.48990i | −0.180902 | − | 0.556758i | ||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | −1.23607 | − | 3.07768i | −0.263531 | − | 0.656164i | ||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | −0.309017 | − | 0.951057i | −0.0630778 | − | 0.194134i | ||||
\(25\) | −1.50000 | − | 1.08981i | −0.300000 | − | 0.217963i | ||||
\(26\) | −3.92705 | + | 2.85317i | −0.770158 | + | 0.559553i | ||||
\(27\) | 1.54508 | − | 4.75528i | 0.297352 | − | 0.915155i | ||||
\(28\) | 0.500000 | − | 1.53884i | 0.0944911 | − | 0.290814i | ||||
\(29\) | 7.23607 | − | 5.25731i | 1.34370 | − | 0.976258i | 0.344405 | − | 0.938821i | \(-0.388081\pi\) |
0.999299 | − | 0.0374370i | \(-0.0119194\pi\) | |||||||
\(30\) | −2.11803 | − | 1.53884i | −0.386698 | − | 0.280953i | ||||
\(31\) | 2.69098 | + | 8.28199i | 0.483315 | + | 1.48749i | 0.834407 | + | 0.551149i | \(0.185810\pi\) |
−0.351092 | + | 0.936341i | \(0.614190\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.80902 | − | 1.76336i | −0.488987 | − | 0.306961i | ||||
\(34\) | 0.236068 | 0.0404853 | ||||||||
\(35\) | −1.30902 | − | 4.02874i | −0.221264 | − | 0.680981i | ||||
\(36\) | 1.61803 | + | 1.17557i | 0.269672 | + | 0.195928i | ||||
\(37\) | −7.59017 | + | 5.51458i | −1.24782 | + | 0.906592i | −0.998093 | − | 0.0617257i | \(-0.980340\pi\) |
−0.249723 | + | 0.968317i | \(0.580340\pi\) | |||||||
\(38\) | −0.309017 | + | 0.951057i | −0.0501292 | + | 0.154282i | ||||
\(39\) | −1.50000 | + | 4.61653i | −0.240192 | + | 0.739236i | ||||
\(40\) | 2.11803 | − | 1.53884i | 0.334891 | − | 0.243312i | ||||
\(41\) | 4.92705 | + | 3.57971i | 0.769476 | + | 0.559057i | 0.901802 | − | 0.432149i | \(-0.142245\pi\) |
−0.132326 | + | 0.991206i | \(0.542245\pi\) | |||||||
\(42\) | −0.500000 | − | 1.53884i | −0.0771517 | − | 0.237448i | ||||
\(43\) | −7.70820 | −1.17549 | −0.587745 | − | 0.809046i | \(-0.699984\pi\) | ||||
−0.587745 | + | 0.809046i | \(0.699984\pi\) | |||||||
\(44\) | 2.54508 | − | 2.12663i | 0.383686 | − | 0.320601i | ||||
\(45\) | 5.23607 | 0.780547 | ||||||||
\(46\) | −0.309017 | − | 0.951057i | −0.0455621 | − | 0.140226i | ||||
\(47\) | 7.04508 | + | 5.11855i | 1.02763 | + | 0.746618i | 0.967833 | − | 0.251593i | \(-0.0809543\pi\) |
0.0597980 | + | 0.998210i | \(0.480954\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | −1.35410 | + | 4.16750i | −0.193443 | + | 0.595357i | ||||
\(50\) | 0.572949 | − | 1.76336i | 0.0810272 | − | 0.249376i | ||||
\(51\) | 0.190983 | − | 0.138757i | 0.0267430 | − | 0.0194299i | ||||
\(52\) | −3.92705 | − | 2.85317i | −0.544584 | − | 0.395663i | ||||
\(53\) | 1.39919 | + | 4.30625i | 0.192193 | + | 0.591510i | 0.999998 | + | 0.00205944i | \(0.000655539\pi\) |
−0.807805 | + | 0.589450i | \(0.799344\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 2.11803 | − | 8.42075i | 0.285596 | − | 1.13545i | ||||
\(56\) | 1.61803 | 0.216219 | ||||||||
\(57\) | 0.309017 | + | 0.951057i | 0.0409303 | + | 0.125971i | ||||
\(58\) | 7.23607 | + | 5.25731i | 0.950142 | + | 0.690319i | ||||
\(59\) | 4.73607 | − | 3.44095i | 0.616584 | − | 0.447974i | −0.235143 | − | 0.971961i | \(-0.575556\pi\) |
0.851726 | + | 0.523987i | \(0.175556\pi\) | |||||||
\(60\) | 0.809017 | − | 2.48990i | 0.104444 | − | 0.321444i | ||||
\(61\) | 4.50000 | − | 13.8496i | 0.576166 | − | 1.77326i | −0.0560084 | − | 0.998430i | \(-0.517837\pi\) |
0.632174 | − | 0.774826i | \(-0.282163\pi\) | |||||||
\(62\) | −7.04508 | + | 5.11855i | −0.894727 | + | 0.650057i | ||||
\(63\) | 2.61803 | + | 1.90211i | 0.329841 | + | 0.239644i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −12.7082 | −1.57626 | ||||||||
\(66\) | 0.809017 | − | 3.21644i | 0.0995831 | − | 0.395916i | ||||
\(67\) | −5.61803 | −0.686352 | −0.343176 | − | 0.939271i | \(-0.611503\pi\) | ||||
−0.343176 | + | 0.939271i | \(0.611503\pi\) | |||||||
\(68\) | 0.0729490 | + | 0.224514i | 0.00884637 | + | 0.0272263i | ||||
\(69\) | −0.809017 | − | 0.587785i | −0.0973942 | − | 0.0707610i | ||||
\(70\) | 3.42705 | − | 2.48990i | 0.409611 | − | 0.297600i | ||||
\(71\) | 3.01722 | − | 9.28605i | 0.358078 | − | 1.10205i | −0.596125 | − | 0.802892i | \(-0.703294\pi\) |
0.954203 | − | 0.299160i | \(-0.0967063\pi\) | |||||||
\(72\) | −0.618034 | + | 1.90211i | −0.0728360 | + | 0.224166i | ||||
\(73\) | −0.309017 | + | 0.224514i | −0.0361677 | + | 0.0262774i | −0.605722 | − | 0.795676i | \(-0.707116\pi\) |
0.569555 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(74\) | −7.59017 | − | 5.51458i | −0.882339 | − | 0.641057i | ||||
\(75\) | −0.572949 | − | 1.76336i | −0.0661585 | − | 0.203615i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.11803 | − | 3.44095i | 0.469294 | − | 0.392133i | ||||
\(78\) | −4.85410 | −0.549619 | ||||||||
\(79\) | 4.63525 | + | 14.2658i | 0.521507 | + | 1.60503i | 0.771122 | + | 0.636688i | \(0.219696\pi\) |
−0.249615 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(80\) | 2.11803 | + | 1.53884i | 0.236803 | + | 0.172048i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −1.88197 | + | 5.79210i | −0.207828 | + | 0.639630i | ||||
\(83\) | 2.71885 | − | 8.36775i | 0.298432 | − | 0.918480i | −0.683615 | − | 0.729843i | \(-0.739593\pi\) |
0.982047 | − | 0.188637i | \(-0.0604069\pi\) | |||||||
\(84\) | 1.30902 | − | 0.951057i | 0.142825 | − | 0.103769i | ||||
\(85\) | 0.500000 | + | 0.363271i | 0.0542326 | + | 0.0394023i | ||||
\(86\) | −2.38197 | − | 7.33094i | −0.256854 | − | 0.790515i | ||||
\(87\) | 8.94427 | 0.958927 | ||||||||
\(88\) | 2.80902 | + | 1.76336i | 0.299442 | + | 0.187974i | ||||
\(89\) | 18.4164 | 1.95214 | 0.976068 | − | 0.217467i | \(-0.0697795\pi\) | ||||
0.976068 | + | 0.217467i | \(0.0697795\pi\) | |||||||
\(90\) | 1.61803 | + | 4.97980i | 0.170556 | + | 0.524917i | ||||
\(91\) | −6.35410 | − | 4.61653i | −0.666091 | − | 0.483943i | ||||
\(92\) | 0.809017 | − | 0.587785i | 0.0843459 | − | 0.0612808i | ||||
\(93\) | −2.69098 | + | 8.28199i | −0.279042 | + | 0.858803i | ||||
\(94\) | −2.69098 | + | 8.28199i | −0.277554 | + | 0.854222i | ||||
\(95\) | −2.11803 | + | 1.53884i | −0.217306 | + | 0.157882i | ||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | 2.83688 | + | 8.73102i | 0.288042 | + | 0.886501i | 0.985470 | + | 0.169847i | \(0.0543273\pi\) |
−0.697429 | + | 0.716654i | \(0.745673\pi\) | |||||||
\(98\) | −4.38197 | −0.442645 | ||||||||
\(99\) | 2.47214 | + | 6.15537i | 0.248459 | + | 0.618638i | ||||
\(100\) | 1.85410 | 0.185410 | ||||||||
\(101\) | −2.83688 | − | 8.73102i | −0.282280 | − | 0.868769i | −0.987201 | − | 0.159483i | \(-0.949017\pi\) |
0.704920 | − | 0.709286i | \(-0.250983\pi\) | |||||||
\(102\) | 0.190983 | + | 0.138757i | 0.0189101 | + | 0.0137390i | ||||
\(103\) | −7.54508 | + | 5.48183i | −0.743439 | + | 0.540140i | −0.893786 | − | 0.448493i | \(-0.851961\pi\) |
0.150347 | + | 0.988633i | \(0.451961\pi\) | |||||||
\(104\) | 1.50000 | − | 4.61653i | 0.147087 | − | 0.452688i | ||||
\(105\) | 1.30902 | − | 4.02874i | 0.127747 | − | 0.393165i | ||||
\(106\) | −3.66312 | + | 2.66141i | −0.355794 | + | 0.258499i | ||||
\(107\) | −4.66312 | − | 3.38795i | −0.450801 | − | 0.327526i | 0.339111 | − | 0.940746i | \(-0.389874\pi\) |
−0.789912 | + | 0.613220i | \(0.789874\pi\) | |||||||
\(108\) | 1.54508 | + | 4.75528i | 0.148676 | + | 0.457577i | ||||
\(109\) | 13.0902 | 1.25381 | 0.626905 | − | 0.779095i | \(-0.284321\pi\) | ||||
0.626905 | + | 0.779095i | \(0.284321\pi\) | |||||||
\(110\) | 8.66312 | − | 0.587785i | 0.825996 | − | 0.0560431i | ||||
\(111\) | −9.38197 | −0.890497 | ||||||||
\(112\) | 0.500000 | + | 1.53884i | 0.0472456 | + | 0.145407i | ||||
\(113\) | 5.80902 | + | 4.22050i | 0.546466 | + | 0.397031i | 0.826481 | − | 0.562965i | \(-0.190339\pi\) |
−0.280015 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(114\) | −0.809017 | + | 0.587785i | −0.0757714 | + | 0.0550511i | ||||
\(115\) | 0.809017 | − | 2.48990i | 0.0754412 | − | 0.232184i | ||||
\(116\) | −2.76393 | + | 8.50651i | −0.256625 | + | 0.789809i | ||||
\(117\) | 7.85410 | − | 5.70634i | 0.726112 | − | 0.527551i | ||||
\(118\) | 4.73607 | + | 3.44095i | 0.435990 | + | 0.316766i | ||||
\(119\) | 0.118034 | + | 0.363271i | 0.0108202 | + | 0.0333010i | ||||
\(120\) | 2.61803 | 0.238993 | ||||||||
\(121\) | 10.8992 | − | 1.48584i | 0.990835 | − | 0.135076i | ||||
\(122\) | 14.5623 | 1.31841 | ||||||||
\(123\) | 1.88197 | + | 5.79210i | 0.169691 | + | 0.522256i | ||||
\(124\) | −7.04508 | − | 5.11855i | −0.632667 | − | 0.459660i | ||||
\(125\) | −6.66312 | + | 4.84104i | −0.595967 | + | 0.432996i | ||||
\(126\) | −1.00000 | + | 3.07768i | −0.0890871 | + | 0.274182i | ||||
\(127\) | 4.54508 | − | 13.9883i | 0.403311 | − | 1.24126i | −0.518986 | − | 0.854783i | \(-0.673690\pi\) |
0.922297 | − | 0.386481i | \(-0.126310\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | −6.23607 | − | 4.53077i | −0.549055 | − | 0.398912i | ||||
\(130\) | −3.92705 | − | 12.0862i | −0.344425 | − | 1.06003i | ||||
\(131\) | −10.7639 | −0.940449 | −0.470225 | − | 0.882547i | \(-0.655827\pi\) | ||||
−0.470225 | + | 0.882547i | \(0.655827\pi\) | |||||||
\(132\) | 3.30902 | − | 0.224514i | 0.288013 | − | 0.0195414i | ||||
\(133\) | −1.61803 | −0.140301 | ||||||||
\(134\) | −1.73607 | − | 5.34307i | −0.149973 | − | 0.461571i | ||||
\(135\) | 10.5902 | + | 7.69421i | 0.911457 | + | 0.662212i | ||||
\(136\) | −0.190983 | + | 0.138757i | −0.0163767 | + | 0.0118983i | ||||
\(137\) | −0.781153 | + | 2.40414i | −0.0667384 | + | 0.205400i | −0.978864 | − | 0.204510i | \(-0.934440\pi\) |
0.912126 | + | 0.409910i | \(0.134440\pi\) | |||||||
\(138\) | 0.309017 | − | 0.951057i | 0.0263053 | − | 0.0809593i | ||||
\(139\) | 2.07295 | − | 1.50609i | 0.175825 | − | 0.127745i | −0.496392 | − | 0.868099i | \(-0.665342\pi\) |
0.672217 | + | 0.740354i | \(0.265342\pi\) | |||||||
\(140\) | 3.42705 | + | 2.48990i | 0.289639 | + | 0.210435i | ||||
\(141\) | 2.69098 | + | 8.28199i | 0.226622 | + | 0.697470i | ||||
\(142\) | 9.76393 | 0.819371 | ||||||||
\(143\) | −6.00000 | − | 14.9394i | −0.501745 | − | 1.24929i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 7.23607 | + | 22.2703i | 0.600923 | + | 1.84945i | ||||
\(146\) | −0.309017 | − | 0.224514i | −0.0255744 | − | 0.0185809i | ||||
\(147\) | −3.54508 | + | 2.57565i | −0.292394 | + | 0.212436i | ||||
\(148\) | 2.89919 | − | 8.92278i | 0.238312 | − | 0.733448i | ||||
\(149\) | 1.21885 | − | 3.75123i | 0.0998518 | − | 0.307312i | −0.888636 | − | 0.458613i | \(-0.848346\pi\) |
0.988488 | + | 0.151301i | \(0.0483463\pi\) | |||||||
\(150\) | 1.50000 | − | 1.08981i | 0.122474 | − | 0.0889829i | ||||
\(151\) | −7.47214 | − | 5.42882i | −0.608074 | − | 0.441791i | 0.240662 | − | 0.970609i | \(-0.422636\pi\) |
−0.848736 | + | 0.528818i | \(0.822636\pi\) | |||||||
\(152\) | −0.309017 | − | 0.951057i | −0.0250646 | − | 0.0771409i | ||||
\(153\) | −0.472136 | −0.0381699 | ||||||||
\(154\) | 4.54508 | + | 2.85317i | 0.366253 | + | 0.229915i | ||||
\(155\) | −22.7984 | −1.83121 | ||||||||
\(156\) | −1.50000 | − | 4.61653i | −0.120096 | − | 0.369618i | ||||
\(157\) | −4.23607 | − | 3.07768i | −0.338075 | − | 0.245626i | 0.405774 | − | 0.913973i | \(-0.367002\pi\) |
−0.743849 | + | 0.668347i | \(0.767002\pi\) | |||||||
\(158\) | −12.1353 | + | 8.81678i | −0.965429 | + | 0.701425i | ||||
\(159\) | −1.39919 | + | 4.30625i | −0.110963 | + | 0.341508i | ||||
\(160\) | −0.809017 | + | 2.48990i | −0.0639584 | + | 0.196844i | ||||
\(161\) | 1.30902 | − | 0.951057i | 0.103165 | − | 0.0749538i | ||||
\(162\) | −0.809017 | − | 0.587785i | −0.0635624 | − | 0.0461808i | ||||
\(163\) | −3.50000 | − | 10.7719i | −0.274141 | − | 0.843720i | −0.989445 | − | 0.144907i | \(-0.953712\pi\) |
0.715304 | − | 0.698813i | \(-0.246288\pi\) | |||||||
\(164\) | −6.09017 | −0.475562 | ||||||||
\(165\) | 6.66312 | − | 5.56758i | 0.518723 | − | 0.433436i | ||||
\(166\) | 8.79837 | 0.682886 | ||||||||
\(167\) | −0.881966 | − | 2.71441i | −0.0682486 | − | 0.210048i | 0.911116 | − | 0.412151i | \(-0.135222\pi\) |
−0.979364 | + | 0.202103i | \(0.935222\pi\) | |||||||
\(168\) | 1.30902 | + | 0.951057i | 0.100993 | + | 0.0733756i | ||||
\(169\) | −8.54508 | + | 6.20837i | −0.657314 | + | 0.477567i | ||||
\(170\) | −0.190983 | + | 0.587785i | −0.0146477 | + | 0.0450811i | ||||
\(171\) | 0.618034 | − | 1.90211i | 0.0472622 | − | 0.145458i | ||||
\(172\) | 6.23607 | − | 4.53077i | 0.475496 | − | 0.345468i | ||||
\(173\) | −6.59017 | − | 4.78804i | −0.501041 | − | 0.364028i | 0.308373 | − | 0.951265i | \(-0.400215\pi\) |
−0.809415 | + | 0.587238i | \(0.800215\pi\) | |||||||
\(174\) | 2.76393 | + | 8.50651i | 0.209533 | + | 0.644877i | ||||
\(175\) | 3.00000 | 0.226779 | ||||||||
\(176\) | −0.809017 | + | 3.21644i | −0.0609820 | + | 0.242448i | ||||
\(177\) | 5.85410 | 0.440021 | ||||||||
\(178\) | 5.69098 | + | 17.5150i | 0.426557 | + | 1.31281i | ||||
\(179\) | −9.47214 | − | 6.88191i | −0.707981 | − | 0.514378i | 0.174541 | − | 0.984650i | \(-0.444156\pi\) |
−0.882522 | + | 0.470272i | \(0.844156\pi\) | |||||||
\(180\) | −4.23607 | + | 3.07768i | −0.315738 | + | 0.229397i | ||||
\(181\) | −3.36475 | + | 10.3556i | −0.250100 | + | 0.769727i | 0.744656 | + | 0.667448i | \(0.232613\pi\) |
−0.994756 | + | 0.102279i | \(0.967387\pi\) | |||||||
\(182\) | 2.42705 | − | 7.46969i | 0.179905 | − | 0.553691i | ||||
\(183\) | 11.7812 | − | 8.55951i | 0.870888 | − | 0.632737i | ||||
\(184\) | 0.809017 | + | 0.587785i | 0.0596415 | + | 0.0433321i | ||||
\(185\) | −7.59017 | − | 23.3601i | −0.558040 | − | 1.71747i | ||||
\(186\) | −8.70820 | −0.638516 | ||||||||
\(187\) | −0.190983 | + | 0.759299i | −0.0139661 | + | 0.0555254i | ||||
\(188\) | −8.70820 | −0.635111 | ||||||||
\(189\) | 2.50000 | + | 7.69421i | 0.181848 | + | 0.559671i | ||||
\(190\) | −2.11803 | − | 1.53884i | −0.153658 | − | 0.111639i | ||||
\(191\) | −7.04508 | + | 5.11855i | −0.509764 | + | 0.370366i | −0.812734 | − | 0.582635i | \(-0.802022\pi\) |
0.302970 | + | 0.953000i | \(0.402022\pi\) | |||||||
\(192\) | −0.309017 | + | 0.951057i | −0.0223014 | + | 0.0686366i | ||||
\(193\) | −0.0450850 | + | 0.138757i | −0.00324529 | + | 0.00998797i | −0.952666 | − | 0.304019i | \(-0.901671\pi\) |
0.949421 | + | 0.314007i | \(0.101671\pi\) | |||||||
\(194\) | −7.42705 | + | 5.39607i | −0.533231 | + | 0.387415i | ||||
\(195\) | −10.2812 | − | 7.46969i | −0.736249 | − | 0.534916i | ||||
\(196\) | −1.35410 | − | 4.16750i | −0.0967216 | − | 0.297678i | ||||
\(197\) | 23.0000 | 1.63868 | 0.819341 | − | 0.573306i | \(-0.194340\pi\) | ||||
0.819341 | + | 0.573306i | \(0.194340\pi\) | |||||||
\(198\) | −5.09017 | + | 4.25325i | −0.361743 | + | 0.302266i | ||||
\(199\) | −3.41641 | −0.242183 | −0.121091 | − | 0.992641i | \(-0.538639\pi\) | ||||
−0.121091 | + | 0.992641i | \(0.538639\pi\) | |||||||
\(200\) | 0.572949 | + | 1.76336i | 0.0405136 | + | 0.124688i | ||||
\(201\) | −4.54508 | − | 3.30220i | −0.320586 | − | 0.232919i | ||||
\(202\) | 7.42705 | − | 5.39607i | 0.522565 | − | 0.379666i | ||||
\(203\) | −4.47214 | + | 13.7638i | −0.313882 | + | 0.966031i | ||||
\(204\) | −0.0729490 | + | 0.224514i | −0.00510745 | + | 0.0157191i | ||||
\(205\) | −12.8992 | + | 9.37181i | −0.900918 | + | 0.654555i | ||||
\(206\) | −7.54508 | − | 5.48183i | −0.525691 | − | 0.381937i | ||||
\(207\) | 0.618034 | + | 1.90211i | 0.0429563 | + | 0.132206i | ||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | −2.80902 | − | 1.76336i | −0.194304 | − | 0.121974i | ||||
\(210\) | 4.23607 | 0.292316 | ||||||||
\(211\) | −5.92705 | − | 18.2416i | −0.408035 | − | 1.25580i | −0.918334 | − | 0.395806i | \(-0.870465\pi\) |
0.510299 | − | 0.859997i | \(-0.329535\pi\) | |||||||
\(212\) | −3.66312 | − | 2.66141i | −0.251584 | − | 0.182787i | ||||
\(213\) | 7.89919 | − | 5.73910i | 0.541243 | − | 0.393236i | ||||
\(214\) | 1.78115 | − | 5.48183i | 0.121757 | − | 0.374730i | ||||
\(215\) | 6.23607 | − | 19.1926i | 0.425296 | − | 1.30893i | ||||
\(216\) | −4.04508 | + | 2.93893i | −0.275233 | + | 0.199969i | ||||
\(217\) | −11.3992 | − | 8.28199i | −0.773827 | − | 0.562218i | ||||
\(218\) | 4.04508 | + | 12.4495i | 0.273968 | + | 0.843186i | ||||
\(219\) | −0.381966 | −0.0258109 | ||||||||
\(220\) | 3.23607 | + | 8.05748i | 0.218176 | + | 0.543235i | ||||
\(221\) | 1.14590 | 0.0770814 | ||||||||
\(222\) | −2.89919 | − | 8.92278i | −0.194581 | − | 0.598858i | ||||
\(223\) | −10.4721 | − | 7.60845i | −0.701266 | − | 0.509500i | 0.179078 | − | 0.983835i | \(-0.442688\pi\) |
−0.880344 | + | 0.474335i | \(0.842688\pi\) | |||||||
\(224\) | −1.30902 | + | 0.951057i | −0.0874624 | + | 0.0635451i | ||||
\(225\) | −1.14590 | + | 3.52671i | −0.0763932 | + | 0.235114i | ||||
\(226\) | −2.21885 | + | 6.82891i | −0.147596 | + | 0.454252i | ||||
\(227\) | −13.8713 | + | 10.0781i | −0.920672 | + | 0.668907i | −0.943691 | − | 0.330828i | \(-0.892672\pi\) |
0.0230192 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(228\) | −0.809017 | − | 0.587785i | −0.0535785 | − | 0.0389270i | ||||
\(229\) | 5.42705 | + | 16.7027i | 0.358630 | + | 1.10375i | 0.953875 | + | 0.300204i | \(0.0970549\pi\) |
−0.595245 | + | 0.803544i | \(0.702945\pi\) | |||||||
\(230\) | 2.61803 | 0.172628 | ||||||||
\(231\) | 5.35410 | − | 0.363271i | 0.352274 | − | 0.0239015i | ||||
\(232\) | −8.94427 | −0.587220 | ||||||||
\(233\) | 0.218847 | + | 0.673542i | 0.0143371 | + | 0.0441252i | 0.957969 | − | 0.286871i | \(-0.0926152\pi\) |
−0.943632 | + | 0.330996i | \(0.892615\pi\) | |||||||
\(234\) | 7.85410 | + | 5.70634i | 0.513439 | + | 0.373035i | ||||
\(235\) | −18.4443 | + | 13.4005i | −1.20317 | + | 0.874155i | ||||
\(236\) | −1.80902 | + | 5.56758i | −0.117757 | + | 0.362419i | ||||
\(237\) | −4.63525 | + | 14.2658i | −0.301092 | + | 0.926666i | ||||
\(238\) | −0.309017 | + | 0.224514i | −0.0200306 | + | 0.0145531i | ||||
\(239\) | −4.30902 | − | 3.13068i | −0.278727 | − | 0.202507i | 0.439635 | − | 0.898177i | \(-0.355108\pi\) |
−0.718362 | + | 0.695669i | \(0.755108\pi\) | |||||||
\(240\) | 0.809017 | + | 2.48990i | 0.0522218 | + | 0.160722i | ||||
\(241\) | −6.09017 | −0.392302 | −0.196151 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196151 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(242\) | 4.78115 | + | 9.90659i | 0.307344 | + | 0.636820i | ||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 4.50000 | + | 13.8496i | 0.288083 | + | 0.886628i | ||||
\(245\) | −9.28115 | − | 6.74315i | −0.592951 | − | 0.430804i | ||||
\(246\) | −4.92705 | + | 3.57971i | −0.314137 | + | 0.228234i | ||||
\(247\) | −1.50000 | + | 4.61653i | −0.0954427 | + | 0.293742i | ||||
\(248\) | 2.69098 | − | 8.28199i | 0.170878 | − | 0.525907i | ||||
\(249\) | 7.11803 | − | 5.17155i | 0.451087 | − | 0.327734i | ||||
\(250\) | −6.66312 | − | 4.84104i | −0.421413 | − | 0.306174i | ||||
\(251\) | 4.76393 | + | 14.6619i | 0.300697 | + | 0.925449i | 0.981248 | + | 0.192749i | \(0.0617403\pi\) |
−0.680551 | + | 0.732700i | \(0.738260\pi\) | |||||||
\(252\) | −3.23607 | −0.203853 | ||||||||
\(253\) | 3.30902 | − | 0.224514i | 0.208036 | − | 0.0141151i | ||||
\(254\) | 14.7082 | 0.922875 | ||||||||
\(255\) | 0.190983 | + | 0.587785i | 0.0119598 | + | 0.0368085i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −13.9721 | + | 10.1514i | −0.871558 | + | 0.633224i | −0.931005 | − | 0.365008i | \(-0.881066\pi\) |
0.0594466 | + | 0.998231i | \(0.481066\pi\) | |||||||
\(258\) | 2.38197 | − | 7.33094i | 0.148295 | − | 0.456404i | ||||
\(259\) | 4.69098 | − | 14.4374i | 0.291484 | − | 0.897094i | ||||
\(260\) | 10.2812 | − | 7.46969i | 0.637610 | − | 0.463251i | ||||
\(261\) | −14.4721 | − | 10.5146i | −0.895803 | − | 0.650839i | ||||
\(262\) | −3.32624 | − | 10.2371i | −0.205496 | − | 0.632451i | ||||
\(263\) | −12.3820 | −0.763505 | −0.381752 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381752 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(264\) | 1.23607 | + | 3.07768i | 0.0760747 | + | 0.189418i | ||||
\(265\) | −11.8541 | −0.728192 | ||||||||
\(266\) | −0.500000 | − | 1.53884i | −0.0306570 | − | 0.0943524i | ||||
\(267\) | 14.8992 | + | 10.8249i | 0.911815 | + | 0.662473i | ||||
\(268\) | 4.54508 | − | 3.30220i | 0.277635 | − | 0.201714i | ||||
\(269\) | 6.01722 | − | 18.5191i | 0.366876 | − | 1.12913i | −0.581921 | − | 0.813245i | \(-0.697699\pi\) |
0.948798 | − | 0.315884i | \(-0.102301\pi\) | |||||||
\(270\) | −4.04508 | + | 12.4495i | −0.246176 | + | 0.757652i | ||||
\(271\) | 11.4721 | − | 8.33499i | 0.696883 | − | 0.506315i | −0.182033 | − | 0.983292i | \(-0.558268\pi\) |
0.878915 | + | 0.476978i | \(0.158268\pi\) | |||||||
\(272\) | −0.190983 | − | 0.138757i | −0.0115800 | − | 0.00841340i | ||||
\(273\) | −2.42705 | − | 7.46969i | −0.146892 | − | 0.452086i | ||||
\(274\) | −2.52786 | −0.152714 | ||||||||
\(275\) | 5.20820 | + | 3.26944i | 0.314067 | + | 0.197155i | ||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 5.29837 | + | 16.3067i | 0.318348 | + | 0.979776i | 0.974354 | + | 0.225020i | \(0.0722447\pi\) |
−0.656006 | + | 0.754756i | \(0.727755\pi\) | |||||||
\(278\) | 2.07295 | + | 1.50609i | 0.124327 | + | 0.0903290i | ||||
\(279\) | 14.0902 | − | 10.2371i | 0.843556 | − | 0.612880i | ||||
\(280\) | −1.30902 | + | 4.02874i | −0.0782287 | + | 0.240763i | ||||
\(281\) | 6.53444 | − | 20.1109i | 0.389812 | − | 1.19972i | −0.543117 | − | 0.839657i | \(-0.682756\pi\) |
0.932929 | − | 0.360061i | \(-0.117244\pi\) | |||||||
\(282\) | −7.04508 | + | 5.11855i | −0.419529 | + | 0.304805i | ||||
\(283\) | 13.8992 | + | 10.0984i | 0.826221 | + | 0.600285i | 0.918488 | − | 0.395450i | \(-0.129411\pi\) |
−0.0922667 | + | 0.995734i | \(0.529411\pi\) | |||||||
\(284\) | 3.01722 | + | 9.28605i | 0.179039 | + | 0.551026i | ||||
\(285\) | −2.61803 | −0.155079 | ||||||||
\(286\) | 12.3541 | − | 10.3229i | 0.730513 | − | 0.610404i | ||||
\(287\) | −9.85410 | −0.581669 | ||||||||
\(288\) | −0.618034 | − | 1.90211i | −0.0364180 | − | 0.112083i | ||||
\(289\) | 13.7082 | + | 9.95959i | 0.806365 | + | 0.585858i | ||||
\(290\) | −18.9443 | + | 13.7638i | −1.11245 | + | 0.808239i | ||||
\(291\) | −2.83688 | + | 8.73102i | −0.166301 | + | 0.511822i | ||||
\(292\) | 0.118034 | − | 0.363271i | 0.00690742 | − | 0.0212588i | ||||
\(293\) | 19.7533 | − | 14.3516i | 1.15400 | − | 0.838430i | 0.164992 | − | 0.986295i | \(-0.447240\pi\) |
0.989008 | + | 0.147865i | \(0.0472402\pi\) | |||||||
\(294\) | −3.54508 | − | 2.57565i | −0.206754 | − | 0.150215i | ||||
\(295\) | 4.73607 | + | 14.5761i | 0.275745 | + | 0.848654i | ||||
\(296\) | 9.38197 | 0.545316 | ||||||||
\(297\) | −4.04508 | + | 16.0822i | −0.234720 | + | 0.933184i | ||||
\(298\) | 3.94427 | 0.228486 | ||||||||
\(299\) | −1.50000 | − | 4.61653i | −0.0867472 | − | 0.266981i | ||||
\(300\) | 1.50000 | + | 1.08981i | 0.0866025 | + | 0.0629204i | ||||
\(301\) | 10.0902 | − | 7.33094i | 0.581588 | − | 0.422548i | ||||
\(302\) | 2.85410 | − | 8.78402i | 0.164235 | − | 0.505464i | ||||
\(303\) | 2.83688 | − | 8.73102i | 0.162975 | − | 0.501584i | ||||
\(304\) | 0.809017 | − | 0.587785i | 0.0464003 | − | 0.0337118i | ||||
\(305\) | 30.8435 | + | 22.4091i | 1.76609 | + | 1.28314i | ||||
\(306\) | −0.145898 | − | 0.449028i | −0.00834044 | − | 0.0256692i | ||||
\(307\) | 23.0000 | 1.31268 | 0.656340 | − | 0.754466i | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(308\) | −1.30902 | + | 5.20431i | −0.0745882 | + | 0.296543i | ||||
\(309\) | −9.32624 | −0.530551 | ||||||||
\(310\) | −7.04508 | − | 21.6825i | −0.400134 | − | 1.23149i | ||||
\(311\) | −1.61803 | − | 1.17557i | −0.0917503 | − | 0.0666605i | 0.540964 | − | 0.841046i | \(-0.318059\pi\) |
−0.632715 | + | 0.774385i | \(0.718059\pi\) | |||||||
\(312\) | 3.92705 | − | 2.85317i | 0.222325 | − | 0.161529i | ||||
\(313\) | −6.16312 | + | 18.9681i | −0.348360 | + | 1.07214i | 0.611400 | + | 0.791322i | \(0.290607\pi\) |
−0.959760 | + | 0.280821i | \(0.909393\pi\) | |||||||
\(314\) | 1.61803 | − | 4.97980i | 0.0913109 | − | 0.281026i | ||||
\(315\) | −6.85410 | + | 4.97980i | −0.386185 | + | 0.280580i | ||||
\(316\) | −12.1353 | − | 8.81678i | −0.682661 | − | 0.495983i | ||||
\(317\) | −5.25329 | − | 16.1680i | −0.295054 | − | 0.908083i | −0.983203 | − | 0.182514i | \(-0.941577\pi\) |
0.688149 | − | 0.725569i | \(-0.258423\pi\) | |||||||
\(318\) | −4.52786 | −0.253910 | ||||||||
\(319\) | −22.7639 | + | 19.0211i | −1.27454 | + | 1.06498i | ||||
\(320\) | −2.61803 | −0.146353 | ||||||||
\(321\) | −1.78115 | − | 5.48183i | −0.0994143 | − | 0.305966i | ||||
\(322\) | 1.30902 | + | 0.951057i | 0.0729487 | + | 0.0530003i | ||||
\(323\) | 0.190983 | − | 0.138757i | 0.0106266 | − | 0.00772066i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 2.78115 | − | 8.55951i | 0.154271 | − | 0.474796i | ||||
\(326\) | 9.16312 | − | 6.65740i | 0.507498 | − | 0.368719i | ||||
\(327\) | 10.5902 | + | 7.69421i | 0.585638 | + | 0.425491i | ||||
\(328\) | −1.88197 | − | 5.79210i | −0.103914 | − | 0.319815i | ||||
\(329\) | −14.0902 | −0.776816 | ||||||||
\(330\) | 7.35410 | + | 4.61653i | 0.404830 | + | 0.254131i | ||||
\(331\) | −24.1803 | −1.32907 | −0.664536 | − | 0.747256i | \(-0.731371\pi\) | ||||
−0.664536 | + | 0.747256i | \(0.731371\pi\) | |||||||
\(332\) | 2.71885 | + | 8.36775i | 0.149216 | + | 0.459240i | ||||
\(333\) | 15.1803 | + | 11.0292i | 0.831878 | + | 0.604394i | ||||
\(334\) | 2.30902 | − | 1.67760i | 0.126344 | − | 0.0917941i | ||||
\(335\) | 4.54508 | − | 13.9883i | 0.248325 | − | 0.764264i | ||||
\(336\) | −0.500000 | + | 1.53884i | −0.0272772 | + | 0.0839507i | ||||
\(337\) | 5.66312 | − | 4.11450i | 0.308490 | − | 0.224131i | −0.422758 | − | 0.906242i | \(-0.638938\pi\) |
0.731248 | + | 0.682111i | \(0.238938\pi\) | |||||||
\(338\) | −8.54508 | − | 6.20837i | −0.464791 | − | 0.337691i | ||||
\(339\) | 2.21885 | + | 6.82891i | 0.120511 | + | 0.370895i | ||||
\(340\) | −0.618034 | −0.0335176 | ||||||||
\(341\) | −10.7639 | − | 26.8011i | −0.582900 | − | 1.45136i | ||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | −5.69098 | − | 17.5150i | −0.307284 | − | 0.945724i | ||||
\(344\) | 6.23607 | + | 4.53077i | 0.336226 | + | 0.244283i | ||||
\(345\) | 2.11803 | − | 1.53884i | 0.114031 | − | 0.0828485i | ||||
\(346\) | 2.51722 | − | 7.74721i | 0.135327 | − | 0.416493i | ||||
\(347\) | −3.90983 | + | 12.0332i | −0.209891 | + | 0.645977i | 0.789586 | + | 0.613639i | \(0.210295\pi\) |
−0.999477 | + | 0.0323376i | \(0.989705\pi\) | |||||||
\(348\) | −7.23607 | + | 5.25731i | −0.387894 | + | 0.281821i | ||||
\(349\) | 12.9271 | + | 9.39205i | 0.691969 | + | 0.502745i | 0.877307 | − | 0.479930i | \(-0.159338\pi\) |
−0.185338 | + | 0.982675i | \(0.559338\pi\) | |||||||
\(350\) | 0.927051 | + | 2.85317i | 0.0495530 | + | 0.152508i | ||||
\(351\) | 24.2705 | 1.29546 | ||||||||
\(352\) | −3.30902 | + | 0.224514i | −0.176371 | + | 0.0119666i | ||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 1.80902 | + | 5.56758i | 0.0961482 | + | 0.295914i | ||||
\(355\) | 20.6803 | + | 15.0251i | 1.09760 | + | 0.797452i | ||||
\(356\) | −14.8992 | + | 10.8249i | −0.789655 | + | 0.573718i | ||||
\(357\) | −0.118034 | + | 0.363271i | −0.00624702 | + | 0.0192264i | ||||
\(358\) | 3.61803 | − | 11.1352i | 0.191219 | − | 0.588512i | ||||
\(359\) | −21.4443 | + | 15.5802i | −1.13179 | + | 0.822290i | −0.985954 | − | 0.167019i | \(-0.946586\pi\) |
−0.145832 | + | 0.989309i | \(0.546586\pi\) | |||||||
\(360\) | −4.23607 | − | 3.07768i | −0.223260 | − | 0.162208i | ||||
\(361\) | 0.309017 | + | 0.951057i | 0.0162641 | + | 0.0500556i | ||||
\(362\) | −10.8885 | −0.572289 | ||||||||
\(363\) | 9.69098 | + | 5.20431i | 0.508645 | + | 0.273155i | ||||
\(364\) | 7.85410 | 0.411667 | ||||||||
\(365\) | −0.309017 | − | 0.951057i | −0.0161747 | − | 0.0497806i | ||||
\(366\) | 11.7812 | + | 8.55951i | 0.615811 | + | 0.447413i | ||||
\(367\) | 11.2533 | − | 8.17599i | 0.587417 | − | 0.426783i | −0.253973 | − | 0.967211i | \(-0.581738\pi\) |
0.841390 | + | 0.540428i | \(0.181738\pi\) | |||||||
\(368\) | −0.309017 | + | 0.951057i | −0.0161086 | + | 0.0495772i | ||||
\(369\) | 3.76393 | − | 11.5842i | 0.195942 | − | 0.603049i | ||||
\(370\) | 19.8713 | − | 14.4374i | 1.03306 | − | 0.750563i | ||||
\(371\) | −5.92705 | − | 4.30625i | −0.307717 | − | 0.223570i | ||||
\(372\) | −2.69098 | − | 8.28199i | −0.139521 | − | 0.429401i | ||||
\(373\) | 21.2361 | 1.09956 | 0.549781 | − | 0.835309i | \(-0.314711\pi\) | ||||
0.549781 | + | 0.835309i | \(0.314711\pi\) | |||||||
\(374\) | −0.781153 | + | 0.0530006i | −0.0403925 | + | 0.00274059i | ||||
\(375\) | −8.23607 | −0.425309 | ||||||||
\(376\) | −2.69098 | − | 8.28199i | −0.138777 | − | 0.427111i | ||||
\(377\) | 35.1246 | + | 25.5195i | 1.80901 | + | 1.31432i | ||||
\(378\) | −6.54508 | + | 4.75528i | −0.336643 | + | 0.244585i | ||||
\(379\) | 7.86475 | − | 24.2052i | 0.403985 | − | 1.24334i | −0.517755 | − | 0.855529i | \(-0.673232\pi\) |
0.921740 | − | 0.387809i | \(-0.126768\pi\) | |||||||
\(380\) | 0.809017 | − | 2.48990i | 0.0415017 | − | 0.127729i | ||||
\(381\) | 11.8992 | − | 8.64527i | 0.609614 | − | 0.442910i | ||||
\(382\) | −7.04508 | − | 5.11855i | −0.360458 | − | 0.261888i | ||||
\(383\) | 4.42705 | + | 13.6251i | 0.226212 | + | 0.696208i | 0.998166 | + | 0.0605305i | \(0.0192792\pi\) |
−0.771955 | + | 0.635678i | \(0.780721\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 5.23607 | + | 13.0373i | 0.266855 | + | 0.664441i | ||||
\(386\) | −0.145898 | −0.00742601 | ||||||||
\(387\) | 4.76393 | + | 14.6619i | 0.242164 | + | 0.745305i | ||||
\(388\) | −7.42705 | − | 5.39607i | −0.377051 | − | 0.273944i | ||||
\(389\) | 21.1803 | − | 15.3884i | 1.07389 | − | 0.780224i | 0.0972792 | − | 0.995257i | \(-0.468986\pi\) |
0.976607 | + | 0.215033i | \(0.0689860\pi\) | |||||||
\(390\) | 3.92705 | − | 12.0862i | 0.198854 | − | 0.612010i | ||||
\(391\) | −0.0729490 | + | 0.224514i | −0.00368919 | + | 0.0113542i | ||||
\(392\) | 3.54508 | − | 2.57565i | 0.179054 | − | 0.130090i | ||||
\(393\) | −8.70820 | − | 6.32688i | −0.439271 | − | 0.319149i | ||||
\(394\) | 7.10739 | + | 21.8743i | 0.358065 | + | 1.10201i | ||||
\(395\) | −39.2705 | −1.97591 | ||||||||
\(396\) | −5.61803 | − | 3.52671i | −0.282317 | − | 0.177224i | ||||
\(397\) | −10.8197 | −0.543023 | −0.271512 | − | 0.962435i | \(-0.587524\pi\) | ||||
−0.271512 | + | 0.962435i | \(0.587524\pi\) | |||||||
\(398\) | −1.05573 | − | 3.24920i | −0.0529189 | − | 0.162868i | ||||
\(399\) | −1.30902 | − | 0.951057i | −0.0655328 | − | 0.0476124i | ||||
\(400\) | −1.50000 | + | 1.08981i | −0.0750000 | + | 0.0544907i | ||||
\(401\) | 5.12868 | − | 15.7844i | 0.256114 | − | 0.788238i | −0.737494 | − | 0.675353i | \(-0.763991\pi\) |
0.993608 | − | 0.112884i | \(-0.0360089\pi\) | |||||||
\(402\) | 1.73607 | − | 5.34307i | 0.0865872 | − | 0.266488i | ||||
\(403\) | −34.1976 | + | 24.8460i | −1.70350 | + | 1.23767i | ||||
\(404\) | 7.42705 | + | 5.39607i | 0.369510 | + | 0.268464i | ||||
\(405\) | −0.809017 | − | 2.48990i | −0.0402004 | − | 0.123724i | ||||
\(406\) | −14.4721 | −0.718240 | ||||||||
\(407\) | 23.8779 | − | 19.9519i | 1.18358 | − | 0.988981i | ||||
\(408\) | −0.236068 | −0.0116871 | ||||||||
\(409\) | 1.01722 | + | 3.13068i | 0.0502983 | + | 0.154802i | 0.973051 | − | 0.230591i | \(-0.0740659\pi\) |
−0.922752 | + | 0.385393i | \(0.874066\pi\) | |||||||
\(410\) | −12.8992 | − | 9.37181i | −0.637045 | − | 0.462841i | ||||
\(411\) | −2.04508 | + | 1.48584i | −0.100877 | + | 0.0732911i | ||||
\(412\) | 2.88197 | − | 8.86978i | 0.141984 | − | 0.436983i | ||||
\(413\) | −2.92705 | + | 9.00854i | −0.144031 | + | 0.443281i | ||||
\(414\) | −1.61803 | + | 1.17557i | −0.0795220 | + | 0.0577761i | ||||
\(415\) | 18.6353 | + | 13.5393i | 0.914769 | + | 0.664618i | ||||
\(416\) | 1.50000 | + | 4.61653i | 0.0735436 | + | 0.226344i | ||||
\(417\) | 2.56231 | 0.125477 | ||||||||
\(418\) | 0.809017 | − | 3.21644i | 0.0395703 | − | 0.157321i | ||||
\(419\) | 25.5279 | 1.24712 | 0.623559 | − | 0.781776i | \(-0.285686\pi\) | ||||
0.623559 | + | 0.781776i | \(0.285686\pi\) | |||||||
\(420\) | 1.30902 | + | 4.02874i | 0.0638735 | + | 0.196582i | ||||
\(421\) | −20.1353 | − | 14.6291i | −0.981332 | − | 0.712980i | −0.0233263 | − | 0.999728i | \(-0.507426\pi\) |
−0.958006 | + | 0.286748i | \(0.907426\pi\) | |||||||
\(422\) | 15.5172 | − | 11.2739i | 0.755366 | − | 0.548806i | ||||
\(423\) | 5.38197 | − | 16.5640i | 0.261680 | − | 0.805369i | ||||
\(424\) | 1.39919 | − | 4.30625i | 0.0679505 | − | 0.209130i | ||||
\(425\) | −0.354102 | + | 0.257270i | −0.0171765 | + | 0.0124794i | ||||
\(426\) | 7.89919 | + | 5.73910i | 0.382717 | + | 0.278060i | ||||
\(427\) | 7.28115 | + | 22.4091i | 0.352360 | + | 1.08445i | ||||
\(428\) | 5.76393 | 0.278610 | ||||||||
\(429\) | 3.92705 | − | 15.6129i | 0.189600 | − | 0.753799i | ||||
\(430\) | 20.1803 | 0.973182 | ||||||||
\(431\) | 11.5344 | + | 35.4994i | 0.555595 | + | 1.70994i | 0.694368 | + | 0.719620i | \(0.255684\pi\) |
−0.138774 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(432\) | −4.04508 | − | 2.93893i | −0.194619 | − | 0.141399i | ||||
\(433\) | 19.3262 | − | 14.0413i | 0.928760 | − | 0.674783i | −0.0169291 | − | 0.999857i | \(-0.505389\pi\) |
0.945689 | + | 0.325073i | \(0.105389\pi\) | |||||||
\(434\) | 4.35410 | − | 13.4005i | 0.209004 | − | 0.643247i | ||||
\(435\) | −7.23607 | + | 22.2703i | −0.346943 | + | 1.06778i | ||||
\(436\) | −10.5902 | + | 7.69421i | −0.507177 | + | 0.368486i | ||||
\(437\) | −0.809017 | − | 0.587785i | −0.0387005 | − | 0.0281176i | ||||
\(438\) | −0.118034 | − | 0.363271i | −0.00563988 | − | 0.0173578i | ||||
\(439\) | 10.8541 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(440\) | −6.66312 | + | 5.56758i | −0.317652 | + | 0.265424i | ||||
\(441\) | 8.76393 | 0.417330 | ||||||||
\(442\) | 0.354102 | + | 1.08981i | 0.0168429 | + | 0.0518372i | ||||
\(443\) | 8.73607 | + | 6.34712i | 0.415063 | + | 0.301561i | 0.775648 | − | 0.631165i | \(-0.217423\pi\) |
−0.360585 | + | 0.932726i | \(0.617423\pi\) | |||||||
\(444\) | 7.59017 | − | 5.51458i | 0.360214 | − | 0.261710i | ||||
\(445\) | −14.8992 | + | 45.8550i | −0.706289 | + | 2.17373i | ||||
\(446\) | 4.00000 | − | 12.3107i | 0.189405 | − | 0.582930i | ||||
\(447\) | 3.19098 | − | 2.31838i | 0.150928 | − | 0.109656i | ||||
\(448\) | −1.30902 | − | 0.951057i | −0.0618452 | − | 0.0449332i | ||||
\(449\) | 3.98278 | + | 12.2577i | 0.187959 | + | 0.578478i | 0.999987 | − | 0.00514051i | \(-0.00163628\pi\) |
−0.812028 | + | 0.583619i | \(0.801636\pi\) | |||||||
\(450\) | −3.70820 | −0.174806 | ||||||||
\(451\) | −17.1074 | − | 10.7391i | −0.805556 | − | 0.505686i | ||||
\(452\) | −7.18034 | −0.337735 | ||||||||
\(453\) | −2.85410 | − | 8.78402i | −0.134097 | − | 0.412709i | ||||
\(454\) | −13.8713 | − | 10.0781i | −0.651013 | − | 0.472989i | ||||
\(455\) | 16.6353 | − | 12.0862i | 0.779873 | − | 0.566611i | ||||
\(456\) | 0.309017 | − | 0.951057i | 0.0144710 | − | 0.0445373i | ||||
\(457\) | 0.600813 | − | 1.84911i | 0.0281048 | − | 0.0864978i | −0.936020 | − | 0.351946i | \(-0.885520\pi\) |
0.964125 | + | 0.265448i | \(0.0855200\pi\) | |||||||
\(458\) | −14.2082 | + | 10.3229i | −0.663906 | + | 0.482356i | ||||
\(459\) | −0.954915 | − | 0.693786i | −0.0445716 | − | 0.0323832i | ||||
\(460\) | 0.809017 | + | 2.48990i | 0.0377206 | + | 0.116092i | ||||
\(461\) | −20.2361 | −0.942488 | −0.471244 | − | 0.882003i | \(-0.656195\pi\) | ||||
−0.471244 | + | 0.882003i | \(0.656195\pi\) | |||||||
\(462\) | 2.00000 | + | 4.97980i | 0.0930484 | + | 0.231681i | ||||
\(463\) | 29.8541 | 1.38744 | 0.693719 | − | 0.720246i | \(-0.255971\pi\) | ||||
0.693719 | + | 0.720246i | \(0.255971\pi\) | |||||||
\(464\) | −2.76393 | − | 8.50651i | −0.128312 | − | 0.394905i | ||||
\(465\) | −18.4443 | − | 13.4005i | −0.855333 | − | 0.621436i | ||||
\(466\) | −0.572949 | + | 0.416272i | −0.0265414 | + | 0.0192834i | ||||
\(467\) | −0.718847 | + | 2.21238i | −0.0332643 | + | 0.102377i | −0.966310 | − | 0.257381i | \(-0.917141\pi\) |
0.933046 | + | 0.359758i | \(0.117141\pi\) | |||||||
\(468\) | −3.00000 | + | 9.23305i | −0.138675 | + | 0.426798i | ||||
\(469\) | 7.35410 | − | 5.34307i | 0.339581 | − | 0.246720i | ||||
\(470\) | −18.4443 | − | 13.4005i | −0.850771 | − | 0.618121i | ||||
\(471\) | −1.61803 | − | 4.97980i | −0.0745551 | − | 0.229457i | ||||
\(472\) | −5.85410 | −0.269457 | ||||||||
\(473\) | 25.5066 | − | 1.73060i | 1.17279 | − | 0.0795731i | ||||
\(474\) | −15.0000 | −0.688973 | ||||||||
\(475\) | −0.572949 | − | 1.76336i | −0.0262887 | − | 0.0809083i | ||||
\(476\) | −0.309017 | − | 0.224514i | −0.0141638 | − | 0.0102906i | ||||
\(477\) | 7.32624 | − | 5.32282i | 0.335445 | − | 0.243715i | ||||
\(478\) | 1.64590 | − | 5.06555i | 0.0752816 | − | 0.231693i | ||||
\(479\) | 5.69098 | − | 17.5150i | 0.260028 | − | 0.800283i | −0.732770 | − | 0.680477i | \(-0.761773\pi\) |
0.992797 | − | 0.119806i | \(-0.0382273\pi\) | |||||||
\(480\) | −2.11803 | + | 1.53884i | −0.0966746 | + | 0.0702382i | ||||
\(481\) | −36.8435 | − | 26.7683i | −1.67992 | − | 1.22053i | ||||
\(482\) | −1.88197 | − | 5.79210i | −0.0857212 | − | 0.263823i | ||||
\(483\) | 1.61803 | 0.0736231 | ||||||||
\(484\) | −7.94427 | + | 7.60845i | −0.361103 | + | 0.345839i | ||||
\(485\) | −24.0344 | −1.09135 | ||||||||
\(486\) | −4.94427 | − | 15.2169i | −0.224277 | − | 0.690253i | ||||
\(487\) | 30.9894 | + | 22.5151i | 1.40426 | + | 1.02026i | 0.994126 | + | 0.108232i | \(0.0345188\pi\) |
0.410136 | + | 0.912024i | \(0.365481\pi\) | |||||||
\(488\) | −11.7812 | + | 8.55951i | −0.533308 | + | 0.387471i | ||||
\(489\) | 3.50000 | − | 10.7719i | 0.158275 | − | 0.487122i | ||||
\(490\) | 3.54508 | − | 10.9106i | 0.160151 | − | 0.492893i | ||||
\(491\) | 5.78115 | − | 4.20025i | 0.260900 | − | 0.189555i | −0.449644 | − | 0.893208i | \(-0.648449\pi\) |
0.710544 | + | 0.703653i | \(0.248449\pi\) | |||||||
\(492\) | −4.92705 | − | 3.57971i | −0.222129 | − | 0.161386i | ||||
\(493\) | −0.652476 | − | 2.00811i | −0.0293860 | − | 0.0904409i | ||||
\(494\) | −4.85410 | −0.218396 | ||||||||
\(495\) | −17.3262 | + | 1.17557i | −0.778756 | + | 0.0528380i | ||||
\(496\) | 8.70820 | 0.391010 | ||||||||
\(497\) | 4.88197 | + | 15.0251i | 0.218986 | + | 0.673970i | ||||
\(498\) | 7.11803 | + | 5.17155i | 0.318967 | + | 0.231743i | ||||
\(499\) | 26.6074 | − | 19.3314i | 1.19111 | − | 0.865392i | 0.197729 | − | 0.980257i | \(-0.436643\pi\) |
0.993381 | + | 0.114864i | \(0.0366433\pi\) | |||||||
\(500\) | 2.54508 | − | 7.83297i | 0.113820 | − | 0.350301i | ||||
\(501\) | 0.881966 | − | 2.71441i | 0.0394033 | − | 0.121271i | ||||
\(502\) | −12.4721 | + | 9.06154i | −0.556659 | + | 0.404436i | ||||
\(503\) | 21.8262 | + | 15.8577i | 0.973184 | + | 0.707059i | 0.956175 | − | 0.292796i | \(-0.0945856\pi\) |
0.0170089 | + | 0.999855i | \(0.494586\pi\) | |||||||
\(504\) | −1.00000 | − | 3.07768i | −0.0445435 | − | 0.137091i | ||||
\(505\) | 24.0344 | 1.06952 | ||||||||
\(506\) | 1.23607 | + | 3.07768i | 0.0549499 | + | 0.136820i | ||||
\(507\) | −10.5623 | −0.469088 | ||||||||
\(508\) | 4.54508 | + | 13.9883i | 0.201656 | + | 0.620632i | ||||
\(509\) | 3.51722 | + | 2.55541i | 0.155898 | + | 0.113267i | 0.663000 | − | 0.748620i | \(-0.269283\pi\) |
−0.507102 | + | 0.861886i | \(0.669283\pi\) | |||||||
\(510\) | −0.500000 | + | 0.363271i | −0.0221404 | + | 0.0160859i | ||||
\(511\) | 0.190983 | − | 0.587785i | 0.00844859 | − | 0.0260021i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | 4.04508 | − | 2.93893i | 0.178595 | − | 0.129757i | ||||
\(514\) | −13.9721 | − | 10.1514i | −0.616284 | − | 0.447757i | ||||
\(515\) | −7.54508 | − | 23.2214i | −0.332476 | − | 1.02326i | ||||
\(516\) | 7.70820 | 0.339335 | ||||||||
\(517\) | −24.4615 | − | 15.3557i | −1.07582 | − | 0.675341i | ||||
\(518\) | 15.1803 | 0.666986 | ||||||||
\(519\) | −2.51722 | − | 7.74721i | −0.110494 | − | 0.340065i | ||||
\(520\) | 10.2812 | + | 7.46969i | 0.450858 | + | 0.327568i | ||||
\(521\) | −5.13525 | + | 3.73098i | −0.224980 | + | 0.163457i | −0.694565 | − | 0.719430i | \(-0.744403\pi\) |
0.469586 | + | 0.882887i | \(0.344403\pi\) | |||||||
\(522\) | 5.52786 | − | 17.0130i | 0.241948 | − | 0.744639i | ||||
\(523\) | −0.774575 | + | 2.38390i | −0.0338698 | + | 0.104241i | −0.966562 | − | 0.256432i | \(-0.917453\pi\) |
0.932692 | + | 0.360673i | \(0.117453\pi\) | |||||||
\(524\) | 8.70820 | − | 6.32688i | 0.380420 | − | 0.276391i | ||||
\(525\) | 2.42705 | + | 1.76336i | 0.105925 | + | 0.0769592i | ||||
\(526\) | −3.82624 | − | 11.7759i | −0.166832 | − | 0.513456i | ||||
\(527\) | 2.05573 | 0.0895489 | ||||||||
\(528\) | −2.54508 | + | 2.12663i | −0.110761 | + | 0.0925496i | ||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | −3.66312 | − | 11.2739i | −0.159116 | − | 0.489708i | ||||
\(531\) | −9.47214 | − | 6.88191i | −0.411056 | − | 0.298649i | ||||
\(532\) | 1.30902 | − | 0.951057i | 0.0567531 | − | 0.0412335i | ||||
\(533\) | −9.13525 | + | 28.1154i | −0.395692 | + | 1.21781i | ||||
\(534\) | −5.69098 | + | 17.5150i | −0.246273 | + | 0.757950i | ||||
\(535\) | 12.2082 | − | 8.86978i | 0.527807 | − | 0.383474i | ||||
\(536\) | 4.54508 | + | 3.30220i | 0.196318 | + | 0.142633i | ||||
\(537\) | −3.61803 | − | 11.1352i | −0.156130 | − | 0.480518i | ||||
\(538\) | 19.4721 | 0.839503 | ||||||||
\(539\) | 3.54508 | − | 14.0943i | 0.152698 | − | 0.607086i | ||||
\(540\) | −13.0902 | −0.563311 | ||||||||
\(541\) | 12.2254 | + | 37.6260i | 0.525612 | + | 1.61767i | 0.763102 | + | 0.646278i | \(0.223675\pi\) |
−0.237490 | + | 0.971390i | \(0.576325\pi\) | |||||||
\(542\) | 11.4721 | + | 8.33499i | 0.492770 | + | 0.358019i | ||||
\(543\) | −8.80902 | + | 6.40013i | −0.378031 | + | 0.274656i | ||||
\(544\) | 0.0729490 | − | 0.224514i | 0.00312766 | − | 0.00962596i | ||||
\(545\) | −10.5902 | + | 32.5932i | −0.453633 | + | 1.39614i | ||||
\(546\) | 6.35410 | − | 4.61653i | 0.271930 | − | 0.197569i | ||||
\(547\) | 1.88197 | + | 1.36733i | 0.0804671 | + | 0.0584627i | 0.627291 | − | 0.778785i | \(-0.284163\pi\) |
−0.546824 | + | 0.837247i | \(0.684163\pi\) | |||||||
\(548\) | −0.781153 | − | 2.40414i | −0.0333692 | − | 0.102700i | ||||
\(549\) | −29.1246 | −1.24301 | ||||||||
\(550\) | −1.50000 | + | 5.96361i | −0.0639602 | + | 0.254289i | ||||
\(551\) | 8.94427 | 0.381039 | ||||||||
\(552\) | 0.309017 | + | 0.951057i | 0.0131526 | + | 0.0404797i | ||||
\(553\) | −19.6353 | − | 14.2658i | −0.834976 | − | 0.606646i | ||||
\(554\) | −13.8713 | + | 10.0781i | −0.589336 | + | 0.428178i | ||||
\(555\) | 7.59017 | − | 23.3601i | 0.322185 | − | 0.991583i | ||||
\(556\) | −0.791796 | + | 2.43690i | −0.0335796 | + | 0.103347i | ||||
\(557\) | −12.8541 | + | 9.33905i | −0.544646 | + | 0.395708i | −0.825808 | − | 0.563952i | \(-0.809280\pi\) |
0.281162 | + | 0.959660i | \(0.409280\pi\) | |||||||
\(558\) | 14.0902 | + | 10.2371i | 0.596484 | + | 0.433371i | ||||
\(559\) | −11.5623 | − | 35.5851i | −0.489033 | − | 1.50509i | ||||
\(560\) | −4.23607 | −0.179007 | ||||||||
\(561\) | −0.600813 | + | 0.502029i | −0.0253663 | + | 0.0211957i | ||||
\(562\) | 21.1459 | 0.891986 | ||||||||
\(563\) | −7.54508 | − | 23.2214i | −0.317987 | − | 0.978665i | −0.974507 | − | 0.224356i | \(-0.927972\pi\) |
0.656520 | − | 0.754309i | \(-0.272028\pi\) | |||||||
\(564\) | −7.04508 | − | 5.11855i | −0.296652 | − | 0.215530i | ||||
\(565\) | −15.2082 | + | 11.0494i | −0.639814 | + | 0.464852i | ||||
\(566\) | −5.30902 | + | 16.3395i | −0.223155 | + | 0.686799i | ||||
\(567\) | 0.500000 | − | 1.53884i | 0.0209980 | − | 0.0646253i | ||||
\(568\) | −7.89919 | + | 5.73910i | −0.331443 | + | 0.240807i | ||||
\(569\) | 16.1803 | + | 11.7557i | 0.678315 | + | 0.492825i | 0.872798 | − | 0.488081i | \(-0.162303\pi\) |
−0.194483 | + | 0.980906i | \(0.562303\pi\) | |||||||
\(570\) | −0.809017 | − | 2.48990i | −0.0338860 | − | 0.104290i | ||||
\(571\) | 19.3607 | 0.810219 | 0.405110 | − | 0.914268i | \(-0.367233\pi\) | ||||
0.405110 | + | 0.914268i | \(0.367233\pi\) | |||||||
\(572\) | 13.6353 | + | 8.55951i | 0.570119 | + | 0.357891i | ||||
\(573\) | −8.70820 | −0.363790 | ||||||||
\(574\) | −3.04508 | − | 9.37181i | −0.127099 | − | 0.391172i | ||||
\(575\) | 1.50000 | + | 1.08981i | 0.0625543 | + | 0.0454484i | ||||
\(576\) | 1.61803 | − | 1.17557i | 0.0674181 | − | 0.0489821i | ||||
\(577\) | 1.19098 | − | 3.66547i | 0.0495813 | − | 0.152595i | −0.923200 | − | 0.384319i | \(-0.874436\pi\) |
0.972782 | + | 0.231723i | \(0.0744364\pi\) | |||||||
\(578\) | −5.23607 | + | 16.1150i | −0.217792 | + | 0.670294i | ||||
\(579\) | −0.118034 | + | 0.0857567i | −0.00490533 | + | 0.00356393i | ||||
\(580\) | −18.9443 | − | 13.7638i | −0.786618 | − | 0.571511i | ||||
\(581\) | 4.39919 | + | 13.5393i | 0.182509 | + | 0.561705i | ||||
\(582\) | −9.18034 | −0.380537 | ||||||||
\(583\) | −5.59675 | − | 13.9353i | −0.231794 | − | 0.577143i | ||||
\(584\) | 0.381966 | 0.0158059 | ||||||||
\(585\) | 7.85410 | + | 24.1724i | 0.324727 | + | 0.999407i | ||||
\(586\) | 19.7533 | + | 14.3516i | 0.816001 | + | 0.592859i | ||||
\(587\) | −4.13525 | + | 3.00444i | −0.170680 | + | 0.124006i | −0.669846 | − | 0.742500i | \(-0.733640\pi\) |
0.499166 | + | 0.866507i | \(0.333640\pi\) | |||||||
\(588\) | 1.35410 | − | 4.16750i | 0.0558422 | − | 0.171865i | ||||
\(589\) | −2.69098 | + | 8.28199i | −0.110880 | + | 0.341254i | ||||
\(590\) | −12.3992 | + | 9.00854i | −0.510466 | + | 0.370876i | ||||
\(591\) | 18.6074 | + | 13.5191i | 0.765406 | + | 0.556100i | ||||
\(592\) | 2.89919 | + | 8.92278i | 0.119156 | + | 0.366724i | ||||
\(593\) | −19.9443 | −0.819013 | −0.409507 | − | 0.912307i | \(-0.634299\pi\) | ||||
−0.409507 | + | 0.912307i | \(0.634299\pi\) | |||||||
\(594\) | −16.5451 | + | 1.12257i | −0.678853 | + | 0.0460596i | ||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 1.21885 | + | 3.75123i | 0.0499259 | + | 0.153656i | ||||
\(597\) | −2.76393 | − | 2.00811i | −0.113120 | − | 0.0821866i | ||||
\(598\) | 3.92705 | − | 2.85317i | 0.160589 | − | 0.116675i | ||||
\(599\) | 4.40983 | − | 13.5721i | 0.180181 | − | 0.554539i | −0.819651 | − | 0.572863i | \(-0.805833\pi\) |
0.999832 | + | 0.0183233i | \(0.00583282\pi\) | |||||||
\(600\) | −0.572949 | + | 1.76336i | −0.0233905 | + | 0.0719887i | ||||
\(601\) | −23.5902 | + | 17.1393i | −0.962263 | + | 0.699125i | −0.953675 | − | 0.300838i | \(-0.902734\pi\) |
−0.00858786 | + | 0.999963i | \(0.502734\pi\) | |||||||
\(602\) | 10.0902 | + | 7.33094i | 0.411245 | + | 0.298787i | ||||
\(603\) | 3.47214 | + | 10.6861i | 0.141396 | + | 0.435173i | ||||
\(604\) | 9.23607 | 0.375810 | ||||||||
\(605\) | −5.11803 | + | 28.3399i | −0.208078 | + | 1.15218i | ||||
\(606\) | 9.18034 | 0.372926 | ||||||||
\(607\) | −10.1287 | − | 31.1729i | −0.411110 | − | 1.26527i | −0.915684 | − | 0.401899i | \(-0.868350\pi\) |
0.504574 | − | 0.863369i | \(-0.331650\pi\) | |||||||
\(608\) | 0.809017 | + | 0.587785i | 0.0328100 | + | 0.0238378i | ||||
\(609\) | −11.7082 | + | 8.50651i | −0.474440 | + | 0.344701i | ||||
\(610\) | −11.7812 | + | 36.2587i | −0.477005 | + | 1.46807i | ||||
\(611\) | −13.0623 | + | 40.2016i | −0.528444 | + | 1.62638i | ||||
\(612\) | 0.381966 | − | 0.277515i | 0.0154401 | − | 0.0112179i | ||||
\(613\) | −4.61803 | − | 3.35520i | −0.186521 | − | 0.135515i | 0.490606 | − | 0.871381i | \(-0.336775\pi\) |
−0.677127 | + | 0.735866i | \(0.736775\pi\) | |||||||
\(614\) | 7.10739 | + | 21.8743i | 0.286831 | + | 0.882775i | ||||
\(615\) | −15.9443 | −0.642935 | ||||||||
\(616\) | −5.35410 | + | 0.363271i | −0.215723 | + | 0.0146366i | ||||
\(617\) | 22.2705 | 0.896577 | 0.448288 | − | 0.893889i | \(-0.352034\pi\) | ||||
0.448288 | + | 0.893889i | \(0.352034\pi\) | |||||||
\(618\) | −2.88197 | − | 8.86978i | −0.115930 | − | 0.356795i | ||||
\(619\) | 14.2082 | + | 10.3229i | 0.571076 | + | 0.414911i | 0.835496 | − | 0.549497i | \(-0.185181\pi\) |
−0.264420 | + | 0.964408i | \(0.585181\pi\) | |||||||
\(620\) | 18.4443 | − | 13.4005i | 0.740740 | − | 0.538179i | ||||
\(621\) | −1.54508 | + | 4.75528i | −0.0620021 | + | 0.190823i | ||||
\(622\) | 0.618034 | − | 1.90211i | 0.0247809 | − | 0.0762678i | ||||
\(623\) | −24.1074 | + | 17.5150i | −0.965842 | + | 0.701725i | ||||
\(624\) | 3.92705 | + | 2.85317i | 0.157208 | + | 0.114218i | ||||
\(625\) | −9.52786 | − | 29.3238i | −0.381115 | − | 1.17295i | ||||
\(626\) | −19.9443 | −0.797133 | ||||||||
\(627\) | −1.23607 | − | 3.07768i | −0.0493638 | − | 0.122911i | ||||
\(628\) | 5.23607 | 0.208942 | ||||||||
\(629\) | 0.684405 | + | 2.10638i | 0.0272890 | + | 0.0839870i | ||||
\(630\) | −6.85410 | − | 4.97980i | −0.273074 | − | 0.198400i | ||||
\(631\) | −15.2984 | + | 11.1149i | −0.609019 | + | 0.442478i | −0.849069 | − | 0.528283i | \(-0.822836\pi\) |
0.240050 | + | 0.970761i | \(0.422836\pi\) | |||||||
\(632\) | 4.63525 | − | 14.2658i | 0.184381 | − | 0.567465i | ||||
\(633\) | 5.92705 | − | 18.2416i | 0.235579 | − | 0.725038i | ||||
\(634\) | 13.7533 | − | 9.99235i | 0.546213 | − | 0.396847i | ||||
\(635\) | 31.1525 | + | 22.6336i | 1.23625 | + | 0.898187i | ||||
\(636\) | −1.39919 | − | 4.30625i | −0.0554814 | − | 0.170754i | ||||
\(637\) | −21.2705 | −0.842768 | ||||||||
\(638\) | −25.1246 | − | 15.7719i | −0.994693 | − | 0.624417i | ||||
\(639\) | −19.5279 | −0.772510 | ||||||||
\(640\) | −0.809017 | − | 2.48990i | −0.0319792 | − | 0.0984219i | ||||
\(641\) | −18.3262 | − | 13.3148i | −0.723843 | − | 0.525903i | 0.163767 | − | 0.986499i | \(-0.447636\pi\) |
−0.887610 | + | 0.460596i | \(0.847636\pi\) | |||||||
\(642\) | 4.66312 | − | 3.38795i | 0.184039 | − | 0.133712i | ||||
\(643\) | −5.27051 | + | 16.2210i | −0.207849 | + | 0.639692i | 0.791736 | + | 0.610864i | \(0.209178\pi\) |
−0.999584 | + | 0.0288285i | \(0.990822\pi\) | |||||||
\(644\) | −0.500000 | + | 1.53884i | −0.0197028 | + | 0.0606389i | ||||
\(645\) | 16.3262 | − | 11.8617i | 0.642845 | − | 0.467054i | ||||
\(646\) | 0.190983 | + | 0.138757i | 0.00751413 | + | 0.00545933i | ||||
\(647\) | 7.37132 | + | 22.6866i | 0.289797 | + | 0.891902i | 0.984920 | + | 0.173012i | \(0.0553498\pi\) |
−0.695123 | + | 0.718891i | \(0.744650\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −14.8992 | + | 12.4495i | −0.584844 | + | 0.488685i | ||||
\(650\) | 9.00000 | 0.353009 | ||||||||
\(651\) | −4.35410 | − | 13.4005i | −0.170651 | − | 0.525209i | ||||
\(652\) | 9.16312 | + | 6.65740i | 0.358855 | + | 0.260724i | ||||
\(653\) | 31.2984 | − | 22.7396i | 1.22480 | − | 0.889869i | 0.228311 | − | 0.973588i | \(-0.426680\pi\) |
0.996489 | + | 0.0837190i | \(0.0266798\pi\) | |||||||
\(654\) | −4.04508 | + | 12.4495i | −0.158175 | + | 0.486814i | ||||
\(655\) | 8.70820 | − | 26.8011i | 0.340258 | − | 1.04721i | ||||
\(656\) | 4.92705 | − | 3.57971i | 0.192369 | − | 0.139764i | ||||
\(657\) | 0.618034 | + | 0.449028i | 0.0241118 | + | 0.0175182i | ||||
\(658\) | −4.35410 | − | 13.4005i | −0.169741 | − | 0.522408i | ||||
\(659\) | −15.6525 | −0.609734 | −0.304867 | − | 0.952395i | \(-0.598612\pi\) | ||||
−0.304867 | + | 0.952395i | \(0.598612\pi\) | |||||||
\(660\) | −2.11803 | + | 8.42075i | −0.0824444 | + | 0.327777i | ||||
\(661\) | −23.8541 | −0.927817 | −0.463909 | − | 0.885883i | \(-0.653553\pi\) | ||||
−0.463909 | + | 0.885883i | \(0.653553\pi\) | |||||||
\(662\) | −7.47214 | − | 22.9969i | −0.290413 | − | 0.893799i | ||||
\(663\) | 0.927051 | + | 0.673542i | 0.0360037 | + | 0.0261582i | ||||
\(664\) | −7.11803 | + | 5.17155i | −0.276233 | + | 0.200695i | ||||
\(665\) | 1.30902 | − | 4.02874i | 0.0507615 | − | 0.156228i | ||||
\(666\) | −5.79837 | + | 17.8456i | −0.224682 | + | 0.691501i | ||||
\(667\) | −7.23607 | + | 5.25731i | −0.280182 | + | 0.203564i | ||||
\(668\) | 2.30902 | + | 1.67760i | 0.0893385 | + | 0.0649083i | ||||
\(669\) | −4.00000 | − | 12.3107i | −0.154649 | − | 0.475960i | ||||
\(670\) | 14.7082 | 0.568227 | ||||||||
\(671\) | −11.7812 | + | 46.8388i | −0.454806 | + | 1.80819i | ||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | 4.42705 | + | 13.6251i | 0.170650 | + | 0.525208i | 0.999408 | − | 0.0343998i | \(-0.0109520\pi\) |
−0.828758 | + | 0.559607i | \(0.810952\pi\) | |||||||
\(674\) | 5.66312 | + | 4.11450i | 0.218135 | + | 0.158484i | ||||
\(675\) | −7.50000 | + | 5.44907i | −0.288675 | + | 0.209735i | ||||
\(676\) | 3.26393 | − | 10.0453i | 0.125536 | − | 0.386360i | ||||
\(677\) | −1.83688 | + | 5.65334i | −0.0705971 | + | 0.217275i | −0.980130 | − | 0.198357i | \(-0.936440\pi\) |
0.909533 | + | 0.415632i | \(0.136440\pi\) | |||||||
\(678\) | −5.80902 | + | 4.22050i | −0.223094 | + | 0.162087i | ||||
\(679\) | −12.0172 | − | 8.73102i | −0.461179 | − | 0.335066i | ||||
\(680\) | −0.190983 | − | 0.587785i | −0.00732386 | − | 0.0225405i | ||||
\(681\) | −17.1459 | −0.657032 | ||||||||
\(682\) | 22.1631 | − | 18.5191i | 0.848670 | − | 0.709133i | ||||
\(683\) | −1.97871 | −0.0757134 | −0.0378567 | − | 0.999283i | \(-0.512053\pi\) | ||||
−0.0378567 | + | 0.999283i | \(0.512053\pi\) | |||||||
\(684\) | 0.618034 | + | 1.90211i | 0.0236311 | + | 0.0727291i | ||||
\(685\) | −5.35410 | − | 3.88998i | −0.204570 | − | 0.148629i | ||||
\(686\) | 14.8992 | − | 10.8249i | 0.568854 | − | 0.413296i | ||||
\(687\) | −5.42705 | + | 16.7027i | −0.207055 | + | 0.637249i | ||||
\(688\) | −2.38197 | + | 7.33094i | −0.0908116 | + | 0.279489i | ||||
\(689\) | −17.7812 | + | 12.9188i | −0.677408 | + | 0.492166i | ||||
\(690\) | 2.11803 | + | 1.53884i | 0.0806322 | + | 0.0585827i | ||||
\(691\) | 3.58359 | + | 11.0292i | 0.136326 | + | 0.419569i | 0.995794 | − | 0.0916210i | \(-0.0292048\pi\) |
−0.859468 | + | 0.511190i | \(0.829205\pi\) | |||||||
\(692\) | 8.14590 | 0.309661 | ||||||||
\(693\) | −9.09017 | − | 5.70634i | −0.345307 | − | 0.216766i | ||||
\(694\) | −12.6525 | −0.480281 | ||||||||
\(695\) | 2.07295 | + | 6.37988i | 0.0786314 | + | 0.242003i | ||||
\(696\) | −7.23607 | − | 5.25731i | −0.274282 | − | 0.199278i | ||||
\(697\) | 1.16312 | − | 0.845055i | 0.0440563 | − | 0.0320088i | ||||
\(698\) | −4.93769 | + | 15.1967i | −0.186894 | + | 0.575202i | ||||
\(699\) | −0.218847 | + | 0.673542i | −0.00827756 | + | 0.0254757i | ||||
\(700\) | −2.42705 | + | 1.76336i | −0.0917339 | + | 0.0666486i | ||||
\(701\) | −21.2533 | − | 15.4414i | −0.802726 | − | 0.583214i | 0.108987 | − | 0.994043i | \(-0.465239\pi\) |
−0.911712 | + | 0.410829i | \(0.865239\pi\) | |||||||
\(702\) | 7.50000 | + | 23.0826i | 0.283069 | + | 0.871198i | ||||
\(703\) | −9.38197 | −0.353848 | ||||||||
\(704\) | −1.23607 | − | 3.07768i | −0.0465861 | − | 0.115995i | ||||
\(705\) | −22.7984 | −0.858636 | ||||||||
\(706\) | −8.03444 | − | 24.7275i | −0.302380 | − | 0.930631i | ||||
\(707\) | 12.0172 | + | 8.73102i | 0.451954 | + | 0.328364i | ||||
\(708\) | −4.73607 | + | 3.44095i | −0.177992 | + | 0.129319i | ||||
\(709\) | −14.9615 | + | 46.0467i | −0.561891 | + | 1.72932i | 0.115123 | + | 0.993351i | \(0.463274\pi\) |
−0.677014 | + | 0.735970i | \(0.736726\pi\) | |||||||
\(710\) | −7.89919 | + | 24.3112i | −0.296451 | + | 0.912383i | ||||
\(711\) | 24.2705 | − | 17.6336i | 0.910215 | − | 0.661310i | ||||
\(712\) | −14.8992 | − | 10.8249i | −0.558371 | − | 0.405680i | ||||
\(713\) | −2.69098 | − | 8.28199i | −0.100778 | − | 0.310163i | ||||
\(714\) | −0.381966 | −0.0142947 | ||||||||
\(715\) | 42.0517 | − | 2.85317i | 1.57264 | − | 0.106702i | ||||
\(716\) | 11.7082 | 0.437556 | ||||||||
\(717\) | −1.64590 | − | 5.06555i | −0.0614672 | − | 0.189177i | ||||
\(718\) | −21.4443 | − | 15.5802i | −0.800293 | − | 0.581447i | ||||
\(719\) | 11.0172 | − | 8.00448i | 0.410873 | − | 0.298517i | −0.363082 | − | 0.931757i | \(-0.618276\pi\) |
0.773955 | + | 0.633240i | \(0.218276\pi\) | |||||||
\(720\) | 1.61803 | − | 4.97980i | 0.0603006 | − | 0.185586i | ||||
\(721\) | 4.66312 | − | 14.3516i | 0.173664 | − | 0.534482i | ||||
\(722\) | −0.809017 | + | 0.587785i | −0.0301085 | + | 0.0218751i | ||||
\(723\) | −4.92705 | − | 3.57971i | −0.183239 | − | 0.133131i | ||||
\(724\) | −3.36475 | − | 10.3556i | −0.125050 | − | 0.384864i | ||||
\(725\) | −16.5836 | −0.615899 | ||||||||
\(726\) | −1.95492 | + | 10.8249i | −0.0725537 | + | 0.401749i | ||||
\(727\) | 31.2918 | 1.16055 | 0.580274 | − | 0.814421i | \(-0.302945\pi\) | ||||
0.580274 | + | 0.814421i | \(0.302945\pi\) | |||||||
\(728\) | 2.42705 | + | 7.46969i | 0.0899525 | + | 0.276845i | ||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | 0.809017 | − | 0.587785i | 0.0299431 | − | 0.0217549i | ||||
\(731\) | −0.562306 | + | 1.73060i | −0.0207976 | + | 0.0640085i | ||||
\(732\) | −4.50000 | + | 13.8496i | −0.166325 | + | 0.511895i | ||||
\(733\) | −17.8713 | + | 12.9843i | −0.660092 | + | 0.479585i | −0.866694 | − | 0.498840i | \(-0.833760\pi\) |
0.206602 | + | 0.978425i | \(0.433760\pi\) | |||||||
\(734\) | 11.2533 | + | 8.17599i | 0.415366 | + | 0.301781i | ||||
\(735\) | −3.54508 | − | 10.9106i | −0.130762 | − | 0.402445i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 18.5902 | − | 1.26133i | 0.684778 | − | 0.0464616i | ||||
\(738\) | 12.1803 | 0.448365 | ||||||||
\(739\) | −9.79837 | − | 30.1563i | −0.360439 | − | 1.10932i | −0.952788 | − | 0.303636i | \(-0.901799\pi\) |
0.592349 | − | 0.805681i | \(-0.298201\pi\) | |||||||
\(740\) | 19.8713 | + | 14.4374i | 0.730484 | + | 0.530728i | ||||
\(741\) | −3.92705 | + | 2.85317i | −0.144264 | + | 0.104814i | ||||
\(742\) | 2.26393 | − | 6.96767i | 0.0831116 | − | 0.255791i | ||||
\(743\) | 4.52786 | − | 13.9353i | 0.166111 | − | 0.511238i | −0.833005 | − | 0.553265i | \(-0.813382\pi\) |
0.999116 | + | 0.0420273i | \(0.0133817\pi\) | |||||||
\(744\) | 7.04508 | − | 5.11855i | 0.258285 | − | 0.187655i | ||||
\(745\) | 8.35410 | + | 6.06961i | 0.306071 | + | 0.222373i | ||||
\(746\) | 6.56231 | + | 20.1967i | 0.240263 | + | 0.739454i | ||||
\(747\) | −17.5967 | −0.643831 | ||||||||
\(748\) | −0.291796 | − | 0.726543i | −0.0106691 | − | 0.0265650i | ||||
\(749\) | 9.32624 | 0.340773 | ||||||||
\(750\) | −2.54508 | − | 7.83297i | −0.0929334 | − | 0.286019i | ||||
\(751\) | −9.28115 | − | 6.74315i | −0.338674 | − | 0.246061i | 0.405428 | − | 0.914127i | \(-0.367122\pi\) |
−0.744102 | + | 0.668066i | \(0.767122\pi\) | |||||||
\(752\) | 7.04508 | − | 5.11855i | 0.256908 | − | 0.186654i | ||||
\(753\) | −4.76393 | + | 14.6619i | −0.173607 | + | 0.534308i | ||||
\(754\) | −13.4164 | + | 41.2915i | −0.488597 | + | 1.50375i | ||||
\(755\) | 19.5623 | − | 14.2128i | 0.711945 | − | 0.517258i | ||||
\(756\) | −6.54508 | − | 4.75528i | −0.238042 | − | 0.172948i | ||||
\(757\) | −14.9894 | − | 46.1325i | −0.544797 | − | 1.67671i | −0.721471 | − | 0.692445i | \(-0.756534\pi\) |
0.176674 | − | 0.984269i | \(-0.443466\pi\) | |||||||
\(758\) | 25.4508 | 0.924416 | ||||||||
\(759\) | 2.80902 | + | 1.76336i | 0.101961 | + | 0.0640058i | ||||
\(760\) | 2.61803 | 0.0949661 | ||||||||
\(761\) | −15.7254 | − | 48.3979i | −0.570046 | − | 1.75442i | −0.652460 | − | 0.757824i | \(-0.726263\pi\) |
0.0824133 | − | 0.996598i | \(-0.473737\pi\) | |||||||
\(762\) | 11.8992 | + | 8.64527i | 0.431062 | + | 0.313185i | ||||
\(763\) | −17.1353 | + | 12.4495i | −0.620338 | + | 0.450702i | ||||
\(764\) | 2.69098 | − | 8.28199i | 0.0973563 | − | 0.299632i | ||||
\(765\) | 0.381966 | − | 1.17557i | 0.0138100 | − | 0.0425028i | ||||
\(766\) | −11.5902 | + | 8.42075i | −0.418770 | + | 0.304254i | ||||
\(767\) | 22.9894 | + | 16.7027i | 0.830098 | + | 0.603101i | ||||
\(768\) | −0.309017 | − | 0.951057i | −0.0111507 | − | 0.0343183i | ||||
\(769\) | 3.29180 | 0.118705 | 0.0593526 | − | 0.998237i | \(-0.481096\pi\) | ||||
0.0593526 | + | 0.998237i | \(0.481096\pi\) | |||||||
\(770\) | −10.7812 | + | 9.00854i | −0.388526 | + | 0.324645i | ||||
\(771\) | −17.2705 | −0.621982 | ||||||||
\(772\) | −0.0450850 | − | 0.138757i | −0.00162264 | − | 0.00499398i | ||||
\(773\) | 14.9164 | + | 10.8374i | 0.536506 | + | 0.389794i | 0.822786 | − | 0.568352i | \(-0.192419\pi\) |
−0.286280 | + | 0.958146i | \(0.592419\pi\) | |||||||
\(774\) | −12.4721 | + | 9.06154i | −0.448302 | + | 0.325710i | ||||
\(775\) | 4.98936 | − | 15.3557i | 0.179223 | − | 0.551592i | ||||
\(776\) | 2.83688 | − | 8.73102i | 0.101838 | − | 0.313425i | ||||
\(777\) | 12.2812 | − | 8.92278i | 0.440584 | − | 0.320103i | ||||
\(778\) | 21.1803 | + | 15.3884i | 0.759352 | + | 0.551702i | ||||
\(779\) | 1.88197 | + | 5.79210i | 0.0674284 | + | 0.207523i | ||||
\(780\) | 12.7082 | 0.455027 | ||||||||
\(781\) | −7.89919 | + | 31.4051i | −0.282655 | + | 1.12376i | ||||
\(782\) | −0.236068 | −0.00844177 | ||||||||
\(783\) | −13.8197 | − | 42.5325i | −0.493874 | − | 1.51999i | ||||
\(784\) | 3.54508 | + | 2.57565i | 0.126610 | + | 0.0919877i | ||||
\(785\) | 11.0902 | − | 8.05748i | 0.395825 | − | 0.287584i | ||||
\(786\) | 3.32624 | − | 10.2371i | 0.118643 | − | 0.365146i | ||||
\(787\) | 10.9656 | − | 33.7485i | 0.390880 | − | 1.20300i | −0.541244 | − | 0.840866i | \(-0.682046\pi\) |
0.932124 | − | 0.362139i | \(-0.117954\pi\) | |||||||
\(788\) | −18.6074 | + | 13.5191i | −0.662861 | + | 0.481597i | ||||
\(789\) | −10.0172 | − | 7.27794i | −0.356623 | − | 0.259101i | ||||
\(790\) | −12.1353 | − | 37.3485i | −0.431753 | − | 1.32880i | ||||
\(791\) | −11.6180 | −0.413090 | ||||||||
\(792\) | 1.61803 | − | 6.43288i | 0.0574943 | − | 0.228582i | ||||
\(793\) | 70.6869 | 2.51017 | ||||||||
\(794\) | −3.34346 | − | 10.2901i | −0.118655 | − | 0.365182i | ||||
\(795\) | −9.59017 | − | 6.96767i | −0.340128 | − | 0.247118i | ||||
\(796\) | 2.76393 | − | 2.00811i | 0.0979650 | − | 0.0711757i | ||||
\(797\) | −4.50000 | + | 13.8496i | −0.159398 | + | 0.490577i | −0.998580 | − | 0.0532739i | \(-0.983034\pi\) |
0.839182 | + | 0.543851i | \(0.183034\pi\) | |||||||
\(798\) | 0.500000 | − | 1.53884i | 0.0176998 | − | 0.0544744i | ||||
\(799\) | 1.66312 | − | 1.20833i | 0.0588369 | − | 0.0427475i | ||||
\(800\) | −1.50000 | − | 1.08981i | −0.0530330 | − | 0.0385307i | ||||
\(801\) | −11.3820 | − | 35.0301i | −0.402162 | − | 1.23773i | ||||
\(802\) | 16.5967 | 0.586052 | ||||||||
\(803\) | 0.972136 | − | 0.812299i | 0.0343059 | − | 0.0286654i | ||||
\(804\) | 5.61803 | 0.198133 | ||||||||
\(805\) | 1.30902 | + | 4.02874i | 0.0461368 | + | 0.141994i | ||||
\(806\) | −34.1976 | − | 24.8460i | −1.20456 | − | 0.875162i | ||||
\(807\) | 15.7533 | − | 11.4454i | 0.554542 | − | 0.402898i | ||||
\(808\) | −2.83688 | + | 8.73102i | −0.0998011 | + | 0.307156i | ||||
\(809\) | −5.52786 | + | 17.0130i | −0.194349 | + | 0.598146i | 0.805634 | + | 0.592413i | \(0.201825\pi\) |
−0.999984 | + | 0.00573251i | \(0.998175\pi\) | |||||||
\(810\) | 2.11803 | − | 1.53884i | 0.0744201 | − | 0.0540694i | ||||
\(811\) | −21.4164 | − | 15.5599i | −0.752032 | − | 0.546383i | 0.144424 | − | 0.989516i | \(-0.453867\pi\) |
−0.896456 | + | 0.443133i | \(0.853867\pi\) | |||||||
\(812\) | −4.47214 | − | 13.7638i | −0.156941 | − | 0.483015i | ||||
\(813\) | 14.1803 | 0.497326 | ||||||||
\(814\) | 26.3541 | + | 16.5437i | 0.923711 | + | 0.579858i | ||||
\(815\) | 29.6525 | 1.03868 | ||||||||
\(816\) | −0.0729490 | − | 0.224514i | −0.00255373 | − | 0.00785956i | ||||
\(817\) | −6.23607 | − | 4.53077i | −0.218172 | − | 0.158512i | ||||
\(818\) | −2.66312 | + | 1.93487i | −0.0931138 | + | 0.0676511i | ||||
\(819\) | −4.85410 | + | 14.9394i | −0.169616 | + | 0.522025i | ||||
\(820\) | 4.92705 | − | 15.1639i | 0.172060 | − | 0.529546i | ||||
\(821\) | 11.2082 | − | 8.14324i | 0.391169 | − | 0.284201i | −0.374765 | − | 0.927120i | \(-0.622277\pi\) |
0.765934 | + | 0.642919i | \(0.222277\pi\) | |||||||
\(822\) | −2.04508 | − | 1.48584i | −0.0713305 | − | 0.0518247i | ||||
\(823\) | 1.76393 | + | 5.42882i | 0.0614868 | + | 0.189237i | 0.977082 | − | 0.212865i | \(-0.0682796\pi\) |
−0.915595 | + | 0.402102i | \(0.868280\pi\) | |||||||
\(824\) | 9.32624 | 0.324895 | ||||||||
\(825\) | 2.29180 | + | 5.70634i | 0.0797901 | + | 0.198669i | ||||
\(826\) | −9.47214 | −0.329578 | ||||||||
\(827\) | 6.68034 | + | 20.5600i | 0.232298 | + | 0.714940i | 0.997468 | + | 0.0711122i | \(0.0226548\pi\) |
−0.765170 | + | 0.643828i | \(0.777345\pi\) | |||||||
\(828\) | −1.61803 | − | 1.17557i | −0.0562306 | − | 0.0408539i | ||||
\(829\) | 35.1246 | − | 25.5195i | 1.21993 | − | 0.886330i | 0.223834 | − | 0.974627i | \(-0.428143\pi\) |
0.996094 | + | 0.0882976i | \(0.0281426\pi\) | |||||||
\(830\) | −7.11803 | + | 21.9071i | −0.247071 | + | 0.760405i | ||||
\(831\) | −5.29837 | + | 16.3067i | −0.183799 | + | 0.565674i | ||||
\(832\) | −3.92705 | + | 2.85317i | −0.136146 | + | 0.0989159i | ||||
\(833\) | 0.836881 | + | 0.608030i | 0.0289962 | + | 0.0210670i | ||||
\(834\) | 0.791796 | + | 2.43690i | 0.0274177 | + | 0.0843829i | ||||
\(835\) | 7.47214 | 0.258584 | ||||||||
\(836\) | 3.30902 | − | 0.224514i | 0.114445 | − | 0.00776498i | ||||
\(837\) | 43.5410 | 1.50500 | ||||||||
\(838\) | 7.88854 | + | 24.2784i | 0.272505 | + | 0.838685i | ||||
\(839\) | −4.73607 | − | 3.44095i | −0.163507 | − | 0.118795i | 0.503023 | − | 0.864273i | \(-0.332221\pi\) |
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(840\) | −3.42705 | + | 2.48990i | −0.118244 | + | 0.0859097i | ||||
\(841\) | 15.7599 | − | 48.5039i | 0.543444 | − | 1.67255i | ||||
\(842\) | 7.69098 | − | 23.6704i | 0.265049 | − | 0.815736i | ||||
\(843\) | 17.1074 | − | 12.4292i | 0.589210 | − | 0.428086i | ||||
\(844\) | 15.5172 | + | 11.2739i | 0.534125 | + | 0.388064i | ||||
\(845\) | −8.54508 | − | 26.2991i | −0.293960 | − | 0.904715i | ||||
\(846\) | 17.4164 | 0.598788 | ||||||||
\(847\) | −12.8541 | + | 12.3107i | −0.441672 | + | 0.423002i | ||||
\(848\) | 4.52786 | 0.155487 | ||||||||
\(849\) | 5.30902 | + | 16.3395i | 0.182205 | + | 0.560769i | ||||
\(850\) | −0.354102 | − | 0.257270i | −0.0121456 | − | 0.00882429i | ||||
\(851\) | 7.59017 | − | 5.51458i | 0.260188 | − | 0.189037i | ||||
\(852\) | −3.01722 | + | 9.28605i | −0.103368 | + | 0.318135i | ||||
\(853\) | 7.15248 | − | 22.0131i | 0.244896 | − | 0.753713i | −0.750757 | − | 0.660578i | \(-0.770311\pi\) |
0.995654 | − | 0.0931347i | \(-0.0296887\pi\) | |||||||
\(854\) | −19.0623 | + | 13.8496i | −0.652299 | + | 0.473923i | ||||
\(855\) | 4.23607 | + | 3.07768i | 0.144870 | + | 0.105255i | ||||
\(856\) | 1.78115 | + | 5.48183i | 0.0608786 | + | 0.187365i | ||||
\(857\) | 33.8541 | 1.15643 | 0.578217 | − | 0.815883i | \(-0.303749\pi\) | ||||
0.578217 | + | 0.815883i | \(0.303749\pi\) | |||||||
\(858\) | 16.0623 | − | 1.08981i | 0.548358 | − | 0.0372056i | ||||
\(859\) | −16.3050 | −0.556318 | −0.278159 | − | 0.960535i | \(-0.589724\pi\) | ||||
−0.278159 | + | 0.960535i | \(0.589724\pi\) | |||||||
\(860\) | 6.23607 | + | 19.1926i | 0.212648 | + | 0.654464i | ||||
\(861\) | −7.97214 | − | 5.79210i | −0.271690 | − | 0.197394i | ||||
\(862\) | −30.1976 | + | 21.9398i | −1.02853 | + | 0.747273i | ||||
\(863\) | 0.381966 | − | 1.17557i | 0.0130023 | − | 0.0400169i | −0.944345 | − | 0.328957i | \(-0.893303\pi\) |
0.957347 | + | 0.288940i | \(0.0933029\pi\) | |||||||
\(864\) | 1.54508 | − | 4.75528i | 0.0525649 | − | 0.161778i | ||||
\(865\) | 17.2533 | − | 12.5352i | 0.586629 | − | 0.426211i | ||||
\(866\) | 19.3262 | + | 14.0413i | 0.656732 | + | 0.477144i | ||||
\(867\) | 5.23607 | + | 16.1150i | 0.177826 | + | 0.547293i | ||||
\(868\) | 14.0902 | 0.478252 | ||||||||
\(869\) | −18.5410 | − | 46.1653i | −0.628961 | − | 1.56605i | ||||
\(870\) | −23.4164 | −0.793891 | ||||||||
\(871\) | −8.42705 | − | 25.9358i | −0.285540 | − | 0.878801i | ||||
\(872\) | −10.5902 | − | 7.69421i | −0.358628 | − | 0.260559i | ||||
\(873\) | 14.8541 | − | 10.7921i | 0.502735 | − | 0.365258i | ||||
\(874\) | 0.309017 | − | 0.951057i | 0.0104527 | − | 0.0321700i | ||||
\(875\) | 4.11803 | − | 12.6740i | 0.139215 | − | 0.428460i | ||||
\(876\) | 0.309017 | − | 0.224514i | 0.0104407 | − | 0.00758562i | ||||
\(877\) | 12.7361 | + | 9.25330i | 0.430066 | + | 0.312462i | 0.781675 | − | 0.623685i | \(-0.214365\pi\) |
−0.351609 | + | 0.936147i | \(0.614365\pi\) | |||||||
\(878\) | 3.35410 | + | 10.3229i | 0.113195 | + | 0.348380i | ||||
\(879\) | 24.4164 | 0.823545 | ||||||||
\(880\) | −7.35410 | − | 4.61653i | −0.247907 | − | 0.155623i | ||||
\(881\) | −31.4164 | −1.05845 | −0.529223 | − | 0.848483i | \(-0.677516\pi\) | ||||
−0.529223 | + | 0.848483i | \(0.677516\pi\) | |||||||
\(882\) | 2.70820 | + | 8.33499i | 0.0911900 | + | 0.280654i | ||||
\(883\) | −42.5066 | − | 30.8828i | −1.43046 | − | 1.03929i | −0.989931 | − | 0.141552i | \(-0.954791\pi\) |
−0.440529 | − | 0.897738i | \(-0.645209\pi\) | |||||||
\(884\) | −0.927051 | + | 0.673542i | −0.0311801 | + | 0.0226537i | ||||
\(885\) | −4.73607 | + | 14.5761i | −0.159201 | + | 0.489971i | ||||
\(886\) | −3.33688 | + | 10.2699i | −0.112105 | + | 0.345023i | ||||
\(887\) | −25.5172 | + | 18.5393i | −0.856784 | + | 0.622490i | −0.927008 | − | 0.375041i | \(-0.877629\pi\) |
0.0702238 | + | 0.997531i | \(0.477629\pi\) | |||||||
\(888\) | 7.59017 | + | 5.51458i | 0.254709 | + | 0.185057i | ||||
\(889\) | 7.35410 | + | 22.6336i | 0.246649 | + | 0.759107i | ||||
\(890\) | −48.2148 | −1.61616 | ||||||||
\(891\) | 2.54508 | − | 2.12663i | 0.0852636 | − | 0.0712447i | ||||
\(892\) | 12.9443 | 0.433406 | ||||||||
\(893\) | 2.69098 | + | 8.28199i | 0.0900503 | + | 0.277146i | ||||
\(894\) | 3.19098 | + | 2.31838i | 0.106722 | + | 0.0775384i | ||||
\(895\) | 24.7984 | − | 18.0171i | 0.828918 | − | 0.602244i | ||||
\(896\) | 0.500000 | − | 1.53884i | 0.0167038 | − | 0.0514091i | ||||
\(897\) | 1.50000 | − | 4.61653i | 0.0500835 | − | 0.154141i | ||||
\(898\) | −10.4271 | + | 7.57570i | −0.347955 | + | 0.252804i | ||||
\(899\) | 63.0132 | + | 45.7817i | 2.10161 | + | 1.52691i | ||||
\(900\) | −1.14590 | − | 3.52671i | −0.0381966 | − | 0.117557i | ||||
\(901\) | 1.06888 | 0.0356097 | ||||||||
\(902\) | 4.92705 | − | 19.5887i | 0.164053 | − | 0.652231i | ||||
\(903\) | 12.4721 | 0.415047 | ||||||||
\(904\) | −2.21885 | − | 6.82891i | −0.0737978 | − | 0.227126i | ||||
\(905\) | −23.0623 | − | 16.7557i | −0.766617 | − | 0.556980i | ||||
\(906\) | 7.47214 | − | 5.42882i | 0.248245 | − | 0.180361i | ||||
\(907\) | −14.8262 | + | 45.6305i | −0.492297 | + | 1.51513i | 0.328830 | + | 0.944389i | \(0.393346\pi\) |
−0.821127 | + | 0.570746i | \(0.806654\pi\) | |||||||
\(908\) | 5.29837 | − | 16.3067i | 0.175833 | − | 0.541157i | ||||
\(909\) | −14.8541 | + | 10.7921i | −0.492679 | + | 0.357953i | ||||
\(910\) | 16.6353 | + | 12.0862i | 0.551453 | + | 0.400654i | ||||
\(911\) | 9.88854 | + | 30.4338i | 0.327622 | + | 1.00832i | 0.970243 | + | 0.242133i | \(0.0778470\pi\) |
−0.642621 | + | 0.766184i | \(0.722153\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −7.11803 | + | 28.2994i | −0.235573 | + | 0.936575i | ||||
\(914\) | 1.94427 | 0.0643108 | ||||||||
\(915\) | 11.7812 | + | 36.2587i | 0.389473 | + | 1.19867i | ||||
\(916\) | −14.2082 | − | 10.3229i | −0.469452 | − | 0.341077i | ||||
\(917\) | 14.0902 | − | 10.2371i | 0.465298 | − | 0.338059i | ||||
\(918\) | 0.364745 | − | 1.12257i | 0.0120384 | − | 0.0370503i | ||||
\(919\) | 8.90576 | − | 27.4091i | 0.293774 | − | 0.904144i | −0.689856 | − | 0.723946i | \(-0.742326\pi\) |
0.983630 | − | 0.180197i | \(-0.0576737\pi\) | |||||||
\(920\) | −2.11803 | + | 1.53884i | −0.0698295 | + | 0.0507341i | ||||
\(921\) | 18.6074 | + | 13.5191i | 0.613134 | + | 0.445468i | ||||
\(922\) | −6.25329 | − | 19.2456i | −0.205941 | − | 0.633822i | ||||
\(923\) | 47.3951 | 1.56003 | ||||||||
\(924\) | −4.11803 | + | 3.44095i | −0.135473 | + | 0.113199i | ||||
\(925\) | 17.3951 | 0.571948 | ||||||||
\(926\) | 9.22542 | + | 28.3929i | 0.303166 | + | 0.933050i | ||||
\(927\) | 15.0902 | + | 10.9637i | 0.495626 | + | 0.360094i | ||||
\(928\) | 7.23607 | − | 5.25731i | 0.237536 | − | 0.172580i | ||||
\(929\) | 12.6008 | − | 38.7813i | 0.413419 | − | 1.27237i | −0.500238 | − | 0.865888i | \(-0.666754\pi\) |
0.913657 | − | 0.406486i | \(-0.133246\pi\) | |||||||
\(930\) | 7.04508 | − | 21.6825i | 0.231017 | − | 0.710999i | ||||
\(931\) | −3.54508 | + | 2.57565i | −0.116185 | + | 0.0844137i | ||||
\(932\) | −0.572949 | − | 0.416272i | −0.0187676 | − | 0.0136354i | ||||
\(933\) | −0.618034 | − | 1.90211i | −0.0202335 | − | 0.0622724i | ||||
\(934\) | −2.32624 | −0.0761168 | ||||||||
\(935\) | −1.73607 | − | 1.08981i | −0.0567755 | − | 0.0356407i | ||||
\(936\) | −9.70820 | −0.317323 | ||||||||
\(937\) | −16.6738 | − | 51.3166i | −0.544708 | − | 1.67644i | −0.721683 | − | 0.692224i | \(-0.756631\pi\) |
0.176975 | − | 0.984215i | \(-0.443369\pi\) | |||||||
\(938\) | 7.35410 | + | 5.34307i | 0.240120 | + | 0.174457i | ||||
\(939\) | −16.1353 | + | 11.7229i | −0.526554 | + | 0.382564i | ||||
\(940\) | 7.04508 | − | 21.6825i | 0.229785 | − | 0.707207i | ||||
\(941\) | −3.28773 | + | 10.1186i | −0.107177 | + | 0.329857i | −0.990235 | − | 0.139407i | \(-0.955481\pi\) |
0.883058 | + | 0.469263i | \(0.155481\pi\) | |||||||
\(942\) | 4.23607 | − | 3.07768i | 0.138019 | − | 0.100276i | ||||
\(943\) | −4.92705 | − | 3.57971i | −0.160447 | − | 0.116571i | ||||
\(944\) | −1.80902 | − | 5.56758i | −0.0588785 | − | 0.181209i | ||||
\(945\) | −21.1803 | −0.688997 | ||||||||
\(946\) | 9.52786 | + | 23.7234i | 0.309778 | + | 0.771315i | ||||
\(947\) | 20.8885 | 0.678786 | 0.339393 | − | 0.940645i | \(-0.389778\pi\) | ||||
0.339393 | + | 0.940645i | \(0.389778\pi\) | |||||||
\(948\) | −4.63525 | − | 14.2658i | −0.150546 | − | 0.463333i | ||||
\(949\) | −1.50000 | − | 1.08981i | −0.0486921 | − | 0.0353769i | ||||
\(950\) | 1.50000 | − | 1.08981i | 0.0486664 | − | 0.0353582i | ||||
\(951\) | 5.25329 | − | 16.1680i | 0.170350 | − | 0.524282i | ||||
\(952\) | 0.118034 | − | 0.363271i | 0.00382550 | − | 0.0117737i | ||||
\(953\) | −0.145898 | + | 0.106001i | −0.00472610 | + | 0.00343371i | −0.590146 | − | 0.807297i | \(-0.700930\pi\) |
0.585420 | + | 0.810730i | \(0.300930\pi\) | |||||||
\(954\) | 7.32624 | + | 5.32282i | 0.237196 | + | 0.172333i | ||||
\(955\) | −7.04508 | − | 21.6825i | −0.227974 | − | 0.701631i | ||||
\(956\) | 5.32624 | 0.172263 | ||||||||
\(957\) | −29.5967 | + | 2.00811i | −0.956727 | + | 0.0649131i | ||||
\(958\) | 18.4164 | 0.595007 | ||||||||
\(959\) | −1.26393 | − | 3.88998i | −0.0408145 | − | 0.125614i | ||||
\(960\) | −2.11803 | − | 1.53884i | −0.0683593 | − | 0.0496659i | ||||
\(961\) | −36.2705 | + | 26.3521i | −1.17002 | + | 0.850067i | ||||
\(962\) | 14.0729 | − | 43.3121i | 0.453730 | − | 1.39644i | ||||
\(963\) | −3.56231 | + | 10.9637i | −0.114794 | + | 0.353299i | ||||
\(964\) | 4.92705 | − | 3.57971i | 0.158690 | − | 0.115295i | ||||
\(965\) | −0.309017 | − | 0.224514i | −0.00994761 | − | 0.00722736i | ||||
\(966\) | 0.500000 | + | 1.53884i | 0.0160872 | + | 0.0495114i | ||||
\(967\) | 11.7426 | 0.377618 | 0.188809 | − | 0.982014i | \(-0.439537\pi\) | ||||
0.188809 | + | 0.982014i | \(0.439537\pi\) | |||||||
\(968\) | −9.69098 | − | 5.20431i | −0.311480 | − | 0.167273i | ||||
\(969\) | 0.236068 | 0.00758360 | ||||||||
\(970\) | −7.42705 | − | 22.8581i | −0.238468 | − | 0.733930i | ||||
\(971\) | −13.2639 | − | 9.63681i | −0.425660 | − | 0.309260i | 0.354251 | − | 0.935150i | \(-0.384736\pi\) |
−0.779911 | + | 0.625890i | \(0.784736\pi\) | |||||||
\(972\) | 12.9443 | − | 9.40456i | 0.415188 | − | 0.301652i | ||||
\(973\) | −1.28115 | + | 3.94298i | −0.0410719 | + | 0.126406i | ||||
\(974\) | −11.8369 | + | 36.4302i | −0.379278 | + | 1.16730i | ||||
\(975\) | 7.28115 | − | 5.29007i | 0.233184 | − | 0.169418i | ||||
\(976\) | −11.7812 | − | 8.55951i | −0.377106 | − | 0.273983i | ||||
\(977\) | 1.61803 | + | 4.97980i | 0.0517655 | + | 0.159318i | 0.973597 | − | 0.228272i | \(-0.0733076\pi\) |
−0.921832 | + | 0.387590i | \(0.873308\pi\) | |||||||
\(978\) | 11.3262 | 0.362173 | ||||||||
\(979\) | −60.9402 | + | 4.13474i | −1.94766 | + | 0.132147i | ||||
\(980\) | 11.4721 | 0.366464 | ||||||||
\(981\) | −8.09017 | − | 24.8990i | −0.258299 | − | 0.794963i | ||||
\(982\) | 5.78115 | + | 4.20025i | 0.184484 | + | 0.134035i | ||||
\(983\) | −9.94427 | + | 7.22494i | −0.317173 | + | 0.230440i | −0.734968 | − | 0.678102i | \(-0.762803\pi\) |
0.417795 | + | 0.908541i | \(0.362803\pi\) | |||||||
\(984\) | 1.88197 | − | 5.79210i | 0.0599949 | − | 0.184645i | ||||
\(985\) | −18.6074 | + | 57.2677i | −0.592881 | + | 1.82470i | ||||
\(986\) | 1.70820 | − | 1.24108i | 0.0544003 | − | 0.0395241i | ||||
\(987\) | −11.3992 | − | 8.28199i | −0.362840 | − | 0.263619i | ||||
\(988\) | −1.50000 | − | 4.61653i | −0.0477214 | − | 0.146871i | ||||
\(989\) | 7.70820 | 0.245107 | ||||||||
\(990\) | −6.47214 | − | 16.1150i | −0.205698 | − | 0.512167i | ||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | 2.69098 | + | 8.28199i | 0.0854388 | + | 0.262954i | ||||
\(993\) | −19.5623 | − | 14.2128i | −0.620791 | − | 0.451031i | ||||
\(994\) | −12.7812 | + | 9.28605i | −0.405394 | + | 0.294536i | ||||
\(995\) | 2.76393 | − | 8.50651i | 0.0876225 | − | 0.269674i | ||||
\(996\) | −2.71885 | + | 8.36775i | −0.0861500 | + | 0.265142i | ||||
\(997\) | 15.1353 | − | 10.9964i | 0.479338 | − | 0.348260i | −0.321731 | − | 0.946831i | \(-0.604265\pi\) |
0.801069 | + | 0.598571i | \(0.204265\pi\) | |||||||
\(998\) | 26.6074 | + | 19.3314i | 0.842242 | + | 0.611925i | ||||
\(999\) | 14.4959 | + | 44.6139i | 0.458631 | + | 1.41152i |
(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 | 418.2.f.c.115.1 | ✓ | 4 | |
11.3 | even | 5 | 4598.2.a.bd.1.1 | 2 | |||
11.8 | odd | 10 | 4598.2.a.u.1.1 | 2 | |||
11.9 | even | 5 | inner | 418.2.f.c.229.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.c.115.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
418.2.f.c.229.1 | yes | 4 | 11.9 | even | 5 | inner | |
4598.2.a.u.1.1 | 2 | 11.8 | odd | 10 | |||
4598.2.a.bd.1.1 | 2 | 11.3 | even | 5 |