Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(28,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 136.2 | ||
Root | \(0.500000 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.136 |
Dual form | 243.2.e.b.109.2 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.83975 | + | 1.54373i | 1.30090 | + | 1.09158i | 0.989989 | + | 0.141144i | \(0.0450781\pi\) |
0.310910 | + | 0.950439i | \(0.399366\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.654269 | + | 3.71054i | 0.327134 | + | 1.85527i | ||||
\(5\) | 0.0874698 | + | 0.0318364i | 0.0391177 | + | 0.0142377i | 0.361505 | − | 0.932370i | \(-0.382263\pi\) |
−0.322387 | + | 0.946608i | \(0.604485\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.100692 | + | 0.571052i | −0.0380579 | + | 0.215837i | −0.997906 | − | 0.0646837i | \(-0.979396\pi\) |
0.959848 | + | 0.280521i | \(0.0905073\pi\) | |||||||
\(8\) | −2.12277 | + | 3.67675i | −0.750514 | + | 1.29993i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.111776 | + | 0.193601i | 0.0353465 | + | 0.0612220i | ||||
\(11\) | −2.90655 | + | 1.05790i | −0.876357 | + | 0.318968i | −0.740739 | − | 0.671793i | \(-0.765524\pi\) |
−0.135618 | + | 0.990761i | \(0.543302\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.21871 | − | 2.70082i | 0.892711 | − | 0.749073i | −0.0760413 | − | 0.997105i | \(-0.524228\pi\) |
0.968752 | + | 0.248031i | \(0.0797836\pi\) | |||||||
\(14\) | −1.06680 | + | 0.895151i | −0.285114 | + | 0.239239i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.50017 | + | 0.909989i | −0.625044 | + | 0.227497i | ||||
\(17\) | −0.995493 | − | 1.72424i | −0.241443 | − | 0.418191i | 0.719683 | − | 0.694303i | \(-0.244287\pi\) |
−0.961125 | + | 0.276112i | \(0.910954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92271 | − | 3.33023i | 0.441100 | − | 0.764008i | −0.556671 | − | 0.830733i | \(-0.687922\pi\) |
0.997771 | + | 0.0667249i | \(0.0212550\pi\) | |||||||
\(20\) | −0.0609016 | + | 0.345390i | −0.0136180 | + | 0.0772316i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.98043 | − | 2.54067i | −1.48823 | − | 0.541672i | ||||
\(23\) | 0.773223 | + | 4.38517i | 0.161228 | + | 0.914371i | 0.952869 | + | 0.303383i | \(0.0981163\pi\) |
−0.791640 | + | 0.610987i | \(0.790773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.82358 | − | 3.20837i | −0.764717 | − | 0.641674i | ||||
\(26\) | 10.0910 | 1.97900 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.18479 | −0.412887 | ||||||||
\(29\) | −4.90231 | − | 4.11353i | −0.910336 | − | 0.763862i | 0.0618470 | − | 0.998086i | \(-0.480301\pi\) |
−0.972183 | + | 0.234223i | \(0.924745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.287822 | + | 1.63232i | 0.0516943 | + | 0.293173i | 0.999684 | − | 0.0251272i | \(-0.00799908\pi\) |
−0.947990 | + | 0.318300i | \(0.896888\pi\) | |||||||
\(32\) | 1.97455 | + | 0.718677i | 0.349054 | + | 0.127045i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.830315 | − | 4.70895i | 0.142398 | − | 0.807578i | ||||
\(35\) | −0.0269877 | + | 0.0467441i | −0.00456176 | + | 0.00790120i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.01505 | − | 3.49016i | −0.331272 | − | 0.573779i | 0.651490 | − | 0.758657i | \(-0.274144\pi\) |
−0.982761 | + | 0.184878i | \(0.940811\pi\) | |||||||
\(38\) | 8.67830 | − | 3.15864i | 1.40781 | − | 0.512399i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.302733 | + | 0.254023i | −0.0478663 | + | 0.0401646i | ||||
\(41\) | 0.839704 | − | 0.704595i | 0.131140 | − | 0.110039i | −0.574859 | − | 0.818253i | \(-0.694943\pi\) |
0.705998 | + | 0.708213i | \(0.250499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.48493 | − | 2.36032i | 0.988943 | − | 0.359946i | 0.203632 | − | 0.979047i | \(-0.434725\pi\) |
0.785311 | + | 0.619102i | \(0.212503\pi\) | |||||||
\(44\) | −5.82704 | − | 10.0927i | −0.878459 | − | 1.52154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.34699 | + | 9.26126i | −0.788370 | + | 1.36550i | ||||
\(47\) | −0.623952 | + | 3.53861i | −0.0910127 | + | 0.516159i | 0.904884 | + | 0.425659i | \(0.139958\pi\) |
−0.995896 | + | 0.0904999i | \(0.971154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.26189 | + | 2.27914i | 0.894555 | + | 0.325591i | ||||
\(50\) | −2.08157 | − | 11.8052i | −0.294379 | − | 1.66951i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.1274 | + | 10.1761i | 1.68177 | + | 1.41117i | ||||
\(53\) | −5.40034 | −0.741793 | −0.370897 | − | 0.928674i | \(-0.620950\pi\) | ||||
−0.370897 | + | 0.928674i | \(0.620950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.287915 | −0.0388224 | ||||||||
\(56\) | −1.88587 | − | 1.58243i | −0.252010 | − | 0.211462i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.66883 | − | 15.1357i | −0.350435 | − | 1.98742i | ||||
\(59\) | −9.66442 | − | 3.51756i | −1.25820 | − | 0.457947i | −0.375035 | − | 0.927011i | \(-0.622369\pi\) |
−0.883165 | + | 0.469063i | \(0.844592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.29152 | + | 12.9958i | −0.293399 | + | 1.66395i | 0.380242 | + | 0.924887i | \(0.375841\pi\) |
−0.673640 | + | 0.739059i | \(0.735270\pi\) | |||||||
\(62\) | −1.99034 | + | 3.44738i | −0.252774 | + | 0.437817i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.18386 | + | 8.97871i | 0.647982 | + | 1.12234i | ||||
\(65\) | 0.367525 | − | 0.133768i | 0.0455858 | − | 0.0165919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.76976 | + | 5.68050i | −0.827058 | + | 0.693984i | −0.954613 | − | 0.297848i | \(-0.903731\pi\) |
0.127556 | + | 0.991831i | \(0.459287\pi\) | |||||||
\(68\) | 5.74656 | − | 4.82194i | 0.696873 | − | 0.584746i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.121811 | + | 0.0443356i | −0.0145592 | + | 0.00529912i | ||||
\(71\) | 0.572473 | + | 0.991553i | 0.0679401 | + | 0.117676i | 0.897994 | − | 0.440007i | \(-0.145024\pi\) |
−0.830054 | + | 0.557683i | \(0.811691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0977361 | + | 0.169284i | −0.0114391 | + | 0.0198132i | −0.871688 | − | 0.490061i | \(-0.836975\pi\) |
0.860249 | + | 0.509874i | \(0.170308\pi\) | |||||||
\(74\) | 1.68070 | − | 9.53172i | 0.195377 | − | 1.10804i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.6149 | + | 4.95544i | 1.56174 | + | 0.568427i | ||||
\(77\) | −0.311448 | − | 1.76631i | −0.0354928 | − | 0.201290i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.52164 | − | 4.63321i | −0.621233 | − | 0.521277i | 0.276958 | − | 0.960882i | \(-0.410674\pi\) |
−0.898191 | + | 0.439605i | \(0.855118\pi\) | |||||||
\(80\) | −0.247661 | −0.0276893 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.63255 | 0.290717 | ||||||||
\(83\) | 11.4144 | + | 9.57782i | 1.25289 | + | 1.05130i | 0.996402 | + | 0.0847562i | \(0.0270111\pi\) |
0.256492 | + | 0.966546i | \(0.417433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0321818 | − | 0.182512i | −0.00349061 | − | 0.0197962i | ||||
\(86\) | 15.5744 | + | 5.66860i | 1.67943 | + | 0.611261i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.28032 | − | 12.9323i | 0.243083 | − | 1.37859i | ||||
\(89\) | −0.776563 | + | 1.34505i | −0.0823155 | + | 0.142575i | −0.904244 | − | 0.427016i | \(-0.859565\pi\) |
0.821929 | + | 0.569590i | \(0.192898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.21821 | + | 2.11000i | 0.127703 | + | 0.221189i | ||||
\(92\) | −15.7655 | + | 5.73816i | −1.64366 | + | 0.598244i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.61057 | + | 5.54693i | −0.681829 | + | 0.572122i | ||||
\(95\) | 0.274202 | − | 0.230083i | 0.0281325 | − | 0.0236060i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.97617 | + | 1.81118i | −0.505254 | + | 0.183897i | −0.582056 | − | 0.813149i | \(-0.697751\pi\) |
0.0768016 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(98\) | 8.00191 | + | 13.8597i | 0.808315 | + | 1.40004i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.40314 | − | 16.2867i | 0.940314 | − | 1.62867i | ||||
\(101\) | 1.26225 | − | 7.15855i | 0.125598 | − | 0.712302i | −0.855353 | − | 0.518046i | \(-0.826660\pi\) |
0.980951 | − | 0.194256i | \(-0.0622293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.01532 | − | 2.18940i | −0.592707 | − | 0.215728i | 0.0282124 | − | 0.999602i | \(-0.491019\pi\) |
−0.620920 | + | 0.783874i | \(0.713241\pi\) | |||||||
\(104\) | 3.09765 | + | 17.5677i | 0.303750 | + | 1.72265i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.93526 | − | 8.33667i | −0.964998 | − | 0.809729i | ||||
\(107\) | 5.54365 | 0.535925 | 0.267963 | − | 0.963429i | \(-0.413650\pi\) | ||||
0.267963 | + | 0.963429i | \(0.413650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.23137 | −0.596857 | −0.298428 | − | 0.954432i | \(-0.596462\pi\) | ||||
−0.298428 | + | 0.954432i | \(0.596462\pi\) | |||||||
\(110\) | −0.529691 | − | 0.444463i | −0.0505040 | − | 0.0423779i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.267904 | − | 1.51936i | −0.0253145 | − | 0.143566i | ||||
\(113\) | −11.1297 | − | 4.05088i | −1.04699 | − | 0.381075i | −0.239467 | − | 0.970905i | \(-0.576973\pi\) |
−0.807528 | + | 0.589830i | \(0.799195\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0719743 | + | 0.408186i | −0.00671164 | + | 0.0380636i | ||||
\(116\) | 12.0560 | − | 20.8816i | 1.11937 | − | 1.93881i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.3499 | − | 21.3907i | −1.13690 | − | 1.96917i | ||||
\(119\) | 1.08487 | − | 0.394861i | 0.0994500 | − | 0.0361968i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.09762 | + | 0.921009i | −0.0997832 | + | 0.0837281i | ||||
\(122\) | −24.2779 | + | 20.3716i | −2.19802 | + | 1.84436i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.86848 | + | 2.13595i | −0.527005 | + | 0.191814i | ||||
\(125\) | −0.465014 | − | 0.805428i | −0.0415921 | − | 0.0720396i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76469 | + | 9.98473i | −0.511533 | + | 0.886002i | 0.488377 | + | 0.872633i | \(0.337589\pi\) |
−0.999911 | + | 0.0133693i | \(0.995744\pi\) | |||||||
\(128\) | −3.59396 | + | 20.3824i | −0.317664 | + | 1.80156i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.882655 | + | 0.321260i | 0.0774140 | + | 0.0281764i | ||||
\(131\) | 1.56488 | + | 8.87487i | 0.136724 | + | 0.775401i | 0.973644 | + | 0.228075i | \(0.0732431\pi\) |
−0.836920 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70814 | + | 1.43330i | 0.148114 | + | 0.124282i | ||||
\(134\) | −21.2238 | −1.83346 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.45283 | 0.724824 | ||||||||
\(137\) | −8.82501 | − | 7.40506i | −0.753971 | − | 0.632657i | 0.182579 | − | 0.983191i | \(-0.441556\pi\) |
−0.936550 | + | 0.350534i | \(0.886000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.295868 | + | 1.67795i | 0.0250952 | + | 0.142322i | 0.994781 | − | 0.102033i | \(-0.0325348\pi\) |
−0.969686 | + | 0.244355i | \(0.921424\pi\) | |||||||
\(140\) | −0.191103 | − | 0.0695559i | −0.0161512 | − | 0.00587855i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.477485 | + | 2.70795i | −0.0400697 | + | 0.227246i | ||||
\(143\) | −6.49816 | + | 11.2551i | −0.543403 | + | 0.941202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.297844 | − | 0.515881i | −0.0247346 | − | 0.0428416i | ||||
\(146\) | −0.441139 | + | 0.160561i | −0.0365089 | + | 0.0132882i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.6320 | − | 9.76042i | 0.956146 | − | 0.802302i | ||||
\(149\) | 16.5870 | − | 13.9181i | 1.35886 | − | 1.14022i | 0.382525 | − | 0.923945i | \(-0.375054\pi\) |
0.976333 | − | 0.216273i | \(-0.0693900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.45557 | − | 1.62170i | 0.362589 | − | 0.131972i | −0.154300 | − | 0.988024i | \(-0.549312\pi\) |
0.516889 | + | 0.856052i | \(0.327090\pi\) | |||||||
\(152\) | 8.16296 | + | 14.1387i | 0.662104 | + | 1.14680i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.15373 | − | 3.73036i | 0.173552 | − | 0.300601i | ||||
\(155\) | −0.0267914 | + | 0.151942i | −0.00215194 | + | 0.0122043i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.196589 | + | 0.0715526i | 0.0156895 | + | 0.00571052i | 0.349853 | − | 0.936805i | \(-0.386232\pi\) |
−0.334163 | + | 0.942515i | \(0.608454\pi\) | |||||||
\(158\) | −3.00600 | − | 17.0479i | −0.239145 | − | 1.35626i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.149833 | + | 0.125725i | 0.0118454 | + | 0.00993944i | ||||
\(161\) | −2.58202 | −0.203491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.62384 | 0.440493 | 0.220247 | − | 0.975444i | \(-0.429314\pi\) | ||||
0.220247 | + | 0.975444i | \(0.429314\pi\) | |||||||
\(164\) | 3.16382 | + | 2.65476i | 0.247053 | + | 0.207302i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.21404 | + | 35.2416i | 0.482303 | + | 2.73528i | ||||
\(167\) | 15.6745 | + | 5.70507i | 1.21293 | + | 0.441471i | 0.867720 | − | 0.497053i | \(-0.165585\pi\) |
0.345212 | + | 0.938525i | \(0.387807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.808256 | − | 4.58385i | 0.0621735 | − | 0.352604i | ||||
\(170\) | 0.222544 | − | 0.385457i | 0.0170683 | − | 0.0295632i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.0010 | + | 22.5183i | 0.991315 | + | 1.71701i | ||||
\(173\) | 17.8562 | − | 6.49912i | 1.35758 | − | 0.494119i | 0.442275 | − | 0.896880i | \(-0.354172\pi\) |
0.915305 | + | 0.402761i | \(0.131949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.21715 | − | 1.86041i | 0.167601 | − | 0.140634i | ||||
\(176\) | 6.30420 | − | 5.28985i | 0.475197 | − | 0.398738i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.50507 | + | 1.27574i | −0.262716 | + | 0.0956209i | ||||
\(179\) | 8.11761 | + | 14.0601i | 0.606739 | + | 1.05090i | 0.991774 | + | 0.128001i | \(0.0408560\pi\) |
−0.385035 | + | 0.922902i | \(0.625811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49579 | − | 2.59078i | 0.111181 | − | 0.192571i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) |
0.916247 | + | 0.400614i | \(0.131203\pi\) | |||||||
\(182\) | −1.01608 | + | 5.76247i | −0.0753168 | + | 0.427143i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.7646 | − | 6.46577i | −1.30962 | − | 0.476663i | ||||
\(185\) | −0.0651415 | − | 0.369436i | −0.00478930 | − | 0.0271615i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.71752 | + | 3.95847i | 0.344979 | + | 0.289472i | ||||
\(188\) | −13.5384 | −0.987388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.859649 | 0.0623655 | ||||||||
\(191\) | 1.72652 | + | 1.44873i | 0.124927 | + | 0.104826i | 0.703111 | − | 0.711081i | \(-0.251794\pi\) |
−0.578184 | + | 0.815907i | \(0.696238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.152858 | − | 0.866900i | −0.0110029 | − | 0.0624008i | 0.978812 | − | 0.204761i | \(-0.0656418\pi\) |
−0.989815 | + | 0.142361i | \(0.954531\pi\) | |||||||
\(194\) | −11.9509 | − | 4.34977i | −0.858024 | − | 0.312295i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.35989 | + | 24.7262i | −0.311421 | + | 1.76616i | ||||
\(197\) | 10.1383 | − | 17.5600i | 0.722322 | − | 1.25110i | −0.237744 | − | 0.971328i | \(-0.576408\pi\) |
0.960067 | − | 0.279771i | \(-0.0902586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50472 | + | 16.4627i | 0.673772 | + | 1.16701i | 0.976826 | + | 0.214034i | \(0.0686603\pi\) |
−0.303054 | + | 0.952973i | \(0.598006\pi\) | |||||||
\(200\) | 19.9130 | − | 7.24773i | 1.40806 | − | 0.512492i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.3731 | − | 11.2214i | 0.940928 | − | 0.789532i | ||||
\(203\) | 2.84266 | − | 2.38527i | 0.199516 | − | 0.167413i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0958805 | − | 0.0348977i | 0.00669659 | − | 0.00243736i | ||||
\(206\) | −7.68684 | − | 13.3140i | −0.535567 | − | 0.927630i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.58963 | + | 9.68152i | −0.387571 | + | 0.671293i | ||||
\(209\) | −2.06541 | + | 11.7135i | −0.142867 | + | 0.810241i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2080 | − | 5.53528i | −1.04697 | − | 0.381064i | −0.239449 | − | 0.970909i | \(-0.576967\pi\) |
−0.807517 | + | 0.589845i | \(0.799189\pi\) | |||||||
\(212\) | −3.53327 | − | 20.0382i | −0.242666 | − | 1.37623i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.1989 | + | 8.55792i | 0.697184 | + | 0.585007i | ||||
\(215\) | 0.642380 | 0.0438100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.961120 | −0.0652451 | ||||||||
\(218\) | −11.4642 | − | 9.61957i | −0.776450 | − | 0.651519i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.188374 | − | 1.06832i | −0.0127002 | − | 0.0720261i | ||||
\(221\) | −7.86109 | − | 2.86120i | −0.528794 | − | 0.192465i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.72602 | − | 21.1313i | 0.249513 | − | 1.41506i | −0.560261 | − | 0.828316i | \(-0.689299\pi\) |
0.809774 | − | 0.586742i | \(-0.199590\pi\) | |||||||
\(224\) | −0.609223 | + | 1.05520i | −0.0407054 | + | 0.0705038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2224 | − | 24.6339i | −0.946058 | − | 1.63862i | ||||
\(227\) | −17.9615 | + | 6.53746i | −1.19215 | + | 0.433906i | −0.860477 | − | 0.509489i | \(-0.829834\pi\) |
−0.331671 | + | 0.943395i | \(0.607612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2131 | − | 14.4435i | 1.13748 | − | 0.954456i | 0.138123 | − | 0.990415i | \(-0.455893\pi\) |
0.999353 | + | 0.0359590i | \(0.0114486\pi\) | |||||||
\(230\) | −0.762545 | + | 0.639851i | −0.0502807 | + | 0.0421905i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.5309 | − | 9.29249i | 1.67619 | − | 0.610082i | ||||
\(233\) | −8.84074 | − | 15.3126i | −0.579176 | − | 1.00316i | −0.995574 | − | 0.0939796i | \(-0.970041\pi\) |
0.416398 | − | 0.909182i | \(-0.363292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.167233 | + | 0.289657i | −0.0109091 | + | 0.0188951i | ||||
\(236\) | 6.72893 | − | 38.1617i | 0.438016 | − | 2.48411i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.60545 | + | 0.948306i | 0.168886 | + | 0.0614696i | ||||
\(239\) | 2.67771 | + | 15.1860i | 0.173207 | + | 0.982304i | 0.940193 | + | 0.340641i | \(0.110644\pi\) |
−0.766987 | + | 0.641663i | \(0.778245\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0746 | + | 8.45359i | 0.648962 | + | 0.544544i | 0.906756 | − | 0.421656i | \(-0.138551\pi\) |
−0.257794 | + | 0.966200i | \(0.582996\pi\) | |||||||
\(242\) | −3.44113 | −0.221204 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −49.7209 | −3.18305 | ||||||||
\(245\) | 0.475166 | + | 0.398712i | 0.0303573 | + | 0.0254728i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.80571 | − | 15.9120i | −0.178523 | − | 1.01245i | ||||
\(248\) | −6.61261 | − | 2.40679i | −0.419901 | − | 0.152832i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.387856 | − | 2.19964i | 0.0245302 | − | 0.139118i | ||||
\(251\) | 8.70830 | − | 15.0832i | 0.549663 | − | 0.952045i | −0.448634 | − | 0.893716i | \(-0.648089\pi\) |
0.998297 | − | 0.0583292i | \(-0.0185773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.88646 | − | 11.9277i | −0.432948 | − | 0.749889i | ||||
\(254\) | −26.0193 | + | 9.47026i | −1.63260 | + | 0.594217i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.1926 | + | 18.6218i | −1.38704 | + | 1.16386i | ||||
\(257\) | −8.57018 | + | 7.19124i | −0.534593 | + | 0.448577i | −0.869684 | − | 0.493609i | \(-0.835677\pi\) |
0.335091 | + | 0.942186i | \(0.391233\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.19596 | − | 0.799265i | 0.136451 | − | 0.0496639i | ||||
\(260\) | 0.736812 | + | 1.27620i | 0.0456952 | + | 0.0791463i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.8214 | + | 18.7433i | −0.668550 | + | 1.15796i | ||||
\(263\) | 3.59641 | − | 20.3962i | 0.221764 | − | 1.25769i | −0.647012 | − | 0.762480i | \(-0.723982\pi\) |
0.868776 | − | 0.495206i | \(-0.164907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.472366 | − | 0.171927i | −0.0290172 | − | 0.0105614i | ||||
\(266\) | 0.929914 | + | 5.27381i | 0.0570167 | + | 0.323358i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.5070 | − | 21.4029i | −1.55809 | − | 1.30739i | ||||
\(269\) | 28.2449 | 1.72212 | 0.861060 | − | 0.508504i | \(-0.169801\pi\) | ||||
0.861060 | + | 0.508504i | \(0.169801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.2626 | 1.04863 | 0.524316 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524316 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(272\) | 4.05795 | + | 3.40502i | 0.246049 | + | 0.206460i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.80436 | − | 27.2469i | −0.290242 | − | 1.64605i | ||||
\(275\) | 14.5076 | + | 5.28032i | 0.874838 | + | 0.318415i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.897584 | − | 5.09045i | 0.0539306 | − | 0.305855i | −0.945896 | − | 0.324469i | \(-0.894814\pi\) |
0.999827 | + | 0.0186140i | \(0.00592536\pi\) | |||||||
\(278\) | −2.04598 | + | 3.54375i | −0.122710 | + | 0.212540i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.114578 | − | 0.198454i | −0.00684733 | − | 0.0118599i | ||||
\(281\) | −3.09764 | + | 1.12745i | −0.184790 | + | 0.0672580i | −0.432758 | − | 0.901510i | \(-0.642459\pi\) |
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.99454 | + | 5.86911i | −0.415782 | + | 0.348883i | −0.826556 | − | 0.562855i | \(-0.809703\pi\) |
0.410774 | + | 0.911737i | \(0.365259\pi\) | |||||||
\(284\) | −3.30465 | + | 2.77293i | −0.196095 | + | 0.164543i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.3299 | + | 10.6752i | −1.73431 | + | 0.631238i | ||||
\(287\) | 0.317809 | + | 0.550462i | 0.0187597 | + | 0.0324927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.51799 | − | 11.2895i | 0.383411 | − | 0.664087i | ||||
\(290\) | 0.248424 | − | 1.40888i | 0.0145880 | − | 0.0827325i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.692081 | − | 0.251897i | −0.0405010 | − | 0.0147411i | ||||
\(293\) | 0.490805 | + | 2.78349i | 0.0286731 | + | 0.162613i | 0.995782 | − | 0.0917487i | \(-0.0292456\pi\) |
−0.967109 | + | 0.254362i | \(0.918135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.733358 | − | 0.615360i | −0.0426978 | − | 0.0358277i | ||||
\(296\) | 17.1100 | 0.994496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 52.0017 | 3.01238 | ||||||||
\(299\) | 14.3323 | + | 12.0263i | 0.828861 | + | 0.695497i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.694887 | + | 3.94090i | 0.0400526 | + | 0.227150i | ||||
\(302\) | 10.7006 | + | 3.89470i | 0.615750 | + | 0.224115i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.77664 | + | 10.0758i | −0.101897 | + | 0.577888i | ||||
\(305\) | −0.614179 | + | 1.06379i | −0.0351678 | + | 0.0609124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.14723 | − | 5.45116i | −0.179622 | − | 0.311114i | 0.762129 | − | 0.647425i | \(-0.224154\pi\) |
−0.941751 | + | 0.336311i | \(0.890821\pi\) | |||||||
\(308\) | 6.35020 | − | 2.31129i | 0.361836 | − | 0.131698i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.283847 | + | 0.238176i | −0.0161214 | + | 0.0135275i | ||||
\(311\) | 5.64796 | − | 4.73920i | 0.320266 | − | 0.268735i | −0.468453 | − | 0.883488i | \(-0.655189\pi\) |
0.788720 | + | 0.614753i | \(0.210744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.01319 | − | 1.46068i | 0.226839 | − | 0.0825627i | −0.226100 | − | 0.974104i | \(-0.572598\pi\) |
0.452939 | + | 0.891541i | \(0.350375\pi\) | |||||||
\(314\) | 0.251217 | + | 0.435120i | 0.0141770 | + | 0.0245552i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5791 | − | 23.5197i | 0.763883 | − | 1.32308i | ||||
\(317\) | −2.80400 | + | 15.9023i | −0.157488 | + | 0.893160i | 0.798988 | + | 0.601348i | \(0.205369\pi\) |
−0.956476 | + | 0.291812i | \(0.905742\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.6005 | + | 6.77002i | 1.04143 | + | 0.379048i | ||||
\(320\) | 0.167581 | + | 0.950401i | 0.00936808 | + | 0.0531290i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.75026 | − | 3.98594i | −0.264722 | − | 0.222128i | ||||
\(323\) | −7.65618 | −0.426001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.9723 | −1.16333 | ||||||||
\(326\) | 10.3465 | + | 8.68171i | 0.573037 | + | 0.480835i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.808121 | + | 4.58308i | 0.0446210 | + | 0.253058i | ||||
\(329\) | −1.95790 | − | 0.712618i | −0.107943 | − | 0.0392879i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.33895 | − | 18.9361i | 0.183525 | − | 1.04082i | −0.744311 | − | 0.667834i | \(-0.767222\pi\) |
0.927836 | − | 0.372989i | \(-0.121667\pi\) | |||||||
\(332\) | −28.0708 | + | 48.6201i | −1.54059 | + | 2.66838i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0301 | + | 34.6932i | 1.09600 | + | 1.89833i | ||||
\(335\) | −0.772996 | + | 0.281348i | −0.0422333 | + | 0.0153717i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.5698 | + | 18.9383i | −1.22945 | + | 1.03163i | −0.231180 | + | 0.972911i | \(0.574259\pi\) |
−0.998274 | + | 0.0587237i | \(0.981297\pi\) | |||||||
\(338\) | 8.56322 | − | 7.18540i | 0.465778 | − | 0.390834i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.656164 | − | 0.238824i | 0.0355855 | − | 0.0129521i | ||||
\(341\) | −2.56339 | − | 4.43993i | −0.138815 | − | 0.240435i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.96154 | + | 6.86159i | −0.213903 | + | 0.370491i | ||||
\(344\) | −5.08773 | + | 28.8539i | −0.274312 | + | 1.55570i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 42.8838 | + | 15.6084i | 2.30545 | + | 0.839114i | ||||
\(347\) | −1.97907 | − | 11.2239i | −0.106242 | − | 0.602530i | −0.990717 | − | 0.135941i | \(-0.956594\pi\) |
0.884475 | − | 0.466588i | \(-0.154517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.5731 | + | 18.1019i | 1.15478 | + | 0.968975i | 0.999821 | − | 0.0189464i | \(-0.00603120\pi\) |
0.154958 | + | 0.987921i | \(0.450476\pi\) | |||||||
\(350\) | 6.95097 | 0.371545 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.49941 | −0.346419 | ||||||||
\(353\) | −21.9503 | − | 18.4185i | −1.16830 | − | 0.980318i | −0.168312 | − | 0.985734i | \(-0.553832\pi\) |
−0.999985 | + | 0.00541596i | \(0.998276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0185067 | + | 0.104956i | 0.000982231 | + | 0.00557051i | ||||
\(356\) | −5.49893 | − | 2.00145i | −0.291443 | − | 0.106077i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.77069 | + | 38.3985i | −0.357842 | + | 2.02942i | ||||
\(359\) | −15.5161 | + | 26.8747i | −0.818909 | + | 1.41839i | 0.0875770 | + | 0.996158i | \(0.472088\pi\) |
−0.906486 | + | 0.422235i | \(0.861246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10636 | + | 3.64833i | 0.110861 | + | 0.192017i | ||||
\(362\) | 6.75136 | − | 2.45729i | 0.354843 | − | 0.129152i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.03222 | + | 5.90074i | −0.368589 | + | 0.309283i | ||||
\(365\) | −0.0139383 | + | 0.0116957i | −0.000729566 | + | 0.000612179i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.6694 | + | 8.25097i | −1.18333 | + | 0.430697i | −0.857377 | − | 0.514689i | \(-0.827907\pi\) |
−0.325953 | + | 0.945386i | \(0.605685\pi\) | |||||||
\(368\) | −5.92365 | − | 10.2601i | −0.308791 | − | 0.534843i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.450466 | − | 0.780230i | 0.0234186 | − | 0.0405622i | ||||
\(371\) | 0.543770 | − | 3.08387i | 0.0282311 | − | 0.160107i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8266 | + | 4.30453i | 0.612359 | + | 0.222880i | 0.629535 | − | 0.776972i | \(-0.283245\pi\) |
−0.0171764 | + | 0.999852i | \(0.505468\pi\) | |||||||
\(374\) | 2.56823 | + | 14.5652i | 0.132800 | + | 0.753147i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.6861 | − | 9.80578i | −0.602663 | − | 0.505694i | ||||
\(377\) | −26.8890 | −1.38486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.70522 | −0.395790 | −0.197895 | − | 0.980223i | \(-0.563411\pi\) | ||||
−0.197895 | + | 0.980223i | \(0.563411\pi\) | |||||||
\(380\) | 1.03313 | + | 0.866902i | 0.0529986 | + | 0.0444711i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.939925 | + | 5.33058i | 0.0480908 | + | 0.272736i | ||||
\(383\) | −16.7844 | − | 6.10904i | −0.857645 | − | 0.312157i | −0.124492 | − | 0.992221i | \(-0.539730\pi\) |
−0.733153 | + | 0.680063i | \(0.761952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0289907 | − | 0.164414i | 0.00147750 | − | 0.00837933i | ||||
\(386\) | 1.05704 | − | 1.83085i | 0.0538020 | − | 0.0931878i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.97622 | − | 17.2793i | −0.506466 | − | 0.877224i | ||||
\(389\) | 25.7367 | − | 9.36740i | 1.30490 | − | 0.474946i | 0.406313 | − | 0.913734i | \(-0.366814\pi\) |
0.898591 | + | 0.438788i | \(0.144592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.79136 | − | 5.69863i | 0.343454 | − | 0.288192i | ||||
\(392\) | −21.6724 | + | 18.1853i | −1.09462 | + | 0.918497i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 45.7598 | − | 16.6552i | 2.30535 | − | 0.839078i | ||||
\(395\) | −0.335472 | − | 0.581055i | −0.0168794 | − | 0.0292361i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.10799 | + | 3.65115i | −0.105797 | + | 0.183246i | −0.914064 | − | 0.405571i | \(-0.867073\pi\) |
0.808266 | + | 0.588817i | \(0.200406\pi\) | |||||||
\(398\) | −7.92764 | + | 44.9599i | −0.397377 | + | 2.25364i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.4792 | + | 4.54206i | 0.623961 | + | 0.227103i | ||||
\(401\) | −2.63468 | − | 14.9420i | −0.131569 | − | 0.746168i | −0.977187 | − | 0.212379i | \(-0.931879\pi\) |
0.845618 | − | 0.533789i | \(-0.179232\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.33502 | + | 4.47661i | 0.265756 | + | 0.222996i | ||||
\(404\) | 27.3880 | 1.36260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.91200 | 0.442295 | ||||||||
\(407\) | 9.54906 | + | 8.01262i | 0.473330 | + | 0.397171i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.817816 | + | 4.63806i | 0.0404384 | + | 0.229337i | 0.998328 | − | 0.0577983i | \(-0.0184080\pi\) |
−0.957890 | + | 0.287136i | \(0.907297\pi\) | |||||||
\(410\) | 0.230269 | + | 0.0838110i | 0.0113722 | + | 0.00413913i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.18822 | − | 23.7526i | 0.206339 | − | 1.17021i | ||||
\(413\) | 2.98184 | − | 5.16469i | 0.146727 | − | 0.254138i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.693492 | + | 1.20116i | 0.0340422 | + | 0.0589628i | ||||
\(416\) | 8.29653 | − | 3.01969i | 0.406771 | − | 0.148052i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.8824 | + | 18.3615i | −1.07030 | + | 0.898089i | ||||
\(419\) | −15.1609 | + | 12.7215i | −0.740658 | + | 0.621486i | −0.933014 | − | 0.359839i | \(-0.882831\pi\) |
0.192356 | + | 0.981325i | \(0.438387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.4859 | + | 9.64008i | −1.29084 | + | 0.469829i | −0.894004 | − | 0.448059i | \(-0.852115\pi\) |
−0.396840 | + | 0.917888i | \(0.629893\pi\) | |||||||
\(422\) | −19.4340 | − | 33.6607i | −0.946032 | − | 1.63858i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.4637 | − | 19.8557i | 0.556726 | − | 0.964278i | ||||
\(425\) | −1.72566 | + | 9.78670i | −0.0837068 | + | 0.474725i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.19056 | − | 2.61715i | −0.347976 | − | 0.126653i | ||||
\(428\) | 3.62704 | + | 20.5700i | 0.175320 | + | 0.994287i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.18182 | + | 0.991663i | 0.0569923 | + | 0.0478222i | ||||
\(431\) | 5.19681 | 0.250321 | 0.125161 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125161 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3285 | 1.21721 | 0.608605 | − | 0.793473i | \(-0.291730\pi\) | ||||
0.608605 | + | 0.793473i | \(0.291730\pi\) | |||||||
\(434\) | −1.76822 | − | 1.48371i | −0.0848772 | − | 0.0712205i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.07699 | − | 23.1218i | −0.195252 | − | 1.10733i | ||||
\(437\) | 16.0903 | + | 5.85640i | 0.769704 | + | 0.280149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.71955 | + | 15.4233i | −0.129797 | + | 0.736114i | 0.848546 | + | 0.529122i | \(0.177479\pi\) |
−0.978343 | + | 0.206992i | \(0.933633\pi\) | |||||||
\(440\) | 0.611178 | − | 1.05859i | 0.0291368 | − | 0.0504664i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.0455 | − | 17.3993i | −0.477815 | − | 0.827600i | ||||
\(443\) | −17.1530 | + | 6.24318i | −0.814964 | + | 0.296623i | −0.715673 | − | 0.698436i | \(-0.753880\pi\) |
−0.0992911 | + | 0.995058i | \(0.531658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.110747 | + | 0.0929280i | −0.00524992 | + | 0.00440521i | ||||
\(446\) | 39.4760 | − | 33.1243i | 1.86924 | − | 1.56848i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.64928 | + | 2.05617i | −0.266903 | + | 0.0971449i | ||||
\(449\) | 14.3608 | + | 24.8737i | 0.677729 | + | 1.17386i | 0.975663 | + | 0.219274i | \(0.0703690\pi\) |
−0.297934 | + | 0.954586i | \(0.596298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69525 | + | 2.93626i | −0.0798262 | + | 0.138263i | ||||
\(452\) | 7.74915 | − | 43.9476i | 0.364489 | − | 2.06712i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43.1368 | − | 15.7005i | −2.02451 | − | 0.736861i | ||||
\(455\) | 0.0393818 | + | 0.223345i | 0.00184625 | + | 0.0104706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1087 | − | 22.7469i | −1.26809 | − | 1.06406i | −0.994771 | − | 0.102133i | \(-0.967433\pi\) |
−0.273321 | − | 0.961923i | \(-0.588122\pi\) | |||||||
\(458\) | 53.9648 | 2.52161 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.56168 | −0.0728139 | ||||||||
\(461\) | −1.74408 | − | 1.46345i | −0.0812297 | − | 0.0681598i | 0.601269 | − | 0.799047i | \(-0.294662\pi\) |
−0.682498 | + | 0.730887i | \(0.739107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.19070 | + | 18.0954i | 0.148285 | + | 0.840964i | 0.964671 | + | 0.263458i | \(0.0848629\pi\) |
−0.816386 | + | 0.577506i | \(0.804026\pi\) | |||||||
\(464\) | 15.9999 | + | 5.82348i | 0.742776 | + | 0.270348i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.37383 | − | 41.8191i | 0.341586 | − | 1.93723i | ||||
\(467\) | 2.32935 | − | 4.03455i | 0.107789 | − | 0.186697i | −0.807085 | − | 0.590435i | \(-0.798956\pi\) |
0.914874 | + | 0.403738i | \(0.132289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.56220 | − | 4.43786i | −0.118312 | − | 0.204922i | ||||
\(470\) | −0.754820 | + | 0.274732i | −0.0348172 | + | 0.0126724i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 33.4486 | − | 28.0667i | 1.53960 | − | 1.29187i | ||||
\(473\) | −16.3518 | + | 13.7208i | −0.751856 | + | 0.630882i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0363 | + | 6.56466i | −0.827561 | + | 0.301207i | ||||
\(476\) | 2.17495 | + | 3.76712i | 0.0996885 | + | 0.172666i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.5169 | + | 32.0722i | −0.846942 | + | 1.46695i | ||||
\(479\) | 2.46162 | − | 13.9605i | 0.112474 | − | 0.637873i | −0.875496 | − | 0.483226i | \(-0.839465\pi\) |
0.987970 | − | 0.154647i | \(-0.0494240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.9122 | − | 5.79156i | −0.725533 | − | 0.264072i | ||||
\(482\) | 5.48464 | + | 31.1050i | 0.249819 | + | 1.41679i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.13558 | − | 3.47016i | −0.187981 | − | 0.157735i | ||||
\(485\) | −0.492926 | −0.0223826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4338 | −0.971258 | −0.485629 | − | 0.874165i | \(-0.661409\pi\) | ||||
−0.485629 | + | 0.874165i | \(0.661409\pi\) | |||||||
\(488\) | −42.9181 | − | 36.0126i | −1.94281 | − | 1.63021i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.258682 | + | 1.46706i | 0.0116861 | + | 0.0662750i | ||||
\(491\) | −13.2382 | − | 4.81833i | −0.597434 | − | 0.217448i | 0.0255621 | − | 0.999673i | \(-0.491862\pi\) |
−0.622996 | + | 0.782225i | \(0.714085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.21251 | + | 12.5478i | −0.0996464 | + | 0.565123i | ||||
\(494\) | 19.4020 | − | 33.6053i | 0.872938 | − | 1.51197i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20500 | − | 3.81917i | −0.0990073 | − | 0.171486i | ||||
\(497\) | −0.623872 | + | 0.227071i | −0.0279845 | + | 0.0101855i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4212 | − | 9.58353i | 0.511284 | − | 0.429018i | −0.350297 | − | 0.936639i | \(-0.613919\pi\) |
0.861581 | + | 0.507621i | \(0.169475\pi\) | |||||||
\(500\) | 2.68433 | − | 2.25242i | 0.120047 | − | 0.100731i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 39.3056 | − | 14.3061i | 1.75429 | − | 0.638510i | ||||
\(503\) | −7.93153 | − | 13.7378i | −0.353650 | − | 0.612539i | 0.633236 | − | 0.773958i | \(-0.281726\pi\) |
−0.986886 | + | 0.161420i | \(0.948393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.338311 | − | 0.585972i | 0.0150546 | − | 0.0260754i | ||||
\(506\) | 5.74382 | − | 32.5748i | 0.255344 | − | 1.44813i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −40.8204 | − | 14.8574i | −1.81111 | − | 0.659192i | ||||
\(509\) | −5.89131 | − | 33.4113i | −0.261128 | − | 1.48093i | −0.779839 | − | 0.625980i | \(-0.784699\pi\) |
0.518712 | − | 0.854949i | \(-0.326412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0868286 | − | 0.0728579i | −0.00384107 | − | 0.00322304i | ||||
\(512\) | −28.1824 | −1.24550 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.8683 | −1.18511 | ||||||||
\(515\) | −0.456457 | − | 0.383013i | −0.0201139 | − | 0.0168775i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.92993 | − | 10.9452i | −0.0848784 | − | 0.481369i | ||||
\(518\) | 5.27387 | + | 1.91953i | 0.231721 | + | 0.0843394i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.288340 | + | 1.63526i | −0.0126445 | + | 0.0717108i | ||||
\(521\) | −21.3899 | + | 37.0484i | −0.937108 | + | 1.62312i | −0.166277 | + | 0.986079i | \(0.553175\pi\) |
−0.770831 | + | 0.637040i | \(0.780159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.38893 | + | 2.40569i | 0.0607335 | + | 0.105193i | 0.894793 | − | 0.446480i | \(-0.147323\pi\) |
−0.834060 | + | 0.551674i | \(0.813989\pi\) | |||||||
\(524\) | −31.9067 | + | 11.6131i | −1.39385 | + | 0.507321i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.1028 | − | 31.9721i | 1.66136 | − | 1.39405i | ||||
\(527\) | 2.52799 | − | 2.12124i | 0.110121 | − | 0.0924025i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.98111 | − | 1.08504i | 0.129614 | − | 0.0471755i | ||||
\(530\) | −0.603626 | − | 1.04551i | −0.0262198 | − | 0.0454141i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.20073 | + | 7.27587i | −0.182125 | + | 0.315449i | ||||
\(533\) | 0.799781 | − | 4.53578i | 0.0346424 | − | 0.196467i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.484902 | + | 0.176490i | 0.0209642 | + | 0.00763033i | ||||
\(536\) | −6.51513 | − | 36.9492i | −0.281411 | − | 1.59596i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 51.9634 | + | 43.6025i | 2.24030 | + | 1.87984i | ||||
\(539\) | −20.6116 | −0.887803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.59390 | −0.154514 | −0.0772570 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772570 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(542\) | 31.7589 | + | 26.6489i | 1.36416 | + | 1.14467i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.726475 | − | 4.12004i | −0.0311473 | − | 0.176645i | ||||
\(545\) | −0.545057 | − | 0.198384i | −0.0233477 | − | 0.00849785i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.87401 | + | 38.9844i | −0.293911 | + | 1.66685i | 0.377683 | + | 0.925935i | \(0.376721\pi\) |
−0.671594 | + | 0.740919i | \(0.734390\pi\) | |||||||
\(548\) | 21.7029 | − | 37.5905i | 0.927101 | − | 1.60579i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.5389 | + | 32.1102i | 0.790499 | + | 1.36919i | ||||
\(551\) | −23.1247 | + | 8.41671i | −0.985146 | + | 0.358564i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.20179 | − | 2.68662i | 0.136154 | − | 0.114247i | ||||
\(554\) | 9.50962 | − | 7.97952i | 0.404025 | − | 0.339017i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.03253 | + | 2.19566i | −0.255836 | + | 0.0931167i | ||||
\(557\) | −5.71731 | − | 9.90267i | −0.242250 | − | 0.419590i | 0.719105 | − | 0.694902i | \(-0.244552\pi\) |
−0.961355 | + | 0.275312i | \(0.911219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.4983 | − | 25.1119i | 0.613214 | − | 1.06212i | ||||
\(560\) | 0.0249374 | − | 0.141427i | 0.00105380 | − | 0.00597638i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.43936 | − | 2.70771i | −0.313810 | − | 0.114218i | ||||
\(563\) | −2.51977 | − | 14.2903i | −0.106196 | − | 0.602266i | −0.990736 | − | 0.135802i | \(-0.956639\pi\) |
0.884540 | − | 0.466464i | \(-0.154472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.844547 | − | 0.708659i | −0.0355304 | − | 0.0298135i | ||||
\(566\) | −21.9285 | −0.921725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86093 | −0.203960 | ||||||||
\(569\) | 0.995232 | + | 0.835099i | 0.0417223 | + | 0.0350092i | 0.663410 | − | 0.748256i | \(-0.269108\pi\) |
−0.621688 | + | 0.783265i | \(0.713553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.78833 | + | 15.8134i | 0.116688 | + | 0.661769i | 0.985901 | + | 0.167331i | \(0.0535150\pi\) |
−0.869213 | + | 0.494438i | \(0.835374\pi\) | |||||||
\(572\) | −46.0142 | − | 16.7478i | −1.92395 | − | 0.700261i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.265077 | + | 1.50332i | −0.0110641 | + | 0.0627475i | ||||
\(575\) | 11.1127 | − | 19.2478i | 0.463434 | − | 0.802691i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.23017 | + | 7.32686i | 0.176104 | + | 0.305021i | 0.940543 | − | 0.339675i | \(-0.110317\pi\) |
−0.764439 | + | 0.644696i | \(0.776984\pi\) | |||||||
\(578\) | 29.4194 | − | 10.7078i | 1.22369 | − | 0.445385i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.71933 | − | 1.44269i | 0.0713912 | − | 0.0599044i | ||||
\(581\) | −6.61877 | + | 5.55381i | −0.274593 | + | 0.230411i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.6963 | − | 5.71300i | 0.650076 | − | 0.236608i | ||||
\(584\) | −0.414943 | − | 0.718703i | −0.0171705 | − | 0.0297401i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.39401 | + | 5.87860i | −0.140205 | + | 0.242843i | ||||
\(587\) | 3.19256 | − | 18.1059i | 0.131771 | − | 0.747310i | −0.845283 | − | 0.534319i | \(-0.820568\pi\) |
0.977054 | − | 0.212991i | \(-0.0683206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.98940 | + | 2.17996i | 0.246789 | + | 0.0898238i | ||||
\(590\) | −0.399243 | − | 2.26422i | −0.0164366 | − | 0.0932163i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.21398 | + | 6.89235i | 0.337593 | + | 0.283274i | ||||
\(593\) | −13.5128 | −0.554905 | −0.277452 | − | 0.960739i | \(-0.589490\pi\) | ||||
−0.277452 | + | 0.960739i | \(0.589490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.107464 | 0.00440561 | ||||||||
\(596\) | 62.4962 | + | 52.4405i | 2.55994 | + | 2.14805i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.80257 | + | 44.2506i | 0.319071 | + | 1.80954i | ||||
\(599\) | 10.3627 | + | 3.77170i | 0.423407 | + | 0.154108i | 0.544931 | − | 0.838481i | \(-0.316556\pi\) |
−0.121524 | + | 0.992589i | \(0.538778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.47976 | − | 25.4060i | 0.182733 | − | 1.03633i | −0.746100 | − | 0.665834i | \(-0.768076\pi\) |
0.928833 | − | 0.370498i | \(-0.120813\pi\) | |||||||
\(602\) | −4.80528 | + | 8.32298i | −0.195848 | + | 0.339219i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.93252 | + | 15.4716i | 0.363459 | + | 0.629529i | ||||
\(605\) | −0.125330 | + | 0.0456163i | −0.00509538 | + | 0.00185457i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3297 | + | 9.50675i | −0.459858 | + | 0.385867i | −0.843079 | − | 0.537790i | \(-0.819259\pi\) |
0.383221 | + | 0.923657i | \(0.374815\pi\) | |||||||
\(608\) | 6.18985 | − | 5.19390i | 0.251032 | − | 0.210640i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.77214 | + | 1.00898i | −0.112241 | + | 0.0408523i | ||||
\(611\) | 7.54882 | + | 13.0749i | 0.305393 | + | 0.528956i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1370 | + | 31.4141i | −0.732545 | + | 1.26880i | 0.223248 | + | 0.974762i | \(0.428334\pi\) |
−0.955792 | + | 0.294043i | \(0.904999\pi\) | |||||||
\(614\) | 2.62502 | − | 14.8873i | 0.105937 | − | 0.600801i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.15542 | + | 2.60436i | 0.288300 | + | 0.104933i | ||||
\(617\) | 7.01079 | + | 39.7602i | 0.282244 | + | 1.60068i | 0.714967 | + | 0.699158i | \(0.246442\pi\) |
−0.432724 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.28058 | − | 4.43093i | −0.212244 | − | 0.178094i | 0.530468 | − | 0.847705i | \(-0.322016\pi\) |
−0.742712 | + | 0.669611i | \(0.766461\pi\) | |||||||
\(620\) | −0.581315 | −0.0233462 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7069 | 0.709981 | ||||||||
\(623\) | −0.689898 | − | 0.578893i | −0.0276402 | − | 0.0231929i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.31865 | + | 24.4923i | 0.172746 | + | 0.979691i | ||||
\(626\) | 9.63817 | + | 3.50801i | 0.385219 | + | 0.140208i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.136877 | + | 0.776267i | −0.00546198 | + | 0.0309764i | ||||
\(629\) | −4.01193 | + | 6.94887i | −0.159966 | + | 0.277070i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9095 | − | 25.8241i | −0.593539 | − | 1.02804i | −0.993751 | − | 0.111617i | \(-0.964397\pi\) |
0.400212 | − | 0.916423i | \(-0.368936\pi\) | |||||||
\(632\) | 28.7564 | − | 10.4665i | 1.14387 | − | 0.416334i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.7075 | + | 24.9275i | −1.17983 | + | 0.989999i | ||||
\(635\) | −0.822114 | + | 0.689836i | −0.0326246 | + | 0.0273753i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.3108 | − | 9.57634i | 1.04247 | − | 0.379428i | ||||
\(638\) | 23.7691 | + | 41.1693i | 0.941028 | + | 1.62991i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.963264 | + | 1.66842i | −0.0380763 | + | 0.0659502i | ||||
\(641\) | −7.44616 | + | 42.2293i | −0.294106 | + | 1.66796i | 0.376709 | + | 0.926331i | \(0.377056\pi\) |
−0.670815 | + | 0.741625i | \(0.734056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.7600 | + | 9.37589i | 1.01588 | + | 0.369749i | 0.795687 | − | 0.605708i | \(-0.207110\pi\) |
0.220190 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(644\) | −1.68933 | − | 9.58068i | −0.0665690 | − | 0.377532i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.0855 | − | 11.8191i | −0.554185 | − | 0.465016i | ||||
\(647\) | 16.1623 | 0.635407 | 0.317703 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317703 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8113 | 1.24870 | ||||||||
\(650\) | −38.5837 | − | 32.3756i | −1.51338 | − | 1.26987i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.67951 | + | 20.8675i | 0.144101 | + | 0.817235i | ||||
\(653\) | 30.3016 | + | 11.0289i | 1.18579 | + | 0.431593i | 0.858245 | − | 0.513241i | \(-0.171555\pi\) |
0.327549 | + | 0.944834i | \(0.393777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.145664 | + | 0.826103i | −0.00569157 | + | 0.0322785i | ||||
\(656\) | −1.45823 | + | 2.52573i | −0.0569344 | + | 0.0986133i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.50195 | − | 4.33351i | −0.0975363 | − | 0.168938i | ||||
\(659\) | 26.1409 | − | 9.51452i | 1.01831 | − | 0.370633i | 0.221689 | − | 0.975117i | \(-0.428843\pi\) |
0.796617 | + | 0.604485i | \(0.206621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5854 | − | 19.7905i | 0.917367 | − | 0.769763i | −0.0561388 | − | 0.998423i | \(-0.517879\pi\) |
0.973506 | + | 0.228660i | \(0.0734345\pi\) | |||||||
\(662\) | 35.3751 | − | 29.6832i | 1.37489 | − | 1.15367i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.4455 | + | 21.6364i | −2.30693 | + | 0.839655i | ||||
\(665\) | 0.103779 | + | 0.179751i | 0.00402439 | + | 0.00697044i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2479 | − | 24.6781i | 0.551682 | − | 0.955540i | ||||
\(668\) | −10.9135 | + | 61.8937i | −0.422257 | + | 2.39474i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.85644 | − | 0.675690i | −0.0717207 | − | 0.0261042i | ||||
\(671\) | −7.08785 | − | 40.1972i | −0.273624 | − | 1.55180i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.0172 | − | 16.7964i | −0.771607 | − | 0.647455i | 0.169513 | − | 0.985528i | \(-0.445780\pi\) |
−0.941120 | + | 0.338073i | \(0.890225\pi\) | |||||||
\(674\) | −70.7584 | −2.72551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5374 | 0.674515 | ||||||||
\(677\) | −13.9378 | − | 11.6952i | −0.535673 | − | 0.449483i | 0.334382 | − | 0.942438i | \(-0.391472\pi\) |
−0.870055 | + | 0.492955i | \(0.835917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.533217 | − | 3.02403i | −0.0204630 | − | 0.116051i | ||||
\(680\) | 0.739367 | + | 0.269108i | 0.0283534 | + | 0.0103198i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.13806 | − | 12.1255i | 0.0818705 | − | 0.464311i | ||||
\(683\) | 11.7486 | − | 20.3491i | 0.449546 | − | 0.778636i | −0.548811 | − | 0.835947i | \(-0.684919\pi\) |
0.998356 | + | 0.0573104i | \(0.0182525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.536171 | − | 0.928676i | −0.0204860 | − | 0.0354829i | ||||
\(686\) | −17.8807 | + | 6.50805i | −0.682689 | + | 0.248478i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.0656 | + | 11.8024i | −0.536246 | + | 0.449964i | ||||
\(689\) | −17.3821 | + | 14.5853i | −0.662207 | + | 0.555657i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.8520 | − | 15.2329i | 1.59212 | − | 0.579486i | 0.614329 | − | 0.789050i | \(-0.289427\pi\) |
0.977795 | + | 0.209565i | \(0.0672046\pi\) | |||||||
\(692\) | 35.7980 | + | 62.0039i | 1.36084 | + | 2.35704i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.6857 | − | 23.7043i | 0.519501 | − | 0.899802i | ||||
\(695\) | −0.0275404 | + | 0.156189i | −0.00104467 | + | 0.00592460i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.05081 | − | 0.746435i | −0.0776801 | − | 0.0282733i | ||||
\(698\) | 11.7444 | + | 66.6060i | 0.444534 | + | 2.52108i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.35374 | + | 7.00962i | 0.315742 | + | 0.264939i | ||||
\(701\) | 25.2567 | 0.953934 | 0.476967 | − | 0.878921i | \(-0.341736\pi\) | ||||
0.476967 | + | 0.878921i | \(0.341736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4974 | −0.584496 | ||||||||
\(704\) | −24.5657 | − | 20.6130i | −0.925854 | − | 0.776884i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.9498 | − | 67.7708i | −0.449738 | − | 2.55059i | ||||
\(707\) | 3.96081 | + | 1.44162i | 0.148961 | + | 0.0542175i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.72350 | + | 15.4457i | −0.102283 | + | 0.580077i | 0.889987 | + | 0.455985i | \(0.150713\pi\) |
−0.992271 | + | 0.124092i | \(0.960398\pi\) | |||||||
\(710\) | −0.127977 | + | 0.221663i | −0.00480289 | + | 0.00831886i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.29694 | − | 5.71046i | −0.123558 | − | 0.214009i | ||||
\(713\) | −6.93544 | + | 2.52429i | −0.259734 | + | 0.0945355i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.926715 | + | 0.777607i | −0.0346572 | + | 0.0290808i | ||||
\(716\) | −46.8596 | + | 39.3199i | −1.75122 | + | 1.46945i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −70.0331 | + | 25.4900i | −2.61361 | + | 0.951277i | ||||
\(719\) | −26.5804 | − | 46.0385i | −0.991280 | − | 1.71695i | −0.609757 | − | 0.792588i | \(-0.708733\pi\) |
−0.381523 | − | 0.924359i | \(-0.624600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85595 | − | 3.21461i | 0.0691194 | − | 0.119718i | ||||
\(722\) | −1.75686 | + | 9.96366i | −0.0653836 | + | 0.370809i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.5919 | + | 3.85512i | 0.393644 | + | 0.143275i | ||||
\(725\) | 5.54669 | + | 31.4568i | 0.205999 | + | 1.16828i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.359407 | + | 0.301578i | 0.0133297 | + | 0.0111849i | 0.649428 | − | 0.760423i | \(-0.275008\pi\) |
−0.636098 | + | 0.771608i | \(0.719453\pi\) | |||||||
\(728\) | −10.3440 | −0.383372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0436980 | −0.00161734 | ||||||||
\(731\) | −10.5255 | − | 8.83193i | −0.389299 | − | 0.326661i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.05837 | − | 45.7013i | −0.297643 | − | 1.68801i | −0.656264 | − | 0.754532i | \(-0.727864\pi\) |
0.358621 | − | 0.933483i | \(-0.383247\pi\) | |||||||
\(734\) | −54.4432 | − | 19.8157i | −2.00953 | − | 0.731411i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.62475 | + | 9.21442i | −0.0598891 | + | 0.339648i | ||||
\(737\) | 13.6672 | − | 23.6724i | 0.503439 | − | 0.871983i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9047 | − | 22.3515i | −0.474706 | − | 0.822214i | 0.524875 | − | 0.851179i | \(-0.324112\pi\) |
−0.999580 | + | 0.0289653i | \(0.990779\pi\) | |||||||
\(740\) | 1.32819 | − | 0.483421i | 0.0488251 | − | 0.0177709i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.76107 | − | 4.83411i | 0.211496 | − | 0.177466i | ||||
\(743\) | −26.5891 | + | 22.3109i | −0.975460 | + | 0.818508i | −0.983398 | − | 0.181460i | \(-0.941918\pi\) |
0.00793799 | + | 0.999968i | \(0.497473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.89396 | − | 0.689346i | 0.0693894 | − | 0.0252557i | ||||
\(746\) | 15.1129 | + | 26.1764i | 0.553324 | + | 0.958385i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.6015 | + | 20.0945i | −0.424195 | + | 0.734727i | ||||
\(749\) | −0.558201 | + | 3.16571i | −0.0203962 | + | 0.115673i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5393 | − | 8.20364i | −0.822472 | − | 0.299355i | −0.103706 | − | 0.994608i | \(-0.533070\pi\) |
−0.718765 | + | 0.695253i | \(0.755292\pi\) | |||||||
\(752\) | −1.66010 | − | 9.41492i | −0.0605378 | − | 0.343327i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −49.4691 | − | 41.5095i | −1.80156 | − | 1.51169i | ||||
\(755\) | 0.441357 | 0.0160626 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.78780 | −0.319398 | −0.159699 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159699 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(758\) | −14.1757 | − | 11.8948i | −0.514883 | − | 0.432038i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.263888 | + | 1.49659i | 0.00957224 | + | 0.0542869i | ||||
\(761\) | 12.9244 | + | 4.70410i | 0.468510 | + | 0.170524i | 0.565477 | − | 0.824764i | \(-0.308692\pi\) |
−0.0969675 | + | 0.995288i | \(0.530914\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.627448 | − | 3.55844i | 0.0227152 | − | 0.128824i | ||||
\(764\) | −4.24595 | + | 7.35420i | −0.153613 | + | 0.266066i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.4484 | − | 37.1498i | −0.774963 | − | 1.34228i | ||||
\(767\) | −40.6073 | + | 14.7798i | −1.46624 | + | 0.533669i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0216 | + | 20.1565i | −0.866240 | + | 0.726862i | −0.963303 | − | 0.268417i | \(-0.913500\pi\) |
0.0970630 | + | 0.995278i | \(0.469055\pi\) | |||||||
\(770\) | 0.307147 | − | 0.257727i | 0.0110688 | − | 0.00928784i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.11666 | − | 1.13437i | 0.112171 | − | 0.0408269i | ||||
\(773\) | 14.0607 | + | 24.3539i | 0.505729 | + | 0.875948i | 0.999978 | + | 0.00662776i | \(0.00210970\pi\) |
−0.494249 | + | 0.869320i | \(0.664557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.13657 | − | 7.16475i | 0.148590 | − | 0.257365i | ||||
\(776\) | 3.90404 | − | 22.1409i | 0.140147 | − | 0.794812i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 61.8099 | + | 22.4970i | 2.21599 | + | 0.806555i | ||||
\(779\) | −0.731959 | − | 4.15114i | −0.0262251 | − | 0.148730i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.71288 | − | 2.27638i | −0.0970745 | − | 0.0814552i | ||||
\(782\) | 21.2916 | 0.761385 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.7298 | −0.633207 | ||||||||
\(785\) | 0.0149176 | + | 0.0125174i | 0.000532433 | + | 0.000446764i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.28609 | − | 35.6502i | −0.224075 | − | 1.27079i | −0.864446 | − | 0.502726i | \(-0.832330\pi\) |
0.640371 | − | 0.768066i | \(-0.278781\pi\) | |||||||
\(788\) | 71.7903 | + | 26.1295i | 2.55742 | + | 0.930827i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.279809 | − | 1.58687i | 0.00995515 | − | 0.0564585i | ||||
\(791\) | 3.43393 | − | 5.94775i | 0.122097 | − | 0.211478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7237 | + | 48.0189i | 0.984498 | + | 1.70520i | ||||
\(794\) | −9.51458 | + | 3.46302i | −0.337660 | + | 0.122898i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −54.8668 | + | 46.0387i | −1.94470 | + | 1.63180i | ||||
\(797\) | 22.6750 | − | 19.0266i | 0.803189 | − | 0.673956i | −0.145782 | − | 0.989317i | \(-0.546570\pi\) |
0.948972 | + | 0.315361i | \(0.102126\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.72256 | − | 2.44681i | 0.237827 | − | 0.0865620i | ||||
\(800\) | −5.24407 | − | 9.08300i | −0.185406 | − | 0.321133i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2193 | − | 31.5568i | 0.643346 | − | 1.11431i | ||||
\(803\) | 0.104990 | − | 0.595426i | 0.00370501 | − | 0.0210121i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.225848 | − | 0.0822021i | −0.00796011 | − | 0.00289724i | ||||
\(806\) | 2.90440 | + | 16.4717i | 0.102303 | + | 0.580190i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23.6408 | + | 19.8370i | 0.831679 | + | 0.697861i | ||||
\(809\) | 5.75943 | 0.202491 | 0.101245 | − | 0.994861i | \(-0.467717\pi\) | ||||
0.101245 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4896 | 0.438569 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(812\) | 10.7105 | + | 8.98720i | 0.375866 | + | 0.315389i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.19854 | + | 29.4824i | 0.182209 | + | 1.03336i | ||||
\(815\) | 0.491916 | + | 0.179043i | 0.0172311 | + | 0.00627160i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.60823 | − | 26.1346i | 0.161222 | − | 0.914333i | ||||
\(818\) | −5.65535 | + | 9.79536i | −0.197735 | + | 0.342487i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.192221 | + | 0.332936i | 0.00671265 | + | 0.0116266i | ||||
\(821\) | 40.4695 | − | 14.7297i | 1.41240 | − | 0.514070i | 0.480564 | − | 0.876960i | \(-0.340432\pi\) |
0.931832 | + | 0.362890i | \(0.118210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.87807 | − | 6.61049i | 0.274612 | − | 0.230427i | −0.495072 | − | 0.868852i | \(-0.664858\pi\) |
0.769684 | + | 0.638425i | \(0.220414\pi\) | |||||||
\(824\) | 20.8190 | − | 17.4693i | 0.725266 | − | 0.608570i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.4587 | − | 4.89858i | 0.468289 | − | 0.170443i | ||||
\(827\) | 3.04731 | + | 5.27810i | 0.105965 | + | 0.183538i | 0.914132 | − | 0.405416i | \(-0.132873\pi\) |
−0.808167 | + | 0.588954i | \(0.799540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8489 | − | 29.1832i | 0.585188 | − | 1.01358i | −0.409664 | − | 0.912236i | \(-0.634354\pi\) |
0.994852 | − | 0.101339i | \(-0.0323126\pi\) | |||||||
\(830\) | −0.578424 | + | 3.28041i | −0.0200774 | + | 0.113865i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 40.9352 | + | 14.8992i | 1.41917 | + | 0.516537i | ||||
\(833\) | −2.30387 | − | 13.0659i | −0.0798243 | − | 0.452706i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.18942 | + | 0.998042i | 0.0411616 | + | 0.0345387i | ||||
\(836\) | −44.8148 | −1.54995 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.5308 | −1.64192 | ||||||||
\(839\) | 32.3472 | + | 27.1425i | 1.11675 | + | 0.937063i | 0.998436 | − | 0.0559139i | \(-0.0178072\pi\) |
0.118312 | + | 0.992976i | \(0.462252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.07574 | + | 11.7721i | 0.0715773 | + | 0.405935i | ||||
\(842\) | −63.6091 | − | 23.1518i | −2.19211 | − | 0.797865i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.5887 | − | 60.0517i | 0.364479 | − | 2.06706i | ||||
\(845\) | 0.216631 | − | 0.375216i | 0.00745234 | − | 0.0129078i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.415423 | − | 0.719533i | −0.0142741 | − | 0.0247235i | ||||
\(848\) | 13.5018 | − | 4.91425i | 0.463653 | − | 0.168756i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.2828 | + | 15.3411i | −0.627096 | + | 0.526196i | ||||
\(851\) | 13.7469 | − | 11.5350i | 0.471237 | − | 0.395415i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5748 | − | 12.2202i | 1.14958 | − | 0.418413i | 0.304216 | − | 0.952603i | \(-0.401606\pi\) |
0.845364 | + | 0.534190i | \(0.179383\pi\) | |||||||
\(854\) | −9.18865 | − | 15.9152i | −0.314429 | − | 0.544607i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7679 | + | 20.3826i | −0.402219 | + | 0.696664i | ||||
\(857\) | −1.37332 | + | 7.78850i | −0.0469118 | + | 0.266050i | −0.999238 | − | 0.0390316i | \(-0.987573\pi\) |
0.952326 | + | 0.305082i | \(0.0986838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.0223 | + | 15.2948i | 1.43378 | + | 0.521853i | 0.938013 | − | 0.346601i | \(-0.112664\pi\) |
0.495768 | + | 0.868455i | \(0.334887\pi\) | |||||||
\(860\) | 0.420289 | + | 2.38358i | 0.0143317 | + | 0.0812794i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.56081 | + | 8.02248i | 0.325643 | + | 0.273247i | ||||
\(863\) | 22.9170 | 0.780103 | 0.390052 | − | 0.920793i | \(-0.372457\pi\) | ||||
0.390052 | + | 0.920793i | \(0.372457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76878 | 0.0601405 | ||||||||
\(866\) | 46.5981 | + | 39.1004i | 1.58347 | + | 1.32869i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.628831 | − | 3.56628i | −0.0213439 | − | 0.121047i | ||||
\(869\) | 20.9504 | + | 7.62531i | 0.710693 | + | 0.258671i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.44790 | + | 36.5678i | −0.218479 | + | 1.23905i | ||||
\(872\) | 13.2278 | − | 22.9112i | 0.447950 | − | 0.775871i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.5614 | + | 35.6134i | 0.695501 | + | 1.20464i | ||||
\(875\) | 0.506764 | − | 0.184447i | 0.0171318 | − | 0.00623545i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.9584 | + | 14.2298i | −0.572645 | + | 0.480506i | −0.882522 | − | 0.470270i | \(-0.844156\pi\) |
0.309877 | + | 0.950776i | \(0.399712\pi\) | |||||||
\(878\) | −28.8127 | + | 24.1768i | −0.972383 | + | 0.815926i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.719837 | − | 0.261999i | 0.0242657 | − | 0.00883200i | ||||
\(881\) | 4.93202 | + | 8.54251i | 0.166164 | + | 0.287804i | 0.937068 | − | 0.349147i | \(-0.113529\pi\) |
−0.770904 | + | 0.636951i | \(0.780195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7865 | + | 41.1995i | −0.800481 | + | 1.38647i | 0.118819 | + | 0.992916i | \(0.462089\pi\) |
−0.919300 | + | 0.393558i | \(0.871244\pi\) | |||||||
\(884\) | 5.47335 | − | 31.0409i | 0.184089 | − | 1.04402i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.1950 | − | 14.9938i | −1.38397 | − | 0.503725i | ||||
\(887\) | −2.31947 | − | 13.1544i | −0.0778801 | − | 0.441680i | −0.998667 | − | 0.0516143i | \(-0.983563\pi\) |
0.920787 | − | 0.390066i | \(-0.127548\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.12134 | − | 4.29732i | −0.171764 | − | 0.144127i | ||||
\(890\) | −0.347203 | −0.0116383 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 80.8465 | 2.70694 | ||||||||
\(893\) | 10.5847 | + | 8.88162i | 0.354204 | + | 0.297212i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.262422 | + | 1.48827i | 0.00877181 | + | 0.0497474i | ||||
\(896\) | −11.2775 | − | 4.10468i | −0.376755 | − | 0.137128i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.9780 | + | 67.9306i | −0.399711 | + | 2.26687i | ||||
\(899\) | 5.30359 | − | 9.18609i | 0.176885 | − | 0.306373i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37600 | + | 9.31150i | 0.179100 | + | 0.310211i | ||||
\(902\) | −7.65164 | + | 2.78497i | −0.254772 | + | 0.0927293i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.5199 | − | 32.3221i | 1.28115 | − | 1.07502i | ||||
\(905\) | 0.213318 | − | 0.178995i | 0.00709092 | − | 0.00594999i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.7316 | + | 12.6413i | −1.15325 | + | 0.419747i | −0.846680 | − | 0.532103i | \(-0.821402\pi\) |
−0.306565 | + | 0.951850i | \(0.599180\pi\) | |||||||
\(908\) | −36.0092 | − | 62.3697i | −1.19501 | − | 2.06981i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.272332 | + | 0.471694i | −0.00902773 | + | 0.0156365i | ||||
\(911\) | 8.40650 | − | 47.6756i | 0.278520 | − | 1.57956i | −0.449035 | − | 0.893514i | \(-0.648232\pi\) |
0.727555 | − | 0.686050i | \(-0.240657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.3089 | − | 15.7631i | −1.43331 | − | 0.521684i | ||||
\(914\) | −14.7581 | − | 83.6972i | −0.488154 | − | 2.76846i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 64.8554 | + | 54.4201i | 2.14288 | + | 1.79809i | ||||
\(917\) | −5.22558 | −0.172564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.93459 | 0.294725 | 0.147363 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147363 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(920\) | −1.34802 | − | 1.13112i | −0.0444427 | − | 0.0372919i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.949481 | − | 5.38477i | −0.0312695 | − | 0.177338i | ||||
\(923\) | 4.52064 | + | 1.64538i | 0.148799 | + | 0.0541582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.49303 | + | 19.8100i | −0.114850 | + | 0.651347i | ||||
\(926\) | −22.0643 | + | 38.2165i | −0.725079 | + | 1.25587i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.72355 | − | 11.6455i | −0.220711 | − | 0.382283i | ||||
\(929\) | −5.86758 | + | 2.13562i | −0.192509 | + | 0.0700676i | −0.436476 | − | 0.899716i | \(-0.643774\pi\) |
0.243967 | + | 0.969784i | \(0.421551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.6299 | − | 16.4714i | 0.643343 | − | 0.539829i | ||||
\(932\) | 51.0339 | − | 42.8225i | 1.67167 | − | 1.40270i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.5137 | − | 3.82667i | 0.344018 | − | 0.125212i | ||||
\(935\) | 0.286617 | + | 0.496435i | 0.00937338 | + | 0.0162352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9212 | + | 39.7006i | −0.748802 | + | 1.29696i | 0.199595 | + | 0.979878i | \(0.436037\pi\) |
−0.948397 | + | 0.317085i | \(0.897296\pi\) | |||||||
\(938\) | 2.13707 | − | 12.1199i | 0.0697777 | − | 0.395729i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.18420 | − | 0.431013i | −0.0386243 | − | 0.0140581i | ||||
\(941\) | 0.755827 | + | 4.28651i | 0.0246392 | + | 0.139736i | 0.994646 | − | 0.103343i | \(-0.0329538\pi\) |
−0.970007 | + | 0.243079i | \(0.921843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.73905 | + | 3.13743i | 0.121760 | + | 0.102169i | ||||
\(944\) | 27.3637 | 0.890612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.2644 | −1.66675 | ||||||||
\(947\) | −1.54491 | − | 1.29633i | −0.0502028 | − | 0.0421251i | 0.617341 | − | 0.786696i | \(-0.288210\pi\) |
−0.667544 | + | 0.744571i | \(0.732654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.142621 | + | 0.808844i | 0.00462967 | + | 0.0262562i | ||||
\(950\) | −43.3163 | − | 15.7658i | −1.40537 | − | 0.511511i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.851131 | + | 4.82700i | −0.0275853 | + | 0.156444i | ||||
\(953\) | −17.8644 | + | 30.9420i | −0.578684 | + | 1.00231i | 0.416947 | + | 0.908931i | \(0.363100\pi\) |
−0.995631 | + | 0.0933786i | \(0.970233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.104896 | + | 0.181686i | 0.00339437 | + | 0.00587922i | ||||
\(956\) | −54.5965 | + | 19.8715i | −1.76578 | + | 0.642691i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.0801 | − | 21.8838i | 0.842609 | − | 0.707033i | ||||
\(959\) | 5.11728 | − | 4.29391i | 0.165246 | − | 0.138658i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.5488 | − | 9.66299i | 0.856414 | − | 0.311709i | ||||
\(962\) | −20.3338 | − | 35.2191i | −0.655587 | − | 1.13551i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.7759 | + | 42.9131i | −0.797978 | + | 1.38214i | ||||
\(965\) | 0.0142285 | − | 0.0806940i | 0.000458032 | − | 0.00259763i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.651505 | + | 0.237128i | 0.0209510 | + | 0.00762553i | 0.352474 | − | 0.935821i | \(-0.385340\pi\) |
−0.331523 | + | 0.943447i | \(0.607563\pi\) | |||||||
\(968\) | −1.05633 | − | 5.99075i | −0.0339518 | − | 0.192550i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.906861 | − | 0.760946i | −0.0291175 | − | 0.0244325i | ||||
\(971\) | −47.4942 | −1.52416 | −0.762081 | − | 0.647482i | \(-0.775822\pi\) | ||||
−0.762081 | + | 0.647482i | \(0.775822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.987988 | −0.0316734 | ||||||||
\(974\) | −39.4328 | − | 33.0881i | −1.26351 | − | 1.06021i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.09688 | − | 34.5771i | −0.195156 | − | 1.10679i | ||||
\(977\) | −11.8432 | − | 4.31059i | −0.378899 | − | 0.137908i | 0.145548 | − | 0.989351i | \(-0.453506\pi\) |
−0.524447 | + | 0.851443i | \(0.675728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.834197 | − | 4.73096i | 0.0266610 | − | 0.151202i | ||||
\(980\) | −1.16855 | + | 2.02399i | −0.0373280 | + | 0.0646540i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.9168 | − | 29.3008i | −0.539838 | − | 0.935027i | ||||
\(983\) | 10.8488 | − | 3.94863i | 0.346022 | − | 0.125942i | −0.163162 | − | 0.986599i | \(-0.552169\pi\) |
0.509184 | + | 0.860657i | \(0.329947\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.44584 | − | 1.21320i | 0.0460683 | − | 0.0386559i | ||||
\(986\) | −23.4409 | + | 19.6692i | −0.746509 | + | 0.626395i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57.2064 | − | 20.8214i | 1.81998 | − | 0.662418i | ||||
\(989\) | 15.3647 | + | 26.6125i | 0.488569 | + | 0.846227i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.34676 | + | 16.1891i | −0.296910 | + | 0.514263i | −0.975427 | − | 0.220322i | \(-0.929289\pi\) |
0.678518 | + | 0.734584i | \(0.262623\pi\) | |||||||
\(992\) | −0.604792 | + | 3.42994i | −0.0192022 | + | 0.108901i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.49830 | − | 0.545338i | −0.0475233 | − | 0.0172971i | ||||
\(995\) | 0.307264 | + | 1.74258i | 0.00974093 | + | 0.0552436i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.57299 | + | 2.15900i | 0.0814875 | + | 0.0683762i | 0.682622 | − | 0.730772i | \(-0.260840\pi\) |
−0.601134 | + | 0.799148i | \(0.705284\pi\) | |||||||
\(998\) | 35.8066 | 1.13344 | ||||||||
\(999\) | 0 | 0 |
(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 | 243.2.e.b.136.2 | 12 | ||
3.2 | odd | 2 | 243.2.e.c.136.1 | 12 | |||
9.2 | odd | 6 | 27.2.e.a.25.1 | yes | 12 | ||
9.4 | even | 3 | 243.2.e.a.55.1 | 12 | |||
9.5 | odd | 6 | 243.2.e.d.55.2 | 12 | |||
9.7 | even | 3 | 81.2.e.a.73.2 | 12 | |||
27.2 | odd | 18 | 729.2.c.e.244.6 | 12 | |||
27.4 | even | 9 | 81.2.e.a.10.2 | 12 | |||
27.5 | odd | 18 | 243.2.e.c.109.1 | 12 | |||
27.7 | even | 9 | 729.2.a.d.1.6 | 6 | |||
27.11 | odd | 18 | 729.2.c.e.487.6 | 12 | |||
27.13 | even | 9 | 243.2.e.a.190.1 | 12 | |||
27.14 | odd | 18 | 243.2.e.d.190.2 | 12 | |||
27.16 | even | 9 | 729.2.c.b.487.1 | 12 | |||
27.20 | odd | 18 | 729.2.a.a.1.1 | 6 | |||
27.22 | even | 9 | inner | 243.2.e.b.109.2 | 12 | ||
27.23 | odd | 18 | 27.2.e.a.13.1 | ✓ | 12 | ||
27.25 | even | 9 | 729.2.c.b.244.1 | 12 | |||
36.11 | even | 6 | 432.2.u.c.241.1 | 12 | |||
45.2 | even | 12 | 675.2.u.b.349.1 | 24 | |||
45.29 | odd | 6 | 675.2.l.c.376.2 | 12 | |||
45.38 | even | 12 | 675.2.u.b.349.4 | 24 | |||
108.23 | even | 18 | 432.2.u.c.337.1 | 12 | |||
135.23 | even | 36 | 675.2.u.b.499.1 | 24 | |||
135.77 | even | 36 | 675.2.u.b.499.4 | 24 | |||
135.104 | odd | 18 | 675.2.l.c.526.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.1 | ✓ | 12 | 27.23 | odd | 18 | ||
27.2.e.a.25.1 | yes | 12 | 9.2 | odd | 6 | ||
81.2.e.a.10.2 | 12 | 27.4 | even | 9 | |||
81.2.e.a.73.2 | 12 | 9.7 | even | 3 | |||
243.2.e.a.55.1 | 12 | 9.4 | even | 3 | |||
243.2.e.a.190.1 | 12 | 27.13 | even | 9 | |||
243.2.e.b.109.2 | 12 | 27.22 | even | 9 | inner | ||
243.2.e.b.136.2 | 12 | 1.1 | even | 1 | trivial | ||
243.2.e.c.109.1 | 12 | 27.5 | odd | 18 | |||
243.2.e.c.136.1 | 12 | 3.2 | odd | 2 | |||
243.2.e.d.55.2 | 12 | 9.5 | odd | 6 | |||
243.2.e.d.190.2 | 12 | 27.14 | odd | 18 | |||
432.2.u.c.241.1 | 12 | 36.11 | even | 6 | |||
432.2.u.c.337.1 | 12 | 108.23 | even | 18 | |||
675.2.l.c.376.2 | 12 | 45.29 | odd | 6 | |||
675.2.l.c.526.2 | 12 | 135.104 | odd | 18 | |||
675.2.u.b.349.1 | 24 | 45.2 | even | 12 | |||
675.2.u.b.349.4 | 24 | 45.38 | even | 12 | |||
675.2.u.b.499.1 | 24 | 135.23 | even | 36 | |||
675.2.u.b.499.4 | 24 | 135.77 | even | 36 | |||
729.2.a.a.1.1 | 6 | 27.20 | odd | 18 | |||
729.2.a.d.1.6 | 6 | 27.7 | even | 9 | |||
729.2.c.b.244.1 | 12 | 27.25 | even | 9 | |||
729.2.c.b.487.1 | 12 | 27.16 | even | 9 | |||
729.2.c.e.244.6 | 12 | 27.2 | odd | 18 | |||
729.2.c.e.487.6 | 12 | 27.11 | odd | 18 |