Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(35,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.ce (of order \(18\), degree \(6\), 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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 359.3 | ||
Character | \(\chi\) | \(=\) | 684.359 |
Dual form | 684.2.ce.a.503.3 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39232 | + | 0.247874i | −0.984520 | + | 0.175273i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.87712 | − | 0.690240i | 0.938559 | − | 0.345120i | ||||
\(5\) | 0.294744 | + | 0.809802i | 0.131813 | + | 0.362154i | 0.987988 | − | 0.154533i | \(-0.0493872\pi\) |
−0.856174 | + | 0.516687i | \(0.827165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07545 | + | 1.19826i | −0.784445 | + | 0.452900i | −0.838003 | − | 0.545665i | \(-0.816277\pi\) |
0.0535581 | + | 0.998565i | \(0.482944\pi\) | |||||||
\(8\) | −2.44246 | + | 1.42632i | −0.863539 | + | 0.504281i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.611107 | − | 1.05445i | −0.193249 | − | 0.333445i | ||||
\(11\) | −1.68767 | + | 2.92312i | −0.508850 | + | 0.881355i | 0.491097 | + | 0.871105i | \(0.336596\pi\) |
−0.999947 | + | 0.0102500i | \(0.996737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.65614 | − | 1.38967i | 0.459331 | − | 0.385425i | −0.383554 | − | 0.923519i | \(-0.625300\pi\) |
0.842885 | + | 0.538094i | \(0.180855\pi\) | |||||||
\(14\) | 2.59267 | − | 2.18281i | 0.692921 | − | 0.583381i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.04714 | − | 2.59132i | 0.761785 | − | 0.647830i | ||||
\(17\) | −7.72199 | − | 1.36160i | −1.87286 | − | 0.330235i | −0.882672 | − | 0.469989i | \(-0.844258\pi\) |
−0.990186 | + | 0.139754i | \(0.955369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.789602 | − | 4.28679i | −0.181147 | − | 0.983456i | ||||
\(20\) | 1.11223 | + | 1.31665i | 0.248701 | + | 0.294412i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.62521 | − | 4.48825i | 0.346496 | − | 0.956899i | ||||
\(23\) | −2.80559 | − | 1.02115i | −0.585007 | − | 0.212925i | 0.0325250 | − | 0.999471i | \(-0.489645\pi\) |
−0.617532 | + | 0.786546i | \(0.711867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.26132 | − | 2.73657i | 0.652263 | − | 0.547314i | ||||
\(26\) | −1.96142 | + | 2.34538i | −0.384666 | + | 0.459967i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.06877 | + | 3.68183i | −0.579943 | + | 0.695800i | ||||
\(29\) | 4.45240 | − | 0.785078i | 0.826789 | − | 0.145785i | 0.255786 | − | 0.966733i | \(-0.417666\pi\) |
0.571003 | + | 0.820948i | \(0.306555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.62096 | + | 4.39996i | −1.36876 | + | 0.790257i | −0.990770 | − | 0.135551i | \(-0.956719\pi\) |
−0.377994 | + | 0.925808i | \(0.623386\pi\) | |||||||
\(32\) | −3.60028 | + | 4.36326i | −0.636445 | + | 0.771322i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.0890 | − | 0.0182998i | 1.90175 | − | 0.00313839i | ||||
\(35\) | −1.58208 | − | 1.32752i | −0.267420 | − | 0.224392i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.33783 | −1.20633 | −0.603166 | − | 0.797615i | \(-0.706094\pi\) | ||||
−0.603166 | + | 0.797615i | \(0.706094\pi\) | |||||||
\(38\) | 2.16196 | + | 5.77286i | 0.350716 | + | 0.936482i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.87494 | − | 1.55751i | −0.296454 | − | 0.246264i | ||||
\(41\) | 4.47507 | − | 5.33318i | 0.698888 | − | 0.832903i | −0.293512 | − | 0.955955i | \(-0.594824\pi\) |
0.992400 | + | 0.123053i | \(0.0392685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61673 | + | 4.44193i | 0.246549 | + | 0.677388i | 0.999807 | + | 0.0196624i | \(0.00625914\pi\) |
−0.753258 | + | 0.657726i | \(0.771519\pi\) | |||||||
\(44\) | −1.15029 | + | 6.65194i | −0.173413 | + | 1.00282i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.15941 | + | 0.726340i | 0.613271 | + | 0.107093i | ||||
\(47\) | −1.49426 | − | 8.47439i | −0.217961 | − | 1.23612i | −0.875694 | − | 0.482866i | \(-0.839596\pi\) |
0.657734 | − | 0.753251i | \(-0.271515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.628347 | + | 1.08833i | −0.0897638 | + | 0.155475i | ||||
\(50\) | −3.86248 | + | 4.61858i | −0.546237 | + | 0.653166i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.14957 | − | 3.75171i | 0.298092 | − | 0.520268i | ||||
\(53\) | 0.0611610 | − | 0.168038i | 0.00840111 | − | 0.0230819i | −0.935421 | − | 0.353535i | \(-0.884979\pi\) |
0.943822 | + | 0.330453i | \(0.107202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.86458 | − | 0.505103i | −0.386260 | − | 0.0681080i | ||||
\(56\) | 3.36009 | − | 5.88696i | 0.449011 | − | 0.786678i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00457 | + | 2.19671i | −0.788438 | + | 0.288442i | ||||
\(59\) | −0.802194 | + | 4.54947i | −0.104437 | + | 0.592291i | 0.887007 | + | 0.461756i | \(0.152780\pi\) |
−0.991444 | + | 0.130534i | \(0.958331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.65253 | − | 0.965440i | −0.339621 | − | 0.123612i | 0.166579 | − | 0.986028i | \(-0.446728\pi\) |
−0.506200 | + | 0.862416i | \(0.668950\pi\) | |||||||
\(62\) | 9.52019 | − | 8.01520i | 1.20907 | − | 1.01793i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.93120 | − | 6.96747i | 0.491401 | − | 0.870934i | ||||
\(65\) | 1.61349 | + | 0.931551i | 0.200129 | + | 0.115545i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8747 | + | 2.09382i | −1.45072 | + | 0.255801i | −0.842813 | − | 0.538207i | \(-0.819102\pi\) |
−0.607907 | + | 0.794008i | \(0.707991\pi\) | |||||||
\(68\) | −15.4349 | + | 2.77415i | −1.87176 | + | 0.336415i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.53182 | + | 1.45618i | 0.302610 | + | 0.174047i | ||||
\(71\) | −9.81994 | + | 3.57417i | −1.16541 | + | 0.424176i | −0.851028 | − | 0.525120i | \(-0.824020\pi\) |
−0.314385 | + | 0.949296i | \(0.601798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.28753 | − | 4.43677i | −0.618859 | − | 0.519284i | 0.278586 | − | 0.960411i | \(-0.410134\pi\) |
−0.897445 | + | 0.441127i | \(0.854579\pi\) | |||||||
\(74\) | 10.2166 | − | 1.81886i | 1.18766 | − | 0.211438i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.44108 | − | 7.50178i | −0.509427 | − | 0.860514i | ||||
\(77\) | − | 8.08905i | − | 0.921833i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.94292 | + | 4.69899i | −0.443613 | + | 0.528677i | −0.940798 | − | 0.338967i | \(-0.889922\pi\) |
0.497185 | + | 0.867644i | \(0.334367\pi\) | |||||||
\(80\) | 2.99658 | + | 1.70380i | 0.335028 | + | 0.190491i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.90878 | + | 8.53475i | −0.542084 | + | 0.942505i | ||||
\(83\) | −7.58820 | − | 13.1432i | −0.832914 | − | 1.44265i | −0.895718 | − | 0.444623i | \(-0.853338\pi\) |
0.0628044 | − | 0.998026i | \(-0.479996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17339 | − | 6.65461i | −0.127272 | − | 0.721793i | ||||
\(86\) | −3.35205 | − | 5.78385i | −0.361460 | − | 0.623689i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0472644 | − | 9.54676i | −0.00503841 | − | 1.01769i | ||||
\(89\) | −2.98845 | − | 3.56150i | −0.316775 | − | 0.377518i | 0.584037 | − | 0.811727i | \(-0.301472\pi\) |
−0.900812 | + | 0.434209i | \(0.857028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.77205 | + | 4.86867i | −0.185762 | + | 0.510376i | ||||
\(92\) | −5.97127 | + | 0.0197084i | −0.622548 | + | 0.00205474i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.18107 | + | 11.4287i | 0.431245 | + | 1.17878i | ||||
\(95\) | 3.23872 | − | 1.90292i | 0.332285 | − | 0.195236i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.117541 | − | 0.666610i | 0.0119345 | − | 0.0676840i | −0.978259 | − | 0.207388i | \(-0.933504\pi\) |
0.990193 | + | 0.139704i | \(0.0446150\pi\) | |||||||
\(98\) | 0.605092 | − | 1.67105i | 0.0611236 | − | 0.168802i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.23299 | − | 7.38795i | 0.423299 | − | 0.738795i | ||||
\(101\) | 1.47271 | + | 1.75510i | 0.146540 | + | 0.174639i | 0.834321 | − | 0.551278i | \(-0.185860\pi\) |
−0.687782 | + | 0.725918i | \(0.741415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5341 | + | 8.96861i | 1.53062 | + | 0.883704i | 0.999333 | + | 0.0365116i | \(0.0116246\pi\) |
0.531287 | + | 0.847192i | \(0.321709\pi\) | |||||||
\(104\) | −2.06294 | + | 5.75640i | −0.202288 | + | 0.564462i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0435034 | + | 0.249124i | −0.00422543 | + | 0.0241970i | ||||
\(107\) | 1.32317 | + | 2.29180i | 0.127916 | + | 0.221557i | 0.922869 | − | 0.385114i | \(-0.125838\pi\) |
−0.794953 | + | 0.606671i | \(0.792505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.06044 | − | 1.47788i | 0.388920 | − | 0.141555i | −0.140157 | − | 0.990129i | \(-0.544761\pi\) |
0.529077 | + | 0.848574i | \(0.322538\pi\) | |||||||
\(110\) | 4.11362 | − | 0.00678856i | 0.392218 | − | 0.000647264i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.21910 | + | 9.02941i | −0.304176 | + | 0.853199i | ||||
\(113\) | 13.1332i | 1.23546i | 0.786389 | + | 0.617732i | \(0.211948\pi\) | ||||
−0.786389 | + | 0.617732i | \(0.788052\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.57295i | − | 0.239929i | ||||||
\(116\) | 7.81578 | − | 4.54690i | 0.725677 | − | 0.422169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0107815 | − | 6.53317i | −0.000992514 | − | 0.601427i | ||||
\(119\) | 17.6581 | − | 6.42703i | 1.61872 | − | 0.589165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.196433 | − | 0.340233i | −0.0178576 | − | 0.0309302i | ||||
\(122\) | 3.93247 | + | 0.686712i | 0.356030 | + | 0.0621720i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.2684 | + | 13.5195i | −1.01193 | + | 1.21409i | ||||
\(125\) | 6.90892 | + | 3.98887i | 0.617953 | + | 0.356775i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.91926 | + | 5.86255i | 0.436514 | + | 0.520217i | 0.938790 | − | 0.344490i | \(-0.111948\pi\) |
−0.502276 | + | 0.864707i | \(0.667504\pi\) | |||||||
\(128\) | −3.74645 | + | 10.6754i | −0.331142 | + | 0.943581i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.47741 | − | 0.897076i | −0.217283 | − | 0.0786788i | ||||
\(131\) | 1.44419 | − | 8.19039i | 0.126179 | − | 0.715598i | −0.854421 | − | 0.519581i | \(-0.826088\pi\) |
0.980600 | − | 0.196017i | \(-0.0628008\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.77546 | + | 7.95085i | 0.587507 | + | 0.689426i | ||||
\(134\) | 16.0143 | − | 5.85869i | 1.38343 | − | 0.506114i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.8027 | − | 7.68842i | 1.78382 | − | 0.659276i | ||||
\(137\) | −2.75030 | + | 7.55638i | −0.234974 | + | 0.645585i | 0.765025 | + | 0.644001i | \(0.222727\pi\) |
−0.999999 | + | 0.00158449i | \(0.999496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.11738 | − | 6.09866i | −0.434051 | − | 0.517282i | 0.504036 | − | 0.863683i | \(-0.331848\pi\) |
−0.938086 | + | 0.346401i | \(0.887404\pi\) | |||||||
\(140\) | −3.88605 | − | 1.39990i | −0.328432 | − | 0.118313i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7866 | − | 7.41049i | 1.07303 | − | 0.621875i | ||||
\(143\) | 1.26716 | + | 7.18641i | 0.105965 | + | 0.600958i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.94807 | + | 3.37416i | 0.161779 | + | 0.280209i | ||||
\(146\) | 8.46170 | + | 4.86677i | 0.700296 | + | 0.402776i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.7740 | + | 5.06486i | −1.13221 | + | 0.416329i | ||||
\(149\) | 1.57760 | − | 1.88011i | 0.129242 | − | 0.154025i | −0.697542 | − | 0.716543i | \(-0.745723\pi\) |
0.826785 | + | 0.562519i | \(0.190168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.55905i | − | 0.126874i | −0.997986 | − | 0.0634370i | \(-0.979794\pi\) | ||
0.997986 | − | 0.0634370i | \(-0.0202062\pi\) | |||||||
\(152\) | 8.04291 | + | 9.34407i | 0.652366 | + | 0.757904i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00506 | + | 11.2626i | 0.161573 | + | 0.907563i | ||||
\(155\) | −5.80933 | − | 4.87461i | −0.466617 | − | 0.391538i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.7845 | + | 4.28921i | −0.940506 | + | 0.342316i | −0.766366 | − | 0.642405i | \(-0.777937\pi\) |
−0.174140 | + | 0.984721i | \(0.555715\pi\) | |||||||
\(158\) | 4.32505 | − | 7.51984i | 0.344083 | − | 0.598247i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.59453 | − | 1.62947i | −0.363230 | − | 0.128821i | ||||
\(161\) | 7.04647 | − | 1.24248i | 0.555340 | − | 0.0979214i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5297 | − | 6.07933i | −0.824750 | − | 0.476170i | 0.0273018 | − | 0.999627i | \(-0.491308\pi\) |
−0.852052 | + | 0.523458i | \(0.824642\pi\) | |||||||
\(164\) | 4.71906 | − | 13.0999i | 0.368496 | − | 1.02293i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.8231 | + | 16.4186i | 1.07288 | + | 1.27433i | ||||
\(167\) | 9.20385 | + | 3.34993i | 0.712215 | + | 0.259225i | 0.672617 | − | 0.739991i | \(-0.265170\pi\) |
0.0395978 | + | 0.999216i | \(0.487392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.44580 | + | 8.19952i | −0.111215 | + | 0.630732i | ||||
\(170\) | 3.28323 | + | 8.97450i | 0.251812 | + | 0.688313i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.10079 | + | 7.22209i | 0.465181 | + | 0.550679i | ||||
\(173\) | 14.7175 | + | 2.59509i | 1.11895 | + | 0.197301i | 0.702380 | − | 0.711802i | \(-0.252121\pi\) |
0.416571 | + | 0.909103i | \(0.363232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.48957 | + | 9.58751i | −0.263787 | + | 0.724748i | ||||
\(176\) | 2.43220 | + | 13.2804i | 0.183334 | + | 1.00105i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.04368 | + | 4.21799i | 0.378040 | + | 0.316152i | ||||
\(179\) | −4.64063 | + | 8.03781i | −0.346857 | + | 0.600774i | −0.985689 | − | 0.168572i | \(-0.946084\pi\) |
0.638832 | + | 0.769346i | \(0.279418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.37903 | + | 24.8347i | 0.325491 | + | 1.84595i | 0.506203 | + | 0.862414i | \(0.331049\pi\) |
−0.180712 | + | 0.983536i | \(0.557840\pi\) | |||||||
\(182\) | 1.26045 | − | 7.21800i | 0.0934308 | − | 0.535034i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.30904 | − | 1.50756i | 0.612551 | − | 0.111139i | ||||
\(185\) | −2.16278 | − | 5.94219i | −0.159011 | − | 0.436879i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.0123 | − | 20.2744i | 1.24406 | − | 1.48261i | ||||
\(188\) | −8.65426 | − | 14.8760i | −0.631177 | − | 1.08495i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.03765 | + | 3.45228i | −0.292922 | + | 0.250454i | ||||
\(191\) | 24.9747 | 1.80710 | 0.903551 | − | 0.428480i | \(-0.140951\pi\) | ||||
0.903551 | + | 0.428480i | \(0.140951\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.61468 | − | 8.06768i | −0.692080 | − | 0.580724i | 0.227428 | − | 0.973795i | \(-0.426968\pi\) |
−0.919508 | + | 0.393071i | \(0.871413\pi\) | |||||||
\(194\) | 0.00157975 | + | 0.957270i | 0.000113419 | + | 0.0687280i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.428273 | + | 2.47663i | −0.0305909 | + | 0.176902i | ||||
\(197\) | −17.3740 | + | 10.0309i | −1.23785 | + | 0.714672i | −0.968654 | − | 0.248414i | \(-0.920091\pi\) |
−0.269195 | + | 0.963086i | \(0.586757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6219 | − | 3.28354i | 1.32007 | − | 0.232764i | 0.531161 | − | 0.847271i | \(-0.321756\pi\) |
0.788911 | + | 0.614507i | \(0.210645\pi\) | |||||||
\(200\) | −4.06240 | + | 11.3356i | −0.287255 | + | 0.801551i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.48553 | − | 2.07862i | −0.174881 | − | 0.146251i | ||||
\(203\) | −8.29999 | + | 6.96451i | −0.582545 | + | 0.488813i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.63782 | + | 2.05200i | 0.393762 | + | 0.143318i | ||||
\(206\) | −23.8515 | − | 8.63670i | −1.66182 | − | 0.601747i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.44542 | − | 8.52611i | 0.100222 | − | 0.591179i | ||||
\(209\) | 13.8634 | + | 4.92656i | 0.958951 | + | 0.340777i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5643 | + | 2.74440i | 1.07149 | + | 0.188933i | 0.681450 | − | 0.731865i | \(-0.261350\pi\) |
0.390041 | + | 0.920798i | \(0.372461\pi\) | |||||||
\(212\) | −0.00118042 | − | 0.357644i | −8.10714e−5 | − | 0.0245631i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.41036 | − | 2.86295i | −0.164769 | − | 0.195707i | ||||
\(215\) | −3.12056 | + | 2.61846i | −0.212821 | + | 0.178578i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5446 | − | 18.2638i | 0.715814 | − | 1.23983i | ||||
\(218\) | −5.28711 | + | 3.06416i | −0.358089 | + | 0.207531i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.72579 | + | 1.02911i | −0.386033 | + | 0.0693825i | ||||
\(221\) | −14.6809 | + | 8.47602i | −0.987544 | + | 0.570159i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.278472 | − | 0.765095i | −0.0186479 | − | 0.0512346i | 0.930019 | − | 0.367510i | \(-0.119790\pi\) |
−0.948667 | + | 0.316276i | \(0.897568\pi\) | |||||||
\(224\) | 2.24387 | − | 13.3698i | 0.149925 | − | 0.893306i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.25537 | − | 18.2856i | −0.216544 | − | 1.21634i | ||||
\(227\) | 4.39878 | 0.291958 | 0.145979 | − | 0.989288i | \(-0.453367\pi\) | ||||
0.145979 | + | 0.989288i | \(0.453367\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.48158 | 0.296151 | 0.148076 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148076 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(230\) | 0.637768 | + | 3.58238i | 0.0420531 | + | 0.236215i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.75502 | + | 8.26807i | −0.640448 | + | 0.542826i | ||||
\(233\) | −5.42325 | − | 14.9003i | −0.355289 | − | 0.976148i | −0.980643 | − | 0.195807i | \(-0.937268\pi\) |
0.625354 | − | 0.780341i | \(-0.284955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.42215 | − | 3.70783i | 0.418935 | − | 0.241872i | ||||
\(236\) | 1.63441 | + | 9.09359i | 0.106391 | + | 0.591943i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.9927 | + | 13.3255i | −1.49040 | + | 0.863763i | ||||
\(239\) | 8.37012 | − | 14.4975i | 0.541418 | − | 0.937764i | −0.457405 | − | 0.889259i | \(-0.651221\pi\) |
0.998823 | − | 0.0485054i | \(-0.0154458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.8812 | + | 15.8432i | −1.21624 | + | 1.02055i | −0.217231 | + | 0.976120i | \(0.569703\pi\) |
−0.999013 | + | 0.0444297i | \(0.985853\pi\) | |||||||
\(242\) | 0.357833 | + | 0.425022i | 0.0230024 | + | 0.0273215i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.64549 | + | 0.0186332i | −0.361415 | + | 0.00119287i | ||||
\(245\) | −1.06653 | − | 0.188058i | −0.0681382 | − | 0.0120146i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.26491 | − | 6.00224i | −0.462255 | − | 0.381914i | ||||
\(248\) | 12.3381 | − | 21.6167i | 0.783471 | − | 1.37266i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.6082 | − | 3.84125i | −0.670920 | − | 0.242942i | ||||
\(251\) | −15.4669 | − | 5.62948i | −0.976261 | − | 0.355330i | −0.195875 | − | 0.980629i | \(-0.562755\pi\) |
−0.780385 | + | 0.625299i | \(0.784977\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.71986 | − | 6.47773i | 0.485344 | − | 0.407252i | ||||
\(254\) | −8.30236 | − | 6.94320i | −0.520937 | − | 0.435655i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.57011 | − | 15.7922i | 0.160632 | − | 0.987014i | ||||
\(257\) | −8.62199 | + | 1.52029i | −0.537825 | + | 0.0948331i | −0.435962 | − | 0.899965i | \(-0.643592\pi\) |
−0.101864 | + | 0.994798i | \(0.532481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.2293 | − | 8.79263i | 0.946302 | − | 0.546348i | ||||
\(260\) | 3.67171 | + | 0.634934i | 0.227710 | + | 0.0393769i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0194098 | + | 11.7616i | 0.00119914 | + | 0.726636i | ||||
\(263\) | 15.4391 | + | 12.9549i | 0.952016 | + | 0.798836i | 0.979636 | − | 0.200782i | \(-0.0643483\pi\) |
−0.0276198 | + | 0.999618i | \(0.508793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.154105 | 0.00946657 | ||||||||
\(266\) | −11.4044 | − | 9.39068i | −0.699250 | − | 0.575779i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.8449 | + | 12.1267i | −1.27330 | + | 0.740757i | ||||
\(269\) | −4.82085 | + | 5.74526i | −0.293932 | + | 0.350295i | −0.892719 | − | 0.450614i | \(-0.851205\pi\) |
0.598787 | + | 0.800908i | \(0.295650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.169153 | + | 0.464745i | 0.0102753 | + | 0.0282313i | 0.944724 | − | 0.327866i | \(-0.106329\pi\) |
−0.934449 | + | 0.356097i | \(0.884107\pi\) | |||||||
\(272\) | −27.0583 | + | 15.8612i | −1.64065 | + | 0.961726i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.95627 | − | 11.2026i | 0.118183 | − | 0.676776i | ||||
\(275\) | 2.49532 | + | 14.1516i | 0.150473 | + | 0.853376i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0558 | − | 20.8812i | 0.724361 | − | 1.25463i | −0.234875 | − | 0.972026i | \(-0.575468\pi\) |
0.959236 | − | 0.282605i | \(-0.0911986\pi\) | |||||||
\(278\) | 8.63674 | + | 7.22283i | 0.517997 | + | 0.433197i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.75763 | + | 0.985861i | 0.344084 | + | 0.0589164i | ||||
\(281\) | 3.69312 | − | 10.1468i | 0.220313 | − | 0.605305i | −0.779464 | − | 0.626448i | \(-0.784508\pi\) |
0.999776 | + | 0.0211428i | \(0.00673047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1383 | − | 2.31664i | −0.780990 | − | 0.137710i | −0.231082 | − | 0.972934i | \(-0.574226\pi\) |
−0.549909 | + | 0.835225i | \(0.685338\pi\) | |||||||
\(284\) | −15.9662 | + | 13.4872i | −0.947417 | + | 0.800321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.54561 | − | 9.69169i | −0.209656 | − | 0.573082i | ||||
\(287\) | −2.89723 | + | 16.4310i | −0.171018 | + | 0.969893i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.8005 | + | 15.2141i | 2.45885 | + | 0.894948i | ||||
\(290\) | −3.54871 | − | 4.21504i | −0.208387 | − | 0.247516i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.9878 | − | 4.67867i | −0.760051 | − | 0.273798i | ||||
\(293\) | −22.8738 | − | 13.2062i | −1.33630 | − | 0.771513i | −0.350043 | − | 0.936733i | \(-0.613833\pi\) |
−0.986257 | + | 0.165220i | \(0.947167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.92061 | + | 0.691310i | −0.228267 | + | 0.0402496i | ||||
\(296\) | 17.9224 | − | 10.4661i | 1.04172 | − | 0.608331i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.73050 | + | 3.00877i | −0.100245 | + | 0.174293i | ||||
\(299\) | −6.06553 | + | 2.20767i | −0.350779 | + | 0.127673i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.67803 | − | 7.28173i | −0.500193 | − | 0.419712i | ||||
\(302\) | 0.386448 | + | 2.17070i | 0.0222376 | + | 0.124910i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.5145 | − | 11.0163i | −0.775108 | − | 0.631829i | ||||
\(305\) | − | 2.43258i | − | 0.139289i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2323 | − | 13.3861i | 0.641059 | − | 0.763985i | −0.343478 | − | 0.939161i | \(-0.611605\pi\) |
0.984537 | + | 0.175176i | \(0.0560495\pi\) | |||||||
\(308\) | −5.58338 | − | 15.1841i | −0.318143 | − | 0.865194i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.29674 | + | 5.34704i | 0.528019 | + | 0.303691i | ||||
\(311\) | −8.24491 | − | 14.2806i | −0.467526 | − | 0.809779i | 0.531786 | − | 0.846879i | \(-0.321521\pi\) |
−0.999312 | + | 0.0371003i | \(0.988188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.926830 | − | 5.25632i | −0.0523875 | − | 0.297105i | 0.947345 | − | 0.320213i | \(-0.103755\pi\) |
−0.999733 | + | 0.0231090i | \(0.992644\pi\) | |||||||
\(314\) | 15.3446 | − | 8.89303i | 0.865948 | − | 0.501863i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.15789 | + | 11.5421i | −0.233900 | + | 0.649294i | ||||
\(317\) | 14.4777 | + | 17.2539i | 0.813149 | + | 0.969073i | 0.999911 | − | 0.0133319i | \(-0.00424380\pi\) |
−0.186762 | + | 0.982405i | \(0.559799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.21928 | + | 14.3399i | −0.292224 | + | 0.802878i | ||||
\(320\) | 6.80097 | + | 1.12988i | 0.380186 | + | 0.0631621i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.50297 | + | 3.47657i | −0.529580 | + | 0.193742i | ||||
\(323\) | 0.260433 | + | 34.1776i | 0.0144909 | + | 1.90170i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.59828 | − | 9.06430i | 0.0886567 | − | 0.502797i | ||||
\(326\) | 16.1676 | + | 5.85434i | 0.895442 | + | 0.324242i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.32333 | + | 19.4090i | −0.183500 | + | 1.07168i | ||||
\(329\) | 13.2558 | + | 15.7976i | 0.730815 | + | 0.870951i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.85664 | − | 2.80398i | −0.266945 | − | 0.154121i | 0.360553 | − | 0.932739i | \(-0.382588\pi\) |
−0.627499 | + | 0.778618i | \(0.715921\pi\) | |||||||
\(332\) | −23.3159 | − | 19.4336i | −1.27962 | − | 1.06656i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.6451 | − | 2.38278i | −0.746625 | − | 0.130380i | ||||
\(335\) | −5.19556 | − | 8.99898i | −0.283864 | − | 0.491667i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1701 | + | 8.43324i | −1.26216 | + | 0.459388i | −0.884493 | − | 0.466554i | \(-0.845495\pi\) |
−0.377665 | + | 0.925942i | \(0.623273\pi\) | |||||||
\(338\) | −0.0194315 | − | 11.7747i | −0.00105693 | − | 0.640462i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.79586 | − | 11.6816i | −0.368557 | − | 0.633521i | ||||
\(341\) | − | 29.7027i | − | 1.60849i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.7873i | − | 1.06842i | ||||||
\(344\) | −10.2844 | − | 8.54325i | −0.554499 | − | 0.460621i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.1347 | + | 0.0348779i | −1.13621 | + | 0.00187505i | ||||
\(347\) | −15.8250 | + | 5.75983i | −0.849531 | + | 0.309204i | −0.729849 | − | 0.683608i | \(-0.760410\pi\) |
−0.119682 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.63536 | − | 2.83252i | −0.0875387 | − | 0.151621i | 0.818932 | − | 0.573891i | \(-0.194567\pi\) |
−0.906470 | + | 0.422270i | \(0.861233\pi\) | |||||||
\(350\) | 2.48211 | − | 14.2139i | 0.132674 | − | 0.759763i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.67827 | − | 17.8878i | −0.355953 | − | 0.953421i | ||||
\(353\) | −9.30139 | − | 5.37016i | −0.495063 | − | 0.285825i | 0.231609 | − | 0.972809i | \(-0.425601\pi\) |
−0.726673 | + | 0.686984i | \(0.758934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.78873 | − | 6.89874i | −0.307234 | − | 0.366147i | ||||
\(356\) | −8.06795 | − | 4.62260i | −0.427601 | − | 0.244997i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.46889 | − | 12.3415i | 0.236188 | − | 0.652269i | ||||
\(359\) | −1.27735 | + | 7.24418i | −0.0674157 | + | 0.382333i | 0.932368 | + | 0.361512i | \(0.117739\pi\) |
−0.999783 | + | 0.0208216i | \(0.993372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7531 | + | 6.76971i | −0.934371 | + | 0.356300i | ||||
\(362\) | −12.2529 | − | 33.4925i | −0.643998 | − | 1.76032i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0342009 | + | 10.3622i | 0.00179261 | + | 0.543127i | ||||
\(365\) | 2.03443 | − | 5.58956i | 0.106487 | − | 0.292571i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.86751 | + | 9.37613i | 0.410680 | + | 0.489430i | 0.931246 | − | 0.364392i | \(-0.118723\pi\) |
−0.520565 | + | 0.853822i | \(0.674279\pi\) | |||||||
\(368\) | −11.1952 | + | 4.15860i | −0.583589 | + | 0.216782i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.48420 | + | 7.73735i | 0.233122 | + | 0.402245i | ||||
\(371\) | 0.0744173 | + | 0.422042i | 0.00386356 | + | 0.0219113i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.64556 | − | 13.2425i | −0.395872 | − | 0.685671i | 0.597340 | − | 0.801988i | \(-0.296224\pi\) |
−0.993212 | + | 0.116317i | \(0.962891\pi\) | |||||||
\(374\) | −18.6610 | + | 32.4454i | −0.964939 | + | 1.67771i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7369 | + | 18.5670i | 0.811568 | + | 0.957522i | ||||
\(377\) | 6.28281 | − | 7.48756i | 0.323581 | − | 0.385629i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.8226i | − | 1.84008i | −0.391820 | − | 0.920042i | \(-0.628155\pi\) | ||
0.391820 | − | 0.920042i | \(-0.371845\pi\) | |||||||
\(380\) | 4.76598 | − | 5.80750i | 0.244489 | − | 0.297919i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −34.7727 | + | 6.19056i | −1.77913 | + | 0.316737i | ||||
\(383\) | 25.6781 | + | 21.5465i | 1.31209 | + | 1.10097i | 0.987918 | + | 0.154976i | \(0.0495299\pi\) |
0.324171 | + | 0.945998i | \(0.394915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.55053 | − | 2.38420i | 0.333846 | − | 0.121510i | ||||
\(386\) | 15.3865 | + | 8.84957i | 0.783152 | + | 0.450431i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.239482 | − | 1.33244i | −0.0121578 | − | 0.0676442i | ||||
\(389\) | −16.6303 | + | 2.93236i | −0.843187 | + | 0.148677i | −0.578525 | − | 0.815665i | \(-0.696372\pi\) |
−0.264662 | + | 0.964341i | \(0.585260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.2744 | + | 11.7054i | 1.02532 | + | 0.591969i | ||||
\(392\) | −0.0175973 | − | 3.55442i | −0.000888800 | − | 0.179525i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.7038 | − | 18.2728i | 1.09342 | − | 0.920571i | ||||
\(395\) | −4.96740 | − | 1.80799i | −0.249937 | − | 0.0909696i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.52241 | + | 36.9904i | −0.327350 | + | 1.85650i | 0.165266 | + | 0.986249i | \(0.447152\pi\) |
−0.492616 | + | 0.870247i | \(0.663959\pi\) | |||||||
\(398\) | −25.1138 | + | 9.18763i | −1.25884 | + | 0.460534i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.84635 | − | 16.7898i | 0.142318 | − | 0.839491i | ||||
\(401\) | 30.9269 | + | 5.45325i | 1.54442 | + | 0.272322i | 0.879976 | − | 0.475018i | \(-0.157559\pi\) |
0.664441 | + | 0.747341i | \(0.268670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.50691 | + | 17.8776i | −0.324132 | + | 0.890546i | ||||
\(404\) | 3.97589 | + | 2.27802i | 0.197808 | + | 0.113335i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.82993 | − | 11.7542i | 0.487851 | − | 0.583351i | ||||
\(407\) | 12.3838 | − | 21.4494i | 0.613843 | − | 1.06321i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.46956 | − | 8.33427i | −0.0726649 | − | 0.412103i | −0.999343 | − | 0.0362469i | \(-0.988460\pi\) |
0.926678 | − | 0.375856i | \(-0.122651\pi\) | |||||||
\(410\) | −8.35829 | − | 1.45957i | −0.412786 | − | 0.0720832i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 35.3498 | + | 6.11289i | 1.74156 | + | 0.301161i | ||||
\(413\) | −3.78654 | − | 10.4034i | −0.186323 | − | 0.511919i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.40678 | − | 10.0188i | 0.412672 | − | 0.491804i | ||||
\(416\) | 0.100911 | + | 12.2294i | 0.00494756 | + | 0.599594i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.5235 | − | 3.42298i | −1.00383 | − | 0.167424i | ||||
\(419\) | 16.7413 | 0.817867 | 0.408933 | − | 0.912564i | \(-0.365901\pi\) | ||||
0.408933 | + | 0.912564i | \(0.365901\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.74700 | + | 1.46590i | 0.0851434 | + | 0.0714438i | 0.684366 | − | 0.729139i | \(-0.260079\pi\) |
−0.599223 | + | 0.800583i | \(0.704524\pi\) | |||||||
\(422\) | −22.3508 | + | 0.0368847i | −1.08802 | + | 0.00179552i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0902939 | + | 0.497662i | 0.00438506 | + | 0.0241686i | ||||
\(425\) | −28.9100 | + | 16.6912i | −1.40234 | + | 0.809641i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.66202 | − | 1.17469i | 0.322398 | − | 0.0568475i | ||||
\(428\) | 4.06565 | + | 3.38868i | 0.196520 | + | 0.163798i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.69578 | − | 4.41925i | 0.178226 | − | 0.213115i | ||||
\(431\) | −6.09376 | + | 5.11327i | −0.293526 | + | 0.246298i | −0.777644 | − | 0.628705i | \(-0.783585\pi\) |
0.484118 | + | 0.875003i | \(0.339141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.28136 | + | 3.37814i | 0.446034 | + | 0.162343i | 0.555265 | − | 0.831673i | \(-0.312617\pi\) |
−0.109231 | + | 0.994016i | \(0.534839\pi\) | |||||||
\(434\) | −10.1544 | + | 28.0428i | −0.487425 | + | 1.34610i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.60184 | − | 5.57683i | 0.316171 | − | 0.267082i | ||||
\(437\) | −2.16216 | + | 12.8333i | −0.103430 | + | 0.613899i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.4928 | − | 3.78976i | −1.02579 | − | 0.180875i | −0.364658 | − | 0.931141i | \(-0.618814\pi\) |
−0.661136 | + | 0.750266i | \(0.729925\pi\) | |||||||
\(440\) | 7.71706 | − | 2.85212i | 0.367896 | − | 0.135970i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.3395 | − | 15.4403i | 0.872323 | − | 0.734422i | ||||
\(443\) | −14.9033 | + | 12.5054i | −0.708078 | + | 0.594148i | −0.924059 | − | 0.382250i | \(-0.875149\pi\) |
0.215981 | + | 0.976397i | \(0.430705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00328 | − | 3.46978i | 0.0949645 | − | 0.164483i | ||||
\(446\) | 0.577369 | + | 0.996232i | 0.0273392 | + | 0.0471730i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.189832 | + | 19.1712i | 0.00896870 | + | 0.905755i | ||||
\(449\) | −15.9971 | + | 9.23594i | −0.754951 | + | 0.435871i | −0.827480 | − | 0.561495i | \(-0.810226\pi\) |
0.0725292 | + | 0.997366i | \(0.476893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.03712 | + | 22.0818i | 0.378453 | + | 1.03979i | ||||
\(452\) | 9.06503 | + | 24.6525i | 0.426383 | + | 1.15956i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.12452 | + | 1.09034i | −0.287438 | + | 0.0511723i | ||||
\(455\) | −4.46496 | −0.209321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.9109 | 1.86695 | 0.933477 | − | 0.358637i | \(-0.116758\pi\) | ||||
0.933477 | + | 0.358637i | \(0.116758\pi\) | |||||||
\(458\) | −6.23980 | + | 1.11087i | −0.291567 | + | 0.0519073i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.77595 | − | 4.82974i | −0.0828043 | − | 0.225188i | ||||
\(461\) | −5.09196 | − | 13.9900i | −0.237156 | − | 0.651581i | −0.999988 | − | 0.00498392i | \(-0.998414\pi\) |
0.762831 | − | 0.646598i | \(-0.223809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1531 | + | 6.43926i | −0.518329 | + | 0.299258i | −0.736251 | − | 0.676709i | \(-0.763406\pi\) |
0.217922 | + | 0.975966i | \(0.430072\pi\) | |||||||
\(464\) | 11.5327 | − | 13.9298i | 0.535391 | − | 0.646676i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.2443 | + | 19.4017i | 0.520881 | + | 0.898765i | ||||
\(467\) | −7.54976 | + | 13.0766i | −0.349361 | + | 0.605111i | −0.986136 | − | 0.165938i | \(-0.946935\pi\) |
0.636775 | + | 0.771050i | \(0.280268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.1363 | − | 18.5745i | 1.02216 | − | 0.857693i | ||||
\(470\) | −8.02262 | + | 6.75437i | −0.370056 | + | 0.311556i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.52969 | − | 12.2561i | −0.208496 | − | 0.564132i | ||||
\(473\) | −15.7128 | − | 2.77059i | −0.722476 | − | 0.127392i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.3062 | − | 11.8198i | −0.656415 | − | 0.542328i | ||||
\(476\) | 28.7102 | − | 24.2526i | 1.31593 | − | 1.11162i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.06036 | + | 22.2599i | −0.368672 | + | 1.01814i | ||||
\(479\) | 6.31766 | + | 2.29944i | 0.288661 | + | 0.105064i | 0.482292 | − | 0.876010i | \(-0.339804\pi\) |
−0.193631 | + | 0.981074i | \(0.562026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1525 | + | 10.1972i | −0.554106 | + | 0.464950i | ||||
\(482\) | 22.3616 | − | 26.7390i | 1.01854 | − | 1.21793i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.603570 | − | 0.503070i | −0.0274350 | − | 0.0228668i | ||||
\(485\) | 0.574466 | − | 0.101294i | 0.0260852 | − | 0.00459952i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.89672 | − | 4.55917i | 0.357834 | − | 0.206596i | −0.310296 | − | 0.950640i | \(-0.600428\pi\) |
0.668130 | + | 0.744044i | \(0.267095\pi\) | |||||||
\(488\) | 7.85571 | − | 1.42531i | 0.355611 | − | 0.0645208i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.53157 | − | 0.00252750i | 0.0691892 | − | 0.000114181i | ||||
\(491\) | −28.3728 | − | 23.8076i | −1.28045 | − | 1.07442i | −0.993182 | − | 0.116571i | \(-0.962810\pi\) |
−0.287264 | − | 0.957851i | \(-0.592746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.4503 | −1.59660 | ||||||||
\(494\) | 11.6029 | + | 6.55627i | 0.522038 | + | 0.294981i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.8204 | + | 33.1557i | −0.530752 | + | 1.48873i | ||||
\(497\) | 16.0980 | − | 19.1848i | 0.722093 | − | 0.860558i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.82010 | − | 21.4856i | −0.350076 | − | 0.961825i | −0.982345 | − | 0.187077i | \(-0.940099\pi\) |
0.632269 | − | 0.774749i | \(-0.282124\pi\) | |||||||
\(500\) | 15.7221 | + | 2.71876i | 0.703115 | + | 0.121587i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.9303 | + | 4.00422i | 1.02343 | + | 0.178717i | ||||
\(503\) | 3.18840 | + | 18.0823i | 0.142164 | + | 0.806250i | 0.969601 | + | 0.244692i | \(0.0786868\pi\) |
−0.827437 | + | 0.561558i | \(0.810202\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.987215 | + | 1.70991i | −0.0439305 | + | 0.0760899i | ||||
\(506\) | −9.14287 | + | 10.9326i | −0.406450 | + | 0.486015i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2806 | + | 7.60922i | 0.589231 | + | 0.337605i | ||||
\(509\) | −1.37680 | + | 3.78273i | −0.0610256 | + | 0.167666i | −0.966458 | − | 0.256823i | \(-0.917324\pi\) |
0.905433 | + | 0.424490i | \(0.139546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2904 | + | 2.87244i | 0.720645 | + | 0.127069i | ||||
\(512\) | 0.336059 | + | 22.6249i | 0.0148518 | + | 0.999890i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.6277 | − | 4.25390i | 0.512878 | − | 0.187631i | ||||
\(515\) | −2.68422 | + | 15.2230i | −0.118281 | + | 0.670805i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.2935 | + | 9.93402i | 1.20037 | + | 0.436898i | ||||
\(518\) | −19.0246 | + | 16.0171i | −0.835893 | + | 0.703751i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.26959 | + | 0.0260888i | −0.231087 | + | 0.00114407i | ||||
\(521\) | −0.605646 | − | 0.349670i | −0.0265338 | − | 0.0153193i | 0.486674 | − | 0.873583i | \(-0.338210\pi\) |
−0.513208 | + | 0.858264i | \(0.671543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.9707 | + | 4.75567i | −1.17935 | + | 0.207951i | −0.728753 | − | 0.684777i | \(-0.759900\pi\) |
−0.450596 | + | 0.892728i | \(0.648788\pi\) | |||||||
\(524\) | −2.94242 | − | 16.3712i | −0.128540 | − | 0.715177i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.7074 | − | 14.2105i | −1.07729 | − | 0.619607i | ||||
\(527\) | 64.8400 | − | 23.5998i | 2.82447 | − | 1.02802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7904 | − | 9.05423i | −0.469148 | − | 0.393662i | ||||
\(530\) | −0.214563 | + | 0.0381985i | −0.00932003 | + | 0.00165924i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.2063 | + | 10.2480i | 0.789344 | + | 0.444306i | ||||
\(533\) | − | 15.0514i | − | 0.651947i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.46591 | + | 1.74700i | −0.0633768 | + | 0.0755296i | ||||
\(536\) | 26.0169 | − | 22.0512i | 1.12376 | − | 0.952466i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.28807 | − | 9.19421i | 0.227985 | − | 0.396391i | ||||
\(539\) | −2.12088 | − | 3.67347i | −0.0913527 | − | 0.158227i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.20240 | − | 35.1756i | −0.266662 | − | 1.51232i | −0.764260 | − | 0.644908i | \(-0.776896\pi\) |
0.497598 | − | 0.867408i | \(-0.334215\pi\) | |||||||
\(542\) | −0.350714 | − | 0.605146i | −0.0150645 | − | 0.0259932i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 33.7423 | − | 28.7909i | 1.44669 | − | 1.23440i | ||||
\(545\) | 2.39358 | + | 2.85256i | 0.102530 | + | 0.122190i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.02410 | − | 19.2985i | 0.300329 | − | 0.825146i | −0.694114 | − | 0.719865i | \(-0.744204\pi\) |
0.994443 | − | 0.105281i | \(-0.0335742\pi\) | |||||||
\(548\) | 0.0530812 | + | 16.0826i | 0.00226752 | + | 0.687014i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.98210 | − | 19.0851i | −0.297718 | − | 0.813792i | ||||
\(551\) | −6.88108 | − | 18.4666i | −0.293144 | − | 0.786702i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.55271 | − | 14.4771i | 0.108552 | − | 0.615630i | ||||
\(554\) | −11.6096 | + | 32.0617i | −0.493245 | + | 1.36217i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.8155 | − | 7.91568i | −0.585906 | − | 0.335700i | ||||
\(557\) | 6.07847 | + | 7.24404i | 0.257553 | + | 0.306940i | 0.879290 | − | 0.476286i | \(-0.158017\pi\) |
−0.621737 | + | 0.783226i | \(0.713573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.85035 | + | 5.10975i | 0.374330 | + | 0.216119i | ||||
\(560\) | −8.26085 | + | 0.0545311i | −0.349084 | + | 0.00230436i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.62689 | + | 15.0430i | −0.110809 | + | 0.634549i | ||||
\(563\) | −13.3746 | − | 23.1654i | −0.563671 | − | 0.976306i | −0.997172 | − | 0.0751534i | \(-0.976055\pi\) |
0.433501 | − | 0.901153i | \(-0.357278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.6353 | + | 3.87092i | −0.447429 | + | 0.162851i | ||||
\(566\) | 18.8670 | − | 0.0311355i | 0.793037 | − | 0.00130872i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.8869 | − | 22.7362i | 0.792476 | − | 0.953988i | ||||
\(569\) | 30.3341i | 1.27167i | 0.771825 | + | 0.635835i | \(0.219344\pi\) | ||||
−0.771825 | + | 0.635835i | \(0.780656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5696i | 1.53039i | 0.643799 | + | 0.765195i | \(0.277357\pi\) | ||||
−0.643799 | + | 0.765195i | \(0.722643\pi\) | |||||||
\(572\) | 7.33894 | + | 12.6151i | 0.306857 | + | 0.527463i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0389387 | − | 23.5954i | −0.00162527 | − | 0.984854i | ||||
\(575\) | −11.9444 | + | 4.34740i | −0.498115 | + | 0.181299i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.56387 | + | 9.63690i | 0.231627 | + | 0.401189i | 0.958287 | − | 0.285808i | \(-0.0922618\pi\) |
−0.726660 | + | 0.686997i | \(0.758929\pi\) | |||||||
\(578\) | −61.9708 | − | 10.8217i | −2.57765 | − | 0.450124i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.98574 | + | 4.98906i | 0.248544 | + | 0.207159i | ||||
\(581\) | 31.4978 | + | 18.1853i | 1.30675 | + | 0.754453i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.387978 | + | 0.462374i | 0.0160684 | + | 0.0191496i | ||||
\(584\) | 19.2428 | + | 3.29489i | 0.796275 | + | 0.136343i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.1211 | + | 12.7174i | 1.45084 | + | 0.525353i | ||||
\(587\) | 5.71714 | − | 32.4235i | 0.235971 | − | 1.33826i | −0.604587 | − | 0.796539i | \(-0.706662\pi\) |
0.840558 | − | 0.541721i | \(-0.182227\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.8792 | + | 29.1952i | 1.02513 | + | 1.20297i | ||||
\(590\) | 5.28739 | − | 1.93434i | 0.217679 | − | 0.0796356i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.3594 | + | 19.0147i | −0.918966 | + | 0.781499i | ||||
\(593\) | −12.0571 | + | 33.1267i | −0.495126 | + | 1.36035i | 0.400808 | + | 0.916162i | \(0.368729\pi\) |
−0.895934 | + | 0.444187i | \(0.853493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.4092 | + | 12.4053i | 0.426738 | + | 0.508566i | ||||
\(596\) | 1.66361 | − | 4.61811i | 0.0681443 | − | 0.189165i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.89794 | − | 4.57727i | 0.322971 | − | 0.187179i | ||||
\(599\) | −5.37209 | − | 30.4666i | −0.219498 | − | 1.24483i | −0.872929 | − | 0.487847i | \(-0.837782\pi\) |
0.653432 | − | 0.756985i | \(-0.273329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3151 | + | 26.5266i | 0.624717 | + | 1.08204i | 0.988596 | + | 0.150595i | \(0.0481189\pi\) |
−0.363879 | + | 0.931446i | \(0.618548\pi\) | |||||||
\(602\) | 13.8875 | + | 7.98745i | 0.566014 | + | 0.325544i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.07612 | − | 2.92653i | −0.0437867 | − | 0.119079i | ||||
\(605\) | 0.217623 | − | 0.259354i | 0.00884765 | − | 0.0105442i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0703i | 0.774038i | 0.922072 | + | 0.387019i | \(0.126495\pi\) | ||||
−0.922072 | + | 0.387019i | \(0.873505\pi\) | |||||||
\(608\) | 21.5471 | + | 11.9884i | 0.873852 | + | 0.486193i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.602972 | + | 3.38693i | 0.0244136 | + | 0.137133i | ||||
\(611\) | −14.2513 | − | 11.9583i | −0.576546 | − | 0.483780i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.7090 | + | 13.3610i | −1.48266 | + | 0.539645i | −0.951506 | − | 0.307629i | \(-0.900464\pi\) |
−0.531156 | + | 0.847274i | \(0.678242\pi\) | |||||||
\(614\) | −12.3209 | + | 21.4219i | −0.497230 | + | 0.864518i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.5376 | + | 19.7572i | 0.464863 | + | 0.796039i | ||||
\(617\) | 13.9514 | − | 2.46001i | 0.561662 | − | 0.0990362i | 0.114393 | − | 0.993436i | \(-0.463508\pi\) |
0.447269 | + | 0.894399i | \(0.352397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.86407 | + | 5.69503i | 0.396471 | + | 0.228902i | 0.684960 | − | 0.728581i | \(-0.259820\pi\) |
−0.288489 | + | 0.957483i | \(0.593153\pi\) | |||||||
\(620\) | −14.2694 | − | 5.14038i | −0.573074 | − | 0.206443i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0193 | + | 17.8395i | 0.602221 | + | 0.715299i | ||||
\(623\) | 10.4700 | + | 3.81076i | 0.419470 | + | 0.152675i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.50257 | − | 14.1928i | 0.100103 | − | 0.567712i | ||||
\(626\) | 2.59335 | + | 7.08874i | 0.103651 | + | 0.283323i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.1603 | + | 16.1855i | −0.764580 | + | 0.645871i | ||||
\(629\) | 56.6627 | + | 9.99116i | 2.25929 | + | 0.398374i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5251 | + | 39.9073i | −0.578234 | + | 1.58869i | 0.212920 | + | 0.977070i | \(0.431703\pi\) |
−0.791155 | + | 0.611616i | \(0.790520\pi\) | |||||||
\(632\) | 2.92814 | − | 17.1010i | 0.116475 | − | 0.680239i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.4344 | − | 20.4343i | −0.970414 | − | 0.811549i | ||||
\(635\) | −3.29758 | + | 5.71158i | −0.130861 | + | 0.226657i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.471784 | + | 2.67562i | 0.0186928 | + | 0.106012i | ||||
\(638\) | 3.71244 | − | 21.2594i | 0.146977 | − | 0.841668i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.74920 | + | 0.112626i | −0.385371 | + | 0.00445195i | ||||
\(641\) | −8.79213 | − | 24.1562i | −0.347268 | − | 0.954111i | −0.983227 | − | 0.182388i | \(-0.941617\pi\) |
0.635959 | − | 0.771723i | \(-0.280605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1027 | + | 13.2317i | −0.437847 | + | 0.521806i | −0.939169 | − | 0.343455i | \(-0.888403\pi\) |
0.501322 | + | 0.865261i | \(0.332847\pi\) | |||||||
\(644\) | 12.3694 | − | 7.19604i | 0.487424 | − | 0.283564i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.83434 | − | 47.5217i | −0.347583 | − | 1.86972i | ||||
\(647\) | 2.56660 | 0.100904 | 0.0504518 | − | 0.998726i | \(-0.483934\pi\) | ||||
0.0504518 | + | 0.998726i | \(0.483934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.9448 | − | 10.0229i | −0.468875 | − | 0.393433i | ||||
\(650\) | 0.0214808 | + | 13.0166i | 0.000842548 | + | 0.510553i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.9617 | − | 4.14359i | −0.938412 | − | 0.162276i | ||||
\(653\) | −1.23323 | + | 0.712004i | −0.0482599 | + | 0.0278629i | −0.523936 | − | 0.851758i | \(-0.675537\pi\) |
0.475676 | + | 0.879621i | \(0.342204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.05826 | − | 1.24456i | 0.275789 | − | 0.0486290i | ||||
\(656\) | −0.183824 | − | 27.8473i | −0.00717713 | − | 1.08725i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.3721 | − | 18.7096i | −0.872156 | − | 0.729377i | ||||
\(659\) | 5.23948 | − | 4.39644i | 0.204101 | − | 0.171261i | −0.535008 | − | 0.844847i | \(-0.679691\pi\) |
0.739109 | + | 0.673586i | \(0.235247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.12000 | + | 2.22750i | 0.238040 | + | 0.0866396i | 0.458286 | − | 0.888805i | \(-0.348464\pi\) |
−0.220246 | + | 0.975444i | \(0.570686\pi\) | |||||||
\(662\) | 7.45704 | + | 2.70021i | 0.289826 | + | 0.104947i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.2803 | + | 21.2784i | 1.44675 | + | 0.825761i | ||||
\(665\) | −4.44159 | + | 7.83024i | −0.172237 | + | 0.303644i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.2933 | − | 2.34397i | −0.514719 | − | 0.0907588i | ||||
\(668\) | 19.5889 | − | 0.0646541i | 0.757919 | − | 0.00250154i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.46450 | + | 11.2416i | 0.365646 | + | 0.434302i | ||||
\(671\) | 7.29868 | − | 6.12432i | 0.281762 | − | 0.236427i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.77884 | − | 11.7413i | 0.261305 | − | 0.452594i | −0.705284 | − | 0.708925i | \(-0.749180\pi\) |
0.966589 | + | 0.256331i | \(0.0825138\pi\) | |||||||
\(674\) | 30.1699 | − | 17.4850i | 1.16210 | − | 0.673499i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.94570 | + | 16.3894i | 0.113296 | + | 0.630362i | ||||
\(677\) | 12.1931 | − | 7.03971i | 0.468620 | − | 0.270558i | −0.247042 | − | 0.969005i | \(-0.579458\pi\) |
0.715662 | + | 0.698447i | \(0.246125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.554821 | + | 1.52436i | 0.0212921 | + | 0.0584995i | ||||
\(680\) | 12.3576 | + | 14.5800i | 0.473891 | + | 0.559116i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.36251 | + | 41.3557i | 0.281925 | + | 1.58359i | ||||
\(683\) | −43.9380 | −1.68124 | −0.840621 | − | 0.541624i | \(-0.817810\pi\) | ||||
−0.840621 | + | 0.541624i | \(0.817810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.92980 | −0.264774 | ||||||||
\(686\) | 4.90476 | + | 27.5503i | 0.187264 | + | 1.05188i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.4369 | + | 9.34571i | 0.626650 | + | 0.356302i | ||||
\(689\) | −0.132226 | − | 0.363289i | −0.00503743 | − | 0.0138402i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.64458 | + | 3.83625i | −0.252772 | + | 0.145938i | −0.621033 | − | 0.783785i | \(-0.713287\pi\) |
0.368261 | + | 0.929722i | \(0.379953\pi\) | |||||||
\(692\) | 29.4177 | − | 5.28731i | 1.11829 | − | 0.200993i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.6058 | − | 11.9421i | 0.782185 | − | 0.453317i | ||||
\(695\) | 3.43039 | − | 5.94161i | 0.130122 | − | 0.225378i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.8181 | + | 35.0895i | −1.58397 | + | 1.32911i | ||||
\(698\) | 2.97905 | + | 3.53842i | 0.112759 | + | 0.133931i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.0673493 | + | 20.4055i | 0.00254556 | + | 0.771256i | ||||
\(701\) | −9.62261 | − | 1.69673i | −0.363441 | − | 0.0640845i | −0.0110543 | − | 0.999939i | \(-0.503519\pi\) |
−0.352387 | + | 0.935854i | \(0.614630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.79397 | + | 31.4557i | 0.218524 | + | 1.18638i | ||||
\(704\) | 13.7322 | + | 23.2502i | 0.517552 | + | 0.876273i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.2817 | + | 5.17142i | 0.537497 | + | 0.194629i | ||||
\(707\) | −5.15960 | − | 1.87794i | −0.194047 | − | 0.0706272i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8648 | + | 13.3121i | −0.595814 | + | 0.499947i | −0.890097 | − | 0.455771i | \(-0.849364\pi\) |
0.294283 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(710\) | 9.76979 | + | 8.17039i | 0.366654 | + | 0.306629i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.3790 | + | 4.43631i | 0.463923 | + | 0.166258i | ||||
\(713\) | 25.8744 | − | 4.56235i | 0.969002 | − | 0.170861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.44608 | + | 3.14430i | −0.203672 | + | 0.117590i | ||||
\(716\) | −3.16300 | + | 18.2911i | −0.118207 | + | 0.683569i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.0171675 | − | 10.4029i | −0.000640684 | − | 0.388231i | ||||
\(719\) | 15.4370 | + | 12.9532i | 0.575704 | + | 0.483073i | 0.883533 | − | 0.468368i | \(-0.155158\pi\) |
−0.307829 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.9869 | −1.60092 | ||||||||
\(722\) | 23.0399 | − | 13.8261i | 0.857457 | − | 0.514555i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.3619 | + | 43.5951i | 0.942566 | + | 1.62020i | ||||
\(725\) | 12.3723 | − | 14.7447i | 0.459494 | − | 0.547604i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.3825 | − | 50.5056i | −0.681771 | − | 1.87315i | −0.417372 | − | 0.908735i | \(-0.637049\pi\) |
−0.264398 | − | 0.964414i | \(-0.585173\pi\) | |||||||
\(728\) | −2.61614 | − | 14.4191i | −0.0969605 | − | 0.534406i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.44708 | + | 8.28675i | −0.0535589 | + | 0.306706i | ||||
\(731\) | −6.43627 | − | 36.5019i | −0.238054 | − | 1.35007i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0451 | − | 19.1307i | 0.407961 | − | 0.706609i | −0.586700 | − | 0.809804i | \(-0.699573\pi\) |
0.994661 | + | 0.103195i | \(0.0329067\pi\) | |||||||
\(734\) | −13.2782 | − | 11.1044i | −0.490107 | − | 0.409872i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.5565 | − | 8.56510i | 0.536559 | − | 0.315714i | ||||
\(737\) | 13.9200 | − | 38.2448i | 0.512748 | − | 1.40876i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.9753 | − | 7.93037i | −1.65444 | − | 0.291723i | −0.732999 | − | 0.680230i | \(-0.761880\pi\) |
−0.921446 | + | 0.388506i | \(0.872991\pi\) | |||||||
\(740\) | −8.16133 | − | 9.66136i | −0.300016 | − | 0.355158i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.208226 | − | 0.569171i | −0.00764421 | − | 0.0208949i | ||||
\(743\) | −1.88482 | + | 10.6893i | −0.0691474 | + | 0.392154i | 0.930517 | + | 0.366249i | \(0.119358\pi\) |
−0.999664 | + | 0.0259055i | \(0.991753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.98751 | + | 0.723393i | 0.0728166 | + | 0.0265031i | ||||
\(746\) | 13.9275 | + | 16.5427i | 0.509924 | + | 0.605671i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.9398 | − | 49.8000i | 0.655944 | − | 1.82087i | ||||
\(749\) | −5.49236 | − | 3.17101i | −0.200686 | − | 0.115866i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.46846 | − | 0.258930i | 0.0535849 | − | 0.00944847i | −0.146791 | − | 0.989167i | \(-0.546895\pi\) |
0.200376 | + | 0.979719i | \(0.435784\pi\) | |||||||
\(752\) | −26.5131 | − | 21.9505i | −0.966833 | − | 0.800453i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.89172 | + | 11.9824i | −0.250982 | + | 0.436374i | ||||
\(755\) | 1.26252 | − | 0.459521i | 0.0459480 | − | 0.0167237i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.1287 | − | 32.8329i | −1.42216 | − | 1.19333i | −0.950173 | − | 0.311724i | \(-0.899094\pi\) |
−0.471984 | − | 0.881607i | \(-0.656462\pi\) | |||||||
\(758\) | 8.87948 | + | 49.8766i | 0.322517 | + | 1.81160i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.19624 | + | 9.26727i | −0.188488 | + | 0.336159i | ||||
\(761\) | − | 21.3388i | − | 0.773530i | −0.922178 | − | 0.386765i | \(-0.873592\pi\) | ||
0.922178 | − | 0.386765i | \(-0.126408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.65635 | + | 7.93273i | −0.240976 | + | 0.287184i | ||||
\(764\) | 46.8804 | − | 17.2385i | 1.69607 | − | 0.623667i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.0930 | − | 23.6347i | −1.48475 | − | 0.853957i | ||||
\(767\) | 4.99371 | + | 8.64936i | 0.180312 | + | 0.312310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.44886 | − | 47.9159i | −0.304674 | − | 1.72789i | −0.625036 | − | 0.780596i | \(-0.714916\pi\) |
0.320362 | − | 0.947295i | \(-0.396195\pi\) | |||||||
\(770\) | −8.52946 | + | 4.94327i | −0.307380 | + | 0.178143i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.6165 | − | 8.50754i | −0.849977 | − | 0.306193i | ||||
\(773\) | −15.0239 | − | 17.9048i | −0.540373 | − | 0.643992i | 0.424898 | − | 0.905241i | \(-0.360310\pi\) |
−0.965271 | + | 0.261249i | \(0.915866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.8136 | + | 35.2050i | −0.460277 | + | 1.26460i | ||||
\(776\) | 0.663711 | + | 1.79582i | 0.0238258 | + | 0.0644661i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.4278 | − | 8.20499i | 0.804076 | − | 0.294163i | ||||
\(779\) | −26.3957 | − | 14.9726i | −0.945725 | − | 0.536448i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.12505 | − | 34.7369i | 0.219172 | − | 1.24298i | ||||
\(782\) | −31.1299 | − | 11.2722i | −1.11320 | − | 0.403094i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.905548 | + | 4.94453i | 0.0323410 | + | 0.176591i | ||||
\(785\) | −6.94682 | − | 8.27890i | −0.247943 | − | 0.295487i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9135 | + | 6.87826i | 0.424670 | + | 0.245184i | 0.697074 | − | 0.717000i | \(-0.254485\pi\) |
−0.272403 | + | 0.962183i | \(0.587818\pi\) | |||||||
\(788\) | −25.6894 | + | 30.8214i | −0.915146 | + | 1.09797i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.36437 | + | 1.28601i | 0.262012 | + | 0.0457542i | ||||
\(791\) | −15.7369 | − | 27.2572i | −0.559541 | − | 0.969154i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.73460 | + | 2.08722i | −0.203642 | + | 0.0741195i | ||||
\(794\) | −0.0876609 | − | 53.1193i | −0.00311097 | − | 1.88513i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.6891 | − | 19.0172i | 1.15863 | − | 0.674046i | ||||
\(797\) | 10.8460i | 0.384185i | 0.981377 | + | 0.192093i | \(0.0615274\pi\) | ||||
−0.981377 | + | 0.192093i | \(0.938473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.4737i | 2.38705i | ||||||||
\(800\) | 0.198716 | + | 24.0824i | 0.00702567 | + | 0.851440i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −44.4119 | + | 0.0732915i | −1.56824 | + | 0.00258801i | ||||
\(803\) | 21.8928 | − | 7.96833i | 0.772580 | − | 0.281196i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.08307 | + | 5.34003i | 0.108664 | + | 0.188211i | ||||
\(806\) | 4.62832 | − | 26.5042i | 0.163026 | − | 0.933571i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.10037 | − | 2.18621i | −0.214610 | − | 0.0769107i | ||||
\(809\) | −17.9152 | − | 10.3433i | −0.629864 | − | 0.363652i | 0.150835 | − | 0.988559i | \(-0.451804\pi\) |
−0.780700 | + | 0.624907i | \(0.785137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.57226 | − | 7.83251i | −0.230783 | − | 0.275037i | 0.638208 | − | 0.769864i | \(-0.279676\pi\) |
−0.868991 | + | 0.494827i | \(0.835231\pi\) | |||||||
\(812\) | −10.7729 | + | 18.8022i | −0.378053 | + | 0.659827i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.9255 | + | 32.9341i | −0.417989 | + | 1.15434i | ||||
\(815\) | 1.81949 | − | 10.3188i | 0.0637338 | − | 0.361452i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.7650 | − | 10.4379i | 0.621520 | − | 0.365177i | ||||
\(818\) | 4.11194 | + | 11.2397i | 0.143771 | + | 0.392988i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.9992 | − | 0.0396039i | 0.419031 | − | 0.00138303i | ||||
\(821\) | −17.0854 | + | 46.9419i | −0.596286 | + | 1.63828i | 0.162324 | + | 0.986737i | \(0.448101\pi\) |
−0.758610 | + | 0.651545i | \(0.774121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3566 | − | 12.3425i | −0.361008 | − | 0.430232i | 0.554717 | − | 0.832039i | \(-0.312827\pi\) |
−0.915724 | + | 0.401807i | \(0.868382\pi\) | |||||||
\(824\) | −50.7335 | + | 0.251173i | −1.76739 | + | 0.00875003i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.85081 | + | 13.5463i | 0.273165 | + | 0.471337i | ||||
\(827\) | 1.54355 | + | 8.75389i | 0.0536744 | + | 0.304403i | 0.999813 | − | 0.0193604i | \(-0.00616300\pi\) |
−0.946138 | + | 0.323763i | \(0.895052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.48543 | + | 12.9651i | 0.259980 | + | 0.450298i | 0.966236 | − | 0.257658i | \(-0.0829508\pi\) |
−0.706256 | + | 0.707956i | \(0.749617\pi\) | |||||||
\(830\) | −9.22154 | + | 16.0332i | −0.320084 | + | 0.556521i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.17184 | − | 17.0022i | −0.109964 | − | 0.589445i | ||||
\(833\) | 6.33395 | − | 7.54851i | 0.219458 | − | 0.261540i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.44066i | 0.292101i | ||||||||
\(836\) | 29.4237 | − | 0.321330i | 1.01764 | − | 0.0111134i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.3093 | + | 4.14973i | −0.805206 | + | 0.143350i | ||||
\(839\) | 19.4852 | + | 16.3500i | 0.672704 | + | 0.564465i | 0.913864 | − | 0.406020i | \(-0.133084\pi\) |
−0.241161 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.04360 | + | 2.92763i | −0.277366 | + | 0.100953i | ||||
\(842\) | −2.79574 | − | 1.60798i | −0.0963475 | − | 0.0554145i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 31.1103 | − | 5.59152i | 1.07086 | − | 0.192468i | ||||
\(845\) | −7.06613 | + | 1.24595i | −0.243082 | + | 0.0428619i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.815374 | + | 0.470756i | 0.0280166 | + | 0.0161754i | ||||
\(848\) | −0.249076 | − | 0.670524i | −0.00855329 | − | 0.0230259i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 36.1147 | − | 30.4055i | 1.23872 | − | 1.04290i | ||||
\(851\) | 20.5870 | + | 7.49305i | 0.705713 | + | 0.256859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.208823 | − | 1.18429i | 0.00714995 | − | 0.0405494i | −0.981024 | − | 0.193886i | \(-0.937891\pi\) |
0.988174 | + | 0.153337i | \(0.0490019\pi\) | |||||||
\(854\) | −8.98450 | + | 3.28689i | −0.307443 | + | 0.112475i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50065 | − | 3.71036i | −0.222188 | − | 0.126818i | ||||
\(857\) | 24.2624 | + | 4.27811i | 0.828786 | + | 0.146137i | 0.571920 | − | 0.820309i | \(-0.306199\pi\) |
0.256867 | + | 0.966447i | \(0.417310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3498 | − | 50.4156i | 0.626086 | − | 1.72016i | −0.0654906 | − | 0.997853i | \(-0.520861\pi\) |
0.691576 | − | 0.722303i | \(-0.256917\pi\) | |||||||
\(860\) | −4.05030 | + | 7.06910i | −0.138114 | + | 0.241054i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.21703 | − | 8.62980i | 0.245813 | − | 0.293932i | ||||
\(863\) | 15.4850 | − | 26.8209i | 0.527117 | − | 0.912993i | −0.472384 | − | 0.881393i | \(-0.656606\pi\) |
0.999501 | − | 0.0316000i | \(-0.0100603\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23638 | + | 12.6831i | 0.0760392 | + | 0.431240i | ||||
\(866\) | −13.7600 | − | 2.40285i | −0.467584 | − | 0.0816522i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.18707 | − | 41.5616i | 0.243945 | − | 1.41069i | ||||
\(869\) | −7.08139 | − | 19.4560i | −0.240220 | − | 0.659998i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7564 | + | 19.9695i | −0.567769 | + | 0.676641i | ||||
\(872\) | −7.80953 | + | 9.40116i | −0.264464 | + | 0.318364i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.170612 | − | 18.4040i | −0.00577103 | − | 0.622525i | ||||
\(875\) | −19.1188 | −0.646333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.1372 | + | 34.5182i | 1.38910 | + | 1.16560i | 0.965701 | + | 0.259655i | \(0.0836090\pi\) |
0.423403 | + | 0.905941i | \(0.360835\pi\) | |||||||
\(878\) | 30.8642 | − | 0.0509342i | 1.04162 | − | 0.00171895i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.0377 | + | 5.88393i | −0.338369 | + | 0.198347i | ||||
\(881\) | −10.8128 | + | 6.24276i | −0.364292 | + | 0.210324i | −0.670962 | − | 0.741492i | \(-0.734119\pi\) |
0.306670 | + | 0.951816i | \(0.400785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.870075 | + | 0.153418i | −0.0292803 | + | 0.00516291i | −0.188269 | − | 0.982117i | \(-0.560288\pi\) |
0.158989 | + | 0.987280i | \(0.449177\pi\) | |||||||
\(884\) | −21.7073 | + | 26.0438i | −0.730095 | + | 0.875948i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.6504 | − | 21.1056i | 0.592978 | − | 0.709057i | ||||
\(887\) | −20.0221 | + | 16.8005i | −0.672276 | + | 0.564106i | −0.913738 | − | 0.406304i | \(-0.866817\pi\) |
0.241462 | + | 0.970410i | \(0.422373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.2345 | − | 6.27285i | −0.578027 | − | 0.210385i | ||||
\(890\) | −1.92914 | + | 5.32761i | −0.0646649 | + | 0.178582i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.05082 | − | 1.24396i | −0.0351842 | − | 0.0416509i | ||||
\(893\) | −35.1480 | + | 13.0970i | −1.17618 | + | 0.438274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.87683 | − | 1.38890i | −0.263293 | − | 0.0464257i | ||||
\(896\) | −5.01635 | − | 26.6454i | −0.167584 | − | 0.890162i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.9838 | − | 16.8247i | 0.666868 | − | 0.561446i | ||||
\(899\) | −30.4772 | + | 25.5734i | −1.01647 | + | 0.852921i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.701085 | + | 1.21432i | −0.0233565 | + | 0.0404547i | ||||
\(902\) | −16.6637 | − | 28.7528i | −0.554842 | − | 0.957363i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.7321 | − | 32.0772i | −0.623022 | − | 1.06687i | ||||
\(905\) | −18.8205 | + | 10.8660i | −0.625615 | + | 0.361199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.9326 | − | 46.5219i | −0.562238 | − | 1.54473i | −0.816348 | − | 0.577560i | \(-0.804005\pi\) |
0.254111 | − | 0.967175i | \(-0.418217\pi\) | |||||||
\(908\) | 8.25703 | − | 3.03621i | 0.274019 | − | 0.100760i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.21666 | − | 1.10675i | 0.206080 | − | 0.0366883i | ||||
\(911\) | −40.7601 | −1.35044 | −0.675221 | − | 0.737615i | \(-0.735952\pi\) | ||||
−0.675221 | + | 0.737615i | \(0.735952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.2254 | 1.69531 | ||||||||
\(914\) | −55.5688 | + | 9.89286i | −1.83805 | + | 0.327227i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.41245 | − | 3.09336i | 0.277955 | − | 0.102208i | ||||
\(917\) | 6.81688 | + | 18.7292i | 0.225113 | + | 0.618494i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.4780 | − | 7.20419i | 0.411612 | − | 0.237644i | −0.279870 | − | 0.960038i | \(-0.590291\pi\) |
0.691482 | + | 0.722394i | \(0.256958\pi\) | |||||||
\(920\) | 3.66986 | + | 6.28433i | 0.120992 | + | 0.207188i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.5574 | + | 18.2165i | 0.347690 | + | 0.599928i | ||||
\(923\) | −11.2963 | + | 19.5658i | −0.371823 | + | 0.644016i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9310 | + | 20.0805i | −0.786847 | + | 0.660243i | ||||
\(926\) | 13.9326 | − | 11.7301i | 0.457854 | − | 0.385474i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.6044 | + | 22.2534i | −0.413758 | + | 0.730505i | ||||
\(929\) | −23.3111 | − | 4.11037i | −0.764812 | − | 0.134857i | −0.222384 | − | 0.974959i | \(-0.571384\pi\) |
−0.542428 | + | 0.840102i | \(0.682495\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.16157 | + | 1.83424i | 0.169164 | + | 0.0601148i | ||||
\(932\) | −20.4648 | − | 24.2262i | −0.670347 | − | 0.793555i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.27036 | − | 20.0782i | 0.237893 | − | 0.656978i | ||||
\(935\) | 21.4325 | + | 7.80080i | 0.700918 | + | 0.255113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.2829 | − | 34.6405i | 1.34865 | − | 1.13166i | 0.369344 | − | 0.929293i | \(-0.379583\pi\) |
0.979311 | − | 0.202362i | \(-0.0648619\pi\) | |||||||
\(938\) | −26.2167 | + | 31.3487i | −0.856005 | + | 1.02357i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.49584 | − | 11.3929i | 0.309720 | − | 0.371594i | ||||
\(941\) | 35.2664 | − | 6.21841i | 1.14965 | − | 0.202714i | 0.433828 | − | 0.900996i | \(-0.357163\pi\) |
0.715823 | + | 0.698281i | \(0.246052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0012 | + | 10.3930i | −0.586200 | + | 0.338443i | ||||
\(944\) | 9.34474 | + | 15.9416i | 0.304145 | + | 0.518855i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.5640 | − | 0.0372367i | 0.733620 | − | 0.00121067i | ||||
\(947\) | 7.68149 | + | 6.44553i | 0.249615 | + | 0.209452i | 0.759006 | − | 0.651083i | \(-0.225685\pi\) |
−0.509392 | + | 0.860535i | \(0.670130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9225 | −0.484406 | ||||||||
\(950\) | 22.8487 | + | 12.9108i | 0.741309 | + | 0.418881i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −33.9622 | + | 40.8840i | −1.10072 | + | 1.32506i | ||||
\(953\) | −7.01559 | + | 8.36085i | −0.227257 | + | 0.270835i | −0.867609 | − | 0.497247i | \(-0.834344\pi\) |
0.640352 | + | 0.768082i | \(0.278789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.36113 | + | 20.2245i | 0.238200 | + | 0.654450i | ||||
\(956\) | 5.70497 | − | 32.9909i | 0.184512 | − | 1.06700i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.36619 | − | 1.63558i | −0.302608 | − | 0.0528432i | ||||
\(959\) | −3.34641 | − | 18.9784i | −0.108061 | − | 0.612846i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.2194 | − | 40.2171i | 0.749011 | − | 1.29733i | ||||
\(962\) | 14.3926 | − | 17.2100i | 0.464035 | − | 0.554873i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.5066 | + | 42.7721i | −0.789304 | + | 1.37760i | ||||
\(965\) | 3.69935 | − | 10.1639i | 0.119086 | − | 0.327187i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.74891 | − | 0.837361i | −0.152715 | − | 0.0269277i | 0.0967681 | − | 0.995307i | \(-0.469149\pi\) |
−0.249483 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(968\) | 0.965062 | + | 0.550826i | 0.0310183 | + | 0.0177042i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.774734 | + | 0.283429i | −0.0248752 | + | 0.00910035i | ||||
\(971\) | −8.78529 | + | 49.8239i | −0.281933 | + | 1.59892i | 0.434105 | + | 0.900862i | \(0.357065\pi\) |
−0.716038 | + | 0.698061i | \(0.754046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.9286 | + | 6.52549i | 0.574766 | + | 0.209198i | ||||
\(974\) | −9.86467 | + | 8.30522i | −0.316084 | + | 0.266116i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.5844 | + | 3.93171i | −0.338798 | + | 0.125851i | ||||
\(977\) | 27.0288 | + | 15.6051i | 0.864728 | + | 0.499251i | 0.865593 | − | 0.500749i | \(-0.166942\pi\) |
−0.000864660 | 1.00000i | \(0.500275\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.4542 | − | 2.72499i | 0.493918 | − | 0.0870911i | ||||
\(980\) | −2.13181 | + | 0.383155i | −0.0680982 | + | 0.0122394i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45.4053 | + | 26.1150i | 1.44894 | + | 0.833362i | ||||
\(983\) | −1.24629 | + | 0.453613i | −0.0397505 | + | 0.0144680i | −0.361819 | − | 0.932248i | \(-0.617844\pi\) |
0.322068 | + | 0.946716i | \(0.395622\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.2439 | − | 11.1130i | −0.421987 | − | 0.354089i | ||||
\(986\) | 49.3583 | − | 8.78720i | 1.57189 | − | 0.279842i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.7801 | − | 6.25239i | −0.565659 | − | 0.198915i | ||||
\(989\) | − | 14.1132i | − | 0.448773i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0462 | − | 16.7396i | 0.446192 | − | 0.531751i | −0.495329 | − | 0.868705i | \(-0.664953\pi\) |
0.941521 | + | 0.336955i | \(0.109397\pi\) | |||||||
\(992\) | 8.23939 | − | 49.0933i | 0.261601 | − | 1.55871i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.6582 | + | 30.7017i | −0.560083 | + | 0.973800i | ||||
\(995\) | 8.14771 | + | 14.1123i | 0.258300 | + | 0.447388i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.63415 | + | 48.9667i | 0.273446 | + | 1.55079i | 0.743855 | + | 0.668341i | \(0.232995\pi\) |
−0.470408 | + | 0.882449i | \(0.655893\pi\) | |||||||
\(998\) | 16.2138 | + | 27.9764i | 0.513239 | + | 0.885577i | ||||
\(999\) | 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 | 684.2.ce.a.359.3 | ✓ | 240 | |
3.2 | odd | 2 | inner | 684.2.ce.a.359.38 | yes | 240 | |
4.3 | odd | 2 | inner | 684.2.ce.a.359.8 | yes | 240 | |
12.11 | even | 2 | inner | 684.2.ce.a.359.33 | yes | 240 | |
19.9 | even | 9 | inner | 684.2.ce.a.503.33 | yes | 240 | |
57.47 | odd | 18 | inner | 684.2.ce.a.503.8 | yes | 240 | |
76.47 | odd | 18 | inner | 684.2.ce.a.503.38 | yes | 240 | |
228.47 | even | 18 | inner | 684.2.ce.a.503.3 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.ce.a.359.3 | ✓ | 240 | 1.1 | even | 1 | trivial | |
684.2.ce.a.359.8 | yes | 240 | 4.3 | odd | 2 | inner | |
684.2.ce.a.359.33 | yes | 240 | 12.11 | even | 2 | inner | |
684.2.ce.a.359.38 | yes | 240 | 3.2 | odd | 2 | inner | |
684.2.ce.a.503.3 | yes | 240 | 228.47 | even | 18 | inner | |
684.2.ce.a.503.8 | yes | 240 | 57.47 | odd | 18 | inner | |
684.2.ce.a.503.33 | yes | 240 | 19.9 | even | 9 | inner | |
684.2.ce.a.503.38 | yes | 240 | 76.47 | odd | 18 | inner |