Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.10 | ||
Character | \(\chi\) | \(=\) | 1110.43 |
Dual form | 1110.2.l.a.697.10 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.87641 | + | 1.21617i | 0.839158 | + | 0.543888i | ||||
\(6\) | 0.707107 | + | 0.707107i | 0.288675 | + | 0.288675i | ||||
\(7\) | −2.24767 | + | 2.24767i | −0.849539 | + | 0.849539i | −0.990075 | − | 0.140537i | \(-0.955117\pi\) |
0.140537 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.21617 | + | 1.87641i | −0.384587 | + | 0.593374i | ||||
\(11\) | 5.65930i | 1.70634i | 0.521632 | + | 0.853171i | \(0.325324\pi\) | ||||
−0.521632 | + | 0.853171i | \(0.674676\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | − | 4.81453i | − | 1.33531i | −0.744471 | − | 0.667655i | \(-0.767298\pi\) | ||
0.744471 | − | 0.667655i | \(-0.232702\pi\) | |||||||
\(14\) | −2.24767 | − | 2.24767i | −0.600715 | − | 0.600715i | ||||
\(15\) | 2.18679 | − | 0.466864i | 0.564626 | − | 0.120544i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.58373 | −1.83932 | −0.919662 | − | 0.392710i | \(-0.871537\pi\) | ||||
−0.919662 | + | 0.392710i | \(0.871537\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.73408 | + | 3.73408i | −0.856657 | + | 0.856657i | −0.990943 | − | 0.134285i | \(-0.957126\pi\) |
0.134285 | + | 0.990943i | \(0.457126\pi\) | |||||||
\(20\) | −1.87641 | − | 1.21617i | −0.419579 | − | 0.271944i | ||||
\(21\) | 3.17868i | 0.693646i | ||||||||
\(22\) | −5.65930 | −1.20657 | ||||||||
\(23\) | 4.23021i | 0.882059i | 0.897493 | + | 0.441030i | \(0.145387\pi\) | ||||
−0.897493 | + | 0.441030i | \(0.854613\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | 2.04186 | + | 4.56408i | 0.408373 | + | 0.912815i | ||||
\(26\) | 4.81453 | 0.944207 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 2.24767 | − | 2.24767i | 0.424769 | − | 0.424769i | ||||
\(29\) | 3.26498 | + | 3.26498i | 0.606291 | + | 0.606291i | 0.941975 | − | 0.335684i | \(-0.108967\pi\) |
−0.335684 | + | 0.941975i | \(0.608967\pi\) | |||||||
\(30\) | 0.466864 | + | 2.18679i | 0.0852373 | + | 0.399251i | ||||
\(31\) | 1.98809 | − | 1.98809i | 0.357071 | − | 0.357071i | −0.505661 | − | 0.862732i | \(-0.668751\pi\) |
0.862732 | + | 0.505661i | \(0.168751\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.00173 | + | 4.00173i | 0.696611 | + | 0.696611i | ||||
\(34\) | − | 7.58373i | − | 1.30060i | ||||||
\(35\) | −6.95110 | + | 1.48401i | −1.17495 | + | 0.250844i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −4.17208 | − | 4.42648i | −0.685886 | − | 0.727709i | ||||
\(38\) | −3.73408 | − | 3.73408i | −0.605748 | − | 0.605748i | ||||
\(39\) | −3.40439 | − | 3.40439i | −0.545138 | − | 0.545138i | ||||
\(40\) | 1.21617 | − | 1.87641i | 0.192293 | − | 0.296687i | ||||
\(41\) | − | 2.43043i | − | 0.379570i | −0.981826 | − | 0.189785i | \(-0.939221\pi\) | ||
0.981826 | − | 0.189785i | \(-0.0607791\pi\) | |||||||
\(42\) | −3.17868 | −0.490482 | ||||||||
\(43\) | − | 3.34656i | − | 0.510346i | −0.966895 | − | 0.255173i | \(-0.917868\pi\) | ||
0.966895 | − | 0.255173i | \(-0.0821324\pi\) | |||||||
\(44\) | − | 5.65930i | − | 0.853171i | ||||||
\(45\) | 1.21617 | − | 1.87641i | 0.181296 | − | 0.279719i | ||||
\(46\) | −4.23021 | −0.623710 | ||||||||
\(47\) | 6.04560 | − | 6.04560i | 0.881842 | − | 0.881842i | −0.111880 | − | 0.993722i | \(-0.535687\pi\) |
0.993722 | + | 0.111880i | \(0.0356873\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 3.10403i | − | 0.443433i | ||||||
\(50\) | −4.56408 | + | 2.04186i | −0.645458 | + | 0.288763i | ||||
\(51\) | −5.36251 | + | 5.36251i | −0.750901 | + | 0.750901i | ||||
\(52\) | 4.81453i | 0.667655i | ||||||||
\(53\) | 8.02058 | + | 8.02058i | 1.10171 | + | 1.10171i | 0.994204 | + | 0.107507i | \(0.0342868\pi\) |
0.107507 | + | 0.994204i | \(0.465713\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | −6.88266 | + | 10.6192i | −0.928058 | + | 1.43189i | ||||
\(56\) | 2.24767 | + | 2.24767i | 0.300357 | + | 0.300357i | ||||
\(57\) | 5.28079i | 0.699458i | ||||||||
\(58\) | −3.26498 | + | 3.26498i | −0.428712 | + | 0.428712i | ||||
\(59\) | −9.84721 | + | 9.84721i | −1.28200 | + | 1.28200i | −0.342468 | + | 0.939530i | \(0.611263\pi\) |
−0.939530 | + | 0.342468i | \(0.888737\pi\) | |||||||
\(60\) | −2.18679 | + | 0.466864i | −0.282313 | + | 0.0602718i | ||||
\(61\) | −1.11855 | + | 1.11855i | −0.143216 | + | 0.143216i | −0.775080 | − | 0.631864i | \(-0.782290\pi\) |
0.631864 | + | 0.775080i | \(0.282290\pi\) | |||||||
\(62\) | 1.98809 | + | 1.98809i | 0.252487 | + | 0.252487i | ||||
\(63\) | 2.24767 | + | 2.24767i | 0.283180 | + | 0.283180i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.85528 | − | 9.03405i | 0.726259 | − | 1.12054i | ||||
\(66\) | −4.00173 | + | 4.00173i | −0.492578 | + | 0.492578i | ||||
\(67\) | 6.91167 | + | 6.91167i | 0.844395 | + | 0.844395i | 0.989427 | − | 0.145032i | \(-0.0463284\pi\) |
−0.145032 | + | 0.989427i | \(0.546328\pi\) | |||||||
\(68\) | 7.58373 | 0.919662 | ||||||||
\(69\) | 2.99121 | + | 2.99121i | 0.360099 | + | 0.360099i | ||||
\(70\) | −1.48401 | − | 6.95110i | −0.177373 | − | 0.830816i | ||||
\(71\) | −6.12087 | −0.726413 | −0.363207 | − | 0.931709i | \(-0.618318\pi\) | ||||
−0.363207 | + | 0.931709i | \(0.618318\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.58794 | + | 2.58794i | −0.302896 | + | 0.302896i | −0.842146 | − | 0.539250i | \(-0.818708\pi\) |
0.539250 | + | 0.842146i | \(0.318708\pi\) | |||||||
\(74\) | 4.42648 | − | 4.17208i | 0.514568 | − | 0.484995i | ||||
\(75\) | 4.67110 | + | 1.78347i | 0.539373 | + | 0.205938i | ||||
\(76\) | 3.73408 | − | 3.73408i | 0.428329 | − | 0.428329i | ||||
\(77\) | −12.7202 | − | 12.7202i | −1.44960 | − | 1.44960i | ||||
\(78\) | 3.40439 | − | 3.40439i | 0.385471 | − | 0.385471i | ||||
\(79\) | −2.85317 | + | 2.85317i | −0.321007 | + | 0.321007i | −0.849153 | − | 0.528146i | \(-0.822887\pi\) |
0.528146 | + | 0.849153i | \(0.322887\pi\) | |||||||
\(80\) | 1.87641 | + | 1.21617i | 0.209790 | + | 0.135972i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.43043 | 0.268396 | ||||||||
\(83\) | 0.906248 | + | 0.906248i | 0.0994737 | + | 0.0994737i | 0.755092 | − | 0.655619i | \(-0.227592\pi\) |
−0.655619 | + | 0.755092i | \(0.727592\pi\) | |||||||
\(84\) | − | 3.17868i | − | 0.346823i | ||||||
\(85\) | −14.2302 | − | 9.22310i | −1.54348 | − | 1.00039i | ||||
\(86\) | 3.34656 | 0.360869 | ||||||||
\(87\) | 4.61737 | 0.495034 | ||||||||
\(88\) | 5.65930 | 0.603283 | ||||||||
\(89\) | 10.1878 | + | 10.1878i | 1.07990 | + | 1.07990i | 0.996518 | + | 0.0833830i | \(0.0265725\pi\) |
0.0833830 | + | 0.996518i | \(0.473428\pi\) | |||||||
\(90\) | 1.87641 | + | 1.21617i | 0.197791 | + | 0.128196i | ||||
\(91\) | 10.8215 | + | 10.8215i | 1.13440 | + | 1.13440i | ||||
\(92\) | − | 4.23021i | − | 0.441030i | ||||||
\(93\) | − | 2.81158i | − | 0.291547i | ||||||
\(94\) | 6.04560 | + | 6.04560i | 0.623556 | + | 0.623556i | ||||
\(95\) | −11.5480 | + | 2.46541i | −1.18480 | + | 0.252946i | ||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | −2.87834 | −0.292251 | −0.146125 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146125 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(98\) | 3.10403 | 0.313554 | ||||||||
\(99\) | 5.65930 | 0.568781 | ||||||||
\(100\) | −2.04186 | − | 4.56408i | −0.204186 | − | 0.456408i | ||||
\(101\) | − | 16.0893i | − | 1.60095i | −0.599367 | − | 0.800474i | \(-0.704581\pi\) | ||
0.599367 | − | 0.800474i | \(-0.295419\pi\) | |||||||
\(102\) | −5.36251 | − | 5.36251i | −0.530967 | − | 0.530967i | ||||
\(103\) | 11.0997 | 1.09369 | 0.546845 | − | 0.837234i | \(-0.315829\pi\) | ||||
0.546845 | + | 0.837234i | \(0.315829\pi\) | |||||||
\(104\) | −4.81453 | −0.472103 | ||||||||
\(105\) | −3.86582 | + | 5.96453i | −0.377265 | + | 0.582078i | ||||
\(106\) | −8.02058 | + | 8.02058i | −0.779028 | + | 0.779028i | ||||
\(107\) | 8.64549 | − | 8.64549i | 0.835791 | − | 0.835791i | −0.152511 | − | 0.988302i | \(-0.548736\pi\) |
0.988302 | + | 0.152511i | \(0.0487359\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −13.7592 | + | 13.7592i | −1.31790 | + | 1.31790i | −0.402458 | + | 0.915438i | \(0.631844\pi\) |
−0.915438 | + | 0.402458i | \(0.868156\pi\) | |||||||
\(110\) | −10.6192 | − | 6.88266i | −1.01250 | − | 0.656236i | ||||
\(111\) | −6.08010 | − | 0.179886i | −0.577098 | − | 0.0170740i | ||||
\(112\) | −2.24767 | + | 2.24767i | −0.212385 | + | 0.212385i | ||||
\(113\) | 4.68689 | 0.440906 | 0.220453 | − | 0.975398i | \(-0.429246\pi\) | ||||
0.220453 | + | 0.975398i | \(0.429246\pi\) | |||||||
\(114\) | −5.28079 | −0.494591 | ||||||||
\(115\) | −5.14465 | + | 7.93762i | −0.479741 | + | 0.740187i | ||||
\(116\) | −3.26498 | − | 3.26498i | −0.303145 | − | 0.303145i | ||||
\(117\) | −4.81453 | −0.445103 | ||||||||
\(118\) | −9.84721 | − | 9.84721i | −0.906509 | − | 0.906509i | ||||
\(119\) | 17.0457 | − | 17.0457i | 1.56258 | − | 1.56258i | ||||
\(120\) | −0.466864 | − | 2.18679i | −0.0426186 | − | 0.199625i | ||||
\(121\) | −21.0276 | −1.91160 | ||||||||
\(122\) | −1.11855 | − | 1.11855i | −0.101269 | − | 0.101269i | ||||
\(123\) | −1.71858 | − | 1.71858i | −0.154959 | − | 0.154959i | ||||
\(124\) | −1.98809 | + | 1.98809i | −0.178535 | + | 0.178535i | ||||
\(125\) | −1.71931 | + | 11.0474i | −0.153780 | + | 0.988105i | ||||
\(126\) | −2.24767 | + | 2.24767i | −0.200238 | + | 0.200238i | ||||
\(127\) | −14.6086 | + | 14.6086i | −1.29630 | + | 1.29630i | −0.365488 | + | 0.930816i | \(0.619098\pi\) |
−0.930816 | + | 0.365488i | \(0.880902\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −2.36638 | − | 2.36638i | −0.208348 | − | 0.208348i | ||||
\(130\) | 9.03405 | + | 5.85528i | 0.792339 | + | 0.513542i | ||||
\(131\) | 9.26219 | − | 9.26219i | 0.809241 | − | 0.809241i | −0.175278 | − | 0.984519i | \(-0.556082\pi\) |
0.984519 | + | 0.175278i | \(0.0560824\pi\) | |||||||
\(132\) | −4.00173 | − | 4.00173i | −0.348306 | − | 0.348306i | ||||
\(133\) | − | 16.7860i | − | 1.45553i | ||||||
\(134\) | −6.91167 | + | 6.91167i | −0.597078 | + | 0.597078i | ||||
\(135\) | −0.466864 | − | 2.18679i | −0.0401812 | − | 0.188209i | ||||
\(136\) | 7.58373i | 0.650299i | ||||||||
\(137\) | 1.63948 | − | 1.63948i | 0.140071 | − | 0.140071i | −0.633595 | − | 0.773665i | \(-0.718421\pi\) |
0.773665 | + | 0.633595i | \(0.218421\pi\) | |||||||
\(138\) | −2.99121 | + | 2.99121i | −0.254629 | + | 0.254629i | ||||
\(139\) | 17.9432 | 1.52192 | 0.760959 | − | 0.648800i | \(-0.224729\pi\) | ||||
0.760959 | + | 0.648800i | \(0.224729\pi\) | |||||||
\(140\) | 6.95110 | − | 1.48401i | 0.587476 | − | 0.125422i | ||||
\(141\) | − | 8.54977i | − | 0.720021i | ||||||
\(142\) | − | 6.12087i | − | 0.513652i | ||||||
\(143\) | 27.2468 | 2.27850 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 2.15568 | + | 10.0972i | 0.179020 | + | 0.838528i | ||||
\(146\) | −2.58794 | − | 2.58794i | −0.214180 | − | 0.214180i | ||||
\(147\) | −2.19488 | − | 2.19488i | −0.181031 | − | 0.181031i | ||||
\(148\) | 4.17208 | + | 4.42648i | 0.342943 | + | 0.363854i | ||||
\(149\) | − | 9.20482i | − | 0.754088i | −0.926195 | − | 0.377044i | \(-0.876941\pi\) | ||
0.926195 | − | 0.377044i | \(-0.123059\pi\) | |||||||
\(150\) | −1.78347 | + | 4.67110i | −0.145620 | + | 0.381394i | ||||
\(151\) | 5.59713i | 0.455488i | 0.973721 | + | 0.227744i | \(0.0731349\pi\) | ||||
−0.973721 | + | 0.227744i | \(0.926865\pi\) | |||||||
\(152\) | 3.73408 | + | 3.73408i | 0.302874 | + | 0.302874i | ||||
\(153\) | 7.58373i | 0.613108i | ||||||||
\(154\) | 12.7202 | − | 12.7202i | 1.02502 | − | 1.02502i | ||||
\(155\) | 6.14832 | − | 1.31262i | 0.493845 | − | 0.105432i | ||||
\(156\) | 3.40439 | + | 3.40439i | 0.272569 | + | 0.272569i | ||||
\(157\) | −0.998661 | + | 0.998661i | −0.0797019 | + | 0.0797019i | −0.745834 | − | 0.666132i | \(-0.767949\pi\) |
0.666132 | + | 0.745834i | \(0.267949\pi\) | |||||||
\(158\) | −2.85317 | − | 2.85317i | −0.226986 | − | 0.226986i | ||||
\(159\) | 11.3428 | 0.899543 | ||||||||
\(160\) | −1.21617 | + | 1.87641i | −0.0961466 | + | 0.148344i | ||||
\(161\) | −9.50811 | − | 9.50811i | −0.749344 | − | 0.749344i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −7.74976 | −0.607008 | −0.303504 | − | 0.952830i | \(-0.598157\pi\) | ||||
−0.303504 | + | 0.952830i | \(0.598157\pi\) | |||||||
\(164\) | 2.43043i | 0.189785i | ||||||||
\(165\) | 2.64212 | + | 12.3757i | 0.205689 | + | 0.963445i | ||||
\(166\) | −0.906248 | + | 0.906248i | −0.0703385 | + | 0.0703385i | ||||
\(167\) | 19.2547 | 1.48997 | 0.744985 | − | 0.667081i | \(-0.232457\pi\) | ||||
0.744985 | + | 0.667081i | \(0.232457\pi\) | |||||||
\(168\) | 3.17868 | 0.245241 | ||||||||
\(169\) | −10.1797 | −0.783053 | ||||||||
\(170\) | 9.22310 | − | 14.2302i | 0.707379 | − | 1.09141i | ||||
\(171\) | 3.73408 | + | 3.73408i | 0.285552 | + | 0.285552i | ||||
\(172\) | 3.34656i | 0.255173i | ||||||||
\(173\) | 8.58579 | − | 8.58579i | 0.652765 | − | 0.652765i | −0.300893 | − | 0.953658i | \(-0.597285\pi\) |
0.953658 | + | 0.300893i | \(0.0972846\pi\) | |||||||
\(174\) | 4.61737i | 0.350042i | ||||||||
\(175\) | −14.8480 | − | 5.66910i | −1.12240 | − | 0.428544i | ||||
\(176\) | 5.65930i | 0.426585i | ||||||||
\(177\) | 13.9261i | 1.04675i | ||||||||
\(178\) | −10.1878 | + | 10.1878i | −0.763605 | + | 0.763605i | ||||
\(179\) | −14.0961 | − | 14.0961i | −1.05359 | − | 1.05359i | −0.998480 | − | 0.0551080i | \(-0.982450\pi\) |
−0.0551080 | − | 0.998480i | \(-0.517550\pi\) | |||||||
\(180\) | −1.21617 | + | 1.87641i | −0.0906479 | + | 0.139860i | ||||
\(181\) | 13.7831 | 1.02449 | 0.512245 | − | 0.858839i | \(-0.328814\pi\) | ||||
0.512245 | + | 0.858839i | \(0.328814\pi\) | |||||||
\(182\) | −10.8215 | + | 10.8215i | −0.802140 | + | 0.802140i | ||||
\(183\) | 1.58187i | 0.116935i | ||||||||
\(184\) | 4.23021 | 0.311855 | ||||||||
\(185\) | −2.44521 | − | 13.3799i | −0.179775 | − | 0.983708i | ||||
\(186\) | 2.81158 | 0.206155 | ||||||||
\(187\) | − | 42.9186i | − | 3.13852i | ||||||
\(188\) | −6.04560 | + | 6.04560i | −0.440921 | + | 0.440921i | ||||
\(189\) | 3.17868 | 0.231215 | ||||||||
\(190\) | −2.46541 | − | 11.5480i | −0.178860 | − | 0.837777i | ||||
\(191\) | 18.4453 | + | 18.4453i | 1.33466 | + | 1.33466i | 0.901149 | + | 0.433509i | \(0.142725\pi\) |
0.433509 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | − | 22.9897i | − | 1.65484i | −0.561585 | − | 0.827419i | \(-0.689808\pi\) | ||
0.561585 | − | 0.827419i | \(-0.310192\pi\) | |||||||
\(194\) | − | 2.87834i | − | 0.206652i | ||||||
\(195\) | −2.24773 | − | 10.5284i | −0.160963 | − | 0.753951i | ||||
\(196\) | 3.10403i | 0.221716i | ||||||||
\(197\) | −1.69341 | + | 1.69341i | −0.120650 | + | 0.120650i | −0.764854 | − | 0.644204i | \(-0.777189\pi\) |
0.644204 | + | 0.764854i | \(0.277189\pi\) | |||||||
\(198\) | 5.65930i | 0.402189i | ||||||||
\(199\) | 7.33672 | + | 7.33672i | 0.520087 | + | 0.520087i | 0.917597 | − | 0.397511i | \(-0.130126\pi\) |
−0.397511 | + | 0.917597i | \(0.630126\pi\) | |||||||
\(200\) | 4.56408 | − | 2.04186i | 0.322729 | − | 0.144382i | ||||
\(201\) | 9.77458 | 0.689446 | ||||||||
\(202\) | 16.0893 | 1.13204 | ||||||||
\(203\) | −14.6772 | −1.03014 | ||||||||
\(204\) | 5.36251 | − | 5.36251i | 0.375451 | − | 0.375451i | ||||
\(205\) | 2.95582 | − | 4.56050i | 0.206443 | − | 0.318519i | ||||
\(206\) | 11.0997i | 0.773355i | ||||||||
\(207\) | 4.23021 | 0.294020 | ||||||||
\(208\) | − | 4.81453i | − | 0.333828i | ||||||
\(209\) | −21.1323 | − | 21.1323i | −1.46175 | − | 1.46175i | ||||
\(210\) | −5.96453 | − | 3.86582i | −0.411592 | − | 0.266767i | ||||
\(211\) | 11.9466 | 0.822435 | 0.411218 | − | 0.911537i | \(-0.365104\pi\) | ||||
0.411218 | + | 0.911537i | \(0.365104\pi\) | |||||||
\(212\) | −8.02058 | − | 8.02058i | −0.550856 | − | 0.550856i | ||||
\(213\) | −4.32811 | + | 4.32811i | −0.296557 | + | 0.296557i | ||||
\(214\) | 8.64549 | + | 8.64549i | 0.590993 | + | 0.590993i | ||||
\(215\) | 4.06999 | − | 6.27954i | 0.277571 | − | 0.428261i | ||||
\(216\) | −0.707107 | + | 0.707107i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | 8.93712i | 0.606691i | ||||||||
\(218\) | −13.7592 | − | 13.7592i | −0.931894 | − | 0.931894i | ||||
\(219\) | 3.65991i | 0.247314i | ||||||||
\(220\) | 6.88266 | − | 10.6192i | 0.464029 | − | 0.715945i | ||||
\(221\) | 36.5121i | 2.45607i | ||||||||
\(222\) | 0.179886 | − | 6.08010i | 0.0120732 | − | 0.408070i | ||||
\(223\) | 11.0520 | + | 11.0520i | 0.740100 | + | 0.740100i | 0.972597 | − | 0.232497i | \(-0.0746896\pi\) |
−0.232497 | + | 0.972597i | \(0.574690\pi\) | |||||||
\(224\) | −2.24767 | − | 2.24767i | −0.150179 | − | 0.150179i | ||||
\(225\) | 4.56408 | − | 2.04186i | 0.304272 | − | 0.136124i | ||||
\(226\) | 4.68689i | 0.311768i | ||||||||
\(227\) | −6.40168 | −0.424894 | −0.212447 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212447 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(228\) | − | 5.28079i | − | 0.349729i | ||||||
\(229\) | − | 16.3225i | − | 1.07862i | −0.842107 | − | 0.539310i | \(-0.818685\pi\) | ||
0.842107 | − | 0.539310i | \(-0.181315\pi\) | |||||||
\(230\) | −7.93762 | − | 5.14465i | −0.523391 | − | 0.339228i | ||||
\(231\) | −17.9891 | −1.18360 | ||||||||
\(232\) | 3.26498 | − | 3.26498i | 0.214356 | − | 0.214356i | ||||
\(233\) | 0.738837 | − | 0.738837i | 0.0484028 | − | 0.0484028i | −0.682491 | − | 0.730894i | \(-0.739103\pi\) |
0.730894 | + | 0.682491i | \(0.239103\pi\) | |||||||
\(234\) | − | 4.81453i | − | 0.314736i | ||||||
\(235\) | 18.6965 | − | 3.99158i | 1.21963 | − | 0.260382i | ||||
\(236\) | 9.84721 | − | 9.84721i | 0.640999 | − | 0.640999i | ||||
\(237\) | 4.03499i | 0.262101i | ||||||||
\(238\) | 17.0457 | + | 17.0457i | 1.10491 | + | 1.10491i | ||||
\(239\) | 5.10981 | − | 5.10981i | 0.330526 | − | 0.330526i | −0.522260 | − | 0.852786i | \(-0.674911\pi\) |
0.852786 | + | 0.522260i | \(0.174911\pi\) | |||||||
\(240\) | 2.18679 | − | 0.466864i | 0.141157 | − | 0.0301359i | ||||
\(241\) | −8.22613 | − | 8.22613i | −0.529892 | − | 0.529892i | 0.390648 | − | 0.920540i | \(-0.372251\pi\) |
−0.920540 | + | 0.390648i | \(0.872251\pi\) | |||||||
\(242\) | − | 21.0276i | − | 1.35171i | ||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 1.11855 | − | 1.11855i | 0.0716080 | − | 0.0716080i | ||||
\(245\) | 3.77503 | − | 5.82445i | 0.241178 | − | 0.372110i | ||||
\(246\) | 1.71858 | − | 1.71858i | 0.109572 | − | 0.109572i | ||||
\(247\) | 17.9778 | + | 17.9778i | 1.14390 | + | 1.14390i | ||||
\(248\) | −1.98809 | − | 1.98809i | −0.126244 | − | 0.126244i | ||||
\(249\) | 1.28163 | 0.0812199 | ||||||||
\(250\) | −11.0474 | − | 1.71931i | −0.698696 | − | 0.108739i | ||||
\(251\) | −10.0396 | + | 10.0396i | −0.633694 | + | 0.633694i | −0.948992 | − | 0.315299i | \(-0.897895\pi\) |
0.315299 | + | 0.948992i | \(0.397895\pi\) | |||||||
\(252\) | −2.24767 | − | 2.24767i | −0.141590 | − | 0.141590i | ||||
\(253\) | −23.9400 | −1.50509 | ||||||||
\(254\) | −14.6086 | − | 14.6086i | −0.916626 | − | 0.916626i | ||||
\(255\) | −16.5840 | + | 3.54057i | −1.03853 | + | 0.221719i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.5767 | 0.971645 | 0.485823 | − | 0.874057i | \(-0.338520\pi\) | ||||
0.485823 | + | 0.874057i | \(0.338520\pi\) | |||||||
\(258\) | 2.36638 | − | 2.36638i | 0.147324 | − | 0.147324i | ||||
\(259\) | 19.3267 | + | 0.571801i | 1.20090 | + | 0.0355300i | ||||
\(260\) | −5.85528 | + | 9.03405i | −0.363129 | + | 0.560268i | ||||
\(261\) | 3.26498 | − | 3.26498i | 0.202097 | − | 0.202097i | ||||
\(262\) | 9.26219 | + | 9.26219i | 0.572220 | + | 0.572220i | ||||
\(263\) | 17.2063 | − | 17.2063i | 1.06099 | − | 1.06099i | 0.0629697 | − | 0.998015i | \(-0.479943\pi\) |
0.998015 | − | 0.0629697i | \(-0.0200571\pi\) | |||||||
\(264\) | 4.00173 | − | 4.00173i | 0.246289 | − | 0.246289i | ||||
\(265\) | 5.29555 | + | 24.8043i | 0.325303 | + | 1.52372i | ||||
\(266\) | 16.7860 | 1.02921 | ||||||||
\(267\) | 14.4077 | 0.881735 | ||||||||
\(268\) | −6.91167 | − | 6.91167i | −0.422198 | − | 0.422198i | ||||
\(269\) | 16.7896i | 1.02368i | 0.859080 | + | 0.511841i | \(0.171036\pi\) | ||||
−0.859080 | + | 0.511841i | \(0.828964\pi\) | |||||||
\(270\) | 2.18679 | − | 0.466864i | 0.133084 | − | 0.0284124i | ||||
\(271\) | −3.47058 | −0.210823 | −0.105411 | − | 0.994429i | \(-0.533616\pi\) | ||||
−0.105411 | + | 0.994429i | \(0.533616\pi\) | |||||||
\(272\) | −7.58373 | −0.459831 | ||||||||
\(273\) | 15.3039 | 0.926232 | ||||||||
\(274\) | 1.63948 | + | 1.63948i | 0.0990449 | + | 0.0990449i | ||||
\(275\) | −25.8295 | + | 11.5555i | −1.55757 | + | 0.696823i | ||||
\(276\) | −2.99121 | − | 2.99121i | −0.180050 | − | 0.180050i | ||||
\(277\) | 5.08835i | 0.305730i | 0.988247 | + | 0.152865i | \(0.0488499\pi\) | ||||
−0.988247 | + | 0.152865i | \(0.951150\pi\) | |||||||
\(278\) | 17.9432i | 1.07616i | ||||||||
\(279\) | −1.98809 | − | 1.98809i | −0.119024 | − | 0.119024i | ||||
\(280\) | 1.48401 | + | 6.95110i | 0.0886867 | + | 0.415408i | ||||
\(281\) | 22.3585 | + | 22.3585i | 1.33380 | + | 1.33380i | 0.901943 | + | 0.431856i | \(0.142141\pi\) |
0.431856 | + | 0.901943i | \(0.357859\pi\) | |||||||
\(282\) | 8.54977 | 0.509131 | ||||||||
\(283\) | −4.97011 | −0.295442 | −0.147721 | − | 0.989029i | \(-0.547194\pi\) | ||||
−0.147721 | + | 0.989029i | \(0.547194\pi\) | |||||||
\(284\) | 6.12087 | 0.363207 | ||||||||
\(285\) | −6.42234 | + | 9.90895i | −0.380426 | + | 0.586956i | ||||
\(286\) | 27.2468i | 1.61114i | ||||||||
\(287\) | 5.46281 | + | 5.46281i | 0.322459 | + | 0.322459i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 40.5129 | 2.38311 | ||||||||
\(290\) | −10.0972 | + | 2.15568i | −0.592929 | + | 0.126586i | ||||
\(291\) | −2.03529 | + | 2.03529i | −0.119311 | + | 0.119311i | ||||
\(292\) | 2.58794 | − | 2.58794i | 0.151448 | − | 0.151448i | ||||
\(293\) | −3.76385 | − | 3.76385i | −0.219886 | − | 0.219886i | 0.588564 | − | 0.808450i | \(-0.299693\pi\) |
−0.808450 | + | 0.588564i | \(0.799693\pi\) | |||||||
\(294\) | 2.19488 | − | 2.19488i | 0.128008 | − | 0.128008i | ||||
\(295\) | −30.4533 | + | 6.50157i | −1.77306 | + | 0.378536i | ||||
\(296\) | −4.42648 | + | 4.17208i | −0.257284 | + | 0.242497i | ||||
\(297\) | 4.00173 | − | 4.00173i | 0.232204 | − | 0.232204i | ||||
\(298\) | 9.20482 | 0.533221 | ||||||||
\(299\) | 20.3665 | 1.17782 | ||||||||
\(300\) | −4.67110 | − | 1.78347i | −0.269686 | − | 0.102969i | ||||
\(301\) | 7.52196 | + | 7.52196i | 0.433559 | + | 0.433559i | ||||
\(302\) | −5.59713 | −0.322078 | ||||||||
\(303\) | −11.3769 | − | 11.3769i | −0.653584 | − | 0.653584i | ||||
\(304\) | −3.73408 | + | 3.73408i | −0.214164 | + | 0.214164i | ||||
\(305\) | −3.45922 | + | 0.738519i | −0.198074 | + | 0.0422875i | ||||
\(306\) | −7.58373 | −0.433533 | ||||||||
\(307\) | −10.3413 | − | 10.3413i | −0.590210 | − | 0.590210i | 0.347478 | − | 0.937688i | \(-0.387038\pi\) |
−0.937688 | + | 0.347478i | \(0.887038\pi\) | |||||||
\(308\) | 12.7202 | + | 12.7202i | 0.724802 | + | 0.724802i | ||||
\(309\) | 7.84870 | − | 7.84870i | 0.446497 | − | 0.446497i | ||||
\(310\) | 1.31262 | + | 6.14832i | 0.0745520 | + | 0.349201i | ||||
\(311\) | 2.08224 | − | 2.08224i | 0.118073 | − | 0.118073i | −0.645601 | − | 0.763675i | \(-0.723393\pi\) |
0.763675 | + | 0.645601i | \(0.223393\pi\) | |||||||
\(312\) | −3.40439 | + | 3.40439i | −0.192735 | + | 0.192735i | ||||
\(313\) | − | 5.86237i | − | 0.331361i | −0.986179 | − | 0.165681i | \(-0.947018\pi\) | ||
0.986179 | − | 0.165681i | \(-0.0529820\pi\) | |||||||
\(314\) | −0.998661 | − | 0.998661i | −0.0563577 | − | 0.0563577i | ||||
\(315\) | 1.48401 | + | 6.95110i | 0.0836146 | + | 0.391650i | ||||
\(316\) | 2.85317 | − | 2.85317i | 0.160503 | − | 0.160503i | ||||
\(317\) | −3.30695 | − | 3.30695i | −0.185737 | − | 0.185737i | 0.608113 | − | 0.793850i | \(-0.291927\pi\) |
−0.793850 | + | 0.608113i | \(0.791927\pi\) | |||||||
\(318\) | 11.3428i | 0.636073i | ||||||||
\(319\) | −18.4775 | + | 18.4775i | −1.03454 | + | 1.03454i | ||||
\(320\) | −1.87641 | − | 1.21617i | −0.104895 | − | 0.0679859i | ||||
\(321\) | − | 12.2266i | − | 0.682421i | ||||||
\(322\) | 9.50811 | − | 9.50811i | 0.529866 | − | 0.529866i | ||||
\(323\) | 28.3183 | − | 28.3183i | 1.57567 | − | 1.57567i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 21.9739 | − | 9.83061i | 1.21889 | − | 0.545304i | ||||
\(326\) | − | 7.74976i | − | 0.429220i | ||||||
\(327\) | 19.4585i | 1.07606i | ||||||||
\(328\) | −2.43043 | −0.134198 | ||||||||
\(329\) | 27.1770i | 1.49832i | ||||||||
\(330\) | −12.3757 | + | 2.64212i | −0.681258 | + | 0.145444i | ||||
\(331\) | 2.03744 | + | 2.03744i | 0.111988 | + | 0.111988i | 0.760880 | − | 0.648892i | \(-0.224768\pi\) |
−0.648892 | + | 0.760880i | \(0.724768\pi\) | |||||||
\(332\) | −0.906248 | − | 0.906248i | −0.0497368 | − | 0.0497368i | ||||
\(333\) | −4.42648 | + | 4.17208i | −0.242570 | + | 0.228629i | ||||
\(334\) | 19.2547i | 1.05357i | ||||||||
\(335\) | 4.56340 | + | 21.3749i | 0.249325 | + | 1.16784i | ||||
\(336\) | 3.17868i | 0.173411i | ||||||||
\(337\) | 4.38679 | + | 4.38679i | 0.238963 | + | 0.238963i | 0.816421 | − | 0.577457i | \(-0.195955\pi\) |
−0.577457 | + | 0.816421i | \(0.695955\pi\) | |||||||
\(338\) | − | 10.1797i | − | 0.553702i | ||||||
\(339\) | 3.31414 | − | 3.31414i | 0.179999 | − | 0.179999i | ||||
\(340\) | 14.2302 | + | 9.22310i | 0.771742 | + | 0.500193i | ||||
\(341\) | 11.2512 | + | 11.2512i | 0.609285 | + | 0.609285i | ||||
\(342\) | −3.73408 | + | 3.73408i | −0.201916 | + | 0.201916i | ||||
\(343\) | −8.75685 | − | 8.75685i | −0.472826 | − | 0.472826i | ||||
\(344\) | −3.34656 | −0.180435 | ||||||||
\(345\) | 1.97493 | + | 9.25056i | 0.106327 | + | 0.498034i | ||||
\(346\) | 8.58579 | + | 8.58579i | 0.461575 | + | 0.461575i | ||||
\(347\) | − | 6.84918i | − | 0.367683i | −0.982956 | − | 0.183842i | \(-0.941147\pi\) | ||
0.982956 | − | 0.183842i | \(-0.0588533\pi\) | |||||||
\(348\) | −4.61737 | −0.247517 | ||||||||
\(349\) | 11.3003i | 0.604891i | 0.953167 | + | 0.302445i | \(0.0978030\pi\) | ||||
−0.953167 | + | 0.302445i | \(0.902197\pi\) | |||||||
\(350\) | 5.66910 | − | 14.8480i | 0.303026 | − | 0.793657i | ||||
\(351\) | −3.40439 | + | 3.40439i | −0.181713 | + | 0.181713i | ||||
\(352\) | −5.65930 | −0.301641 | ||||||||
\(353\) | −21.3525 | −1.13648 | −0.568240 | − | 0.822863i | \(-0.692375\pi\) | ||||
−0.568240 | + | 0.822863i | \(0.692375\pi\) | |||||||
\(354\) | −13.9261 | −0.740162 | ||||||||
\(355\) | −11.4853 | − | 7.44401i | −0.609576 | − | 0.395087i | ||||
\(356\) | −10.1878 | − | 10.1878i | −0.539950 | − | 0.539950i | ||||
\(357\) | − | 24.1063i | − | 1.27584i | ||||||
\(358\) | 14.0961 | − | 14.0961i | 0.745000 | − | 0.745000i | ||||
\(359\) | − | 5.23042i | − | 0.276051i | −0.990429 | − | 0.138025i | \(-0.955924\pi\) | ||
0.990429 | − | 0.138025i | \(-0.0440756\pi\) | |||||||
\(360\) | −1.87641 | − | 1.21617i | −0.0988957 | − | 0.0640978i | ||||
\(361\) | − | 8.88674i | − | 0.467723i | ||||||
\(362\) | 13.7831i | 0.724424i | ||||||||
\(363\) | −14.8688 | + | 14.8688i | −0.780408 | + | 0.780408i | ||||
\(364\) | −10.8215 | − | 10.8215i | −0.567199 | − | 0.567199i | ||||
\(365\) | −8.00344 | + | 1.70868i | −0.418919 | + | 0.0894362i | ||||
\(366\) | −1.58187 | −0.0826858 | ||||||||
\(367\) | −0.560713 | + | 0.560713i | −0.0292690 | + | 0.0292690i | −0.721590 | − | 0.692321i | \(-0.756588\pi\) |
0.692321 | + | 0.721590i | \(0.256588\pi\) | |||||||
\(368\) | 4.23021i | 0.220515i | ||||||||
\(369\) | −2.43043 | −0.126523 | ||||||||
\(370\) | 13.3799 | − | 2.44521i | 0.695586 | − | 0.127120i | ||||
\(371\) | −36.0552 | −1.87189 | ||||||||
\(372\) | 2.81158i | 0.145774i | ||||||||
\(373\) | 3.16048 | − | 3.16048i | 0.163643 | − | 0.163643i | −0.620535 | − | 0.784179i | \(-0.713085\pi\) |
0.784179 | + | 0.620535i | \(0.213085\pi\) | |||||||
\(374\) | 42.9186 | 2.21927 | ||||||||
\(375\) | 6.59592 | + | 9.02739i | 0.340612 | + | 0.466173i | ||||
\(376\) | −6.04560 | − | 6.04560i | −0.311778 | − | 0.311778i | ||||
\(377\) | 15.7193 | − | 15.7193i | 0.809586 | − | 0.809586i | ||||
\(378\) | 3.17868i | 0.163494i | ||||||||
\(379\) | − | 1.59897i | − | 0.0821335i | −0.999156 | − | 0.0410667i | \(-0.986924\pi\) | ||
0.999156 | − | 0.0410667i | \(-0.0130756\pi\) | |||||||
\(380\) | 11.5480 | − | 2.46541i | 0.592398 | − | 0.126473i | ||||
\(381\) | 20.6597i | 1.05843i | ||||||||
\(382\) | −18.4453 | + | 18.4453i | −0.943746 | + | 0.943746i | ||||
\(383\) | 1.83857i | 0.0939464i | 0.998896 | + | 0.0469732i | \(0.0149575\pi\) | ||||
−0.998896 | + | 0.0469732i | \(0.985042\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | −8.39846 | − | 39.3384i | −0.428025 | − | 2.00487i | ||||
\(386\) | 22.9897 | 1.17015 | ||||||||
\(387\) | −3.34656 | −0.170115 | ||||||||
\(388\) | 2.87834 | 0.146125 | ||||||||
\(389\) | −21.9756 | + | 21.9756i | −1.11421 | + | 1.11421i | −0.121630 | + | 0.992575i | \(0.538812\pi\) |
−0.992575 | + | 0.121630i | \(0.961188\pi\) | |||||||
\(390\) | 10.5284 | − | 2.24773i | 0.533124 | − | 0.113818i | ||||
\(391\) | − | 32.0807i | − | 1.62239i | ||||||
\(392\) | −3.10403 | −0.156777 | ||||||||
\(393\) | − | 13.0987i | − | 0.660743i | ||||||
\(394\) | −1.69341 | − | 1.69341i | −0.0853126 | − | 0.0853126i | ||||
\(395\) | −8.82367 | + | 1.88379i | −0.443967 | + | 0.0947838i | ||||
\(396\) | −5.65930 | −0.284390 | ||||||||
\(397\) | −14.3901 | − | 14.3901i | −0.722218 | − | 0.722218i | 0.246838 | − | 0.969057i | \(-0.420608\pi\) |
−0.969057 | + | 0.246838i | \(0.920608\pi\) | |||||||
\(398\) | −7.33672 | + | 7.33672i | −0.367757 | + | 0.367757i | ||||
\(399\) | −11.8695 | − | 11.8695i | −0.594217 | − | 0.594217i | ||||
\(400\) | 2.04186 | + | 4.56408i | 0.102093 | + | 0.228204i | ||||
\(401\) | −1.56403 | + | 1.56403i | −0.0781040 | + | 0.0781040i | −0.745080 | − | 0.666976i | \(-0.767589\pi\) |
0.666976 | + | 0.745080i | \(0.267589\pi\) | |||||||
\(402\) | 9.77458i | 0.487512i | ||||||||
\(403\) | −9.57170 | − | 9.57170i | −0.476800 | − | 0.476800i | ||||
\(404\) | 16.0893i | 0.800474i | ||||||||
\(405\) | −1.87641 | − | 1.21617i | −0.0932398 | − | 0.0604320i | ||||
\(406\) | − | 14.6772i | − | 0.728416i | ||||||
\(407\) | 25.0508 | − | 23.6110i | 1.24172 | − | 1.17036i | ||||
\(408\) | 5.36251 | + | 5.36251i | 0.265484 | + | 0.265484i | ||||
\(409\) | −6.64945 | − | 6.64945i | −0.328794 | − | 0.328794i | 0.523334 | − | 0.852128i | \(-0.324688\pi\) |
−0.852128 | + | 0.523334i | \(0.824688\pi\) | |||||||
\(410\) | 4.56050 | + | 2.95582i | 0.225227 | + | 0.145978i | ||||
\(411\) | − | 2.31858i | − | 0.114367i | ||||||
\(412\) | −11.0997 | −0.546845 | ||||||||
\(413\) | − | 44.2665i | − | 2.17821i | ||||||
\(414\) | 4.23021i | 0.207903i | ||||||||
\(415\) | 0.598346 | + | 2.80265i | 0.0293716 | + | 0.137577i | ||||
\(416\) | 4.81453 | 0.236052 | ||||||||
\(417\) | 12.6877 | − | 12.6877i | 0.621321 | − | 0.621321i | ||||
\(418\) | 21.1323 | − | 21.1323i | 1.03361 | − | 1.03361i | ||||
\(419\) | 22.2951i | 1.08919i | 0.838701 | + | 0.544593i | \(0.183316\pi\) | ||||
−0.838701 | + | 0.544593i | \(0.816684\pi\) | |||||||
\(420\) | 3.86582 | − | 5.96453i | 0.188633 | − | 0.291039i | ||||
\(421\) | −1.74485 | + | 1.74485i | −0.0850387 | + | 0.0850387i | −0.748347 | − | 0.663308i | \(-0.769152\pi\) |
0.663308 | + | 0.748347i | \(0.269152\pi\) | |||||||
\(422\) | 11.9466i | 0.581549i | ||||||||
\(423\) | −6.04560 | − | 6.04560i | −0.293947 | − | 0.293947i | ||||
\(424\) | 8.02058 | − | 8.02058i | 0.389514 | − | 0.389514i | ||||
\(425\) | −15.4849 | − | 34.6127i | −0.751130 | − | 1.67896i | ||||
\(426\) | −4.32811 | − | 4.32811i | −0.209697 | − | 0.209697i | ||||
\(427\) | − | 5.02827i | − | 0.243335i | ||||||
\(428\) | −8.64549 | + | 8.64549i | −0.417896 | + | 0.417896i | ||||
\(429\) | 19.2664 | − | 19.2664i | 0.930192 | − | 0.930192i | ||||
\(430\) | 6.27954 | + | 4.06999i | 0.302826 | + | 0.196272i | ||||
\(431\) | −23.7856 | + | 23.7856i | −1.14571 | + | 1.14571i | −0.158327 | + | 0.987387i | \(0.550610\pi\) |
−0.987387 | + | 0.158327i | \(0.949390\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −9.00285 | − | 9.00285i | −0.432649 | − | 0.432649i | 0.456879 | − | 0.889529i | \(-0.348967\pi\) |
−0.889529 | + | 0.456879i | \(0.848967\pi\) | |||||||
\(434\) | −8.93712 | −0.428995 | ||||||||
\(435\) | 8.66411 | + | 5.61551i | 0.415412 | + | 0.269243i | ||||
\(436\) | 13.7592 | − | 13.7592i | 0.658948 | − | 0.658948i | ||||
\(437\) | −15.7959 | − | 15.7959i | −0.755622 | − | 0.755622i | ||||
\(438\) | −3.65991 | −0.174877 | ||||||||
\(439\) | −4.79636 | − | 4.79636i | −0.228918 | − | 0.228918i | 0.583323 | − | 0.812240i | \(-0.301752\pi\) |
−0.812240 | + | 0.583323i | \(0.801752\pi\) | |||||||
\(440\) | 10.6192 | + | 6.88266i | 0.506250 | + | 0.328118i | ||||
\(441\) | −3.10403 | −0.147811 | ||||||||
\(442\) | −36.5121 | −1.73670 | ||||||||
\(443\) | 7.85980 | − | 7.85980i | 0.373430 | − | 0.373430i | −0.495295 | − | 0.868725i | \(-0.664940\pi\) |
0.868725 | + | 0.495295i | \(0.164940\pi\) | |||||||
\(444\) | 6.08010 | + | 0.179886i | 0.288549 | + | 0.00853702i | ||||
\(445\) | 6.72642 | + | 31.5065i | 0.318863 | + | 1.49355i | ||||
\(446\) | −11.0520 | + | 11.0520i | −0.523330 | + | 0.523330i | ||||
\(447\) | −6.50879 | − | 6.50879i | −0.307855 | − | 0.307855i | ||||
\(448\) | 2.24767 | − | 2.24767i | 0.106192 | − | 0.106192i | ||||
\(449\) | 16.4657 | − | 16.4657i | 0.777066 | − | 0.777066i | −0.202265 | − | 0.979331i | \(-0.564830\pi\) |
0.979331 | + | 0.202265i | \(0.0648303\pi\) | |||||||
\(450\) | 2.04186 | + | 4.56408i | 0.0962543 | + | 0.215153i | ||||
\(451\) | 13.7545 | 0.647676 | ||||||||
\(452\) | −4.68689 | −0.220453 | ||||||||
\(453\) | 3.95777 | + | 3.95777i | 0.185952 | + | 0.185952i | ||||
\(454\) | − | 6.40168i | − | 0.300446i | ||||||
\(455\) | 7.14482 | + | 33.4663i | 0.334954 | + | 1.56892i | ||||
\(456\) | 5.28079 | 0.247296 | ||||||||
\(457\) | −5.42876 | −0.253947 | −0.126973 | − | 0.991906i | \(-0.540526\pi\) | ||||
−0.126973 | + | 0.991906i | \(0.540526\pi\) | |||||||
\(458\) | 16.3225 | 0.762699 | ||||||||
\(459\) | 5.36251 | + | 5.36251i | 0.250300 | + | 0.250300i | ||||
\(460\) | 5.14465 | − | 7.93762i | 0.239871 | − | 0.370094i | ||||
\(461\) | 12.8604 | + | 12.8604i | 0.598967 | + | 0.598967i | 0.940038 | − | 0.341071i | \(-0.110790\pi\) |
−0.341071 | + | 0.940038i | \(0.610790\pi\) | |||||||
\(462\) | − | 17.9891i | − | 0.836929i | ||||||
\(463\) | 36.1282i | 1.67902i | 0.543345 | + | 0.839509i | \(0.317157\pi\) | ||||
−0.543345 | + | 0.839509i | \(0.682843\pi\) | |||||||
\(464\) | 3.26498 | + | 3.26498i | 0.151573 | + | 0.151573i | ||||
\(465\) | 3.41936 | − | 5.27569i | 0.158569 | − | 0.244654i | ||||
\(466\) | 0.738837 | + | 0.738837i | 0.0342260 | + | 0.0342260i | ||||
\(467\) | 4.96873 | 0.229925 | 0.114963 | − | 0.993370i | \(-0.463325\pi\) | ||||
0.114963 | + | 0.993370i | \(0.463325\pi\) | |||||||
\(468\) | 4.81453 | 0.222552 | ||||||||
\(469\) | −31.0703 | −1.43469 | ||||||||
\(470\) | 3.99158 | + | 18.6965i | 0.184118 | + | 0.862407i | ||||
\(471\) | 1.41232i | 0.0650763i | ||||||||
\(472\) | 9.84721 | + | 9.84721i | 0.453255 | + | 0.453255i | ||||
\(473\) | 18.9392 | 0.870825 | ||||||||
\(474\) | −4.03499 | −0.185333 | ||||||||
\(475\) | −24.6671 | − | 9.41815i | −1.13181 | − | 0.432135i | ||||
\(476\) | −17.0457 | + | 17.0457i | −0.781289 | + | 0.781289i | ||||
\(477\) | 8.02058 | − | 8.02058i | 0.367237 | − | 0.367237i | ||||
\(478\) | 5.10981 | + | 5.10981i | 0.233717 | + | 0.233717i | ||||
\(479\) | −21.0873 | + | 21.0873i | −0.963504 | + | 0.963504i | −0.999357 | − | 0.0358527i | \(-0.988585\pi\) |
0.0358527 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(480\) | 0.466864 | + | 2.18679i | 0.0213093 | + | 0.0998127i | ||||
\(481\) | −21.3114 | + | 20.0866i | −0.971717 | + | 0.915871i | ||||
\(482\) | 8.22613 | − | 8.22613i | 0.374690 | − | 0.374690i | ||||
\(483\) | −13.4465 | −0.611837 | ||||||||
\(484\) | 21.0276 | 0.955801 | ||||||||
\(485\) | −5.40095 | − | 3.50054i | −0.245245 | − | 0.158952i | ||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −10.6041 | −0.480519 | −0.240259 | − | 0.970709i | \(-0.577233\pi\) | ||||
−0.240259 | + | 0.970709i | \(0.577233\pi\) | |||||||
\(488\) | 1.11855 | + | 1.11855i | 0.0506345 | + | 0.0506345i | ||||
\(489\) | −5.47991 | + | 5.47991i | −0.247810 | + | 0.247810i | ||||
\(490\) | 5.82445 | + | 3.77503i | 0.263122 | + | 0.170538i | ||||
\(491\) | 2.33716 | 0.105475 | 0.0527373 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527373 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(492\) | 1.71858 | + | 1.71858i | 0.0774794 | + | 0.0774794i | ||||
\(493\) | −24.7607 | − | 24.7607i | −1.11517 | − | 1.11517i | ||||
\(494\) | −17.9778 | + | 17.9778i | −0.808862 | + | 0.808862i | ||||
\(495\) | 10.6192 | + | 6.88266i | 0.477297 | + | 0.309353i | ||||
\(496\) | 1.98809 | − | 1.98809i | 0.0892677 | − | 0.0892677i | ||||
\(497\) | 13.7577 | − | 13.7577i | 0.617116 | − | 0.617116i | ||||
\(498\) | 1.28163i | 0.0574312i | ||||||||
\(499\) | 15.9396 | + | 15.9396i | 0.713555 | + | 0.713555i | 0.967277 | − | 0.253723i | \(-0.0816550\pi\) |
−0.253723 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(500\) | 1.71931 | − | 11.0474i | 0.0768899 | − | 0.494053i | ||||
\(501\) | 13.6151 | − | 13.6151i | 0.608278 | − | 0.608278i | ||||
\(502\) | −10.0396 | − | 10.0396i | −0.448089 | − | 0.448089i | ||||
\(503\) | 18.1285i | 0.808309i | 0.914691 | + | 0.404155i | \(0.132434\pi\) | ||||
−0.914691 | + | 0.404155i | \(0.867566\pi\) | |||||||
\(504\) | 2.24767 | − | 2.24767i | 0.100119 | − | 0.100119i | ||||
\(505\) | 19.5674 | − | 30.1903i | 0.870736 | − | 1.34345i | ||||
\(506\) | − | 23.9400i | − | 1.06426i | ||||||
\(507\) | −7.19813 | + | 7.19813i | −0.319680 | + | 0.319680i | ||||
\(508\) | 14.6086 | − | 14.6086i | 0.648152 | − | 0.648152i | ||||
\(509\) | −14.6649 | −0.650010 | −0.325005 | − | 0.945712i | \(-0.605366\pi\) | ||||
−0.325005 | + | 0.945712i | \(0.605366\pi\) | |||||||
\(510\) | −3.54057 | − | 16.5840i | −0.156779 | − | 0.734352i | ||||
\(511\) | − | 11.6337i | − | 0.514644i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.28079 | 0.233153 | ||||||||
\(514\) | 15.5767i | 0.687057i | ||||||||
\(515\) | 20.8277 | + | 13.4992i | 0.917778 | + | 0.594844i | ||||
\(516\) | 2.36638 | + | 2.36638i | 0.104174 | + | 0.104174i | ||||
\(517\) | 34.2138 | + | 34.2138i | 1.50472 | + | 1.50472i | ||||
\(518\) | −0.571801 | + | 19.3267i | −0.0251235 | + | 0.849167i | ||||
\(519\) | − | 12.1421i | − | 0.532981i | ||||||
\(520\) | −9.03405 | − | 5.85528i | −0.396169 | − | 0.256771i | ||||
\(521\) | − | 13.9917i | − | 0.612988i | −0.951873 | − | 0.306494i | \(-0.900844\pi\) | ||
0.951873 | − | 0.306494i | \(-0.0991560\pi\) | |||||||
\(522\) | 3.26498 | + | 3.26498i | 0.142904 | + | 0.142904i | ||||
\(523\) | 16.6140i | 0.726479i | 0.931696 | + | 0.363239i | \(0.118329\pi\) | ||||
−0.931696 | + | 0.363239i | \(0.881671\pi\) | |||||||
\(524\) | −9.26219 | + | 9.26219i | −0.404621 | + | 0.404621i | ||||
\(525\) | −14.5078 | + | 6.49044i | −0.633170 | + | 0.283266i | ||||
\(526\) | 17.2063 | + | 17.2063i | 0.750230 | + | 0.750230i | ||||
\(527\) | −15.0771 | + | 15.0771i | −0.656769 | + | 0.656769i | ||||
\(528\) | 4.00173 | + | 4.00173i | 0.174153 | + | 0.174153i | ||||
\(529\) | 5.10534 | 0.221971 | ||||||||
\(530\) | −24.8043 | + | 5.29555i | −1.07743 | + | 0.230024i | ||||
\(531\) | 9.84721 | + | 9.84721i | 0.427332 | + | 0.427332i | ||||
\(532\) | 16.7860i | 0.727764i | ||||||||
\(533\) | −11.7014 | −0.506844 | ||||||||
\(534\) | 14.4077i | 0.623481i | ||||||||
\(535\) | 26.7369 | − | 5.70814i | 1.15594 | − | 0.246784i | ||||
\(536\) | 6.91167 | − | 6.91167i | 0.298539 | − | 0.298539i | ||||
\(537\) | −19.9348 | −0.860251 | ||||||||
\(538\) | −16.7896 | −0.723853 | ||||||||
\(539\) | 17.5666 | 0.756648 | ||||||||
\(540\) | 0.466864 | + | 2.18679i | 0.0200906 | + | 0.0941043i | ||||
\(541\) | −15.0297 | − | 15.0297i | −0.646177 | − | 0.646177i | 0.305890 | − | 0.952067i | \(-0.401046\pi\) |
−0.952067 | + | 0.305890i | \(0.901046\pi\) | |||||||
\(542\) | − | 3.47058i | − | 0.149074i | ||||||
\(543\) | 9.74613 | − | 9.74613i | 0.418246 | − | 0.418246i | ||||
\(544\) | − | 7.58373i | − | 0.325150i | ||||||
\(545\) | −42.5516 | + | 9.08447i | −1.82271 | + | 0.389136i | ||||
\(546\) | 15.3039i | 0.654945i | ||||||||
\(547\) | 1.60901i | 0.0687964i | 0.999408 | + | 0.0343982i | \(0.0109514\pi\) | ||||
−0.999408 | + | 0.0343982i | \(0.989049\pi\) | |||||||
\(548\) | −1.63948 | + | 1.63948i | −0.0700353 | + | 0.0700353i | ||||
\(549\) | 1.11855 | + | 1.11855i | 0.0477387 | + | 0.0477387i | ||||
\(550\) | −11.5555 | − | 25.8295i | −0.492728 | − | 1.10137i | ||||
\(551\) | −24.3834 | −1.03877 | ||||||||
\(552\) | 2.99121 | − | 2.99121i | 0.127314 | − | 0.127314i | ||||
\(553\) | − | 12.8260i | − | 0.545416i | ||||||
\(554\) | −5.08835 | −0.216183 | ||||||||
\(555\) | −11.1900 | − | 7.73198i | −0.474990 | − | 0.328204i | ||||
\(556\) | −17.9432 | −0.760959 | ||||||||
\(557\) | 13.8846i | 0.588309i | 0.955758 | + | 0.294155i | \(0.0950381\pi\) | ||||
−0.955758 | + | 0.294155i | \(0.904962\pi\) | |||||||
\(558\) | 1.98809 | − | 1.98809i | 0.0841624 | − | 0.0841624i | ||||
\(559\) | −16.1121 | −0.681470 | ||||||||
\(560\) | −6.95110 | + | 1.48401i | −0.293738 | + | 0.0627109i | ||||
\(561\) | −30.3480 | − | 30.3480i | −1.28129 | − | 1.28129i | ||||
\(562\) | −22.3585 | + | 22.3585i | −0.943138 | + | 0.943138i | ||||
\(563\) | − | 36.2994i | − | 1.52984i | −0.644126 | − | 0.764919i | \(-0.722779\pi\) | ||
0.644126 | − | 0.764919i | \(-0.277221\pi\) | |||||||
\(564\) | 8.54977i | 0.360010i | ||||||||
\(565\) | 8.79456 | + | 5.70006i | 0.369990 | + | 0.239803i | ||||
\(566\) | − | 4.97011i | − | 0.208909i | ||||||
\(567\) | 2.24767 | − | 2.24767i | 0.0943932 | − | 0.0943932i | ||||
\(568\) | 6.12087i | 0.256826i | ||||||||
\(569\) | −4.09043 | − | 4.09043i | −0.171480 | − | 0.171480i | 0.616149 | − | 0.787629i | \(-0.288692\pi\) |
−0.787629 | + | 0.616149i | \(0.788692\pi\) | |||||||
\(570\) | −9.90895 | − | 6.42234i | −0.415040 | − | 0.269002i | ||||
\(571\) | 9.17017 | 0.383760 | 0.191880 | − | 0.981418i | \(-0.438542\pi\) | ||||
0.191880 | + | 0.981418i | \(0.438542\pi\) | |||||||
\(572\) | −27.2468 | −1.13925 | ||||||||
\(573\) | 26.0857 | 1.08974 | ||||||||
\(574\) | −5.46281 | + | 5.46281i | −0.228013 | + | 0.228013i | ||||
\(575\) | −19.3070 | + | 8.63750i | −0.805157 | + | 0.360209i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −35.0406 | −1.45876 | −0.729381 | − | 0.684108i | \(-0.760192\pi\) | ||||
−0.729381 | + | 0.684108i | \(0.760192\pi\) | |||||||
\(578\) | 40.5129i | 1.68512i | ||||||||
\(579\) | −16.2562 | − | 16.2562i | −0.675585 | − | 0.675585i | ||||
\(580\) | −2.15568 | − | 10.0972i | −0.0895099 | − | 0.419264i | ||||
\(581\) | −4.07389 | −0.169014 | ||||||||
\(582\) | −2.03529 | − | 2.03529i | −0.0843655 | − | 0.0843655i | ||||
\(583\) | −45.3908 | + | 45.3908i | −1.87990 | + | 1.87990i | ||||
\(584\) | 2.58794 | + | 2.58794i | 0.107090 | + | 0.107090i | ||||
\(585\) | −9.03405 | − | 5.85528i | −0.373512 | − | 0.242086i | ||||
\(586\) | 3.76385 | − | 3.76385i | 0.155483 | − | 0.155483i | ||||
\(587\) | − | 33.5312i | − | 1.38398i | −0.721907 | − | 0.691990i | \(-0.756734\pi\) | ||
0.721907 | − | 0.691990i | \(-0.243266\pi\) | |||||||
\(588\) | 2.19488 | + | 2.19488i | 0.0905153 | + | 0.0905153i | ||||
\(589\) | 14.8474i | 0.611775i | ||||||||
\(590\) | −6.50157 | − | 30.4533i | −0.267665 | − | 1.25374i | ||||
\(591\) | 2.39484i | 0.0985106i | ||||||||
\(592\) | −4.17208 | − | 4.42648i | −0.171472 | − | 0.181927i | ||||
\(593\) | 1.10793 | + | 1.10793i | 0.0454971 | + | 0.0454971i | 0.729489 | − | 0.683992i | \(-0.239758\pi\) |
−0.683992 | + | 0.729489i | \(0.739758\pi\) | |||||||
\(594\) | 4.00173 | + | 4.00173i | 0.164193 | + | 0.164193i | ||||
\(595\) | 52.7153 | − | 11.2543i | 2.16112 | − | 0.461383i | ||||
\(596\) | 9.20482i | 0.377044i | ||||||||
\(597\) | 10.3757 | 0.424649 | ||||||||
\(598\) | 20.3665i | 0.832846i | ||||||||
\(599\) | 0.823976i | 0.0336668i | 0.999858 | + | 0.0168334i | \(0.00535848\pi\) | ||||
−0.999858 | + | 0.0168334i | \(0.994642\pi\) | |||||||
\(600\) | 1.78347 | − | 4.67110i | 0.0728100 | − | 0.190697i | ||||
\(601\) | 7.88760 | 0.321742 | 0.160871 | − | 0.986975i | \(-0.448570\pi\) | ||||
0.160871 | + | 0.986975i | \(0.448570\pi\) | |||||||
\(602\) | −7.52196 | + | 7.52196i | −0.306572 | + | 0.306572i | ||||
\(603\) | 6.91167 | − | 6.91167i | 0.281465 | − | 0.281465i | ||||
\(604\) | − | 5.59713i | − | 0.227744i | ||||||
\(605\) | −39.4565 | − | 25.5732i | −1.60414 | − | 1.03970i | ||||
\(606\) | 11.3769 | − | 11.3769i | 0.462154 | − | 0.462154i | ||||
\(607\) | − | 1.34105i | − | 0.0544316i | −0.999630 | − | 0.0272158i | \(-0.991336\pi\) | ||
0.999630 | − | 0.0272158i | \(-0.00866413\pi\) | |||||||
\(608\) | −3.73408 | − | 3.73408i | −0.151437 | − | 0.151437i | ||||
\(609\) | −10.3783 | + | 10.3783i | −0.420551 | + | 0.420551i | ||||
\(610\) | −0.738519 | − | 3.45922i | −0.0299018 | − | 0.140060i | ||||
\(611\) | −29.1067 | − | 29.1067i | −1.17753 | − | 1.17753i | ||||
\(612\) | − | 7.58373i | − | 0.306554i | ||||||
\(613\) | 3.50859 | − | 3.50859i | 0.141711 | − | 0.141711i | −0.632693 | − | 0.774403i | \(-0.718050\pi\) |
0.774403 | + | 0.632693i | \(0.218050\pi\) | |||||||
\(614\) | 10.3413 | − | 10.3413i | 0.417342 | − | 0.417342i | ||||
\(615\) | −1.13468 | − | 5.31484i | −0.0457548 | − | 0.214315i | ||||
\(616\) | −12.7202 | + | 12.7202i | −0.512512 | + | 0.512512i | ||||
\(617\) | 1.91217 | + | 1.91217i | 0.0769810 | + | 0.0769810i | 0.744549 | − | 0.667568i | \(-0.232665\pi\) |
−0.667568 | + | 0.744549i | \(0.732665\pi\) | |||||||
\(618\) | 7.84870 | + | 7.84870i | 0.315721 | + | 0.315721i | ||||
\(619\) | 19.7786 | 0.794968 | 0.397484 | − | 0.917609i | \(-0.369883\pi\) | ||||
0.397484 | + | 0.917609i | \(0.369883\pi\) | |||||||
\(620\) | −6.14832 | + | 1.31262i | −0.246923 | + | 0.0527162i | ||||
\(621\) | 2.99121 | − | 2.99121i | 0.120033 | − | 0.120033i | ||||
\(622\) | 2.08224 | + | 2.08224i | 0.0834904 | + | 0.0834904i | ||||
\(623\) | −45.7974 | −1.83484 | ||||||||
\(624\) | −3.40439 | − | 3.40439i | −0.136285 | − | 0.136285i | ||||
\(625\) | −16.6616 | + | 18.6384i | −0.666464 | + | 0.745538i | ||||
\(626\) | 5.86237 | 0.234308 | ||||||||
\(627\) | −29.8855 | −1.19351 | ||||||||
\(628\) | 0.998661 | − | 0.998661i | 0.0398509 | − | 0.0398509i | ||||
\(629\) | 31.6399 | + | 33.5692i | 1.26157 | + | 1.33849i | ||||
\(630\) | −6.95110 | + | 1.48401i | −0.276939 | + | 0.0591244i | ||||
\(631\) | −2.64808 | + | 2.64808i | −0.105418 | + | 0.105418i | −0.757849 | − | 0.652430i | \(-0.773749\pi\) |
0.652430 | + | 0.757849i | \(0.273749\pi\) | |||||||
\(632\) | 2.85317 | + | 2.85317i | 0.113493 | + | 0.113493i | ||||
\(633\) | 8.44749 | − | 8.44749i | 0.335758 | − | 0.335758i | ||||
\(634\) | 3.30695 | − | 3.30695i | 0.131336 | − | 0.131336i | ||||
\(635\) | −45.1783 | + | 9.64526i | −1.79285 | + | 0.382760i | ||||
\(636\) | −11.3428 | −0.449772 | ||||||||
\(637\) | −14.9444 | −0.592120 | ||||||||
\(638\) | −18.4775 | − | 18.4775i | −0.731530 | − | 0.731530i | ||||
\(639\) | 6.12087i | 0.242138i | ||||||||
\(640\) | 1.21617 | − | 1.87641i | 0.0480733 | − | 0.0741718i | ||||
\(641\) | −25.9245 | −1.02395 | −0.511977 | − | 0.858999i | \(-0.671087\pi\) | ||||
−0.511977 | + | 0.858999i | \(0.671087\pi\) | |||||||
\(642\) | 12.2266 | 0.482544 | ||||||||
\(643\) | −6.75346 | −0.266331 | −0.133165 | − | 0.991094i | \(-0.542514\pi\) | ||||
−0.133165 | + | 0.991094i | \(0.542514\pi\) | |||||||
\(644\) | 9.50811 | + | 9.50811i | 0.374672 | + | 0.374672i | ||||
\(645\) | −1.56239 | − | 7.31822i | −0.0615190 | − | 0.288155i | ||||
\(646\) | 28.3183 | + | 28.3183i | 1.11417 | + | 1.11417i | ||||
\(647\) | − | 17.0199i | − | 0.669122i | −0.942374 | − | 0.334561i | \(-0.891412\pi\) | ||
0.942374 | − | 0.334561i | \(-0.108588\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −55.7283 | − | 55.7283i | −2.18753 | − | 2.18753i | ||||
\(650\) | 9.83061 | + | 21.9739i | 0.385588 | + | 0.861886i | ||||
\(651\) | 6.31950 | + | 6.31950i | 0.247681 | + | 0.247681i | ||||
\(652\) | 7.74976 | 0.303504 | ||||||||
\(653\) | 2.21356 | 0.0866234 | 0.0433117 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433117 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(654\) | −19.4585 | −0.760888 | ||||||||
\(655\) | 28.6441 | − | 6.11531i | 1.11922 | − | 0.238945i | ||||
\(656\) | − | 2.43043i | − | 0.0948925i | ||||||
\(657\) | 2.58794 | + | 2.58794i | 0.100965 | + | 0.100965i | ||||
\(658\) | −27.1770 | −1.05947 | ||||||||
\(659\) | −10.5454 | −0.410790 | −0.205395 | − | 0.978679i | \(-0.565848\pi\) | ||||
−0.205395 | + | 0.978679i | \(0.565848\pi\) | |||||||
\(660\) | −2.64212 | − | 12.3757i | −0.102844 | − | 0.481722i | ||||
\(661\) | 26.5280 | − | 26.5280i | 1.03182 | − | 1.03182i | 0.0323414 | − | 0.999477i | \(-0.489704\pi\) |
0.999477 | − | 0.0323414i | \(-0.0102964\pi\) | |||||||
\(662\) | −2.03744 | + | 2.03744i | −0.0791872 | + | 0.0791872i | ||||
\(663\) | 25.8179 | + | 25.8179i | 1.00269 | + | 1.00269i | ||||
\(664\) | 0.906248 | − | 0.906248i | 0.0351693 | − | 0.0351693i | ||||
\(665\) | 20.4146 | − | 31.4974i | 0.791643 | − | 1.22142i | ||||
\(666\) | −4.17208 | − | 4.42648i | −0.161665 | − | 0.171523i | ||||
\(667\) | −13.8115 | + | 13.8115i | −0.534784 | + | 0.534784i | ||||
\(668\) | −19.2547 | −0.744985 | ||||||||
\(669\) | 15.6300 | 0.604289 | ||||||||
\(670\) | −21.3749 | + | 4.56340i | −0.825786 | + | 0.176299i | ||||
\(671\) | −6.33022 | − | 6.33022i | −0.244375 | − | 0.244375i | ||||
\(672\) | −3.17868 | −0.122620 | ||||||||
\(673\) | −18.5100 | − | 18.5100i | −0.713507 | − | 0.713507i | 0.253760 | − | 0.967267i | \(-0.418333\pi\) |
−0.967267 | + | 0.253760i | \(0.918333\pi\) | |||||||
\(674\) | −4.38679 | + | 4.38679i | −0.168973 | + | 0.168973i | ||||
\(675\) | 1.78347 | − | 4.67110i | 0.0686460 | − | 0.179791i | ||||
\(676\) | 10.1797 | 0.391527 | ||||||||
\(677\) | 19.4458 | + | 19.4458i | 0.747364 | + | 0.747364i | 0.973983 | − | 0.226620i | \(-0.0727674\pi\) |
−0.226620 | + | 0.973983i | \(0.572767\pi\) | |||||||
\(678\) | 3.31414 | + | 3.31414i | 0.127279 | + | 0.127279i | ||||
\(679\) | 6.46955 | − | 6.46955i | 0.248278 | − | 0.248278i | ||||
\(680\) | −9.22310 | + | 14.2302i | −0.353690 | + | 0.545704i | ||||
\(681\) | −4.52667 | + | 4.52667i | −0.173462 | + | 0.173462i | ||||
\(682\) | −11.2512 | + | 11.2512i | −0.430830 | + | 0.430830i | ||||
\(683\) | 45.5661i | 1.74354i | 0.489916 | + | 0.871770i | \(0.337028\pi\) | ||||
−0.489916 | + | 0.871770i | \(0.662972\pi\) | |||||||
\(684\) | −3.73408 | − | 3.73408i | −0.142776 | − | 0.142776i | ||||
\(685\) | 5.07024 | − | 1.08246i | 0.193724 | − | 0.0413587i | ||||
\(686\) | 8.75685 | − | 8.75685i | 0.334338 | − | 0.334338i | ||||
\(687\) | −11.5417 | − | 11.5417i | −0.440345 | − | 0.440345i | ||||
\(688\) | − | 3.34656i | − | 0.127587i | ||||||
\(689\) | 38.6153 | − | 38.6153i | 1.47113 | − | 1.47113i | ||||
\(690\) | −9.25056 | + | 1.97493i | −0.352163 | + | 0.0751843i | ||||
\(691\) | 14.6674i | 0.557973i | 0.960295 | + | 0.278986i | \(0.0899984\pi\) | ||||
−0.960295 | + | 0.278986i | \(0.910002\pi\) | |||||||
\(692\) | −8.58579 | + | 8.58579i | −0.326383 | + | 0.326383i | ||||
\(693\) | −12.7202 | + | 12.7202i | −0.483201 | + | 0.483201i | ||||
\(694\) | 6.84918 | 0.259991 | ||||||||
\(695\) | 33.6688 | + | 21.8219i | 1.27713 | + | 0.827753i | ||||
\(696\) | − | 4.61737i | − | 0.175021i | ||||||
\(697\) | 18.4317i | 0.698152i | ||||||||
\(698\) | −11.3003 | −0.427722 | ||||||||
\(699\) | − | 1.04487i | − | 0.0395207i | ||||||
\(700\) | 14.8480 | + | 5.66910i | 0.561200 | + | 0.214272i | ||||
\(701\) | −2.72887 | − | 2.72887i | −0.103068 | − | 0.103068i | 0.653692 | − | 0.756760i | \(-0.273219\pi\) |
−0.756760 | + | 0.653692i | \(0.773219\pi\) | |||||||
\(702\) | −3.40439 | − | 3.40439i | −0.128490 | − | 0.128490i | ||||
\(703\) | 32.1077 | + | 0.949941i | 1.21097 | + | 0.0358277i | ||||
\(704\) | − | 5.65930i | − | 0.213293i | ||||||
\(705\) | 10.3980 | − | 16.0429i | 0.391610 | − | 0.604211i | ||||
\(706\) | − | 21.3525i | − | 0.803612i | ||||||
\(707\) | 36.1635 | + | 36.1635i | 1.36007 | + | 1.36007i | ||||
\(708\) | − | 13.9261i | − | 0.523373i | ||||||
\(709\) | −1.20334 | + | 1.20334i | −0.0451926 | + | 0.0451926i | −0.729342 | − | 0.684149i | \(-0.760174\pi\) |
0.684149 | + | 0.729342i | \(0.260174\pi\) | |||||||
\(710\) | 7.44401 | − | 11.4853i | 0.279369 | − | 0.431035i | ||||
\(711\) | 2.85317 | + | 2.85317i | 0.107002 | + | 0.107002i | ||||
\(712\) | 10.1878 | − | 10.1878i | 0.381803 | − | 0.381803i | ||||
\(713\) | 8.41002 | + | 8.41002i | 0.314958 | + | 0.314958i | ||||
\(714\) | 24.1063 | 0.902155 | ||||||||
\(715\) | 51.1264 | + | 33.1368i | 1.91202 | + | 1.23925i | ||||
\(716\) | 14.0961 | + | 14.0961i | 0.526794 | + | 0.526794i | ||||
\(717\) | − | 7.22636i | − | 0.269873i | ||||||
\(718\) | 5.23042 | 0.195197 | ||||||||
\(719\) | − | 34.8068i | − | 1.29807i | −0.760757 | − | 0.649037i | \(-0.775172\pi\) | ||
0.760757 | − | 0.649037i | \(-0.224828\pi\) | |||||||
\(720\) | 1.21617 | − | 1.87641i | 0.0453240 | − | 0.0699298i | ||||
\(721\) | −24.9485 | + | 24.9485i | −0.929131 | + | 0.929131i | ||||
\(722\) | 8.88674 | 0.330730 | ||||||||
\(723\) | −11.6335 | −0.432655 | ||||||||
\(724\) | −13.7831 | −0.512245 | ||||||||
\(725\) | −8.23497 | + | 21.5682i | −0.305839 | + | 0.801024i | ||||
\(726\) | −14.8688 | − | 14.8688i | −0.551832 | − | 0.551832i | ||||
\(727\) | 29.0229i | 1.07640i | 0.842817 | + | 0.538200i | \(0.180895\pi\) | ||||
−0.842817 | + | 0.538200i | \(0.819105\pi\) | |||||||
\(728\) | 10.8215 | − | 10.8215i | 0.401070 | − | 0.401070i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.70868 | − | 8.00344i | −0.0632410 | − | 0.296220i | ||||
\(731\) | 25.3794i | 0.938692i | ||||||||
\(732\) | − | 1.58187i | − | 0.0584677i | ||||||
\(733\) | −6.55654 | + | 6.55654i | −0.242171 | + | 0.242171i | −0.817748 | − | 0.575577i | \(-0.804778\pi\) |
0.575577 | + | 0.817748i | \(0.304778\pi\) | |||||||
\(734\) | −0.560713 | − | 0.560713i | −0.0206963 | − | 0.0206963i | ||||
\(735\) | −1.44916 | − | 6.78785i | −0.0534530 | − | 0.250374i | ||||
\(736\) | −4.23021 | −0.155928 | ||||||||
\(737\) | −39.1152 | + | 39.1152i | −1.44083 | + | 1.44083i | ||||
\(738\) | − | 2.43043i | − | 0.0894655i | ||||||
\(739\) | −3.57785 | −0.131613 | −0.0658067 | − | 0.997832i | \(-0.520962\pi\) | ||||
−0.0658067 | + | 0.997832i | \(0.520962\pi\) | |||||||
\(740\) | 2.44521 | + | 13.3799i | 0.0898876 | + | 0.491854i | ||||
\(741\) | 25.4245 | 0.933993 | ||||||||
\(742\) | − | 36.0552i | − | 1.32363i | ||||||
\(743\) | −29.2655 | + | 29.2655i | −1.07365 | + | 1.07365i | −0.0765832 | + | 0.997063i | \(0.524401\pi\) |
−0.997063 | + | 0.0765832i | \(0.975599\pi\) | |||||||
\(744\) | −2.81158 | −0.103077 | ||||||||
\(745\) | 11.1946 | − | 17.2720i | 0.410139 | − | 0.632799i | ||||
\(746\) | 3.16048 | + | 3.16048i | 0.115713 | + | 0.115713i | ||||
\(747\) | 0.906248 | − | 0.906248i | 0.0331579 | − | 0.0331579i | ||||
\(748\) | 42.9186i | 1.56926i | ||||||||
\(749\) | 38.8644i | 1.42007i | ||||||||
\(750\) | −9.02739 | + | 6.59592i | −0.329634 | + | 0.240849i | ||||
\(751\) | − | 17.5101i | − | 0.638951i | −0.947595 | − | 0.319476i | \(-0.896493\pi\) | ||
0.947595 | − | 0.319476i | \(-0.103507\pi\) | |||||||
\(752\) | 6.04560 | − | 6.04560i | 0.220460 | − | 0.220460i | ||||
\(753\) | 14.1981i | 0.517409i | ||||||||
\(754\) | 15.7193 | + | 15.7193i | 0.572464 | + | 0.572464i | ||||
\(755\) | −6.80705 | + | 10.5025i | −0.247734 | + | 0.382226i | ||||
\(756\) | −3.17868 | −0.115608 | ||||||||
\(757\) | −15.4393 | −0.561153 | −0.280576 | − | 0.959832i | \(-0.590526\pi\) | ||||
−0.280576 | + | 0.959832i | \(0.590526\pi\) | |||||||
\(758\) | 1.59897 | 0.0580771 | ||||||||
\(759\) | −16.9281 | + | 16.9281i | −0.614452 | + | 0.614452i | ||||
\(760\) | 2.46541 | + | 11.5480i | 0.0894298 | + | 0.418889i | ||||
\(761\) | − | 19.6274i | − | 0.711492i | −0.934583 | − | 0.355746i | \(-0.884227\pi\) | ||
0.934583 | − | 0.355746i | \(-0.115773\pi\) | |||||||
\(762\) | −20.6597 | −0.748422 | ||||||||
\(763\) | − | 61.8524i | − | 2.23921i | ||||||
\(764\) | −18.4453 | − | 18.4453i | −0.667329 | − | 0.667329i | ||||
\(765\) | −9.22310 | + | 14.2302i | −0.333462 | + | 0.514495i | ||||
\(766\) | −1.83857 | −0.0664301 | ||||||||
\(767\) | 47.4097 | + | 47.4097i | 1.71186 | + | 1.71186i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 38.3252 | + | 38.3252i | 1.38204 | + | 1.38204i | 0.840985 | + | 0.541058i | \(0.181976\pi\) |
0.541058 | + | 0.840985i | \(0.318024\pi\) | |||||||
\(770\) | 39.3384 | − | 8.39846i | 1.41766 | − | 0.302660i | ||||
\(771\) | 11.0144 | − | 11.0144i | 0.396672 | − | 0.396672i | ||||
\(772\) | 22.9897i | 0.827419i | ||||||||
\(773\) | 13.6080 | + | 13.6080i | 0.489445 | + | 0.489445i | 0.908131 | − | 0.418686i | \(-0.137509\pi\) |
−0.418686 | + | 0.908131i | \(0.637509\pi\) | |||||||
\(774\) | − | 3.34656i | − | 0.120290i | ||||||
\(775\) | 13.1332 | + | 5.01438i | 0.471758 | + | 0.180122i | ||||
\(776\) | 2.87834i | 0.103326i | ||||||||
\(777\) | 14.0704 | − | 13.2617i | 0.504772 | − | 0.475762i | ||||
\(778\) | −21.9756 | − | 21.9756i | −0.787862 | − | 0.787862i | ||||
\(779\) | 9.07544 | + | 9.07544i | 0.325161 | + | 0.325161i | ||||
\(780\) | 2.24773 | + | 10.5284i | 0.0804816 | + | 0.376975i | ||||
\(781\) | − | 34.6398i | − | 1.23951i | ||||||
\(782\) | 32.0807 | 1.14721 | ||||||||
\(783\) | − | 4.61737i | − | 0.165011i | ||||||
\(784\) | − | 3.10403i | − | 0.110858i | ||||||
\(785\) | −3.08844 | + | 0.659361i | −0.110231 | + | 0.0235336i | ||||
\(786\) | 13.0987 | 0.467216 | ||||||||
\(787\) | 0.848326 | − | 0.848326i | 0.0302396 | − | 0.0302396i | −0.691825 | − | 0.722065i | \(-0.743193\pi\) |
0.722065 | + | 0.691825i | \(0.243193\pi\) | |||||||
\(788\) | 1.69341 | − | 1.69341i | 0.0603251 | − | 0.0603251i | ||||
\(789\) | − | 24.3334i | − | 0.866291i | ||||||
\(790\) | −1.88379 | − | 8.82367i | −0.0670223 | − | 0.313932i | ||||
\(791\) | −10.5346 | + | 10.5346i | −0.374567 | + | 0.374567i | ||||
\(792\) | − | 5.65930i | − | 0.201094i | ||||||
\(793\) | 5.38530 | + | 5.38530i | 0.191238 | + | 0.191238i | ||||
\(794\) | 14.3901 | − | 14.3901i | 0.510686 | − | 0.510686i | ||||
\(795\) | 21.2838 | + | 13.7948i | 0.754859 | + | 0.489251i | ||||
\(796\) | −7.33672 | − | 7.33672i | −0.260043 | − | 0.260043i | ||||
\(797\) | 54.9817i | 1.94755i | 0.227510 | + | 0.973776i | \(0.426942\pi\) | ||||
−0.227510 | + | 0.973776i | \(0.573058\pi\) | |||||||
\(798\) | 11.8695 | − | 11.8695i | 0.420175 | − | 0.420175i | ||||
\(799\) | −45.8482 | + | 45.8482i | −1.62199 | + | 1.62199i | ||||
\(800\) | −4.56408 | + | 2.04186i | −0.161364 | + | 0.0721908i | ||||
\(801\) | 10.1878 | − | 10.1878i | 0.359967 | − | 0.359967i | ||||
\(802\) | −1.56403 | − | 1.56403i | −0.0552279 | − | 0.0552279i | ||||
\(803\) | −14.6459 | − | 14.6459i | −0.516844 | − | 0.516844i | ||||
\(804\) | −9.77458 | −0.344723 | ||||||||
\(805\) | −6.27768 | − | 29.4046i | −0.221259 | − | 1.03638i | ||||
\(806\) | 9.57170 | − | 9.57170i | 0.337149 | − | 0.337149i | ||||
\(807\) | 11.8721 | + | 11.8721i | 0.417916 | + | 0.417916i | ||||
\(808\) | −16.0893 | −0.566021 | ||||||||
\(809\) | −4.86721 | − | 4.86721i | −0.171122 | − | 0.171122i | 0.616350 | − | 0.787472i | \(-0.288611\pi\) |
−0.787472 | + | 0.616350i | \(0.788611\pi\) | |||||||
\(810\) | 1.21617 | − | 1.87641i | 0.0427318 | − | 0.0659305i | ||||
\(811\) | −13.3290 | −0.468044 | −0.234022 | − | 0.972231i | \(-0.575189\pi\) | ||||
−0.234022 | + | 0.972231i | \(0.575189\pi\) | |||||||
\(812\) | 14.6772 | 0.515068 | ||||||||
\(813\) | −2.45407 | + | 2.45407i | −0.0860680 | + | 0.0860680i | ||||
\(814\) | 23.6110 | + | 25.0508i | 0.827567 | + | 0.878029i | ||||
\(815\) | −14.5418 | − | 9.42503i | −0.509376 | − | 0.330144i | ||||
\(816\) | −5.36251 | + | 5.36251i | −0.187725 | + | 0.187725i | ||||
\(817\) | 12.4963 | + | 12.4963i | 0.437192 | + | 0.437192i | ||||
\(818\) | 6.64945 | − | 6.64945i | 0.232493 | − | 0.232493i | ||||
\(819\) | 10.8215 | − | 10.8215i | 0.378133 | − | 0.378133i | ||||
\(820\) | −2.95582 | + | 4.56050i | −0.103222 | + | 0.159260i | ||||
\(821\) | 43.5087 | 1.51846 | 0.759232 | − | 0.650820i | \(-0.225575\pi\) | ||||
0.759232 | + | 0.650820i | \(0.225575\pi\) | |||||||
\(822\) | 2.31858 | 0.0808698 | ||||||||
\(823\) | −0.673165 | − | 0.673165i | −0.0234651 | − | 0.0234651i | 0.695277 | − | 0.718742i | \(-0.255282\pi\) |
−0.718742 | + | 0.695277i | \(0.755282\pi\) | |||||||
\(824\) | − | 11.0997i | − | 0.386677i | ||||||
\(825\) | −10.0932 | + | 26.4352i | −0.351400 | + | 0.920354i | ||||
\(826\) | 44.2665 | 1.54023 | ||||||||
\(827\) | 33.1455 | 1.15258 | 0.576290 | − | 0.817245i | \(-0.304500\pi\) | ||||
0.576290 | + | 0.817245i | \(0.304500\pi\) | |||||||
\(828\) | −4.23021 | −0.147010 | ||||||||
\(829\) | −17.7173 | − | 17.7173i | −0.615349 | − | 0.615349i | 0.328986 | − | 0.944335i | \(-0.393293\pi\) |
−0.944335 | + | 0.328986i | \(0.893293\pi\) | |||||||
\(830\) | −2.80265 | + | 0.598346i | −0.0972814 | + | 0.0207689i | ||||
\(831\) | 3.59801 | + | 3.59801i | 0.124814 | + | 0.124814i | ||||
\(832\) | 4.81453i | 0.166914i | ||||||||
\(833\) | 23.5401i | 0.815617i | ||||||||
\(834\) | 12.6877 | + | 12.6877i | 0.439340 | + | 0.439340i | ||||
\(835\) | 36.1297 | + | 23.4169i | 1.25032 | + | 0.810376i | ||||
\(836\) | 21.1323 | + | 21.1323i | 0.730875 | + | 0.730875i | ||||
\(837\) | −2.81158 | −0.0971824 | ||||||||
\(838\) | −22.2951 | −0.770170 | ||||||||
\(839\) | −40.9132 | −1.41248 | −0.706240 | − | 0.707973i | \(-0.749610\pi\) | ||||
−0.706240 | + | 0.707973i | \(0.749610\pi\) | |||||||
\(840\) | 5.96453 | + | 3.86582i | 0.205796 | + | 0.133383i | ||||
\(841\) | − | 7.67986i | − | 0.264823i | ||||||
\(842\) | −1.74485 | − | 1.74485i | −0.0601315 | − | 0.0601315i | ||||
\(843\) | 31.6197 | 1.08904 | ||||||||
\(844\) | −11.9466 | −0.411218 | ||||||||
\(845\) | −19.1013 | − | 12.3802i | −0.657105 | − | 0.425893i | ||||
\(846\) | 6.04560 | − | 6.04560i | 0.207852 | − | 0.207852i | ||||
\(847\) | 47.2631 | − | 47.2631i | 1.62398 | − | 1.62398i | ||||
\(848\) | 8.02058 | + | 8.02058i | 0.275428 | + | 0.275428i | ||||
\(849\) | −3.51440 | + | 3.51440i | −0.120614 | + | 0.120614i | ||||
\(850\) | 34.6127 | − | 15.4849i | 1.18721 | − | 0.531129i | ||||
\(851\) | 18.7249 | − | 17.6488i | 0.641882 | − | 0.604992i | ||||
\(852\) | 4.32811 | − | 4.32811i | 0.148279 | − | 0.148279i | ||||
\(853\) | −42.0289 | −1.43904 | −0.719520 | − | 0.694471i | \(-0.755638\pi\) | ||||
−0.719520 | + | 0.694471i | \(0.755638\pi\) | |||||||
\(854\) | 5.02827 | 0.172064 | ||||||||
\(855\) | 2.46541 | + | 11.5480i | 0.0843152 | + | 0.394932i | ||||
\(856\) | −8.64549 | − | 8.64549i | −0.295497 | − | 0.295497i | ||||
\(857\) | 34.3759 | 1.17426 | 0.587129 | − | 0.809494i | \(-0.300258\pi\) | ||||
0.587129 | + | 0.809494i | \(0.300258\pi\) | |||||||
\(858\) | 19.2664 | + | 19.2664i | 0.657745 | + | 0.657745i | ||||
\(859\) | 29.2733 | − | 29.2733i | 0.998794 | − | 0.998794i | −0.00120570 | − | 0.999999i | \(-0.500384\pi\) |
0.999999 | + | 0.00120570i | \(0.000383786\pi\) | |||||||
\(860\) | −4.06999 | + | 6.27954i | −0.138785 | + | 0.214130i | ||||
\(861\) | 7.72558 | 0.263287 | ||||||||
\(862\) | −23.7856 | − | 23.7856i | −0.810142 | − | 0.810142i | ||||
\(863\) | 11.0183 | + | 11.0183i | 0.375069 | + | 0.375069i | 0.869319 | − | 0.494251i | \(-0.164558\pi\) |
−0.494251 | + | 0.869319i | \(0.664558\pi\) | |||||||
\(864\) | 0.707107 | − | 0.707107i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | 26.5523 | − | 5.66872i | 0.902804 | − | 0.192742i | ||||
\(866\) | 9.00285 | − | 9.00285i | 0.305929 | − | 0.305929i | ||||
\(867\) | 28.6470 | − | 28.6470i | 0.972902 | − | 0.972902i | ||||
\(868\) | − | 8.93712i | − | 0.303346i | ||||||
\(869\) | −16.1469 | − | 16.1469i | −0.547747 | − | 0.547747i | ||||
\(870\) | −5.61551 | + | 8.66411i | −0.190384 | + | 0.293741i | ||||
\(871\) | 33.2765 | − | 33.2765i | 1.12753 | − | 1.12753i | ||||
\(872\) | 13.7592 | + | 13.7592i | 0.465947 | + | 0.465947i | ||||
\(873\) | 2.87834i | 0.0974169i | ||||||||
\(874\) | 15.7959 | − | 15.7959i | 0.534306 | − | 0.534306i | ||||
\(875\) | −20.9663 | − | 28.6952i | −0.708792 | − | 0.970076i | ||||
\(876\) | − | 3.65991i | − | 0.123657i | ||||||
\(877\) | −5.02653 | + | 5.02653i | −0.169734 | + | 0.169734i | −0.786862 | − | 0.617129i | \(-0.788296\pi\) |
0.617129 | + | 0.786862i | \(0.288296\pi\) | |||||||
\(878\) | 4.79636 | − | 4.79636i | 0.161869 | − | 0.161869i | ||||
\(879\) | −5.32288 | −0.179536 | ||||||||
\(880\) | −6.88266 | + | 10.6192i | −0.232015 | + | 0.357973i | ||||
\(881\) | − | 29.2467i | − | 0.985345i | −0.870215 | − | 0.492673i | \(-0.836020\pi\) | ||
0.870215 | − | 0.492673i | \(-0.163980\pi\) | |||||||
\(882\) | − | 3.10403i | − | 0.104518i | ||||||
\(883\) | −28.8964 | −0.972441 | −0.486220 | − | 0.873836i | \(-0.661625\pi\) | ||||
−0.486220 | + | 0.873836i | \(0.661625\pi\) | |||||||
\(884\) | − | 36.5121i | − | 1.22803i | ||||||
\(885\) | −16.9364 | + | 26.1311i | −0.569312 | + | 0.878386i | ||||
\(886\) | 7.85980 | + | 7.85980i | 0.264055 | + | 0.264055i | ||||
\(887\) | 8.58020 | + | 8.58020i | 0.288095 | + | 0.288095i | 0.836327 | − | 0.548232i | \(-0.184699\pi\) |
−0.548232 | + | 0.836327i | \(0.684699\pi\) | |||||||
\(888\) | −0.179886 | + | 6.08010i | −0.00603658 | + | 0.204035i | ||||
\(889\) | − | 65.6706i | − | 2.20252i | ||||||
\(890\) | −31.5065 | + | 6.72642i | −1.05610 | + | 0.225470i | ||||
\(891\) | − | 5.65930i | − | 0.189594i | ||||||
\(892\) | −11.0520 | − | 11.0520i | −0.370050 | − | 0.370050i | ||||
\(893\) | 45.1495i | 1.51087i | ||||||||
\(894\) | 6.50879 | − | 6.50879i | 0.217686 | − | 0.217686i | ||||
\(895\) | −9.30685 | − | 43.5932i | −0.311094 | − | 1.45716i | ||||
\(896\) | 2.24767 | + | 2.24767i | 0.0750893 | + | 0.0750893i | ||||
\(897\) | 14.4013 | − | 14.4013i | 0.480844 | − | 0.480844i | ||||
\(898\) | 16.4657 | + | 16.4657i | 0.549468 | + | 0.549468i | ||||
\(899\) | 12.9821 | 0.432978 | ||||||||
\(900\) | −4.56408 | + | 2.04186i | −0.152136 | + | 0.0680621i | ||||
\(901\) | −60.8259 | − | 60.8259i | −2.02640 | − | 2.02640i | ||||
\(902\) | 13.7545i | 0.457976i | ||||||||
\(903\) | 10.6377 | 0.353999 | ||||||||
\(904\) | − | 4.68689i | − | 0.155884i | ||||||
\(905\) | 25.8628 | + | 16.7626i | 0.859709 | + | 0.557208i | ||||
\(906\) | −3.95777 | + | 3.95777i | −0.131488 | + | 0.131488i | ||||
\(907\) | 0.367882 | 0.0122153 | 0.00610766 | − | 0.999981i | \(-0.498056\pi\) | ||||
0.00610766 | + | 0.999981i | \(0.498056\pi\) | |||||||
\(908\) | 6.40168 | 0.212447 | ||||||||
\(909\) | −16.0893 | −0.533649 | ||||||||
\(910\) | −33.4663 | + | 7.14482i | −1.10940 | + | 0.236848i | ||||
\(911\) | −28.3530 | − | 28.3530i | −0.939377 | − | 0.939377i | 0.0588872 | − | 0.998265i | \(-0.481245\pi\) |
−0.998265 | + | 0.0588872i | \(0.981245\pi\) | |||||||
\(912\) | 5.28079i | 0.174864i | ||||||||
\(913\) | −5.12873 | + | 5.12873i | −0.169736 | + | 0.169736i | ||||
\(914\) | − | 5.42876i | − | 0.179568i | ||||||
\(915\) | −1.92383 | + | 2.96825i | −0.0635997 | + | 0.0981273i | ||||
\(916\) | 16.3225i | 0.539310i | ||||||||
\(917\) | 41.6367i | 1.37496i | ||||||||
\(918\) | −5.36251 | + | 5.36251i | −0.176989 | + | 0.176989i | ||||
\(919\) | 6.98899 | + | 6.98899i | 0.230546 | + | 0.230546i | 0.812920 | − | 0.582375i | \(-0.197876\pi\) |
−0.582375 | + | 0.812920i | \(0.697876\pi\) | |||||||
\(920\) | 7.93762 | + | 5.14465i | 0.261696 | + | 0.169614i | ||||
\(921\) | −14.6248 | −0.481905 | ||||||||
\(922\) | −12.8604 | + | 12.8604i | −0.423534 | + | 0.423534i | ||||
\(923\) | 29.4691i | 0.969987i | ||||||||
\(924\) | 17.9891 | 0.591798 | ||||||||
\(925\) | 11.6840 | − | 28.0800i | 0.384167 | − | 0.923264i | ||||
\(926\) | −36.1282 | −1.18725 | ||||||||
\(927\) | − | 11.0997i | − | 0.364563i | ||||||
\(928\) | −3.26498 | + | 3.26498i | −0.107178 | + | 0.107178i | ||||
\(929\) | 31.4501 | 1.03184 | 0.515922 | − | 0.856636i | \(-0.327450\pi\) | ||||
0.515922 | + | 0.856636i | \(0.327450\pi\) | |||||||
\(930\) | 5.27569 | + | 3.41936i | 0.172997 | + | 0.112125i | ||||
\(931\) | 11.5907 | + | 11.5907i | 0.379870 | + | 0.379870i | ||||
\(932\) | −0.738837 | + | 0.738837i | −0.0242014 | + | 0.0242014i | ||||
\(933\) | − | 2.94474i | − | 0.0964064i | ||||||
\(934\) | 4.96873i | 0.162582i | ||||||||
\(935\) | 52.1962 | − | 80.5330i | 1.70700 | − | 2.63371i | ||||
\(936\) | 4.81453i | 0.157368i | ||||||||
\(937\) | 16.7719 | − | 16.7719i | 0.547915 | − | 0.547915i | −0.377922 | − | 0.925837i | \(-0.623361\pi\) |
0.925837 | + | 0.377922i | \(0.123361\pi\) | |||||||
\(938\) | − | 31.0703i | − | 1.01448i | ||||||
\(939\) | −4.14532 | − | 4.14532i | −0.135278 | − | 0.135278i | ||||
\(940\) | −18.6965 | + | 3.99158i | −0.609814 | + | 0.130191i | ||||
\(941\) | 16.4771 | 0.537139 | 0.268570 | − | 0.963260i | \(-0.413449\pi\) | ||||
0.268570 | + | 0.963260i | \(0.413449\pi\) | |||||||
\(942\) | −1.41232 | −0.0460159 | ||||||||
\(943\) | 10.2812 | 0.334803 | ||||||||
\(944\) | −9.84721 | + | 9.84721i | −0.320499 | + | 0.320499i | ||||
\(945\) | 5.96453 | + | 3.86582i | 0.194026 | + | 0.125755i | ||||
\(946\) | 18.9392i | 0.615766i | ||||||||
\(947\) | −56.8823 | −1.84843 | −0.924214 | − | 0.381876i | \(-0.875278\pi\) | ||||
−0.924214 | + | 0.381876i | \(0.875278\pi\) | |||||||
\(948\) | − | 4.03499i | − | 0.131050i | ||||||
\(949\) | 12.4597 | + | 12.4597i | 0.404460 | + | 0.404460i | ||||
\(950\) | 9.41815 | − | 24.6671i | 0.305565 | − | 0.800307i | ||||
\(951\) | −4.67673 | −0.151653 | ||||||||
\(952\) | −17.0457 | − | 17.0457i | −0.552455 | − | 0.552455i | ||||
\(953\) | 3.27877 | − | 3.27877i | 0.106210 | − | 0.106210i | −0.652005 | − | 0.758215i | \(-0.726072\pi\) |
0.758215 | + | 0.652005i | \(0.226072\pi\) | |||||||
\(954\) | 8.02058 | + | 8.02058i | 0.259676 | + | 0.259676i | ||||
\(955\) | 12.1784 | + | 57.0438i | 0.394085 | + | 1.84589i | ||||
\(956\) | −5.10981 | + | 5.10981i | −0.165263 | + | 0.165263i | ||||
\(957\) | 26.1311i | 0.844698i | ||||||||
\(958\) | −21.0873 | − | 21.0873i | −0.681300 | − | 0.681300i | ||||
\(959\) | 7.37004i | 0.237991i | ||||||||
\(960\) | −2.18679 | + | 0.466864i | −0.0705783 | + | 0.0150680i | ||||
\(961\) | 23.0950i | 0.745001i | ||||||||
\(962\) | −20.0866 | − | 21.3114i | −0.647618 | − | 0.687108i | ||||
\(963\) | −8.64549 | − | 8.64549i | −0.278597 | − | 0.278597i | ||||
\(964\) | 8.22613 | + | 8.22613i | 0.264946 | + | 0.264946i | ||||
\(965\) | 27.9594 | − | 43.1383i | 0.900046 | − | 1.38867i | ||||
\(966\) | − | 13.4465i | − | 0.432634i | ||||||
\(967\) | −38.2625 | −1.23044 | −0.615219 | − | 0.788356i | \(-0.710932\pi\) | ||||
−0.615219 | + | 0.788356i | \(0.710932\pi\) | |||||||
\(968\) | 21.0276i | 0.675853i | ||||||||
\(969\) | − | 40.0481i | − | 1.28653i | ||||||
\(970\) | 3.50054 | − | 5.40095i | 0.112396 | − | 0.173414i | ||||
\(971\) | −30.0272 | −0.963620 | −0.481810 | − | 0.876276i | \(-0.660020\pi\) | ||||
−0.481810 | + | 0.876276i | \(0.660020\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −40.3303 | + | 40.3303i | −1.29293 | + | 1.29293i | ||||
\(974\) | − | 10.6041i | − | 0.339778i | ||||||
\(975\) | 8.58659 | − | 22.4892i | 0.274991 | − | 0.720230i | ||||
\(976\) | −1.11855 | + | 1.11855i | −0.0358040 | + | 0.0358040i | ||||
\(977\) | − | 23.6886i | − | 0.757865i | −0.925424 | − | 0.378932i | \(-0.876291\pi\) | ||
0.925424 | − | 0.378932i | \(-0.123709\pi\) | |||||||
\(978\) | −5.47991 | − | 5.47991i | −0.175228 | − | 0.175228i | ||||
\(979\) | −57.6556 | + | 57.6556i | −1.84268 | + | 1.84268i | ||||
\(980\) | −3.77503 | + | 5.82445i | −0.120589 | + | 0.186055i | ||||
\(981\) | 13.7592 | + | 13.7592i | 0.439299 | + | 0.439299i | ||||
\(982\) | 2.33716i | 0.0745819i | ||||||||
\(983\) | 29.2431 | − | 29.2431i | 0.932711 | − | 0.932711i | −0.0651639 | − | 0.997875i | \(-0.520757\pi\) |
0.997875 | + | 0.0651639i | \(0.0207570\pi\) | |||||||
\(984\) | −1.71858 | + | 1.71858i | −0.0547862 | + | 0.0547862i | ||||
\(985\) | −5.23701 | + | 1.11806i | −0.166865 | + | 0.0356245i | ||||
\(986\) | 24.7607 | − | 24.7607i | 0.788541 | − | 0.788541i | ||||
\(987\) | 19.2171 | + | 19.2171i | 0.611686 | + | 0.611686i | ||||
\(988\) | −17.9778 | − | 17.9778i | −0.571952 | − | 0.571952i | ||||
\(989\) | 14.1567 | 0.450155 | ||||||||
\(990\) | −6.88266 | + | 10.6192i | −0.218745 | + | 0.337500i | ||||
\(991\) | 6.15758 | − | 6.15758i | 0.195602 | − | 0.195602i | −0.602510 | − | 0.798112i | \(-0.705833\pi\) |
0.798112 | + | 0.602510i | \(0.205833\pi\) | |||||||
\(992\) | 1.98809 | + | 1.98809i | 0.0631218 | + | 0.0631218i | ||||
\(993\) | 2.88137 | 0.0914375 | ||||||||
\(994\) | 13.7577 | + | 13.7577i | 0.436367 | + | 0.436367i | ||||
\(995\) | 4.84403 | + | 22.6894i | 0.153566 | + | 0.719303i | ||||
\(996\) | −1.28163 | −0.0406100 | ||||||||
\(997\) | 14.2061 | 0.449913 | 0.224957 | − | 0.974369i | \(-0.427776\pi\) | ||||
0.224957 | + | 0.974369i | \(0.427776\pi\) | |||||||
\(998\) | −15.9396 | + | 15.9396i | −0.504559 | + | 0.504559i | ||||
\(999\) | −0.179886 | + | 6.08010i | −0.00569134 | + | 0.192366i |
(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 | 1110.2.l.a.43.10 | ✓ | 36 | |
5.2 | odd | 4 | 1110.2.o.a.487.9 | yes | 36 | ||
37.31 | odd | 4 | 1110.2.o.a.253.9 | yes | 36 | ||
185.142 | even | 4 | inner | 1110.2.l.a.697.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.10 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1110.2.l.a.697.10 | yes | 36 | 185.142 | even | 4 | inner | |
1110.2.o.a.253.9 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.487.9 | yes | 36 | 5.2 | odd | 4 |