Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.45474709504.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 38x^{6} + 481x^{4} + 2112x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.3 | ||
Root | \(-0.742317i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.a.239.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.23200 | + | 2.23200i | −0.998183 | + | 0.998183i | −0.999998 | − | 0.00181579i | \(-0.999422\pi\) |
0.00181579 | + | 0.999998i | \(0.499422\pi\) | |||||||
\(6\) | −1.70711 | + | 0.292893i | −0.696923 | + | 0.119573i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 3.15653i | 0.998183i | ||||||||
\(11\) | 3.38853 | + | 3.38853i | 1.02168 | + | 1.02168i | 0.999760 | + | 0.0219219i | \(0.00697852\pi\) |
0.0219219 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(12\) | −1.00000 | + | 1.41421i | −0.288675 | + | 0.408248i | ||||
\(13\) | −1.52490 | + | 3.26721i | −0.422930 | + | 0.906162i | ||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 5.38853 | − | 0.924526i | 1.39131 | − | 0.238712i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.15653 | 1.25064 | 0.625321 | − | 0.780368i | \(-0.284968\pi\) | ||||
0.625321 | + | 0.780368i | \(0.284968\pi\) | |||||||
\(18\) | 2.70711 | + | 1.29289i | 0.638071 | + | 0.304738i | ||||
\(19\) | −4.23200 | − | 4.23200i | −0.970888 | − | 0.970888i | 0.0286998 | − | 0.999588i | \(-0.490863\pi\) |
−0.999588 | + | 0.0286998i | \(0.990863\pi\) | |||||||
\(20\) | 2.23200 | + | 2.23200i | 0.499091 | + | 0.499091i | ||||
\(21\) | −1.70711 | + | 0.292893i | −0.372521 | + | 0.0639145i | ||||
\(22\) | 4.79211 | 1.02168 | ||||||||
\(23\) | 6.67033 | 1.39086 | 0.695430 | − | 0.718594i | \(-0.255214\pi\) | ||||
0.695430 | + | 0.718594i | \(0.255214\pi\) | |||||||
\(24\) | 0.292893 | + | 1.70711i | 0.0597866 | + | 0.348462i | ||||
\(25\) | − | 4.96368i | − | 0.992737i | ||||||
\(26\) | 1.23200 | + | 3.38853i | 0.241616 | + | 0.664546i | ||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 4.20632i | 0.781095i | 0.920583 | + | 0.390547i | \(0.127714\pi\) | ||||
−0.920583 | + | 0.390547i | \(0.872286\pi\) | |||||||
\(30\) | 3.15653 | − | 4.46401i | 0.576301 | − | 0.815013i | ||||
\(31\) | 3.41421 | + | 3.41421i | 0.613211 | + | 0.613211i | 0.943781 | − | 0.330570i | \(-0.107241\pi\) |
−0.330570 | + | 0.943781i | \(0.607241\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −1.40358 | − | 8.18065i | −0.244331 | − | 1.42407i | ||||
\(34\) | 3.64622 | − | 3.64622i | 0.625321 | − | 0.625321i | ||||
\(35\) | 3.15653i | 0.533551i | ||||||||
\(36\) | 2.82843 | − | 1.00000i | 0.471405 | − | 0.166667i | ||||
\(37\) | −0.0256791 | + | 0.0256791i | −0.00422161 | + | 0.00422161i | −0.709214 | − | 0.704993i | \(-0.750950\pi\) |
0.704993 | + | 0.709214i | \(0.250950\pi\) | |||||||
\(38\) | −5.98496 | −0.970888 | ||||||||
\(39\) | 5.42374 | − | 3.09564i | 0.868494 | − | 0.495699i | ||||
\(40\) | 3.15653 | 0.499091 | ||||||||
\(41\) | −7.20632 | + | 7.20632i | −1.12544 | + | 1.12544i | −0.134529 | + | 0.990910i | \(0.542952\pi\) |
−0.990910 | + | 0.134529i | \(0.957048\pi\) | |||||||
\(42\) | −1.00000 | + | 1.41421i | −0.154303 | + | 0.218218i | ||||
\(43\) | 8.08455i | 1.23288i | 0.787401 | + | 0.616441i | \(0.211426\pi\) | ||||
−0.787401 | + | 0.616441i | \(0.788574\pi\) | |||||||
\(44\) | 3.38853 | − | 3.38853i | 0.510841 | − | 0.510841i | ||||
\(45\) | −8.54506 | − | 4.08106i | −1.27382 | − | 0.608368i | ||||
\(46\) | 4.71664 | − | 4.71664i | 0.695430 | − | 0.695430i | ||||
\(47\) | 4.24264 | + | 4.24264i | 0.618853 | + | 0.618853i | 0.945237 | − | 0.326384i | \(-0.105830\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(48\) | 1.41421 | + | 1.00000i | 0.204124 | + | 0.144338i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −3.50985 | − | 3.50985i | −0.496368 | − | 0.496368i | ||||
\(51\) | −7.29244 | − | 5.15653i | −1.02115 | − | 0.722059i | ||||
\(52\) | 3.26721 | + | 1.52490i | 0.453081 | + | 0.211465i | ||||
\(53\) | 2.87757i | 0.395265i | 0.980276 | + | 0.197633i | \(0.0633253\pi\) | ||||
−0.980276 | + | 0.197633i | \(0.936675\pi\) | |||||||
\(54\) | −2.53553 | − | 4.53553i | −0.345042 | − | 0.617208i | ||||
\(55\) | −15.1264 | −2.03965 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.75295 | + | 10.2170i | 0.232184 | + | 1.35327i | ||||
\(58\) | 2.97432 | + | 2.97432i | 0.390547 | + | 0.390547i | ||||
\(59\) | 2.48463 | + | 2.48463i | 0.323472 | + | 0.323472i | 0.850097 | − | 0.526626i | \(-0.176543\pi\) |
−0.526626 | + | 0.850097i | \(0.676543\pi\) | |||||||
\(60\) | −0.924526 | − | 5.38853i | −0.119356 | − | 0.695657i | ||||
\(61\) | 2.47115 | 0.316399 | 0.158199 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158199 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(62\) | 4.82843 | 0.613211 | ||||||||
\(63\) | 2.70711 | + | 1.29289i | 0.341063 | + | 0.162889i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.88886 | − | 10.6960i | −0.482354 | − | 1.32668i | ||||
\(66\) | −6.77707 | − | 4.79211i | −0.834200 | − | 0.589868i | ||||
\(67\) | −7.19128 | − | 7.19128i | −0.878555 | − | 0.878555i | 0.114830 | − | 0.993385i | \(-0.463368\pi\) |
−0.993385 | + | 0.114830i | \(0.963368\pi\) | |||||||
\(68\) | − | 5.15653i | − | 0.625321i | ||||||
\(69\) | −9.43328 | − | 6.67033i | −1.13563 | − | 0.803014i | ||||
\(70\) | 2.23200 | + | 2.23200i | 0.266776 | + | 0.266776i | ||||
\(71\) | 2.25768 | − | 2.25768i | 0.267938 | − | 0.267938i | −0.560331 | − | 0.828269i | \(-0.689326\pi\) |
0.828269 | + | 0.560331i | \(0.189326\pi\) | |||||||
\(72\) | 1.29289 | − | 2.70711i | 0.152369 | − | 0.319036i | ||||
\(73\) | 8.14654 | − | 8.14654i | 0.953481 | − | 0.953481i | −0.0454845 | − | 0.998965i | \(-0.514483\pi\) |
0.998965 | + | 0.0454845i | \(0.0144832\pi\) | |||||||
\(74\) | 0.0363157i | 0.00422161i | ||||||||
\(75\) | −4.96368 | + | 7.01971i | −0.573157 | + | 0.810566i | ||||
\(76\) | −4.23200 | + | 4.23200i | −0.485444 | + | 0.485444i | ||||
\(77\) | 4.79211 | 0.546112 | ||||||||
\(78\) | 1.64622 | − | 6.02412i | 0.186397 | − | 0.682097i | ||||
\(79\) | 2.36442 | 0.266018 | 0.133009 | − | 0.991115i | \(-0.457536\pi\) | ||||
0.133009 | + | 0.991115i | \(0.457536\pi\) | |||||||
\(80\) | 2.23200 | − | 2.23200i | 0.249546 | − | 0.249546i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 10.1913i | 1.12544i | ||||||||
\(83\) | −6.15653 | + | 6.15653i | −0.675767 | + | 0.675767i | −0.959039 | − | 0.283272i | \(-0.908580\pi\) |
0.283272 | + | 0.959039i | \(0.408580\pi\) | |||||||
\(84\) | 0.292893 | + | 1.70711i | 0.0319573 | + | 0.186261i | ||||
\(85\) | −11.5094 | + | 11.5094i | −1.24837 | + | 1.24837i | ||||
\(86\) | 5.71664 | + | 5.71664i | 0.616441 | + | 0.616441i | ||||
\(87\) | 4.20632 | − | 5.94864i | 0.450965 | − | 0.637761i | ||||
\(88\) | − | 4.79211i | − | 0.510841i | ||||||
\(89\) | −9.55570 | − | 9.55570i | −1.01290 | − | 1.01290i | −0.999916 | − | 0.0129867i | \(-0.995866\pi\) |
−0.0129867 | − | 0.999916i | \(-0.504134\pi\) | |||||||
\(90\) | −8.92802 | + | 3.15653i | −0.941096 | + | 0.332728i | ||||
\(91\) | 1.23200 | + | 3.38853i | 0.129149 | + | 0.355215i | ||||
\(92\) | − | 6.67033i | − | 0.695430i | ||||||
\(93\) | −1.41421 | − | 8.24264i | −0.146647 | − | 0.854722i | ||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 18.8917 | 1.93825 | ||||||||
\(96\) | 1.70711 | − | 0.292893i | 0.174231 | − | 0.0298933i | ||||
\(97\) | 2.58579 | + | 2.58579i | 0.262547 | + | 0.262547i | 0.826088 | − | 0.563541i | \(-0.190561\pi\) |
−0.563541 | + | 0.826088i | \(0.690561\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | −6.19569 | + | 12.9728i | −0.622690 | + | 1.30381i | ||||
\(100\) | −4.96368 | −0.496368 | ||||||||
\(101\) | −0.291788 | −0.0290340 | −0.0145170 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145170 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(102\) | −8.80275 | + | 1.51031i | −0.871602 | + | 0.149543i | ||||
\(103\) | 18.2758i | 1.80077i | 0.435093 | + | 0.900385i | \(0.356715\pi\) | ||||
−0.435093 | + | 0.900385i | \(0.643285\pi\) | |||||||
\(104\) | 3.38853 | − | 1.23200i | 0.332273 | − | 0.120808i | ||||
\(105\) | 3.15653 | − | 4.46401i | 0.308046 | − | 0.435643i | ||||
\(106\) | 2.03475 | + | 2.03475i | 0.197633 | + | 0.197633i | ||||
\(107\) | 4.82843i | 0.466782i | 0.972383 | + | 0.233391i | \(0.0749821\pi\) | ||||
−0.972383 | + | 0.233391i | \(0.925018\pi\) | |||||||
\(108\) | −5.00000 | − | 1.41421i | −0.481125 | − | 0.136083i | ||||
\(109\) | −12.3870 | − | 12.3870i | −1.18646 | − | 1.18646i | −0.978040 | − | 0.208416i | \(-0.933169\pi\) |
−0.208416 | − | 0.978040i | \(-0.566831\pi\) | |||||||
\(110\) | −10.6960 | + | 10.6960i | −1.01982 | + | 1.01982i | ||||
\(111\) | 0.0619948 | − | 0.0106366i | 0.00588428 | − | 0.00100958i | ||||
\(112\) | −0.707107 | + | 0.707107i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | 12.4853i | 1.17452i | 0.809400 | + | 0.587258i | \(0.199793\pi\) | ||||
−0.809400 | + | 0.587258i | \(0.800207\pi\) | |||||||
\(114\) | 8.46401 | + | 5.98496i | 0.792727 | + | 0.560543i | ||||
\(115\) | −14.8882 | + | 14.8882i | −1.38833 | + | 1.38833i | ||||
\(116\) | 4.20632 | 0.390547 | ||||||||
\(117\) | −10.7660 | − | 1.04585i | −0.995315 | − | 0.0966886i | ||||
\(118\) | 3.51380 | 0.323472 | ||||||||
\(119\) | 3.64622 | − | 3.64622i | 0.334248 | − | 0.334248i | ||||
\(120\) | −4.46401 | − | 3.15653i | −0.407506 | − | 0.288150i | ||||
\(121\) | 11.9643i | 1.08767i | ||||||||
\(122\) | 1.74737 | − | 1.74737i | 0.158199 | − | 0.158199i | ||||
\(123\) | 17.3976 | − | 2.98496i | 1.56869 | − | 0.269145i | ||||
\(124\) | 3.41421 | − | 3.41421i | 0.306605 | − | 0.306605i | ||||
\(125\) | −0.0810568 | − | 0.0810568i | −0.00724994 | − | 0.00724994i | ||||
\(126\) | 2.82843 | − | 1.00000i | 0.251976 | − | 0.0890871i | ||||
\(127\) | − | 13.4647i | − | 1.19479i | −0.801945 | − | 0.597397i | \(-0.796201\pi\) | ||
0.801945 | − | 0.597397i | \(-0.203799\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.08455 | − | 11.4333i | 0.711805 | − | 1.00664i | ||||
\(130\) | −10.3131 | − | 4.81338i | −0.904515 | − | 0.422162i | ||||
\(131\) | − | 2.34938i | − | 0.205266i | −0.994719 | − | 0.102633i | \(-0.967273\pi\) | ||
0.994719 | − | 0.102633i | \(-0.0327267\pi\) | |||||||
\(132\) | −8.18065 | + | 1.40358i | −0.712034 | + | 0.122166i | ||||
\(133\) | −5.98496 | −0.518962 | ||||||||
\(134\) | −10.1700 | −0.878555 | ||||||||
\(135\) | 8.00349 | + | 14.3166i | 0.688831 | + | 1.23217i | ||||
\(136\) | −3.64622 | − | 3.64622i | −0.312661 | − | 0.312661i | ||||
\(137\) | −12.1102 | − | 12.1102i | −1.03465 | − | 1.03465i | −0.999378 | − | 0.0352685i | \(-0.988771\pi\) |
−0.0352685 | − | 0.999378i | \(-0.511229\pi\) | |||||||
\(138\) | −11.3870 | + | 1.95370i | −0.969323 | + | 0.166310i | ||||
\(139\) | 8.51537 | 0.722264 | 0.361132 | − | 0.932515i | \(-0.382390\pi\) | ||||
0.361132 | + | 0.932515i | \(0.382390\pi\) | |||||||
\(140\) | 3.15653 | 0.266776 | ||||||||
\(141\) | −1.75736 | − | 10.2426i | −0.147996 | − | 0.862586i | ||||
\(142\) | − | 3.19285i | − | 0.267938i | ||||||
\(143\) | −16.2382 | + | 5.90390i | −1.35791 | + | 0.493709i | ||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | −9.38853 | − | 9.38853i | −0.779675 | − | 0.779675i | ||||
\(146\) | − | 11.5209i | − | 0.953481i | ||||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | 0.0256791 | + | 0.0256791i | 0.00211081 | + | 0.00211081i | ||||
\(149\) | 11.7201 | − | 11.7201i | 0.960150 | − | 0.960150i | −0.0390856 | − | 0.999236i | \(-0.512445\pi\) |
0.999236 | + | 0.0390856i | \(0.0124445\pi\) | |||||||
\(150\) | 1.45383 | + | 8.47354i | 0.118705 | + | 0.691862i | ||||
\(151\) | 7.88886 | − | 7.88886i | 0.641986 | − | 0.641986i | −0.309057 | − | 0.951043i | \(-0.600013\pi\) |
0.951043 | + | 0.309057i | \(0.100013\pi\) | |||||||
\(152\) | 5.98496i | 0.485444i | ||||||||
\(153\) | 5.15653 | + | 14.5849i | 0.416881 | + | 1.17912i | ||||
\(154\) | 3.38853 | − | 3.38853i | 0.273056 | − | 0.273056i | ||||
\(155\) | −15.2411 | −1.22419 | ||||||||
\(156\) | −3.09564 | − | 5.42374i | −0.247850 | − | 0.434247i | ||||
\(157\) | 18.5676 | 1.48186 | 0.740929 | − | 0.671584i | \(-0.234386\pi\) | ||||
0.740929 | + | 0.671584i | \(0.234386\pi\) | |||||||
\(158\) | 1.67190 | − | 1.67190i | 0.133009 | − | 0.133009i | ||||
\(159\) | 2.87757 | − | 4.06950i | 0.228206 | − | 0.322733i | ||||
\(160\) | − | 3.15653i | − | 0.249546i | ||||||
\(161\) | 4.71664 | − | 4.71664i | 0.371723 | − | 0.371723i | ||||
\(162\) | −0.949747 | + | 8.94975i | −0.0746192 | + | 0.703159i | ||||
\(163\) | 7.34223 | − | 7.34223i | 0.575088 | − | 0.575088i | −0.358458 | − | 0.933546i | \(-0.616697\pi\) |
0.933546 | + | 0.358458i | \(0.116697\pi\) | |||||||
\(164\) | 7.20632 | + | 7.20632i | 0.562719 | + | 0.562719i | ||||
\(165\) | 21.3920 | + | 15.1264i | 1.66537 | + | 1.17759i | ||||
\(166\) | 8.70665i | 0.675767i | ||||||||
\(167\) | −5.31811 | − | 5.31811i | −0.411528 | − | 0.411528i | 0.470743 | − | 0.882271i | \(-0.343986\pi\) |
−0.882271 | + | 0.470743i | \(0.843986\pi\) | |||||||
\(168\) | 1.41421 | + | 1.00000i | 0.109109 | + | 0.0771517i | ||||
\(169\) | −8.34938 | − | 9.96433i | −0.642260 | − | 0.766487i | ||||
\(170\) | 16.2767i | 1.24837i | ||||||||
\(171\) | 7.73791 | − | 16.2019i | 0.591733 | − | 1.23899i | ||||
\(172\) | 8.08455 | 0.616441 | ||||||||
\(173\) | 14.0425 | 1.06764 | 0.533818 | − | 0.845600i | \(-0.320757\pi\) | ||||
0.533818 | + | 0.845600i | \(0.320757\pi\) | |||||||
\(174\) | −1.23200 | − | 7.18065i | −0.0933980 | − | 0.544363i | ||||
\(175\) | −3.50985 | − | 3.50985i | −0.265320 | − | 0.265320i | ||||
\(176\) | −3.38853 | − | 3.38853i | −0.255420 | − | 0.255420i | ||||
\(177\) | −1.02917 | − | 5.99844i | −0.0773571 | − | 0.450870i | ||||
\(178\) | −13.5138 | −1.01290 | ||||||||
\(179\) | −2.05136 | −0.153326 | −0.0766629 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766629 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(180\) | −4.08106 | + | 8.54506i | −0.304184 | + | 0.636912i | ||||
\(181\) | − | 14.5344i | − | 1.08034i | −0.841557 | − | 0.540168i | \(-0.818361\pi\) | ||
0.841557 | − | 0.540168i | \(-0.181639\pi\) | |||||||
\(182\) | 3.26721 | + | 1.52490i | 0.242182 | + | 0.113033i | ||||
\(183\) | −3.49474 | − | 2.47115i | −0.258339 | − | 0.182673i | ||||
\(184\) | −4.71664 | − | 4.71664i | −0.347715 | − | 0.347715i | ||||
\(185\) | − | 0.114632i | − | 0.00842788i | ||||||
\(186\) | −6.82843 | − | 4.82843i | −0.500685 | − | 0.354037i | ||||
\(187\) | 17.4731 | + | 17.4731i | 1.27776 | + | 1.27776i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | −2.53553 | − | 4.53553i | −0.184433 | − | 0.329912i | ||||
\(190\) | 13.3584 | − | 13.3584i | 0.969124 | − | 0.969124i | ||||
\(191\) | 10.0141i | 0.724597i | 0.932062 | + | 0.362298i | \(0.118008\pi\) | ||||
−0.932062 | + | 0.362298i | \(0.881992\pi\) | |||||||
\(192\) | 1.00000 | − | 1.41421i | 0.0721688 | − | 0.102062i | ||||
\(193\) | −9.59991 | + | 9.59991i | −0.691017 | + | 0.691017i | −0.962456 | − | 0.271439i | \(-0.912501\pi\) |
0.271439 | + | 0.962456i | \(0.412501\pi\) | |||||||
\(194\) | 3.65685 | 0.262547 | ||||||||
\(195\) | −5.19634 | + | 19.0153i | −0.372117 | + | 1.36171i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −4.64116 | + | 4.64116i | −0.330669 | + | 0.330669i | −0.852841 | − | 0.522171i | \(-0.825122\pi\) |
0.522171 | + | 0.852841i | \(0.325122\pi\) | |||||||
\(198\) | 4.79211 | + | 13.5541i | 0.340561 | + | 0.963251i | ||||
\(199\) | − | 9.76046i | − | 0.691901i | −0.938253 | − | 0.345950i | \(-0.887557\pi\) | ||
0.938253 | − | 0.345950i | \(-0.112443\pi\) | |||||||
\(200\) | −3.50985 | + | 3.50985i | −0.248184 | + | 0.248184i | ||||
\(201\) | 2.97873 | + | 17.3613i | 0.210103 | + | 1.22457i | ||||
\(202\) | −0.206325 | + | 0.206325i | −0.0145170 | + | 0.0145170i | ||||
\(203\) | 2.97432 | + | 2.97432i | 0.208756 | + | 0.208756i | ||||
\(204\) | −5.15653 | + | 7.29244i | −0.361029 | + | 0.510573i | ||||
\(205\) | − | 32.1691i | − | 2.24679i | ||||||
\(206\) | 12.9230 | + | 12.9230i | 0.900385 | + | 0.900385i | ||||
\(207\) | 6.67033 | + | 18.8666i | 0.463620 | + | 1.31132i | ||||
\(208\) | 1.52490 | − | 3.26721i | 0.105733 | − | 0.226541i | ||||
\(209\) | − | 28.6806i | − | 1.98388i | ||||||
\(210\) | −0.924526 | − | 5.38853i | −0.0637984 | − | 0.371844i | ||||
\(211\) | −9.59927 | −0.660841 | −0.330420 | − | 0.943834i | \(-0.607191\pi\) | ||||
−0.330420 | + | 0.943834i | \(0.607191\pi\) | |||||||
\(212\) | 2.87757 | 0.197633 | ||||||||
\(213\) | −5.45053 | + | 0.935163i | −0.373464 | + | 0.0640763i | ||||
\(214\) | 3.41421 | + | 3.41421i | 0.233391 | + | 0.233391i | ||||
\(215\) | −18.0447 | − | 18.0447i | −1.23064 | − | 1.23064i | ||||
\(216\) | −4.53553 | + | 2.53553i | −0.308604 | + | 0.172521i | ||||
\(217\) | 4.82843 | 0.327775 | ||||||||
\(218\) | −17.5178 | −1.18646 | ||||||||
\(219\) | −19.6675 | + | 3.37441i | −1.32901 | + | 0.228021i | ||||
\(220\) | 15.1264i | 1.01982i | ||||||||
\(221\) | −7.86318 | + | 16.8475i | −0.528935 | + | 1.13328i | ||||
\(222\) | 0.0363157 | − | 0.0513581i | 0.00243735 | − | 0.00344693i | ||||
\(223\) | 16.2467 | + | 16.2467i | 1.08796 | + | 1.08796i | 0.995739 | + | 0.0922180i | \(0.0293957\pi\) |
0.0922180 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | 14.0394 | − | 4.96368i | 0.935961 | − | 0.330912i | ||||
\(226\) | 8.82843 | + | 8.82843i | 0.587258 | + | 0.587258i | ||||
\(227\) | −1.92802 | + | 1.92802i | −0.127967 | + | 0.127967i | −0.768189 | − | 0.640223i | \(-0.778842\pi\) |
0.640223 | + | 0.768189i | \(0.278842\pi\) | |||||||
\(228\) | 10.2170 | − | 1.75295i | 0.676635 | − | 0.116092i | ||||
\(229\) | −1.19285 | + | 1.19285i | −0.0788255 | + | 0.0788255i | −0.745420 | − | 0.666595i | \(-0.767751\pi\) |
0.666595 | + | 0.745420i | \(0.267751\pi\) | |||||||
\(230\) | 21.0551i | 1.38833i | ||||||||
\(231\) | −6.77707 | − | 4.79211i | −0.445898 | − | 0.315298i | ||||
\(232\) | 2.97432 | − | 2.97432i | 0.195274 | − | 0.195274i | ||||
\(233\) | 19.9486 | 1.30688 | 0.653439 | − | 0.756979i | \(-0.273325\pi\) | ||||
0.653439 | + | 0.756979i | \(0.273325\pi\) | |||||||
\(234\) | −8.35222 | + | 6.87317i | −0.546002 | + | 0.449313i | ||||
\(235\) | −18.9392 | −1.23546 | ||||||||
\(236\) | 2.48463 | − | 2.48463i | 0.161736 | − | 0.161736i | ||||
\(237\) | −3.34379 | − | 2.36442i | −0.217203 | − | 0.153586i | ||||
\(238\) | − | 5.15653i | − | 0.334248i | ||||||
\(239\) | 7.48463 | − | 7.48463i | 0.484141 | − | 0.484141i | −0.422311 | − | 0.906451i | \(-0.638781\pi\) |
0.906451 | + | 0.422311i | \(0.138781\pi\) | |||||||
\(240\) | −5.38853 | + | 0.924526i | −0.347828 | + | 0.0596779i | ||||
\(241\) | −3.43549 | + | 3.43549i | −0.221299 | + | 0.221299i | −0.809045 | − | 0.587746i | \(-0.800015\pi\) |
0.587746 | + | 0.809045i | \(0.300015\pi\) | |||||||
\(242\) | 8.46006 | + | 8.46006i | 0.543833 | + | 0.543833i | ||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | − | 2.47115i | − | 0.158199i | ||||||
\(245\) | 2.23200 | + | 2.23200i | 0.142598 | + | 0.142598i | ||||
\(246\) | 10.1913 | − | 14.4126i | 0.649772 | − | 0.918917i | ||||
\(247\) | 20.2802 | − | 7.37349i | 1.29040 | − | 0.469164i | ||||
\(248\) | − | 4.82843i | − | 0.306605i | ||||||
\(249\) | 14.8632 | − | 2.55012i | 0.941916 | − | 0.161607i | ||||
\(250\) | −0.114632 | −0.00724994 | ||||||||
\(251\) | 8.93425 | 0.563925 | 0.281962 | − | 0.959425i | \(-0.409015\pi\) | ||||
0.281962 | + | 0.959425i | \(0.409015\pi\) | |||||||
\(252\) | 1.29289 | − | 2.70711i | 0.0814446 | − | 0.170532i | ||||
\(253\) | 22.6027 | + | 22.6027i | 1.42102 | + | 1.42102i | ||||
\(254\) | −9.52095 | − | 9.52095i | −0.597397 | − | 0.597397i | ||||
\(255\) | 27.7861 | − | 4.76735i | 1.74004 | − | 0.298543i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.75580 | −0.421415 | −0.210707 | − | 0.977549i | \(-0.567577\pi\) | ||||
−0.210707 | + | 0.977549i | \(0.567577\pi\) | |||||||
\(258\) | −2.36791 | − | 13.8012i | −0.147420 | − | 0.859224i | ||||
\(259\) | 0.0363157i | 0.00225655i | ||||||||
\(260\) | −10.6960 | + | 3.88886i | −0.663339 | + | 0.241177i | ||||
\(261\) | −11.8973 | + | 4.20632i | −0.736423 | + | 0.260365i | ||||
\(262\) | −1.66126 | − | 1.66126i | −0.102633 | − | 0.102633i | ||||
\(263\) | − | 5.77551i | − | 0.356133i | −0.984018 | − | 0.178066i | \(-0.943016\pi\) | ||
0.984018 | − | 0.178066i | \(-0.0569842\pi\) | |||||||
\(264\) | −4.79211 | + | 6.77707i | −0.294934 | + | 0.417100i | ||||
\(265\) | −6.42276 | − | 6.42276i | −0.394547 | − | 0.394547i | ||||
\(266\) | −4.23200 | + | 4.23200i | −0.259481 | + | 0.259481i | ||||
\(267\) | 3.95810 | + | 23.0695i | 0.242232 | + | 1.41183i | ||||
\(268\) | −7.19128 | + | 7.19128i | −0.439277 | + | 0.439277i | ||||
\(269\) | − | 5.94864i | − | 0.362695i | −0.983419 | − | 0.181348i | \(-0.941954\pi\) | ||
0.983419 | − | 0.181348i | \(-0.0580459\pi\) | |||||||
\(270\) | 15.7827 | + | 4.46401i | 0.960502 | + | 0.271671i | ||||
\(271\) | −0.843470 | + | 0.843470i | −0.0512371 | + | 0.0512371i | −0.732261 | − | 0.681024i | \(-0.761535\pi\) |
0.681024 | + | 0.732261i | \(0.261535\pi\) | |||||||
\(272\) | −5.15653 | −0.312661 | ||||||||
\(273\) | 1.64622 | − | 6.02412i | 0.0996336 | − | 0.364596i | ||||
\(274\) | −17.1264 | −1.03465 | ||||||||
\(275\) | 16.8196 | − | 16.8196i | 1.01426 | − | 1.01426i | ||||
\(276\) | −6.67033 | + | 9.43328i | −0.401507 | + | 0.567816i | ||||
\(277\) | 3.74634i | 0.225096i | 0.993646 | + | 0.112548i | \(0.0359011\pi\) | ||||
−0.993646 | + | 0.112548i | \(0.964099\pi\) | |||||||
\(278\) | 6.02127 | − | 6.02127i | 0.361132 | − | 0.361132i | ||||
\(279\) | −6.24264 | + | 13.0711i | −0.373737 | + | 0.782544i | ||||
\(280\) | 2.23200 | − | 2.23200i | 0.133388 | − | 0.133388i | ||||
\(281\) | −10.6340 | − | 10.6340i | −0.634372 | − | 0.634372i | 0.314789 | − | 0.949162i | \(-0.398066\pi\) |
−0.949162 | + | 0.314789i | \(0.898066\pi\) | |||||||
\(282\) | −8.48528 | − | 6.00000i | −0.505291 | − | 0.357295i | ||||
\(283\) | − | 32.1320i | − | 1.91005i | −0.296524 | − | 0.955025i | \(-0.595827\pi\) | ||
0.296524 | − | 0.955025i | \(-0.404173\pi\) | |||||||
\(284\) | −2.25768 | − | 2.25768i | −0.133969 | − | 0.133969i | ||||
\(285\) | −26.7169 | − | 18.8917i | −1.58257 | − | 1.11905i | ||||
\(286\) | −7.30748 | + | 15.6569i | −0.432100 | + | 0.925809i | ||||
\(287\) | 10.1913i | 0.601572i | ||||||||
\(288\) | −2.70711 | − | 1.29289i | −0.159518 | − | 0.0761845i | ||||
\(289\) | 9.58981 | 0.564106 | ||||||||
\(290\) | −13.2774 | −0.779675 | ||||||||
\(291\) | −1.07107 | − | 6.24264i | −0.0627871 | − | 0.365950i | ||||
\(292\) | −8.14654 | − | 8.14654i | −0.476740 | − | 0.476740i | ||||
\(293\) | 12.3613 | + | 12.3613i | 0.722154 | + | 0.722154i | 0.969044 | − | 0.246889i | \(-0.0794084\pi\) |
−0.246889 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(294\) | 0.292893 | + | 1.70711i | 0.0170819 | + | 0.0995605i | ||||
\(295\) | −11.0914 | −0.645768 | ||||||||
\(296\) | 0.0363157 | 0.00211081 | ||||||||
\(297\) | 21.7348 | − | 12.1506i | 1.26118 | − | 0.705047i | ||||
\(298\) | − | 16.5748i | − | 0.960150i | ||||||
\(299\) | −10.1716 | + | 21.7934i | −0.588237 | + | 1.26035i | ||||
\(300\) | 7.01971 | + | 4.96368i | 0.405283 | + | 0.286578i | ||||
\(301\) | 5.71664 | + | 5.71664i | 0.329502 | + | 0.329502i | ||||
\(302\) | − | 11.1565i | − | 0.641986i | ||||||
\(303\) | 0.412650 | + | 0.291788i | 0.0237061 | + | 0.0167628i | ||||
\(304\) | 4.23200 | + | 4.23200i | 0.242722 | + | 0.242722i | ||||
\(305\) | −5.51563 | + | 5.51563i | −0.315824 | + | 0.315824i | ||||
\(306\) | 13.9593 | + | 6.66684i | 0.797999 | + | 0.381118i | ||||
\(307\) | 12.3914 | − | 12.3914i | 0.707213 | − | 0.707213i | −0.258735 | − | 0.965948i | \(-0.583306\pi\) |
0.965948 | + | 0.258735i | \(0.0833057\pi\) | |||||||
\(308\) | − | 4.79211i | − | 0.273056i | ||||||
\(309\) | 18.2758 | − | 25.8459i | 1.03968 | − | 1.47032i | ||||
\(310\) | −10.7771 | + | 10.7771i | −0.612096 | + | 0.612096i | ||||
\(311\) | −24.3613 | −1.38140 | −0.690701 | − | 0.723140i | \(-0.742698\pi\) | ||||
−0.690701 | + | 0.723140i | \(0.742698\pi\) | |||||||
\(312\) | −6.02412 | − | 1.64622i | −0.341048 | − | 0.0931987i | ||||
\(313\) | −20.9462 | −1.18395 | −0.591974 | − | 0.805957i | \(-0.701651\pi\) | ||||
−0.591974 | + | 0.805957i | \(0.701651\pi\) | |||||||
\(314\) | 13.1293 | − | 13.1293i | 0.740929 | − | 0.740929i | ||||
\(315\) | −8.92802 | + | 3.15653i | −0.503037 | + | 0.177850i | ||||
\(316\) | − | 2.36442i | − | 0.133009i | ||||||
\(317\) | −12.7580 | + | 12.7580i | −0.716561 | + | 0.716561i | −0.967899 | − | 0.251338i | \(-0.919129\pi\) |
0.251338 | + | 0.967899i | \(0.419129\pi\) | |||||||
\(318\) | −0.842822 | − | 4.91233i | −0.0472631 | − | 0.275470i | ||||
\(319\) | −14.2533 | + | 14.2533i | −0.798030 | + | 0.798030i | ||||
\(320\) | −2.23200 | − | 2.23200i | −0.124773 | − | 0.124773i | ||||
\(321\) | 4.82843 | − | 6.82843i | 0.269497 | − | 0.381126i | ||||
\(322\) | − | 6.67033i | − | 0.371723i | ||||||
\(323\) | −21.8225 | − | 21.8225i | −1.21423 | − | 1.21423i | ||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | 16.2174 | + | 7.56911i | 0.899581 | + | 0.419859i | ||||
\(326\) | − | 10.3835i | − | 0.575088i | ||||||
\(327\) | 5.13085 | + | 29.9048i | 0.283737 | + | 1.65374i | ||||
\(328\) | 10.1913 | 0.562719 | ||||||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | 25.8225 | − | 4.43043i | 1.42148 | − | 0.243887i | ||||
\(331\) | −12.8269 | − | 12.8269i | −0.705028 | − | 0.705028i | 0.260457 | − | 0.965485i | \(-0.416127\pi\) |
−0.965485 | + | 0.260457i | \(0.916127\pi\) | |||||||
\(332\) | 6.15653 | + | 6.15653i | 0.337884 | + | 0.337884i | ||||
\(333\) | −0.0983105 | − | 0.0469523i | −0.00538738 | − | 0.00257297i | ||||
\(334\) | −7.52095 | −0.411528 | ||||||||
\(335\) | 32.1019 | 1.75392 | ||||||||
\(336\) | 1.70711 | − | 0.292893i | 0.0931303 | − | 0.0159786i | ||||
\(337\) | − | 7.72325i | − | 0.420712i | −0.977625 | − | 0.210356i | \(-0.932538\pi\) | ||
0.977625 | − | 0.210356i | \(-0.0674624\pi\) | |||||||
\(338\) | −12.9497 | − | 1.14195i | −0.704373 | − | 0.0621137i | ||||
\(339\) | 12.4853 | − | 17.6569i | 0.678107 | − | 0.958989i | ||||
\(340\) | 11.5094 | + | 11.5094i | 0.624185 | + | 0.624185i | ||||
\(341\) | 23.1384i | 1.25301i | ||||||||
\(342\) | −5.98496 | − | 16.9280i | −0.323629 | − | 0.915362i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 5.71664 | − | 5.71664i | 0.308220 | − | 0.308220i | ||||
\(345\) | 35.9433 | − | 6.16690i | 1.93512 | − | 0.332015i | ||||
\(346\) | 9.92958 | − | 9.92958i | 0.533818 | − | 0.533818i | ||||
\(347\) | 2.65621i | 0.142593i | 0.997455 | + | 0.0712963i | \(0.0227136\pi\) | ||||
−0.997455 | + | 0.0712963i | \(0.977286\pi\) | |||||||
\(348\) | −5.94864 | − | 4.20632i | −0.318881 | − | 0.225483i | ||||
\(349\) | −18.9130 | + | 18.9130i | −1.01239 | + | 1.01239i | −0.0124660 | + | 0.999922i | \(0.503968\pi\) |
−0.999922 | + | 0.0124660i | \(0.996032\pi\) | |||||||
\(350\) | −4.96368 | −0.265320 | ||||||||
\(351\) | 14.1795 | + | 12.2450i | 0.756848 | + | 0.653591i | ||||
\(352\) | −4.79211 | −0.255420 | ||||||||
\(353\) | 18.4837 | − | 18.4837i | 0.983789 | − | 0.983789i | −0.0160816 | − | 0.999871i | \(-0.505119\pi\) |
0.999871 | + | 0.0160816i | \(0.00511917\pi\) | |||||||
\(354\) | −4.96927 | − | 3.51380i | −0.264114 | − | 0.186757i | ||||
\(355\) | 10.0783i | 0.534901i | ||||||||
\(356\) | −9.55570 | + | 9.55570i | −0.506451 | + | 0.506451i | ||||
\(357\) | −8.80275 | + | 1.51031i | −0.465891 | + | 0.0799342i | ||||
\(358\) | −1.45053 | + | 1.45053i | −0.0766629 | + | 0.0766629i | ||||
\(359\) | 19.1556 | + | 19.1556i | 1.01099 | + | 1.01099i | 0.999939 | + | 0.0110558i | \(0.00351924\pi\) |
0.0110558 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(360\) | 3.15653 | + | 8.92802i | 0.166364 | + | 0.470548i | ||||
\(361\) | 16.8197i | 0.885248i | ||||||||
\(362\) | −10.2774 | − | 10.2774i | −0.540168 | − | 0.540168i | ||||
\(363\) | 11.9643 | − | 16.9201i | 0.627965 | − | 0.888076i | ||||
\(364\) | 3.38853 | − | 1.23200i | 0.177607 | − | 0.0645746i | ||||
\(365\) | 36.3662i | 1.90350i | ||||||||
\(366\) | −4.21853 | + | 0.723784i | −0.220506 | + | 0.0378328i | ||||
\(367\) | 21.7343 | 1.13452 | 0.567259 | − | 0.823539i | \(-0.308004\pi\) | ||||
0.567259 | + | 0.823539i | \(0.308004\pi\) | |||||||
\(368\) | −6.67033 | −0.347715 | ||||||||
\(369\) | −27.5889 | − | 13.1762i | −1.43622 | − | 0.685928i | ||||
\(370\) | −0.0810568 | − | 0.0810568i | −0.00421394 | − | 0.00421394i | ||||
\(371\) | 2.03475 | + | 2.03475i | 0.105639 | + | 0.105639i | ||||
\(372\) | −8.24264 | + | 1.41421i | −0.427361 | + | 0.0733236i | ||||
\(373\) | −3.19285 | −0.165319 | −0.0826597 | − | 0.996578i | \(-0.526341\pi\) | ||||
−0.0826597 | + | 0.996578i | \(0.526341\pi\) | |||||||
\(374\) | 24.7107 | 1.27776 | ||||||||
\(375\) | 0.0335748 | + | 0.195688i | 0.00173380 | + | 0.0101053i | ||||
\(376\) | − | 6.00000i | − | 0.309426i | ||||||
\(377\) | −13.7430 | − | 6.41421i | −0.707799 | − | 0.330349i | ||||
\(378\) | −5.00000 | − | 1.41421i | −0.257172 | − | 0.0727393i | ||||
\(379\) | 17.5920 | + | 17.5920i | 0.903641 | + | 0.903641i | 0.995749 | − | 0.0921078i | \(-0.0293604\pi\) |
−0.0921078 | + | 0.995749i | \(0.529360\pi\) | |||||||
\(380\) | − | 18.8917i | − | 0.969124i | ||||||
\(381\) | −13.4647 | + | 19.0419i | −0.689815 | + | 0.975546i | ||||
\(382\) | 7.08106 | + | 7.08106i | 0.362298 | + | 0.362298i | ||||
\(383\) | 16.3870 | − | 16.3870i | 0.837335 | − | 0.837335i | −0.151172 | − | 0.988507i | \(-0.548305\pi\) |
0.988507 | + | 0.151172i | \(0.0483048\pi\) | |||||||
\(384\) | −0.292893 | − | 1.70711i | −0.0149466 | − | 0.0871154i | ||||
\(385\) | −10.6960 | + | 10.6960i | −0.545119 | + | 0.545119i | ||||
\(386\) | 13.5763i | 0.691017i | ||||||||
\(387\) | −22.8666 | + | 8.08455i | −1.16237 | + | 0.410961i | ||||
\(388\) | 2.58579 | − | 2.58579i | 0.131273 | − | 0.131273i | ||||
\(389\) | 28.0616 | 1.42278 | 0.711390 | − | 0.702797i | \(-0.248066\pi\) | ||||
0.711390 | + | 0.702797i | \(0.248066\pi\) | |||||||
\(390\) | 9.77149 | + | 17.1202i | 0.494798 | + | 0.866916i | ||||
\(391\) | 34.3958 | 1.73947 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −2.34938 | + | 3.32252i | −0.118510 | + | 0.167599i | ||||
\(394\) | 6.56360i | 0.330669i | ||||||||
\(395\) | −5.27739 | + | 5.27739i | −0.265534 | + | 0.265534i | ||||
\(396\) | 12.9728 | + | 6.19569i | 0.651906 | + | 0.311345i | ||||
\(397\) | −14.8625 | + | 14.8625i | −0.745929 | + | 0.745929i | −0.973712 | − | 0.227783i | \(-0.926852\pi\) |
0.227783 | + | 0.973712i | \(0.426852\pi\) | |||||||
\(398\) | −6.90169 | − | 6.90169i | −0.345950 | − | 0.345950i | ||||
\(399\) | 8.46401 | + | 5.98496i | 0.423730 | + | 0.299623i | ||||
\(400\) | 4.96368i | 0.248184i | ||||||||
\(401\) | −10.4862 | − | 10.4862i | −0.523656 | − | 0.523656i | 0.395018 | − | 0.918673i | \(-0.370738\pi\) |
−0.918673 | + | 0.395018i | \(0.870738\pi\) | |||||||
\(402\) | 14.3826 | + | 10.1700i | 0.717337 | + | 0.507234i | ||||
\(403\) | −16.3613 | + | 5.94864i | −0.815014 | + | 0.296323i | ||||
\(404\) | 0.291788i | 0.0145170i | ||||||||
\(405\) | 2.99791 | − | 28.2502i | 0.148967 | − | 1.40376i | ||||
\(406\) | 4.20632 | 0.208756 | ||||||||
\(407\) | −0.174029 | −0.00862629 | ||||||||
\(408\) | 1.51031 | + | 8.80275i | 0.0747716 | + | 0.435801i | ||||
\(409\) | 7.23667 | + | 7.23667i | 0.357830 | + | 0.357830i | 0.863013 | − | 0.505182i | \(-0.168575\pi\) |
−0.505182 | + | 0.863013i | \(0.668575\pi\) | |||||||
\(410\) | −22.7470 | − | 22.7470i | −1.12339 | − | 1.12339i | ||||
\(411\) | 5.01622 | + | 29.2367i | 0.247432 | + | 1.44214i | ||||
\(412\) | 18.2758 | 0.900385 | ||||||||
\(413\) | 3.51380 | 0.172903 | ||||||||
\(414\) | 18.0573 | + | 8.62403i | 0.887468 | + | 0.423848i | ||||
\(415\) | − | 27.4828i | − | 1.34908i | ||||||
\(416\) | −1.23200 | − | 3.38853i | −0.0604040 | − | 0.166137i | ||||
\(417\) | −12.0425 | − | 8.51537i | −0.589726 | − | 0.416999i | ||||
\(418\) | −20.2802 | − | 20.2802i | −0.991939 | − | 0.991939i | ||||
\(419\) | 3.69317i | 0.180423i | 0.995923 | + | 0.0902116i | \(0.0287543\pi\) | ||||
−0.995923 | + | 0.0902116i | \(0.971246\pi\) | |||||||
\(420\) | −4.46401 | − | 3.15653i | −0.217821 | − | 0.154023i | ||||
\(421\) | 20.3905 | + | 20.3905i | 0.993770 | + | 0.993770i | 0.999981 | − | 0.00621046i | \(-0.00197686\pi\) |
−0.00621046 | + | 0.999981i | \(0.501977\pi\) | |||||||
\(422\) | −6.78771 | + | 6.78771i | −0.330420 | + | 0.330420i | ||||
\(423\) | −7.75736 | + | 16.2426i | −0.377176 | + | 0.789744i | ||||
\(424\) | 2.03475 | − | 2.03475i | 0.0988163 | − | 0.0988163i | ||||
\(425\) | − | 25.5954i | − | 1.24156i | ||||||
\(426\) | −3.19285 | + | 4.51537i | −0.154694 | + | 0.218770i | ||||
\(427\) | 1.74737 | − | 1.74737i | 0.0845612 | − | 0.0845612i | ||||
\(428\) | 4.82843 | 0.233391 | ||||||||
\(429\) | 28.8682 | + | 7.88886i | 1.39377 | + | 0.380878i | ||||
\(430\) | −25.5191 | −1.23064 | ||||||||
\(431\) | 7.55635 | − | 7.55635i | 0.363977 | − | 0.363977i | −0.501298 | − | 0.865275i | \(-0.667144\pi\) |
0.865275 | + | 0.501298i | \(0.167144\pi\) | |||||||
\(432\) | −1.41421 | + | 5.00000i | −0.0680414 | + | 0.240563i | ||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | 3.41421 | − | 3.41421i | 0.163887 | − | 0.163887i | ||||
\(435\) | 3.88886 | + | 22.6659i | 0.186456 | + | 1.08675i | ||||
\(436\) | −12.3870 | + | 12.3870i | −0.593228 | + | 0.593228i | ||||
\(437\) | −28.2289 | − | 28.2289i | −1.35037 | − | 1.35037i | ||||
\(438\) | −11.5209 | + | 16.2931i | −0.550492 | + | 0.778514i | ||||
\(439\) | − | 39.3066i | − | 1.87600i | −0.346635 | − | 0.938000i | \(-0.612676\pi\) | ||
0.346635 | − | 0.938000i | \(-0.387324\pi\) | |||||||
\(440\) | 10.6960 | + | 10.6960i | 0.509912 | + | 0.509912i | ||||
\(441\) | 2.82843 | − | 1.00000i | 0.134687 | − | 0.0476190i | ||||
\(442\) | 6.35287 | + | 17.4731i | 0.302175 | + | 0.831110i | ||||
\(443\) | − | 7.37075i | − | 0.350195i | −0.984551 | − | 0.175097i | \(-0.943976\pi\) | ||
0.984551 | − | 0.175097i | \(-0.0560241\pi\) | |||||||
\(444\) | −0.0106366 | − | 0.0619948i | −0.000504792 | − | 0.00294214i | ||||
\(445\) | 42.6567 | 2.02212 | ||||||||
\(446\) | 22.9762 | 1.08796 | ||||||||
\(447\) | −28.2949 | + | 4.85464i | −1.33830 | + | 0.229616i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −9.39255 | − | 9.39255i | −0.443262 | − | 0.443262i | 0.449845 | − | 0.893107i | \(-0.351479\pi\) |
−0.893107 | + | 0.449845i | \(0.851479\pi\) | |||||||
\(450\) | 6.41751 | − | 13.4372i | 0.302525 | − | 0.633437i | ||||
\(451\) | −48.8378 | −2.29968 | ||||||||
\(452\) | 12.4853 | 0.587258 | ||||||||
\(453\) | −19.0454 | + | 3.26767i | −0.894830 | + | 0.153529i | ||||
\(454\) | 2.72663i | 0.127967i | ||||||||
\(455\) | −10.3131 | − | 4.81338i | −0.483484 | − | 0.225655i | ||||
\(456\) | 5.98496 | − | 8.46401i | 0.280271 | − | 0.396363i | ||||
\(457\) | 8.79276 | + | 8.79276i | 0.411308 | + | 0.411308i | 0.882194 | − | 0.470886i | \(-0.156066\pi\) |
−0.470886 | + | 0.882194i | \(0.656066\pi\) | |||||||
\(458\) | 1.68694i | 0.0788255i | ||||||||
\(459\) | 7.29244 | − | 25.7827i | 0.340382 | − | 1.20343i | ||||
\(460\) | 14.8882 | + | 14.8882i | 0.694166 | + | 0.694166i | ||||
\(461\) | −19.2327 | + | 19.2327i | −0.895754 | + | 0.895754i | −0.995057 | − | 0.0993033i | \(-0.968339\pi\) |
0.0993033 | + | 0.995057i | \(0.468339\pi\) | |||||||
\(462\) | −8.18065 | + | 1.40358i | −0.380598 | + | 0.0653003i | ||||
\(463\) | −6.23200 | + | 6.23200i | −0.289626 | + | 0.289626i | −0.836932 | − | 0.547306i | \(-0.815653\pi\) |
0.547306 | + | 0.836932i | \(0.315653\pi\) | |||||||
\(464\) | − | 4.20632i | − | 0.195274i | ||||||
\(465\) | 21.5541 | + | 15.2411i | 0.999549 | + | 0.706788i | ||||
\(466\) | 14.1058 | − | 14.1058i | 0.653439 | − | 0.653439i | ||||
\(467\) | 0.932952 | 0.0431719 | 0.0215859 | − | 0.999767i | \(-0.493128\pi\) | ||||
0.0215859 | + | 0.999767i | \(0.493128\pi\) | |||||||
\(468\) | −1.04585 | + | 10.7660i | −0.0483443 | + | 0.497657i | ||||
\(469\) | −10.1700 | −0.469607 | ||||||||
\(470\) | −13.3920 | + | 13.3920i | −0.617728 | + | 0.617728i | ||||
\(471\) | −26.2586 | − | 18.5676i | −1.20993 | − | 0.855551i | ||||
\(472\) | − | 3.51380i | − | 0.161736i | ||||||
\(473\) | −27.3948 | + | 27.3948i | −1.25961 | + | 1.25961i | ||||
\(474\) | −4.03632 | + | 0.692522i | −0.185394 | + | 0.0318086i | ||||
\(475\) | −21.0063 | + | 21.0063i | −0.963837 | + | 0.963837i | ||||
\(476\) | −3.64622 | − | 3.64622i | −0.167124 | − | 0.167124i | ||||
\(477\) | −8.13901 | + | 2.87757i | −0.372660 | + | 0.131755i | ||||
\(478\) | − | 10.5849i | − | 0.484141i | ||||||
\(479\) | −25.7489 | − | 25.7489i | −1.17650 | − | 1.17650i | −0.980630 | − | 0.195867i | \(-0.937248\pi\) |
−0.195867 | − | 0.980630i | \(-0.562752\pi\) | |||||||
\(480\) | −3.15653 | + | 4.46401i | −0.144075 | + | 0.203753i | ||||
\(481\) | −0.0447411 | − | 0.123057i | −0.00204002 | − | 0.00561092i | ||||
\(482\) | 4.85851i | 0.221299i | ||||||||
\(483\) | −11.3870 | + | 1.95370i | −0.518125 | + | 0.0888962i | ||||
\(484\) | 11.9643 | 0.543833 | ||||||||
\(485\) | −11.5430 | −0.524139 | ||||||||
\(486\) | 10.2929 | − | 11.7071i | 0.466895 | − | 0.531045i | ||||
\(487\) | 18.4640 | + | 18.4640i | 0.836684 | + | 0.836684i | 0.988421 | − | 0.151737i | \(-0.0484866\pi\) |
−0.151737 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(488\) | −1.74737 | − | 1.74737i | −0.0790997 | − | 0.0790997i | ||||
\(489\) | −17.7257 | + | 3.04125i | −0.801584 | + | 0.137530i | ||||
\(490\) | 3.15653 | 0.142598 | ||||||||
\(491\) | 1.56608 | 0.0706761 | 0.0353380 | − | 0.999375i | \(-0.488749\pi\) | ||||
0.0353380 | + | 0.999375i | \(0.488749\pi\) | |||||||
\(492\) | −2.98496 | − | 17.3976i | −0.134572 | − | 0.784345i | ||||
\(493\) | 21.6900i | 0.976870i | ||||||||
\(494\) | 9.12645 | − | 19.5541i | 0.410618 | − | 0.879782i | ||||
\(495\) | −15.1264 | − | 42.7840i | −0.679883 | − | 1.92300i | ||||
\(496\) | −3.41421 | − | 3.41421i | −0.153303 | − | 0.153303i | ||||
\(497\) | − | 3.19285i | − | 0.143219i | ||||||
\(498\) | 8.70665 | − | 12.3131i | 0.390154 | − | 0.551761i | ||||
\(499\) | −21.8475 | − | 21.8475i | −0.978028 | − | 0.978028i | 0.0217358 | − | 0.999764i | \(-0.493081\pi\) |
−0.999764 | + | 0.0217358i | \(0.993081\pi\) | |||||||
\(500\) | −0.0810568 | + | 0.0810568i | −0.00362497 | + | 0.00362497i | ||||
\(501\) | 2.20284 | + | 12.8391i | 0.0984154 | + | 0.573607i | ||||
\(502\) | 6.31747 | − | 6.31747i | 0.281962 | − | 0.281962i | ||||
\(503\) | − | 16.4853i | − | 0.735042i | −0.930015 | − | 0.367521i | \(-0.880207\pi\) | ||
0.930015 | − | 0.367521i | \(-0.119793\pi\) | |||||||
\(504\) | −1.00000 | − | 2.82843i | −0.0445435 | − | 0.125988i | ||||
\(505\) | 0.651271 | − | 0.651271i | 0.0289812 | − | 0.0289812i | ||||
\(506\) | 31.9650 | 1.42102 | ||||||||
\(507\) | 1.84347 | + | 22.4411i | 0.0818714 | + | 0.996643i | ||||
\(508\) | −13.4647 | −0.597397 | ||||||||
\(509\) | −11.2526 | + | 11.2526i | −0.498764 | + | 0.498764i | −0.911053 | − | 0.412289i | \(-0.864729\pi\) |
0.412289 | + | 0.911053i | \(0.364729\pi\) | |||||||
\(510\) | 16.2767 | − | 23.0188i | 0.720746 | − | 1.01929i | ||||
\(511\) | − | 11.5209i | − | 0.509657i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −27.1450 | + | 15.1751i | −1.19848 | + | 0.669995i | ||||
\(514\) | −4.77707 | + | 4.77707i | −0.210707 | + | 0.210707i | ||||
\(515\) | −40.7917 | − | 40.7917i | −1.79750 | − | 1.79750i | ||||
\(516\) | −11.4333 | − | 8.08455i | −0.503322 | − | 0.355902i | ||||
\(517\) | 28.7527i | 1.26454i | ||||||||
\(518\) | 0.0256791 | + | 0.0256791i | 0.00112827 | + | 0.00112827i | ||||
\(519\) | −19.8592 | − | 14.0425i | −0.871720 | − | 0.616399i | ||||
\(520\) | −4.81338 | + | 10.3131i | −0.211081 | + | 0.452258i | ||||
\(521\) | 12.5304i | 0.548967i | 0.961592 | + | 0.274484i | \(0.0885069\pi\) | ||||
−0.961592 | + | 0.274484i | \(0.911493\pi\) | |||||||
\(522\) | −5.43833 | + | 11.3870i | −0.238029 | + | 0.498394i | ||||
\(523\) | 14.2148 | 0.621568 | 0.310784 | − | 0.950481i | \(-0.399408\pi\) | ||||
0.310784 | + | 0.950481i | \(0.399408\pi\) | |||||||
\(524\) | −2.34938 | −0.102633 | ||||||||
\(525\) | 1.45383 | + | 8.47354i | 0.0634503 | + | 0.369816i | ||||
\(526\) | −4.08390 | − | 4.08390i | −0.178066 | − | 0.178066i | ||||
\(527\) | 17.6055 | + | 17.6055i | 0.766907 | + | 0.766907i | ||||
\(528\) | 1.40358 | + | 8.18065i | 0.0610828 | + | 0.356017i | ||||
\(529\) | 21.4933 | 0.934493 | ||||||||
\(530\) | −9.08315 | −0.394547 | ||||||||
\(531\) | −4.54297 | + | 9.51224i | −0.197148 | + | 0.412796i | ||||
\(532\) | 5.98496i | 0.259481i | ||||||||
\(533\) | −12.5557 | − | 34.5335i | −0.543848 | − | 1.49581i | ||||
\(534\) | 19.1114 | + | 13.5138i | 0.827031 | + | 0.584799i | ||||
\(535\) | −10.7771 | − | 10.7771i | −0.465933 | − | 0.465933i | ||||
\(536\) | 10.1700i | 0.439277i | ||||||||
\(537\) | 2.90106 | + | 2.05136i | 0.125190 | + | 0.0885226i | ||||
\(538\) | −4.20632 | − | 4.20632i | −0.181348 | − | 0.181348i | ||||
\(539\) | 3.38853 | − | 3.38853i | 0.145955 | − | 0.145955i | ||||
\(540\) | 14.3166 | − | 8.00349i | 0.616086 | − | 0.344415i | ||||
\(541\) | −25.4872 | + | 25.4872i | −1.09578 | + | 1.09578i | −0.100882 | + | 0.994898i | \(0.532167\pi\) |
−0.994898 | + | 0.100882i | \(0.967833\pi\) | |||||||
\(542\) | 1.19285i | 0.0512371i | ||||||||
\(543\) | −14.5344 | + | 20.5548i | −0.623732 | + | 0.882090i | ||||
\(544\) | −3.64622 | + | 3.64622i | −0.156330 | + | 0.156330i | ||||
\(545\) | 55.2955 | 2.36860 | ||||||||
\(546\) | −3.09564 | − | 5.42374i | −0.132481 | − | 0.232115i | ||||
\(547\) | −31.3407 | −1.34003 | −0.670015 | − | 0.742348i | \(-0.733712\pi\) | ||||
−0.670015 | + | 0.742348i | \(0.733712\pi\) | |||||||
\(548\) | −12.1102 | + | 12.1102i | −0.517323 | + | 0.517323i | ||||
\(549\) | 2.47115 | + | 6.98948i | 0.105466 | + | 0.298304i | ||||
\(550\) | − | 23.7865i | − | 1.01426i | ||||||
\(551\) | 17.8012 | − | 17.8012i | 0.758356 | − | 0.758356i | ||||
\(552\) | 1.95370 | + | 11.3870i | 0.0831548 | + | 0.484662i | ||||
\(553\) | 1.67190 | − | 1.67190i | 0.0710963 | − | 0.0710963i | ||||
\(554\) | 2.64906 | + | 2.64906i | 0.112548 | + | 0.112548i | ||||
\(555\) | −0.114632 | + | 0.162114i | −0.00486584 | + | 0.00688134i | ||||
\(556\) | − | 8.51537i | − | 0.361132i | ||||||
\(557\) | 18.4198 | + | 18.4198i | 0.780472 | + | 0.780472i | 0.979910 | − | 0.199439i | \(-0.0639118\pi\) |
−0.199439 | + | 0.979910i | \(0.563912\pi\) | |||||||
\(558\) | 4.82843 | + | 13.6569i | 0.204404 | + | 0.578141i | ||||
\(559\) | −26.4139 | − | 12.3281i | −1.11719 | − | 0.521423i | ||||
\(560\) | − | 3.15653i | − | 0.133388i | ||||||
\(561\) | −7.23759 | − | 42.1837i | −0.305571 | − | 1.78100i | ||||
\(562\) | −15.0388 | −0.634372 | ||||||||
\(563\) | 22.9944 | 0.969099 | 0.484550 | − | 0.874764i | \(-0.338984\pi\) | ||||
0.484550 | + | 0.874764i | \(0.338984\pi\) | |||||||
\(564\) | −10.2426 | + | 1.75736i | −0.431293 | + | 0.0739982i | ||||
\(565\) | −27.8672 | − | 27.8672i | −1.17238 | − | 1.17238i | ||||
\(566\) | −22.7208 | − | 22.7208i | −0.955025 | − | 0.955025i | ||||
\(567\) | −0.949747 | + | 8.94975i | −0.0398856 | + | 0.375854i | ||||
\(568\) | −3.19285 | −0.133969 | ||||||||
\(569\) | −44.0664 | −1.84736 | −0.923679 | − | 0.383166i | \(-0.874834\pi\) | ||||
−0.923679 | + | 0.383166i | \(0.874834\pi\) | |||||||
\(570\) | −32.2502 | + | 5.53325i | −1.35081 | + | 0.231762i | ||||
\(571\) | − | 19.0689i | − | 0.798007i | −0.916949 | − | 0.399003i | \(-0.869356\pi\) | ||
0.916949 | − | 0.399003i | \(-0.130644\pi\) | |||||||
\(572\) | 5.90390 | + | 16.2382i | 0.246854 | + | 0.678955i | ||||
\(573\) | 10.0141 | − | 14.1621i | 0.418346 | − | 0.591631i | ||||
\(574\) | 7.20632 | + | 7.20632i | 0.300786 | + | 0.300786i | ||||
\(575\) | − | 33.1094i | − | 1.38076i | ||||||
\(576\) | −2.82843 | + | 1.00000i | −0.117851 | + | 0.0416667i | ||||
\(577\) | −22.9201 | − | 22.9201i | −0.954177 | − | 0.954177i | 0.0448181 | − | 0.998995i | \(-0.485729\pi\) |
−0.998995 | + | 0.0448181i | \(0.985729\pi\) | |||||||
\(578\) | 6.78102 | − | 6.78102i | 0.282053 | − | 0.282053i | ||||
\(579\) | 23.1762 | − | 3.97641i | 0.963172 | − | 0.165254i | ||||
\(580\) | −9.38853 | + | 9.38853i | −0.389838 | + | 0.389838i | ||||
\(581\) | 8.70665i | 0.361213i | ||||||||
\(582\) | −5.17157 | − | 3.65685i | −0.214369 | − | 0.151581i | ||||
\(583\) | −9.75076 | + | 9.75076i | −0.403835 | + | 0.403835i | ||||
\(584\) | −11.5209 | −0.476740 | ||||||||
\(585\) | 26.3640 | − | 21.6954i | 1.09002 | − | 0.896993i | ||||
\(586\) | 17.4815 | 0.722154 | ||||||||
\(587\) | −10.7264 | + | 10.7264i | −0.442724 | + | 0.442724i | −0.892927 | − | 0.450202i | \(-0.851352\pi\) |
0.450202 | + | 0.892927i | \(0.351352\pi\) | |||||||
\(588\) | 1.41421 | + | 1.00000i | 0.0583212 | + | 0.0412393i | ||||
\(589\) | − | 28.8979i | − | 1.19072i | ||||||
\(590\) | −7.84282 | + | 7.84282i | −0.322884 | + | 0.322884i | ||||
\(591\) | 11.2048 | − | 1.92243i | 0.460902 | − | 0.0790783i | ||||
\(592\) | 0.0256791 | − | 0.0256791i | 0.00105540 | − | 0.00105540i | ||||
\(593\) | 28.7454 | + | 28.7454i | 1.18043 | + | 1.18043i | 0.979632 | + | 0.200801i | \(0.0643544\pi\) |
0.200801 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(594\) | 6.77707 | − | 23.9606i | 0.278067 | − | 0.983114i | ||||
\(595\) | 16.2767i | 0.667281i | ||||||||
\(596\) | −11.7201 | − | 11.7201i | −0.480075 | − | 0.480075i | ||||
\(597\) | −9.76046 | + | 13.8034i | −0.399469 | + | 0.564935i | ||||
\(598\) | 8.21788 | + | 22.6027i | 0.336054 | + | 0.924291i | ||||
\(599\) | − | 17.6396i | − | 0.720735i | −0.932811 | − | 0.360367i | \(-0.882651\pi\) | ||
0.932811 | − | 0.360367i | \(-0.117349\pi\) | |||||||
\(600\) | 8.47354 | − | 1.45383i | 0.345931 | − | 0.0593523i | ||||
\(601\) | 5.17287 | 0.211006 | 0.105503 | − | 0.994419i | \(-0.466355\pi\) | ||||
0.105503 | + | 0.994419i | \(0.466355\pi\) | |||||||
\(602\) | 8.08455 | 0.329502 | ||||||||
\(603\) | 13.1487 | − | 27.5313i | 0.535458 | − | 1.12116i | ||||
\(604\) | −7.88886 | − | 7.88886i | −0.320993 | − | 0.320993i | ||||
\(605\) | −26.7044 | − | 26.7044i | −1.08569 | − | 1.08569i | ||||
\(606\) | 0.498113 | − | 0.0854626i | 0.0202344 | − | 0.00347168i | ||||
\(607\) | 40.2727 | 1.63462 | 0.817309 | − | 0.576199i | \(-0.195465\pi\) | ||||
0.817309 | + | 0.576199i | \(0.195465\pi\) | |||||||
\(608\) | 5.98496 | 0.242722 | ||||||||
\(609\) | −1.23200 | − | 7.18065i | −0.0499233 | − | 0.290974i | ||||
\(610\) | 7.80028i | 0.315824i | ||||||||
\(611\) | −20.3312 | + | 7.39202i | −0.822513 | + | 0.299049i | ||||
\(612\) | 14.5849 | − | 5.15653i | 0.589558 | − | 0.208440i | ||||
\(613\) | −28.3087 | − | 28.3087i | −1.14338 | − | 1.14338i | −0.987828 | − | 0.155547i | \(-0.950286\pi\) |
−0.155547 | − | 0.987828i | \(-0.549714\pi\) | |||||||
\(614\) | − | 17.5241i | − | 0.707213i | ||||||
\(615\) | −32.1691 | + | 45.4940i | −1.29718 | + | 1.83449i | ||||
\(616\) | −3.38853 | − | 3.38853i | −0.136528 | − | 0.136528i | ||||
\(617\) | −28.8059 | + | 28.8059i | −1.15968 | + | 1.15968i | −0.175136 | + | 0.984544i | \(0.556036\pi\) |
−0.984544 | + | 0.175136i | \(0.943964\pi\) | |||||||
\(618\) | −5.35287 | − | 31.1988i | −0.215324 | − | 1.25500i | ||||
\(619\) | 10.9608 | − | 10.9608i | 0.440553 | − | 0.440553i | −0.451645 | − | 0.892198i | \(-0.649162\pi\) |
0.892198 | + | 0.451645i | \(0.149162\pi\) | |||||||
\(620\) | 15.2411i | 0.612096i | ||||||||
\(621\) | 9.43328 | − | 33.3517i | 0.378544 | − | 1.33836i | ||||
\(622\) | −17.2260 | + | 17.2260i | −0.690701 | + | 0.690701i | ||||
\(623\) | −13.5138 | −0.541419 | ||||||||
\(624\) | −5.42374 | + | 3.09564i | −0.217124 | + | 0.123925i | ||||
\(625\) | 25.1803 | 1.00721 | ||||||||
\(626\) | −14.8112 | + | 14.8112i | −0.591974 | + | 0.591974i | ||||
\(627\) | −28.6806 | + | 40.5605i | −1.14539 | + | 1.61983i | ||||
\(628\) | − | 18.5676i | − | 0.740929i | ||||||
\(629\) | −0.132415 | + | 0.132415i | −0.00527973 | + | 0.00527973i | ||||
\(630\) | −4.08106 | + | 8.54506i | −0.162593 | + | 0.340444i | ||||
\(631\) | 10.9064 | − | 10.9064i | 0.434175 | − | 0.434175i | −0.455871 | − | 0.890046i | \(-0.650672\pi\) |
0.890046 | + | 0.455871i | \(0.150672\pi\) | |||||||
\(632\) | −1.67190 | − | 1.67190i | −0.0665045 | − | 0.0665045i | ||||
\(633\) | 13.5754 | + | 9.59927i | 0.539574 | + | 0.381537i | ||||
\(634\) | 18.0425i | 0.716561i | ||||||||
\(635\) | 30.0532 | + | 30.0532i | 1.19262 | + | 1.19262i | ||||
\(636\) | −4.06950 | − | 2.87757i | −0.161366 | − | 0.114103i | ||||
\(637\) | 3.26721 | + | 1.52490i | 0.129452 | + | 0.0604186i | ||||
\(638\) | 20.1572i | 0.798030i | ||||||||
\(639\) | 8.64338 | + | 4.12801i | 0.341927 | + | 0.163302i | ||||
\(640\) | −3.15653 | −0.124773 | ||||||||
\(641\) | −19.7733 | −0.780998 | −0.390499 | − | 0.920603i | \(-0.627698\pi\) | ||||
−0.390499 | + | 0.920603i | \(0.627698\pi\) | |||||||
\(642\) | −1.41421 | − | 8.24264i | −0.0558146 | − | 0.325311i | ||||
\(643\) | 25.4731 | + | 25.4731i | 1.00456 | + | 1.00456i | 0.999990 | + | 0.00457070i | \(0.00145491\pi\) |
0.00457070 | + | 0.999990i | \(0.498545\pi\) | |||||||
\(644\) | −4.71664 | − | 4.71664i | −0.185862 | − | 0.185862i | ||||
\(645\) | 7.47438 | + | 43.5639i | 0.294303 | + | 1.71533i | ||||
\(646\) | −30.8616 | −1.21423 | ||||||||
\(647\) | −3.91856 | −0.154054 | −0.0770272 | − | 0.997029i | \(-0.524543\pi\) | ||||
−0.0770272 | + | 0.997029i | \(0.524543\pi\) | |||||||
\(648\) | 8.94975 | + | 0.949747i | 0.351579 | + | 0.0373096i | ||||
\(649\) | 16.8385i | 0.660970i | ||||||||
\(650\) | 16.8196 | − | 6.11528i | 0.659720 | − | 0.239861i | ||||
\(651\) | −6.82843 | − | 4.82843i | −0.267627 | − | 0.189241i | ||||
\(652\) | −7.34223 | − | 7.34223i | −0.287544 | − | 0.287544i | ||||
\(653\) | − | 2.45301i | − | 0.0959937i | −0.998847 | − | 0.0479968i | \(-0.984716\pi\) | ||
0.998847 | − | 0.0479968i | \(-0.0152837\pi\) | |||||||
\(654\) | 24.7739 | + | 17.5178i | 0.968738 | + | 0.685001i | ||||
\(655\) | 5.24382 | + | 5.24382i | 0.204893 | + | 0.204893i | ||||
\(656\) | 7.20632 | − | 7.20632i | 0.281360 | − | 0.281360i | ||||
\(657\) | 31.1884 | + | 14.8954i | 1.21678 | + | 0.581123i | ||||
\(658\) | 4.24264 | − | 4.24264i | 0.165395 | − | 0.165395i | ||||
\(659\) | 21.5272i | 0.838580i | 0.907852 | + | 0.419290i | \(0.137721\pi\) | ||||
−0.907852 | + | 0.419290i | \(0.862279\pi\) | |||||||
\(660\) | 15.1264 | − | 21.3920i | 0.588796 | − | 0.832683i | ||||
\(661\) | 10.4361 | − | 10.4361i | 0.405919 | − | 0.405919i | −0.474394 | − | 0.880313i | \(-0.657333\pi\) |
0.880313 | + | 0.474394i | \(0.157333\pi\) | |||||||
\(662\) | −18.1399 | −0.705028 | ||||||||
\(663\) | 27.9677 | − | 15.9628i | 1.08618 | − | 0.619943i | ||||
\(664\) | 8.70665 | 0.337884 | ||||||||
\(665\) | 13.3584 | − | 13.3584i | 0.518018 | − | 0.518018i | ||||
\(666\) | −0.102716 | + | 0.0363157i | −0.00398018 | + | 0.00140720i | ||||
\(667\) | 28.0576i | 1.08639i | ||||||||
\(668\) | −5.31811 | + | 5.31811i | −0.205764 | + | 0.205764i | ||||
\(669\) | −6.72959 | − | 39.2229i | −0.260181 | − | 1.51645i | ||||
\(670\) | 22.6995 | − | 22.6995i | 0.876958 | − | 0.876958i | ||||
\(671\) | 8.37359 | + | 8.37359i | 0.323259 | + | 0.323259i | ||||
\(672\) | 1.00000 | − | 1.41421i | 0.0385758 | − | 0.0545545i | ||||
\(673\) | 12.8064i | 0.493651i | 0.969060 | + | 0.246825i | \(0.0793874\pi\) | ||||
−0.969060 | + | 0.246825i | \(0.920613\pi\) | |||||||
\(674\) | −5.46117 | − | 5.46117i | −0.210356 | − | 0.210356i | ||||
\(675\) | −24.8184 | − | 7.01971i | −0.955261 | − | 0.270189i | ||||
\(676\) | −9.96433 | + | 8.34938i | −0.383244 | + | 0.321130i | ||||
\(677\) | 5.56424i | 0.213851i | 0.994267 | + | 0.106926i | \(0.0341007\pi\) | ||||
−0.994267 | + | 0.106926i | \(0.965899\pi\) | |||||||
\(678\) | −3.65685 | − | 21.3137i | −0.140441 | − | 0.818548i | ||||
\(679\) | 3.65685 | 0.140337 | ||||||||
\(680\) | 16.2767 | 0.624185 | ||||||||
\(681\) | 4.65464 | − | 0.798610i | 0.178366 | − | 0.0306028i | ||||
\(682\) | 16.3613 | + | 16.3613i | 0.626506 | + | 0.626506i | ||||
\(683\) | 22.6991 | + | 22.6991i | 0.868558 | + | 0.868558i | 0.992313 | − | 0.123755i | \(-0.0394938\pi\) |
−0.123755 | + | 0.992313i | \(0.539494\pi\) | |||||||
\(684\) | −16.2019 | − | 7.73791i | −0.619496 | − | 0.295866i | ||||
\(685\) | 54.0601 | 2.06553 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 2.87979 | − | 0.494093i | 0.109871 | − | 0.0188508i | ||||
\(688\) | − | 8.08455i | − | 0.308220i | ||||||
\(689\) | −9.40165 | − | 4.38800i | −0.358174 | − | 0.167170i | ||||
\(690\) | 21.0551 | − | 29.7764i | 0.801554 | − | 1.13357i | ||||
\(691\) | −3.18274 | − | 3.18274i | −0.121077 | − | 0.121077i | 0.643972 | − | 0.765049i | \(-0.277285\pi\) |
−0.765049 | + | 0.643972i | \(0.777285\pi\) | |||||||
\(692\) | − | 14.0425i | − | 0.533818i | ||||||
\(693\) | 4.79211 | + | 13.5541i | 0.182037 | + | 0.514879i | ||||
\(694\) | 1.87822 | + | 1.87822i | 0.0712963 | + | 0.0712963i | ||||
\(695\) | −19.0063 | + | 19.0063i | −0.720951 | + | 0.720951i | ||||
\(696\) | −7.18065 | + | 1.23200i | −0.272182 | + | 0.0466990i | ||||
\(697\) | −37.1596 | + | 37.1596i | −1.40752 | + | 1.40752i | ||||
\(698\) | 26.7470i | 1.01239i | ||||||||
\(699\) | −28.2116 | − | 19.9486i | −1.06706 | − | 0.754527i | ||||
\(700\) | −3.50985 | + | 3.50985i | −0.132660 | + | 0.132660i | ||||
\(701\) | 2.11061 | 0.0797167 | 0.0398584 | − | 0.999205i | \(-0.487309\pi\) | ||||
0.0398584 | + | 0.999205i | \(0.487309\pi\) | |||||||
\(702\) | 18.6850 | − | 1.36791i | 0.705219 | − | 0.0516284i | ||||
\(703\) | 0.217348 | 0.00819743 | ||||||||
\(704\) | −3.38853 | + | 3.38853i | −0.127710 | + | 0.127710i | ||||
\(705\) | 26.7840 | + | 18.9392i | 1.00875 | + | 0.713291i | ||||
\(706\) | − | 26.1399i | − | 0.983789i | ||||||
\(707\) | −0.206325 | + | 0.206325i | −0.00775965 | + | 0.00775965i | ||||
\(708\) | −5.99844 | + | 1.02917i | −0.225435 | + | 0.0386785i | ||||
\(709\) | 27.5250 | − | 27.5250i | 1.03372 | − | 1.03372i | 0.0343107 | − | 0.999411i | \(-0.489076\pi\) |
0.999411 | − | 0.0343107i | \(-0.0109236\pi\) | |||||||
\(710\) | 7.12645 | + | 7.12645i | 0.267451 | + | 0.267451i | ||||
\(711\) | 2.36442 | + | 6.68759i | 0.0886726 | + | 0.250804i | ||||
\(712\) | 13.5138i | 0.506451i | ||||||||
\(713\) | 22.7739 | + | 22.7739i | 0.852891 | + | 0.852891i | ||||
\(714\) | −5.15653 | + | 7.29244i | −0.192978 | + | 0.272913i | ||||
\(715\) | 23.0663 | − | 49.4213i | 0.862630 | − | 1.84825i | ||||
\(716\) | 2.05136i | 0.0766629i | ||||||||
\(717\) | −18.0695 | + | 3.10024i | −0.674818 | + | 0.115780i | ||||
\(718\) | 27.0901 | 1.01099 | ||||||||
\(719\) | 47.6706 | 1.77781 | 0.888906 | − | 0.458089i | \(-0.151466\pi\) | ||||
0.888906 | + | 0.458089i | \(0.151466\pi\) | |||||||
\(720\) | 8.54506 | + | 4.08106i | 0.318456 | + | 0.152092i | ||||
\(721\) | 12.9230 | + | 12.9230i | 0.481276 | + | 0.481276i | ||||
\(722\) | 11.8933 | + | 11.8933i | 0.442624 | + | 0.442624i | ||||
\(723\) | 8.29400 | − | 1.42303i | 0.308457 | − | 0.0529229i | ||||
\(724\) | −14.5344 | −0.540168 | ||||||||
\(725\) | 20.8789 | 0.775422 | ||||||||
\(726\) | −3.50427 | − | 20.4244i | −0.130056 | − | 0.758020i | ||||
\(727\) | 37.3478i | 1.38515i | 0.721344 | + | 0.692577i | \(0.243525\pi\) | ||||
−0.721344 | + | 0.692577i | \(0.756475\pi\) | |||||||
\(728\) | 1.52490 | − | 3.26721i | 0.0565165 | − | 0.121091i | ||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 25.7148 | + | 25.7148i | 0.951748 | + | 0.951748i | ||||
\(731\) | 41.6882i | 1.54189i | ||||||||
\(732\) | −2.47115 | + | 3.49474i | −0.0913365 | + | 0.129169i | ||||
\(733\) | −24.1834 | − | 24.1834i | −0.893234 | − | 0.893234i | 0.101592 | − | 0.994826i | \(-0.467606\pi\) |
−0.994826 | + | 0.101592i | \(0.967606\pi\) | |||||||
\(734\) | 15.3684 | − | 15.3684i | 0.567259 | − | 0.567259i | ||||
\(735\) | −0.924526 | − | 5.38853i | −0.0341017 | − | 0.198759i | ||||
\(736\) | −4.71664 | + | 4.71664i | −0.173858 | + | 0.173858i | ||||
\(737\) | − | 48.7358i | − | 1.79521i | ||||||
\(738\) | −28.8253 | + | 10.1913i | −1.06107 | + | 0.375146i | ||||
\(739\) | 4.86811 | − | 4.86811i | 0.179076 | − | 0.179076i | −0.611877 | − | 0.790953i | \(-0.709585\pi\) |
0.790953 | + | 0.611877i | \(0.209585\pi\) | |||||||
\(740\) | −0.114632 | −0.00421394 | ||||||||
\(741\) | −36.0541 | − | 9.85254i | −1.32448 | − | 0.361942i | ||||
\(742\) | 2.87757 | 0.105639 | ||||||||
\(743\) | −15.2292 | + | 15.2292i | −0.558704 | + | 0.558704i | −0.928938 | − | 0.370235i | \(-0.879277\pi\) |
0.370235 | + | 0.928938i | \(0.379277\pi\) | |||||||
\(744\) | −4.82843 | + | 6.82843i | −0.177019 | + | 0.250342i | ||||
\(745\) | 52.3187i | 1.91681i | ||||||||
\(746\) | −2.25768 | + | 2.25768i | −0.0826597 | + | 0.0826597i | ||||
\(747\) | −23.5698 | − | 11.2568i | −0.862375 | − | 0.411864i | ||||
\(748\) | 17.4731 | − | 17.4731i | 0.638879 | − | 0.638879i | ||||
\(749\) | 3.41421 | + | 3.41421i | 0.124753 | + | 0.124753i | ||||
\(750\) | 0.162114 | + | 0.114632i | 0.00591955 | + | 0.00418575i | ||||
\(751\) | − | 18.3857i | − | 0.670903i | −0.942057 | − | 0.335452i | \(-0.891111\pi\) | ||
0.942057 | − | 0.335452i | \(-0.108889\pi\) | |||||||
\(752\) | −4.24264 | − | 4.24264i | −0.154713 | − | 0.154713i | ||||
\(753\) | −12.6349 | − | 8.93425i | −0.460443 | − | 0.325582i | ||||
\(754\) | −14.2533 | + | 5.18221i | −0.519074 | + | 0.188725i | ||||
\(755\) | 35.2159i | 1.28164i | ||||||||
\(756\) | −4.53553 | + | 2.53553i | −0.164956 | + | 0.0922165i | ||||
\(757\) | −30.2116 | −1.09806 | −0.549030 | − | 0.835802i | \(-0.685003\pi\) | ||||
−0.549030 | + | 0.835802i | \(0.685003\pi\) | |||||||
\(758\) | 24.8789 | 0.903641 | ||||||||
\(759\) | −9.36233 | − | 54.5676i | −0.339831 | − | 1.98068i | ||||
\(760\) | −13.3584 | − | 13.3584i | −0.484562 | − | 0.484562i | ||||
\(761\) | −8.02284 | − | 8.02284i | −0.290828 | − | 0.290828i | 0.546580 | − | 0.837407i | \(-0.315930\pi\) |
−0.837407 | + | 0.546580i | \(0.815930\pi\) | |||||||
\(762\) | 3.94371 | + | 22.9856i | 0.142865 | + | 0.832681i | ||||
\(763\) | −17.5178 | −0.634188 | ||||||||
\(764\) | 10.0141 | 0.362298 | ||||||||
\(765\) | −44.0629 | − | 21.0441i | −1.59310 | − | 0.760851i | ||||
\(766\) | − | 23.1747i | − | 0.837335i | ||||||
\(767\) | −11.9066 | + | 4.32902i | −0.429924 | + | 0.156312i | ||||
\(768\) | −1.41421 | − | 1.00000i | −0.0510310 | − | 0.0360844i | ||||
\(769\) | −7.07326 | − | 7.07326i | −0.255068 | − | 0.255068i | 0.567976 | − | 0.823045i | \(-0.307726\pi\) |
−0.823045 | + | 0.567976i | \(0.807726\pi\) | |||||||
\(770\) | 15.1264i | 0.545119i | ||||||||
\(771\) | 9.55414 | + | 6.75580i | 0.344084 | + | 0.243304i | ||||
\(772\) | 9.59991 | + | 9.59991i | 0.345508 | + | 0.345508i | ||||
\(773\) | 32.8081 | − | 32.8081i | 1.18002 | − | 1.18002i | 0.200287 | − | 0.979737i | \(-0.435813\pi\) |
0.979737 | − | 0.200287i | \(-0.0641874\pi\) | |||||||
\(774\) | −10.4525 | + | 21.8857i | −0.375706 | + | 0.786666i | ||||
\(775\) | 16.9471 | − | 16.9471i | 0.608757 | − | 0.608757i | ||||
\(776\) | − | 3.65685i | − | 0.131273i | ||||||
\(777\) | 0.0363157 | − | 0.0513581i | 0.00130282 | − | 0.00184246i | ||||
\(778\) | 19.8426 | − | 19.8426i | 0.711390 | − | 0.711390i | ||||
\(779\) | 60.9944 | 2.18535 | ||||||||
\(780\) | 19.0153 | + | 5.19634i | 0.680857 | + | 0.186059i | ||||
\(781\) | 15.3005 | 0.547494 | ||||||||
\(782\) | 24.3215 | − | 24.3215i | 0.869735 | − | 0.869735i | ||||
\(783\) | 21.0316 | + | 5.94864i | 0.751609 | + | 0.212587i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | −41.4430 | + | 41.4430i | −1.47916 | + | 1.47916i | ||||
\(786\) | 0.688116 | + | 4.01064i | 0.0245443 | + | 0.143055i | ||||
\(787\) | 19.9270 | − | 19.9270i | 0.710320 | − | 0.710320i | −0.256282 | − | 0.966602i | \(-0.582498\pi\) |
0.966602 | + | 0.256282i | \(0.0824975\pi\) | |||||||
\(788\) | 4.64116 | + | 4.64116i | 0.165335 | + | 0.165335i | ||||
\(789\) | −5.77551 | + | 8.16780i | −0.205613 | + | 0.290781i | ||||
\(790\) | 7.46336i | 0.265534i | ||||||||
\(791\) | 8.82843 | + | 8.82843i | 0.313903 | + | 0.313903i | ||||
\(792\) | 13.5541 | − | 4.79211i | 0.481625 | − | 0.170280i | ||||
\(793\) | −3.76826 | + | 8.07379i | −0.133815 | + | 0.286709i | ||||
\(794\) | 21.0188i | 0.745929i | ||||||||
\(795\) | 2.66039 | + | 15.5059i | 0.0943544 | + | 0.549938i | ||||
\(796\) | −9.76046 | −0.345950 | ||||||||
\(797\) | 8.12086 | 0.287656 | 0.143828 | − | 0.989603i | \(-0.454059\pi\) | ||||
0.143828 | + | 0.989603i | \(0.454059\pi\) | |||||||
\(798\) | 10.2170 | − | 1.75295i | 0.361677 | − | 0.0620539i | ||||
\(799\) | 21.8773 | + | 21.8773i | 0.773963 | + | 0.773963i | ||||
\(800\) | 3.50985 | + | 3.50985i | 0.124092 | + | 0.124092i | ||||
\(801\) | 17.4719 | − | 36.5833i | 0.617339 | − | 1.29261i | ||||
\(802\) | −14.8297 | −0.523656 | ||||||||
\(803\) | 55.2097 | 1.94831 | ||||||||
\(804\) | 17.3613 | − | 2.97873i | 0.612286 | − | 0.105052i | ||||
\(805\) | 21.0551i | 0.742095i | ||||||||
\(806\) | −7.36286 | + | 15.7755i | −0.259346 | + | 0.555668i | ||||
\(807\) | −5.94864 | + | 8.41265i | −0.209402 | + | 0.296139i | ||||
\(808\) | 0.206325 | + | 0.206325i | 0.00725849 | + | 0.00725849i | ||||
\(809\) | 13.7365i | 0.482948i | 0.970407 | + | 0.241474i | \(0.0776309\pi\) | ||||
−0.970407 | + | 0.241474i | \(0.922369\pi\) | |||||||
\(810\) | −17.8560 | − | 22.0957i | −0.627397 | − | 0.776364i | ||||
\(811\) | −28.7767 | − | 28.7767i | −1.01049 | − | 1.01049i | −0.999944 | − | 0.0105416i | \(-0.996644\pi\) |
−0.0105416 | − | 0.999944i | \(-0.503356\pi\) | |||||||
\(812\) | 2.97432 | − | 2.97432i | 0.104378 | − | 0.104378i | ||||
\(813\) | 2.03632 | − | 0.349377i | 0.0714167 | − | 0.0122532i | ||||
\(814\) | −0.123057 | + | 0.123057i | −0.00431315 | + | 0.00431315i | ||||
\(815\) | 32.7758i | 1.14809i | ||||||||
\(816\) | 7.29244 | + | 5.15653i | 0.255286 | + | 0.180515i | ||||
\(817\) | 34.2138 | − | 34.2138i | 1.19699 | − | 1.19699i | ||||
\(818\) | 10.2342 | 0.357830 | ||||||||
\(819\) | −8.35222 | + | 6.87317i | −0.291850 | + | 0.240168i | ||||
\(820\) | −32.1691 | −1.12339 | ||||||||
\(821\) | −1.49566 | + | 1.49566i | −0.0521988 | + | 0.0521988i | −0.732724 | − | 0.680526i | \(-0.761752\pi\) |
0.680526 | + | 0.732724i | \(0.261752\pi\) | |||||||
\(822\) | 24.2205 | + | 17.1264i | 0.844785 | + | 0.597353i | ||||
\(823\) | − | 46.5104i | − | 1.62125i | −0.585565 | − | 0.810625i | \(-0.699127\pi\) | ||
0.585565 | − | 0.810625i | \(-0.300873\pi\) | |||||||
\(824\) | 12.9230 | − | 12.9230i | 0.450193 | − | 0.450193i | ||||
\(825\) | −40.6061 | + | 6.96691i | −1.41372 | + | 0.242557i | ||||
\(826\) | 2.48463 | − | 2.48463i | 0.0864515 | − | 0.0864515i | ||||
\(827\) | 3.72157 | + | 3.72157i | 0.129412 | + | 0.129412i | 0.768846 | − | 0.639434i | \(-0.220831\pi\) |
−0.639434 | + | 0.768846i | \(0.720831\pi\) | |||||||
\(828\) | 18.8666 | − | 6.67033i | 0.655658 | − | 0.231810i | ||||
\(829\) | 28.7523i | 0.998609i | 0.866427 | + | 0.499304i | \(0.166411\pi\) | ||||
−0.866427 | + | 0.499304i | \(0.833589\pi\) | |||||||
\(830\) | −19.4333 | − | 19.4333i | −0.674539 | − | 0.674539i | ||||
\(831\) | 3.74634 | − | 5.29812i | 0.129959 | − | 0.183790i | ||||
\(832\) | −3.26721 | − | 1.52490i | −0.113270 | − | 0.0528663i | ||||
\(833\) | − | 5.15653i | − | 0.178663i | ||||||
\(834\) | −14.5366 | + | 2.49409i | −0.503363 | + | 0.0863634i | ||||
\(835\) | 23.7401 | 0.821560 | ||||||||
\(836\) | −28.6806 | −0.991939 | ||||||||
\(837\) | 21.8995 | − | 12.2426i | 0.756957 | − | 0.423168i | ||||
\(838\) | 2.61147 | + | 2.61147i | 0.0902116 | + | 0.0902116i | ||||
\(839\) | −10.8049 | − | 10.8049i | −0.373028 | − | 0.373028i | 0.495551 | − | 0.868579i | \(-0.334966\pi\) |
−0.868579 | + | 0.495551i | \(0.834966\pi\) | |||||||
\(840\) | −5.38853 | + | 0.924526i | −0.185922 | + | 0.0318992i | ||||
\(841\) | 11.3068 | 0.389891 | ||||||||
\(842\) | 28.8365 | 0.993770 | ||||||||
\(843\) | 4.40475 | + | 25.6728i | 0.151708 | + | 0.884218i | ||||
\(844\) | 9.59927i | 0.330420i | ||||||||
\(845\) | 40.8763 | + | 3.60459i | 1.40619 | + | 0.124002i | ||||
\(846\) | 6.00000 | + | 16.9706i | 0.206284 | + | 0.583460i | ||||
\(847\) | 8.46006 | + | 8.46006i | 0.290691 | + | 0.290691i | ||||
\(848\) | − | 2.87757i | − | 0.0988163i | ||||||
\(849\) | −32.1320 | + | 45.4416i | −1.10277 | + | 1.55955i | ||||
\(850\) | −18.0987 | − | 18.0987i | −0.620779 | − | 0.620779i | ||||
\(851\) | −0.171288 | + | 0.171288i | −0.00587168 | + | 0.00587168i | ||||
\(852\) | 0.935163 | + | 5.45053i | 0.0320382 | + | 0.186732i | ||||
\(853\) | 11.8751 | − | 11.8751i | 0.406595 | − | 0.406595i | −0.473954 | − | 0.880550i | \(-0.657174\pi\) |
0.880550 | + | 0.473954i | \(0.157174\pi\) | |||||||
\(854\) | − | 2.47115i | − | 0.0845612i | ||||||
\(855\) | 18.8917 | + | 53.4338i | 0.646083 | + | 1.82740i | ||||
\(856\) | 3.41421 | − | 3.41421i | 0.116695 | − | 0.116695i | ||||
\(857\) | −20.3032 | −0.693544 | −0.346772 | − | 0.937950i | \(-0.612722\pi\) | ||||
−0.346772 | + | 0.937950i | \(0.612722\pi\) | |||||||
\(858\) | 25.9912 | − | 14.8347i | 0.887325 | − | 0.506447i | ||||
\(859\) | 1.71625 | 0.0585577 | 0.0292789 | − | 0.999571i | \(-0.490679\pi\) | ||||
0.0292789 | + | 0.999571i | \(0.490679\pi\) | |||||||
\(860\) | −18.0447 | + | 18.0447i | −0.615321 | + | 0.615321i | ||||
\(861\) | 10.1913 | − | 14.4126i | 0.347318 | − | 0.491182i | ||||
\(862\) | − | 10.6863i | − | 0.363977i | ||||||
\(863\) | −12.8939 | + | 12.8939i | −0.438914 | + | 0.438914i | −0.891646 | − | 0.452733i | \(-0.850449\pi\) |
0.452733 | + | 0.891646i | \(0.350449\pi\) | |||||||
\(864\) | 2.53553 | + | 4.53553i | 0.0862606 | + | 0.154302i | ||||
\(865\) | −31.3430 | + | 31.3430i | −1.06569 | + | 1.06569i | ||||
\(866\) | −9.89949 | − | 9.89949i | −0.336399 | − | 0.336399i | ||||
\(867\) | −13.5620 | − | 9.58981i | −0.460591 | − | 0.325687i | ||||
\(868\) | − | 4.82843i | − | 0.163887i | ||||||
\(869\) | 8.01192 | + | 8.01192i | 0.271786 | + | 0.271786i | ||||
\(870\) | 18.7771 | + | 13.2774i | 0.636602 | + | 0.450146i | ||||
\(871\) | 34.4614 | − | 12.5295i | 1.16768 | − | 0.424546i | ||||
\(872\) | 17.5178i | 0.593228i | ||||||||
\(873\) | −4.72792 | + | 9.89949i | −0.160016 | + | 0.335047i | ||||
\(874\) | −39.9217 | −1.35037 | ||||||||
\(875\) | −0.114632 | −0.00387526 | ||||||||
\(876\) | 3.37441 | + | 19.6675i | 0.114011 | + | 0.664503i | ||||
\(877\) | 7.74542 | + | 7.74542i | 0.261544 | + | 0.261544i | 0.825681 | − | 0.564137i | \(-0.190791\pi\) |
−0.564137 | + | 0.825681i | \(0.690791\pi\) | |||||||
\(878\) | −27.7939 | − | 27.7939i | −0.938000 | − | 0.938000i | ||||
\(879\) | −5.12021 | − | 29.8428i | −0.172701 | − | 1.00657i | ||||
\(880\) | 15.1264 | 0.509912 | ||||||||
\(881\) | 40.1553 | 1.35287 | 0.676434 | − | 0.736503i | \(-0.263524\pi\) | ||||
0.676434 | + | 0.736503i | \(0.263524\pi\) | |||||||
\(882\) | 1.29289 | − | 2.70711i | 0.0435340 | − | 0.0911530i | ||||
\(883\) | − | 33.9136i | − | 1.14128i | −0.821199 | − | 0.570642i | \(-0.806694\pi\) | ||
0.821199 | − | 0.570642i | \(-0.193306\pi\) | |||||||
\(884\) | 16.8475 | + | 7.86318i | 0.566642 | + | 0.264467i | ||||
\(885\) | 15.6856 | + | 11.0914i | 0.527267 | + | 0.372834i | ||||
\(886\) | −5.21191 | − | 5.21191i | −0.175097 | − | 0.175097i | ||||
\(887\) | − | 24.5348i | − | 0.823798i | −0.911229 | − | 0.411899i | \(-0.864866\pi\) | ||
0.911229 | − | 0.411899i | \(-0.135134\pi\) | |||||||
\(888\) | −0.0513581 | − | 0.0363157i | −0.00172347 | − | 0.00121867i | ||||
\(889\) | −9.52095 | − | 9.52095i | −0.319322 | − | 0.319322i | ||||
\(890\) | 30.1629 | − | 30.1629i | 1.01106 | − | 1.01106i | ||||
\(891\) | −42.8882 | − | 4.55130i | −1.43681 | − | 0.152474i | ||||
\(892\) | 16.2467 | − | 16.2467i | 0.543978 | − | 0.543978i | ||||
\(893\) | − | 35.9097i | − | 1.20167i | ||||||
\(894\) | −16.5748 | + | 23.4403i | −0.554343 | + | 0.783959i | ||||
\(895\) | 4.57864 | − | 4.57864i | 0.153047 | − | 0.153047i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 36.1782 | − | 20.6490i | 1.20795 | − | 0.689449i | ||||
\(898\) | −13.2831 | −0.443262 | ||||||||
\(899\) | −14.3613 | + | 14.3613i | −0.478976 | + | 0.478976i | ||||
\(900\) | −4.96368 | − | 14.0394i | −0.165456 | − | 0.467981i | ||||
\(901\) | 14.8383i | 0.494335i | ||||||||
\(902\) | −34.5335 | + | 34.5335i | −1.14984 | + | 1.14984i | ||||
\(903\) | −2.36791 | − | 13.8012i | −0.0787991 | − | 0.459275i | ||||
\(904\) | 8.82843 | − | 8.82843i | 0.293629 | − | 0.293629i | ||||
\(905\) | 32.4409 | + | 32.4409i | 1.07837 | + | 1.07837i | ||||
\(906\) | −11.1565 | + | 15.7777i | −0.370651 | + | 0.524180i | ||||
\(907\) | − | 13.8986i | − | 0.461495i | −0.973014 | − | 0.230747i | \(-0.925883\pi\) | ||
0.973014 | − | 0.230747i | \(-0.0741171\pi\) | |||||||
\(908\) | 1.92802 | + | 1.92802i | 0.0639835 | + | 0.0639835i | ||||
\(909\) | −0.291788 | − | 0.825300i | −0.00967798 | − | 0.0273735i | ||||
\(910\) | −10.6960 | + | 3.88886i | −0.354569 | + | 0.128914i | ||||
\(911\) | − | 25.8388i | − | 0.856077i | −0.903761 | − | 0.428038i | \(-0.859205\pi\) | ||
0.903761 | − | 0.428038i | \(-0.140795\pi\) | |||||||
\(912\) | −1.75295 | − | 10.2170i | −0.0580461 | − | 0.338317i | ||||
\(913\) | −41.7232 | −1.38084 | ||||||||
\(914\) | 12.4348 | 0.411308 | ||||||||
\(915\) | 13.3159 | − | 2.28465i | 0.440210 | − | 0.0755281i | ||||
\(916\) | 1.19285 | + | 1.19285i | 0.0394127 | + | 0.0394127i | ||||
\(917\) | −1.66126 | − | 1.66126i | −0.0548596 | − | 0.0548596i | ||||
\(918\) | −13.0746 | − | 23.3876i | −0.431525 | − | 0.771906i | ||||
\(919\) | 44.2498 | 1.45967 | 0.729833 | − | 0.683626i | \(-0.239598\pi\) | ||||
0.729833 | + | 0.683626i | \(0.239598\pi\) | |||||||
\(920\) | 21.0551 | 0.694166 | ||||||||
\(921\) | −29.9154 | + | 5.13268i | −0.985747 | + | 0.169127i | ||||
\(922\) | 27.1991i | 0.895754i | ||||||||
\(923\) | 3.93360 | + | 10.8191i | 0.129476 | + | 0.356114i | ||||
\(924\) | −4.79211 | + | 6.77707i | −0.157649 | + | 0.222949i | ||||
\(925\) | 0.127463 | + | 0.127463i | 0.00419095 | + | 0.00419095i | ||||
\(926\) | 8.81338i | 0.289626i | ||||||||
\(927\) | −51.6919 | + | 18.2758i | −1.69778 | + | 0.600257i | ||||
\(928\) | −2.97432 | − | 2.97432i | −0.0976369 | − | 0.0976369i | ||||
\(929\) | 4.05990 | − | 4.05990i | 0.133201 | − | 0.133201i | −0.637363 | − | 0.770564i | \(-0.719975\pi\) |
0.770564 | + | 0.637363i | \(0.219975\pi\) | |||||||
\(930\) | 26.0181 | − | 4.46401i | 0.853169 | − | 0.146381i | ||||
\(931\) | −4.23200 | + | 4.23200i | −0.138698 | + | 0.138698i | ||||
\(932\) | − | 19.9486i | − | 0.653439i | ||||||
\(933\) | 34.4521 | + | 24.3613i | 1.12791 | + | 0.797553i | ||||
\(934\) | 0.659697 | − | 0.659697i | 0.0215859 | − | 0.0215859i | ||||
\(935\) | −78.0000 | −2.55087 | ||||||||
\(936\) | 6.87317 | + | 8.35222i | 0.224657 | + | 0.273001i | ||||
\(937\) | −46.3976 | −1.51574 | −0.757872 | − | 0.652404i | \(-0.773761\pi\) | ||||
−0.757872 | + | 0.652404i | \(0.773761\pi\) | |||||||
\(938\) | −7.19128 | + | 7.19128i | −0.234804 | + | 0.234804i | ||||
\(939\) | 29.6223 | + | 20.9462i | 0.966689 | + | 0.683552i | ||||
\(940\) | 18.9392i | 0.617728i | ||||||||
\(941\) | 7.70821 | − | 7.70821i | 0.251281 | − | 0.251281i | −0.570215 | − | 0.821496i | \(-0.693140\pi\) |
0.821496 | + | 0.570215i | \(0.193140\pi\) | |||||||
\(942\) | −31.6969 | + | 5.43833i | −1.03274 | + | 0.177190i | ||||
\(943\) | −48.0686 | + | 48.0686i | −1.56533 | + | 1.56533i | ||||
\(944\) | −2.48463 | − | 2.48463i | −0.0808679 | − | 0.0808679i | ||||
\(945\) | 15.7827 | + | 4.46401i | 0.513410 | + | 0.145214i | ||||
\(946\) | 38.7420i | 1.25961i | ||||||||
\(947\) | −20.7705 | − | 20.7705i | −0.674949 | − | 0.674949i | 0.283904 | − | 0.958853i | \(-0.408370\pi\) |
−0.958853 | + | 0.283904i | \(0.908370\pi\) | |||||||
\(948\) | −2.36442 | + | 3.34379i | −0.0767928 | + | 0.108601i | ||||
\(949\) | 14.1939 | + | 39.0391i | 0.460752 | + | 1.26726i | ||||
\(950\) | 29.7074i | 0.963837i | ||||||||
\(951\) | 30.8006 | − | 5.28454i | 0.998776 | − | 0.171363i | ||||
\(952\) | −5.15653 | −0.167124 | ||||||||
\(953\) | 41.5409 | 1.34564 | 0.672821 | − | 0.739805i | \(-0.265082\pi\) | ||||
0.672821 | + | 0.739805i | \(0.265082\pi\) | |||||||
\(954\) | −3.72040 | + | 7.78990i | −0.120452 | + | 0.252207i | ||||
\(955\) | −22.3516 | − | 22.3516i | −0.723280 | − | 0.723280i | ||||
\(956\) | −7.48463 | − | 7.48463i | −0.242070 | − | 0.242070i | ||||
\(957\) | 34.4105 | − | 5.90390i | 1.11233 | − | 0.190846i | ||||
\(958\) | −36.4145 | −1.17650 | ||||||||
\(959\) | −17.1264 | −0.553042 | ||||||||
\(960\) | 0.924526 | + | 5.38853i | 0.0298390 | + | 0.173914i | ||||
\(961\) | − | 7.68629i | − | 0.247945i | ||||||
\(962\) | −0.118651 | − | 0.0553777i | −0.00382547 | − | 0.00178545i | ||||
\(963\) | −13.6569 | + | 4.82843i | −0.440086 | + | 0.155594i | ||||
\(964\) | 3.43549 | + | 3.43549i | 0.110650 | + | 0.110650i | ||||
\(965\) | − | 42.8541i | − | 1.37952i | ||||||
\(966\) | −6.67033 | + | 9.43328i | −0.214614 | + | 0.303511i | ||||
\(967\) | 0.304635 | + | 0.304635i | 0.00979642 | + | 0.00979642i | 0.711988 | − | 0.702192i | \(-0.247795\pi\) |
−0.702192 | + | 0.711988i | \(0.747795\pi\) | |||||||
\(968\) | 8.46006 | − | 8.46006i | 0.271917 | − | 0.271917i | ||||
\(969\) | 9.03916 | + | 52.6841i | 0.290380 | + | 1.69246i | ||||
\(970\) | −8.16211 | + | 8.16211i | −0.262070 | + | 0.262070i | ||||
\(971\) | 15.6680i | 0.502811i | 0.967882 | + | 0.251405i | \(0.0808927\pi\) | ||||
−0.967882 | + | 0.251405i | \(0.919107\pi\) | |||||||
\(972\) | −1.00000 | − | 15.5563i | −0.0320750 | − | 0.498970i | ||||
\(973\) | 6.02127 | − | 6.02127i | 0.193033 | − | 0.193033i | ||||
\(974\) | 26.1121 | 0.836684 | ||||||||
\(975\) | −15.3658 | − | 26.9218i | −0.492099 | − | 0.862186i | ||||
\(976\) | −2.47115 | −0.0790997 | ||||||||
\(977\) | −3.39698 | + | 3.39698i | −0.108679 | + | 0.108679i | −0.759355 | − | 0.650676i | \(-0.774485\pi\) |
0.650676 | + | 0.759355i | \(0.274485\pi\) | |||||||
\(978\) | −10.3835 | + | 14.6845i | −0.332027 | + | 0.469557i | ||||
\(979\) | − | 64.7596i | − | 2.06973i | ||||||
\(980\) | 2.23200 | − | 2.23200i | 0.0712988 | − | 0.0712988i | ||||
\(981\) | 22.6487 | − | 47.4226i | 0.723116 | − | 1.51409i | ||||
\(982\) | 1.10738 | − | 1.10738i | 0.0353380 | − | 0.0353380i | ||||
\(983\) | 0.279343 | + | 0.279343i | 0.00890965 | + | 0.00890965i | 0.711548 | − | 0.702638i | \(-0.247995\pi\) |
−0.702638 | + | 0.711548i | \(0.747995\pi\) | |||||||
\(984\) | −14.4126 | − | 10.1913i | −0.459459 | − | 0.324886i | ||||
\(985\) | − | 20.7182i | − | 0.660137i | ||||||
\(986\) | 15.3372 | + | 15.3372i | 0.488435 | + | 0.488435i | ||||
\(987\) | −8.48528 | − | 6.00000i | −0.270089 | − | 0.190982i | ||||
\(988\) | −7.37349 | − | 20.2802i | −0.234582 | − | 0.645200i | ||||
\(989\) | 53.9266i | 1.71477i | ||||||||
\(990\) | −40.9489 | − | 19.5569i | −1.30144 | − | 0.621558i | ||||
\(991\) | −16.1603 | −0.513348 | −0.256674 | − | 0.966498i | \(-0.582627\pi\) | ||||
−0.256674 | + | 0.966498i | \(0.582627\pi\) | |||||||
\(992\) | −4.82843 | −0.153303 | ||||||||
\(993\) | 5.31306 | + | 30.9668i | 0.168605 | + | 0.982701i | ||||
\(994\) | −2.25768 | − | 2.25768i | −0.0716094 | − | 0.0716094i | ||||
\(995\) | 21.7854 | + | 21.7854i | 0.690643 | + | 0.690643i | ||||
\(996\) | −2.55012 | − | 14.8632i | −0.0808036 | − | 0.470958i | ||||
\(997\) | 20.7730 | 0.657888 | 0.328944 | − | 0.944349i | \(-0.393307\pi\) | ||||
0.328944 | + | 0.944349i | \(0.393307\pi\) | |||||||
\(998\) | −30.8970 | −0.978028 | ||||||||
\(999\) | 0.0920797 | + | 0.164711i | 0.00291327 | + | 0.00521123i |
(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 | 546.2.p.a.281.3 | yes | 8 | |
3.2 | odd | 2 | 546.2.p.b.281.2 | yes | 8 | ||
13.5 | odd | 4 | 546.2.p.b.239.2 | yes | 8 | ||
39.5 | even | 4 | inner | 546.2.p.a.239.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.a.239.3 | ✓ | 8 | 39.5 | even | 4 | inner | |
546.2.p.a.281.3 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.p.b.239.2 | yes | 8 | 13.5 | odd | 4 | ||
546.2.p.b.281.2 | yes | 8 | 3.2 | odd | 2 |