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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
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 | 281.7 | ||
Root | \(1.72893 - 0.103975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.c.239.7 |
$q$-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 | ||||
\(3\) | −1.14901 | + | 1.29606i | −0.663384 | + | 0.748279i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.237140 | − | 0.237140i | 0.106052 | − | 0.106052i | −0.652090 | − | 0.758142i | \(-0.726107\pi\) |
0.758142 | + | 0.652090i | \(0.226107\pi\) | |||||||
\(6\) | 0.103975 | + | 1.72893i | 0.0424477 | + | 0.705832i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −0.359531 | − | 2.97838i | −0.119844 | − | 0.992793i | ||||
\(10\) | − | 0.335367i | − | 0.106052i | ||||||
\(11\) | 2.55493 | + | 2.55493i | 0.770341 | + | 0.770341i | 0.978166 | − | 0.207825i | \(-0.0666386\pi\) |
−0.207825 | + | 0.978166i | \(0.566639\pi\) | |||||||
\(12\) | 1.29606 | + | 1.14901i | 0.374140 | + | 0.331692i | ||||
\(13\) | 3.37961 | + | 1.25628i | 0.937335 | + | 0.348430i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0.0348698 | + | 0.579825i | 0.00900335 | + | 0.149710i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.26383 | 1.27667 | 0.638334 | − | 0.769760i | \(-0.279624\pi\) | ||||
0.638334 | + | 0.769760i | \(0.279624\pi\) | |||||||
\(18\) | −2.36026 | − | 1.85180i | −0.556318 | − | 0.436475i | ||||
\(19\) | 0.906991 | + | 0.906991i | 0.208078 | + | 0.208078i | 0.803450 | − | 0.595372i | \(-0.202995\pi\) |
−0.595372 | + | 0.803450i | \(0.702995\pi\) | |||||||
\(20\) | −0.237140 | − | 0.237140i | −0.0530262 | − | 0.0530262i | ||||
\(21\) | −0.103975 | − | 1.72893i | −0.0226892 | − | 0.377283i | ||||
\(22\) | 3.61322 | 0.770341 | ||||||||
\(23\) | −1.48838 | −0.310349 | −0.155175 | − | 0.987887i | \(-0.549594\pi\) | ||||
−0.155175 | + | 0.987887i | \(0.549594\pi\) | |||||||
\(24\) | 1.72893 | − | 0.103975i | 0.352916 | − | 0.0212238i | ||||
\(25\) | 4.88753i | 0.977506i | ||||||||
\(26\) | 3.27807 | − | 1.50142i | 0.642882 | − | 0.294452i | ||||
\(27\) | 4.27326 | + | 2.95623i | 0.822389 | + | 0.568926i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | − | 7.36454i | − | 1.36756i | −0.729688 | − | 0.683780i | \(-0.760335\pi\) | ||
0.729688 | − | 0.683780i | \(-0.239665\pi\) | |||||||
\(30\) | 0.434655 | + | 0.385342i | 0.0793568 | + | 0.0703534i | ||||
\(31\) | 7.20598 | + | 7.20598i | 1.29423 | + | 1.29423i | 0.932143 | + | 0.362089i | \(0.117936\pi\) |
0.362089 | + | 0.932143i | \(0.382064\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.24699 | + | 0.375685i | −1.08746 | + | 0.0653983i | ||||
\(34\) | 3.72209 | − | 3.72209i | 0.638334 | − | 0.638334i | ||||
\(35\) | 0.335367i | 0.0566874i | ||||||||
\(36\) | −2.97838 | + | 0.359531i | −0.496396 | + | 0.0599218i | ||||
\(37\) | −2.83332 | + | 2.83332i | −0.465795 | + | 0.465795i | −0.900549 | − | 0.434754i | \(-0.856835\pi\) |
0.434754 | + | 0.900549i | \(0.356835\pi\) | |||||||
\(38\) | 1.28268 | 0.208078 | ||||||||
\(39\) | −5.51143 | + | 2.93668i | −0.882536 | + | 0.470245i | ||||
\(40\) | −0.335367 | −0.0530262 | ||||||||
\(41\) | 1.32329 | − | 1.32329i | 0.206664 | − | 0.206664i | −0.596184 | − | 0.802848i | \(-0.703317\pi\) |
0.802848 | + | 0.596184i | \(0.203317\pi\) | |||||||
\(42\) | −1.29606 | − | 1.14901i | −0.199986 | − | 0.177297i | ||||
\(43\) | 2.75805i | 0.420598i | 0.977637 | + | 0.210299i | \(0.0674437\pi\) | ||||
−0.977637 | + | 0.210299i | \(0.932556\pi\) | |||||||
\(44\) | 2.55493 | − | 2.55493i | 0.385170 | − | 0.385170i | ||||
\(45\) | −0.791553 | − | 0.621034i | −0.117998 | − | 0.0925783i | ||||
\(46\) | −1.05244 | + | 1.05244i | −0.155175 | + | 0.155175i | ||||
\(47\) | −2.27264 | − | 2.27264i | −0.331499 | − | 0.331499i | 0.521657 | − | 0.853156i | \(-0.325314\pi\) |
−0.853156 | + | 0.521657i | \(0.825314\pi\) | |||||||
\(48\) | 1.14901 | − | 1.29606i | 0.165846 | − | 0.187070i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 3.45600 | + | 3.45600i | 0.488753 | + | 0.488753i | ||||
\(51\) | −6.04822 | + | 6.82223i | −0.846920 | + | 0.955304i | ||||
\(52\) | 1.25628 | − | 3.37961i | 0.174215 | − | 0.468667i | ||||
\(53\) | − | 8.80608i | − | 1.20961i | −0.796374 | − | 0.604804i | \(-0.793251\pi\) | ||
0.796374 | − | 0.604804i | \(-0.206749\pi\) | |||||||
\(54\) | 5.11202 | − | 0.931280i | 0.695657 | − | 0.126731i | ||||
\(55\) | 1.21175 | 0.163393 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.21766 | + | 0.133367i | −0.293736 | + | 0.0176648i | ||||
\(58\) | −5.20752 | − | 5.20752i | −0.683780 | − | 0.683780i | ||||
\(59\) | −0.785394 | − | 0.785394i | −0.102250 | − | 0.102250i | 0.654131 | − | 0.756381i | \(-0.273034\pi\) |
−0.756381 | + | 0.654131i | \(0.773034\pi\) | |||||||
\(60\) | 0.579825 | − | 0.0348698i | 0.0748551 | − | 0.00450167i | ||||
\(61\) | 8.74912 | 1.12021 | 0.560105 | − | 0.828422i | \(-0.310761\pi\) | ||||
0.560105 | + | 0.828422i | \(0.310761\pi\) | |||||||
\(62\) | 10.1908 | 1.29423 | ||||||||
\(63\) | 2.36026 | + | 1.85180i | 0.297365 | + | 0.233305i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.09936 | − | 0.503526i | 0.136358 | − | 0.0624547i | ||||
\(66\) | −4.15164 | + | 4.68294i | −0.511032 | + | 0.576430i | ||||
\(67\) | −9.68048 | − | 9.68048i | −1.18266 | − | 1.18266i | −0.979053 | − | 0.203606i | \(-0.934734\pi\) |
−0.203606 | − | 0.979053i | \(-0.565266\pi\) | |||||||
\(68\) | − | 5.26383i | − | 0.638334i | ||||||
\(69\) | 1.71017 | − | 1.92903i | 0.205881 | − | 0.232228i | ||||
\(70\) | 0.237140 | + | 0.237140i | 0.0283437 | + | 0.0283437i | ||||
\(71\) | 4.94294 | − | 4.94294i | 0.586619 | − | 0.586619i | −0.350095 | − | 0.936714i | \(-0.613851\pi\) |
0.936714 | + | 0.350095i | \(0.113851\pi\) | |||||||
\(72\) | −1.85180 | + | 2.36026i | −0.218237 | + | 0.278159i | ||||
\(73\) | −4.00560 | + | 4.00560i | −0.468821 | + | 0.468821i | −0.901532 | − | 0.432712i | \(-0.857557\pi\) |
0.432712 | + | 0.901532i | \(0.357557\pi\) | |||||||
\(74\) | 4.00692i | 0.465795i | ||||||||
\(75\) | −6.33452 | − | 5.61584i | −0.731447 | − | 0.648462i | ||||
\(76\) | 0.906991 | − | 0.906991i | 0.104039 | − | 0.104039i | ||||
\(77\) | −3.61322 | −0.411764 | ||||||||
\(78\) | −1.82063 | + | 5.97372i | −0.206145 | + | 0.676390i | ||||
\(79\) | −8.50862 | −0.957294 | −0.478647 | − | 0.878007i | \(-0.658873\pi\) | ||||
−0.478647 | + | 0.878007i | \(0.658873\pi\) | |||||||
\(80\) | −0.237140 | + | 0.237140i | −0.0265131 | + | 0.0265131i | ||||
\(81\) | −8.74148 | + | 2.14164i | −0.971275 | + | 0.237960i | ||||
\(82\) | − | 1.87142i | − | 0.206664i | ||||||
\(83\) | −3.05668 | + | 3.05668i | −0.335515 | + | 0.335515i | −0.854676 | − | 0.519162i | \(-0.826244\pi\) |
0.519162 | + | 0.854676i | \(0.326244\pi\) | |||||||
\(84\) | −1.72893 | + | 0.103975i | −0.188641 | + | 0.0113446i | ||||
\(85\) | 1.24827 | − | 1.24827i | 0.135394 | − | 0.135394i | ||||
\(86\) | 1.95023 | + | 1.95023i | 0.210299 | + | 0.210299i | ||||
\(87\) | 9.54487 | + | 8.46196i | 1.02332 | + | 0.907218i | ||||
\(88\) | − | 3.61322i | − | 0.385170i | ||||||
\(89\) | 1.62293 | + | 1.62293i | 0.172030 | + | 0.172030i | 0.787871 | − | 0.615840i | \(-0.211183\pi\) |
−0.615840 | + | 0.787871i | \(0.711183\pi\) | |||||||
\(90\) | −0.998850 | + | 0.120575i | −0.105288 | + | 0.0127097i | ||||
\(91\) | −3.27807 | + | 1.50142i | −0.343635 | + | 0.157391i | ||||
\(92\) | 1.48838i | 0.155175i | ||||||||
\(93\) | −17.6191 | + | 1.05959i | −1.82702 | + | 0.109874i | ||||
\(94\) | −3.21400 | −0.331499 | ||||||||
\(95\) | 0.430168 | 0.0441343 | ||||||||
\(96\) | −0.103975 | − | 1.72893i | −0.0106119 | − | 0.176458i | ||||
\(97\) | −4.86305 | − | 4.86305i | −0.493768 | − | 0.493768i | 0.415723 | − | 0.909491i | \(-0.363529\pi\) |
−0.909491 | + | 0.415723i | \(0.863529\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 6.69097 | − | 8.52813i | 0.672468 | − | 0.857109i | ||||
\(100\) | 4.88753 | 0.488753 | ||||||||
\(101\) | −18.5302 | −1.84382 | −0.921911 | − | 0.387402i | \(-0.873373\pi\) | ||||
−0.921911 | + | 0.387402i | \(0.873373\pi\) | |||||||
\(102\) | 0.547308 | + | 9.10078i | 0.0541915 | + | 0.901112i | ||||
\(103\) | 5.76073i | 0.567622i | 0.958880 | + | 0.283811i | \(0.0915988\pi\) | ||||
−0.958880 | + | 0.283811i | \(0.908401\pi\) | |||||||
\(104\) | −1.50142 | − | 3.27807i | −0.147226 | − | 0.321441i | ||||
\(105\) | −0.434655 | − | 0.385342i | −0.0424180 | − | 0.0376055i | ||||
\(106\) | −6.22684 | − | 6.22684i | −0.604804 | − | 0.604804i | ||||
\(107\) | 18.3125i | 1.77034i | 0.465270 | + | 0.885169i | \(0.345957\pi\) | ||||
−0.465270 | + | 0.885169i | \(0.654043\pi\) | |||||||
\(108\) | 2.95623 | − | 4.27326i | 0.284463 | − | 0.411194i | ||||
\(109\) | −6.72226 | − | 6.72226i | −0.643876 | − | 0.643876i | 0.307630 | − | 0.951506i | \(-0.400464\pi\) |
−0.951506 | + | 0.307630i | \(0.900464\pi\) | |||||||
\(110\) | 0.856839 | − | 0.856839i | 0.0816964 | − | 0.0816964i | ||||
\(111\) | −0.416620 | − | 6.92768i | −0.0395439 | − | 0.657546i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | − | 15.8812i | − | 1.49398i | −0.664835 | − | 0.746990i | \(-0.731498\pi\) | ||
0.664835 | − | 0.746990i | \(-0.268502\pi\) | |||||||
\(114\) | −1.47382 | + | 1.66243i | −0.138036 | + | 0.155700i | ||||
\(115\) | −0.352955 | + | 0.352955i | −0.0329132 | + | 0.0329132i | ||||
\(116\) | −7.36454 | −0.683780 | ||||||||
\(117\) | 2.52661 | − | 10.5174i | 0.233585 | − | 0.972336i | ||||
\(118\) | −1.11071 | −0.102250 | ||||||||
\(119\) | −3.72209 | + | 3.72209i | −0.341204 | + | 0.341204i | ||||
\(120\) | 0.385342 | − | 0.434655i | 0.0351767 | − | 0.0396784i | ||||
\(121\) | 2.05534i | 0.186849i | ||||||||
\(122\) | 6.18656 | − | 6.18656i | 0.560105 | − | 0.560105i | ||||
\(123\) | 0.194581 | + | 3.23555i | 0.0175448 | + | 0.291739i | ||||
\(124\) | 7.20598 | − | 7.20598i | 0.647116 | − | 0.647116i | ||||
\(125\) | 2.34473 | + | 2.34473i | 0.209719 | + | 0.209719i | ||||
\(126\) | 2.97838 | − | 0.359531i | 0.265335 | − | 0.0320295i | ||||
\(127\) | 8.38087i | 0.743682i | 0.928297 | + | 0.371841i | \(0.121273\pi\) | ||||
−0.928297 | + | 0.371841i | \(0.878727\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −3.57459 | − | 3.16903i | −0.314725 | − | 0.279018i | ||||
\(130\) | 0.421316 | − | 1.13341i | 0.0369518 | − | 0.0994066i | ||||
\(131\) | − | 14.5927i | − | 1.27497i | −0.770464 | − | 0.637484i | \(-0.779975\pi\) | ||
0.770464 | − | 0.637484i | \(-0.220025\pi\) | |||||||
\(132\) | 0.375685 | + | 6.24699i | 0.0326992 | + | 0.543731i | ||||
\(133\) | −1.28268 | −0.111222 | ||||||||
\(134\) | −13.6903 | −1.18266 | ||||||||
\(135\) | 1.71440 | − | 0.312321i | 0.147552 | − | 0.0268803i | ||||
\(136\) | −3.72209 | − | 3.72209i | −0.319167 | − | 0.319167i | ||||
\(137\) | 11.5852 | + | 11.5852i | 0.989790 | + | 0.989790i | 0.999948 | − | 0.0101587i | \(-0.00323368\pi\) |
−0.0101587 | + | 0.999948i | \(0.503234\pi\) | |||||||
\(138\) | −0.154755 | − | 2.57330i | −0.0131736 | − | 0.219054i | ||||
\(139\) | 11.9801 | 1.01614 | 0.508070 | − | 0.861316i | \(-0.330359\pi\) | ||||
0.508070 | + | 0.861316i | \(0.330359\pi\) | |||||||
\(140\) | 0.335367 | 0.0283437 | ||||||||
\(141\) | 5.55677 | − | 0.334176i | 0.467965 | − | 0.0281427i | ||||
\(142\) | − | 6.99038i | − | 0.586619i | ||||||
\(143\) | 5.42495 | + | 11.8444i | 0.453657 | + | 0.990477i | ||||
\(144\) | 0.359531 | + | 2.97838i | 0.0299609 | + | 0.248198i | ||||
\(145\) | −1.74643 | − | 1.74643i | −0.145033 | − | 0.145033i | ||||
\(146\) | 5.66478i | 0.468821i | ||||||||
\(147\) | 1.29606 | + | 1.14901i | 0.106897 | + | 0.0947691i | ||||
\(148\) | 2.83332 | + | 2.83332i | 0.232898 | + | 0.232898i | ||||
\(149\) | 2.17899 | − | 2.17899i | 0.178510 | − | 0.178510i | −0.612196 | − | 0.790706i | \(-0.709714\pi\) |
0.790706 | + | 0.612196i | \(0.209714\pi\) | |||||||
\(150\) | −8.45018 | + | 0.508181i | −0.689954 | + | 0.0414928i | ||||
\(151\) | 9.34711 | − | 9.34711i | 0.760657 | − | 0.760657i | −0.215784 | − | 0.976441i | \(-0.569231\pi\) |
0.976441 | + | 0.215784i | \(0.0692307\pi\) | |||||||
\(152\) | − | 1.28268i | − | 0.104039i | ||||||
\(153\) | −1.89251 | − | 15.6777i | −0.153000 | − | 1.26747i | ||||
\(154\) | −2.55493 | + | 2.55493i | −0.205882 | + | 0.205882i | ||||
\(155\) | 3.41766 | 0.274513 | ||||||||
\(156\) | 2.93668 | + | 5.51143i | 0.235123 | + | 0.441268i | ||||
\(157\) | −17.6346 | −1.40740 | −0.703698 | − | 0.710499i | \(-0.748469\pi\) | ||||
−0.703698 | + | 0.710499i | \(0.748469\pi\) | |||||||
\(158\) | −6.01650 | + | 6.01650i | −0.478647 | + | 0.478647i | ||||
\(159\) | 11.4132 | + | 10.1183i | 0.905125 | + | 0.802435i | ||||
\(160\) | 0.335367i | 0.0265131i | ||||||||
\(161\) | 1.05244 | − | 1.05244i | 0.0829443 | − | 0.0829443i | ||||
\(162\) | −4.66679 | + | 7.69552i | −0.366658 | + | 0.604617i | ||||
\(163\) | −2.26457 | + | 2.26457i | −0.177375 | + | 0.177375i | −0.790210 | − | 0.612836i | \(-0.790029\pi\) |
0.612836 | + | 0.790210i | \(0.290029\pi\) | |||||||
\(164\) | −1.32329 | − | 1.32329i | −0.103332 | − | 0.103332i | ||||
\(165\) | −1.39232 | + | 1.57050i | −0.108392 | + | 0.122263i | ||||
\(166\) | 4.32280i | 0.335515i | ||||||||
\(167\) | 12.4482 | + | 12.4482i | 0.963272 | + | 0.963272i | 0.999349 | − | 0.0360774i | \(-0.0114863\pi\) |
−0.0360774 | + | 0.999349i | \(0.511486\pi\) | |||||||
\(168\) | −1.14901 | + | 1.29606i | −0.0886484 | + | 0.0999930i | ||||
\(169\) | 9.84351 | + | 8.49149i | 0.757193 | + | 0.653192i | ||||
\(170\) | − | 1.76532i | − | 0.135394i | ||||||
\(171\) | 2.37527 | − | 3.02745i | 0.181641 | − | 0.231515i | ||||
\(172\) | 2.75805 | 0.210299 | ||||||||
\(173\) | −12.8517 | −0.977096 | −0.488548 | − | 0.872537i | \(-0.662473\pi\) | ||||
−0.488548 | + | 0.872537i | \(0.662473\pi\) | |||||||
\(174\) | 12.7328 | − | 0.765729i | 0.965267 | − | 0.0580497i | ||||
\(175\) | −3.45600 | − | 3.45600i | −0.261249 | − | 0.261249i | ||||
\(176\) | −2.55493 | − | 2.55493i | −0.192585 | − | 0.192585i | ||||
\(177\) | 1.92034 | − | 0.115487i | 0.144342 | − | 0.00868051i | ||||
\(178\) | 2.29517 | 0.172030 | ||||||||
\(179\) | −13.7258 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(180\) | −0.621034 | + | 0.791553i | −0.0462892 | + | 0.0589989i | ||||
\(181\) | 17.7979i | 1.32291i | 0.749986 | + | 0.661454i | \(0.230060\pi\) | ||||
−0.749986 | + | 0.661454i | \(0.769940\pi\) | |||||||
\(182\) | −1.25628 | + | 3.37961i | −0.0931219 | + | 0.250513i | ||||
\(183\) | −10.0529 | + | 11.3394i | −0.743129 | + | 0.838230i | ||||
\(184\) | 1.05244 | + | 1.05244i | 0.0775873 | + | 0.0775873i | ||||
\(185\) | 1.34379i | 0.0987974i | ||||||||
\(186\) | −11.7094 | + | 13.2079i | −0.858573 | + | 0.968447i | ||||
\(187\) | 13.4487 | + | 13.4487i | 0.983469 | + | 0.983469i | ||||
\(188\) | −2.27264 | + | 2.27264i | −0.165749 | + | 0.165749i | ||||
\(189\) | −5.11202 | + | 0.931280i | −0.371845 | + | 0.0677406i | ||||
\(190\) | 0.304175 | − | 0.304175i | 0.0220672 | − | 0.0220672i | ||||
\(191\) | 0.449102i | 0.0324959i | 0.999868 | + | 0.0162479i | \(0.00517211\pi\) | ||||
−0.999868 | + | 0.0162479i | \(0.994828\pi\) | |||||||
\(192\) | −1.29606 | − | 1.14901i | −0.0935349 | − | 0.0829230i | ||||
\(193\) | −5.53933 | + | 5.53933i | −0.398730 | + | 0.398730i | −0.877785 | − | 0.479055i | \(-0.840979\pi\) |
0.479055 | + | 0.877785i | \(0.340979\pi\) | |||||||
\(194\) | −6.87739 | −0.493768 | ||||||||
\(195\) | −0.610578 | + | 2.00339i | −0.0437244 | + | 0.143466i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 15.8126 | − | 15.8126i | 1.12660 | − | 1.12660i | 0.135878 | − | 0.990726i | \(-0.456614\pi\) |
0.990726 | − | 0.135878i | \(-0.0433855\pi\) | |||||||
\(198\) | −1.29906 | − | 10.7615i | −0.0923204 | − | 0.764789i | ||||
\(199\) | − | 26.3160i | − | 1.86549i | −0.360531 | − | 0.932747i | \(-0.617405\pi\) | ||
0.360531 | − | 0.932747i | \(-0.382595\pi\) | |||||||
\(200\) | 3.45600 | − | 3.45600i | 0.244376 | − | 0.244376i | ||||
\(201\) | 23.6695 | − | 1.42345i | 1.66952 | − | 0.100402i | ||||
\(202\) | −13.1028 | + | 13.1028i | −0.921911 | + | 0.921911i | ||||
\(203\) | 5.20752 | + | 5.20752i | 0.365496 | + | 0.365496i | ||||
\(204\) | 6.82223 | + | 6.04822i | 0.477652 | + | 0.423460i | ||||
\(205\) | − | 0.627612i | − | 0.0438343i | ||||||
\(206\) | 4.07345 | + | 4.07345i | 0.283811 | + | 0.283811i | ||||
\(207\) | 0.535119 | + | 4.43296i | 0.0371933 | + | 0.308112i | ||||
\(208\) | −3.37961 | − | 1.25628i | −0.234334 | − | 0.0871076i | ||||
\(209\) | 4.63460i | 0.320582i | ||||||||
\(210\) | −0.579825 | + | 0.0348698i | −0.0400117 | + | 0.00240625i | ||||
\(211\) | −11.4416 | −0.787669 | −0.393835 | − | 0.919181i | \(-0.628852\pi\) | ||||
−0.393835 | + | 0.919181i | \(0.628852\pi\) | |||||||
\(212\) | −8.80608 | −0.604804 | ||||||||
\(213\) | 0.726825 | + | 12.0859i | 0.0498012 | + | 0.828109i | ||||
\(214\) | 12.9489 | + | 12.9489i | 0.885169 | + | 0.885169i | ||||
\(215\) | 0.654044 | + | 0.654044i | 0.0446054 | + | 0.0446054i | ||||
\(216\) | −0.931280 | − | 5.11202i | −0.0633656 | − | 0.347829i | ||||
\(217\) | −10.1908 | −0.691796 | ||||||||
\(218\) | −9.50671 | −0.643876 | ||||||||
\(219\) | −0.588996 | − | 9.79399i | −0.0398007 | − | 0.661817i | ||||
\(220\) | − | 1.21175i | − | 0.0816964i | ||||||
\(221\) | 17.7897 | + | 6.61287i | 1.19666 | + | 0.444829i | ||||
\(222\) | −5.19320 | − | 4.60401i | −0.348545 | − | 0.309001i | ||||
\(223\) | −9.06520 | − | 9.06520i | −0.607051 | − | 0.607051i | 0.335124 | − | 0.942174i | \(-0.391222\pi\) |
−0.942174 | + | 0.335124i | \(0.891222\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 14.5569 | − | 1.75722i | 0.970461 | − | 0.117148i | ||||
\(226\) | −11.2297 | − | 11.2297i | −0.746990 | − | 0.746990i | ||||
\(227\) | 1.95892 | − | 1.95892i | 0.130018 | − | 0.130018i | −0.639103 | − | 0.769121i | \(-0.720694\pi\) |
0.769121 | + | 0.639103i | \(0.220694\pi\) | |||||||
\(228\) | 0.133367 | + | 2.21766i | 0.00883242 | + | 0.146868i | ||||
\(229\) | 19.6908 | − | 19.6908i | 1.30120 | − | 1.30120i | 0.373622 | − | 0.927581i | \(-0.378116\pi\) |
0.927581 | − | 0.373622i | \(-0.121884\pi\) | |||||||
\(230\) | 0.499154i | 0.0329132i | ||||||||
\(231\) | 4.15164 | − | 4.68294i | 0.273158 | − | 0.308115i | ||||
\(232\) | −5.20752 | + | 5.20752i | −0.341890 | + | 0.341890i | ||||
\(233\) | 8.08237 | 0.529494 | 0.264747 | − | 0.964318i | \(-0.414712\pi\) | ||||
0.264747 | + | 0.964318i | \(0.414712\pi\) | |||||||
\(234\) | −5.65036 | − | 9.22353i | −0.369375 | − | 0.602961i | ||||
\(235\) | −1.07787 | −0.0703125 | ||||||||
\(236\) | −0.785394 | + | 0.785394i | −0.0511248 | + | 0.0511248i | ||||
\(237\) | 9.77652 | − | 11.0277i | 0.635053 | − | 0.716323i | ||||
\(238\) | 5.26383i | 0.341204i | ||||||||
\(239\) | 17.1098 | − | 17.1098i | 1.10674 | − | 1.10674i | 0.113167 | − | 0.993576i | \(-0.463901\pi\) |
0.993576 | − | 0.113167i | \(-0.0360994\pi\) | |||||||
\(240\) | −0.0348698 | − | 0.579825i | −0.00225084 | − | 0.0374275i | ||||
\(241\) | −1.64646 | + | 1.64646i | −0.106058 | + | 0.106058i | −0.758144 | − | 0.652087i | \(-0.773894\pi\) |
0.652087 | + | 0.758144i | \(0.273894\pi\) | |||||||
\(242\) | 1.45335 | + | 1.45335i | 0.0934247 | + | 0.0934247i | ||||
\(243\) | 7.26840 | − | 13.7902i | 0.466268 | − | 0.884644i | ||||
\(244\) | − | 8.74912i | − | 0.560105i | ||||||
\(245\) | −0.237140 | − | 0.237140i | −0.0151503 | − | 0.0151503i | ||||
\(246\) | 2.42547 | + | 2.15029i | 0.154642 | + | 0.137097i | ||||
\(247\) | 1.92584 | + | 4.20471i | 0.122538 | + | 0.267539i | ||||
\(248\) | − | 10.1908i | − | 0.647116i | ||||||
\(249\) | −0.449464 | − | 7.47381i | −0.0284836 | − | 0.473633i | ||||
\(250\) | 3.31595 | 0.209719 | ||||||||
\(251\) | −5.59492 | −0.353148 | −0.176574 | − | 0.984287i | \(-0.556501\pi\) | ||||
−0.176574 | + | 0.984287i | \(0.556501\pi\) | |||||||
\(252\) | 1.85180 | − | 2.36026i | 0.116653 | − | 0.148682i | ||||
\(253\) | −3.80271 | − | 3.80271i | −0.239074 | − | 0.239074i | ||||
\(254\) | 5.92617 | + | 5.92617i | 0.371841 | + | 0.371841i | ||||
\(255\) | 0.183549 | + | 3.05210i | 0.0114943 | + | 0.191130i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.37697 | 0.584920 | 0.292460 | − | 0.956278i | \(-0.405526\pi\) | ||||
0.292460 | + | 0.956278i | \(0.405526\pi\) | |||||||
\(258\) | −4.76846 | + | 0.286768i | −0.296871 | + | 0.0178534i | ||||
\(259\) | − | 4.00692i | − | 0.248978i | ||||||
\(260\) | −0.503526 | − | 1.09936i | −0.0312274 | − | 0.0681792i | ||||
\(261\) | −21.9344 | + | 2.64778i | −1.35770 | + | 0.163893i | ||||
\(262\) | −10.3186 | − | 10.3186i | −0.637484 | − | 0.637484i | ||||
\(263\) | 7.28774i | 0.449382i | 0.974430 | + | 0.224691i | \(0.0721372\pi\) | ||||
−0.974430 | + | 0.224691i | \(0.927863\pi\) | |||||||
\(264\) | 4.68294 | + | 4.15164i | 0.288215 | + | 0.255516i | ||||
\(265\) | −2.08828 | − | 2.08828i | −0.128282 | − | 0.128282i | ||||
\(266\) | −0.906991 | + | 0.906991i | −0.0556112 | + | 0.0556112i | ||||
\(267\) | −3.96818 | + | 0.238641i | −0.242849 | + | 0.0146046i | ||||
\(268\) | −9.68048 | + | 9.68048i | −0.591330 | + | 0.591330i | ||||
\(269\) | − | 16.4964i | − | 1.00580i | −0.864344 | − | 0.502901i | \(-0.832266\pi\) | ||
0.864344 | − | 0.502901i | \(-0.167734\pi\) | |||||||
\(270\) | 0.991421 | − | 1.43311i | 0.0603360 | − | 0.0872162i | ||||
\(271\) | −2.57036 | + | 2.57036i | −0.156138 | + | 0.156138i | −0.780853 | − | 0.624715i | \(-0.785215\pi\) |
0.624715 | + | 0.780853i | \(0.285215\pi\) | |||||||
\(272\) | −5.26383 | −0.319167 | ||||||||
\(273\) | 1.82063 | − | 5.97372i | 0.110189 | − | 0.361546i | ||||
\(274\) | 16.3839 | 0.989790 | ||||||||
\(275\) | −12.4873 | + | 12.4873i | −0.753012 | + | 0.753012i | ||||
\(276\) | −1.92903 | − | 1.71017i | −0.116114 | − | 0.102940i | ||||
\(277\) | 7.42795i | 0.446302i | 0.974784 | + | 0.223151i | \(0.0716344\pi\) | ||||
−0.974784 | + | 0.223151i | \(0.928366\pi\) | |||||||
\(278\) | 8.47121 | − | 8.47121i | 0.508070 | − | 0.508070i | ||||
\(279\) | 18.8714 | − | 24.0529i | 1.12980 | − | 1.44001i | ||||
\(280\) | 0.237140 | − | 0.237140i | 0.0141718 | − | 0.0141718i | ||||
\(281\) | −9.42247 | − | 9.42247i | −0.562097 | − | 0.562097i | 0.367805 | − | 0.929903i | \(-0.380109\pi\) |
−0.929903 | + | 0.367805i | \(0.880109\pi\) | |||||||
\(282\) | 3.69293 | − | 4.16553i | 0.219911 | − | 0.248054i | ||||
\(283\) | 21.5878i | 1.28326i | 0.767014 | + | 0.641631i | \(0.221742\pi\) | ||||
−0.767014 | + | 0.641631i | \(0.778258\pi\) | |||||||
\(284\) | −4.94294 | − | 4.94294i | −0.293310 | − | 0.293310i | ||||
\(285\) | −0.494269 | + | 0.557523i | −0.0292780 | + | 0.0330248i | ||||
\(286\) | 12.2113 | + | 4.53922i | 0.722067 | + | 0.268410i | ||||
\(287\) | 1.87142i | 0.110466i | ||||||||
\(288\) | 2.36026 | + | 1.85180i | 0.139080 | + | 0.109119i | ||||
\(289\) | 10.7079 | 0.629879 | ||||||||
\(290\) | −2.46982 | −0.145033 | ||||||||
\(291\) | 11.8905 | − | 0.715078i | 0.697034 | − | 0.0419186i | ||||
\(292\) | 4.00560 | + | 4.00560i | 0.234410 | + | 0.234410i | ||||
\(293\) | −3.94771 | − | 3.94771i | −0.230628 | − | 0.230628i | 0.582327 | − | 0.812955i | \(-0.302142\pi\) |
−0.812955 | + | 0.582327i | \(0.802142\pi\) | |||||||
\(294\) | 1.72893 | − | 0.103975i | 0.100833 | − | 0.00606395i | ||||
\(295\) | −0.372497 | −0.0216876 | ||||||||
\(296\) | 4.00692 | 0.232898 | ||||||||
\(297\) | 3.36492 | + | 18.4708i | 0.195252 | + | 1.07179i | ||||
\(298\) | − | 3.08156i | − | 0.178510i | ||||||
\(299\) | −5.03015 | − | 1.86983i | −0.290901 | − | 0.108135i | ||||
\(300\) | −5.61584 | + | 6.33452i | −0.324231 | + | 0.365724i | ||||
\(301\) | −1.95023 | − | 1.95023i | −0.112410 | − | 0.112410i | ||||
\(302\) | − | 13.2188i | − | 0.760657i | ||||||
\(303\) | 21.2915 | − | 24.0162i | 1.22316 | − | 1.37969i | ||||
\(304\) | −0.906991 | − | 0.906991i | −0.0520195 | − | 0.0520195i | ||||
\(305\) | 2.07477 | − | 2.07477i | 0.118801 | − | 0.118801i | ||||
\(306\) | −12.4240 | − | 9.74759i | −0.710233 | − | 0.557233i | ||||
\(307\) | −11.8118 | + | 11.8118i | −0.674136 | + | 0.674136i | −0.958667 | − | 0.284531i | \(-0.908162\pi\) |
0.284531 | + | 0.958667i | \(0.408162\pi\) | |||||||
\(308\) | 3.61322i | 0.205882i | ||||||||
\(309\) | −7.46624 | − | 6.61917i | −0.424740 | − | 0.376551i | ||||
\(310\) | 2.41665 | − | 2.41665i | 0.137256 | − | 0.137256i | ||||
\(311\) | −20.8401 | −1.18174 | −0.590868 | − | 0.806769i | \(-0.701214\pi\) | ||||
−0.590868 | + | 0.806769i | \(0.701214\pi\) | |||||||
\(312\) | 5.97372 | + | 1.82063i | 0.338195 | + | 0.103073i | ||||
\(313\) | 9.67697 | 0.546975 | 0.273487 | − | 0.961876i | \(-0.411823\pi\) | ||||
0.273487 | + | 0.961876i | \(0.411823\pi\) | |||||||
\(314\) | −12.4696 | + | 12.4696i | −0.703698 | + | 0.703698i | ||||
\(315\) | 0.998850 | − | 0.120575i | 0.0562788 | − | 0.00679362i | ||||
\(316\) | 8.50862i | 0.478647i | ||||||||
\(317\) | −14.4793 | + | 14.4793i | −0.813239 | + | 0.813239i | −0.985118 | − | 0.171879i | \(-0.945016\pi\) |
0.171879 | + | 0.985118i | \(0.445016\pi\) | |||||||
\(318\) | 15.2251 | − | 0.915613i | 0.853780 | − | 0.0513450i | ||||
\(319\) | 18.8159 | − | 18.8159i | 1.05349 | − | 1.05349i | ||||
\(320\) | 0.237140 | + | 0.237140i | 0.0132565 | + | 0.0132565i | ||||
\(321\) | −23.7341 | − | 21.0414i | −1.32471 | − | 1.17441i | ||||
\(322\) | − | 1.48838i | − | 0.0829443i | ||||||
\(323\) | 4.77425 | + | 4.77425i | 0.265646 | + | 0.265646i | ||||
\(324\) | 2.14164 | + | 8.74148i | 0.118980 | + | 0.485638i | ||||
\(325\) | −6.14012 | + | 16.5179i | −0.340593 | + | 0.916250i | ||||
\(326\) | 3.20259i | 0.177375i | ||||||||
\(327\) | 16.4364 | − | 0.988462i | 0.908936 | − | 0.0546620i | ||||
\(328\) | −1.87142 | −0.103332 | ||||||||
\(329\) | 3.21400 | 0.177194 | ||||||||
\(330\) | 0.125992 | + | 2.09503i | 0.00693565 | + | 0.115328i | ||||
\(331\) | 23.9019 | + | 23.9019i | 1.31377 | + | 1.31377i | 0.918617 | + | 0.395149i | \(0.129307\pi\) |
0.395149 | + | 0.918617i | \(0.370693\pi\) | |||||||
\(332\) | 3.05668 | + | 3.05668i | 0.167757 | + | 0.167757i | ||||
\(333\) | 9.45737 | + | 7.42004i | 0.518261 | + | 0.406616i | ||||
\(334\) | 17.6044 | 0.963272 | ||||||||
\(335\) | −4.59126 | −0.250848 | ||||||||
\(336\) | 0.103975 | + | 1.72893i | 0.00567231 | + | 0.0943207i | ||||
\(337\) | − | 19.1386i | − | 1.04254i | −0.853390 | − | 0.521272i | \(-0.825458\pi\) | ||
0.853390 | − | 0.521272i | \(-0.174542\pi\) | |||||||
\(338\) | 12.9648 | − | 0.956020i | 0.705192 | − | 0.0520006i | ||||
\(339\) | 20.5830 | + | 18.2478i | 1.11791 | + | 0.991083i | ||||
\(340\) | −1.24827 | − | 1.24827i | −0.0676968 | − | 0.0676968i | ||||
\(341\) | 36.8216i | 1.99400i | ||||||||
\(342\) | −0.461162 | − | 3.82030i | −0.0249368 | − | 0.206578i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 1.95023 | − | 1.95023i | 0.105149 | − | 0.105149i | ||||
\(345\) | −0.0518996 | − | 0.863001i | −0.00279418 | − | 0.0464624i | ||||
\(346\) | −9.08752 | + | 9.08752i | −0.488548 | + | 0.488548i | ||||
\(347\) | − | 22.2918i | − | 1.19669i | −0.801240 | − | 0.598343i | \(-0.795826\pi\) | ||
0.801240 | − | 0.598343i | \(-0.204174\pi\) | |||||||
\(348\) | 8.46196 | − | 9.54487i | 0.453609 | − | 0.511659i | ||||
\(349\) | −11.5388 | + | 11.5388i | −0.617658 | + | 0.617658i | −0.944930 | − | 0.327272i | \(-0.893871\pi\) |
0.327272 | + | 0.944930i | \(0.393871\pi\) | |||||||
\(350\) | −4.88753 | −0.261249 | ||||||||
\(351\) | 10.7281 | + | 15.3593i | 0.572622 | + | 0.819819i | ||||
\(352\) | −3.61322 | −0.192585 | ||||||||
\(353\) | −10.9867 | + | 10.9867i | −0.584765 | + | 0.584765i | −0.936209 | − | 0.351444i | \(-0.885691\pi\) |
0.351444 | + | 0.936209i | \(0.385691\pi\) | |||||||
\(354\) | 1.27623 | − | 1.43955i | 0.0678307 | − | 0.0765112i | ||||
\(355\) | − | 2.34434i | − | 0.124425i | ||||||
\(356\) | 1.62293 | − | 1.62293i | 0.0860152 | − | 0.0860152i | ||||
\(357\) | −0.547308 | − | 9.10078i | −0.0289666 | − | 0.481665i | ||||
\(358\) | −9.70564 | + | 9.70564i | −0.512959 | + | 0.512959i | ||||
\(359\) | −12.3937 | − | 12.3937i | −0.654116 | − | 0.654116i | 0.299865 | − | 0.953982i | \(-0.403058\pi\) |
−0.953982 | + | 0.299865i | \(0.903058\pi\) | |||||||
\(360\) | 0.120575 | + | 0.998850i | 0.00635485 | + | 0.0526440i | ||||
\(361\) | − | 17.3547i | − | 0.913407i | ||||||
\(362\) | 12.5850 | + | 12.5850i | 0.661454 | + | 0.661454i | ||||
\(363\) | −2.66384 | − | 2.36162i | −0.139816 | − | 0.123953i | ||||
\(364\) | 1.50142 | + | 3.27807i | 0.0786957 | + | 0.171818i | ||||
\(365\) | 1.89978i | 0.0994390i | ||||||||
\(366\) | 0.909691 | + | 15.1266i | 0.0475503 | + | 0.790679i | ||||
\(367\) | −19.3712 | −1.01117 | −0.505583 | − | 0.862778i | \(-0.668723\pi\) | ||||
−0.505583 | + | 0.862778i | \(0.668723\pi\) | |||||||
\(368\) | 1.48838 | 0.0775873 | ||||||||
\(369\) | −4.41703 | − | 3.46550i | −0.229941 | − | 0.180407i | ||||
\(370\) | 0.950203 | + | 0.950203i | 0.0493987 | + | 0.0493987i | ||||
\(371\) | 6.22684 | + | 6.22684i | 0.323281 | + | 0.323281i | ||||
\(372\) | 1.05959 | + | 17.6191i | 0.0549372 | + | 0.913510i | ||||
\(373\) | 26.6583 | 1.38031 | 0.690157 | − | 0.723659i | \(-0.257541\pi\) | ||||
0.690157 | + | 0.723659i | \(0.257541\pi\) | |||||||
\(374\) | 19.0194 | 0.983469 | ||||||||
\(375\) | −5.73304 | + | 0.344776i | −0.296053 | + | 0.0178042i | ||||
\(376\) | 3.21400i | 0.165749i | ||||||||
\(377\) | 9.25195 | − | 24.8893i | 0.476499 | − | 1.28186i | ||||
\(378\) | −2.95623 | + | 4.27326i | −0.152052 | + | 0.219793i | ||||
\(379\) | −7.17262 | − | 7.17262i | −0.368433 | − | 0.368433i | 0.498473 | − | 0.866905i | \(-0.333894\pi\) |
−0.866905 | + | 0.498473i | \(0.833894\pi\) | |||||||
\(380\) | − | 0.430168i | − | 0.0220672i | ||||||
\(381\) | −10.8621 | − | 9.62974i | −0.556482 | − | 0.493346i | ||||
\(382\) | 0.317563 | + | 0.317563i | 0.0162479 | + | 0.0162479i | ||||
\(383\) | 1.75953 | − | 1.75953i | 0.0899076 | − | 0.0899076i | −0.660723 | − | 0.750630i | \(-0.729750\pi\) |
0.750630 | + | 0.660723i | \(0.229750\pi\) | |||||||
\(384\) | −1.72893 | + | 0.103975i | −0.0882289 | + | 0.00530596i | ||||
\(385\) | −0.856839 | + | 0.856839i | −0.0436686 | + | 0.0436686i | ||||
\(386\) | 7.83380i | 0.398730i | ||||||||
\(387\) | 8.21450 | − | 0.991602i | 0.417567 | − | 0.0504060i | ||||
\(388\) | −4.86305 | + | 4.86305i | −0.246884 | + | 0.246884i | ||||
\(389\) | −23.3995 | −1.18640 | −0.593200 | − | 0.805055i | \(-0.702136\pi\) | ||||
−0.593200 | + | 0.805055i | \(0.702136\pi\) | |||||||
\(390\) | 0.984865 | + | 1.84835i | 0.0498706 | + | 0.0935950i | ||||
\(391\) | −7.83459 | −0.396212 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 18.9130 | + | 16.7672i | 0.954032 | + | 0.845793i | ||||
\(394\) | − | 22.3624i | − | 1.12660i | ||||||
\(395\) | −2.01774 | + | 2.01774i | −0.101523 | + | 0.101523i | ||||
\(396\) | −8.52813 | − | 6.69097i | −0.428555 | − | 0.336234i | ||||
\(397\) | 12.7022 | − | 12.7022i | 0.637506 | − | 0.637506i | −0.312434 | − | 0.949940i | \(-0.601144\pi\) |
0.949940 | + | 0.312434i | \(0.101144\pi\) | |||||||
\(398\) | −18.6082 | − | 18.6082i | −0.932747 | − | 0.932747i | ||||
\(399\) | 1.47382 | − | 1.66243i | 0.0737831 | − | 0.0832254i | ||||
\(400\) | − | 4.88753i | − | 0.244376i | ||||||
\(401\) | −4.63460 | − | 4.63460i | −0.231441 | − | 0.231441i | 0.581853 | − | 0.813294i | \(-0.302328\pi\) |
−0.813294 | + | 0.581853i | \(0.802328\pi\) | |||||||
\(402\) | 15.7303 | − | 17.7434i | 0.784557 | − | 0.884959i | ||||
\(403\) | 15.3006 | + | 33.4062i | 0.762179 | + | 1.66408i | ||||
\(404\) | 18.5302i | 0.921911i | ||||||||
\(405\) | −1.56509 | + | 2.58082i | −0.0777698 | + | 0.128242i | ||||
\(406\) | 7.36454 | 0.365496 | ||||||||
\(407\) | −14.4779 | −0.717642 | ||||||||
\(408\) | 9.10078 | − | 0.547308i | 0.450556 | − | 0.0270958i | ||||
\(409\) | 20.9632 | + | 20.9632i | 1.03656 | + | 1.03656i | 0.999306 | + | 0.0372568i | \(0.0118619\pi\) |
0.0372568 | + | 0.999306i | \(0.488138\pi\) | |||||||
\(410\) | −0.443789 | − | 0.443789i | −0.0219172 | − | 0.0219172i | ||||
\(411\) | −28.3266 | + | 1.70352i | −1.39725 | + | 0.0840285i | ||||
\(412\) | 5.76073 | 0.283811 | ||||||||
\(413\) | 1.11071 | 0.0546547 | ||||||||
\(414\) | 3.51297 | + | 2.75619i | 0.172653 | + | 0.135459i | ||||
\(415\) | 1.44973i | 0.0711642i | ||||||||
\(416\) | −3.27807 | + | 1.50142i | −0.160721 | + | 0.0736131i | ||||
\(417\) | −13.7653 | + | 15.5269i | −0.674091 | + | 0.760356i | ||||
\(418\) | 3.27716 | + | 3.27716i | 0.160291 | + | 0.160291i | ||||
\(419\) | 2.30031i | 0.112377i | 0.998420 | + | 0.0561886i | \(0.0178948\pi\) | ||||
−0.998420 | + | 0.0561886i | \(0.982105\pi\) | |||||||
\(420\) | −0.385342 | + | 0.434655i | −0.0188027 | + | 0.0212090i | ||||
\(421\) | −5.27352 | − | 5.27352i | −0.257016 | − | 0.257016i | 0.566823 | − | 0.823839i | \(-0.308172\pi\) |
−0.823839 | + | 0.566823i | \(0.808172\pi\) | |||||||
\(422\) | −8.09040 | + | 8.09040i | −0.393835 | + | 0.393835i | ||||
\(423\) | −5.95170 | + | 7.58587i | −0.289382 | + | 0.368838i | ||||
\(424\) | −6.22684 | + | 6.22684i | −0.302402 | + | 0.302402i | ||||
\(425\) | 25.7271i | 1.24795i | ||||||||
\(426\) | 9.05993 | + | 8.03204i | 0.438955 | + | 0.389154i | ||||
\(427\) | −6.18656 | + | 6.18656i | −0.299389 | + | 0.299389i | ||||
\(428\) | 18.3125 | 0.885169 | ||||||||
\(429\) | −21.5843 | − | 6.57832i | −1.04210 | − | 0.317604i | ||||
\(430\) | 0.924957 | 0.0446054 | ||||||||
\(431\) | 4.81808 | − | 4.81808i | 0.232079 | − | 0.232079i | −0.581481 | − | 0.813560i | \(-0.697527\pi\) |
0.813560 | + | 0.581481i | \(0.197527\pi\) | |||||||
\(432\) | −4.27326 | − | 2.95623i | −0.205597 | − | 0.142232i | ||||
\(433\) | − | 4.81966i | − | 0.231618i | −0.993272 | − | 0.115809i | \(-0.963054\pi\) | ||
0.993272 | − | 0.115809i | \(-0.0369460\pi\) | |||||||
\(434\) | −7.20598 | + | 7.20598i | −0.345898 | + | 0.345898i | ||||
\(435\) | 4.27014 | − | 0.256800i | 0.204738 | − | 0.0123126i | ||||
\(436\) | −6.72226 | + | 6.72226i | −0.321938 | + | 0.321938i | ||||
\(437\) | −1.34995 | − | 1.34995i | −0.0645768 | − | 0.0645768i | ||||
\(438\) | −7.34188 | − | 6.50891i | −0.350809 | − | 0.311008i | ||||
\(439\) | − | 13.0143i | − | 0.621137i | −0.950551 | − | 0.310569i | \(-0.899481\pi\) | ||
0.950551 | − | 0.310569i | \(-0.100519\pi\) | |||||||
\(440\) | −0.856839 | − | 0.856839i | −0.0408482 | − | 0.0408482i | ||||
\(441\) | −2.97838 | + | 0.359531i | −0.141828 | + | 0.0171205i | ||||
\(442\) | 17.2552 | − | 7.90321i | 0.820747 | − | 0.375918i | ||||
\(443\) | 23.1864i | 1.10162i | 0.834631 | + | 0.550810i | \(0.185681\pi\) | ||||
−0.834631 | + | 0.550810i | \(0.814319\pi\) | |||||||
\(444\) | −6.92768 | + | 0.416620i | −0.328773 | + | 0.0197719i | ||||
\(445\) | 0.769725 | 0.0364884 | ||||||||
\(446\) | −12.8201 | −0.607051 | ||||||||
\(447\) | 0.320406 | + | 5.32779i | 0.0151547 | + | 0.251996i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 7.31378 | + | 7.31378i | 0.345159 | + | 0.345159i | 0.858303 | − | 0.513144i | \(-0.171519\pi\) |
−0.513144 | + | 0.858303i | \(0.671519\pi\) | |||||||
\(450\) | 9.05075 | − | 11.5358i | 0.426656 | − | 0.543804i | ||||
\(451\) | 6.76184 | 0.318403 | ||||||||
\(452\) | −15.8812 | −0.746990 | ||||||||
\(453\) | 1.37443 | + | 22.8544i | 0.0645762 | + | 1.07379i | ||||
\(454\) | − | 2.77033i | − | 0.130018i | ||||||
\(455\) | −0.421316 | + | 1.13341i | −0.0197516 | + | 0.0531350i | ||||
\(456\) | 1.66243 | + | 1.47382i | 0.0778502 | + | 0.0690178i | ||||
\(457\) | 7.58631 | + | 7.58631i | 0.354873 | + | 0.354873i | 0.861919 | − | 0.507046i | \(-0.169263\pi\) |
−0.507046 | + | 0.861919i | \(0.669263\pi\) | |||||||
\(458\) | − | 27.8470i | − | 1.30120i | ||||||
\(459\) | 22.4937 | + | 15.5611i | 1.04992 | + | 0.726329i | ||||
\(460\) | 0.352955 | + | 0.352955i | 0.0164566 | + | 0.0164566i | ||||
\(461\) | −9.45526 | + | 9.45526i | −0.440375 | + | 0.440375i | −0.892138 | − | 0.451763i | \(-0.850795\pi\) |
0.451763 | + | 0.892138i | \(0.350795\pi\) | |||||||
\(462\) | −0.375685 | − | 6.24699i | −0.0174784 | − | 0.290636i | ||||
\(463\) | 24.1674 | − | 24.1674i | 1.12315 | − | 1.12315i | 0.131890 | − | 0.991264i | \(-0.457895\pi\) |
0.991264 | − | 0.131890i | \(-0.0421046\pi\) | |||||||
\(464\) | 7.36454i | 0.341890i | ||||||||
\(465\) | −3.92694 | + | 4.42948i | −0.182107 | + | 0.205412i | ||||
\(466\) | 5.71510 | − | 5.71510i | 0.264747 | − | 0.264747i | ||||
\(467\) | −23.9765 | −1.10950 | −0.554750 | − | 0.832017i | \(-0.687186\pi\) | ||||
−0.554750 | + | 0.832017i | \(0.687186\pi\) | |||||||
\(468\) | −10.5174 | − | 2.52661i | −0.486168 | − | 0.116793i | ||||
\(469\) | 13.6903 | 0.632158 | ||||||||
\(470\) | −0.762169 | + | 0.762169i | −0.0351562 | + | 0.0351562i | ||||
\(471\) | 20.2624 | − | 22.8555i | 0.933644 | − | 1.05313i | ||||
\(472\) | 1.11071i | 0.0511248i | ||||||||
\(473\) | −7.04661 | + | 7.04661i | −0.324004 | + | 0.324004i | ||||
\(474\) | −0.884684 | − | 14.7108i | −0.0406349 | − | 0.675688i | ||||
\(475\) | −4.43294 | + | 4.43294i | −0.203397 | + | 0.203397i | ||||
\(476\) | 3.72209 | + | 3.72209i | 0.170602 | + | 0.170602i | ||||
\(477\) | −26.2278 | + | 3.16606i | −1.20089 | + | 0.144964i | ||||
\(478\) | − | 24.1969i | − | 1.10674i | ||||||
\(479\) | 13.3006 | + | 13.3006i | 0.607720 | + | 0.607720i | 0.942350 | − | 0.334630i | \(-0.108611\pi\) |
−0.334630 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(480\) | −0.434655 | − | 0.385342i | −0.0198392 | − | 0.0175884i | ||||
\(481\) | −13.1350 | + | 6.01607i | −0.598903 | + | 0.274309i | ||||
\(482\) | 2.32844i | 0.106058i | ||||||||
\(483\) | 0.154755 | + | 2.57330i | 0.00704158 | + | 0.117089i | ||||
\(484\) | 2.05534 | 0.0934247 | ||||||||
\(485\) | −2.30645 | −0.104731 | ||||||||
\(486\) | −4.61163 | − | 14.8907i | −0.209188 | − | 0.675456i | ||||
\(487\) | −12.0715 | − | 12.0715i | −0.547013 | − | 0.547013i | 0.378563 | − | 0.925576i | \(-0.376418\pi\) |
−0.925576 | + | 0.378563i | \(0.876418\pi\) | |||||||
\(488\) | −6.18656 | − | 6.18656i | −0.280052 | − | 0.280052i | ||||
\(489\) | −0.332989 | − | 5.53704i | −0.0150583 | − | 0.250393i | ||||
\(490\) | −0.335367 | −0.0151503 | ||||||||
\(491\) | −28.9991 | −1.30871 | −0.654356 | − | 0.756187i | \(-0.727060\pi\) | ||||
−0.654356 | + | 0.756187i | \(0.727060\pi\) | |||||||
\(492\) | 3.23555 | − | 0.194581i | 0.145870 | − | 0.00877239i | ||||
\(493\) | − | 38.7657i | − | 1.74592i | ||||||
\(494\) | 4.33495 | + | 1.61141i | 0.195039 | + | 0.0725007i | ||||
\(495\) | −0.435663 | − | 3.60906i | −0.0195816 | − | 0.162215i | ||||
\(496\) | −7.20598 | − | 7.20598i | −0.323558 | − | 0.323558i | ||||
\(497\) | 6.99038i | 0.313561i | ||||||||
\(498\) | −5.60260 | − | 4.96696i | −0.251059 | − | 0.222575i | ||||
\(499\) | −16.4961 | − | 16.4961i | −0.738468 | − | 0.738468i | 0.233814 | − | 0.972281i | \(-0.424879\pi\) |
−0.972281 | + | 0.233814i | \(0.924879\pi\) | |||||||
\(500\) | 2.34473 | − | 2.34473i | 0.104860 | − | 0.104860i | ||||
\(501\) | −30.4368 | + | 1.83042i | −1.35982 | + | 0.0817773i | ||||
\(502\) | −3.95620 | + | 3.95620i | −0.176574 | + | 0.176574i | ||||
\(503\) | − | 3.30047i | − | 0.147161i | −0.997289 | − | 0.0735804i | \(-0.976557\pi\) | ||
0.997289 | − | 0.0735804i | \(-0.0234425\pi\) | |||||||
\(504\) | −0.359531 | − | 2.97838i | −0.0160148 | − | 0.132668i | ||||
\(505\) | −4.39425 | + | 4.39425i | −0.195542 | + | 0.195542i | ||||
\(506\) | −5.37785 | −0.239074 | ||||||||
\(507\) | −22.3158 | + | 3.00090i | −0.991079 | + | 0.133275i | ||||
\(508\) | 8.38087 | 0.371841 | ||||||||
\(509\) | 4.74000 | − | 4.74000i | 0.210097 | − | 0.210097i | −0.594212 | − | 0.804309i | \(-0.702536\pi\) |
0.804309 | + | 0.594212i | \(0.202536\pi\) | |||||||
\(510\) | 2.28795 | + | 2.02837i | 0.101312 | + | 0.0898179i | ||||
\(511\) | − | 5.66478i | − | 0.250595i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 1.19453 | + | 6.55708i | 0.0527399 | + | 0.289502i | ||||
\(514\) | 6.63052 | − | 6.63052i | 0.292460 | − | 0.292460i | ||||
\(515\) | 1.36610 | + | 1.36610i | 0.0601976 | + | 0.0601976i | ||||
\(516\) | −3.16903 | + | 3.57459i | −0.139509 | + | 0.157362i | ||||
\(517\) | − | 11.6129i | − | 0.510734i | ||||||
\(518\) | −2.83332 | − | 2.83332i | −0.124489 | − | 0.124489i | ||||
\(519\) | 14.7668 | − | 16.6565i | 0.648190 | − | 0.731140i | ||||
\(520\) | −1.13341 | − | 0.421316i | −0.0497033 | − | 0.0184759i | ||||
\(521\) | − | 23.6757i | − | 1.03725i | −0.855001 | − | 0.518627i | \(-0.826443\pi\) | ||
0.855001 | − | 0.518627i | \(-0.173557\pi\) | |||||||
\(522\) | −13.6377 | + | 17.3822i | −0.596905 | + | 0.760799i | ||||
\(523\) | −39.0606 | −1.70800 | −0.854000 | − | 0.520272i | \(-0.825830\pi\) | ||||
−0.854000 | + | 0.520272i | \(0.825830\pi\) | |||||||
\(524\) | −14.5927 | −0.637484 | ||||||||
\(525\) | 8.45018 | − | 0.508181i | 0.368796 | − | 0.0221789i | ||||
\(526\) | 5.15321 | + | 5.15321i | 0.224691 | + | 0.224691i | ||||
\(527\) | 37.9311 | + | 37.9311i | 1.65230 | + | 1.65230i | ||||
\(528\) | 6.24699 | − | 0.375685i | 0.271865 | − | 0.0163496i | ||||
\(529\) | −20.7847 | −0.903683 | ||||||||
\(530\) | −2.95327 | −0.128282 | ||||||||
\(531\) | −2.05683 | + | 2.62157i | −0.0892586 | + | 0.113767i | ||||
\(532\) | 1.28268i | 0.0556112i | ||||||||
\(533\) | 6.13464 | − | 2.80978i | 0.265721 | − | 0.121705i | ||||
\(534\) | −2.63719 | + | 2.97467i | −0.114122 | + | 0.128727i | ||||
\(535\) | 4.34264 | + | 4.34264i | 0.187749 | + | 0.187749i | ||||
\(536\) | 13.6903i | 0.591330i | ||||||||
\(537\) | 15.7712 | − | 17.7895i | 0.680577 | − | 0.767673i | ||||
\(538\) | −11.6647 | − | 11.6647i | −0.502901 | − | 0.502901i | ||||
\(539\) | 2.55493 | − | 2.55493i | 0.110049 | − | 0.110049i | ||||
\(540\) | −0.312321 | − | 1.71440i | −0.0134401 | − | 0.0737761i | ||||
\(541\) | −19.3541 | + | 19.3541i | −0.832100 | + | 0.832100i | −0.987804 | − | 0.155704i | \(-0.950235\pi\) |
0.155704 | + | 0.987804i | \(0.450235\pi\) | |||||||
\(542\) | 3.63504i | 0.156138i | ||||||||
\(543\) | −23.0671 | − | 20.4500i | −0.989904 | − | 0.877595i | ||||
\(544\) | −3.72209 | + | 3.72209i | −0.159583 | + | 0.159583i | ||||
\(545\) | −3.18824 | −0.136569 | ||||||||
\(546\) | −2.93668 | − | 5.51143i | −0.125678 | − | 0.235868i | ||||
\(547\) | −17.0333 | −0.728292 | −0.364146 | − | 0.931342i | \(-0.618639\pi\) | ||||
−0.364146 | + | 0.931342i | \(0.618639\pi\) | |||||||
\(548\) | 11.5852 | − | 11.5852i | 0.494895 | − | 0.494895i | ||||
\(549\) | −3.14558 | − | 26.0582i | −0.134250 | − | 1.11214i | ||||
\(550\) | 17.6597i | 0.753012i | ||||||||
\(551\) | 6.67957 | − | 6.67957i | 0.284559 | − | 0.284559i | ||||
\(552\) | −2.57330 | + | 0.154755i | −0.109527 | + | 0.00658680i | ||||
\(553\) | 6.01650 | − | 6.01650i | 0.255848 | − | 0.255848i | ||||
\(554\) | 5.25236 | + | 5.25236i | 0.223151 | + | 0.223151i | ||||
\(555\) | −1.74163 | − | 1.54403i | −0.0739280 | − | 0.0655406i | ||||
\(556\) | − | 11.9801i | − | 0.508070i | ||||||
\(557\) | −17.6970 | − | 17.6970i | −0.749846 | − | 0.749846i | 0.224604 | − | 0.974450i | \(-0.427891\pi\) |
−0.974450 | + | 0.224604i | \(0.927891\pi\) | |||||||
\(558\) | −3.66391 | − | 30.3521i | −0.155106 | − | 1.28490i | ||||
\(559\) | −3.46489 | + | 9.32111i | −0.146549 | + | 0.394241i | ||||
\(560\) | − | 0.335367i | − | 0.0141718i | ||||||
\(561\) | −32.8831 | + | 1.97754i | −1.38833 | + | 0.0834919i | ||||
\(562\) | −13.3254 | −0.562097 | ||||||||
\(563\) | 1.91330 | 0.0806362 | 0.0403181 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403181 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(564\) | −0.334176 | − | 5.55677i | −0.0140714 | − | 0.233982i | ||||
\(565\) | −3.76608 | − | 3.76608i | −0.158440 | − | 0.158440i | ||||
\(566\) | 15.2649 | + | 15.2649i | 0.641631 | + | 0.641631i | ||||
\(567\) | 4.66679 | − | 7.69552i | 0.195987 | − | 0.323182i | ||||
\(568\) | −6.99038 | −0.293310 | ||||||||
\(569\) | −16.3399 | −0.685003 | −0.342501 | − | 0.939517i | \(-0.611274\pi\) | ||||
−0.342501 | + | 0.939517i | \(0.611274\pi\) | |||||||
\(570\) | 0.0447268 | + | 0.743729i | 0.00187340 | + | 0.0311514i | ||||
\(571\) | − | 42.0194i | − | 1.75846i | −0.476400 | − | 0.879229i | \(-0.658059\pi\) | ||
0.476400 | − | 0.879229i | \(-0.341941\pi\) | |||||||
\(572\) | 11.8444 | − | 5.42495i | 0.495238 | − | 0.226829i | ||||
\(573\) | −0.582062 | − | 0.516025i | −0.0243160 | − | 0.0215572i | ||||
\(574\) | 1.32329 | + | 1.32329i | 0.0552332 | + | 0.0552332i | ||||
\(575\) | − | 7.27451i | − | 0.303368i | ||||||
\(576\) | 2.97838 | − | 0.359531i | 0.124099 | − | 0.0149804i | ||||
\(577\) | 24.8112 | + | 24.8112i | 1.03290 | + | 1.03290i | 0.999440 | + | 0.0334650i | \(0.0106542\pi\) |
0.0334650 | + | 0.999440i | \(0.489346\pi\) | |||||||
\(578\) | 7.57166 | − | 7.57166i | 0.314940 | − | 0.314940i | ||||
\(579\) | −0.814520 | − | 13.5441i | −0.0338503 | − | 0.562872i | ||||
\(580\) | −1.74643 | + | 1.74643i | −0.0725165 | + | 0.0725165i | ||||
\(581\) | − | 4.32280i | − | 0.179340i | ||||||
\(582\) | 7.90223 | − | 8.91350i | 0.327558 | − | 0.369476i | ||||
\(583\) | 22.4989 | − | 22.4989i | 0.931810 | − | 0.931810i | ||||
\(584\) | 5.66478 | 0.234410 | ||||||||
\(585\) | −1.89494 | − | 3.09327i | −0.0783463 | − | 0.127891i | ||||
\(586\) | −5.58290 | −0.230628 | ||||||||
\(587\) | −9.34332 | + | 9.34332i | −0.385640 | + | 0.385640i | −0.873129 | − | 0.487489i | \(-0.837913\pi\) |
0.487489 | + | 0.873129i | \(0.337913\pi\) | |||||||
\(588\) | 1.14901 | − | 1.29606i | 0.0473846 | − | 0.0534485i | ||||
\(589\) | 13.0715i | 0.538603i | ||||||||
\(590\) | −0.263395 | + | 0.263395i | −0.0108438 | + | 0.0108438i | ||||
\(591\) | 2.32514 | + | 38.6630i | 0.0956434 | + | 1.59038i | ||||
\(592\) | 2.83332 | − | 2.83332i | 0.116449 | − | 0.116449i | ||||
\(593\) | 8.89198 | + | 8.89198i | 0.365150 | + | 0.365150i | 0.865705 | − | 0.500555i | \(-0.166871\pi\) |
−0.500555 | + | 0.865705i | \(0.666871\pi\) | |||||||
\(594\) | 15.4402 | + | 10.6815i | 0.633519 | + | 0.438267i | ||||
\(595\) | 1.76532i | 0.0723709i | ||||||||
\(596\) | −2.17899 | − | 2.17899i | −0.0892550 | − | 0.0892550i | ||||
\(597\) | 34.1071 | + | 30.2375i | 1.39591 | + | 1.23754i | ||||
\(598\) | −4.87902 | + | 2.23468i | −0.199518 | + | 0.0913830i | ||||
\(599\) | − | 39.8265i | − | 1.62727i | −0.581379 | − | 0.813633i | \(-0.697487\pi\) | ||
0.581379 | − | 0.813633i | \(-0.302513\pi\) | |||||||
\(600\) | 0.508181 | + | 8.45018i | 0.0207464 | + | 0.344977i | ||||
\(601\) | 40.3328 | 1.64521 | 0.822605 | − | 0.568613i | \(-0.192520\pi\) | ||||
0.822605 | + | 0.568613i | \(0.192520\pi\) | |||||||
\(602\) | −2.75805 | −0.112410 | ||||||||
\(603\) | −25.3517 | + | 32.3126i | −1.03240 | + | 1.31587i | ||||
\(604\) | −9.34711 | − | 9.34711i | −0.380329 | − | 0.380329i | ||||
\(605\) | 0.487405 | + | 0.487405i | 0.0198158 | + | 0.0198158i | ||||
\(606\) | −1.92668 | − | 32.0373i | −0.0782659 | − | 1.30143i | ||||
\(607\) | −29.9002 | −1.21361 | −0.606805 | − | 0.794851i | \(-0.707549\pi\) | ||||
−0.606805 | + | 0.794851i | \(0.707549\pi\) | |||||||
\(608\) | −1.28268 | −0.0520195 | ||||||||
\(609\) | −12.7328 | + | 0.765729i | −0.515957 | + | 0.0310289i | ||||
\(610\) | − | 2.93417i | − | 0.118801i | ||||||
\(611\) | −4.82556 | − | 10.5357i | −0.195221 | − | 0.426230i | ||||
\(612\) | −15.6777 | + | 1.89251i | −0.633733 | + | 0.0765002i | ||||
\(613\) | 0.240034 | + | 0.240034i | 0.00969490 | + | 0.00969490i | 0.711938 | − | 0.702243i | \(-0.247818\pi\) |
−0.702243 | + | 0.711938i | \(0.747818\pi\) | |||||||
\(614\) | 16.7044i | 0.674136i | ||||||||
\(615\) | 0.813421 | + | 0.721135i | 0.0328003 | + | 0.0290790i | ||||
\(616\) | 2.55493 | + | 2.55493i | 0.102941 | + | 0.102941i | ||||
\(617\) | −25.7734 | + | 25.7734i | −1.03760 | + | 1.03760i | −0.0383316 | + | 0.999265i | \(0.512204\pi\) |
−0.999265 | + | 0.0383316i | \(0.987796\pi\) | |||||||
\(618\) | −9.95989 | + | 0.598973i | −0.400645 | + | 0.0240942i | ||||
\(619\) | −26.3806 | + | 26.3806i | −1.06033 | + | 1.06033i | −0.0622679 | + | 0.998059i | \(0.519833\pi\) |
−0.998059 | + | 0.0622679i | \(0.980167\pi\) | |||||||
\(620\) | − | 3.41766i | − | 0.137256i | ||||||
\(621\) | −6.36024 | − | 4.40000i | −0.255227 | − | 0.176566i | ||||
\(622\) | −14.7362 | + | 14.7362i | −0.590868 | + | 0.590868i | ||||
\(623\) | −2.29517 | −0.0919541 | ||||||||
\(624\) | 5.51143 | − | 2.93668i | 0.220634 | − | 0.117561i | ||||
\(625\) | −23.3256 | −0.933023 | ||||||||
\(626\) | 6.84265 | − | 6.84265i | 0.273487 | − | 0.273487i | ||||
\(627\) | −6.00671 | − | 5.32522i | −0.239885 | − | 0.212669i | ||||
\(628\) | 17.6346i | 0.703698i | ||||||||
\(629\) | −14.9141 | + | 14.9141i | −0.594666 | + | 0.594666i | ||||
\(630\) | 0.621034 | − | 0.791553i | 0.0247426 | − | 0.0315362i | ||||
\(631\) | −4.98978 | + | 4.98978i | −0.198640 | + | 0.198640i | −0.799417 | − | 0.600777i | \(-0.794858\pi\) |
0.600777 | + | 0.799417i | \(0.294858\pi\) | |||||||
\(632\) | 6.01650 | + | 6.01650i | 0.239324 | + | 0.239324i | ||||
\(633\) | 13.1465 | − | 14.8289i | 0.522527 | − | 0.589396i | ||||
\(634\) | 20.4768i | 0.813239i | ||||||||
\(635\) | 1.98744 | + | 1.98744i | 0.0788692 | + | 0.0788692i | ||||
\(636\) | 10.1183 | − | 11.4132i | 0.401217 | − | 0.452562i | ||||
\(637\) | 1.25628 | − | 3.37961i | 0.0497757 | − | 0.133905i | ||||
\(638\) | − | 26.6097i | − | 1.05349i | ||||||
\(639\) | −16.4991 | − | 12.9448i | −0.652694 | − | 0.512089i | ||||
\(640\) | 0.335367 | 0.0132565 | ||||||||
\(641\) | 6.77888 | 0.267750 | 0.133875 | − | 0.990998i | \(-0.457258\pi\) | ||||
0.133875 | + | 0.990998i | \(0.457258\pi\) | |||||||
\(642\) | −31.6610 | + | 1.90405i | −1.24956 | + | 0.0751467i | ||||
\(643\) | −11.9887 | − | 11.9887i | −0.472790 | − | 0.472790i | 0.430026 | − | 0.902816i | \(-0.358504\pi\) |
−0.902816 | + | 0.430026i | \(0.858504\pi\) | |||||||
\(644\) | −1.05244 | − | 1.05244i | −0.0414721 | − | 0.0414721i | ||||
\(645\) | −1.59918 | + | 0.0961725i | −0.0629678 | + | 0.00378679i | ||||
\(646\) | 6.75181 | 0.265646 | ||||||||
\(647\) | −4.90621 | −0.192883 | −0.0964415 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964415 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(648\) | 7.69552 | + | 4.66679i | 0.302309 | + | 0.183329i | ||||
\(649\) | − | 4.01325i | − | 0.157534i | ||||||
\(650\) | 7.33822 | + | 16.0217i | 0.287829 | + | 0.628421i | ||||
\(651\) | 11.7094 | − | 13.2079i | 0.458927 | − | 0.517657i | ||||
\(652\) | 2.26457 | + | 2.26457i | 0.0886874 | + | 0.0886874i | ||||
\(653\) | − | 16.9184i | − | 0.662069i | −0.943619 | − | 0.331035i | \(-0.892602\pi\) | ||
0.943619 | − | 0.331035i | \(-0.107398\pi\) | |||||||
\(654\) | 10.9234 | − | 12.3212i | 0.427137 | − | 0.481799i | ||||
\(655\) | −3.46051 | − | 3.46051i | −0.135213 | − | 0.135213i | ||||
\(656\) | −1.32329 | + | 1.32329i | −0.0516659 | + | 0.0516659i | ||||
\(657\) | 13.3703 | + | 10.4901i | 0.521627 | + | 0.409256i | ||||
\(658\) | 2.27264 | − | 2.27264i | 0.0885968 | − | 0.0885968i | ||||
\(659\) | − | 42.8877i | − | 1.67067i | −0.549744 | − | 0.835333i | \(-0.685275\pi\) | ||
0.549744 | − | 0.835333i | \(-0.314725\pi\) | |||||||
\(660\) | 1.57050 | + | 1.39232i | 0.0611317 | + | 0.0541961i | ||||
\(661\) | 23.1466 | − | 23.1466i | 0.900299 | − | 0.900299i | −0.0951631 | − | 0.995462i | \(-0.530337\pi\) |
0.995462 | + | 0.0951631i | \(0.0303373\pi\) | |||||||
\(662\) | 33.8024 | 1.31377 | ||||||||
\(663\) | −29.0113 | + | 15.4582i | −1.12670 | + | 0.600346i | ||||
\(664\) | 4.32280 | 0.167757 | ||||||||
\(665\) | −0.304175 | + | 0.304175i | −0.0117954 | + | 0.0117954i | ||||
\(666\) | 11.9341 | − | 1.44061i | 0.462438 | − | 0.0558226i | ||||
\(667\) | 10.9612i | 0.424421i | ||||||||
\(668\) | 12.4482 | − | 12.4482i | 0.481636 | − | 0.481636i | ||||
\(669\) | 22.1651 | − | 1.33297i | 0.856951 | − | 0.0515357i | ||||
\(670\) | −3.24651 | + | 3.24651i | −0.125424 | + | 0.125424i | ||||
\(671\) | 22.3534 | + | 22.3534i | 0.862943 | + | 0.862943i | ||||
\(672\) | 1.29606 | + | 1.14901i | 0.0499965 | + | 0.0443242i | ||||
\(673\) | 29.7951i | 1.14852i | 0.818674 | + | 0.574259i | \(0.194710\pi\) | ||||
−0.818674 | + | 0.574259i | \(0.805290\pi\) | |||||||
\(674\) | −13.5330 | − | 13.5330i | −0.521272 | − | 0.521272i | ||||
\(675\) | −14.4486 | + | 20.8857i | −0.556129 | + | 0.803890i | ||||
\(676\) | 8.49149 | − | 9.84351i | 0.326596 | − | 0.378596i | ||||
\(677\) | 21.9759i | 0.844602i | 0.906456 | + | 0.422301i | \(0.138778\pi\) | ||||
−0.906456 | + | 0.422301i | \(0.861222\pi\) | |||||||
\(678\) | 27.4575 | − | 1.65125i | 1.05450 | − | 0.0634160i | ||||
\(679\) | 6.87739 | 0.263930 | ||||||||
\(680\) | −1.76532 | −0.0676968 | ||||||||
\(681\) | 0.288045 | + | 4.78970i | 0.0110379 | + | 0.183542i | ||||
\(682\) | 26.0368 | + | 26.0368i | 0.997000 | + | 0.997000i | ||||
\(683\) | −5.21995 | − | 5.21995i | −0.199736 | − | 0.199736i | 0.600151 | − | 0.799887i | \(-0.295107\pi\) |
−0.799887 | + | 0.600151i | \(0.795107\pi\) | |||||||
\(684\) | −3.02745 | − | 2.37527i | −0.115758 | − | 0.0908207i | ||||
\(685\) | 5.49463 | 0.209939 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 2.89539 | + | 48.1454i | 0.110466 | + | 1.83686i | ||||
\(688\) | − | 2.75805i | − | 0.105149i | ||||||
\(689\) | 11.0629 | − | 29.7611i | 0.421464 | − | 1.13381i | ||||
\(690\) | −0.646932 | − | 0.573535i | −0.0246283 | − | 0.0218341i | ||||
\(691\) | −16.8889 | − | 16.8889i | −0.642485 | − | 0.642485i | 0.308681 | − | 0.951166i | \(-0.400112\pi\) |
−0.951166 | + | 0.308681i | \(0.900112\pi\) | |||||||
\(692\) | 12.8517i | 0.488548i | ||||||||
\(693\) | 1.29906 | + | 10.7615i | 0.0493473 | + | 0.408797i | ||||
\(694\) | −15.7627 | − | 15.7627i | −0.598343 | − | 0.598343i | ||||
\(695\) | 2.84097 | − | 2.84097i | 0.107764 | − | 0.107764i | ||||
\(696\) | −0.765729 | − | 12.7328i | −0.0290249 | − | 0.482634i | ||||
\(697\) | 6.96559 | − | 6.96559i | 0.263841 | − | 0.263841i | ||||
\(698\) | 16.3183i | 0.617658i | ||||||||
\(699\) | −9.28676 | + | 10.4752i | −0.351258 | + | 0.396209i | ||||
\(700\) | −3.45600 | + | 3.45600i | −0.130625 | + | 0.130625i | ||||
\(701\) | 37.1491 | 1.40310 | 0.701550 | − | 0.712620i | \(-0.252491\pi\) | ||||
0.701550 | + | 0.712620i | \(0.252491\pi\) | |||||||
\(702\) | 18.4466 | + | 3.27478i | 0.696221 | + | 0.123599i | ||||
\(703\) | −5.13960 | −0.193844 | ||||||||
\(704\) | −2.55493 | + | 2.55493i | −0.0962926 | + | 0.0962926i | ||||
\(705\) | 1.23849 | − | 1.39698i | 0.0466442 | − | 0.0526134i | ||||
\(706\) | 15.5376i | 0.584765i | ||||||||
\(707\) | 13.1028 | − | 13.1028i | 0.492782 | − | 0.492782i | ||||
\(708\) | −0.115487 | − | 1.92034i | −0.00434025 | − | 0.0721709i | ||||
\(709\) | 17.2343 | − | 17.2343i | 0.647249 | − | 0.647249i | −0.305078 | − | 0.952327i | \(-0.598683\pi\) |
0.952327 | + | 0.305078i | \(0.0986826\pi\) | |||||||
\(710\) | −1.65770 | − | 1.65770i | −0.0622124 | − | 0.0622124i | ||||
\(711\) | 3.05911 | + | 25.3419i | 0.114726 | + | 0.950395i | ||||
\(712\) | − | 2.29517i | − | 0.0860152i | ||||||
\(713\) | −10.7253 | − | 10.7253i | −0.401664 | − | 0.401664i | ||||
\(714\) | −6.82223 | − | 6.04822i | −0.255316 | − | 0.226349i | ||||
\(715\) | 4.09525 | + | 1.52231i | 0.153154 | + | 0.0569310i | ||||
\(716\) | 13.7258i | 0.512959i | ||||||||
\(717\) | 2.51588 | + | 41.8348i | 0.0939573 | + | 1.56235i | ||||
\(718\) | −17.5274 | −0.654116 | ||||||||
\(719\) | −2.42778 | −0.0905411 | −0.0452705 | − | 0.998975i | \(-0.514415\pi\) | ||||
−0.0452705 | + | 0.998975i | \(0.514415\pi\) | |||||||
\(720\) | 0.791553 | + | 0.621034i | 0.0294994 | + | 0.0231446i | ||||
\(721\) | −4.07345 | − | 4.07345i | −0.151703 | − | 0.151703i | ||||
\(722\) | −12.2717 | − | 12.2717i | −0.456704 | − | 0.456704i | ||||
\(723\) | −0.242100 | − | 4.02570i | −0.00900379 | − | 0.149718i | ||||
\(724\) | 17.7979 | 0.661454 | ||||||||
\(725\) | 35.9944 | 1.33680 | ||||||||
\(726\) | −3.55354 | + | 0.213705i | −0.131884 | + | 0.00793132i | ||||
\(727\) | − | 2.06159i | − | 0.0764603i | −0.999269 | − | 0.0382301i | \(-0.987828\pi\) | ||
0.999269 | − | 0.0382301i | \(-0.0121720\pi\) | |||||||
\(728\) | 3.37961 | + | 1.25628i | 0.125257 | + | 0.0465609i | ||||
\(729\) | 9.52144 | + | 25.2654i | 0.352646 | + | 0.935757i | ||||
\(730\) | 1.34335 | + | 1.34335i | 0.0497195 | + | 0.0497195i | ||||
\(731\) | 14.5179i | 0.536964i | ||||||||
\(732\) | 11.3394 | + | 10.0529i | 0.419115 | + | 0.371565i | ||||
\(733\) | 16.8266 | + | 16.8266i | 0.621505 | + | 0.621505i | 0.945916 | − | 0.324412i | \(-0.105166\pi\) |
−0.324412 | + | 0.945916i | \(0.605166\pi\) | |||||||
\(734\) | −13.6975 | + | 13.6975i | −0.505583 | + | 0.505583i | ||||
\(735\) | 0.579825 | − | 0.0348698i | 0.0213872 | − | 0.00128619i | ||||
\(736\) | 1.05244 | − | 1.05244i | 0.0387936 | − | 0.0387936i | ||||
\(737\) | − | 49.4659i | − | 1.82210i | ||||||
\(738\) | −5.57379 | + | 0.672833i | −0.205174 | + | 0.0247673i | ||||
\(739\) | −29.5329 | + | 29.5329i | −1.08638 | + | 1.08638i | −0.0904869 | + | 0.995898i | \(0.528842\pi\) |
−0.995898 | + | 0.0904869i | \(0.971158\pi\) | |||||||
\(740\) | 1.34379 | 0.0493987 | ||||||||
\(741\) | −7.66236 | − | 2.33528i | −0.281484 | − | 0.0857886i | ||||
\(742\) | 8.80608 | 0.323281 | ||||||||
\(743\) | 21.2462 | − | 21.2462i | 0.779446 | − | 0.779446i | −0.200290 | − | 0.979737i | \(-0.564189\pi\) |
0.979737 | + | 0.200290i | \(0.0641886\pi\) | |||||||
\(744\) | 13.2079 | + | 11.7094i | 0.484224 | + | 0.429287i | ||||
\(745\) | − | 1.03345i | − | 0.0378628i | ||||||
\(746\) | 18.8503 | − | 18.8503i | 0.690157 | − | 0.690157i | ||||
\(747\) | 10.2029 | + | 8.00499i | 0.373306 | + | 0.292887i | ||||
\(748\) | 13.4487 | − | 13.4487i | 0.491734 | − | 0.491734i | ||||
\(749\) | −12.9489 | − | 12.9489i | −0.473143 | − | 0.473143i | ||||
\(750\) | −3.81008 | + | 4.29766i | −0.139124 | + | 0.156928i | ||||
\(751\) | 22.6437i | 0.826281i | 0.910667 | + | 0.413140i | \(0.135568\pi\) | ||||
−0.910667 | + | 0.413140i | \(0.864432\pi\) | |||||||
\(752\) | 2.27264 | + | 2.27264i | 0.0828747 | + | 0.0828747i | ||||
\(753\) | 6.42864 | − | 7.25133i | 0.234273 | − | 0.264253i | ||||
\(754\) | −11.0572 | − | 24.1415i | −0.402681 | − | 0.879181i | ||||
\(755\) | − | 4.43315i | − | 0.161339i | ||||||
\(756\) | 0.931280 | + | 5.11202i | 0.0338703 | + | 0.185922i | ||||
\(757\) | 28.9363 | 1.05171 | 0.525853 | − | 0.850575i | \(-0.323746\pi\) | ||||
0.525853 | + | 0.850575i | \(0.323746\pi\) | |||||||
\(758\) | −10.1436 | −0.368433 | ||||||||
\(759\) | 9.29791 | − | 0.559162i | 0.337493 | − | 0.0202963i | ||||
\(760\) | −0.304175 | − | 0.304175i | −0.0110336 | − | 0.0110336i | ||||
\(761\) | 34.0212 | + | 34.0212i | 1.23327 | + | 1.23327i | 0.962701 | + | 0.270567i | \(0.0872113\pi\) |
0.270567 | + | 0.962701i | \(0.412789\pi\) | |||||||
\(762\) | −14.4899 | + | 0.871402i | −0.524914 | + | 0.0315675i | ||||
\(763\) | 9.50671 | 0.344166 | ||||||||
\(764\) | 0.449102 | 0.0162479 | ||||||||
\(765\) | −4.16660 | − | 3.26902i | −0.150644 | − | 0.118192i | ||||
\(766\) | − | 2.48835i | − | 0.0899076i | ||||||
\(767\) | −1.66765 | − | 3.64100i | −0.0602152 | − | 0.131469i | ||||
\(768\) | −1.14901 | + | 1.29606i | −0.0414615 | + | 0.0467675i | ||||
\(769\) | 14.2161 | + | 14.2161i | 0.512647 | + | 0.512647i | 0.915337 | − | 0.402690i | \(-0.131925\pi\) |
−0.402690 | + | 0.915337i | \(0.631925\pi\) | |||||||
\(770\) | 1.21175i | 0.0436686i | ||||||||
\(771\) | −10.7743 | + | 12.1531i | −0.388026 | + | 0.437683i | ||||
\(772\) | 5.53933 | + | 5.53933i | 0.199365 | + | 0.199365i | ||||
\(773\) | −29.6369 | + | 29.6369i | −1.06596 | + | 1.06596i | −0.0682992 | + | 0.997665i | \(0.521757\pi\) |
−0.997665 | + | 0.0682992i | \(0.978243\pi\) | |||||||
\(774\) | 5.10736 | − | 6.50970i | 0.183580 | − | 0.233986i | ||||
\(775\) | −35.2194 | + | 35.2194i | −1.26512 | + | 1.26512i | ||||
\(776\) | 6.87739i | 0.246884i | ||||||||
\(777\) | 5.19320 | + | 4.60401i | 0.186305 | + | 0.165168i | ||||
\(778\) | −16.5459 | + | 16.5459i | −0.593200 | + | 0.593200i | ||||
\(779\) | 2.40043 | 0.0860043 | ||||||||
\(780\) | 2.00339 | + | 0.610578i | 0.0717328 | + | 0.0218622i | ||||
\(781\) | 25.2577 | 0.903793 | ||||||||
\(782\) | −5.53989 | + | 5.53989i | −0.198106 | + | 0.198106i | ||||
\(783\) | 21.7713 | − | 31.4706i | 0.778041 | − | 1.12467i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | −4.18188 | + | 4.18188i | −0.149258 | + | 0.149258i | ||||
\(786\) | 25.2297 | − | 1.51728i | 0.899913 | − | 0.0541194i | ||||
\(787\) | 37.0266 | − | 37.0266i | 1.31986 | − | 1.31986i | 0.405969 | − | 0.913887i | \(-0.366934\pi\) |
0.913887 | − | 0.405969i | \(-0.133066\pi\) | |||||||
\(788\) | −15.8126 | − | 15.8126i | −0.563302 | − | 0.563302i | ||||
\(789\) | −9.44534 | − | 8.37373i | −0.336263 | − | 0.298113i | ||||
\(790\) | 2.85351i | 0.101523i | ||||||||
\(791\) | 11.2297 | + | 11.2297i | 0.399283 | + | 0.399283i | ||||
\(792\) | −10.7615 | + | 1.29906i | −0.382394 | + | 0.0461602i | ||||
\(793\) | 29.5686 | + | 10.9914i | 1.05001 | + | 0.390315i | ||||
\(794\) | − | 17.9636i | − | 0.637506i | ||||||
\(795\) | 5.10599 | − | 0.307066i | 0.181091 | − | 0.0108905i | ||||
\(796\) | −26.3160 | −0.932747 | ||||||||
\(797\) | −16.8981 | −0.598562 | −0.299281 | − | 0.954165i | \(-0.596747\pi\) | ||||
−0.299281 | + | 0.954165i | \(0.596747\pi\) | |||||||
\(798\) | −0.133367 | − | 2.21766i | −0.00472113 | − | 0.0785042i | ||||
\(799\) | −11.9628 | − | 11.9628i | −0.423214 | − | 0.423214i | ||||
\(800\) | −3.45600 | − | 3.45600i | −0.122188 | − | 0.122188i | ||||
\(801\) | 4.25021 | − | 5.41720i | 0.150174 | − | 0.191407i | ||||
\(802\) | −6.55431 | −0.231441 | ||||||||
\(803\) | −20.4681 | −0.722303 | ||||||||
\(804\) | −1.42345 | − | 23.6695i | −0.0502011 | − | 0.834758i | ||||
\(805\) | − | 0.499154i | − | 0.0175929i | ||||||
\(806\) | 34.4409 | + | 12.8025i | 1.21313 | + | 0.450950i | ||||
\(807\) | 21.3802 | + | 18.9546i | 0.752620 | + | 0.667232i | ||||
\(808\) | 13.1028 | + | 13.1028i | 0.460956 | + | 0.460956i | ||||
\(809\) | − | 5.97793i | − | 0.210173i | −0.994463 | − | 0.105086i | \(-0.966488\pi\) | ||
0.994463 | − | 0.105086i | \(-0.0335119\pi\) | |||||||
\(810\) | 0.718235 | + | 2.93160i | 0.0252362 | + | 0.103006i | ||||
\(811\) | −3.24299 | − | 3.24299i | −0.113877 | − | 0.113877i | 0.647872 | − | 0.761749i | \(-0.275659\pi\) |
−0.761749 | + | 0.647872i | \(0.775659\pi\) | |||||||
\(812\) | 5.20752 | − | 5.20752i | 0.182748 | − | 0.182748i | ||||
\(813\) | −0.377954 | − | 6.28472i | −0.0132554 | − | 0.220415i | ||||
\(814\) | −10.2374 | + | 10.2374i | −0.358821 | + | 0.358821i | ||||
\(815\) | 1.07404i | 0.0376220i | ||||||||
\(816\) | 6.04822 | − | 6.82223i | 0.211730 | − | 0.238826i | ||||
\(817\) | −2.50152 | + | 2.50152i | −0.0875172 | + | 0.0875172i | ||||
\(818\) | 29.6464 | 1.03656 | ||||||||
\(819\) | 5.65036 | + | 9.22353i | 0.197439 | + | 0.322296i | ||||
\(820\) | −0.627612 | −0.0219172 | ||||||||
\(821\) | −8.79510 | + | 8.79510i | −0.306951 | + | 0.306951i | −0.843726 | − | 0.536775i | \(-0.819643\pi\) |
0.536775 | + | 0.843726i | \(0.319643\pi\) | |||||||
\(822\) | −18.8254 | + | 21.2345i | −0.656611 | + | 0.740639i | ||||
\(823\) | − | 0.483844i | − | 0.0168658i | −0.999964 | − | 0.00843288i | \(-0.997316\pi\) | ||
0.999964 | − | 0.00843288i | \(-0.00268430\pi\) | |||||||
\(824\) | 4.07345 | − | 4.07345i | 0.141905 | − | 0.141905i | ||||
\(825\) | −1.83617 | − | 30.5323i | −0.0639272 | − | 1.06300i | ||||
\(826\) | 0.785394 | − | 0.785394i | 0.0273273 | − | 0.0273273i | ||||
\(827\) | 0.304974 | + | 0.304974i | 0.0106050 | + | 0.0106050i | 0.712389 | − | 0.701784i | \(-0.247613\pi\) |
−0.701784 | + | 0.712389i | \(0.747613\pi\) | |||||||
\(828\) | 4.43296 | − | 0.535119i | 0.154056 | − | 0.0185967i | ||||
\(829\) | 1.15353i | 0.0400637i | 0.999799 | + | 0.0200319i | \(0.00637677\pi\) | ||||
−0.999799 | + | 0.0200319i | \(0.993623\pi\) | |||||||
\(830\) | 1.02511 | + | 1.02511i | 0.0355821 | + | 0.0355821i | ||||
\(831\) | −9.62705 | − | 8.53483i | −0.333959 | − | 0.296070i | ||||
\(832\) | −1.25628 | + | 3.37961i | −0.0435538 | + | 0.117167i | ||||
\(833\) | − | 5.26383i | − | 0.182381i | ||||||
\(834\) | 1.24563 | + | 20.7127i | 0.0431327 | + | 0.717223i | ||||
\(835\) | 5.90395 | 0.204314 | ||||||||
\(836\) | 4.63460 | 0.160291 | ||||||||
\(837\) | 9.49048 | + | 52.0955i | 0.328039 | + | 1.80069i | ||||
\(838\) | 1.62656 | + | 1.62656i | 0.0561886 | + | 0.0561886i | ||||
\(839\) | 34.5315 | + | 34.5315i | 1.19216 | + | 1.19216i | 0.976460 | + | 0.215701i | \(0.0692036\pi\) |
0.215701 | + | 0.976460i | \(0.430796\pi\) | |||||||
\(840\) | 0.0348698 | + | 0.579825i | 0.00120312 | + | 0.0200059i | ||||
\(841\) | −25.2364 | −0.870222 | ||||||||
\(842\) | −7.45789 | −0.257016 | ||||||||
\(843\) | 23.0386 | − | 1.38551i | 0.793492 | − | 0.0477194i | ||||
\(844\) | 11.4416i | 0.393835i | ||||||||
\(845\) | 4.34797 | − | 0.320617i | 0.149575 | − | 0.0110296i | ||||
\(846\) | 1.15553 | + | 9.57251i | 0.0397280 | + | 0.329110i | ||||
\(847\) | −1.45335 | − | 1.45335i | −0.0499376 | − | 0.0499376i | ||||
\(848\) | 8.80608i | 0.302402i | ||||||||
\(849\) | −27.9790 | − | 24.8047i | −0.960238 | − | 0.851295i | ||||
\(850\) | 18.1918 | + | 18.1918i | 0.623975 | + | 0.623975i | ||||
\(851\) | 4.21707 | − | 4.21707i | 0.144559 | − | 0.144559i | ||||
\(852\) | 12.0859 | − | 0.726825i | 0.414054 | − | 0.0249006i | ||||
\(853\) | 33.2316 | − | 33.2316i | 1.13783 | − | 1.13783i | 0.148989 | − | 0.988839i | \(-0.452398\pi\) |
0.988839 | − | 0.148989i | \(-0.0476018\pi\) | |||||||
\(854\) | 8.74912i | 0.299389i | ||||||||
\(855\) | −0.154659 | − | 1.28120i | −0.00528922 | − | 0.0438162i | ||||
\(856\) | 12.9489 | − | 12.9489i | 0.442585 | − | 0.442585i | ||||
\(857\) | −16.7687 | −0.572808 | −0.286404 | − | 0.958109i | \(-0.592460\pi\) | ||||
−0.286404 | + | 0.958109i | \(0.592460\pi\) | |||||||
\(858\) | −19.9140 | + | 10.6109i | −0.679853 | + | 0.362249i | ||||
\(859\) | −3.03581 | −0.103581 | −0.0517903 | − | 0.998658i | \(-0.516493\pi\) | ||||
−0.0517903 | + | 0.998658i | \(0.516493\pi\) | |||||||
\(860\) | 0.654044 | − | 0.654044i | 0.0223027 | − | 0.0223027i | ||||
\(861\) | −2.42547 | − | 2.15029i | −0.0826597 | − | 0.0732816i | ||||
\(862\) | − | 6.81380i | − | 0.232079i | ||||||
\(863\) | 13.1182 | − | 13.1182i | 0.446549 | − | 0.446549i | −0.447656 | − | 0.894206i | \(-0.647741\pi\) |
0.894206 | + | 0.447656i | \(0.147741\pi\) | |||||||
\(864\) | −5.11202 | + | 0.931280i | −0.173914 | + | 0.0316828i | ||||
\(865\) | −3.04765 | + | 3.04765i | −0.103623 | + | 0.103623i | ||||
\(866\) | −3.40801 | − | 3.40801i | −0.115809 | − | 0.115809i | ||||
\(867\) | −12.3036 | + | 13.8781i | −0.417852 | + | 0.471325i | ||||
\(868\) | 10.1908i | 0.345898i | ||||||||
\(869\) | −21.7389 | − | 21.7389i | −0.737443 | − | 0.737443i | ||||
\(870\) | 2.83786 | − | 3.20103i | 0.0962126 | − | 0.108525i | ||||
\(871\) | −20.5548 | − | 44.8777i | −0.696473 | − | 1.52062i | ||||
\(872\) | 9.50671i | 0.321938i | ||||||||
\(873\) | −12.7356 | + | 16.2324i | −0.431034 | + | 0.549384i | ||||
\(874\) | −1.90912 | −0.0645768 | ||||||||
\(875\) | −3.31595 | −0.112100 | ||||||||
\(876\) | −9.79399 | + | 0.588996i | −0.330908 | + | 0.0199003i | ||||
\(877\) | −11.1099 | − | 11.1099i | −0.375156 | − | 0.375156i | 0.494195 | − | 0.869351i | \(-0.335463\pi\) |
−0.869351 | + | 0.494195i | \(0.835463\pi\) | |||||||
\(878\) | −9.20248 | − | 9.20248i | −0.310569 | − | 0.310569i | ||||
\(879\) | 9.65243 | − | 0.580483i | 0.325569 | − | 0.0195792i | ||||
\(880\) | −1.21175 | −0.0408482 | ||||||||
\(881\) | 42.5418 | 1.43327 | 0.716634 | − | 0.697449i | \(-0.245682\pi\) | ||||
0.716634 | + | 0.697449i | \(0.245682\pi\) | |||||||
\(882\) | −1.85180 | + | 2.36026i | −0.0623535 | + | 0.0794740i | ||||
\(883\) | 27.0567i | 0.910530i | 0.890356 | + | 0.455265i | \(0.150455\pi\) | ||||
−0.890356 | + | 0.455265i | \(0.849545\pi\) | |||||||
\(884\) | 6.61287 | − | 17.7897i | 0.222415 | − | 0.598332i | ||||
\(885\) | 0.428004 | − | 0.482777i | 0.0143872 | − | 0.0162284i | ||||
\(886\) | 16.3953 | + | 16.3953i | 0.550810 | + | 0.550810i | ||||
\(887\) | − | 5.81160i | − | 0.195134i | −0.995229 | − | 0.0975672i | \(-0.968894\pi\) | ||
0.995229 | − | 0.0975672i | \(-0.0311061\pi\) | |||||||
\(888\) | −4.60401 | + | 5.19320i | −0.154501 | + | 0.174273i | ||||
\(889\) | −5.92617 | − | 5.92617i | −0.198757 | − | 0.198757i | ||||
\(890\) | 0.544278 | − | 0.544278i | 0.0182442 | − | 0.0182442i | ||||
\(891\) | −27.8056 | − | 16.8621i | −0.931523 | − | 0.564903i | ||||
\(892\) | −9.06520 | + | 9.06520i | −0.303525 | + | 0.303525i | ||||
\(893\) | − | 4.12253i | − | 0.137955i | ||||||
\(894\) | 3.99388 | + | 3.54076i | 0.133575 | + | 0.118421i | ||||
\(895\) | −3.25495 | + | 3.25495i | −0.108801 | + | 0.108801i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 8.20312 | − | 4.37090i | 0.273894 | − | 0.145940i | ||||
\(898\) | 10.3432 | 0.345159 | ||||||||
\(899\) | 53.0687 | − | 53.0687i | 1.76994 | − | 1.76994i | ||||
\(900\) | −1.75722 | − | 14.5569i | −0.0585739 | − | 0.485230i | ||||
\(901\) | − | 46.3537i | − | 1.54427i | ||||||
\(902\) | 4.78134 | − | 4.78134i | 0.159201 | − | 0.159201i | ||||
\(903\) | 4.76846 | − | 0.286768i | 0.158684 | − | 0.00954304i | ||||
\(904\) | −11.2297 | + | 11.2297i | −0.373495 | + | 0.373495i | ||||
\(905\) | 4.22060 | + | 4.22060i | 0.140297 | + | 0.140297i | ||||
\(906\) | 17.1323 | + | 15.1886i | 0.569184 | + | 0.504608i | ||||
\(907\) | − | 12.1476i | − | 0.403356i | −0.979452 | − | 0.201678i | \(-0.935361\pi\) | ||
0.979452 | − | 0.201678i | \(-0.0646394\pi\) | |||||||
\(908\) | −1.95892 | − | 1.95892i | −0.0650090 | − | 0.0650090i | ||||
\(909\) | 6.66217 | + | 55.1899i | 0.220970 | + | 1.83053i | ||||
\(910\) | 0.503526 | + | 1.09936i | 0.0166917 | + | 0.0364433i | ||||
\(911\) | − | 5.85676i | − | 0.194043i | −0.995282 | − | 0.0970216i | \(-0.969068\pi\) | ||
0.995282 | − | 0.0970216i | \(-0.0309316\pi\) | |||||||
\(912\) | 2.21766 | − | 0.133367i | 0.0734340 | − | 0.00441621i | ||||
\(913\) | −15.6192 | −0.516921 | ||||||||
\(914\) | 10.7287 | 0.354873 | ||||||||
\(915\) | 0.305080 | + | 5.07296i | 0.0100856 | + | 0.167707i | ||||
\(916\) | −19.6908 | − | 19.6908i | −0.650601 | − | 0.650601i | ||||
\(917\) | 10.3186 | + | 10.3186i | 0.340750 | + | 0.340750i | ||||
\(918\) | 26.9088 | − | 4.90210i | 0.888123 | − | 0.161793i | ||||
\(919\) | 30.9858 | 1.02213 | 0.511064 | − | 0.859543i | \(-0.329252\pi\) | ||||
0.511064 | + | 0.859543i | \(0.329252\pi\) | |||||||
\(920\) | 0.499154 | 0.0164566 | ||||||||
\(921\) | −1.73685 | − | 28.8808i | −0.0572310 | − | 0.951654i | ||||
\(922\) | 13.3718i | 0.440375i | ||||||||
\(923\) | 22.9149 | − | 10.4955i | 0.754255 | − | 0.345463i | ||||
\(924\) | −4.68294 | − | 4.15164i | −0.154057 | − | 0.136579i | ||||
\(925\) | −13.8479 | − | 13.8479i | −0.455318 | − | 0.455318i | ||||
\(926\) | − | 34.1779i | − | 1.12315i | ||||||
\(927\) | 17.1576 | − | 2.07116i | 0.563531 | − | 0.0680258i | ||||
\(928\) | 5.20752 | + | 5.20752i | 0.170945 | + | 0.170945i | ||||
\(929\) | −4.17792 | + | 4.17792i | −0.137073 | + | 0.137073i | −0.772314 | − | 0.635241i | \(-0.780901\pi\) |
0.635241 | + | 0.772314i | \(0.280901\pi\) | |||||||
\(930\) | 0.355351 | + | 5.90888i | 0.0116524 | + | 0.193760i | ||||
\(931\) | 0.906991 | − | 0.906991i | 0.0297254 | − | 0.0297254i | ||||
\(932\) | − | 8.08237i | − | 0.264747i | ||||||
\(933\) | 23.9456 | − | 27.0100i | 0.783944 | − | 0.884268i | ||||
\(934\) | −16.9539 | + | 16.9539i | −0.554750 | + | 0.554750i | ||||
\(935\) | 6.37847 | 0.208598 | ||||||||
\(936\) | −9.22353 | + | 5.65036i | −0.301480 | + | 0.184688i | ||||
\(937\) | −7.86277 | −0.256865 | −0.128433 | − | 0.991718i | \(-0.540995\pi\) | ||||
−0.128433 | + | 0.991718i | \(0.540995\pi\) | |||||||
\(938\) | 9.68048 | − | 9.68048i | 0.316079 | − | 0.316079i | ||||
\(939\) | −11.1190 | + | 12.5419i | −0.362854 | + | 0.409290i | ||||
\(940\) | 1.07787i | 0.0351562i | ||||||||
\(941\) | 38.2300 | − | 38.2300i | 1.24626 | − | 1.24626i | 0.288904 | − | 0.957358i | \(-0.406709\pi\) |
0.957358 | − | 0.288904i | \(-0.0932909\pi\) | |||||||
\(942\) | −1.83356 | − | 30.4890i | −0.0597407 | − | 0.993385i | ||||
\(943\) | −1.96956 | + | 1.96956i | −0.0641378 | + | 0.0641378i | ||||
\(944\) | 0.785394 | + | 0.785394i | 0.0255624 | + | 0.0255624i | ||||
\(945\) | −0.991421 | + | 1.43311i | −0.0322509 | + | 0.0466190i | ||||
\(946\) | 9.96542i | 0.324004i | ||||||||
\(947\) | −37.9375 | − | 37.9375i | −1.23280 | − | 1.23280i | −0.962883 | − | 0.269918i | \(-0.913003\pi\) |
−0.269918 | − | 0.962883i | \(-0.586997\pi\) | |||||||
\(948\) | −11.0277 | − | 9.77652i | −0.358162 | − | 0.317527i | ||||
\(949\) | −18.5695 | + | 8.50520i | −0.602793 | + | 0.276091i | ||||
\(950\) | 6.26913i | 0.203397i | ||||||||
\(951\) | −2.12908 | − | 35.4030i | −0.0690402 | − | 1.14802i | ||||
\(952\) | 5.26383 | 0.170602 | ||||||||
\(953\) | −3.17735 | −0.102924 | −0.0514622 | − | 0.998675i | \(-0.516388\pi\) | ||||
−0.0514622 | + | 0.998675i | \(0.516388\pi\) | |||||||
\(954\) | −16.3071 | + | 20.7846i | −0.527963 | + | 0.672927i | ||||
\(955\) | 0.106500 | + | 0.106500i | 0.00344627 | + | 0.00344627i | ||||
\(956\) | −17.1098 | − | 17.1098i | −0.553371 | − | 0.553371i | ||||
\(957\) | 2.76674 | + | 46.0062i | 0.0894362 | + | 1.48717i | ||||
\(958\) | 18.8099 | 0.607720 | ||||||||
\(959\) | −16.3839 | −0.529065 | ||||||||
\(960\) | −0.579825 | + | 0.0348698i | −0.0187138 | + | 0.00112542i | ||||
\(961\) | 72.8524i | 2.35008i | ||||||||
\(962\) | −5.03383 | + | 13.5418i | −0.162297 | + | 0.436606i | ||||
\(963\) | 54.5416 | − | 6.58391i | 1.75758 | − | 0.212164i | ||||
\(964\) | 1.64646 | + | 1.64646i | 0.0530288 | + | 0.0530288i | ||||
\(965\) | 2.62720i | 0.0845725i | ||||||||
\(966\) | 1.92903 | + | 1.71017i | 0.0620655 | + | 0.0550239i | ||||
\(967\) | −9.01267 | − | 9.01267i | −0.289828 | − | 0.289828i | 0.547184 | − | 0.837012i | \(-0.315700\pi\) |
−0.837012 | + | 0.547184i | \(0.815700\pi\) | |||||||
\(968\) | 1.45335 | − | 1.45335i | 0.0467124 | − | 0.0467124i | ||||
\(969\) | −11.6734 | + | 0.702020i | −0.375003 | + | 0.0225521i | ||||
\(970\) | −1.63091 | + | 1.63091i | −0.0523653 | + | 0.0523653i | ||||
\(971\) | 50.8888i | 1.63310i | 0.577276 | + | 0.816549i | \(0.304116\pi\) | ||||
−0.577276 | + | 0.816549i | \(0.695884\pi\) | |||||||
\(972\) | −13.7902 | − | 7.26840i | −0.442322 | − | 0.233134i | ||||
\(973\) | −8.47121 | + | 8.47121i | −0.271575 | + | 0.271575i | ||||
\(974\) | −17.0717 | −0.547013 | ||||||||
\(975\) | −14.3531 | − | 26.9373i | −0.459667 | − | 0.862684i | ||||
\(976\) | −8.74912 | −0.280052 | ||||||||
\(977\) | 22.6267 | − | 22.6267i | 0.723891 | − | 0.723891i | −0.245505 | − | 0.969395i | \(-0.578954\pi\) |
0.969395 | + | 0.245505i | \(0.0789536\pi\) | |||||||
\(978\) | −4.15074 | − | 3.67982i | −0.132726 | − | 0.117668i | ||||
\(979\) | 8.29295i | 0.265044i | ||||||||
\(980\) | −0.237140 | + | 0.237140i | −0.00757517 | + | 0.00757517i | ||||
\(981\) | −17.6046 | + | 22.4383i | −0.562071 | + | 0.716400i | ||||
\(982\) | −20.5055 | + | 20.5055i | −0.654356 | + | 0.654356i | ||||
\(983\) | 12.3141 | + | 12.3141i | 0.392758 | + | 0.392758i | 0.875669 | − | 0.482911i | \(-0.160421\pi\) |
−0.482911 | + | 0.875669i | \(0.660421\pi\) | |||||||
\(984\) | 2.15029 | − | 2.42547i | 0.0685486 | − | 0.0773210i | ||||
\(985\) | − | 7.49963i | − | 0.238958i | ||||||
\(986\) | −27.4115 | − | 27.4115i | −0.872960 | − | 0.872960i | ||||
\(987\) | −3.69293 | + | 4.16553i | −0.117547 | + | 0.132590i | ||||
\(988\) | 4.20471 | − | 1.92584i | 0.133770 | − | 0.0612690i | ||||
\(989\) | − | 4.10502i | − | 0.130532i | ||||||
\(990\) | −2.86005 | − | 2.24393i | −0.0908984 | − | 0.0713168i | ||||
\(991\) | 14.7119 | 0.467338 | 0.233669 | − | 0.972316i | \(-0.424927\pi\) | ||||
0.233669 | + | 0.972316i | \(0.424927\pi\) | |||||||
\(992\) | −10.1908 | −0.323558 | ||||||||
\(993\) | −58.4418 | + | 3.51460i | −1.85460 | + | 0.111533i | ||||
\(994\) | 4.94294 | + | 4.94294i | 0.156781 | + | 0.156781i | ||||
\(995\) | −6.24059 | − | 6.24059i | −0.197840 | − | 0.197840i | ||||
\(996\) | −7.47381 | + | 0.449464i | −0.236817 | + | 0.0142418i | ||||
\(997\) | −17.6061 | −0.557591 | −0.278795 | − | 0.960351i | \(-0.589935\pi\) | ||||
−0.278795 | + | 0.960351i | \(0.589935\pi\) | |||||||
\(998\) | −23.3290 | −0.738468 | ||||||||
\(999\) | −20.4835 | + | 3.73157i | −0.648068 | + | 0.118062i |
(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.c.281.7 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.d.281.2 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.d.239.2 | yes | 20 | ||
39.5 | even | 4 | inner | 546.2.p.c.239.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.7 | ✓ | 20 | 39.5 | even | 4 | inner | |
546.2.p.c.281.7 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.239.2 | yes | 20 | 13.5 | odd | 4 | ||
546.2.p.d.281.2 | yes | 20 | 3.2 | odd | 2 |