Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.15 | ||
Root | \(1.76011i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.6 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76011i | 1.24459i | 0.782784 | + | 0.622293i | \(0.213799\pi\) | ||||
−0.782784 | + | 0.622293i | \(0.786201\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.09799 | −0.548994 | ||||||||
\(5\) | 2.22415 | + | 0.230563i | 0.994670 | + | 0.103111i | ||||
\(6\) | −1.76011 | −0.718562 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.58764i | 0.561316i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.405817 | + | 3.91475i | −0.128331 | + | 1.23795i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − | 1.09799i | − | 0.316962i | ||||||
\(13\) | 4.21462i | 1.16893i | 0.811420 | + | 0.584463i | \(0.198695\pi\) | ||||
−0.811420 | + | 0.584463i | \(0.801305\pi\) | |||||||
\(14\) | 1.76011 | 0.470409 | ||||||||
\(15\) | −0.230563 | + | 2.22415i | −0.0595312 | + | 0.574273i | ||||
\(16\) | −4.99040 | −1.24760 | ||||||||
\(17\) | 1.43361i | 0.347701i | 0.984772 | + | 0.173850i | \(0.0556209\pi\) | ||||
−0.984772 | + | 0.173850i | \(0.944379\pi\) | |||||||
\(18\) | − | 1.76011i | − | 0.414862i | ||||||
\(19\) | 6.78233 | 1.55597 | 0.777987 | − | 0.628281i | \(-0.216241\pi\) | ||||
0.777987 | + | 0.628281i | \(0.216241\pi\) | |||||||
\(20\) | −2.44209 | − | 0.253156i | −0.546067 | − | 0.0566073i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 1.76011i | − | 0.375257i | ||||||
\(23\) | − | 2.64270i | − | 0.551041i | −0.961295 | − | 0.275521i | \(-0.911150\pi\) | ||
0.961295 | − | 0.275521i | \(-0.0888502\pi\) | |||||||
\(24\) | −1.58764 | −0.324076 | ||||||||
\(25\) | 4.89368 | + | 1.02561i | 0.978736 | + | 0.205123i | ||||
\(26\) | −7.41820 | −1.45483 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.09799i | 0.207500i | ||||||||
\(29\) | −8.97759 | −1.66710 | −0.833548 | − | 0.552447i | \(-0.813694\pi\) | ||||
−0.833548 | + | 0.552447i | \(0.813694\pi\) | |||||||
\(30\) | −3.91475 | − | 0.405817i | −0.714732 | − | 0.0740917i | ||||
\(31\) | −0.288914 | −0.0518904 | −0.0259452 | − | 0.999663i | \(-0.508260\pi\) | ||||
−0.0259452 | + | 0.999663i | \(0.508260\pi\) | |||||||
\(32\) | − | 5.60837i | − | 0.991429i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | −2.52331 | −0.432744 | ||||||||
\(35\) | 0.230563 | − | 2.22415i | 0.0389723 | − | 0.375950i | ||||
\(36\) | 1.09799 | 0.182998 | ||||||||
\(37\) | 10.7089i | 1.76053i | 0.474481 | + | 0.880266i | \(0.342636\pi\) | ||||
−0.474481 | + | 0.880266i | \(0.657364\pi\) | |||||||
\(38\) | 11.9377i | 1.93654i | ||||||||
\(39\) | −4.21462 | −0.674880 | ||||||||
\(40\) | −0.366052 | + | 3.53115i | −0.0578779 | + | 0.558324i | ||||
\(41\) | 1.62215 | 0.253337 | 0.126669 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126669 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(42\) | 1.76011i | 0.271591i | ||||||||
\(43\) | 8.21640i | 1.25299i | 0.779426 | + | 0.626494i | \(0.215511\pi\) | ||||
−0.779426 | + | 0.626494i | \(0.784489\pi\) | |||||||
\(44\) | 1.09799 | 0.165528 | ||||||||
\(45\) | −2.22415 | − | 0.230563i | −0.331557 | − | 0.0343704i | ||||
\(46\) | 4.65144 | 0.685818 | ||||||||
\(47\) | 3.94493i | 0.575427i | 0.957717 | + | 0.287714i | \(0.0928951\pi\) | ||||
−0.957717 | + | 0.287714i | \(0.907105\pi\) | |||||||
\(48\) | − | 4.99040i | − | 0.720302i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.80519 | + | 8.61342i | −0.255293 | + | 1.21812i | ||||
\(51\) | −1.43361 | −0.200745 | ||||||||
\(52\) | − | 4.62760i | − | 0.641733i | ||||||
\(53\) | − | 5.94827i | − | 0.817057i | −0.912746 | − | 0.408529i | \(-0.866042\pi\) | ||
0.912746 | − | 0.408529i | \(-0.133958\pi\) | |||||||
\(54\) | 1.76011 | 0.239521 | ||||||||
\(55\) | −2.22415 | − | 0.230563i | −0.299904 | − | 0.0310892i | ||||
\(56\) | 1.58764 | 0.212158 | ||||||||
\(57\) | 6.78233i | 0.898342i | ||||||||
\(58\) | − | 15.8015i | − | 2.07484i | ||||||
\(59\) | −6.45500 | −0.840369 | −0.420185 | − | 0.907439i | \(-0.638035\pi\) | ||||
−0.420185 | + | 0.907439i | \(0.638035\pi\) | |||||||
\(60\) | 0.253156 | − | 2.44209i | 0.0326823 | − | 0.315272i | ||||
\(61\) | 4.07606 | 0.521886 | 0.260943 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260943 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(62\) | − | 0.508520i | − | 0.0645821i | ||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −0.109452 | −0.0136816 | ||||||||
\(65\) | −0.971738 | + | 9.37395i | −0.120529 | + | 1.16270i | ||||
\(66\) | 1.76011 | 0.216655 | ||||||||
\(67\) | − | 12.3695i | − | 1.51117i | −0.655050 | − | 0.755585i | \(-0.727352\pi\) | ||
0.655050 | − | 0.755585i | \(-0.272648\pi\) | |||||||
\(68\) | − | 1.57408i | − | 0.190886i | ||||||
\(69\) | 2.64270 | 0.318144 | ||||||||
\(70\) | 3.91475 | + | 0.405817i | 0.467902 | + | 0.0485044i | ||||
\(71\) | 15.0283 | 1.78353 | 0.891767 | − | 0.452494i | \(-0.149466\pi\) | ||||
0.891767 | + | 0.452494i | \(0.149466\pi\) | |||||||
\(72\) | − | 1.58764i | − | 0.187105i | ||||||
\(73\) | − | 8.54550i | − | 1.00018i | −0.865975 | − | 0.500088i | \(-0.833301\pi\) | ||
0.865975 | − | 0.500088i | \(-0.166699\pi\) | |||||||
\(74\) | −18.8488 | −2.19113 | ||||||||
\(75\) | −1.02561 | + | 4.89368i | −0.118428 | + | 0.565074i | ||||
\(76\) | −7.44692 | −0.854220 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | − | 7.41820i | − | 0.839946i | ||||||
\(79\) | 0.690394 | 0.0776754 | 0.0388377 | − | 0.999246i | \(-0.487634\pi\) | ||||
0.0388377 | + | 0.999246i | \(0.487634\pi\) | |||||||
\(80\) | −11.0994 | − | 1.15060i | −1.24095 | − | 0.128641i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.85516i | 0.315300i | ||||||||
\(83\) | 8.67547i | 0.952256i | 0.879376 | + | 0.476128i | \(0.157960\pi\) | ||||
−0.879376 | + | 0.476128i | \(0.842040\pi\) | |||||||
\(84\) | −1.09799 | −0.119800 | ||||||||
\(85\) | −0.330537 | + | 3.18856i | −0.0358518 | + | 0.345848i | ||||
\(86\) | −14.4618 | −1.55945 | ||||||||
\(87\) | − | 8.97759i | − | 0.962499i | ||||||
\(88\) | − | 1.58764i | − | 0.169243i | ||||||
\(89\) | −16.3392 | −1.73195 | −0.865975 | − | 0.500087i | \(-0.833302\pi\) | ||||
−0.865975 | + | 0.500087i | \(0.833302\pi\) | |||||||
\(90\) | 0.405817 | − | 3.91475i | 0.0427769 | − | 0.412651i | ||||
\(91\) | 4.21462 | 0.441813 | ||||||||
\(92\) | 2.90165i | 0.302518i | ||||||||
\(93\) | − | 0.288914i | − | 0.0299589i | ||||||
\(94\) | −6.94351 | −0.716168 | ||||||||
\(95\) | 15.0849 | + | 1.56376i | 1.54768 | + | 0.160438i | ||||
\(96\) | 5.60837 | 0.572402 | ||||||||
\(97\) | − | 15.4515i | − | 1.56886i | −0.620217 | − | 0.784430i | \(-0.712956\pi\) | ||
0.620217 | − | 0.784430i | \(-0.287044\pi\) | |||||||
\(98\) | − | 1.76011i | − | 0.177798i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −5.37320 | − | 1.12611i | −0.537320 | − | 0.112611i | ||||
\(101\) | 6.16833 | 0.613772 | 0.306886 | − | 0.951746i | \(-0.400713\pi\) | ||||
0.306886 | + | 0.951746i | \(0.400713\pi\) | |||||||
\(102\) | − | 2.52331i | − | 0.249845i | ||||||
\(103\) | − | 8.41237i | − | 0.828896i | −0.910073 | − | 0.414448i | \(-0.863975\pi\) | ||
0.910073 | − | 0.414448i | \(-0.136025\pi\) | |||||||
\(104\) | −6.69131 | −0.656137 | ||||||||
\(105\) | 2.22415 | + | 0.230563i | 0.217055 | + | 0.0225007i | ||||
\(106\) | 10.4696 | 1.01690 | ||||||||
\(107\) | − | 6.91382i | − | 0.668384i | −0.942505 | − | 0.334192i | \(-0.891537\pi\) | ||
0.942505 | − | 0.334192i | \(-0.108463\pi\) | |||||||
\(108\) | 1.09799i | 0.105654i | ||||||||
\(109\) | 12.2807 | 1.17628 | 0.588141 | − | 0.808759i | \(-0.299860\pi\) | ||||
0.588141 | + | 0.808759i | \(0.299860\pi\) | |||||||
\(110\) | 0.405817 | − | 3.91475i | 0.0386931 | − | 0.373257i | ||||
\(111\) | −10.7089 | −1.01644 | ||||||||
\(112\) | 4.99040i | 0.471548i | ||||||||
\(113\) | − | 9.86801i | − | 0.928304i | −0.885755 | − | 0.464152i | \(-0.846359\pi\) | ||
0.885755 | − | 0.464152i | \(-0.153641\pi\) | |||||||
\(114\) | −11.9377 | −1.11806 | ||||||||
\(115\) | 0.609310 | − | 5.87776i | 0.0568184 | − | 0.548104i | ||||
\(116\) | 9.85728 | 0.915226 | ||||||||
\(117\) | − | 4.21462i | − | 0.389642i | ||||||
\(118\) | − | 11.3615i | − | 1.04591i | ||||||
\(119\) | 1.43361 | 0.131419 | ||||||||
\(120\) | −3.53115 | − | 0.366052i | −0.322349 | − | 0.0334158i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.17432i | 0.649532i | ||||||||
\(123\) | 1.62215i | 0.146264i | ||||||||
\(124\) | 0.317224 | 0.0284875 | ||||||||
\(125\) | 10.6478 | + | 3.40942i | 0.952369 | + | 0.304948i | ||||
\(126\) | −1.76011 | −0.156803 | ||||||||
\(127\) | 11.9392i | 1.05943i | 0.848176 | + | 0.529715i | \(0.177701\pi\) | ||||
−0.848176 | + | 0.529715i | \(0.822299\pi\) | |||||||
\(128\) | − | 11.4094i | − | 1.00846i | ||||||
\(129\) | −8.21640 | −0.723413 | ||||||||
\(130\) | −16.4992 | − | 1.71037i | −1.44707 | − | 0.150009i | ||||
\(131\) | −3.51910 | −0.307465 | −0.153733 | − | 0.988112i | \(-0.549129\pi\) | ||||
−0.153733 | + | 0.988112i | \(0.549129\pi\) | |||||||
\(132\) | 1.09799i | 0.0955675i | ||||||||
\(133\) | − | 6.78233i | − | 0.588103i | ||||||
\(134\) | 21.7716 | 1.88078 | ||||||||
\(135\) | 0.230563 | − | 2.22415i | 0.0198437 | − | 0.191424i | ||||
\(136\) | −2.27605 | −0.195170 | ||||||||
\(137\) | 8.26959i | 0.706518i | 0.935525 | + | 0.353259i | \(0.114927\pi\) | ||||
−0.935525 | + | 0.353259i | \(0.885073\pi\) | |||||||
\(138\) | 4.65144i | 0.395957i | ||||||||
\(139\) | 15.6717 | 1.32926 | 0.664628 | − | 0.747174i | \(-0.268590\pi\) | ||||
0.664628 | + | 0.747174i | \(0.268590\pi\) | |||||||
\(140\) | −0.253156 | + | 2.44209i | −0.0213956 | + | 0.206394i | ||||
\(141\) | −3.94493 | −0.332223 | ||||||||
\(142\) | 26.4515i | 2.21976i | ||||||||
\(143\) | − | 4.21462i | − | 0.352445i | ||||||
\(144\) | 4.99040 | 0.415867 | ||||||||
\(145\) | −19.9675 | − | 2.06990i | −1.65821 | − | 0.171896i | ||||
\(146\) | 15.0410 | 1.24480 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | − | 11.7582i | − | 0.966521i | ||||||
\(149\) | −11.8212 | −0.968428 | −0.484214 | − | 0.874950i | \(-0.660894\pi\) | ||||
−0.484214 | + | 0.874950i | \(0.660894\pi\) | |||||||
\(150\) | −8.61342 | − | 1.80519i | −0.703283 | − | 0.147394i | ||||
\(151\) | 16.7850 | 1.36594 | 0.682972 | − | 0.730445i | \(-0.260687\pi\) | ||||
0.682972 | + | 0.730445i | \(0.260687\pi\) | |||||||
\(152\) | 10.7679i | 0.873393i | ||||||||
\(153\) | − | 1.43361i | − | 0.115900i | ||||||
\(154\) | −1.76011 | −0.141834 | ||||||||
\(155\) | −0.642587 | − | 0.0666129i | −0.0516138 | − | 0.00535048i | ||||
\(156\) | 4.62760 | 0.370505 | ||||||||
\(157\) | − | 6.22134i | − | 0.496517i | −0.968694 | − | 0.248258i | \(-0.920142\pi\) | ||
0.968694 | − | 0.248258i | \(-0.0798582\pi\) | |||||||
\(158\) | 1.21517i | 0.0966737i | ||||||||
\(159\) | 5.94827 | 0.471728 | ||||||||
\(160\) | 1.29308 | − | 12.4738i | 0.102227 | − | 0.986144i | ||||
\(161\) | −2.64270 | −0.208274 | ||||||||
\(162\) | 1.76011i | 0.138287i | ||||||||
\(163\) | 7.54879i | 0.591267i | 0.955301 | + | 0.295633i | \(0.0955307\pi\) | ||||
−0.955301 | + | 0.295633i | \(0.904469\pi\) | |||||||
\(164\) | −1.78110 | −0.139081 | ||||||||
\(165\) | 0.230563 | − | 2.22415i | 0.0179493 | − | 0.173150i | ||||
\(166\) | −15.2698 | −1.18516 | ||||||||
\(167\) | − | 8.21780i | − | 0.635913i | −0.948105 | − | 0.317956i | \(-0.897003\pi\) | ||
0.948105 | − | 0.317956i | \(-0.102997\pi\) | |||||||
\(168\) | 1.58764i | 0.122489i | ||||||||
\(169\) | −4.76305 | −0.366388 | ||||||||
\(170\) | −5.61221 | − | 0.581782i | −0.430437 | − | 0.0446206i | ||||
\(171\) | −6.78233 | −0.518658 | ||||||||
\(172\) | − | 9.02150i | − | 0.687883i | ||||||
\(173\) | 14.7464i | 1.12115i | 0.828104 | + | 0.560575i | \(0.189420\pi\) | ||||
−0.828104 | + | 0.560575i | \(0.810580\pi\) | |||||||
\(174\) | 15.8015 | 1.19791 | ||||||||
\(175\) | 1.02561 | − | 4.89368i | 0.0775292 | − | 0.369928i | ||||
\(176\) | 4.99040 | 0.376165 | ||||||||
\(177\) | − | 6.45500i | − | 0.485188i | ||||||
\(178\) | − | 28.7588i | − | 2.15556i | ||||||
\(179\) | 0.455241 | 0.0340263 | 0.0170132 | − | 0.999855i | \(-0.494584\pi\) | ||||
0.0170132 | + | 0.999855i | \(0.494584\pi\) | |||||||
\(180\) | 2.44209 | + | 0.253156i | 0.182022 | + | 0.0188691i | ||||
\(181\) | 8.07223 | 0.600004 | 0.300002 | − | 0.953939i | \(-0.403013\pi\) | ||||
0.300002 | + | 0.953939i | \(0.403013\pi\) | |||||||
\(182\) | 7.41820i | 0.549874i | ||||||||
\(183\) | 4.07606i | 0.301311i | ||||||||
\(184\) | 4.19566 | 0.309308 | ||||||||
\(185\) | −2.46908 | + | 23.8182i | −0.181530 | + | 1.75115i | ||||
\(186\) | 0.508520 | 0.0372865 | ||||||||
\(187\) | − | 1.43361i | − | 0.104836i | ||||||
\(188\) | − | 4.33148i | − | 0.315906i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −2.75238 | + | 26.5511i | −0.199679 | + | 1.92622i | ||||
\(191\) | 15.5526 | 1.12535 | 0.562673 | − | 0.826679i | \(-0.309773\pi\) | ||||
0.562673 | + | 0.826679i | \(0.309773\pi\) | |||||||
\(192\) | − | 0.109452i | − | 0.00789905i | ||||||
\(193\) | − | 19.9679i | − | 1.43732i | −0.695363 | − | 0.718659i | \(-0.744756\pi\) | ||
0.695363 | − | 0.718659i | \(-0.255244\pi\) | |||||||
\(194\) | 27.1963 | 1.95258 | ||||||||
\(195\) | −9.37395 | − | 0.971738i | −0.671283 | − | 0.0695876i | ||||
\(196\) | 1.09799 | 0.0784277 | ||||||||
\(197\) | − | 15.0465i | − | 1.07202i | −0.844213 | − | 0.536008i | \(-0.819932\pi\) | ||
0.844213 | − | 0.536008i | \(-0.180068\pi\) | |||||||
\(198\) | 1.76011i | 0.125086i | ||||||||
\(199\) | 6.25560 | 0.443448 | 0.221724 | − | 0.975109i | \(-0.428832\pi\) | ||||
0.221724 | + | 0.975109i | \(0.428832\pi\) | |||||||
\(200\) | −1.62831 | + | 7.76941i | −0.115139 | + | 0.549380i | ||||
\(201\) | 12.3695 | 0.872475 | ||||||||
\(202\) | 10.8569i | 0.763891i | ||||||||
\(203\) | 8.97759i | 0.630103i | ||||||||
\(204\) | 1.57408 | 0.110208 | ||||||||
\(205\) | 3.60791 | + | 0.374008i | 0.251987 | + | 0.0261219i | ||||
\(206\) | 14.8067 | 1.03163 | ||||||||
\(207\) | 2.64270i | 0.183680i | ||||||||
\(208\) | − | 21.0326i | − | 1.45835i | ||||||
\(209\) | −6.78233 | −0.469144 | ||||||||
\(210\) | −0.405817 | + | 3.91475i | −0.0280040 | + | 0.270143i | ||||
\(211\) | 15.7435 | 1.08383 | 0.541913 | − | 0.840435i | \(-0.317700\pi\) | ||||
0.541913 | + | 0.840435i | \(0.317700\pi\) | |||||||
\(212\) | 6.53112i | 0.448559i | ||||||||
\(213\) | 15.0283i | 1.02972i | ||||||||
\(214\) | 12.1691 | 0.831862 | ||||||||
\(215\) | −1.89440 | + | 18.2745i | −0.129197 | + | 1.24631i | ||||
\(216\) | 1.58764 | 0.108025 | ||||||||
\(217\) | 0.288914i | 0.0196127i | ||||||||
\(218\) | 21.6154i | 1.46398i | ||||||||
\(219\) | 8.54550 | 0.577452 | ||||||||
\(220\) | 2.44209 | + | 0.253156i | 0.164646 | + | 0.0170678i | ||||
\(221\) | −6.04212 | −0.406437 | ||||||||
\(222\) | − | 18.8488i | − | 1.26505i | ||||||
\(223\) | − | 10.0023i | − | 0.669802i | −0.942253 | − | 0.334901i | \(-0.891297\pi\) | ||
0.942253 | − | 0.334901i | \(-0.108703\pi\) | |||||||
\(224\) | −5.60837 | −0.374725 | ||||||||
\(225\) | −4.89368 | − | 1.02561i | −0.326245 | − | 0.0683743i | ||||
\(226\) | 17.3688 | 1.15535 | ||||||||
\(227\) | 15.8599i | 1.05266i | 0.850280 | + | 0.526330i | \(0.176432\pi\) | ||||
−0.850280 | + | 0.526330i | \(0.823568\pi\) | |||||||
\(228\) | − | 7.44692i | − | 0.493184i | ||||||
\(229\) | −23.1722 | −1.53126 | −0.765632 | − | 0.643279i | \(-0.777573\pi\) | ||||
−0.765632 | + | 0.643279i | \(0.777573\pi\) | |||||||
\(230\) | 10.3455 | + | 1.07245i | 0.682162 | + | 0.0707154i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | − | 14.2532i | − | 0.935768i | ||||||
\(233\) | 18.5186i | 1.21319i | 0.795010 | + | 0.606597i | \(0.207466\pi\) | ||||
−0.795010 | + | 0.606597i | \(0.792534\pi\) | |||||||
\(234\) | 7.41820 | 0.484943 | ||||||||
\(235\) | −0.909556 | + | 8.77411i | −0.0593329 | + | 0.572360i | ||||
\(236\) | 7.08751 | 0.461358 | ||||||||
\(237\) | 0.690394i | 0.0448459i | ||||||||
\(238\) | 2.52331i | 0.163562i | ||||||||
\(239\) | 28.1822 | 1.82295 | 0.911477 | − | 0.411351i | \(-0.134943\pi\) | ||||
0.911477 | + | 0.411351i | \(0.134943\pi\) | |||||||
\(240\) | 1.15060 | − | 11.0994i | 0.0742711 | − | 0.716463i | ||||
\(241\) | −7.08108 | −0.456132 | −0.228066 | − | 0.973646i | \(-0.573240\pi\) | ||||
−0.228066 | + | 0.973646i | \(0.573240\pi\) | |||||||
\(242\) | 1.76011i | 0.113144i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.47547 | −0.286512 | ||||||||
\(245\) | −2.22415 | − | 0.230563i | −0.142096 | − | 0.0147302i | ||||
\(246\) | −2.85516 | −0.182039 | ||||||||
\(247\) | 28.5850i | 1.81882i | ||||||||
\(248\) | − | 0.458691i | − | 0.0291269i | ||||||
\(249\) | −8.67547 | −0.549785 | ||||||||
\(250\) | −6.00096 | + | 18.7413i | −0.379534 | + | 1.18530i | ||||
\(251\) | −8.74303 | −0.551855 | −0.275927 | − | 0.961178i | \(-0.588985\pi\) | ||||
−0.275927 | + | 0.961178i | \(0.588985\pi\) | |||||||
\(252\) | − | 1.09799i | − | 0.0691667i | ||||||
\(253\) | 2.64270i | 0.166145i | ||||||||
\(254\) | −21.0142 | −1.31855 | ||||||||
\(255\) | −3.18856 | − | 0.330537i | −0.199675 | − | 0.0206991i | ||||
\(256\) | 19.8629 | 1.24143 | ||||||||
\(257\) | − | 20.9626i | − | 1.30761i | −0.756662 | − | 0.653806i | \(-0.773171\pi\) | ||
0.756662 | − | 0.653806i | \(-0.226829\pi\) | |||||||
\(258\) | − | 14.4618i | − | 0.900350i | ||||||
\(259\) | 10.7089 | 0.665419 | ||||||||
\(260\) | 1.06696 | − | 10.2925i | 0.0661698 | − | 0.638313i | ||||
\(261\) | 8.97759 | 0.555699 | ||||||||
\(262\) | − | 6.19401i | − | 0.382667i | ||||||
\(263\) | − | 6.30742i | − | 0.388932i | −0.980909 | − | 0.194466i | \(-0.937703\pi\) | ||
0.980909 | − | 0.194466i | \(-0.0622974\pi\) | |||||||
\(264\) | 1.58764 | 0.0977126 | ||||||||
\(265\) | 1.37145 | − | 13.2298i | 0.0842476 | − | 0.812702i | ||||
\(266\) | 11.9377 | 0.731944 | ||||||||
\(267\) | − | 16.3392i | − | 0.999942i | ||||||
\(268\) | 13.5815i | 0.829623i | ||||||||
\(269\) | −24.8014 | −1.51217 | −0.756083 | − | 0.654476i | \(-0.772889\pi\) | ||||
−0.756083 | + | 0.654476i | \(0.772889\pi\) | |||||||
\(270\) | 3.91475 | + | 0.405817i | 0.238244 | + | 0.0246972i | ||||
\(271\) | 9.73698 | 0.591479 | 0.295740 | − | 0.955269i | \(-0.404434\pi\) | ||||
0.295740 | + | 0.955269i | \(0.404434\pi\) | |||||||
\(272\) | − | 7.15427i | − | 0.433791i | ||||||
\(273\) | 4.21462i | 0.255081i | ||||||||
\(274\) | −14.5554 | −0.879323 | ||||||||
\(275\) | −4.89368 | − | 1.02561i | −0.295100 | − | 0.0618469i | ||||
\(276\) | −2.90165 | −0.174659 | ||||||||
\(277\) | 0.787221i | 0.0472995i | 0.999720 | + | 0.0236498i | \(0.00752866\pi\) | ||||
−0.999720 | + | 0.0236498i | \(0.992471\pi\) | |||||||
\(278\) | 27.5839i | 1.65437i | ||||||||
\(279\) | 0.288914 | 0.0172968 | ||||||||
\(280\) | 3.53115 | + | 0.366052i | 0.211027 | + | 0.0218758i | ||||
\(281\) | 12.4309 | 0.741565 | 0.370782 | − | 0.928720i | \(-0.379090\pi\) | ||||
0.370782 | + | 0.928720i | \(0.379090\pi\) | |||||||
\(282\) | − | 6.94351i | − | 0.413480i | ||||||
\(283\) | 2.09042i | 0.124263i | 0.998068 | + | 0.0621314i | \(0.0197898\pi\) | ||||
−0.998068 | + | 0.0621314i | \(0.980210\pi\) | |||||||
\(284\) | −16.5009 | −0.979149 | ||||||||
\(285\) | −1.56376 | + | 15.0849i | −0.0926290 | + | 0.893554i | ||||
\(286\) | 7.41820 | 0.438647 | ||||||||
\(287\) | − | 1.62215i | − | 0.0957525i | ||||||
\(288\) | 5.60837i | 0.330476i | ||||||||
\(289\) | 14.9448 | 0.879104 | ||||||||
\(290\) | 3.64326 | − | 35.1450i | 0.213939 | − | 2.06379i | ||||
\(291\) | 15.4515 | 0.905782 | ||||||||
\(292\) | 9.38286i | 0.549090i | ||||||||
\(293\) | − | 10.4989i | − | 0.613353i | −0.951814 | − | 0.306676i | \(-0.900783\pi\) | ||
0.951814 | − | 0.306676i | \(-0.0992169\pi\) | |||||||
\(294\) | 1.76011 | 0.102652 | ||||||||
\(295\) | −14.3569 | − | 1.48829i | −0.835890 | − | 0.0866514i | ||||
\(296\) | −17.0019 | −0.988215 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − | 20.8066i | − | 1.20529i | ||||||
\(299\) | 11.1380 | 0.644126 | ||||||||
\(300\) | 1.12611 | − | 5.37320i | 0.0650161 | − | 0.310222i | ||||
\(301\) | 8.21640 | 0.473585 | ||||||||
\(302\) | 29.5434i | 1.70003i | ||||||||
\(303\) | 6.16833i | 0.354361i | ||||||||
\(304\) | −33.8465 | −1.94123 | ||||||||
\(305\) | 9.06577 | + | 0.939791i | 0.519105 | + | 0.0538123i | ||||
\(306\) | 2.52331 | 0.144248 | ||||||||
\(307\) | 26.9278i | 1.53685i | 0.639939 | + | 0.768426i | \(0.278960\pi\) | ||||
−0.639939 | + | 0.768426i | \(0.721040\pi\) | |||||||
\(308\) | − | 1.09799i | − | 0.0625636i | ||||||
\(309\) | 8.41237 | 0.478563 | ||||||||
\(310\) | 0.117246 | − | 1.13102i | 0.00665913 | − | 0.0642378i | ||||
\(311\) | 15.0673 | 0.854391 | 0.427195 | − | 0.904159i | \(-0.359502\pi\) | ||||
0.427195 | + | 0.904159i | \(0.359502\pi\) | |||||||
\(312\) | − | 6.69131i | − | 0.378821i | ||||||
\(313\) | 23.5904i | 1.33341i | 0.745322 | + | 0.666704i | \(0.232296\pi\) | ||||
−0.745322 | + | 0.666704i | \(0.767704\pi\) | |||||||
\(314\) | 10.9502 | 0.617958 | ||||||||
\(315\) | −0.230563 | + | 2.22415i | −0.0129908 | + | 0.125317i | ||||
\(316\) | −0.758044 | −0.0426433 | ||||||||
\(317\) | 24.0122i | 1.34866i | 0.738430 | + | 0.674330i | \(0.235568\pi\) | ||||
−0.738430 | + | 0.674330i | \(0.764432\pi\) | |||||||
\(318\) | 10.4696i | 0.587106i | ||||||||
\(319\) | 8.97759 | 0.502649 | ||||||||
\(320\) | −0.243439 | − | 0.0252357i | −0.0136086 | − | 0.00141072i | ||||
\(321\) | 6.91382 | 0.385892 | ||||||||
\(322\) | − | 4.65144i | − | 0.259215i | ||||||
\(323\) | 9.72320i | 0.541013i | ||||||||
\(324\) | −1.09799 | −0.0609993 | ||||||||
\(325\) | −4.32258 | + | 20.6250i | −0.239774 | + | 1.14407i | ||||
\(326\) | −13.2867 | −0.735882 | ||||||||
\(327\) | 12.2807i | 0.679126i | ||||||||
\(328\) | 2.57539i | 0.142202i | ||||||||
\(329\) | 3.94493 | 0.217491 | ||||||||
\(330\) | 3.91475 | + | 0.405817i | 0.215500 | + | 0.0223395i | ||||
\(331\) | −21.5409 | −1.18400 | −0.591998 | − | 0.805940i | \(-0.701661\pi\) | ||||
−0.591998 | + | 0.805940i | \(0.701661\pi\) | |||||||
\(332\) | − | 9.52555i | − | 0.522783i | ||||||
\(333\) | − | 10.7089i | − | 0.586844i | ||||||
\(334\) | 14.4642 | 0.791448 | ||||||||
\(335\) | 2.85195 | − | 27.5115i | 0.155818 | − | 1.50312i | ||||
\(336\) | −4.99040 | −0.272249 | ||||||||
\(337\) | 1.35270i | 0.0736864i | 0.999321 | + | 0.0368432i | \(0.0117302\pi\) | ||||
−0.999321 | + | 0.0368432i | \(0.988270\pi\) | |||||||
\(338\) | − | 8.38349i | − | 0.456002i | ||||||
\(339\) | 9.86801 | 0.535957 | ||||||||
\(340\) | 0.362926 | − | 3.50100i | 0.0196824 | − | 0.189868i | ||||
\(341\) | 0.288914 | 0.0156455 | ||||||||
\(342\) | − | 11.9377i | − | 0.645514i | ||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −13.0447 | −0.703323 | ||||||||
\(345\) | 5.87776 | + | 0.609310i | 0.316448 | + | 0.0328041i | ||||
\(346\) | −25.9553 | −1.39537 | ||||||||
\(347\) | 6.68647i | 0.358948i | 0.983763 | + | 0.179474i | \(0.0574396\pi\) | ||||
−0.983763 | + | 0.179474i | \(0.942560\pi\) | |||||||
\(348\) | 9.85728i | 0.528406i | ||||||||
\(349\) | −4.60906 | −0.246718 | −0.123359 | − | 0.992362i | \(-0.539367\pi\) | ||||
−0.123359 | + | 0.992362i | \(0.539367\pi\) | |||||||
\(350\) | 8.61342 | + | 1.80519i | 0.460407 | + | 0.0964917i | ||||
\(351\) | 4.21462 | 0.224960 | ||||||||
\(352\) | 5.60837i | 0.298927i | ||||||||
\(353\) | − | 17.5120i | − | 0.932071i | −0.884766 | − | 0.466036i | \(-0.845682\pi\) | ||
0.884766 | − | 0.466036i | \(-0.154318\pi\) | |||||||
\(354\) | 11.3615 | 0.603857 | ||||||||
\(355\) | 33.4253 | + | 3.46498i | 1.77403 | + | 0.183902i | ||||
\(356\) | 17.9402 | 0.950830 | ||||||||
\(357\) | 1.43361i | 0.0758746i | ||||||||
\(358\) | 0.801274i | 0.0423487i | ||||||||
\(359\) | −21.3097 | −1.12469 | −0.562343 | − | 0.826904i | \(-0.690100\pi\) | ||||
−0.562343 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(360\) | 0.366052 | − | 3.53115i | 0.0192926 | − | 0.186108i | ||||
\(361\) | 27.0000 | 1.42105 | ||||||||
\(362\) | 14.2080i | 0.746756i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −4.62760 | −0.242552 | ||||||||
\(365\) | 1.97028 | − | 19.0065i | 0.103129 | − | 0.994844i | ||||
\(366\) | −7.17432 | −0.375008 | ||||||||
\(367\) | − | 19.0886i | − | 0.996414i | −0.867058 | − | 0.498207i | \(-0.833992\pi\) | ||
0.867058 | − | 0.498207i | \(-0.166008\pi\) | |||||||
\(368\) | 13.1881i | 0.687479i | ||||||||
\(369\) | −1.62215 | −0.0844458 | ||||||||
\(370\) | −41.9226 | − | 4.34585i | −2.17945 | − | 0.225930i | ||||
\(371\) | −5.94827 | −0.308819 | ||||||||
\(372\) | 0.317224i | 0.0164473i | ||||||||
\(373\) | 17.0590i | 0.883282i | 0.897192 | + | 0.441641i | \(0.145603\pi\) | ||||
−0.897192 | + | 0.441641i | \(0.854397\pi\) | |||||||
\(374\) | 2.52331 | 0.130477 | ||||||||
\(375\) | −3.40942 | + | 10.6478i | −0.176062 | + | 0.549850i | ||||
\(376\) | −6.26313 | −0.322996 | ||||||||
\(377\) | − | 37.8372i | − | 1.94871i | ||||||
\(378\) | − | 1.76011i | − | 0.0905303i | ||||||
\(379\) | −33.8078 | −1.73659 | −0.868295 | − | 0.496048i | \(-0.834784\pi\) | ||||
−0.868295 | + | 0.496048i | \(0.834784\pi\) | |||||||
\(380\) | −16.5631 | − | 1.71699i | −0.849667 | − | 0.0880795i | ||||
\(381\) | −11.9392 | −0.611662 | ||||||||
\(382\) | 27.3743i | 1.40059i | ||||||||
\(383\) | − | 12.6409i | − | 0.645920i | −0.946413 | − | 0.322960i | \(-0.895322\pi\) | ||
0.946413 | − | 0.322960i | \(-0.104678\pi\) | |||||||
\(384\) | 11.4094 | 0.582233 | ||||||||
\(385\) | −0.230563 | + | 2.22415i | −0.0117506 | + | 0.113353i | ||||
\(386\) | 35.1456 | 1.78887 | ||||||||
\(387\) | − | 8.21640i | − | 0.417663i | ||||||
\(388\) | 16.9655i | 0.861294i | ||||||||
\(389\) | −2.90831 | −0.147457 | −0.0737285 | − | 0.997278i | \(-0.523490\pi\) | ||||
−0.0737285 | + | 0.997278i | \(0.523490\pi\) | |||||||
\(390\) | 1.71037 | − | 16.4992i | 0.0866077 | − | 0.835469i | ||||
\(391\) | 3.78859 | 0.191597 | ||||||||
\(392\) | − | 1.58764i | − | 0.0801880i | ||||||
\(393\) | − | 3.51910i | − | 0.177515i | ||||||
\(394\) | 26.4834 | 1.33422 | ||||||||
\(395\) | 1.53554 | + | 0.159180i | 0.0772614 | + | 0.00800920i | ||||
\(396\) | −1.09799 | −0.0551759 | ||||||||
\(397\) | − | 11.6301i | − | 0.583700i | −0.956464 | − | 0.291850i | \(-0.905729\pi\) | ||
0.956464 | − | 0.291850i | \(-0.0942708\pi\) | |||||||
\(398\) | 11.0106i | 0.551909i | ||||||||
\(399\) | 6.78233 | 0.339541 | ||||||||
\(400\) | −24.4214 | − | 5.11823i | −1.22107 | − | 0.255911i | ||||
\(401\) | 22.4120 | 1.11920 | 0.559602 | − | 0.828761i | \(-0.310954\pi\) | ||||
0.559602 | + | 0.828761i | \(0.310954\pi\) | |||||||
\(402\) | 21.7716i | 1.08587i | ||||||||
\(403\) | − | 1.21766i | − | 0.0606561i | ||||||
\(404\) | −6.77275 | −0.336957 | ||||||||
\(405\) | 2.22415 | + | 0.230563i | 0.110519 | + | 0.0114568i | ||||
\(406\) | −15.8015 | −0.784218 | ||||||||
\(407\) | − | 10.7089i | − | 0.530820i | ||||||
\(408\) | − | 2.27605i | − | 0.112681i | ||||||
\(409\) | 12.4627 | 0.616239 | 0.308120 | − | 0.951348i | \(-0.400300\pi\) | ||||
0.308120 | + | 0.951348i | \(0.400300\pi\) | |||||||
\(410\) | −0.658296 | + | 6.35031i | −0.0325109 | + | 0.313619i | ||||
\(411\) | −8.26959 | −0.407909 | ||||||||
\(412\) | 9.23668i | 0.455058i | ||||||||
\(413\) | 6.45500i | 0.317630i | ||||||||
\(414\) | −4.65144 | −0.228606 | ||||||||
\(415\) | −2.00024 | + | 19.2955i | −0.0981881 | + | 0.947180i | ||||
\(416\) | 23.6372 | 1.15891 | ||||||||
\(417\) | 15.6717i | 0.767447i | ||||||||
\(418\) | − | 11.9377i | − | 0.583890i | ||||||
\(419\) | 7.16999 | 0.350277 | 0.175139 | − | 0.984544i | \(-0.443963\pi\) | ||||
0.175139 | + | 0.984544i | \(0.443963\pi\) | |||||||
\(420\) | −2.44209 | − | 0.253156i | −0.119162 | − | 0.0123527i | ||||
\(421\) | 26.8929 | 1.31068 | 0.655341 | − | 0.755334i | \(-0.272525\pi\) | ||||
0.655341 | + | 0.755334i | \(0.272525\pi\) | |||||||
\(422\) | 27.7103i | 1.34891i | ||||||||
\(423\) | − | 3.94493i | − | 0.191809i | ||||||
\(424\) | 9.44371 | 0.458627 | ||||||||
\(425\) | −1.47033 | + | 7.01562i | −0.0713214 | + | 0.340307i | ||||
\(426\) | −26.4515 | −1.28158 | ||||||||
\(427\) | − | 4.07606i | − | 0.197255i | ||||||
\(428\) | 7.59129i | 0.366939i | ||||||||
\(429\) | 4.21462 | 0.203484 | ||||||||
\(430\) | −32.1651 | − | 3.33435i | −1.55114 | − | 0.160797i | ||||
\(431\) | 8.06019 | 0.388246 | 0.194123 | − | 0.980977i | \(-0.437814\pi\) | ||||
0.194123 | + | 0.980977i | \(0.437814\pi\) | |||||||
\(432\) | 4.99040i | 0.240101i | ||||||||
\(433\) | − | 14.4948i | − | 0.696576i | −0.937388 | − | 0.348288i | \(-0.886763\pi\) | ||
0.937388 | − | 0.348288i | \(-0.113237\pi\) | |||||||
\(434\) | −0.508520 | −0.0244097 | ||||||||
\(435\) | 2.06990 | − | 19.9675i | 0.0992443 | − | 0.957368i | ||||
\(436\) | −13.4841 | −0.645771 | ||||||||
\(437\) | − | 17.9237i | − | 0.857405i | ||||||
\(438\) | 15.0410i | 0.718688i | ||||||||
\(439\) | −4.28674 | −0.204595 | −0.102298 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102298 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(440\) | 0.366052 | − | 3.53115i | 0.0174508 | − | 0.168341i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 10.6348i | − | 0.505845i | ||||||
\(443\) | 4.83452i | 0.229695i | 0.993383 | + | 0.114848i | \(0.0366380\pi\) | ||||
−0.993383 | + | 0.114848i | \(0.963362\pi\) | |||||||
\(444\) | 11.7582 | 0.558021 | ||||||||
\(445\) | −36.3408 | − | 3.76722i | −1.72272 | − | 0.178583i | ||||
\(446\) | 17.6051 | 0.833626 | ||||||||
\(447\) | − | 11.8212i | − | 0.559122i | ||||||
\(448\) | 0.109452i | 0.00517114i | ||||||||
\(449\) | −35.7884 | −1.68896 | −0.844479 | − | 0.535588i | \(-0.820090\pi\) | ||||
−0.844479 | + | 0.535588i | \(0.820090\pi\) | |||||||
\(450\) | 1.80519 | − | 8.61342i | 0.0850977 | − | 0.406040i | ||||
\(451\) | −1.62215 | −0.0763841 | ||||||||
\(452\) | 10.8350i | 0.509633i | ||||||||
\(453\) | 16.7850i | 0.788628i | ||||||||
\(454\) | −27.9152 | −1.31013 | ||||||||
\(455\) | 9.37395 | + | 0.971738i | 0.439458 | + | 0.0455558i | ||||
\(456\) | −10.7679 | −0.504254 | ||||||||
\(457\) | − | 15.6563i | − | 0.732370i | −0.930542 | − | 0.366185i | \(-0.880664\pi\) | ||
0.930542 | − | 0.366185i | \(-0.119336\pi\) | |||||||
\(458\) | − | 40.7856i | − | 1.90579i | ||||||
\(459\) | 1.43361 | 0.0669151 | ||||||||
\(460\) | −0.669014 | + | 6.45371i | −0.0311930 | + | 0.300906i | ||||
\(461\) | −38.1784 | −1.77815 | −0.889073 | − | 0.457766i | \(-0.848650\pi\) | ||||
−0.889073 | + | 0.457766i | \(0.848650\pi\) | |||||||
\(462\) | − | 1.76011i | − | 0.0818877i | ||||||
\(463\) | − | 13.4364i | − | 0.624442i | −0.950010 | − | 0.312221i | \(-0.898927\pi\) | ||
0.950010 | − | 0.312221i | \(-0.101073\pi\) | |||||||
\(464\) | 44.8017 | 2.07987 | ||||||||
\(465\) | 0.0666129 | − | 0.642587i | 0.00308910 | − | 0.0297993i | ||||
\(466\) | −32.5948 | −1.50992 | ||||||||
\(467\) | − | 37.5213i | − | 1.73628i | −0.496321 | − | 0.868139i | \(-0.665316\pi\) | ||
0.496321 | − | 0.868139i | \(-0.334684\pi\) | |||||||
\(468\) | 4.62760i | 0.213911i | ||||||||
\(469\) | −12.3695 | −0.571169 | ||||||||
\(470\) | −15.4434 | − | 1.60092i | −0.712351 | − | 0.0738449i | ||||
\(471\) | 6.22134 | 0.286664 | ||||||||
\(472\) | − | 10.2482i | − | 0.471713i | ||||||
\(473\) | − | 8.21640i | − | 0.377790i | ||||||
\(474\) | −1.21517 | −0.0558146 | ||||||||
\(475\) | 33.1906 | + | 6.95606i | 1.52289 | + | 0.319166i | ||||
\(476\) | −1.57408 | −0.0721480 | ||||||||
\(477\) | 5.94827i | 0.272352i | ||||||||
\(478\) | 49.6037i | 2.26882i | ||||||||
\(479\) | 19.6828 | 0.899329 | 0.449665 | − | 0.893198i | \(-0.351544\pi\) | ||||
0.449665 | + | 0.893198i | \(0.351544\pi\) | |||||||
\(480\) | 12.4738 | + | 1.29308i | 0.569351 | + | 0.0590209i | ||||
\(481\) | −45.1340 | −2.05793 | ||||||||
\(482\) | − | 12.4635i | − | 0.567696i | ||||||
\(483\) | − | 2.64270i | − | 0.120247i | ||||||
\(484\) | −1.09799 | −0.0499085 | ||||||||
\(485\) | 3.56254 | − | 34.3664i | 0.161767 | − | 1.56050i | ||||
\(486\) | −1.76011 | −0.0798402 | ||||||||
\(487\) | 24.5893i | 1.11425i | 0.830430 | + | 0.557123i | \(0.188095\pi\) | ||||
−0.830430 | + | 0.557123i | \(0.811905\pi\) | |||||||
\(488\) | 6.47133i | 0.292943i | ||||||||
\(489\) | −7.54879 | −0.341368 | ||||||||
\(490\) | 0.405817 | − | 3.91475i | 0.0183329 | − | 0.176850i | ||||
\(491\) | 32.0804 | 1.44777 | 0.723883 | − | 0.689922i | \(-0.242355\pi\) | ||||
0.723883 | + | 0.689922i | \(0.242355\pi\) | |||||||
\(492\) | − | 1.78110i | − | 0.0802982i | ||||||
\(493\) | − | 12.8703i | − | 0.579651i | ||||||
\(494\) | −50.3127 | −2.26368 | ||||||||
\(495\) | 2.22415 | + | 0.230563i | 0.0999681 | + | 0.0103631i | ||||
\(496\) | 1.44179 | 0.0647385 | ||||||||
\(497\) | − | 15.0283i | − | 0.674113i | ||||||
\(498\) | − | 15.2698i | − | 0.684255i | ||||||
\(499\) | 42.5393 | 1.90432 | 0.952161 | − | 0.305597i | \(-0.0988559\pi\) | ||||
0.952161 | + | 0.305597i | \(0.0988559\pi\) | |||||||
\(500\) | −11.6912 | − | 3.74350i | −0.522845 | − | 0.167415i | ||||
\(501\) | 8.21780 | 0.367144 | ||||||||
\(502\) | − | 15.3887i | − | 0.686831i | ||||||
\(503\) | − | 25.6136i | − | 1.14205i | −0.820931 | − | 0.571027i | \(-0.806545\pi\) | ||
0.820931 | − | 0.571027i | \(-0.193455\pi\) | |||||||
\(504\) | −1.58764 | −0.0707192 | ||||||||
\(505\) | 13.7193 | + | 1.42219i | 0.610500 | + | 0.0632866i | ||||
\(506\) | −4.65144 | −0.206782 | ||||||||
\(507\) | − | 4.76305i | − | 0.211534i | ||||||
\(508\) | − | 13.1091i | − | 0.581620i | ||||||
\(509\) | −32.8590 | −1.45645 | −0.728226 | − | 0.685337i | \(-0.759655\pi\) | ||||
−0.728226 | + | 0.685337i | \(0.759655\pi\) | |||||||
\(510\) | 0.581782 | − | 5.61221i | 0.0257617 | − | 0.248513i | ||||
\(511\) | −8.54550 | −0.378031 | ||||||||
\(512\) | 12.1421i | 0.536608i | ||||||||
\(513\) | − | 6.78233i | − | 0.299447i | ||||||
\(514\) | 36.8965 | 1.62744 | ||||||||
\(515\) | 1.93958 | − | 18.7104i | 0.0854683 | − | 0.824477i | ||||
\(516\) | 9.02150 | 0.397149 | ||||||||
\(517\) | − | 3.94493i | − | 0.173498i | ||||||
\(518\) | 18.8488i | 0.828170i | ||||||||
\(519\) | −14.7464 | −0.647296 | ||||||||
\(520\) | −14.8825 | − | 1.54277i | −0.652640 | − | 0.0676550i | ||||
\(521\) | 32.2802 | 1.41422 | 0.707111 | − | 0.707103i | \(-0.249998\pi\) | ||||
0.707111 | + | 0.707103i | \(0.249998\pi\) | |||||||
\(522\) | 15.8015i | 0.691615i | ||||||||
\(523\) | − | 17.5863i | − | 0.768996i | −0.923126 | − | 0.384498i | \(-0.874375\pi\) | ||
0.923126 | − | 0.384498i | \(-0.125625\pi\) | |||||||
\(524\) | 3.86393 | 0.168797 | ||||||||
\(525\) | 4.89368 | + | 1.02561i | 0.213578 | + | 0.0447615i | ||||
\(526\) | 11.1018 | 0.484060 | ||||||||
\(527\) | − | 0.414189i | − | 0.0180423i | ||||||
\(528\) | 4.99040i | 0.217179i | ||||||||
\(529\) | 16.0161 | 0.696354 | ||||||||
\(530\) | 23.2860 | + | 2.41391i | 1.01148 | + | 0.104853i | ||||
\(531\) | 6.45500 | 0.280123 | ||||||||
\(532\) | 7.44692i | 0.322865i | ||||||||
\(533\) | 6.83675i | 0.296133i | ||||||||
\(534\) | 28.7588 | 1.24451 | ||||||||
\(535\) | 1.59407 | − | 15.3774i | 0.0689178 | − | 0.664822i | ||||
\(536\) | 19.6383 | 0.848244 | ||||||||
\(537\) | 0.455241i | 0.0196451i | ||||||||
\(538\) | − | 43.6531i | − | 1.88202i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −0.253156 | + | 2.44209i | −0.0108941 | + | 0.105091i | ||||
\(541\) | −30.5935 | −1.31532 | −0.657659 | − | 0.753316i | \(-0.728453\pi\) | ||||
−0.657659 | + | 0.753316i | \(0.728453\pi\) | |||||||
\(542\) | 17.1382i | 0.736147i | ||||||||
\(543\) | 8.07223i | 0.346412i | ||||||||
\(544\) | 8.04020 | 0.344721 | ||||||||
\(545\) | 27.3142 | + | 2.83149i | 1.17001 | + | 0.121288i | ||||
\(546\) | −7.41820 | −0.317470 | ||||||||
\(547\) | 42.4854i | 1.81655i | 0.418378 | + | 0.908273i | \(0.362599\pi\) | ||||
−0.418378 | + | 0.908273i | \(0.637401\pi\) | |||||||
\(548\) | − | 9.07990i | − | 0.387874i | ||||||
\(549\) | −4.07606 | −0.173962 | ||||||||
\(550\) | 1.80519 | − | 8.61342i | 0.0769738 | − | 0.367277i | ||||
\(551\) | −60.8890 | −2.59396 | ||||||||
\(552\) | 4.19566i | 0.178579i | ||||||||
\(553\) | − | 0.690394i | − | 0.0293586i | ||||||
\(554\) | −1.38560 | −0.0588683 | ||||||||
\(555\) | −23.8182 | − | 2.46908i | −1.01103 | − | 0.104807i | ||||
\(556\) | −17.2073 | −0.729753 | ||||||||
\(557\) | − | 29.1333i | − | 1.23442i | −0.786799 | − | 0.617209i | \(-0.788263\pi\) | ||
0.786799 | − | 0.617209i | \(-0.211737\pi\) | |||||||
\(558\) | 0.508520i | 0.0215274i | ||||||||
\(559\) | −34.6290 | −1.46465 | ||||||||
\(560\) | −1.15060 | + | 11.0994i | −0.0486218 | + | 0.469035i | ||||
\(561\) | 1.43361 | 0.0605270 | ||||||||
\(562\) | 21.8797i | 0.922941i | ||||||||
\(563\) | 37.5476i | 1.58244i | 0.611531 | + | 0.791221i | \(0.290554\pi\) | ||||
−0.611531 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(564\) | 4.33148 | 0.182388 | ||||||||
\(565\) | 2.27520 | − | 21.9479i | 0.0957185 | − | 0.923356i | ||||
\(566\) | −3.67938 | −0.154656 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 23.8596i | 1.00113i | ||||||||
\(569\) | −0.484384 | −0.0203064 | −0.0101532 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101532 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(570\) | −26.5511 | − | 2.75238i | −1.11210 | − | 0.115285i | ||||
\(571\) | 7.23540 | 0.302792 | 0.151396 | − | 0.988473i | \(-0.451623\pi\) | ||||
0.151396 | + | 0.988473i | \(0.451623\pi\) | |||||||
\(572\) | 4.62760i | 0.193490i | ||||||||
\(573\) | 15.5526i | 0.649719i | ||||||||
\(574\) | 2.85516 | 0.119172 | ||||||||
\(575\) | 2.71039 | − | 12.9325i | 0.113031 | − | 0.539324i | ||||
\(576\) | 0.109452 | 0.00456052 | ||||||||
\(577\) | − | 23.8497i | − | 0.992878i | −0.868072 | − | 0.496439i | \(-0.834641\pi\) | ||
0.868072 | − | 0.496439i | \(-0.165359\pi\) | |||||||
\(578\) | 26.3044i | 1.09412i | ||||||||
\(579\) | 19.9679 | 0.829836 | ||||||||
\(580\) | 21.9241 | + | 2.27273i | 0.910347 | + | 0.0943699i | ||||
\(581\) | 8.67547 | 0.359919 | ||||||||
\(582\) | 27.1963i | 1.12732i | ||||||||
\(583\) | 5.94827i | 0.246352i | ||||||||
\(584\) | 13.5672 | 0.561415 | ||||||||
\(585\) | 0.971738 | − | 9.37395i | 0.0401764 | − | 0.387565i | ||||
\(586\) | 18.4792 | 0.763370 | ||||||||
\(587\) | − | 25.6673i | − | 1.05940i | −0.848184 | − | 0.529701i | \(-0.822304\pi\) | ||
0.848184 | − | 0.529701i | \(-0.177696\pi\) | |||||||
\(588\) | 1.09799i | 0.0452802i | ||||||||
\(589\) | −1.95951 | −0.0807401 | ||||||||
\(590\) | 2.61955 | − | 25.2697i | 0.107845 | − | 1.04034i | ||||
\(591\) | 15.0465 | 0.618929 | ||||||||
\(592\) | − | 53.4417i | − | 2.19644i | ||||||
\(593\) | 25.8664i | 1.06221i | 0.847308 | + | 0.531103i | \(0.178222\pi\) | ||||
−0.847308 | + | 0.531103i | \(0.821778\pi\) | |||||||
\(594\) | −1.76011 | −0.0722182 | ||||||||
\(595\) | 3.18856 | + | 0.330537i | 0.130718 | + | 0.0135507i | ||||
\(596\) | 12.9795 | 0.531661 | ||||||||
\(597\) | 6.25560i | 0.256025i | ||||||||
\(598\) | 19.6041i | 0.801670i | ||||||||
\(599\) | −23.1007 | −0.943870 | −0.471935 | − | 0.881633i | \(-0.656444\pi\) | ||||
−0.471935 | + | 0.881633i | \(0.656444\pi\) | |||||||
\(600\) | −7.76941 | − | 1.62831i | −0.317185 | − | 0.0664754i | ||||
\(601\) | −25.3840 | −1.03544 | −0.517718 | − | 0.855551i | \(-0.673218\pi\) | ||||
−0.517718 | + | 0.855551i | \(0.673218\pi\) | |||||||
\(602\) | 14.4618i | 0.589417i | ||||||||
\(603\) | 12.3695i | 0.503724i | ||||||||
\(604\) | −18.4297 | −0.749895 | ||||||||
\(605\) | 2.22415 | + | 0.230563i | 0.0904245 | + | 0.00937373i | ||||
\(606\) | −10.8569 | −0.441033 | ||||||||
\(607\) | − | 25.9728i | − | 1.05420i | −0.849802 | − | 0.527102i | \(-0.823278\pi\) | ||
0.849802 | − | 0.527102i | \(-0.176722\pi\) | |||||||
\(608\) | − | 38.0378i | − | 1.54264i | ||||||
\(609\) | −8.97759 | −0.363790 | ||||||||
\(610\) | −1.65414 | + | 15.9568i | −0.0669740 | + | 0.646070i | ||||
\(611\) | −16.6264 | −0.672632 | ||||||||
\(612\) | 1.57408i | 0.0636285i | ||||||||
\(613\) | − | 18.6868i | − | 0.754753i | −0.926060 | − | 0.377377i | \(-0.876826\pi\) | ||
0.926060 | − | 0.377377i | \(-0.123174\pi\) | |||||||
\(614\) | −47.3959 | −1.91274 | ||||||||
\(615\) | −0.374008 | + | 3.60791i | −0.0150815 | + | 0.145485i | ||||
\(616\) | −1.58764 | −0.0639679 | ||||||||
\(617\) | − | 12.4067i | − | 0.499476i | −0.968313 | − | 0.249738i | \(-0.919656\pi\) | ||
0.968313 | − | 0.249738i | \(-0.0803445\pi\) | |||||||
\(618\) | 14.8067i | 0.595613i | ||||||||
\(619\) | 3.23070 | 0.129853 | 0.0649265 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649265 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(620\) | 0.705553 | + | 0.0731401i | 0.0283357 | + | 0.00293738i | ||||
\(621\) | −2.64270 | −0.106048 | ||||||||
\(622\) | 26.5202i | 1.06336i | ||||||||
\(623\) | 16.3392i | 0.654616i | ||||||||
\(624\) | 21.0326 | 0.841980 | ||||||||
\(625\) | 22.8962 | + | 10.0381i | 0.915849 | + | 0.401522i | ||||
\(626\) | −41.5217 | −1.65954 | ||||||||
\(627\) | − | 6.78233i | − | 0.270860i | ||||||
\(628\) | 6.83095i | 0.272585i | ||||||||
\(629\) | −15.3524 | −0.612139 | ||||||||
\(630\) | −3.91475 | − | 0.405817i | −0.155967 | − | 0.0161681i | ||||
\(631\) | −15.6686 | −0.623758 | −0.311879 | − | 0.950122i | \(-0.600958\pi\) | ||||
−0.311879 | + | 0.950122i | \(0.600958\pi\) | |||||||
\(632\) | 1.09610i | 0.0436005i | ||||||||
\(633\) | 15.7435i | 0.625747i | ||||||||
\(634\) | −42.2641 | −1.67852 | ||||||||
\(635\) | −2.75273 | + | 26.5545i | −0.109239 | + | 1.05378i | ||||
\(636\) | −6.53112 | −0.258976 | ||||||||
\(637\) | − | 4.21462i | − | 0.166989i | ||||||
\(638\) | 15.8015i | 0.625589i | ||||||||
\(639\) | −15.0283 | −0.594512 | ||||||||
\(640\) | 2.63059 | − | 25.3762i | 0.103983 | − | 1.00308i | ||||
\(641\) | −40.4745 | −1.59865 | −0.799323 | − | 0.600901i | \(-0.794809\pi\) | ||||
−0.799323 | + | 0.600901i | \(0.794809\pi\) | |||||||
\(642\) | 12.1691i | 0.480276i | ||||||||
\(643\) | 27.5878i | 1.08796i | 0.839099 | + | 0.543979i | \(0.183083\pi\) | ||||
−0.839099 | + | 0.543979i | \(0.816917\pi\) | |||||||
\(644\) | 2.90165 | 0.114341 | ||||||||
\(645\) | −18.2745 | − | 1.89440i | −0.719557 | − | 0.0745919i | ||||
\(646\) | −17.1139 | −0.673338 | ||||||||
\(647\) | − | 12.5975i | − | 0.495257i | −0.968855 | − | 0.247628i | \(-0.920349\pi\) | ||
0.968855 | − | 0.247628i | \(-0.0796512\pi\) | |||||||
\(648\) | 1.58764i | 0.0623684i | ||||||||
\(649\) | 6.45500 | 0.253381 | ||||||||
\(650\) | −36.3023 | − | 7.60822i | −1.42389 | − | 0.298419i | ||||
\(651\) | −0.288914 | −0.0113234 | ||||||||
\(652\) | − | 8.28848i | − | 0.324602i | ||||||
\(653\) | − | 27.9716i | − | 1.09461i | −0.836932 | − | 0.547307i | \(-0.815653\pi\) | ||
0.836932 | − | 0.547307i | \(-0.184347\pi\) | |||||||
\(654\) | −21.6154 | −0.845231 | ||||||||
\(655\) | −7.82701 | − | 0.811376i | −0.305827 | − | 0.0317031i | ||||
\(656\) | −8.09518 | −0.316064 | ||||||||
\(657\) | 8.54550i | 0.333392i | ||||||||
\(658\) | 6.94351i | 0.270686i | ||||||||
\(659\) | −25.4690 | −0.992130 | −0.496065 | − | 0.868285i | \(-0.665222\pi\) | ||||
−0.496065 | + | 0.868285i | \(0.665222\pi\) | |||||||
\(660\) | −0.253156 | + | 2.44209i | −0.00985407 | + | 0.0950581i | ||||
\(661\) | 34.5066 | 1.34215 | 0.671075 | − | 0.741390i | \(-0.265833\pi\) | ||||
0.671075 | + | 0.741390i | \(0.265833\pi\) | |||||||
\(662\) | − | 37.9144i | − | 1.47358i | ||||||
\(663\) | − | 6.04212i | − | 0.234656i | ||||||
\(664\) | −13.7735 | −0.534517 | ||||||||
\(665\) | 1.56376 | − | 15.0849i | 0.0606399 | − | 0.584968i | ||||
\(666\) | 18.8488 | 0.730378 | ||||||||
\(667\) | 23.7251i | 0.918639i | ||||||||
\(668\) | 9.02304i | 0.349112i | ||||||||
\(669\) | 10.0023 | 0.386711 | ||||||||
\(670\) | 48.4233 | + | 5.01974i | 1.87076 | + | 0.193929i | ||||
\(671\) | −4.07606 | −0.157355 | ||||||||
\(672\) | − | 5.60837i | − | 0.216347i | ||||||
\(673\) | 38.8076i | 1.49592i | 0.663743 | + | 0.747961i | \(0.268967\pi\) | ||||
−0.663743 | + | 0.747961i | \(0.731033\pi\) | |||||||
\(674\) | −2.38091 | −0.0917090 | ||||||||
\(675\) | 1.02561 | − | 4.89368i | 0.0394759 | − | 0.188358i | ||||
\(676\) | 5.22977 | 0.201145 | ||||||||
\(677\) | − | 24.9110i | − | 0.957407i | −0.877977 | − | 0.478704i | \(-0.841107\pi\) | ||
0.877977 | − | 0.478704i | \(-0.158893\pi\) | |||||||
\(678\) | 17.3688i | 0.667044i | ||||||||
\(679\) | −15.4515 | −0.592973 | ||||||||
\(680\) | −5.06229 | − | 0.524775i | −0.194130 | − | 0.0201242i | ||||
\(681\) | −15.8599 | −0.607754 | ||||||||
\(682\) | 0.508520i | 0.0194722i | ||||||||
\(683\) | 2.62542i | 0.100459i | 0.998738 | + | 0.0502295i | \(0.0159953\pi\) | ||||
−0.998738 | + | 0.0502295i | \(0.984005\pi\) | |||||||
\(684\) | 7.44692 | 0.284740 | ||||||||
\(685\) | −1.90666 | + | 18.3928i | −0.0728499 | + | 0.702753i | ||||
\(686\) | −1.76011 | −0.0672013 | ||||||||
\(687\) | − | 23.1722i | − | 0.884075i | ||||||
\(688\) | − | 41.0031i | − | 1.56323i | ||||||
\(689\) | 25.0697 | 0.955079 | ||||||||
\(690\) | −1.07245 | + | 10.3455i | −0.0408276 | + | 0.393847i | ||||
\(691\) | −20.8124 | −0.791741 | −0.395871 | − | 0.918306i | \(-0.629557\pi\) | ||||
−0.395871 | + | 0.918306i | \(0.629557\pi\) | |||||||
\(692\) | − | 16.1914i | − | 0.615504i | ||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | −11.7689 | −0.446742 | ||||||||
\(695\) | 34.8562 | + | 3.61332i | 1.32217 | + | 0.137061i | ||||
\(696\) | 14.2532 | 0.540266 | ||||||||
\(697\) | 2.32553i | 0.0880856i | ||||||||
\(698\) | − | 8.11246i | − | 0.307061i | ||||||
\(699\) | −18.5186 | −0.700437 | ||||||||
\(700\) | −1.12611 | + | 5.37320i | −0.0425630 | + | 0.203088i | ||||
\(701\) | 3.23339 | 0.122124 | 0.0610618 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610618 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(702\) | 7.41820i | 0.279982i | ||||||||
\(703\) | 72.6313i | 2.73934i | ||||||||
\(704\) | 0.109452 | 0.00412514 | ||||||||
\(705\) | −8.77411 | − | 0.909556i | −0.330452 | − | 0.0342559i | ||||
\(706\) | 30.8231 | 1.16004 | ||||||||
\(707\) | − | 6.16833i | − | 0.231984i | ||||||
\(708\) | 7.08751i | 0.266365i | ||||||||
\(709\) | −2.02814 | −0.0761684 | −0.0380842 | − | 0.999275i | \(-0.512126\pi\) | ||||
−0.0380842 | + | 0.999275i | \(0.512126\pi\) | |||||||
\(710\) | −6.09875 | + | 58.8321i | −0.228882 | + | 2.20793i | ||||
\(711\) | −0.690394 | −0.0258918 | ||||||||
\(712\) | − | 25.9408i | − | 0.972172i | ||||||
\(713\) | 0.763512i | 0.0285938i | ||||||||
\(714\) | −2.52331 | −0.0944324 | ||||||||
\(715\) | 0.971738 | − | 9.37395i | 0.0363409 | − | 0.350566i | ||||
\(716\) | −0.499849 | −0.0186802 | ||||||||
\(717\) | 28.1822i | 1.05248i | ||||||||
\(718\) | − | 37.5075i | − | 1.39977i | ||||||
\(719\) | −24.9232 | −0.929477 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(720\) | 11.0994 | + | 1.15060i | 0.413650 | + | 0.0428804i | ||||
\(721\) | −8.41237 | −0.313293 | ||||||||
\(722\) | 47.5230i | 1.76862i | ||||||||
\(723\) | − | 7.08108i | − | 0.263348i | ||||||
\(724\) | −8.86321 | −0.329398 | ||||||||
\(725\) | −43.9335 | − | 9.20755i | −1.63165 | − | 0.341960i | ||||
\(726\) | −1.76011 | −0.0653238 | ||||||||
\(727\) | − | 2.18158i | − | 0.0809104i | −0.999181 | − | 0.0404552i | \(-0.987119\pi\) | ||
0.999181 | − | 0.0404552i | \(-0.0128808\pi\) | |||||||
\(728\) | 6.69131i | 0.247996i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 33.4535 | + | 3.46791i | 1.23817 | + | 0.128353i | ||||
\(731\) | −11.7791 | −0.435665 | ||||||||
\(732\) | − | 4.47547i | − | 0.165418i | ||||||
\(733\) | − | 17.1410i | − | 0.633118i | −0.948573 | − | 0.316559i | \(-0.897473\pi\) | ||
0.948573 | − | 0.316559i | \(-0.102527\pi\) | |||||||
\(734\) | 33.5980 | 1.24012 | ||||||||
\(735\) | 0.230563 | − | 2.22415i | 0.00850446 | − | 0.0820390i | ||||
\(736\) | −14.8212 | −0.546318 | ||||||||
\(737\) | 12.3695i | 0.455635i | ||||||||
\(738\) | − | 2.85516i | − | 0.105100i | ||||||
\(739\) | 0.235487 | 0.00866254 | 0.00433127 | − | 0.999991i | \(-0.498621\pi\) | ||||
0.00433127 | + | 0.999991i | \(0.498621\pi\) | |||||||
\(740\) | 2.71102 | − | 26.1521i | 0.0996590 | − | 0.961369i | ||||
\(741\) | −28.5850 | −1.05010 | ||||||||
\(742\) | − | 10.4696i | − | 0.384351i | ||||||
\(743\) | − | 18.2853i | − | 0.670823i | −0.942072 | − | 0.335412i | \(-0.891125\pi\) | ||
0.942072 | − | 0.335412i | \(-0.108875\pi\) | |||||||
\(744\) | 0.458691 | 0.0168164 | ||||||||
\(745\) | −26.2921 | − | 2.72553i | −0.963266 | − | 0.0998557i | ||||
\(746\) | −30.0257 | −1.09932 | ||||||||
\(747\) | − | 8.67547i | − | 0.317419i | ||||||
\(748\) | 1.57408i | 0.0575542i | ||||||||
\(749\) | −6.91382 | −0.252626 | ||||||||
\(750\) | −18.7413 | − | 6.00096i | −0.684336 | − | 0.219124i | ||||
\(751\) | 40.5425 | 1.47942 | 0.739708 | − | 0.672928i | \(-0.234963\pi\) | ||||
0.739708 | + | 0.672928i | \(0.234963\pi\) | |||||||
\(752\) | − | 19.6868i | − | 0.717903i | ||||||
\(753\) | − | 8.74303i | − | 0.318614i | ||||||
\(754\) | 66.5976 | 2.42534 | ||||||||
\(755\) | 37.3323 | + | 3.87001i | 1.35866 | + | 0.140844i | ||||
\(756\) | 1.09799 | 0.0399334 | ||||||||
\(757\) | 16.5593i | 0.601857i | 0.953647 | + | 0.300928i | \(0.0972965\pi\) | ||||
−0.953647 | + | 0.300928i | \(0.902703\pi\) | |||||||
\(758\) | − | 59.5055i | − | 2.16134i | ||||||
\(759\) | −2.64270 | −0.0959239 | ||||||||
\(760\) | −2.48269 | + | 23.9494i | −0.0900565 | + | 0.868738i | ||||
\(761\) | −37.4981 | −1.35930 | −0.679652 | − | 0.733534i | \(-0.737869\pi\) | ||||
−0.679652 | + | 0.733534i | \(0.737869\pi\) | |||||||
\(762\) | − | 21.0142i | − | 0.761266i | ||||||
\(763\) | − | 12.2807i | − | 0.444593i | ||||||
\(764\) | −17.0766 | −0.617808 | ||||||||
\(765\) | 0.330537 | − | 3.18856i | 0.0119506 | − | 0.115283i | ||||
\(766\) | 22.2494 | 0.803902 | ||||||||
\(767\) | − | 27.2054i | − | 0.982330i | ||||||
\(768\) | 19.8629i | 0.716739i | ||||||||
\(769\) | −0.466341 | −0.0168167 | −0.00840835 | − | 0.999965i | \(-0.502676\pi\) | ||||
−0.00840835 | + | 0.999965i | \(0.502676\pi\) | |||||||
\(770\) | −3.91475 | − | 0.405817i | −0.141078 | − | 0.0146246i | ||||
\(771\) | 20.9626 | 0.754950 | ||||||||
\(772\) | 21.9245i | 0.789078i | ||||||||
\(773\) | 15.0027i | 0.539608i | 0.962915 | + | 0.269804i | \(0.0869590\pi\) | ||||
−0.962915 | + | 0.269804i | \(0.913041\pi\) | |||||||
\(774\) | 14.4618 | 0.519817 | ||||||||
\(775\) | −1.41385 | − | 0.296314i | −0.0507870 | − | 0.0106439i | ||||
\(776\) | 24.5314 | 0.880626 | ||||||||
\(777\) | 10.7089i | 0.384180i | ||||||||
\(778\) | − | 5.11894i | − | 0.183523i | ||||||
\(779\) | 11.0020 | 0.394186 | ||||||||
\(780\) | 10.2925 | + | 1.06696i | 0.368530 | + | 0.0382031i | ||||
\(781\) | −15.0283 | −0.537756 | ||||||||
\(782\) | 6.66834i | 0.238459i | ||||||||
\(783\) | 8.97759i | 0.320833i | ||||||||
\(784\) | 4.99040 | 0.178229 | ||||||||
\(785\) | 1.43441 | − | 13.8372i | 0.0511964 | − | 0.493870i | ||||
\(786\) | 6.19401 | 0.220933 | ||||||||
\(787\) | − | 32.4641i | − | 1.15722i | −0.815604 | − | 0.578610i | \(-0.803595\pi\) | ||
0.815604 | − | 0.578610i | \(-0.196405\pi\) | |||||||
\(788\) | 16.5208i | 0.588530i | ||||||||
\(789\) | 6.30742 | 0.224550 | ||||||||
\(790\) | −0.280174 | + | 2.70272i | −0.00996813 | + | 0.0961584i | ||||
\(791\) | −9.86801 | −0.350866 | ||||||||
\(792\) | 1.58764i | 0.0564144i | ||||||||
\(793\) | 17.1791i | 0.610047i | ||||||||
\(794\) | 20.4703 | 0.726465 | ||||||||
\(795\) | 13.2298 | + | 1.37145i | 0.469214 | + | 0.0486404i | ||||
\(796\) | −6.86857 | −0.243450 | ||||||||
\(797\) | 13.9482i | 0.494072i | 0.969006 | + | 0.247036i | \(0.0794566\pi\) | ||||
−0.969006 | + | 0.247036i | \(0.920543\pi\) | |||||||
\(798\) | 11.9377i | 0.422588i | ||||||||
\(799\) | −5.65548 | −0.200077 | ||||||||
\(800\) | 5.75202 | − | 27.4456i | 0.203365 | − | 0.970347i | ||||
\(801\) | 16.3392 | 0.577317 | ||||||||
\(802\) | 39.4477i | 1.39295i | ||||||||
\(803\) | 8.54550i | 0.301564i | ||||||||
\(804\) | −13.5815 | −0.478983 | ||||||||
\(805\) | −5.87776 | − | 0.609310i | −0.207164 | − | 0.0214753i | ||||
\(806\) | 2.14322 | 0.0754917 | ||||||||
\(807\) | − | 24.8014i | − | 0.873049i | ||||||
\(808\) | 9.79309i | 0.344520i | ||||||||
\(809\) | −27.3872 | −0.962883 | −0.481442 | − | 0.876478i | \(-0.659887\pi\) | ||||
−0.481442 | + | 0.876478i | \(0.659887\pi\) | |||||||
\(810\) | −0.405817 | + | 3.91475i | −0.0142590 | + | 0.137550i | ||||
\(811\) | −17.7628 | −0.623736 | −0.311868 | − | 0.950125i | \(-0.600955\pi\) | ||||
−0.311868 | + | 0.950125i | \(0.600955\pi\) | |||||||
\(812\) | − | 9.85728i | − | 0.345923i | ||||||
\(813\) | 9.73698i | 0.341491i | ||||||||
\(814\) | 18.8488 | 0.660651 | ||||||||
\(815\) | −1.74047 | + | 16.7896i | −0.0609662 | + | 0.588115i | ||||
\(816\) | 7.15427 | 0.250450 | ||||||||
\(817\) | 55.7263i | 1.94962i | ||||||||
\(818\) | 21.9357i | 0.766963i | ||||||||
\(819\) | −4.21462 | −0.147271 | ||||||||
\(820\) | −3.96143 | − | 0.410657i | −0.138339 | − | 0.0143408i | ||||
\(821\) | 23.0623 | 0.804879 | 0.402440 | − | 0.915447i | \(-0.368162\pi\) | ||||
0.402440 | + | 0.915447i | \(0.368162\pi\) | |||||||
\(822\) | − | 14.5554i | − | 0.507677i | ||||||
\(823\) | − | 36.9625i | − | 1.28843i | −0.764844 | − | 0.644216i | \(-0.777184\pi\) | ||
0.764844 | − | 0.644216i | \(-0.222816\pi\) | |||||||
\(824\) | 13.3558 | 0.465272 | ||||||||
\(825\) | 1.02561 | − | 4.89368i | 0.0357073 | − | 0.170376i | ||||
\(826\) | −11.3615 | −0.395318 | ||||||||
\(827\) | − | 1.32975i | − | 0.0462398i | −0.999733 | − | 0.0231199i | \(-0.992640\pi\) | ||
0.999733 | − | 0.0231199i | \(-0.00735995\pi\) | |||||||
\(828\) | − | 2.90165i | − | 0.100839i | ||||||
\(829\) | −26.1935 | −0.909738 | −0.454869 | − | 0.890558i | \(-0.650314\pi\) | ||||
−0.454869 | + | 0.890558i | \(0.650314\pi\) | |||||||
\(830\) | −33.9623 | − | 3.52065i | −1.17885 | − | 0.122204i | ||||
\(831\) | −0.787221 | −0.0273084 | ||||||||
\(832\) | − | 0.461301i | − | 0.0159927i | ||||||
\(833\) | − | 1.43361i | − | 0.0496716i | ||||||
\(834\) | −27.5839 | −0.955153 | ||||||||
\(835\) | 1.89472 | − | 18.2776i | 0.0655696 | − | 0.632523i | ||||
\(836\) | 7.44692 | 0.257557 | ||||||||
\(837\) | 0.288914i | 0.00998632i | ||||||||
\(838\) | 12.6200i | 0.435950i | ||||||||
\(839\) | −14.9850 | −0.517340 | −0.258670 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258670 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(840\) | −0.366052 | + | 3.53115i | −0.0126300 | + | 0.121836i | ||||
\(841\) | 51.5971 | 1.77921 | ||||||||
\(842\) | 47.3345i | 1.63126i | ||||||||
\(843\) | 12.4309i | 0.428143i | ||||||||
\(844\) | −17.2861 | −0.595014 | ||||||||
\(845\) | −10.5937 | − | 1.09818i | −0.364436 | − | 0.0377787i | ||||
\(846\) | 6.94351 | 0.238723 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 29.6842i | 1.01936i | ||||||||
\(849\) | −2.09042 | −0.0717432 | ||||||||
\(850\) | −12.3483 | − | 2.58794i | −0.423542 | − | 0.0887656i | ||||
\(851\) | 28.3004 | 0.970125 | ||||||||
\(852\) | − | 16.5009i | − | 0.565312i | ||||||
\(853\) | 2.04939i | 0.0701697i | 0.999384 | + | 0.0350849i | \(0.0111702\pi\) | ||||
−0.999384 | + | 0.0350849i | \(0.988830\pi\) | |||||||
\(854\) | 7.17432 | 0.245500 | ||||||||
\(855\) | −15.0849 | − | 1.56376i | −0.515893 | − | 0.0534794i | ||||
\(856\) | 10.9767 | 0.375175 | ||||||||
\(857\) | − | 2.00984i | − | 0.0686550i | −0.999411 | − | 0.0343275i | \(-0.989071\pi\) | ||
0.999411 | − | 0.0343275i | \(-0.0109289\pi\) | |||||||
\(858\) | 7.41820i | 0.253253i | ||||||||
\(859\) | −40.9339 | −1.39665 | −0.698323 | − | 0.715782i | \(-0.746070\pi\) | ||||
−0.698323 | + | 0.715782i | \(0.746070\pi\) | |||||||
\(860\) | 2.08003 | − | 20.0652i | 0.0709283 | − | 0.684216i | ||||
\(861\) | 1.62215 | 0.0552827 | ||||||||
\(862\) | 14.1868i | 0.483205i | ||||||||
\(863\) | 48.3974i | 1.64747i | 0.566978 | + | 0.823733i | \(0.308112\pi\) | ||||
−0.566978 | + | 0.823733i | \(0.691888\pi\) | |||||||
\(864\) | −5.60837 | −0.190801 | ||||||||
\(865\) | −3.39998 | + | 32.7982i | −0.115603 | + | 1.11517i | ||||
\(866\) | 25.5125 | 0.866949 | ||||||||
\(867\) | 14.9448i | 0.507551i | ||||||||
\(868\) | − | 0.317224i | − | 0.0107673i | ||||||
\(869\) | −0.690394 | −0.0234200 | ||||||||
\(870\) | 35.1450 | + | 3.64326i | 1.19153 | + | 0.123518i | ||||
\(871\) | 52.1326 | 1.76645 | ||||||||
\(872\) | 19.4974i | 0.660265i | ||||||||
\(873\) | 15.4515i | 0.522953i | ||||||||
\(874\) | 31.5476 | 1.06711 | ||||||||
\(875\) | 3.40942 | − | 10.6478i | 0.115260 | − | 0.359962i | ||||
\(876\) | −9.38286 | −0.317017 | ||||||||
\(877\) | 0.951733i | 0.0321377i | 0.999871 | + | 0.0160689i | \(0.00511510\pi\) | ||||
−0.999871 | + | 0.0160689i | \(0.994885\pi\) | |||||||
\(878\) | − | 7.54514i | − | 0.254636i | ||||||
\(879\) | 10.4989 | 0.354119 | ||||||||
\(880\) | 11.0994 | + | 1.15060i | 0.374160 | + | 0.0387868i | ||||
\(881\) | −37.9056 | −1.27707 | −0.638535 | − | 0.769593i | \(-0.720459\pi\) | ||||
−0.638535 | + | 0.769593i | \(0.720459\pi\) | |||||||
\(882\) | 1.76011i | 0.0592660i | ||||||||
\(883\) | − | 41.8084i | − | 1.40696i | −0.710713 | − | 0.703482i | \(-0.751628\pi\) | ||
0.710713 | − | 0.703482i | \(-0.248372\pi\) | |||||||
\(884\) | 6.63417 | 0.223131 | ||||||||
\(885\) | 1.48829 | − | 14.3569i | 0.0500282 | − | 0.482601i | ||||
\(886\) | −8.50929 | −0.285875 | ||||||||
\(887\) | 23.7956i | 0.798979i | 0.916738 | + | 0.399490i | \(0.130813\pi\) | ||||
−0.916738 | + | 0.399490i | \(0.869187\pi\) | |||||||
\(888\) | − | 17.0019i | − | 0.570546i | ||||||
\(889\) | 11.9392 | 0.400427 | ||||||||
\(890\) | 6.63072 | − | 63.9638i | 0.222262 | − | 2.14407i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 10.9824i | 0.367717i | ||||||||
\(893\) | 26.7558i | 0.895350i | ||||||||
\(894\) | 20.8066 | 0.695876 | ||||||||
\(895\) | 1.01252 | + | 0.104962i | 0.0338449 | + | 0.00350849i | ||||
\(896\) | −11.4094 | −0.381161 | ||||||||
\(897\) | 11.1380i | 0.371887i | ||||||||
\(898\) | − | 62.9915i | − | 2.10205i | ||||||
\(899\) | 2.59375 | 0.0865063 | ||||||||
\(900\) | 5.37320 | + | 1.12611i | 0.179107 | + | 0.0375371i | ||||
\(901\) | 8.52748 | 0.284091 | ||||||||
\(902\) | − | 2.85516i | − | 0.0950665i | ||||||
\(903\) | 8.21640i | 0.273425i | ||||||||
\(904\) | 15.6669 | 0.521072 | ||||||||
\(905\) | 17.9538 | + | 1.86116i | 0.596806 | + | 0.0618670i | ||||
\(906\) | −29.5434 | −0.981515 | ||||||||
\(907\) | − | 43.3339i | − | 1.43888i | −0.694556 | − | 0.719439i | \(-0.744399\pi\) | ||
0.694556 | − | 0.719439i | \(-0.255601\pi\) | |||||||
\(908\) | − | 17.4140i | − | 0.577904i | ||||||
\(909\) | −6.16833 | −0.204591 | ||||||||
\(910\) | −1.71037 | + | 16.4992i | −0.0566981 | + | 0.546943i | ||||
\(911\) | 3.13409 | 0.103837 | 0.0519185 | − | 0.998651i | \(-0.483466\pi\) | ||||
0.0519185 | + | 0.998651i | \(0.483466\pi\) | |||||||
\(912\) | − | 33.8465i | − | 1.12077i | ||||||
\(913\) | − | 8.67547i | − | 0.287116i | ||||||
\(914\) | 27.5568 | 0.911497 | ||||||||
\(915\) | −0.939791 | + | 9.06577i | −0.0310685 | + | 0.299705i | ||||
\(916\) | 25.4428 | 0.840654 | ||||||||
\(917\) | 3.51910i | 0.116211i | ||||||||
\(918\) | 2.52331i | 0.0832815i | ||||||||
\(919\) | 19.9236 | 0.657219 | 0.328610 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328610 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(920\) | 9.33177 | + | 0.967365i | 0.307660 | + | 0.0318931i | ||||
\(921\) | −26.9278 | −0.887302 | ||||||||
\(922\) | − | 67.1982i | − | 2.21305i | ||||||
\(923\) | 63.3388i | 2.08482i | ||||||||
\(924\) | 1.09799 | 0.0361211 | ||||||||
\(925\) | −10.9832 | + | 52.4059i | −0.361125 | + | 1.72310i | ||||
\(926\) | 23.6495 | 0.777171 | ||||||||
\(927\) | 8.41237i | 0.276299i | ||||||||
\(928\) | 50.3496i | 1.65281i | ||||||||
\(929\) | 36.3569 | 1.19283 | 0.596415 | − | 0.802676i | \(-0.296591\pi\) | ||||
0.596415 | + | 0.802676i | \(0.296591\pi\) | |||||||
\(930\) | 1.13102 | + | 0.117246i | 0.0370877 | + | 0.00384465i | ||||
\(931\) | −6.78233 | −0.222282 | ||||||||
\(932\) | − | 20.3332i | − | 0.666035i | ||||||
\(933\) | 15.0673i | 0.493283i | ||||||||
\(934\) | 66.0416 | 2.16095 | ||||||||
\(935\) | 0.330537 | − | 3.18856i | 0.0108097 | − | 0.104277i | ||||
\(936\) | 6.69131 | 0.218712 | ||||||||
\(937\) | 33.4114i | 1.09150i | 0.837947 | + | 0.545752i | \(0.183756\pi\) | ||||
−0.837947 | + | 0.545752i | \(0.816244\pi\) | |||||||
\(938\) | − | 21.7716i | − | 0.710869i | ||||||
\(939\) | −23.5904 | −0.769844 | ||||||||
\(940\) | 0.998681 | − | 9.63387i | 0.0325734 | − | 0.314222i | ||||
\(941\) | 53.7688 | 1.75281 | 0.876406 | − | 0.481572i | \(-0.159934\pi\) | ||||
0.876406 | + | 0.481572i | \(0.159934\pi\) | |||||||
\(942\) | 10.9502i | 0.356778i | ||||||||
\(943\) | − | 4.28686i | − | 0.139599i | ||||||
\(944\) | 32.2130 | 1.04844 | ||||||||
\(945\) | −2.22415 | − | 0.230563i | −0.0723516 | − | 0.00750023i | ||||
\(946\) | 14.4618 | 0.470192 | ||||||||
\(947\) | 22.0800i | 0.717504i | 0.933433 | + | 0.358752i | \(0.116798\pi\) | ||||
−0.933433 | + | 0.358752i | \(0.883202\pi\) | |||||||
\(948\) | − | 0.758044i | − | 0.0246201i | ||||||
\(949\) | 36.0161 | 1.16913 | ||||||||
\(950\) | −12.2434 | + | 58.4191i | −0.397229 | + | 1.89536i | ||||
\(951\) | −24.0122 | −0.778649 | ||||||||
\(952\) | 2.27605i | 0.0737674i | ||||||||
\(953\) | − | 14.4516i | − | 0.468134i | −0.972221 | − | 0.234067i | \(-0.924797\pi\) | ||
0.972221 | − | 0.234067i | \(-0.0752035\pi\) | |||||||
\(954\) | −10.4696 | −0.338966 | ||||||||
\(955\) | 34.5913 | + | 3.58586i | 1.11935 | + | 0.116036i | ||||
\(956\) | −30.9437 | −1.00079 | ||||||||
\(957\) | 8.97759i | 0.290204i | ||||||||
\(958\) | 34.6439i | 1.11929i | ||||||||
\(959\) | 8.26959 | 0.267039 | ||||||||
\(960\) | 0.0252357 | − | 0.243439i | 0.000814479 | − | 0.00785694i | ||||
\(961\) | −30.9165 | −0.997307 | ||||||||
\(962\) | − | 79.4408i | − | 2.56127i | ||||||
\(963\) | 6.91382i | 0.222795i | ||||||||
\(964\) | 7.77493 | 0.250414 | ||||||||
\(965\) | 4.60386 | − | 44.4115i | 0.148203 | − | 1.42966i | ||||
\(966\) | 4.65144 | 0.149658 | ||||||||
\(967\) | − | 42.3008i | − | 1.36030i | −0.733072 | − | 0.680152i | \(-0.761914\pi\) | ||
0.733072 | − | 0.680152i | \(-0.238086\pi\) | |||||||
\(968\) | 1.58764i | 0.0510287i | ||||||||
\(969\) | −9.72320 | −0.312354 | ||||||||
\(970\) | 60.4886 | + | 6.27047i | 1.94217 | + | 0.201333i | ||||
\(971\) | −30.0533 | −0.964457 | −0.482229 | − | 0.876045i | \(-0.660173\pi\) | ||||
−0.482229 | + | 0.876045i | \(0.660173\pi\) | |||||||
\(972\) | − | 1.09799i | − | 0.0352180i | ||||||
\(973\) | − | 15.6717i | − | 0.502412i | ||||||
\(974\) | −43.2798 | −1.38677 | ||||||||
\(975\) | −20.6250 | − | 4.32258i | −0.660529 | − | 0.138433i | ||||
\(976\) | −20.3412 | −0.651105 | ||||||||
\(977\) | − | 11.9074i | − | 0.380952i | −0.981692 | − | 0.190476i | \(-0.938997\pi\) | ||
0.981692 | − | 0.190476i | \(-0.0610031\pi\) | |||||||
\(978\) | − | 13.2867i | − | 0.424862i | ||||||
\(979\) | 16.3392 | 0.522203 | ||||||||
\(980\) | 2.44209 | + | 0.253156i | 0.0780096 | + | 0.00808676i | ||||
\(981\) | −12.2807 | −0.392094 | ||||||||
\(982\) | 56.4650i | 1.80187i | ||||||||
\(983\) | − | 23.1043i | − | 0.736913i | −0.929645 | − | 0.368456i | \(-0.879886\pi\) | ||
0.929645 | − | 0.368456i | \(-0.120114\pi\) | |||||||
\(984\) | −2.57539 | −0.0821005 | ||||||||
\(985\) | 3.46916 | − | 33.4656i | 0.110537 | − | 1.06630i | ||||
\(986\) | 22.6532 | 0.721425 | ||||||||
\(987\) | 3.94493i | 0.125568i | ||||||||
\(988\) | − | 31.3859i | − | 0.998520i | ||||||
\(989\) | 21.7135 | 0.690448 | ||||||||
\(990\) | −0.405817 | + | 3.91475i | −0.0128977 | + | 0.124419i | ||||
\(991\) | 20.8358 | 0.661871 | 0.330936 | − | 0.943653i | \(-0.392636\pi\) | ||||
0.330936 | + | 0.943653i | \(0.392636\pi\) | |||||||
\(992\) | 1.62033i | 0.0514457i | ||||||||
\(993\) | − | 21.5409i | − | 0.683580i | ||||||
\(994\) | 26.4515 | 0.838991 | ||||||||
\(995\) | 13.9134 | + | 1.44231i | 0.441084 | + | 0.0457244i | ||||
\(996\) | 9.52555 | 0.301829 | ||||||||
\(997\) | 53.0422i | 1.67986i | 0.542693 | + | 0.839931i | \(0.317405\pi\) | ||||
−0.542693 | + | 0.839931i | \(0.682595\pi\) | |||||||
\(998\) | 74.8739i | 2.37009i | ||||||||
\(999\) | 10.7089 | 0.338815 |
(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 | 1155.2.c.e.694.15 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cp.1.3 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cm.1.8 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.6 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.e.694.15 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cm.1.8 | 10 | 5.3 | odd | 4 | |||
5775.2.a.cp.1.3 | 10 | 5.2 | odd | 4 |