Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
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: | yes |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 9x^{7} + 29x^{6} + 23x^{5} - 84x^{4} - 23x^{3} + 89x^{2} + 8x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.92391\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92391 | 1.36041 | 0.680205 | − | 0.733022i | \(-0.261891\pi\) | ||||
0.680205 | + | 0.733022i | \(0.261891\pi\) | |||||||
\(3\) | 0.621031 | 0.358552 | 0.179276 | − | 0.983799i | \(-0.442624\pi\) | ||||
0.179276 | + | 0.983799i | \(0.442624\pi\) | |||||||
\(4\) | 1.70143 | 0.850715 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.19481 | 0.487778 | ||||||||
\(7\) | 5.15278 | 1.94757 | 0.973785 | − | 0.227471i | \(-0.0730458\pi\) | ||||
0.973785 | + | 0.227471i | \(0.0730458\pi\) | |||||||
\(8\) | −0.574421 | −0.203088 | ||||||||
\(9\) | −2.61432 | −0.871440 | ||||||||
\(10\) | 1.92391 | 0.608394 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.05664 | 0.305026 | ||||||||
\(13\) | 0.138167 | 0.0383206 | 0.0191603 | − | 0.999816i | \(-0.493901\pi\) | ||||
0.0191603 | + | 0.999816i | \(0.493901\pi\) | |||||||
\(14\) | 9.91350 | 2.64949 | ||||||||
\(15\) | 0.621031 | 0.160350 | ||||||||
\(16\) | −4.50800 | −1.12700 | ||||||||
\(17\) | 1.86183 | 0.451561 | 0.225780 | − | 0.974178i | \(-0.427507\pi\) | ||||
0.225780 | + | 0.974178i | \(0.427507\pi\) | |||||||
\(18\) | −5.02972 | −1.18552 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.70143 | 0.380451 | ||||||||
\(21\) | 3.20004 | 0.698306 | ||||||||
\(22\) | 1.92391 | 0.410179 | ||||||||
\(23\) | 0.167646 | 0.0349567 | 0.0174783 | − | 0.999847i | \(-0.494436\pi\) | ||||
0.0174783 | + | 0.999847i | \(0.494436\pi\) | |||||||
\(24\) | −0.356733 | −0.0728178 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.265820 | 0.0521317 | ||||||||
\(27\) | −3.48667 | −0.671009 | ||||||||
\(28\) | 8.76711 | 1.65683 | ||||||||
\(29\) | 4.80913 | 0.893033 | 0.446516 | − | 0.894775i | \(-0.352664\pi\) | ||||
0.446516 | + | 0.894775i | \(0.352664\pi\) | |||||||
\(30\) | 1.19481 | 0.218141 | ||||||||
\(31\) | −1.73000 | −0.310718 | −0.155359 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155359 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(32\) | −7.52414 | −1.33009 | ||||||||
\(33\) | 0.621031 | 0.108108 | ||||||||
\(34\) | 3.58200 | 0.614308 | ||||||||
\(35\) | 5.15278 | 0.870980 | ||||||||
\(36\) | −4.44808 | −0.741347 | ||||||||
\(37\) | 0.442598 | 0.0727626 | 0.0363813 | − | 0.999338i | \(-0.488417\pi\) | ||||
0.0363813 | + | 0.999338i | \(0.488417\pi\) | |||||||
\(38\) | 1.92391 | 0.312099 | ||||||||
\(39\) | 0.0858058 | 0.0137399 | ||||||||
\(40\) | −0.574421 | −0.0908239 | ||||||||
\(41\) | −12.1984 | −1.90506 | −0.952532 | − | 0.304437i | \(-0.901532\pi\) | ||||
−0.952532 | + | 0.304437i | \(0.901532\pi\) | |||||||
\(42\) | 6.15659 | 0.949982 | ||||||||
\(43\) | −8.67909 | −1.32355 | −0.661774 | − | 0.749703i | \(-0.730196\pi\) | ||||
−0.661774 | + | 0.749703i | \(0.730196\pi\) | |||||||
\(44\) | 1.70143 | 0.256500 | ||||||||
\(45\) | −2.61432 | −0.389720 | ||||||||
\(46\) | 0.322537 | 0.0475554 | ||||||||
\(47\) | 2.21857 | 0.323611 | 0.161806 | − | 0.986823i | \(-0.448268\pi\) | ||||
0.161806 | + | 0.986823i | \(0.448268\pi\) | |||||||
\(48\) | −2.79960 | −0.404088 | ||||||||
\(49\) | 19.5512 | 2.79303 | ||||||||
\(50\) | 1.92391 | 0.272082 | ||||||||
\(51\) | 1.15626 | 0.161908 | ||||||||
\(52\) | 0.235081 | 0.0325999 | ||||||||
\(53\) | 1.34355 | 0.184550 | 0.0922751 | − | 0.995734i | \(-0.470586\pi\) | ||||
0.0922751 | + | 0.995734i | \(0.470586\pi\) | |||||||
\(54\) | −6.70803 | −0.912848 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −2.95987 | −0.395529 | ||||||||
\(57\) | 0.621031 | 0.0822576 | ||||||||
\(58\) | 9.25233 | 1.21489 | ||||||||
\(59\) | 3.15592 | 0.410866 | 0.205433 | − | 0.978671i | \(-0.434140\pi\) | ||||
0.205433 | + | 0.978671i | \(0.434140\pi\) | |||||||
\(60\) | 1.05664 | 0.136412 | ||||||||
\(61\) | 1.90706 | 0.244174 | 0.122087 | − | 0.992519i | \(-0.461041\pi\) | ||||
0.122087 | + | 0.992519i | \(0.461041\pi\) | |||||||
\(62\) | −3.32837 | −0.422703 | ||||||||
\(63\) | −13.4710 | −1.69719 | ||||||||
\(64\) | −5.45977 | −0.682472 | ||||||||
\(65\) | 0.138167 | 0.0171375 | ||||||||
\(66\) | 1.19481 | 0.147071 | ||||||||
\(67\) | −10.7534 | −1.31373 | −0.656867 | − | 0.754007i | \(-0.728119\pi\) | ||||
−0.656867 | + | 0.754007i | \(0.728119\pi\) | |||||||
\(68\) | 3.16778 | 0.384150 | ||||||||
\(69\) | 0.104114 | 0.0125338 | ||||||||
\(70\) | 9.91350 | 1.18489 | ||||||||
\(71\) | 11.2883 | 1.33968 | 0.669840 | − | 0.742505i | \(-0.266363\pi\) | ||||
0.669840 | + | 0.742505i | \(0.266363\pi\) | |||||||
\(72\) | 1.50172 | 0.176979 | ||||||||
\(73\) | −9.78050 | −1.14472 | −0.572361 | − | 0.820002i | \(-0.693972\pi\) | ||||
−0.572361 | + | 0.820002i | \(0.693972\pi\) | |||||||
\(74\) | 0.851518 | 0.0989870 | ||||||||
\(75\) | 0.621031 | 0.0717105 | ||||||||
\(76\) | 1.70143 | 0.195167 | ||||||||
\(77\) | 5.15278 | 0.587214 | ||||||||
\(78\) | 0.165083 | 0.0186919 | ||||||||
\(79\) | −6.14010 | −0.690816 | −0.345408 | − | 0.938453i | \(-0.612259\pi\) | ||||
−0.345408 | + | 0.938453i | \(0.612259\pi\) | |||||||
\(80\) | −4.50800 | −0.504009 | ||||||||
\(81\) | 5.67763 | 0.630848 | ||||||||
\(82\) | −23.4686 | −2.59167 | ||||||||
\(83\) | −0.190459 | −0.0209056 | −0.0104528 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104528 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(84\) | 5.44464 | 0.594059 | ||||||||
\(85\) | 1.86183 | 0.201944 | ||||||||
\(86\) | −16.6978 | −1.80057 | ||||||||
\(87\) | 2.98662 | 0.320199 | ||||||||
\(88\) | −0.574421 | −0.0612335 | ||||||||
\(89\) | −8.94416 | −0.948079 | −0.474040 | − | 0.880504i | \(-0.657205\pi\) | ||||
−0.474040 | + | 0.880504i | \(0.657205\pi\) | |||||||
\(90\) | −5.02972 | −0.530179 | ||||||||
\(91\) | 0.711944 | 0.0746320 | ||||||||
\(92\) | 0.285239 | 0.0297382 | ||||||||
\(93\) | −1.07439 | −0.111409 | ||||||||
\(94\) | 4.26832 | 0.440244 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | −4.67272 | −0.476908 | ||||||||
\(97\) | 6.74261 | 0.684609 | 0.342304 | − | 0.939589i | \(-0.388793\pi\) | ||||
0.342304 | + | 0.939589i | \(0.388793\pi\) | |||||||
\(98\) | 37.6147 | 3.79966 | ||||||||
\(99\) | −2.61432 | −0.262749 | ||||||||
\(100\) | 1.70143 | 0.170143 | ||||||||
\(101\) | 2.79639 | 0.278251 | 0.139126 | − | 0.990275i | \(-0.455571\pi\) | ||||
0.139126 | + | 0.990275i | \(0.455571\pi\) | |||||||
\(102\) | 2.22453 | 0.220262 | ||||||||
\(103\) | −7.49046 | −0.738057 | −0.369028 | − | 0.929418i | \(-0.620309\pi\) | ||||
−0.369028 | + | 0.929418i | \(0.620309\pi\) | |||||||
\(104\) | −0.0793659 | −0.00778246 | ||||||||
\(105\) | 3.20004 | 0.312292 | ||||||||
\(106\) | 2.58486 | 0.251064 | ||||||||
\(107\) | 3.26297 | 0.315443 | 0.157722 | − | 0.987484i | \(-0.449585\pi\) | ||||
0.157722 | + | 0.987484i | \(0.449585\pi\) | |||||||
\(108\) | −5.93232 | −0.570838 | ||||||||
\(109\) | 1.46274 | 0.140105 | 0.0700526 | − | 0.997543i | \(-0.477683\pi\) | ||||
0.0700526 | + | 0.997543i | \(0.477683\pi\) | |||||||
\(110\) | 1.92391 | 0.183438 | ||||||||
\(111\) | 0.274867 | 0.0260892 | ||||||||
\(112\) | −23.2287 | −2.19491 | ||||||||
\(113\) | 8.58423 | 0.807537 | 0.403768 | − | 0.914861i | \(-0.367700\pi\) | ||||
0.403768 | + | 0.914861i | \(0.367700\pi\) | |||||||
\(114\) | 1.19481 | 0.111904 | ||||||||
\(115\) | 0.167646 | 0.0156331 | ||||||||
\(116\) | 8.18240 | 0.759717 | ||||||||
\(117\) | −0.361212 | −0.0333941 | ||||||||
\(118\) | 6.07171 | 0.558946 | ||||||||
\(119\) | 9.59363 | 0.879446 | ||||||||
\(120\) | −0.356733 | −0.0325651 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.66901 | 0.332176 | ||||||||
\(123\) | −7.57556 | −0.683066 | ||||||||
\(124\) | −2.94348 | −0.264332 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −25.9171 | −2.30887 | ||||||||
\(127\) | −4.66887 | −0.414295 | −0.207148 | − | 0.978310i | \(-0.566418\pi\) | ||||
−0.207148 | + | 0.978310i | \(0.566418\pi\) | |||||||
\(128\) | 4.54416 | 0.401651 | ||||||||
\(129\) | −5.38998 | −0.474561 | ||||||||
\(130\) | 0.265820 | 0.0233140 | ||||||||
\(131\) | 0.940241 | 0.0821492 | 0.0410746 | − | 0.999156i | \(-0.486922\pi\) | ||||
0.0410746 | + | 0.999156i | \(0.486922\pi\) | |||||||
\(132\) | 1.05664 | 0.0919688 | ||||||||
\(133\) | 5.15278 | 0.446803 | ||||||||
\(134\) | −20.6885 | −1.78722 | ||||||||
\(135\) | −3.48667 | −0.300085 | ||||||||
\(136\) | −1.06948 | −0.0917068 | ||||||||
\(137\) | −12.8192 | −1.09522 | −0.547610 | − | 0.836734i | \(-0.684462\pi\) | ||||
−0.547610 | + | 0.836734i | \(0.684462\pi\) | |||||||
\(138\) | 0.200305 | 0.0170511 | ||||||||
\(139\) | −20.5940 | −1.74676 | −0.873379 | − | 0.487042i | \(-0.838076\pi\) | ||||
−0.873379 | + | 0.487042i | \(0.838076\pi\) | |||||||
\(140\) | 8.76711 | 0.740956 | ||||||||
\(141\) | 1.37780 | 0.116032 | ||||||||
\(142\) | 21.7178 | 1.82251 | ||||||||
\(143\) | 0.138167 | 0.0115541 | ||||||||
\(144\) | 11.7853 | 0.982112 | ||||||||
\(145\) | 4.80913 | 0.399376 | ||||||||
\(146\) | −18.8168 | −1.55729 | ||||||||
\(147\) | 12.1419 | 1.00145 | ||||||||
\(148\) | 0.753049 | 0.0619003 | ||||||||
\(149\) | 19.5366 | 1.60050 | 0.800250 | − | 0.599666i | \(-0.204700\pi\) | ||||
0.800250 | + | 0.599666i | \(0.204700\pi\) | |||||||
\(150\) | 1.19481 | 0.0975556 | ||||||||
\(151\) | −13.4871 | −1.09756 | −0.548781 | − | 0.835966i | \(-0.684908\pi\) | ||||
−0.548781 | + | 0.835966i | \(0.684908\pi\) | |||||||
\(152\) | −0.574421 | −0.0465917 | ||||||||
\(153\) | −4.86743 | −0.393508 | ||||||||
\(154\) | 9.91350 | 0.798852 | ||||||||
\(155\) | −1.73000 | −0.138957 | ||||||||
\(156\) | 0.145993 | 0.0116888 | ||||||||
\(157\) | −6.15820 | −0.491478 | −0.245739 | − | 0.969336i | \(-0.579031\pi\) | ||||
−0.245739 | + | 0.969336i | \(0.579031\pi\) | |||||||
\(158\) | −11.8130 | −0.939793 | ||||||||
\(159\) | 0.834384 | 0.0661709 | ||||||||
\(160\) | −7.52414 | −0.594835 | ||||||||
\(161\) | 0.863846 | 0.0680806 | ||||||||
\(162\) | 10.9233 | 0.858212 | ||||||||
\(163\) | −15.7457 | −1.23330 | −0.616649 | − | 0.787238i | \(-0.711510\pi\) | ||||
−0.616649 | + | 0.787238i | \(0.711510\pi\) | |||||||
\(164\) | −20.7547 | −1.62067 | ||||||||
\(165\) | 0.621031 | 0.0483472 | ||||||||
\(166\) | −0.366426 | −0.0284402 | ||||||||
\(167\) | −1.49742 | −0.115874 | −0.0579369 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579369 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(168\) | −1.83817 | −0.141818 | ||||||||
\(169\) | −12.9809 | −0.998532 | ||||||||
\(170\) | 3.58200 | 0.274727 | ||||||||
\(171\) | −2.61432 | −0.199922 | ||||||||
\(172\) | −14.7669 | −1.12596 | ||||||||
\(173\) | −25.3734 | −1.92910 | −0.964550 | − | 0.263898i | \(-0.914992\pi\) | ||||
−0.964550 | + | 0.263898i | \(0.914992\pi\) | |||||||
\(174\) | 5.74598 | 0.435602 | ||||||||
\(175\) | 5.15278 | 0.389514 | ||||||||
\(176\) | −4.50800 | −0.339803 | ||||||||
\(177\) | 1.95992 | 0.147317 | ||||||||
\(178\) | −17.2078 | −1.28978 | ||||||||
\(179\) | −1.45676 | −0.108883 | −0.0544416 | − | 0.998517i | \(-0.517338\pi\) | ||||
−0.0544416 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(180\) | −4.44808 | −0.331541 | ||||||||
\(181\) | −10.1387 | −0.753605 | −0.376803 | − | 0.926294i | \(-0.622976\pi\) | ||||
−0.376803 | + | 0.926294i | \(0.622976\pi\) | |||||||
\(182\) | 1.36972 | 0.101530 | ||||||||
\(183\) | 1.18434 | 0.0875490 | ||||||||
\(184\) | −0.0962996 | −0.00709930 | ||||||||
\(185\) | 0.442598 | 0.0325404 | ||||||||
\(186\) | −2.06702 | −0.151561 | ||||||||
\(187\) | 1.86183 | 0.136151 | ||||||||
\(188\) | 3.77474 | 0.275301 | ||||||||
\(189\) | −17.9660 | −1.30684 | ||||||||
\(190\) | 1.92391 | 0.139575 | ||||||||
\(191\) | −8.99086 | −0.650556 | −0.325278 | − | 0.945619i | \(-0.605458\pi\) | ||||
−0.325278 | + | 0.945619i | \(0.605458\pi\) | |||||||
\(192\) | −3.39069 | −0.244702 | ||||||||
\(193\) | −4.44729 | −0.320123 | −0.160061 | − | 0.987107i | \(-0.551169\pi\) | ||||
−0.160061 | + | 0.987107i | \(0.551169\pi\) | |||||||
\(194\) | 12.9722 | 0.931348 | ||||||||
\(195\) | 0.0858058 | 0.00614468 | ||||||||
\(196\) | 33.2650 | 2.37607 | ||||||||
\(197\) | 21.9424 | 1.56333 | 0.781664 | − | 0.623699i | \(-0.214371\pi\) | ||||
0.781664 | + | 0.623699i | \(0.214371\pi\) | |||||||
\(198\) | −5.02972 | −0.357446 | ||||||||
\(199\) | 13.7659 | 0.975840 | 0.487920 | − | 0.872888i | \(-0.337756\pi\) | ||||
0.487920 | + | 0.872888i | \(0.337756\pi\) | |||||||
\(200\) | −0.574421 | −0.0406177 | ||||||||
\(201\) | −6.67818 | −0.471042 | ||||||||
\(202\) | 5.38000 | 0.378536 | ||||||||
\(203\) | 24.7804 | 1.73924 | ||||||||
\(204\) | 1.96729 | 0.137738 | ||||||||
\(205\) | −12.1984 | −0.851971 | ||||||||
\(206\) | −14.4110 | −1.00406 | ||||||||
\(207\) | −0.438282 | −0.0304627 | ||||||||
\(208\) | −0.622855 | −0.0431872 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 6.15659 | 0.424845 | ||||||||
\(211\) | −21.5479 | −1.48342 | −0.741710 | − | 0.670721i | \(-0.765985\pi\) | ||||
−0.741710 | + | 0.670721i | \(0.765985\pi\) | |||||||
\(212\) | 2.28595 | 0.157000 | ||||||||
\(213\) | 7.01041 | 0.480346 | ||||||||
\(214\) | 6.27766 | 0.429132 | ||||||||
\(215\) | −8.67909 | −0.591909 | ||||||||
\(216\) | 2.00281 | 0.136274 | ||||||||
\(217\) | −8.91433 | −0.605144 | ||||||||
\(218\) | 2.81418 | 0.190600 | ||||||||
\(219\) | −6.07399 | −0.410442 | ||||||||
\(220\) | 1.70143 | 0.114710 | ||||||||
\(221\) | 0.257243 | 0.0173041 | ||||||||
\(222\) | 0.528819 | 0.0354920 | ||||||||
\(223\) | 25.5722 | 1.71244 | 0.856221 | − | 0.516610i | \(-0.172806\pi\) | ||||
0.856221 | + | 0.516610i | \(0.172806\pi\) | |||||||
\(224\) | −38.7703 | −2.59045 | ||||||||
\(225\) | −2.61432 | −0.174288 | ||||||||
\(226\) | 16.5153 | 1.09858 | ||||||||
\(227\) | 9.06540 | 0.601692 | 0.300846 | − | 0.953673i | \(-0.402731\pi\) | ||||
0.300846 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(228\) | 1.05664 | 0.0699778 | ||||||||
\(229\) | 27.5774 | 1.82236 | 0.911182 | − | 0.412005i | \(-0.135171\pi\) | ||||
0.911182 | + | 0.412005i | \(0.135171\pi\) | |||||||
\(230\) | 0.322537 | 0.0212674 | ||||||||
\(231\) | 3.20004 | 0.210547 | ||||||||
\(232\) | −2.76246 | −0.181365 | ||||||||
\(233\) | 13.5037 | 0.884654 | 0.442327 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442327 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(234\) | −0.694940 | −0.0454296 | ||||||||
\(235\) | 2.21857 | 0.144723 | ||||||||
\(236\) | 5.36958 | 0.349530 | ||||||||
\(237\) | −3.81319 | −0.247694 | ||||||||
\(238\) | 18.4573 | 1.19641 | ||||||||
\(239\) | 2.50739 | 0.162190 | 0.0810949 | − | 0.996706i | \(-0.474158\pi\) | ||||
0.0810949 | + | 0.996706i | \(0.474158\pi\) | |||||||
\(240\) | −2.79960 | −0.180714 | ||||||||
\(241\) | 24.4676 | 1.57610 | 0.788050 | − | 0.615611i | \(-0.211091\pi\) | ||||
0.788050 | + | 0.615611i | \(0.211091\pi\) | |||||||
\(242\) | 1.92391 | 0.123674 | ||||||||
\(243\) | 13.9860 | 0.897201 | ||||||||
\(244\) | 3.24472 | 0.207722 | ||||||||
\(245\) | 19.5512 | 1.24908 | ||||||||
\(246\) | −14.5747 | −0.929249 | ||||||||
\(247\) | 0.138167 | 0.00879134 | ||||||||
\(248\) | 0.993750 | 0.0631032 | ||||||||
\(249\) | −0.118281 | −0.00749576 | ||||||||
\(250\) | 1.92391 | 0.121679 | ||||||||
\(251\) | −9.98514 | −0.630256 | −0.315128 | − | 0.949049i | \(-0.602048\pi\) | ||||
−0.315128 | + | 0.949049i | \(0.602048\pi\) | |||||||
\(252\) | −22.9200 | −1.44383 | ||||||||
\(253\) | 0.167646 | 0.0105398 | ||||||||
\(254\) | −8.98249 | −0.563612 | ||||||||
\(255\) | 1.15626 | 0.0724076 | ||||||||
\(256\) | 19.6621 | 1.22888 | ||||||||
\(257\) | −23.5112 | −1.46659 | −0.733294 | − | 0.679912i | \(-0.762018\pi\) | ||||
−0.733294 | + | 0.679912i | \(0.762018\pi\) | |||||||
\(258\) | −10.3698 | −0.645598 | ||||||||
\(259\) | 2.28061 | 0.141710 | ||||||||
\(260\) | 0.235081 | 0.0145791 | ||||||||
\(261\) | −12.5726 | −0.778225 | ||||||||
\(262\) | 1.80894 | 0.111757 | ||||||||
\(263\) | 22.8248 | 1.40744 | 0.703720 | − | 0.710478i | \(-0.251521\pi\) | ||||
0.703720 | + | 0.710478i | \(0.251521\pi\) | |||||||
\(264\) | −0.356733 | −0.0219554 | ||||||||
\(265\) | 1.34355 | 0.0825334 | ||||||||
\(266\) | 9.91350 | 0.607835 | ||||||||
\(267\) | −5.55460 | −0.339936 | ||||||||
\(268\) | −18.2961 | −1.11761 | ||||||||
\(269\) | 18.7957 | 1.14599 | 0.572997 | − | 0.819557i | \(-0.305781\pi\) | ||||
0.572997 | + | 0.819557i | \(0.305781\pi\) | |||||||
\(270\) | −6.70803 | −0.408238 | ||||||||
\(271\) | 11.0978 | 0.674146 | 0.337073 | − | 0.941479i | \(-0.390563\pi\) | ||||
0.337073 | + | 0.941479i | \(0.390563\pi\) | |||||||
\(272\) | −8.39314 | −0.508909 | ||||||||
\(273\) | 0.442139 | 0.0267595 | ||||||||
\(274\) | −24.6630 | −1.48995 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.177142 | 0.0106627 | ||||||||
\(277\) | 27.1795 | 1.63306 | 0.816529 | − | 0.577305i | \(-0.195896\pi\) | ||||
0.816529 | + | 0.577305i | \(0.195896\pi\) | |||||||
\(278\) | −39.6209 | −2.37631 | ||||||||
\(279\) | 4.52278 | 0.270772 | ||||||||
\(280\) | −2.95987 | −0.176886 | ||||||||
\(281\) | 11.4050 | 0.680364 | 0.340182 | − | 0.940360i | \(-0.389511\pi\) | ||||
0.340182 | + | 0.940360i | \(0.389511\pi\) | |||||||
\(282\) | 2.65076 | 0.157850 | ||||||||
\(283\) | 21.8388 | 1.29818 | 0.649090 | − | 0.760711i | \(-0.275150\pi\) | ||||
0.649090 | + | 0.760711i | \(0.275150\pi\) | |||||||
\(284\) | 19.2063 | 1.13969 | ||||||||
\(285\) | 0.621031 | 0.0367867 | ||||||||
\(286\) | 0.265820 | 0.0157183 | ||||||||
\(287\) | −62.8556 | −3.71025 | ||||||||
\(288\) | 19.6705 | 1.15910 | ||||||||
\(289\) | −13.5336 | −0.796093 | ||||||||
\(290\) | 9.25233 | 0.543316 | ||||||||
\(291\) | 4.18737 | 0.245468 | ||||||||
\(292\) | −16.6408 | −0.973832 | ||||||||
\(293\) | −5.49779 | −0.321184 | −0.160592 | − | 0.987021i | \(-0.551340\pi\) | ||||
−0.160592 | + | 0.987021i | \(0.551340\pi\) | |||||||
\(294\) | 23.3599 | 1.36238 | ||||||||
\(295\) | 3.15592 | 0.183745 | ||||||||
\(296\) | −0.254237 | −0.0147772 | ||||||||
\(297\) | −3.48667 | −0.202317 | ||||||||
\(298\) | 37.5867 | 2.17734 | ||||||||
\(299\) | 0.0231632 | 0.00133956 | ||||||||
\(300\) | 1.05664 | 0.0610052 | ||||||||
\(301\) | −44.7215 | −2.57770 | ||||||||
\(302\) | −25.9479 | −1.49314 | ||||||||
\(303\) | 1.73665 | 0.0997677 | ||||||||
\(304\) | −4.50800 | −0.258551 | ||||||||
\(305\) | 1.90706 | 0.109198 | ||||||||
\(306\) | −9.36450 | −0.535333 | ||||||||
\(307\) | 9.90065 | 0.565060 | 0.282530 | − | 0.959258i | \(-0.408826\pi\) | ||||
0.282530 | + | 0.959258i | \(0.408826\pi\) | |||||||
\(308\) | 8.76711 | 0.499552 | ||||||||
\(309\) | −4.65181 | −0.264632 | ||||||||
\(310\) | −3.32837 | −0.189039 | ||||||||
\(311\) | 27.6617 | 1.56855 | 0.784276 | − | 0.620412i | \(-0.213035\pi\) | ||||
0.784276 | + | 0.620412i | \(0.213035\pi\) | |||||||
\(312\) | −0.0492887 | −0.00279042 | ||||||||
\(313\) | −18.3016 | −1.03447 | −0.517234 | − | 0.855844i | \(-0.673038\pi\) | ||||
−0.517234 | + | 0.855844i | \(0.673038\pi\) | |||||||
\(314\) | −11.8478 | −0.668611 | ||||||||
\(315\) | −13.4710 | −0.759007 | ||||||||
\(316\) | −10.4470 | −0.587687 | ||||||||
\(317\) | −3.72231 | −0.209066 | −0.104533 | − | 0.994521i | \(-0.533335\pi\) | ||||
−0.104533 | + | 0.994521i | \(0.533335\pi\) | |||||||
\(318\) | 1.60528 | 0.0900196 | ||||||||
\(319\) | 4.80913 | 0.269259 | ||||||||
\(320\) | −5.45977 | −0.305211 | ||||||||
\(321\) | 2.02641 | 0.113103 | ||||||||
\(322\) | 1.66196 | 0.0926175 | ||||||||
\(323\) | 1.86183 | 0.103595 | ||||||||
\(324\) | 9.66010 | 0.536672 | ||||||||
\(325\) | 0.138167 | 0.00766411 | ||||||||
\(326\) | −30.2933 | −1.67779 | ||||||||
\(327\) | 0.908408 | 0.0502351 | ||||||||
\(328\) | 7.00700 | 0.386897 | ||||||||
\(329\) | 11.4318 | 0.630255 | ||||||||
\(330\) | 1.19481 | 0.0657720 | ||||||||
\(331\) | −10.3313 | −0.567858 | −0.283929 | − | 0.958845i | \(-0.591638\pi\) | ||||
−0.283929 | + | 0.958845i | \(0.591638\pi\) | |||||||
\(332\) | −0.324053 | −0.0177847 | ||||||||
\(333\) | −1.15709 | −0.0634083 | ||||||||
\(334\) | −2.88090 | −0.157636 | ||||||||
\(335\) | −10.7534 | −0.587519 | ||||||||
\(336\) | −14.4258 | −0.786990 | ||||||||
\(337\) | −9.86777 | −0.537532 | −0.268766 | − | 0.963206i | \(-0.586616\pi\) | ||||
−0.268766 | + | 0.963206i | \(0.586616\pi\) | |||||||
\(338\) | −24.9741 | −1.35841 | ||||||||
\(339\) | 5.33107 | 0.289544 | ||||||||
\(340\) | 3.16778 | 0.171797 | ||||||||
\(341\) | −1.73000 | −0.0936849 | ||||||||
\(342\) | −5.02972 | −0.271976 | ||||||||
\(343\) | 64.6736 | 3.49205 | ||||||||
\(344\) | 4.98545 | 0.268797 | ||||||||
\(345\) | 0.104114 | 0.00560529 | ||||||||
\(346\) | −48.8161 | −2.62437 | ||||||||
\(347\) | 17.4270 | 0.935529 | 0.467764 | − | 0.883853i | \(-0.345060\pi\) | ||||
0.467764 | + | 0.883853i | \(0.345060\pi\) | |||||||
\(348\) | 5.08152 | 0.272398 | ||||||||
\(349\) | −0.187343 | −0.0100282 | −0.00501411 | − | 0.999987i | \(-0.501596\pi\) | ||||
−0.00501411 | + | 0.999987i | \(0.501596\pi\) | |||||||
\(350\) | 9.91350 | 0.529899 | ||||||||
\(351\) | −0.481741 | −0.0257135 | ||||||||
\(352\) | −7.52414 | −0.401038 | ||||||||
\(353\) | −27.6872 | −1.47364 | −0.736821 | − | 0.676088i | \(-0.763674\pi\) | ||||
−0.736821 | + | 0.676088i | \(0.763674\pi\) | |||||||
\(354\) | 3.77072 | 0.200411 | ||||||||
\(355\) | 11.2883 | 0.599123 | ||||||||
\(356\) | −15.2179 | −0.806545 | ||||||||
\(357\) | 5.95794 | 0.315328 | ||||||||
\(358\) | −2.80267 | −0.148126 | ||||||||
\(359\) | 11.8587 | 0.625878 | 0.312939 | − | 0.949773i | \(-0.398686\pi\) | ||||
0.312939 | + | 0.949773i | \(0.398686\pi\) | |||||||
\(360\) | 1.50172 | 0.0791476 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.5060 | −1.02521 | ||||||||
\(363\) | 0.621031 | 0.0325957 | ||||||||
\(364\) | 1.21132 | 0.0634906 | ||||||||
\(365\) | −9.78050 | −0.511935 | ||||||||
\(366\) | 2.27857 | 0.119103 | ||||||||
\(367\) | 22.6382 | 1.18170 | 0.590852 | − | 0.806780i | \(-0.298792\pi\) | ||||
0.590852 | + | 0.806780i | \(0.298792\pi\) | |||||||
\(368\) | −0.755749 | −0.0393962 | ||||||||
\(369\) | 31.8904 | 1.66015 | ||||||||
\(370\) | 0.851518 | 0.0442683 | ||||||||
\(371\) | 6.92300 | 0.359425 | ||||||||
\(372\) | −1.82799 | −0.0947770 | ||||||||
\(373\) | 18.2379 | 0.944322 | 0.472161 | − | 0.881512i | \(-0.343474\pi\) | ||||
0.472161 | + | 0.881512i | \(0.343474\pi\) | |||||||
\(374\) | 3.58200 | 0.185221 | ||||||||
\(375\) | 0.621031 | 0.0320699 | ||||||||
\(376\) | −1.27439 | −0.0657217 | ||||||||
\(377\) | 0.664462 | 0.0342215 | ||||||||
\(378\) | −34.5651 | −1.77783 | ||||||||
\(379\) | 36.4789 | 1.87380 | 0.936898 | − | 0.349604i | \(-0.113684\pi\) | ||||
0.936898 | + | 0.349604i | \(0.113684\pi\) | |||||||
\(380\) | 1.70143 | 0.0872815 | ||||||||
\(381\) | −2.89951 | −0.148547 | ||||||||
\(382\) | −17.2976 | −0.885022 | ||||||||
\(383\) | 21.4254 | 1.09479 | 0.547393 | − | 0.836876i | \(-0.315620\pi\) | ||||
0.547393 | + | 0.836876i | \(0.315620\pi\) | |||||||
\(384\) | 2.82206 | 0.144013 | ||||||||
\(385\) | 5.15278 | 0.262610 | ||||||||
\(386\) | −8.55619 | −0.435498 | ||||||||
\(387\) | 22.6899 | 1.15339 | ||||||||
\(388\) | 11.4721 | 0.582407 | ||||||||
\(389\) | −7.30513 | −0.370385 | −0.185192 | − | 0.982702i | \(-0.559291\pi\) | ||||
−0.185192 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(390\) | 0.165083 | 0.00835929 | ||||||||
\(391\) | 0.312130 | 0.0157851 | ||||||||
\(392\) | −11.2306 | −0.567232 | ||||||||
\(393\) | 0.583919 | 0.0294548 | ||||||||
\(394\) | 42.2151 | 2.12677 | ||||||||
\(395\) | −6.14010 | −0.308942 | ||||||||
\(396\) | −4.44808 | −0.223525 | ||||||||
\(397\) | 27.3333 | 1.37182 | 0.685909 | − | 0.727688i | \(-0.259405\pi\) | ||||
0.685909 | + | 0.727688i | \(0.259405\pi\) | |||||||
\(398\) | 26.4844 | 1.32754 | ||||||||
\(399\) | 3.20004 | 0.160202 | ||||||||
\(400\) | −4.50800 | −0.225400 | ||||||||
\(401\) | 19.4498 | 0.971274 | 0.485637 | − | 0.874161i | \(-0.338588\pi\) | ||||
0.485637 | + | 0.874161i | \(0.338588\pi\) | |||||||
\(402\) | −12.8482 | −0.640810 | ||||||||
\(403\) | −0.239029 | −0.0119069 | ||||||||
\(404\) | 4.75786 | 0.236713 | ||||||||
\(405\) | 5.67763 | 0.282124 | ||||||||
\(406\) | 47.6753 | 2.36608 | ||||||||
\(407\) | 0.442598 | 0.0219387 | ||||||||
\(408\) | −0.664178 | −0.0328817 | ||||||||
\(409\) | −4.01732 | −0.198644 | −0.0993219 | − | 0.995055i | \(-0.531667\pi\) | ||||
−0.0993219 | + | 0.995055i | \(0.531667\pi\) | |||||||
\(410\) | −23.4686 | −1.15903 | ||||||||
\(411\) | −7.96113 | −0.392694 | ||||||||
\(412\) | −12.7445 | −0.627876 | ||||||||
\(413\) | 16.2618 | 0.800190 | ||||||||
\(414\) | −0.843214 | −0.0414417 | ||||||||
\(415\) | −0.190459 | −0.00934927 | ||||||||
\(416\) | −1.03959 | −0.0509699 | ||||||||
\(417\) | −12.7895 | −0.626304 | ||||||||
\(418\) | 1.92391 | 0.0941015 | ||||||||
\(419\) | 23.9878 | 1.17188 | 0.585940 | − | 0.810354i | \(-0.300725\pi\) | ||||
0.585940 | + | 0.810354i | \(0.300725\pi\) | |||||||
\(420\) | 5.44464 | 0.265671 | ||||||||
\(421\) | −20.3725 | −0.992894 | −0.496447 | − | 0.868067i | \(-0.665362\pi\) | ||||
−0.496447 | + | 0.868067i | \(0.665362\pi\) | |||||||
\(422\) | −41.4562 | −2.01806 | ||||||||
\(423\) | −5.80004 | −0.282008 | ||||||||
\(424\) | −0.771761 | −0.0374800 | ||||||||
\(425\) | 1.86183 | 0.0903122 | ||||||||
\(426\) | 13.4874 | 0.653467 | ||||||||
\(427\) | 9.82665 | 0.475545 | ||||||||
\(428\) | 5.55172 | 0.268352 | ||||||||
\(429\) | 0.0858058 | 0.00414275 | ||||||||
\(430\) | −16.6978 | −0.805239 | ||||||||
\(431\) | −17.8520 | −0.859901 | −0.429950 | − | 0.902853i | \(-0.641469\pi\) | ||||
−0.429950 | + | 0.902853i | \(0.641469\pi\) | |||||||
\(432\) | 15.7179 | 0.756227 | ||||||||
\(433\) | −37.5810 | −1.80603 | −0.903015 | − | 0.429609i | \(-0.858651\pi\) | ||||
−0.903015 | + | 0.429609i | \(0.858651\pi\) | |||||||
\(434\) | −17.1504 | −0.823244 | ||||||||
\(435\) | 2.98662 | 0.143197 | ||||||||
\(436\) | 2.48875 | 0.119190 | ||||||||
\(437\) | 0.167646 | 0.00801962 | ||||||||
\(438\) | −11.6858 | −0.558370 | ||||||||
\(439\) | −17.9023 | −0.854430 | −0.427215 | − | 0.904150i | \(-0.640505\pi\) | ||||
−0.427215 | + | 0.904150i | \(0.640505\pi\) | |||||||
\(440\) | −0.574421 | −0.0273844 | ||||||||
\(441\) | −51.1131 | −2.43396 | ||||||||
\(442\) | 0.494913 | 0.0235406 | ||||||||
\(443\) | −21.7096 | −1.03146 | −0.515728 | − | 0.856752i | \(-0.672479\pi\) | ||||
−0.515728 | + | 0.856752i | \(0.672479\pi\) | |||||||
\(444\) | 0.467667 | 0.0221945 | ||||||||
\(445\) | −8.94416 | −0.423994 | ||||||||
\(446\) | 49.1986 | 2.32962 | ||||||||
\(447\) | 12.1328 | 0.573863 | ||||||||
\(448\) | −28.1330 | −1.32916 | ||||||||
\(449\) | −35.7775 | −1.68844 | −0.844222 | − | 0.535994i | \(-0.819937\pi\) | ||||
−0.844222 | + | 0.535994i | \(0.819937\pi\) | |||||||
\(450\) | −5.02972 | −0.237103 | ||||||||
\(451\) | −12.1984 | −0.574399 | ||||||||
\(452\) | 14.6055 | 0.686984 | ||||||||
\(453\) | −8.37589 | −0.393534 | ||||||||
\(454\) | 17.4410 | 0.818548 | ||||||||
\(455\) | 0.711944 | 0.0333764 | ||||||||
\(456\) | −0.356733 | −0.0167056 | ||||||||
\(457\) | 4.03494 | 0.188747 | 0.0943733 | − | 0.995537i | \(-0.469915\pi\) | ||||
0.0943733 | + | 0.995537i | \(0.469915\pi\) | |||||||
\(458\) | 53.0564 | 2.47916 | ||||||||
\(459\) | −6.49159 | −0.303002 | ||||||||
\(460\) | 0.285239 | 0.0132993 | ||||||||
\(461\) | −16.5876 | −0.772563 | −0.386281 | − | 0.922381i | \(-0.626241\pi\) | ||||
−0.386281 | + | 0.922381i | \(0.626241\pi\) | |||||||
\(462\) | 6.15659 | 0.286430 | ||||||||
\(463\) | 20.1731 | 0.937523 | 0.468761 | − | 0.883325i | \(-0.344700\pi\) | ||||
0.468761 | + | 0.883325i | \(0.344700\pi\) | |||||||
\(464\) | −21.6795 | −1.00645 | ||||||||
\(465\) | −1.07439 | −0.0498234 | ||||||||
\(466\) | 25.9798 | 1.20349 | ||||||||
\(467\) | 24.2739 | 1.12326 | 0.561632 | − | 0.827387i | \(-0.310174\pi\) | ||||
0.561632 | + | 0.827387i | \(0.310174\pi\) | |||||||
\(468\) | −0.614578 | −0.0284089 | ||||||||
\(469\) | −55.4098 | −2.55859 | ||||||||
\(470\) | 4.26832 | 0.196883 | ||||||||
\(471\) | −3.82443 | −0.176221 | ||||||||
\(472\) | −1.81283 | −0.0834421 | ||||||||
\(473\) | −8.67909 | −0.399065 | ||||||||
\(474\) | −7.33624 | −0.336965 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 16.3229 | 0.748158 | ||||||||
\(477\) | −3.51246 | −0.160825 | ||||||||
\(478\) | 4.82400 | 0.220645 | ||||||||
\(479\) | −1.94923 | −0.0890625 | −0.0445312 | − | 0.999008i | \(-0.514179\pi\) | ||||
−0.0445312 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(480\) | −4.67272 | −0.213280 | ||||||||
\(481\) | 0.0611523 | 0.00278830 | ||||||||
\(482\) | 47.0736 | 2.14414 | ||||||||
\(483\) | 0.536475 | 0.0244105 | ||||||||
\(484\) | 1.70143 | 0.0773378 | ||||||||
\(485\) | 6.74261 | 0.306166 | ||||||||
\(486\) | 26.9078 | 1.22056 | ||||||||
\(487\) | 18.1312 | 0.821605 | 0.410802 | − | 0.911724i | \(-0.365249\pi\) | ||||
0.410802 | + | 0.911724i | \(0.365249\pi\) | |||||||
\(488\) | −1.09545 | −0.0495888 | ||||||||
\(489\) | −9.77857 | −0.442202 | ||||||||
\(490\) | 37.6147 | 1.69926 | ||||||||
\(491\) | 20.7470 | 0.936298 | 0.468149 | − | 0.883649i | \(-0.344921\pi\) | ||||
0.468149 | + | 0.883649i | \(0.344921\pi\) | |||||||
\(492\) | −12.8893 | −0.581094 | ||||||||
\(493\) | 8.95379 | 0.403259 | ||||||||
\(494\) | 0.265820 | 0.0119598 | ||||||||
\(495\) | −2.61432 | −0.117505 | ||||||||
\(496\) | 7.79884 | 0.350178 | ||||||||
\(497\) | 58.1664 | 2.60912 | ||||||||
\(498\) | −0.227562 | −0.0101973 | ||||||||
\(499\) | −23.1410 | −1.03593 | −0.517967 | − | 0.855400i | \(-0.673311\pi\) | ||||
−0.517967 | + | 0.855400i | \(0.673311\pi\) | |||||||
\(500\) | 1.70143 | 0.0760903 | ||||||||
\(501\) | −0.929944 | −0.0415469 | ||||||||
\(502\) | −19.2105 | −0.857407 | ||||||||
\(503\) | 31.2204 | 1.39205 | 0.696024 | − | 0.718018i | \(-0.254951\pi\) | ||||
0.696024 | + | 0.718018i | \(0.254951\pi\) | |||||||
\(504\) | 7.73804 | 0.344680 | ||||||||
\(505\) | 2.79639 | 0.124438 | ||||||||
\(506\) | 0.322537 | 0.0143385 | ||||||||
\(507\) | −8.06155 | −0.358026 | ||||||||
\(508\) | −7.94376 | −0.352447 | ||||||||
\(509\) | 11.1936 | 0.496147 | 0.248073 | − | 0.968741i | \(-0.420203\pi\) | ||||
0.248073 | + | 0.968741i | \(0.420203\pi\) | |||||||
\(510\) | 2.22453 | 0.0985040 | ||||||||
\(511\) | −50.3968 | −2.22942 | ||||||||
\(512\) | 28.7398 | 1.27013 | ||||||||
\(513\) | −3.48667 | −0.153940 | ||||||||
\(514\) | −45.2334 | −1.99516 | ||||||||
\(515\) | −7.49046 | −0.330069 | ||||||||
\(516\) | −9.17068 | −0.403717 | ||||||||
\(517\) | 2.21857 | 0.0975724 | ||||||||
\(518\) | 4.38769 | 0.192784 | ||||||||
\(519\) | −15.7576 | −0.691684 | ||||||||
\(520\) | −0.0793659 | −0.00348042 | ||||||||
\(521\) | 9.76912 | 0.427993 | 0.213996 | − | 0.976834i | \(-0.431352\pi\) | ||||
0.213996 | + | 0.976834i | \(0.431352\pi\) | |||||||
\(522\) | −24.1886 | −1.05870 | ||||||||
\(523\) | 10.2890 | 0.449905 | 0.224952 | − | 0.974370i | \(-0.427777\pi\) | ||||
0.224952 | + | 0.974370i | \(0.427777\pi\) | |||||||
\(524\) | 1.59975 | 0.0698856 | ||||||||
\(525\) | 3.20004 | 0.139661 | ||||||||
\(526\) | 43.9129 | 1.91469 | ||||||||
\(527\) | −3.22098 | −0.140308 | ||||||||
\(528\) | −2.79960 | −0.121837 | ||||||||
\(529\) | −22.9719 | −0.998778 | ||||||||
\(530\) | 2.58486 | 0.112279 | ||||||||
\(531\) | −8.25059 | −0.358045 | ||||||||
\(532\) | 8.76711 | 0.380102 | ||||||||
\(533\) | −1.68541 | −0.0730032 | ||||||||
\(534\) | −10.6866 | −0.462452 | ||||||||
\(535\) | 3.26297 | 0.141071 | ||||||||
\(536\) | 6.17696 | 0.266804 | ||||||||
\(537\) | −0.904691 | −0.0390403 | ||||||||
\(538\) | 36.1613 | 1.55902 | ||||||||
\(539\) | 19.5512 | 0.842129 | ||||||||
\(540\) | −5.93232 | −0.255286 | ||||||||
\(541\) | −21.0839 | −0.906468 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(542\) | 21.3512 | 0.917115 | ||||||||
\(543\) | −6.29646 | −0.270207 | ||||||||
\(544\) | −14.0087 | −0.600618 | ||||||||
\(545\) | 1.46274 | 0.0626569 | ||||||||
\(546\) | 0.850636 | 0.0364039 | ||||||||
\(547\) | −14.5523 | −0.622212 | −0.311106 | − | 0.950375i | \(-0.600699\pi\) | ||||
−0.311106 | + | 0.950375i | \(0.600699\pi\) | |||||||
\(548\) | −21.8110 | −0.931720 | ||||||||
\(549\) | −4.98566 | −0.212783 | ||||||||
\(550\) | 1.92391 | 0.0820358 | ||||||||
\(551\) | 4.80913 | 0.204876 | ||||||||
\(552\) | −0.0598050 | −0.00254547 | ||||||||
\(553\) | −31.6386 | −1.34541 | ||||||||
\(554\) | 52.2909 | 2.22163 | ||||||||
\(555\) | 0.274867 | 0.0116674 | ||||||||
\(556\) | −35.0392 | −1.48599 | ||||||||
\(557\) | 11.1213 | 0.471226 | 0.235613 | − | 0.971847i | \(-0.424290\pi\) | ||||
0.235613 | + | 0.971847i | \(0.424290\pi\) | |||||||
\(558\) | 8.70143 | 0.368361 | ||||||||
\(559\) | −1.19916 | −0.0507191 | ||||||||
\(560\) | −23.2287 | −0.981593 | ||||||||
\(561\) | 1.15626 | 0.0488172 | ||||||||
\(562\) | 21.9422 | 0.925574 | ||||||||
\(563\) | 22.9586 | 0.967589 | 0.483794 | − | 0.875182i | \(-0.339258\pi\) | ||||
0.483794 | + | 0.875182i | \(0.339258\pi\) | |||||||
\(564\) | 2.34423 | 0.0987098 | ||||||||
\(565\) | 8.58423 | 0.361141 | ||||||||
\(566\) | 42.0159 | 1.76606 | ||||||||
\(567\) | 29.2556 | 1.22862 | ||||||||
\(568\) | −6.48426 | −0.272074 | ||||||||
\(569\) | −35.9363 | −1.50653 | −0.753263 | − | 0.657719i | \(-0.771521\pi\) | ||||
−0.753263 | + | 0.657719i | \(0.771521\pi\) | |||||||
\(570\) | 1.19481 | 0.0500450 | ||||||||
\(571\) | 13.4752 | 0.563919 | 0.281959 | − | 0.959426i | \(-0.409016\pi\) | ||||
0.281959 | + | 0.959426i | \(0.409016\pi\) | |||||||
\(572\) | 0.235081 | 0.00982924 | ||||||||
\(573\) | −5.58360 | −0.233258 | ||||||||
\(574\) | −120.928 | −5.04746 | ||||||||
\(575\) | 0.167646 | 0.00699134 | ||||||||
\(576\) | 14.2736 | 0.594733 | ||||||||
\(577\) | −20.7453 | −0.863640 | −0.431820 | − | 0.901960i | \(-0.642128\pi\) | ||||
−0.431820 | + | 0.901960i | \(0.642128\pi\) | |||||||
\(578\) | −26.0374 | −1.08301 | ||||||||
\(579\) | −2.76190 | −0.114781 | ||||||||
\(580\) | 8.18240 | 0.339756 | ||||||||
\(581\) | −0.981395 | −0.0407151 | ||||||||
\(582\) | 8.05613 | 0.333937 | ||||||||
\(583\) | 1.34355 | 0.0556440 | ||||||||
\(584\) | 5.61812 | 0.232480 | ||||||||
\(585\) | −0.361212 | −0.0149343 | ||||||||
\(586\) | −10.5772 | −0.436942 | ||||||||
\(587\) | 15.0468 | 0.621048 | 0.310524 | − | 0.950565i | \(-0.399495\pi\) | ||||
0.310524 | + | 0.950565i | \(0.399495\pi\) | |||||||
\(588\) | 20.6586 | 0.851946 | ||||||||
\(589\) | −1.73000 | −0.0712835 | ||||||||
\(590\) | 6.07171 | 0.249968 | ||||||||
\(591\) | 13.6269 | 0.560535 | ||||||||
\(592\) | −1.99523 | −0.0820034 | ||||||||
\(593\) | −12.7120 | −0.522019 | −0.261009 | − | 0.965336i | \(-0.584055\pi\) | ||||
−0.261009 | + | 0.965336i | \(0.584055\pi\) | |||||||
\(594\) | −6.70803 | −0.275234 | ||||||||
\(595\) | 9.59363 | 0.393300 | ||||||||
\(596\) | 33.2402 | 1.36157 | ||||||||
\(597\) | 8.54906 | 0.349890 | ||||||||
\(598\) | 0.0445639 | 0.00182235 | ||||||||
\(599\) | −17.3589 | −0.709267 | −0.354634 | − | 0.935005i | \(-0.615394\pi\) | ||||
−0.354634 | + | 0.935005i | \(0.615394\pi\) | |||||||
\(600\) | −0.356733 | −0.0145636 | ||||||||
\(601\) | −9.95232 | −0.405964 | −0.202982 | − | 0.979183i | \(-0.565063\pi\) | ||||
−0.202982 | + | 0.979183i | \(0.565063\pi\) | |||||||
\(602\) | −86.0401 | −3.50673 | ||||||||
\(603\) | 28.1128 | 1.14484 | ||||||||
\(604\) | −22.9473 | −0.933713 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 3.34115 | 0.135725 | ||||||||
\(607\) | 31.0381 | 1.25980 | 0.629900 | − | 0.776677i | \(-0.283096\pi\) | ||||
0.629900 | + | 0.776677i | \(0.283096\pi\) | |||||||
\(608\) | −7.52414 | −0.305144 | ||||||||
\(609\) | 15.3894 | 0.623610 | ||||||||
\(610\) | 3.66901 | 0.148554 | ||||||||
\(611\) | 0.306532 | 0.0124010 | ||||||||
\(612\) | −8.28159 | −0.334764 | ||||||||
\(613\) | −18.2820 | −0.738401 | −0.369201 | − | 0.929350i | \(-0.620369\pi\) | ||||
−0.369201 | + | 0.929350i | \(0.620369\pi\) | |||||||
\(614\) | 19.0480 | 0.768713 | ||||||||
\(615\) | −7.57556 | −0.305476 | ||||||||
\(616\) | −2.95987 | −0.119256 | ||||||||
\(617\) | 35.8243 | 1.44223 | 0.721115 | − | 0.692815i | \(-0.243630\pi\) | ||||
0.721115 | + | 0.692815i | \(0.243630\pi\) | |||||||
\(618\) | −8.94966 | −0.360008 | ||||||||
\(619\) | −33.3475 | −1.34035 | −0.670175 | − | 0.742203i | \(-0.733781\pi\) | ||||
−0.670175 | + | 0.742203i | \(0.733781\pi\) | |||||||
\(620\) | −2.94348 | −0.118213 | ||||||||
\(621\) | −0.584527 | −0.0234563 | ||||||||
\(622\) | 53.2187 | 2.13387 | ||||||||
\(623\) | −46.0873 | −1.84645 | ||||||||
\(624\) | −0.386812 | −0.0154849 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.2106 | −1.40730 | ||||||||
\(627\) | 0.621031 | 0.0248016 | ||||||||
\(628\) | −10.4778 | −0.418108 | ||||||||
\(629\) | 0.824043 | 0.0328567 | ||||||||
\(630\) | −25.9171 | −1.03256 | ||||||||
\(631\) | −41.2198 | −1.64094 | −0.820468 | − | 0.571692i | \(-0.806287\pi\) | ||||
−0.820468 | + | 0.571692i | \(0.806287\pi\) | |||||||
\(632\) | 3.52700 | 0.140297 | ||||||||
\(633\) | −13.3819 | −0.531883 | ||||||||
\(634\) | −7.16140 | −0.284415 | ||||||||
\(635\) | −4.66887 | −0.185279 | ||||||||
\(636\) | 1.41965 | 0.0562926 | ||||||||
\(637\) | 2.70132 | 0.107030 | ||||||||
\(638\) | 9.25233 | 0.366303 | ||||||||
\(639\) | −29.5114 | −1.16745 | ||||||||
\(640\) | 4.54416 | 0.179624 | ||||||||
\(641\) | 12.8023 | 0.505662 | 0.252831 | − | 0.967510i | \(-0.418638\pi\) | ||||
0.252831 | + | 0.967510i | \(0.418638\pi\) | |||||||
\(642\) | 3.89862 | 0.153866 | ||||||||
\(643\) | 24.6826 | 0.973386 | 0.486693 | − | 0.873573i | \(-0.338203\pi\) | ||||
0.486693 | + | 0.873573i | \(0.338203\pi\) | |||||||
\(644\) | 1.46977 | 0.0579172 | ||||||||
\(645\) | −5.38998 | −0.212230 | ||||||||
\(646\) | 3.58200 | 0.140932 | ||||||||
\(647\) | −27.4253 | −1.07820 | −0.539101 | − | 0.842241i | \(-0.681236\pi\) | ||||
−0.539101 | + | 0.842241i | \(0.681236\pi\) | |||||||
\(648\) | −3.26135 | −0.128118 | ||||||||
\(649\) | 3.15592 | 0.123881 | ||||||||
\(650\) | 0.265820 | 0.0104263 | ||||||||
\(651\) | −5.53608 | −0.216976 | ||||||||
\(652\) | −26.7902 | −1.04919 | ||||||||
\(653\) | 44.1678 | 1.72842 | 0.864210 | − | 0.503131i | \(-0.167819\pi\) | ||||
0.864210 | + | 0.503131i | \(0.167819\pi\) | |||||||
\(654\) | 1.74769 | 0.0683403 | ||||||||
\(655\) | 0.940241 | 0.0367382 | ||||||||
\(656\) | 54.9902 | 2.14701 | ||||||||
\(657\) | 25.5694 | 0.997556 | ||||||||
\(658\) | 21.9937 | 0.857406 | ||||||||
\(659\) | −19.2583 | −0.750198 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(660\) | 1.05664 | 0.0411297 | ||||||||
\(661\) | 30.1994 | 1.17462 | 0.587311 | − | 0.809361i | \(-0.300186\pi\) | ||||
0.587311 | + | 0.809361i | \(0.300186\pi\) | |||||||
\(662\) | −19.8764 | −0.772519 | ||||||||
\(663\) | 0.159756 | 0.00620442 | ||||||||
\(664\) | 0.109404 | 0.00424569 | ||||||||
\(665\) | 5.15278 | 0.199816 | ||||||||
\(666\) | −2.22614 | −0.0862612 | ||||||||
\(667\) | 0.806233 | 0.0312175 | ||||||||
\(668\) | −2.54776 | −0.0985757 | ||||||||
\(669\) | 15.8811 | 0.614000 | ||||||||
\(670\) | −20.6885 | −0.799267 | ||||||||
\(671\) | 1.90706 | 0.0736211 | ||||||||
\(672\) | −24.0775 | −0.928811 | ||||||||
\(673\) | 30.5163 | 1.17632 | 0.588159 | − | 0.808746i | \(-0.299853\pi\) | ||||
0.588159 | + | 0.808746i | \(0.299853\pi\) | |||||||
\(674\) | −18.9847 | −0.731264 | ||||||||
\(675\) | −3.48667 | −0.134202 | ||||||||
\(676\) | −22.0861 | −0.849466 | ||||||||
\(677\) | 26.1491 | 1.00499 | 0.502497 | − | 0.864579i | \(-0.332415\pi\) | ||||
0.502497 | + | 0.864579i | \(0.332415\pi\) | |||||||
\(678\) | 10.2565 | 0.393899 | ||||||||
\(679\) | 34.7432 | 1.33332 | ||||||||
\(680\) | −1.06948 | −0.0410125 | ||||||||
\(681\) | 5.62989 | 0.215738 | ||||||||
\(682\) | −3.32837 | −0.127450 | ||||||||
\(683\) | 6.55898 | 0.250972 | 0.125486 | − | 0.992095i | \(-0.459951\pi\) | ||||
0.125486 | + | 0.992095i | \(0.459951\pi\) | |||||||
\(684\) | −4.44808 | −0.170077 | ||||||||
\(685\) | −12.8192 | −0.489797 | ||||||||
\(686\) | 124.426 | 4.75061 | ||||||||
\(687\) | 17.1264 | 0.653413 | ||||||||
\(688\) | 39.1253 | 1.49164 | ||||||||
\(689\) | 0.185633 | 0.00707207 | ||||||||
\(690\) | 0.200305 | 0.00762549 | ||||||||
\(691\) | 26.3501 | 1.00240 | 0.501202 | − | 0.865330i | \(-0.332891\pi\) | ||||
0.501202 | + | 0.865330i | \(0.332891\pi\) | |||||||
\(692\) | −43.1710 | −1.64112 | ||||||||
\(693\) | −13.4710 | −0.511722 | ||||||||
\(694\) | 33.5279 | 1.27270 | ||||||||
\(695\) | −20.5940 | −0.781174 | ||||||||
\(696\) | −1.71558 | −0.0650287 | ||||||||
\(697\) | −22.7113 | −0.860253 | ||||||||
\(698\) | −0.360431 | −0.0136425 | ||||||||
\(699\) | 8.38619 | 0.317195 | ||||||||
\(700\) | 8.76711 | 0.331365 | ||||||||
\(701\) | 13.5154 | 0.510470 | 0.255235 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255235 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(702\) | −0.926827 | −0.0349808 | ||||||||
\(703\) | 0.442598 | 0.0166929 | ||||||||
\(704\) | −5.45977 | −0.205773 | ||||||||
\(705\) | 1.37780 | 0.0518909 | ||||||||
\(706\) | −53.2677 | −2.00476 | ||||||||
\(707\) | 14.4092 | 0.541914 | ||||||||
\(708\) | 3.33468 | 0.125325 | ||||||||
\(709\) | −17.7736 | −0.667503 | −0.333751 | − | 0.942661i | \(-0.608315\pi\) | ||||
−0.333751 | + | 0.942661i | \(0.608315\pi\) | |||||||
\(710\) | 21.7178 | 0.815053 | ||||||||
\(711\) | 16.0522 | 0.602005 | ||||||||
\(712\) | 5.13771 | 0.192544 | ||||||||
\(713\) | −0.290029 | −0.0108617 | ||||||||
\(714\) | 11.4625 | 0.428975 | ||||||||
\(715\) | 0.138167 | 0.00516714 | ||||||||
\(716\) | −2.47857 | −0.0926285 | ||||||||
\(717\) | 1.55717 | 0.0581535 | ||||||||
\(718\) | 22.8151 | 0.851450 | ||||||||
\(719\) | 27.2414 | 1.01593 | 0.507966 | − | 0.861377i | \(-0.330397\pi\) | ||||
0.507966 | + | 0.861377i | \(0.330397\pi\) | |||||||
\(720\) | 11.7853 | 0.439214 | ||||||||
\(721\) | −38.5967 | −1.43742 | ||||||||
\(722\) | 1.92391 | 0.0716005 | ||||||||
\(723\) | 15.1952 | 0.565114 | ||||||||
\(724\) | −17.2503 | −0.641103 | ||||||||
\(725\) | 4.80913 | 0.178607 | ||||||||
\(726\) | 1.19481 | 0.0443435 | ||||||||
\(727\) | 20.2128 | 0.749651 | 0.374826 | − | 0.927095i | \(-0.377703\pi\) | ||||
0.374826 | + | 0.927095i | \(0.377703\pi\) | |||||||
\(728\) | −0.408955 | −0.0151569 | ||||||||
\(729\) | −8.34717 | −0.309154 | ||||||||
\(730\) | −18.8168 | −0.696441 | ||||||||
\(731\) | −16.1590 | −0.597663 | ||||||||
\(732\) | 2.01507 | 0.0744793 | ||||||||
\(733\) | −27.9563 | −1.03259 | −0.516295 | − | 0.856411i | \(-0.672689\pi\) | ||||
−0.516295 | + | 0.856411i | \(0.672689\pi\) | |||||||
\(734\) | 43.5538 | 1.60760 | ||||||||
\(735\) | 12.1419 | 0.447861 | ||||||||
\(736\) | −1.26139 | −0.0464956 | ||||||||
\(737\) | −10.7534 | −0.396105 | ||||||||
\(738\) | 61.3543 | 2.25848 | ||||||||
\(739\) | −38.5940 | −1.41971 | −0.709853 | − | 0.704350i | \(-0.751238\pi\) | ||||
−0.709853 | + | 0.704350i | \(0.751238\pi\) | |||||||
\(740\) | 0.753049 | 0.0276826 | ||||||||
\(741\) | 0.0858058 | 0.00315216 | ||||||||
\(742\) | 13.3192 | 0.488965 | ||||||||
\(743\) | −32.7873 | −1.20285 | −0.601425 | − | 0.798929i | \(-0.705400\pi\) | ||||
−0.601425 | + | 0.798929i | \(0.705400\pi\) | |||||||
\(744\) | 0.617149 | 0.0226258 | ||||||||
\(745\) | 19.5366 | 0.715766 | ||||||||
\(746\) | 35.0881 | 1.28467 | ||||||||
\(747\) | 0.497921 | 0.0182180 | ||||||||
\(748\) | 3.16778 | 0.115826 | ||||||||
\(749\) | 16.8134 | 0.614348 | ||||||||
\(750\) | 1.19481 | 0.0436282 | ||||||||
\(751\) | 3.21182 | 0.117201 | 0.0586005 | − | 0.998282i | \(-0.481336\pi\) | ||||
0.0586005 | + | 0.998282i | \(0.481336\pi\) | |||||||
\(752\) | −10.0013 | −0.364709 | ||||||||
\(753\) | −6.20108 | −0.225980 | ||||||||
\(754\) | 1.27836 | 0.0465553 | ||||||||
\(755\) | −13.4871 | −0.490845 | ||||||||
\(756\) | −30.5680 | −1.11175 | ||||||||
\(757\) | −19.6023 | −0.712459 | −0.356230 | − | 0.934398i | \(-0.615938\pi\) | ||||
−0.356230 | + | 0.934398i | \(0.615938\pi\) | |||||||
\(758\) | 70.1821 | 2.54913 | ||||||||
\(759\) | 0.104114 | 0.00377909 | ||||||||
\(760\) | −0.574421 | −0.0208364 | ||||||||
\(761\) | 14.2807 | 0.517674 | 0.258837 | − | 0.965921i | \(-0.416661\pi\) | ||||
0.258837 | + | 0.965921i | \(0.416661\pi\) | |||||||
\(762\) | −5.57841 | −0.202084 | ||||||||
\(763\) | 7.53719 | 0.272865 | ||||||||
\(764\) | −15.2973 | −0.553437 | ||||||||
\(765\) | −4.86743 | −0.175982 | ||||||||
\(766\) | 41.2205 | 1.48936 | ||||||||
\(767\) | 0.436043 | 0.0157446 | ||||||||
\(768\) | 12.2108 | 0.440618 | ||||||||
\(769\) | 21.9005 | 0.789751 | 0.394875 | − | 0.918735i | \(-0.370788\pi\) | ||||
0.394875 | + | 0.918735i | \(0.370788\pi\) | |||||||
\(770\) | 9.91350 | 0.357258 | ||||||||
\(771\) | −14.6012 | −0.525849 | ||||||||
\(772\) | −7.56676 | −0.272333 | ||||||||
\(773\) | −49.0337 | −1.76362 | −0.881810 | − | 0.471605i | \(-0.843675\pi\) | ||||
−0.881810 | + | 0.471605i | \(0.843675\pi\) | |||||||
\(774\) | 43.6534 | 1.56909 | ||||||||
\(775\) | −1.73000 | −0.0621435 | ||||||||
\(776\) | −3.87310 | −0.139036 | ||||||||
\(777\) | 1.41633 | 0.0508105 | ||||||||
\(778\) | −14.0544 | −0.503875 | ||||||||
\(779\) | −12.1984 | −0.437052 | ||||||||
\(780\) | 0.145993 | 0.00522738 | ||||||||
\(781\) | 11.2883 | 0.403929 | ||||||||
\(782\) | 0.600510 | 0.0214742 | ||||||||
\(783\) | −16.7678 | −0.599233 | ||||||||
\(784\) | −88.1367 | −3.14774 | ||||||||
\(785\) | −6.15820 | −0.219796 | ||||||||
\(786\) | 1.12341 | 0.0400706 | ||||||||
\(787\) | 46.8687 | 1.67069 | 0.835345 | − | 0.549726i | \(-0.185268\pi\) | ||||
0.835345 | + | 0.549726i | \(0.185268\pi\) | |||||||
\(788\) | 37.3334 | 1.32995 | ||||||||
\(789\) | 14.1749 | 0.504641 | ||||||||
\(790\) | −11.8130 | −0.420288 | ||||||||
\(791\) | 44.2327 | 1.57273 | ||||||||
\(792\) | 1.50172 | 0.0533613 | ||||||||
\(793\) | 0.263492 | 0.00935687 | ||||||||
\(794\) | 52.5868 | 1.86623 | ||||||||
\(795\) | 0.834384 | 0.0295925 | ||||||||
\(796\) | 23.4217 | 0.830162 | ||||||||
\(797\) | 38.5922 | 1.36701 | 0.683503 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683503 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(798\) | 6.15659 | 0.217941 | ||||||||
\(799\) | 4.13060 | 0.146130 | ||||||||
\(800\) | −7.52414 | −0.266018 | ||||||||
\(801\) | 23.3829 | 0.826194 | ||||||||
\(802\) | 37.4196 | 1.32133 | ||||||||
\(803\) | −9.78050 | −0.345146 | ||||||||
\(804\) | −11.3625 | −0.400723 | ||||||||
\(805\) | 0.863846 | 0.0304466 | ||||||||
\(806\) | −0.459870 | −0.0161982 | ||||||||
\(807\) | 11.6727 | 0.410899 | ||||||||
\(808\) | −1.60630 | −0.0565096 | ||||||||
\(809\) | −24.9581 | −0.877478 | −0.438739 | − | 0.898614i | \(-0.644575\pi\) | ||||
−0.438739 | + | 0.898614i | \(0.644575\pi\) | |||||||
\(810\) | 10.9233 | 0.383804 | ||||||||
\(811\) | 2.91522 | 0.102367 | 0.0511836 | − | 0.998689i | \(-0.483701\pi\) | ||||
0.0511836 | + | 0.998689i | \(0.483701\pi\) | |||||||
\(812\) | 42.1621 | 1.47960 | ||||||||
\(813\) | 6.89210 | 0.241717 | ||||||||
\(814\) | 0.851518 | 0.0298457 | ||||||||
\(815\) | −15.7457 | −0.551548 | ||||||||
\(816\) | −5.21240 | −0.182470 | ||||||||
\(817\) | −8.67909 | −0.303643 | ||||||||
\(818\) | −7.72897 | −0.270237 | ||||||||
\(819\) | −1.86125 | −0.0650373 | ||||||||
\(820\) | −20.7547 | −0.724785 | ||||||||
\(821\) | −44.1959 | −1.54245 | −0.771225 | − | 0.636563i | \(-0.780355\pi\) | ||||
−0.771225 | + | 0.636563i | \(0.780355\pi\) | |||||||
\(822\) | −15.3165 | −0.534224 | ||||||||
\(823\) | −7.80327 | −0.272005 | −0.136002 | − | 0.990709i | \(-0.543425\pi\) | ||||
−0.136002 | + | 0.990709i | \(0.543425\pi\) | |||||||
\(824\) | 4.30267 | 0.149891 | ||||||||
\(825\) | 0.621031 | 0.0216215 | ||||||||
\(826\) | 31.2862 | 1.08859 | ||||||||
\(827\) | 30.7160 | 1.06810 | 0.534051 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534051 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(828\) | −0.745706 | −0.0259151 | ||||||||
\(829\) | 30.3940 | 1.05563 | 0.527813 | − | 0.849361i | \(-0.323012\pi\) | ||||
0.527813 | + | 0.849361i | \(0.323012\pi\) | |||||||
\(830\) | −0.366426 | −0.0127188 | ||||||||
\(831\) | 16.8793 | 0.585537 | ||||||||
\(832\) | −0.754359 | −0.0261527 | ||||||||
\(833\) | 36.4011 | 1.26122 | ||||||||
\(834\) | −24.6058 | −0.852030 | ||||||||
\(835\) | −1.49742 | −0.0518204 | ||||||||
\(836\) | 1.70143 | 0.0588452 | ||||||||
\(837\) | 6.03194 | 0.208494 | ||||||||
\(838\) | 46.1504 | 1.59424 | ||||||||
\(839\) | −37.9883 | −1.31150 | −0.655750 | − | 0.754978i | \(-0.727648\pi\) | ||||
−0.655750 | + | 0.754978i | \(0.727648\pi\) | |||||||
\(840\) | −1.83817 | −0.0634229 | ||||||||
\(841\) | −5.87228 | −0.202493 | ||||||||
\(842\) | −39.1948 | −1.35074 | ||||||||
\(843\) | 7.08285 | 0.243946 | ||||||||
\(844\) | −36.6623 | −1.26197 | ||||||||
\(845\) | −12.9809 | −0.446557 | ||||||||
\(846\) | −11.1588 | −0.383646 | ||||||||
\(847\) | 5.15278 | 0.177052 | ||||||||
\(848\) | −6.05670 | −0.207988 | ||||||||
\(849\) | 13.5626 | 0.465466 | ||||||||
\(850\) | 3.58200 | 0.122862 | ||||||||
\(851\) | 0.0741999 | 0.00254354 | ||||||||
\(852\) | 11.9277 | 0.408637 | ||||||||
\(853\) | −25.5855 | −0.876032 | −0.438016 | − | 0.898967i | \(-0.644319\pi\) | ||||
−0.438016 | + | 0.898967i | \(0.644319\pi\) | |||||||
\(854\) | 18.9056 | 0.646936 | ||||||||
\(855\) | −2.61432 | −0.0894079 | ||||||||
\(856\) | −1.87432 | −0.0640629 | ||||||||
\(857\) | −47.7536 | −1.63123 | −0.815616 | − | 0.578593i | \(-0.803602\pi\) | ||||
−0.815616 | + | 0.578593i | \(0.803602\pi\) | |||||||
\(858\) | 0.165083 | 0.00563583 | ||||||||
\(859\) | 26.0637 | 0.889282 | 0.444641 | − | 0.895709i | \(-0.353331\pi\) | ||||
0.444641 | + | 0.895709i | \(0.353331\pi\) | |||||||
\(860\) | −14.7669 | −0.503546 | ||||||||
\(861\) | −39.0352 | −1.33032 | ||||||||
\(862\) | −34.3457 | −1.16982 | ||||||||
\(863\) | 16.9616 | 0.577380 | 0.288690 | − | 0.957423i | \(-0.406780\pi\) | ||||
0.288690 | + | 0.957423i | \(0.406780\pi\) | |||||||
\(864\) | 26.2342 | 0.892504 | ||||||||
\(865\) | −25.3734 | −0.862720 | ||||||||
\(866\) | −72.3026 | −2.45694 | ||||||||
\(867\) | −8.40477 | −0.285441 | ||||||||
\(868\) | −15.1671 | −0.514805 | ||||||||
\(869\) | −6.14010 | −0.208289 | ||||||||
\(870\) | 5.74598 | 0.194807 | ||||||||
\(871\) | −1.48576 | −0.0503430 | ||||||||
\(872\) | −0.840229 | −0.0284537 | ||||||||
\(873\) | −17.6274 | −0.596595 | ||||||||
\(874\) | 0.322537 | 0.0109100 | ||||||||
\(875\) | 5.15278 | 0.174196 | ||||||||
\(876\) | −10.3345 | −0.349170 | ||||||||
\(877\) | −4.50622 | −0.152164 | −0.0760822 | − | 0.997102i | \(-0.524241\pi\) | ||||
−0.0760822 | + | 0.997102i | \(0.524241\pi\) | |||||||
\(878\) | −34.4424 | −1.16238 | ||||||||
\(879\) | −3.41429 | −0.115161 | ||||||||
\(880\) | −4.50800 | −0.151964 | ||||||||
\(881\) | 6.05500 | 0.203998 | 0.101999 | − | 0.994784i | \(-0.467476\pi\) | ||||
0.101999 | + | 0.994784i | \(0.467476\pi\) | |||||||
\(882\) | −98.3370 | −3.31118 | ||||||||
\(883\) | −40.0852 | −1.34897 | −0.674487 | − | 0.738287i | \(-0.735635\pi\) | ||||
−0.674487 | + | 0.738287i | \(0.735635\pi\) | |||||||
\(884\) | 0.437682 | 0.0147208 | ||||||||
\(885\) | 1.95992 | 0.0658821 | ||||||||
\(886\) | −41.7674 | −1.40320 | ||||||||
\(887\) | −9.84825 | −0.330672 | −0.165336 | − | 0.986237i | \(-0.552871\pi\) | ||||
−0.165336 | + | 0.986237i | \(0.552871\pi\) | |||||||
\(888\) | −0.157889 | −0.00529842 | ||||||||
\(889\) | −24.0577 | −0.806869 | ||||||||
\(890\) | −17.2078 | −0.576805 | ||||||||
\(891\) | 5.67763 | 0.190208 | ||||||||
\(892\) | 43.5093 | 1.45680 | ||||||||
\(893\) | 2.21857 | 0.0742415 | ||||||||
\(894\) | 23.3425 | 0.780689 | ||||||||
\(895\) | −1.45676 | −0.0486940 | ||||||||
\(896\) | 23.4151 | 0.782243 | ||||||||
\(897\) | 0.0143850 | 0.000480303 0 | ||||||||
\(898\) | −68.8327 | −2.29698 | ||||||||
\(899\) | −8.31980 | −0.277481 | ||||||||
\(900\) | −4.44808 | −0.148269 | ||||||||
\(901\) | 2.50146 | 0.0833357 | ||||||||
\(902\) | −23.4686 | −0.781418 | ||||||||
\(903\) | −27.7734 | −0.924241 | ||||||||
\(904\) | −4.93096 | −0.164001 | ||||||||
\(905\) | −10.1387 | −0.337022 | ||||||||
\(906\) | −16.1145 | −0.535367 | ||||||||
\(907\) | 7.41910 | 0.246347 | 0.123174 | − | 0.992385i | \(-0.460693\pi\) | ||||
0.123174 | + | 0.992385i | \(0.460693\pi\) | |||||||
\(908\) | 15.4242 | 0.511868 | ||||||||
\(909\) | −7.31066 | −0.242479 | ||||||||
\(910\) | 1.36972 | 0.0454056 | ||||||||
\(911\) | 41.2334 | 1.36612 | 0.683062 | − | 0.730360i | \(-0.260648\pi\) | ||||
0.683062 | + | 0.730360i | \(0.260648\pi\) | |||||||
\(912\) | −2.79960 | −0.0927042 | ||||||||
\(913\) | −0.190459 | −0.00630328 | ||||||||
\(914\) | 7.76287 | 0.256773 | ||||||||
\(915\) | 1.18434 | 0.0391531 | ||||||||
\(916\) | 46.9210 | 1.55031 | ||||||||
\(917\) | 4.84486 | 0.159991 | ||||||||
\(918\) | −12.4892 | −0.412206 | ||||||||
\(919\) | −2.28384 | −0.0753370 | −0.0376685 | − | 0.999290i | \(-0.511993\pi\) | ||||
−0.0376685 | + | 0.999290i | \(0.511993\pi\) | |||||||
\(920\) | −0.0962996 | −0.00317490 | ||||||||
\(921\) | 6.14861 | 0.202604 | ||||||||
\(922\) | −31.9131 | −1.05100 | ||||||||
\(923\) | 1.55967 | 0.0513373 | ||||||||
\(924\) | 5.44464 | 0.179116 | ||||||||
\(925\) | 0.442598 | 0.0145525 | ||||||||
\(926\) | 38.8112 | 1.27542 | ||||||||
\(927\) | 19.5825 | 0.643172 | ||||||||
\(928\) | −36.1845 | −1.18782 | ||||||||
\(929\) | 0.727324 | 0.0238627 | 0.0119314 | − | 0.999929i | \(-0.496202\pi\) | ||||
0.0119314 | + | 0.999929i | \(0.496202\pi\) | |||||||
\(930\) | −2.06702 | −0.0677803 | ||||||||
\(931\) | 19.5512 | 0.640764 | ||||||||
\(932\) | 22.9755 | 0.752589 | ||||||||
\(933\) | 17.1788 | 0.562408 | ||||||||
\(934\) | 46.7009 | 1.52810 | ||||||||
\(935\) | 1.86183 | 0.0608885 | ||||||||
\(936\) | 0.207488 | 0.00678195 | ||||||||
\(937\) | 7.67144 | 0.250615 | 0.125308 | − | 0.992118i | \(-0.460008\pi\) | ||||
0.125308 | + | 0.992118i | \(0.460008\pi\) | |||||||
\(938\) | −106.603 | −3.48073 | ||||||||
\(939\) | −11.3659 | −0.370911 | ||||||||
\(940\) | 3.77474 | 0.123118 | ||||||||
\(941\) | 33.4104 | 1.08915 | 0.544574 | − | 0.838713i | \(-0.316691\pi\) | ||||
0.544574 | + | 0.838713i | \(0.316691\pi\) | |||||||
\(942\) | −7.35787 | −0.239732 | ||||||||
\(943\) | −2.04501 | −0.0665948 | ||||||||
\(944\) | −14.2269 | −0.463045 | ||||||||
\(945\) | −17.9660 | −0.584435 | ||||||||
\(946\) | −16.6978 | −0.542892 | ||||||||
\(947\) | −53.7974 | −1.74818 | −0.874091 | − | 0.485762i | \(-0.838542\pi\) | ||||
−0.874091 | + | 0.485762i | \(0.838542\pi\) | |||||||
\(948\) | −6.48789 | −0.210717 | ||||||||
\(949\) | −1.35134 | −0.0438664 | ||||||||
\(950\) | 1.92391 | 0.0624199 | ||||||||
\(951\) | −2.31167 | −0.0749611 | ||||||||
\(952\) | −5.51078 | −0.178605 | ||||||||
\(953\) | −14.6240 | −0.473719 | −0.236859 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236859 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(954\) | −6.75766 | −0.218787 | ||||||||
\(955\) | −8.99086 | −0.290937 | ||||||||
\(956\) | 4.26615 | 0.137977 | ||||||||
\(957\) | 2.98662 | 0.0965436 | ||||||||
\(958\) | −3.75014 | −0.121161 | ||||||||
\(959\) | −66.0547 | −2.13302 | ||||||||
\(960\) | −3.39069 | −0.109434 | ||||||||
\(961\) | −28.0071 | −0.903455 | ||||||||
\(962\) | 0.117651 | 0.00379324 | ||||||||
\(963\) | −8.53045 | −0.274890 | ||||||||
\(964\) | 41.6300 | 1.34081 | ||||||||
\(965\) | −4.44729 | −0.143163 | ||||||||
\(966\) | 1.03213 | 0.0332082 | ||||||||
\(967\) | −35.2412 | −1.13328 | −0.566640 | − | 0.823965i | \(-0.691757\pi\) | ||||
−0.566640 | + | 0.823965i | \(0.691757\pi\) | |||||||
\(968\) | −0.574421 | −0.0184626 | ||||||||
\(969\) | 1.15626 | 0.0371443 | ||||||||
\(970\) | 12.9722 | 0.416512 | ||||||||
\(971\) | 30.8760 | 0.990858 | 0.495429 | − | 0.868649i | \(-0.335011\pi\) | ||||
0.495429 | + | 0.868649i | \(0.335011\pi\) | |||||||
\(972\) | 23.7962 | 0.763263 | ||||||||
\(973\) | −106.116 | −3.40193 | ||||||||
\(974\) | 34.8829 | 1.11772 | ||||||||
\(975\) | 0.0858058 | 0.00274799 | ||||||||
\(976\) | −8.59700 | −0.275183 | ||||||||
\(977\) | −43.8813 | −1.40389 | −0.701943 | − | 0.712233i | \(-0.747684\pi\) | ||||
−0.701943 | + | 0.712233i | \(0.747684\pi\) | |||||||
\(978\) | −18.8131 | −0.601576 | ||||||||
\(979\) | −8.94416 | −0.285857 | ||||||||
\(980\) | 33.2650 | 1.06261 | ||||||||
\(981\) | −3.82407 | −0.122093 | ||||||||
\(982\) | 39.9153 | 1.27375 | ||||||||
\(983\) | −59.9692 | −1.91272 | −0.956360 | − | 0.292191i | \(-0.905616\pi\) | ||||
−0.956360 | + | 0.292191i | \(0.905616\pi\) | |||||||
\(984\) | 4.35156 | 0.138723 | ||||||||
\(985\) | 21.9424 | 0.699142 | ||||||||
\(986\) | 17.2263 | 0.548597 | ||||||||
\(987\) | 7.09950 | 0.225980 | ||||||||
\(988\) | 0.235081 | 0.00747893 | ||||||||
\(989\) | −1.45502 | −0.0462669 | ||||||||
\(990\) | −5.02972 | −0.159855 | ||||||||
\(991\) | −44.2019 | −1.40412 | −0.702060 | − | 0.712118i | \(-0.747736\pi\) | ||||
−0.702060 | + | 0.712118i | \(0.747736\pi\) | |||||||
\(992\) | 13.0168 | 0.413283 | ||||||||
\(993\) | −6.41604 | −0.203607 | ||||||||
\(994\) | 111.907 | 3.54947 | ||||||||
\(995\) | 13.7659 | 0.436409 | ||||||||
\(996\) | −0.201247 | −0.00637675 | ||||||||
\(997\) | 55.6039 | 1.76099 | 0.880496 | − | 0.474054i | \(-0.157210\pi\) | ||||
0.880496 | + | 0.474054i | \(0.157210\pi\) | |||||||
\(998\) | −44.5213 | −1.40930 | ||||||||
\(999\) | −1.54319 | −0.0488244 |
(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 | 1045.2.a.k.1.7 | ✓ | 9 | |
3.2 | odd | 2 | 9405.2.a.bh.1.3 | 9 | |||
5.4 | even | 2 | 5225.2.a.p.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.k.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial | |
5225.2.a.p.1.3 | 9 | 5.4 | even | 2 | |||
9405.2.a.bh.1.3 | 9 | 3.2 | odd | 2 |