Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.24 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.9 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.44935i | 1.02484i | 0.858734 | + | 0.512422i | \(0.171252\pi\) | ||||
−0.858734 | + | 0.512422i | \(0.828748\pi\) | |||||||
\(3\) | 0.0382575 | 0.0220880 | 0.0110440 | − | 0.999939i | \(-0.496485\pi\) | ||||
0.0110440 | + | 0.999939i | \(0.496485\pi\) | |||||||
\(4\) | −0.100611 | −0.0503057 | ||||||||
\(5\) | − | 3.85977i | − | 1.72614i | −0.505083 | − | 0.863071i | \(-0.668538\pi\) | ||
0.505083 | − | 0.863071i | \(-0.331462\pi\) | |||||||
\(6\) | 0.0554484i | 0.0226367i | ||||||||
\(7\) | − | 1.66255i | − | 0.628384i | −0.949359 | − | 0.314192i | \(-0.898266\pi\) | ||
0.949359 | − | 0.314192i | \(-0.101734\pi\) | |||||||
\(8\) | 2.75288i | 0.973289i | ||||||||
\(9\) | −2.99854 | −0.999512 | ||||||||
\(10\) | 5.59415 | 1.76903 | ||||||||
\(11\) | − | 1.88038i | − | 0.566955i | −0.958979 | − | 0.283477i | \(-0.908512\pi\) | ||
0.958979 | − | 0.283477i | \(-0.0914881\pi\) | |||||||
\(12\) | −0.00384914 | −0.00111115 | ||||||||
\(13\) | 1.08571 | − | 3.43820i | 0.301122 | − | 0.953586i | ||||
\(14\) | 2.40961 | 0.643996 | ||||||||
\(15\) | − | 0.147665i | − | 0.0381270i | ||||||
\(16\) | −4.19110 | −1.04778 | ||||||||
\(17\) | 3.75015 | 0.909546 | 0.454773 | − | 0.890607i | \(-0.349720\pi\) | ||||
0.454773 | + | 0.890607i | \(0.349720\pi\) | |||||||
\(18\) | − | 4.34592i | − | 1.02434i | ||||||
\(19\) | − | 3.26949i | − | 0.750073i | −0.927010 | − | 0.375036i | \(-0.877630\pi\) | ||
0.927010 | − | 0.375036i | \(-0.122370\pi\) | |||||||
\(20\) | 0.388337i | 0.0868349i | ||||||||
\(21\) | − | 0.0636049i | − | 0.0138797i | ||||||
\(22\) | 2.72532 | 0.581040 | ||||||||
\(23\) | 5.31401 | 1.10805 | 0.554023 | − | 0.832501i | \(-0.313092\pi\) | ||||
0.554023 | + | 0.832501i | \(0.313092\pi\) | |||||||
\(24\) | 0.105318i | 0.0214980i | ||||||||
\(25\) | −9.89783 | −1.97957 | ||||||||
\(26\) | 4.98315 | + | 1.57358i | 0.977277 | + | 0.308603i | ||||
\(27\) | −0.229489 | −0.0441651 | ||||||||
\(28\) | 0.167271i | 0.0316113i | ||||||||
\(29\) | 3.11168 | 0.577824 | 0.288912 | − | 0.957356i | \(-0.406706\pi\) | ||||
0.288912 | + | 0.957356i | \(0.406706\pi\) | |||||||
\(30\) | 0.214018 | 0.0390742 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | − | 0.568613i | − | 0.100518i | ||||||
\(33\) | − | 0.0719384i | − | 0.0125229i | ||||||
\(34\) | 5.43528i | 0.932143i | ||||||||
\(35\) | −6.41705 | −1.08468 | ||||||||
\(36\) | 0.301687 | 0.0502812 | ||||||||
\(37\) | 11.5806i | 1.90383i | 0.306361 | + | 0.951915i | \(0.400888\pi\) | ||||
−0.306361 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(38\) | 4.73863 | 0.768708 | ||||||||
\(39\) | 0.0415366 | − | 0.131537i | 0.00665118 | − | 0.0210628i | ||||
\(40\) | 10.6255 | 1.68003 | ||||||||
\(41\) | 7.94532i | 1.24085i | 0.784266 | + | 0.620425i | \(0.213040\pi\) | ||||
−0.784266 | + | 0.620425i | \(0.786960\pi\) | |||||||
\(42\) | 0.0921856 | 0.0142246 | ||||||||
\(43\) | −9.24319 | −1.40957 | −0.704786 | − | 0.709420i | \(-0.748957\pi\) | ||||
−0.704786 | + | 0.709420i | \(0.748957\pi\) | |||||||
\(44\) | 0.189187i | 0.0285211i | ||||||||
\(45\) | 11.5737i | 1.72530i | ||||||||
\(46\) | 7.70185i | 1.13558i | ||||||||
\(47\) | − | 6.97995i | − | 1.01813i | −0.860728 | − | 0.509065i | \(-0.829991\pi\) | ||
0.860728 | − | 0.509065i | \(-0.170009\pi\) | |||||||
\(48\) | −0.160341 | −0.0231432 | ||||||||
\(49\) | 4.23593 | 0.605133 | ||||||||
\(50\) | − | 14.3454i | − | 2.02875i | ||||||
\(51\) | 0.143471 | 0.0200900 | ||||||||
\(52\) | −0.109235 | + | 0.345923i | −0.0151482 | + | 0.0479708i | ||||
\(53\) | 6.11470 | 0.839918 | 0.419959 | − | 0.907543i | \(-0.362044\pi\) | ||||
0.419959 | + | 0.907543i | \(0.362044\pi\) | |||||||
\(54\) | − | 0.332609i | − | 0.0452624i | ||||||
\(55\) | −7.25782 | −0.978644 | ||||||||
\(56\) | 4.57679 | 0.611599 | ||||||||
\(57\) | − | 0.125082i | − | 0.0165676i | ||||||
\(58\) | 4.50991i | 0.592180i | ||||||||
\(59\) | 12.1104i | 1.57664i | 0.615268 | + | 0.788318i | \(0.289048\pi\) | ||||
−0.615268 | + | 0.788318i | \(0.710952\pi\) | |||||||
\(60\) | 0.0148568i | 0.00191801i | ||||||||
\(61\) | 1.75416 | 0.224598 | 0.112299 | − | 0.993674i | \(-0.464179\pi\) | ||||
0.112299 | + | 0.993674i | \(0.464179\pi\) | |||||||
\(62\) | 1.44935 | 0.184067 | ||||||||
\(63\) | 4.98521i | 0.628078i | ||||||||
\(64\) | −7.55808 | −0.944760 | ||||||||
\(65\) | −13.2707 | − | 4.19060i | −1.64602 | − | 0.519780i | ||||
\(66\) | 0.104264 | 0.0128340 | ||||||||
\(67\) | − | 7.94479i | − | 0.970611i | −0.874345 | − | 0.485306i | \(-0.838708\pi\) | ||
0.874345 | − | 0.485306i | \(-0.161292\pi\) | |||||||
\(68\) | −0.377308 | −0.0457554 | ||||||||
\(69\) | 0.203300 | 0.0244745 | ||||||||
\(70\) | − | 9.30055i | − | 1.11163i | ||||||
\(71\) | − | 0.735383i | − | 0.0872739i | −0.999047 | − | 0.0436369i | \(-0.986106\pi\) | ||
0.999047 | − | 0.0436369i | \(-0.0138945\pi\) | |||||||
\(72\) | − | 8.25460i | − | 0.972814i | ||||||
\(73\) | − | 13.5423i | − | 1.58500i | −0.609870 | − | 0.792501i | \(-0.708778\pi\) | ||
0.609870 | − | 0.792501i | \(-0.291222\pi\) | |||||||
\(74\) | −16.7843 | −1.95113 | ||||||||
\(75\) | −0.378666 | −0.0437246 | ||||||||
\(76\) | 0.328948i | 0.0377330i | ||||||||
\(77\) | −3.12622 | −0.356265 | ||||||||
\(78\) | 0.190643 | + | 0.0602010i | 0.0215860 | + | 0.00681642i | ||||
\(79\) | −5.66333 | −0.637174 | −0.318587 | − | 0.947894i | \(-0.603208\pi\) | ||||
−0.318587 | + | 0.947894i | \(0.603208\pi\) | |||||||
\(80\) | 16.1767i | 1.80861i | ||||||||
\(81\) | 8.98683 | 0.998537 | ||||||||
\(82\) | −11.5155 | −1.27168 | ||||||||
\(83\) | 13.7729i | 1.51177i | 0.654704 | + | 0.755886i | \(0.272793\pi\) | ||||
−0.654704 | + | 0.755886i | \(0.727207\pi\) | |||||||
\(84\) | 0.00639938i | 0.000698230i | ||||||||
\(85\) | − | 14.4747i | − | 1.57001i | ||||||
\(86\) | − | 13.3966i | − | 1.44459i | ||||||
\(87\) | 0.119045 | 0.0127630 | ||||||||
\(88\) | 5.17644 | 0.551811 | ||||||||
\(89\) | − | 10.2781i | − | 1.08948i | −0.838606 | − | 0.544738i | \(-0.816629\pi\) | ||
0.838606 | − | 0.544738i | \(-0.183371\pi\) | |||||||
\(90\) | −16.7743 | −1.76816 | ||||||||
\(91\) | −5.71618 | − | 1.80505i | −0.599218 | − | 0.189220i | ||||
\(92\) | −0.534650 | −0.0557411 | ||||||||
\(93\) | − | 0.0382575i | − | 0.00396711i | ||||||
\(94\) | 10.1164 | 1.04342 | ||||||||
\(95\) | −12.6195 | −1.29473 | ||||||||
\(96\) | − | 0.0217537i | − | 0.00222023i | ||||||
\(97\) | 8.34364i | 0.847169i | 0.905857 | + | 0.423584i | \(0.139228\pi\) | ||||
−0.905857 | + | 0.423584i | \(0.860772\pi\) | |||||||
\(98\) | 6.13935i | 0.620168i | ||||||||
\(99\) | 5.63838i | 0.566678i | ||||||||
\(100\) | 0.995836 | 0.0995836 | ||||||||
\(101\) | 8.36630 | 0.832478 | 0.416239 | − | 0.909255i | \(-0.363348\pi\) | ||||
0.416239 | + | 0.909255i | \(0.363348\pi\) | |||||||
\(102\) | 0.207940i | 0.0205891i | ||||||||
\(103\) | 14.0180 | 1.38123 | 0.690616 | − | 0.723222i | \(-0.257340\pi\) | ||||
0.690616 | + | 0.723222i | \(0.257340\pi\) | |||||||
\(104\) | 9.46494 | + | 2.98883i | 0.928114 | + | 0.293079i | ||||
\(105\) | −0.245500 | −0.0239584 | ||||||||
\(106\) | 8.86233i | 0.860785i | ||||||||
\(107\) | −0.569178 | −0.0550245 | −0.0275122 | − | 0.999621i | \(-0.508759\pi\) | ||||
−0.0275122 | + | 0.999621i | \(0.508759\pi\) | |||||||
\(108\) | 0.0230892 | 0.00222176 | ||||||||
\(109\) | 10.7415i | 1.02885i | 0.857537 | + | 0.514423i | \(0.171994\pi\) | ||||
−0.857537 | + | 0.514423i | \(0.828006\pi\) | |||||||
\(110\) | − | 10.5191i | − | 1.00296i | ||||||
\(111\) | 0.443043i | 0.0420517i | ||||||||
\(112\) | 6.96791i | 0.658405i | ||||||||
\(113\) | −7.41542 | −0.697584 | −0.348792 | − | 0.937200i | \(-0.613408\pi\) | ||||
−0.348792 | + | 0.937200i | \(0.613408\pi\) | |||||||
\(114\) | 0.181288 | 0.0169792 | ||||||||
\(115\) | − | 20.5108i | − | 1.91265i | ||||||
\(116\) | −0.313071 | −0.0290679 | ||||||||
\(117\) | −3.25555 | + | 10.3096i | −0.300975 | + | 0.953120i | ||||
\(118\) | −17.5522 | −1.61581 | ||||||||
\(119\) | − | 6.23481i | − | 0.571544i | ||||||
\(120\) | 0.406504 | 0.0371085 | ||||||||
\(121\) | 7.46419 | 0.678562 | ||||||||
\(122\) | 2.54240i | 0.230178i | ||||||||
\(123\) | 0.303968i | 0.0274079i | ||||||||
\(124\) | 0.100611i | 0.00903518i | ||||||||
\(125\) | 18.9045i | 1.69087i | ||||||||
\(126\) | −7.22531 | −0.643682 | ||||||||
\(127\) | −18.2144 | −1.61627 | −0.808133 | − | 0.589000i | \(-0.799522\pi\) | ||||
−0.808133 | + | 0.589000i | \(0.799522\pi\) | |||||||
\(128\) | − | 12.0915i | − | 1.06875i | ||||||
\(129\) | −0.353621 | −0.0311346 | ||||||||
\(130\) | 6.07364 | − | 19.2338i | 0.532693 | − | 1.68692i | ||||
\(131\) | 18.5465 | 1.62042 | 0.810209 | − | 0.586141i | \(-0.199354\pi\) | ||||
0.810209 | + | 0.586141i | \(0.199354\pi\) | |||||||
\(132\) | 0.00723783i | 0.000629972i | ||||||||
\(133\) | −5.43568 | −0.471334 | ||||||||
\(134\) | 11.5148 | 0.994725 | ||||||||
\(135\) | 0.885774i | 0.0762353i | ||||||||
\(136\) | 10.3237i | 0.885251i | ||||||||
\(137\) | − | 3.12119i | − | 0.266661i | −0.991072 | − | 0.133331i | \(-0.957433\pi\) | ||
0.991072 | − | 0.133331i | \(-0.0425672\pi\) | |||||||
\(138\) | 0.294653i | 0.0250825i | ||||||||
\(139\) | −16.0910 | −1.36482 | −0.682410 | − | 0.730970i | \(-0.739068\pi\) | ||||
−0.682410 | + | 0.730970i | \(0.739068\pi\) | |||||||
\(140\) | 0.645629 | 0.0545657 | ||||||||
\(141\) | − | 0.267035i | − | 0.0224884i | ||||||
\(142\) | 1.06583 | 0.0894421 | ||||||||
\(143\) | −6.46511 | − | 2.04155i | −0.540640 | − | 0.170723i | ||||
\(144\) | 12.5672 | 1.04726 | ||||||||
\(145\) | − | 12.0104i | − | 0.997407i | ||||||
\(146\) | 19.6275 | 1.62438 | ||||||||
\(147\) | 0.162056 | 0.0133662 | ||||||||
\(148\) | − | 1.16514i | − | 0.0957736i | ||||||
\(149\) | 18.8430i | 1.54368i | 0.635820 | + | 0.771838i | \(0.280662\pi\) | ||||
−0.635820 | + | 0.771838i | \(0.719338\pi\) | |||||||
\(150\) | − | 0.548819i | − | 0.0448109i | ||||||
\(151\) | 0.726888i | 0.0591533i | 0.999563 | + | 0.0295767i | \(0.00941591\pi\) | ||||
−0.999563 | + | 0.0295767i | \(0.990584\pi\) | |||||||
\(152\) | 9.00050 | 0.730037 | ||||||||
\(153\) | −11.2450 | −0.909102 | ||||||||
\(154\) | − | 4.53098i | − | 0.365116i | ||||||
\(155\) | −3.85977 | −0.310024 | ||||||||
\(156\) | −0.00417906 | + | 0.0132341i | −0.000334592 | + | 0.00105958i | ||||
\(157\) | −5.75901 | −0.459619 | −0.229809 | − | 0.973236i | \(-0.573810\pi\) | ||||
−0.229809 | + | 0.973236i | \(0.573810\pi\) | |||||||
\(158\) | − | 8.20814i | − | 0.653004i | ||||||
\(159\) | 0.233933 | 0.0185521 | ||||||||
\(160\) | −2.19472 | −0.173508 | ||||||||
\(161\) | − | 8.83479i | − | 0.696279i | ||||||
\(162\) | 13.0250i | 1.02334i | ||||||||
\(163\) | 3.17279i | 0.248512i | 0.992250 | + | 0.124256i | \(0.0396544\pi\) | ||||
−0.992250 | + | 0.124256i | \(0.960346\pi\) | |||||||
\(164\) | − | 0.799390i | − | 0.0624219i | ||||||
\(165\) | −0.277666 | −0.0216163 | ||||||||
\(166\) | −19.9617 | −1.54933 | ||||||||
\(167\) | − | 4.97051i | − | 0.384630i | −0.981333 | − | 0.192315i | \(-0.938400\pi\) | ||
0.981333 | − | 0.192315i | \(-0.0615995\pi\) | |||||||
\(168\) | 0.175096 | 0.0135090 | ||||||||
\(169\) | −10.6425 | − | 7.46579i | −0.818651 | − | 0.574292i | ||||
\(170\) | 20.9789 | 1.60901 | ||||||||
\(171\) | 9.80369i | 0.749707i | ||||||||
\(172\) | 0.929971 | 0.0709096 | ||||||||
\(173\) | −1.97560 | −0.150202 | −0.0751009 | − | 0.997176i | \(-0.523928\pi\) | ||||
−0.0751009 | + | 0.997176i | \(0.523928\pi\) | |||||||
\(174\) | 0.172538i | 0.0130800i | ||||||||
\(175\) | 16.4556i | 1.24393i | ||||||||
\(176\) | 7.88084i | 0.594041i | ||||||||
\(177\) | 0.463312i | 0.0348247i | ||||||||
\(178\) | 14.8965 | 1.11654 | ||||||||
\(179\) | 6.07427 | 0.454012 | 0.227006 | − | 0.973893i | \(-0.427106\pi\) | ||||
0.227006 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(180\) | − | 1.16444i | − | 0.0867925i | ||||||
\(181\) | 20.6084 | 1.53181 | 0.765906 | − | 0.642953i | \(-0.222291\pi\) | ||||
0.765906 | + | 0.642953i | \(0.222291\pi\) | |||||||
\(182\) | 2.61614 | − | 8.28473i | 0.193922 | − | 0.614105i | ||||
\(183\) | 0.0671099 | 0.00496091 | ||||||||
\(184\) | 14.6288i | 1.07845i | ||||||||
\(185\) | 44.6983 | 3.28628 | ||||||||
\(186\) | 0.0554484 | 0.00406567 | ||||||||
\(187\) | − | 7.05170i | − | 0.515671i | ||||||
\(188\) | 0.702263i | 0.0512178i | ||||||||
\(189\) | 0.381536i | 0.0277527i | ||||||||
\(190\) | − | 18.2900i | − | 1.32690i | ||||||
\(191\) | 6.78433 | 0.490897 | 0.245448 | − | 0.969410i | \(-0.421065\pi\) | ||||
0.245448 | + | 0.969410i | \(0.421065\pi\) | |||||||
\(192\) | −0.289153 | −0.0208678 | ||||||||
\(193\) | − | 22.3446i | − | 1.60840i | −0.594361 | − | 0.804198i | \(-0.702595\pi\) | ||
0.594361 | − | 0.804198i | \(-0.297405\pi\) | |||||||
\(194\) | −12.0928 | −0.868216 | ||||||||
\(195\) | −0.507702 | − | 0.160322i | −0.0363573 | − | 0.0114809i | ||||
\(196\) | −0.426184 | −0.0304417 | ||||||||
\(197\) | 6.85560i | 0.488441i | 0.969720 | + | 0.244221i | \(0.0785321\pi\) | ||||
−0.969720 | + | 0.244221i | \(0.921468\pi\) | |||||||
\(198\) | −8.17197 | −0.580757 | ||||||||
\(199\) | −6.55363 | −0.464575 | −0.232287 | − | 0.972647i | \(-0.574621\pi\) | ||||
−0.232287 | + | 0.972647i | \(0.574621\pi\) | |||||||
\(200\) | − | 27.2475i | − | 1.92669i | ||||||
\(201\) | − | 0.303948i | − | 0.0214388i | ||||||
\(202\) | 12.1257i | 0.853160i | ||||||||
\(203\) | − | 5.17332i | − | 0.363096i | ||||||
\(204\) | −0.0144349 | −0.00101064 | ||||||||
\(205\) | 30.6671 | 2.14188 | ||||||||
\(206\) | 20.3169i | 1.41555i | ||||||||
\(207\) | −15.9342 | −1.10751 | ||||||||
\(208\) | −4.55033 | + | 14.4098i | −0.315508 | + | 0.999143i | ||||
\(209\) | −6.14787 | −0.425257 | ||||||||
\(210\) | − | 0.355815i | − | 0.0245536i | ||||||
\(211\) | 21.8282 | 1.50271 | 0.751356 | − | 0.659897i | \(-0.229400\pi\) | ||||
0.751356 | + | 0.659897i | \(0.229400\pi\) | |||||||
\(212\) | −0.615209 | −0.0422527 | ||||||||
\(213\) | − | 0.0281339i | − | 0.00192770i | ||||||
\(214\) | − | 0.824937i | − | 0.0563915i | ||||||
\(215\) | 35.6766i | 2.43312i | ||||||||
\(216\) | − | 0.631754i | − | 0.0429854i | ||||||
\(217\) | −1.66255 | −0.112861 | ||||||||
\(218\) | −15.5681 | −1.05441 | ||||||||
\(219\) | − | 0.518093i | − | 0.0350095i | ||||||
\(220\) | 0.730220 | 0.0492314 | ||||||||
\(221\) | 4.07159 | − | 12.8938i | 0.273884 | − | 0.867330i | ||||
\(222\) | −0.642123 | −0.0430965 | ||||||||
\(223\) | 1.22551i | 0.0820659i | 0.999158 | + | 0.0410330i | \(0.0130649\pi\) | ||||
−0.999158 | + | 0.0410330i | \(0.986935\pi\) | |||||||
\(224\) | −0.945347 | −0.0631636 | ||||||||
\(225\) | 29.6790 | 1.97860 | ||||||||
\(226\) | − | 10.7475i | − | 0.714915i | ||||||
\(227\) | 9.82473i | 0.652090i | 0.945354 | + | 0.326045i | \(0.105716\pi\) | ||||
−0.945354 | + | 0.326045i | \(0.894284\pi\) | |||||||
\(228\) | 0.0125847i | 0.000833444i | ||||||||
\(229\) | 1.46932i | 0.0970954i | 0.998821 | + | 0.0485477i | \(0.0154593\pi\) | ||||
−0.998821 | + | 0.0485477i | \(0.984541\pi\) | |||||||
\(230\) | 29.7274 | 1.96016 | ||||||||
\(231\) | −0.119601 | −0.00786917 | ||||||||
\(232\) | 8.56607i | 0.562390i | ||||||||
\(233\) | 14.1766 | 0.928737 | 0.464369 | − | 0.885642i | \(-0.346281\pi\) | ||||
0.464369 | + | 0.885642i | \(0.346281\pi\) | |||||||
\(234\) | −14.9422 | − | 4.71842i | −0.976800 | − | 0.308453i | ||||
\(235\) | −26.9410 | −1.75744 | ||||||||
\(236\) | − | 1.21844i | − | 0.0793139i | ||||||
\(237\) | −0.216665 | −0.0140739 | ||||||||
\(238\) | 9.03641 | 0.585744 | ||||||||
\(239\) | 12.4101i | 0.802745i | 0.915915 | + | 0.401372i | \(0.131467\pi\) | ||||
−0.915915 | + | 0.401372i | \(0.868533\pi\) | |||||||
\(240\) | 0.618879i | 0.0399485i | ||||||||
\(241\) | 9.96203i | 0.641711i | 0.947128 | + | 0.320855i | \(0.103970\pi\) | ||||
−0.947128 | + | 0.320855i | \(0.896030\pi\) | |||||||
\(242\) | 10.8182i | 0.695421i | ||||||||
\(243\) | 1.03228 | 0.0662208 | ||||||||
\(244\) | −0.176489 | −0.0112986 | ||||||||
\(245\) | − | 16.3497i | − | 1.04455i | ||||||
\(246\) | −0.440555 | −0.0280888 | ||||||||
\(247\) | −11.2412 | − | 3.54972i | −0.715258 | − | 0.225864i | ||||
\(248\) | 2.75288 | 0.174808 | ||||||||
\(249\) | 0.526916i | 0.0333919i | ||||||||
\(250\) | −27.3992 | −1.73288 | ||||||||
\(251\) | −2.57983 | −0.162837 | −0.0814187 | − | 0.996680i | \(-0.525945\pi\) | ||||
−0.0814187 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(252\) | − | 0.501570i | − | 0.0315959i | ||||||
\(253\) | − | 9.99233i | − | 0.628212i | ||||||
\(254\) | − | 26.3990i | − | 1.65642i | ||||||
\(255\) | − | 0.553767i | − | 0.0346782i | ||||||
\(256\) | 2.40867 | 0.150542 | ||||||||
\(257\) | 8.69963 | 0.542668 | 0.271334 | − | 0.962485i | \(-0.412535\pi\) | ||||
0.271334 | + | 0.962485i | \(0.412535\pi\) | |||||||
\(258\) | − | 0.512520i | − | 0.0319081i | ||||||
\(259\) | 19.2532 | 1.19634 | ||||||||
\(260\) | 1.33518 | + | 0.421622i | 0.0828045 | + | 0.0261479i | ||||
\(261\) | −9.33048 | −0.577542 | ||||||||
\(262\) | 26.8804i | 1.66068i | ||||||||
\(263\) | 4.64597 | 0.286483 | 0.143241 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143241 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(264\) | 0.198038 | 0.0121884 | ||||||||
\(265\) | − | 23.6013i | − | 1.44982i | ||||||
\(266\) | − | 7.87820i | − | 0.483044i | ||||||
\(267\) | − | 0.393214i | − | 0.0240643i | ||||||
\(268\) | 0.799338i | 0.0488273i | ||||||||
\(269\) | −1.50231 | −0.0915976 | −0.0457988 | − | 0.998951i | \(-0.514583\pi\) | ||||
−0.0457988 | + | 0.998951i | \(0.514583\pi\) | |||||||
\(270\) | −1.28380 | −0.0781293 | ||||||||
\(271\) | 8.71423i | 0.529352i | 0.964337 | + | 0.264676i | \(0.0852650\pi\) | ||||
−0.964337 | + | 0.264676i | \(0.914735\pi\) | |||||||
\(272\) | −15.7173 | −0.952999 | ||||||||
\(273\) | −0.218686 | − | 0.0690566i | −0.0132355 | − | 0.00417949i | ||||
\(274\) | 4.52369 | 0.273286 | ||||||||
\(275\) | 18.6116i | 1.12232i | ||||||||
\(276\) | −0.0204544 | −0.00123121 | ||||||||
\(277\) | 4.24495 | 0.255054 | 0.127527 | − | 0.991835i | \(-0.459296\pi\) | ||||
0.127527 | + | 0.991835i | \(0.459296\pi\) | |||||||
\(278\) | − | 23.3214i | − | 1.39873i | ||||||
\(279\) | 2.99854i | 0.179518i | ||||||||
\(280\) | − | 17.6654i | − | 1.05571i | ||||||
\(281\) | 5.08775i | 0.303510i | 0.988418 | + | 0.151755i | \(0.0484924\pi\) | ||||
−0.988418 | + | 0.151755i | \(0.951508\pi\) | |||||||
\(282\) | 0.387027 | 0.0230471 | ||||||||
\(283\) | −32.6740 | −1.94227 | −0.971134 | − | 0.238533i | \(-0.923334\pi\) | ||||
−0.971134 | + | 0.238533i | \(0.923334\pi\) | |||||||
\(284\) | 0.0739880i | 0.00439038i | ||||||||
\(285\) | −0.482789 | −0.0285980 | ||||||||
\(286\) | 2.95891 | − | 9.37020i | 0.174964 | − | 0.554072i | ||||
\(287\) | 13.2095 | 0.779731 | ||||||||
\(288\) | 1.70501i | 0.100469i | ||||||||
\(289\) | −2.93635 | −0.172727 | ||||||||
\(290\) | 17.4072 | 1.02219 | ||||||||
\(291\) | 0.319207i | 0.0187122i | ||||||||
\(292\) | 1.36251i | 0.0797347i | ||||||||
\(293\) | − | 10.6513i | − | 0.622254i | −0.950368 | − | 0.311127i | \(-0.899293\pi\) | ||
0.950368 | − | 0.311127i | \(-0.100707\pi\) | |||||||
\(294\) | 0.234876i | 0.0136982i | ||||||||
\(295\) | 46.7433 | 2.72150 | ||||||||
\(296\) | −31.8798 | −1.85298 | ||||||||
\(297\) | 0.431525i | 0.0250396i | ||||||||
\(298\) | −27.3100 | −1.58203 | ||||||||
\(299\) | 5.76948 | − | 18.2706i | 0.333658 | − | 1.05662i | ||||
\(300\) | 0.0380982 | 0.00219960 | ||||||||
\(301\) | 15.3672i | 0.885753i | ||||||||
\(302\) | −1.05351 | −0.0606229 | ||||||||
\(303\) | 0.320073 | 0.0183877 | ||||||||
\(304\) | 13.7028i | 0.785907i | ||||||||
\(305\) | − | 6.77067i | − | 0.387688i | ||||||
\(306\) | − | 16.2979i | − | 0.931688i | ||||||
\(307\) | − | 11.4536i | − | 0.653691i | −0.945078 | − | 0.326845i | \(-0.894014\pi\) | ||
0.945078 | − | 0.326845i | \(-0.105986\pi\) | |||||||
\(308\) | 0.314533 | 0.0179222 | ||||||||
\(309\) | 0.536292 | 0.0305086 | ||||||||
\(310\) | − | 5.59415i | − | 0.317727i | ||||||
\(311\) | −14.2666 | −0.808983 | −0.404492 | − | 0.914542i | \(-0.632552\pi\) | ||||
−0.404492 | + | 0.914542i | \(0.632552\pi\) | |||||||
\(312\) | 0.362105 | + | 0.114345i | 0.0205001 | + | 0.00647352i | ||||
\(313\) | 10.3671 | 0.585983 | 0.292991 | − | 0.956115i | \(-0.405349\pi\) | ||||
0.292991 | + | 0.956115i | \(0.405349\pi\) | |||||||
\(314\) | − | 8.34681i | − | 0.471038i | ||||||
\(315\) | 19.2418 | 1.08415 | ||||||||
\(316\) | 0.569796 | 0.0320535 | ||||||||
\(317\) | − | 5.67935i | − | 0.318984i | −0.987199 | − | 0.159492i | \(-0.949014\pi\) | ||
0.987199 | − | 0.159492i | \(-0.0509857\pi\) | |||||||
\(318\) | 0.339050i | 0.0190130i | ||||||||
\(319\) | − | 5.85113i | − | 0.327600i | ||||||
\(320\) | 29.1725i | 1.63079i | ||||||||
\(321\) | −0.0217753 | −0.00121538 | ||||||||
\(322\) | 12.8047 | 0.713577 | ||||||||
\(323\) | − | 12.2611i | − | 0.682225i | ||||||
\(324\) | −0.904178 | −0.0502321 | ||||||||
\(325\) | −10.7462 | + | 34.0307i | −0.596092 | + | 1.88769i | ||||
\(326\) | −4.59848 | −0.254686 | ||||||||
\(327\) | 0.410941i | 0.0227251i | ||||||||
\(328\) | −21.8725 | −1.20771 | ||||||||
\(329\) | −11.6045 | −0.639777 | ||||||||
\(330\) | − | 0.402435i | − | 0.0221533i | ||||||
\(331\) | − | 0.676975i | − | 0.0372099i | −0.999827 | − | 0.0186050i | \(-0.994078\pi\) | ||
0.999827 | − | 0.0186050i | \(-0.00592248\pi\) | |||||||
\(332\) | − | 1.38571i | − | 0.0760508i | ||||||
\(333\) | − | 34.7247i | − | 1.90290i | ||||||
\(334\) | 7.20401 | 0.394186 | ||||||||
\(335\) | −30.6651 | −1.67541 | ||||||||
\(336\) | 0.266574i | 0.0145428i | ||||||||
\(337\) | 4.73721 | 0.258052 | 0.129026 | − | 0.991641i | \(-0.458815\pi\) | ||||
0.129026 | + | 0.991641i | \(0.458815\pi\) | |||||||
\(338\) | 10.8205 | − | 15.4246i | 0.588560 | − | 0.838989i | ||||
\(339\) | −0.283695 | −0.0154082 | ||||||||
\(340\) | 1.45632i | 0.0789803i | ||||||||
\(341\) | −1.88038 | −0.101828 | ||||||||
\(342\) | −14.2090 | −0.768332 | ||||||||
\(343\) | − | 18.6803i | − | 1.00864i | ||||||
\(344\) | − | 25.4453i | − | 1.37192i | ||||||
\(345\) | − | 0.784693i | − | 0.0422464i | ||||||
\(346\) | − | 2.86333i | − | 0.153933i | ||||||
\(347\) | −31.6786 | −1.70059 | −0.850297 | − | 0.526303i | \(-0.823578\pi\) | ||||
−0.850297 | + | 0.526303i | \(0.823578\pi\) | |||||||
\(348\) | −0.0119773 | −0.000642050 | ||||||||
\(349\) | 8.64433i | 0.462720i | 0.972868 | + | 0.231360i | \(0.0743176\pi\) | ||||
−0.972868 | + | 0.231360i | \(0.925682\pi\) | |||||||
\(350\) | −23.8499 | −1.27483 | ||||||||
\(351\) | −0.249159 | + | 0.789029i | −0.0132991 | + | 0.0421152i | ||||
\(352\) | −1.06921 | −0.0569889 | ||||||||
\(353\) | 11.6266i | 0.618820i | 0.950929 | + | 0.309410i | \(0.100131\pi\) | ||||
−0.950929 | + | 0.309410i | \(0.899869\pi\) | |||||||
\(354\) | −0.671501 | −0.0356899 | ||||||||
\(355\) | −2.83841 | −0.150647 | ||||||||
\(356\) | 1.03409i | 0.0548069i | ||||||||
\(357\) | − | 0.238528i | − | 0.0126242i | ||||||
\(358\) | 8.80373i | 0.465292i | ||||||||
\(359\) | 5.12526i | 0.270501i | 0.990811 | + | 0.135250i | \(0.0431839\pi\) | ||||
−0.990811 | + | 0.135250i | \(0.956816\pi\) | |||||||
\(360\) | −31.8609 | −1.67921 | ||||||||
\(361\) | 8.31043 | 0.437391 | ||||||||
\(362\) | 29.8688i | 1.56987i | ||||||||
\(363\) | 0.285561 | 0.0149881 | ||||||||
\(364\) | 0.575113 | + | 0.181609i | 0.0301441 | + | 0.00951888i | ||||
\(365\) | −52.2701 | −2.73594 | ||||||||
\(366\) | 0.0972656i | 0.00508416i | ||||||||
\(367\) | −35.1284 | −1.83369 | −0.916844 | − | 0.399246i | \(-0.869272\pi\) | ||||
−0.916844 | + | 0.399246i | \(0.869272\pi\) | |||||||
\(368\) | −22.2715 | −1.16098 | ||||||||
\(369\) | − | 23.8243i | − | 1.24024i | ||||||
\(370\) | 64.7834i | 3.36793i | ||||||||
\(371\) | − | 10.1660i | − | 0.527791i | ||||||
\(372\) | 0.00384914i | 0.000199569i | ||||||||
\(373\) | 3.37056 | 0.174521 | 0.0872604 | − | 0.996186i | \(-0.472189\pi\) | ||||
0.0872604 | + | 0.996186i | \(0.472189\pi\) | |||||||
\(374\) | 10.2204 | 0.528483 | ||||||||
\(375\) | 0.723239i | 0.0373479i | ||||||||
\(376\) | 19.2149 | 0.990934 | ||||||||
\(377\) | 3.37839 | − | 10.6986i | 0.173996 | − | 0.551005i | ||||
\(378\) | −0.552979 | −0.0284422 | ||||||||
\(379\) | 15.5733i | 0.799945i | 0.916527 | + | 0.399972i | \(0.130980\pi\) | ||||
−0.916527 | + | 0.399972i | \(0.869020\pi\) | |||||||
\(380\) | 1.26967 | 0.0651324 | ||||||||
\(381\) | −0.696837 | −0.0357000 | ||||||||
\(382\) | 9.83285i | 0.503092i | ||||||||
\(383\) | − | 14.2746i | − | 0.729396i | −0.931126 | − | 0.364698i | \(-0.881172\pi\) | ||
0.931126 | − | 0.364698i | \(-0.118828\pi\) | |||||||
\(384\) | − | 0.462591i | − | 0.0236065i | ||||||
\(385\) | 12.0665i | 0.614964i | ||||||||
\(386\) | 32.3851 | 1.64836 | ||||||||
\(387\) | 27.7160 | 1.40888 | ||||||||
\(388\) | − | 0.839467i | − | 0.0426175i | ||||||
\(389\) | 10.3188 | 0.523185 | 0.261592 | − | 0.965178i | \(-0.415752\pi\) | ||||
0.261592 | + | 0.965178i | \(0.415752\pi\) | |||||||
\(390\) | 0.232362 | − | 0.735838i | 0.0117661 | − | 0.0372606i | ||||
\(391\) | 19.9283 | 1.00782 | ||||||||
\(392\) | 11.6610i | 0.588970i | ||||||||
\(393\) | 0.709543 | 0.0357917 | ||||||||
\(394\) | −9.93615 | −0.500576 | ||||||||
\(395\) | 21.8591i | 1.09985i | ||||||||
\(396\) | − | 0.567285i | − | 0.0285072i | ||||||
\(397\) | 24.3801i | 1.22360i | 0.791012 | + | 0.611801i | \(0.209554\pi\) | ||||
−0.791012 | + | 0.611801i | \(0.790446\pi\) | |||||||
\(398\) | − | 9.49850i | − | 0.476117i | ||||||
\(399\) | −0.207956 | −0.0104108 | ||||||||
\(400\) | 41.4828 | 2.07414 | ||||||||
\(401\) | − | 15.7425i | − | 0.786141i | −0.919508 | − | 0.393071i | \(-0.871413\pi\) | ||
0.919508 | − | 0.393071i | \(-0.128587\pi\) | |||||||
\(402\) | 0.440526 | 0.0219714 | ||||||||
\(403\) | −3.43820 | − | 1.08571i | −0.171269 | − | 0.0540832i | ||||
\(404\) | −0.841746 | −0.0418784 | ||||||||
\(405\) | − | 34.6871i | − | 1.72362i | ||||||
\(406\) | 7.49794 | 0.372116 | ||||||||
\(407\) | 21.7758 | 1.07939 | ||||||||
\(408\) | 0.394959i | 0.0195534i | ||||||||
\(409\) | 13.4932i | 0.667196i | 0.942716 | + | 0.333598i | \(0.108263\pi\) | ||||
−0.942716 | + | 0.333598i | \(0.891737\pi\) | |||||||
\(410\) | 44.4473i | 2.19510i | ||||||||
\(411\) | − | 0.119409i | − | 0.00589000i | ||||||
\(412\) | −1.41037 | −0.0694839 | ||||||||
\(413\) | 20.1341 | 0.990733 | ||||||||
\(414\) | − | 23.0943i | − | 1.13502i | ||||||
\(415\) | 53.1602 | 2.60953 | ||||||||
\(416\) | −1.95501 | − | 0.617350i | −0.0958521 | − | 0.0302681i | ||||
\(417\) | −0.615600 | −0.0301461 | ||||||||
\(418\) | − | 8.91041i | − | 0.435822i | ||||||
\(419\) | −30.1496 | −1.47290 | −0.736451 | − | 0.676491i | \(-0.763500\pi\) | ||||
−0.736451 | + | 0.676491i | \(0.763500\pi\) | |||||||
\(420\) | 0.0247001 | 0.00120524 | ||||||||
\(421\) | 29.2902i | 1.42752i | 0.700393 | + | 0.713758i | \(0.253008\pi\) | ||||
−0.700393 | + | 0.713758i | \(0.746992\pi\) | |||||||
\(422\) | 31.6366i | 1.54005i | ||||||||
\(423\) | 20.9296i | 1.01763i | ||||||||
\(424\) | 16.8330i | 0.817483i | ||||||||
\(425\) | −37.1184 | −1.80051 | ||||||||
\(426\) | 0.0407758 | 0.00197559 | ||||||||
\(427\) | − | 2.91638i | − | 0.141134i | ||||||
\(428\) | 0.0572658 | 0.00276805 | ||||||||
\(429\) | −0.247339 | − | 0.0781044i | −0.0119416 | − | 0.00377092i | ||||
\(430\) | −51.7078 | −2.49357 | ||||||||
\(431\) | 35.3794i | 1.70416i | 0.523408 | + | 0.852082i | \(0.324660\pi\) | ||||
−0.523408 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(432\) | 0.961811 | 0.0462751 | ||||||||
\(433\) | 12.7072 | 0.610671 | 0.305335 | − | 0.952245i | \(-0.401231\pi\) | ||||
0.305335 | + | 0.952245i | \(0.401231\pi\) | |||||||
\(434\) | − | 2.40961i | − | 0.115665i | ||||||
\(435\) | − | 0.459486i | − | 0.0220307i | ||||||
\(436\) | − | 1.08071i | − | 0.0517568i | ||||||
\(437\) | − | 17.3741i | − | 0.831115i | ||||||
\(438\) | 0.750897 | 0.0358793 | ||||||||
\(439\) | 18.4508 | 0.880609 | 0.440305 | − | 0.897849i | \(-0.354870\pi\) | ||||
0.440305 | + | 0.897849i | \(0.354870\pi\) | |||||||
\(440\) | − | 19.9799i | − | 0.952503i | ||||||
\(441\) | −12.7016 | −0.604838 | ||||||||
\(442\) | 18.6876 | + | 5.90115i | 0.888878 | + | 0.280689i | ||||
\(443\) | 10.8749 | 0.516680 | 0.258340 | − | 0.966054i | \(-0.416824\pi\) | ||||
0.258340 | + | 0.966054i | \(0.416824\pi\) | |||||||
\(444\) | − | 0.0445752i | − | 0.00211544i | ||||||
\(445\) | −39.6711 | −1.88059 | ||||||||
\(446\) | −1.77619 | −0.0841048 | ||||||||
\(447\) | 0.720884i | 0.0340966i | ||||||||
\(448\) | 12.5657i | 0.593672i | ||||||||
\(449\) | − | 11.8359i | − | 0.558569i | −0.960208 | − | 0.279284i | \(-0.909903\pi\) | ||
0.960208 | − | 0.279284i | \(-0.0900972\pi\) | |||||||
\(450\) | 43.0152i | 2.02776i | ||||||||
\(451\) | 14.9402 | 0.703506 | ||||||||
\(452\) | 0.746076 | 0.0350925 | ||||||||
\(453\) | 0.0278089i | 0.00130658i | ||||||||
\(454\) | −14.2395 | −0.668291 | ||||||||
\(455\) | −6.96707 | + | 22.0631i | −0.326621 | + | 1.03434i | ||||
\(456\) | 0.344336 | 0.0161250 | ||||||||
\(457\) | − | 32.9139i | − | 1.53965i | −0.638258 | − | 0.769823i | \(-0.720345\pi\) | ||
0.638258 | − | 0.769823i | \(-0.279655\pi\) | |||||||
\(458\) | −2.12956 | −0.0995077 | ||||||||
\(459\) | −0.860618 | −0.0401702 | ||||||||
\(460\) | 2.06363i | 0.0962171i | ||||||||
\(461\) | − | 25.2638i | − | 1.17665i | −0.808625 | − | 0.588325i | \(-0.799788\pi\) | ||
0.808625 | − | 0.588325i | \(-0.200212\pi\) | |||||||
\(462\) | − | 0.173344i | − | 0.00806468i | ||||||
\(463\) | − | 19.8975i | − | 0.924714i | −0.886694 | − | 0.462357i | \(-0.847004\pi\) | ||
0.886694 | − | 0.462357i | \(-0.152996\pi\) | |||||||
\(464\) | −13.0414 | −0.605430 | ||||||||
\(465\) | −0.147665 | −0.00684780 | ||||||||
\(466\) | 20.5468i | 0.951811i | ||||||||
\(467\) | −19.7000 | −0.911608 | −0.455804 | − | 0.890080i | \(-0.650648\pi\) | ||||
−0.455804 | + | 0.890080i | \(0.650648\pi\) | |||||||
\(468\) | 0.327545 | − | 1.03726i | 0.0151408 | − | 0.0479474i | ||||
\(469\) | −13.2086 | −0.609917 | ||||||||
\(470\) | − | 39.0469i | − | 1.80110i | ||||||
\(471\) | −0.220325 | −0.0101520 | ||||||||
\(472\) | −33.3384 | −1.53452 | ||||||||
\(473\) | 17.3807i | 0.799164i | ||||||||
\(474\) | − | 0.314022i | − | 0.0144235i | ||||||
\(475\) | 32.3609i | 1.48482i | ||||||||
\(476\) | 0.627294i | 0.0287520i | ||||||||
\(477\) | −18.3351 | −0.839508 | ||||||||
\(478\) | −17.9866 | −0.822688 | ||||||||
\(479\) | − | 24.1566i | − | 1.10374i | −0.833929 | − | 0.551872i | \(-0.813914\pi\) | ||
0.833929 | − | 0.551872i | \(-0.186086\pi\) | |||||||
\(480\) | −0.0839643 | −0.00383243 | ||||||||
\(481\) | 39.8163 | + | 12.5731i | 1.81547 | + | 0.573286i | ||||
\(482\) | −14.4385 | −0.657653 | ||||||||
\(483\) | − | 0.337997i | − | 0.0153794i | ||||||
\(484\) | −0.750983 | −0.0341356 | ||||||||
\(485\) | 32.2046 | 1.46233 | ||||||||
\(486\) | 1.49613i | 0.0678660i | ||||||||
\(487\) | − | 21.5211i | − | 0.975213i | −0.873063 | − | 0.487607i | \(-0.837870\pi\) | ||
0.873063 | − | 0.487607i | \(-0.162130\pi\) | |||||||
\(488\) | 4.82900i | 0.218598i | ||||||||
\(489\) | 0.121383i | 0.00548913i | ||||||||
\(490\) | 23.6965 | 1.07050 | ||||||||
\(491\) | 1.06521 | 0.0480723 | 0.0240361 | − | 0.999711i | \(-0.492348\pi\) | ||||
0.0240361 | + | 0.999711i | \(0.492348\pi\) | |||||||
\(492\) | − | 0.0305827i | − | 0.00137877i | ||||||
\(493\) | 11.6693 | 0.525558 | ||||||||
\(494\) | 5.14479 | − | 16.2924i | 0.231475 | − | 0.733028i | ||||
\(495\) | 21.7628 | 0.978167 | ||||||||
\(496\) | 4.19110i | 0.188186i | ||||||||
\(497\) | −1.22261 | −0.0548415 | ||||||||
\(498\) | −0.763685 | −0.0342215 | ||||||||
\(499\) | 21.7718i | 0.974641i | 0.873223 | + | 0.487321i | \(0.162026\pi\) | ||||
−0.873223 | + | 0.487321i | \(0.837974\pi\) | |||||||
\(500\) | − | 1.90201i | − | 0.0850605i | ||||||
\(501\) | − | 0.190159i | − | 0.00849569i | ||||||
\(502\) | − | 3.73907i | − | 0.166883i | ||||||
\(503\) | −19.9950 | −0.891531 | −0.445766 | − | 0.895150i | \(-0.647068\pi\) | ||||
−0.445766 | + | 0.895150i | \(0.647068\pi\) | |||||||
\(504\) | −13.7237 | −0.611301 | ||||||||
\(505\) | − | 32.2920i | − | 1.43697i | ||||||
\(506\) | 14.4824 | 0.643820 | ||||||||
\(507\) | −0.407154 | − | 0.285622i | −0.0180823 | − | 0.0126849i | ||||
\(508\) | 1.83258 | 0.0813075 | ||||||||
\(509\) | − | 18.7005i | − | 0.828883i | −0.910076 | − | 0.414442i | \(-0.863977\pi\) | ||
0.910076 | − | 0.414442i | \(-0.136023\pi\) | |||||||
\(510\) | 0.802601 | 0.0355398 | ||||||||
\(511\) | −22.5147 | −0.995990 | ||||||||
\(512\) | − | 20.6920i | − | 0.914468i | ||||||
\(513\) | 0.750311i | 0.0331271i | ||||||||
\(514\) | 12.6088i | 0.556150i | ||||||||
\(515\) | − | 54.1062i | − | 2.38420i | ||||||
\(516\) | 0.0355783 | 0.00156625 | ||||||||
\(517\) | −13.1249 | −0.577234 | ||||||||
\(518\) | 27.9046i | 1.22606i | ||||||||
\(519\) | −0.0755813 | −0.00331765 | ||||||||
\(520\) | 11.5362 | − | 36.5325i | 0.505896 | − | 1.60206i | ||||
\(521\) | 21.5470 | 0.943992 | 0.471996 | − | 0.881601i | \(-0.343534\pi\) | ||||
0.471996 | + | 0.881601i | \(0.343534\pi\) | |||||||
\(522\) | − | 13.5231i | − | 0.591891i | ||||||
\(523\) | −35.8946 | −1.56956 | −0.784781 | − | 0.619773i | \(-0.787225\pi\) | ||||
−0.784781 | + | 0.619773i | \(0.787225\pi\) | |||||||
\(524\) | −1.86599 | −0.0815163 | ||||||||
\(525\) | 0.629550i | 0.0274758i | ||||||||
\(526\) | 6.73363i | 0.293600i | ||||||||
\(527\) | − | 3.75015i | − | 0.163359i | ||||||
\(528\) | 0.301501i | 0.0131212i | ||||||||
\(529\) | 5.23865 | 0.227768 | ||||||||
\(530\) | 34.2065 | 1.48584 | ||||||||
\(531\) | − | 36.3134i | − | 1.57587i | ||||||
\(532\) | 0.546892 | 0.0237108 | ||||||||
\(533\) | 27.3176 | + | 8.62633i | 1.18326 | + | 0.373648i | ||||
\(534\) | 0.569904 | 0.0246622 | ||||||||
\(535\) | 2.19690i | 0.0949801i | ||||||||
\(536\) | 21.8710 | 0.944685 | ||||||||
\(537\) | 0.232386 | 0.0100282 | ||||||||
\(538\) | − | 2.17737i | − | 0.0938733i | ||||||
\(539\) | − | 7.96515i | − | 0.343083i | ||||||
\(540\) | − | 0.0891191i | − | 0.00383507i | ||||||
\(541\) | 12.8955i | 0.554420i | 0.960809 | + | 0.277210i | \(0.0894097\pi\) | ||||
−0.960809 | + | 0.277210i | \(0.910590\pi\) | |||||||
\(542\) | −12.6300 | −0.542503 | ||||||||
\(543\) | 0.788426 | 0.0338346 | ||||||||
\(544\) | − | 2.13239i | − | 0.0914253i | ||||||
\(545\) | 41.4596 | 1.77593 | ||||||||
\(546\) | 0.100087 | − | 0.316953i | 0.00428333 | − | 0.0135643i | ||||
\(547\) | 28.8880 | 1.23516 | 0.617582 | − | 0.786507i | \(-0.288113\pi\) | ||||
0.617582 | + | 0.786507i | \(0.288113\pi\) | |||||||
\(548\) | 0.314027i | 0.0134146i | ||||||||
\(549\) | −5.25993 | −0.224488 | ||||||||
\(550\) | −26.9748 | −1.15021 | ||||||||
\(551\) | − | 10.1736i | − | 0.433410i | ||||||
\(552\) | 0.559661i | 0.0238207i | ||||||||
\(553\) | 9.41555i | 0.400390i | ||||||||
\(554\) | 6.15241i | 0.261391i | ||||||||
\(555\) | 1.71004 | 0.0725873 | ||||||||
\(556\) | 1.61894 | 0.0686583 | ||||||||
\(557\) | − | 8.61442i | − | 0.365005i | −0.983205 | − | 0.182502i | \(-0.941580\pi\) | ||
0.983205 | − | 0.182502i | \(-0.0584197\pi\) | |||||||
\(558\) | −4.34592 | −0.183978 | ||||||||
\(559\) | −10.0354 | + | 31.7799i | −0.424454 | + | 1.34415i | ||||
\(560\) | 26.8945 | 1.13650 | ||||||||
\(561\) | − | 0.269780i | − | 0.0113901i | ||||||
\(562\) | −7.37392 | −0.311050 | ||||||||
\(563\) | 5.36118 | 0.225947 | 0.112973 | − | 0.993598i | \(-0.463963\pi\) | ||||
0.112973 | + | 0.993598i | \(0.463963\pi\) | |||||||
\(564\) | 0.0268668i | 0.00113130i | ||||||||
\(565\) | 28.6218i | 1.20413i | ||||||||
\(566\) | − | 47.3560i | − | 1.99052i | ||||||
\(567\) | − | 14.9410i | − | 0.627465i | ||||||
\(568\) | 2.02442 | 0.0849427 | ||||||||
\(569\) | −13.1854 | −0.552760 | −0.276380 | − | 0.961048i | \(-0.589135\pi\) | ||||
−0.276380 | + | 0.961048i | \(0.589135\pi\) | |||||||
\(570\) | − | 0.699730i | − | 0.0293085i | ||||||
\(571\) | 36.6258 | 1.53274 | 0.766372 | − | 0.642397i | \(-0.222060\pi\) | ||||
0.766372 | + | 0.642397i | \(0.222060\pi\) | |||||||
\(572\) | 0.650464 | + | 0.205403i | 0.0271973 | + | 0.00858833i | ||||
\(573\) | 0.259551 | 0.0108429 | ||||||||
\(574\) | 19.1451i | 0.799102i | ||||||||
\(575\) | −52.5971 | −2.19345 | ||||||||
\(576\) | 22.6632 | 0.944299 | ||||||||
\(577\) | − | 26.2411i | − | 1.09243i | −0.837645 | − | 0.546215i | \(-0.816068\pi\) | ||
0.837645 | − | 0.546215i | \(-0.183932\pi\) | |||||||
\(578\) | − | 4.25580i | − | 0.177018i | ||||||
\(579\) | − | 0.854846i | − | 0.0355262i | ||||||
\(580\) | 1.20838i | 0.0501753i | ||||||||
\(581\) | 22.8981 | 0.949973 | ||||||||
\(582\) | −0.462642 | −0.0191771 | ||||||||
\(583\) | − | 11.4979i | − | 0.476195i | ||||||
\(584\) | 37.2802 | 1.54267 | ||||||||
\(585\) | 39.7926 | + | 12.5657i | 1.64522 | + | 0.519526i | ||||
\(586\) | 15.4374 | 0.637714 | ||||||||
\(587\) | 15.9650i | 0.658945i | 0.944165 | + | 0.329472i | \(0.106871\pi\) | ||||
−0.944165 | + | 0.329472i | \(0.893129\pi\) | |||||||
\(588\) | −0.0163047 | −0.000672395 | ||||||||
\(589\) | −3.26949 | −0.134717 | ||||||||
\(590\) | 67.7473i | 2.78911i | ||||||||
\(591\) | 0.262278i | 0.0107887i | ||||||||
\(592\) | − | 48.5352i | − | 1.99479i | ||||||
\(593\) | 20.7033i | 0.850181i | 0.905151 | + | 0.425091i | \(0.139758\pi\) | ||||
−0.905151 | + | 0.425091i | \(0.860242\pi\) | |||||||
\(594\) | −0.625430 | −0.0256617 | ||||||||
\(595\) | −24.0649 | −0.986566 | ||||||||
\(596\) | − | 1.89582i | − | 0.0776558i | ||||||
\(597\) | −0.250725 | −0.0102615 | ||||||||
\(598\) | 26.4805 | + | 8.36199i | 1.08287 | + | 0.341947i | ||||
\(599\) | −31.4587 | −1.28537 | −0.642685 | − | 0.766131i | \(-0.722179\pi\) | ||||
−0.642685 | + | 0.766131i | \(0.722179\pi\) | |||||||
\(600\) | − | 1.04242i | − | 0.0425566i | ||||||
\(601\) | 14.5688 | 0.594274 | 0.297137 | − | 0.954835i | \(-0.403968\pi\) | ||||
0.297137 | + | 0.954835i | \(0.403968\pi\) | |||||||
\(602\) | −22.2725 | −0.907759 | ||||||||
\(603\) | 23.8228i | 0.970137i | ||||||||
\(604\) | − | 0.0731333i | − | 0.00297575i | ||||||
\(605\) | − | 28.8101i | − | 1.17130i | ||||||
\(606\) | 0.463898i | 0.0188446i | ||||||||
\(607\) | −8.19708 | −0.332709 | −0.166355 | − | 0.986066i | \(-0.553200\pi\) | ||||
−0.166355 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(608\) | −1.85908 | −0.0753955 | ||||||||
\(609\) | − | 0.197918i | − | 0.00802004i | ||||||
\(610\) | 9.81307 | 0.397319 | ||||||||
\(611\) | −23.9985 | − | 7.57821i | −0.970874 | − | 0.306582i | ||||
\(612\) | 1.13137 | 0.0457331 | ||||||||
\(613\) | − | 5.02425i | − | 0.202927i | −0.994839 | − | 0.101464i | \(-0.967647\pi\) | ||
0.994839 | − | 0.101464i | \(-0.0323526\pi\) | |||||||
\(614\) | 16.6002 | 0.669931 | ||||||||
\(615\) | 1.17325 | 0.0473098 | ||||||||
\(616\) | − | 8.60608i | − | 0.346749i | ||||||
\(617\) | 20.3301i | 0.818460i | 0.912431 | + | 0.409230i | \(0.134203\pi\) | ||||
−0.912431 | + | 0.409230i | \(0.865797\pi\) | |||||||
\(618\) | 0.777274i | 0.0312666i | ||||||||
\(619\) | 9.73194i | 0.391160i | 0.980688 | + | 0.195580i | \(0.0626589\pi\) | ||||
−0.980688 | + | 0.195580i | \(0.937341\pi\) | |||||||
\(620\) | 0.388337 | 0.0155960 | ||||||||
\(621\) | −1.21950 | −0.0489370 | ||||||||
\(622\) | − | 20.6772i | − | 0.829082i | ||||||
\(623\) | −17.0878 | −0.684609 | ||||||||
\(624\) | −0.174084 | + | 0.551284i | −0.00696894 | + | 0.0220690i | ||||
\(625\) | 23.4779 | 0.939117 | ||||||||
\(626\) | 15.0255i | 0.600541i | ||||||||
\(627\) | −0.235202 | −0.00939306 | ||||||||
\(628\) | 0.579422 | 0.0231215 | ||||||||
\(629\) | 43.4288i | 1.73162i | ||||||||
\(630\) | 27.8880i | 1.11109i | ||||||||
\(631\) | − | 46.9356i | − | 1.86848i | −0.356651 | − | 0.934238i | \(-0.616081\pi\) | ||
0.356651 | − | 0.934238i | \(-0.383919\pi\) | |||||||
\(632\) | − | 15.5904i | − | 0.620154i | ||||||
\(633\) | 0.835090 | 0.0331919 | ||||||||
\(634\) | 8.23136 | 0.326909 | ||||||||
\(635\) | 70.3034i | 2.78991i | ||||||||
\(636\) | −0.0235363 | −0.000933276 | ||||||||
\(637\) | 4.59900 | − | 14.5640i | 0.182219 | − | 0.577046i | ||||
\(638\) | 8.48032 | 0.335739 | ||||||||
\(639\) | 2.20507i | 0.0872313i | ||||||||
\(640\) | −46.6705 | −1.84481 | ||||||||
\(641\) | −27.2007 | −1.07436 | −0.537181 | − | 0.843467i | \(-0.680511\pi\) | ||||
−0.537181 | + | 0.843467i | \(0.680511\pi\) | |||||||
\(642\) | − | 0.0315600i | − | 0.00124557i | ||||||
\(643\) | − | 41.5545i | − | 1.63875i | −0.573257 | − | 0.819375i | \(-0.694320\pi\) | ||
0.573257 | − | 0.819375i | \(-0.305680\pi\) | |||||||
\(644\) | 0.888881i | 0.0350268i | ||||||||
\(645\) | 1.36490i | 0.0537427i | ||||||||
\(646\) | 17.7706 | 0.699175 | ||||||||
\(647\) | −12.4684 | −0.490184 | −0.245092 | − | 0.969500i | \(-0.578818\pi\) | ||||
−0.245092 | + | 0.969500i | \(0.578818\pi\) | |||||||
\(648\) | 24.7396i | 0.971864i | ||||||||
\(649\) | 22.7720 | 0.893881 | ||||||||
\(650\) | −49.3224 | − | 15.5750i | −1.93458 | − | 0.610901i | ||||
\(651\) | −0.0636049 | −0.00249287 | ||||||||
\(652\) | − | 0.319219i | − | 0.0125016i | ||||||
\(653\) | 48.1876 | 1.88572 | 0.942862 | − | 0.333182i | \(-0.108122\pi\) | ||||
0.942862 | + | 0.333182i | \(0.108122\pi\) | |||||||
\(654\) | −0.595597 | −0.0232897 | ||||||||
\(655\) | − | 71.5854i | − | 2.79707i | ||||||
\(656\) | − | 33.2996i | − | 1.30013i | ||||||
\(657\) | 40.6070i | 1.58423i | ||||||||
\(658\) | − | 16.8190i | − | 0.655672i | ||||||
\(659\) | −8.64394 | −0.336720 | −0.168360 | − | 0.985726i | \(-0.553847\pi\) | ||||
−0.168360 | + | 0.985726i | \(0.553847\pi\) | |||||||
\(660\) | 0.0279364 | 0.00108742 | ||||||||
\(661\) | − | 25.8464i | − | 1.00531i | −0.864487 | − | 0.502654i | \(-0.832357\pi\) | ||
0.864487 | − | 0.502654i | \(-0.167643\pi\) | |||||||
\(662\) | 0.981173 | 0.0381344 | ||||||||
\(663\) | 0.155769 | − | 0.493283i | 0.00604955 | − | 0.0191575i | ||||
\(664\) | −37.9151 | −1.47139 | ||||||||
\(665\) | 20.9805i | 0.813589i | ||||||||
\(666\) | 50.3282 | 1.95018 | ||||||||
\(667\) | 16.5355 | 0.640256 | ||||||||
\(668\) | 0.500091i | 0.0193491i | ||||||||
\(669\) | 0.0468847i | 0.00181267i | ||||||||
\(670\) | − | 44.4444i | − | 1.71704i | ||||||
\(671\) | − | 3.29849i | − | 0.127337i | ||||||
\(672\) | −0.0361666 | −0.00139516 | ||||||||
\(673\) | −13.1020 | −0.505044 | −0.252522 | − | 0.967591i | \(-0.581260\pi\) | ||||
−0.252522 | + | 0.967591i | \(0.581260\pi\) | |||||||
\(674\) | 6.86586i | 0.264463i | ||||||||
\(675\) | 2.27144 | 0.0874278 | ||||||||
\(676\) | 1.07075 | + | 0.751145i | 0.0411828 | + | 0.0288902i | ||||
\(677\) | −44.8541 | −1.72388 | −0.861941 | − | 0.507008i | \(-0.830752\pi\) | ||||
−0.861941 | + | 0.507008i | \(0.830752\pi\) | |||||||
\(678\) | − | 0.411173i | − | 0.0157910i | ||||||
\(679\) | 13.8717 | 0.532347 | ||||||||
\(680\) | 39.8471 | 1.52807 | ||||||||
\(681\) | 0.375869i | 0.0144033i | ||||||||
\(682\) | − | 2.72532i | − | 0.104358i | ||||||
\(683\) | − | 0.979482i | − | 0.0374788i | −0.999824 | − | 0.0187394i | \(-0.994035\pi\) | ||
0.999824 | − | 0.0187394i | \(-0.00596529\pi\) | |||||||
\(684\) | − | 0.986363i | − | 0.0377146i | ||||||
\(685\) | −12.0471 | −0.460295 | ||||||||
\(686\) | 27.0742 | 1.03370 | ||||||||
\(687\) | 0.0562125i | 0.00214464i | ||||||||
\(688\) | 38.7391 | 1.47692 | ||||||||
\(689\) | 6.63880 | − | 21.0236i | 0.252918 | − | 0.800934i | ||||
\(690\) | 1.13729 | 0.0432960 | ||||||||
\(691\) | − | 40.0083i | − | 1.52199i | −0.648759 | − | 0.760994i | \(-0.724711\pi\) | ||
0.648759 | − | 0.760994i | \(-0.275289\pi\) | |||||||
\(692\) | 0.198768 | 0.00755602 | ||||||||
\(693\) | 9.37407 | 0.356091 | ||||||||
\(694\) | − | 45.9133i | − | 1.74284i | ||||||
\(695\) | 62.1075i | 2.35587i | ||||||||
\(696\) | 0.327716i | 0.0124220i | ||||||||
\(697\) | 29.7962i | 1.12861i | ||||||||
\(698\) | −12.5287 | −0.474216 | ||||||||
\(699\) | 0.542359 | 0.0205139 | ||||||||
\(700\) | − | 1.65562i | − | 0.0625767i | ||||||
\(701\) | −37.1969 | −1.40491 | −0.702454 | − | 0.711729i | \(-0.747912\pi\) | ||||
−0.702454 | + | 0.711729i | \(0.747912\pi\) | |||||||
\(702\) | −1.14358 | − | 0.361118i | −0.0431616 | − | 0.0136295i | ||||
\(703\) | 37.8625 | 1.42801 | ||||||||
\(704\) | 14.2120i | 0.535636i | ||||||||
\(705\) | −1.03069 | −0.0388182 | ||||||||
\(706\) | −16.8509 | −0.634194 | ||||||||
\(707\) | − | 13.9094i | − | 0.523116i | ||||||
\(708\) | − | 0.0466145i | − | 0.00175188i | ||||||
\(709\) | 33.3437i | 1.25225i | 0.779722 | + | 0.626125i | \(0.215360\pi\) | ||||
−0.779722 | + | 0.626125i | \(0.784640\pi\) | |||||||
\(710\) | − | 4.11384i | − | 0.154390i | ||||||
\(711\) | 16.9817 | 0.636863 | ||||||||
\(712\) | 28.2943 | 1.06037 | ||||||||
\(713\) | − | 5.31401i | − | 0.199011i | ||||||
\(714\) | 0.345710 | 0.0129379 | ||||||||
\(715\) | −7.87990 | + | 24.9538i | −0.294692 | + | 0.933221i | ||||
\(716\) | −0.611141 | −0.0228394 | ||||||||
\(717\) | 0.474780i | 0.0177310i | ||||||||
\(718\) | −7.42828 | −0.277221 | ||||||||
\(719\) | −23.1357 | −0.862815 | −0.431407 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431407 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(720\) | − | 48.5064i | − | 1.80773i | ||||||
\(721\) | − | 23.3056i | − | 0.867944i | ||||||
\(722\) | 12.0447i | 0.448258i | ||||||||
\(723\) | 0.381122i | 0.0141741i | ||||||||
\(724\) | −2.07344 | −0.0770589 | ||||||||
\(725\) | −30.7989 | −1.14384 | ||||||||
\(726\) | 0.413877i | 0.0153604i | ||||||||
\(727\) | −4.47177 | −0.165849 | −0.0829243 | − | 0.996556i | \(-0.526426\pi\) | ||||
−0.0829243 | + | 0.996556i | \(0.526426\pi\) | |||||||
\(728\) | 4.96907 | − | 15.7359i | 0.184166 | − | 0.583212i | ||||
\(729\) | −26.9210 | −0.997074 | ||||||||
\(730\) | − | 75.7575i | − | 2.80391i | ||||||
\(731\) | −34.6634 | −1.28207 | ||||||||
\(732\) | −0.00675203 | −0.000249562 | ||||||||
\(733\) | 50.4881i | 1.86482i | 0.361402 | + | 0.932410i | \(0.382298\pi\) | ||||
−0.361402 | + | 0.932410i | \(0.617702\pi\) | |||||||
\(734\) | − | 50.9133i | − | 1.87924i | ||||||
\(735\) | − | 0.625499i | − | 0.0230719i | ||||||
\(736\) | − | 3.02161i | − | 0.111378i | ||||||
\(737\) | −14.9392 | −0.550292 | ||||||||
\(738\) | 34.5298 | 1.27106 | ||||||||
\(739\) | 51.2533i | 1.88538i | 0.333666 | + | 0.942691i | \(0.391714\pi\) | ||||
−0.333666 | + | 0.942691i | \(0.608286\pi\) | |||||||
\(740\) | −4.49716 | −0.165319 | ||||||||
\(741\) | −0.430059 | − | 0.135803i | −0.0157986 | − | 0.00498887i | ||||
\(742\) | 14.7340 | 0.540904 | ||||||||
\(743\) | 26.3425i | 0.966411i | 0.875507 | + | 0.483206i | \(0.160528\pi\) | ||||
−0.875507 | + | 0.483206i | \(0.839472\pi\) | |||||||
\(744\) | 0.105318 | 0.00386115 | ||||||||
\(745\) | 72.7295 | 2.66460 | ||||||||
\(746\) | 4.88511i | 0.178857i | ||||||||
\(747\) | − | 41.2985i | − | 1.51103i | ||||||
\(748\) | 0.709482i | 0.0259412i | ||||||||
\(749\) | 0.946285i | 0.0345765i | ||||||||
\(750\) | −1.04823 | −0.0382758 | ||||||||
\(751\) | −34.0846 | −1.24377 | −0.621883 | − | 0.783110i | \(-0.713632\pi\) | ||||
−0.621883 | + | 0.783110i | \(0.713632\pi\) | |||||||
\(752\) | 29.2537i | 1.06677i | ||||||||
\(753\) | −0.0986978 | −0.00359675 | ||||||||
\(754\) | 15.5060 | + | 4.89646i | 0.564694 | + | 0.178319i | ||||
\(755\) | 2.80562 | 0.102107 | ||||||||
\(756\) | − | 0.0383869i | − | 0.00139612i | ||||||
\(757\) | −50.7996 | −1.84634 | −0.923171 | − | 0.384389i | \(-0.874412\pi\) | ||||
−0.923171 | + | 0.384389i | \(0.874412\pi\) | |||||||
\(758\) | −22.5711 | −0.819819 | ||||||||
\(759\) | − | 0.382281i | − | 0.0138759i | ||||||
\(760\) | − | 34.7399i | − | 1.26015i | ||||||
\(761\) | − | 9.08920i | − | 0.329483i | −0.986337 | − | 0.164742i | \(-0.947321\pi\) | ||
0.986337 | − | 0.164742i | \(-0.0526790\pi\) | |||||||
\(762\) | − | 1.00996i | − | 0.0365870i | ||||||
\(763\) | 17.8582 | 0.646510 | ||||||||
\(764\) | −0.682581 | −0.0246949 | ||||||||
\(765\) | 43.4030i | 1.56924i | ||||||||
\(766\) | 20.6888 | 0.747518 | ||||||||
\(767\) | 41.6379 | + | 13.1484i | 1.50346 | + | 0.474760i | ||||
\(768\) | 0.0921495 | 0.00332516 | ||||||||
\(769\) | 11.9781i | 0.431942i | 0.976400 | + | 0.215971i | \(0.0692917\pi\) | ||||
−0.976400 | + | 0.215971i | \(0.930708\pi\) | |||||||
\(770\) | −17.4885 | −0.630243 | ||||||||
\(771\) | 0.332826 | 0.0119864 | ||||||||
\(772\) | 2.24812i | 0.0809116i | ||||||||
\(773\) | 29.6744i | 1.06731i | 0.845701 | + | 0.533657i | \(0.179183\pi\) | ||||
−0.845701 | + | 0.533657i | \(0.820817\pi\) | |||||||
\(774\) | 40.1702i | 1.44389i | ||||||||
\(775\) | 9.89783i | 0.355541i | ||||||||
\(776\) | −22.9690 | −0.824540 | ||||||||
\(777\) | 0.736579 | 0.0264246 | ||||||||
\(778\) | 14.9556i | 0.536183i | ||||||||
\(779\) | 25.9771 | 0.930728 | ||||||||
\(780\) | 0.0510807 | + | 0.0161302i | 0.00182898 | + | 0.000577554i | ||||
\(781\) | −1.38280 | −0.0494803 | ||||||||
\(782\) | 28.8831i | 1.03286i | ||||||||
\(783\) | −0.714095 | −0.0255197 | ||||||||
\(784\) | −17.7532 | −0.634044 | ||||||||
\(785\) | 22.2284i | 0.793367i | ||||||||
\(786\) | 1.02838i | 0.0366809i | ||||||||
\(787\) | − | 31.7791i | − | 1.13280i | −0.824129 | − | 0.566402i | \(-0.808335\pi\) | ||
0.824129 | − | 0.566402i | \(-0.191665\pi\) | |||||||
\(788\) | − | 0.689752i | − | 0.0245714i | ||||||
\(789\) | 0.177743 | 0.00632782 | ||||||||
\(790\) | −31.6815 | −1.12718 | ||||||||
\(791\) | 12.3285i | 0.438351i | ||||||||
\(792\) | −15.5217 | −0.551541 | ||||||||
\(793\) | 1.90452 | − | 6.03117i | 0.0676314 | − | 0.214173i | ||||
\(794\) | −35.3352 | −1.25400 | ||||||||
\(795\) | − | 0.902927i | − | 0.0320235i | ||||||
\(796\) | 0.659371 | 0.0233708 | ||||||||
\(797\) | 3.59563 | 0.127364 | 0.0636819 | − | 0.997970i | \(-0.479716\pi\) | ||||
0.0636819 | + | 0.997970i | \(0.479716\pi\) | |||||||
\(798\) | − | 0.301400i | − | 0.0106694i | ||||||
\(799\) | − | 26.1759i | − | 0.926036i | ||||||
\(800\) | 5.62804i | 0.198981i | ||||||||
\(801\) | 30.8192i | 1.08894i | ||||||||
\(802\) | 22.8163 | 0.805672 | ||||||||
\(803\) | −25.4646 | −0.898625 | ||||||||
\(804\) | 0.0305806i | 0.00107850i | ||||||||
\(805\) | −34.1003 | −1.20188 | ||||||||
\(806\) | 1.57358 | − | 4.98315i | 0.0554268 | − | 0.175524i | ||||
\(807\) | −0.0574747 | −0.00202320 | ||||||||
\(808\) | 23.0314i | 0.810241i | ||||||||
\(809\) | 13.4626 | 0.473321 | 0.236660 | − | 0.971592i | \(-0.423947\pi\) | ||||
0.236660 | + | 0.971592i | \(0.423947\pi\) | |||||||
\(810\) | 50.2737 | 1.76644 | ||||||||
\(811\) | 24.6877i | 0.866902i | 0.901177 | + | 0.433451i | \(0.142704\pi\) | ||||
−0.901177 | + | 0.433451i | \(0.857296\pi\) | |||||||
\(812\) | 0.520495i | 0.0182658i | ||||||||
\(813\) | 0.333384i | 0.0116923i | ||||||||
\(814\) | 31.5607i | 1.10620i | ||||||||
\(815\) | 12.2462 | 0.428967 | ||||||||
\(816\) | −0.601303 | −0.0210498 | ||||||||
\(817\) | 30.2205i | 1.05728i | ||||||||
\(818\) | −19.5563 | −0.683771 | ||||||||
\(819\) | 17.1402 | + | 5.41250i | 0.598926 | + | 0.189128i | ||||
\(820\) | −3.08546 | −0.107749 | ||||||||
\(821\) | − | 0.766000i | − | 0.0267336i | −0.999911 | − | 0.0133668i | \(-0.995745\pi\) | ||
0.999911 | − | 0.0133668i | \(-0.00425491\pi\) | |||||||
\(822\) | 0.173065 | 0.00603633 | ||||||||
\(823\) | −10.3978 | −0.362445 | −0.181222 | − | 0.983442i | \(-0.558005\pi\) | ||||
−0.181222 | + | 0.983442i | \(0.558005\pi\) | |||||||
\(824\) | 38.5897i | 1.34434i | ||||||||
\(825\) | 0.712034i | 0.0247899i | ||||||||
\(826\) | 29.1813i | 1.01535i | ||||||||
\(827\) | − | 28.3555i | − | 0.986017i | −0.870024 | − | 0.493009i | \(-0.835897\pi\) | ||
0.870024 | − | 0.493009i | \(-0.164103\pi\) | |||||||
\(828\) | 1.60317 | 0.0557139 | ||||||||
\(829\) | −35.5293 | −1.23398 | −0.616991 | − | 0.786970i | \(-0.711649\pi\) | ||||
−0.616991 | + | 0.786970i | \(0.711649\pi\) | |||||||
\(830\) | 77.0477i | 2.67436i | ||||||||
\(831\) | 0.162401 | 0.00563363 | ||||||||
\(832\) | −8.20590 | + | 25.9862i | −0.284488 | + | 0.900910i | ||||
\(833\) | 15.8854 | 0.550396 | ||||||||
\(834\) | − | 0.892220i | − | 0.0308950i | ||||||
\(835\) | −19.1850 | −0.663926 | ||||||||
\(836\) | 0.618546 | 0.0213929 | ||||||||
\(837\) | 0.229489i | 0.00793229i | ||||||||
\(838\) | − | 43.6972i | − | 1.50950i | ||||||
\(839\) | − | 19.1269i | − | 0.660333i | −0.943923 | − | 0.330167i | \(-0.892895\pi\) | ||
0.943923 | − | 0.330167i | \(-0.107105\pi\) | |||||||
\(840\) | − | 0.675832i | − | 0.0233184i | ||||||
\(841\) | −19.3175 | −0.666119 | ||||||||
\(842\) | −42.4517 | −1.46298 | ||||||||
\(843\) | 0.194644i | 0.00670391i | ||||||||
\(844\) | −2.19616 | −0.0755951 | ||||||||
\(845\) | −28.8163 | + | 41.0775i | −0.991309 | + | 1.41311i | ||||
\(846\) | −30.3343 | −1.04292 | ||||||||
\(847\) | − | 12.4096i | − | 0.426398i | ||||||
\(848\) | −25.6273 | −0.880045 | ||||||||
\(849\) | −1.25003 | −0.0429008 | ||||||||
\(850\) | − | 53.7975i | − | 1.84524i | ||||||
\(851\) | 61.5391i | 2.10953i | ||||||||
\(852\) | 0.00283059i | 9.69745e-5i | ||||||||
\(853\) | 45.3232i | 1.55184i | 0.630833 | + | 0.775919i | \(0.282713\pi\) | ||||
−0.630833 | + | 0.775919i | \(0.717287\pi\) | |||||||
\(854\) | 4.22686 | 0.144640 | ||||||||
\(855\) | 37.8400 | 1.29410 | ||||||||
\(856\) | − | 1.56688i | − | 0.0535547i | ||||||
\(857\) | 35.9135 | 1.22678 | 0.613391 | − | 0.789779i | \(-0.289805\pi\) | ||||
0.613391 | + | 0.789779i | \(0.289805\pi\) | |||||||
\(858\) | 0.113200 | − | 0.358480i | 0.00386460 | − | 0.0122383i | ||||
\(859\) | 32.4843 | 1.10835 | 0.554176 | − | 0.832400i | \(-0.313034\pi\) | ||||
0.554176 | + | 0.832400i | \(0.313034\pi\) | |||||||
\(860\) | − | 3.58947i | − | 0.122400i | ||||||
\(861\) | 0.505361 | 0.0172227 | ||||||||
\(862\) | −51.2771 | −1.74650 | ||||||||
\(863\) | − | 6.12078i | − | 0.208354i | −0.994559 | − | 0.104177i | \(-0.966779\pi\) | ||
0.994559 | − | 0.104177i | \(-0.0332208\pi\) | |||||||
\(864\) | 0.130490i | 0.00443937i | ||||||||
\(865\) | 7.62535i | 0.259270i | ||||||||
\(866\) | 18.4172i | 0.625842i | ||||||||
\(867\) | −0.112337 | −0.00381518 | ||||||||
\(868\) | 0.167271 | 0.00567756 | ||||||||
\(869\) | 10.6492i | 0.361249i | ||||||||
\(870\) | 0.665956 | 0.0225780 | ||||||||
\(871\) | −27.3158 | − | 8.62576i | −0.925561 | − | 0.292273i | ||||
\(872\) | −29.5699 | −1.00136 | ||||||||
\(873\) | − | 25.0187i | − | 0.846755i | ||||||
\(874\) | 25.1811 | 0.851764 | ||||||||
\(875\) | 31.4297 | 1.06252 | ||||||||
\(876\) | 0.0521261i | 0.00176118i | ||||||||
\(877\) | − | 13.2533i | − | 0.447533i | −0.974643 | − | 0.223766i | \(-0.928165\pi\) | ||
0.974643 | − | 0.223766i | \(-0.0718353\pi\) | |||||||
\(878\) | 26.7417i | 0.902487i | ||||||||
\(879\) | − | 0.407491i | − | 0.0137443i | ||||||
\(880\) | 30.4183 | 1.02540 | ||||||||
\(881\) | 4.71128 | 0.158727 | 0.0793635 | − | 0.996846i | \(-0.474711\pi\) | ||||
0.0793635 | + | 0.996846i | \(0.474711\pi\) | |||||||
\(882\) | − | 18.4090i | − | 0.619865i | ||||||
\(883\) | −37.7426 | −1.27014 | −0.635070 | − | 0.772455i | \(-0.719029\pi\) | ||||
−0.635070 | + | 0.772455i | \(0.719029\pi\) | |||||||
\(884\) | −0.409648 | + | 1.29726i | −0.0137780 | + | 0.0436317i | ||||
\(885\) | 1.78828 | 0.0601123 | ||||||||
\(886\) | 15.7615i | 0.529517i | ||||||||
\(887\) | 57.0438 | 1.91534 | 0.957671 | − | 0.287864i | \(-0.0929450\pi\) | ||||
0.957671 | + | 0.287864i | \(0.0929450\pi\) | |||||||
\(888\) | −1.21964 | −0.0409285 | ||||||||
\(889\) | 30.2823i | 1.01564i | ||||||||
\(890\) | − | 57.4973i | − | 1.92731i | ||||||
\(891\) | − | 16.8986i | − | 0.566125i | ||||||
\(892\) | − | 0.123300i | − | 0.00412839i | ||||||
\(893\) | −22.8209 | −0.763671 | ||||||||
\(894\) | −1.04481 | −0.0349437 | ||||||||
\(895\) | − | 23.4453i | − | 0.783690i | ||||||
\(896\) | −20.1027 | −0.671585 | ||||||||
\(897\) | 0.220726 | − | 0.698988i | 0.00736982 | − | 0.0233385i | ||||
\(898\) | 17.1543 | 0.572446 | ||||||||
\(899\) | − | 3.11168i | − | 0.103780i | ||||||
\(900\) | −2.98605 | −0.0995350 | ||||||||
\(901\) | 22.9310 | 0.763944 | ||||||||
\(902\) | 21.6535i | 0.720984i | ||||||||
\(903\) | 0.587912i | 0.0195645i | ||||||||
\(904\) | − | 20.4137i | − | 0.678950i | ||||||
\(905\) | − | 79.5438i | − | 2.64412i | ||||||
\(906\) | −0.0403048 | −0.00133904 | ||||||||
\(907\) | −22.9446 | −0.761863 | −0.380931 | − | 0.924603i | \(-0.624397\pi\) | ||||
−0.380931 | + | 0.924603i | \(0.624397\pi\) | |||||||
\(908\) | − | 0.988481i | − | 0.0328039i | ||||||
\(909\) | −25.0866 | −0.832072 | ||||||||
\(910\) | −31.9772 | − | 10.0977i | −1.06003 | − | 0.334736i | ||||
\(911\) | 11.9059 | 0.394460 | 0.197230 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197230 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(912\) | 0.524233i | 0.0173591i | ||||||||
\(913\) | 25.8982 | 0.857106 | ||||||||
\(914\) | 47.7037 | 1.57790 | ||||||||
\(915\) | − | 0.259029i | − | 0.00856323i | ||||||
\(916\) | − | 0.147830i | − | 0.00488446i | ||||||
\(917\) | − | 30.8345i | − | 1.01824i | ||||||
\(918\) | − | 1.24734i | − | 0.0411682i | ||||||
\(919\) | −3.50789 | −0.115714 | −0.0578572 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578572 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(920\) | 56.4638 | 1.86156 | ||||||||
\(921\) | − | 0.438185i | − | 0.0144387i | ||||||
\(922\) | 36.6160 | 1.20588 | ||||||||
\(923\) | −2.52839 | − | 0.798414i | −0.0832231 | − | 0.0262801i | ||||
\(924\) | 0.0120332 | 0.000395865 | ||||||||
\(925\) | − | 114.622i | − | 3.76876i | ||||||
\(926\) | 28.8384 | 0.947688 | ||||||||
\(927\) | −42.0334 | −1.38056 | ||||||||
\(928\) | − | 1.76934i | − | 0.0580815i | ||||||
\(929\) | − | 12.0272i | − | 0.394599i | −0.980343 | − | 0.197300i | \(-0.936783\pi\) | ||
0.980343 | − | 0.197300i | \(-0.0632172\pi\) | |||||||
\(930\) | − | 0.214018i | − | 0.00701793i | ||||||
\(931\) | − | 13.8493i | − | 0.453894i | ||||||
\(932\) | −1.42632 | −0.0467208 | ||||||||
\(933\) | −0.545803 | −0.0178688 | ||||||||
\(934\) | − | 28.5522i | − | 0.934256i | ||||||
\(935\) | −27.2179 | −0.890122 | ||||||||
\(936\) | −28.3810 | − | 8.96212i | −0.927661 | − | 0.292936i | ||||
\(937\) | 15.4940 | 0.506167 | 0.253083 | − | 0.967445i | \(-0.418555\pi\) | ||||
0.253083 | + | 0.967445i | \(0.418555\pi\) | |||||||
\(938\) | − | 19.1439i | − | 0.625069i | ||||||
\(939\) | 0.396619 | 0.0129432 | ||||||||
\(940\) | 2.71057 | 0.0884092 | ||||||||
\(941\) | − | 4.92655i | − | 0.160601i | −0.996771 | − | 0.0803005i | \(-0.974412\pi\) | ||
0.996771 | − | 0.0803005i | \(-0.0255880\pi\) | |||||||
\(942\) | − | 0.319328i | − | 0.0104043i | ||||||
\(943\) | 42.2215i | 1.37492i | ||||||||
\(944\) | − | 50.7558i | − | 1.65196i | ||||||
\(945\) | 1.47264 | 0.0479051 | ||||||||
\(946\) | −25.1906 | −0.819018 | ||||||||
\(947\) | − | 21.8513i | − | 0.710072i | −0.934853 | − | 0.355036i | \(-0.884469\pi\) | ||
0.934853 | − | 0.355036i | \(-0.115531\pi\) | |||||||
\(948\) | 0.0217989 | 0.000707997 | ||||||||
\(949\) | −46.5610 | − | 14.7030i | −1.51144 | − | 0.477280i | ||||
\(950\) | −46.9022 | −1.52171 | ||||||||
\(951\) | − | 0.217278i | − | 0.00704571i | ||||||
\(952\) | 17.1637 | 0.556277 | ||||||||
\(953\) | −26.5138 | −0.858866 | −0.429433 | − | 0.903099i | \(-0.641286\pi\) | ||||
−0.429433 | + | 0.903099i | \(0.641286\pi\) | |||||||
\(954\) | − | 26.5740i | − | 0.860365i | ||||||
\(955\) | − | 26.1859i | − | 0.847357i | ||||||
\(956\) | − | 1.24860i | − | 0.0403827i | ||||||
\(957\) | − | 0.223849i | − | 0.00723602i | ||||||
\(958\) | 35.0113 | 1.13117 | ||||||||
\(959\) | −5.18913 | −0.167566 | ||||||||
\(960\) | 1.11606i | 0.0360208i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −18.2229 | + | 57.7076i | −0.587529 | + | 1.86057i | ||||
\(963\) | 1.70670 | 0.0549976 | ||||||||
\(964\) | − | 1.00229i | − | 0.0322817i | ||||||
\(965\) | −86.2449 | −2.77632 | ||||||||
\(966\) | 0.489875 | 0.0157615 | ||||||||
\(967\) | 16.7775i | 0.539528i | 0.962927 | + | 0.269764i | \(0.0869456\pi\) | ||||
−0.962927 | + | 0.269764i | \(0.913054\pi\) | |||||||
\(968\) | 20.5480i | 0.660437i | ||||||||
\(969\) | − | 0.469078i | − | 0.0150690i | ||||||
\(970\) | 46.6756i | 1.49866i | ||||||||
\(971\) | 6.43434 | 0.206488 | 0.103244 | − | 0.994656i | \(-0.467078\pi\) | ||||
0.103244 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(972\) | −0.103859 | −0.00333129 | ||||||||
\(973\) | 26.7520i | 0.857631i | ||||||||
\(974\) | 31.1915 | 0.999442 | ||||||||
\(975\) | −0.411122 | + | 1.30193i | −0.0131664 | + | 0.0416951i | ||||
\(976\) | −7.35188 | −0.235328 | ||||||||
\(977\) | 38.4778i | 1.23101i | 0.788132 | + | 0.615506i | \(0.211048\pi\) | ||||
−0.788132 | + | 0.615506i | \(0.788952\pi\) | |||||||
\(978\) | −0.175926 | −0.00562550 | ||||||||
\(979\) | −19.3267 | −0.617683 | ||||||||
\(980\) | 1.64497i | 0.0525467i | ||||||||
\(981\) | − | 32.2087i | − | 1.02834i | ||||||
\(982\) | 1.54386i | 0.0492666i | ||||||||
\(983\) | 28.3956i | 0.905678i | 0.891592 | + | 0.452839i | \(0.149589\pi\) | ||||
−0.891592 | + | 0.452839i | \(0.850411\pi\) | |||||||
\(984\) | −0.836786 | −0.0266758 | ||||||||
\(985\) | 26.4610 | 0.843119 | ||||||||
\(986\) | 16.9128i | 0.538615i | ||||||||
\(987\) | −0.443959 | −0.0141314 | ||||||||
\(988\) | 1.13099 | + | 0.357143i | 0.0359816 | + | 0.0113622i | ||||
\(989\) | −49.1183 | −1.56187 | ||||||||
\(990\) | 31.5419i | 1.00247i | ||||||||
\(991\) | −33.6179 | −1.06791 | −0.533954 | − | 0.845513i | \(-0.679295\pi\) | ||||
−0.533954 | + | 0.845513i | \(0.679295\pi\) | |||||||
\(992\) | −0.568613 | −0.0180535 | ||||||||
\(993\) | − | 0.0258994i | − | 0.000821891i | ||||||
\(994\) | − | 1.77199i | − | 0.0562040i | ||||||
\(995\) | 25.2955i | 0.801922i | ||||||||
\(996\) | − | 0.0530138i | − | 0.00167981i | ||||||
\(997\) | −57.9223 | −1.83442 | −0.917208 | − | 0.398408i | \(-0.869563\pi\) | ||||
−0.917208 | + | 0.398408i | \(0.869563\pi\) | |||||||
\(998\) | −31.5550 | −0.998855 | ||||||||
\(999\) | − | 2.65761i | − | 0.0840830i |
(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 | 403.2.c.b.311.24 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.11 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.6 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.9 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.9 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.24 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.6 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.11 | 16 | 13.5 | odd | 4 |