Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), degree \(2\), not 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 481.3 | ||
Root | \(1.71903 - 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.481 |
Dual form | 720.2.q.j.241.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71903 | + | 0.211943i | 0.992485 | + | 0.122365i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.719035 | + | 1.24540i | 0.271770 | + | 0.470719i | 0.969315 | − | 0.245822i | \(-0.0790578\pi\) |
−0.697545 | + | 0.716541i | \(0.745724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.91016 | + | 0.728674i | 0.970054 | + | 0.242891i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.675970 | − | 1.17081i | −0.203813 | − | 0.353014i | 0.745941 | − | 0.666012i | \(-0.232000\pi\) |
−0.949754 | + | 0.312998i | \(0.898667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.76210 | − | 4.78410i | 0.766069 | − | 1.32687i | −0.173611 | − | 0.984814i | \(-0.555544\pi\) |
0.939680 | − | 0.342056i | \(-0.111123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.04307 | + | 1.38276i | −0.269318 | + | 0.357026i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.82032 | 1.16910 | 0.584550 | − | 0.811358i | \(-0.301271\pi\) | ||||
0.584550 | + | 0.811358i | \(0.301271\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.648061 | 0.148675 | 0.0743377 | − | 0.997233i | \(-0.476316\pi\) | ||||
0.0743377 | + | 0.997233i | \(0.476316\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.972091 | + | 2.29329i | 0.212128 | + | 0.500436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.45323 | + | 7.71321i | −0.928562 | + | 1.60832i | −0.142831 | + | 0.989747i | \(0.545621\pi\) |
−0.785730 | + | 0.618569i | \(0.787713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.84823 | + | 1.86940i | 0.933042 | + | 0.359767i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.58613 | + | 6.21136i | 0.665928 | + | 1.15342i | 0.979033 | + | 0.203702i | \(0.0652974\pi\) |
−0.313105 | + | 0.949718i | \(0.601369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.32403 | + | 4.02534i | −0.417408 | + | 0.722972i | −0.995678 | − | 0.0928735i | \(-0.970395\pi\) |
0.578270 | + | 0.815846i | \(0.303728\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.913870 | − | 2.15594i | −0.159084 | − | 0.375300i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.43807 | −0.243078 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.35194 | 0.222257 | 0.111129 | − | 0.993806i | \(-0.464553\pi\) | ||||
0.111129 | + | 0.993806i | \(0.464553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.76210 | − | 7.63862i | 0.922674 | − | 1.22316i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.175970 | + | 0.304788i | −0.0274818 | + | 0.0475999i | −0.879439 | − | 0.476011i | \(-0.842082\pi\) |
0.851957 | + | 0.523611i | \(0.175416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41016 | + | 4.17452i | 0.367546 | + | 0.636608i | 0.989181 | − | 0.146698i | \(-0.0468647\pi\) |
−0.621635 | + | 0.783307i | \(0.713531\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.08613 | + | 2.15594i | −0.310982 | + | 0.321388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.74694 | − | 8.22195i | −0.692413 | − | 1.19929i | −0.971045 | − | 0.238896i | \(-0.923214\pi\) |
0.278632 | − | 0.960398i | \(-0.410119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.46598 | − | 4.27120i | 0.352283 | − | 0.610171i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.28630 | + | 1.02163i | 1.16031 | + | 0.143057i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.17226 | −1.12255 | −0.561273 | − | 0.827631i | \(-0.689688\pi\) | ||||
−0.561273 | + | 0.827631i | \(0.689688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35194 | 0.182295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.11404 | + | 0.137352i | 0.147558 | + | 0.0181927i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.734191 | − | 1.27166i | 0.0955835 | − | 0.165556i | −0.814268 | − | 0.580488i | \(-0.802862\pi\) |
0.909852 | + | 0.414933i | \(0.136195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.34823 | − | 5.79930i | −0.428697 | − | 0.742525i | 0.568061 | − | 0.822987i | \(-0.307694\pi\) |
−0.996758 | + | 0.0804618i | \(0.974361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.18501 | + | 4.14827i | 0.149298 | + | 0.522633i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.76210 | + | 4.78410i | 0.342596 | + | 0.593394i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.21533 | − | 10.7653i | 0.759323 | − | 1.31519i | −0.183873 | − | 0.982950i | \(-0.558864\pi\) |
0.943196 | − | 0.332236i | \(-0.107803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.29001 | + | 12.3155i | −1.11839 | + | 1.48261i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.22808 | −0.264424 | −0.132212 | − | 0.991221i | \(-0.542208\pi\) | ||||
−0.132212 | + | 0.991221i | \(0.542208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.34452 | −0.508488 | −0.254244 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254244 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.675970 | − | 1.59470i | −0.0780542 | − | 0.184140i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.972091 | − | 1.68371i | 0.110780 | − | 0.191877i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.52420 | − | 11.3002i | −0.734030 | − | 1.27138i | −0.955148 | − | 0.296130i | \(-0.904304\pi\) |
0.221118 | − | 0.975247i | \(-0.429029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.93807 | + | 4.24111i | 0.882008 | + | 0.471235i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.63290 | − | 4.56032i | −0.288999 | − | 0.500561i | 0.684572 | − | 0.728945i | \(-0.259989\pi\) |
−0.973571 | + | 0.228384i | \(0.926656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.41016 | + | 4.17452i | −0.261419 | + | 0.452790i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.84823 | + | 11.4376i | 0.519785 | + | 1.22624i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0000 | −1.16600 | −0.582999 | − | 0.812473i | \(-0.698121\pi\) | ||||
−0.582999 | + | 0.812473i | \(0.698121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.94418 | 0.832777 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.84823 | + | 6.42714i | −0.502738 | + | 0.666463i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.324030 | + | 0.561237i | −0.0332448 | + | 0.0575817i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.79001 | − | 15.2247i | −0.892490 | − | 1.54584i | −0.836880 | − | 0.547386i | \(-0.815623\pi\) |
−0.0556097 | − | 0.998453i | \(-0.517710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.11404 | − | 3.89982i | −0.111965 | − | 0.391946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.43807 | − | 2.49081i | −0.143093 | − | 0.247845i | 0.785567 | − | 0.618777i | \(-0.212372\pi\) |
−0.928660 | + | 0.370932i | \(0.879038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.93436 | + | 13.7427i | −0.781796 | + | 1.35411i | 0.149099 | + | 0.988822i | \(0.452363\pi\) |
−0.930895 | + | 0.365288i | \(0.880971\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.47209 | − | 0.304788i | −0.241251 | − | 0.0297443i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.314208 | −0.0303757 | −0.0151878 | − | 0.999885i | \(-0.504835\pi\) | ||||
−0.0151878 | + | 0.999885i | \(0.504835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9320 | 1.52600 | 0.763002 | − | 0.646396i | \(-0.223724\pi\) | ||||
0.763002 | + | 0.646396i | \(0.223724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.32403 | + | 0.286534i | 0.220587 | + | 0.0271966i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25839 | + | 5.64370i | −0.306524 | + | 0.530914i | −0.977599 | − | 0.210474i | \(-0.932499\pi\) |
0.671076 | + | 0.741389i | \(0.265833\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.45323 | − | 7.71321i | −0.415265 | − | 0.719261i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5242 | − | 11.9098i | 1.06541 | − | 1.10106i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46598 | + | 6.00325i | 0.317726 | + | 0.550317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.58613 | − | 7.94341i | 0.416921 | − | 0.722128i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.367095 | + | 0.486646i | −0.0330999 | + | 0.0438794i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.19777 | 0.727434 | 0.363717 | − | 0.931509i | \(-0.381508\pi\) | ||||
0.363717 | + | 0.931509i | \(0.381508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.25839 | + | 7.68696i | 0.286885 | + | 0.676799i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.64806 | + | 6.31863i | −0.318733 | + | 0.552061i | −0.980224 | − | 0.197892i | \(-0.936591\pi\) |
0.661491 | + | 0.749953i | \(0.269924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.465978 | + | 0.807098i | 0.0404054 | + | 0.0699843i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.04307 | + | 3.26399i | −0.347972 | + | 0.280919i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.43807 | + | 11.1511i | 0.550041 | + | 0.952700i | 0.998271 | + | 0.0587811i | \(0.0187214\pi\) |
−0.448230 | + | 0.893919i | \(0.647945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.70388 | − | 4.68325i | 0.229340 | − | 0.397228i | −0.728273 | − | 0.685287i | \(-0.759677\pi\) |
0.957613 | + | 0.288059i | \(0.0930099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.41758 | − | 15.1399i | −0.540458 | − | 1.27501i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.46838 | −0.624537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.17226 | −0.595624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.14435 | − | 6.81969i | 0.424299 | − | 0.562479i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.44178 | − | 2.49723i | 0.118115 | − | 0.204581i | −0.800906 | − | 0.598791i | \(-0.795648\pi\) |
0.919021 | + | 0.394209i | \(0.128981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.32403 | − | 9.22149i | −0.433263 | − | 0.750434i | 0.563889 | − | 0.825851i | \(-0.309305\pi\) |
−0.997152 | + | 0.0754165i | \(0.975971\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0279 | + | 3.51244i | 1.13409 | + | 0.283964i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.32403 | − | 4.02534i | −0.186671 | − | 0.323323i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.14195 | + | 14.1023i | −0.649798 | + | 1.12548i | 0.333373 | + | 0.942795i | \(0.391813\pi\) |
−0.983171 | + | 0.182688i | \(0.941520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0484 | − | 1.73205i | −1.11411 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.8081 | −1.00942 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.1164 | −1.10569 | −0.552843 | − | 0.833286i | \(-0.686457\pi\) | ||||
−0.552843 | + | 0.833286i | \(0.686457\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.32403 | + | 0.286534i | 0.180926 | + | 0.0223066i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.30146 | + | 16.1106i | −0.719768 | + | 1.24668i | 0.241323 | + | 0.970445i | \(0.422419\pi\) |
−0.961091 | + | 0.276230i | \(0.910915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.75839 | − | 15.1700i | −0.673722 | − | 1.16692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.88596 | + | 0.472225i | 0.144223 | + | 0.0361119i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4003 | − | 21.4780i | −0.942780 | − | 1.63294i | −0.760136 | − | 0.649764i | \(-0.774868\pi\) |
−0.182645 | − | 0.983179i | \(-0.558466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.719035 | − | 1.24540i | 0.0543539 | − | 0.0941437i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.53162 | − | 2.03041i | 0.115123 | − | 0.152615i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.8687 | 1.18608 | 0.593042 | − | 0.805172i | \(-0.297927\pi\) | ||||
0.593042 | + | 0.805172i | \(0.297927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5168 | 0.856036 | 0.428018 | − | 0.903770i | \(-0.359212\pi\) | ||||
0.428018 | + | 0.903770i | \(0.359212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.52660 | − | 10.6788i | −0.334616 | − | 0.789402i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.675970 | + | 1.17081i | −0.0496983 | + | 0.0860799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.25839 | − | 5.64370i | −0.238277 | − | 0.412708i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.15788 | + | 7.38217i | 0.0842236 | + | 0.536974i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.114039 | + | 0.197521i | 0.00825157 | + | 0.0142921i | 0.870122 | − | 0.492837i | \(-0.164040\pi\) |
−0.861870 | + | 0.507129i | \(0.830707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9344 | + | 22.4030i | −0.931036 | + | 1.61260i | −0.149481 | + | 0.988765i | \(0.547760\pi\) |
−0.781555 | + | 0.623836i | \(0.785573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.73419 | + | 8.80944i | 0.267411 | + | 0.630857i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.419983 | −0.0299225 | −0.0149613 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149613 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0410 | −0.853562 | −0.426781 | − | 0.904355i | \(-0.640353\pi\) | ||||
−0.426781 | + | 0.904355i | \(0.640353\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9660 | − | 17.1886i | 0.914550 | − | 1.21239i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.15710 | + | 8.93237i | −0.361958 | + | 0.626929i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.175970 | − | 0.304788i | −0.0122903 | − | 0.0212873i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.5800 | + | 19.2017i | −1.29140 | + | 1.33461i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.438069 | − | 0.758758i | −0.0303019 | − | 0.0524844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.49629 | − | 6.05575i | 0.240695 | − | 0.416895i | −0.720218 | − | 0.693748i | \(-0.755958\pi\) |
0.960912 | + | 0.276853i | \(0.0892915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.83014 | − | 0.472225i | −0.262437 | − | 0.0323563i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.82032 | −0.328743 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.68423 | −0.453755 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.46838 | − | 0.920789i | −0.504666 | − | 0.0622212i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.3142 | − | 23.0609i | 0.895611 | − | 1.55124i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.04307 | − | 12.1989i | −0.471639 | − | 0.816902i | 0.527835 | − | 0.849347i | \(-0.323004\pi\) |
−0.999474 | + | 0.0324450i | \(0.989671\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.824030 | − | 2.88461i | −0.0549354 | − | 0.192307i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7244 | − | 20.3072i | −0.778174 | − | 1.34784i | −0.932993 | − | 0.359894i | \(-0.882813\pi\) |
0.154820 | − | 0.987943i | \(-0.450520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.40645 | − | 11.0963i | 0.423350 | − | 0.733264i | −0.572915 | − | 0.819615i | \(-0.694187\pi\) |
0.996265 | + | 0.0863510i | \(0.0275207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.02791 | − | 2.68833i | 0.133427 | − | 0.176879i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.7449 | −1.88314 | −0.941569 | − | 0.336820i | \(-0.890649\pi\) | ||||
−0.941569 | + | 0.336820i | \(0.890649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.49389 | 0.619313 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.82032 | − | 20.8083i | −0.572941 | − | 1.35164i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.321627 | + | 0.557074i | −0.0208043 | + | 0.0360341i | −0.876240 | − | 0.481875i | \(-0.839956\pi\) |
0.855436 | + | 0.517909i | \(0.173289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4344 | + | 18.0728i | 0.672136 | + | 1.16417i | 0.977297 | + | 0.211873i | \(0.0679564\pi\) |
−0.305161 | + | 0.952301i | \(0.598710\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7469 | + | 8.97304i | 0.817717 | + | 0.575621i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.46598 | + | 4.27120i | 0.157546 | + | 0.272877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.79001 | − | 3.10039i | 0.113896 | − | 0.197273i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.55953 | − | 8.39738i | −0.225576 | − | 0.532162i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.8687 | 1.12786 | 0.563932 | − | 0.825821i | \(-0.309288\pi\) | ||||
0.563932 | + | 0.825821i | \(0.309288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0410 | 0.757010 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.02791 | + | 6.66533i | −0.314860 | + | 0.417399i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.70388 | + | 9.87941i | −0.355798 | + | 0.616260i | −0.987254 | − | 0.159151i | \(-0.949124\pi\) |
0.631456 | + | 0.775412i | \(0.282458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.972091 | + | 1.68371i | 0.0604028 | + | 0.104621i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.91016 | + | 20.6892i | 0.365830 | + | 1.28063i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.237900 | + | 0.412055i | 0.0146696 | + | 0.0254084i | 0.873267 | − | 0.487242i | \(-0.161997\pi\) |
−0.858597 | + | 0.512650i | \(0.828664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.08613 | − | 7.07739i | 0.251009 | − | 0.434760i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.9094 | − | 2.33137i | −1.15724 | − | 0.142677i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.57260 | −0.461709 | −0.230855 | − | 0.972988i | \(-0.574152\pi\) | ||||
−0.230855 | + | 0.972988i | \(0.574152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6965 | 1.19647 | 0.598237 | − | 0.801319i | \(-0.295868\pi\) | ||||
0.598237 | + | 0.801319i | \(0.295868\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.6563 | + | 1.68371i | 0.826518 | + | 0.101903i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.675970 | + | 1.17081i | −0.0407625 | + | 0.0706027i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7547 | + | 18.6277i | 0.646186 | + | 1.11923i | 0.984026 | + | 0.178024i | \(0.0569704\pi\) |
−0.337840 | + | 0.941204i | \(0.609696\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.69646 | + | 10.0209i | −0.580512 | + | 0.599937i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.08242 | + | 8.80301i | 0.303192 | + | 0.525144i | 0.976857 | − | 0.213893i | \(-0.0686144\pi\) |
−0.673665 | + | 0.739037i | \(0.735281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.2432 | + | 19.4739i | −0.668341 | + | 1.15760i | 0.310027 | + | 0.950728i | \(0.399662\pi\) |
−0.978368 | + | 0.206873i | \(0.933671\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.675970 | + | 0.896110i | −0.0400410 | + | 0.0530810i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.506113 | −0.0298749 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.23550 | 0.366794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.8836 | − | 28.0348i | −0.696626 | − | 1.64343i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.99760 | − | 5.19199i | 0.175121 | − | 0.303319i | −0.765082 | − | 0.643933i | \(-0.777302\pi\) |
0.940203 | + | 0.340614i | \(0.110635\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.734191 | + | 1.27166i | 0.0427463 | + | 0.0740387i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.08853 | − | 6.94003i | −0.0631631 | − | 0.402702i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.6005 | + | 42.6093i | 1.42268 | + | 2.46416i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.46598 | + | 6.00325i | −0.199776 | + | 0.346022i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.94418 | − | 4.58658i | −0.111690 | − | 0.263492i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.69646 | 0.383438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9549 | 1.36718 | 0.683588 | − | 0.729868i | \(-0.260419\pi\) | ||||
0.683588 | + | 0.729868i | \(0.260419\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5521 | + | 21.9426i | −0.941617 | + | 1.24827i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7547 | − | 23.8238i | 0.779956 | − | 1.35092i | −0.152010 | − | 0.988379i | \(-0.548575\pi\) |
0.931966 | − | 0.362545i | \(-0.118092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.50371 | − | 2.60450i | −0.0849947 | − | 0.147215i | 0.820394 | − | 0.571798i | \(-0.193754\pi\) |
−0.905389 | + | 0.424583i | \(0.860421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.18501 | − | 1.04788i | −0.235799 | − | 0.0590415i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.20017 | − | 9.00696i | −0.292071 | − | 0.505881i | 0.682229 | − | 0.731139i | \(-0.261011\pi\) |
−0.974299 | + | 0.225258i | \(0.927678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.84823 | − | 8.39738i | 0.271449 | − | 0.470163i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.540135 | − | 0.0665941i | −0.0301474 | − | 0.00371692i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12386 | 0.173816 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.52420 | −0.306427 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.3876 | + | 3.37666i | 1.51454 | + | 0.186730i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.82643 | − | 11.8237i | 0.376353 | − | 0.651863i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.61775 | − | 7.99817i | −0.253814 | − | 0.439619i | 0.710758 | − | 0.703436i | \(-0.248352\pi\) |
−0.964573 | + | 0.263817i | \(0.915019\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.93436 | + | 0.985122i | 0.215602 | + | 0.0539844i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.21533 | + | 10.7653i | 0.339580 | + | 0.588169i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3748 | + | 30.0941i | −0.946467 | + | 1.63933i | −0.193681 | + | 0.981064i | \(0.562043\pi\) |
−0.752786 | + | 0.658265i | \(0.771291\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.79743 | + | 9.01112i | −0.369186 | + | 0.489417i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.28390 | 0.340292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1590 | 0.926498 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.02049 | − | 14.2031i | −0.324132 | − | 0.764670i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.8105 | − | 18.7243i | 0.580338 | − | 1.00517i | −0.415101 | − | 0.909775i | \(-0.636254\pi\) |
0.995439 | − | 0.0953996i | \(-0.0304129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.61644 | − | 6.26386i | −0.193584 | − | 0.335297i | 0.752852 | − | 0.658190i | \(-0.228678\pi\) |
−0.946435 | + | 0.322893i | \(0.895344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.3347 | − | 18.0309i | 1.19214 | − | 0.962420i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6406 | + | 20.1622i | 0.619569 | + | 1.07312i | 0.989564 | + | 0.144091i | \(0.0460259\pi\) |
−0.369996 | + | 0.929034i | \(0.620641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.11404 | − | 1.92957i | 0.0591271 | − | 0.102411i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.68579 | + | 11.0544i | 0.247998 | + | 0.585060i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.9655 | 1.68708 | 0.843538 | − | 0.537070i | \(-0.180469\pi\) | ||||
0.843538 | + | 0.537070i | \(0.180469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.56726 | − | 12.6830i | 0.502151 | − | 0.665685i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.17226 | − | 3.76247i | 0.113701 | − | 0.196936i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.76210 | + | 13.4444i | 0.405178 | + | 0.701789i | 0.994342 | − | 0.106224i | \(-0.0338761\pi\) |
−0.589164 | + | 0.808014i | \(0.700543\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.734191 | + | 0.758758i | −0.0382205 | + | 0.0394994i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.87614 | − | 10.1778i | −0.305074 | − | 0.528404i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6661 | + | 27.1346i | −0.811162 | + | 1.40497i | 0.100889 | + | 0.994898i | \(0.467831\pi\) |
−0.912051 | + | 0.410077i | \(0.865502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.71903 | + | 0.211943i | 0.0887706 | + | 0.0109447i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.6210 | 2.04059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.0000 | −1.13006 | −0.565032 | − | 0.825069i | \(-0.691136\pi\) | ||||
−0.565032 | + | 0.825069i | \(0.691136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0922 | + | 1.73746i | 0.721967 | + | 0.0890126i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.6382 | − | 25.3542i | 0.747979 | − | 1.29554i | −0.200811 | − | 0.979630i | \(-0.564358\pi\) |
0.948790 | − | 0.315908i | \(-0.102309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.972091 | + | 1.68371i | 0.0495424 | + | 0.0858099i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.97209 | + | 13.9047i | 0.201913 | + | 0.706818i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00371 | + | 1.73848i | 0.0508901 | + | 0.0881442i | 0.890348 | − | 0.455280i | \(-0.150461\pi\) |
−0.839458 | + | 0.543424i | \(0.817128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4660 | + | 37.1802i | −1.08558 | + | 1.88028i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.61033 | + | 10.0888i | −0.383890 | + | 0.508911i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.0484 | 0.656536 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9368 | 0.850032 | 0.425016 | − | 0.905186i | \(-0.360268\pi\) | ||||
0.425016 | + | 0.905186i | \(0.360268\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.629974 | + | 1.48619i | 0.0315382 | + | 0.0744026i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.9065 | + | 18.8905i | −0.544642 | + | 0.943348i | 0.453987 | + | 0.891008i | \(0.350001\pi\) |
−0.998629 | + | 0.0523397i | \(0.983332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.8384 | + | 22.2368i | 0.639527 | + | 1.10769i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.64195 | + | 4.75401i | −0.379731 | + | 0.236229i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.913870 | − | 1.58287i | −0.0452988 | − | 0.0784599i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.40034 | − | 12.8178i | 0.365923 | − | 0.633798i | −0.623001 | − | 0.782221i | \(-0.714087\pi\) |
0.988924 | + | 0.148424i | \(0.0474200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.70388 | + | 20.5336i | 0.429331 | + | 1.01285i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.11164 | 0.103907 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.26581 | 0.258488 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.64064 | − | 7.47761i | 0.276223 | − | 0.366180i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.14435 | + | 10.6423i | −0.300171 | + | 0.519912i | −0.976175 | − | 0.216987i | \(-0.930377\pi\) |
0.676003 | + | 0.736899i | \(0.263710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.69646 | + | 11.5986i | 0.326365 | + | 0.565282i | 0.981788 | − | 0.189981i | \(-0.0608426\pi\) |
−0.655422 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.82325 | − | 27.3862i | −0.380380 | − | 1.33156i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.41016 | − | 4.17452i | −0.116910 | − | 0.202494i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.81499 | − | 8.33980i | 0.233014 | − | 0.403591i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.8384 | − | 1.58287i | −0.619844 | − | 0.0764216i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0968 | −0.582682 | −0.291341 | − | 0.956619i | \(-0.594101\pi\) | ||||
−0.291341 | + | 0.956619i | \(0.594101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1648 | 1.01712 | 0.508559 | − | 0.861027i | \(-0.330178\pi\) | ||||
0.508559 | + | 0.861027i | \(0.330178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.3294 | − | 1.52011i | −0.591148 | − | 0.0728836i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.88596 | + | 4.99863i | −0.138054 | + | 0.239117i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.741609 | − | 1.28451i | −0.0353951 | − | 0.0613061i | 0.847785 | − | 0.530340i | \(-0.177936\pi\) |
−0.883180 | + | 0.469034i | \(0.844602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.2887 | − | 10.6330i | 0.489938 | − | 0.506333i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.77726 | − | 3.07830i | −0.0844400 | − | 0.146254i | 0.820712 | − | 0.571341i | \(-0.193577\pi\) |
−0.905152 | + | 0.425087i | \(0.860243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.50000 | − | 9.52628i | 0.260725 | − | 0.451589i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.00774 | − | 3.98726i | 0.142261 | − | 0.188591i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.3659 | 1.90498 | 0.952491 | − | 0.304566i | \(-0.0985114\pi\) | ||||
0.952491 | + | 0.304566i | \(0.0985114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.475800 | 0.0224046 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.19777 | − | 16.9805i | −0.338181 | − | 0.797811i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.97209 | + | 6.87986i | −0.186215 | + | 0.322533i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2002 | − | 24.5954i | −0.664256 | − | 1.15052i | −0.979486 | − | 0.201510i | \(-0.935415\pi\) |
0.315231 | − | 0.949015i | \(-0.397918\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.3700 | + | 9.01112i | 1.09082 | + | 0.420603i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.87483 | − | 17.1037i | −0.459917 | − | 0.796599i | 0.539039 | − | 0.842281i | \(-0.318787\pi\) |
−0.998956 | + | 0.0456813i | \(0.985454\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0885340 | − | 0.153345i | 0.00411452 | − | 0.00712656i | −0.863961 | − | 0.503559i | \(-0.832024\pi\) |
0.868075 | + | 0.496432i | \(0.165357\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.14195 | − | 7.41226i | −0.145704 | − | 0.343735i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.5094 | −0.995335 | −0.497667 | − | 0.867368i | \(-0.665810\pi\) | ||||
−0.497667 | + | 0.867368i | \(0.665810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.8761 | 0.825443 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9852 | + | 22.5167i | −0.782635 | + | 1.03751i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.25839 | − | 5.64370i | 0.149821 | − | 0.259498i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.324030 | − | 0.561237i | −0.0148675 | − | 0.0257513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.7826 | − | 5.95491i | −1.08893 | − | 0.272657i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.655479 | + | 1.13532i | 0.0299496 | + | 0.0518742i | 0.880612 | − | 0.473839i | \(-0.157132\pi\) |
−0.850662 | + | 0.525713i | \(0.823799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.73419 | − | 6.46781i | 0.170264 | − | 0.294907i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.0176 | − | 2.71458i | −1.00183 | − | 0.123518i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.5800 | 0.798267 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4152 | −0.471957 | −0.235978 | − | 0.971758i | \(-0.575829\pi\) | ||||
−0.235978 | + | 0.971758i | \(0.575829\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2667 | − | 2.99188i | −1.09738 | − | 0.135297i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0935486 | − | 0.162031i | 0.00422179 | − | 0.00731235i | −0.863907 | − | 0.503652i | \(-0.831989\pi\) |
0.868129 | + | 0.496339i | \(0.165323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2863 | + | 29.9407i | 0.778536 | + | 1.34846i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.93436 | + | 0.985122i | 0.176836 | + | 0.0442780i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.60207 | − | 2.77486i | −0.0718625 | − | 0.124469i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8990 | + | 29.2700i | −0.756505 | + | 1.31030i | 0.188118 | + | 0.982146i | \(0.439761\pi\) |
−0.944623 | + | 0.328158i | \(0.893572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.4040 | + | 25.7233i | −0.866909 | + | 1.14923i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.9623 | −0.934661 | −0.467331 | − | 0.884083i | \(-0.654784\pi\) | ||||
−0.467331 | + | 0.884083i | \(0.654784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.87614 | 0.127986 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8408 | − | 27.9340i | −0.525869 | − | 1.24059i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.3687 | − | 21.4233i | 0.548234 | − | 0.949569i | −0.450162 | − | 0.892947i | \(-0.648634\pi\) |
0.998396 | − | 0.0566220i | \(-0.0180330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.12386 | − | 5.41069i | −0.138191 | − | 0.239355i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.14195 | + | 1.21149i | 0.138720 | + | 0.0534884i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.93436 | − | 13.7427i | −0.349630 | − | 0.605576i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.41758 | + | 11.1156i | −0.282245 | + | 0.488862i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.7645 | − | 39.5496i | −0.735880 | − | 1.73604i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.28390 | −0.319113 | −0.159557 | − | 0.987189i | \(-0.551006\pi\) | ||||
−0.159557 | + | 0.987189i | \(0.551006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0255 | −0.525839 | −0.262919 | − | 0.964818i | \(-0.584685\pi\) | ||||
−0.262919 | + | 0.964818i | \(0.584685\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.50000 | − | 1.98850i | 0.0654654 | − | 0.0867852i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.2026 | + | 19.4034i | −0.487992 | + | 0.845226i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.1624 | − | 48.7788i | −1.22445 | − | 2.12082i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.06324 | − | 3.16574i | 0.132933 | − | 0.137381i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.972091 | + | 1.68371i | 0.0421059 | + | 0.0729296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.157104 | − | 0.272112i | 0.00679220 | − | 0.0117644i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.2789 | + | 3.36326i | 1.17717 | + | 0.145135i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.66771 | −0.287198 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6890 | −1.01847 | −0.509236 | − | 0.860627i | \(-0.670072\pi\) | ||||
−0.509236 | + | 0.860627i | \(0.670072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.7977 | + | 2.44090i | 0.849603 | + | 0.104749i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.96598 | + | 13.7975i | −0.341225 | + | 0.591019i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.77485 | + | 13.4664i | 0.332429 | + | 0.575783i | 0.982987 | − | 0.183673i | \(-0.0587986\pi\) |
−0.650559 | + | 0.759456i | \(0.725465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.51809 | − | 19.3167i | −0.235506 | − | 0.824416i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.32403 | + | 4.02534i | 0.0990070 | + | 0.171485i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.38225 | − | 16.2505i | 0.398974 | − | 0.691043i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.41016 | + | 1.86940i | −0.0598580 | + | 0.0793517i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2477 | 0.518953 | 0.259476 | − | 0.965749i | \(-0.416450\pi\) | ||||
0.259476 | + | 0.965749i | \(0.416450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.6284 | 1.12626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.40515 | − | 10.3923i | −0.185985 | − | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0989 | − | 19.2238i | 0.467762 | − | 0.810188i | −0.531559 | − | 0.847021i | \(-0.678394\pi\) |
0.999321 | + | 0.0368333i | \(0.0117271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.25839 | − | 5.64370i | −0.137082 | − | 0.237432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.425843 | + | 12.9356i | 0.0178837 | + | 0.543245i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.4078 | + | 18.0268i | 0.436316 | + | 0.755721i | 0.997402 | − | 0.0720362i | \(-0.0229497\pi\) |
−0.561086 | + | 0.827757i | \(0.689616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.8007 | + | 39.4919i | −0.954179 | + | 1.65269i | −0.217942 | + | 0.975962i | \(0.569934\pi\) |
−0.736237 | + | 0.676724i | \(0.763399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.154174 | + | 0.363716i | 0.00644070 | + | 0.0151944i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.90645 | 0.371425 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.172260 | −0.00717129 | −0.00358565 | − | 0.999994i | \(-0.501141\pi\) | ||||
−0.00358565 | + | 0.999994i | \(0.501141\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.9828 | + | 35.7701i | −1.12137 | + | 1.48656i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.78630 | − | 6.55806i | 0.157082 | − | 0.272074i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.52420 | + | 9.56819i | 0.228789 | + | 0.396274i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.55211 | + | 15.9352i | 0.188207 | + | 0.658838i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.22515 | − | 10.7823i | −0.256939 | − | 0.445032i | 0.708481 | − | 0.705730i | \(-0.249381\pi\) |
−0.965420 | + | 0.260698i | \(0.916047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.50611 | + | 2.60866i | −0.0620583 | + | 0.107488i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.721965 | − | 0.0890123i | −0.0296977 | − | 0.00366148i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.2403 | 0.543714 | 0.271857 | − | 0.962338i | \(-0.412362\pi\) | ||||
0.271857 | + | 0.962338i | \(0.412362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.93196 | −0.284183 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6989 | − | 2.55200i | −0.847148 | − | 0.104446i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6406 | − | 39.2147i | 0.925072 | − | 1.60227i | 0.133626 | − | 0.991032i | \(-0.457338\pi\) |
0.791446 | − | 0.611239i | \(-0.209329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0558 | + | 26.0774i | 0.614140 | + | 1.06372i | 0.990535 | + | 0.137262i | \(0.0438302\pi\) |
−0.376395 | + | 0.926459i | \(0.622837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.9320 | − | 26.7997i | 1.05603 | − | 1.09137i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.58613 | + | 7.94341i | 0.186453 | + | 0.322946i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2153 | + | 24.6217i | −0.576982 | + | 0.999363i | 0.418841 | + | 0.908060i | \(0.362436\pi\) |
−0.995823 | + | 0.0913030i | \(0.970897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.7584 | + | 14.2620i | −0.435952 | + | 0.577927i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.4461 | −2.12174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.06804 | 0.123917 | 0.0619586 | − | 0.998079i | \(-0.480265\pi\) | ||||
0.0619586 | + | 0.998079i | \(0.480265\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.237900 | − | 0.561237i | −0.00959306 | − | 0.0226313i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.741609 | + | 1.28451i | −0.0298561 | + | 0.0517122i | −0.880567 | − | 0.473921i | \(-0.842838\pi\) |
0.850711 | + | 0.525633i | \(0.176172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.552108 | − | 0.956280i | −0.0221911 | − | 0.0384361i | 0.854717 | − | 0.519095i | \(-0.173731\pi\) |
−0.876908 | + | 0.480659i | \(0.840398\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −36.0094 | + | 29.0706i | −1.44501 | + | 1.16656i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.90938 | − | 13.6995i | −0.316883 | − | 0.548857i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.592243 | − | 1.39718i | −0.0236519 | − | 0.0557979i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.51678 | 0.259841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.07546 | 0.321479 | 0.160740 | − | 0.986997i | \(-0.448612\pi\) | ||||
0.160740 | + | 0.986997i | \(0.448612\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.29372 | − | 9.66904i | 0.289899 | − | 0.384310i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.09888 | + | 7.09947i | −0.162659 | + | 0.281734i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.6226 | − | 23.5950i | −0.539745 | − | 0.934866i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.48406 | − | 1.62354i | −0.256506 | − | 0.0642263i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.269518 | − | 0.466819i | −0.0106453 | − | 0.0184383i | 0.860654 | − | 0.509191i | \(-0.170055\pi\) |
−0.871299 | + | 0.490753i | \(0.836722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.51145 | − | 14.7423i | 0.335659 | − | 0.581378i | −0.647952 | − | 0.761681i | \(-0.724374\pi\) |
0.983611 | + | 0.180303i | \(0.0577078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.28630 | − | 1.02163i | −0.326273 | − | 0.0402267i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.1952 | 1.77680 | 0.888402 | − | 0.459065i | \(-0.151816\pi\) | ||||
0.888402 | + | 0.459065i | \(0.151816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.98516 | −0.0779245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.4904 | − | 1.41667i | −0.450345 | − | 0.0555239i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.62015 | − | 14.9305i | 0.337333 | − | 0.584277i | −0.646597 | − | 0.762831i | \(-0.723809\pi\) |
0.983930 | + | 0.178554i | \(0.0571420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.64806 | − | 6.31863i | −0.142542 | − | 0.246889i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.6433 | − | 3.16574i | −0.493260 | − | 0.123507i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.25839 | + | 9.10780i | 0.204838 | + | 0.354790i | 0.950081 | − | 0.312003i | \(-0.101000\pi\) |
−0.745243 | + | 0.666793i | \(0.767667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.23550 | − | 3.87199i | 0.0869507 | − | 0.150603i | −0.819270 | − | 0.573408i | \(-0.805621\pi\) |
0.906221 | + | 0.422805i | \(0.138954\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.7752 | − | 36.8206i | 1.07870 | − | 1.42999i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.931956 | −0.0361397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −63.8794 | −2.47342 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.52180 | − | 22.4631i | −0.368134 | − | 0.868475i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.52660 | + | 7.84031i | −0.174748 | + | 0.302672i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.43567 | − | 4.21870i | −0.0938880 | − | 0.162619i | 0.815256 | − | 0.579101i | \(-0.196596\pi\) |
−0.909144 | + | 0.416482i | \(0.863263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.805165 | − | 5.13339i | −0.0309908 | − | 0.197584i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.85565 | − | 11.8743i | −0.263484 | − | 0.456368i | 0.703681 | − | 0.710516i | \(-0.251538\pi\) |
−0.967165 | + | 0.254148i | \(0.918205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.6406 | − | 21.8942i | 0.485103 | − | 0.840224i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.8506 | − | 37.3937i | −0.607398 | − | 1.43293i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.8687 | −1.21942 | −0.609711 | − | 0.792624i | \(-0.708715\pi\) | ||||
−0.609711 | + | 0.792624i | \(0.708715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.8761 | −0.491972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.3647 | − | 17.7171i | 0.509895 | − | 0.675950i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.5726 | + | 39.0969i | −0.859948 | + | 1.48947i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0484 | + | 27.7966i | 0.610510 | + | 1.05743i | 0.991155 | + | 0.132713i | \(0.0423688\pi\) |
−0.380645 | + | 0.924721i | \(0.624298\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.05582 | − | 4.19153i | 0.154068 | − | 0.159223i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.70388 | + | 4.68325i | 0.102564 | + | 0.177646i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.848230 | + | 1.46918i | −0.0321290 | + | 0.0556491i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.4134 | − | 6.09226i | −1.86899 | − | 0.230431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5268 | 0.435362 | 0.217681 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217681 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.876139 | 0.0330442 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.3203 | + | 2.01216i | 0.614659 | + | 0.0757823i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.06804 | − | 3.58196i | 0.0777768 | − | 0.134713i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6345 | + | 21.8836i | 0.474500 | + | 0.821858i | 0.999574 | − | 0.0291990i | \(-0.00929566\pi\) |
−0.525074 | + | 0.851057i | \(0.675962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.7523 | − | 37.6395i | −0.403242 | − | 1.41159i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.6989 | − | 35.8515i | −0.775179 | − | 1.34265i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.73419 | − | 6.46781i | 0.139651 | − | 0.241882i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.670955 | + | 0.889462i | −0.0250573 | + | 0.0332176i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.6284 | −0.769310 | −0.384655 | − | 0.923060i | \(-0.625680\pi\) | ||||
−0.384655 | + | 0.923060i | \(0.625680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.8203 | −0.849873 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.1066 | + | 33.2793i | 0.524631 | + | 1.23767i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58613 | − | 6.21136i | 0.133186 | − | 0.230684i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9979 | + | 20.7810i | 0.444978 | + | 0.770725i | 0.998051 | − | 0.0624084i | \(-0.0198781\pi\) |
−0.553073 | + | 0.833133i | \(0.686545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0107 | + | 18.1266i | 0.741136 | + | 0.671355i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6177 | + | 20.1225i | 0.429698 | + | 0.744259i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.64064 | − | 8.03783i | 0.171406 | − | 0.296884i | −0.767506 | − | 0.641042i | \(-0.778502\pi\) |
0.938912 | + | 0.344158i | \(0.111836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.33385 | + | 7.86499i | 0.122971 | + | 0.290104i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.8055 | −0.619038 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3323 | 1.15258 | 0.576289 | − | 0.817246i | \(-0.304500\pi\) | ||||
0.576289 | + | 0.817246i | \(0.304500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.73419 | − | 4.95029i | 0.137179 | − | 0.181854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.9216 | − | 22.3809i | 0.474048 | − | 0.821075i | −0.525511 | − | 0.850787i | \(-0.676126\pi\) |
0.999558 | + | 0.0297121i | \(0.00945905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.44178 | + | 2.49723i | 0.0528227 | + | 0.0914916i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.33919 | − | 15.1898i | −0.158763 | − | 0.555766i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.225927 | − | 0.391316i | −0.00825518 | − | 0.0142984i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58984 | − | 2.75368i | 0.0580141 | − | 0.100483i | −0.835560 | − | 0.549400i | \(-0.814857\pi\) |
0.893574 | + | 0.448916i | \(0.148190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.7170 | + | 3.78714i | 1.11939 | + | 0.138011i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.6481 | 0.387523 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.0288 | 1.63660 | 0.818299 | − | 0.574793i | \(-0.194917\pi\) | ||||
0.818299 | + | 0.574793i | \(0.194917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.6989 | + | 2.55200i | 0.751321 | + | 0.0926317i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.5107 | + | 25.1332i | −0.526011 | + | 0.911078i | 0.473530 | + | 0.880778i | \(0.342980\pi\) |
−0.999541 | + | 0.0303004i | \(0.990354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4556 | + | 19.8417i | 0.414722 | + | 0.718319i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0558 | + | 10.3923i | −0.363569 | + | 0.375735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.05582 | − | 7.02488i | −0.146447 | − | 0.253654i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.80679 | + | 11.7897i | −0.245459 | + | 0.425148i | −0.962261 | − | 0.272130i | \(-0.912272\pi\) |
0.716801 | + | 0.697277i | \(0.245605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8990 | + | 15.7741i | −0.428533 | + | 0.568092i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.7523 | −0.638505 | −0.319253 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319253 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.64806 | 0.166963 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.31421 | + | 3.10039i | 0.0471470 | + | 0.111226i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.114039 | + | 0.197521i | −0.00408587 | + | 0.00707694i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50611 | + | 2.60866i | 0.0538930 | + | 0.0933453i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.77485 | + | 36.8180i | 0.206376 | + | 1.31577i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.14195 | − | 14.1023i | −0.290599 | − | 0.503332i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.9344 | − | 48.3837i | 0.995752 | − | 1.72469i | 0.418140 | − | 0.908383i | \(-0.362682\pi\) |
0.577612 | − | 0.816311i | \(-0.303985\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.321627 | + | 0.758758i | 0.0114502 | + | 0.0270125i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.37158 | −0.333215 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.9926 | −1.31365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.52420 | − | 11.3002i | 0.302322 | − | 0.400778i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.7850 | + | 36.0007i | −0.736242 | + | 1.27521i | 0.217934 | + | 0.975964i | \(0.430068\pi\) |
−0.954176 | + | 0.299245i | \(0.903265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.8818 | − | 39.6324i | −0.809500 | − | 1.40209i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0118 | − | 8.01541i | −1.13108 | − | 0.283211i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.93676 | + | 5.08662i | 0.103636 | + | 0.179503i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.40405 | − | 11.0921i | 0.225713 | − | 0.390946i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0176 | − | 1.60496i | −0.458240 | − | 0.0564972i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.6917 | 0.622005 | 0.311003 | − | 0.950409i | \(-0.399335\pi\) | ||||
0.311003 | + | 0.950409i | \(0.399335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5438 | −0.475589 | −0.237794 | − | 0.971316i | \(-0.576424\pi\) | ||||
−0.237794 | + | 0.971316i | \(0.576424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.8589 | + | 4.17452i | 1.18748 | + | 0.146407i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.05822 | − | 12.2252i | 0.247239 | − | 0.428230i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.56193 | + | 2.70534i | 0.0546450 | + | 0.0946480i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.1188 | + | 5.78872i | 0.807838 | + | 0.202274i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.768213 | + | 1.33058i | 0.0268108 | + | 0.0464377i | 0.879119 | − | 0.476601i | \(-0.158131\pi\) |
−0.852309 | + | 0.523039i | \(0.824798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.43274 | + | 7.67772i | −0.154515 | + | 0.267629i | −0.932882 | − | 0.360181i | \(-0.882715\pi\) |
0.778367 | + | 0.627809i | \(0.216048\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.41016 | + | 1.86940i | −0.0490955 | + | 0.0650842i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4307 | 0.501803 | 0.250901 | − | 0.968013i | \(-0.419273\pi\) | ||||
0.250901 | + | 0.968013i | \(0.419273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.30354 | −0.114737 | −0.0573683 | − | 0.998353i | \(-0.518271\pi\) | ||||
−0.0573683 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5397 | + | 34.3010i | 0.504376 | + | 1.18989i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.8868 | − | 20.5886i | 0.411853 | − | 0.713351i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.30146 | − | 16.1106i | −0.321890 | − | 0.557530i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.7924 | + | 15.1712i | −0.649561 | + | 0.524394i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.0353272 | + | 0.0611885i | 0.00121963 | + | 0.00211246i | 0.866635 | − | 0.498943i | \(-0.166278\pi\) |
−0.865415 | + | 0.501056i | \(0.832945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2207 | + | 19.4348i | −0.386919 | + | 0.670164i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.87112 | + | 16.2099i | 0.236654 | + | 0.558297i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.5168 | 0.602596 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1903 | 0.453226 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.4549 | + | 31.0933i | −0.804968 | + | 1.06712i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.02049 | + | 10.4278i | −0.206380 | + | 0.357460i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.62015 | − | 13.1985i | −0.260909 | − | 0.451908i | 0.705575 | − | 0.708636i | \(-0.250689\pi\) |
−0.966484 | + | 0.256728i | \(0.917356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.35194 | + | 1.39718i | −0.0462353 | + | 0.0477825i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5702 | − | 39.0927i | −0.770983 | − | 1.33538i | −0.937025 | − | 0.349263i | \(-0.886432\pi\) |
0.166041 | − | 0.986119i | \(-0.446901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5144 | − | 44.1922i | 0.870539 | − | 1.50782i | 0.00909955 | − | 0.999959i | \(-0.497103\pi\) |
0.861440 | − | 0.507860i | \(-0.169563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.870026 | − | 0.107267i | −0.0296504 | − | 0.00365565i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.6784 | 0.431577 | 0.215788 | − | 0.976440i | \(-0.430768\pi\) | ||||
0.215788 | + | 0.976440i | \(0.430768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.8007 | 0.843248 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.7190 | + | 1.32157i | 0.364038 | + | 0.0448828i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.82032 | + | 15.2772i | −0.299209 | + | 0.518245i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.3347 | − | 59.4694i | −1.16339 | − | 2.01505i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.4865 | − | 50.7115i | −0.490293 | − | 1.71632i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.719035 | + | 1.24540i | 0.0243078 | + | 0.0421024i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1747 | − | 28.0153i | 0.546180 | − | 0.946011i | −0.452352 | − | 0.891839i | \(-0.649415\pi\) |
0.998532 | − | 0.0541714i | \(-0.0172517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.25338 | − | 8.28989i | 0.210921 | − | 0.279611i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.6816 | −1.37060 | −0.685299 | − | 0.728261i | \(-0.740329\pi\) | ||||
−0.685299 | + | 0.728261i | \(0.740329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3700 | 0.348979 | 0.174490 | − | 0.984659i | \(-0.444172\pi\) | ||||
0.174490 | + | 0.984659i | \(0.444172\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.992582 | + | 2.34163i | 0.0333653 | + | 0.0787129i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.24532 | + | 9.08516i | −0.176121 | + | 0.305050i | −0.940548 | − | 0.339659i | \(-0.889688\pi\) |
0.764428 | + | 0.644709i | \(0.223022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.89448 | + | 10.2095i | 0.197694 | + | 0.342417i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.400338 | − | 12.1609i | −0.0134118 | − | 0.407404i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.07631 | − | 5.32832i | −0.102945 | − | 0.178305i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.93436 | + | 13.7427i | −0.265216 | + | 0.459368i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.2584 | + | 78.4608i | 1.11047 | + | 2.61973i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.3371 | −1.11185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.3929 | −1.31237 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.23048 | + | 9.58521i | −0.240615 | + | 0.318976i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.75839 | + | 9.97383i | −0.191415 | + | 0.331541i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.556597 | + | 0.964053i | 0.0184815 | + | 0.0320109i | 0.875118 | − | 0.483909i | \(-0.160783\pi\) |
−0.856637 | + | 0.515920i | \(0.827450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.37003 | − | 8.29654i | −0.0786088 | − | 0.275179i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.61775 | − | 14.9264i | −0.285519 | − | 0.494533i | 0.687216 | − | 0.726453i | \(-0.258833\pi\) |
−0.972735 | + | 0.231920i | \(0.925499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.55953 | + | 6.16528i | −0.117803 | + | 0.204041i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.5114 | + | 1.41927i | 0.380557 | + | 0.0469195i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.4923 | −0.346487 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.4413 | −0.938193 | −0.469096 | − | 0.883147i | \(-0.655420\pi\) | ||||
−0.469096 | + | 0.883147i | \(0.655420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.1792 | + | 5.07706i | 1.35690 | + | 0.167295i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.15417 | + | 10.6593i | −0.202567 | + | 0.350857i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.675970 | − | 1.17081i | −0.0222257 | − | 0.0384961i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.1042 | + | 34.2119i | −1.08729 | + | 1.12367i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.4610 | + | 51.0279i | 0.966583 | + | 1.67417i | 0.705301 | + | 0.708908i | \(0.250812\pi\) |
0.261282 | + | 0.965263i | \(0.415855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.59810 | − | 2.76800i | 0.0523757 | − | 0.0907174i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.6941 | − | 38.0387i | 0.939401 | − | 1.24533i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.51678 | 0.213122 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0458 | −1.04689 | −0.523445 | − | 0.852059i | \(-0.675353\pi\) | ||||
−0.523445 | + | 0.852059i | \(0.675353\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.03292 | − | 4.79593i | −0.0663419 | − | 0.156509i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.1661 | + | 19.3403i | −0.364006 | + | 0.630477i | −0.988616 | − | 0.150460i | \(-0.951925\pi\) |
0.624610 | + | 0.780937i | \(0.285258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56726 | − | 2.71458i | −0.0510372 | − | 0.0883990i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.97209 | − | 2.68833i | −0.226802 | − | 0.0874514i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.0915 | + | 33.0674i | 0.620389 | + | 1.07455i | 0.989413 | + | 0.145126i | \(0.0463587\pi\) |
−0.369024 | + | 0.929420i | \(0.620308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.03031 | − | 16.5854i | −0.227974 | − | 0.537819i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1771 | 0.459240 | 0.229620 | − | 0.973280i | \(-0.426252\pi\) | ||||
0.229620 | + | 0.973280i | \(0.426252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.228078 | −0.00738043 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.1140 | − | 13.4078i | 0.326940 | − | 0.433414i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.25839 | + | 16.0360i | −0.298969 | + | 0.517830i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.69777 | + | 8.13677i | 0.151541 | + | 0.262476i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.914396 | − | 0.228955i | −0.0294660 | − | 0.00737798i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.9344 | − | 22.4030i | −0.416372 | − | 0.721177i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7042 | + | 20.2723i | −0.376382 | + | 0.651912i | −0.990533 | − | 0.137276i | \(-0.956165\pi\) |
0.614151 | + | 0.789188i | \(0.289499\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.37003 | + | 0.662080i | 0.172510 | + | 0.0212691i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.7300 | 1.05036 | 0.525178 | − | 0.850992i | \(-0.323999\pi\) | ||||
0.525178 | + | 0.850992i | \(0.323999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.77673 | 0.249311 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.49629 | − | 1.17081i | −0.304125 | − | 0.0374960i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.7802 | − | 25.6000i | 0.472860 | − | 0.819018i | −0.526657 | − | 0.850078i | \(-0.676555\pi\) |
0.999518 | + | 0.0310599i | \(0.00988828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.43567 | + | 12.8790i | 0.237645 | + | 0.411613i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.3646 | + | 11.6092i | 1.48031 | + | 0.370653i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.8233 | + | 39.5310i | 0.727949 | + | 1.26084i | 0.957749 | + | 0.287606i | \(0.0928594\pi\) |
−0.229800 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.209991 | − | 0.363716i | 0.00669088 | − | 0.0115889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.2408 | − | 18.8786i | 0.453291 | − | 0.600912i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.9320 | −1.36516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.9245 | 1.45884 | 0.729421 | − | 0.684066i | \(-0.239790\pi\) | ||||
0.729421 | + | 0.684066i | \(0.239790\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.24291 | − | 14.7278i | −0.198113 | − | 0.467374i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.02049 | − | 10.4278i | 0.190862 | − | 0.330583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3700 | + | 24.8896i | 0.455103 | + | 0.788262i | 0.998694 | − | 0.0510883i | \(-0.0162690\pi\) |
−0.543591 | + | 0.839350i | \(0.682936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.55451 | + | 2.52732i | 0.207376 | + | 0.0799608i |
(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 | 720.2.q.j.481.3 | 6 | ||
3.2 | odd | 2 | 2160.2.q.j.1441.3 | 6 | |||
4.3 | odd | 2 | 360.2.q.d.121.1 | ✓ | 6 | ||
9.2 | odd | 6 | 2160.2.q.j.721.3 | 6 | |||
9.4 | even | 3 | 6480.2.a.bx.1.1 | 3 | |||
9.5 | odd | 6 | 6480.2.a.bu.1.1 | 3 | |||
9.7 | even | 3 | inner | 720.2.q.j.241.3 | 6 | ||
12.11 | even | 2 | 1080.2.q.d.361.1 | 6 | |||
36.7 | odd | 6 | 360.2.q.d.241.1 | yes | 6 | ||
36.11 | even | 6 | 1080.2.q.d.721.1 | 6 | |||
36.23 | even | 6 | 3240.2.a.q.1.3 | 3 | |||
36.31 | odd | 6 | 3240.2.a.r.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.d.121.1 | ✓ | 6 | 4.3 | odd | 2 | ||
360.2.q.d.241.1 | yes | 6 | 36.7 | odd | 6 | ||
720.2.q.j.241.3 | 6 | 9.7 | even | 3 | inner | ||
720.2.q.j.481.3 | 6 | 1.1 | even | 1 | trivial | ||
1080.2.q.d.361.1 | 6 | 12.11 | even | 2 | |||
1080.2.q.d.721.1 | 6 | 36.11 | even | 6 | |||
2160.2.q.j.721.3 | 6 | 9.2 | odd | 6 | |||
2160.2.q.j.1441.3 | 6 | 3.2 | odd | 2 | |||
3240.2.a.q.1.3 | 3 | 36.23 | even | 6 | |||
3240.2.a.r.1.3 | 3 | 36.31 | odd | 6 | |||
6480.2.a.bu.1.1 | 3 | 9.5 | odd | 6 | |||
6480.2.a.bx.1.1 | 3 | 9.4 | even | 3 |