Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(442,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.442");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.f (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 883.3 | ||
Character | \(\chi\) | \(=\) | 1323.883 |
Dual form | 1323.2.f.h.442.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.863305 | + | 1.49529i | −0.610449 | + | 1.05733i | 0.380716 | + | 0.924692i | \(0.375678\pi\) |
−0.991165 | + | 0.132637i | \(0.957656\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.490592 | − | 0.849731i | −0.245296 | − | 0.424865i | ||||
\(5\) | −1.75616 | − | 3.04175i | −0.785377 | − | 1.36031i | −0.928774 | − | 0.370647i | \(-0.879136\pi\) |
0.143397 | − | 0.989665i | \(-0.454197\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.75910 | −0.621935 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.06439 | 1.91773 | ||||||||
\(11\) | −3.04532 | + | 5.27465i | −0.918199 | + | 1.59037i | −0.116049 | + | 0.993244i | \(0.537023\pi\) |
−0.802150 | + | 0.597123i | \(0.796310\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.560139 | − | 0.970190i | −0.155355 | − | 0.269082i | 0.777833 | − | 0.628471i | \(-0.216319\pi\) |
−0.933188 | + | 0.359388i | \(0.882985\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49982 | − | 4.32982i | 0.624956 | − | 1.08246i | ||||
\(17\) | 1.20396 | 0.292002 | 0.146001 | − | 0.989284i | \(-0.453360\pi\) | ||||
0.146001 | + | 0.989284i | \(0.453360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.20537 | 0.505947 | 0.252974 | − | 0.967473i | \(-0.418591\pi\) | ||||
0.252974 | + | 0.967473i | \(0.418591\pi\) | |||||||
\(20\) | −1.72311 | + | 2.98452i | −0.385300 | + | 0.667359i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25808 | − | 9.10727i | −1.12103 | − | 1.94168i | ||||
\(23\) | −0.636695 | − | 1.10279i | −0.132760 | − | 0.229947i | 0.791980 | − | 0.610548i | \(-0.209051\pi\) |
−0.924740 | + | 0.380601i | \(0.875717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66817 | + | 6.35345i | −0.733633 | + | 1.27069i | ||||
\(26\) | 1.93429 | 0.379345 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.10262 | − | 5.37390i | 0.576142 | − | 0.997907i | −0.419774 | − | 0.907628i | \(-0.637891\pi\) |
0.995917 | − | 0.0902789i | \(-0.0287758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0942019 | − | 0.163162i | −0.0169192 | − | 0.0293048i | 0.857442 | − | 0.514581i | \(-0.172052\pi\) |
−0.874361 | + | 0.485276i | \(0.838719\pi\) | |||||||
\(32\) | 2.55712 | + | 4.42907i | 0.452040 | + | 0.782956i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.03938 | + | 1.80026i | −0.178252 | + | 0.308742i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.57670 | 0.588006 | 0.294003 | − | 0.955804i | \(-0.405012\pi\) | ||||
0.294003 | + | 0.955804i | \(0.405012\pi\) | |||||||
\(38\) | −1.90391 | + | 3.29767i | −0.308855 | + | 0.534953i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.08925 | + | 5.35074i | 0.488453 | + | 0.846026i | ||||
\(41\) | 1.68320 | + | 2.91538i | 0.262871 | + | 0.455307i | 0.967004 | − | 0.254762i | \(-0.0819972\pi\) |
−0.704132 | + | 0.710069i | \(0.748664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90276 | + | 3.29567i | −0.290168 | + | 0.502585i | −0.973849 | − | 0.227195i | \(-0.927044\pi\) |
0.683681 | + | 0.729781i | \(0.260378\pi\) | |||||||
\(44\) | 5.97604 | 0.900922 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19865 | 0.324173 | ||||||||
\(47\) | 2.86035 | − | 4.95427i | 0.417225 | − | 0.722654i | −0.578434 | − | 0.815729i | \(-0.696336\pi\) |
0.995659 | + | 0.0930746i | \(0.0296695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.33349 | − | 10.9699i | −0.895691 | − | 1.55138i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.549600 | + | 0.951935i | −0.0762158 | + | 0.132010i | ||||
\(53\) | 8.33827 | 1.14535 | 0.572675 | − | 0.819783i | \(-0.305906\pi\) | ||||
0.572675 | + | 0.819783i | \(0.305906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.3922 | 2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.35702 | + | 9.27862i | 0.703411 | + | 1.21834i | ||||
\(59\) | 5.63427 | + | 9.75883i | 0.733519 | + | 1.27049i | 0.955370 | + | 0.295411i | \(0.0954567\pi\) |
−0.221851 | + | 0.975081i | \(0.571210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00109 | − | 10.3942i | 0.768361 | − | 1.33084i | −0.170091 | − | 0.985428i | \(-0.554406\pi\) |
0.938451 | − | 0.345411i | \(-0.112261\pi\) | |||||||
\(62\) | 0.325300 | 0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | −1.96738 | + | 3.40761i | −0.244024 | + | 0.422662i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.95652 | + | 6.85289i | 0.483366 | + | 0.837214i | 0.999818 | − | 0.0191025i | \(-0.00608088\pi\) |
−0.516452 | + | 0.856316i | \(0.672748\pi\) | |||||||
\(68\) | −0.590651 | − | 1.02304i | −0.0716270 | − | 0.124062i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2052 | 1.44850 | 0.724248 | − | 0.689540i | \(-0.242187\pi\) | ||||
0.724248 | + | 0.689540i | \(0.242187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.31473 | 0.622042 | 0.311021 | − | 0.950403i | \(-0.399329\pi\) | ||||
0.311021 | + | 0.950403i | \(0.399329\pi\) | |||||||
\(74\) | −3.08779 | + | 5.34820i | −0.358948 | + | 0.621716i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.08194 | − | 1.87397i | −0.124107 | − | 0.214959i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.60855 | + | 7.98225i | −0.518503 | + | 0.898073i | 0.481266 | + | 0.876575i | \(0.340177\pi\) |
−0.999769 | + | 0.0214988i | \(0.993156\pi\) | |||||||
\(80\) | −17.5603 | −1.96330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.81246 | −0.641878 | ||||||||
\(83\) | 0.624950 | − | 1.08245i | 0.0685972 | − | 0.118814i | −0.829687 | − | 0.558229i | \(-0.811481\pi\) |
0.898284 | + | 0.439415i | \(0.144814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11433 | − | 3.66213i | −0.229332 | − | 0.397214i | ||||
\(86\) | −3.28532 | − | 5.69034i | −0.354265 | − | 0.613605i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.35702 | − | 9.27862i | 0.571060 | − | 0.989105i | ||||
\(89\) | 5.54131 | 0.587378 | 0.293689 | − | 0.955901i | \(-0.405117\pi\) | ||||
0.293689 | + | 0.955901i | \(0.405117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.624715 | + | 1.08204i | −0.0651310 | + | 0.112810i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.93871 | + | 8.55409i | 0.509389 | + | 0.882287i | ||||
\(95\) | −3.87298 | − | 6.70820i | −0.397359 | − | 0.688246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.24277 | + | 14.2769i | −0.836926 | + | 1.44960i | 0.0555261 | + | 0.998457i | \(0.482316\pi\) |
−0.892452 | + | 0.451142i | \(0.851017\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.19829 | 0.719829 | ||||||||
\(101\) | 6.48192 | − | 11.2270i | 0.644975 | − | 1.11713i | −0.339332 | − | 0.940667i | \(-0.610201\pi\) |
0.984307 | − | 0.176463i | \(-0.0564657\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.35091 | + | 2.33984i | 0.133109 | + | 0.230552i | 0.924873 | − | 0.380275i | \(-0.124171\pi\) |
−0.791765 | + | 0.610826i | \(0.790837\pi\) | |||||||
\(104\) | 0.985340 | + | 1.70666i | 0.0966205 | + | 0.167352i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.19847 | + | 12.4681i | −0.699177 | + | 1.21101i | ||||
\(107\) | 0.178480 | 0.0172544 | 0.00862718 | − | 0.999963i | \(-0.497254\pi\) | ||||
0.00862718 | + | 0.999963i | \(0.497254\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.35853 | 0.896385 | 0.448192 | − | 0.893937i | \(-0.352068\pi\) | ||||
0.448192 | + | 0.893937i | \(0.352068\pi\) | |||||||
\(110\) | −18.4680 | + | 31.9876i | −1.76086 | + | 3.04989i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.21019 | − | 7.29226i | −0.396061 | − | 0.685998i | 0.597175 | − | 0.802111i | \(-0.296290\pi\) |
−0.993236 | + | 0.116113i | \(0.962957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.23627 | + | 3.87333i | −0.208533 | + | 0.361190i | ||||
\(116\) | −6.08848 | −0.565302 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.4564 | −1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0479 | − | 22.5997i | −1.18618 | − | 2.05452i | ||||
\(122\) | 10.3615 | + | 17.9467i | 0.938090 | + | 1.62482i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0924294 | + | 0.160092i | −0.00830040 | + | 0.0143767i | ||||
\(125\) | 8.20593 | 0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | −6.12343 | + | 10.6061i | −0.541240 | + | 0.937455i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.39691 | − | 5.88361i | −0.297928 | − | 0.516027i | ||||
\(131\) | 7.62335 | + | 13.2040i | 0.666055 | + | 1.15364i | 0.978998 | + | 0.203870i | \(0.0653519\pi\) |
−0.312943 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.6627 | −1.18028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.11788 | −0.181606 | ||||||||
\(137\) | 3.07350 | − | 5.32346i | 0.262587 | − | 0.454814i | −0.704342 | − | 0.709861i | \(-0.748758\pi\) |
0.966929 | + | 0.255047i | \(0.0820910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.438687 | − | 0.759829i | −0.0372090 | − | 0.0644478i | 0.846821 | − | 0.531878i | \(-0.178513\pi\) |
−0.884030 | + | 0.467430i | \(0.845180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.5368 | + | 18.2504i | −0.884233 | + | 1.53154i | ||||
\(143\) | 6.82321 | 0.570586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7947 | −1.80995 | ||||||||
\(146\) | −4.58824 | + | 7.94706i | −0.379725 | + | 0.657703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.75470 | − | 3.03923i | −0.144236 | − | 0.249823i | ||||
\(149\) | 2.88776 | + | 5.00175i | 0.236575 | + | 0.409760i | 0.959729 | − | 0.280927i | \(-0.0906418\pi\) |
−0.723154 | + | 0.690686i | \(0.757308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01321 | − | 1.75494i | 0.0824541 | − | 0.142815i | −0.821849 | − | 0.569705i | \(-0.807058\pi\) |
0.904304 | + | 0.426890i | \(0.140391\pi\) | |||||||
\(152\) | −3.87947 | −0.314666 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.330866 | + | 0.573077i | −0.0265758 | + | 0.0460307i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.52378 | − | 2.63927i | −0.121611 | − | 0.210636i | 0.798792 | − | 0.601607i | \(-0.205473\pi\) |
−0.920403 | + | 0.390971i | \(0.872139\pi\) | |||||||
\(158\) | −7.95718 | − | 13.7822i | −0.633039 | − | 1.09646i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.98141 | − | 15.5563i | 0.710043 | − | 1.22983i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.38891 | −0.422092 | −0.211046 | − | 0.977476i | \(-0.567687\pi\) | ||||
−0.211046 | + | 0.977476i | \(0.567687\pi\) | |||||||
\(164\) | 1.65153 | − | 2.86053i | 0.128963 | − | 0.223370i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.07905 | + | 1.86896i | 0.0837502 | + | 0.145060i | ||||
\(167\) | −8.30480 | − | 14.3843i | −0.642645 | − | 1.11309i | −0.984840 | − | 0.173464i | \(-0.944504\pi\) |
0.342196 | − | 0.939629i | \(-0.388829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87249 | − | 10.1714i | 0.451730 | − | 0.782419i | ||||
\(170\) | 7.30126 | 0.559981 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.73391 | 0.284708 | ||||||||
\(173\) | 8.82516 | − | 15.2856i | 0.670965 | − | 1.16214i | −0.306666 | − | 0.951817i | \(-0.599214\pi\) |
0.977631 | − | 0.210328i | \(-0.0674531\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.2255 | + | 26.3714i | 1.14767 | + | 1.98782i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.78384 | + | 8.28586i | −0.358564 | + | 0.621051i | ||||
\(179\) | −2.62844 | −0.196459 | −0.0982294 | − | 0.995164i | \(-0.531318\pi\) | ||||
−0.0982294 | + | 0.995164i | \(0.531318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.97391 | −0.295378 | −0.147689 | − | 0.989034i | \(-0.547184\pi\) | ||||
−0.147689 | + | 0.989034i | \(0.547184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.12001 | + | 1.93991i | 0.0825681 | + | 0.143012i | ||||
\(185\) | −6.28125 | − | 10.8794i | −0.461806 | − | 0.799872i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.66643 | + | 6.35045i | −0.268116 | + | 0.464391i | ||||
\(188\) | −5.61306 | −0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | −9.10295 | + | 15.7668i | −0.658666 | + | 1.14084i | 0.322295 | + | 0.946639i | \(0.395546\pi\) |
−0.980961 | + | 0.194204i | \(0.937787\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.101193 | + | 0.175271i | 0.00728401 | + | 0.0126163i | 0.869644 | − | 0.493679i | \(-0.164348\pi\) |
−0.862360 | + | 0.506295i | \(0.831015\pi\) | |||||||
\(194\) | −14.2321 | − | 24.6506i | −1.02180 | − | 1.76981i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.63136 | 0.116229 | 0.0581147 | − | 0.998310i | \(-0.481491\pi\) | ||||
0.0581147 | + | 0.998310i | \(0.481491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.29211 | −0.446036 | −0.223018 | − | 0.974814i | \(-0.571591\pi\) | ||||
−0.223018 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(200\) | 6.45266 | − | 11.1763i | 0.456272 | − | 0.790287i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.1918 | + | 19.3847i | 0.787449 | + | 1.36390i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.91192 | − | 10.2397i | 0.412906 | − | 0.715174i | ||||
\(206\) | −4.66499 | −0.325025 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.60100 | −0.388359 | ||||||||
\(209\) | −6.71607 | + | 11.6326i | −0.464560 | + | 0.804642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14368 | + | 14.1053i | 0.560634 | + | 0.971046i | 0.997441 | + | 0.0714912i | \(0.0227758\pi\) |
−0.436807 | + | 0.899555i | \(0.643891\pi\) | |||||||
\(212\) | −4.09069 | − | 7.08528i | −0.280950 | − | 0.486619i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.154083 | + | 0.266880i | −0.0105329 | + | 0.0182435i | ||||
\(215\) | 13.3662 | 0.911564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.07927 | + | 13.9937i | −0.547197 | + | 0.947773i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.4949 | − | 18.1776i | −0.707563 | − | 1.22554i | ||||
\(221\) | −0.674383 | − | 1.16807i | −0.0453639 | − | 0.0785726i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.98472 | − | 17.2940i | 0.668626 | − | 1.15809i | −0.309662 | − | 0.950847i | \(-0.600216\pi\) |
0.978288 | − | 0.207248i | \(-0.0664507\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.5387 | 0.967101 | ||||||||
\(227\) | −1.80642 | + | 3.12880i | −0.119896 | + | 0.207666i | −0.919726 | − | 0.392560i | \(-0.871589\pi\) |
0.799830 | + | 0.600226i | \(0.204923\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.85733 | + | 11.8772i | 0.453145 | + | 0.784870i | 0.998579 | − | 0.0532835i | \(-0.0169687\pi\) |
−0.545435 | + | 0.838153i | \(0.683635\pi\) | |||||||
\(230\) | −3.86117 | − | 6.68774i | −0.254598 | − | 0.440976i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45781 | + | 9.45321i | −0.358323 | + | 0.620634i | ||||
\(233\) | 25.2542 | 1.65445 | 0.827227 | − | 0.561867i | \(-0.189917\pi\) | ||||
0.827227 | + | 0.561867i | \(0.189917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0929 | −1.31071 | ||||||||
\(236\) | 5.52825 | − | 9.57521i | 0.359859 | − | 0.623293i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.49495 | + | 7.78549i | 0.290754 | + | 0.503601i | 0.973988 | − | 0.226598i | \(-0.0727604\pi\) |
−0.683234 | + | 0.730200i | \(0.739427\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.62862 | − | 8.01701i | 0.298156 | − | 0.516421i | −0.677558 | − | 0.735469i | \(-0.736962\pi\) |
0.975714 | + | 0.219048i | \(0.0702952\pi\) | |||||||
\(242\) | 45.0575 | 2.89640 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.7763 | −0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23532 | − | 2.13963i | −0.0786013 | − | 0.136141i | ||||
\(248\) | 0.165710 | + | 0.287019i | 0.0105226 | + | 0.0182257i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.08422 | + | 12.2702i | −0.448045 | + | 0.776037i | ||||
\(251\) | 20.6517 | 1.30353 | 0.651763 | − | 0.758422i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758422i | \(0.274030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | 8.56777 | − | 14.8398i | 0.537590 | − | 0.931133i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.40380 | − | 16.2879i | −0.587738 | − | 1.01799i | ||||
\(257\) | 1.22289 | + | 2.11811i | 0.0762819 | + | 0.132124i | 0.901643 | − | 0.432481i | \(-0.142362\pi\) |
−0.825361 | + | 0.564605i | \(0.809028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.86073 | 0.239432 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −26.3251 | −1.62637 | ||||||||
\(263\) | −12.2814 | + | 21.2720i | −0.757302 | + | 1.31169i | 0.186919 | + | 0.982375i | \(0.440150\pi\) |
−0.944222 | + | 0.329311i | \(0.893184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.6433 | − | 25.3629i | −0.899531 | − | 1.55803i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.88207 | − | 6.72395i | 0.237135 | − | 0.410730i | ||||
\(269\) | −29.5703 | −1.80293 | −0.901466 | − | 0.432849i | \(-0.857508\pi\) | ||||
−0.901466 | + | 0.432849i | \(0.857508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7915 | 1.50598 | 0.752989 | − | 0.658034i | \(-0.228612\pi\) | ||||
0.752989 | + | 0.658034i | \(0.228612\pi\) | |||||||
\(272\) | 3.00968 | − | 5.21291i | 0.182488 | − | 0.316079i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30674 | + | 9.19154i | 0.320592 | + | 0.555281i | ||||
\(275\) | −22.3415 | − | 38.6966i | −1.34724 | − | 2.33349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.939249 | + | 1.62683i | −0.0564340 | + | 0.0977466i | −0.892862 | − | 0.450330i | \(-0.851306\pi\) |
0.836428 | + | 0.548076i | \(0.184640\pi\) | |||||||
\(278\) | 1.51488 | 0.0908567 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.03965 | + | 10.4610i | −0.360295 | + | 0.624049i | −0.988009 | − | 0.154395i | \(-0.950657\pi\) |
0.627714 | + | 0.778444i | \(0.283991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9859 | − | 24.2244i | −0.831378 | − | 1.43999i | −0.896946 | − | 0.442140i | \(-0.854219\pi\) |
0.0655680 | − | 0.997848i | \(-0.479114\pi\) | |||||||
\(284\) | −5.98779 | − | 10.3712i | −0.355310 | − | 0.615415i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.89052 | + | 10.2027i | −0.348314 | + | 0.603297i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5505 | −0.914735 | ||||||||
\(290\) | 18.8155 | − | 32.5894i | 1.10488 | − | 1.91372i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.60736 | − | 4.51609i | −0.152584 | − | 0.264284i | ||||
\(293\) | −4.41163 | − | 7.64117i | −0.257730 | − | 0.446402i | 0.707903 | − | 0.706309i | \(-0.249641\pi\) |
−0.965634 | + | 0.259908i | \(0.916308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7893 | − | 34.2761i | 1.15218 | − | 1.99563i | ||||
\(296\) | −6.29177 | −0.365702 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.97209 | −0.577668 | ||||||||
\(299\) | −0.713276 | + | 1.23543i | −0.0412498 | + | 0.0714467i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.74942 | + | 3.03009i | 0.100668 | + | 0.174362i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.51304 | − | 9.54887i | 0.316195 | − | 0.547665i | ||||
\(305\) | −42.1554 | −2.41381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.05532 | −0.0602304 | −0.0301152 | − | 0.999546i | \(-0.509587\pi\) | ||||
−0.0301152 | + | 0.999546i | \(0.509587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.571277 | − | 0.989481i | −0.0324464 | − | 0.0561988i | ||||
\(311\) | −1.53608 | − | 2.66056i | −0.0871029 | − | 0.150867i | 0.819182 | − | 0.573533i | \(-0.194428\pi\) |
−0.906285 | + | 0.422666i | \(0.861094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0810 | − | 24.3891i | 0.795907 | − | 1.37855i | −0.126355 | − | 0.991985i | \(-0.540328\pi\) |
0.922262 | − | 0.386566i | \(-0.126339\pi\) | |||||||
\(314\) | 5.26196 | 0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | 6.42324 | − | 11.1254i | 0.360765 | − | 0.624863i | −0.627322 | − | 0.778760i | \(-0.715849\pi\) |
0.988087 | + | 0.153897i | \(0.0491823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8969 | + | 32.7305i | 1.05803 | + | 1.83255i | ||||
\(320\) | −2.05291 | − | 3.55575i | −0.114761 | − | 0.198772i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.65517 | 0.147738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.21874 | 0.455893 | ||||||||
\(326\) | 4.65227 | − | 8.05797i | 0.257665 | − | 0.446290i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.96091 | − | 5.12845i | −0.163489 | − | 0.283171i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7780 | − | 18.6681i | 0.592413 | − | 1.02609i | −0.401493 | − | 0.915862i | \(-0.631509\pi\) |
0.993906 | − | 0.110228i | \(-0.0351581\pi\) | |||||||
\(332\) | −1.22638 | −0.0673065 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.6783 | 1.56921 | ||||||||
\(335\) | 13.8965 | − | 24.0695i | 0.759248 | − | 1.31506i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30340 | + | 10.9178i | 0.343368 | + | 0.594731i | 0.985056 | − | 0.172235i | \(-0.0550989\pi\) |
−0.641688 | + | 0.766966i | \(0.721766\pi\) | |||||||
\(338\) | 10.1395 | + | 17.5621i | 0.551516 | + | 0.955254i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.07455 | + | 3.59323i | −0.112508 | + | 0.194870i | ||||
\(341\) | 1.14750 | 0.0621406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.34714 | − | 5.79741i | 0.180466 | − | 0.312575i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.2376 | + | 26.3923i | 0.819179 | + | 1.41886i | ||||
\(347\) | 11.5683 | + | 20.0369i | 0.621020 | + | 1.07564i | 0.989296 | + | 0.145922i | \(0.0466147\pi\) |
−0.368276 | + | 0.929716i | \(0.620052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.24346 | + | 14.2781i | −0.441262 | + | 0.764289i | −0.997783 | − | 0.0665448i | \(-0.978802\pi\) |
0.556521 | + | 0.830833i | \(0.312136\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −31.1490 | −1.66025 | ||||||||
\(353\) | 12.2438 | − | 21.2068i | 0.651669 | − | 1.12872i | −0.331049 | − | 0.943614i | \(-0.607402\pi\) |
0.982718 | − | 0.185110i | \(-0.0592642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.4343 | − | 37.1253i | −1.13761 | − | 1.97041i | ||||
\(356\) | −2.71852 | − | 4.70862i | −0.144081 | − | 0.249556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.26915 | − | 3.93028i | 0.119928 | − | 0.207722i | ||||
\(359\) | −20.4777 | −1.08077 | −0.540386 | − | 0.841417i | \(-0.681722\pi\) | ||||
−0.540386 | + | 0.841417i | \(0.681722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1363 | −0.744017 | ||||||||
\(362\) | 3.43070 | − | 5.94214i | 0.180313 | − | 0.312312i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.33349 | − | 16.1661i | −0.488537 | − | 0.846172i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1269 | − | 19.2724i | 0.580821 | − | 1.00601i | −0.414561 | − | 0.910021i | \(-0.636065\pi\) |
0.995382 | − | 0.0959900i | \(-0.0306017\pi\) | |||||||
\(368\) | −6.36650 | −0.331877 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.6905 | 1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2684 | + | 28.1777i | 0.842347 | + | 1.45899i | 0.887905 | + | 0.460027i | \(0.152160\pi\) |
−0.0455576 | + | 0.998962i | \(0.514506\pi\) | |||||||
\(374\) | −6.33050 | − | 10.9647i | −0.327342 | − | 0.566974i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.03163 | + | 8.71504i | −0.259487 | + | 0.449444i | ||||
\(377\) | −6.95160 | −0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | −3.80011 | + | 6.58198i | −0.194941 | + | 0.337648i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.7173 | − | 27.2231i | −0.804165 | − | 1.39285i | ||||
\(383\) | −15.8147 | − | 27.3919i | −0.808093 | − | 1.39966i | −0.914183 | − | 0.405302i | \(-0.867166\pi\) |
0.106090 | − | 0.994357i | \(-0.466167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.349441 | −0.0177861 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.1753 | 0.821179 | ||||||||
\(389\) | −2.62313 | + | 4.54340i | −0.132998 | + | 0.230359i | −0.924831 | − | 0.380378i | \(-0.875794\pi\) |
0.791833 | + | 0.610738i | \(0.209127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.766552 | − | 1.32771i | −0.0387662 | − | 0.0671451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.40836 | + | 2.43935i | −0.0709521 | + | 0.122893i | ||||
\(395\) | 32.3734 | 1.62888 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0276349 | −0.00138696 | −0.000693478 | − | 1.00000i | \(-0.500221\pi\) | ||||
−0.000693478 | 1.00000i | \(0.500221\pi\) | ||||||||
\(398\) | 5.43201 | − | 9.40851i | 0.272282 | − | 0.471606i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3395 | + | 31.7650i | 0.916977 | + | 1.58825i | ||||
\(401\) | 6.06885 | + | 10.5115i | 0.303064 | + | 0.524922i | 0.976828 | − | 0.214024i | \(-0.0686572\pi\) |
−0.673765 | + | 0.738946i | \(0.735324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.105532 | + | 0.182787i | −0.00525694 | + | 0.00910529i | ||||
\(404\) | −12.7199 | −0.632840 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.8922 | + | 18.8659i | −0.539907 | + | 0.935146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6726 | + | 27.1458i | 0.774963 | + | 1.34227i | 0.934816 | + | 0.355134i | \(0.115565\pi\) |
−0.159853 | + | 0.987141i | \(0.551102\pi\) | |||||||
\(410\) | 10.2076 | + | 17.6800i | 0.504116 | + | 0.873155i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.32549 | − | 2.29582i | 0.0653022 | − | 0.113107i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.39004 | −0.215499 | ||||||||
\(416\) | 2.86469 | − | 4.96179i | 0.140453 | − | 0.243272i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.5960 | − | 20.0849i | −0.567181 | − | 0.982385i | ||||
\(419\) | 7.44319 | + | 12.8920i | 0.363623 | + | 0.629814i | 0.988554 | − | 0.150866i | \(-0.0482061\pi\) |
−0.624931 | + | 0.780680i | \(0.714873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.54213 | + | 7.86721i | −0.221370 | + | 0.383424i | −0.955224 | − | 0.295883i | \(-0.904386\pi\) |
0.733854 | + | 0.679307i | \(0.237720\pi\) | |||||||
\(422\) | −28.1219 | −1.36895 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.6678 | −0.712333 | ||||||||
\(425\) | −4.41631 | + | 7.64927i | −0.214223 | + | 0.371044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.0875611 | − | 0.151660i | −0.00423243 | − | 0.00733078i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.5391 | + | 19.9863i | −0.556463 | + | 0.963823i | ||||
\(431\) | 16.6355 | 0.801305 | 0.400652 | − | 0.916230i | \(-0.368784\pi\) | ||||
0.400652 | + | 0.916230i | \(0.368784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.7423 | −0.948756 | −0.474378 | − | 0.880321i | \(-0.657327\pi\) | ||||
−0.474378 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.59122 | − | 7.95223i | −0.219880 | − | 0.380843i | ||||
\(437\) | −1.40415 | − | 2.43206i | −0.0671696 | − | 0.116341i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.36757 | + | 5.83280i | −0.160725 | + | 0.278384i | −0.935129 | − | 0.354307i | \(-0.884717\pi\) |
0.774404 | + | 0.632692i | \(0.218050\pi\) | |||||||
\(440\) | −37.6310 | −1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | 14.3202 | − | 24.8033i | 0.680372 | − | 1.17844i | −0.294496 | − | 0.955653i | \(-0.595152\pi\) |
0.974867 | − | 0.222786i | \(-0.0715150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.73141 | − | 16.8553i | −0.461313 | − | 0.799017i | ||||
\(446\) | 17.2397 | + | 29.8601i | 0.816324 | + | 1.41392i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.66872 | 0.314716 | 0.157358 | − | 0.987542i | \(-0.449702\pi\) | ||||
0.157358 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.5035 | −0.965473 | ||||||||
\(452\) | −4.13097 | + | 7.15505i | −0.194305 | + | 0.336545i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.11898 | − | 5.40223i | −0.146381 | − | 0.253539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3287 | − | 24.8180i | 0.670266 | − | 1.16093i | −0.307563 | − | 0.951528i | \(-0.599513\pi\) |
0.977829 | − | 0.209407i | \(-0.0671533\pi\) | |||||||
\(458\) | −23.6799 | −1.10649 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.38839 | 0.204610 | ||||||||
\(461\) | −10.0087 | + | 17.3355i | −0.466150 | + | 0.807395i | −0.999253 | − | 0.0386554i | \(-0.987693\pi\) |
0.533103 | + | 0.846050i | \(0.321026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95789 | − | 8.58731i | −0.230413 | − | 0.399086i | 0.727517 | − | 0.686090i | \(-0.240674\pi\) |
−0.957930 | + | 0.287003i | \(0.907341\pi\) | |||||||
\(464\) | −15.5120 | − | 26.8676i | −0.720127 | − | 1.24730i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.8020 | + | 37.7623i | −1.00996 | + | 1.74930i | ||||
\(467\) | −16.0807 | −0.744126 | −0.372063 | − | 0.928207i | \(-0.621349\pi\) | ||||
−0.372063 | + | 0.928207i | \(0.621349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.3463 | − | 30.0446i | 0.800124 | − | 1.38586i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.91123 | − | 17.1667i | −0.456201 | − | 0.790164i | ||||
\(473\) | −11.5890 | − | 20.0728i | −0.532863 | − | 0.922946i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.08967 | + | 14.0117i | −0.371180 | + | 0.642902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.5221 | −0.709963 | ||||||||
\(479\) | −4.10128 | + | 7.10362i | −0.187392 | + | 0.324573i | −0.944380 | − | 0.328856i | \(-0.893337\pi\) |
0.756988 | + | 0.653429i | \(0.226670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00345 | − | 3.47008i | −0.0913496 | − | 0.158222i | ||||
\(482\) | 7.99183 | + | 13.8423i | 0.364018 | + | 0.630497i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8024 | + | 22.1745i | −0.581929 | + | 1.00793i | ||||
\(485\) | 57.9023 | 2.62921 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.73680 | 0.124016 | 0.0620081 | − | 0.998076i | \(-0.480250\pi\) | ||||
0.0620081 | + | 0.998076i | \(0.480250\pi\) | |||||||
\(488\) | −10.5565 | + | 18.2844i | −0.477871 | + | 0.827696i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.85482 | − | 17.0690i | −0.444742 | − | 0.770315i | 0.553293 | − | 0.832987i | \(-0.313371\pi\) |
−0.998034 | + | 0.0626719i | \(0.980038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.73542 | − | 6.46993i | 0.168235 | − | 0.291391i | ||||
\(494\) | 4.26582 | 0.191928 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.941952 | −0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5480 | + | 28.6619i | 0.740789 | + | 1.28309i | 0.952136 | + | 0.305674i | \(0.0988817\pi\) |
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(500\) | −4.02576 | − | 6.97283i | −0.180038 | − | 0.311834i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.8288 | + | 30.8803i | −0.795737 | + | 1.37826i | ||||
\(503\) | −12.1860 | −0.543346 | −0.271673 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271673 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | −6.69559 | + | 11.5971i | −0.297655 | + | 0.515554i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.86882 | + | 8.43305i | 0.216019 | + | 0.374156i | ||||
\(509\) | 6.81965 | + | 11.8120i | 0.302276 | + | 0.523557i | 0.976651 | − | 0.214832i | \(-0.0689204\pi\) |
−0.674375 | + | 0.738389i | \(0.735587\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.97968 | 0.352656 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.22292 | −0.186265 | ||||||||
\(515\) | 4.74481 | − | 8.21826i | 0.209081 | − | 0.362140i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.4214 | + | 30.1747i | 0.766190 | + | 1.32708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.46082 | − | 5.99432i | 0.151767 | − | 0.262868i | ||||
\(521\) | 35.5490 | 1.55743 | 0.778714 | − | 0.627379i | \(-0.215872\pi\) | ||||
0.778714 | + | 0.627379i | \(0.215872\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.7187 | 1.16833 | 0.584163 | − | 0.811636i | \(-0.301423\pi\) | ||||
0.584163 | + | 0.811636i | \(0.301423\pi\) | |||||||
\(524\) | 7.47991 | − | 12.9556i | 0.326761 | − | 0.565967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2052 | − | 36.7284i | −0.924589 | − | 1.60143i | ||||
\(527\) | −0.113415 | − | 0.196440i | −0.00494043 | − | 0.00855708i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6892 | − | 18.5143i | 0.464750 | − | 0.804970i | ||||
\(530\) | 50.5665 | 2.19647 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88565 | − | 3.26604i | 0.0816766 | − | 0.141468i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.313440 | − | 0.542893i | −0.0135512 | − | 0.0234713i | ||||
\(536\) | −6.95990 | − | 12.0549i | −0.300622 | − | 0.520693i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.5282 | − | 44.2161i | 1.10060 | − | 1.90629i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.5855 | 1.61593 | 0.807963 | − | 0.589233i | \(-0.200570\pi\) | ||||
0.807963 | + | 0.589233i | \(0.200570\pi\) | |||||||
\(542\) | −21.4026 | + | 37.0705i | −0.919322 | + | 1.59231i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.07866 | + | 5.33240i | 0.131997 | + | 0.228625i | ||||
\(545\) | −16.4350 | − | 28.4663i | −0.704000 | − | 1.21936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13381 | + | 15.8202i | −0.390533 | + | 0.676424i | −0.992520 | − | 0.122082i | \(-0.961043\pi\) |
0.601986 | + | 0.798506i | \(0.294376\pi\) | |||||||
\(548\) | −6.03134 | −0.257646 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 77.1501 | 3.28969 | ||||||||
\(551\) | 6.84243 | − | 11.8514i | 0.291498 | − | 0.504889i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.62172 | − | 2.80890i | −0.0689002 | − | 0.119339i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.430433 | + | 0.745532i | −0.0182544 | + | 0.0316176i | ||||
\(557\) | 3.89272 | 0.164940 | 0.0824698 | − | 0.996594i | \(-0.473719\pi\) | ||||
0.0824698 | + | 0.996594i | \(0.473719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.26324 | 0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.4281 | − | 18.0620i | −0.439884 | − | 0.761901i | ||||
\(563\) | −1.66428 | − | 2.88261i | −0.0701409 | − | 0.121488i | 0.828822 | − | 0.559512i | \(-0.189012\pi\) |
−0.898963 | + | 0.438025i | \(0.855678\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.7875 | + | 25.6127i | −0.622115 | + | 1.07753i | ||||
\(566\) | 48.2965 | 2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | −18.3122 | + | 31.7177i | −0.767688 | + | 1.32967i | 0.171126 | + | 0.985249i | \(0.445259\pi\) |
−0.938814 | + | 0.344425i | \(0.888074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2912 | + | 19.5569i | 0.472522 | + | 0.818432i | 0.999506 | − | 0.0314435i | \(-0.0100104\pi\) |
−0.526984 | + | 0.849875i | \(0.676677\pi\) | |||||||
\(572\) | −3.34742 | − | 5.79789i | −0.139962 | − | 0.242422i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.34201 | 0.389589 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5449 | −0.938557 | −0.469279 | − | 0.883050i | \(-0.655486\pi\) | ||||
−0.469279 | + | 0.883050i | \(0.655486\pi\) | |||||||
\(578\) | 13.4248 | − | 23.2525i | 0.558399 | − | 0.967175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.6923 | + | 18.5197i | 0.443975 | + | 0.768987i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3927 | + | 43.9814i | −1.05166 | + | 1.82152i | ||||
\(584\) | −9.34913 | −0.386870 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.2343 | 0.629325 | ||||||||
\(587\) | −12.1198 | + | 20.9921i | −0.500237 | + | 0.866436i | 0.499763 | + | 0.866162i | \(0.333421\pi\) |
−1.00000 | 0.000273884i | \(0.999913\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.207750 | − | 0.359834i | −0.00856020 | − | 0.0148267i | ||||
\(590\) | 34.1684 | + | 59.1814i | 1.40669 | + | 2.43646i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.94112 | − | 15.4865i | 0.367478 | − | 0.636490i | ||||
\(593\) | −45.7326 | −1.87801 | −0.939007 | − | 0.343898i | \(-0.888253\pi\) | ||||
−0.939007 | + | 0.343898i | \(0.888253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.83343 | − | 4.90764i | 0.116062 | − | 0.201025i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.23155 | − | 2.13311i | −0.0503618 | − | 0.0872292i | ||||
\(599\) | −15.0834 | − | 26.1252i | −0.616290 | − | 1.06745i | −0.990157 | − | 0.139963i | \(-0.955302\pi\) |
0.373866 | − | 0.927483i | \(-0.378032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.36933 | + | 12.7641i | −0.300601 | + | 0.520657i | −0.976272 | − | 0.216547i | \(-0.930521\pi\) |
0.675671 | + | 0.737203i | \(0.263854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.98830 | −0.0809027 | ||||||||
\(605\) | −45.8285 | + | 79.3772i | −1.86319 | + | 3.22714i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.03918 | − | 5.26401i | −0.123356 | − | 0.213660i | 0.797733 | − | 0.603011i | \(-0.206033\pi\) |
−0.921089 | + | 0.389351i | \(0.872699\pi\) | |||||||
\(608\) | 5.63941 | + | 9.76774i | 0.228708 | + | 0.396134i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.3930 | − | 63.0345i | 1.47351 | − | 2.55219i | ||||
\(611\) | −6.40877 | −0.259271 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7734 | 0.475522 | 0.237761 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237761 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(614\) | 0.911065 | − | 1.57801i | 0.0367676 | − | 0.0636833i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0319 | + | 27.7680i | 0.645418 | + | 1.11790i | 0.984205 | + | 0.177034i | \(0.0566503\pi\) |
−0.338786 | + | 0.940863i | \(0.610016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.27588 | + | 10.8701i | −0.252249 | + | 0.436908i | −0.964145 | − | 0.265377i | \(-0.914504\pi\) |
0.711896 | + | 0.702285i | \(0.247837\pi\) | |||||||
\(620\) | 0.649282 | 0.0260758 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.30441 | 0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.92995 | + | 6.80687i | 0.157198 | + | 0.272275i | ||||
\(626\) | 24.3125 | + | 42.1104i | 0.971721 | + | 1.68307i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.49511 | + | 2.58961i | −0.0596614 | + | 0.103337i | ||||
\(629\) | 4.30619 | 0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | 8.10690 | − | 14.0416i | 0.322475 | − | 0.558543i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.0904 | + | 19.2092i | 0.440457 | + | 0.762894i | ||||
\(635\) | 17.4288 | + | 30.1875i | 0.691639 | + | 1.19795i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −65.2553 | −2.58348 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.0148 | 1.70031 | ||||||||
\(641\) | −9.49183 | + | 16.4403i | −0.374905 | + | 0.649354i | −0.990313 | − | 0.138855i | \(-0.955658\pi\) |
0.615408 | + | 0.788209i | \(0.288991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.81347 | − | 8.33718i | −0.189825 | − | 0.328786i | 0.755367 | − | 0.655302i | \(-0.227459\pi\) |
−0.945192 | + | 0.326516i | \(0.894125\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.29222 | + | 3.97025i | −0.0901864 | + | 0.156207i | ||||
\(647\) | −7.81214 | −0.307127 | −0.153564 | − | 0.988139i | \(-0.549075\pi\) | ||||
−0.153564 | + | 0.988139i | \(0.549075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −68.6326 | −2.69406 | ||||||||
\(650\) | −7.09528 | + | 12.2894i | −0.278300 | + | 0.482029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64376 | + | 4.57912i | 0.103537 | + | 0.179332i | ||||
\(653\) | 15.8714 | + | 27.4901i | 0.621097 | + | 1.07577i | 0.989282 | + | 0.146019i | \(0.0466461\pi\) |
−0.368185 | + | 0.929753i | \(0.620021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.7756 | − | 46.3767i | 1.04621 | − | 1.81209i | ||||
\(656\) | 16.8308 | 0.657132 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.10685 | + | 5.38122i | −0.121026 | + | 0.209623i | −0.920172 | − | 0.391513i | \(-0.871952\pi\) |
0.799147 | + | 0.601136i | \(0.205285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7631 | + | 23.8384i | 0.535324 | + | 0.927208i | 0.999148 | + | 0.0412802i | \(0.0131436\pi\) |
−0.463824 | + | 0.885927i | \(0.653523\pi\) | |||||||
\(662\) | 18.6094 | + | 32.2325i | 0.723276 | + | 1.25275i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.09935 | + | 1.90413i | −0.0426630 | + | 0.0738945i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.90169 | −0.305955 | ||||||||
\(668\) | −8.14854 | + | 14.1137i | −0.315276 | + | 0.546075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.9939 | + | 41.5586i | 0.926965 | + | 1.60555i | ||||
\(671\) | 36.5505 | + | 63.3073i | 1.41102 | + | 2.44395i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.10894 | + | 14.0451i | −0.312577 | + | 0.541399i | −0.978919 | − | 0.204247i | \(-0.934526\pi\) |
0.666343 | + | 0.745646i | \(0.267859\pi\) | |||||||
\(674\) | −21.7670 | −0.838434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5240 | −0.443230 | ||||||||
\(677\) | 10.2545 | − | 17.7613i | 0.394112 | − | 0.682623i | −0.598875 | − | 0.800842i | \(-0.704385\pi\) |
0.992987 | + | 0.118220i | \(0.0377188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.71932 | + | 6.44205i | 0.142629 | + | 0.247041i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.990642 | + | 1.71584i | −0.0379337 | + | 0.0657030i | ||||
\(683\) | 0.112308 | 0.00429736 | 0.00214868 | − | 0.999998i | \(-0.499316\pi\) | ||||
0.00214868 | + | 0.999998i | \(0.499316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.5902 | −0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.51311 | + | 16.4772i | 0.362684 | + | 0.628187i | ||||
\(689\) | −4.67059 | − | 8.08970i | −0.177935 | − | 0.308193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.43351 | − | 16.3393i | 0.358868 | − | 0.621577i | −0.628904 | − | 0.777483i | \(-0.716496\pi\) |
0.987772 | + | 0.155906i | \(0.0498296\pi\) | |||||||
\(692\) | −17.3182 | −0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | −1.54081 | + | 2.66876i | −0.0584461 | + | 0.101232i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.02650 | + | 3.51000i | 0.0767590 | + | 0.132951i | ||||
\(698\) | −14.2332 | − | 24.6527i | −0.538736 | − | 0.933118i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.16006 | 0.119354 | 0.0596770 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596770 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.88796 | 0.297500 | ||||||||
\(704\) | −3.55992 | + | 6.16596i | −0.134170 | + | 0.232388i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.1402 | + | 36.6159i | 0.795622 | + | 1.37806i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7606 | − | 18.6378i | 0.404121 | − | 0.699959i | −0.590097 | − | 0.807332i | \(-0.700911\pi\) |
0.994219 | + | 0.107373i | \(0.0342440\pi\) | |||||||
\(710\) | 74.0174 | 2.77782 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.74771 | −0.365311 | ||||||||
\(713\) | −0.119956 | + | 0.207769i | −0.00449237 | + | 0.00778102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9826 | − | 20.7545i | −0.448125 | − | 0.776175i | ||||
\(716\) | 1.28949 | + | 2.23347i | 0.0481906 | + | 0.0834685i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.6785 | − | 30.6201i | 0.659757 | − | 1.14273i | ||||
\(719\) | −18.8302 | −0.702246 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.2040 | − | 21.1379i | 0.454185 | − | 0.786671i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.94957 | + | 3.37675i | 0.0724551 | + | 0.125496i | ||||
\(725\) | 22.7618 | + | 39.4247i | 0.845354 | + | 1.46420i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5426 | − | 33.8489i | 0.724797 | − | 1.25538i | −0.234261 | − | 0.972174i | \(-0.575267\pi\) |
0.959058 | − | 0.283211i | \(-0.0913996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.2306 | 1.19291 | ||||||||
\(731\) | −2.29084 | + | 3.96784i | −0.0847296 | + | 0.146756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.29924 | + | 16.1068i | 0.343475 | + | 0.594917i | 0.985076 | − | 0.172123i | \(-0.0550625\pi\) |
−0.641600 | + | 0.767039i | \(0.721729\pi\) | |||||||
\(734\) | 19.2119 | + | 33.2759i | 0.709123 | + | 1.22824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.25621 | − | 5.63993i | 0.120026 | − | 0.207890i | ||||
\(737\) | −48.1954 | −1.77530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.50136 | 0.202371 | 0.101185 | − | 0.994868i | \(-0.467736\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467736\pi\) | |||||||
\(740\) | −6.16306 | + | 10.6747i | −0.226559 | + | 0.392411i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2326 | − | 17.7234i | −0.375399 | − | 0.650210i | 0.614988 | − | 0.788537i | \(-0.289161\pi\) |
−0.990387 | + | 0.138327i | \(0.955828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.1427 | − | 17.5677i | 0.371601 | − | 0.643631i | ||||
\(746\) | −56.1785 | −2.05684 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.19489 | 0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0230 | − | 32.9488i | −0.694159 | − | 1.20232i | −0.970463 | − | 0.241248i | \(-0.922443\pi\) |
0.276305 | − | 0.961070i | \(-0.410890\pi\) | |||||||
\(752\) | −14.3007 | − | 24.7696i | −0.521494 | − | 0.903254i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00135 | − | 10.3946i | 0.218556 | − | 0.378551i | ||||
\(755\) | −7.11744 | −0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | −1.33329 | + | 2.30933i | −0.0484273 | + | 0.0838786i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.81295 | + | 11.8004i | 0.247132 | + | 0.428045i | ||||
\(761\) | 20.0375 | + | 34.7059i | 0.726357 | + | 1.25809i | 0.958413 | + | 0.285385i | \(0.0921216\pi\) |
−0.232055 | + | 0.972703i | \(0.574545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.8633 | 0.646273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.6116 | 1.97320 | ||||||||
\(767\) | 6.31195 | − | 10.9326i | 0.227911 | − | 0.394754i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4828 | − | 38.9414i | −0.810751 | − | 1.40426i | −0.912339 | − | 0.409436i | \(-0.865726\pi\) |
0.101587 | − | 0.994827i | \(-0.467608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.0992886 | − | 0.171973i | 0.00357348 | − | 0.00618944i | ||||
\(773\) | −24.3561 | −0.876029 | −0.438014 | − | 0.898968i | \(-0.644318\pi\) | ||||
−0.438014 | + | 0.898968i | \(0.644318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.38219 | 0.0496498 | ||||||||
\(776\) | 14.4998 | − | 25.1145i | 0.520514 | − | 0.901556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.52913 | − | 7.84468i | −0.162377 | − | 0.281245i | ||||
\(779\) | 3.71208 | + | 6.42951i | 0.132999 | + | 0.230361i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.1689 | + | 64.3784i | −1.33001 | + | 2.30364i | ||||
\(782\) | 2.64707 | 0.0946592 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.35200 | + | 9.26993i | −0.191021 | + | 0.330858i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7617 | + | 35.9603i | 0.740073 | + | 1.28184i | 0.952461 | + | 0.304659i | \(0.0985426\pi\) |
−0.212388 | + | 0.977185i | \(0.568124\pi\) | |||||||
\(788\) | −0.800331 | − | 1.38621i | −0.0285106 | − | 0.0493818i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.9481 | + | 48.4075i | −0.994349 | + | 1.72226i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4458 | −0.477474 | ||||||||
\(794\) | 0.0238574 | − | 0.0413222i | 0.000846666 | − | 0.00146647i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.08686 | + | 5.34659i | 0.109411 | + | 0.189505i | ||||
\(797\) | −17.3018 | − | 29.9676i | −0.612861 | − | 1.06151i | −0.990756 | − | 0.135657i | \(-0.956685\pi\) |
0.377895 | − | 0.925848i | \(-0.376648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44373 | − | 5.96472i | 0.121831 | − | 0.211017i | ||||
\(800\) | −37.5198 | −1.32653 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.9571 | −0.740020 | ||||||||
\(803\) | −16.1851 | + | 28.0333i | −0.571158 | + | 0.989275i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.182213 | − | 0.315603i | −0.00641819 | − | 0.0111166i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.4023 | + | 19.7494i | −0.401133 | + | 0.694782i | ||||
\(809\) | 11.2519 | 0.395597 | 0.197799 | − | 0.980243i | \(-0.436621\pi\) | ||||
0.197799 | + | 0.980243i | \(0.436621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6803 | 1.04222 | 0.521108 | − | 0.853491i | \(-0.325519\pi\) | ||||
0.521108 | + | 0.853491i | \(0.325519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.8066 | − | 32.5740i | −0.659171 | − | 1.14172i | ||||
\(815\) | 9.46376 | + | 16.3917i | 0.331501 | + | 0.574177i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.19629 | + | 7.26819i | −0.146810 | + | 0.254282i | ||||
\(818\) | −54.1211 | −1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | 17.3215 | − | 30.0018i | 0.604526 | − | 1.04707i | −0.387600 | − | 0.921828i | \(-0.626696\pi\) |
0.992126 | − | 0.125242i | \(-0.0399709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1935 | − | 31.5121i | −0.634186 | − | 1.09844i | −0.986687 | − | 0.162631i | \(-0.948002\pi\) |
0.352501 | − | 0.935811i | \(-0.385331\pi\) | |||||||
\(824\) | −2.37638 | − | 4.11601i | −0.0827851 | − | 0.143388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.3576 | 0.846997 | 0.423498 | − | 0.905897i | \(-0.360802\pi\) | ||||
0.423498 | + | 0.905897i | \(0.360802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.1702 | −1.36044 | −0.680219 | − | 0.733009i | \(-0.738115\pi\) | ||||
−0.680219 | + | 0.733009i | \(0.738115\pi\) | |||||||
\(830\) | 3.78994 | − | 6.56438i | 0.131551 | − | 0.227853i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.654792 | − | 1.13413i | −0.0227008 | − | 0.0393190i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.1690 | + | 50.5223i | −1.00944 | + | 1.74839i | ||||
\(836\) | 13.1794 | 0.455819 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.7030 | −0.887894 | ||||||||
\(839\) | −17.1739 | + | 29.7460i | −0.592907 | + | 1.02695i | 0.400931 | + | 0.916108i | \(0.368687\pi\) |
−0.993839 | + | 0.110838i | \(0.964647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.75250 | − | 8.23157i | −0.163879 | − | 0.283847i | ||||
\(842\) | −7.84250 | − | 13.5836i | −0.270270 | − | 0.468122i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.99045 | − | 13.8399i | 0.275043 | − | 0.476388i | ||||
\(845\) | −41.2520 | −1.41911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.8442 | − | 36.1032i | 0.715793 | − | 1.23979i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.62525 | − | 13.2073i | −0.261544 | − | 0.453007i | ||||
\(851\) | −2.27727 | − | 3.94434i | −0.0780637 | − | 0.135210i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.3371 | − | 28.2967i | 0.559373 | − | 0.968862i | −0.438176 | − | 0.898889i | \(-0.644375\pi\) |
0.997549 | − | 0.0699730i | \(-0.0222913\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.313965 | −0.0107311 | ||||||||
\(857\) | 28.8340 | − | 49.9419i | 0.984950 | − | 1.70598i | 0.342791 | − | 0.939412i | \(-0.388628\pi\) |
0.642159 | − | 0.766571i | \(-0.278039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9884 | + | 25.9607i | 0.511397 | + | 0.885766i | 0.999913 | + | 0.0132108i | \(0.00420525\pi\) |
−0.488515 | + | 0.872555i | \(0.662461\pi\) | |||||||
\(860\) | −6.55733 | − | 11.3576i | −0.223603 | − | 0.387292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3615 | + | 24.8749i | −0.489156 | + | 0.847243i | ||||
\(863\) | 23.1776 | 0.788974 | 0.394487 | − | 0.918901i | \(-0.370922\pi\) | ||||
0.394487 | + | 0.918901i | \(0.370922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.9934 | −2.10784 | ||||||||
\(866\) | 17.0437 | − | 29.5205i | 0.579167 | − | 1.00315i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0690 | − | 48.6170i | −0.952177 | − | 1.64922i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.43240 | − | 7.67715i | 0.150186 | − | 0.260130i | ||||
\(872\) | −16.4626 | −0.557493 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.84884 | 0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.369978 | + | 0.640820i | 0.0124933 | + | 0.0216390i | 0.872204 | − | 0.489141i | \(-0.162690\pi\) |
−0.859711 | + | 0.510780i | \(0.829357\pi\) | |||||||
\(878\) | −5.81448 | − | 10.0710i | −0.196229 | − | 0.339879i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 53.4768 | − | 92.6245i | 1.80270 | − | 3.12237i | ||||
\(881\) | −18.0285 | −0.607395 | −0.303697 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303697 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | −0.661694 | + | 1.14609i | −0.0222552 | + | 0.0385471i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.7254 | + | 42.8256i | 0.830664 | + | 1.43875i | ||||
\(887\) | 15.4763 | + | 26.8058i | 0.519645 | + | 0.900051i | 0.999739 | + | 0.0228344i | \(0.00726904\pi\) |
−0.480094 | + | 0.877217i | \(0.659398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 33.6047 | 1.12643 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.5937 | −0.656046 | ||||||||
\(893\) | 6.30813 | − | 10.9260i | 0.211094 | − | 0.365625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.61595 | + | 7.99506i | 0.154294 | + | 0.267245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.75714 | + | 9.97165i | −0.192118 | + | 0.332758i | ||||
\(899\) | −1.16909 | −0.0389913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0389 | 0.334444 | ||||||||
\(902\) | 17.7008 | − | 30.6587i | 0.589372 | − | 1.02082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.40614 | + | 12.8278i | 0.246324 | + | 0.426646i | ||||
\(905\) | 6.97880 | + | 12.0876i | 0.231983 | + | 0.401807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4042 | − | 37.0731i | 0.710714 | − | 1.23099i | −0.253876 | − | 0.967237i | \(-0.581706\pi\) |
0.964590 | − | 0.263755i | \(-0.0849611\pi\) | |||||||
\(908\) | 3.54485 | 0.117640 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.04869 | + | 5.28049i | −0.101008 | + | 0.174950i | −0.912100 | − | 0.409968i | \(-0.865540\pi\) |
0.811092 | + | 0.584918i | \(0.198873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.80635 | + | 6.59278i | 0.125972 | + | 0.218189i | ||||
\(914\) | 24.7400 | + | 42.8509i | 0.818327 | + | 1.41738i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.72830 | − | 11.6538i | 0.222309 | − | 0.385051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8613 | 0.820100 | 0.410050 | − | 0.912063i | \(-0.365511\pi\) | ||||
0.410050 | + | 0.912063i | \(0.365511\pi\) | |||||||
\(920\) | 3.93382 | − | 6.81357i | 0.129694 | − | 0.224637i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.2811 | − | 29.9317i | −0.569121 | − | 0.985747i | ||||
\(923\) | −6.83664 | − | 11.8414i | −0.225031 | − | 0.389764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1199 | + | 22.7244i | −0.431381 | + | 0.747174i | ||||
\(926\) | 17.1207 | 0.562621 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.7351 | 1.04176 | ||||||||
\(929\) | 20.9201 | − | 36.2347i | 0.686366 | − | 1.18882i | −0.286639 | − | 0.958039i | \(-0.592538\pi\) |
0.973005 | − | 0.230783i | \(-0.0741287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.3895 | − | 21.4592i | −0.405831 | − | 0.702920i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.8826 | − | 24.0453i | 0.454251 | − | 0.786786i | ||||
\(935\) | 25.7553 | 0.842288 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.2537 | 0.955676 | 0.477838 | − | 0.878448i | \(-0.341421\pi\) | ||||
0.477838 | + | 0.878448i | \(0.341421\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.85740 | + | 17.0735i | 0.321513 | + | 0.556877i | ||||
\(941\) | 1.67869 | + | 2.90757i | 0.0547236 | + | 0.0947841i | 0.892090 | − | 0.451859i | \(-0.149239\pi\) |
−0.837366 | + | 0.546643i | \(0.815906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.14337 | − | 3.71242i | 0.0697976 | − | 0.120893i | ||||
\(944\) | 56.3387 | 1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | 2.63300 | − | 4.56050i | 0.0855612 | − | 0.148196i | −0.820069 | − | 0.572265i | \(-0.806065\pi\) |
0.905630 | + | 0.424068i | \(0.139398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.97699 | − | 5.15630i | −0.0966372 | − | 0.167381i | ||||
\(950\) | −13.9677 | − | 24.1928i | −0.453173 | − | 0.784918i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.2520 | −1.82218 | −0.911090 | − | 0.412208i | \(-0.864758\pi\) | ||||
−0.911090 | + | 0.412208i | \(0.864758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.9448 | 2.06921 | ||||||||
\(956\) | 4.41038 | − | 7.63900i | 0.142642 | − | 0.247063i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.08131 | − | 12.2652i | −0.228787 | − | 0.396270i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4823 | − | 26.8160i | 0.499427 | − | 0.865034i | ||||
\(962\) | 6.91836 | 0.223057 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.08306 | −0.292546 | ||||||||
\(965\) | 0.355420 | − | 0.615606i | 0.0114414 | − | 0.0198171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.88641 | − | 11.9276i | −0.221452 | − | 0.383566i | 0.733797 | − | 0.679369i | \(-0.237746\pi\) |
−0.955249 | + | 0.295803i | \(0.904413\pi\) | |||||||
\(968\) | 22.9526 | + | 39.7551i | 0.737725 | + | 1.27778i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −49.9874 | + | 86.5807i | −1.60500 | + | 2.77994i | ||||
\(971\) | 51.3254 | 1.64711 | 0.823555 | − | 0.567236i | \(-0.191987\pi\) | ||||
0.823555 | + | 0.567236i | \(0.191987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.36269 | + | 4.09230i | −0.0757055 | + | 0.131126i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.0033 | − | 51.9673i | −0.960383 | − | 1.66343i | ||||
\(977\) | 8.84252 | + | 15.3157i | 0.282897 | + | 0.489992i | 0.972097 | − | 0.234579i | \(-0.0753711\pi\) |
−0.689200 | + | 0.724571i | \(0.742038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.8751 | + | 29.2285i | −0.539329 | + | 0.934146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.0309 | 1.08597 | ||||||||
\(983\) | −8.00207 | + | 13.8600i | −0.255226 | + | 0.442065i | −0.964957 | − | 0.262408i | \(-0.915483\pi\) |
0.709731 | + | 0.704473i | \(0.248817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.86492 | − | 4.96218i | −0.0912839 | − | 0.158108i | ||||
\(986\) | 6.44961 | + | 11.1711i | 0.205397 | + | 0.355759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.21207 | + | 2.09937i | −0.0385612 | + | 0.0667899i | ||||
\(989\) | 4.84590 | 0.154091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8664 | −0.345182 | −0.172591 | − | 0.984994i | \(-0.555214\pi\) | ||||
−0.172591 | + | 0.984994i | \(0.555214\pi\) | |||||||
\(992\) | 0.481771 | − | 0.834453i | 0.0152963 | − | 0.0264939i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0499 | + | 19.1390i | 0.350306 | + | 0.606748i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.5187 | + | 35.5395i | −0.649835 | + | 1.12555i | 0.333327 | + | 0.942811i | \(0.391829\pi\) |
−0.983162 | + | 0.182736i | \(0.941505\pi\) | |||||||
\(998\) | −57.1438 | −1.80886 | ||||||||
\(999\) | 0 | 0 |
(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 | 1323.2.f.h.883.3 | 24 | ||
3.2 | odd | 2 | 441.2.f.h.295.9 | yes | 24 | ||
7.2 | even | 3 | 1323.2.h.h.802.10 | 24 | |||
7.3 | odd | 6 | 1323.2.g.h.667.3 | 24 | |||
7.4 | even | 3 | 1323.2.g.h.667.4 | 24 | |||
7.5 | odd | 6 | 1323.2.h.h.802.9 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.f.h.883.4 | 24 | ||
9.2 | odd | 6 | 3969.2.a.bh.1.3 | 12 | |||
9.4 | even | 3 | inner | 1323.2.f.h.442.3 | 24 | ||
9.5 | odd | 6 | 441.2.f.h.148.9 | ✓ | 24 | ||
9.7 | even | 3 | 3969.2.a.bi.1.10 | 12 | |||
21.2 | odd | 6 | 441.2.h.h.214.4 | 24 | |||
21.5 | even | 6 | 441.2.h.h.214.3 | 24 | |||
21.11 | odd | 6 | 441.2.g.h.79.9 | 24 | |||
21.17 | even | 6 | 441.2.g.h.79.10 | 24 | |||
21.20 | even | 2 | 441.2.f.h.295.10 | yes | 24 | ||
63.4 | even | 3 | 1323.2.h.h.226.10 | 24 | |||
63.5 | even | 6 | 441.2.g.h.67.10 | 24 | |||
63.13 | odd | 6 | inner | 1323.2.f.h.442.4 | 24 | ||
63.20 | even | 6 | 3969.2.a.bh.1.4 | 12 | |||
63.23 | odd | 6 | 441.2.g.h.67.9 | 24 | |||
63.31 | odd | 6 | 1323.2.h.h.226.9 | 24 | |||
63.32 | odd | 6 | 441.2.h.h.373.4 | 24 | |||
63.34 | odd | 6 | 3969.2.a.bi.1.9 | 12 | |||
63.40 | odd | 6 | 1323.2.g.h.361.3 | 24 | |||
63.41 | even | 6 | 441.2.f.h.148.10 | yes | 24 | ||
63.58 | even | 3 | 1323.2.g.h.361.4 | 24 | |||
63.59 | even | 6 | 441.2.h.h.373.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 9.5 | odd | 6 | ||
441.2.f.h.148.10 | yes | 24 | 63.41 | even | 6 | ||
441.2.f.h.295.9 | yes | 24 | 3.2 | odd | 2 | ||
441.2.f.h.295.10 | yes | 24 | 21.20 | even | 2 | ||
441.2.g.h.67.9 | 24 | 63.23 | odd | 6 | |||
441.2.g.h.67.10 | 24 | 63.5 | even | 6 | |||
441.2.g.h.79.9 | 24 | 21.11 | odd | 6 | |||
441.2.g.h.79.10 | 24 | 21.17 | even | 6 | |||
441.2.h.h.214.3 | 24 | 21.5 | even | 6 | |||
441.2.h.h.214.4 | 24 | 21.2 | odd | 6 | |||
441.2.h.h.373.3 | 24 | 63.59 | even | 6 | |||
441.2.h.h.373.4 | 24 | 63.32 | odd | 6 | |||
1323.2.f.h.442.3 | 24 | 9.4 | even | 3 | inner | ||
1323.2.f.h.442.4 | 24 | 63.13 | odd | 6 | inner | ||
1323.2.f.h.883.3 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.f.h.883.4 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.g.h.361.3 | 24 | 63.40 | odd | 6 | |||
1323.2.g.h.361.4 | 24 | 63.58 | even | 3 | |||
1323.2.g.h.667.3 | 24 | 7.3 | odd | 6 | |||
1323.2.g.h.667.4 | 24 | 7.4 | even | 3 | |||
1323.2.h.h.226.9 | 24 | 63.31 | odd | 6 | |||
1323.2.h.h.226.10 | 24 | 63.4 | even | 3 | |||
1323.2.h.h.802.9 | 24 | 7.5 | odd | 6 | |||
1323.2.h.h.802.10 | 24 | 7.2 | even | 3 | |||
3969.2.a.bh.1.3 | 12 | 9.2 | odd | 6 | |||
3969.2.a.bh.1.4 | 12 | 63.20 | even | 6 | |||
3969.2.a.bi.1.9 | 12 | 63.34 | odd | 6 | |||
3969.2.a.bi.1.10 | 12 | 9.7 | even | 3 |