Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (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 | 667.7 | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.h.361.7 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0341870 | + | 0.0592136i | 0.0241739 | + | 0.0418703i | 0.877859 | − | 0.478919i | \(-0.158971\pi\) |
−0.853685 | + | 0.520789i | \(0.825638\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.997662 | − | 1.72800i | 0.498831 | − | 0.864001i | ||||
\(5\) | −2.66379 | −1.19128 | −0.595642 | − | 0.803250i | \(-0.703102\pi\) | ||||
−0.595642 | + | 0.803250i | \(0.703102\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.273176 | 0.0965824 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0910670 | − | 0.157733i | −0.0287979 | − | 0.0498794i | ||||
\(11\) | 1.59913 | 0.482155 | 0.241077 | − | 0.970506i | \(-0.422499\pi\) | ||||
0.241077 | + | 0.970506i | \(0.422499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62690 | + | 4.54992i | 0.728571 | + | 1.26192i | 0.957487 | + | 0.288476i | \(0.0931485\pi\) |
−0.228916 | + | 0.973446i | \(0.573518\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.98599 | − | 3.43983i | −0.496496 | − | 0.859957i | ||||
\(17\) | 3.27360 | + | 5.67005i | 0.793966 | + | 1.37519i | 0.923494 | + | 0.383613i | \(0.125320\pi\) |
−0.129528 | + | 0.991576i | \(0.541346\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.950968 | − | 1.64713i | 0.218167 | − | 0.377877i | −0.736081 | − | 0.676894i | \(-0.763326\pi\) |
0.954248 | + | 0.299017i | \(0.0966589\pi\) | |||||||
\(20\) | −2.65756 | + | 4.60304i | −0.594249 | + | 1.02927i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0546693 | + | 0.0946900i | 0.0116555 | + | 0.0201880i | ||||
\(23\) | 3.06837 | 0.639800 | 0.319900 | − | 0.947451i | \(-0.396351\pi\) | ||||
0.319900 | + | 0.947451i | \(0.396351\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.09578 | 0.419157 | ||||||||
\(26\) | −0.179612 | + | 0.311096i | −0.0352247 | + | 0.0610110i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.19452 | − | 5.53306i | 0.593207 | − | 1.02746i | −0.400591 | − | 0.916257i | \(-0.631195\pi\) |
0.993797 | − | 0.111207i | \(-0.0354716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.35961 | − | 5.81902i | 0.603405 | − | 1.04513i | −0.388897 | − | 0.921281i | \(-0.627144\pi\) |
0.992301 | − | 0.123846i | \(-0.0395229\pi\) | |||||||
\(32\) | 0.408966 | − | 0.708350i | 0.0722957 | − | 0.125220i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.223829 | + | 0.387684i | −0.0383864 | + | 0.0664872i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.11477 | + | 3.66290i | −0.347667 | + | 0.602176i | −0.985835 | − | 0.167721i | \(-0.946359\pi\) |
0.638168 | + | 0.769897i | \(0.279693\pi\) | |||||||
\(38\) | 0.130043 | 0.0210958 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.727684 | −0.115057 | ||||||||
\(41\) | −3.69648 | − | 6.40249i | −0.577293 | − | 0.999901i | −0.995788 | − | 0.0916820i | \(-0.970776\pi\) |
0.418495 | − | 0.908219i | \(-0.362558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.63176 | − | 9.75450i | 0.858836 | − | 1.48755i | −0.0142043 | − | 0.999899i | \(-0.504522\pi\) |
0.873040 | − | 0.487648i | \(-0.162145\pi\) | |||||||
\(44\) | 1.59539 | − | 2.76329i | 0.240514 | − | 0.416582i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.104898 | + | 0.181689i | 0.0154664 | + | 0.0267887i | ||||
\(47\) | −1.89959 | − | 3.29018i | −0.277083 | − | 0.479922i | 0.693575 | − | 0.720384i | \(-0.256034\pi\) |
−0.970659 | + | 0.240462i | \(0.922701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.0716485 | + | 0.124099i | 0.0101326 | + | 0.0175502i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.4830 | 1.45374 | ||||||||
\(53\) | 4.44931 | + | 7.70643i | 0.611160 | + | 1.05856i | 0.991045 | + | 0.133527i | \(0.0426301\pi\) |
−0.379885 | + | 0.925034i | \(0.624037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.25974 | −0.574383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.436843 | 0.0573604 | ||||||||
\(59\) | 5.44639 | − | 9.43343i | 0.709060 | − | 1.22813i | −0.256146 | − | 0.966638i | \(-0.582453\pi\) |
0.965206 | − | 0.261490i | \(-0.0842138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.35693 | + | 2.35027i | 0.173737 | + | 0.300922i | 0.939724 | − | 0.341935i | \(-0.111082\pi\) |
−0.765986 | + | 0.642857i | \(0.777749\pi\) | |||||||
\(62\) | 0.459420 | 0.0583465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88802 | −0.986002 | ||||||||
\(65\) | −6.99751 | − | 12.1200i | −0.867935 | − | 1.50331i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66267 | − | 2.87982i | 0.203127 | − | 0.351826i | −0.746407 | − | 0.665489i | \(-0.768223\pi\) |
0.949534 | + | 0.313663i | \(0.101556\pi\) | |||||||
\(68\) | 13.0638 | 1.58422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3890 | 1.47031 | 0.735154 | − | 0.677900i | \(-0.237110\pi\) | ||||
0.735154 | + | 0.677900i | \(0.237110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.09932 | + | 1.90407i | 0.128665 | + | 0.222855i | 0.923160 | − | 0.384417i | \(-0.125597\pi\) |
−0.794494 | + | 0.607271i | \(0.792264\pi\) | |||||||
\(74\) | −0.289191 | −0.0336178 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.89749 | − | 3.28655i | −0.217657 | − | 0.376993i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.406778 | − | 0.704560i | −0.0457661 | − | 0.0792692i | 0.842235 | − | 0.539111i | \(-0.181240\pi\) |
−0.888001 | + | 0.459841i | \(0.847906\pi\) | |||||||
\(80\) | 5.29025 | + | 9.16298i | 0.591468 | + | 1.02445i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.252743 | − | 0.437764i | 0.0279108 | − | 0.0483429i | ||||
\(83\) | −3.41842 | + | 5.92088i | −0.375220 | + | 0.649901i | −0.990360 | − | 0.138517i | \(-0.955766\pi\) |
0.615140 | + | 0.788418i | \(0.289100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.72020 | − | 15.1038i | −0.945838 | − | 1.63824i | ||||
\(86\) | 0.770132 | 0.0830455 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.436843 | 0.0465677 | ||||||||
\(89\) | −0.235286 | + | 0.407527i | −0.0249403 | + | 0.0431978i | −0.878226 | − | 0.478246i | \(-0.841273\pi\) |
0.853286 | + | 0.521443i | \(0.174606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.06120 | − | 5.30216i | 0.319152 | − | 0.552788i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.129882 | − | 0.224963i | 0.0133963 | − | 0.0232031i | ||||
\(95\) | −2.53318 | + | 4.38760i | −0.259899 | + | 0.450158i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.57623 | + | 4.46216i | −0.261576 | + | 0.453064i | −0.966661 | − | 0.256059i | \(-0.917576\pi\) |
0.705085 | + | 0.709123i | \(0.250909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.09088 | − | 3.62152i | 0.209088 | − | 0.362152i | ||||
\(101\) | −1.84488 | −0.183572 | −0.0917862 | − | 0.995779i | \(-0.529258\pi\) | ||||
−0.0917862 | + | 0.995779i | \(0.529258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17802 | −0.510206 | −0.255103 | − | 0.966914i | \(-0.582109\pi\) | ||||
−0.255103 | + | 0.966914i | \(0.582109\pi\) | |||||||
\(104\) | 0.717607 | + | 1.24293i | 0.0703671 | + | 0.121879i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.304217 | + | 0.526920i | −0.0295482 | + | 0.0511790i | ||||
\(107\) | −8.47445 | + | 14.6782i | −0.819256 | + | 1.41899i | 0.0869755 | + | 0.996210i | \(0.472280\pi\) |
−0.906231 | + | 0.422782i | \(0.861054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.24996 | + | 7.36115i | 0.407073 | + | 0.705070i | 0.994560 | − | 0.104163i | \(-0.0332163\pi\) |
−0.587488 | + | 0.809233i | \(0.699883\pi\) | |||||||
\(110\) | −0.145628 | − | 0.252235i | −0.0138851 | − | 0.0240496i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.95196 | + | 3.38089i | 0.183625 | + | 0.318048i | 0.943112 | − | 0.332474i | \(-0.107884\pi\) |
−0.759487 | + | 0.650522i | \(0.774550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.17351 | −0.762183 | ||||||||
\(116\) | −6.37410 | − | 11.0403i | −0.591820 | − | 1.02506i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.744783 | 0.0685628 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.44279 | −0.767527 | ||||||||
\(122\) | −0.0927788 | + | 0.160698i | −0.00839980 | + | 0.0145489i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.70352 | − | 11.6108i | −0.601994 | − | 1.04268i | ||||
\(125\) | 7.73623 | 0.691949 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9533 | 0.971946 | 0.485973 | − | 0.873974i | \(-0.338465\pi\) | ||||
0.485973 | + | 0.873974i | \(0.338465\pi\) | |||||||
\(128\) | −1.08760 | − | 1.88378i | −0.0961311 | − | 0.166504i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.478448 | − | 0.828696i | 0.0419626 | − | 0.0726814i | ||||
\(131\) | −4.45342 | −0.389097 | −0.194549 | − | 0.980893i | \(-0.562324\pi\) | ||||
−0.194549 | + | 0.980893i | \(0.562324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.227366 | 0.0196414 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.894271 | + | 1.54892i | 0.0766831 | + | 0.132819i | ||||
\(137\) | 19.5360 | 1.66907 | 0.834537 | − | 0.550952i | \(-0.185735\pi\) | ||||
0.834537 | + | 0.550952i | \(0.185735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.31540 | + | 2.27833i | 0.111570 | + | 0.193246i | 0.916404 | − | 0.400256i | \(-0.131079\pi\) |
−0.804833 | + | 0.593501i | \(0.797745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.423544 | + | 0.733599i | 0.0355430 | + | 0.0615623i | ||||
\(143\) | 4.20075 | + | 7.27590i | 0.351284 | + | 0.608442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.50952 | + | 14.7389i | −0.706677 | + | 1.22400i | ||||
\(146\) | −0.0751647 | + | 0.130189i | −0.00622067 | + | 0.0107745i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.21966 | + | 7.30867i | 0.346854 | + | 0.600769i | ||||
\(149\) | 8.81281 | 0.721973 | 0.360987 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360987 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.66422 | 0.379569 | 0.189784 | − | 0.981826i | \(-0.439221\pi\) | ||||
0.189784 | + | 0.981826i | \(0.439221\pi\) | |||||||
\(152\) | 0.259782 | − | 0.449956i | 0.0210711 | − | 0.0364962i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94931 | + | 15.5007i | −0.718826 | + | 1.24504i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.03647 | + | 3.52727i | −0.162528 | + | 0.281506i | −0.935775 | − | 0.352599i | \(-0.885298\pi\) |
0.773247 | + | 0.634105i | \(0.218631\pi\) | |||||||
\(158\) | 0.0278130 | − | 0.0481736i | 0.00221269 | − | 0.00383249i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.08940 | + | 1.88690i | −0.0861246 | + | 0.149172i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.06112 | − | 10.4982i | 0.474744 | − | 0.822280i | −0.524838 | − | 0.851202i | \(-0.675874\pi\) |
0.999582 | + | 0.0289220i | \(0.00920745\pi\) | |||||||
\(164\) | −14.7514 | −1.15189 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.467462 | −0.0362821 | ||||||||
\(167\) | 2.39951 | + | 4.15608i | 0.185680 | + | 0.321607i | 0.943805 | − | 0.330502i | \(-0.107218\pi\) |
−0.758126 | + | 0.652109i | \(0.773885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.30121 | + | 12.6461i | −0.561631 | + | 0.972774i | ||||
\(170\) | 0.596235 | − | 1.03271i | 0.0457291 | − | 0.0792051i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.2372 | − | 19.4634i | −0.856828 | − | 1.48407i | ||||
\(173\) | −2.51585 | − | 4.35759i | −0.191277 | − | 0.331301i | 0.754397 | − | 0.656419i | \(-0.227929\pi\) |
−0.945674 | + | 0.325118i | \(0.894596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.17584 | − | 5.50072i | −0.239388 | − | 0.414632i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.0321749 | −0.00241161 | ||||||||
\(179\) | −8.19896 | − | 14.2010i | −0.612819 | − | 1.06143i | −0.990763 | − | 0.135605i | \(-0.956702\pi\) |
0.377944 | − | 0.925828i | \(-0.376631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4345 | 1.07291 | 0.536454 | − | 0.843930i | \(-0.319763\pi\) | ||||
0.536454 | + | 0.843930i | \(0.319763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.838207 | 0.0617934 | ||||||||
\(185\) | 5.63332 | − | 9.75719i | 0.414170 | − | 0.717363i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.23491 | + | 9.06713i | 0.382814 | + | 0.663054i | ||||
\(188\) | −7.58059 | −0.552871 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.346407 | −0.0251310 | ||||||||
\(191\) | 1.42066 | + | 2.46065i | 0.102795 | + | 0.178046i | 0.912835 | − | 0.408328i | \(-0.133888\pi\) |
−0.810040 | + | 0.586374i | \(0.800555\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.41443 | + | 7.64601i | −0.317758 | + | 0.550372i | −0.980020 | − | 0.198900i | \(-0.936263\pi\) |
0.662262 | + | 0.749272i | \(0.269596\pi\) | |||||||
\(194\) | −0.352294 | −0.0252932 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.72354 | −0.407785 | −0.203893 | − | 0.978993i | \(-0.565359\pi\) | ||||
−0.203893 | + | 0.978993i | \(0.565359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.70752 | − | 9.88572i | −0.404596 | − | 0.700780i | 0.589679 | − | 0.807638i | \(-0.299254\pi\) |
−0.994274 | + | 0.106858i | \(0.965921\pi\) | |||||||
\(200\) | 0.572518 | 0.0404832 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.0630709 | − | 0.109242i | −0.00443765 | − | 0.00768624i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.84665 | + | 17.0549i | 0.687720 | + | 1.19117i | ||||
\(206\) | −0.177021 | − | 0.306609i | −0.0123336 | − | 0.0213625i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.4340 | − | 18.0722i | 0.723466 | − | 1.25308i | ||||
\(209\) | 1.52072 | − | 2.63396i | 0.105190 | − | 0.182195i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6919 | + | 18.5189i | 0.736059 | + | 1.27489i | 0.954257 | + | 0.298986i | \(0.0966486\pi\) |
−0.218199 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(212\) | 17.7556 | 1.21946 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.15886 | −0.0792183 | ||||||||
\(215\) | −15.0018 | + | 25.9840i | −1.02312 | + | 1.77209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.290587 | + | 0.503311i | −0.0196810 | + | 0.0340885i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.24978 | + | 7.36084i | −0.286520 | + | 0.496268i | ||||
\(221\) | −17.1989 | + | 29.7893i | −1.15692 | + | 2.00385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.58387 | − | 6.20744i | 0.239994 | − | 0.415681i | −0.720719 | − | 0.693228i | \(-0.756188\pi\) |
0.960712 | + | 0.277547i | \(0.0895213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.133463 | + | 0.231165i | −0.00887784 | + | 0.0153769i | ||||
\(227\) | −13.7887 | −0.915187 | −0.457593 | − | 0.889162i | \(-0.651288\pi\) | ||||
−0.457593 | + | 0.889162i | \(0.651288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3943 | 1.74418 | 0.872092 | − | 0.489341i | \(-0.162763\pi\) | ||||
0.872092 | + | 0.489341i | \(0.162763\pi\) | |||||||
\(230\) | −0.279428 | − | 0.483983i | −0.0184249 | − | 0.0319129i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.872666 | − | 1.51150i | 0.0572933 | − | 0.0992349i | ||||
\(233\) | −6.32230 | + | 10.9505i | −0.414187 | + | 0.717394i | −0.995343 | − | 0.0963989i | \(-0.969268\pi\) |
0.581155 | + | 0.813793i | \(0.302601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.06010 | + | 8.76436i | 0.330085 | + | 0.571724i | ||||
\(236\) | −10.8673 | − | 18.8228i | −0.707403 | − | 1.22526i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71640 | − | 13.3652i | −0.499133 | − | 0.864523i | 0.500867 | − | 0.865524i | \(-0.333015\pi\) |
−0.999999 | + | 0.00100121i | \(0.999681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.17988 | −0.0760029 | −0.0380015 | − | 0.999278i | \(-0.512099\pi\) | ||||
−0.0380015 | + | 0.999278i | \(0.512099\pi\) | |||||||
\(242\) | −0.288634 | − | 0.499928i | −0.0185541 | − | 0.0321366i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.41504 | 0.346662 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.99240 | 0.635801 | ||||||||
\(248\) | 0.917767 | − | 1.58962i | 0.0582783 | − | 0.100941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.264478 | + | 0.458090i | 0.0167271 | + | 0.0289721i | ||||
\(251\) | 5.54970 | 0.350294 | 0.175147 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175147 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.90672 | 0.308483 | ||||||||
\(254\) | 0.374459 | + | 0.648583i | 0.0234957 | + | 0.0406957i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.81365 | + | 13.5336i | −0.488353 | + | 0.845853i | ||||
\(257\) | 9.83076 | 0.613226 | 0.306613 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306613 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.9246 | −1.73181 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.152249 | − | 0.263703i | −0.00940598 | − | 0.0162916i | ||||
\(263\) | −11.9322 | −0.735774 | −0.367887 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367887 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.8520 | − | 20.5283i | −0.728065 | − | 1.26105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.31756 | − | 5.74618i | −0.202652 | − | 0.351004i | ||||
\(269\) | −14.9824 | − | 25.9503i | −0.913494 | − | 1.58222i | −0.809092 | − | 0.587682i | \(-0.800041\pi\) |
−0.104401 | − | 0.994535i | \(-0.533293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.54825 | + | 6.14575i | −0.215541 | + | 0.373328i | −0.953440 | − | 0.301584i | \(-0.902485\pi\) |
0.737899 | + | 0.674911i | \(0.235818\pi\) | |||||||
\(272\) | 13.0027 | − | 22.5213i | 0.788402 | − | 1.36555i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.667877 | + | 1.15680i | 0.0403479 | + | 0.0698847i | ||||
\(275\) | 3.35142 | 0.202098 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.82351 | −0.590237 | −0.295119 | − | 0.955461i | \(-0.595359\pi\) | ||||
−0.295119 | + | 0.955461i | \(0.595359\pi\) | |||||||
\(278\) | −0.0899388 | + | 0.155779i | −0.00539417 | + | 0.00934298i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.9389 | + | 20.6787i | −0.712213 | + | 1.23359i | 0.251812 | + | 0.967776i | \(0.418974\pi\) |
−0.964025 | + | 0.265813i | \(0.914360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50798 | + | 2.61189i | −0.0896399 | + | 0.155261i | −0.907359 | − | 0.420357i | \(-0.861905\pi\) |
0.817719 | + | 0.575618i | \(0.195238\pi\) | |||||||
\(284\) | 12.3601 | − | 21.4083i | 0.733435 | − | 1.27035i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.287222 | + | 0.497483i | −0.0169838 | + | 0.0294168i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9330 | + | 22.4006i | −0.760763 | + | 1.31768i | ||||
\(290\) | −1.16366 | −0.0683324 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.38699 | 0.256729 | ||||||||
\(293\) | −8.52913 | − | 14.7729i | −0.498277 | − | 0.863041i | 0.501721 | − | 0.865030i | \(-0.332700\pi\) |
−0.999998 | + | 0.00198814i | \(0.999367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5081 | + | 25.1287i | −0.844692 | + | 1.46305i | ||||
\(296\) | −0.577706 | + | 1.00062i | −0.0335785 | + | 0.0581596i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.301283 | + | 0.521838i | 0.0174529 | + | 0.0302293i | ||||
\(299\) | 8.06031 | + | 13.9609i | 0.466140 | + | 0.807378i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.159456 | + | 0.276185i | 0.00917564 | + | 0.0158927i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.55444 | −0.433277 | ||||||||
\(305\) | −3.61458 | − | 6.26064i | −0.206970 | − | 0.358483i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.2178 | −1.32511 | −0.662554 | − | 0.749014i | \(-0.730527\pi\) | ||||
−0.662554 | + | 0.749014i | \(0.730527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.22380 | −0.0695072 | ||||||||
\(311\) | −0.895467 | + | 1.55100i | −0.0507773 | + | 0.0879489i | −0.890297 | − | 0.455381i | \(-0.849503\pi\) |
0.839520 | + | 0.543329i | \(0.182837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.30458 | + | 3.99166i | 0.130263 | + | 0.225622i | 0.923778 | − | 0.382929i | \(-0.125085\pi\) |
−0.793515 | + | 0.608551i | \(0.791751\pi\) | |||||||
\(314\) | −0.278483 | −0.0157157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62331 | −0.0913183 | ||||||||
\(317\) | −12.9421 | − | 22.4163i | −0.726898 | − | 1.25902i | −0.958188 | − | 0.286140i | \(-0.907628\pi\) |
0.231290 | − | 0.972885i | \(-0.425705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.10843 | − | 8.84807i | 0.286017 | − | 0.495397i | ||||
\(320\) | 21.0120 | 1.17461 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4524 | 0.692869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50541 | + | 9.53566i | 0.305385 | + | 0.528943i | ||||
\(326\) | 0.828846 | 0.0459055 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00979 | − | 1.74901i | −0.0557563 | − | 0.0965728i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0806617 | − | 0.139710i | −0.00443357 | − | 0.00767917i | 0.863800 | − | 0.503835i | \(-0.168078\pi\) |
−0.868234 | + | 0.496156i | \(0.834745\pi\) | |||||||
\(332\) | 6.82086 | + | 11.8141i | 0.374343 | + | 0.648382i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.164064 | + | 0.284168i | −0.00897719 | + | 0.0155490i | ||||
\(335\) | −4.42899 | + | 7.67124i | −0.241982 | + | 0.419125i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.52675 | + | 7.84057i | 0.246588 | + | 0.427103i | 0.962577 | − | 0.271009i | \(-0.0873572\pi\) |
−0.715989 | + | 0.698112i | \(0.754024\pi\) | |||||||
\(338\) | −0.998425 | −0.0543072 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.7993 | −1.88725 | ||||||||
\(341\) | 5.37245 | − | 9.30535i | 0.290934 | − | 0.503913i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.53846 | − | 2.66470i | 0.0829484 | − | 0.143671i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.172019 | − | 0.297945i | 0.00924779 | − | 0.0160176i | ||||
\(347\) | −2.90984 | + | 5.03999i | −0.156208 | + | 0.270561i | −0.933498 | − | 0.358582i | \(-0.883260\pi\) |
0.777290 | + | 0.629142i | \(0.216594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6310 | − | 23.6095i | 0.729648 | − | 1.26379i | −0.227384 | − | 0.973805i | \(-0.573017\pi\) |
0.957032 | − | 0.289983i | \(-0.0936496\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.653988 | − | 1.13274i | 0.0348577 | − | 0.0603753i | ||||
\(353\) | −24.1896 | −1.28748 | −0.643741 | − | 0.765244i | \(-0.722618\pi\) | ||||
−0.643741 | + | 0.765244i | \(0.722618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.0018 | −1.75155 | ||||||||
\(356\) | 0.469472 | + | 0.813149i | 0.0248820 | + | 0.0430968i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.560595 | − | 0.970979i | 0.0296284 | − | 0.0513179i | ||||
\(359\) | −10.5188 | + | 18.2191i | −0.555161 | + | 0.961567i | 0.442730 | + | 0.896655i | \(0.354010\pi\) |
−0.997891 | + | 0.0649124i | \(0.979323\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.69132 | + | 13.3218i | 0.404806 | + | 0.701145i | ||||
\(362\) | 0.493472 | + | 0.854719i | 0.0259363 | + | 0.0449230i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.92835 | − | 5.07205i | −0.153277 | − | 0.265483i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.0380 | −1.82897 | −0.914485 | − | 0.404620i | \(-0.867404\pi\) | ||||
−0.914485 | + | 0.404620i | \(0.867404\pi\) | |||||||
\(368\) | −6.09375 | − | 10.5547i | −0.317659 | − | 0.550201i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.770345 | 0.0400483 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.12862 | 0.0584377 | 0.0292189 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292189 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(374\) | −0.357931 | + | 0.619955i | −0.0185082 | + | 0.0320571i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.518922 | − | 0.898800i | −0.0267614 | − | 0.0463521i | ||||
\(377\) | 33.5667 | 1.72877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9619 | −1.12811 | −0.564054 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564054 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(380\) | 5.05452 | + | 8.75468i | 0.259291 | + | 0.449106i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0971359 | + | 0.168244i | −0.00496991 | + | 0.00860813i | ||||
\(383\) | −23.0401 | −1.17729 | −0.588647 | − | 0.808390i | \(-0.700339\pi\) | ||||
−0.588647 | + | 0.808390i | \(0.700339\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.603664 | −0.0307257 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.14042 | + | 8.90346i | 0.260965 | + | 0.452005i | ||||
\(389\) | −15.7751 | −0.799828 | −0.399914 | − | 0.916553i | \(-0.630960\pi\) | ||||
−0.399914 | + | 0.916553i | \(0.630960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0446 | + | 17.3978i | 0.507979 | + | 0.879846i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.195671 | − | 0.338912i | −0.00985774 | − | 0.0170741i | ||||
\(395\) | 1.08357 | + | 1.87680i | 0.0545204 | + | 0.0944321i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.25277 | − | 14.2942i | 0.414195 | − | 0.717406i | −0.581149 | − | 0.813797i | \(-0.697397\pi\) |
0.995344 | + | 0.0963911i | \(0.0307300\pi\) | |||||||
\(398\) | 0.390246 | − | 0.675926i | 0.0195613 | − | 0.0338811i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.16220 | − | 7.20914i | −0.208110 | − | 0.360457i | ||||
\(401\) | −21.6600 | −1.08165 | −0.540823 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540823 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.3015 | 1.75849 | ||||||||
\(404\) | −1.84057 | + | 3.18796i | −0.0915716 | + | 0.158607i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.38179 | + | 5.85743i | −0.167629 | + | 0.290342i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2860 | + | 26.4762i | −0.755846 | + | 1.30916i | 0.189107 | + | 0.981956i | \(0.439441\pi\) |
−0.944953 | + | 0.327207i | \(0.893893\pi\) | |||||||
\(410\) | −0.673255 | + | 1.16611i | −0.0332497 | + | 0.0575901i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.16592 | + | 8.94763i | −0.254507 | + | 0.440818i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.10596 | − | 15.7720i | 0.446994 | − | 0.774216i | ||||
\(416\) | 4.29725 | 0.210690 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.207955 | 0.0101714 | ||||||||
\(419\) | 10.8081 | + | 18.7202i | 0.528011 | + | 0.914542i | 0.999467 | + | 0.0326524i | \(0.0103954\pi\) |
−0.471456 | + | 0.881890i | \(0.656271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6217 | − | 23.5935i | 0.663881 | − | 1.14988i | −0.315706 | − | 0.948857i | \(-0.602241\pi\) |
0.979587 | − | 0.201019i | \(-0.0644252\pi\) | |||||||
\(422\) | −0.731046 | + | 1.26621i | −0.0355867 | + | 0.0616380i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.21545 | + | 2.10521i | 0.0590273 | + | 0.102238i | ||||
\(425\) | 6.86077 | + | 11.8832i | 0.332796 | + | 0.576420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.9093 | + | 29.2877i | 0.817341 | + | 1.41568i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.05147 | −0.0989307 | ||||||||
\(431\) | 4.09843 | + | 7.09869i | 0.197415 | + | 0.341932i | 0.947689 | − | 0.319194i | \(-0.103412\pi\) |
−0.750275 | + | 0.661126i | \(0.770079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.41468 | −0.164099 | −0.0820494 | − | 0.996628i | \(-0.526147\pi\) | ||||
−0.0820494 | + | 0.996628i | \(0.526147\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9601 | 0.812242 | ||||||||
\(437\) | 2.91793 | − | 5.05400i | 0.139583 | − | 0.241765i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.29416 | + | 5.70564i | 0.157221 | + | 0.272316i | 0.933866 | − | 0.357624i | \(-0.116413\pi\) |
−0.776644 | + | 0.629939i | \(0.783080\pi\) | |||||||
\(440\) | −1.16366 | −0.0554753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35191 | −0.111869 | ||||||||
\(443\) | 14.3456 | + | 24.8473i | 0.681581 | + | 1.18053i | 0.974498 | + | 0.224395i | \(0.0720407\pi\) |
−0.292917 | + | 0.956138i | \(0.594626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.626752 | − | 1.08557i | 0.0297109 | − | 0.0514608i | ||||
\(446\) | 0.490087 | 0.0232063 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.457724 | −0.0216013 | −0.0108007 | − | 0.999942i | \(-0.503438\pi\) | ||||
−0.0108007 | + | 0.999942i | \(0.503438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.91114 | − | 10.2384i | −0.278345 | − | 0.482107i | ||||
\(452\) | 7.78958 | 0.366391 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.471393 | − | 0.816477i | −0.0221236 | − | 0.0383192i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1105 | − | 17.5119i | −0.472950 | − | 0.819173i | 0.526571 | − | 0.850131i | \(-0.323477\pi\) |
−0.999521 | + | 0.0309581i | \(0.990144\pi\) | |||||||
\(458\) | 0.902342 | + | 1.56290i | 0.0421637 | + | 0.0730296i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.15440 | + | 14.1238i | −0.380201 | + | 0.658527i | ||||
\(461\) | −12.1036 | + | 20.9640i | −0.563719 | + | 0.976390i | 0.433449 | + | 0.901178i | \(0.357297\pi\) |
−0.997168 | + | 0.0752117i | \(0.976037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.40242 | + | 4.16111i | 0.111650 | + | 0.193383i | 0.916436 | − | 0.400182i | \(-0.131053\pi\) |
−0.804786 | + | 0.593565i | \(0.797720\pi\) | |||||||
\(464\) | −25.3770 | −1.17810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.864561 | −0.0400500 | ||||||||
\(467\) | 13.6228 | − | 23.5954i | 0.630389 | − | 1.09187i | −0.357083 | − | 0.934073i | \(-0.616229\pi\) |
0.987472 | − | 0.157793i | \(-0.0504379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.345979 | + | 0.599254i | −0.0159588 | + | 0.0276415i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.48783 | − | 2.57699i | 0.0684827 | − | 0.118616i | ||||
\(473\) | 9.00590 | − | 15.5987i | 0.414092 | − | 0.717228i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.99302 | − | 3.45202i | 0.0914462 | − | 0.158389i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.527601 | − | 0.913832i | 0.0241319 | − | 0.0417977i | ||||
\(479\) | 20.5255 | 0.937834 | 0.468917 | − | 0.883242i | \(-0.344644\pi\) | ||||
0.468917 | + | 0.883242i | \(0.344644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2212 | −1.01320 | ||||||||
\(482\) | −0.0403366 | − | 0.0698651i | −0.00183728 | − | 0.00318227i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.42306 | + | 14.5892i | −0.382866 | + | 0.663144i | ||||
\(485\) | 6.86254 | − | 11.8863i | 0.311612 | − | 0.539727i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9224 | − | 22.3823i | −0.585571 | − | 1.01424i | −0.994804 | − | 0.101809i | \(-0.967537\pi\) |
0.409233 | − | 0.912430i | \(-0.365796\pi\) | |||||||
\(488\) | 0.370682 | + | 0.642039i | 0.0167800 | + | 0.0290638i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.80775 | + | 13.5234i | 0.352359 | + | 0.610303i | 0.986662 | − | 0.162781i | \(-0.0520463\pi\) |
−0.634303 | + | 0.773084i | \(0.718713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.8303 | 1.88394 | ||||||||
\(494\) | 0.341610 | + | 0.591686i | 0.0153698 | + | 0.0266212i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.6886 | −1.19835 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2690 | 0.952133 | 0.476066 | − | 0.879409i | \(-0.342062\pi\) | ||||
0.476066 | + | 0.879409i | \(0.342062\pi\) | |||||||
\(500\) | 7.71814 | − | 13.3682i | 0.345166 | − | 0.597845i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.189728 | + | 0.328618i | 0.00846795 | + | 0.0146669i | ||||
\(503\) | −16.3298 | −0.728110 | −0.364055 | − | 0.931377i | \(-0.618608\pi\) | ||||
−0.364055 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.91437 | 0.218687 | ||||||||
\(506\) | 0.167746 | + | 0.290544i | 0.00745722 | + | 0.0129163i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.9277 | − | 18.9273i | 0.484837 | − | 0.839762i | ||||
\(509\) | −13.4618 | −0.596683 | −0.298342 | − | 0.954459i | \(-0.596433\pi\) | ||||
−0.298342 | + | 0.954459i | \(0.596433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.41890 | −0.239484 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.336084 | + | 0.582115i | 0.0148240 | + | 0.0256760i | ||||
\(515\) | 13.7932 | 0.607800 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.03768 | − | 5.26142i | −0.133597 | − | 0.231397i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.91155 | − | 3.31091i | −0.0838272 | − | 0.145193i | ||||
\(521\) | 0.713095 | + | 1.23512i | 0.0312413 | + | 0.0541115i | 0.881223 | − | 0.472700i | \(-0.156721\pi\) |
−0.849982 | + | 0.526812i | \(0.823387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.85530 | + | 6.67758i | −0.168581 | + | 0.291990i | −0.937921 | − | 0.346849i | \(-0.887252\pi\) |
0.769340 | + | 0.638839i | \(0.220585\pi\) | |||||||
\(524\) | −4.44301 | + | 7.69553i | −0.194094 | + | 0.336181i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.407928 | − | 0.706551i | −0.0177865 | − | 0.0308071i | ||||
\(527\) | 43.9922 | 1.91633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5851 | −0.590656 | ||||||||
\(530\) | 0.810371 | − | 1.40360i | 0.0352003 | − | 0.0609686i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4206 | − | 33.6374i | 0.841198 | − | 1.45700i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.5742 | − | 39.0996i | 0.975966 | − | 1.69042i | ||||
\(536\) | 0.454201 | − | 0.786699i | 0.0196185 | − | 0.0339802i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.02441 | − | 1.77432i | 0.0441653 | − | 0.0764966i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0228 | + | 24.2882i | −0.602886 | + | 1.04423i | 0.389495 | + | 0.921028i | \(0.372649\pi\) |
−0.992382 | + | 0.123201i | \(0.960684\pi\) | |||||||
\(542\) | −0.485216 | −0.0208418 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.35517 | 0.229601 | ||||||||
\(545\) | −11.3210 | − | 19.6086i | −0.484939 | − | 0.839939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7305 | − | 30.7101i | 0.758101 | − | 1.31307i | −0.185717 | − | 0.982603i | \(-0.559461\pi\) |
0.943818 | − | 0.330466i | \(-0.107206\pi\) | |||||||
\(548\) | 19.4903 | − | 33.7583i | 0.832586 | − | 1.44208i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.114575 | + | 0.198450i | 0.00488550 | + | 0.00846193i | ||||
\(551\) | −6.07577 | − | 10.5235i | −0.258836 | − | 0.448318i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.335836 | − | 0.581685i | −0.0142683 | − | 0.0247134i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.24928 | 0.222619 | ||||||||
\(557\) | 17.5209 | + | 30.3472i | 0.742386 | + | 1.28585i | 0.951406 | + | 0.307940i | \(0.0996395\pi\) |
−0.209019 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 59.1763 | 2.50289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.63262 | −0.0688677 | ||||||||
\(563\) | −8.01311 | + | 13.8791i | −0.337712 | + | 0.584935i | −0.984002 | − | 0.178157i | \(-0.942986\pi\) |
0.646290 | + | 0.763092i | \(0.276320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.19961 | − | 9.00599i | −0.218749 | − | 0.378885i | ||||
\(566\) | −0.206213 | −0.00866776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.38439 | 0.142006 | ||||||||
\(569\) | 0.185651 | + | 0.321557i | 0.00778290 | + | 0.0134804i | 0.869891 | − | 0.493245i | \(-0.164189\pi\) |
−0.862108 | + | 0.506725i | \(0.830856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6152 | + | 25.3142i | −0.611626 | + | 1.05937i | 0.379340 | + | 0.925257i | \(0.376151\pi\) |
−0.990966 | + | 0.134110i | \(0.957182\pi\) | |||||||
\(572\) | 16.7637 | 0.700926 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.43065 | 0.268177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.52852 | − | 13.0398i | −0.313417 | − | 0.542853i | 0.665683 | − | 0.746235i | \(-0.268140\pi\) |
−0.979100 | + | 0.203381i | \(0.934807\pi\) | |||||||
\(578\) | −1.76856 | −0.0735623 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.9793 | + | 29.4089i | 0.705025 | + | 1.22114i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.11501 | + | 12.3236i | 0.294674 | + | 0.510390i | ||||
\(584\) | 0.300307 | + | 0.520148i | 0.0124268 | + | 0.0215239i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.583171 | − | 1.01008i | 0.0240906 | − | 0.0417261i | ||||
\(587\) | −0.835901 | + | 1.44782i | −0.0345013 | + | 0.0597580i | −0.882760 | − | 0.469823i | \(-0.844318\pi\) |
0.848259 | + | 0.529581i | \(0.177651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.38977 | − | 11.0674i | −0.263286 | − | 0.456025i | ||||
\(590\) | −1.98395 | −0.0816778 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.7996 | 0.690461 | ||||||||
\(593\) | 5.40871 | − | 9.36816i | 0.222109 | − | 0.384704i | −0.733339 | − | 0.679863i | \(-0.762039\pi\) |
0.955448 | + | 0.295159i | \(0.0953726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.79221 | − | 15.2286i | 0.360143 | − | 0.623786i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.551116 | + | 0.954560i | −0.0225368 | + | 0.0390349i | ||||
\(599\) | 8.32007 | − | 14.4108i | 0.339949 | − | 0.588809i | −0.644474 | − | 0.764626i | \(-0.722924\pi\) |
0.984423 | + | 0.175817i | \(0.0562568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9011 | + | 22.3453i | −0.526246 | + | 0.911485i | 0.473286 | + | 0.880909i | \(0.343068\pi\) |
−0.999532 | + | 0.0305765i | \(0.990266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.65332 | − | 8.05978i | 0.189341 | − | 0.327948i | ||||
\(605\) | 22.4898 | 0.914342 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.8049 | 1.53445 | 0.767227 | − | 0.641376i | \(-0.221636\pi\) | ||||
0.767227 | + | 0.641376i | \(0.221636\pi\) | |||||||
\(608\) | −0.777828 | − | 1.34724i | −0.0315451 | − | 0.0546377i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.247143 | − | 0.428065i | 0.0100065 | − | 0.0173318i | ||||
\(611\) | 9.98005 | − | 17.2860i | 0.403750 | − | 0.699315i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.47719 | + | 11.2188i | 0.261611 | + | 0.453124i | 0.966670 | − | 0.256025i | \(-0.0824129\pi\) |
−0.705059 | + | 0.709149i | \(0.749080\pi\) | |||||||
\(614\) | −0.793745 | − | 1.37481i | −0.0320330 | − | 0.0554827i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2202 | − | 28.0941i | −0.652999 | − | 1.13103i | −0.982391 | − | 0.186834i | \(-0.940177\pi\) |
0.329393 | − | 0.944193i | \(-0.393156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1974 | 1.33431 | 0.667157 | − | 0.744917i | \(-0.267511\pi\) | ||||
0.667157 | + | 0.744917i | \(0.267511\pi\) | |||||||
\(620\) | 17.8568 | + | 30.9289i | 0.717146 | + | 1.24213i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.122453 | −0.00490993 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0866 | −1.24346 | ||||||||
\(626\) | −0.157574 | + | 0.272925i | −0.00629791 | + | 0.0109083i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.06342 | + | 7.03804i | 0.162148 | + | 0.280848i | ||||
\(629\) | −27.6917 | −1.10414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2773 | 1.28494 | 0.642470 | − | 0.766311i | \(-0.277910\pi\) | ||||
0.642470 | + | 0.766311i | \(0.277910\pi\) | |||||||
\(632\) | −0.111122 | − | 0.192469i | −0.00442020 | − | 0.00765601i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.884900 | − | 1.53269i | 0.0351439 | − | 0.0608709i | ||||
\(635\) | −29.1772 | −1.15786 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.698568 | 0.0276566 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.89714 | + | 5.01799i | 0.114519 | + | 0.198353i | ||||
\(641\) | −43.0814 | −1.70161 | −0.850806 | − | 0.525480i | \(-0.823886\pi\) | ||||
−0.850806 | + | 0.525480i | \(0.823886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.20088 | − | 5.54409i | −0.126230 | − | 0.218638i | 0.795983 | − | 0.605319i | \(-0.206955\pi\) |
−0.922213 | + | 0.386682i | \(0.873621\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.425709 | + | 0.737350i | 0.0167493 | + | 0.0290107i | ||||
\(647\) | 1.94403 | + | 3.36716i | 0.0764278 | + | 0.132377i | 0.901706 | − | 0.432349i | \(-0.142315\pi\) |
−0.825278 | + | 0.564726i | \(0.808982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.70947 | − | 15.0852i | 0.341877 | − | 0.592148i | ||||
\(650\) | −0.376427 | + | 0.651991i | −0.0147647 | + | 0.0255732i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0939 | − | 20.9473i | −0.473634 | − | 0.820358i | ||||
\(653\) | −15.1035 | −0.591044 | −0.295522 | − | 0.955336i | \(-0.595494\pi\) | ||||
−0.295522 | + | 0.955336i | \(0.595494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8630 | 0.463525 | ||||||||
\(656\) | −14.6823 | + | 25.4305i | −0.573248 | + | 0.992895i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.13002 | − | 12.3496i | 0.277746 | − | 0.481070i | −0.693078 | − | 0.720862i | \(-0.743746\pi\) |
0.970824 | + | 0.239792i | \(0.0770793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.70965 | − | 16.8176i | 0.377662 | − | 0.654129i | −0.613060 | − | 0.790036i | \(-0.710062\pi\) |
0.990722 | + | 0.135907i | \(0.0433949\pi\) | |||||||
\(662\) | 0.00551516 | − | 0.00955254i | 0.000214353 | − | 0.000371270i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.933832 | + | 1.61744i | −0.0362397 | + | 0.0627690i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.80197 | − | 16.9775i | 0.379534 | − | 0.657372i | ||||
\(668\) | 9.57561 | 0.370492 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.605656 | −0.0233985 | ||||||||
\(671\) | 2.16991 | + | 3.75839i | 0.0837683 | + | 0.145091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.96563 | + | 5.13663i | −0.114317 | + | 0.198002i | −0.917506 | − | 0.397721i | \(-0.869801\pi\) |
0.803190 | + | 0.595723i | \(0.203135\pi\) | |||||||
\(674\) | −0.309512 | + | 0.536091i | −0.0119220 | + | 0.0206494i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.5683 | + | 25.2330i | 0.560318 | + | 0.970500i | ||||
\(677\) | 18.4913 | + | 32.0278i | 0.710678 | + | 1.23093i | 0.964603 | + | 0.263706i | \(0.0849449\pi\) |
−0.253925 | + | 0.967224i | \(0.581722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.38215 | − | 4.12601i | −0.0913513 | − | 0.158225i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.734671 | 0.0281320 | ||||||||
\(683\) | 6.56800 | + | 11.3761i | 0.251317 | + | 0.435294i | 0.963889 | − | 0.266305i | \(-0.0858029\pi\) |
−0.712571 | + | 0.701600i | \(0.752470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −52.0398 | −1.98834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.7384 | −1.70564 | ||||||||
\(689\) | −23.3758 | + | 40.4881i | −0.890547 | + | 1.54247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.38292 | − | 12.7876i | −0.280860 | − | 0.486463i | 0.690737 | − | 0.723106i | \(-0.257286\pi\) |
−0.971597 | + | 0.236643i | \(0.923953\pi\) | |||||||
\(692\) | −10.0399 | −0.381659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.397915 | −0.0151046 | ||||||||
\(695\) | −3.50394 | − | 6.06900i | −0.132912 | − | 0.230210i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.2016 | − | 41.9184i | 0.916702 | − | 1.58777i | ||||
\(698\) | 1.86401 | 0.0705536 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4627 | 1.15056 | 0.575281 | − | 0.817956i | \(-0.304893\pi\) | ||||
0.575281 | + | 0.817956i | \(0.304893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.02217 | + | 6.96660i | 0.151699 | + | 0.262750i | ||||
\(704\) | −12.6139 | −0.475406 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.826969 | − | 1.43235i | −0.0311234 | − | 0.0539073i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.05152 | − | 12.2136i | −0.264825 | − | 0.458691i | 0.702693 | − | 0.711494i | \(-0.251981\pi\) |
−0.967518 | + | 0.252803i | \(0.918648\pi\) | |||||||
\(710\) | −1.12823 | − | 1.95415i | −0.0423418 | − | 0.0733381i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.0642745 | + | 0.111327i | −0.00240879 | + | 0.00417215i | ||||
\(713\) | 10.3086 | − | 17.8549i | 0.386058 | − | 0.668673i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1899 | − | 19.3815i | −0.418479 | − | 0.724827i | ||||
\(716\) | −32.7192 | −1.22277 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.43842 | −0.0536815 | ||||||||
\(719\) | 7.49790 | − | 12.9867i | 0.279624 | − | 0.484324i | −0.691667 | − | 0.722217i | \(-0.743123\pi\) |
0.971291 | + | 0.237893i | \(0.0764567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.525886 | + | 0.910861i | −0.0195715 | + | 0.0338987i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.4008 | − | 24.9429i | 0.535200 | − | 0.926994i | ||||
\(725\) | 6.69501 | − | 11.5961i | 0.248646 | − | 0.430668i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.0527 | + | 22.6080i | −0.484099 | + | 0.838485i | −0.999833 | − | 0.0182642i | \(-0.994186\pi\) |
0.515734 | + | 0.856749i | \(0.327519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.200223 | − | 0.346796i | 0.00741059 | − | 0.0128355i | ||||
\(731\) | 73.7447 | 2.72754 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.3821 | 1.04832 | 0.524159 | − | 0.851621i | \(-0.324380\pi\) | ||||
0.524159 | + | 0.851621i | \(0.324380\pi\) | |||||||
\(734\) | −1.19784 | − | 2.07473i | −0.0442132 | − | 0.0765796i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25486 | − | 2.17348i | 0.0462548 | − | 0.0801156i | ||||
\(737\) | 2.65881 | − | 4.60520i | 0.0979386 | − | 0.169635i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2933 | − | 40.3451i | −0.856857 | − | 1.48412i | −0.874912 | − | 0.484282i | \(-0.839081\pi\) |
0.0180552 | − | 0.999837i | \(-0.494253\pi\) | |||||||
\(740\) | −11.2403 | − | 19.4688i | −0.413202 | − | 0.715686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.169513 | + | 0.293606i | 0.00621884 | + | 0.0107713i | 0.869118 | − | 0.494605i | \(-0.164687\pi\) |
−0.862899 | + | 0.505376i | \(0.831354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.4755 | −0.860075 | ||||||||
\(746\) | 0.0385841 | + | 0.0668297i | 0.00141267 | + | 0.00244681i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.8907 | 0.763839 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.3662 | −1.32702 | −0.663510 | − | 0.748168i | \(-0.730934\pi\) | ||||
−0.663510 | + | 0.748168i | \(0.730934\pi\) | |||||||
\(752\) | −7.54511 | + | 13.0685i | −0.275142 | + | 0.476560i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.14754 | + | 1.98760i | 0.0417911 | + | 0.0723843i | ||||
\(755\) | −12.4245 | −0.452174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4703 | −0.998424 | −0.499212 | − | 0.866480i | \(-0.666377\pi\) | ||||
−0.499212 | + | 0.866480i | \(0.666377\pi\) | |||||||
\(758\) | −0.750812 | − | 1.30044i | −0.0272707 | − | 0.0472343i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.692005 | + | 1.19859i | −0.0251017 | + | 0.0434773i | ||||
\(761\) | −33.0357 | −1.19754 | −0.598771 | − | 0.800920i | \(-0.704344\pi\) | ||||
−0.598771 | + | 0.800920i | \(0.704344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.66934 | 0.205110 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.787671 | − | 1.36429i | −0.0284597 | − | 0.0492937i | ||||
\(767\) | 57.2285 | 2.06640 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.28876 | − | 2.23219i | −0.0464738 | − | 0.0804949i | 0.841853 | − | 0.539707i | \(-0.181465\pi\) |
−0.888327 | + | 0.459212i | \(0.848132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.80822 | + | 15.2563i | 0.317015 | + | 0.549086i | ||||
\(773\) | 3.36486 | + | 5.82811i | 0.121026 | + | 0.209623i | 0.920172 | − | 0.391513i | \(-0.128048\pi\) |
−0.799147 | + | 0.601136i | \(0.794715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.04102 | − | 12.1954i | 0.252921 | − | 0.438072i | ||||
\(776\) | −0.703765 | + | 1.21896i | −0.0252637 | + | 0.0437580i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.539302 | − | 0.934099i | −0.0193349 | − | 0.0334891i | ||||
\(779\) | −14.0609 | −0.503785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.8116 | 0.708916 | ||||||||
\(782\) | −0.686792 | + | 1.18956i | −0.0245596 | + | 0.0425385i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.42473 | − | 9.39590i | 0.193617 | − | 0.335354i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3341 | + | 24.8274i | −0.510956 | + | 0.885003i | 0.488963 | + | 0.872305i | \(0.337375\pi\) |
−0.999919 | + | 0.0126980i | \(0.995958\pi\) | |||||||
\(788\) | −5.71016 | + | 9.89029i | −0.203416 | + | 0.352327i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0740881 | + | 0.128324i | −0.00263594 | + | 0.00456558i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.12905 | + | 12.3479i | −0.253160 | + | 0.438486i | ||||
\(794\) | 1.12855 | 0.0400507 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.7767 | −0.807300 | ||||||||
\(797\) | −11.4913 | − | 19.9035i | −0.407042 | − | 0.705017i | 0.587515 | − | 0.809213i | \(-0.300106\pi\) |
−0.994557 | + | 0.104196i | \(0.966773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4370 | − | 21.5415i | 0.439989 | − | 0.762084i | ||||
\(800\) | 0.857104 | − | 1.48455i | 0.0303032 | − | 0.0524867i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.740489 | − | 1.28256i | −0.0261476 | − | 0.0452889i | ||||
\(803\) | 1.75795 | + | 3.04485i | 0.0620366 | + | 0.107451i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.20685 | + | 2.09033i | 0.0425095 | + | 0.0736287i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.503977 | −0.0177299 | ||||||||
\(809\) | −8.23894 | − | 14.2703i | −0.289666 | − | 0.501716i | 0.684064 | − | 0.729422i | \(-0.260211\pi\) |
−0.973730 | + | 0.227706i | \(0.926878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.4318 | 1.41975 | 0.709876 | − | 0.704326i | \(-0.248751\pi\) | ||||
0.709876 | + | 0.704326i | \(0.248751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.462453 | −0.0162090 | ||||||||
\(815\) | −16.1456 | + | 27.9649i | −0.565554 | + | 0.979569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7113 | − | 18.5524i | −0.374739 | − | 0.649068i | ||||
\(818\) | −2.09033 | −0.0730868 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.2945 | 1.37222 | ||||||||
\(821\) | −14.0543 | − | 24.3428i | −0.490499 | − | 0.849569i | 0.509441 | − | 0.860506i | \(-0.329852\pi\) |
−0.999940 | + | 0.0109361i | \(0.996519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9529 | + | 22.4351i | −0.451510 | + | 0.782038i | −0.998480 | − | 0.0551142i | \(-0.982448\pi\) |
0.546970 | + | 0.837152i | \(0.315781\pi\) | |||||||
\(824\) | −1.41451 | −0.0492769 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.7998 | 0.618961 | 0.309480 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309480 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.85344 | + | 13.6026i | 0.272761 | + | 0.472436i | 0.969568 | − | 0.244823i | \(-0.0787297\pi\) |
−0.696807 | + | 0.717259i | \(0.745396\pi\) | |||||||
\(830\) | 1.24522 | 0.0432223 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.7210 | − | 35.8899i | −0.718373 | − | 1.24426i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.39180 | − | 11.0709i | −0.221197 | − | 0.383125i | ||||
\(836\) | −3.03433 | − | 5.25561i | −0.104944 | − | 0.181769i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.738994 | + | 1.27998i | −0.0255281 | + | 0.0442160i | ||||
\(839\) | 3.69822 | − | 6.40550i | 0.127677 | − | 0.221142i | −0.795099 | − | 0.606479i | \(-0.792581\pi\) |
0.922776 | + | 0.385337i | \(0.125915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.90986 | − | 10.2362i | −0.203788 | − | 0.352971i | ||||
\(842\) | 1.86274 | 0.0641942 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42.6675 | 1.46868 | ||||||||
\(845\) | 19.4489 | − | 33.6865i | 0.669062 | − | 1.15885i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.6725 | − | 30.6097i | 0.606878 | − | 1.05114i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.469098 | + | 0.812501i | −0.0160899 | + | 0.0278686i | ||||
\(851\) | −6.48892 | + | 11.2391i | −0.222437 | + | 0.385273i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5631 | + | 46.0086i | −0.909503 | + | 1.57530i | −0.0947464 | + | 0.995501i | \(0.530204\pi\) |
−0.814756 | + | 0.579804i | \(0.803129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.31502 | + | 4.00973i | −0.0791257 | + | 0.137050i | ||||
\(857\) | −3.81530 | −0.130328 | −0.0651640 | − | 0.997875i | \(-0.520757\pi\) | ||||
−0.0651640 | + | 0.997875i | \(0.520757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9768 | −1.32987 | −0.664936 | − | 0.746901i | \(-0.731541\pi\) | ||||
−0.664936 | + | 0.746901i | \(0.731541\pi\) | |||||||
\(860\) | 29.9336 | + | 51.8464i | 1.02073 | + | 1.76795i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.280226 | + | 0.485366i | −0.00954454 | + | 0.0165316i | ||||
\(863\) | 13.3368 | − | 23.1000i | 0.453989 | − | 0.786332i | −0.544640 | − | 0.838670i | \(-0.683334\pi\) |
0.998629 | + | 0.0523375i | \(0.0166672\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.70171 | + | 11.6077i | 0.227865 | + | 0.394674i | ||||
\(866\) | −0.116737 | − | 0.202195i | −0.00396690 | − | 0.00687087i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.650490 | − | 1.12668i | −0.0220664 | − | 0.0382200i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.4706 | 0.591970 | ||||||||
\(872\) | 1.16099 | + | 2.01089i | 0.0393160 | + | 0.0680974i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.399020 | 0.0134971 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0135 | 0.810879 | 0.405440 | − | 0.914122i | \(-0.367118\pi\) | ||||
0.405440 | + | 0.914122i | \(0.367118\pi\) | |||||||
\(878\) | −0.225235 | + | 0.390118i | −0.00760130 | + | 0.0131658i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.45978 | + | 14.6528i | 0.285179 | + | 0.493945i | ||||
\(881\) | −4.67326 | −0.157446 | −0.0787231 | − | 0.996897i | \(-0.525084\pi\) | ||||
−0.0787231 | + | 0.996897i | \(0.525084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6948 | −1.20122 | −0.600612 | − | 0.799541i | \(-0.705076\pi\) | ||||
−0.600612 | + | 0.799541i | \(0.705076\pi\) | |||||||
\(884\) | 34.3173 | + | 59.4393i | 1.15422 | + | 1.99916i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.980867 | + | 1.69891i | −0.0329529 | + | 0.0570761i | ||||
\(887\) | 29.1032 | 0.977191 | 0.488596 | − | 0.872510i | \(-0.337509\pi\) | ||||
0.488596 | + | 0.872510i | \(0.337509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.0857071 | 0.00287291 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.15098 | − | 12.3859i | −0.239433 | − | 0.414710i | ||||
\(893\) | −7.22579 | −0.241802 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.8403 | + | 37.8285i | 0.730041 | + | 1.26447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0156482 | − | 0.0271035i | −0.000522187 | − | 0.000904455i | ||||
\(899\) | −21.4647 | − | 37.1779i | −0.715887 | − | 1.23995i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.1306 | + | 50.4556i | −0.970480 | + | 1.68092i | ||||
\(902\) | 0.404168 | − | 0.700040i | 0.0134573 | − | 0.0233088i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.533229 | + | 0.923579i | 0.0177349 | + | 0.0307178i | ||||
\(905\) | −38.4505 | −1.27814 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.2142 | −1.36849 | −0.684247 | − | 0.729250i | \(-0.739869\pi\) | ||||
−0.684247 | + | 0.729250i | \(0.739869\pi\) | |||||||
\(908\) | −13.7564 | + | 23.8269i | −0.456524 | + | 0.790722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8619 | + | 49.9903i | −0.956239 | + | 1.65625i | −0.224731 | + | 0.974421i | \(0.572150\pi\) |
−0.731508 | + | 0.681833i | \(0.761183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.46649 | + | 9.46824i | −0.180914 | + | 0.313353i | ||||
\(914\) | 0.691296 | − | 1.19736i | 0.0228660 | − | 0.0396051i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.3326 | − | 45.6094i | 0.870054 | − | 1.50698i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.7799 | − | 44.6521i | 0.850400 | − | 1.47294i | −0.0304476 | − | 0.999536i | \(-0.509693\pi\) |
0.880848 | − | 0.473400i | \(-0.156973\pi\) | |||||||
\(920\) | −2.23281 | −0.0736135 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.65514 | −0.0545090 | ||||||||
\(923\) | 32.5447 | + | 56.3691i | 1.07122 | + | 1.85541i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.43211 | + | 7.67664i | −0.145727 | + | 0.252406i | ||||
\(926\) | −0.164263 | + | 0.284511i | −0.00539801 | + | 0.00934962i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.61290 | − | 4.52567i | −0.0857725 | − | 0.148562i | ||||
\(929\) | 25.1412 | + | 43.5458i | 0.824856 | + | 1.42869i | 0.902029 | + | 0.431675i | \(0.142077\pi\) |
−0.0771732 | + | 0.997018i | \(0.524589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.6150 | + | 21.8499i | 0.413219 | + | 0.715717i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.86289 | 0.0609557 | ||||||||
\(935\) | −13.9447 | − | 24.1529i | −0.456040 | − | 0.789885i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.1400 | −0.592607 | −0.296303 | − | 0.955094i | \(-0.595754\pi\) | ||||
−0.296303 | + | 0.955094i | \(0.595754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.1931 | 0.658627 | ||||||||
\(941\) | 8.51660 | − | 14.7512i | 0.277633 | − | 0.480875i | −0.693163 | − | 0.720781i | \(-0.743783\pi\) |
0.970796 | + | 0.239906i | \(0.0771166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3422 | − | 19.6452i | −0.369352 | − | 0.639737i | ||||
\(944\) | −43.2658 | −1.40818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.23154 | 0.0400408 | ||||||||
\(947\) | 15.7530 | + | 27.2849i | 0.511903 | + | 0.886641i | 0.999905 | + | 0.0137988i | \(0.00439243\pi\) |
−0.488002 | + | 0.872842i | \(0.662274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.77559 | + | 10.0036i | −0.187484 | + | 0.324731i | ||||
\(950\) | 0.272542 | 0.00884243 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0677 | −0.520485 | −0.260242 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260242 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.78433 | − | 6.55465i | −0.122458 | − | 0.212104i | ||||
\(956\) | −30.7935 | −0.995932 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.701705 | + | 1.21539i | 0.0226711 | + | 0.0392674i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.07402 | − | 12.2526i | −0.228194 | − | 0.395244i | ||||
\(962\) | −0.759676 | − | 1.31580i | −0.0244929 | − | 0.0424230i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.17713 | + | 2.03884i | −0.0379126 | + | 0.0656666i | ||||
\(965\) | 11.7591 | − | 20.3674i | 0.378539 | − | 0.655649i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3049 | + | 23.0448i | 0.427857 | + | 0.741069i | 0.996682 | − | 0.0813886i | \(-0.0259355\pi\) |
−0.568826 | + | 0.822458i | \(0.692602\pi\) | |||||||
\(968\) | −2.30637 | −0.0741296 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.938438 | 0.0301314 | ||||||||
\(971\) | 28.2839 | − | 48.9892i | 0.907674 | − | 1.57214i | 0.0903867 | − | 0.995907i | \(-0.471190\pi\) |
0.817287 | − | 0.576231i | \(-0.195477\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.883558 | − | 1.53037i | 0.0283110 | − | 0.0490361i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.38969 | − | 9.33522i | 0.172520 | − | 0.298813i | ||||
\(977\) | 26.8780 | − | 46.5541i | 0.859904 | − | 1.48940i | −0.0121160 | − | 0.999927i | \(-0.503857\pi\) |
0.872020 | − | 0.489471i | \(-0.162810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.376252 | + | 0.651687i | −0.0120251 | + | 0.0208280i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.533847 | + | 0.924650i | −0.0170357 | + | 0.0295068i | ||||
\(983\) | 27.4102 | 0.874249 | 0.437125 | − | 0.899401i | \(-0.355997\pi\) | ||||
0.437125 | + | 0.899401i | \(0.355997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2463 | 0.485788 | ||||||||
\(986\) | 1.43005 | + | 2.47692i | 0.0455421 | + | 0.0788813i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.96904 | − | 17.2669i | 0.317157 | − | 0.549333i | ||||
\(989\) | 17.2804 | − | 29.9305i | 0.549483 | − | 0.951733i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.66869 | + | 15.0146i | 0.275370 | + | 0.476955i | 0.970228 | − | 0.242192i | \(-0.0778663\pi\) |
−0.694858 | + | 0.719147i | \(0.744533\pi\) | |||||||
\(992\) | −2.74794 | − | 4.75957i | −0.0872471 | − | 0.151116i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2037 | + | 26.3335i | 0.481988 | + | 0.834828i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6638 | 1.12948 | 0.564742 | − | 0.825268i | \(-0.308976\pi\) | ||||
0.564742 | + | 0.825268i | \(0.308976\pi\) | |||||||
\(998\) | 0.727124 | + | 1.25942i | 0.0230167 | + | 0.0398661i | ||||
\(999\) | 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.g.h.667.7 | 24 | ||
3.2 | odd | 2 | 441.2.g.h.79.6 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.883.8 | 24 | |||
7.3 | odd | 6 | 1323.2.h.h.802.6 | 24 | |||
7.4 | even | 3 | 1323.2.h.h.802.5 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.883.7 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.g.h.667.8 | 24 | ||
9.4 | even | 3 | 1323.2.h.h.226.5 | 24 | |||
9.5 | odd | 6 | 441.2.h.h.373.8 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.295.5 | yes | 24 | ||
21.5 | even | 6 | 441.2.f.h.295.6 | yes | 24 | ||
21.11 | odd | 6 | 441.2.h.h.214.8 | 24 | |||
21.17 | even | 6 | 441.2.h.h.214.7 | 24 | |||
21.20 | even | 2 | 441.2.g.h.79.5 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bh.1.8 | 12 | |||
63.4 | even | 3 | inner | 1323.2.g.h.361.7 | 24 | ||
63.5 | even | 6 | 441.2.f.h.148.6 | yes | 24 | ||
63.13 | odd | 6 | 1323.2.h.h.226.6 | 24 | |||
63.16 | even | 3 | 3969.2.a.bi.1.5 | 12 | |||
63.23 | odd | 6 | 441.2.f.h.148.5 | ✓ | 24 | ||
63.31 | odd | 6 | inner | 1323.2.g.h.361.8 | 24 | ||
63.32 | odd | 6 | 441.2.g.h.67.6 | 24 | |||
63.40 | odd | 6 | 1323.2.f.h.442.7 | 24 | |||
63.41 | even | 6 | 441.2.h.h.373.7 | 24 | |||
63.47 | even | 6 | 3969.2.a.bh.1.7 | 12 | |||
63.58 | even | 3 | 1323.2.f.h.442.8 | 24 | |||
63.59 | even | 6 | 441.2.g.h.67.5 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bi.1.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.5 | ✓ | 24 | 63.23 | odd | 6 | ||
441.2.f.h.148.6 | yes | 24 | 63.5 | even | 6 | ||
441.2.f.h.295.5 | yes | 24 | 21.2 | odd | 6 | ||
441.2.f.h.295.6 | yes | 24 | 21.5 | even | 6 | ||
441.2.g.h.67.5 | 24 | 63.59 | even | 6 | |||
441.2.g.h.67.6 | 24 | 63.32 | odd | 6 | |||
441.2.g.h.79.5 | 24 | 21.20 | even | 2 | |||
441.2.g.h.79.6 | 24 | 3.2 | odd | 2 | |||
441.2.h.h.214.7 | 24 | 21.17 | even | 6 | |||
441.2.h.h.214.8 | 24 | 21.11 | odd | 6 | |||
441.2.h.h.373.7 | 24 | 63.41 | even | 6 | |||
441.2.h.h.373.8 | 24 | 9.5 | odd | 6 | |||
1323.2.f.h.442.7 | 24 | 63.40 | odd | 6 | |||
1323.2.f.h.442.8 | 24 | 63.58 | even | 3 | |||
1323.2.f.h.883.7 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.883.8 | 24 | 7.2 | even | 3 | |||
1323.2.g.h.361.7 | 24 | 63.4 | even | 3 | inner | ||
1323.2.g.h.361.8 | 24 | 63.31 | odd | 6 | inner | ||
1323.2.g.h.667.7 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.g.h.667.8 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.226.5 | 24 | 9.4 | even | 3 | |||
1323.2.h.h.226.6 | 24 | 63.13 | odd | 6 | |||
1323.2.h.h.802.5 | 24 | 7.4 | even | 3 | |||
1323.2.h.h.802.6 | 24 | 7.3 | odd | 6 | |||
3969.2.a.bh.1.7 | 12 | 63.47 | even | 6 | |||
3969.2.a.bh.1.8 | 12 | 63.2 | odd | 6 | |||
3969.2.a.bi.1.5 | 12 | 63.16 | even | 3 | |||
3969.2.a.bi.1.6 | 12 | 63.61 | odd | 6 |