Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.6 | ||
Character | \(\chi\) | \(=\) | 1008.529 |
Dual form | 1008.2.q.l.625.6 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.633073 | − | 1.61221i | 0.365505 | − | 0.930809i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.70368 | + | 2.95086i | −0.761909 | + | 1.31967i | 0.179956 | + | 0.983675i | \(0.442404\pi\) |
−0.941865 | + | 0.335991i | \(0.890929\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.410295 | − | 2.61374i | 0.155077 | − | 0.987902i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.19844 | − | 2.04129i | −0.732812 | − | 0.680431i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.69819 | + | 4.67340i | 0.813535 | + | 1.40908i | 0.910375 | + | 0.413784i | \(0.135793\pi\) |
−0.0968406 | + | 0.995300i | \(0.530874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.89598 | + | 3.28393i | 0.525850 | + | 0.910800i | 0.999547 | + | 0.0301113i | \(0.00958618\pi\) |
−0.473696 | + | 0.880688i | \(0.657080\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.67885 | + | 4.61480i | 0.949875 | + | 1.19154i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.411976 | − | 0.713564i | 0.0999190 | − | 0.173065i | −0.811732 | − | 0.584030i | \(-0.801475\pi\) |
0.911651 | + | 0.410965i | \(0.134808\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.233611 | − | 0.404626i | −0.0535940 | − | 0.0928275i | 0.837984 | − | 0.545695i | \(-0.183734\pi\) |
−0.891578 | + | 0.452868i | \(0.850401\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.95416 | − | 2.31617i | −0.862867 | − | 0.505430i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.74950 | + | 4.76227i | −0.573309 | + | 0.993001i | 0.422914 | + | 0.906170i | \(0.361007\pi\) |
−0.996223 | + | 0.0868310i | \(0.972326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30506 | − | 5.72452i | −0.661011 | − | 1.14490i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.68276 | + | 2.25205i | −0.901198 | + | 0.433407i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.400332 | − | 0.693396i | 0.0743399 | − | 0.128760i | −0.826459 | − | 0.562997i | \(-0.809648\pi\) |
0.900799 | + | 0.434236i | \(0.142982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.90732 | 1.77941 | 0.889703 | − | 0.456539i | \(-0.150911\pi\) | ||||
0.889703 | + | 0.456539i | \(0.150911\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.24265 | − | 1.39144i | 1.60894 | − | 0.242219i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.01378 | + | 5.66371i | 1.18555 | + | 0.957342i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.34210 | + | 7.52074i | 0.713837 | + | 1.23640i | 0.963406 | + | 0.268045i | \(0.0863777\pi\) |
−0.249569 | + | 0.968357i | \(0.580289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.49468 | − | 0.977746i | 1.03998 | − | 0.156565i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.84467 | + | 3.19507i | 0.288090 | + | 0.498986i | 0.973354 | − | 0.229309i | \(-0.0736465\pi\) |
−0.685264 | + | 0.728295i | \(0.740313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.36356 | − | 7.55790i | 0.665436 | − | 1.15257i | −0.313731 | − | 0.949512i | \(-0.601579\pi\) |
0.979167 | − | 0.203057i | \(-0.0650878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.76901 | − | 3.00957i | 1.45628 | − | 0.448640i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4991 | 1.53146 | 0.765728 | − | 0.643164i | \(-0.222379\pi\) | ||||
0.765728 | + | 0.643164i | \(0.222379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66332 | − | 2.14481i | −0.951902 | − | 0.306402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.889603 | − | 1.11593i | −0.124569 | − | 0.156262i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.71820 | + | 8.17217i | −0.648095 | + | 1.12253i | 0.335483 | + | 0.942046i | \(0.391101\pi\) |
−0.983577 | + | 0.180487i | \(0.942233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.3874 | −2.47936 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.800234 | + | 0.120472i | −0.105994 | + | 0.0159569i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.66069 | 0.216203 | 0.108102 | − | 0.994140i | \(-0.465523\pi\) | ||||
0.108102 | + | 0.994140i | \(0.465523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.948811 | 0.121483 | 0.0607414 | − | 0.998154i | \(-0.480654\pi\) | ||||
0.0607414 | + | 0.998154i | \(0.480654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.23743 | + | 4.90862i | −0.785842 | + | 0.618428i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.9206 | −1.60260 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.539184 | −0.0658718 | −0.0329359 | − | 0.999457i | \(-0.510486\pi\) | ||||
−0.0329359 | + | 0.999457i | \(0.510486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.93714 | + | 7.44762i | 0.714747 | + | 0.896589i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.86901 | 0.459167 | 0.229583 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229583 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.58943 | − | 4.48502i | 0.303070 | − | 0.524932i | −0.673760 | − | 0.738950i | \(-0.735322\pi\) |
0.976830 | + | 0.214018i | \(0.0686551\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.3215 | + | 1.70440i | −1.30729 | + | 0.196807i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.3221 | − | 5.13490i | 1.51820 | − | 0.585176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.82899 | −0.880830 | −0.440415 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440415 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.666244 | + | 8.97531i | 0.0740272 | + | 0.997256i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.79623 | − | 6.57527i | 0.416691 | − | 0.721729i | −0.578914 | − | 0.815389i | \(-0.696523\pi\) |
0.995604 | + | 0.0936595i | \(0.0298565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40375 | + | 2.43137i | 0.152258 | + | 0.263719i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.864460 | − | 1.08439i | −0.0926798 | − | 0.116259i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.73498 | − | 6.46917i | −0.395907 | − | 0.685730i | 0.597310 | − | 0.802011i | \(-0.296236\pi\) |
−0.993216 | + | 0.116280i | \(0.962903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.36128 | − | 3.60823i | 0.981328 | − | 0.378245i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.27206 | − | 15.9727i | 0.650382 | − | 1.65629i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59199 | 0.163335 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22500 | + | 5.58587i | −0.327450 | + | 0.567159i | −0.982005 | − | 0.188855i | \(-0.939522\pi\) |
0.654555 | + | 0.756014i | \(0.272856\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.60798 | − | 15.7820i | 0.362616 | − | 1.58615i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.09973 | + | 14.0291i | 0.805953 | + | 1.39595i | 0.915646 | + | 0.401987i | \(0.131680\pi\) |
−0.109692 | + | 0.993966i | \(0.534986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.84930 | + | 13.5954i | −0.773414 | + | 1.33959i | 0.162267 | + | 0.986747i | \(0.448119\pi\) |
−0.935681 | + | 0.352846i | \(0.885214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.5713 | − | 7.72214i | 1.32443 | − | 0.753604i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.85024 | − | 4.93675i | −0.275543 | − | 0.477254i | 0.694729 | − | 0.719271i | \(-0.255524\pi\) |
−0.970272 | + | 0.242017i | \(0.922191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19196 | + | 3.79659i | −0.209952 | + | 0.363648i | −0.951699 | − | 0.307032i | \(-0.900664\pi\) |
0.741747 | + | 0.670680i | \(0.233997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8739 | − | 2.23920i | 1.41177 | − | 0.212535i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.96607 | − | 8.60149i | −0.467169 | − | 0.809160i | 0.532128 | − | 0.846664i | \(-0.321393\pi\) |
−0.999296 | + | 0.0375041i | \(0.988059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.36852 | − | 16.2268i | −0.873619 | − | 1.51315i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.53528 | − | 11.0898i | 0.234387 | − | 1.02525i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.69604 | − | 1.36957i | −0.155476 | − | 0.125549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.06045 | + | 15.6932i | −0.823677 | + | 1.42665i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.31894 | − | 0.951288i | 0.569759 | − | 0.0857747i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.48623 | 0.490703 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1122 | −1.42973 | −0.714864 | − | 0.699263i | \(-0.753512\pi\) | ||||
−0.714864 | + | 0.699263i | \(0.753512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.42247 | − | 11.8197i | −0.829602 | − | 1.04066i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.97039 | − | 12.0731i | 0.609006 | − | 1.05483i | −0.382399 | − | 0.923997i | \(-0.624902\pi\) |
0.991405 | − | 0.130832i | \(-0.0417648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15344 | + | 0.444583i | −0.100016 | + | 0.0385502i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.33244 | − | 17.6550i | 0.114678 | − | 1.51950i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.57598 | + | 9.65787i | 0.476388 | + | 0.825128i | 0.999634 | − | 0.0270537i | \(-0.00861250\pi\) |
−0.523246 | + | 0.852182i | \(0.675279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17737 | − | 5.50337i | −0.269501 | − | 0.466790i | 0.699232 | − | 0.714895i | \(-0.253526\pi\) |
−0.968733 | + | 0.248105i | \(0.920192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.64672 | − | 16.9268i | 0.559755 | − | 1.42549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2314 | + | 17.7214i | −0.855595 | + | 1.48193i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.36408 | + | 2.36265i | 0.113280 | + | 0.196207i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.67625 | + | 9.38483i | −0.633127 | + | 0.774048i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.76521 | − | 9.98564i | 0.472304 | − | 0.818055i | −0.527193 | − | 0.849745i | \(-0.676756\pi\) |
0.999498 | + | 0.0316900i | \(0.0100889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.347317 | − | 0.601571i | −0.0282643 | − | 0.0489551i | 0.851547 | − | 0.524278i | \(-0.175665\pi\) |
−0.879812 | + | 0.475323i | \(0.842331\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.36230 | + | 0.727761i | −0.190980 | + | 0.0588360i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.8789 | + | 29.2351i | −1.35575 | + | 2.34822i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.04845 | −0.323102 | −0.161551 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161551 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.1883 | + | 12.7803i | 0.807982 | + | 1.01354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3192 | + | 9.14041i | 0.892081 | + | 0.720365i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.05968 | + | 8.76363i | 0.396305 | + | 0.686420i | 0.993267 | − | 0.115849i | \(-0.0369590\pi\) |
−0.596962 | + | 0.802270i | \(0.703626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.6406 | + | 29.6444i | −0.906218 | + | 2.30781i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.76377 | − | 15.1793i | −0.678161 | − | 1.17461i | −0.975534 | − | 0.219847i | \(-0.929444\pi\) |
0.297374 | − | 0.954761i | \(-0.403889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.689486 | + | 1.19422i | −0.0530374 | + | 0.0918634i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.312381 | + | 1.36641i | −0.0238884 | + | 0.104492i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.83515 | −0.595695 | −0.297848 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297848 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.3185 | + | 6.28982i | −1.23356 | + | 0.475466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.05134 | − | 2.67738i | 0.0790234 | − | 0.201244i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.61920 | + | 8.00069i | −0.345255 | + | 0.597999i | −0.985400 | − | 0.170255i | \(-0.945541\pi\) |
0.640145 | + | 0.768254i | \(0.278874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.45977 | 0.703139 | 0.351569 | − | 0.936162i | \(-0.385648\pi\) | ||||
0.351569 | + | 0.936162i | \(0.385648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.600667 | − | 1.52968i | 0.0444026 | − | 0.113077i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.5902 | −2.17552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44636 | 0.325150 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.96497 | + | 13.1635i | 0.288409 | + | 0.957507i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0452967 | −0.00327756 | −0.00163878 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163878 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8198 | −1.35468 | −0.677340 | − | 0.735670i | \(-0.736868\pi\) | ||||
−0.677340 | + | 0.735670i | \(0.736868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.17968 | + | 20.8307i | −0.585759 | + | 1.49172i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.3886 | −1.59512 | −0.797561 | − | 0.603239i | \(-0.793877\pi\) | ||||
−0.797561 | + | 0.603239i | \(0.793877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3709 | − | 19.6949i | 0.806060 | − | 1.39614i | −0.109513 | − | 0.993985i | \(-0.534929\pi\) |
0.915573 | − | 0.402152i | \(-0.131738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.341343 | + | 0.869277i | −0.0240765 | + | 0.0613141i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.64811 | − | 1.33086i | −0.115674 | − | 0.0934083i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5709 | −0.877993 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.7658 | − | 4.85701i | 1.09580 | − | 0.337586i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.26065 | − | 2.18351i | 0.0872011 | − | 0.151037i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.95868 | + | 5.12458i | 0.203684 | + | 0.352791i | 0.949713 | − | 0.313123i | \(-0.101375\pi\) |
−0.746029 | + | 0.665914i | \(0.768042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.44937 | − | 6.23765i | 0.167828 | − | 0.427397i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.8682 | + | 25.7525i | 1.01400 | + | 1.75631i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.06492 | − | 25.8952i | 0.275945 | − | 1.75788i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.59150 | − | 7.01405i | −0.377838 | − | 0.473966i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.12440 | 0.210170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.20124 | − | 2.08062i | 0.0804412 | − | 0.139328i | −0.822998 | − | 0.568044i | \(-0.807700\pi\) |
0.903440 | + | 0.428716i | \(0.141034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41948 | + | 19.3316i | −0.294632 | + | 1.28877i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.48851 | − | 6.04227i | −0.231540 | − | 0.401040i | 0.726721 | − | 0.686933i | \(-0.241043\pi\) |
−0.958262 | + | 0.285893i | \(0.907710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.60782 | − | 16.6412i | 0.634903 | − | 1.09968i | −0.351633 | − | 0.936138i | \(-0.614374\pi\) |
0.986536 | − | 0.163546i | \(-0.0522931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.155347 | − | 24.7288i | 0.0102211 | − | 1.62704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9002 | + | 22.3439i | 0.845122 | + | 1.46379i | 0.885515 | + | 0.464611i | \(0.153806\pi\) |
−0.0403930 | + | 0.999184i | \(0.512861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8872 | + | 30.9815i | −1.16683 | + | 2.02101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.95632 | + | 12.6220i | −0.321948 | + | 0.819885i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.65732 | + | 11.5308i | 0.430626 | + | 0.745866i | 0.996927 | − | 0.0783322i | \(-0.0249595\pi\) |
−0.566301 | + | 0.824198i | \(0.691626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.928238 | − | 1.60776i | −0.0597931 | − | 0.103565i | 0.834579 | − | 0.550888i | \(-0.185711\pi\) |
−0.894372 | + | 0.447323i | \(0.852377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8919 | + | 4.60790i | 0.955313 | + | 0.295597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.6812 | − | 16.0084i | 1.12961 | − | 1.02274i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.885843 | − | 1.53432i | 0.0563648 | − | 0.0976267i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.19741 | − | 10.2829i | −0.519490 | − | 0.651655i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6947 | −0.738165 | −0.369083 | − | 0.929397i | \(-0.620328\pi\) | ||||
−0.369083 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.6746 | −1.86563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.80856 | − | 0.723907i | 0.301123 | − | 0.0453328i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.46594 | + | 2.53908i | −0.0914429 | + | 0.158384i | −0.908118 | − | 0.418713i | \(-0.862481\pi\) |
0.816676 | + | 0.577097i | \(0.195815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4388 | − | 8.26342i | 1.33214 | − | 0.513464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.29553 | + | 0.707191i | −0.142090 | + | 0.0437740i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1420 | − | 24.4946i | −0.872032 | − | 1.51040i | −0.859891 | − | 0.510477i | \(-0.829469\pi\) |
−0.0121407 | − | 0.999926i | \(-0.503865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0766 | − | 27.8455i | −0.987579 | − | 1.71054i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.7942 | + | 1.92610i | −0.782990 | + | 0.117876i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.79128 | − | 8.29874i | 0.292129 | − | 0.505983i | −0.682184 | − | 0.731181i | \(-0.738970\pi\) |
0.974313 | + | 0.225198i | \(0.0723028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.14220 | − | 15.8348i | −0.555349 | − | 0.961893i | −0.997876 | − | 0.0651381i | \(-0.979251\pi\) |
0.442527 | − | 0.896755i | \(-0.354082\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.109160 | − | 17.3766i | 0.00660668 | − | 1.05168i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.8353 | − | 30.8917i | 1.07551 | − | 1.86284i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.32776 | − | 4.03180i | −0.139862 | − | 0.242248i | 0.787582 | − | 0.616209i | \(-0.211332\pi\) |
−0.927444 | + | 0.373962i | \(0.877999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.7806 | − | 20.2237i | −1.30397 | − | 1.21076i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.06669 | + | 15.7040i | −0.540873 | + | 0.936820i | 0.457981 | + | 0.888962i | \(0.348573\pi\) |
−0.998854 | + | 0.0478580i | \(0.984760\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.6194 | 0.987920 | 0.493960 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493960 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00785 | − | 2.56662i | 0.0596997 | − | 0.152034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.10796 | − | 3.51059i | 0.537626 | − | 0.207223i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.16055 | + | 14.1345i | 0.480032 | + | 0.831441i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.96393 | + | 8.73565i | 0.408233 | + | 0.512093i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.94284 | + | 3.36510i | 0.113502 | + | 0.196591i | 0.917180 | − | 0.398473i | \(-0.130460\pi\) |
−0.803678 | + | 0.595064i | \(0.797127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82928 | + | 4.90046i | −0.164727 | + | 0.285316i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.1597 | − | 15.8080i | −1.34386 | − | 0.917271i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.8520 | −1.20590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.9641 | − | 14.5062i | −1.03543 | − | 0.836123i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.7456 | − | 4.17698i | 1.59395 | − | 0.239961i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.61647 | + | 2.79981i | −0.0925588 | + | 0.160317i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48452 | 0.198872 | 0.0994361 | − | 0.995044i | \(-0.468296\pi\) | ||||
0.0994361 | + | 0.995044i | \(0.468296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.9494 | + | 21.2616i | 0.964219 | + | 1.20953i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9855 | 0.736338 | 0.368169 | − | 0.929759i | \(-0.379985\pi\) | ||||
0.368169 | + | 0.929759i | \(0.379985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0439 | 0.850329 | 0.425164 | − | 0.905116i | \(-0.360216\pi\) | ||||
0.425164 | + | 0.905116i | \(0.360216\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.85807 | − | 26.7685i | −0.217378 | − | 1.50823i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.45839 | −0.475070 | −0.237535 | − | 0.971379i | \(-0.576340\pi\) | ||||
−0.237535 | + | 0.971379i | \(0.576340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.32069 | 0.241912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.76349 | + | 1.46985i | −0.544945 | + | 0.0820390i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.384968 | −0.0214202 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5326 | − | 21.7072i | 0.695186 | − | 1.20410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.73323 | + | 5.93743i | 0.261748 | + | 0.328341i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.30774 | − | 27.4421i | 0.237494 | − | 1.51293i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0245 | −0.550996 | −0.275498 | − | 0.961302i | \(-0.588843\pi\) | ||||
−0.275498 | + | 0.961302i | \(0.588843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.80620 | − | 25.3974i | 0.318178 | − | 1.39177i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.918597 | − | 1.59106i | 0.0501883 | − | 0.0869287i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.33242 | − | 16.1642i | −0.508369 | − | 0.880522i | −0.999953 | − | 0.00969119i | \(-0.996915\pi\) |
0.491584 | − | 0.870830i | \(-0.336418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.0113 | + | 2.56097i | −0.923926 | + | 0.139093i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.7318 | + | 46.3009i | 1.44761 | + | 2.50733i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.33992 | + | 16.5362i | −0.450313 | + | 0.892871i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.0919 | + | 4.83129i | −1.72777 | + | 0.260108i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.8048 | −0.848446 | −0.424223 | − | 0.905558i | \(-0.639453\pi\) | ||||
−0.424223 | + | 0.905558i | \(0.639453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.51578 | − | 7.82156i | 0.241724 | − | 0.418678i | −0.719481 | − | 0.694512i | \(-0.755620\pi\) |
0.961205 | + | 0.275833i | \(0.0889538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.2740 | − | 11.1080i | −0.868643 | − | 0.592904i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.23939 | − | 12.5390i | −0.385314 | − | 0.667383i | 0.606499 | − | 0.795084i | \(-0.292573\pi\) |
−0.991813 | + | 0.127701i | \(0.959240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.59155 | + | 11.4169i | −0.349843 | + | 0.605947i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.28176 | + | 1.86733i | −0.173689 | + | 0.0988298i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.85517 | − | 13.6056i | −0.414580 | − | 0.718074i | 0.580804 | − | 0.814043i | \(-0.302738\pi\) |
−0.995384 | + | 0.0959695i | \(0.969405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.39085 | − | 16.2654i | 0.494255 | − | 0.856075i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.5647 | + | 24.5423i | 1.02688 | + | 1.28813i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.82312 | + | 15.2821i | 0.461823 | + | 0.799902i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.42947 | − | 16.3323i | −0.492214 | − | 0.852540i | 0.507746 | − | 0.861507i | \(-0.330479\pi\) |
−0.999960 | + | 0.00896710i | \(0.997146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.46668 | − | 10.7897i | 0.128410 | − | 0.561688i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4241 | + | 15.6852i | 1.00845 | + | 0.814334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8568 | − | 29.1969i | 0.872814 | − | 1.51176i | 0.0137417 | − | 0.999906i | \(-0.495626\pi\) |
0.859073 | − | 0.511853i | \(-0.171041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.47318 | − | 8.84495i | 0.179354 | − | 0.456751i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.03609 | 0.156367 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.7263 | 1.73241 | 0.866203 | − | 0.499693i | \(-0.166554\pi\) | ||||
0.866203 | + | 0.499693i | \(0.166554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.2002 | + | 25.9763i | −0.522573 | + | 1.33080i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.16201 | + | 15.8691i | −0.468157 | + | 0.810871i | −0.999338 | − | 0.0363870i | \(-0.988415\pi\) |
0.531181 | + | 0.847258i | \(0.321748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.54427 | + | 48.0600i | −0.384491 | + | 2.44936i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.0209 | + | 7.70827i | −1.27188 | + | 0.391833i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.13744 | − | 3.70216i | −0.108373 | − | 0.187707i | 0.806739 | − | 0.590909i | \(-0.201231\pi\) |
−0.915111 | + | 0.403202i | \(0.867897\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.26545 | + | 3.92388i | 0.114569 | + | 0.198439i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.0516 | − | 18.8809i | −0.759250 | − | 0.952414i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3381 | − | 23.1023i | 0.671112 | − | 1.16240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9312 | + | 31.0577i | 0.899939 | + | 1.55874i | 0.827570 | + | 0.561362i | \(0.189723\pi\) |
0.0723687 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0134500 | + | 2.14104i | −0.000673344 | + | 0.107186i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7007 | − | 20.2663i | 0.584307 | − | 1.01205i | −0.410654 | − | 0.911791i | \(-0.634700\pi\) |
0.994961 | − | 0.100259i | \(-0.0319670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.7841 | + | 32.5350i | 0.935702 | + | 1.62068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.6200 | − | 13.3251i | −1.37245 | − | 0.662128i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4316 | + | 40.5848i | −1.16146 | + | 2.01171i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.8032 | 1.72091 | 0.860453 | − | 0.509530i | \(-0.170181\pi\) | ||||
0.860453 | + | 0.509530i | \(0.170181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.1005 | − | 2.87550i | 0.942159 | − | 0.141838i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.681372 | − | 4.34062i | 0.0335281 | − | 0.213588i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9351 | + | 22.4043i | 0.634961 | + | 1.09978i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.8841 | + | 1.63855i | −0.532997 | + | 0.0802403i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.90894 | + | 5.03843i | 0.142111 | + | 0.246143i | 0.928291 | − | 0.371854i | \(-0.121278\pi\) |
−0.786180 | + | 0.617997i | \(0.787944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7765 | + | 30.7898i | −0.866375 | + | 1.50061i | −0.000699237 | 1.00000i | \(0.500223\pi\) | |
−0.865676 | + | 0.500605i | \(0.833111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.0817 | − | 21.4318i | −1.12227 | − | 1.04205i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.44642 | −0.264190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.389292 | − | 2.47995i | 0.0188392 | − | 0.120013i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.0933 | + | 27.7141i | 1.06667 | + | 1.33805i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.48374 | + | 4.30196i | −0.119637 | + | 0.207218i | −0.919624 | − | 0.392800i | \(-0.871507\pi\) |
0.799987 | + | 0.600018i | \(0.204840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.9062 | 1.10080 | 0.550401 | − | 0.834900i | \(-0.314475\pi\) | ||||
0.550401 | + | 0.834900i | \(0.314475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.67265 | − | 0.703446i | 0.224036 | − | 0.0337277i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.56925 | 0.122904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.05894 | 0.384632 | 0.192316 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192316 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.2707 | + | 18.3170i | 0.489080 | + | 0.872239i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.77766 | −0.179482 | −0.0897410 | − | 0.995965i | \(-0.528604\pi\) | ||||
−0.0897410 | + | 0.995965i | \(0.528604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.4528 | 1.20658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4491 | − | 15.6164i | −0.588824 | − | 0.738629i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.5069 | 1.58129 | 0.790644 | − | 0.612276i | \(-0.209746\pi\) | ||||
0.790644 | + | 0.612276i | \(0.209746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.95457 | + | 17.2418i | −0.468742 | + | 0.811885i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.18973 | + | 0.179109i | −0.0558986 | + | 0.00841529i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.30125 | + | 33.7711i | −0.248527 | + | 1.58321i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.739506 | 0.0345926 | 0.0172963 | − | 0.999850i | \(-0.494494\pi\) | ||||
0.0172963 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.322205 | + | 4.26924i | −0.0150393 | + | 0.199271i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.30465 | + | 5.72383i | −0.153913 | + | 0.266585i | −0.932663 | − | 0.360750i | \(-0.882521\pi\) |
0.778750 | + | 0.627335i | \(0.215854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.96606 | − | 10.3335i | −0.277266 | − | 0.480239i | 0.693438 | − | 0.720516i | \(-0.256095\pi\) |
−0.970704 | + | 0.240277i | \(0.922762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.4475 | + | 45.7203i | 1.69021 | + | 2.12023i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.11184 | − | 8.85396i | −0.236548 | − | 0.409713i | 0.723174 | − | 0.690666i | \(-0.242683\pi\) |
−0.959721 | + | 0.280954i | \(0.909349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.221225 | + | 1.40929i | −0.0102152 | + | 0.0650749i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.56297 | + | 6.52695i | −0.118095 | + | 0.300746i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.0948 | 2.16542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54419 | + | 2.67462i | −0.0708524 | + | 0.122720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.0545 | − | 8.33475i | 1.23874 | − | 0.381622i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.01896 | + | 1.76488i | 0.0465573 | + | 0.0806395i | 0.888365 | − | 0.459138i | \(-0.151842\pi\) |
−0.841808 | + | 0.539778i | \(0.818508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4651 | + | 28.5184i | −0.750743 | + | 1.30033i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.9022 | − | 12.4624i | 0.996583 | − | 0.567060i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9888 | − | 19.0331i | −0.498974 | − | 0.864248i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5958 | − | 30.4767i | 0.797340 | − | 1.38103i | −0.124003 | − | 0.992282i | \(-0.539573\pi\) |
0.921343 | − | 0.388751i | \(-0.127093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.3319 | − | 2.60925i | 0.783778 | − | 0.117994i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.5708 | − | 30.4335i | −0.792958 | − | 1.37344i | −0.924128 | − | 0.382083i | \(-0.875207\pi\) |
0.131170 | − | 0.991360i | \(-0.458127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.329855 | − | 0.571326i | −0.0148559 | − | 0.0257312i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 40.4236 | + | 37.5341i | 1.81690 | + | 1.68703i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.58744 | − | 10.1126i | 0.0712062 | − | 0.453612i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.32633 | + | 4.02932i | −0.104141 | + | 0.180377i | −0.913387 | − | 0.407093i | \(-0.866543\pi\) |
0.809246 | + | 0.587470i | \(0.199876\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.0203 | + | 4.51942i | −1.34121 | + | 0.201913i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0660 | 0.537997 | 0.268999 | − | 0.963141i | \(-0.413307\pi\) | ||||
0.268999 | + | 0.963141i | \(0.413307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.1974 | −2.45625 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.48884 | + | 1.86763i | 0.0661219 | + | 0.0829442i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.1739 | + | 19.3537i | −0.495273 | + | 0.857838i | −0.999985 | − | 0.00544958i | \(-0.998265\pi\) |
0.504712 | + | 0.863288i | \(0.331599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6603 | − | 8.60829i | −0.471583 | − | 0.380808i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00518 | + | 1.36866i | 0.0885309 | + | 0.0604279i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.7454 | − | 46.3244i | −1.17854 | − | 2.04130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.3287 | + | 49.0667i | 1.24589 | + | 2.15795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.96022 | + | 12.6319i | −0.217730 | + | 0.554479i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.854260 | − | 1.47962i | 0.0374258 | − | 0.0648234i | −0.846706 | − | 0.532061i | \(-0.821418\pi\) |
0.884132 | + | 0.467238i | \(0.154751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6036 | − | 18.3659i | −0.463662 | − | 0.803087i | 0.535478 | − | 0.844549i | \(-0.320132\pi\) |
−0.999140 | + | 0.0414627i | \(0.986798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.190287 | + | 30.2907i | −0.00830481 | + | 1.32200i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.08158 | − | 7.06951i | 0.177796 | − | 0.307952i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.61945 | − | 6.26907i | −0.157367 | − | 0.272568i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.65092 | − | 3.38995i | −0.158436 | − | 0.147111i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.99494 | + | 12.1156i | −0.302984 | + | 0.524784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4236 | 0.839754 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.97449 | + | 12.5121i | 0.430431 | + | 0.539939i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.95532 | − | 36.9275i | −0.342660 | − | 1.59058i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.79443 | + | 8.30419i | 0.206129 | + | 0.357025i | 0.950492 | − | 0.310750i | \(-0.100580\pi\) |
−0.744363 | + | 0.667775i | \(0.767247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.98873 | − | 15.2511i | 0.257001 | − | 0.654488i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.46882 | − | 12.9364i | −0.319929 | − | 0.554133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.65927 | + | 9.80214i | −0.241973 | + | 0.419109i | −0.961276 | − | 0.275587i | \(-0.911128\pi\) |
0.719303 | + | 0.694696i | \(0.244461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.08590 | − | 1.93680i | −0.0890240 | − | 0.0826606i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.374088 | −0.0159367 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.21220 | + | 20.4630i | −0.136596 | + | 0.870174i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.7328 | + | 47.7056i | −0.795162 | + | 2.02499i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.68102 | − | 2.91162i | 0.0712272 | − | 0.123369i | −0.828212 | − | 0.560415i | \(-0.810642\pi\) |
0.899439 | + | 0.437045i | \(0.143975\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.0929 | 1.39968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.81487 | − | 7.16846i | 0.118844 | − | 0.302653i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0914 | −0.804606 | −0.402303 | − | 0.915506i | \(-0.631790\pi\) | ||||
−0.402303 | + | 0.915506i | \(0.631790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.8424 | 1.42376 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7325 | + | 1.94113i | 0.996672 | + | 0.0815199i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.62726 | 0.110140 | 0.0550702 | − | 0.998482i | \(-0.482462\pi\) | ||||
0.0550702 | + | 0.998482i | \(0.482462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.98226 | −0.417745 | −0.208872 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208872 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.0286761 | + | 0.0730278i | −0.00119796 | + | 0.00305078i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.3489 | 1.51586 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.05761 | − | 10.4921i | 0.252182 | − | 0.436791i | −0.711945 | − | 0.702236i | \(-0.752185\pi\) |
0.964126 | + | 0.265444i | \(0.0855187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9143 | + | 30.3415i | −0.495143 | + | 1.26095i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.6285 | − | 12.6202i | −0.648379 | − | 0.523573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.9224 | −2.10899 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.4051 | + | 26.3747i | 1.17441 | + | 1.09046i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1857 | − | 26.3025i | 0.626782 | − | 1.08562i | −0.361411 | − | 0.932407i | \(-0.617705\pi\) |
0.988193 | − | 0.153212i | \(-0.0489618\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.31446 | − | 4.00875i | −0.0953655 | − | 0.165178i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.1736 | + | 36.0951i | −0.583025 | + | 1.48475i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5788 | − | 35.6434i | −0.845068 | − | 1.46370i | −0.885562 | − | 0.464521i | \(-0.846226\pi\) |
0.0404940 | − | 0.999180i | \(-0.487107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.93093 | − | 2.67147i | 0.284141 | − | 0.109520i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.5538 | − | 30.8006i | −1.00492 | − | 1.26058i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.11041 | 0.331382 | 0.165691 | − | 0.986178i | \(-0.447014\pi\) | ||||
0.165691 | + | 0.986178i | \(0.447014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8320 | − | 27.4218i | 0.645801 | − | 1.11856i | −0.338315 | − | 0.941033i | \(-0.609857\pi\) |
0.984116 | − | 0.177527i | \(-0.0568098\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.18536 | + | 1.10063i | 0.0482717 | + | 0.0448212i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.8722 | − | 53.4723i | −1.25513 | − | 2.17396i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5131 | − | 19.9412i | 0.467300 | − | 0.809388i | −0.532002 | − | 0.846743i | \(-0.678560\pi\) |
0.999302 | + | 0.0373552i | \(0.0118933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.18900 | + | 1.81456i | −0.129225 | + | 0.0735295i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.9062 | + | 34.4785i | 0.805317 | + | 1.39485i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4750 | − | 19.8752i | 0.463470 | − | 0.802753i | −0.535661 | − | 0.844433i | \(-0.679938\pi\) |
0.999131 | + | 0.0416796i | \(0.0132709\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.95833 | + | 20.2670i | −0.320911 | + | 0.817244i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1183 | + | 19.2574i | 0.447605 | + | 0.775274i | 0.998230 | − | 0.0594788i | \(-0.0189439\pi\) |
−0.550625 | + | 0.834753i | \(0.685611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.75302 | + | 4.76836i | 0.110653 | + | 0.191657i | 0.916034 | − | 0.401101i | \(-0.131372\pi\) |
−0.805381 | + | 0.592758i | \(0.798039\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.15037 | − | 28.4926i | 0.0862914 | − | 1.14337i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.4412 | + | 7.10800i | −0.738831 | + | 0.284776i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.17850 | − | 12.4335i | 0.287140 | − | 0.497341i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.72219 | − | 3.41476i | −0.108714 | − | 0.136372i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.15538 | 0.285303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.9276 | −1.31083 | −0.655413 | − | 0.755271i | \(-0.727505\pi\) | ||||
−0.655413 | + | 0.755271i | \(0.727505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1350 | − | 1.52577i | 0.402829 | − | 0.0606440i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.4501 | − | 47.5449i | 1.08932 | − | 1.88676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.59009 | − | 25.9484i | −0.221488 | − | 1.02811i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.50577 | − | 7.89778i | −0.336483 | − | 0.312431i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.945880 | + | 1.63831i | 0.0373600 | + | 0.0647095i | 0.884101 | − | 0.467296i | \(-0.154772\pi\) |
−0.846741 | + | 0.532006i | \(0.821438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8742 | + | 39.6193i | 0.902070 | + | 1.56243i | 0.824803 | + | 0.565421i | \(0.191286\pi\) |
0.0772675 | + | 0.997010i | \(0.475380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 50.9311 | − | 7.66745i | 2.00541 | − | 0.301906i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.98067 | − | 15.5550i | 0.353066 | − | 0.611529i | −0.633719 | − | 0.773564i | \(-0.718472\pi\) |
0.986785 | + | 0.162035i | \(0.0518056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48085 | + | 7.76106i | 0.175889 | + | 0.304648i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −39.1751 | − | 22.9471i | −1.53539 | − | 0.899366i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0741 | − | 19.1809i | 0.433363 | − | 0.750607i | −0.563797 | − | 0.825913i | \(-0.690660\pi\) |
0.997160 | + | 0.0753063i | \(0.0239935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7506 | + | 41.1373i | 0.928015 | + | 1.60737i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.8479 | + | 4.57425i | −0.579274 | + | 0.178459i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.39543 | + | 9.34515i | −0.210176 | + | 0.364035i | −0.951769 | − | 0.306814i | \(-0.900737\pi\) |
0.741594 | + | 0.670850i | \(0.234070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.13907 | −0.199887 | −0.0999434 | − | 0.994993i | \(-0.531866\pi\) | ||||
−0.0999434 | + | 0.994993i | \(0.531866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.97797 | − | 5.03718i | 0.0768181 | − | 0.195628i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.653187 | − | 4.16106i | 0.0253295 | − | 0.161359i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.20142 | + | 3.81298i | 0.0852395 | + | 0.147639i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.59391 | − | 3.25384i | −0.100286 | − | 0.125801i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.56007 | + | 4.43417i | 0.0988304 | + | 0.171179i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9290 | − | 18.9295i | 0.421281 | − | 0.729680i | −0.574784 | − | 0.818305i | \(-0.694914\pi\) |
0.996065 | + | 0.0886254i | \(0.0282474\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.3687 | + | 19.3634i | 1.09191 | + | 0.745299i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.7296 | −0.450807 | −0.225403 | − | 0.974266i | \(-0.572370\pi\) | ||||
−0.225403 | + | 0.974266i | \(0.572370\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2768 | + | 10.7212i | 0.509518 | + | 0.411442i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9499 | + | 1.79900i | −0.457921 | + | 0.0689379i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.260358 | + | 0.450954i | −0.00996234 | + | 0.0172553i | −0.870964 | − | 0.491348i | \(-0.836504\pi\) |
0.861001 | + | 0.508603i | \(0.169838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.9987 | −1.45186 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.7467 | − | 26.0249i | −0.791536 | − | 0.992913i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.7825 | −1.36320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.1912 | 1.75720 | 0.878599 | − | 0.477561i | \(-0.158479\pi\) | ||||
0.878599 | + | 0.477561i | \(0.158479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −39.7697 | − | 15.9056i | −1.51073 | − | 0.604204i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.6529 | 0.821342 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.03985 | 0.115143 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.1898 | − | 6.65257i | 1.67141 | − | 0.251623i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7166 | −1.23569 | −0.617844 | − | 0.786301i | \(-0.711994\pi\) | ||||
−0.617844 | + | 0.786301i | \(0.711994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.02872 | − | 3.51385i | 0.0765148 | − | 0.132527i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38.6248 | + | 48.4514i | 1.45469 | + | 1.82479i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.9919 | − | 15.4145i | 1.50405 | − | 0.579723i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.4551 | −1.25643 | −0.628216 | − | 0.778039i | \(-0.716215\pi\) | ||||
−0.628216 | + | 0.778039i | \(0.716215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.2115 | + | 15.9813i | 0.645483 | + | 0.599344i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.2401 | + | 47.1813i | −1.02015 | + | 1.76695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.8622 | − | 60.3831i | −1.30377 | − | 2.25820i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.8046 | − | 3.43314i | 0.851655 | − | 0.128213i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.42685 | + | 16.3278i | 0.351562 | + | 0.608924i | 0.986523 | − | 0.163621i | \(-0.0523173\pi\) |
−0.634961 | + | 0.772544i | \(0.718984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.3143 | + | 26.0942i | 1.20345 | + | 0.971798i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.17968 | + | 0.478687i | −0.118254 | + | 0.0178026i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.29248 | −0.196558 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3107 | + | 33.4471i | −0.716194 | + | 1.24048i | 0.246303 | + | 0.969193i | \(0.420784\pi\) |
−0.962497 | + | 0.271291i | \(0.912549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.8565 | − | 21.0916i | 0.624316 | − | 0.781172i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.59537 | − | 6.22736i | −0.132979 | − | 0.230327i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.35591 | − | 16.2049i | 0.345569 | − | 0.598542i | −0.639888 | − | 0.768468i | \(-0.721019\pi\) |
0.985457 | + | 0.169926i | \(0.0543527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.6155 | − | 38.6403i | −0.539099 | − | 1.42527i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.45482 | − | 2.51982i | −0.0535890 | − | 0.0928189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.15949 | − | 12.4006i | 0.263366 | − | 0.456163i | −0.703768 | − | 0.710430i | \(-0.748501\pi\) |
0.967134 | + | 0.254266i | \(0.0818340\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.91285 | − | 2.39950i | −0.0702703 | − | 0.0881480i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2068 | + | 24.6069i | 0.521197 | + | 0.902740i | 0.999696 | + | 0.0246519i | \(0.00784775\pi\) |
−0.478499 | + | 0.878088i | \(0.658819\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.6442 | + | 34.0247i | 0.719706 | + | 1.24657i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.7678 | + | 6.70608i | −0.796443 | + | 0.245363i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0729 | + | 5.42426i | −0.514211 | + | 0.198198i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7209 | − | 27.2294i | 0.573663 | − | 0.993614i | −0.422522 | − | 0.906353i | \(-0.638855\pi\) |
0.996185 | − | 0.0872612i | \(-0.0278115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.40362 | + | 18.8544i | −0.269803 | + | 0.687091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.36687 | 0.0861392 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.405916 | 0.0147533 | 0.00737663 | − | 0.999973i | \(-0.497652\pi\) | ||||
0.00737663 | + | 0.999973i | \(0.497652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.7862 | + | 47.8417i | −0.681897 | + | 1.73654i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.65688 | + | 4.60184i | −0.0963117 | + | 0.166817i | −0.910155 | − | 0.414267i | \(-0.864038\pi\) |
0.813844 | + | 0.581084i | \(0.197371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.02397 | + | 7.28696i | 0.326690 | + | 0.263806i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.87708 | − | 8.21068i | 0.0678660 | − | 0.296858i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.14863 | + | 5.45359i | 0.113691 | + | 0.196918i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9430 | + | 20.6858i | 0.430674 | + | 0.745949i | 0.996931 | − | 0.0782793i | \(-0.0249426\pi\) |
−0.566258 | + | 0.824228i | \(0.691609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16549 | + | 3.97083i | 0.114002 | + | 0.143006i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.8525 | − | 22.2613i | 0.462274 | − | 0.800682i | −0.536800 | − | 0.843710i | \(-0.680367\pi\) |
0.999074 | + | 0.0430274i | \(0.0137003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.7442 | − | 56.7147i | −1.17621 | − | 2.03725i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.249995 | − | 39.7952i | 0.00896851 | − | 1.42765i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.861872 | − | 1.49281i | 0.0308798 | − | 0.0534853i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4393 | + | 18.0814i | 0.373548 | + | 0.647004i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.313099 | + | 4.14858i | −0.0111892 | + | 0.148258i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.89727 | − | 11.9464i | 0.246174 | − | 0.426386i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1109 | 0.574292 | 0.287146 | − | 0.957887i | \(-0.407293\pi\) | ||||
0.287146 | + | 0.957887i | \(0.407293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.4434 | + | 7.29293i | −1.72463 | + | 0.259635i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.5196 | + | 9.45089i | −0.871818 | + | 0.336035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.79893 | + | 3.11583i | 0.0638818 | + | 0.110646i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55.0705 | + | 8.29061i | −1.95315 | + | 0.294038i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.556852 | + | 0.964495i | 0.0197247 | + | 0.0341642i | 0.875719 | − | 0.482821i | \(-0.160388\pi\) |
−0.855995 | + | 0.516985i | \(0.827054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.32540 | − | 7.49181i | 0.153022 | − | 0.265041i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.99436 | + | 21.8462i | −0.176467 | + | 0.771899i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.9471 | 0.986231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.2565 | + | 17.8292i | −1.63033 | + | 0.628395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.3461 | − | 12.9783i | −0.364199 | − | 0.456856i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.1461 | − | 17.5736i | 0.356718 | − | 0.617853i | −0.630693 | − | 0.776033i | \(-0.717229\pi\) |
0.987410 | + | 0.158179i | \(0.0505624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.72686 | −0.341556 | −0.170778 | − | 0.985310i | \(-0.554628\pi\) | ||||
−0.170778 | + | 0.985310i | \(0.554628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.3166 | + | 4.71458i | −1.09832 | + | 0.165348i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.4803 | −1.20779 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.07749 | −0.142653 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.9456 | − | 11.1767i | −0.976499 | − | 0.390544i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.07104 | −0.142080 | −0.0710401 | − | 0.997473i | \(-0.522632\pi\) | ||||
−0.0710401 | + | 0.997473i | \(0.522632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.61200 | 0.0910485 | 0.0455242 | − | 0.998963i | \(-0.485504\pi\) | ||||
0.0455242 | + | 0.998963i | \(0.485504\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.5128 | − | 48.3110i | −1.34084 | − | 1.68197i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.0054 | −1.04339 | −0.521695 | − | 0.853132i | \(-0.674700\pi\) | ||||
−0.521695 | + | 0.853132i | \(0.674700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0676 | + | 24.3658i | −0.488588 | + | 0.846260i | −0.999914 | − | 0.0131272i | \(-0.995821\pi\) |
0.511325 | + | 0.859387i | \(0.329155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.97375 | + | 1.20041i | −0.276606 | + | 0.0416419i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.27559 | + | 3.87109i | −0.148140 | + | 0.134125i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.7226 | 2.06679 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.3936 | + | 22.3118i | −1.60360 | + | 0.771208i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.61277 | + | 6.25750i | −0.124727 | + | 0.216033i | −0.921626 | − | 0.388079i | \(-0.873139\pi\) |
0.796899 | + | 0.604112i | \(0.206472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1795 | + | 24.5596i | 0.488947 | + | 0.846881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5782 | + | 24.5592i | 0.674309 | + | 0.845862i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.34933 | − | 4.06915i | −0.0808193 | − | 0.139983i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.3005 | + | 30.1205i | 1.28166 | + | 1.03495i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5213 | − | 26.7939i | 0.361090 | − | 0.919565i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.7544 | −1.63700 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0767 | − | 27.8457i | 0.550457 | − | 0.953419i | −0.447785 | − | 0.894141i | \(-0.647787\pi\) |
0.998242 | − | 0.0592779i | \(-0.0188798\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.49989 | − | 3.24972i | −0.119694 | − | 0.111138i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.48585 | + | 6.03767i | 0.119074 | + | 0.206243i | 0.919401 | − | 0.393321i | \(-0.128674\pi\) |
−0.800327 | + | 0.599564i | \(0.795341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3523 | − | 30.0551i | 0.592054 | − | 1.02547i | −0.401901 | − | 0.915683i | \(-0.631650\pi\) |
0.993955 | − | 0.109785i | \(-0.0350162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.106206 | − | 16.9064i | 0.00361950 | − | 0.576168i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.9863 | + | 45.0095i | 0.884583 | + | 1.53214i | 0.846191 | + | 0.532879i | \(0.178890\pi\) |
0.0383914 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3486 | − | 23.1204i | 0.453866 | − | 0.786119i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.9540 | − | 4.20835i | 0.949367 | − | 0.142923i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.1241 | − | 36.5880i | −0.716586 | − | 1.24116i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.02228 | − | 1.77064i | −0.0346387 | − | 0.0599960i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4924 | − | 5.69700i | 0.625872 | − | 0.192814i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.25097 | − | 14.3396i | 0.0760968 | − | 0.484767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3822 | + | 35.3029i | −0.688257 | + | 1.19210i | 0.284145 | + | 0.958781i | \(0.408290\pi\) |
−0.972401 | + | 0.233314i | \(0.925043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.65520 | − | 1.00191i | 0.224474 | − | 0.0337936i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.07339 | −0.204618 | −0.102309 | − | 0.994753i | \(-0.532623\pi\) | ||||
−0.102309 | + | 0.994753i | \(0.532623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0958 | −0.339751 | −0.169875 | − | 0.985466i | \(-0.554336\pi\) | ||||
−0.169875 | + | 0.985466i | \(0.554336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.10943 | + | 7.66375i | 0.205366 | + | 0.257614i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.55215 | + | 11.3487i | −0.220000 | + | 0.381051i | −0.954808 | − | 0.297225i | \(-0.903939\pi\) |
0.734808 | + | 0.678275i | \(0.237272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.61077 | + | 42.1132i | −0.221718 | + | 1.41243i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.1476 | + | 27.3307i | −1.34499 | + | 0.915613i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.45271 | − | 4.24822i | −0.0820768 | − | 0.142161i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7393 | − | 27.2612i | −0.526106 | − | 0.911242i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.2008 | + | 33.6177i | −0.440763 | + | 1.12246i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.96622 | − | 6.86969i | 0.132281 | − | 0.229117i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.88758 | + | 6.73348i | 0.129514 | + | 0.224325i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.7596 | + | 19.7784i | −1.15673 | + | 0.658183i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.1164 | + | 27.9145i | −0.535728 | + | 0.927908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.41698 | − | 11.1145i | −0.213072 | − | 0.369052i | 0.739602 | − | 0.673044i | \(-0.235014\pi\) |
−0.952674 | + | 0.303992i | \(0.901680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.8309 | − | 47.3761i | 0.359237 | − | 1.57137i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.5089 | − | 30.3262i | 0.580094 | − | 1.00475i | −0.415373 | − | 0.909651i | \(-0.636349\pi\) |
0.995468 | − | 0.0951015i | \(-0.0303176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.9718 | 1.35597 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.49053 | + | 4.37857i | 0.115393 | + | 0.144751i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.6960 | − | 23.1723i | −0.947626 | − | 0.765218i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.12422 | − | 7.14336i | −0.136046 | − | 0.235638i | 0.789951 | − | 0.613170i | \(-0.210106\pi\) |
−0.925996 | + | 0.377532i | \(0.876773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.20596 | − | 5.61778i | 0.0726888 | − | 0.185112i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.33557 | + | 12.7056i | 0.241453 | + | 0.418209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.7018 | − | 49.7129i | 0.943709 | − | 1.63455i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.0083 | − | 13.8659i | 1.47827 | − | 0.455415i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.8512 | −1.86523 | −0.932614 | − | 0.360876i | \(-0.882478\pi\) | ||||
−0.932614 | + | 0.360876i | \(0.882478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.688776 | + | 3.19720i | 0.0225737 | + | 0.104784i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.22075 | − | 20.9353i | 0.269135 | − | 0.685390i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.57518 | + | 13.1206i | −0.247735 | + | 0.429089i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.6213 | −1.52305 | −0.761526 | − | 0.648134i | \(-0.775550\pi\) | ||||
−0.761526 | + | 0.648134i | \(0.775550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.52386 | − | 24.2538i | 0.310800 | − | 0.791494i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.3402 | 0.826067 | 0.413033 | − | 0.910716i | \(-0.364469\pi\) | ||||
0.413033 | + | 0.910716i | \(0.364469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.2877 | −0.660658 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45.5988 | − | 10.7264i | −1.48333 | − | 0.348930i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.9572 | −0.973478 | −0.486739 | − | 0.873548i | \(-0.661814\pi\) | ||||
−0.486739 | + | 0.873548i | \(0.661814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.6380 | 0.637478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.35478 | + | 13.6367i | −0.173641 | + | 0.442200i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.6721 | 1.25271 | 0.626356 | − | 0.779537i | \(-0.284546\pi\) | ||||
0.626356 | + | 0.779537i | \(0.284546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0771711 | − | 0.133664i | 0.00249720 | − | 0.00432528i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.73531 | − | 6.96586i | 0.0884201 | − | 0.225174i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.5310 | − | 10.6116i | 0.889023 | − | 0.342666i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.1549 | 2.16629 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.81130 | + | 16.6713i | −0.122817 | + | 0.537225i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.0630 | − | 55.5347i | 1.03214 | − | 1.78773i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2161 | − | 28.0870i | −0.521473 | − | 0.903218i | −0.999688 | − | 0.0249755i | \(-0.992049\pi\) |
0.478215 | − | 0.878243i | \(-0.341284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.243713 | + | 0.620650i | −0.00782920 | + | 0.0199381i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.53128 | − | 14.7766i | −0.273782 | − | 0.474204i | 0.696045 | − | 0.717998i | \(-0.254941\pi\) |
−0.969827 | + | 0.243794i | \(0.921608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.6881 | + | 6.04683i | −0.502936 | + | 0.193853i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.0624 | − | 33.9475i | −0.866691 | − | 1.08719i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.5513 | −0.465538 | −0.232769 | − | 0.972532i | \(-0.574779\pi\) | ||||
−0.232769 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.1553 | − | 34.9101i | 0.644168 | − | 1.11573i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.5689 | − | 3.87213i | 0.401293 | − | 0.123628i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1926 | − | 28.0463i | −0.516463 | − | 0.894540i | −0.999817 | − | 0.0191149i | \(-0.993915\pi\) |
0.483355 | − | 0.875425i | \(-0.339418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.1430 | − | 66.0657i | 1.21534 | − | 2.10503i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.5152 | − | 24.3178i | −1.32144 | − | 0.774045i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.9952 | + | 41.5608i | 0.763002 | + | 1.32156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7165 | + | 22.0256i | −0.403952 | + | 0.699665i | −0.994199 | − | 0.107558i | \(-0.965697\pi\) |
0.590247 | + | 0.807223i | \(0.299030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.34624 | + | 16.1616i | −0.201392 | + | 0.512872i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.7447 | + | 67.1078i | 1.22829 | + | 2.12746i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.696665 | + | 1.20666i | 0.0220636 | + | 0.0382153i | 0.876846 | − | 0.480771i | \(-0.159643\pi\) |
−0.854783 | + | 0.518986i | \(0.826310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.2701 | − | 25.4392i | −1.17917 | − | 0.804861i |
(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 | 1008.2.q.l.529.6 | 22 | ||
3.2 | odd | 2 | 3024.2.q.l.2881.11 | 22 | |||
4.3 | odd | 2 | 504.2.q.c.25.6 | ✓ | 22 | ||
7.2 | even | 3 | 1008.2.t.l.961.9 | 22 | |||
9.4 | even | 3 | 1008.2.t.l.193.9 | 22 | |||
9.5 | odd | 6 | 3024.2.t.k.1873.1 | 22 | |||
12.11 | even | 2 | 1512.2.q.d.1369.11 | 22 | |||
21.2 | odd | 6 | 3024.2.t.k.289.1 | 22 | |||
28.23 | odd | 6 | 504.2.t.c.457.3 | yes | 22 | ||
36.23 | even | 6 | 1512.2.t.c.361.1 | 22 | |||
36.31 | odd | 6 | 504.2.t.c.193.3 | yes | 22 | ||
63.23 | odd | 6 | 3024.2.q.l.2305.11 | 22 | |||
63.58 | even | 3 | inner | 1008.2.q.l.625.6 | 22 | ||
84.23 | even | 6 | 1512.2.t.c.289.1 | 22 | |||
252.23 | even | 6 | 1512.2.q.d.793.11 | 22 | |||
252.247 | odd | 6 | 504.2.q.c.121.6 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.6 | ✓ | 22 | 4.3 | odd | 2 | ||
504.2.q.c.121.6 | yes | 22 | 252.247 | odd | 6 | ||
504.2.t.c.193.3 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.c.457.3 | yes | 22 | 28.23 | odd | 6 | ||
1008.2.q.l.529.6 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.q.l.625.6 | 22 | 63.58 | even | 3 | inner | ||
1008.2.t.l.193.9 | 22 | 9.4 | even | 3 | |||
1008.2.t.l.961.9 | 22 | 7.2 | even | 3 | |||
1512.2.q.d.793.11 | 22 | 252.23 | even | 6 | |||
1512.2.q.d.1369.11 | 22 | 12.11 | even | 2 | |||
1512.2.t.c.289.1 | 22 | 84.23 | even | 6 | |||
1512.2.t.c.361.1 | 22 | 36.23 | even | 6 | |||
3024.2.q.l.2305.11 | 22 | 63.23 | odd | 6 | |||
3024.2.q.l.2881.11 | 22 | 3.2 | odd | 2 | |||
3024.2.t.k.289.1 | 22 | 21.2 | odd | 6 | |||
3024.2.t.k.1873.1 | 22 | 9.5 | odd | 6 |