Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(593,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.w (of order \(4\), 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: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.33973862400.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 44x^{4} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.2 | ||
Root | \(1.79576 - 1.79576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1457 |
Dual form | 2160.2.w.e.593.2 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.403587 | − | 2.19934i | −0.180490 | − | 0.983577i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.224745 | − | 0.224745i | −0.0849456 | − | 0.0849456i | 0.663357 | − | 0.748303i | \(-0.269131\pi\) |
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.78434i | 0.839510i | 0.907637 | + | 0.419755i | \(0.137884\pi\) | ||||
−0.907637 | + | 0.419755i | \(0.862116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22474 | + | 1.22474i | −0.339683 | + | 0.339683i | −0.856248 | − | 0.516565i | \(-0.827210\pi\) |
0.516565 | + | 0.856248i | \(0.327210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.78434 | − | 2.78434i | 0.675302 | − | 0.675302i | −0.283632 | − | 0.958933i | \(-0.591539\pi\) |
0.958933 | + | 0.283632i | \(0.0915393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.89898i | 0.894487i | 0.894412 | + | 0.447244i | \(0.147594\pi\) | ||||
−0.894412 | + | 0.447244i | \(0.852406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.19445 | + | 6.19445i | 1.29163 | + | 1.29163i | 0.933778 | + | 0.357854i | \(0.116491\pi\) |
0.357854 | + | 0.933778i | \(0.383509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.67423 | + | 1.77526i | −0.934847 | + | 0.355051i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.78434 | 0.517039 | 0.258520 | − | 0.966006i | \(-0.416765\pi\) | ||||
0.258520 | + | 0.966006i | \(0.416765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.449490 | −0.0807307 | −0.0403654 | − | 0.999185i | \(-0.512852\pi\) | ||||
−0.0403654 | + | 0.999185i | \(0.512852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.403587 | + | 0.584996i | −0.0682187 | + | 0.0988823i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.67423 | + | 3.67423i | 0.604040 | + | 0.604040i | 0.941382 | − | 0.337342i | \(-0.109528\pi\) |
−0.337342 | + | 0.941382i | \(0.609528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.60455i | − | 1.49998i | −0.661450 | − | 0.749990i | \(-0.730058\pi\) | ||
0.661450 | − | 0.749990i | \(-0.269942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.550510 | + | 0.550510i | −0.0839520 | + | 0.0839520i | −0.747836 | − | 0.663884i | \(-0.768907\pi\) |
0.663884 | + | 0.747836i | \(0.268907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.89898i | − | 0.985568i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.19445 | + | 6.19445i | 0.850873 | + | 0.850873i | 0.990241 | − | 0.139368i | \(-0.0445071\pi\) |
−0.139368 | + | 0.990241i | \(0.544507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.12372 | − | 1.12372i | 0.825723 | − | 0.151523i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3889 | 1.61290 | 0.806448 | − | 0.591305i | \(-0.201387\pi\) | ||||
0.806448 | + | 0.591305i | \(0.201387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7980 | 1.63861 | 0.819305 | − | 0.573357i | \(-0.194359\pi\) | ||||
0.819305 | + | 0.573357i | \(0.194359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.18793 | + | 2.19934i | 0.395414 | + | 0.272795i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.67423 | − | 8.67423i | −1.05973 | − | 1.05973i | −0.998099 | − | 0.0616272i | \(-0.980371\pi\) |
−0.0616272 | − | 0.998099i | \(-0.519629\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.60455i | − | 1.13985i | −0.821696 | − | 0.569925i | \(-0.806972\pi\) | ||
0.821696 | − | 0.569925i | \(-0.193028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22474 | + | 6.22474i | −0.728551 | + | 0.728551i | −0.970331 | − | 0.241780i | \(-0.922269\pi\) |
0.241780 | + | 0.970331i | \(0.422269\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.625766 | − | 0.625766i | 0.0713127 | − | 0.0713127i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.24745i | 1.04042i | 0.854039 | + | 0.520210i | \(0.174146\pi\) | ||||
−0.854039 | + | 0.520210i | \(0.825854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.41011 | − | 3.41011i | −0.374308 | − | 0.374308i | 0.494736 | − | 0.869044i | \(-0.335265\pi\) |
−0.869044 | + | 0.494736i | \(0.835265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.24745 | − | 5.00000i | −0.786096 | − | 0.542326i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.3889 | 1.31322 | 0.656610 | − | 0.754230i | \(-0.271990\pi\) | ||||
0.656610 | + | 0.754230i | \(0.271990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.550510 | 0.0577092 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.57520 | − | 1.57358i | 0.879797 | − | 0.161446i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.77526 | − | 4.77526i | −0.484854 | − | 0.484854i | 0.421824 | − | 0.906678i | \(-0.361390\pi\) |
−0.906678 | + | 0.421824i | \(0.861390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.9576i | 1.78685i | 0.449217 | + | 0.893423i | \(0.351703\pi\) | ||||
−0.449217 | + | 0.893423i | \(0.648297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.22474 | − | 6.22474i | 0.613342 | − | 0.613342i | −0.330473 | − | 0.943815i | \(-0.607208\pi\) |
0.943815 | + | 0.330473i | \(0.107208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.97879 | − | 8.97879i | 0.868012 | − | 0.868012i | −0.124240 | − | 0.992252i | \(-0.539649\pi\) |
0.992252 | + | 0.124240i | \(0.0396493\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.3485i | − | 1.08699i | −0.839414 | − | 0.543493i | \(-0.817101\pi\) | ||
0.839414 | − | 0.543493i | \(-0.182899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.625766 | − | 0.625766i | −0.0588671 | − | 0.0588671i | 0.677060 | − | 0.735927i | \(-0.263254\pi\) |
−0.735927 | + | 0.677060i | \(0.763254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1237 | − | 16.1237i | 1.03729 | − | 1.50355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.25153 | −0.114728 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.24745 | 0.295223 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.79086 | + | 9.56378i | 0.517950 | + | 0.855411i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.89898 | − | 9.89898i | −0.878392 | − | 0.878392i | 0.114976 | − | 0.993368i | \(-0.463321\pi\) |
−0.993368 | + | 0.114976i | \(0.963321\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.56868i | − | 0.486538i | −0.969959 | − | 0.243269i | \(-0.921780\pi\) | ||
0.969959 | − | 0.243269i | \(-0.0782198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.876276 | − | 0.876276i | 0.0759827 | − | 0.0759827i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.41011 | + | 3.41011i | −0.291345 | + | 0.291345i | −0.837611 | − | 0.546266i | \(-0.816049\pi\) |
0.546266 | + | 0.837611i | \(0.316049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2474i | 1.63255i | 0.577665 | + | 0.816274i | \(0.303964\pi\) | ||||
−0.577665 | + | 0.816274i | \(0.696036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41011 | − | 3.41011i | −0.285167 | − | 0.285167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.12372 | − | 6.12372i | −0.0933202 | − | 0.508548i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.82021 | 0.558734 | 0.279367 | − | 0.960184i | \(-0.409875\pi\) | ||||
0.279367 | + | 0.960184i | \(0.409875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5505 | −0.858588 | −0.429294 | − | 0.903165i | \(-0.641238\pi\) | ||||
−0.429294 | + | 0.903165i | \(0.641238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.181408 | + | 0.988583i | 0.0145711 | + | 0.0794049i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3485 | + | 13.3485i | 1.06532 | + | 1.06532i | 0.997712 | + | 0.0676121i | \(0.0215380\pi\) |
0.0676121 | + | 0.997712i | \(0.478462\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.78434i | − | 0.219437i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.77526 | + | 3.77526i | −0.295701 | + | 0.295701i | −0.839327 | − | 0.543626i | \(-0.817051\pi\) |
0.543626 | + | 0.839327i | \(0.317051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.60455 | − | 9.60455i | 0.743223 | − | 0.743223i | −0.229974 | − | 0.973197i | \(-0.573864\pi\) |
0.973197 | + | 0.229974i | \(0.0738641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000i | 0.769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.56868 | + | 5.56868i | 0.423379 | + | 0.423379i | 0.886365 | − | 0.462986i | \(-0.153222\pi\) |
−0.462986 | + | 0.886365i | \(0.653222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44949 | + | 0.651531i | 0.109571 | + | 0.0492511i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.60455 | 0.717878 | 0.358939 | − | 0.933361i | \(-0.383139\pi\) | ||||
0.358939 | + | 0.933361i | \(0.383139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2474 | 0.836016 | 0.418008 | − | 0.908443i | \(-0.362728\pi\) | ||||
0.418008 | + | 0.908443i | \(0.362728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.59803 | − | 9.56378i | 0.485097 | − | 0.703143i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.75255 | + | 7.75255i | 0.566923 | + | 0.566923i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3889i | 0.896429i | 0.893926 | + | 0.448214i | \(0.147940\pi\) | ||||
−0.893926 | + | 0.448214i | \(0.852060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5732 | + | 11.5732i | −0.833058 | + | 0.833058i | −0.987934 | − | 0.154876i | \(-0.950502\pi\) |
0.154876 | + | 0.987934i | \(0.450502\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.82021 | − | 6.82021i | 0.485920 | − | 0.485920i | −0.421096 | − | 0.907016i | \(-0.638354\pi\) |
0.907016 | + | 0.421096i | \(0.138354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.24745i | 0.655534i | 0.944759 | + | 0.327767i | \(0.106296\pi\) | ||||
−0.944759 | + | 0.327767i | \(0.893704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.625766 | − | 0.625766i | −0.0439202 | − | 0.0439202i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.1237 | + | 3.87628i | −1.47534 | + | 0.270731i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.8561 | −0.750931 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2474 | 0.911992 | 0.455996 | − | 0.889982i | \(-0.349283\pi\) | ||||
0.455996 | + | 0.889982i | \(0.349283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.43294 | + | 0.988583i | 0.0977257 | + | 0.0674208i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.101021 | + | 0.101021i | 0.00685772 | + | 0.00685772i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.82021i | 0.458777i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7980 | + | 12.7980i | −0.857015 | + | 0.857015i | −0.990985 | − | 0.133971i | \(-0.957227\pi\) |
0.133971 | + | 0.990985i | \(0.457227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7990 | + | 15.7990i | −1.04862 | + | 1.04862i | −0.0498603 | + | 0.998756i | \(0.515878\pi\) |
−0.998756 | + | 0.0498603i | \(0.984122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.34847i | − | 0.0891094i | −0.999007 | − | 0.0445547i | \(-0.985813\pi\) | ||
0.999007 | − | 0.0445547i | \(-0.0141869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.1732 | − | 15.1732i | −0.994032 | − | 0.994032i | 0.00595067 | − | 0.999982i | \(-0.498106\pi\) |
−0.999982 | + | 0.00595067i | \(0.998106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.35302 | −0.540312 | −0.270156 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270156 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0000 | 1.22390 | 0.611949 | − | 0.790897i | \(-0.290386\pi\) | ||||
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.1732 | + | 2.78434i | −0.969382 | + | 0.177885i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.77526 | − | 4.77526i | −0.303842 | − | 0.303842i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9934i | 1.38821i | 0.719872 | + | 0.694107i | \(0.244201\pi\) | ||||
−0.719872 | + | 0.694107i | \(0.755799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.2474 | + | 17.2474i | −1.08434 | + | 1.08434i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7419 | − | 20.7419i | 1.29385 | − | 1.29385i | 0.361456 | − | 0.932389i | \(-0.382280\pi\) |
0.932389 | − | 0.361456i | \(-0.117720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.65153i | − | 0.102621i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3889 | + | 12.3889i | 0.763932 | + | 0.763932i | 0.977031 | − | 0.213099i | \(-0.0683556\pi\) |
−0.213099 | + | 0.977031i | \(0.568356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1237 | − | 16.1237i | 0.683325 | − | 0.990473i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3889 | −0.755364 | −0.377682 | − | 0.925935i | \(-0.623279\pi\) | ||||
−0.377682 | + | 0.925935i | \(0.623279\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0000 | 1.27566 | 0.637830 | − | 0.770178i | \(-0.279832\pi\) | ||||
0.637830 | + | 0.770178i | \(0.279832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.94291 | − | 13.0147i | −0.298069 | − | 0.784814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8990 | − | 13.8990i | −0.835109 | − | 0.835109i | 0.153102 | − | 0.988210i | \(-0.451074\pi\) |
−0.988210 | + | 0.153102i | \(0.951074\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.5263i | − | 1.40346i | −0.712444 | − | 0.701729i | \(-0.752412\pi\) | ||
0.712444 | − | 0.701729i | \(-0.247588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.79796 | + | 2.79796i | −0.166321 | + | 0.166321i | −0.785360 | − | 0.619039i | \(-0.787522\pi\) |
0.619039 | + | 0.785360i | \(0.287522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.15857 | + | 2.15857i | −0.127417 | + | 0.127417i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.49490i | 0.0879351i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2303 | + | 10.2303i | 0.597662 | + | 0.597662i | 0.939690 | − | 0.342028i | \(-0.111114\pi\) |
−0.342028 | + | 0.939690i | \(0.611114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.00000 | − | 27.2474i | −0.291111 | − | 1.58641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.1732 | −0.877491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.247449 | 0.0142627 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.16509 | − | 28.1471i | −0.295752 | − | 1.61170i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.3485 | − | 13.3485i | −0.761837 | − | 0.761837i | 0.214817 | − | 0.976654i | \(-0.431085\pi\) |
−0.976654 | + | 0.214817i | \(0.931085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.25153i | − | 0.0709679i | −0.999370 | − | 0.0354839i | \(-0.988703\pi\) | ||
0.999370 | − | 0.0354839i | \(-0.0112973\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7753 | − | 13.7753i | 0.778623 | − | 0.778623i | −0.200973 | − | 0.979597i | \(-0.564410\pi\) |
0.979597 | + | 0.200973i | \(0.0644104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.9934 | + | 21.9934i | −1.23528 | + | 1.23528i | −0.273365 | + | 0.961910i | \(0.588137\pi\) |
−0.961910 | + | 0.273365i | \(0.911863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.75255i | 0.434060i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8561 | + | 10.8561i | 0.604049 | + | 0.604049i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.55051 | − | 7.89898i | 0.196947 | − | 0.438157i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.75255 | −0.371154 | −0.185577 | − | 0.982630i | \(-0.559415\pi\) | ||||
−0.185577 | + | 0.982630i | \(0.559415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.5768 | + | 22.5784i | −0.851053 | + | 1.23359i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.42679 | + | 6.42679i | 0.350089 | + | 0.350089i | 0.860143 | − | 0.510053i | \(-0.170374\pi\) |
−0.510053 | + | 0.860143i | \(0.670374\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.25153i | − | 0.0677743i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.12372 | + | 3.12372i | −0.168665 | + | 0.168665i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.625766 | − | 0.625766i | 0.0335929 | − | 0.0335929i | −0.690111 | − | 0.723704i | \(-0.742438\pi\) |
0.723704 | + | 0.690111i | \(0.242438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0000i | 0.695874i | 0.937518 | + | 0.347937i | \(0.113118\pi\) | ||||
−0.937518 | + | 0.347937i | \(0.886882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1732 | − | 15.1732i | −0.807590 | − | 0.807590i | 0.176679 | − | 0.984269i | \(-0.443465\pi\) |
−0.984269 | + | 0.176679i | \(0.943465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.1237 | + | 3.87628i | −1.12113 | + | 0.205731i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.03587 | −0.213005 | −0.106503 | − | 0.994312i | \(-0.533965\pi\) | ||||
−0.106503 | + | 0.994312i | \(0.533965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.79796 | 0.199893 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.2026 | + | 11.1781i | 0.848082 | + | 0.585090i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5732 | + | 18.5732i | 0.969514 | + | 0.969514i | 0.999549 | − | 0.0300350i | \(-0.00956186\pi\) |
−0.0300350 | + | 0.999549i | \(0.509562\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.78434i | − | 0.144556i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.32577 | + | 4.32577i | −0.223980 | + | 0.223980i | −0.810172 | − | 0.586192i | \(-0.800626\pi\) |
0.586192 | + | 0.810172i | \(0.300626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.41011 | + | 3.41011i | −0.175629 | + | 0.175629i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.0000i | − | 0.667765i | −0.942615 | − | 0.333883i | \(-0.891641\pi\) | ||
0.942615 | − | 0.333883i | \(-0.108359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5263 | − | 23.5263i | −1.20214 | − | 1.20214i | −0.973516 | − | 0.228620i | \(-0.926579\pi\) |
−0.228620 | − | 0.973516i | \(-0.573421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.62883 | − | 1.12372i | −0.0830127 | − | 0.0572703i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.7060 | −0.847030 | −0.423515 | − | 0.905889i | \(-0.639204\pi\) | ||||
−0.423515 | + | 0.905889i | \(0.639204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.4949 | 1.74448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.3383 | − | 3.73215i | 1.02333 | − | 0.187785i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1464 | − | 16.1464i | −0.810366 | − | 0.810366i | 0.174323 | − | 0.984689i | \(-0.444226\pi\) |
−0.984689 | + | 0.174323i | \(0.944226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.53281i | − | 0.0765448i | −0.999267 | − | 0.0382724i | \(-0.987815\pi\) | ||
0.999267 | − | 0.0382724i | \(-0.0121855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.550510 | − | 0.550510i | 0.0274229 | − | 0.0274229i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2303 | + | 10.2303i | −0.507098 | + | 0.507098i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.4949i | 1.35954i | 0.733428 | + | 0.679768i | \(0.237919\pi\) | ||||
−0.733428 | + | 0.679768i | \(0.762081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.78434 | − | 2.78434i | −0.137008 | − | 0.137008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.12372 | + | 8.87628i | −0.300602 | + | 0.435719i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.3465 | −1.48252 | −0.741261 | − | 0.671217i | \(-0.765772\pi\) | ||||
−0.741261 | + | 0.671217i | \(0.765772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.2474 | 0.548167 | 0.274084 | − | 0.961706i | \(-0.411626\pi\) | ||||
0.274084 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.07175 | + | 17.9576i | −0.391537 | + | 0.871070i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.87628 | − | 2.87628i | −0.139193 | − | 0.139193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.7419i | − | 0.999103i | −0.866284 | − | 0.499551i | \(-0.833498\pi\) | ||
0.866284 | − | 0.499551i | \(-0.166502\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.79796 | − | 2.79796i | 0.134461 | − | 0.134461i | −0.636673 | − | 0.771134i | \(-0.719690\pi\) |
0.771134 | + | 0.636673i | \(0.219690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.1520 | + | 24.1520i | −1.15535 | + | 1.15535i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.1464i | − | 0.627445i | −0.949515 | − | 0.313722i | \(-0.898424\pi\) | ||
0.949515 | − | 0.313722i | \(-0.101576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.82021 | − | 6.82021i | −0.324038 | − | 0.324038i | 0.526276 | − | 0.850314i | \(-0.323588\pi\) |
−0.850314 | + | 0.526276i | \(0.823588\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | − | 27.2474i | −0.237023 | − | 1.29165i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.3889 | −0.584668 | −0.292334 | − | 0.956316i | \(-0.594432\pi\) | ||||
−0.292334 | + | 0.956316i | \(0.594432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.7423 | 1.25925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.222179 | − | 1.21076i | −0.0104159 | − | 0.0567614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.3485 | − | 22.3485i | −1.04542 | − | 1.04542i | −0.998918 | − | 0.0464990i | \(-0.985194\pi\) |
−0.0464990 | − | 0.998918i | \(-0.514806\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.0949i | 1.35509i | 0.735483 | + | 0.677543i | \(0.236955\pi\) | ||||
−0.735483 | + | 0.677543i | \(0.763045\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.02270 | + | 1.02270i | −0.0475291 | + | 0.0475291i | −0.730472 | − | 0.682943i | \(-0.760700\pi\) |
0.682943 | + | 0.730472i | \(0.260700\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4248 | + | 16.4248i | −0.760048 | + | 0.760048i | −0.976331 | − | 0.216283i | \(-0.930607\pi\) |
0.216283 | + | 0.976331i | \(0.430607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.89898i | 0.180038i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.53281 | − | 1.53281i | −0.0704786 | − | 0.0704786i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.92168 | − | 18.2247i | −0.317589 | − | 0.836209i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.03587 | 0.184404 | 0.0922019 | − | 0.995740i | \(-0.470609\pi\) | ||||
0.0922019 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | −0.410365 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.57520 | + | 12.4297i | −0.389380 | + | 0.564402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.6742 | − | 18.6742i | −0.846210 | − | 0.846210i | 0.143448 | − | 0.989658i | \(-0.454181\pi\) |
−0.989658 | + | 0.143448i | \(0.954181\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 39.9510i | − | 1.80296i | −0.432816 | − | 0.901482i | \(-0.642480\pi\) | ||
0.432816 | − | 0.901482i | \(-0.357520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.75255 | − | 7.75255i | 0.349157 | − | 0.349157i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.15857 | + | 2.15857i | −0.0968253 | + | 0.0968253i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.898979i | − | 0.0402438i | −0.999798 | − | 0.0201219i | \(-0.993595\pi\) | ||
0.999798 | − | 0.0201219i | \(-0.00640544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.5833 | − | 18.5833i | −0.828590 | − | 0.828590i | 0.158732 | − | 0.987322i | \(-0.449260\pi\) |
−0.987322 | + | 0.158732i | \(0.949260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.4949 | − | 7.24745i | 1.75750 | − | 0.322507i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.4248 | 0.728015 | 0.364007 | − | 0.931396i | \(-0.381408\pi\) | ||||
0.364007 | + | 0.931396i | \(0.381408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.79796 | 0.123774 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.2026 | − | 11.1781i | −0.713971 | − | 0.492567i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.1732i | − | 0.664751i | −0.943147 | − | 0.332376i | \(-0.892150\pi\) | ||
0.943147 | − | 0.332376i | \(-0.107850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9217 | + | 27.9217i | −1.22093 | + | 1.22093i | −0.253628 | + | 0.967302i | \(0.581624\pi\) |
−0.967302 | + | 0.253628i | \(0.918376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.25153 | + | 1.25153i | −0.0545176 | + | 0.0545176i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.7423i | 2.33662i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7631 | + | 11.7631i | 0.509518 | + | 0.509518i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.3712 | − | 16.1237i | −1.01042 | − | 0.697089i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.2091 | 0.827395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5505 | 0.453602 | 0.226801 | − | 0.973941i | \(-0.427173\pi\) | ||||
0.226801 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.9592 | + | 4.58010i | −1.06913 | + | 0.196190i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.5732 | + | 23.5732i | 1.00792 | + | 1.00792i | 0.999968 | + | 0.00794945i | \(0.00253042\pi\) |
0.00794945 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8561i | 0.462485i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.07832 | − | 2.07832i | 0.0883790 | − | 0.0883790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.5263 | + | 23.5263i | −0.996839 | + | 0.996839i | −0.999995 | − | 0.00315559i | \(-0.998996\pi\) |
0.00315559 | + | 0.999995i | \(0.498996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.34847i | − | 0.0570342i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.35302 | − | 8.35302i | −0.352038 | − | 0.352038i | 0.508829 | − | 0.860867i | \(-0.330078\pi\) |
−0.860867 | + | 0.508829i | \(0.830078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.12372 | + | 1.62883i | −0.0472754 | + | 0.0685253i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.9576 | −0.752821 | −0.376410 | − | 0.926453i | \(-0.622842\pi\) | ||||
−0.376410 | + | 0.926453i | \(0.622842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.44949 | 0.395449 | 0.197724 | − | 0.980258i | \(-0.436645\pi\) | ||||
0.197724 | + | 0.980258i | \(0.436645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.9510 | − | 17.9576i | −1.66607 | − | 0.748883i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0227 | − | 22.0227i | −0.916817 | − | 0.916817i | 0.0799794 | − | 0.996797i | \(-0.474515\pi\) |
−0.996797 | + | 0.0799794i | \(0.974515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.53281i | 0.0635916i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2474 | + | 17.2474i | −0.714316 | + | 0.714316i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2303 | − | 10.2303i | 0.422250 | − | 0.422250i | −0.463727 | − | 0.885978i | \(-0.653488\pi\) |
0.885978 | + | 0.463727i | \(0.153488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.75255i | − | 0.0722126i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.97879 | + | 8.97879i | 0.368715 | + | 0.368715i | 0.867008 | − | 0.498294i | \(-0.166040\pi\) |
−0.498294 | + | 0.867008i | \(0.666040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.505103 | + | 2.75255i | 0.0207072 | + | 0.112844i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.3823 | 1.40482 | 0.702412 | − | 0.711770i | \(-0.252106\pi\) | ||||
0.702412 | + | 0.711770i | \(0.252106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0454 | −0.572924 | −0.286462 | − | 0.958092i | \(-0.592479\pi\) | ||||
−0.286462 | + | 0.958092i | \(0.592479\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.31063 | − | 7.14226i | −0.0532846 | − | 0.290374i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.67423 | − | 3.67423i | −0.149133 | − | 0.149133i | 0.628598 | − | 0.777730i | \(-0.283629\pi\) |
−0.777730 | + | 0.628598i | \(0.783629\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2247 | + | 31.2247i | −1.26116 | + | 1.26116i | −0.310622 | + | 0.950533i | \(0.600537\pi\) |
−0.950533 | + | 0.310622i | \(0.899463\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7631 | − | 11.7631i | 0.473566 | − | 0.473566i | −0.429501 | − | 0.903066i | \(-0.641310\pi\) |
0.903066 | + | 0.429501i | \(0.141310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.65153i | 0.0663806i | 0.999449 | + | 0.0331903i | \(0.0105667\pi\) | ||||
−0.999449 | + | 0.0331903i | \(0.989433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.78434 | − | 2.78434i | −0.111552 | − | 0.111552i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6969 | − | 16.5959i | 0.747878 | − | 0.663837i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.4606 | 0.815819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.4949 | 1.41303 | 0.706515 | − | 0.707698i | \(-0.250266\pi\) | ||||
0.706515 | + | 0.707698i | \(0.250266\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.7762 | + | 25.7664i | −0.705426 | + | 1.02251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.44949 | + | 8.44949i | 0.334781 | + | 0.334781i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.07175i | 0.318815i | 0.987213 | + | 0.159407i | \(0.0509583\pi\) | ||||
−0.987213 | + | 0.159407i | \(0.949042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5505 | − | 12.5505i | 0.494944 | − | 0.494944i | −0.414916 | − | 0.909860i | \(-0.636189\pi\) |
0.909860 | + | 0.414916i | \(0.136189\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0147 | − | 13.0147i | 0.511659 | − | 0.511659i | −0.403375 | − | 0.915035i | \(-0.632163\pi\) |
0.915035 | + | 0.403375i | \(0.132163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.4949i | 1.35404i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.9934 | − | 21.9934i | −0.860670 | − | 0.860670i | 0.130746 | − | 0.991416i | \(-0.458263\pi\) |
−0.991416 | + | 0.130746i | \(0.958263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2474 | + | 2.24745i | −0.478547 | + | 0.0878151i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.5556 | −1.93041 | −0.965206 | − | 0.261492i | \(-0.915785\pi\) | ||||
−0.965206 | + | 0.261492i | \(0.915785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | −0.0388955 | −0.0194477 | − | 0.999811i | \(-0.506191\pi\) | ||||
−0.0194477 | + | 0.999811i | \(0.506191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.28089 | − | 1.57358i | −0.0884490 | − | 0.0610208i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.2474 | + | 17.2474i | 0.667824 | + | 0.667824i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.6339i | 1.37563i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2702 | − | 18.2702i | 0.704263 | − | 0.704263i | −0.261060 | − | 0.965323i | \(-0.584072\pi\) |
0.965323 | + | 0.261060i | \(0.0840720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1374 | − | 11.1374i | 0.428044 | − | 0.428044i | −0.459918 | − | 0.887961i | \(-0.652121\pi\) |
0.887961 | + | 0.459918i | \(0.152121\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.14643i | 0.0823724i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1161 | + | 20.1161i | 0.769723 | + | 0.769723i | 0.978058 | − | 0.208335i | \(-0.0668043\pi\) |
−0.208335 | + | 0.978058i | \(0.566804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.87628 | + | 6.12372i | 0.339145 | + | 0.233975i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.1732 | −0.578054 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.247449 | 0.00941339 | 0.00470670 | − | 0.999989i | \(-0.498502\pi\) | ||||
0.00470670 | + | 0.999989i | \(0.498502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 42.3318 | − | 7.76803i | 1.60574 | − | 0.294658i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.7423 | − | 26.7423i | −1.01294 | − | 1.01294i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6763i | 0.667625i | 0.942640 | + | 0.333812i | \(0.108335\pi\) | ||||
−0.942640 | + | 0.333812i | \(0.891665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3258 | + | 14.3258i | −0.540306 | + | 0.540306i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.03587 | − | 4.03587i | 0.151785 | − | 0.151785i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.34847i | 0.313533i | 0.987636 | + | 0.156767i | \(0.0501071\pi\) | ||||
−0.987636 | + | 0.156767i | \(0.949893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.78434 | − | 2.78434i | −0.104274 | − | 0.104274i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.12372 | + | 8.87628i | −0.229014 | + | 0.331954i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.8369 | −1.85860 | −0.929300 | − | 0.369325i | \(-0.879589\pi\) | ||||
−0.929300 | + | 0.369325i | \(0.879589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.79796 | −0.104201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.0147 | + | 4.94291i | −0.483352 | + | 0.183575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8990 | + | 13.8990i | 0.515485 | + | 0.515485i | 0.916202 | − | 0.400717i | \(-0.131239\pi\) |
−0.400717 | + | 0.916202i | \(0.631239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.06562i | 0.113386i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.55051 | + | 2.55051i | −0.0942052 | + | 0.0942052i | −0.752639 | − | 0.658434i | \(-0.771219\pi\) |
0.658434 | + | 0.752639i | \(0.271219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.1520 | − | 24.1520i | 0.889651 | − | 0.889651i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.2474i | − | 0.965528i | −0.875750 | − | 0.482764i | \(-0.839633\pi\) | ||
0.875750 | − | 0.482764i | \(-0.160367\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.3823 | + | 34.3823i | 1.26137 | + | 1.26137i | 0.950431 | + | 0.310934i | \(0.100642\pi\) |
0.310934 | + | 0.950431i | \(0.399358\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.75255 | − | 15.0000i | −0.100846 | − | 0.549557i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.03587 | −0.147468 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.00000 | −0.328415 | −0.164207 | − | 0.986426i | \(-0.552507\pi\) | ||||
−0.164207 | + | 0.986426i | \(0.552507\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.25805 | + | 23.2042i | 0.154966 | + | 0.844488i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7196 | + | 19.7196i | 0.716723 | + | 0.716723i | 0.967933 | − | 0.251210i | \(-0.0808285\pi\) |
−0.251210 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 23.2450i | − | 0.842630i | −0.906914 | − | 0.421315i | \(-0.861569\pi\) | ||
0.906914 | − | 0.421315i | \(-0.138431\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.55051 | + | 2.55051i | −0.0923347 | + | 0.0923347i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.1732 | + | 15.1732i | −0.547874 | + | 0.547874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.7423i | 1.07254i | 0.844048 | + | 0.536268i | \(0.180166\pi\) | ||||
−0.844048 | + | 0.536268i | \(0.819834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.41011 | + | 3.41011i | 0.122653 | + | 0.122653i | 0.765769 | − | 0.643116i | \(-0.222359\pi\) |
−0.643116 | + | 0.765769i | \(0.722359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.10102 | − | 0.797959i | 0.0754709 | − | 0.0286635i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.4480 | 1.34171 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7423 | 0.956916 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.9706 | − | 34.7452i | 0.855548 | − | 1.24011i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4722 | − | 17.4722i | −0.622816 | − | 0.622816i | 0.323434 | − | 0.946251i | \(-0.395163\pi\) |
−0.946251 | + | 0.323434i | \(0.895163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.281275i | 0.0100010i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.6742 | + | 15.6742i | −0.556608 | + | 0.556608i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.9934 | − | 21.9934i | 0.779048 | − | 0.779048i | −0.200621 | − | 0.979669i | \(-0.564296\pi\) |
0.979669 | + | 0.200621i | \(0.0642960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.3318 | − | 17.3318i | −0.611626 | − | 0.611626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.12372 | + | 1.12372i | −0.215833 | + | 0.0396061i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.25153 | −0.0440015 | −0.0220008 | − | 0.999758i | \(-0.507004\pi\) | ||||
−0.0220008 | + | 0.999758i | \(0.507004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5505 | 0.686511 | 0.343256 | − | 0.939242i | \(-0.388470\pi\) | ||||
0.343256 | + | 0.939242i | \(0.388470\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.82673 | + | 6.77944i | 0.344215 | + | 0.237474i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.14643 | − | 2.14643i | −0.0750940 | − | 0.0750940i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 17.9576i | − | 0.626724i | −0.949634 | − | 0.313362i | \(-0.898545\pi\) | ||
0.949634 | − | 0.313362i | \(-0.101455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.0227 | + | 31.0227i | −1.08138 | + | 1.08138i | −0.0850028 | + | 0.996381i | \(0.527090\pi\) |
−0.996381 | + | 0.0850028i | \(0.972910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.82021 | − | 6.82021i | 0.237162 | − | 0.237162i | −0.578512 | − | 0.815674i | \(-0.696366\pi\) |
0.815674 | + | 0.578512i | \(0.196366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 49.2474i | − | 1.71043i | −0.518270 | − | 0.855217i | \(-0.673424\pi\) | ||
0.518270 | − | 0.855217i | \(-0.326576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.2091 | − | 19.2091i | −0.665556 | − | 0.665556i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.0000 | − | 17.2474i | −0.865161 | − | 0.596873i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.7778 | 0.855424 | 0.427712 | − | 0.903915i | \(-0.359320\pi\) | ||||
0.427712 | + | 0.903915i | \(0.359320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2474 | −0.732671 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9934 | − | 4.03587i | 0.756598 | − | 0.138838i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.729847 | − | 0.729847i | −0.0250779 | − | 0.0250779i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.5197i | 1.56040i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.47219 | + | 3.47219i | −0.118886 | + | 0.118886i | −0.764047 | − | 0.645161i | \(-0.776790\pi\) |
0.645161 | + | 0.764047i | \(0.276790\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.41011 | + | 3.41011i | −0.116487 | + | 0.116487i | −0.762947 | − | 0.646460i | \(-0.776249\pi\) |
0.646460 | + | 0.762947i | \(0.276249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.24745i | − | 0.179041i | −0.995985 | − | 0.0895203i | \(-0.971467\pi\) | ||
0.995985 | − | 0.0895203i | \(-0.0285334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.8561 | − | 10.8561i | −0.369545 | − | 0.369545i | 0.497766 | − | 0.867311i | \(-0.334154\pi\) |
−0.867311 | + | 0.497766i | \(0.834154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | − | 14.4949i | 0.340010 | − | 0.492841i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.7480 | −0.873443 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2474 | 0.719942 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.847945 | − | 3.45088i | 0.0286658 | − | 0.116661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2247 | + | 10.2247i | 0.345265 | + | 0.345265i | 0.858342 | − | 0.513077i | \(-0.171495\pi\) |
−0.513077 | + | 0.858342i | \(0.671495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.78434i | − | 0.0938068i | −0.998899 | − | 0.0469034i | \(-0.985065\pi\) | ||
0.998899 | − | 0.0469034i | \(-0.0149353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.9217 | + | 22.9217i | −0.771376 | + | 0.771376i | −0.978347 | − | 0.206971i | \(-0.933639\pi\) |
0.206971 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6404 | + | 13.6404i | −0.458001 | + | 0.458001i | −0.897999 | − | 0.439998i | \(-0.854979\pi\) |
0.439998 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.44949i | 0.149231i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.87628 | − | 21.1237i | −0.129570 | − | 0.706088i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.25153 | −0.0417409 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4949 | 1.14919 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.53933 | − | 24.7370i | −0.150892 | − | 0.822286i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.6742 | − | 13.6742i | −0.454046 | − | 0.454046i | 0.442649 | − | 0.896695i | \(-0.354039\pi\) |
−0.896695 | + | 0.442649i | \(0.854039\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.31715i | − | 0.143034i | −0.997439 | − | 0.0715168i | \(-0.977216\pi\) | ||
0.997439 | − | 0.0715168i | \(-0.0227839\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.49490 | − | 9.49490i | 0.314235 | − | 0.314235i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.25153 | + | 1.25153i | −0.0413292 | + | 0.0413292i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.6515i | − | 0.615257i | −0.951507 | − | 0.307629i | \(-0.900465\pi\) | ||
0.951507 | − | 0.307629i | \(-0.0995354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.7631 | + | 11.7631i | 0.387188 | + | 0.387188i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6969 | − | 10.6515i | −0.779151 | − | 0.350220i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.6571 | 1.85886 | 0.929429 | − | 0.369001i | \(-0.120300\pi\) | ||||
0.929429 | + | 0.369001i | \(0.120300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8990 | 0.881578 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.9217 | − | 20.1794i | 0.455288 | − | 0.659936i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.77526 | − | 9.77526i | −0.319344 | − | 0.319344i | 0.529171 | − | 0.848515i | \(-0.322503\pi\) |
−0.848515 | + | 0.529171i | \(0.822503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.1732i | − | 0.494633i | −0.968935 | − | 0.247317i | \(-0.920451\pi\) | ||
0.968935 | − | 0.247317i | \(-0.0795488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.4949 | − | 59.4949i | 1.93742 | − | 1.93742i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.4248 | − | 16.4248i | 0.533733 | − | 0.533733i | −0.387948 | − | 0.921681i | \(-0.626816\pi\) |
0.921681 | + | 0.387948i | \(0.126816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.2474i | − | 0.494953i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.5263 | + | 23.5263i | 0.762090 | + | 0.762090i | 0.976700 | − | 0.214610i | \(-0.0688480\pi\) |
−0.214610 | + | 0.976700i | \(0.568848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.2474 | − | 5.00000i | 0.881707 | − | 0.161796i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.53281 | 0.0494969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7980 | −0.993483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.1243 | + | 20.7827i | 0.969735 | + | 0.669018i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3258 | + | 31.3258i | 1.00737 | + | 1.00737i | 0.999973 | + | 0.00739605i | \(0.00235426\pi\) |
0.00739605 | + | 0.999973i | \(0.497646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.50306i | 0.0803272i | 0.999193 | + | 0.0401636i | \(0.0127879\pi\) | ||||
−0.999193 | + | 0.0401636i | \(0.987212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.32577 | − | 4.32577i | 0.138678 | − | 0.138678i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.7566 | + | 33.7566i | −1.07997 | + | 1.07997i | −0.0834572 | + | 0.996511i | \(0.526596\pi\) |
−0.996511 | + | 0.0834572i | \(0.973404\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.4949i | 1.10246i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.6848 | + | 25.6848i | 0.819219 | + | 0.819219i | 0.985995 | − | 0.166776i | \(-0.0533357\pi\) |
−0.166776 | + | 0.985995i | \(0.553336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.7526 | − | 12.2474i | −0.565643 | − | 0.390236i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.82021 | −0.216870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.0454 | −1.11325 | −0.556627 | − | 0.830763i | \(-0.687905\pi\) | ||||
−0.556627 | + | 0.830763i | \(0.687905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.3383 | − | 3.73215i | 0.644768 | − | 0.118317i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.101021 | − | 0.101021i | −0.00319935 | − | 0.00319935i | 0.705505 | − | 0.708705i | \(-0.250720\pi\) |
−0.708705 | + | 0.705505i | \(0.750720\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2160.2.w.e.1457.2 | 8 | ||
3.2 | odd | 2 | inner | 2160.2.w.e.1457.3 | 8 | ||
4.3 | odd | 2 | 540.2.j.a.377.2 | yes | 8 | ||
5.3 | odd | 4 | inner | 2160.2.w.e.593.3 | 8 | ||
12.11 | even | 2 | 540.2.j.a.377.3 | yes | 8 | ||
15.8 | even | 4 | inner | 2160.2.w.e.593.2 | 8 | ||
20.3 | even | 4 | 540.2.j.a.53.3 | yes | 8 | ||
20.7 | even | 4 | 2700.2.j.j.593.1 | 8 | |||
20.19 | odd | 2 | 2700.2.j.j.1457.1 | 8 | |||
36.7 | odd | 6 | 1620.2.x.d.377.4 | 16 | |||
36.11 | even | 6 | 1620.2.x.d.377.1 | 16 | |||
36.23 | even | 6 | 1620.2.x.d.917.4 | 16 | |||
36.31 | odd | 6 | 1620.2.x.d.917.1 | 16 | |||
60.23 | odd | 4 | 540.2.j.a.53.2 | ✓ | 8 | ||
60.47 | odd | 4 | 2700.2.j.j.593.2 | 8 | |||
60.59 | even | 2 | 2700.2.j.j.1457.2 | 8 | |||
180.23 | odd | 12 | 1620.2.x.d.593.4 | 16 | |||
180.43 | even | 12 | 1620.2.x.d.53.4 | 16 | |||
180.83 | odd | 12 | 1620.2.x.d.53.1 | 16 | |||
180.103 | even | 12 | 1620.2.x.d.593.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.2.j.a.53.2 | ✓ | 8 | 60.23 | odd | 4 | ||
540.2.j.a.53.3 | yes | 8 | 20.3 | even | 4 | ||
540.2.j.a.377.2 | yes | 8 | 4.3 | odd | 2 | ||
540.2.j.a.377.3 | yes | 8 | 12.11 | even | 2 | ||
1620.2.x.d.53.1 | 16 | 180.83 | odd | 12 | |||
1620.2.x.d.53.4 | 16 | 180.43 | even | 12 | |||
1620.2.x.d.377.1 | 16 | 36.11 | even | 6 | |||
1620.2.x.d.377.4 | 16 | 36.7 | odd | 6 | |||
1620.2.x.d.593.1 | 16 | 180.103 | even | 12 | |||
1620.2.x.d.593.4 | 16 | 180.23 | odd | 12 | |||
1620.2.x.d.917.1 | 16 | 36.31 | odd | 6 | |||
1620.2.x.d.917.4 | 16 | 36.23 | even | 6 | |||
2160.2.w.e.593.2 | 8 | 15.8 | even | 4 | inner | ||
2160.2.w.e.593.3 | 8 | 5.3 | odd | 4 | inner | ||
2160.2.w.e.1457.2 | 8 | 1.1 | even | 1 | trivial | ||
2160.2.w.e.1457.3 | 8 | 3.2 | odd | 2 | inner | ||
2700.2.j.j.593.1 | 8 | 20.7 | even | 4 | |||
2700.2.j.j.593.2 | 8 | 60.47 | odd | 4 | |||
2700.2.j.j.1457.1 | 8 | 20.19 | odd | 2 | |||
2700.2.j.j.1457.2 | 8 | 60.59 | even | 2 |