Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.2 | ||
Character | \(\chi\) | \(=\) | 2100.493 |
Dual form | 2100.2.ce.e.1657.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.258819 | − | 0.965926i | −0.149429 | − | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70817 | − | 2.02043i | 0.645628 | − | 0.763652i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.21556 | − | 2.10542i | 0.366506 | − | 0.634808i | −0.622510 | − | 0.782612i | \(-0.713887\pi\) |
0.989017 | + | 0.147804i | \(0.0472204\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.728866 | − | 0.728866i | 0.202151 | − | 0.202151i | −0.598770 | − | 0.800921i | \(-0.704344\pi\) |
0.800921 | + | 0.598770i | \(0.204344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.33552 | − | 1.96555i | 1.77913 | − | 0.476715i | 0.788702 | − | 0.614776i | \(-0.210753\pi\) |
0.990424 | + | 0.138060i | \(0.0440867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.84965 | + | 3.20369i | 0.424339 | + | 0.734977i | 0.996358 | − | 0.0852629i | \(-0.0271730\pi\) |
−0.572019 | + | 0.820240i | \(0.693840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.39370 | − | 1.12704i | −0.522347 | − | 0.245940i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.759994 | + | 2.83634i | −0.158470 | + | 0.591417i | 0.840313 | + | 0.542101i | \(0.182371\pi\) |
−0.998783 | + | 0.0493165i | \(0.984296\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.99120i | 0.369757i | 0.982761 | + | 0.184878i | \(0.0591891\pi\) | ||||
−0.982761 | + | 0.184878i | \(0.940811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.02262 | + | 3.47716i | 1.08169 | + | 0.624517i | 0.931353 | − | 0.364117i | \(-0.118629\pi\) |
0.150342 | + | 0.988634i | \(0.451963\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.34829 | − | 0.629222i | −0.408785 | − | 0.109534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.22068 | − | 2.20273i | −1.35147 | − | 0.362126i | −0.490794 | − | 0.871276i | \(-0.663293\pi\) |
−0.860678 | + | 0.509150i | \(0.829960\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.892675 | − | 0.515386i | −0.142942 | − | 0.0825278i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.08701i | − | 0.169762i | −0.996391 | − | 0.0848810i | \(-0.972949\pi\) | ||
0.996391 | − | 0.0848810i | \(-0.0270510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.91785 | − | 5.91785i | −0.902464 | − | 0.902464i | 0.0931848 | − | 0.995649i | \(-0.470295\pi\) |
−0.995649 | + | 0.0931848i | \(0.970295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.28906 | − | 4.81085i | 0.188029 | − | 0.701735i | −0.805932 | − | 0.592007i | \(-0.798336\pi\) |
0.993962 | − | 0.109727i | \(-0.0349978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.16431 | − | 6.90249i | −0.166329 | − | 0.986070i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.79715 | − | 6.57685i | −0.531707 | − | 0.920943i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.56972 | − | 1.76035i | 0.902420 | − | 0.241803i | 0.222365 | − | 0.974964i | \(-0.428622\pi\) |
0.680055 | + | 0.733161i | \(0.261956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.61580 | − | 2.61580i | 0.346472 | − | 0.346472i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.39403 | + | 2.41454i | −0.181488 | + | 0.314346i | −0.942387 | − | 0.334523i | \(-0.891425\pi\) |
0.760900 | + | 0.648870i | \(0.224758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.217574 | − | 0.125616i | 0.0278575 | − | 0.0160835i | −0.486007 | − | 0.873955i | \(-0.661547\pi\) |
0.513864 | + | 0.857872i | \(0.328214\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.469102 | + | 2.60383i | −0.0591013 | + | 0.328052i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.08758 | + | 7.79096i | 0.255039 | + | 0.951818i | 0.968069 | + | 0.250684i | \(0.0806556\pi\) |
−0.713030 | + | 0.701133i | \(0.752678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.93639 | 0.353500 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5737 | 1.72958 | 0.864790 | − | 0.502133i | \(-0.167451\pi\) | ||||
0.864790 | + | 0.502133i | \(0.167451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.73216 | − | 6.46450i | −0.202734 | − | 0.756612i | −0.990128 | − | 0.140163i | \(-0.955237\pi\) |
0.787395 | − | 0.616449i | \(-0.211429\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.17747 | − | 6.05238i | −0.248146 | − | 0.689733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.54459 | − | 5.51057i | 1.07385 | − | 0.619987i | 0.144619 | − | 0.989487i | \(-0.453804\pi\) |
0.929231 | + | 0.369500i | \(0.120471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.90994 | + | 9.90994i | −1.08776 | + | 1.08776i | −0.0919976 | + | 0.995759i | \(0.529325\pi\) |
−0.995759 | + | 0.0919976i | \(0.970675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.92335 | − | 0.515361i | 0.206205 | − | 0.0552525i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.81468 | − | 10.0713i | −0.616354 | − | 1.06756i | −0.990145 | − | 0.140044i | \(-0.955276\pi\) |
0.373791 | − | 0.927513i | \(-0.378058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.227598 | − | 2.71765i | −0.0238587 | − | 0.284887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.79991 | − | 6.71736i | 0.186642 | − | 0.696558i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8833 | − | 10.8833i | −1.10503 | − | 1.10503i | −0.993794 | − | 0.111236i | \(-0.964519\pi\) |
−0.111236 | − | 0.993794i | \(-0.535481\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.43113i | 0.244338i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.44655 | + | 3.14457i | 0.541952 | + | 0.312896i | 0.745870 | − | 0.666092i | \(-0.232034\pi\) |
−0.203918 | + | 0.978988i | \(0.565367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5741 | − | 3.90512i | −1.43603 | − | 0.384782i | −0.544887 | − | 0.838510i | \(-0.683427\pi\) |
−0.891141 | + | 0.453727i | \(0.850094\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1277 | + | 3.78551i | 1.36578 | + | 0.365960i | 0.865935 | − | 0.500156i | \(-0.166724\pi\) |
0.499844 | + | 0.866115i | \(0.333391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3565 | − | 5.97935i | −0.991976 | − | 0.572718i | −0.0861118 | − | 0.996285i | \(-0.527444\pi\) |
−0.905864 | + | 0.423568i | \(0.860778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.51068i | 0.807798i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.10715 | + | 5.10715i | 0.480441 | + | 0.480441i | 0.905272 | − | 0.424832i | \(-0.139667\pi\) |
−0.424832 | + | 0.905272i | \(0.639667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.266783 | + | 0.995650i | −0.0246641 | + | 0.0920478i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.55907 | − | 18.1784i | 0.784609 | − | 1.66641i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54481 | + | 4.40773i | 0.231346 | + | 0.400703i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.04997 | + | 0.281338i | −0.0946724 | + | 0.0253674i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0263367 | − | 0.0263367i | 0.00233701 | − | 0.00233701i | −0.705937 | − | 0.708274i | \(-0.749474\pi\) |
0.708274 | + | 0.705937i | \(0.249474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.18455 | + | 7.24786i | −0.368429 | + | 0.638138i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.58485 | − | 4.95646i | 0.750062 | − | 0.433048i | −0.0756546 | − | 0.997134i | \(-0.524105\pi\) |
0.825716 | + | 0.564086i | \(0.190771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.63237 | + | 1.73535i | 0.835232 | + | 0.150474i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.71987 | − | 13.8828i | −0.317810 | − | 1.18608i | −0.921345 | − | 0.388747i | \(-0.872908\pi\) |
0.603535 | − | 0.797337i | \(-0.293759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0917 | −0.940787 | −0.470394 | − | 0.882457i | \(-0.655888\pi\) | ||||
−0.470394 | + | 0.882457i | \(0.655888\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.98056 | −0.419439 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.648585 | − | 2.42055i | −0.0542374 | − | 0.202417i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.36595 | + | 2.91113i | −0.525055 | + | 0.240106i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.66332 | − | 4.42442i | 0.627804 | − | 0.362463i | −0.152097 | − | 0.988366i | \(-0.548603\pi\) |
0.779901 | + | 0.625903i | \(0.215269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.901062 | + | 1.56068i | −0.0733274 | + | 0.127007i | −0.900358 | − | 0.435151i | \(-0.856695\pi\) |
0.827030 | + | 0.562157i | \(0.190028\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.36998 | + | 5.36998i | −0.434137 | + | 0.434137i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0832 | − | 2.96972i | 0.884532 | − | 0.237010i | 0.212171 | − | 0.977233i | \(-0.431947\pi\) |
0.672361 | + | 0.740223i | \(0.265280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.40074 | − | 5.89025i | −0.269696 | − | 0.467127i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.43243 | + | 6.38047i | 0.349325 | + | 0.502851i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0813198 | − | 0.303489i | 0.00636946 | − | 0.0237711i | −0.962668 | − | 0.270685i | \(-0.912750\pi\) |
0.969037 | + | 0.246914i | \(0.0794165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.10159 | − | 2.10159i | −0.162626 | − | 0.162626i | 0.621103 | − | 0.783729i | \(-0.286685\pi\) |
−0.783729 | + | 0.621103i | \(0.786685\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9375i | 0.918270i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.20369 | − | 1.84965i | −0.244992 | − | 0.141446i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.48720 | − | 2.54209i | −0.721298 | − | 0.193271i | −0.120547 | − | 0.992708i | \(-0.538465\pi\) |
−0.600751 | + | 0.799436i | \(0.705132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.69307 | + | 0.721606i | 0.202423 | + | 0.0542392i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8512 | − | 9.15169i | −1.18477 | − | 0.684030i | −0.227660 | − | 0.973741i | \(-0.573107\pi\) |
−0.957114 | + | 0.289711i | \(0.906441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.1817i | − | 1.50009i | −0.661387 | − | 0.750045i | \(-0.730032\pi\) | ||
0.661387 | − | 0.750045i | \(-0.269968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.177648 | − | 0.177648i | −0.0131321 | − | 0.0131321i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.77850 | − | 17.8336i | 0.349439 | − | 1.30412i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.63652 | − | 0.220803i | 0.191779 | − | 0.0160611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.24147 | − | 2.15029i | −0.0898297 | − | 0.155590i | 0.817609 | − | 0.575773i | \(-0.195299\pi\) |
−0.907439 | + | 0.420184i | \(0.861966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8390 | − | 3.44019i | 0.924169 | − | 0.247630i | 0.234802 | − | 0.972043i | \(-0.424556\pi\) |
0.689366 | + | 0.724413i | \(0.257889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.45204 | − | 5.45204i | 0.388442 | − | 0.388442i | −0.485690 | − | 0.874131i | \(-0.661431\pi\) |
0.874131 | + | 0.485690i | \(0.161431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.32953 | + | 10.9631i | −0.448689 | + | 0.777152i | −0.998301 | − | 0.0582681i | \(-0.981442\pi\) |
0.549612 | + | 0.835420i | \(0.314776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.98519 | − | 4.03290i | 0.492697 | − | 0.284459i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.02309 | + | 3.40131i | 0.282366 | + | 0.238725i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.759994 | − | 2.83634i | −0.0528233 | − | 0.197139i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.99349 | 0.622093 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.37636 | −0.370124 | −0.185062 | − | 0.982727i | \(-0.559249\pi\) | ||||
−0.185062 | + | 0.982727i | \(0.559249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.77195 | − | 14.0771i | −0.258450 | − | 0.964548i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.3130 | − | 6.22872i | 1.17529 | − | 0.422833i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.79591 | + | 3.34627i | −0.391651 | + | 0.226120i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.91399 | − | 6.77924i | 0.263284 | − | 0.456021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2847 | + | 17.2847i | −1.15747 | + | 1.15747i | −0.172452 | + | 0.985018i | \(0.555169\pi\) |
−0.985018 | + | 0.172452i | \(0.944831\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.81901 | − | 0.487401i | 0.120732 | − | 0.0323499i | −0.197947 | − | 0.980213i | \(-0.563427\pi\) |
0.318679 | + | 0.947863i | \(0.396761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5383 | + | 21.7171i | 0.828557 | + | 1.43510i | 0.899170 | + | 0.437600i | \(0.144171\pi\) |
−0.0706123 | + | 0.997504i | \(0.522495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.28258 | + | 3.66975i | −0.347568 | + | 0.241452i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.80563 | − | 21.6669i | 0.380340 | − | 1.41945i | −0.465044 | − | 0.885287i | \(-0.653962\pi\) |
0.845384 | − | 0.534159i | \(-0.179372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.79312 | − | 7.79312i | −0.506218 | − | 0.506218i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.38917i | 0.413281i | 0.978417 | + | 0.206641i | \(0.0662531\pi\) | ||||
−0.978417 | + | 0.206641i | \(0.933747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1337 | − | 9.31479i | −1.03926 | − | 0.600018i | −0.119638 | − | 0.992818i | \(-0.538173\pi\) |
−0.919624 | + | 0.392799i | \(0.871507\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.965926 | − | 0.258819i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.68321 | + | 0.986914i | 0.234357 | + | 0.0627958i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.1371 | + | 7.00738i | 0.769160 | + | 0.444075i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 31.5776i | 1.99316i | 0.0826181 | + | 0.996581i | \(0.473672\pi\) | ||||
−0.0826181 | + | 0.996581i | \(0.526328\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.04786 | + | 5.04786i | 0.317356 | + | 0.317356i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.81126 | + | 17.9559i | −0.300118 | + | 1.12006i | 0.636949 | + | 0.770906i | \(0.280196\pi\) |
−0.937067 | + | 0.349150i | \(0.886470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.4928 | + | 12.8467i | −1.14909 | + | 0.798256i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.995601 | − | 1.72443i | −0.0616261 | − | 0.106740i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.52178 | + | 1.47956i | −0.340488 | + | 0.0912334i | −0.425011 | − | 0.905188i | \(-0.639730\pi\) |
0.0845235 | + | 0.996421i | \(0.473063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.22319 | + | 8.22319i | −0.503251 | + | 0.503251i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.22482 | − | 2.12145i | 0.0746785 | − | 0.129347i | −0.826268 | − | 0.563277i | \(-0.809540\pi\) |
0.900946 | + | 0.433930i | \(0.142874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.9156 | + | 12.6530i | −1.33128 | + | 0.768613i | −0.985495 | − | 0.169702i | \(-0.945720\pi\) |
−0.345782 | + | 0.938315i | \(0.612386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.56614 | + | 0.923223i | −0.155310 | + | 0.0558760i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.27697 | + | 30.8901i | 0.497315 | + | 1.85600i | 0.516660 | + | 0.856191i | \(0.327175\pi\) |
−0.0193451 | + | 0.999813i | \(0.506158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.95433 | −0.416345 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3044 | 0.734020 | 0.367010 | − | 0.930217i | \(-0.380382\pi\) | ||||
0.367010 | + | 0.930217i | \(0.380382\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.584999 | − | 2.18325i | −0.0347746 | − | 0.129780i | 0.946356 | − | 0.323125i | \(-0.104733\pi\) |
−0.981131 | + | 0.193344i | \(0.938067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.19623 | − | 1.85679i | −0.129639 | − | 0.109603i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.2241 | − | 20.3366i | 2.07201 | − | 1.19627i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.69564 | + | 13.3292i | −0.451126 | + | 0.781374i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.19458 | − | 3.19458i | 0.186629 | − | 0.186629i | −0.607608 | − | 0.794237i | \(-0.707871\pi\) |
0.794237 | + | 0.607608i | \(0.207871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.34829 | − | 0.629222i | 0.136262 | − | 0.0365112i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.51338 | + | 2.62124i | 0.0875208 | + | 0.151590i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0653 | + | 1.84793i | −1.27182 | + | 0.106513i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.62775 | − | 6.07484i | 0.0935117 | − | 0.348990i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.74597 | + | 5.74597i | 0.327940 | + | 0.327940i | 0.851803 | − | 0.523863i | \(-0.175510\pi\) |
−0.523863 | + | 0.851803i | \(0.675510\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0882i | 0.858338i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5238 | + | 7.23064i | 0.710161 | + | 0.410012i | 0.811121 | − | 0.584879i | \(-0.198858\pi\) |
−0.100959 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.14185 | + | 0.305958i | 0.0645412 | + | 0.0172938i | 0.290945 | − | 0.956740i | \(-0.406030\pi\) |
−0.226404 | + | 0.974033i | \(0.572697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.53996 | − | 2.28828i | −0.479652 | − | 0.128522i | 0.0108885 | − | 0.999941i | \(-0.496534\pi\) |
−0.490541 | + | 0.871418i | \(0.663201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.19231 | + | 2.42043i | 0.234725 | + | 0.135518i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 14.6261i | − | 0.816350i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.8652 | + | 19.8652i | 1.10533 | + | 1.10533i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.09514 | + | 11.5512i | −0.171162 | + | 0.638784i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.51807 | − | 10.8222i | −0.414484 | − | 0.596649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9304 | − | 18.9320i | −0.600789 | − | 1.04060i | −0.992702 | − | 0.120595i | \(-0.961520\pi\) |
0.391913 | − | 0.920002i | \(-0.371814\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.22068 | − | 2.20273i | 0.450491 | − | 0.120709i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0987 | + | 18.0987i | −0.985900 | + | 0.985900i | −0.999902 | − | 0.0140019i | \(-0.995543\pi\) |
0.0140019 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.61130 | − | 6.25496i | 0.196139 | − | 0.339723i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6418 | − | 8.45343i | 0.792896 | − | 0.457779i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9349 | − | 9.43823i | −0.860402 | − | 0.509617i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.08442 | + | 4.04711i | 0.0582148 | + | 0.217261i | 0.988905 | − | 0.148547i | \(-0.0474596\pi\) |
−0.930691 | + | 0.365807i | \(0.880793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.8258 | −1.81065 | −0.905327 | − | 0.424715i | \(-0.860374\pi\) | ||||
−0.905327 | + | 0.424715i | \(0.860374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.03077 | 0.0550186 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.70598 | + | 32.4911i | 0.463372 | + | 1.72933i | 0.662230 | + | 0.749301i | \(0.269610\pi\) |
−0.198857 | + | 0.980028i | \(0.563723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.7743 | − | 3.56250i | −1.04657 | − | 0.188548i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0177 | − | 8.09313i | 0.739826 | − | 0.427139i | −0.0821800 | − | 0.996618i | \(-0.526188\pi\) |
0.822006 | + | 0.569479i | \(0.192855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.65757 | − | 4.60305i | 0.139872 | − | 0.242266i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.59890 | − | 3.59890i | 0.188893 | − | 0.188893i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6293 | + | 4.18786i | −0.815842 | + | 0.218604i | −0.642528 | − | 0.766262i | \(-0.722114\pi\) |
−0.173314 | + | 0.984867i | \(0.555448\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.543504 | + | 0.941376i | 0.0282937 | + | 0.0490061i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.66553 | − | 16.2807i | 0.397974 | − | 0.845250i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.962517 | − | 3.59216i | 0.0498372 | − | 0.185995i | −0.936520 | − | 0.350614i | \(-0.885973\pi\) |
0.986357 | + | 0.164619i | \(0.0526395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.45132 | + | 1.45132i | 0.0747467 | + | 0.0747467i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.149127i | 0.00766015i | 0.999993 | + | 0.00383007i | \(0.00121915\pi\) | ||||
−0.999993 | + | 0.00383007i | \(0.998781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0322558 | − | 0.0186229i | −0.00165251 | − | 0.000954080i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.4767 | + | 8.97006i | 1.71058 | + | 0.458349i | 0.975567 | − | 0.219703i | \(-0.0705089\pi\) |
0.735014 | + | 0.678052i | \(0.237176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.08394 | + | 2.16608i | 0.410930 | + | 0.110108i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.3146 | + | 16.3474i | 1.43561 | + | 0.828847i | 0.997540 | − | 0.0700961i | \(-0.0223306\pi\) |
0.438065 | + | 0.898943i | \(0.355664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.2998i | 1.12775i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.00950 | − | 7.00950i | −0.353582 | − | 0.353582i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.73087 | + | 17.6559i | −0.237436 | + | 0.886122i | 0.739600 | + | 0.673047i | \(0.235015\pi\) |
−0.977036 | + | 0.213076i | \(0.931652\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.816819 | − | 9.75330i | −0.0408921 | − | 0.488276i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.590882 | − | 1.02344i | −0.0295072 | − | 0.0511080i | 0.850895 | − | 0.525336i | \(-0.176060\pi\) |
−0.880402 | + | 0.474228i | \(0.842727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.92407 | − | 1.85530i | 0.344913 | − | 0.0924190i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6304 | + | 14.6304i | −0.725203 | + | 0.725203i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.11235 | − | 14.0510i | 0.401130 | − | 0.694777i | −0.592733 | − | 0.805399i | \(-0.701951\pi\) |
0.993863 | + | 0.110622i | \(0.0352843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4469 | + | 7.18624i | −0.613962 | + | 0.354471i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.49717 | + | 6.94100i | 0.122878 | + | 0.341544i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.87075 | + | 10.7138i | 0.140581 | + | 0.524656i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.4289 | −0.753750 | −0.376875 | − | 0.926264i | \(-0.623001\pi\) | ||||
−0.376875 | + | 0.926264i | \(0.623001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6085 | 1.29682 | 0.648409 | − | 0.761292i | \(-0.275435\pi\) | ||||
0.648409 | + | 0.761292i | \(0.275435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.28906 | + | 4.81085i | 0.0626764 | + | 0.233912i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.117854 | − | 0.654167i | 0.00570335 | − | 0.0316574i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.17021 | + | 1.25297i | −0.104779 | + | 0.0604940i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.83304 | + | 3.17492i | −0.0882944 | + | 0.152930i | −0.906790 | − | 0.421582i | \(-0.861475\pi\) |
0.818496 | + | 0.574512i | \(0.194808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.74318 | − | 9.74318i | 0.468227 | − | 0.468227i | −0.433112 | − | 0.901340i | \(-0.642585\pi\) |
0.901340 | + | 0.433112i | \(0.142585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.4925 | + | 2.81145i | −0.501923 | + | 0.134490i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00918 | + | 5.21204i | 0.143620 | + | 0.248757i | 0.928857 | − | 0.370438i | \(-0.120792\pi\) |
−0.785237 | + | 0.619195i | \(0.787459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.45956 | + | 5.39558i | 0.212360 | + | 0.256932i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25355 | + | 19.6065i | −0.249604 | + | 0.931534i | 0.721410 | + | 0.692509i | \(0.243495\pi\) |
−0.971013 | + | 0.239025i | \(0.923172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.25708 | − | 6.25708i | −0.295950 | − | 0.295950i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7251i | 0.600534i | 0.953855 | + | 0.300267i | \(0.0970758\pi\) | ||||
−0.953855 | + | 0.300267i | \(0.902924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.28861 | − | 1.32133i | −0.107766 | − | 0.0622189i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.74072 | + | 0.466424i | 0.0817860 | + | 0.0219145i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.1623 | − | 8.08197i | −1.41093 | − | 0.378058i | −0.528675 | − | 0.848824i | \(-0.677311\pi\) |
−0.882258 | + | 0.470766i | \(0.843978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.57685 | + | 3.79715i | 0.306981 | + | 0.177236i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4059i | 1.09012i | 0.838397 | + | 0.545060i | \(0.183493\pi\) | ||||
−0.838397 | + | 0.545060i | \(0.816507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.8382 | + | 16.8382i | 0.782539 | + | 0.782539i | 0.980259 | − | 0.197720i | \(-0.0633537\pi\) |
−0.197720 | + | 0.980259i | \(0.563354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0990 | + | 37.6898i | −0.467324 | + | 1.74408i | 0.181744 | + | 0.983346i | \(0.441826\pi\) |
−0.649068 | + | 0.760730i | \(0.724841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3071 | + | 9.09048i | 0.891518 | + | 0.419759i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.73706 | − | 9.93688i | −0.264350 | − | 0.457867i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.6531 | + | 5.26603i | −0.903650 | + | 0.242132i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.80937 | + | 4.80937i | −0.220206 | + | 0.220206i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.66084 | − | 13.2690i | 0.350033 | − | 0.606275i | −0.636222 | − | 0.771506i | \(-0.719504\pi\) |
0.986255 | + | 0.165231i | \(0.0528371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.59727 | + | 4.38628i | −0.346406 | + | 0.199997i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.01586 | − | 5.93279i | 0.228230 | − | 0.269951i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.32465 | + | 16.1398i | 0.195968 | + | 0.731364i | 0.992014 | + | 0.126127i | \(0.0402548\pi\) |
−0.796046 | + | 0.605237i | \(0.793079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.314195 | −0.0142084 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.188878 | 0.00852393 | 0.00426196 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426196 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.91380 | + | 14.6065i | 0.176269 | + | 0.657844i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.8944 | − | 29.4452i | 1.11667 | − | 1.32080i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1410 | + | 7.00959i | −0.543504 | + | 0.313792i | −0.746498 | − | 0.665388i | \(-0.768266\pi\) |
0.202994 | + | 0.979180i | \(0.434933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.48605 | + | 2.57391i | −0.0663917 | + | 0.114994i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0052 | − | 20.0052i | 0.891989 | − | 0.891989i | −0.102721 | − | 0.994710i | \(-0.532755\pi\) |
0.994710 | + | 0.102721i | \(0.0327549\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5307 | − | 3.08965i | 0.512098 | − | 0.137216i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.58364 | − | 11.4032i | −0.291815 | − | 0.505438i | 0.682424 | − | 0.730956i | \(-0.260926\pi\) |
−0.974239 | + | 0.225518i | \(0.927592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0199 | − | 7.54276i | −0.708679 | − | 0.333672i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.957451 | + | 3.57325i | −0.0422725 | + | 0.157763i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.56192 | − | 8.56192i | −0.376553 | − | 0.376553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.82187i | 0.431132i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.6255 | − | 13.0628i | −0.991242 | − | 0.572294i | −0.0855965 | − | 0.996330i | \(-0.527280\pi\) |
−0.905645 | + | 0.424036i | \(0.860613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.53573 | + | 1.48330i | 0.242061 | + | 0.0648600i | 0.377810 | − | 0.925883i | \(-0.376677\pi\) |
−0.135749 | + | 0.990743i | \(0.543344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.0136 | + | 13.6691i | 2.22219 | + | 0.595434i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4514 | + | 7.18880i | 0.541364 | + | 0.312556i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.78807i | − | 0.120992i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.792283 | − | 0.792283i | −0.0343176 | − | 0.0343176i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.73727 | + | 17.6797i | −0.204428 | + | 0.762936i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.9479 | − | 5.93907i | −0.686926 | − | 0.255814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1293 | − | 24.4727i | −0.607468 | − | 1.05217i | −0.991656 | − | 0.128910i | \(-0.958852\pi\) |
0.384188 | − | 0.923255i | \(-0.374481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.4940 | + | 5.22340i | −0.836567 | + | 0.224157i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0515 | + | 20.0515i | −0.857341 | + | 0.857341i | −0.991024 | − | 0.133683i | \(-0.957320\pi\) |
0.133683 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.125616 | + | 0.217574i | −0.00536117 | + | 0.00928582i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.37920 | + | 3.68303i | −0.271763 | + | 0.156902i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.17004 | − | 28.6972i | 0.219853 | − | 1.22033i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.73283 | − | 21.3952i | −0.242908 | − | 0.906544i | −0.974423 | − | 0.224720i | \(-0.927853\pi\) |
0.731516 | − | 0.681825i | \(-0.238813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.62664 | −0.364868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.4627 | −0.779496 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.337839 | + | 1.26083i | 0.0142382 | + | 0.0531378i | 0.972679 | − | 0.232152i | \(-0.0745768\pi\) |
−0.958441 | + | 0.285290i | \(0.907910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.895662 | − | 2.48954i | −0.0376143 | − | 0.104551i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.426999 | + | 0.246528i | −0.0179007 | + | 0.0103350i | −0.508924 | − | 0.860812i | \(-0.669956\pi\) |
0.491023 | + | 0.871147i | \(0.336623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.79895 | + | 3.11588i | −0.0752839 | + | 0.130395i | −0.901210 | − | 0.433383i | \(-0.857320\pi\) |
0.825926 | + | 0.563779i | \(0.190653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.75571 | + | 1.75571i | −0.0733456 | + | 0.0733456i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2308 | − | 3.27724i | 0.509177 | − | 0.136433i | 0.00492102 | − | 0.999988i | \(-0.498434\pi\) |
0.504256 | + | 0.863554i | \(0.331767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.64594 | − | 11.5111i | −0.276196 | − | 0.478385i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.09451 | + | 36.9502i | 0.128382 | + | 1.53295i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.27964 | − | 15.9718i | 0.177245 | − | 0.661486i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.84683 | − | 2.84683i | −0.117501 | − | 0.117501i | 0.645911 | − | 0.763413i | \(-0.276478\pi\) |
−0.763413 | + | 0.645911i | \(0.776478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.7262i | 1.06003i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.67736 | − | 3.85517i | −0.274670 | − | 0.158581i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.7485 | + | 8.23903i | 1.26269 | + | 0.338336i | 0.827226 | − | 0.561870i | \(-0.189918\pi\) |
0.435463 | + | 0.900206i | \(0.356585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.2277 | + | 3.27641i | 0.500447 | + | 0.134094i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.3274 | + | 19.2416i | 1.36172 | + | 0.786191i | 0.989853 | − | 0.142095i | \(-0.0453837\pi\) |
0.371869 | + | 0.928285i | \(0.378717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.6842i | 1.86350i | 0.363102 | + | 0.931750i | \(0.381718\pi\) | ||||
−0.363102 | + | 0.931750i | \(0.618282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.70338 | − | 5.70338i | −0.232260 | − | 0.232260i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.42220 | − | 23.9680i | 0.260669 | − | 0.972831i | −0.704179 | − | 0.710023i | \(-0.748685\pi\) |
0.964848 | − | 0.262808i | \(-0.0846487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.24416 | − | 4.76633i | 0.0909381 | − | 0.193141i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.56691 | − | 4.44602i | −0.103846 | − | 0.179867i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.06899 | − | 0.286436i | 0.0431762 | − | 0.0115690i | −0.237166 | − | 0.971469i | \(-0.576219\pi\) |
0.280343 | + | 0.959900i | \(0.409552\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.353089 | − | 0.353089i | 0.0142148 | − | 0.0142148i | −0.699964 | − | 0.714178i | \(-0.746800\pi\) |
0.714178 | + | 0.699964i | \(0.246800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6067 | − | 20.1034i | 0.466513 | − | 0.808024i | −0.532756 | − | 0.846269i | \(-0.678844\pi\) |
0.999268 | + | 0.0382453i | \(0.0121768\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.54299 | + | 1.46820i | −0.102047 | + | 0.0589167i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.2809 | − | 5.45536i | −1.21318 | − | 0.218564i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.32769 | − | 8.68704i | −0.0929588 | − | 0.346927i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −64.6326 | −2.57707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8761 | 0.751445 | 0.375723 | − | 0.926732i | \(-0.377395\pi\) | ||||
0.375723 | + | 0.926732i | \(0.377395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.39150 | + | 5.19316i | 0.0553073 | + | 0.206410i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.87961 | − | 4.18237i | −0.232959 | − | 0.165712i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.6212 | + | 7.28685i | −0.499287 | + | 0.288263i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.7675 | − | 32.5062i | 0.741271 | − | 1.28392i | −0.210646 | − | 0.977562i | \(-0.567557\pi\) |
0.951917 | − | 0.306356i | \(-0.0991099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0570 | + | 12.0570i | −0.475483 | + | 0.475483i | −0.903684 | − | 0.428201i | \(-0.859148\pi\) |
0.428201 | + | 0.903684i | \(0.359148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0130 | + | 4.82656i | −0.708163 | + | 0.189752i | −0.594884 | − | 0.803812i | \(-0.702802\pi\) |
−0.113279 | + | 0.993563i | \(0.536135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.38908 | + | 5.87006i | 0.133033 | + | 0.230420i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4974 | − | 15.1110i | −0.411427 | − | 0.592247i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.34601 | − | 16.2195i | 0.170073 | − | 0.634719i | −0.827266 | − | 0.561810i | \(-0.810105\pi\) |
0.997339 | − | 0.0729090i | \(-0.0232283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.73234 | + | 4.73234i | 0.184626 | + | 0.184626i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.4270i | 1.84749i | 0.383005 | + | 0.923746i | \(0.374889\pi\) | ||||
−0.383005 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5554 | + | 6.09418i | 0.410558 | + | 0.237036i | 0.691030 | − | 0.722826i | \(-0.257157\pi\) |
−0.280471 | + | 0.959862i | \(0.590491\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.56125 | − | 2.02603i | −0.293655 | − | 0.0786846i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.64772 | − | 1.51330i | −0.218681 | − | 0.0585953i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.1694 | + | 12.2221i | 0.818455 | + | 0.472535i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 0.610779i | − | 0.0235789i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.19597 | − | 1.19597i | −0.0461011 | − | 0.0461011i | 0.683680 | − | 0.729782i | \(-0.260378\pi\) |
−0.729782 | + | 0.683680i | \(0.760378\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.45115 | − | 9.14780i | 0.0942052 | − | 0.351578i | −0.902693 | − | 0.430286i | \(-0.858413\pi\) |
0.996898 | + | 0.0787076i | \(0.0250794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40.5794 | + | 3.39845i | −1.55730 | + | 0.130420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.941587 | − | 1.63088i | −0.0360817 | − | 0.0624953i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7804 | + | 5.56809i | −0.795139 | + | 0.213057i | −0.633449 | − | 0.773785i | \(-0.718361\pi\) |
−0.161690 | + | 0.986842i | \(0.551695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7319 | − | 17.7319i | 0.676514 | − | 0.676514i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.50538 | − | 6.07150i | 0.133544 | − | 0.231306i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.42242 | − | 3.13064i | 0.206279 | − | 0.119095i | −0.393302 | − | 0.919409i | \(-0.628667\pi\) |
0.599581 | + | 0.800314i | \(0.295334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.91193 | + | 4.15278i | 0.186589 | + | 0.157751i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.13656 | − | 7.97377i | −0.0809281 | − | 0.302028i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.4312 | −0.848427 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.6155 | −1.57180 | −0.785899 | − | 0.618355i | \(-0.787799\pi\) | ||||
−0.785899 | + | 0.618355i | \(0.787799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.14855 | − | 30.4108i | −0.307328 | − | 1.14697i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.6570 | − | 5.63294i | 0.588843 | − | 0.211848i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.279672 | − | 0.161469i | 0.0105033 | − | 0.00606409i | −0.494739 | − | 0.869042i | \(-0.664736\pi\) |
0.505242 | + | 0.862977i | \(0.331403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.51057 | + | 9.54459i | −0.206662 | + | 0.357950i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.4396 | + | 14.4396i | −0.540766 | + | 0.540766i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.17147 | − | 1.65364i | 0.230478 | − | 0.0617563i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1034 | + | 17.4996i | 0.376792 | + | 0.652623i | 0.990594 | − | 0.136837i | \(-0.0436938\pi\) |
−0.613801 | + | 0.789460i | \(0.710360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.7851 | + | 22.7754i | −1.22098 | + | 0.848199i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.82169 | + | 17.9948i | −0.179321 | + | 0.669234i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.29844 | + | 3.29844i | 0.122332 | + | 0.122332i | 0.765622 | − | 0.643290i | \(-0.222431\pi\) |
−0.643290 | + | 0.765622i | \(0.722431\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.0424 | − | 31.7787i | −2.03582 | − | 1.17538i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6701 | − | 3.93084i | −0.541852 | − | 0.145189i | −0.0224964 | − | 0.999747i | \(-0.507161\pi\) |
−0.519356 | + | 0.854558i | \(0.673828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.9408 | + | 5.07518i | 0.697695 | + | 0.186947i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.6624 | + | 9.04272i | 0.576153 | + | 0.332642i | 0.759603 | − | 0.650387i | \(-0.225393\pi\) |
−0.183450 | + | 0.983029i | \(0.558727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.81314i | − | 0.140079i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.73236 | + | 4.73236i | 0.173613 | + | 0.173613i | 0.788565 | − | 0.614952i | \(-0.210824\pi\) |
−0.614952 | + | 0.788565i | \(0.710824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.62729 | − | 13.5372i | 0.132716 | − | 0.495301i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.7810 | − | 22.0778i | 1.16125 | − | 0.806707i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.6070 | + | 39.1564i | 0.824940 | + | 1.42884i | 0.901965 | + | 0.431809i | \(0.142124\pi\) |
−0.0770253 | + | 0.997029i | \(0.524542\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.5017 | − | 8.17289i | 1.11154 | − | 0.297837i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.8934 | + | 13.8934i | −0.504964 | + | 0.504964i | −0.912976 | − | 0.408012i | \(-0.866222\pi\) |
0.408012 | + | 0.912976i | \(0.366222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.56938 | − | 6.18234i | 0.129560 | − | 0.224405i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.4013 | + | 12.9334i | −0.812046 | + | 0.468835i | −0.847666 | − | 0.530531i | \(-0.821993\pi\) |
0.0356201 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.7716 | + | 10.7109i | −1.07780 | + | 0.387762i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.743811 | + | 2.77594i | 0.0268575 | + | 0.100233i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.97934 | −0.143499 | −0.0717493 | − | 0.997423i | \(-0.522858\pi\) | ||||
−0.0717493 | + | 0.997423i | \(0.522858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5893 | 0.669476 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.53332 | + | 28.1147i | 0.270955 | + | 1.01122i | 0.958504 | + | 0.285079i | \(0.0920198\pi\) |
−0.687549 | + | 0.726138i | \(0.741314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.1953 | + | 14.5377i | 0.616876 | + | 0.521537i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.48244 | − | 2.01059i | 0.124771 | − | 0.0720367i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.7153 | − | 30.6838i | 0.633903 | − | 1.09795i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.40799 | + | 1.40799i | −0.0503175 | + | 0.0503175i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.3783 | + | 7.87190i | −1.04722 | + | 0.280603i | −0.741104 | − | 0.671390i | \(-0.765698\pi\) |
−0.306120 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.85829 | + | 4.95070i | 0.101758 | + | 0.176249i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.0426 | − | 1.59477i | 0.677075 | − | 0.0567037i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0670247 | − | 0.250140i | 0.00238012 | − | 0.00888272i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.04054 | − | 4.04054i | −0.143123 | − | 0.143123i | 0.631915 | − | 0.775038i | \(-0.282269\pi\) |
−0.775038 | + | 0.631915i | \(0.782269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 37.8238i | − | 1.33811i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0713 | + | 5.81468i | 0.355852 | + | 0.205451i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.7160 | − | 4.21110i | −0.554607 | − | 0.148606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.36617 | − | 0.634013i | −0.0832931 | − | 0.0223183i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.9488 | − | 21.9098i | −1.33421 | − | 0.770306i | −0.348268 | − | 0.937395i | \(-0.613230\pi\) |
−0.985942 | + | 0.167089i | \(0.946563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.74791i | 0.0613774i | 0.999529 | + | 0.0306887i | \(0.00977005\pi\) | ||||
−0.999529 | + | 0.0306887i | \(0.990230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8940 | + | 17.8940i | 0.627570 | + | 0.627570i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.01301 | − | 29.9049i | 0.280340 | − | 1.04624i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.55593 | + | 2.23976i | 0.0543687 | + | 0.0782635i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5210 | + | 23.4191i | 0.471886 | + | 0.817331i | 0.999483 | − | 0.0321643i | \(-0.0102400\pi\) |
−0.527596 | + | 0.849495i | \(0.676907\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50063 | + | 0.670043i | −0.0871667 | + | 0.0233562i | −0.302139 | − | 0.953264i | \(-0.597701\pi\) |
0.214972 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.3013 | + | 37.3013i | −1.29709 | + | 1.29709i | −0.366787 | + | 0.930305i | \(0.619542\pi\) |
−0.930305 | + | 0.366787i | \(0.880458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0559 | − | 33.0057i | 0.661837 | − | 1.14634i | −0.318295 | − | 0.947992i | \(-0.603110\pi\) |
0.980132 | − | 0.198344i | \(-0.0635563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.6953 | − | 15.9899i | 0.960738 | − | 0.554682i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.1080 | − | 48.3449i | −0.765996 | − | 1.67505i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.79991 | + | 6.71736i | 0.0622141 | + | 0.232186i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.2101 | 0.939398 | 0.469699 | − | 0.882827i | \(-0.344362\pi\) | ||||
0.469699 | + | 0.882827i | \(0.344362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0351 | 0.863280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.18462 | − | 11.8852i | −0.109684 | − | 0.409346i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.2525 | + | 2.38755i | 0.455361 | + | 0.0820372i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.95744 | + | 1.13013i | −0.0671793 | + | 0.0387860i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.4953 | − | 21.6426i | 0.428335 | − | 0.741898i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1745 | − | 12.1745i | 0.416848 | − | 0.416848i | −0.467268 | − | 0.884116i | \(-0.654762\pi\) |
0.884116 | + | 0.467268i | \(0.154762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.5825 | + | 8.99840i | −1.14716 | + | 0.307379i | −0.781825 | − | 0.623498i | \(-0.785711\pi\) |
−0.365331 | + | 0.930878i | \(0.619044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7607 | − | 29.0304i | −0.571869 | − | 0.990506i | −0.996374 | − | 0.0850805i | \(-0.972885\pi\) |
0.424505 | − | 0.905426i | \(-0.360448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.22510 | + | 2.60196i | −0.0417513 | + | 0.0886747i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.79609 | − | 32.8275i | 0.299422 | − | 1.11746i | −0.638219 | − | 0.769855i | \(-0.720329\pi\) |
0.937641 | − | 0.347605i | \(-0.113005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.7604 | − | 28.7604i | −0.976753 | − | 0.976753i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26.7938i | − | 0.908918i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.20014 | + | 4.15700i | 0.243967 | + | 0.140855i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.8668 | + | 3.98356i | 0.503166 | + | 0.134823i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6931 | + | 4.74085i | 0.597454 | + | 0.160087i | 0.544858 | − | 0.838529i | \(-0.316584\pi\) |
0.0525963 | + | 0.998616i | \(0.483250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.91255 | − | 2.25891i | −0.131967 | − | 0.0761911i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.5109i | − | 0.589956i | −0.955504 | − | 0.294978i | \(-0.904688\pi\) | ||
0.955504 | − | 0.294978i | \(-0.0953123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.5448 | + | 33.5448i | 1.12887 | + | 1.12887i | 0.990361 | + | 0.138510i | \(0.0442312\pi\) |
0.138510 | + | 0.990361i | \(0.455769\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.10104 | − | 26.5015i | 0.238430 | − | 0.889832i | −0.738143 | − | 0.674644i | \(-0.764297\pi\) |
0.976573 | − | 0.215188i | \(-0.0690363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.00822399 | − | 0.0981993i | −0.000275824 | − | 0.00329350i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.21556 | − | 2.10542i | −0.0407229 | − | 0.0705342i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.7968 | − | 4.76864i | 0.595547 | − | 0.159576i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.14024 | − | 2.14024i | 0.0714604 | − | 0.0714604i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.92373 | + | 11.9923i | −0.230919 | + | 0.399964i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7323 | − | 25.8262i | 1.49025 | − | 0.860395i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.49589 | + | 20.8352i | 0.249448 | + | 0.693352i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.829631 | + | 3.09623i | 0.0275475 | + | 0.102809i | 0.978331 | − | 0.207048i | \(-0.0663856\pi\) |
−0.950783 | + | 0.309857i | \(0.899719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.28914 | −0.208597 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.5087 | 1.70656 | 0.853279 | − | 0.521454i | \(-0.174610\pi\) | ||||
0.853279 | + | 0.521454i | \(0.174610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.81841 | + | 32.9107i | 0.291847 | + | 1.08919i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.65018 | − | 25.8116i | 0.153562 | − | 0.852374i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.7186 | − | 24.0862i | 1.37617 | − | 0.794531i | 0.384473 | − | 0.923136i | \(-0.374383\pi\) |
0.991696 | + | 0.128605i | \(0.0410499\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.06301 | − | 7.03734i | 0.133881 | − | 0.231888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6223 | − | 10.6223i | 0.349637 | − | 0.349637i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.5741 | − | 3.90512i | 0.478676 | − | 0.128261i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.4707 | − | 25.0639i | −0.474767 | − | 0.822321i | 0.524815 | − | 0.851216i | \(-0.324134\pi\) |
−0.999582 | + | 0.0288955i | \(0.990801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.9599 | − | 16.4973i | 0.654159 | − | 0.540677i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.74285 | − | 13.9685i | 0.122536 | − | 0.457309i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.57644 | − | 9.57644i | −0.312849 | − | 0.312849i | 0.533164 | − | 0.846012i | \(-0.321003\pi\) |
−0.846012 | + | 0.533164i | \(0.821003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.18213i | − | 0.0385774i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8414 | + | 7.99136i | 0.451218 | + | 0.260511i | 0.708344 | − | 0.705867i | \(-0.249442\pi\) |
−0.257127 | + | 0.966378i | \(0.582776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.08312 | + | 0.826119i | 0.100400 | + | 0.0269021i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.97060 | + | 2.13572i | 0.259010 | + | 0.0694015i | 0.385987 | − | 0.922504i | \(-0.373861\pi\) |
−0.126977 | + | 0.991906i | \(0.540528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.97426 | − | 3.44924i | −0.193933 | − | 0.111967i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.84122i | 0.286696i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.2246 | − | 25.2246i | −0.817104 | − | 0.817104i | 0.168584 | − | 0.985687i | \(-0.446081\pi\) |
−0.985687 | + | 0.168584i | \(0.946081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.25291 | − | 4.67592i | 0.0405008 | − | 0.151151i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.4034 | − | 16.1984i | −1.11094 | − | 0.523072i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.68132 | + | 15.0365i | 0.280043 | + | 0.485048i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.1277 | + | 3.78551i | −0.455260 | + | 0.121987i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3072 | − | 16.3072i | 0.524405 | − | 0.524405i | −0.394494 | − | 0.918899i | \(-0.629080\pi\) |
0.918899 | + | 0.394494i | \(0.129080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.0468 | − | 24.3298i | 0.451248 | − | 0.781585i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.80744 | + | 2.19823i | −0.122187 | + | 0.0705445i | −0.559848 | − | 0.828596i | \(-0.689140\pi\) |
0.437661 | + | 0.899140i | \(0.355807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9466 | + | 22.4101i | −0.607399 | + | 0.718434i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.6307 | − | 39.6743i | −0.340106 | − | 1.26929i | −0.898226 | − | 0.439534i | \(-0.855144\pi\) |
0.558120 | − | 0.829760i | \(-0.311523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.2725 | −0.903592 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9587 | 0.381812 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.682478 | − | 2.54704i | −0.0217677 | − | 0.0812380i | 0.954188 | − | 0.299209i | \(-0.0967228\pi\) |
−0.975955 | + | 0.217971i | \(0.930056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.50765 | + | 10.0629i | −0.270801 | + | 0.320305i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.2826 | − | 12.2875i | 0.676746 | − | 0.390720i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.658365 | − | 1.14032i | 0.0209136 | − | 0.0362235i | −0.855379 | − | 0.518002i | \(-0.826676\pi\) |
0.876293 | + | 0.481779i | \(0.160009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.4579 | + | 15.4579i | −0.490542 | + | 0.490542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.5044 | − | 13.2647i | 1.56782 | − | 0.420096i | 0.632692 | − | 0.774404i | \(-0.281950\pi\) |
0.935129 | + | 0.354307i | \(0.115283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.25534 | − | 7.37046i | −0.134633 | − | 0.233191i |
(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 | 2100.2.ce.e.493.2 | 32 | ||
5.2 | odd | 4 | inner | 2100.2.ce.e.157.4 | 32 | ||
5.3 | odd | 4 | 420.2.bo.a.157.5 | yes | 32 | ||
5.4 | even | 2 | 420.2.bo.a.73.7 | ✓ | 32 | ||
7.5 | odd | 6 | inner | 2100.2.ce.e.1993.4 | 32 | ||
15.8 | even | 4 | 1260.2.dq.c.577.7 | 32 | |||
15.14 | odd | 2 | 1260.2.dq.c.73.4 | 32 | |||
35.3 | even | 12 | 2940.2.x.c.97.15 | 32 | |||
35.4 | even | 6 | 2940.2.x.c.1273.15 | 32 | |||
35.12 | even | 12 | inner | 2100.2.ce.e.1657.2 | 32 | ||
35.18 | odd | 12 | 2940.2.x.c.97.4 | 32 | |||
35.19 | odd | 6 | 420.2.bo.a.313.5 | yes | 32 | ||
35.24 | odd | 6 | 2940.2.x.c.1273.4 | 32 | |||
35.33 | even | 12 | 420.2.bo.a.397.7 | yes | 32 | ||
105.68 | odd | 12 | 1260.2.dq.c.397.4 | 32 | |||
105.89 | even | 6 | 1260.2.dq.c.1153.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bo.a.73.7 | ✓ | 32 | 5.4 | even | 2 | ||
420.2.bo.a.157.5 | yes | 32 | 5.3 | odd | 4 | ||
420.2.bo.a.313.5 | yes | 32 | 35.19 | odd | 6 | ||
420.2.bo.a.397.7 | yes | 32 | 35.33 | even | 12 | ||
1260.2.dq.c.73.4 | 32 | 15.14 | odd | 2 | |||
1260.2.dq.c.397.4 | 32 | 105.68 | odd | 12 | |||
1260.2.dq.c.577.7 | 32 | 15.8 | even | 4 | |||
1260.2.dq.c.1153.7 | 32 | 105.89 | even | 6 | |||
2100.2.ce.e.157.4 | 32 | 5.2 | odd | 4 | inner | ||
2100.2.ce.e.493.2 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.ce.e.1657.2 | 32 | 35.12 | even | 12 | inner | ||
2100.2.ce.e.1993.4 | 32 | 7.5 | odd | 6 | inner | ||
2940.2.x.c.97.4 | 32 | 35.18 | odd | 12 | |||
2940.2.x.c.97.15 | 32 | 35.3 | even | 12 | |||
2940.2.x.c.1273.4 | 32 | 35.24 | odd | 6 | |||
2940.2.x.c.1273.15 | 32 | 35.4 | even | 6 |