Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(121,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bd (of order \(6\), degree \(2\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(0.960282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.121 |
Dual form | 546.2.bd.a.361.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.620092 | − | 0.358010i | −0.277314 | − | 0.160107i | 0.354893 | − | 0.934907i | \(-0.384517\pi\) |
−0.632207 | + | 0.774800i | \(0.717851\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −2.52418 | + | 0.792781i | −0.954051 | + | 0.299643i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.716021 | 0.226426 | ||||||||
\(11\) | 2.57068i | 0.775089i | 0.921851 | + | 0.387544i | \(0.126677\pi\) | ||||
−0.921851 | + | 0.387544i | \(0.873323\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 3.57509 | + | 0.467723i | 0.991550 | + | 0.129723i | ||||
\(14\) | 1.78962 | − | 1.94866i | 0.478295 | − | 0.520801i | ||||
\(15\) | 0.620092 | + | 0.358010i | 0.160107 | + | 0.0924379i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.0124180 | + | 0.0215086i | −0.00301181 | + | 0.00521661i | −0.867527 | − | 0.497389i | \(-0.834292\pi\) |
0.864516 | + | 0.502606i | \(0.167625\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | − | 6.91088i | − | 1.58546i | −0.609571 | − | 0.792732i | \(-0.708658\pi\) | ||
0.609571 | − | 0.792732i | \(-0.291342\pi\) | |||||||
\(20\) | −0.620092 | + | 0.358010i | −0.138657 | + | 0.0800535i | ||||
\(21\) | 2.52418 | − | 0.792781i | 0.550822 | − | 0.172999i | ||||
\(22\) | −1.28534 | − | 2.22627i | −0.274035 | − | 0.474643i | ||||
\(23\) | −4.69938 | − | 8.13957i | −0.979889 | − | 1.69722i | −0.662755 | − | 0.748836i | \(-0.730613\pi\) |
−0.317134 | − | 0.948381i | \(-0.602720\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −2.24366 | − | 3.88613i | −0.448731 | − | 0.777226i | ||||
\(26\) | −3.32998 | + | 1.38248i | −0.653062 | + | 0.271127i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.575523 | + | 2.58240i | −0.108764 | + | 0.488027i | ||||
\(29\) | −2.77589 | + | 4.80797i | −0.515469 | + | 0.892818i | 0.484370 | + | 0.874863i | \(0.339049\pi\) |
−0.999839 | + | 0.0179551i | \(0.994284\pi\) | |||||||
\(30\) | −0.716021 | −0.130727 | ||||||||
\(31\) | 4.92140 | − | 2.84137i | 0.883909 | − | 0.510325i | 0.0119639 | − | 0.999928i | \(-0.496192\pi\) |
0.871945 | + | 0.489603i | \(0.162858\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | − | 2.57068i | − | 0.447498i | ||||||
\(34\) | − | 0.0248360i | − | 0.00425935i | ||||||
\(35\) | 1.84905 | + | 0.412087i | 0.312546 | + | 0.0696553i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 3.61229 | − | 2.08556i | 0.593856 | − | 0.342863i | −0.172764 | − | 0.984963i | \(-0.555270\pi\) |
0.766621 | + | 0.642100i | \(0.221937\pi\) | |||||||
\(38\) | 3.45544 | + | 5.98499i | 0.560546 | + | 0.970894i | ||||
\(39\) | −3.57509 | − | 0.467723i | −0.572472 | − | 0.0748956i | ||||
\(40\) | 0.358010 | − | 0.620092i | 0.0566064 | − | 0.0980452i | ||||
\(41\) | 4.54901 | + | 2.62637i | 0.710436 | + | 0.410171i | 0.811223 | − | 0.584737i | \(-0.198802\pi\) |
−0.100786 | + | 0.994908i | \(0.532136\pi\) | |||||||
\(42\) | −1.78962 | + | 1.94866i | −0.276144 | + | 0.300685i | ||||
\(43\) | −6.37475 | − | 11.0414i | −0.972141 | − | 1.68380i | −0.689065 | − | 0.724699i | \(-0.741979\pi\) |
−0.283075 | − | 0.959098i | \(-0.591355\pi\) | |||||||
\(44\) | 2.22627 | + | 1.28534i | 0.335623 | + | 0.193772i | ||||
\(45\) | −0.620092 | − | 0.358010i | −0.0924379 | − | 0.0533690i | ||||
\(46\) | 8.13957 | + | 4.69938i | 1.20011 | + | 0.692886i | ||||
\(47\) | −4.32056 | − | 2.49448i | −0.630219 | − | 0.363857i | 0.150618 | − | 0.988592i | \(-0.451874\pi\) |
−0.780837 | + | 0.624735i | \(0.785207\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 5.74300 | − | 4.00225i | 0.820428 | − | 0.571749i | ||||
\(50\) | 3.88613 | + | 2.24366i | 0.549582 | + | 0.317301i | ||||
\(51\) | 0.0124180 | − | 0.0215086i | 0.00173887 | − | 0.00301181i | ||||
\(52\) | 2.19260 | − | 2.86225i | 0.304059 | − | 0.396923i | ||||
\(53\) | −4.72462 | − | 8.18328i | −0.648977 | − | 1.12406i | −0.983368 | − | 0.181626i | \(-0.941864\pi\) |
0.334391 | − | 0.942434i | \(-0.391469\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0.920330 | − | 1.59406i | 0.124097 | − | 0.214943i | ||||
\(56\) | −0.792781 | − | 2.52418i | −0.105940 | − | 0.337308i | ||||
\(57\) | 6.91088i | 0.915368i | ||||||||
\(58\) | − | 5.55177i | − | 0.728983i | ||||||
\(59\) | 1.95045 | + | 1.12610i | 0.253928 | + | 0.146605i | 0.621561 | − | 0.783365i | \(-0.286499\pi\) |
−0.367634 | + | 0.929971i | \(0.619832\pi\) | |||||||
\(60\) | 0.620092 | − | 0.358010i | 0.0800535 | − | 0.0462189i | ||||
\(61\) | −0.652006 | −0.0834808 | −0.0417404 | − | 0.999128i | \(-0.513290\pi\) | ||||
−0.0417404 | + | 0.999128i | \(0.513290\pi\) | |||||||
\(62\) | −2.84137 | + | 4.92140i | −0.360854 | + | 0.625018i | ||||
\(63\) | −2.52418 | + | 0.792781i | −0.318017 | + | 0.0998810i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.04943 | − | 1.56995i | −0.254201 | − | 0.194728i | ||||
\(66\) | 1.28534 | + | 2.22627i | 0.158214 | + | 0.274035i | ||||
\(67\) | 1.87610i | 0.229203i | 0.993412 | + | 0.114601i | \(0.0365591\pi\) | ||||
−0.993412 | + | 0.114601i | \(0.963441\pi\) | |||||||
\(68\) | 0.0124180 | + | 0.0215086i | 0.00150591 | + | 0.00260831i | ||||
\(69\) | 4.69938 | + | 8.13957i | 0.565739 | + | 0.979889i | ||||
\(70\) | −1.80737 | + | 0.567647i | −0.216022 | + | 0.0678468i | ||||
\(71\) | 7.52246 | − | 4.34310i | 0.892752 | − | 0.515431i | 0.0179106 | − | 0.999840i | \(-0.494299\pi\) |
0.874842 | + | 0.484409i | \(0.160965\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 13.7568 | − | 7.94250i | 1.61011 | − | 0.929600i | 0.620772 | − | 0.783991i | \(-0.286819\pi\) |
0.989342 | − | 0.145608i | \(-0.0465139\pi\) | |||||||
\(74\) | −2.08556 | + | 3.61229i | −0.242441 | + | 0.419920i | ||||
\(75\) | 2.24366 | + | 3.88613i | 0.259075 | + | 0.448731i | ||||
\(76\) | −5.98499 | − | 3.45544i | −0.686526 | − | 0.396366i | ||||
\(77\) | −2.03798 | − | 6.48886i | −0.232250 | − | 0.739475i | ||||
\(78\) | 3.32998 | − | 1.38248i | 0.377046 | − | 0.156535i | ||||
\(79\) | −0.194223 | + | 0.336404i | −0.0218518 | + | 0.0378484i | −0.876744 | − | 0.480956i | \(-0.840290\pi\) |
0.854893 | + | 0.518805i | \(0.173623\pi\) | |||||||
\(80\) | 0.716021i | 0.0800535i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.25275 | −0.580069 | ||||||||
\(83\) | 8.85439i | 0.971895i | 0.873988 | + | 0.485948i | \(0.161525\pi\) | ||||
−0.873988 | + | 0.485948i | \(0.838475\pi\) | |||||||
\(84\) | 0.575523 | − | 2.58240i | 0.0627947 | − | 0.281763i | ||||
\(85\) | 0.0154006 | − | 0.00889156i | 0.00167043 | − | 0.000964425i | ||||
\(86\) | 11.0414 | + | 6.37475i | 1.19062 | + | 0.687407i | ||||
\(87\) | 2.77589 | − | 4.80797i | 0.297606 | − | 0.515469i | ||||
\(88\) | −2.57068 | −0.274035 | ||||||||
\(89\) | −12.8502 | + | 7.41908i | −1.36212 | + | 0.786420i | −0.989906 | − | 0.141726i | \(-0.954735\pi\) |
−0.372214 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(90\) | 0.716021 | 0.0754752 | ||||||||
\(91\) | −9.39497 | + | 1.65364i | −0.984861 | + | 0.173349i | ||||
\(92\) | −9.39876 | −0.979889 | ||||||||
\(93\) | −4.92140 | + | 2.84137i | −0.510325 | + | 0.294636i | ||||
\(94\) | 4.98896 | 0.514572 | ||||||||
\(95\) | −2.47416 | + | 4.28538i | −0.253844 | + | 0.439671i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −1.78702 | + | 1.03174i | −0.181445 | + | 0.104757i | −0.587971 | − | 0.808882i | \(-0.700073\pi\) |
0.406527 | + | 0.913639i | \(0.366740\pi\) | |||||||
\(98\) | −2.97246 | + | 6.33755i | −0.300264 | + | 0.640189i | ||||
\(99\) | 2.57068i | 0.258363i | ||||||||
\(100\) | −4.48731 | −0.448731 | ||||||||
\(101\) | 11.5903 | 1.15328 | 0.576638 | − | 0.817000i | \(-0.304364\pi\) | ||||
0.576638 | + | 0.817000i | \(0.304364\pi\) | |||||||
\(102\) | 0.0248360i | 0.00245913i | ||||||||
\(103\) | −7.89706 | + | 13.6781i | −0.778120 | + | 1.34774i | 0.154903 | + | 0.987930i | \(0.450493\pi\) |
−0.933024 | + | 0.359814i | \(0.882840\pi\) | |||||||
\(104\) | −0.467723 | + | 3.57509i | −0.0458640 | + | 0.350566i | ||||
\(105\) | −1.84905 | − | 0.412087i | −0.180449 | − | 0.0402155i | ||||
\(106\) | 8.18328 | + | 4.72462i | 0.794831 | + | 0.458896i | ||||
\(107\) | 0.241343 | + | 0.418019i | 0.0233315 | + | 0.0404114i | 0.877455 | − | 0.479658i | \(-0.159239\pi\) |
−0.854124 | + | 0.520070i | \(0.825906\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −2.77524 | + | 1.60228i | −0.265819 | + | 0.153471i | −0.626986 | − | 0.779030i | \(-0.715712\pi\) |
0.361167 | + | 0.932501i | \(0.382378\pi\) | |||||||
\(110\) | 1.84066i | 0.175500i | ||||||||
\(111\) | −3.61229 | + | 2.08556i | −0.342863 | + | 0.197952i | ||||
\(112\) | 1.94866 | + | 1.78962i | 0.184131 | + | 0.169103i | ||||
\(113\) | −4.18781 | − | 7.25350i | −0.393956 | − | 0.682352i | 0.599011 | − | 0.800741i | \(-0.295560\pi\) |
−0.992967 | + | 0.118389i | \(0.962227\pi\) | |||||||
\(114\) | −3.45544 | − | 5.98499i | −0.323631 | − | 0.560546i | ||||
\(115\) | 6.72971i | 0.627548i | ||||||||
\(116\) | 2.77589 | + | 4.80797i | 0.257734 | + | 0.446409i | ||||
\(117\) | 3.57509 | + | 0.467723i | 0.330517 | + | 0.0432410i | ||||
\(118\) | −2.25219 | −0.207331 | ||||||||
\(119\) | 0.0142937 | − | 0.0641365i | 0.00131030 | − | 0.00587939i | ||||
\(120\) | −0.358010 | + | 0.620092i | −0.0326817 | + | 0.0566064i | ||||
\(121\) | 4.39161 | 0.399237 | ||||||||
\(122\) | 0.564654 | − | 0.326003i | 0.0511214 | − | 0.0295149i | ||||
\(123\) | −4.54901 | − | 2.62637i | −0.410171 | − | 0.236812i | ||||
\(124\) | − | 5.68274i | − | 0.510325i | ||||||
\(125\) | 6.79311i | 0.607594i | ||||||||
\(126\) | 1.78962 | − | 1.94866i | 0.159432 | − | 0.173600i | ||||
\(127\) | −11.0533 | + | 19.1448i | −0.980820 | + | 1.69883i | −0.321610 | + | 0.946872i | \(0.604224\pi\) |
−0.659211 | + | 0.751958i | \(0.729109\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.37475 | + | 11.0414i | 0.561266 | + | 0.972141i | ||||
\(130\) | 2.55983 | + | 0.334899i | 0.224512 | + | 0.0293726i | ||||
\(131\) | 5.57371 | − | 9.65394i | 0.486977 | − | 0.843469i | −0.512911 | − | 0.858442i | \(-0.671433\pi\) |
0.999888 | + | 0.0149731i | \(0.00476625\pi\) | |||||||
\(132\) | −2.22627 | − | 1.28534i | −0.193772 | − | 0.111874i | ||||
\(133\) | 5.47881 | + | 17.4443i | 0.475073 | + | 1.51261i | ||||
\(134\) | −0.938052 | − | 1.62475i | −0.0810354 | − | 0.140357i | ||||
\(135\) | 0.620092 | + | 0.358010i | 0.0533690 | + | 0.0308126i | ||||
\(136\) | −0.0215086 | − | 0.0124180i | −0.00184435 | − | 0.00106484i | ||||
\(137\) | −14.5467 | − | 8.39853i | −1.24281 | − | 0.717534i | −0.273142 | − | 0.961974i | \(-0.588063\pi\) |
−0.969665 | + | 0.244439i | \(0.921396\pi\) | |||||||
\(138\) | −8.13957 | − | 4.69938i | −0.692886 | − | 0.400038i | ||||
\(139\) | −9.50946 | − | 16.4709i | −0.806582 | − | 1.39704i | −0.915218 | − | 0.402959i | \(-0.867982\pi\) |
0.108636 | − | 0.994082i | \(-0.465352\pi\) | |||||||
\(140\) | 1.28140 | − | 1.39528i | 0.108298 | − | 0.117923i | ||||
\(141\) | 4.32056 | + | 2.49448i | 0.363857 | + | 0.210073i | ||||
\(142\) | −4.34310 | + | 7.52246i | −0.364465 | + | 0.631271i | ||||
\(143\) | −1.20237 | + | 9.19040i | −0.100547 | + | 0.768540i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 3.44261 | − | 1.98759i | 0.285893 | − | 0.165060i | ||||
\(146\) | −7.94250 | + | 13.7568i | −0.657326 | + | 1.13852i | ||||
\(147\) | −5.74300 | + | 4.00225i | −0.473674 | + | 0.330100i | ||||
\(148\) | − | 4.17111i | − | 0.342863i | ||||||
\(149\) | − | 12.2538i | − | 1.00387i | −0.864906 | − | 0.501934i | \(-0.832622\pi\) | ||
0.864906 | − | 0.501934i | \(-0.167378\pi\) | |||||||
\(150\) | −3.88613 | − | 2.24366i | −0.317301 | − | 0.183194i | ||||
\(151\) | −11.5364 | + | 6.66053i | −0.938817 | + | 0.542026i | −0.889589 | − | 0.456761i | \(-0.849009\pi\) |
−0.0492279 | + | 0.998788i | \(0.515676\pi\) | |||||||
\(152\) | 6.91088 | 0.560546 | ||||||||
\(153\) | −0.0124180 | + | 0.0215086i | −0.00100394 | + | 0.00173887i | ||||
\(154\) | 5.00938 | + | 4.60053i | 0.403667 | + | 0.370721i | ||||
\(155\) | −4.06896 | −0.326827 | ||||||||
\(156\) | −2.19260 | + | 2.86225i | −0.175549 | + | 0.229164i | ||||
\(157\) | −3.49931 | − | 6.06098i | −0.279275 | − | 0.483719i | 0.691930 | − | 0.721965i | \(-0.256761\pi\) |
−0.971205 | + | 0.238246i | \(0.923427\pi\) | |||||||
\(158\) | − | 0.388445i | − | 0.0309031i | ||||||
\(159\) | 4.72462 | + | 8.18328i | 0.374687 | + | 0.648977i | ||||
\(160\) | −0.358010 | − | 0.620092i | −0.0283032 | − | 0.0490226i | ||||
\(161\) | 18.3150 | + | 16.8202i | 1.44342 | + | 1.32562i | ||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | − | 10.1930i | − | 0.798376i | −0.916869 | − | 0.399188i | \(-0.869292\pi\) | ||
0.916869 | − | 0.399188i | \(-0.130708\pi\) | |||||||
\(164\) | 4.54901 | − | 2.62637i | 0.355218 | − | 0.205085i | ||||
\(165\) | −0.920330 | + | 1.59406i | −0.0716476 | + | 0.124097i | ||||
\(166\) | −4.42719 | − | 7.66812i | −0.343617 | − | 0.595162i | ||||
\(167\) | −6.33732 | − | 3.65885i | −0.490397 | − | 0.283131i | 0.234342 | − | 0.972154i | \(-0.424706\pi\) |
−0.724739 | + | 0.689023i | \(0.758040\pi\) | |||||||
\(168\) | 0.792781 | + | 2.52418i | 0.0611643 | + | 0.194745i | ||||
\(169\) | 12.5625 | + | 3.34430i | 0.966344 | + | 0.257254i | ||||
\(170\) | −0.00889156 | + | 0.0154006i | −0.000681951 | + | 0.00118117i | ||||
\(171\) | − | 6.91088i | − | 0.528488i | ||||||
\(172\) | −12.7495 | −0.972141 | ||||||||
\(173\) | 6.48507 | 0.493051 | 0.246525 | − | 0.969136i | \(-0.420711\pi\) | ||||
0.246525 | + | 0.969136i | \(0.420711\pi\) | |||||||
\(174\) | 5.55177i | 0.420879i | ||||||||
\(175\) | 8.74425 | + | 8.03057i | 0.661003 | + | 0.607054i | ||||
\(176\) | 2.22627 | − | 1.28534i | 0.167812 | − | 0.0968861i | ||||
\(177\) | −1.95045 | − | 1.12610i | −0.146605 | − | 0.0846425i | ||||
\(178\) | 7.41908 | − | 12.8502i | 0.556083 | − | 0.963164i | ||||
\(179\) | 23.2228 | 1.73576 | 0.867878 | − | 0.496777i | \(-0.165483\pi\) | ||||
0.867878 | + | 0.496777i | \(0.165483\pi\) | |||||||
\(180\) | −0.620092 | + | 0.358010i | −0.0462189 | + | 0.0266845i | ||||
\(181\) | −5.61910 | −0.417664 | −0.208832 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208832 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(182\) | 7.30946 | − | 6.12958i | 0.541813 | − | 0.454355i | ||||
\(183\) | 0.652006 | 0.0481977 | ||||||||
\(184\) | 8.13957 | − | 4.69938i | 0.600057 | − | 0.346443i | ||||
\(185\) | −2.98660 | −0.219579 | ||||||||
\(186\) | 2.84137 | − | 4.92140i | 0.208339 | − | 0.360854i | ||||
\(187\) | −0.0552918 | − | 0.0319228i | −0.00404334 | − | 0.00233442i | ||||
\(188\) | −4.32056 | + | 2.49448i | −0.315109 | + | 0.181929i | ||||
\(189\) | 2.52418 | − | 0.792781i | 0.183607 | − | 0.0576663i | ||||
\(190\) | − | 4.94833i | − | 0.358990i | ||||||
\(191\) | −23.8945 | −1.72894 | −0.864472 | − | 0.502681i | \(-0.832347\pi\) | ||||
−0.864472 | + | 0.502681i | \(0.832347\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 20.9972i | 1.51141i | 0.654910 | + | 0.755707i | \(0.272707\pi\) | ||||
−0.654910 | + | 0.755707i | \(0.727293\pi\) | |||||||
\(194\) | 1.03174 | − | 1.78702i | 0.0740744 | − | 0.128301i | ||||
\(195\) | 2.04943 | + | 1.56995i | 0.146763 | + | 0.112426i | ||||
\(196\) | −0.594548 | − | 6.97471i | −0.0424677 | − | 0.498193i | ||||
\(197\) | −4.48984 | − | 2.59221i | −0.319888 | − | 0.184688i | 0.331455 | − | 0.943471i | \(-0.392461\pi\) |
−0.651343 | + | 0.758784i | \(0.725794\pi\) | |||||||
\(198\) | −1.28534 | − | 2.22627i | −0.0913451 | − | 0.158214i | ||||
\(199\) | 8.07086 | − | 13.9791i | 0.572128 | − | 0.990955i | −0.424219 | − | 0.905560i | \(-0.639451\pi\) |
0.996347 | − | 0.0853954i | \(-0.0272153\pi\) | |||||||
\(200\) | 3.88613 | − | 2.24366i | 0.274791 | − | 0.158651i | ||||
\(201\) | − | 1.87610i | − | 0.132330i | ||||||
\(202\) | −10.0375 | + | 5.79514i | −0.706235 | + | 0.407745i | ||||
\(203\) | 3.19517 | − | 14.3369i | 0.224257 | − | 1.00625i | ||||
\(204\) | −0.0124180 | − | 0.0215086i | −0.000869435 | − | 0.00150591i | ||||
\(205\) | −1.88054 | − | 3.25719i | −0.131342 | − | 0.227492i | ||||
\(206\) | − | 15.7941i | − | 1.10043i | ||||||
\(207\) | −4.69938 | − | 8.13957i | −0.326630 | − | 0.565739i | ||||
\(208\) | −1.38248 | − | 3.32998i | −0.0958579 | − | 0.230892i | ||||
\(209\) | 17.7656 | 1.22888 | ||||||||
\(210\) | 1.80737 | − | 0.567647i | 0.124720 | − | 0.0391714i | ||||
\(211\) | 7.68735 | − | 13.3149i | 0.529219 | − | 0.916635i | −0.470200 | − | 0.882560i | \(-0.655818\pi\) |
0.999419 | − | 0.0340747i | \(-0.0108484\pi\) | |||||||
\(212\) | −9.44924 | −0.648977 | ||||||||
\(213\) | −7.52246 | + | 4.34310i | −0.515431 | + | 0.297584i | ||||
\(214\) | −0.418019 | − | 0.241343i | −0.0285752 | − | 0.0164979i | ||||
\(215\) | 9.12891i | 0.622586i | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −10.1699 | + | 11.0737i | −0.690380 | + | 0.751734i | ||||
\(218\) | 1.60228 | − | 2.77524i | 0.108520 | − | 0.187963i | ||||
\(219\) | −13.7568 | + | 7.94250i | −0.929600 | + | 0.536705i | ||||
\(220\) | −0.920330 | − | 1.59406i | −0.0620486 | − | 0.107471i | ||||
\(221\) | −0.0544556 | + | 0.0710871i | −0.00366308 | + | 0.00478183i | ||||
\(222\) | 2.08556 | − | 3.61229i | 0.139973 | − | 0.242441i | ||||
\(223\) | 11.0984 | + | 6.40769i | 0.743207 | + | 0.429091i | 0.823234 | − | 0.567702i | \(-0.192167\pi\) |
−0.0800273 | + | 0.996793i | \(0.525501\pi\) | |||||||
\(224\) | −2.58240 | − | 0.575523i | −0.172544 | − | 0.0384538i | ||||
\(225\) | −2.24366 | − | 3.88613i | −0.149577 | − | 0.259075i | ||||
\(226\) | 7.25350 | + | 4.18781i | 0.482496 | + | 0.278569i | ||||
\(227\) | 17.4536 | + | 10.0768i | 1.15843 | + | 0.668823i | 0.950928 | − | 0.309411i | \(-0.100132\pi\) |
0.207506 | + | 0.978234i | \(0.433465\pi\) | |||||||
\(228\) | 5.98499 | + | 3.45544i | 0.396366 | + | 0.228842i | ||||
\(229\) | 8.89145 | + | 5.13348i | 0.587564 | + | 0.339230i | 0.764134 | − | 0.645058i | \(-0.223167\pi\) |
−0.176570 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(230\) | −3.36485 | − | 5.82810i | −0.221872 | − | 0.384293i | ||||
\(231\) | 2.03798 | + | 6.48886i | 0.134090 | + | 0.426936i | ||||
\(232\) | −4.80797 | − | 2.77589i | −0.315659 | − | 0.182246i | ||||
\(233\) | −1.56117 | + | 2.70402i | −0.102276 | + | 0.177146i | −0.912622 | − | 0.408805i | \(-0.865946\pi\) |
0.810346 | + | 0.585951i | \(0.199279\pi\) | |||||||
\(234\) | −3.32998 | + | 1.38248i | −0.217687 | + | 0.0903757i | ||||
\(235\) | 1.78610 | + | 3.09361i | 0.116512 | + | 0.201805i | ||||
\(236\) | 1.95045 | − | 1.12610i | 0.126964 | − | 0.0733026i | ||||
\(237\) | 0.194223 | − | 0.336404i | 0.0126161 | − | 0.0218518i | ||||
\(238\) | 0.0196895 | + | 0.0626907i | 0.00127628 | + | 0.00406364i | ||||
\(239\) | 12.2325i | 0.791253i | 0.918411 | + | 0.395627i | \(0.129473\pi\) | ||||
−0.918411 | + | 0.395627i | \(0.870527\pi\) | |||||||
\(240\) | − | 0.716021i | − | 0.0462189i | ||||||
\(241\) | −1.63586 | − | 0.944462i | −0.105375 | − | 0.0608382i | 0.446386 | − | 0.894840i | \(-0.352711\pi\) |
−0.551761 | + | 0.834002i | \(0.686044\pi\) | |||||||
\(242\) | −3.80324 | + | 2.19580i | −0.244482 | + | 0.141152i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.326003 | + | 0.564654i | −0.0208702 | + | 0.0361483i | ||||
\(245\) | −4.99403 | + | 0.425708i | −0.319057 | + | 0.0271975i | ||||
\(246\) | 5.25275 | 0.334903 | ||||||||
\(247\) | 3.23238 | − | 24.7070i | 0.205671 | − | 1.57207i | ||||
\(248\) | 2.84137 | + | 4.92140i | 0.180427 | + | 0.312509i | ||||
\(249\) | − | 8.85439i | − | 0.561124i | ||||||
\(250\) | −3.39656 | − | 5.88301i | −0.214817 | − | 0.372074i | ||||
\(251\) | −7.56052 | − | 13.0952i | −0.477216 | − | 0.826562i | 0.522443 | − | 0.852674i | \(-0.325021\pi\) |
−0.999659 | + | 0.0261123i | \(0.991687\pi\) | |||||||
\(252\) | −0.575523 | + | 2.58240i | −0.0362546 | + | 0.162676i | ||||
\(253\) | 20.9242 | − | 12.0806i | 1.31549 | − | 0.759501i | ||||
\(254\) | − | 22.1066i | − | 1.38709i | ||||||
\(255\) | −0.0154006 | + | 0.00889156i | −0.000964425 | + | 0.000556811i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.82704 | − | 4.89658i | −0.176346 | − | 0.305440i | 0.764280 | − | 0.644884i | \(-0.223094\pi\) |
−0.940626 | + | 0.339444i | \(0.889761\pi\) | |||||||
\(258\) | −11.0414 | − | 6.37475i | −0.687407 | − | 0.396875i | ||||
\(259\) | −7.46469 | + | 8.12807i | −0.463833 | + | 0.505054i | ||||
\(260\) | −2.38433 | + | 0.989886i | −0.147870 | + | 0.0613901i | ||||
\(261\) | −2.77589 | + | 4.80797i | −0.171823 | + | 0.297606i | ||||
\(262\) | 11.1474i | 0.688689i | ||||||||
\(263\) | −14.5482 | −0.897083 | −0.448541 | − | 0.893762i | \(-0.648056\pi\) | ||||
−0.448541 | + | 0.893762i | \(0.648056\pi\) | |||||||
\(264\) | 2.57068 | 0.158214 | ||||||||
\(265\) | 6.76585i | 0.415623i | ||||||||
\(266\) | −13.4669 | − | 12.3678i | −0.825711 | − | 0.758319i | ||||
\(267\) | 12.8502 | − | 7.41908i | 0.786420 | − | 0.454040i | ||||
\(268\) | 1.62475 | + | 0.938052i | 0.0992477 | + | 0.0573007i | ||||
\(269\) | −1.73031 | + | 2.99698i | −0.105499 | + | 0.182729i | −0.913942 | − | 0.405845i | \(-0.866977\pi\) |
0.808443 | + | 0.588574i | \(0.200311\pi\) | |||||||
\(270\) | −0.716021 | −0.0435756 | ||||||||
\(271\) | −10.0207 | + | 5.78543i | −0.608712 | + | 0.351440i | −0.772461 | − | 0.635062i | \(-0.780975\pi\) |
0.163749 | + | 0.986502i | \(0.447641\pi\) | |||||||
\(272\) | 0.0248360 | 0.00150591 | ||||||||
\(273\) | 9.39497 | − | 1.65364i | 0.568609 | − | 0.100083i | ||||
\(274\) | 16.7971 | 1.01475 | ||||||||
\(275\) | 9.98999 | − | 5.76772i | 0.602419 | − | 0.347807i | ||||
\(276\) | 9.39876 | 0.565739 | ||||||||
\(277\) | −2.31998 | + | 4.01832i | −0.139394 | + | 0.241438i | −0.927267 | − | 0.374400i | \(-0.877849\pi\) |
0.787873 | + | 0.615837i | \(0.211182\pi\) | |||||||
\(278\) | 16.4709 | + | 9.50946i | 0.987857 | + | 0.570340i | ||||
\(279\) | 4.92140 | − | 2.84137i | 0.294636 | − | 0.170108i | ||||
\(280\) | −0.412087 | + | 1.84905i | −0.0246269 | + | 0.110502i | ||||
\(281\) | − | 20.9621i | − | 1.25049i | −0.780428 | − | 0.625246i | \(-0.784999\pi\) | ||
0.780428 | − | 0.625246i | \(-0.215001\pi\) | |||||||
\(282\) | −4.98896 | −0.297088 | ||||||||
\(283\) | −4.72036 | −0.280596 | −0.140298 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140298 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(284\) | − | 8.68619i | − | 0.515431i | ||||||
\(285\) | 2.47416 | − | 4.28538i | 0.146557 | − | 0.253844i | ||||
\(286\) | −3.55392 | − | 8.56030i | −0.210148 | − | 0.506181i | ||||
\(287\) | −13.5647 | − | 3.02308i | −0.800698 | − | 0.178447i | ||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 8.49969 | + | 14.7219i | 0.499982 | + | 0.865994i | ||||
\(290\) | −1.98759 | + | 3.44261i | −0.116715 | + | 0.202157i | ||||
\(291\) | 1.78702 | − | 1.03174i | 0.104757 | − | 0.0604815i | ||||
\(292\) | − | 15.8850i | − | 0.929600i | ||||||
\(293\) | 29.0541 | − | 16.7744i | 1.69736 | − | 0.979970i | 0.749105 | − | 0.662451i | \(-0.230484\pi\) |
0.948252 | − | 0.317518i | \(-0.102850\pi\) | |||||||
\(294\) | 2.97246 | − | 6.33755i | 0.173357 | − | 0.369613i | ||||
\(295\) | −0.806308 | − | 1.39657i | −0.0469450 | − | 0.0813112i | ||||
\(296\) | 2.08556 | + | 3.61229i | 0.121220 | + | 0.209960i | ||||
\(297\) | − | 2.57068i | − | 0.149166i | ||||||
\(298\) | 6.12689 | + | 10.6121i | 0.354921 | + | 0.614741i | ||||
\(299\) | −12.9936 | − | 31.2977i | −0.751441 | − | 1.80999i | ||||
\(300\) | 4.48731 | 0.259075 | ||||||||
\(301\) | 24.8444 | + | 22.8167i | 1.43201 | + | 1.31513i | ||||
\(302\) | 6.66053 | − | 11.5364i | 0.383271 | − | 0.663844i | ||||
\(303\) | −11.5903 | −0.665845 | ||||||||
\(304\) | −5.98499 | + | 3.45544i | −0.343263 | + | 0.198183i | ||||
\(305\) | 0.404304 | + | 0.233425i | 0.0231504 | + | 0.0133659i | ||||
\(306\) | − | 0.0248360i | − | 0.00141978i | ||||||
\(307\) | 5.49245i | 0.313471i | 0.987641 | + | 0.156735i | \(0.0500970\pi\) | ||||
−0.987641 | + | 0.156735i | \(0.949903\pi\) | |||||||
\(308\) | −6.63851 | − | 1.47949i | −0.378264 | − | 0.0843015i | ||||
\(309\) | 7.89706 | − | 13.6781i | 0.449248 | − | 0.778120i | ||||
\(310\) | 3.52382 | − | 2.03448i | 0.200140 | − | 0.115551i | ||||
\(311\) | 7.45213 | + | 12.9075i | 0.422572 | + | 0.731916i | 0.996190 | − | 0.0872069i | \(-0.0277941\pi\) |
−0.573619 | + | 0.819123i | \(0.694461\pi\) | |||||||
\(312\) | 0.467723 | − | 3.57509i | 0.0264796 | − | 0.202399i | ||||
\(313\) | 1.80173 | − | 3.12069i | 0.101840 | − | 0.176392i | −0.810603 | − | 0.585596i | \(-0.800860\pi\) |
0.912443 | + | 0.409205i | \(0.134194\pi\) | |||||||
\(314\) | 6.06098 | + | 3.49931i | 0.342041 | + | 0.197477i | ||||
\(315\) | 1.84905 | + | 0.412087i | 0.104182 | + | 0.0232184i | ||||
\(316\) | 0.194223 | + | 0.336404i | 0.0109259 | + | 0.0189242i | ||||
\(317\) | −3.54331 | − | 2.04573i | −0.199012 | − | 0.114900i | 0.397183 | − | 0.917740i | \(-0.369988\pi\) |
−0.596194 | + | 0.802840i | \(0.703321\pi\) | |||||||
\(318\) | −8.18328 | − | 4.72462i | −0.458896 | − | 0.264944i | ||||
\(319\) | −12.3598 | − | 7.13591i | −0.692014 | − | 0.399534i | ||||
\(320\) | 0.620092 | + | 0.358010i | 0.0346642 | + | 0.0200134i | ||||
\(321\) | −0.241343 | − | 0.418019i | −0.0134705 | − | 0.0233315i | ||||
\(322\) | −24.2713 | − | 5.40921i | −1.35259 | − | 0.301443i | ||||
\(323\) | 0.148644 | + | 0.0858194i | 0.00827075 | + | 0.00477512i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −6.20363 | − | 14.9427i | −0.344116 | − | 0.828869i | ||||
\(326\) | 5.09649 | + | 8.82738i | 0.282268 | + | 0.488903i | ||||
\(327\) | 2.77524 | − | 1.60228i | 0.153471 | − | 0.0886065i | ||||
\(328\) | −2.62637 | + | 4.54901i | −0.145017 | + | 0.251177i | ||||
\(329\) | 12.8835 | + | 2.87126i | 0.710289 | + | 0.158298i | ||||
\(330\) | − | 1.84066i | − | 0.101325i | ||||||
\(331\) | 19.4070i | 1.06670i | 0.845893 | + | 0.533352i | \(0.179068\pi\) | ||||
−0.845893 | + | 0.533352i | \(0.820932\pi\) | |||||||
\(332\) | 7.66812 | + | 4.42719i | 0.420843 | + | 0.242974i | ||||
\(333\) | 3.61229 | − | 2.08556i | 0.197952 | − | 0.114288i | ||||
\(334\) | 7.31771 | 0.400407 | ||||||||
\(335\) | 0.671665 | − | 1.16336i | 0.0366970 | − | 0.0635610i | ||||
\(336\) | −1.94866 | − | 1.78962i | −0.106308 | − | 0.0976316i | ||||
\(337\) | −23.0545 | −1.25586 | −0.627929 | − | 0.778271i | \(-0.716097\pi\) | ||||
−0.627929 | + | 0.778271i | \(0.716097\pi\) | |||||||
\(338\) | −12.5516 | + | 3.38499i | −0.682715 | + | 0.184119i | ||||
\(339\) | 4.18781 | + | 7.25350i | 0.227451 | + | 0.393956i | ||||
\(340\) | − | 0.0177831i | − | 0.000964425i | ||||||
\(341\) | 7.30425 | + | 12.6513i | 0.395547 | + | 0.685108i | ||||
\(342\) | 3.45544 | + | 5.98499i | 0.186849 | + | 0.323631i | ||||
\(343\) | −11.3235 | + | 14.6553i | −0.611410 | + | 0.791314i | ||||
\(344\) | 11.0414 | − | 6.37475i | 0.595312 | − | 0.343704i | ||||
\(345\) | − | 6.72971i | − | 0.362315i | ||||||
\(346\) | −5.61624 | + | 3.24254i | −0.301931 | + | 0.174320i | ||||
\(347\) | 2.30078 | − | 3.98507i | 0.123513 | − | 0.213930i | −0.797638 | − | 0.603136i | \(-0.793917\pi\) |
0.921151 | + | 0.389207i | \(0.127251\pi\) | |||||||
\(348\) | −2.77589 | − | 4.80797i | −0.148803 | − | 0.257734i | ||||
\(349\) | −3.23204 | − | 1.86602i | −0.173007 | − | 0.0998858i | 0.410996 | − | 0.911637i | \(-0.365181\pi\) |
−0.584003 | + | 0.811751i | \(0.698514\pi\) | |||||||
\(350\) | −11.5880 | − | 2.58255i | −0.619406 | − | 0.138043i | ||||
\(351\) | −3.57509 | − | 0.467723i | −0.190824 | − | 0.0249652i | ||||
\(352\) | −1.28534 | + | 2.22627i | −0.0685088 | + | 0.118661i | ||||
\(353\) | − | 26.3529i | − | 1.40262i | −0.712854 | − | 0.701312i | \(-0.752598\pi\) | ||
0.712854 | − | 0.701312i | \(-0.247402\pi\) | |||||||
\(354\) | 2.25219 | 0.119703 | ||||||||
\(355\) | −6.21949 | −0.330096 | ||||||||
\(356\) | 14.8382i | 0.786420i | ||||||||
\(357\) | −0.0142937 | + | 0.0641365i | −0.000756504 | + | 0.00339446i | ||||
\(358\) | −20.1116 | + | 11.6114i | −1.06293 | + | 0.613683i | ||||
\(359\) | −7.11568 | − | 4.10824i | −0.375551 | − | 0.216825i | 0.300330 | − | 0.953835i | \(-0.402903\pi\) |
−0.675881 | + | 0.737011i | \(0.736237\pi\) | |||||||
\(360\) | 0.358010 | − | 0.620092i | 0.0188688 | − | 0.0326817i | ||||
\(361\) | −28.7602 | −1.51370 | ||||||||
\(362\) | 4.86628 | − | 2.80955i | 0.255766 | − | 0.147667i | ||||
\(363\) | −4.39161 | −0.230500 | ||||||||
\(364\) | −3.26539 | + | 8.96310i | −0.171153 | + | 0.469794i | ||||
\(365\) | −11.3740 | −0.595342 | ||||||||
\(366\) | −0.564654 | + | 0.326003i | −0.0295149 | + | 0.0170405i | ||||
\(367\) | 0.428797 | 0.0223830 | 0.0111915 | − | 0.999937i | \(-0.496438\pi\) | ||||
0.0111915 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(368\) | −4.69938 | + | 8.13957i | −0.244972 | + | 0.424304i | ||||
\(369\) | 4.54901 | + | 2.62637i | 0.236812 | + | 0.136724i | ||||
\(370\) | 2.58647 | − | 1.49330i | 0.134464 | − | 0.0776330i | ||||
\(371\) | 18.4134 | + | 16.9105i | 0.955974 | + | 0.877950i | ||||
\(372\) | 5.68274i | 0.294636i | ||||||||
\(373\) | −2.01507 | −0.104336 | −0.0521682 | − | 0.998638i | \(-0.516613\pi\) | ||||
−0.0521682 | + | 0.998638i | \(0.516613\pi\) | |||||||
\(374\) | 0.0638455 | 0.00330137 | ||||||||
\(375\) | − | 6.79311i | − | 0.350795i | ||||||
\(376\) | 2.49448 | − | 4.32056i | 0.128643 | − | 0.222816i | ||||
\(377\) | −12.1728 | + | 15.8906i | −0.626932 | + | 0.818406i | ||||
\(378\) | −1.78962 | + | 1.94866i | −0.0920479 | + | 0.100228i | ||||
\(379\) | 15.0823 | + | 8.70779i | 0.774727 | + | 0.447289i | 0.834558 | − | 0.550920i | \(-0.185723\pi\) |
−0.0598312 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(380\) | 2.47416 | + | 4.28538i | 0.126922 | + | 0.219835i | ||||
\(381\) | 11.0533 | − | 19.1448i | 0.566277 | − | 0.980820i | ||||
\(382\) | 20.6932 | − | 11.9472i | 1.05876 | − | 0.611274i | ||||
\(383\) | − | 0.328330i | − | 0.0167769i | −0.999965 | − | 0.00838845i | \(-0.997330\pi\) | ||
0.999965 | − | 0.00838845i | \(-0.00267016\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | −1.05934 | + | 4.75331i | −0.0539891 | + | 0.242251i | ||||
\(386\) | −10.4986 | − | 18.1841i | −0.534365 | − | 0.925548i | ||||
\(387\) | −6.37475 | − | 11.0414i | −0.324047 | − | 0.561266i | ||||
\(388\) | 2.06347i | 0.104757i | ||||||||
\(389\) | −4.30458 | − | 7.45575i | −0.218251 | − | 0.378022i | 0.736022 | − | 0.676957i | \(-0.236702\pi\) |
−0.954273 | + | 0.298935i | \(0.903368\pi\) | |||||||
\(390\) | −2.55983 | − | 0.334899i | −0.129622 | − | 0.0169583i | ||||
\(391\) | 0.233428 | 0.0118050 | ||||||||
\(392\) | 4.00225 | + | 5.74300i | 0.202144 | + | 0.290065i | ||||
\(393\) | −5.57371 | + | 9.65394i | −0.281156 | + | 0.486977i | ||||
\(394\) | 5.18443 | 0.261188 | ||||||||
\(395\) | 0.240872 | − | 0.139067i | 0.0121196 | − | 0.00699724i | ||||
\(396\) | 2.22627 | + | 1.28534i | 0.111874 | + | 0.0645907i | ||||
\(397\) | 1.72832i | 0.0867420i | 0.999059 | + | 0.0433710i | \(0.0138097\pi\) | ||||
−0.999059 | + | 0.0433710i | \(0.986190\pi\) | |||||||
\(398\) | 16.1417i | 0.809111i | ||||||||
\(399\) | −5.47881 | − | 17.4443i | −0.274283 | − | 0.873308i | ||||
\(400\) | −2.24366 | + | 3.88613i | −0.112183 | + | 0.194306i | ||||
\(401\) | −11.7488 | + | 6.78319i | −0.586709 | + | 0.338737i | −0.763795 | − | 0.645459i | \(-0.776666\pi\) |
0.177086 | + | 0.984195i | \(0.443333\pi\) | |||||||
\(402\) | 0.938052 | + | 1.62475i | 0.0467858 | + | 0.0810354i | ||||
\(403\) | 18.9234 | − | 7.85629i | 0.942641 | − | 0.391350i | ||||
\(404\) | 5.79514 | − | 10.0375i | 0.288319 | − | 0.499383i | ||||
\(405\) | −0.620092 | − | 0.358010i | −0.0308126 | − | 0.0177897i | ||||
\(406\) | 4.40134 | + | 14.0137i | 0.218435 | + | 0.695487i | ||||
\(407\) | 5.36129 | + | 9.28603i | 0.265749 | + | 0.460292i | ||||
\(408\) | 0.0215086 | + | 0.0124180i | 0.00106484 | + | 0.000614784i | ||||
\(409\) | 1.00634 | + | 0.581012i | 0.0497605 | + | 0.0287292i | 0.524674 | − | 0.851303i | \(-0.324187\pi\) |
−0.474913 | + | 0.880033i | \(0.657521\pi\) | |||||||
\(410\) | 3.25719 | + | 1.88054i | 0.160861 | + | 0.0928731i | ||||
\(411\) | 14.5467 | + | 8.39853i | 0.717534 | + | 0.414269i | ||||
\(412\) | 7.89706 | + | 13.6781i | 0.389060 | + | 0.673872i | ||||
\(413\) | −5.81605 | − | 1.29619i | −0.286189 | − | 0.0637813i | ||||
\(414\) | 8.13957 | + | 4.69938i | 0.400038 | + | 0.230962i | ||||
\(415\) | 3.16996 | − | 5.49053i | 0.155607 | − | 0.269520i | ||||
\(416\) | 2.86225 | + | 2.19260i | 0.140334 | + | 0.107501i | ||||
\(417\) | 9.50946 | + | 16.4709i | 0.465680 | + | 0.806582i | ||||
\(418\) | −15.3855 | + | 8.88282i | −0.752529 | + | 0.434473i | ||||
\(419\) | 16.6656 | − | 28.8657i | 0.814169 | − | 1.41018i | −0.0957534 | − | 0.995405i | \(-0.530526\pi\) |
0.909923 | − | 0.414778i | \(-0.136141\pi\) | |||||||
\(420\) | −1.28140 | + | 1.39528i | −0.0625260 | + | 0.0680827i | ||||
\(421\) | 17.4686i | 0.851367i | 0.904872 | + | 0.425684i | \(0.139966\pi\) | ||||
−0.904872 | + | 0.425684i | \(0.860034\pi\) | |||||||
\(422\) | 15.3747i | 0.748429i | ||||||||
\(423\) | −4.32056 | − | 2.49448i | −0.210073 | − | 0.121286i | ||||
\(424\) | 8.18328 | − | 4.72462i | 0.397415 | − | 0.229448i | ||||
\(425\) | 0.111447 | 0.00540598 | ||||||||
\(426\) | 4.34310 | − | 7.52246i | 0.210424 | − | 0.364465i | ||||
\(427\) | 1.64578 | − | 0.516898i | 0.0796450 | − | 0.0250144i | ||||
\(428\) | 0.482687 | 0.0233315 | ||||||||
\(429\) | 1.20237 | − | 9.19040i | 0.0580508 | − | 0.443717i | ||||
\(430\) | −4.56445 | − | 7.90587i | −0.220118 | − | 0.381255i | ||||
\(431\) | − | 22.8866i | − | 1.10241i | −0.834370 | − | 0.551205i | \(-0.814168\pi\) | ||
0.834370 | − | 0.551205i | \(-0.185832\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −9.81620 | − | 17.0022i | −0.471736 | − | 0.817071i | 0.527741 | − | 0.849405i | \(-0.323039\pi\) |
−0.999477 | + | 0.0323342i | \(0.989706\pi\) | |||||||
\(434\) | 3.27055 | − | 14.6751i | 0.156991 | − | 0.704427i | ||||
\(435\) | −3.44261 | + | 1.98759i | −0.165060 | + | 0.0952977i | ||||
\(436\) | 3.20457i | 0.153471i | ||||||||
\(437\) | −56.2515 | + | 32.4768i | −2.69088 | + | 1.55358i | ||||
\(438\) | 7.94250 | − | 13.7568i | 0.379507 | − | 0.657326i | ||||
\(439\) | 12.7988 | + | 22.1682i | 0.610854 | + | 1.05803i | 0.991097 | + | 0.133144i | \(0.0425072\pi\) |
−0.380242 | + | 0.924887i | \(0.624159\pi\) | |||||||
\(440\) | 1.59406 | + | 0.920330i | 0.0759937 | + | 0.0438750i | ||||
\(441\) | 5.74300 | − | 4.00225i | 0.273476 | − | 0.190583i | ||||
\(442\) | 0.0116164 | − | 0.0887910i | 0.000552535 | − | 0.00422336i | ||||
\(443\) | 10.9535 | − | 18.9721i | 0.520418 | − | 0.901390i | −0.479301 | − | 0.877651i | \(-0.659110\pi\) |
0.999718 | − | 0.0237390i | \(-0.00755706\pi\) | |||||||
\(444\) | 4.17111i | 0.197952i | ||||||||
\(445\) | 10.6244 | 0.503646 | ||||||||
\(446\) | −12.8154 | −0.606826 | ||||||||
\(447\) | 12.2538i | 0.579584i | ||||||||
\(448\) | 2.52418 | − | 0.792781i | 0.119256 | − | 0.0374554i | ||||
\(449\) | −23.0029 | + | 13.2807i | −1.08557 | + | 0.626756i | −0.932394 | − | 0.361443i | \(-0.882284\pi\) |
−0.153179 | + | 0.988198i | \(0.548951\pi\) | |||||||
\(450\) | 3.88613 | + | 2.24366i | 0.183194 | + | 0.105767i | ||||
\(451\) | −6.75156 | + | 11.6941i | −0.317919 | + | 0.550651i | ||||
\(452\) | −8.37562 | −0.393956 | ||||||||
\(453\) | 11.5364 | − | 6.66053i | 0.542026 | − | 0.312939i | ||||
\(454\) | −20.1537 | −0.945858 | ||||||||
\(455\) | 6.41777 | + | 2.33809i | 0.300870 | + | 0.109611i | ||||
\(456\) | −6.91088 | −0.323631 | ||||||||
\(457\) | 25.3660 | − | 14.6451i | 1.18657 | − | 0.685068i | 0.229046 | − | 0.973416i | \(-0.426439\pi\) |
0.957526 | + | 0.288348i | \(0.0931060\pi\) | |||||||
\(458\) | −10.2670 | −0.479744 | ||||||||
\(459\) | 0.0124180 | − | 0.0215086i | 0.000579624 | − | 0.00100394i | ||||
\(460\) | 5.82810 | + | 3.36485i | 0.271736 | + | 0.156887i | ||||
\(461\) | −1.95594 | + | 1.12927i | −0.0910974 | + | 0.0525951i | −0.544857 | − | 0.838529i | \(-0.683416\pi\) |
0.453759 | + | 0.891124i | \(0.350083\pi\) | |||||||
\(462\) | −5.00938 | − | 4.60053i | −0.233057 | − | 0.214036i | ||||
\(463\) | − | 2.33300i | − | 0.108424i | −0.998529 | − | 0.0542119i | \(-0.982735\pi\) | ||
0.998529 | − | 0.0542119i | \(-0.0172647\pi\) | |||||||
\(464\) | 5.55177 | 0.257734 | ||||||||
\(465\) | 4.06896 | 0.188694 | ||||||||
\(466\) | − | 3.12234i | − | 0.144639i | ||||||
\(467\) | −21.1203 | + | 36.5814i | −0.977329 | + | 1.69278i | −0.305305 | + | 0.952255i | \(0.598758\pi\) |
−0.672025 | + | 0.740529i | \(0.734575\pi\) | |||||||
\(468\) | 2.19260 | − | 2.86225i | 0.101353 | − | 0.132308i | ||||
\(469\) | −1.48734 | − | 4.73563i | −0.0686789 | − | 0.218671i | ||||
\(470\) | −3.09361 | − | 1.78610i | −0.142698 | − | 0.0823866i | ||||
\(471\) | 3.49931 | + | 6.06098i | 0.161240 | + | 0.279275i | ||||
\(472\) | −1.12610 | + | 1.95045i | −0.0518328 | + | 0.0897770i | ||||
\(473\) | 28.3839 | − | 16.3874i | 1.30509 | − | 0.753495i | ||||
\(474\) | 0.388445i | 0.0178419i | ||||||||
\(475\) | −26.8566 | + | 15.5056i | −1.23226 | + | 0.711447i | ||||
\(476\) | −0.0483970 | − | 0.0444470i | −0.00221827 | − | 0.00203722i | ||||
\(477\) | −4.72462 | − | 8.18328i | −0.216326 | − | 0.374687i | ||||
\(478\) | −6.11624 | − | 10.5936i | −0.279750 | − | 0.484542i | ||||
\(479\) | 19.3019i | 0.881925i | 0.897526 | + | 0.440962i | \(0.145363\pi\) | ||||
−0.897526 | + | 0.440962i | \(0.854637\pi\) | |||||||
\(480\) | 0.358010 | + | 0.620092i | 0.0163409 | + | 0.0283032i | ||||
\(481\) | 13.8897 | − | 5.76649i | 0.633316 | − | 0.262929i | ||||
\(482\) | 1.88892 | 0.0860382 | ||||||||
\(483\) | −18.3150 | − | 16.8202i | −0.833361 | − | 0.765345i | ||||
\(484\) | 2.19580 | − | 3.80324i | 0.0998093 | − | 0.172875i | ||||
\(485\) | 1.47749 | 0.0670894 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −12.9928 | − | 7.50142i | −0.588762 | − | 0.339922i | 0.175846 | − | 0.984418i | \(-0.443734\pi\) |
−0.764608 | + | 0.644496i | \(0.777067\pi\) | |||||||
\(488\) | − | 0.652006i | − | 0.0295149i | ||||||
\(489\) | 10.1930i | 0.460942i | ||||||||
\(490\) | 4.11210 | − | 2.86569i | 0.185766 | − | 0.129459i | ||||
\(491\) | 14.2048 | − | 24.6034i | 0.641052 | − | 1.11033i | −0.344147 | − | 0.938916i | \(-0.611832\pi\) |
0.985198 | − | 0.171418i | \(-0.0548350\pi\) | |||||||
\(492\) | −4.54901 | + | 2.62637i | −0.205085 | + | 0.118406i | ||||
\(493\) | −0.0689420 | − | 0.119411i | −0.00310499 | − | 0.00537800i | ||||
\(494\) | 9.55417 | + | 23.0131i | 0.429862 | + | 1.03541i | ||||
\(495\) | 0.920330 | − | 1.59406i | 0.0413657 | − | 0.0716476i | ||||
\(496\) | −4.92140 | − | 2.84137i | −0.220977 | − | 0.127581i | ||||
\(497\) | −15.5450 | + | 16.9264i | −0.697286 | + | 0.759254i | ||||
\(498\) | 4.42719 | + | 7.66812i | 0.198387 | + | 0.343617i | ||||
\(499\) | 3.33919 | + | 1.92788i | 0.149482 | + | 0.0863038i | 0.572876 | − | 0.819642i | \(-0.305828\pi\) |
−0.423393 | + | 0.905946i | \(0.639161\pi\) | |||||||
\(500\) | 5.88301 | + | 3.39656i | 0.263096 | + | 0.151899i | ||||
\(501\) | 6.33732 | + | 3.65885i | 0.283131 | + | 0.163466i | ||||
\(502\) | 13.0952 | + | 7.56052i | 0.584467 | + | 0.337442i | ||||
\(503\) | 16.3872 | + | 28.3835i | 0.730670 | + | 1.26556i | 0.956597 | + | 0.291413i | \(0.0941254\pi\) |
−0.225927 | + | 0.974144i | \(0.572541\pi\) | |||||||
\(504\) | −0.792781 | − | 2.52418i | −0.0353133 | − | 0.112436i | ||||
\(505\) | −7.18704 | − | 4.14944i | −0.319819 | − | 0.184648i | ||||
\(506\) | −12.0806 | + | 20.9242i | −0.537048 | + | 0.930195i | ||||
\(507\) | −12.5625 | − | 3.34430i | −0.557919 | − | 0.148526i | ||||
\(508\) | 11.0533 | + | 19.1448i | 0.490410 | + | 0.849415i | ||||
\(509\) | −30.9031 | + | 17.8419i | −1.36976 | + | 0.790829i | −0.990897 | − | 0.134625i | \(-0.957017\pi\) |
−0.378859 | + | 0.925454i | \(0.623684\pi\) | |||||||
\(510\) | 0.00889156 | − | 0.0154006i | 0.000393725 | − | 0.000681951i | ||||
\(511\) | −28.4281 | + | 30.9545i | −1.25758 | + | 1.36935i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.91088i | 0.305123i | ||||||||
\(514\) | 4.89658 | + | 2.82704i | 0.215979 | + | 0.124695i | ||||
\(515\) | 9.79381 | − | 5.65446i | 0.431567 | − | 0.249165i | ||||
\(516\) | 12.7495 | 0.561266 | ||||||||
\(517\) | 6.41250 | − | 11.1068i | 0.282022 | − | 0.488476i | ||||
\(518\) | 2.40057 | − | 10.7715i | 0.105475 | − | 0.473271i | ||||
\(519\) | −6.48507 | −0.284663 | ||||||||
\(520\) | 1.56995 | − | 2.04943i | 0.0688468 | − | 0.0898735i | ||||
\(521\) | −0.555626 | − | 0.962372i | −0.0243424 | − | 0.0421623i | 0.853598 | − | 0.520933i | \(-0.174416\pi\) |
−0.877940 | + | 0.478771i | \(0.841083\pi\) | |||||||
\(522\) | − | 5.55177i | − | 0.242994i | ||||||
\(523\) | −0.368072 | − | 0.637520i | −0.0160947 | − | 0.0278768i | 0.857866 | − | 0.513874i | \(-0.171790\pi\) |
−0.873961 | + | 0.485997i | \(0.838457\pi\) | |||||||
\(524\) | −5.57371 | − | 9.65394i | −0.243488 | − | 0.421734i | ||||
\(525\) | −8.74425 | − | 8.03057i | −0.381630 | − | 0.350483i | ||||
\(526\) | 12.5991 | − | 7.27412i | 0.549349 | − | 0.317167i | ||||
\(527\) | 0.141137i | 0.00614802i | ||||||||
\(528\) | −2.22627 | + | 1.28534i | −0.0968861 | + | 0.0559372i | ||||
\(529\) | −32.6684 | + | 56.5833i | −1.42036 | + | 2.46014i | ||||
\(530\) | −3.38293 | − | 5.85940i | −0.146945 | − | 0.254516i | ||||
\(531\) | 1.95045 | + | 1.12610i | 0.0846425 | + | 0.0488684i | ||||
\(532\) | 17.8466 | + | 3.97737i | 0.773749 | + | 0.172441i | ||||
\(533\) | 15.0347 | + | 11.5172i | 0.651225 | + | 0.498865i | ||||
\(534\) | −7.41908 | + | 12.8502i | −0.321055 | + | 0.556083i | ||||
\(535\) | − | 0.345613i | − | 0.0149422i | ||||||
\(536\) | −1.87610 | −0.0810354 | ||||||||
\(537\) | −23.2228 | −1.00214 | ||||||||
\(538\) | − | 3.46062i | − | 0.149198i | ||||||
\(539\) | 10.2885 | + | 14.7634i | 0.443157 | + | 0.635905i | ||||
\(540\) | 0.620092 | − | 0.358010i | 0.0266845 | − | 0.0154063i | ||||
\(541\) | 3.31356 | + | 1.91309i | 0.142461 | + | 0.0822500i | 0.569536 | − | 0.821966i | \(-0.307123\pi\) |
−0.427075 | + | 0.904216i | \(0.640456\pi\) | |||||||
\(542\) | 5.78543 | − | 10.0207i | 0.248506 | − | 0.430424i | ||||
\(543\) | 5.61910 | 0.241139 | ||||||||
\(544\) | −0.0215086 | + | 0.0124180i | −0.000922176 | + | 0.000532418i | ||||
\(545\) | 2.29454 | 0.0982871 | ||||||||
\(546\) | −7.30946 | + | 6.12958i | −0.312816 | + | 0.262322i | ||||
\(547\) | −5.24598 | −0.224302 | −0.112151 | − | 0.993691i | \(-0.535774\pi\) | ||||
−0.112151 | + | 0.993691i | \(0.535774\pi\) | |||||||
\(548\) | −14.5467 | + | 8.39853i | −0.621403 | + | 0.358767i | ||||
\(549\) | −0.652006 | −0.0278269 | ||||||||
\(550\) | −5.76772 | + | 9.98999i | −0.245937 | + | 0.425975i | ||||
\(551\) | 33.2273 | + | 19.1838i | 1.41553 | + | 0.817257i | ||||
\(552\) | −8.13957 | + | 4.69938i | −0.346443 | + | 0.200019i | ||||
\(553\) | 0.223559 | − | 1.00312i | 0.00950671 | − | 0.0426570i | ||||
\(554\) | − | 4.63996i | − | 0.197133i | ||||||
\(555\) | 2.98660 | 0.126774 | ||||||||
\(556\) | −19.0189 | −0.806582 | ||||||||
\(557\) | − | 19.4339i | − | 0.823440i | −0.911310 | − | 0.411720i | \(-0.864928\pi\) | ||
0.911310 | − | 0.411720i | \(-0.135072\pi\) | |||||||
\(558\) | −2.84137 | + | 4.92140i | −0.120285 | + | 0.208339i | ||||
\(559\) | −17.6260 | − | 42.4555i | −0.745499 | − | 1.79568i | ||||
\(560\) | −0.567647 | − | 1.80737i | −0.0239875 | − | 0.0763752i | ||||
\(561\) | 0.0552918 | + | 0.0319228i | 0.00233442 | + | 0.00134778i | ||||
\(562\) | 10.4810 | + | 18.1537i | 0.442116 | + | 0.765767i | ||||
\(563\) | −2.06339 | + | 3.57390i | −0.0869616 | + | 0.150622i | −0.906225 | − | 0.422795i | \(-0.861049\pi\) |
0.819264 | + | 0.573417i | \(0.194382\pi\) | |||||||
\(564\) | 4.32056 | − | 2.49448i | 0.181929 | − | 0.105036i | ||||
\(565\) | 5.99712i | 0.252301i | ||||||||
\(566\) | 4.08795 | − | 2.36018i | 0.171829 | − | 0.0992057i | ||||
\(567\) | −2.52418 | + | 0.792781i | −0.106006 | + | 0.0332937i | ||||
\(568\) | 4.34310 | + | 7.52246i | 0.182232 | + | 0.315636i | ||||
\(569\) | 12.5267 | + | 21.6969i | 0.525147 | + | 0.909581i | 0.999571 | + | 0.0292850i | \(0.00932303\pi\) |
−0.474424 | + | 0.880296i | \(0.657344\pi\) | |||||||
\(570\) | 4.94833i | 0.207263i | ||||||||
\(571\) | −15.9460 | − | 27.6192i | −0.667318 | − | 1.15583i | −0.978651 | − | 0.205528i | \(-0.934109\pi\) |
0.311333 | − | 0.950301i | \(-0.399224\pi\) | |||||||
\(572\) | 7.35793 | + | 5.63648i | 0.307651 | + | 0.235673i | ||||
\(573\) | 23.8945 | 0.998206 | ||||||||
\(574\) | 13.2589 | − | 4.16428i | 0.553416 | − | 0.173814i | ||||
\(575\) | −21.0876 | + | 36.5248i | −0.879414 | + | 1.52319i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 19.6398 | − | 11.3390i | 0.817614 | − | 0.472050i | −0.0319788 | − | 0.999489i | \(-0.510181\pi\) |
0.849593 | + | 0.527439i | \(0.176848\pi\) | |||||||
\(578\) | −14.7219 | − | 8.49969i | −0.612350 | − | 0.353541i | ||||
\(579\) | − | 20.9972i | − | 0.872615i | ||||||
\(580\) | − | 3.97518i | − | 0.165060i | ||||||
\(581\) | −7.01959 | − | 22.3501i | −0.291221 | − | 0.927238i | ||||
\(582\) | −1.03174 | + | 1.78702i | −0.0427669 | + | 0.0740744i | ||||
\(583\) | 21.0366 | − | 12.1455i | 0.871247 | − | 0.503015i | ||||
\(584\) | 7.94250 | + | 13.7568i | 0.328663 | + | 0.569261i | ||||
\(585\) | −2.04943 | − | 1.56995i | −0.0847336 | − | 0.0649094i | ||||
\(586\) | −16.7744 | + | 29.0541i | −0.692943 | + | 1.20021i | ||||
\(587\) | −2.99085 | − | 1.72677i | −0.123446 | − | 0.0712714i | 0.437006 | − | 0.899459i | \(-0.356039\pi\) |
−0.560451 | + | 0.828187i | \(0.689372\pi\) | |||||||
\(588\) | 0.594548 | + | 6.97471i | 0.0245187 | + | 0.287632i | ||||
\(589\) | −19.6364 | − | 34.0112i | −0.809102 | − | 1.40141i | ||||
\(590\) | 1.39657 | + | 0.806308i | 0.0574957 | + | 0.0331952i | ||||
\(591\) | 4.48984 | + | 2.59221i | 0.184688 | + | 0.106629i | ||||
\(592\) | −3.61229 | − | 2.08556i | −0.148464 | − | 0.0857158i | ||||
\(593\) | 12.0235 | + | 6.94179i | 0.493747 | + | 0.285065i | 0.726128 | − | 0.687560i | \(-0.241318\pi\) |
−0.232380 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(594\) | 1.28534 | + | 2.22627i | 0.0527381 | + | 0.0913451i | ||||
\(595\) | −0.0318250 | + | 0.0346532i | −0.00130470 | + | 0.00142064i | ||||
\(596\) | −10.6121 | − | 6.12689i | −0.434688 | − | 0.250967i | ||||
\(597\) | −8.07086 | + | 13.9791i | −0.330318 | + | 0.572128i | ||||
\(598\) | 26.9016 | + | 20.6078i | 1.10009 | + | 0.842714i | ||||
\(599\) | −1.37576 | − | 2.38289i | −0.0562122 | − | 0.0973624i | 0.836550 | − | 0.547891i | \(-0.184569\pi\) |
−0.892762 | + | 0.450528i | \(0.851236\pi\) | |||||||
\(600\) | −3.88613 | + | 2.24366i | −0.158651 | + | 0.0915969i | ||||
\(601\) | 17.0005 | − | 29.4457i | 0.693464 | − | 1.20112i | −0.277231 | − | 0.960803i | \(-0.589417\pi\) |
0.970696 | − | 0.240312i | \(-0.0772499\pi\) | |||||||
\(602\) | −32.9243 | − | 7.33764i | −1.34189 | − | 0.299060i | ||||
\(603\) | 1.87610i | 0.0764009i | ||||||||
\(604\) | 13.3211i | 0.542026i | ||||||||
\(605\) | −2.72320 | − | 1.57224i | −0.110714 | − | 0.0639207i | ||||
\(606\) | 10.0375 | − | 5.79514i | 0.407745 | − | 0.235412i | ||||
\(607\) | 30.9167 | 1.25487 | 0.627434 | − | 0.778669i | \(-0.284105\pi\) | ||||
0.627434 | + | 0.778669i | \(0.284105\pi\) | |||||||
\(608\) | 3.45544 | − | 5.98499i | 0.140137 | − | 0.242724i | ||||
\(609\) | −3.19517 | + | 14.3369i | −0.129475 | + | 0.580959i | ||||
\(610\) | −0.466850 | −0.0189022 | ||||||||
\(611\) | −14.2797 | − | 10.9388i | −0.577693 | − | 0.442537i | ||||
\(612\) | 0.0124180 | + | 0.0215086i | 0.000501969 | + | 0.000869435i | ||||
\(613\) | − | 6.52803i | − | 0.263665i | −0.991272 | − | 0.131832i | \(-0.957914\pi\) | ||
0.991272 | − | 0.131832i | \(-0.0420860\pi\) | |||||||
\(614\) | −2.74622 | − | 4.75660i | −0.110829 | − | 0.191961i | ||||
\(615\) | 1.88054 | + | 3.25719i | 0.0758306 | + | 0.131342i | ||||
\(616\) | 6.48886 | − | 2.03798i | 0.261444 | − | 0.0821127i | ||||
\(617\) | −10.8491 | + | 6.26373i | −0.436768 | + | 0.252168i | −0.702226 | − | 0.711954i | \(-0.747810\pi\) |
0.265458 | + | 0.964123i | \(0.414477\pi\) | |||||||
\(618\) | 15.7941i | 0.635333i | ||||||||
\(619\) | 3.04630 | − | 1.75878i | 0.122441 | − | 0.0706914i | −0.437529 | − | 0.899205i | \(-0.644146\pi\) |
0.559970 | + | 0.828513i | \(0.310813\pi\) | |||||||
\(620\) | −2.03448 | + | 3.52382i | −0.0817067 | + | 0.141520i | ||||
\(621\) | 4.69938 | + | 8.13957i | 0.188580 | + | 0.326630i | ||||
\(622\) | −12.9075 | − | 7.45213i | −0.517543 | − | 0.298803i | ||||
\(623\) | 26.5546 | − | 28.9145i | 1.06389 | − | 1.15844i | ||||
\(624\) | 1.38248 | + | 3.32998i | 0.0553436 | + | 0.133306i | ||||
\(625\) | −8.78628 | + | 15.2183i | −0.351451 | + | 0.608731i | ||||
\(626\) | 3.60346i | 0.144023i | ||||||||
\(627\) | −17.7656 | −0.709492 | ||||||||
\(628\) | −6.99861 | −0.279275 | ||||||||
\(629\) | 0.103594i | 0.00413056i | ||||||||
\(630\) | −1.80737 | + | 0.567647i | −0.0720072 | + | 0.0226156i | ||||
\(631\) | −17.1805 | + | 9.91915i | −0.683944 | + | 0.394875i | −0.801339 | − | 0.598210i | \(-0.795879\pi\) |
0.117395 | + | 0.993085i | \(0.462545\pi\) | |||||||
\(632\) | −0.336404 | − | 0.194223i | −0.0133814 | − | 0.00772577i | ||||
\(633\) | −7.68735 | + | 13.3149i | −0.305545 | + | 0.529219i | ||||
\(634\) | 4.09146 | 0.162493 | ||||||||
\(635\) | 13.7081 | − | 7.91438i | 0.543990 | − | 0.314073i | ||||
\(636\) | 9.44924 | 0.374687 | ||||||||
\(637\) | 22.4037 | − | 11.6222i | 0.887665 | − | 0.460490i | ||||
\(638\) | 14.2718 | 0.565027 | ||||||||
\(639\) | 7.52246 | − | 4.34310i | 0.297584 | − | 0.171810i | ||||
\(640\) | −0.716021 | −0.0283032 | ||||||||
\(641\) | −1.57697 | + | 2.73139i | −0.0622865 | + | 0.107883i | −0.895487 | − | 0.445088i | \(-0.853173\pi\) |
0.833201 | + | 0.552971i | \(0.186506\pi\) | |||||||
\(642\) | 0.418019 | + | 0.241343i | 0.0164979 | + | 0.00952506i | ||||
\(643\) | 29.0975 | − | 16.7994i | 1.14749 | − | 0.662505i | 0.199217 | − | 0.979955i | \(-0.436160\pi\) |
0.948275 | + | 0.317451i | \(0.102827\pi\) | |||||||
\(644\) | 23.7242 | − | 7.45116i | 0.934864 | − | 0.293617i | ||||
\(645\) | − | 9.12891i | − | 0.359450i | ||||||
\(646\) | −0.171639 | −0.00675304 | ||||||||
\(647\) | −22.3012 | −0.876750 | −0.438375 | − | 0.898792i | \(-0.644446\pi\) | ||||
−0.438375 | + | 0.898792i | \(0.644446\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −2.89483 | + | 5.01399i | −0.113632 | + | 0.196816i | ||||
\(650\) | 12.8438 | + | 9.83890i | 0.503776 | + | 0.385913i | ||||
\(651\) | 10.1699 | − | 11.0737i | 0.398591 | − | 0.434014i | ||||
\(652\) | −8.82738 | − | 5.09649i | −0.345707 | − | 0.199594i | ||||
\(653\) | 3.74174 | + | 6.48088i | 0.146426 | + | 0.253616i | 0.929904 | − | 0.367803i | \(-0.119890\pi\) |
−0.783478 | + | 0.621419i | \(0.786556\pi\) | |||||||
\(654\) | −1.60228 | + | 2.77524i | −0.0626542 | + | 0.108520i | ||||
\(655\) | −6.91242 | + | 3.99089i | −0.270091 | + | 0.155937i | ||||
\(656\) | − | 5.25275i | − | 0.205085i | ||||||
\(657\) | 13.7568 | − | 7.94250i | 0.536705 | − | 0.309867i | ||||
\(658\) | −12.5930 | + | 3.95515i | −0.490928 | + | 0.154188i | ||||
\(659\) | 4.51922 | + | 7.82751i | 0.176044 | + | 0.304917i | 0.940522 | − | 0.339733i | \(-0.110337\pi\) |
−0.764478 | + | 0.644650i | \(0.777003\pi\) | |||||||
\(660\) | 0.920330 | + | 1.59406i | 0.0358238 | + | 0.0620486i | ||||
\(661\) | − | 11.6240i | − | 0.452120i | −0.974113 | − | 0.226060i | \(-0.927415\pi\) | ||
0.974113 | − | 0.226060i | \(-0.0725846\pi\) | |||||||
\(662\) | −9.70350 | − | 16.8069i | −0.377137 | − | 0.653221i | ||||
\(663\) | 0.0544556 | − | 0.0710871i | 0.00211488 | − | 0.00276079i | ||||
\(664\) | −8.85439 | −0.343617 | ||||||||
\(665\) | 2.84788 | − | 12.7785i | 0.110436 | − | 0.495531i | ||||
\(666\) | −2.08556 | + | 3.61229i | −0.0808136 | + | 0.139973i | ||||
\(667\) | 52.1798 | 2.02041 | ||||||||
\(668\) | −6.33732 | + | 3.65885i | −0.245198 | + | 0.141565i | ||||
\(669\) | −11.0984 | − | 6.40769i | −0.429091 | − | 0.247736i | ||||
\(670\) | 1.34333i | 0.0518973i | ||||||||
\(671\) | − | 1.67610i | − | 0.0647051i | ||||||
\(672\) | 2.58240 | + | 0.575523i | 0.0996181 | + | 0.0222013i | ||||
\(673\) | 5.44014 | − | 9.42260i | 0.209702 | − | 0.363214i | −0.741919 | − | 0.670490i | \(-0.766084\pi\) |
0.951621 | + | 0.307275i | \(0.0994173\pi\) | |||||||
\(674\) | 19.9658 | − | 11.5272i | 0.769053 | − | 0.444013i | ||||
\(675\) | 2.24366 | + | 3.88613i | 0.0863584 | + | 0.149577i | ||||
\(676\) | 9.17748 | − | 9.20727i | 0.352980 | − | 0.354126i | ||||
\(677\) | 8.71040 | − | 15.0869i | 0.334768 | − | 0.579835i | −0.648672 | − | 0.761068i | \(-0.724675\pi\) |
0.983440 | + | 0.181233i | \(0.0580087\pi\) | |||||||
\(678\) | −7.25350 | − | 4.18781i | −0.278569 | − | 0.160832i | ||||
\(679\) | 3.69283 | − | 4.02101i | 0.141718 | − | 0.154312i | ||||
\(680\) | 0.00889156 | + | 0.0154006i | 0.000340976 | + | 0.000590587i | ||||
\(681\) | −17.4536 | − | 10.0768i | −0.668823 | − | 0.386145i | ||||
\(682\) | −12.6513 | − | 7.30425i | −0.484445 | − | 0.279694i | ||||
\(683\) | 30.8882 | + | 17.8333i | 1.18190 | + | 0.682372i | 0.956454 | − | 0.291883i | \(-0.0942819\pi\) |
0.225449 | + | 0.974255i | \(0.427615\pi\) | |||||||
\(684\) | −5.98499 | − | 3.45544i | −0.228842 | − | 0.132122i | ||||
\(685\) | 6.01352 | + | 10.4157i | 0.229765 | + | 0.397964i | ||||
\(686\) | 2.47875 | − | 18.3536i | 0.0946390 | − | 0.700745i | ||||
\(687\) | −8.89145 | − | 5.13348i | −0.339230 | − | 0.195855i | ||||
\(688\) | −6.37475 | + | 11.0414i | −0.243035 | + | 0.420949i | ||||
\(689\) | −13.0634 | − | 31.4658i | −0.497676 | − | 1.19875i | ||||
\(690\) | 3.36485 | + | 5.82810i | 0.128098 | + | 0.221872i | ||||
\(691\) | −2.62439 | + | 1.51519i | −0.0998365 | + | 0.0576406i | −0.549087 | − | 0.835765i | \(-0.685024\pi\) |
0.449250 | + | 0.893406i | \(0.351691\pi\) | |||||||
\(692\) | 3.24254 | − | 5.61624i | 0.123263 | − | 0.213497i | ||||
\(693\) | −2.03798 | − | 6.48886i | −0.0774166 | − | 0.246492i | ||||
\(694\) | 4.60157i | 0.174673i | ||||||||
\(695\) | 13.6179i | 0.516558i | ||||||||
\(696\) | 4.80797 | + | 2.77589i | 0.182246 | + | 0.105220i | ||||
\(697\) | −0.112979 | + | 0.0652287i | −0.00427940 | + | 0.00247071i | ||||
\(698\) | 3.73204 | 0.141260 | ||||||||
\(699\) | 1.56117 | − | 2.70402i | 0.0590488 | − | 0.102276i | ||||
\(700\) | 11.3268 | − | 3.55746i | 0.428113 | − | 0.134459i | ||||
\(701\) | −27.7372 | −1.04762 | −0.523810 | − | 0.851835i | \(-0.675490\pi\) | ||||
−0.523810 | + | 0.851835i | \(0.675490\pi\) | |||||||
\(702\) | 3.32998 | − | 1.38248i | 0.125682 | − | 0.0521784i | ||||
\(703\) | −14.4130 | − | 24.9641i | −0.543597 | − | 0.941538i | ||||
\(704\) | − | 2.57068i | − | 0.0968861i | ||||||
\(705\) | −1.78610 | − | 3.09361i | −0.0672683 | − | 0.116512i | ||||
\(706\) | 13.1765 | + | 22.8223i | 0.495903 | + | 0.858928i | ||||
\(707\) | −29.2560 | + | 9.18855i | −1.10029 | + | 0.345571i | ||||
\(708\) | −1.95045 | + | 1.12610i | −0.0733026 | + | 0.0423213i | ||||
\(709\) | − | 16.3014i | − | 0.612214i | −0.951997 | − | 0.306107i | \(-0.900974\pi\) | ||
0.951997 | − | 0.306107i | \(-0.0990265\pi\) | |||||||
\(710\) | 5.38624 | − | 3.10975i | 0.202142 | − | 0.116707i | ||||
\(711\) | −0.194223 | + | 0.336404i | −0.00728392 | + | 0.0126161i | ||||
\(712\) | −7.41908 | − | 12.8502i | −0.278042 | − | 0.481582i | ||||
\(713\) | −46.2551 | − | 26.7054i | −1.73227 | − | 1.00012i | ||||
\(714\) | −0.0196895 | − | 0.0626907i | −0.000736862 | − | 0.00234614i | ||||
\(715\) | 4.03583 | − | 5.26843i | 0.150932 | − | 0.197028i | ||||
\(716\) | 11.6114 | − | 20.1116i | 0.433939 | − | 0.751605i | ||||
\(717\) | − | 12.2325i | − | 0.456830i | ||||||
\(718\) | 8.21648 | 0.306636 | ||||||||
\(719\) | 6.89552 | 0.257159 | 0.128580 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128580 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(720\) | 0.716021i | 0.0266845i | ||||||||
\(721\) | 9.08988 | − | 40.7867i | 0.338525 | − | 1.51898i | ||||
\(722\) | 24.9071 | − | 14.3801i | 0.926945 | − | 0.535172i | ||||
\(723\) | 1.63586 | + | 0.944462i | 0.0608382 | + | 0.0351249i | ||||
\(724\) | −2.80955 | + | 4.86628i | −0.104416 | + | 0.180854i | ||||
\(725\) | 24.9125 | 0.925229 | ||||||||
\(726\) | 3.80324 | − | 2.19580i | 0.141152 | − | 0.0814939i | ||||
\(727\) | −26.6965 | −0.990119 | −0.495059 | − | 0.868859i | \(-0.664854\pi\) | ||||
−0.495059 | + | 0.868859i | \(0.664854\pi\) | |||||||
\(728\) | −1.65364 | − | 9.39497i | −0.0612880 | − | 0.348201i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.85017 | − | 5.68700i | 0.364571 | − | 0.210485i | ||||
\(731\) | 0.316647 | 0.0117116 | ||||||||
\(732\) | 0.326003 | − | 0.564654i | 0.0120494 | − | 0.0208702i | ||||
\(733\) | −27.0290 | − | 15.6052i | −0.998337 | − | 0.576390i | −0.0905813 | − | 0.995889i | \(-0.528872\pi\) |
−0.907756 | + | 0.419499i | \(0.862206\pi\) | |||||||
\(734\) | −0.371350 | + | 0.214399i | −0.0137068 | + | 0.00791360i | ||||
\(735\) | 4.99403 | − | 0.425708i | 0.184208 | − | 0.0157025i | ||||
\(736\) | − | 9.39876i | − | 0.346443i | ||||||
\(737\) | −4.82286 | −0.177652 | ||||||||
\(738\) | −5.25275 | −0.193356 | ||||||||
\(739\) | 21.7423i | 0.799804i | 0.916558 | + | 0.399902i | \(0.130956\pi\) | ||||
−0.916558 | + | 0.399902i | \(0.869044\pi\) | |||||||
\(740\) | −1.49330 | + | 2.58647i | −0.0548948 | + | 0.0950806i | ||||
\(741\) | −3.23238 | + | 24.7070i | −0.118744 | + | 0.907633i | ||||
\(742\) | −24.4017 | − | 5.43826i | −0.895814 | − | 0.199645i | ||||
\(743\) | 8.60858 | + | 4.97016i | 0.315818 | + | 0.182338i | 0.649527 | − | 0.760339i | \(-0.274967\pi\) |
−0.333709 | + | 0.942676i | \(0.608300\pi\) | |||||||
\(744\) | −2.84137 | − | 4.92140i | −0.104170 | − | 0.180427i | ||||
\(745\) | −4.38698 | + | 7.59847i | −0.160726 | + | 0.278386i | ||||
\(746\) | 1.74510 | − | 1.00753i | 0.0638927 | − | 0.0368885i | ||||
\(747\) | 8.85439i | 0.323965i | ||||||||
\(748\) | −0.0552918 | + | 0.0319228i | −0.00202167 | + | 0.00116721i | ||||
\(749\) | −0.940592 | − | 0.863824i | −0.0343685 | − | 0.0315634i | ||||
\(750\) | 3.39656 | + | 5.88301i | 0.124025 | + | 0.214817i | ||||
\(751\) | 4.27457 | + | 7.40378i | 0.155981 | + | 0.270168i | 0.933416 | − | 0.358796i | \(-0.116813\pi\) |
−0.777435 | + | 0.628964i | \(0.783479\pi\) | |||||||
\(752\) | 4.98896i | 0.181929i | ||||||||
\(753\) | 7.56052 | + | 13.0952i | 0.275521 | + | 0.477216i | ||||
\(754\) | 2.59669 | − | 19.8481i | 0.0945659 | − | 0.722823i | ||||
\(755\) | 9.53816 | 0.347129 | ||||||||
\(756\) | 0.575523 | − | 2.58240i | 0.0209316 | − | 0.0939209i | ||||
\(757\) | 3.50974 | − | 6.07905i | 0.127564 | − | 0.220947i | −0.795168 | − | 0.606389i | \(-0.792618\pi\) |
0.922732 | + | 0.385442i | \(0.125951\pi\) | |||||||
\(758\) | −17.4156 | −0.632562 | ||||||||
\(759\) | −20.9242 | + | 12.0806i | −0.759501 | + | 0.438498i | ||||
\(760\) | −4.28538 | − | 2.47416i | −0.155447 | − | 0.0897474i | ||||
\(761\) | − | 16.1732i | − | 0.586279i | −0.956070 | − | 0.293139i | \(-0.905300\pi\) | ||
0.956070 | − | 0.293139i | \(-0.0947000\pi\) | |||||||
\(762\) | 22.1066i | 0.800836i | ||||||||
\(763\) | 5.73494 | − | 6.24461i | 0.207619 | − | 0.226070i | ||||
\(764\) | −11.9472 | + | 20.6932i | −0.432236 | + | 0.748655i | ||||
\(765\) | 0.0154006 | − | 0.00889156i | 0.000556811 | − | 0.000321475i | ||||
\(766\) | 0.164165 | + | 0.284342i | 0.00593153 | + | 0.0102737i | ||||
\(767\) | 6.44634 | + | 4.93816i | 0.232764 | + | 0.178307i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 22.6397 | + | 13.0710i | 0.816409 | + | 0.471354i | 0.849176 | − | 0.528109i | \(-0.177099\pi\) |
−0.0327678 | + | 0.999463i | \(0.510432\pi\) | |||||||
\(770\) | −1.45924 | − | 4.64616i | −0.0525873 | − | 0.167436i | ||||
\(771\) | 2.82704 | + | 4.89658i | 0.101813 | + | 0.176346i | ||||
\(772\) | 18.1841 | + | 10.4986i | 0.654461 | + | 0.377853i | ||||
\(773\) | 3.03108 | + | 1.74999i | 0.109020 | + | 0.0629429i | 0.553519 | − | 0.832837i | \(-0.313285\pi\) |
−0.444498 | + | 0.895780i | \(0.646618\pi\) | |||||||
\(774\) | 11.0414 | + | 6.37475i | 0.396875 | + | 0.229136i | ||||
\(775\) | −22.0839 | − | 12.7501i | −0.793276 | − | 0.457998i | ||||
\(776\) | −1.03174 | − | 1.78702i | −0.0370372 | − | 0.0641503i | ||||
\(777\) | 7.46469 | − | 8.12807i | 0.267794 | − | 0.291593i | ||||
\(778\) | 7.45575 | + | 4.30458i | 0.267302 | + | 0.154327i | ||||
\(779\) | 18.1505 | − | 31.4377i | 0.650311 | − | 1.12637i | ||||
\(780\) | 2.38433 | − | 0.989886i | 0.0853728 | − | 0.0354436i | ||||
\(781\) | 11.1647 | + | 19.3378i | 0.399505 | + | 0.691962i | ||||
\(782\) | −0.202155 | + | 0.116714i | −0.00722904 | + | 0.00417369i | ||||
\(783\) | 2.77589 | − | 4.80797i | 0.0992020 | − | 0.171823i | ||||
\(784\) | −6.33755 | − | 2.97246i | −0.226341 | − | 0.106159i | ||||
\(785\) | 5.01115i | 0.178856i | ||||||||
\(786\) | − | 11.1474i | − | 0.397615i | ||||||
\(787\) | −10.6680 | − | 6.15919i | −0.380274 | − | 0.219551i | 0.297664 | − | 0.954671i | \(-0.403793\pi\) |
−0.677937 | + | 0.735120i | \(0.737126\pi\) | |||||||
\(788\) | −4.48984 | + | 2.59221i | −0.159944 | + | 0.0923438i | ||||
\(789\) | 14.5482 | 0.517931 | ||||||||
\(790\) | −0.139067 | + | 0.240872i | −0.00494780 | + | 0.00856984i | ||||
\(791\) | 16.3212 | + | 14.9892i | 0.580316 | + | 0.532953i | ||||
\(792\) | −2.57068 | −0.0913451 | ||||||||
\(793\) | −2.33098 | − | 0.304958i | −0.0827754 | − | 0.0108294i | ||||
\(794\) | −0.864161 | − | 1.49677i | −0.0306679 | − | 0.0531184i | ||||
\(795\) | − | 6.76585i | − | 0.239960i | ||||||
\(796\) | −8.07086 | − | 13.9791i | −0.286064 | − | 0.495478i | ||||
\(797\) | 18.9472 | + | 32.8176i | 0.671145 | + | 1.16246i | 0.977580 | + | 0.210566i | \(0.0675306\pi\) |
−0.306435 | + | 0.951892i | \(0.599136\pi\) | |||||||
\(798\) | 13.4669 | + | 12.3678i | 0.476725 | + | 0.437816i | ||||
\(799\) | 0.107306 | − | 0.0619530i | 0.00379620 | − | 0.00219174i | ||||
\(800\) | − | 4.48731i | − | 0.158651i | ||||||
\(801\) | −12.8502 | + | 7.41908i | −0.454040 | + | 0.262140i | ||||
\(802\) | 6.78319 | − | 11.7488i | 0.239523 | − | 0.414866i | ||||
\(803\) | 20.4176 | + | 35.3644i | 0.720522 | + | 1.24798i | ||||
\(804\) | −1.62475 | − | 0.938052i | −0.0573007 | − | 0.0330826i | ||||
\(805\) | −5.33518 | − | 16.9870i | −0.188040 | − | 0.598713i | ||||
\(806\) | −12.4600 | + | 16.2654i | −0.438885 | + | 0.572926i | ||||
\(807\) | 1.73031 | − | 2.99698i | 0.0609098 | − | 0.105499i | ||||
\(808\) | 11.5903i | 0.407745i | ||||||||
\(809\) | 21.0649 | 0.740603 | 0.370301 | − | 0.928912i | \(-0.379254\pi\) | ||||
0.370301 | + | 0.928912i | \(0.379254\pi\) | |||||||
\(810\) | 0.716021 | 0.0251584 | ||||||||
\(811\) | − | 46.4549i | − | 1.63125i | −0.578578 | − | 0.815627i | \(-0.696392\pi\) | ||
0.578578 | − | 0.815627i | \(-0.303608\pi\) | |||||||
\(812\) | −10.8185 | − | 9.93554i | −0.379655 | − | 0.348669i | ||||
\(813\) | 10.0207 | − | 5.78543i | 0.351440 | − | 0.202904i | ||||
\(814\) | −9.28603 | − | 5.36129i | −0.325475 | − | 0.187913i | ||||
\(815\) | −3.64919 | + | 6.32059i | −0.127826 | + | 0.221400i | ||||
\(816\) | −0.0248360 | −0.000869435 | ||||||||
\(817\) | −76.3057 | + | 44.0551i | −2.66960 | + | 1.54129i | ||||
\(818\) | −1.16202 | −0.0406292 | ||||||||
\(819\) | −9.39497 | + | 1.65364i | −0.328287 | + | 0.0577828i | ||||
\(820\) | −3.76108 | −0.131342 | ||||||||
\(821\) | −5.65583 | + | 3.26539i | −0.197390 | + | 0.113963i | −0.595437 | − | 0.803402i | \(-0.703021\pi\) |
0.398048 | + | 0.917365i | \(0.369688\pi\) | |||||||
\(822\) | −16.7971 | −0.585864 | ||||||||
\(823\) | 3.71035 | − | 6.42651i | 0.129335 | − | 0.224014i | −0.794084 | − | 0.607808i | \(-0.792049\pi\) |
0.923419 | + | 0.383793i | \(0.125383\pi\) | |||||||
\(824\) | −13.6781 | − | 7.89706i | −0.476499 | − | 0.275107i | ||||
\(825\) | −9.98999 | + | 5.76772i | −0.347807 | + | 0.200806i | ||||
\(826\) | 5.68494 | − | 1.78549i | 0.197804 | − | 0.0621253i | ||||
\(827\) | 38.3288i | 1.33282i | 0.745584 | + | 0.666411i | \(0.232170\pi\) | ||||
−0.745584 | + | 0.666411i | \(0.767830\pi\) | |||||||
\(828\) | −9.39876 | −0.326630 | ||||||||
\(829\) | −10.9300 | −0.379616 | −0.189808 | − | 0.981821i | \(-0.560787\pi\) | ||||
−0.189808 | + | 0.981821i | \(0.560787\pi\) | |||||||
\(830\) | 6.33992i | 0.220062i | ||||||||
\(831\) | 2.31998 | − | 4.01832i | 0.0804792 | − | 0.139394i | ||||
\(832\) | −3.57509 | − | 0.467723i | −0.123944 | − | 0.0162154i | ||||
\(833\) | 0.0147662 | + | 0.173224i | 0.000511619 | + | 0.00600186i | ||||
\(834\) | −16.4709 | − | 9.50946i | −0.570340 | − | 0.329286i | ||||
\(835\) | 2.61982 | + | 4.53765i | 0.0906624 | + | 0.157032i | ||||
\(836\) | 8.88282 | − | 15.3855i | 0.307219 | − | 0.532119i | ||||
\(837\) | −4.92140 | + | 2.84137i | −0.170108 | + | 0.0982121i | ||||
\(838\) | 33.3313i | 1.15141i | ||||||||
\(839\) | −1.82881 | + | 1.05586i | −0.0631375 | + | 0.0364525i | −0.531236 | − | 0.847224i | \(-0.678272\pi\) |
0.468099 | + | 0.883676i | \(0.344939\pi\) | |||||||
\(840\) | 0.412087 | − | 1.84905i | 0.0142183 | − | 0.0637983i | ||||
\(841\) | −0.911078 | − | 1.57803i | −0.0314165 | − | 0.0544150i | ||||
\(842\) | −8.73430 | − | 15.1282i | −0.301004 | − | 0.521354i | ||||
\(843\) | 20.9621i | 0.721972i | ||||||||
\(844\) | −7.68735 | − | 13.3149i | −0.264610 | − | 0.458317i | ||||
\(845\) | −6.59259 | − | 6.57127i | −0.226792 | − | 0.226058i | ||||
\(846\) | 4.98896 | 0.171524 | ||||||||
\(847\) | −11.0852 | + | 3.48158i | −0.380893 | + | 0.119629i | ||||
\(848\) | −4.72462 | + | 8.18328i | −0.162244 | + | 0.281015i | ||||
\(849\) | 4.72036 | 0.162002 | ||||||||
\(850\) | −0.0965161 | + | 0.0557236i | −0.00331047 | + | 0.00191130i | ||||
\(851\) | −33.9510 | − | 19.6016i | −1.16383 | − | 0.671935i | ||||
\(852\) | 8.68619i | 0.297584i | ||||||||
\(853\) | 1.58650i | 0.0543207i | 0.999631 | + | 0.0271604i | \(0.00864647\pi\) | ||||
−0.999631 | + | 0.0271604i | \(0.991354\pi\) | |||||||
\(854\) | −1.16684 | + | 1.27054i | −0.0399285 | + | 0.0434769i | ||||
\(855\) | −2.47416 | + | 4.28538i | −0.0846146 | + | 0.146557i | ||||
\(856\) | −0.418019 | + | 0.241343i | −0.0142876 | + | 0.00824894i | ||||
\(857\) | −15.0692 | − | 26.1007i | −0.514756 | − | 0.891583i | −0.999853 | − | 0.0171229i | \(-0.994549\pi\) |
0.485098 | − | 0.874460i | \(-0.338784\pi\) | |||||||
\(858\) | 3.55392 | + | 8.56030i | 0.121329 | + | 0.292244i | ||||
\(859\) | 7.96343 | − | 13.7931i | 0.271709 | − | 0.470614i | −0.697591 | − | 0.716497i | \(-0.745745\pi\) |
0.969300 | + | 0.245883i | \(0.0790779\pi\) | |||||||
\(860\) | 7.90587 | + | 4.56445i | 0.269588 | + | 0.155647i | ||||
\(861\) | 13.5647 | + | 3.02308i | 0.462283 | + | 0.103026i | ||||
\(862\) | 11.4433 | + | 19.8204i | 0.389761 | + | 0.675085i | ||||
\(863\) | 19.4948 | + | 11.2553i | 0.663609 | + | 0.383135i | 0.793651 | − | 0.608373i | \(-0.208178\pi\) |
−0.130041 | + | 0.991509i | \(0.541511\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | −4.02134 | − | 2.32172i | −0.136730 | − | 0.0789409i | ||||
\(866\) | 17.0022 | + | 9.81620i | 0.577757 | + | 0.333568i | ||||
\(867\) | −8.49969 | − | 14.7219i | −0.288665 | − | 0.499982i | ||||
\(868\) | 4.50517 | + | 14.3443i | 0.152915 | + | 0.486877i | ||||
\(869\) | −0.864786 | − | 0.499284i | −0.0293359 | − | 0.0169371i | ||||
\(870\) | 1.98759 | − | 3.44261i | 0.0673856 | − | 0.116715i | ||||
\(871\) | −0.877497 | + | 6.70723i | −0.0297329 | + | 0.227266i | ||||
\(872\) | −1.60228 | − | 2.77524i | −0.0542601 | − | 0.0939813i | ||||
\(873\) | −1.78702 | + | 1.03174i | −0.0604815 | + | 0.0349190i | ||||
\(874\) | 32.4768 | − | 56.2515i | 1.09855 | − | 1.90274i | ||||
\(875\) | −5.38545 | − | 17.1471i | −0.182061 | − | 0.579676i | ||||
\(876\) | 15.8850i | 0.536705i | ||||||||
\(877\) | 24.9627i | 0.842930i | 0.906845 | + | 0.421465i | \(0.138484\pi\) | ||||
−0.906845 | + | 0.421465i | \(0.861516\pi\) | |||||||
\(878\) | −22.1682 | − | 12.7988i | −0.748141 | − | 0.431939i | ||||
\(879\) | −29.0541 | + | 16.7744i | −0.979970 | + | 0.565786i | ||||
\(880\) | −1.84066 | −0.0620486 | ||||||||
\(881\) | 21.0029 | − | 36.3780i | 0.707605 | − | 1.22561i | −0.258138 | − | 0.966108i | \(-0.583109\pi\) |
0.965743 | − | 0.259500i | \(-0.0835576\pi\) | |||||||
\(882\) | −2.97246 | + | 6.33755i | −0.100088 | + | 0.213396i | ||||
\(883\) | 19.4571 | 0.654782 | 0.327391 | − | 0.944889i | \(-0.393831\pi\) | ||||
0.327391 | + | 0.944889i | \(0.393831\pi\) | |||||||
\(884\) | 0.0343354 | + | 0.0827034i | 0.00115482 | + | 0.00278162i | ||||
\(885\) | 0.806308 | + | 1.39657i | 0.0271037 | + | 0.0469450i | ||||
\(886\) | 21.9070i | 0.735982i | ||||||||
\(887\) | −24.0070 | − | 41.5813i | −0.806075 | − | 1.39616i | −0.915563 | − | 0.402175i | \(-0.868254\pi\) |
0.109488 | − | 0.993988i | \(-0.465079\pi\) | |||||||
\(888\) | −2.08556 | − | 3.61229i | −0.0699866 | − | 0.121220i | ||||
\(889\) | 12.7228 | − | 57.0879i | 0.426711 | − | 1.91467i | ||||
\(890\) | −9.20102 | + | 5.31221i | −0.308419 | + | 0.178066i | ||||
\(891\) | 2.57068i | 0.0861210i | ||||||||
\(892\) | 11.0984 | − | 6.40769i | 0.371603 | − | 0.214545i | ||||
\(893\) | −17.2390 | + | 29.8589i | −0.576882 | + | 0.999189i | ||||
\(894\) | −6.12689 | − | 10.6121i | −0.204914 | − | 0.354921i | ||||
\(895\) | −14.4003 | − | 8.31401i | −0.481349 | − | 0.277907i | ||||
\(896\) | −1.78962 | + | 1.94866i | −0.0597869 | + | 0.0651001i | ||||
\(897\) | 12.9936 | + | 31.2977i | 0.433845 | + | 1.04500i | ||||
\(898\) | 13.2807 | − | 23.0029i | 0.443183 | − | 0.767616i | ||||
\(899\) | 31.5493i | 1.05223i | ||||||||
\(900\) | −4.48731 | −0.149577 | ||||||||
\(901\) | 0.234682 | 0.00781838 | ||||||||
\(902\) | − | 13.5031i | − | 0.449605i | ||||||
\(903\) | −24.8444 | − | 22.8167i | −0.826771 | − | 0.759293i | ||||
\(904\) | 7.25350 | − | 4.18781i | 0.241248 | − | 0.139285i | ||||
\(905\) | 3.48436 | + | 2.01169i | 0.115824 | + | 0.0668710i | ||||
\(906\) | −6.66053 | + | 11.5364i | −0.221281 | + | 0.383271i | ||||
\(907\) | 32.9344 | 1.09357 | 0.546785 | − | 0.837273i | \(-0.315852\pi\) | ||||
0.546785 | + | 0.837273i | \(0.315852\pi\) | |||||||
\(908\) | 17.4536 | − | 10.0768i | 0.579217 | − | 0.334411i | ||||
\(909\) | 11.5903 | 0.384426 | ||||||||
\(910\) | −6.72699 | + | 1.18404i | −0.222998 | + | 0.0392505i | ||||
\(911\) | 36.6136 | 1.21306 | 0.606532 | − | 0.795059i | \(-0.292560\pi\) | ||||
0.606532 | + | 0.795059i | \(0.292560\pi\) | |||||||
\(912\) | 5.98499 | − | 3.45544i | 0.198183 | − | 0.114421i | ||||
\(913\) | −22.7618 | −0.753305 | ||||||||
\(914\) | −14.6451 | + | 25.3660i | −0.484416 | + | 0.839033i | ||||
\(915\) | −0.404304 | − | 0.233425i | −0.0133659 | − | 0.00771679i | ||||
\(916\) | 8.89145 | − | 5.13348i | 0.293782 | − | 0.169615i | ||||
\(917\) | −6.41560 | + | 28.7870i | −0.211862 | + | 0.950632i | ||||
\(918\) | 0.0248360i | 0.000819712i | ||||||||
\(919\) | 19.9240 | 0.657231 | 0.328615 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328615 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(920\) | −6.72971 | −0.221872 | ||||||||
\(921\) | − | 5.49245i | − | 0.180982i | ||||||
\(922\) | 1.12927 | − | 1.95594i | 0.0371904 | − | 0.0644156i | ||||
\(923\) | 28.9248 | − | 12.0085i | 0.952072 | − | 0.395265i | ||||
\(924\) | 6.63851 | + | 1.47949i | 0.218391 | + | 0.0486715i | ||||
\(925\) | −16.2095 | − | 9.35854i | −0.532964 | − | 0.307707i | ||||
\(926\) | 1.16650 | + | 2.02044i | 0.0383336 | + | 0.0663958i | ||||
\(927\) | −7.89706 | + | 13.6781i | −0.259373 | + | 0.449248i | ||||
\(928\) | −4.80797 | + | 2.77589i | −0.157829 | + | 0.0911229i | ||||
\(929\) | 4.48490i | 0.147145i | 0.997290 | + | 0.0735724i | \(0.0234400\pi\) | ||||
−0.997290 | + | 0.0735724i | \(0.976560\pi\) | |||||||
\(930\) | −3.52382 | + | 2.03448i | −0.115551 | + | 0.0667132i | ||||
\(931\) | −27.6590 | − | 39.6891i | −0.906488 | − | 1.30076i | ||||
\(932\) | 1.56117 | + | 2.70402i | 0.0511378 | + | 0.0885732i | ||||
\(933\) | −7.45213 | − | 12.9075i | −0.243972 | − | 0.422572i | ||||
\(934\) | − | 42.2405i | − | 1.38215i | ||||||
\(935\) | 0.0228573 | + | 0.0395901i | 0.000747515 | + | 0.00129473i | ||||
\(936\) | −0.467723 | + | 3.57509i | −0.0152880 | + | 0.116855i | ||||
\(937\) | −1.54887 | −0.0505995 | −0.0252997 | − | 0.999680i | \(-0.508054\pi\) | ||||
−0.0252997 | + | 0.999680i | \(0.508054\pi\) | |||||||
\(938\) | 3.65589 | + | 3.35751i | 0.119369 | + | 0.109626i | ||||
\(939\) | −1.80173 | + | 3.12069i | −0.0587972 | + | 0.101840i | ||||
\(940\) | 3.57220 | 0.116512 | ||||||||
\(941\) | 0.0220362 | − | 0.0127226i | 0.000718359 | − | 0.000414745i | −0.499641 | − | 0.866233i | \(-0.666535\pi\) |
0.500359 | + | 0.865818i | \(0.333201\pi\) | |||||||
\(942\) | −6.06098 | − | 3.49931i | −0.197477 | − | 0.114014i | ||||
\(943\) | − | 49.3693i | − | 1.60769i | ||||||
\(944\) | − | 2.25219i | − | 0.0733026i | ||||||
\(945\) | −1.84905 | − | 0.412087i | −0.0601496 | − | 0.0134052i | ||||
\(946\) | −16.3874 | + | 28.3839i | −0.532802 | + | 0.922840i | ||||
\(947\) | 5.91870 | − | 3.41716i | 0.192332 | − | 0.111043i | −0.400742 | − | 0.916191i | \(-0.631248\pi\) |
0.593074 | + | 0.805148i | \(0.297914\pi\) | |||||||
\(948\) | −0.194223 | − | 0.336404i | −0.00630806 | − | 0.0109259i | ||||
\(949\) | 52.8967 | − | 21.9607i | 1.71710 | − | 0.712876i | ||||
\(950\) | 15.5056 | − | 26.8566i | 0.503069 | − | 0.871342i | ||||
\(951\) | 3.54331 | + | 2.04573i | 0.114900 | + | 0.0663373i | ||||
\(952\) | 0.0641365 | + | 0.0142937i | 0.00207868 | + | 0.000463262i | ||||
\(953\) | 23.9163 | + | 41.4242i | 0.774724 | + | 1.34186i | 0.934949 | + | 0.354782i | \(0.115445\pi\) |
−0.160225 | + | 0.987081i | \(0.551222\pi\) | |||||||
\(954\) | 8.18328 | + | 4.72462i | 0.264944 | + | 0.152965i | ||||
\(955\) | 14.8168 | + | 8.55447i | 0.479460 | + | 0.276816i | ||||
\(956\) | 10.5936 | + | 6.11624i | 0.342623 | + | 0.197813i | ||||
\(957\) | 12.3598 | + | 7.13591i | 0.399534 | + | 0.230671i | ||||
\(958\) | −9.65093 | − | 16.7159i | −0.311807 | − | 0.540066i | ||||
\(959\) | 43.3766 | + | 9.66709i | 1.40070 | + | 0.312167i | ||||
\(960\) | −0.620092 | − | 0.358010i | −0.0200134 | − | 0.0115547i | ||||
\(961\) | 0.646777 | − | 1.12025i | 0.0208638 | − | 0.0361371i | ||||
\(962\) | −9.14559 | + | 11.9388i | −0.294866 | + | 0.384921i | ||||
\(963\) | 0.241343 | + | 0.418019i | 0.00777718 | + | 0.0134705i | ||||
\(964\) | −1.63586 | + | 0.944462i | −0.0526874 | + | 0.0304191i | ||||
\(965\) | 7.51722 | − | 13.0202i | 0.241988 | − | 0.419136i | ||||
\(966\) | 24.2713 | + | 5.40921i | 0.780917 | + | 0.174038i | ||||
\(967\) | 14.3721i | 0.462175i | 0.972933 | + | 0.231088i | \(0.0742284\pi\) | ||||
−0.972933 | + | 0.231088i | \(0.925772\pi\) | |||||||
\(968\) | 4.39161i | 0.141152i | ||||||||
\(969\) | −0.148644 | − | 0.0858194i | −0.00477512 | − | 0.00275692i | ||||
\(970\) | −1.27954 | + | 0.738745i | −0.0410837 | + | 0.0237197i | ||||
\(971\) | −8.15870 | −0.261825 | −0.130913 | − | 0.991394i | \(-0.541791\pi\) | ||||
−0.130913 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 37.0614 | + | 34.0366i | 1.18813 | + | 1.09116i | ||||
\(974\) | 15.0028 | 0.480722 | ||||||||
\(975\) | 6.20363 | + | 14.9427i | 0.198675 | + | 0.478548i | ||||
\(976\) | 0.326003 | + | 0.564654i | 0.0104351 | + | 0.0180741i | ||||
\(977\) | − | 14.2110i | − | 0.454650i | −0.973819 | − | 0.227325i | \(-0.927002\pi\) | ||
0.973819 | − | 0.227325i | \(-0.0729979\pi\) | |||||||
\(978\) | −5.09649 | − | 8.82738i | −0.162968 | − | 0.282268i | ||||
\(979\) | −19.0721 | − | 33.0338i | −0.609546 | − | 1.05576i | ||||
\(980\) | −2.12834 | + | 4.53781i | −0.0679874 | + | 0.144955i | ||||
\(981\) | −2.77524 | + | 1.60228i | −0.0886065 | + | 0.0511570i | ||||
\(982\) | 28.4095i | 0.906584i | ||||||||
\(983\) | −3.80375 | + | 2.19610i | −0.121321 | + | 0.0700447i | −0.559432 | − | 0.828876i | \(-0.688981\pi\) |
0.438111 | + | 0.898921i | \(0.355648\pi\) | |||||||
\(984\) | 2.62637 | − | 4.54901i | 0.0837257 | − | 0.145017i | ||||
\(985\) | 1.85608 | + | 3.21482i | 0.0591396 | + | 0.102433i | ||||
\(986\) | 0.119411 | + | 0.0689420i | 0.00380282 | + | 0.00219556i | ||||
\(987\) | −12.8835 | − | 2.87126i | −0.410085 | − | 0.0913933i | ||||
\(988\) | −19.7807 | − | 15.1528i | −0.629307 | − | 0.482075i | ||||
\(989\) | −59.9148 | + | 103.775i | −1.90518 | + | 3.29987i | ||||
\(990\) | 1.84066i | 0.0585000i | ||||||||
\(991\) | −13.4728 | −0.427978 | −0.213989 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213989 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(992\) | 5.68274 | 0.180427 | ||||||||
\(993\) | − | 19.4070i | − | 0.615862i | ||||||
\(994\) | 4.99911 | − | 22.4312i | 0.158562 | − | 0.711474i | ||||
\(995\) | −10.0094 | + | 5.77890i | −0.317318 | + | 0.183204i | ||||
\(996\) | −7.66812 | − | 4.42719i | −0.242974 | − | 0.140281i | ||||
\(997\) | 8.41844 | − | 14.5812i | 0.266615 | − | 0.461790i | −0.701371 | − | 0.712797i | \(-0.747428\pi\) |
0.967985 | + | 0.251007i | \(0.0807616\pi\) | |||||||
\(998\) | −3.85576 | −0.122052 | ||||||||
\(999\) | −3.61229 | + | 2.08556i | −0.114288 | + | 0.0659840i |
(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 | 546.2.bd.a.121.2 | ✓ | 16 | |
3.2 | odd | 2 | 1638.2.cr.a.667.7 | 16 | |||
7.4 | even | 3 | 546.2.bm.a.277.3 | yes | 16 | ||
13.10 | even | 6 | 546.2.bm.a.205.7 | yes | 16 | ||
21.11 | odd | 6 | 1638.2.dt.a.1369.6 | 16 | |||
39.23 | odd | 6 | 1638.2.dt.a.1297.2 | 16 | |||
91.88 | even | 6 | inner | 546.2.bd.a.361.2 | yes | 16 | |
273.179 | odd | 6 | 1638.2.cr.a.361.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bd.a.121.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
546.2.bd.a.361.2 | yes | 16 | 91.88 | even | 6 | inner | |
546.2.bm.a.205.7 | yes | 16 | 13.10 | even | 6 | ||
546.2.bm.a.277.3 | yes | 16 | 7.4 | even | 3 | ||
1638.2.cr.a.361.7 | 16 | 273.179 | odd | 6 | |||
1638.2.cr.a.667.7 | 16 | 3.2 | odd | 2 | |||
1638.2.dt.a.1297.2 | 16 | 39.23 | odd | 6 | |||
1638.2.dt.a.1369.6 | 16 | 21.11 | odd | 6 |