Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(499,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.r (of order \(4\), 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(56\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 619.17 | ||
Character | \(\chi\) | \(=\) | 624.619 |
Dual form | 624.2.r.a.499.17 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.815469 | − | 1.15543i | −0.576624 | − | 0.817010i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −0.670020 | + | 1.88443i | −0.335010 | + | 0.942215i | ||||
\(5\) | 2.34860i | 1.05033i | 0.851002 | + | 0.525163i | \(0.175996\pi\) | ||||
−0.851002 | + | 0.525163i | \(0.824004\pi\) | |||||||
\(6\) | 0.240386 | − | 1.39363i | 0.0981372 | − | 0.568949i | ||||
\(7\) | 3.19154 | − | 3.19154i | 1.20629 | − | 1.20629i | 0.234070 | − | 0.972220i | \(-0.424796\pi\) |
0.972220 | − | 0.234070i | \(-0.0752043\pi\) | |||||||
\(8\) | 2.72370 | − | 0.762534i | 0.962973 | − | 0.269597i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.71364 | − | 1.91521i | 0.858127 | − | 0.605643i | ||||
\(11\) | − | 5.07397i | − | 1.52986i | −0.644114 | − | 0.764930i | \(-0.722774\pi\) | ||
0.644114 | − | 0.764930i | \(-0.277226\pi\) | |||||||
\(12\) | −1.80627 | + | 0.858717i | −0.521425 | + | 0.247890i | ||||
\(13\) | 1.19005 | + | 3.40350i | 0.330061 | + | 0.943960i | ||||
\(14\) | −6.29020 | − | 1.08499i | −1.68113 | − | 0.289975i | ||||
\(15\) | −1.66071 | + | 1.66071i | −0.428794 | + | 0.428794i | ||||
\(16\) | −3.10215 | − | 2.52521i | −0.775536 | − | 0.631303i | ||||
\(17\) | 3.26734i | 0.792447i | 0.918154 | + | 0.396224i | \(0.129679\pi\) | ||||
−0.918154 | + | 0.396224i | \(0.870321\pi\) | |||||||
\(18\) | 1.15543 | − | 0.815469i | 0.272337 | − | 0.192208i | ||||
\(19\) | − | 0.605369i | − | 0.138881i | −0.997586 | − | 0.0694405i | \(-0.977879\pi\) | ||
0.997586 | − | 0.0694405i | \(-0.0221214\pi\) | |||||||
\(20\) | −4.42577 | − | 1.57361i | −0.989633 | − | 0.351870i | ||||
\(21\) | 4.51352 | 0.984931 | ||||||||
\(22\) | −5.86260 | + | 4.13766i | −1.24991 | + | 0.882153i | ||||
\(23\) | 2.94806i | 0.614714i | 0.951594 | + | 0.307357i | \(0.0994446\pi\) | ||||
−0.951594 | + | 0.307357i | \(0.900555\pi\) | |||||||
\(24\) | 2.46514 | + | 1.38675i | 0.503195 | + | 0.283070i | ||||
\(25\) | −0.515926 | −0.103185 | ||||||||
\(26\) | 2.96204 | − | 4.15046i | 0.580904 | − | 0.813972i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 3.87584 | + | 8.15263i | 0.732464 | + | 1.54070i | ||||
\(29\) | 0.887645 | − | 0.887645i | 0.164831 | − | 0.164831i | −0.619872 | − | 0.784703i | \(-0.712815\pi\) |
0.784703 | + | 0.619872i | \(0.212815\pi\) | |||||||
\(30\) | 3.27309 | + | 0.564571i | 0.597582 | + | 0.103076i | ||||
\(31\) | 5.17321 | − | 5.17321i | 0.929137 | − | 0.929137i | −0.0685136 | − | 0.997650i | \(-0.521826\pi\) |
0.997650 | + | 0.0685136i | \(0.0218256\pi\) | |||||||
\(32\) | −0.387993 | + | 5.64353i | −0.0685880 | + | 0.997645i | ||||
\(33\) | 3.58784 | − | 3.58784i | 0.624562 | − | 0.624562i | ||||
\(34\) | 3.77518 | − | 2.66442i | 0.647437 | − | 0.456944i | ||||
\(35\) | 7.49566 | + | 7.49566i | 1.26700 | + | 1.26700i | ||||
\(36\) | −1.88443 | − | 0.670020i | −0.314072 | − | 0.111670i | ||||
\(37\) | 7.71814 | 1.26886 | 0.634428 | − | 0.772982i | \(-0.281236\pi\) | ||||
0.634428 | + | 0.772982i | \(0.281236\pi\) | |||||||
\(38\) | −0.699459 | + | 0.493659i | −0.113467 | + | 0.0800821i | ||||
\(39\) | −1.56514 | + | 3.24813i | −0.250623 | + | 0.520117i | ||||
\(40\) | 1.79089 | + | 6.39688i | 0.283164 | + | 1.01144i | ||||
\(41\) | −1.94035 | + | 1.94035i | −0.303032 | + | 0.303032i | −0.842199 | − | 0.539167i | \(-0.818739\pi\) |
0.539167 | + | 0.842199i | \(0.318739\pi\) | |||||||
\(42\) | −3.68064 | − | 5.21504i | −0.567935 | − | 0.804698i | ||||
\(43\) | 6.13961 | + | 6.13961i | 0.936281 | + | 0.936281i | 0.998088 | − | 0.0618071i | \(-0.0196863\pi\) |
−0.0618071 | + | 0.998088i | \(0.519686\pi\) | |||||||
\(44\) | 9.56153 | + | 3.39966i | 1.44146 | + | 0.512518i | ||||
\(45\) | −2.34860 | −0.350109 | ||||||||
\(46\) | 3.40627 | − | 2.40406i | 0.502227 | − | 0.354459i | ||||
\(47\) | −5.45813 | − | 5.45813i | −0.796151 | − | 0.796151i | 0.186336 | − | 0.982486i | \(-0.440339\pi\) |
−0.982486 | + | 0.186336i | \(0.940339\pi\) | |||||||
\(48\) | −0.407954 | − | 3.97914i | −0.0588831 | − | 0.574340i | ||||
\(49\) | − | 13.3719i | − | 1.91027i | ||||||
\(50\) | 0.420722 | + | 0.596114i | 0.0594990 | + | 0.0843033i | ||||
\(51\) | −2.31036 | + | 2.31036i | −0.323515 | + | 0.323515i | ||||
\(52\) | −7.21100 | − | 0.0378447i | −0.999986 | − | 0.00524812i | ||||
\(53\) | 0.417744 | + | 0.417744i | 0.0573816 | + | 0.0573816i | 0.735215 | − | 0.677834i | \(-0.237081\pi\) |
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(54\) | 1.39363 | + | 0.240386i | 0.189650 | + | 0.0327124i | ||||
\(55\) | 11.9167 | 1.60685 | ||||||||
\(56\) | 6.25914 | − | 11.1265i | 0.836413 | − | 1.48684i | ||||
\(57\) | 0.428060 | − | 0.428060i | 0.0566980 | − | 0.0566980i | ||||
\(58\) | −1.74945 | − | 0.301761i | −0.229715 | − | 0.0396232i | ||||
\(59\) | 12.6521i | 1.64716i | 0.567198 | + | 0.823582i | \(0.308027\pi\) | ||||
−0.567198 | + | 0.823582i | \(0.691973\pi\) | |||||||
\(60\) | −2.01678 | − | 4.24220i | −0.260365 | − | 0.547666i | ||||
\(61\) | −5.83218 | + | 5.83218i | −0.746734 | + | 0.746734i | −0.973864 | − | 0.227131i | \(-0.927066\pi\) |
0.227131 | + | 0.973864i | \(0.427066\pi\) | |||||||
\(62\) | −10.1959 | − | 1.75867i | −1.29488 | − | 0.223352i | ||||
\(63\) | 3.19154 | + | 3.19154i | 0.402096 | + | 0.402096i | ||||
\(64\) | 6.83708 | − | 4.15383i | 0.854635 | − | 0.519229i | ||||
\(65\) | −7.99345 | + | 2.79495i | −0.991466 | + | 0.346671i | ||||
\(66\) | −7.07125 | − | 1.21971i | −0.870411 | − | 0.150136i | ||||
\(67\) | − | 1.52125i | − | 0.185850i | −0.995673 | − | 0.0929250i | \(-0.970378\pi\) | ||
0.995673 | − | 0.0929250i | \(-0.0296217\pi\) | |||||||
\(68\) | −6.15708 | − | 2.18919i | −0.746655 | − | 0.265478i | ||||
\(69\) | −2.08460 | + | 2.08460i | −0.250956 | + | 0.250956i | ||||
\(70\) | 2.54820 | − | 14.7732i | 0.304569 | − | 1.76573i | ||||
\(71\) | −8.15417 | − | 8.15417i | −0.967722 | − | 0.967722i | 0.0317731 | − | 0.999495i | \(-0.489885\pi\) |
−0.999495 | + | 0.0317731i | \(0.989885\pi\) | |||||||
\(72\) | 0.762534 | + | 2.72370i | 0.0898655 | + | 0.320991i | ||||
\(73\) | −1.51786 | − | 1.51786i | −0.177652 | − | 0.177652i | 0.612680 | − | 0.790331i | \(-0.290092\pi\) |
−0.790331 | + | 0.612680i | \(0.790092\pi\) | |||||||
\(74\) | −6.29391 | − | 8.91775i | −0.731652 | − | 1.03667i | ||||
\(75\) | −0.364815 | − | 0.364815i | −0.0421252 | − | 0.0421252i | ||||
\(76\) | 1.14077 | + | 0.405609i | 0.130856 | + | 0.0465266i | ||||
\(77\) | −16.1938 | − | 16.1938i | −1.84545 | − | 1.84545i | ||||
\(78\) | 5.02930 | − | 0.840342i | 0.569456 | − | 0.0951500i | ||||
\(79\) | 1.03583i | 0.116540i | 0.998301 | + | 0.0582699i | \(0.0185584\pi\) | ||||
−0.998301 | + | 0.0582699i | \(0.981442\pi\) | |||||||
\(80\) | 5.93071 | − | 7.28570i | 0.663074 | − | 0.814566i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.82423 | + | 0.659636i | 0.422315 | + | 0.0728446i | ||||
\(83\) | 13.5933i | 1.49206i | 0.665911 | + | 0.746031i | \(0.268043\pi\) | ||||
−0.665911 | + | 0.746031i | \(0.731957\pi\) | |||||||
\(84\) | −3.02415 | + | 8.50541i | −0.329962 | + | 0.928016i | ||||
\(85\) | −7.67369 | −0.832328 | ||||||||
\(86\) | 2.08720 | − | 12.1005i | 0.225069 | − | 1.30483i | ||||
\(87\) | 1.25532 | 0.134584 | ||||||||
\(88\) | −3.86908 | − | 13.8200i | −0.412445 | − | 1.47321i | ||||
\(89\) | 0.249708 | + | 0.249708i | 0.0264690 | + | 0.0264690i | 0.720217 | − | 0.693748i | \(-0.244042\pi\) |
−0.693748 | + | 0.720217i | \(0.744042\pi\) | |||||||
\(90\) | 1.91521 | + | 2.71364i | 0.201881 | + | 0.286042i | ||||
\(91\) | 14.6605 | + | 7.06430i | 1.53684 | + | 0.740540i | ||||
\(92\) | −5.55542 | − | 1.97526i | −0.579192 | − | 0.205935i | ||||
\(93\) | 7.31603 | 0.758637 | ||||||||
\(94\) | −1.85553 | + | 10.7574i | −0.191384 | + | 1.10954i | ||||
\(95\) | 1.42177 | 0.145870 | ||||||||
\(96\) | −4.26493 | + | 3.71623i | −0.435288 | + | 0.379286i | ||||
\(97\) | 0.664032 | + | 0.664032i | 0.0674222 | + | 0.0674222i | 0.740014 | − | 0.672592i | \(-0.234819\pi\) |
−0.672592 | + | 0.740014i | \(0.734819\pi\) | |||||||
\(98\) | −15.4502 | + | 10.9044i | −1.56071 | + | 1.10151i | ||||
\(99\) | 5.07397 | 0.509953 | ||||||||
\(100\) | 0.345681 | − | 0.972226i | 0.0345681 | − | 0.0972226i | ||||
\(101\) | 2.46756 | − | 2.46756i | 0.245531 | − | 0.245531i | −0.573603 | − | 0.819134i | \(-0.694455\pi\) |
0.819134 | + | 0.573603i | \(0.194455\pi\) | |||||||
\(102\) | 4.55348 | + | 0.785424i | 0.450862 | + | 0.0777686i | ||||
\(103\) | − | 14.8904i | − | 1.46719i | −0.679586 | − | 0.733596i | \(-0.737840\pi\) | ||
0.679586 | − | 0.733596i | \(-0.262160\pi\) | |||||||
\(104\) | 5.83662 | + | 8.36264i | 0.572328 | + | 0.820025i | ||||
\(105\) | 10.6005i | 1.03450i | ||||||||
\(106\) | 0.142015 | − | 0.823330i | 0.0137937 | − | 0.0799689i | ||||
\(107\) | 10.3264 | − | 10.3264i | 0.998293 | − | 0.998293i | −0.00170580 | − | 0.999999i | \(-0.500543\pi\) |
0.999999 | + | 0.00170580i | \(0.000542973\pi\) | |||||||
\(108\) | −0.858717 | − | 1.80627i | −0.0826300 | − | 0.173808i | ||||
\(109\) | 10.1680 | 0.973916 | 0.486958 | − | 0.873425i | \(-0.338107\pi\) | ||||
0.486958 | + | 0.873425i | \(0.338107\pi\) | |||||||
\(110\) | −9.71772 | − | 13.7689i | −0.926548 | − | 1.31281i | ||||
\(111\) | 5.45755 | + | 5.45755i | 0.518008 | + | 0.518008i | ||||
\(112\) | −17.9599 | + | 1.84131i | −1.69706 | + | 0.173987i | ||||
\(113\) | −3.58121 | −0.336892 | −0.168446 | − | 0.985711i | \(-0.553875\pi\) | ||||
−0.168446 | + | 0.985711i | \(0.553875\pi\) | |||||||
\(114\) | −0.843662 | − | 0.145522i | −0.0790162 | − | 0.0136294i | ||||
\(115\) | −6.92383 | −0.645650 | ||||||||
\(116\) | 1.07796 | + | 2.26744i | 0.100086 | + | 0.210527i | ||||
\(117\) | −3.40350 | + | 1.19005i | −0.314653 | + | 0.110020i | ||||
\(118\) | 14.6186 | − | 10.3174i | 1.34575 | − | 0.949793i | ||||
\(119\) | 10.4279 | + | 10.4279i | 0.955921 | + | 0.955921i | ||||
\(120\) | −3.25693 | + | 5.78963i | −0.297316 | + | 0.528518i | ||||
\(121\) | −14.7452 | −1.34047 | ||||||||
\(122\) | 11.4946 | + | 1.98269i | 1.04067 | + | 0.179504i | ||||
\(123\) | −2.74407 | −0.247424 | ||||||||
\(124\) | 6.28240 | + | 13.2147i | 0.564176 | + | 1.18672i | ||||
\(125\) | 10.5313i | 0.941948i | ||||||||
\(126\) | 1.08499 | − | 6.29020i | 0.0966584 | − | 0.560375i | ||||
\(127\) | −20.5514 | −1.82364 | −0.911819 | − | 0.410593i | \(-0.865322\pi\) | ||||
−0.911819 | + | 0.410593i | \(0.865322\pi\) | |||||||
\(128\) | −10.3749 | − | 4.51243i | −0.917018 | − | 0.398846i | ||||
\(129\) | 8.68271i | 0.764470i | ||||||||
\(130\) | 9.74778 | + | 6.95665i | 0.854937 | + | 0.610138i | ||||
\(131\) | −8.31734 | − | 8.31734i | −0.726689 | − | 0.726689i | 0.243269 | − | 0.969959i | \(-0.421780\pi\) |
−0.969959 | + | 0.243269i | \(0.921780\pi\) | |||||||
\(132\) | 4.35710 | + | 9.16495i | 0.379237 | + | 0.797706i | ||||
\(133\) | −1.93206 | − | 1.93206i | −0.167531 | − | 0.167531i | ||||
\(134\) | −1.75769 | + | 1.24053i | −0.151841 | + | 0.107166i | ||||
\(135\) | −1.66071 | − | 1.66071i | −0.142931 | − | 0.142931i | ||||
\(136\) | 2.49146 | + | 8.89926i | 0.213641 | + | 0.763106i | ||||
\(137\) | −4.42870 | − | 4.42870i | −0.378369 | − | 0.378369i | 0.492144 | − | 0.870514i | \(-0.336213\pi\) |
−0.870514 | + | 0.492144i | \(0.836213\pi\) | |||||||
\(138\) | 4.10852 | + | 0.708674i | 0.349741 | + | 0.0603263i | ||||
\(139\) | −6.67075 | + | 6.67075i | −0.565806 | + | 0.565806i | −0.930951 | − | 0.365145i | \(-0.881019\pi\) |
0.365145 | + | 0.930951i | \(0.381019\pi\) | |||||||
\(140\) | −19.1473 | + | 9.10279i | −1.61824 | + | 0.769326i | ||||
\(141\) | − | 7.71897i | − | 0.650054i | ||||||
\(142\) | −2.77207 | + | 16.0710i | −0.232627 | + | 1.34865i | ||||
\(143\) | 17.2692 | − | 6.03828i | 1.44413 | − | 0.504946i | ||||
\(144\) | 2.52521 | − | 3.10215i | 0.210434 | − | 0.258512i | ||||
\(145\) | 2.08472 | + | 2.08472i | 0.173127 | + | 0.173127i | ||||
\(146\) | −0.516006 | + | 2.99153i | −0.0427050 | + | 0.247581i | ||||
\(147\) | 9.45535 | − | 9.45535i | 0.779864 | − | 0.779864i | ||||
\(148\) | −5.17131 | + | 14.5443i | −0.425079 | + | 1.19553i | ||||
\(149\) | − | 19.8312i | − | 1.62463i | −0.583217 | − | 0.812316i | \(-0.698206\pi\) | ||
0.583217 | − | 0.812316i | \(-0.301794\pi\) | |||||||
\(150\) | −0.124021 | + | 0.719012i | −0.0101263 | + | 0.0587071i | ||||
\(151\) | −3.38860 | + | 3.38860i | −0.275760 | + | 0.275760i | −0.831414 | − | 0.555654i | \(-0.812468\pi\) |
0.555654 | + | 0.831414i | \(0.312468\pi\) | |||||||
\(152\) | −0.461614 | − | 1.64884i | −0.0374419 | − | 0.133739i | ||||
\(153\) | −3.26734 | −0.264149 | ||||||||
\(154\) | −5.50520 | + | 31.9163i | −0.443621 | + | 2.57188i | ||||
\(155\) | 12.1498 | + | 12.1498i | 0.975897 | + | 0.975897i | ||||
\(156\) | −5.07219 | − | 5.12571i | −0.406100 | − | 0.410385i | ||||
\(157\) | −4.37013 | + | 4.37013i | −0.348774 | + | 0.348774i | −0.859653 | − | 0.510879i | \(-0.829320\pi\) |
0.510879 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(158\) | 1.19682 | − | 0.844686i | 0.0952142 | − | 0.0671996i | ||||
\(159\) | 0.590780i | 0.0468519i | ||||||||
\(160\) | −13.2544 | − | 0.911240i | −1.04785 | − | 0.0720398i | ||||
\(161\) | 9.40887 | + | 9.40887i | 0.741523 | + | 0.741523i | ||||
\(162\) | 0.815469 | + | 1.15543i | 0.0640693 | + | 0.0907789i | ||||
\(163\) | −21.6413 | −1.69508 | −0.847540 | − | 0.530732i | \(-0.821917\pi\) | ||||
−0.847540 | + | 0.530732i | \(0.821917\pi\) | |||||||
\(164\) | −2.35638 | − | 4.95653i | −0.184002 | − | 0.387040i | ||||
\(165\) | 8.42640 | + | 8.42640i | 0.655994 | + | 0.655994i | ||||
\(166\) | 15.7061 | − | 11.0849i | 1.21903 | − | 0.860359i | ||||
\(167\) | 12.2294 | − | 12.2294i | 0.946340 | − | 0.946340i | −0.0522917 | − | 0.998632i | \(-0.516653\pi\) |
0.998632 | + | 0.0522917i | \(0.0166526\pi\) | |||||||
\(168\) | 12.2935 | − | 3.44172i | 0.948462 | − | 0.265534i | ||||
\(169\) | −10.1676 | + | 8.10066i | −0.782120 | + | 0.623128i | ||||
\(170\) | 6.25765 | + | 8.86638i | 0.479940 | + | 0.680020i | ||||
\(171\) | 0.605369 | 0.0462937 | ||||||||
\(172\) | −15.6833 | + | 7.45599i | −1.19584 | + | 0.568514i | ||||
\(173\) | −10.6506 | − | 10.6506i | −0.809750 | − | 0.809750i | 0.174846 | − | 0.984596i | \(-0.444057\pi\) |
−0.984596 | + | 0.174846i | \(0.944057\pi\) | |||||||
\(174\) | −1.02367 | − | 1.45043i | −0.0776045 | − | 0.109957i | ||||
\(175\) | −1.64660 | + | 1.64660i | −0.124471 | + | 0.124471i | ||||
\(176\) | −12.8128 | + | 15.7402i | −0.965805 | + | 1.18646i | ||||
\(177\) | −8.94639 | + | 8.94639i | −0.672452 | + | 0.672452i | ||||
\(178\) | 0.0848901 | − | 0.492149i | 0.00636278 | − | 0.0368881i | ||||
\(179\) | −11.2150 | + | 11.2150i | −0.838248 | + | 0.838248i | −0.988628 | − | 0.150381i | \(-0.951950\pi\) |
0.150381 | + | 0.988628i | \(0.451950\pi\) | |||||||
\(180\) | 1.57361 | − | 4.42577i | 0.117290 | − | 0.329878i | ||||
\(181\) | 3.78980 | − | 3.78980i | 0.281693 | − | 0.281693i | −0.552091 | − | 0.833784i | \(-0.686170\pi\) |
0.833784 | + | 0.552091i | \(0.186170\pi\) | |||||||
\(182\) | −3.79290 | − | 22.6998i | −0.281149 | − | 1.68262i | ||||
\(183\) | −8.24794 | −0.609706 | ||||||||
\(184\) | 2.24800 | + | 8.02964i | 0.165725 | + | 0.591953i | ||||
\(185\) | 18.1268i | 1.33271i | ||||||||
\(186\) | −5.96600 | − | 8.45313i | −0.437448 | − | 0.619814i | ||||
\(187\) | 16.5784 | 1.21233 | ||||||||
\(188\) | 13.9425 | − | 6.62840i | 1.01686 | − | 0.483426i | ||||
\(189\) | 4.51352i | 0.328310i | ||||||||
\(190\) | −1.15941 | − | 1.64275i | −0.0841123 | − | 0.119178i | ||||
\(191\) | 0.595035i | 0.0430552i | 0.999768 | + | 0.0215276i | \(0.00685298\pi\) | ||||
−0.999768 | + | 0.0215276i | \(0.993147\pi\) | |||||||
\(192\) | 7.77175 | + | 1.89735i | 0.560878 | + | 0.136929i | ||||
\(193\) | −16.1069 | + | 16.1069i | −1.15940 | + | 1.15940i | −0.174797 | + | 0.984604i | \(0.555927\pi\) |
−0.984604 | + | 0.174797i | \(0.944073\pi\) | |||||||
\(194\) | 0.225743 | − | 1.30874i | 0.0162074 | − | 0.0939619i | ||||
\(195\) | −7.62855 | − | 3.67589i | −0.546292 | − | 0.263236i | ||||
\(196\) | 25.1984 | + | 8.95943i | 1.79988 | + | 0.639959i | ||||
\(197\) | − | 17.9886i | − | 1.28164i | −0.767693 | − | 0.640818i | \(-0.778595\pi\) | ||
0.767693 | − | 0.640818i | \(-0.221405\pi\) | |||||||
\(198\) | −4.13766 | − | 5.86260i | −0.294051 | − | 0.416637i | ||||
\(199\) | − | 10.0707i | − | 0.713890i | −0.934125 | − | 0.356945i | \(-0.883818\pi\) | ||
0.934125 | − | 0.356945i | \(-0.116182\pi\) | |||||||
\(200\) | −1.40523 | + | 0.393411i | −0.0993646 | + | 0.0278184i | ||||
\(201\) | 1.07568 | − | 1.07568i | 0.0758730 | − | 0.0758730i | ||||
\(202\) | −4.86330 | − | 0.838864i | −0.342180 | − | 0.0590223i | ||||
\(203\) | − | 5.66591i | − | 0.397669i | ||||||
\(204\) | −2.80572 | − | 5.90170i | −0.196440 | − | 0.413202i | ||||
\(205\) | −4.55711 | − | 4.55711i | −0.318282 | − | 0.318282i | ||||
\(206\) | −17.2047 | + | 12.1426i | −1.19871 | + | 0.846018i | ||||
\(207\) | −2.94806 | −0.204905 | ||||||||
\(208\) | 4.90283 | − | 13.5633i | 0.339950 | − | 0.940443i | ||||
\(209\) | −3.07162 | −0.212468 | ||||||||
\(210\) | 12.2481 | − | 8.64435i | 0.845196 | − | 0.596517i | ||||
\(211\) | −18.4212 | − | 18.4212i | −1.26817 | − | 1.26817i | −0.947033 | − | 0.321137i | \(-0.895935\pi\) |
−0.321137 | − | 0.947033i | \(-0.604065\pi\) | |||||||
\(212\) | −1.06711 | + | 0.507312i | −0.0732892 | + | 0.0348424i | ||||
\(213\) | − | 11.5317i | − | 0.790142i | ||||||
\(214\) | −20.3523 | − | 3.51054i | −1.39125 | − | 0.239976i | ||||
\(215\) | −14.4195 | + | 14.4195i | −0.983401 | + | 0.983401i | ||||
\(216\) | −1.38675 | + | 2.46514i | −0.0943566 | + | 0.167732i | ||||
\(217\) | − | 33.0211i | − | 2.24162i | ||||||
\(218\) | −8.29167 | − | 11.7483i | −0.561583 | − | 0.795699i | ||||
\(219\) | − | 2.14657i | − | 0.145052i | ||||||
\(220\) | −7.98445 | + | 22.4562i | −0.538311 | + | 1.51400i | ||||
\(221\) | −11.1204 | + | 3.88831i | −0.748038 | + | 0.261556i | ||||
\(222\) | 1.85533 | − | 10.7563i | 0.124522 | − | 0.721913i | ||||
\(223\) | 1.37101 | − | 1.37101i | 0.0918098 | − | 0.0918098i | −0.659710 | − | 0.751520i | \(-0.729321\pi\) |
0.751520 | + | 0.659710i | \(0.229321\pi\) | |||||||
\(224\) | 16.7733 | + | 19.2499i | 1.12071 | + | 1.28619i | ||||
\(225\) | − | 0.515926i | − | 0.0343951i | ||||||
\(226\) | 2.92037 | + | 4.13783i | 0.194260 | + | 0.275244i | ||||
\(227\) | 12.5858i | 0.835350i | 0.908597 | + | 0.417675i | \(0.137155\pi\) | ||||
−0.908597 | + | 0.417675i | \(0.862845\pi\) | |||||||
\(228\) | 0.519840 | + | 1.09346i | 0.0344272 | + | 0.0724160i | ||||
\(229\) | 11.2091 | 0.740720 | 0.370360 | − | 0.928888i | \(-0.379234\pi\) | ||||
0.370360 | + | 0.928888i | \(0.379234\pi\) | |||||||
\(230\) | 5.64617 | + | 7.99997i | 0.372297 | + | 0.527503i | ||||
\(231\) | − | 22.9015i | − | 1.50681i | ||||||
\(232\) | 1.74082 | − | 3.09454i | 0.114290 | − | 0.203166i | ||||
\(233\) | −0.489336 | −0.0320575 | −0.0160287 | − | 0.999872i | \(-0.505102\pi\) | ||||
−0.0160287 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(234\) | 4.15046 | + | 2.96204i | 0.271324 | + | 0.193635i | ||||
\(235\) | 12.8190 | − | 12.8190i | 0.836218 | − | 0.836218i | ||||
\(236\) | −23.8420 | − | 8.47716i | −1.55198 | − | 0.551816i | ||||
\(237\) | −0.732441 | + | 0.732441i | −0.0475772 | + | 0.0475772i | ||||
\(238\) | 3.54503 | − | 20.5522i | 0.229790 | − | 1.33220i | ||||
\(239\) | −7.05526 | + | 7.05526i | −0.456367 | + | 0.456367i | −0.897461 | − | 0.441094i | \(-0.854590\pi\) |
0.441094 | + | 0.897461i | \(0.354590\pi\) | |||||||
\(240\) | 9.34542 | − | 0.958121i | 0.603244 | − | 0.0618464i | ||||
\(241\) | −8.20705 | + | 8.20705i | −0.528663 | + | 0.528663i | −0.920174 | − | 0.391511i | \(-0.871953\pi\) |
0.391511 | + | 0.920174i | \(0.371953\pi\) | |||||||
\(242\) | 12.0242 | + | 17.0369i | 0.772946 | + | 1.09518i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −7.08265 | − | 14.8980i | −0.453420 | − | 0.953747i | ||||
\(245\) | 31.4052 | 2.00640 | ||||||||
\(246\) | 2.23770 | + | 3.17057i | 0.142671 | + | 0.202148i | ||||
\(247\) | 2.06037 | − | 0.720419i | 0.131098 | − | 0.0458392i | ||||
\(248\) | 10.1455 | − | 18.0350i | 0.644242 | − | 1.14523i | ||||
\(249\) | −9.61194 | + | 9.61194i | −0.609132 | + | 0.609132i | ||||
\(250\) | 12.1681 | − | 8.58795i | 0.769581 | − | 0.543150i | ||||
\(251\) | 14.6130 | + | 14.6130i | 0.922366 | + | 0.922366i | 0.997196 | − | 0.0748299i | \(-0.0238414\pi\) |
−0.0748299 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(252\) | −8.15263 | + | 3.87584i | −0.513568 | + | 0.244155i | ||||
\(253\) | 14.9584 | 0.940426 | ||||||||
\(254\) | 16.7590 | + | 23.7456i | 1.05155 | + | 1.48993i | ||||
\(255\) | −5.42612 | − | 5.42612i | −0.339797 | − | 0.339797i | ||||
\(256\) | 3.24661 | + | 15.6671i | 0.202913 | + | 0.979197i | ||||
\(257\) | − | 13.6561i | − | 0.851841i | −0.904761 | − | 0.425921i | \(-0.859950\pi\) | ||
0.904761 | − | 0.425921i | \(-0.140050\pi\) | |||||||
\(258\) | 10.0322 | − | 7.08048i | 0.624580 | − | 0.440812i | ||||
\(259\) | 24.6328 | − | 24.6328i | 1.53061 | − | 1.53061i | ||||
\(260\) | 0.0888822 | − | 16.9358i | 0.00551224 | − | 1.05031i | ||||
\(261\) | 0.887645 | + | 0.887645i | 0.0549438 | + | 0.0549438i | ||||
\(262\) | −2.82754 | + | 16.3926i | −0.174686 | + | 1.01274i | ||||
\(263\) | 24.4841 | 1.50975 | 0.754877 | − | 0.655867i | \(-0.227697\pi\) | ||||
0.754877 | + | 0.655867i | \(0.227697\pi\) | |||||||
\(264\) | 7.03634 | − | 12.5080i | 0.433057 | − | 0.769817i | ||||
\(265\) | −0.981115 | + | 0.981115i | −0.0602694 | + | 0.0602694i | ||||
\(266\) | −0.656818 | + | 3.80789i | −0.0402721 | + | 0.233476i | ||||
\(267\) | 0.353141i | 0.0216119i | ||||||||
\(268\) | 2.86668 | + | 1.01927i | 0.175111 | + | 0.0622617i | ||||
\(269\) | −19.8278 | + | 19.8278i | −1.20892 | + | 1.20892i | −0.237545 | + | 0.971377i | \(0.576343\pi\) |
−0.971377 | + | 0.237545i | \(0.923657\pi\) | |||||||
\(270\) | −0.564571 | + | 3.27309i | −0.0343587 | + | 0.199194i | ||||
\(271\) | −18.4596 | − | 18.4596i | −1.12134 | − | 1.12134i | −0.991540 | − | 0.129798i | \(-0.958567\pi\) |
−0.129798 | − | 0.991540i | \(-0.541433\pi\) | |||||||
\(272\) | 8.25073 | − | 10.1358i | 0.500274 | − | 0.614572i | ||||
\(273\) | 5.37132 | + | 15.3617i | 0.325087 | + | 0.929735i | ||||
\(274\) | −1.50557 | + | 8.72850i | −0.0909547 | + | 0.527308i | ||||
\(275\) | 2.61779i | 0.157859i | ||||||||
\(276\) | −2.53155 | − | 5.32500i | −0.152382 | − | 0.320527i | ||||
\(277\) | −12.3053 | + | 12.3053i | −0.739353 | + | 0.739353i | −0.972453 | − | 0.233100i | \(-0.925113\pi\) |
0.233100 | + | 0.972453i | \(0.425113\pi\) | |||||||
\(278\) | 13.1474 | + | 2.26777i | 0.788526 | + | 0.136012i | ||||
\(279\) | 5.17321 | + | 5.17321i | 0.309712 | + | 0.309712i | ||||
\(280\) | 26.1316 | + | 14.7002i | 1.56166 | + | 0.878507i | ||||
\(281\) | −8.83183 | − | 8.83183i | −0.526863 | − | 0.526863i | 0.392773 | − | 0.919636i | \(-0.371516\pi\) |
−0.919636 | + | 0.392773i | \(0.871516\pi\) | |||||||
\(282\) | −8.91870 | + | 6.29458i | −0.531101 | + | 0.374837i | ||||
\(283\) | 10.2657 | + | 10.2657i | 0.610233 | + | 0.610233i | 0.943007 | − | 0.332773i | \(-0.107984\pi\) |
−0.332773 | + | 0.943007i | \(0.607984\pi\) | |||||||
\(284\) | 20.8294 | − | 9.90250i | 1.23600 | − | 0.587605i | ||||
\(285\) | 1.00534 | + | 1.00534i | 0.0595514 | + | 0.0595514i | ||||
\(286\) | −21.0593 | − | 15.0293i | −1.24526 | − | 0.888701i | ||||
\(287\) | 12.3854i | 0.731088i | ||||||||
\(288\) | −5.64353 | − | 0.387993i | −0.332548 | − | 0.0228627i | ||||
\(289\) | 6.32447 | 0.372027 | ||||||||
\(290\) | 0.708717 | − | 4.10877i | 0.0416173 | − | 0.241275i | ||||
\(291\) | 0.939083i | 0.0550500i | ||||||||
\(292\) | 3.87729 | − | 1.84330i | 0.226901 | − | 0.107871i | ||||
\(293\) | 15.3619 | 0.897452 | 0.448726 | − | 0.893669i | \(-0.351878\pi\) | ||||
0.448726 | + | 0.893669i | \(0.351878\pi\) | |||||||
\(294\) | −18.6355 | − | 3.21441i | −1.08684 | − | 0.187468i | ||||
\(295\) | −29.7147 | −1.73006 | ||||||||
\(296\) | 21.0219 | − | 5.88535i | 1.22187 | − | 0.342079i | ||||
\(297\) | 3.58784 | + | 3.58784i | 0.208187 | + | 0.208187i | ||||
\(298\) | −22.9135 | + | 16.1717i | −1.32734 | + | 0.936802i | ||||
\(299\) | −10.0337 | + | 3.50835i | −0.580265 | + | 0.202893i | ||||
\(300\) | 0.931901 | − | 0.443034i | 0.0538033 | − | 0.0255786i | ||||
\(301\) | 39.1896 | 2.25885 | ||||||||
\(302\) | 6.67857 | + | 1.15198i | 0.384309 | + | 0.0662889i | ||||
\(303\) | 3.48965 | 0.200475 | ||||||||
\(304\) | −1.52868 | + | 1.87794i | −0.0876760 | + | 0.107707i | ||||
\(305\) | −13.6975 | − | 13.6975i | −0.784314 | − | 0.784314i | ||||
\(306\) | 2.66442 | + | 3.77518i | 0.152315 | + | 0.215812i | ||||
\(307\) | 28.3820 | 1.61985 | 0.809924 | − | 0.586535i | \(-0.199508\pi\) | ||||
0.809924 | + | 0.586535i | \(0.199508\pi\) | |||||||
\(308\) | 41.3662 | − | 19.6659i | 2.35706 | − | 1.12057i | ||||
\(309\) | 10.5291 | − | 10.5291i | 0.598979 | − | 0.598979i | ||||
\(310\) | 4.13042 | − | 23.9460i | 0.234592 | − | 1.36004i | ||||
\(311\) | 6.73675i | 0.382006i | 0.981589 | + | 0.191003i | \(0.0611740\pi\) | ||||
−0.981589 | + | 0.191003i | \(0.938826\pi\) | |||||||
\(312\) | −1.78617 | + | 10.0404i | −0.101122 | + | 0.568426i | ||||
\(313\) | − | 2.41263i | − | 0.136370i | −0.997673 | − | 0.0681848i | \(-0.978279\pi\) | ||
0.997673 | − | 0.0681848i | \(-0.0217208\pi\) | |||||||
\(314\) | 8.61306 | + | 1.48566i | 0.486063 | + | 0.0838405i | ||||
\(315\) | −7.49566 | + | 7.49566i | −0.422332 | + | 0.422332i | ||||
\(316\) | −1.95195 | − | 0.694026i | −0.109806 | − | 0.0390420i | ||||
\(317\) | −16.1230 | −0.905557 | −0.452779 | − | 0.891623i | \(-0.649567\pi\) | ||||
−0.452779 | + | 0.891623i | \(0.649567\pi\) | |||||||
\(318\) | 0.682602 | − | 0.481763i | 0.0382784 | − | 0.0270159i | ||||
\(319\) | −4.50388 | − | 4.50388i | −0.252169 | − | 0.252169i | ||||
\(320\) | 9.75569 | + | 16.0576i | 0.545360 | + | 0.897646i | ||||
\(321\) | 14.6038 | 0.815103 | ||||||||
\(322\) | 3.19861 | − | 18.5439i | 0.178252 | − | 1.03341i | ||||
\(323\) | 1.97795 | 0.110056 | ||||||||
\(324\) | 0.670020 | − | 1.88443i | 0.0372234 | − | 0.104691i | ||||
\(325\) | −0.613978 | − | 1.75595i | −0.0340574 | − | 0.0974026i | ||||
\(326\) | 17.6478 | + | 25.0050i | 0.977423 | + | 1.38490i | ||||
\(327\) | 7.18985 | + | 7.18985i | 0.397599 | + | 0.397599i | ||||
\(328\) | −3.80535 | + | 6.76452i | −0.210115 | + | 0.373508i | ||||
\(329\) | −34.8397 | −1.92078 | ||||||||
\(330\) | 2.86462 | − | 16.6076i | 0.157692 | − | 0.914216i | ||||
\(331\) | −10.0815 | −0.554128 | −0.277064 | − | 0.960851i | \(-0.589361\pi\) | ||||
−0.277064 | + | 0.960851i | \(0.589361\pi\) | |||||||
\(332\) | −25.6157 | − | 9.10781i | −1.40584 | − | 0.499856i | ||||
\(333\) | 7.71814i | 0.422952i | ||||||||
\(334\) | −24.1029 | − | 4.15748i | −1.31885 | − | 0.227487i | ||||
\(335\) | 3.57280 | 0.195203 | ||||||||
\(336\) | −14.0016 | − | 11.3976i | −0.763850 | − | 0.621790i | ||||
\(337\) | − | 6.69041i | − | 0.364450i | −0.983257 | − | 0.182225i | \(-0.941670\pi\) | ||
0.983257 | − | 0.182225i | \(-0.0583299\pi\) | |||||||
\(338\) | 17.6511 | + | 5.14202i | 0.960091 | + | 0.279689i | ||||
\(339\) | −2.53230 | − | 2.53230i | −0.137536 | − | 0.137536i | ||||
\(340\) | 5.14153 | − | 14.4605i | 0.278838 | − | 0.784232i | ||||
\(341\) | −26.2487 | − | 26.2487i | −1.42145 | − | 1.42145i | ||||
\(342\) | −0.493659 | − | 0.699459i | −0.0266940 | − | 0.0378224i | ||||
\(343\) | −20.3361 | − | 20.3361i | −1.09805 | − | 1.09805i | ||||
\(344\) | 21.4041 | + | 12.0408i | 1.15403 | + | 0.649196i | ||||
\(345\) | −4.89588 | − | 4.89588i | −0.263586 | − | 0.263586i | ||||
\(346\) | −3.62075 | + | 20.9912i | −0.194653 | + | 1.12849i | ||||
\(347\) | 11.0016 | − | 11.0016i | 0.590597 | − | 0.590597i | −0.347196 | − | 0.937793i | \(-0.612866\pi\) |
0.937793 | + | 0.347196i | \(0.112866\pi\) | |||||||
\(348\) | −0.841089 | + | 2.36556i | −0.0450871 | + | 0.126807i | ||||
\(349\) | − | 21.8772i | − | 1.17106i | −0.810651 | − | 0.585529i | \(-0.800887\pi\) | ||
0.810651 | − | 0.585529i | \(-0.199113\pi\) | |||||||
\(350\) | 3.24527 | + | 0.559773i | 0.173467 | + | 0.0299211i | ||||
\(351\) | −3.24813 | − | 1.56514i | −0.173372 | − | 0.0835411i | ||||
\(352\) | 28.6351 | + | 1.96866i | 1.52626 | + | 0.104930i | ||||
\(353\) | 10.7964 | + | 10.7964i | 0.574633 | + | 0.574633i | 0.933420 | − | 0.358787i | \(-0.116809\pi\) |
−0.358787 | + | 0.933420i | \(0.616809\pi\) | |||||||
\(354\) | 17.6324 | + | 3.04139i | 0.937151 | + | 0.161648i | ||||
\(355\) | 19.1509 | − | 19.1509i | 1.01642 | − | 1.01642i | ||||
\(356\) | −0.637867 | + | 0.303248i | −0.0338069 | + | 0.0160721i | ||||
\(357\) | 14.7472i | 0.780506i | ||||||||
\(358\) | 22.1036 | + | 3.81262i | 1.16821 | + | 0.201503i | ||||
\(359\) | −0.370371 | + | 0.370371i | −0.0195475 | + | 0.0195475i | −0.716813 | − | 0.697266i | \(-0.754400\pi\) |
0.697266 | + | 0.716813i | \(0.254400\pi\) | |||||||
\(360\) | −6.39688 | + | 1.79089i | −0.337145 | + | 0.0943881i | ||||
\(361\) | 18.6335 | 0.980712 | ||||||||
\(362\) | −7.46929 | − | 1.28837i | −0.392577 | − | 0.0677152i | ||||
\(363\) | −10.4264 | − | 10.4264i | −0.547244 | − | 0.547244i | ||||
\(364\) | −23.1350 | + | 22.8934i | −1.21260 | + | 1.19994i | ||||
\(365\) | 3.56484 | − | 3.56484i | 0.186592 | − | 0.186592i | ||||
\(366\) | 6.72594 | + | 9.52989i | 0.351571 | + | 0.498135i | ||||
\(367\) | 7.18887i | 0.375256i | 0.982240 | + | 0.187628i | \(0.0600799\pi\) | ||||
−0.982240 | + | 0.187628i | \(0.939920\pi\) | |||||||
\(368\) | 7.44449 | − | 9.14532i | 0.388071 | − | 0.476733i | ||||
\(369\) | −1.94035 | − | 1.94035i | −0.101011 | − | 0.101011i | ||||
\(370\) | 20.9442 | − | 14.7819i | 1.08884 | − | 0.768473i | ||||
\(371\) | 2.66650 | 0.138438 | ||||||||
\(372\) | −4.90189 | + | 13.7865i | −0.254151 | + | 0.714799i | ||||
\(373\) | −21.4840 | − | 21.4840i | −1.11240 | − | 1.11240i | −0.992825 | − | 0.119573i | \(-0.961847\pi\) |
−0.119573 | − | 0.992825i | \(-0.538153\pi\) | |||||||
\(374\) | −13.5192 | − | 19.1551i | −0.699060 | − | 0.990488i | ||||
\(375\) | −7.44675 | + | 7.44675i | −0.384549 | + | 0.384549i | ||||
\(376\) | −19.0283 | − | 10.7043i | −0.981311 | − | 0.552032i | ||||
\(377\) | 4.07744 | + | 1.96475i | 0.209999 | + | 0.101190i | ||||
\(378\) | 5.21504 | − | 3.68064i | 0.268233 | − | 0.189312i | ||||
\(379\) | −21.5692 | −1.10793 | −0.553967 | − | 0.832538i | \(-0.686887\pi\) | ||||
−0.553967 | + | 0.832538i | \(0.686887\pi\) | |||||||
\(380\) | −0.952614 | + | 2.67922i | −0.0488681 | + | 0.137441i | ||||
\(381\) | −14.5320 | − | 14.5320i | −0.744497 | − | 0.744497i | ||||
\(382\) | 0.687519 | − | 0.485233i | 0.0351766 | − | 0.0248267i | ||||
\(383\) | 15.2878 | − | 15.2878i | 0.781169 | − | 0.781169i | −0.198859 | − | 0.980028i | \(-0.563724\pi\) |
0.980028 | + | 0.198859i | \(0.0637237\pi\) | |||||||
\(384\) | −4.14538 | − | 10.5269i | −0.211543 | − | 0.537199i | ||||
\(385\) | 38.0327 | − | 38.0327i | 1.93833 | − | 1.93833i | ||||
\(386\) | 31.7451 | + | 5.47567i | 1.61578 | + | 0.278704i | ||||
\(387\) | −6.13961 | + | 6.13961i | −0.312094 | + | 0.312094i | ||||
\(388\) | −1.69624 | + | 0.806406i | −0.0861134 | + | 0.0409391i | ||||
\(389\) | 13.0026 | − | 13.0026i | 0.659257 | − | 0.659257i | −0.295947 | − | 0.955204i | \(-0.595635\pi\) |
0.955204 | + | 0.295947i | \(0.0956352\pi\) | |||||||
\(390\) | 1.97363 | + | 11.8118i | 0.0999385 | + | 0.598114i | ||||
\(391\) | −9.63234 | −0.487128 | ||||||||
\(392\) | −10.1965 | − | 36.4210i | −0.515002 | − | 1.83954i | ||||
\(393\) | − | 11.7625i | − | 0.593339i | ||||||
\(394\) | −20.7845 | + | 14.6692i | −1.04711 | + | 0.739022i | ||||
\(395\) | −2.43275 | −0.122405 | ||||||||
\(396\) | −3.39966 | + | 9.56153i | −0.170839 | + | 0.480485i | ||||
\(397\) | 18.6653i | 0.936785i | 0.883521 | + | 0.468392i | \(0.155167\pi\) | ||||
−0.883521 | + | 0.468392i | \(0.844833\pi\) | |||||||
\(398\) | −11.6359 | + | 8.21231i | −0.583255 | + | 0.411646i | ||||
\(399\) | − | 2.73234i | − | 0.136788i | ||||||
\(400\) | 1.60048 | + | 1.30282i | 0.0800239 | + | 0.0651411i | ||||
\(401\) | 12.4375 | − | 12.4375i | 0.621101 | − | 0.621101i | −0.324712 | − | 0.945813i | \(-0.605267\pi\) |
0.945813 | + | 0.324712i | \(0.105267\pi\) | |||||||
\(402\) | −2.12006 | − | 0.365687i | −0.105739 | − | 0.0182388i | ||||
\(403\) | 23.7634 | + | 11.4506i | 1.18374 | + | 0.570396i | ||||
\(404\) | 2.99662 | + | 6.30325i | 0.149088 | + | 0.313598i | ||||
\(405\) | − | 2.34860i | − | 0.116703i | ||||||
\(406\) | −6.54654 | + | 4.62037i | −0.324899 | + | 0.229305i | ||||
\(407\) | − | 39.1616i | − | 1.94117i | ||||||
\(408\) | −4.53100 | + | 8.05446i | −0.224318 | + | 0.398755i | ||||
\(409\) | −18.2627 | + | 18.2627i | −0.903032 | + | 0.903032i | −0.995697 | − | 0.0926651i | \(-0.970461\pi\) |
0.0926651 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(410\) | −1.54922 | + | 8.98158i | −0.0765106 | + | 0.443569i | ||||
\(411\) | − | 6.26313i | − | 0.308937i | ||||||
\(412\) | 28.0599 | + | 9.97686i | 1.38241 | + | 0.491524i | ||||
\(413\) | 40.3797 | + | 40.3797i | 1.98696 | + | 1.98696i | ||||
\(414\) | 2.40406 | + | 3.40627i | 0.118153 | + | 0.167409i | ||||
\(415\) | −31.9253 | −1.56715 | ||||||||
\(416\) | −19.6695 | + | 5.39556i | −0.964375 | + | 0.264539i | ||||
\(417\) | −9.43386 | −0.461978 | ||||||||
\(418\) | 2.50481 | + | 3.54903i | 0.122514 | + | 0.173589i | ||||
\(419\) | −10.9612 | − | 10.9612i | −0.535491 | − | 0.535491i | 0.386710 | − | 0.922201i | \(-0.373611\pi\) |
−0.922201 | + | 0.386710i | \(0.873611\pi\) | |||||||
\(420\) | −19.9758 | − | 7.10252i | −0.974720 | − | 0.346568i | ||||
\(421\) | 21.1607i | 1.03131i | 0.856796 | + | 0.515656i | \(0.172452\pi\) | ||||
−0.856796 | + | 0.515656i | \(0.827548\pi\) | |||||||
\(422\) | −6.26243 | + | 36.3063i | −0.304850 | + | 1.76736i | ||||
\(423\) | 5.45813 | − | 5.45813i | 0.265384 | − | 0.265384i | ||||
\(424\) | 1.45635 | + | 0.819266i | 0.0707268 | + | 0.0397871i | ||||
\(425\) | − | 1.68571i | − | 0.0817688i | ||||||
\(426\) | −13.3241 | + | 9.40378i | −0.645554 | + | 0.455614i | ||||
\(427\) | 37.2273i | 1.80155i | ||||||||
\(428\) | 12.5405 | + | 26.3783i | 0.606168 | + | 1.27504i | ||||
\(429\) | 16.4809 | + | 7.94148i | 0.795705 | + | 0.383418i | ||||
\(430\) | 28.4193 | + | 4.90201i | 1.37050 | + | 0.236396i | ||||
\(431\) | −24.2194 | + | 24.2194i | −1.16661 | + | 1.16661i | −0.183606 | + | 0.983000i | \(0.558777\pi\) |
−0.983000 | + | 0.183606i | \(0.941223\pi\) | |||||||
\(432\) | 3.97914 | − | 0.407954i | 0.191447 | − | 0.0196277i | ||||
\(433\) | − | 11.2157i | − | 0.538990i | −0.963002 | − | 0.269495i | \(-0.913143\pi\) | ||
0.963002 | − | 0.269495i | \(-0.0868567\pi\) | |||||||
\(434\) | −38.1534 | + | 26.9276i | −1.83142 | + | 1.29257i | ||||
\(435\) | 2.94824i | 0.141357i | ||||||||
\(436\) | −6.81275 | + | 19.1608i | −0.326272 | + | 0.917637i | ||||
\(437\) | 1.78467 | 0.0853721 | ||||||||
\(438\) | −2.48021 | + | 1.75046i | −0.118509 | + | 0.0836404i | ||||
\(439\) | 26.1909i | 1.25002i | 0.780616 | + | 0.625012i | \(0.214906\pi\) | ||||
−0.780616 | + | 0.625012i | \(0.785094\pi\) | |||||||
\(440\) | 32.4576 | − | 9.08691i | 1.54735 | − | 0.433202i | ||||
\(441\) | 13.3719 | 0.636756 | ||||||||
\(442\) | 13.5610 | + | 9.67800i | 0.645030 | + | 0.460335i | ||||
\(443\) | −4.34169 | + | 4.34169i | −0.206280 | + | 0.206280i | −0.802684 | − | 0.596404i | \(-0.796596\pi\) |
0.596404 | + | 0.802684i | \(0.296596\pi\) | |||||||
\(444\) | −13.9410 | + | 6.62770i | −0.661612 | + | 0.314537i | ||||
\(445\) | −0.586465 | + | 0.586465i | −0.0278011 | + | 0.0278011i | ||||
\(446\) | −2.70212 | − | 0.466086i | −0.127949 | − | 0.0220698i | ||||
\(447\) | 14.0228 | − | 14.0228i | 0.663253 | − | 0.663253i | ||||
\(448\) | 8.56371 | − | 35.0780i | 0.404597 | − | 1.65728i | ||||
\(449\) | −5.51808 | + | 5.51808i | −0.260414 | + | 0.260414i | −0.825222 | − | 0.564808i | \(-0.808950\pi\) |
0.564808 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(450\) | −0.596114 | + | 0.420722i | −0.0281011 | + | 0.0198330i | ||||
\(451\) | 9.84528 | + | 9.84528i | 0.463596 | + | 0.463596i | ||||
\(452\) | 2.39949 | − | 6.74855i | 0.112862 | − | 0.317425i | ||||
\(453\) | −4.79220 | −0.225157 | ||||||||
\(454\) | 14.5420 | − | 10.2633i | 0.682489 | − | 0.481682i | ||||
\(455\) | −16.5912 | + | 34.4316i | −0.777808 | + | 1.61418i | ||||
\(456\) | 0.839497 | − | 1.49232i | 0.0393130 | − | 0.0698842i | ||||
\(457\) | 15.4363 | − | 15.4363i | 0.722081 | − | 0.722081i | −0.246948 | − | 0.969029i | \(-0.579428\pi\) |
0.969029 | + | 0.246948i | \(0.0794275\pi\) | |||||||
\(458\) | −9.14070 | − | 12.9513i | −0.427117 | − | 0.605175i | ||||
\(459\) | −2.31036 | − | 2.31036i | −0.107838 | − | 0.107838i | ||||
\(460\) | 4.63910 | − | 13.0475i | 0.216299 | − | 0.608341i | ||||
\(461\) | 15.3480 | 0.714829 | 0.357414 | − | 0.933946i | \(-0.383658\pi\) | ||||
0.357414 | + | 0.933946i | \(0.383658\pi\) | |||||||
\(462\) | −26.4610 | + | 18.6754i | −1.23108 | + | 0.868860i | ||||
\(463\) | −11.8554 | − | 11.8554i | −0.550967 | − | 0.550967i | 0.375753 | − | 0.926720i | \(-0.377384\pi\) |
−0.926720 | + | 0.375753i | \(0.877384\pi\) | |||||||
\(464\) | −4.99509 | + | 0.512112i | −0.231891 | + | 0.0237742i | ||||
\(465\) | 17.1824i | 0.796816i | ||||||||
\(466\) | 0.399038 | + | 0.565392i | 0.0184851 | + | 0.0261913i | ||||
\(467\) | −20.9330 | + | 20.9330i | −0.968663 | + | 0.968663i | −0.999524 | − | 0.0308608i | \(-0.990175\pi\) |
0.0308608 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(468\) | 0.0378447 | − | 7.21100i | 0.00174937 | − | 0.333329i | ||||
\(469\) | −4.85513 | − | 4.85513i | −0.224189 | − | 0.224189i | ||||
\(470\) | −25.2649 | − | 4.35791i | −1.16538 | − | 0.201015i | ||||
\(471\) | −6.18029 | −0.284773 | ||||||||
\(472\) | 9.64766 | + | 34.4605i | 0.444070 | + | 1.58617i | ||||
\(473\) | 31.1522 | − | 31.1522i | 1.43238 | − | 1.43238i | ||||
\(474\) | 1.44357 | + | 0.248999i | 0.0663052 | + | 0.0114369i | ||||
\(475\) | 0.312325i | 0.0143305i | ||||||||
\(476\) | −26.6375 | + | 12.6637i | −1.22093 | + | 0.580439i | ||||
\(477\) | −0.417744 | + | 0.417744i | −0.0191272 | + | 0.0191272i | ||||
\(478\) | 13.9052 | + | 2.39849i | 0.636008 | + | 0.109704i | ||||
\(479\) | −11.3939 | − | 11.3939i | −0.520600 | − | 0.520600i | 0.397153 | − | 0.917752i | \(-0.369998\pi\) |
−0.917752 | + | 0.397153i | \(0.869998\pi\) | |||||||
\(480\) | −8.72794 | − | 10.0166i | −0.398374 | − | 0.457194i | ||||
\(481\) | 9.18498 | + | 26.2687i | 0.418799 | + | 1.19775i | ||||
\(482\) | 16.1752 | + | 2.79005i | 0.736762 | + | 0.127083i | ||||
\(483\) | 13.3062i | 0.605451i | ||||||||
\(484\) | 9.87956 | − | 27.7862i | 0.449071 | − | 1.26301i | ||||
\(485\) | −1.55955 | + | 1.55955i | −0.0708154 | + | 0.0708154i | ||||
\(486\) | −0.240386 | + | 1.39363i | −0.0109041 | + | 0.0632165i | ||||
\(487\) | −19.6521 | − | 19.6521i | −0.890522 | − | 0.890522i | 0.104050 | − | 0.994572i | \(-0.466820\pi\) |
−0.994572 | + | 0.104050i | \(0.966820\pi\) | |||||||
\(488\) | −11.4379 | + | 20.3323i | −0.517768 | + | 0.920402i | ||||
\(489\) | −15.3027 | − | 15.3027i | −0.692013 | − | 0.692013i | ||||
\(490\) | −25.6100 | − | 36.2864i | −1.15694 | − | 1.63925i | ||||
\(491\) | 6.80270 | + | 6.80270i | 0.307002 | + | 0.307002i | 0.843745 | − | 0.536744i | \(-0.180346\pi\) |
−0.536744 | + | 0.843745i | \(0.680346\pi\) | |||||||
\(492\) | 1.83858 | − | 5.17100i | 0.0828897 | − | 0.233127i | ||||
\(493\) | 2.90024 | + | 2.90024i | 0.130620 | + | 0.130620i | ||||
\(494\) | −2.51256 | − | 1.79312i | −0.113045 | − | 0.0806765i | ||||
\(495\) | 11.9167i | 0.535617i | ||||||||
\(496\) | −29.1115 | + | 2.98460i | −1.30715 | + | 0.134013i | ||||
\(497\) | −52.0488 | −2.33471 | ||||||||
\(498\) | 18.9441 | + | 3.26765i | 0.848907 | + | 0.146427i | ||||
\(499\) | 25.9141i | 1.16008i | 0.814590 | + | 0.580038i | \(0.196962\pi\) | ||||
−0.814590 | + | 0.580038i | \(0.803038\pi\) | |||||||
\(500\) | −19.8455 | − | 7.05619i | −0.887517 | − | 0.315562i | ||||
\(501\) | 17.2950 | 0.772684 | ||||||||
\(502\) | 4.96781 | − | 28.8008i | 0.221724 | − | 1.28544i | ||||
\(503\) | 24.0888 | 1.07407 | 0.537034 | − | 0.843561i | \(-0.319545\pi\) | ||||
0.537034 | + | 0.843561i | \(0.319545\pi\) | |||||||
\(504\) | 11.1265 | + | 6.25914i | 0.495612 | + | 0.278804i | ||||
\(505\) | 5.79531 | + | 5.79531i | 0.257888 | + | 0.257888i | ||||
\(506\) | −12.1981 | − | 17.2833i | −0.542272 | − | 0.768337i | ||||
\(507\) | −12.9176 | − | 1.46151i | −0.573690 | − | 0.0649081i | ||||
\(508\) | 13.7698 | − | 38.7276i | 0.610937 | − | 1.71826i | ||||
\(509\) | 40.2715 | 1.78500 | 0.892501 | − | 0.451046i | \(-0.148949\pi\) | ||||
0.892501 | + | 0.451046i | \(0.148949\pi\) | |||||||
\(510\) | −1.84465 | + | 10.6943i | −0.0816824 | + | 0.473552i | ||||
\(511\) | −9.68860 | −0.428598 | ||||||||
\(512\) | 15.4547 | − | 16.5273i | 0.683009 | − | 0.730410i | ||||
\(513\) | 0.428060 | + | 0.428060i | 0.0188993 | + | 0.0188993i | ||||
\(514\) | −15.7786 | + | 11.1361i | −0.695962 | + | 0.491192i | ||||
\(515\) | 34.9715 | 1.54103 | ||||||||
\(516\) | −16.3620 | − | 5.81759i | −0.720295 | − | 0.256105i | ||||
\(517\) | −27.6944 | + | 27.6944i | −1.21800 | + | 1.21800i | ||||
\(518\) | −48.5486 | − | 8.37409i | −2.13310 | − | 0.367937i | ||||
\(519\) | − | 15.0622i | − | 0.661158i | ||||||
\(520\) | −19.6405 | + | 13.7079i | −0.861294 | + | 0.601131i | ||||
\(521\) | − | 8.52149i | − | 0.373333i | −0.982423 | − | 0.186667i | \(-0.940232\pi\) | ||
0.982423 | − | 0.186667i | \(-0.0597684\pi\) | |||||||
\(522\) | 0.301761 | − | 1.74945i | 0.0132077 | − | 0.0765716i | ||||
\(523\) | −21.1778 | + | 21.1778i | −0.926040 | + | 0.926040i | −0.997447 | − | 0.0714073i | \(-0.977251\pi\) |
0.0714073 | + | 0.997447i | \(0.477251\pi\) | |||||||
\(524\) | 21.2462 | − | 10.1006i | 0.928146 | − | 0.441249i | ||||
\(525\) | −2.32864 | −0.101630 | ||||||||
\(526\) | −19.9660 | − | 28.2896i | −0.870560 | − | 1.23348i | ||||
\(527\) | 16.9027 | + | 16.9027i | 0.736292 | + | 0.736292i | ||||
\(528\) | −20.1900 | + | 2.06994i | −0.878659 | + | 0.0900828i | ||||
\(529\) | 14.3089 | 0.622127 | ||||||||
\(530\) | 1.93367 | + | 0.333537i | 0.0839934 | + | 0.0144879i | ||||
\(531\) | −12.6521 | −0.549054 | ||||||||
\(532\) | 4.93535 | − | 2.34631i | 0.213974 | − | 0.101725i | ||||
\(533\) | −8.91309 | − | 4.29486i | −0.386069 | − | 0.186031i | ||||
\(534\) | 0.408028 | − | 0.287975i | 0.0176571 | − | 0.0124619i | ||||
\(535\) | 24.2526 | + | 24.2526i | 1.04853 | + | 1.04853i | ||||
\(536\) | −1.16000 | − | 4.14342i | −0.0501045 | − | 0.178969i | ||||
\(537\) | −15.8604 | −0.684426 | ||||||||
\(538\) | 39.0785 | + | 6.74060i | 1.68479 | + | 0.290608i | ||||
\(539\) | −67.8485 | −2.92244 | ||||||||
\(540\) | 4.24220 | − | 2.01678i | 0.182555 | − | 0.0867885i | ||||
\(541\) | 10.5379i | 0.453060i | 0.974004 | + | 0.226530i | \(0.0727381\pi\) | ||||
−0.974004 | + | 0.226530i | \(0.927262\pi\) | |||||||
\(542\) | −6.27546 | + | 36.3819i | −0.269554 | + | 1.56274i | ||||
\(543\) | 5.35958 | 0.230002 | ||||||||
\(544\) | −18.4394 | − | 1.26771i | −0.790581 | − | 0.0543524i | ||||
\(545\) | 23.8805i | 1.02293i | ||||||||
\(546\) | 13.3692 | − | 18.7332i | 0.572150 | − | 0.801707i | ||||
\(547\) | −9.83786 | − | 9.83786i | −0.420636 | − | 0.420636i | 0.464786 | − | 0.885423i | \(-0.346131\pi\) |
−0.885423 | + | 0.464786i | \(0.846131\pi\) | |||||||
\(548\) | 11.3129 | − | 5.37825i | 0.483263 | − | 0.229747i | ||||
\(549\) | −5.83218 | − | 5.83218i | −0.248911 | − | 0.248911i | ||||
\(550\) | 3.02467 | − | 2.13473i | 0.128972 | − | 0.0910251i | ||||
\(551\) | −0.537352 | − | 0.537352i | −0.0228920 | − | 0.0228920i | ||||
\(552\) | −4.08824 | + | 7.26739i | −0.174007 | + | 0.309321i | ||||
\(553\) | 3.30589 | + | 3.30589i | 0.140581 | + | 0.140581i | ||||
\(554\) | 24.2524 | + | 4.18327i | 1.03039 | + | 0.177730i | ||||
\(555\) | −12.8176 | + | 12.8176i | −0.544077 | + | 0.544077i | ||||
\(556\) | −8.10102 | − | 17.0401i | −0.343560 | − | 0.722661i | ||||
\(557\) | 2.17656i | 0.0922239i | 0.998936 | + | 0.0461120i | \(0.0146831\pi\) | ||||
−0.998936 | + | 0.0461120i | \(0.985317\pi\) | |||||||
\(558\) | 1.75867 | − | 10.1959i | 0.0744505 | − | 0.431625i | ||||
\(559\) | −13.5897 | + | 28.2026i | −0.574782 | + | 1.19284i | ||||
\(560\) | −4.32450 | − | 42.1807i | −0.182743 | − | 1.78246i | ||||
\(561\) | 11.7227 | + | 11.7227i | 0.494933 | + | 0.494933i | ||||
\(562\) | −3.00245 | + | 17.4066i | −0.126651 | + | 0.734254i | ||||
\(563\) | −9.43668 | + | 9.43668i | −0.397709 | + | 0.397709i | −0.877424 | − | 0.479715i | \(-0.840740\pi\) |
0.479715 | + | 0.877424i | \(0.340740\pi\) | |||||||
\(564\) | 14.5458 | + | 5.17186i | 0.612491 | + | 0.217775i | ||||
\(565\) | − | 8.41084i | − | 0.353847i | ||||||
\(566\) | 3.48990 | − | 20.2326i | 0.146692 | − | 0.850442i | ||||
\(567\) | −3.19154 | + | 3.19154i | −0.134032 | + | 0.134032i | ||||
\(568\) | −28.4274 | − | 15.9917i | −1.19279 | − | 0.670996i | ||||
\(569\) | 0.604977 | 0.0253620 | 0.0126810 | − | 0.999920i | \(-0.495963\pi\) | ||||
0.0126810 | + | 0.999920i | \(0.495963\pi\) | |||||||
\(570\) | 0.341774 | − | 1.98143i | 0.0143153 | − | 0.0829928i | ||||
\(571\) | −16.7611 | − | 16.7611i | −0.701431 | − | 0.701431i | 0.263287 | − | 0.964718i | \(-0.415193\pi\) |
−0.964718 | + | 0.263287i | \(0.915193\pi\) | |||||||
\(572\) | −0.192023 | + | 36.5884i | −0.00802889 | + | 1.52984i | ||||
\(573\) | −0.420753 | + | 0.420753i | −0.0175772 | + | 0.0175772i | ||||
\(574\) | 14.3104 | − | 10.0999i | 0.597306 | − | 0.421563i | ||||
\(575\) | − | 1.52098i | − | 0.0634294i | ||||||
\(576\) | 4.15383 | + | 6.83708i | 0.173076 | + | 0.284878i | ||||
\(577\) | 9.27339 | + | 9.27339i | 0.386056 | + | 0.386056i | 0.873278 | − | 0.487222i | \(-0.161990\pi\) |
−0.487222 | + | 0.873278i | \(0.661990\pi\) | |||||||
\(578\) | −5.15741 | − | 7.30745i | −0.214520 | − | 0.303950i | ||||
\(579\) | −22.7786 | −0.946648 | ||||||||
\(580\) | −5.32532 | + | 2.53171i | −0.221122 | + | 0.105123i | ||||
\(581\) | 43.3837 | + | 43.3837i | 1.79986 | + | 1.79986i | ||||
\(582\) | 1.08504 | − | 0.765793i | 0.0449764 | − | 0.0317432i | ||||
\(583\) | 2.11962 | − | 2.11962i | 0.0877858 | − | 0.0877858i | ||||
\(584\) | −5.29160 | − | 2.97677i | −0.218968 | − | 0.123179i | ||||
\(585\) | −2.79495 | − | 7.99345i | −0.115557 | − | 0.330489i | ||||
\(586\) | −12.5272 | − | 17.7495i | −0.517492 | − | 0.733227i | ||||
\(587\) | 18.0193 | 0.743735 | 0.371867 | − | 0.928286i | \(-0.378718\pi\) | ||||
0.371867 | + | 0.928286i | \(0.378718\pi\) | |||||||
\(588\) | 11.4827 | + | 24.1532i | 0.473537 | + | 0.996061i | ||||
\(589\) | −3.13170 | − | 3.13170i | −0.129039 | − | 0.129039i | ||||
\(590\) | 24.2314 | + | 34.3332i | 0.997593 | + | 1.41347i | ||||
\(591\) | 12.7199 | − | 12.7199i | 0.523226 | − | 0.523226i | ||||
\(592\) | −23.9428 | − | 19.4899i | −0.984043 | − | 0.801032i | ||||
\(593\) | 16.9494 | − | 16.9494i | 0.696027 | − | 0.696027i | −0.267524 | − | 0.963551i | \(-0.586205\pi\) |
0.963551 | + | 0.267524i | \(0.0862054\pi\) | |||||||
\(594\) | 1.21971 | − | 7.07125i | 0.0500454 | − | 0.290137i | ||||
\(595\) | −24.4909 | + | 24.4909i | −1.00403 | + | 1.00403i | ||||
\(596\) | 37.3704 | + | 13.2873i | 1.53075 | + | 0.544268i | ||||
\(597\) | 7.12103 | − | 7.12103i | 0.291445 | − | 0.291445i | ||||
\(598\) | 12.2358 | + | 8.73228i | 0.500360 | + | 0.357089i | ||||
\(599\) | 26.4515 | 1.08078 | 0.540389 | − | 0.841415i | \(-0.318277\pi\) | ||||
0.540389 | + | 0.841415i | \(0.318277\pi\) | |||||||
\(600\) | −1.27183 | − | 0.715462i | −0.0519222 | − | 0.0292086i | ||||
\(601\) | 46.9067i | 1.91336i | 0.291137 | + | 0.956681i | \(0.405967\pi\) | ||||
−0.291137 | + | 0.956681i | \(0.594033\pi\) | |||||||
\(602\) | −31.9579 | − | 45.2807i | −1.30251 | − | 1.84550i | ||||
\(603\) | 1.52125 | 0.0619500 | ||||||||
\(604\) | −4.11514 | − | 8.65600i | −0.167443 | − | 0.352208i | ||||
\(605\) | − | 34.6305i | − | 1.40793i | ||||||
\(606\) | −2.84570 | − | 4.03204i | −0.115599 | − | 0.163790i | ||||
\(607\) | 33.6440i | 1.36557i | 0.730620 | + | 0.682784i | \(0.239231\pi\) | ||||
−0.730620 | + | 0.682784i | \(0.760769\pi\) | |||||||
\(608\) | 3.41642 | + | 0.234879i | 0.138554 | + | 0.00952558i | ||||
\(609\) | 4.00640 | − | 4.00640i | 0.162348 | − | 0.162348i | ||||
\(610\) | −4.65655 | + | 26.9963i | −0.188538 | + | 1.09305i | ||||
\(611\) | 12.0813 | − | 25.0722i | 0.488756 | − | 1.01431i | ||||
\(612\) | 2.18919 | − | 6.15708i | 0.0884926 | − | 0.248885i | ||||
\(613\) | 30.3615i | 1.22629i | 0.789971 | + | 0.613145i | \(0.210096\pi\) | ||||
−0.789971 | + | 0.613145i | \(0.789904\pi\) | |||||||
\(614\) | −23.1447 | − | 32.7934i | −0.934043 | − | 1.32343i | ||||
\(615\) | − | 6.44472i | − | 0.259876i | ||||||
\(616\) | −56.4553 | − | 31.7587i | −2.27465 | − | 1.27959i | ||||
\(617\) | −17.2302 | + | 17.2302i | −0.693662 | + | 0.693662i | −0.963036 | − | 0.269373i | \(-0.913183\pi\) |
0.269373 | + | 0.963036i | \(0.413183\pi\) | |||||||
\(618\) | −20.7517 | − | 3.57944i | −0.834757 | − | 0.143986i | ||||
\(619\) | − | 36.8840i | − | 1.48249i | −0.671232 | − | 0.741247i | \(-0.734235\pi\) | ||
0.671232 | − | 0.741247i | \(-0.265765\pi\) | |||||||
\(620\) | −31.0361 | + | 14.7548i | −1.24644 | + | 0.592569i | ||||
\(621\) | −2.08460 | − | 2.08460i | −0.0836520 | − | 0.0836520i | ||||
\(622\) | 7.78382 | − | 5.49361i | 0.312103 | − | 0.220274i | ||||
\(623\) | 1.59391 | 0.0638586 | ||||||||
\(624\) | 13.0575 | − | 6.12385i | 0.522719 | − | 0.245150i | ||||
\(625\) | −27.3134 | −1.09254 | ||||||||
\(626\) | −2.78761 | + | 1.96742i | −0.111415 | + | 0.0786340i | ||||
\(627\) | −2.17196 | − | 2.17196i | −0.0867399 | − | 0.0867399i | ||||
\(628\) | −5.30712 | − | 11.1633i | −0.211777 | − | 0.445463i | ||||
\(629\) | 25.2178i | 1.00550i | ||||||||
\(630\) | 14.7732 | + | 2.54820i | 0.588577 | + | 0.101523i | ||||
\(631\) | 19.5087 | − | 19.5087i | 0.776629 | − | 0.776629i | −0.202627 | − | 0.979256i | \(-0.564948\pi\) |
0.979256 | + | 0.202627i | \(0.0649480\pi\) | |||||||
\(632\) | 0.789855 | + | 2.82129i | 0.0314187 | + | 0.112225i | ||||
\(633\) | − | 26.0516i | − | 1.03546i | ||||||
\(634\) | 13.1478 | + | 18.6289i | 0.522166 | + | 0.739849i | ||||
\(635\) | − | 48.2669i | − | 1.91541i | ||||||
\(636\) | −1.11328 | − | 0.395834i | −0.0441445 | − | 0.0156959i | ||||
\(637\) | 45.5111 | − | 15.9132i | 1.80322 | − | 0.630504i | ||||
\(638\) | −1.53113 | + | 8.87668i | −0.0606179 | + | 0.351431i | ||||
\(639\) | 8.15417 | − | 8.15417i | 0.322574 | − | 0.322574i | ||||
\(640\) | 10.5979 | − | 24.3664i | 0.418918 | − | 0.963168i | ||||
\(641\) | 44.5896i | 1.76119i | 0.473874 | + | 0.880593i | \(0.342855\pi\) | ||||
−0.473874 | + | 0.880593i | \(0.657145\pi\) | |||||||
\(642\) | −11.9089 | − | 16.8736i | −0.470007 | − | 0.665947i | ||||
\(643\) | − | 10.3204i | − | 0.406995i | −0.979075 | − | 0.203497i | \(-0.934769\pi\) | ||
0.979075 | − | 0.203497i | \(-0.0652309\pi\) | |||||||
\(644\) | −24.0345 | + | 11.4262i | −0.947091 | + | 0.450256i | ||||
\(645\) | −20.3922 | −0.802943 | ||||||||
\(646\) | −1.61295 | − | 2.28537i | −0.0634609 | − | 0.0899168i | ||||
\(647\) | − | 6.39306i | − | 0.251337i | −0.992072 | − | 0.125669i | \(-0.959892\pi\) | ||
0.992072 | − | 0.125669i | \(-0.0401076\pi\) | |||||||
\(648\) | −2.72370 | + | 0.762534i | −0.106997 | + | 0.0299552i | ||||
\(649\) | 64.1964 | 2.51993 | ||||||||
\(650\) | −1.52819 | + | 2.14133i | −0.0599406 | + | 0.0839899i | ||||
\(651\) | 23.3494 | − | 23.3494i | 0.915136 | − | 0.915136i | ||||
\(652\) | 14.5001 | − | 40.7815i | 0.567869 | − | 1.59713i | ||||
\(653\) | −9.91722 | + | 9.91722i | −0.388091 | + | 0.388091i | −0.874006 | − | 0.485915i | \(-0.838486\pi\) |
0.485915 | + | 0.874006i | \(0.338486\pi\) | |||||||
\(654\) | 2.44424 | − | 14.1704i | 0.0955774 | − | 0.554108i | ||||
\(655\) | 19.5341 | − | 19.5341i | 0.763261 | − | 0.763261i | ||||
\(656\) | 10.9190 | − | 1.11945i | 0.426317 | − | 0.0437073i | ||||
\(657\) | 1.51786 | − | 1.51786i | 0.0592172 | − | 0.0592172i | ||||
\(658\) | 28.4107 | + | 40.2547i | 1.10756 | + | 1.56929i | ||||
\(659\) | −5.98583 | − | 5.98583i | −0.233175 | − | 0.233175i | 0.580842 | − | 0.814017i | \(-0.302724\pi\) |
−0.814017 | + | 0.580842i | \(0.802724\pi\) | |||||||
\(660\) | −21.5248 | + | 10.2331i | −0.837852 | + | 0.398323i | ||||
\(661\) | 20.1520 | 0.783820 | 0.391910 | − | 0.920004i | \(-0.371814\pi\) | ||||
0.391910 | + | 0.920004i | \(0.371814\pi\) | |||||||
\(662\) | 8.22114 | + | 11.6484i | 0.319524 | + | 0.452728i | ||||
\(663\) | −10.6127 | − | 5.11386i | −0.412165 | − | 0.198606i | ||||
\(664\) | 10.3654 | + | 37.0242i | 0.402255 | + | 1.43682i | ||||
\(665\) | 4.53764 | − | 4.53764i | 0.175962 | − | 0.175962i | ||||
\(666\) | 8.91775 | − | 6.29391i | 0.345556 | − | 0.243884i | ||||
\(667\) | 2.61683 | + | 2.61683i | 0.101324 | + | 0.101324i | ||||
\(668\) | 14.8515 | + | 31.2394i | 0.574622 | + | 1.20869i | ||||
\(669\) | 1.93891 | 0.0749624 | ||||||||
\(670\) | −2.91351 | − | 4.12811i | −0.112559 | − | 0.159483i | ||||
\(671\) | 29.5923 | + | 29.5923i | 1.14240 | + | 1.14240i | ||||
\(672\) | −1.75121 | + | 25.4722i | −0.0675545 | + | 0.982612i | ||||
\(673\) | − | 16.5370i | − | 0.637454i | −0.947847 | − | 0.318727i | \(-0.896745\pi\) | ||
0.947847 | − | 0.318727i | \(-0.103255\pi\) | |||||||
\(674\) | −7.73028 | + | 5.45582i | −0.297759 | + | 0.210151i | ||||
\(675\) | 0.364815 | − | 0.364815i | 0.0140417 | − | 0.0140417i | ||||
\(676\) | −8.45266 | − | 24.5877i | −0.325102 | − | 0.945679i | ||||
\(677\) | −8.18314 | − | 8.18314i | −0.314504 | − | 0.314504i | 0.532148 | − | 0.846651i | \(-0.321385\pi\) |
−0.846651 | + | 0.532148i | \(0.821385\pi\) | |||||||
\(678\) | −0.860874 | + | 4.99090i | −0.0330617 | + | 0.191674i | ||||
\(679\) | 4.23857 | 0.162661 | ||||||||
\(680\) | −20.9008 | + | 5.85145i | −0.801510 | + | 0.224393i | ||||
\(681\) | −8.89951 | + | 8.89951i | −0.341030 | + | 0.341030i | ||||
\(682\) | −8.92345 | + | 51.7335i | −0.341696 | + | 1.98098i | ||||
\(683\) | − | 35.1244i | − | 1.34400i | −0.740553 | − | 0.671998i | \(-0.765436\pi\) | ||
0.740553 | − | 0.671998i | \(-0.234564\pi\) | |||||||
\(684\) | −0.405609 | + | 1.14077i | −0.0155089 | + | 0.0436186i | ||||
\(685\) | 10.4012 | − | 10.4012i | 0.397411 | − | 0.397411i | ||||
\(686\) | −6.91341 | + | 40.0804i | −0.263955 | + | 1.53028i | ||||
\(687\) | 7.92605 | + | 7.92605i | 0.302398 | + | 0.302398i | ||||
\(688\) | −3.54215 | − | 34.5498i | −0.135043 | − | 1.31720i | ||||
\(689\) | −0.924654 | + | 1.91893i | −0.0352265 | + | 0.0731053i | ||||
\(690\) | −1.66439 | + | 9.64928i | −0.0633623 | + | 0.367342i | ||||
\(691\) | − | 5.86497i | − | 0.223114i | −0.993758 | − | 0.111557i | \(-0.964416\pi\) | ||
0.993758 | − | 0.111557i | \(-0.0355838\pi\) | |||||||
\(692\) | 27.2064 | − | 12.9342i | 1.03423 | − | 0.491684i | ||||
\(693\) | 16.1938 | − | 16.1938i | 0.615151 | − | 0.615151i | ||||
\(694\) | −21.6830 | − | 3.74008i | −0.823076 | − | 0.141971i | ||||
\(695\) | −15.6669 | − | 15.6669i | −0.594280 | − | 0.594280i | ||||
\(696\) | 3.41911 | − | 0.957224i | 0.129601 | − | 0.0362835i | ||||
\(697\) | −6.33979 | − | 6.33979i | −0.240137 | − | 0.240137i | ||||
\(698\) | −25.2775 | + | 17.8402i | −0.956766 | + | 0.675260i | ||||
\(699\) | −0.346013 | − | 0.346013i | −0.0130874 | − | 0.0130874i | ||||
\(700\) | −1.99964 | − | 4.20615i | −0.0755794 | − | 0.158978i | ||||
\(701\) | −21.2812 | − | 21.2812i | −0.803778 | − | 0.803778i | 0.179906 | − | 0.983684i | \(-0.442421\pi\) |
−0.983684 | + | 0.179906i | \(0.942421\pi\) | |||||||
\(702\) | 0.840342 | + | 5.02930i | 0.0317167 | + | 0.189819i | ||||
\(703\) | − | 4.67232i | − | 0.176220i | ||||||
\(704\) | −21.0764 | − | 34.6911i | −0.794347 | − | 1.30747i | ||||
\(705\) | 18.1288 | 0.682769 | ||||||||
\(706\) | 3.67031 | − | 21.2785i | 0.138134 | − | 0.800828i | ||||
\(707\) | − | 15.7506i | − | 0.592363i | ||||||
\(708\) | −10.8646 | − | 22.8531i | −0.408315 | − | 0.858872i | ||||
\(709\) | −11.7721 | −0.442111 | −0.221056 | − | 0.975261i | \(-0.570950\pi\) | ||||
−0.221056 | + | 0.975261i | \(0.570950\pi\) | |||||||
\(710\) | −37.7444 | − | 6.51049i | −1.41652 | − | 0.244334i | ||||
\(711\) | −1.03583 | −0.0388466 | ||||||||
\(712\) | 0.870541 | + | 0.489719i | 0.0326249 | + | 0.0183530i | ||||
\(713\) | 15.2510 | + | 15.2510i | 0.571153 | + | 0.571153i | ||||
\(714\) | 17.0393 | − | 12.0259i | 0.637681 | − | 0.450058i | ||||
\(715\) | 14.1815 | + | 40.5585i | 0.530358 | + | 1.51680i | ||||
\(716\) | −13.6196 | − | 28.6481i | −0.508988 | − | 1.07063i | ||||
\(717\) | −9.97764 | −0.372622 | ||||||||
\(718\) | 0.729963 | + | 0.125910i | 0.0272420 | + | 0.00469894i | ||||
\(719\) | 17.1587 | 0.639912 | 0.319956 | − | 0.947432i | \(-0.396332\pi\) | ||||
0.319956 | + | 0.947432i | \(0.396332\pi\) | |||||||
\(720\) | 7.28570 | + | 5.93071i | 0.271522 | + | 0.221025i | ||||
\(721\) | −47.5233 | − | 47.5233i | −1.76986 | − | 1.76986i | ||||
\(722\) | −15.1951 | − | 21.5297i | −0.565502 | − | 0.801251i | ||||
\(723\) | −11.6065 | −0.431651 | ||||||||
\(724\) | 4.60236 | + | 9.68084i | 0.171045 | + | 0.359786i | ||||
\(725\) | −0.457959 | + | 0.457959i | −0.0170082 | + | 0.0170082i | ||||
\(726\) | −3.54453 | + | 20.5493i | −0.131550 | + | 0.762658i | ||||
\(727\) | − | 43.8878i | − | 1.62771i | −0.581070 | − | 0.813854i | \(-0.697366\pi\) | ||
0.581070 | − | 0.813854i | \(-0.302634\pi\) | |||||||
\(728\) | 45.3176 | + | 8.06190i | 1.67958 | + | 0.298794i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −7.02592 | − | 1.21189i | −0.260041 | − | 0.0448542i | ||||
\(731\) | −20.0602 | + | 20.0602i | −0.741953 | + | 0.741953i | ||||
\(732\) | 5.52629 | − | 15.5427i | 0.204258 | − | 0.574473i | ||||
\(733\) | −34.6520 | −1.27990 | −0.639950 | − | 0.768417i | \(-0.721045\pi\) | ||||
−0.639950 | + | 0.768417i | \(0.721045\pi\) | |||||||
\(734\) | 8.30621 | − | 5.86230i | 0.306588 | − | 0.216382i | ||||
\(735\) | 22.2068 | + | 22.2068i | 0.819111 | + | 0.819111i | ||||
\(736\) | −16.6375 | − | 1.14383i | −0.613266 | − | 0.0421620i | ||||
\(737\) | −7.71877 | −0.284324 | ||||||||
\(738\) | −0.659636 | + | 3.82423i | −0.0242815 | + | 0.140772i | ||||
\(739\) | −40.2781 | −1.48165 | −0.740827 | − | 0.671696i | \(-0.765566\pi\) | ||||
−0.740827 | + | 0.671696i | \(0.765566\pi\) | |||||||
\(740\) | −34.1587 | − | 12.1454i | −1.25570 | − | 0.446472i | ||||
\(741\) | 1.96631 | + | 0.947487i | 0.0722344 | + | 0.0348068i | ||||
\(742\) | −2.17445 | − | 3.08094i | −0.0798264 | − | 0.113105i | ||||
\(743\) | 21.6457 | + | 21.6457i | 0.794102 | + | 0.794102i | 0.982158 | − | 0.188056i | \(-0.0602186\pi\) |
−0.188056 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(744\) | 19.9267 | − | 5.57872i | 0.730547 | − | 0.204526i | ||||
\(745\) | 46.5755 | 1.70639 | ||||||||
\(746\) | −7.30364 | + | 42.3427i | −0.267405 | + | 1.55028i | ||||
\(747\) | −13.5933 | −0.497354 | ||||||||
\(748\) | −11.1079 | + | 31.2408i | −0.406144 | + | 1.14228i | ||||
\(749\) | − | 65.9144i | − | 2.40846i | ||||||
\(750\) | 14.6768 | + | 2.53158i | 0.535920 | + | 0.0924402i | ||||
\(751\) | 38.5993 | 1.40851 | 0.704255 | − | 0.709947i | \(-0.251281\pi\) | ||||
0.704255 | + | 0.709947i | \(0.251281\pi\) | |||||||
\(752\) | 3.14898 | + | 30.7149i | 0.114832 | + | 1.12006i | ||||
\(753\) | 20.6659i | 0.753109i | ||||||||
\(754\) | −1.05490 | − | 6.31337i | −0.0384171 | − | 0.229919i | ||||
\(755\) | −7.95847 | − | 7.95847i | −0.289638 | − | 0.289638i | ||||
\(756\) | −8.50541 | − | 3.02415i | −0.309339 | − | 0.109987i | ||||
\(757\) | 34.6082 | + | 34.6082i | 1.25786 | + | 1.25786i | 0.952114 | + | 0.305742i | \(0.0989046\pi\) |
0.305742 | + | 0.952114i | \(0.401095\pi\) | |||||||
\(758\) | 17.5890 | + | 24.9216i | 0.638861 | + | 0.905193i | ||||
\(759\) | 10.5772 | + | 10.5772i | 0.383927 | + | 0.383927i | ||||
\(760\) | 3.87247 | − | 1.08415i | 0.140469 | − | 0.0393262i | ||||
\(761\) | 6.26732 | + | 6.26732i | 0.227190 | + | 0.227190i | 0.811518 | − | 0.584328i | \(-0.198642\pi\) |
−0.584328 | + | 0.811518i | \(0.698642\pi\) | |||||||
\(762\) | −4.94026 | + | 28.6411i | −0.178967 | + | 1.03756i | ||||
\(763\) | 32.4515 | − | 32.4515i | 1.17482 | − | 1.17482i | ||||
\(764\) | −1.12130 | − | 0.398686i | −0.0405673 | − | 0.0144239i | ||||
\(765\) | − | 7.67369i | − | 0.277443i | ||||||
\(766\) | −30.1306 | − | 5.19719i | −1.08866 | − | 0.187782i | ||||
\(767\) | −43.0614 | + | 15.0566i | −1.55486 | + | 0.543664i | ||||
\(768\) | −8.78264 | + | 13.3740i | −0.316916 | + | 0.482594i | ||||
\(769\) | 8.39417 | + | 8.39417i | 0.302702 | + | 0.302702i | 0.842070 | − | 0.539368i | \(-0.181337\pi\) |
−0.539368 | + | 0.842070i | \(0.681337\pi\) | |||||||
\(770\) | −74.9585 | − | 12.9295i | −2.70132 | − | 0.465947i | ||||
\(771\) | 9.65629 | − | 9.65629i | 0.347763 | − | 0.347763i | ||||
\(772\) | −19.5604 | − | 41.1443i | −0.703994 | − | 1.48082i | ||||
\(773\) | 3.76569i | 0.135442i | 0.997704 | + | 0.0677212i | \(0.0215728\pi\) | ||||
−0.997704 | + | 0.0677212i | \(0.978427\pi\) | |||||||
\(774\) | 12.1005 | + | 2.08720i | 0.434944 | + | 0.0750230i | ||||
\(775\) | −2.66899 | + | 2.66899i | −0.0958731 | + | 0.0958731i | ||||
\(776\) | 2.31497 | + | 1.30228i | 0.0831026 | + | 0.0467490i | ||||
\(777\) | 34.8360 | 1.24973 | ||||||||
\(778\) | −25.6267 | − | 4.42033i | −0.918763 | − | 0.158476i | ||||
\(779\) | 1.17463 | + | 1.17463i | 0.0420854 | + | 0.0420854i | ||||
\(780\) | 12.0382 | − | 11.9125i | 0.431038 | − | 0.426538i | ||||
\(781\) | −41.3740 | + | 41.3740i | −1.48048 | + | 1.48048i | ||||
\(782\) | 7.85487 | + | 11.1295i | 0.280890 | + | 0.397989i | ||||
\(783\) | 1.25532i | 0.0448614i | ||||||||
\(784\) | −33.7668 | + | 41.4815i | −1.20596 | + | 1.48148i | ||||
\(785\) | −10.2637 | − | 10.2637i | −0.366327 | − | 0.366327i | ||||
\(786\) | −13.5907 | + | 9.59195i | −0.484764 | + | 0.342134i | ||||
\(787\) | 35.0770 | 1.25036 | 0.625180 | − | 0.780480i | \(-0.285025\pi\) | ||||
0.625180 | + | 0.780480i | \(0.285025\pi\) | |||||||
\(788\) | 33.8983 | + | 12.0527i | 1.20758 | + | 0.429361i | ||||
\(789\) | 17.3129 | + | 17.3129i | 0.616354 | + | 0.616354i | ||||
\(790\) | 1.98383 | + | 2.81086i | 0.0705815 | + | 0.100006i | ||||
\(791\) | −11.4296 | + | 11.4296i | −0.406390 | + | 0.406390i | ||||
\(792\) | 13.8200 | − | 3.86908i | 0.491071 | − | 0.137482i | ||||
\(793\) | −26.7904 | − | 12.9092i | −0.951354 | − | 0.458419i | ||||
\(794\) | 21.5664 | − | 15.2210i | 0.765362 | − | 0.540172i | ||||
\(795\) | −1.38751 | −0.0492098 | ||||||||
\(796\) | 18.9775 | + | 6.74755i | 0.672638 | + | 0.239161i | ||||
\(797\) | 7.66354 | + | 7.66354i | 0.271457 | + | 0.271457i | 0.829686 | − | 0.558230i | \(-0.188519\pi\) |
−0.558230 | + | 0.829686i | \(0.688519\pi\) | |||||||
\(798\) | −3.15702 | + | 2.22814i | −0.111757 | + | 0.0788754i | ||||
\(799\) | 17.8336 | − | 17.8336i | 0.630907 | − | 0.630907i | ||||
\(800\) | 0.200175 | − | 2.91164i | 0.00707727 | − | 0.102942i | ||||
\(801\) | −0.249708 | + | 0.249708i | −0.00882300 | + | 0.00882300i | ||||
\(802\) | −24.5131 | − | 4.22823i | −0.865587 | − | 0.149304i | ||||
\(803\) | −7.70155 | + | 7.70155i | −0.271782 | + | 0.271782i | ||||
\(804\) | 1.30632 | + | 2.74778i | 0.0460704 | + | 0.0969068i | ||||
\(805\) | −22.0977 | + | 22.0977i | −0.778841 | + | 0.778841i | ||||
\(806\) | −6.14796 | − | 36.7945i | −0.216553 | − | 1.29603i | ||||
\(807\) | −28.0407 | −0.987080 | ||||||||
\(808\) | 4.83929 | − | 8.60248i | 0.170246 | − | 0.302634i | ||||
\(809\) | 22.5956i | 0.794420i | 0.917728 | + | 0.397210i | \(0.130022\pi\) | ||||
−0.917728 | + | 0.397210i | \(0.869978\pi\) | |||||||
\(810\) | −2.71364 | + | 1.91521i | −0.0953474 | + | 0.0672937i | ||||
\(811\) | 35.4063 | 1.24328 | 0.621642 | − | 0.783302i | \(-0.286466\pi\) | ||||
0.621642 | + | 0.783302i | \(0.286466\pi\) | |||||||
\(812\) | 10.6770 | + | 3.79627i | 0.374689 | + | 0.133223i | ||||
\(813\) | − | 26.1058i | − | 0.915569i | ||||||
\(814\) | −45.2484 | + | 31.9351i | −1.58595 | + | 1.11932i | ||||
\(815\) | − | 50.8268i | − | 1.78039i | ||||||
\(816\) | 13.0012 | − | 1.33293i | 0.455134 | − | 0.0466617i | ||||
\(817\) | 3.71672 | − | 3.71672i | 0.130032 | − | 0.130032i | ||||
\(818\) | 35.9939 | + | 6.20854i | 1.25850 | + | 0.217076i | ||||
\(819\) | −7.06430 | + | 14.6605i | −0.246847 | + | 0.512279i | ||||
\(820\) | 11.6409 | − | 5.53419i | 0.406518 | − | 0.193262i | ||||
\(821\) | − | 17.6202i | − | 0.614950i | −0.951556 | − | 0.307475i | \(-0.900516\pi\) | ||
0.951556 | − | 0.307475i | \(-0.0994840\pi\) | |||||||
\(822\) | −7.23658 | + | 5.10738i | −0.252405 | + | 0.178141i | ||||
\(823\) | 49.1646i | 1.71377i | 0.515508 | + | 0.856885i | \(0.327603\pi\) | ||||
−0.515508 | + | 0.856885i | \(0.672397\pi\) | |||||||
\(824\) | −11.3544 | − | 40.5569i | −0.395550 | − | 1.41287i | ||||
\(825\) | −1.85106 | + | 1.85106i | −0.0644456 | + | 0.0644456i | ||||
\(826\) | 13.7274 | − | 79.5842i | 0.477637 | − | 2.76909i | ||||
\(827\) | 7.99820i | 0.278125i | 0.990284 | + | 0.139062i | \(0.0444088\pi\) | ||||
−0.990284 | + | 0.139062i | \(0.955591\pi\) | |||||||
\(828\) | 1.97526 | − | 5.55542i | 0.0686451 | − | 0.193064i | ||||
\(829\) | −4.58085 | − | 4.58085i | −0.159100 | − | 0.159100i | 0.623068 | − | 0.782168i | \(-0.285886\pi\) |
−0.782168 | + | 0.623068i | \(0.785886\pi\) | |||||||
\(830\) | 26.0341 | + | 36.8874i | 0.903657 | + | 1.28038i | ||||
\(831\) | −17.4023 | −0.603679 | ||||||||
\(832\) | 22.2740 | + | 18.3267i | 0.772213 | + | 0.635364i | ||||
\(833\) | 43.6905 | 1.51379 | ||||||||
\(834\) | 7.69302 | + | 10.9001i | 0.266388 | + | 0.377441i | ||||
\(835\) | 28.7220 | + | 28.7220i | 0.993966 | + | 0.993966i | ||||
\(836\) | 2.05805 | − | 5.78825i | 0.0711791 | − | 0.200191i | ||||
\(837\) | 7.31603i | 0.252879i | ||||||||
\(838\) | −3.72635 | + | 21.6034i | −0.128725 | + | 0.746279i | ||||
\(839\) | −13.0875 | + | 13.0875i | −0.451830 | + | 0.451830i | −0.895962 | − | 0.444131i | \(-0.853512\pi\) |
0.444131 | + | 0.895962i | \(0.353512\pi\) | |||||||
\(840\) | 8.08322 | + | 28.8725i | 0.278897 | + | 0.996195i | ||||
\(841\) | 27.4242i | 0.945661i | ||||||||
\(842\) | 24.4497 | − | 17.2559i | 0.842591 | − | 0.594678i | ||||
\(843\) | − | 12.4901i | − | 0.430182i | ||||||
\(844\) | 47.0561 | − | 22.3709i | 1.61974 | − | 0.770038i | ||||
\(845\) | −19.0252 | − | 23.8795i | −0.654488 | − | 0.821481i | ||||
\(846\) | −10.7574 | − | 1.85553i | −0.369847 | − | 0.0637945i | ||||
\(847\) | −47.0598 | + | 47.0598i | −1.61699 | + | 1.61699i | ||||
\(848\) | −0.241011 | − | 2.35080i | −0.00827634 | − | 0.0807267i | ||||
\(849\) | 14.5179i | 0.498253i | ||||||||
\(850\) | −1.94771 | + | 1.37464i | −0.0668059 | + | 0.0471498i | ||||
\(851\) | 22.7536i | 0.779983i | ||||||||
\(852\) | 21.7307 | + | 7.72650i | 0.744483 | + | 0.264706i | ||||
\(853\) | −44.9975 | −1.54069 | −0.770343 | − | 0.637630i | \(-0.779915\pi\) | ||||
−0.770343 | + | 0.637630i | \(0.779915\pi\) | |||||||
\(854\) | 43.0134 | − | 30.3577i | 1.47189 | − | 1.03882i | ||||
\(855\) | 1.42177i | 0.0486235i | ||||||||
\(856\) | 20.2518 | − | 36.0003i | 0.692193 | − | 1.23047i | ||||
\(857\) | −11.7268 | −0.400581 | −0.200291 | − | 0.979737i | \(-0.564189\pi\) | ||||
−0.200291 | + | 0.979737i | \(0.564189\pi\) | |||||||
\(858\) | −4.26387 | − | 25.5185i | −0.145566 | − | 0.871187i | ||||
\(859\) | −25.5881 | + | 25.5881i | −0.873055 | + | 0.873055i | −0.992804 | − | 0.119750i | \(-0.961791\pi\) |
0.119750 | + | 0.992804i | \(0.461791\pi\) | |||||||
\(860\) | −17.5111 | − | 36.8338i | −0.597125 | − | 1.25602i | ||||
\(861\) | −8.75781 | + | 8.75781i | −0.298465 | + | 0.298465i | ||||
\(862\) | 47.7338 | + | 8.23355i | 1.62582 | + | 0.280436i | ||||
\(863\) | 24.6589 | − | 24.6589i | 0.839400 | − | 0.839400i | −0.149380 | − | 0.988780i | \(-0.547728\pi\) |
0.988780 | + | 0.149380i | \(0.0477279\pi\) | |||||||
\(864\) | −3.71623 | − | 4.26493i | −0.126429 | − | 0.145096i | ||||
\(865\) | 25.0140 | − | 25.0140i | 0.850501 | − | 0.850501i | ||||
\(866\) | −12.9589 | + | 9.14602i | −0.440360 | + | 0.310794i | ||||
\(867\) | 4.47207 | + | 4.47207i | 0.151880 | + | 0.151880i | ||||
\(868\) | 62.2258 | + | 22.1248i | 2.11208 | + | 0.750964i | ||||
\(869\) | 5.25576 | 0.178290 | ||||||||
\(870\) | 3.40648 | − | 2.40420i | 0.115490 | − | 0.0815101i | ||||
\(871\) | 5.17756 | − | 1.81036i | 0.175435 | − | 0.0613418i | ||||
\(872\) | 27.6945 | − | 7.75343i | 0.937855 | − | 0.262564i | ||||
\(873\) | −0.664032 | + | 0.664032i | −0.0224741 | + | 0.0224741i | ||||
\(874\) | −1.45534 | − | 2.06205i | −0.0492276 | − | 0.0697499i | ||||
\(875\) | 33.6111 | + | 33.6111i | 1.13626 | + | 1.13626i | ||||
\(876\) | 4.04506 | + | 1.43825i | 0.136670 | + | 0.0485939i | ||||
\(877\) | −23.4692 | −0.792497 | −0.396248 | − | 0.918143i | \(-0.629688\pi\) | ||||
−0.396248 | + | 0.918143i | \(0.629688\pi\) | |||||||
\(878\) | 30.2616 | − | 21.3579i | 1.02128 | − | 0.720793i | ||||
\(879\) | 10.8625 | + | 10.8625i | 0.366383 | + | 0.366383i | ||||
\(880\) | −36.9674 | − | 30.0923i | −1.24617 | − | 1.01441i | ||||
\(881\) | 9.71971i | 0.327465i | 0.986505 | + | 0.163733i | \(0.0523535\pi\) | ||||
−0.986505 | + | 0.163733i | \(0.947647\pi\) | |||||||
\(882\) | −10.9044 | − | 15.4502i | −0.367169 | − | 0.520236i | ||||
\(883\) | 29.1466 | − | 29.1466i | 0.980862 | − | 0.980862i | −0.0189579 | − | 0.999820i | \(-0.506035\pi\) |
0.999820 | + | 0.0189579i | \(0.00603486\pi\) | |||||||
\(884\) | 0.123652 | − | 23.5608i | 0.00415886 | − | 0.792436i | ||||
\(885\) | −21.0115 | − | 21.0115i | −0.706293 | − | 0.706293i | ||||
\(886\) | 8.55703 | + | 1.47599i | 0.287479 | + | 0.0495869i | ||||
\(887\) | −46.5887 | −1.56430 | −0.782148 | − | 0.623093i | \(-0.785876\pi\) | ||||
−0.782148 | + | 0.623093i | \(0.785876\pi\) | |||||||
\(888\) | 19.0263 | + | 10.7032i | 0.638481 | + | 0.359175i | ||||
\(889\) | −65.5905 | + | 65.5905i | −2.19983 | + | 2.19983i | ||||
\(890\) | 1.15586 | + | 0.199373i | 0.0387445 | + | 0.00668300i | ||||
\(891\) | 5.07397i | 0.169984i | ||||||||
\(892\) | 1.66497 | + | 3.50218i | 0.0557473 | + | 0.117262i | ||||
\(893\) | −3.30418 | + | 3.30418i | −0.110570 | + | 0.110570i | ||||
\(894\) | −27.6374 | − | 4.76714i | −0.924332 | − | 0.159437i | ||||
\(895\) | −26.3395 | − | 26.3395i | −0.880433 | − | 0.880433i | ||||
\(896\) | −47.5134 | + | 18.7102i | −1.58731 | + | 0.625065i | ||||
\(897\) | −9.57569 | − | 4.61414i | −0.319723 | − | 0.154062i | ||||
\(898\) | 10.8756 | + | 1.87591i | 0.362922 | + | 0.0626000i | ||||
\(899\) | − | 9.18395i | − | 0.306302i | ||||||
\(900\) | 0.972226 | + | 0.345681i | 0.0324075 | + | 0.0115227i | ||||
\(901\) | −1.36491 | + | 1.36491i | −0.0454719 | + | 0.0454719i | ||||
\(902\) | 3.34697 | − | 19.4040i | 0.111442 | − | 0.646083i | ||||
\(903\) | 27.7112 | + | 27.7112i | 0.922172 | + | 0.922172i | ||||
\(904\) | −9.75415 | + | 2.73080i | −0.324418 | + | 0.0908250i | ||||
\(905\) | 8.90072 | + | 8.90072i | 0.295870 | + | 0.295870i | ||||
\(906\) | 3.90789 | + | 5.53704i | 0.129831 | + | 0.183956i | ||||
\(907\) | 3.88182 | + | 3.88182i | 0.128894 | + | 0.128894i | 0.768611 | − | 0.639717i | \(-0.220948\pi\) |
−0.639717 | + | 0.768611i | \(0.720948\pi\) | |||||||
\(908\) | −23.7171 | − | 8.43275i | −0.787078 | − | 0.279851i | ||||
\(909\) | 2.46756 | + | 2.46756i | 0.0818437 | + | 0.0818437i | ||||
\(910\) | 53.3129 | − | 8.90801i | 1.76730 | − | 0.295298i | ||||
\(911\) | 29.5097i | 0.977702i | 0.872367 | + | 0.488851i | \(0.162584\pi\) | ||||
−0.872367 | + | 0.488851i | \(0.837416\pi\) | |||||||
\(912\) | −2.40885 | + | 0.246962i | −0.0797649 | + | 0.00817774i | ||||
\(913\) | 68.9722 | 2.28265 | ||||||||
\(914\) | −30.4234 | − | 5.24770i | −1.00632 | − | 0.173578i | ||||
\(915\) | − | 19.3711i | − | 0.640390i | ||||||
\(916\) | −7.51034 | + | 21.1228i | −0.248149 | + | 0.697917i | ||||
\(917\) | −53.0903 | −1.75320 | ||||||||
\(918\) | −0.785424 | + | 4.55348i | −0.0259229 | + | 0.150287i | ||||
\(919\) | 12.2113 | 0.402813 | 0.201407 | − | 0.979508i | \(-0.435449\pi\) | ||||
0.201407 | + | 0.979508i | \(0.435449\pi\) | |||||||
\(920\) | −18.8584 | + | 5.27966i | −0.621744 | + | 0.174065i | ||||
\(921\) | 20.0691 | + | 20.0691i | 0.661300 | + | 0.661300i | ||||
\(922\) | −12.5158 | − | 17.7335i | −0.412187 | − | 0.584022i | ||||
\(923\) | 18.0488 | − | 37.4566i | 0.594084 | − | 1.23290i | ||||
\(924\) | 43.1562 | + | 15.3444i | 1.41973 | + | 0.504795i | ||||
\(925\) | −3.98199 | −0.130927 | ||||||||
\(926\) | −4.03033 | + | 23.3657i | −0.132445 | + | 0.767846i | ||||
\(927\) | 14.8904 | 0.489064 | ||||||||
\(928\) | 4.66505 | + | 5.35385i | 0.153138 | + | 0.175749i | ||||
\(929\) | −22.7859 | − | 22.7859i | −0.747580 | − | 0.747580i | 0.226444 | − | 0.974024i | \(-0.427290\pi\) |
−0.974024 | + | 0.226444i | \(0.927290\pi\) | |||||||
\(930\) | 19.8530 | − | 14.0117i | 0.651007 | − | 0.459463i | ||||
\(931\) | −8.09491 | −0.265300 | ||||||||
\(932\) | 0.327865 | − | 0.922119i | 0.0107396 | − | 0.0302050i | ||||
\(933\) | −4.76360 | + | 4.76360i | −0.155953 | + | 0.155953i | ||||
\(934\) | 41.2567 | + | 7.11632i | 1.34996 | + | 0.232853i | ||||
\(935\) | 38.9360i | 1.27334i | ||||||||
\(936\) | −8.36264 | + | 5.83662i | −0.273342 | + | 0.190776i | ||||
\(937\) | − | 37.4559i | − | 1.22363i | −0.791001 | − | 0.611815i | \(-0.790440\pi\) | ||
0.791001 | − | 0.611815i | \(-0.209560\pi\) | |||||||
\(938\) | −1.65054 | + | 9.56895i | −0.0538919 | + | 0.312437i | ||||
\(939\) | 1.70598 | − | 1.70598i | 0.0556727 | − | 0.0556727i | ||||
\(940\) | 15.5675 | + | 32.7454i | 0.507755 | + | 1.06804i | ||||
\(941\) | 26.5950 | 0.866971 | 0.433485 | − | 0.901161i | \(-0.357284\pi\) | ||||
0.433485 | + | 0.901161i | \(0.357284\pi\) | |||||||
\(942\) | 5.03984 | + | 7.14087i | 0.164207 | + | 0.232662i | ||||
\(943\) | −5.72028 | − | 5.72028i | −0.186278 | − | 0.186278i | ||||
\(944\) | 31.9492 | − | 39.2487i | 1.03986 | − | 1.27743i | ||||
\(945\) | −10.6005 | −0.344833 | ||||||||
\(946\) | −61.3977 | − | 10.5904i | −1.99621 | − | 0.344324i | ||||
\(947\) | 54.6006 | 1.77428 | 0.887141 | − | 0.461499i | \(-0.152688\pi\) | ||||
0.887141 | + | 0.461499i | \(0.152688\pi\) | |||||||
\(948\) | −0.889483 | − | 1.87098i | −0.0288891 | − | 0.0607668i | ||||
\(949\) | 3.35969 | − | 6.97234i | 0.109060 | − | 0.226332i | ||||
\(950\) | 0.360869 | − | 0.254692i | 0.0117081 | − | 0.00826329i | ||||
\(951\) | −11.4007 | − | 11.4007i | −0.369692 | − | 0.369692i | ||||
\(952\) | 36.3540 | + | 20.4508i | 1.17824 | + | 0.662813i | ||||
\(953\) | 3.58901 | 0.116259 | 0.0581297 | − | 0.998309i | \(-0.481486\pi\) | ||||
0.0581297 | + | 0.998309i | \(0.481486\pi\) | |||||||
\(954\) | 0.823330 | + | 0.142015i | 0.0266563 | + | 0.00459791i | ||||
\(955\) | −1.39750 | −0.0452220 | ||||||||
\(956\) | −8.56797 | − | 18.0223i | −0.277108 | − | 0.582883i | ||||
\(957\) | − | 6.36945i | − | 0.205895i | ||||||
\(958\) | −3.87343 | + | 22.4561i | −0.125145 | + | 0.725525i | ||||
\(959\) | −28.2688 | −0.912846 | ||||||||
\(960\) | −4.45611 | + | 18.2527i | −0.143820 | + | 0.589104i | ||||
\(961\) | − | 22.5243i | − | 0.726590i | ||||||
\(962\) | 22.8614 | − | 32.0339i | 0.737082 | − | 1.03281i | ||||
\(963\) | 10.3264 | + | 10.3264i | 0.332764 | + | 0.332764i | ||||
\(964\) | −9.96672 | − | 20.9645i | −0.321006 | − | 0.675221i | ||||
\(965\) | −37.8287 | − | 37.8287i | −1.21775 | − | 1.21775i | ||||
\(966\) | 15.3743 | − | 10.8508i | 0.494659 | − | 0.349117i | ||||
\(967\) | 7.15030 | + | 7.15030i | 0.229938 | + | 0.229938i | 0.812667 | − | 0.582729i | \(-0.198015\pi\) |
−0.582729 | + | 0.812667i | \(0.698015\pi\) | |||||||
\(968\) | −40.1614 | + | 11.2437i | −1.29084 | + | 0.361386i | ||||
\(969\) | 1.39862 | + | 1.39862i | 0.0449301 | + | 0.0449301i | ||||
\(970\) | 3.07370 | + | 0.530179i | 0.0986907 | + | 0.0170230i | ||||
\(971\) | 9.57899 | − | 9.57899i | 0.307404 | − | 0.307404i | −0.536498 | − | 0.843902i | \(-0.680253\pi\) |
0.843902 | + | 0.536498i | \(0.180253\pi\) | |||||||
\(972\) | 1.80627 | − | 0.858717i | 0.0579361 | − | 0.0275433i | ||||
\(973\) | 42.5800i | 1.36505i | ||||||||
\(974\) | −6.68088 | + | 38.7323i | −0.214069 | + | 1.24106i | ||||
\(975\) | 0.807497 | − | 1.67579i | 0.0258606 | − | 0.0536683i | ||||
\(976\) | 32.8197 | − | 3.36478i | 1.05053 | − | 0.107704i | ||||
\(977\) | 8.41417 | + | 8.41417i | 0.269193 | + | 0.269193i | 0.828775 | − | 0.559582i | \(-0.189038\pi\) |
−0.559582 | + | 0.828775i | \(0.689038\pi\) | |||||||
\(978\) | −5.20228 | + | 30.1601i | −0.166350 | + | 0.964413i | ||||
\(979\) | 1.26701 | − | 1.26701i | 0.0404938 | − | 0.0404938i | ||||
\(980\) | −21.0421 | + | 59.1809i | −0.672166 | + | 1.89046i | ||||
\(981\) | 10.1680i | 0.324639i | ||||||||
\(982\) | 2.31263 | − | 13.4074i | 0.0737990 | − | 0.427848i | ||||
\(983\) | 16.4160 | − | 16.4160i | 0.523589 | − | 0.523589i | −0.395064 | − | 0.918653i | \(-0.629278\pi\) |
0.918653 | + | 0.395064i | \(0.129278\pi\) | |||||||
\(984\) | −7.47402 | + | 2.09245i | −0.238263 | + | 0.0667048i | ||||
\(985\) | 42.2481 | 1.34614 | ||||||||
\(986\) | 0.985958 | − | 5.71607i | 0.0313993 | − | 0.182037i | ||||
\(987\) | −24.6354 | − | 24.6354i | −0.784154 | − | 0.784154i | ||||
\(988\) | −0.0229100 | + | 4.36531i | −0.000728865 | + | 0.138879i | ||||
\(989\) | −18.1000 | + | 18.1000i | −0.575545 | + | 0.575545i | ||||
\(990\) | 13.7689 | − | 9.71772i | 0.437604 | − | 0.308849i | ||||
\(991\) | 13.1248i | 0.416923i | 0.978031 | + | 0.208462i | \(0.0668456\pi\) | ||||
−0.978031 | + | 0.208462i | \(0.933154\pi\) | |||||||
\(992\) | 27.1880 | + | 31.2024i | 0.863221 | + | 0.990676i | ||||
\(993\) | −7.12869 | − | 7.12869i | −0.226222 | − | 0.226222i | ||||
\(994\) | 42.4441 | + | 60.1385i | 1.34625 | + | 1.90748i | ||||
\(995\) | 23.6520 | 0.749818 | ||||||||
\(996\) | −11.6728 | − | 24.5532i | −0.369868 | − | 0.777998i | ||||
\(997\) | 20.4149 | + | 20.4149i | 0.646546 | + | 0.646546i | 0.952157 | − | 0.305611i | \(-0.0988606\pi\) |
−0.305611 | + | 0.952157i | \(0.598861\pi\) | |||||||
\(998\) | 29.9419 | − | 21.1322i | 0.947793 | − | 0.668927i | ||||
\(999\) | −5.45755 | + | 5.45755i | −0.172669 | + | 0.172669i |
(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 | 624.2.r.a.619.17 | yes | 112 | |
13.5 | odd | 4 | 624.2.bn.a.187.12 | yes | 112 | ||
16.3 | odd | 4 | 624.2.bn.a.307.12 | yes | 112 | ||
208.83 | even | 4 | inner | 624.2.r.a.499.17 | ✓ | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.r.a.499.17 | ✓ | 112 | 208.83 | even | 4 | inner | |
624.2.r.a.619.17 | yes | 112 | 1.1 | even | 1 | trivial | |
624.2.bn.a.187.12 | yes | 112 | 13.5 | odd | 4 | ||
624.2.bn.a.307.12 | yes | 112 | 16.3 | odd | 4 |