Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(143,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([27, 34]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.bb (of order \(36\), degree \(12\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{36})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 243.4 | ||
Character | \(\chi\) | \(=\) | 950.243 |
Dual form | 950.2.bb.c.907.4 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{11}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.422618 | + | 0.906308i | 0.298836 | + | 0.640856i | ||||
\(3\) | −1.84087 | − | 1.28899i | −1.06283 | − | 0.744200i | −0.0949146 | − | 0.995485i | \(-0.530258\pi\) |
−0.967913 | + | 0.251285i | \(0.919147\pi\) | |||||||
\(4\) | −0.642788 | + | 0.766044i | −0.321394 | + | 0.383022i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.390238 | − | 2.21315i | 0.159314 | − | 0.903514i | ||||
\(7\) | 0.947246 | + | 3.53517i | 0.358026 | + | 1.33617i | 0.876634 | + | 0.481158i | \(0.159784\pi\) |
−0.518609 | + | 0.855012i | \(0.673550\pi\) | |||||||
\(8\) | −0.965926 | − | 0.258819i | −0.341506 | − | 0.0915064i | ||||
\(9\) | 0.701247 | + | 1.92666i | 0.233749 | + | 0.642220i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.01780 | − | 1.76288i | −0.306877 | − | 0.531527i | 0.670800 | − | 0.741638i | \(-0.265951\pi\) |
−0.977678 | + | 0.210111i | \(0.932617\pi\) | |||||||
\(12\) | 2.17071 | − | 0.581641i | 0.626631 | − | 0.167905i | ||||
\(13\) | −0.228201 | − | 0.325905i | −0.0632917 | − | 0.0903899i | 0.786258 | − | 0.617898i | \(-0.212015\pi\) |
−0.849550 | + | 0.527508i | \(0.823127\pi\) | |||||||
\(14\) | −2.80363 | + | 2.35253i | −0.749302 | + | 0.628739i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.173648 | − | 0.984808i | −0.0434120 | − | 0.246202i | ||||
\(17\) | −3.29740 | + | 1.53760i | −0.799738 | + | 0.372924i | −0.779129 | − | 0.626864i | \(-0.784338\pi\) |
−0.0206090 | + | 0.999788i | \(0.506560\pi\) | |||||||
\(18\) | −1.44979 | + | 1.44979i | −0.341718 | + | 0.341718i | ||||
\(19\) | 2.20191 | − | 3.76186i | 0.505152 | − | 0.863030i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.81305 | − | 7.72879i | 0.613858 | − | 1.68656i | ||||
\(22\) | 1.16757 | − | 1.66746i | 0.248926 | − | 0.355504i | ||||
\(23\) | 0.331390 | + | 3.78781i | 0.0690997 | + | 0.789813i | 0.949128 | + | 0.314891i | \(0.101968\pi\) |
−0.880028 | + | 0.474922i | \(0.842476\pi\) | |||||||
\(24\) | 1.44453 | + | 1.72152i | 0.294863 | + | 0.351404i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.198929 | − | 0.344554i | 0.0390131 | − | 0.0675727i | ||||
\(27\) | −0.552380 | + | 2.06151i | −0.106306 | + | 0.396738i | ||||
\(28\) | −3.31698 | − | 1.54673i | −0.626850 | − | 0.292305i | ||||
\(29\) | −4.56508 | + | 1.66155i | −0.847714 | + | 0.308542i | −0.729108 | − | 0.684399i | \(-0.760065\pi\) |
−0.118606 | + | 0.992941i | \(0.537842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28120 | − | 1.89440i | −0.589321 | − | 0.340245i | 0.175508 | − | 0.984478i | \(-0.443843\pi\) |
−0.764829 | + | 0.644233i | \(0.777177\pi\) | |||||||
\(32\) | 0.819152 | − | 0.573576i | 0.144807 | − | 0.101395i | ||||
\(33\) | −0.398700 | + | 4.55716i | −0.0694047 | + | 0.793300i | ||||
\(34\) | −2.78709 | − | 2.33864i | −0.477981 | − | 0.401074i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.92666 | − | 0.701247i | −0.321110 | − | 0.116874i | ||||
\(37\) | −7.90769 | − | 7.90769i | −1.30002 | − | 1.30002i | −0.928378 | − | 0.371638i | \(-0.878796\pi\) |
−0.371638 | − | 0.928378i | \(-0.621204\pi\) | |||||||
\(38\) | 4.33997 | + | 0.405773i | 0.704036 | + | 0.0658251i | ||||
\(39\) | 0.894100i | 0.143171i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.75160 | + | 0.308853i | −0.273553 | + | 0.0482348i | −0.308742 | − | 0.951146i | \(-0.599908\pi\) |
0.0351886 | + | 0.999381i | \(0.488797\pi\) | |||||||
\(42\) | 8.19351 | − | 0.716839i | 1.26429 | − | 0.110611i | ||||
\(43\) | 0.840994 | + | 0.0735774i | 0.128250 | + | 0.0112205i | 0.151100 | − | 0.988518i | \(-0.451718\pi\) |
−0.0228498 | + | 0.999739i | \(0.507274\pi\) | |||||||
\(44\) | 2.00467 | + | 0.353477i | 0.302215 | + | 0.0532887i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.29287 | + | 1.90114i | −0.485507 | + | 0.280308i | ||||
\(47\) | −1.80812 | + | 3.87752i | −0.263741 | + | 0.565595i | −0.992928 | − | 0.118720i | \(-0.962121\pi\) |
0.729186 | + | 0.684315i | \(0.239899\pi\) | |||||||
\(48\) | −0.949745 | + | 2.03674i | −0.137084 | + | 0.293977i | ||||
\(49\) | −5.53799 | + | 3.19736i | −0.791141 | + | 0.456765i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.05206 | + | 1.41979i | 1.12751 | + | 0.198811i | ||||
\(52\) | 0.396343 | + | 0.0346755i | 0.0549629 | + | 0.00480863i | ||||
\(53\) | −11.2417 | + | 0.983524i | −1.54417 | + | 0.135097i | −0.827160 | − | 0.561966i | \(-0.810045\pi\) |
−0.717010 | + | 0.697063i | \(0.754490\pi\) | |||||||
\(54\) | −2.10181 | + | 0.370605i | −0.286020 | + | 0.0504330i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.65988i | − | 0.489072i | ||||||
\(57\) | −8.90244 | + | 4.08686i | −1.17916 | + | 0.541318i | ||||
\(58\) | −3.43516 | − | 3.43516i | −0.451059 | − | 0.451059i | ||||
\(59\) | −5.19883 | − | 1.89222i | −0.676830 | − | 0.246346i | −0.0193440 | − | 0.999813i | \(-0.506158\pi\) |
−0.657486 | + | 0.753467i | \(0.728380\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.06628 | − | 5.92932i | −0.904745 | − | 0.759171i | 0.0663671 | − | 0.997795i | \(-0.478859\pi\) |
−0.971112 | + | 0.238624i | \(0.923304\pi\) | |||||||
\(62\) | 0.330216 | − | 3.77439i | 0.0419375 | − | 0.479347i | ||||
\(63\) | −6.14682 | + | 4.30405i | −0.774426 | + | 0.542259i | ||||
\(64\) | 0.866025 | + | 0.500000i | 0.108253 | + | 0.0625000i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.29869 | + | 1.56459i | −0.529132 | + | 0.192588i | ||||
\(67\) | −13.1012 | − | 6.10920i | −1.60057 | − | 0.746358i | −0.601933 | − | 0.798547i | \(-0.705603\pi\) |
−0.998637 | + | 0.0521887i | \(0.983380\pi\) | |||||||
\(68\) | 0.941657 | − | 3.51431i | 0.114193 | − | 0.426173i | ||||
\(69\) | 4.27241 | − | 7.40003i | 0.514338 | − | 0.890859i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65737 | + | 6.74219i | 0.671406 | + | 0.800150i | 0.988975 | − | 0.148085i | \(-0.0473109\pi\) |
−0.317569 | + | 0.948235i | \(0.602866\pi\) | |||||||
\(72\) | −0.178696 | − | 2.04251i | −0.0210595 | − | 0.240712i | ||||
\(73\) | −6.07023 | + | 8.66918i | −0.710466 | + | 1.01465i | 0.287908 | + | 0.957658i | \(0.407040\pi\) |
−0.998375 | + | 0.0569931i | \(0.981849\pi\) | |||||||
\(74\) | 3.82487 | − | 10.5087i | 0.444632 | − | 1.22162i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.46640 | + | 4.10484i | 0.168207 | + | 0.470857i | ||||
\(77\) | 5.26797 | − | 5.26797i | 0.600340 | − | 0.600340i | ||||
\(78\) | −0.810330 | + | 0.377863i | −0.0917518 | + | 0.0427845i | ||||
\(79\) | −0.813612 | − | 4.61423i | −0.0915386 | − | 0.519141i | −0.995753 | − | 0.0920627i | \(-0.970654\pi\) |
0.904215 | − | 0.427078i | \(-0.140457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.38601 | − | 7.03670i | 0.931779 | − | 0.781855i | ||||
\(82\) | −1.02017 | − | 1.45696i | −0.112659 | − | 0.160894i | ||||
\(83\) | −1.85941 | + | 0.498229i | −0.204097 | + | 0.0546877i | −0.359419 | − | 0.933176i | \(-0.617025\pi\) |
0.155322 | + | 0.987864i | \(0.450359\pi\) | |||||||
\(84\) | 4.11240 | + | 7.12289i | 0.448700 | + | 0.777171i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.288736 | + | 0.793294i | 0.0311352 | + | 0.0855431i | ||||
\(87\) | 10.5454 | + | 2.82564i | 1.13059 | + | 0.302941i | ||||
\(88\) | 0.526850 | + | 1.96623i | 0.0561624 | + | 0.209601i | ||||
\(89\) | −1.99769 | + | 11.3295i | −0.211755 | + | 1.20092i | 0.674694 | + | 0.738097i | \(0.264275\pi\) |
−0.886450 | + | 0.462825i | \(0.846836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.935969 | − | 1.11544i | 0.0981162 | − | 0.116930i | ||||
\(92\) | −3.11464 | − | 2.18090i | −0.324724 | − | 0.227374i | ||||
\(93\) | 3.59840 | + | 7.71679i | 0.373136 | + | 0.800194i | ||||
\(94\) | −4.27837 | −0.441281 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.24729 | −0.229363 | ||||||||
\(97\) | −3.74799 | − | 8.03759i | −0.380551 | − | 0.816094i | −0.999529 | − | 0.0306856i | \(-0.990231\pi\) |
0.618978 | − | 0.785408i | \(-0.287547\pi\) | |||||||
\(98\) | −5.23825 | − | 3.66786i | −0.529143 | − | 0.370510i | ||||
\(99\) | 2.68274 | − | 3.19716i | 0.269625 | − | 0.321327i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.12745 | + | 6.39408i | −0.112185 | + | 0.636235i | 0.875920 | + | 0.482456i | \(0.160255\pi\) |
−0.988105 | + | 0.153778i | \(0.950856\pi\) | |||||||
\(102\) | 2.11618 | + | 7.89767i | 0.209533 | + | 0.781986i | ||||
\(103\) | 15.6168 | + | 4.18451i | 1.53877 | + | 0.412312i | 0.925868 | − | 0.377847i | \(-0.123335\pi\) |
0.612902 | + | 0.790159i | \(0.290002\pi\) | |||||||
\(104\) | 0.136075 | + | 0.373863i | 0.0133433 | + | 0.0366603i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.64233 | − | 9.77281i | −0.548032 | − | 0.949219i | ||||
\(107\) | 12.3055 | − | 3.29724i | 1.18961 | − | 0.318756i | 0.390881 | − | 0.920441i | \(-0.372170\pi\) |
0.798733 | + | 0.601685i | \(0.205504\pi\) | |||||||
\(108\) | −1.22415 | − | 1.74826i | −0.117793 | − | 0.168226i | ||||
\(109\) | −7.69581 | + | 6.45755i | −0.737124 | + | 0.618521i | −0.932064 | − | 0.362294i | \(-0.881993\pi\) |
0.194939 | + | 0.980815i | \(0.437549\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.36409 | + | 24.7500i | 0.414221 | + | 2.34916i | ||||
\(112\) | 3.31698 | − | 1.54673i | 0.313425 | − | 0.146152i | ||||
\(113\) | 11.5628 | − | 11.5628i | 1.08774 | − | 1.08774i | 0.0919767 | − | 0.995761i | \(-0.470681\pi\) |
0.995761 | − | 0.0919767i | \(-0.0293185\pi\) | |||||||
\(114\) | −7.46629 | − | 6.34116i | −0.699282 | − | 0.593904i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.66155 | − | 4.56508i | 0.154271 | − | 0.423857i | ||||
\(117\) | 0.467883 | − | 0.668206i | 0.0432558 | − | 0.0617757i | ||||
\(118\) | −0.482187 | − | 5.51142i | −0.0443889 | − | 0.507368i | ||||
\(119\) | −8.55915 | − | 10.2004i | −0.784616 | − | 0.935069i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.42818 | − | 5.93778i | 0.311653 | − | 0.539798i | ||||
\(122\) | 2.38744 | − | 8.91006i | 0.216149 | − | 0.806679i | ||||
\(123\) | 3.62257 | + | 1.68923i | 0.326636 | + | 0.152313i | ||||
\(124\) | 3.56031 | − | 1.29585i | 0.319725 | − | 0.116370i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.49855 | − | 3.75194i | −0.578937 | − | 0.334249i | ||||
\(127\) | −4.21307 | + | 2.95002i | −0.373849 | + | 0.261772i | −0.745368 | − | 0.666653i | \(-0.767726\pi\) |
0.371518 | + | 0.928426i | \(0.378837\pi\) | |||||||
\(128\) | −0.0871557 | + | 0.996195i | −0.00770355 | + | 0.0880520i | ||||
\(129\) | −1.45332 | − | 1.21948i | −0.127958 | − | 0.107369i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.43460 | + | 2.70597i | 0.649564 | + | 0.236422i | 0.645724 | − | 0.763571i | \(-0.276556\pi\) |
0.00383987 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(132\) | −3.23471 | − | 3.23471i | −0.281545 | − | 0.281545i | ||||
\(133\) | 15.3846 | + | 4.22071i | 1.33401 | + | 0.365982i | ||||
\(134\) | − | 14.4556i | − | 1.24877i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.58301 | − | 0.631781i | 0.307240 | − | 0.0541748i | ||||
\(137\) | 0.0646282 | − | 0.00565423i | 0.00552156 | − | 0.000483074i | −0.0843946 | − | 0.996432i | \(-0.526896\pi\) |
0.0899162 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(138\) | 8.51230 | + | 0.744730i | 0.724615 | + | 0.0633956i | ||||
\(139\) | 17.1262 | + | 3.01982i | 1.45263 | + | 0.256137i | 0.843583 | − | 0.536998i | \(-0.180442\pi\) |
0.609045 | + | 0.793136i | \(0.291553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.32661 | − | 4.80737i | 0.701227 | − | 0.404854i | ||||
\(142\) | −3.71959 | + | 7.97669i | −0.312141 | + | 0.669389i | ||||
\(143\) | −0.342268 | + | 0.733996i | −0.0286219 | + | 0.0613798i | ||||
\(144\) | 1.77562 | − | 1.02515i | 0.147968 | − | 0.0854295i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.4223 | − | 1.83774i | −0.862559 | − | 0.152092i | ||||
\(147\) | 14.3161 | + | 1.25250i | 1.18077 | + | 0.103304i | ||||
\(148\) | 11.1406 | − | 0.974677i | 0.915752 | − | 0.0801179i | ||||
\(149\) | −15.4981 | + | 2.73273i | −1.26965 | + | 0.223874i | −0.767582 | − | 0.640951i | \(-0.778540\pi\) |
−0.502073 | + | 0.864825i | \(0.667429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.12444i | 0.742536i | 0.928526 | + | 0.371268i | \(0.121077\pi\) | ||||
−0.928526 | + | 0.371268i | \(0.878923\pi\) | |||||||
\(152\) | −3.10052 | + | 3.06378i | −0.251485 | + | 0.248506i | ||||
\(153\) | −5.27473 | − | 5.27473i | −0.426437 | − | 0.426437i | ||||
\(154\) | 7.00074 | + | 2.54806i | 0.564135 | + | 0.205328i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.684920 | − | 0.574716i | −0.0548375 | − | 0.0460141i | ||||
\(157\) | −1.49617 | + | 17.1013i | −0.119407 | + | 1.36483i | 0.666045 | + | 0.745911i | \(0.267986\pi\) |
−0.785453 | + | 0.618922i | \(0.787570\pi\) | |||||||
\(158\) | 3.83806 | − | 2.68744i | 0.305340 | − | 0.213801i | ||||
\(159\) | 21.9623 | + | 12.6800i | 1.74173 | + | 1.00559i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0766 | + | 4.75951i | −1.03058 | + | 0.375102i | ||||
\(162\) | 9.92150 | + | 4.62647i | 0.779506 | + | 0.363490i | ||||
\(163\) | 4.17250 | − | 15.5720i | 0.326816 | − | 1.21969i | −0.585659 | − | 0.810558i | \(-0.699164\pi\) |
0.912474 | − | 0.409134i | \(-0.134169\pi\) | |||||||
\(164\) | 0.889308 | − | 1.54033i | 0.0694433 | − | 0.120279i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.23737 | − | 1.47464i | −0.0960386 | − | 0.114454i | ||||
\(167\) | 0.984333 | + | 11.2510i | 0.0761700 | + | 0.870627i | 0.934135 | + | 0.356919i | \(0.116173\pi\) |
−0.857965 | + | 0.513708i | \(0.828272\pi\) | |||||||
\(168\) | −4.71756 | + | 6.73737i | −0.363967 | + | 0.519799i | ||||
\(169\) | 4.39212 | − | 12.0673i | 0.337856 | − | 0.928251i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.79191 | + | 1.60433i | 0.672334 | + | 0.122686i | ||||
\(172\) | −0.596944 | + | 0.596944i | −0.0455165 | + | 0.0455165i | ||||
\(173\) | 19.6625 | − | 9.16877i | 1.49491 | − | 0.697088i | 0.508451 | − | 0.861091i | \(-0.330218\pi\) |
0.986460 | + | 0.164003i | \(0.0524406\pi\) | |||||||
\(174\) | 1.89580 | + | 10.7516i | 0.143720 | + | 0.815076i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.55936 | + | 1.30845i | −0.117541 | + | 0.0986285i | ||||
\(177\) | 7.13132 | + | 10.1846i | 0.536023 | + | 0.765520i | ||||
\(178\) | −11.1123 | + | 2.97752i | −0.832899 | + | 0.223175i | ||||
\(179\) | 11.0624 | + | 19.1607i | 0.826843 | + | 1.43213i | 0.900503 | + | 0.434851i | \(0.143199\pi\) |
−0.0736594 | + | 0.997283i | \(0.523468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.62297 | − | 12.7015i | −0.343623 | − | 0.944096i | −0.984334 | − | 0.176314i | \(-0.943583\pi\) |
0.640711 | − | 0.767782i | \(-0.278640\pi\) | |||||||
\(182\) | 1.40649 | + | 0.376869i | 0.104256 | + | 0.0279354i | ||||
\(183\) | 5.36528 | + | 20.0235i | 0.396613 | + | 1.48018i | ||||
\(184\) | 0.660259 | − | 3.74451i | 0.0486749 | − | 0.276049i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.47304 | + | 6.52251i | −0.401303 | + | 0.478254i | ||||
\(187\) | 6.06669 | + | 4.24794i | 0.443641 | + | 0.310640i | ||||
\(188\) | −1.80812 | − | 3.87752i | −0.131871 | − | 0.282798i | ||||
\(189\) | −7.81103 | −0.568169 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2634 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(192\) | −0.949745 | − | 2.03674i | −0.0685420 | − | 0.146989i | ||||
\(193\) | −4.09257 | − | 2.86565i | −0.294590 | − | 0.206274i | 0.416933 | − | 0.908937i | \(-0.363105\pi\) |
−0.711522 | + | 0.702664i | \(0.751994\pi\) | |||||||
\(194\) | 5.70056 | − | 6.79366i | 0.409276 | − | 0.487757i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.11043 | − | 6.29757i | 0.0793165 | − | 0.449826i | ||||
\(197\) | 2.56441 | + | 9.57051i | 0.182707 | + | 0.681870i | 0.995110 | + | 0.0987743i | \(0.0314922\pi\) |
−0.812403 | + | 0.583096i | \(0.801841\pi\) | |||||||
\(198\) | 4.03138 | + | 1.08021i | 0.286498 | + | 0.0767669i | ||||
\(199\) | 3.43559 | + | 9.43920i | 0.243542 | + | 0.669127i | 0.999888 | + | 0.0149552i | \(0.00476057\pi\) |
−0.756346 | + | 0.654172i | \(0.773017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.2430 | + | 28.1336i | 1.14569 | + | 1.98439i | ||||
\(202\) | −6.27148 | + | 1.68044i | −0.441260 | + | 0.118235i | ||||
\(203\) | −10.1981 | − | 14.5644i | −0.715768 | − | 1.02222i | ||||
\(204\) | −6.26339 | + | 5.25561i | −0.438525 | + | 0.367966i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.80749 | + | 15.9221i | 0.195607 | + | 1.10934i | ||||
\(207\) | −7.06543 | + | 3.29467i | −0.491082 | + | 0.228995i | ||||
\(208\) | −0.281327 | + | 0.281327i | −0.0195065 | + | 0.0195065i | ||||
\(209\) | −8.87279 | − | 0.0528762i | −0.613744 | − | 0.00365753i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.63145 | − | 15.4723i | 0.387685 | − | 1.06516i | −0.580356 | − | 0.814363i | \(-0.697086\pi\) |
0.968041 | − | 0.250793i | \(-0.0806913\pi\) | |||||||
\(212\) | 6.47262 | − | 9.24386i | 0.444541 | − | 0.634871i | ||||
\(213\) | −1.72386 | − | 19.7038i | −0.118117 | − | 1.35008i | ||||
\(214\) | 8.18883 | + | 9.75907i | 0.559777 | + | 0.667116i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.06712 | − | 1.84830i | 0.0726080 | − | 0.125761i | ||||
\(217\) | 3.58893 | − | 13.3941i | 0.243632 | − | 0.909249i | ||||
\(218\) | −9.10491 | − | 4.24569i | −0.616663 | − | 0.287554i | ||||
\(219\) | 22.3490 | − | 8.13438i | 1.51021 | − | 0.549670i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.25359 | + | 0.723758i | 0.0843253 | + | 0.0486852i | ||||
\(222\) | −20.5868 | + | 14.4150i | −1.38169 | + | 0.967472i | ||||
\(223\) | 1.76268 | − | 20.1475i | 0.118038 | − | 1.34918i | −0.674011 | − | 0.738721i | \(-0.735430\pi\) |
0.792049 | − | 0.610457i | \(-0.209014\pi\) | |||||||
\(224\) | 2.80363 | + | 2.35253i | 0.187325 | + | 0.157185i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.3661 | + | 5.59281i | 1.02214 | + | 0.372028i | ||||
\(227\) | −16.9824 | − | 16.9824i | −1.12716 | − | 1.12716i | −0.990637 | − | 0.136525i | \(-0.956407\pi\) |
−0.136525 | − | 0.990637i | \(-0.543593\pi\) | |||||||
\(228\) | 2.59166 | − | 9.44665i | 0.171637 | − | 0.625620i | ||||
\(229\) | 8.20517i | 0.542213i | 0.962549 | + | 0.271107i | \(0.0873896\pi\) | ||||
−0.962549 | + | 0.271107i | \(0.912610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.4880 | + | 2.90728i | −1.08483 | + | 0.191285i | ||||
\(232\) | 4.83957 | − | 0.423407i | 0.317733 | − | 0.0277980i | ||||
\(233\) | −9.93045 | − | 0.868802i | −0.650566 | − | 0.0569171i | −0.242904 | − | 0.970050i | \(-0.578100\pi\) |
−0.407661 | + | 0.913133i | \(0.633656\pi\) | |||||||
\(234\) | 0.803337 | + | 0.141650i | 0.0525158 | + | 0.00925995i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.79127 | − | 2.76624i | 0.311885 | − | 0.180067i | ||||
\(237\) | −4.44994 | + | 9.54294i | −0.289055 | + | 0.619880i | ||||
\(238\) | 5.62745 | − | 12.0681i | 0.364773 | − | 0.782259i | ||||
\(239\) | −9.17350 | + | 5.29632i | −0.593384 | + | 0.342591i | −0.766435 | − | 0.642322i | \(-0.777971\pi\) |
0.173050 | + | 0.984913i | \(0.444638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.98759 | − | 1.05577i | −0.385695 | − | 0.0680084i | −0.0225612 | − | 0.999745i | \(-0.507182\pi\) |
−0.363134 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(242\) | 6.83027 | + | 0.597571i | 0.439066 | + | 0.0384133i | ||||
\(243\) | −18.1295 | + | 1.58612i | −1.16301 | + | 0.101750i | ||||
\(244\) | 9.08424 | − | 1.60180i | 0.581559 | − | 0.102545i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.99707i | 0.254844i | ||||||||
\(247\) | −1.72849 | + | 0.140849i | −0.109981 | + | 0.00896201i | ||||
\(248\) | 2.67909 | + | 2.67909i | 0.170122 | + | 0.170122i | ||||
\(249\) | 4.06516 | + | 1.47960i | 0.257619 | + | 0.0937656i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.99608 | + | 4.19221i | 0.315350 | + | 0.264610i | 0.786699 | − | 0.617337i | \(-0.211788\pi\) |
−0.471349 | + | 0.881947i | \(0.656233\pi\) | |||||||
\(252\) | 0.654006 | − | 7.47533i | 0.0411985 | − | 0.470901i | ||||
\(253\) | 6.34015 | − | 4.43942i | 0.398602 | − | 0.279104i | ||||
\(254\) | −4.45415 | − | 2.57160i | −0.279478 | − | 0.161357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | + | 0.342020i | −0.0587308 | + | 0.0213763i | ||||
\(257\) | −14.0201 | − | 6.53770i | −0.874553 | − | 0.407811i | −0.0671022 | − | 0.997746i | \(-0.521375\pi\) |
−0.807450 | + | 0.589936i | \(0.799153\pi\) | |||||||
\(258\) | 0.491025 | − | 1.83253i | 0.0305699 | − | 0.114088i | ||||
\(259\) | 20.4645 | − | 35.4456i | 1.27160 | − | 2.20248i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.40249 | − | 7.63019i | −0.396304 | − | 0.472297i | ||||
\(262\) | 0.689553 | + | 7.88163i | 0.0426008 | + | 0.486929i | ||||
\(263\) | −11.4410 | + | 16.3395i | −0.705484 | + | 1.00754i | 0.293190 | + | 0.956054i | \(0.405283\pi\) |
−0.998674 | + | 0.0514815i | \(0.983606\pi\) | |||||||
\(264\) | 1.56459 | − | 4.29869i | 0.0962941 | − | 0.264566i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.67654 | + | 15.7269i | 0.164109 | + | 0.964279i | ||||
\(267\) | 18.2811 | − | 18.2811i | 1.11879 | − | 1.11879i | ||||
\(268\) | 13.1012 | − | 6.10920i | 0.800285 | − | 0.373179i | ||||
\(269\) | 2.78396 | + | 15.7886i | 0.169741 | + | 0.962651i | 0.944040 | + | 0.329831i | \(0.106992\pi\) |
−0.774299 | + | 0.632820i | \(0.781897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.427071 | + | 0.358355i | −0.0259427 | + | 0.0217685i | −0.655667 | − | 0.755050i | \(-0.727612\pi\) |
0.629724 | + | 0.776819i | \(0.283168\pi\) | |||||||
\(272\) | 2.08683 | + | 2.98031i | 0.126533 | + | 0.180708i | ||||
\(273\) | −3.16080 | + | 0.846933i | −0.191300 | + | 0.0512587i | ||||
\(274\) | 0.0324375 | + | 0.0561834i | 0.00195962 | + | 0.00339416i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.92250 | + | 8.02950i | 0.175914 | + | 0.483319i | ||||
\(277\) | −23.4935 | − | 6.29506i | −1.41159 | − | 0.378233i | −0.529095 | − | 0.848563i | \(-0.677468\pi\) |
−0.882491 | + | 0.470330i | \(0.844135\pi\) | |||||||
\(278\) | 4.50097 | + | 16.7979i | 0.269950 | + | 1.00747i | ||||
\(279\) | 1.34894 | − | 7.65020i | 0.0807587 | − | 0.458005i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7044 | + | 19.9075i | −0.996502 | + | 1.18758i | −0.0142727 | + | 0.999898i | \(0.504543\pi\) |
−0.982229 | + | 0.187686i | \(0.939901\pi\) | |||||||
\(282\) | 7.87594 | + | 5.51479i | 0.469005 | + | 0.328401i | ||||
\(283\) | 10.6442 | + | 22.8265i | 0.632730 | + | 1.35689i | 0.917284 | + | 0.398233i | \(0.130377\pi\) |
−0.284554 | + | 0.958660i | \(0.591846\pi\) | |||||||
\(284\) | −8.80130 | −0.522261 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.809875 | −0.0478889 | ||||||||
\(287\) | −2.75104 | − | 5.89963i | −0.162389 | − | 0.348244i | ||||
\(288\) | 1.67951 | + | 1.17601i | 0.0989663 | + | 0.0692970i | ||||
\(289\) | −2.41875 | + | 2.88255i | −0.142279 | + | 0.169562i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.46082 | + | 19.6273i | −0.202877 | + | 1.15057i | ||||
\(292\) | −2.73911 | − | 10.2225i | −0.160294 | − | 0.598227i | ||||
\(293\) | −15.6986 | − | 4.20642i | −0.917121 | − | 0.245742i | −0.230767 | − | 0.973009i | \(-0.574123\pi\) |
−0.686354 | + | 0.727267i | \(0.740790\pi\) | |||||||
\(294\) | 4.91510 | + | 13.5041i | 0.286654 | + | 0.787576i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.59158 | + | 9.68490i | 0.325004 | + | 0.562923i | ||||
\(297\) | 4.19640 | − | 1.12442i | 0.243500 | − | 0.0652455i | ||||
\(298\) | −9.02648 | − | 12.8912i | −0.522890 | − | 0.746764i | ||||
\(299\) | 1.15884 | − | 0.972385i | 0.0670177 | − | 0.0562345i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.536520 | + | 3.04275i | 0.0309245 | + | 0.175381i | ||||
\(302\) | −8.26955 | + | 3.85615i | −0.475859 | + | 0.221897i | ||||
\(303\) | 10.3174 | − | 10.3174i | 0.592719 | − | 0.592719i | ||||
\(304\) | −4.08707 | − | 1.51521i | −0.234409 | − | 0.0869035i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.55133 | − | 7.00973i | 0.145850 | − | 0.400720i | ||||
\(307\) | −13.4826 | + | 19.2552i | −0.769494 | + | 1.09895i | 0.222778 | + | 0.974869i | \(0.428488\pi\) |
−0.992272 | + | 0.124082i | \(0.960401\pi\) | |||||||
\(308\) | 0.649313 | + | 7.42168i | 0.0369980 | + | 0.422889i | ||||
\(309\) | −23.3547 | − | 27.8331i | −1.32860 | − | 1.58337i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.83904 | + | 10.1135i | −0.331102 | + | 0.573485i | −0.982728 | − | 0.185055i | \(-0.940754\pi\) |
0.651626 | + | 0.758540i | \(0.274087\pi\) | |||||||
\(312\) | 0.231410 | − | 0.863634i | 0.0131010 | − | 0.0488936i | ||||
\(313\) | −4.39298 | − | 2.04848i | −0.248306 | − | 0.115787i | 0.294481 | − | 0.955657i | \(-0.404853\pi\) |
−0.542787 | + | 0.839870i | \(0.682631\pi\) | |||||||
\(314\) | −16.1314 | + | 5.87133i | −0.910345 | + | 0.331338i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.05768 | + | 2.34270i | 0.228262 | + | 0.131787i | ||||
\(317\) | 23.5662 | − | 16.5012i | 1.32361 | − | 0.926802i | 0.323797 | − | 0.946127i | \(-0.395041\pi\) |
0.999813 | + | 0.0193247i | \(0.00615163\pi\) | |||||||
\(318\) | −2.21026 | + | 25.2634i | −0.123945 | + | 1.41670i | ||||
\(319\) | 7.57543 | + | 6.35654i | 0.424143 | + | 0.355898i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.9029 | − | 9.79185i | −1.50157 | − | 0.546528i | ||||
\(322\) | −9.84001 | − | 9.84001i | −0.548362 | − | 0.548362i | ||||
\(323\) | −1.47632 | + | 15.7900i | −0.0821445 | + | 0.878581i | ||||
\(324\) | 10.9472i | 0.608176i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.8764 | − | 2.79944i | 0.879312 | − | 0.155046i | ||||
\(327\) | 22.4907 | − | 1.96768i | 1.24374 | − | 0.108813i | ||||
\(328\) | 1.77185 | + | 0.155017i | 0.0978339 | + | 0.00855936i | ||||
\(329\) | −15.4204 | − | 2.71904i | −0.850157 | − | 0.149906i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3599 | − | 9.44539i | 0.899221 | − | 0.519166i | 0.0222740 | − | 0.999752i | \(-0.492909\pi\) |
0.876948 | + | 0.480586i | \(0.159576\pi\) | |||||||
\(332\) | 0.813543 | − | 1.74465i | 0.0446490 | − | 0.0957501i | ||||
\(333\) | 9.69018 | − | 20.7807i | 0.531019 | − | 1.13877i | ||||
\(334\) | −9.78085 | + | 5.64698i | −0.535184 | + | 0.308989i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.09985 | − | 1.42822i | −0.441883 | − | 0.0779159i | ||||
\(337\) | −4.83922 | − | 0.423377i | −0.263609 | − | 0.0230628i | −0.0454151 | − | 0.998968i | \(-0.514461\pi\) |
−0.218194 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(338\) | 12.7928 | − | 1.11923i | 0.695839 | − | 0.0608780i | ||||
\(339\) | −36.1900 | + | 6.38128i | −1.96557 | + | 0.346583i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.71246i | 0.417653i | ||||||||
\(342\) | 2.26160 | + | 8.64619i | 0.122294 | + | 0.467533i | ||||
\(343\) | 1.56643 | + | 1.56643i | 0.0845791 | + | 0.0845791i | ||||
\(344\) | −0.793294 | − | 0.288736i | −0.0427716 | − | 0.0155676i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.6194 | + | 13.9454i | 0.893467 | + | 0.749708i | ||||
\(347\) | 2.05622 | − | 23.5028i | 0.110384 | − | 1.26169i | −0.715805 | − | 0.698300i | \(-0.753940\pi\) |
0.826189 | − | 0.563394i | \(-0.190504\pi\) | |||||||
\(348\) | −8.94305 | + | 6.26199i | −0.479398 | + | 0.335678i | ||||
\(349\) | 27.7330 | + | 16.0117i | 1.48451 | + | 0.857085i | 0.999845 | − | 0.0176130i | \(-0.00560669\pi\) |
0.484669 | + | 0.874698i | \(0.338940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.797911 | − | 0.290416i | 0.0425893 | − | 0.0155013i | ||||
\(352\) | −1.84487 | − | 0.860279i | −0.0983321 | − | 0.0458530i | ||||
\(353\) | 1.43103 | − | 5.34067i | 0.0761660 | − | 0.284255i | −0.917329 | − | 0.398130i | \(-0.869659\pi\) |
0.993495 | + | 0.113874i | \(0.0363261\pi\) | |||||||
\(354\) | −6.21654 | + | 10.7674i | −0.330405 | + | 0.572279i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.39479 | − | 8.81277i | −0.391923 | − | 0.467076i | ||||
\(357\) | 2.60806 | + | 29.8103i | 0.138033 | + | 1.57773i | ||||
\(358\) | −12.6903 | + | 18.1236i | −0.670702 | + | 0.957861i | ||||
\(359\) | 9.48616 | − | 26.0630i | 0.500660 | − | 1.37555i | −0.389971 | − | 0.920827i | \(-0.627515\pi\) |
0.890631 | − | 0.454726i | \(-0.150263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30322 | − | 16.5665i | −0.489643 | − | 0.871923i | ||||
\(362\) | 9.55773 | − | 9.55773i | 0.502343 | − | 0.502343i | ||||
\(363\) | −13.9646 | + | 6.51179i | −0.732951 | + | 0.341781i | ||||
\(364\) | 0.252851 | + | 1.43399i | 0.0132530 | + | 0.0751613i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.8800 | + | 13.3249i | −0.830060 | + | 0.696503i | ||||
\(367\) | 5.06478 | + | 7.23325i | 0.264379 | + | 0.377573i | 0.929291 | − | 0.369350i | \(-0.120420\pi\) |
−0.664911 | + | 0.746922i | \(0.731531\pi\) | |||||||
\(368\) | 3.67272 | − | 0.984102i | 0.191454 | − | 0.0512999i | ||||
\(369\) | −1.82336 | − | 3.15815i | −0.0949201 | − | 0.164406i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1256 | − | 38.8098i | −0.733365 | − | 2.01490i | ||||
\(372\) | −8.22441 | − | 2.20372i | −0.426416 | − | 0.114258i | ||||
\(373\) | 2.17694 | + | 8.12447i | 0.112718 | + | 0.420669i | 0.999106 | − | 0.0422739i | \(-0.0134602\pi\) |
−0.886388 | + | 0.462943i | \(0.846794\pi\) | |||||||
\(374\) | −1.28605 | + | 7.29355i | −0.0665000 | + | 0.377141i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.75009 | − | 3.27742i | 0.141825 | − | 0.169020i | ||||
\(377\) | 1.58327 | + | 1.10861i | 0.0815423 | + | 0.0570966i | ||||
\(378\) | −3.30108 | − | 7.07920i | −0.169789 | − | 0.364115i | ||||
\(379\) | 37.0435 | 1.90280 | 0.951399 | − | 0.307962i | \(-0.0996471\pi\) | ||||
0.951399 | + | 0.307962i | \(0.0996471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.5583 | 0.592148 | ||||||||
\(382\) | −6.02799 | − | 12.9271i | −0.308419 | − | 0.661406i | ||||
\(383\) | 21.8129 | + | 15.2735i | 1.11459 | + | 0.780442i | 0.977671 | − | 0.210141i | \(-0.0673923\pi\) |
0.136915 | + | 0.990583i | \(0.456281\pi\) | |||||||
\(384\) | 1.44453 | − | 1.72152i | 0.0737158 | − | 0.0878511i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.867564 | − | 4.92020i | 0.0441579 | − | 0.250432i | ||||
\(387\) | 0.447985 | + | 1.67190i | 0.0227724 | + | 0.0849877i | ||||
\(388\) | 8.56631 | + | 2.29534i | 0.434889 | + | 0.116528i | ||||
\(389\) | 10.3560 | + | 28.4529i | 0.525071 | + | 1.44262i | 0.864810 | + | 0.502100i | \(0.167439\pi\) |
−0.339739 | + | 0.940520i | \(0.610339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.91688 | − | 11.9804i | −0.349802 | − | 0.605874i | ||||
\(392\) | 6.17682 | − | 1.65507i | 0.311977 | − | 0.0835939i | ||||
\(393\) | −10.1982 | − | 14.5645i | −0.514430 | − | 0.734682i | ||||
\(394\) | −7.59006 | + | 6.36881i | −0.382382 | + | 0.320856i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.724737 | + | 4.11019i | 0.0364194 | + | 0.206545i | ||||
\(397\) | −12.9106 | + | 6.02029i | −0.647962 | + | 0.302150i | −0.718674 | − | 0.695347i | \(-0.755251\pi\) |
0.0707119 | + | 0.997497i | \(0.477473\pi\) | |||||||
\(398\) | −7.10288 | + | 7.10288i | −0.356035 | + | 0.356035i | ||||
\(399\) | −22.8806 | − | 27.6004i | −1.14546 | − | 1.38175i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.57197 | + | 7.06642i | −0.128438 | + | 0.352880i | −0.987198 | − | 0.159497i | \(-0.949013\pi\) |
0.858761 | + | 0.512377i | \(0.171235\pi\) | |||||||
\(402\) | −18.6332 | + | 26.6109i | −0.929338 | + | 1.32723i | ||||
\(403\) | 0.131379 | + | 1.50167i | 0.00654444 | + | 0.0748033i | ||||
\(404\) | −4.17344 | − | 4.97371i | −0.207636 | − | 0.247451i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.88995 | − | 15.3978i | 0.441201 | − | 0.764182i | ||||
\(407\) | −5.89185 | + | 21.9887i | −0.292048 | + | 1.08994i | ||||
\(408\) | −7.41022 | − | 3.45544i | −0.366861 | − | 0.171070i | ||||
\(409\) | −9.23982 | + | 3.36302i | −0.456880 | + | 0.166291i | −0.560200 | − | 0.828358i | \(-0.689276\pi\) |
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.126260 | − | 0.0728965i | −0.00622797 | − | 0.00359572i | ||||
\(412\) | −13.2438 | + | 9.27342i | −0.652476 | + | 0.456868i | ||||
\(413\) | 1.76475 | − | 20.1711i | 0.0868375 | − | 0.992557i | ||||
\(414\) | −5.97196 | − | 5.01107i | −0.293506 | − | 0.246281i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.373863 | − | 0.136075i | −0.0183302 | − | 0.00667163i | ||||
\(417\) | −27.6347 | − | 27.6347i | −1.35328 | − | 1.35328i | ||||
\(418\) | −3.70188 | − | 8.06383i | −0.181065 | − | 0.394415i | ||||
\(419\) | 22.6846i | 1.10821i | 0.832446 | + | 0.554107i | \(0.186940\pi\) | ||||
−0.832446 | + | 0.554107i | \(0.813060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7480 | − | 2.77679i | 0.767510 | − | 0.135333i | 0.223833 | − | 0.974627i | \(-0.428143\pi\) |
0.543677 | + | 0.839295i | \(0.317032\pi\) | |||||||
\(422\) | 16.4026 | − | 1.43504i | 0.798466 | − | 0.0698568i | ||||
\(423\) | −8.73861 | − | 0.764529i | −0.424886 | − | 0.0371727i | ||||
\(424\) | 11.1132 | + | 1.95956i | 0.539706 | + | 0.0951648i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.1292 | − | 9.88953i | 0.829911 | − | 0.479149i | ||||
\(427\) | 14.2676 | − | 30.5971i | 0.690459 | − | 1.48070i | ||||
\(428\) | −5.38397 | + | 11.5460i | −0.260244 | + | 0.558095i | ||||
\(429\) | 1.57619 | − | 0.910012i | 0.0760990 | − | 0.0439358i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1562 | − | 1.96715i | −0.537377 | − | 0.0947541i | −0.101628 | − | 0.994822i | \(-0.532405\pi\) |
−0.435749 | + | 0.900068i | \(0.643516\pi\) | |||||||
\(432\) | 2.12611 | + | 0.186011i | 0.102293 | + | 0.00894944i | ||||
\(433\) | −0.262954 | + | 0.0230055i | −0.0126367 | + | 0.00110557i | −0.0934724 | − | 0.995622i | \(-0.529797\pi\) |
0.0808356 | + | 0.996727i | \(0.474241\pi\) | |||||||
\(434\) | 13.6559 | − | 2.40790i | 0.655504 | − | 0.115583i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 10.0462i | − | 0.481124i | ||||||
\(437\) | 14.9789 | + | 7.09376i | 0.716538 | + | 0.339340i | ||||
\(438\) | 16.8174 | + | 16.8174i | 0.803564 | + | 0.803564i | ||||
\(439\) | −13.1779 | − | 4.79637i | −0.628948 | − | 0.228918i | 0.00782562 | − | 0.999969i | \(-0.497509\pi\) |
−0.636773 | + | 0.771051i | \(0.719731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.0437 | − | 8.42768i | −0.478272 | − | 0.401318i | ||||
\(442\) | −0.126159 | + | 1.44201i | −0.00600079 | + | 0.0685893i | ||||
\(443\) | −20.6262 | + | 14.4427i | −0.979983 | + | 0.686191i | −0.949638 | − | 0.313348i | \(-0.898549\pi\) |
−0.0303444 | + | 0.999540i | \(0.509660\pi\) | |||||||
\(444\) | −21.7648 | − | 12.5659i | −1.03291 | − | 0.596351i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.0048 | − | 6.91718i | 0.899904 | − | 0.327538i | ||||
\(447\) | 32.0525 | + | 14.9463i | 1.51603 | + | 0.706937i | ||||
\(448\) | −0.947246 | + | 3.53517i | −0.0447532 | + | 0.167021i | ||||
\(449\) | 8.85846 | − | 15.3433i | 0.418057 | − | 0.724095i | −0.577687 | − | 0.816258i | \(-0.696045\pi\) |
0.995744 | + | 0.0921629i | \(0.0293780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.32724 | + | 2.77349i | 0.109585 | + | 0.130599i | ||||
\(452\) | 1.42520 | + | 16.2901i | 0.0670356 | + | 0.766220i | ||||
\(453\) | 11.7613 | − | 16.7969i | 0.552595 | − | 0.789188i | ||||
\(454\) | 8.21421 | − | 22.5683i | 0.385512 | − | 1.05919i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.65685 | − | 1.64349i | 0.452224 | − | 0.0769634i | ||||
\(457\) | 22.0911 | − | 22.0911i | 1.03338 | − | 1.03338i | 0.0339529 | − | 0.999423i | \(-0.489190\pi\) |
0.999423 | − | 0.0339529i | \(-0.0108096\pi\) | |||||||
\(458\) | −7.43641 | + | 3.46766i | −0.347481 | + | 0.162033i | ||||
\(459\) | −1.34837 | − | 7.64697i | −0.0629364 | − | 0.356930i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.00960 | − | 6.72085i | 0.373044 | − | 0.313021i | −0.436920 | − | 0.899500i | \(-0.643931\pi\) |
0.809964 | + | 0.586479i | \(0.199486\pi\) | |||||||
\(462\) | −9.60303 | − | 13.7145i | −0.446773 | − | 0.638058i | ||||
\(463\) | −22.5965 | + | 6.05471i | −1.05015 | + | 0.281386i | −0.742312 | − | 0.670054i | \(-0.766271\pi\) |
−0.307835 | + | 0.951440i | \(0.599604\pi\) | |||||||
\(464\) | 2.42903 | + | 4.20720i | 0.112765 | + | 0.195314i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.40939 | − | 9.36722i | −0.157937 | − | 0.433928i | ||||
\(467\) | 25.3644 | + | 6.79636i | 1.17372 | + | 0.314498i | 0.792434 | − | 0.609958i | \(-0.208814\pi\) |
0.381289 | + | 0.924456i | \(0.375480\pi\) | |||||||
\(468\) | 0.211126 | + | 0.787934i | 0.00975932 | + | 0.0364223i | ||||
\(469\) | 9.18699 | − | 52.1020i | 0.424216 | − | 2.40585i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.7977 | − | 29.5528i | 1.14262 | − | 1.36172i | ||||
\(472\) | 4.53194 | + | 3.17330i | 0.208599 | + | 0.146063i | ||||
\(473\) | −0.726253 | − | 1.55745i | −0.0333931 | − | 0.0716118i | ||||
\(474\) | −10.5295 | −0.483634 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.3157 | 0.610323 | ||||||||
\(477\) | −9.77814 | − | 20.9693i | −0.447710 | − | 0.960118i | ||||
\(478\) | −8.67698 | − | 6.07569i | −0.396876 | − | 0.277896i | ||||
\(479\) | −10.6969 | + | 12.7481i | −0.488755 | + | 0.582475i | −0.952900 | − | 0.303284i | \(-0.901917\pi\) |
0.464146 | + | 0.885759i | \(0.346361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.772613 | + | 4.38170i | −0.0352281 | + | 0.199788i | ||||
\(482\) | −1.57361 | − | 5.87279i | −0.0716760 | − | 0.267498i | ||||
\(483\) | 30.2074 | + | 8.09405i | 1.37448 | + | 0.368292i | ||||
\(484\) | 2.34501 | + | 6.44287i | 0.106591 | + | 0.292858i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.09937 | − | 15.7606i | −0.412756 | − | 0.714914i | ||||
\(487\) | 3.93208 | − | 1.05360i | 0.178180 | − | 0.0477431i | −0.168626 | − | 0.985680i | \(-0.553933\pi\) |
0.346806 | + | 0.937937i | \(0.387266\pi\) | |||||||
\(488\) | 5.29089 | + | 7.55617i | 0.239507 | + | 0.342052i | ||||
\(489\) | −27.7532 | + | 23.2877i | −1.25504 | + | 1.05311i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.77015 | − | 32.7241i | −0.260403 | − | 1.47682i | −0.781813 | − | 0.623513i | \(-0.785705\pi\) |
0.521409 | − | 0.853307i | \(-0.325406\pi\) | |||||||
\(492\) | −3.62257 | + | 1.68923i | −0.163318 | + | 0.0761565i | ||||
\(493\) | 12.4981 | − | 12.4981i | 0.562886 | − | 0.562886i | ||||
\(494\) | −0.858144 | − | 1.50702i | −0.0386097 | − | 0.0678039i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.29585 | + | 3.56031i | −0.0581852 | + | 0.159863i | ||||
\(497\) | −18.4759 | + | 26.3863i | −0.828756 | + | 1.18359i | ||||
\(498\) | 0.377040 | + | 4.30959i | 0.0168956 | + | 0.193117i | ||||
\(499\) | 0.189710 | + | 0.226087i | 0.00849258 | + | 0.0101211i | 0.770274 | − | 0.637713i | \(-0.220119\pi\) |
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.6904 | − | 21.9804i | 0.566965 | − | 0.982012i | ||||
\(502\) | −1.68800 | + | 6.29969i | −0.0753390 | + | 0.281169i | ||||
\(503\) | −31.4925 | − | 14.6852i | −1.40418 | − | 0.654781i | −0.434843 | − | 0.900506i | \(-0.643196\pi\) |
−0.969340 | + | 0.245725i | \(0.920974\pi\) | |||||||
\(504\) | 7.05134 | − | 2.56648i | 0.314092 | − | 0.114320i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.70294 | + | 3.86995i | 0.297982 | + | 0.172040i | ||||
\(507\) | −23.6399 | + | 16.5529i | −1.04989 | + | 0.735138i | ||||
\(508\) | 0.448260 | − | 5.12364i | 0.0198883 | − | 0.227325i | ||||
\(509\) | −7.54692 | − | 6.33262i | −0.334512 | − | 0.280689i | 0.460024 | − | 0.887907i | \(-0.347841\pi\) |
−0.794535 | + | 0.607218i | \(0.792285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.3971 | − | 13.2474i | −1.61011 | − | 0.586032i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 6.53883 | + | 6.61723i | 0.288696 | + | 0.292158i | ||||
\(514\) | − | 15.4695i | − | 0.682331i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.86835 | − | 0.329441i | 0.0822497 | − | 0.0145028i | ||||
\(517\) | 8.67589 | − | 0.759042i | 0.381565 | − | 0.0333826i | ||||
\(518\) | 40.7733 | + | 3.56720i | 1.79147 | + | 0.156734i | ||||
\(519\) | −48.0146 | − | 8.46626i | −2.10761 | − | 0.371628i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9420 | − | 13.2456i | 1.00511 | − | 0.580300i | 0.0953526 | − | 0.995444i | \(-0.469602\pi\) |
0.909756 | + | 0.415144i | \(0.136269\pi\) | |||||||
\(522\) | 4.20949 | − | 9.02729i | 0.184244 | − | 0.395114i | ||||
\(523\) | −13.7727 | + | 29.5357i | −0.602239 | + | 1.29151i | 0.334803 | + | 0.942288i | \(0.391330\pi\) |
−0.937042 | + | 0.349218i | \(0.886447\pi\) | |||||||
\(524\) | −6.85177 | + | 3.95587i | −0.299321 | + | 0.172813i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.6438 | − | 3.46373i | −0.856510 | − | 0.151026i | ||||
\(527\) | 13.7323 | + | 1.20142i | 0.598187 | + | 0.0523346i | ||||
\(528\) | 4.55716 | − | 0.398700i | 0.198325 | − | 0.0173512i | ||||
\(529\) | 8.41290 | − | 1.48342i | 0.365778 | − | 0.0644966i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 11.3433i | − | 0.492257i | ||||||
\(532\) | −13.1223 | + | 9.07225i | −0.568922 | + | 0.393332i | ||||
\(533\) | 0.500373 | + | 0.500373i | 0.0216736 | + | 0.0216736i | ||||
\(534\) | 24.2942 | + | 8.84238i | 1.05131 | + | 0.382647i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.0736 | + | 9.29189i | 0.478308 | + | 0.401348i | ||||
\(537\) | 4.33346 | − | 49.5316i | 0.187003 | − | 2.13745i | ||||
\(538\) | −13.1328 | + | 9.19570i | −0.566196 | + | 0.396455i | ||||
\(539\) | 11.2731 | + | 6.50852i | 0.485566 | + | 0.280342i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6337 | + | 4.96227i | −0.586160 | + | 0.213345i | −0.618039 | − | 0.786147i | \(-0.712073\pi\) |
0.0318799 | + | 0.999492i | \(0.489851\pi\) | |||||||
\(542\) | −0.505268 | − | 0.235610i | −0.0217031 | − | 0.0101203i | ||||
\(543\) | −7.86185 | + | 29.3408i | −0.337384 | + | 1.25914i | ||||
\(544\) | −1.81914 | + | 3.15085i | −0.0779950 | + | 0.135091i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.10339 | − | 2.50672i | −0.0900169 | − | 0.107278i | ||||
\(547\) | −0.899184 | − | 10.2777i | −0.0384463 | − | 0.439444i | −0.990885 | − | 0.134712i | \(-0.956989\pi\) |
0.952438 | − | 0.304731i | \(-0.0985666\pi\) | |||||||
\(548\) | −0.0372108 | + | 0.0531425i | −0.00158957 | + | 0.00227014i | ||||
\(549\) | 6.46856 | − | 17.7722i | 0.276072 | − | 0.758501i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.80134 | + | 20.8318i | −0.161943 | + | 0.887463i | ||||
\(552\) | −6.04210 | + | 6.04210i | −0.257169 | + | 0.257169i | ||||
\(553\) | 15.5414 | − | 7.24707i | 0.660887 | − | 0.308177i | ||||
\(554\) | −4.22351 | − | 23.9527i | −0.179440 | − | 1.01765i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.3218 | + | 11.1784i | −0.564972 | + | 0.474068i | ||||
\(557\) | 21.4053 | + | 30.5699i | 0.906970 | + | 1.29529i | 0.955050 | + | 0.296444i | \(0.0958009\pi\) |
−0.0480799 | + | 0.998843i | \(0.515310\pi\) | |||||||
\(558\) | 7.50352 | − | 2.01056i | 0.317649 | − | 0.0851139i | ||||
\(559\) | −0.167937 | − | 0.290875i | −0.00710296 | − | 0.0123027i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.69244 | − | 15.6398i | −0.240335 | − | 0.660315i | ||||
\(562\) | −25.1020 | − | 6.72605i | −1.05886 | − | 0.283721i | ||||
\(563\) | 2.49018 | + | 9.29350i | 0.104949 | + | 0.391674i | 0.998339 | − | 0.0576067i | \(-0.0183469\pi\) |
−0.893391 | + | 0.449281i | \(0.851680\pi\) | |||||||
\(564\) | −1.66958 | + | 9.46867i | −0.0703021 | + | 0.398703i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.1894 | + | 19.2938i | −0.680491 | + | 0.810978i | ||||
\(567\) | 32.8196 | + | 22.9805i | 1.37829 | + | 0.965090i | ||||
\(568\) | −3.71959 | − | 7.97669i | −0.156071 | − | 0.334694i | ||||
\(569\) | −19.0127 | −0.797055 | −0.398527 | − | 0.917156i | \(-0.630479\pi\) | ||||
−0.398527 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.873418 | 0.0365514 | 0.0182757 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182757 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(572\) | −0.342268 | − | 0.733996i | −0.0143109 | − | 0.0306899i | ||||
\(573\) | 26.2571 | + | 18.3854i | 1.09691 | + | 0.768063i | ||||
\(574\) | 4.18424 | − | 4.98658i | 0.174647 | − | 0.208136i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.356032 | + | 2.01916i | −0.0148347 | + | 0.0841316i | ||||
\(577\) | −2.00055 | − | 7.46617i | −0.0832841 | − | 0.310821i | 0.911700 | − | 0.410857i | \(-0.134771\pi\) |
−0.994984 | + | 0.100037i | \(0.968104\pi\) | |||||||
\(578\) | −3.63468 | − | 0.973910i | −0.151183 | − | 0.0405093i | ||||
\(579\) | 3.84010 | + | 10.5506i | 0.159589 | + | 0.438467i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.52265 | − | 6.10141i | −0.146144 | − | 0.253129i | ||||
\(582\) | −19.2510 | + | 5.15828i | −0.797979 | + | 0.213818i | ||||
\(583\) | 13.1756 | + | 18.8167i | 0.545679 | + | 0.779310i | ||||
\(584\) | 8.10714 | − | 6.80270i | 0.335476 | − | 0.281498i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.82219 | − | 16.0055i | −0.116584 | − | 0.661179i | ||||
\(587\) | −31.1379 | + | 14.5198i | −1.28520 | + | 0.599297i | −0.940620 | − | 0.339461i | \(-0.889755\pi\) |
−0.344577 | + | 0.938758i | \(0.611978\pi\) | |||||||
\(588\) | −10.1617 | + | 10.1617i | −0.419060 | + | 0.419060i | ||||
\(589\) | −14.3514 | + | 8.17213i | −0.591338 | + | 0.336727i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.61556 | − | 20.9236i | 0.313262 | − | 0.860681i | ||||
\(592\) | −6.41440 | + | 9.16071i | −0.263630 | + | 0.376503i | ||||
\(593\) | −0.638147 | − | 7.29405i | −0.0262055 | − | 0.299531i | −0.997975 | − | 0.0636002i | \(-0.979742\pi\) |
0.971770 | − | 0.235931i | \(-0.0758138\pi\) | |||||||
\(594\) | 2.79255 | + | 3.32803i | 0.114580 | + | 0.136551i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.86860 | − | 13.6288i | 0.322310 | − | 0.558258i | ||||
\(597\) | 5.84258 | − | 21.8048i | 0.239121 | − | 0.892411i | ||||
\(598\) | 1.37103 | + | 0.639321i | 0.0560655 | + | 0.0261438i | ||||
\(599\) | 0.0335506 | − | 0.0122114i | 0.00137084 | − | 0.000498945i | −0.341335 | − | 0.939942i | \(-0.610879\pi\) |
0.342705 | + | 0.939443i | \(0.388657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8767 | + | 16.0946i | 1.13711 | + | 0.656512i | 0.945714 | − | 0.325000i | \(-0.105364\pi\) |
0.191399 | + | 0.981512i | \(0.438698\pi\) | |||||||
\(602\) | −2.53093 | + | 1.77218i | −0.103153 | + | 0.0722285i | ||||
\(603\) | 2.58316 | − | 29.5257i | 0.105194 | − | 1.20238i | ||||
\(604\) | −6.98972 | − | 5.86508i | −0.284408 | − | 0.238647i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.7111 | + | 4.99042i | 0.556974 | + | 0.202722i | ||||
\(607\) | −18.1942 | − | 18.1942i | −0.738478 | − | 0.738478i | 0.233806 | − | 0.972283i | \(-0.424882\pi\) |
−0.972283 | + | 0.233806i | \(0.924882\pi\) | |||||||
\(608\) | −0.354019 | − | 4.34450i | −0.0143574 | − | 0.176193i | ||||
\(609\) | 39.9566i | 1.61912i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.67632 | − | 0.295581i | 0.0678167 | − | 0.0119579i | ||||
\(612\) | 7.43121 | − | 0.650147i | 0.300389 | − | 0.0262806i | ||||
\(613\) | −47.8974 | − | 4.19048i | −1.93456 | − | 0.169252i | −0.946433 | − | 0.322899i | \(-0.895342\pi\) |
−0.988126 | + | 0.153647i | \(0.950898\pi\) | |||||||
\(614\) | −23.1491 | − | 4.08182i | −0.934223 | − | 0.164729i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.45191 | + | 3.72501i | −0.259955 | + | 0.150085i | ||||
\(617\) | 13.5042 | − | 28.9599i | 0.543659 | − | 1.16588i | −0.422126 | − | 0.906537i | \(-0.638716\pi\) |
0.965785 | − | 0.259343i | \(-0.0835061\pi\) | |||||||
\(618\) | 15.3552 | − | 32.9294i | 0.617677 | − | 1.32461i | ||||
\(619\) | −6.33757 | + | 3.65900i | −0.254728 | + | 0.147067i | −0.621927 | − | 0.783075i | \(-0.713650\pi\) |
0.367199 | + | 0.930142i | \(0.380317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.99166 | − | 1.40915i | −0.320694 | − | 0.0565470i | ||||
\(622\) | −11.6337 | − | 1.01781i | −0.466467 | − | 0.0408106i | ||||
\(623\) | −41.9440 | + | 3.66962i | −1.68045 | + | 0.147020i | ||||
\(624\) | 0.880516 | − | 0.155259i | 0.0352489 | − | 0.00621533i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 4.84712i | − | 0.193730i | ||||||
\(627\) | 16.2655 | + | 11.5343i | 0.649582 | + | 0.460635i | ||||
\(628\) | −12.1386 | − | 12.1386i | −0.484384 | − | 0.484384i | ||||
\(629\) | 38.2337 | + | 13.9159i | 1.52448 | + | 0.554865i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.97788 | − | 3.33784i | −0.158357 | − | 0.132877i | 0.560166 | − | 0.828380i | \(-0.310737\pi\) |
−0.718523 | + | 0.695503i | \(0.755182\pi\) | |||||||
\(632\) | −0.408360 | + | 4.66758i | −0.0162437 | + | 0.185666i | ||||
\(633\) | −30.3104 | + | 21.2236i | −1.20473 | + | 0.843562i | ||||
\(634\) | 24.9147 | + | 14.3845i | 0.989490 | + | 0.571282i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −23.8305 | + | 8.67360i | −0.944942 | + | 0.343931i | ||||
\(637\) | 2.30581 | + | 1.07522i | 0.0913596 | + | 0.0426017i | ||||
\(638\) | −2.55947 | + | 9.55206i | −0.101330 | + | 0.378170i | ||||
\(639\) | −9.02269 | + | 15.6278i | −0.356932 | + | 0.618224i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.52712 | + | 8.97047i | 0.297303 | + | 0.354312i | 0.893930 | − | 0.448207i | \(-0.147937\pi\) |
−0.596627 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(642\) | −2.49522 | − | 28.5205i | −0.0984786 | − | 1.12562i | ||||
\(643\) | 1.15385 | − | 1.64787i | 0.0455035 | − | 0.0649858i | −0.795756 | − | 0.605618i | \(-0.792926\pi\) |
0.841259 | + | 0.540632i | \(0.181815\pi\) | |||||||
\(644\) | 4.75951 | − | 13.0766i | 0.187551 | − | 0.515292i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9346 | + | 5.33516i | −0.587592 | + | 0.209909i | ||||
\(647\) | −19.1316 | + | 19.1316i | −0.752140 | + | 0.752140i | −0.974878 | − | 0.222739i | \(-0.928500\pi\) |
0.222739 | + | 0.974878i | \(0.428500\pi\) | |||||||
\(648\) | −9.92150 | + | 4.62647i | −0.389753 | + | 0.181745i | ||||
\(649\) | 1.95560 | + | 11.0908i | 0.0767642 | + | 0.435351i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.8716 | + | 20.0307i | −0.935602 | + | 0.785063i | ||||
\(652\) | 9.24680 | + | 13.2058i | 0.362133 | + | 0.517179i | ||||
\(653\) | 5.77046 | − | 1.54619i | 0.225816 | − | 0.0605071i | −0.144137 | − | 0.989558i | \(-0.546041\pi\) |
0.369953 | + | 0.929051i | \(0.379374\pi\) | |||||||
\(654\) | 11.2883 | + | 19.5519i | 0.441408 | + | 0.764541i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.608323 | + | 1.67135i | 0.0237510 | + | 0.0652554i | ||||
\(657\) | −20.9593 | − | 5.61602i | −0.817700 | − | 0.219102i | ||||
\(658\) | −4.05268 | − | 15.1248i | −0.157990 | − | 0.589626i | ||||
\(659\) | 2.71452 | − | 15.3948i | 0.105743 | − | 0.599697i | −0.885178 | − | 0.465252i | \(-0.845964\pi\) |
0.990921 | − | 0.134445i | \(-0.0429252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.941384 | + | 1.12190i | −0.0366156 | + | 0.0436368i | −0.784041 | − | 0.620708i | \(-0.786845\pi\) |
0.747426 | + | 0.664345i | \(0.231290\pi\) | |||||||
\(662\) | 15.4744 | + | 10.8353i | 0.601431 | + | 0.421126i | ||||
\(663\) | −1.37477 | − | 2.94821i | −0.0533917 | − | 0.114499i | ||||
\(664\) | 1.92501 | 0.0747048 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 22.9289 | 0.888478 | ||||||||
\(667\) | −7.80647 | − | 16.7410i | −0.302268 | − | 0.648215i | ||||
\(668\) | −9.25147 | − | 6.47795i | −0.357950 | − | 0.250639i | ||||
\(669\) | −29.2149 | + | 34.8169i | −1.12951 | + | 1.34610i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.26061 | + | 18.4918i | −0.125874 | + | 0.713869i | ||||
\(672\) | −2.12874 | − | 7.94455i | −0.0821178 | − | 0.306468i | ||||
\(673\) | 22.5231 | + | 6.03504i | 0.868201 | + | 0.232634i | 0.665310 | − | 0.746567i | \(-0.268300\pi\) |
0.202891 | + | 0.979201i | \(0.434966\pi\) | |||||||
\(674\) | −1.66143 | − | 4.56475i | −0.0639961 | − | 0.175828i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.42085 | + | 11.1212i | 0.246956 | + | 0.427740i | ||||
\(677\) | −19.4948 | + | 5.22361i | −0.749245 | + | 0.200760i | −0.613183 | − | 0.789941i | \(-0.710111\pi\) |
−0.136062 | + | 0.990700i | \(0.543445\pi\) | |||||||
\(678\) | −21.0780 | − | 30.1025i | −0.809494 | − | 1.15608i | ||||
\(679\) | 24.8640 | − | 20.8634i | 0.954192 | − | 0.800663i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.37223 | + | 53.1526i | 0.359145 | + | 2.03681i | ||||
\(682\) | −6.98987 | + | 3.25943i | −0.267656 | + | 0.124810i | ||||
\(683\) | −8.02116 | + | 8.02116i | −0.306921 | + | 0.306921i | −0.843714 | − | 0.536793i | \(-0.819636\pi\) |
0.536793 | + | 0.843714i | \(0.319636\pi\) | |||||||
\(684\) | −6.88032 | + | 5.70375i | −0.263076 | + | 0.218088i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.757665 | + | 2.08167i | −0.0289278 | + | 0.0794784i | ||||
\(687\) | 10.5764 | − | 15.1047i | 0.403515 | − | 0.576279i | ||||
\(688\) | −0.0735774 | − | 0.840994i | −0.00280511 | − | 0.0320626i | ||||
\(689\) | 2.88591 | + | 3.43930i | 0.109945 | + | 0.131027i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.21068 | + | 10.7572i | −0.236265 | + | 0.409223i | −0.959640 | − | 0.281233i | \(-0.909257\pi\) |
0.723374 | + | 0.690456i | \(0.242590\pi\) | |||||||
\(692\) | −5.61512 | + | 20.9559i | −0.213455 | + | 0.796624i | ||||
\(693\) | 13.8437 | + | 6.45543i | 0.525879 | + | 0.245222i | ||||
\(694\) | 22.1697 | − | 8.06912i | 0.841551 | − | 0.306300i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.45479 | − | 5.45873i | −0.358383 | − | 0.206912i | ||||
\(697\) | 5.30082 | − | 3.71168i | 0.200783 | − | 0.140590i | ||||
\(698\) | −2.79102 | + | 31.9015i | −0.105642 | + | 1.20749i | ||||
\(699\) | 17.1608 | + | 14.3996i | 0.649081 | + | 0.544644i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8105 | − | 7.21044i | −0.748233 | − | 0.272334i | −0.0603709 | − | 0.998176i | \(-0.519228\pi\) |
−0.687862 | + | 0.725842i | \(0.741451\pi\) | |||||||
\(702\) | 0.600418 | + | 0.600418i | 0.0226613 | + | 0.0226613i | ||||
\(703\) | −47.1596 | + | 12.3356i | −1.77866 | + | 0.465248i | ||||
\(704\) | − | 2.03559i | − | 0.0767193i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.44507 | − | 0.960113i | 0.204928 | − | 0.0361343i | ||||
\(707\) | −23.6721 | + | 2.07104i | −0.890282 | + | 0.0778896i | ||||
\(708\) | −12.3858 | − | 1.08361i | −0.465486 | − | 0.0407247i | ||||
\(709\) | −11.4026 | − | 2.01058i | −0.428232 | − | 0.0755088i | −0.0446217 | − | 0.999004i | \(-0.514208\pi\) |
−0.383610 | + | 0.923495i | \(0.625319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.31950 | − | 4.80326i | 0.312006 | − | 0.180137i | ||||
\(712\) | 4.86191 | − | 10.4264i | 0.182208 | − | 0.390746i | ||||
\(713\) | 6.08827 | − | 13.0563i | 0.228008 | − | 0.488964i | ||||
\(714\) | −25.9151 | + | 14.9621i | −0.969848 | + | 0.559942i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.7887 | − | 3.84193i | −0.814281 | − | 0.143580i | ||||
\(717\) | 23.7141 | + | 2.07472i | 0.885621 | + | 0.0774818i | ||||
\(718\) | 27.6301 | − | 2.41732i | 1.03115 | − | 0.0902137i | ||||
\(719\) | −27.0863 | + | 4.77604i | −1.01015 | + | 0.178116i | −0.654145 | − | 0.756369i | \(-0.726972\pi\) |
−0.356002 | + | 0.934485i | \(0.615860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.1719i | 2.20368i | ||||||||
\(722\) | 11.0827 | − | 15.4329i | 0.412454 | − | 0.574353i | ||||
\(723\) | 9.66151 | + | 9.66151i | 0.359315 | + | 0.359315i | ||||
\(724\) | 12.7015 | + | 4.62297i | 0.472048 | + | 0.171811i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.8034 | − | 9.90421i | −0.438065 | − | 0.367580i | ||||
\(727\) | −0.752266 | + | 8.59844i | −0.0279000 | + | 0.318899i | 0.969401 | + | 0.245481i | \(0.0789460\pi\) |
−0.997301 | + | 0.0734172i | \(0.976610\pi\) | |||||||
\(728\) | −1.19277 | + | 0.835190i | −0.0442072 | + | 0.0309542i | ||||
\(729\) | 6.97700 | + | 4.02817i | 0.258407 | + | 0.149192i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.88623 | + | 1.05050i | −0.106751 | + | 0.0388542i | ||||
\(732\) | −18.7876 | − | 8.76081i | −0.694410 | − | 0.323809i | ||||
\(733\) | 2.61866 | − | 9.77299i | 0.0967226 | − | 0.360974i | −0.900552 | − | 0.434747i | \(-0.856838\pi\) |
0.997275 | + | 0.0737739i | \(0.0235043\pi\) | |||||||
\(734\) | −4.41509 | + | 7.64715i | −0.162964 | + | 0.282262i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.44406 | + | 2.91271i | 0.0900891 | + | 0.107364i | ||||
\(737\) | 2.56462 | + | 29.3138i | 0.0944691 | + | 1.07979i | ||||
\(738\) | 2.09167 | − | 2.98721i | 0.0769954 | − | 0.109961i | ||||
\(739\) | −5.21626 | + | 14.3316i | −0.191883 | + | 0.527195i | −0.997905 | − | 0.0646905i | \(-0.979394\pi\) |
0.806022 | + | 0.591885i | \(0.201616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.36348 | + | 1.96872i | 0.123561 | + | 0.0723229i | ||||
\(742\) | 29.2039 | − | 29.2039i | 1.07211 | − | 1.07211i | ||||
\(743\) | 12.9587 | − | 6.04272i | 0.475407 | − | 0.221686i | −0.170120 | − | 0.985423i | \(-0.554416\pi\) |
0.645527 | + | 0.763737i | \(0.276638\pi\) | |||||||
\(744\) | −1.47853 | − | 8.38518i | −0.0542057 | − | 0.307416i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.44325 | + | 5.40653i | −0.235904 | + | 0.197947i | ||||
\(747\) | −2.26383 | − | 3.23308i | −0.0828290 | − | 0.118292i | ||||
\(748\) | −7.15371 | + | 1.91683i | −0.261566 | + | 0.0700863i | ||||
\(749\) | 23.3126 | + | 40.3786i | 0.851824 | + | 1.47540i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.373454 | − | 1.02606i | −0.0136275 | − | 0.0374414i | 0.932692 | − | 0.360673i | \(-0.117453\pi\) |
−0.946320 | + | 0.323232i | \(0.895231\pi\) | |||||||
\(752\) | 4.13259 | + | 1.10732i | 0.150700 | + | 0.0403800i | ||||
\(753\) | −3.79342 | − | 14.1572i | −0.138240 | − | 0.515918i | ||||
\(754\) | −0.335629 | + | 1.90345i | −0.0122229 | + | 0.0693194i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.02083 | − | 5.98360i | 0.182606 | − | 0.217621i | ||||
\(757\) | 15.3020 | + | 10.7146i | 0.556160 | + | 0.389428i | 0.817595 | − | 0.575793i | \(-0.195307\pi\) |
−0.261435 | + | 0.965221i | \(0.584196\pi\) | |||||||
\(758\) | 15.6553 | + | 33.5728i | 0.568625 | + | 1.21942i | ||||
\(759\) | −17.3938 | −0.631354 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7464 | 1.22330 | 0.611652 | − | 0.791127i | \(-0.290505\pi\) | ||||
0.611652 | + | 0.791127i | \(0.290505\pi\) | |||||||
\(762\) | 4.88474 | + | 10.4754i | 0.176955 | + | 0.379482i | ||||
\(763\) | −30.1184 | − | 21.0891i | −1.09036 | − | 0.763477i | ||||
\(764\) | 9.16835 | − | 10.9264i | 0.331699 | − | 0.395304i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.62401 | + | 26.2241i | −0.167072 | + | 0.947514i | ||||
\(767\) | 0.569696 | + | 2.12613i | 0.0205705 | + | 0.0767702i | ||||
\(768\) | 2.17071 | + | 0.581641i | 0.0783289 | + | 0.0209882i | ||||
\(769\) | −10.2512 | − | 28.1649i | −0.369667 | − | 1.01565i | −0.975488 | − | 0.220051i | \(-0.929377\pi\) |
0.605821 | − | 0.795601i | \(-0.292845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.3822 | + | 30.1069i | 0.626006 | + | 1.08427i | ||||
\(772\) | 4.82587 | − | 1.29309i | 0.173687 | − | 0.0465392i | ||||
\(773\) | −8.28226 | − | 11.8283i | −0.297892 | − | 0.425434i | 0.642105 | − | 0.766617i | \(-0.278061\pi\) |
−0.939997 | + | 0.341183i | \(0.889172\pi\) | |||||||
\(774\) | −1.32593 | + | 1.11259i | −0.0476597 | + | 0.0399912i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.54000 | + | 8.73377i | 0.0552827 | + | 0.313524i | ||||
\(777\) | −83.3616 | + | 38.8721i | −2.99058 | + | 1.39453i | ||||
\(778\) | −21.4104 | + | 21.4104i | −0.767602 | + | 0.767602i | ||||
\(779\) | −2.69498 | + | 7.26933i | −0.0965578 | + | 0.260451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.12759 | − | 16.8354i | 0.219262 | − | 0.602418i | ||||
\(782\) | 7.93472 | − | 11.3320i | 0.283745 | − | 0.405230i | ||||
\(783\) | −0.903649 | − | 10.3288i | −0.0322938 | − | 0.369120i | ||||
\(784\) | 4.11044 | + | 4.89864i | 0.146802 | + | 0.174951i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.88998 | − | 15.3979i | 0.317095 | − | 0.549225i | ||||
\(787\) | 5.87046 | − | 21.9089i | 0.209259 | − | 0.780967i | −0.778849 | − | 0.627211i | \(-0.784196\pi\) |
0.988109 | − | 0.153756i | \(-0.0491369\pi\) | |||||||
\(788\) | −8.97980 | − | 4.18735i | −0.319892 | − | 0.149168i | ||||
\(789\) | 42.1229 | − | 15.3315i | 1.49962 | − | 0.545816i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.8294 | + | 29.9237i | 1.84284 | + | 1.06396i | ||||
\(792\) | −3.41881 | + | 2.39388i | −0.121482 | + | 0.0850627i | ||||
\(793\) | −0.319860 | + | 3.65602i | −0.0113586 | + | 0.129829i | ||||
\(794\) | −10.9125 | − | 9.15665i | −0.387269 | − | 0.324957i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.43920 | − | 3.43559i | −0.334564 | − | 0.121771i | ||||
\(797\) | 37.2856 | + | 37.2856i | 1.32072 | + | 1.32072i | 0.913190 | + | 0.407534i | \(0.133611\pi\) |
0.407534 | + | 0.913190i | \(0.366389\pi\) | |||||||
\(798\) | 15.3447 | − | 32.4013i | 0.543196 | − | 1.14699i | ||||
\(799\) | − | 15.5659i | − | 0.550683i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.2289 | + | 4.09589i | −0.820754 | + | 0.144721i | ||||
\(802\) | −7.49131 | + | 0.655405i | −0.264527 | + | 0.0231431i | ||||
\(803\) | 21.4610 | + | 1.87759i | 0.757341 | + | 0.0662587i | ||||
\(804\) | −31.9924 | − | 5.64112i | −1.12828 | − | 0.198947i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.30545 | + | 0.753701i | −0.0459825 | + | 0.0265480i | ||||
\(807\) | 15.2265 | − | 32.6534i | 0.535999 | − | 1.14945i | ||||
\(808\) | 2.74394 | − | 5.88440i | 0.0965315 | − | 0.207012i | ||||
\(809\) | 32.1500 | − | 18.5618i | 1.13033 | − | 0.652598i | 0.186314 | − | 0.982490i | \(-0.440346\pi\) |
0.944019 | + | 0.329892i | \(0.107012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.1066 | − | 5.83759i | −1.16253 | − | 0.204985i | −0.441090 | − | 0.897463i | \(-0.645408\pi\) |
−0.721440 | + | 0.692477i | \(0.756519\pi\) | |||||||
\(812\) | 17.7122 | + | 1.54962i | 0.621577 | + | 0.0543810i | ||||
\(813\) | 1.24810 | − | 0.109195i | 0.0437728 | − | 0.00382962i | ||||
\(814\) | −22.4185 | + | 3.95299i | −0.785769 | + | 0.138552i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 8.17627i | − | 0.286227i | ||||||
\(817\) | 2.12858 | − | 3.00169i | 0.0744695 | − | 0.105016i | ||||
\(818\) | −6.95285 | − | 6.95285i | −0.243101 | − | 0.243101i | ||||
\(819\) | 2.80543 | + | 1.02109i | 0.0980295 | + | 0.0356798i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.4020 | − | 30.5449i | −1.27044 | − | 1.06602i | −0.994488 | − | 0.104852i | \(-0.966563\pi\) |
−0.275950 | − | 0.961172i | \(-0.588992\pi\) | |||||||
\(822\) | 0.0127067 | − | 0.145238i | 0.000443197 | − | 0.00506576i | ||||
\(823\) | 44.5572 | − | 31.1993i | 1.55317 | − | 1.08754i | 0.594086 | − | 0.804402i | \(-0.297514\pi\) |
0.959080 | − | 0.283137i | \(-0.0913750\pi\) | |||||||
\(824\) | −14.0016 | − | 8.08385i | −0.487771 | − | 0.281614i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.0271 | − | 6.92529i | 0.662037 | − | 0.240962i | ||||
\(827\) | −36.4111 | − | 16.9788i | −1.26614 | − | 0.590410i | −0.330646 | − | 0.943755i | \(-0.607267\pi\) |
−0.935493 | + | 0.353345i | \(0.885044\pi\) | |||||||
\(828\) | 2.01771 | − | 7.53021i | 0.0701204 | − | 0.261693i | ||||
\(829\) | 1.42975 | − | 2.47640i | 0.0496573 | − | 0.0860089i | −0.840128 | − | 0.542388i | \(-0.817520\pi\) |
0.889786 | + | 0.456379i | \(0.150854\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.1342 | + | 41.8713i | 1.21879 | + | 1.45250i | ||||
\(832\) | −0.0346755 | − | 0.396343i | −0.00120216 | − | 0.0137407i | ||||
\(833\) | 13.3447 | − | 19.0582i | 0.462367 | − | 0.660328i | ||||
\(834\) | 13.3666 | − | 36.7244i | 0.462847 | − | 1.27166i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.74383 | − | 6.76296i | 0.198654 | − | 0.233902i | ||||
\(837\) | 5.71780 | − | 5.71780i | 0.197636 | − | 0.197636i | ||||
\(838\) | −20.5592 | + | 9.58691i | −0.710206 | + | 0.331174i | ||||
\(839\) | −5.21072 | − | 29.5514i | −0.179894 | − | 1.02023i | −0.932342 | − | 0.361578i | \(-0.882238\pi\) |
0.752448 | − | 0.658652i | \(-0.228873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.13612 | + | 3.47061i | −0.142625 | + | 0.119676i | ||||
\(842\) | 9.17202 | + | 13.0990i | 0.316089 | + | 0.451421i | ||||
\(843\) | 56.4113 | − | 15.1154i | 1.94291 | − | 0.520601i | ||||
\(844\) | 8.23263 | + | 14.2593i | 0.283379 | + | 0.490827i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00020 | − | 8.24297i | −0.103149 | − | 0.283399i | ||||
\(847\) | 24.2384 | + | 6.49466i | 0.832841 | + | 0.223159i | ||||
\(848\) | 2.92069 | + | 10.9002i | 0.100297 | + | 0.374313i | ||||
\(849\) | 9.82862 | − | 55.7408i | 0.337317 | − | 1.91302i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.3323 | − | 32.5733i | 0.936939 | − | 1.11660i | ||||
\(852\) | 16.2021 | + | 11.3448i | 0.555073 | + | 0.388667i | ||||
\(853\) | −15.0441 | − | 32.2621i | −0.515100 | − | 1.10463i | −0.976117 | − | 0.217244i | \(-0.930293\pi\) |
0.461018 | − | 0.887391i | \(-0.347484\pi\) | |||||||
\(854\) | 33.7601 | 1.15525 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.7396 | −0.435429 | ||||||||
\(857\) | −3.36904 | − | 7.22494i | −0.115084 | − | 0.246799i | 0.840325 | − | 0.542082i | \(-0.182364\pi\) |
−0.955410 | + | 0.295283i | \(0.904586\pi\) | |||||||
\(858\) | 1.49088 | + | 1.04392i | 0.0508977 | + | 0.0356389i | ||||
\(859\) | 3.63063 | − | 4.32681i | 0.123875 | − | 0.147629i | −0.700542 | − | 0.713611i | \(-0.747058\pi\) |
0.824418 | + | 0.565982i | \(0.191503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.54026 | + | 14.4065i | −0.0865718 | + | 0.490973i | ||||
\(862\) | −2.93199 | − | 10.9423i | −0.0998640 | − | 0.372698i | ||||
\(863\) | 3.20720 | + | 0.859366i | 0.109174 | + | 0.0292532i | 0.312993 | − | 0.949756i | \(-0.398669\pi\) |
−0.203818 | + | 0.979009i | \(0.565335\pi\) | |||||||
\(864\) | 0.729950 | + | 2.00552i | 0.0248334 | + | 0.0682292i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.131979 | − | 0.228594i | −0.00448483 | − | 0.00776795i | ||||
\(867\) | 8.16818 | − | 2.18866i | 0.277406 | − | 0.0743307i | ||||
\(868\) | 7.95353 | + | 11.3588i | 0.269960 | + | 0.385544i | ||||
\(869\) | −7.30621 | + | 6.13064i | −0.247846 | + | 0.207968i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.998697 | + | 5.66389i | 0.0338395 | + | 0.191914i | ||||
\(872\) | 9.10491 | − | 4.24569i | 0.308331 | − | 0.143777i | ||||
\(873\) | 12.8574 | − | 12.8574i | 0.435158 | − | 0.435158i | ||||
\(874\) | −0.0987673 | + | 16.5735i | −0.00334085 | + | 0.560605i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.13438 | + | 22.3490i | −0.274835 | + | 0.755103i | ||||
\(877\) | −3.89826 | + | 5.56729i | −0.131635 | + | 0.187994i | −0.879559 | − | 0.475791i | \(-0.842162\pi\) |
0.747924 | + | 0.663785i | \(0.231051\pi\) | |||||||
\(878\) | −1.22224 | − | 13.9703i | −0.0412486 | − | 0.471474i | ||||
\(879\) | 23.4770 | + | 27.9788i | 0.791860 | + | 0.943702i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.0976 | + | 29.6140i | −0.576034 | + | 0.997720i | 0.419895 | + | 0.907573i | \(0.362067\pi\) |
−0.995928 | + | 0.0901468i | \(0.971266\pi\) | |||||||
\(882\) | 3.39341 | − | 12.6644i | 0.114262 | − | 0.426432i | ||||
\(883\) | 49.4000 | + | 23.0356i | 1.66244 | + | 0.775210i | 0.999651 | + | 0.0264069i | \(0.00840654\pi\) |
0.662792 | + | 0.748803i | \(0.269371\pi\) | |||||||
\(884\) | −1.36022 | + | 0.495080i | −0.0457492 | + | 0.0166513i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.8065 | − | 12.5900i | −0.732604 | − | 0.422969i | ||||
\(887\) | −33.3094 | + | 23.3235i | −1.11842 | + | 0.783127i | −0.978338 | − | 0.207013i | \(-0.933626\pi\) |
−0.140083 | + | 0.990140i | \(0.544737\pi\) | |||||||
\(888\) | 2.19038 | − | 25.0362i | 0.0735043 | − | 0.840159i | ||||
\(889\) | −14.4197 | − | 12.0995i | −0.483620 | − | 0.405805i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.9401 | − | 7.62157i | −0.701519 | − | 0.255332i | ||||
\(892\) | 14.3009 | + | 14.3009i | 0.478829 | + | 0.478829i | ||||
\(893\) | 10.6054 | + | 15.3398i | 0.354896 | + | 0.513328i | ||||
\(894\) | 35.3660i | 1.18282i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.60428 | + | 0.635531i | −0.120410 | + | 0.0212316i | ||||
\(897\) | −3.38668 | + | 0.296296i | −0.113078 | + | 0.00989304i | ||||
\(898\) | 17.6495 | + | 1.54413i | 0.588972 | + | 0.0515283i | ||||
\(899\) | 18.1266 | + | 3.19620i | 0.604555 | + | 0.106599i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.5562 | − | 20.5284i | 1.18455 | − | 0.683900i | ||||
\(902\) | −1.53011 | + | 3.28132i | −0.0509470 | + | 0.109256i | ||||
\(903\) | 2.93442 | − | 6.29289i | 0.0976514 | − | 0.209414i | ||||
\(904\) | −14.1615 | + | 8.17614i | −0.471004 | + | 0.271934i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.1937 | + | 3.56070i | 0.670892 | + | 0.118296i | ||||
\(907\) | −38.0915 | − | 3.33257i | −1.26481 | − | 0.110656i | −0.565062 | − | 0.825048i | \(-0.691148\pi\) |
−0.699746 | + | 0.714392i | \(0.746703\pi\) | |||||||
\(908\) | 23.9253 | − | 2.09320i | 0.793990 | − | 0.0694652i | ||||
\(909\) | −13.1098 | + | 2.31162i | −0.434826 | + | 0.0766715i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.9349i | − | 0.362288i | −0.983457 | − | 0.181144i | \(-0.942020\pi\) | ||
0.983457 | − | 0.181144i | \(-0.0579801\pi\) | |||||||
\(912\) | 5.57067 | + | 8.05751i | 0.184463 | + | 0.266811i | ||||
\(913\) | 2.77082 | + | 2.77082i | 0.0917008 | + | 0.0917008i | ||||
\(914\) | 29.3574 | + | 10.6852i | 0.971056 | + | 0.353436i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.28553 | − | 5.27418i | −0.207680 | − | 0.174264i | ||||
\(917\) | −2.52368 | + | 28.8458i | −0.0833393 | + | 0.952573i | ||||
\(918\) | 6.36067 | − | 4.45379i | 0.209933 | − | 0.146997i | ||||
\(919\) | 41.8138 | + | 24.1412i | 1.37931 | + | 0.796345i | 0.992076 | − | 0.125636i | \(-0.0400972\pi\) |
0.387234 | + | 0.921981i | \(0.373431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.6396 | − | 18.0673i | 1.63568 | − | 0.595339i | ||||
\(922\) | 9.47616 | + | 4.41881i | 0.312081 | + | 0.145526i | ||||
\(923\) | 0.906296 | − | 3.38234i | 0.0298311 | − | 0.111331i | ||||
\(924\) | 8.37118 | − | 14.4993i | 0.275392 | − | 0.476992i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.0371 | − | 17.9205i | −0.494150 | − | 0.588905i | ||||
\(927\) | 2.88911 | + | 33.0226i | 0.0948907 | + | 1.08461i | ||||
\(928\) | −2.78647 | + | 3.97948i | −0.0914702 | + | 0.130633i | ||||
\(929\) | 2.79049 | − | 7.66681i | 0.0915530 | − | 0.251540i | −0.885461 | − | 0.464713i | \(-0.846158\pi\) |
0.977014 | + | 0.213173i | \(0.0683798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.166108 | + | 27.8734i | −0.00544397 | + | 0.913515i | ||||
\(932\) | 7.04871 | − | 7.04871i | 0.230888 | − | 0.230888i | ||||
\(933\) | 23.7852 | − | 11.0912i | 0.778692 | − | 0.363110i | ||||
\(934\) | 4.55985 | + | 25.8602i | 0.149203 | + | 0.846171i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.624885 | + | 0.524341i | −0.0204250 | + | 0.0171386i | ||||
\(937\) | 4.79704 | + | 6.85088i | 0.156712 | + | 0.223809i | 0.889829 | − | 0.456295i | \(-0.150824\pi\) |
−0.733116 | + | 0.680103i | \(0.761935\pi\) | |||||||
\(938\) | 51.1031 | − | 13.6930i | 1.66857 | − | 0.447093i | ||||
\(939\) | 5.44644 | + | 9.43350i | 0.177738 | + | 0.307851i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.65059 | + | 26.5148i | 0.314600 | + | 0.864357i | 0.991712 | + | 0.128477i | \(0.0410089\pi\) |
−0.677112 | + | 0.735880i | \(0.736769\pi\) | |||||||
\(942\) | 37.2639 | + | 9.98482i | 1.21412 | + | 0.325323i | ||||
\(943\) | −1.75034 | − | 6.53236i | −0.0569989 | − | 0.212723i | ||||
\(944\) | −0.960705 | + | 5.44843i | −0.0312683 | + | 0.177331i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.10461 | − | 1.31642i | 0.0359138 | − | 0.0428004i | ||||
\(947\) | −11.1199 | − | 7.78627i | −0.361350 | − | 0.253020i | 0.378776 | − | 0.925488i | \(-0.376345\pi\) |
−0.740126 | + | 0.672469i | \(0.765234\pi\) | |||||||
\(948\) | −4.44994 | − | 9.54294i | −0.144527 | − | 0.309940i | ||||
\(949\) | 4.21057 | 0.136681 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −64.6523 | −2.09650 | ||||||||
\(952\) | 5.62745 | + | 12.0681i | 0.182387 | + | 0.391129i | ||||
\(953\) | 14.4384 | + | 10.1098i | 0.467704 | + | 0.327490i | 0.783559 | − | 0.621318i | \(-0.213402\pi\) |
−0.315855 | + | 0.948808i | \(0.602291\pi\) | |||||||
\(954\) | 14.8722 | − | 17.7240i | 0.481506 | − | 0.573836i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.83939 | − | 10.4317i | 0.0594902 | − | 0.337386i | ||||
\(957\) | −5.75186 | − | 21.4662i | −0.185931 | − | 0.693905i | ||||
\(958\) | −16.0744 | − | 4.30712i | −0.519341 | − | 0.139157i | ||||
\(959\) | 0.0812075 | + | 0.223116i | 0.00262233 | + | 0.00720478i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.32249 | − | 14.4150i | −0.268467 | − | 0.464999i | ||||
\(962\) | −4.29769 | + | 1.15156i | −0.138563 | + | 0.0371279i | ||||
\(963\) | 14.9818 | + | 21.3963i | 0.482783 | + | 0.689485i | ||||
\(964\) | 4.65752 | − | 3.90812i | 0.150009 | − | 0.125872i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.43050 | + | 30.7979i | 0.174723 | + | 0.990906i | ||||
\(967\) | −21.6762 | + | 10.1078i | −0.697059 | + | 0.325044i | −0.738648 | − | 0.674091i | \(-0.764536\pi\) |
0.0415896 | + | 0.999135i | \(0.486758\pi\) | |||||||
\(968\) | −4.84818 | + | 4.84818i | −0.155826 | + | 0.155826i | ||||
\(969\) | 23.0709 | − | 27.1645i | 0.741146 | − | 0.872649i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.15941 | − | 3.18546i | 0.0372073 | − | 0.102226i | −0.919698 | − | 0.392627i | \(-0.871566\pi\) |
0.956905 | + | 0.290401i | \(0.0937886\pi\) | |||||||
\(972\) | 10.4384 | − | 14.9075i | 0.334811 | − | 0.478159i | ||||
\(973\) | 5.54719 | + | 63.4047i | 0.177835 | + | 2.03266i | ||||
\(974\) | 2.61666 | + | 3.11841i | 0.0838431 | + | 0.0999203i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.61219 | + | 7.98855i | −0.147633 | + | 0.255707i | ||||
\(977\) | 7.39660 | − | 27.6045i | 0.236638 | − | 0.883146i | −0.740765 | − | 0.671764i | \(-0.765537\pi\) |
0.977404 | − | 0.211382i | \(-0.0677963\pi\) | |||||||
\(978\) | −32.8348 | − | 15.3111i | −1.04994 | − | 0.489596i | ||||
\(979\) | 22.0057 | − | 8.00942i | 0.703306 | − | 0.255982i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8382 | − | 10.2989i | −0.569528 | − | 0.328817i | ||||
\(982\) | 27.2196 | − | 19.0594i | 0.868612 | − | 0.608208i | ||||
\(983\) | −2.03577 | + | 23.2689i | −0.0649309 | + | 0.742164i | 0.892036 | + | 0.451965i | \(0.149277\pi\) |
−0.956966 | + | 0.290198i | \(0.906279\pi\) | |||||||
\(984\) | −3.06193 | − | 2.56926i | −0.0976107 | − | 0.0819051i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.6090 | + | 6.04520i | 0.528940 | + | 0.192518i | ||||
\(987\) | 24.8822 | + | 24.8822i | 0.792010 | + | 0.792010i | ||||
\(988\) | 1.00315 | − | 1.41464i | 0.0319146 | − | 0.0450056i | ||||
\(989\) | 3.20991i | 0.102069i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9141 | − | 4.92201i | 0.886721 | − | 0.156353i | 0.288305 | − | 0.957539i | \(-0.406908\pi\) |
0.598416 | + | 0.801186i | \(0.295797\pi\) | |||||||
\(992\) | −3.77439 | + | 0.330216i | −0.119837 | + | 0.0104844i | ||||
\(993\) | −42.2915 | − | 3.70003i | −1.34208 | − | 0.117417i | ||||
\(994\) | −31.7223 | − | 5.59350i | −1.00617 | − | 0.177415i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.74647 | + | 2.16302i | −0.118711 | + | 0.0685381i | ||||
\(997\) | −11.7072 | + | 25.1061i | −0.370770 | + | 0.795119i | 0.629072 | + | 0.777347i | \(0.283435\pi\) |
−0.999842 | + | 0.0177719i | \(0.994343\pi\) | |||||||
\(998\) | −0.124730 | + | 0.267484i | −0.00394826 | + | 0.00846706i | ||||
\(999\) | 20.6698 | − | 11.9337i | 0.653964 | − | 0.377566i |
(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 | 950.2.bb.c.243.4 | yes | 72 | |
5.2 | odd | 4 | inner | 950.2.bb.c.357.1 | yes | 72 | |
5.3 | odd | 4 | inner | 950.2.bb.c.357.6 | yes | 72 | |
5.4 | even | 2 | inner | 950.2.bb.c.243.3 | ✓ | 72 | |
19.14 | odd | 18 | inner | 950.2.bb.c.793.1 | yes | 72 | |
95.14 | odd | 18 | inner | 950.2.bb.c.793.6 | yes | 72 | |
95.33 | even | 36 | inner | 950.2.bb.c.907.3 | yes | 72 | |
95.52 | even | 36 | inner | 950.2.bb.c.907.4 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.bb.c.243.3 | ✓ | 72 | 5.4 | even | 2 | inner | |
950.2.bb.c.243.4 | yes | 72 | 1.1 | even | 1 | trivial | |
950.2.bb.c.357.1 | yes | 72 | 5.2 | odd | 4 | inner | |
950.2.bb.c.357.6 | yes | 72 | 5.3 | odd | 4 | inner | |
950.2.bb.c.793.1 | yes | 72 | 19.14 | odd | 18 | inner | |
950.2.bb.c.793.6 | yes | 72 | 95.14 | odd | 18 | inner | |
950.2.bb.c.907.3 | yes | 72 | 95.33 | even | 36 | inner | |
950.2.bb.c.907.4 | yes | 72 | 95.52 | even | 36 | inner |