Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(37,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.e (of order \(3\), 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: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(-0.527336 - 0.913372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.37 |
Dual form | 201.2.e.b.163.4 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.527336 | + | 0.913372i | 0.372883 | + | 0.645852i | 0.990008 | − | 0.141013i | \(-0.0450360\pi\) |
−0.617125 | + | 0.786865i | \(0.711703\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.443834 | − | 0.768743i | 0.221917 | − | 0.384371i | ||||
\(5\) | 0.832996 | 0.372527 | 0.186264 | − | 0.982500i | \(-0.440362\pi\) | ||||
0.186264 | + | 0.982500i | \(0.440362\pi\) | |||||||
\(6\) | −0.527336 | − | 0.913372i | −0.215284 | − | 0.372883i | ||||
\(7\) | 1.13029 | − | 1.95772i | 0.427209 | − | 0.739947i | −0.569415 | − | 0.822050i | \(-0.692830\pi\) |
0.996624 | + | 0.0821028i | \(0.0261636\pi\) | |||||||
\(8\) | 3.04554 | 1.07676 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.439269 | + | 0.760836i | 0.138909 | + | 0.240597i | ||||
\(11\) | −0.713790 | + | 1.23632i | −0.215216 | + | 0.372765i | −0.953339 | − | 0.301901i | \(-0.902379\pi\) |
0.738123 | + | 0.674666i | \(0.235712\pi\) | |||||||
\(12\) | −0.443834 | + | 0.768743i | −0.128124 | + | 0.221917i | ||||
\(13\) | 0.308980 | + | 0.535170i | 0.0856958 | + | 0.148429i | 0.905687 | − | 0.423946i | \(-0.139355\pi\) |
−0.819992 | + | 0.572375i | \(0.806022\pi\) | |||||||
\(14\) | 2.38417 | 0.637195 | ||||||||
\(15\) | −0.832996 | −0.215079 | ||||||||
\(16\) | 0.718355 | + | 1.24423i | 0.179589 | + | 0.311057i | ||||
\(17\) | 2.57744 | + | 4.46426i | 0.625122 | + | 1.08274i | 0.988517 | + | 0.151107i | \(0.0482840\pi\) |
−0.363396 | + | 0.931635i | \(0.618383\pi\) | |||||||
\(18\) | 0.527336 | + | 0.913372i | 0.124294 | + | 0.215284i | ||||
\(19\) | −0.939269 | − | 1.62686i | −0.215483 | − | 0.373228i | 0.737939 | − | 0.674868i | \(-0.235799\pi\) |
−0.953422 | + | 0.301640i | \(0.902466\pi\) | |||||||
\(20\) | 0.369712 | − | 0.640360i | 0.0826701 | − | 0.143189i | ||||
\(21\) | −1.13029 | + | 1.95772i | −0.246649 | + | 0.427209i | ||||
\(22\) | −1.50563 | −0.321001 | ||||||||
\(23\) | −1.55467 | − | 2.69277i | −0.324171 | − | 0.561481i | 0.657173 | − | 0.753740i | \(-0.271752\pi\) |
−0.981344 | + | 0.192258i | \(0.938419\pi\) | |||||||
\(24\) | −3.04554 | −0.621669 | ||||||||
\(25\) | −4.30612 | −0.861224 | ||||||||
\(26\) | −0.325873 | + | 0.564428i | −0.0639089 | + | 0.110694i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00332 | − | 1.73780i | −0.189610 | − | 0.328414i | ||||
\(29\) | −0.962039 | + | 1.66630i | −0.178646 | + | 0.309424i | −0.941417 | − | 0.337245i | \(-0.890505\pi\) |
0.762771 | + | 0.646669i | \(0.223838\pi\) | |||||||
\(30\) | −0.439269 | − | 0.760836i | −0.0801991 | − | 0.138909i | ||||
\(31\) | −0.286210 | + | 0.495730i | −0.0514048 | + | 0.0890357i | −0.890583 | − | 0.454821i | \(-0.849703\pi\) |
0.839178 | + | 0.543857i | \(0.183037\pi\) | |||||||
\(32\) | 2.28791 | − | 3.96278i | 0.404450 | − | 0.700527i | ||||
\(33\) | 0.713790 | − | 1.23632i | 0.124255 | − | 0.215216i | ||||
\(34\) | −2.71836 | + | 4.70833i | −0.466194 | + | 0.807472i | ||||
\(35\) | 0.941526 | − | 1.63077i | 0.159147 | − | 0.275650i | ||||
\(36\) | 0.443834 | − | 0.768743i | 0.0739723 | − | 0.128124i | ||||
\(37\) | −2.67890 | − | 4.63999i | −0.440408 | − | 0.762810i | 0.557311 | − | 0.830304i | \(-0.311833\pi\) |
−0.997720 | + | 0.0674938i | \(0.978500\pi\) | |||||||
\(38\) | 0.990620 | − | 1.71580i | 0.160700 | − | 0.278340i | ||||
\(39\) | −0.308980 | − | 0.535170i | −0.0494765 | − | 0.0856958i | ||||
\(40\) | 2.53692 | 0.401123 | ||||||||
\(41\) | −4.25132 | + | 7.36350i | −0.663945 | + | 1.14999i | 0.315626 | + | 0.948884i | \(0.397786\pi\) |
−0.979570 | + | 0.201102i | \(0.935548\pi\) | |||||||
\(42\) | −2.38417 | −0.367885 | ||||||||
\(43\) | −7.16863 | −1.09321 | −0.546603 | − | 0.837392i | \(-0.684079\pi\) | ||||
−0.546603 | + | 0.837392i | \(0.684079\pi\) | |||||||
\(44\) | 0.633608 | + | 1.09744i | 0.0955201 | + | 0.165446i | ||||
\(45\) | 0.832996 | 0.124176 | ||||||||
\(46\) | 1.63967 | − | 2.83999i | 0.241756 | − | 0.418733i | ||||
\(47\) | 0.624228 | − | 1.08120i | 0.0910531 | − | 0.157709i | −0.816901 | − | 0.576777i | \(-0.804310\pi\) |
0.907955 | + | 0.419069i | \(0.137643\pi\) | |||||||
\(48\) | −0.718355 | − | 1.24423i | −0.103686 | − | 0.179589i | ||||
\(49\) | 0.944897 | + | 1.63661i | 0.134985 | + | 0.233801i | ||||
\(50\) | −2.27077 | − | 3.93309i | −0.321135 | − | 0.556223i | ||||
\(51\) | −2.57744 | − | 4.46426i | −0.360914 | − | 0.625122i | ||||
\(52\) | 0.548544 | 0.0760694 | ||||||||
\(53\) | −4.80713 | −0.660310 | −0.330155 | − | 0.943927i | \(-0.607101\pi\) | ||||
−0.330155 | + | 0.943927i | \(0.607101\pi\) | |||||||
\(54\) | −0.527336 | − | 0.913372i | −0.0717613 | − | 0.124294i | ||||
\(55\) | −0.594584 | + | 1.02985i | −0.0801737 | + | 0.138865i | ||||
\(56\) | 3.44234 | − | 5.96231i | 0.460002 | − | 0.796747i | ||||
\(57\) | 0.939269 | + | 1.62686i | 0.124409 | + | 0.215483i | ||||
\(58\) | −2.02927 | −0.266456 | ||||||||
\(59\) | 7.75196 | 1.00922 | 0.504610 | − | 0.863348i | \(-0.331636\pi\) | ||||
0.504610 | + | 0.863348i | \(0.331636\pi\) | |||||||
\(60\) | −0.369712 | + | 0.640360i | −0.0477296 | + | 0.0826701i | ||||
\(61\) | −1.96992 | − | 3.41201i | −0.252223 | − | 0.436863i | 0.711915 | − | 0.702266i | \(-0.247828\pi\) |
−0.964138 | + | 0.265403i | \(0.914495\pi\) | |||||||
\(62\) | −0.603715 | −0.0766719 | ||||||||
\(63\) | 1.13029 | − | 1.95772i | 0.142403 | − | 0.246649i | ||||
\(64\) | 7.69941 | 0.962427 | ||||||||
\(65\) | 0.257379 | + | 0.445794i | 0.0319240 | + | 0.0552940i | ||||
\(66\) | 1.50563 | 0.185330 | ||||||||
\(67\) | −7.67540 | − | 2.84399i | −0.937699 | − | 0.347448i | ||||
\(68\) | 4.57582 | 0.554900 | ||||||||
\(69\) | 1.55467 | + | 2.69277i | 0.187160 | + | 0.324171i | ||||
\(70\) | 1.98600 | 0.237372 | ||||||||
\(71\) | −4.64824 | + | 8.05099i | −0.551645 | + | 0.955477i | 0.446511 | + | 0.894778i | \(0.352666\pi\) |
−0.998156 | + | 0.0606992i | \(0.980667\pi\) | |||||||
\(72\) | 3.04554 | 0.358920 | ||||||||
\(73\) | 7.88356 | + | 13.6547i | 0.922701 | + | 1.59816i | 0.795218 | + | 0.606324i | \(0.207357\pi\) |
0.127483 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(74\) | 2.82536 | − | 4.89367i | 0.328441 | − | 0.568877i | ||||
\(75\) | 4.30612 | 0.497228 | ||||||||
\(76\) | −1.66752 | −0.191277 | ||||||||
\(77\) | 1.61358 | + | 2.79480i | 0.183884 | + | 0.318497i | ||||
\(78\) | 0.325873 | − | 0.564428i | 0.0368978 | − | 0.0639089i | ||||
\(79\) | −0.745691 | + | 1.29158i | −0.0838968 | + | 0.145314i | −0.904921 | − | 0.425580i | \(-0.860070\pi\) |
0.821024 | + | 0.570894i | \(0.193403\pi\) | |||||||
\(80\) | 0.598387 | + | 1.03644i | 0.0669017 | + | 0.115877i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.96749 | −0.990294 | ||||||||
\(83\) | −0.355767 | − | 0.616206i | −0.0390505 | − | 0.0676374i | 0.845840 | − | 0.533437i | \(-0.179100\pi\) |
−0.884890 | + | 0.465800i | \(0.845767\pi\) | |||||||
\(84\) | 1.00332 | + | 1.73780i | 0.109471 | + | 0.189610i | ||||
\(85\) | 2.14700 | + | 3.71871i | 0.232875 | + | 0.403351i | ||||
\(86\) | −3.78028 | − | 6.54763i | −0.407638 | − | 0.706049i | ||||
\(87\) | 0.962039 | − | 1.66630i | 0.103141 | − | 0.178646i | ||||
\(88\) | −2.17388 | + | 3.76527i | −0.231736 | + | 0.401379i | ||||
\(89\) | −0.514759 | −0.0545643 | −0.0272822 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272822 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(90\) | 0.439269 | + | 0.760836i | 0.0463030 | + | 0.0801991i | ||||
\(91\) | 1.39695 | 0.146440 | ||||||||
\(92\) | −2.76006 | −0.287757 | ||||||||
\(93\) | 0.286210 | − | 0.495730i | 0.0296786 | − | 0.0514048i | ||||
\(94\) | 1.31671 | 0.135808 | ||||||||
\(95\) | −0.782407 | − | 1.35517i | −0.0802733 | − | 0.139037i | ||||
\(96\) | −2.28791 | + | 3.96278i | −0.233509 | + | 0.404450i | ||||
\(97\) | 0.590375 | + | 1.02256i | 0.0599435 | + | 0.103825i | 0.894440 | − | 0.447188i | \(-0.147575\pi\) |
−0.834496 | + | 0.551014i | \(0.814241\pi\) | |||||||
\(98\) | −0.996556 | + | 1.72609i | −0.100667 | + | 0.174361i | ||||
\(99\) | −0.713790 | + | 1.23632i | −0.0717386 | + | 0.124255i | ||||
\(100\) | −1.91120 | + | 3.31030i | −0.191120 | + | 0.331030i | ||||
\(101\) | −5.28898 | + | 9.16077i | −0.526273 | + | 0.911531i | 0.473259 | + | 0.880923i | \(0.343078\pi\) |
−0.999531 | + | 0.0306077i | \(0.990256\pi\) | |||||||
\(102\) | 2.71836 | − | 4.70833i | 0.269157 | − | 0.466194i | ||||
\(103\) | 6.21562 | − | 10.7658i | 0.612443 | − | 1.06078i | −0.378385 | − | 0.925648i | \(-0.623520\pi\) |
0.990827 | − | 0.135134i | \(-0.0431464\pi\) | |||||||
\(104\) | 0.941013 | + | 1.62988i | 0.0922739 | + | 0.159823i | ||||
\(105\) | −0.941526 | + | 1.63077i | −0.0918835 | + | 0.159147i | ||||
\(106\) | −2.53497 | − | 4.39070i | −0.246218 | − | 0.426462i | ||||
\(107\) | −13.4452 | −1.29980 | −0.649900 | − | 0.760020i | \(-0.725189\pi\) | ||||
−0.649900 | + | 0.760020i | \(0.725189\pi\) | |||||||
\(108\) | −0.443834 | + | 0.768743i | −0.0427079 | + | 0.0739723i | ||||
\(109\) | 17.6159 | 1.68730 | 0.843648 | − | 0.536897i | \(-0.180404\pi\) | ||||
0.843648 | + | 0.536897i | \(0.180404\pi\) | |||||||
\(110\) | −1.25418 | −0.119582 | ||||||||
\(111\) | 2.67890 | + | 4.63999i | 0.254270 | + | 0.440408i | ||||
\(112\) | 3.24779 | 0.306888 | ||||||||
\(113\) | 2.90861 | − | 5.03786i | 0.273619 | − | 0.473922i | −0.696167 | − | 0.717880i | \(-0.745113\pi\) |
0.969786 | + | 0.243958i | \(0.0784458\pi\) | |||||||
\(114\) | −0.990620 | + | 1.71580i | −0.0927801 | + | 0.160700i | ||||
\(115\) | −1.29504 | − | 2.24307i | −0.120763 | − | 0.209167i | ||||
\(116\) | 0.853971 | + | 1.47912i | 0.0792892 | + | 0.137333i | ||||
\(117\) | 0.308980 | + | 0.535170i | 0.0285653 | + | 0.0494765i | ||||
\(118\) | 4.08789 | + | 7.08043i | 0.376320 | + | 0.651806i | ||||
\(119\) | 11.6530 | 1.06823 | ||||||||
\(120\) | −2.53692 | −0.231588 | ||||||||
\(121\) | 4.48101 | + | 7.76133i | 0.407364 | + | 0.705576i | ||||
\(122\) | 2.07762 | − | 3.59855i | 0.188099 | − | 0.325797i | ||||
\(123\) | 4.25132 | − | 7.36350i | 0.383329 | − | 0.663945i | ||||
\(124\) | 0.254059 | + | 0.440043i | 0.0228152 | + | 0.0395171i | ||||
\(125\) | −7.75196 | −0.693356 | ||||||||
\(126\) | 2.38417 | 0.212398 | ||||||||
\(127\) | 8.35473 | − | 14.4708i | 0.741362 | − | 1.28408i | −0.210513 | − | 0.977591i | \(-0.567513\pi\) |
0.951875 | − | 0.306486i | \(-0.0991533\pi\) | |||||||
\(128\) | −0.515648 | − | 0.893128i | −0.0455772 | − | 0.0789421i | ||||
\(129\) | 7.16863 | 0.631163 | ||||||||
\(130\) | −0.271451 | + | 0.470167i | −0.0238078 | + | 0.0412363i | ||||
\(131\) | −6.06892 | −0.530244 | −0.265122 | − | 0.964215i | \(-0.585412\pi\) | ||||
−0.265122 | + | 0.964215i | \(0.585412\pi\) | |||||||
\(132\) | −0.633608 | − | 1.09744i | −0.0551485 | − | 0.0955201i | ||||
\(133\) | −4.24658 | −0.368225 | ||||||||
\(134\) | −1.44989 | − | 8.51023i | −0.125252 | − | 0.735172i | ||||
\(135\) | −0.832996 | −0.0716929 | ||||||||
\(136\) | 7.84971 | + | 13.5961i | 0.673107 | + | 1.16586i | ||||
\(137\) | 5.12537 | 0.437890 | 0.218945 | − | 0.975737i | \(-0.429739\pi\) | ||||
0.218945 | + | 0.975737i | \(0.429739\pi\) | |||||||
\(138\) | −1.63967 | + | 2.83999i | −0.139578 | + | 0.241756i | ||||
\(139\) | 20.9364 | 1.77580 | 0.887899 | − | 0.460037i | \(-0.152164\pi\) | ||||
0.887899 | + | 0.460037i | \(0.152164\pi\) | |||||||
\(140\) | −0.835762 | − | 1.44758i | −0.0706348 | − | 0.122343i | ||||
\(141\) | −0.624228 | + | 1.08120i | −0.0525695 | + | 0.0910531i | ||||
\(142\) | −9.80474 | −0.822796 | ||||||||
\(143\) | −0.882189 | −0.0737723 | ||||||||
\(144\) | 0.718355 | + | 1.24423i | 0.0598629 | + | 0.103686i | ||||
\(145\) | −0.801375 | + | 1.38802i | −0.0665506 | + | 0.115269i | ||||
\(146\) | −8.31457 | + | 14.4013i | −0.688118 | + | 1.19186i | ||||
\(147\) | −0.944897 | − | 1.63661i | −0.0779338 | − | 0.134985i | ||||
\(148\) | −4.75595 | −0.390936 | ||||||||
\(149\) | 1.46100 | 0.119690 | 0.0598450 | − | 0.998208i | \(-0.480939\pi\) | ||||
0.0598450 | + | 0.998208i | \(0.480939\pi\) | |||||||
\(150\) | 2.27077 | + | 3.93309i | 0.185408 | + | 0.321135i | ||||
\(151\) | −4.04073 | − | 6.99874i | −0.328830 | − | 0.569550i | 0.653450 | − | 0.756969i | \(-0.273321\pi\) |
−0.982280 | + | 0.187420i | \(0.939988\pi\) | |||||||
\(152\) | −2.86058 | − | 4.95467i | −0.232024 | − | 0.401877i | ||||
\(153\) | 2.57744 | + | 4.46426i | 0.208374 | + | 0.360914i | ||||
\(154\) | −1.70179 | + | 2.94759i | −0.137134 | + | 0.237524i | ||||
\(155\) | −0.238412 | + | 0.412941i | −0.0191497 | + | 0.0331682i | ||||
\(156\) | −0.548544 | −0.0439187 | ||||||||
\(157\) | −7.92335 | − | 13.7236i | −0.632352 | − | 1.09527i | −0.987070 | − | 0.160292i | \(-0.948756\pi\) |
0.354718 | − | 0.934973i | \(-0.384577\pi\) | |||||||
\(158\) | −1.57292 | −0.125135 | ||||||||
\(159\) | 4.80713 | 0.381230 | ||||||||
\(160\) | 1.90582 | − | 3.30098i | 0.150668 | − | 0.260965i | ||||
\(161\) | −7.02891 | −0.553956 | ||||||||
\(162\) | 0.527336 | + | 0.913372i | 0.0414314 | + | 0.0717613i | ||||
\(163\) | 7.13366 | − | 12.3559i | 0.558751 | − | 0.967786i | −0.438850 | − | 0.898560i | \(-0.644614\pi\) |
0.997601 | − | 0.0692253i | \(-0.0220527\pi\) | |||||||
\(164\) | 3.77376 | + | 6.53634i | 0.294681 | + | 0.510403i | ||||
\(165\) | 0.594584 | − | 1.02985i | 0.0462883 | − | 0.0801737i | ||||
\(166\) | 0.375217 | − | 0.649895i | 0.0291225 | − | 0.0504416i | ||||
\(167\) | 1.47723 | − | 2.55864i | 0.114311 | − | 0.197993i | −0.803193 | − | 0.595719i | \(-0.796867\pi\) |
0.917504 | + | 0.397726i | \(0.130200\pi\) | |||||||
\(168\) | −3.44234 | + | 5.96231i | −0.265582 | + | 0.460002i | ||||
\(169\) | 6.30906 | − | 10.9276i | 0.485312 | − | 0.840586i | ||||
\(170\) | −2.26438 | + | 3.92202i | −0.173670 | + | 0.300805i | ||||
\(171\) | −0.939269 | − | 1.62686i | −0.0718277 | − | 0.124409i | ||||
\(172\) | −3.18168 | + | 5.51083i | −0.242601 | + | 0.420197i | ||||
\(173\) | −11.5206 | − | 19.9543i | −0.875895 | − | 1.51709i | −0.855807 | − | 0.517296i | \(-0.826939\pi\) |
−0.0200880 | − | 0.999798i | \(-0.506395\pi\) | |||||||
\(174\) | 2.02927 | 0.153839 | ||||||||
\(175\) | −4.86715 | + | 8.43016i | −0.367922 | + | 0.637260i | ||||
\(176\) | −2.05102 | −0.154601 | ||||||||
\(177\) | −7.75196 | −0.582673 | ||||||||
\(178\) | −0.271451 | − | 0.470167i | −0.0203461 | − | 0.0352405i | ||||
\(179\) | −10.6867 | −0.798761 | −0.399380 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399380 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(180\) | 0.369712 | − | 0.640360i | 0.0275567 | − | 0.0477296i | ||||
\(181\) | −4.37430 | + | 7.57652i | −0.325139 | + | 0.563158i | −0.981541 | − | 0.191254i | \(-0.938745\pi\) |
0.656401 | + | 0.754412i | \(0.272078\pi\) | |||||||
\(182\) | 0.736661 | + | 1.27593i | 0.0546049 | + | 0.0945785i | ||||
\(183\) | 1.96992 | + | 3.41201i | 0.145621 | + | 0.252223i | ||||
\(184\) | −4.73482 | − | 8.20094i | −0.349055 | − | 0.604582i | ||||
\(185\) | −2.23151 | − | 3.86509i | −0.164064 | − | 0.284167i | ||||
\(186\) | 0.603715 | 0.0442665 | ||||||||
\(187\) | −7.35901 | −0.538144 | ||||||||
\(188\) | −0.554107 | − | 0.959742i | −0.0404124 | − | 0.0699964i | ||||
\(189\) | −1.13029 | + | 1.95772i | −0.0822164 | + | 0.142403i | ||||
\(190\) | 0.825183 | − | 1.42926i | 0.0598650 | − | 0.103689i | ||||
\(191\) | −8.08452 | − | 14.0028i | −0.584976 | − | 1.01321i | −0.994878 | − | 0.101078i | \(-0.967771\pi\) |
0.409903 | − | 0.912129i | \(-0.365563\pi\) | |||||||
\(192\) | −7.69941 | −0.555657 | ||||||||
\(193\) | 7.15854 | 0.515283 | 0.257641 | − | 0.966241i | \(-0.417055\pi\) | ||||
0.257641 | + | 0.966241i | \(0.417055\pi\) | |||||||
\(194\) | −0.622652 | + | 1.07847i | −0.0447038 | + | 0.0774293i | ||||
\(195\) | −0.257379 | − | 0.445794i | −0.0184313 | − | 0.0319240i | ||||
\(196\) | 1.67751 | 0.119822 | ||||||||
\(197\) | 0.218605 | − | 0.378635i | 0.0155750 | − | 0.0269766i | −0.858133 | − | 0.513428i | \(-0.828375\pi\) |
0.873708 | + | 0.486451i | \(0.161709\pi\) | |||||||
\(198\) | −1.50563 | −0.107000 | ||||||||
\(199\) | 8.10268 | + | 14.0342i | 0.574384 | + | 0.994862i | 0.996108 | + | 0.0881377i | \(0.0280915\pi\) |
−0.421725 | + | 0.906724i | \(0.638575\pi\) | |||||||
\(200\) | −13.1145 | −0.927332 | ||||||||
\(201\) | 7.67540 | + | 2.84399i | 0.541381 | + | 0.200599i | ||||
\(202\) | −11.1563 | −0.784952 | ||||||||
\(203\) | 2.17476 | + | 3.76680i | 0.152638 | + | 0.264378i | ||||
\(204\) | −4.57582 | −0.320372 | ||||||||
\(205\) | −3.54133 | + | 6.13377i | −0.247337 | + | 0.428401i | ||||
\(206\) | 13.1109 | 0.913477 | ||||||||
\(207\) | −1.55467 | − | 2.69277i | −0.108057 | − | 0.187160i | ||||
\(208\) | −0.443916 | + | 0.768884i | −0.0307800 | + | 0.0533125i | ||||
\(209\) | 2.68176 | 0.185501 | ||||||||
\(210\) | −1.98600 | −0.137047 | ||||||||
\(211\) | −2.15714 | − | 3.73628i | −0.148504 | − | 0.257216i | 0.782171 | − | 0.623064i | \(-0.214112\pi\) |
−0.930675 | + | 0.365848i | \(0.880779\pi\) | |||||||
\(212\) | −2.13357 | + | 3.69545i | −0.146534 | + | 0.253804i | ||||
\(213\) | 4.64824 | − | 8.05099i | 0.318492 | − | 0.551645i | ||||
\(214\) | −7.09015 | − | 12.2805i | −0.484673 | − | 0.839478i | ||||
\(215\) | −5.97144 | −0.407249 | ||||||||
\(216\) | −3.04554 | −0.207223 | ||||||||
\(217\) | 0.646999 | + | 1.12064i | 0.0439212 | + | 0.0760737i | ||||
\(218\) | 9.28949 | + | 16.0899i | 0.629164 | + | 1.08974i | ||||
\(219\) | −7.88356 | − | 13.6547i | −0.532722 | − | 0.922701i | ||||
\(220\) | 0.527793 | + | 0.914165i | 0.0355838 | + | 0.0616330i | ||||
\(221\) | −1.59276 | + | 2.75874i | −0.107141 | + | 0.185573i | ||||
\(222\) | −2.82536 | + | 4.89367i | −0.189626 | + | 0.328441i | ||||
\(223\) | −18.9649 | −1.26998 | −0.634992 | − | 0.772518i | \(-0.718997\pi\) | ||||
−0.634992 | + | 0.772518i | \(0.718997\pi\) | |||||||
\(224\) | −5.17200 | − | 8.95817i | −0.345569 | − | 0.598543i | ||||
\(225\) | −4.30612 | −0.287075 | ||||||||
\(226\) | 6.13526 | 0.408112 | ||||||||
\(227\) | −1.90313 | + | 3.29632i | −0.126315 | + | 0.218785i | −0.922246 | − | 0.386603i | \(-0.873648\pi\) |
0.795931 | + | 0.605387i | \(0.206982\pi\) | |||||||
\(228\) | 1.66752 | 0.110434 | ||||||||
\(229\) | 6.42081 | + | 11.1212i | 0.424299 | + | 0.734908i | 0.996355 | − | 0.0853070i | \(-0.0271871\pi\) |
−0.572055 | + | 0.820215i | \(0.693854\pi\) | |||||||
\(230\) | 1.36584 | − | 2.36570i | 0.0900606 | − | 0.155990i | ||||
\(231\) | −1.61358 | − | 2.79480i | −0.106166 | − | 0.183884i | ||||
\(232\) | −2.92993 | + | 5.07479i | −0.192359 | + | 0.333176i | ||||
\(233\) | −4.61173 | + | 7.98774i | −0.302124 | + | 0.523295i | −0.976617 | − | 0.214987i | \(-0.931029\pi\) |
0.674493 | + | 0.738282i | \(0.264362\pi\) | |||||||
\(234\) | −0.325873 | + | 0.564428i | −0.0213030 | + | 0.0368978i | ||||
\(235\) | 0.519980 | − | 0.900632i | 0.0339197 | − | 0.0587507i | ||||
\(236\) | 3.44058 | − | 5.95926i | 0.223963 | − | 0.387915i | ||||
\(237\) | 0.745691 | − | 1.29158i | 0.0484378 | − | 0.0838968i | ||||
\(238\) | 6.14505 | + | 10.6435i | 0.398324 | + | 0.689918i | ||||
\(239\) | −9.01312 | + | 15.6112i | −0.583010 | + | 1.00980i | 0.412110 | + | 0.911134i | \(0.364792\pi\) |
−0.995120 | + | 0.0986690i | \(0.968541\pi\) | |||||||
\(240\) | −0.598387 | − | 1.03644i | −0.0386257 | − | 0.0669017i | ||||
\(241\) | −3.90380 | −0.251466 | −0.125733 | − | 0.992064i | \(-0.540128\pi\) | ||||
−0.125733 | + | 0.992064i | \(0.540128\pi\) | |||||||
\(242\) | −4.72599 | + | 8.18566i | −0.303798 | + | 0.526194i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.49728 | −0.223890 | ||||||||
\(245\) | 0.787096 | + | 1.36329i | 0.0502857 | + | 0.0870974i | ||||
\(246\) | 8.96749 | 0.571746 | ||||||||
\(247\) | 0.580431 | − | 1.00534i | 0.0369320 | − | 0.0639680i | ||||
\(248\) | −0.871664 | + | 1.50977i | −0.0553507 | + | 0.0958702i | ||||
\(249\) | 0.355767 | + | 0.616206i | 0.0225458 | + | 0.0390505i | ||||
\(250\) | −4.08789 | − | 7.08043i | −0.258541 | − | 0.447805i | ||||
\(251\) | 9.53385 | + | 16.5131i | 0.601771 | + | 1.04230i | 0.992553 | + | 0.121815i | \(0.0388715\pi\) |
−0.390781 | + | 0.920484i | \(0.627795\pi\) | |||||||
\(252\) | −1.00332 | − | 1.73780i | −0.0632032 | − | 0.109471i | ||||
\(253\) | 4.43884 | 0.279067 | ||||||||
\(254\) | 17.6230 | 1.10576 | ||||||||
\(255\) | −2.14700 | − | 3.71871i | −0.134450 | − | 0.232875i | ||||
\(256\) | 8.24325 | − | 14.2777i | 0.515203 | − | 0.892358i | ||||
\(257\) | 14.3517 | − | 24.8579i | 0.895237 | − | 1.55060i | 0.0617259 | − | 0.998093i | \(-0.480340\pi\) |
0.833511 | − | 0.552503i | \(-0.186327\pi\) | |||||||
\(258\) | 3.78028 | + | 6.54763i | 0.235350 | + | 0.407638i | ||||
\(259\) | −12.1117 | −0.752585 | ||||||||
\(260\) | 0.456935 | 0.0283379 | ||||||||
\(261\) | −0.962039 | + | 1.66630i | −0.0595487 | + | 0.103141i | ||||
\(262\) | −3.20036 | − | 5.54318i | −0.197719 | − | 0.342459i | ||||
\(263\) | 28.5607 | 1.76113 | 0.880565 | − | 0.473926i | \(-0.157164\pi\) | ||||
0.880565 | + | 0.473926i | \(0.157164\pi\) | |||||||
\(264\) | 2.17388 | − | 3.76527i | 0.133793 | − | 0.231736i | ||||
\(265\) | −4.00432 | −0.245983 | ||||||||
\(266\) | −2.23937 | − | 3.87871i | −0.137305 | − | 0.237819i | ||||
\(267\) | 0.514759 | 0.0315027 | ||||||||
\(268\) | −5.59290 | + | 4.63815i | −0.341640 | + | 0.283320i | ||||
\(269\) | 32.3731 | 1.97382 | 0.986912 | − | 0.161259i | \(-0.0515554\pi\) | ||||
0.986912 | + | 0.161259i | \(0.0515554\pi\) | |||||||
\(270\) | −0.439269 | − | 0.760836i | −0.0267330 | − | 0.0463030i | ||||
\(271\) | 21.0856 | 1.28086 | 0.640429 | − | 0.768018i | \(-0.278757\pi\) | ||||
0.640429 | + | 0.768018i | \(0.278757\pi\) | |||||||
\(272\) | −3.70304 | + | 6.41385i | −0.224530 | + | 0.388897i | ||||
\(273\) | −1.39695 | −0.0845471 | ||||||||
\(274\) | 2.70279 | + | 4.68137i | 0.163281 | + | 0.282812i | ||||
\(275\) | 3.07366 | − | 5.32374i | 0.185349 | − | 0.321034i | ||||
\(276\) | 2.76006 | 0.166136 | ||||||||
\(277\) | −12.7228 | −0.764438 | −0.382219 | − | 0.924072i | \(-0.624840\pi\) | ||||
−0.382219 | + | 0.924072i | \(0.624840\pi\) | |||||||
\(278\) | 11.0405 | + | 19.1227i | 0.662165 | + | 1.14690i | ||||
\(279\) | −0.286210 | + | 0.495730i | −0.0171349 | + | 0.0296786i | ||||
\(280\) | 2.86745 | − | 4.96658i | 0.171363 | − | 0.296810i | ||||
\(281\) | −7.58597 | − | 13.1393i | −0.452541 | − | 0.783824i | 0.546002 | − | 0.837784i | \(-0.316149\pi\) |
−0.998543 | + | 0.0539600i | \(0.982816\pi\) | |||||||
\(282\) | −1.31671 | −0.0784091 | ||||||||
\(283\) | −18.9563 | −1.12684 | −0.563419 | − | 0.826172i | \(-0.690514\pi\) | ||||
−0.563419 | + | 0.826172i | \(0.690514\pi\) | |||||||
\(284\) | 4.12610 | + | 7.14661i | 0.244839 | + | 0.424073i | ||||
\(285\) | 0.782407 | + | 1.35517i | 0.0463458 | + | 0.0802733i | ||||
\(286\) | −0.465210 | − | 0.805767i | −0.0275084 | − | 0.0476460i | ||||
\(287\) | 9.61043 | + | 16.6458i | 0.567286 | + | 0.982568i | ||||
\(288\) | 2.28791 | − | 3.96278i | 0.134817 | − | 0.233509i | ||||
\(289\) | −4.78642 | + | 8.29032i | −0.281554 | + | 0.487666i | ||||
\(290\) | −1.69037 | −0.0992622 | ||||||||
\(291\) | −0.590375 | − | 1.02256i | −0.0346084 | − | 0.0599435i | ||||
\(292\) | 13.9960 | 0.819052 | ||||||||
\(293\) | 31.2734 | 1.82701 | 0.913506 | − | 0.406825i | \(-0.133364\pi\) | ||||
0.913506 | + | 0.406825i | \(0.133364\pi\) | |||||||
\(294\) | 0.996556 | − | 1.72609i | 0.0581203 | − | 0.100667i | ||||
\(295\) | 6.45735 | 0.375961 | ||||||||
\(296\) | −8.15870 | − | 14.1313i | −0.474215 | − | 0.821364i | ||||
\(297\) | 0.713790 | − | 1.23632i | 0.0414183 | − | 0.0717386i | ||||
\(298\) | 0.770439 | + | 1.33444i | 0.0446303 | + | 0.0773020i | ||||
\(299\) | 0.960726 | − | 1.66403i | 0.0555602 | − | 0.0962332i | ||||
\(300\) | 1.91120 | − | 3.31030i | 0.110343 | − | 0.191120i | ||||
\(301\) | −8.10262 | + | 14.0341i | −0.467027 | + | 0.808915i | ||||
\(302\) | 4.26164 | − | 7.38138i | 0.245230 | − | 0.424750i | ||||
\(303\) | 5.28898 | − | 9.16077i | 0.303844 | − | 0.526273i | ||||
\(304\) | 1.34946 | − | 2.33733i | 0.0773967 | − | 0.134055i | ||||
\(305\) | −1.64094 | − | 2.84219i | −0.0939599 | − | 0.162743i | ||||
\(306\) | −2.71836 | + | 4.70833i | −0.155398 | + | 0.269157i | ||||
\(307\) | −5.85184 | − | 10.1357i | −0.333982 | − | 0.578474i | 0.649307 | − | 0.760527i | \(-0.275059\pi\) |
−0.983289 | + | 0.182053i | \(0.941726\pi\) | |||||||
\(308\) | 2.86464 | 0.163228 | ||||||||
\(309\) | −6.21562 | + | 10.7658i | −0.353594 | + | 0.612443i | ||||
\(310\) | −0.502892 | −0.0285623 | ||||||||
\(311\) | −0.574859 | −0.0325973 | −0.0162986 | − | 0.999867i | \(-0.505188\pi\) | ||||
−0.0162986 | + | 0.999867i | \(0.505188\pi\) | |||||||
\(312\) | −0.941013 | − | 1.62988i | −0.0532744 | − | 0.0922739i | ||||
\(313\) | 6.04001 | 0.341402 | 0.170701 | − | 0.985323i | \(-0.445397\pi\) | ||||
0.170701 | + | 0.985323i | \(0.445397\pi\) | |||||||
\(314\) | 8.35653 | − | 14.4739i | 0.471586 | − | 0.816811i | ||||
\(315\) | 0.941526 | − | 1.63077i | 0.0530490 | − | 0.0918835i | ||||
\(316\) | 0.661926 | + | 1.14649i | 0.0372362 | + | 0.0644951i | ||||
\(317\) | −3.10752 | − | 5.38238i | −0.174536 | − | 0.302304i | 0.765465 | − | 0.643478i | \(-0.222509\pi\) |
−0.940000 | + | 0.341173i | \(0.889176\pi\) | |||||||
\(318\) | 2.53497 | + | 4.39070i | 0.142154 | + | 0.246218i | ||||
\(319\) | −1.37339 | − | 2.37878i | −0.0768950 | − | 0.133186i | ||||
\(320\) | 6.41358 | 0.358530 | ||||||||
\(321\) | 13.4452 | 0.750440 | ||||||||
\(322\) | −3.70660 | − | 6.42001i | −0.206560 | − | 0.357773i | ||||
\(323\) | 4.84182 | − | 8.38628i | 0.269406 | − | 0.466625i | ||||
\(324\) | 0.443834 | − | 0.768743i | 0.0246574 | − | 0.0427079i | ||||
\(325\) | −1.33051 | − | 2.30450i | −0.0738032 | − | 0.127831i | ||||
\(326\) | 15.0473 | 0.833395 | ||||||||
\(327\) | −17.6159 | −0.974161 | ||||||||
\(328\) | −12.9476 | + | 22.4258i | −0.714910 | + | 1.23826i | ||||
\(329\) | −1.41112 | − | 2.44412i | −0.0777974 | − | 0.134749i | ||||
\(330\) | 1.25418 | 0.0690405 | ||||||||
\(331\) | 1.65108 | − | 2.85976i | 0.0907517 | − | 0.157186i | −0.817076 | − | 0.576530i | \(-0.804406\pi\) |
0.907828 | + | 0.419344i | \(0.137740\pi\) | |||||||
\(332\) | −0.631605 | −0.0346638 | ||||||||
\(333\) | −2.67890 | − | 4.63999i | −0.146803 | − | 0.254270i | ||||
\(334\) | 3.11598 | 0.170499 | ||||||||
\(335\) | −6.39358 | − | 2.36903i | −0.349318 | − | 0.129434i | ||||
\(336\) | −3.24779 | −0.177182 | ||||||||
\(337\) | 15.2528 | + | 26.4186i | 0.830871 | + | 1.43911i | 0.897348 | + | 0.441324i | \(0.145491\pi\) |
−0.0664766 | + | 0.997788i | \(0.521176\pi\) | |||||||
\(338\) | 13.3080 | 0.723859 | ||||||||
\(339\) | −2.90861 | + | 5.03786i | −0.157974 | + | 0.273619i | ||||
\(340\) | 3.81164 | 0.206715 | ||||||||
\(341\) | −0.408588 | − | 0.707694i | −0.0221263 | − | 0.0383238i | ||||
\(342\) | 0.990620 | − | 1.71580i | 0.0535666 | − | 0.0927801i | ||||
\(343\) | 20.0961 | 1.08509 | ||||||||
\(344\) | −21.8324 | −1.17712 | ||||||||
\(345\) | 1.29504 | + | 2.24307i | 0.0697224 | + | 0.120763i | ||||
\(346\) | 12.1504 | − | 21.0452i | 0.653212 | − | 1.13140i | ||||
\(347\) | −7.38767 | + | 12.7958i | −0.396591 | + | 0.686915i | −0.993303 | − | 0.115540i | \(-0.963140\pi\) |
0.596712 | + | 0.802455i | \(0.296473\pi\) | |||||||
\(348\) | −0.853971 | − | 1.47912i | −0.0457777 | − | 0.0792892i | ||||
\(349\) | −29.0181 | −1.55330 | −0.776651 | − | 0.629931i | \(-0.783083\pi\) | ||||
−0.776651 | + | 0.629931i | \(0.783083\pi\) | |||||||
\(350\) | −10.2665 | −0.548767 | ||||||||
\(351\) | −0.308980 | − | 0.535170i | −0.0164922 | − | 0.0285653i | ||||
\(352\) | 3.26618 | + | 5.65719i | 0.174088 | + | 0.301529i | ||||
\(353\) | −3.46490 | − | 6.00139i | −0.184418 | − | 0.319422i | 0.758962 | − | 0.651135i | \(-0.225707\pi\) |
−0.943380 | + | 0.331713i | \(0.892373\pi\) | |||||||
\(354\) | −4.08789 | − | 7.08043i | −0.217269 | − | 0.376320i | ||||
\(355\) | −3.87197 | + | 6.70645i | −0.205503 | + | 0.355941i | ||||
\(356\) | −0.228467 | + | 0.395717i | −0.0121088 | + | 0.0209730i | ||||
\(357\) | −11.6530 | −0.616743 | ||||||||
\(358\) | −5.63548 | − | 9.76093i | −0.297844 | − | 0.515881i | ||||
\(359\) | 10.4060 | 0.549206 | 0.274603 | − | 0.961558i | \(-0.411454\pi\) | ||||
0.274603 | + | 0.961558i | \(0.411454\pi\) | |||||||
\(360\) | 2.53692 | 0.133708 | ||||||||
\(361\) | 7.73555 | − | 13.3984i | 0.407134 | − | 0.705177i | ||||
\(362\) | −9.22691 | −0.484956 | ||||||||
\(363\) | −4.48101 | − | 7.76133i | −0.235192 | − | 0.407364i | ||||
\(364\) | 0.620013 | − | 1.07389i | 0.0324975 | − | 0.0562873i | ||||
\(365\) | 6.56697 | + | 11.3743i | 0.343731 | + | 0.595360i | ||||
\(366\) | −2.07762 | + | 3.59855i | −0.108599 | + | 0.188099i | ||||
\(367\) | −16.3874 | + | 28.3839i | −0.855418 | + | 1.48163i | 0.0208394 | + | 0.999783i | \(0.493366\pi\) |
−0.876257 | + | 0.481844i | \(0.839967\pi\) | |||||||
\(368\) | 2.23361 | − | 3.86873i | 0.116435 | − | 0.201672i | ||||
\(369\) | −4.25132 | + | 7.36350i | −0.221315 | + | 0.383329i | ||||
\(370\) | 2.35351 | − | 4.07641i | 0.122353 | − | 0.211922i | ||||
\(371\) | −5.43344 | + | 9.41100i | −0.282090 | + | 0.488595i | ||||
\(372\) | −0.254059 | − | 0.440043i | −0.0131724 | − | 0.0228152i | ||||
\(373\) | −7.05241 | + | 12.2151i | −0.365160 | + | 0.632476i | −0.988802 | − | 0.149234i | \(-0.952319\pi\) |
0.623642 | + | 0.781710i | \(0.285652\pi\) | |||||||
\(374\) | −3.88067 | − | 6.72152i | −0.200665 | − | 0.347561i | ||||
\(375\) | 7.75196 | 0.400309 | ||||||||
\(376\) | 1.90111 | − | 3.29283i | 0.0980425 | − | 0.169815i | ||||
\(377\) | −1.18901 | −0.0612369 | ||||||||
\(378\) | −2.38417 | −0.122628 | ||||||||
\(379\) | −4.53066 | − | 7.84733i | −0.232724 | − | 0.403090i | 0.725885 | − | 0.687816i | \(-0.241431\pi\) |
−0.958609 | + | 0.284726i | \(0.908097\pi\) | |||||||
\(380\) | −1.38903 | −0.0712560 | ||||||||
\(381\) | −8.35473 | + | 14.4708i | −0.428026 | + | 0.741362i | ||||
\(382\) | 8.52652 | − | 14.7684i | 0.436255 | − | 0.755615i | ||||
\(383\) | 10.2326 | + | 17.7233i | 0.522859 | + | 0.905619i | 0.999646 | + | 0.0266000i | \(0.00846805\pi\) |
−0.476787 | + | 0.879019i | \(0.658199\pi\) | |||||||
\(384\) | 0.515648 | + | 0.893128i | 0.0263140 | + | 0.0455772i | ||||
\(385\) | 1.34410 | + | 2.32806i | 0.0685019 | + | 0.118649i | ||||
\(386\) | 3.77495 | + | 6.53841i | 0.192140 | + | 0.332796i | ||||
\(387\) | −7.16863 | −0.364402 | ||||||||
\(388\) | 1.04811 | 0.0532100 | ||||||||
\(389\) | −6.13345 | − | 10.6235i | −0.310978 | − | 0.538630i | 0.667596 | − | 0.744524i | \(-0.267323\pi\) |
−0.978574 | + | 0.205893i | \(0.933990\pi\) | |||||||
\(390\) | 0.271451 | − | 0.470167i | 0.0137454 | − | 0.0238078i | ||||
\(391\) | 8.01415 | − | 13.8809i | 0.405293 | − | 0.701988i | ||||
\(392\) | 2.87772 | + | 4.98436i | 0.145347 | + | 0.251748i | ||||
\(393\) | 6.06892 | 0.306136 | ||||||||
\(394\) | 0.461113 | 0.0232305 | ||||||||
\(395\) | −0.621158 | + | 1.07588i | −0.0312538 | + | 0.0541332i | ||||
\(396\) | 0.633608 | + | 1.09744i | 0.0318400 | + | 0.0551485i | ||||
\(397\) | 9.35080 | 0.469303 | 0.234652 | − | 0.972080i | \(-0.424605\pi\) | ||||
0.234652 | + | 0.972080i | \(0.424605\pi\) | |||||||
\(398\) | −8.54566 | + | 14.8015i | −0.428355 | + | 0.741933i | ||||
\(399\) | 4.24658 | 0.212595 | ||||||||
\(400\) | −3.09332 | − | 5.35779i | −0.154666 | − | 0.267890i | ||||
\(401\) | −37.4643 | −1.87088 | −0.935438 | − | 0.353491i | \(-0.884994\pi\) | ||||
−0.935438 | + | 0.353491i | \(0.884994\pi\) | |||||||
\(402\) | 1.44989 | + | 8.51023i | 0.0723141 | + | 0.424452i | ||||
\(403\) | −0.353733 | −0.0176207 | ||||||||
\(404\) | 4.69485 | + | 8.13172i | 0.233578 | + | 0.404568i | ||||
\(405\) | 0.832996 | 0.0413919 | ||||||||
\(406\) | −2.29366 | + | 3.97274i | −0.113832 | + | 0.197164i | ||||
\(407\) | 7.64869 | 0.379132 | ||||||||
\(408\) | −7.84971 | − | 13.5961i | −0.388618 | − | 0.673107i | ||||
\(409\) | −10.5166 | + | 18.2153i | −0.520013 | + | 0.900689i | 0.479716 | + | 0.877424i | \(0.340740\pi\) |
−0.999729 | + | 0.0232654i | \(0.992594\pi\) | |||||||
\(410\) | −7.46989 | −0.368911 | ||||||||
\(411\) | −5.12537 | −0.252816 | ||||||||
\(412\) | −5.51740 | − | 9.55642i | −0.271823 | − | 0.470811i | ||||
\(413\) | 8.76195 | − | 15.1761i | 0.431147 | − | 0.746769i | ||||
\(414\) | 1.63967 | − | 2.83999i | 0.0805853 | − | 0.139578i | ||||
\(415\) | −0.296352 | − | 0.513297i | −0.0145474 | − | 0.0251968i | ||||
\(416\) | 2.82768 | 0.138638 | ||||||||
\(417\) | −20.9364 | −1.02526 | ||||||||
\(418\) | 1.41419 | + | 2.44945i | 0.0691703 | + | 0.119806i | ||||
\(419\) | 15.2100 | + | 26.3445i | 0.743057 | + | 1.28701i | 0.951097 | + | 0.308892i | \(0.0999582\pi\) |
−0.208040 | + | 0.978120i | \(0.566708\pi\) | |||||||
\(420\) | 0.835762 | + | 1.44758i | 0.0407810 | + | 0.0706348i | ||||
\(421\) | 0.300281 | + | 0.520102i | 0.0146348 | + | 0.0253482i | 0.873250 | − | 0.487272i | \(-0.162008\pi\) |
−0.858615 | + | 0.512621i | \(0.828675\pi\) | |||||||
\(422\) | 2.27508 | − | 3.94055i | 0.110749 | − | 0.191823i | ||||
\(423\) | 0.624228 | − | 1.08120i | 0.0303510 | − | 0.0525695i | ||||
\(424\) | −14.6403 | −0.710996 | ||||||||
\(425\) | −11.0988 | − | 19.2236i | −0.538369 | − | 0.932483i | ||||
\(426\) | 9.80474 | 0.475041 | ||||||||
\(427\) | −8.90633 | −0.431008 | ||||||||
\(428\) | −5.96745 | + | 10.3359i | −0.288448 | + | 0.499606i | ||||
\(429\) | 0.882189 | 0.0425925 | ||||||||
\(430\) | −3.14896 | − | 5.45415i | −0.151856 | − | 0.263022i | ||||
\(431\) | 9.37537 | − | 16.2386i | 0.451596 | − | 0.782187i | −0.546890 | − | 0.837205i | \(-0.684188\pi\) |
0.998485 | + | 0.0550178i | \(0.0175216\pi\) | |||||||
\(432\) | −0.718355 | − | 1.24423i | −0.0345619 | − | 0.0598629i | ||||
\(433\) | 0.462064 | − | 0.800319i | 0.0222054 | − | 0.0384609i | −0.854709 | − | 0.519107i | \(-0.826265\pi\) |
0.876915 | + | 0.480646i | \(0.159598\pi\) | |||||||
\(434\) | −0.682372 | + | 1.18190i | −0.0327549 | + | 0.0567331i | ||||
\(435\) | 0.801375 | − | 1.38802i | 0.0384230 | − | 0.0665506i | ||||
\(436\) | 7.81853 | − | 13.5421i | 0.374440 | − | 0.648548i | ||||
\(437\) | −2.92051 | + | 5.05847i | −0.139707 | + | 0.241979i | ||||
\(438\) | 8.31457 | − | 14.4013i | 0.397285 | − | 0.688118i | ||||
\(439\) | −4.46070 | − | 7.72616i | −0.212898 | − | 0.368750i | 0.739723 | − | 0.672912i | \(-0.234957\pi\) |
−0.952620 | + | 0.304162i | \(0.901623\pi\) | |||||||
\(440\) | −1.81083 | + | 3.13645i | −0.0863280 | + | 0.149524i | ||||
\(441\) | 0.944897 | + | 1.63661i | 0.0449951 | + | 0.0779338i | ||||
\(442\) | −3.35967 | −0.159803 | ||||||||
\(443\) | −17.5449 | + | 30.3886i | −0.833583 | + | 1.44381i | 0.0615964 | + | 0.998101i | \(0.480381\pi\) |
−0.895179 | + | 0.445707i | \(0.852952\pi\) | |||||||
\(444\) | 4.75595 | 0.225707 | ||||||||
\(445\) | −0.428792 | −0.0203267 | ||||||||
\(446\) | −10.0009 | − | 17.3220i | −0.473555 | − | 0.820222i | ||||
\(447\) | −1.46100 | −0.0691030 | ||||||||
\(448\) | 8.70256 | − | 15.0733i | 0.411157 | − | 0.712145i | ||||
\(449\) | −3.18088 | + | 5.50945i | −0.150115 | + | 0.260007i | −0.931270 | − | 0.364331i | \(-0.881298\pi\) |
0.781155 | + | 0.624338i | \(0.214631\pi\) | |||||||
\(450\) | −2.27077 | − | 3.93309i | −0.107045 | − | 0.185408i | ||||
\(451\) | −6.06910 | − | 10.5120i | −0.285783 | − | 0.494990i | ||||
\(452\) | −2.58188 | − | 4.47195i | −0.121441 | − | 0.210343i | ||||
\(453\) | 4.04073 | + | 6.99874i | 0.189850 | + | 0.328830i | ||||
\(454\) | −4.01436 | −0.188403 | ||||||||
\(455\) | 1.16365 | 0.0545528 | ||||||||
\(456\) | 2.86058 | + | 4.95467i | 0.133959 | + | 0.232024i | ||||
\(457\) | 17.1029 | − | 29.6231i | 0.800039 | − | 1.38571i | −0.119550 | − | 0.992828i | \(-0.538145\pi\) |
0.919590 | − | 0.392880i | \(-0.128521\pi\) | |||||||
\(458\) | −6.77185 | + | 11.7292i | −0.316428 | + | 0.548069i | ||||
\(459\) | −2.57744 | − | 4.46426i | −0.120305 | − | 0.208374i | ||||
\(460\) | −2.29912 | −0.107197 | ||||||||
\(461\) | −1.67330 | −0.0779331 | −0.0389666 | − | 0.999241i | \(-0.512407\pi\) | ||||
−0.0389666 | + | 0.999241i | \(0.512407\pi\) | |||||||
\(462\) | 1.70179 | − | 2.94759i | 0.0791746 | − | 0.137134i | ||||
\(463\) | 4.92715 | + | 8.53407i | 0.228984 | + | 0.396612i | 0.957507 | − | 0.288409i | \(-0.0931263\pi\) |
−0.728523 | + | 0.685021i | \(0.759793\pi\) | |||||||
\(464\) | −2.76434 | −0.128331 | ||||||||
\(465\) | 0.238412 | − | 0.412941i | 0.0110561 | − | 0.0191497i | ||||
\(466\) | −9.72771 | −0.450628 | ||||||||
\(467\) | −13.6240 | − | 23.5975i | −0.630444 | − | 1.09196i | −0.987461 | − | 0.157863i | \(-0.949540\pi\) |
0.357017 | − | 0.934098i | \(-0.383794\pi\) | |||||||
\(468\) | 0.548544 | 0.0253565 | ||||||||
\(469\) | −14.2431 | + | 11.8117i | −0.657687 | + | 0.545415i | ||||
\(470\) | 1.09682 | 0.0505924 | ||||||||
\(471\) | 7.92335 | + | 13.7236i | 0.365089 | + | 0.632352i | ||||
\(472\) | 23.6089 | 1.08669 | ||||||||
\(473\) | 5.11690 | − | 8.86273i | 0.235275 | − | 0.407509i | ||||
\(474\) | 1.57292 | 0.0722466 | ||||||||
\(475\) | 4.04460 | + | 7.00545i | 0.185579 | + | 0.321432i | ||||
\(476\) | 5.17200 | − | 8.95817i | 0.237058 | − | 0.410597i | ||||
\(477\) | −4.80713 | −0.220103 | ||||||||
\(478\) | −19.0118 | −0.869577 | ||||||||
\(479\) | 3.40234 | + | 5.89303i | 0.155457 | + | 0.269260i | 0.933225 | − | 0.359292i | \(-0.116982\pi\) |
−0.777768 | + | 0.628551i | \(0.783648\pi\) | |||||||
\(480\) | −1.90582 | + | 3.30098i | −0.0869885 | + | 0.150668i | ||||
\(481\) | 1.65546 | − | 2.86733i | 0.0754823 | − | 0.130739i | ||||
\(482\) | −2.05861 | − | 3.56562i | −0.0937673 | − | 0.162410i | ||||
\(483\) | 7.02891 | 0.319826 | ||||||||
\(484\) | 7.95529 | 0.361604 | ||||||||
\(485\) | 0.491780 | + | 0.851789i | 0.0223306 | + | 0.0386777i | ||||
\(486\) | −0.527336 | − | 0.913372i | −0.0239204 | − | 0.0414314i | ||||
\(487\) | −8.21278 | − | 14.2249i | −0.372157 | − | 0.644594i | 0.617741 | − | 0.786382i | \(-0.288048\pi\) |
−0.989897 | + | 0.141788i | \(0.954715\pi\) | |||||||
\(488\) | −5.99949 | − | 10.3914i | −0.271584 | − | 0.470397i | ||||
\(489\) | −7.13366 | + | 12.3559i | −0.322595 | + | 0.558751i | ||||
\(490\) | −0.830127 | + | 1.43782i | −0.0375013 | + | 0.0649542i | ||||
\(491\) | −35.8410 | −1.61748 | −0.808740 | − | 0.588166i | \(-0.799850\pi\) | ||||
−0.808740 | + | 0.588166i | \(0.799850\pi\) | |||||||
\(492\) | −3.77376 | − | 6.53634i | −0.170134 | − | 0.294681i | ||||
\(493\) | −9.91840 | −0.446702 | ||||||||
\(494\) | 1.22433 | 0.0550852 | ||||||||
\(495\) | −0.594584 | + | 1.02985i | −0.0267246 | + | 0.0462883i | ||||
\(496\) | −0.822401 | −0.0369269 | ||||||||
\(497\) | 10.5077 | + | 18.1999i | 0.471335 | + | 0.816377i | ||||
\(498\) | −0.375217 | + | 0.649895i | −0.0168139 | + | 0.0291225i | ||||
\(499\) | −11.2462 | − | 19.4790i | −0.503449 | − | 0.871999i | −0.999992 | − | 0.00398722i | \(-0.998731\pi\) |
0.496543 | − | 0.868012i | \(-0.334603\pi\) | |||||||
\(500\) | −3.44058 | + | 5.95926i | −0.153867 | + | 0.266506i | ||||
\(501\) | −1.47723 | + | 2.55864i | −0.0659977 | + | 0.114311i | ||||
\(502\) | −10.0551 | + | 17.4159i | −0.448780 | + | 0.777310i | ||||
\(503\) | 13.6267 | − | 23.6021i | 0.607583 | − | 1.05236i | −0.384054 | − | 0.923310i | \(-0.625472\pi\) |
0.991638 | − | 0.129054i | \(-0.0411942\pi\) | |||||||
\(504\) | 3.44234 | − | 5.96231i | 0.153334 | − | 0.265582i | ||||
\(505\) | −4.40570 | + | 7.63089i | −0.196051 | + | 0.339570i | ||||
\(506\) | 2.34076 | + | 4.05431i | 0.104059 | + | 0.180236i | ||||
\(507\) | −6.30906 | + | 10.9276i | −0.280195 | + | 0.485312i | ||||
\(508\) | −7.41622 | − | 12.8453i | −0.329042 | − | 0.569917i | ||||
\(509\) | −12.9035 | −0.571939 | −0.285970 | − | 0.958239i | \(-0.592316\pi\) | ||||
−0.285970 | + | 0.958239i | \(0.592316\pi\) | |||||||
\(510\) | 2.26438 | − | 3.92202i | 0.100268 | − | 0.173670i | ||||
\(511\) | 35.6428 | 1.57674 | ||||||||
\(512\) | 15.3253 | 0.677287 | ||||||||
\(513\) | 0.939269 | + | 1.62686i | 0.0414697 | + | 0.0718277i | ||||
\(514\) | 30.2727 | 1.33527 | ||||||||
\(515\) | 5.17758 | − | 8.96784i | 0.228152 | − | 0.395170i | ||||
\(516\) | 3.18168 | − | 5.51083i | 0.140066 | − | 0.242601i | ||||
\(517\) | 0.891136 | + | 1.54349i | 0.0391921 | + | 0.0678828i | ||||
\(518\) | −6.38694 | − | 11.0625i | −0.280626 | − | 0.486059i | ||||
\(519\) | 11.5206 | + | 19.9543i | 0.505698 | + | 0.875895i | ||||
\(520\) | 0.783860 | + | 1.35769i | 0.0343745 | + | 0.0595384i | ||||
\(521\) | −27.9102 | −1.22277 | −0.611385 | − | 0.791333i | \(-0.709387\pi\) | ||||
−0.611385 | + | 0.791333i | \(0.709387\pi\) | |||||||
\(522\) | −2.02927 | −0.0888188 | ||||||||
\(523\) | −3.12709 | − | 5.41628i | −0.136738 | − | 0.236837i | 0.789522 | − | 0.613722i | \(-0.210329\pi\) |
−0.926260 | + | 0.376885i | \(0.876995\pi\) | |||||||
\(524\) | −2.69359 | + | 4.66544i | −0.117670 | + | 0.203811i | ||||
\(525\) | 4.86715 | − | 8.43016i | 0.212420 | − | 0.367922i | ||||
\(526\) | 15.0611 | + | 26.0866i | 0.656695 | + | 1.13743i | ||||
\(527\) | −2.95076 | −0.128537 | ||||||||
\(528\) | 2.05102 | 0.0892592 | ||||||||
\(529\) | 6.66599 | − | 11.5458i | 0.289826 | − | 0.501993i | ||||
\(530\) | −2.11162 | − | 3.65744i | −0.0917230 | − | 0.158869i | ||||
\(531\) | 7.75196 | 0.336406 | ||||||||
\(532\) | −1.88477 | + | 3.26453i | −0.0817153 | + | 0.141535i | ||||
\(533\) | −5.25430 | −0.227589 | ||||||||
\(534\) | 0.271451 | + | 0.470167i | 0.0117468 | + | 0.0203461i | ||||
\(535\) | −11.1998 | −0.484211 | ||||||||
\(536\) | −23.3757 | − | 8.66148i | −1.00968 | − | 0.374119i | ||||
\(537\) | 10.6867 | 0.461165 | ||||||||
\(538\) | 17.0715 | + | 29.5687i | 0.736005 | + | 1.27480i | ||||
\(539\) | −2.69783 | −0.116204 | ||||||||
\(540\) | −0.369712 | + | 0.640360i | −0.0159099 | + | 0.0275567i | ||||
\(541\) | 38.8177 | 1.66890 | 0.834451 | − | 0.551082i | \(-0.185785\pi\) | ||||
0.834451 | + | 0.551082i | \(0.185785\pi\) | |||||||
\(542\) | 11.1192 | + | 19.2590i | 0.477610 | + | 0.827244i | ||||
\(543\) | 4.37430 | − | 7.57652i | 0.187719 | − | 0.325139i | ||||
\(544\) | 23.5878 | 1.01132 | ||||||||
\(545\) | 14.6740 | 0.628564 | ||||||||
\(546\) | −0.736661 | − | 1.27593i | −0.0315262 | − | 0.0546049i | ||||
\(547\) | −15.9091 | + | 27.5553i | −0.680222 | + | 1.17818i | 0.294691 | + | 0.955593i | \(0.404783\pi\) |
−0.974913 | + | 0.222586i | \(0.928550\pi\) | |||||||
\(548\) | 2.27481 | − | 3.94009i | 0.0971751 | − | 0.168312i | ||||
\(549\) | −1.96992 | − | 3.41201i | −0.0840743 | − | 0.145621i | ||||
\(550\) | 6.48341 | 0.276454 | ||||||||
\(551\) | 3.61445 | 0.153981 | ||||||||
\(552\) | 4.73482 | + | 8.20094i | 0.201527 | + | 0.349055i | ||||
\(553\) | 1.68569 | + | 2.91970i | 0.0716829 | + | 0.124158i | ||||
\(554\) | −6.70918 | − | 11.6206i | −0.285046 | − | 0.493714i | ||||
\(555\) | 2.23151 | + | 3.86509i | 0.0947225 | + | 0.164064i | ||||
\(556\) | 9.29227 | − | 16.0947i | 0.394080 | − | 0.682566i | ||||
\(557\) | 4.56572 | − | 7.90806i | 0.193456 | − | 0.335075i | −0.752937 | − | 0.658092i | \(-0.771364\pi\) |
0.946393 | + | 0.323017i | \(0.104697\pi\) | |||||||
\(558\) | −0.603715 | −0.0255573 | ||||||||
\(559\) | −2.21497 | − | 3.83644i | −0.0936831 | − | 0.162264i | ||||
\(560\) | 2.70540 | 0.114324 | ||||||||
\(561\) | 7.35901 | 0.310698 | ||||||||
\(562\) | 8.00070 | − | 13.8576i | 0.337489 | − | 0.584549i | ||||
\(563\) | −0.692468 | −0.0291841 | −0.0145920 | − | 0.999894i | \(-0.504645\pi\) | ||||
−0.0145920 | + | 0.999894i | \(0.504645\pi\) | |||||||
\(564\) | 0.554107 | + | 0.959742i | 0.0233321 | + | 0.0404124i | ||||
\(565\) | 2.42286 | − | 4.19652i | 0.101931 | − | 0.176549i | ||||
\(566\) | −9.99636 | − | 17.3142i | −0.420178 | − | 0.727770i | ||||
\(567\) | 1.13029 | − | 1.95772i | 0.0474676 | − | 0.0822164i | ||||
\(568\) | −14.1564 | + | 24.5196i | −0.593990 | + | 1.02882i | ||||
\(569\) | 14.2321 | − | 24.6508i | 0.596642 | − | 1.03341i | −0.396671 | − | 0.917961i | \(-0.629835\pi\) |
0.993313 | − | 0.115453i | \(-0.0368320\pi\) | |||||||
\(570\) | −0.825183 | + | 1.42926i | −0.0345631 | + | 0.0598650i | ||||
\(571\) | 4.17007 | − | 7.22278i | 0.174512 | − | 0.302264i | −0.765480 | − | 0.643460i | \(-0.777498\pi\) |
0.939992 | + | 0.341196i | \(0.110832\pi\) | |||||||
\(572\) | −0.391545 | + | 0.678176i | −0.0163713 | + | 0.0283560i | ||||
\(573\) | 8.08452 | + | 14.0028i | 0.337736 | + | 0.584976i | ||||
\(574\) | −10.1359 | + | 17.5558i | −0.423062 | + | 0.732765i | ||||
\(575\) | 6.69460 | + | 11.5954i | 0.279184 | + | 0.483561i | ||||
\(576\) | 7.69941 | 0.320809 | ||||||||
\(577\) | 8.79468 | − | 15.2328i | 0.366127 | − | 0.634151i | −0.622829 | − | 0.782358i | \(-0.714017\pi\) |
0.988956 | + | 0.148207i | \(0.0473502\pi\) | |||||||
\(578\) | −10.0962 | −0.419946 | ||||||||
\(579\) | −7.15854 | −0.297499 | ||||||||
\(580\) | 0.711355 | + | 1.23210i | 0.0295374 | + | 0.0511603i | ||||
\(581\) | −1.60848 | −0.0667308 | ||||||||
\(582\) | 0.622652 | − | 1.07847i | 0.0258098 | − | 0.0447038i | ||||
\(583\) | 3.43128 | − | 5.94315i | 0.142109 | − | 0.246140i | ||||
\(584\) | 24.0097 | + | 41.5860i | 0.993529 | + | 1.72084i | ||||
\(585\) | 0.257379 | + | 0.445794i | 0.0106413 | + | 0.0184313i | ||||
\(586\) | 16.4916 | + | 28.5643i | 0.681261 | + | 1.17998i | ||||
\(587\) | 9.13198 | + | 15.8171i | 0.376917 | + | 0.652840i | 0.990612 | − | 0.136703i | \(-0.0436508\pi\) |
−0.613695 | + | 0.789543i | \(0.710317\pi\) | |||||||
\(588\) | −1.67751 | −0.0691793 | ||||||||
\(589\) | 1.07531 | 0.0443074 | ||||||||
\(590\) | 3.40519 | + | 5.89797i | 0.140190 | + | 0.242815i | ||||
\(591\) | −0.218605 | + | 0.378635i | −0.00899221 | + | 0.0155750i | ||||
\(592\) | 3.84880 | − | 6.66633i | 0.158185 | − | 0.273984i | ||||
\(593\) | −21.3179 | − | 36.9237i | −0.875422 | − | 1.51628i | −0.856312 | − | 0.516458i | \(-0.827250\pi\) |
−0.0191096 | − | 0.999817i | \(-0.506083\pi\) | |||||||
\(594\) | 1.50563 | 0.0617767 | ||||||||
\(595\) | 9.70691 | 0.397945 | ||||||||
\(596\) | 0.648442 | − | 1.12313i | 0.0265612 | − | 0.0460054i | ||||
\(597\) | −8.10268 | − | 14.0342i | −0.331621 | − | 0.574384i | ||||
\(598\) | 2.02650 | 0.0828698 | ||||||||
\(599\) | −6.13494 | + | 10.6260i | −0.250667 | + | 0.434168i | −0.963710 | − | 0.266953i | \(-0.913983\pi\) |
0.713043 | + | 0.701121i | \(0.247317\pi\) | |||||||
\(600\) | 13.1145 | 0.535396 | ||||||||
\(601\) | 8.80483 | + | 15.2504i | 0.359156 | + | 0.622077i | 0.987820 | − | 0.155600i | \(-0.0497311\pi\) |
−0.628664 | + | 0.777677i | \(0.716398\pi\) | |||||||
\(602\) | −17.0912 | −0.696586 | ||||||||
\(603\) | −7.67540 | − | 2.84399i | −0.312566 | − | 0.115816i | ||||
\(604\) | −7.17364 | −0.291891 | ||||||||
\(605\) | 3.73266 | + | 6.46516i | 0.151754 | + | 0.262846i | ||||
\(606\) | 11.1563 | 0.453192 | ||||||||
\(607\) | −11.8160 | + | 20.4658i | −0.479595 | + | 0.830683i | −0.999726 | − | 0.0234037i | \(-0.992550\pi\) |
0.520131 | + | 0.854086i | \(0.325883\pi\) | |||||||
\(608\) | −8.59586 | −0.348608 | ||||||||
\(609\) | −2.17476 | − | 3.76680i | −0.0881259 | − | 0.152638i | ||||
\(610\) | 1.73065 | − | 2.99758i | 0.0700721 | − | 0.121368i | ||||
\(611\) | 0.771498 | 0.0312115 | ||||||||
\(612\) | 4.57582 | 0.184967 | ||||||||
\(613\) | −6.80455 | − | 11.7858i | −0.274833 | − | 0.476025i | 0.695260 | − | 0.718758i | \(-0.255289\pi\) |
−0.970093 | + | 0.242734i | \(0.921956\pi\) | |||||||
\(614\) | 6.17177 | − | 10.6898i | 0.249072 | − | 0.431406i | ||||
\(615\) | 3.54133 | − | 6.13377i | 0.142800 | − | 0.247337i | ||||
\(616\) | 4.91422 | + | 8.51167i | 0.197999 | + | 0.342945i | ||||
\(617\) | −40.7431 | −1.64026 | −0.820128 | − | 0.572181i | \(-0.806098\pi\) | ||||
−0.820128 | + | 0.572181i | \(0.806098\pi\) | |||||||
\(618\) | −13.1109 | −0.527396 | ||||||||
\(619\) | −1.21800 | − | 2.10964i | −0.0489555 | − | 0.0847934i | 0.840509 | − | 0.541797i | \(-0.182256\pi\) |
−0.889465 | + | 0.457004i | \(0.848923\pi\) | |||||||
\(620\) | 0.211630 | + | 0.366554i | 0.00849928 | + | 0.0147212i | ||||
\(621\) | 1.55467 | + | 2.69277i | 0.0623868 | + | 0.108057i | ||||
\(622\) | −0.303144 | − | 0.525061i | −0.0121550 | − | 0.0210530i | ||||
\(623\) | −0.581826 | + | 1.00775i | −0.0233104 | + | 0.0403747i | ||||
\(624\) | 0.443916 | − | 0.768884i | 0.0177708 | − | 0.0307800i | ||||
\(625\) | 15.0732 | 0.602930 | ||||||||
\(626\) | 3.18511 | + | 5.51678i | 0.127303 | + | 0.220495i | ||||
\(627\) | −2.68176 | −0.107099 | ||||||||
\(628\) | −14.0666 | −0.561318 | ||||||||
\(629\) | 13.8094 | − | 23.9186i | 0.550618 | − | 0.953698i | ||||
\(630\) | 1.98600 | 0.0791242 | ||||||||
\(631\) | 18.1408 | + | 31.4208i | 0.722173 | + | 1.25084i | 0.960127 | + | 0.279564i | \(0.0901901\pi\) |
−0.237954 | + | 0.971277i | \(0.576477\pi\) | |||||||
\(632\) | −2.27103 | + | 3.93355i | −0.0903369 | + | 0.156468i | ||||
\(633\) | 2.15714 | + | 3.73628i | 0.0857387 | + | 0.148504i | ||||
\(634\) | 3.27741 | − | 5.67664i | 0.130163 | − | 0.225448i | ||||
\(635\) | 6.95946 | − | 12.0541i | 0.276178 | − | 0.478354i | ||||
\(636\) | 2.13357 | − | 3.69545i | 0.0846014 | − | 0.146534i | ||||
\(637\) | −0.583910 | + | 1.01136i | −0.0231353 | + | 0.0400716i | ||||
\(638\) | 1.44847 | − | 2.50883i | 0.0573456 | − | 0.0993255i | ||||
\(639\) | −4.64824 | + | 8.05099i | −0.183882 | + | 0.318492i | ||||
\(640\) | −0.429532 | − | 0.743972i | −0.0169788 | − | 0.0294081i | ||||
\(641\) | −4.46785 | + | 7.73854i | −0.176469 | + | 0.305654i | −0.940669 | − | 0.339326i | \(-0.889801\pi\) |
0.764199 | + | 0.644980i | \(0.223134\pi\) | |||||||
\(642\) | 7.09015 | + | 12.2805i | 0.279826 | + | 0.484673i | ||||
\(643\) | −26.1480 | −1.03118 | −0.515589 | − | 0.856836i | \(-0.672427\pi\) | ||||
−0.515589 | + | 0.856836i | \(0.672427\pi\) | |||||||
\(644\) | −3.11967 | + | 5.40342i | −0.122932 | + | 0.212925i | ||||
\(645\) | 5.97144 | 0.235125 | ||||||||
\(646\) | 10.2131 | 0.401828 | ||||||||
\(647\) | 20.3952 | + | 35.3256i | 0.801819 | + | 1.38879i | 0.918418 | + | 0.395612i | \(0.129468\pi\) |
−0.116599 | + | 0.993179i | \(0.537199\pi\) | |||||||
\(648\) | 3.04554 | 0.119640 | ||||||||
\(649\) | −5.53327 | + | 9.58391i | −0.217200 | + | 0.376201i | ||||
\(650\) | 1.40325 | − | 2.43050i | 0.0550399 | − | 0.0953319i | ||||
\(651\) | −0.646999 | − | 1.12064i | −0.0253579 | − | 0.0439212i | ||||
\(652\) | −6.33232 | − | 10.9679i | −0.247993 | − | 0.429536i | ||||
\(653\) | 12.4495 | + | 21.5632i | 0.487188 | + | 0.843835i | 0.999891 | − | 0.0147309i | \(-0.00468916\pi\) |
−0.512703 | + | 0.858566i | \(0.671356\pi\) | |||||||
\(654\) | −9.28949 | − | 16.0899i | −0.363248 | − | 0.629164i | ||||
\(655\) | −5.05538 | −0.197530 | ||||||||
\(656\) | −12.2158 | −0.476948 | ||||||||
\(657\) | 7.88356 | + | 13.6547i | 0.307567 | + | 0.532722i | ||||
\(658\) | 1.48826 | − | 2.57775i | 0.0580186 | − | 0.100491i | ||||
\(659\) | 11.1988 | − | 19.3970i | 0.436245 | − | 0.755599i | −0.561151 | − | 0.827713i | \(-0.689641\pi\) |
0.997396 | + | 0.0721146i | \(0.0229747\pi\) | |||||||
\(660\) | −0.527793 | − | 0.914165i | −0.0205443 | − | 0.0355838i | ||||
\(661\) | −38.7373 | −1.50671 | −0.753354 | − | 0.657616i | \(-0.771565\pi\) | ||||
−0.753354 | + | 0.657616i | \(0.771565\pi\) | |||||||
\(662\) | 3.48270 | 0.135359 | ||||||||
\(663\) | 1.59276 | − | 2.75874i | 0.0618576 | − | 0.107141i | ||||
\(664\) | −1.08350 | − | 1.87668i | −0.0420480 | − | 0.0728293i | ||||
\(665\) | −3.53738 | −0.137174 | ||||||||
\(666\) | 2.82536 | − | 4.89367i | 0.109480 | − | 0.189626i | ||||
\(667\) | 5.98262 | 0.231648 | ||||||||
\(668\) | −1.31129 | − | 2.27122i | −0.0507353 | − | 0.0878761i | ||||
\(669\) | 18.9649 | 0.733226 | ||||||||
\(670\) | −1.20776 | − | 7.08899i | −0.0466597 | − | 0.273872i | ||||
\(671\) | 5.62445 | 0.217130 | ||||||||
\(672\) | 5.17200 | + | 8.95817i | 0.199514 | + | 0.345569i | ||||
\(673\) | 23.4903 | 0.905483 | 0.452741 | − | 0.891642i | \(-0.350446\pi\) | ||||
0.452741 | + | 0.891642i | \(0.350446\pi\) | |||||||
\(674\) | −16.0867 | + | 27.8629i | −0.619635 | + | 1.07324i | ||||
\(675\) | 4.30612 | 0.165743 | ||||||||
\(676\) | −5.60035 | − | 9.70009i | −0.215398 | − | 0.373080i | ||||
\(677\) | 20.6440 | − | 35.7564i | 0.793413 | − | 1.37423i | −0.130429 | − | 0.991458i | \(-0.541635\pi\) |
0.923842 | − | 0.382774i | \(-0.125031\pi\) | |||||||
\(678\) | −6.13526 | −0.235623 | ||||||||
\(679\) | 2.66918 | 0.102434 | ||||||||
\(680\) | 6.53877 | + | 11.3255i | 0.250751 | + | 0.434313i | ||||
\(681\) | 1.90313 | − | 3.29632i | 0.0729282 | − | 0.126315i | ||||
\(682\) | 0.430926 | − | 0.746385i | 0.0165010 | − | 0.0285806i | ||||
\(683\) | −4.97437 | − | 8.61586i | −0.190339 | − | 0.329677i | 0.755024 | − | 0.655698i | \(-0.227625\pi\) |
−0.945363 | + | 0.326021i | \(0.894292\pi\) | |||||||
\(684\) | −1.66752 | −0.0637591 | ||||||||
\(685\) | 4.26941 | 0.163126 | ||||||||
\(686\) | 10.5974 | + | 18.3552i | 0.404610 | + | 0.700804i | ||||
\(687\) | −6.42081 | − | 11.1212i | −0.244969 | − | 0.424299i | ||||
\(688\) | −5.14963 | − | 8.91941i | −0.196328 | − | 0.340049i | ||||
\(689\) | −1.48531 | − | 2.57263i | −0.0565858 | − | 0.0980094i | ||||
\(690\) | −1.36584 | + | 2.36570i | −0.0519965 | + | 0.0900606i | ||||
\(691\) | −12.3699 | + | 21.4252i | −0.470572 | + | 0.815054i | −0.999434 | − | 0.0336538i | \(-0.989286\pi\) |
0.528862 | + | 0.848708i | \(0.322619\pi\) | |||||||
\(692\) | −20.4529 | −0.777503 | ||||||||
\(693\) | 1.61358 | + | 2.79480i | 0.0612947 | + | 0.106166i | ||||
\(694\) | −15.5831 | −0.591527 | ||||||||
\(695\) | 17.4399 | 0.661533 | ||||||||
\(696\) | 2.92993 | − | 5.07479i | 0.111059 | − | 0.192359i | ||||
\(697\) | −43.8301 | −1.66018 | ||||||||
\(698\) | −15.3023 | − | 26.5043i | −0.579199 | − | 1.00320i | ||||
\(699\) | 4.61173 | − | 7.98774i | 0.174432 | − | 0.302124i | ||||
\(700\) | 4.32042 | + | 7.48318i | 0.163296 | + | 0.282838i | ||||
\(701\) | 25.7172 | − | 44.5435i | 0.971326 | − | 1.68239i | 0.279763 | − | 0.960069i | \(-0.409744\pi\) |
0.691563 | − | 0.722317i | \(-0.256923\pi\) | |||||||
\(702\) | 0.325873 | − | 0.564428i | 0.0122993 | − | 0.0213030i | ||||
\(703\) | −5.03241 | + | 8.71640i | −0.189801 | + | 0.328745i | ||||
\(704\) | −5.49577 | + | 9.51895i | −0.207129 | + | 0.358759i | ||||
\(705\) | −0.519980 | + | 0.900632i | −0.0195836 | + | 0.0339197i | ||||
\(706\) | 3.65433 | − | 6.32949i | 0.137533 | − | 0.238214i | ||||
\(707\) | 11.9561 | + | 20.7086i | 0.449657 | + | 0.778828i | ||||
\(708\) | −3.44058 | + | 5.95926i | −0.129305 | + | 0.223963i | ||||
\(709\) | −8.33267 | − | 14.4326i | −0.312940 | − | 0.542028i | 0.666058 | − | 0.745900i | \(-0.267980\pi\) |
−0.978997 | + | 0.203873i | \(0.934647\pi\) | |||||||
\(710\) | −8.16731 | −0.306514 | ||||||||
\(711\) | −0.745691 | + | 1.29158i | −0.0279656 | + | 0.0484378i | ||||
\(712\) | −1.56772 | −0.0587528 | ||||||||
\(713\) | 1.77985 | 0.0666559 | ||||||||
\(714\) | −6.14505 | − | 10.6435i | −0.229973 | − | 0.398324i | ||||
\(715\) | −0.734860 | −0.0274822 | ||||||||
\(716\) | −4.74312 | + | 8.21532i | −0.177259 | + | 0.307021i | ||||
\(717\) | 9.01312 | − | 15.6112i | 0.336601 | − | 0.583010i | ||||
\(718\) | 5.48744 | + | 9.50452i | 0.204789 | + | 0.354706i | ||||
\(719\) | 3.97866 | + | 6.89124i | 0.148379 | + | 0.257000i | 0.930628 | − | 0.365965i | \(-0.119261\pi\) |
−0.782250 | + | 0.622965i | \(0.785928\pi\) | |||||||
\(720\) | 0.598387 | + | 1.03644i | 0.0223006 | + | 0.0386257i | ||||
\(721\) | −14.0509 | − | 24.3368i | −0.523282 | − | 0.906351i | ||||
\(722\) | 16.3169 | 0.607253 | ||||||||
\(723\) | 3.90380 | 0.145184 | ||||||||
\(724\) | 3.88293 | + | 6.72543i | 0.144308 | + | 0.249949i | ||||
\(725\) | 4.14265 | − | 7.17529i | 0.153854 | − | 0.266483i | ||||
\(726\) | 4.72599 | − | 8.18566i | 0.175398 | − | 0.303798i | ||||
\(727\) | 18.4741 | + | 31.9981i | 0.685167 | + | 1.18674i | 0.973384 | + | 0.229179i | \(0.0736042\pi\) |
−0.288217 | + | 0.957565i | \(0.593062\pi\) | |||||||
\(728\) | 4.25446 | 0.157681 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.92600 | + | 11.9962i | −0.256343 | + | 0.443999i | ||||
\(731\) | −18.4767 | − | 32.0026i | −0.683387 | − | 1.18366i | ||||
\(732\) | 3.49728 | 0.129263 | ||||||||
\(733\) | 17.7298 | − | 30.7089i | 0.654864 | − | 1.13426i | −0.327064 | − | 0.945002i | \(-0.606059\pi\) |
0.981928 | − | 0.189255i | \(-0.0606074\pi\) | |||||||
\(734\) | −34.5667 | −1.27588 | ||||||||
\(735\) | −0.787096 | − | 1.36329i | −0.0290325 | − | 0.0502857i | ||||
\(736\) | −14.2278 | −0.524444 | ||||||||
\(737\) | 8.99470 | − | 7.45925i | 0.331324 | − | 0.274765i | ||||
\(738\) | −8.96749 | −0.330098 | ||||||||
\(739\) | −12.8612 | − | 22.2763i | −0.473107 | − | 0.819445i | 0.526419 | − | 0.850225i | \(-0.323534\pi\) |
−0.999526 | + | 0.0307797i | \(0.990201\pi\) | |||||||
\(740\) | −3.96168 | −0.145634 | ||||||||
\(741\) | −0.580431 | + | 1.00534i | −0.0213227 | + | 0.0369320i | ||||
\(742\) | −11.4610 | −0.420746 | ||||||||
\(743\) | 12.2309 | + | 21.1846i | 0.448709 | + | 0.777187i | 0.998302 | − | 0.0582451i | \(-0.0185505\pi\) |
−0.549593 | + | 0.835433i | \(0.685217\pi\) | |||||||
\(744\) | 0.871664 | − | 1.50977i | 0.0319567 | − | 0.0553507i | ||||
\(745\) | 1.21701 | 0.0445878 | ||||||||
\(746\) | −14.8760 | −0.544648 | ||||||||
\(747\) | −0.355767 | − | 0.616206i | −0.0130168 | − | 0.0225458i | ||||
\(748\) | −3.26618 | + | 5.65719i | −0.119423 | + | 0.206847i | ||||
\(749\) | −15.1970 | + | 26.3220i | −0.555286 | + | 0.961783i | ||||
\(750\) | 4.08789 | + | 7.08043i | 0.149268 | + | 0.258541i | ||||
\(751\) | 11.0637 | 0.403720 | 0.201860 | − | 0.979414i | \(-0.435301\pi\) | ||||
0.201860 | + | 0.979414i | \(0.435301\pi\) | |||||||
\(752\) | 1.79367 | 0.0654085 | ||||||||
\(753\) | −9.53385 | − | 16.5131i | −0.347433 | − | 0.601771i | ||||
\(754\) | −0.627005 | − | 1.08600i | −0.0228342 | − | 0.0395500i | ||||
\(755\) | −3.36591 | − | 5.82993i | −0.122498 | − | 0.212173i | ||||
\(756\) | 1.00332 | + | 1.73780i | 0.0364904 | + | 0.0632032i | ||||
\(757\) | −10.4668 | + | 18.1290i | −0.380422 | + | 0.658910i | −0.991123 | − | 0.132952i | \(-0.957554\pi\) |
0.610701 | + | 0.791861i | \(0.290888\pi\) | |||||||
\(758\) | 4.77835 | − | 8.27635i | 0.173558 | − | 0.300611i | ||||
\(759\) | −4.43884 | −0.161120 | ||||||||
\(760\) | −2.38285 | − | 4.12722i | −0.0864352 | − | 0.149710i | ||||
\(761\) | −12.1681 | −0.441093 | −0.220547 | − | 0.975376i | \(-0.570784\pi\) | ||||
−0.220547 | + | 0.975376i | \(0.570784\pi\) | |||||||
\(762\) | −17.6230 | −0.638414 | ||||||||
\(763\) | 19.9110 | − | 34.4869i | 0.720828 | − | 1.24851i | ||||
\(764\) | −14.3527 | −0.519264 | ||||||||
\(765\) | 2.14700 | + | 3.71871i | 0.0776249 | + | 0.134450i | ||||
\(766\) | −10.7920 | + | 18.6923i | −0.389930 | + | 0.675379i | ||||
\(767\) | 2.39520 | + | 4.14861i | 0.0864858 | + | 0.149798i | ||||
\(768\) | −8.24325 | + | 14.2777i | −0.297453 | + | 0.515203i | ||||
\(769\) | 13.1071 | − | 22.7022i | 0.472655 | − | 0.818662i | −0.526855 | − | 0.849955i | \(-0.676629\pi\) |
0.999510 | + | 0.0312927i | \(0.00996242\pi\) | |||||||
\(770\) | −1.41759 | + | 2.45533i | −0.0510863 | + | 0.0884841i | ||||
\(771\) | −14.3517 | + | 24.8579i | −0.516865 | + | 0.895237i | ||||
\(772\) | 3.17720 | − | 5.50307i | 0.114350 | − | 0.198060i | ||||
\(773\) | −4.49338 | + | 7.78277i | −0.161616 | + | 0.279927i | −0.935448 | − | 0.353464i | \(-0.885004\pi\) |
0.773833 | + | 0.633390i | \(0.218337\pi\) | |||||||
\(774\) | −3.78028 | − | 6.54763i | −0.135879 | − | 0.235350i | ||||
\(775\) | 1.23245 | − | 2.13467i | 0.0442710 | − | 0.0766797i | ||||
\(776\) | 1.79801 | + | 3.11425i | 0.0645449 | + | 0.111795i | ||||
\(777\) | 12.1117 | 0.434505 | ||||||||
\(778\) | 6.46878 | − | 11.2043i | 0.231917 | − | 0.401692i | ||||
\(779\) | 15.9725 | 0.572275 | ||||||||
\(780\) | −0.456935 | −0.0163609 | ||||||||
\(781\) | −6.63574 | − | 11.4934i | −0.237446 | − | 0.411268i | ||||
\(782\) | 16.9046 | 0.604507 | ||||||||
\(783\) | 0.962039 | − | 1.66630i | 0.0343805 | − | 0.0595487i | ||||
\(784\) | −1.35754 | + | 2.35134i | −0.0484837 | + | 0.0839763i | ||||
\(785\) | −6.60012 | − | 11.4317i | −0.235568 | − | 0.408016i | ||||
\(786\) | 3.20036 | + | 5.54318i | 0.114153 | + | 0.197719i | ||||
\(787\) | 4.82133 | + | 8.35079i | 0.171862 | + | 0.297674i | 0.939071 | − | 0.343724i | \(-0.111688\pi\) |
−0.767209 | + | 0.641397i | \(0.778355\pi\) | |||||||
\(788\) | −0.194049 | − | 0.336102i | −0.00691269 | − | 0.0119731i | ||||
\(789\) | −28.5607 | −1.01679 | ||||||||
\(790\) | −1.31024 | −0.0466161 | ||||||||
\(791\) | −6.57514 | − | 11.3885i | −0.233785 | − | 0.404928i | ||||
\(792\) | −2.17388 | + | 3.76527i | −0.0772454 | + | 0.133793i | ||||
\(793\) | 1.21734 | − | 2.10849i | 0.0432289 | − | 0.0748746i | ||||
\(794\) | 4.93101 | + | 8.54076i | 0.174995 | + | 0.303100i | ||||
\(795\) | 4.00432 | 0.142019 | ||||||||
\(796\) | 14.3850 | 0.509862 | ||||||||
\(797\) | 22.8239 | − | 39.5322i | 0.808466 | − | 1.40030i | −0.105461 | − | 0.994423i | \(-0.533632\pi\) |
0.913926 | − | 0.405880i | \(-0.133035\pi\) | |||||||
\(798\) | 2.23937 | + | 3.87871i | 0.0792729 | + | 0.137305i | ||||
\(799\) | 6.43565 | 0.227677 | ||||||||
\(800\) | −9.85202 | + | 17.0642i | −0.348321 | + | 0.603310i | ||||
\(801\) | −0.514759 | −0.0181881 | ||||||||
\(802\) | −19.7562 | − | 34.2188i | −0.697617 | − | 1.20831i | ||||
\(803\) | −22.5088 | −0.794319 | ||||||||
\(804\) | 5.59290 | − | 4.63815i | 0.197246 | − | 0.163575i | ||||
\(805\) | −5.85505 | −0.206363 | ||||||||
\(806\) | −0.186536 | − | 0.323090i | −0.00657045 | − | 0.0113804i | ||||
\(807\) | −32.3731 | −1.13959 | ||||||||
\(808\) | −16.1078 | + | 27.8995i | −0.566670 | + | 0.981502i | ||||
\(809\) | 20.7668 | 0.730121 | 0.365060 | − | 0.930984i | \(-0.381048\pi\) | ||||
0.365060 | + | 0.930984i | \(0.381048\pi\) | |||||||
\(810\) | 0.439269 | + | 0.760836i | 0.0154343 | + | 0.0267330i | ||||
\(811\) | 7.02612 | − | 12.1696i | 0.246720 | − | 0.427332i | −0.715894 | − | 0.698209i | \(-0.753980\pi\) |
0.962614 | + | 0.270877i | \(0.0873138\pi\) | |||||||
\(812\) | 3.86093 | 0.135492 | ||||||||
\(813\) | −21.0856 | −0.739503 | ||||||||
\(814\) | 4.03343 | + | 6.98610i | 0.141372 | + | 0.244863i | ||||
\(815\) | 5.94231 | − | 10.2924i | 0.208150 | − | 0.360526i | ||||
\(816\) | 3.70304 | − | 6.41385i | 0.129632 | − | 0.224530i | ||||
\(817\) | 6.73327 | + | 11.6624i | 0.235567 | + | 0.408015i | ||||
\(818\) | −22.1831 | −0.775616 | ||||||||
\(819\) | 1.39695 | 0.0488133 | ||||||||
\(820\) | 3.14353 | + | 5.44475i | 0.109777 | + | 0.190139i | ||||
\(821\) | 15.2618 | + | 26.4341i | 0.532639 | + | 0.922558i | 0.999274 | + | 0.0381079i | \(0.0121331\pi\) |
−0.466634 | + | 0.884450i | \(0.654534\pi\) | |||||||
\(822\) | −2.70279 | − | 4.68137i | −0.0942706 | − | 0.163281i | ||||
\(823\) | −23.9634 | − | 41.5058i | −0.835311 | − | 1.44680i | −0.893777 | − | 0.448511i | \(-0.851954\pi\) |
0.0584667 | − | 0.998289i | \(-0.481379\pi\) | |||||||
\(824\) | 18.9299 | − | 32.7876i | 0.659455 | − | 1.14221i | ||||
\(825\) | −3.07366 | + | 5.32374i | −0.107011 | + | 0.185349i | ||||
\(826\) | 18.4820 | 0.643069 | ||||||||
\(827\) | 10.9411 | + | 18.9506i | 0.380461 | + | 0.658978i | 0.991128 | − | 0.132910i | \(-0.0424320\pi\) |
−0.610667 | + | 0.791887i | \(0.709099\pi\) | |||||||
\(828\) | −2.76006 | −0.0959188 | ||||||||
\(829\) | −0.363130 | −0.0126120 | −0.00630600 | − | 0.999980i | \(-0.502007\pi\) | ||||
−0.00630600 | + | 0.999980i | \(0.502007\pi\) | |||||||
\(830\) | 0.312554 | − | 0.541360i | 0.0108489 | − | 0.0187909i | ||||
\(831\) | 12.7228 | 0.441349 | ||||||||
\(832\) | 2.37897 | + | 4.12049i | 0.0824759 | + | 0.142852i | ||||
\(833\) | −4.87084 | + | 8.43654i | −0.168764 | + | 0.292309i | ||||
\(834\) | −11.0405 | − | 19.1227i | −0.382301 | − | 0.662165i | ||||
\(835\) | 1.23053 | − | 2.13133i | 0.0425841 | − | 0.0737578i | ||||
\(836\) | 1.19026 | − | 2.06159i | 0.0411659 | − | 0.0713014i | ||||
\(837\) | 0.286210 | − | 0.495730i | 0.00989286 | − | 0.0171349i | ||||
\(838\) | −16.0416 | + | 27.7848i | −0.554146 | + | 0.959809i | ||||
\(839\) | −11.2480 | + | 19.4822i | −0.388326 | + | 0.672600i | −0.992224 | − | 0.124461i | \(-0.960280\pi\) |
0.603899 | + | 0.797061i | \(0.293613\pi\) | |||||||
\(840\) | −2.86745 | + | 4.96658i | −0.0989366 | + | 0.171363i | ||||
\(841\) | 12.6490 | + | 21.9086i | 0.436171 | + | 0.755470i | ||||
\(842\) | −0.316698 | + | 0.548537i | −0.0109141 | + | 0.0189038i | ||||
\(843\) | 7.58597 | + | 13.1393i | 0.261275 | + | 0.452541i | ||||
\(844\) | −3.82965 | −0.131822 | ||||||||
\(845\) | 5.25542 | − | 9.10266i | 0.180792 | − | 0.313141i | ||||
\(846\) | 1.31671 | 0.0452695 | ||||||||
\(847\) | 20.2593 | 0.696118 | ||||||||
\(848\) | −3.45323 | − | 5.98117i | −0.118584 | − | 0.205394i | ||||
\(849\) | 18.9563 | 0.650580 | ||||||||
\(850\) | 11.7056 | − | 20.2746i | 0.401497 | − | 0.695414i | ||||
\(851\) | −8.32962 | + | 14.4273i | −0.285536 | + | 0.494562i | ||||
\(852\) | −4.12610 | − | 7.14661i | −0.141358 | − | 0.244839i | ||||
\(853\) | −2.83112 | − | 4.90365i | −0.0969358 | − | 0.167898i | 0.813479 | − | 0.581594i | \(-0.197571\pi\) |
−0.910415 | + | 0.413696i | \(0.864237\pi\) | |||||||
\(854\) | −4.69663 | − | 8.13480i | −0.160715 | − | 0.278367i | ||||
\(855\) | −0.782407 | − | 1.35517i | −0.0267578 | − | 0.0463458i | ||||
\(856\) | −40.9480 | −1.39957 | ||||||||
\(857\) | −14.8633 | −0.507721 | −0.253861 | − | 0.967241i | \(-0.581700\pi\) | ||||
−0.253861 | + | 0.967241i | \(0.581700\pi\) | |||||||
\(858\) | 0.465210 | + | 0.805767i | 0.0158820 | + | 0.0275084i | ||||
\(859\) | −21.4760 | + | 37.1975i | −0.732751 | + | 1.26916i | 0.222953 | + | 0.974829i | \(0.428430\pi\) |
−0.955703 | + | 0.294332i | \(0.904903\pi\) | |||||||
\(860\) | −2.65033 | + | 4.59050i | −0.0903754 | + | 0.156535i | ||||
\(861\) | −9.61043 | − | 16.6458i | −0.327523 | − | 0.567286i | ||||
\(862\) | 19.7759 | 0.673569 | ||||||||
\(863\) | 22.5825 | 0.768716 | 0.384358 | − | 0.923184i | \(-0.374423\pi\) | ||||
0.384358 | + | 0.923184i | \(0.374423\pi\) | |||||||
\(864\) | −2.28791 | + | 3.96278i | −0.0778364 | + | 0.134817i | ||||
\(865\) | −9.59661 | − | 16.6218i | −0.326295 | − | 0.565159i | ||||
\(866\) | 0.974652 | 0.0331200 | ||||||||
\(867\) | 4.78642 | − | 8.29032i | 0.162555 | − | 0.281554i | ||||
\(868\) | 1.14864 | 0.0389874 | ||||||||
\(869\) | −1.06453 | − | 1.84383i | −0.0361118 | − | 0.0625476i | ||||
\(870\) | 1.69037 | 0.0573091 | ||||||||
\(871\) | −0.849532 | − | 4.98638i | −0.0287853 | − | 0.168957i | ||||
\(872\) | 53.6499 | 1.81682 | ||||||||
\(873\) | 0.590375 | + | 1.02256i | 0.0199812 | + | 0.0346084i | ||||
\(874\) | −6.16036 | −0.208377 | ||||||||
\(875\) | −8.76195 | + | 15.1761i | −0.296208 | + | 0.513047i | ||||
\(876\) | −13.9960 | −0.472880 | ||||||||
\(877\) | −0.732725 | − | 1.26912i | −0.0247424 | − | 0.0428550i | 0.853389 | − | 0.521274i | \(-0.174543\pi\) |
−0.878131 | + | 0.478419i | \(0.841210\pi\) | |||||||
\(878\) | 4.70458 | − | 8.14856i | 0.158772 | − | 0.275001i | ||||
\(879\) | −31.2734 | −1.05483 | ||||||||
\(880\) | −1.70849 | −0.0575932 | ||||||||
\(881\) | 17.4077 | + | 30.1509i | 0.586479 | + | 1.01581i | 0.994689 | + | 0.102923i | \(0.0328196\pi\) |
−0.408210 | + | 0.912888i | \(0.633847\pi\) | |||||||
\(882\) | −0.996556 | + | 1.72609i | −0.0335558 | + | 0.0581203i | ||||
\(883\) | 8.29415 | − | 14.3659i | 0.279120 | − | 0.483451i | −0.692046 | − | 0.721853i | \(-0.743290\pi\) |
0.971166 | + | 0.238403i | \(0.0766238\pi\) | |||||||
\(884\) | 1.41384 | + | 2.44884i | 0.0475526 | + | 0.0823635i | ||||
\(885\) | −6.45735 | −0.217061 | ||||||||
\(886\) | −37.0082 | −1.24331 | ||||||||
\(887\) | 22.9646 | + | 39.7758i | 0.771075 | + | 1.33554i | 0.936974 | + | 0.349399i | \(0.113614\pi\) |
−0.165899 | + | 0.986143i | \(0.553053\pi\) | |||||||
\(888\) | 8.15870 | + | 14.1313i | 0.273788 | + | 0.474215i | ||||
\(889\) | −18.8865 | − | 32.7124i | −0.633433 | − | 1.09714i | ||||
\(890\) | −0.226117 | − | 0.391647i | −0.00757947 | − | 0.0131280i | ||||
\(891\) | −0.713790 | + | 1.23632i | −0.0239129 | + | 0.0414183i | ||||
\(892\) | −8.41727 | + | 14.5791i | −0.281831 | + | 0.488146i | ||||
\(893\) | −2.34527 | −0.0784816 | ||||||||
\(894\) | −0.770439 | − | 1.33444i | −0.0257673 | − | 0.0446303i | ||||
\(895\) | −8.90197 | −0.297560 | ||||||||
\(896\) | −2.33132 | −0.0778840 | ||||||||
\(897\) | −0.960726 | + | 1.66403i | −0.0320777 | + | 0.0555602i | ||||
\(898\) | −6.70957 | −0.223901 | ||||||||
\(899\) | −0.550690 | − | 0.953823i | −0.0183665 | − | 0.0318118i | ||||
\(900\) | −1.91120 | + | 3.31030i | −0.0637067 | + | 0.110343i | ||||
\(901\) | −12.3901 | − | 21.4603i | −0.412774 | − | 0.714946i | ||||
\(902\) | 6.40091 | − | 11.0867i | 0.213127 | − | 0.369147i | ||||
\(903\) | 8.10262 | − | 14.0341i | 0.269638 | − | 0.467027i | ||||
\(904\) | 8.85830 | − | 15.3430i | 0.294623 | − | 0.510301i | ||||
\(905\) | −3.64378 | + | 6.31121i | −0.121123 | + | 0.209792i | ||||
\(906\) | −4.26164 | + | 7.38138i | −0.141583 | + | 0.245230i | ||||
\(907\) | −13.8915 | + | 24.0607i | −0.461259 | + | 0.798924i | −0.999024 | − | 0.0441708i | \(-0.985935\pi\) |
0.537765 | + | 0.843095i | \(0.319269\pi\) | |||||||
\(908\) | 1.68935 | + | 2.92604i | 0.0560631 | + | 0.0971041i | ||||
\(909\) | −5.28898 | + | 9.16077i | −0.175424 | + | 0.303844i | ||||
\(910\) | 0.613635 | + | 1.06285i | 0.0203418 | + | 0.0352331i | ||||
\(911\) | −26.1508 | −0.866416 | −0.433208 | − | 0.901294i | \(-0.642618\pi\) | ||||
−0.433208 | + | 0.901294i | \(0.642618\pi\) | |||||||
\(912\) | −1.34946 | + | 2.33733i | −0.0446850 | + | 0.0773967i | ||||
\(913\) | 1.01577 | 0.0336171 | ||||||||
\(914\) | 36.0759 | 1.19328 | ||||||||
\(915\) | 1.64094 | + | 2.84219i | 0.0542478 | + | 0.0939599i | ||||
\(916\) | 11.3991 | 0.376637 | ||||||||
\(917\) | −6.85963 | + | 11.8812i | −0.226525 | + | 0.392352i | ||||
\(918\) | 2.71836 | − | 4.70833i | 0.0897191 | − | 0.155398i | ||||
\(919\) | 23.3286 | + | 40.4063i | 0.769539 | + | 1.33288i | 0.937813 | + | 0.347140i | \(0.112847\pi\) |
−0.168275 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(920\) | −3.94408 | − | 6.83135i | −0.130033 | − | 0.225223i | ||||
\(921\) | 5.85184 | + | 10.1357i | 0.192825 | + | 0.333982i | ||||
\(922\) | −0.882388 | − | 1.52834i | −0.0290599 | − | 0.0503333i | ||||
\(923\) | −5.74487 | −0.189095 | ||||||||
\(924\) | −2.86464 | −0.0942398 | ||||||||
\(925\) | 11.5357 | + | 19.9803i | 0.379290 | + | 0.656950i | ||||
\(926\) | −5.19652 | + | 9.00064i | −0.170768 | + | 0.295780i | ||||
\(927\) | 6.21562 | − | 10.7658i | 0.204148 | − | 0.353594i | ||||
\(928\) | 4.40212 | + | 7.62470i | 0.144507 | + | 0.250293i | ||||
\(929\) | −33.2073 | −1.08950 | −0.544748 | − | 0.838600i | \(-0.683375\pi\) | ||||
−0.544748 | + | 0.838600i | \(0.683375\pi\) | |||||||
\(930\) | 0.502892 | 0.0164905 | ||||||||
\(931\) | 1.77502 | − | 3.07443i | 0.0581741 | − | 0.100760i | ||||
\(932\) | 4.09368 | + | 7.09046i | 0.134093 | + | 0.232256i | ||||
\(933\) | 0.574859 | 0.0188201 | ||||||||
\(934\) | 14.3689 | − | 24.8876i | 0.470163 | − | 0.814347i | ||||
\(935\) | −6.13003 | −0.200473 | ||||||||
\(936\) | 0.941013 | + | 1.62988i | 0.0307580 | + | 0.0532744i | ||||
\(937\) | −27.4424 | −0.896505 | −0.448253 | − | 0.893907i | \(-0.647954\pi\) | ||||
−0.448253 | + | 0.893907i | \(0.647954\pi\) | |||||||
\(938\) | −18.2994 | − | 6.78054i | −0.597497 | − | 0.221392i | ||||
\(939\) | −6.04001 | −0.197108 | ||||||||
\(940\) | −0.461569 | − | 0.799461i | −0.0150547 | − | 0.0260756i | ||||
\(941\) | −21.4206 | −0.698293 | −0.349147 | − | 0.937068i | \(-0.613528\pi\) | ||||
−0.349147 | + | 0.937068i | \(0.613528\pi\) | |||||||
\(942\) | −8.35653 | + | 14.4739i | −0.272270 | + | 0.471586i | ||||
\(943\) | 26.4376 | 0.860928 | ||||||||
\(944\) | 5.56866 | + | 9.64520i | 0.181244 | + | 0.313925i | ||||
\(945\) | −0.941526 | + | 1.63077i | −0.0306278 | + | 0.0530490i | ||||
\(946\) | 10.7933 | 0.350920 | ||||||||
\(947\) | 53.6910 | 1.74472 | 0.872361 | − | 0.488862i | \(-0.162588\pi\) | ||||
0.872361 | + | 0.488862i | \(0.162588\pi\) | |||||||
\(948\) | −0.661926 | − | 1.14649i | −0.0214984 | − | 0.0372362i | ||||
\(949\) | −4.87173 | + | 8.43809i | −0.158143 | + | 0.273912i | ||||
\(950\) | −4.26573 | + | 7.38845i | −0.138398 | + | 0.239713i | ||||
\(951\) | 3.10752 | + | 5.38238i | 0.100768 | + | 0.174536i | ||||
\(952\) | 35.4897 | 1.15023 | ||||||||
\(953\) | −0.108986 | −0.00353040 | −0.00176520 | − | 0.999998i | \(-0.500562\pi\) | ||||
−0.00176520 | + | 0.999998i | \(0.500562\pi\) | |||||||
\(954\) | −2.53497 | − | 4.39070i | −0.0820727 | − | 0.142154i | ||||
\(955\) | −6.73438 | − | 11.6643i | −0.217919 | − | 0.377447i | ||||
\(956\) | 8.00065 | + | 13.8575i | 0.258760 | + | 0.448185i | ||||
\(957\) | 1.37339 | + | 2.37878i | 0.0443953 | + | 0.0768950i | ||||
\(958\) | −3.58836 | + | 6.21522i | −0.115935 | + | 0.200805i | ||||
\(959\) | 5.79314 | − | 10.0340i | 0.187070 | − | 0.324015i | ||||
\(960\) | −6.41358 | −0.206997 | ||||||||
\(961\) | 15.3362 | + | 26.5630i | 0.494715 | + | 0.856872i | ||||
\(962\) | 3.49192 | 0.112584 | ||||||||
\(963\) | −13.4452 | −0.433267 | ||||||||
\(964\) | −1.73264 | + | 3.00102i | −0.0558046 | + | 0.0966563i | ||||
\(965\) | 5.96303 | 0.191957 | ||||||||
\(966\) | 3.70660 | + | 6.42001i | 0.119258 | + | 0.206560i | ||||
\(967\) | 22.1707 | − | 38.4007i | 0.712961 | − | 1.23488i | −0.250780 | − | 0.968044i | \(-0.580687\pi\) |
0.963741 | − | 0.266840i | \(-0.0859795\pi\) | |||||||
\(968\) | 13.6471 | + | 23.6375i | 0.438634 | + | 0.759737i | ||||
\(969\) | −4.84182 | + | 8.38628i | −0.155542 | + | 0.269406i | ||||
\(970\) | −0.518667 | + | 0.898357i | −0.0166534 | + | 0.0288445i | ||||
\(971\) | 11.8519 | − | 20.5281i | 0.380345 | − | 0.658778i | −0.610766 | − | 0.791811i | \(-0.709138\pi\) |
0.991112 | + | 0.133033i | \(0.0424718\pi\) | |||||||
\(972\) | −0.443834 | + | 0.768743i | −0.0142360 | + | 0.0246574i | ||||
\(973\) | 23.6641 | − | 40.9875i | 0.758637 | − | 1.31400i | ||||
\(974\) | 8.66178 | − | 15.0027i | 0.277541 | − | 0.480716i | ||||
\(975\) | 1.33051 | + | 2.30450i | 0.0426103 | + | 0.0738032i | ||||
\(976\) | 2.83021 | − | 4.90207i | 0.0905929 | − | 0.156911i | ||||
\(977\) | 13.1525 | + | 22.7808i | 0.420785 | + | 0.728821i | 0.996016 | − | 0.0891697i | \(-0.0284213\pi\) |
−0.575231 | + | 0.817991i | \(0.695088\pi\) | |||||||
\(978\) | −15.0473 | −0.481161 | ||||||||
\(979\) | 0.367430 | − | 0.636407i | 0.0117431 | − | 0.0203397i | ||||
\(980\) | 1.39736 | 0.0446370 | ||||||||
\(981\) | 17.6159 | 0.562432 | ||||||||
\(982\) | −18.9002 | − | 32.7362i | −0.603130 | − | 1.04465i | ||||
\(983\) | 9.50229 | 0.303076 | 0.151538 | − | 0.988451i | \(-0.451577\pi\) | ||||
0.151538 | + | 0.988451i | \(0.451577\pi\) | |||||||
\(984\) | 12.9476 | − | 22.4258i | 0.412753 | − | 0.714910i | ||||
\(985\) | 0.182097 | − | 0.315401i | 0.00580209 | − | 0.0100495i | ||||
\(986\) | −5.23033 | − | 9.05920i | −0.166568 | − | 0.288504i | ||||
\(987\) | 1.41112 | + | 2.44412i | 0.0449163 | + | 0.0777974i | ||||
\(988\) | −0.515230 | − | 0.892405i | −0.0163917 | − | 0.0283912i | ||||
\(989\) | 11.1449 | + | 19.3035i | 0.354386 | + | 0.613815i | ||||
\(990\) | −1.25418 | −0.0398605 | ||||||||
\(991\) | −10.2654 | −0.326090 | −0.163045 | − | 0.986619i | \(-0.552132\pi\) | ||||
−0.163045 | + | 0.986619i | \(0.552132\pi\) | |||||||
\(992\) | 1.30965 | + | 2.26837i | 0.0415813 | + | 0.0720209i | ||||
\(993\) | −1.65108 | + | 2.85976i | −0.0523955 | + | 0.0907517i | ||||
\(994\) | −11.0822 | + | 19.1949i | −0.351506 | + | 0.608825i | ||||
\(995\) | 6.74950 | + | 11.6905i | 0.213973 | + | 0.370613i | ||||
\(996\) | 0.631605 | 0.0200132 | ||||||||
\(997\) | 32.6943 | 1.03544 | 0.517719 | − | 0.855551i | \(-0.326781\pi\) | ||||
0.517719 | + | 0.855551i | \(0.326781\pi\) | |||||||
\(998\) | 11.8610 | − | 20.5439i | 0.375455 | − | 0.650307i | ||||
\(999\) | 2.67890 | + | 4.63999i | 0.0847567 | + | 0.146803i |
(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 | 201.2.e.b.37.4 | ✓ | 10 | |
3.2 | odd | 2 | 603.2.g.g.37.2 | 10 | |||
67.29 | even | 3 | inner | 201.2.e.b.163.4 | yes | 10 | |
201.29 | odd | 6 | 603.2.g.g.163.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.e.b.37.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
201.2.e.b.163.4 | yes | 10 | 67.29 | even | 3 | inner | |
603.2.g.g.37.2 | 10 | 3.2 | odd | 2 | |||
603.2.g.g.163.2 | 10 | 201.29 | odd | 6 |