Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(-1.27597 - 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.901 |
Dual form | 1170.2.bs.g.361.1 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24653 | + | 0.719687i | −0.471146 | + | 0.272016i | −0.716719 | − | 0.697362i | \(-0.754357\pi\) |
0.245574 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −3.49837 | − | 2.01978i | −1.05480 | − | 0.608988i | −0.130809 | − | 0.991408i | \(-0.541758\pi\) |
−0.923989 | + | 0.382420i | \(0.875091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.13234 | + | 1.78561i | 0.868756 | + | 0.495240i | ||||
\(14\) | 1.43937 | 0.384689 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.15376 | − | 1.99837i | −0.279828 | − | 0.484676i | 0.691514 | − | 0.722363i | \(-0.256944\pi\) |
−0.971342 | + | 0.237687i | \(0.923611\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.346241 | + | 0.199902i | −0.0794331 | + | 0.0458607i | −0.539190 | − | 0.842184i | \(-0.681270\pi\) |
0.459757 | + | 0.888045i | \(0.347936\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.01978 | + | 3.49837i | 0.430620 | + | 0.745855i | ||||
\(23\) | −0.780313 | + | 1.35154i | −0.162707 | + | 0.281816i | −0.935838 | − | 0.352429i | \(-0.885356\pi\) |
0.773132 | + | 0.634245i | \(0.218689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.81988 | − | 3.11256i | −0.356908 | − | 0.610423i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.24653 | − | 0.719687i | −0.235573 | − | 0.136008i | ||||
\(29\) | −3.93244 | + | 6.81119i | −0.730236 | + | 1.26481i | 0.226546 | + | 0.974000i | \(0.427257\pi\) |
−0.956782 | + | 0.290806i | \(0.906077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.10713i | − | 0.558057i | −0.960283 | − | 0.279028i | \(-0.909988\pi\) | ||
0.960283 | − | 0.279028i | \(-0.0900123\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.30752i | 0.395736i | ||||||||
\(35\) | −0.719687 | − | 1.24653i | −0.121649 | − | 0.210703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.40029 | − | 3.11786i | −0.887803 | − | 0.512573i | −0.0145796 | − | 0.999894i | \(-0.504641\pi\) |
−0.873223 | + | 0.487321i | \(0.837974\pi\) | |||||||
\(38\) | 0.399804 | 0.0648568 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.659061 | + | 0.380509i | 0.102928 | + | 0.0594255i | 0.550580 | − | 0.834782i | \(-0.314406\pi\) |
−0.447652 | + | 0.894208i | \(0.647740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50367 | − | 9.53264i | −0.839302 | − | 1.45371i | −0.890479 | − | 0.455024i | \(-0.849631\pi\) |
0.0511772 | − | 0.998690i | \(-0.483703\pi\) | |||||||
\(44\) | − | 4.03957i | − | 0.608988i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.35154 | − | 0.780313i | 0.199274 | − | 0.115051i | ||||
\(47\) | − | 5.84016i | − | 0.851874i | −0.904753 | − | 0.425937i | \(-0.859944\pi\) | ||
0.904753 | − | 0.425937i | \(-0.140056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.46410 | + | 4.26795i | −0.352015 | + | 0.609707i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0197847 | + | 3.60550i | 0.00274365 | + | 0.499992i | ||||
\(53\) | −10.6249 | −1.45945 | −0.729723 | − | 0.683743i | \(-0.760351\pi\) | ||||
−0.729723 | + | 0.683743i | \(0.760351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.01978 | − | 3.49837i | 0.272348 | − | 0.471720i | ||||
\(56\) | 0.719687 | + | 1.24653i | 0.0961722 | + | 0.166575i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.81119 | − | 3.93244i | 0.894353 | − | 0.516355i | ||||
\(59\) | 3.00000 | − | 1.73205i | 0.390567 | − | 0.225494i | −0.291839 | − | 0.956467i | \(-0.594267\pi\) |
0.682406 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.84624 | + | 4.92983i | 0.364424 | + | 0.631200i | 0.988684 | − | 0.150016i | \(-0.0479326\pi\) |
−0.624260 | + | 0.781217i | \(0.714599\pi\) | |||||||
\(62\) | −1.55356 | + | 2.69085i | −0.197303 | + | 0.341738i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.78561 | + | 3.13234i | −0.221478 | + | 0.388519i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00734 | − | 5.20039i | −1.10042 | − | 0.635329i | −0.164090 | − | 0.986445i | \(-0.552469\pi\) |
−0.936332 | + | 0.351116i | \(0.885802\pi\) | |||||||
\(68\) | 1.15376 | − | 1.99837i | 0.139914 | − | 0.242338i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.43937i | 0.172038i | ||||||||
\(71\) | −5.19615 | + | 3.00000i | −0.616670 | + | 0.356034i | −0.775571 | − | 0.631260i | \(-0.782538\pi\) |
0.158901 | + | 0.987294i | \(0.449205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.4608i | − | 1.57547i | −0.616013 | − | 0.787736i | \(-0.711253\pi\) | ||
0.616013 | − | 0.787736i | \(-0.288747\pi\) | |||||||
\(74\) | 3.11786 | + | 5.40029i | 0.362444 | + | 0.627771i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.346241 | − | 0.199902i | −0.0397165 | − | 0.0229303i | ||||
\(77\) | 5.81445 | 0.662618 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.931464 | 0.104798 | 0.0523989 | − | 0.998626i | \(-0.483313\pi\) | ||||
0.0523989 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.380509 | − | 0.659061i | −0.0420202 | − | 0.0727811i | ||||
\(83\) | − | 10.3867i | − | 1.14008i | −0.821616 | − | 0.570042i | \(-0.806927\pi\) | ||
0.821616 | − | 0.570042i | \(-0.193073\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.99837 | − | 1.15376i | 0.216754 | − | 0.125143i | ||||
\(86\) | 11.0073i | 1.18695i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.01978 | + | 3.49837i | −0.215310 | + | 0.372927i | ||||
\(89\) | 0.840939 | + | 0.485517i | 0.0891394 | + | 0.0514647i | 0.543907 | − | 0.839145i | \(-0.316944\pi\) |
−0.454768 | + | 0.890610i | \(0.650278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.18966 | + | 0.0284776i | −0.544024 | + | 0.00298526i | ||||
\(92\) | −1.56063 | −0.162707 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.92008 | + | 5.05772i | −0.301183 | + | 0.521664i | ||||
\(95\) | −0.199902 | − | 0.346241i | −0.0205095 | − | 0.0355235i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6680 | + | 6.15919i | −1.08317 | + | 0.625371i | −0.931751 | − | 0.363098i | \(-0.881719\pi\) |
−0.151424 | + | 0.988469i | \(0.548386\pi\) | |||||||
\(98\) | 4.26795 | − | 2.46410i | 0.431128 | − | 0.248912i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −2.41747 | + | 4.18718i | −0.240547 | + | 0.416640i | −0.960870 | − | 0.276999i | \(-0.910660\pi\) |
0.720323 | + | 0.693639i | \(0.243994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.73205 | −0.564796 | −0.282398 | − | 0.959297i | \(-0.591130\pi\) | ||||
−0.282398 | + | 0.959297i | \(0.591130\pi\) | |||||||
\(104\) | 1.78561 | − | 3.13234i | 0.175094 | − | 0.307152i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.20145 | + | 5.31246i | 0.893724 | + | 0.515992i | ||||
\(107\) | −6.43774 | + | 11.1505i | −0.622360 | + | 1.07796i | 0.366685 | + | 0.930345i | \(0.380493\pi\) |
−0.989045 | + | 0.147614i | \(0.952841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.214254i | − | 0.0205219i | −0.999947 | − | 0.0102609i | \(-0.996734\pi\) | ||
0.999947 | − | 0.0102609i | \(-0.00326621\pi\) | |||||||
\(110\) | −3.49837 | + | 2.01978i | −0.333556 | + | 0.192579i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.43937i | − | 0.136008i | ||||||
\(113\) | −0.0642973 | − | 0.111366i | −0.00604858 | − | 0.0104765i | 0.862985 | − | 0.505229i | \(-0.168592\pi\) |
−0.869034 | + | 0.494753i | \(0.835259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.35154 | − | 0.780313i | −0.126032 | − | 0.0727646i | ||||
\(116\) | −7.86488 | −0.730236 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.46410 | −0.318896 | ||||||||
\(119\) | 2.87640 | + | 1.66069i | 0.263679 | + | 0.152235i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65906 | + | 4.60563i | 0.241733 | + | 0.418693i | ||||
\(122\) | − | 5.69248i | − | 0.515373i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.69085 | − | 1.55356i | 0.241646 | − | 0.139514i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.06218 | + | 13.9641i | −0.715403 | + | 1.23911i | 0.247401 | + | 0.968913i | \(0.420423\pi\) |
−0.962804 | + | 0.270201i | \(0.912910\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.11256 | − | 1.81988i | 0.272990 | − | 0.159614i | ||||
\(131\) | −2.78010 | −0.242898 | −0.121449 | − | 0.992598i | \(-0.538754\pi\) | ||||
−0.121449 | + | 0.992598i | \(0.538754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.287734 | − | 0.498370i | 0.0249497 | − | 0.0432141i | ||||
\(134\) | 5.20039 | + | 9.00734i | 0.449245 | + | 0.778116i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.99837 | + | 1.15376i | −0.171359 | + | 0.0989340i | ||||
\(137\) | 4.73487 | − | 2.73368i | 0.404528 | − | 0.233554i | −0.283908 | − | 0.958851i | \(-0.591631\pi\) |
0.688436 | + | 0.725297i | \(0.258298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.107258 | + | 0.185777i | 0.00909753 | + | 0.0157574i | 0.870538 | − | 0.492101i | \(-0.163771\pi\) |
−0.861441 | + | 0.507858i | \(0.830437\pi\) | |||||||
\(140\) | 0.719687 | − | 1.24653i | 0.0608246 | − | 0.105351i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −7.35154 | − | 12.5734i | −0.614767 | − | 1.05144i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.81119 | − | 3.93244i | −0.565639 | − | 0.326572i | ||||
\(146\) | −6.73042 | + | 11.6574i | −0.557014 | + | 0.964776i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.23572i | − | 0.512573i | ||||||
\(149\) | −14.3149 | + | 8.26469i | −1.17272 | + | 0.677070i | −0.954319 | − | 0.298790i | \(-0.903417\pi\) |
−0.218400 | + | 0.975859i | \(0.570084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.70830i | 0.545914i | 0.962026 | + | 0.272957i | \(0.0880016\pi\) | ||||
−0.962026 | + | 0.272957i | \(0.911998\pi\) | |||||||
\(152\) | 0.199902 | + | 0.346241i | 0.0162142 | + | 0.0280838i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.03546 | − | 2.90723i | −0.405769 | − | 0.234271i | ||||
\(155\) | 3.10713 | 0.249570 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.81684 | 0.464234 | 0.232117 | − | 0.972688i | \(-0.425435\pi\) | ||||
0.232117 | + | 0.972688i | \(0.425435\pi\) | |||||||
\(158\) | −0.806671 | − | 0.465732i | −0.0641753 | − | 0.0370516i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | − | 2.24632i | − | 0.177035i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.61341 | − | 2.08620i | 0.283024 | − | 0.163404i | −0.351768 | − | 0.936087i | \(-0.614419\pi\) |
0.634792 | + | 0.772683i | \(0.281086\pi\) | |||||||
\(164\) | 0.761018i | 0.0594255i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.19333 | + | 8.99511i | −0.403080 | + | 0.698156i | ||||
\(167\) | 13.5174 | + | 7.80426i | 1.04601 | + | 0.603912i | 0.921528 | − | 0.388311i | \(-0.126941\pi\) |
0.124477 | + | 0.992222i | \(0.460275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.62316 | + | 11.1863i | 0.509474 | + | 0.860486i | ||||
\(170\) | −2.30752 | −0.176979 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.50367 | − | 9.53264i | 0.419651 | − | 0.726857i | ||||
\(173\) | −2.90723 | − | 5.03546i | −0.221032 | − | 0.382839i | 0.734089 | − | 0.679053i | \(-0.237609\pi\) |
−0.955122 | + | 0.296214i | \(0.904276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.24653 | − | 0.719687i | 0.0942291 | − | 0.0544032i | ||||
\(176\) | 3.49837 | − | 2.01978i | 0.263700 | − | 0.152247i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.485517 | − | 0.840939i | −0.0363910 | − | 0.0630311i | ||||
\(179\) | 8.43611 | − | 14.6118i | 0.630545 | − | 1.09214i | −0.356896 | − | 0.934144i | \(-0.616165\pi\) |
0.987441 | − | 0.157991i | \(-0.0505018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6207 | 0.938088 | 0.469044 | − | 0.883175i | \(-0.344599\pi\) | ||||
0.469044 | + | 0.883175i | \(0.344599\pi\) | |||||||
\(182\) | 4.50861 | + | 2.57017i | 0.334201 | + | 0.190513i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.35154 | + | 0.780313i | 0.0996370 | + | 0.0575254i | ||||
\(185\) | 3.11786 | − | 5.40029i | 0.229230 | − | 0.397037i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.32138i | 0.681647i | ||||||||
\(188\) | 5.05772 | − | 2.92008i | 0.368872 | − | 0.212969i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.399804i | 0.0290049i | ||||||||
\(191\) | 0.670362 | + | 1.16110i | 0.0485057 | + | 0.0840143i | 0.889259 | − | 0.457404i | \(-0.151221\pi\) |
−0.840753 | + | 0.541419i | \(0.817887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5004 | − | 8.37182i | −1.04376 | − | 0.602616i | −0.122866 | − | 0.992423i | \(-0.539208\pi\) |
−0.920897 | + | 0.389807i | \(0.872542\pi\) | |||||||
\(194\) | 12.3184 | 0.884408 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.92820 | −0.352015 | ||||||||
\(197\) | −0.863202 | − | 0.498370i | −0.0615006 | − | 0.0355074i | 0.468934 | − | 0.883233i | \(-0.344638\pi\) |
−0.530435 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.30752 | − | 2.26469i | −0.0926875 | − | 0.160540i | 0.815954 | − | 0.578117i | \(-0.196212\pi\) |
−0.908641 | + | 0.417578i | \(0.862879\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.18718 | − | 2.41747i | 0.294609 | − | 0.170093i | ||||
\(203\) | − | 11.3205i | − | 0.794544i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.380509 | + | 0.659061i | −0.0265759 | + | 0.0460308i | ||||
\(206\) | 4.96410 | + | 2.86603i | 0.345865 | + | 0.199685i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.11256 | + | 1.81988i | −0.215817 | + | 0.126186i | ||||
\(209\) | 1.61504 | 0.111714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.56691 | − | 7.91011i | 0.314399 | − | 0.544555i | −0.664911 | − | 0.746923i | \(-0.731530\pi\) |
0.979310 | + | 0.202368i | \(0.0648638\pi\) | |||||||
\(212\) | −5.31246 | − | 9.20145i | −0.364861 | − | 0.631958i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.1505 | − | 6.43774i | 0.762232 | − | 0.440075i | ||||
\(215\) | 9.53264 | − | 5.50367i | 0.650121 | − | 0.375347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.23616 | + | 3.87314i | 0.151800 | + | 0.262926i | ||||
\(218\) | −0.107127 | + | 0.185550i | −0.00725557 | + | 0.0125670i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.03957 | 0.272348 | ||||||||
\(221\) | −0.0456536 | − | 8.31975i | −0.00307099 | − | 0.559647i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.03326 | + | 2.90595i | 0.337052 | + | 0.194597i | 0.658968 | − | 0.752171i | \(-0.270993\pi\) |
−0.321916 | + | 0.946768i | \(0.604327\pi\) | |||||||
\(224\) | −0.719687 | + | 1.24653i | −0.0480861 | + | 0.0832876i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.128595i | 0.00855399i | ||||||||
\(227\) | 9.99674 | − | 5.77162i | 0.663507 | − | 0.383076i | −0.130105 | − | 0.991500i | \(-0.541531\pi\) |
0.793612 | + | 0.608424i | \(0.208198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8755i | 0.850836i | 0.904997 | + | 0.425418i | \(0.139873\pi\) | ||||
−0.904997 | + | 0.425418i | \(0.860127\pi\) | |||||||
\(230\) | 0.780313 | + | 1.35154i | 0.0514523 | + | 0.0891180i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.81119 | + | 3.93244i | 0.447177 | + | 0.258177i | ||||
\(233\) | 10.4149 | 0.682303 | 0.341152 | − | 0.940008i | \(-0.389183\pi\) | ||||
0.341152 | + | 0.940008i | \(0.389183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.84016 | 0.380970 | ||||||||
\(236\) | 3.00000 | + | 1.73205i | 0.195283 | + | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.66069 | − | 2.87640i | −0.107647 | − | 0.186449i | ||||
\(239\) | 18.3801i | 1.18891i | 0.804128 | + | 0.594456i | \(0.202633\pi\) | ||||
−0.804128 | + | 0.594456i | \(0.797367\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.536681 | − | 0.309853i | 0.0345707 | − | 0.0199594i | −0.482615 | − | 0.875833i | \(-0.660313\pi\) |
0.517186 | + | 0.855873i | \(0.326980\pi\) | |||||||
\(242\) | − | 5.31812i | − | 0.341862i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.84624 | + | 4.92983i | −0.182212 | + | 0.315600i | ||||
\(245\) | −4.26795 | − | 2.46410i | −0.272669 | − | 0.157426i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.44149 | + | 0.00791002i | −0.0917200 | + | 0.000503302i | ||||
\(248\) | −3.10713 | −0.197303 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 2.65376 | + | 4.59645i | 0.167504 | + | 0.290125i | 0.937542 | − | 0.347873i | \(-0.113096\pi\) |
−0.770038 | + | 0.637998i | \(0.779763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.45965 | − | 3.15213i | 0.343245 | − | 0.198173i | ||||
\(254\) | 13.9641 | − | 8.06218i | 0.876186 | − | 0.505866i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.3686 | + | 21.4230i | −0.771529 | + | 1.33633i | 0.165195 | + | 0.986261i | \(0.447175\pi\) |
−0.936725 | + | 0.350067i | \(0.886159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.97553 | 0.557713 | ||||||||
\(260\) | −3.60550 | + | 0.0197847i | −0.223603 | + | 0.00122700i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.40764 | + | 1.39005i | 0.148744 | + | 0.0858775i | ||||
\(263\) | 2.56466 | − | 4.44211i | 0.158143 | − | 0.273912i | −0.776056 | − | 0.630664i | \(-0.782782\pi\) |
0.934199 | + | 0.356752i | \(0.116116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.6249i | − | 0.652684i | ||||||
\(266\) | −0.498370 | + | 0.287734i | −0.0305570 | + | 0.0176421i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 10.4008i | − | 0.635329i | ||||||
\(269\) | 3.40687 | + | 5.90087i | 0.207720 | + | 0.359782i | 0.950996 | − | 0.309203i | \(-0.100062\pi\) |
−0.743276 | + | 0.668985i | \(0.766729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0709 | − | 11.0106i | −1.15848 | − | 0.668846i | −0.207538 | − | 0.978227i | \(-0.566545\pi\) |
−0.950938 | + | 0.309381i | \(0.899878\pi\) | |||||||
\(272\) | 2.30752 | 0.139914 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.46736 | −0.330295 | ||||||||
\(275\) | 3.49837 | + | 2.01978i | 0.210960 | + | 0.121798i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7152 | + | 22.0233i | 0.763980 | + | 1.32325i | 0.940784 | + | 0.339006i | \(0.110091\pi\) |
−0.176805 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(278\) | − | 0.214517i | − | 0.0128659i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.24653 | + | 0.719687i | −0.0744947 | + | 0.0430095i | ||||
\(281\) | − | 25.0954i | − | 1.49707i | −0.663098 | − | 0.748533i | \(-0.730759\pi\) | ||
0.663098 | − | 0.748533i | \(-0.269241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.882986 | − | 1.52938i | 0.0524881 | − | 0.0909120i | −0.838588 | − | 0.544767i | \(-0.816618\pi\) |
0.891076 | + | 0.453855i | \(0.149952\pi\) | |||||||
\(284\) | −5.19615 | − | 3.00000i | −0.308335 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0799217 | + | 14.5647i | 0.00472587 | + | 0.861226i | ||||
\(287\) | −1.09539 | −0.0646588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.83768 | − | 10.1112i | 0.343393 | − | 0.594774i | ||||
\(290\) | 3.93244 | + | 6.81119i | 0.230921 | + | 0.399967i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6574 | − | 6.73042i | 0.682200 | − | 0.393868i | ||||
\(293\) | 15.9374 | − | 9.20145i | 0.931072 | − | 0.537555i | 0.0439215 | − | 0.999035i | \(-0.486015\pi\) |
0.887150 | + | 0.461480i | \(0.152682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73205 | + | 3.00000i | 0.100844 | + | 0.174667i | ||||
\(296\) | −3.11786 | + | 5.40029i | −0.181222 | + | 0.313886i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.5294 | 0.957521 | ||||||||
\(299\) | −4.85754 | + | 2.84016i | −0.280919 | + | 0.164250i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.7210 | + | 7.92184i | 0.790867 | + | 0.456607i | ||||
\(302\) | 3.35415 | − | 5.80956i | 0.193010 | − | 0.334303i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.399804i | − | 0.0229303i | ||||||
\(305\) | −4.92983 | + | 2.84624i | −0.282281 | + | 0.162975i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.40730i | − | 0.479830i | −0.970794 | − | 0.239915i | \(-0.922880\pi\) | ||
0.970794 | − | 0.239915i | \(-0.0771196\pi\) | |||||||
\(308\) | 2.90723 | + | 5.03546i | 0.165655 | + | 0.286922i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.69085 | − | 1.55356i | −0.152830 | − | 0.0882365i | ||||
\(311\) | 33.6601 | 1.90869 | 0.954344 | − | 0.298708i | \(-0.0965557\pi\) | ||||
0.954344 | + | 0.298708i | \(0.0965557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0008 | 1.52618 | 0.763088 | − | 0.646294i | \(-0.223682\pi\) | ||||
0.763088 | + | 0.646294i | \(0.223682\pi\) | |||||||
\(314\) | −5.03753 | − | 2.90842i | −0.284284 | − | 0.164132i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.465732 | + | 0.806671i | 0.0261995 | + | 0.0453788i | ||||
\(317\) | 10.2569i | 0.576086i | 0.957617 | + | 0.288043i | \(0.0930047\pi\) | ||||
−0.957617 | + | 0.288043i | \(0.906995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.5143 | − | 15.8854i | 1.54050 | − | 0.889410i | ||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.12316 | + | 1.94537i | −0.0625914 | + | 0.108411i | ||||
\(323\) | 0.798957 | + | 0.461278i | 0.0444551 | + | 0.0256662i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.13234 | − | 1.78561i | −0.173751 | − | 0.0990481i | ||||
\(326\) | −4.17240 | −0.231088 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.380509 | − | 0.659061i | 0.0210101 | − | 0.0363905i | ||||
\(329\) | 4.20308 | + | 7.27995i | 0.231724 | + | 0.401357i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.92256 | + | 2.26469i | −0.215603 | + | 0.124479i | −0.603913 | − | 0.797050i | \(-0.706392\pi\) |
0.388310 | + | 0.921529i | \(0.373059\pi\) | |||||||
\(332\) | 8.99511 | − | 5.19333i | 0.493671 | − | 0.285021i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.80426 | − | 13.5174i | −0.427030 | − | 0.739638i | ||||
\(335\) | 5.20039 | − | 9.00734i | 0.284128 | − | 0.492124i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.72755 | 0.366473 | 0.183236 | − | 0.983069i | \(-0.441343\pi\) | ||||
0.183236 | + | 0.983069i | \(0.441343\pi\) | |||||||
\(338\) | −0.142667 | − | 12.9992i | −0.00776009 | − | 0.707064i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.99837 | + | 1.15376i | 0.108377 | + | 0.0625714i | ||||
\(341\) | −6.27573 | + | 10.8699i | −0.339850 | + | 0.588637i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.1691i | − | 0.927047i | ||||||
\(344\) | −9.53264 | + | 5.50367i | −0.513965 | + | 0.296738i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.81445i | 0.312587i | ||||||||
\(347\) | 1.57286 | + | 2.72427i | 0.0844355 | + | 0.146247i | 0.905151 | − | 0.425091i | \(-0.139758\pi\) |
−0.820715 | + | 0.571338i | \(0.806425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.09752 | − | 5.25246i | −0.486979 | − | 0.281158i | 0.236341 | − | 0.971670i | \(-0.424052\pi\) |
−0.723320 | + | 0.690513i | \(0.757385\pi\) | |||||||
\(350\) | −1.43937 | −0.0769378 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.03957 | −0.215310 | ||||||||
\(353\) | 28.5767 | + | 16.4988i | 1.52099 | + | 0.878141i | 0.999693 | + | 0.0247633i | \(0.00788320\pi\) |
0.521292 | + | 0.853378i | \(0.325450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00000 | − | 5.19615i | −0.159223 | − | 0.275783i | ||||
\(356\) | 0.971033i | 0.0514647i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.6118 | + | 8.43611i | −0.772256 | + | 0.445862i | ||||
\(359\) | − | 24.2487i | − | 1.27980i | −0.768459 | − | 0.639899i | \(-0.778976\pi\) | ||
0.768459 | − | 0.639899i | \(-0.221024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.42008 | + | 16.3161i | −0.495794 | + | 0.858740i | ||||
\(362\) | −10.9298 | − | 6.31034i | −0.574459 | − | 0.331664i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.61949 | − | 4.48014i | −0.137299 | − | 0.234823i | ||||
\(365\) | 13.4608 | 0.704573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.89924 | − | 17.1460i | 0.516736 | − | 0.895013i | −0.483075 | − | 0.875579i | \(-0.660480\pi\) |
0.999811 | − | 0.0194340i | \(-0.00618643\pi\) | |||||||
\(368\) | −0.780313 | − | 1.35154i | −0.0406766 | − | 0.0704540i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.40029 | + | 3.11786i | −0.280748 | + | 0.162090i | ||||
\(371\) | 13.2443 | − | 7.64662i | 0.687611 | − | 0.396993i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.39557 | − | 4.14924i | −0.124038 | − | 0.214840i | 0.797319 | − | 0.603559i | \(-0.206251\pi\) |
−0.921356 | + | 0.388719i | \(0.872918\pi\) | |||||||
\(374\) | 4.66069 | − | 8.07255i | 0.240999 | − | 0.417422i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.84016 | −0.301183 | ||||||||
\(377\) | −24.4799 | + | 14.3132i | −1.26078 | + | 0.737166i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8833 | − | 9.74760i | −0.867239 | − | 0.500700i | −0.000808945 | − | 1.00000i | \(-0.500257\pi\) |
−0.866430 | + | 0.499299i | \(0.833591\pi\) | |||||||
\(380\) | 0.199902 | − | 0.346241i | 0.0102548 | − | 0.0177618i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 1.34072i | − | 0.0685974i | ||||||
\(383\) | −11.1383 | + | 6.43068i | −0.569139 | + | 0.328592i | −0.756805 | − | 0.653640i | \(-0.773241\pi\) |
0.187667 | + | 0.982233i | \(0.439908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.81445i | 0.296332i | ||||||||
\(386\) | 8.37182 | + | 14.5004i | 0.426114 | + | 0.738051i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.6680 | − | 6.15919i | −0.541587 | − | 0.312686i | ||||
\(389\) | −6.94233 | −0.351990 | −0.175995 | − | 0.984391i | \(-0.556314\pi\) | ||||
−0.175995 | + | 0.984391i | \(0.556314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.60117 | 0.182119 | ||||||||
\(392\) | 4.26795 | + | 2.46410i | 0.215564 | + | 0.124456i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.498370 | + | 0.863202i | 0.0251075 | + | 0.0434875i | ||||
\(395\) | 0.931464i | 0.0468670i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.75184 | + | 2.16612i | −0.188299 | + | 0.108715i | −0.591186 | − | 0.806535i | \(-0.701340\pi\) |
0.402887 | + | 0.915250i | \(0.368007\pi\) | |||||||
\(398\) | 2.61504i | 0.131080i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 20.5448 | + | 11.8616i | 1.02596 | + | 0.592339i | 0.915825 | − | 0.401578i | \(-0.131538\pi\) |
0.110136 | + | 0.993917i | \(0.464871\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.54813 | − | 9.73259i | 0.276372 | − | 0.484815i | ||||
\(404\) | −4.83494 | −0.240547 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.66025 | + | 9.80385i | −0.280914 | + | 0.486557i | ||||
\(407\) | 12.5948 | + | 21.8149i | 0.624302 | + | 1.08132i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.2373 | + | 19.1896i | −1.64348 | + | 0.948864i | −0.663897 | + | 0.747824i | \(0.731099\pi\) |
−0.979583 | + | 0.201039i | \(0.935568\pi\) | |||||||
\(410\) | 0.659061 | − | 0.380509i | 0.0325487 | − | 0.0187920i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.86603 | − | 4.96410i | −0.141199 | − | 0.244564i | ||||
\(413\) | −2.49307 | + | 4.31812i | −0.122676 | + | 0.212481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3867 | 0.509861 | ||||||||
\(416\) | 3.60550 | − | 0.0197847i | 0.176774 | − | 0.000970026i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.39866 | − | 0.807519i | −0.0684109 | − | 0.0394970i | ||||
\(419\) | −19.2946 | + | 33.4192i | −0.942602 | + | 1.63263i | −0.182120 | + | 0.983276i | \(0.558296\pi\) |
−0.760482 | + | 0.649359i | \(0.775037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.6199i | 1.97969i | 0.142134 | + | 0.989847i | \(0.454603\pi\) | ||||
−0.142134 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(422\) | −7.91011 | + | 4.56691i | −0.385058 | + | 0.222314i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.6249i | 0.515992i | ||||||||
\(425\) | 1.15376 | + | 1.99837i | 0.0559655 | + | 0.0969352i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.09587 | − | 4.09680i | −0.343393 | − | 0.198258i | ||||
\(428\) | −12.8755 | −0.622360 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.0073 | −0.530821 | ||||||||
\(431\) | −10.1945 | − | 5.88581i | −0.491053 | − | 0.283509i | 0.233958 | − | 0.972247i | \(-0.424832\pi\) |
−0.725011 | + | 0.688737i | \(0.758165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.5004 | − | 28.5795i | −0.792959 | − | 1.37345i | −0.924127 | − | 0.382085i | \(-0.875206\pi\) |
0.131168 | − | 0.991360i | \(-0.458127\pi\) | |||||||
\(434\) | − | 4.47232i | − | 0.214678i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.185550 | − | 0.107127i | 0.00888622 | − | 0.00513046i | ||||
\(437\) | − | 0.623945i | − | 0.0298473i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.348718 | − | 0.603998i | 0.0166434 | − | 0.0288272i | −0.857584 | − | 0.514344i | \(-0.828035\pi\) |
0.874227 | + | 0.485517i | \(0.161369\pi\) | |||||||
\(440\) | −3.49837 | − | 2.01978i | −0.166778 | − | 0.0962895i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.12034 | + | 7.22794i | −0.195985 | + | 0.343798i | ||||
\(443\) | −28.6297 | −1.36024 | −0.680120 | − | 0.733101i | \(-0.738072\pi\) | ||||
−0.680120 | + | 0.733101i | \(0.738072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.485517 | + | 0.840939i | −0.0230157 | + | 0.0398644i | ||||
\(446\) | −2.90595 | − | 5.03326i | −0.137601 | − | 0.238332i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.24653 | − | 0.719687i | 0.0588932 | − | 0.0340020i | ||||
\(449\) | 5.87601 | − | 3.39251i | 0.277306 | − | 0.160103i | −0.354897 | − | 0.934905i | \(-0.615484\pi\) |
0.632203 | + | 0.774803i | \(0.282151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.53709 | − | 2.66232i | −0.0723788 | − | 0.125364i | ||||
\(452\) | 0.0642973 | − | 0.111366i | 0.00302429 | − | 0.00523823i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.5432 | −0.541751 | ||||||||
\(455\) | −0.0284776 | − | 5.18966i | −0.00133505 | − | 0.243295i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5355 | + | 8.96940i | 0.726718 | + | 0.419571i | 0.817220 | − | 0.576325i | \(-0.195514\pi\) |
−0.0905021 | + | 0.995896i | \(0.528847\pi\) | |||||||
\(458\) | 6.43774 | − | 11.1505i | 0.300816 | − | 0.521029i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 1.56063i | − | 0.0727646i | ||||||
\(461\) | 23.2937 | − | 13.4486i | 1.08489 | − | 0.626364i | 0.152682 | − | 0.988275i | \(-0.451209\pi\) |
0.932213 | + | 0.361911i | \(0.117876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.8402i | − | 1.24737i | −0.781677 | − | 0.623684i | \(-0.785635\pi\) | ||
0.781677 | − | 0.623684i | \(-0.214365\pi\) | |||||||
\(464\) | −3.93244 | − | 6.81119i | −0.182559 | − | 0.316202i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.01957 | − | 5.20745i | −0.417824 | − | 0.241231i | ||||
\(467\) | −9.48726 | −0.439018 | −0.219509 | − | 0.975610i | \(-0.570446\pi\) | ||||
−0.219509 | + | 0.975610i | \(0.570446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.9706 | 0.691279 | ||||||||
\(470\) | −5.05772 | − | 2.92008i | −0.233295 | − | 0.134693i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.73205 | − | 3.00000i | −0.0797241 | − | 0.138086i | ||||
\(473\) | 44.4649i | 2.04450i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.346241 | − | 0.199902i | 0.0158866 | − | 0.00917214i | ||||
\(476\) | 3.32138i | 0.152235i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.19007 | − | 15.9177i | 0.420344 | − | 0.728057i | ||||
\(479\) | −9.71206 | − | 5.60726i | −0.443755 | − | 0.256202i | 0.261434 | − | 0.965221i | \(-0.415805\pi\) |
−0.705189 | + | 0.709019i | \(0.749138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3483 | − | 19.4091i | −0.517437 | − | 0.884977i | ||||
\(482\) | −0.619706 | −0.0282268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.65906 | + | 4.60563i | −0.120866 | + | 0.209347i | ||||
\(485\) | −6.15919 | − | 10.6680i | −0.279674 | − | 0.484410i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0137 | − | 13.8643i | 1.08816 | − | 0.628252i | 0.155077 | − | 0.987902i | \(-0.450437\pi\) |
0.933087 | + | 0.359650i | \(0.117104\pi\) | |||||||
\(488\) | 4.92983 | − | 2.84624i | 0.223163 | − | 0.128843i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.46410 | + | 4.26795i | 0.111317 | + | 0.192806i | ||||
\(491\) | −13.9377 | + | 24.1409i | −0.629002 | + | 1.08946i | 0.358751 | + | 0.933433i | \(0.383203\pi\) |
−0.987752 | + | 0.156029i | \(0.950131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1484 | 0.817361 | ||||||||
\(494\) | 1.25232 | + | 0.713896i | 0.0563448 | + | 0.0321197i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.69085 | + | 1.55356i | 0.120823 | + | 0.0697571i | ||||
\(497\) | 4.31812 | − | 7.47921i | 0.193694 | − | 0.335488i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.8040i | 1.64757i | 0.566901 | + | 0.823786i | \(0.308142\pi\) | ||||
−0.566901 | + | 0.823786i | \(0.691858\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.30752i | − | 0.236886i | ||||||
\(503\) | −19.2848 | − | 33.4022i | −0.859865 | − | 1.48933i | −0.872057 | − | 0.489404i | \(-0.837215\pi\) |
0.0121928 | − | 0.999926i | \(-0.496119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.18718 | − | 2.41747i | −0.186327 | − | 0.107576i | ||||
\(506\) | −6.30426 | −0.280258 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.1244 | −0.715403 | ||||||||
\(509\) | −24.9870 | − | 14.4262i | −1.10753 | − | 0.639431i | −0.169340 | − | 0.985558i | \(-0.554163\pi\) |
−0.938188 | + | 0.346126i | \(0.887497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.68759 | + | 16.7794i | 0.428554 | + | 0.742277i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.4230 | − | 12.3686i | 0.944927 | − | 0.545554i | ||||
\(515\) | − | 5.73205i | − | 0.252584i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7959 | + | 20.4310i | −0.518781 | + | 0.898556i | ||||
\(518\) | −7.77304 | − | 4.48777i | −0.341528 | − | 0.197181i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.13234 | + | 1.78561i | 0.137362 | + | 0.0783044i | ||||
\(521\) | 10.6422 | 0.466241 | 0.233121 | − | 0.972448i | \(-0.425106\pi\) | ||||
0.233121 | + | 0.972448i | \(0.425106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0759 | + | 33.0404i | −0.834130 | + | 1.44476i | 0.0606070 | + | 0.998162i | \(0.480696\pi\) |
−0.894737 | + | 0.446594i | \(0.852637\pi\) | |||||||
\(524\) | −1.39005 | − | 2.40764i | −0.0607246 | − | 0.105178i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.44211 | + | 2.56466i | −0.193685 | + | 0.111824i | ||||
\(527\) | −6.20919 | + | 3.58488i | −0.270477 | + | 0.156160i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2822 | + | 17.8093i | 0.447053 | + | 0.774319i | ||||
\(530\) | −5.31246 | + | 9.20145i | −0.230759 | + | 0.399686i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.575468 | 0.0249497 | ||||||||
\(533\) | 1.38496 | + | 2.36871i | 0.0599894 | + | 0.102600i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1505 | − | 6.43774i | −0.482078 | − | 0.278328i | ||||
\(536\) | −5.20039 | + | 9.00734i | −0.224623 | + | 0.389058i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 6.81373i | − | 0.293761i | ||||||
\(539\) | 17.2407 | − | 9.95391i | 0.742609 | − | 0.428745i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.46593i | 0.0630252i | 0.999503 | + | 0.0315126i | \(0.0100324\pi\) | ||||
−0.999503 | + | 0.0315126i | \(0.989968\pi\) | |||||||
\(542\) | 11.0106 | + | 19.0709i | 0.472946 | + | 0.819166i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.99837 | − | 1.15376i | −0.0856794 | − | 0.0494670i | ||||
\(545\) | 0.214254 | 0.00917765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2374 | −0.694262 | −0.347131 | − | 0.937817i | \(-0.612844\pi\) | ||||
−0.347131 | + | 0.937817i | \(0.612844\pi\) | |||||||
\(548\) | 4.73487 | + | 2.73368i | 0.202264 | + | 0.116777i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.01978 | − | 3.49837i | −0.0861239 | − | 0.149171i | ||||
\(551\) | − | 3.14441i | − | 0.133957i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.16110 | + | 0.670362i | −0.0493751 | + | 0.0285067i | ||||
\(554\) | − | 25.4303i | − | 1.08043i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.107258 | + | 0.185777i | −0.00454877 | + | 0.00787869i | ||||
\(557\) | −28.8599 | − | 16.6623i | −1.22283 | − | 0.706004i | −0.257314 | − | 0.966328i | \(-0.582837\pi\) |
−0.965521 | + | 0.260324i | \(0.916171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.217777 | − | 39.6869i | −0.00921099 | − | 1.67858i | ||||
\(560\) | 1.43937 | 0.0608246 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.5477 | + | 21.7332i | −0.529293 | + | 0.916762i | ||||
\(563\) | −3.75678 | − | 6.50693i | −0.158329 | − | 0.274234i | 0.775937 | − | 0.630810i | \(-0.217277\pi\) |
−0.934266 | + | 0.356576i | \(0.883944\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.111366 | − | 0.0642973i | 0.00468521 | − | 0.00270501i | ||||
\(566\) | −1.52938 | + | 0.882986i | −0.0642845 | + | 0.0371147i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | −6.45619 | + | 11.1825i | −0.270658 | + | 0.468793i | −0.969030 | − | 0.246941i | \(-0.920574\pi\) |
0.698373 | + | 0.715734i | \(0.253908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.47470 | 0.145412 | 0.0727059 | − | 0.997353i | \(-0.476837\pi\) | ||||
0.0727059 | + | 0.997353i | \(0.476837\pi\) | |||||||
\(572\) | 7.21311 | − | 12.6533i | 0.301595 | − | 0.529062i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.948635 | + | 0.547694i | 0.0395952 | + | 0.0228603i | ||||
\(575\) | 0.780313 | − | 1.35154i | 0.0325413 | − | 0.0563632i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.80287i | 0.366468i | 0.983069 | + | 0.183234i | \(0.0586566\pi\) | ||||
−0.983069 | + | 0.183234i | \(0.941343\pi\) | |||||||
\(578\) | −10.1112 | + | 5.83768i | −0.420569 | + | 0.242815i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 7.86488i | − | 0.326572i | ||||||
\(581\) | 7.47514 | + | 12.9473i | 0.310121 | + | 0.537146i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.1699 | + | 21.4601i | 1.53942 | + | 0.888785i | ||||
\(584\) | −13.4608 | −0.557014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.4029 | −0.760217 | ||||||||
\(587\) | −30.9967 | − | 17.8960i | −1.27937 | − | 0.738646i | −0.302639 | − | 0.953105i | \(-0.597868\pi\) |
−0.976733 | + | 0.214459i | \(0.931201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.621121 | + | 1.07581i | 0.0255929 | + | 0.0443281i | ||||
\(590\) | − | 3.46410i | − | 0.142615i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.40029 | − | 3.11786i | 0.221951 | − | 0.128143i | ||||
\(593\) | 3.93555i | 0.161613i | 0.996730 | + | 0.0808067i | \(0.0257497\pi\) | ||||
−0.996730 | + | 0.0808067i | \(0.974250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.66069 | + | 2.87640i | −0.0680817 | + | 0.117921i | ||||
\(596\) | −14.3149 | − | 8.26469i | −0.586360 | − | 0.338535i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.62683 | − | 0.0308766i | 0.230098 | − | 0.00126264i | ||||
\(599\) | 9.50704 | 0.388447 | 0.194223 | − | 0.980957i | \(-0.437781\pi\) | ||||
0.194223 | + | 0.980957i | \(0.437781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4935 | + | 30.2996i | −0.713574 | + | 1.23595i | 0.249933 | + | 0.968263i | \(0.419591\pi\) |
−0.963507 | + | 0.267683i | \(0.913742\pi\) | |||||||
\(602\) | −7.92184 | − | 13.7210i | −0.322870 | − | 0.559227i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.80956 | + | 3.35415i | −0.236388 | + | 0.136478i | ||||
\(605\) | −4.60563 | + | 2.65906i | −0.187245 | + | 0.108106i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.08054 | + | 13.9959i | 0.327979 | + | 0.568076i | 0.982111 | − | 0.188304i | \(-0.0602991\pi\) |
−0.654132 | + | 0.756381i | \(0.726966\pi\) | |||||||
\(608\) | −0.199902 | + | 0.346241i | −0.00810710 | + | 0.0140419i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.69248 | 0.230482 | ||||||||
\(611\) | 10.4283 | − | 18.2934i | 0.421883 | − | 0.740071i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.68335 | − | 4.43598i | −0.310327 | − | 0.179168i | 0.336746 | − | 0.941596i | \(-0.390674\pi\) |
−0.647073 | + | 0.762428i | \(0.724007\pi\) | |||||||
\(614\) | −4.20365 | + | 7.28094i | −0.169646 | + | 0.293835i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 5.81445i | − | 0.234271i | ||||||
\(617\) | 9.39557 | − | 5.42453i | 0.378251 | − | 0.218383i | −0.298806 | − | 0.954314i | \(-0.596588\pi\) |
0.677057 | + | 0.735930i | \(0.263255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.82727i | 0.234218i | 0.993119 | + | 0.117109i | \(0.0373627\pi\) | ||||
−0.993119 | + | 0.117109i | \(0.962637\pi\) | |||||||
\(620\) | 1.55356 | + | 2.69085i | 0.0623926 | + | 0.108067i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.1505 | − | 16.8300i | −1.16883 | − | 0.674823i | ||||
\(623\) | −1.39768 | −0.0559969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.3834 | − | 13.5004i | −0.934589 | − | 0.539585i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.90842 | + | 5.03753i | 0.116059 | + | 0.201019i | ||||
\(629\) | 14.3890i | 0.573729i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.17169 | + | 4.71793i | −0.325310 | + | 0.187818i | −0.653757 | − | 0.756705i | \(-0.726808\pi\) |
0.328447 | + | 0.944522i | \(0.393475\pi\) | |||||||
\(632\) | − | 0.931464i | − | 0.0370516i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.12846 | − | 8.88276i | 0.203677 | − | 0.352779i | ||||
\(635\) | −13.9641 | − | 8.06218i | −0.554148 | − | 0.319938i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.3393 | + | 8.96875i | −0.607766 | + | 0.355355i | ||||
\(638\) | −31.7707 | −1.25782 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −20.2877 | − | 35.1392i | −0.801314 | − | 1.38792i | −0.918751 | − | 0.394837i | \(-0.870801\pi\) |
0.117437 | − | 0.993080i | \(-0.462532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.08527 | + | 2.93598i | −0.200543 | + | 0.115784i | −0.596909 | − | 0.802309i | \(-0.703605\pi\) |
0.396365 | + | 0.918093i | \(0.370271\pi\) | |||||||
\(644\) | 1.94537 | − | 1.12316i | 0.0766585 | − | 0.0442588i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.461278 | − | 0.798957i | −0.0181487 | − | 0.0314345i | ||||
\(647\) | −19.3652 | + | 33.5416i | −0.761326 | + | 1.31866i | 0.180841 | + | 0.983512i | \(0.442118\pi\) |
−0.942167 | + | 0.335143i | \(0.891215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9935 | −0.549292 | ||||||||
\(650\) | 1.81988 | + | 3.11256i | 0.0713817 | + | 0.122085i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.61341 | + | 2.08620i | 0.141512 | + | 0.0817020i | ||||
\(653\) | −6.45492 | + | 11.1802i | −0.252601 | + | 0.437517i | −0.964241 | − | 0.265027i | \(-0.914619\pi\) |
0.711641 | + | 0.702544i | \(0.247953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.78010i | − | 0.108627i | ||||||
\(656\) | −0.659061 | + | 0.380509i | −0.0257320 | + | 0.0148564i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 8.40617i | − | 0.327707i | ||||||
\(659\) | −3.20654 | − | 5.55389i | −0.124909 | − | 0.216349i | 0.796788 | − | 0.604259i | \(-0.206531\pi\) |
−0.921697 | + | 0.387910i | \(0.873197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.05300 | − | 3.49470i | −0.235434 | − | 0.135928i | 0.377642 | − | 0.925952i | \(-0.376735\pi\) |
−0.613076 | + | 0.790024i | \(0.710068\pi\) | |||||||
\(662\) | 4.52938 | 0.176039 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3867 | −0.403080 | ||||||||
\(665\) | 0.498370 | + | 0.287734i | 0.0193260 | + | 0.0111578i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.13707 | − | 10.6297i | −0.237628 | − | 0.411584i | ||||
\(668\) | 15.6085i | 0.603912i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.00734 | + | 5.20039i | −0.347984 | + | 0.200909i | ||||
\(671\) | − | 22.9952i | − | 0.887719i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3083 | + | 40.3712i | −0.898470 | + | 1.55620i | −0.0690207 | + | 0.997615i | \(0.521987\pi\) |
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(674\) | −5.82623 | − | 3.36377i | −0.224418 | − | 0.129568i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.37605 | + | 11.3290i | −0.245233 | + | 0.435730i | ||||
\(677\) | −6.85102 | −0.263306 | −0.131653 | − | 0.991296i | \(-0.542028\pi\) | ||||
−0.131653 | + | 0.991296i | \(0.542028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.86538 | − | 15.3553i | 0.340222 | − | 0.589282i | ||||
\(680\) | −1.15376 | − | 1.99837i | −0.0442446 | − | 0.0766340i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.8699 | − | 6.27573i | 0.416229 | − | 0.240310i | ||||
\(683\) | 21.2374 | − | 12.2614i | 0.812627 | − | 0.469171i | −0.0352402 | − | 0.999379i | \(-0.511220\pi\) |
0.847867 | + | 0.530208i | \(0.177886\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.73368 | + | 4.73487i | 0.104449 | + | 0.180910i | ||||
\(686\) | −8.58457 | + | 14.8689i | −0.327760 | + | 0.567698i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.0073 | 0.419651 | ||||||||
\(689\) | −33.2809 | − | 18.9720i | −1.26790 | − | 0.722776i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.72060 | + | 5.03484i | 0.331747 | + | 0.191534i | 0.656617 | − | 0.754225i | \(-0.271987\pi\) |
−0.324869 | + | 0.945759i | \(0.605320\pi\) | |||||||
\(692\) | 2.90723 | − | 5.03546i | 0.110516 | − | 0.191420i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 3.14572i | − | 0.119410i | ||||||
\(695\) | −0.185777 | + | 0.107258i | −0.00704692 | + | 0.00406854i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.75606i | − | 0.0665156i | ||||||
\(698\) | 5.25246 | + | 9.09752i | 0.198808 | + | 0.344346i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.24653 | + | 0.719687i | 0.0471146 | + | 0.0272016i | ||||
\(701\) | 10.4149 | 0.393366 | 0.196683 | − | 0.980467i | \(-0.436983\pi\) | ||||
0.196683 | + | 0.980467i | \(0.436983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.49307 | 0.0940279 | ||||||||
\(704\) | 3.49837 | + | 2.01978i | 0.131850 | + | 0.0761235i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.4988 | − | 28.5767i | −0.620940 | − | 1.07550i | ||||
\(707\) | − | 6.95928i | − | 0.261731i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.325446 | + | 0.187896i | −0.0122224 | + | 0.00705660i | −0.506099 | − | 0.862476i | \(-0.668913\pi\) |
0.493876 | + | 0.869532i | \(0.335580\pi\) | |||||||
\(710\) | 6.00000i | 0.225176i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.485517 | − | 0.840939i | 0.0181955 | − | 0.0315155i | ||||
\(713\) | 4.19941 | + | 2.42453i | 0.157269 | + | 0.0907994i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5734 | − | 7.35154i | 0.470219 | − | 0.274932i | ||||
\(716\) | 16.8722 | 0.630545 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.1244 | + | 21.0000i | −0.452477 | + | 0.783713i | ||||
\(719\) | 9.66547 | + | 16.7411i | 0.360461 | + | 0.624337i | 0.988037 | − | 0.154218i | \(-0.0492860\pi\) |
−0.627576 | + | 0.778556i | \(0.715953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.14520 | − | 4.12528i | 0.266101 | − | 0.153634i | ||||
\(722\) | 16.3161 | − | 9.42008i | 0.607221 | − | 0.350579i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.31034 | + | 10.9298i | 0.234522 | + | 0.406204i | ||||
\(725\) | 3.93244 | − | 6.81119i | 0.146047 | − | 0.252961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.3390 | 1.16230 | 0.581150 | − | 0.813797i | \(-0.302603\pi\) | ||||
0.581150 | + | 0.813797i | \(0.302603\pi\) | |||||||
\(728\) | 0.0284776 | + | 5.18966i | 0.00105545 | + | 0.192342i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.6574 | − | 6.73042i | −0.431461 | − | 0.249104i | ||||
\(731\) | −12.6998 | + | 21.9967i | −0.469720 | + | 0.813579i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6207i | 0.724707i | 0.932041 | + | 0.362353i | \(0.118027\pi\) | ||||
−0.932041 | + | 0.362353i | \(0.881973\pi\) | |||||||
\(734\) | −17.1460 | + | 9.89924i | −0.632870 | + | 0.365387i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.56063i | 0.0575254i | ||||||||
\(737\) | 21.0073 | + | 36.3858i | 0.773815 | + | 1.34029i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3601 | − | 5.98141i | −0.381103 | − | 0.220030i | 0.297195 | − | 0.954817i | \(-0.403949\pi\) |
−0.678298 | + | 0.734787i | \(0.737282\pi\) | |||||||
\(740\) | 6.23572 | 0.229230 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.2932 | −0.561432 | ||||||||
\(743\) | 17.2540 | + | 9.96162i | 0.632989 | + | 0.365457i | 0.781909 | − | 0.623393i | \(-0.214246\pi\) |
−0.148920 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.26469 | − | 14.3149i | −0.302795 | − | 0.524456i | ||||
\(746\) | 4.79113i | 0.175416i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.07255 | + | 4.66069i | −0.295162 | + | 0.170412i | ||||
\(749\) | − | 18.5326i | − | 0.677168i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4608 | − | 37.1713i | 0.783117 | − | 1.35640i | −0.147000 | − | 0.989136i | \(-0.546962\pi\) |
0.930117 | − | 0.367262i | \(-0.119705\pi\) | |||||||
\(752\) | 5.05772 | + | 2.92008i | 0.184436 | + | 0.106484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28.3568 | − | 0.155605i | 1.03269 | − | 0.00566678i | ||||
\(755\) | −6.70830 | −0.244140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8750 | − | 30.9604i | 0.649678 | − | 1.12528i | −0.333522 | − | 0.942742i | \(-0.608237\pi\) |
0.983200 | − | 0.182533i | \(-0.0584295\pi\) | |||||||
\(758\) | 9.74760 | + | 16.8833i | 0.354049 | + | 0.613230i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.346241 | + | 0.199902i | −0.0125595 | + | 0.00725121i | ||||
\(761\) | −26.1232 | + | 15.0822i | −0.946965 | + | 0.546731i | −0.892137 | − | 0.451765i | \(-0.850795\pi\) |
−0.0548284 | + | 0.998496i | \(0.517461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.154196 | + | 0.267076i | 0.00558227 | + | 0.00966878i | ||||
\(764\) | −0.670362 | + | 1.16110i | −0.0242529 | + | 0.0420072i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.8614 | 0.464700 | ||||||||
\(767\) | 12.4898 | − | 0.0685363i | 0.450981 | − | 0.00247470i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0236 | − | 12.1380i | −0.758132 | − | 0.437708i | 0.0704928 | − | 0.997512i | \(-0.477543\pi\) |
−0.828625 | + | 0.559805i | \(0.810876\pi\) | |||||||
\(770\) | 2.90723 | − | 5.03546i | 0.104769 | − | 0.181465i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 16.7436i | − | 0.602616i | ||||||
\(773\) | 38.5671 | − | 22.2667i | 1.38716 | − | 0.800879i | 0.394168 | − | 0.919038i | \(-0.371033\pi\) |
0.992995 | + | 0.118160i | \(0.0376995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.10713i | 0.111611i | ||||||||
\(776\) | 6.15919 | + | 10.6680i | 0.221102 | + | 0.382960i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.01223 | + | 3.47116i | 0.215549 | + | 0.124447i | ||||
\(779\) | −0.304258 | −0.0109012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.2374 | 0.867283 | ||||||||
\(782\) | −3.11871 | − | 1.80059i | −0.111525 | − | 0.0643889i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.46410 | − | 4.26795i | −0.0880036 | − | 0.152427i | ||||
\(785\) | 5.81684i | 0.207612i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0864 | + | 8.71015i | −0.537773 | + | 0.310483i | −0.744176 | − | 0.667984i | \(-0.767158\pi\) |
0.206403 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(788\) | − | 0.996740i | − | 0.0355074i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.465732 | − | 0.806671i | 0.0165700 | − | 0.0287001i | ||||
\(791\) | 0.160298 | + | 0.0925479i | 0.00569953 | + | 0.00329062i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.112624 | + | 20.5242i | 0.00399940 | + | 0.728837i | ||||
\(794\) | 4.33225 | 0.153746 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.30752 | − | 2.26469i | 0.0463438 | − | 0.0802698i | ||||
\(797\) | −16.4801 | − | 28.5444i | −0.583756 | − | 1.01110i | −0.995029 | − | 0.0995834i | \(-0.968249\pi\) |
0.411273 | − | 0.911512i | \(-0.365084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6708 | + | 6.73813i | −0.412883 | + | 0.238378i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.8616 | − | 20.5448i | −0.418847 | − | 0.725464i | ||||
\(803\) | −27.1880 | + | 47.0910i | −0.959444 | + | 1.66181i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.24632 | 0.0791725 | ||||||||
\(806\) | −9.67112 | + | 5.65461i | −0.340651 | + | 0.199175i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.18718 | + | 2.41747i | 0.147304 | + | 0.0850463i | ||||
\(809\) | 12.6664 | − | 21.9389i | 0.445327 | − | 0.771329i | −0.552748 | − | 0.833348i | \(-0.686421\pi\) |
0.998075 | + | 0.0620195i | \(0.0197541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.4806i | − | 1.49170i | −0.666117 | − | 0.745848i | \(-0.732045\pi\) | ||
0.666117 | − | 0.745848i | \(-0.267955\pi\) | |||||||
\(812\) | 9.80385 | − | 5.66025i | 0.344048 | − | 0.198636i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 25.1896i | − | 0.882896i | ||||||
\(815\) | 2.08620 | + | 3.61341i | 0.0730765 | + | 0.126572i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.81119 | + | 2.20039i | 0.133337 | + | 0.0769820i | ||||
\(818\) | 38.3792 | 1.34190 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.761018 | −0.0265759 | ||||||||
\(821\) | −15.3744 | − | 8.87640i | −0.536569 | − | 0.309789i | 0.207118 | − | 0.978316i | \(-0.433592\pi\) |
−0.743687 | + | 0.668527i | \(0.766925\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2840 | + | 28.2048i | 0.567626 | + | 0.983157i | 0.996800 | + | 0.0799351i | \(0.0254713\pi\) |
−0.429174 | + | 0.903222i | \(0.641195\pi\) | |||||||
\(824\) | 5.73205i | 0.199685i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.31812 | − | 2.49307i | 0.150247 | − | 0.0867449i | ||||
\(827\) | 26.6419i | 0.926429i | 0.886246 | + | 0.463215i | \(0.153304\pi\) | ||||
−0.886246 | + | 0.463215i | \(0.846696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.58281 | + | 14.8659i | −0.298093 | + | 0.516313i | −0.975700 | − | 0.219112i | \(-0.929684\pi\) |
0.677606 | + | 0.735425i | \(0.263017\pi\) | |||||||
\(830\) | −8.99511 | − | 5.19333i | −0.312225 | − | 0.180263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.13234 | − | 1.78561i | −0.108595 | − | 0.0619050i | ||||
\(833\) | 11.3719 | 0.394014 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.80426 | + | 13.5174i | −0.270077 | + | 0.467788i | ||||
\(836\) | 0.807519 | + | 1.39866i | 0.0279286 | + | 0.0483738i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.4192 | − | 19.2946i | 1.15445 | − | 0.666520i | ||||
\(839\) | 38.9951 | − | 22.5138i | 1.34626 | − | 0.777264i | 0.358543 | − | 0.933513i | \(-0.383274\pi\) |
0.987718 | + | 0.156249i | \(0.0499403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4282 | − | 28.4545i | −0.566490 | − | 0.981189i | ||||
\(842\) | 20.3100 | − | 35.1779i | 0.699928 | − | 1.21231i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.13381 | 0.314399 | ||||||||
\(845\) | −11.1863 | + | 6.62316i | −0.384821 | + | 0.227844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.62922 | − | 3.82738i | −0.227783 | − | 0.131510i | ||||
\(848\) | 5.31246 | − | 9.20145i | 0.182431 | − | 0.315979i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 2.30752i | − | 0.0791472i | ||||||
\(851\) | 8.42784 | − | 4.86582i | 0.288903 | − | 0.166798i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31.0013i | − | 1.06146i | −0.847540 | − | 0.530731i | \(-0.821917\pi\) | ||
0.847540 | − | 0.530731i | \(-0.178083\pi\) | |||||||
\(854\) | 4.09680 | + | 7.09587i | 0.140190 | + | 0.242816i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1505 | + | 6.43774i | 0.381116 | + | 0.220038i | ||||
\(857\) | 27.3813 | 0.935326 | 0.467663 | − | 0.883907i | \(-0.345096\pi\) | ||||
0.467663 | + | 0.883907i | \(0.345096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.36050 | 0.285256 | 0.142628 | − | 0.989776i | \(-0.454445\pi\) | ||||
0.142628 | + | 0.989776i | \(0.454445\pi\) | |||||||
\(860\) | 9.53264 | + | 5.50367i | 0.325060 | + | 0.187674i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.88581 | + | 10.1945i | 0.200471 | + | 0.347227i | ||||
\(863\) | 40.2398i | 1.36978i | 0.728647 | + | 0.684889i | \(0.240150\pi\) | ||||
−0.728647 | + | 0.684889i | \(0.759850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.03546 | − | 2.90723i | 0.171211 | − | 0.0988486i | ||||
\(866\) | 33.0008i | 1.12141i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.23616 | + | 3.87314i | −0.0759002 | + | 0.131463i | ||||
\(869\) | −3.25860 | − | 1.88136i | −0.110541 | − | 0.0638206i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.9282 | − | 32.3731i | −0.641358 | − | 1.09692i | ||||
\(872\) | −0.214254 | −0.00725557 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.311973 | + | 0.540352i | −0.0105526 | + | 0.0182777i | ||||
\(875\) | 0.719687 | + | 1.24653i | 0.0243299 | + | 0.0421405i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.0918 | + | 26.0338i | −1.52264 | + | 0.879098i | −0.523000 | + | 0.852333i | \(0.675187\pi\) |
−0.999642 | + | 0.0267652i | \(0.991479\pi\) | |||||||
\(878\) | −0.603998 | + | 0.348718i | −0.0203839 | + | 0.0117687i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.01978 | + | 3.49837i | 0.0680869 | + | 0.117930i | ||||
\(881\) | 17.2542 | − | 29.8852i | 0.581310 | − | 1.00686i | −0.414015 | − | 0.910270i | \(-0.635874\pi\) |
0.995324 | − | 0.0965881i | \(-0.0307929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.2064 | −0.949222 | −0.474611 | − | 0.880196i | \(-0.657411\pi\) | ||||
−0.474611 | + | 0.880196i | \(0.657411\pi\) | |||||||
\(884\) | 7.18229 | − | 4.19941i | 0.241567 | − | 0.141242i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.7941 | + | 14.3149i | 0.832973 | + | 0.480917i | ||||
\(887\) | 1.06098 | − | 1.83768i | 0.0356244 | − | 0.0617032i | −0.847664 | − | 0.530534i | \(-0.821991\pi\) |
0.883288 | + | 0.468831i | \(0.155325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.2090i | − | 0.778404i | ||||||
\(890\) | 0.840939 | − | 0.485517i | 0.0281884 | − | 0.0162746i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.81191i | 0.194597i | ||||||||
\(893\) | 1.16746 | + | 2.02210i | 0.0390676 | + | 0.0676670i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6118 | + | 8.43611i | 0.488418 | + | 0.281988i | ||||
\(896\) | −1.43937 | −0.0480861 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.78503 | −0.226419 | ||||||||
\(899\) | 21.1632 | + | 12.2186i | 0.705833 | + | 0.407513i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2586 | + | 21.2325i | 0.408393 | + | 0.707358i | ||||
\(902\) | 3.07418i | 0.102359i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.111366 | + | 0.0642973i | −0.00370398 | + | 0.00213850i | ||||
\(905\) | 12.6207i | 0.419526i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.7272 | − | 25.5082i | 0.489007 | − | 0.846986i | −0.510913 | − | 0.859633i | \(-0.670692\pi\) |
0.999920 | + | 0.0126471i | \(0.00402580\pi\) | |||||||
\(908\) | 9.99674 | + | 5.77162i | 0.331753 | + | 0.191538i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.57017 | + | 4.50861i | −0.0852002 | + | 0.149459i | ||||
\(911\) | −19.9986 | −0.662582 | −0.331291 | − | 0.943529i | \(-0.607484\pi\) | ||||
−0.331291 | + | 0.943529i | \(0.607484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.9788 | + | 36.3364i | −0.694297 | + | 1.20256i | ||||
\(914\) | −8.96940 | − | 15.5355i | −0.296681 | − | 0.513867i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.1505 | + | 6.43774i | −0.368423 | + | 0.212709i | ||||
\(917\) | 3.46549 | − | 2.00080i | 0.114440 | − | 0.0660722i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8564 | + | 25.7321i | 0.490068 | + | 0.848822i | 0.999935 | − | 0.0114312i | \(-0.00363874\pi\) |
−0.509867 | + | 0.860253i | \(0.670305\pi\) | |||||||
\(920\) | −0.780313 | + | 1.35154i | −0.0257262 | + | 0.0445590i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.8972 | −0.885813 | ||||||||
\(923\) | −21.6330 | + | 0.118708i | −0.712058 | + | 0.00390733i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.40029 | + | 3.11786i | 0.177561 | + | 0.102515i | ||||
\(926\) | −13.4201 | + | 23.2443i | −0.441011 | + | 0.763854i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.86488i | 0.258177i | ||||||||
\(929\) | 7.99348 | − | 4.61504i | 0.262258 | − | 0.151414i | −0.363106 | − | 0.931748i | \(-0.618284\pi\) |
0.625364 | + | 0.780333i | \(0.284951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.97032i | − | 0.0645745i | ||||||
\(932\) | 5.20745 | + | 9.01957i | 0.170576 | + | 0.295446i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.21621 | + | 4.74363i | 0.268843 | + | 0.155216i | ||||
\(935\) | −9.32138 | −0.304842 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.58731 | −0.149861 | −0.0749305 | − | 0.997189i | \(-0.523873\pi\) | ||||
−0.0749305 | + | 0.997189i | \(0.523873\pi\) | |||||||
\(938\) | −12.9649 | − | 7.48531i | −0.423320 | − | 0.244404i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.92008 | + | 5.05772i | 0.0952425 | + | 0.164965i | ||||
\(941\) | 9.00734i | 0.293631i | 0.989164 | + | 0.146815i | \(0.0469024\pi\) | ||||
−0.989164 | + | 0.146815i | \(0.953098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.02855 | + | 0.593832i | −0.0334941 | + | 0.0193378i | ||||
\(944\) | 3.46410i | 0.112747i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.2325 | − | 38.5078i | 0.722840 | − | 1.25200i | ||||
\(947\) | −47.3100 | − | 27.3144i | −1.53737 | − | 0.887600i | −0.998992 | − | 0.0448946i | \(-0.985705\pi\) |
−0.538376 | − | 0.842705i | \(-0.680962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0359 | − | 42.1640i | 0.780237 | − | 1.36870i | ||||
\(950\) | −0.399804 | −0.0129714 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.66069 | − | 2.87640i | 0.0538233 | − | 0.0932247i | ||||
\(953\) | 9.46862 | + | 16.4001i | 0.306719 | + | 0.531252i | 0.977643 | − | 0.210274i | \(-0.0674356\pi\) |
−0.670924 | + | 0.741526i | \(0.734102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.16110 | + | 0.670362i | −0.0375724 | + | 0.0216924i | ||||
\(956\) | −15.9177 | + | 9.19007i | −0.514814 | + | 0.297228i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.60726 | + | 9.71206i | 0.181162 | + | 0.313782i | ||||
\(959\) | −3.93479 | + | 6.81525i | −0.127061 | + | 0.220076i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.3458 | 0.688573 | ||||||||
\(962\) | 0.123372 | + | 22.4829i | 0.00397767 | + | 0.724877i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.536681 | + | 0.309853i | 0.0172853 | + | 0.00997970i | ||||
\(965\) | 8.37182 | − | 14.5004i | 0.269498 | − | 0.466785i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1583i | 0.616089i | 0.951372 | + | 0.308044i | \(0.0996745\pi\) | ||||
−0.951372 | + | 0.308044i | \(0.900325\pi\) | |||||||
\(968\) | 4.60563 | − | 2.65906i | 0.148030 | − | 0.0854654i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.3184i | 0.395519i | ||||||||
\(971\) | 11.1876 | + | 19.3775i | 0.359027 | + | 0.621853i | 0.987799 | − | 0.155737i | \(-0.0497753\pi\) |
−0.628772 | + | 0.777590i | \(0.716442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.267402 | − | 0.154385i | −0.00857253 | − | 0.00494935i | ||||
\(974\) | −27.7286 | −0.888483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.69248 | −0.182212 | ||||||||
\(977\) | −3.91962 | − | 2.26299i | −0.125400 | − | 0.0723996i | 0.435988 | − | 0.899952i | \(-0.356399\pi\) |
−0.561388 | + | 0.827553i | \(0.689732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.96128 | − | 3.39703i | −0.0626827 | − | 0.108570i | ||||
\(980\) | − | 4.92820i | − | 0.157426i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.1409 | − | 13.9377i | 0.770366 | − | 0.444771i | ||||
\(983\) | − | 12.1598i | − | 0.387839i | −0.981017 | − | 0.193919i | \(-0.937880\pi\) | ||
0.981017 | − | 0.193919i | \(-0.0621200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.498370 | − | 0.863202i | 0.0158794 | − | 0.0275039i | ||||
\(986\) | −15.7169 | − | 9.07418i | −0.500530 | − | 0.288981i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.727597 | − | 1.24441i | −0.0231479 | − | 0.0395901i | ||||
\(989\) | 17.1783 | 0.546240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.1367 | − | 48.7341i | 0.893790 | − | 1.54809i | 0.0584955 | − | 0.998288i | \(-0.481370\pi\) |
0.835295 | − | 0.549802i | \(-0.185297\pi\) | |||||||
\(992\) | −1.55356 | − | 2.69085i | −0.0493257 | − | 0.0854346i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.47921 | + | 4.31812i | −0.237226 | + | 0.136962i | ||||
\(995\) | 2.26469 | − | 1.30752i | 0.0717955 | − | 0.0414511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.33056 | + | 4.03665i | 0.0738097 | + | 0.127842i | 0.900568 | − | 0.434715i | \(-0.143151\pi\) |
−0.826758 | + | 0.562557i | \(0.809818\pi\) | |||||||
\(998\) | 18.4020 | − | 31.8732i | 0.582504 | − | 1.00893i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.bs.g.901.1 | 8 | ||
3.2 | odd | 2 | 130.2.l.b.121.3 | yes | 8 | ||
12.11 | even | 2 | 1040.2.da.d.641.4 | 8 | |||
13.10 | even | 6 | inner | 1170.2.bs.g.361.1 | 8 | ||
15.2 | even | 4 | 650.2.n.d.199.4 | 8 | |||
15.8 | even | 4 | 650.2.n.e.199.1 | 8 | |||
15.14 | odd | 2 | 650.2.m.c.251.2 | 8 | |||
39.2 | even | 12 | 1690.2.e.t.991.1 | 8 | |||
39.5 | even | 4 | 1690.2.e.t.191.1 | 8 | |||
39.8 | even | 4 | 1690.2.e.s.191.1 | 8 | |||
39.11 | even | 12 | 1690.2.e.s.991.1 | 8 | |||
39.17 | odd | 6 | 1690.2.d.k.1351.8 | 8 | |||
39.20 | even | 12 | 1690.2.a.u.1.4 | 4 | |||
39.23 | odd | 6 | 130.2.l.b.101.3 | ✓ | 8 | ||
39.29 | odd | 6 | 1690.2.l.j.361.1 | 8 | |||
39.32 | even | 12 | 1690.2.a.t.1.4 | 4 | |||
39.35 | odd | 6 | 1690.2.d.k.1351.4 | 8 | |||
39.38 | odd | 2 | 1690.2.l.j.1161.1 | 8 | |||
156.23 | even | 6 | 1040.2.da.d.881.4 | 8 | |||
195.23 | even | 12 | 650.2.n.d.49.4 | 8 | |||
195.59 | even | 12 | 8450.2.a.ci.1.1 | 4 | |||
195.62 | even | 12 | 650.2.n.e.49.1 | 8 | |||
195.149 | even | 12 | 8450.2.a.cm.1.1 | 4 | |||
195.179 | odd | 6 | 650.2.m.c.101.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.b.101.3 | ✓ | 8 | 39.23 | odd | 6 | ||
130.2.l.b.121.3 | yes | 8 | 3.2 | odd | 2 | ||
650.2.m.c.101.2 | 8 | 195.179 | odd | 6 | |||
650.2.m.c.251.2 | 8 | 15.14 | odd | 2 | |||
650.2.n.d.49.4 | 8 | 195.23 | even | 12 | |||
650.2.n.d.199.4 | 8 | 15.2 | even | 4 | |||
650.2.n.e.49.1 | 8 | 195.62 | even | 12 | |||
650.2.n.e.199.1 | 8 | 15.8 | even | 4 | |||
1040.2.da.d.641.4 | 8 | 12.11 | even | 2 | |||
1040.2.da.d.881.4 | 8 | 156.23 | even | 6 | |||
1170.2.bs.g.361.1 | 8 | 13.10 | even | 6 | inner | ||
1170.2.bs.g.901.1 | 8 | 1.1 | even | 1 | trivial | ||
1690.2.a.t.1.4 | 4 | 39.32 | even | 12 | |||
1690.2.a.u.1.4 | 4 | 39.20 | even | 12 | |||
1690.2.d.k.1351.4 | 8 | 39.35 | odd | 6 | |||
1690.2.d.k.1351.8 | 8 | 39.17 | odd | 6 | |||
1690.2.e.s.191.1 | 8 | 39.8 | even | 4 | |||
1690.2.e.s.991.1 | 8 | 39.11 | even | 12 | |||
1690.2.e.t.191.1 | 8 | 39.5 | even | 4 | |||
1690.2.e.t.991.1 | 8 | 39.2 | even | 12 | |||
1690.2.l.j.361.1 | 8 | 39.29 | odd | 6 | |||
1690.2.l.j.1161.1 | 8 | 39.38 | odd | 2 | |||
8450.2.a.ci.1.1 | 4 | 195.59 | even | 12 | |||
8450.2.a.cm.1.1 | 4 | 195.149 | even | 12 |