Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(307,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 811.3 | ||
Root | \(2.06644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.811 |
Dual form | 1638.2.x.a.307.3 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.16830 | − | 2.16830i | −0.969692 | − | 0.969692i | 0.0298617 | − | 0.999554i | \(-0.490493\pi\) |
−0.999554 | + | 0.0298617i | \(0.990493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.292893 | + | 2.62949i | −0.110703 | + | 0.993854i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.06644 | −0.969692 | ||||||||
\(11\) | −0.516075 | − | 0.516075i | −0.155603 | − | 0.155603i | 0.625012 | − | 0.780615i | \(-0.285094\pi\) |
−0.780615 | + | 0.625012i | \(0.785094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60525 | + | 0.0469777i | −0.999915 | + | 0.0130293i | ||||
\(14\) | 1.65222 | + | 2.06644i | 0.441575 | + | 0.552278i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.57461 | −0.624434 | −0.312217 | − | 0.950011i | \(-0.601072\pi\) | ||||
−0.312217 | + | 0.950011i | \(0.601072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.82052 | + | 3.82052i | 0.876488 | + | 0.876488i | 0.993169 | − | 0.116682i | \(-0.0372258\pi\) |
−0.116682 | + | 0.993169i | \(0.537226\pi\) | |||||||
\(20\) | −2.16830 | + | 2.16830i | −0.484846 | + | 0.484846i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.729840 | −0.155603 | ||||||||
\(23\) | 6.97248i | 1.45386i | 0.686710 | + | 0.726931i | \(0.259054\pi\) | ||||
−0.686710 | + | 0.726931i | \(0.740946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.40303i | 0.880606i | ||||||||
\(26\) | −2.51608 | + | 2.58251i | −0.493443 | + | 0.506472i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.62949 | + | 0.292893i | 0.496927 | + | 0.0553516i | ||||
\(29\) | 6.32541 | 1.17460 | 0.587300 | − | 0.809369i | \(-0.300191\pi\) | ||||
0.587300 | + | 0.809369i | \(0.300191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.33660 | + | 4.33660i | 0.778876 | + | 0.778876i | 0.979640 | − | 0.200764i | \(-0.0643424\pi\) |
−0.200764 | + | 0.979640i | \(0.564342\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.82052 | + | 1.82052i | −0.312217 | + | 0.312217i | ||||
\(35\) | 6.33660 | − | 5.06644i | 1.07108 | − | 0.856384i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58251 | − | 3.58251i | −0.588961 | − | 0.588961i | 0.348389 | − | 0.937350i | \(-0.386729\pi\) |
−0.937350 | + | 0.348389i | \(0.886729\pi\) | |||||||
\(38\) | 5.40303 | 0.876488 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06644i | 0.484846i | ||||||||
\(41\) | −0.176204 | − | 0.176204i | −0.0275185 | − | 0.0275185i | 0.693214 | − | 0.720732i | \(-0.256194\pi\) |
−0.720732 | + | 0.693214i | \(0.756194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.89486i | 1.20396i | 0.798513 | + | 0.601978i | \(0.205620\pi\) | ||||
−0.798513 | + | 0.601978i | \(0.794380\pi\) | |||||||
\(44\) | −0.516075 | + | 0.516075i | −0.0778013 | + | 0.0778013i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.93029 | + | 4.93029i | 0.726931 | + | 0.726931i | ||||
\(47\) | 1.41421 | − | 1.41421i | 0.206284 | − | 0.206284i | −0.596402 | − | 0.802686i | \(-0.703403\pi\) |
0.802686 | + | 0.596402i | \(0.203403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82843 | − | 1.54032i | −0.975490 | − | 0.220046i | ||||
\(50\) | 3.11341 | + | 3.11341i | 0.440303 | + | 0.440303i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0469777 | + | 3.60525i | 0.00651463 | + | 0.499958i | ||||
\(53\) | 0.514936 | 0.0707319 | 0.0353660 | − | 0.999374i | \(-0.488740\pi\) | ||||
0.0353660 | + | 0.999374i | \(0.488740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.23801i | 0.301773i | ||||||||
\(56\) | 2.06644 | − | 1.65222i | 0.276139 | − | 0.220788i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.47274 | − | 4.47274i | 0.587300 | − | 0.587300i | ||||
\(59\) | −3.17834 | + | 3.17834i | −0.413785 | + | 0.413785i | −0.883055 | − | 0.469270i | \(-0.844517\pi\) |
0.469270 | + | 0.883055i | \(0.344517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.41208i | − | 0.820982i | −0.911865 | − | 0.410491i | \(-0.865357\pi\) | ||
0.911865 | − | 0.410491i | \(-0.134643\pi\) | |||||||
\(62\) | 6.13287 | 0.778876 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.91911 | + | 7.71538i | 0.982244 | + | 0.956976i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96130 | + | 3.96130i | −0.483950 | + | 0.483950i | −0.906391 | − | 0.422441i | \(-0.861173\pi\) |
0.422441 | + | 0.906391i | \(0.361173\pi\) | |||||||
\(68\) | 2.57461i | 0.312217i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.898138 | − | 8.06316i | 0.107348 | − | 0.963732i | ||||
\(71\) | −8.12169 | + | 8.12169i | −0.963867 | + | 0.963867i | −0.999370 | − | 0.0355021i | \(-0.988697\pi\) |
0.0355021 | + | 0.999370i | \(0.488697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6056 | + | 11.6056i | −1.35833 | + | 1.35833i | −0.482364 | + | 0.875971i | \(0.660222\pi\) |
−0.875971 | + | 0.482364i | \(0.839778\pi\) | |||||||
\(74\) | −5.06644 | −0.588961 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.82052 | − | 3.82052i | 0.438244 | − | 0.438244i | ||||
\(77\) | 1.50817 | − | 1.20586i | 0.171872 | − | 0.137420i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9455 | 1.23146 | 0.615732 | − | 0.787956i | \(-0.288860\pi\) | ||||
0.615732 | + | 0.787956i | \(0.288860\pi\) | |||||||
\(80\) | 2.16830 | + | 2.16830i | 0.242423 | + | 0.242423i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.249190 | −0.0275185 | ||||||||
\(83\) | 1.01118 | + | 1.01118i | 0.110992 | + | 0.110992i | 0.760421 | − | 0.649430i | \(-0.224992\pi\) |
−0.649430 | + | 0.760421i | \(0.724992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.58251 | + | 5.58251i | 0.605508 | + | 0.605508i | ||||
\(86\) | 5.58251 | + | 5.58251i | 0.601978 | + | 0.601978i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.729840i | 0.0778013i | ||||||||
\(89\) | 1.10977 | − | 1.10977i | 0.117635 | − | 0.117635i | −0.645839 | − | 0.763474i | \(-0.723492\pi\) |
0.763474 | + | 0.645839i | \(0.223492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.932425 | − | 9.49371i | 0.0977447 | − | 0.995212i | ||||
\(92\) | 6.97248 | 0.726931 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.00000i | − | 0.206284i | ||||||
\(95\) | − | 16.5681i | − | 1.69985i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.34336 | + | 9.34336i | 0.948675 | + | 0.948675i | 0.998746 | − | 0.0500709i | \(-0.0159447\pi\) |
−0.0500709 | + | 0.998746i | \(0.515945\pi\) | |||||||
\(98\) | −5.91760 | + | 3.73926i | −0.597768 | + | 0.377722i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.40303 | 0.440303 | ||||||||
\(101\) | −5.86058 | −0.583149 | −0.291575 | − | 0.956548i | \(-0.594179\pi\) | ||||
−0.291575 | + | 0.956548i | \(0.594179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16965 | 0.903513 | 0.451756 | − | 0.892141i | \(-0.350798\pi\) | ||||
0.451756 | + | 0.892141i | \(0.350798\pi\) | |||||||
\(104\) | 2.58251 | + | 2.51608i | 0.253236 | + | 0.246721i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.364115 | − | 0.364115i | 0.0353660 | − | 0.0353660i | ||||
\(107\) | −7.91334 | −0.765011 | −0.382506 | − | 0.923953i | \(-0.624939\pi\) | ||||
−0.382506 | + | 0.923953i | \(0.624939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.90330 | − | 9.90330i | 0.948564 | − | 0.948564i | −0.0501767 | − | 0.998740i | \(-0.515978\pi\) |
0.998740 | + | 0.0501767i | \(0.0159785\pi\) | |||||||
\(110\) | 1.58251 | + | 1.58251i | 0.150887 | + | 0.150887i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.292893 | − | 2.62949i | 0.0276758 | − | 0.248463i | ||||
\(113\) | −11.9450 | −1.12369 | −0.561844 | − | 0.827243i | \(-0.689908\pi\) | ||||
−0.561844 | + | 0.827243i | \(0.689908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.1184 | − | 15.1184i | 1.40980 | − | 1.40980i | ||||
\(116\) | − | 6.32541i | − | 0.587300i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.49485i | 0.413785i | ||||||||
\(119\) | 0.754084 | − | 6.76990i | 0.0691268 | − | 0.620595i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4673i | − | 0.951576i | ||||||
\(122\) | −4.53402 | − | 4.53402i | −0.410491 | − | 0.410491i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.33660 | − | 4.33660i | 0.389438 | − | 0.389438i | ||||
\(125\) | −1.29440 | + | 1.29440i | −0.115775 | + | 0.115775i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2112i | 1.70472i | 0.522954 | + | 0.852361i | \(0.324830\pi\) | ||||
−0.522954 | + | 0.852361i | \(0.675170\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.0553 | − | 0.144054i | 0.969610 | − | 0.0126344i | ||||
\(131\) | 9.83056i | 0.858900i | 0.903091 | + | 0.429450i | \(0.141293\pi\) | ||||
−0.903091 | + | 0.429450i | \(0.858707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.1650 | + | 8.92701i | −0.968130 | + | 0.774070i | ||||
\(134\) | 5.60212i | 0.483950i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.82052 | + | 1.82052i | 0.156108 | + | 0.156108i | ||||
\(137\) | −3.88019 | − | 3.88019i | −0.331507 | − | 0.331507i | 0.521652 | − | 0.853159i | \(-0.325316\pi\) |
−0.853159 | + | 0.521652i | \(0.825316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.32681i | 0.282176i | 0.989997 | + | 0.141088i | \(0.0450601\pi\) | ||||
−0.989997 | + | 0.141088i | \(0.954940\pi\) | |||||||
\(140\) | −5.06644 | − | 6.33660i | −0.428192 | − | 0.535540i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.4858i | 0.963867i | ||||||||
\(143\) | 1.88482 | + | 1.83633i | 0.157617 | + | 0.153562i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.7154 | − | 13.7154i | −1.13900 | − | 1.13900i | ||||
\(146\) | 16.4128i | 1.35833i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.58251 | + | 3.58251i | −0.294481 | + | 0.294481i | ||||
\(149\) | −8.02774 | + | 8.02774i | −0.657658 | + | 0.657658i | −0.954825 | − | 0.297168i | \(-0.903958\pi\) |
0.297168 | + | 0.954825i | \(0.403958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5417 | + | 13.5417i | 1.10201 | + | 1.10201i | 0.994169 | + | 0.107837i | \(0.0343926\pi\) |
0.107837 | + | 0.994169i | \(0.465607\pi\) | |||||||
\(152\) | − | 5.40303i | − | 0.438244i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.213765 | − | 1.91911i | 0.0172257 | − | 0.154646i | ||||
\(155\) | − | 18.8061i | − | 1.51054i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.14458i | − | 0.250965i | −0.992096 | − | 0.125482i | \(-0.959952\pi\) | ||
0.992096 | − | 0.125482i | \(-0.0400479\pi\) | |||||||
\(158\) | 7.73963 | − | 7.73963i | 0.615732 | − | 0.615732i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.06644 | 0.242423 | ||||||||
\(161\) | −18.3341 | − | 2.04219i | −1.44493 | − | 0.160947i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.2816 | − | 15.2816i | −1.19694 | − | 1.19694i | −0.975077 | − | 0.221867i | \(-0.928785\pi\) |
−0.221867 | − | 0.975077i | \(-0.571215\pi\) | |||||||
\(164\) | −0.176204 | + | 0.176204i | −0.0137592 | + | 0.0137592i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.43003 | 0.110992 | ||||||||
\(167\) | −9.21892 | + | 9.21892i | −0.713382 | + | 0.713382i | −0.967241 | − | 0.253860i | \(-0.918300\pi\) |
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9956 | − | 0.338732i | 0.999660 | − | 0.0260563i | ||||
\(170\) | 7.89486 | 0.605508 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.89486 | 0.601978 | ||||||||
\(173\) | 17.4793 | 1.32892 | 0.664462 | − | 0.747322i | \(-0.268661\pi\) | ||||
0.664462 | + | 0.747322i | \(0.268661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5777 | − | 1.28962i | −0.875194 | − | 0.0974860i | ||||
\(176\) | 0.516075 | + | 0.516075i | 0.0389006 | + | 0.0389006i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1.56945i | − | 0.117635i | ||||||
\(179\) | − | 18.3235i | − | 1.36956i | −0.728749 | − | 0.684781i | \(-0.759898\pi\) | ||
0.728749 | − | 0.684781i | \(-0.240102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.96432 | −0.368995 | −0.184498 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184498 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(182\) | −6.05374 | − | 7.37239i | −0.448733 | − | 0.546478i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.93029 | − | 4.93029i | 0.363466 | − | 0.363466i | ||||
\(185\) | 15.5359i | 1.14222i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.32869 | + | 1.32869i | 0.0971634 | + | 0.0971634i | ||||
\(188\) | −1.41421 | − | 1.41421i | −0.103142 | − | 0.103142i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.7154 | − | 11.7154i | −0.849923 | − | 0.849923i | ||||
\(191\) | −10.5427 | −0.762841 | −0.381421 | − | 0.924402i | \(-0.624565\pi\) | ||||
−0.381421 | + | 0.924402i | \(0.624565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6366 | − | 13.6366i | −0.981586 | − | 0.981586i | 0.0182475 | − | 0.999833i | \(-0.494191\pi\) |
−0.999833 | + | 0.0182475i | \(0.994191\pi\) | |||||||
\(194\) | 13.2135 | 0.948675 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.54032 | + | 6.82843i | −0.110023 | + | 0.487745i | ||||
\(197\) | −13.4673 | + | 13.4673i | −0.959508 | + | 0.959508i | −0.999211 | − | 0.0397038i | \(-0.987359\pi\) |
0.0397038 | + | 0.999211i | \(0.487359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.92452 | −0.419978 | −0.209989 | − | 0.977704i | \(-0.567343\pi\) | ||||
−0.209989 | + | 0.977704i | \(0.567343\pi\) | |||||||
\(200\) | 3.11341 | − | 3.11341i | 0.220152 | − | 0.220152i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.14405 | + | 4.14405i | −0.291575 | + | 0.291575i | ||||
\(203\) | −1.85267 | + | 16.6326i | −0.130032 | + | 1.16738i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.764127i | 0.0533689i | ||||||||
\(206\) | 6.48392 | − | 6.48392i | 0.451756 | − | 0.451756i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.60525 | − | 0.0469777i | 0.249979 | − | 0.00325731i | ||||
\(209\) | − | 3.94335i | − | 0.272767i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.04407 | −0.484934 | −0.242467 | − | 0.970160i | \(-0.577957\pi\) | ||||
−0.242467 | + | 0.970160i | \(0.577957\pi\) | |||||||
\(212\) | − | 0.514936i | − | 0.0353660i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.59557 | + | 5.59557i | −0.382506 | + | 0.382506i | ||||
\(215\) | 17.1184 | − | 17.1184i | 1.16747 | − | 1.16747i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.6732 | + | 10.1329i | −0.860312 | + | 0.687864i | ||||
\(218\) | − | 14.0054i | − | 0.948564i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.23801 | 0.150887 | ||||||||
\(221\) | 9.28208 | − | 0.120949i | 0.624381 | − | 0.00813591i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.71425 | − | 9.71425i | −0.650514 | − | 0.650514i | 0.302603 | − | 0.953117i | \(-0.402144\pi\) |
−0.953117 | + | 0.302603i | \(0.902144\pi\) | |||||||
\(224\) | −1.65222 | − | 2.06644i | −0.110394 | − | 0.138070i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.44636 | + | 8.44636i | −0.561844 | + | 0.561844i | ||||
\(227\) | −13.9000 | − | 13.9000i | −0.922577 | − | 0.922577i | 0.0746342 | − | 0.997211i | \(-0.476221\pi\) |
−0.997211 | + | 0.0746342i | \(0.976221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.97035 | − | 5.97035i | 0.394532 | − | 0.394532i | −0.481768 | − | 0.876299i | \(-0.660005\pi\) |
0.876299 | + | 0.481768i | \(0.160005\pi\) | |||||||
\(230\) | − | 21.3807i | − | 1.40980i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47274 | − | 4.47274i | −0.293650 | − | 0.293650i | ||||
\(233\) | 1.35293i | 0.0886336i | 0.999018 | + | 0.0443168i | \(0.0141111\pi\) | ||||
−0.999018 | + | 0.0443168i | \(0.985889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.13287 | −0.400065 | ||||||||
\(236\) | 3.17834 | + | 3.17834i | 0.206892 | + | 0.206892i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.25382 | − | 5.32026i | −0.275734 | − | 0.344861i | ||||
\(239\) | −20.8904 | + | 20.8904i | −1.35129 | + | 1.35129i | −0.467071 | + | 0.884220i | \(0.654691\pi\) |
−0.884220 | + | 0.467071i | \(0.845309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1816 | + | 11.1816i | −0.720269 | + | 0.720269i | −0.968660 | − | 0.248391i | \(-0.920098\pi\) |
0.248391 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(242\) | −7.40152 | − | 7.40152i | −0.475788 | − | 0.475788i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.41208 | −0.410491 | ||||||||
\(245\) | 11.4662 | + | 18.1459i | 0.732548 | + | 1.15930i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.9534 | − | 13.5944i | −0.887833 | − | 0.864993i | ||||
\(248\) | − | 6.13287i | − | 0.389438i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.83056i | 0.115775i | ||||||||
\(251\) | 20.6366 | 1.30257 | 0.651286 | − | 0.758832i | \(-0.274230\pi\) | ||||
0.651286 | + | 0.758832i | \(0.274230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.59832 | − | 3.59832i | 0.226225 | − | 0.226225i | ||||
\(254\) | 13.5844 | + | 13.5844i | 0.852361 | + | 0.852361i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.21351 | −0.574723 | −0.287362 | − | 0.957822i | \(-0.592778\pi\) | ||||
−0.287362 | + | 0.957822i | \(0.592778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4695 | − | 8.37088i | 0.650541 | − | 0.520141i | ||||
\(260\) | 7.71538 | − | 7.91911i | 0.478488 | − | 0.491122i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.95126 | + | 6.95126i | 0.429450 | + | 0.429450i | ||||
\(263\) | −9.50464 | −0.586081 | −0.293041 | − | 0.956100i | \(-0.594667\pi\) | ||||
−0.293041 | + | 0.956100i | \(0.594667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.11654 | − | 1.11654i | −0.0685882 | − | 0.0685882i | ||||
\(266\) | −1.58251 | + | 14.2072i | −0.0970300 | + | 0.871100i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.96130 | + | 3.96130i | 0.241975 | + | 0.241975i | ||||
\(269\) | − | 15.7423i | − | 0.959824i | −0.877317 | − | 0.479912i | \(-0.840669\pi\) | ||
0.877317 | − | 0.479912i | \(-0.159331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4746 | − | 17.4746i | 1.06151 | − | 1.06151i | 0.0635278 | − | 0.997980i | \(-0.479765\pi\) |
0.997980 | − | 0.0635278i | \(-0.0202352\pi\) | |||||||
\(272\) | 2.57461 | 0.156108 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.48742 | −0.331507 | ||||||||
\(275\) | 2.27230 | − | 2.27230i | 0.137025 | − | 0.137025i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3991i | 1.28575i | 0.765971 | + | 0.642875i | \(0.222259\pi\) | ||||
−0.765971 | + | 0.642875i | \(0.777741\pi\) | |||||||
\(278\) | 2.35241 | + | 2.35241i | 0.141088 | + | 0.141088i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.06316 | − | 0.898138i | −0.481866 | − | 0.0536740i | ||||
\(281\) | −0.634274 | − | 0.634274i | −0.0378376 | − | 0.0378376i | 0.687935 | − | 0.725772i | \(-0.258517\pi\) |
−0.725772 | + | 0.687935i | \(0.758517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6503 | 0.692539 | 0.346269 | − | 0.938135i | \(-0.387448\pi\) | ||||
0.346269 | + | 0.938135i | \(0.387448\pi\) | |||||||
\(284\) | 8.12169 | + | 8.12169i | 0.481934 | + | 0.481934i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.63125 | − | 0.0342862i | 0.155589 | − | 0.00202739i | ||||
\(287\) | 0.514936 | − | 0.411718i | 0.0303957 | − | 0.0243030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3714 | −0.610083 | ||||||||
\(290\) | −19.3965 | −1.13900 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6056 | + | 11.6056i | 0.679167 | + | 0.679167i | ||||
\(293\) | 16.3755 | − | 16.3755i | 0.956668 | − | 0.956668i | −0.0424317 | − | 0.999099i | \(-0.513510\pi\) |
0.999099 | + | 0.0424317i | \(0.0135105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7832 | 0.802488 | ||||||||
\(296\) | 5.06644i | 0.294481i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3529i | 0.657658i | ||||||||
\(299\) | −0.327551 | − | 25.1375i | −0.0189428 | − | 1.45374i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.7595 | − | 2.31235i | −1.19656 | − | 0.133282i | ||||
\(302\) | 19.1508 | 1.10201 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.82052 | − | 3.82052i | −0.219122 | − | 0.219122i | ||||
\(305\) | −13.9033 | + | 13.9033i | −0.796100 | + | 0.796100i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8704 | + | 14.8704i | −0.848697 | + | 0.848697i | −0.989971 | − | 0.141274i | \(-0.954880\pi\) |
0.141274 | + | 0.989971i | \(0.454880\pi\) | |||||||
\(308\) | −1.20586 | − | 1.50817i | −0.0687102 | − | 0.0859359i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.2979 | − | 13.2979i | −0.755270 | − | 0.755270i | ||||
\(311\) | 26.0489 | 1.47710 | 0.738549 | − | 0.674199i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674199i | \(0.235511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.1007i | − | 0.740497i | −0.928933 | − | 0.370248i | \(-0.879273\pi\) | ||
0.928933 | − | 0.370248i | \(-0.120727\pi\) | |||||||
\(314\) | −2.22355 | − | 2.22355i | −0.125482 | − | 0.125482i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 10.9455i | − | 0.615732i | ||||||
\(317\) | 15.6157 | − | 15.6157i | 0.877063 | − | 0.877063i | −0.116167 | − | 0.993230i | \(-0.537061\pi\) |
0.993230 | + | 0.116167i | \(0.0370608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.26439 | − | 3.26439i | −0.182771 | − | 0.182771i | ||||
\(320\) | 2.16830 | − | 2.16830i | 0.121212 | − | 0.121212i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.4082 | + | 11.5201i | −0.802937 | + | 0.641990i | ||||
\(323\) | −9.83633 | − | 9.83633i | −0.547308 | − | 0.547308i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.206844 | − | 15.8740i | −0.0114736 | − | 0.880532i | ||||
\(326\) | −21.6114 | −1.19694 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.249190i | 0.0137592i | ||||||||
\(329\) | 3.30445 | + | 4.13287i | 0.182180 | + | 0.227853i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.01634 | + | 6.01634i | −0.330688 | + | 0.330688i | −0.852848 | − | 0.522160i | \(-0.825126\pi\) |
0.522160 | + | 0.852848i | \(0.325126\pi\) | |||||||
\(332\) | 1.01118 | − | 1.01118i | 0.0554958 | − | 0.0554958i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.0375i | 0.713382i | ||||||||
\(335\) | 17.1786 | 0.938565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.23748i | − | 0.0674101i | −0.999432 | − | 0.0337050i | \(-0.989269\pi\) | ||
0.999432 | − | 0.0337050i | \(-0.0107307\pi\) | |||||||
\(338\) | 8.94975 | − | 9.42879i | 0.486802 | − | 0.512858i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.58251 | − | 5.58251i | 0.302754 | − | 0.302754i | ||||
\(341\) | − | 4.47602i | − | 0.242390i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.05025 | − | 17.5041i | 0.326683 | − | 0.945134i | ||||
\(344\) | 5.58251 | − | 5.58251i | 0.300989 | − | 0.300989i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3597 | − | 12.3597i | 0.664462 | − | 0.664462i | ||||
\(347\) | 12.1613 | 0.652852 | 0.326426 | − | 0.945223i | \(-0.394156\pi\) | ||||
0.326426 | + | 0.945223i | \(0.394156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.9622 | + | 17.9622i | −0.961494 | + | 0.961494i | −0.999286 | − | 0.0377919i | \(-0.987968\pi\) |
0.0377919 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(350\) | −9.09859 | + | 7.27479i | −0.486340 | + | 0.388854i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.729840 | 0.0389006 | ||||||||
\(353\) | 21.2045 | + | 21.2045i | 1.12860 | + | 1.12860i | 0.990405 | + | 0.138195i | \(0.0441300\pi\) |
0.138195 | + | 0.990405i | \(0.455870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.2205 | 1.86931 | ||||||||
\(356\) | −1.10977 | − | 1.10977i | −0.0588176 | − | 0.0588176i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9567 | − | 12.9567i | −0.684781 | − | 0.684781i | ||||
\(359\) | −20.4359 | − | 20.4359i | −1.07857 | − | 1.07857i | −0.996638 | − | 0.0819287i | \(-0.973892\pi\) |
−0.0819287 | − | 0.996638i | \(-0.526108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1928i | 0.536461i | ||||||||
\(362\) | −3.51030 | + | 3.51030i | −0.184498 | + | 0.184498i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.49371 | − | 0.932425i | −0.497606 | − | 0.0488723i | ||||
\(365\) | 50.3289 | 2.63433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.09998i | − | 0.0574185i | −0.999588 | − | 0.0287092i | \(-0.990860\pi\) | ||
0.999588 | − | 0.0287092i | \(-0.00913969\pi\) | |||||||
\(368\) | − | 6.97248i | − | 0.363466i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.9855 | + | 10.9855i | 0.571111 | + | 0.571111i | ||||
\(371\) | −0.150821 | + | 1.35402i | −0.00783025 | + | 0.0702972i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6382 | 1.06861 | 0.534304 | − | 0.845293i | \(-0.320574\pi\) | ||||
0.534304 | + | 0.845293i | \(0.320574\pi\) | |||||||
\(374\) | 1.87905 | 0.0971634 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −22.8047 | + | 0.297153i | −1.17450 | + | 0.0153042i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.82027 | + | 5.82027i | −0.298967 | + | 0.298967i | −0.840609 | − | 0.541642i | \(-0.817803\pi\) |
0.541642 | + | 0.840609i | \(0.317803\pi\) | |||||||
\(380\) | −16.5681 | −0.849923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.45480 | + | 7.45480i | −0.381421 | + | 0.381421i | ||||
\(383\) | −9.25710 | − | 9.25710i | −0.473016 | − | 0.473016i | 0.429874 | − | 0.902889i | \(-0.358558\pi\) |
−0.902889 | + | 0.429874i | \(0.858558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.88482 | − | 0.655498i | −0.299918 | − | 0.0334073i | ||||
\(386\) | −19.2851 | −0.981586 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.34336 | − | 9.34336i | 0.474337 | − | 0.474337i | ||||
\(389\) | 33.6641i | 1.70684i | 0.521224 | + | 0.853420i | \(0.325476\pi\) | ||||
−0.521224 | + | 0.853420i | \(0.674524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.9514i | − | 0.907841i | ||||||
\(392\) | 3.73926 | + | 5.91760i | 0.188861 | + | 0.298884i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.0457i | 0.959508i | ||||||||
\(395\) | −23.7331 | − | 23.7331i | −1.19414 | − | 1.19414i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.1629 | − | 24.1629i | 1.21270 | − | 1.21270i | 0.242566 | − | 0.970135i | \(-0.422011\pi\) |
0.970135 | − | 0.242566i | \(-0.0779889\pi\) | |||||||
\(398\) | −4.18927 | + | 4.18927i | −0.209989 | + | 0.209989i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 4.40303i | − | 0.220152i | ||||||
\(401\) | 8.28885 | + | 8.28885i | 0.413925 | + | 0.413925i | 0.883104 | − | 0.469178i | \(-0.155450\pi\) |
−0.469178 | + | 0.883104i | \(0.655450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.8382 | − | 15.4308i | −0.788958 | − | 0.768661i | ||||
\(404\) | 5.86058i | 0.291575i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.4510 | + | 13.0711i | 0.518674 | + | 0.648706i | ||||
\(407\) | 3.69769i | 0.183288i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.74077 | − | 7.74077i | −0.382756 | − | 0.382756i | 0.489338 | − | 0.872094i | \(-0.337238\pi\) |
−0.872094 | + | 0.489338i | \(0.837238\pi\) | |||||||
\(410\) | 0.540319 | + | 0.540319i | 0.0266845 | + | 0.0266845i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 9.16965i | − | 0.451756i | ||||||
\(413\) | −7.42650 | − | 9.28833i | −0.365434 | − | 0.457049i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.38508i | − | 0.215255i | ||||||
\(416\) | 2.51608 | − | 2.58251i | 0.123361 | − | 0.126618i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.78837 | − | 2.78837i | −0.136384 | − | 0.136384i | ||||
\(419\) | 37.2548i | 1.82002i | 0.414592 | + | 0.910008i | \(0.363924\pi\) | ||||
−0.414592 | + | 0.910008i | \(0.636076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.1725 | − | 26.1725i | 1.27557 | − | 1.27557i | 0.332451 | − | 0.943121i | \(-0.392125\pi\) |
0.943121 | − | 0.332451i | \(-0.107875\pi\) | |||||||
\(422\) | −4.98091 | + | 4.98091i | −0.242467 | + | 0.242467i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.364115 | − | 0.364115i | −0.0176830 | − | 0.0176830i | ||||
\(425\) | − | 11.3361i | − | 0.549880i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.8605 | + | 1.87805i | 0.815936 | + | 0.0908854i | ||||
\(428\) | 7.91334i | 0.382506i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 24.2091i | − | 1.16747i | ||||||
\(431\) | −2.05151 | + | 2.05151i | −0.0988177 | + | 0.0988177i | −0.754787 | − | 0.655970i | \(-0.772260\pi\) |
0.655970 | + | 0.754787i | \(0.272260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7613 | 0.757441 | 0.378720 | − | 0.925511i | \(-0.376364\pi\) | ||||
0.378720 | + | 0.925511i | \(0.376364\pi\) | |||||||
\(434\) | −1.79628 | + | 16.1263i | −0.0862240 | + | 0.774088i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.90330 | − | 9.90330i | −0.474282 | − | 0.474282i | ||||
\(437\) | −26.6385 | + | 26.6385i | −1.27429 | + | 1.27429i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8489 | 0.517788 | 0.258894 | − | 0.965906i | \(-0.416642\pi\) | ||||
0.258894 | + | 0.965906i | \(0.416642\pi\) | |||||||
\(440\) | 1.58251 | − | 1.58251i | 0.0754433 | − | 0.0754433i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.47790 | − | 6.64895i | 0.308122 | − | 0.316258i | ||||
\(443\) | 9.19115 | 0.436685 | 0.218342 | − | 0.975872i | \(-0.429935\pi\) | ||||
0.218342 | + | 0.975872i | \(0.429935\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.81261 | −0.228140 | ||||||||
\(446\) | −13.7380 | −0.650514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.62949 | − | 0.292893i | −0.124232 | − | 0.0138379i | ||||
\(449\) | −15.6122 | − | 15.6122i | −0.736784 | − | 0.736784i | 0.235170 | − | 0.971954i | \(-0.424435\pi\) |
−0.971954 | + | 0.235170i | \(0.924435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.181869i | 0.00856389i | ||||||||
\(452\) | 11.9450i | 0.561844i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.6576 | −0.922577 | ||||||||
\(455\) | −22.6070 | + | 18.5634i | −1.05983 | + | 0.870267i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7396 | + | 26.7396i | −1.25083 | + | 1.25083i | −0.295477 | + | 0.955350i | \(0.595479\pi\) |
−0.955350 | + | 0.295477i | \(0.904521\pi\) | |||||||
\(458\) | − | 8.44334i | − | 0.394532i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.1184 | − | 15.1184i | −0.704900 | − | 0.704900i | ||||
\(461\) | 17.1846 | + | 17.1846i | 0.800368 | + | 0.800368i | 0.983153 | − | 0.182785i | \(-0.0585111\pi\) |
−0.182785 | + | 0.983153i | \(0.558511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9948 | − | 16.9948i | −0.789816 | − | 0.789816i | 0.191648 | − | 0.981464i | \(-0.438617\pi\) |
−0.981464 | + | 0.191648i | \(0.938617\pi\) | |||||||
\(464\) | −6.32541 | −0.293650 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.956669 | + | 0.956669i | 0.0443168 | + | 0.0443168i | ||||
\(467\) | −7.72653 | −0.357541 | −0.178771 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178771 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.25596 | − | 11.5764i | −0.427400 | − | 0.534550i | ||||
\(470\) | −4.33660 | + | 4.33660i | −0.200032 | + | 0.200032i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.49485 | 0.206892 | ||||||||
\(473\) | 4.07434 | − | 4.07434i | 0.187338 | − | 0.187338i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.8219 | + | 16.8219i | −0.771841 | + | 0.771841i | ||||
\(476\) | −6.76990 | − | 0.754084i | −0.310298 | − | 0.0345634i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29.5436i | 1.35129i | ||||||||
\(479\) | −26.0081 | + | 26.0081i | −1.18834 | + | 1.18834i | −0.210816 | + | 0.977526i | \(0.567612\pi\) |
−0.977526 | + | 0.210816i | \(0.932388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0841 | + | 12.7475i | 0.596585 | + | 0.581238i | ||||
\(482\) | 15.8131i | 0.720269i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.4673 | −0.475788 | ||||||||
\(485\) | − | 40.5184i | − | 1.83985i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7641 | + | 12.7641i | −0.578398 | + | 0.578398i | −0.934462 | − | 0.356064i | \(-0.884119\pi\) |
0.356064 | + | 0.934462i | \(0.384119\pi\) | |||||||
\(488\) | −4.53402 | + | 4.53402i | −0.205246 | + | 0.205246i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 20.9389 | + | 4.72329i | 0.945925 | + | 0.213377i | ||||
\(491\) | − | 43.7292i | − | 1.97347i | −0.162337 | − | 0.986735i | \(-0.551903\pi\) | ||
0.162337 | − | 0.986735i | \(-0.448097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.2854 | −0.733460 | ||||||||
\(494\) | −19.4793 | + | 0.253822i | −0.876413 | + | 0.0114200i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.33660 | − | 4.33660i | −0.194719 | − | 0.194719i | ||||
\(497\) | −18.9771 | − | 23.7347i | −0.851240 | − | 1.06465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.31100 | − | 6.31100i | 0.282519 | − | 0.282519i | −0.551594 | − | 0.834113i | \(-0.685980\pi\) |
0.834113 | + | 0.551594i | \(0.185980\pi\) | |||||||
\(500\) | 1.29440 | + | 1.29440i | 0.0578875 | + | 0.0578875i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.5923 | − | 14.5923i | 0.651286 | − | 0.651286i | ||||
\(503\) | 23.4423i | 1.04524i | 0.852565 | + | 0.522620i | \(0.175046\pi\) | ||||
−0.852565 | + | 0.522620i | \(0.824954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.7075 | + | 12.7075i | 0.565475 | + | 0.565475i | ||||
\(506\) | − | 5.08880i | − | 0.226225i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2112 | 0.852361 | ||||||||
\(509\) | 16.5795 | + | 16.5795i | 0.734874 | + | 0.734874i | 0.971581 | − | 0.236707i | \(-0.0760682\pi\) |
−0.236707 | + | 0.971581i | \(0.576068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.1176 | − | 33.9161i | −1.19961 | − | 1.50036i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.51494 | + | 6.51494i | −0.287362 | + | 0.287362i | ||||
\(515\) | −19.8825 | − | 19.8825i | −0.876130 | − | 0.876130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.45968 | −0.0641967 | ||||||||
\(518\) | 1.48392 | − | 13.3221i | 0.0651999 | − | 0.585341i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.144054 | − | 11.0553i | −0.00631719 | − | 0.484805i | ||||
\(521\) | − | 32.3153i | − | 1.41576i | −0.706332 | − | 0.707880i | \(-0.749652\pi\) | ||
0.706332 | − | 0.707880i | \(-0.250348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3376i | 0.495757i | 0.968791 | + | 0.247878i | \(0.0797333\pi\) | ||||
−0.968791 | + | 0.247878i | \(0.920267\pi\) | |||||||
\(524\) | 9.83056 | 0.429450 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.72080 | + | 6.72080i | −0.293041 | + | 0.293041i | ||||
\(527\) | −11.1650 | − | 11.1650i | −0.486356 | − | 0.486356i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.6155 | −1.11372 | ||||||||
\(530\) | −1.57902 | −0.0685882 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.92701 | + | 11.1650i | 0.387035 | + | 0.484065i | ||||
\(533\) | 0.643537 | + | 0.626982i | 0.0278747 | + | 0.0271576i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.1585 | + | 17.1585i | 0.741825 | + | 0.741825i | ||||
\(536\) | 5.60212 | 0.241975 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.1315 | − | 11.1315i | −0.479912 | − | 0.479912i | ||||
\(539\) | 2.72906 | + | 4.31890i | 0.117549 | + | 0.186028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1266 | + | 17.1266i | 0.736329 | + | 0.736329i | 0.971866 | − | 0.235536i | \(-0.0756847\pi\) |
−0.235536 | + | 0.971866i | \(0.575685\pi\) | |||||||
\(542\) | − | 24.7129i | − | 1.06151i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.82052 | − | 1.82052i | 0.0780542 | − | 0.0780542i | ||||
\(545\) | −42.9466 | −1.83963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.145972 | 0.00624133 | 0.00312066 | − | 0.999995i | \(-0.499007\pi\) | ||||
0.00312066 | + | 0.999995i | \(0.499007\pi\) | |||||||
\(548\) | −3.88019 | + | 3.88019i | −0.165754 | + | 0.165754i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 3.21351i | − | 0.137025i | ||||||
\(551\) | 24.1664 | + | 24.1664i | 1.02952 | + | 1.02952i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.20586 | + | 28.7810i | −0.136327 | + | 1.22389i | ||||
\(554\) | 15.1315 | + | 15.1315i | 0.642875 | + | 0.642875i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.32681 | 0.141088 | ||||||||
\(557\) | 18.1533 | + | 18.1533i | 0.769181 | + | 0.769181i | 0.977962 | − | 0.208782i | \(-0.0669498\pi\) |
−0.208782 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.370882 | − | 28.4629i | −0.0156866 | − | 1.20385i | ||||
\(560\) | −6.33660 | + | 5.06644i | −0.267770 | + | 0.214096i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.897000 | −0.0378376 | ||||||||
\(563\) | 21.4249 | 0.902951 | 0.451476 | − | 0.892283i | \(-0.350898\pi\) | ||||
0.451476 | + | 0.892283i | \(0.350898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.9002 | + | 25.9002i | 1.08963 | + | 1.08963i | ||||
\(566\) | 8.23801 | − | 8.23801i | 0.346269 | − | 0.346269i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.4858 | 0.481934 | ||||||||
\(569\) | 26.3627i | 1.10518i | 0.833452 | + | 0.552591i | \(0.186361\pi\) | ||||
−0.833452 | + | 0.552591i | \(0.813639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 21.5077i | − | 0.900068i | −0.893012 | − | 0.450034i | \(-0.851412\pi\) | ||
0.893012 | − | 0.450034i | \(-0.148588\pi\) | |||||||
\(572\) | 1.83633 | − | 1.88482i | 0.0767810 | − | 0.0788083i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0729862 | − | 0.655244i | 0.00304638 | − | 0.0273493i | ||||
\(575\) | −30.7001 | −1.28028 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5787 | + | 11.5787i | 0.482028 | + | 0.482028i | 0.905779 | − | 0.423751i | \(-0.139287\pi\) |
−0.423751 | + | 0.905779i | \(0.639287\pi\) | |||||||
\(578\) | −7.33369 | + | 7.33369i | −0.305041 | + | 0.305041i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.7154 | + | 13.7154i | −0.569500 | + | 0.569500i | ||||
\(581\) | −2.95506 | + | 2.36272i | −0.122596 | + | 0.0980222i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.265746 | − | 0.265746i | −0.0110061 | − | 0.0110061i | ||||
\(584\) | 16.4128 | 0.679167 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 23.1585i | − | 0.956668i | ||||||
\(587\) | −27.3890 | − | 27.3890i | −1.13047 | − | 1.13047i | −0.990099 | − | 0.140368i | \(-0.955172\pi\) |
−0.140368 | − | 0.990099i | \(-0.544828\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.1361i | 1.36535i | ||||||||
\(590\) | 9.74618 | − | 9.74618i | 0.401244 | − | 0.401244i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.58251 | + | 3.58251i | 0.147240 | + | 0.147240i | ||||
\(593\) | 12.3499 | − | 12.3499i | 0.507150 | − | 0.507150i | −0.406500 | − | 0.913651i | \(-0.633251\pi\) |
0.913651 | + | 0.406500i | \(0.133251\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.3142 | + | 13.0441i | −0.668818 | + | 0.534755i | ||||
\(596\) | 8.02774 | + | 8.02774i | 0.328829 | + | 0.328829i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.0065 | − | 17.5433i | −0.736341 | − | 0.717398i | ||||
\(599\) | 29.0798 | 1.18817 | 0.594084 | − | 0.804403i | \(-0.297515\pi\) | ||||
0.594084 | + | 0.804403i | \(0.297515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.7194i | 1.17149i | 0.810496 | + | 0.585744i | \(0.199198\pi\) | ||||
−0.810496 | + | 0.585744i | \(0.800802\pi\) | |||||||
\(602\) | −16.3142 | + | 13.0441i | −0.664919 | + | 0.531637i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.5417 | − | 13.5417i | 0.551003 | − | 0.551003i | ||||
\(605\) | −22.6963 | + | 22.6963i | −0.922736 | + | 0.922736i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.9366i | − | 0.930967i | −0.885056 | − | 0.465484i | \(-0.845880\pi\) | ||
0.885056 | − | 0.465484i | \(-0.154120\pi\) | |||||||
\(608\) | −5.40303 | −0.219122 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.6622i | 0.796100i | ||||||||
\(611\) | −5.03215 | + | 5.16502i | −0.203579 | + | 0.208954i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.54006 | + | 5.54006i | −0.223761 | + | 0.223761i | −0.810080 | − | 0.586319i | \(-0.800576\pi\) |
0.586319 | + | 0.810080i | \(0.300576\pi\) | |||||||
\(614\) | 21.0299i | 0.848697i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.91911 | − | 0.213765i | −0.0773230 | − | 0.00861285i | ||||
\(617\) | 3.86438 | − | 3.86438i | 0.155574 | − | 0.155574i | −0.625028 | − | 0.780602i | \(-0.714913\pi\) |
0.780602 | + | 0.625028i | \(0.214913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.0182 | + | 25.0182i | −1.00557 | + | 1.00557i | −0.00558273 | + | 0.999984i | \(0.501777\pi\) |
−0.999984 | + | 0.00558273i | \(0.998223\pi\) | |||||||
\(620\) | −18.8061 | −0.755270 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.4194 | − | 18.4194i | 0.738549 | − | 0.738549i | ||||
\(623\) | 2.59308 | + | 3.24317i | 0.103890 | + | 0.129935i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.6285 | 1.10514 | ||||||||
\(626\) | −9.26361 | − | 9.26361i | −0.370248 | − | 0.370248i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.14458 | −0.125482 | ||||||||
\(629\) | 9.22355 | + | 9.22355i | 0.367767 | + | 0.367767i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.12549 | − | 8.12549i | −0.323471 | − | 0.323471i | 0.526626 | − | 0.850097i | \(-0.323457\pi\) |
−0.850097 | + | 0.526626i | \(0.823457\pi\) | |||||||
\(632\) | −7.73963 | − | 7.73963i | −0.307866 | − | 0.307866i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 22.0839i | − | 0.877063i | ||||||
\(635\) | 41.6557 | − | 41.6557i | 1.65306 | − | 1.65306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.6905 | + | 5.23244i | 0.978274 | + | 0.207317i | ||||
\(638\) | −4.61654 | −0.182771 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.06644i | − | 0.121212i | ||||||
\(641\) | 42.7580i | 1.68884i | 0.535682 | + | 0.844420i | \(0.320055\pi\) | ||||
−0.535682 | + | 0.844420i | \(0.679945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.37341 | − | 7.37341i | −0.290779 | − | 0.290779i | 0.546609 | − | 0.837388i | \(-0.315918\pi\) |
−0.837388 | + | 0.546609i | \(0.815918\pi\) | |||||||
\(644\) | −2.04219 | + | 18.3341i | −0.0804737 | + | 0.722463i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.9107 | −0.547308 | ||||||||
\(647\) | 22.7445 | 0.894178 | 0.447089 | − | 0.894490i | \(-0.352461\pi\) | ||||
0.447089 | + | 0.894490i | \(0.352461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.28052 | 0.128772 | ||||||||
\(650\) | −11.3709 | − | 11.0784i | −0.446003 | − | 0.434529i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.2816 | + | 15.2816i | −0.598472 | + | 0.598472i | ||||
\(653\) | 28.5645 | 1.11782 | 0.558908 | − | 0.829230i | \(-0.311220\pi\) | ||||
0.558908 | + | 0.829230i | \(0.311220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.3156 | − | 21.3156i | 0.832869 | − | 0.832869i | ||||
\(656\) | 0.176204 | + | 0.176204i | 0.00687962 | + | 0.00687962i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.25898 | + | 0.585786i | 0.205016 | + | 0.0228363i | ||||
\(659\) | 24.6149 | 0.958862 | 0.479431 | − | 0.877580i | \(-0.340843\pi\) | ||||
0.479431 | + | 0.877580i | \(0.340843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7668 | − | 14.7668i | 0.574363 | − | 0.574363i | −0.358981 | − | 0.933345i | \(-0.616876\pi\) |
0.933345 | + | 0.358981i | \(0.116876\pi\) | |||||||
\(662\) | 8.50839i | 0.330688i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.43003i | − | 0.0554958i | ||||||
\(665\) | 43.5655 | + | 4.85267i | 1.68940 | + | 0.188179i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.1038i | 1.70771i | ||||||||
\(668\) | 9.21892 | + | 9.21892i | 0.356691 | + | 0.356691i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.1471 | − | 12.1471i | 0.469282 | − | 0.469282i | ||||
\(671\) | −3.30911 | + | 3.30911i | −0.127747 | + | 0.127747i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 50.9335i | − | 1.96334i | −0.190584 | − | 0.981671i | \(-0.561038\pi\) | ||
0.190584 | − | 0.981671i | \(-0.438962\pi\) | |||||||
\(674\) | −0.875033 | − | 0.875033i | −0.0337050 | − | 0.0337050i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.338732 | − | 12.9956i | −0.0130282 | − | 0.499830i | ||||
\(677\) | − | 4.02891i | − | 0.154844i | −0.996998 | − | 0.0774218i | \(-0.975331\pi\) | ||
0.996998 | − | 0.0774218i | \(-0.0246688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.3049 | + | 21.8317i | −1.04787 | + | 0.837822i | ||||
\(680\) | − | 7.89486i | − | 0.302754i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.16502 | − | 3.16502i | −0.121195 | − | 0.121195i | ||||
\(683\) | 17.3021 | + | 17.3021i | 0.662045 | + | 0.662045i | 0.955862 | − | 0.293817i | \(-0.0949256\pi\) |
−0.293817 | + | 0.955862i | \(0.594926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8268i | 0.642920i | ||||||||
\(686\) | −8.09911 | − | 16.6555i | −0.309226 | − | 0.635908i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 7.89486i | − | 0.300989i | ||||||
\(689\) | −1.85647 | + | 0.0241905i | −0.0707259 | + | 0.000921585i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49183 | − | 2.49183i | −0.0947937 | − | 0.0947937i | 0.658120 | − | 0.752913i | \(-0.271352\pi\) |
−0.752913 | + | 0.658120i | \(0.771352\pi\) | |||||||
\(692\) | − | 17.4793i | − | 0.664462i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.59932 | − | 8.59932i | 0.326426 | − | 0.326426i | ||||
\(695\) | 7.21351 | − | 7.21351i | 0.273624 | − | 0.273624i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.453656 | + | 0.453656i | 0.0171835 | + | 0.0171835i | ||||
\(698\) | 25.4024i | 0.961494i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.28962 | + | 11.5777i | −0.0487430 | + | 0.437597i | ||||
\(701\) | − | 0.236091i | − | 0.00891703i | −0.999990 | − | 0.00445852i | \(-0.998581\pi\) | ||
0.999990 | − | 0.00445852i | \(-0.00141919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.3741i | − | 1.03243i | ||||||
\(704\) | 0.516075 | − | 0.516075i | 0.0194503 | − | 0.0194503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.9876 | 1.12860 | ||||||||
\(707\) | 1.71652 | − | 15.4103i | 0.0645565 | − | 0.579565i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.68526 | + | 9.68526i | 0.363737 | + | 0.363737i | 0.865187 | − | 0.501449i | \(-0.167200\pi\) |
−0.501449 | + | 0.865187i | \(0.667200\pi\) | |||||||
\(710\) | 24.9047 | − | 24.9047i | 0.934655 | − | 0.934655i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.56945 | −0.0588176 | ||||||||
\(713\) | −30.2368 | + | 30.2368i | −1.13238 | + | 1.13238i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.105136 | − | 8.06857i | −0.00393188 | − | 0.301747i | ||||
\(716\) | −18.3235 | −0.684781 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.9008 | −1.07857 | ||||||||
\(719\) | 47.6518 | 1.77711 | 0.888556 | − | 0.458768i | \(-0.151709\pi\) | ||||
0.888556 | + | 0.458768i | \(0.151709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.68573 | + | 24.1115i | −0.100022 | + | 0.897959i | ||||
\(722\) | 7.20737 | + | 7.20737i | 0.268231 | + | 0.268231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.96432i | 0.184498i | ||||||||
\(725\) | 27.8510i | 1.03436i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6947 | 0.396644 | 0.198322 | − | 0.980137i | \(-0.436451\pi\) | ||||
0.198322 | + | 0.980137i | \(0.436451\pi\) | |||||||
\(728\) | −7.37239 | + | 6.05374i | −0.273239 | + | 0.224367i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 35.5879 | − | 35.5879i | 1.31717 | − | 1.31717i | ||||
\(731\) | − | 20.3262i | − | 0.751790i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.22630 | − | 1.22630i | −0.0452945 | − | 0.0452945i | 0.684097 | − | 0.729391i | \(-0.260197\pi\) |
−0.729391 | + | 0.684097i | \(0.760197\pi\) | |||||||
\(734\) | −0.777803 | − | 0.777803i | −0.0287092 | − | 0.0287092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.93029 | − | 4.93029i | −0.181733 | − | 0.181733i | ||||
\(737\) | 4.08866 | 0.150608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0141 | + | 10.0141i | 0.368373 | + | 0.368373i | 0.866884 | − | 0.498511i | \(-0.166119\pi\) |
−0.498511 | + | 0.866884i | \(0.666119\pi\) | |||||||
\(740\) | 15.5359 | 0.571111 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.850789 | + | 1.06408i | 0.0312335 | + | 0.0390637i | ||||
\(743\) | 17.3229 | − | 17.3229i | 0.635516 | − | 0.635516i | −0.313930 | − | 0.949446i | \(-0.601646\pi\) |
0.949446 | + | 0.313930i | \(0.101646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.8130 | 1.27545 | ||||||||
\(746\) | 14.5934 | − | 14.5934i | 0.534304 | − | 0.534304i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.32869 | − | 1.32869i | 0.0485817 | − | 0.0485817i | ||||
\(749\) | 2.31776 | − | 20.8080i | 0.0846892 | − | 0.760309i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.8207i | − | 1.41659i | −0.705919 | − | 0.708293i | \(-0.749466\pi\) | ||
0.705919 | − | 0.708293i | \(-0.250534\pi\) | |||||||
\(752\) | −1.41421 | + | 1.41421i | −0.0515711 | + | 0.0515711i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.9152 | + | 16.3355i | −0.579598 | + | 0.594902i | ||||
\(755\) | − | 58.7248i | − | 2.13721i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6121 | −0.458395 | −0.229198 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229198 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(758\) | 8.23110i | 0.298967i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.7154 | + | 11.7154i | −0.424962 | + | 0.424962i | ||||
\(761\) | −30.3727 | + | 30.3727i | −1.10101 | + | 1.10101i | −0.106721 | + | 0.994289i | \(0.534035\pi\) |
−0.994289 | + | 0.106721i | \(0.965965\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.1400 | + | 28.9412i | 0.837724 | + | 1.04774i | ||||
\(764\) | 10.5427i | 0.381421i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.0915 | −0.473016 | ||||||||
\(767\) | 11.3094 | − | 11.6080i | 0.408358 | − | 0.419141i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.566917 | − | 0.566917i | −0.0204435 | − | 0.0204435i | 0.696811 | − | 0.717255i | \(-0.254602\pi\) |
−0.717255 | + | 0.696811i | \(0.754602\pi\) | |||||||
\(770\) | −4.62470 | + | 3.69769i | −0.166663 | + | 0.133256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.6366 | + | 13.6366i | −0.490793 | + | 0.490793i | ||||
\(773\) | 23.9977 | + | 23.9977i | 0.863137 | + | 0.863137i | 0.991701 | − | 0.128564i | \(-0.0410369\pi\) |
−0.128564 | + | 0.991701i | \(0.541037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.0942 | + | 19.0942i | −0.685883 | + | 0.685883i | ||||
\(776\) | − | 13.2135i | − | 0.474337i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.8041 | + | 23.8041i | 0.853420 | + | 0.853420i | ||||
\(779\) | − | 1.34638i | − | 0.0482392i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.38281 | 0.299960 | ||||||||
\(782\) | −12.6935 | − | 12.6935i | −0.453920 | − | 0.453920i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.82843 | + | 1.54032i | 0.243872 | + | 0.0550114i | ||||
\(785\) | −6.81838 | + | 6.81838i | −0.243359 | + | 0.243359i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.7888 | + | 32.7888i | −1.16879 | + | 1.16879i | −0.186302 | + | 0.982492i | \(0.559650\pi\) |
−0.982492 | + | 0.186302i | \(0.940350\pi\) | |||||||
\(788\) | 13.4673 | + | 13.4673i | 0.479754 | + | 0.479754i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.5636 | −1.19414 | ||||||||
\(791\) | 3.49860 | − | 31.4091i | 0.124396 | − | 1.11678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.301224 | + | 23.1171i | 0.0106968 | + | 0.820913i | ||||
\(794\) | − | 34.1715i | − | 1.21270i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.92452i | 0.209989i | ||||||||
\(797\) | 0.606614 | 0.0214874 | 0.0107437 | − | 0.999942i | \(-0.496580\pi\) | ||||
0.0107437 | + | 0.999942i | \(0.496580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.64104 | + | 3.64104i | −0.128811 | + | 0.128811i | ||||
\(800\) | −3.11341 | − | 3.11341i | −0.110076 | − | 0.110076i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.7222 | 0.413925 | ||||||||
\(803\) | 11.9787 | 0.422721 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.3256 | + | 44.1818i | 1.24506 | + | 1.55720i | ||||
\(806\) | −22.1105 | + | 0.288108i | −0.778810 | + | 0.0101482i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.14405 | + | 4.14405i | 0.145787 | + | 0.145787i | ||||
\(809\) | −1.54084 | −0.0541732 | −0.0270866 | − | 0.999633i | \(-0.508623\pi\) | ||||
−0.0270866 | + | 0.999633i | \(0.508623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4392 | + | 17.4392i | 0.612373 | + | 0.612373i | 0.943564 | − | 0.331191i | \(-0.107450\pi\) |
−0.331191 | + | 0.943564i | \(0.607450\pi\) | |||||||
\(812\) | 16.6326 | + | 1.85267i | 0.583690 | + | 0.0650160i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.61466 | + | 2.61466i | 0.0916438 | + | 0.0916438i | ||||
\(815\) | 66.2699i | 2.32133i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.1625 | + | 30.1625i | −1.05525 | + | 1.05525i | ||||
\(818\) | −10.9471 | −0.382756 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.764127 | 0.0266845 | ||||||||
\(821\) | 20.4659 | − | 20.4659i | 0.714266 | − | 0.714266i | −0.253159 | − | 0.967425i | \(-0.581469\pi\) |
0.967425 | + | 0.253159i | \(0.0814694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.39538i | 0.257787i | 0.991658 | + | 0.128893i | \(0.0411425\pi\) | ||||
−0.991658 | + | 0.128893i | \(0.958858\pi\) | |||||||
\(824\) | −6.48392 | − | 6.48392i | −0.225878 | − | 0.225878i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.8192 | − | 1.31651i | −0.411241 | − | 0.0458073i | ||||
\(827\) | 0.405564 | + | 0.405564i | 0.0141029 | + | 0.0141029i | 0.714123 | − | 0.700020i | \(-0.246826\pi\) |
−0.700020 | + | 0.714123i | \(0.746826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.28950 | −0.114249 | −0.0571245 | − | 0.998367i | \(-0.518193\pi\) | ||||
−0.0571245 | + | 0.998367i | \(0.518193\pi\) | |||||||
\(830\) | −3.10072 | − | 3.10072i | −0.107628 | − | 0.107628i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0469777 | − | 3.60525i | −0.00162866 | − | 0.124989i | ||||
\(833\) | 17.5805 | + | 3.96571i | 0.609128 | + | 0.137404i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.9787 | 1.38352 | ||||||||
\(836\) | −3.94335 | −0.136384 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.3431 | + | 26.3431i | 0.910008 | + | 0.910008i | ||||
\(839\) | −8.32703 | + | 8.32703i | −0.287481 | + | 0.287481i | −0.836083 | − | 0.548602i | \(-0.815160\pi\) |
0.548602 | + | 0.836083i | \(0.315160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0109 | 0.379685 | ||||||||
\(842\) | − | 37.0136i | − | 1.27557i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.04407i | 0.242467i | ||||||||
\(845\) | −28.9128 | − | 27.4438i | −0.994630 | − | 0.944097i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5237 | + | 3.06581i | 0.945727 | + | 0.105343i | ||||
\(848\) | −0.514936 | −0.0176830 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.01581 | − | 8.01581i | −0.274940 | − | 0.274940i | ||||
\(851\) | 24.9790 | − | 24.9790i | 0.856269 | − | 0.856269i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6895 | − | 11.6895i | 0.400242 | − | 0.400242i | −0.478076 | − | 0.878318i | \(-0.658666\pi\) |
0.878318 | + | 0.478076i | \(0.158666\pi\) | |||||||
\(854\) | 13.2502 | − | 10.5942i | 0.453411 | − | 0.362525i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.59557 | + | 5.59557i | 0.191253 | + | 0.191253i | ||||
\(857\) | 17.6693 | 0.603573 | 0.301787 | − | 0.953376i | \(-0.402417\pi\) | ||||
0.301787 | + | 0.953376i | \(0.402417\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.1971i | − | 1.40563i | −0.711374 | − | 0.702813i | \(-0.751927\pi\) | ||
0.711374 | − | 0.702813i | \(-0.248073\pi\) | |||||||
\(860\) | −17.1184 | − | 17.1184i | −0.583733 | − | 0.583733i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.90127i | 0.0988177i | ||||||||
\(863\) | −5.50354 | + | 5.50354i | −0.187343 | + | 0.187343i | −0.794546 | − | 0.607204i | \(-0.792291\pi\) |
0.607204 | + | 0.794546i | \(0.292291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.9002 | − | 37.9002i | −1.28865 | − | 1.28865i | ||||
\(866\) | 11.1449 | − | 11.1449i | 0.378720 | − | 0.378720i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.1329 | + | 12.6732i | 0.343932 | + | 0.430156i | ||||
\(869\) | −5.64869 | − | 5.64869i | −0.191619 | − | 0.191619i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0954 | − | 14.4676i | 0.477603 | − | 0.490214i | ||||
\(872\) | −14.0054 | −0.474282 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.6725i | 1.27429i | ||||||||
\(875\) | −3.02450 | − | 3.78274i | −0.102247 | − | 0.127880i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.6890 | − | 14.6890i | 0.496012 | − | 0.496012i | −0.414182 | − | 0.910194i | \(-0.635932\pi\) |
0.910194 | + | 0.414182i | \(0.135932\pi\) | |||||||
\(878\) | 7.67131 | − | 7.67131i | 0.258894 | − | 0.258894i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 2.23801i | − | 0.0754433i | ||||||
\(881\) | −9.22544 | −0.310813 | −0.155406 | − | 0.987851i | \(-0.549669\pi\) | ||||
−0.155406 | + | 0.987851i | \(0.549669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.4515i | − | 0.890165i | −0.895490 | − | 0.445083i | \(-0.853174\pi\) | ||
0.895490 | − | 0.445083i | \(-0.146826\pi\) | |||||||
\(884\) | −0.120949 | − | 9.28208i | −0.00406795 | − | 0.312190i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.49912 | − | 6.49912i | 0.218342 | − | 0.218342i | ||||
\(887\) | − | 11.7136i | − | 0.393303i | −0.980473 | − | 0.196651i | \(-0.936993\pi\) | ||
0.980473 | − | 0.196651i | \(-0.0630067\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.5157 | − | 5.62684i | −1.69424 | − | 0.188718i | ||||
\(890\) | −3.40303 | + | 3.40303i | −0.114070 | + | 0.114070i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.71425 | + | 9.71425i | −0.325257 | + | 0.325257i | ||||
\(893\) | 10.8061 | 0.361611 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.7308 | + | 39.7308i | −1.32805 | + | 1.32805i | ||||
\(896\) | −2.06644 | + | 1.65222i | −0.0690348 | + | 0.0551969i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0789 | −0.736784 | ||||||||
\(899\) | 27.4308 | + | 27.4308i | 0.914867 | + | 0.914867i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32576 | −0.0441674 | ||||||||
\(902\) | 0.128601 | + | 0.128601i | 0.00428194 | + | 0.00428194i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.44636 | + | 8.44636i | 0.280922 | + | 0.280922i | ||||
\(905\) | 10.7641 | + | 10.7641i | 0.357812 | + | 0.357812i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4074i | 0.810436i | 0.914220 | + | 0.405218i | \(0.132804\pi\) | ||||
−0.914220 | + | 0.405218i | \(0.867196\pi\) | |||||||
\(908\) | −13.9000 | + | 13.9000i | −0.461288 | + | 0.461288i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.85922 | + | 29.1119i | −0.0947822 | + | 0.965049i | ||||
\(911\) | 35.7796 | 1.18543 | 0.592715 | − | 0.805412i | \(-0.298056\pi\) | ||||
0.592715 | + | 0.805412i | \(0.298056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.04369i | − | 0.0345411i | ||||||
\(914\) | 37.8155i | 1.25083i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.97035 | − | 5.97035i | −0.197266 | − | 0.197266i | ||||
\(917\) | −25.8494 | − | 2.87931i | −0.853621 | − | 0.0950830i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.9957 | 0.725572 | 0.362786 | − | 0.931872i | \(-0.381826\pi\) | ||||
0.362786 | + | 0.931872i | \(0.381826\pi\) | |||||||
\(920\) | −21.3807 | −0.704900 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.3027 | 0.800368 | ||||||||
\(923\) | 28.8992 | − | 29.6622i | 0.951227 | − | 0.976344i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7739 | − | 15.7739i | 0.518643 | − | 0.518643i | ||||
\(926\) | −24.0343 | −0.789816 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.47274 | + | 4.47274i | −0.146825 | + | 0.146825i | ||||
\(929\) | −11.1005 | − | 11.1005i | −0.364196 | − | 0.364196i | 0.501159 | − | 0.865355i | \(-0.332907\pi\) |
−0.865355 | + | 0.501159i | \(0.832907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2033 | − | 31.9730i | −0.662137 | − | 1.04787i | ||||
\(932\) | 1.35293 | 0.0443168 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.46348 | + | 5.46348i | −0.178771 | + | 0.178771i | ||||
\(935\) | − | 5.76199i | − | 0.188437i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.9296i | − | 1.07576i | −0.843020 | − | 0.537882i | \(-0.819225\pi\) | ||
0.843020 | − | 0.537882i | \(-0.180775\pi\) | |||||||
\(938\) | −14.7307 | − | 1.64082i | −0.480975 | − | 0.0535748i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.13287i | 0.200032i | ||||||||
\(941\) | −16.5400 | − | 16.5400i | −0.539189 | − | 0.539189i | 0.384102 | − | 0.923291i | \(-0.374511\pi\) |
−0.923291 | + | 0.384102i | \(0.874511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22858 | − | 1.22858i | 0.0400081 | − | 0.0400081i | ||||
\(944\) | 3.17834 | − | 3.17834i | 0.103446 | − | 0.103446i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 5.76199i | − | 0.187338i | ||||||
\(947\) | −8.74592 | − | 8.74592i | −0.284204 | − | 0.284204i | 0.550579 | − | 0.834783i | \(-0.314407\pi\) |
−0.834783 | + | 0.550579i | \(0.814407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.2959 | − | 42.3863i | 1.34052 | − | 1.37592i | ||||
\(950\) | 23.7897i | 0.771841i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.32026 | + | 4.25382i | −0.172431 | + | 0.137867i | ||||
\(953\) | 14.1171i | 0.457296i | 0.973509 | + | 0.228648i | \(0.0734306\pi\) | ||||
−0.973509 | + | 0.228648i | \(0.926569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.8597 | + | 22.8597i | 0.739721 | + | 0.739721i | ||||
\(956\) | 20.8904 | + | 20.8904i | 0.675645 | + | 0.675645i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.7810i | 1.18834i | ||||||||
\(959\) | 11.3394 | − | 9.06644i | 0.366168 | − | 0.292771i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.61213i | 0.213295i | ||||||||
\(962\) | 18.2657 | − | 0.238009i | 0.588911 | − | 0.00767373i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.1816 | + | 11.1816i | 0.360134 | + | 0.360134i | ||||
\(965\) | 59.1365i | 1.90367i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8079 | + | 17.8079i | −0.572664 | + | 0.572664i | −0.932872 | − | 0.360208i | \(-0.882706\pi\) |
0.360208 | + | 0.932872i | \(0.382706\pi\) | |||||||
\(968\) | −7.40152 | + | 7.40152i | −0.237894 | + | 0.237894i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.6508 | − | 28.6508i | −0.919923 | − | 0.919923i | ||||
\(971\) | 21.1673i | 0.679291i | 0.940554 | + | 0.339646i | \(0.110307\pi\) | ||||
−0.940554 | + | 0.339646i | \(0.889693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.74781 | − | 0.974400i | −0.280442 | − | 0.0312378i | ||||
\(974\) | 18.0512i | 0.578398i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.41208i | 0.205246i | ||||||||
\(977\) | −19.6568 | + | 19.6568i | −0.628877 | + | 0.628877i | −0.947786 | − | 0.318908i | \(-0.896684\pi\) |
0.318908 | + | 0.947786i | \(0.396684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.14545 | −0.0366086 | ||||||||
\(980\) | 18.1459 | − | 11.4662i | 0.579651 | − | 0.366274i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.9212 | − | 30.9212i | −0.986735 | − | 0.986735i | ||||
\(983\) | −17.7065 | + | 17.7065i | −0.564749 | + | 0.564749i | −0.930653 | − | 0.365904i | \(-0.880760\pi\) |
0.365904 | + | 0.930653i | \(0.380760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58.4024 | 1.86085 | ||||||||
\(986\) | −11.5155 | + | 11.5155i | −0.366730 | + | 0.366730i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.5944 | + | 13.9534i | −0.432497 | + | 0.443917i | ||||
\(989\) | −55.0468 | −1.75039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3147 | 0.835913 | 0.417957 | − | 0.908467i | \(-0.362746\pi\) | ||||
0.417957 | + | 0.908467i | \(0.362746\pi\) | |||||||
\(992\) | −6.13287 | −0.194719 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.2018 | − | 3.36411i | −0.957943 | − | 0.106703i | ||||
\(995\) | 12.8461 | + | 12.8461i | 0.407249 | + | 0.407249i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.40444i | 0.107820i | 0.998546 | + | 0.0539099i | \(0.0171684\pi\) | ||||
−0.998546 | + | 0.0539099i | \(0.982832\pi\) | |||||||
\(998\) | − | 8.92510i | − | 0.282519i | ||||||
\(999\) | 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 | 1638.2.x.a.811.3 | 8 | ||
3.2 | odd | 2 | 546.2.o.c.265.2 | yes | 8 | ||
7.6 | odd | 2 | 1638.2.x.c.811.4 | 8 | |||
13.8 | odd | 4 | 1638.2.x.c.307.4 | 8 | |||
21.20 | even | 2 | 546.2.o.b.265.1 | ✓ | 8 | ||
39.8 | even | 4 | 546.2.o.b.307.1 | yes | 8 | ||
91.34 | even | 4 | inner | 1638.2.x.a.307.3 | 8 | ||
273.125 | odd | 4 | 546.2.o.c.307.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.1 | ✓ | 8 | 21.20 | even | 2 | ||
546.2.o.b.307.1 | yes | 8 | 39.8 | even | 4 | ||
546.2.o.c.265.2 | yes | 8 | 3.2 | odd | 2 | ||
546.2.o.c.307.2 | yes | 8 | 273.125 | odd | 4 | ||
1638.2.x.a.307.3 | 8 | 91.34 | even | 4 | inner | ||
1638.2.x.a.811.3 | 8 | 1.1 | even | 1 | trivial | ||
1638.2.x.c.307.4 | 8 | 13.8 | odd | 4 | |||
1638.2.x.c.811.4 | 8 | 7.6 | odd | 2 |