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 | 307.4 | ||
Root | \(-2.06644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.307 |
Dual form | 1638.2.x.c.811.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | \(-0.509507\pi\) |
0.999554 | + | 0.0298617i | \(0.00950669\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62949 | + | 0.292893i | 0.993854 | + | 0.110703i | ||||
\(8\) | −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 | −0.780615 | − | 0.625012i | \(-0.785094\pi\) |
0.625012 | + | 0.780615i | \(0.285094\pi\) | |||||||
\(12\) | 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 | \(-0.398928\pi\) | ||||
0.312217 | + | 0.950011i | \(0.398928\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.82052 | + | 3.82052i | −0.876488 | + | 0.876488i | −0.993169 | − | 0.116682i | \(-0.962774\pi\) |
0.116682 | + | 0.993169i | \(0.462774\pi\) | |||||||
\(20\) | 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 | \(-0.740946\pi\) | ||
0.686710 | − | 0.726931i | \(-0.259054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.40303i | − | 0.880606i | ||||||
\(26\) | 2.51608 | + | 2.58251i | 0.493443 | + | 0.506472i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.292893 | + | 2.62949i | −0.0553516 | + | 0.496927i | ||||
\(29\) | 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 | \(-0.935658\pi\) |
0.200764 | + | 0.979640i | \(0.435658\pi\) | |||||||
\(32\) | −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 | −0.937350 | − | 0.348389i | \(-0.886729\pi\) |
0.348389 | + | 0.937350i | \(0.386729\pi\) | |||||||
\(38\) | −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 | \(-0.743806\pi\) |
0.720732 | + | 0.693214i | \(0.243806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.89486i | − | 1.20396i | −0.798513 | − | 0.601978i | \(-0.794380\pi\) | ||
0.798513 | − | 0.601978i | \(-0.205620\pi\) | |||||||
\(44\) | −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 | \(-0.296597\pi\) |
−0.802686 | + | 0.596402i | \(0.796597\pi\) | |||||||
\(48\) | 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 | \(-0.155483\pi\) |
−0.469270 | + | 0.883055i | \(0.655483\pi\) | |||||||
\(60\) | 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 | 0.422441 | − | 0.906391i | \(-0.361173\pi\) |
−0.906391 | + | 0.422441i | \(0.861173\pi\) | |||||||
\(68\) | 2.57461i | 0.312217i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.06316 | + | 0.898138i | 0.963732 | + | 0.107348i | ||||
\(71\) | −8.12169 | − | 8.12169i | −0.963867 | − | 0.963867i | 0.0355021 | − | 0.999370i | \(-0.488697\pi\) |
−0.999370 | + | 0.0355021i | \(0.988697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6056 | + | 11.6056i | 1.35833 | + | 1.35833i | 0.875971 | + | 0.482364i | \(0.160222\pi\) |
0.482364 | + | 0.875971i | \(0.339778\pi\) | |||||||
\(74\) | −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 | \(-0.775008\pi\) |
0.649430 | + | 0.760421i | \(0.275008\pi\) | |||||||
\(84\) | 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 | \(-0.276508\pi\) |
−0.763474 | + | 0.645839i | \(0.776508\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.46619 | + | 1.17948i | 0.992327 | + | 0.123643i | ||||
\(92\) | 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 | \(-0.984055\pi\) |
0.0500709 | + | 0.998746i | \(0.484055\pi\) | |||||||
\(98\) | 3.73926 | + | 5.91760i | 0.377722 | + | 0.597768i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.40303 | 0.440303 | ||||||||
\(101\) | 5.86058 | 0.583149 | 0.291575 | − | 0.956548i | \(-0.405821\pi\) | ||||
0.291575 | + | 0.956548i | \(0.405821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.16965 | −0.903513 | −0.451756 | − | 0.892141i | \(-0.649202\pi\) | ||||
−0.451756 | + | 0.892141i | \(0.649202\pi\) | |||||||
\(104\) | −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 | 0.998740 | − | 0.0501767i | \(-0.0159785\pi\) |
−0.0501767 | + | 0.998740i | \(0.515978\pi\) | |||||||
\(110\) | −1.58251 | + | 1.58251i | −0.150887 | + | 0.150887i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.62949 | − | 0.292893i | −0.248463 | − | 0.0276758i | ||||
\(113\) | −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 | ||||||||
\(119\) | 6.76990 | + | 0.754084i | 0.620595 | + | 0.0691268i | ||||
\(120\) | 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 | \(-0.675170\pi\) | ||
0.522954 | − | 0.852361i | \(-0.324830\pi\) | |||||||
\(128\) | 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 | −0.853159 | − | 0.521652i | \(-0.825316\pi\) |
0.521652 | + | 0.853159i | \(0.325316\pi\) | |||||||
\(138\) | 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 | 0.297168 | − | 0.954825i | \(-0.403958\pi\) |
−0.954825 | + | 0.297168i | \(0.903958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5417 | − | 13.5417i | 1.10201 | − | 1.10201i | 0.107837 | − | 0.994169i | \(-0.465607\pi\) |
0.994169 | − | 0.107837i | \(-0.0343926\pi\) | |||||||
\(152\) | − | 5.40303i | − | 0.438244i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.91911 | − | 0.213765i | −0.154646 | − | 0.0172257i | ||||
\(155\) | 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 | ||||||||
\(161\) | 2.04219 | − | 18.3341i | 0.160947 | − | 1.44493i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.2816 | + | 15.2816i | −1.19694 | + | 1.19694i | −0.221867 | + | 0.975077i | \(0.571215\pi\) |
−0.975077 | + | 0.221867i | \(0.928785\pi\) | |||||||
\(164\) | 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 | \(-0.0817001\pi\) |
−0.253860 | + | 0.967241i | \(0.581700\pi\) | |||||||
\(168\) | 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 | \(-0.731339\pi\) | ||||
−0.664462 | + | 0.747322i | \(0.731339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.28962 | − | 11.5777i | 0.0974860 | − | 0.875194i | ||||
\(176\) | 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 | \(0.240102\pi\) | ||||
−0.728749 | + | 0.684781i | \(0.759898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.96432 | 0.368995 | 0.184498 | − | 0.982833i | \(-0.440934\pi\) | ||||
0.184498 | + | 0.982833i | \(0.440934\pi\) | |||||||
\(182\) | 5.85959 | + | 7.52763i | 0.434342 | + | 0.557985i | ||||
\(183\) | 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 | −0.999833 | − | 0.0182475i | \(-0.994191\pi\) |
0.0182475 | + | 0.999833i | \(0.494191\pi\) | |||||||
\(194\) | −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 | 0.0397038 | − | 0.999211i | \(-0.487359\pi\) |
−0.999211 | + | 0.0397038i | \(0.987359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.92452 | 0.419978 | 0.209989 | − | 0.977704i | \(-0.432657\pi\) | ||||
0.209989 | + | 0.977704i | \(0.432657\pi\) | |||||||
\(200\) | 3.11341 | + | 3.11341i | 0.220152 | + | 0.220152i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.14405 | + | 4.14405i | 0.291575 | + | 0.291575i | ||||
\(203\) | 16.6326 | + | 1.85267i | 1.16738 | + | 0.130032i | ||||
\(204\) | 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 | \(-0.597856\pi\) |
0.953117 | + | 0.302603i | \(0.0978555\pi\) | |||||||
\(224\) | −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 | \(-0.523779\pi\) |
0.997211 | + | 0.0746342i | \(0.0237789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.97035 | − | 5.97035i | −0.394532 | − | 0.394532i | 0.481768 | − | 0.876299i | \(-0.339995\pi\) |
−0.876299 | + | 0.481768i | \(0.839995\pi\) | |||||||
\(230\) | − | 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 | \(-0.985889\pi\) | ||
0.999018 | − | 0.0443168i | \(-0.0141111\pi\) | |||||||
\(234\) | 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 | −0.884220 | − | 0.467071i | \(-0.845309\pi\) |
−0.467071 | − | 0.884220i | \(-0.654691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1816 | + | 11.1816i | 0.720269 | + | 0.720269i | 0.968660 | − | 0.248391i | \(-0.0799018\pi\) |
−0.248391 | + | 0.968660i | \(0.579902\pi\) | |||||||
\(242\) | −7.40152 | + | 7.40152i | −0.475788 | + | 0.475788i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.41208 | 0.410491 | ||||||||
\(245\) | 18.1459 | − | 11.4662i | 1.15930 | − | 0.732548i | ||||
\(246\) | 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 | \(-0.725770\pi\) | ||||
−0.651286 | + | 0.758832i | \(0.725770\pi\) | |||||||
\(252\) | 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 | \(-0.407222\pi\) | ||||
0.287362 | + | 0.957822i | \(0.407222\pi\) | |||||||
\(258\) | 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 | ||||
\(266\) | −14.2072 | − | 1.58251i | −0.871100 | − | 0.0970300i | ||||
\(267\) | 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 | −0.997980 | − | 0.0635278i | \(-0.979765\pi\) |
−0.0635278 | − | 0.997980i | \(-0.520235\pi\) | |||||||
\(272\) | −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 | \(-0.777741\pi\) | ||
0.765971 | − | 0.642875i | \(-0.222259\pi\) | |||||||
\(278\) | −2.35241 | + | 2.35241i | −0.141088 | + | 0.141088i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.898138 | + | 8.06316i | −0.0536740 | + | 0.481866i | ||||
\(281\) | −0.634274 | + | 0.634274i | −0.0378376 | + | 0.0378376i | −0.725772 | − | 0.687935i | \(-0.758517\pi\) |
0.687935 | + | 0.725772i | \(0.258517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6503 | −0.692539 | −0.346269 | − | 0.938135i | \(-0.612552\pi\) | ||||
−0.346269 | + | 0.938135i | \(0.612552\pi\) | |||||||
\(284\) | 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 | \(-0.486490\pi\) |
−0.999099 | + | 0.0424317i | \(0.986490\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 2.31235 | − | 20.7595i | 0.133282 | − | 1.19656i | ||||
\(302\) | 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 | \(-0.0451198\pi\) |
−0.141274 | + | 0.989971i | \(0.545120\pi\) | |||||||
\(308\) | −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 | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674199i | \(0.764489\pi\) | |||||||
\(312\) | 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 | 0.993230 | − | 0.116167i | \(-0.0370608\pi\) |
−0.116167 | + | 0.993230i | \(0.537061\pi\) | |||||||
\(318\) | 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 | 0.522160 | − | 0.852848i | \(-0.325126\pi\) |
−0.852848 | + | 0.522160i | \(0.825126\pi\) | |||||||
\(332\) | −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 | \(0.0107307\pi\) | ||||
−0.999432 | + | 0.0337050i | \(0.989269\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 17.5041 | + | 6.05025i | 0.945134 | + | 0.326683i | ||||
\(344\) | 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 | \(-0.0120324\pi\) |
−0.0377919 | + | 0.999286i | \(0.512032\pi\) | |||||||
\(350\) | 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 | −0.138195 | + | 0.990405i | \(0.544130\pi\) |
−0.990405 | + | 0.138195i | \(0.955870\pi\) | |||||||
\(354\) | 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 | −0.0819287 | + | 0.996638i | \(0.526108\pi\) |
−0.996638 | + | 0.0819287i | \(0.973892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 10.1928i | − | 0.536461i | ||||||
\(362\) | 3.51030 | + | 3.51030i | 0.184498 | + | 0.184498i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.17948 | + | 9.46619i | −0.0618215 | + | 0.496163i | ||||
\(365\) | 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 | ||||
\(371\) | 1.35402 | + | 0.150821i | 0.0702972 | + | 0.00783025i | ||||
\(372\) | 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 | 0.541642 | − | 0.840609i | \(-0.317803\pi\) |
−0.840609 | + | 0.541642i | \(0.817803\pi\) | |||||||
\(380\) | −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 | \(-0.641442\pi\) |
0.902889 | + | 0.429874i | \(0.141442\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.655498 | + | 5.88482i | −0.0334073 | + | 0.299918i | ||||
\(386\) | −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 | \(-0.674524\pi\) | ||
0.521224 | − | 0.853420i | \(-0.325476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.9514i | − | 0.907841i | ||||||
\(392\) | −5.91760 | + | 3.73926i | −0.298884 | + | 0.188861i | ||||
\(393\) | 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 | −0.970135 | − | 0.242566i | \(-0.922011\pi\) |
−0.242566 | − | 0.970135i | \(-0.577989\pi\) | |||||||
\(398\) | 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 | −0.469178 | − | 0.883104i | \(-0.655450\pi\) |
0.883104 | + | 0.469178i | \(0.155450\pi\) | |||||||
\(402\) | 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 | \(-0.662762\pi\) |
0.872094 | + | 0.489338i | \(0.162762\pi\) | |||||||
\(410\) | 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 | 0.943121 | + | 0.332451i | \(0.107875\pi\) |
0.332451 | + | 0.943121i | \(0.392125\pi\) | |||||||
\(422\) | −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 | ||||||||
\(427\) | 1.87805 | − | 16.8605i | 0.0908854 | − | 0.815936i | ||||
\(428\) | − | 7.91334i | − | 0.382506i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 24.2091i | − | 1.16747i | ||||||
\(431\) | −2.05151 | − | 2.05151i | −0.0988177 | − | 0.0988177i | 0.655970 | − | 0.754787i | \(-0.272260\pi\) |
−0.754787 | + | 0.655970i | \(0.772260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7613 | −0.757441 | −0.378720 | − | 0.925511i | \(-0.623636\pi\) | ||||
−0.378720 | + | 0.925511i | \(0.623636\pi\) | |||||||
\(434\) | −16.1263 | − | 1.79628i | −0.774088 | − | 0.0862240i | ||||
\(435\) | 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 | \(-0.583358\pi\) | ||||
−0.258894 | + | 0.965906i | \(0.583358\pi\) | |||||||
\(440\) | −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 | ||||||||
\(448\) | 0.292893 | − | 2.62949i | 0.0138379 | − | 0.124232i | ||||
\(449\) | −15.6122 | + | 15.6122i | −0.736784 | + | 0.736784i | −0.971954 | − | 0.235170i | \(-0.924435\pi\) |
0.235170 | + | 0.971954i | \(0.424435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.181869i | 0.00856389i | ||||||||
\(452\) | − | 11.9450i | − | 0.561844i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.6576 | 0.922577 | ||||||||
\(455\) | 23.0830 | − | 17.9681i | 1.08215 | − | 0.842356i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7396 | − | 26.7396i | −1.25083 | − | 1.25083i | −0.955350 | − | 0.295477i | \(-0.904521\pi\) |
−0.295477 | − | 0.955350i | \(-0.595479\pi\) | |||||||
\(458\) | − | 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 | \(-0.941489\pi\) |
0.182785 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9948 | + | 16.9948i | −0.789816 | + | 0.789816i | −0.981464 | − | 0.191648i | \(-0.938617\pi\) |
0.191648 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(464\) | −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 | \(-0.442788\pi\) | ||||
0.178771 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(468\) | 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 | ||||
\(476\) | −0.754084 | + | 6.76990i | −0.0345634 | + | 0.310298i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 29.5436i | − | 1.35129i | ||||||
\(479\) | 26.0081 | + | 26.0081i | 1.18834 | + | 1.18834i | 0.977526 | + | 0.210816i | \(0.0676120\pi\) |
0.210816 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(480\) | 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 | 0.356064 | − | 0.934462i | \(-0.384119\pi\) |
−0.934462 | + | 0.356064i | \(0.884119\pi\) | |||||||
\(488\) | 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 | \(0.448097\pi\) | ||||
−0.162337 | + | 0.986735i | \(0.551903\pi\) | |||||||
\(492\) | 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 | 0.834113 | − | 0.551594i | \(-0.185980\pi\) |
−0.551594 | + | 0.834113i | \(0.685980\pi\) | |||||||
\(500\) | −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 | \(-0.923932\pi\) |
0.236707 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(510\) | 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 | ||||||||
\(518\) | −13.3221 | − | 1.48392i | −0.585341 | − | 0.0651999i | ||||
\(519\) | 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 | ||||
\(539\) | −4.31890 | + | 2.72906i | −0.186028 | + | 0.117549i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1266 | − | 17.1266i | 0.736329 | − | 0.736329i | −0.235536 | − | 0.971866i | \(-0.575685\pi\) |
0.971866 | + | 0.235536i | \(0.0756847\pi\) | |||||||
\(542\) | − | 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 | ||||||||
\(553\) | 28.7810 | + | 3.20586i | 1.22389 | + | 0.136327i | ||||
\(554\) | 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 | −0.208782 | − | 0.977962i | \(-0.566950\pi\) |
0.977962 | + | 0.208782i | \(0.0669498\pi\) | |||||||
\(558\) | 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 | \(-0.649102\pi\) | ||||
−0.451476 | + | 0.892283i | \(0.649102\pi\) | |||||||
\(564\) | 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 | \(-0.813639\pi\) | ||
0.833452 | − | 0.552591i | \(-0.186361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5077i | 0.900068i | 0.893012 | + | 0.450034i | \(0.148588\pi\) | ||||
−0.893012 | + | 0.450034i | \(0.851412\pi\) | |||||||
\(572\) | −1.83633 | − | 1.88482i | −0.0767810 | − | 0.0788083i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.655244 | + | 0.0729862i | 0.0273493 | + | 0.00304638i | ||||
\(575\) | −30.7001 | −1.28028 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5787 | + | 11.5787i | −0.482028 | + | 0.482028i | −0.905779 | − | 0.423751i | \(-0.860713\pi\) |
0.423751 | + | 0.905779i | \(0.360713\pi\) | |||||||
\(578\) | −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 | 0.140368 | − | 0.990099i | \(-0.455172\pi\) |
0.990099 | − | 0.140368i | \(-0.0448284\pi\) | |||||||
\(588\) | 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 | \(-0.366749\pi\) |
−0.913651 | + | 0.406500i | \(0.866749\pi\) | |||||||
\(594\) | 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 | 0.586319 | − | 0.810080i | \(-0.300576\pi\) |
−0.810080 | + | 0.586319i | \(0.800576\pi\) | |||||||
\(614\) | 21.0299i | 0.848697i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.213765 | − | 1.91911i | 0.00861285 | − | 0.0773230i | ||||
\(617\) | 3.86438 | + | 3.86438i | 0.155574 | + | 0.155574i | 0.780602 | − | 0.625028i | \(-0.214913\pi\) |
−0.625028 | + | 0.780602i | \(0.714913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0182 | + | 25.0182i | 1.00557 | + | 1.00557i | 0.999984 | + | 0.00558273i | \(0.00177705\pi\) |
0.00558273 | + | 0.999984i | \(0.498223\pi\) | |||||||
\(620\) | −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 | −0.850097 | − | 0.526626i | \(-0.823457\pi\) |
0.526626 | + | 0.850097i | \(0.323457\pi\) | |||||||
\(632\) | −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 | ||||||||
\(637\) | 24.5458 | + | 5.87401i | 0.972540 | + | 0.232737i | ||||
\(638\) | −4.61654 | −0.182771 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.06644i | − | 0.121212i | ||||||
\(641\) | − | 42.7580i | − | 1.68884i | −0.535682 | − | 0.844420i | \(-0.679945\pi\) | ||
0.535682 | − | 0.844420i | \(-0.320055\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.37341 | − | 7.37341i | 0.290779 | − | 0.290779i | −0.546609 | − | 0.837388i | \(-0.684082\pi\) |
0.837388 | + | 0.546609i | \(0.184082\pi\) | |||||||
\(644\) | 18.3341 | + | 2.04219i | 0.722463 | + | 0.0804737i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.9107 | −0.547308 | ||||||||
\(647\) | −22.7445 | −0.894178 | −0.447089 | − | 0.894490i | \(-0.647539\pi\) | ||||
−0.447089 | + | 0.894490i | \(0.647539\pi\) | |||||||
\(648\) | 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 | ||||||||
\(658\) | 0.585786 | − | 5.25898i | 0.0228363 | − | 0.205016i | ||||
\(659\) | 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 | \(-0.383124\pi\) |
−0.933345 | + | 0.358981i | \(0.883124\pi\) | |||||||
\(662\) | − | 8.50839i | − | 0.330688i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.43003i | − | 0.0554958i | ||||||
\(665\) | −4.85267 | + | 43.5655i | −0.188179 | + | 1.68940i | ||||
\(666\) | 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 | \(0.438962\pi\) | ||||
−0.190584 | + | 0.981671i | \(0.561038\pi\) | |||||||
\(674\) | −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 | −0.293817 | − | 0.955862i | \(-0.594926\pi\) |
0.955862 | + | 0.293817i | \(0.0949256\pi\) | |||||||
\(684\) | 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 | \(-0.728648\pi\) |
0.752913 | + | 0.658120i | \(0.228648\pi\) | |||||||
\(692\) | − | 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 | ||||||||
\(700\) | 11.5777 | + | 1.28962i | 0.437597 | + | 0.0487430i | ||||
\(701\) | 0.236091i | 0.00891703i | 0.999990 | + | 0.00445852i | \(0.00141919\pi\) | ||||
−0.999990 | + | 0.00445852i | \(0.998581\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.3741i | − | 1.03243i | ||||||
\(704\) | 0.516075 | + | 0.516075i | 0.0194503 | + | 0.0194503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.9876 | −1.12860 | ||||||||
\(707\) | 15.4103 | + | 1.71652i | 0.579565 | + | 0.0645565i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.68526 | − | 9.68526i | 0.363737 | − | 0.363737i | −0.501449 | − | 0.865187i | \(-0.667200\pi\) |
0.865187 | + | 0.501449i | \(0.167200\pi\) | |||||||
\(710\) | −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 | \(-0.848291\pi\) | ||||
−0.888556 | + | 0.458768i | \(0.848291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.1115 | − | 2.68573i | −0.897959 | − | 0.100022i | ||||
\(722\) | 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 | \(-0.563549\pi\) | ||||
−0.198322 | + | 0.980137i | \(0.563549\pi\) | |||||||
\(728\) | −7.52763 | + | 5.85959i | −0.278992 | + | 0.217171i | ||||
\(729\) | 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 | \(-0.739803\pi\) |
0.729391 | + | 0.684097i | \(0.239803\pi\) | |||||||
\(734\) | 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 | −0.498511 | − | 0.866884i | \(-0.666119\pi\) |
0.866884 | + | 0.498511i | \(0.166119\pi\) | |||||||
\(740\) | −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 | 0.949446 | − | 0.313930i | \(-0.101646\pi\) |
−0.313930 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(744\) | 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 | ||||
\(749\) | −20.8080 | − | 2.31776i | −0.760309 | − | 0.0846892i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.8207i | 1.41659i | 0.705919 | + | 0.708293i | \(0.250534\pi\) | ||||
−0.705919 | + | 0.708293i | \(0.749466\pi\) | |||||||
\(752\) | 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 | 0.994289 | + | 0.106721i | \(0.0340351\pi\) |
0.106721 | + | 0.994289i | \(0.465965\pi\) | |||||||
\(762\) | 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 | \(-0.745398\pi\) |
0.717255 | + | 0.696811i | \(0.245398\pi\) | |||||||
\(770\) | −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 | \(-0.958963\pi\) |
0.128564 | + | 0.991701i | \(0.458963\pi\) | |||||||
\(774\) | 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 | 0.982492 | + | 0.186302i | \(0.0596504\pi\) |
0.186302 | + | 0.982492i | \(0.440350\pi\) | |||||||
\(788\) | 13.4673 | − | 13.4673i | 0.479754 | − | 0.479754i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.5636 | 1.19414 | ||||||||
\(791\) | −31.4091 | − | 3.49860i | −1.11678 | − | 0.124396i | ||||
\(792\) | 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 | \(-0.503420\pi\) | ||||
−0.0107437 | + | 0.999942i | \(0.503420\pi\) | |||||||
\(798\) | 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 | \(-0.892550\pi\) |
0.331191 | + | 0.943564i | \(0.392550\pi\) | |||||||
\(812\) | −1.85267 | + | 16.6326i | −0.0650160 | + | 0.583690i | ||||
\(813\) | 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 | 0.967425 | − | 0.253159i | \(-0.0814694\pi\) |
−0.253159 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.39538i | − | 0.257787i | −0.991658 | − | 0.128893i | \(-0.958858\pi\) | ||
0.991658 | − | 0.128893i | \(-0.0411425\pi\) | |||||||
\(824\) | 6.48392 | − | 6.48392i | 0.225878 | − | 0.225878i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.31651 | + | 11.8192i | −0.0458073 | + | 0.411241i | ||||
\(827\) | 0.405564 | − | 0.405564i | 0.0141029 | − | 0.0141029i | −0.700020 | − | 0.714123i | \(-0.746826\pi\) |
0.714123 | + | 0.700020i | \(0.246826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.28950 | 0.114249 | 0.0571245 | − | 0.998367i | \(-0.481807\pi\) | ||||
0.0571245 | + | 0.998367i | \(0.481807\pi\) | |||||||
\(830\) | −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 | \(-0.184840\pi\) |
−0.548602 | + | 0.836083i | \(0.684840\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | −3.06581 | + | 27.5237i | −0.105343 | + | 0.945727i | ||||
\(848\) | −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 | \(-0.341334\pi\) |
−0.878318 | + | 0.478076i | \(0.841334\pi\) | |||||||
\(854\) | 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 | \(-0.597583\pi\) | ||||
−0.301787 | + | 0.953376i | \(0.597583\pi\) | |||||||
\(858\) | 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 | 0.607204 | − | 0.794546i | \(-0.292291\pi\) |
−0.794546 | + | 0.607204i | \(0.792291\pi\) | |||||||
\(864\) | 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 | 0.910194 | − | 0.414182i | \(-0.135932\pi\) |
−0.414182 | + | 0.910194i | \(0.635932\pi\) | |||||||
\(878\) | −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 | \(-0.450331\pi\) | ||||
0.155406 | + | 0.987851i | \(0.450331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4515i | 0.890165i | 0.895490 | + | 0.445083i | \(0.146826\pi\) | ||||
−0.895490 | + | 0.445083i | \(0.853174\pi\) | |||||||
\(884\) | −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 | ||||||||
\(889\) | 5.62684 | − | 50.5157i | 0.188718 | − | 1.69424i | ||||
\(890\) | −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 | \(-0.867196\pi\) | ||
0.914220 | − | 0.405218i | \(-0.132804\pi\) | |||||||
\(908\) | 13.9000 | + | 13.9000i | 0.461288 | + | 0.461288i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.0275 | + | 3.61680i | 0.962252 | + | 0.119896i | ||||
\(911\) | 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 | ||||
\(917\) | −2.87931 | + | 25.8494i | −0.0950830 | + | 0.853621i | ||||
\(918\) | 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 | \(-0.667093\pi\) |
0.865355 | + | 0.501159i | \(0.167093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.9730 | + | 20.2033i | −1.04787 | + | 0.662137i | ||||
\(932\) | 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 | \(-0.180775\pi\) | |||||||
\(938\) | 1.64082 | − | 14.7307i | 0.0535748 | − | 0.480975i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 6.13287i | − | 0.200032i | ||||||
\(941\) | 16.5400 | − | 16.5400i | 0.539189 | − | 0.539189i | −0.384102 | − | 0.923291i | \(-0.625489\pi\) |
0.923291 | + | 0.384102i | \(0.125489\pi\) | |||||||
\(942\) | 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 | −0.834783 | − | 0.550579i | \(-0.814407\pi\) |
0.550579 | + | 0.834783i | \(0.314407\pi\) | |||||||
\(948\) | 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 | \(-0.926569\pi\) | ||
0.973509 | − | 0.228648i | \(-0.0734306\pi\) | |||||||
\(954\) | 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 | 0.360208 | − | 0.932872i | \(-0.382706\pi\) |
−0.932872 | + | 0.360208i | \(0.882706\pi\) | |||||||
\(968\) | −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 | ||||||||
\(973\) | −0.974400 | + | 8.74781i | −0.0312378 | + | 0.280442i | ||||
\(974\) | − | 18.0512i | − | 0.578398i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.41208i | 0.205246i | ||||||||
\(977\) | −19.6568 | − | 19.6568i | −0.628877 | − | 0.628877i | 0.318908 | − | 0.947786i | \(-0.396684\pi\) |
−0.947786 | + | 0.318908i | \(0.896684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14545 | 0.0366086 | ||||||||
\(980\) | 11.4662 | + | 18.1459i | 0.366274 | + | 0.579651i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.9212 | + | 30.9212i | −0.986735 | + | 0.986735i | ||||
\(983\) | 17.7065 | + | 17.7065i | 0.564749 | + | 0.564749i | 0.930653 | − | 0.365904i | \(-0.119240\pi\) |
−0.365904 | + | 0.930653i | \(0.619240\pi\) | |||||||
\(984\) | 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 | ||||||||
\(994\) | 3.36411 | − | 30.2018i | 0.106703 | − | 0.957943i | ||||
\(995\) | 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.c.307.4 | 8 | ||
3.2 | odd | 2 | 546.2.o.b.307.1 | yes | 8 | ||
7.6 | odd | 2 | 1638.2.x.a.307.3 | 8 | |||
13.5 | odd | 4 | 1638.2.x.a.811.3 | 8 | |||
21.20 | even | 2 | 546.2.o.c.307.2 | yes | 8 | ||
39.5 | even | 4 | 546.2.o.c.265.2 | yes | 8 | ||
91.83 | even | 4 | inner | 1638.2.x.c.811.4 | 8 | ||
273.83 | odd | 4 | 546.2.o.b.265.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.1 | ✓ | 8 | 273.83 | odd | 4 | ||
546.2.o.b.307.1 | yes | 8 | 3.2 | odd | 2 | ||
546.2.o.c.265.2 | yes | 8 | 39.5 | even | 4 | ||
546.2.o.c.307.2 | yes | 8 | 21.20 | even | 2 | ||
1638.2.x.a.307.3 | 8 | 7.6 | odd | 2 | |||
1638.2.x.a.811.3 | 8 | 13.5 | odd | 4 | |||
1638.2.x.c.307.4 | 8 | 1.1 | even | 1 | trivial | ||
1638.2.x.c.811.4 | 8 | 91.83 | even | 4 | inner |