Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22545.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.27060\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15561 | 1.52425 | 0.762124 | − | 0.647431i | \(-0.224157\pi\) | ||||
0.762124 | + | 0.647431i | \(0.224157\pi\) | |||||||
\(3\) | 2.62393 | 1.51493 | 0.757464 | − | 0.652877i | \(-0.226438\pi\) | ||||
0.757464 | + | 0.652877i | \(0.226438\pi\) | |||||||
\(4\) | 2.64667 | 1.32333 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.65618 | 2.30913 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.39396 | 0.492840 | ||||||||
\(9\) | 3.88502 | 1.29501 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15561 | 0.951453 | 0.475727 | − | 0.879593i | \(-0.342185\pi\) | ||||
0.475727 | + | 0.879593i | \(0.342185\pi\) | |||||||
\(12\) | 6.94467 | 2.00475 | ||||||||
\(13\) | 1.72940 | 0.479650 | 0.239825 | − | 0.970816i | \(-0.422910\pi\) | ||||
0.239825 | + | 0.970816i | \(0.422910\pi\) | |||||||
\(14\) | 2.15561 | 0.576112 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.28849 | −0.572123 | ||||||||
\(17\) | 5.38558 | 1.30620 | 0.653098 | − | 0.757274i | \(-0.273469\pi\) | ||||
0.653098 | + | 0.757274i | \(0.273469\pi\) | |||||||
\(18\) | 8.37459 | 1.97391 | ||||||||
\(19\) | −3.42621 | −0.786027 | −0.393013 | − | 0.919533i | \(-0.628567\pi\) | ||||
−0.393013 | + | 0.919533i | \(0.628567\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.62393 | 0.572589 | ||||||||
\(22\) | 6.80228 | 1.45025 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 3.65766 | 0.746617 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.72792 | 0.731106 | ||||||||
\(27\) | 2.32222 | 0.446911 | ||||||||
\(28\) | 2.64667 | 0.500173 | ||||||||
\(29\) | −2.54119 | −0.471888 | −0.235944 | − | 0.971767i | \(-0.575818\pi\) | ||||
−0.235944 | + | 0.971767i | \(0.575818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.96741 | −1.79020 | −0.895099 | − | 0.445867i | \(-0.852896\pi\) | ||||
−0.895099 | + | 0.445867i | \(0.852896\pi\) | |||||||
\(32\) | −7.72102 | −1.36490 | ||||||||
\(33\) | 8.28011 | 1.44138 | ||||||||
\(34\) | 11.6092 | 1.99097 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.2823 | 1.71372 | ||||||||
\(37\) | 5.69681 | 0.936549 | 0.468275 | − | 0.883583i | \(-0.344876\pi\) | ||||
0.468275 | + | 0.883583i | \(0.344876\pi\) | |||||||
\(38\) | −7.38558 | −1.19810 | ||||||||
\(39\) | 4.53783 | 0.726635 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.30285 | 1.14051 | 0.570256 | − | 0.821467i | \(-0.306844\pi\) | ||||
0.570256 | + | 0.821467i | \(0.306844\pi\) | |||||||
\(42\) | 5.65618 | 0.872767 | ||||||||
\(43\) | −4.93516 | −0.752604 | −0.376302 | − | 0.926497i | \(-0.622805\pi\) | ||||
−0.376302 | + | 0.926497i | \(0.622805\pi\) | |||||||
\(44\) | 8.35185 | 1.25909 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.15561 | −0.317828 | ||||||||
\(47\) | 7.42621 | 1.08322 | 0.541612 | − | 0.840629i | \(-0.317814\pi\) | ||||
0.541612 | + | 0.840629i | \(0.317814\pi\) | |||||||
\(48\) | −6.00484 | −0.866724 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.1314 | 1.97879 | ||||||||
\(52\) | 4.57715 | 0.634737 | ||||||||
\(53\) | 3.20575 | 0.440344 | 0.220172 | − | 0.975461i | \(-0.429338\pi\) | ||||
0.220172 | + | 0.975461i | \(0.429338\pi\) | |||||||
\(54\) | 5.00581 | 0.681204 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.39396 | 0.186276 | ||||||||
\(57\) | −8.99014 | −1.19077 | ||||||||
\(58\) | −5.47783 | −0.719275 | ||||||||
\(59\) | 8.27060 | 1.07674 | 0.538370 | − | 0.842709i | \(-0.319040\pi\) | ||||
0.538370 | + | 0.842709i | \(0.319040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.95789 | −1.01890 | −0.509452 | − | 0.860499i | \(-0.670152\pi\) | ||||
−0.509452 | + | 0.860499i | \(0.670152\pi\) | |||||||
\(62\) | −21.4859 | −2.72871 | ||||||||
\(63\) | 3.88502 | 0.489466 | ||||||||
\(64\) | −12.0666 | −1.50832 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.8487 | 2.19702 | ||||||||
\(67\) | −5.20723 | −0.636165 | −0.318082 | − | 0.948063i | \(-0.603039\pi\) | ||||
−0.318082 | + | 0.948063i | \(0.603039\pi\) | |||||||
\(68\) | 14.2538 | 1.72853 | ||||||||
\(69\) | −2.62393 | −0.315884 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.0308 | 1.54647 | 0.773234 | − | 0.634121i | \(-0.218638\pi\) | ||||
0.773234 | + | 0.634121i | \(0.218638\pi\) | |||||||
\(72\) | 5.41556 | 0.638230 | ||||||||
\(73\) | −8.81031 | −1.03117 | −0.515585 | − | 0.856839i | \(-0.672425\pi\) | ||||
−0.515585 | + | 0.856839i | \(0.672425\pi\) | |||||||
\(74\) | 12.2801 | 1.42753 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.06803 | −1.04017 | ||||||||
\(77\) | 3.15561 | 0.359615 | ||||||||
\(78\) | 9.78181 | 1.10757 | ||||||||
\(79\) | −4.05014 | −0.455677 | −0.227838 | − | 0.973699i | \(-0.573166\pi\) | ||||
−0.227838 | + | 0.973699i | \(0.573166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.56170 | −0.617967 | ||||||||
\(82\) | 15.7421 | 1.73842 | ||||||||
\(83\) | −12.0597 | −1.32372 | −0.661860 | − | 0.749628i | \(-0.730232\pi\) | ||||
−0.661860 | + | 0.749628i | \(0.730232\pi\) | |||||||
\(84\) | 6.94467 | 0.757726 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.6383 | −1.14716 | ||||||||
\(87\) | −6.66792 | −0.714876 | ||||||||
\(88\) | 4.39880 | 0.468914 | ||||||||
\(89\) | 5.22011 | 0.553330 | 0.276665 | − | 0.960966i | \(-0.410771\pi\) | ||||
0.276665 | + | 0.960966i | \(0.410771\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72940 | 0.181291 | ||||||||
\(92\) | −2.64667 | −0.275934 | ||||||||
\(93\) | −26.1538 | −2.71202 | ||||||||
\(94\) | 16.0080 | 1.65110 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20.2594 | −2.06772 | ||||||||
\(97\) | −4.36621 | −0.443321 | −0.221661 | − | 0.975124i | \(-0.571148\pi\) | ||||
−0.221661 | + | 0.975124i | \(0.571148\pi\) | |||||||
\(98\) | 2.15561 | 0.217750 | ||||||||
\(99\) | 12.2596 | 1.23214 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.60958 | 0.458670 | 0.229335 | − | 0.973348i | \(-0.426345\pi\) | ||||
0.229335 | + | 0.973348i | \(0.426345\pi\) | |||||||
\(102\) | 30.4618 | 3.01617 | ||||||||
\(103\) | −5.73407 | −0.564995 | −0.282498 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282498 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(104\) | 2.41072 | 0.236391 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.91036 | 0.671194 | ||||||||
\(107\) | −18.6320 | −1.80122 | −0.900610 | − | 0.434628i | \(-0.856880\pi\) | ||||
−0.900610 | + | 0.434628i | \(0.856880\pi\) | |||||||
\(108\) | 6.14614 | 0.591413 | ||||||||
\(109\) | −6.26912 | −0.600473 | −0.300236 | − | 0.953865i | \(-0.597066\pi\) | ||||
−0.300236 | + | 0.953865i | \(0.597066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.9480 | 1.41880 | ||||||||
\(112\) | −2.28849 | −0.216242 | ||||||||
\(113\) | −6.58330 | −0.619305 | −0.309653 | − | 0.950850i | \(-0.600213\pi\) | ||||
−0.309653 | + | 0.950850i | \(0.600213\pi\) | |||||||
\(114\) | −19.3793 | −1.81503 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.72569 | −0.624465 | ||||||||
\(117\) | 6.71876 | 0.621149 | ||||||||
\(118\) | 17.8282 | 1.64122 | ||||||||
\(119\) | 5.38558 | 0.493696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.04211 | −0.0947371 | ||||||||
\(122\) | −17.1541 | −1.55306 | ||||||||
\(123\) | 19.1622 | 1.72779 | ||||||||
\(124\) | −26.3804 | −2.36903 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.37459 | 0.746068 | ||||||||
\(127\) | 17.4907 | 1.55205 | 0.776025 | − | 0.630703i | \(-0.217233\pi\) | ||||
0.776025 | + | 0.630703i | \(0.217233\pi\) | |||||||
\(128\) | −10.5688 | −0.934156 | ||||||||
\(129\) | −12.9495 | −1.14014 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.83453 | −0.160283 | −0.0801417 | − | 0.996783i | \(-0.525537\pi\) | ||||
−0.0801417 | + | 0.996783i | \(0.525537\pi\) | |||||||
\(132\) | 21.9147 | 1.90743 | ||||||||
\(133\) | −3.42621 | −0.297090 | ||||||||
\(134\) | −11.2248 | −0.969673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.50730 | 0.643745 | ||||||||
\(137\) | 16.5865 | 1.41708 | 0.708540 | − | 0.705671i | \(-0.249354\pi\) | ||||
0.708540 | + | 0.705671i | \(0.249354\pi\) | |||||||
\(138\) | −5.65618 | −0.481486 | ||||||||
\(139\) | 2.79425 | 0.237005 | 0.118502 | − | 0.992954i | \(-0.462191\pi\) | ||||
0.118502 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.4859 | 1.64101 | ||||||||
\(142\) | 28.0893 | 2.35720 | ||||||||
\(143\) | 5.45732 | 0.456364 | ||||||||
\(144\) | −8.89082 | −0.740902 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.9916 | −1.57176 | ||||||||
\(147\) | 2.62393 | 0.216418 | ||||||||
\(148\) | 15.0775 | 1.23937 | ||||||||
\(149\) | −21.7613 | −1.78276 | −0.891378 | − | 0.453261i | \(-0.850260\pi\) | ||||
−0.891378 | + | 0.453261i | \(0.850260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7598 | 1.77079 | 0.885395 | − | 0.464840i | \(-0.153888\pi\) | ||||
0.885395 | + | 0.464840i | \(0.153888\pi\) | |||||||
\(152\) | −4.77601 | −0.387385 | ||||||||
\(153\) | 20.9231 | 1.69153 | ||||||||
\(154\) | 6.80228 | 0.548143 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.0101 | 0.961580 | ||||||||
\(157\) | −9.73892 | −0.777250 | −0.388625 | − | 0.921396i | \(-0.627050\pi\) | ||||
−0.388625 | + | 0.921396i | \(0.627050\pi\) | |||||||
\(158\) | −8.73054 | −0.694564 | ||||||||
\(159\) | 8.41168 | 0.667089 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −11.9889 | −0.941935 | ||||||||
\(163\) | −10.7712 | −0.843663 | −0.421831 | − | 0.906674i | \(-0.638613\pi\) | ||||
−0.421831 | + | 0.906674i | \(0.638613\pi\) | |||||||
\(164\) | 19.3282 | 1.50928 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.9959 | −2.01768 | ||||||||
\(167\) | 18.0066 | 1.39339 | 0.696694 | − | 0.717368i | \(-0.254653\pi\) | ||||
0.696694 | + | 0.717368i | \(0.254653\pi\) | |||||||
\(168\) | 3.65766 | 0.282195 | ||||||||
\(169\) | −10.0092 | −0.769936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.3109 | −1.01791 | ||||||||
\(172\) | −13.0617 | −0.995946 | ||||||||
\(173\) | −14.2380 | −1.08250 | −0.541248 | − | 0.840863i | \(-0.682048\pi\) | ||||
−0.541248 | + | 0.840863i | \(0.682048\pi\) | |||||||
\(174\) | −14.3735 | −1.08965 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.22159 | −0.544348 | ||||||||
\(177\) | 21.7015 | 1.63118 | ||||||||
\(178\) | 11.2525 | 0.843413 | ||||||||
\(179\) | 9.07436 | 0.678249 | 0.339125 | − | 0.940741i | \(-0.389869\pi\) | ||||
0.339125 | + | 0.940741i | \(0.389869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.15413 | 0.0857860 | 0.0428930 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428930 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(182\) | 3.72792 | 0.276332 | ||||||||
\(183\) | −20.8810 | −1.54357 | ||||||||
\(184\) | −1.39396 | −0.102764 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −56.3774 | −4.13379 | ||||||||
\(187\) | 16.9948 | 1.24278 | ||||||||
\(188\) | 19.6547 | 1.43347 | ||||||||
\(189\) | 2.32222 | 0.168917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.0321 | 1.66654 | 0.833271 | − | 0.552864i | \(-0.186465\pi\) | ||||
0.833271 | + | 0.552864i | \(0.186465\pi\) | |||||||
\(192\) | −31.6618 | −2.28499 | ||||||||
\(193\) | −4.27060 | −0.307404 | −0.153702 | − | 0.988117i | \(-0.549120\pi\) | ||||
−0.153702 | + | 0.988117i | \(0.549120\pi\) | |||||||
\(194\) | −9.41185 | −0.675732 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.64667 | 0.189048 | ||||||||
\(197\) | −0.444103 | −0.0316410 | −0.0158205 | − | 0.999875i | \(-0.505036\pi\) | ||||
−0.0158205 | + | 0.999875i | \(0.505036\pi\) | |||||||
\(198\) | 26.4270 | 1.87808 | ||||||||
\(199\) | −2.18171 | −0.154657 | −0.0773286 | − | 0.997006i | \(-0.524639\pi\) | ||||
−0.0773286 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.6634 | −0.963744 | ||||||||
\(202\) | 9.93646 | 0.699127 | ||||||||
\(203\) | −2.54119 | −0.178357 | ||||||||
\(204\) | 37.4011 | 2.61860 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.3604 | −0.861193 | ||||||||
\(207\) | −3.88502 | −0.270027 | ||||||||
\(208\) | −3.95772 | −0.274419 | ||||||||
\(209\) | −10.8118 | −0.747867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7018 | 0.736744 | 0.368372 | − | 0.929678i | \(-0.379915\pi\) | ||||
0.368372 | + | 0.929678i | \(0.379915\pi\) | |||||||
\(212\) | 8.48456 | 0.582722 | ||||||||
\(213\) | 34.1918 | 2.34279 | ||||||||
\(214\) | −40.1633 | −2.74551 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.23708 | 0.220256 | ||||||||
\(217\) | −9.96741 | −0.676632 | ||||||||
\(218\) | −13.5138 | −0.915269 | ||||||||
\(219\) | −23.1177 | −1.56215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.31384 | 0.626517 | ||||||||
\(222\) | 32.2222 | 2.16261 | ||||||||
\(223\) | −20.9249 | −1.40124 | −0.700619 | − | 0.713535i | \(-0.747093\pi\) | ||||
−0.700619 | + | 0.713535i | \(0.747093\pi\) | |||||||
\(224\) | −7.72102 | −0.515883 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.1911 | −0.943975 | ||||||||
\(227\) | −16.4346 | −1.09080 | −0.545401 | − | 0.838175i | \(-0.683623\pi\) | ||||
−0.545401 | + | 0.838175i | \(0.683623\pi\) | |||||||
\(228\) | −23.7939 | −1.57579 | ||||||||
\(229\) | 5.76855 | 0.381197 | 0.190598 | − | 0.981668i | \(-0.438957\pi\) | ||||
0.190598 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.28011 | 0.544791 | ||||||||
\(232\) | −3.54233 | −0.232565 | ||||||||
\(233\) | −24.0692 | −1.57682 | −0.788412 | − | 0.615148i | \(-0.789096\pi\) | ||||
−0.788412 | + | 0.615148i | \(0.789096\pi\) | |||||||
\(234\) | 14.4830 | 0.946786 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.8895 | 1.42489 | ||||||||
\(237\) | −10.6273 | −0.690317 | ||||||||
\(238\) | 11.6092 | 0.752515 | ||||||||
\(239\) | 14.8308 | 0.959326 | 0.479663 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479663 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8088 | −1.08275 | −0.541376 | − | 0.840781i | \(-0.682096\pi\) | ||||
−0.541376 | + | 0.840781i | \(0.682096\pi\) | |||||||
\(242\) | −2.24638 | −0.144403 | ||||||||
\(243\) | −21.5602 | −1.38309 | ||||||||
\(244\) | −21.0619 | −1.34835 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 41.3062 | 2.63359 | ||||||||
\(247\) | −5.92530 | −0.377018 | ||||||||
\(248\) | −13.8942 | −0.882281 | ||||||||
\(249\) | −31.6437 | −2.00534 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3401 | 0.842020 | 0.421010 | − | 0.907056i | \(-0.361676\pi\) | ||||
0.421010 | + | 0.907056i | \(0.361676\pi\) | |||||||
\(252\) | 10.2823 | 0.647726 | ||||||||
\(253\) | −3.15561 | −0.198392 | ||||||||
\(254\) | 37.7032 | 2.36571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.35093 | 0.0844331 | ||||||||
\(257\) | 29.0985 | 1.81511 | 0.907556 | − | 0.419931i | \(-0.137946\pi\) | ||||
0.907556 | + | 0.419931i | \(0.137946\pi\) | |||||||
\(258\) | −27.9141 | −1.73786 | ||||||||
\(259\) | 5.69681 | 0.353982 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.87258 | −0.611097 | ||||||||
\(262\) | −3.95453 | −0.244312 | ||||||||
\(263\) | 8.98547 | 0.554068 | 0.277034 | − | 0.960860i | \(-0.410649\pi\) | ||||
0.277034 | + | 0.960860i | \(0.410649\pi\) | |||||||
\(264\) | 11.5422 | 0.710371 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.38558 | −0.452839 | ||||||||
\(267\) | 13.6972 | 0.838256 | ||||||||
\(268\) | −13.7818 | −0.841858 | ||||||||
\(269\) | 12.3996 | 0.756016 | 0.378008 | − | 0.925802i | \(-0.376609\pi\) | ||||
0.378008 | + | 0.925802i | \(0.376609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65055 | 0.100264 | 0.0501319 | − | 0.998743i | \(-0.484036\pi\) | ||||
0.0501319 | + | 0.998743i | \(0.484036\pi\) | |||||||
\(272\) | −12.3249 | −0.747304 | ||||||||
\(273\) | 4.53783 | 0.274642 | ||||||||
\(274\) | 35.7541 | 2.15998 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.94467 | −0.418020 | ||||||||
\(277\) | 8.00951 | 0.481245 | 0.240623 | − | 0.970619i | \(-0.422648\pi\) | ||||
0.240623 | + | 0.970619i | \(0.422648\pi\) | |||||||
\(278\) | 6.02331 | 0.361254 | ||||||||
\(279\) | −38.7235 | −2.31832 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.90256 | −0.411772 | −0.205886 | − | 0.978576i | \(-0.566008\pi\) | ||||
−0.205886 | + | 0.978576i | \(0.566008\pi\) | |||||||
\(282\) | 42.0040 | 2.50130 | ||||||||
\(283\) | 2.96627 | 0.176327 | 0.0881633 | − | 0.996106i | \(-0.471900\pi\) | ||||
0.0881633 | + | 0.996106i | \(0.471900\pi\) | |||||||
\(284\) | 34.4881 | 2.04649 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7639 | 0.695613 | ||||||||
\(287\) | 7.30285 | 0.431073 | ||||||||
\(288\) | −29.9963 | −1.76755 | ||||||||
\(289\) | 12.0045 | 0.706147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4566 | −0.671600 | ||||||||
\(292\) | −23.3180 | −1.36458 | ||||||||
\(293\) | 6.83151 | 0.399101 | 0.199551 | − | 0.979888i | \(-0.436052\pi\) | ||||
0.199551 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(294\) | 5.65618 | 0.329875 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.94113 | 0.461569 | ||||||||
\(297\) | 7.32802 | 0.425215 | ||||||||
\(298\) | −46.9089 | −2.71736 | ||||||||
\(299\) | −1.72940 | −0.100014 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.93516 | −0.284458 | ||||||||
\(302\) | 46.9058 | 2.69912 | ||||||||
\(303\) | 12.0952 | 0.694852 | ||||||||
\(304\) | 7.84085 | 0.449704 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 45.1020 | 2.57831 | ||||||||
\(307\) | −23.0999 | −1.31838 | −0.659191 | − | 0.751975i | \(-0.729101\pi\) | ||||
−0.659191 | + | 0.751975i | \(0.729101\pi\) | |||||||
\(308\) | 8.35185 | 0.475891 | ||||||||
\(309\) | −15.0458 | −0.855927 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.21208 | 0.0687305 | 0.0343653 | − | 0.999409i | \(-0.489059\pi\) | ||||
0.0343653 | + | 0.999409i | \(0.489059\pi\) | |||||||
\(312\) | 6.32557 | 0.358115 | ||||||||
\(313\) | −24.2346 | −1.36982 | −0.684911 | − | 0.728626i | \(-0.740159\pi\) | ||||
−0.684911 | + | 0.728626i | \(0.740159\pi\) | |||||||
\(314\) | −20.9933 | −1.18472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7194 | −0.603012 | ||||||||
\(317\) | −17.5337 | −0.984793 | −0.492396 | − | 0.870371i | \(-0.663879\pi\) | ||||
−0.492396 | + | 0.870371i | \(0.663879\pi\) | |||||||
\(318\) | 18.1323 | 1.01681 | ||||||||
\(319\) | −8.01903 | −0.448979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −48.8890 | −2.72872 | ||||||||
\(322\) | −2.15561 | −0.120128 | ||||||||
\(323\) | −18.4521 | −1.02670 | ||||||||
\(324\) | −14.7200 | −0.817776 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.2185 | −1.28595 | ||||||||
\(327\) | −16.4497 | −0.909672 | ||||||||
\(328\) | 10.1799 | 0.562090 | ||||||||
\(329\) | 7.42621 | 0.409420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2555 | 0.893486 | 0.446743 | − | 0.894662i | \(-0.352584\pi\) | ||||
0.446743 | + | 0.894662i | \(0.352584\pi\) | |||||||
\(332\) | −31.9179 | −1.75172 | ||||||||
\(333\) | 22.1322 | 1.21284 | ||||||||
\(334\) | 38.8152 | 2.12387 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00484 | −0.327591 | ||||||||
\(337\) | 11.1765 | 0.608824 | 0.304412 | − | 0.952540i | \(-0.401540\pi\) | ||||
0.304412 | + | 0.952540i | \(0.401540\pi\) | |||||||
\(338\) | −21.5759 | −1.17357 | ||||||||
\(339\) | −17.2741 | −0.938202 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.4533 | −1.70329 | ||||||||
\(342\) | −28.6931 | −1.55155 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.87942 | −0.370913 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.6916 | −1.64999 | ||||||||
\(347\) | −11.4812 | −0.616343 | −0.308171 | − | 0.951331i | \(-0.599717\pi\) | ||||
−0.308171 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(348\) | −17.6478 | −0.946019 | ||||||||
\(349\) | 16.6091 | 0.889062 | 0.444531 | − | 0.895763i | \(-0.353370\pi\) | ||||
0.444531 | + | 0.895763i | \(0.353370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.01605 | 0.214361 | ||||||||
\(352\) | −24.3646 | −1.29864 | ||||||||
\(353\) | 14.1601 | 0.753666 | 0.376833 | − | 0.926281i | \(-0.377013\pi\) | ||||
0.376833 | + | 0.926281i | \(0.377013\pi\) | |||||||
\(354\) | 46.7800 | 2.48633 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.8159 | 0.732241 | ||||||||
\(357\) | 14.1314 | 0.747913 | ||||||||
\(358\) | 19.5608 | 1.03382 | ||||||||
\(359\) | −11.2009 | −0.591162 | −0.295581 | − | 0.955318i | \(-0.595513\pi\) | ||||
−0.295581 | + | 0.955318i | \(0.595513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.26108 | −0.382162 | ||||||||
\(362\) | 2.48786 | 0.130759 | ||||||||
\(363\) | −2.73442 | −0.143520 | ||||||||
\(364\) | 4.57715 | 0.239908 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −45.0113 | −2.35278 | ||||||||
\(367\) | 23.2104 | 1.21157 | 0.605787 | − | 0.795627i | \(-0.292858\pi\) | ||||
0.605787 | + | 0.795627i | \(0.292858\pi\) | |||||||
\(368\) | 2.28849 | 0.119296 | ||||||||
\(369\) | 28.3717 | 1.47697 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.20575 | 0.166434 | ||||||||
\(372\) | −69.2203 | −3.58891 | ||||||||
\(373\) | −4.68843 | −0.242758 | −0.121379 | − | 0.992606i | \(-0.538732\pi\) | ||||
−0.121379 | + | 0.992606i | \(0.538732\pi\) | |||||||
\(374\) | 36.6342 | 1.89431 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3519 | 0.533856 | ||||||||
\(377\) | −4.39475 | −0.226341 | ||||||||
\(378\) | 5.00581 | 0.257471 | ||||||||
\(379\) | −11.4540 | −0.588351 | −0.294175 | − | 0.955751i | \(-0.595045\pi\) | ||||
−0.294175 | + | 0.955751i | \(0.595045\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45.8944 | 2.35124 | ||||||||
\(382\) | 49.6482 | 2.54022 | ||||||||
\(383\) | −27.2946 | −1.39469 | −0.697346 | − | 0.716735i | \(-0.745636\pi\) | ||||
−0.697346 | + | 0.716735i | \(0.745636\pi\) | |||||||
\(384\) | −27.7317 | −1.41518 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.20575 | −0.468561 | ||||||||
\(387\) | −19.1732 | −0.974626 | ||||||||
\(388\) | −11.5559 | −0.586662 | ||||||||
\(389\) | 28.2460 | 1.43213 | 0.716065 | − | 0.698033i | \(-0.245941\pi\) | ||||
0.716065 | + | 0.698033i | \(0.245941\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.38558 | −0.272361 | ||||||||
\(392\) | 1.39396 | 0.0704057 | ||||||||
\(393\) | −4.81367 | −0.242818 | ||||||||
\(394\) | −0.957315 | −0.0482288 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 32.4471 | 1.63053 | ||||||||
\(397\) | −30.9383 | −1.55275 | −0.776376 | − | 0.630271i | \(-0.782944\pi\) | ||||
−0.776376 | + | 0.630271i | \(0.782944\pi\) | |||||||
\(398\) | −4.70292 | −0.235736 | ||||||||
\(399\) | −8.99014 | −0.450070 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2509 | −1.11116 | −0.555578 | − | 0.831464i | \(-0.687503\pi\) | ||||
−0.555578 | + | 0.831464i | \(0.687503\pi\) | |||||||
\(402\) | −29.4531 | −1.46898 | ||||||||
\(403\) | −17.2377 | −0.858669 | ||||||||
\(404\) | 12.2000 | 0.606973 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.47783 | −0.271860 | ||||||||
\(407\) | 17.9769 | 0.891083 | ||||||||
\(408\) | 19.6986 | 0.975227 | ||||||||
\(409\) | 5.84941 | 0.289234 | 0.144617 | − | 0.989488i | \(-0.453805\pi\) | ||||
0.144617 | + | 0.989488i | \(0.453805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 43.5218 | 2.14677 | ||||||||
\(412\) | −15.1762 | −0.747677 | ||||||||
\(413\) | 8.27060 | 0.406969 | ||||||||
\(414\) | −8.37459 | −0.411589 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.3528 | −0.654673 | ||||||||
\(417\) | 7.33191 | 0.359045 | ||||||||
\(418\) | −23.3060 | −1.13994 | ||||||||
\(419\) | −25.7082 | −1.25593 | −0.627964 | − | 0.778242i | \(-0.716111\pi\) | ||||
−0.627964 | + | 0.778242i | \(0.716111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3849 | 0.944762 | 0.472381 | − | 0.881395i | \(-0.343395\pi\) | ||||
0.472381 | + | 0.881395i | \(0.343395\pi\) | |||||||
\(422\) | 23.0690 | 1.12298 | ||||||||
\(423\) | 28.8509 | 1.40278 | ||||||||
\(424\) | 4.46870 | 0.217019 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 73.7044 | 3.57099 | ||||||||
\(427\) | −7.95789 | −0.385109 | ||||||||
\(428\) | −49.3126 | −2.38361 | ||||||||
\(429\) | 14.3196 | 0.691359 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.90474 | −0.139916 | −0.0699581 | − | 0.997550i | \(-0.522287\pi\) | ||||
−0.0699581 | + | 0.997550i | \(0.522287\pi\) | |||||||
\(432\) | −5.31438 | −0.255688 | ||||||||
\(433\) | −24.8312 | −1.19331 | −0.596656 | − | 0.802497i | \(-0.703504\pi\) | ||||
−0.596656 | + | 0.802497i | \(0.703504\pi\) | |||||||
\(434\) | −21.4859 | −1.03135 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.5923 | −0.794625 | ||||||||
\(437\) | 3.42621 | 0.163898 | ||||||||
\(438\) | −49.8327 | −2.38110 | ||||||||
\(439\) | 18.6918 | 0.892110 | 0.446055 | − | 0.895005i | \(-0.352828\pi\) | ||||
0.446055 | + | 0.895005i | \(0.352828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.88502 | 0.185001 | ||||||||
\(442\) | 20.0770 | 0.954967 | ||||||||
\(443\) | 21.0951 | 1.00226 | 0.501129 | − | 0.865373i | \(-0.332918\pi\) | ||||
0.501129 | + | 0.865373i | \(0.332918\pi\) | |||||||
\(444\) | 39.5624 | 1.87755 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −45.1061 | −2.13584 | ||||||||
\(447\) | −57.1002 | −2.70075 | ||||||||
\(448\) | −12.0666 | −0.570091 | ||||||||
\(449\) | 3.43961 | 0.162325 | 0.0811626 | − | 0.996701i | \(-0.474137\pi\) | ||||
0.0811626 | + | 0.996701i | \(0.474137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.0450 | 1.08514 | ||||||||
\(452\) | −17.4238 | −0.819547 | ||||||||
\(453\) | 57.0963 | 2.68262 | ||||||||
\(454\) | −35.4266 | −1.66265 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.5319 | −0.586861 | ||||||||
\(457\) | 3.47356 | 0.162486 | 0.0812432 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812432 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(458\) | 12.4348 | 0.581038 | ||||||||
\(459\) | 12.5065 | 0.583754 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.4226 | −1.64979 | −0.824896 | − | 0.565284i | \(-0.808767\pi\) | ||||
−0.824896 | + | 0.565284i | \(0.808767\pi\) | |||||||
\(462\) | 17.8487 | 0.830397 | ||||||||
\(463\) | 41.0574 | 1.90810 | 0.954050 | − | 0.299647i | \(-0.0968688\pi\) | ||||
0.954050 | + | 0.299647i | \(0.0968688\pi\) | |||||||
\(464\) | 5.81550 | 0.269978 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −51.8838 | −2.40347 | ||||||||
\(467\) | −26.1893 | −1.21190 | −0.605949 | − | 0.795503i | \(-0.707206\pi\) | ||||
−0.605949 | + | 0.795503i | \(0.707206\pi\) | |||||||
\(468\) | 17.7823 | 0.821987 | ||||||||
\(469\) | −5.20723 | −0.240448 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.5542 | −1.17748 | ||||||||
\(472\) | 11.5289 | 0.530661 | ||||||||
\(473\) | −15.5734 | −0.716068 | ||||||||
\(474\) | −22.9083 | −1.05221 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.2538 | 0.653324 | ||||||||
\(477\) | 12.4544 | 0.570248 | ||||||||
\(478\) | 31.9695 | 1.46225 | ||||||||
\(479\) | −28.7194 | −1.31222 | −0.656111 | − | 0.754665i | \(-0.727800\pi\) | ||||
−0.656111 | + | 0.754665i | \(0.727800\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.85207 | 0.449216 | ||||||||
\(482\) | −36.2333 | −1.65038 | ||||||||
\(483\) | −2.62393 | −0.119393 | ||||||||
\(484\) | −2.75811 | −0.125369 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −46.4754 | −2.10817 | ||||||||
\(487\) | 10.1974 | 0.462087 | 0.231044 | − | 0.972943i | \(-0.425786\pi\) | ||||
0.231044 | + | 0.972943i | \(0.425786\pi\) | |||||||
\(488\) | −11.0930 | −0.502156 | ||||||||
\(489\) | −28.2628 | −1.27809 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4829 | −0.518216 | −0.259108 | − | 0.965848i | \(-0.583429\pi\) | ||||
−0.259108 | + | 0.965848i | \(0.583429\pi\) | |||||||
\(492\) | 50.7159 | 2.28645 | ||||||||
\(493\) | −13.6858 | −0.616378 | ||||||||
\(494\) | −12.7726 | −0.574668 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.8103 | 1.02421 | ||||||||
\(497\) | 13.0308 | 0.584510 | ||||||||
\(498\) | −68.2116 | −3.05663 | ||||||||
\(499\) | −3.89636 | −0.174425 | −0.0872124 | − | 0.996190i | \(-0.527796\pi\) | ||||
−0.0872124 | + | 0.996190i | \(0.527796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 47.2480 | 2.11088 | ||||||||
\(502\) | 28.7561 | 1.28345 | ||||||||
\(503\) | 39.2844 | 1.75161 | 0.875803 | − | 0.482668i | \(-0.160332\pi\) | ||||
0.875803 | + | 0.482668i | \(0.160332\pi\) | |||||||
\(504\) | 5.41556 | 0.241228 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.80228 | −0.302398 | ||||||||
\(507\) | −26.2634 | −1.16640 | ||||||||
\(508\) | 46.2921 | 2.05388 | ||||||||
\(509\) | −42.4548 | −1.88178 | −0.940888 | − | 0.338718i | \(-0.890007\pi\) | ||||
−0.940888 | + | 0.338718i | \(0.890007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.81031 | −0.389745 | ||||||||
\(512\) | 24.0496 | 1.06285 | ||||||||
\(513\) | −7.95641 | −0.351284 | ||||||||
\(514\) | 62.7250 | 2.76668 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −34.2730 | −1.50879 | ||||||||
\(517\) | 23.4342 | 1.03064 | ||||||||
\(518\) | 12.2801 | 0.539557 | ||||||||
\(519\) | −37.3595 | −1.63990 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.7986 | 1.65599 | 0.827993 | − | 0.560739i | \(-0.189483\pi\) | ||||
0.827993 | + | 0.560739i | \(0.189483\pi\) | |||||||
\(522\) | −21.2815 | −0.931464 | ||||||||
\(523\) | 10.8004 | 0.472268 | 0.236134 | − | 0.971720i | \(-0.424119\pi\) | ||||
0.236134 | + | 0.971720i | \(0.424119\pi\) | |||||||
\(524\) | −4.85538 | −0.212108 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.3692 | 0.844537 | ||||||||
\(527\) | −53.6803 | −2.33835 | ||||||||
\(528\) | −18.9490 | −0.824647 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.1314 | 1.39438 | ||||||||
\(532\) | −9.06803 | −0.393149 | ||||||||
\(533\) | 12.6296 | 0.547047 | ||||||||
\(534\) | 29.5259 | 1.27771 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.25869 | −0.313527 | ||||||||
\(537\) | 23.8105 | 1.02750 | ||||||||
\(538\) | 26.7287 | 1.15236 | ||||||||
\(539\) | 3.15561 | 0.135922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.8362 | 1.28276 | 0.641380 | − | 0.767223i | \(-0.278362\pi\) | ||||
0.641380 | + | 0.767223i | \(0.278362\pi\) | |||||||
\(542\) | 3.55795 | 0.152827 | ||||||||
\(543\) | 3.02836 | 0.129960 | ||||||||
\(544\) | −41.5822 | −1.78282 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.78181 | 0.418623 | ||||||||
\(547\) | 31.8433 | 1.36152 | 0.680762 | − | 0.732505i | \(-0.261649\pi\) | ||||
0.680762 | + | 0.732505i | \(0.261649\pi\) | |||||||
\(548\) | 43.8989 | 1.87527 | ||||||||
\(549\) | −30.9165 | −1.31949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.70667 | 0.370917 | ||||||||
\(552\) | −3.65766 | −0.155680 | ||||||||
\(553\) | −4.05014 | −0.172230 | ||||||||
\(554\) | 17.2654 | 0.733537 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.39544 | 0.313636 | ||||||||
\(557\) | −43.2395 | −1.83212 | −0.916059 | − | 0.401044i | \(-0.868648\pi\) | ||||
−0.916059 | + | 0.401044i | \(0.868648\pi\) | |||||||
\(558\) | −83.4729 | −3.53369 | ||||||||
\(559\) | −8.53487 | −0.360987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.5932 | 1.88273 | ||||||||
\(562\) | −14.8792 | −0.627643 | ||||||||
\(563\) | 6.58034 | 0.277328 | 0.138664 | − | 0.990339i | \(-0.455719\pi\) | ||||
0.138664 | + | 0.990339i | \(0.455719\pi\) | |||||||
\(564\) | 51.5726 | 2.17160 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.39413 | 0.268765 | ||||||||
\(567\) | −5.56170 | −0.233570 | ||||||||
\(568\) | 18.1644 | 0.762161 | ||||||||
\(569\) | 37.6191 | 1.57708 | 0.788538 | − | 0.614986i | \(-0.210838\pi\) | ||||
0.788538 | + | 0.614986i | \(0.210838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.913726 | 0.0382382 | 0.0191191 | − | 0.999817i | \(-0.493914\pi\) | ||||
0.0191191 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(572\) | 14.4437 | 0.603922 | ||||||||
\(573\) | 60.4346 | 2.52469 | ||||||||
\(574\) | 15.7421 | 0.657063 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −46.8787 | −1.95328 | ||||||||
\(577\) | −22.0692 | −0.918751 | −0.459376 | − | 0.888242i | \(-0.651927\pi\) | ||||
−0.459376 | + | 0.888242i | \(0.651927\pi\) | |||||||
\(578\) | 25.8770 | 1.07634 | ||||||||
\(579\) | −11.2058 | −0.465695 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0597 | −0.500319 | ||||||||
\(582\) | −24.6961 | −1.02368 | ||||||||
\(583\) | 10.1161 | 0.418967 | ||||||||
\(584\) | −12.2812 | −0.508201 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7261 | 0.608329 | ||||||||
\(587\) | −42.9058 | −1.77091 | −0.885455 | − | 0.464725i | \(-0.846153\pi\) | ||||
−0.885455 | + | 0.464725i | \(0.846153\pi\) | |||||||
\(588\) | 6.94467 | 0.286393 | ||||||||
\(589\) | 34.1504 | 1.40714 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.16530 | −0.0479339 | ||||||||
\(592\) | −13.0371 | −0.535821 | ||||||||
\(593\) | 29.4911 | 1.21105 | 0.605527 | − | 0.795825i | \(-0.292962\pi\) | ||||
0.605527 | + | 0.795825i | \(0.292962\pi\) | |||||||
\(594\) | 15.7964 | 0.648133 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −57.5949 | −2.35918 | ||||||||
\(597\) | −5.72465 | −0.234295 | ||||||||
\(598\) | −3.72792 | −0.152446 | ||||||||
\(599\) | 5.76536 | 0.235566 | 0.117783 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117783 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5587 | −0.512282 | −0.256141 | − | 0.966639i | \(-0.582451\pi\) | ||||
−0.256141 | + | 0.966639i | \(0.582451\pi\) | |||||||
\(602\) | −10.6383 | −0.433584 | ||||||||
\(603\) | −20.2302 | −0.823837 | ||||||||
\(604\) | 57.5910 | 2.34334 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 26.0726 | 1.05913 | ||||||||
\(607\) | −4.76165 | −0.193269 | −0.0966347 | − | 0.995320i | \(-0.530808\pi\) | ||||
−0.0966347 | + | 0.995320i | \(0.530808\pi\) | |||||||
\(608\) | 26.4538 | 1.07285 | ||||||||
\(609\) | −6.66792 | −0.270198 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.8429 | 0.519568 | ||||||||
\(612\) | 55.3764 | 2.23846 | ||||||||
\(613\) | −11.1622 | −0.450836 | −0.225418 | − | 0.974262i | \(-0.572375\pi\) | ||||
−0.225418 | + | 0.974262i | \(0.572375\pi\) | |||||||
\(614\) | −49.7945 | −2.00954 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.39880 | 0.177233 | ||||||||
\(617\) | −13.5572 | −0.545793 | −0.272896 | − | 0.962043i | \(-0.587982\pi\) | ||||
−0.272896 | + | 0.962043i | \(0.587982\pi\) | |||||||
\(618\) | −32.4330 | −1.30464 | ||||||||
\(619\) | −7.23539 | −0.290815 | −0.145407 | − | 0.989372i | \(-0.546449\pi\) | ||||
−0.145407 | + | 0.989372i | \(0.546449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32222 | −0.0931874 | ||||||||
\(622\) | 2.61277 | 0.104762 | ||||||||
\(623\) | 5.22011 | 0.209139 | ||||||||
\(624\) | −10.3848 | −0.415724 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −52.2405 | −2.08795 | ||||||||
\(627\) | −28.3694 | −1.13296 | ||||||||
\(628\) | −25.7757 | −1.02856 | ||||||||
\(629\) | 30.6806 | 1.22332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6513 | −0.543451 | −0.271726 | − | 0.962375i | \(-0.587594\pi\) | ||||
−0.271726 | + | 0.962375i | \(0.587594\pi\) | |||||||
\(632\) | −5.64574 | −0.224576 | ||||||||
\(633\) | 28.0809 | 1.11611 | ||||||||
\(634\) | −37.7960 | −1.50107 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 22.2629 | 0.882782 | ||||||||
\(637\) | 1.72940 | 0.0685214 | ||||||||
\(638\) | −17.2859 | −0.684356 | ||||||||
\(639\) | 50.6247 | 2.00268 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.9739 | −0.986410 | −0.493205 | − | 0.869913i | \(-0.664175\pi\) | ||||
−0.493205 | + | 0.869913i | \(0.664175\pi\) | |||||||
\(642\) | −105.386 | −4.15924 | ||||||||
\(643\) | 34.5414 | 1.36218 | 0.681090 | − | 0.732199i | \(-0.261506\pi\) | ||||
0.681090 | + | 0.732199i | \(0.261506\pi\) | |||||||
\(644\) | −2.64667 | −0.104293 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.7757 | −1.56495 | ||||||||
\(647\) | 40.9669 | 1.61057 | 0.805287 | − | 0.592885i | \(-0.202011\pi\) | ||||
0.805287 | + | 0.592885i | \(0.202011\pi\) | |||||||
\(648\) | −7.75280 | −0.304559 | ||||||||
\(649\) | 26.0988 | 1.02447 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.1538 | −1.02505 | ||||||||
\(652\) | −28.5077 | −1.11645 | ||||||||
\(653\) | 38.9770 | 1.52529 | 0.762643 | − | 0.646819i | \(-0.223901\pi\) | ||||
0.762643 | + | 0.646819i | \(0.223901\pi\) | |||||||
\(654\) | −35.4593 | −1.38657 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.7125 | −0.652513 | ||||||||
\(657\) | −34.2282 | −1.33537 | ||||||||
\(658\) | 16.0080 | 0.624058 | ||||||||
\(659\) | 36.2460 | 1.41195 | 0.705973 | − | 0.708239i | \(-0.250510\pi\) | ||||
0.705973 | + | 0.708239i | \(0.250510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.05310 | 0.157647 | 0.0788237 | − | 0.996889i | \(-0.474884\pi\) | ||||
0.0788237 | + | 0.996889i | \(0.474884\pi\) | |||||||
\(662\) | 35.0407 | 1.36189 | ||||||||
\(663\) | 24.4389 | 0.949127 | ||||||||
\(664\) | −16.8107 | −0.652382 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 47.7084 | 1.84866 | ||||||||
\(667\) | 2.54119 | 0.0983955 | ||||||||
\(668\) | 47.6573 | 1.84392 | ||||||||
\(669\) | −54.9056 | −2.12277 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.1120 | −0.969439 | ||||||||
\(672\) | −20.2594 | −0.781525 | ||||||||
\(673\) | 43.0790 | 1.66057 | 0.830287 | − | 0.557336i | \(-0.188176\pi\) | ||||
0.830287 | + | 0.557336i | \(0.188176\pi\) | |||||||
\(674\) | 24.0922 | 0.927999 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.4909 | −1.01888 | ||||||||
\(677\) | −38.0161 | −1.46108 | −0.730538 | − | 0.682872i | \(-0.760731\pi\) | ||||
−0.730538 | + | 0.682872i | \(0.760731\pi\) | |||||||
\(678\) | −37.2363 | −1.43005 | ||||||||
\(679\) | −4.36621 | −0.167560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −43.1232 | −1.65249 | ||||||||
\(682\) | −67.8011 | −2.59624 | ||||||||
\(683\) | −46.7213 | −1.78774 | −0.893870 | − | 0.448327i | \(-0.852020\pi\) | ||||
−0.893870 | + | 0.448327i | \(0.852020\pi\) | |||||||
\(684\) | −35.2295 | −1.34703 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.15561 | 0.0823017 | ||||||||
\(687\) | 15.1363 | 0.577485 | ||||||||
\(688\) | 11.2941 | 0.430582 | ||||||||
\(689\) | 5.54404 | 0.211211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9309 | −0.682125 | −0.341062 | − | 0.940041i | \(-0.610787\pi\) | ||||
−0.341062 | + | 0.940041i | \(0.610787\pi\) | |||||||
\(692\) | −37.6832 | −1.43250 | ||||||||
\(693\) | 12.2596 | 0.465704 | ||||||||
\(694\) | −24.7490 | −0.939459 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.29483 | −0.352320 | ||||||||
\(697\) | 39.3301 | 1.48973 | ||||||||
\(698\) | 35.8027 | 1.35515 | ||||||||
\(699\) | −63.1558 | −2.38877 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5215 | 0.472930 | 0.236465 | − | 0.971640i | \(-0.424011\pi\) | ||||
0.236465 | + | 0.971640i | \(0.424011\pi\) | |||||||
\(702\) | 8.65705 | 0.326739 | ||||||||
\(703\) | −19.5185 | −0.736153 | ||||||||
\(704\) | −38.0774 | −1.43509 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.5237 | 1.14877 | ||||||||
\(707\) | 4.60958 | 0.173361 | ||||||||
\(708\) | 57.4366 | 2.15860 | ||||||||
\(709\) | 19.5766 | 0.735216 | 0.367608 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367608 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.7349 | −0.590103 | ||||||||
\(712\) | 7.27663 | 0.272703 | ||||||||
\(713\) | 9.96741 | 0.373282 | ||||||||
\(714\) | 30.4618 | 1.14000 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0168 | 0.897550 | ||||||||
\(717\) | 38.9151 | 1.45331 | ||||||||
\(718\) | −24.1448 | −0.901077 | ||||||||
\(719\) | −1.11818 | −0.0417009 | −0.0208505 | − | 0.999783i | \(-0.506637\pi\) | ||||
−0.0208505 | + | 0.999783i | \(0.506637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.73407 | −0.213548 | ||||||||
\(722\) | −15.6521 | −0.582510 | ||||||||
\(723\) | −44.1052 | −1.64029 | ||||||||
\(724\) | 3.05460 | 0.113523 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.89435 | −0.218760 | ||||||||
\(727\) | −11.1732 | −0.414390 | −0.207195 | − | 0.978300i | \(-0.566433\pi\) | ||||
−0.207195 | + | 0.978300i | \(0.566433\pi\) | |||||||
\(728\) | 2.41072 | 0.0893473 | ||||||||
\(729\) | −39.8873 | −1.47731 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.5787 | −0.983048 | ||||||||
\(732\) | −55.2649 | −2.04265 | ||||||||
\(733\) | 16.9333 | 0.625445 | 0.312722 | − | 0.949845i | \(-0.398759\pi\) | ||||
0.312722 | + | 0.949845i | \(0.398759\pi\) | |||||||
\(734\) | 50.0327 | 1.84674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.72102 | 0.284601 | ||||||||
\(737\) | −16.4320 | −0.605281 | ||||||||
\(738\) | 61.1583 | 2.25127 | ||||||||
\(739\) | 18.4339 | 0.678102 | 0.339051 | − | 0.940768i | \(-0.389894\pi\) | ||||
0.339051 | + | 0.940768i | \(0.389894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.5476 | −0.571154 | ||||||||
\(742\) | 6.91036 | 0.253687 | ||||||||
\(743\) | −6.08445 | −0.223217 | −0.111608 | − | 0.993752i | \(-0.535600\pi\) | ||||
−0.111608 | + | 0.993752i | \(0.535600\pi\) | |||||||
\(744\) | −36.4574 | −1.33659 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.1064 | −0.370023 | ||||||||
\(747\) | −46.8519 | −1.71422 | ||||||||
\(748\) | 44.9796 | 1.64462 | ||||||||
\(749\) | −18.6320 | −0.680797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6886 | 0.499504 | 0.249752 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249752 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(752\) | −16.9948 | −0.619737 | ||||||||
\(753\) | 35.0035 | 1.27560 | ||||||||
\(754\) | −9.47338 | −0.345000 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.14614 | 0.223533 | ||||||||
\(757\) | 27.9301 | 1.01514 | 0.507569 | − | 0.861611i | \(-0.330544\pi\) | ||||
0.507569 | + | 0.861611i | \(0.330544\pi\) | |||||||
\(758\) | −24.6903 | −0.896792 | ||||||||
\(759\) | −8.28011 | −0.300549 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.7557 | −0.426143 | −0.213071 | − | 0.977037i | \(-0.568347\pi\) | ||||
−0.213071 | + | 0.977037i | \(0.568347\pi\) | |||||||
\(762\) | 98.9306 | 3.58388 | ||||||||
\(763\) | −6.26912 | −0.226957 | ||||||||
\(764\) | 60.9582 | 2.20539 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −58.8367 | −2.12586 | ||||||||
\(767\) | 14.3032 | 0.516458 | ||||||||
\(768\) | 3.54475 | 0.127910 | ||||||||
\(769\) | −36.1868 | −1.30493 | −0.652464 | − | 0.757820i | \(-0.726265\pi\) | ||||
−0.652464 | + | 0.757820i | \(0.726265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 76.3523 | 2.74976 | ||||||||
\(772\) | −11.3028 | −0.406798 | ||||||||
\(773\) | 29.4969 | 1.06093 | 0.530464 | − | 0.847707i | \(-0.322018\pi\) | ||||
0.530464 | + | 0.847707i | \(0.322018\pi\) | |||||||
\(774\) | −41.3299 | −1.48557 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.08633 | −0.218486 | ||||||||
\(777\) | 14.9480 | 0.536258 | ||||||||
\(778\) | 60.8875 | 2.18292 | ||||||||
\(779\) | −25.0211 | −0.896473 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.1201 | 1.47139 | ||||||||
\(782\) | −11.6092 | −0.415145 | ||||||||
\(783\) | −5.90121 | −0.210892 | ||||||||
\(784\) | −2.28849 | −0.0817318 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.3764 | −0.370114 | ||||||||
\(787\) | 26.9176 | 0.959509 | 0.479755 | − | 0.877403i | \(-0.340726\pi\) | ||||
0.479755 | + | 0.877403i | \(0.340726\pi\) | |||||||
\(788\) | −1.17539 | −0.0418716 | ||||||||
\(789\) | 23.5773 | 0.839372 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.58330 | −0.234075 | ||||||||
\(792\) | 17.0894 | 0.607246 | ||||||||
\(793\) | −13.7624 | −0.488717 | ||||||||
\(794\) | −66.6911 | −2.36678 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.77426 | −0.204663 | ||||||||
\(797\) | 39.8228 | 1.41060 | 0.705299 | − | 0.708910i | \(-0.250813\pi\) | ||||
0.705299 | + | 0.708910i | \(0.250813\pi\) | |||||||
\(798\) | −19.3793 | −0.686018 | ||||||||
\(799\) | 39.9945 | 1.41490 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.2802 | 0.716566 | ||||||||
\(802\) | −47.9643 | −1.69368 | ||||||||
\(803\) | −27.8019 | −0.981109 | ||||||||
\(804\) | −36.1625 | −1.27535 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37.1577 | −1.30882 | ||||||||
\(807\) | 32.5357 | 1.14531 | ||||||||
\(808\) | 6.42557 | 0.226051 | ||||||||
\(809\) | −14.2056 | −0.499442 | −0.249721 | − | 0.968318i | \(-0.580339\pi\) | ||||
−0.249721 | + | 0.968318i | \(0.580339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.06992 | 0.318488 | 0.159244 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159244 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(812\) | −6.72569 | −0.236026 | ||||||||
\(813\) | 4.33093 | 0.151892 | ||||||||
\(814\) | 38.7513 | 1.35823 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −32.3396 | −1.13211 | ||||||||
\(817\) | 16.9089 | 0.591567 | ||||||||
\(818\) | 12.6091 | 0.440865 | ||||||||
\(819\) | 6.71876 | 0.234772 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8448 | 1.39059 | 0.695297 | − | 0.718722i | \(-0.255273\pi\) | ||||
0.695297 | + | 0.718722i | \(0.255273\pi\) | |||||||
\(822\) | 93.8162 | 3.27222 | ||||||||
\(823\) | 13.6308 | 0.475141 | 0.237570 | − | 0.971370i | \(-0.423649\pi\) | ||||
0.237570 | + | 0.971370i | \(0.423649\pi\) | |||||||
\(824\) | −7.99308 | −0.278452 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8282 | 0.620323 | ||||||||
\(827\) | 27.3750 | 0.951921 | 0.475961 | − | 0.879467i | \(-0.342100\pi\) | ||||
0.475961 | + | 0.879467i | \(0.342100\pi\) | |||||||
\(828\) | −10.2823 | −0.357336 | ||||||||
\(829\) | −34.1484 | −1.18602 | −0.593012 | − | 0.805194i | \(-0.702061\pi\) | ||||
−0.593012 | + | 0.805194i | \(0.702061\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0164 | 0.729051 | ||||||||
\(832\) | −20.8679 | −0.723465 | ||||||||
\(833\) | 5.38558 | 0.186599 | ||||||||
\(834\) | 15.8048 | 0.547274 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.6152 | −0.989678 | ||||||||
\(837\) | −23.1465 | −0.800060 | ||||||||
\(838\) | −55.4169 | −1.91435 | ||||||||
\(839\) | 39.9352 | 1.37872 | 0.689358 | − | 0.724421i | \(-0.257893\pi\) | ||||
0.689358 | + | 0.724421i | \(0.257893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5423 | −0.777322 | ||||||||
\(842\) | 41.7863 | 1.44005 | ||||||||
\(843\) | −18.1118 | −0.623805 | ||||||||
\(844\) | 28.3242 | 0.974958 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 62.1915 | 2.13819 | ||||||||
\(847\) | −1.04211 | −0.0358073 | ||||||||
\(848\) | −7.33634 | −0.251931 | ||||||||
\(849\) | 7.78329 | 0.267122 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.69681 | −0.195284 | ||||||||
\(852\) | 90.4944 | 3.10029 | ||||||||
\(853\) | −0.378296 | −0.0129526 | −0.00647631 | − | 0.999979i | \(-0.502061\pi\) | ||||
−0.00647631 | + | 0.999979i | \(0.502061\pi\) | |||||||
\(854\) | −17.1541 | −0.587002 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.9722 | −0.887713 | ||||||||
\(857\) | −21.7667 | −0.743535 | −0.371768 | − | 0.928326i | \(-0.621248\pi\) | ||||
−0.371768 | + | 0.928326i | \(0.621248\pi\) | |||||||
\(858\) | 30.8676 | 1.05380 | ||||||||
\(859\) | −11.5199 | −0.393055 | −0.196528 | − | 0.980498i | \(-0.562967\pi\) | ||||
−0.196528 | + | 0.980498i | \(0.562967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.1622 | 0.653045 | ||||||||
\(862\) | −6.26148 | −0.213267 | ||||||||
\(863\) | −6.32314 | −0.215242 | −0.107621 | − | 0.994192i | \(-0.534323\pi\) | ||||
−0.107621 | + | 0.994192i | \(0.534323\pi\) | |||||||
\(864\) | −17.9299 | −0.609988 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −53.5265 | −1.81890 | ||||||||
\(867\) | 31.4990 | 1.06976 | ||||||||
\(868\) | −26.3804 | −0.895409 | ||||||||
\(869\) | −12.7807 | −0.433555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00540 | −0.305136 | ||||||||
\(872\) | −8.73891 | −0.295937 | ||||||||
\(873\) | −16.9628 | −0.574103 | ||||||||
\(874\) | 7.38558 | 0.249821 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −61.1847 | −2.06724 | ||||||||
\(877\) | −50.6948 | −1.71184 | −0.855921 | − | 0.517107i | \(-0.827009\pi\) | ||||
−0.855921 | + | 0.517107i | \(0.827009\pi\) | |||||||
\(878\) | 40.2923 | 1.35980 | ||||||||
\(879\) | 17.9254 | 0.604609 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.9010 | −0.603101 | −0.301550 | − | 0.953450i | \(-0.597504\pi\) | ||||
−0.301550 | + | 0.953450i | \(0.597504\pi\) | |||||||
\(882\) | 8.37459 | 0.281987 | ||||||||
\(883\) | 42.2971 | 1.42341 | 0.711706 | − | 0.702478i | \(-0.247923\pi\) | ||||
0.711706 | + | 0.702478i | \(0.247923\pi\) | |||||||
\(884\) | 24.6506 | 0.829090 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.4729 | 1.52769 | ||||||||
\(887\) | 34.6437 | 1.16322 | 0.581612 | − | 0.813467i | \(-0.302422\pi\) | ||||
0.581612 | + | 0.813467i | \(0.302422\pi\) | |||||||
\(888\) | 20.8370 | 0.699243 | ||||||||
\(889\) | 17.4907 | 0.586619 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.5506 | −0.587966 | ||||||||
\(892\) | −55.3814 | −1.85430 | ||||||||
\(893\) | −25.4438 | −0.851443 | ||||||||
\(894\) | −123.086 | −4.11661 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.5688 | −0.353078 | ||||||||
\(897\) | −4.53783 | −0.151514 | ||||||||
\(898\) | 7.41446 | 0.247424 | ||||||||
\(899\) | 25.3291 | 0.844773 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.2649 | 0.575176 | ||||||||
\(902\) | 49.6760 | 1.65403 | ||||||||
\(903\) | −12.9495 | −0.430933 | ||||||||
\(904\) | −9.17687 | −0.305218 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 123.077 | 4.08898 | ||||||||
\(907\) | −12.2650 | −0.407252 | −0.203626 | − | 0.979049i | \(-0.565273\pi\) | ||||
−0.203626 | + | 0.979049i | \(0.565273\pi\) | |||||||
\(908\) | −43.4969 | −1.44349 | ||||||||
\(909\) | 17.9083 | 0.593980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.6665 | 0.982894 | 0.491447 | − | 0.870907i | \(-0.336468\pi\) | ||||
0.491447 | + | 0.870907i | \(0.336468\pi\) | |||||||
\(912\) | 20.5738 | 0.681268 | ||||||||
\(913\) | −38.0556 | −1.25946 | ||||||||
\(914\) | 7.48765 | 0.247670 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.2674 | 0.504450 | ||||||||
\(917\) | −1.83453 | −0.0605814 | ||||||||
\(918\) | 26.9592 | 0.889785 | ||||||||
\(919\) | 21.5442 | 0.710678 | 0.355339 | − | 0.934738i | \(-0.384365\pi\) | ||||
0.355339 | + | 0.934738i | \(0.384365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −60.6126 | −1.99725 | ||||||||
\(922\) | −76.3573 | −2.51469 | ||||||||
\(923\) | 22.5354 | 0.741763 | ||||||||
\(924\) | 21.9147 | 0.720940 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 88.5039 | 2.90842 | ||||||||
\(927\) | −22.2770 | −0.731672 | ||||||||
\(928\) | 19.6206 | 0.644079 | ||||||||
\(929\) | 49.0601 | 1.60961 | 0.804805 | − | 0.593540i | \(-0.202270\pi\) | ||||
0.804805 | + | 0.593540i | \(0.202270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.42621 | −0.112290 | ||||||||
\(932\) | −63.7031 | −2.08666 | ||||||||
\(933\) | 3.18041 | 0.104122 | ||||||||
\(934\) | −56.4541 | −1.84723 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.36569 | 0.306127 | ||||||||
\(937\) | −50.1197 | −1.63734 | −0.818670 | − | 0.574265i | \(-0.805288\pi\) | ||||
−0.818670 | + | 0.574265i | \(0.805288\pi\) | |||||||
\(938\) | −11.2248 | −0.366502 | ||||||||
\(939\) | −63.5900 | −2.07518 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.29965 | −0.172764 | −0.0863819 | − | 0.996262i | \(-0.527531\pi\) | ||||
−0.0863819 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(942\) | −55.0851 | −1.79477 | ||||||||
\(943\) | −7.30285 | −0.237813 | ||||||||
\(944\) | −18.9272 | −0.616027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.5703 | −1.09146 | ||||||||
\(947\) | 26.0370 | 0.846088 | 0.423044 | − | 0.906109i | \(-0.360962\pi\) | ||||
0.423044 | + | 0.906109i | \(0.360962\pi\) | |||||||
\(948\) | −28.1269 | −0.913519 | ||||||||
\(949\) | −15.2366 | −0.494600 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −46.0073 | −1.49189 | ||||||||
\(952\) | 7.50730 | 0.243313 | ||||||||
\(953\) | 24.8848 | 0.806099 | 0.403050 | − | 0.915178i | \(-0.367950\pi\) | ||||
0.403050 | + | 0.915178i | \(0.367950\pi\) | |||||||
\(954\) | 26.8469 | 0.869200 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 39.2522 | 1.26951 | ||||||||
\(957\) | −21.0414 | −0.680171 | ||||||||
\(958\) | −61.9078 | −2.00015 | ||||||||
\(959\) | 16.5865 | 0.535606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.3492 | 2.20481 | ||||||||
\(962\) | 21.2373 | 0.684717 | ||||||||
\(963\) | −72.3855 | −2.33259 | ||||||||
\(964\) | −44.4874 | −1.43284 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.65618 | −0.181985 | ||||||||
\(967\) | 26.8969 | 0.864947 | 0.432474 | − | 0.901647i | \(-0.357641\pi\) | ||||
0.432474 | + | 0.901647i | \(0.357641\pi\) | |||||||
\(968\) | −1.45266 | −0.0466902 | ||||||||
\(969\) | −48.4171 | −1.55538 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.0213 | 0.867153 | 0.433577 | − | 0.901117i | \(-0.357251\pi\) | ||||
0.433577 | + | 0.901117i | \(0.357251\pi\) | |||||||
\(972\) | −57.0626 | −1.83028 | ||||||||
\(973\) | 2.79425 | 0.0895794 | ||||||||
\(974\) | 21.9816 | 0.704336 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.2116 | 0.582938 | ||||||||
\(977\) | 56.9300 | 1.82135 | 0.910676 | − | 0.413120i | \(-0.135561\pi\) | ||||
0.910676 | + | 0.413120i | \(0.135561\pi\) | |||||||
\(978\) | −60.9236 | −1.94812 | ||||||||
\(979\) | 16.4726 | 0.526468 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.3556 | −0.777615 | ||||||||
\(982\) | −24.7527 | −0.789890 | ||||||||
\(983\) | −58.9417 | −1.87995 | −0.939974 | − | 0.341245i | \(-0.889151\pi\) | ||||
−0.939974 | + | 0.341245i | \(0.889151\pi\) | |||||||
\(984\) | 26.7113 | 0.851526 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.5013 | −0.939513 | ||||||||
\(987\) | 19.4859 | 0.620242 | ||||||||
\(988\) | −15.6823 | −0.498920 | ||||||||
\(989\) | 4.93516 | 0.156929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.4471 | 1.69780 | 0.848902 | − | 0.528551i | \(-0.177264\pi\) | ||||
0.848902 | + | 0.528551i | \(0.177264\pi\) | |||||||
\(992\) | 76.9586 | 2.44344 | ||||||||
\(993\) | 42.6534 | 1.35357 | ||||||||
\(994\) | 28.0893 | 0.890938 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −83.7503 | −2.65373 | ||||||||
\(997\) | 3.09915 | 0.0981510 | 0.0490755 | − | 0.998795i | \(-0.484373\pi\) | ||||
0.0490755 | + | 0.998795i | \(0.484373\pi\) | |||||||
\(998\) | −8.39903 | −0.265867 | ||||||||
\(999\) | 13.2292 | 0.418555 |
(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 | 4025.2.a.n.1.3 | 4 | ||
5.4 | even | 2 | 805.2.a.h.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 7245.2.a.be.1.3 | 4 | |||
35.34 | odd | 2 | 5635.2.a.t.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.h.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
4025.2.a.n.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5635.2.a.t.1.2 | 4 | 35.34 | odd | 2 | |||
7245.2.a.be.1.3 | 4 | 15.14 | odd | 2 |