Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.8405.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 8x^{2} - 7x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.4 | ||
Root | \(0.500000 + 2.53999i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.m.451.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85078 | + | 0.758030i | 0.925391 | + | 0.379015i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.85078 | + | 2.80590i | 0.712695 | + | 0.701474i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.09573i | 0.585104i | 0.956250 | + | 0.292552i | \(0.0945045\pi\) | ||||
−0.956250 | + | 0.292552i | \(0.905495\pi\) | |||||||
\(8\) | 3.14922 | + | 7.35408i | 0.393652 | + | 0.919259i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.984255i | − | 0.0894777i | −0.998999 | − | 0.0447389i | \(-0.985754\pi\) | ||
0.998999 | − | 0.0447389i | \(-0.0142456\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.8062 | −1.13894 | −0.569471 | − | 0.822011i | \(-0.692852\pi\) | ||||
−0.569471 | + | 0.822011i | \(0.692852\pi\) | |||||||
\(14\) | −3.10469 | + | 7.58030i | −0.221763 | + | 0.541450i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.253905 | + | 15.9980i | 0.0158691 | + | 0.999874i | ||||
\(17\) | −9.80625 | −0.576838 | −0.288419 | − | 0.957504i | \(-0.593130\pi\) | ||||
−0.288419 | + | 0.957504i | \(0.593130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.3684i | 1.44044i | 0.693744 | + | 0.720222i | \(0.255960\pi\) | ||||
−0.693744 | + | 0.720222i | \(0.744040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.746095 | − | 1.82164i | 0.0339134 | − | 0.0828018i | ||||
\(23\) | 18.3514i | 0.797888i | 0.916975 | + | 0.398944i | \(0.130623\pi\) | ||||
−0.916975 | + | 0.398944i | \(0.869377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −27.4031 | − | 11.2236i | −1.05397 | − | 0.431676i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −11.4922 | + | 11.6760i | −0.410435 | + | 0.417001i | ||||
\(29\) | 2.80625 | 0.0967672 | 0.0483836 | − | 0.998829i | \(-0.484593\pi\) | ||||
0.0483836 | + | 0.998829i | \(0.484593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.96851i | − | 0.0635003i | −0.999496 | − | 0.0317502i | \(-0.989892\pi\) | ||
0.999496 | − | 0.0317502i | \(-0.0101081\pi\) | |||||||
\(32\) | −11.6570 | + | 29.8012i | −0.364282 | + | 0.931289i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.1492 | − | 7.43343i | −0.533801 | − | 0.218630i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.8062 | 1.21098 | 0.605490 | − | 0.795853i | \(-0.292977\pi\) | ||||
0.605490 | + | 0.795853i | \(0.292977\pi\) | |||||||
\(38\) | −20.7461 | + | 50.6530i | −0.545950 | + | 1.33297i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.0000 | −0.414634 | −0.207317 | − | 0.978274i | \(-0.566473\pi\) | ||||
−0.207317 | + | 0.978274i | \(0.566473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.8956i | 1.27664i | 0.769771 | + | 0.638321i | \(0.220371\pi\) | ||||
−0.769771 | + | 0.638321i | \(0.779629\pi\) | |||||||
\(44\) | 2.76172 | − | 2.80590i | 0.0627663 | − | 0.0637703i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.9109 | + | 33.9645i | −0.302412 | + | 0.738358i | ||||
\(47\) | − | 58.8326i | − | 1.25176i | −0.779920 | − | 0.625879i | \(-0.784740\pi\) | ||
0.779920 | − | 0.625879i | \(-0.215260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 32.2250 | 0.657653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −42.2094 | − | 41.5448i | −0.811719 | − | 0.798938i | ||||
\(53\) | −89.2250 | −1.68349 | −0.841745 | − | 0.539875i | \(-0.818472\pi\) | ||||
−0.841745 | + | 0.539875i | \(0.818472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −30.1203 | + | 12.8984i | −0.537863 | + | 0.230328i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.19375 | + | 2.12722i | 0.0895474 | + | 0.0366762i | ||||
\(59\) | − | 67.3415i | − | 1.14138i | −0.821165 | − | 0.570691i | \(-0.806676\pi\) | ||
0.821165 | − | 0.570691i | \(-0.193324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.0312 | 0.590676 | 0.295338 | − | 0.955393i | \(-0.404568\pi\) | ||||
0.295338 | + | 0.955393i | \(0.404568\pi\) | |||||||
\(62\) | 1.49219 | − | 3.64328i | 0.0240676 | − | 0.0587626i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.1648 | + | 46.3192i | −0.690076 | + | 0.723737i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.5586i | 0.381472i | 0.981641 | + | 0.190736i | \(0.0610875\pi\) | ||||
−0.981641 | + | 0.190736i | \(0.938913\pi\) | |||||||
\(68\) | −27.9555 | − | 27.5153i | −0.411110 | − | 0.404637i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 120.110i | 1.69169i | 0.533430 | + | 0.845844i | \(0.320903\pi\) | ||||
−0.533430 | + | 0.845844i | \(0.679097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −69.8062 | −0.956250 | −0.478125 | − | 0.878292i | \(-0.658683\pi\) | ||||
−0.478125 | + | 0.878292i | \(0.658683\pi\) | |||||||
\(74\) | 82.9266 | + | 33.9645i | 1.12063 | + | 0.458979i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76.7930 | + | 78.0214i | −1.01043 | + | 1.02660i | ||||
\(77\) | 4.03124 | 0.0523538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 32.2897i | − | 0.408730i | −0.978895 | − | 0.204365i | \(-0.934487\pi\) | ||
0.978895 | − | 0.204365i | \(-0.0655130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −31.4633 | − | 12.8865i | −0.383699 | − | 0.157153i | ||||
\(83\) | 68.1670i | 0.821289i | 0.911795 | + | 0.410645i | \(0.134696\pi\) | ||||
−0.911795 | + | 0.410645i | \(0.865304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −41.6125 | + | 101.600i | −0.483866 | + | 1.18139i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.23828 | − | 3.09963i | 0.0822532 | − | 0.0352231i | ||||
\(89\) | 67.8062 | 0.761868 | 0.380934 | − | 0.924602i | \(-0.375603\pi\) | ||||
0.380934 | + | 0.924602i | \(0.375603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 60.6424i | − | 0.666400i | ||||||
\(92\) | −51.4922 | + | 52.3159i | −0.559698 | + | 0.568651i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 44.5969 | − | 108.886i | 0.474435 | − | 1.15836i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.16251 | −0.0119846 | −0.00599232 | − | 0.999982i | \(-0.501907\pi\) | ||||
−0.00599232 | + | 0.999982i | \(0.501907\pi\) | |||||||
\(98\) | 59.6414 | + | 24.4275i | 0.608586 | + | 0.249260i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 132.031 | 1.30724 | 0.653620 | − | 0.756823i | \(-0.273249\pi\) | ||||
0.653620 | + | 0.756823i | \(0.273249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111.601i | 1.08350i | 0.840538 | + | 0.541752i | \(0.182239\pi\) | ||||
−0.840538 | + | 0.541752i | \(0.817761\pi\) | |||||||
\(104\) | −46.6281 | − | 108.886i | −0.448347 | − | 1.04698i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −165.136 | − | 67.6352i | −1.55789 | − | 0.638068i | ||||
\(107\) | 62.2615i | 0.581883i | 0.956741 | + | 0.290942i | \(0.0939685\pi\) | ||||
−0.956741 | + | 0.290942i | \(0.906031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 87.1938 | 0.799943 | 0.399971 | − | 0.916528i | \(-0.369020\pi\) | ||||
0.399971 | + | 0.916528i | \(0.369020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −65.5234 | + | 1.03993i | −0.585031 | + | 0.00928507i | ||||
\(113\) | −84.2250 | −0.745354 | −0.372677 | − | 0.927961i | \(-0.621560\pi\) | ||||
−0.372677 | + | 0.927961i | \(0.621560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.00000 | + | 7.87404i | 0.0689655 | + | 0.0678796i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 51.0469 | − | 124.634i | 0.432601 | − | 1.05622i | ||||
\(119\) | − | 40.1637i | − | 0.337510i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.031 | 0.991994 | ||||||||
\(122\) | 66.6859 | + | 27.3128i | 0.546606 | + | 0.223875i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.52343 | − | 5.61179i | 0.0445438 | − | 0.0452564i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 75.0568i | − | 0.590999i | −0.955343 | − | 0.295499i | \(-0.904514\pi\) | ||
0.955343 | − | 0.295499i | \(-0.0954860\pi\) | |||||||
\(128\) | −116.851 | + | 52.2484i | −0.912897 | + | 0.408191i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 139.795i | − | 1.06714i | −0.845757 | − | 0.533568i | \(-0.820851\pi\) | ||
0.845757 | − | 0.533568i | \(-0.179149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −112.094 | −0.842810 | ||||||||
\(134\) | −19.3742 | + | 47.3034i | −0.144584 | + | 0.353011i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.8820 | − | 72.1159i | −0.227074 | − | 0.530264i | ||||
\(137\) | 56.1625 | 0.409945 | 0.204973 | − | 0.978768i | \(-0.434289\pi\) | ||||
0.204973 | + | 0.978768i | \(0.434289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 194.341i | − | 1.39814i | −0.715054 | − | 0.699069i | \(-0.753598\pi\) | ||
0.715054 | − | 0.699069i | \(-0.246402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −91.0469 | + | 222.297i | −0.641175 | + | 1.56547i | ||||
\(143\) | 14.5731i | 0.101910i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −129.196 | − | 52.9152i | −0.884905 | − | 0.362433i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 127.733 | + | 125.722i | 0.863059 | + | 0.849470i | ||||
\(149\) | 110.869 | 0.744085 | 0.372043 | − | 0.928216i | \(-0.378657\pi\) | ||||
0.372043 | + | 0.928216i | \(0.378657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 141.763i | − | 0.938831i | −0.882977 | − | 0.469415i | \(-0.844465\pi\) | ||
0.882977 | − | 0.469415i | \(-0.155535\pi\) | |||||||
\(152\) | −201.270 | + | 86.1892i | −1.32414 | + | 0.567034i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.46095 | + | 3.05580i | 0.0484477 | + | 0.0198429i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 178.837 | 1.13909 | 0.569546 | − | 0.821959i | \(-0.307119\pi\) | ||||
0.569546 | + | 0.821959i | \(0.307119\pi\) | |||||||
\(158\) | 24.4766 | − | 59.7612i | 0.154915 | − | 0.378235i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.1625 | −0.466848 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 222.535i | − | 1.36525i | −0.730771 | − | 0.682623i | \(-0.760839\pi\) | ||
0.730771 | − | 0.682623i | \(-0.239161\pi\) | |||||||
\(164\) | −48.4633 | − | 47.7002i | −0.295508 | − | 0.290855i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −51.6727 | + | 126.162i | −0.311281 | + | 0.760014i | ||||
\(167\) | 212.883i | 1.27475i | 0.770554 | + | 0.637375i | \(0.219980\pi\) | ||||
−0.770554 | + | 0.637375i | \(0.780020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 50.2250 | 0.297189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −154.031 | + | 156.495i | −0.895530 | + | 0.909856i | ||||
\(173\) | 20.7750 | 0.120087 | 0.0600434 | − | 0.998196i | \(-0.480876\pi\) | ||||
0.0600434 | + | 0.998196i | \(0.480876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.7461 | − | 0.249908i | 0.0894664 | − | 0.00141993i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 125.495 | + | 51.3992i | 0.705025 | + | 0.288759i | ||||
\(179\) | 37.2110i | 0.207883i | 0.994583 | + | 0.103941i | \(0.0331454\pi\) | ||||
−0.994583 | + | 0.103941i | \(0.966855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 318.125 | 1.75760 | 0.878798 | − | 0.477193i | \(-0.158346\pi\) | ||||
0.878798 | + | 0.477193i | \(0.158346\pi\) | |||||||
\(182\) | 45.9688 | − | 112.236i | 0.252576 | − | 0.616680i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −134.958 | + | 57.7927i | −0.733466 | + | 0.314091i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65185i | 0.0516142i | ||||||||
\(188\) | 165.078 | − | 167.719i | 0.878075 | − | 0.892122i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 257.936i | − | 1.35045i | −0.737611 | − | 0.675226i | \(-0.764046\pi\) | ||
0.737611 | − | 0.675226i | \(-0.235954\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −127.869 | −0.662532 | −0.331266 | − | 0.943537i | \(-0.607476\pi\) | ||||
−0.331266 | + | 0.943537i | \(0.607476\pi\) | |||||||
\(194\) | −2.15155 | − | 0.881217i | −0.0110905 | − | 0.00454235i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 91.8664 | + | 90.4200i | 0.468706 | + | 0.461326i | ||||
\(197\) | 97.2875 | 0.493845 | 0.246923 | − | 0.969035i | \(-0.420581\pi\) | ||||
0.246923 | + | 0.969035i | \(0.420581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.6851i | − | 0.0989201i | −0.998776 | − | 0.0494600i | \(-0.984250\pi\) | ||
0.998776 | − | 0.0494600i | \(-0.0157500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 244.361 | + | 100.084i | 1.20971 | + | 0.495464i | ||||
\(203\) | 11.4936i | 0.0566189i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −84.5969 | + | 206.549i | −0.410664 | + | 1.00266i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.75938 | − | 236.870i | −0.0180740 | − | 1.13880i | ||||
\(209\) | 26.9375 | 0.128888 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 235.298i | 1.11516i | 0.830124 | + | 0.557579i | \(0.188270\pi\) | ||||
−0.830124 | + | 0.557579i | \(0.811730\pi\) | |||||||
\(212\) | −254.361 | − | 250.356i | −1.19982 | − | 1.18092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −47.1961 | + | 115.232i | −0.220542 | + | 0.538469i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.06248 | 0.0371543 | ||||||||
\(218\) | 161.377 | + | 66.0955i | 0.740259 | + | 0.303190i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 145.194 | 0.656985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 32.4484i | 0.145509i | 0.997350 | + | 0.0727543i | \(0.0231789\pi\) | ||||
−0.997350 | + | 0.0727543i | \(0.976821\pi\) | |||||||
\(224\) | −122.058 | − | 47.7440i | −0.544901 | − | 0.213143i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −155.882 | − | 63.8451i | −0.689743 | − | 0.282500i | ||||
\(227\) | − | 289.591i | − | 1.27573i | −0.770147 | − | 0.637866i | \(-0.779817\pi\) | ||
0.770147 | − | 0.637866i | \(-0.220183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 99.2875 | 0.433570 | 0.216785 | − | 0.976219i | \(-0.430443\pi\) | ||||
0.216785 | + | 0.976219i | \(0.430443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.83749 | + | 20.6374i | 0.0380926 | + | 0.0889541i | ||||
\(233\) | 50.7750 | 0.217918 | 0.108959 | − | 0.994046i | \(-0.465248\pi\) | ||||
0.108959 | + | 0.994046i | \(0.465248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 188.953 | − | 191.976i | 0.800649 | − | 0.813457i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 30.4453 | − | 74.3343i | 0.127922 | − | 0.312329i | ||||
\(239\) | 311.498i | 1.30334i | 0.758503 | + | 0.651670i | \(0.225931\pi\) | ||||
−0.758503 | + | 0.651670i | \(0.774069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 319.094 | 1.32404 | 0.662020 | − | 0.749486i | \(-0.269699\pi\) | ||||
0.662020 | + | 0.749486i | \(0.269699\pi\) | |||||||
\(242\) | 222.152 | + | 90.9873i | 0.917982 | + | 0.375981i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 102.717 | + | 101.100i | 0.420972 | + | 0.414344i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 405.224i | − | 1.64058i | ||||||
\(248\) | 14.4766 | − | 6.19927i | 0.0583733 | − | 0.0249970i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 87.6294i | − | 0.349121i | −0.984646 | − | 0.174561i | \(-0.944149\pi\) | ||
0.984646 | − | 0.174561i | \(-0.0558505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0625 | 0.0713932 | ||||||||
\(254\) | 56.8953 | − | 138.914i | 0.223997 | − | 0.546904i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −255.871 | + | 8.12395i | −0.999496 | + | 0.0317342i | ||||
\(257\) | 117.287 | 0.456372 | 0.228186 | − | 0.973618i | \(-0.426721\pi\) | ||||
0.228186 | + | 0.973618i | \(0.426721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 183.514i | 0.708549i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 105.969 | − | 258.730i | 0.404461 | − | 0.987518i | ||||
\(263\) | − | 47.8151i | − | 0.181806i | −0.995860 | − | 0.0909032i | \(-0.971025\pi\) | ||
0.995860 | − | 0.0909032i | \(-0.0289754\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −207.461 | − | 84.9704i | −0.779928 | − | 0.319438i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −71.7149 | + | 72.8621i | −0.267593 | + | 0.271873i | ||||
\(269\) | −479.287 | −1.78174 | −0.890869 | − | 0.454260i | \(-0.849904\pi\) | ||||
−0.890869 | + | 0.454260i | \(0.849904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 242.188i | − | 0.893683i | −0.894613 | − | 0.446842i | \(-0.852549\pi\) | ||
0.894613 | − | 0.446842i | \(-0.147451\pi\) | |||||||
\(272\) | −2.48986 | − | 156.880i | −0.00915389 | − | 0.576766i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 103.945 | + | 42.5729i | 0.379360 | + | 0.155375i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −33.2562 | −0.120059 | −0.0600293 | − | 0.998197i | \(-0.519119\pi\) | ||||
−0.0600293 | + | 0.998197i | \(0.519119\pi\) | |||||||
\(278\) | 147.316 | − | 359.683i | 0.529915 | − | 1.29382i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 246.062 | 0.875667 | 0.437834 | − | 0.899056i | \(-0.355746\pi\) | ||||
0.437834 | + | 0.899056i | \(0.355746\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.52437i | 0.00538646i | 0.999996 | + | 0.00269323i | \(0.000857282\pi\) | ||||
−0.999996 | + | 0.00269323i | \(0.999143\pi\) | |||||||
\(284\) | −337.016 | + | 342.407i | −1.18667 | + | 1.20566i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.0469 | + | 26.9717i | −0.0386254 | + | 0.0943065i | ||||
\(287\) | − | 69.6274i | − | 0.242604i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −192.837 | −0.667258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −199.002 | − | 195.869i | −0.681515 | − | 0.670784i | ||||
\(293\) | 448.994 | 1.53240 | 0.766201 | − | 0.642601i | \(-0.222145\pi\) | ||||
0.766201 | + | 0.642601i | \(0.222145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 141.105 | + | 329.509i | 0.476705 | + | 1.11320i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 205.194 | + | 84.0418i | 0.688570 | + | 0.282020i | ||||
\(299\) | − | 271.716i | − | 0.908749i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −224.837 | −0.746968 | ||||||||
\(302\) | 107.461 | − | 262.373i | 0.355831 | − | 0.868785i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −437.840 | + | 6.94899i | −1.44026 | + | 0.0228585i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.6681i | − | 0.0347495i | −0.999849 | − | 0.0173747i | \(-0.994469\pi\) | ||
0.999849 | − | 0.0173747i | \(-0.00553083\pi\) | |||||||
\(308\) | 11.4922 | + | 11.3112i | 0.0373123 | + | 0.0367248i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 370.172i | 1.19026i | 0.803628 | + | 0.595132i | \(0.202900\pi\) | ||||
−0.803628 | + | 0.595132i | \(0.797100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −42.7125 | −0.136462 | −0.0682309 | − | 0.997670i | \(-0.521735\pi\) | ||||
−0.0682309 | + | 0.997670i | \(0.521735\pi\) | |||||||
\(314\) | 330.989 | + | 135.564i | 1.05411 | + | 0.431733i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 90.6015 | − | 92.0509i | 0.286714 | − | 0.291300i | ||||
\(317\) | 143.100 | 0.451420 | 0.225710 | − | 0.974195i | \(-0.427530\pi\) | ||||
0.225710 | + | 0.974195i | \(0.427530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.76206i | − | 0.00865851i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −139.109 | − | 56.9754i | −0.432017 | − | 0.176942i | ||||
\(323\) | − | 268.382i | − | 0.830903i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 168.688 | − | 411.864i | 0.517449 | − | 1.26339i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −53.5367 | − | 125.019i | −0.163222 | − | 0.381156i | ||||
\(329\) | 240.962 | 0.732409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 52.1655i | 0.157600i | 0.996890 | + | 0.0787999i | \(0.0251088\pi\) | ||||
−0.996890 | + | 0.0787999i | \(0.974891\pi\) | |||||||
\(332\) | −191.270 | + | 194.329i | −0.576113 | + | 0.585329i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −161.372 | + | 394.000i | −0.483149 | + | 1.17964i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 441.900 | 1.31128 | 0.655638 | − | 0.755075i | \(-0.272400\pi\) | ||||
0.655638 | + | 0.755075i | \(0.272400\pi\) | |||||||
\(338\) | 92.9555 | + | 38.0721i | 0.275016 | + | 0.112639i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.93752 | −0.00568186 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 332.676i | 0.969900i | ||||||||
\(344\) | −403.706 | + | 172.878i | −1.17356 | + | 0.502553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.4500 | + | 15.7481i | 0.111127 | + | 0.0455147i | ||||
\(347\) | − | 85.8196i | − | 0.247319i | −0.992325 | − | 0.123659i | \(-0.960537\pi\) | ||
0.992325 | − | 0.123659i | \(-0.0394630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −408.931 | −1.17172 | −0.585861 | − | 0.810411i | \(-0.699244\pi\) | ||||
−0.585861 | + | 0.810411i | \(0.699244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 29.3320 | + | 11.4735i | 0.0833296 | + | 0.0325951i | ||||
\(353\) | −441.163 | −1.24975 | −0.624876 | − | 0.780724i | \(-0.714851\pi\) | ||||
−0.624876 | + | 0.780724i | \(0.714851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 193.301 | + | 190.257i | 0.542980 | + | 0.534430i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.2070 | + | 68.8694i | −0.0787906 | + | 0.192373i | ||||
\(359\) | 430.814i | 1.20004i | 0.799985 | + | 0.600020i | \(0.204841\pi\) | ||||
−0.799985 | + | 0.600020i | \(0.795159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −388.031 | −1.07488 | ||||||||
\(362\) | 588.780 | + | 241.148i | 1.62646 | + | 0.666155i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 170.156 | − | 172.878i | 0.467462 | − | 0.474940i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 346.709i | 0.944710i | 0.881408 | + | 0.472355i | \(0.156596\pi\) | ||||
−0.881408 | + | 0.472355i | \(0.843404\pi\) | |||||||
\(368\) | −293.586 | + | 4.65953i | −0.797788 | + | 0.0126618i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 365.442i | − | 0.985018i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 577.287 | 1.54769 | 0.773844 | − | 0.633376i | \(-0.218332\pi\) | ||||
0.773844 | + | 0.633376i | \(0.218332\pi\) | |||||||
\(374\) | −7.31639 | + | 17.8635i | −0.0195625 | + | 0.0477633i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 432.659 | − | 185.277i | 1.15069 | − | 0.492757i | ||||
\(377\) | −41.5500 | −0.110212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 500.315i | 1.32009i | 0.751225 | + | 0.660046i | \(0.229463\pi\) | ||||
−0.751225 | + | 0.660046i | \(0.770537\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 195.523 | − | 477.384i | 0.511841 | − | 1.24970i | ||||
\(383\) | − | 393.159i | − | 1.02653i | −0.858231 | − | 0.513263i | \(-0.828437\pi\) | ||
0.858231 | − | 0.513263i | \(-0.171563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −236.657 | − | 96.9283i | −0.613101 | − | 0.251110i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.31406 | − | 3.26188i | −0.00854139 | − | 0.00840690i | ||||
\(389\) | 98.7750 | 0.253920 | 0.126960 | − | 0.991908i | \(-0.459478\pi\) | ||||
0.126960 | + | 0.991908i | \(0.459478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 179.959i | − | 0.460252i | ||||||
\(392\) | 101.484 | + | 236.985i | 0.258887 | + | 0.604554i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 180.058 | + | 73.7468i | 0.457000 | + | 0.187175i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −199.225 | −0.501826 | −0.250913 | − | 0.968010i | \(-0.580731\pi\) | ||||
−0.250913 | + | 0.968010i | \(0.580731\pi\) | |||||||
\(398\) | 14.9219 | − | 36.4328i | 0.0374922 | − | 0.0915397i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 105.094 | 0.262079 | 0.131040 | − | 0.991377i | \(-0.458169\pi\) | ||||
0.131040 | + | 0.991377i | \(0.458169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.1462i | 0.0723232i | ||||||||
\(404\) | 376.392 | + | 370.466i | 0.931664 | + | 0.916995i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.71252 | + | 21.2722i | −0.0214594 | + | 0.0523946i | ||||
\(407\) | − | 44.1008i | − | 0.108356i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 368.163 | 0.900153 | 0.450076 | − | 0.892990i | \(-0.351397\pi\) | ||||
0.450076 | + | 0.892990i | \(0.351397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −313.141 | + | 318.150i | −0.760050 | + | 0.772209i | ||||
\(413\) | 275.813 | 0.667827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 172.597 | − | 441.245i | 0.414896 | − | 1.06068i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 49.8554 | + | 20.4194i | 0.119271 | + | 0.0488503i | ||||
\(419\) | − | 47.0535i | − | 0.112300i | −0.998422 | − | 0.0561498i | \(-0.982118\pi\) | ||
0.998422 | − | 0.0561498i | \(-0.0178824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.81255 | 0.0185571 | 0.00927856 | − | 0.999957i | \(-0.497047\pi\) | ||||
0.00927856 | + | 0.999957i | \(0.497047\pi\) | |||||||
\(422\) | −178.363 | + | 435.486i | −0.422662 | + | 1.03196i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −280.989 | − | 656.167i | −0.662710 | − | 1.54756i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 147.574i | 0.345607i | ||||||||
\(428\) | −174.699 | + | 177.494i | −0.408176 | + | 0.414705i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 681.258i | 1.58065i | 0.612691 | + | 0.790323i | \(0.290087\pi\) | ||||
−0.612691 | + | 0.790323i | \(0.709913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.06878 | 0.00939673 | 0.00469836 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469836 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(434\) | 14.9219 | + | 6.11161i | 0.0343822 | + | 0.0140820i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 248.570 | + | 244.657i | 0.570115 | + | 0.561139i | ||||
\(437\) | −502.250 | −1.14931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 176.815i | 0.402768i | 0.979512 | + | 0.201384i | \(0.0645439\pi\) | ||||
−0.979512 | + | 0.201384i | \(0.935456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 268.722 | + | 110.061i | 0.607968 | + | 0.249007i | ||||
\(443\) | 469.454i | 1.05972i | 0.848087 | + | 0.529858i | \(0.177755\pi\) | ||||
−0.848087 | + | 0.529858i | \(0.822245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.5969 | + | 60.0549i | −0.0551499 | + | 0.134652i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −189.711 | − | 180.887i | −0.423462 | − | 0.403766i | ||||
\(449\) | −514.444 | −1.14575 | −0.572877 | − | 0.819641i | \(-0.694173\pi\) | ||||
−0.572877 | + | 0.819641i | \(0.694173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7323i | 0.0371005i | ||||||||
\(452\) | −240.107 | − | 236.326i | −0.531210 | − | 0.522846i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 219.519 | − | 535.970i | 0.483522 | − | 1.18055i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −684.537 | −1.49789 | −0.748947 | − | 0.662630i | \(-0.769440\pi\) | ||||
−0.748947 | + | 0.662630i | \(0.769440\pi\) | |||||||
\(458\) | 183.759 | + | 75.2629i | 0.401221 | + | 0.164329i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −204.250 | −0.443058 | −0.221529 | − | 0.975154i | \(-0.571105\pi\) | ||||
−0.221529 | + | 0.975154i | \(0.571105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 550.353i | − | 1.18867i | −0.804218 | − | 0.594334i | \(-0.797416\pi\) | ||
0.804218 | − | 0.594334i | \(-0.202584\pi\) | |||||||
\(464\) | 0.712521 | + | 44.8943i | 0.00153561 | + | 0.0967550i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 93.9734 | + | 38.4890i | 0.201660 | + | 0.0825944i | ||||
\(467\) | − | 10.0013i | − | 0.0214160i | −0.999943 | − | 0.0107080i | \(-0.996591\pi\) | ||
0.999943 | − | 0.0107080i | \(-0.00340852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −104.681 | −0.223201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 495.234 | − | 212.073i | 1.04923 | − | 0.449307i | ||||
\(473\) | 54.0312 | 0.114231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 112.695 | − | 114.498i | 0.236755 | − | 0.240542i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −236.125 | + | 576.515i | −0.493985 | + | 1.20610i | ||||
\(479\) | − | 548.574i | − | 1.14525i | −0.819818 | − | 0.572625i | \(-0.805925\pi\) | ||
0.819818 | − | 0.572625i | \(-0.194075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −663.412 | −1.37924 | ||||||||
\(482\) | 590.573 | + | 241.883i | 1.22525 | + | 0.501831i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 342.183 | + | 336.795i | 0.706989 | + | 0.695858i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 429.005i | 0.880913i | 0.897774 | + | 0.440457i | \(0.145183\pi\) | ||||
−0.897774 | + | 0.440457i | \(0.854817\pi\) | |||||||
\(488\) | 113.470 | + | 264.976i | 0.232521 | + | 0.542985i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 380.015i | − | 0.773961i | −0.922088 | − | 0.386980i | \(-0.873518\pi\) | ||
0.922088 | − | 0.386980i | \(-0.126482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.5188 | −0.0558190 | ||||||||
\(494\) | 307.172 | − | 749.981i | 0.621805 | − | 1.51818i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.4922 | − | 0.499815i | 0.0634923 | − | 0.00100769i | ||||
\(497\) | −491.938 | −0.989814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 395.763i | − | 0.793112i | −0.918011 | − | 0.396556i | \(-0.870205\pi\) | ||
0.918011 | − | 0.396556i | \(-0.129795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 66.4257 | − | 162.183i | 0.132322 | − | 0.323073i | ||||
\(503\) | − | 325.436i | − | 0.646991i | −0.946230 | − | 0.323495i | \(-0.895142\pi\) | ||
0.946230 | − | 0.323495i | \(-0.104858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.4297 | + | 13.6919i | 0.0660666 | + | 0.0270591i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 210.602 | − | 213.971i | 0.414570 | − | 0.421202i | ||||
\(509\) | −1.22499 | −0.00240667 | −0.00120333 | − | 0.999999i | \(-0.500383\pi\) | ||||
−0.00120333 | + | 0.999999i | \(0.500383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 285.908i | − | 0.559506i | ||||||
\(512\) | −479.720 | − | 178.922i | −0.936952 | − | 0.349458i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 217.073 | + | 88.9074i | 0.422322 | + | 0.172972i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.9063 | −0.112004 | ||||||||
\(518\) | −139.109 | + | 339.645i | −0.268551 | + | 0.655685i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −865.375 | −1.66099 | −0.830494 | − | 0.557027i | \(-0.811942\pi\) | ||||
−0.830494 | + | 0.557027i | \(0.811942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 295.370i | − | 0.564761i | −0.959302 | − | 0.282380i | \(-0.908876\pi\) | ||
0.959302 | − | 0.282380i | \(-0.0911240\pi\) | |||||||
\(524\) | 392.250 | − | 398.525i | 0.748569 | − | 0.760543i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.2453 | − | 88.4953i | 0.0689074 | − | 0.168242i | ||||
\(527\) | 19.3037i | 0.0366294i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 192.225 | 0.363374 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −319.555 | − | 314.523i | −0.600667 | − | 0.591209i | ||||
\(533\) | 251.706 | 0.472244 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −187.960 | + | 80.4897i | −0.350672 | + | 0.150167i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −887.056 | − | 363.314i | −1.64880 | − | 0.675305i | ||||
\(539\) | − | 31.7176i | − | 0.0588453i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −200.250 | −0.370148 | −0.185074 | − | 0.982725i | \(-0.559252\pi\) | ||||
−0.185074 | + | 0.982725i | \(0.559252\pi\) | |||||||
\(542\) | 183.586 | − | 448.237i | 0.338719 | − | 0.827006i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 114.312 | − | 292.238i | 0.210132 | − | 0.537203i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 989.581i | 1.80911i | 0.426361 | + | 0.904553i | \(0.359795\pi\) | ||||
−0.426361 | + | 0.904553i | \(0.640205\pi\) | |||||||
\(548\) | 160.107 | + | 157.586i | 0.292166 | + | 0.287566i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 76.8026i | 0.139388i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 132.250 | 0.239150 | ||||||||
\(554\) | −61.5500 | − | 25.2092i | −0.111101 | − | 0.0455040i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 545.301 | − | 554.024i | 0.980757 | − | 0.996446i | ||||
\(557\) | 641.319 | 1.15138 | 0.575690 | − | 0.817668i | \(-0.304733\pi\) | ||||
0.575690 | + | 0.817668i | \(0.304733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 812.798i | − | 1.45402i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 455.408 | + | 186.523i | 0.810334 | + | 0.331891i | ||||
\(563\) | 382.237i | 0.678928i | 0.940619 | + | 0.339464i | \(0.110246\pi\) | ||||
−0.940619 | + | 0.339464i | \(0.889754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.15552 | + | 2.82127i | −0.00204155 | + | 0.00498458i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −883.297 | + | 378.252i | −1.55510 | + | 0.665937i | ||||
\(569\) | 576.025 | 1.01235 | 0.506173 | − | 0.862432i | \(-0.331060\pi\) | ||||
0.506173 | + | 0.862432i | \(0.331060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1100.67i | 1.92762i | 0.266582 | + | 0.963812i | \(0.414106\pi\) | ||||
−0.266582 | + | 0.963812i | \(0.585894\pi\) | |||||||
\(572\) | −40.8907 | + | 41.5448i | −0.0714872 | + | 0.0726307i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 52.7797 | − | 128.865i | 0.0919506 | − | 0.224504i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −326.475 | −0.565814 | −0.282907 | − | 0.959147i | \(-0.591299\pi\) | ||||
−0.282907 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(578\) | −356.900 | − | 146.177i | −0.617474 | − | 0.252901i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −279.194 | −0.480540 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 87.8201i | 0.150635i | ||||||||
\(584\) | −219.835 | − | 513.360i | −0.376430 | − | 0.879042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 830.989 | + | 340.351i | 1.41807 | + | 0.580803i | ||||
\(587\) | − | 90.5502i | − | 0.154259i | −0.997021 | − | 0.0771296i | \(-0.975424\pi\) | ||
0.997021 | − | 0.0771296i | \(-0.0245755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.8750 | 0.0914686 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.3765 | + | 716.810i | 0.0192171 | + | 1.21083i | ||||
\(593\) | −896.163 | −1.51124 | −0.755618 | − | 0.655013i | \(-0.772663\pi\) | ||||
−0.755618 | + | 0.655013i | \(0.772663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 316.062 | + | 311.086i | 0.530306 | + | 0.521956i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 205.969 | − | 502.887i | 0.344429 | − | 0.840947i | ||||
\(599\) | − | 1157.76i | − | 1.93282i | −0.257001 | − | 0.966411i | \(-0.582734\pi\) | ||
0.257001 | − | 0.966411i | \(-0.417266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −438.969 | −0.730397 | −0.365199 | − | 0.930930i | \(-0.618999\pi\) | ||||
−0.365199 | + | 0.930930i | \(0.618999\pi\) | |||||||
\(602\) | −416.125 | − | 170.434i | −0.691237 | − | 0.283112i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 397.773 | − | 404.137i | 0.658565 | − | 0.669100i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1156.84i | − | 1.90583i | −0.303237 | − | 0.952915i | \(-0.598067\pi\) | ||
0.303237 | − | 0.952915i | \(-0.401933\pi\) | |||||||
\(608\) | −815.613 | − | 319.035i | −1.34147 | − | 0.524728i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 871.090i | 1.42568i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 409.225 | 0.667577 | 0.333789 | − | 0.942648i | \(-0.391673\pi\) | ||||
0.333789 | + | 0.942648i | \(0.391673\pi\) | |||||||
\(614\) | 8.08673 | − | 19.7443i | 0.0131706 | − | 0.0321568i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.6953 | + | 29.6461i | 0.0206092 | + | 0.0481267i | ||||
\(617\) | −999.150 | −1.61937 | −0.809684 | − | 0.586866i | \(-0.800361\pi\) | ||||
−0.809684 | + | 0.586866i | \(0.800361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 266.604i | 0.430701i | 0.976537 | + | 0.215350i | \(0.0690894\pi\) | ||||
−0.976537 | + | 0.215350i | \(0.930911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −280.602 | + | 685.107i | −0.451128 | + | 1.10146i | ||||
\(623\) | 277.716i | 0.445772i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −79.0515 | − | 32.3774i | −0.126280 | − | 0.0517210i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 509.827 | + | 501.799i | 0.811826 | + | 0.799043i | ||||
\(629\) | −439.381 | −0.698539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1053.40i | 1.66941i | 0.550696 | + | 0.834706i | \(0.314362\pi\) | ||||
−0.550696 | + | 0.834706i | \(0.685638\pi\) | |||||||
\(632\) | 237.461 | − | 101.687i | 0.375729 | − | 0.160898i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 264.847 | + | 108.474i | 0.417739 | + | 0.171095i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −477.131 | −0.749029 | ||||||||
\(638\) | 2.09373 | − | 5.11198i | 0.00328170 | − | 0.00801250i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −686.187 | −1.07050 | −0.535248 | − | 0.844695i | \(-0.679782\pi\) | ||||
−0.535248 | + | 0.844695i | \(0.679782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 454.690i | − | 0.707138i | −0.935408 | − | 0.353569i | \(-0.884968\pi\) | ||
0.935408 | − | 0.353569i | \(-0.115032\pi\) | |||||||
\(644\) | −214.272 | − | 210.898i | −0.332720 | − | 0.327482i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 203.441 | − | 496.716i | 0.314925 | − | 0.768910i | ||||
\(647\) | 928.430i | 1.43498i | 0.696570 | + | 0.717489i | \(0.254708\pi\) | ||||
−0.696570 | + | 0.717489i | \(0.745292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −66.2812 | −0.102128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 624.410 | − | 634.399i | 0.957684 | − | 0.973004i | ||||
\(653\) | 536.744 | 0.821966 | 0.410983 | − | 0.911643i | \(-0.365186\pi\) | ||||
0.410983 | + | 0.911643i | \(0.365186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.31639 | − | 271.966i | −0.00657986 | − | 0.414582i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 445.969 | + | 182.657i | 0.677764 | + | 0.277594i | ||||
\(659\) | 967.387i | 1.46796i | 0.679170 | + | 0.733981i | \(0.262340\pi\) | ||||
−0.679170 | + | 0.733981i | \(0.737660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −534.281 | −0.808292 | −0.404146 | − | 0.914694i | \(-0.632431\pi\) | ||||
−0.404146 | + | 0.914694i | \(0.632431\pi\) | |||||||
\(662\) | −39.5430 | + | 96.5469i | −0.0597327 | + | 0.145841i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −501.305 | + | 214.673i | −0.754978 | + | 0.323303i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.4987i | 0.0772094i | ||||||||
\(668\) | −597.328 | + | 606.884i | −0.894204 | + | 0.908508i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 35.4639i | − | 0.0528523i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 129.225 | 0.192013 | 0.0960067 | − | 0.995381i | \(-0.469393\pi\) | ||||
0.0960067 | + | 0.995381i | \(0.469393\pi\) | |||||||
\(674\) | 817.860 | + | 334.973i | 1.21344 | + | 0.496993i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 143.180 | + | 140.926i | 0.211805 | + | 0.208471i | ||||
\(677\) | 111.163 | 0.164199 | 0.0820993 | − | 0.996624i | \(-0.473838\pi\) | ||||
0.0820993 | + | 0.996624i | \(0.473838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.76132i | − | 0.00701226i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.58592 | − | 1.46869i | −0.00525794 | − | 0.00215351i | ||||
\(683\) | 710.467i | 1.04022i | 0.854101 | + | 0.520108i | \(0.174108\pi\) | ||||
−0.854101 | + | 0.520108i | \(0.825892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −252.178 | + | 615.710i | −0.367607 | + | 0.897536i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −878.219 | + | 13.9383i | −1.27648 | + | 0.0202591i | ||||
\(689\) | 1321.09 | 1.91740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 64.0073i | − | 0.0926300i | −0.998927 | − | 0.0463150i | \(-0.985252\pi\) | ||
0.998927 | − | 0.0463150i | \(-0.0147478\pi\) | |||||||
\(692\) | 59.2250 | + | 58.2925i | 0.0855853 | + | 0.0842377i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 65.0539 | − | 158.833i | 0.0937375 | − | 0.228867i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 166.706 | 0.239177 | ||||||||
\(698\) | −756.842 | − | 309.982i | −1.08430 | − | 0.444100i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 122.031 | 0.174082 | 0.0870408 | − | 0.996205i | \(-0.472259\pi\) | ||||
0.0870408 | + | 0.996205i | \(0.472259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1226.28i | 1.74435i | ||||||||
\(704\) | 45.5899 | + | 43.4695i | 0.0647584 | + | 0.0617464i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −816.495 | − | 334.414i | −1.15651 | − | 0.473675i | ||||
\(707\) | 540.764i | 0.764872i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1349.09 | −1.90280 | −0.951402 | − | 0.307953i | \(-0.900356\pi\) | ||||
−0.951402 | + | 0.307953i | \(0.900356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 213.537 | + | 498.652i | 0.299911 | + | 0.700354i | ||||
\(713\) | 36.1250 | 0.0506662 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −104.410 | + | 106.080i | −0.145824 | + | 0.148157i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −326.570 | + | 797.343i | −0.454833 | + | 1.11051i | ||||
\(719\) | 1101.82i | 1.53243i | 0.642584 | + | 0.766216i | \(0.277862\pi\) | ||||
−0.642584 | + | 0.766216i | \(0.722138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −457.087 | −0.633963 | ||||||||
\(722\) | −718.161 | − | 294.139i | −0.994683 | − | 0.407395i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 906.905 | + | 892.625i | 1.25263 | + | 1.23291i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.7188i | − | 0.0436298i | −0.999762 | − | 0.0218149i | \(-0.993056\pi\) | ||
0.999762 | − | 0.0218149i | \(-0.00694445\pi\) | |||||||
\(728\) | 445.969 | − | 190.976i | 0.612594 | − | 0.262330i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 538.320i | − | 0.736415i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 121.319 | 0.165510 | 0.0827549 | − | 0.996570i | \(-0.473628\pi\) | ||||
0.0827549 | + | 0.996570i | \(0.473628\pi\) | |||||||
\(734\) | −262.816 | + | 641.682i | −0.358059 | + | 0.874226i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −546.895 | − | 213.923i | −0.743064 | − | 0.290656i | ||||
\(737\) | 25.1562 | 0.0341333 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 311.498i | − | 0.421513i | −0.977539 | − | 0.210757i | \(-0.932407\pi\) | ||
0.977539 | − | 0.210757i | \(-0.0675927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 277.016 | − | 676.352i | 0.373336 | − | 0.911526i | ||||
\(743\) | − | 298.259i | − | 0.401425i | −0.979650 | − | 0.200712i | \(-0.935674\pi\) | ||
0.979650 | − | 0.200712i | \(-0.0643257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1068.43 | + | 437.601i | 1.43222 | + | 0.586597i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.0821 | + | 27.5153i | −0.0362060 | + | 0.0367852i | ||||
\(749\) | −255.006 | −0.340462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 580.864i | − | 0.773454i | −0.922194 | − | 0.386727i | \(-0.873606\pi\) | ||
0.922194 | − | 0.386727i | \(-0.126394\pi\) | |||||||
\(752\) | 941.203 | − | 14.9379i | 1.25160 | − | 0.0198642i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −76.9000 | − | 31.4962i | −0.101989 | − | 0.0417721i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −507.600 | −0.670541 | −0.335271 | − | 0.942122i | \(-0.608828\pi\) | ||||
−0.335271 | + | 0.942122i | \(0.608828\pi\) | |||||||
\(758\) | −379.254 | + | 925.974i | −0.500335 | + | 1.22160i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −240.875 | −0.316524 | −0.158262 | − | 0.987397i | \(-0.550589\pi\) | ||||
−0.158262 | + | 0.987397i | \(0.550589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 357.122i | 0.468050i | ||||||||
\(764\) | 723.742 | − | 735.320i | 0.947306 | − | 0.962461i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 298.027 | − | 727.652i | 0.389069 | − | 0.949937i | ||||
\(767\) | 997.075i | 1.29997i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −161.681 | −0.210249 | −0.105124 | − | 0.994459i | \(-0.533524\pi\) | ||||
−0.105124 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −364.526 | − | 358.786i | −0.472184 | − | 0.464749i | ||||
\(773\) | −545.506 | −0.705700 | −0.352850 | − | 0.935680i | \(-0.614787\pi\) | ||||
−0.352850 | + | 0.935680i | \(0.614787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.66100 | − | 8.54918i | −0.00471778 | − | 0.0110170i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 182.811 | + | 74.8744i | 0.234975 | + | 0.0962396i | ||||
\(779\) | − | 465.263i | − | 0.597257i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 118.219 | 0.151368 | ||||||||
\(782\) | 136.414 | − | 333.064i | 0.174443 | − | 0.425913i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.18210 | + | 515.535i | 0.0104363 | + | 0.657570i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 953.227i | − | 1.21122i | −0.795763 | − | 0.605608i | \(-0.792930\pi\) | ||
0.795763 | − | 0.605608i | \(-0.207070\pi\) | |||||||
\(788\) | 277.345 | + | 272.978i | 0.351961 | + | 0.346419i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 344.963i | − | 0.436110i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −533.488 | −0.672746 | ||||||||
\(794\) | −368.722 | − | 151.019i | −0.464385 | − | 0.190200i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.2343 | − | 56.1179i | 0.0693898 | − | 0.0704999i | ||||
\(797\) | 456.975 | 0.573369 | 0.286684 | − | 0.958025i | \(-0.407447\pi\) | ||||
0.286684 | + | 0.958025i | \(0.407447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 576.927i | 0.722061i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 194.505 | + | 79.6642i | 0.242526 | + | 0.0993319i | ||||
\(803\) | 68.7071i | 0.0855631i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.0937 | + | 53.9433i | −0.0274116 | + | 0.0669272i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 415.795 | + | 970.968i | 0.514598 | + | 1.20169i | ||||
\(809\) | −1073.79 | −1.32730 | −0.663651 | − | 0.748042i | \(-0.730994\pi\) | ||||
−0.663651 | + | 0.748042i | \(0.730994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 108.299i | 0.133537i | 0.997768 | + | 0.0667687i | \(0.0212690\pi\) | ||||
−0.997768 | + | 0.0667687i | \(0.978731\pi\) | |||||||
\(812\) | −32.2499 | + | 32.7658i | −0.0397167 | + | 0.0403520i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.4297 | − | 81.6209i | 0.0410684 | − | 0.100271i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1502.41 | −1.83893 | ||||||||
\(818\) | 681.388 | + | 279.078i | 0.832993 | + | 0.341171i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1262.19 | 1.53738 | 0.768689 | − | 0.639623i | \(-0.220909\pi\) | ||||
0.768689 | + | 0.639623i | \(0.220909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 862.264i | − | 1.04771i | −0.851808 | − | 0.523854i | \(-0.824494\pi\) | ||
0.851808 | − | 0.523854i | \(-0.175506\pi\) | |||||||
\(824\) | −820.722 | + | 351.456i | −0.996022 | + | 0.426524i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 510.469 | + | 209.074i | 0.618001 | + | 0.253116i | ||||
\(827\) | − | 720.596i | − | 0.871338i | −0.900107 | − | 0.435669i | \(-0.856512\pi\) | ||
0.900107 | − | 0.435669i | \(-0.143488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 385.569 | 0.465101 | 0.232550 | − | 0.972584i | \(-0.425293\pi\) | ||||
0.232550 | + | 0.972584i | \(0.425293\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 653.916 | − | 685.813i | 0.785956 | − | 0.824295i | ||||
\(833\) | −316.006 | −0.379359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 76.7930 | + | 75.5838i | 0.0918576 | + | 0.0904113i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.6680 | − | 87.0858i | 0.0425632 | − | 0.103921i | ||||
\(839\) | 561.530i | 0.669284i | 0.942345 | + | 0.334642i | \(0.108615\pi\) | ||||
−0.942345 | + | 0.334642i | \(0.891385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −833.125 | −0.990636 | ||||||||
\(842\) | 14.4593 | + | 5.92214i | 0.0171726 | + | 0.00703343i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −660.223 | + | 670.784i | −0.782254 | + | 0.794768i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 491.616i | 0.580420i | ||||||||
\(848\) | −22.6547 | − | 1427.42i | −0.0267154 | − | 1.68328i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 822.259i | 0.966227i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −151.087 | −0.177125 | −0.0885624 | − | 0.996071i | \(-0.528227\pi\) | ||||
−0.0885624 | + | 0.996071i | \(0.528227\pi\) | |||||||
\(854\) | −111.866 | + | 273.128i | −0.130990 | + | 0.319822i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −457.876 | + | 196.075i | −0.534902 | + | 0.229060i | ||||
\(857\) | 444.225 | 0.518349 | 0.259174 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259174 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 731.867i | 0.851999i | 0.904723 | + | 0.426000i | \(0.140077\pi\) | ||||
−0.904723 | + | 0.426000i | \(0.859923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −516.414 | + | 1260.86i | −0.599088 | + | 1.46271i | ||||
\(863\) | 965.801i | 1.11912i | 0.828790 | + | 0.559560i | \(0.189030\pi\) | ||||
−0.828790 | + | 0.559560i | \(0.810970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.53042 | + | 3.08426i | 0.00869564 | + | 0.00356150i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.9844 | + | 22.6225i | 0.0264797 | + | 0.0260628i | ||||
\(869\) | −31.7813 | −0.0365723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 378.428i | − | 0.434475i | ||||||
\(872\) | 274.592 | + | 641.229i | 0.314899 | + | 0.735355i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −929.555 | − | 380.721i | −1.06356 | − | 0.435607i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1440.78 | 1.64284 | 0.821422 | − | 0.570320i | \(-0.193181\pi\) | ||||
0.821422 | + | 0.570320i | \(0.193181\pi\) | |||||||
\(878\) | −134.031 | + | 327.246i | −0.152655 | + | 0.372718i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1538.44 | −1.74624 | −0.873120 | − | 0.487505i | \(-0.837907\pi\) | ||||
−0.873120 | + | 0.487505i | \(0.837907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 229.616i | − | 0.260040i | −0.991511 | − | 0.130020i | \(-0.958496\pi\) | ||
0.991511 | − | 0.130020i | \(-0.0415042\pi\) | |||||||
\(884\) | 413.916 | + | 407.398i | 0.468230 | + | 0.460858i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −355.860 | + | 868.856i | −0.401648 | + | 0.980650i | ||||
\(887\) | − | 456.945i | − | 0.515158i | −0.966257 | − | 0.257579i | \(-0.917075\pi\) | ||
0.966257 | − | 0.257579i | \(-0.0829248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 307.412 | 0.345796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −91.0469 | + | 92.5033i | −0.102070 | + | 0.103703i | ||||
\(893\) | 1610.16 | 1.80309 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −213.995 | − | 478.589i | −0.238834 | − | 0.534140i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −952.123 | − | 389.964i | −1.06027 | − | 0.434258i | ||||
\(899\) | − | 5.52413i | − | 0.00614475i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 874.962 | 0.971102 | ||||||||
\(902\) | −12.6836 | + | 30.9679i | −0.0140617 | + | 0.0343325i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −265.243 | − | 619.397i | −0.293410 | − | 0.685174i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 797.272i | − | 0.879021i | −0.898237 | − | 0.439511i | \(-0.855152\pi\) | ||
0.898237 | − | 0.439511i | \(-0.144848\pi\) | |||||||
\(908\) | 812.562 | − | 825.561i | 0.894892 | − | 0.909208i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 531.621i | 0.583557i | 0.956486 | + | 0.291779i | \(0.0942470\pi\) | ||||
−0.956486 | + | 0.291779i | \(0.905753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.0937 | 0.0734871 | ||||||||
\(914\) | −1266.93 | − | 518.900i | −1.38614 | − | 0.567724i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 283.047 | + | 278.590i | 0.309003 | + | 0.304138i | ||||
\(917\) | 572.562 | 0.624386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 593.469i | 0.645777i | 0.946437 | + | 0.322888i | \(0.104654\pi\) | ||||
−0.946437 | + | 0.322888i | \(0.895346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −378.022 | − | 154.828i | −0.410002 | − | 0.167926i | ||||
\(923\) | − | 1778.38i | − | 1.92673i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 417.184 | − | 1018.58i | 0.450523 | − | 1.09998i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.7125 | + | 83.6297i | −0.0352506 | + | 0.0901182i | ||||
\(929\) | 198.775 | 0.213967 | 0.106983 | − | 0.994261i | \(-0.465881\pi\) | ||||
0.106983 | + | 0.994261i | \(0.465881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 881.948i | 0.947312i | ||||||||
\(932\) | 144.748 | + | 142.469i | 0.155309 | + | 0.152864i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.58125 | − | 18.5101i | 0.00811697 | − | 0.0198181i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1200.43 | 1.28114 | 0.640572 | − | 0.767898i | \(-0.278697\pi\) | ||||
0.640572 | + | 0.767898i | \(0.278697\pi\) | |||||||
\(938\) | −193.742 | − | 79.3515i | −0.206548 | − | 0.0845965i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1338.16 | 1.42206 | 0.711029 | − | 0.703163i | \(-0.248230\pi\) | ||||
0.711029 | + | 0.703163i | \(0.248230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 311.974i | − | 0.330832i | ||||||
\(944\) | 1077.33 | − | 17.0984i | 1.14124 | − | 0.0181127i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 100.000 | + | 40.9573i | 0.105708 | + | 0.0432952i | ||||
\(947\) | − | 586.516i | − | 0.619341i | −0.950844 | − | 0.309671i | \(-0.899781\pi\) | ||
0.950844 | − | 0.309671i | \(-0.100219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1033.57 | 1.08911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 295.367 | − | 126.484i | 0.310260 | − | 0.132862i | ||||
\(953\) | −1598.72 | −1.67757 | −0.838785 | − | 0.544462i | \(-0.816734\pi\) | ||||
−0.838785 | + | 0.544462i | \(0.816734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −874.031 | + | 888.013i | −0.914259 | + | 0.928884i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 415.836 | − | 1015.29i | 0.434067 | − | 1.05980i | ||||
\(959\) | 230.026i | 0.239861i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 957.125 | 0.995968 | ||||||||
\(962\) | −1227.83 | − | 502.887i | −1.27633 | − | 0.522751i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 909.666 | + | 895.344i | 0.943637 | + | 0.928780i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 320.675i | 0.331619i | 0.986158 | + | 0.165809i | \(0.0530236\pi\) | ||||
−0.986158 | + | 0.165809i | \(0.946976\pi\) | |||||||
\(968\) | 378.005 | + | 882.719i | 0.390501 | + | 0.911900i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1402.93i | − | 1.44483i | −0.691459 | − | 0.722416i | \(-0.743032\pi\) | ||
0.691459 | − | 0.722416i | \(-0.256968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 795.969 | 0.818056 | ||||||||
\(974\) | −325.198 | + | 793.994i | −0.333879 | + | 0.815189i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.14852 | + | 576.427i | 0.00937349 | + | 0.590602i | ||||
\(977\) | −1226.24 | −1.25511 | −0.627556 | − | 0.778572i | \(-0.715944\pi\) | ||||
−0.627556 | + | 0.778572i | \(0.715944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 66.7386i | − | 0.0681702i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 288.062 | − | 703.324i | 0.293343 | − | 0.716216i | ||||
\(983\) | − | 1372.96i | − | 1.39670i | −0.715754 | − | 0.698352i | \(-0.753917\pi\) | ||
0.715754 | − | 0.698352i | \(-0.246083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −50.9312 | − | 20.8601i | −0.0516544 | − | 0.0211562i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1137.02 | − | 1155.20i | 1.15083 | − | 1.16924i | ||||
\(989\) | −1007.41 | −1.01862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 362.298i | − | 0.365588i | −0.983151 | − | 0.182794i | \(-0.941486\pi\) | ||
0.983151 | − | 0.182794i | \(-0.0585142\pi\) | |||||||
\(992\) | 58.6640 | + | 22.9470i | 0.0591371 | + | 0.0231320i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −910.469 | − | 372.903i | −0.915964 | − | 0.375154i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 941.087 | 0.943919 | 0.471960 | − | 0.881620i | \(-0.343547\pi\) | ||||
0.471960 | + | 0.881620i | \(0.343547\pi\) | |||||||
\(998\) | 300.000 | − | 732.470i | 0.300601 | − | 0.733938i | ||||
\(999\) | 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 | 900.3.c.m.451.4 | 4 | ||
3.2 | odd | 2 | 100.3.b.d.51.1 | ✓ | 4 | ||
4.3 | odd | 2 | inner | 900.3.c.m.451.3 | 4 | ||
5.2 | odd | 4 | 900.3.f.d.199.4 | 8 | |||
5.3 | odd | 4 | 900.3.f.d.199.5 | 8 | |||
5.4 | even | 2 | 900.3.c.l.451.1 | 4 | |||
12.11 | even | 2 | 100.3.b.d.51.2 | yes | 4 | ||
15.2 | even | 4 | 100.3.d.a.99.5 | 8 | |||
15.8 | even | 4 | 100.3.d.a.99.4 | 8 | |||
15.14 | odd | 2 | 100.3.b.e.51.4 | yes | 4 | ||
20.3 | even | 4 | 900.3.f.d.199.3 | 8 | |||
20.7 | even | 4 | 900.3.f.d.199.6 | 8 | |||
20.19 | odd | 2 | 900.3.c.l.451.2 | 4 | |||
24.5 | odd | 2 | 1600.3.b.p.1151.1 | 4 | |||
24.11 | even | 2 | 1600.3.b.p.1151.4 | 4 | |||
60.23 | odd | 4 | 100.3.d.a.99.6 | 8 | |||
60.47 | odd | 4 | 100.3.d.a.99.3 | 8 | |||
60.59 | even | 2 | 100.3.b.e.51.3 | yes | 4 | ||
120.29 | odd | 2 | 1600.3.b.o.1151.4 | 4 | |||
120.53 | even | 4 | 1600.3.h.o.1599.7 | 8 | |||
120.59 | even | 2 | 1600.3.b.o.1151.1 | 4 | |||
120.77 | even | 4 | 1600.3.h.o.1599.1 | 8 | |||
120.83 | odd | 4 | 1600.3.h.o.1599.2 | 8 | |||
120.107 | odd | 4 | 1600.3.h.o.1599.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.3.b.d.51.1 | ✓ | 4 | 3.2 | odd | 2 | ||
100.3.b.d.51.2 | yes | 4 | 12.11 | even | 2 | ||
100.3.b.e.51.3 | yes | 4 | 60.59 | even | 2 | ||
100.3.b.e.51.4 | yes | 4 | 15.14 | odd | 2 | ||
100.3.d.a.99.3 | 8 | 60.47 | odd | 4 | |||
100.3.d.a.99.4 | 8 | 15.8 | even | 4 | |||
100.3.d.a.99.5 | 8 | 15.2 | even | 4 | |||
100.3.d.a.99.6 | 8 | 60.23 | odd | 4 | |||
900.3.c.l.451.1 | 4 | 5.4 | even | 2 | |||
900.3.c.l.451.2 | 4 | 20.19 | odd | 2 | |||
900.3.c.m.451.3 | 4 | 4.3 | odd | 2 | inner | ||
900.3.c.m.451.4 | 4 | 1.1 | even | 1 | trivial | ||
900.3.f.d.199.3 | 8 | 20.3 | even | 4 | |||
900.3.f.d.199.4 | 8 | 5.2 | odd | 4 | |||
900.3.f.d.199.5 | 8 | 5.3 | odd | 4 | |||
900.3.f.d.199.6 | 8 | 20.7 | even | 4 | |||
1600.3.b.o.1151.1 | 4 | 120.59 | even | 2 | |||
1600.3.b.o.1151.4 | 4 | 120.29 | odd | 2 | |||
1600.3.b.p.1151.1 | 4 | 24.5 | odd | 2 | |||
1600.3.b.p.1151.4 | 4 | 24.11 | even | 2 | |||
1600.3.h.o.1599.1 | 8 | 120.77 | even | 4 | |||
1600.3.h.o.1599.2 | 8 | 120.83 | odd | 4 | |||
1600.3.h.o.1599.7 | 8 | 120.53 | even | 4 | |||
1600.3.h.o.1599.8 | 8 | 120.107 | odd | 4 |