Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
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.f (of order \(2\), degree \(1\), not 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: | \(8\) |
Coefficient field: | 8.0.18084870400.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 40x^{4} + 17x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(-2.53999 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.d.199.5 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.758030 | + | 1.85078i | 0.379015 | + | 0.925391i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.85078 | + | 2.80590i | −0.712695 | + | 0.701474i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.09573 | 0.585104 | 0.292552 | − | 0.956250i | \(-0.405495\pi\) | ||||
0.292552 | + | 0.956250i | \(0.405495\pi\) | |||||||
\(8\) | −7.35408 | − | 3.14922i | −0.919259 | − | 0.393652i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.984255i | 0.0894777i | 0.998999 | + | 0.0447389i | \(0.0142456\pi\) | ||||
−0.998999 | + | 0.0447389i | \(0.985754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.8062i | 1.13894i | 0.822011 | + | 0.569471i | \(0.192852\pi\) | ||||
−0.822011 | + | 0.569471i | \(0.807148\pi\) | |||||||
\(14\) | 3.10469 | + | 7.58030i | 0.221763 | + | 0.541450i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.253905 | − | 15.9980i | 0.0158691 | − | 0.999874i | ||||
\(17\) | − | 9.80625i | − | 0.576838i | −0.957504 | − | 0.288419i | \(-0.906870\pi\) | ||
0.957504 | − | 0.288419i | \(-0.0931296\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | −1.82164 | + | 0.746095i | −0.0828018 | + | 0.0339134i | ||||
\(23\) | −18.3514 | −0.797888 | −0.398944 | − | 0.916975i | \(-0.630623\pi\) | ||||
−0.398944 | + | 0.916975i | \(0.630623\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −27.4031 | + | 11.2236i | −1.05397 | + | 0.431676i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −11.6760 | + | 11.4922i | −0.417001 | + | 0.410435i | ||||
\(29\) | −2.80625 | −0.0967672 | −0.0483836 | − | 0.998829i | \(-0.515407\pi\) | ||||
−0.0483836 | + | 0.998829i | \(0.515407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.96851i | 0.0635003i | 0.999496 | + | 0.0317502i | \(0.0101081\pi\) | ||||
−0.999496 | + | 0.0317502i | \(0.989892\pi\) | |||||||
\(32\) | 29.8012 | − | 11.6570i | 0.931289 | − | 0.364282i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.1492 | − | 7.43343i | 0.533801 | − | 0.218630i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.8062i | 1.21098i | 0.795853 | + | 0.605490i | \(0.207023\pi\) | ||||
−0.795853 | + | 0.605490i | \(0.792977\pi\) | |||||||
\(38\) | −50.6530 | + | 20.7461i | −1.33297 | + | 0.545950i | ||||
\(39\) | 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 | ||||||||
\(43\) | −54.8956 | −1.27664 | −0.638321 | − | 0.769771i | \(-0.720371\pi\) | ||||
−0.638321 | + | 0.769771i | \(0.720371\pi\) | |||||||
\(44\) | −2.76172 | − | 2.80590i | −0.0627663 | − | 0.0637703i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.9109 | − | 33.9645i | −0.302412 | − | 0.738358i | ||||
\(47\) | −58.8326 | −1.25176 | −0.625879 | − | 0.779920i | \(-0.715260\pi\) | ||||
−0.625879 | + | 0.779920i | \(0.715260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −32.2250 | −0.657653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −41.5448 | − | 42.2094i | −0.798938 | − | 0.811719i | ||||
\(53\) | 89.2250i | 1.68349i | 0.539875 | + | 0.841745i | \(0.318472\pi\) | ||||
−0.539875 | + | 0.841745i | \(0.681528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −30.1203 | − | 12.8984i | −0.537863 | − | 0.230328i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.12722 | − | 5.19375i | −0.0366762 | − | 0.0895474i | ||||
\(59\) | − | 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 | \(0.404568\pi\) | |||||||
\(62\) | −3.64328 | + | 1.49219i | −0.0587626 | + | 0.0240676i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 44.1648 | + | 46.3192i | 0.690076 | + | 0.723737i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.5586 | 0.381472 | 0.190736 | − | 0.981641i | \(-0.438913\pi\) | ||||
0.190736 | + | 0.981641i | \(0.438913\pi\) | |||||||
\(68\) | 27.5153 | + | 27.9555i | 0.404637 | + | 0.411110i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 120.110i | − | 1.69169i | −0.533430 | − | 0.845844i | \(-0.679097\pi\) | ||
0.533430 | − | 0.845844i | \(-0.320903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 69.8062i | 0.956250i | 0.878292 | + | 0.478125i | \(0.158683\pi\) | ||||
−0.878292 | + | 0.478125i | \(0.841317\pi\) | |||||||
\(74\) | −82.9266 | + | 33.9645i | −1.12063 | + | 0.458979i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76.7930 | − | 78.0214i | −1.01043 | − | 1.02660i | ||||
\(77\) | 4.03124i | 0.0523538i | ||||||||
\(78\) | 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 | ||||||||
\(82\) | −12.8865 | − | 31.4633i | −0.157153 | − | 0.383699i | ||||
\(83\) | −68.1670 | −0.821289 | −0.410645 | − | 0.911795i | \(-0.634696\pi\) | ||||
−0.410645 | + | 0.911795i | \(0.634696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −41.6125 | − | 101.600i | −0.483866 | − | 1.18139i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.09963 | − | 7.23828i | 0.0352231 | − | 0.0822532i | ||||
\(89\) | −67.8062 | −0.761868 | −0.380934 | − | 0.924602i | \(-0.624397\pi\) | ||||
−0.380934 | + | 0.924602i | \(0.624397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 60.6424i | 0.666400i | ||||||||
\(92\) | 52.3159 | − | 51.4922i | 0.568651 | − | 0.559698i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −44.5969 | − | 108.886i | −0.474435 | − | 1.15836i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.16251i | − | 0.0119846i | −0.999982 | − | 0.00599232i | \(-0.998093\pi\) | ||
0.999982 | − | 0.00599232i | \(-0.00190742\pi\) | |||||||
\(98\) | −24.4275 | − | 59.6414i | −0.249260 | − | 0.608586i | ||||
\(99\) | 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 | ||||||||
\(103\) | −111.601 | −1.08350 | −0.541752 | − | 0.840538i | \(-0.682239\pi\) | ||||
−0.541752 | + | 0.840538i | \(0.682239\pi\) | |||||||
\(104\) | 46.6281 | − | 108.886i | 0.448347 | − | 1.04698i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −165.136 | + | 67.6352i | −1.55789 | + | 0.638068i | ||||
\(107\) | 62.2615 | 0.581883 | 0.290942 | − | 0.956741i | \(-0.406031\pi\) | ||||
0.290942 | + | 0.956741i | \(0.406031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −87.1938 | −0.799943 | −0.399971 | − | 0.916528i | \(-0.630980\pi\) | ||||
−0.399971 | + | 0.916528i | \(0.630980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.03993 | − | 65.5234i | 0.00928507 | − | 0.585031i | ||||
\(113\) | 84.2250i | 0.745354i | 0.927961 | + | 0.372677i | \(0.121560\pi\) | ||||
−0.927961 | + | 0.372677i | \(0.878440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.00000 | − | 7.87404i | 0.0689655 | − | 0.0678796i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 124.634 | − | 51.0469i | 1.05622 | − | 0.432601i | ||||
\(119\) | − | 40.1637i | − | 0.337510i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.031 | 0.991994 | ||||||||
\(122\) | 27.3128 | + | 66.6859i | 0.223875 | + | 0.546606i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.52343 | − | 5.61179i | −0.0445438 | − | 0.0452564i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −75.0568 | −0.590999 | −0.295499 | − | 0.955343i | \(-0.595486\pi\) | ||||
−0.295499 | + | 0.955343i | \(0.595486\pi\) | |||||||
\(128\) | −52.2484 | + | 116.851i | −0.408191 | + | 0.912897i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 139.795i | 1.06714i | 0.845757 | + | 0.533568i | \(0.179149\pi\) | ||||
−0.845757 | + | 0.533568i | \(0.820851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 112.094i | 0.842810i | ||||||||
\(134\) | 19.3742 | + | 47.3034i | 0.144584 | + | 0.353011i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.8820 | + | 72.1159i | −0.227074 | + | 0.530264i | ||||
\(137\) | 56.1625i | 0.409945i | 0.978768 | + | 0.204973i | \(0.0657105\pi\) | ||||
−0.978768 | + | 0.204973i | \(0.934289\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 222.297 | − | 91.0469i | 1.56547 | − | 0.641175i | ||||
\(143\) | −14.5731 | −0.101910 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −129.196 | + | 52.9152i | −0.884905 | + | 0.362433i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −125.722 | − | 127.733i | −0.849470 | − | 0.863059i | ||||
\(149\) | −110.869 | −0.744085 | −0.372043 | − | 0.928216i | \(-0.621343\pi\) | ||||
−0.372043 | + | 0.928216i | \(0.621343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 141.763i | 0.938831i | 0.882977 | + | 0.469415i | \(0.155535\pi\) | ||||
−0.882977 | + | 0.469415i | \(0.844465\pi\) | |||||||
\(152\) | 86.1892 | − | 201.270i | 0.567034 | − | 1.32414i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.46095 | + | 3.05580i | −0.0484477 | + | 0.0198429i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 178.837i | 1.13909i | 0.821959 | + | 0.569546i | \(0.192881\pi\) | ||||
−0.821959 | + | 0.569546i | \(0.807119\pi\) | |||||||
\(158\) | 59.7612 | − | 24.4766i | 0.378235 | − | 0.154915i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.1625 | −0.466848 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.535 | 1.36525 | 0.682623 | − | 0.730771i | \(-0.260839\pi\) | ||||
0.682623 | + | 0.730771i | \(0.260839\pi\) | |||||||
\(164\) | 48.4633 | − | 47.7002i | 0.295508 | − | 0.290855i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −51.6727 | − | 126.162i | −0.311281 | − | 0.760014i | ||||
\(167\) | 212.883 | 1.27475 | 0.637375 | − | 0.770554i | \(-0.280020\pi\) | ||||
0.637375 | + | 0.770554i | \(0.280020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −50.2250 | −0.297189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 156.495 | − | 154.031i | 0.909856 | − | 0.895530i | ||||
\(173\) | − | 20.7750i | − | 0.120087i | −0.998196 | − | 0.0600434i | \(-0.980876\pi\) | ||
0.998196 | − | 0.0600434i | \(-0.0191239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.7461 | + | 0.249908i | 0.0894664 | + | 0.00141993i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −51.3992 | − | 125.495i | −0.288759 | − | 0.705025i | ||||
\(179\) | 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 | \(0.158346\pi\) | |||||||
\(182\) | −112.236 | + | 45.9688i | −0.616680 | + | 0.252576i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 134.958 | + | 57.7927i | 0.733466 | + | 0.314091i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65185 | 0.0516142 | ||||||||
\(188\) | 167.719 | − | 165.078i | 0.892122 | − | 0.878075i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 257.936i | 1.35045i | 0.737611 | + | 0.675226i | \(0.235954\pi\) | ||||
−0.737611 | + | 0.675226i | \(0.764046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 127.869i | 0.662532i | 0.943537 | + | 0.331266i | \(0.107476\pi\) | ||||
−0.943537 | + | 0.331266i | \(0.892524\pi\) | |||||||
\(194\) | 2.15155 | − | 0.881217i | 0.0110905 | − | 0.00454235i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 91.8664 | − | 90.4200i | 0.468706 | − | 0.461326i | ||||
\(197\) | 97.2875i | 0.493845i | 0.969035 | + | 0.246923i | \(0.0794193\pi\) | ||||
−0.969035 | + | 0.246923i | \(0.920581\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | 100.084 | + | 244.361i | 0.495464 | + | 1.20971i | ||||
\(203\) | −11.4936 | −0.0566189 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −84.5969 | − | 206.549i | −0.410664 | − | 1.00266i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 236.870 | + | 3.75938i | 1.13880 | + | 0.0180740i | ||||
\(209\) | −26.9375 | −0.128888 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 235.298i | − | 1.11516i | −0.830124 | − | 0.557579i | \(-0.811730\pi\) | ||
0.830124 | − | 0.557579i | \(-0.188270\pi\) | |||||||
\(212\) | −250.356 | − | 254.361i | −1.18092 | − | 1.19982i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 47.1961 | + | 115.232i | 0.220542 | + | 0.538469i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.06248i | 0.0371543i | ||||||||
\(218\) | −66.0955 | − | 161.377i | −0.303190 | − | 0.740259i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 145.194 | 0.656985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −32.4484 | −0.145509 | −0.0727543 | − | 0.997350i | \(-0.523179\pi\) | ||||
−0.0727543 | + | 0.997350i | \(0.523179\pi\) | |||||||
\(224\) | 122.058 | − | 47.7440i | 0.544901 | − | 0.213143i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −155.882 | + | 63.8451i | −0.689743 | + | 0.282500i | ||||
\(227\) | −289.591 | −1.27573 | −0.637866 | − | 0.770147i | \(-0.720183\pi\) | ||||
−0.637866 | + | 0.770147i | \(0.720183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −99.2875 | −0.433570 | −0.216785 | − | 0.976219i | \(-0.569557\pi\) | ||||
−0.216785 | + | 0.976219i | \(0.569557\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.6374 | + | 8.83749i | 0.0889541 | + | 0.0380926i | ||||
\(233\) | − | 50.7750i | − | 0.217918i | −0.994046 | − | 0.108959i | \(-0.965248\pi\) | ||
0.994046 | − | 0.108959i | \(-0.0347518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 188.953 | + | 191.976i | 0.800649 | + | 0.813457i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 74.3343 | − | 30.4453i | 0.312329 | − | 0.127922i | ||||
\(239\) | 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 | \(0.269699\pi\) | |||||||
\(242\) | 90.9873 | + | 222.152i | 0.375981 | + | 0.917982i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −102.717 | + | 101.100i | −0.420972 | + | 0.414344i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −405.224 | −1.64058 | ||||||||
\(248\) | 6.19927 | − | 14.4766i | 0.0249970 | − | 0.0583733i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 87.6294i | 0.349121i | 0.984646 | + | 0.174561i | \(0.0558505\pi\) | ||||
−0.984646 | + | 0.174561i | \(0.944149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.0625i | − | 0.0713932i | ||||||
\(254\) | −56.8953 | − | 138.914i | −0.223997 | − | 0.546904i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −255.871 | − | 8.12395i | −0.999496 | − | 0.0317342i | ||||
\(257\) | 117.287i | 0.456372i | 0.973618 | + | 0.228186i | \(0.0732794\pi\) | ||||
−0.973618 | + | 0.228186i | \(0.926721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 183.514i | 0.708549i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −258.730 | + | 105.969i | −0.987518 | + | 0.404461i | ||||
\(263\) | 47.8151 | 0.181806 | 0.0909032 | − | 0.995860i | \(-0.471025\pi\) | ||||
0.0909032 | + | 0.995860i | \(0.471025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −207.461 | + | 84.9704i | −0.779928 | + | 0.319438i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −72.8621 | + | 71.7149i | −0.271873 | + | 0.267593i | ||||
\(269\) | 479.287 | 1.78174 | 0.890869 | − | 0.454260i | \(-0.150096\pi\) | ||||
0.890869 | + | 0.454260i | \(0.150096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 242.188i | 0.893683i | 0.894613 | + | 0.446842i | \(0.147451\pi\) | ||||
−0.894613 | + | 0.446842i | \(0.852549\pi\) | |||||||
\(272\) | −156.880 | − | 2.48986i | −0.576766 | − | 0.00915389i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −103.945 | + | 42.5729i | −0.379360 | + | 0.155375i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 33.2562i | − | 0.120059i | −0.998197 | − | 0.0600293i | \(-0.980881\pi\) | ||
0.998197 | − | 0.0600293i | \(-0.0191194\pi\) | |||||||
\(278\) | 359.683 | − | 147.316i | 1.29382 | − | 0.529915i | ||||
\(279\) | 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 | ||||||||
\(283\) | −1.52437 | −0.00538646 | −0.00269323 | − | 0.999996i | \(-0.500857\pi\) | ||||
−0.00269323 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(284\) | 337.016 | + | 342.407i | 1.18667 | + | 1.20566i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.0469 | − | 26.9717i | −0.0386254 | − | 0.0943065i | ||||
\(287\) | −69.6274 | −0.242604 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 192.837 | 0.667258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −195.869 | − | 199.002i | −0.670784 | − | 0.681515i | ||||
\(293\) | − | 448.994i | − | 1.53240i | −0.642601 | − | 0.766201i | \(-0.722145\pi\) | ||
0.642601 | − | 0.766201i | \(-0.277855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 141.105 | − | 329.509i | 0.476705 | − | 1.11320i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −84.0418 | − | 205.194i | −0.282020 | − | 0.688570i | ||||
\(299\) | − | 271.716i | − | 0.908749i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −224.837 | −0.746968 | ||||||||
\(302\) | −262.373 | + | 107.461i | −0.868785 | + | 0.355831i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 437.840 | + | 6.94899i | 1.44026 | + | 0.0228585i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6681 | −0.0347495 | −0.0173747 | − | 0.999849i | \(-0.505531\pi\) | ||||
−0.0173747 | + | 0.999849i | \(0.505531\pi\) | |||||||
\(308\) | −11.3112 | − | 11.4922i | −0.0367248 | − | 0.0373123i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 370.172i | − | 1.19026i | −0.803628 | − | 0.595132i | \(-0.797100\pi\) | ||
0.803628 | − | 0.595132i | \(-0.202900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 42.7125i | 0.136462i | 0.997670 | + | 0.0682309i | \(0.0217354\pi\) | ||||
−0.997670 | + | 0.0682309i | \(0.978265\pi\) | |||||||
\(314\) | −330.989 | + | 135.564i | −1.05411 | + | 0.431733i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 90.6015 | + | 92.0509i | 0.286714 | + | 0.291300i | ||||
\(317\) | 143.100i | 0.451420i | 0.974195 | + | 0.225710i | \(0.0724701\pi\) | ||||
−0.974195 | + | 0.225710i | \(0.927530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.76206i | − | 0.00865851i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −56.9754 | − | 139.109i | −0.176942 | − | 0.432017i | ||||
\(323\) | 268.382 | 0.830903 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 168.688 | + | 411.864i | 0.517449 | + | 1.26339i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 125.019 | + | 53.5367i | 0.381156 | + | 0.163222i | ||||
\(329\) | −240.962 | −0.732409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 52.1655i | − | 0.157600i | −0.996890 | − | 0.0787999i | \(-0.974891\pi\) | ||
0.996890 | − | 0.0787999i | \(-0.0251088\pi\) | |||||||
\(332\) | 194.329 | − | 191.270i | 0.585329 | − | 0.576113i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 161.372 | + | 394.000i | 0.483149 | + | 1.17964i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 441.900i | 1.31128i | 0.755075 | + | 0.655638i | \(0.227600\pi\) | ||||
−0.755075 | + | 0.655638i | \(0.772400\pi\) | |||||||
\(338\) | −38.0721 | − | 92.9555i | −0.112639 | − | 0.275016i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.93752 | −0.00568186 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −332.676 | −0.969900 | ||||||||
\(344\) | 403.706 | + | 172.878i | 1.17356 | + | 0.502553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.4500 | − | 15.7481i | 0.111127 | − | 0.0455147i | ||||
\(347\) | −85.8196 | −0.247319 | −0.123659 | − | 0.992325i | \(-0.539463\pi\) | ||||
−0.123659 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 408.931 | 1.17172 | 0.585861 | − | 0.810411i | \(-0.300756\pi\) | ||||
0.585861 | + | 0.810411i | \(0.300756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.4735 | + | 29.3320i | 0.0325951 | + | 0.0833296i | ||||
\(353\) | 441.163i | 1.24975i | 0.780724 | + | 0.624876i | \(0.214851\pi\) | ||||
−0.780724 | + | 0.624876i | \(0.785149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 193.301 | − | 190.257i | 0.542980 | − | 0.534430i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −68.8694 | + | 28.2070i | −0.192373 | + | 0.0787906i | ||||
\(359\) | 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 | ||||||||
\(362\) | 241.148 | + | 588.780i | 0.666155 | + | 1.62646i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −170.156 | − | 172.878i | −0.467462 | − | 0.474940i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 346.709 | 0.944710 | 0.472355 | − | 0.881408i | \(-0.343404\pi\) | ||||
0.472355 | + | 0.881408i | \(0.343404\pi\) | |||||||
\(368\) | −4.65953 | + | 293.586i | −0.0126618 | + | 0.797788i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 365.442i | 0.985018i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 577.287i | − | 1.54769i | −0.633376 | − | 0.773844i | \(-0.718332\pi\) | ||
0.633376 | − | 0.773844i | \(-0.281668\pi\) | |||||||
\(374\) | 7.31639 | + | 17.8635i | 0.0195625 | + | 0.0477633i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 432.659 | + | 185.277i | 1.15069 | + | 0.492757i | ||||
\(377\) | − | 41.5500i | − | 0.110212i | ||||||
\(378\) | 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 | ||||||||
\(382\) | −477.384 | + | 195.523i | −1.24970 | + | 0.511841i | ||||
\(383\) | 393.159 | 1.02653 | 0.513263 | − | 0.858231i | \(-0.328437\pi\) | ||||
0.513263 | + | 0.858231i | \(0.328437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −236.657 | + | 96.9283i | −0.613101 | + | 0.251110i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.26188 | + | 3.31406i | 0.00840690 | + | 0.00854139i | ||||
\(389\) | −98.7750 | −0.253920 | −0.126960 | − | 0.991908i | \(-0.540522\pi\) | ||||
−0.126960 | + | 0.991908i | \(0.540522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 179.959i | 0.460252i | ||||||||
\(392\) | 236.985 | + | 101.484i | 0.604554 | + | 0.258887i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −180.058 | + | 73.7468i | −0.457000 | + | 0.187175i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 199.225i | − | 0.501826i | −0.968010 | − | 0.250913i | \(-0.919269\pi\) | ||
0.968010 | − | 0.250913i | \(-0.0807308\pi\) | |||||||
\(398\) | 36.4328 | − | 14.9219i | 0.0915397 | − | 0.0374922i | ||||
\(399\) | 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 | ||||||||
\(403\) | −29.1462 | −0.0723232 | ||||||||
\(404\) | −376.392 | + | 370.466i | −0.931664 | + | 0.916995i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.71252 | − | 21.2722i | −0.0214594 | − | 0.0523946i | ||||
\(407\) | −44.1008 | −0.108356 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −368.163 | −0.900153 | −0.450076 | − | 0.892990i | \(-0.648603\pi\) | ||||
−0.450076 | + | 0.892990i | \(0.648603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 318.150 | − | 313.141i | 0.772209 | − | 0.760050i | ||||
\(413\) | − | 275.813i | − | 0.667827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 172.597 | + | 441.245i | 0.414896 | + | 1.06068i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.4194 | − | 49.8554i | −0.0488503 | − | 0.119271i | ||||
\(419\) | − | 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 | \(0.497047\pi\) | |||||||
\(422\) | 435.486 | − | 178.363i | 1.03196 | − | 0.422662i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 280.989 | − | 656.167i | 0.662710 | − | 1.54756i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 147.574 | 0.345607 | ||||||||
\(428\) | −177.494 | + | 174.699i | −0.414705 | + | 0.408176i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 681.258i | − | 1.58065i | −0.612691 | − | 0.790323i | \(-0.709913\pi\) | ||
0.612691 | − | 0.790323i | \(-0.290087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.06878i | − | 0.00939673i | −0.999989 | − | 0.00469836i | \(-0.998504\pi\) | ||
0.999989 | − | 0.00469836i | \(-0.00149554\pi\) | |||||||
\(434\) | −14.9219 | + | 6.11161i | −0.0343822 | + | 0.0140820i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 248.570 | − | 244.657i | 0.570115 | − | 0.561139i | ||||
\(437\) | − | 502.250i | − | 1.14931i | ||||||
\(438\) | 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 | ||||||||
\(442\) | 110.061 | + | 268.722i | 0.249007 | + | 0.607968i | ||||
\(443\) | −469.454 | −1.05972 | −0.529858 | − | 0.848087i | \(-0.677755\pi\) | ||||
−0.529858 | + | 0.848087i | \(0.677755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.5969 | − | 60.0549i | −0.0551499 | − | 0.134652i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 180.887 | + | 189.711i | 0.403766 | + | 0.423462i | ||||
\(449\) | 514.444 | 1.14575 | 0.572877 | − | 0.819641i | \(-0.305827\pi\) | ||||
0.572877 | + | 0.819641i | \(0.305827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.7323i | − | 0.0371005i | ||||||
\(452\) | −236.326 | − | 240.107i | −0.522846 | − | 0.531210i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −219.519 | − | 535.970i | −0.483522 | − | 1.18055i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 684.537i | − | 1.49789i | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||
0.662630 | − | 0.748947i | \(-0.269440\pi\) | |||||||
\(458\) | −75.2629 | − | 183.759i | −0.164329 | − | 0.401221i | ||||
\(459\) | 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 | ||||||||
\(463\) | 550.353 | 1.18867 | 0.594334 | − | 0.804218i | \(-0.297416\pi\) | ||||
0.594334 | + | 0.804218i | \(0.297416\pi\) | |||||||
\(464\) | −0.712521 | + | 44.8943i | −0.00153561 | + | 0.0967550i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 93.9734 | − | 38.4890i | 0.201660 | − | 0.0825944i | ||||
\(467\) | −10.0013 | −0.0214160 | −0.0107080 | − | 0.999943i | \(-0.503409\pi\) | ||||
−0.0107080 | + | 0.999943i | \(0.503409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 104.681 | 0.223201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −212.073 | + | 495.234i | −0.449307 | + | 1.04923i | ||||
\(473\) | − | 54.0312i | − | 0.114231i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 112.695 | + | 114.498i | 0.236755 | + | 0.240542i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −576.515 | + | 236.125i | −1.20610 | + | 0.493985i | ||||
\(479\) | − | 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 | ||||||||
\(482\) | 241.883 | + | 590.573i | 0.501831 | + | 1.22525i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −342.183 | + | 336.795i | −0.706989 | + | 0.695858i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 429.005 | 0.880913 | 0.440457 | − | 0.897774i | \(-0.354817\pi\) | ||||
0.440457 | + | 0.897774i | \(0.354817\pi\) | |||||||
\(488\) | −264.976 | − | 113.470i | −0.542985 | − | 0.232521i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 380.015i | 0.773961i | 0.922088 | + | 0.386980i | \(0.126482\pi\) | ||||
−0.922088 | + | 0.386980i | \(0.873518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.5188i | 0.0558190i | ||||||||
\(494\) | −307.172 | − | 749.981i | −0.621805 | − | 1.51818i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.4922 | + | 0.499815i | 0.0634923 | + | 0.00100769i | ||||
\(497\) | − | 491.938i | − | 0.989814i | ||||||
\(498\) | 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 | ||||||||
\(502\) | −162.183 | + | 66.4257i | −0.323073 | + | 0.132322i | ||||
\(503\) | 325.436 | 0.646991 | 0.323495 | − | 0.946230i | \(-0.395142\pi\) | ||||
0.323495 | + | 0.946230i | \(0.395142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.4297 | − | 13.6919i | 0.0660666 | − | 0.0270591i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 213.971 | − | 210.602i | 0.421202 | − | 0.414570i | ||||
\(509\) | 1.22499 | 0.00240667 | 0.00120333 | − | 0.999999i | \(-0.499617\pi\) | ||||
0.00120333 | + | 0.999999i | \(0.499617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 285.908i | 0.559506i | ||||||||
\(512\) | −178.922 | − | 479.720i | −0.349458 | − | 0.936952i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −217.073 | + | 88.9074i | −0.422322 | + | 0.172972i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 57.9063i | − | 0.112004i | ||||||
\(518\) | −339.645 | + | 139.109i | −0.655685 | + | 0.268551i | ||||
\(519\) | 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 | ||||||||
\(523\) | 295.370 | 0.564761 | 0.282380 | − | 0.959302i | \(-0.408876\pi\) | ||||
0.282380 | + | 0.959302i | \(0.408876\pi\) | |||||||
\(524\) | −392.250 | − | 398.525i | −0.748569 | − | 0.760543i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.2453 | + | 88.4953i | 0.0689074 | + | 0.168242i | ||||
\(527\) | 19.3037 | 0.0366294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −192.225 | −0.363374 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −314.523 | − | 319.555i | −0.591209 | − | 0.600667i | ||||
\(533\) | − | 251.706i | − | 0.472244i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −187.960 | − | 80.4897i | −0.350672 | − | 0.150167i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 363.314 | + | 887.056i | 0.675305 | + | 1.64880i | ||||
\(539\) | − | 31.7176i | − | 0.0588453i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −200.250 | −0.370148 | −0.185074 | − | 0.982725i | \(-0.559252\pi\) | ||||
−0.185074 | + | 0.982725i | \(0.559252\pi\) | |||||||
\(542\) | −448.237 | + | 183.586i | −0.827006 | + | 0.338719i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −114.312 | − | 292.238i | −0.210132 | − | 0.537203i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 989.581 | 1.80911 | 0.904553 | − | 0.426361i | \(-0.140205\pi\) | ||||
0.904553 | + | 0.426361i | \(0.140205\pi\) | |||||||
\(548\) | −157.586 | − | 160.107i | −0.287566 | − | 0.292166i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 76.8026i | − | 0.139388i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 132.250i | − | 0.239150i | ||||||
\(554\) | 61.5500 | − | 25.2092i | 0.111101 | − | 0.0455040i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 545.301 | + | 554.024i | 0.980757 | + | 0.996446i | ||||
\(557\) | 641.319i | 1.15138i | 0.817668 | + | 0.575690i | \(0.195267\pi\) | ||||
−0.817668 | + | 0.575690i | \(0.804733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 812.798i | − | 1.45402i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 186.523 | + | 455.408i | 0.331891 | + | 0.810334i | ||||
\(563\) | −382.237 | −0.678928 | −0.339464 | − | 0.940619i | \(-0.610246\pi\) | ||||
−0.339464 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.15552 | − | 2.82127i | −0.00204155 | − | 0.00498458i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −378.252 | + | 883.297i | −0.665937 | + | 1.55510i | ||||
\(569\) | −576.025 | −1.01235 | −0.506173 | − | 0.862432i | \(-0.668940\pi\) | ||||
−0.506173 | + | 0.862432i | \(0.668940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1100.67i | − | 1.92762i | −0.266582 | − | 0.963812i | \(-0.585894\pi\) | ||
0.266582 | − | 0.963812i | \(-0.414106\pi\) | |||||||
\(572\) | 41.5448 | − | 40.8907i | 0.0726307 | − | 0.0714872i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −52.7797 | − | 128.865i | −0.0919506 | − | 0.224504i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 326.475i | − | 0.565814i | −0.959147 | − | 0.282907i | \(-0.908701\pi\) | ||
0.959147 | − | 0.282907i | \(-0.0912989\pi\) | |||||||
\(578\) | 146.177 | + | 356.900i | 0.252901 | + | 0.617474i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −279.194 | −0.480540 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −87.8201 | −0.150635 | ||||||||
\(584\) | 219.835 | − | 513.360i | 0.376430 | − | 0.879042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 830.989 | − | 340.351i | 1.41807 | − | 0.580803i | ||||
\(587\) | −90.5502 | −0.154259 | −0.0771296 | − | 0.997021i | \(-0.524576\pi\) | ||||
−0.0771296 | + | 0.997021i | \(0.524576\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.8750 | −0.0914686 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 716.810 | + | 11.3765i | 1.21083 | + | 0.0192171i | ||||
\(593\) | 896.163i | 1.51124i | 0.655013 | + | 0.755618i | \(0.272663\pi\) | ||||
−0.655013 | + | 0.755618i | \(0.727337\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 316.062 | − | 311.086i | 0.530306 | − | 0.521956i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 502.887 | − | 205.969i | 0.840947 | − | 0.344429i | ||||
\(599\) | − | 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 | \(0.618999\pi\) | |||||||
\(602\) | −170.434 | − | 416.125i | −0.283112 | − | 0.691237i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −397.773 | − | 404.137i | −0.658565 | − | 0.669100i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1156.84 | −1.90583 | −0.952915 | − | 0.303237i | \(-0.901933\pi\) | ||||
−0.952915 | + | 0.303237i | \(0.901933\pi\) | |||||||
\(608\) | 319.035 | + | 815.613i | 0.524728 | + | 1.34147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 871.090i | − | 1.42568i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 409.225i | − | 0.667577i | −0.942648 | − | 0.333789i | \(-0.891673\pi\) | ||
0.942648 | − | 0.333789i | \(-0.108327\pi\) | |||||||
\(614\) | −8.08673 | − | 19.7443i | −0.0131706 | − | 0.0321568i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.6953 | − | 29.6461i | 0.0206092 | − | 0.0481267i | ||||
\(617\) | − | 999.150i | − | 1.61937i | −0.586866 | − | 0.809684i | \(-0.699639\pi\) | ||
0.586866 | − | 0.809684i | \(-0.300361\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | 685.107 | − | 280.602i | 1.10146 | − | 0.451128i | ||||
\(623\) | −277.716 | −0.445772 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −79.0515 | + | 32.3774i | −0.126280 | + | 0.0517210i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −501.799 | − | 509.827i | −0.799043 | − | 0.811826i | ||||
\(629\) | 439.381 | 0.698539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1053.40i | − | 1.66941i | −0.550696 | − | 0.834706i | \(-0.685638\pi\) | ||
0.550696 | − | 0.834706i | \(-0.314362\pi\) | |||||||
\(632\) | −101.687 | + | 237.461i | −0.160898 | + | 0.375729i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −264.847 | + | 108.474i | −0.417739 | + | 0.171095i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 477.131i | − | 0.749029i | ||||||
\(638\) | 5.11198 | − | 2.09373i | 0.00801250 | − | 0.00328170i | ||||
\(639\) | 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 | ||||||||
\(643\) | 454.690 | 0.707138 | 0.353569 | − | 0.935408i | \(-0.384968\pi\) | ||||
0.353569 | + | 0.935408i | \(0.384968\pi\) | |||||||
\(644\) | 214.272 | − | 210.898i | 0.332720 | − | 0.327482i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 203.441 | + | 496.716i | 0.314925 | + | 0.768910i | ||||
\(647\) | 928.430 | 1.43498 | 0.717489 | − | 0.696570i | \(-0.245292\pi\) | ||||
0.717489 | + | 0.696570i | \(0.245292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 66.2812 | 0.102128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −634.399 | + | 624.410i | −0.973004 | + | 0.957684i | ||||
\(653\) | − | 536.744i | − | 0.821966i | −0.911643 | − | 0.410983i | \(-0.865186\pi\) | ||
0.911643 | − | 0.410983i | \(-0.134814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.31639 | + | 271.966i | −0.00657986 | + | 0.414582i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −182.657 | − | 445.969i | −0.277594 | − | 0.677764i | ||||
\(659\) | 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 | \(0.632431\pi\) | |||||||
\(662\) | 96.5469 | − | 39.5430i | 0.145841 | − | 0.0597327i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 501.305 | + | 214.673i | 0.754978 | + | 0.323303i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.4987 | 0.0772094 | ||||||||
\(668\) | −606.884 | + | 597.328i | −0.908508 | + | 0.894204i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.4639i | 0.0528523i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 129.225i | − | 0.192013i | −0.995381 | − | 0.0960067i | \(-0.969393\pi\) | ||
0.995381 | − | 0.0960067i | \(-0.0306070\pi\) | |||||||
\(674\) | −817.860 | + | 334.973i | −1.21344 | + | 0.496993i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 143.180 | − | 140.926i | 0.211805 | − | 0.208471i | ||||
\(677\) | 111.163i | 0.164199i | 0.996624 | + | 0.0820993i | \(0.0261625\pi\) | ||||
−0.996624 | + | 0.0820993i | \(0.973838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.76132i | − | 0.00701226i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.46869 | − | 3.58592i | −0.00215351 | − | 0.00525794i | ||||
\(683\) | −710.467 | −1.04022 | −0.520108 | − | 0.854101i | \(-0.674108\pi\) | ||||
−0.520108 | + | 0.854101i | \(0.674108\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −252.178 | − | 615.710i | −0.367607 | − | 0.897536i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.9383 | + | 878.219i | −0.0202591 | + | 1.27648i | ||||
\(689\) | −1321.09 | −1.91740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 64.0073i | 0.0926300i | 0.998927 | + | 0.0463150i | \(0.0147478\pi\) | ||||
−0.998927 | + | 0.0463150i | \(0.985252\pi\) | |||||||
\(692\) | 58.2925 | + | 59.2250i | 0.0842377 | + | 0.0855853i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −65.0539 | − | 158.833i | −0.0937375 | − | 0.228867i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 166.706i | 0.239177i | ||||||||
\(698\) | 309.982 | + | 756.842i | 0.444100 | + | 1.08430i | ||||
\(699\) | 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 | ||||||||
\(703\) | −1226.28 | −1.74435 | ||||||||
\(704\) | −45.5899 | + | 43.4695i | −0.0647584 | + | 0.0617464i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −816.495 | + | 334.414i | −1.15651 | + | 0.473675i | ||||
\(707\) | 540.764 | 0.764872 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1349.09 | 1.90280 | 0.951402 | − | 0.307953i | \(-0.0996440\pi\) | ||||
0.951402 | + | 0.307953i | \(0.0996440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 498.652 | + | 213.537i | 0.700354 | + | 0.299911i | ||||
\(713\) | − | 36.1250i | − | 0.0506662i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −104.410 | − | 106.080i | −0.145824 | − | 0.148157i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −797.343 | + | 326.570i | −1.11051 | + | 0.454833i | ||||
\(719\) | 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 | ||||||||
\(722\) | −294.139 | − | 718.161i | −0.407395 | − | 0.994683i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −906.905 | + | 892.625i | −1.25263 | + | 1.23291i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7188 | −0.0436298 | −0.0218149 | − | 0.999762i | \(-0.506944\pi\) | ||||
−0.0218149 | + | 0.999762i | \(0.506944\pi\) | |||||||
\(728\) | 190.976 | − | 445.969i | 0.262330 | − | 0.612594i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 538.320i | 0.736415i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 121.319i | − | 0.165510i | −0.996570 | − | 0.0827549i | \(-0.973628\pi\) | ||
0.996570 | − | 0.0827549i | \(-0.0263719\pi\) | |||||||
\(734\) | 262.816 | + | 641.682i | 0.358059 | + | 0.874226i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −546.895 | + | 213.923i | −0.743064 | + | 0.290656i | ||||
\(737\) | 25.1562i | 0.0341333i | ||||||||
\(738\) | 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 | ||||||||
\(742\) | −676.352 | + | 277.016i | −0.911526 | + | 0.373336i | ||||
\(743\) | 298.259 | 0.401425 | 0.200712 | − | 0.979650i | \(-0.435674\pi\) | ||||
0.200712 | + | 0.979650i | \(0.435674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1068.43 | − | 437.601i | 1.43222 | − | 0.586597i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.5153 | + | 27.0821i | −0.0367852 | + | 0.0362060i | ||||
\(749\) | 255.006 | 0.340462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 580.864i | 0.773454i | 0.922194 | + | 0.386727i | \(0.126394\pi\) | ||||
−0.922194 | + | 0.386727i | \(0.873606\pi\) | |||||||
\(752\) | −14.9379 | + | 941.203i | −0.0198642 | + | 1.25160i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 76.9000 | − | 31.4962i | 0.101989 | − | 0.0417721i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 507.600i | − | 0.670541i | −0.942122 | − | 0.335271i | \(-0.891172\pi\) | ||
0.942122 | − | 0.335271i | \(-0.108828\pi\) | |||||||
\(758\) | −925.974 | + | 379.254i | −1.22160 | + | 0.500335i | ||||
\(759\) | 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 | ||||||||
\(763\) | −357.122 | −0.468050 | ||||||||
\(764\) | −723.742 | − | 735.320i | −0.947306 | − | 0.962461i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 298.027 | + | 727.652i | 0.389069 | + | 0.949937i | ||||
\(767\) | 997.075 | 1.29997 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 161.681 | 0.210249 | 0.105124 | − | 0.994459i | \(-0.466476\pi\) | ||||
0.105124 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −358.786 | − | 364.526i | −0.464749 | − | 0.472184i | ||||
\(773\) | 545.506i | 0.705700i | 0.935680 | + | 0.352850i | \(0.114787\pi\) | ||||
−0.935680 | + | 0.352850i | \(0.885213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.66100 | + | 8.54918i | −0.00471778 | + | 0.0110170i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −74.8744 | − | 182.811i | −0.0962396 | − | 0.234975i | ||||
\(779\) | − | 465.263i | − | 0.597257i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 118.219 | 0.151368 | ||||||||
\(782\) | −333.064 | + | 136.414i | −0.425913 | + | 0.174443i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.18210 | + | 515.535i | −0.0104363 | + | 0.657570i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −953.227 | −1.21122 | −0.605608 | − | 0.795763i | \(-0.707070\pi\) | ||||
−0.605608 | + | 0.795763i | \(0.707070\pi\) | |||||||
\(788\) | −272.978 | − | 277.345i | −0.346419 | − | 0.351961i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 344.963i | 0.436110i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 533.488i | 0.672746i | ||||||||
\(794\) | 368.722 | − | 151.019i | 0.464385 | − | 0.190200i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.2343 | + | 56.1179i | 0.0693898 | + | 0.0704999i | ||||
\(797\) | 456.975i | 0.573369i | 0.958025 | + | 0.286684i | \(0.0925531\pi\) | ||||
−0.958025 | + | 0.286684i | \(0.907447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 576.927i | 0.722061i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 79.6642 | + | 194.505i | 0.0993319 | + | 0.242526i | ||||
\(803\) | −68.7071 | −0.0855631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.0937 | − | 53.9433i | −0.0274116 | − | 0.0669272i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −970.968 | − | 415.795i | −1.20169 | − | 0.514598i | ||||
\(809\) | 1073.79 | 1.32730 | 0.663651 | − | 0.748042i | \(-0.269006\pi\) | ||||
0.663651 | + | 0.748042i | \(0.269006\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 108.299i | − | 0.133537i | −0.997768 | − | 0.0667687i | \(-0.978731\pi\) | ||
0.997768 | − | 0.0667687i | \(-0.0212690\pi\) | |||||||
\(812\) | 32.7658 | − | 32.2499i | 0.0403520 | − | 0.0397167i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33.4297 | − | 81.6209i | −0.0410684 | − | 0.100271i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1502.41i | − | 1.83893i | ||||||
\(818\) | −279.078 | − | 681.388i | −0.341171 | − | 0.832993i | ||||
\(819\) | 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 | ||||||||
\(823\) | 862.264 | 1.04771 | 0.523854 | − | 0.851808i | \(-0.324494\pi\) | ||||
0.523854 | + | 0.851808i | \(0.324494\pi\) | |||||||
\(824\) | 820.722 | + | 351.456i | 0.996022 | + | 0.426524i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 510.469 | − | 209.074i | 0.618001 | − | 0.253116i | ||||
\(827\) | −720.596 | −0.871338 | −0.435669 | − | 0.900107i | \(-0.643488\pi\) | ||||
−0.435669 | + | 0.900107i | \(0.643488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −385.569 | −0.465101 | −0.232550 | − | 0.972584i | \(-0.574707\pi\) | ||||
−0.232550 | + | 0.972584i | \(0.574707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −685.813 | + | 653.916i | −0.824295 | + | 0.785956i | ||||
\(833\) | 316.006i | 0.379359i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 76.7930 | − | 75.5838i | 0.0918576 | − | 0.0904113i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 87.0858 | − | 35.6680i | 0.103921 | − | 0.0425632i | ||||
\(839\) | 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 | ||||||||
\(842\) | 5.92214 | + | 14.4593i | 0.00703343 | + | 0.0171726i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 660.223 | + | 670.784i | 0.782254 | + | 0.794768i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 491.616 | 0.580420 | ||||||||
\(848\) | 1427.42 | + | 22.6547i | 1.68328 | + | 0.0267154i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 822.259i | − | 0.966227i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 151.087i | 0.177125i | 0.996071 | + | 0.0885624i | \(0.0282273\pi\) | ||||
−0.996071 | + | 0.0885624i | \(0.971773\pi\) | |||||||
\(854\) | 111.866 | + | 273.128i | 0.130990 | + | 0.319822i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −457.876 | − | 196.075i | −0.534902 | − | 0.229060i | ||||
\(857\) | 444.225i | 0.518349i | 0.965831 | + | 0.259174i | \(0.0834505\pi\) | ||||
−0.965831 | + | 0.259174i | \(0.916550\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | 1260.86 | − | 516.414i | 1.46271 | − | 0.599088i | ||||
\(863\) | −965.801 | −1.11912 | −0.559560 | − | 0.828790i | \(-0.689030\pi\) | ||||
−0.559560 | + | 0.828790i | \(0.689030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.53042 | − | 3.08426i | 0.00869564 | − | 0.00356150i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.6225 | − | 22.9844i | −0.0260628 | − | 0.0264797i | ||||
\(869\) | 31.7813 | 0.0365723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 378.428i | 0.434475i | ||||||||
\(872\) | 641.229 | + | 274.592i | 0.735355 | + | 0.314899i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 929.555 | − | 380.721i | 1.06356 | − | 0.435607i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1440.78i | 1.64284i | 0.570320 | + | 0.821422i | \(0.306819\pi\) | ||||
−0.570320 | + | 0.821422i | \(0.693181\pi\) | |||||||
\(878\) | −327.246 | + | 134.031i | −0.372718 | + | 0.152655i | ||||
\(879\) | 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 | ||||||||
\(883\) | 229.616 | 0.260040 | 0.130020 | − | 0.991511i | \(-0.458496\pi\) | ||||
0.130020 | + | 0.991511i | \(0.458496\pi\) | |||||||
\(884\) | −413.916 | + | 407.398i | −0.468230 | + | 0.460858i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −355.860 | − | 868.856i | −0.401648 | − | 0.980650i | ||||
\(887\) | −456.945 | −0.515158 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −307.412 | −0.345796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 92.5033 | − | 91.0469i | 0.103703 | − | 0.102070i | ||||
\(893\) | − | 1610.16i | − | 1.80309i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −213.995 | + | 478.589i | −0.238834 | + | 0.534140i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 389.964 | + | 952.123i | 0.434258 | + | 1.06027i | ||||
\(899\) | − | 5.52413i | − | 0.00614475i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 874.962 | 0.971102 | ||||||||
\(902\) | 30.9679 | − | 12.6836i | 0.0343325 | − | 0.0140617i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 265.243 | − | 619.397i | 0.293410 | − | 0.685174i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −797.272 | −0.879021 | −0.439511 | − | 0.898237i | \(-0.644848\pi\) | ||||
−0.439511 | + | 0.898237i | \(0.644848\pi\) | |||||||
\(908\) | 825.561 | − | 812.562i | 0.909208 | − | 0.894892i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 531.621i | − | 0.583557i | −0.956486 | − | 0.291779i | \(-0.905753\pi\) | ||
0.956486 | − | 0.291779i | \(-0.0942470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 67.0937i | − | 0.0734871i | ||||||
\(914\) | 1266.93 | − | 518.900i | 1.38614 | − | 0.567724i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 283.047 | − | 278.590i | 0.309003 | − | 0.304138i | ||||
\(917\) | 572.562i | 0.624386i | ||||||||
\(918\) | 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 | ||||||||
\(922\) | −154.828 | − | 378.022i | −0.167926 | − | 0.410002i | ||||
\(923\) | 1778.38 | 1.92673 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 417.184 | + | 1018.58i | 0.450523 | + | 1.09998i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −83.6297 | + | 32.7125i | −0.0901182 | + | 0.0352506i | ||||
\(929\) | −198.775 | −0.213967 | −0.106983 | − | 0.994261i | \(-0.534119\pi\) | ||||
−0.106983 | + | 0.994261i | \(0.534119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 881.948i | − | 0.947312i | ||||||
\(932\) | 142.469 | + | 144.748i | 0.152864 | + | 0.155309i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.58125 | − | 18.5101i | −0.00811697 | − | 0.0198181i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1200.43i | 1.28114i | 0.767898 | + | 0.640572i | \(0.221303\pi\) | ||||
−0.767898 | + | 0.640572i | \(0.778697\pi\) | |||||||
\(938\) | 79.3515 | + | 193.742i | 0.0845965 | + | 0.206548i | ||||
\(939\) | 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 | ||||||||
\(943\) | 311.974 | 0.330832 | ||||||||
\(944\) | −1077.33 | − | 17.0984i | −1.14124 | − | 0.0181127i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 100.000 | − | 40.9573i | 0.105708 | − | 0.0432952i | ||||
\(947\) | −586.516 | −0.619341 | −0.309671 | − | 0.950844i | \(-0.600219\pi\) | ||||
−0.309671 | + | 0.950844i | \(0.600219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1033.57 | −1.08911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −126.484 | + | 295.367i | −0.132862 | + | 0.310260i | ||||
\(953\) | 1598.72i | 1.67757i | 0.544462 | + | 0.838785i | \(0.316734\pi\) | ||||
−0.544462 | + | 0.838785i | \(0.683266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −874.031 | − | 888.013i | −0.914259 | − | 0.928884i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1015.29 | − | 415.836i | 1.05980 | − | 0.434067i | ||||
\(959\) | 230.026i | 0.239861i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 957.125 | 0.995968 | ||||||||
\(962\) | −502.887 | − | 1227.83i | −0.522751 | − | 1.27633i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −909.666 | + | 895.344i | −0.943637 | + | 0.928780i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 320.675 | 0.331619 | 0.165809 | − | 0.986158i | \(-0.446976\pi\) | ||||
0.165809 | + | 0.986158i | \(0.446976\pi\) | |||||||
\(968\) | −882.719 | − | 378.005i | −0.911900 | − | 0.390501i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1402.93i | 1.44483i | 0.691459 | + | 0.722416i | \(0.256968\pi\) | ||||
−0.691459 | + | 0.722416i | \(0.743032\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 795.969i | − | 0.818056i | ||||||
\(974\) | 325.198 | + | 793.994i | 0.333879 | + | 0.815189i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.14852 | − | 576.427i | 0.00937349 | − | 0.590602i | ||||
\(977\) | − | 1226.24i | − | 1.25511i | −0.778572 | − | 0.627556i | \(-0.784056\pi\) | ||
0.778572 | − | 0.627556i | \(-0.215944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 66.7386i | − | 0.0681702i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −703.324 | + | 288.062i | −0.716216 | + | 0.293343i | ||||
\(983\) | 1372.96 | 1.39670 | 0.698352 | − | 0.715754i | \(-0.253917\pi\) | ||||
0.698352 | + | 0.715754i | \(0.253917\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −50.9312 | + | 20.8601i | −0.0516544 | + | 0.0211562i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1155.20 | − | 1137.02i | 1.16924 | − | 1.15083i | ||||
\(989\) | 1007.41 | 1.01862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 362.298i | 0.365588i | 0.983151 | + | 0.182794i | \(0.0585142\pi\) | ||||
−0.983151 | + | 0.182794i | \(0.941486\pi\) | |||||||
\(992\) | 22.9470 | + | 58.6640i | 0.0231320 | + | 0.0591371i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 910.469 | − | 372.903i | 0.915964 | − | 0.375154i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 941.087i | 0.943919i | 0.881620 | + | 0.471960i | \(0.156453\pi\) | ||||
−0.881620 | + | 0.471960i | \(0.843547\pi\) | |||||||
\(998\) | 732.470 | − | 300.000i | 0.733938 | − | 0.300601i | ||||
\(999\) | 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.f.d.199.6 | 8 | ||
3.2 | odd | 2 | 100.3.d.a.99.3 | 8 | |||
4.3 | odd | 2 | inner | 900.3.f.d.199.4 | 8 | ||
5.2 | odd | 4 | 900.3.c.l.451.2 | 4 | |||
5.3 | odd | 4 | 900.3.c.m.451.3 | 4 | |||
5.4 | even | 2 | inner | 900.3.f.d.199.3 | 8 | ||
12.11 | even | 2 | 100.3.d.a.99.5 | 8 | |||
15.2 | even | 4 | 100.3.b.e.51.3 | yes | 4 | ||
15.8 | even | 4 | 100.3.b.d.51.2 | yes | 4 | ||
15.14 | odd | 2 | 100.3.d.a.99.6 | 8 | |||
20.3 | even | 4 | 900.3.c.m.451.4 | 4 | |||
20.7 | even | 4 | 900.3.c.l.451.1 | 4 | |||
20.19 | odd | 2 | inner | 900.3.f.d.199.5 | 8 | ||
24.5 | odd | 2 | 1600.3.h.o.1599.8 | 8 | |||
24.11 | even | 2 | 1600.3.h.o.1599.1 | 8 | |||
60.23 | odd | 4 | 100.3.b.d.51.1 | ✓ | 4 | ||
60.47 | odd | 4 | 100.3.b.e.51.4 | yes | 4 | ||
60.59 | even | 2 | 100.3.d.a.99.4 | 8 | |||
120.29 | odd | 2 | 1600.3.h.o.1599.2 | 8 | |||
120.53 | even | 4 | 1600.3.b.p.1151.4 | 4 | |||
120.59 | even | 2 | 1600.3.h.o.1599.7 | 8 | |||
120.77 | even | 4 | 1600.3.b.o.1151.1 | 4 | |||
120.83 | odd | 4 | 1600.3.b.p.1151.1 | 4 | |||
120.107 | odd | 4 | 1600.3.b.o.1151.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.3.b.d.51.1 | ✓ | 4 | 60.23 | odd | 4 | ||
100.3.b.d.51.2 | yes | 4 | 15.8 | even | 4 | ||
100.3.b.e.51.3 | yes | 4 | 15.2 | even | 4 | ||
100.3.b.e.51.4 | yes | 4 | 60.47 | odd | 4 | ||
100.3.d.a.99.3 | 8 | 3.2 | odd | 2 | |||
100.3.d.a.99.4 | 8 | 60.59 | even | 2 | |||
100.3.d.a.99.5 | 8 | 12.11 | even | 2 | |||
100.3.d.a.99.6 | 8 | 15.14 | odd | 2 | |||
900.3.c.l.451.1 | 4 | 20.7 | even | 4 | |||
900.3.c.l.451.2 | 4 | 5.2 | odd | 4 | |||
900.3.c.m.451.3 | 4 | 5.3 | odd | 4 | |||
900.3.c.m.451.4 | 4 | 20.3 | even | 4 | |||
900.3.f.d.199.3 | 8 | 5.4 | even | 2 | inner | ||
900.3.f.d.199.4 | 8 | 4.3 | odd | 2 | inner | ||
900.3.f.d.199.5 | 8 | 20.19 | odd | 2 | inner | ||
900.3.f.d.199.6 | 8 | 1.1 | even | 1 | trivial | ||
1600.3.b.o.1151.1 | 4 | 120.77 | even | 4 | |||
1600.3.b.o.1151.4 | 4 | 120.107 | odd | 4 | |||
1600.3.b.p.1151.1 | 4 | 120.83 | odd | 4 | |||
1600.3.b.p.1151.4 | 4 | 120.53 | even | 4 | |||
1600.3.h.o.1599.1 | 8 | 24.11 | even | 2 | |||
1600.3.h.o.1599.2 | 8 | 120.29 | odd | 2 | |||
1600.3.h.o.1599.7 | 8 | 120.59 | even | 2 | |||
1600.3.h.o.1599.8 | 8 | 24.5 | odd | 2 |