Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,4,Mod(169,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.169");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.g (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: | \(12.3904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(2.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.169 |
Dual form | 210.4.g.b.169.3 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −0.582576 | + | 11.1652i | −0.0521072 | + | 0.998641i | ||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 22.3303 | + | 1.16515i | 0.706146 | + | 0.0368453i | ||||
\(11\) | −42.6606 | −1.16933 | −0.584666 | − | 0.811274i | \(-0.698775\pi\) | ||||
−0.584666 | + | 0.811274i | \(0.698775\pi\) | |||||||
\(12\) | − | 12.0000i | − | 0.288675i | ||||||
\(13\) | − | 73.1652i | − | 1.56095i | −0.625186 | − | 0.780475i | \(-0.714977\pi\) | ||
0.625186 | − | 0.780475i | \(-0.285023\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | −33.4955 | − | 1.74773i | −0.576566 | − | 0.0300841i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 48.4864i | − | 0.691745i | −0.938281 | − | 0.345873i | \(-0.887583\pi\) | ||
0.938281 | − | 0.345873i | \(-0.112417\pi\) | |||||||
\(18\) | 18.0000i | 0.235702i | ||||||||
\(19\) | −77.6515 | −0.937604 | −0.468802 | − | 0.883303i | \(-0.655314\pi\) | ||||
−0.468802 | + | 0.883303i | \(0.655314\pi\) | |||||||
\(20\) | 2.33030 | − | 44.6606i | 0.0260536 | − | 0.499321i | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 85.3212i | 0.826843i | ||||||||
\(23\) | − | 12.3485i | − | 0.111949i | −0.998432 | − | 0.0559747i | \(-0.982173\pi\) | ||
0.998432 | − | 0.0559747i | \(-0.0178266\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −124.321 | − | 13.0091i | −0.994570 | − | 0.104073i | ||||
\(26\) | −146.330 | −1.10376 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | − | 28.0000i | − | 0.188982i | ||||||
\(29\) | 47.8439 | 0.306359 | 0.153179 | − | 0.988198i | \(-0.451049\pi\) | ||||
0.153179 | + | 0.988198i | \(0.451049\pi\) | |||||||
\(30\) | −3.49545 | + | 66.9909i | −0.0212727 | + | 0.407694i | ||||
\(31\) | −151.808 | −0.879530 | −0.439765 | − | 0.898113i | \(-0.644938\pi\) | ||||
−0.439765 | + | 0.898113i | \(0.644938\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | − | 127.982i | − | 0.675114i | ||||||
\(34\) | −96.9727 | −0.489138 | ||||||||
\(35\) | −78.1561 | − | 4.07803i | −0.377451 | − | 0.0196947i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 212.486i | 0.944123i | 0.881566 | + | 0.472061i | \(0.156490\pi\) | ||||
−0.881566 | + | 0.472061i | \(0.843510\pi\) | |||||||
\(38\) | 155.303i | 0.662986i | ||||||||
\(39\) | 219.495 | 0.901215 | ||||||||
\(40\) | −89.3212 | − | 4.66061i | −0.353073 | − | 0.0184227i | ||||
\(41\) | −227.808 | −0.867746 | −0.433873 | − | 0.900974i | \(-0.642853\pi\) | ||||
−0.433873 | + | 0.900974i | \(0.642853\pi\) | |||||||
\(42\) | 42.0000i | 0.154303i | ||||||||
\(43\) | − | 299.165i | − | 1.06098i | −0.847690 | − | 0.530491i | \(-0.822007\pi\) | ||
0.847690 | − | 0.530491i | \(-0.177993\pi\) | |||||||
\(44\) | 170.642 | 0.584666 | ||||||||
\(45\) | 5.24318 | − | 100.486i | 0.0173691 | − | 0.332880i | ||||
\(46\) | −24.6970 | −0.0791602 | ||||||||
\(47\) | 542.744i | 1.68441i | 0.539156 | + | 0.842206i | \(0.318743\pi\) | ||||
−0.539156 | + | 0.842206i | \(0.681257\pi\) | |||||||
\(48\) | 48.0000i | 0.144338i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −26.0182 | + | 248.642i | −0.0735905 | + | 0.703267i | ||||
\(51\) | 145.459 | 0.399379 | ||||||||
\(52\) | 292.661i | 0.780475i | ||||||||
\(53\) | 152.367i | 0.394890i | 0.980314 | + | 0.197445i | \(0.0632644\pi\) | ||||
−0.980314 | + | 0.197445i | \(0.936736\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 24.8530 | − | 476.312i | 0.0609306 | − | 1.16774i | ||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | − | 232.955i | − | 0.541326i | ||||||
\(58\) | − | 95.6879i | − | 0.216628i | ||||||
\(59\) | 238.606 | 0.526506 | 0.263253 | − | 0.964727i | \(-0.415205\pi\) | ||||
0.263253 | + | 0.964727i | \(0.415205\pi\) | |||||||
\(60\) | 133.982 | + | 6.99091i | 0.288283 | + | 0.0150420i | ||||
\(61\) | −768.744 | −1.61357 | −0.806783 | − | 0.590847i | \(-0.798794\pi\) | ||||
−0.806783 | + | 0.590847i | \(0.798794\pi\) | |||||||
\(62\) | 303.615i | 0.621922i | ||||||||
\(63\) | − | 63.0000i | − | 0.125988i | ||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 816.900 | + | 42.6242i | 1.55883 | + | 0.0813367i | ||||
\(66\) | −255.964 | −0.477378 | ||||||||
\(67\) | − | 313.386i | − | 0.571436i | −0.958314 | − | 0.285718i | \(-0.907768\pi\) | ||
0.958314 | − | 0.285718i | \(-0.0922321\pi\) | |||||||
\(68\) | 193.945i | 0.345873i | ||||||||
\(69\) | 37.0455 | 0.0646340 | ||||||||
\(70\) | −8.15606 | + | 156.312i | −0.0139262 | + | 0.266898i | ||||
\(71\) | 122.065 | 0.204035 | 0.102017 | − | 0.994783i | \(-0.467470\pi\) | ||||
0.102017 | + | 0.994783i | \(0.467470\pi\) | |||||||
\(72\) | − | 72.0000i | − | 0.117851i | ||||||
\(73\) | − | 31.8076i | − | 0.0509972i | −0.999675 | − | 0.0254986i | \(-0.991883\pi\) | ||
0.999675 | − | 0.0254986i | \(-0.00811733\pi\) | |||||||
\(74\) | 424.973 | 0.667596 | ||||||||
\(75\) | 39.0273 | − | 372.964i | 0.0600864 | − | 0.574215i | ||||
\(76\) | 310.606 | 0.468802 | ||||||||
\(77\) | − | 298.624i | − | 0.441966i | ||||||
\(78\) | − | 438.991i | − | 0.637256i | ||||||
\(79\) | −419.579 | −0.597548 | −0.298774 | − | 0.954324i | \(-0.596578\pi\) | ||||
−0.298774 | + | 0.954324i | \(0.596578\pi\) | |||||||
\(80\) | −9.32121 | + | 178.642i | −0.0130268 | + | 0.249660i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 455.615i | 0.613589i | ||||||||
\(83\) | 981.633i | 1.29817i | 0.760715 | + | 0.649086i | \(0.224848\pi\) | ||||
−0.760715 | + | 0.649086i | \(0.775152\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | 541.358 | + | 28.2470i | 0.690806 | + | 0.0360449i | ||||
\(86\) | −598.330 | −0.750228 | ||||||||
\(87\) | 143.532i | 0.176876i | ||||||||
\(88\) | − | 341.285i | − | 0.413421i | ||||||
\(89\) | −157.477 | −0.187557 | −0.0937784 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937784 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(90\) | −200.973 | − | 10.4864i | −0.235382 | − | 0.0122818i | ||||
\(91\) | 512.156 | 0.589984 | ||||||||
\(92\) | 49.3939i | 0.0559747i | ||||||||
\(93\) | − | 455.423i | − | 0.507797i | ||||||
\(94\) | 1085.49 | 1.19106 | ||||||||
\(95\) | 45.2379 | − | 866.991i | 0.0488559 | − | 0.936330i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | − | 1752.63i | − | 1.83457i | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||
0.398234 | − | 0.917284i | \(-0.369623\pi\) | |||||||
\(98\) | 98.0000i | 0.101015i | ||||||||
\(99\) | 383.945 | 0.389777 | ||||||||
\(100\) | 497.285 | + | 52.0364i | 0.497285 | + | 0.0520364i | ||||
\(101\) | 1081.96 | 1.06593 | 0.532964 | − | 0.846138i | \(-0.321078\pi\) | ||||
0.532964 | + | 0.846138i | \(0.321078\pi\) | |||||||
\(102\) | − | 290.918i | − | 0.282404i | ||||||
\(103\) | − | 718.330i | − | 0.687177i | −0.939120 | − | 0.343588i | \(-0.888358\pi\) | ||
0.939120 | − | 0.343588i | \(-0.111642\pi\) | |||||||
\(104\) | 585.321 | 0.551879 | ||||||||
\(105\) | 12.2341 | − | 234.468i | 0.0113707 | − | 0.217921i | ||||
\(106\) | 304.733 | 0.279229 | ||||||||
\(107\) | 1950.95i | 1.76267i | 0.472490 | + | 0.881336i | \(0.343355\pi\) | ||||
−0.472490 | + | 0.881336i | \(0.656645\pi\) | |||||||
\(108\) | 108.000i | 0.0962250i | ||||||||
\(109\) | 1298.24 | 1.14081 | 0.570407 | − | 0.821362i | \(-0.306785\pi\) | ||||
0.570407 | + | 0.821362i | \(0.306785\pi\) | |||||||
\(110\) | −952.624 | − | 49.7061i | −0.825720 | − | 0.0430844i | ||||
\(111\) | −637.459 | −0.545090 | ||||||||
\(112\) | 112.000i | 0.0944911i | ||||||||
\(113\) | − | 1010.55i | − | 0.841280i | −0.907228 | − | 0.420640i | \(-0.861805\pi\) | ||
0.907228 | − | 0.420640i | \(-0.138195\pi\) | |||||||
\(114\) | −465.909 | −0.382775 | ||||||||
\(115\) | 137.873 | + | 7.19393i | 0.111797 | + | 0.00583337i | ||||
\(116\) | −191.376 | −0.153179 | ||||||||
\(117\) | 658.486i | 0.520317i | ||||||||
\(118\) | − | 477.212i | − | 0.372296i | ||||||
\(119\) | 339.405 | 0.261455 | ||||||||
\(120\) | 13.9818 | − | 267.964i | 0.0106363 | − | 0.203847i | ||||
\(121\) | 488.927 | 0.367338 | ||||||||
\(122\) | 1537.49i | 1.14096i | ||||||||
\(123\) | − | 683.423i | − | 0.500993i | ||||||
\(124\) | 607.230 | 0.439765 | ||||||||
\(125\) | 217.675 | − | 1380.49i | 0.155756 | − | 0.987796i | ||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | 1688.52i | 1.17978i | 0.807485 | + | 0.589888i | \(0.200828\pi\) | ||||
−0.807485 | + | 0.589888i | \(0.799172\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 897.495 | 0.612559 | ||||||||
\(130\) | 85.2485 | − | 1633.80i | 0.0575137 | − | 1.10226i | ||||
\(131\) | −919.194 | −0.613056 | −0.306528 | − | 0.951862i | \(-0.599167\pi\) | ||||
−0.306528 | + | 0.951862i | \(0.599167\pi\) | |||||||
\(132\) | 511.927i | 0.337557i | ||||||||
\(133\) | − | 543.561i | − | 0.354381i | ||||||
\(134\) | −626.773 | −0.404067 | ||||||||
\(135\) | 301.459 | + | 15.7295i | 0.192189 | + | 0.0100280i | ||||
\(136\) | 387.891 | 0.244569 | ||||||||
\(137\) | 1154.24i | 0.719805i | 0.932990 | + | 0.359903i | \(0.117190\pi\) | ||||
−0.932990 | + | 0.359903i | \(0.882810\pi\) | |||||||
\(138\) | − | 74.0909i | − | 0.0457032i | ||||||
\(139\) | −3050.52 | −1.86145 | −0.930724 | − | 0.365722i | \(-0.880822\pi\) | ||||
−0.930724 | + | 0.365722i | \(0.880822\pi\) | |||||||
\(140\) | 312.624 | + | 16.3121i | 0.188726 | + | 0.00984733i | ||||
\(141\) | −1628.23 | −0.972495 | ||||||||
\(142\) | − | 244.130i | − | 0.144274i | ||||||
\(143\) | 3121.27i | 1.82527i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | −27.8727 | + | 534.185i | −0.0159635 | + | 0.305942i | ||||
\(146\) | −63.6151 | −0.0360605 | ||||||||
\(147\) | − | 147.000i | − | 0.0824786i | ||||||
\(148\) | − | 849.945i | − | 0.472061i | ||||||
\(149\) | −1194.36 | −0.656681 | −0.328340 | − | 0.944559i | \(-0.606489\pi\) | ||||
−0.328340 | + | 0.944559i | \(0.606489\pi\) | |||||||
\(150\) | −745.927 | − | 78.0545i | −0.406031 | − | 0.0424875i | ||||
\(151\) | 1398.61 | 0.753755 | 0.376877 | − | 0.926263i | \(-0.376998\pi\) | ||||
0.376877 | + | 0.926263i | \(0.376998\pi\) | |||||||
\(152\) | − | 621.212i | − | 0.331493i | ||||||
\(153\) | 436.377i | 0.230582i | ||||||||
\(154\) | −597.248 | −0.312517 | ||||||||
\(155\) | 88.4394 | − | 1694.95i | 0.0458298 | − | 0.878336i | ||||
\(156\) | −877.982 | −0.450608 | ||||||||
\(157\) | 3465.39i | 1.76158i | 0.473506 | + | 0.880790i | \(0.342988\pi\) | ||||
−0.473506 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(158\) | 839.158i | 0.422530i | ||||||||
\(159\) | −457.100 | −0.227990 | ||||||||
\(160\) | 357.285 | + | 18.6424i | 0.176537 | + | 0.00921133i | ||||
\(161\) | 86.4394 | 0.0423129 | ||||||||
\(162\) | − | 162.000i | − | 0.0785674i | ||||||
\(163\) | 2697.83i | 1.29638i | 0.761478 | + | 0.648191i | \(0.224474\pi\) | ||||
−0.761478 | + | 0.648191i | \(0.775526\pi\) | |||||||
\(164\) | 911.230 | 0.433873 | ||||||||
\(165\) | 1428.94 | + | 74.5591i | 0.674197 | + | 0.0351783i | ||||
\(166\) | 1963.27 | 0.917946 | ||||||||
\(167\) | 3203.92i | 1.48459i | 0.670073 | + | 0.742296i | \(0.266263\pi\) | ||||
−0.670073 | + | 0.742296i | \(0.733737\pi\) | |||||||
\(168\) | − | 168.000i | − | 0.0771517i | ||||||
\(169\) | −3156.14 | −1.43657 | ||||||||
\(170\) | 56.4940 | − | 1082.72i | 0.0254876 | − | 0.488473i | ||||
\(171\) | 698.864 | 0.312535 | ||||||||
\(172\) | 1196.66i | 0.530491i | ||||||||
\(173\) | − | 231.906i | − | 0.101916i | −0.998701 | − | 0.0509581i | \(-0.983773\pi\) | ||
0.998701 | − | 0.0509581i | \(-0.0162275\pi\) | |||||||
\(174\) | 287.064 | 0.125070 | ||||||||
\(175\) | 91.0636 | − | 870.248i | 0.0393358 | − | 0.375912i | ||||
\(176\) | −682.570 | −0.292333 | ||||||||
\(177\) | 715.818i | 0.303978i | ||||||||
\(178\) | 314.955i | 0.132623i | ||||||||
\(179\) | −2906.13 | −1.21349 | −0.606744 | − | 0.794897i | \(-0.707525\pi\) | ||||
−0.606744 | + | 0.794897i | \(0.707525\pi\) | |||||||
\(180\) | −20.9727 | + | 401.945i | −0.00868453 | + | 0.166440i | ||||
\(181\) | −999.865 | −0.410604 | −0.205302 | − | 0.978699i | \(-0.565818\pi\) | ||||
−0.205302 | + | 0.978699i | \(0.565818\pi\) | |||||||
\(182\) | − | 1024.31i | − | 0.417182i | ||||||
\(183\) | − | 2306.23i | − | 0.931593i | ||||||
\(184\) | 98.7879 | 0.0395801 | ||||||||
\(185\) | −2372.44 | − | 123.789i | −0.942840 | − | 0.0491956i | ||||
\(186\) | −910.845 | −0.359067 | ||||||||
\(187\) | 2068.46i | 0.808880i | ||||||||
\(188\) | − | 2170.98i | − | 0.842206i | ||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −1733.98 | − | 90.4758i | −0.662086 | − | 0.0345463i | ||||
\(191\) | 2745.04 | 1.03992 | 0.519959 | − | 0.854191i | \(-0.325947\pi\) | ||||
0.519959 | + | 0.854191i | \(0.325947\pi\) | |||||||
\(192\) | − | 192.000i | − | 0.0721688i | ||||||
\(193\) | − | 3825.38i | − | 1.42672i | −0.700798 | − | 0.713360i | \(-0.747173\pi\) | ||
0.700798 | − | 0.713360i | \(-0.252827\pi\) | |||||||
\(194\) | −3505.27 | −1.29724 | ||||||||
\(195\) | −127.873 | + | 2450.70i | −0.0469598 | + | 0.899991i | ||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | − | 4449.00i | − | 1.60902i | −0.593936 | − | 0.804512i | \(-0.702427\pi\) | ||
0.593936 | − | 0.804512i | \(-0.297573\pi\) | |||||||
\(198\) | − | 767.891i | − | 0.275614i | ||||||
\(199\) | −4383.22 | −1.56140 | −0.780699 | − | 0.624907i | \(-0.785137\pi\) | ||||
−0.780699 | + | 0.624907i | \(0.785137\pi\) | |||||||
\(200\) | 104.073 | − | 994.570i | 0.0367953 | − | 0.351633i | ||||
\(201\) | 940.159 | 0.329919 | ||||||||
\(202\) | − | 2163.91i | − | 0.753724i | ||||||
\(203\) | 334.908i | 0.115793i | ||||||||
\(204\) | −581.836 | −0.199690 | ||||||||
\(205\) | 132.715 | − | 2543.51i | 0.0452157 | − | 0.866567i | ||||
\(206\) | −1436.66 | −0.485907 | ||||||||
\(207\) | 111.136i | 0.0373165i | ||||||||
\(208\) | − | 1170.64i | − | 0.390238i | ||||||
\(209\) | 3312.66 | 1.09637 | ||||||||
\(210\) | −468.936 | − | 24.4682i | −0.154094 | − | 0.00804031i | ||||
\(211\) | −145.655 | −0.0475226 | −0.0237613 | − | 0.999718i | \(-0.507564\pi\) | ||||
−0.0237613 | + | 0.999718i | \(0.507564\pi\) | |||||||
\(212\) | − | 609.467i | − | 0.197445i | ||||||
\(213\) | 366.195i | 0.117800i | ||||||||
\(214\) | 3901.91 | 1.24640 | ||||||||
\(215\) | 3340.22 | + | 174.286i | 1.05954 | + | 0.0552848i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | − | 1062.65i | − | 0.332431i | ||||||
\(218\) | − | 2596.48i | − | 0.806678i | ||||||
\(219\) | 95.4227 | 0.0294432 | ||||||||
\(220\) | −99.4121 | + | 1905.25i | −0.0304653 | + | 0.583872i | ||||
\(221\) | −3547.51 | −1.07978 | ||||||||
\(222\) | 1274.92i | 0.385437i | ||||||||
\(223\) | − | 1911.17i | − | 0.573908i | −0.957944 | − | 0.286954i | \(-0.907357\pi\) | ||
0.957944 | − | 0.286954i | \(-0.0926428\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 1118.89 | + | 117.082i | 0.331523 | + | 0.0346909i | ||||
\(226\) | −2021.10 | −0.594875 | ||||||||
\(227\) | 2083.60i | 0.609222i | 0.952477 | + | 0.304611i | \(0.0985265\pi\) | ||||
−0.952477 | + | 0.304611i | \(0.901474\pi\) | |||||||
\(228\) | 931.818i | 0.270663i | ||||||||
\(229\) | −2002.03 | −0.577720 | −0.288860 | − | 0.957371i | \(-0.593276\pi\) | ||||
−0.288860 | + | 0.957371i | \(0.593276\pi\) | |||||||
\(230\) | 14.3879 | − | 275.745i | 0.00412481 | − | 0.0790527i | ||||
\(231\) | 895.873 | 0.255169 | ||||||||
\(232\) | 382.752i | 0.108314i | ||||||||
\(233\) | 3245.52i | 0.912537i | 0.889842 | + | 0.456269i | \(0.150814\pi\) | ||||
−0.889842 | + | 0.456269i | \(0.849186\pi\) | |||||||
\(234\) | 1316.97 | 0.367920 | ||||||||
\(235\) | −6059.82 | − | 316.189i | −1.68212 | − | 0.0877699i | ||||
\(236\) | −954.424 | −0.263253 | ||||||||
\(237\) | − | 1258.74i | − | 0.344995i | ||||||
\(238\) | − | 678.809i | − | 0.184877i | ||||||
\(239\) | 5602.03 | 1.51617 | 0.758086 | − | 0.652155i | \(-0.226135\pi\) | ||||
0.758086 | + | 0.652155i | \(0.226135\pi\) | |||||||
\(240\) | −535.927 | − | 27.9636i | −0.144141 | − | 0.00752102i | ||||
\(241\) | 4789.93 | 1.28028 | 0.640138 | − | 0.768260i | \(-0.278877\pi\) | ||||
0.640138 | + | 0.768260i | \(0.278877\pi\) | |||||||
\(242\) | − | 977.855i | − | 0.259747i | ||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 3074.98 | 0.806783 | ||||||||
\(245\) | 28.5462 | − | 547.092i | 0.00744388 | − | 0.142663i | ||||
\(246\) | −1366.85 | −0.354256 | ||||||||
\(247\) | 5681.38i | 1.46355i | ||||||||
\(248\) | − | 1214.46i | − | 0.310961i | ||||||
\(249\) | −2944.90 | −0.749500 | ||||||||
\(250\) | −2760.97 | − | 435.350i | −0.698477 | − | 0.110136i | ||||
\(251\) | −337.467 | −0.0848634 | −0.0424317 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424317 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(252\) | 252.000i | 0.0629941i | ||||||||
\(253\) | 526.794i | 0.130906i | ||||||||
\(254\) | 3377.03 | 0.834227 | ||||||||
\(255\) | −84.7409 | + | 1624.07i | −0.0208105 | + | 0.398837i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2226.69i | 0.540455i | 0.962797 | + | 0.270227i | \(0.0870989\pi\) | ||||
−0.962797 | + | 0.270227i | \(0.912901\pi\) | |||||||
\(258\) | − | 1794.99i | − | 0.433144i | ||||||
\(259\) | −1487.40 | −0.356845 | ||||||||
\(260\) | −3267.60 | − | 170.497i | −0.779415 | − | 0.0406684i | ||||
\(261\) | −430.595 | −0.102120 | ||||||||
\(262\) | 1838.39i | 0.433496i | ||||||||
\(263\) | − | 6474.78i | − | 1.51807i | −0.651051 | − | 0.759034i | \(-0.725672\pi\) | ||
0.651051 | − | 0.759034i | \(-0.274328\pi\) | |||||||
\(264\) | 1023.85 | 0.238689 | ||||||||
\(265\) | −1701.20 | − | 88.7651i | −0.394354 | − | 0.0205766i | ||||
\(266\) | −1087.12 | −0.250585 | ||||||||
\(267\) | − | 472.432i | − | 0.108286i | ||||||
\(268\) | 1253.55i | 0.285718i | ||||||||
\(269\) | −4980.38 | −1.12884 | −0.564422 | − | 0.825486i | \(-0.690901\pi\) | ||||
−0.564422 | + | 0.825486i | \(0.690901\pi\) | |||||||
\(270\) | 31.4591 | − | 602.918i | 0.00709089 | − | 0.135898i | ||||
\(271\) | 7829.76 | 1.75507 | 0.877535 | − | 0.479513i | \(-0.159186\pi\) | ||||
0.877535 | + | 0.479513i | \(0.159186\pi\) | |||||||
\(272\) | − | 775.782i | − | 0.172936i | ||||||
\(273\) | 1536.47i | 0.340627i | ||||||||
\(274\) | 2308.48 | 0.508979 | ||||||||
\(275\) | 5303.62 | + | 554.976i | 1.16298 | + | 0.121696i | ||||
\(276\) | −148.182 | −0.0323170 | ||||||||
\(277\) | 3104.10i | 0.673312i | 0.941628 | + | 0.336656i | \(0.109296\pi\) | ||||
−0.941628 | + | 0.336656i | \(0.890704\pi\) | |||||||
\(278\) | 6101.03i | 1.31624i | ||||||||
\(279\) | 1366.27 | 0.293177 | ||||||||
\(280\) | 32.6242 | − | 625.248i | 0.00696311 | − | 0.133449i | ||||
\(281\) | 2916.45 | 0.619148 | 0.309574 | − | 0.950875i | \(-0.399814\pi\) | ||||
0.309574 | + | 0.950875i | \(0.399814\pi\) | |||||||
\(282\) | 3256.46i | 0.687658i | ||||||||
\(283\) | 8199.29i | 1.72225i | 0.508391 | + | 0.861126i | \(0.330240\pi\) | ||||
−0.508391 | + | 0.861126i | \(0.669760\pi\) | |||||||
\(284\) | −488.261 | −0.102017 | ||||||||
\(285\) | 2600.97 | + | 135.714i | 0.540591 | + | 0.0282070i | ||||
\(286\) | 6242.54 | 1.29066 | ||||||||
\(287\) | − | 1594.65i | − | 0.327977i | ||||||
\(288\) | 288.000i | 0.0589256i | ||||||||
\(289\) | 2562.07 | 0.521488 | ||||||||
\(290\) | 1068.37 | + | 55.7454i | 0.216334 | + | 0.0112879i | ||||
\(291\) | 5257.90 | 1.05919 | ||||||||
\(292\) | 127.230i | 0.0254986i | ||||||||
\(293\) | − | 8448.78i | − | 1.68458i | −0.539022 | − | 0.842291i | \(-0.681206\pi\) | ||
0.539022 | − | 0.842291i | \(-0.318794\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | −139.006 | + | 2664.07i | −0.0274347 | + | 0.525791i | ||||
\(296\) | −1699.89 | −0.333798 | ||||||||
\(297\) | 1151.84i | 0.225038i | ||||||||
\(298\) | 2388.71i | 0.464344i | ||||||||
\(299\) | −903.479 | −0.174748 | ||||||||
\(300\) | −156.109 | + | 1491.85i | −0.0300432 | + | 0.287108i | ||||
\(301\) | 2094.16 | 0.401014 | ||||||||
\(302\) | − | 2797.21i | − | 0.532985i | ||||||
\(303\) | 3245.87i | 0.615413i | ||||||||
\(304\) | −1242.42 | −0.234401 | ||||||||
\(305\) | 447.852 | − | 8583.14i | 0.0840784 | − | 1.61137i | ||||
\(306\) | 872.755 | 0.163046 | ||||||||
\(307\) | − | 2011.52i | − | 0.373953i | −0.982364 | − | 0.186977i | \(-0.940131\pi\) | ||
0.982364 | − | 0.186977i | \(-0.0598688\pi\) | |||||||
\(308\) | 1194.50i | 0.220983i | ||||||||
\(309\) | 2154.99 | 0.396742 | ||||||||
\(310\) | −3389.91 | − | 176.879i | −0.621077 | − | 0.0324066i | ||||
\(311\) | −3741.47 | −0.682185 | −0.341092 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341092 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(312\) | 1755.96i | 0.318628i | ||||||||
\(313\) | − | 8474.92i | − | 1.53045i | −0.643763 | − | 0.765225i | \(-0.722628\pi\) | ||
0.643763 | − | 0.765225i | \(-0.277372\pi\) | |||||||
\(314\) | 6930.78 | 1.24563 | ||||||||
\(315\) | 703.405 | + | 36.7023i | 0.125817 | + | 0.00656488i | ||||
\(316\) | 1678.32 | 0.298774 | ||||||||
\(317\) | − | 9371.15i | − | 1.66037i | −0.557490 | − | 0.830183i | \(-0.688236\pi\) | ||
0.557490 | − | 0.830183i | \(-0.311764\pi\) | |||||||
\(318\) | 914.200i | 0.161213i | ||||||||
\(319\) | −2041.05 | −0.358235 | ||||||||
\(320\) | 37.2848 | − | 714.570i | 0.00651339 | − | 0.124830i | ||||
\(321\) | −5852.86 | −1.01768 | ||||||||
\(322\) | − | 172.879i | − | 0.0299197i | ||||||
\(323\) | 3765.04i | 0.648583i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | −951.812 | + | 9095.98i | −0.162452 | + | 1.55247i | ||||
\(326\) | 5395.66 | 0.916680 | ||||||||
\(327\) | 3894.72i | 0.658650i | ||||||||
\(328\) | − | 1822.46i | − | 0.306794i | ||||||
\(329\) | −3799.21 | −0.636648 | ||||||||
\(330\) | 149.118 | − | 2857.87i | 0.0248748 | − | 0.476729i | ||||
\(331\) | −1757.55 | −0.291853 | −0.145927 | − | 0.989295i | \(-0.546616\pi\) | ||||
−0.145927 | + | 0.989295i | \(0.546616\pi\) | |||||||
\(332\) | − | 3926.53i | − | 0.649086i | ||||||
\(333\) | − | 1912.38i | − | 0.314708i | ||||||
\(334\) | 6407.84 | 1.04976 | ||||||||
\(335\) | 3499.01 | + | 182.571i | 0.570660 | + | 0.0297759i | ||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | − | 2901.49i | − | 0.469003i | −0.972116 | − | 0.234502i | \(-0.924654\pi\) | ||
0.972116 | − | 0.234502i | \(-0.0753458\pi\) | |||||||
\(338\) | 6312.28i | 1.01581i | ||||||||
\(339\) | 3031.65 | 0.485713 | ||||||||
\(340\) | −2165.43 | − | 112.988i | −0.345403 | − | 0.0180224i | ||||
\(341\) | 6476.20 | 1.02846 | ||||||||
\(342\) | − | 1397.73i | − | 0.220995i | ||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 2393.32 | 0.375114 | ||||||||
\(345\) | −21.5818 | + | 413.618i | −0.00336790 | + | 0.0645462i | ||||
\(346\) | −463.812 | −0.0720656 | ||||||||
\(347\) | 261.576i | 0.0404672i | 0.999795 | + | 0.0202336i | \(0.00644100\pi\) | ||||
−0.999795 | + | 0.0202336i | \(0.993559\pi\) | |||||||
\(348\) | − | 574.127i | − | 0.0884381i | ||||||
\(349\) | −10958.6 | −1.68081 | −0.840404 | − | 0.541961i | \(-0.817682\pi\) | ||||
−0.840404 | + | 0.541961i | \(0.817682\pi\) | |||||||
\(350\) | −1740.50 | − | 182.127i | −0.265810 | − | 0.0278146i | ||||
\(351\) | −1975.46 | −0.300405 | ||||||||
\(352\) | 1365.14i | 0.206711i | ||||||||
\(353\) | 4138.16i | 0.623943i | 0.950091 | + | 0.311971i | \(0.100989\pi\) | ||||
−0.950091 | + | 0.311971i | \(0.899011\pi\) | |||||||
\(354\) | 1431.64 | 0.214945 | ||||||||
\(355\) | −71.1122 | + | 1362.88i | −0.0106317 | + | 0.203758i | ||||
\(356\) | 629.909 | 0.0937784 | ||||||||
\(357\) | 1018.21i | 0.150951i | ||||||||
\(358\) | 5812.26i | 0.858066i | ||||||||
\(359\) | 7383.25 | 1.08544 | 0.542720 | − | 0.839914i | \(-0.317395\pi\) | ||||
0.542720 | + | 0.839914i | \(0.317395\pi\) | |||||||
\(360\) | 803.891 | + | 41.9455i | 0.117691 | + | 0.00614089i | ||||
\(361\) | −829.242 | −0.120898 | ||||||||
\(362\) | 1999.73i | 0.290341i | ||||||||
\(363\) | 1466.78i | 0.212083i | ||||||||
\(364\) | −2048.62 | −0.294992 | ||||||||
\(365\) | 355.136 | + | 18.5303i | 0.0509279 | + | 0.00265732i | ||||
\(366\) | −4612.46 | −0.658736 | ||||||||
\(367\) | − | 11585.4i | − | 1.64782i | −0.566718 | − | 0.823912i | \(-0.691787\pi\) | ||
0.566718 | − | 0.823912i | \(-0.308213\pi\) | |||||||
\(368\) | − | 197.576i | − | 0.0279874i | ||||||
\(369\) | 2050.27 | 0.289249 | ||||||||
\(370\) | −247.579 | + | 4744.88i | −0.0347865 | + | 0.666689i | ||||
\(371\) | −1066.57 | −0.149254 | ||||||||
\(372\) | 1821.69i | 0.253899i | ||||||||
\(373\) | − | 7712.37i | − | 1.07059i | −0.844664 | − | 0.535297i | \(-0.820200\pi\) | ||
0.844664 | − | 0.535297i | \(-0.179800\pi\) | |||||||
\(374\) | 4136.92 | 0.571965 | ||||||||
\(375\) | 4141.46 | + | 653.025i | 0.570304 | + | 0.0899255i | ||||
\(376\) | −4341.95 | −0.595529 | ||||||||
\(377\) | − | 3500.51i | − | 0.478211i | ||||||
\(378\) | − | 378.000i | − | 0.0514344i | ||||||
\(379\) | 6663.16 | 0.903071 | 0.451535 | − | 0.892253i | \(-0.350877\pi\) | ||||
0.451535 | + | 0.892253i | \(0.350877\pi\) | |||||||
\(380\) | −180.952 | + | 3467.96i | −0.0244279 | + | 0.468165i | ||||
\(381\) | −5065.55 | −0.681144 | ||||||||
\(382\) | − | 5490.08i | − | 0.735333i | ||||||
\(383\) | − | 8432.12i | − | 1.12496i | −0.826810 | − | 0.562482i | \(-0.809847\pi\) | ||
0.826810 | − | 0.562482i | \(-0.190153\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 3334.18 | + | 173.971i | 0.441366 | + | 0.0230296i | ||||
\(386\) | −7650.76 | −1.00884 | ||||||||
\(387\) | 2692.49i | 0.353661i | ||||||||
\(388\) | 7010.54i | 0.917284i | ||||||||
\(389\) | −5931.40 | −0.773095 | −0.386547 | − | 0.922270i | \(-0.626332\pi\) | ||||
−0.386547 | + | 0.922270i | \(0.626332\pi\) | |||||||
\(390\) | 4901.40 | + | 255.745i | 0.636390 | + | 0.0332056i | ||||
\(391\) | −598.733 | −0.0774405 | ||||||||
\(392\) | − | 392.000i | − | 0.0505076i | ||||||
\(393\) | − | 2757.58i | − | 0.353948i | ||||||
\(394\) | −8897.99 | −1.13775 | ||||||||
\(395\) | 244.436 | − | 4684.66i | 0.0311365 | − | 0.596736i | ||||
\(396\) | −1535.78 | −0.194889 | ||||||||
\(397\) | − | 690.377i | − | 0.0872772i | −0.999047 | − | 0.0436386i | \(-0.986105\pi\) | ||
0.999047 | − | 0.0436386i | \(-0.0138950\pi\) | |||||||
\(398\) | 8766.44i | 1.10408i | ||||||||
\(399\) | 1630.68 | 0.204602 | ||||||||
\(400\) | −1989.14 | − | 208.145i | −0.248642 | − | 0.0260182i | ||||
\(401\) | −2314.18 | −0.288191 | −0.144096 | − | 0.989564i | \(-0.546027\pi\) | ||||
−0.144096 | + | 0.989564i | \(0.546027\pi\) | |||||||
\(402\) | − | 1880.32i | − | 0.233288i | ||||||
\(403\) | 11107.0i | 1.37290i | ||||||||
\(404\) | −4327.82 | −0.532964 | ||||||||
\(405\) | −47.1886 | + | 904.377i | −0.00578968 | + | 0.110960i | ||||
\(406\) | 669.815 | 0.0818778 | ||||||||
\(407\) | − | 9064.80i | − | 1.10399i | ||||||
\(408\) | 1163.67i | 0.141202i | ||||||||
\(409\) | 11899.3 | 1.43859 | 0.719294 | − | 0.694706i | \(-0.244466\pi\) | ||||
0.719294 | + | 0.694706i | \(0.244466\pi\) | |||||||
\(410\) | −5087.01 | − | 265.430i | −0.612755 | − | 0.0319724i | ||||
\(411\) | −3462.72 | −0.415580 | ||||||||
\(412\) | 2873.32i | 0.343588i | ||||||||
\(413\) | 1670.24i | 0.199001i | ||||||||
\(414\) | 222.273 | 0.0263867 | ||||||||
\(415\) | −10960.1 | − | 571.876i | −1.29641 | − | 0.0676440i | ||||
\(416\) | −2341.28 | −0.275940 | ||||||||
\(417\) | − | 9151.55i | − | 1.07471i | ||||||
\(418\) | − | 6625.32i | − | 0.775251i | ||||||
\(419\) | −14383.1 | −1.67700 | −0.838498 | − | 0.544904i | \(-0.816566\pi\) | ||||
−0.838498 | + | 0.544904i | \(0.816566\pi\) | |||||||
\(420\) | −48.9364 | + | 937.873i | −0.00568536 | + | 0.108961i | ||||
\(421\) | 4620.71 | 0.534916 | 0.267458 | − | 0.963569i | \(-0.413816\pi\) | ||||
0.267458 | + | 0.963569i | \(0.413816\pi\) | |||||||
\(422\) | 291.309i | 0.0336036i | ||||||||
\(423\) | − | 4884.70i | − | 0.561470i | ||||||
\(424\) | −1218.93 | −0.139615 | ||||||||
\(425\) | −630.764 | + | 6027.88i | −0.0719918 | + | 0.687989i | ||||
\(426\) | 732.391 | 0.0832968 | ||||||||
\(427\) | − | 5381.21i | − | 0.609871i | ||||||
\(428\) | − | 7803.82i | − | 0.881336i | ||||||
\(429\) | −9363.81 | −1.05382 | ||||||||
\(430\) | 348.573 | − | 6680.45i | 0.0390923 | − | 0.749209i | ||||
\(431\) | −12339.5 | −1.37905 | −0.689527 | − | 0.724260i | \(-0.742181\pi\) | ||||
−0.689527 | + | 0.724260i | \(0.742181\pi\) | |||||||
\(432\) | − | 432.000i | − | 0.0481125i | ||||||
\(433\) | 11280.9i | 1.25202i | 0.779813 | + | 0.626012i | \(0.215314\pi\) | ||||
−0.779813 | + | 0.626012i | \(0.784686\pi\) | |||||||
\(434\) | −2125.31 | −0.235064 | ||||||||
\(435\) | −1602.55 | − | 83.6182i | −0.176636 | − | 0.00921651i | ||||
\(436\) | −5192.96 | −0.570407 | ||||||||
\(437\) | 958.879i | 0.104964i | ||||||||
\(438\) | − | 190.845i | − | 0.0208195i | ||||||
\(439\) | −6585.30 | −0.715943 | −0.357972 | − | 0.933733i | \(-0.616532\pi\) | ||||
−0.357972 | + | 0.933733i | \(0.616532\pi\) | |||||||
\(440\) | 3810.50 | + | 198.824i | 0.412860 | + | 0.0215422i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 7095.02i | 0.763520i | ||||||||
\(443\) | 5521.10i | 0.592134i | 0.955167 | + | 0.296067i | \(0.0956752\pi\) | ||||
−0.955167 | + | 0.296067i | \(0.904325\pi\) | |||||||
\(444\) | 2549.84 | 0.272545 | ||||||||
\(445\) | 91.7424 | − | 1758.26i | 0.00977305 | − | 0.187302i | ||||
\(446\) | −3822.35 | −0.405815 | ||||||||
\(447\) | − | 3583.07i | − | 0.379135i | ||||||
\(448\) | − | 448.000i | − | 0.0472456i | ||||||
\(449\) | 10012.7 | 1.05240 | 0.526199 | − | 0.850361i | \(-0.323617\pi\) | ||||
0.526199 | + | 0.850361i | \(0.323617\pi\) | |||||||
\(450\) | 234.164 | − | 2237.78i | 0.0245302 | − | 0.234422i | ||||
\(451\) | 9718.41 | 1.01468 | ||||||||
\(452\) | 4042.21i | 0.420640i | ||||||||
\(453\) | 4195.82i | 0.435180i | ||||||||
\(454\) | 4167.20 | 0.430785 | ||||||||
\(455\) | −298.370 | + | 5718.30i | −0.0307424 | + | 0.589182i | ||||
\(456\) | 1863.64 | 0.191388 | ||||||||
\(457\) | − | 12128.7i | − | 1.24148i | −0.784017 | − | 0.620740i | \(-0.786832\pi\) | ||
0.784017 | − | 0.620740i | \(-0.213168\pi\) | |||||||
\(458\) | 4004.06i | 0.408509i | ||||||||
\(459\) | −1309.13 | −0.133126 | ||||||||
\(460\) | −551.491 | − | 28.7757i | −0.0558987 | − | 0.00291668i | ||||
\(461\) | −8279.82 | −0.836507 | −0.418254 | − | 0.908330i | \(-0.637358\pi\) | ||||
−0.418254 | + | 0.908330i | \(0.637358\pi\) | |||||||
\(462\) | − | 1791.75i | − | 0.180432i | ||||||
\(463\) | − | 12932.7i | − | 1.29813i | −0.760734 | − | 0.649064i | \(-0.775161\pi\) | ||
0.760734 | − | 0.649064i | \(-0.224839\pi\) | |||||||
\(464\) | 765.503 | 0.0765896 | ||||||||
\(465\) | 5084.86 | + | 265.318i | 0.507107 | + | 0.0264599i | ||||
\(466\) | 6491.04 | 0.645261 | ||||||||
\(467\) | 7326.71i | 0.725995i | 0.931790 | + | 0.362997i | \(0.118247\pi\) | ||||
−0.931790 | + | 0.362997i | \(0.881753\pi\) | |||||||
\(468\) | − | 2633.95i | − | 0.260158i | ||||||
\(469\) | 2193.70 | 0.215983 | ||||||||
\(470\) | −632.379 | + | 12119.6i | −0.0620627 | + | 1.18944i | ||||
\(471\) | −10396.2 | −1.01705 | ||||||||
\(472\) | 1908.85i | 0.186148i | ||||||||
\(473\) | 12762.6i | 1.24064i | ||||||||
\(474\) | −2517.47 | −0.243948 | ||||||||
\(475\) | 9653.73 | + | 1010.18i | 0.932513 | + | 0.0975790i | ||||
\(476\) | −1357.62 | −0.130728 | ||||||||
\(477\) | − | 1371.30i | − | 0.131630i | ||||||
\(478\) | − | 11204.1i | − | 1.07210i | ||||||
\(479\) | −12568.4 | −1.19888 | −0.599442 | − | 0.800418i | \(-0.704611\pi\) | ||||
−0.599442 | + | 0.800418i | \(0.704611\pi\) | |||||||
\(480\) | −55.9273 | + | 1071.85i | −0.00531816 | + | 0.101923i | ||||
\(481\) | 15546.6 | 1.47373 | ||||||||
\(482\) | − | 9579.85i | − | 0.905291i | ||||||
\(483\) | 259.318i | 0.0244294i | ||||||||
\(484\) | −1955.71 | −0.183669 | ||||||||
\(485\) | 19568.4 | + | 1021.04i | 1.83208 | + | 0.0955941i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 10464.8i | 0.973729i | 0.873477 | + | 0.486865i | \(0.161860\pi\) | ||||
−0.873477 | + | 0.486865i | \(0.838140\pi\) | |||||||
\(488\) | − | 6149.95i | − | 0.570482i | ||||||
\(489\) | −8093.49 | −0.748466 | ||||||||
\(490\) | −1094.18 | − | 57.0924i | −0.100878 | − | 0.00526362i | ||||
\(491\) | −1536.22 | −0.141199 | −0.0705995 | − | 0.997505i | \(-0.522491\pi\) | ||||
−0.0705995 | + | 0.997505i | \(0.522491\pi\) | |||||||
\(492\) | 2733.69i | 0.250497i | ||||||||
\(493\) | − | 2319.78i | − | 0.211922i | ||||||
\(494\) | 11362.8 | 1.03489 | ||||||||
\(495\) | −223.677 | + | 4286.81i | −0.0203102 | + | 0.389248i | ||||
\(496\) | −2428.92 | −0.219883 | ||||||||
\(497\) | 854.456i | 0.0771179i | ||||||||
\(498\) | 5889.80i | 0.529976i | ||||||||
\(499\) | −12736.8 | −1.14264 | −0.571320 | − | 0.820728i | \(-0.693568\pi\) | ||||
−0.571320 | + | 0.820728i | \(0.693568\pi\) | |||||||
\(500\) | −870.700 | + | 5521.95i | −0.0778778 | + | 0.493898i | ||||
\(501\) | −9611.76 | −0.857129 | ||||||||
\(502\) | 674.933i | 0.0600075i | ||||||||
\(503\) | 6113.67i | 0.541938i | 0.962588 | + | 0.270969i | \(0.0873441\pi\) | ||||
−0.962588 | + | 0.270969i | \(0.912656\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −630.321 | + | 12080.2i | −0.0555424 | + | 1.06448i | ||||
\(506\) | 1053.59 | 0.0925646 | ||||||||
\(507\) | − | 9468.42i | − | 0.829403i | ||||||
\(508\) | − | 6754.06i | − | 0.589888i | ||||||
\(509\) | −14565.5 | −1.26837 | −0.634187 | − | 0.773179i | \(-0.718665\pi\) | ||||
−0.634187 | + | 0.773179i | \(0.718665\pi\) | |||||||
\(510\) | 3248.15 | + | 169.482i | 0.282020 | + | 0.0147153i | ||||
\(511\) | 222.653 | 0.0192751 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 2096.59i | 0.180442i | ||||||||
\(514\) | 4453.37 | 0.382159 | ||||||||
\(515\) | 8020.27 | + | 418.482i | 0.686243 | + | 0.0358068i | ||||
\(516\) | −3589.98 | −0.306279 | ||||||||
\(517\) | − | 23153.8i | − | 1.96964i | ||||||
\(518\) | 2974.81i | 0.252327i | ||||||||
\(519\) | 695.718 | 0.0588413 | ||||||||
\(520\) | −340.994 | + | 6535.20i | −0.0287569 | + | 0.551130i | ||||
\(521\) | −18007.0 | −1.51420 | −0.757102 | − | 0.653297i | \(-0.773385\pi\) | ||||
−0.757102 | + | 0.653297i | \(0.773385\pi\) | |||||||
\(522\) | 861.191i | 0.0722094i | ||||||||
\(523\) | 8077.14i | 0.675313i | 0.941269 | + | 0.337657i | \(0.109634\pi\) | ||||
−0.941269 | + | 0.337657i | \(0.890366\pi\) | |||||||
\(524\) | 3676.78 | 0.306528 | ||||||||
\(525\) | 2610.75 | + | 273.191i | 0.217033 | + | 0.0227105i | ||||
\(526\) | −12949.6 | −1.07344 | ||||||||
\(527\) | 7360.60i | 0.608411i | ||||||||
\(528\) | − | 2047.71i | − | 0.168779i | ||||||
\(529\) | 12014.5 | 0.987467 | ||||||||
\(530\) | −177.530 | + | 3402.39i | −0.0145499 | + | 0.278850i | ||||
\(531\) | −2147.45 | −0.175502 | ||||||||
\(532\) | 2174.24i | 0.177191i | ||||||||
\(533\) | 16667.6i | 1.35451i | ||||||||
\(534\) | −944.864 | −0.0765698 | ||||||||
\(535\) | −21782.7 | − | 1136.58i | −1.76028 | − | 0.0918478i | ||||
\(536\) | 2507.09 | 0.202033 | ||||||||
\(537\) | − | 8718.39i | − | 0.700608i | ||||||
\(538\) | 9960.76i | 0.798214i | ||||||||
\(539\) | 2090.37 | 0.167047 | ||||||||
\(540\) | −1205.84 | − | 62.9182i | −0.0960943 | − | 0.00501401i | ||||
\(541\) | 17455.2 | 1.38717 | 0.693585 | − | 0.720375i | \(-0.256030\pi\) | ||||
0.693585 | + | 0.720375i | \(0.256030\pi\) | |||||||
\(542\) | − | 15659.5i | − | 1.24102i | ||||||
\(543\) | − | 2999.60i | − | 0.237063i | ||||||
\(544\) | −1551.56 | −0.122284 | ||||||||
\(545\) | −756.323 | + | 14495.0i | −0.0594446 | + | 1.13926i | ||||
\(546\) | 3072.94 | 0.240860 | ||||||||
\(547\) | 5333.74i | 0.416918i | 0.978031 | + | 0.208459i | \(0.0668448\pi\) | ||||
−0.978031 | + | 0.208459i | \(0.933155\pi\) | |||||||
\(548\) | − | 4616.96i | − | 0.359903i | ||||||
\(549\) | 6918.70 | 0.537856 | ||||||||
\(550\) | 1109.95 | − | 10607.2i | 0.0860518 | − | 0.822353i | ||||
\(551\) | −3715.15 | −0.287243 | ||||||||
\(552\) | 296.364i | 0.0228516i | ||||||||
\(553\) | − | 2937.05i | − | 0.225852i | ||||||
\(554\) | 6208.20 | 0.476103 | ||||||||
\(555\) | 371.368 | − | 7117.33i | 0.0284031 | − | 0.544349i | ||||
\(556\) | 12202.1 | 0.930724 | ||||||||
\(557\) | 23117.7i | 1.75858i | 0.476291 | + | 0.879288i | \(0.341981\pi\) | ||||
−0.476291 | + | 0.879288i | \(0.658019\pi\) | |||||||
\(558\) | − | 2732.54i | − | 0.207307i | ||||||
\(559\) | −21888.5 | −1.65614 | ||||||||
\(560\) | −1250.50 | − | 65.2485i | −0.0943628 | − | 0.00492366i | ||||
\(561\) | −6205.37 | −0.467007 | ||||||||
\(562\) | − | 5832.89i | − | 0.437804i | ||||||
\(563\) | − | 10931.0i | − | 0.818273i | −0.912473 | − | 0.409137i | \(-0.865830\pi\) | ||
0.912473 | − | 0.409137i | \(-0.134170\pi\) | |||||||
\(564\) | 6512.93 | 0.486248 | ||||||||
\(565\) | 11283.0 | + | 588.723i | 0.840138 | + | 0.0438367i | ||||
\(566\) | 16398.6 | 1.21782 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 976.521i | 0.0721372i | ||||||||
\(569\) | 14484.1 | 1.06714 | 0.533571 | − | 0.845755i | \(-0.320850\pi\) | ||||
0.533571 | + | 0.845755i | \(0.320850\pi\) | |||||||
\(570\) | 271.427 | − | 5201.95i | 0.0199453 | − | 0.382255i | ||||
\(571\) | 13431.3 | 0.984381 | 0.492190 | − | 0.870488i | \(-0.336196\pi\) | ||||
0.492190 | + | 0.870488i | \(0.336196\pi\) | |||||||
\(572\) | − | 12485.1i | − | 0.912635i | ||||||
\(573\) | 8235.12i | 0.600396i | ||||||||
\(574\) | −3189.31 | −0.231915 | ||||||||
\(575\) | −160.643 | + | 1535.18i | −0.0116509 | + | 0.111342i | ||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | − | 19865.0i | − | 1.43326i | −0.697452 | − | 0.716631i | \(-0.745683\pi\) | ||
0.697452 | − | 0.716631i | \(-0.254317\pi\) | |||||||
\(578\) | − | 5124.15i | − | 0.368748i | ||||||
\(579\) | 11476.1 | 0.823717 | ||||||||
\(580\) | 111.491 | − | 2136.74i | 0.00798173 | − | 0.152971i | ||||
\(581\) | −6871.43 | −0.490663 | ||||||||
\(582\) | − | 10515.8i | − | 0.748959i | ||||||
\(583\) | − | 6500.05i | − | 0.461758i | ||||||
\(584\) | 254.461 | 0.0180302 | ||||||||
\(585\) | −7352.10 | − | 383.618i | −0.519610 | − | 0.0271122i | ||||
\(586\) | −16897.6 | −1.19118 | ||||||||
\(587\) | 12110.3i | 0.851526i | 0.904835 | + | 0.425763i | \(0.139994\pi\) | ||||
−0.904835 | + | 0.425763i | \(0.860006\pi\) | |||||||
\(588\) | 588.000i | 0.0412393i | ||||||||
\(589\) | 11788.1 | 0.824651 | ||||||||
\(590\) | 5328.15 | + | 278.012i | 0.371790 | + | 0.0193993i | ||||
\(591\) | 13347.0 | 0.928971 | ||||||||
\(592\) | 3399.78i | 0.236031i | ||||||||
\(593\) | − | 12185.9i | − | 0.843868i | −0.906627 | − | 0.421934i | \(-0.861351\pi\) | ||
0.906627 | − | 0.421934i | \(-0.138649\pi\) | |||||||
\(594\) | 2303.67 | 0.159126 | ||||||||
\(595\) | −197.729 | + | 3789.50i | −0.0136237 | + | 0.261100i | ||||
\(596\) | 4777.42 | 0.328340 | ||||||||
\(597\) | − | 13149.7i | − | 0.901474i | ||||||
\(598\) | 1806.96i | 0.123565i | ||||||||
\(599\) | 11323.5 | 0.772398 | 0.386199 | − | 0.922416i | \(-0.373788\pi\) | ||||
0.386199 | + | 0.922416i | \(0.373788\pi\) | |||||||
\(600\) | 2983.71 | + | 312.218i | 0.203016 | + | 0.0212438i | ||||
\(601\) | 1769.31 | 0.120086 | 0.0600429 | − | 0.998196i | \(-0.480876\pi\) | ||||
0.0600429 | + | 0.998196i | \(0.480876\pi\) | |||||||
\(602\) | − | 4188.31i | − | 0.283560i | ||||||
\(603\) | 2820.48i | 0.190479i | ||||||||
\(604\) | −5594.42 | −0.376877 | ||||||||
\(605\) | −284.837 | + | 5458.95i | −0.0191410 | + | 0.366839i | ||||
\(606\) | 6491.74 | 0.435163 | ||||||||
\(607\) | − | 9715.83i | − | 0.649676i | −0.945770 | − | 0.324838i | \(-0.894690\pi\) | ||
0.945770 | − | 0.324838i | \(-0.105310\pi\) | |||||||
\(608\) | 2484.85i | 0.165747i | ||||||||
\(609\) | −1004.72 | −0.0668529 | ||||||||
\(610\) | −17166.3 | − | 895.703i | −1.13941 | − | 0.0594524i | ||||
\(611\) | 39709.9 | 2.62928 | ||||||||
\(612\) | − | 1745.51i | − | 0.115291i | ||||||
\(613\) | 29107.8i | 1.91786i | 0.283635 | + | 0.958932i | \(0.408460\pi\) | ||||
−0.283635 | + | 0.958932i | \(0.591540\pi\) | |||||||
\(614\) | −4023.04 | −0.264425 | ||||||||
\(615\) | 7630.52 | + | 398.145i | 0.500313 | + | 0.0261053i | ||||
\(616\) | 2388.99 | 0.156259 | ||||||||
\(617\) | 7034.18i | 0.458972i | 0.973312 | + | 0.229486i | \(0.0737045\pi\) | ||||
−0.973312 | + | 0.229486i | \(0.926296\pi\) | |||||||
\(618\) | − | 4309.98i | − | 0.280539i | ||||||
\(619\) | 574.633 | 0.0373125 | 0.0186563 | − | 0.999826i | \(-0.494061\pi\) | ||||
0.0186563 | + | 0.999826i | \(0.494061\pi\) | |||||||
\(620\) | −353.758 | + | 6779.82i | −0.0229149 | + | 0.439168i | ||||
\(621\) | −333.409 | −0.0215447 | ||||||||
\(622\) | 7482.95i | 0.482377i | ||||||||
\(623\) | − | 1102.34i | − | 0.0708898i | ||||||
\(624\) | 3511.93 | 0.225304 | ||||||||
\(625\) | 15286.5 | + | 3234.61i | 0.978338 | + | 0.207015i | ||||
\(626\) | −16949.8 | −1.08219 | ||||||||
\(627\) | 9937.98i | 0.632990i | ||||||||
\(628\) | − | 13861.6i | − | 0.880790i | ||||||
\(629\) | 10302.7 | 0.653093 | ||||||||
\(630\) | 73.4045 | − | 1406.81i | 0.00464207 | − | 0.0889661i | ||||
\(631\) | 3009.42 | 0.189862 | 0.0949310 | − | 0.995484i | \(-0.469737\pi\) | ||||
0.0949310 | + | 0.995484i | \(0.469737\pi\) | |||||||
\(632\) | − | 3356.63i | − | 0.211265i | ||||||
\(633\) | − | 436.964i | − | 0.0274372i | ||||||
\(634\) | −18742.3 | −1.17406 | ||||||||
\(635\) | −18852.5 | − | 983.688i | −1.17817 | − | 0.0614747i | ||||
\(636\) | 1828.40 | 0.113995 | ||||||||
\(637\) | 3585.09i | 0.222993i | ||||||||
\(638\) | 4082.10i | 0.253310i | ||||||||
\(639\) | −1098.59 | −0.0680116 | ||||||||
\(640\) | −1429.14 | − | 74.5697i | −0.0882683 | − | 0.00460567i | ||||
\(641\) | −25041.6 | −1.54303 | −0.771516 | − | 0.636209i | \(-0.780501\pi\) | ||||
−0.771516 | + | 0.636209i | \(0.780501\pi\) | |||||||
\(642\) | 11705.7i | 0.719608i | ||||||||
\(643\) | 4245.80i | 0.260401i | 0.991488 | + | 0.130201i | \(0.0415622\pi\) | ||||
−0.991488 | + | 0.130201i | \(0.958438\pi\) | |||||||
\(644\) | −345.758 | −0.0211565 | ||||||||
\(645\) | −522.859 | + | 10020.7i | −0.0319187 | + | 0.611727i | ||||
\(646\) | 7530.08 | 0.458618 | ||||||||
\(647\) | − | 6388.02i | − | 0.388159i | −0.980986 | − | 0.194079i | \(-0.937828\pi\) | ||
0.980986 | − | 0.194079i | \(-0.0621720\pi\) | |||||||
\(648\) | 648.000i | 0.0392837i | ||||||||
\(649\) | −10179.1 | −0.615661 | ||||||||
\(650\) | 18192.0 | + | 1903.62i | 1.09777 | + | 0.114871i | ||||
\(651\) | 3187.96 | 0.191929 | ||||||||
\(652\) | − | 10791.3i | − | 0.648191i | ||||||
\(653\) | − | 13791.6i | − | 0.826504i | −0.910617 | − | 0.413252i | \(-0.864393\pi\) | ||
0.910617 | − | 0.413252i | \(-0.135607\pi\) | |||||||
\(654\) | 7789.44 | 0.465736 | ||||||||
\(655\) | 535.500 | − | 10262.9i | 0.0319446 | − | 0.612223i | ||||
\(656\) | −3644.92 | −0.216936 | ||||||||
\(657\) | 286.268i | 0.0169991i | ||||||||
\(658\) | 7598.42i | 0.450178i | ||||||||
\(659\) | 28080.4 | 1.65987 | 0.829937 | − | 0.557856i | \(-0.188376\pi\) | ||||
0.829937 | + | 0.557856i | \(0.188376\pi\) | |||||||
\(660\) | −5715.75 | − | 298.236i | −0.337099 | − | 0.0175891i | ||||
\(661\) | 9133.28 | 0.537433 | 0.268717 | − | 0.963219i | \(-0.413400\pi\) | ||||
0.268717 | + | 0.963219i | \(0.413400\pi\) | |||||||
\(662\) | 3515.09i | 0.206371i | ||||||||
\(663\) | − | 10642.5i | − | 0.623412i | ||||||
\(664\) | −7853.07 | −0.458973 | ||||||||
\(665\) | 6068.94 | + | 316.665i | 0.353900 | + | 0.0184658i | ||||
\(666\) | −3824.75 | −0.222532 | ||||||||
\(667\) | − | 590.800i | − | 0.0342967i | ||||||
\(668\) | − | 12815.7i | − | 0.742296i | ||||||
\(669\) | 5733.52 | 0.331346 | ||||||||
\(670\) | 365.143 | − | 6998.01i | 0.0210548 | − | 0.403518i | ||||
\(671\) | 32795.1 | 1.88680 | ||||||||
\(672\) | 672.000i | 0.0385758i | ||||||||
\(673\) | 13542.6i | 0.775672i | 0.921728 | + | 0.387836i | \(0.126777\pi\) | ||||
−0.921728 | + | 0.387836i | \(0.873223\pi\) | |||||||
\(674\) | −5802.98 | −0.331635 | ||||||||
\(675\) | −351.245 | + | 3356.67i | −0.0200288 | + | 0.191405i | ||||
\(676\) | 12624.6 | 0.718284 | ||||||||
\(677\) | 22203.2i | 1.26047i | 0.776405 | + | 0.630235i | \(0.217041\pi\) | ||||
−0.776405 | + | 0.630235i | \(0.782959\pi\) | |||||||
\(678\) | − | 6063.31i | − | 0.343451i | ||||||
\(679\) | 12268.4 | 0.693402 | ||||||||
\(680\) | −225.976 | + | 4330.86i | −0.0127438 | + | 0.244237i | ||||
\(681\) | −6250.80 | −0.351734 | ||||||||
\(682\) | − | 12952.4i | − | 0.727234i | ||||||
\(683\) | − | 13294.8i | − | 0.744817i | −0.928069 | − | 0.372409i | \(-0.878532\pi\) | ||
0.928069 | − | 0.372409i | \(-0.121468\pi\) | |||||||
\(684\) | −2795.45 | −0.156267 | ||||||||
\(685\) | −12887.3 | − | 672.432i | −0.718827 | − | 0.0375070i | ||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | − | 6006.09i | − | 0.333547i | ||||||
\(688\) | − | 4786.64i | − | 0.265246i | ||||||
\(689\) | 11147.9 | 0.616404 | ||||||||
\(690\) | 827.236 | + | 43.1636i | 0.0456411 | + | 0.00238146i | ||||
\(691\) | 8047.01 | 0.443014 | 0.221507 | − | 0.975159i | \(-0.428902\pi\) | ||||
0.221507 | + | 0.975159i | \(0.428902\pi\) | |||||||
\(692\) | 927.624i | 0.0509581i | ||||||||
\(693\) | 2687.62i | 0.147322i | ||||||||
\(694\) | 523.152 | 0.0286146 | ||||||||
\(695\) | 1777.16 | − | 34059.5i | 0.0969948 | − | 1.85892i | ||||
\(696\) | −1148.25 | −0.0625352 | ||||||||
\(697\) | 11045.6i | 0.600259i | ||||||||
\(698\) | 21917.3i | 1.18851i | ||||||||
\(699\) | −9736.56 | −0.526854 | ||||||||
\(700\) | −364.255 | + | 3480.99i | −0.0196679 | + | 0.187956i | ||||
\(701\) | −29114.5 | −1.56867 | −0.784336 | − | 0.620336i | \(-0.786996\pi\) | ||||
−0.784336 | + | 0.620336i | \(0.786996\pi\) | |||||||
\(702\) | 3950.92i | 0.212419i | ||||||||
\(703\) | − | 16499.9i | − | 0.885213i | ||||||
\(704\) | 2730.28 | 0.146167 | ||||||||
\(705\) | 948.568 | − | 18179.5i | 0.0506740 | − | 0.971174i | ||||
\(706\) | 8276.31 | 0.441194 | ||||||||
\(707\) | 7573.69i | 0.402883i | ||||||||
\(708\) | − | 2863.27i | − | 0.151989i | ||||||
\(709\) | −18269.1 | −0.967717 | −0.483858 | − | 0.875146i | \(-0.660765\pi\) | ||||
−0.483858 | + | 0.875146i | \(0.660765\pi\) | |||||||
\(710\) | 2725.75 | + | 142.224i | 0.144078 | + | 0.00751773i | ||||
\(711\) | 3776.21 | 0.199183 | ||||||||
\(712\) | − | 1259.82i | − | 0.0663114i | ||||||
\(713\) | 1874.59i | 0.0984630i | ||||||||
\(714\) | 2036.43 | 0.106739 | ||||||||
\(715\) | −34849.4 | − | 1818.38i | −1.82279 | − | 0.0951097i | ||||
\(716\) | 11624.5 | 0.606744 | ||||||||
\(717\) | 16806.1i | 0.875362i | ||||||||
\(718\) | − | 14766.5i | − | 0.767522i | ||||||
\(719\) | −19308.5 | −1.00151 | −0.500755 | − | 0.865589i | \(-0.666944\pi\) | ||||
−0.500755 | + | 0.865589i | \(0.666944\pi\) | |||||||
\(720\) | 83.8909 | − | 1607.78i | 0.00434226 | − | 0.0832201i | ||||
\(721\) | 5028.31 | 0.259728 | ||||||||
\(722\) | 1658.48i | 0.0854881i | ||||||||
\(723\) | 14369.8i | 0.739167i | ||||||||
\(724\) | 3999.46 | 0.205302 | ||||||||
\(725\) | −5948.02 | − | 622.406i | −0.304695 | − | 0.0318836i | ||||
\(726\) | 2933.56 | 0.149965 | ||||||||
\(727\) | − | 608.482i | − | 0.0310417i | −0.999880 | − | 0.0155209i | \(-0.995059\pi\) | ||
0.999880 | − | 0.0155209i | \(-0.00494064\pi\) | |||||||
\(728\) | 4097.25i | 0.208591i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 37.0606 | − | 710.273i | 0.00187901 | − | 0.0360115i | ||||
\(731\) | −14505.4 | −0.733930 | ||||||||
\(732\) | 9224.93i | 0.465797i | ||||||||
\(733\) | 3210.00i | 0.161752i | 0.996724 | + | 0.0808759i | \(0.0257718\pi\) | ||||
−0.996724 | + | 0.0808759i | \(0.974228\pi\) | |||||||
\(734\) | −23170.7 | −1.16519 | ||||||||
\(735\) | 1641.28 | + | 85.6386i | 0.0823666 | + | 0.00429773i | ||||
\(736\) | −395.152 | −0.0197901 | ||||||||
\(737\) | 13369.3i | 0.668199i | ||||||||
\(738\) | − | 4100.54i | − | 0.204530i | ||||||
\(739\) | −11630.3 | −0.578930 | −0.289465 | − | 0.957189i | \(-0.593477\pi\) | ||||
−0.289465 | + | 0.957189i | \(0.593477\pi\) | |||||||
\(740\) | 9489.77 | + | 495.158i | 0.471420 | + | 0.0245978i | ||||
\(741\) | −17044.2 | −0.844983 | ||||||||
\(742\) | 2133.13i | 0.105539i | ||||||||
\(743\) | 3312.11i | 0.163539i | 0.996651 | + | 0.0817695i | \(0.0260571\pi\) | ||||
−0.996651 | + | 0.0817695i | \(0.973943\pi\) | |||||||
\(744\) | 3643.38 | 0.179533 | ||||||||
\(745\) | 695.803 | − | 13335.2i | 0.0342178 | − | 0.655789i | ||||
\(746\) | −15424.7 | −0.757024 | ||||||||
\(747\) | − | 8834.70i | − | 0.432724i | ||||||
\(748\) | − | 8273.83i | − | 0.404440i | ||||||
\(749\) | −13656.7 | −0.666227 | ||||||||
\(750\) | 1306.05 | − | 8282.92i | 0.0635869 | − | 0.403266i | ||||
\(751\) | −1536.93 | −0.0746783 | −0.0373391 | − | 0.999303i | \(-0.511888\pi\) | ||||
−0.0373391 | + | 0.999303i | \(0.511888\pi\) | |||||||
\(752\) | 8683.90i | 0.421103i | ||||||||
\(753\) | − | 1012.40i | − | 0.0489959i | ||||||
\(754\) | −7001.02 | −0.338146 | ||||||||
\(755\) | −814.794 | + | 15615.6i | −0.0392760 | + | 0.752731i | ||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 19998.4i | 0.960179i | 0.877220 | + | 0.480089i | \(0.159396\pi\) | ||||
−0.877220 | + | 0.480089i | \(0.840604\pi\) | |||||||
\(758\) | − | 13326.3i | − | 0.638567i | ||||||
\(759\) | −1580.38 | −0.0755787 | ||||||||
\(760\) | 6935.93 | + | 361.903i | 0.331043 | + | 0.0172732i | ||||
\(761\) | −19227.9 | −0.915915 | −0.457957 | − | 0.888974i | \(-0.651419\pi\) | ||||
−0.457957 | + | 0.888974i | \(0.651419\pi\) | |||||||
\(762\) | 10131.1i | 0.481641i | ||||||||
\(763\) | 9087.68i | 0.431187i | ||||||||
\(764\) | −10980.2 | −0.519959 | ||||||||
\(765\) | −4872.22 | − | 254.223i | −0.230269 | − | 0.0120150i | ||||
\(766\) | −16864.2 | −0.795469 | ||||||||
\(767\) | − | 17457.6i | − | 0.821850i | ||||||
\(768\) | 768.000i | 0.0360844i | ||||||||
\(769\) | 5846.72 | 0.274172 | 0.137086 | − | 0.990559i | \(-0.456226\pi\) | ||||
0.137086 | + | 0.990559i | \(0.456226\pi\) | |||||||
\(770\) | 347.942 | − | 6668.37i | 0.0162844 | − | 0.312093i | ||||
\(771\) | −6680.06 | −0.312032 | ||||||||
\(772\) | 15301.5i | 0.713360i | ||||||||
\(773\) | − | 26893.4i | − | 1.25134i | −0.780086 | − | 0.625672i | \(-0.784825\pi\) | ||
0.780086 | − | 0.625672i | \(-0.215175\pi\) | |||||||
\(774\) | 5384.97 | 0.250076 | ||||||||
\(775\) | 18872.9 | + | 1974.88i | 0.874754 | + | 0.0915351i | ||||
\(776\) | 14021.1 | 0.648618 | ||||||||
\(777\) | − | 4462.21i | − | 0.206024i | ||||||
\(778\) | 11862.8i | 0.546660i | ||||||||
\(779\) | 17689.6 | 0.813602 | ||||||||
\(780\) | 511.491 | − | 9802.80i | 0.0234799 | − | 0.449996i | ||||
\(781\) | −5207.37 | −0.238584 | ||||||||
\(782\) | 1197.47i | 0.0547587i | ||||||||
\(783\) | − | 1291.79i | − | 0.0589587i | ||||||
\(784\) | −784.000 | −0.0357143 | ||||||||
\(785\) | −38691.6 | − | 2018.85i | −1.75919 | − | 0.0917910i | ||||
\(786\) | −5515.16 | −0.250279 | ||||||||
\(787\) | − | 38318.9i | − | 1.73560i | −0.496910 | − | 0.867802i | \(-0.665532\pi\) | ||
0.496910 | − | 0.867802i | \(-0.334468\pi\) | |||||||
\(788\) | 17796.0i | 0.804512i | ||||||||
\(789\) | 19424.3 | 0.876457 | ||||||||
\(790\) | −9369.32 | − | 488.873i | −0.421956 | − | 0.0220169i | ||||
\(791\) | 7073.86 | 0.317974 | ||||||||
\(792\) | 3071.56i | 0.137807i | ||||||||
\(793\) | 56245.3i | 2.51870i | ||||||||
\(794\) | −1380.75 | −0.0617143 | ||||||||
\(795\) | 266.295 | − | 5103.59i | 0.0118799 | − | 0.227680i | ||||
\(796\) | 17532.9 | 0.780699 | ||||||||
\(797\) | − | 4597.04i | − | 0.204311i | −0.994768 | − | 0.102155i | \(-0.967426\pi\) | ||
0.994768 | − | 0.102155i | \(-0.0325739\pi\) | |||||||
\(798\) | − | 3261.36i | − | 0.144675i | ||||||
\(799\) | 26315.7 | 1.16518 | ||||||||
\(800\) | −416.291 | + | 3978.28i | −0.0183976 | + | 0.175817i | ||||
\(801\) | 1417.30 | 0.0625189 | ||||||||
\(802\) | 4628.36i | 0.203782i | ||||||||
\(803\) | 1356.93i | 0.0596327i | ||||||||
\(804\) | −3760.64 | −0.164959 | ||||||||
\(805\) | −50.3575 | + | 965.109i | −0.00220481 | + | 0.0422554i | ||||
\(806\) | 22214.0 | 0.970790 | ||||||||
\(807\) | − | 14941.1i | − | 0.651739i | ||||||
\(808\) | 8655.65i | 0.376862i | ||||||||
\(809\) | 22083.1 | 0.959706 | 0.479853 | − | 0.877349i | \(-0.340690\pi\) | ||||
0.479853 | + | 0.877349i | \(0.340690\pi\) | |||||||
\(810\) | 1808.75 | + | 94.3773i | 0.0784607 | + | 0.00409392i | ||||
\(811\) | 1458.44 | 0.0631478 | 0.0315739 | − | 0.999501i | \(-0.489948\pi\) | ||||
0.0315739 | + | 0.999501i | \(0.489948\pi\) | |||||||
\(812\) | − | 1339.63i | − | 0.0578963i | ||||||
\(813\) | 23489.3i | 1.01329i | ||||||||
\(814\) | −18129.6 | −0.780641 | ||||||||
\(815\) | −30121.7 | − | 1571.69i | −1.29462 | − | 0.0675508i | ||||
\(816\) | 2327.35 | 0.0998448 | ||||||||
\(817\) | 23230.6i | 0.994782i | ||||||||
\(818\) | − | 23798.6i | − | 1.01724i | ||||||
\(819\) | −4609.40 | −0.196661 | ||||||||
\(820\) | −530.861 | + | 10174.0i | −0.0226079 | + | 0.433283i | ||||
\(821\) | 10466.2 | 0.444911 | 0.222456 | − | 0.974943i | \(-0.428593\pi\) | ||||
0.222456 | + | 0.974943i | \(0.428593\pi\) | |||||||
\(822\) | 6925.44i | 0.293859i | ||||||||
\(823\) | − | 33033.9i | − | 1.39914i | −0.714566 | − | 0.699568i | \(-0.753376\pi\) | ||
0.714566 | − | 0.699568i | \(-0.246624\pi\) | |||||||
\(824\) | 5746.64 | 0.242954 | ||||||||
\(825\) | −1664.93 | + | 15910.9i | −0.0702610 | + | 0.671448i | ||||
\(826\) | 3340.48 | 0.140715 | ||||||||
\(827\) | 26197.7i | 1.10155i | 0.834653 | + | 0.550777i | \(0.185668\pi\) | ||||
−0.834653 | + | 0.550777i | \(0.814332\pi\) | |||||||
\(828\) | − | 444.545i | − | 0.0186582i | ||||||
\(829\) | 46489.0 | 1.94768 | 0.973841 | − | 0.227229i | \(-0.0729664\pi\) | ||||
0.973841 | + | 0.227229i | \(0.0729664\pi\) | |||||||
\(830\) | −1143.75 | + | 21920.2i | −0.0478316 | + | 0.916699i | ||||
\(831\) | −9312.30 | −0.388737 | ||||||||
\(832\) | 4682.57i | 0.195119i | ||||||||
\(833\) | 2375.83i | 0.0988208i | ||||||||
\(834\) | −18303.1 | −0.759933 | ||||||||
\(835\) | −35772.2 | − | 1866.53i | −1.48257 | − | 0.0773578i | ||||
\(836\) | −13250.6 | −0.548185 | ||||||||
\(837\) | 4098.80i | 0.169266i | ||||||||
\(838\) | 28766.2i | 1.18582i | ||||||||
\(839\) | −29036.9 | −1.19484 | −0.597418 | − | 0.801930i | \(-0.703806\pi\) | ||||
−0.597418 | + | 0.801930i | \(0.703806\pi\) | |||||||
\(840\) | 1875.75 | + | 97.8727i | 0.0770469 | + | 0.00402015i | ||||
\(841\) | −22100.0 | −0.906144 | ||||||||
\(842\) | − | 9241.42i | − | 0.378243i | ||||||
\(843\) | 8749.34i | 0.357465i | ||||||||
\(844\) | 582.618 | 0.0237613 | ||||||||
\(845\) | 1838.69 | − | 35238.8i | 0.0748555 | − | 1.43462i | ||||
\(846\) | −9769.39 | −0.397020 | ||||||||
\(847\) | 3422.49i | 0.138841i | ||||||||
\(848\) | 2437.87i | 0.0987225i | ||||||||
\(849\) | −24597.9 | −0.994343 | ||||||||
\(850\) | 12055.8 | + | 1261.53i | 0.486482 | + | 0.0509059i | ||||
\(851\) | 2623.88 | 0.105694 | ||||||||
\(852\) | − | 1464.78i | − | 0.0588998i | ||||||
\(853\) | − | 6062.80i | − | 0.243360i | −0.992569 | − | 0.121680i | \(-0.961172\pi\) | ||
0.992569 | − | 0.121680i | \(-0.0388282\pi\) | |||||||
\(854\) | −10762.4 | −0.431244 | ||||||||
\(855\) | −407.141 | + | 7802.92i | −0.0162853 | + | 0.312110i | ||||
\(856\) | −15607.6 | −0.623199 | ||||||||
\(857\) | − | 2836.79i | − | 0.113072i | −0.998401 | − | 0.0565362i | \(-0.981994\pi\) | ||
0.998401 | − | 0.0565362i | \(-0.0180056\pi\) | |||||||
\(858\) | 18727.6i | 0.745164i | ||||||||
\(859\) | −25527.2 | −1.01394 | −0.506972 | − | 0.861962i | \(-0.669235\pi\) | ||||
−0.506972 | + | 0.861962i | \(0.669235\pi\) | |||||||
\(860\) | −13360.9 | − | 697.145i | −0.529771 | − | 0.0276424i | ||||
\(861\) | 4783.96 | 0.189358 | ||||||||
\(862\) | 24679.0i | 0.975138i | ||||||||
\(863\) | − | 24340.9i | − | 0.960109i | −0.877239 | − | 0.480055i | \(-0.840617\pi\) | ||
0.877239 | − | 0.480055i | \(-0.159383\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 2589.27 | + | 135.103i | 0.101778 | + | 0.00531056i | ||||
\(866\) | 22561.9 | 0.885315 | ||||||||
\(867\) | 7686.22i | 0.301081i | ||||||||
\(868\) | 4250.61i | 0.166216i | ||||||||
\(869\) | 17899.5 | 0.698732 | ||||||||
\(870\) | −167.236 | + | 3205.11i | −0.00651706 | + | 0.124900i | ||||
\(871\) | −22929.0 | −0.891984 | ||||||||
\(872\) | 10385.9i | 0.403339i | ||||||||
\(873\) | 15773.7i | 0.611523i | ||||||||
\(874\) | 1917.76 | 0.0742209 | ||||||||
\(875\) | 9663.40 | + | 1523.72i | 0.373352 | + | 0.0588701i | ||||
\(876\) | −381.691 | −0.0147216 | ||||||||
\(877\) | 144.805i | 0.00557550i | 0.999996 | + | 0.00278775i | \(0.000887369\pi\) | ||||
−0.999996 | + | 0.00278775i | \(0.999113\pi\) | |||||||
\(878\) | 13170.6i | 0.506248i | ||||||||
\(879\) | 25346.3 | 0.972594 | ||||||||
\(880\) | 397.649 | − | 7620.99i | 0.0152326 | − | 0.291936i | ||||
\(881\) | −10781.9 | −0.412319 | −0.206159 | − | 0.978518i | \(-0.566097\pi\) | ||||
−0.206159 | + | 0.978518i | \(0.566097\pi\) | |||||||
\(882\) | − | 882.000i | − | 0.0336718i | ||||||
\(883\) | − | 20688.7i | − | 0.788483i | −0.919007 | − | 0.394241i | \(-0.871007\pi\) | ||
0.919007 | − | 0.394241i | \(-0.128993\pi\) | |||||||
\(884\) | 14190.0 | 0.539890 | ||||||||
\(885\) | −7992.22 | − | 417.018i | −0.303566 | − | 0.0158395i | ||||
\(886\) | 11042.2 | 0.418702 | ||||||||
\(887\) | − | 35310.9i | − | 1.33667i | −0.743862 | − | 0.668334i | \(-0.767008\pi\) | ||
0.743862 | − | 0.668334i | \(-0.232992\pi\) | |||||||
\(888\) | − | 5099.67i | − | 0.192718i | ||||||
\(889\) | −11819.6 | −0.445913 | ||||||||
\(890\) | −3516.52 | − | 183.485i | −0.132443 | − | 0.00691059i | ||||
\(891\) | −3455.51 | −0.129926 | ||||||||
\(892\) | 7644.69i | 0.286954i | ||||||||
\(893\) | − | 42144.9i | − | 1.57931i | ||||||
\(894\) | −7166.14 | −0.268089 | ||||||||
\(895\) | 1693.04 | − | 32447.4i | 0.0632314 | − | 1.21184i | ||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | − | 2710.44i | − | 0.100891i | ||||||
\(898\) | − | 20025.3i | − | 0.744158i | ||||||
\(899\) | −7263.07 | −0.269452 | ||||||||
\(900\) | −4475.56 | − | 468.327i | −0.165762 | − | 0.0173455i | ||||
\(901\) | 7387.71 | 0.273163 | ||||||||
\(902\) | − | 19436.8i | − | 0.717489i | ||||||
\(903\) | 6282.47i | 0.231525i | ||||||||
\(904\) | 8084.41 | 0.297438 | ||||||||
\(905\) | 582.497 | − | 11163.6i | 0.0213954 | − | 0.410047i | ||||
\(906\) | 8391.64 | 0.307719 | ||||||||
\(907\) | 46702.8i | 1.70975i | 0.518835 | + | 0.854875i | \(0.326366\pi\) | ||||
−0.518835 | + | 0.854875i | \(0.673634\pi\) | |||||||
\(908\) | − | 8334.40i | − | 0.304611i | ||||||
\(909\) | −9737.60 | −0.355309 | ||||||||
\(910\) | 11436.6 | + | 596.739i | 0.416615 | + | 0.0217382i | ||||
\(911\) | 31094.5 | 1.13085 | 0.565426 | − | 0.824799i | \(-0.308712\pi\) | ||||
0.565426 | + | 0.824799i | \(0.308712\pi\) | |||||||
\(912\) | − | 3727.27i | − | 0.135332i | ||||||
\(913\) | − | 41877.1i | − | 1.51799i | ||||||
\(914\) | −24257.4 | −0.877859 | ||||||||
\(915\) | 25749.4 | + | 1343.55i | 0.930328 | + | 0.0485427i | ||||
\(916\) | 8008.12 | 0.288860 | ||||||||
\(917\) | − | 6434.36i | − | 0.231713i | ||||||
\(918\) | 2618.26i | 0.0941346i | ||||||||
\(919\) | −12244.5 | −0.439509 | −0.219755 | − | 0.975555i | \(-0.570526\pi\) | ||||
−0.219755 | + | 0.975555i | \(0.570526\pi\) | |||||||
\(920\) | −57.5514 | + | 1102.98i | −0.00206241 | + | 0.0395263i | ||||
\(921\) | 6034.56 | 0.215902 | ||||||||
\(922\) | 16559.6i | 0.591500i | ||||||||
\(923\) | − | 8930.91i | − | 0.318488i | ||||||
\(924\) | −3583.49 | −0.127585 | ||||||||
\(925\) | 2764.25 | − | 26416.6i | 0.0982574 | − | 0.938996i | ||||
\(926\) | −25865.4 | −0.917915 | ||||||||
\(927\) | 6464.97i | 0.229059i | ||||||||
\(928\) | − | 1531.01i | − | 0.0541570i | ||||||
\(929\) | −40170.0 | −1.41866 | −0.709331 | − | 0.704876i | \(-0.751003\pi\) | ||||
−0.709331 | + | 0.704876i | \(0.751003\pi\) | |||||||
\(930\) | 530.636 | − | 10169.7i | 0.0187100 | − | 0.358579i | ||||
\(931\) | 3804.92 | 0.133943 | ||||||||
\(932\) | − | 12982.1i | − | 0.456269i | ||||||
\(933\) | − | 11224.4i | − | 0.393860i | ||||||
\(934\) | 14653.4 | 0.513356 | ||||||||
\(935\) | −23094.6 | − | 1205.03i | −0.807781 | − | 0.0421484i | ||||
\(936\) | −5267.89 | −0.183960 | ||||||||
\(937\) | 30532.4i | 1.06452i | 0.846582 | + | 0.532258i | \(0.178656\pi\) | ||||
−0.846582 | + | 0.532258i | \(0.821344\pi\) | |||||||
\(938\) | − | 4387.41i | − | 0.152723i | ||||||
\(939\) | 25424.8 | 0.883606 | ||||||||
\(940\) | 24239.3 | + | 1264.76i | 0.841062 | + | 0.0438849i | ||||
\(941\) | 22126.9 | 0.766544 | 0.383272 | − | 0.923636i | \(-0.374797\pi\) | ||||
0.383272 | + | 0.923636i | \(0.374797\pi\) | |||||||
\(942\) | 20792.3i | 0.719162i | ||||||||
\(943\) | 2813.08i | 0.0971436i | ||||||||
\(944\) | 3817.70 | 0.131627 | ||||||||
\(945\) | −110.107 | + | 2110.21i | −0.00379024 | + | 0.0726405i | ||||
\(946\) | 25525.1 | 0.877266 | ||||||||
\(947\) | 14922.2i | 0.512046i | 0.966671 | + | 0.256023i | \(0.0824123\pi\) | ||||
−0.966671 | + | 0.256023i | \(0.917588\pi\) | |||||||
\(948\) | 5034.95i | 0.172497i | ||||||||
\(949\) | −2327.21 | −0.0796041 | ||||||||
\(950\) | 2020.35 | − | 19307.5i | 0.0689988 | − | 0.659386i | ||||
\(951\) | 28113.5 | 0.958613 | ||||||||
\(952\) | 2715.24i | 0.0924384i | ||||||||
\(953\) | − | 20720.7i | − | 0.704313i | −0.935941 | − | 0.352156i | \(-0.885448\pi\) | ||
0.935941 | − | 0.352156i | \(-0.114552\pi\) | |||||||
\(954\) | −2742.60 | −0.0930765 | ||||||||
\(955\) | −1599.19 | + | 30648.8i | −0.0541871 | + | 1.03850i | ||||
\(956\) | −22408.1 | −0.758086 | ||||||||
\(957\) | − | 6123.15i | − | 0.206827i | ||||||
\(958\) | 25136.8i | 0.847739i | ||||||||
\(959\) | −8079.68 | −0.272061 | ||||||||
\(960\) | 2143.71 | + | 111.855i | 0.0720707 | + | 0.00376051i | ||||
\(961\) | −6745.46 | −0.226426 | ||||||||
\(962\) | − | 31093.2i | − | 1.04208i | ||||||
\(963\) | − | 17558.6i | − | 0.587557i | ||||||
\(964\) | −19159.7 | −0.640138 | ||||||||
\(965\) | 42710.9 | + | 2228.57i | 1.42478 | + | 0.0743423i | ||||
\(966\) | 518.636 | 0.0172742 | ||||||||
\(967\) | − | 34075.1i | − | 1.13318i | −0.824001 | − | 0.566589i | \(-0.808263\pi\) | ||
0.824001 | − | 0.566589i | \(-0.191737\pi\) | |||||||
\(968\) | 3911.42i | 0.129874i | ||||||||
\(969\) | −11295.1 | −0.374460 | ||||||||
\(970\) | 2042.08 | − | 39136.9i | 0.0675953 | − | 1.29547i | ||||
\(971\) | 36786.0 | 1.21578 | 0.607889 | − | 0.794022i | \(-0.292017\pi\) | ||||
0.607889 | + | 0.794022i | \(0.292017\pi\) | |||||||
\(972\) | − | 972.000i | − | 0.0320750i | ||||||
\(973\) | − | 21353.6i | − | 0.703561i | ||||||
\(974\) | 20929.6 | 0.688531 | ||||||||
\(975\) | −27287.9 | − | 2855.44i | −0.896322 | − | 0.0937920i | ||||
\(976\) | −12299.9 | −0.403392 | ||||||||
\(977\) | 29429.9i | 0.963711i | 0.876251 | + | 0.481855i | \(0.160037\pi\) | ||||
−0.876251 | + | 0.481855i | \(0.839963\pi\) | |||||||
\(978\) | 16187.0i | 0.529246i | ||||||||
\(979\) | 6718.08 | 0.219316 | ||||||||
\(980\) | −114.185 | + | 2188.37i | −0.00372194 | + | 0.0713315i | ||||
\(981\) | −11684.2 | −0.380272 | ||||||||
\(982\) | 3072.44i | 0.0998427i | ||||||||
\(983\) | − | 209.332i | − | 0.00679212i | −0.999994 | − | 0.00339606i | \(-0.998919\pi\) | ||
0.999994 | − | 0.00339606i | \(-0.00108100\pi\) | |||||||
\(984\) | 5467.38 | 0.177128 | ||||||||
\(985\) | 49673.7 | + | 2591.88i | 1.60684 | + | 0.0838417i | ||||
\(986\) | −4639.56 | −0.149852 | ||||||||
\(987\) | − | 11397.6i | − | 0.367569i | ||||||
\(988\) | − | 22725.5i | − | 0.731777i | ||||||
\(989\) | −3694.24 | −0.118776 | ||||||||
\(990\) | 8573.62 | + | 447.355i | 0.275240 | + | 0.0143615i | ||||
\(991\) | 221.264 | 0.00709250 | 0.00354625 | − | 0.999994i | \(-0.498871\pi\) | ||||
0.00354625 | + | 0.999994i | \(0.498871\pi\) | |||||||
\(992\) | 4857.84i | 0.155480i | ||||||||
\(993\) | − | 5272.64i | − | 0.168502i | ||||||
\(994\) | 1708.91 | 0.0545306 | ||||||||
\(995\) | 2553.56 | − | 48939.3i | 0.0813600 | − | 1.55928i | ||||
\(996\) | 11779.6 | 0.374750 | ||||||||
\(997\) | 25509.1i | 0.810313i | 0.914247 | + | 0.405157i | \(0.132783\pi\) | ||||
−0.914247 | + | 0.405157i | \(0.867217\pi\) | |||||||
\(998\) | 25473.6i | 0.807968i | ||||||||
\(999\) | 5737.13 | 0.181697 |
(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 | 210.4.g.b.169.1 | ✓ | 4 | |
3.2 | odd | 2 | 630.4.g.d.379.4 | 4 | |||
5.2 | odd | 4 | 1050.4.a.bh.1.1 | 2 | |||
5.3 | odd | 4 | 1050.4.a.ba.1.1 | 2 | |||
5.4 | even | 2 | inner | 210.4.g.b.169.3 | yes | 4 | |
15.14 | odd | 2 | 630.4.g.d.379.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.g.b.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
210.4.g.b.169.3 | yes | 4 | 5.4 | even | 2 | inner | |
630.4.g.d.379.2 | 4 | 15.14 | odd | 2 | |||
630.4.g.d.379.4 | 4 | 3.2 | odd | 2 | |||
1050.4.a.ba.1.1 | 2 | 5.3 | odd | 4 | |||
1050.4.a.bh.1.1 | 2 | 5.2 | odd | 4 |