Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(323,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.e (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.17 | ||
Character | \(\chi\) | \(=\) | 756.323 |
Dual form | 756.2.e.b.323.18 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.932512 | − | 1.06321i | 0.659385 | − | 0.751805i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.260844 | − | 1.98292i | −0.130422 | − | 0.991459i | ||||
\(5\) | − | 0.546170i | − | 0.244255i | −0.992514 | − | 0.122127i | \(-0.961028\pi\) | ||
0.992514 | − | 0.122127i | \(-0.0389716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.35150 | − | 1.57176i | −0.831382 | − | 0.555702i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.580695 | − | 0.509310i | −0.183632 | − | 0.161058i | ||||
\(11\) | −4.32940 | −1.30536 | −0.652682 | − | 0.757632i | \(-0.726356\pi\) | ||||
−0.652682 | + | 0.757632i | \(0.726356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.39014 | −0.940256 | −0.470128 | − | 0.882598i | \(-0.655792\pi\) | ||||
−0.470128 | + | 0.882598i | \(0.655792\pi\) | |||||||
\(14\) | −1.06321 | − | 0.932512i | −0.284156 | − | 0.249224i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.86392 | + | 1.03446i | −0.965980 | + | 0.258616i | ||||
\(17\) | − | 0.0960161i | − | 0.0232873i | −0.999932 | − | 0.0116437i | \(-0.996294\pi\) | ||
0.999932 | − | 0.0116437i | \(-0.00370638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.78185i | − | 1.78528i | −0.450772 | − | 0.892639i | \(-0.648851\pi\) | ||
0.450772 | − | 0.892639i | \(-0.351149\pi\) | |||||||
\(20\) | −1.08301 | + | 0.142465i | −0.242168 | + | 0.0318561i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.03722 | + | 4.60308i | −0.860738 | + | 0.981379i | ||||
\(23\) | 0.716100 | 0.149317 | 0.0746585 | − | 0.997209i | \(-0.476213\pi\) | ||||
0.0746585 | + | 0.997209i | \(0.476213\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.70170 | 0.940340 | ||||||||
\(26\) | −3.16135 | + | 3.60444i | −0.619991 | + | 0.706889i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.98292 | + | 0.260844i | −0.374736 | + | 0.0492948i | ||||
\(29\) | − | 2.80103i | − | 0.520137i | −0.965590 | − | 0.260069i | \(-0.916255\pi\) | ||
0.965590 | − | 0.260069i | \(-0.0837452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.38048i | − | 0.247942i | −0.992286 | − | 0.123971i | \(-0.960437\pi\) | ||
0.992286 | − | 0.123971i | \(-0.0395629\pi\) | |||||||
\(32\) | −2.50330 | + | 5.07282i | −0.442525 | + | 0.896756i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.102086 | − | 0.0895361i | −0.0175075 | − | 0.0153553i | ||||
\(35\) | −0.546170 | −0.0923196 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.87923 | 1.62414 | 0.812068 | − | 0.583563i | \(-0.198342\pi\) | ||||
0.812068 | + | 0.583563i | \(0.198342\pi\) | |||||||
\(38\) | −8.27376 | − | 7.25666i | −1.34218 | − | 1.17719i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.858449 | + | 1.28432i | −0.135733 | + | 0.203069i | ||||
\(41\) | 9.42938i | 1.47262i | 0.676644 | + | 0.736311i | \(0.263434\pi\) | ||||
−0.676644 | + | 0.736311i | \(0.736566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.12293i | − | 0.171245i | −0.996328 | − | 0.0856226i | \(-0.972712\pi\) | ||
0.996328 | − | 0.0856226i | \(-0.0272879\pi\) | |||||||
\(44\) | 1.12930 | + | 8.58485i | 0.170248 | + | 1.29421i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.667771 | − | 0.761366i | 0.0984575 | − | 0.112257i | ||||
\(47\) | −10.2208 | −1.49085 | −0.745426 | − | 0.666588i | \(-0.767754\pi\) | ||||
−0.745426 | + | 0.666588i | \(0.767754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.38439 | − | 4.99891i | 0.620046 | − | 0.706952i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.884297 | + | 6.72237i | 0.122630 | + | 0.932225i | ||||
\(53\) | − | 10.3377i | − | 1.41999i | −0.704208 | − | 0.709994i | \(-0.748698\pi\) | ||
0.704208 | − | 0.709994i | \(-0.251302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.36459i | 0.318841i | ||||||||
\(56\) | −1.57176 | + | 2.35150i | −0.210035 | + | 0.314233i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.97809 | − | 2.61199i | −0.391042 | − | 0.342971i | ||||
\(59\) | −7.15116 | −0.931001 | −0.465501 | − | 0.885048i | \(-0.654126\pi\) | ||||
−0.465501 | + | 0.885048i | \(0.654126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47260 | 0.572658 | 0.286329 | − | 0.958131i | \(-0.407565\pi\) | ||||
0.286329 | + | 0.958131i | \(0.407565\pi\) | |||||||
\(62\) | −1.46775 | − | 1.28732i | −0.186404 | − | 0.163489i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.05913 | + | 7.39200i | 0.382392 | + | 0.924000i | ||||
\(65\) | 1.85159i | 0.229662i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.1781i | − | 1.24346i | −0.783233 | − | 0.621728i | \(-0.786431\pi\) | ||
0.783233 | − | 0.621728i | \(-0.213569\pi\) | |||||||
\(68\) | −0.190392 | + | 0.0250452i | −0.0230884 | + | 0.00303717i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.509310 | + | 0.580695i | −0.0608742 | + | 0.0694064i | ||||
\(71\) | 5.68379 | 0.674542 | 0.337271 | − | 0.941408i | \(-0.390496\pi\) | ||||
0.337271 | + | 0.941408i | \(0.390496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.760273 | 0.0889832 | 0.0444916 | − | 0.999010i | \(-0.485833\pi\) | ||||
0.0444916 | + | 0.999010i | \(0.485833\pi\) | |||||||
\(74\) | 9.21250 | − | 10.5037i | 1.07093 | − | 1.22103i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.4308 | + | 2.02985i | −1.77003 | + | 0.232839i | ||||
\(77\) | 4.32940i | 0.493381i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95953i | 0.220464i | 0.993906 | + | 0.110232i | \(0.0351594\pi\) | ||||
−0.993906 | + | 0.110232i | \(0.964841\pi\) | |||||||
\(80\) | 0.564993 | + | 2.11036i | 0.0631681 | + | 0.235945i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.0254 | + | 8.79301i | 1.10712 | + | 0.971025i | ||||
\(83\) | 3.56402 | 0.391202 | 0.195601 | − | 0.980684i | \(-0.437334\pi\) | ||||
0.195601 | + | 0.980684i | \(0.437334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0524411 | −0.00568804 | ||||||||
\(86\) | −1.19391 | − | 1.04715i | −0.128743 | − | 0.112917i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.1806 | + | 6.80479i | 1.08526 | + | 0.725393i | ||||
\(89\) | 5.30500i | 0.562329i | 0.959660 | + | 0.281164i | \(0.0907206\pi\) | ||||
−0.959660 | + | 0.281164i | \(0.909279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.39014i | 0.355383i | ||||||||
\(92\) | −0.186790 | − | 1.41997i | −0.0194742 | − | 0.148042i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.53098 | + | 10.8669i | −0.983046 | + | 1.12083i | ||||
\(95\) | −4.25021 | −0.436063 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8514 | 1.40639 | 0.703197 | − | 0.710995i | \(-0.251755\pi\) | ||||
0.703197 | + | 0.710995i | \(0.251755\pi\) | |||||||
\(98\) | −0.932512 | + | 1.06321i | −0.0941979 | + | 0.107401i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.22641 | − | 9.32308i | −0.122641 | − | 0.932308i | ||||
\(101\) | − | 7.60411i | − | 0.756637i | −0.925675 | − | 0.378319i | \(-0.876502\pi\) | ||
0.925675 | − | 0.378319i | \(-0.123498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.70783i | − | 0.168278i | −0.996454 | − | 0.0841388i | \(-0.973186\pi\) | ||
0.996454 | − | 0.0841388i | \(-0.0268139\pi\) | |||||||
\(104\) | 7.97193 | + | 5.32849i | 0.781712 | + | 0.522502i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9911 | − | 9.64000i | −1.06755 | − | 0.936320i | ||||
\(107\) | 12.0437 | 1.16431 | 0.582155 | − | 0.813078i | \(-0.302210\pi\) | ||||
0.582155 | + | 0.813078i | \(0.302210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6297 | 1.40127 | 0.700634 | − | 0.713521i | \(-0.252900\pi\) | ||||
0.700634 | + | 0.713521i | \(0.252900\pi\) | |||||||
\(110\) | 2.51406 | + | 2.20501i | 0.239707 | + | 0.210239i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.03446 | + | 3.86392i | 0.0977475 | + | 0.365106i | ||||
\(113\) | − | 15.7696i | − | 1.48348i | −0.670688 | − | 0.741740i | \(-0.734001\pi\) | ||
0.670688 | − | 0.741740i | \(-0.265999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.391112i | − | 0.0364714i | ||||||
\(116\) | −5.55420 | + | 0.730630i | −0.515695 | + | 0.0678373i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.66854 | + | 7.60320i | −0.613889 | + | 0.699931i | ||||
\(119\) | −0.0960161 | −0.00880178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.74373 | 0.703976 | ||||||||
\(122\) | 4.17075 | − | 4.75533i | 0.377602 | − | 0.430527i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.73738 | + | 0.360090i | −0.245824 | + | 0.0323370i | ||||
\(125\) | − | 5.29878i | − | 0.473937i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.02905i | 0.534992i | 0.963559 | + | 0.267496i | \(0.0861961\pi\) | ||||
−0.963559 | + | 0.267496i | \(0.913804\pi\) | |||||||
\(128\) | 10.7120 | + | 3.64062i | 0.946812 | + | 0.321788i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.96864 | + | 1.72663i | 0.172661 | + | 0.151436i | ||||
\(131\) | 16.0875 | 1.40558 | 0.702788 | − | 0.711399i | \(-0.251938\pi\) | ||||
0.702788 | + | 0.711399i | \(0.251938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.78185 | −0.674772 | ||||||||
\(134\) | −10.8215 | − | 9.49122i | −0.934836 | − | 0.819917i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.150914 | + | 0.225782i | −0.0129408 | + | 0.0193607i | ||||
\(137\) | 12.5367i | 1.07108i | 0.844509 | + | 0.535541i | \(0.179892\pi\) | ||||
−0.844509 | + | 0.535541i | \(0.820108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.60676i | 0.136283i | 0.997676 | + | 0.0681417i | \(0.0217070\pi\) | ||||
−0.997676 | + | 0.0681417i | \(0.978293\pi\) | |||||||
\(140\) | 0.142465 | + | 1.08301i | 0.0120405 | + | 0.0915311i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.30020 | − | 6.04308i | 0.444783 | − | 0.507124i | ||||
\(143\) | 14.6773 | 1.22738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.52984 | −0.127046 | ||||||||
\(146\) | 0.708963 | − | 0.808332i | 0.0586742 | − | 0.0668980i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.57693 | − | 19.5897i | −0.211823 | − | 1.61026i | ||||
\(149\) | 13.8728i | 1.13651i | 0.822854 | + | 0.568253i | \(0.192380\pi\) | ||||
−0.822854 | + | 0.568253i | \(0.807620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 20.3035i | − | 1.65228i | −0.563468 | − | 0.826138i | \(-0.690533\pi\) | ||
0.563468 | − | 0.826138i | \(-0.309467\pi\) | |||||||
\(152\) | −12.2312 | + | 18.2990i | −0.992082 | + | 1.48425i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.60308 | + | 4.03722i | 0.370927 | + | 0.325328i | ||||
\(155\) | −0.753978 | −0.0605610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8258 | −1.66208 | −0.831041 | − | 0.556212i | \(-0.812254\pi\) | ||||
−0.831041 | + | 0.556212i | \(0.812254\pi\) | |||||||
\(158\) | 2.08340 | + | 1.82728i | 0.165746 | + | 0.145371i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.77062 | + | 1.36723i | 0.219037 | + | 0.108089i | ||||
\(161\) | − | 0.716100i | − | 0.0564366i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.81556i | 0.768814i | 0.923164 | + | 0.384407i | \(0.125594\pi\) | ||||
−0.923164 | + | 0.384407i | \(0.874406\pi\) | |||||||
\(164\) | 18.6977 | − | 2.45959i | 1.46004 | − | 0.192062i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.32349 | − | 3.78931i | 0.257953 | − | 0.294108i | ||||
\(167\) | −7.70531 | −0.596255 | −0.298127 | − | 0.954526i | \(-0.596362\pi\) | ||||
−0.298127 | + | 0.954526i | \(0.596362\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50694 | −0.115918 | ||||||||
\(170\) | −0.0489020 | + | 0.0557561i | −0.00375061 | + | 0.00427630i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.22668 | + | 0.292909i | −0.169783 | + | 0.0223341i | ||||
\(173\) | 15.3623i | 1.16797i | 0.811763 | + | 0.583986i | \(0.198508\pi\) | ||||
−0.811763 | + | 0.583986i | \(0.801492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.70170i | − | 0.355415i | ||||||
\(176\) | 16.7285 | − | 4.47861i | 1.26096 | − | 0.337588i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.64035 | + | 4.94698i | 0.422762 | + | 0.370791i | ||||
\(179\) | 18.7031 | 1.39794 | 0.698968 | − | 0.715153i | \(-0.253643\pi\) | ||||
0.698968 | + | 0.715153i | \(0.253643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.07751 | −0.600397 | −0.300198 | − | 0.953877i | \(-0.597053\pi\) | ||||
−0.300198 | + | 0.953877i | \(0.597053\pi\) | |||||||
\(182\) | 3.60444 | + | 3.16135i | 0.267179 | + | 0.234335i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.68391 | − | 1.12554i | −0.124140 | − | 0.0829757i | ||||
\(185\) | − | 5.39574i | − | 0.396703i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.415692i | 0.0303984i | ||||||||
\(188\) | 2.66602 | + | 20.2669i | 0.194440 | + | 1.47812i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.96337 | + | 4.51888i | −0.287533 | + | 0.327834i | ||||
\(191\) | −8.39933 | −0.607754 | −0.303877 | − | 0.952711i | \(-0.598281\pi\) | ||||
−0.303877 | + | 0.952711i | \(0.598281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.8492 | −1.06887 | −0.534436 | − | 0.845209i | \(-0.679476\pi\) | ||||
−0.534436 | + | 0.845209i | \(0.679476\pi\) | |||||||
\(194\) | 12.9166 | − | 14.7270i | 0.927355 | − | 1.05733i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.260844 | + | 1.98292i | 0.0186317 | + | 0.141637i | ||||
\(197\) | − | 23.5310i | − | 1.67651i | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||
0.545275 | − | 0.838257i | \(-0.316425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.6792i | − | 1.67857i | −0.543690 | − | 0.839286i | \(-0.682973\pi\) | ||
0.543690 | − | 0.839286i | \(-0.317027\pi\) | |||||||
\(200\) | −11.0561 | − | 7.38995i | −0.781781 | − | 0.522548i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.08479 | − | 7.09092i | −0.568844 | − | 0.498916i | ||||
\(203\) | −2.80103 | −0.196593 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.15005 | 0.359695 | ||||||||
\(206\) | −1.81579 | − | 1.59257i | −0.126512 | − | 0.110960i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.0992 | − | 3.50697i | 0.908269 | − | 0.243165i | ||||
\(209\) | 33.6908i | 2.33044i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.20308i | 0.220509i | 0.993903 | + | 0.110255i | \(0.0351666\pi\) | ||||
−0.993903 | + | 0.110255i | \(0.964833\pi\) | |||||||
\(212\) | −20.4987 | + | 2.69652i | −1.40786 | + | 0.185197i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.2309 | − | 12.8050i | 0.767729 | − | 0.875334i | ||||
\(215\) | −0.613311 | −0.0418275 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.38048 | −0.0937132 | ||||||||
\(218\) | 13.6423 | − | 15.5545i | 0.923976 | − | 1.05348i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.68879 | − | 0.616788i | 0.316118 | − | 0.0415839i | ||||
\(221\) | 0.325508i | 0.0218961i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1778i | 1.41817i | 0.705121 | + | 0.709087i | \(0.250892\pi\) | ||||
−0.705121 | + | 0.709087i | \(0.749108\pi\) | |||||||
\(224\) | 5.07282 | + | 2.50330i | 0.338942 | + | 0.167259i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.7665 | − | 14.7053i | −1.11529 | − | 0.978185i | ||||
\(227\) | −4.15700 | −0.275910 | −0.137955 | − | 0.990439i | \(-0.544053\pi\) | ||||
−0.137955 | + | 0.990439i | \(0.544053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.319653 | 0.0211232 | 0.0105616 | − | 0.999944i | \(-0.496638\pi\) | ||||
0.0105616 | + | 0.999944i | \(0.496638\pi\) | |||||||
\(230\) | −0.415836 | − | 0.364717i | −0.0274194 | − | 0.0240487i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.40254 | + | 6.58662i | −0.289041 | + | 0.432433i | ||||
\(233\) | − | 3.81568i | − | 0.249974i | −0.992158 | − | 0.124987i | \(-0.960111\pi\) | ||
0.992158 | − | 0.124987i | \(-0.0398889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.58228i | 0.364148i | ||||||||
\(236\) | 1.86533 | + | 14.1802i | 0.121423 | + | 0.923049i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0895361 | + | 0.102086i | −0.00580377 | + | 0.00661722i | ||||
\(239\) | 5.19473 | 0.336019 | 0.168009 | − | 0.985785i | \(-0.446266\pi\) | ||||
0.168009 | + | 0.985785i | \(0.446266\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4806 | −1.12603 | −0.563013 | − | 0.826448i | \(-0.690358\pi\) | ||||
−0.563013 | + | 0.826448i | \(0.690358\pi\) | |||||||
\(242\) | 7.22112 | − | 8.23324i | 0.464191 | − | 0.529253i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.16665 | − | 8.86880i | −0.0746871 | − | 0.567767i | ||||
\(245\) | 0.546170i | 0.0348935i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.3816i | 1.67862i | ||||||||
\(248\) | −2.16979 | + | 3.24621i | −0.137782 | + | 0.206134i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.63373 | − | 4.94117i | −0.356308 | − | 0.312507i | ||||
\(251\) | −7.32620 | −0.462426 | −0.231213 | − | 0.972903i | \(-0.574269\pi\) | ||||
−0.231213 | + | 0.972903i | \(0.574269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10028 | −0.194913 | ||||||||
\(254\) | 6.41016 | + | 5.62216i | 0.402209 | + | 0.352766i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8598 | − | 7.99416i | 0.866236 | − | 0.499635i | ||||
\(257\) | 15.5523i | 0.970123i | 0.874480 | + | 0.485062i | \(0.161203\pi\) | ||||
−0.874480 | + | 0.485062i | \(0.838797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.87923i | − | 0.613865i | ||||||
\(260\) | 3.67156 | − | 0.482977i | 0.227700 | − | 0.0299529i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0018 | − | 17.1045i | 0.926816 | − | 1.05672i | ||||
\(263\) | 21.9908 | 1.35601 | 0.678005 | − | 0.735057i | \(-0.262845\pi\) | ||||
0.678005 | + | 0.735057i | \(0.262845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.64613 | −0.346839 | ||||||||
\(266\) | −7.25666 | + | 8.27376i | −0.444935 | + | 0.507297i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.1824 | + | 2.65490i | −1.23283 | + | 0.162174i | ||||
\(269\) | − | 26.0711i | − | 1.58958i | −0.606883 | − | 0.794791i | \(-0.707580\pi\) | ||
0.606883 | − | 0.794791i | \(-0.292420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.3875i | − | 1.11696i | −0.829517 | − | 0.558481i | \(-0.811384\pi\) | ||
0.829517 | − | 0.558481i | \(-0.188616\pi\) | |||||||
\(272\) | 0.0993251 | + | 0.370999i | 0.00602247 | + | 0.0224951i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.3292 | + | 11.6906i | 0.805246 | + | 0.706256i | ||||
\(275\) | −20.3555 | −1.22749 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.01025 | 0.0607003 | 0.0303502 | − | 0.999539i | \(-0.490338\pi\) | ||||
0.0303502 | + | 0.999539i | \(0.490338\pi\) | |||||||
\(278\) | 1.70833 | + | 1.49832i | 0.102459 | + | 0.0898633i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.28432 | + | 0.858449i | 0.0767529 | + | 0.0513022i | ||||
\(281\) | − | 15.0496i | − | 0.897784i | −0.893586 | − | 0.448892i | \(-0.851819\pi\) | ||
0.893586 | − | 0.448892i | \(-0.148181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.14369i | − | 0.0679851i | −0.999422 | − | 0.0339926i | \(-0.989178\pi\) | ||
0.999422 | − | 0.0339926i | \(-0.0108223\pi\) | |||||||
\(284\) | −1.48258 | − | 11.2705i | −0.0879749 | − | 0.668780i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6867 | − | 15.6051i | 0.809314 | − | 0.922748i | ||||
\(287\) | 9.42938 | 0.556599 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9908 | 0.999458 | ||||||||
\(290\) | −1.42659 | + | 1.62654i | −0.0837723 | + | 0.0955139i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.198312 | − | 1.50756i | −0.0116054 | − | 0.0882232i | ||||
\(293\) | − | 31.3747i | − | 1.83293i | −0.400113 | − | 0.916466i | \(-0.631029\pi\) | ||
0.400113 | − | 0.916466i | \(-0.368971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.90575i | 0.227401i | ||||||||
\(296\) | −23.2310 | − | 15.5278i | −1.35028 | − | 0.902534i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.7498 | + | 12.9366i | 0.854430 | + | 0.749395i | ||||
\(299\) | −2.42768 | −0.140396 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12293 | −0.0647246 | ||||||||
\(302\) | −21.5870 | − | 18.9333i | −1.24219 | − | 1.08949i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.05003 | + | 30.0684i | 0.461701 | + | 1.72454i | ||||
\(305\) | − | 2.44280i | − | 0.139874i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0117i | 1.48457i | 0.670086 | + | 0.742284i | \(0.266257\pi\) | ||||
−0.670086 | + | 0.742284i | \(0.733743\pi\) | |||||||
\(308\) | 8.58485 | − | 1.12930i | 0.489167 | − | 0.0643477i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.703093 | + | 0.801639i | −0.0399330 | + | 0.0455300i | ||||
\(311\) | −1.17950 | −0.0668835 | −0.0334418 | − | 0.999441i | \(-0.510647\pi\) | ||||
−0.0334418 | + | 0.999441i | \(0.510647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.0849 | −1.41788 | −0.708942 | − | 0.705267i | \(-0.750827\pi\) | ||||
−0.708942 | + | 0.705267i | \(0.750827\pi\) | |||||||
\(314\) | −19.4203 | + | 22.1423i | −1.09595 | + | 1.24956i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.88559 | − | 0.511131i | 0.218581 | − | 0.0287534i | ||||
\(317\) | − | 8.10102i | − | 0.454998i | −0.973778 | − | 0.227499i | \(-0.926945\pi\) | ||
0.973778 | − | 0.227499i | \(-0.0730549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1268i | 0.678969i | ||||||||
\(320\) | 4.03729 | − | 1.67081i | 0.225691 | − | 0.0934010i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.761366 | − | 0.667771i | −0.0424293 | − | 0.0372134i | ||||
\(323\) | −0.747183 | −0.0415744 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.9394 | −0.884160 | ||||||||
\(326\) | 10.4360 | + | 9.15313i | 0.577998 | + | 0.506945i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.8207 | − | 22.1732i | 0.818338 | − | 1.22431i | ||||
\(329\) | 10.2208i | 0.563489i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5057i | 1.62178i | 0.585199 | + | 0.810890i | \(0.301016\pi\) | ||||
−0.585199 | + | 0.810890i | \(0.698984\pi\) | |||||||
\(332\) | −0.929651 | − | 7.06715i | −0.0510212 | − | 0.387860i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.18529 | + | 8.19239i | −0.393162 | + | 0.448268i | ||||
\(335\) | −5.55899 | −0.303720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7381 | 1.12968 | 0.564838 | − | 0.825202i | \(-0.308939\pi\) | ||||
0.564838 | + | 0.825202i | \(0.308939\pi\) | |||||||
\(338\) | −1.40524 | + | 1.60220i | −0.0764349 | + | 0.0871480i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0136789 | + | 0.103986i | 0.000741844 | + | 0.00563946i | ||||
\(341\) | 5.97666i | 0.323654i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −1.76498 | + | 2.64057i | −0.0951613 | + | 0.142370i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.3334 | + | 14.3255i | 0.878088 | + | 0.770144i | ||||
\(347\) | −34.9712 | −1.87735 | −0.938676 | − | 0.344799i | \(-0.887947\pi\) | ||||
−0.938676 | + | 0.344799i | \(0.887947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.321498 | −0.0172094 | −0.00860469 | − | 0.999963i | \(-0.502739\pi\) | ||||
−0.00860469 | + | 0.999963i | \(0.502739\pi\) | |||||||
\(350\) | −4.99891 | − | 4.38439i | −0.267203 | − | 0.234355i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.8378 | − | 21.9623i | 0.577656 | − | 1.17059i | ||||
\(353\) | 25.5472i | 1.35974i | 0.733331 | + | 0.679871i | \(0.237964\pi\) | ||||
−0.733331 | + | 0.679871i | \(0.762036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.10432i | − | 0.164760i | ||||||
\(356\) | 10.5194 | − | 1.38378i | 0.557526 | − | 0.0733399i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4409 | − | 19.8854i | 0.921778 | − | 1.05098i | ||||
\(359\) | −3.16705 | −0.167151 | −0.0835753 | − | 0.996501i | \(-0.526634\pi\) | ||||
−0.0835753 | + | 0.996501i | \(0.526634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −41.5572 | −2.18722 | ||||||||
\(362\) | −7.53238 | + | 8.58812i | −0.395893 | + | 0.451381i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.72237 | − | 0.884297i | 0.352348 | − | 0.0463497i | ||||
\(365\) | − | 0.415238i | − | 0.0217346i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3530i | 1.58442i | 0.610251 | + | 0.792208i | \(0.291069\pi\) | ||||
−0.610251 | + | 0.792208i | \(0.708931\pi\) | |||||||
\(368\) | −2.76695 | + | 0.740778i | −0.144237 | + | 0.0386157i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.73682 | − | 5.03159i | −0.298243 | − | 0.261580i | ||||
\(371\) | −10.3377 | −0.536705 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0260 | 0.881572 | 0.440786 | − | 0.897612i | \(-0.354700\pi\) | ||||
0.440786 | + | 0.897612i | \(0.354700\pi\) | |||||||
\(374\) | 0.441970 | + | 0.387638i | 0.0228537 | + | 0.0200443i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.0342 | + | 16.0646i | 1.23947 | + | 0.828469i | ||||
\(377\) | 9.49587i | 0.489062i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.0613i | 1.90371i | 0.306543 | + | 0.951857i | \(0.400828\pi\) | ||||
−0.306543 | + | 0.951857i | \(0.599172\pi\) | |||||||
\(380\) | 1.10864 | + | 8.42782i | 0.0568721 | + | 0.432338i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.83248 | + | 8.93028i | −0.400744 | + | 0.456913i | ||||
\(383\) | 10.8566 | 0.554749 | 0.277374 | − | 0.960762i | \(-0.410536\pi\) | ||||
0.277374 | + | 0.960762i | \(0.410536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.36459 | 0.120511 | ||||||||
\(386\) | −13.8471 | + | 15.7879i | −0.704798 | + | 0.803583i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.61304 | − | 27.4661i | −0.183424 | − | 1.39438i | ||||
\(389\) | − | 27.3658i | − | 1.38750i | −0.720215 | − | 0.693751i | \(-0.755957\pi\) | ||
0.720215 | − | 0.693751i | \(-0.244043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.0687571i | − | 0.00347720i | ||||||
\(392\) | 2.35150 | + | 1.57176i | 0.118769 | + | 0.0793859i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.0185 | − | 21.9429i | −1.26041 | − | 1.10547i | ||||
\(395\) | 1.07024 | 0.0538495 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2105 | −1.26528 | −0.632640 | − | 0.774446i | \(-0.718029\pi\) | ||||
−0.632640 | + | 0.774446i | \(0.718029\pi\) | |||||||
\(398\) | −25.1760 | − | 22.0811i | −1.26196 | − | 1.10683i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.1670 | + | 4.86373i | −0.908350 | + | 0.243187i | ||||
\(401\) | 30.1462i | 1.50543i | 0.658347 | + | 0.752714i | \(0.271256\pi\) | ||||
−0.658347 | + | 0.752714i | \(0.728744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.68003i | 0.233129i | ||||||||
\(404\) | −15.0783 | + | 1.98348i | −0.750175 | + | 0.0986820i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.61199 | + | 2.97809i | −0.129631 | + | 0.147800i | ||||
\(407\) | −42.7712 | −2.12009 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.5021 | 1.06321 | 0.531605 | − | 0.846993i | \(-0.321589\pi\) | ||||
0.531605 | + | 0.846993i | \(0.321589\pi\) | |||||||
\(410\) | 4.80248 | − | 5.47559i | 0.237177 | − | 0.270420i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.38649 | + | 0.445477i | −0.166840 | + | 0.0219471i | ||||
\(413\) | 7.15116i | 0.351885i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.94656i | − | 0.0955529i | ||||||
\(416\) | 8.48654 | − | 17.1976i | 0.416087 | − | 0.843181i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.8205 | + | 31.4170i | 1.75204 | + | 1.53666i | ||||
\(419\) | −0.917403 | −0.0448181 | −0.0224090 | − | 0.999749i | \(-0.507134\pi\) | ||||
−0.0224090 | + | 0.999749i | \(0.507134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.17383 | −0.154683 | −0.0773416 | − | 0.997005i | \(-0.524643\pi\) | ||||
−0.0773416 | + | 0.997005i | \(0.524643\pi\) | |||||||
\(422\) | 3.40556 | + | 2.98691i | 0.165780 | + | 0.145401i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.2484 | + | 24.3091i | −0.789090 | + | 1.18055i | ||||
\(425\) | − | 0.451439i | − | 0.0218980i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.47260i | − | 0.216444i | ||||||
\(428\) | −3.14153 | − | 23.8817i | −0.151851 | − | 1.15437i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.571920 | + | 0.652080i | −0.0275804 | + | 0.0314461i | ||||
\(431\) | −7.01129 | −0.337722 | −0.168861 | − | 0.985640i | \(-0.554009\pi\) | ||||
−0.168861 | + | 0.985640i | \(0.554009\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.6529 | 0.800288 | 0.400144 | − | 0.916452i | \(-0.368960\pi\) | ||||
0.400144 | + | 0.916452i | \(0.368960\pi\) | |||||||
\(434\) | −1.28732 | + | 1.46775i | −0.0617931 | + | 0.0704540i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.81606 | − | 29.0094i | −0.182756 | − | 1.38930i | ||||
\(437\) | − | 5.57258i | − | 0.266573i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.8377i | − | 0.755894i | −0.925827 | − | 0.377947i | \(-0.876630\pi\) | ||
0.925827 | − | 0.377947i | \(-0.123370\pi\) | |||||||
\(440\) | 3.71657 | − | 5.56034i | 0.177181 | − | 0.265079i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.346085 | + | 0.303540i | 0.0164616 | + | 0.0144379i | ||||
\(443\) | −11.7934 | −0.560321 | −0.280161 | − | 0.959953i | \(-0.590388\pi\) | ||||
−0.280161 | + | 0.959953i | \(0.590388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.89743 | 0.137352 | ||||||||
\(446\) | 22.5166 | + | 19.7486i | 1.06619 | + | 0.935123i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.39200 | − | 3.05913i | 0.349239 | − | 0.144530i | ||||
\(449\) | 11.4729i | 0.541441i | 0.962658 | + | 0.270720i | \(0.0872619\pi\) | ||||
−0.962658 | + | 0.270720i | \(0.912738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 40.8236i | − | 1.92231i | ||||||
\(452\) | −31.2698 | + | 4.11340i | −1.47081 | + | 0.193478i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.87645 | + | 4.41977i | −0.181931 | + | 0.207430i | ||||
\(455\) | 1.85159 | 0.0868041 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.716248 | 0.0335047 | 0.0167523 | − | 0.999860i | \(-0.494667\pi\) | ||||
0.0167523 | + | 0.999860i | \(0.494667\pi\) | |||||||
\(458\) | 0.298080 | − | 0.339859i | 0.0139284 | − | 0.0158806i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.775543 | + | 0.102019i | −0.0361599 | + | 0.00475667i | ||||
\(461\) | 25.6559i | 1.19492i | 0.801900 | + | 0.597458i | \(0.203823\pi\) | ||||
−0.801900 | + | 0.597458i | \(0.796177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.41981i | − | 0.391302i | −0.980674 | − | 0.195651i | \(-0.937318\pi\) | ||
0.980674 | − | 0.195651i | \(-0.0626820\pi\) | |||||||
\(464\) | 2.89756 | + | 10.8229i | 0.134516 | + | 0.502443i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.05689 | − | 3.55817i | −0.187932 | − | 0.164829i | ||||
\(467\) | −27.6632 | −1.28010 | −0.640050 | − | 0.768333i | \(-0.721086\pi\) | ||||
−0.640050 | + | 0.768333i | \(0.721086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1781 | −0.469982 | ||||||||
\(470\) | 5.93515 | + | 5.20554i | 0.273768 | + | 0.240114i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.8160 | + | 11.2399i | 0.774018 | + | 0.517359i | ||||
\(473\) | 4.86162i | 0.223537i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 36.5879i | − | 1.67877i | ||||||
\(476\) | 0.0250452 | + | 0.190392i | 0.00114794 | + | 0.00872660i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.84414 | − | 5.52310i | 0.221566 | − | 0.252621i | ||||
\(479\) | 20.8002 | 0.950383 | 0.475192 | − | 0.879882i | \(-0.342379\pi\) | ||||
0.475192 | + | 0.879882i | \(0.342379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.4920 | −1.52710 | ||||||||
\(482\) | −16.3009 | + | 18.5856i | −0.742485 | + | 0.846552i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.01990 | − | 15.3552i | −0.0918138 | − | 0.697963i | ||||
\(485\) | − | 7.56520i | − | 0.343518i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8907i | 0.674761i | 0.941368 | + | 0.337380i | \(0.109541\pi\) | ||||
−0.941368 | + | 0.337380i | \(0.890459\pi\) | |||||||
\(488\) | −10.5173 | − | 7.02986i | −0.476097 | − | 0.318227i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.580695 | + | 0.509310i | 0.0262331 | + | 0.0230083i | ||||
\(491\) | 43.0692 | 1.94369 | 0.971844 | − | 0.235626i | \(-0.0757140\pi\) | ||||
0.971844 | + | 0.235626i | \(0.0757140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.268944 | −0.0121126 | ||||||||
\(494\) | 28.0492 | + | 24.6011i | 1.26199 | + | 1.10686i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.42806 | + | 5.33407i | 0.0641216 | + | 0.239507i | ||||
\(497\) | − | 5.68379i | − | 0.254953i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.6899i | 1.10527i | 0.833423 | + | 0.552636i | \(0.186378\pi\) | ||||
−0.833423 | + | 0.552636i | \(0.813622\pi\) | |||||||
\(500\) | −10.5070 | + | 1.38215i | −0.469889 | + | 0.0618117i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.83177 | + | 7.78931i | −0.304917 | + | 0.347654i | ||||
\(503\) | 8.81804 | 0.393177 | 0.196588 | − | 0.980486i | \(-0.437014\pi\) | ||||
0.196588 | + | 0.980486i | \(0.437014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.15314 | −0.184812 | ||||||||
\(506\) | −2.89105 | + | 3.29626i | −0.128523 | + | 0.146537i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9551 | − | 1.57264i | 0.530422 | − | 0.0697746i | ||||
\(509\) | − | 24.9542i | − | 1.10607i | −0.833157 | − | 0.553037i | \(-0.813469\pi\) | ||
0.833157 | − | 0.553037i | \(-0.186531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.760273i | − | 0.0336325i | ||||||
\(512\) | 4.42491 | − | 22.1905i | 0.195555 | − | 0.980693i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.5354 | + | 14.5027i | 0.729344 | + | 0.639685i | ||||
\(515\) | −0.932767 | −0.0411026 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2498 | 1.94610 | ||||||||
\(518\) | −10.5037 | − | 9.21250i | −0.461507 | − | 0.404774i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.91026 | − | 4.35403i | 0.127624 | − | 0.190937i | ||||
\(521\) | − | 12.2860i | − | 0.538261i | −0.963104 | − | 0.269131i | \(-0.913264\pi\) | ||
0.963104 | − | 0.269131i | \(-0.0867363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.88092i | 0.344609i | 0.985044 | + | 0.172304i | \(0.0551212\pi\) | ||||
−0.985044 | + | 0.172304i | \(0.944879\pi\) | |||||||
\(524\) | −4.19633 | − | 31.9003i | −0.183318 | − | 1.39357i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5067 | − | 23.3809i | 0.894134 | − | 1.01946i | ||||
\(527\) | −0.132548 | −0.00577390 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4872 | −0.977704 | ||||||||
\(530\) | −5.26508 | + | 6.00304i | −0.228701 | + | 0.260755i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.02985 | + | 15.4308i | 0.0880049 | + | 0.669008i | ||||
\(533\) | − | 31.9669i | − | 1.38464i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.57792i | − | 0.284388i | ||||||
\(536\) | −15.9976 | + | 23.9339i | −0.690990 | + | 1.03379i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.7191 | − | 24.3116i | −1.19506 | − | 1.04815i | ||||
\(539\) | 4.32940 | 0.186481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0419231 | −0.00180241 | −0.000901207 | − | 1.00000i | \(-0.500287\pi\) | ||||
−0.000901207 | 1.00000i | \(0.500287\pi\) | ||||||||
\(542\) | −19.5498 | − | 17.1466i | −0.839737 | − | 0.736508i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.487072 | + | 0.240357i | 0.0208831 | + | 0.0103052i | ||||
\(545\) | − | 7.99029i | − | 0.342266i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.7201i | − | 1.52728i | −0.645642 | − | 0.763640i | \(-0.723410\pi\) | ||
0.645642 | − | 0.763640i | \(-0.276590\pi\) | |||||||
\(548\) | 24.8592 | − | 3.27012i | 1.06193 | − | 0.139693i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.9818 | + | 21.6423i | −0.809386 | + | 0.922830i | ||||
\(551\) | −21.7972 | −0.928590 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.95953 | 0.0833277 | ||||||||
\(554\) | 0.942074 | − | 1.07412i | 0.0400249 | − | 0.0456348i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.18607 | − | 0.419112i | 0.135119 | − | 0.0177743i | ||||
\(557\) | − | 13.6147i | − | 0.576873i | −0.957499 | − | 0.288437i | \(-0.906865\pi\) | ||
0.957499 | − | 0.288437i | \(-0.0931354\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.80689i | 0.161014i | ||||||||
\(560\) | 2.11036 | − | 0.564993i | 0.0891789 | − | 0.0238753i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.0009 | − | 14.0339i | −0.674959 | − | 0.591986i | ||||
\(563\) | −6.20546 | −0.261529 | −0.130765 | − | 0.991413i | \(-0.541743\pi\) | ||||
−0.130765 | + | 0.991413i | \(0.541743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.61289 | −0.362347 | ||||||||
\(566\) | −1.21598 | − | 1.06650i | −0.0511116 | − | 0.0448284i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.3654 | − | 8.93356i | −0.560802 | − | 0.374844i | ||||
\(569\) | − | 14.1054i | − | 0.591330i | −0.955292 | − | 0.295665i | \(-0.904459\pi\) | ||
0.955292 | − | 0.295665i | \(-0.0955412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.5054i | − | 1.23476i | −0.786664 | − | 0.617381i | \(-0.788194\pi\) | ||
0.786664 | − | 0.617381i | \(-0.211806\pi\) | |||||||
\(572\) | −3.82848 | − | 29.1039i | −0.160077 | − | 1.21689i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.79301 | − | 10.0254i | 0.367013 | − | 0.418454i | ||||
\(575\) | 3.36688 | 0.140409 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0674 | −0.544004 | −0.272002 | − | 0.962297i | \(-0.587686\pi\) | ||||
−0.272002 | + | 0.962297i | \(0.587686\pi\) | |||||||
\(578\) | 15.8441 | − | 18.0648i | 0.659028 | − | 0.751397i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.399048 | + | 3.03354i | 0.0165696 | + | 0.125961i | ||||
\(581\) | − | 3.56402i | − | 0.147860i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.7559i | 1.85360i | ||||||||
\(584\) | −1.78778 | − | 1.19497i | −0.0739790 | − | 0.0494481i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33.3580 | − | 29.2573i | −1.37801 | − | 1.20861i | ||||
\(587\) | 46.4897 | 1.91883 | 0.959417 | − | 0.281992i | \(-0.0909951\pi\) | ||||
0.959417 | + | 0.281992i | \(0.0909951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7427 | −0.442645 | ||||||||
\(590\) | 4.15264 | + | 3.64216i | 0.170962 | + | 0.149945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −38.1726 | + | 10.2197i | −1.56888 | + | 0.420027i | ||||
\(593\) | 31.7588i | 1.30418i | 0.758143 | + | 0.652089i | \(0.226107\pi\) | ||||
−0.758143 | + | 0.652089i | \(0.773893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0524411i | 0.00214988i | ||||||||
\(596\) | 27.5086 | − | 3.61863i | 1.12680 | − | 0.148225i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.26384 | + | 2.58114i | −0.0925753 | + | 0.105551i | ||||
\(599\) | 6.57765 | 0.268755 | 0.134378 | − | 0.990930i | \(-0.457096\pi\) | ||||
0.134378 | + | 0.990930i | \(0.457096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6923 | 0.640103 | 0.320052 | − | 0.947400i | \(-0.396300\pi\) | ||||
0.320052 | + | 0.947400i | \(0.396300\pi\) | |||||||
\(602\) | −1.04715 | + | 1.19391i | −0.0426785 | + | 0.0486603i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −40.2602 | + | 5.29604i | −1.63816 | + | 0.215493i | ||||
\(605\) | − | 4.22940i | − | 0.171949i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.44562i | 0.180442i | 0.995922 | + | 0.0902210i | \(0.0287573\pi\) | ||||
−0.995922 | + | 0.0902210i | \(0.971243\pi\) | |||||||
\(608\) | 39.4759 | + | 19.4803i | 1.60096 | + | 0.790030i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.59722 | − | 2.27794i | −0.105158 | − | 0.0922312i | ||||
\(611\) | 34.6498 | 1.40178 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.2778 | −0.455507 | −0.227753 | − | 0.973719i | \(-0.573138\pi\) | ||||
−0.227753 | + | 0.973719i | \(0.573138\pi\) | |||||||
\(614\) | 27.6560 | + | 24.2562i | 1.11611 | + | 0.978902i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.80479 | − | 10.1806i | 0.274173 | − | 0.410188i | ||||
\(617\) | 35.3409i | 1.42277i | 0.702802 | + | 0.711385i | \(0.251932\pi\) | ||||
−0.702802 | + | 0.711385i | \(0.748068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.1363i | − | 1.21128i | −0.795738 | − | 0.605641i | \(-0.792917\pi\) | ||
0.795738 | − | 0.605641i | \(-0.207083\pi\) | |||||||
\(620\) | 0.196670 | + | 1.49508i | 0.00789847 | + | 0.0600437i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.09990 | + | 1.25406i | −0.0441020 | + | 0.0502834i | ||||
\(623\) | 5.30500 | 0.212540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.6145 | 0.824578 | ||||||||
\(626\) | −23.3920 | + | 26.6706i | −0.934932 | + | 1.06597i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.43228 | + | 41.2959i | 0.216772 | + | 1.64788i | ||||
\(629\) | − | 0.948565i | − | 0.0378218i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.06139i | − | 0.0422535i | −0.999777 | − | 0.0211267i | \(-0.993275\pi\) | ||
0.999777 | − | 0.0211267i | \(-0.00672535\pi\) | |||||||
\(632\) | 3.07991 | − | 4.60784i | 0.122512 | − | 0.183290i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.61311 | − | 7.55429i | −0.342070 | − | 0.300019i | ||||
\(635\) | 3.29289 | 0.130674 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.39014 | 0.134322 | ||||||||
\(638\) | 12.8933 | + | 11.3084i | 0.510452 | + | 0.447702i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.98840 | − | 5.85055i | 0.0785984 | − | 0.231263i | ||||
\(641\) | 17.6125i | 0.695651i | 0.937559 | + | 0.347825i | \(0.113080\pi\) | ||||
−0.937559 | + | 0.347825i | \(0.886920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.86528i | 0.310176i | 0.987901 | + | 0.155088i | \(0.0495662\pi\) | ||||
−0.987901 | + | 0.155088i | \(0.950434\pi\) | |||||||
\(644\) | −1.41997 | + | 0.186790i | −0.0559545 | + | 0.00736056i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.696757 | + | 0.794414i | −0.0274135 | + | 0.0312558i | ||||
\(647\) | −27.9700 | −1.09962 | −0.549808 | − | 0.835291i | \(-0.685299\pi\) | ||||
−0.549808 | + | 0.835291i | \(0.685299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.9602 | 1.21530 | ||||||||
\(650\) | −14.8637 | + | 16.9470i | −0.583002 | + | 0.664716i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.4634 | − | 2.56033i | 0.762247 | − | 0.100270i | ||||
\(653\) | − | 14.0209i | − | 0.548679i | −0.961633 | − | 0.274340i | \(-0.911541\pi\) | ||
0.961633 | − | 0.274340i | \(-0.0884592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.78654i | − | 0.343319i | ||||||
\(656\) | −9.75434 | − | 36.4344i | −0.380843 | − | 1.42252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.8669 | + | 9.53098i | 0.423634 | + | 0.371556i | ||||
\(659\) | 10.0407 | 0.391130 | 0.195565 | − | 0.980691i | \(-0.437346\pi\) | ||||
0.195565 | + | 0.980691i | \(0.437346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.09723 | −0.159364 | −0.0796818 | − | 0.996820i | \(-0.525390\pi\) | ||||
−0.0796818 | + | 0.996820i | \(0.525390\pi\) | |||||||
\(662\) | 31.3708 | + | 27.5144i | 1.21926 | + | 1.06938i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.38080 | − | 5.60179i | −0.325238 | − | 0.217391i | ||||
\(665\) | 4.25021i | 0.164816i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.00581i | − | 0.0776654i | ||||||
\(668\) | 2.00988 | + | 15.2790i | 0.0777646 | + | 0.591162i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.18382 | + | 5.91039i | −0.200269 | + | 0.228338i | ||||
\(671\) | −19.3637 | −0.747527 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2300 | 0.702716 | 0.351358 | − | 0.936241i | \(-0.385720\pi\) | ||||
0.351358 | + | 0.936241i | \(0.385720\pi\) | |||||||
\(674\) | 19.3385 | − | 22.0490i | 0.744892 | − | 0.849296i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.393075 | + | 2.98813i | 0.0151183 | + | 0.114928i | ||||
\(677\) | − | 41.9357i | − | 1.61172i | −0.592106 | − | 0.805860i | \(-0.701703\pi\) | ||
0.592106 | − | 0.805860i | \(-0.298297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.8514i | − | 0.531567i | ||||||
\(680\) | 0.123315 | + | 0.0824250i | 0.00472893 | + | 0.00316085i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.35446 | + | 5.57331i | 0.243325 | + | 0.213413i | ||||
\(683\) | −15.5075 | −0.593379 | −0.296689 | − | 0.954974i | \(-0.595883\pi\) | ||||
−0.296689 | + | 0.954974i | \(0.595883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.84717 | 0.261617 | ||||||||
\(686\) | 1.06321 | + | 0.932512i | 0.0405937 | + | 0.0356035i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.16163 | + | 4.33891i | 0.0442867 | + | 0.165420i | ||||
\(689\) | 35.0462i | 1.33515i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.133779i | 0.00508917i | 0.999997 | + | 0.00254459i | \(0.000809968\pi\) | ||||
−0.999997 | + | 0.00254459i | \(0.999190\pi\) | |||||||
\(692\) | 30.4621 | − | 4.00715i | 1.15800 | − | 0.152329i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.6111 | + | 37.1818i | −1.23790 | + | 1.41140i | ||||
\(695\) | 0.877563 | 0.0332879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.905372 | 0.0342934 | ||||||||
\(698\) | −0.299800 | + | 0.341820i | −0.0113476 | + | 0.0129381i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.32308 | + | 1.22641i | −0.352379 | + | 0.0463539i | ||||
\(701\) | 34.1981i | 1.29164i | 0.763488 | + | 0.645822i | \(0.223485\pi\) | ||||
−0.763488 | + | 0.645822i | \(0.776515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 76.8786i | − | 2.89953i | ||||||
\(704\) | −13.2442 | − | 32.0030i | −0.499160 | − | 1.20616i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.1622 | + | 23.8231i | 1.02226 | + | 0.896595i | ||||
\(707\) | −7.60411 | −0.285982 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.7558 | 1.90617 | 0.953087 | − | 0.302697i | \(-0.0978869\pi\) | ||||
0.953087 | + | 0.302697i | \(0.0978869\pi\) | |||||||
\(710\) | −3.30055 | − | 2.89481i | −0.123867 | − | 0.108640i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.33819 | − | 12.4747i | 0.312487 | − | 0.467510i | ||||
\(713\) | − | 0.988562i | − | 0.0370219i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.01630i | − | 0.299793i | ||||||
\(716\) | −4.87858 | − | 37.0867i | −0.182321 | − | 1.38600i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.95331 | + | 3.36725i | −0.110217 | + | 0.125665i | ||||
\(719\) | 38.0420 | 1.41873 | 0.709364 | − | 0.704843i | \(-0.248982\pi\) | ||||
0.709364 | + | 0.704843i | \(0.248982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.70783 | −0.0636030 | ||||||||
\(722\) | −38.7525 | + | 44.1841i | −1.44222 | + | 1.64436i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.10697 | + | 16.0170i | 0.0783048 | + | 0.595269i | ||||
\(725\) | − | 13.1696i | − | 0.489106i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.97341i | 0.369893i | 0.982749 | + | 0.184947i | \(0.0592112\pi\) | ||||
−0.982749 | + | 0.184947i | \(0.940789\pi\) | |||||||
\(728\) | 5.32849 | − | 7.97193i | 0.197487 | − | 0.295459i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.441487 | − | 0.387215i | −0.0163402 | − | 0.0143315i | ||||
\(731\) | −0.107819 | −0.00398784 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.6381 | 0.799221 | 0.399610 | − | 0.916685i | \(-0.369145\pi\) | ||||
0.399610 | + | 0.916685i | \(0.369145\pi\) | |||||||
\(734\) | 32.2718 | + | 28.3046i | 1.19117 | + | 1.04474i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.79261 | + | 3.63264i | −0.0660765 | + | 0.133901i | ||||
\(737\) | 44.0652i | 1.62316i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.62532i | − | 0.0597882i | −0.999553 | − | 0.0298941i | \(-0.990483\pi\) | ||
0.999553 | − | 0.0298941i | \(-0.00951700\pi\) | |||||||
\(740\) | −10.6993 | + | 1.40744i | −0.393314 | + | 0.0517387i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.64000 | + | 10.9911i | −0.353896 | + | 0.403498i | ||||
\(743\) | −0.901684 | −0.0330796 | −0.0165398 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165398 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.57692 | 0.277597 | ||||||||
\(746\) | 15.8769 | − | 18.1023i | 0.581296 | − | 0.662771i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.824284 | − | 0.108431i | 0.0301388 | − | 0.00396462i | ||||
\(749\) | − | 12.0437i | − | 0.440068i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.79695i | 0.211534i | 0.994391 | + | 0.105767i | \(0.0337297\pi\) | ||||
−0.994391 | + | 0.105767i | \(0.966270\pi\) | |||||||
\(752\) | 39.4922 | − | 10.5730i | 1.44013 | − | 0.385558i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.0961 | + | 8.85501i | 0.367680 | + | 0.322481i | ||||
\(755\) | −11.0892 | −0.403576 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.8699 | 1.23102 | 0.615511 | − | 0.788128i | \(-0.288950\pi\) | ||||
0.615511 | + | 0.788128i | \(0.288950\pi\) | |||||||
\(758\) | 39.4041 | + | 34.5601i | 1.43122 | + | 1.25528i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.99439 | + | 6.68032i | 0.362535 | + | 0.242321i | ||||
\(761\) | − | 13.2036i | − | 0.478630i | −0.970942 | − | 0.239315i | \(-0.923077\pi\) | ||
0.970942 | − | 0.239315i | \(-0.0769229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.6297i | − | 0.529630i | ||||||
\(764\) | 2.19091 | + | 16.6552i | 0.0792644 | + | 0.602563i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.1240 | − | 11.5429i | 0.365793 | − | 0.417063i | ||||
\(767\) | 24.2434 | 0.875380 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8172 | 0.858872 | 0.429436 | − | 0.903097i | \(-0.358712\pi\) | ||||
0.429436 | + | 0.903097i | \(0.358712\pi\) | |||||||
\(770\) | 2.20501 | − | 2.51406i | 0.0794630 | − | 0.0906006i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.87333 | + | 29.4448i | 0.139404 | + | 1.05974i | ||||
\(773\) | 26.4363i | 0.950847i | 0.879757 | + | 0.475423i | \(0.157705\pi\) | ||||
−0.879757 | + | 0.475423i | \(0.842295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.49061i | − | 0.233149i | ||||||
\(776\) | −32.5715 | − | 21.7710i | −1.16925 | − | 0.781535i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.0957 | − | 25.5189i | −1.04313 | − | 0.914898i | ||||
\(779\) | 73.3780 | 2.62904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.6074 | −0.880522 | ||||||||
\(782\) | −0.0731034 | − | 0.0641168i | −0.00261417 | − | 0.00229281i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.86392 | − | 1.03446i | 0.137997 | − | 0.0369451i | ||||
\(785\) | 11.3744i | 0.405971i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.3744i | 0.833207i | 0.909088 | + | 0.416604i | \(0.136780\pi\) | ||||
−0.909088 | + | 0.416604i | \(0.863220\pi\) | |||||||
\(788\) | −46.6600 | + | 6.13791i | −1.66219 | + | 0.218654i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.998008 | − | 1.13789i | 0.0355075 | − | 0.0404843i | ||||
\(791\) | −15.7696 | −0.560703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.1628 | −0.538445 | ||||||||
\(794\) | −23.5091 | + | 26.8041i | −0.834307 | + | 0.951244i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −46.9539 | + | 6.17656i | −1.66424 | + | 0.218922i | ||||
\(797\) | − | 10.6022i | − | 0.375549i | −0.982212 | − | 0.187775i | \(-0.939873\pi\) | ||
0.982212 | − | 0.187775i | \(-0.0601274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.981358i | 0.0347180i | ||||||||
\(800\) | −11.7698 | + | 23.8509i | −0.416124 | + | 0.843255i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.0518 | + | 28.1117i | 1.13179 | + | 0.992658i | ||||
\(803\) | −3.29153 | −0.116155 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.391112 | −0.0137849 | ||||||||
\(806\) | 4.97587 | + | 4.36418i | 0.175267 | + | 0.153722i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.9518 | + | 17.8811i | −0.420465 | + | 0.629055i | ||||
\(809\) | 0.238439i | 0.00838306i | 0.999991 | + | 0.00419153i | \(0.00133421\pi\) | ||||
−0.999991 | + | 0.00419153i | \(0.998666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2987i | 1.34485i | 0.740166 | + | 0.672425i | \(0.234747\pi\) | ||||
−0.740166 | + | 0.672425i | \(0.765253\pi\) | |||||||
\(812\) | 0.730630 | + | 5.55420i | 0.0256401 | + | 0.194914i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −39.8846 | + | 45.4749i | −1.39795 | + | 1.59389i | ||||
\(815\) | 5.36097 | 0.187787 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.73847 | −0.305720 | ||||||||
\(818\) | 20.0509 | − | 22.8613i | 0.701065 | − | 0.799326i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.34336 | − | 10.2121i | −0.0469120 | − | 0.356622i | ||||
\(821\) | − | 38.3125i | − | 1.33712i | −0.743660 | − | 0.668558i | \(-0.766912\pi\) | ||
0.743660 | − | 0.668558i | \(-0.233088\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0368i | 0.384718i | 0.981325 | + | 0.192359i | \(0.0616138\pi\) | ||||
−0.981325 | + | 0.192359i | \(0.938386\pi\) | |||||||
\(824\) | −2.68430 | + | 4.01597i | −0.0935122 | + | 0.139903i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.60320 | + | 6.66854i | 0.264549 | + | 0.232028i | ||||
\(827\) | −21.5781 | −0.750342 | −0.375171 | − | 0.926956i | \(-0.622416\pi\) | ||||
−0.375171 | + | 0.926956i | \(0.622416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.2618 | 1.36362 | 0.681809 | − | 0.731531i | \(-0.261194\pi\) | ||||
0.681809 | + | 0.731531i | \(0.261194\pi\) | |||||||
\(830\) | −2.06961 | − | 1.81519i | −0.0718372 | − | 0.0630062i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.3709 | − | 25.0599i | −0.359546 | − | 0.868797i | ||||
\(833\) | 0.0960161i | 0.00332676i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.20841i | 0.145638i | ||||||||
\(836\) | 66.8060 | − | 8.78802i | 2.31053 | − | 0.303940i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.855489 | + | 0.975395i | −0.0295524 | + | 0.0336944i | ||||
\(839\) | 45.4839 | 1.57028 | 0.785140 | − | 0.619319i | \(-0.212591\pi\) | ||||
0.785140 | + | 0.619319i | \(0.212591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1543 | 0.729457 | ||||||||
\(842\) | −2.95964 | + | 3.37446i | −0.101996 | + | 0.116292i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.35144 | − | 0.835503i | 0.218626 | − | 0.0287592i | ||||
\(845\) | 0.823045i | 0.0283136i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.74373i | − | 0.266078i | ||||||
\(848\) | 10.6939 | + | 39.9439i | 0.367231 | + | 1.37168i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.479975 | − | 0.420972i | −0.0164630 | − | 0.0144392i | ||||
\(851\) | 7.07451 | 0.242511 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.2554 | −1.37832 | −0.689159 | − | 0.724610i | \(-0.742020\pi\) | ||||
−0.689159 | + | 0.724610i | \(0.742020\pi\) | |||||||
\(854\) | −4.75533 | − | 4.17075i | −0.162724 | − | 0.142720i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.3208 | − | 18.9299i | −0.967986 | − | 0.647009i | ||||
\(857\) | − | 38.9387i | − | 1.33012i | −0.746789 | − | 0.665061i | \(-0.768406\pi\) | ||
0.746789 | − | 0.665061i | \(-0.231594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 49.6846i | − | 1.69522i | −0.530622 | − | 0.847608i | \(-0.678042\pi\) | ||
0.530622 | − | 0.847608i | \(-0.321958\pi\) | |||||||
\(860\) | 0.159978 | + | 1.21615i | 0.00545521 | + | 0.0414702i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.53811 | + | 7.45450i | −0.222689 | + | 0.253901i | ||||
\(863\) | −31.3183 | −1.06609 | −0.533044 | − | 0.846088i | \(-0.678952\pi\) | ||||
−0.533044 | + | 0.846088i | \(0.678952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.39042 | 0.285283 | ||||||||
\(866\) | 15.5290 | − | 17.7056i | 0.527698 | − | 0.601661i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.360090 | + | 2.73738i | 0.0122222 | + | 0.0929127i | ||||
\(869\) | − | 8.48359i | − | 0.287786i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.5053i | 1.16917i | ||||||||
\(872\) | −34.4017 | − | 22.9944i | −1.16499 | − | 0.778687i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.92484 | − | 5.19649i | −0.200411 | − | 0.175774i | ||||
\(875\) | −5.29878 | −0.179131 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.69361 | −0.124724 | −0.0623621 | − | 0.998054i | \(-0.519863\pi\) | ||||
−0.0623621 | + | 0.998054i | \(0.519863\pi\) | |||||||
\(878\) | −16.8389 | − | 14.7689i | −0.568285 | − | 0.498425i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.44608 | − | 9.13659i | −0.0824574 | − | 0.307995i | ||||
\(881\) | − | 53.3419i | − | 1.79713i | −0.438836 | − | 0.898567i | \(-0.644609\pi\) | ||
0.438836 | − | 0.898567i | \(-0.355391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.3560i | 1.56001i | 0.625776 | + | 0.780003i | \(0.284782\pi\) | ||||
−0.625776 | + | 0.780003i | \(0.715218\pi\) | |||||||
\(884\) | 0.645456 | − | 0.0849067i | 0.0217090 | − | 0.00285572i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9975 | + | 12.5389i | −0.369468 | + | 0.421252i | ||||
\(887\) | 30.4446 | 1.02223 | 0.511115 | − | 0.859512i | \(-0.329233\pi\) | ||||
0.511115 | + | 0.859512i | \(0.329233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.02905 | 0.202208 | ||||||||
\(890\) | 2.70189 | − | 3.08059i | 0.0905676 | − | 0.103262i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.9939 | − | 5.52410i | 1.40606 | − | 0.184961i | ||||
\(893\) | 79.5364i | 2.66159i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.2151i | − | 0.341452i | ||||||
\(896\) | 3.64062 | − | 10.7120i | 0.121625 | − | 0.357861i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.1982 | + | 10.6986i | 0.407058 | + | 0.357018i | ||||
\(899\) | −3.86676 | −0.128964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.992583 | −0.0330677 | ||||||||
\(902\) | −43.4042 | − | 38.0685i | −1.44520 | − | 1.26754i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.7861 | + | 37.0823i | −0.824372 | + | 1.23334i | ||||
\(905\) | 4.41170i | 0.146650i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.3798i | − | 0.610291i | −0.952306 | − | 0.305145i | \(-0.901295\pi\) | ||
0.952306 | − | 0.305145i | \(-0.0987051\pi\) | |||||||
\(908\) | 1.08433 | + | 8.24298i | 0.0359846 | + | 0.273553i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.72663 | − | 1.96864i | 0.0572374 | − | 0.0652598i | ||||
\(911\) | 13.4574 | 0.445863 | 0.222932 | − | 0.974834i | \(-0.428437\pi\) | ||||
0.222932 | + | 0.974834i | \(0.428437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4301 | −0.510661 | ||||||||
\(914\) | 0.667910 | − | 0.761524i | 0.0220925 | − | 0.0251890i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0833793 | − | 0.633845i | −0.00275493 | − | 0.0209428i | ||||
\(917\) | − | 16.0875i | − | 0.531258i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 56.3374i | − | 1.85840i | −0.369579 | − | 0.929199i | \(-0.620498\pi\) | ||
0.369579 | − | 0.929199i | \(-0.379502\pi\) | |||||||
\(920\) | −0.614735 | + | 0.919702i | −0.0202672 | + | 0.0303217i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.2777 | + | 23.9245i | 0.898344 | + | 0.787910i | ||||
\(923\) | −19.2688 | −0.634242 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.4491 | 1.52724 | ||||||||
\(926\) | −8.95205 | − | 7.85157i | −0.294183 | − | 0.258019i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 14.2091 | + | 7.01180i | 0.466437 | + | 0.230174i | ||||
\(929\) | 10.6011i | 0.347812i | 0.984762 | + | 0.173906i | \(0.0556389\pi\) | ||||
−0.984762 | + | 0.173906i | \(0.944361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.78185i | 0.255040i | ||||||||
\(932\) | −7.56619 | + | 0.995297i | −0.247839 | + | 0.0326020i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.7962 | + | 29.4119i | −0.844079 | + | 0.962385i | ||||
\(935\) | 0.227039 | 0.00742496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1206 | 0.657312 | 0.328656 | − | 0.944450i | \(-0.393404\pi\) | ||||
0.328656 | + | 0.944450i | \(0.393404\pi\) | |||||||
\(938\) | −9.49122 | + | 10.8215i | −0.309899 | + | 0.353335i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.0692 | − | 1.45610i | 0.361037 | − | 0.0474928i | ||||
\(941\) | − | 31.6197i | − | 1.03077i | −0.856958 | − | 0.515386i | \(-0.827649\pi\) | ||
0.856958 | − | 0.515386i | \(-0.172351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.75237i | 0.219888i | ||||||||
\(944\) | 27.6315 | − | 7.39760i | 0.899329 | − | 0.240771i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.16894 | + | 4.53352i | 0.168057 | + | 0.147397i | ||||
\(947\) | −17.3640 | −0.564255 | −0.282127 | − | 0.959377i | \(-0.591040\pi\) | ||||
−0.282127 | + | 0.959377i | \(0.591040\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.57743 | −0.0836670 | ||||||||
\(950\) | −38.9007 | − | 34.1186i | −1.26211 | − | 1.10696i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.225782 | + | 0.150914i | 0.00731764 | + | 0.00489116i | ||||
\(953\) | 33.7037i | 1.09177i | 0.837860 | + | 0.545886i | \(0.183807\pi\) | ||||
−0.837860 | + | 0.545886i | \(0.816193\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.58747i | 0.148447i | ||||||||
\(956\) | −1.35501 | − | 10.3007i | −0.0438242 | − | 0.333149i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.3964 | − | 22.1150i | 0.626669 | − | 0.714503i | ||||
\(959\) | 12.5367 | 0.404831 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.0943 | 0.938525 | ||||||||
\(962\) | −31.2317 | + | 35.6091i | −1.00695 | + | 1.14808i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.55971 | + | 34.6626i | 0.146858 | + | 1.11641i | ||||
\(965\) | 8.11021i | 0.261077i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.7843i | − | 0.443272i | −0.975129 | − | 0.221636i | \(-0.928860\pi\) | ||
0.975129 | − | 0.221636i | \(-0.0711397\pi\) | |||||||
\(968\) | −18.2094 | − | 12.1713i | −0.585273 | − | 0.391200i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.04342 | − | 7.05464i | −0.258259 | − | 0.226511i | ||||
\(971\) | −48.4808 | −1.55582 | −0.777911 | − | 0.628374i | \(-0.783721\pi\) | ||||
−0.777911 | + | 0.628374i | \(0.783721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.60676 | 0.0515103 | ||||||||
\(974\) | 15.8320 | + | 13.8857i | 0.507288 | + | 0.444927i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.2818 | + | 4.62674i | −0.553176 | + | 0.148098i | ||||
\(977\) | − | 13.2147i | − | 0.422775i | −0.977402 | − | 0.211388i | \(-0.932202\pi\) | ||
0.977402 | − | 0.211388i | \(-0.0677983\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.9675i | − | 0.734044i | ||||||
\(980\) | 1.08301 | − | 0.142465i | 0.0345955 | − | 0.00455088i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.1626 | − | 45.7918i | 1.28164 | − | 1.46127i | ||||
\(983\) | 23.1147 | 0.737243 | 0.368621 | − | 0.929580i | \(-0.379830\pi\) | ||||
0.368621 | + | 0.929580i | \(0.379830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8519 | −0.409497 | ||||||||
\(986\) | −0.250793 | + | 0.285944i | −0.00798688 | + | 0.00910632i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 52.3125 | − | 6.88146i | 1.66428 | − | 0.218929i | ||||
\(989\) | − | 0.804130i | − | 0.0255698i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.38292i | − | 0.139228i | −0.997574 | − | 0.0696140i | \(-0.977823\pi\) | ||
0.997574 | − | 0.0696140i | \(-0.0221768\pi\) | |||||||
\(992\) | 7.00293 | + | 3.45576i | 0.222343 | + | 0.109720i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.04308 | − | 5.30020i | −0.191675 | − | 0.168112i | ||||
\(995\) | −12.9329 | −0.409999 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.6903 | −1.41536 | −0.707679 | − | 0.706534i | \(-0.750258\pi\) | ||||
−0.707679 | + | 0.706534i | \(0.750258\pi\) | |||||||
\(998\) | 26.2506 | + | 23.0236i | 0.830949 | + | 0.728800i | ||||
\(999\) | 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 | 756.2.e.b.323.17 | yes | 24 | |
3.2 | odd | 2 | inner | 756.2.e.b.323.8 | yes | 24 | |
4.3 | odd | 2 | inner | 756.2.e.b.323.7 | ✓ | 24 | |
12.11 | even | 2 | inner | 756.2.e.b.323.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.e.b.323.7 | ✓ | 24 | 4.3 | odd | 2 | inner | |
756.2.e.b.323.8 | yes | 24 | 3.2 | odd | 2 | inner | |
756.2.e.b.323.17 | yes | 24 | 1.1 | even | 1 | trivial | |
756.2.e.b.323.18 | yes | 24 | 12.11 | even | 2 | inner |