Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.8 | ||
Root | \(1.23362 - 1.23362i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.g.369.7 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.189375i | 0.109336i | 0.998505 | + | 0.0546680i | \(0.0174100\pi\) | ||||
−0.998505 | + | 0.0546680i | \(0.982590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60280 | + | 1.55918i | −0.716793 | + | 0.697286i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65661i | 0.626139i | 0.949730 | + | 0.313070i | \(0.101357\pi\) | ||||
−0.949730 | + | 0.313070i | \(0.898643\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.96414 | 0.988046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0759321 | −0.0228944 | −0.0114472 | − | 0.999934i | \(-0.503644\pi\) | ||||
−0.0114472 | + | 0.999934i | \(0.503644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24146i | 0.344319i | 0.985069 | + | 0.172159i | \(0.0550744\pi\) | ||||
−0.985069 | + | 0.172159i | \(0.944926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.295270 | − | 0.303531i | −0.0762384 | − | 0.0783713i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.17593i | 1.25535i | 0.778477 | + | 0.627673i | \(0.215993\pi\) | ||||
−0.778477 | + | 0.627673i | \(0.784007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.792262 | 0.181757 | 0.0908787 | − | 0.995862i | \(-0.471032\pi\) | ||||
0.0908787 | + | 0.995862i | \(0.471032\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.313721 | −0.0684595 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.137925 | − | 4.99810i | 0.0275850 | − | 0.999619i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.12946i | 0.217365i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.85401 | 0.529976 | 0.264988 | − | 0.964252i | \(-0.414632\pi\) | ||||
0.264988 | + | 0.964252i | \(0.414632\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.90112 | −1.59869 | −0.799345 | − | 0.600873i | \(-0.794820\pi\) | ||||
−0.799345 | + | 0.600873i | \(0.794820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.0143797i | − | 0.00250318i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.58295 | − | 2.65521i | −0.436598 | − | 0.448812i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92065i | 1.13775i | 0.822425 | + | 0.568874i | \(0.192621\pi\) | ||||
−0.822425 | + | 0.568874i | \(0.807379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.235102 | −0.0376464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.64279 | 0.725082 | 0.362541 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362541 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.75255i | − | 0.267262i | −0.991031 | − | 0.133631i | \(-0.957336\pi\) | ||
0.991031 | − | 0.133631i | \(-0.0426636\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.75091 | + | 4.62162i | −0.708224 | + | 0.688950i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.0033i | − | 1.45913i | −0.683914 | − | 0.729563i | \(-0.739724\pi\) | ||
0.683914 | − | 0.729563i | \(-0.260276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.25565 | 0.607950 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.980193 | −0.137254 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1284i | 1.52860i | 0.644859 | + | 0.764301i | \(0.276916\pi\) | ||||
−0.644859 | + | 0.764301i | \(0.723084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.121704 | − | 0.118392i | 0.0164105 | − | 0.0159639i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.150035i | 0.0198726i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4581 | −1.62191 | −0.810955 | − | 0.585108i | \(-0.801052\pi\) | ||||
−0.810955 | + | 0.585108i | \(0.801052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0098 | −1.53770 | −0.768849 | − | 0.639430i | \(-0.779170\pi\) | ||||
−0.768849 | + | 0.639430i | \(0.779170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.91041i | 0.618654i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.93566 | − | 1.98981i | −0.240089 | − | 0.246806i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.96067i | 0.850381i | 0.905104 | + | 0.425191i | \(0.139793\pi\) | ||||
−0.905104 | + | 0.425191i | \(0.860207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.189375 | 0.0227981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.71650 | 0.915779 | 0.457890 | − | 0.889009i | \(-0.348605\pi\) | ||||
0.457890 | + | 0.889009i | \(0.348605\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.49476i | 0.877196i | 0.898683 | + | 0.438598i | \(0.144525\pi\) | ||||
−0.898683 | + | 0.438598i | \(0.855475\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.946517 | + | 0.0261196i | 0.109294 | + | 0.00301604i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.125790i | − | 0.0143351i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6615 | −1.76206 | −0.881029 | − | 0.473063i | \(-0.843148\pi\) | ||||
−0.881029 | + | 0.473063i | \(0.843148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.67852 | 0.964280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.68518i | 0.733793i | 0.930262 | + | 0.366897i | \(0.119580\pi\) | ||||
−0.930262 | + | 0.366897i | \(0.880420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.07019 | − | 8.29597i | −0.875335 | − | 0.899824i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.540478i | 0.0579454i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.03333 | 0.321532 | 0.160766 | − | 0.986993i | \(-0.448604\pi\) | ||||
0.160766 | + | 0.986993i | \(0.448604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.05661 | −0.215592 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.68565i | − | 0.174794i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.26984 | + | 1.23528i | −0.130282 | + | 0.126737i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.21747i | − | 0.326684i | −0.986569 | − | 0.163342i | \(-0.947773\pi\) | ||
0.986569 | − | 0.163342i | \(-0.0522275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.225073 | −0.0226207 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.6059 | −1.65235 | −0.826173 | − | 0.563417i | \(-0.809486\pi\) | ||||
−0.826173 | + | 0.563417i | \(0.809486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.30241i | 0.719528i | 0.933043 | + | 0.359764i | \(0.117143\pi\) | ||||
−0.933043 | + | 0.359764i | \(0.882857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.502831 | − | 0.489147i | 0.0490713 | − | 0.0477358i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.356936i | − | 0.0345063i | −0.999851 | − | 0.0172532i | \(-0.994508\pi\) | ||
0.999851 | − | 0.0172532i | \(-0.00549213\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0359 | −1.34440 | −0.672198 | − | 0.740371i | \(-0.734650\pi\) | ||||
−0.672198 | + | 0.740371i | \(0.734650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.31060 | −0.124397 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.17924i | − | 0.110933i | −0.998461 | − | 0.0554667i | \(-0.982335\pi\) | ||
0.998461 | − | 0.0554667i | \(-0.0176647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.55918 | + | 1.60280i | 0.145394 | + | 0.149462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.67986i | 0.340203i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.57448 | −0.786022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9942 | −0.999476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.879230i | 0.0792775i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.57186 | + | 8.22599i | 0.677248 | + | 0.735755i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.0097i | 1.68684i | 0.537255 | + | 0.843420i | \(0.319461\pi\) | ||||
−0.537255 | + | 0.843420i | \(0.680539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.331890 | 0.0292213 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29043 | −0.374857 | −0.187428 | − | 0.982278i | \(-0.560015\pi\) | ||||
−0.187428 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.31247i | 0.113805i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.76103 | − | 1.81030i | −0.151565 | − | 0.155806i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.2499i | − | 1.04658i | −0.852155 | − | 0.523290i | \(-0.824704\pi\) | ||
0.852155 | − | 0.523290i | \(-0.175296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.61437 | 0.221748 | 0.110874 | − | 0.993834i | \(-0.464635\pi\) | ||||
0.110874 | + | 0.993834i | \(0.464635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.89437 | 0.159535 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.0942666i | − | 0.00788297i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.57440 | + | 4.44990i | −0.379883 | + | 0.369544i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.805915i | 0.0664707i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.0404 | 1.55985 | 0.779927 | − | 0.625870i | \(-0.215256\pi\) | ||||
0.779927 | + | 0.625870i | \(0.215256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3252 | 1.49128 | 0.745640 | − | 0.666349i | \(-0.232144\pi\) | ||||
0.745640 | + | 0.666349i | \(0.232144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.3422i | 1.24034i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.2667 | − | 13.8784i | 1.14593 | − | 1.11474i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.37467i | − | 0.349137i | −0.984645 | − | 0.174569i | \(-0.944147\pi\) | ||
0.984645 | − | 0.174569i | \(-0.0558530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.10744 | −0.167131 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.65661 | 0.130559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8050i | 0.924639i | 0.886714 | + | 0.462319i | \(0.152983\pi\) | ||||
−0.886714 | + | 0.462319i | \(0.847017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0224205 | + | 0.0230477i | 0.00174543 | + | 0.00179426i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.19760i | − | 0.402202i | −0.979570 | − | 0.201101i | \(-0.935548\pi\) | ||
0.979570 | − | 0.201101i | \(-0.0644520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4588 | 0.881444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34837 | 0.179585 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.61834i | 0.199069i | 0.995034 | + | 0.0995345i | \(0.0317354\pi\) | ||||
−0.995034 | + | 0.0995345i | \(0.968265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.27989 | + | 0.228488i | 0.625901 | + | 0.0172721i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.35926i | − | 0.177333i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.627563 | 0.0469062 | 0.0234531 | − | 0.999725i | \(-0.492534\pi\) | ||||
0.0234531 | + | 0.999725i | \(0.492534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.15848 | −0.457756 | −0.228878 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228878 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.27436i | − | 0.168126i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.7905 | − | 11.0924i | −0.793335 | − | 0.815530i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.393019i | − | 0.0287404i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.87107 | −0.136101 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1343 | 1.38451 | 0.692254 | − | 0.721654i | \(-0.256618\pi\) | ||||
0.692254 | + | 0.721654i | \(0.256618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.810900i | 0.0583698i | 0.999574 | + | 0.0291849i | \(0.00929117\pi\) | ||||
−0.999574 | + | 0.0291849i | \(0.990709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.376821 | − | 0.366566i | 0.0269847 | − | 0.0262503i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.15110i | − | 0.438248i | −0.975697 | − | 0.219124i | \(-0.929680\pi\) | ||
0.975697 | − | 0.219124i | \(-0.0703199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.03061 | 0.498387 | 0.249193 | − | 0.968454i | \(-0.419834\pi\) | ||||
0.249193 | + | 0.968454i | \(0.419834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.31818 | −0.0929772 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.72797i | 0.331838i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.44146 | + | 7.23894i | −0.519734 | + | 0.505589i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.96414i | − | 0.206022i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0601581 | −0.00416122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.12120 | −0.559086 | −0.279543 | − | 0.960133i | \(-0.590183\pi\) | ||||
−0.279543 | + | 0.960133i | \(0.590183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.46131i | 0.100128i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.73254 | + | 2.80899i | 0.186358 | + | 0.191571i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.7457i | − | 1.00100i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.41932 | −0.0959090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.42570 | −0.432240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.86268i | 0.191699i | 0.995396 | + | 0.0958495i | \(0.0305568\pi\) | ||||
−0.995396 | + | 0.0958495i | \(0.969443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.408829 | − | 14.8150i | 0.0272553 | − | 0.987670i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 27.4500i | − | 1.82192i | −0.412496 | − | 0.910960i | \(-0.635343\pi\) | ||
0.412496 | − | 0.910960i | \(-0.364657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.11319 | −0.0735613 | −0.0367807 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367807 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0238215 | 0.00156734 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.2957i | − | 1.39513i | −0.716523 | − | 0.697564i | \(-0.754267\pi\) | ||
0.716523 | − | 0.697564i | \(-0.245733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.5969 | + | 16.0332i | 1.01743 | + | 1.04589i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.96590i | − | 0.192656i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.68036 | 0.496801 | 0.248401 | − | 0.968657i | \(-0.420095\pi\) | ||||
0.248401 | + | 0.968657i | \(0.420095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.42476 | 0.542687 | 0.271343 | − | 0.962483i | \(-0.412532\pi\) | ||||
0.271343 | + | 0.962483i | \(0.412532\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.03188i | 0.322795i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.82095 | + | 6.63531i | −0.435774 | + | 0.423915i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.983561i | 0.0625825i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.26601 | −0.0802300 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.56210 | 0.161718 | 0.0808590 | − | 0.996726i | \(-0.474234\pi\) | ||||
0.0808590 | + | 0.996726i | \(0.474234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0759321i | 0.00477381i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.57105 | − | 1.52830i | 0.0983831 | − | 0.0957056i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.39999i | 0.274464i | 0.990539 | + | 0.137232i | \(0.0438206\pi\) | ||||
−0.990539 | + | 0.137232i | \(0.956179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4648 | −0.712388 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.45966 | 0.523640 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8510i | 1.53238i | 0.642613 | + | 0.766191i | \(0.277850\pi\) | ||||
−0.642613 | + | 0.766191i | \(0.722150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.3512 | − | 17.8366i | −1.06587 | − | 1.09569i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.574437i | 0.0351550i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.8742 | 0.663012 | 0.331506 | − | 0.943453i | \(-0.392443\pi\) | ||||
0.331506 | + | 0.943453i | \(0.392443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.60290 | 0.158115 | 0.0790575 | − | 0.996870i | \(-0.474809\pi\) | ||||
0.0790575 | + | 0.996870i | \(0.474809\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.389472i | − | 0.0235719i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0104729 | + | 0.379516i | −0.000631542 | + | 0.0228857i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.1918i | − | 0.732537i | −0.930509 | − | 0.366269i | \(-0.880635\pi\) | ||
0.930509 | − | 0.366269i | \(-0.119365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.3842 | −1.57958 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.85068 | 0.349022 | 0.174511 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174511 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7223i | 0.637375i | 0.947860 | + | 0.318688i | \(0.103242\pi\) | ||||
−0.947860 | + | 0.318688i | \(0.896758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.233931 | − | 0.240476i | −0.0138569 | − | 0.0142446i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.69129i | 0.454002i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.79021 | −0.575895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.609309 | 0.0357183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.72596i | 0.159252i | 0.996825 | + | 0.0796261i | \(0.0253726\pi\) | ||||
−0.996825 | + | 0.0796261i | \(0.974627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.9679 | − | 19.4245i | 1.16257 | − | 1.13094i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.0857623i | − | 0.00497643i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24146 | 0.0717955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90329 | 0.167343 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.14474i | − | 0.180661i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.2493 | − | 18.7254i | 1.10221 | − | 1.07222i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.4979i | − | 1.28402i | −0.766695 | − | 0.642012i | \(-0.778100\pi\) | ||
0.766695 | − | 0.642012i | \(-0.221900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.38290 | −0.0786703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9597 | −1.01840 | −0.509200 | − | 0.860648i | \(-0.670058\pi\) | ||||
−0.509200 | + | 0.860648i | \(0.670058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4728i | 0.818052i | 0.912523 | + | 0.409026i | \(0.134131\pi\) | ||||
−0.912523 | + | 0.409026i | \(0.865869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.65621 | − | 7.87040i | −0.431379 | − | 0.443447i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.47689i | 0.419944i | 0.977707 | + | 0.209972i | \(0.0673373\pi\) | ||||
−0.977707 | + | 0.209972i | \(0.932663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.216711 | −0.0121335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0675949 | 0.00377278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.10069i | 0.228168i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.20494 | + | 0.171229i | 0.344188 | + | 0.00949805i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.65806i | − | 0.146991i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5715 | 0.913616 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3565 | 1.50365 | 0.751826 | − | 0.659362i | \(-0.229173\pi\) | ||||
0.751826 | + | 0.659362i | \(0.229173\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.5137i | 1.12415i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.8529 | − | 11.1565i | −0.592959 | − | 0.609547i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.65271i | − | 0.307923i | −0.988077 | − | 0.153961i | \(-0.950797\pi\) | ||
0.988077 | − | 0.153961i | \(-0.0492032\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.223319 | 0.0121290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.675881 | 0.0366010 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6462i | 1.00680i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.303531 | + | 0.295270i | −0.0163415 | + | 0.0158968i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5293i | 0.833658i | 0.908985 | + | 0.416829i | \(0.136859\pi\) | ||||
−0.908985 | + | 0.416829i | \(0.863141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0559 | −0.591810 | −0.295905 | − | 0.955217i | \(-0.595621\pi\) | ||||
−0.295905 | + | 0.955217i | \(0.595621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.40218 | −0.0748428 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.85381i | 0.364792i | 0.983225 | + | 0.182396i | \(0.0583852\pi\) | ||||
−0.983225 | + | 0.182396i | \(0.941615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3680 | + | 12.0314i | −0.656425 | + | 0.638560i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.62380i | − | 0.0859404i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3104 | 0.860832 | 0.430416 | − | 0.902631i | \(-0.358367\pi\) | ||||
0.430416 | + | 0.902631i | \(0.358367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3723 | −0.966964 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.08204i | − | 0.109279i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.6857 | − | 12.0126i | −0.611656 | − | 0.628768i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 31.6200i | − | 1.65055i | −0.564731 | − | 0.825275i | \(-0.691020\pi\) | ||
0.564731 | − | 0.825275i | \(-0.308980\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.7619 | 0.716414 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4354 | −0.957118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2458i | 1.46251i | 0.682104 | + | 0.731256i | \(0.261065\pi\) | ||||
−0.682104 | + | 0.731256i | \(0.738935\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.55780 | + | 1.43392i | −0.0804445 | + | 0.0740475i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.54313i | 0.182481i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.98772 | 0.153469 | 0.0767345 | − | 0.997052i | \(-0.475551\pi\) | ||||
0.0767345 | + | 0.997052i | \(0.475551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.59997 | −0.184432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 12.5176i | − | 0.639621i | −0.947482 | − | 0.319810i | \(-0.896381\pi\) | ||
0.947482 | − | 0.319810i | \(-0.103619\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.196129 | + | 0.201616i | 0.00999564 | + | 0.0102753i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 5.19480i | − | 0.264067i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4861 | 0.987982 | 0.493991 | − | 0.869467i | \(-0.335538\pi\) | ||||
0.493991 | + | 0.869467i | \(0.335538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.17593 | 0.261758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.812503i | − | 0.0409853i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.1022 | − | 24.4191i | 1.26303 | − | 1.22866i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.3203i | − | 0.869281i | −0.900604 | − | 0.434640i | \(-0.856876\pi\) | ||
0.900604 | − | 0.434640i | \(-0.143124\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.248549 | −0.0124430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3727 | 0.867553 | 0.433777 | − | 0.901020i | \(-0.357181\pi\) | ||||
0.433777 | + | 0.901020i | \(0.357181\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.0504i | − | 0.550459i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.9099 | + | 13.5314i | −0.691189 | + | 0.672379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.525499i | − | 0.0260480i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6874 | 0.627350 | 0.313675 | − | 0.949530i | \(-0.398440\pi\) | ||||
0.313675 | + | 0.949530i | \(0.398440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.31983 | 0.114429 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 20.6383i | − | 1.01554i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4234 | − | 10.7150i | −0.511664 | − | 0.525978i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.495098i | 0.0242450i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.23468 | −0.206878 | −0.103439 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103439 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.17837 | 0.203641 | 0.101821 | − | 0.994803i | \(-0.467533\pi\) | ||||
0.101821 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 29.6510i | − | 1.44168i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.8698 | + | 0.713891i | 1.25487 | + | 0.0346288i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.8956i | − | 0.962813i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0178518 | 0.000861892 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9197 | 1.05583 | 0.527917 | − | 0.849296i | \(-0.322973\pi\) | ||||
0.527917 | + | 0.849296i | \(0.322973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.2195i | − | 0.971688i | −0.874046 | − | 0.485844i | \(-0.838512\pi\) | ||
0.874046 | − | 0.485844i | \(-0.161488\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.842702 | − | 0.866278i | −0.0404045 | − | 0.0415348i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.792262i | − | 0.0378990i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.3149 | −0.778666 | −0.389333 | − | 0.921097i | \(-0.627294\pi\) | ||||
−0.389333 | + | 0.921097i | \(0.627294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6143 | 0.600682 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 28.0868i | − | 1.33444i | −0.744859 | − | 0.667222i | \(-0.767483\pi\) | ||
0.744859 | − | 0.667222i | \(-0.232517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.86181 | + | 4.72950i | −0.230472 | + | 0.224200i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.60579i | 0.170548i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5071 | 1.15656 | 0.578282 | − | 0.815837i | \(-0.303723\pi\) | ||||
0.578282 | + | 0.815837i | \(0.303723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.352537 | −0.0166003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.47033i | 0.163050i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.29634 | − | 3.20663i | 0.154535 | − | 0.150329i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.87128i | 0.134313i | 0.997742 | + | 0.0671564i | \(0.0213927\pi\) | ||||
−0.997742 | + | 0.0671564i | \(0.978607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.84601 | −0.272868 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2264 | 0.709162 | 0.354581 | − | 0.935025i | \(-0.384623\pi\) | ||||
0.354581 | + | 0.935025i | \(0.384623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.6480i | 1.70318i | 0.524212 | + | 0.851588i | \(0.324360\pi\) | ||||
−0.524212 | + | 0.851588i | \(0.675640\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.62824 | + | 2.70176i | 0.121881 | + | 0.125291i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9765i | 0.693031i | 0.938044 | + | 0.346516i | \(0.112635\pi\) | ||||
−0.938044 | + | 0.346516i | \(0.887365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5311 | −0.532457 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.828456 | 0.0381732 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.133075i | 0.00611879i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.109273 | − | 3.95980i | 0.00501378 | − | 0.181688i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.9861i | 1.51033i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.03398 | 0.184317 | 0.0921587 | − | 0.995744i | \(-0.470623\pi\) | ||||
0.0921587 | + | 0.995744i | \(0.470623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.59171 | −0.391748 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.313721i | 0.0142748i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.01661 | + | 5.15695i | 0.227792 | + | 0.234165i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.28846i | 0.194329i | 0.995268 | + | 0.0971643i | \(0.0309772\pi\) | ||||
−0.995268 | + | 0.0971643i | \(0.969023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.23558 | −0.101096 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.8754 | 1.66416 | 0.832081 | − | 0.554654i | \(-0.187149\pi\) | ||||
0.832081 | + | 0.554654i | \(0.187149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.7721i | 0.665303i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.360747 | − | 0.350929i | 0.0162144 | − | 0.0157731i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7832i | 0.573405i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.74707 | −0.257274 | −0.128637 | − | 0.991692i | \(-0.541060\pi\) | ||||
−0.128637 | + | 0.991692i | \(0.541060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.984298 | 0.0439752 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 18.7850i | − | 0.837583i | −0.908082 | − | 0.418792i | \(-0.862454\pi\) | ||
0.908082 | − | 0.418792i | \(-0.137546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.6158 | − | 25.8915i | 1.18439 | − | 1.15216i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17001i | 0.0963735i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2669 | 0.898313 | 0.449157 | − | 0.893453i | \(-0.351725\pi\) | ||||
0.449157 | + | 0.893453i | \(0.351725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4159 | −0.549247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.894829i | 0.0395077i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3858 | − | 11.7043i | −0.501717 | − | 0.515753i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.759568i | 0.0334058i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.495850 | −0.0217654 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.47593 | 0.283716 | 0.141858 | − | 0.989887i | \(-0.454692\pi\) | ||||
0.141858 | + | 0.989887i | \(0.454692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.414671i | − | 0.0181323i | −0.999959 | − | 0.00906615i | \(-0.997114\pi\) | ||
0.999959 | − | 0.00906615i | \(-0.00288588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0432700 | + | 1.56801i | −0.00188846 | + | 0.0684335i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 46.0716i | − | 2.00691i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.9276 | −1.60252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.76384i | 0.249659i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.556527 | + | 0.572097i | 0.0240608 | + | 0.0247339i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.118845i | 0.00512854i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.323140 | −0.0139186 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5708 | 1.22835 | 0.614177 | − | 0.789169i | \(-0.289488\pi\) | ||||
0.614177 | + | 0.789169i | \(0.289488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.16626i | − | 0.0500492i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.4967 | − | 21.8845i | 0.963654 | − | 0.937428i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.0974i | 1.67168i | 0.548971 | + | 0.835841i | \(0.315020\pi\) | ||||
−0.548971 | + | 0.835841i | \(0.684980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.5987 | −1.51932 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.26112 | 0.0963270 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 25.9450i | − | 1.10329i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.10063 | − | 2.04346i | 0.0891667 | − | 0.0867400i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 33.9136i | − | 1.43696i | −0.695546 | − | 0.718482i | \(-0.744837\pi\) | ||
0.695546 | − | 0.718482i | \(-0.255163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.17572 | 0.0920232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0744281 | 0.00314236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6390i | 1.08056i | 0.841486 | + | 0.540278i | \(0.181681\pi\) | ||||
−0.841486 | + | 0.540278i | \(0.818319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.83864 | + | 1.89008i | 0.0773523 | + | 0.0795163i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.3769i | 0.603773i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.6257 | 0.571218 | 0.285609 | − | 0.958346i | \(-0.407804\pi\) | ||||
0.285609 | + | 0.958346i | \(0.407804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.354294 | −0.0148267 | −0.00741337 | − | 0.999973i | \(-0.502360\pi\) | ||||
−0.00741337 | + | 0.999973i | \(0.502360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.62356i | 0.151376i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.99810 | − | 0.137925i | −0.208435 | − | 0.00575188i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.5870i | − | 0.773788i | −0.922124 | − | 0.386894i | \(-0.873548\pi\) | ||
0.922124 | − | 0.386894i | \(-0.126452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.153564 | −0.00638192 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0747 | −0.459457 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.845002i | − | 0.0349964i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.73755 | − | 5.89807i | −0.237219 | − | 0.243855i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.75193i | − | 0.319956i | −0.987121 | − | 0.159978i | \(-0.948858\pi\) | ||
0.987121 | − | 0.159978i | \(-0.0511424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.05202 | −0.290573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.16487 | 0.0479162 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.3828i | 0.960215i | 0.877210 | + | 0.480107i | \(0.159402\pi\) | ||||
−0.877210 | + | 0.480107i | \(0.840598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.7432 | − | 13.3692i | 0.563415 | − | 0.548082i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.33142i | 0.0544916i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6075 | −1.04629 | −0.523146 | − | 0.852243i | \(-0.675242\pi\) | ||||
−0.523146 | + | 0.852243i | \(0.675242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.03750 | 0.164693 | 0.0823466 | − | 0.996604i | \(-0.473759\pi\) | ||||
0.0823466 | + | 0.996604i | \(0.473759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.6324i | 0.840215i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.6215 | − | 17.1420i | 0.716418 | − | 0.696920i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.8176i | − | 1.85968i | −0.367967 | − | 0.929839i | \(-0.619946\pi\) | ||
0.367967 | − | 0.929839i | \(-0.380054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.895361 | −0.0362819 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4186 | 0.502405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.1714i | 1.17822i | 0.808052 | + | 0.589112i | \(0.200522\pi\) | ||||
−0.808052 | + | 0.589112i | \(0.799478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.37088 | − | 1.40923i | −0.0552791 | − | 0.0568256i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0562i | 0.686659i | 0.939215 | + | 0.343329i | \(0.111555\pi\) | ||||
−0.939215 | + | 0.343329i | \(0.888445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0620 | 1.44946 | 0.724728 | − | 0.689035i | \(-0.241966\pi\) | ||||
0.724728 | + | 0.689035i | \(0.241966\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12946 | 0.0453237 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.02503i | 0.201324i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9620 | − | 1.37873i | −0.998478 | − | 0.0551491i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.0113925i | − | 0.000454971i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.8208 | −1.42827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4958 | −0.696496 | −0.348248 | − | 0.937402i | \(-0.613223\pi\) | ||||
−0.348248 | + | 0.937402i | \(0.613223\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.53795i | − | 0.0611282i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.6395 | − | 30.4687i | −1.17621 | − | 1.20911i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.28322i | 0.209329i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.8727 | 0.904832 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.9200 | −1.57675 | −0.788373 | − | 0.615197i | \(-0.789076\pi\) | ||||
−0.788373 | + | 0.615197i | \(0.789076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.8187i | 1.64917i | 0.565740 | + | 0.824584i | \(0.308591\pi\) | ||||
−0.565740 | + | 0.824584i | \(0.691409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.531953 | + | 0.517476i | −0.0209456 | + | 0.0203756i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.8026i | 1.52549i | 0.646702 | + | 0.762743i | \(0.276148\pi\) | ||||
−0.646702 | + | 0.762743i | \(0.723852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.945972 | 0.0371327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.79247 | 0.109445 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.8995i | 1.56139i | 0.624914 | + | 0.780694i | \(0.285134\pi\) | ||||
−0.624914 | + | 0.780694i | \(0.714866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.87670 | − | 6.68955i | 0.268695 | − | 0.261382i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.2155i | 0.866709i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9449 | 0.893808 | 0.446904 | − | 0.894582i | \(-0.352527\pi\) | ||||
0.446904 | + | 0.894582i | \(0.352527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2759 | 0.749745 | 0.374873 | − | 0.927076i | \(-0.377686\pi\) | ||||
0.374873 | + | 0.927076i | \(0.377686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.21687i | − | 0.0472593i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.04637 | − | 2.10362i | −0.0793549 | − | 0.0815749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.85401i | − | 0.110508i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.542121 | −0.0209596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.911930 | 0.0352047 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.0041i | − | 1.46495i | −0.680793 | − | 0.732476i | \(-0.738365\pi\) | ||
0.680793 | − | 0.732476i | \(-0.261635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.64515 | + | 0.155781i | 0.217282 | + | 0.00599602i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 41.0387i | − | 1.57725i | −0.614878 | − | 0.788623i | \(-0.710795\pi\) | ||
0.614878 | − | 0.788623i | \(-0.289205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.33008 | 0.204550 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.19835 | 0.199201 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 27.6705i | − | 1.05878i | −0.848378 | − | 0.529390i | \(-0.822421\pi\) | ||
0.848378 | − | 0.529390i | \(-0.177579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.0998 | + | 19.6341i | 0.729765 | + | 0.750181i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.210810i | − | 0.00804290i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.8155 | −0.526327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.8078 | −1.28611 | −0.643056 | − | 0.765820i | \(-0.722334\pi\) | ||||
−0.643056 | + | 0.765820i | \(0.722334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.372858i | − | 0.0141637i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.19031 | + | 4.07627i | −0.158948 | + | 0.154622i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0307i | 0.910229i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.03288 | 0.152538 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.4878 | −1.75582 | −0.877909 | − | 0.478827i | \(-0.841062\pi\) | ||||
−0.877909 | + | 0.478827i | \(0.841062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48297i | 0.206794i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.03630 | + | 2.95366i | −0.114353 | + | 0.111241i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 27.5094i | − | 1.03460i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5298 | 0.508122 | 0.254061 | − | 0.967188i | \(-0.418234\pi\) | ||||
0.254061 | + | 0.967188i | \(0.418234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −46.4229 | −1.74099 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.90112i | 0.333350i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.146979 | + | 0.151090i | 0.00549668 | + | 0.00565046i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.45447i | 0.0543182i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.64955 | −0.0988115 | −0.0494057 | − | 0.998779i | \(-0.515733\pi\) | ||||
−0.0494057 | + | 0.998779i | \(0.515733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0972 | −0.450525 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.59544i | 0.0593351i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.393639 | − | 14.2646i | 0.0146194 | − | 0.529774i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.8796i | 1.73867i | 0.494226 | + | 0.869334i | \(0.335452\pi\) | ||||
−0.494226 | + | 0.869334i | \(0.664548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0826 | 0.928987 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.07108 | 0.335506 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.1389i | 1.33482i | 0.744691 | + | 0.667410i | \(0.232597\pi\) | ||||
−0.744691 | + | 0.667410i | \(0.767403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.25657 | − | 1.29172i | −0.0463491 | − | 0.0476458i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.528538i | − | 0.0194690i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6473 | 0.833095 | 0.416547 | − | 0.909114i | \(-0.363240\pi\) | ||||
0.416547 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.186262 | −0.00684252 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.04015i | − | 0.258278i | −0.991627 | − | 0.129139i | \(-0.958779\pi\) | ||
0.991627 | − | 0.129139i | \(-0.0412213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.5180 | + | 29.6875i | −1.11809 | + | 1.08766i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.8158i | 0.725021i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.591304 | 0.0216058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.94539 | 0.216950 | 0.108475 | − | 0.994099i | \(-0.465403\pi\) | ||||
0.108475 | + | 0.994099i | \(0.465403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.485198i | 0.0176816i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.3715 | + | 28.5722i | −1.06894 | + | 1.03985i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 43.9519i | − | 1.59746i | −0.601691 | − | 0.798729i | \(-0.705506\pi\) | ||
0.601691 | − | 0.798729i | \(-0.294494\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0143797 | −0.000521949 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0290 | 0.798549 | 0.399274 | − | 0.916831i | \(-0.369262\pi\) | ||||
0.399274 | + | 0.916831i | \(0.369262\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 23.2520i | − | 0.841779i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.9212 | − | 24.5904i | −0.864871 | − | 0.889067i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.4663i | − | 0.558455i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6958 | 0.638128 | 0.319064 | − | 0.947733i | \(-0.396632\pi\) | ||||
0.319064 | + | 0.947733i | \(0.396632\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.833250 | −0.0300088 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.63758i | 0.0588997i | 0.999566 | + | 0.0294498i | \(0.00937553\pi\) | ||||
−0.999566 | + | 0.0294498i | \(0.990624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22769 | + | 44.4887i | −0.0440999 | + | 1.59808i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.17115i | − | 0.0778896i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.67831 | 0.131789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.585930 | −0.0209662 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.22349i | 0.115198i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.82090 | + | 7.01172i | 0.243448 | + | 0.250259i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6760i | 0.986543i | 0.869875 | + | 0.493272i | \(0.164199\pi\) | ||||
−0.869875 | + | 0.493272i | \(0.835801\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.70618 | −0.167544 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.95354 | 0.0694598 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 14.9097i | − | 0.529459i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.37781 | − | 3.28588i | 0.119799 | − | 0.116538i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.29831i | 0.329363i | 0.986347 | + | 0.164681i | \(0.0526596\pi\) | ||||
−0.986347 | + | 0.164681i | \(0.947340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.7761 | 1.83171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.99119 | 0.317688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 0.569093i | − | 0.0200829i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.65521 | + | 2.58295i | −0.0935838 | + | 0.0910370i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.05931i | 0.0724911i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.8800 | −1.71853 | −0.859264 | − | 0.511532i | \(-0.829078\pi\) | ||||
−0.859264 | + | 0.511532i | \(0.829078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0615 | −1.54721 | −0.773604 | − | 0.633669i | \(-0.781548\pi\) | ||||
−0.773604 | + | 0.633669i | \(0.781548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.492926i | 0.0172877i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.4061 | − | 18.9210i | −0.644737 | − | 0.662775i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.38848i | − | 0.0485768i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.09608 | −0.213014 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.1832 | 1.05340 | 0.526700 | − | 0.850051i | \(-0.323429\pi\) | ||||
0.526700 | + | 0.850051i | \(0.323429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0171i | 1.11605i | 0.829826 | + | 0.558023i | \(0.188440\pi\) | ||||
−0.829826 | + | 0.558023i | \(0.811560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0718710 | − | 0.00198332i | −0.00250223 | − | 6.90503e-5i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.5192i | − | 0.713523i | −0.934196 | − | 0.356761i | \(-0.883881\pi\) | ||
0.934196 | − | 0.356761i | \(-0.116119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0551 | −1.32171 | −0.660854 | − | 0.750515i | \(-0.729806\pi\) | ||||
−0.660854 | + | 0.750515i | \(0.729806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.30884 | 0.0800926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.0269i | 0.763188i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.10399 | + | 8.33071i | 0.280450 | + | 0.288296i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.0535i | − | 0.347499i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6946 | 0.852553 | 0.426277 | − | 0.904593i | \(-0.359825\pi\) | ||||
0.426277 | + | 0.904593i | \(0.359825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8547 | −0.719126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.10797i | 0.0381607i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.3661 | + | 17.8663i | −0.631813 | + | 0.614619i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 18.2131i | − | 0.625811i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.03054 | −0.0696880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.92065 | 0.237237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.4770i | − | 0.803837i | −0.915675 | − | 0.401919i | \(-0.868343\pi\) | ||
0.915675 | − | 0.401919i | \(-0.131657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.76397 | + | 3.66153i | −0.128725 | + | 0.125222i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9632i | 0.716090i | 0.933704 | + | 0.358045i | \(0.116557\pi\) | ||||
−0.933704 | + | 0.358045i | \(0.883443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.7273 | 1.21900 | 0.609500 | − | 0.792786i | \(-0.291370\pi\) | ||||
0.609500 | + | 0.792786i | \(0.291370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.45654 | −0.0496388 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5880i | 0.666784i | 0.942788 | + | 0.333392i | \(0.108193\pi\) | ||||
−0.942788 | + | 0.333392i | \(0.891807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.08246 | − | 4.19668i | −0.138808 | − | 0.142691i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.85403i | − | 0.0629660i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.18921 | 0.0403412 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.64139 | −0.292802 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.53702i | − | 0.322779i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.6272 | + | 12.5436i | −0.460685 | + | 0.424051i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 49.5791i | − | 1.67417i | −0.547074 | − | 0.837084i | \(-0.684259\pi\) | ||
0.547074 | − | 0.837084i | \(-0.315741\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.516230 | −0.0174120 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4406 | 0.722353 | 0.361177 | − | 0.932497i | \(-0.382375\pi\) | ||||
0.361177 | + | 0.932497i | \(0.382375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.7646i | 1.77567i | 0.460161 | + | 0.887836i | \(0.347792\pi\) | ||||
−0.460161 | + | 0.887836i | \(0.652208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.67851 | + | 3.78142i | 0.123652 | + | 0.127111i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.1462i | 1.01221i | 0.862472 | + | 0.506105i | \(0.168915\pi\) | ||||
−0.862472 | + | 0.506105i | \(0.831085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.4917 | −1.05620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.658978 | −0.0220766 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.92520i | − | 0.265207i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.00586 | + | 0.978482i | −0.0336221 | + | 0.0327071i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.235102i | 0.00784982i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.4039 | −0.847266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.5998 | −1.91893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.549812i | 0.0182966i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.87080 | − | 9.60217i | 0.328117 | − | 0.319187i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3987i | 0.677329i | 0.940907 | + | 0.338665i | \(0.109975\pi\) | ||||
−0.940907 | + | 0.338665i | \(0.890025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −49.2221 | −1.63259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.7921 | 1.91474 | 0.957369 | − | 0.288869i | \(-0.0932792\pi\) | ||||
0.957369 | + | 0.288869i | \(0.0932792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.507619i | − | 0.0167998i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.54614 | + | 3.64534i | 0.117232 | + | 0.120511i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.10757i | − | 0.234713i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0255 | −0.858502 | −0.429251 | − | 0.903185i | \(-0.641222\pi\) | ||||
−0.429251 | + | 0.903185i | \(0.641222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.26055 | 0.140390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.57972i | 0.315320i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5901 | + | 0.954531i | 1.13731 | + | 0.0313848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.6454i | 0.710927i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.9839 | −0.885313 | −0.442656 | − | 0.896691i | \(-0.645964\pi\) | ||||
−0.442656 | + | 0.896691i | \(0.645964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.37159 | 0.110499 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3.40112i | − | 0.111348i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.612787 | + | 0.629930i | 0.0200403 | + | 0.0206009i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.8201i | 1.17019i | 0.810964 | + | 0.585096i | \(0.198943\pi\) | ||||
−0.810964 | + | 0.585096i | \(0.801057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.74079 | −0.0894424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.0416 | −1.04453 | −0.522263 | − | 0.852785i | \(-0.674912\pi\) | ||||
−0.522263 | + | 0.852785i | \(0.674912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.64279i | − | 0.151190i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.99895 | − | 2.91734i | 0.0975560 | − | 0.0949010i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.53256i | 0.277271i | 0.990343 | + | 0.138635i | \(0.0442716\pi\) | ||||
−0.990343 | + | 0.138635i | \(0.955728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.30445 | −0.302035 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.41594 | −0.0459150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.4054i | − | 1.37365i | −0.726825 | − | 0.686823i | \(-0.759005\pi\) | ||
0.726825 | − | 0.686823i | \(-0.240995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.6684 | + | 29.8338i | −0.992406 | + | 0.965398i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.0410397i | − | 0.00132662i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.2933 | 0.655305 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.2300 | 1.55581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.05801i | − | 0.0340938i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.26434 | − | 1.29971i | −0.0407005 | − | 0.0418391i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.0988i | − | 0.324755i | −0.986729 | − | 0.162377i | \(-0.948084\pi\) | ||
0.986729 | − | 0.162377i | \(-0.0519162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.776570 | −0.0249470 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7943 | 0.506863 | 0.253431 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253431 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.33099i | 0.138845i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0324265 | + | 1.17506i | −0.00103848 | + | 0.0376321i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0055i | 0.863984i | 0.901877 | + | 0.431992i | \(0.142189\pi\) | ||||
−0.901877 | + | 0.431992i | \(0.857811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.230327 | −0.00736128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.6043 | −1.32832 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0647i | 0.512384i | 0.966626 | + | 0.256192i | \(0.0824679\pi\) | ||||
−0.966626 | + | 0.256192i | \(0.917532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.59066 | + | 9.85897i | 0.305584 | + | 0.314133i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.13823i | 0.0998910i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.75255 | −0.0557279 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.4433 | −1.63415 | −0.817075 | − | 0.576532i | \(-0.804406\pi\) | ||||
−0.817075 | + | 0.576532i | \(0.804406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.18066i | 0.164403i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.2687 | + | 10.9620i | −0.357240 | + | 0.347518i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.2639i | 1.24350i | 0.783215 | + | 0.621751i | \(0.213578\pi\) | ||||
−0.783215 | + | 0.621751i | \(0.786422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.81660 | −0.247306 |
(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 | 1840.2.e.g.369.8 | 14 | ||
4.3 | odd | 2 | 920.2.e.b.369.7 | ✓ | 14 | ||
5.2 | odd | 4 | 9200.2.a.dc.1.3 | 7 | |||
5.3 | odd | 4 | 9200.2.a.cz.1.5 | 7 | |||
5.4 | even | 2 | inner | 1840.2.e.g.369.7 | 14 | ||
20.3 | even | 4 | 4600.2.a.bi.1.3 | 7 | |||
20.7 | even | 4 | 4600.2.a.bh.1.5 | 7 | |||
20.19 | odd | 2 | 920.2.e.b.369.8 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.7 | ✓ | 14 | 4.3 | odd | 2 | ||
920.2.e.b.369.8 | yes | 14 | 20.19 | odd | 2 | ||
1840.2.e.g.369.7 | 14 | 5.4 | even | 2 | inner | ||
1840.2.e.g.369.8 | 14 | 1.1 | even | 1 | trivial | ||
4600.2.a.bh.1.5 | 7 | 20.7 | even | 4 | |||
4600.2.a.bi.1.3 | 7 | 20.3 | even | 4 | |||
9200.2.a.cz.1.5 | 7 | 5.3 | odd | 4 | |||
9200.2.a.dc.1.3 | 7 | 5.2 | odd | 4 |