Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(449,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.cu (of order \(6\), degree \(2\), 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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.8 | ||
Root | \(3.16384 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.449 |
Dual form | 1368.2.cu.b.521.8 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.76516 | − | 1.01912i | 0.789404 | − | 0.455763i | −0.0503486 | − | 0.998732i | \(-0.516033\pi\) |
0.839753 | + | 0.542969i | \(0.182700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.69902 | 1.39810 | 0.699050 | − | 0.715073i | \(-0.253607\pi\) | ||||
0.699050 | + | 0.715073i | \(0.253607\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.605557i | − | 0.182582i | −0.995824 | − | 0.0912912i | \(-0.970901\pi\) | ||
0.995824 | − | 0.0912912i | \(-0.0290994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65015 | + | 1.53006i | 0.735019 | + | 0.424364i | 0.820256 | − | 0.571997i | \(-0.193831\pi\) |
−0.0852364 | + | 0.996361i | \(0.527165\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.40852 | − | 1.39056i | 0.584153 | − | 0.337261i | −0.178629 | − | 0.983916i | \(-0.557166\pi\) |
0.762782 | + | 0.646656i | \(0.223833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.780721 | − | 4.28841i | 0.179110 | − | 0.983829i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23644 | − | 1.29121i | −0.466330 | − | 0.269236i | 0.248372 | − | 0.968665i | \(-0.420104\pi\) |
−0.714702 | + | 0.699429i | \(0.753438\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.422804 | + | 0.732318i | −0.0845607 | + | 0.146464i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.70567 | + | 2.95430i | −0.316734 | + | 0.548600i | −0.979805 | − | 0.199957i | \(-0.935920\pi\) |
0.663070 | + | 0.748557i | \(0.269253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.42738i | 0.795181i | 0.917563 | + | 0.397591i | \(0.130154\pi\) | ||||
−0.917563 | + | 0.397591i | \(0.869846\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.52937 | − | 3.76973i | 1.10367 | − | 0.637201i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34720i | 0.550276i | 0.961405 | + | 0.275138i | \(0.0887236\pi\) | ||||
−0.961405 | + | 0.275138i | \(0.911276\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50349 | − | 2.60412i | −0.234806 | − | 0.406696i | 0.724410 | − | 0.689369i | \(-0.242112\pi\) |
−0.959216 | + | 0.282673i | \(0.908779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.562914 | + | 0.974996i | 0.0858436 | + | 0.148686i | 0.905750 | − | 0.423812i | \(-0.139308\pi\) |
−0.819907 | + | 0.572497i | \(0.805975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.05695 | − | 1.76493i | −0.445903 | − | 0.257442i | 0.260196 | − | 0.965556i | \(-0.416213\pi\) |
−0.706098 | + | 0.708114i | \(0.749546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.68277 | 0.954681 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.984893 | + | 1.70588i | −0.135285 | + | 0.234321i | −0.925706 | − | 0.378243i | \(-0.876528\pi\) |
0.790421 | + | 0.612564i | \(0.209862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.617133 | − | 1.06891i | −0.0832142 | − | 0.144131i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.48434 | − | 6.03505i | −0.453622 | − | 0.785696i | 0.544986 | − | 0.838445i | \(-0.316535\pi\) |
−0.998608 | + | 0.0527492i | \(0.983202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.98180 | − | 8.62874i | 0.637855 | − | 1.10480i | −0.348048 | − | 0.937477i | \(-0.613155\pi\) |
0.985903 | − | 0.167320i | \(-0.0535113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.23725 | 0.773636 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.324291 | + | 0.187230i | 0.0396185 | + | 0.0228738i | 0.519678 | − | 0.854362i | \(-0.326052\pi\) |
−0.480060 | + | 0.877236i | \(0.659385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.03969 | − | 13.9252i | −0.954136 | − | 1.65261i | −0.736334 | − | 0.676618i | \(-0.763445\pi\) |
−0.217802 | − | 0.975993i | \(-0.569889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.09850 | + | 14.0270i | 0.947858 | + | 1.64174i | 0.749925 | + | 0.661523i | \(0.230090\pi\) |
0.197934 | + | 0.980215i | \(0.436577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.23997i | − | 0.255268i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.44995 | + | 4.30123i | −0.838185 | + | 0.483926i | −0.856647 | − | 0.515903i | \(-0.827456\pi\) |
0.0184618 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.17251i | − | 0.787285i | −0.919264 | − | 0.393643i | \(-0.871215\pi\) | ||
0.919264 | − | 0.393643i | \(-0.128785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.83429 | − | 4.90913i | 0.307422 | − | 0.532470i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.91340 | + | 6.77822i | −0.414820 | + | 0.718489i | −0.995410 | − | 0.0957070i | \(-0.969489\pi\) |
0.580590 | + | 0.814196i | \(0.302822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.80296 | + | 5.65974i | 1.02763 | + | 0.593302i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.99229 | − | 8.36538i | −0.307003 | − | 0.858270i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.57756 | − | 4.95226i | 0.870919 | − | 0.502826i | 0.00326577 | − | 0.999995i | \(-0.498960\pi\) |
0.867654 | + | 0.497169i | \(0.165627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3741 | + | 7.72154i | 1.33077 | + | 0.768322i | 0.985418 | − | 0.170150i | \(-0.0544253\pi\) |
0.345355 | + | 0.938472i | \(0.387759\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3067i | 1.31114i | 0.755133 | + | 0.655572i | \(0.227572\pi\) | ||||
−0.755133 | + | 0.655572i | \(0.772428\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.95982 | 0.769505 | 0.384753 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384753 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.06803 | − | 4.08073i | 0.676995 | − | 0.390863i | −0.121727 | − | 0.992564i | \(-0.538843\pi\) |
0.798722 | + | 0.601700i | \(0.205510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.63294 | 0.341759 | 0.170879 | − | 0.985292i | \(-0.445339\pi\) | ||||
0.170879 | + | 0.985292i | \(0.445339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.26357 | −0.490831 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.90918 | − | 5.14372i | 0.816704 | − | 0.471524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6333 | 0.966664 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9147i | 1.06568i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.69581 | − | 3.28848i | −0.505421 | − | 0.291805i | 0.225528 | − | 0.974237i | \(-0.427589\pi\) |
−0.730950 | + | 0.682431i | \(0.760923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.27444 | − | 1.89050i | 0.286089 | − | 0.165174i | −0.350088 | − | 0.936717i | \(-0.613848\pi\) |
0.636177 | + | 0.771543i | \(0.280515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.88790 | − | 15.8629i | 0.250413 | − | 1.37549i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5831 | − | 7.26483i | −1.07504 | − | 0.620676i | −0.145488 | − | 0.989360i | \(-0.546475\pi\) |
−0.929555 | + | 0.368684i | \(0.879808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.79838 | − | 6.57899i | 0.322175 | − | 0.558023i | −0.658762 | − | 0.752352i | \(-0.728920\pi\) |
0.980936 | + | 0.194329i | \(0.0622529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.926541 | − | 1.60482i | 0.0774813 | − | 0.134202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.95309i | 0.577423i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.06792 | + | 1.77127i | −0.251334 | + | 0.145108i | −0.620375 | − | 0.784305i | \(-0.713020\pi\) |
0.369041 | + | 0.929413i | \(0.379686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10333i | 0.0897877i | 0.998992 | + | 0.0448938i | \(0.0142950\pi\) | ||||
−0.998992 | + | 0.0448938i | \(0.985705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.51202 | + | 7.81504i | 0.362414 | + | 0.627719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.691234 | − | 1.19725i | −0.0551665 | − | 0.0955511i | 0.837123 | − | 0.547014i | \(-0.184236\pi\) |
−0.892290 | + | 0.451463i | \(0.850902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.27265 | − | 4.77622i | −0.651976 | − | 0.376419i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.3481 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.45424 | + | 4.25087i | −0.189915 | + | 0.328942i | −0.945222 | − | 0.326429i | \(-0.894155\pi\) |
0.755307 | + | 0.655371i | \(0.227488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.81781 | − | 3.14853i | −0.139831 | − | 0.242195i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.2798 | + | 21.2693i | 0.933619 | + | 1.61708i | 0.777078 | + | 0.629404i | \(0.216701\pi\) |
0.156541 | + | 0.987671i | \(0.449966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56396 | + | 2.70886i | −0.118224 | + | 0.204770i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5239 | −1.16031 | −0.580155 | − | 0.814506i | \(-0.697008\pi\) | ||||
−0.580155 | + | 0.814506i | \(0.697008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6668 | − | 6.73585i | −0.867189 | − | 0.500672i | −0.000775855 | − | 1.00000i | \(-0.500247\pi\) |
−0.866413 | + | 0.499328i | \(0.833580\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.41119 | + | 5.90835i | 0.250795 | + | 0.434390i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.842065 | − | 1.45850i | −0.0615779 | − | 0.106656i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3381i | 1.03747i | 0.854935 | + | 0.518734i | \(0.173597\pi\) | ||||
−0.854935 | + | 0.518734i | \(0.826403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7819 | + | 9.68904i | −1.20799 | + | 0.697432i | −0.962319 | − | 0.271922i | \(-0.912341\pi\) |
−0.245668 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.2122i | − | 1.01257i | −0.862365 | − | 0.506287i | \(-0.831018\pi\) | ||
0.862365 | − | 0.506287i | \(-0.168982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3046 | − | 19.5801i | 0.801360 | − | 1.38800i | −0.117362 | − | 0.993089i | \(-0.537444\pi\) |
0.918721 | − | 0.394906i | \(-0.129223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.30930 | + | 10.9280i | −0.442826 | + | 0.766997i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.30781 | − | 3.06447i | −0.370714 | − | 0.214032i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.59688 | − | 0.472771i | −0.179630 | − | 0.0327022i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1117 | + | 5.83798i | −0.696116 | + | 0.401903i | −0.805899 | − | 0.592053i | \(-0.798318\pi\) |
0.109783 | + | 0.993956i | \(0.464984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98727 | + | 1.14735i | 0.135531 | + | 0.0782487i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.3770i | 1.11174i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.51060 | 0.572485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6238 | + | 8.44308i | −0.979285 | + | 0.565391i | −0.902054 | − | 0.431623i | \(-0.857941\pi\) |
−0.0772310 | + | 0.997013i | \(0.524608\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3183 | 1.01671 | 0.508354 | − | 0.861148i | \(-0.330254\pi\) | ||||
0.508354 | + | 0.861148i | \(0.330254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5798 | −1.16171 | −0.580854 | − | 0.814008i | \(-0.697281\pi\) | ||||
−0.580854 | + | 0.814008i | \(0.697281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.4561 | + | 10.6556i | −1.20910 | + | 0.698074i | −0.962563 | − | 0.271059i | \(-0.912626\pi\) |
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.19469 | −0.469330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.70885i | 0.369275i | 0.982807 | + | 0.184638i | \(0.0591111\pi\) | ||||
−0.982807 | + | 0.184638i | \(0.940889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3638 | − | 8.87029i | −0.989668 | − | 0.571385i | −0.0844932 | − | 0.996424i | \(-0.526927\pi\) |
−0.905175 | + | 0.425039i | \(0.860260\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7962 | − | 6.81052i | 0.753629 | − | 0.435108i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.63057 | − | 10.1704i | 0.549150 | − | 0.647126i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.8199 | − | 14.3298i | −1.56662 | − | 0.904489i | −0.996559 | − | 0.0828875i | \(-0.973586\pi\) |
−0.570062 | − | 0.821602i | \(-0.693081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.781902 | + | 1.35429i | −0.0491577 | + | 0.0851437i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.27016 | + | 10.8602i | −0.391122 | + | 0.677443i | −0.992598 | − | 0.121448i | \(-0.961246\pi\) |
0.601476 | + | 0.798891i | \(0.294580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.3814i | 0.769341i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.42476 | + | 0.822587i | −0.0878546 | + | 0.0507229i | −0.543284 | − | 0.839549i | \(-0.682819\pi\) |
0.455429 | + | 0.890272i | \(0.349486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.01488i | 0.246632i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.25176 | − | 9.09632i | −0.320206 | − | 0.554612i | 0.660325 | − | 0.750980i | \(-0.270419\pi\) |
−0.980530 | + | 0.196368i | \(0.937085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.37145 | − | 11.0357i | −0.387038 | − | 0.670370i | 0.605012 | − | 0.796217i | \(-0.293168\pi\) |
−0.992050 | + | 0.125847i | \(0.959835\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.443460 | + | 0.256032i | 0.0267416 | + | 0.0154393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4101 | 1.16624 | 0.583119 | − | 0.812387i | \(-0.301832\pi\) | ||||
0.583119 | + | 0.812387i | \(0.301832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.78424 | + | 13.4827i | −0.464369 | + | 0.804311i | −0.999173 | − | 0.0406655i | \(-0.987052\pi\) |
0.534804 | + | 0.844976i | \(0.320386\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.22827 | − | 9.05563i | −0.310788 | − | 0.538301i | 0.667745 | − | 0.744390i | \(-0.267260\pi\) |
−0.978533 | + | 0.206089i | \(0.933926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.56145 | − | 9.63271i | −0.328282 | − | 0.568601i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.63267 | + | 8.02403i | −0.272510 | + | 0.472002i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1390 | 1.64390 | 0.821949 | − | 0.569561i | \(-0.192887\pi\) | ||||
0.821949 | + | 0.569561i | \(0.192887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3008 | − | 7.10189i | −0.716182 | − | 0.413488i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.95127 | − | 6.84380i | −0.228508 | − | 0.395787i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08223 | + | 3.60653i | 0.120018 | + | 0.207877i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 20.3082i | − | 1.16284i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.1659 | − | 6.44663i | 0.637271 | − | 0.367929i | −0.146292 | − | 0.989242i | \(-0.546734\pi\) |
0.783563 | + | 0.621313i | \(0.213400\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6008i | 0.771228i | 0.922660 | + | 0.385614i | \(0.126010\pi\) | ||||
−0.922660 | + | 0.385614i | \(0.873990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12148 | − | 1.94246i | 0.0633899 | − | 0.109794i | −0.832589 | − | 0.553892i | \(-0.813142\pi\) |
0.895979 | + | 0.444097i | \(0.146476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3488 | + | 28.3170i | −0.918242 | + | 1.59044i | −0.116159 | + | 0.993231i | \(0.537058\pi\) |
−0.802084 | + | 0.597212i | \(0.796275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.78900 | + | 1.03288i | 0.100165 | + | 0.0578301i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.08292 | − | 11.4144i | −0.227180 | − | 0.635113i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.24099 | + | 1.29383i | −0.124308 | + | 0.0717690i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3077 | − | 6.52853i | −0.623416 | − | 0.359929i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7734i | 1.03188i | 0.856625 | + | 0.515940i | \(0.172557\pi\) | ||||
−0.856625 | + | 0.515940i | \(0.827443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.763236 | 0.0417000 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.38982 | + | 4.84387i | −0.457023 | + | 0.263862i | −0.710792 | − | 0.703403i | \(-0.751663\pi\) |
0.253769 | + | 0.967265i | \(0.418330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.68103 | 0.145186 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.17346 | −0.0633606 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.2531 | + | 6.49698i | −0.604098 | + | 0.348776i | −0.770652 | − | 0.637256i | \(-0.780069\pi\) |
0.166554 | + | 0.986032i | \(0.446736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.98962 | 0.374146 | 0.187073 | − | 0.982346i | \(-0.440100\pi\) | ||||
0.187073 | + | 0.982346i | \(0.440100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.60313i | 0.0853258i | 0.999090 | + | 0.0426629i | \(0.0135842\pi\) | ||||
−0.999090 | + | 0.0426629i | \(0.986416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.3827 | − | 16.3868i | −1.50640 | − | 0.869719i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1453 | − | 11.0535i | 1.01045 | − | 0.583383i | 0.0991256 | − | 0.995075i | \(-0.468395\pi\) |
0.911323 | + | 0.411692i | \(0.135062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7810 | − | 6.69610i | −0.935840 | − | 0.352426i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.5903 | + | 16.5066i | 1.49649 | + | 0.863997i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.97781 | − | 8.62182i | 0.259840 | − | 0.450055i | −0.706359 | − | 0.707854i | \(-0.749664\pi\) |
0.966199 | + | 0.257798i | \(0.0829970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.64314 | + | 6.31011i | −0.189142 | + | 0.327604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.4257i | − | 0.850489i | −0.905078 | − | 0.425245i | \(-0.860188\pi\) | ||
0.905078 | − | 0.425245i | \(-0.139812\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.04054 | + | 5.21956i | −0.465612 | + | 0.268821i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2429i | 1.29664i | 0.761367 | + | 0.648322i | \(0.224529\pi\) | ||||
−0.761367 | + | 0.648322i | \(0.775471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5496 | + | 30.3968i | 0.896742 | + | 1.55320i | 0.831633 | + | 0.555325i | \(0.187406\pi\) |
0.0651092 | + | 0.997878i | \(0.479260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.28279 | − | 3.95391i | −0.116342 | − | 0.201510i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8623 | + | 9.73543i | 0.854950 | + | 0.493606i | 0.862318 | − | 0.506367i | \(-0.169012\pi\) |
−0.00736774 | + | 0.999973i | \(0.502345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.18203 | −0.363211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.76691 | + | 15.1847i | −0.441111 | + | 0.764027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.78901 | − | 15.2230i | −0.441108 | − | 0.764021i | 0.556664 | − | 0.830738i | \(-0.312081\pi\) |
−0.997772 | + | 0.0667165i | \(0.978748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.54092 | + | 14.7933i | 0.426513 | + | 0.738743i | 0.996560 | − | 0.0828693i | \(-0.0264084\pi\) |
−0.570047 | + | 0.821612i | \(0.693075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.77418 | + | 11.7332i | −0.337446 | + | 0.584473i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.02692 | 0.100471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3939 | + | 7.73296i | 0.662284 | + | 0.382370i | 0.793147 | − | 0.609030i | \(-0.208441\pi\) |
−0.130862 | + | 0.991401i | \(0.541775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.8886 | − | 22.3238i | −0.634208 | − | 1.09848i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.30962 | − | 12.6606i | −0.358815 | − | 0.621486i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.5092i | 1.24621i | 0.782140 | + | 0.623103i | \(0.214128\pi\) | ||||
−0.782140 | + | 0.623103i | \(0.785872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.76334 | − | 3.90482i | 0.329625 | − | 0.190309i | −0.326050 | − | 0.945353i | \(-0.605718\pi\) |
0.655675 | + | 0.755044i | \(0.272384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.35174i | 0.114076i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4278 | − | 31.9179i | 0.891784 | − | 1.54461i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.26660 | + | 16.0502i | −0.446356 | + | 0.773112i | −0.998146 | − | 0.0608716i | \(-0.980612\pi\) |
0.551789 | + | 0.833984i | \(0.313945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.2020 | − | 16.2824i | −1.35530 | − | 0.782484i | −0.366316 | − | 0.930491i | \(-0.619381\pi\) |
−0.988986 | + | 0.148007i | \(0.952714\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.28328 | + | 8.58271i | −0.348406 | + | 0.410567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5290 | + | 6.07891i | −0.502521 | + | 0.290131i | −0.729754 | − | 0.683710i | \(-0.760365\pi\) |
0.227233 | + | 0.973840i | \(0.427032\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7476 | + | 6.20513i | 0.510634 | + | 0.294815i | 0.733094 | − | 0.680127i | \(-0.238075\pi\) |
−0.222460 | + | 0.974942i | \(0.571409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.9529i | 0.756238i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.8022 | −1.83119 | −0.915596 | − | 0.402100i | \(-0.868280\pi\) | ||||
−0.915596 | + | 0.402100i | \(0.868280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.57695 | + | 0.910450i | −0.0742555 | + | 0.0428714i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.0717 | 1.08162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4392 | −1.47066 | −0.735331 | − | 0.677708i | \(-0.762973\pi\) | ||||
−0.735331 | + | 0.677708i | \(0.762973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.76189 | − | 1.59458i | 0.128634 | − | 0.0742669i | −0.434302 | − | 0.900767i | \(-0.643005\pi\) |
0.562936 | + | 0.826500i | \(0.309672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6707 | 1.00712 | 0.503562 | − | 0.863959i | \(-0.332022\pi\) | ||||
0.503562 | + | 0.863959i | \(0.332022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 19.0633i | − | 0.882144i | −0.897472 | − | 0.441072i | \(-0.854598\pi\) | ||
0.897472 | − | 0.441072i | \(-0.145402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.19956 | + | 0.692567i | 0.0553906 | + | 0.0319798i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.590416 | − | 0.340877i | 0.0271474 | − | 0.0156735i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.81039 | + | 2.38489i | 0.128949 | + | 0.109426i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.51906 | + | 4.34113i | 0.343554 | + | 0.198351i | 0.661843 | − | 0.749643i | \(-0.269775\pi\) |
−0.318288 | + | 0.947994i | \(0.603108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.12143 | + | 8.87058i | −0.233517 | + | 0.404464i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0939 | − | 17.4831i | 0.458338 | − | 0.793865i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.7742i | − | 0.805425i | −0.915326 | − | 0.402713i | \(-0.868067\pi\) | ||
0.915326 | − | 0.402713i | \(-0.131933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.13906 | − | 0.657635i | 0.0514050 | − | 0.0296787i | −0.474077 | − | 0.880483i | \(-0.657218\pi\) |
0.525482 | + | 0.850805i | \(0.323885\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.48734i | 0.427288i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.7390 | − | 51.5094i | −1.33398 | − | 2.31051i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7952 | − | 18.6979i | −0.483261 | − | 0.837033i | 0.516554 | − | 0.856255i | \(-0.327215\pi\) |
−0.999815 | + | 0.0192214i | \(0.993881\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.2076 | − | 16.2857i | −1.25772 | − | 0.726143i | −0.285086 | − | 0.958502i | \(-0.592022\pi\) |
−0.972630 | + | 0.232359i | \(0.925356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.4766 | 1.40069 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4800 | − | 19.8839i | 0.508842 | − | 0.881339i | −0.491106 | − | 0.871100i | \(-0.663407\pi\) |
0.999948 | − | 0.0102396i | \(-0.00325942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.9565 | + | 51.8863i | 1.32520 | + | 2.29531i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5610 | + | 23.4884i | 0.597570 | + | 1.03502i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.06877 | + | 1.85116i | −0.0470044 | + | 0.0814139i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0841 | 0.617035 | 0.308517 | − | 0.951219i | \(-0.400167\pi\) | ||||
0.308517 | + | 0.951219i | \(0.400167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1343 | + | 19.1301i | 1.44886 | + | 0.836501i | 0.998414 | − | 0.0563014i | \(-0.0179308\pi\) |
0.450448 | + | 0.892802i | \(0.351264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.15655 | + | 10.6635i | 0.268183 | + | 0.464507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.16555 | − | 14.1431i | −0.355024 | − | 0.614920i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.20176i | − | 0.398572i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0504 | − | 8.11199i | 0.607450 | − | 0.350712i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.04680i | − | 0.174308i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.22232 | − | 3.84916i | 0.0955448 | − | 0.165489i | −0.814291 | − | 0.580457i | \(-0.802874\pi\) |
0.909836 | + | 0.414968i | \(0.136207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.31748 | − | 14.4063i | 0.356282 | − | 0.617098i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2229 | + | 10.5210i | 0.779156 | + | 0.449846i | 0.836131 | − | 0.548530i | \(-0.184812\pi\) |
−0.0569750 | + | 0.998376i | \(0.518146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3376 | + | 9.62108i | 0.482998 | + | 0.409872i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.5575 | + | 15.9104i | −1.17187 | + | 0.676577i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.4094 | − | 12.3607i | −0.907145 | − | 0.523740i | −0.0276336 | − | 0.999618i | \(-0.508797\pi\) |
−0.879511 | + | 0.475878i | \(0.842131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.44518i | 0.145716i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.1514 | 0.849281 | 0.424640 | − | 0.905362i | \(-0.360401\pi\) | ||||
0.424640 | + | 0.905362i | \(0.360401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.41273 | − | 3.70239i | 0.269786 | − | 0.155761i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.91264 | 0.122104 | 0.0610520 | − | 0.998135i | \(-0.480554\pi\) | ||||
0.0610520 | + | 0.998135i | \(0.480554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.30300 | 0.221924 | 0.110962 | − | 0.993825i | \(-0.464607\pi\) | ||||
0.110962 | + | 0.993825i | \(0.464607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.89115 | − | 1.09186i | 0.0788665 | − | 0.0455336i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0613 | 1.20984 | 0.604919 | − | 0.796287i | \(-0.293205\pi\) | ||||
0.604919 | + | 0.796287i | \(0.293205\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 26.5313i | − | 1.10070i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.03301 | + | 0.596409i | 0.0427829 | + | 0.0247007i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.60901 | + | 3.81571i | −0.272783 | + | 0.157491i | −0.630152 | − | 0.776472i | \(-0.717007\pi\) |
0.357369 | + | 0.933963i | \(0.383674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9864 | + | 3.45655i | 0.782322 | + | 0.142425i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.1987 | − | 13.3938i | −0.952657 | − | 0.550017i | −0.0587516 | − | 0.998273i | \(-0.518712\pi\) |
−0.893905 | + | 0.448256i | \(0.852045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.4841 | − | 18.1590i | 0.429806 | − | 0.744446i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4393 | − | 33.6699i | 0.794270 | − | 1.37572i | −0.129032 | − | 0.991640i | \(-0.541187\pi\) |
0.923302 | − | 0.384075i | \(-0.125480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4550i | 0.834377i | 0.908820 | + | 0.417188i | \(0.136985\pi\) | ||||
−0.908820 | + | 0.417188i | \(0.863015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.7695 | − | 10.8366i | 0.763088 | − | 0.440569i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.65988i | − | 0.189139i | −0.995518 | − | 0.0945694i | \(-0.969853\pi\) | ||
0.995518 | − | 0.0945694i | \(-0.0301474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.40092 | − | 9.35467i | −0.218498 | − | 0.378450i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.90269 | − | 10.2238i | −0.238408 | − | 0.412934i | 0.721850 | − | 0.692050i | \(-0.243292\pi\) |
−0.960258 | + | 0.279116i | \(0.909959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.1238 | − | 24.3202i | −1.69584 | − | 0.979094i | −0.949625 | − | 0.313389i | \(-0.898536\pi\) |
−0.746215 | − | 0.665705i | \(-0.768131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.7915 | 1.71993 | 0.859967 | − | 0.510350i | \(-0.170484\pi\) | ||||
0.859967 | + | 0.510350i | \(0.170484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.4758 | + | 25.0728i | −0.579959 | + | 1.00452i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0285 | + | 17.3698i | 0.401138 | + | 0.694792i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.65449 | + | 8.06181i | 0.185587 | + | 0.321445i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6092 | + | 32.2321i | −0.740820 | + | 1.28314i | 0.211302 | + | 0.977421i | \(0.432230\pi\) |
−0.952122 | + | 0.305717i | \(0.901104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4054 | −0.531976 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7103 | + | 10.2251i | 0.701709 | + | 0.405132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.29142 | + | 5.70091i | 0.130003 | + | 0.225172i | 0.923678 | − | 0.383171i | \(-0.125168\pi\) |
−0.793674 | + | 0.608343i | \(0.791835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.24623 | + | 10.8188i | 0.246327 | + | 0.426651i | 0.962504 | − | 0.271268i | \(-0.0874429\pi\) |
−0.716177 | + | 0.697919i | \(0.754110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.23117i | 0.166344i | 0.996535 | + | 0.0831722i | \(0.0265052\pi\) | ||||
−0.996535 | + | 0.0831722i | \(0.973495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.65456 | + | 2.10996i | −0.143454 | + | 0.0828233i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.95004i | − | 0.115444i | −0.998333 | − | 0.0577219i | \(-0.981616\pi\) | ||
0.998333 | − | 0.0577219i | \(-0.0183837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.85328 | − | 6.67408i | 0.150560 | − | 0.260778i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.557166 | + | 0.965039i | −0.0217041 | + | 0.0375926i | −0.876673 | − | 0.481086i | \(-0.840243\pi\) |
0.854969 | + | 0.518679i | \(0.173576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5103 | − | 12.4190i | −0.836653 | − | 0.483042i | 0.0194720 | − | 0.999810i | \(-0.493801\pi\) |
−0.856125 | + | 0.516768i | \(0.827135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0686 | − | 30.9437i | −0.429220 | − | 1.19995i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.62925 | − | 4.40475i | 0.295406 | − | 0.170553i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.22519 | − | 3.01677i | −0.201716 | − | 0.116461i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.51767i | − | 0.174144i | −0.996202 | − | 0.0870718i | \(-0.972249\pi\) | ||
0.996202 | − | 0.0870718i | \(-0.0277509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.8210 | 0.454319 | 0.227159 | − | 0.973858i | \(-0.427056\pi\) | ||||
0.227159 | + | 0.973858i | \(0.427056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.7286 | − | 18.3185i | 1.21763 | − | 0.703000i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.2681 | 0.813803 | 0.406901 | − | 0.913472i | \(-0.366609\pi\) | ||||
0.406901 | + | 0.913472i | \(0.366609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.6148 | −1.13152 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.22023 | + | 3.01390i | −0.198875 | + | 0.114820i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.9630 | −1.33006 | −0.665028 | − | 0.746819i | \(-0.731580\pi\) | ||||
−0.665028 | + | 0.746819i | \(0.731580\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15.4840i | − | 0.587341i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.24239 | − | 4.18140i | −0.274325 | − | 0.158382i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.1442 | − | 22.0226i | 1.44069 | − | 0.831781i | 0.442791 | − | 0.896625i | \(-0.353988\pi\) |
0.997895 | + | 0.0648442i | \(0.0206550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3542 | + | 2.61323i | 0.541378 | + | 0.0985598i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 49.4711 | + | 28.5622i | 1.86055 | + | 1.07419i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9260 | − | 29.3166i | 0.635668 | − | 1.10101i | −0.350705 | − | 0.936486i | \(-0.614058\pi\) |
0.986373 | − | 0.164523i | \(-0.0526085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.71668 | − | 9.90158i | 0.214091 | − | 0.370817i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.77701i | − | 0.141252i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.9929 | + | 26.5540i | −1.71525 | + | 0.990298i | −0.788144 | + | 0.615491i | \(0.788958\pi\) |
−0.927103 | + | 0.374807i | \(0.877709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.2216i | 1.83311i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.44232 | − | 2.49818i | −0.0535666 | − | 0.0927800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.59081 | − | 6.21946i | −0.133176 | − | 0.230667i | 0.791723 | − | 0.610880i | \(-0.209184\pi\) |
−0.924899 | + | 0.380213i | \(0.875851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.71159 | + | 1.56553i | 0.100292 | + | 0.0579034i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.8680 | 1.06626 | 0.533132 | − | 0.846032i | \(-0.321015\pi\) | ||||
0.533132 | + | 0.846032i | \(0.321015\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.113378 | − | 0.196377i | 0.00417634 | − | 0.00723364i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1981 | + | 28.0559i | 0.595855 | + | 1.03205i | 0.993426 | + | 0.114480i | \(0.0365202\pi\) |
−0.397570 | + | 0.917572i | \(0.630146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.2449 | − | 29.8690i | −0.632654 | − | 1.09579i | −0.987007 | − | 0.160677i | \(-0.948632\pi\) |
0.354353 | − | 0.935112i | \(-0.384701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.61025 | + | 6.25314i | −0.132269 | + | 0.229097i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.4436 | 1.07584 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7822 | + | 11.4212i | 0.721861 | + | 0.416767i | 0.815437 | − | 0.578845i | \(-0.196496\pi\) |
−0.0935759 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.12442 | + | 1.94755i | 0.0409219 | + | 0.0708788i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.87620 | + | 4.98173i | 0.104537 | + | 0.181064i | 0.913549 | − | 0.406728i | \(-0.133330\pi\) |
−0.809012 | + | 0.587792i | \(0.799997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.7434i | 1.76695i | 0.468481 | + | 0.883474i | \(0.344801\pi\) | ||||
−0.468481 | + | 0.883474i | \(0.655199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.1448 | − | 15.0947i | 0.946506 | − | 0.546465i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.3250i | − | 0.770002i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.50200 | + | 6.06565i | −0.126285 | + | 0.218733i | −0.922235 | − | 0.386631i | \(-0.873639\pi\) |
0.795949 | + | 0.605363i | \(0.206972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.00414 | + | 8.66743i | −0.179987 | + | 0.311746i | −0.941876 | − | 0.335962i | \(-0.890939\pi\) |
0.761889 | + | 0.647707i | \(0.224272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.24225 | − | 1.87191i | −0.116465 | − | 0.0672411i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.3414 | + | 4.41450i | −0.442175 | + | 0.158166i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.43247 | + | 4.86849i | −0.301738 | + | 0.174208i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.44028 | − | 1.40890i | −0.0870973 | − | 0.0502856i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 34.2689i | − | 1.22155i | −0.791803 | − | 0.610777i | \(-0.790857\pi\) | ||
0.791803 | − | 0.610777i | \(-0.209143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4383 | 0.477812 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.4050 | − | 15.2450i | 0.937671 | − | 0.541364i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.8026 | −0.984817 | −0.492409 | − | 0.870364i | \(-0.663883\pi\) | ||||
−0.492409 | + | 0.870364i | \(0.663883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.81700 | −0.347300 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.49416 | − | 4.90411i | 0.299752 | − | 0.173062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.4701 | −0.686230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 38.6452i | − | 1.35869i | −0.733817 | − | 0.679347i | \(-0.762263\pi\) | ||
0.733817 | − | 0.679347i | \(-0.237737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9998 | − | 21.9392i | −1.33435 | − | 0.770390i | −0.348390 | − | 0.937350i | \(-0.613272\pi\) |
−0.985964 | + | 0.166960i | \(0.946605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0919 | + | 15.6415i | −0.948989 | + | 0.547899i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.62066 | − | 1.65281i | 0.161657 | − | 0.0578245i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.8864 | + | 26.4925i | 1.60145 | + | 0.924596i | 0.991198 | + | 0.132387i | \(0.0422642\pi\) |
0.610250 | + | 0.792209i | \(0.291069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0908 | − | 24.4059i | 0.491174 | − | 0.850737i | −0.508775 | − | 0.860900i | \(-0.669901\pi\) |
0.999948 | + | 0.0101621i | \(0.00323476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.9263 | − | 31.0492i | 0.623358 | − | 1.07969i | −0.365498 | − | 0.930812i | \(-0.619101\pi\) |
0.988856 | − | 0.148876i | \(-0.0475654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.7685i | − | 1.31175i | −0.754868 | − | 0.655877i | \(-0.772299\pi\) | ||
0.754868 | − | 0.655877i | \(-0.227701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.0956 | − | 9.29280i | 0.557680 | − | 0.321976i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0046i | 0.346225i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.3542 | + | 19.6660i | 0.391989 | + | 0.678945i | 0.992712 | − | 0.120513i | \(-0.0384538\pi\) |
−0.600723 | + | 0.799457i | \(0.705120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.68140 | + | 15.0366i | 0.299359 | + | 0.518505i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.41744 | − | 3.70511i | −0.220767 | − | 0.127460i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.3328 | 1.35149 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.32194 | − | 7.48582i | 0.148154 | − | 0.256611i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3713 | + | 31.8200i | 0.629021 | + | 1.08950i | 0.987749 | + | 0.156054i | \(0.0498772\pi\) |
−0.358728 | + | 0.933442i | \(0.616789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.42058 | − | 5.92462i | −0.116845 | − | 0.202381i | 0.801671 | − | 0.597766i | \(-0.203945\pi\) |
−0.918516 | + | 0.395385i | \(0.870611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3794 | + | 19.7097i | −0.388261 | + | 0.672488i | −0.992216 | − | 0.124531i | \(-0.960257\pi\) |
0.603955 | + | 0.797019i | \(0.293591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6907 | −0.670279 | −0.335139 | − | 0.942169i | \(-0.608783\pi\) | ||||
−0.335139 | + | 0.942169i | \(0.608783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.3518 | + | 25.0292i | 1.47401 | + | 0.851017i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.60464 | + | 4.51137i | 0.0883564 | + | 0.153038i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.572947 | + | 0.992374i | 0.0194136 | + | 0.0336253i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44.0728i | 1.48993i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0986 | − | 7.56250i | 0.442309 | − | 0.255367i | −0.262267 | − | 0.964995i | \(-0.584470\pi\) |
0.704577 | + | 0.709628i | \(0.251137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.3230i | 1.39221i | 0.717942 | + | 0.696103i | \(0.245084\pi\) | ||||
−0.717942 | + | 0.696103i | \(0.754916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.1270 | − | 40.0572i | 0.778286 | − | 1.34803i | −0.154642 | − | 0.987971i | \(-0.549422\pi\) |
0.932929 | − | 0.360061i | \(-0.117244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.7167 | − | 22.0260i | 0.426986 | − | 0.739561i | −0.569618 | − | 0.821910i | \(-0.692909\pi\) |
0.996604 | + | 0.0823488i | \(0.0262422\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.0689 | − | 12.1641i | −0.706629 | − | 0.407972i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.95539 | + | 11.7316i | −0.333144 | + | 0.392582i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.4021 | + | 15.8206i | −0.915953 | + | 0.528826i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.0798 | − | 7.55164i | −0.436236 | − | 0.251861i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.47822i | 0.182506i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.4585 | −0.912750 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5518 | − | 11.2882i | 0.649205 | − | 0.374819i | −0.138946 | − | 0.990300i | \(-0.544372\pi\) |
0.788152 | + | 0.615481i | \(0.211038\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.6150 | 1.67695 | 0.838475 | − | 0.544940i | \(-0.183448\pi\) | ||||
0.838475 | + | 0.544940i | \(0.183448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.34336 | −0.143744 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.1122 | − | 6.99300i | 0.399981 | − | 0.230929i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.3240 | −1.00030 | −0.500148 | − | 0.865940i | \(-0.666721\pi\) | ||||
−0.500148 | + | 0.865940i | \(0.666721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 49.2050i | − | 1.61960i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.45121 | − | 1.41521i | −0.0805954 | − | 0.0465318i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.7976 | − | 14.8943i | 0.846393 | − | 0.488665i | −0.0130391 | − | 0.999915i | \(-0.504151\pi\) |
0.859432 | + | 0.511250i | \(0.170817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21737 | − | 28.6585i | 0.170993 | − | 0.939243i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.97276 | − | 1.71632i | −0.0972196 | − | 0.0561298i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1927 | + | 22.8504i | −0.430985 | + | 0.746488i | −0.996958 | − | 0.0779353i | \(-0.975167\pi\) |
0.565973 | + | 0.824424i | \(0.308501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.47207 | − | 2.54971i | 0.0479883 | − | 0.0831181i | −0.841034 | − | 0.540983i | \(-0.818052\pi\) |
0.889022 | + | 0.457865i | \(0.151386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.76530i | 0.252873i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.65210 | − | 1.53119i | 0.0861815 | − | 0.0497569i | −0.456290 | − | 0.889831i | \(-0.650822\pi\) |
0.542471 | + | 0.840074i | \(0.317489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.5649i | 1.60895i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.84291 | + | 3.19201i | 0.0596977 | + | 0.103399i | 0.894330 | − | 0.447409i | \(-0.147653\pi\) |
−0.834632 | + | 0.550808i | \(0.814320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6122 | + | 25.3091i | 0.472840 | + | 0.818982i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.5450 | − | 26.8728i | −1.50302 | − | 0.867767i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3983 | 0.367687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.7485 | + | 34.2054i | −0.635727 | + | 1.10111i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0399 | + | 27.7819i | 0.515808 | + | 0.893405i | 0.999832 | + | 0.0183505i | \(0.00584147\pi\) |
−0.484024 | + | 0.875055i | \(0.660825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.26555 | + | 12.5843i | 0.233163 | + | 0.403849i | 0.958737 | − | 0.284294i | \(-0.0917592\pi\) |
−0.725575 | + | 0.688144i | \(0.758426\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0503 | − | 24.3358i | 0.450432 | − | 0.780171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.611504 | 0.0195637 | 0.00978187 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978187 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.10460 | + | 2.36979i | 0.131183 | + | 0.0757388i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.61045 | + | 2.78937i | 0.0513652 | + | 0.0889672i | 0.890565 | − | 0.454856i | \(-0.150309\pi\) |
−0.839200 | + | 0.543824i | \(0.816976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4838 | − | 25.0867i | −0.461493 | − | 0.799330i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.90736i | − | 0.0924488i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.9740 | + | 20.1923i | −1.11099 | + | 0.641428i | −0.939085 | − | 0.343686i | \(-0.888325\pi\) |
−0.171902 | + | 0.985114i | \(0.554991\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 46.0827i | − | 1.46092i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5964 | − | 47.7983i | 0.873986 | − | 1.51379i | 0.0161464 | − | 0.999870i | \(-0.494860\pi\) |
0.857839 | − | 0.513918i | \(-0.171806\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1368.2.cu.b.449.8 | yes | 20 | |
3.2 | odd | 2 | 1368.2.cu.a.449.3 | ✓ | 20 | ||
4.3 | odd | 2 | 2736.2.dc.f.449.8 | 20 | |||
12.11 | even | 2 | 2736.2.dc.e.449.3 | 20 | |||
19.8 | odd | 6 | 1368.2.cu.a.521.3 | yes | 20 | ||
57.8 | even | 6 | inner | 1368.2.cu.b.521.8 | yes | 20 | |
76.27 | even | 6 | 2736.2.dc.e.1889.3 | 20 | |||
228.179 | odd | 6 | 2736.2.dc.f.1889.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.cu.a.449.3 | ✓ | 20 | 3.2 | odd | 2 | ||
1368.2.cu.a.521.3 | yes | 20 | 19.8 | odd | 6 | ||
1368.2.cu.b.449.8 | yes | 20 | 1.1 | even | 1 | trivial | |
1368.2.cu.b.521.8 | yes | 20 | 57.8 | even | 6 | inner | |
2736.2.dc.e.449.3 | 20 | 12.11 | even | 2 | |||
2736.2.dc.e.1889.3 | 20 | 76.27 | even | 6 | |||
2736.2.dc.f.449.8 | 20 | 4.3 | odd | 2 | |||
2736.2.dc.f.1889.8 | 20 | 228.179 | odd | 6 |