Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(26,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.26");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(-1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.26 |
Dual form | 45.3.c.a.26.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.821854i | − 0.410927i | −0.978665 | − | 0.205464i | \(-0.934130\pi\) | ||||
0.978665 | − | 0.205464i | \(-0.0658702\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.32456 | 0.831139 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.837722 | 0.119675 | 0.0598373 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598373 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(8\) | − 6.01972i | − 0.752465i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.83772 | −0.183772 | ||||||||
\(11\) | 14.3716i | 1.30651i | 0.757137 | + | 0.653256i | \(0.226597\pi\) | ||||
−0.757137 | + | 0.653256i | \(0.773403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.8114 | −1.67780 | −0.838900 | − | 0.544286i | \(-0.816801\pi\) | ||||
−0.838900 | + | 0.544286i | \(0.816801\pi\) | |||||||
\(14\) | − 0.688486i | − 0.0491776i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.35089 | 0.521931 | ||||||||
\(17\) | 23.5454i | 1.38502i | 0.721407 | + | 0.692512i | \(0.243496\pi\) | ||||
−0.721407 | + | 0.692512i | \(0.756504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.32456 | −0.332871 | −0.166436 | − | 0.986052i | \(-0.553226\pi\) | ||||
−0.166436 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(20\) | − 7.43393i | − 0.371697i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.8114 | 0.536881 | ||||||||
\(23\) | − 38.8723i | − 1.69010i | −0.534689 | − | 0.845049i | \(-0.679571\pi\) | ||||
0.534689 | − | 0.845049i | \(-0.320429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 17.9258i | 0.689453i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.78505 | 0.0994662 | ||||||||
\(29\) | − 0.266737i | − 0.00919784i | −0.999989 | − | 0.00459892i | \(-0.998536\pi\) | ||||
0.999989 | − | 0.00459892i | \(-0.00146389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.2719 | 0.976512 | 0.488256 | − | 0.872700i | \(-0.337633\pi\) | ||||
0.488256 | + | 0.872700i | \(0.337633\pi\) | |||||||
\(32\) | − 30.9421i | − 0.966940i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 19.3509 | 0.569144 | ||||||||
\(35\) | − 1.87320i | − 0.0535201i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.53950 | 0.257824 | 0.128912 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128912 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(38\) | 5.19786i | 0.136786i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.4605 | −0.336512 | ||||||||
\(41\) | − 19.3028i | − 0.470799i | −0.971899 | − | 0.235399i | \(-0.924360\pi\) | ||||
0.971899 | − | 0.235399i | \(-0.0756398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.6228 | 0.456344 | 0.228172 | − | 0.973621i | \(-0.426725\pi\) | ||||
0.228172 | + | 0.973621i | \(0.426725\pi\) | |||||||
\(44\) | 47.7793i | 1.08589i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −31.9473 | −0.694507 | ||||||||
\(47\) | 22.1684i | 0.471669i | 0.971793 | + | 0.235834i | \(0.0757823\pi\) | ||||
−0.971793 | + | 0.235834i | \(0.924218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2982 | −0.985678 | ||||||||
\(50\) | 4.10927i | 0.0821854i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −72.5132 | −1.39448 | ||||||||
\(53\) | 49.0012i | 0.924552i | 0.886736 | + | 0.462276i | \(0.152967\pi\) | ||||
−0.886736 | + | 0.462276i | \(0.847033\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 32.1359 | 0.584290 | ||||||||
\(56\) | − 5.04285i | − 0.0900509i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.219219 | −0.00377964 | ||||||||
\(59\) | − 73.2351i | − 1.24127i | −0.784098 | − | 0.620637i | \(-0.786874\pi\) | ||||
0.784098 | − | 0.620637i | \(-0.213126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.3246 | −0.792206 | −0.396103 | − | 0.918206i | \(-0.629638\pi\) | ||||
−0.396103 | + | 0.918206i | \(0.629638\pi\) | |||||||
\(62\) | − 24.8791i | − 0.401276i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.97367 | 0.124589 | ||||||||
\(65\) | 48.7717i | 0.750335i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.2982 | 1.15370 | 0.576852 | − | 0.816848i | \(-0.304281\pi\) | ||||
0.576852 | + | 0.816848i | \(0.304281\pi\) | |||||||
\(68\) | 78.2780i | 1.15115i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.53950 | −0.0219929 | ||||||||
\(71\) | − 104.044i | − 1.46541i | −0.680548 | − | 0.732703i | \(-0.738258\pi\) | ||||
0.680548 | − | 0.732703i | \(-0.261742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.6754 | 0.653088 | 0.326544 | − | 0.945182i | \(-0.394116\pi\) | ||||
0.326544 | + | 0.945182i | \(0.394116\pi\) | |||||||
\(74\) | − 7.84008i | − 0.105947i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.0263 | −0.276662 | ||||||||
\(77\) | 12.0394i | 0.156356i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.2192 | 0.863534 | 0.431767 | − | 0.901985i | \(-0.357890\pi\) | ||||
0.431767 | + | 0.901985i | \(0.357890\pi\) | |||||||
\(80\) | − 18.6732i | − 0.233414i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.8641 | −0.193464 | ||||||||
\(83\) | 28.2098i | 0.339877i | 0.985455 | + | 0.169938i | \(0.0543569\pi\) | ||||
−0.985455 | + | 0.169938i | \(0.945643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 52.6491 | 0.619401 | ||||||||
\(86\) | − 16.1271i | − 0.187524i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 86.5132 | 0.983104 | ||||||||
\(89\) | − 53.7774i | − 0.604240i | −0.953270 | − | 0.302120i | \(-0.902306\pi\) | ||||
0.953270 | − | 0.302120i | \(-0.0976943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.2719 | −0.200790 | ||||||||
\(92\) | − 129.233i | − 1.40471i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.2192 | 0.193821 | ||||||||
\(95\) | 14.1421i | 0.148865i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.921 | −1.18475 | −0.592376 | − | 0.805661i | \(-0.701810\pi\) | ||||
−0.592376 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(98\) | 39.6941i | 0.405042i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.6228 | −0.166228 | ||||||||
\(101\) | 17.5473i | 0.173736i | 0.996220 | + | 0.0868679i | \(0.0276858\pi\) | ||||
−0.996220 | + | 0.0868679i | \(0.972314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −71.5395 | −0.694558 | −0.347279 | − | 0.937762i | \(-0.612894\pi\) | ||||
−0.347279 | + | 0.937762i | \(0.612894\pi\) | |||||||
\(104\) | 131.298i | 1.26248i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 40.2719 | 0.379923 | ||||||||
\(107\) | 76.3675i | 0.713715i | 0.934159 | + | 0.356858i | \(0.116152\pi\) | ||||
−0.934159 | + | 0.356858i | \(0.883848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −126.921 | −1.16441 | −0.582206 | − | 0.813041i | \(-0.697810\pi\) | ||||
−0.582206 | + | 0.813041i | \(0.697810\pi\) | |||||||
\(110\) | − 26.4111i | − 0.240101i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.99573 | 0.0624618 | ||||||||
\(113\) | 15.0601i | 0.133275i | 0.997777 | + | 0.0666377i | \(0.0212272\pi\) | ||||
−0.997777 | + | 0.0666377i | \(0.978773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −86.9210 | −0.755835 | ||||||||
\(116\) | − 0.886783i | − 0.00764468i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −60.1886 | −0.510073 | ||||||||
\(119\) | 19.7245i | 0.165752i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.5438 | −0.706973 | ||||||||
\(122\) | 39.7157i | 0.325539i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 100.641 | 0.811617 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 158.031 | 1.24434 | 0.622168 | − | 0.782884i | \(-0.286252\pi\) | ||||
0.622168 | + | 0.782884i | \(0.286252\pi\) | |||||||
\(128\) | − 130.322i | − 1.01814i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 40.0833 | 0.308333 | ||||||||
\(131\) | 211.220i | 1.61237i | 0.591665 | + | 0.806184i | \(0.298471\pi\) | ||||
−0.591665 | + | 0.806184i | \(0.701529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.29822 | −0.0398363 | ||||||||
\(134\) | − 63.5279i | − 0.474089i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 141.737 | 1.04218 | ||||||||
\(137\) | 69.2592i | 0.505542i | 0.967526 | + | 0.252771i | \(0.0813419\pi\) | ||||
−0.967526 | + | 0.252771i | \(0.918658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −159.842 | −1.14994 | −0.574971 | − | 0.818174i | \(-0.694987\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(140\) | − 6.22757i | − 0.0444826i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −85.5089 | −0.602175 | ||||||||
\(143\) | − 313.465i | − 2.19206i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.596443 | −0.00411340 | ||||||||
\(146\) | − 39.1823i | − 0.268372i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31.7146 | 0.214288 | ||||||||
\(149\) | 9.81897i | 0.0658991i | 0.999457 | + | 0.0329496i | \(0.0104901\pi\) | ||||
−0.999457 | + | 0.0329496i | \(0.989510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 210.649 | 1.39503 | 0.697514 | − | 0.716572i | \(-0.254290\pi\) | ||||
0.697514 | + | 0.716572i | \(0.254290\pi\) | |||||||
\(152\) | 38.0720i | 0.250474i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.89466 | 0.0642511 | ||||||||
\(155\) | − 67.6900i | − 0.436710i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 211.276 | 1.34571 | 0.672854 | − | 0.739775i | \(-0.265068\pi\) | ||||
0.672854 | + | 0.739775i | \(0.265068\pi\) | |||||||
\(158\) | − 56.0663i | − 0.354850i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −69.1886 | −0.432429 | ||||||||
\(161\) | − 32.5642i | − 0.202262i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222.763 | −1.36664 | −0.683322 | − | 0.730117i | \(-0.739465\pi\) | ||||
−0.683322 | + | 0.730117i | \(0.739465\pi\) | |||||||
\(164\) | − 64.1731i | − 0.391299i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.1843 | 0.139665 | ||||||||
\(167\) | 33.3644i | 0.199787i | 0.994998 | + | 0.0998933i | \(0.0318501\pi\) | ||||
−0.994998 | + | 0.0998933i | \(0.968150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 306.737 | 1.81501 | ||||||||
\(170\) | − 43.2699i | − 0.254529i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 65.2370 | 0.379285 | ||||||||
\(173\) | 29.8102i | 0.172313i | 0.996282 | + | 0.0861567i | \(0.0274586\pi\) | ||||
−0.996282 | + | 0.0861567i | \(0.972541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.18861 | −0.0239349 | ||||||||
\(176\) | 120.016i | 0.681909i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −44.1972 | −0.248299 | ||||||||
\(179\) | 111.841i | 0.624808i | 0.949949 | + | 0.312404i | \(0.101134\pi\) | ||||
−0.949949 | + | 0.312404i | \(0.898866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −49.0790 | −0.271155 | −0.135577 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135577 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(182\) | 15.0168i | 0.0825101i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −234.000 | −1.27174 | ||||||||
\(185\) | − 21.3310i | − 0.115303i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −338.386 | −1.80955 | ||||||||
\(188\) | 73.7002i | 0.392022i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.6228 | 0.0611725 | ||||||||
\(191\) | 278.947i | 1.46046i | 0.683203 | + | 0.730229i | \(0.260586\pi\) | ||||
−0.683203 | + | 0.730229i | \(0.739414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89.8947 | 0.465775 | 0.232888 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232888 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(194\) | 94.4483i | 0.486847i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −160.570 | −0.819235 | ||||||||
\(197\) | − 212.709i | − 1.07974i | −0.841748 | − | 0.539870i | \(-0.818473\pi\) | ||||
0.841748 | − | 0.539870i | \(-0.181527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 96.4911 | 0.484880 | 0.242440 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242440 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(200\) | 30.0986i | 0.150493i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.4213 | 0.0713928 | ||||||||
\(203\) | − 0.223452i | − 0.00110075i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43.1623 | −0.210548 | ||||||||
\(206\) | 58.7951i | 0.285413i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −182.144 | −0.875695 | ||||||||
\(209\) | − 90.8942i | − 0.434900i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −65.7893 | −0.311798 | −0.155899 | − | 0.987773i | \(-0.549827\pi\) | ||||
−0.155899 | + | 0.987773i | \(0.549827\pi\) | |||||||
\(212\) | 162.907i | 0.768431i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 62.7630 | 0.293285 | ||||||||
\(215\) | − 43.8779i | − 0.204083i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.3594 | 0.116864 | ||||||||
\(218\) | 104.311i | 0.478489i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 106.838 | 0.485626 | ||||||||
\(221\) | − 513.558i | − 2.32379i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 102.302 | 0.458756 | 0.229378 | − | 0.973337i | \(-0.426331\pi\) | ||||
0.229378 | + | 0.973337i | \(0.426331\pi\) | |||||||
\(224\) | − 25.9209i | − 0.115718i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3772 | 0.0547665 | ||||||||
\(227\) | − 12.5296i | − 0.0551966i | −0.999619 | − | 0.0275983i | \(-0.991214\pi\) | ||||
0.999619 | − | 0.0275983i | \(-0.00878593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2982 | 0.101739 | 0.0508695 | − | 0.998705i | \(-0.483801\pi\) | ||||
0.0508695 | + | 0.998705i | \(0.483801\pi\) | |||||||
\(230\) | 71.4364i | 0.310593i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.60568 | −0.00692105 | ||||||||
\(233\) | 356.382i | 1.52954i | 0.644306 | + | 0.764768i | \(0.277146\pi\) | ||||
−0.644306 | + | 0.764768i | \(0.722854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 49.5701 | 0.210937 | ||||||||
\(236\) | − 243.474i | − 1.03167i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.2107 | 0.0681121 | ||||||||
\(239\) | − 175.524i | − 0.734408i | −0.930140 | − | 0.367204i | \(-0.880315\pi\) | ||||
0.930140 | − | 0.367204i | \(-0.119685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.438 | 0.433355 | 0.216677 | − | 0.976243i | \(-0.430478\pi\) | ||||
0.216677 | + | 0.976243i | \(0.430478\pi\) | |||||||
\(242\) | 70.3045i | 0.290515i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −160.658 | −0.658433 | ||||||||
\(245\) | 107.998i | 0.440809i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 137.947 | 0.558491 | ||||||||
\(248\) | − 182.228i | − 0.734791i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.18861 | 0.0367544 | ||||||||
\(251\) | 130.945i | 0.521694i | 0.965380 | + | 0.260847i | \(0.0840018\pi\) | ||||
−0.965380 | + | 0.260847i | \(0.915998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 558.658 | 2.20813 | ||||||||
\(254\) | − 129.878i | − 0.511331i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −75.2107 | −0.293792 | ||||||||
\(257\) | − 425.641i | − 1.65619i | −0.560587 | − | 0.828095i | \(-0.689425\pi\) | ||||
0.560587 | − | 0.828095i | \(-0.310575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.99145 | 0.0308550 | ||||||||
\(260\) | 162.144i | 0.623632i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 173.592 | 0.662566 | ||||||||
\(263\) | 74.5004i | 0.283271i | 0.989919 | + | 0.141636i | \(0.0452362\pi\) | ||||
−0.989919 | + | 0.141636i | \(0.954764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 109.570 | 0.413472 | ||||||||
\(266\) | 4.35437i | 0.0163698i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 256.982 | 0.958889 | ||||||||
\(269\) | 205.067i | 0.762331i | 0.924507 | + | 0.381165i | \(0.124477\pi\) | ||||
−0.924507 | + | 0.381165i | \(0.875523\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −233.351 | −0.861073 | −0.430537 | − | 0.902573i | \(-0.641676\pi\) | ||||
−0.430537 | + | 0.902573i | \(0.641676\pi\) | |||||||
\(272\) | 196.625i | 0.722886i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 56.9210 | 0.207741 | ||||||||
\(275\) | − 71.8582i | − 0.261302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −423.715 | −1.52966 | −0.764828 | − | 0.644235i | \(-0.777176\pi\) | ||||
−0.764828 | + | 0.644235i | \(0.777176\pi\) | |||||||
\(278\) | 131.367i | 0.472543i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.2762 | −0.0402720 | ||||||||
\(281\) | − 402.604i | − 1.43275i | −0.697713 | − | 0.716377i | \(-0.745799\pi\) | ||||
0.697713 | − | 0.716377i | \(-0.254201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −272.333 | −0.962308 | −0.481154 | − | 0.876636i | \(-0.659782\pi\) | ||||
−0.481154 | + | 0.876636i | \(0.659782\pi\) | |||||||
\(284\) | − 345.900i | − 1.21796i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −257.623 | −0.900779 | ||||||||
\(287\) | − 16.1704i | − 0.0563427i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −265.386 | −0.918290 | ||||||||
\(290\) | 0.490189i | 0.00169031i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 158.500 | 0.542807 | ||||||||
\(293\) | 443.188i | 1.51259i | 0.654232 | + | 0.756294i | \(0.272992\pi\) | ||||
−0.654232 | + | 0.756294i | \(0.727008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −163.759 | −0.555114 | ||||||||
\(296\) | − 57.4251i | − 0.194004i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.06976 | 0.0270797 | ||||||||
\(299\) | 847.858i | 2.83564i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4384 | 0.0546128 | ||||||||
\(302\) | − 173.123i | − 0.573255i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −52.8157 | −0.173736 | ||||||||
\(305\) | 108.057i | 0.354285i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −390.824 | −1.27304 | −0.636522 | − | 0.771259i | \(-0.719627\pi\) | ||||
−0.636522 | + | 0.771259i | \(0.719627\pi\) | |||||||
\(308\) | 40.0258i | 0.129954i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −55.6313 | −0.179456 | ||||||||
\(311\) | 2.97739i | 0.00957362i | 0.999989 | + | 0.00478681i | \(0.00152369\pi\) | ||||
−0.999989 | + | 0.00478681i | \(0.998476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 130.105 | 0.415672 | 0.207836 | − | 0.978164i | \(-0.433358\pi\) | ||||
0.207836 | + | 0.978164i | \(0.433358\pi\) | |||||||
\(314\) | − 173.638i | − 0.552988i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 226.799 | 0.717717 | ||||||||
\(317\) | − 131.677i | − 0.415384i | −0.978194 | − | 0.207692i | \(-0.933405\pi\) | ||||
0.978194 | − | 0.207692i | \(-0.0665953\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.83345 | 0.0120171 | ||||||||
\(320\) | − 17.8297i | − 0.0557177i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −26.7630 | −0.0831149 | ||||||||
\(323\) | − 148.914i | − 0.461035i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 109.057 | 0.335560 | ||||||||
\(326\) | 183.079i | 0.561591i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −116.197 | −0.354260 | ||||||||
\(329\) | 18.5710i | 0.0564468i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 160.483 | 0.484842 | 0.242421 | − | 0.970171i | \(-0.422059\pi\) | ||||
0.242421 | + | 0.970171i | \(0.422059\pi\) | |||||||
\(332\) | 93.7850i | 0.282485i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.4207 | 0.0820978 | ||||||||
\(335\) | − 172.844i | − 0.515952i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −128.114 | −0.380160 | −0.190080 | − | 0.981769i | \(-0.560875\pi\) | ||||
−0.190080 | + | 0.981769i | \(0.560875\pi\) | |||||||
\(338\) | − 252.093i | − 0.745837i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 175.035 | 0.514808 | ||||||||
\(341\) | 435.056i | 1.27583i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −81.5089 | −0.237635 | ||||||||
\(344\) | − 118.124i | − 0.343383i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.4997 | 0.0708082 | ||||||||
\(347\) | 219.637i | 0.632959i | 0.948599 | + | 0.316480i | \(0.102501\pi\) | ||||
−0.948599 | + | 0.316480i | \(0.897499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 403.465 | 1.15606 | 0.578030 | − | 0.816016i | \(-0.303822\pi\) | ||||
0.578030 | + | 0.816016i | \(0.303822\pi\) | |||||||
\(350\) | 3.44243i | 0.00983551i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 444.688 | 1.26332 | ||||||||
\(353\) | − 54.8192i | − 0.155295i | −0.996981 | − | 0.0776475i | \(-0.975259\pi\) | ||||
0.996981 | − | 0.0776475i | \(-0.0247409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −232.649 | −0.655350 | ||||||||
\(356\) | − 178.786i | − 0.502207i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 91.9167 | 0.256751 | ||||||||
\(359\) | − 480.460i | − 1.33833i | −0.743114 | − | 0.669165i | \(-0.766652\pi\) | ||||
0.743114 | − | 0.669165i | \(-0.233348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −321.000 | −0.889197 | ||||||||
\(362\) | 40.3358i | 0.111425i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −60.7459 | −0.166884 | ||||||||
\(365\) | − 106.606i | − 0.292070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 522.364 | 1.42333 | 0.711667 | − | 0.702517i | \(-0.247940\pi\) | ||||
0.711667 | + | 0.702517i | \(0.247940\pi\) | |||||||
\(368\) | − 324.618i | − 0.882114i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.5310 | −0.0473810 | ||||||||
\(371\) | 41.0494i | 0.110645i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −233.285 | −0.625428 | −0.312714 | − | 0.949847i | \(-0.601238\pi\) | ||||
−0.312714 | + | 0.949847i | \(0.601238\pi\) | |||||||
\(374\) | 278.104i | 0.743593i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 133.448 | 0.354914 | ||||||||
\(377\) | 5.81791i | 0.0154321i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 248.596 | 0.655927 | 0.327964 | − | 0.944690i | \(-0.393638\pi\) | ||||
0.327964 | + | 0.944690i | \(0.393638\pi\) | |||||||
\(380\) | 47.0163i | 0.123727i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 229.254 | 0.600142 | ||||||||
\(383\) | − 468.291i | − 1.22269i | −0.791364 | − | 0.611346i | \(-0.790628\pi\) | ||||
0.791364 | − | 0.611346i | \(-0.209372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.9210 | 0.0699247 | ||||||||
\(386\) | − 73.8803i | − 0.191400i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −382.061 | −0.984694 | ||||||||
\(389\) | − 484.238i | − 1.24483i | −0.782688 | − | 0.622414i | \(-0.786152\pi\) | ||||
0.782688 | − | 0.622414i | \(-0.213848\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 915.263 | 2.34083 | ||||||||
\(392\) | 290.742i | 0.741688i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −174.816 | −0.443695 | ||||||||
\(395\) | − 152.543i | − 0.386184i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −298.943 | −0.753005 | −0.376503 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376503 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(398\) | − 79.3016i | − 0.199250i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −41.7544 | −0.104386 | ||||||||
\(401\) | 467.509i | 1.16586i | 0.812523 | + | 0.582929i | \(0.198093\pi\) | ||||
−0.812523 | + | 0.582929i | \(0.801907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −660.272 | −1.63839 | ||||||||
\(404\) | 58.3370i | 0.144399i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.183645 | −0.000452327 0 | ||||||||
\(407\) | 137.098i | 0.336851i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −184.158 | −0.450264 | −0.225132 | − | 0.974328i | \(-0.572281\pi\) | ||||
−0.225132 | + | 0.974328i | \(0.572281\pi\) | |||||||
\(410\) | 35.4731i | 0.0865198i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −237.837 | −0.577274 | ||||||||
\(413\) | − 61.3507i | − 0.148549i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 63.0790 | 0.151998 | ||||||||
\(416\) | 674.890i | 1.62233i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −74.7018 | −0.178712 | ||||||||
\(419\) | 429.840i | 1.02587i | 0.858427 | + | 0.512936i | \(0.171442\pi\) | ||||
−0.858427 | + | 0.512936i | \(0.828558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −305.035 | −0.724548 | −0.362274 | − | 0.932072i | \(-0.618000\pi\) | ||||
−0.362274 | + | 0.932072i | \(0.618000\pi\) | |||||||
\(422\) | 54.0692i | 0.128126i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 294.974 | 0.695693 | ||||||||
\(425\) | − 117.727i | − 0.277005i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.4826 | −0.0948069 | ||||||||
\(428\) | 253.888i | 0.593196i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.0612 | −0.0838633 | ||||||||
\(431\) | 128.880i | 0.299025i | 0.988760 | + | 0.149512i | \(0.0477704\pi\) | ||||
−0.988760 | + | 0.149512i | \(0.952230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 243.886 | 0.563247 | 0.281624 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281624 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(434\) | − 20.8418i | − 0.0480225i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −421.956 | −0.967789 | ||||||||
\(437\) | 245.850i | 0.562585i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −259.614 | −0.591376 | −0.295688 | − | 0.955285i | \(-0.595549\pi\) | ||||
−0.295688 | + | 0.955285i | \(0.595549\pi\) | |||||||
\(440\) | − 193.449i | − 0.439658i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −422.070 | −0.954909 | ||||||||
\(443\) | − 541.011i | − 1.22124i | −0.791923 | − | 0.610622i | \(-0.790920\pi\) | ||||
0.791923 | − | 0.610622i | \(-0.209080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −120.250 | −0.270224 | ||||||||
\(446\) | − 84.0778i | − 0.188515i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.67972 | 0.0149101 | ||||||||
\(449\) | 791.947i | 1.76380i | 0.471436 | + | 0.881900i | \(0.343736\pi\) | ||||
−0.471436 | + | 0.881900i | \(0.656264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 277.412 | 0.615104 | ||||||||
\(452\) | 50.0682i | 0.110770i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.2975 | −0.0226818 | ||||||||
\(455\) | 40.8572i | 0.0897960i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 611.359 | 1.33777 | 0.668883 | − | 0.743367i | \(-0.266773\pi\) | ||||
0.668883 | + | 0.743367i | \(0.266773\pi\) | |||||||
\(458\) | − 19.1477i | − 0.0418073i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −288.974 | −0.628204 | ||||||||
\(461\) | − 586.991i | − 1.27330i | −0.771153 | − | 0.636650i | \(-0.780320\pi\) | ||||
0.771153 | − | 0.636650i | \(-0.219680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 195.285 | 0.421781 | 0.210891 | − | 0.977510i | \(-0.432364\pi\) | ||||
0.210891 | + | 0.977510i | \(0.432364\pi\) | |||||||
\(464\) | − 2.22749i | − 0.00480063i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 292.894 | 0.628528 | ||||||||
\(467\) | − 753.763i | − 1.61405i | −0.590515 | − | 0.807027i | \(-0.701075\pi\) | ||||
0.590515 | − | 0.807027i | \(-0.298925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 64.7544 | 0.138069 | ||||||||
\(470\) | − 40.7394i | − 0.0866796i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −440.855 | −0.934014 | ||||||||
\(473\) | 282.011i | 0.596218i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6228 | 0.0665743 | ||||||||
\(476\) | 65.5752i | 0.137763i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −144.255 | −0.301788 | ||||||||
\(479\) | − 614.848i | − 1.28361i | −0.766869 | − | 0.641803i | \(-0.778186\pi\) | ||||
0.766869 | − | 0.641803i | \(-0.221814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −208.070 | −0.432577 | ||||||||
\(482\) | − 85.8332i | − 0.178077i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −284.395 | −0.587593 | ||||||||
\(485\) | 256.971i | 0.529837i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 478.197 | 0.981924 | 0.490962 | − | 0.871181i | \(-0.336645\pi\) | ||||
0.490962 | + | 0.871181i | \(0.336645\pi\) | |||||||
\(488\) | 290.900i | 0.596107i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 88.7587 | 0.181140 | ||||||||
\(491\) | 617.223i | 1.25707i | 0.777780 | + | 0.628537i | \(0.216346\pi\) | ||||
−0.777780 | + | 0.628537i | \(0.783654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.28043 | 0.0127392 | ||||||||
\(494\) | − 113.373i | − 0.229499i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 252.797 | 0.509672 | ||||||||
\(497\) | − 87.1599i | − 0.175372i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 783.096 | 1.56933 | 0.784665 | − | 0.619919i | \(-0.212835\pi\) | ||||
0.784665 | + | 0.619919i | \(0.212835\pi\) | |||||||
\(500\) | 37.1697i | 0.0743393i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 107.618 | 0.214378 | ||||||||
\(503\) | − 369.395i | − 0.734383i | −0.930145 | − | 0.367191i | \(-0.880319\pi\) | ||||
0.930145 | − | 0.367191i | \(-0.119681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.2370 | 0.0776970 | ||||||||
\(506\) | − 459.135i | − 0.907382i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 525.381 | 1.03422 | ||||||||
\(509\) | − 225.635i | − 0.443291i | −0.975127 | − | 0.221645i | \(-0.928857\pi\) | ||||
0.975127 | − | 0.221645i | \(-0.0711427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.9388 | 0.0781581 | ||||||||
\(512\) | − 459.474i | − 0.897410i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −349.815 | −0.680574 | ||||||||
\(515\) | 159.967i | 0.310616i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −318.596 | −0.616241 | ||||||||
\(518\) | − 6.56781i | − 0.0126792i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 293.592 | 0.564600 | ||||||||
\(521\) | − 1007.73i | − 1.93422i | −0.254367 | − | 0.967108i | \(-0.581867\pi\) | ||||
0.254367 | − | 0.967108i | \(-0.418133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 935.517 | 1.78875 | 0.894376 | − | 0.447316i | \(-0.147620\pi\) | ||||
0.894376 | + | 0.447316i | \(0.147620\pi\) | |||||||
\(524\) | 702.213i | 1.34010i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 61.2285 | 0.116404 | ||||||||
\(527\) | 712.764i | 1.35249i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −982.052 | −1.85643 | ||||||||
\(530\) | − 90.0507i | − 0.169907i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.6142 | −0.0331095 | ||||||||
\(533\) | 421.020i | 0.789906i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 170.763 | 0.319183 | ||||||||
\(536\) | − 465.314i | − 0.868122i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 168.535 | 0.313263 | ||||||||
\(539\) | − 694.124i | − 1.28780i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −399.149 | −0.737798 | −0.368899 | − | 0.929469i | \(-0.620265\pi\) | ||||
−0.368899 | + | 0.929469i | \(0.620265\pi\) | |||||||
\(542\) | 191.780i | 0.353838i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 728.544 | 1.33923 | ||||||||
\(545\) | 283.804i | 0.520741i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 480.833 | 0.879036 | 0.439518 | − | 0.898234i | \(-0.355149\pi\) | ||||
0.439518 | + | 0.898234i | \(0.355149\pi\) | |||||||
\(548\) | 230.256i | 0.420175i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −59.0569 | −0.107376 | ||||||||
\(551\) | 1.68699i | 0.00306170i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 57.1488 | 0.103343 | ||||||||
\(554\) | 348.232i | 0.628577i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −531.404 | −0.955762 | ||||||||
\(557\) | 751.542i | 1.34927i | 0.738152 | + | 0.674634i | \(0.235699\pi\) | ||||
−0.738152 | + | 0.674634i | \(0.764301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −428.000 | −0.765653 | ||||||||
\(560\) | − 15.6429i | − 0.0279338i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −330.882 | −0.588758 | ||||||||
\(563\) | 670.820i | 1.19151i | 0.803166 | + | 0.595755i | \(0.203147\pi\) | ||||
−0.803166 | + | 0.595755i | \(0.796853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.6754 | 0.0596026 | ||||||||
\(566\) | 223.818i | 0.395438i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −626.315 | −1.10267 | ||||||||
\(569\) | − 275.325i | − 0.483875i | −0.970292 | − | 0.241937i | \(-0.922217\pi\) | ||||
0.970292 | − | 0.241937i | \(-0.0777829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −900.289 | −1.57669 | −0.788344 | − | 0.615235i | \(-0.789061\pi\) | ||||
−0.788344 | + | 0.615235i | \(0.789061\pi\) | |||||||
\(572\) | − 1042.13i | − 1.82191i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.2897 | −0.0231527 | ||||||||
\(575\) | 194.361i | 0.338020i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −596.236 | −1.03334 | −0.516669 | − | 0.856185i | \(-0.672828\pi\) | ||||
−0.516669 | + | 0.856185i | \(0.672828\pi\) | |||||||
\(578\) | 218.108i | 0.377350i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.98291 | −0.00341880 | ||||||||
\(581\) | 23.6320i | 0.0406746i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −704.228 | −1.20794 | ||||||||
\(584\) | − 286.993i | − 0.491426i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 364.236 | 0.621564 | ||||||||
\(587\) | − 497.431i | − 0.847412i | −0.905800 | − | 0.423706i | \(-0.860729\pi\) | ||||
0.905800 | − | 0.423706i | \(-0.139271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −191.456 | −0.325053 | ||||||||
\(590\) | 134.586i | 0.228112i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 79.6633 | 0.134566 | ||||||||
\(593\) | 898.856i | 1.51578i | 0.652384 | + | 0.757889i | \(0.273769\pi\) | ||||
−0.652384 | + | 0.757889i | \(0.726231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.1053 | 0.0741266 | ||||||||
\(596\) | 32.6437i | 0.0547713i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 696.816 | 1.16524 | ||||||||
\(599\) | − 28.5701i | − 0.0476964i | −0.999716 | − | 0.0238482i | \(-0.992408\pi\) | ||||
0.999716 | − | 0.0238482i | \(-0.00759183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2107 | −0.0336284 | −0.0168142 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168142 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(602\) | − 13.5100i | − 0.0224419i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 700.315 | 1.15946 | ||||||||
\(605\) | 191.282i | 0.316168i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −713.626 | −1.17566 | −0.587831 | − | 0.808984i | \(-0.700018\pi\) | ||||
−0.587831 | + | 0.808984i | \(0.700018\pi\) | |||||||
\(608\) | 195.695i | 0.321867i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 88.8071 | 0.145585 | ||||||||
\(611\) | − 483.524i | − 0.791365i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −76.1530 | −0.124230 | −0.0621150 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621150 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(614\) | 321.201i | 0.523128i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 72.4740 | 0.117653 | ||||||||
\(617\) | − 201.599i | − 0.326741i | −0.986565 | − | 0.163371i | \(-0.947763\pi\) | ||||
0.986565 | − | 0.163371i | \(-0.0522367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −204.263 | −0.329989 | −0.164995 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164995 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(620\) | − 225.039i | − 0.362966i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.44699 | 0.00393406 | ||||||||
\(623\) | − 45.0505i | − 0.0723122i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 106.928i | − 0.170811i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 702.399 | 1.11847 | ||||||||
\(629\) | 224.611i | 0.357093i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −639.903 | −1.01411 | −0.507055 | − | 0.861914i | \(-0.669266\pi\) | ||||
−0.507055 | + | 0.861914i | \(0.669266\pi\) | |||||||
\(632\) | − 410.660i | − 0.649779i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −108.219 | −0.170693 | ||||||||
\(635\) | − 353.367i | − 0.556484i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1053.45 | 1.65377 | ||||||||
\(638\) | − 3.15054i | − 0.00493815i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −291.408 | −0.455325 | ||||||||
\(641\) | 570.709i | 0.890342i | 0.895446 | + | 0.445171i | \(0.146857\pi\) | ||||
−0.895446 | + | 0.445171i | \(0.853143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 453.693 | 0.705587 | 0.352794 | − | 0.935701i | \(-0.385232\pi\) | ||||
0.352794 | + | 0.935701i | \(0.385232\pi\) | |||||||
\(644\) | − 108.261i | − 0.168108i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −122.386 | −0.189452 | ||||||||
\(647\) | 983.536i | 1.52015i | 0.649837 | + | 0.760074i | \(0.274837\pi\) | ||||
−0.649837 | + | 0.760074i | \(0.725163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1052.51 | 1.62174 | ||||||||
\(650\) | − 89.6289i | − 0.137891i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −740.588 | −1.13587 | ||||||||
\(653\) | − 544.478i | − 0.833811i | −0.908950 | − | 0.416905i | \(-0.863115\pi\) | ||||
0.908950 | − | 0.416905i | \(-0.136885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 472.302 | 0.721073 | ||||||||
\(656\) | − 161.195i | − 0.245724i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.2626 | 0.0231955 | ||||||||
\(659\) | 107.933i | 0.163783i | 0.996641 | + | 0.0818916i | \(0.0260961\pi\) | ||||
−0.996641 | + | 0.0818916i | \(0.973904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 345.728 | 0.523038 | 0.261519 | − | 0.965198i | \(-0.415777\pi\) | ||||
0.261519 | + | 0.965198i | \(0.415777\pi\) | |||||||
\(662\) | − 131.893i | − 0.199235i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 169.815 | 0.255745 | ||||||||
\(665\) | 11.8472i | 0.0178153i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3687 | −0.0155452 | ||||||||
\(668\) | 110.922i | 0.166050i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −142.053 | −0.212019 | ||||||||
\(671\) | − 694.503i | − 1.03503i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1204.78 | −1.79016 | −0.895082 | − | 0.445902i | \(-0.852883\pi\) | ||||
−0.895082 | + | 0.445902i | \(0.852883\pi\) | |||||||
\(674\) | 105.291i | 0.156218i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1019.76 | 1.50853 | ||||||||
\(677\) | − 574.598i | − 0.848742i | −0.905488 | − | 0.424371i | \(-0.860495\pi\) | ||||
0.905488 | − | 0.424371i | \(-0.139505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −96.2719 | −0.141785 | ||||||||
\(680\) | − 316.933i | − 0.466078i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 357.553 | 0.524271 | ||||||||
\(683\) | − 334.387i | − 0.489585i | −0.969575 | − | 0.244792i | \(-0.921280\pi\) | ||||
0.969575 | − | 0.244792i | \(-0.0787198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 154.868 | 0.226085 | ||||||||
\(686\) | 66.9884i | 0.0976508i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 163.868 | 0.238180 | ||||||||
\(689\) | − 1068.79i | − 1.55121i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 901.149 | 1.30412 | 0.652061 | − | 0.758166i | \(-0.273904\pi\) | ||||
0.652061 | + | 0.758166i | \(0.273904\pi\) | |||||||
\(692\) | 99.1057i | 0.143216i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 180.510 | 0.260100 | ||||||||
\(695\) | 357.418i | 0.514270i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 454.491 | 0.652068 | ||||||||
\(698\) | − 331.589i | − 0.475056i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.9253 | −0.0198932 | ||||||||
\(701\) | 887.934i | 1.26667i | 0.773879 | + | 0.633334i | \(0.218314\pi\) | ||||
−0.773879 | + | 0.633334i | \(0.781686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.3331 | −0.0858223 | ||||||||
\(704\) | 114.595i | 0.162776i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.0534 | −0.0638150 | ||||||||
\(707\) | 14.6998i | 0.0207918i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1026.35 | −1.44760 | −0.723801 | − | 0.690008i | \(-0.757607\pi\) | ||||
−0.723801 | + | 0.690008i | \(0.757607\pi\) | |||||||
\(710\) | 191.204i | 0.269301i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −323.725 | −0.454669 | ||||||||
\(713\) | − 1176.74i | − 1.65040i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −700.930 | −0.980321 | ||||||||
\(716\) | 371.820i | 0.519302i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −394.868 | −0.549956 | ||||||||
\(719\) | 740.080i | 1.02932i | 0.857395 | + | 0.514659i | \(0.172081\pi\) | ||||
−0.857395 | + | 0.514659i | \(0.827919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.9302 | −0.0831210 | ||||||||
\(722\) | 263.815i | 0.365395i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −163.166 | −0.225367 | ||||||||
\(725\) | 1.33369i | 0.00183957i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1063.75 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238773\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238773\pi\) | |||||||
\(728\) | 109.992i | 0.151087i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −87.6142 | −0.120019 | ||||||||
\(731\) | 462.026i | 0.632047i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 134.749 | 0.183833 | 0.0919164 | − | 0.995767i | \(-0.470701\pi\) | ||||
0.0919164 | + | 0.995767i | \(0.470701\pi\) | |||||||
\(734\) | − 429.307i | − 0.584887i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1202.79 | −1.63422 | ||||||||
\(737\) | 1110.90i | 1.50733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −711.429 | −0.962692 | −0.481346 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481346 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(740\) | − 70.9160i | − 0.0958324i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33.7367 | 0.0454672 | ||||||||
\(743\) | − 466.330i | − 0.627631i | −0.949484 | − | 0.313816i | \(-0.898393\pi\) | ||||
0.949484 | − | 0.313816i | \(-0.101607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.9559 | 0.0294710 | ||||||||
\(746\) | 191.726i | 0.257005i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1124.98 | −1.50399 | ||||||||
\(749\) | 63.9748i | 0.0854136i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 227.359 | 0.302742 | 0.151371 | − | 0.988477i | \(-0.451631\pi\) | ||||
0.151371 | + | 0.988477i | \(0.451631\pi\) | |||||||
\(752\) | 185.126i | 0.246178i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.78147 | 0.00634148 | ||||||||
\(755\) | − 471.026i | − 0.623875i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −552.258 | −0.729535 | −0.364768 | − | 0.931099i | \(-0.618852\pi\) | ||||
−0.364768 | + | 0.931099i | \(0.618852\pi\) | |||||||
\(758\) | − 204.310i | − 0.269538i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 85.1317 | 0.112015 | ||||||||
\(761\) | 303.051i | 0.398228i | 0.979976 | + | 0.199114i | \(0.0638064\pi\) | ||||
−0.979976 | + | 0.199114i | \(0.936194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −106.325 | −0.139351 | ||||||||
\(764\) | 927.376i | 1.21384i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −384.867 | −0.502437 | ||||||||
\(767\) | 1597.36i | 2.08261i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 739.684 | 0.961878 | 0.480939 | − | 0.876754i | \(-0.340296\pi\) | ||||
0.480939 | + | 0.876754i | \(0.340296\pi\) | |||||||
\(770\) | − 22.1251i | − 0.0287339i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 298.860 | 0.387124 | ||||||||
\(773\) | − 603.479i | − 0.780697i | −0.920667 | − | 0.390348i | \(-0.872355\pi\) | ||||
0.920667 | − | 0.390348i | \(-0.127645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −151.359 | −0.195302 | ||||||||
\(776\) | 691.792i | 0.891485i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −397.973 | −0.511533 | ||||||||
\(779\) | 122.081i | 0.156715i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1495.28 | 1.91457 | ||||||||
\(782\) | − 752.213i | − 0.961909i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −403.333 | −0.514455 | ||||||||
\(785\) | − 472.428i | − 0.601819i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −660.483 | −0.839241 | −0.419620 | − | 0.907700i | \(-0.637837\pi\) | ||||
−0.419620 | + | 0.907700i | \(0.637837\pi\) | |||||||
\(788\) | − 707.162i | − 0.897414i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −125.368 | −0.158694 | ||||||||
\(791\) | 12.6162i | 0.0159497i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1054.03 | 1.32916 | ||||||||
\(794\) | 245.688i | 0.309430i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 320.790 | 0.403003 | ||||||||
\(797\) | − 634.969i | − 0.796699i | −0.917234 | − | 0.398349i | \(-0.869583\pi\) | ||||
0.917234 | − | 0.398349i | \(-0.130417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −521.964 | −0.653272 | ||||||||
\(800\) | 154.710i | 0.193388i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 384.224 | 0.479083 | ||||||||
\(803\) | 685.174i | 0.853268i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −72.8157 | −0.0904542 | ||||||||
\(806\) | 542.647i | 0.673260i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 105.630 | 0.130730 | ||||||||
\(809\) | − 405.048i | − 0.500677i | −0.968158 | − | 0.250339i | \(-0.919458\pi\) | ||||
0.968158 | − | 0.250339i | \(-0.0805419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 406.034 | 0.500659 | 0.250329 | − | 0.968161i | \(-0.419461\pi\) | ||||
0.250329 | + | 0.968161i | \(0.419461\pi\) | |||||||
\(812\) | − 0.742878i | 0 0.000914874i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 112.675 | 0.138421 | ||||||||
\(815\) | 498.113i | 0.611182i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −124.105 | −0.151904 | ||||||||
\(818\) | 151.351i | 0.185026i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −143.495 | −0.174994 | ||||||||
\(821\) | − 550.073i | − 0.670003i | −0.942218 | − | 0.335002i | \(-0.891263\pi\) | ||||
0.942218 | − | 0.335002i | \(-0.108737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1472.51 | −1.78920 | −0.894600 | − | 0.446868i | \(-0.852540\pi\) | ||||
−0.894600 | + | 0.446868i | \(0.852540\pi\) | |||||||
\(824\) | 430.648i | 0.522631i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −50.4213 | −0.0610428 | ||||||||
\(827\) | − 1510.47i | − 1.82644i | −0.407466 | − | 0.913220i | \(-0.633587\pi\) | ||||
0.407466 | − | 0.913220i | \(-0.366413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 712.692 | 0.859701 | 0.429850 | − | 0.902900i | \(-0.358566\pi\) | ||||
0.429850 | + | 0.902900i | \(0.358566\pi\) | |||||||
\(830\) | − 51.8418i | − 0.0624599i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −173.917 | −0.209035 | ||||||||
\(833\) | − 1137.20i | − 1.36519i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.6050 | 0.0893473 | ||||||||
\(836\) | − 302.183i | − 0.361463i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 353.266 | 0.421559 | ||||||||
\(839\) | − 530.579i | − 0.632394i | −0.948694 | − | 0.316197i | \(-0.897594\pi\) | ||||
0.948694 | − | 0.316197i | \(-0.102406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.929 | 0.999915 | ||||||||
\(842\) | 250.694i | 0.297737i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −218.720 | −0.259147 | ||||||||
\(845\) | − 685.884i | − 0.811697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −71.6619 | −0.0846068 | ||||||||
\(848\) | 409.204i | 0.482552i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −96.7544 | −0.113829 | ||||||||
\(851\) | − 370.822i | − 0.435748i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 215.232 | 0.252324 | 0.126162 | − | 0.992010i | \(-0.459734\pi\) | ||||
0.126162 | + | 0.992010i | \(0.459734\pi\) | |||||||
\(854\) | 33.2708i | 0.0389587i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 459.711 | 0.537046 | ||||||||
\(857\) | 4.97441i | 0.00580445i | 0.999996 | + | 0.00290222i | \(0.000923808\pi\) | ||||
−0.999996 | + | 0.00290222i | \(0.999076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1652.28 | 1.92349 | 0.961746 | − | 0.273941i | \(-0.0883273\pi\) | ||||
0.961746 | + | 0.273941i | \(0.0883273\pi\) | |||||||
\(860\) | − 145.874i | − 0.169621i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 105.920 | 0.122877 | ||||||||
\(863\) | 379.077i | 0.439255i | 0.975584 | + | 0.219627i | \(0.0704841\pi\) | ||||
−0.975584 | + | 0.219627i | \(0.929516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.6577 | 0.0770609 | ||||||||
\(866\) | − 200.439i | − 0.231454i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 84.3088 | 0.0971300 | ||||||||
\(869\) | 980.421i | 1.12822i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1685.98 | −1.93568 | ||||||||
\(872\) | 764.029i | 0.876180i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 202.053 | 0.231182 | ||||||||
\(875\) | 9.36602i | 0.0107040i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1101.60 | 1.25610 | 0.628051 | − | 0.778173i | \(-0.283853\pi\) | ||||
0.628051 | + | 0.778173i | \(0.283853\pi\) | |||||||
\(878\) | 213.365i | 0.243013i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 268.364 | 0.304959 | ||||||||
\(881\) | 184.877i | 0.209850i | 0.994480 | + | 0.104925i | \(0.0334602\pi\) | ||||
−0.994480 | + | 0.104925i | \(0.966540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 978.236 | 1.10786 | 0.553928 | − | 0.832565i | \(-0.313128\pi\) | ||||
0.553928 | + | 0.832565i | \(0.313128\pi\) | |||||||
\(884\) | − 1707.35i | − 1.93139i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −444.632 | −0.501842 | ||||||||
\(887\) | − 667.937i | − 0.753029i | −0.926411 | − | 0.376514i | \(-0.877123\pi\) | ||||
0.926411 | − | 0.376514i | \(-0.122877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 132.386 | 0.148915 | ||||||||
\(890\) | 98.8279i | 0.111043i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 340.110 | 0.381290 | ||||||||
\(893\) | − 140.205i | − 0.157005i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 250.083 | 0.279423 | ||||||||
\(896\) | − 109.173i | − 0.121845i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 650.865 | 0.724794 | ||||||||
\(899\) | − 8.07464i | − 0.00898180i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1153.75 | −1.28053 | ||||||||
\(902\) | − 227.992i | − 0.252763i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 90.6577 | 0.100285 | ||||||||
\(905\) | 109.744i | 0.121264i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −832.622 | −0.917996 | −0.458998 | − | 0.888437i | \(-0.651791\pi\) | ||||
−0.458998 | + | 0.888437i | \(0.651791\pi\) | |||||||
\(908\) | − 41.6554i | − 0.0458760i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 33.5787 | 0.0368996 | ||||||||
\(911\) | 565.263i | 0.620486i | 0.950657 | + | 0.310243i | \(0.100410\pi\) | ||||
−0.950657 | + | 0.310243i | \(0.899590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −405.421 | −0.444053 | ||||||||
\(914\) | − 502.448i | − 0.549725i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 77.4562 | 0.0845592 | ||||||||
\(917\) | 176.944i | 0.192959i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1185.75 | −1.29026 | −0.645128 | − | 0.764075i | \(-0.723196\pi\) | ||||
−0.645128 | + | 0.764075i | \(0.723196\pi\) | |||||||
\(920\) | 523.240i | 0.568739i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −482.421 | −0.523234 | ||||||||
\(923\) | 2269.34i | 2.45866i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.6975 | −0.0515649 | ||||||||
\(926\) | − 160.496i | − 0.173321i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.25341 | −0.00889376 | ||||||||
\(929\) | 942.995i | 1.01506i | 0.861633 | + | 0.507532i | \(0.169442\pi\) | ||||
−0.861633 | + | 0.507532i | \(0.830558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 305.465 | 0.328104 | ||||||||
\(932\) | 1184.81i | 1.27126i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −619.483 | −0.663258 | ||||||||
\(935\) | 756.654i | 0.809255i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −531.281 | −0.567002 | −0.283501 | − | 0.958972i | \(-0.591496\pi\) | ||||
−0.283501 | + | 0.958972i | \(0.591496\pi\) | |||||||
\(938\) | − 53.2187i | − 0.0567364i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 164.799 | 0.175318 | ||||||||
\(941\) | − 595.650i | − 0.632996i | −0.948593 | − | 0.316498i | \(-0.897493\pi\) | ||||
0.948593 | − | 0.316498i | \(-0.102507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −750.342 | −0.795696 | ||||||||
\(944\) | − 611.578i | − 0.647859i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 231.772 | 0.245002 | ||||||||
\(947\) | − 782.246i | − 0.826026i | −0.910725 | − | 0.413013i | \(-0.864476\pi\) | ||||
0.910725 | − | 0.413013i | \(-0.135524\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1039.87 | −1.09575 | ||||||||
\(950\) | − 25.9893i | − 0.0273572i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 118.736 | 0.124723 | ||||||||
\(953\) | 426.708i | 0.447752i | 0.974618 | + | 0.223876i | \(0.0718711\pi\) | ||||
−0.974618 | + | 0.223876i | \(0.928129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 623.745 | 0.653136 | ||||||||
\(956\) | − 583.538i | − 0.610395i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −505.315 | −0.527469 | ||||||||
\(959\) | 58.0200i | 0.0605005i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.6128 | −0.0464234 | ||||||||
\(962\) | 171.003i | 0.177758i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 347.211 | 0.360178 | ||||||||
\(965\) | − 201.011i | − 0.208301i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1210.91 | −1.25223 | −0.626116 | − | 0.779730i | \(-0.715356\pi\) | ||||
−0.626116 | + | 0.779730i | \(0.715356\pi\) | |||||||
\(968\) | 514.949i | 0.531973i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 211.193 | 0.217725 | ||||||||
\(971\) | − 1193.69i | − 1.22934i | −0.788784 | − | 0.614670i | \(-0.789289\pi\) | ||||
0.788784 | − | 0.614670i | \(-0.210711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −133.903 | −0.137619 | ||||||||
\(974\) | − 393.008i | − 0.403499i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −403.553 | −0.413476 | ||||||||
\(977\) | 909.475i | 0.930886i | 0.885078 | + | 0.465443i | \(0.154105\pi\) | ||||
−0.885078 | + | 0.465443i | \(0.845895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 772.868 | 0.789447 | ||||||||
\(980\) | 359.046i | 0.366373i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 507.268 | 0.516566 | ||||||||
\(983\) | 1560.88i | 1.58788i | 0.607999 | + | 0.793938i | \(0.291972\pi\) | ||||
−0.607999 | + | 0.793938i | \(0.708028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −475.631 | −0.482874 | ||||||||
\(986\) | − 5.16160i | − 0.00523489i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 458.614 | 0.464184 | ||||||||
\(989\) | − 762.782i | − 0.771265i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1692.63 | −1.70800 | −0.854001 | − | 0.520271i | \(-0.825831\pi\) | ||||
−0.854001 | + | 0.520271i | \(0.825831\pi\) | |||||||
\(992\) | − 936.675i | − 0.944229i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −71.6327 | −0.0720651 | ||||||||
\(995\) | − 215.761i | − 0.216845i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.5744 | 0.0166243 | 0.00831213 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831213 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(998\) | − 643.591i | − 0.644881i | ||||||||
\(999\) | 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 | 45.3.c.a.26.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 45.3.c.a.26.3 | yes | 4 | |
4.3 | odd | 2 | 720.3.l.a.161.2 | 4 | |||
5.2 | odd | 4 | 225.3.d.b.224.6 | 8 | |||
5.3 | odd | 4 | 225.3.d.b.224.3 | 8 | |||
5.4 | even | 2 | 225.3.c.c.26.3 | 4 | |||
8.3 | odd | 2 | 2880.3.l.c.1601.4 | 4 | |||
8.5 | even | 2 | 2880.3.l.g.1601.3 | 4 | |||
9.2 | odd | 6 | 405.3.i.d.296.3 | 8 | |||
9.4 | even | 3 | 405.3.i.d.26.3 | 8 | |||
9.5 | odd | 6 | 405.3.i.d.26.2 | 8 | |||
9.7 | even | 3 | 405.3.i.d.296.2 | 8 | |||
12.11 | even | 2 | 720.3.l.a.161.4 | 4 | |||
15.2 | even | 4 | 225.3.d.b.224.4 | 8 | |||
15.8 | even | 4 | 225.3.d.b.224.5 | 8 | |||
15.14 | odd | 2 | 225.3.c.c.26.2 | 4 | |||
20.3 | even | 4 | 3600.3.c.i.449.5 | 8 | |||
20.7 | even | 4 | 3600.3.c.i.449.3 | 8 | |||
20.19 | odd | 2 | 3600.3.l.v.1601.1 | 4 | |||
24.5 | odd | 2 | 2880.3.l.g.1601.1 | 4 | |||
24.11 | even | 2 | 2880.3.l.c.1601.2 | 4 | |||
60.23 | odd | 4 | 3600.3.c.i.449.6 | 8 | |||
60.47 | odd | 4 | 3600.3.c.i.449.4 | 8 | |||
60.59 | even | 2 | 3600.3.l.v.1601.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.c.a.26.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
45.3.c.a.26.3 | yes | 4 | 3.2 | odd | 2 | inner | |
225.3.c.c.26.2 | 4 | 15.14 | odd | 2 | |||
225.3.c.c.26.3 | 4 | 5.4 | even | 2 | |||
225.3.d.b.224.3 | 8 | 5.3 | odd | 4 | |||
225.3.d.b.224.4 | 8 | 15.2 | even | 4 | |||
225.3.d.b.224.5 | 8 | 15.8 | even | 4 | |||
225.3.d.b.224.6 | 8 | 5.2 | odd | 4 | |||
405.3.i.d.26.2 | 8 | 9.5 | odd | 6 | |||
405.3.i.d.26.3 | 8 | 9.4 | even | 3 | |||
405.3.i.d.296.2 | 8 | 9.7 | even | 3 | |||
405.3.i.d.296.3 | 8 | 9.2 | odd | 6 | |||
720.3.l.a.161.2 | 4 | 4.3 | odd | 2 | |||
720.3.l.a.161.4 | 4 | 12.11 | even | 2 | |||
2880.3.l.c.1601.2 | 4 | 24.11 | even | 2 | |||
2880.3.l.c.1601.4 | 4 | 8.3 | odd | 2 | |||
2880.3.l.g.1601.1 | 4 | 24.5 | odd | 2 | |||
2880.3.l.g.1601.3 | 4 | 8.5 | even | 2 | |||
3600.3.c.i.449.3 | 8 | 20.7 | even | 4 | |||
3600.3.c.i.449.4 | 8 | 60.47 | odd | 4 | |||
3600.3.c.i.449.5 | 8 | 20.3 | even | 4 | |||
3600.3.c.i.449.6 | 8 | 60.23 | odd | 4 | |||
3600.3.l.v.1601.1 | 4 | 20.19 | odd | 2 | |||
3600.3.l.v.1601.2 | 4 | 60.59 | even | 2 |