Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.586186\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.586186 | −0.414496 | −0.207248 | − | 0.978288i | \(-0.566451\pi\) | ||||
−0.207248 | + | 0.978288i | \(0.566451\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.65639 | −0.828193 | ||||||||
\(5\) | 0.842866 | 0.376941 | 0.188471 | − | 0.982079i | \(-0.439647\pi\) | ||||
0.188471 | + | 0.982079i | \(0.439647\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23837 | 0.468058 | 0.234029 | − | 0.972230i | \(-0.424809\pi\) | ||||
0.234029 | + | 0.972230i | \(0.424809\pi\) | |||||||
\(8\) | 2.14332 | 0.757779 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.494076 | −0.156241 | ||||||||
\(11\) | −1.47020 | −0.443283 | −0.221641 | − | 0.975128i | \(-0.571141\pi\) | ||||
−0.221641 | + | 0.975128i | \(0.571141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.26028 | −0.904238 | −0.452119 | − | 0.891958i | \(-0.649332\pi\) | ||||
−0.452119 | + | 0.891958i | \(0.649332\pi\) | |||||||
\(14\) | −0.725912 | −0.194008 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.05639 | 0.514097 | ||||||||
\(17\) | 4.93493 | 1.19690 | 0.598448 | − | 0.801161i | \(-0.295784\pi\) | ||||
0.598448 | + | 0.801161i | \(0.295784\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.260886 | 0.0598514 | 0.0299257 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299257 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(20\) | −1.39611 | −0.312180 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.861812 | 0.183739 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.28958 | −0.857915 | ||||||||
\(26\) | 1.91113 | 0.374803 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.05121 | −0.387643 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.101716 | −0.0182688 | −0.00913438 | − | 0.999958i | \(-0.502908\pi\) | ||||
−0.00913438 | + | 0.999958i | \(0.502908\pi\) | |||||||
\(32\) | −5.49207 | −0.970870 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.89279 | −0.496109 | ||||||||
\(35\) | 1.04378 | 0.176430 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.33423 | −0.548144 | −0.274072 | − | 0.961709i | \(-0.588371\pi\) | ||||
−0.274072 | + | 0.961709i | \(0.588371\pi\) | |||||||
\(38\) | −0.152928 | −0.0248082 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.80653 | 0.285638 | ||||||||
\(41\) | 0.732484 | 0.114395 | 0.0571974 | − | 0.998363i | \(-0.481784\pi\) | ||||
0.0571974 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.01063 | −0.764114 | −0.382057 | − | 0.924139i | \(-0.624784\pi\) | ||||
−0.382057 | + | 0.924139i | \(0.624784\pi\) | |||||||
\(44\) | 2.43522 | 0.367124 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.586186 | 0.0864284 | ||||||||
\(47\) | 8.71377 | 1.27103 | 0.635517 | − | 0.772087i | \(-0.280787\pi\) | ||||
0.635517 | + | 0.772087i | \(0.280787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.46645 | −0.780922 | ||||||||
\(50\) | 2.51449 | 0.355602 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.40027 | 0.748883 | ||||||||
\(53\) | 4.24097 | 0.582541 | 0.291271 | − | 0.956641i | \(-0.405922\pi\) | ||||
0.291271 | + | 0.956641i | \(0.405922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23918 | −0.167091 | ||||||||
\(56\) | 2.65422 | 0.354685 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.586186 | −0.0769700 | ||||||||
\(59\) | −8.76778 | −1.14147 | −0.570734 | − | 0.821135i | \(-0.693341\pi\) | ||||
−0.570734 | + | 0.821135i | \(0.693341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.88602 | −0.241481 | −0.120740 | − | 0.992684i | \(-0.538527\pi\) | ||||
−0.120740 | + | 0.992684i | \(0.538527\pi\) | |||||||
\(62\) | 0.0596245 | 0.00757232 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.893403 | −0.111675 | ||||||||
\(65\) | −2.74797 | −0.340844 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.21685 | −0.393001 | −0.196500 | − | 0.980504i | \(-0.562958\pi\) | ||||
−0.196500 | + | 0.980504i | \(0.562958\pi\) | |||||||
\(68\) | −8.17415 | −0.991262 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.611847 | −0.0731297 | ||||||||
\(71\) | 1.72395 | 0.204595 | 0.102297 | − | 0.994754i | \(-0.467381\pi\) | ||||
0.102297 | + | 0.994754i | \(0.467381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.64612 | −0.309705 | −0.154852 | − | 0.987938i | \(-0.549490\pi\) | ||||
−0.154852 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(74\) | 1.95448 | 0.227203 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.432129 | −0.0495685 | ||||||||
\(77\) | −1.82065 | −0.207482 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.465342 | 0.0523551 | 0.0261775 | − | 0.999657i | \(-0.491666\pi\) | ||||
0.0261775 | + | 0.999657i | \(0.491666\pi\) | |||||||
\(80\) | 1.73326 | 0.193784 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.429372 | −0.0474162 | ||||||||
\(83\) | 8.34128 | 0.915575 | 0.457787 | − | 0.889062i | \(-0.348642\pi\) | ||||
0.457787 | + | 0.889062i | \(0.348642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.15949 | 0.451160 | ||||||||
\(86\) | 2.93716 | 0.316722 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.15112 | −0.335910 | ||||||||
\(89\) | 5.13593 | 0.544408 | 0.272204 | − | 0.962240i | \(-0.412247\pi\) | ||||
0.272204 | + | 0.962240i | \(0.412247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.03741 | −0.423236 | ||||||||
\(92\) | 1.65639 | 0.172690 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.10789 | −0.526838 | ||||||||
\(95\) | 0.219892 | 0.0225605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.87730 | −0.698284 | −0.349142 | − | 0.937070i | \(-0.613527\pi\) | ||||
−0.349142 | + | 0.937070i | \(0.613527\pi\) | |||||||
\(98\) | 3.20436 | 0.323689 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.10520 | 0.710520 | ||||||||
\(101\) | 15.4552 | 1.53785 | 0.768923 | − | 0.639342i | \(-0.220793\pi\) | ||||
0.768923 | + | 0.639342i | \(0.220793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.59885 | 0.945803 | 0.472901 | − | 0.881115i | \(-0.343207\pi\) | ||||
0.472901 | + | 0.881115i | \(0.343207\pi\) | |||||||
\(104\) | −6.98782 | −0.685212 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.48599 | −0.241461 | ||||||||
\(107\) | −18.4638 | −1.78496 | −0.892480 | − | 0.451088i | \(-0.851036\pi\) | ||||
−0.892480 | + | 0.451088i | \(0.851036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.6145 | −1.30403 | −0.652017 | − | 0.758204i | \(-0.726077\pi\) | ||||
−0.652017 | + | 0.758204i | \(0.726077\pi\) | |||||||
\(110\) | 0.726391 | 0.0692587 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.54656 | 0.240627 | ||||||||
\(113\) | 9.49007 | 0.892750 | 0.446375 | − | 0.894846i | \(-0.352715\pi\) | ||||
0.446375 | + | 0.894846i | \(0.352715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.842866 | −0.0785976 | ||||||||
\(116\) | −1.65639 | −0.153792 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.13955 | 0.473134 | ||||||||
\(119\) | 6.11125 | 0.560217 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.83851 | −0.803501 | ||||||||
\(122\) | 1.10556 | 0.100093 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.168481 | 0.0151301 | ||||||||
\(125\) | −7.82987 | −0.700325 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1350 | 1.69796 | 0.848980 | − | 0.528426i | \(-0.177217\pi\) | ||||
0.848980 | + | 0.528426i | \(0.177217\pi\) | |||||||
\(128\) | 11.5078 | 1.01716 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.61082 | 0.141279 | ||||||||
\(131\) | −14.4038 | −1.25846 | −0.629232 | − | 0.777218i | \(-0.716630\pi\) | ||||
−0.629232 | + | 0.777218i | \(0.716630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.323073 | 0.0280140 | ||||||||
\(134\) | 1.88567 | 0.162897 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.5771 | 0.906983 | ||||||||
\(137\) | −10.9664 | −0.936922 | −0.468461 | − | 0.883484i | \(-0.655191\pi\) | ||||
−0.468461 | + | 0.883484i | \(0.655191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7820 | −0.914519 | −0.457259 | − | 0.889333i | \(-0.651169\pi\) | ||||
−0.457259 | + | 0.889333i | \(0.651169\pi\) | |||||||
\(140\) | −1.72890 | −0.146118 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.01055 | −0.0848038 | ||||||||
\(143\) | 4.79326 | 0.400833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.842866 | 0.0699962 | ||||||||
\(146\) | 1.55112 | 0.128371 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.52277 | 0.453969 | ||||||||
\(149\) | 14.9598 | 1.22555 | 0.612776 | − | 0.790257i | \(-0.290053\pi\) | ||||
0.612776 | + | 0.790257i | \(0.290053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.51476 | −0.367406 | −0.183703 | − | 0.982982i | \(-0.558808\pi\) | ||||
−0.183703 | + | 0.982982i | \(0.558808\pi\) | |||||||
\(152\) | 0.559163 | 0.0453541 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.06724 | 0.0860005 | ||||||||
\(155\) | −0.0857330 | −0.00688624 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2289 | −1.29521 | −0.647604 | − | 0.761977i | \(-0.724229\pi\) | ||||
−0.647604 | + | 0.761977i | \(0.724229\pi\) | |||||||
\(158\) | −0.272777 | −0.0217010 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.62908 | −0.365961 | ||||||||
\(161\) | −1.23837 | −0.0975969 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.54577 | −0.199400 | −0.0997001 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0997001 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(164\) | −1.21328 | −0.0947410 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.88954 | −0.379502 | ||||||||
\(167\) | −19.0688 | −1.47559 | −0.737794 | − | 0.675026i | \(-0.764132\pi\) | ||||
−0.737794 | + | 0.675026i | \(0.764132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.37061 | −0.182354 | ||||||||
\(170\) | −2.43823 | −0.187004 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.29954 | 0.632834 | ||||||||
\(173\) | 9.37891 | 0.713065 | 0.356533 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356533 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.31207 | −0.401554 | ||||||||
\(176\) | −3.02331 | −0.227890 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.01061 | −0.225655 | ||||||||
\(179\) | −4.33101 | −0.323715 | −0.161857 | − | 0.986814i | \(-0.551748\pi\) | ||||
−0.161857 | + | 0.986814i | \(0.551748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4714 | 1.52163 | 0.760813 | − | 0.648971i | \(-0.224801\pi\) | ||||
0.760813 | + | 0.648971i | \(0.224801\pi\) | |||||||
\(182\) | 2.36667 | 0.175430 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.14332 | −0.158008 | ||||||||
\(185\) | −2.81031 | −0.206618 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.25535 | −0.530564 | ||||||||
\(188\) | −14.4334 | −1.05266 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.128898 | −0.00935122 | ||||||||
\(191\) | −7.10652 | −0.514210 | −0.257105 | − | 0.966383i | \(-0.582769\pi\) | ||||
−0.257105 | + | 0.966383i | \(0.582769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.37896 | 0.171242 | 0.0856208 | − | 0.996328i | \(-0.472713\pi\) | ||||
0.0856208 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(194\) | 4.03138 | 0.289436 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.05455 | 0.646754 | ||||||||
\(197\) | −4.61033 | −0.328472 | −0.164236 | − | 0.986421i | \(-0.552516\pi\) | ||||
−0.164236 | + | 0.986421i | \(0.552516\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7702 | −0.905254 | −0.452627 | − | 0.891700i | \(-0.649513\pi\) | ||||
−0.452627 | + | 0.891700i | \(0.649513\pi\) | |||||||
\(200\) | −9.19394 | −0.650110 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.05959 | −0.637431 | ||||||||
\(203\) | 1.23837 | 0.0869162 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.617386 | 0.0431201 | ||||||||
\(206\) | −5.62671 | −0.392031 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.70439 | −0.464866 | ||||||||
\(209\) | −0.383556 | −0.0265311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.75135 | −0.602468 | −0.301234 | − | 0.953550i | \(-0.597398\pi\) | ||||
−0.301234 | + | 0.953550i | \(0.597398\pi\) | |||||||
\(212\) | −7.02468 | −0.482457 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.8232 | 0.739858 | ||||||||
\(215\) | −4.22329 | −0.288026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.125962 | −0.00855084 | ||||||||
\(218\) | 7.98064 | 0.540517 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.05257 | 0.138384 | ||||||||
\(221\) | −16.0892 | −1.08228 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.3753 | 1.96712 | 0.983559 | − | 0.180586i | \(-0.0577993\pi\) | ||||
0.983559 | + | 0.180586i | \(0.0577993\pi\) | |||||||
\(224\) | −6.80119 | −0.454424 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.56294 | −0.370041 | ||||||||
\(227\) | −21.4702 | −1.42503 | −0.712514 | − | 0.701658i | \(-0.752443\pi\) | ||||
−0.712514 | + | 0.701658i | \(0.752443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.14700 | 0.406205 | 0.203103 | − | 0.979157i | \(-0.434898\pi\) | ||||
0.203103 | + | 0.979157i | \(0.434898\pi\) | |||||||
\(230\) | 0.494076 | 0.0325784 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.14332 | 0.140716 | ||||||||
\(233\) | −21.0310 | −1.37778 | −0.688892 | − | 0.724864i | \(-0.741903\pi\) | ||||
−0.688892 | + | 0.724864i | \(0.741903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.34454 | 0.479105 | ||||||||
\(236\) | 14.5228 | 0.945355 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.58233 | −0.232208 | ||||||||
\(239\) | 22.6235 | 1.46339 | 0.731697 | − | 0.681630i | \(-0.238729\pi\) | ||||
0.731697 | + | 0.681630i | \(0.238729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1684 | 1.04150 | 0.520749 | − | 0.853710i | \(-0.325653\pi\) | ||||
0.520749 | + | 0.853710i | \(0.325653\pi\) | |||||||
\(242\) | 5.18101 | 0.333048 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.12398 | 0.199993 | ||||||||
\(245\) | −4.60748 | −0.294361 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.850561 | −0.0541199 | ||||||||
\(248\) | −0.218010 | −0.0138437 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.58976 | 0.290282 | ||||||||
\(251\) | −4.88555 | −0.308373 | −0.154186 | − | 0.988042i | \(-0.549276\pi\) | ||||
−0.154186 | + | 0.988042i | \(0.549276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.47020 | 0.0924308 | ||||||||
\(254\) | −11.2167 | −0.703797 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.95892 | −0.309933 | ||||||||
\(257\) | −14.0680 | −0.877539 | −0.438770 | − | 0.898600i | \(-0.644586\pi\) | ||||
−0.438770 | + | 0.898600i | \(0.644586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.12899 | −0.256563 | ||||||||
\(260\) | 4.55171 | 0.282285 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.44329 | 0.521628 | ||||||||
\(263\) | 15.7419 | 0.970687 | 0.485344 | − | 0.874323i | \(-0.338694\pi\) | ||||
0.485344 | + | 0.874323i | \(0.338694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.57456 | 0.219584 | ||||||||
\(266\) | −0.189381 | −0.0116117 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.32834 | 0.325480 | ||||||||
\(269\) | −5.80954 | −0.354214 | −0.177107 | − | 0.984192i | \(-0.556674\pi\) | ||||
−0.177107 | + | 0.984192i | \(0.556674\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5144 | 0.820944 | 0.410472 | − | 0.911873i | \(-0.365364\pi\) | ||||
0.410472 | + | 0.911873i | \(0.365364\pi\) | |||||||
\(272\) | 10.1481 | 0.615321 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.42834 | 0.388350 | ||||||||
\(275\) | 6.30655 | 0.380299 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1794 | −0.851956 | −0.425978 | − | 0.904733i | \(-0.640070\pi\) | ||||
−0.425978 | + | 0.904733i | \(0.640070\pi\) | |||||||
\(278\) | 6.32027 | 0.379064 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.23715 | 0.133695 | ||||||||
\(281\) | 0.303631 | 0.0181131 | 0.00905656 | − | 0.999959i | \(-0.497117\pi\) | ||||
0.00905656 | + | 0.999959i | \(0.497117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4684 | 1.03839 | 0.519195 | − | 0.854656i | \(-0.326232\pi\) | ||||
0.519195 | + | 0.854656i | \(0.326232\pi\) | |||||||
\(284\) | −2.85552 | −0.169444 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.80974 | −0.166144 | ||||||||
\(287\) | 0.907084 | 0.0535434 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.35356 | 0.432562 | ||||||||
\(290\) | −0.494076 | −0.0290131 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.38300 | 0.256495 | ||||||||
\(293\) | −18.0182 | −1.05263 | −0.526317 | − | 0.850289i | \(-0.676427\pi\) | ||||
−0.526317 | + | 0.850289i | \(0.676427\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.39006 | −0.430266 | ||||||||
\(296\) | −7.14632 | −0.415371 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.76920 | −0.507986 | ||||||||
\(299\) | 3.26028 | 0.188547 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.20499 | −0.357650 | ||||||||
\(302\) | 2.64649 | 0.152288 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.536484 | 0.0307694 | ||||||||
\(305\) | −1.58966 | −0.0910239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8992 | 0.850340 | 0.425170 | − | 0.905113i | \(-0.360214\pi\) | ||||
0.425170 | + | 0.905113i | \(0.360214\pi\) | |||||||
\(308\) | 3.01570 | 0.171835 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0502555 | 0.00285432 | ||||||||
\(311\) | 1.83728 | 0.104183 | 0.0520914 | − | 0.998642i | \(-0.483411\pi\) | ||||
0.0520914 | + | 0.998642i | \(0.483411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.46857 | 0.252579 | 0.126289 | − | 0.991993i | \(-0.459693\pi\) | ||||
0.126289 | + | 0.991993i | \(0.459693\pi\) | |||||||
\(314\) | 9.51315 | 0.536858 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.770786 | −0.0433601 | ||||||||
\(317\) | −15.9563 | −0.896194 | −0.448097 | − | 0.893985i | \(-0.647898\pi\) | ||||
−0.448097 | + | 0.893985i | \(0.647898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.47020 | −0.0823155 | ||||||||
\(320\) | −0.753019 | −0.0420950 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.725912 | 0.0404535 | ||||||||
\(323\) | 1.28746 | 0.0716360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.9852 | 0.775759 | ||||||||
\(326\) | 1.49230 | 0.0826506 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.56995 | 0.0866860 | ||||||||
\(329\) | 10.7908 | 0.594918 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.5195 | −1.95233 | −0.976164 | − | 0.217035i | \(-0.930362\pi\) | ||||
−0.976164 | + | 0.217035i | \(0.930362\pi\) | |||||||
\(332\) | −13.8164 | −0.758273 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.1779 | 0.611625 | ||||||||
\(335\) | −2.71137 | −0.148138 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6824 | −1.12664 | −0.563322 | − | 0.826237i | \(-0.690477\pi\) | ||||
−0.563322 | + | 0.826237i | \(0.690477\pi\) | |||||||
\(338\) | 1.38962 | 0.0755851 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.88971 | −0.373647 | ||||||||
\(341\) | 0.149543 | 0.00809822 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4380 | −0.833575 | ||||||||
\(344\) | −10.7394 | −0.579029 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.49778 | −0.295563 | ||||||||
\(347\) | −13.4784 | −0.723557 | −0.361779 | − | 0.932264i | \(-0.617830\pi\) | ||||
−0.361779 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.9095 | −1.76160 | −0.880801 | − | 0.473486i | \(-0.842995\pi\) | ||||
−0.880801 | + | 0.473486i | \(0.842995\pi\) | |||||||
\(350\) | 3.11386 | 0.166443 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.07445 | 0.430370 | ||||||||
\(353\) | −23.8249 | −1.26807 | −0.634035 | − | 0.773305i | \(-0.718602\pi\) | ||||
−0.634035 | + | 0.773305i | \(0.718602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.45306 | 0.0771202 | ||||||||
\(356\) | −8.50709 | −0.450875 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.53877 | 0.134178 | ||||||||
\(359\) | −26.2175 | −1.38370 | −0.691852 | − | 0.722039i | \(-0.743205\pi\) | ||||
−0.691852 | + | 0.722039i | \(0.743205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9319 | −0.996418 | ||||||||
\(362\) | −12.0000 | −0.630708 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.68751 | 0.350521 | ||||||||
\(365\) | −2.23032 | −0.116740 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.01887 | 0.470781 | 0.235391 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235391 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(368\) | −2.05639 | −0.107197 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.64736 | 0.0856422 | ||||||||
\(371\) | 5.25187 | 0.272663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.59391 | −0.444976 | −0.222488 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222488 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(374\) | 4.25298 | 0.219916 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.6764 | 0.963162 | ||||||||
\(377\) | −3.26028 | −0.167913 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.48972 | 0.436088 | 0.218044 | − | 0.975939i | \(-0.430032\pi\) | ||||
0.218044 | + | 0.975939i | \(0.430032\pi\) | |||||||
\(380\) | −0.364226 | −0.0186844 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.16574 | 0.213138 | ||||||||
\(383\) | −10.6436 | −0.543865 | −0.271933 | − | 0.962316i | \(-0.587663\pi\) | ||||
−0.271933 | + | 0.962316i | \(0.587663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.53456 | −0.0782085 | ||||||||
\(386\) | −1.39451 | −0.0709789 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.3915 | 0.578314 | ||||||||
\(389\) | 14.6896 | 0.744794 | 0.372397 | − | 0.928074i | \(-0.378536\pi\) | ||||
0.372397 | + | 0.928074i | \(0.378536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.93493 | −0.249570 | ||||||||
\(392\) | −11.7164 | −0.591766 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.70251 | 0.136150 | ||||||||
\(395\) | 0.392221 | 0.0197348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.75333 | 0.389128 | 0.194564 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194564 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(398\) | 7.48570 | 0.375224 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.82103 | −0.441052 | ||||||||
\(401\) | 1.17706 | 0.0587797 | 0.0293899 | − | 0.999568i | \(-0.490644\pi\) | ||||
0.0293899 | + | 0.999568i | \(0.490644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.331623 | 0.0165193 | ||||||||
\(404\) | −25.5997 | −1.27363 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.725912 | −0.0360264 | ||||||||
\(407\) | 4.90199 | 0.242982 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6328 | −1.16857 | −0.584283 | − | 0.811550i | \(-0.698624\pi\) | ||||
−0.584283 | + | 0.811550i | \(0.698624\pi\) | |||||||
\(410\) | −0.361903 | −0.0178731 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.8994 | −0.783307 | ||||||||
\(413\) | −10.8577 | −0.534273 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.03058 | 0.345118 | ||||||||
\(416\) | 17.9057 | 0.877897 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.224835 | 0.0109970 | ||||||||
\(419\) | −18.6252 | −0.909901 | −0.454951 | − | 0.890517i | \(-0.650343\pi\) | ||||
−0.454951 | + | 0.890517i | \(0.650343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.0986 | −1.51565 | −0.757827 | − | 0.652456i | \(-0.773739\pi\) | ||||
−0.757827 | + | 0.652456i | \(0.773739\pi\) | |||||||
\(422\) | 5.12992 | 0.249720 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.08975 | 0.441437 | ||||||||
\(425\) | −21.1688 | −1.02684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.33559 | −0.113027 | ||||||||
\(428\) | 30.5831 | 1.47829 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.47563 | 0.119386 | ||||||||
\(431\) | −9.88560 | −0.476173 | −0.238086 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238086 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.91141 | −0.428255 | −0.214127 | − | 0.976806i | \(-0.568691\pi\) | ||||
−0.214127 | + | 0.976806i | \(0.568691\pi\) | |||||||
\(434\) | 0.0738370 | 0.00354429 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.5509 | 1.07999 | ||||||||
\(437\) | −0.260886 | −0.0124799 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.9814 | −1.52639 | −0.763193 | − | 0.646170i | \(-0.776370\pi\) | ||||
−0.763193 | + | 0.646170i | \(0.776370\pi\) | |||||||
\(440\) | −2.65597 | −0.126618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.43128 | 0.448600 | ||||||||
\(443\) | −20.8775 | −0.991921 | −0.495960 | − | 0.868345i | \(-0.665184\pi\) | ||||
−0.495960 | + | 0.868345i | \(0.665184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.32890 | 0.205210 | ||||||||
\(446\) | −17.2194 | −0.815363 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.10636 | −0.0522706 | ||||||||
\(449\) | 13.7130 | 0.647158 | 0.323579 | − | 0.946201i | \(-0.395114\pi\) | ||||
0.323579 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07690 | −0.0507092 | ||||||||
\(452\) | −15.7192 | −0.739370 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.5855 | 0.590668 | ||||||||
\(455\) | −3.40300 | −0.159535 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8613 | 0.601627 | 0.300813 | − | 0.953683i | \(-0.402742\pi\) | ||||
0.300813 | + | 0.953683i | \(0.402742\pi\) | |||||||
\(458\) | −3.60328 | −0.168370 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.39611 | 0.0650940 | ||||||||
\(461\) | 24.1332 | 1.12400 | 0.561998 | − | 0.827139i | \(-0.310033\pi\) | ||||
0.561998 | + | 0.827139i | \(0.310033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.5906 | −1.88640 | −0.943202 | − | 0.332219i | \(-0.892203\pi\) | ||||
−0.943202 | + | 0.332219i | \(0.892203\pi\) | |||||||
\(464\) | 2.05639 | 0.0954654 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.3281 | 0.571086 | ||||||||
\(467\) | 16.4110 | 0.759413 | 0.379706 | − | 0.925107i | \(-0.376025\pi\) | ||||
0.379706 | + | 0.925107i | \(0.376025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.98363 | −0.183947 | ||||||||
\(470\) | −4.30526 | −0.198587 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.7922 | −0.864979 | ||||||||
\(473\) | 7.36664 | 0.338718 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.11909 | −0.0513475 | ||||||||
\(476\) | −10.1226 | −0.463968 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.2616 | −0.606571 | ||||||||
\(479\) | 11.5781 | 0.529017 | 0.264508 | − | 0.964383i | \(-0.414790\pi\) | ||||
0.264508 | + | 0.964383i | \(0.414790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.8705 | 0.495652 | ||||||||
\(482\) | −9.47768 | −0.431697 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.6400 | 0.665454 | ||||||||
\(485\) | −5.79664 | −0.263212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.57197 | −0.252490 | −0.126245 | − | 0.991999i | \(-0.540293\pi\) | ||||
−0.126245 | + | 0.991999i | \(0.540293\pi\) | |||||||
\(488\) | −4.04236 | −0.182989 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.70084 | 0.122012 | ||||||||
\(491\) | −20.4086 | −0.921028 | −0.460514 | − | 0.887653i | \(-0.652335\pi\) | ||||
−0.460514 | + | 0.887653i | \(0.652335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.93493 | 0.222258 | ||||||||
\(494\) | 0.498587 | 0.0224325 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.209168 | −0.00939191 | ||||||||
\(497\) | 2.13488 | 0.0957624 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.6022 | −1.45947 | −0.729737 | − | 0.683728i | \(-0.760357\pi\) | ||||
−0.729737 | + | 0.683728i | \(0.760357\pi\) | |||||||
\(500\) | 12.9693 | 0.580004 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.86384 | 0.127819 | ||||||||
\(503\) | −6.33199 | −0.282330 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0266 | 0.579677 | ||||||||
\(506\) | −0.861812 | −0.0383122 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −31.6950 | −1.40624 | ||||||||
\(509\) | −27.0573 | −1.19929 | −0.599646 | − | 0.800265i | \(-0.704692\pi\) | ||||
−0.599646 | + | 0.800265i | \(0.704692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27686 | −0.144960 | ||||||||
\(512\) | −20.1088 | −0.888693 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.24647 | 0.363736 | ||||||||
\(515\) | 8.09054 | 0.356512 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.8110 | −0.563427 | ||||||||
\(518\) | 2.42036 | 0.106344 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.88979 | −0.258284 | ||||||||
\(521\) | 5.85670 | 0.256587 | 0.128293 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128293 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.29727 | 0.362814 | 0.181407 | − | 0.983408i | \(-0.441935\pi\) | ||||
0.181407 | + | 0.983408i | \(0.441935\pi\) | |||||||
\(524\) | 23.8582 | 1.04225 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.22768 | −0.402346 | ||||||||
\(527\) | −0.501962 | −0.0218658 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.09536 | −0.0910166 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.535133 | −0.0232010 | ||||||||
\(533\) | −2.38810 | −0.103440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.5625 | −0.672824 | ||||||||
\(536\) | −6.89474 | −0.297807 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.40547 | 0.146820 | ||||||||
\(539\) | 8.03679 | 0.346169 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0825 | 0.476473 | 0.238237 | − | 0.971207i | \(-0.423431\pi\) | ||||
0.238237 | + | 0.971207i | \(0.423431\pi\) | |||||||
\(542\) | −7.92197 | −0.340278 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.1030 | −1.16203 | ||||||||
\(545\) | −11.4752 | −0.491544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4790 | 0.918375 | 0.459187 | − | 0.888339i | \(-0.348141\pi\) | ||||
0.459187 | + | 0.888339i | \(0.348141\pi\) | |||||||
\(548\) | 18.1646 | 0.775952 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.69681 | −0.157632 | ||||||||
\(551\) | 0.260886 | 0.0111141 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.576264 | 0.0245052 | ||||||||
\(554\) | 8.31175 | 0.353132 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.8592 | 0.757398 | ||||||||
\(557\) | −38.2929 | −1.62252 | −0.811262 | − | 0.584683i | \(-0.801219\pi\) | ||||
−0.811262 | + | 0.584683i | \(0.801219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3360 | 0.690940 | ||||||||
\(560\) | 2.14641 | 0.0907023 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.177984 | −0.00750781 | ||||||||
\(563\) | 4.52231 | 0.190592 | 0.0952962 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952962 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.99885 | 0.336514 | ||||||||
\(566\) | −10.2397 | −0.430409 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.69497 | 0.155038 | ||||||||
\(569\) | −44.8603 | −1.88064 | −0.940321 | − | 0.340289i | \(-0.889475\pi\) | ||||
−0.940321 | + | 0.340289i | \(0.889475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.417218 | 0.0174600 | 0.00873001 | − | 0.999962i | \(-0.497221\pi\) | ||||
0.00873001 | + | 0.999962i | \(0.497221\pi\) | |||||||
\(572\) | −7.93949 | −0.331967 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.531719 | −0.0221935 | ||||||||
\(575\) | 4.28958 | 0.178888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8343 | −0.492670 | −0.246335 | − | 0.969185i | \(-0.579226\pi\) | ||||
−0.246335 | + | 0.969185i | \(0.579226\pi\) | |||||||
\(578\) | −4.31055 | −0.179295 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.39611 | −0.0579704 | ||||||||
\(581\) | 10.3296 | 0.428542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.23508 | −0.258230 | ||||||||
\(584\) | −5.67148 | −0.234688 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.5620 | 0.436312 | ||||||||
\(587\) | 18.5466 | 0.765501 | 0.382750 | − | 0.923852i | \(-0.374977\pi\) | ||||
0.382750 | + | 0.923852i | \(0.374977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0265363 | −0.00109341 | ||||||||
\(590\) | 4.33195 | 0.178343 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.85646 | −0.281799 | ||||||||
\(593\) | 29.0821 | 1.19426 | 0.597129 | − | 0.802145i | \(-0.296308\pi\) | ||||
0.597129 | + | 0.802145i | \(0.296308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.15096 | 0.211169 | ||||||||
\(596\) | −24.7792 | −1.01499 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.91113 | −0.0781518 | ||||||||
\(599\) | −29.5204 | −1.20617 | −0.603085 | − | 0.797677i | \(-0.706062\pi\) | ||||
−0.603085 | + | 0.797677i | \(0.706062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.49768 | 0.142673 | 0.0713367 | − | 0.997452i | \(-0.477274\pi\) | ||||
0.0713367 | + | 0.997452i | \(0.477274\pi\) | |||||||
\(602\) | 3.63728 | 0.148244 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.47819 | 0.304283 | ||||||||
\(605\) | −7.44967 | −0.302872 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.88945 | 0.320223 | 0.160111 | − | 0.987099i | \(-0.448815\pi\) | ||||
0.160111 | + | 0.987099i | \(0.448815\pi\) | |||||||
\(608\) | −1.43281 | −0.0581079 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.931839 | 0.0377291 | ||||||||
\(611\) | −28.4093 | −1.14932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.4560 | −1.35127 | −0.675637 | − | 0.737235i | \(-0.736131\pi\) | ||||
−0.675637 | + | 0.737235i | \(0.736131\pi\) | |||||||
\(614\) | −8.73368 | −0.352463 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.90223 | −0.157225 | ||||||||
\(617\) | 33.2433 | 1.33832 | 0.669162 | − | 0.743117i | \(-0.266653\pi\) | ||||
0.669162 | + | 0.743117i | \(0.266653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.1547 | −0.930668 | −0.465334 | − | 0.885135i | \(-0.654066\pi\) | ||||
−0.465334 | + | 0.885135i | \(0.654066\pi\) | |||||||
\(620\) | 0.142007 | 0.00570314 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.07699 | −0.0431834 | ||||||||
\(623\) | 6.36016 | 0.254815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8484 | 0.593934 | ||||||||
\(626\) | −2.61941 | −0.104693 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.8813 | 1.07268 | ||||||||
\(629\) | −16.4542 | −0.656071 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7854 | −0.708027 | −0.354014 | − | 0.935240i | \(-0.615183\pi\) | ||||
−0.354014 | + | 0.935240i | \(0.615183\pi\) | |||||||
\(632\) | 0.997378 | 0.0396735 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.35334 | 0.371469 | ||||||||
\(635\) | 16.1283 | 0.640030 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8221 | 0.706139 | ||||||||
\(638\) | 0.861812 | 0.0341194 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.69956 | 0.383409 | ||||||||
\(641\) | −27.7374 | −1.09556 | −0.547782 | − | 0.836621i | \(-0.684528\pi\) | ||||
−0.547782 | + | 0.836621i | \(0.684528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3293 | 0.604528 | 0.302264 | − | 0.953224i | \(-0.402258\pi\) | ||||
0.302264 | + | 0.953224i | \(0.402258\pi\) | |||||||
\(644\) | 2.05121 | 0.0808291 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.754689 | −0.0296928 | ||||||||
\(647\) | 41.3220 | 1.62454 | 0.812268 | − | 0.583284i | \(-0.198233\pi\) | ||||
0.812268 | + | 0.583284i | \(0.198233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8904 | 0.505993 | ||||||||
\(650\) | −8.19793 | −0.321549 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.21678 | 0.165142 | ||||||||
\(653\) | 31.9364 | 1.24977 | 0.624883 | − | 0.780718i | \(-0.285146\pi\) | ||||
0.624883 | + | 0.780718i | \(0.285146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1405 | −0.474367 | ||||||||
\(656\) | 1.50627 | 0.0588100 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.32543 | −0.246591 | ||||||||
\(659\) | 39.4143 | 1.53536 | 0.767681 | − | 0.640833i | \(-0.221411\pi\) | ||||
0.767681 | + | 0.640833i | \(0.221411\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5791 | 0.644850 | 0.322425 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322425 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(662\) | 20.8210 | 0.809232 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.8781 | 0.693803 | ||||||||
\(665\) | 0.272307 | 0.0105596 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 31.5853 | 1.22207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.58937 | 0.0614026 | ||||||||
\(671\) | 2.77284 | 0.107044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0131 | −0.501618 | −0.250809 | − | 0.968037i | \(-0.580697\pi\) | ||||
−0.250809 | + | 0.968037i | \(0.580697\pi\) | |||||||
\(674\) | 12.1237 | 0.466989 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.92664 | 0.151025 | ||||||||
\(677\) | −12.2182 | −0.469583 | −0.234792 | − | 0.972046i | \(-0.575441\pi\) | ||||
−0.234792 | + | 0.972046i | \(0.575441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.51661 | −0.326838 | ||||||||
\(680\) | 8.91512 | 0.341879 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0876601 | −0.00335668 | ||||||||
\(683\) | −1.56826 | −0.0600076 | −0.0300038 | − | 0.999550i | \(-0.509552\pi\) | ||||
−0.0300038 | + | 0.999550i | \(0.509552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.24319 | −0.353164 | ||||||||
\(686\) | 9.04955 | 0.345513 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.3038 | −0.392829 | ||||||||
\(689\) | −13.8267 | −0.526756 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.57025 | 0.249944 | 0.124972 | − | 0.992160i | \(-0.460116\pi\) | ||||
0.124972 | + | 0.992160i | \(0.460116\pi\) | |||||||
\(692\) | −15.5351 | −0.590556 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.90084 | 0.299912 | ||||||||
\(695\) | −9.08779 | −0.344720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.61476 | 0.136919 | ||||||||
\(698\) | 19.2911 | 0.730177 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.79883 | 0.332565 | ||||||||
\(701\) | −16.6273 | −0.628004 | −0.314002 | − | 0.949422i | \(-0.601670\pi\) | ||||
−0.314002 | + | 0.949422i | \(0.601670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.869854 | −0.0328072 | ||||||||
\(704\) | 1.31348 | 0.0495038 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.9658 | 0.525610 | ||||||||
\(707\) | 19.1391 | 0.719801 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.39341 | −0.352777 | −0.176389 | − | 0.984321i | \(-0.556442\pi\) | ||||
−0.176389 | + | 0.984321i | \(0.556442\pi\) | |||||||
\(710\) | −0.851761 | −0.0319660 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.0080 | 0.412541 | ||||||||
\(713\) | 0.101716 | 0.00380930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.04008 | 0.151090 | ||||||||
\(716\) | 7.17382 | 0.268098 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.3683 | 0.573540 | ||||||||
\(719\) | 0.289428 | 0.0107939 | 0.00539693 | − | 0.999985i | \(-0.498282\pi\) | ||||
0.00539693 | + | 0.999985i | \(0.498282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8869 | 0.442691 | ||||||||
\(722\) | 11.0976 | 0.413011 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −33.9085 | −1.26020 | ||||||||
\(725\) | −4.28958 | −0.159311 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8787 | 0.477644 | 0.238822 | − | 0.971063i | \(-0.423239\pi\) | ||||
0.238822 | + | 0.971063i | \(0.423239\pi\) | |||||||
\(728\) | −8.65347 | −0.320719 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.30738 | 0.0483884 | ||||||||
\(731\) | −24.7271 | −0.914566 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.0973 | −1.22248 | −0.611239 | − | 0.791446i | \(-0.709328\pi\) | ||||
−0.611239 | + | 0.791446i | \(0.709328\pi\) | |||||||
\(734\) | −5.28673 | −0.195137 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.49207 | 0.202440 | ||||||||
\(737\) | 4.72942 | 0.174210 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1818 | 0.632043 | 0.316022 | − | 0.948752i | \(-0.397653\pi\) | ||||
0.316022 | + | 0.948752i | \(0.397653\pi\) | |||||||
\(740\) | 4.65495 | 0.171119 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.07857 | −0.113018 | ||||||||
\(743\) | 21.8990 | 0.803395 | 0.401697 | − | 0.915772i | \(-0.368420\pi\) | ||||
0.401697 | + | 0.915772i | \(0.368420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6091 | 0.461961 | ||||||||
\(746\) | 5.03763 | 0.184441 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0177 | 0.439409 | ||||||||
\(749\) | −22.8649 | −0.835465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.1136 | 1.82867 | 0.914336 | − | 0.404956i | \(-0.132713\pi\) | ||||
0.914336 | + | 0.404956i | \(0.132713\pi\) | |||||||
\(752\) | 17.9189 | 0.653435 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.91113 | 0.0695991 | ||||||||
\(755\) | −3.80534 | −0.138490 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.4866 | 1.79862 | 0.899311 | − | 0.437309i | \(-0.144068\pi\) | ||||
0.899311 | + | 0.437309i | \(0.144068\pi\) | |||||||
\(758\) | −4.97655 | −0.180757 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.471300 | 0.0170958 | ||||||||
\(761\) | 18.5155 | 0.671186 | 0.335593 | − | 0.942007i | \(-0.391063\pi\) | ||||
0.335593 | + | 0.942007i | \(0.391063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.8598 | −0.610364 | ||||||||
\(764\) | 11.7711 | 0.425865 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.23916 | 0.225430 | ||||||||
\(767\) | 28.5854 | 1.03216 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.36922 | 0.337863 | 0.168931 | − | 0.985628i | \(-0.445968\pi\) | ||||
0.168931 | + | 0.985628i | \(0.445968\pi\) | |||||||
\(770\) | 0.899538 | 0.0324171 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.94048 | −0.141821 | ||||||||
\(773\) | −3.24015 | −0.116540 | −0.0582700 | − | 0.998301i | \(-0.518558\pi\) | ||||
−0.0582700 | + | 0.998301i | \(0.518558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.436319 | 0.0156730 | ||||||||
\(776\) | −14.7403 | −0.529145 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.61085 | −0.308714 | ||||||||
\(779\) | 0.191095 | 0.00684670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.53455 | −0.0906934 | ||||||||
\(782\) | 2.89279 | 0.103446 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.2411 | −0.401469 | ||||||||
\(785\) | −13.6788 | −0.488217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2199 | 1.21981 | 0.609905 | − | 0.792475i | \(-0.291208\pi\) | ||||
0.609905 | + | 0.792475i | \(0.291208\pi\) | |||||||
\(788\) | 7.63648 | 0.272038 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.229914 | −0.00817998 | ||||||||
\(791\) | 11.7522 | 0.417859 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.14896 | 0.218356 | ||||||||
\(794\) | −4.54489 | −0.161292 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.1524 | 0.749725 | ||||||||
\(797\) | 9.08039 | 0.321644 | 0.160822 | − | 0.986983i | \(-0.448585\pi\) | ||||
0.160822 | + | 0.986983i | \(0.448585\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.0019 | 1.52130 | ||||||||
\(800\) | 23.5587 | 0.832924 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.689978 | −0.0243640 | ||||||||
\(803\) | 3.89033 | 0.137287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.04378 | −0.0367883 | ||||||||
\(806\) | −0.194392 | −0.00684718 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.1254 | 1.16535 | ||||||||
\(809\) | 2.55646 | 0.0898804 | 0.0449402 | − | 0.998990i | \(-0.485690\pi\) | ||||
0.0449402 | + | 0.998990i | \(0.485690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90277 | 0.0668153 | 0.0334077 | − | 0.999442i | \(-0.489364\pi\) | ||||
0.0334077 | + | 0.999442i | \(0.489364\pi\) | |||||||
\(812\) | −2.05121 | −0.0719834 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.87348 | −0.100715 | ||||||||
\(815\) | −2.14574 | −0.0751621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.30720 | −0.0457333 | ||||||||
\(818\) | 13.8532 | 0.484366 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.02263 | −0.0357118 | ||||||||
\(821\) | 13.7415 | 0.479581 | 0.239790 | − | 0.970825i | \(-0.422921\pi\) | ||||
0.239790 | + | 0.970825i | \(0.422921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.1853 | −0.355039 | −0.177519 | − | 0.984117i | \(-0.556807\pi\) | ||||
−0.177519 | + | 0.984117i | \(0.556807\pi\) | |||||||
\(824\) | 20.5734 | 0.716709 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.36464 | 0.221454 | ||||||||
\(827\) | −26.7391 | −0.929809 | −0.464905 | − | 0.885361i | \(-0.653911\pi\) | ||||
−0.464905 | + | 0.885361i | \(0.653911\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5489 | −1.79037 | −0.895184 | − | 0.445697i | \(-0.852956\pi\) | ||||
−0.895184 | + | 0.445697i | \(0.852956\pi\) | |||||||
\(830\) | −4.12123 | −0.143050 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.91274 | 0.100981 | ||||||||
\(833\) | −26.9766 | −0.934683 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0724 | −0.556210 | ||||||||
\(836\) | 0.635316 | 0.0219729 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.9178 | 0.377150 | ||||||||
\(839\) | −4.54360 | −0.156862 | −0.0784312 | − | 0.996920i | \(-0.524991\pi\) | ||||
−0.0784312 | + | 0.996920i | \(0.524991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 18.2296 | 0.628232 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.4956 | 0.498960 | ||||||||
\(845\) | −1.99810 | −0.0687368 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9453 | −0.376085 | ||||||||
\(848\) | 8.72107 | 0.299483 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.4088 | 0.425620 | ||||||||
\(851\) | 3.33423 | 0.114296 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.2400 | −0.487568 | −0.243784 | − | 0.969830i | \(-0.578389\pi\) | ||||
−0.243784 | + | 0.969830i | \(0.578389\pi\) | |||||||
\(854\) | 1.36909 | 0.0468492 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.5738 | −1.35260 | ||||||||
\(857\) | 2.90828 | 0.0993451 | 0.0496726 | − | 0.998766i | \(-0.484182\pi\) | ||||
0.0496726 | + | 0.998766i | \(0.484182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.525329 | 0.0179240 | 0.00896200 | − | 0.999960i | \(-0.497147\pi\) | ||||
0.00896200 | + | 0.999960i | \(0.497147\pi\) | |||||||
\(860\) | 6.99540 | 0.238541 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.79480 | 0.197372 | ||||||||
\(863\) | 35.2839 | 1.20108 | 0.600539 | − | 0.799595i | \(-0.294953\pi\) | ||||
0.600539 | + | 0.799595i | \(0.294953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.90516 | 0.268784 | ||||||||
\(866\) | 5.22374 | 0.177510 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.208641 | 0.00708175 | ||||||||
\(869\) | −0.684147 | −0.0232081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4878 | 0.355366 | ||||||||
\(872\) | −29.1803 | −0.988170 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.152928 | 0.00517286 | ||||||||
\(875\) | −9.69624 | −0.327793 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.9988 | −1.11429 | −0.557145 | − | 0.830415i | \(-0.688103\pi\) | ||||
−0.557145 | + | 0.830415i | \(0.688103\pi\) | |||||||
\(878\) | 18.7470 | 0.632681 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.54824 | −0.0859012 | ||||||||
\(881\) | 8.43036 | 0.284026 | 0.142013 | − | 0.989865i | \(-0.454642\pi\) | ||||
0.142013 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.7930 | −0.901656 | −0.450828 | − | 0.892611i | \(-0.648871\pi\) | ||||
−0.450828 | + | 0.892611i | \(0.648871\pi\) | |||||||
\(884\) | 26.6500 | 0.896336 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.2381 | 0.411147 | ||||||||
\(887\) | −18.0659 | −0.606594 | −0.303297 | − | 0.952896i | \(-0.598087\pi\) | ||||
−0.303297 | + | 0.952896i | \(0.598087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.6962 | 0.794744 | ||||||||
\(890\) | −2.53754 | −0.0850585 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −48.6569 | −1.62915 | ||||||||
\(893\) | 2.27330 | 0.0760732 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.65046 | −0.122021 | ||||||||
\(896\) | 14.2509 | 0.476089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.03838 | −0.268244 | ||||||||
\(899\) | −0.101716 | −0.00339242 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9289 | 0.697242 | ||||||||
\(902\) | 0.631264 | 0.0210188 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.3403 | 0.676507 | ||||||||
\(905\) | 17.2546 | 0.573563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.2869 | 1.66975 | 0.834874 | − | 0.550441i | \(-0.185540\pi\) | ||||
0.834874 | + | 0.550441i | \(0.185540\pi\) | |||||||
\(908\) | 35.5630 | 1.18020 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.99479 | 0.0661266 | ||||||||
\(911\) | 25.2794 | 0.837544 | 0.418772 | − | 0.908091i | \(-0.362461\pi\) | ||||
0.418772 | + | 0.908091i | \(0.362461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.2634 | −0.405858 | ||||||||
\(914\) | −7.53912 | −0.249372 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.1818 | −0.336416 | ||||||||
\(917\) | −17.8371 | −0.589034 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0884 | −1.58629 | −0.793146 | − | 0.609032i | \(-0.791558\pi\) | ||||
−0.793146 | + | 0.609032i | \(0.791558\pi\) | |||||||
\(920\) | −1.80653 | −0.0595596 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.1465 | −0.465891 | ||||||||
\(923\) | −5.62054 | −0.185002 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3024 | 0.470261 | ||||||||
\(926\) | 23.7936 | 0.781907 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.49207 | −0.180286 | ||||||||
\(929\) | 32.8357 | 1.07731 | 0.538653 | − | 0.842528i | \(-0.318934\pi\) | ||||
0.538653 | + | 0.842528i | \(0.318934\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.42612 | −0.0467393 | ||||||||
\(932\) | 34.8354 | 1.14107 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.61992 | −0.314773 | ||||||||
\(935\) | −6.11528 | −0.199991 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5880 | −0.933930 | −0.466965 | − | 0.884276i | \(-0.654653\pi\) | ||||
−0.466965 | + | 0.884276i | \(0.654653\pi\) | |||||||
\(938\) | 2.33515 | 0.0762453 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.1654 | −0.396791 | ||||||||
\(941\) | 13.1403 | 0.428361 | 0.214181 | − | 0.976794i | \(-0.431292\pi\) | ||||
0.214181 | + | 0.976794i | \(0.431292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.732484 | −0.0238530 | ||||||||
\(944\) | −18.0299 | −0.586825 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.31822 | −0.140397 | ||||||||
\(947\) | 35.6856 | 1.15963 | 0.579813 | − | 0.814750i | \(-0.303126\pi\) | ||||
0.579813 | + | 0.814750i | \(0.303126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.62708 | 0.280047 | ||||||||
\(950\) | 0.655996 | 0.0212833 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.0984 | 0.424521 | ||||||||
\(953\) | 14.8964 | 0.482541 | 0.241270 | − | 0.970458i | \(-0.422436\pi\) | ||||
0.241270 | + | 0.970458i | \(0.422436\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.98985 | −0.193827 | ||||||||
\(956\) | −37.4733 | −1.21197 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.78691 | −0.219275 | ||||||||
\(959\) | −13.5804 | −0.438534 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9897 | −0.999666 | ||||||||
\(962\) | −6.37213 | −0.205446 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.7811 | −0.862561 | ||||||||
\(965\) | 2.00515 | 0.0645480 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5500 | −0.500053 | −0.250026 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250026 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(968\) | −18.9438 | −0.608876 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.39791 | 0.109100 | ||||||||
\(971\) | 40.0985 | 1.28682 | 0.643410 | − | 0.765522i | \(-0.277519\pi\) | ||||
0.643410 | + | 0.765522i | \(0.277519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.3521 | −0.428048 | ||||||||
\(974\) | 3.26621 | 0.104656 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.87840 | −0.124144 | ||||||||
\(977\) | 12.6678 | 0.405277 | 0.202639 | − | 0.979254i | \(-0.435048\pi\) | ||||
0.202639 | + | 0.979254i | \(0.435048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.55086 | −0.241326 | ||||||||
\(980\) | 7.63177 | 0.243788 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.9632 | 0.381762 | ||||||||
\(983\) | 41.8116 | 1.33358 | 0.666792 | − | 0.745244i | \(-0.267667\pi\) | ||||
0.666792 | + | 0.745244i | \(0.267667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.88589 | −0.123815 | ||||||||
\(986\) | −2.89279 | −0.0921251 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.40886 | 0.0448217 | ||||||||
\(989\) | 5.01063 | 0.159329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.44884 | 0.204854 | 0.102427 | − | 0.994741i | \(-0.467339\pi\) | ||||
0.102427 | + | 0.994741i | \(0.467339\pi\) | |||||||
\(992\) | 0.558632 | 0.0177366 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.25143 | −0.0396931 | ||||||||
\(995\) | −10.7635 | −0.341227 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.3269 | 0.897123 | 0.448562 | − | 0.893752i | \(-0.351936\pi\) | ||||
0.448562 | + | 0.893752i | \(0.351936\pi\) | |||||||
\(998\) | 19.1109 | 0.604946 | ||||||||
\(999\) | 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 | 6003.2.a.j.1.3 | 7 | ||
3.2 | odd | 2 | 2001.2.a.i.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.i.1.5 | ✓ | 7 | 3.2 | odd | 2 | ||
6003.2.a.j.1.3 | 7 | 1.1 | even | 1 | trivial |