Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, 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("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.06607\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06607 | 0.753828 | 0.376914 | − | 0.926248i | \(-0.376985\pi\) | ||||
0.376914 | + | 0.926248i | \(0.376985\pi\) | |||||||
\(3\) | 3.07491 | 1.77530 | 0.887650 | − | 0.460519i | \(-0.152337\pi\) | ||||
0.887650 | + | 0.460519i | \(0.152337\pi\) | |||||||
\(4\) | −0.863486 | −0.431743 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.27808 | 1.33827 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.05269 | −1.07929 | ||||||||
\(9\) | 6.45507 | 2.15169 | ||||||||
\(10\) | −1.06607 | −0.337122 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.65514 | −0.766473 | ||||||||
\(13\) | 2.06228 | 0.571973 | 0.285986 | − | 0.958234i | \(-0.407679\pi\) | ||||
0.285986 | + | 0.958234i | \(0.407679\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.07491 | −0.793938 | ||||||||
\(16\) | −1.52742 | −0.381855 | ||||||||
\(17\) | −1.12330 | −0.272441 | −0.136221 | − | 0.990679i | \(-0.543496\pi\) | ||||
−0.136221 | + | 0.990679i | \(0.543496\pi\) | |||||||
\(18\) | 6.88158 | 1.62200 | ||||||||
\(19\) | 8.47065 | 1.94330 | 0.971650 | − | 0.236424i | \(-0.0759753\pi\) | ||||
0.971650 | + | 0.236424i | \(0.0759753\pi\) | |||||||
\(20\) | 0.863486 | 0.193081 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.06607 | 0.227288 | ||||||||
\(23\) | 3.99926 | 0.833903 | 0.416951 | − | 0.908929i | \(-0.363099\pi\) | ||||
0.416951 | + | 0.908929i | \(0.363099\pi\) | |||||||
\(24\) | −9.38674 | −1.91606 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.19854 | 0.431169 | ||||||||
\(27\) | 10.6240 | 2.04459 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.01868 | −0.746250 | −0.373125 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373125 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(30\) | −3.27808 | −0.598493 | ||||||||
\(31\) | −0.325585 | −0.0584768 | −0.0292384 | − | 0.999572i | \(-0.509308\pi\) | ||||
−0.0292384 | + | 0.999572i | \(0.509308\pi\) | |||||||
\(32\) | 4.47703 | 0.791435 | ||||||||
\(33\) | 3.07491 | 0.535273 | ||||||||
\(34\) | −1.19753 | −0.205374 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.57386 | −0.928977 | ||||||||
\(37\) | 5.40922 | 0.889270 | 0.444635 | − | 0.895712i | \(-0.353333\pi\) | ||||
0.444635 | + | 0.895712i | \(0.353333\pi\) | |||||||
\(38\) | 9.03034 | 1.46491 | ||||||||
\(39\) | 6.34131 | 1.01542 | ||||||||
\(40\) | 3.05269 | 0.482672 | ||||||||
\(41\) | 1.23247 | 0.192480 | 0.0962399 | − | 0.995358i | \(-0.469318\pi\) | ||||
0.0962399 | + | 0.995358i | \(0.469318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0838 | −1.84276 | −0.921381 | − | 0.388660i | \(-0.872938\pi\) | ||||
−0.921381 | + | 0.388660i | \(0.872938\pi\) | |||||||
\(44\) | −0.863486 | −0.130175 | ||||||||
\(45\) | −6.45507 | −0.962265 | ||||||||
\(46\) | 4.26350 | 0.628619 | ||||||||
\(47\) | −1.05368 | −0.153695 | −0.0768477 | − | 0.997043i | \(-0.524486\pi\) | ||||
−0.0768477 | + | 0.997043i | \(0.524486\pi\) | |||||||
\(48\) | −4.69668 | −0.677908 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.06607 | 0.150766 | ||||||||
\(51\) | −3.45406 | −0.483665 | ||||||||
\(52\) | −1.78075 | −0.246945 | ||||||||
\(53\) | −0.884442 | −0.121487 | −0.0607437 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607437 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(54\) | 11.3260 | 1.54127 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26.0465 | 3.44994 | ||||||||
\(58\) | −4.28421 | −0.562545 | ||||||||
\(59\) | 13.8692 | 1.80562 | 0.902809 | − | 0.430041i | \(-0.141501\pi\) | ||||
0.902809 | + | 0.430041i | \(0.141501\pi\) | |||||||
\(60\) | 2.65514 | 0.342777 | ||||||||
\(61\) | 1.63867 | 0.209810 | 0.104905 | − | 0.994482i | \(-0.466546\pi\) | ||||
0.104905 | + | 0.994482i | \(0.466546\pi\) | |||||||
\(62\) | −0.347098 | −0.0440815 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.82769 | 0.978461 | ||||||||
\(65\) | −2.06228 | −0.255794 | ||||||||
\(66\) | 3.27808 | 0.403504 | ||||||||
\(67\) | 10.7570 | 1.31418 | 0.657091 | − | 0.753811i | \(-0.271787\pi\) | ||||
0.657091 | + | 0.753811i | \(0.271787\pi\) | |||||||
\(68\) | 0.969957 | 0.117625 | ||||||||
\(69\) | 12.2974 | 1.48043 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.18682 | 0.971597 | 0.485799 | − | 0.874071i | \(-0.338529\pi\) | ||||
0.485799 | + | 0.874071i | \(0.338529\pi\) | |||||||
\(72\) | −19.7053 | −2.32229 | ||||||||
\(73\) | −12.9612 | −1.51700 | −0.758499 | − | 0.651674i | \(-0.774067\pi\) | ||||
−0.758499 | + | 0.651674i | \(0.774067\pi\) | |||||||
\(74\) | 5.76663 | 0.670357 | ||||||||
\(75\) | 3.07491 | 0.355060 | ||||||||
\(76\) | −7.31428 | −0.839006 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.76031 | 0.765454 | ||||||||
\(79\) | 7.43983 | 0.837047 | 0.418523 | − | 0.908206i | \(-0.362548\pi\) | ||||
0.418523 | + | 0.908206i | \(0.362548\pi\) | |||||||
\(80\) | 1.52742 | 0.170771 | ||||||||
\(81\) | 13.3027 | 1.47808 | ||||||||
\(82\) | 1.31391 | 0.145097 | ||||||||
\(83\) | 4.20154 | 0.461179 | 0.230590 | − | 0.973051i | \(-0.425935\pi\) | ||||
0.230590 | + | 0.973051i | \(0.425935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12330 | 0.121839 | ||||||||
\(86\) | −12.8822 | −1.38913 | ||||||||
\(87\) | −12.3571 | −1.32482 | ||||||||
\(88\) | −3.05269 | −0.325418 | ||||||||
\(89\) | −14.0917 | −1.49371 | −0.746856 | − | 0.664986i | \(-0.768438\pi\) | ||||
−0.746856 | + | 0.664986i | \(0.768438\pi\) | |||||||
\(90\) | −6.88158 | −0.725383 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.45330 | −0.360031 | ||||||||
\(93\) | −1.00115 | −0.103814 | ||||||||
\(94\) | −1.12330 | −0.115860 | ||||||||
\(95\) | −8.47065 | −0.869070 | ||||||||
\(96\) | 13.7665 | 1.40503 | ||||||||
\(97\) | −16.8254 | −1.70836 | −0.854180 | − | 0.519977i | \(-0.825940\pi\) | ||||
−0.854180 | + | 0.519977i | \(0.825940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.45507 | 0.648759 | ||||||||
\(100\) | −0.863486 | −0.0863486 | ||||||||
\(101\) | 14.2529 | 1.41822 | 0.709109 | − | 0.705099i | \(-0.249098\pi\) | ||||
0.709109 | + | 0.705099i | \(0.249098\pi\) | |||||||
\(102\) | −3.68228 | −0.364600 | ||||||||
\(103\) | −16.2582 | −1.60197 | −0.800985 | − | 0.598684i | \(-0.795691\pi\) | ||||
−0.800985 | + | 0.598684i | \(0.795691\pi\) | |||||||
\(104\) | −6.29549 | −0.617323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.942881 | −0.0915807 | ||||||||
\(107\) | 8.58032 | 0.829491 | 0.414745 | − | 0.909937i | \(-0.363871\pi\) | ||||
0.414745 | + | 0.909937i | \(0.363871\pi\) | |||||||
\(108\) | −9.17369 | −0.882739 | ||||||||
\(109\) | 4.14170 | 0.396703 | 0.198351 | − | 0.980131i | \(-0.436441\pi\) | ||||
0.198351 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(110\) | −1.06607 | −0.101646 | ||||||||
\(111\) | 16.6329 | 1.57872 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.95520 | 0.278002 | 0.139001 | − | 0.990292i | \(-0.455611\pi\) | ||||
0.139001 | + | 0.990292i | \(0.455611\pi\) | |||||||
\(114\) | 27.7675 | 2.60066 | ||||||||
\(115\) | −3.99926 | −0.372933 | ||||||||
\(116\) | 3.47007 | 0.322188 | ||||||||
\(117\) | 13.3121 | 1.23071 | ||||||||
\(118\) | 14.7856 | 1.36113 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.38674 | 0.856888 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.74694 | 0.158161 | ||||||||
\(123\) | 3.78974 | 0.341709 | ||||||||
\(124\) | 0.281138 | 0.0252470 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.78852 | −0.602383 | −0.301192 | − | 0.953564i | \(-0.597384\pi\) | ||||
−0.301192 | + | 0.953564i | \(0.597384\pi\) | |||||||
\(128\) | −0.609164 | −0.0538430 | ||||||||
\(129\) | −37.1566 | −3.27146 | ||||||||
\(130\) | −2.19854 | −0.192825 | ||||||||
\(131\) | −4.12189 | −0.360131 | −0.180065 | − | 0.983655i | \(-0.557631\pi\) | ||||
−0.180065 | + | 0.983655i | \(0.557631\pi\) | |||||||
\(132\) | −2.65514 | −0.231100 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.4678 | 0.990668 | ||||||||
\(135\) | −10.6240 | −0.914370 | ||||||||
\(136\) | 3.42910 | 0.294043 | ||||||||
\(137\) | 11.5079 | 0.983188 | 0.491594 | − | 0.870825i | \(-0.336414\pi\) | ||||
0.491594 | + | 0.870825i | \(0.336414\pi\) | |||||||
\(138\) | 13.1099 | 1.11599 | ||||||||
\(139\) | −0.783249 | −0.0664343 | −0.0332172 | − | 0.999448i | \(-0.510575\pi\) | ||||
−0.0332172 | + | 0.999448i | \(0.510575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.23998 | −0.272855 | ||||||||
\(142\) | 8.72776 | 0.732417 | ||||||||
\(143\) | 2.06228 | 0.172456 | ||||||||
\(144\) | −9.85961 | −0.821634 | ||||||||
\(145\) | 4.01868 | 0.333733 | ||||||||
\(146\) | −13.8176 | −1.14356 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.67078 | −0.383936 | ||||||||
\(149\) | 10.9739 | 0.899017 | 0.449509 | − | 0.893276i | \(-0.351599\pi\) | ||||
0.449509 | + | 0.893276i | \(0.351599\pi\) | |||||||
\(150\) | 3.27808 | 0.267654 | ||||||||
\(151\) | −9.62635 | −0.783381 | −0.391691 | − | 0.920097i | \(-0.628110\pi\) | ||||
−0.391691 | + | 0.920097i | \(0.628110\pi\) | |||||||
\(152\) | −25.8583 | −2.09738 | ||||||||
\(153\) | −7.25101 | −0.586209 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.325585 | 0.0261516 | ||||||||
\(156\) | −5.47563 | −0.438401 | ||||||||
\(157\) | −19.3521 | −1.54446 | −0.772231 | − | 0.635341i | \(-0.780859\pi\) | ||||
−0.772231 | + | 0.635341i | \(0.780859\pi\) | |||||||
\(158\) | 7.93142 | 0.630990 | ||||||||
\(159\) | −2.71958 | −0.215677 | ||||||||
\(160\) | −4.47703 | −0.353940 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 14.1817 | 1.11422 | ||||||||
\(163\) | 16.1186 | 1.26251 | 0.631254 | − | 0.775576i | \(-0.282541\pi\) | ||||
0.631254 | + | 0.775576i | \(0.282541\pi\) | |||||||
\(164\) | −1.06422 | −0.0831018 | ||||||||
\(165\) | −3.07491 | −0.239381 | ||||||||
\(166\) | 4.47916 | 0.347650 | ||||||||
\(167\) | −9.27253 | −0.717530 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.74702 | −0.672847 | ||||||||
\(170\) | 1.19753 | 0.0918460 | ||||||||
\(171\) | 54.6786 | 4.18138 | ||||||||
\(172\) | 10.4342 | 0.795599 | ||||||||
\(173\) | −19.2414 | −1.46290 | −0.731448 | − | 0.681897i | \(-0.761155\pi\) | ||||
−0.731448 | + | 0.681897i | \(0.761155\pi\) | |||||||
\(174\) | −13.1736 | −0.998685 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.52742 | −0.115134 | ||||||||
\(177\) | 42.6466 | 3.20552 | ||||||||
\(178\) | −15.0227 | −1.12600 | ||||||||
\(179\) | −8.34322 | −0.623601 | −0.311801 | − | 0.950148i | \(-0.600932\pi\) | ||||
−0.311801 | + | 0.950148i | \(0.600932\pi\) | |||||||
\(180\) | 5.57386 | 0.415451 | ||||||||
\(181\) | −18.9132 | −1.40580 | −0.702902 | − | 0.711287i | \(-0.748113\pi\) | ||||
−0.702902 | + | 0.711287i | \(0.748113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.03876 | 0.372476 | ||||||||
\(184\) | −12.2085 | −0.900021 | ||||||||
\(185\) | −5.40922 | −0.397694 | ||||||||
\(186\) | −1.06730 | −0.0782579 | ||||||||
\(187\) | −1.12330 | −0.0821441 | ||||||||
\(188\) | 0.909840 | 0.0663569 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.03034 | −0.655130 | ||||||||
\(191\) | 1.19403 | 0.0863972 | 0.0431986 | − | 0.999067i | \(-0.486245\pi\) | ||||
0.0431986 | + | 0.999067i | \(0.486245\pi\) | |||||||
\(192\) | 24.0694 | 1.73706 | ||||||||
\(193\) | −22.2090 | −1.59864 | −0.799319 | − | 0.600907i | \(-0.794806\pi\) | ||||
−0.799319 | + | 0.600907i | \(0.794806\pi\) | |||||||
\(194\) | −17.9371 | −1.28781 | ||||||||
\(195\) | −6.34131 | −0.454111 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.35087 | −0.381234 | −0.190617 | − | 0.981664i | \(-0.561049\pi\) | ||||
−0.190617 | + | 0.981664i | \(0.561049\pi\) | |||||||
\(198\) | 6.88158 | 0.489053 | ||||||||
\(199\) | −11.0229 | −0.781394 | −0.390697 | − | 0.920519i | \(-0.627766\pi\) | ||||
−0.390697 | + | 0.920519i | \(0.627766\pi\) | |||||||
\(200\) | −3.05269 | −0.215858 | ||||||||
\(201\) | 33.0769 | 2.33307 | ||||||||
\(202\) | 15.1947 | 1.06909 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.98253 | 0.208819 | ||||||||
\(205\) | −1.23247 | −0.0860796 | ||||||||
\(206\) | −17.3325 | −1.20761 | ||||||||
\(207\) | 25.8155 | 1.79430 | ||||||||
\(208\) | −3.14996 | −0.218411 | ||||||||
\(209\) | 8.47065 | 0.585927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.84291 | 0.333400 | 0.166700 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166700 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(212\) | 0.763703 | 0.0524513 | ||||||||
\(213\) | 25.1737 | 1.72488 | ||||||||
\(214\) | 9.14726 | 0.625294 | ||||||||
\(215\) | 12.0838 | 0.824108 | ||||||||
\(216\) | −32.4318 | −2.20671 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.41536 | 0.299046 | ||||||||
\(219\) | −39.8546 | −2.69313 | ||||||||
\(220\) | 0.863486 | 0.0582162 | ||||||||
\(221\) | −2.31656 | −0.155829 | ||||||||
\(222\) | 17.7319 | 1.19008 | ||||||||
\(223\) | −10.7581 | −0.720412 | −0.360206 | − | 0.932873i | \(-0.617294\pi\) | ||||
−0.360206 | + | 0.932873i | \(0.617294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.45507 | 0.430338 | ||||||||
\(226\) | 3.15046 | 0.209566 | ||||||||
\(227\) | 4.62447 | 0.306937 | 0.153469 | − | 0.988154i | \(-0.450956\pi\) | ||||
0.153469 | + | 0.988154i | \(0.450956\pi\) | |||||||
\(228\) | −22.4908 | −1.48949 | ||||||||
\(229\) | −1.65401 | −0.109300 | −0.0546500 | − | 0.998506i | \(-0.517404\pi\) | ||||
−0.0546500 | + | 0.998506i | \(0.517404\pi\) | |||||||
\(230\) | −4.26350 | −0.281127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.2678 | 0.805419 | ||||||||
\(233\) | 2.09030 | 0.136940 | 0.0684700 | − | 0.997653i | \(-0.478188\pi\) | ||||
0.0684700 | + | 0.997653i | \(0.478188\pi\) | |||||||
\(234\) | 14.1917 | 0.927742 | ||||||||
\(235\) | 1.05368 | 0.0687347 | ||||||||
\(236\) | −11.9759 | −0.779563 | ||||||||
\(237\) | 22.8768 | 1.48601 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1060 | −0.847754 | −0.423877 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423877 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(240\) | 4.69668 | 0.303170 | ||||||||
\(241\) | 5.92643 | 0.381755 | 0.190877 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190877 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(242\) | 1.06607 | 0.0685298 | ||||||||
\(243\) | 9.03255 | 0.579438 | ||||||||
\(244\) | −1.41497 | −0.0905840 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.04014 | 0.257590 | ||||||||
\(247\) | 17.4688 | 1.11151 | ||||||||
\(248\) | 0.993910 | 0.0631134 | ||||||||
\(249\) | 12.9194 | 0.818731 | ||||||||
\(250\) | −1.06607 | −0.0674245 | ||||||||
\(251\) | 8.12067 | 0.512572 | 0.256286 | − | 0.966601i | \(-0.417501\pi\) | ||||
0.256286 | + | 0.966601i | \(0.417501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.99926 | 0.251431 | ||||||||
\(254\) | −7.23706 | −0.454094 | ||||||||
\(255\) | 3.45406 | 0.216302 | ||||||||
\(256\) | −16.3048 | −1.01905 | ||||||||
\(257\) | 26.3816 | 1.64564 | 0.822818 | − | 0.568304i | \(-0.192400\pi\) | ||||
0.822818 | + | 0.568304i | \(0.192400\pi\) | |||||||
\(258\) | −39.6117 | −2.46612 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.78075 | 0.110437 | ||||||||
\(261\) | −25.9409 | −1.60570 | ||||||||
\(262\) | −4.39424 | −0.271477 | ||||||||
\(263\) | −20.7690 | −1.28067 | −0.640337 | − | 0.768094i | \(-0.721205\pi\) | ||||
−0.640337 | + | 0.768094i | \(0.721205\pi\) | |||||||
\(264\) | −9.38674 | −0.577714 | ||||||||
\(265\) | 0.884442 | 0.0543308 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −43.3306 | −2.65179 | ||||||||
\(268\) | −9.28855 | −0.567389 | ||||||||
\(269\) | −10.6726 | −0.650717 | −0.325359 | − | 0.945591i | \(-0.605485\pi\) | ||||
−0.325359 | + | 0.945591i | \(0.605485\pi\) | |||||||
\(270\) | −11.3260 | −0.689278 | ||||||||
\(271\) | −5.24361 | −0.318527 | −0.159263 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159263 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(272\) | 1.71576 | 0.104033 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.2683 | 0.741155 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −10.6186 | −0.639164 | ||||||||
\(277\) | −18.3766 | −1.10414 | −0.552072 | − | 0.833797i | \(-0.686163\pi\) | ||||
−0.552072 | + | 0.833797i | \(0.686163\pi\) | |||||||
\(278\) | −0.835002 | −0.0500801 | ||||||||
\(279\) | −2.10168 | −0.125824 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.89615 | −0.172770 | −0.0863849 | − | 0.996262i | \(-0.527531\pi\) | ||||
−0.0863849 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(282\) | −3.45406 | −0.205686 | ||||||||
\(283\) | 4.39212 | 0.261084 | 0.130542 | − | 0.991443i | \(-0.458328\pi\) | ||||
0.130542 | + | 0.991443i | \(0.458328\pi\) | |||||||
\(284\) | −7.06920 | −0.419480 | ||||||||
\(285\) | −26.0465 | −1.54286 | ||||||||
\(286\) | 2.19854 | 0.130002 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 28.8996 | 1.70292 | ||||||||
\(289\) | −15.7382 | −0.925776 | ||||||||
\(290\) | 4.28421 | 0.251578 | ||||||||
\(291\) | −51.7366 | −3.03285 | ||||||||
\(292\) | 11.1918 | 0.654953 | ||||||||
\(293\) | −21.0343 | −1.22884 | −0.614418 | − | 0.788981i | \(-0.710609\pi\) | ||||
−0.614418 | + | 0.788981i | \(0.710609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.8692 | −0.807497 | ||||||||
\(296\) | −16.5127 | −0.959779 | ||||||||
\(297\) | 10.6240 | 0.616468 | ||||||||
\(298\) | 11.6990 | 0.677705 | ||||||||
\(299\) | 8.24757 | 0.476969 | ||||||||
\(300\) | −2.65514 | −0.153295 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.2624 | −0.590535 | ||||||||
\(303\) | 43.8264 | 2.51776 | ||||||||
\(304\) | −12.9382 | −0.742059 | ||||||||
\(305\) | −1.63867 | −0.0938299 | ||||||||
\(306\) | −7.73011 | −0.441901 | ||||||||
\(307\) | 24.8681 | 1.41930 | 0.709648 | − | 0.704556i | \(-0.248854\pi\) | ||||
0.709648 | + | 0.704556i | \(0.248854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −49.9926 | −2.84398 | ||||||||
\(310\) | 0.347098 | 0.0197138 | ||||||||
\(311\) | −24.3484 | −1.38067 | −0.690336 | − | 0.723489i | \(-0.742537\pi\) | ||||
−0.690336 | + | 0.723489i | \(0.742537\pi\) | |||||||
\(312\) | −19.3581 | −1.09593 | ||||||||
\(313\) | 1.14902 | 0.0649464 | 0.0324732 | − | 0.999473i | \(-0.489662\pi\) | ||||
0.0324732 | + | 0.999473i | \(0.489662\pi\) | |||||||
\(314\) | −20.6307 | −1.16426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.42419 | −0.361389 | ||||||||
\(317\) | 19.3547 | 1.08707 | 0.543533 | − | 0.839387i | \(-0.317086\pi\) | ||||
0.543533 | + | 0.839387i | \(0.317086\pi\) | |||||||
\(318\) | −2.89927 | −0.162583 | ||||||||
\(319\) | −4.01868 | −0.225003 | ||||||||
\(320\) | −7.82769 | −0.437581 | ||||||||
\(321\) | 26.3837 | 1.47260 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.51511 | −0.529435 | ||||||||
\(324\) | −11.4867 | −0.638150 | ||||||||
\(325\) | 2.06228 | 0.114395 | ||||||||
\(326\) | 17.1836 | 0.951714 | ||||||||
\(327\) | 12.7353 | 0.704266 | ||||||||
\(328\) | −3.76235 | −0.207741 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.27808 | −0.180452 | ||||||||
\(331\) | −3.25973 | −0.179171 | −0.0895856 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895856 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(332\) | −3.62797 | −0.199111 | ||||||||
\(333\) | 34.9169 | 1.91343 | ||||||||
\(334\) | −9.88521 | −0.540894 | ||||||||
\(335\) | −10.7570 | −0.587720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.431489 | −0.0235047 | −0.0117523 | − | 0.999931i | \(-0.503741\pi\) | ||||
−0.0117523 | + | 0.999931i | \(0.503741\pi\) | |||||||
\(338\) | −9.32497 | −0.507211 | ||||||||
\(339\) | 9.08697 | 0.493536 | ||||||||
\(340\) | −0.969957 | −0.0526033 | ||||||||
\(341\) | −0.325585 | −0.0176314 | ||||||||
\(342\) | 58.2915 | 3.15204 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 36.8881 | 1.98887 | ||||||||
\(345\) | −12.2974 | −0.662067 | ||||||||
\(346\) | −20.5128 | −1.10277 | ||||||||
\(347\) | −2.59500 | −0.139307 | −0.0696535 | − | 0.997571i | \(-0.522189\pi\) | ||||
−0.0696535 | + | 0.997571i | \(0.522189\pi\) | |||||||
\(348\) | 10.6702 | 0.571981 | ||||||||
\(349\) | −11.7944 | −0.631340 | −0.315670 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315670 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.9097 | 1.16945 | ||||||||
\(352\) | 4.47703 | 0.238627 | ||||||||
\(353\) | −2.07304 | −0.110337 | −0.0551685 | − | 0.998477i | \(-0.517570\pi\) | ||||
−0.0551685 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(354\) | 45.4644 | 2.41641 | ||||||||
\(355\) | −8.18682 | −0.434511 | ||||||||
\(356\) | 12.1679 | 0.644899 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.89449 | −0.470088 | ||||||||
\(359\) | −30.2756 | −1.59789 | −0.798943 | − | 0.601407i | \(-0.794607\pi\) | ||||
−0.798943 | + | 0.601407i | \(0.794607\pi\) | |||||||
\(360\) | 19.7053 | 1.03856 | ||||||||
\(361\) | 52.7519 | 2.77642 | ||||||||
\(362\) | −20.1628 | −1.05974 | ||||||||
\(363\) | 3.07491 | 0.161391 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.9612 | 0.678422 | ||||||||
\(366\) | 5.37169 | 0.280783 | ||||||||
\(367\) | 8.03951 | 0.419659 | 0.209830 | − | 0.977738i | \(-0.432709\pi\) | ||||
0.209830 | + | 0.977738i | \(0.432709\pi\) | |||||||
\(368\) | −6.10855 | −0.318430 | ||||||||
\(369\) | 7.95569 | 0.414157 | ||||||||
\(370\) | −5.76663 | −0.299793 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.864474 | 0.0448209 | ||||||||
\(373\) | −29.9656 | −1.55156 | −0.775780 | − | 0.631003i | \(-0.782644\pi\) | ||||
−0.775780 | + | 0.631003i | \(0.782644\pi\) | |||||||
\(374\) | −1.19753 | −0.0619226 | ||||||||
\(375\) | −3.07491 | −0.158788 | ||||||||
\(376\) | 3.21657 | 0.165882 | ||||||||
\(377\) | −8.28763 | −0.426835 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3330 | 0.993068 | 0.496534 | − | 0.868017i | \(-0.334606\pi\) | ||||
0.496534 | + | 0.868017i | \(0.334606\pi\) | |||||||
\(380\) | 7.31428 | 0.375215 | ||||||||
\(381\) | −20.8741 | −1.06941 | ||||||||
\(382\) | 1.27293 | 0.0651287 | ||||||||
\(383\) | −10.0923 | −0.515693 | −0.257846 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257846 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(384\) | −1.87312 | −0.0955875 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.6764 | −1.20510 | ||||||||
\(387\) | −78.0018 | −3.96505 | ||||||||
\(388\) | 14.5285 | 0.737572 | ||||||||
\(389\) | 27.2856 | 1.38343 | 0.691717 | − | 0.722169i | \(-0.256855\pi\) | ||||
0.691717 | + | 0.722169i | \(0.256855\pi\) | |||||||
\(390\) | −6.76031 | −0.342322 | ||||||||
\(391\) | −4.49238 | −0.227189 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.6744 | −0.639340 | ||||||||
\(394\) | −5.70443 | −0.287385 | ||||||||
\(395\) | −7.43983 | −0.374339 | ||||||||
\(396\) | −5.57386 | −0.280097 | ||||||||
\(397\) | −25.2595 | −1.26774 | −0.633870 | − | 0.773440i | \(-0.718535\pi\) | ||||
−0.633870 | + | 0.773440i | \(0.718535\pi\) | |||||||
\(398\) | −11.7512 | −0.589037 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.52742 | −0.0763711 | ||||||||
\(401\) | 5.31132 | 0.265235 | 0.132617 | − | 0.991167i | \(-0.457662\pi\) | ||||
0.132617 | + | 0.991167i | \(0.457662\pi\) | |||||||
\(402\) | 35.2625 | 1.75873 | ||||||||
\(403\) | −0.671447 | −0.0334471 | ||||||||
\(404\) | −12.3072 | −0.612305 | ||||||||
\(405\) | −13.3027 | −0.661017 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.40922 | 0.268125 | ||||||||
\(408\) | 10.5442 | 0.522014 | ||||||||
\(409\) | −30.0680 | −1.48677 | −0.743384 | − | 0.668865i | \(-0.766780\pi\) | ||||
−0.743384 | + | 0.668865i | \(0.766780\pi\) | |||||||
\(410\) | −1.31391 | −0.0648892 | ||||||||
\(411\) | 35.3858 | 1.74545 | ||||||||
\(412\) | 14.0387 | 0.691639 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 27.5212 | 1.35259 | ||||||||
\(415\) | −4.20154 | −0.206246 | ||||||||
\(416\) | 9.23288 | 0.452679 | ||||||||
\(417\) | −2.40842 | −0.117941 | ||||||||
\(418\) | 9.03034 | 0.441688 | ||||||||
\(419\) | 12.9969 | 0.634938 | 0.317469 | − | 0.948269i | \(-0.397167\pi\) | ||||
0.317469 | + | 0.948269i | \(0.397167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.56078 | −0.124805 | −0.0624024 | − | 0.998051i | \(-0.519876\pi\) | ||||
−0.0624024 | + | 0.998051i | \(0.519876\pi\) | |||||||
\(422\) | 5.16291 | 0.251326 | ||||||||
\(423\) | −6.80159 | −0.330705 | ||||||||
\(424\) | 2.69993 | 0.131120 | ||||||||
\(425\) | −1.12330 | −0.0544883 | ||||||||
\(426\) | 26.8371 | 1.30026 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.40898 | −0.358127 | ||||||||
\(429\) | 6.34131 | 0.306161 | ||||||||
\(430\) | 12.8822 | 0.621236 | ||||||||
\(431\) | 0.989866 | 0.0476802 | 0.0238401 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238401 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(432\) | −16.2274 | −0.780739 | ||||||||
\(433\) | 32.4815 | 1.56096 | 0.780482 | − | 0.625179i | \(-0.214974\pi\) | ||||
0.780482 | + | 0.625179i | \(0.214974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.3571 | 0.592477 | ||||||||
\(436\) | −3.57630 | −0.171274 | ||||||||
\(437\) | 33.8763 | 1.62052 | ||||||||
\(438\) | −42.4880 | −2.03016 | ||||||||
\(439\) | 2.44093 | 0.116499 | 0.0582495 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582495 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(440\) | 3.05269 | 0.145531 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.46963 | −0.117468 | ||||||||
\(443\) | 29.7927 | 1.41549 | 0.707746 | − | 0.706467i | \(-0.249712\pi\) | ||||
0.707746 | + | 0.706467i | \(0.249712\pi\) | |||||||
\(444\) | −14.3622 | −0.681602 | ||||||||
\(445\) | 14.0917 | 0.668008 | ||||||||
\(446\) | −11.4689 | −0.543067 | ||||||||
\(447\) | 33.7438 | 1.59603 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.6965 | 1.54304 | 0.771521 | − | 0.636203i | \(-0.219496\pi\) | ||||
0.771521 | + | 0.636203i | \(0.219496\pi\) | |||||||
\(450\) | 6.88158 | 0.324401 | ||||||||
\(451\) | 1.23247 | 0.0580348 | ||||||||
\(452\) | −2.55177 | −0.120025 | ||||||||
\(453\) | −29.6002 | −1.39074 | ||||||||
\(454\) | 4.93003 | 0.231378 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −79.5118 | −3.72348 | ||||||||
\(457\) | 12.3905 | 0.579603 | 0.289801 | − | 0.957087i | \(-0.406411\pi\) | ||||
0.289801 | + | 0.957087i | \(0.406411\pi\) | |||||||
\(458\) | −1.76330 | −0.0823935 | ||||||||
\(459\) | −11.9340 | −0.557032 | ||||||||
\(460\) | 3.45330 | 0.161011 | ||||||||
\(461\) | −36.7587 | −1.71202 | −0.856011 | − | 0.516957i | \(-0.827065\pi\) | ||||
−0.856011 | + | 0.516957i | \(0.827065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1518 | 0.843585 | 0.421793 | − | 0.906692i | \(-0.361401\pi\) | ||||
0.421793 | + | 0.906692i | \(0.361401\pi\) | |||||||
\(464\) | 6.13822 | 0.284960 | ||||||||
\(465\) | 1.00115 | 0.0464270 | ||||||||
\(466\) | 2.22841 | 0.103229 | ||||||||
\(467\) | 33.6677 | 1.55795 | 0.778977 | − | 0.627052i | \(-0.215739\pi\) | ||||
0.778977 | + | 0.627052i | \(0.215739\pi\) | |||||||
\(468\) | −11.4948 | −0.531349 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.12330 | 0.0518142 | ||||||||
\(471\) | −59.5059 | −2.74188 | ||||||||
\(472\) | −42.3384 | −1.94878 | ||||||||
\(473\) | −12.0838 | −0.555614 | ||||||||
\(474\) | 24.3884 | 1.12020 | ||||||||
\(475\) | 8.47065 | 0.388660 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.70913 | −0.261403 | ||||||||
\(478\) | −13.9719 | −0.639061 | ||||||||
\(479\) | 21.9471 | 1.00279 | 0.501393 | − | 0.865219i | \(-0.332821\pi\) | ||||
0.501393 | + | 0.865219i | \(0.332821\pi\) | |||||||
\(480\) | −13.7665 | −0.628350 | ||||||||
\(481\) | 11.1553 | 0.508638 | ||||||||
\(482\) | 6.31801 | 0.287778 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.863486 | −0.0392493 | ||||||||
\(485\) | 16.8254 | 0.764002 | ||||||||
\(486\) | 9.62937 | 0.436797 | ||||||||
\(487\) | 19.4520 | 0.881454 | 0.440727 | − | 0.897641i | \(-0.354721\pi\) | ||||
0.440727 | + | 0.897641i | \(0.354721\pi\) | |||||||
\(488\) | −5.00235 | −0.226446 | ||||||||
\(489\) | 49.5633 | 2.24133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.22618 | 0.280984 | 0.140492 | − | 0.990082i | \(-0.455132\pi\) | ||||
0.140492 | + | 0.990082i | \(0.455132\pi\) | |||||||
\(492\) | −3.27239 | −0.147531 | ||||||||
\(493\) | 4.51420 | 0.203309 | ||||||||
\(494\) | 18.6231 | 0.837891 | ||||||||
\(495\) | −6.45507 | −0.290134 | ||||||||
\(496\) | 0.497306 | 0.0223297 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.7730 | 0.617183 | ||||||||
\(499\) | 10.3643 | 0.463968 | 0.231984 | − | 0.972720i | \(-0.425478\pi\) | ||||
0.231984 | + | 0.972720i | \(0.425478\pi\) | |||||||
\(500\) | 0.863486 | 0.0386163 | ||||||||
\(501\) | −28.5122 | −1.27383 | ||||||||
\(502\) | 8.65723 | 0.386391 | ||||||||
\(503\) | −4.68935 | −0.209088 | −0.104544 | − | 0.994520i | \(-0.533338\pi\) | ||||
−0.104544 | + | 0.994520i | \(0.533338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.2529 | −0.634246 | ||||||||
\(506\) | 4.26350 | 0.189536 | ||||||||
\(507\) | −26.8963 | −1.19451 | ||||||||
\(508\) | 5.86179 | 0.260075 | ||||||||
\(509\) | 30.3913 | 1.34707 | 0.673535 | − | 0.739155i | \(-0.264775\pi\) | ||||
0.673535 | + | 0.739155i | \(0.264775\pi\) | |||||||
\(510\) | 3.68228 | 0.163054 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.1638 | −0.714346 | ||||||||
\(513\) | 89.9924 | 3.97326 | ||||||||
\(514\) | 28.1247 | 1.24053 | ||||||||
\(515\) | 16.2582 | 0.716423 | ||||||||
\(516\) | 32.0842 | 1.41243 | ||||||||
\(517\) | −1.05368 | −0.0463409 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −59.1656 | −2.59708 | ||||||||
\(520\) | 6.29549 | 0.276075 | ||||||||
\(521\) | 20.3815 | 0.892932 | 0.446466 | − | 0.894801i | \(-0.352682\pi\) | ||||
0.446466 | + | 0.894801i | \(0.352682\pi\) | |||||||
\(522\) | −27.6549 | −1.21042 | ||||||||
\(523\) | 2.05927 | 0.0900458 | 0.0450229 | − | 0.998986i | \(-0.485664\pi\) | ||||
0.0450229 | + | 0.998986i | \(0.485664\pi\) | |||||||
\(524\) | 3.55919 | 0.155484 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.1413 | −0.965408 | ||||||||
\(527\) | 0.365731 | 0.0159315 | ||||||||
\(528\) | −4.69668 | −0.204397 | ||||||||
\(529\) | −7.00595 | −0.304606 | ||||||||
\(530\) | 0.942881 | 0.0409561 | ||||||||
\(531\) | 89.5268 | 3.88513 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.54170 | 0.110093 | ||||||||
\(534\) | −46.1936 | −1.99899 | ||||||||
\(535\) | −8.58032 | −0.370960 | ||||||||
\(536\) | −32.8379 | −1.41838 | ||||||||
\(537\) | −25.6546 | −1.10708 | ||||||||
\(538\) | −11.3777 | −0.490529 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.17369 | 0.394773 | ||||||||
\(541\) | 2.61676 | 0.112503 | 0.0562516 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562516 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(542\) | −5.59008 | −0.240114 | ||||||||
\(543\) | −58.1563 | −2.49572 | ||||||||
\(544\) | −5.02907 | −0.215620 | ||||||||
\(545\) | −4.14170 | −0.177411 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.6670 | 1.90982 | 0.954910 | − | 0.296894i | \(-0.0959507\pi\) | ||||
0.954910 | + | 0.296894i | \(0.0959507\pi\) | |||||||
\(548\) | −9.93692 | −0.424484 | ||||||||
\(549\) | 10.5777 | 0.451446 | ||||||||
\(550\) | 1.06607 | 0.0454576 | ||||||||
\(551\) | −34.0408 | −1.45019 | ||||||||
\(552\) | −37.5400 | −1.59781 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19.5908 | −0.832335 | ||||||||
\(555\) | −16.6329 | −0.706026 | ||||||||
\(556\) | 0.676324 | 0.0286825 | ||||||||
\(557\) | 27.6836 | 1.17299 | 0.586497 | − | 0.809952i | \(-0.300507\pi\) | ||||
0.586497 | + | 0.809952i | \(0.300507\pi\) | |||||||
\(558\) | −2.24054 | −0.0948497 | ||||||||
\(559\) | −24.9201 | −1.05401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45406 | −0.145830 | ||||||||
\(562\) | −3.08751 | −0.130239 | ||||||||
\(563\) | −17.8633 | −0.752849 | −0.376425 | − | 0.926447i | \(-0.622847\pi\) | ||||
−0.376425 | + | 0.926447i | \(0.622847\pi\) | |||||||
\(564\) | 2.79768 | 0.117803 | ||||||||
\(565\) | −2.95520 | −0.124326 | ||||||||
\(566\) | 4.68232 | 0.196813 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.9918 | −1.04863 | ||||||||
\(569\) | 27.0943 | 1.13585 | 0.567925 | − | 0.823080i | \(-0.307746\pi\) | ||||
0.567925 | + | 0.823080i | \(0.307746\pi\) | |||||||
\(570\) | −27.7675 | −1.16305 | ||||||||
\(571\) | 33.6184 | 1.40689 | 0.703443 | − | 0.710752i | \(-0.251645\pi\) | ||||
0.703443 | + | 0.710752i | \(0.251645\pi\) | |||||||
\(572\) | −1.78075 | −0.0744567 | ||||||||
\(573\) | 3.67154 | 0.153381 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.99926 | 0.166781 | ||||||||
\(576\) | 50.5283 | 2.10535 | ||||||||
\(577\) | 0.511024 | 0.0212742 | 0.0106371 | − | 0.999943i | \(-0.496614\pi\) | ||||
0.0106371 | + | 0.999943i | \(0.496614\pi\) | |||||||
\(578\) | −16.7781 | −0.697876 | ||||||||
\(579\) | −68.2906 | −2.83806 | ||||||||
\(580\) | −3.47007 | −0.144087 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −55.1550 | −2.28625 | ||||||||
\(583\) | −0.884442 | −0.0366298 | ||||||||
\(584\) | 39.5666 | 1.63728 | ||||||||
\(585\) | −13.3121 | −0.550389 | ||||||||
\(586\) | −22.4241 | −0.926331 | ||||||||
\(587\) | 24.8042 | 1.02378 | 0.511889 | − | 0.859052i | \(-0.328946\pi\) | ||||
0.511889 | + | 0.859052i | \(0.328946\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.75792 | −0.113638 | ||||||||
\(590\) | −14.7856 | −0.608714 | ||||||||
\(591\) | −16.4535 | −0.676805 | ||||||||
\(592\) | −8.26216 | −0.339573 | ||||||||
\(593\) | −29.2813 | −1.20244 | −0.601219 | − | 0.799084i | \(-0.705318\pi\) | ||||
−0.601219 | + | 0.799084i | \(0.705318\pi\) | |||||||
\(594\) | 11.3260 | 0.464711 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.47581 | −0.388144 | ||||||||
\(597\) | −33.8945 | −1.38721 | ||||||||
\(598\) | 8.79252 | 0.359553 | ||||||||
\(599\) | −15.8331 | −0.646922 | −0.323461 | − | 0.946241i | \(-0.604846\pi\) | ||||
−0.323461 | + | 0.946241i | \(0.604846\pi\) | |||||||
\(600\) | −9.38674 | −0.383212 | ||||||||
\(601\) | 16.8302 | 0.686516 | 0.343258 | − | 0.939241i | \(-0.388469\pi\) | ||||
0.343258 | + | 0.939241i | \(0.388469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 69.4374 | 2.82771 | ||||||||
\(604\) | 8.31221 | 0.338219 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 46.7222 | 1.89796 | ||||||||
\(607\) | 9.72751 | 0.394828 | 0.197414 | − | 0.980320i | \(-0.436746\pi\) | ||||
0.197414 | + | 0.980320i | \(0.436746\pi\) | |||||||
\(608\) | 37.9234 | 1.53800 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.74694 | −0.0707317 | ||||||||
\(611\) | −2.17298 | −0.0879096 | ||||||||
\(612\) | 6.26114 | 0.253092 | ||||||||
\(613\) | 10.7530 | 0.434311 | 0.217156 | − | 0.976137i | \(-0.430322\pi\) | ||||
0.217156 | + | 0.976137i | \(0.430322\pi\) | |||||||
\(614\) | 26.5112 | 1.06991 | ||||||||
\(615\) | −3.78974 | −0.152817 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5288 | −0.745942 | −0.372971 | − | 0.927843i | \(-0.621661\pi\) | ||||
−0.372971 | + | 0.927843i | \(0.621661\pi\) | |||||||
\(618\) | −53.2958 | −2.14387 | ||||||||
\(619\) | −24.4585 | −0.983070 | −0.491535 | − | 0.870858i | \(-0.663564\pi\) | ||||
−0.491535 | + | 0.870858i | \(0.663564\pi\) | |||||||
\(620\) | −0.281138 | −0.0112908 | ||||||||
\(621\) | 42.4882 | 1.70499 | ||||||||
\(622\) | −25.9572 | −1.04079 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.68586 | −0.387745 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.22494 | 0.0489584 | ||||||||
\(627\) | 26.0465 | 1.04020 | ||||||||
\(628\) | 16.7102 | 0.666811 | ||||||||
\(629\) | −6.07620 | −0.242274 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.3589 | −1.52704 | −0.763522 | − | 0.645782i | \(-0.776532\pi\) | ||||
−0.763522 | + | 0.645782i | \(0.776532\pi\) | |||||||
\(632\) | −22.7115 | −0.903415 | ||||||||
\(633\) | 14.8915 | 0.591885 | ||||||||
\(634\) | 20.6335 | 0.819462 | ||||||||
\(635\) | 6.78852 | 0.269394 | ||||||||
\(636\) | 2.34832 | 0.0931168 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.28421 | −0.169614 | ||||||||
\(639\) | 52.8465 | 2.09058 | ||||||||
\(640\) | 0.609164 | 0.0240793 | ||||||||
\(641\) | −32.1823 | −1.27113 | −0.635563 | − | 0.772049i | \(-0.719232\pi\) | ||||
−0.635563 | + | 0.772049i | \(0.719232\pi\) | |||||||
\(642\) | 28.1270 | 1.11008 | ||||||||
\(643\) | −12.1417 | −0.478821 | −0.239410 | − | 0.970918i | \(-0.576954\pi\) | ||||
−0.239410 | + | 0.970918i | \(0.576954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.1566 | 1.46304 | ||||||||
\(646\) | −10.1438 | −0.399103 | ||||||||
\(647\) | 22.2116 | 0.873229 | 0.436615 | − | 0.899649i | \(-0.356177\pi\) | ||||
0.436615 | + | 0.899649i | \(0.356177\pi\) | |||||||
\(648\) | −40.6090 | −1.59527 | ||||||||
\(649\) | 13.8692 | 0.544415 | ||||||||
\(650\) | 2.19854 | 0.0862338 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.9182 | −0.545079 | ||||||||
\(653\) | 41.7877 | 1.63528 | 0.817640 | − | 0.575730i | \(-0.195282\pi\) | ||||
0.817640 | + | 0.575730i | \(0.195282\pi\) | |||||||
\(654\) | 13.5768 | 0.530896 | ||||||||
\(655\) | 4.12189 | 0.161055 | ||||||||
\(656\) | −1.88250 | −0.0734994 | ||||||||
\(657\) | −83.6657 | −3.26411 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.0308 | −0.429700 | −0.214850 | − | 0.976647i | \(-0.568926\pi\) | ||||
−0.214850 | + | 0.976647i | \(0.568926\pi\) | |||||||
\(660\) | 2.65514 | 0.103351 | ||||||||
\(661\) | 40.6832 | 1.58239 | 0.791196 | − | 0.611562i | \(-0.209459\pi\) | ||||
0.791196 | + | 0.611562i | \(0.209459\pi\) | |||||||
\(662\) | −3.47512 | −0.135064 | ||||||||
\(663\) | −7.12322 | −0.276643 | ||||||||
\(664\) | −12.8260 | −0.497745 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 37.2240 | 1.44240 | ||||||||
\(667\) | −16.0717 | −0.622300 | ||||||||
\(668\) | 8.00670 | 0.309788 | ||||||||
\(669\) | −33.0800 | −1.27895 | ||||||||
\(670\) | −11.4678 | −0.443040 | ||||||||
\(671\) | 1.63867 | 0.0632601 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.01027 | −0.347320 | −0.173660 | − | 0.984806i | \(-0.555559\pi\) | ||||
−0.173660 | + | 0.984806i | \(0.555559\pi\) | |||||||
\(674\) | −0.459999 | −0.0177185 | ||||||||
\(675\) | 10.6240 | 0.408919 | ||||||||
\(676\) | 7.55292 | 0.290497 | ||||||||
\(677\) | −48.6358 | −1.86922 | −0.934612 | − | 0.355669i | \(-0.884253\pi\) | ||||
−0.934612 | + | 0.355669i | \(0.884253\pi\) | |||||||
\(678\) | 9.68738 | 0.372042 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.42910 | −0.131500 | ||||||||
\(681\) | 14.2198 | 0.544905 | ||||||||
\(682\) | −0.347098 | −0.0132911 | ||||||||
\(683\) | −10.4881 | −0.401316 | −0.200658 | − | 0.979661i | \(-0.564308\pi\) | ||||
−0.200658 | + | 0.979661i | \(0.564308\pi\) | |||||||
\(684\) | −47.2142 | −1.80528 | ||||||||
\(685\) | −11.5079 | −0.439695 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.08593 | −0.194040 | ||||||||
\(688\) | 18.4571 | 0.703669 | ||||||||
\(689\) | −1.82396 | −0.0694875 | ||||||||
\(690\) | −13.1099 | −0.499085 | ||||||||
\(691\) | 22.5536 | 0.857978 | 0.428989 | − | 0.903310i | \(-0.358870\pi\) | ||||
0.428989 | + | 0.903310i | \(0.358870\pi\) | |||||||
\(692\) | 16.6147 | 0.631595 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.76647 | −0.105014 | ||||||||
\(695\) | 0.783249 | 0.0297103 | ||||||||
\(696\) | 37.7223 | 1.42986 | ||||||||
\(697\) | −1.38444 | −0.0524394 | ||||||||
\(698\) | −12.5737 | −0.475922 | ||||||||
\(699\) | 6.42748 | 0.243110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9143 | −0.978769 | −0.489385 | − | 0.872068i | \(-0.662779\pi\) | ||||
−0.489385 | + | 0.872068i | \(0.662779\pi\) | |||||||
\(702\) | 23.3573 | 0.881566 | ||||||||
\(703\) | 45.8196 | 1.72812 | ||||||||
\(704\) | 7.82769 | 0.295017 | ||||||||
\(705\) | 3.23998 | 0.122025 | ||||||||
\(706\) | −2.21002 | −0.0831751 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −36.8247 | −1.38396 | ||||||||
\(709\) | −52.0656 | −1.95536 | −0.977682 | − | 0.210089i | \(-0.932625\pi\) | ||||
−0.977682 | + | 0.210089i | \(0.932625\pi\) | |||||||
\(710\) | −8.72776 | −0.327547 | ||||||||
\(711\) | 48.0246 | 1.80106 | ||||||||
\(712\) | 43.0174 | 1.61215 | ||||||||
\(713\) | −1.30210 | −0.0487640 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.06228 | −0.0771248 | ||||||||
\(716\) | 7.20425 | 0.269235 | ||||||||
\(717\) | −40.2996 | −1.50502 | ||||||||
\(718\) | −32.2761 | −1.20453 | ||||||||
\(719\) | 33.1393 | 1.23589 | 0.617944 | − | 0.786222i | \(-0.287966\pi\) | ||||
0.617944 | + | 0.786222i | \(0.287966\pi\) | |||||||
\(720\) | 9.85961 | 0.367446 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 56.2374 | 2.09294 | ||||||||
\(723\) | 18.2232 | 0.677729 | ||||||||
\(724\) | 16.3312 | 0.606946 | ||||||||
\(725\) | −4.01868 | −0.149250 | ||||||||
\(726\) | 3.27808 | 0.121661 | ||||||||
\(727\) | 2.62195 | 0.0972428 | 0.0486214 | − | 0.998817i | \(-0.484517\pi\) | ||||
0.0486214 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.1339 | −0.449402 | ||||||||
\(730\) | 13.8176 | 0.511414 | ||||||||
\(731\) | 13.5738 | 0.502044 | ||||||||
\(732\) | −4.35090 | −0.160814 | ||||||||
\(733\) | −13.7308 | −0.507158 | −0.253579 | − | 0.967315i | \(-0.581608\pi\) | ||||
−0.253579 | + | 0.967315i | \(0.581608\pi\) | |||||||
\(734\) | 8.57072 | 0.316351 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.9048 | 0.659980 | ||||||||
\(737\) | 10.7570 | 0.396241 | ||||||||
\(738\) | 8.48136 | 0.312203 | ||||||||
\(739\) | 4.54057 | 0.167028 | 0.0835138 | − | 0.996507i | \(-0.473386\pi\) | ||||
0.0835138 | + | 0.996507i | \(0.473386\pi\) | |||||||
\(740\) | 4.67078 | 0.171701 | ||||||||
\(741\) | 53.7150 | 1.97327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7757 | 0.872245 | 0.436123 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436123 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(744\) | 3.05618 | 0.112045 | ||||||||
\(745\) | −10.9739 | −0.402053 | ||||||||
\(746\) | −31.9456 | −1.16961 | ||||||||
\(747\) | 27.1213 | 0.992315 | ||||||||
\(748\) | 0.969957 | 0.0354651 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.27808 | −0.119699 | ||||||||
\(751\) | 35.2109 | 1.28486 | 0.642432 | − | 0.766343i | \(-0.277925\pi\) | ||||
0.642432 | + | 0.766343i | \(0.277925\pi\) | |||||||
\(752\) | 1.60942 | 0.0586894 | ||||||||
\(753\) | 24.9703 | 0.909969 | ||||||||
\(754\) | −8.83523 | −0.321760 | ||||||||
\(755\) | 9.62635 | 0.350339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.66097 | 0.205752 | 0.102876 | − | 0.994694i | \(-0.467196\pi\) | ||||
0.102876 | + | 0.994694i | \(0.467196\pi\) | |||||||
\(758\) | 20.6104 | 0.748603 | ||||||||
\(759\) | 12.2974 | 0.446366 | ||||||||
\(760\) | 25.8583 | 0.937977 | ||||||||
\(761\) | −15.5703 | −0.564422 | −0.282211 | − | 0.959352i | \(-0.591068\pi\) | ||||
−0.282211 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(762\) | −22.2533 | −0.806152 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.03103 | −0.0373014 | ||||||||
\(765\) | 7.25101 | 0.262161 | ||||||||
\(766\) | −10.7591 | −0.388744 | ||||||||
\(767\) | 28.6022 | 1.03276 | ||||||||
\(768\) | −50.1358 | −1.80912 | ||||||||
\(769\) | −11.4329 | −0.412281 | −0.206140 | − | 0.978522i | \(-0.566090\pi\) | ||||
−0.206140 | + | 0.978522i | \(0.566090\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 81.1209 | 2.92150 | ||||||||
\(772\) | 19.1771 | 0.690200 | ||||||||
\(773\) | 8.33168 | 0.299670 | 0.149835 | − | 0.988711i | \(-0.452126\pi\) | ||||
0.149835 | + | 0.988711i | \(0.452126\pi\) | |||||||
\(774\) | −83.1557 | −2.98897 | ||||||||
\(775\) | −0.325585 | −0.0116954 | ||||||||
\(776\) | 51.3627 | 1.84381 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.0884 | 1.04287 | ||||||||
\(779\) | 10.4398 | 0.374046 | ||||||||
\(780\) | 5.47563 | 0.196059 | ||||||||
\(781\) | 8.18682 | 0.292948 | ||||||||
\(782\) | −4.78921 | −0.171262 | ||||||||
\(783\) | −42.6946 | −1.52578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.3521 | 0.690705 | ||||||||
\(786\) | −13.5119 | −0.481953 | ||||||||
\(787\) | −20.3518 | −0.725463 | −0.362731 | − | 0.931894i | \(-0.618156\pi\) | ||||
−0.362731 | + | 0.931894i | \(0.618156\pi\) | |||||||
\(788\) | 4.62040 | 0.164595 | ||||||||
\(789\) | −63.8629 | −2.27358 | ||||||||
\(790\) | −7.93142 | −0.282187 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −19.7053 | −0.700198 | ||||||||
\(793\) | 3.37939 | 0.120006 | ||||||||
\(794\) | −26.9285 | −0.955658 | ||||||||
\(795\) | 2.71958 | 0.0964535 | ||||||||
\(796\) | 9.51813 | 0.337361 | ||||||||
\(797\) | −11.4434 | −0.405345 | −0.202672 | − | 0.979247i | \(-0.564963\pi\) | ||||
−0.202672 | + | 0.979247i | \(0.564963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.18361 | 0.0418730 | ||||||||
\(800\) | 4.47703 | 0.158287 | ||||||||
\(801\) | −90.9626 | −3.21400 | ||||||||
\(802\) | 5.66227 | 0.199942 | ||||||||
\(803\) | −12.9612 | −0.457392 | ||||||||
\(804\) | −28.5615 | −1.00728 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.715812 | −0.0252134 | ||||||||
\(807\) | −32.8172 | −1.15522 | ||||||||
\(808\) | −43.5097 | −1.53067 | ||||||||
\(809\) | −41.2939 | −1.45182 | −0.725908 | − | 0.687792i | \(-0.758580\pi\) | ||||
−0.725908 | + | 0.687792i | \(0.758580\pi\) | |||||||
\(810\) | −14.1817 | −0.498293 | ||||||||
\(811\) | −7.63142 | −0.267976 | −0.133988 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133988 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.1236 | −0.565480 | ||||||||
\(814\) | 5.76663 | 0.202120 | ||||||||
\(815\) | −16.1186 | −0.564610 | ||||||||
\(816\) | 5.27580 | 0.184690 | ||||||||
\(817\) | −102.358 | −3.58104 | ||||||||
\(818\) | −32.0547 | −1.12077 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.06422 | 0.0371642 | ||||||||
\(821\) | 55.5421 | 1.93843 | 0.969216 | − | 0.246214i | \(-0.0791864\pi\) | ||||
0.969216 | + | 0.246214i | \(0.0791864\pi\) | |||||||
\(822\) | 37.7239 | 1.31577 | ||||||||
\(823\) | −4.45307 | −0.155224 | −0.0776122 | − | 0.996984i | \(-0.524730\pi\) | ||||
−0.0776122 | + | 0.996984i | \(0.524730\pi\) | |||||||
\(824\) | 49.6313 | 1.72899 | ||||||||
\(825\) | 3.07491 | 0.107055 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.60111 | −0.125223 | −0.0626114 | − | 0.998038i | \(-0.519943\pi\) | ||||
−0.0626114 | + | 0.998038i | \(0.519943\pi\) | |||||||
\(828\) | −22.2913 | −0.774676 | ||||||||
\(829\) | −16.0872 | −0.558732 | −0.279366 | − | 0.960185i | \(-0.590124\pi\) | ||||
−0.279366 | + | 0.960185i | \(0.590124\pi\) | |||||||
\(830\) | −4.47916 | −0.155474 | ||||||||
\(831\) | −56.5064 | −1.96019 | ||||||||
\(832\) | 16.1429 | 0.559653 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.56755 | −0.0889071 | ||||||||
\(835\) | 9.27253 | 0.320889 | ||||||||
\(836\) | −7.31428 | −0.252970 | ||||||||
\(837\) | −3.45903 | −0.119561 | ||||||||
\(838\) | 13.8556 | 0.478634 | ||||||||
\(839\) | −14.6263 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581246\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.8502 | −0.443110 | ||||||||
\(842\) | −2.72998 | −0.0940814 | ||||||||
\(843\) | −8.90540 | −0.306718 | ||||||||
\(844\) | −4.18179 | −0.143943 | ||||||||
\(845\) | 8.74702 | 0.300907 | ||||||||
\(846\) | −7.25101 | −0.249295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.35092 | 0.0463906 | ||||||||
\(849\) | 13.5054 | 0.463503 | ||||||||
\(850\) | −1.19753 | −0.0410748 | ||||||||
\(851\) | 21.6329 | 0.741565 | ||||||||
\(852\) | −21.7372 | −0.744703 | ||||||||
\(853\) | −44.9908 | −1.54046 | −0.770228 | − | 0.637769i | \(-0.779857\pi\) | ||||
−0.770228 | + | 0.637769i | \(0.779857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −54.6786 | −1.86997 | ||||||||
\(856\) | −26.1930 | −0.895260 | ||||||||
\(857\) | −38.9813 | −1.33158 | −0.665789 | − | 0.746140i | \(-0.731905\pi\) | ||||
−0.665789 | + | 0.746140i | \(0.731905\pi\) | |||||||
\(858\) | 6.76031 | 0.230793 | ||||||||
\(859\) | 27.5179 | 0.938898 | 0.469449 | − | 0.882960i | \(-0.344453\pi\) | ||||
0.469449 | + | 0.882960i | \(0.344453\pi\) | |||||||
\(860\) | −10.4342 | −0.355803 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.05527 | 0.0359427 | ||||||||
\(863\) | −21.6767 | −0.737882 | −0.368941 | − | 0.929453i | \(-0.620280\pi\) | ||||
−0.368941 | + | 0.929453i | \(0.620280\pi\) | |||||||
\(864\) | 47.5641 | 1.61816 | ||||||||
\(865\) | 19.2414 | 0.654227 | ||||||||
\(866\) | 34.6277 | 1.17670 | ||||||||
\(867\) | −48.3935 | −1.64353 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.43983 | 0.252379 | ||||||||
\(870\) | 13.1736 | 0.446626 | ||||||||
\(871\) | 22.1840 | 0.751676 | ||||||||
\(872\) | −12.6433 | −0.428156 | ||||||||
\(873\) | −108.609 | −3.67586 | ||||||||
\(874\) | 36.1146 | 1.22160 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 34.4139 | 1.16274 | ||||||||
\(877\) | −21.1178 | −0.713097 | −0.356549 | − | 0.934277i | \(-0.616047\pi\) | ||||
−0.356549 | + | 0.934277i | \(0.616047\pi\) | |||||||
\(878\) | 2.60221 | 0.0878202 | ||||||||
\(879\) | −64.6785 | −2.18155 | ||||||||
\(880\) | 1.52742 | 0.0514894 | ||||||||
\(881\) | 12.4701 | 0.420128 | 0.210064 | − | 0.977688i | \(-0.432633\pi\) | ||||
0.210064 | + | 0.977688i | \(0.432633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.8363 | 1.00407 | 0.502035 | − | 0.864847i | \(-0.332585\pi\) | ||||
0.502035 | + | 0.864847i | \(0.332585\pi\) | |||||||
\(884\) | 2.00032 | 0.0672780 | ||||||||
\(885\) | −42.6466 | −1.43355 | ||||||||
\(886\) | 31.7612 | 1.06704 | ||||||||
\(887\) | 28.4571 | 0.955495 | 0.477748 | − | 0.878497i | \(-0.341453\pi\) | ||||
0.477748 | + | 0.878497i | \(0.341453\pi\) | |||||||
\(888\) | −50.7749 | −1.70390 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15.0227 | 0.503564 | ||||||||
\(891\) | 13.3027 | 0.445657 | ||||||||
\(892\) | 9.28942 | 0.311033 | ||||||||
\(893\) | −8.92538 | −0.298676 | ||||||||
\(894\) | 35.9734 | 1.20313 | ||||||||
\(895\) | 8.34322 | 0.278883 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.3605 | 0.846764 | ||||||||
\(898\) | 34.8569 | 1.16319 | ||||||||
\(899\) | 1.30842 | 0.0436384 | ||||||||
\(900\) | −5.57386 | −0.185795 | ||||||||
\(901\) | 0.993497 | 0.0330982 | ||||||||
\(902\) | 1.31391 | 0.0437483 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.02130 | −0.300044 | ||||||||
\(905\) | 18.9132 | 0.628695 | ||||||||
\(906\) | −31.5560 | −1.04838 | ||||||||
\(907\) | −10.9305 | −0.362941 | −0.181471 | − | 0.983396i | \(-0.558086\pi\) | ||||
−0.181471 | + | 0.983396i | \(0.558086\pi\) | |||||||
\(908\) | −3.99317 | −0.132518 | ||||||||
\(909\) | 92.0035 | 3.05156 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.19124 | 0.138862 | 0.0694310 | − | 0.997587i | \(-0.477882\pi\) | ||||
0.0694310 | + | 0.997587i | \(0.477882\pi\) | |||||||
\(912\) | −39.7839 | −1.31738 | ||||||||
\(913\) | 4.20154 | 0.139051 | ||||||||
\(914\) | 13.2092 | 0.436921 | ||||||||
\(915\) | −5.03876 | −0.166576 | ||||||||
\(916\) | 1.42821 | 0.0471895 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.7225 | −0.419906 | ||||||||
\(919\) | 29.8465 | 0.984545 | 0.492272 | − | 0.870441i | \(-0.336166\pi\) | ||||
0.492272 | + | 0.870441i | \(0.336166\pi\) | |||||||
\(920\) | 12.2085 | 0.402502 | ||||||||
\(921\) | 76.4671 | 2.51968 | ||||||||
\(922\) | −39.1875 | −1.29057 | ||||||||
\(923\) | 16.8835 | 0.555727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.40922 | 0.177854 | ||||||||
\(926\) | 19.3512 | 0.635918 | ||||||||
\(927\) | −104.948 | −3.44694 | ||||||||
\(928\) | −17.9918 | −0.590609 | ||||||||
\(929\) | −16.6544 | −0.546414 | −0.273207 | − | 0.961955i | \(-0.588084\pi\) | ||||
−0.273207 | + | 0.961955i | \(0.588084\pi\) | |||||||
\(930\) | 1.06730 | 0.0349980 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.80494 | −0.0591229 | ||||||||
\(933\) | −74.8692 | −2.45111 | ||||||||
\(934\) | 35.8923 | 1.17443 | ||||||||
\(935\) | 1.12330 | 0.0367360 | ||||||||
\(936\) | −40.6378 | −1.32829 | ||||||||
\(937\) | 8.35998 | 0.273109 | 0.136554 | − | 0.990633i | \(-0.456397\pi\) | ||||
0.136554 | + | 0.990633i | \(0.456397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.53313 | 0.115299 | ||||||||
\(940\) | −0.909840 | −0.0296757 | ||||||||
\(941\) | 21.3159 | 0.694880 | 0.347440 | − | 0.937702i | \(-0.387051\pi\) | ||||
0.347440 | + | 0.937702i | \(0.387051\pi\) | |||||||
\(942\) | −63.4377 | −2.06691 | ||||||||
\(943\) | 4.92897 | 0.160509 | ||||||||
\(944\) | −21.1841 | −0.689485 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.8822 | −0.418837 | ||||||||
\(947\) | −12.6887 | −0.412327 | −0.206164 | − | 0.978518i | \(-0.566098\pi\) | ||||
−0.206164 | + | 0.978518i | \(0.566098\pi\) | |||||||
\(948\) | −19.7538 | −0.641574 | ||||||||
\(949\) | −26.7297 | −0.867681 | ||||||||
\(950\) | 9.03034 | 0.292983 | ||||||||
\(951\) | 59.5139 | 1.92987 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.6944 | −1.25343 | −0.626717 | − | 0.779247i | \(-0.715602\pi\) | ||||
−0.626717 | + | 0.779247i | \(0.715602\pi\) | |||||||
\(954\) | −6.08636 | −0.197053 | ||||||||
\(955\) | −1.19403 | −0.0386380 | ||||||||
\(956\) | 11.3168 | 0.366012 | ||||||||
\(957\) | −12.3571 | −0.399448 | ||||||||
\(958\) | 23.3972 | 0.755929 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.0694 | −0.776838 | ||||||||
\(961\) | −30.8940 | −0.996580 | ||||||||
\(962\) | 11.8924 | 0.383426 | ||||||||
\(963\) | 55.3866 | 1.78481 | ||||||||
\(964\) | −5.11739 | −0.164820 | ||||||||
\(965\) | 22.2090 | 0.714933 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.1619 | −0.423259 | −0.211630 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211630 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(968\) | −3.05269 | −0.0981171 | ||||||||
\(969\) | −29.2581 | −0.939906 | ||||||||
\(970\) | 17.9371 | 0.575926 | ||||||||
\(971\) | −35.5953 | −1.14231 | −0.571153 | − | 0.820844i | \(-0.693504\pi\) | ||||
−0.571153 | + | 0.820844i | \(0.693504\pi\) | |||||||
\(972\) | −7.79948 | −0.250168 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.7373 | 0.664465 | ||||||||
\(975\) | 6.34131 | 0.203085 | ||||||||
\(976\) | −2.50294 | −0.0801171 | ||||||||
\(977\) | −19.2003 | −0.614273 | −0.307136 | − | 0.951666i | \(-0.599371\pi\) | ||||
−0.307136 | + | 0.951666i | \(0.599371\pi\) | |||||||
\(978\) | 52.8381 | 1.68958 | ||||||||
\(979\) | −14.0917 | −0.450371 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.7349 | 0.853581 | ||||||||
\(982\) | 6.63757 | 0.211813 | ||||||||
\(983\) | −32.8956 | −1.04921 | −0.524603 | − | 0.851347i | \(-0.675786\pi\) | ||||
−0.524603 | + | 0.851347i | \(0.675786\pi\) | |||||||
\(984\) | −11.5689 | −0.368803 | ||||||||
\(985\) | 5.35087 | 0.170493 | ||||||||
\(986\) | 4.81247 | 0.153260 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.0841 | −0.479888 | ||||||||
\(989\) | −48.3262 | −1.53668 | ||||||||
\(990\) | −6.88158 | −0.218711 | ||||||||
\(991\) | −19.9760 | −0.634560 | −0.317280 | − | 0.948332i | \(-0.602770\pi\) | ||||
−0.317280 | + | 0.948332i | \(0.602770\pi\) | |||||||
\(992\) | −1.45766 | −0.0462806 | ||||||||
\(993\) | −10.0234 | −0.318083 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0229 | 0.349450 | ||||||||
\(996\) | −11.1557 | −0.353481 | ||||||||
\(997\) | −4.04129 | −0.127989 | −0.0639945 | − | 0.997950i | \(-0.520384\pi\) | ||||
−0.0639945 | + | 0.997950i | \(0.520384\pi\) | |||||||
\(998\) | 11.0491 | 0.349752 | ||||||||
\(999\) | 57.4677 | 1.81820 |
(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 | 2695.2.a.y.1.6 | 10 | ||
7.2 | even | 3 | 385.2.i.d.221.5 | ✓ | 20 | ||
7.4 | even | 3 | 385.2.i.d.331.5 | yes | 20 | ||
7.6 | odd | 2 | 2695.2.a.z.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.d.221.5 | ✓ | 20 | 7.2 | even | 3 | ||
385.2.i.d.331.5 | yes | 20 | 7.4 | even | 3 | ||
2695.2.a.y.1.6 | 10 | 1.1 | even | 1 | trivial | ||
2695.2.a.z.1.6 | 10 | 7.6 | odd | 2 |