Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(1\) |
Dimension: | \(83\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50484 | −1.77119 | −0.885594 | − | 0.464460i | \(-0.846249\pi\) | ||||
−0.885594 | + | 0.464460i | \(0.846249\pi\) | |||||||
\(3\) | 1.86042 | 1.07411 | 0.537056 | − | 0.843547i | \(-0.319537\pi\) | ||||
0.537056 | + | 0.843547i | \(0.319537\pi\) | |||||||
\(4\) | 4.27422 | 2.13711 | ||||||||
\(5\) | 2.20949 | 0.988114 | 0.494057 | − | 0.869429i | \(-0.335513\pi\) | ||||
0.494057 | + | 0.869429i | \(0.335513\pi\) | |||||||
\(6\) | −4.66004 | −1.90245 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.69655 | −2.01403 | ||||||||
\(9\) | 0.461144 | 0.153715 | ||||||||
\(10\) | −5.53442 | −1.75014 | ||||||||
\(11\) | 3.98616 | 1.20187 | 0.600936 | − | 0.799297i | \(-0.294795\pi\) | ||||
0.600936 | + | 0.799297i | \(0.294795\pi\) | |||||||
\(12\) | 7.95182 | 2.29549 | ||||||||
\(13\) | −3.32354 | −0.921783 | −0.460892 | − | 0.887456i | \(-0.652470\pi\) | ||||
−0.460892 | + | 0.887456i | \(0.652470\pi\) | |||||||
\(14\) | −2.50484 | −0.669446 | ||||||||
\(15\) | 4.11057 | 1.06134 | ||||||||
\(16\) | 5.72051 | 1.43013 | ||||||||
\(17\) | −3.47214 | −0.842117 | −0.421059 | − | 0.907033i | \(-0.638341\pi\) | ||||
−0.421059 | + | 0.907033i | \(0.638341\pi\) | |||||||
\(18\) | −1.15509 | −0.272258 | ||||||||
\(19\) | −1.58300 | −0.363164 | −0.181582 | − | 0.983376i | \(-0.558122\pi\) | ||||
−0.181582 | + | 0.983376i | \(0.558122\pi\) | |||||||
\(20\) | 9.44384 | 2.11171 | ||||||||
\(21\) | 1.86042 | 0.405976 | ||||||||
\(22\) | −9.98469 | −2.12874 | ||||||||
\(23\) | −1.29720 | −0.270486 | −0.135243 | − | 0.990812i | \(-0.543181\pi\) | ||||
−0.135243 | + | 0.990812i | \(0.543181\pi\) | |||||||
\(24\) | −10.5979 | −2.16330 | ||||||||
\(25\) | −0.118152 | −0.0236305 | ||||||||
\(26\) | 8.32493 | 1.63265 | ||||||||
\(27\) | −4.72333 | −0.909004 | ||||||||
\(28\) | 4.27422 | 0.807751 | ||||||||
\(29\) | −6.45859 | −1.19933 | −0.599665 | − | 0.800251i | \(-0.704700\pi\) | ||||
−0.599665 | + | 0.800251i | \(0.704700\pi\) | |||||||
\(30\) | −10.2963 | −1.87984 | ||||||||
\(31\) | −1.02891 | −0.184798 | −0.0923988 | − | 0.995722i | \(-0.529453\pi\) | ||||
−0.0923988 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(32\) | −2.93584 | −0.518989 | ||||||||
\(33\) | 7.41591 | 1.29094 | ||||||||
\(34\) | 8.69715 | 1.49155 | ||||||||
\(35\) | 2.20949 | 0.373472 | ||||||||
\(36\) | 1.97103 | 0.328505 | ||||||||
\(37\) | −3.48735 | −0.573317 | −0.286658 | − | 0.958033i | \(-0.592544\pi\) | ||||
−0.286658 | + | 0.958033i | \(0.592544\pi\) | |||||||
\(38\) | 3.96515 | 0.643232 | ||||||||
\(39\) | −6.18316 | −0.990098 | ||||||||
\(40\) | −12.5865 | −1.99010 | ||||||||
\(41\) | 2.91634 | 0.455456 | 0.227728 | − | 0.973725i | \(-0.426870\pi\) | ||||
0.227728 | + | 0.973725i | \(0.426870\pi\) | |||||||
\(42\) | −4.66004 | −0.719060 | ||||||||
\(43\) | 0.547380 | 0.0834747 | 0.0417373 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417373 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(44\) | 17.0377 | 2.56853 | ||||||||
\(45\) | 1.01889 | 0.151888 | ||||||||
\(46\) | 3.24929 | 0.479081 | ||||||||
\(47\) | −11.2193 | −1.63650 | −0.818251 | − | 0.574861i | \(-0.805056\pi\) | ||||
−0.818251 | + | 0.574861i | \(0.805056\pi\) | |||||||
\(48\) | 10.6425 | 1.53611 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.295953 | 0.0418540 | ||||||||
\(51\) | −6.45962 | −0.904527 | ||||||||
\(52\) | −14.2055 | −1.96995 | ||||||||
\(53\) | −6.72493 | −0.923741 | −0.461870 | − | 0.886947i | \(-0.652821\pi\) | ||||
−0.461870 | + | 0.886947i | \(0.652821\pi\) | |||||||
\(54\) | 11.8312 | 1.61002 | ||||||||
\(55\) | 8.80738 | 1.18759 | ||||||||
\(56\) | −5.69655 | −0.761234 | ||||||||
\(57\) | −2.94503 | −0.390079 | ||||||||
\(58\) | 16.1777 | 2.12424 | ||||||||
\(59\) | −11.2668 | −1.46682 | −0.733409 | − | 0.679788i | \(-0.762072\pi\) | ||||
−0.733409 | + | 0.679788i | \(0.762072\pi\) | |||||||
\(60\) | 17.5695 | 2.26821 | ||||||||
\(61\) | −1.50408 | −0.192578 | −0.0962889 | − | 0.995353i | \(-0.530697\pi\) | ||||
−0.0962889 | + | 0.995353i | \(0.530697\pi\) | |||||||
\(62\) | 2.57725 | 0.327311 | ||||||||
\(63\) | 0.461144 | 0.0580987 | ||||||||
\(64\) | −4.08720 | −0.510899 | ||||||||
\(65\) | −7.34332 | −0.910827 | ||||||||
\(66\) | −18.5757 | −2.28651 | ||||||||
\(67\) | 1.77027 | 0.216273 | 0.108136 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108136 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(68\) | −14.8407 | −1.79970 | ||||||||
\(69\) | −2.41334 | −0.290532 | ||||||||
\(70\) | −5.53442 | −0.661489 | ||||||||
\(71\) | −9.11314 | −1.08153 | −0.540765 | − | 0.841173i | \(-0.681865\pi\) | ||||
−0.540765 | + | 0.841173i | \(0.681865\pi\) | |||||||
\(72\) | −2.62693 | −0.309587 | ||||||||
\(73\) | −0.379090 | −0.0443691 | −0.0221846 | − | 0.999754i | \(-0.507062\pi\) | ||||
−0.0221846 | + | 0.999754i | \(0.507062\pi\) | |||||||
\(74\) | 8.73525 | 1.01545 | ||||||||
\(75\) | −0.219812 | −0.0253817 | ||||||||
\(76\) | −6.76607 | −0.776122 | ||||||||
\(77\) | 3.98616 | 0.454265 | ||||||||
\(78\) | 15.4878 | 1.75365 | ||||||||
\(79\) | 9.57473 | 1.07724 | 0.538621 | − | 0.842548i | \(-0.318946\pi\) | ||||
0.538621 | + | 0.842548i | \(0.318946\pi\) | |||||||
\(80\) | 12.6394 | 1.41313 | ||||||||
\(81\) | −10.1708 | −1.13009 | ||||||||
\(82\) | −7.30497 | −0.806699 | ||||||||
\(83\) | 15.8931 | 1.74449 | 0.872247 | − | 0.489066i | \(-0.162662\pi\) | ||||
0.872247 | + | 0.489066i | \(0.162662\pi\) | |||||||
\(84\) | 7.95182 | 0.867615 | ||||||||
\(85\) | −7.67165 | −0.832108 | ||||||||
\(86\) | −1.37110 | −0.147849 | ||||||||
\(87\) | −12.0157 | −1.28821 | ||||||||
\(88\) | −22.7074 | −2.42061 | ||||||||
\(89\) | −4.04735 | −0.429018 | −0.214509 | − | 0.976722i | \(-0.568815\pi\) | ||||
−0.214509 | + | 0.976722i | \(0.568815\pi\) | |||||||
\(90\) | −2.55217 | −0.269022 | ||||||||
\(91\) | −3.32354 | −0.348401 | ||||||||
\(92\) | −5.54453 | −0.578057 | ||||||||
\(93\) | −1.91420 | −0.198493 | ||||||||
\(94\) | 28.1025 | 2.89855 | ||||||||
\(95\) | −3.49762 | −0.358848 | ||||||||
\(96\) | −5.46189 | −0.557452 | ||||||||
\(97\) | 0.0214864 | 0.00218162 | 0.00109081 | − | 0.999999i | \(-0.499653\pi\) | ||||
0.00109081 | + | 0.999999i | \(0.499653\pi\) | |||||||
\(98\) | −2.50484 | −0.253027 | ||||||||
\(99\) | 1.83820 | 0.184746 | ||||||||
\(100\) | −0.505009 | −0.0505009 | ||||||||
\(101\) | −13.6927 | −1.36248 | −0.681239 | − | 0.732062i | \(-0.738558\pi\) | ||||
−0.681239 | + | 0.732062i | \(0.738558\pi\) | |||||||
\(102\) | 16.1803 | 1.60209 | ||||||||
\(103\) | 2.69409 | 0.265457 | 0.132728 | − | 0.991152i | \(-0.457626\pi\) | ||||
0.132728 | + | 0.991152i | \(0.457626\pi\) | |||||||
\(104\) | 18.9327 | 1.85650 | ||||||||
\(105\) | 4.11057 | 0.401150 | ||||||||
\(106\) | 16.8449 | 1.63612 | ||||||||
\(107\) | 14.7213 | 1.42317 | 0.711583 | − | 0.702602i | \(-0.247979\pi\) | ||||
0.711583 | + | 0.702602i | \(0.247979\pi\) | |||||||
\(108\) | −20.1885 | −1.94264 | ||||||||
\(109\) | −8.12394 | −0.778132 | −0.389066 | − | 0.921210i | \(-0.627202\pi\) | ||||
−0.389066 | + | 0.921210i | \(0.627202\pi\) | |||||||
\(110\) | −22.0611 | −2.10344 | ||||||||
\(111\) | −6.48792 | −0.615806 | ||||||||
\(112\) | 5.72051 | 0.540537 | ||||||||
\(113\) | 16.6924 | 1.57028 | 0.785142 | − | 0.619316i | \(-0.212590\pi\) | ||||
0.785142 | + | 0.619316i | \(0.212590\pi\) | |||||||
\(114\) | 7.37683 | 0.690903 | ||||||||
\(115\) | −2.86616 | −0.267271 | ||||||||
\(116\) | −27.6054 | −2.56310 | ||||||||
\(117\) | −1.53263 | −0.141692 | ||||||||
\(118\) | 28.2216 | 2.59801 | ||||||||
\(119\) | −3.47214 | −0.318290 | ||||||||
\(120\) | −23.4161 | −2.13758 | ||||||||
\(121\) | 4.88947 | 0.444498 | ||||||||
\(122\) | 3.76748 | 0.341091 | ||||||||
\(123\) | 5.42561 | 0.489211 | ||||||||
\(124\) | −4.39778 | −0.394933 | ||||||||
\(125\) | −11.3085 | −1.01146 | ||||||||
\(126\) | −1.15509 | −0.102904 | ||||||||
\(127\) | −2.62536 | −0.232963 | −0.116482 | − | 0.993193i | \(-0.537162\pi\) | ||||
−0.116482 | + | 0.993193i | \(0.537162\pi\) | |||||||
\(128\) | 16.1095 | 1.42389 | ||||||||
\(129\) | 1.01835 | 0.0896611 | ||||||||
\(130\) | 18.3938 | 1.61325 | ||||||||
\(131\) | −12.5517 | −1.09665 | −0.548326 | − | 0.836265i | \(-0.684735\pi\) | ||||
−0.548326 | + | 0.836265i | \(0.684735\pi\) | |||||||
\(132\) | 31.6972 | 2.75889 | ||||||||
\(133\) | −1.58300 | −0.137263 | ||||||||
\(134\) | −4.43424 | −0.383060 | ||||||||
\(135\) | −10.4361 | −0.898200 | ||||||||
\(136\) | 19.7792 | 1.69605 | ||||||||
\(137\) | 9.83236 | 0.840035 | 0.420017 | − | 0.907516i | \(-0.362024\pi\) | ||||
0.420017 | + | 0.907516i | \(0.362024\pi\) | |||||||
\(138\) | 6.04502 | 0.514586 | ||||||||
\(139\) | 0.266687 | 0.0226201 | 0.0113100 | − | 0.999936i | \(-0.496400\pi\) | ||||
0.0113100 | + | 0.999936i | \(0.496400\pi\) | |||||||
\(140\) | 9.44384 | 0.798151 | ||||||||
\(141\) | −20.8725 | −1.75779 | ||||||||
\(142\) | 22.8270 | 1.91560 | ||||||||
\(143\) | −13.2482 | −1.10787 | ||||||||
\(144\) | 2.63798 | 0.219832 | ||||||||
\(145\) | −14.2702 | −1.18508 | ||||||||
\(146\) | 0.949559 | 0.0785861 | ||||||||
\(147\) | 1.86042 | 0.153444 | ||||||||
\(148\) | −14.9057 | −1.22524 | ||||||||
\(149\) | −10.6944 | −0.876120 | −0.438060 | − | 0.898946i | \(-0.644334\pi\) | ||||
−0.438060 | + | 0.898946i | \(0.644334\pi\) | |||||||
\(150\) | 0.550595 | 0.0449559 | ||||||||
\(151\) | −21.2585 | −1.72999 | −0.864995 | − | 0.501780i | \(-0.832679\pi\) | ||||
−0.864995 | + | 0.501780i | \(0.832679\pi\) | |||||||
\(152\) | 9.01762 | 0.731425 | ||||||||
\(153\) | −1.60116 | −0.129446 | ||||||||
\(154\) | −9.98469 | −0.804589 | ||||||||
\(155\) | −2.27337 | −0.182601 | ||||||||
\(156\) | −26.4282 | −2.11595 | ||||||||
\(157\) | −19.0276 | −1.51857 | −0.759283 | − | 0.650760i | \(-0.774450\pi\) | ||||
−0.759283 | + | 0.650760i | \(0.774450\pi\) | |||||||
\(158\) | −23.9832 | −1.90800 | ||||||||
\(159\) | −12.5112 | −0.992200 | ||||||||
\(160\) | −6.48672 | −0.512820 | ||||||||
\(161\) | −1.29720 | −0.102234 | ||||||||
\(162\) | 25.4762 | 2.00160 | ||||||||
\(163\) | −14.4253 | −1.12988 | −0.564939 | − | 0.825132i | \(-0.691100\pi\) | ||||
−0.564939 | + | 0.825132i | \(0.691100\pi\) | |||||||
\(164\) | 12.4651 | 0.973360 | ||||||||
\(165\) | 16.3854 | 1.27560 | ||||||||
\(166\) | −39.8096 | −3.08983 | ||||||||
\(167\) | 11.6529 | 0.901729 | 0.450865 | − | 0.892592i | \(-0.351116\pi\) | ||||
0.450865 | + | 0.892592i | \(0.351116\pi\) | |||||||
\(168\) | −10.5979 | −0.817650 | ||||||||
\(169\) | −1.95410 | −0.150315 | ||||||||
\(170\) | 19.2163 | 1.47382 | ||||||||
\(171\) | −0.729990 | −0.0558237 | ||||||||
\(172\) | 2.33962 | 0.178395 | ||||||||
\(173\) | 12.0786 | 0.918320 | 0.459160 | − | 0.888354i | \(-0.348150\pi\) | ||||
0.459160 | + | 0.888354i | \(0.348150\pi\) | |||||||
\(174\) | 30.0973 | 2.28167 | ||||||||
\(175\) | −0.118152 | −0.00893148 | ||||||||
\(176\) | 22.8029 | 1.71883 | ||||||||
\(177\) | −20.9610 | −1.57553 | ||||||||
\(178\) | 10.1379 | 0.759871 | ||||||||
\(179\) | 19.0548 | 1.42422 | 0.712109 | − | 0.702068i | \(-0.247740\pi\) | ||||
0.712109 | + | 0.702068i | \(0.247740\pi\) | |||||||
\(180\) | 4.35498 | 0.324601 | ||||||||
\(181\) | 2.71672 | 0.201932 | 0.100966 | − | 0.994890i | \(-0.467807\pi\) | ||||
0.100966 | + | 0.994890i | \(0.467807\pi\) | |||||||
\(182\) | 8.32493 | 0.617085 | ||||||||
\(183\) | −2.79821 | −0.206850 | ||||||||
\(184\) | 7.38959 | 0.544768 | ||||||||
\(185\) | −7.70526 | −0.566502 | ||||||||
\(186\) | 4.79476 | 0.351569 | ||||||||
\(187\) | −13.8405 | −1.01212 | ||||||||
\(188\) | −47.9537 | −3.49738 | ||||||||
\(189\) | −4.72333 | −0.343571 | ||||||||
\(190\) | 8.76096 | 0.635587 | ||||||||
\(191\) | −8.21262 | −0.594245 | −0.297122 | − | 0.954839i | \(-0.596027\pi\) | ||||
−0.297122 | + | 0.954839i | \(0.596027\pi\) | |||||||
\(192\) | −7.60388 | −0.548763 | ||||||||
\(193\) | −13.1291 | −0.945051 | −0.472525 | − | 0.881317i | \(-0.656658\pi\) | ||||
−0.472525 | + | 0.881317i | \(0.656658\pi\) | |||||||
\(194\) | −0.0538200 | −0.00386405 | ||||||||
\(195\) | −13.6616 | −0.978330 | ||||||||
\(196\) | 4.27422 | 0.305301 | ||||||||
\(197\) | −5.93017 | −0.422507 | −0.211253 | − | 0.977431i | \(-0.567755\pi\) | ||||
−0.211253 | + | 0.977431i | \(0.567755\pi\) | |||||||
\(198\) | −4.60438 | −0.327219 | ||||||||
\(199\) | −6.45110 | −0.457307 | −0.228653 | − | 0.973508i | \(-0.573432\pi\) | ||||
−0.228653 | + | 0.973508i | \(0.573432\pi\) | |||||||
\(200\) | 0.673061 | 0.0475926 | ||||||||
\(201\) | 3.29343 | 0.232301 | ||||||||
\(202\) | 34.2981 | 2.41320 | ||||||||
\(203\) | −6.45859 | −0.453304 | ||||||||
\(204\) | −27.6098 | −1.93307 | ||||||||
\(205\) | 6.44363 | 0.450043 | ||||||||
\(206\) | −6.74826 | −0.470174 | ||||||||
\(207\) | −0.598198 | −0.0415777 | ||||||||
\(208\) | −19.0123 | −1.31827 | ||||||||
\(209\) | −6.31008 | −0.436477 | ||||||||
\(210\) | −10.2963 | −0.710513 | ||||||||
\(211\) | 6.56557 | 0.451992 | 0.225996 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225996 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(212\) | −28.7438 | −1.97413 | ||||||||
\(213\) | −16.9542 | −1.16168 | ||||||||
\(214\) | −36.8746 | −2.52070 | ||||||||
\(215\) | 1.20943 | 0.0824825 | ||||||||
\(216\) | 26.9067 | 1.83077 | ||||||||
\(217\) | −1.02891 | −0.0698469 | ||||||||
\(218\) | 20.3492 | 1.37822 | ||||||||
\(219\) | −0.705264 | −0.0476574 | ||||||||
\(220\) | 37.6447 | 2.53800 | ||||||||
\(221\) | 11.5398 | 0.776249 | ||||||||
\(222\) | 16.2512 | 1.09071 | ||||||||
\(223\) | 0.244783 | 0.0163919 | 0.00819594 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819594 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(224\) | −2.93584 | −0.196159 | ||||||||
\(225\) | −0.0544853 | −0.00363235 | ||||||||
\(226\) | −41.8117 | −2.78127 | ||||||||
\(227\) | 8.30758 | 0.551393 | 0.275697 | − | 0.961245i | \(-0.411091\pi\) | ||||
0.275697 | + | 0.961245i | \(0.411091\pi\) | |||||||
\(228\) | −12.5877 | −0.833641 | ||||||||
\(229\) | −2.40294 | −0.158791 | −0.0793953 | − | 0.996843i | \(-0.525299\pi\) | ||||
−0.0793953 | + | 0.996843i | \(0.525299\pi\) | |||||||
\(230\) | 7.17927 | 0.473387 | ||||||||
\(231\) | 7.41591 | 0.487931 | ||||||||
\(232\) | 36.7917 | 2.41549 | ||||||||
\(233\) | 14.2580 | 0.934075 | 0.467038 | − | 0.884237i | \(-0.345321\pi\) | ||||
0.467038 | + | 0.884237i | \(0.345321\pi\) | |||||||
\(234\) | 3.83899 | 0.250963 | ||||||||
\(235\) | −24.7889 | −1.61705 | ||||||||
\(236\) | −48.1569 | −3.13475 | ||||||||
\(237\) | 17.8130 | 1.15708 | ||||||||
\(238\) | 8.69715 | 0.563752 | ||||||||
\(239\) | 10.5027 | 0.679362 | 0.339681 | − | 0.940541i | \(-0.389681\pi\) | ||||
0.339681 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(240\) | 23.5145 | 1.51786 | ||||||||
\(241\) | −27.8277 | −1.79254 | −0.896270 | − | 0.443508i | \(-0.853734\pi\) | ||||
−0.896270 | + | 0.443508i | \(0.853734\pi\) | |||||||
\(242\) | −12.2473 | −0.787289 | ||||||||
\(243\) | −4.75190 | −0.304834 | ||||||||
\(244\) | −6.42877 | −0.411560 | ||||||||
\(245\) | 2.20949 | 0.141159 | ||||||||
\(246\) | −13.5903 | −0.866485 | ||||||||
\(247\) | 5.26115 | 0.334759 | ||||||||
\(248\) | 5.86124 | 0.372189 | ||||||||
\(249\) | 29.5677 | 1.87378 | ||||||||
\(250\) | 28.3260 | 1.79149 | ||||||||
\(251\) | 22.1457 | 1.39783 | 0.698913 | − | 0.715207i | \(-0.253667\pi\) | ||||
0.698913 | + | 0.715207i | \(0.253667\pi\) | |||||||
\(252\) | 1.97103 | 0.124163 | ||||||||
\(253\) | −5.17086 | −0.325089 | ||||||||
\(254\) | 6.57612 | 0.412622 | ||||||||
\(255\) | −14.2725 | −0.893776 | ||||||||
\(256\) | −32.1772 | −2.01107 | ||||||||
\(257\) | 19.7499 | 1.23197 | 0.615984 | − | 0.787759i | \(-0.288759\pi\) | ||||
0.615984 | + | 0.787759i | \(0.288759\pi\) | |||||||
\(258\) | −2.55081 | −0.158807 | ||||||||
\(259\) | −3.48735 | −0.216693 | ||||||||
\(260\) | −31.3870 | −1.94654 | ||||||||
\(261\) | −2.97834 | −0.184355 | ||||||||
\(262\) | 31.4401 | 1.94238 | ||||||||
\(263\) | −8.38937 | −0.517311 | −0.258656 | − | 0.965970i | \(-0.583279\pi\) | ||||
−0.258656 | + | 0.965970i | \(0.583279\pi\) | |||||||
\(264\) | −42.2451 | −2.60001 | ||||||||
\(265\) | −14.8587 | −0.912761 | ||||||||
\(266\) | 3.96515 | 0.243119 | ||||||||
\(267\) | −7.52974 | −0.460813 | ||||||||
\(268\) | 7.56651 | 0.462198 | ||||||||
\(269\) | −3.43841 | −0.209644 | −0.104822 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104822 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(270\) | 26.1409 | 1.59088 | ||||||||
\(271\) | 21.0323 | 1.27762 | 0.638811 | − | 0.769364i | \(-0.279427\pi\) | ||||
0.638811 | + | 0.769364i | \(0.279427\pi\) | |||||||
\(272\) | −19.8624 | −1.20433 | ||||||||
\(273\) | −6.18316 | −0.374222 | ||||||||
\(274\) | −24.6285 | −1.48786 | ||||||||
\(275\) | −0.470974 | −0.0284008 | ||||||||
\(276\) | −10.3151 | −0.620898 | ||||||||
\(277\) | −3.40316 | −0.204476 | −0.102238 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102238 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(278\) | −0.668008 | −0.0400644 | ||||||||
\(279\) | −0.474476 | −0.0284061 | ||||||||
\(280\) | −12.5865 | −0.752186 | ||||||||
\(281\) | −0.106490 | −0.00635268 | −0.00317634 | − | 0.999995i | \(-0.501011\pi\) | ||||
−0.00317634 | + | 0.999995i | \(0.501011\pi\) | |||||||
\(282\) | 52.2824 | 3.11337 | ||||||||
\(283\) | 30.1565 | 1.79262 | 0.896309 | − | 0.443430i | \(-0.146238\pi\) | ||||
0.896309 | + | 0.443430i | \(0.146238\pi\) | |||||||
\(284\) | −38.9516 | −2.31135 | ||||||||
\(285\) | −6.50702 | −0.385442 | ||||||||
\(286\) | 33.1845 | 1.96224 | ||||||||
\(287\) | 2.91634 | 0.172146 | ||||||||
\(288\) | −1.35385 | −0.0797763 | ||||||||
\(289\) | −4.94426 | −0.290839 | ||||||||
\(290\) | 35.7445 | 2.09899 | ||||||||
\(291\) | 0.0399737 | 0.00234330 | ||||||||
\(292\) | −1.62031 | −0.0948216 | ||||||||
\(293\) | 18.9673 | 1.10808 | 0.554041 | − | 0.832490i | \(-0.313085\pi\) | ||||
0.554041 | + | 0.832490i | \(0.313085\pi\) | |||||||
\(294\) | −4.66004 | −0.271779 | ||||||||
\(295\) | −24.8940 | −1.44938 | ||||||||
\(296\) | 19.8659 | 1.15468 | ||||||||
\(297\) | −18.8279 | −1.09251 | ||||||||
\(298\) | 26.7878 | 1.55177 | ||||||||
\(299\) | 4.31131 | 0.249329 | ||||||||
\(300\) | −0.939526 | −0.0542436 | ||||||||
\(301\) | 0.547380 | 0.0315505 | ||||||||
\(302\) | 53.2491 | 3.06414 | ||||||||
\(303\) | −25.4742 | −1.46345 | ||||||||
\(304\) | −9.05554 | −0.519371 | ||||||||
\(305\) | −3.32325 | −0.190289 | ||||||||
\(306\) | 4.01064 | 0.229273 | ||||||||
\(307\) | 22.8872 | 1.30624 | 0.653121 | − | 0.757254i | \(-0.273459\pi\) | ||||
0.653121 | + | 0.757254i | \(0.273459\pi\) | |||||||
\(308\) | 17.0377 | 0.970814 | ||||||||
\(309\) | 5.01213 | 0.285130 | ||||||||
\(310\) | 5.69442 | 0.323421 | ||||||||
\(311\) | 22.8738 | 1.29705 | 0.648526 | − | 0.761192i | \(-0.275386\pi\) | ||||
0.648526 | + | 0.761192i | \(0.275386\pi\) | |||||||
\(312\) | 35.2227 | 1.99409 | ||||||||
\(313\) | −4.55585 | −0.257512 | −0.128756 | − | 0.991676i | \(-0.541098\pi\) | ||||
−0.128756 | + | 0.991676i | \(0.541098\pi\) | |||||||
\(314\) | 47.6610 | 2.68967 | ||||||||
\(315\) | 1.01889 | 0.0574082 | ||||||||
\(316\) | 40.9245 | 2.30218 | ||||||||
\(317\) | 3.52818 | 0.198162 | 0.0990811 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990811 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(318\) | 31.3385 | 1.75737 | ||||||||
\(319\) | −25.7450 | −1.44144 | ||||||||
\(320\) | −9.03062 | −0.504827 | ||||||||
\(321\) | 27.3878 | 1.52864 | ||||||||
\(322\) | 3.24929 | 0.181076 | ||||||||
\(323\) | 5.49638 | 0.305827 | ||||||||
\(324\) | −43.4721 | −2.41512 | ||||||||
\(325\) | 0.392684 | 0.0217822 | ||||||||
\(326\) | 36.1331 | 2.00123 | ||||||||
\(327\) | −15.1139 | −0.835800 | ||||||||
\(328\) | −16.6131 | −0.917305 | ||||||||
\(329\) | −11.2193 | −0.618540 | ||||||||
\(330\) | −41.0428 | −2.25933 | ||||||||
\(331\) | −33.0532 | −1.81677 | −0.908385 | − | 0.418134i | \(-0.862684\pi\) | ||||
−0.908385 | + | 0.418134i | \(0.862684\pi\) | |||||||
\(332\) | 67.9305 | 3.72817 | ||||||||
\(333\) | −1.60817 | −0.0881273 | ||||||||
\(334\) | −29.1887 | −1.59713 | ||||||||
\(335\) | 3.91139 | 0.213702 | ||||||||
\(336\) | 10.6425 | 0.580597 | ||||||||
\(337\) | −20.2071 | −1.10075 | −0.550376 | − | 0.834917i | \(-0.685516\pi\) | ||||
−0.550376 | + | 0.834917i | \(0.685516\pi\) | |||||||
\(338\) | 4.89471 | 0.266237 | ||||||||
\(339\) | 31.0547 | 1.68666 | ||||||||
\(340\) | −32.7903 | −1.77831 | ||||||||
\(341\) | −4.10140 | −0.222103 | ||||||||
\(342\) | 1.82851 | 0.0988744 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.11818 | −0.168121 | ||||||||
\(345\) | −5.33225 | −0.287078 | ||||||||
\(346\) | −30.2550 | −1.62652 | ||||||||
\(347\) | 5.40419 | 0.290112 | 0.145056 | − | 0.989423i | \(-0.453664\pi\) | ||||
0.145056 | + | 0.989423i | \(0.453664\pi\) | |||||||
\(348\) | −51.3576 | −2.75305 | ||||||||
\(349\) | −6.96367 | −0.372757 | −0.186378 | − | 0.982478i | \(-0.559675\pi\) | ||||
−0.186378 | + | 0.982478i | \(0.559675\pi\) | |||||||
\(350\) | 0.295953 | 0.0158193 | ||||||||
\(351\) | 15.6981 | 0.837905 | ||||||||
\(352\) | −11.7027 | −0.623758 | ||||||||
\(353\) | −2.61675 | −0.139275 | −0.0696377 | − | 0.997572i | \(-0.522184\pi\) | ||||
−0.0696377 | + | 0.997572i | \(0.522184\pi\) | |||||||
\(354\) | 52.5039 | 2.79055 | ||||||||
\(355\) | −20.1354 | −1.06868 | ||||||||
\(356\) | −17.2992 | −0.916858 | ||||||||
\(357\) | −6.45962 | −0.341879 | ||||||||
\(358\) | −47.7291 | −2.52256 | ||||||||
\(359\) | 15.2528 | 0.805014 | 0.402507 | − | 0.915417i | \(-0.368139\pi\) | ||||
0.402507 | + | 0.915417i | \(0.368139\pi\) | |||||||
\(360\) | −5.80418 | −0.305907 | ||||||||
\(361\) | −16.4941 | −0.868112 | ||||||||
\(362\) | −6.80493 | −0.357659 | ||||||||
\(363\) | 9.09645 | 0.477440 | ||||||||
\(364\) | −14.2055 | −0.744572 | ||||||||
\(365\) | −0.837595 | −0.0438417 | ||||||||
\(366\) | 7.00907 | 0.366370 | ||||||||
\(367\) | 0.396559 | 0.0207002 | 0.0103501 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103501 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(368\) | −7.42066 | −0.386829 | ||||||||
\(369\) | 1.34486 | 0.0700104 | ||||||||
\(370\) | 19.3004 | 1.00338 | ||||||||
\(371\) | −6.72493 | −0.349141 | ||||||||
\(372\) | −8.18170 | −0.424202 | ||||||||
\(373\) | 7.04128 | 0.364583 | 0.182292 | − | 0.983244i | \(-0.441648\pi\) | ||||
0.182292 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(374\) | 34.6682 | 1.79265 | ||||||||
\(375\) | −21.0385 | −1.08642 | ||||||||
\(376\) | 63.9113 | 3.29597 | ||||||||
\(377\) | 21.4654 | 1.10552 | ||||||||
\(378\) | 11.8312 | 0.608530 | ||||||||
\(379\) | 31.8265 | 1.63482 | 0.817408 | − | 0.576059i | \(-0.195410\pi\) | ||||
0.817408 | + | 0.576059i | \(0.195410\pi\) | |||||||
\(380\) | −14.9496 | −0.766897 | ||||||||
\(381\) | −4.88427 | −0.250229 | ||||||||
\(382\) | 20.5713 | 1.05252 | ||||||||
\(383\) | 12.2753 | 0.627240 | 0.313620 | − | 0.949549i | \(-0.398458\pi\) | ||||
0.313620 | + | 0.949549i | \(0.398458\pi\) | |||||||
\(384\) | 29.9703 | 1.52941 | ||||||||
\(385\) | 8.80738 | 0.448866 | ||||||||
\(386\) | 32.8862 | 1.67386 | ||||||||
\(387\) | 0.252421 | 0.0128313 | ||||||||
\(388\) | 0.0918377 | 0.00466235 | ||||||||
\(389\) | 18.8537 | 0.955922 | 0.477961 | − | 0.878381i | \(-0.341376\pi\) | ||||
0.477961 | + | 0.878381i | \(0.341376\pi\) | |||||||
\(390\) | 34.2202 | 1.73281 | ||||||||
\(391\) | 4.50407 | 0.227781 | ||||||||
\(392\) | −5.69655 | −0.287719 | ||||||||
\(393\) | −23.3515 | −1.17793 | ||||||||
\(394\) | 14.8541 | 0.748339 | ||||||||
\(395\) | 21.1553 | 1.06444 | ||||||||
\(396\) | 7.85685 | 0.394822 | ||||||||
\(397\) | −4.55642 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(398\) | 16.1590 | 0.809976 | ||||||||
\(399\) | −2.94503 | −0.147436 | ||||||||
\(400\) | −0.675891 | −0.0337946 | ||||||||
\(401\) | 22.0508 | 1.10116 | 0.550582 | − | 0.834781i | \(-0.314406\pi\) | ||||
0.550582 | + | 0.834781i | \(0.314406\pi\) | |||||||
\(402\) | −8.24952 | −0.411449 | ||||||||
\(403\) | 3.41962 | 0.170343 | ||||||||
\(404\) | −58.5257 | −2.91176 | ||||||||
\(405\) | −22.4722 | −1.11665 | ||||||||
\(406\) | 16.1777 | 0.802887 | ||||||||
\(407\) | −13.9011 | −0.689054 | ||||||||
\(408\) | 36.7975 | 1.82175 | ||||||||
\(409\) | 28.8258 | 1.42535 | 0.712673 | − | 0.701497i | \(-0.247484\pi\) | ||||
0.712673 | + | 0.701497i | \(0.247484\pi\) | |||||||
\(410\) | −16.1403 | −0.797111 | ||||||||
\(411\) | 18.2923 | 0.902291 | ||||||||
\(412\) | 11.5151 | 0.567310 | ||||||||
\(413\) | −11.2668 | −0.554405 | ||||||||
\(414\) | 1.49839 | 0.0736419 | ||||||||
\(415\) | 35.1156 | 1.72376 | ||||||||
\(416\) | 9.75739 | 0.478395 | ||||||||
\(417\) | 0.496148 | 0.0242965 | ||||||||
\(418\) | 15.8057 | 0.773083 | ||||||||
\(419\) | 0.893769 | 0.0436635 | 0.0218317 | − | 0.999762i | \(-0.493050\pi\) | ||||
0.0218317 | + | 0.999762i | \(0.493050\pi\) | |||||||
\(420\) | 17.5695 | 0.857302 | ||||||||
\(421\) | 5.18115 | 0.252514 | 0.126257 | − | 0.991998i | \(-0.459704\pi\) | ||||
0.126257 | + | 0.991998i | \(0.459704\pi\) | |||||||
\(422\) | −16.4457 | −0.800563 | ||||||||
\(423\) | −5.17372 | −0.251555 | ||||||||
\(424\) | 38.3089 | 1.86045 | ||||||||
\(425\) | 0.410241 | 0.0198996 | ||||||||
\(426\) | 42.4676 | 2.05756 | ||||||||
\(427\) | −1.50408 | −0.0727875 | ||||||||
\(428\) | 62.9222 | 3.04146 | ||||||||
\(429\) | −24.6471 | −1.18997 | ||||||||
\(430\) | −3.02943 | −0.146092 | ||||||||
\(431\) | 17.5355 | 0.844657 | 0.422329 | − | 0.906443i | \(-0.361213\pi\) | ||||
0.422329 | + | 0.906443i | \(0.361213\pi\) | |||||||
\(432\) | −27.0198 | −1.29999 | ||||||||
\(433\) | 12.3477 | 0.593391 | 0.296696 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296696 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(434\) | 2.57725 | 0.123712 | ||||||||
\(435\) | −26.5485 | −1.27290 | ||||||||
\(436\) | −34.7235 | −1.66295 | ||||||||
\(437\) | 2.05347 | 0.0982307 | ||||||||
\(438\) | 1.76657 | 0.0844102 | ||||||||
\(439\) | 13.7986 | 0.658572 | 0.329286 | − | 0.944230i | \(-0.393192\pi\) | ||||
0.329286 | + | 0.944230i | \(0.393192\pi\) | |||||||
\(440\) | −50.1717 | −2.39184 | ||||||||
\(441\) | 0.461144 | 0.0219593 | ||||||||
\(442\) | −28.9053 | −1.37488 | ||||||||
\(443\) | −20.8176 | −0.989073 | −0.494536 | − | 0.869157i | \(-0.664662\pi\) | ||||
−0.494536 | + | 0.869157i | \(0.664662\pi\) | |||||||
\(444\) | −27.7308 | −1.31604 | ||||||||
\(445\) | −8.94257 | −0.423918 | ||||||||
\(446\) | −0.613142 | −0.0290331 | ||||||||
\(447\) | −19.8960 | −0.941050 | ||||||||
\(448\) | −4.08720 | −0.193102 | ||||||||
\(449\) | −3.58796 | −0.169326 | −0.0846631 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846631 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(450\) | 0.136477 | 0.00643358 | ||||||||
\(451\) | 11.6250 | 0.547401 | ||||||||
\(452\) | 71.3468 | 3.35587 | ||||||||
\(453\) | −39.5496 | −1.85820 | ||||||||
\(454\) | −20.8091 | −0.976621 | ||||||||
\(455\) | −7.34332 | −0.344260 | ||||||||
\(456\) | 16.7765 | 0.785632 | ||||||||
\(457\) | −9.89547 | −0.462891 | −0.231445 | − | 0.972848i | \(-0.574345\pi\) | ||||
−0.231445 | + | 0.972848i | \(0.574345\pi\) | |||||||
\(458\) | 6.01897 | 0.281248 | ||||||||
\(459\) | 16.4000 | 0.765488 | ||||||||
\(460\) | −12.2506 | −0.571187 | ||||||||
\(461\) | 24.8767 | 1.15862 | 0.579311 | − | 0.815107i | \(-0.303322\pi\) | ||||
0.579311 | + | 0.815107i | \(0.303322\pi\) | |||||||
\(462\) | −18.5757 | −0.864218 | ||||||||
\(463\) | −14.6485 | −0.680773 | −0.340387 | − | 0.940286i | \(-0.610558\pi\) | ||||
−0.340387 | + | 0.940286i | \(0.610558\pi\) | |||||||
\(464\) | −36.9464 | −1.71519 | ||||||||
\(465\) | −4.22940 | −0.196134 | ||||||||
\(466\) | −35.7141 | −1.65442 | ||||||||
\(467\) | 23.9023 | 1.10607 | 0.553033 | − | 0.833160i | \(-0.313470\pi\) | ||||
0.553033 | + | 0.833160i | \(0.313470\pi\) | |||||||
\(468\) | −6.55080 | −0.302811 | ||||||||
\(469\) | 1.77027 | 0.0817434 | ||||||||
\(470\) | 62.0923 | 2.86410 | ||||||||
\(471\) | −35.3992 | −1.63111 | ||||||||
\(472\) | 64.1821 | 2.95422 | ||||||||
\(473\) | 2.18194 | 0.100326 | ||||||||
\(474\) | −44.6186 | −2.04940 | ||||||||
\(475\) | 0.187035 | 0.00858174 | ||||||||
\(476\) | −14.8407 | −0.680221 | ||||||||
\(477\) | −3.10117 | −0.141993 | ||||||||
\(478\) | −26.3075 | −1.20328 | ||||||||
\(479\) | −0.163964 | −0.00749172 | −0.00374586 | − | 0.999993i | \(-0.501192\pi\) | ||||
−0.00374586 | + | 0.999993i | \(0.501192\pi\) | |||||||
\(480\) | −12.0680 | −0.550826 | ||||||||
\(481\) | 11.5903 | 0.528474 | ||||||||
\(482\) | 69.7040 | 3.17493 | ||||||||
\(483\) | −2.41334 | −0.109811 | ||||||||
\(484\) | 20.8987 | 0.949940 | ||||||||
\(485\) | 0.0474740 | 0.00215569 | ||||||||
\(486\) | 11.9027 | 0.539919 | ||||||||
\(487\) | 25.3053 | 1.14669 | 0.573347 | − | 0.819313i | \(-0.305645\pi\) | ||||
0.573347 | + | 0.819313i | \(0.305645\pi\) | |||||||
\(488\) | 8.56807 | 0.387858 | ||||||||
\(489\) | −26.8371 | −1.21362 | ||||||||
\(490\) | −5.53442 | −0.250020 | ||||||||
\(491\) | −5.94539 | −0.268312 | −0.134156 | − | 0.990960i | \(-0.542832\pi\) | ||||
−0.134156 | + | 0.990960i | \(0.542832\pi\) | |||||||
\(492\) | 23.1902 | 1.04550 | ||||||||
\(493\) | 22.4251 | 1.00998 | ||||||||
\(494\) | −13.1783 | −0.592921 | ||||||||
\(495\) | 4.06148 | 0.182550 | ||||||||
\(496\) | −5.88588 | −0.264284 | ||||||||
\(497\) | −9.11314 | −0.408780 | ||||||||
\(498\) | −74.0624 | −3.31882 | ||||||||
\(499\) | −33.6053 | −1.50438 | −0.752190 | − | 0.658947i | \(-0.771002\pi\) | ||||
−0.752190 | + | 0.658947i | \(0.771002\pi\) | |||||||
\(500\) | −48.3350 | −2.16161 | ||||||||
\(501\) | 21.6793 | 0.968558 | ||||||||
\(502\) | −55.4715 | −2.47581 | ||||||||
\(503\) | −0.879890 | −0.0392323 | −0.0196162 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196162 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(504\) | −2.62693 | −0.117013 | ||||||||
\(505\) | −30.2539 | −1.34628 | ||||||||
\(506\) | 12.9522 | 0.575794 | ||||||||
\(507\) | −3.63544 | −0.161455 | ||||||||
\(508\) | −11.2214 | −0.497868 | ||||||||
\(509\) | −35.6092 | −1.57835 | −0.789176 | − | 0.614167i | \(-0.789492\pi\) | ||||
−0.789176 | + | 0.614167i | \(0.789492\pi\) | |||||||
\(510\) | 35.7502 | 1.58305 | ||||||||
\(511\) | −0.379090 | −0.0167699 | ||||||||
\(512\) | 48.3798 | 2.13810 | ||||||||
\(513\) | 7.47701 | 0.330118 | ||||||||
\(514\) | −49.4704 | −2.18205 | ||||||||
\(515\) | 5.95257 | 0.262301 | ||||||||
\(516\) | 4.35267 | 0.191616 | ||||||||
\(517\) | −44.7219 | −1.96687 | ||||||||
\(518\) | 8.73525 | 0.383805 | ||||||||
\(519\) | 22.4712 | 0.986378 | ||||||||
\(520\) | 41.8316 | 1.83444 | ||||||||
\(521\) | −10.6697 | −0.467447 | −0.233724 | − | 0.972303i | \(-0.575091\pi\) | ||||
−0.233724 | + | 0.972303i | \(0.575091\pi\) | |||||||
\(522\) | 7.46027 | 0.326527 | ||||||||
\(523\) | 19.0981 | 0.835103 | 0.417552 | − | 0.908653i | \(-0.362888\pi\) | ||||
0.417552 | + | 0.908653i | \(0.362888\pi\) | |||||||
\(524\) | −53.6489 | −2.34366 | ||||||||
\(525\) | −0.219812 | −0.00959340 | ||||||||
\(526\) | 21.0140 | 0.916255 | ||||||||
\(527\) | 3.57252 | 0.155621 | ||||||||
\(528\) | 42.4228 | 1.84621 | ||||||||
\(529\) | −21.3173 | −0.926837 | ||||||||
\(530\) | 37.2186 | 1.61667 | ||||||||
\(531\) | −5.19564 | −0.225472 | ||||||||
\(532\) | −6.76607 | −0.293346 | ||||||||
\(533\) | −9.69258 | −0.419832 | ||||||||
\(534\) | 18.8608 | 0.816186 | ||||||||
\(535\) | 32.5267 | 1.40625 | ||||||||
\(536\) | −10.0844 | −0.435581 | ||||||||
\(537\) | 35.4497 | 1.52977 | ||||||||
\(538\) | 8.61267 | 0.371318 | ||||||||
\(539\) | 3.98616 | 0.171696 | ||||||||
\(540\) | −44.6063 | −1.91955 | ||||||||
\(541\) | −11.1307 | −0.478544 | −0.239272 | − | 0.970953i | \(-0.576909\pi\) | ||||
−0.239272 | + | 0.970953i | \(0.576909\pi\) | |||||||
\(542\) | −52.6825 | −2.26291 | ||||||||
\(543\) | 5.05422 | 0.216897 | ||||||||
\(544\) | 10.1937 | 0.437049 | ||||||||
\(545\) | −17.9498 | −0.768883 | ||||||||
\(546\) | 15.4878 | 0.662817 | ||||||||
\(547\) | −12.1905 | −0.521228 | −0.260614 | − | 0.965443i | \(-0.583925\pi\) | ||||
−0.260614 | + | 0.965443i | \(0.583925\pi\) | |||||||
\(548\) | 42.0256 | 1.79525 | ||||||||
\(549\) | −0.693598 | −0.0296021 | ||||||||
\(550\) | 1.17971 | 0.0503032 | ||||||||
\(551\) | 10.2239 | 0.435554 | ||||||||
\(552\) | 13.7477 | 0.585141 | ||||||||
\(553\) | 9.57473 | 0.407159 | ||||||||
\(554\) | 8.52436 | 0.362165 | ||||||||
\(555\) | −14.3350 | −0.608486 | ||||||||
\(556\) | 1.13988 | 0.0483416 | ||||||||
\(557\) | −32.4232 | −1.37381 | −0.686907 | − | 0.726745i | \(-0.741032\pi\) | ||||
−0.686907 | + | 0.726745i | \(0.741032\pi\) | |||||||
\(558\) | 1.18849 | 0.0503126 | ||||||||
\(559\) | −1.81924 | −0.0769456 | ||||||||
\(560\) | 12.6394 | 0.534112 | ||||||||
\(561\) | −25.7491 | −1.08713 | ||||||||
\(562\) | 0.266741 | 0.0112518 | ||||||||
\(563\) | 28.6414 | 1.20709 | 0.603546 | − | 0.797328i | \(-0.293754\pi\) | ||||
0.603546 | + | 0.797328i | \(0.293754\pi\) | |||||||
\(564\) | −89.2138 | −3.75658 | ||||||||
\(565\) | 36.8816 | 1.55162 | ||||||||
\(566\) | −75.5372 | −3.17507 | ||||||||
\(567\) | −10.1708 | −0.427133 | ||||||||
\(568\) | 51.9135 | 2.17824 | ||||||||
\(569\) | 23.7488 | 0.995602 | 0.497801 | − | 0.867291i | \(-0.334141\pi\) | ||||
0.497801 | + | 0.867291i | \(0.334141\pi\) | |||||||
\(570\) | 16.2990 | 0.682691 | ||||||||
\(571\) | 25.8537 | 1.08195 | 0.540973 | − | 0.841040i | \(-0.318056\pi\) | ||||
0.540973 | + | 0.841040i | \(0.318056\pi\) | |||||||
\(572\) | −56.6255 | −2.36763 | ||||||||
\(573\) | −15.2789 | −0.638285 | ||||||||
\(574\) | −7.30497 | −0.304904 | ||||||||
\(575\) | 0.153268 | 0.00639170 | ||||||||
\(576\) | −1.88479 | −0.0785328 | ||||||||
\(577\) | −18.3638 | −0.764493 | −0.382247 | − | 0.924060i | \(-0.624850\pi\) | ||||
−0.382247 | + | 0.924060i | \(0.624850\pi\) | |||||||
\(578\) | 12.3846 | 0.515131 | ||||||||
\(579\) | −24.4255 | −1.01509 | ||||||||
\(580\) | −60.9939 | −2.53263 | ||||||||
\(581\) | 15.8931 | 0.659357 | ||||||||
\(582\) | −0.100128 | −0.00415042 | ||||||||
\(583\) | −26.8067 | −1.11022 | ||||||||
\(584\) | 2.15950 | 0.0893609 | ||||||||
\(585\) | −3.38633 | −0.140008 | ||||||||
\(586\) | −47.5100 | −1.96262 | ||||||||
\(587\) | −26.4890 | −1.09332 | −0.546660 | − | 0.837355i | \(-0.684101\pi\) | ||||
−0.546660 | + | 0.837355i | \(0.684101\pi\) | |||||||
\(588\) | 7.95182 | 0.327928 | ||||||||
\(589\) | 1.62876 | 0.0671119 | ||||||||
\(590\) | 62.3554 | 2.56713 | ||||||||
\(591\) | −11.0326 | −0.453819 | ||||||||
\(592\) | −19.9494 | −0.819915 | ||||||||
\(593\) | −13.4733 | −0.553281 | −0.276641 | − | 0.960973i | \(-0.589221\pi\) | ||||
−0.276641 | + | 0.960973i | \(0.589221\pi\) | |||||||
\(594\) | 47.1609 | 1.93504 | ||||||||
\(595\) | −7.67165 | −0.314507 | ||||||||
\(596\) | −45.7102 | −1.87236 | ||||||||
\(597\) | −12.0017 | −0.491198 | ||||||||
\(598\) | −10.7991 | −0.441609 | ||||||||
\(599\) | −17.0337 | −0.695980 | −0.347990 | − | 0.937498i | \(-0.613136\pi\) | ||||
−0.347990 | + | 0.937498i | \(0.613136\pi\) | |||||||
\(600\) | 1.25217 | 0.0511197 | ||||||||
\(601\) | −44.0185 | −1.79555 | −0.897777 | − | 0.440450i | \(-0.854819\pi\) | ||||
−0.897777 | + | 0.440450i | \(0.854819\pi\) | |||||||
\(602\) | −1.37110 | −0.0558818 | ||||||||
\(603\) | 0.816349 | 0.0332443 | ||||||||
\(604\) | −90.8634 | −3.69718 | ||||||||
\(605\) | 10.8032 | 0.439214 | ||||||||
\(606\) | 63.8086 | 2.59205 | ||||||||
\(607\) | −1.31107 | −0.0532147 | −0.0266073 | − | 0.999646i | \(-0.508470\pi\) | ||||
−0.0266073 | + | 0.999646i | \(0.508470\pi\) | |||||||
\(608\) | 4.64743 | 0.188478 | ||||||||
\(609\) | −12.0157 | −0.486899 | ||||||||
\(610\) | 8.32421 | 0.337037 | ||||||||
\(611\) | 37.2877 | 1.50850 | ||||||||
\(612\) | −6.84369 | −0.276640 | ||||||||
\(613\) | 38.4074 | 1.55126 | 0.775629 | − | 0.631189i | \(-0.217433\pi\) | ||||
0.775629 | + | 0.631189i | \(0.217433\pi\) | |||||||
\(614\) | −57.3288 | −2.31360 | ||||||||
\(615\) | 11.9878 | 0.483396 | ||||||||
\(616\) | −22.7074 | −0.914906 | ||||||||
\(617\) | 5.27196 | 0.212241 | 0.106121 | − | 0.994353i | \(-0.466157\pi\) | ||||
0.106121 | + | 0.994353i | \(0.466157\pi\) | |||||||
\(618\) | −12.5546 | −0.505019 | ||||||||
\(619\) | −1.54284 | −0.0620119 | −0.0310059 | − | 0.999519i | \(-0.509871\pi\) | ||||
−0.0310059 | + | 0.999519i | \(0.509871\pi\) | |||||||
\(620\) | −9.71686 | −0.390239 | ||||||||
\(621\) | 6.12712 | 0.245873 | ||||||||
\(622\) | −57.2951 | −2.29732 | ||||||||
\(623\) | −4.04735 | −0.162153 | ||||||||
\(624\) | −35.3708 | −1.41596 | ||||||||
\(625\) | −24.3953 | −0.975811 | ||||||||
\(626\) | 11.4117 | 0.456102 | ||||||||
\(627\) | −11.7394 | −0.468825 | ||||||||
\(628\) | −81.3280 | −3.24534 | ||||||||
\(629\) | 12.1086 | 0.482800 | ||||||||
\(630\) | −2.55217 | −0.101681 | ||||||||
\(631\) | 9.47469 | 0.377182 | 0.188591 | − | 0.982056i | \(-0.439608\pi\) | ||||
0.188591 | + | 0.982056i | \(0.439608\pi\) | |||||||
\(632\) | −54.5430 | −2.16960 | ||||||||
\(633\) | 12.2147 | 0.485490 | ||||||||
\(634\) | −8.83751 | −0.350983 | ||||||||
\(635\) | −5.80072 | −0.230194 | ||||||||
\(636\) | −53.4755 | −2.12044 | ||||||||
\(637\) | −3.32354 | −0.131683 | ||||||||
\(638\) | 64.4870 | 2.55307 | ||||||||
\(639\) | −4.20247 | −0.166247 | ||||||||
\(640\) | 35.5937 | 1.40696 | ||||||||
\(641\) | −0.637557 | −0.0251820 | −0.0125910 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125910 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(642\) | −68.6021 | −2.70751 | ||||||||
\(643\) | 22.5675 | 0.889977 | 0.444989 | − | 0.895536i | \(-0.353208\pi\) | ||||
0.444989 | + | 0.895536i | \(0.353208\pi\) | |||||||
\(644\) | −5.54453 | −0.218485 | ||||||||
\(645\) | 2.25004 | 0.0885954 | ||||||||
\(646\) | −13.7675 | −0.541677 | ||||||||
\(647\) | 19.8306 | 0.779622 | 0.389811 | − | 0.920895i | \(-0.372540\pi\) | ||||
0.389811 | + | 0.920895i | \(0.372540\pi\) | |||||||
\(648\) | 57.9384 | 2.27603 | ||||||||
\(649\) | −44.9114 | −1.76293 | ||||||||
\(650\) | −0.983609 | −0.0385803 | ||||||||
\(651\) | −1.91420 | −0.0750234 | ||||||||
\(652\) | −61.6570 | −2.41467 | ||||||||
\(653\) | −22.6337 | −0.885726 | −0.442863 | − | 0.896589i | \(-0.646037\pi\) | ||||
−0.442863 | + | 0.896589i | \(0.646037\pi\) | |||||||
\(654\) | 37.8579 | 1.48036 | ||||||||
\(655\) | −27.7330 | −1.08362 | ||||||||
\(656\) | 16.6830 | 0.651360 | ||||||||
\(657\) | −0.174815 | −0.00682019 | ||||||||
\(658\) | 28.1025 | 1.09555 | ||||||||
\(659\) | −6.35338 | −0.247492 | −0.123746 | − | 0.992314i | \(-0.539491\pi\) | ||||
−0.123746 | + | 0.992314i | \(0.539491\pi\) | |||||||
\(660\) | 70.0347 | 2.72610 | ||||||||
\(661\) | −3.70713 | −0.144190 | −0.0720952 | − | 0.997398i | \(-0.522969\pi\) | ||||
−0.0720952 | + | 0.997398i | \(0.522969\pi\) | |||||||
\(662\) | 82.7931 | 3.21784 | ||||||||
\(663\) | 21.4688 | 0.833778 | ||||||||
\(664\) | −90.5358 | −3.51347 | ||||||||
\(665\) | −3.49762 | −0.135632 | ||||||||
\(666\) | 4.02821 | 0.156090 | ||||||||
\(667\) | 8.37811 | 0.324402 | ||||||||
\(668\) | 49.8071 | 1.92709 | ||||||||
\(669\) | 0.455398 | 0.0176067 | ||||||||
\(670\) | −9.79740 | −0.378507 | ||||||||
\(671\) | −5.99550 | −0.231454 | ||||||||
\(672\) | −5.46189 | −0.210697 | ||||||||
\(673\) | −6.74909 | −0.260158 | −0.130079 | − | 0.991504i | \(-0.541523\pi\) | ||||
−0.130079 | + | 0.991504i | \(0.541523\pi\) | |||||||
\(674\) | 50.6156 | 1.94964 | ||||||||
\(675\) | 0.558072 | 0.0214802 | ||||||||
\(676\) | −8.35225 | −0.321241 | ||||||||
\(677\) | −15.8817 | −0.610385 | −0.305192 | − | 0.952291i | \(-0.598721\pi\) | ||||
−0.305192 | + | 0.952291i | \(0.598721\pi\) | |||||||
\(678\) | −77.7870 | −2.98739 | ||||||||
\(679\) | 0.0214864 | 0.000824573 0 | ||||||||
\(680\) | 43.7020 | 1.67589 | ||||||||
\(681\) | 15.4555 | 0.592258 | ||||||||
\(682\) | 10.2733 | 0.393387 | ||||||||
\(683\) | 19.4604 | 0.744632 | 0.372316 | − | 0.928106i | \(-0.378564\pi\) | ||||
0.372316 | + | 0.928106i | \(0.378564\pi\) | |||||||
\(684\) | −3.12014 | −0.119301 | ||||||||
\(685\) | 21.7245 | 0.830050 | ||||||||
\(686\) | −2.50484 | −0.0956352 | ||||||||
\(687\) | −4.47046 | −0.170559 | ||||||||
\(688\) | 3.13129 | 0.119379 | ||||||||
\(689\) | 22.3506 | 0.851489 | ||||||||
\(690\) | 13.3564 | 0.508470 | ||||||||
\(691\) | −5.09501 | −0.193823 | −0.0969117 | − | 0.995293i | \(-0.530896\pi\) | ||||
−0.0969117 | + | 0.995293i | \(0.530896\pi\) | |||||||
\(692\) | 51.6266 | 1.96255 | ||||||||
\(693\) | 1.83820 | 0.0698273 | ||||||||
\(694\) | −13.5366 | −0.513843 | ||||||||
\(695\) | 0.589242 | 0.0223512 | ||||||||
\(696\) | 68.4478 | 2.59451 | ||||||||
\(697\) | −10.1259 | −0.383548 | ||||||||
\(698\) | 17.4429 | 0.660222 | ||||||||
\(699\) | 26.5259 | 1.00330 | ||||||||
\(700\) | −0.505009 | −0.0190875 | ||||||||
\(701\) | −12.3684 | −0.467150 | −0.233575 | − | 0.972339i | \(-0.575042\pi\) | ||||
−0.233575 | + | 0.972339i | \(0.575042\pi\) | |||||||
\(702\) | −39.3213 | −1.48409 | ||||||||
\(703\) | 5.52046 | 0.208208 | ||||||||
\(704\) | −16.2922 | −0.614036 | ||||||||
\(705\) | −46.1177 | −1.73689 | ||||||||
\(706\) | 6.55453 | 0.246683 | ||||||||
\(707\) | −13.6927 | −0.514968 | ||||||||
\(708\) | −89.5919 | −3.36707 | ||||||||
\(709\) | 29.7263 | 1.11640 | 0.558198 | − | 0.829708i | \(-0.311493\pi\) | ||||
0.558198 | + | 0.829708i | \(0.311493\pi\) | |||||||
\(710\) | 50.4359 | 1.89283 | ||||||||
\(711\) | 4.41534 | 0.165588 | ||||||||
\(712\) | 23.0559 | 0.864057 | ||||||||
\(713\) | 1.33471 | 0.0499851 | ||||||||
\(714\) | 16.1803 | 0.605533 | ||||||||
\(715\) | −29.2717 | −1.09470 | ||||||||
\(716\) | 81.4442 | 3.04371 | ||||||||
\(717\) | 19.5393 | 0.729710 | ||||||||
\(718\) | −38.2059 | −1.42583 | ||||||||
\(719\) | 4.04614 | 0.150896 | 0.0754478 | − | 0.997150i | \(-0.475961\pi\) | ||||
0.0754478 | + | 0.997150i | \(0.475961\pi\) | |||||||
\(720\) | 5.82859 | 0.217219 | ||||||||
\(721\) | 2.69409 | 0.100333 | ||||||||
\(722\) | 41.3151 | 1.53759 | ||||||||
\(723\) | −51.7711 | −1.92539 | ||||||||
\(724\) | 11.6118 | 0.431550 | ||||||||
\(725\) | 0.763098 | 0.0283407 | ||||||||
\(726\) | −22.7851 | −0.845636 | ||||||||
\(727\) | −29.6643 | −1.10019 | −0.550094 | − | 0.835102i | \(-0.685408\pi\) | ||||
−0.550094 | + | 0.835102i | \(0.685408\pi\) | |||||||
\(728\) | 18.9327 | 0.701692 | ||||||||
\(729\) | 21.6718 | 0.802661 | ||||||||
\(730\) | 2.09804 | 0.0776520 | ||||||||
\(731\) | −1.90058 | −0.0702955 | ||||||||
\(732\) | −11.9602 | −0.442061 | ||||||||
\(733\) | −21.8489 | −0.807009 | −0.403504 | − | 0.914978i | \(-0.632208\pi\) | ||||
−0.403504 | + | 0.914978i | \(0.632208\pi\) | |||||||
\(734\) | −0.993317 | −0.0366640 | ||||||||
\(735\) | 4.11057 | 0.151621 | ||||||||
\(736\) | 3.80839 | 0.140379 | ||||||||
\(737\) | 7.05657 | 0.259932 | ||||||||
\(738\) | −3.36865 | −0.124002 | ||||||||
\(739\) | −24.8060 | −0.912502 | −0.456251 | − | 0.889851i | \(-0.650808\pi\) | ||||
−0.456251 | + | 0.889851i | \(0.650808\pi\) | |||||||
\(740\) | −32.9340 | −1.21068 | ||||||||
\(741\) | 9.78792 | 0.359568 | ||||||||
\(742\) | 16.8449 | 0.618395 | ||||||||
\(743\) | −4.12351 | −0.151277 | −0.0756384 | − | 0.997135i | \(-0.524099\pi\) | ||||
−0.0756384 | + | 0.997135i | \(0.524099\pi\) | |||||||
\(744\) | 10.9043 | 0.399772 | ||||||||
\(745\) | −23.6292 | −0.865707 | ||||||||
\(746\) | −17.6373 | −0.645746 | ||||||||
\(747\) | 7.32901 | 0.268154 | ||||||||
\(748\) | −59.1573 | −2.16301 | ||||||||
\(749\) | 14.7213 | 0.537906 | ||||||||
\(750\) | 52.6981 | 1.92426 | ||||||||
\(751\) | −17.2718 | −0.630256 | −0.315128 | − | 0.949049i | \(-0.602047\pi\) | ||||
−0.315128 | + | 0.949049i | \(0.602047\pi\) | |||||||
\(752\) | −64.1800 | −2.34040 | ||||||||
\(753\) | 41.2002 | 1.50142 | ||||||||
\(754\) | −53.7673 | −1.95809 | ||||||||
\(755\) | −46.9704 | −1.70943 | ||||||||
\(756\) | −20.1885 | −0.734249 | ||||||||
\(757\) | −14.5235 | −0.527867 | −0.263934 | − | 0.964541i | \(-0.585020\pi\) | ||||
−0.263934 | + | 0.964541i | \(0.585020\pi\) | |||||||
\(758\) | −79.7202 | −2.89557 | ||||||||
\(759\) | −9.61995 | −0.349182 | ||||||||
\(760\) | 19.9243 | 0.722732 | ||||||||
\(761\) | −32.8399 | −1.19044 | −0.595222 | − | 0.803561i | \(-0.702936\pi\) | ||||
−0.595222 | + | 0.803561i | \(0.702936\pi\) | |||||||
\(762\) | 12.2343 | 0.443202 | ||||||||
\(763\) | −8.12394 | −0.294106 | ||||||||
\(764\) | −35.1025 | −1.26997 | ||||||||
\(765\) | −3.53774 | −0.127907 | ||||||||
\(766\) | −30.7477 | −1.11096 | ||||||||
\(767\) | 37.4458 | 1.35209 | ||||||||
\(768\) | −59.8629 | −2.16012 | ||||||||
\(769\) | −5.26142 | −0.189732 | −0.0948658 | − | 0.995490i | \(-0.530242\pi\) | ||||
−0.0948658 | + | 0.995490i | \(0.530242\pi\) | |||||||
\(770\) | −22.0611 | −0.795026 | ||||||||
\(771\) | 36.7431 | 1.32327 | ||||||||
\(772\) | −56.1165 | −2.01968 | ||||||||
\(773\) | −42.9071 | −1.54326 | −0.771630 | − | 0.636072i | \(-0.780558\pi\) | ||||
−0.771630 | + | 0.636072i | \(0.780558\pi\) | |||||||
\(774\) | −0.632275 | −0.0227266 | ||||||||
\(775\) | 0.121568 | 0.00436685 | ||||||||
\(776\) | −0.122398 | −0.00439385 | ||||||||
\(777\) | −6.48792 | −0.232753 | ||||||||
\(778\) | −47.2256 | −1.69312 | ||||||||
\(779\) | −4.61656 | −0.165405 | ||||||||
\(780\) | −58.3928 | −2.09080 | ||||||||
\(781\) | −36.3264 | −1.29986 | ||||||||
\(782\) | −11.2820 | −0.403442 | ||||||||
\(783\) | 30.5060 | 1.09020 | ||||||||
\(784\) | 5.72051 | 0.204304 | ||||||||
\(785\) | −42.0413 | −1.50052 | ||||||||
\(786\) | 58.4916 | 2.08633 | ||||||||
\(787\) | 21.4261 | 0.763757 | 0.381878 | − | 0.924213i | \(-0.375277\pi\) | ||||
0.381878 | + | 0.924213i | \(0.375277\pi\) | |||||||
\(788\) | −25.3468 | −0.902943 | ||||||||
\(789\) | −15.6077 | −0.555650 | ||||||||
\(790\) | −52.9906 | −1.88532 | ||||||||
\(791\) | 16.6924 | 0.593512 | ||||||||
\(792\) | −10.4714 | −0.372084 | ||||||||
\(793\) | 4.99887 | 0.177515 | ||||||||
\(794\) | 11.4131 | 0.405036 | ||||||||
\(795\) | −27.6433 | −0.980407 | ||||||||
\(796\) | −27.5734 | −0.977314 | ||||||||
\(797\) | −20.2470 | −0.717187 | −0.358594 | − | 0.933494i | \(-0.616744\pi\) | ||||
−0.358594 | + | 0.933494i | \(0.616744\pi\) | |||||||
\(798\) | 7.37683 | 0.261137 | ||||||||
\(799\) | 38.9549 | 1.37813 | ||||||||
\(800\) | 0.346877 | 0.0122639 | ||||||||
\(801\) | −1.86641 | −0.0659464 | ||||||||
\(802\) | −55.2337 | −1.95037 | ||||||||
\(803\) | −1.51111 | −0.0533260 | ||||||||
\(804\) | 14.0768 | 0.496452 | ||||||||
\(805\) | −2.86616 | −0.101019 | ||||||||
\(806\) | −8.56560 | −0.301710 | ||||||||
\(807\) | −6.39687 | −0.225181 | ||||||||
\(808\) | 78.0013 | 2.74408 | ||||||||
\(809\) | 32.6308 | 1.14724 | 0.573619 | − | 0.819122i | \(-0.305539\pi\) | ||||
0.573619 | + | 0.819122i | \(0.305539\pi\) | |||||||
\(810\) | 56.2893 | 1.97781 | ||||||||
\(811\) | 36.4847 | 1.28115 | 0.640576 | − | 0.767895i | \(-0.278696\pi\) | ||||
0.640576 | + | 0.767895i | \(0.278696\pi\) | |||||||
\(812\) | −27.6054 | −0.968761 | ||||||||
\(813\) | 39.1288 | 1.37231 | ||||||||
\(814\) | 34.8201 | 1.22044 | ||||||||
\(815\) | −31.8726 | −1.11645 | ||||||||
\(816\) | −36.9523 | −1.29359 | ||||||||
\(817\) | −0.866501 | −0.0303150 | ||||||||
\(818\) | −72.2041 | −2.52456 | ||||||||
\(819\) | −1.53263 | −0.0535545 | ||||||||
\(820\) | 27.5415 | 0.961791 | ||||||||
\(821\) | −25.7410 | −0.898368 | −0.449184 | − | 0.893439i | \(-0.648285\pi\) | ||||
−0.449184 | + | 0.893439i | \(0.648285\pi\) | |||||||
\(822\) | −45.8192 | −1.59813 | ||||||||
\(823\) | −48.4857 | −1.69010 | −0.845052 | − | 0.534684i | \(-0.820431\pi\) | ||||
−0.845052 | + | 0.534684i | \(0.820431\pi\) | |||||||
\(824\) | −15.3470 | −0.534639 | ||||||||
\(825\) | −0.876207 | −0.0305056 | ||||||||
\(826\) | 28.2216 | 0.981956 | ||||||||
\(827\) | 2.41438 | 0.0839561 | 0.0419781 | − | 0.999119i | \(-0.486634\pi\) | ||||
0.0419781 | + | 0.999119i | \(0.486634\pi\) | |||||||
\(828\) | −2.55683 | −0.0888560 | ||||||||
\(829\) | −22.0487 | −0.765784 | −0.382892 | − | 0.923793i | \(-0.625072\pi\) | ||||
−0.382892 | + | 0.923793i | \(0.625072\pi\) | |||||||
\(830\) | −87.9590 | −3.05310 | ||||||||
\(831\) | −6.33128 | −0.219630 | ||||||||
\(832\) | 13.5839 | 0.470939 | ||||||||
\(833\) | −3.47214 | −0.120302 | ||||||||
\(834\) | −1.24277 | −0.0430337 | ||||||||
\(835\) | 25.7470 | 0.891011 | ||||||||
\(836\) | −26.9706 | −0.932799 | ||||||||
\(837\) | 4.85987 | 0.167982 | ||||||||
\(838\) | −2.23875 | −0.0773362 | ||||||||
\(839\) | −25.5581 | −0.882364 | −0.441182 | − | 0.897418i | \(-0.645441\pi\) | ||||
−0.441182 | + | 0.897418i | \(0.645441\pi\) | |||||||
\(840\) | −23.4161 | −0.807931 | ||||||||
\(841\) | 12.7134 | 0.438393 | ||||||||
\(842\) | −12.9779 | −0.447250 | ||||||||
\(843\) | −0.198116 | −0.00682348 | ||||||||
\(844\) | 28.0627 | 0.965957 | ||||||||
\(845\) | −4.31757 | −0.148529 | ||||||||
\(846\) | 12.9593 | 0.445551 | ||||||||
\(847\) | 4.88947 | 0.168004 | ||||||||
\(848\) | −38.4700 | −1.32107 | ||||||||
\(849\) | 56.1036 | 1.92547 | ||||||||
\(850\) | −1.02759 | −0.0352460 | ||||||||
\(851\) | 4.52380 | 0.155074 | ||||||||
\(852\) | −72.4661 | −2.48265 | ||||||||
\(853\) | 42.3468 | 1.44993 | 0.724964 | − | 0.688787i | \(-0.241856\pi\) | ||||
0.724964 | + | 0.688787i | \(0.241856\pi\) | |||||||
\(854\) | 3.76748 | 0.128920 | ||||||||
\(855\) | −1.61291 | −0.0551602 | ||||||||
\(856\) | −83.8609 | −2.86631 | ||||||||
\(857\) | 0.526136 | 0.0179725 | 0.00898623 | − | 0.999960i | \(-0.497140\pi\) | ||||
0.00898623 | + | 0.999960i | \(0.497140\pi\) | |||||||
\(858\) | 61.7369 | 2.10766 | ||||||||
\(859\) | −35.0044 | −1.19433 | −0.597167 | − | 0.802117i | \(-0.703707\pi\) | ||||
−0.597167 | + | 0.802117i | \(0.703707\pi\) | |||||||
\(860\) | 5.16937 | 0.176274 | ||||||||
\(861\) | 5.42561 | 0.184904 | ||||||||
\(862\) | −43.9237 | −1.49605 | ||||||||
\(863\) | 1.00000 | 0.0340404 | ||||||||
\(864\) | 13.8669 | 0.471763 | ||||||||
\(865\) | 26.6876 | 0.907405 | ||||||||
\(866\) | −30.9289 | −1.05101 | ||||||||
\(867\) | −9.19838 | −0.312393 | ||||||||
\(868\) | −4.39778 | −0.149271 | ||||||||
\(869\) | 38.1664 | 1.29471 | ||||||||
\(870\) | 66.4997 | 2.25455 | ||||||||
\(871\) | −5.88355 | −0.199356 | ||||||||
\(872\) | 46.2784 | 1.56719 | ||||||||
\(873\) | 0.00990835 | 0.000335347 0 | ||||||||
\(874\) | −5.14361 | −0.173985 | ||||||||
\(875\) | −11.3085 | −0.382297 | ||||||||
\(876\) | −3.01445 | −0.101849 | ||||||||
\(877\) | −23.0587 | −0.778637 | −0.389318 | − | 0.921103i | \(-0.627289\pi\) | ||||
−0.389318 | + | 0.921103i | \(0.627289\pi\) | |||||||
\(878\) | −34.5633 | −1.16646 | ||||||||
\(879\) | 35.2870 | 1.19020 | ||||||||
\(880\) | 50.3827 | 1.69840 | ||||||||
\(881\) | −49.6781 | −1.67370 | −0.836848 | − | 0.547435i | \(-0.815604\pi\) | ||||
−0.836848 | + | 0.547435i | \(0.815604\pi\) | |||||||
\(882\) | −1.15509 | −0.0388940 | ||||||||
\(883\) | 23.7020 | 0.797636 | 0.398818 | − | 0.917030i | \(-0.369421\pi\) | ||||
0.398818 | + | 0.917030i | \(0.369421\pi\) | |||||||
\(884\) | 49.3235 | 1.65893 | ||||||||
\(885\) | −46.3131 | −1.55680 | ||||||||
\(886\) | 52.1447 | 1.75183 | ||||||||
\(887\) | −22.2971 | −0.748663 | −0.374331 | − | 0.927295i | \(-0.622128\pi\) | ||||
−0.374331 | + | 0.927295i | \(0.622128\pi\) | |||||||
\(888\) | 36.9587 | 1.24025 | ||||||||
\(889\) | −2.62536 | −0.0880519 | ||||||||
\(890\) | 22.3997 | 0.750840 | ||||||||
\(891\) | −40.5424 | −1.35822 | ||||||||
\(892\) | 1.04626 | 0.0350312 | ||||||||
\(893\) | 17.7601 | 0.594319 | ||||||||
\(894\) | 49.8364 | 1.66678 | ||||||||
\(895\) | 42.1013 | 1.40729 | ||||||||
\(896\) | 16.1095 | 0.538179 | ||||||||
\(897\) | 8.02082 | 0.267807 | ||||||||
\(898\) | 8.98725 | 0.299909 | ||||||||
\(899\) | 6.64531 | 0.221633 | ||||||||
\(900\) | −0.232882 | −0.00776273 | ||||||||
\(901\) | 23.3499 | 0.777898 | ||||||||
\(902\) | −29.1188 | −0.969550 | ||||||||
\(903\) | 1.01835 | 0.0338887 | ||||||||
\(904\) | −95.0888 | −3.16261 | ||||||||
\(905\) | 6.00256 | 0.199532 | ||||||||
\(906\) | 99.0654 | 3.29123 | ||||||||
\(907\) | −14.7309 | −0.489131 | −0.244566 | − | 0.969633i | \(-0.578645\pi\) | ||||
−0.244566 | + | 0.969633i | \(0.578645\pi\) | |||||||
\(908\) | 35.5084 | 1.17839 | ||||||||
\(909\) | −6.31432 | −0.209433 | ||||||||
\(910\) | 18.3938 | 0.609750 | ||||||||
\(911\) | −17.2748 | −0.572340 | −0.286170 | − | 0.958179i | \(-0.592382\pi\) | ||||
−0.286170 | + | 0.958179i | \(0.592382\pi\) | |||||||
\(912\) | −16.8471 | −0.557862 | ||||||||
\(913\) | 63.3524 | 2.09666 | ||||||||
\(914\) | 24.7866 | 0.819866 | ||||||||
\(915\) | −6.18263 | −0.204391 | ||||||||
\(916\) | −10.2707 | −0.339353 | ||||||||
\(917\) | −12.5517 | −0.414495 | ||||||||
\(918\) | −41.0794 | −1.35582 | ||||||||
\(919\) | 36.2464 | 1.19566 | 0.597829 | − | 0.801624i | \(-0.296030\pi\) | ||||
0.597829 | + | 0.801624i | \(0.296030\pi\) | |||||||
\(920\) | 16.3272 | 0.538293 | ||||||||
\(921\) | 42.5797 | 1.40305 | ||||||||
\(922\) | −62.3120 | −2.05214 | ||||||||
\(923\) | 30.2879 | 0.996937 | ||||||||
\(924\) | 31.6972 | 1.04276 | ||||||||
\(925\) | 0.412038 | 0.0135477 | ||||||||
\(926\) | 36.6921 | 1.20578 | ||||||||
\(927\) | 1.24236 | 0.0408046 | ||||||||
\(928\) | 18.9614 | 0.622439 | ||||||||
\(929\) | 11.8426 | 0.388543 | 0.194271 | − | 0.980948i | \(-0.437766\pi\) | ||||
0.194271 | + | 0.980948i | \(0.437766\pi\) | |||||||
\(930\) | 10.5940 | 0.347390 | ||||||||
\(931\) | −1.58300 | −0.0518806 | ||||||||
\(932\) | 60.9420 | 1.99622 | ||||||||
\(933\) | 42.5547 | 1.39318 | ||||||||
\(934\) | −59.8714 | −1.95905 | ||||||||
\(935\) | −30.5804 | −1.00009 | ||||||||
\(936\) | 8.73071 | 0.285372 | ||||||||
\(937\) | 20.9163 | 0.683304 | 0.341652 | − | 0.939826i | \(-0.389014\pi\) | ||||
0.341652 | + | 0.939826i | \(0.389014\pi\) | |||||||
\(938\) | −4.43424 | −0.144783 | ||||||||
\(939\) | −8.47576 | −0.276596 | ||||||||
\(940\) | −105.953 | −3.45581 | ||||||||
\(941\) | 10.1482 | 0.330820 | 0.165410 | − | 0.986225i | \(-0.447105\pi\) | ||||
0.165410 | + | 0.986225i | \(0.447105\pi\) | |||||||
\(942\) | 88.6693 | 2.88900 | ||||||||
\(943\) | −3.78309 | −0.123194 | ||||||||
\(944\) | −64.4520 | −2.09773 | ||||||||
\(945\) | −10.4361 | −0.339488 | ||||||||
\(946\) | −5.46542 | −0.177696 | ||||||||
\(947\) | −50.5995 | −1.64426 | −0.822132 | − | 0.569297i | \(-0.807216\pi\) | ||||
−0.822132 | + | 0.569297i | \(0.807216\pi\) | |||||||
\(948\) | 76.1366 | 2.47280 | ||||||||
\(949\) | 1.25992 | 0.0408987 | ||||||||
\(950\) | −0.468492 | −0.0151999 | ||||||||
\(951\) | 6.56387 | 0.212848 | ||||||||
\(952\) | 19.7792 | 0.641048 | ||||||||
\(953\) | −39.5231 | −1.28028 | −0.640140 | − | 0.768258i | \(-0.721124\pi\) | ||||
−0.640140 | + | 0.768258i | \(0.721124\pi\) | |||||||
\(954\) | 7.76792 | 0.251496 | ||||||||
\(955\) | −18.1457 | −0.587181 | ||||||||
\(956\) | 44.8907 | 1.45187 | ||||||||
\(957\) | −47.8963 | −1.54827 | ||||||||
\(958\) | 0.410704 | 0.0132692 | ||||||||
\(959\) | 9.83236 | 0.317503 | ||||||||
\(960\) | −16.8007 | −0.542240 | ||||||||
\(961\) | −29.9413 | −0.965850 | ||||||||
\(962\) | −29.0319 | −0.936027 | ||||||||
\(963\) | 6.78867 | 0.218762 | ||||||||
\(964\) | −118.942 | −3.83086 | ||||||||
\(965\) | −29.0085 | −0.933818 | ||||||||
\(966\) | 6.04502 | 0.194495 | ||||||||
\(967\) | −3.80816 | −0.122462 | −0.0612311 | − | 0.998124i | \(-0.519503\pi\) | ||||
−0.0612311 | + | 0.998124i | \(0.519503\pi\) | |||||||
\(968\) | −27.8531 | −0.895233 | ||||||||
\(969\) | 10.2256 | 0.328492 | ||||||||
\(970\) | −0.118915 | −0.00381813 | ||||||||
\(971\) | −40.0942 | −1.28669 | −0.643343 | − | 0.765578i | \(-0.722453\pi\) | ||||
−0.643343 | + | 0.765578i | \(0.722453\pi\) | |||||||
\(972\) | −20.3106 | −0.651464 | ||||||||
\(973\) | 0.266687 | 0.00854959 | ||||||||
\(974\) | −63.3857 | −2.03101 | ||||||||
\(975\) | 0.730555 | 0.0233965 | ||||||||
\(976\) | −8.60410 | −0.275410 | ||||||||
\(977\) | −32.8753 | −1.05177 | −0.525887 | − | 0.850555i | \(-0.676266\pi\) | ||||
−0.525887 | + | 0.850555i | \(0.676266\pi\) | |||||||
\(978\) | 67.2226 | 2.14954 | ||||||||
\(979\) | −16.1334 | −0.515625 | ||||||||
\(980\) | 9.44384 | 0.301673 | ||||||||
\(981\) | −3.74631 | −0.119610 | ||||||||
\(982\) | 14.8922 | 0.475231 | ||||||||
\(983\) | 17.9314 | 0.571923 | 0.285962 | − | 0.958241i | \(-0.407687\pi\) | ||||
0.285962 | + | 0.958241i | \(0.407687\pi\) | |||||||
\(984\) | −30.9073 | −0.985288 | ||||||||
\(985\) | −13.1026 | −0.417485 | ||||||||
\(986\) | −56.1713 | −1.78886 | ||||||||
\(987\) | −20.8725 | −0.664380 | ||||||||
\(988\) | 22.4873 | 0.715416 | ||||||||
\(989\) | −0.710064 | −0.0225787 | ||||||||
\(990\) | −10.1733 | −0.323330 | ||||||||
\(991\) | 47.0682 | 1.49517 | 0.747586 | − | 0.664165i | \(-0.231213\pi\) | ||||
0.747586 | + | 0.664165i | \(0.231213\pi\) | |||||||
\(992\) | 3.02072 | 0.0959079 | ||||||||
\(993\) | −61.4928 | −1.95141 | ||||||||
\(994\) | 22.8270 | 0.724027 | ||||||||
\(995\) | −14.2536 | −0.451871 | ||||||||
\(996\) | 126.379 | 4.00447 | ||||||||
\(997\) | 17.2356 | 0.545856 | 0.272928 | − | 0.962034i | \(-0.412008\pi\) | ||||
0.272928 | + | 0.962034i | \(0.412008\pi\) | |||||||
\(998\) | 84.1758 | 2.66454 | ||||||||
\(999\) | 16.4719 | 0.521147 |
(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 | 6041.2.a.c.1.4 | ✓ | 83 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.c.1.4 | ✓ | 83 | 1.1 | even | 1 | trivial |