Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.315426 | 0.223040 | 0.111520 | − | 0.993762i | \(-0.464428\pi\) | ||||
0.111520 | + | 0.993762i | \(0.464428\pi\) | |||||||
\(3\) | 2.38391 | 1.37635 | 0.688175 | − | 0.725544i | \(-0.258412\pi\) | ||||
0.688175 | + | 0.725544i | \(0.258412\pi\) | |||||||
\(4\) | −1.90051 | −0.950253 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.751948 | 0.306981 | ||||||||
\(7\) | 0.00485401 | 0.00183464 | 0.000917321 | − | 1.00000i | \(-0.499708\pi\) | ||||
0.000917321 | 1.00000i | \(0.499708\pi\) | ||||||||
\(8\) | −1.23032 | −0.434985 | ||||||||
\(9\) | 2.68302 | 0.894342 | ||||||||
\(10\) | −0.315426 | −0.0997465 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.53064 | −1.30788 | ||||||||
\(13\) | 0.139360 | 0.0386515 | 0.0193257 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193257 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(14\) | 0.00153108 | 0.000409199 0 | ||||||||
\(15\) | −2.38391 | −0.615523 | ||||||||
\(16\) | 3.41294 | 0.853234 | ||||||||
\(17\) | −1.09212 | −0.264878 | −0.132439 | − | 0.991191i | \(-0.542281\pi\) | ||||
−0.132439 | + | 0.991191i | \(0.542281\pi\) | |||||||
\(18\) | 0.846296 | 0.199474 | ||||||||
\(19\) | −4.53407 | −1.04019 | −0.520093 | − | 0.854110i | \(-0.674103\pi\) | ||||
−0.520093 | + | 0.854110i | \(0.674103\pi\) | |||||||
\(20\) | 1.90051 | 0.424966 | ||||||||
\(21\) | 0.0115715 | 0.00252511 | ||||||||
\(22\) | 0.315426 | 0.0672491 | ||||||||
\(23\) | 1.37855 | 0.287448 | 0.143724 | − | 0.989618i | \(-0.454092\pi\) | ||||
0.143724 | + | 0.989618i | \(0.454092\pi\) | |||||||
\(24\) | −2.93298 | −0.598691 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.0439578 | 0.00862083 | ||||||||
\(27\) | −0.755641 | −0.145423 | ||||||||
\(28\) | −0.00922507 | −0.00174337 | ||||||||
\(29\) | −9.29049 | −1.72520 | −0.862600 | − | 0.505886i | \(-0.831166\pi\) | ||||
−0.862600 | + | 0.505886i | \(0.831166\pi\) | |||||||
\(30\) | −0.751948 | −0.137286 | ||||||||
\(31\) | −2.10380 | −0.377854 | −0.188927 | − | 0.981991i | \(-0.560501\pi\) | ||||
−0.188927 | + | 0.981991i | \(0.560501\pi\) | |||||||
\(32\) | 3.53717 | 0.625290 | ||||||||
\(33\) | 2.38391 | 0.414985 | ||||||||
\(34\) | −0.344484 | −0.0590784 | ||||||||
\(35\) | −0.00485401 | −0.000820477 0 | ||||||||
\(36\) | −5.09911 | −0.849851 | ||||||||
\(37\) | 10.9268 | 1.79635 | 0.898175 | − | 0.439639i | \(-0.144894\pi\) | ||||
0.898175 | + | 0.439639i | \(0.144894\pi\) | |||||||
\(38\) | −1.43016 | −0.232003 | ||||||||
\(39\) | 0.332221 | 0.0531980 | ||||||||
\(40\) | 1.23032 | 0.194531 | ||||||||
\(41\) | 5.58866 | 0.872803 | 0.436401 | − | 0.899752i | \(-0.356253\pi\) | ||||
0.436401 | + | 0.899752i | \(0.356253\pi\) | |||||||
\(42\) | 0.00364996 | 0.000563201 0 | ||||||||
\(43\) | −6.58975 | −1.00493 | −0.502464 | − | 0.864598i | \(-0.667573\pi\) | ||||
−0.502464 | + | 0.864598i | \(0.667573\pi\) | |||||||
\(44\) | −1.90051 | −0.286512 | ||||||||
\(45\) | −2.68302 | −0.399962 | ||||||||
\(46\) | 0.434831 | 0.0641124 | ||||||||
\(47\) | −3.69707 | −0.539273 | −0.269636 | − | 0.962962i | \(-0.586903\pi\) | ||||
−0.269636 | + | 0.962962i | \(0.586903\pi\) | |||||||
\(48\) | 8.13613 | 1.17435 | ||||||||
\(49\) | −6.99998 | −0.999997 | ||||||||
\(50\) | 0.315426 | 0.0446080 | ||||||||
\(51\) | −2.60352 | −0.364565 | ||||||||
\(52\) | −0.264854 | −0.0367287 | ||||||||
\(53\) | −8.56197 | −1.17608 | −0.588039 | − | 0.808833i | \(-0.700100\pi\) | ||||
−0.588039 | + | 0.808833i | \(0.700100\pi\) | |||||||
\(54\) | −0.238349 | −0.0324352 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −0.00597199 | −0.000798041 0 | ||||||||
\(57\) | −10.8088 | −1.43166 | ||||||||
\(58\) | −2.93046 | −0.384789 | ||||||||
\(59\) | −4.55986 | −0.593643 | −0.296821 | − | 0.954933i | \(-0.595927\pi\) | ||||
−0.296821 | + | 0.954933i | \(0.595927\pi\) | |||||||
\(60\) | 4.53064 | 0.584902 | ||||||||
\(61\) | −10.2471 | −1.31200 | −0.656002 | − | 0.754759i | \(-0.727754\pi\) | ||||
−0.656002 | + | 0.754759i | \(0.727754\pi\) | |||||||
\(62\) | −0.663595 | −0.0842766 | ||||||||
\(63\) | 0.0130234 | 0.00164080 | ||||||||
\(64\) | −5.71016 | −0.713770 | ||||||||
\(65\) | −0.139360 | −0.0172855 | ||||||||
\(66\) | 0.751948 | 0.0925584 | ||||||||
\(67\) | 5.74607 | 0.701994 | 0.350997 | − | 0.936377i | \(-0.385843\pi\) | ||||
0.350997 | + | 0.936377i | \(0.385843\pi\) | |||||||
\(68\) | 2.07558 | 0.251701 | ||||||||
\(69\) | 3.28634 | 0.395629 | ||||||||
\(70\) | −0.00153108 | −0.000182999 0 | ||||||||
\(71\) | 12.5861 | 1.49369 | 0.746845 | − | 0.664998i | \(-0.231568\pi\) | ||||
0.746845 | + | 0.664998i | \(0.231568\pi\) | |||||||
\(72\) | −3.30098 | −0.389025 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 3.44659 | 0.400658 | ||||||||
\(75\) | 2.38391 | 0.275270 | ||||||||
\(76\) | 8.61702 | 0.988440 | ||||||||
\(77\) | 0.00485401 | 0.000553165 0 | ||||||||
\(78\) | 0.104791 | 0.0118653 | ||||||||
\(79\) | −2.38764 | −0.268630 | −0.134315 | − | 0.990939i | \(-0.542883\pi\) | ||||
−0.134315 | + | 0.990939i | \(0.542883\pi\) | |||||||
\(80\) | −3.41294 | −0.381578 | ||||||||
\(81\) | −9.85045 | −1.09449 | ||||||||
\(82\) | 1.76281 | 0.194670 | ||||||||
\(83\) | −17.1570 | −1.88323 | −0.941615 | − | 0.336693i | \(-0.890692\pi\) | ||||
−0.941615 | + | 0.336693i | \(0.890692\pi\) | |||||||
\(84\) | −0.0219917 | −0.00239950 | ||||||||
\(85\) | 1.09212 | 0.118457 | ||||||||
\(86\) | −2.07858 | −0.224139 | ||||||||
\(87\) | −22.1477 | −2.37448 | ||||||||
\(88\) | −1.23032 | −0.131153 | ||||||||
\(89\) | 0.283948 | 0.0300984 | 0.0150492 | − | 0.999887i | \(-0.495210\pi\) | ||||
0.0150492 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(90\) | −0.846296 | −0.0892075 | ||||||||
\(91\) | 0.000676454 0 | 7.09116e−5 0 | ||||||||
\(92\) | −2.61995 | −0.273148 | ||||||||
\(93\) | −5.01528 | −0.520060 | ||||||||
\(94\) | −1.16615 | −0.120279 | ||||||||
\(95\) | 4.53407 | 0.465185 | ||||||||
\(96\) | 8.43230 | 0.860618 | ||||||||
\(97\) | 12.1669 | 1.23536 | 0.617680 | − | 0.786429i | \(-0.288073\pi\) | ||||
0.617680 | + | 0.786429i | \(0.288073\pi\) | |||||||
\(98\) | −2.20798 | −0.223039 | ||||||||
\(99\) | 2.68302 | 0.269654 | ||||||||
\(100\) | −1.90051 | −0.190051 | ||||||||
\(101\) | −2.70486 | −0.269144 | −0.134572 | − | 0.990904i | \(-0.542966\pi\) | ||||
−0.134572 | + | 0.990904i | \(0.542966\pi\) | |||||||
\(102\) | −0.821218 | −0.0813127 | ||||||||
\(103\) | −11.0497 | −1.08875 | −0.544377 | − | 0.838840i | \(-0.683234\pi\) | ||||
−0.544377 | + | 0.838840i | \(0.683234\pi\) | |||||||
\(104\) | −0.171458 | −0.0168128 | ||||||||
\(105\) | −0.0115715 | −0.00112926 | ||||||||
\(106\) | −2.70067 | −0.262312 | ||||||||
\(107\) | 5.94034 | 0.574274 | 0.287137 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287137 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(108\) | 1.43610 | 0.138189 | ||||||||
\(109\) | −15.7267 | −1.50635 | −0.753173 | − | 0.657822i | \(-0.771478\pi\) | ||||
−0.753173 | + | 0.657822i | \(0.771478\pi\) | |||||||
\(110\) | −0.315426 | −0.0300747 | ||||||||
\(111\) | 26.0484 | 2.47241 | ||||||||
\(112\) | 0.0165664 | 0.00156538 | ||||||||
\(113\) | −7.35469 | −0.691871 | −0.345935 | − | 0.938258i | \(-0.612438\pi\) | ||||
−0.345935 | + | 0.938258i | \(0.612438\pi\) | |||||||
\(114\) | −3.40938 | −0.319318 | ||||||||
\(115\) | −1.37855 | −0.128551 | ||||||||
\(116\) | 17.6566 | 1.63938 | ||||||||
\(117\) | 0.373906 | 0.0345676 | ||||||||
\(118\) | −1.43830 | −0.132406 | ||||||||
\(119\) | −0.00530116 | −0.000485957 0 | ||||||||
\(120\) | 2.93298 | 0.267743 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.23220 | −0.292629 | ||||||||
\(123\) | 13.3229 | 1.20128 | ||||||||
\(124\) | 3.99829 | 0.359057 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.00410793 | 0.000365963 0 | ||||||||
\(127\) | 0.465605 | 0.0413157 | 0.0206579 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206579 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(128\) | −8.87548 | −0.784489 | ||||||||
\(129\) | −15.7094 | −1.38313 | ||||||||
\(130\) | −0.0439578 | −0.00385535 | ||||||||
\(131\) | −20.9234 | −1.82809 | −0.914043 | − | 0.405617i | \(-0.867057\pi\) | ||||
−0.914043 | + | 0.405617i | \(0.867057\pi\) | |||||||
\(132\) | −4.53064 | −0.394341 | ||||||||
\(133\) | −0.0220084 | −0.00190837 | ||||||||
\(134\) | 1.81246 | 0.156573 | ||||||||
\(135\) | 0.755641 | 0.0650352 | ||||||||
\(136\) | 1.34366 | 0.115218 | ||||||||
\(137\) | −18.2453 | −1.55880 | −0.779402 | − | 0.626524i | \(-0.784477\pi\) | ||||
−0.779402 | + | 0.626524i | \(0.784477\pi\) | |||||||
\(138\) | 1.03660 | 0.0882411 | ||||||||
\(139\) | 10.1370 | 0.859809 | 0.429904 | − | 0.902874i | \(-0.358547\pi\) | ||||
0.429904 | + | 0.902874i | \(0.358547\pi\) | |||||||
\(140\) | 0.00922507 | 0.000779661 0 | ||||||||
\(141\) | −8.81347 | −0.742228 | ||||||||
\(142\) | 3.96997 | 0.333153 | ||||||||
\(143\) | 0.139360 | 0.0116539 | ||||||||
\(144\) | 9.15699 | 0.763083 | ||||||||
\(145\) | 9.29049 | 0.771533 | ||||||||
\(146\) | 0.315426 | 0.0261049 | ||||||||
\(147\) | −16.6873 | −1.37635 | ||||||||
\(148\) | −20.7664 | −1.70699 | ||||||||
\(149\) | 18.9733 | 1.55436 | 0.777178 | − | 0.629281i | \(-0.216650\pi\) | ||||
0.777178 | + | 0.629281i | \(0.216650\pi\) | |||||||
\(150\) | 0.751948 | 0.0613963 | ||||||||
\(151\) | −1.70211 | −0.138516 | −0.0692579 | − | 0.997599i | \(-0.522063\pi\) | ||||
−0.0692579 | + | 0.997599i | \(0.522063\pi\) | |||||||
\(152\) | 5.57836 | 0.452465 | ||||||||
\(153\) | −2.93019 | −0.236892 | ||||||||
\(154\) | 0.00153108 | 0.000123378 0 | ||||||||
\(155\) | 2.10380 | 0.168982 | ||||||||
\(156\) | −0.631389 | −0.0505516 | ||||||||
\(157\) | 8.60002 | 0.686356 | 0.343178 | − | 0.939270i | \(-0.388497\pi\) | ||||
0.343178 | + | 0.939270i | \(0.388497\pi\) | |||||||
\(158\) | −0.753124 | −0.0599153 | ||||||||
\(159\) | −20.4110 | −1.61869 | ||||||||
\(160\) | −3.53717 | −0.279638 | ||||||||
\(161\) | 0.00669150 | 0.000527364 0 | ||||||||
\(162\) | −3.10709 | −0.244116 | ||||||||
\(163\) | 0.217553 | 0.0170401 | 0.00852003 | − | 0.999964i | \(-0.497288\pi\) | ||||
0.00852003 | + | 0.999964i | \(0.497288\pi\) | |||||||
\(164\) | −10.6213 | −0.829383 | ||||||||
\(165\) | −2.38391 | −0.185587 | ||||||||
\(166\) | −5.41178 | −0.420036 | ||||||||
\(167\) | 10.2115 | 0.790186 | 0.395093 | − | 0.918641i | \(-0.370712\pi\) | ||||
0.395093 | + | 0.918641i | \(0.370712\pi\) | |||||||
\(168\) | −0.0142367 | −0.00109838 | ||||||||
\(169\) | −12.9806 | −0.998506 | ||||||||
\(170\) | 0.344484 | 0.0264207 | ||||||||
\(171\) | −12.1650 | −0.930282 | ||||||||
\(172\) | 12.5239 | 0.954936 | ||||||||
\(173\) | −11.6535 | −0.885999 | −0.443000 | − | 0.896522i | \(-0.646086\pi\) | ||||
−0.443000 | + | 0.896522i | \(0.646086\pi\) | |||||||
\(174\) | −6.98596 | −0.529604 | ||||||||
\(175\) | 0.00485401 | 0.000366928 0 | ||||||||
\(176\) | 3.41294 | 0.257260 | ||||||||
\(177\) | −10.8703 | −0.817061 | ||||||||
\(178\) | 0.0895645 | 0.00671314 | ||||||||
\(179\) | 18.0084 | 1.34601 | 0.673004 | − | 0.739639i | \(-0.265004\pi\) | ||||
0.673004 | + | 0.739639i | \(0.265004\pi\) | |||||||
\(180\) | 5.09911 | 0.380065 | ||||||||
\(181\) | −2.44675 | −0.181865 | −0.0909327 | − | 0.995857i | \(-0.528985\pi\) | ||||
−0.0909327 | + | 0.995857i | \(0.528985\pi\) | |||||||
\(182\) | 0.000213371 0 | 1.58161e−5 0 | ||||||||
\(183\) | −24.4281 | −1.80578 | ||||||||
\(184\) | −1.69606 | −0.125035 | ||||||||
\(185\) | −10.9268 | −0.803352 | ||||||||
\(186\) | −1.58195 | −0.115994 | ||||||||
\(187\) | −1.09212 | −0.0798638 | ||||||||
\(188\) | 7.02630 | 0.512446 | ||||||||
\(189\) | −0.00366789 | −0.000266799 0 | ||||||||
\(190\) | 1.43016 | 0.103755 | ||||||||
\(191\) | −7.30975 | −0.528915 | −0.264458 | − | 0.964397i | \(-0.585193\pi\) | ||||
−0.264458 | + | 0.964397i | \(0.585193\pi\) | |||||||
\(192\) | −13.6125 | −0.982397 | ||||||||
\(193\) | −1.53414 | −0.110430 | −0.0552150 | − | 0.998474i | \(-0.517584\pi\) | ||||
−0.0552150 | + | 0.998474i | \(0.517584\pi\) | |||||||
\(194\) | 3.83776 | 0.275535 | ||||||||
\(195\) | −0.332221 | −0.0237909 | ||||||||
\(196\) | 13.3035 | 0.950250 | ||||||||
\(197\) | −2.86076 | −0.203820 | −0.101910 | − | 0.994794i | \(-0.532495\pi\) | ||||
−0.101910 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(198\) | 0.846296 | 0.0601437 | ||||||||
\(199\) | −21.8748 | −1.55066 | −0.775332 | − | 0.631554i | \(-0.782418\pi\) | ||||
−0.775332 | + | 0.631554i | \(0.782418\pi\) | |||||||
\(200\) | −1.23032 | −0.0869969 | ||||||||
\(201\) | 13.6981 | 0.966190 | ||||||||
\(202\) | −0.853184 | −0.0600298 | ||||||||
\(203\) | −0.0450961 | −0.00316513 | ||||||||
\(204\) | 4.94800 | 0.346429 | ||||||||
\(205\) | −5.58866 | −0.390329 | ||||||||
\(206\) | −3.48535 | −0.242836 | ||||||||
\(207\) | 3.69869 | 0.257077 | ||||||||
\(208\) | 0.475626 | 0.0329788 | ||||||||
\(209\) | −4.53407 | −0.313628 | ||||||||
\(210\) | −0.00364996 | −0.000251871 0 | ||||||||
\(211\) | 9.02054 | 0.621000 | 0.310500 | − | 0.950573i | \(-0.399504\pi\) | ||||
0.310500 | + | 0.950573i | \(0.399504\pi\) | |||||||
\(212\) | 16.2721 | 1.11757 | ||||||||
\(213\) | 30.0040 | 2.05584 | ||||||||
\(214\) | 1.87374 | 0.128086 | ||||||||
\(215\) | 6.58975 | 0.449417 | ||||||||
\(216\) | 0.929681 | 0.0632568 | ||||||||
\(217\) | −0.0102119 | −0.000693227 0 | ||||||||
\(218\) | −4.96062 | −0.335975 | ||||||||
\(219\) | 2.38391 | 0.161090 | ||||||||
\(220\) | 1.90051 | 0.128132 | ||||||||
\(221\) | −0.152198 | −0.0102379 | ||||||||
\(222\) | 8.21636 | 0.551446 | ||||||||
\(223\) | 15.7203 | 1.05271 | 0.526354 | − | 0.850265i | \(-0.323559\pi\) | ||||
0.526354 | + | 0.850265i | \(0.323559\pi\) | |||||||
\(224\) | 0.0171695 | 0.00114718 | ||||||||
\(225\) | 2.68302 | 0.178868 | ||||||||
\(226\) | −2.31986 | −0.154315 | ||||||||
\(227\) | 13.6074 | 0.903155 | 0.451577 | − | 0.892232i | \(-0.350861\pi\) | ||||
0.451577 | + | 0.892232i | \(0.350861\pi\) | |||||||
\(228\) | 20.5422 | 1.36044 | ||||||||
\(229\) | 18.3939 | 1.21550 | 0.607752 | − | 0.794127i | \(-0.292071\pi\) | ||||
0.607752 | + | 0.794127i | \(0.292071\pi\) | |||||||
\(230\) | −0.434831 | −0.0286719 | ||||||||
\(231\) | 0.0115715 | 0.000761350 0 | ||||||||
\(232\) | 11.4303 | 0.750436 | ||||||||
\(233\) | 8.50816 | 0.557388 | 0.278694 | − | 0.960380i | \(-0.410098\pi\) | ||||
0.278694 | + | 0.960380i | \(0.410098\pi\) | |||||||
\(234\) | 0.117940 | 0.00770996 | ||||||||
\(235\) | 3.69707 | 0.241170 | ||||||||
\(236\) | 8.66604 | 0.564111 | ||||||||
\(237\) | −5.69192 | −0.369730 | ||||||||
\(238\) | −0.00167213 | −0.000108388 0 | ||||||||
\(239\) | −11.0629 | −0.715599 | −0.357799 | − | 0.933799i | \(-0.616473\pi\) | ||||
−0.357799 | + | 0.933799i | \(0.616473\pi\) | |||||||
\(240\) | −8.13613 | −0.525185 | ||||||||
\(241\) | −26.8069 | −1.72678 | −0.863391 | − | 0.504535i | \(-0.831664\pi\) | ||||
−0.863391 | + | 0.504535i | \(0.831664\pi\) | |||||||
\(242\) | 0.315426 | 0.0202764 | ||||||||
\(243\) | −21.2157 | −1.36099 | ||||||||
\(244\) | 19.4746 | 1.24674 | ||||||||
\(245\) | 6.99998 | 0.447212 | ||||||||
\(246\) | 4.20238 | 0.267934 | ||||||||
\(247\) | −0.631867 | −0.0402047 | ||||||||
\(248\) | 2.58836 | 0.164361 | ||||||||
\(249\) | −40.9008 | −2.59198 | ||||||||
\(250\) | −0.315426 | −0.0199493 | ||||||||
\(251\) | −14.8704 | −0.938610 | −0.469305 | − | 0.883036i | \(-0.655496\pi\) | ||||
−0.469305 | + | 0.883036i | \(0.655496\pi\) | |||||||
\(252\) | −0.0247511 | −0.00155917 | ||||||||
\(253\) | 1.37855 | 0.0866688 | ||||||||
\(254\) | 0.146864 | 0.00921506 | ||||||||
\(255\) | 2.60352 | 0.163039 | ||||||||
\(256\) | 8.62075 | 0.538797 | ||||||||
\(257\) | −13.0159 | −0.811908 | −0.405954 | − | 0.913893i | \(-0.633061\pi\) | ||||
−0.405954 | + | 0.913893i | \(0.633061\pi\) | |||||||
\(258\) | −4.95515 | −0.308494 | ||||||||
\(259\) | 0.0530386 | 0.00329566 | ||||||||
\(260\) | 0.264854 | 0.0164256 | ||||||||
\(261\) | −24.9266 | −1.54292 | ||||||||
\(262\) | −6.59979 | −0.407736 | ||||||||
\(263\) | 4.55095 | 0.280624 | 0.140312 | − | 0.990107i | \(-0.455190\pi\) | ||||
0.140312 | + | 0.990107i | \(0.455190\pi\) | |||||||
\(264\) | −2.93298 | −0.180512 | ||||||||
\(265\) | 8.56197 | 0.525958 | ||||||||
\(266\) | −0.00694202 | −0.000425643 0 | ||||||||
\(267\) | 0.676905 | 0.0414259 | ||||||||
\(268\) | −10.9204 | −0.667072 | ||||||||
\(269\) | −3.23783 | −0.197414 | −0.0987069 | − | 0.995117i | \(-0.531471\pi\) | ||||
−0.0987069 | + | 0.995117i | \(0.531471\pi\) | |||||||
\(270\) | 0.238349 | 0.0145055 | ||||||||
\(271\) | −18.5739 | −1.12828 | −0.564142 | − | 0.825677i | \(-0.690793\pi\) | ||||
−0.564142 | + | 0.825677i | \(0.690793\pi\) | |||||||
\(272\) | −3.72734 | −0.226003 | ||||||||
\(273\) | 0.00161260 | 9.75993e−5 0 | ||||||||
\(274\) | −5.75506 | −0.347676 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −6.24571 | −0.375948 | ||||||||
\(277\) | −8.10302 | −0.486863 | −0.243431 | − | 0.969918i | \(-0.578273\pi\) | ||||
−0.243431 | + | 0.969918i | \(0.578273\pi\) | |||||||
\(278\) | 3.19747 | 0.191772 | ||||||||
\(279\) | −5.64456 | −0.337931 | ||||||||
\(280\) | 0.00597199 | 0.000356895 0 | ||||||||
\(281\) | 4.37376 | 0.260916 | 0.130458 | − | 0.991454i | \(-0.458355\pi\) | ||||
0.130458 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(282\) | −2.78000 | −0.165547 | ||||||||
\(283\) | 15.7094 | 0.933824 | 0.466912 | − | 0.884304i | \(-0.345366\pi\) | ||||
0.466912 | + | 0.884304i | \(0.345366\pi\) | |||||||
\(284\) | −23.9199 | −1.41938 | ||||||||
\(285\) | 10.8088 | 0.640258 | ||||||||
\(286\) | 0.0439578 | 0.00259928 | ||||||||
\(287\) | 0.0271274 | 0.00160128 | ||||||||
\(288\) | 9.49032 | 0.559223 | ||||||||
\(289\) | −15.8073 | −0.929840 | ||||||||
\(290\) | 2.93046 | 0.172083 | ||||||||
\(291\) | 29.0048 | 1.70029 | ||||||||
\(292\) | −1.90051 | −0.111219 | ||||||||
\(293\) | −1.61737 | −0.0944880 | −0.0472440 | − | 0.998883i | \(-0.515044\pi\) | ||||
−0.0472440 | + | 0.998883i | \(0.515044\pi\) | |||||||
\(294\) | −5.26362 | −0.306980 | ||||||||
\(295\) | 4.55986 | 0.265485 | ||||||||
\(296\) | −13.4434 | −0.781384 | ||||||||
\(297\) | −0.755641 | −0.0438467 | ||||||||
\(298\) | 5.98469 | 0.346684 | ||||||||
\(299\) | 0.192115 | 0.0111103 | ||||||||
\(300\) | −4.53064 | −0.261576 | ||||||||
\(301\) | −0.0319867 | −0.00184368 | ||||||||
\(302\) | −0.536890 | −0.0308945 | ||||||||
\(303\) | −6.44814 | −0.370436 | ||||||||
\(304\) | −15.4745 | −0.887522 | ||||||||
\(305\) | 10.2471 | 0.586746 | ||||||||
\(306\) | −0.924258 | −0.0528363 | ||||||||
\(307\) | −17.3223 | −0.988638 | −0.494319 | − | 0.869281i | \(-0.664583\pi\) | ||||
−0.494319 | + | 0.869281i | \(0.664583\pi\) | |||||||
\(308\) | −0.00922507 | −0.000525647 0 | ||||||||
\(309\) | −26.3414 | −1.49851 | ||||||||
\(310\) | 0.663595 | 0.0376897 | ||||||||
\(311\) | 3.45383 | 0.195849 | 0.0979244 | − | 0.995194i | \(-0.468780\pi\) | ||||
0.0979244 | + | 0.995194i | \(0.468780\pi\) | |||||||
\(312\) | −0.408739 | −0.0231403 | ||||||||
\(313\) | 7.47430 | 0.422472 | 0.211236 | − | 0.977435i | \(-0.432251\pi\) | ||||
0.211236 | + | 0.977435i | \(0.432251\pi\) | |||||||
\(314\) | 2.71267 | 0.153085 | ||||||||
\(315\) | −0.0130234 | −0.000733787 0 | ||||||||
\(316\) | 4.53772 | 0.255267 | ||||||||
\(317\) | −1.95137 | −0.109600 | −0.0547999 | − | 0.998497i | \(-0.517452\pi\) | ||||
−0.0547999 | + | 0.998497i | \(0.517452\pi\) | |||||||
\(318\) | −6.43815 | −0.361034 | ||||||||
\(319\) | −9.29049 | −0.520168 | ||||||||
\(320\) | 5.71016 | 0.319207 | ||||||||
\(321\) | 14.1612 | 0.790403 | ||||||||
\(322\) | 0.00211067 | 0.000117623 0 | ||||||||
\(323\) | 4.95175 | 0.275523 | ||||||||
\(324\) | 18.7208 | 1.04005 | ||||||||
\(325\) | 0.139360 | 0.00773030 | ||||||||
\(326\) | 0.0686219 | 0.00380062 | ||||||||
\(327\) | −37.4911 | −2.07326 | ||||||||
\(328\) | −6.87586 | −0.379656 | ||||||||
\(329\) | −0.0179456 | −0.000989373 0 | ||||||||
\(330\) | −0.751948 | −0.0413934 | ||||||||
\(331\) | 11.7265 | 0.644545 | 0.322272 | − | 0.946647i | \(-0.395553\pi\) | ||||
0.322272 | + | 0.946647i | \(0.395553\pi\) | |||||||
\(332\) | 32.6071 | 1.78954 | ||||||||
\(333\) | 29.3168 | 1.60655 | ||||||||
\(334\) | 3.22096 | 0.176243 | ||||||||
\(335\) | −5.74607 | −0.313941 | ||||||||
\(336\) | 0.0394928 | 0.00215451 | ||||||||
\(337\) | 7.09030 | 0.386233 | 0.193117 | − | 0.981176i | \(-0.438140\pi\) | ||||
0.193117 | + | 0.981176i | \(0.438140\pi\) | |||||||
\(338\) | −4.09442 | −0.222707 | ||||||||
\(339\) | −17.5329 | −0.952257 | ||||||||
\(340\) | −2.07558 | −0.112564 | ||||||||
\(341\) | −2.10380 | −0.113927 | ||||||||
\(342\) | −3.83716 | −0.207490 | ||||||||
\(343\) | −0.0679560 | −0.00366928 | ||||||||
\(344\) | 8.10752 | 0.437128 | ||||||||
\(345\) | −3.28634 | −0.176931 | ||||||||
\(346\) | −3.67582 | −0.197613 | ||||||||
\(347\) | 28.7694 | 1.54442 | 0.772212 | − | 0.635365i | \(-0.219150\pi\) | ||||
0.772212 | + | 0.635365i | \(0.219150\pi\) | |||||||
\(348\) | 42.0918 | 2.25636 | ||||||||
\(349\) | 14.5802 | 0.780462 | 0.390231 | − | 0.920717i | \(-0.372395\pi\) | ||||
0.390231 | + | 0.920717i | \(0.372395\pi\) | |||||||
\(350\) | 0.00153108 | 8.18397e−5 0 | ||||||||
\(351\) | −0.105306 | −0.00562082 | ||||||||
\(352\) | 3.53717 | 0.188532 | ||||||||
\(353\) | 30.8635 | 1.64270 | 0.821349 | − | 0.570426i | \(-0.193222\pi\) | ||||
0.821349 | + | 0.570426i | \(0.193222\pi\) | |||||||
\(354\) | −3.42877 | −0.182237 | ||||||||
\(355\) | −12.5861 | −0.667998 | ||||||||
\(356\) | −0.539644 | −0.0286011 | ||||||||
\(357\) | −0.0126375 | −0.000668847 0 | ||||||||
\(358\) | 5.68031 | 0.300214 | ||||||||
\(359\) | −20.5627 | −1.08526 | −0.542630 | − | 0.839972i | \(-0.682571\pi\) | ||||
−0.542630 | + | 0.839972i | \(0.682571\pi\) | |||||||
\(360\) | 3.30098 | 0.173977 | ||||||||
\(361\) | 1.55776 | 0.0819873 | ||||||||
\(362\) | −0.771768 | −0.0405632 | ||||||||
\(363\) | 2.38391 | 0.125123 | ||||||||
\(364\) | −0.00128560 | −6.73840e−5 0 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −7.70527 | −0.402761 | ||||||||
\(367\) | −4.39747 | −0.229546 | −0.114773 | − | 0.993392i | \(-0.536614\pi\) | ||||
−0.114773 | + | 0.993392i | \(0.536614\pi\) | |||||||
\(368\) | 4.70491 | 0.245260 | ||||||||
\(369\) | 14.9945 | 0.780584 | ||||||||
\(370\) | −3.44659 | −0.179180 | ||||||||
\(371\) | −0.0415599 | −0.00215768 | ||||||||
\(372\) | 9.53157 | 0.494189 | ||||||||
\(373\) | 23.4551 | 1.21446 | 0.607230 | − | 0.794526i | \(-0.292281\pi\) | ||||
0.607230 | + | 0.794526i | \(0.292281\pi\) | |||||||
\(374\) | −0.344484 | −0.0178128 | ||||||||
\(375\) | −2.38391 | −0.123105 | ||||||||
\(376\) | 4.54858 | 0.234575 | ||||||||
\(377\) | −1.29472 | −0.0666816 | ||||||||
\(378\) | −0.00115695 | −5.95069e−5 0 | ||||||||
\(379\) | 20.2474 | 1.04004 | 0.520021 | − | 0.854154i | \(-0.325924\pi\) | ||||
0.520021 | + | 0.854154i | \(0.325924\pi\) | |||||||
\(380\) | −8.61702 | −0.442044 | ||||||||
\(381\) | 1.10996 | 0.0568649 | ||||||||
\(382\) | −2.30569 | −0.117969 | ||||||||
\(383\) | 25.1613 | 1.28568 | 0.642842 | − | 0.765998i | \(-0.277755\pi\) | ||||
0.642842 | + | 0.765998i | \(0.277755\pi\) | |||||||
\(384\) | −21.1583 | −1.07973 | ||||||||
\(385\) | −0.00485401 | −0.000247383 0 | ||||||||
\(386\) | −0.483909 | −0.0246303 | ||||||||
\(387\) | −17.6805 | −0.898749 | ||||||||
\(388\) | −23.1232 | −1.17390 | ||||||||
\(389\) | 34.6084 | 1.75471 | 0.877357 | − | 0.479839i | \(-0.159305\pi\) | ||||
0.877357 | + | 0.479839i | \(0.159305\pi\) | |||||||
\(390\) | −0.104791 | −0.00530632 | ||||||||
\(391\) | −1.50554 | −0.0761387 | ||||||||
\(392\) | 8.61223 | 0.434983 | ||||||||
\(393\) | −49.8795 | −2.51609 | ||||||||
\(394\) | −0.902357 | −0.0454601 | ||||||||
\(395\) | 2.38764 | 0.120135 | ||||||||
\(396\) | −5.09911 | −0.256240 | ||||||||
\(397\) | 16.8514 | 0.845745 | 0.422873 | − | 0.906189i | \(-0.361022\pi\) | ||||
0.422873 | + | 0.906189i | \(0.361022\pi\) | |||||||
\(398\) | −6.89989 | −0.345860 | ||||||||
\(399\) | −0.0524660 | −0.00262659 | ||||||||
\(400\) | 3.41294 | 0.170647 | ||||||||
\(401\) | −17.5010 | −0.873957 | −0.436979 | − | 0.899472i | \(-0.643952\pi\) | ||||
−0.436979 | + | 0.899472i | \(0.643952\pi\) | |||||||
\(402\) | 4.32074 | 0.215499 | ||||||||
\(403\) | −0.293186 | −0.0146046 | ||||||||
\(404\) | 5.14060 | 0.255755 | ||||||||
\(405\) | 9.85045 | 0.489473 | ||||||||
\(406\) | −0.0142245 | −0.000705950 0 | ||||||||
\(407\) | 10.9268 | 0.541620 | ||||||||
\(408\) | 3.20316 | 0.158580 | ||||||||
\(409\) | 18.9926 | 0.939122 | 0.469561 | − | 0.882900i | \(-0.344412\pi\) | ||||
0.469561 | + | 0.882900i | \(0.344412\pi\) | |||||||
\(410\) | −1.76281 | −0.0870590 | ||||||||
\(411\) | −43.4952 | −2.14546 | ||||||||
\(412\) | 20.9999 | 1.03459 | ||||||||
\(413\) | −0.0221336 | −0.00108912 | ||||||||
\(414\) | 1.16666 | 0.0573384 | ||||||||
\(415\) | 17.1570 | 0.842206 | ||||||||
\(416\) | 0.492940 | 0.0241684 | ||||||||
\(417\) | 24.1657 | 1.18340 | ||||||||
\(418\) | −1.43016 | −0.0699516 | ||||||||
\(419\) | −34.8838 | −1.70418 | −0.852092 | − | 0.523393i | \(-0.824666\pi\) | ||||
−0.852092 | + | 0.523393i | \(0.824666\pi\) | |||||||
\(420\) | 0.0219917 | 0.00107309 | ||||||||
\(421\) | 22.1520 | 1.07962 | 0.539812 | − | 0.841786i | \(-0.318495\pi\) | ||||
0.539812 | + | 0.841786i | \(0.318495\pi\) | |||||||
\(422\) | 2.84531 | 0.138508 | ||||||||
\(423\) | −9.91932 | −0.482294 | ||||||||
\(424\) | 10.5340 | 0.511575 | ||||||||
\(425\) | −1.09212 | −0.0529756 | ||||||||
\(426\) | 9.46405 | 0.458535 | ||||||||
\(427\) | −0.0497394 | −0.00240706 | ||||||||
\(428\) | −11.2897 | −0.545706 | ||||||||
\(429\) | 0.332221 | 0.0160398 | ||||||||
\(430\) | 2.07858 | 0.100238 | ||||||||
\(431\) | 21.0720 | 1.01500 | 0.507500 | − | 0.861652i | \(-0.330570\pi\) | ||||
0.507500 | + | 0.861652i | \(0.330570\pi\) | |||||||
\(432\) | −2.57895 | −0.124080 | ||||||||
\(433\) | 18.0179 | 0.865884 | 0.432942 | − | 0.901422i | \(-0.357476\pi\) | ||||
0.432942 | + | 0.901422i | \(0.357476\pi\) | |||||||
\(434\) | −0.00322109 | −0.000154617 0 | ||||||||
\(435\) | 22.1477 | 1.06190 | ||||||||
\(436\) | 29.8887 | 1.43141 | ||||||||
\(437\) | −6.25044 | −0.298999 | ||||||||
\(438\) | 0.751948 | 0.0359294 | ||||||||
\(439\) | −22.5790 | −1.07764 | −0.538819 | − | 0.842421i | \(-0.681130\pi\) | ||||
−0.538819 | + | 0.842421i | \(0.681130\pi\) | |||||||
\(440\) | 1.23032 | 0.0586533 | ||||||||
\(441\) | −18.7811 | −0.894339 | ||||||||
\(442\) | −0.0480072 | −0.00228347 | ||||||||
\(443\) | −2.30299 | −0.109418 | −0.0547091 | − | 0.998502i | \(-0.517423\pi\) | ||||
−0.0547091 | + | 0.998502i | \(0.517423\pi\) | |||||||
\(444\) | −49.5052 | −2.34941 | ||||||||
\(445\) | −0.283948 | −0.0134604 | ||||||||
\(446\) | 4.95859 | 0.234796 | ||||||||
\(447\) | 45.2307 | 2.13934 | ||||||||
\(448\) | −0.0277171 | −0.00130951 | ||||||||
\(449\) | −27.4433 | −1.29513 | −0.647564 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647564 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(450\) | 0.846296 | 0.0398948 | ||||||||
\(451\) | 5.58866 | 0.263160 | ||||||||
\(452\) | 13.9776 | 0.657452 | ||||||||
\(453\) | −4.05768 | −0.190646 | ||||||||
\(454\) | 4.29213 | 0.201440 | ||||||||
\(455\) | −0.000676454 0 | −3.17126e−5 0 | ||||||||
\(456\) | 13.2983 | 0.622750 | ||||||||
\(457\) | 11.3488 | 0.530876 | 0.265438 | − | 0.964128i | \(-0.414484\pi\) | ||||
0.265438 | + | 0.964128i | \(0.414484\pi\) | |||||||
\(458\) | 5.80192 | 0.271106 | ||||||||
\(459\) | 0.825251 | 0.0385194 | ||||||||
\(460\) | 2.61995 | 0.122156 | ||||||||
\(461\) | 14.8536 | 0.691799 | 0.345900 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345900 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(462\) | 0.00364996 | 0.000169811 0 | ||||||||
\(463\) | 26.6457 | 1.23833 | 0.619165 | − | 0.785261i | \(-0.287471\pi\) | ||||
0.619165 | + | 0.785261i | \(0.287471\pi\) | |||||||
\(464\) | −31.7079 | −1.47200 | ||||||||
\(465\) | 5.01528 | 0.232578 | ||||||||
\(466\) | 2.68370 | 0.124320 | ||||||||
\(467\) | −7.88900 | −0.365059 | −0.182530 | − | 0.983200i | \(-0.558429\pi\) | ||||
−0.182530 | + | 0.983200i | \(0.558429\pi\) | |||||||
\(468\) | −0.710611 | −0.0328480 | ||||||||
\(469\) | 0.0278915 | 0.00128791 | ||||||||
\(470\) | 1.16615 | 0.0537906 | ||||||||
\(471\) | 20.5017 | 0.944667 | ||||||||
\(472\) | 5.61009 | 0.258225 | ||||||||
\(473\) | −6.58975 | −0.302997 | ||||||||
\(474\) | −1.79538 | −0.0824645 | ||||||||
\(475\) | −4.53407 | −0.208037 | ||||||||
\(476\) | 0.0100749 | 0.000461782 0 | ||||||||
\(477\) | −22.9720 | −1.05181 | ||||||||
\(478\) | −3.48952 | −0.159607 | ||||||||
\(479\) | 16.5238 | 0.754991 | 0.377496 | − | 0.926011i | \(-0.376785\pi\) | ||||
0.377496 | + | 0.926011i | \(0.376785\pi\) | |||||||
\(480\) | −8.43230 | −0.384880 | ||||||||
\(481\) | 1.52275 | 0.0694316 | ||||||||
\(482\) | −8.45559 | −0.385142 | ||||||||
\(483\) | 0.0159519 | 0.000725838 0 | ||||||||
\(484\) | −1.90051 | −0.0863866 | ||||||||
\(485\) | −12.1669 | −0.552470 | ||||||||
\(486\) | −6.69198 | −0.303554 | ||||||||
\(487\) | 30.4032 | 1.37770 | 0.688849 | − | 0.724905i | \(-0.258116\pi\) | ||||
0.688849 | + | 0.724905i | \(0.258116\pi\) | |||||||
\(488\) | 12.6072 | 0.570702 | ||||||||
\(489\) | 0.518627 | 0.0234531 | ||||||||
\(490\) | 2.20798 | 0.0997462 | ||||||||
\(491\) | 37.2373 | 1.68050 | 0.840248 | − | 0.542203i | \(-0.182410\pi\) | ||||
0.840248 | + | 0.542203i | \(0.182410\pi\) | |||||||
\(492\) | −25.3202 | −1.14152 | ||||||||
\(493\) | 10.1463 | 0.456968 | ||||||||
\(494\) | −0.199307 | −0.00896726 | ||||||||
\(495\) | −2.68302 | −0.120593 | ||||||||
\(496\) | −7.18015 | −0.322398 | ||||||||
\(497\) | 0.0610928 | 0.00274039 | ||||||||
\(498\) | −12.9012 | −0.578116 | ||||||||
\(499\) | −9.64970 | −0.431980 | −0.215990 | − | 0.976396i | \(-0.569298\pi\) | ||||
−0.215990 | + | 0.976396i | \(0.569298\pi\) | |||||||
\(500\) | 1.90051 | 0.0849932 | ||||||||
\(501\) | 24.3432 | 1.08757 | ||||||||
\(502\) | −4.69051 | −0.209348 | ||||||||
\(503\) | 28.4325 | 1.26774 | 0.633872 | − | 0.773438i | \(-0.281465\pi\) | ||||
0.633872 | + | 0.773438i | \(0.281465\pi\) | |||||||
\(504\) | −0.0160230 | −0.000713721 0 | ||||||||
\(505\) | 2.70486 | 0.120365 | ||||||||
\(506\) | 0.434831 | 0.0193306 | ||||||||
\(507\) | −30.9445 | −1.37429 | ||||||||
\(508\) | −0.884885 | −0.0392604 | ||||||||
\(509\) | 13.6772 | 0.606232 | 0.303116 | − | 0.952954i | \(-0.401973\pi\) | ||||
0.303116 | + | 0.952954i | \(0.401973\pi\) | |||||||
\(510\) | 0.821218 | 0.0363641 | ||||||||
\(511\) | 0.00485401 | 0.000214729 0 | ||||||||
\(512\) | 20.4702 | 0.904662 | ||||||||
\(513\) | 3.42613 | 0.151267 | ||||||||
\(514\) | −4.10555 | −0.181088 | ||||||||
\(515\) | 11.0497 | 0.486906 | ||||||||
\(516\) | 29.8558 | 1.31433 | ||||||||
\(517\) | −3.69707 | −0.162597 | ||||||||
\(518\) | 0.0167298 | 0.000735064 0 | ||||||||
\(519\) | −27.7809 | −1.21945 | ||||||||
\(520\) | 0.171458 | 0.00751891 | ||||||||
\(521\) | 20.1311 | 0.881958 | 0.440979 | − | 0.897518i | \(-0.354631\pi\) | ||||
0.440979 | + | 0.897518i | \(0.354631\pi\) | |||||||
\(522\) | −7.86251 | −0.344133 | ||||||||
\(523\) | −15.1986 | −0.664587 | −0.332294 | − | 0.943176i | \(-0.607823\pi\) | ||||
−0.332294 | + | 0.943176i | \(0.607823\pi\) | |||||||
\(524\) | 39.7651 | 1.73715 | ||||||||
\(525\) | 0.0115715 | 0.000505022 0 | ||||||||
\(526\) | 1.43549 | 0.0625903 | ||||||||
\(527\) | 2.29761 | 0.100085 | ||||||||
\(528\) | 8.13613 | 0.354080 | ||||||||
\(529\) | −21.0996 | −0.917374 | ||||||||
\(530\) | 2.70067 | 0.117310 | ||||||||
\(531\) | −12.2342 | −0.530919 | ||||||||
\(532\) | 0.0418271 | 0.00181343 | ||||||||
\(533\) | 0.778836 | 0.0337351 | ||||||||
\(534\) | 0.213514 | 0.00923964 | ||||||||
\(535\) | −5.94034 | −0.256823 | ||||||||
\(536\) | −7.06951 | −0.305356 | ||||||||
\(537\) | 42.9303 | 1.85258 | ||||||||
\(538\) | −1.02130 | −0.0440312 | ||||||||
\(539\) | −6.99998 | −0.301510 | ||||||||
\(540\) | −1.43610 | −0.0617999 | ||||||||
\(541\) | 12.8571 | 0.552770 | 0.276385 | − | 0.961047i | \(-0.410863\pi\) | ||||
0.276385 | + | 0.961047i | \(0.410863\pi\) | |||||||
\(542\) | −5.85870 | −0.251653 | ||||||||
\(543\) | −5.83283 | −0.250310 | ||||||||
\(544\) | −3.86302 | −0.165626 | ||||||||
\(545\) | 15.7267 | 0.673658 | ||||||||
\(546\) | 0.000508658 0 | 2.17685e−5 0 | ||||||||
\(547\) | 0.371232 | 0.0158727 | 0.00793637 | − | 0.999969i | \(-0.497474\pi\) | ||||
0.00793637 | + | 0.999969i | \(0.497474\pi\) | |||||||
\(548\) | 34.6754 | 1.48126 | ||||||||
\(549\) | −27.4932 | −1.17338 | ||||||||
\(550\) | 0.315426 | 0.0134498 | ||||||||
\(551\) | 42.1237 | 1.79453 | ||||||||
\(552\) | −4.04326 | −0.172093 | ||||||||
\(553\) | −0.0115896 | −0.000492841 0 | ||||||||
\(554\) | −2.55590 | −0.108590 | ||||||||
\(555\) | −26.0484 | −1.10569 | ||||||||
\(556\) | −19.2654 | −0.817036 | ||||||||
\(557\) | −35.9498 | −1.52324 | −0.761621 | − | 0.648022i | \(-0.775596\pi\) | ||||
−0.761621 | + | 0.648022i | \(0.775596\pi\) | |||||||
\(558\) | −1.78044 | −0.0753721 | ||||||||
\(559\) | −0.918347 | −0.0388420 | ||||||||
\(560\) | −0.0165664 | −0.000700059 0 | ||||||||
\(561\) | −2.60352 | −0.109921 | ||||||||
\(562\) | 1.37960 | 0.0581948 | ||||||||
\(563\) | −28.0982 | −1.18420 | −0.592098 | − | 0.805866i | \(-0.701700\pi\) | ||||
−0.592098 | + | 0.805866i | \(0.701700\pi\) | |||||||
\(564\) | 16.7501 | 0.705305 | ||||||||
\(565\) | 7.35469 | 0.309414 | ||||||||
\(566\) | 4.95514 | 0.208280 | ||||||||
\(567\) | −0.0478142 | −0.00200801 | ||||||||
\(568\) | −15.4849 | −0.649732 | ||||||||
\(569\) | −30.5378 | −1.28021 | −0.640105 | − | 0.768287i | \(-0.721109\pi\) | ||||
−0.640105 | + | 0.768287i | \(0.721109\pi\) | |||||||
\(570\) | 3.40938 | 0.142803 | ||||||||
\(571\) | 21.6266 | 0.905047 | 0.452523 | − | 0.891752i | \(-0.350524\pi\) | ||||
0.452523 | + | 0.891752i | \(0.350524\pi\) | |||||||
\(572\) | −0.264854 | −0.0110741 | ||||||||
\(573\) | −17.4258 | −0.727973 | ||||||||
\(574\) | 0.00855670 | 0.000357150 0 | ||||||||
\(575\) | 1.37855 | 0.0574896 | ||||||||
\(576\) | −15.3205 | −0.638354 | ||||||||
\(577\) | −6.60725 | −0.275064 | −0.137532 | − | 0.990497i | \(-0.543917\pi\) | ||||
−0.137532 | + | 0.990497i | \(0.543917\pi\) | |||||||
\(578\) | −4.98603 | −0.207391 | ||||||||
\(579\) | −3.65726 | −0.151990 | ||||||||
\(580\) | −17.6566 | −0.733152 | ||||||||
\(581\) | −0.0832804 | −0.00345505 | ||||||||
\(582\) | 9.14886 | 0.379233 | ||||||||
\(583\) | −8.56197 | −0.354601 | ||||||||
\(584\) | −1.23032 | −0.0509111 | ||||||||
\(585\) | −0.373906 | −0.0154591 | ||||||||
\(586\) | −0.510162 | −0.0210746 | ||||||||
\(587\) | −12.4065 | −0.512070 | −0.256035 | − | 0.966668i | \(-0.582416\pi\) | ||||
−0.256035 | + | 0.966668i | \(0.582416\pi\) | |||||||
\(588\) | 31.7143 | 1.30788 | ||||||||
\(589\) | 9.53879 | 0.393039 | ||||||||
\(590\) | 1.43830 | 0.0592138 | ||||||||
\(591\) | −6.81978 | −0.280528 | ||||||||
\(592\) | 37.2924 | 1.53271 | ||||||||
\(593\) | −38.3652 | −1.57547 | −0.787735 | − | 0.616015i | \(-0.788746\pi\) | ||||
−0.787735 | + | 0.616015i | \(0.788746\pi\) | |||||||
\(594\) | −0.238349 | −0.00977957 | ||||||||
\(595\) | 0.00530116 | 0.000217326 0 | ||||||||
\(596\) | −36.0589 | −1.47703 | ||||||||
\(597\) | −52.1476 | −2.13426 | ||||||||
\(598\) | 0.0605980 | 0.00247804 | ||||||||
\(599\) | −38.9043 | −1.58959 | −0.794793 | − | 0.606881i | \(-0.792420\pi\) | ||||
−0.794793 | + | 0.606881i | \(0.792420\pi\) | |||||||
\(600\) | −2.93298 | −0.119738 | ||||||||
\(601\) | 8.26541 | 0.337153 | 0.168577 | − | 0.985689i | \(-0.446083\pi\) | ||||
0.168577 | + | 0.985689i | \(0.446083\pi\) | |||||||
\(602\) | −0.0100894 | −0.000411215 0 | ||||||||
\(603\) | 15.4168 | 0.627822 | ||||||||
\(604\) | 3.23487 | 0.131625 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −2.03391 | −0.0826221 | ||||||||
\(607\) | −4.38807 | −0.178106 | −0.0890531 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890531 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(608\) | −16.0378 | −0.650418 | ||||||||
\(609\) | −0.107505 | −0.00435632 | ||||||||
\(610\) | 3.23220 | 0.130868 | ||||||||
\(611\) | −0.515223 | −0.0208437 | ||||||||
\(612\) | 5.56884 | 0.225107 | ||||||||
\(613\) | 23.0162 | 0.929616 | 0.464808 | − | 0.885412i | \(-0.346123\pi\) | ||||
0.464808 | + | 0.885412i | \(0.346123\pi\) | |||||||
\(614\) | −5.46392 | −0.220506 | ||||||||
\(615\) | −13.3229 | −0.537230 | ||||||||
\(616\) | −0.00597199 | −0.000240618 0 | ||||||||
\(617\) | −18.5534 | −0.746931 | −0.373465 | − | 0.927644i | \(-0.621831\pi\) | ||||
−0.373465 | + | 0.927644i | \(0.621831\pi\) | |||||||
\(618\) | −8.30876 | −0.334227 | ||||||||
\(619\) | 35.6661 | 1.43354 | 0.716770 | − | 0.697309i | \(-0.245620\pi\) | ||||
0.716770 | + | 0.697309i | \(0.245620\pi\) | |||||||
\(620\) | −3.99829 | −0.160575 | ||||||||
\(621\) | −1.04169 | −0.0418016 | ||||||||
\(622\) | 1.08943 | 0.0436821 | ||||||||
\(623\) | 0.00137828 | 5.52198e−5 0 | ||||||||
\(624\) | 1.13385 | 0.0453903 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.35759 | 0.0942282 | ||||||||
\(627\) | −10.8088 | −0.431662 | ||||||||
\(628\) | −16.3444 | −0.652212 | ||||||||
\(629\) | −11.9333 | −0.475814 | ||||||||
\(630\) | −0.00410793 | −0.000163664 0 | ||||||||
\(631\) | −35.7922 | −1.42486 | −0.712432 | − | 0.701741i | \(-0.752406\pi\) | ||||
−0.712432 | + | 0.701741i | \(0.752406\pi\) | |||||||
\(632\) | 2.93757 | 0.116850 | ||||||||
\(633\) | 21.5042 | 0.854713 | ||||||||
\(634\) | −0.615513 | −0.0244452 | ||||||||
\(635\) | −0.465605 | −0.0184770 | ||||||||
\(636\) | 38.7912 | 1.53817 | ||||||||
\(637\) | −0.975516 | −0.0386513 | ||||||||
\(638\) | −2.93046 | −0.116018 | ||||||||
\(639\) | 33.7687 | 1.33587 | ||||||||
\(640\) | 8.87548 | 0.350834 | ||||||||
\(641\) | 20.5756 | 0.812688 | 0.406344 | − | 0.913720i | \(-0.366804\pi\) | ||||
0.406344 | + | 0.913720i | \(0.366804\pi\) | |||||||
\(642\) | 4.46682 | 0.176291 | ||||||||
\(643\) | 3.28637 | 0.129602 | 0.0648009 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648009 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(644\) | −0.0127172 | −0.000501129 0 | ||||||||
\(645\) | 15.7094 | 0.618556 | ||||||||
\(646\) | 1.56191 | 0.0614526 | ||||||||
\(647\) | −33.9477 | −1.33462 | −0.667311 | − | 0.744779i | \(-0.732555\pi\) | ||||
−0.667311 | + | 0.744779i | \(0.732555\pi\) | |||||||
\(648\) | 12.1192 | 0.476088 | ||||||||
\(649\) | −4.55986 | −0.178990 | ||||||||
\(650\) | 0.0439578 | 0.00172417 | ||||||||
\(651\) | −0.0243442 | −0.000954124 0 | ||||||||
\(652\) | −0.413461 | −0.0161924 | ||||||||
\(653\) | 33.9537 | 1.32871 | 0.664356 | − | 0.747416i | \(-0.268706\pi\) | ||||
0.664356 | + | 0.747416i | \(0.268706\pi\) | |||||||
\(654\) | −11.8257 | −0.462420 | ||||||||
\(655\) | 20.9234 | 0.817545 | ||||||||
\(656\) | 19.0738 | 0.744705 | ||||||||
\(657\) | 2.68302 | 0.104675 | ||||||||
\(658\) | −0.00566051 | −0.000220670 0 | ||||||||
\(659\) | −6.02042 | −0.234522 | −0.117261 | − | 0.993101i | \(-0.537411\pi\) | ||||
−0.117261 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(660\) | 4.53064 | 0.176355 | ||||||||
\(661\) | −8.22504 | −0.319917 | −0.159958 | − | 0.987124i | \(-0.551136\pi\) | ||||
−0.159958 | + | 0.987124i | \(0.551136\pi\) | |||||||
\(662\) | 3.69883 | 0.143759 | ||||||||
\(663\) | −0.362826 | −0.0140910 | ||||||||
\(664\) | 21.1087 | 0.819176 | ||||||||
\(665\) | 0.0220084 | 0.000853449 0 | ||||||||
\(666\) | 9.24728 | 0.358325 | ||||||||
\(667\) | −12.8074 | −0.495905 | ||||||||
\(668\) | −19.4069 | −0.750877 | ||||||||
\(669\) | 37.4758 | 1.44890 | ||||||||
\(670\) | −1.81246 | −0.0700215 | ||||||||
\(671\) | −10.2471 | −0.395584 | ||||||||
\(672\) | 0.0409305 | 0.00157893 | ||||||||
\(673\) | −7.11445 | −0.274242 | −0.137121 | − | 0.990554i | \(-0.543785\pi\) | ||||
−0.137121 | + | 0.990554i | \(0.543785\pi\) | |||||||
\(674\) | 2.23647 | 0.0861455 | ||||||||
\(675\) | −0.755641 | −0.0290846 | ||||||||
\(676\) | 24.6697 | 0.948834 | ||||||||
\(677\) | 6.18509 | 0.237712 | 0.118856 | − | 0.992911i | \(-0.462077\pi\) | ||||
0.118856 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(678\) | −5.53034 | −0.212391 | ||||||||
\(679\) | 0.0590582 | 0.00226644 | ||||||||
\(680\) | −1.34366 | −0.0515270 | ||||||||
\(681\) | 32.4388 | 1.24306 | ||||||||
\(682\) | −0.663595 | −0.0254104 | ||||||||
\(683\) | 5.43431 | 0.207938 | 0.103969 | − | 0.994581i | \(-0.466846\pi\) | ||||
0.103969 | + | 0.994581i | \(0.466846\pi\) | |||||||
\(684\) | 23.1197 | 0.884003 | ||||||||
\(685\) | 18.2453 | 0.697118 | ||||||||
\(686\) | −0.0214351 | −0.000818396 0 | ||||||||
\(687\) | 43.8494 | 1.67296 | ||||||||
\(688\) | −22.4904 | −0.857439 | ||||||||
\(689\) | −1.19320 | −0.0454571 | ||||||||
\(690\) | −1.03660 | −0.0394626 | ||||||||
\(691\) | −48.2910 | −1.83708 | −0.918538 | − | 0.395333i | \(-0.870629\pi\) | ||||
−0.918538 | + | 0.395333i | \(0.870629\pi\) | |||||||
\(692\) | 22.1475 | 0.841923 | ||||||||
\(693\) | 0.0130234 | 0.000494719 0 | ||||||||
\(694\) | 9.07463 | 0.344468 | ||||||||
\(695\) | −10.1370 | −0.384518 | ||||||||
\(696\) | 27.2488 | 1.03286 | ||||||||
\(697\) | −6.10350 | −0.231186 | ||||||||
\(698\) | 4.59899 | 0.174074 | ||||||||
\(699\) | 20.2827 | 0.767161 | ||||||||
\(700\) | −0.00922507 | −0.000348675 0 | ||||||||
\(701\) | 25.0342 | 0.945527 | 0.472764 | − | 0.881189i | \(-0.343256\pi\) | ||||
0.472764 | + | 0.881189i | \(0.343256\pi\) | |||||||
\(702\) | −0.0332163 | −0.00125367 | ||||||||
\(703\) | −49.5427 | −1.86854 | ||||||||
\(704\) | −5.71016 | −0.215210 | ||||||||
\(705\) | 8.81347 | 0.331935 | ||||||||
\(706\) | 9.73515 | 0.366387 | ||||||||
\(707\) | −0.0131294 | −0.000493782 0 | ||||||||
\(708\) | 20.6590 | 0.776414 | ||||||||
\(709\) | 48.7032 | 1.82909 | 0.914543 | − | 0.404489i | \(-0.132551\pi\) | ||||
0.914543 | + | 0.404489i | \(0.132551\pi\) | |||||||
\(710\) | −3.96997 | −0.148990 | ||||||||
\(711\) | −6.40610 | −0.240247 | ||||||||
\(712\) | −0.349347 | −0.0130923 | ||||||||
\(713\) | −2.90020 | −0.108613 | ||||||||
\(714\) | −0.00398620 | −0.000149180 0 | ||||||||
\(715\) | −0.139360 | −0.00521176 | ||||||||
\(716\) | −34.2250 | −1.27905 | ||||||||
\(717\) | −26.3729 | −0.984915 | ||||||||
\(718\) | −6.48603 | −0.242056 | ||||||||
\(719\) | −37.4570 | −1.39691 | −0.698456 | − | 0.715653i | \(-0.746129\pi\) | ||||
−0.698456 | + | 0.715653i | \(0.746129\pi\) | |||||||
\(720\) | −9.15699 | −0.341261 | ||||||||
\(721\) | −0.0536351 | −0.00199748 | ||||||||
\(722\) | 0.491358 | 0.0182865 | ||||||||
\(723\) | −63.9052 | −2.37666 | ||||||||
\(724\) | 4.65006 | 0.172818 | ||||||||
\(725\) | −9.29049 | −0.345040 | ||||||||
\(726\) | 0.751948 | 0.0279074 | ||||||||
\(727\) | −48.7135 | −1.80668 | −0.903342 | − | 0.428922i | \(-0.858894\pi\) | ||||
−0.903342 | + | 0.428922i | \(0.858894\pi\) | |||||||
\(728\) | −0.000832256 0 | −3.08455e−5 0 | ||||||||
\(729\) | −21.0249 | −0.778699 | ||||||||
\(730\) | −0.315426 | −0.0116744 | ||||||||
\(731\) | 7.19681 | 0.266184 | ||||||||
\(732\) | 46.4258 | 1.71595 | ||||||||
\(733\) | −50.1163 | −1.85109 | −0.925543 | − | 0.378642i | \(-0.876391\pi\) | ||||
−0.925543 | + | 0.378642i | \(0.876391\pi\) | |||||||
\(734\) | −1.38708 | −0.0511979 | ||||||||
\(735\) | 16.6873 | 0.615521 | ||||||||
\(736\) | 4.87618 | 0.179738 | ||||||||
\(737\) | 5.74607 | 0.211659 | ||||||||
\(738\) | 4.72967 | 0.174101 | ||||||||
\(739\) | 32.9012 | 1.21029 | 0.605145 | − | 0.796115i | \(-0.293115\pi\) | ||||
0.605145 | + | 0.796115i | \(0.293115\pi\) | |||||||
\(740\) | 20.7664 | 0.763388 | ||||||||
\(741\) | −1.50631 | −0.0553358 | ||||||||
\(742\) | −0.0131091 | −0.000481249 0 | ||||||||
\(743\) | −18.3917 | −0.674727 | −0.337363 | − | 0.941374i | \(-0.609535\pi\) | ||||
−0.337363 | + | 0.941374i | \(0.609535\pi\) | |||||||
\(744\) | 6.17041 | 0.226218 | ||||||||
\(745\) | −18.9733 | −0.695129 | ||||||||
\(746\) | 7.39836 | 0.270873 | ||||||||
\(747\) | −46.0327 | −1.68425 | ||||||||
\(748\) | 2.07558 | 0.0758908 | ||||||||
\(749\) | 0.0288345 | 0.00105359 | ||||||||
\(750\) | −0.751948 | −0.0274572 | ||||||||
\(751\) | −0.164906 | −0.00601751 | −0.00300876 | − | 0.999995i | \(-0.500958\pi\) | ||||
−0.00300876 | + | 0.999995i | \(0.500958\pi\) | |||||||
\(752\) | −12.6179 | −0.460126 | ||||||||
\(753\) | −35.4496 | −1.29186 | ||||||||
\(754\) | −0.408389 | −0.0148727 | ||||||||
\(755\) | 1.70211 | 0.0619461 | ||||||||
\(756\) | 0.00697084 | 0.000253527 0 | ||||||||
\(757\) | −28.1034 | −1.02144 | −0.510718 | − | 0.859748i | \(-0.670620\pi\) | ||||
−0.510718 | + | 0.859748i | \(0.670620\pi\) | |||||||
\(758\) | 6.38658 | 0.231971 | ||||||||
\(759\) | 3.28634 | 0.119287 | ||||||||
\(760\) | −5.57836 | −0.202348 | ||||||||
\(761\) | 8.68736 | 0.314917 | 0.157458 | − | 0.987526i | \(-0.449670\pi\) | ||||
0.157458 | + | 0.987526i | \(0.449670\pi\) | |||||||
\(762\) | 0.350110 | 0.0126832 | ||||||||
\(763\) | −0.0763376 | −0.00276361 | ||||||||
\(764\) | 13.8922 | 0.502603 | ||||||||
\(765\) | 2.93019 | 0.105941 | ||||||||
\(766\) | 7.93655 | 0.286759 | ||||||||
\(767\) | −0.635461 | −0.0229452 | ||||||||
\(768\) | 20.5511 | 0.741574 | ||||||||
\(769\) | −26.0966 | −0.941067 | −0.470534 | − | 0.882382i | \(-0.655939\pi\) | ||||
−0.470534 | + | 0.882382i | \(0.655939\pi\) | |||||||
\(770\) | −0.00153108 | −5.51763e−5 0 | ||||||||
\(771\) | −31.0287 | −1.11747 | ||||||||
\(772\) | 2.91565 | 0.104936 | ||||||||
\(773\) | −36.8793 | −1.32645 | −0.663227 | − | 0.748418i | \(-0.730814\pi\) | ||||
−0.663227 | + | 0.748418i | \(0.730814\pi\) | |||||||
\(774\) | −5.57688 | −0.200457 | ||||||||
\(775\) | −2.10380 | −0.0755709 | ||||||||
\(776\) | −14.9692 | −0.537363 | ||||||||
\(777\) | 0.126439 | 0.00453598 | ||||||||
\(778\) | 10.9164 | 0.391371 | ||||||||
\(779\) | −25.3394 | −0.907877 | ||||||||
\(780\) | 0.631389 | 0.0226073 | ||||||||
\(781\) | 12.5861 | 0.450364 | ||||||||
\(782\) | −0.474888 | −0.0169820 | ||||||||
\(783\) | 7.02027 | 0.250884 | ||||||||
\(784\) | −23.8905 | −0.853231 | ||||||||
\(785\) | −8.60002 | −0.306948 | ||||||||
\(786\) | −15.7333 | −0.561188 | ||||||||
\(787\) | 8.78418 | 0.313122 | 0.156561 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156561 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(788\) | 5.43688 | 0.193681 | ||||||||
\(789\) | 10.8491 | 0.386237 | ||||||||
\(790\) | 0.753124 | 0.0267950 | ||||||||
\(791\) | −0.0356997 | −0.00126934 | ||||||||
\(792\) | −3.30098 | −0.117295 | ||||||||
\(793\) | −1.42803 | −0.0507109 | ||||||||
\(794\) | 5.31536 | 0.188635 | ||||||||
\(795\) | 20.4110 | 0.723902 | ||||||||
\(796\) | 41.5732 | 1.47352 | ||||||||
\(797\) | −23.9222 | −0.847366 | −0.423683 | − | 0.905810i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905810i | \(0.639263\pi\) | |||||||
\(798\) | −0.0165492 | −0.000585834 0 | ||||||||
\(799\) | 4.03764 | 0.142842 | ||||||||
\(800\) | 3.53717 | 0.125058 | ||||||||
\(801\) | 0.761838 | 0.0269182 | ||||||||
\(802\) | −5.52027 | −0.194927 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −26.0333 | −0.918125 | ||||||||
\(805\) | −0.00669150 | −0.000235844 0 | ||||||||
\(806\) | −0.0924785 | −0.00325742 | ||||||||
\(807\) | −7.71868 | −0.271711 | ||||||||
\(808\) | 3.32785 | 0.117073 | ||||||||
\(809\) | −42.5025 | −1.49431 | −0.747154 | − | 0.664651i | \(-0.768580\pi\) | ||||
−0.747154 | + | 0.664651i | \(0.768580\pi\) | |||||||
\(810\) | 3.10709 | 0.109172 | ||||||||
\(811\) | −50.4703 | −1.77225 | −0.886127 | − | 0.463443i | \(-0.846614\pi\) | ||||
−0.886127 | + | 0.463443i | \(0.846614\pi\) | |||||||
\(812\) | 0.0857054 | 0.00300767 | ||||||||
\(813\) | −44.2785 | −1.55292 | ||||||||
\(814\) | 3.44659 | 0.120803 | ||||||||
\(815\) | −0.217553 | −0.00762055 | ||||||||
\(816\) | −8.88564 | −0.311060 | ||||||||
\(817\) | 29.8784 | 1.04531 | ||||||||
\(818\) | 5.99075 | 0.209462 | ||||||||
\(819\) | 0.00181494 | 6.34192e−5 0 | ||||||||
\(820\) | 10.6213 | 0.370912 | ||||||||
\(821\) | 17.3414 | 0.605219 | 0.302610 | − | 0.953115i | \(-0.402142\pi\) | ||||
0.302610 | + | 0.953115i | \(0.402142\pi\) | |||||||
\(822\) | −13.7195 | −0.478524 | ||||||||
\(823\) | 49.9996 | 1.74287 | 0.871437 | − | 0.490507i | \(-0.163188\pi\) | ||||
0.871437 | + | 0.490507i | \(0.163188\pi\) | |||||||
\(824\) | 13.5946 | 0.473591 | ||||||||
\(825\) | 2.38391 | 0.0829971 | ||||||||
\(826\) | −0.00698151 | −0.000242918 0 | ||||||||
\(827\) | −5.86933 | −0.204097 | −0.102048 | − | 0.994779i | \(-0.532540\pi\) | ||||
−0.102048 | + | 0.994779i | \(0.532540\pi\) | |||||||
\(828\) | −7.02938 | −0.244288 | ||||||||
\(829\) | 25.0712 | 0.870759 | 0.435379 | − | 0.900247i | \(-0.356614\pi\) | ||||
0.435379 | + | 0.900247i | \(0.356614\pi\) | |||||||
\(830\) | 5.41178 | 0.187846 | ||||||||
\(831\) | −19.3169 | −0.670094 | ||||||||
\(832\) | −0.795767 | −0.0275882 | ||||||||
\(833\) | 7.64482 | 0.264877 | ||||||||
\(834\) | 7.62249 | 0.263945 | ||||||||
\(835\) | −10.2115 | −0.353382 | ||||||||
\(836\) | 8.61702 | 0.298026 | ||||||||
\(837\) | 1.58972 | 0.0549488 | ||||||||
\(838\) | −11.0033 | −0.380101 | ||||||||
\(839\) | 24.8146 | 0.856694 | 0.428347 | − | 0.903614i | \(-0.359096\pi\) | ||||
0.428347 | + | 0.903614i | \(0.359096\pi\) | |||||||
\(840\) | 0.0142367 | 0.000491212 0 | ||||||||
\(841\) | 57.3132 | 1.97632 | ||||||||
\(842\) | 6.98733 | 0.240799 | ||||||||
\(843\) | 10.4266 | 0.359113 | ||||||||
\(844\) | −17.1436 | −0.590107 | ||||||||
\(845\) | 12.9806 | 0.446545 | ||||||||
\(846\) | −3.12881 | −0.107571 | ||||||||
\(847\) | 0.00485401 | 0.000166786 0 | ||||||||
\(848\) | −29.2215 | −1.00347 | ||||||||
\(849\) | 37.4497 | 1.28527 | ||||||||
\(850\) | −0.344484 | −0.0118157 | ||||||||
\(851\) | 15.0631 | 0.516357 | ||||||||
\(852\) | −57.0228 | −1.95357 | ||||||||
\(853\) | 37.0777 | 1.26952 | 0.634758 | − | 0.772711i | \(-0.281100\pi\) | ||||
0.634758 | + | 0.772711i | \(0.281100\pi\) | |||||||
\(854\) | −0.0156891 | −0.000536870 0 | ||||||||
\(855\) | 12.1650 | 0.416035 | ||||||||
\(856\) | −7.30853 | −0.249800 | ||||||||
\(857\) | −48.6119 | −1.66055 | −0.830276 | − | 0.557353i | \(-0.811817\pi\) | ||||
−0.830276 | + | 0.557353i | \(0.811817\pi\) | |||||||
\(858\) | 0.104791 | 0.00357752 | ||||||||
\(859\) | 11.0208 | 0.376026 | 0.188013 | − | 0.982166i | \(-0.439795\pi\) | ||||
0.188013 | + | 0.982166i | \(0.439795\pi\) | |||||||
\(860\) | −12.5239 | −0.427060 | ||||||||
\(861\) | 0.0646693 | 0.00220392 | ||||||||
\(862\) | 6.64665 | 0.226386 | ||||||||
\(863\) | 45.5945 | 1.55205 | 0.776027 | − | 0.630700i | \(-0.217232\pi\) | ||||
0.776027 | + | 0.630700i | \(0.217232\pi\) | |||||||
\(864\) | −2.67283 | −0.0909316 | ||||||||
\(865\) | 11.6535 | 0.396231 | ||||||||
\(866\) | 5.68331 | 0.193127 | ||||||||
\(867\) | −37.6831 | −1.27979 | ||||||||
\(868\) | 0.0194077 | 0.000658742 0 | ||||||||
\(869\) | −2.38764 | −0.0809951 | ||||||||
\(870\) | 6.98596 | 0.236846 | ||||||||
\(871\) | 0.800771 | 0.0271331 | ||||||||
\(872\) | 19.3489 | 0.655237 | ||||||||
\(873\) | 32.6441 | 1.10483 | ||||||||
\(874\) | −1.97155 | −0.0666888 | ||||||||
\(875\) | −0.00485401 | −0.000164095 0 | ||||||||
\(876\) | −4.53064 | −0.153076 | ||||||||
\(877\) | −2.04400 | −0.0690208 | −0.0345104 | − | 0.999404i | \(-0.510987\pi\) | ||||
−0.0345104 | + | 0.999404i | \(0.510987\pi\) | |||||||
\(878\) | −7.12202 | −0.240357 | ||||||||
\(879\) | −3.85567 | −0.130049 | ||||||||
\(880\) | −3.41294 | −0.115050 | ||||||||
\(881\) | −9.92953 | −0.334534 | −0.167267 | − | 0.985912i | \(-0.553494\pi\) | ||||
−0.167267 | + | 0.985912i | \(0.553494\pi\) | |||||||
\(882\) | −5.92405 | −0.199473 | ||||||||
\(883\) | 36.3679 | 1.22388 | 0.611938 | − | 0.790906i | \(-0.290390\pi\) | ||||
0.611938 | + | 0.790906i | \(0.290390\pi\) | |||||||
\(884\) | 0.289253 | 0.00972863 | ||||||||
\(885\) | 10.8703 | 0.365401 | ||||||||
\(886\) | −0.726422 | −0.0244046 | ||||||||
\(887\) | 53.0603 | 1.78159 | 0.890795 | − | 0.454405i | \(-0.150148\pi\) | ||||
0.890795 | + | 0.454405i | \(0.150148\pi\) | |||||||
\(888\) | −32.0479 | −1.07546 | ||||||||
\(889\) | 0.00226005 | 7.57996e−5 0 | ||||||||
\(890\) | −0.0895645 | −0.00300221 | ||||||||
\(891\) | −9.85045 | −0.330003 | ||||||||
\(892\) | −29.8765 | −1.00034 | ||||||||
\(893\) | 16.7627 | 0.560944 | ||||||||
\(894\) | 14.2670 | 0.477158 | ||||||||
\(895\) | −18.0084 | −0.601953 | ||||||||
\(896\) | −0.0430816 | −0.00143926 | ||||||||
\(897\) | 0.457984 | 0.0152916 | ||||||||
\(898\) | −8.65633 | −0.288866 | ||||||||
\(899\) | 19.5454 | 0.651874 | ||||||||
\(900\) | −5.09911 | −0.169970 | ||||||||
\(901\) | 9.35071 | 0.311517 | ||||||||
\(902\) | 1.76281 | 0.0586952 | ||||||||
\(903\) | −0.0762534 | −0.00253756 | ||||||||
\(904\) | 9.04863 | 0.300953 | ||||||||
\(905\) | 2.44675 | 0.0813326 | ||||||||
\(906\) | −1.27990 | −0.0425217 | ||||||||
\(907\) | 34.6596 | 1.15085 | 0.575427 | − | 0.817853i | \(-0.304836\pi\) | ||||
0.575427 | + | 0.817853i | \(0.304836\pi\) | |||||||
\(908\) | −25.8609 | −0.858226 | ||||||||
\(909\) | −7.25721 | −0.240706 | ||||||||
\(910\) | −0.000213371 0 | −7.07319e−6 0 | ||||||||
\(911\) | 7.51658 | 0.249035 | 0.124518 | − | 0.992217i | \(-0.460262\pi\) | ||||
0.124518 | + | 0.992217i | \(0.460262\pi\) | |||||||
\(912\) | −36.8898 | −1.22154 | ||||||||
\(913\) | −17.1570 | −0.567815 | ||||||||
\(914\) | 3.57972 | 0.118407 | ||||||||
\(915\) | 24.4281 | 0.807569 | ||||||||
\(916\) | −34.9578 | −1.15504 | ||||||||
\(917\) | −0.101562 | −0.00335389 | ||||||||
\(918\) | 0.260306 | 0.00859137 | ||||||||
\(919\) | −48.3136 | −1.59372 | −0.796859 | − | 0.604166i | \(-0.793506\pi\) | ||||
−0.796859 | + | 0.604166i | \(0.793506\pi\) | |||||||
\(920\) | 1.69606 | 0.0559175 | ||||||||
\(921\) | −41.2949 | −1.36071 | ||||||||
\(922\) | 4.68520 | 0.154299 | ||||||||
\(923\) | 1.75399 | 0.0577333 | ||||||||
\(924\) | −0.0219917 | −0.000723475 0 | ||||||||
\(925\) | 10.9268 | 0.359270 | ||||||||
\(926\) | 8.40474 | 0.276197 | ||||||||
\(927\) | −29.6465 | −0.973719 | ||||||||
\(928\) | −32.8621 | −1.07875 | ||||||||
\(929\) | 32.6720 | 1.07193 | 0.535967 | − | 0.844239i | \(-0.319947\pi\) | ||||
0.535967 | + | 0.844239i | \(0.319947\pi\) | |||||||
\(930\) | 1.58195 | 0.0518742 | ||||||||
\(931\) | 31.7384 | 1.04018 | ||||||||
\(932\) | −16.1698 | −0.529660 | ||||||||
\(933\) | 8.23362 | 0.269557 | ||||||||
\(934\) | −2.48840 | −0.0814228 | ||||||||
\(935\) | 1.09212 | 0.0357162 | ||||||||
\(936\) | −0.460025 | −0.0150364 | ||||||||
\(937\) | −19.9189 | −0.650724 | −0.325362 | − | 0.945590i | \(-0.605486\pi\) | ||||
−0.325362 | + | 0.945590i | \(0.605486\pi\) | |||||||
\(938\) | 0.00879770 | 0.000287255 0 | ||||||||
\(939\) | 17.8181 | 0.581470 | ||||||||
\(940\) | −7.02630 | −0.229173 | ||||||||
\(941\) | 18.9722 | 0.618476 | 0.309238 | − | 0.950985i | \(-0.399926\pi\) | ||||
0.309238 | + | 0.950985i | \(0.399926\pi\) | |||||||
\(942\) | 6.46676 | 0.210698 | ||||||||
\(943\) | 7.70426 | 0.250885 | ||||||||
\(944\) | −15.5625 | −0.506516 | ||||||||
\(945\) | 0.00366789 | 0.000119316 0 | ||||||||
\(946\) | −2.07858 | −0.0675805 | ||||||||
\(947\) | 14.9553 | 0.485981 | 0.242991 | − | 0.970029i | \(-0.421872\pi\) | ||||
0.242991 | + | 0.970029i | \(0.421872\pi\) | |||||||
\(948\) | 10.8175 | 0.351337 | ||||||||
\(949\) | 0.139360 | 0.00452381 | ||||||||
\(950\) | −1.43016 | −0.0464006 | ||||||||
\(951\) | −4.65189 | −0.150848 | ||||||||
\(952\) | 0.00652214 | 0.000211384 0 | ||||||||
\(953\) | 11.7604 | 0.380956 | 0.190478 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190478 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(954\) | −7.24596 | −0.234597 | ||||||||
\(955\) | 7.30975 | 0.236538 | ||||||||
\(956\) | 21.0251 | 0.680000 | ||||||||
\(957\) | −22.1477 | −0.715933 | ||||||||
\(958\) | 5.21204 | 0.168393 | ||||||||
\(959\) | −0.0885630 | −0.00285985 | ||||||||
\(960\) | 13.6125 | 0.439341 | ||||||||
\(961\) | −26.5740 | −0.857226 | ||||||||
\(962\) | 0.480316 | 0.0154860 | ||||||||
\(963\) | 15.9381 | 0.513597 | ||||||||
\(964\) | 50.9466 | 1.64088 | ||||||||
\(965\) | 1.53414 | 0.0493858 | ||||||||
\(966\) | 0.00503166 | 0.000161891 0 | ||||||||
\(967\) | −30.5066 | −0.981027 | −0.490514 | − | 0.871434i | \(-0.663191\pi\) | ||||
−0.490514 | + | 0.871434i | \(0.663191\pi\) | |||||||
\(968\) | −1.23032 | −0.0395440 | ||||||||
\(969\) | 11.8045 | 0.379216 | ||||||||
\(970\) | −3.83776 | −0.123223 | ||||||||
\(971\) | 47.2156 | 1.51522 | 0.757611 | − | 0.652706i | \(-0.226366\pi\) | ||||
0.757611 | + | 0.652706i | \(0.226366\pi\) | |||||||
\(972\) | 40.3205 | 1.29328 | ||||||||
\(973\) | 0.0492050 | 0.00157744 | ||||||||
\(974\) | 9.58995 | 0.307282 | ||||||||
\(975\) | 0.332221 | 0.0106396 | ||||||||
\(976\) | −34.9726 | −1.11945 | ||||||||
\(977\) | −7.27097 | −0.232619 | −0.116310 | − | 0.993213i | \(-0.537106\pi\) | ||||
−0.116310 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(978\) | 0.163588 | 0.00523098 | ||||||||
\(979\) | 0.283948 | 0.00907500 | ||||||||
\(980\) | −13.3035 | −0.424965 | ||||||||
\(981\) | −42.1952 | −1.34719 | ||||||||
\(982\) | 11.7456 | 0.374818 | ||||||||
\(983\) | 32.1299 | 1.02478 | 0.512392 | − | 0.858752i | \(-0.328760\pi\) | ||||
0.512392 | + | 0.858752i | \(0.328760\pi\) | |||||||
\(984\) | −16.3914 | −0.522539 | ||||||||
\(985\) | 2.86076 | 0.0911513 | ||||||||
\(986\) | 3.20042 | 0.101922 | ||||||||
\(987\) | −0.0427807 | −0.00136172 | ||||||||
\(988\) | 1.20087 | 0.0382047 | ||||||||
\(989\) | −9.08431 | −0.288864 | ||||||||
\(990\) | −0.846296 | −0.0268971 | ||||||||
\(991\) | 15.8575 | 0.503732 | 0.251866 | − | 0.967762i | \(-0.418956\pi\) | ||||
0.251866 | + | 0.967762i | \(0.418956\pi\) | |||||||
\(992\) | −7.44152 | −0.236268 | ||||||||
\(993\) | 27.9548 | 0.887120 | ||||||||
\(994\) | 0.0192703 | 0.000611216 0 | ||||||||
\(995\) | 21.8748 | 0.693478 | ||||||||
\(996\) | 77.7323 | 2.46304 | ||||||||
\(997\) | 32.7127 | 1.03602 | 0.518011 | − | 0.855374i | \(-0.326673\pi\) | ||||
0.518011 | + | 0.855374i | \(0.326673\pi\) | |||||||
\(998\) | −3.04377 | −0.0963488 | ||||||||
\(999\) | −8.25671 | −0.261231 |
(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 | 4015.2.a.f.1.18 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.f.1.18 | ✓ | 31 | 1.1 | even | 1 | trivial |