Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(1\) |
Dimension: | \(139\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39846 | −1.69597 | −0.847984 | − | 0.530022i | \(-0.822184\pi\) | ||||
−0.847984 | + | 0.530022i | \(0.822184\pi\) | |||||||
\(3\) | −2.50987 | −1.44907 | −0.724536 | − | 0.689237i | \(-0.757946\pi\) | ||||
−0.724536 | + | 0.689237i | \(0.757946\pi\) | |||||||
\(4\) | 3.75261 | 1.87631 | ||||||||
\(5\) | 0.204658 | 0.0915257 | 0.0457629 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457629 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(6\) | 6.01982 | 2.45758 | ||||||||
\(7\) | −4.29057 | −1.62168 | −0.810841 | − | 0.585266i | \(-0.800990\pi\) | ||||
−0.810841 | + | 0.585266i | \(0.800990\pi\) | |||||||
\(8\) | −4.20358 | −1.48619 | ||||||||
\(9\) | 3.29943 | 1.09981 | ||||||||
\(10\) | −0.490864 | −0.155225 | ||||||||
\(11\) | 5.44379 | 1.64137 | 0.820683 | − | 0.571384i | \(-0.193593\pi\) | ||||
0.820683 | + | 0.571384i | \(0.193593\pi\) | |||||||
\(12\) | −9.41856 | −2.71891 | ||||||||
\(13\) | 4.38906 | 1.21731 | 0.608653 | − | 0.793437i | \(-0.291710\pi\) | ||||
0.608653 | + | 0.793437i | \(0.291710\pi\) | |||||||
\(14\) | 10.2908 | 2.75032 | ||||||||
\(15\) | −0.513664 | −0.132627 | ||||||||
\(16\) | 2.57688 | 0.644221 | ||||||||
\(17\) | −2.66989 | −0.647543 | −0.323772 | − | 0.946135i | \(-0.604951\pi\) | ||||
−0.323772 | + | 0.946135i | \(0.604951\pi\) | |||||||
\(18\) | −7.91356 | −1.86525 | ||||||||
\(19\) | 5.03946 | 1.15613 | 0.578065 | − | 0.815990i | \(-0.303808\pi\) | ||||
0.578065 | + | 0.815990i | \(0.303808\pi\) | |||||||
\(20\) | 0.768001 | 0.171730 | ||||||||
\(21\) | 10.7688 | 2.34994 | ||||||||
\(22\) | −13.0567 | −2.78370 | ||||||||
\(23\) | −4.73681 | −0.987692 | −0.493846 | − | 0.869549i | \(-0.664409\pi\) | ||||
−0.493846 | + | 0.869549i | \(0.664409\pi\) | |||||||
\(24\) | 10.5504 | 2.15359 | ||||||||
\(25\) | −4.95812 | −0.991623 | ||||||||
\(26\) | −10.5270 | −2.06451 | ||||||||
\(27\) | −0.751541 | −0.144634 | ||||||||
\(28\) | −16.1008 | −3.04277 | ||||||||
\(29\) | −5.83511 | −1.08355 | −0.541776 | − | 0.840523i | \(-0.682248\pi\) | ||||
−0.541776 | + | 0.840523i | \(0.682248\pi\) | |||||||
\(30\) | 1.23200 | 0.224932 | ||||||||
\(31\) | −2.59154 | −0.465455 | −0.232727 | − | 0.972542i | \(-0.574765\pi\) | ||||
−0.232727 | + | 0.972542i | \(0.574765\pi\) | |||||||
\(32\) | 2.22660 | 0.393611 | ||||||||
\(33\) | −13.6632 | −2.37846 | ||||||||
\(34\) | 6.40362 | 1.09821 | ||||||||
\(35\) | −0.878098 | −0.148426 | ||||||||
\(36\) | 12.3815 | 2.06358 | ||||||||
\(37\) | −0.316382 | −0.0520128 | −0.0260064 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260064 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(38\) | −12.0869 | −1.96076 | ||||||||
\(39\) | −11.0160 | −1.76396 | ||||||||
\(40\) | −0.860294 | −0.136024 | ||||||||
\(41\) | 4.20345 | 0.656469 | 0.328234 | − | 0.944596i | \(-0.393546\pi\) | ||||
0.328234 | + | 0.944596i | \(0.393546\pi\) | |||||||
\(42\) | −25.8284 | −3.98541 | ||||||||
\(43\) | −5.47822 | −0.835420 | −0.417710 | − | 0.908580i | \(-0.637167\pi\) | ||||
−0.417710 | + | 0.908580i | \(0.637167\pi\) | |||||||
\(44\) | 20.4285 | 3.07971 | ||||||||
\(45\) | 0.675255 | 0.100661 | ||||||||
\(46\) | 11.3610 | 1.67509 | ||||||||
\(47\) | 0.230350 | 0.0335999 | 0.0168000 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0168000 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(48\) | −6.46763 | −0.933523 | ||||||||
\(49\) | 11.4090 | 1.62985 | ||||||||
\(50\) | 11.8918 | 1.68176 | ||||||||
\(51\) | 6.70107 | 0.938337 | ||||||||
\(52\) | 16.4704 | 2.28404 | ||||||||
\(53\) | 1.38245 | 0.189895 | 0.0949474 | − | 0.995482i | \(-0.469732\pi\) | ||||
0.0949474 | + | 0.995482i | \(0.469732\pi\) | |||||||
\(54\) | 1.80254 | 0.245295 | ||||||||
\(55\) | 1.11411 | 0.150227 | ||||||||
\(56\) | 18.0357 | 2.41013 | ||||||||
\(57\) | −12.6484 | −1.67532 | ||||||||
\(58\) | 13.9953 | 1.83767 | ||||||||
\(59\) | −6.50513 | −0.846896 | −0.423448 | − | 0.905920i | \(-0.639180\pi\) | ||||
−0.423448 | + | 0.905920i | \(0.639180\pi\) | |||||||
\(60\) | −1.92758 | −0.248850 | ||||||||
\(61\) | −3.83527 | −0.491056 | −0.245528 | − | 0.969389i | \(-0.578961\pi\) | ||||
−0.245528 | + | 0.969389i | \(0.578961\pi\) | |||||||
\(62\) | 6.21571 | 0.789396 | ||||||||
\(63\) | −14.1564 | −1.78354 | ||||||||
\(64\) | −10.4942 | −1.31177 | ||||||||
\(65\) | 0.898255 | 0.111415 | ||||||||
\(66\) | 32.7707 | 4.03379 | ||||||||
\(67\) | 7.74657 | 0.946394 | 0.473197 | − | 0.880957i | \(-0.343100\pi\) | ||||
0.473197 | + | 0.880957i | \(0.343100\pi\) | |||||||
\(68\) | −10.0191 | −1.21499 | ||||||||
\(69\) | 11.8888 | 1.43124 | ||||||||
\(70\) | 2.10608 | 0.251725 | ||||||||
\(71\) | 7.88074 | 0.935271 | 0.467636 | − | 0.883921i | \(-0.345106\pi\) | ||||
0.467636 | + | 0.883921i | \(0.345106\pi\) | |||||||
\(72\) | −13.8694 | −1.63453 | ||||||||
\(73\) | −1.60794 | −0.188195 | −0.0940977 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0940977 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(74\) | 0.758829 | 0.0882121 | ||||||||
\(75\) | 12.4442 | 1.43693 | ||||||||
\(76\) | 18.9111 | 2.16926 | ||||||||
\(77\) | −23.3570 | −2.66177 | ||||||||
\(78\) | 26.4213 | 2.99163 | ||||||||
\(79\) | 14.5083 | 1.63231 | 0.816153 | − | 0.577836i | \(-0.196102\pi\) | ||||
0.816153 | + | 0.577836i | \(0.196102\pi\) | |||||||
\(80\) | 0.527379 | 0.0589628 | ||||||||
\(81\) | −8.01203 | −0.890226 | ||||||||
\(82\) | −10.0818 | −1.11335 | ||||||||
\(83\) | −1.36997 | −0.150373 | −0.0751866 | − | 0.997169i | \(-0.523955\pi\) | ||||
−0.0751866 | + | 0.997169i | \(0.523955\pi\) | |||||||
\(84\) | 40.4110 | 4.40920 | ||||||||
\(85\) | −0.546413 | −0.0592668 | ||||||||
\(86\) | 13.1393 | 1.41685 | ||||||||
\(87\) | 14.6453 | 1.57015 | ||||||||
\(88\) | −22.8834 | −2.43938 | ||||||||
\(89\) | −2.34048 | −0.248091 | −0.124045 | − | 0.992277i | \(-0.539587\pi\) | ||||
−0.124045 | + | 0.992277i | \(0.539587\pi\) | |||||||
\(90\) | −1.61957 | −0.170718 | ||||||||
\(91\) | −18.8316 | −1.97408 | ||||||||
\(92\) | −17.7754 | −1.85321 | ||||||||
\(93\) | 6.50443 | 0.674478 | ||||||||
\(94\) | −0.552484 | −0.0569844 | ||||||||
\(95\) | 1.03136 | 0.105816 | ||||||||
\(96\) | −5.58847 | −0.570371 | ||||||||
\(97\) | −17.4363 | −1.77038 | −0.885192 | − | 0.465225i | \(-0.845973\pi\) | ||||
−0.885192 | + | 0.465225i | \(0.845973\pi\) | |||||||
\(98\) | −27.3640 | −2.76418 | ||||||||
\(99\) | 17.9614 | 1.80519 | ||||||||
\(100\) | −18.6059 | −1.86059 | ||||||||
\(101\) | 1.92809 | 0.191852 | 0.0959260 | − | 0.995388i | \(-0.469419\pi\) | ||||
0.0959260 | + | 0.995388i | \(0.469419\pi\) | |||||||
\(102\) | −16.0722 | −1.59139 | ||||||||
\(103\) | 1.85189 | 0.182473 | 0.0912363 | − | 0.995829i | \(-0.470918\pi\) | ||||
0.0912363 | + | 0.995829i | \(0.470918\pi\) | |||||||
\(104\) | −18.4497 | −1.80915 | ||||||||
\(105\) | 2.20391 | 0.215080 | ||||||||
\(106\) | −3.31576 | −0.322055 | ||||||||
\(107\) | 8.95957 | 0.866154 | 0.433077 | − | 0.901357i | \(-0.357428\pi\) | ||||
0.433077 | + | 0.901357i | \(0.357428\pi\) | |||||||
\(108\) | −2.82024 | −0.271378 | ||||||||
\(109\) | −7.30336 | −0.699535 | −0.349768 | − | 0.936836i | \(-0.613739\pi\) | ||||
−0.349768 | + | 0.936836i | \(0.613739\pi\) | |||||||
\(110\) | −2.67216 | −0.254780 | ||||||||
\(111\) | 0.794076 | 0.0753703 | ||||||||
\(112\) | −11.0563 | −1.04472 | ||||||||
\(113\) | −9.67194 | −0.909860 | −0.454930 | − | 0.890527i | \(-0.650336\pi\) | ||||
−0.454930 | + | 0.890527i | \(0.650336\pi\) | |||||||
\(114\) | 30.3366 | 2.84129 | ||||||||
\(115\) | −0.969424 | −0.0903993 | ||||||||
\(116\) | −21.8969 | −2.03308 | ||||||||
\(117\) | 14.4814 | 1.33881 | ||||||||
\(118\) | 15.6023 | 1.43631 | ||||||||
\(119\) | 11.4553 | 1.05011 | ||||||||
\(120\) | 2.15922 | 0.197109 | ||||||||
\(121\) | 18.6349 | 1.69408 | ||||||||
\(122\) | 9.19875 | 0.832815 | ||||||||
\(123\) | −10.5501 | −0.951271 | ||||||||
\(124\) | −9.72506 | −0.873336 | ||||||||
\(125\) | −2.03801 | −0.182285 | ||||||||
\(126\) | 33.9537 | 3.02483 | ||||||||
\(127\) | 10.7486 | 0.953784 | 0.476892 | − | 0.878962i | \(-0.341763\pi\) | ||||
0.476892 | + | 0.878962i | \(0.341763\pi\) | |||||||
\(128\) | 20.7167 | 1.83111 | ||||||||
\(129\) | 13.7496 | 1.21058 | ||||||||
\(130\) | −2.15443 | −0.188956 | ||||||||
\(131\) | 7.27828 | 0.635906 | 0.317953 | − | 0.948106i | \(-0.397005\pi\) | ||||
0.317953 | + | 0.948106i | \(0.397005\pi\) | |||||||
\(132\) | −51.2727 | −4.46272 | ||||||||
\(133\) | −21.6221 | −1.87488 | ||||||||
\(134\) | −18.5798 | −1.60505 | ||||||||
\(135\) | −0.153809 | −0.0132377 | ||||||||
\(136\) | 11.2231 | 0.962371 | ||||||||
\(137\) | 17.6360 | 1.50675 | 0.753373 | − | 0.657594i | \(-0.228426\pi\) | ||||
0.753373 | + | 0.657594i | \(0.228426\pi\) | |||||||
\(138\) | −28.5147 | −2.42733 | ||||||||
\(139\) | 14.9558 | 1.26853 | 0.634265 | − | 0.773115i | \(-0.281303\pi\) | ||||
0.634265 | + | 0.773115i | \(0.281303\pi\) | |||||||
\(140\) | −3.29516 | −0.278492 | ||||||||
\(141\) | −0.578147 | −0.0486887 | ||||||||
\(142\) | −18.9016 | −1.58619 | ||||||||
\(143\) | 23.8931 | 1.99804 | ||||||||
\(144\) | 8.50226 | 0.708521 | ||||||||
\(145\) | −1.19420 | −0.0991729 | ||||||||
\(146\) | 3.85659 | 0.319173 | ||||||||
\(147\) | −28.6350 | −2.36178 | ||||||||
\(148\) | −1.18726 | −0.0975920 | ||||||||
\(149\) | −14.5422 | −1.19135 | −0.595673 | − | 0.803227i | \(-0.703114\pi\) | ||||
−0.595673 | + | 0.803227i | \(0.703114\pi\) | |||||||
\(150\) | −29.8470 | −2.43699 | ||||||||
\(151\) | 5.05088 | 0.411035 | 0.205517 | − | 0.978653i | \(-0.434112\pi\) | ||||
0.205517 | + | 0.978653i | \(0.434112\pi\) | |||||||
\(152\) | −21.1837 | −1.71823 | ||||||||
\(153\) | −8.80912 | −0.712175 | ||||||||
\(154\) | 56.0208 | 4.51428 | ||||||||
\(155\) | −0.530379 | −0.0426011 | ||||||||
\(156\) | −41.3386 | −3.30974 | ||||||||
\(157\) | 5.06912 | 0.404560 | 0.202280 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202280 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(158\) | −34.7975 | −2.76834 | ||||||||
\(159\) | −3.46978 | −0.275171 | ||||||||
\(160\) | 0.455691 | 0.0360255 | ||||||||
\(161\) | 20.3236 | 1.60172 | ||||||||
\(162\) | 19.2166 | 1.50979 | ||||||||
\(163\) | −4.69674 | −0.367877 | −0.183939 | − | 0.982938i | \(-0.558885\pi\) | ||||
−0.183939 | + | 0.982938i | \(0.558885\pi\) | |||||||
\(164\) | 15.7739 | 1.23174 | ||||||||
\(165\) | −2.79628 | −0.217690 | ||||||||
\(166\) | 3.28581 | 0.255028 | ||||||||
\(167\) | −12.2300 | −0.946383 | −0.473191 | − | 0.880960i | \(-0.656898\pi\) | ||||
−0.473191 | + | 0.880960i | \(0.656898\pi\) | |||||||
\(168\) | −45.2673 | −3.49245 | ||||||||
\(169\) | 6.26383 | 0.481833 | ||||||||
\(170\) | 1.31055 | 0.100515 | ||||||||
\(171\) | 16.6274 | 1.27153 | ||||||||
\(172\) | −20.5576 | −1.56750 | ||||||||
\(173\) | 20.7435 | 1.57710 | 0.788550 | − | 0.614970i | \(-0.210832\pi\) | ||||
0.788550 | + | 0.614970i | \(0.210832\pi\) | |||||||
\(174\) | −35.1263 | −2.66292 | ||||||||
\(175\) | 21.2731 | 1.60810 | ||||||||
\(176\) | 14.0280 | 1.05740 | ||||||||
\(177\) | 16.3270 | 1.22721 | ||||||||
\(178\) | 5.61356 | 0.420754 | ||||||||
\(179\) | 24.7729 | 1.85161 | 0.925807 | − | 0.377997i | \(-0.123387\pi\) | ||||
0.925807 | + | 0.377997i | \(0.123387\pi\) | |||||||
\(180\) | 2.53397 | 0.188871 | ||||||||
\(181\) | −20.0145 | −1.48766 | −0.743832 | − | 0.668367i | \(-0.766994\pi\) | ||||
−0.743832 | + | 0.668367i | \(0.766994\pi\) | |||||||
\(182\) | 45.1667 | 3.34798 | ||||||||
\(183\) | 9.62602 | 0.711576 | ||||||||
\(184\) | 19.9115 | 1.46790 | ||||||||
\(185\) | −0.0647499 | −0.00476051 | ||||||||
\(186\) | −15.6006 | −1.14389 | ||||||||
\(187\) | −14.5343 | −1.06285 | ||||||||
\(188\) | 0.864413 | 0.0630438 | ||||||||
\(189\) | 3.22454 | 0.234551 | ||||||||
\(190\) | −2.47369 | −0.179460 | ||||||||
\(191\) | 19.2432 | 1.39239 | 0.696194 | − | 0.717854i | \(-0.254875\pi\) | ||||
0.696194 | + | 0.717854i | \(0.254875\pi\) | |||||||
\(192\) | 26.3390 | 1.90085 | ||||||||
\(193\) | −16.7280 | −1.20411 | −0.602054 | − | 0.798455i | \(-0.705651\pi\) | ||||
−0.602054 | + | 0.798455i | \(0.705651\pi\) | |||||||
\(194\) | 41.8202 | 3.00252 | ||||||||
\(195\) | −2.25450 | −0.161448 | ||||||||
\(196\) | 42.8135 | 3.05810 | ||||||||
\(197\) | 13.3001 | 0.947591 | 0.473796 | − | 0.880635i | \(-0.342884\pi\) | ||||
0.473796 | + | 0.880635i | \(0.342884\pi\) | |||||||
\(198\) | −43.0798 | −3.06155 | ||||||||
\(199\) | −2.39195 | −0.169561 | −0.0847804 | − | 0.996400i | \(-0.527019\pi\) | ||||
−0.0847804 | + | 0.996400i | \(0.527019\pi\) | |||||||
\(200\) | 20.8418 | 1.47374 | ||||||||
\(201\) | −19.4429 | −1.37139 | ||||||||
\(202\) | −4.62445 | −0.325375 | ||||||||
\(203\) | 25.0359 | 1.75718 | ||||||||
\(204\) | 25.1465 | 1.76061 | ||||||||
\(205\) | 0.860269 | 0.0600838 | ||||||||
\(206\) | −4.44170 | −0.309468 | ||||||||
\(207\) | −15.6288 | −1.08628 | ||||||||
\(208\) | 11.3101 | 0.784214 | ||||||||
\(209\) | 27.4338 | 1.89763 | ||||||||
\(210\) | −5.28599 | −0.364768 | ||||||||
\(211\) | −22.5413 | −1.55180 | −0.775902 | − | 0.630853i | \(-0.782705\pi\) | ||||
−0.775902 | + | 0.630853i | \(0.782705\pi\) | |||||||
\(212\) | 5.18782 | 0.356301 | ||||||||
\(213\) | −19.7796 | −1.35528 | ||||||||
\(214\) | −21.4892 | −1.46897 | ||||||||
\(215\) | −1.12116 | −0.0764624 | ||||||||
\(216\) | 3.15916 | 0.214954 | ||||||||
\(217\) | 11.1192 | 0.754820 | ||||||||
\(218\) | 17.5168 | 1.18639 | ||||||||
\(219\) | 4.03572 | 0.272709 | ||||||||
\(220\) | 4.18084 | 0.281872 | ||||||||
\(221\) | −11.7183 | −0.788258 | ||||||||
\(222\) | −1.90456 | −0.127826 | ||||||||
\(223\) | 13.5262 | 0.905780 | 0.452890 | − | 0.891566i | \(-0.350393\pi\) | ||||
0.452890 | + | 0.891566i | \(0.350393\pi\) | |||||||
\(224\) | −9.55337 | −0.638311 | ||||||||
\(225\) | −16.3590 | −1.09060 | ||||||||
\(226\) | 23.1978 | 1.54309 | ||||||||
\(227\) | −11.9248 | −0.791475 | −0.395737 | − | 0.918364i | \(-0.629511\pi\) | ||||
−0.395737 | + | 0.918364i | \(0.629511\pi\) | |||||||
\(228\) | −47.4645 | −3.14341 | ||||||||
\(229\) | −23.8963 | −1.57911 | −0.789557 | − | 0.613677i | \(-0.789690\pi\) | ||||
−0.789557 | + | 0.613677i | \(0.789690\pi\) | |||||||
\(230\) | 2.32513 | 0.153314 | ||||||||
\(231\) | 58.6229 | 3.85710 | ||||||||
\(232\) | 24.5283 | 1.61036 | ||||||||
\(233\) | 0.363211 | 0.0237947 | 0.0118974 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118974 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(234\) | −34.7331 | −2.27057 | ||||||||
\(235\) | 0.0471428 | 0.00307526 | ||||||||
\(236\) | −24.4113 | −1.58904 | ||||||||
\(237\) | −36.4138 | −2.36533 | ||||||||
\(238\) | −27.4752 | −1.78095 | ||||||||
\(239\) | −8.23364 | −0.532590 | −0.266295 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266295 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(240\) | −1.32365 | −0.0854413 | ||||||||
\(241\) | 24.0996 | 1.55239 | 0.776195 | − | 0.630492i | \(-0.217147\pi\) | ||||
0.776195 | + | 0.630492i | \(0.217147\pi\) | |||||||
\(242\) | −44.6951 | −2.87311 | ||||||||
\(243\) | 22.3638 | 1.43464 | ||||||||
\(244\) | −14.3923 | −0.921372 | ||||||||
\(245\) | 2.33493 | 0.149173 | ||||||||
\(246\) | 25.3040 | 1.61332 | ||||||||
\(247\) | 22.1185 | 1.40736 | ||||||||
\(248\) | 10.8937 | 0.691754 | ||||||||
\(249\) | 3.43843 | 0.217902 | ||||||||
\(250\) | 4.88808 | 0.309149 | ||||||||
\(251\) | −24.6273 | −1.55446 | −0.777231 | − | 0.629215i | \(-0.783377\pi\) | ||||
−0.777231 | + | 0.629215i | \(0.783377\pi\) | |||||||
\(252\) | −53.1237 | −3.34648 | ||||||||
\(253\) | −25.7862 | −1.62116 | ||||||||
\(254\) | −25.7801 | −1.61759 | ||||||||
\(255\) | 1.37143 | 0.0858820 | ||||||||
\(256\) | −28.6998 | −1.79374 | ||||||||
\(257\) | 5.82941 | 0.363629 | 0.181814 | − | 0.983333i | \(-0.441803\pi\) | ||||
0.181814 | + | 0.983333i | \(0.441803\pi\) | |||||||
\(258\) | −32.9779 | −2.05311 | ||||||||
\(259\) | 1.35746 | 0.0843483 | ||||||||
\(260\) | 3.37080 | 0.209048 | ||||||||
\(261\) | −19.2526 | −1.19170 | ||||||||
\(262\) | −17.4567 | −1.07848 | ||||||||
\(263\) | 29.9351 | 1.84587 | 0.922937 | − | 0.384950i | \(-0.125781\pi\) | ||||
0.922937 | + | 0.384950i | \(0.125781\pi\) | |||||||
\(264\) | 57.4343 | 3.53484 | ||||||||
\(265\) | 0.282930 | 0.0173803 | ||||||||
\(266\) | 51.8598 | 3.17973 | ||||||||
\(267\) | 5.87430 | 0.359501 | ||||||||
\(268\) | 29.0699 | 1.77573 | ||||||||
\(269\) | 2.02825 | 0.123664 | 0.0618322 | − | 0.998087i | \(-0.480306\pi\) | ||||
0.0618322 | + | 0.998087i | \(0.480306\pi\) | |||||||
\(270\) | 0.368904 | 0.0224508 | ||||||||
\(271\) | −4.78683 | −0.290779 | −0.145390 | − | 0.989374i | \(-0.546444\pi\) | ||||
−0.145390 | + | 0.989374i | \(0.546444\pi\) | |||||||
\(272\) | −6.87999 | −0.417161 | ||||||||
\(273\) | 47.2647 | 2.86059 | ||||||||
\(274\) | −42.2993 | −2.55539 | ||||||||
\(275\) | −26.9910 | −1.62762 | ||||||||
\(276\) | 44.6139 | 2.68544 | ||||||||
\(277\) | −10.4445 | −0.627547 | −0.313774 | − | 0.949498i | \(-0.601593\pi\) | ||||
−0.313774 | + | 0.949498i | \(0.601593\pi\) | |||||||
\(278\) | −35.8708 | −2.15139 | ||||||||
\(279\) | −8.55063 | −0.511913 | ||||||||
\(280\) | 3.69115 | 0.220588 | ||||||||
\(281\) | −16.5320 | −0.986215 | −0.493107 | − | 0.869968i | \(-0.664139\pi\) | ||||
−0.493107 | + | 0.869968i | \(0.664139\pi\) | |||||||
\(282\) | 1.38666 | 0.0825745 | ||||||||
\(283\) | −14.1500 | −0.841128 | −0.420564 | − | 0.907263i | \(-0.638168\pi\) | ||||
−0.420564 | + | 0.907263i | \(0.638168\pi\) | |||||||
\(284\) | 29.5734 | 1.75486 | ||||||||
\(285\) | −2.58859 | −0.153335 | ||||||||
\(286\) | −57.3067 | −3.38862 | ||||||||
\(287\) | −18.0352 | −1.06458 | ||||||||
\(288\) | 7.34652 | 0.432898 | ||||||||
\(289\) | −9.87170 | −0.580688 | ||||||||
\(290\) | 2.86424 | 0.168194 | ||||||||
\(291\) | 43.7627 | 2.56542 | ||||||||
\(292\) | −6.03399 | −0.353112 | ||||||||
\(293\) | 33.5494 | 1.95998 | 0.979988 | − | 0.199056i | \(-0.0637874\pi\) | ||||
0.979988 | + | 0.199056i | \(0.0637874\pi\) | |||||||
\(294\) | 68.6799 | 4.00549 | ||||||||
\(295\) | −1.33133 | −0.0775128 | ||||||||
\(296\) | 1.32993 | 0.0773008 | ||||||||
\(297\) | −4.09124 | −0.237398 | ||||||||
\(298\) | 34.8790 | 2.02048 | ||||||||
\(299\) | −20.7901 | −1.20232 | ||||||||
\(300\) | 46.6983 | 2.69613 | ||||||||
\(301\) | 23.5047 | 1.35479 | ||||||||
\(302\) | −12.1143 | −0.697102 | ||||||||
\(303\) | −4.83925 | −0.278008 | ||||||||
\(304\) | 12.9861 | 0.744804 | ||||||||
\(305\) | −0.784918 | −0.0449443 | ||||||||
\(306\) | 21.1283 | 1.20783 | ||||||||
\(307\) | −22.2473 | −1.26972 | −0.634860 | − | 0.772628i | \(-0.718942\pi\) | ||||
−0.634860 | + | 0.772628i | \(0.718942\pi\) | |||||||
\(308\) | −87.6497 | −4.99430 | ||||||||
\(309\) | −4.64801 | −0.264416 | ||||||||
\(310\) | 1.27209 | 0.0722501 | ||||||||
\(311\) | 22.8842 | 1.29765 | 0.648823 | − | 0.760939i | \(-0.275262\pi\) | ||||
0.648823 | + | 0.760939i | \(0.275262\pi\) | |||||||
\(312\) | 46.3064 | 2.62158 | ||||||||
\(313\) | −14.2580 | −0.805912 | −0.402956 | − | 0.915219i | \(-0.632017\pi\) | ||||
−0.402956 | + | 0.915219i | \(0.632017\pi\) | |||||||
\(314\) | −12.1581 | −0.686120 | ||||||||
\(315\) | −2.89723 | −0.163240 | ||||||||
\(316\) | 54.4439 | 3.06271 | ||||||||
\(317\) | −14.1865 | −0.796794 | −0.398397 | − | 0.917213i | \(-0.630433\pi\) | ||||
−0.398397 | + | 0.917213i | \(0.630433\pi\) | |||||||
\(318\) | 8.32213 | 0.466682 | ||||||||
\(319\) | −31.7651 | −1.77851 | ||||||||
\(320\) | −2.14771 | −0.120061 | ||||||||
\(321\) | −22.4873 | −1.25512 | ||||||||
\(322\) | −48.7453 | −2.71647 | ||||||||
\(323\) | −13.4548 | −0.748645 | ||||||||
\(324\) | −30.0661 | −1.67034 | ||||||||
\(325\) | −21.7615 | −1.20711 | ||||||||
\(326\) | 11.2649 | 0.623908 | ||||||||
\(327\) | 18.3305 | 1.01368 | ||||||||
\(328\) | −17.6695 | −0.975636 | ||||||||
\(329\) | −0.988330 | −0.0544884 | ||||||||
\(330\) | 6.70677 | 0.369195 | ||||||||
\(331\) | 5.32710 | 0.292804 | 0.146402 | − | 0.989225i | \(-0.453231\pi\) | ||||
0.146402 | + | 0.989225i | \(0.453231\pi\) | |||||||
\(332\) | −5.14095 | −0.282146 | ||||||||
\(333\) | −1.04388 | −0.0572043 | ||||||||
\(334\) | 29.3331 | 1.60503 | ||||||||
\(335\) | 1.58540 | 0.0866194 | ||||||||
\(336\) | 27.7498 | 1.51388 | ||||||||
\(337\) | −21.1201 | −1.15048 | −0.575241 | − | 0.817984i | \(-0.695092\pi\) | ||||
−0.575241 | + | 0.817984i | \(0.695092\pi\) | |||||||
\(338\) | −15.0236 | −0.817174 | ||||||||
\(339\) | 24.2753 | 1.31845 | ||||||||
\(340\) | −2.05048 | −0.111203 | ||||||||
\(341\) | −14.1078 | −0.763982 | ||||||||
\(342\) | −39.8801 | −2.15647 | ||||||||
\(343\) | −18.9170 | −1.02142 | ||||||||
\(344\) | 23.0281 | 1.24159 | ||||||||
\(345\) | 2.43313 | 0.130995 | ||||||||
\(346\) | −49.7525 | −2.67471 | ||||||||
\(347\) | −10.9753 | −0.589183 | −0.294592 | − | 0.955623i | \(-0.595184\pi\) | ||||
−0.294592 | + | 0.955623i | \(0.595184\pi\) | |||||||
\(348\) | 54.9583 | 2.94608 | ||||||||
\(349\) | 10.0533 | 0.538141 | 0.269071 | − | 0.963120i | \(-0.413284\pi\) | ||||
0.269071 | + | 0.963120i | \(0.413284\pi\) | |||||||
\(350\) | −51.0228 | −2.72728 | ||||||||
\(351\) | −3.29856 | −0.176064 | ||||||||
\(352\) | 12.1211 | 0.646059 | ||||||||
\(353\) | 20.4812 | 1.09011 | 0.545053 | − | 0.838402i | \(-0.316510\pi\) | ||||
0.545053 | + | 0.838402i | \(0.316510\pi\) | |||||||
\(354\) | −39.1597 | −2.08132 | ||||||||
\(355\) | 1.61285 | 0.0856014 | ||||||||
\(356\) | −8.78293 | −0.465494 | ||||||||
\(357\) | −28.7514 | −1.52168 | ||||||||
\(358\) | −59.4168 | −3.14028 | ||||||||
\(359\) | −19.6592 | −1.03757 | −0.518787 | − | 0.854903i | \(-0.673616\pi\) | ||||
−0.518787 | + | 0.854903i | \(0.673616\pi\) | |||||||
\(360\) | −2.83848 | −0.149601 | ||||||||
\(361\) | 6.39614 | 0.336639 | ||||||||
\(362\) | 48.0039 | 2.52303 | ||||||||
\(363\) | −46.7711 | −2.45485 | ||||||||
\(364\) | −70.6675 | −3.70399 | ||||||||
\(365\) | −0.329078 | −0.0172247 | ||||||||
\(366\) | −23.0876 | −1.20681 | ||||||||
\(367\) | −32.0867 | −1.67491 | −0.837456 | − | 0.546505i | \(-0.815958\pi\) | ||||
−0.837456 | + | 0.546505i | \(0.815958\pi\) | |||||||
\(368\) | −12.2062 | −0.636292 | ||||||||
\(369\) | 13.8690 | 0.721992 | ||||||||
\(370\) | 0.155300 | 0.00807367 | ||||||||
\(371\) | −5.93152 | −0.307949 | ||||||||
\(372\) | 24.4086 | 1.26553 | ||||||||
\(373\) | 29.2769 | 1.51590 | 0.757951 | − | 0.652312i | \(-0.226201\pi\) | ||||
0.757951 | + | 0.652312i | \(0.226201\pi\) | |||||||
\(374\) | 34.8600 | 1.80257 | ||||||||
\(375\) | 5.11512 | 0.264144 | ||||||||
\(376\) | −0.968292 | −0.0499358 | ||||||||
\(377\) | −25.6106 | −1.31901 | ||||||||
\(378\) | −7.73393 | −0.397790 | ||||||||
\(379\) | −17.2225 | −0.884660 | −0.442330 | − | 0.896852i | \(-0.645848\pi\) | ||||
−0.442330 | + | 0.896852i | \(0.645848\pi\) | |||||||
\(380\) | 3.87031 | 0.198543 | ||||||||
\(381\) | −26.9776 | −1.38210 | ||||||||
\(382\) | −46.1540 | −2.36144 | ||||||||
\(383\) | 31.5618 | 1.61273 | 0.806367 | − | 0.591415i | \(-0.201431\pi\) | ||||
0.806367 | + | 0.591415i | \(0.201431\pi\) | |||||||
\(384\) | −51.9961 | −2.65341 | ||||||||
\(385\) | −4.78018 | −0.243621 | ||||||||
\(386\) | 40.1215 | 2.04213 | ||||||||
\(387\) | −18.0750 | −0.918805 | ||||||||
\(388\) | −65.4316 | −3.32178 | ||||||||
\(389\) | 23.6722 | 1.20023 | 0.600115 | − | 0.799914i | \(-0.295122\pi\) | ||||
0.600115 | + | 0.799914i | \(0.295122\pi\) | |||||||
\(390\) | 5.40733 | 0.273811 | ||||||||
\(391\) | 12.6467 | 0.639573 | ||||||||
\(392\) | −47.9585 | −2.42227 | ||||||||
\(393\) | −18.2675 | −0.921474 | ||||||||
\(394\) | −31.8997 | −1.60708 | ||||||||
\(395\) | 2.96923 | 0.149398 | ||||||||
\(396\) | 67.4024 | 3.38710 | ||||||||
\(397\) | −30.8537 | −1.54850 | −0.774251 | − | 0.632879i | \(-0.781873\pi\) | ||||
−0.774251 | + | 0.632879i | \(0.781873\pi\) | |||||||
\(398\) | 5.73700 | 0.287570 | ||||||||
\(399\) | 54.2687 | 2.71683 | ||||||||
\(400\) | −12.7765 | −0.638824 | ||||||||
\(401\) | 7.66836 | 0.382940 | 0.191470 | − | 0.981498i | \(-0.438675\pi\) | ||||
0.191470 | + | 0.981498i | \(0.438675\pi\) | |||||||
\(402\) | 46.6329 | 2.32584 | ||||||||
\(403\) | −11.3744 | −0.566601 | ||||||||
\(404\) | 7.23537 | 0.359973 | ||||||||
\(405\) | −1.63972 | −0.0814786 | ||||||||
\(406\) | −60.0477 | −2.98012 | ||||||||
\(407\) | −1.72232 | −0.0853720 | ||||||||
\(408\) | −28.1684 | −1.39455 | ||||||||
\(409\) | 23.1618 | 1.14528 | 0.572638 | − | 0.819808i | \(-0.305920\pi\) | ||||
0.572638 | + | 0.819808i | \(0.305920\pi\) | |||||||
\(410\) | −2.06332 | −0.101900 | ||||||||
\(411\) | −44.2640 | −2.18338 | ||||||||
\(412\) | 6.94944 | 0.342375 | ||||||||
\(413\) | 27.9107 | 1.37340 | ||||||||
\(414\) | 37.4850 | 1.84229 | ||||||||
\(415\) | −0.280374 | −0.0137630 | ||||||||
\(416\) | 9.77267 | 0.479145 | ||||||||
\(417\) | −37.5370 | −1.83819 | ||||||||
\(418\) | −65.7988 | −3.21833 | ||||||||
\(419\) | −16.7624 | −0.818895 | −0.409447 | − | 0.912334i | \(-0.634278\pi\) | ||||
−0.409447 | + | 0.912334i | \(0.634278\pi\) | |||||||
\(420\) | 8.27042 | 0.403555 | ||||||||
\(421\) | −7.00713 | −0.341507 | −0.170753 | − | 0.985314i | \(-0.554620\pi\) | ||||
−0.170753 | + | 0.985314i | \(0.554620\pi\) | |||||||
\(422\) | 54.0643 | 2.63181 | ||||||||
\(423\) | 0.760023 | 0.0369536 | ||||||||
\(424\) | −5.81125 | −0.282219 | ||||||||
\(425\) | 13.2376 | 0.642119 | ||||||||
\(426\) | 47.4406 | 2.29850 | ||||||||
\(427\) | 16.4555 | 0.796337 | ||||||||
\(428\) | 33.6218 | 1.62517 | ||||||||
\(429\) | −59.9686 | −2.89531 | ||||||||
\(430\) | 2.68906 | 0.129678 | ||||||||
\(431\) | −30.4756 | −1.46796 | −0.733980 | − | 0.679171i | \(-0.762340\pi\) | ||||
−0.733980 | + | 0.679171i | \(0.762340\pi\) | |||||||
\(432\) | −1.93663 | −0.0931763 | ||||||||
\(433\) | 0.765557 | 0.0367903 | 0.0183952 | − | 0.999831i | \(-0.494144\pi\) | ||||
0.0183952 | + | 0.999831i | \(0.494144\pi\) | |||||||
\(434\) | −26.6689 | −1.28015 | ||||||||
\(435\) | 2.99728 | 0.143709 | ||||||||
\(436\) | −27.4067 | −1.31254 | ||||||||
\(437\) | −23.8709 | −1.14190 | ||||||||
\(438\) | −9.67952 | −0.462505 | ||||||||
\(439\) | 6.80740 | 0.324900 | 0.162450 | − | 0.986717i | \(-0.448060\pi\) | ||||
0.162450 | + | 0.986717i | \(0.448060\pi\) | |||||||
\(440\) | −4.68326 | −0.223266 | ||||||||
\(441\) | 37.6432 | 1.79253 | ||||||||
\(442\) | 28.1059 | 1.33686 | ||||||||
\(443\) | −24.5249 | −1.16521 | −0.582605 | − | 0.812755i | \(-0.697967\pi\) | ||||
−0.582605 | + | 0.812755i | \(0.697967\pi\) | |||||||
\(444\) | 2.97986 | 0.141418 | ||||||||
\(445\) | −0.478998 | −0.0227067 | ||||||||
\(446\) | −32.4420 | −1.53617 | ||||||||
\(447\) | 36.4991 | 1.72635 | ||||||||
\(448\) | 45.0260 | 2.12728 | ||||||||
\(449\) | 11.4903 | 0.542261 | 0.271130 | − | 0.962543i | \(-0.412603\pi\) | ||||
0.271130 | + | 0.962543i | \(0.412603\pi\) | |||||||
\(450\) | 39.2364 | 1.84962 | ||||||||
\(451\) | 22.8827 | 1.07751 | ||||||||
\(452\) | −36.2951 | −1.70718 | ||||||||
\(453\) | −12.6770 | −0.595619 | ||||||||
\(454\) | 28.6011 | 1.34232 | ||||||||
\(455\) | −3.85402 | −0.180679 | ||||||||
\(456\) | 53.1684 | 2.48984 | ||||||||
\(457\) | −15.6501 | −0.732079 | −0.366039 | − | 0.930599i | \(-0.619286\pi\) | ||||
−0.366039 | + | 0.930599i | \(0.619286\pi\) | |||||||
\(458\) | 57.3144 | 2.67813 | ||||||||
\(459\) | 2.00653 | 0.0936569 | ||||||||
\(460\) | −3.63787 | −0.169617 | ||||||||
\(461\) | −40.3046 | −1.87717 | −0.938586 | − | 0.345044i | \(-0.887864\pi\) | ||||
−0.938586 | + | 0.345044i | \(0.887864\pi\) | |||||||
\(462\) | −140.605 | −6.54152 | ||||||||
\(463\) | 2.65746 | 0.123503 | 0.0617513 | − | 0.998092i | \(-0.480331\pi\) | ||||
0.0617513 | + | 0.998092i | \(0.480331\pi\) | |||||||
\(464\) | −15.0364 | −0.698047 | ||||||||
\(465\) | 1.33118 | 0.0617321 | ||||||||
\(466\) | −0.871147 | −0.0403551 | ||||||||
\(467\) | −38.0290 | −1.75977 | −0.879887 | − | 0.475183i | \(-0.842382\pi\) | ||||
−0.879887 | + | 0.475183i | \(0.842382\pi\) | |||||||
\(468\) | 54.3431 | 2.51201 | ||||||||
\(469\) | −33.2372 | −1.53475 | ||||||||
\(470\) | −0.113070 | −0.00521554 | ||||||||
\(471\) | −12.7228 | −0.586236 | ||||||||
\(472\) | 27.3448 | 1.25865 | ||||||||
\(473\) | −29.8223 | −1.37123 | ||||||||
\(474\) | 87.3371 | 4.01152 | ||||||||
\(475\) | −24.9862 | −1.14645 | ||||||||
\(476\) | 42.9875 | 1.97033 | ||||||||
\(477\) | 4.56132 | 0.208848 | ||||||||
\(478\) | 19.7481 | 0.903255 | ||||||||
\(479\) | −18.8091 | −0.859410 | −0.429705 | − | 0.902969i | \(-0.641382\pi\) | ||||
−0.429705 | + | 0.902969i | \(0.641382\pi\) | |||||||
\(480\) | −1.14372 | −0.0522036 | ||||||||
\(481\) | −1.38862 | −0.0633155 | ||||||||
\(482\) | −57.8019 | −2.63281 | ||||||||
\(483\) | −51.0095 | −2.32101 | ||||||||
\(484\) | 69.9296 | 3.17862 | ||||||||
\(485\) | −3.56847 | −0.162036 | ||||||||
\(486\) | −53.6386 | −2.43310 | ||||||||
\(487\) | −39.5206 | −1.79085 | −0.895424 | − | 0.445214i | \(-0.853128\pi\) | ||||
−0.895424 | + | 0.445214i | \(0.853128\pi\) | |||||||
\(488\) | 16.1218 | 0.729802 | ||||||||
\(489\) | 11.7882 | 0.533081 | ||||||||
\(490\) | −5.60025 | −0.252993 | ||||||||
\(491\) | −1.77764 | −0.0802238 | −0.0401119 | − | 0.999195i | \(-0.512771\pi\) | ||||
−0.0401119 | + | 0.999195i | \(0.512771\pi\) | |||||||
\(492\) | −39.5905 | −1.78488 | ||||||||
\(493\) | 15.5791 | 0.701647 | ||||||||
\(494\) | −53.0503 | −2.38685 | ||||||||
\(495\) | 3.67595 | 0.165222 | ||||||||
\(496\) | −6.67810 | −0.299856 | ||||||||
\(497\) | −33.8128 | −1.51671 | ||||||||
\(498\) | −8.24694 | −0.369554 | ||||||||
\(499\) | 15.9181 | 0.712591 | 0.356296 | − | 0.934373i | \(-0.384040\pi\) | ||||
0.356296 | + | 0.934373i | \(0.384040\pi\) | |||||||
\(500\) | −7.64785 | −0.342022 | ||||||||
\(501\) | 30.6956 | 1.37138 | ||||||||
\(502\) | 59.0677 | 2.63632 | ||||||||
\(503\) | −3.09482 | −0.137991 | −0.0689956 | − | 0.997617i | \(-0.521979\pi\) | ||||
−0.0689956 | + | 0.997617i | \(0.521979\pi\) | |||||||
\(504\) | 59.5077 | 2.65068 | ||||||||
\(505\) | 0.394598 | 0.0175594 | ||||||||
\(506\) | 61.8472 | 2.74944 | ||||||||
\(507\) | −15.7214 | −0.698211 | ||||||||
\(508\) | 40.3354 | 1.78959 | ||||||||
\(509\) | −3.76643 | −0.166944 | −0.0834721 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834721 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(510\) | −3.28931 | −0.145653 | ||||||||
\(511\) | 6.89898 | 0.305193 | ||||||||
\(512\) | 27.4019 | 1.21101 | ||||||||
\(513\) | −3.78736 | −0.167216 | ||||||||
\(514\) | −13.9816 | −0.616702 | ||||||||
\(515\) | 0.379004 | 0.0167009 | ||||||||
\(516\) | 51.5969 | 2.27143 | ||||||||
\(517\) | 1.25398 | 0.0551498 | ||||||||
\(518\) | −3.25581 | −0.143052 | ||||||||
\(519\) | −52.0635 | −2.28533 | ||||||||
\(520\) | −3.77588 | −0.165583 | ||||||||
\(521\) | 37.4208 | 1.63944 | 0.819718 | − | 0.572767i | \(-0.194130\pi\) | ||||
0.819718 | + | 0.572767i | \(0.194130\pi\) | |||||||
\(522\) | 46.1765 | 2.02109 | ||||||||
\(523\) | −25.7081 | −1.12414 | −0.562069 | − | 0.827090i | \(-0.689995\pi\) | ||||
−0.562069 | + | 0.827090i | \(0.689995\pi\) | |||||||
\(524\) | 27.3126 | 1.19316 | ||||||||
\(525\) | −53.3927 | −2.33025 | ||||||||
\(526\) | −71.7981 | −3.13054 | ||||||||
\(527\) | 6.91913 | 0.301402 | ||||||||
\(528\) | −35.2085 | −1.53225 | ||||||||
\(529\) | −0.562667 | −0.0244638 | ||||||||
\(530\) | −0.678597 | −0.0294764 | ||||||||
\(531\) | −21.4633 | −0.931426 | ||||||||
\(532\) | −81.1395 | −3.51784 | ||||||||
\(533\) | 18.4492 | 0.799123 | ||||||||
\(534\) | −14.0893 | −0.609703 | ||||||||
\(535\) | 1.83365 | 0.0792754 | ||||||||
\(536\) | −32.5633 | −1.40652 | ||||||||
\(537\) | −62.1767 | −2.68312 | ||||||||
\(538\) | −4.86467 | −0.209731 | ||||||||
\(539\) | 62.1081 | 2.67518 | ||||||||
\(540\) | −0.577185 | −0.0248381 | ||||||||
\(541\) | −9.97394 | −0.428813 | −0.214407 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214407 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(542\) | 11.4810 | 0.493152 | ||||||||
\(543\) | 50.2337 | 2.15573 | ||||||||
\(544\) | −5.94477 | −0.254880 | ||||||||
\(545\) | −1.49469 | −0.0640255 | ||||||||
\(546\) | −113.363 | −4.85147 | ||||||||
\(547\) | 28.9440 | 1.23756 | 0.618778 | − | 0.785566i | \(-0.287628\pi\) | ||||
0.618778 | + | 0.785566i | \(0.287628\pi\) | |||||||
\(548\) | 66.1811 | 2.82712 | ||||||||
\(549\) | −12.6542 | −0.540069 | ||||||||
\(550\) | 64.7368 | 2.76038 | ||||||||
\(551\) | −29.4058 | −1.25273 | ||||||||
\(552\) | −49.9753 | −2.12709 | ||||||||
\(553\) | −62.2487 | −2.64708 | ||||||||
\(554\) | 25.0506 | 1.06430 | ||||||||
\(555\) | 0.162514 | 0.00689833 | ||||||||
\(556\) | 56.1232 | 2.38015 | ||||||||
\(557\) | −26.4802 | −1.12200 | −0.561001 | − | 0.827815i | \(-0.689584\pi\) | ||||
−0.561001 | + | 0.827815i | \(0.689584\pi\) | |||||||
\(558\) | 20.5083 | 0.868187 | ||||||||
\(559\) | −24.0442 | −1.01696 | ||||||||
\(560\) | −2.26276 | −0.0956189 | ||||||||
\(561\) | 36.4792 | 1.54015 | ||||||||
\(562\) | 39.6513 | 1.67259 | ||||||||
\(563\) | 24.5064 | 1.03282 | 0.516412 | − | 0.856340i | \(-0.327267\pi\) | ||||
0.516412 | + | 0.856340i | \(0.327267\pi\) | |||||||
\(564\) | −2.16956 | −0.0913550 | ||||||||
\(565\) | −1.97944 | −0.0832756 | ||||||||
\(566\) | 33.9381 | 1.42653 | ||||||||
\(567\) | 34.3762 | 1.44366 | ||||||||
\(568\) | −33.1273 | −1.38999 | ||||||||
\(569\) | −19.7815 | −0.829283 | −0.414641 | − | 0.909985i | \(-0.636093\pi\) | ||||
−0.414641 | + | 0.909985i | \(0.636093\pi\) | |||||||
\(570\) | 6.20862 | 0.260051 | ||||||||
\(571\) | 1.18458 | 0.0495731 | 0.0247866 | − | 0.999693i | \(-0.492109\pi\) | ||||
0.0247866 | + | 0.999693i | \(0.492109\pi\) | |||||||
\(572\) | 89.6617 | 3.74894 | ||||||||
\(573\) | −48.2978 | −2.01767 | ||||||||
\(574\) | 43.2567 | 1.80550 | ||||||||
\(575\) | 23.4856 | 0.979419 | ||||||||
\(576\) | −34.6248 | −1.44270 | ||||||||
\(577\) | −39.6255 | −1.64963 | −0.824815 | − | 0.565403i | \(-0.808721\pi\) | ||||
−0.824815 | + | 0.565403i | \(0.808721\pi\) | |||||||
\(578\) | 23.6769 | 0.984828 | ||||||||
\(579\) | 41.9851 | 1.74484 | ||||||||
\(580\) | −4.48137 | −0.186079 | ||||||||
\(581\) | 5.87793 | 0.243858 | ||||||||
\(582\) | −104.963 | −4.35086 | ||||||||
\(583\) | 7.52580 | 0.311687 | ||||||||
\(584\) | 6.75911 | 0.279694 | ||||||||
\(585\) | 2.96373 | 0.122535 | ||||||||
\(586\) | −80.4669 | −3.32406 | ||||||||
\(587\) | 34.2360 | 1.41307 | 0.706536 | − | 0.707677i | \(-0.250257\pi\) | ||||
0.706536 | + | 0.707677i | \(0.250257\pi\) | |||||||
\(588\) | −107.456 | −4.43142 | ||||||||
\(589\) | −13.0600 | −0.538127 | ||||||||
\(590\) | 3.19313 | 0.131459 | ||||||||
\(591\) | −33.3814 | −1.37313 | ||||||||
\(592\) | −0.815278 | −0.0335077 | ||||||||
\(593\) | −3.10027 | −0.127313 | −0.0636565 | − | 0.997972i | \(-0.520276\pi\) | ||||
−0.0636565 | + | 0.997972i | \(0.520276\pi\) | |||||||
\(594\) | 9.81267 | 0.402619 | ||||||||
\(595\) | 2.34442 | 0.0961120 | ||||||||
\(596\) | −54.5713 | −2.23533 | ||||||||
\(597\) | 6.00348 | 0.245706 | ||||||||
\(598\) | 49.8643 | 2.03910 | ||||||||
\(599\) | −1.47930 | −0.0604424 | −0.0302212 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302212 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(600\) | −52.3102 | −2.13555 | ||||||||
\(601\) | −17.0845 | −0.696892 | −0.348446 | − | 0.937329i | \(-0.613291\pi\) | ||||
−0.348446 | + | 0.937329i | \(0.613291\pi\) | |||||||
\(602\) | −56.3750 | −2.29767 | ||||||||
\(603\) | 25.5593 | 1.04086 | ||||||||
\(604\) | 18.9540 | 0.771227 | ||||||||
\(605\) | 3.81377 | 0.155052 | ||||||||
\(606\) | 11.6067 | 0.471492 | ||||||||
\(607\) | −24.5135 | −0.994972 | −0.497486 | − | 0.867472i | \(-0.665743\pi\) | ||||
−0.497486 | + | 0.867472i | \(0.665743\pi\) | |||||||
\(608\) | 11.2208 | 0.455066 | ||||||||
\(609\) | −62.8368 | −2.54628 | ||||||||
\(610\) | 1.88259 | 0.0762240 | ||||||||
\(611\) | 1.01102 | 0.0409014 | ||||||||
\(612\) | −33.0572 | −1.33626 | ||||||||
\(613\) | 0.0222735 | 0.000899619 0 | 0.000449810 | − | 1.00000i | \(-0.499857\pi\) | ||||
0.000449810 | 1.00000i | \(0.499857\pi\) | ||||||||
\(614\) | 53.3592 | 2.15340 | ||||||||
\(615\) | −2.15916 | −0.0870658 | ||||||||
\(616\) | 98.1828 | 3.95590 | ||||||||
\(617\) | −20.6034 | −0.829461 | −0.414730 | − | 0.909944i | \(-0.636124\pi\) | ||||
−0.414730 | + | 0.909944i | \(0.636124\pi\) | |||||||
\(618\) | 11.1481 | 0.448441 | ||||||||
\(619\) | 31.5214 | 1.26695 | 0.633476 | − | 0.773762i | \(-0.281628\pi\) | ||||
0.633476 | + | 0.773762i | \(0.281628\pi\) | |||||||
\(620\) | −1.99031 | −0.0799327 | ||||||||
\(621\) | 3.55991 | 0.142854 | ||||||||
\(622\) | −54.8869 | −2.20077 | ||||||||
\(623\) | 10.0420 | 0.402324 | ||||||||
\(624\) | −28.3868 | −1.13638 | ||||||||
\(625\) | 24.3735 | 0.974939 | ||||||||
\(626\) | 34.1973 | 1.36680 | ||||||||
\(627\) | −68.8551 | −2.74981 | ||||||||
\(628\) | 19.0224 | 0.759078 | ||||||||
\(629\) | 0.844704 | 0.0336805 | ||||||||
\(630\) | 6.94888 | 0.276850 | ||||||||
\(631\) | 9.21836 | 0.366977 | 0.183489 | − | 0.983022i | \(-0.441261\pi\) | ||||
0.183489 | + | 0.983022i | \(0.441261\pi\) | |||||||
\(632\) | −60.9866 | −2.42591 | ||||||||
\(633\) | 56.5756 | 2.24868 | ||||||||
\(634\) | 34.0258 | 1.35134 | ||||||||
\(635\) | 2.19979 | 0.0872958 | ||||||||
\(636\) | −13.0207 | −0.516306 | ||||||||
\(637\) | 50.0746 | 1.98403 | ||||||||
\(638\) | 76.1874 | 3.01629 | ||||||||
\(639\) | 26.0020 | 1.02862 | ||||||||
\(640\) | 4.23983 | 0.167594 | ||||||||
\(641\) | −16.2032 | −0.639988 | −0.319994 | − | 0.947420i | \(-0.603681\pi\) | ||||
−0.319994 | + | 0.947420i | \(0.603681\pi\) | |||||||
\(642\) | 53.9350 | 2.12864 | ||||||||
\(643\) | 21.3454 | 0.841778 | 0.420889 | − | 0.907112i | \(-0.361718\pi\) | ||||
0.420889 | + | 0.907112i | \(0.361718\pi\) | |||||||
\(644\) | 76.2666 | 3.00532 | ||||||||
\(645\) | 2.81396 | 0.110800 | ||||||||
\(646\) | 32.2708 | 1.26968 | ||||||||
\(647\) | 28.3383 | 1.11409 | 0.557047 | − | 0.830481i | \(-0.311934\pi\) | ||||
0.557047 | + | 0.830481i | \(0.311934\pi\) | |||||||
\(648\) | 33.6792 | 1.32304 | ||||||||
\(649\) | −35.4126 | −1.39007 | ||||||||
\(650\) | 52.1940 | 2.04722 | ||||||||
\(651\) | −27.9077 | −1.09379 | ||||||||
\(652\) | −17.6251 | −0.690250 | ||||||||
\(653\) | 33.5963 | 1.31473 | 0.657363 | − | 0.753574i | \(-0.271672\pi\) | ||||
0.657363 | + | 0.753574i | \(0.271672\pi\) | |||||||
\(654\) | −43.9649 | −1.71916 | ||||||||
\(655\) | 1.48956 | 0.0582018 | ||||||||
\(656\) | 10.8318 | 0.422911 | ||||||||
\(657\) | −5.30530 | −0.206979 | ||||||||
\(658\) | 2.37047 | 0.0924106 | ||||||||
\(659\) | −36.9324 | −1.43868 | −0.719341 | − | 0.694657i | \(-0.755556\pi\) | ||||
−0.719341 | + | 0.694657i | \(0.755556\pi\) | |||||||
\(660\) | −10.4934 | −0.408453 | ||||||||
\(661\) | −15.9484 | −0.620321 | −0.310160 | − | 0.950684i | \(-0.600383\pi\) | ||||
−0.310160 | + | 0.950684i | \(0.600383\pi\) | |||||||
\(662\) | −12.7768 | −0.496586 | ||||||||
\(663\) | 29.4114 | 1.14224 | ||||||||
\(664\) | 5.75875 | 0.223483 | ||||||||
\(665\) | −4.42514 | −0.171599 | ||||||||
\(666\) | 2.50371 | 0.0970166 | ||||||||
\(667\) | 27.6398 | 1.07022 | ||||||||
\(668\) | −45.8943 | −1.77570 | ||||||||
\(669\) | −33.9489 | −1.31254 | ||||||||
\(670\) | −3.80251 | −0.146904 | ||||||||
\(671\) | −20.8784 | −0.806003 | ||||||||
\(672\) | 23.9777 | 0.924960 | ||||||||
\(673\) | −42.2541 | −1.62878 | −0.814388 | − | 0.580320i | \(-0.802927\pi\) | ||||
−0.814388 | + | 0.580320i | \(0.802927\pi\) | |||||||
\(674\) | 50.6556 | 1.95118 | ||||||||
\(675\) | 3.72623 | 0.143423 | ||||||||
\(676\) | 23.5057 | 0.904067 | ||||||||
\(677\) | 35.6139 | 1.36875 | 0.684377 | − | 0.729129i | \(-0.260074\pi\) | ||||
0.684377 | + | 0.729129i | \(0.260074\pi\) | |||||||
\(678\) | −58.2233 | −2.23605 | ||||||||
\(679\) | 74.8115 | 2.87100 | ||||||||
\(680\) | 2.29689 | 0.0880817 | ||||||||
\(681\) | 29.9296 | 1.14690 | ||||||||
\(682\) | 33.8371 | 1.29569 | ||||||||
\(683\) | −10.5247 | −0.402718 | −0.201359 | − | 0.979518i | \(-0.564536\pi\) | ||||
−0.201359 | + | 0.979518i | \(0.564536\pi\) | |||||||
\(684\) | 62.3961 | 2.38577 | ||||||||
\(685\) | 3.60935 | 0.137906 | ||||||||
\(686\) | 45.3716 | 1.73230 | ||||||||
\(687\) | 59.9766 | 2.28825 | ||||||||
\(688\) | −14.1167 | −0.538195 | ||||||||
\(689\) | 6.06767 | 0.231160 | ||||||||
\(690\) | −5.83576 | −0.222163 | ||||||||
\(691\) | 4.48104 | 0.170467 | 0.0852333 | − | 0.996361i | \(-0.472836\pi\) | ||||
0.0852333 | + | 0.996361i | \(0.472836\pi\) | |||||||
\(692\) | 77.8424 | 2.95912 | ||||||||
\(693\) | −77.0648 | −2.92745 | ||||||||
\(694\) | 26.3237 | 0.999236 | ||||||||
\(695\) | 3.06081 | 0.116103 | ||||||||
\(696\) | −61.5628 | −2.33353 | ||||||||
\(697\) | −11.2227 | −0.425092 | ||||||||
\(698\) | −24.1125 | −0.912670 | ||||||||
\(699\) | −0.911611 | −0.0344803 | ||||||||
\(700\) | 79.8298 | 3.01728 | ||||||||
\(701\) | −3.99773 | −0.150992 | −0.0754961 | − | 0.997146i | \(-0.524054\pi\) | ||||
−0.0754961 | + | 0.997146i | \(0.524054\pi\) | |||||||
\(702\) | 7.91146 | 0.298599 | ||||||||
\(703\) | −1.59439 | −0.0601336 | ||||||||
\(704\) | −57.1281 | −2.15310 | ||||||||
\(705\) | −0.118322 | −0.00445627 | ||||||||
\(706\) | −49.1234 | −1.84878 | ||||||||
\(707\) | −8.27260 | −0.311123 | ||||||||
\(708\) | 61.2690 | 2.30263 | ||||||||
\(709\) | 2.98427 | 0.112077 | 0.0560383 | − | 0.998429i | \(-0.482153\pi\) | ||||
0.0560383 | + | 0.998429i | \(0.482153\pi\) | |||||||
\(710\) | −3.86837 | −0.145177 | ||||||||
\(711\) | 47.8690 | 1.79523 | ||||||||
\(712\) | 9.83840 | 0.368710 | ||||||||
\(713\) | 12.2756 | 0.459726 | ||||||||
\(714\) | 68.9591 | 2.58073 | ||||||||
\(715\) | 4.88991 | 0.182872 | ||||||||
\(716\) | 92.9632 | 3.47420 | ||||||||
\(717\) | 20.6653 | 0.771761 | ||||||||
\(718\) | 47.1519 | 1.75969 | ||||||||
\(719\) | 37.6332 | 1.40348 | 0.701741 | − | 0.712432i | \(-0.252406\pi\) | ||||
0.701741 | + | 0.712432i | \(0.252406\pi\) | |||||||
\(720\) | 1.74005 | 0.0648479 | ||||||||
\(721\) | −7.94568 | −0.295912 | ||||||||
\(722\) | −15.3409 | −0.570929 | ||||||||
\(723\) | −60.4868 | −2.24953 | ||||||||
\(724\) | −75.1066 | −2.79131 | ||||||||
\(725\) | 28.9311 | 1.07448 | ||||||||
\(726\) | 112.179 | 4.16334 | ||||||||
\(727\) | 21.0326 | 0.780056 | 0.390028 | − | 0.920803i | \(-0.372465\pi\) | ||||
0.390028 | + | 0.920803i | \(0.372465\pi\) | |||||||
\(728\) | 79.1598 | 2.93386 | ||||||||
\(729\) | −32.0940 | −1.18867 | ||||||||
\(730\) | 0.789280 | 0.0292126 | ||||||||
\(731\) | 14.6262 | 0.540971 | ||||||||
\(732\) | 36.1227 | 1.33513 | ||||||||
\(733\) | 15.2159 | 0.562011 | 0.281006 | − | 0.959706i | \(-0.409332\pi\) | ||||
0.281006 | + | 0.959706i | \(0.409332\pi\) | |||||||
\(734\) | 76.9587 | 2.84060 | ||||||||
\(735\) | −5.86037 | −0.216163 | ||||||||
\(736\) | −10.5470 | −0.388766 | ||||||||
\(737\) | 42.1707 | 1.55338 | ||||||||
\(738\) | −33.2643 | −1.22447 | ||||||||
\(739\) | 9.62533 | 0.354073 | 0.177037 | − | 0.984204i | \(-0.443349\pi\) | ||||
0.177037 | + | 0.984204i | \(0.443349\pi\) | |||||||
\(740\) | −0.242982 | −0.00893218 | ||||||||
\(741\) | −55.5144 | −2.03937 | ||||||||
\(742\) | 14.2265 | 0.522272 | ||||||||
\(743\) | 3.47732 | 0.127570 | 0.0637852 | − | 0.997964i | \(-0.479683\pi\) | ||||
0.0637852 | + | 0.997964i | \(0.479683\pi\) | |||||||
\(744\) | −27.3419 | −1.00240 | ||||||||
\(745\) | −2.97618 | −0.109039 | ||||||||
\(746\) | −70.2196 | −2.57092 | ||||||||
\(747\) | −4.52011 | −0.165382 | ||||||||
\(748\) | −54.5417 | −1.99424 | ||||||||
\(749\) | −38.4416 | −1.40463 | ||||||||
\(750\) | −12.2684 | −0.447979 | ||||||||
\(751\) | 4.63809 | 0.169246 | 0.0846231 | − | 0.996413i | \(-0.473031\pi\) | ||||
0.0846231 | + | 0.996413i | \(0.473031\pi\) | |||||||
\(752\) | 0.593584 | 0.0216458 | ||||||||
\(753\) | 61.8113 | 2.25253 | ||||||||
\(754\) | 61.4261 | 2.23701 | ||||||||
\(755\) | 1.03370 | 0.0376203 | ||||||||
\(756\) | 12.1004 | 0.440089 | ||||||||
\(757\) | −1.31767 | −0.0478916 | −0.0239458 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239458 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(758\) | 41.3074 | 1.50035 | ||||||||
\(759\) | 64.7199 | 2.34918 | ||||||||
\(760\) | −4.33542 | −0.157262 | ||||||||
\(761\) | 25.8210 | 0.936010 | 0.468005 | − | 0.883726i | \(-0.344973\pi\) | ||||
0.468005 | + | 0.883726i | \(0.344973\pi\) | |||||||
\(762\) | 64.7046 | 2.34400 | ||||||||
\(763\) | 31.3356 | 1.13442 | ||||||||
\(764\) | 72.2122 | 2.61255 | ||||||||
\(765\) | −1.80286 | −0.0651824 | ||||||||
\(766\) | −75.6998 | −2.73515 | ||||||||
\(767\) | −28.5514 | −1.03093 | ||||||||
\(768\) | 72.0326 | 2.59925 | ||||||||
\(769\) | −37.1369 | −1.33919 | −0.669596 | − | 0.742726i | \(-0.733533\pi\) | ||||
−0.669596 | + | 0.742726i | \(0.733533\pi\) | |||||||
\(770\) | 11.4651 | 0.413173 | ||||||||
\(771\) | −14.6310 | −0.526924 | ||||||||
\(772\) | −62.7737 | −2.25928 | ||||||||
\(773\) | −31.2596 | −1.12433 | −0.562165 | − | 0.827025i | \(-0.690031\pi\) | ||||
−0.562165 | + | 0.827025i | \(0.690031\pi\) | |||||||
\(774\) | 43.3522 | 1.55826 | ||||||||
\(775\) | 12.8492 | 0.461556 | ||||||||
\(776\) | 73.2947 | 2.63112 | ||||||||
\(777\) | −3.40704 | −0.122227 | ||||||||
\(778\) | −56.7769 | −2.03555 | ||||||||
\(779\) | 21.1831 | 0.758964 | ||||||||
\(780\) | −8.46027 | −0.302926 | ||||||||
\(781\) | 42.9011 | 1.53512 | ||||||||
\(782\) | −30.3327 | −1.08470 | ||||||||
\(783\) | 4.38532 | 0.156719 | ||||||||
\(784\) | 29.3996 | 1.04998 | ||||||||
\(785\) | 1.03743 | 0.0370276 | ||||||||
\(786\) | 43.8139 | 1.56279 | ||||||||
\(787\) | 37.3036 | 1.32973 | 0.664865 | − | 0.746964i | \(-0.268489\pi\) | ||||
0.664865 | + | 0.746964i | \(0.268489\pi\) | |||||||
\(788\) | 49.9101 | 1.77797 | ||||||||
\(789\) | −75.1330 | −2.67481 | ||||||||
\(790\) | −7.12157 | −0.253374 | ||||||||
\(791\) | 41.4981 | 1.47550 | ||||||||
\(792\) | −75.5023 | −2.68286 | ||||||||
\(793\) | −16.8332 | −0.597765 | ||||||||
\(794\) | 74.0013 | 2.62621 | ||||||||
\(795\) | −0.710117 | −0.0251853 | ||||||||
\(796\) | −8.97606 | −0.318148 | ||||||||
\(797\) | 12.9795 | 0.459756 | 0.229878 | − | 0.973219i | \(-0.426167\pi\) | ||||
0.229878 | + | 0.973219i | \(0.426167\pi\) | |||||||
\(798\) | −130.161 | −4.60766 | ||||||||
\(799\) | −0.615007 | −0.0217574 | ||||||||
\(800\) | −11.0397 | −0.390313 | ||||||||
\(801\) | −7.72227 | −0.272853 | ||||||||
\(802\) | −18.3923 | −0.649454 | ||||||||
\(803\) | −8.75331 | −0.308897 | ||||||||
\(804\) | −72.9616 | −2.57316 | ||||||||
\(805\) | 4.15938 | 0.146599 | ||||||||
\(806\) | 27.2811 | 0.960937 | ||||||||
\(807\) | −5.09063 | −0.179199 | ||||||||
\(808\) | −8.10487 | −0.285128 | ||||||||
\(809\) | 27.3774 | 0.962539 | 0.481269 | − | 0.876573i | \(-0.340176\pi\) | ||||
0.481269 | + | 0.876573i | \(0.340176\pi\) | |||||||
\(810\) | 3.93282 | 0.138185 | ||||||||
\(811\) | −46.5830 | −1.63575 | −0.817874 | − | 0.575397i | \(-0.804848\pi\) | ||||
−0.817874 | + | 0.575397i | \(0.804848\pi\) | |||||||
\(812\) | 93.9502 | 3.29700 | ||||||||
\(813\) | 12.0143 | 0.421360 | ||||||||
\(814\) | 4.13091 | 0.144788 | ||||||||
\(815\) | −0.961224 | −0.0336702 | ||||||||
\(816\) | 17.2679 | 0.604496 | ||||||||
\(817\) | −27.6072 | −0.965855 | ||||||||
\(818\) | −55.5526 | −1.94235 | ||||||||
\(819\) | −62.1335 | −2.17112 | ||||||||
\(820\) | 3.22826 | 0.112736 | ||||||||
\(821\) | −54.4996 | −1.90205 | −0.951024 | − | 0.309116i | \(-0.899967\pi\) | ||||
−0.951024 | + | 0.309116i | \(0.899967\pi\) | |||||||
\(822\) | 106.166 | 3.70295 | ||||||||
\(823\) | 22.6504 | 0.789542 | 0.394771 | − | 0.918779i | \(-0.370824\pi\) | ||||
0.394771 | + | 0.918779i | \(0.370824\pi\) | |||||||
\(824\) | −7.78458 | −0.271189 | ||||||||
\(825\) | 67.7437 | 2.35853 | ||||||||
\(826\) | −66.9428 | −2.32924 | ||||||||
\(827\) | −22.0027 | −0.765110 | −0.382555 | − | 0.923933i | \(-0.624956\pi\) | ||||
−0.382555 | + | 0.923933i | \(0.624956\pi\) | |||||||
\(828\) | −58.6488 | −2.03819 | ||||||||
\(829\) | −22.3821 | −0.777363 | −0.388681 | − | 0.921372i | \(-0.627069\pi\) | ||||
−0.388681 | + | 0.921372i | \(0.627069\pi\) | |||||||
\(830\) | 0.672466 | 0.0233416 | ||||||||
\(831\) | 26.2142 | 0.909362 | ||||||||
\(832\) | −46.0595 | −1.59683 | ||||||||
\(833\) | −30.4607 | −1.05540 | ||||||||
\(834\) | 90.0309 | 3.11752 | ||||||||
\(835\) | −2.50296 | −0.0866184 | ||||||||
\(836\) | 102.948 | 3.56054 | ||||||||
\(837\) | 1.94765 | 0.0673207 | ||||||||
\(838\) | 40.2039 | 1.38882 | ||||||||
\(839\) | 7.51523 | 0.259454 | 0.129727 | − | 0.991550i | \(-0.458590\pi\) | ||||
0.129727 | + | 0.991550i | \(0.458590\pi\) | |||||||
\(840\) | −9.26430 | −0.319649 | ||||||||
\(841\) | 5.04848 | 0.174086 | ||||||||
\(842\) | 16.8063 | 0.579184 | ||||||||
\(843\) | 41.4931 | 1.42910 | ||||||||
\(844\) | −84.5887 | −2.91166 | ||||||||
\(845\) | 1.28194 | 0.0441001 | ||||||||
\(846\) | −1.82289 | −0.0626721 | ||||||||
\(847\) | −79.9543 | −2.74726 | ||||||||
\(848\) | 3.56242 | 0.122334 | ||||||||
\(849\) | 35.5145 | 1.21886 | ||||||||
\(850\) | −31.7499 | −1.08901 | ||||||||
\(851\) | 1.49864 | 0.0513727 | ||||||||
\(852\) | −74.2252 | −2.54291 | ||||||||
\(853\) | 38.3776 | 1.31402 | 0.657012 | − | 0.753880i | \(-0.271820\pi\) | ||||
0.657012 | + | 0.753880i | \(0.271820\pi\) | |||||||
\(854\) | −39.4678 | −1.35056 | ||||||||
\(855\) | 3.40292 | 0.116377 | ||||||||
\(856\) | −37.6622 | −1.28727 | ||||||||
\(857\) | −50.0740 | −1.71050 | −0.855248 | − | 0.518219i | \(-0.826595\pi\) | ||||
−0.855248 | + | 0.518219i | \(0.826595\pi\) | |||||||
\(858\) | 143.832 | 4.91035 | ||||||||
\(859\) | −30.5936 | −1.04384 | −0.521920 | − | 0.852994i | \(-0.674784\pi\) | ||||
−0.521920 | + | 0.852994i | \(0.674784\pi\) | |||||||
\(860\) | −4.20728 | −0.143467 | ||||||||
\(861\) | 45.2659 | 1.54266 | ||||||||
\(862\) | 73.0946 | 2.48961 | ||||||||
\(863\) | −42.4567 | −1.44524 | −0.722622 | − | 0.691243i | \(-0.757063\pi\) | ||||
−0.722622 | + | 0.691243i | \(0.757063\pi\) | |||||||
\(864\) | −1.67338 | −0.0569296 | ||||||||
\(865\) | 4.24532 | 0.144345 | ||||||||
\(866\) | −1.83616 | −0.0623952 | ||||||||
\(867\) | 24.7766 | 0.841459 | ||||||||
\(868\) | 41.7260 | 1.41627 | ||||||||
\(869\) | 78.9800 | 2.67921 | ||||||||
\(870\) | −7.18887 | −0.243725 | ||||||||
\(871\) | 34.0001 | 1.15205 | ||||||||
\(872\) | 30.7002 | 1.03964 | ||||||||
\(873\) | −57.5298 | −1.94709 | ||||||||
\(874\) | 57.2535 | 1.93663 | ||||||||
\(875\) | 8.74420 | 0.295608 | ||||||||
\(876\) | 15.1445 | 0.511685 | ||||||||
\(877\) | 6.07266 | 0.205059 | 0.102530 | − | 0.994730i | \(-0.467306\pi\) | ||||
0.102530 | + | 0.994730i | \(0.467306\pi\) | |||||||
\(878\) | −16.3273 | −0.551019 | ||||||||
\(879\) | −84.2045 | −2.84015 | ||||||||
\(880\) | 2.87094 | 0.0967795 | ||||||||
\(881\) | −28.1383 | −0.948004 | −0.474002 | − | 0.880524i | \(-0.657191\pi\) | ||||
−0.474002 | + | 0.880524i | \(0.657191\pi\) | |||||||
\(882\) | −90.2856 | −3.04007 | ||||||||
\(883\) | 8.93733 | 0.300765 | 0.150383 | − | 0.988628i | \(-0.451949\pi\) | ||||
0.150383 | + | 0.988628i | \(0.451949\pi\) | |||||||
\(884\) | −43.9742 | −1.47901 | ||||||||
\(885\) | 3.34145 | 0.112322 | ||||||||
\(886\) | 58.8219 | 1.97616 | ||||||||
\(887\) | 9.64244 | 0.323761 | 0.161881 | − | 0.986810i | \(-0.448244\pi\) | ||||
0.161881 | + | 0.986810i | \(0.448244\pi\) | |||||||
\(888\) | −3.33796 | −0.112015 | ||||||||
\(889\) | −46.1176 | −1.54674 | ||||||||
\(890\) | 1.14886 | 0.0385098 | ||||||||
\(891\) | −43.6159 | −1.46119 | ||||||||
\(892\) | 50.7585 | 1.69952 | ||||||||
\(893\) | 1.16084 | 0.0388459 | ||||||||
\(894\) | −87.5415 | −2.92783 | ||||||||
\(895\) | 5.06997 | 0.169470 | ||||||||
\(896\) | −88.8863 | −2.96948 | ||||||||
\(897\) | 52.1804 | 1.74225 | ||||||||
\(898\) | −27.5590 | −0.919657 | ||||||||
\(899\) | 15.1219 | 0.504345 | ||||||||
\(900\) | −61.3889 | −2.04630 | ||||||||
\(901\) | −3.69100 | −0.122965 | ||||||||
\(902\) | −54.8833 | −1.82741 | ||||||||
\(903\) | −58.9936 | −1.96318 | ||||||||
\(904\) | 40.6567 | 1.35222 | ||||||||
\(905\) | −4.09612 | −0.136160 | ||||||||
\(906\) | 30.4054 | 1.01015 | ||||||||
\(907\) | −31.4379 | −1.04388 | −0.521940 | − | 0.852982i | \(-0.674791\pi\) | ||||
−0.521940 | + | 0.852982i | \(0.674791\pi\) | |||||||
\(908\) | −44.7490 | −1.48505 | ||||||||
\(909\) | 6.36160 | 0.211001 | ||||||||
\(910\) | 9.24372 | 0.306426 | ||||||||
\(911\) | −37.9061 | −1.25588 | −0.627942 | − | 0.778260i | \(-0.716103\pi\) | ||||
−0.627942 | + | 0.778260i | \(0.716103\pi\) | |||||||
\(912\) | −32.5934 | −1.07927 | ||||||||
\(913\) | −7.45781 | −0.246817 | ||||||||
\(914\) | 37.5360 | 1.24158 | ||||||||
\(915\) | 1.97004 | 0.0651275 | ||||||||
\(916\) | −89.6737 | −2.96290 | ||||||||
\(917\) | −31.2279 | −1.03124 | ||||||||
\(918\) | −4.81259 | −0.158839 | ||||||||
\(919\) | −12.4739 | −0.411476 | −0.205738 | − | 0.978607i | \(-0.565959\pi\) | ||||
−0.205738 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(920\) | 4.07505 | 0.134350 | ||||||||
\(921\) | 55.8377 | 1.83992 | ||||||||
\(922\) | 96.6690 | 3.18362 | ||||||||
\(923\) | 34.5890 | 1.13851 | ||||||||
\(924\) | 219.989 | 7.23711 | ||||||||
\(925\) | 1.56866 | 0.0515771 | ||||||||
\(926\) | −6.37381 | −0.209456 | ||||||||
\(927\) | 6.11020 | 0.200685 | ||||||||
\(928\) | −12.9924 | −0.426498 | ||||||||
\(929\) | −23.1401 | −0.759201 | −0.379601 | − | 0.925150i | \(-0.623939\pi\) | ||||
−0.379601 | + | 0.925150i | \(0.623939\pi\) | |||||||
\(930\) | −3.19279 | −0.104696 | ||||||||
\(931\) | 57.4950 | 1.88432 | ||||||||
\(932\) | 1.36299 | 0.0446462 | ||||||||
\(933\) | −57.4364 | −1.88038 | ||||||||
\(934\) | 91.2112 | 2.98452 | ||||||||
\(935\) | −2.97456 | −0.0972786 | ||||||||
\(936\) | −60.8737 | −1.98972 | ||||||||
\(937\) | −7.59503 | −0.248119 | −0.124059 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124059 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(938\) | 79.7181 | 2.60289 | ||||||||
\(939\) | 35.7858 | 1.16782 | ||||||||
\(940\) | 0.176909 | 0.00577013 | ||||||||
\(941\) | 29.3897 | 0.958078 | 0.479039 | − | 0.877794i | \(-0.340985\pi\) | ||||
0.479039 | + | 0.877794i | \(0.340985\pi\) | |||||||
\(942\) | 30.5152 | 0.994238 | ||||||||
\(943\) | −19.9109 | −0.648389 | ||||||||
\(944\) | −16.7630 | −0.545588 | ||||||||
\(945\) | 0.659927 | 0.0214674 | ||||||||
\(946\) | 71.5276 | 2.32556 | ||||||||
\(947\) | 13.0235 | 0.423208 | 0.211604 | − | 0.977355i | \(-0.432131\pi\) | ||||
0.211604 | + | 0.977355i | \(0.432131\pi\) | |||||||
\(948\) | −136.647 | −4.43809 | ||||||||
\(949\) | −7.05735 | −0.229091 | ||||||||
\(950\) | 59.9285 | 1.94434 | ||||||||
\(951\) | 35.6062 | 1.15461 | ||||||||
\(952\) | −48.1534 | −1.56066 | ||||||||
\(953\) | −7.02814 | −0.227664 | −0.113832 | − | 0.993500i | \(-0.536313\pi\) | ||||
−0.113832 | + | 0.993500i | \(0.536313\pi\) | |||||||
\(954\) | −10.9401 | −0.354200 | ||||||||
\(955\) | 3.93827 | 0.127439 | ||||||||
\(956\) | −30.8977 | −0.999302 | ||||||||
\(957\) | 79.7262 | 2.57718 | ||||||||
\(958\) | 45.1129 | 1.45753 | ||||||||
\(959\) | −75.6685 | −2.44346 | ||||||||
\(960\) | 5.39048 | 0.173977 | ||||||||
\(961\) | −24.2839 | −0.783352 | ||||||||
\(962\) | 3.33054 | 0.107381 | ||||||||
\(963\) | 29.5615 | 0.952607 | ||||||||
\(964\) | 90.4364 | 2.91276 | ||||||||
\(965\) | −3.42352 | −0.110207 | ||||||||
\(966\) | 122.344 | 3.93636 | ||||||||
\(967\) | 57.8670 | 1.86088 | 0.930438 | − | 0.366449i | \(-0.119427\pi\) | ||||
0.930438 | + | 0.366449i | \(0.119427\pi\) | |||||||
\(968\) | −78.3332 | −2.51772 | ||||||||
\(969\) | 33.7697 | 1.08484 | ||||||||
\(970\) | 8.55883 | 0.274807 | ||||||||
\(971\) | −8.61825 | −0.276573 | −0.138286 | − | 0.990392i | \(-0.544159\pi\) | ||||
−0.138286 | + | 0.990392i | \(0.544159\pi\) | |||||||
\(972\) | 83.9226 | 2.69182 | ||||||||
\(973\) | −64.1687 | −2.05715 | ||||||||
\(974\) | 94.7886 | 3.03722 | ||||||||
\(975\) | 54.6184 | 1.74919 | ||||||||
\(976\) | −9.88304 | −0.316349 | ||||||||
\(977\) | 13.9995 | 0.447884 | 0.223942 | − | 0.974602i | \(-0.428107\pi\) | ||||
0.223942 | + | 0.974602i | \(0.428107\pi\) | |||||||
\(978\) | −28.2735 | −0.904088 | ||||||||
\(979\) | −12.7411 | −0.407208 | ||||||||
\(980\) | 8.76211 | 0.279895 | ||||||||
\(981\) | −24.0970 | −0.769357 | ||||||||
\(982\) | 4.26360 | 0.136057 | ||||||||
\(983\) | 45.9125 | 1.46438 | 0.732191 | − | 0.681100i | \(-0.238498\pi\) | ||||
0.732191 | + | 0.681100i | \(0.238498\pi\) | |||||||
\(984\) | 44.3482 | 1.41377 | ||||||||
\(985\) | 2.72196 | 0.0867290 | ||||||||
\(986\) | −37.3658 | −1.18997 | ||||||||
\(987\) | 2.48058 | 0.0789577 | ||||||||
\(988\) | 83.0021 | 2.64065 | ||||||||
\(989\) | 25.9492 | 0.825138 | ||||||||
\(990\) | −8.81662 | −0.280210 | ||||||||
\(991\) | −33.9616 | −1.07883 | −0.539413 | − | 0.842041i | \(-0.681354\pi\) | ||||
−0.539413 | + | 0.842041i | \(0.681354\pi\) | |||||||
\(992\) | −5.77033 | −0.183208 | ||||||||
\(993\) | −13.3703 | −0.424294 | ||||||||
\(994\) | 81.0987 | 2.57230 | ||||||||
\(995\) | −0.489531 | −0.0155192 | ||||||||
\(996\) | 12.9031 | 0.408851 | ||||||||
\(997\) | −52.6533 | −1.66755 | −0.833774 | − | 0.552106i | \(-0.813824\pi\) | ||||
−0.833774 | + | 0.552106i | \(0.813824\pi\) | |||||||
\(998\) | −38.1789 | −1.20853 | ||||||||
\(999\) | 0.237774 | 0.00752283 |
(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 | 4007.2.a.a.1.14 | ✓ | 139 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.a.1.14 | ✓ | 139 | 1.1 | even | 1 | trivial |