Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62193 | −1.85398 | −0.926992 | − | 0.375081i | \(-0.877615\pi\) | ||||
−0.926992 | + | 0.375081i | \(0.877615\pi\) | |||||||
\(3\) | 2.84190 | 1.64077 | 0.820385 | − | 0.571812i | \(-0.193759\pi\) | ||||
0.820385 | + | 0.571812i | \(0.193759\pi\) | |||||||
\(4\) | 4.87451 | 2.43726 | ||||||||
\(5\) | 3.72911 | 1.66771 | 0.833853 | − | 0.551986i | \(-0.186130\pi\) | ||||
0.833853 | + | 0.551986i | \(0.186130\pi\) | |||||||
\(6\) | −7.45125 | −3.04196 | ||||||||
\(7\) | −2.25507 | −0.852337 | −0.426169 | − | 0.904644i | \(-0.640137\pi\) | ||||
−0.426169 | + | 0.904644i | \(0.640137\pi\) | |||||||
\(8\) | −7.53678 | −2.66465 | ||||||||
\(9\) | 5.07638 | 1.69213 | ||||||||
\(10\) | −9.77745 | −3.09190 | ||||||||
\(11\) | −3.42407 | −1.03240 | −0.516198 | − | 0.856469i | \(-0.672653\pi\) | ||||
−0.516198 | + | 0.856469i | \(0.672653\pi\) | |||||||
\(12\) | 13.8529 | 3.99898 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 5.91264 | 1.58022 | ||||||||
\(15\) | 10.5977 | 2.73632 | ||||||||
\(16\) | 10.0119 | 2.50297 | ||||||||
\(17\) | 3.16545 | 0.767733 | 0.383867 | − | 0.923389i | \(-0.374592\pi\) | ||||
0.383867 | + | 0.923389i | \(0.374592\pi\) | |||||||
\(18\) | −13.3099 | −3.13717 | ||||||||
\(19\) | −4.50680 | −1.03393 | −0.516965 | − | 0.856006i | \(-0.672938\pi\) | ||||
−0.516965 | + | 0.856006i | \(0.672938\pi\) | |||||||
\(20\) | 18.1776 | 4.06463 | ||||||||
\(21\) | −6.40868 | −1.39849 | ||||||||
\(22\) | 8.97767 | 1.91404 | ||||||||
\(23\) | 8.74374 | 1.82320 | 0.911598 | − | 0.411082i | \(-0.134849\pi\) | ||||
0.911598 | + | 0.411082i | \(0.134849\pi\) | |||||||
\(24\) | −21.4187 | −4.37208 | ||||||||
\(25\) | 8.90623 | 1.78125 | ||||||||
\(26\) | −2.62193 | −0.514203 | ||||||||
\(27\) | 5.90085 | 1.13562 | ||||||||
\(28\) | −10.9924 | −2.07737 | ||||||||
\(29\) | −6.67219 | −1.23899 | −0.619497 | − | 0.784999i | \(-0.712663\pi\) | ||||
−0.619497 | + | 0.784999i | \(0.712663\pi\) | |||||||
\(30\) | −27.7865 | −5.07310 | ||||||||
\(31\) | −5.48594 | −0.985303 | −0.492652 | − | 0.870227i | \(-0.663972\pi\) | ||||
−0.492652 | + | 0.870227i | \(0.663972\pi\) | |||||||
\(32\) | −11.1769 | −1.97581 | ||||||||
\(33\) | −9.73085 | −1.69392 | ||||||||
\(34\) | −8.29958 | −1.42337 | ||||||||
\(35\) | −8.40940 | −1.42145 | ||||||||
\(36\) | 24.7449 | 4.12415 | ||||||||
\(37\) | 2.43963 | 0.401072 | 0.200536 | − | 0.979686i | \(-0.435732\pi\) | ||||
0.200536 | + | 0.979686i | \(0.435732\pi\) | |||||||
\(38\) | 11.8165 | 1.91689 | ||||||||
\(39\) | 2.84190 | 0.455068 | ||||||||
\(40\) | −28.1054 | −4.44386 | ||||||||
\(41\) | 5.37733 | 0.839798 | 0.419899 | − | 0.907571i | \(-0.362065\pi\) | ||||
0.419899 | + | 0.907571i | \(0.362065\pi\) | |||||||
\(42\) | 16.8031 | 2.59278 | ||||||||
\(43\) | 10.9038 | 1.66281 | 0.831407 | − | 0.555664i | \(-0.187536\pi\) | ||||
0.831407 | + | 0.555664i | \(0.187536\pi\) | |||||||
\(44\) | −16.6907 | −2.51621 | ||||||||
\(45\) | 18.9303 | 2.82197 | ||||||||
\(46\) | −22.9255 | −3.38018 | ||||||||
\(47\) | 10.1256 | 1.47697 | 0.738485 | − | 0.674270i | \(-0.235542\pi\) | ||||
0.738485 | + | 0.674270i | \(0.235542\pi\) | |||||||
\(48\) | 28.4527 | 4.10679 | ||||||||
\(49\) | −1.91465 | −0.273521 | ||||||||
\(50\) | −23.3515 | −3.30240 | ||||||||
\(51\) | 8.99587 | 1.25967 | ||||||||
\(52\) | 4.87451 | 0.675974 | ||||||||
\(53\) | 8.19512 | 1.12569 | 0.562843 | − | 0.826564i | \(-0.309707\pi\) | ||||
0.562843 | + | 0.826564i | \(0.309707\pi\) | |||||||
\(54\) | −15.4716 | −2.10542 | ||||||||
\(55\) | −12.7687 | −1.72173 | ||||||||
\(56\) | 16.9960 | 2.27118 | ||||||||
\(57\) | −12.8079 | −1.69644 | ||||||||
\(58\) | 17.4940 | 2.29708 | ||||||||
\(59\) | 4.96930 | 0.646947 | 0.323474 | − | 0.946237i | \(-0.395149\pi\) | ||||
0.323474 | + | 0.946237i | \(0.395149\pi\) | |||||||
\(60\) | 51.6588 | 6.66912 | ||||||||
\(61\) | 0.209772 | 0.0268585 | 0.0134293 | − | 0.999910i | \(-0.495725\pi\) | ||||
0.0134293 | + | 0.999910i | \(0.495725\pi\) | |||||||
\(62\) | 14.3837 | 1.82674 | ||||||||
\(63\) | −11.4476 | −1.44226 | ||||||||
\(64\) | 9.28119 | 1.16015 | ||||||||
\(65\) | 3.72911 | 0.462539 | ||||||||
\(66\) | 25.5136 | 3.14051 | ||||||||
\(67\) | 11.3885 | 1.39133 | 0.695665 | − | 0.718366i | \(-0.255110\pi\) | ||||
0.695665 | + | 0.718366i | \(0.255110\pi\) | |||||||
\(68\) | 15.4300 | 1.87116 | ||||||||
\(69\) | 24.8488 | 2.99145 | ||||||||
\(70\) | 22.0489 | 2.63534 | ||||||||
\(71\) | 6.26110 | 0.743056 | 0.371528 | − | 0.928422i | \(-0.378834\pi\) | ||||
0.371528 | + | 0.928422i | \(0.378834\pi\) | |||||||
\(72\) | −38.2595 | −4.50893 | ||||||||
\(73\) | −0.932277 | −0.109115 | −0.0545574 | − | 0.998511i | \(-0.517375\pi\) | ||||
−0.0545574 | + | 0.998511i | \(0.517375\pi\) | |||||||
\(74\) | −6.39653 | −0.743582 | ||||||||
\(75\) | 25.3106 | 2.92261 | ||||||||
\(76\) | −21.9685 | −2.51995 | ||||||||
\(77\) | 7.72152 | 0.879949 | ||||||||
\(78\) | −7.45125 | −0.843688 | ||||||||
\(79\) | 2.93860 | 0.330618 | 0.165309 | − | 0.986242i | \(-0.447138\pi\) | ||||
0.165309 | + | 0.986242i | \(0.447138\pi\) | |||||||
\(80\) | 37.3353 | 4.17421 | ||||||||
\(81\) | 1.54047 | 0.171164 | ||||||||
\(82\) | −14.0990 | −1.55697 | ||||||||
\(83\) | −6.72996 | −0.738709 | −0.369354 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369354 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(84\) | −31.2392 | −3.40848 | ||||||||
\(85\) | 11.8043 | 1.28035 | ||||||||
\(86\) | −28.5890 | −3.08283 | ||||||||
\(87\) | −18.9617 | −2.03290 | ||||||||
\(88\) | 25.8064 | 2.75097 | ||||||||
\(89\) | −14.5178 | −1.53888 | −0.769440 | − | 0.638719i | \(-0.779465\pi\) | ||||
−0.769440 | + | 0.638719i | \(0.779465\pi\) | |||||||
\(90\) | −49.6340 | −5.23189 | ||||||||
\(91\) | −2.25507 | −0.236396 | ||||||||
\(92\) | 42.6215 | 4.44360 | ||||||||
\(93\) | −15.5905 | −1.61666 | ||||||||
\(94\) | −26.5486 | −2.73828 | ||||||||
\(95\) | −16.8063 | −1.72429 | ||||||||
\(96\) | −31.7635 | −3.24184 | ||||||||
\(97\) | −7.80793 | −0.792775 | −0.396388 | − | 0.918083i | \(-0.629736\pi\) | ||||
−0.396388 | + | 0.918083i | \(0.629736\pi\) | |||||||
\(98\) | 5.02007 | 0.507104 | ||||||||
\(99\) | −17.3819 | −1.74694 | ||||||||
\(100\) | 43.4135 | 4.34135 | ||||||||
\(101\) | 4.41878 | 0.439685 | 0.219842 | − | 0.975535i | \(-0.429446\pi\) | ||||
0.219842 | + | 0.975535i | \(0.429446\pi\) | |||||||
\(102\) | −23.5865 | −2.33542 | ||||||||
\(103\) | 7.91310 | 0.779701 | 0.389850 | − | 0.920878i | \(-0.372527\pi\) | ||||
0.389850 | + | 0.920878i | \(0.372527\pi\) | |||||||
\(104\) | −7.53678 | −0.739042 | ||||||||
\(105\) | −23.8987 | −2.33227 | ||||||||
\(106\) | −21.4870 | −2.08701 | ||||||||
\(107\) | −8.25216 | −0.797766 | −0.398883 | − | 0.917002i | \(-0.630602\pi\) | ||||
−0.398883 | + | 0.917002i | \(0.630602\pi\) | |||||||
\(108\) | 28.7638 | 2.76780 | ||||||||
\(109\) | −5.79536 | −0.555094 | −0.277547 | − | 0.960712i | \(-0.589521\pi\) | ||||
−0.277547 | + | 0.960712i | \(0.589521\pi\) | |||||||
\(110\) | 33.4787 | 3.19206 | ||||||||
\(111\) | 6.93317 | 0.658067 | ||||||||
\(112\) | −22.5775 | −2.13337 | ||||||||
\(113\) | −3.66565 | −0.344836 | −0.172418 | − | 0.985024i | \(-0.555158\pi\) | ||||
−0.172418 | + | 0.985024i | \(0.555158\pi\) | |||||||
\(114\) | 33.5813 | 3.14518 | ||||||||
\(115\) | 32.6063 | 3.04056 | ||||||||
\(116\) | −32.5237 | −3.01975 | ||||||||
\(117\) | 5.07638 | 0.469311 | ||||||||
\(118\) | −13.0291 | −1.19943 | ||||||||
\(119\) | −7.13831 | −0.654368 | ||||||||
\(120\) | −79.8727 | −7.29135 | ||||||||
\(121\) | 0.724242 | 0.0658402 | ||||||||
\(122\) | −0.550007 | −0.0497953 | ||||||||
\(123\) | 15.2818 | 1.37792 | ||||||||
\(124\) | −26.7413 | −2.40144 | ||||||||
\(125\) | 14.5667 | 1.30289 | ||||||||
\(126\) | 30.0148 | 2.67393 | ||||||||
\(127\) | 7.88873 | 0.700011 | 0.350006 | − | 0.936748i | \(-0.386180\pi\) | ||||
0.350006 | + | 0.936748i | \(0.386180\pi\) | |||||||
\(128\) | −1.98093 | −0.175091 | ||||||||
\(129\) | 30.9875 | 2.72829 | ||||||||
\(130\) | −9.77745 | −0.857539 | ||||||||
\(131\) | −2.79361 | −0.244079 | −0.122040 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122040 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(132\) | −47.4332 | −4.12853 | ||||||||
\(133\) | 10.1632 | 0.881257 | ||||||||
\(134\) | −29.8599 | −2.57950 | ||||||||
\(135\) | 22.0049 | 1.89388 | ||||||||
\(136\) | −23.8573 | −2.04574 | ||||||||
\(137\) | −7.62769 | −0.651677 | −0.325839 | − | 0.945425i | \(-0.605647\pi\) | ||||
−0.325839 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(138\) | −65.1518 | −5.54609 | ||||||||
\(139\) | 12.2502 | 1.03905 | 0.519526 | − | 0.854455i | \(-0.326108\pi\) | ||||
0.519526 | + | 0.854455i | \(0.326108\pi\) | |||||||
\(140\) | −40.9918 | −3.46444 | ||||||||
\(141\) | 28.7759 | 2.42337 | ||||||||
\(142\) | −16.4162 | −1.37761 | ||||||||
\(143\) | −3.42407 | −0.286335 | ||||||||
\(144\) | 50.8240 | 4.23533 | ||||||||
\(145\) | −24.8813 | −2.06628 | ||||||||
\(146\) | 2.44436 | 0.202297 | ||||||||
\(147\) | −5.44123 | −0.448785 | ||||||||
\(148\) | 11.8920 | 0.977516 | ||||||||
\(149\) | 13.1013 | 1.07330 | 0.536650 | − | 0.843805i | \(-0.319690\pi\) | ||||
0.536650 | + | 0.843805i | \(0.319690\pi\) | |||||||
\(150\) | −66.3625 | −5.41848 | ||||||||
\(151\) | −6.88641 | −0.560408 | −0.280204 | − | 0.959940i | \(-0.590402\pi\) | ||||
−0.280204 | + | 0.959940i | \(0.590402\pi\) | |||||||
\(152\) | 33.9667 | 2.75507 | ||||||||
\(153\) | 16.0690 | 1.29910 | ||||||||
\(154\) | −20.2453 | −1.63141 | ||||||||
\(155\) | −20.4576 | −1.64320 | ||||||||
\(156\) | 13.8529 | 1.10912 | ||||||||
\(157\) | 3.22834 | 0.257649 | 0.128825 | − | 0.991667i | \(-0.458880\pi\) | ||||
0.128825 | + | 0.991667i | \(0.458880\pi\) | |||||||
\(158\) | −7.70480 | −0.612961 | ||||||||
\(159\) | 23.2897 | 1.84699 | ||||||||
\(160\) | −41.6797 | −3.29507 | ||||||||
\(161\) | −19.7178 | −1.55398 | ||||||||
\(162\) | −4.03901 | −0.317335 | ||||||||
\(163\) | 22.7189 | 1.77948 | 0.889739 | − | 0.456470i | \(-0.150886\pi\) | ||||
0.889739 | + | 0.456470i | \(0.150886\pi\) | |||||||
\(164\) | 26.2119 | 2.04680 | ||||||||
\(165\) | −36.2874 | −2.82497 | ||||||||
\(166\) | 17.6455 | 1.36955 | ||||||||
\(167\) | −8.42879 | −0.652239 | −0.326120 | − | 0.945328i | \(-0.605741\pi\) | ||||
−0.326120 | + | 0.945328i | \(0.605741\pi\) | |||||||
\(168\) | 48.3008 | 3.72649 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −30.9500 | −2.37376 | ||||||||
\(171\) | −22.8782 | −1.74954 | ||||||||
\(172\) | 53.1507 | 4.05271 | ||||||||
\(173\) | −12.3806 | −0.941281 | −0.470640 | − | 0.882325i | \(-0.655977\pi\) | ||||
−0.470640 | + | 0.882325i | \(0.655977\pi\) | |||||||
\(174\) | 49.7162 | 3.76897 | ||||||||
\(175\) | −20.0842 | −1.51822 | ||||||||
\(176\) | −34.2813 | −2.58405 | ||||||||
\(177\) | 14.1222 | 1.06149 | ||||||||
\(178\) | 38.0646 | 2.85306 | ||||||||
\(179\) | −5.19884 | −0.388579 | −0.194290 | − | 0.980944i | \(-0.562240\pi\) | ||||
−0.194290 | + | 0.980944i | \(0.562240\pi\) | |||||||
\(180\) | 92.2762 | 6.87786 | ||||||||
\(181\) | −17.3678 | −1.29093 | −0.645467 | − | 0.763788i | \(-0.723337\pi\) | ||||
−0.645467 | + | 0.763788i | \(0.723337\pi\) | |||||||
\(182\) | 5.91264 | 0.438274 | ||||||||
\(183\) | 0.596149 | 0.0440686 | ||||||||
\(184\) | −65.8996 | −4.85818 | ||||||||
\(185\) | 9.09763 | 0.668871 | ||||||||
\(186\) | 40.8771 | 2.99725 | ||||||||
\(187\) | −10.8387 | −0.792604 | ||||||||
\(188\) | 49.3574 | 3.59976 | ||||||||
\(189\) | −13.3068 | −0.967930 | ||||||||
\(190\) | 44.0650 | 3.19681 | ||||||||
\(191\) | 20.5368 | 1.48599 | 0.742994 | − | 0.669298i | \(-0.233405\pi\) | ||||
0.742994 | + | 0.669298i | \(0.233405\pi\) | |||||||
\(192\) | 26.3762 | 1.90354 | ||||||||
\(193\) | 19.6316 | 1.41312 | 0.706558 | − | 0.707655i | \(-0.250247\pi\) | ||||
0.706558 | + | 0.707655i | \(0.250247\pi\) | |||||||
\(194\) | 20.4718 | 1.46979 | ||||||||
\(195\) | 10.5977 | 0.758919 | ||||||||
\(196\) | −9.33298 | −0.666642 | ||||||||
\(197\) | −15.6084 | −1.11205 | −0.556025 | − | 0.831166i | \(-0.687674\pi\) | ||||
−0.556025 | + | 0.831166i | \(0.687674\pi\) | |||||||
\(198\) | 45.5740 | 3.23880 | ||||||||
\(199\) | −18.8218 | −1.33424 | −0.667120 | − | 0.744951i | \(-0.732473\pi\) | ||||
−0.667120 | + | 0.744951i | \(0.732473\pi\) | |||||||
\(200\) | −67.1242 | −4.74640 | ||||||||
\(201\) | 32.3650 | 2.28285 | ||||||||
\(202\) | −11.5857 | −0.815169 | ||||||||
\(203\) | 15.0463 | 1.05604 | ||||||||
\(204\) | 43.8505 | 3.07015 | ||||||||
\(205\) | 20.0526 | 1.40054 | ||||||||
\(206\) | −20.7476 | −1.44555 | ||||||||
\(207\) | 44.3865 | 3.08508 | ||||||||
\(208\) | 10.0119 | 0.694198 | ||||||||
\(209\) | 15.4316 | 1.06743 | ||||||||
\(210\) | 62.6606 | 4.32399 | ||||||||
\(211\) | −12.9645 | −0.892512 | −0.446256 | − | 0.894905i | \(-0.647243\pi\) | ||||
−0.446256 | + | 0.894905i | \(0.647243\pi\) | |||||||
\(212\) | 39.9472 | 2.74359 | ||||||||
\(213\) | 17.7934 | 1.21918 | ||||||||
\(214\) | 21.6366 | 1.47905 | ||||||||
\(215\) | 40.6614 | 2.77309 | ||||||||
\(216\) | −44.4734 | −3.02603 | ||||||||
\(217\) | 12.3712 | 0.839811 | ||||||||
\(218\) | 15.1950 | 1.02914 | ||||||||
\(219\) | −2.64943 | −0.179032 | ||||||||
\(220\) | −62.2413 | −4.19631 | ||||||||
\(221\) | 3.16545 | 0.212931 | ||||||||
\(222\) | −18.1783 | −1.22005 | ||||||||
\(223\) | −15.5035 | −1.03819 | −0.519097 | − | 0.854715i | \(-0.673732\pi\) | ||||
−0.519097 | + | 0.854715i | \(0.673732\pi\) | |||||||
\(224\) | 25.2046 | 1.68405 | ||||||||
\(225\) | 45.2114 | 3.01409 | ||||||||
\(226\) | 9.61108 | 0.639320 | ||||||||
\(227\) | 10.7779 | 0.715354 | 0.357677 | − | 0.933845i | \(-0.383569\pi\) | ||||
0.357677 | + | 0.933845i | \(0.383569\pi\) | |||||||
\(228\) | −62.4321 | −4.13467 | ||||||||
\(229\) | −5.41258 | −0.357673 | −0.178837 | − | 0.983879i | \(-0.557233\pi\) | ||||
−0.178837 | + | 0.983879i | \(0.557233\pi\) | |||||||
\(230\) | −85.4915 | −5.63714 | ||||||||
\(231\) | 21.9438 | 1.44379 | ||||||||
\(232\) | 50.2868 | 3.30149 | ||||||||
\(233\) | 16.4092 | 1.07500 | 0.537502 | − | 0.843263i | \(-0.319368\pi\) | ||||
0.537502 | + | 0.843263i | \(0.319368\pi\) | |||||||
\(234\) | −13.3099 | −0.870096 | ||||||||
\(235\) | 37.7594 | 2.46315 | ||||||||
\(236\) | 24.2229 | 1.57678 | ||||||||
\(237\) | 8.35119 | 0.542468 | ||||||||
\(238\) | 18.7161 | 1.21319 | ||||||||
\(239\) | 28.8550 | 1.86648 | 0.933238 | − | 0.359260i | \(-0.116971\pi\) | ||||
0.933238 | + | 0.359260i | \(0.116971\pi\) | |||||||
\(240\) | 106.103 | 6.84892 | ||||||||
\(241\) | 8.34062 | 0.537267 | 0.268633 | − | 0.963242i | \(-0.413428\pi\) | ||||
0.268633 | + | 0.963242i | \(0.413428\pi\) | |||||||
\(242\) | −1.89891 | −0.122067 | ||||||||
\(243\) | −13.3247 | −0.854779 | ||||||||
\(244\) | 1.02254 | 0.0654611 | ||||||||
\(245\) | −7.13993 | −0.456153 | ||||||||
\(246\) | −40.0679 | −2.55463 | ||||||||
\(247\) | −4.50680 | −0.286761 | ||||||||
\(248\) | 41.3463 | 2.62549 | ||||||||
\(249\) | −19.1258 | −1.21205 | ||||||||
\(250\) | −38.1929 | −2.41553 | ||||||||
\(251\) | −13.2856 | −0.838579 | −0.419290 | − | 0.907852i | \(-0.637721\pi\) | ||||
−0.419290 | + | 0.907852i | \(0.637721\pi\) | |||||||
\(252\) | −55.8015 | −3.51516 | ||||||||
\(253\) | −29.9392 | −1.88226 | ||||||||
\(254\) | −20.6837 | −1.29781 | ||||||||
\(255\) | 33.5465 | 2.10077 | ||||||||
\(256\) | −13.3685 | −0.835533 | ||||||||
\(257\) | 0.256572 | 0.0160045 | 0.00800227 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800227 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(258\) | −81.2470 | −5.05822 | ||||||||
\(259\) | −5.50154 | −0.341849 | ||||||||
\(260\) | 18.1776 | 1.12733 | ||||||||
\(261\) | −33.8705 | −2.09653 | ||||||||
\(262\) | 7.32465 | 0.452519 | ||||||||
\(263\) | 15.8266 | 0.975911 | 0.487955 | − | 0.872869i | \(-0.337743\pi\) | ||||
0.487955 | + | 0.872869i | \(0.337743\pi\) | |||||||
\(264\) | 73.3392 | 4.51372 | ||||||||
\(265\) | 30.5605 | 1.87731 | ||||||||
\(266\) | −26.6471 | −1.63384 | ||||||||
\(267\) | −41.2580 | −2.52495 | ||||||||
\(268\) | 55.5135 | 3.39103 | ||||||||
\(269\) | −5.84510 | −0.356382 | −0.178191 | − | 0.983996i | \(-0.557025\pi\) | ||||
−0.178191 | + | 0.983996i | \(0.557025\pi\) | |||||||
\(270\) | −57.6953 | −3.51122 | ||||||||
\(271\) | 30.8508 | 1.87405 | 0.937027 | − | 0.349257i | \(-0.113566\pi\) | ||||
0.937027 | + | 0.349257i | \(0.113566\pi\) | |||||||
\(272\) | 31.6920 | 1.92161 | ||||||||
\(273\) | −6.40868 | −0.387871 | ||||||||
\(274\) | 19.9993 | 1.20820 | ||||||||
\(275\) | −30.4955 | −1.83895 | ||||||||
\(276\) | 121.126 | 7.29092 | ||||||||
\(277\) | 21.8280 | 1.31152 | 0.655759 | − | 0.754970i | \(-0.272349\pi\) | ||||
0.655759 | + | 0.754970i | \(0.272349\pi\) | |||||||
\(278\) | −32.1193 | −1.92639 | ||||||||
\(279\) | −27.8487 | −1.66726 | ||||||||
\(280\) | 63.3798 | 3.78767 | ||||||||
\(281\) | −10.8601 | −0.647860 | −0.323930 | − | 0.946081i | \(-0.605004\pi\) | ||||
−0.323930 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(282\) | −75.4484 | −4.49289 | ||||||||
\(283\) | −19.5384 | −1.16144 | −0.580719 | − | 0.814104i | \(-0.697229\pi\) | ||||
−0.580719 | + | 0.814104i | \(0.697229\pi\) | |||||||
\(284\) | 30.5198 | 1.81102 | ||||||||
\(285\) | −47.7618 | −2.82917 | ||||||||
\(286\) | 8.97767 | 0.530860 | ||||||||
\(287\) | −12.1263 | −0.715791 | ||||||||
\(288\) | −56.7379 | −3.34331 | ||||||||
\(289\) | −6.97995 | −0.410585 | ||||||||
\(290\) | 65.2370 | 3.83085 | ||||||||
\(291\) | −22.1893 | −1.30076 | ||||||||
\(292\) | −4.54440 | −0.265941 | ||||||||
\(293\) | 9.35072 | 0.546275 | 0.273137 | − | 0.961975i | \(-0.411939\pi\) | ||||
0.273137 | + | 0.961975i | \(0.411939\pi\) | |||||||
\(294\) | 14.2665 | 0.832041 | ||||||||
\(295\) | 18.5310 | 1.07892 | ||||||||
\(296\) | −18.3869 | −1.06872 | ||||||||
\(297\) | −20.2049 | −1.17241 | ||||||||
\(298\) | −34.3507 | −1.98988 | ||||||||
\(299\) | 8.74374 | 0.505664 | ||||||||
\(300\) | 123.377 | 7.12316 | ||||||||
\(301\) | −24.5889 | −1.41728 | ||||||||
\(302\) | 18.0557 | 1.03899 | ||||||||
\(303\) | 12.5577 | 0.721422 | ||||||||
\(304\) | −45.1215 | −2.58789 | ||||||||
\(305\) | 0.782261 | 0.0447921 | ||||||||
\(306\) | −42.1318 | −2.40851 | ||||||||
\(307\) | 16.2060 | 0.924926 | 0.462463 | − | 0.886639i | \(-0.346966\pi\) | ||||
0.462463 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(308\) | 37.6387 | 2.14466 | ||||||||
\(309\) | 22.4882 | 1.27931 | ||||||||
\(310\) | 53.6385 | 3.04646 | ||||||||
\(311\) | −6.74254 | −0.382335 | −0.191167 | − | 0.981557i | \(-0.561227\pi\) | ||||
−0.191167 | + | 0.981557i | \(0.561227\pi\) | |||||||
\(312\) | −21.4187 | −1.21260 | ||||||||
\(313\) | 34.6469 | 1.95836 | 0.979179 | − | 0.202998i | \(-0.0650685\pi\) | ||||
0.979179 | + | 0.202998i | \(0.0650685\pi\) | |||||||
\(314\) | −8.46448 | −0.477678 | ||||||||
\(315\) | −42.6893 | −2.40527 | ||||||||
\(316\) | 14.3242 | 0.805801 | ||||||||
\(317\) | 1.99174 | 0.111867 | 0.0559336 | − | 0.998434i | \(-0.482186\pi\) | ||||
0.0559336 | + | 0.998434i | \(0.482186\pi\) | |||||||
\(318\) | −61.0639 | −3.42430 | ||||||||
\(319\) | 22.8460 | 1.27913 | ||||||||
\(320\) | 34.6105 | 1.93479 | ||||||||
\(321\) | −23.4518 | −1.30895 | ||||||||
\(322\) | 51.6986 | 2.88105 | ||||||||
\(323\) | −14.2660 | −0.793783 | ||||||||
\(324\) | 7.50905 | 0.417170 | ||||||||
\(325\) | 8.90623 | 0.494029 | ||||||||
\(326\) | −59.5672 | −3.29912 | ||||||||
\(327\) | −16.4698 | −0.910782 | ||||||||
\(328\) | −40.5278 | −2.23777 | ||||||||
\(329\) | −22.8340 | −1.25888 | ||||||||
\(330\) | 95.1429 | 5.23744 | ||||||||
\(331\) | 19.7267 | 1.08427 | 0.542137 | − | 0.840290i | \(-0.317615\pi\) | ||||
0.542137 | + | 0.840290i | \(0.317615\pi\) | |||||||
\(332\) | −32.8053 | −1.80042 | ||||||||
\(333\) | 12.3845 | 0.678665 | ||||||||
\(334\) | 22.0997 | 1.20924 | ||||||||
\(335\) | 42.4690 | 2.32033 | ||||||||
\(336\) | −64.1629 | −3.50037 | ||||||||
\(337\) | 2.12506 | 0.115759 | 0.0578797 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578797 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(338\) | −2.62193 | −0.142614 | ||||||||
\(339\) | −10.4174 | −0.565796 | ||||||||
\(340\) | 57.5401 | 3.12055 | ||||||||
\(341\) | 18.7842 | 1.01722 | ||||||||
\(342\) | 59.9851 | 3.24362 | ||||||||
\(343\) | 20.1032 | 1.08547 | ||||||||
\(344\) | −82.1795 | −4.43082 | ||||||||
\(345\) | 92.6638 | 4.98885 | ||||||||
\(346\) | 32.4611 | 1.74512 | ||||||||
\(347\) | 5.78773 | 0.310702 | 0.155351 | − | 0.987859i | \(-0.450349\pi\) | ||||
0.155351 | + | 0.987859i | \(0.450349\pi\) | |||||||
\(348\) | −92.4289 | −4.95471 | ||||||||
\(349\) | 30.6998 | 1.64332 | 0.821661 | − | 0.569977i | \(-0.193048\pi\) | ||||
0.821661 | + | 0.569977i | \(0.193048\pi\) | |||||||
\(350\) | 52.6593 | 2.81476 | ||||||||
\(351\) | 5.90085 | 0.314964 | ||||||||
\(352\) | 38.2703 | 2.03981 | ||||||||
\(353\) | 1.95836 | 0.104233 | 0.0521165 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521165 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(354\) | −37.0275 | −1.96799 | ||||||||
\(355\) | 23.3483 | 1.23920 | ||||||||
\(356\) | −70.7671 | −3.75065 | ||||||||
\(357\) | −20.2863 | −1.07367 | ||||||||
\(358\) | 13.6310 | 0.720420 | ||||||||
\(359\) | 12.5648 | 0.663143 | 0.331572 | − | 0.943430i | \(-0.392421\pi\) | ||||
0.331572 | + | 0.943430i | \(0.392421\pi\) | |||||||
\(360\) | −142.674 | −7.51957 | ||||||||
\(361\) | 1.31123 | 0.0690123 | ||||||||
\(362\) | 45.5370 | 2.39337 | ||||||||
\(363\) | 2.05822 | 0.108029 | ||||||||
\(364\) | −10.9924 | −0.576157 | ||||||||
\(365\) | −3.47656 | −0.181971 | ||||||||
\(366\) | −1.56306 | −0.0817025 | ||||||||
\(367\) | −3.61386 | −0.188642 | −0.0943210 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943210 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(368\) | 87.5412 | 4.56340 | ||||||||
\(369\) | 27.2974 | 1.42104 | ||||||||
\(370\) | −23.8533 | −1.24008 | ||||||||
\(371\) | −18.4806 | −0.959465 | ||||||||
\(372\) | −75.9959 | −3.94021 | ||||||||
\(373\) | −5.72676 | −0.296520 | −0.148260 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148260 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(374\) | 28.4183 | 1.46948 | ||||||||
\(375\) | 41.3971 | 2.13774 | ||||||||
\(376\) | −76.3143 | −3.93561 | ||||||||
\(377\) | −6.67219 | −0.343635 | ||||||||
\(378\) | 34.8896 | 1.79453 | ||||||||
\(379\) | 20.7953 | 1.06818 | 0.534090 | − | 0.845427i | \(-0.320654\pi\) | ||||
0.534090 | + | 0.845427i | \(0.320654\pi\) | |||||||
\(380\) | −81.9227 | −4.20255 | ||||||||
\(381\) | 22.4190 | 1.14856 | ||||||||
\(382\) | −53.8460 | −2.75500 | ||||||||
\(383\) | −4.63341 | −0.236756 | −0.118378 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118378 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(384\) | −5.62960 | −0.287284 | ||||||||
\(385\) | 28.7944 | 1.46750 | ||||||||
\(386\) | −51.4728 | −2.61990 | ||||||||
\(387\) | 55.3518 | 2.81369 | ||||||||
\(388\) | −38.0599 | −1.93220 | ||||||||
\(389\) | −10.1357 | −0.513898 | −0.256949 | − | 0.966425i | \(-0.582717\pi\) | ||||
−0.256949 | + | 0.966425i | \(0.582717\pi\) | |||||||
\(390\) | −27.7865 | −1.40702 | ||||||||
\(391\) | 27.6778 | 1.39973 | ||||||||
\(392\) | 14.4303 | 0.728839 | ||||||||
\(393\) | −7.93916 | −0.400478 | ||||||||
\(394\) | 40.9240 | 2.06172 | ||||||||
\(395\) | 10.9583 | 0.551374 | ||||||||
\(396\) | −84.7281 | −4.25775 | ||||||||
\(397\) | −12.0080 | −0.602662 | −0.301331 | − | 0.953520i | \(-0.597431\pi\) | ||||
−0.301331 | + | 0.953520i | \(0.597431\pi\) | |||||||
\(398\) | 49.3493 | 2.47366 | ||||||||
\(399\) | 28.8826 | 1.44594 | ||||||||
\(400\) | 89.1679 | 4.45840 | ||||||||
\(401\) | −18.6946 | −0.933563 | −0.466781 | − | 0.884373i | \(-0.654587\pi\) | ||||
−0.466781 | + | 0.884373i | \(0.654587\pi\) | |||||||
\(402\) | −84.8588 | −4.23237 | ||||||||
\(403\) | −5.48594 | −0.273274 | ||||||||
\(404\) | 21.5394 | 1.07163 | ||||||||
\(405\) | 5.74458 | 0.285451 | ||||||||
\(406\) | −39.4503 | −1.95788 | ||||||||
\(407\) | −8.35345 | −0.414065 | ||||||||
\(408\) | −67.7998 | −3.35659 | ||||||||
\(409\) | 2.78300 | 0.137611 | 0.0688053 | − | 0.997630i | \(-0.478081\pi\) | ||||
0.0688053 | + | 0.997630i | \(0.478081\pi\) | |||||||
\(410\) | −52.5766 | −2.59657 | ||||||||
\(411\) | −21.6771 | −1.06925 | ||||||||
\(412\) | 38.5725 | 1.90033 | ||||||||
\(413\) | −11.2061 | −0.551417 | ||||||||
\(414\) | −116.378 | −5.71968 | ||||||||
\(415\) | −25.0967 | −1.23195 | ||||||||
\(416\) | −11.1769 | −0.547990 | ||||||||
\(417\) | 34.8139 | 1.70485 | ||||||||
\(418\) | −40.4605 | −1.97899 | ||||||||
\(419\) | 22.7358 | 1.11072 | 0.555359 | − | 0.831610i | \(-0.312581\pi\) | ||||
0.555359 | + | 0.831610i | \(0.312581\pi\) | |||||||
\(420\) | −116.494 | −5.68434 | ||||||||
\(421\) | 37.4428 | 1.82485 | 0.912426 | − | 0.409243i | \(-0.134207\pi\) | ||||
0.912426 | + | 0.409243i | \(0.134207\pi\) | |||||||
\(422\) | 33.9920 | 1.65470 | ||||||||
\(423\) | 51.4013 | 2.49922 | ||||||||
\(424\) | −61.7648 | −2.99956 | ||||||||
\(425\) | 28.1922 | 1.36752 | ||||||||
\(426\) | −46.6531 | −2.26035 | ||||||||
\(427\) | −0.473050 | −0.0228925 | ||||||||
\(428\) | −40.2253 | −1.94436 | ||||||||
\(429\) | −9.73085 | −0.469810 | ||||||||
\(430\) | −106.611 | −5.14126 | ||||||||
\(431\) | −36.3309 | −1.75000 | −0.875000 | − | 0.484123i | \(-0.839139\pi\) | ||||
−0.875000 | + | 0.484123i | \(0.839139\pi\) | |||||||
\(432\) | 59.0785 | 2.84242 | ||||||||
\(433\) | 28.8949 | 1.38860 | 0.694300 | − | 0.719686i | \(-0.255714\pi\) | ||||
0.694300 | + | 0.719686i | \(0.255714\pi\) | |||||||
\(434\) | −32.4364 | −1.55700 | ||||||||
\(435\) | −70.7101 | −3.39029 | ||||||||
\(436\) | −28.2495 | −1.35291 | ||||||||
\(437\) | −39.4063 | −1.88506 | ||||||||
\(438\) | 6.94663 | 0.331923 | ||||||||
\(439\) | 36.2964 | 1.73233 | 0.866166 | − | 0.499757i | \(-0.166577\pi\) | ||||
0.866166 | + | 0.499757i | \(0.166577\pi\) | |||||||
\(440\) | 96.2349 | 4.58782 | ||||||||
\(441\) | −9.71948 | −0.462832 | ||||||||
\(442\) | −8.29958 | −0.394771 | ||||||||
\(443\) | −11.6530 | −0.553653 | −0.276826 | − | 0.960920i | \(-0.589283\pi\) | ||||
−0.276826 | + | 0.960920i | \(0.589283\pi\) | |||||||
\(444\) | 33.7958 | 1.60388 | ||||||||
\(445\) | −54.1383 | −2.56640 | ||||||||
\(446\) | 40.6492 | 1.92480 | ||||||||
\(447\) | 37.2325 | 1.76104 | ||||||||
\(448\) | −20.9298 | −0.988838 | ||||||||
\(449\) | 32.7532 | 1.54572 | 0.772861 | − | 0.634576i | \(-0.218825\pi\) | ||||
0.772861 | + | 0.634576i | \(0.218825\pi\) | |||||||
\(450\) | −118.541 | −5.58808 | ||||||||
\(451\) | −18.4124 | −0.867004 | ||||||||
\(452\) | −17.8683 | −0.840453 | ||||||||
\(453\) | −19.5705 | −0.919500 | ||||||||
\(454\) | −28.2589 | −1.32625 | ||||||||
\(455\) | −8.40940 | −0.394239 | ||||||||
\(456\) | 96.5299 | 4.52043 | ||||||||
\(457\) | −28.2760 | −1.32270 | −0.661348 | − | 0.750079i | \(-0.730015\pi\) | ||||
−0.661348 | + | 0.750079i | \(0.730015\pi\) | |||||||
\(458\) | 14.1914 | 0.663121 | ||||||||
\(459\) | 18.6788 | 0.871853 | ||||||||
\(460\) | 158.940 | 7.41062 | ||||||||
\(461\) | −3.69114 | −0.171914 | −0.0859569 | − | 0.996299i | \(-0.527395\pi\) | ||||
−0.0859569 | + | 0.996299i | \(0.527395\pi\) | |||||||
\(462\) | −57.5350 | −2.67677 | ||||||||
\(463\) | −41.2551 | −1.91729 | −0.958643 | − | 0.284611i | \(-0.908136\pi\) | ||||
−0.958643 | + | 0.284611i | \(0.908136\pi\) | |||||||
\(464\) | −66.8011 | −3.10116 | ||||||||
\(465\) | −58.1385 | −2.69611 | ||||||||
\(466\) | −43.0238 | −1.99304 | ||||||||
\(467\) | −7.99468 | −0.369950 | −0.184975 | − | 0.982743i | \(-0.559220\pi\) | ||||
−0.184975 | + | 0.982743i | \(0.559220\pi\) | |||||||
\(468\) | 24.7449 | 1.14383 | ||||||||
\(469\) | −25.6819 | −1.18588 | ||||||||
\(470\) | −99.0025 | −4.56665 | ||||||||
\(471\) | 9.17461 | 0.422743 | ||||||||
\(472\) | −37.4525 | −1.72389 | ||||||||
\(473\) | −37.3353 | −1.71668 | ||||||||
\(474\) | −21.8962 | −1.00573 | ||||||||
\(475\) | −40.1386 | −1.84168 | ||||||||
\(476\) | −34.7958 | −1.59486 | ||||||||
\(477\) | 41.6015 | 1.90480 | ||||||||
\(478\) | −75.6558 | −3.46042 | ||||||||
\(479\) | −24.5744 | −1.12283 | −0.561416 | − | 0.827534i | \(-0.689743\pi\) | ||||
−0.561416 | + | 0.827534i | \(0.689743\pi\) | |||||||
\(480\) | −118.449 | −5.40645 | ||||||||
\(481\) | 2.43963 | 0.111237 | ||||||||
\(482\) | −21.8685 | −0.996084 | ||||||||
\(483\) | −56.0359 | −2.54972 | ||||||||
\(484\) | 3.53033 | 0.160469 | ||||||||
\(485\) | −29.1166 | −1.32212 | ||||||||
\(486\) | 34.9364 | 1.58475 | ||||||||
\(487\) | 12.3170 | 0.558136 | 0.279068 | − | 0.960271i | \(-0.409975\pi\) | ||||
0.279068 | + | 0.960271i | \(0.409975\pi\) | |||||||
\(488\) | −1.58100 | −0.0715686 | ||||||||
\(489\) | 64.5646 | 2.91971 | ||||||||
\(490\) | 18.7204 | 0.845701 | ||||||||
\(491\) | −8.87011 | −0.400302 | −0.200151 | − | 0.979765i | \(-0.564143\pi\) | ||||
−0.200151 | + | 0.979765i | \(0.564143\pi\) | |||||||
\(492\) | 74.4915 | 3.35834 | ||||||||
\(493\) | −21.1205 | −0.951217 | ||||||||
\(494\) | 11.8165 | 0.531650 | ||||||||
\(495\) | −64.8188 | −2.91339 | ||||||||
\(496\) | −54.9244 | −2.46618 | ||||||||
\(497\) | −14.1192 | −0.633335 | ||||||||
\(498\) | 50.1466 | 2.24712 | ||||||||
\(499\) | 14.1052 | 0.631435 | 0.315717 | − | 0.948853i | \(-0.397755\pi\) | ||||
0.315717 | + | 0.948853i | \(0.397755\pi\) | |||||||
\(500\) | 71.0057 | 3.17547 | ||||||||
\(501\) | −23.9538 | −1.07017 | ||||||||
\(502\) | 34.8339 | 1.55471 | ||||||||
\(503\) | 30.3883 | 1.35495 | 0.677473 | − | 0.735547i | \(-0.263075\pi\) | ||||
0.677473 | + | 0.735547i | \(0.263075\pi\) | |||||||
\(504\) | 86.2780 | 3.84313 | ||||||||
\(505\) | 16.4781 | 0.733265 | ||||||||
\(506\) | 78.4984 | 3.48968 | ||||||||
\(507\) | 2.84190 | 0.126213 | ||||||||
\(508\) | 38.4537 | 1.70611 | ||||||||
\(509\) | −11.2447 | −0.498412 | −0.249206 | − | 0.968451i | \(-0.580170\pi\) | ||||
−0.249206 | + | 0.968451i | \(0.580170\pi\) | |||||||
\(510\) | −87.9567 | −3.89479 | ||||||||
\(511\) | 2.10235 | 0.0930026 | ||||||||
\(512\) | 39.0132 | 1.72416 | ||||||||
\(513\) | −26.5939 | −1.17415 | ||||||||
\(514\) | −0.672715 | −0.0296722 | ||||||||
\(515\) | 29.5088 | 1.30031 | ||||||||
\(516\) | 151.049 | 6.64956 | ||||||||
\(517\) | −34.6707 | −1.52482 | ||||||||
\(518\) | 14.4246 | 0.633782 | ||||||||
\(519\) | −35.1844 | −1.54443 | ||||||||
\(520\) | −28.1054 | −1.23250 | ||||||||
\(521\) | −43.8867 | −1.92271 | −0.961355 | − | 0.275310i | \(-0.911219\pi\) | ||||
−0.961355 | + | 0.275310i | \(0.911219\pi\) | |||||||
\(522\) | 88.8062 | 3.88694 | ||||||||
\(523\) | −34.1115 | −1.49159 | −0.745795 | − | 0.666175i | \(-0.767930\pi\) | ||||
−0.745795 | + | 0.666175i | \(0.767930\pi\) | |||||||
\(524\) | −13.6175 | −0.594883 | ||||||||
\(525\) | −57.0772 | −2.49105 | ||||||||
\(526\) | −41.4963 | −1.80932 | ||||||||
\(527\) | −17.3654 | −0.756450 | ||||||||
\(528\) | −97.4239 | −4.23983 | ||||||||
\(529\) | 53.4530 | 2.32404 | ||||||||
\(530\) | −80.1274 | −3.48051 | ||||||||
\(531\) | 25.2260 | 1.09472 | ||||||||
\(532\) | 49.5405 | 2.14785 | ||||||||
\(533\) | 5.37733 | 0.232918 | ||||||||
\(534\) | 108.176 | 4.68122 | ||||||||
\(535\) | −30.7732 | −1.33044 | ||||||||
\(536\) | −85.8328 | −3.70741 | ||||||||
\(537\) | −14.7746 | −0.637569 | ||||||||
\(538\) | 15.3255 | 0.660727 | ||||||||
\(539\) | 6.55589 | 0.282382 | ||||||||
\(540\) | 107.263 | 4.61587 | ||||||||
\(541\) | 22.9599 | 0.987125 | 0.493563 | − | 0.869710i | \(-0.335694\pi\) | ||||
0.493563 | + | 0.869710i | \(0.335694\pi\) | |||||||
\(542\) | −80.8887 | −3.47447 | ||||||||
\(543\) | −49.3574 | −2.11813 | ||||||||
\(544\) | −35.3797 | −1.51689 | ||||||||
\(545\) | −21.6115 | −0.925735 | ||||||||
\(546\) | 16.8031 | 0.719107 | ||||||||
\(547\) | −7.53017 | −0.321967 | −0.160984 | − | 0.986957i | \(-0.551467\pi\) | ||||
−0.160984 | + | 0.986957i | \(0.551467\pi\) | |||||||
\(548\) | −37.1813 | −1.58831 | ||||||||
\(549\) | 1.06488 | 0.0454480 | ||||||||
\(550\) | 79.9571 | 3.40938 | ||||||||
\(551\) | 30.0702 | 1.28103 | ||||||||
\(552\) | −187.280 | −7.97116 | ||||||||
\(553\) | −6.62675 | −0.281798 | ||||||||
\(554\) | −57.2315 | −2.43153 | ||||||||
\(555\) | 25.8545 | 1.09746 | ||||||||
\(556\) | 59.7140 | 2.53244 | ||||||||
\(557\) | 21.2656 | 0.901053 | 0.450527 | − | 0.892763i | \(-0.351236\pi\) | ||||
0.450527 | + | 0.892763i | \(0.351236\pi\) | |||||||
\(558\) | 73.0173 | 3.09107 | ||||||||
\(559\) | 10.9038 | 0.461182 | ||||||||
\(560\) | −84.1938 | −3.55784 | ||||||||
\(561\) | −30.8025 | −1.30048 | ||||||||
\(562\) | 28.4745 | 1.20112 | ||||||||
\(563\) | −14.5870 | −0.614769 | −0.307385 | − | 0.951585i | \(-0.599454\pi\) | ||||
−0.307385 | + | 0.951585i | \(0.599454\pi\) | |||||||
\(564\) | 140.269 | 5.90637 | ||||||||
\(565\) | −13.6696 | −0.575084 | ||||||||
\(566\) | 51.2284 | 2.15329 | ||||||||
\(567\) | −3.47388 | −0.145889 | ||||||||
\(568\) | −47.1885 | −1.97999 | ||||||||
\(569\) | −37.5624 | −1.57470 | −0.787349 | − | 0.616507i | \(-0.788547\pi\) | ||||
−0.787349 | + | 0.616507i | \(0.788547\pi\) | |||||||
\(570\) | 125.228 | 5.24523 | ||||||||
\(571\) | 8.33478 | 0.348800 | 0.174400 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174400 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(572\) | −16.6907 | −0.697872 | ||||||||
\(573\) | 58.3634 | 2.43817 | ||||||||
\(574\) | 31.7942 | 1.32707 | ||||||||
\(575\) | 77.8737 | 3.24756 | ||||||||
\(576\) | 47.1148 | 1.96312 | ||||||||
\(577\) | −13.4895 | −0.561577 | −0.280788 | − | 0.959770i | \(-0.590596\pi\) | ||||
−0.280788 | + | 0.959770i | \(0.590596\pi\) | |||||||
\(578\) | 18.3009 | 0.761219 | ||||||||
\(579\) | 55.7911 | 2.31860 | ||||||||
\(580\) | −121.284 | −5.03605 | ||||||||
\(581\) | 15.1765 | 0.629629 | ||||||||
\(582\) | 58.1789 | 2.41159 | ||||||||
\(583\) | −28.0607 | −1.16215 | ||||||||
\(584\) | 7.02636 | 0.290753 | ||||||||
\(585\) | 18.9303 | 0.782673 | ||||||||
\(586\) | −24.5169 | −1.01279 | ||||||||
\(587\) | 3.80675 | 0.157121 | 0.0785607 | − | 0.996909i | \(-0.474968\pi\) | ||||
0.0785607 | + | 0.996909i | \(0.474968\pi\) | |||||||
\(588\) | −26.5234 | −1.09381 | ||||||||
\(589\) | 24.7240 | 1.01874 | ||||||||
\(590\) | −48.5870 | −2.00030 | ||||||||
\(591\) | −44.3573 | −1.82462 | ||||||||
\(592\) | 24.4252 | 1.00387 | ||||||||
\(593\) | 28.0179 | 1.15056 | 0.575279 | − | 0.817957i | \(-0.304893\pi\) | ||||
0.575279 | + | 0.817957i | \(0.304893\pi\) | |||||||
\(594\) | 52.9758 | 2.17363 | ||||||||
\(595\) | −26.6195 | −1.09129 | ||||||||
\(596\) | 63.8625 | 2.61591 | ||||||||
\(597\) | −53.4895 | −2.18918 | ||||||||
\(598\) | −22.9255 | −0.937492 | ||||||||
\(599\) | 0.655518 | 0.0267837 | 0.0133919 | − | 0.999910i | \(-0.495737\pi\) | ||||
0.0133919 | + | 0.999910i | \(0.495737\pi\) | |||||||
\(600\) | −190.760 | −7.78775 | ||||||||
\(601\) | −12.9947 | −0.530066 | −0.265033 | − | 0.964239i | \(-0.585383\pi\) | ||||
−0.265033 | + | 0.964239i | \(0.585383\pi\) | |||||||
\(602\) | 64.4702 | 2.62761 | ||||||||
\(603\) | 57.8124 | 2.35430 | ||||||||
\(604\) | −33.5679 | −1.36586 | ||||||||
\(605\) | 2.70077 | 0.109802 | ||||||||
\(606\) | −32.9254 | −1.33750 | ||||||||
\(607\) | 29.0475 | 1.17900 | 0.589500 | − | 0.807768i | \(-0.299325\pi\) | ||||
0.589500 | + | 0.807768i | \(0.299325\pi\) | |||||||
\(608\) | 50.3718 | 2.04285 | ||||||||
\(609\) | 42.7599 | 1.73272 | ||||||||
\(610\) | −2.05103 | −0.0830439 | ||||||||
\(611\) | 10.1256 | 0.409638 | ||||||||
\(612\) | 78.3286 | 3.16624 | ||||||||
\(613\) | −16.6481 | −0.672411 | −0.336206 | − | 0.941789i | \(-0.609144\pi\) | ||||
−0.336206 | + | 0.941789i | \(0.609144\pi\) | |||||||
\(614\) | −42.4910 | −1.71480 | ||||||||
\(615\) | 56.9875 | 2.29796 | ||||||||
\(616\) | −58.1954 | −2.34476 | ||||||||
\(617\) | −1.00000 | −0.0402585 | ||||||||
\(618\) | −58.9625 | −2.37182 | ||||||||
\(619\) | −40.7759 | −1.63892 | −0.819460 | − | 0.573136i | \(-0.805727\pi\) | ||||
−0.819460 | + | 0.573136i | \(0.805727\pi\) | |||||||
\(620\) | −99.7210 | −4.00489 | ||||||||
\(621\) | 51.5955 | 2.07046 | ||||||||
\(622\) | 17.6785 | 0.708842 | ||||||||
\(623\) | 32.7386 | 1.31165 | ||||||||
\(624\) | 28.4527 | 1.13902 | ||||||||
\(625\) | 9.78973 | 0.391589 | ||||||||
\(626\) | −90.8417 | −3.63077 | ||||||||
\(627\) | 43.8550 | 1.75140 | ||||||||
\(628\) | 15.7366 | 0.627958 | ||||||||
\(629\) | 7.72251 | 0.307917 | ||||||||
\(630\) | 111.928 | 4.45933 | ||||||||
\(631\) | −34.7951 | −1.38517 | −0.692586 | − | 0.721335i | \(-0.743529\pi\) | ||||
−0.692586 | + | 0.721335i | \(0.743529\pi\) | |||||||
\(632\) | −22.1476 | −0.880982 | ||||||||
\(633\) | −36.8437 | −1.46441 | ||||||||
\(634\) | −5.22220 | −0.207400 | ||||||||
\(635\) | 29.4179 | 1.16741 | ||||||||
\(636\) | 113.526 | 4.50160 | ||||||||
\(637\) | −1.91465 | −0.0758611 | ||||||||
\(638\) | −59.9007 | −2.37149 | ||||||||
\(639\) | 31.7837 | 1.25734 | ||||||||
\(640\) | −7.38710 | −0.292001 | ||||||||
\(641\) | −13.6626 | −0.539639 | −0.269820 | − | 0.962911i | \(-0.586964\pi\) | ||||
−0.269820 | + | 0.962911i | \(0.586964\pi\) | |||||||
\(642\) | 61.4889 | 2.42677 | ||||||||
\(643\) | −16.0964 | −0.634779 | −0.317389 | − | 0.948295i | \(-0.602806\pi\) | ||||
−0.317389 | + | 0.948295i | \(0.602806\pi\) | |||||||
\(644\) | −96.1146 | −3.78744 | ||||||||
\(645\) | 115.556 | 4.54999 | ||||||||
\(646\) | 37.4045 | 1.47166 | ||||||||
\(647\) | −13.3231 | −0.523787 | −0.261893 | − | 0.965097i | \(-0.584347\pi\) | ||||
−0.261893 | + | 0.965097i | \(0.584347\pi\) | |||||||
\(648\) | −11.6102 | −0.456091 | ||||||||
\(649\) | −17.0152 | −0.667905 | ||||||||
\(650\) | −23.3515 | −0.915921 | ||||||||
\(651\) | 35.1576 | 1.37794 | ||||||||
\(652\) | 110.743 | 4.33705 | ||||||||
\(653\) | −44.7546 | −1.75138 | −0.875692 | − | 0.482870i | \(-0.839594\pi\) | ||||
−0.875692 | + | 0.482870i | \(0.839594\pi\) | |||||||
\(654\) | 43.1827 | 1.68858 | ||||||||
\(655\) | −10.4177 | −0.407052 | ||||||||
\(656\) | 53.8371 | 2.10199 | ||||||||
\(657\) | −4.73259 | −0.184636 | ||||||||
\(658\) | 59.8690 | 2.33394 | ||||||||
\(659\) | −4.17416 | −0.162602 | −0.0813011 | − | 0.996690i | \(-0.525908\pi\) | ||||
−0.0813011 | + | 0.996690i | \(0.525908\pi\) | |||||||
\(660\) | −176.883 | −6.88517 | ||||||||
\(661\) | −45.7584 | −1.77980 | −0.889898 | − | 0.456159i | \(-0.849225\pi\) | ||||
−0.889898 | + | 0.456159i | \(0.849225\pi\) | |||||||
\(662\) | −51.7219 | −2.01023 | ||||||||
\(663\) | 8.99587 | 0.349371 | ||||||||
\(664\) | 50.7222 | 1.96840 | ||||||||
\(665\) | 37.8995 | 1.46968 | ||||||||
\(666\) | −32.4712 | −1.25823 | ||||||||
\(667\) | −58.3399 | −2.25893 | ||||||||
\(668\) | −41.0863 | −1.58968 | ||||||||
\(669\) | −44.0595 | −1.70344 | ||||||||
\(670\) | −111.351 | −4.30185 | ||||||||
\(671\) | −0.718272 | −0.0277286 | ||||||||
\(672\) | 71.6289 | 2.76315 | ||||||||
\(673\) | 34.7819 | 1.34074 | 0.670372 | − | 0.742025i | \(-0.266134\pi\) | ||||
0.670372 | + | 0.742025i | \(0.266134\pi\) | |||||||
\(674\) | −5.57176 | −0.214616 | ||||||||
\(675\) | 52.5543 | 2.02282 | ||||||||
\(676\) | 4.87451 | 0.187481 | ||||||||
\(677\) | 40.7997 | 1.56806 | 0.784030 | − | 0.620723i | \(-0.213161\pi\) | ||||
0.784030 | + | 0.620723i | \(0.213161\pi\) | |||||||
\(678\) | 27.3137 | 1.04898 | ||||||||
\(679\) | 17.6075 | 0.675712 | ||||||||
\(680\) | −88.9662 | −3.41170 | ||||||||
\(681\) | 30.6296 | 1.17373 | ||||||||
\(682\) | −49.2509 | −1.88591 | ||||||||
\(683\) | 15.2793 | 0.584648 | 0.292324 | − | 0.956319i | \(-0.405571\pi\) | ||||
0.292324 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(684\) | −111.520 | −4.26408 | ||||||||
\(685\) | −28.4444 | −1.08681 | ||||||||
\(686\) | −52.7091 | −2.01244 | ||||||||
\(687\) | −15.3820 | −0.586860 | ||||||||
\(688\) | 109.167 | 4.16197 | ||||||||
\(689\) | 8.19512 | 0.312209 | ||||||||
\(690\) | −242.958 | −9.24926 | ||||||||
\(691\) | 14.2108 | 0.540603 | 0.270302 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270302 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(692\) | −60.3495 | −2.29414 | ||||||||
\(693\) | 39.1974 | 1.48898 | ||||||||
\(694\) | −15.1750 | −0.576036 | ||||||||
\(695\) | 45.6825 | 1.73283 | ||||||||
\(696\) | 142.910 | 5.41698 | ||||||||
\(697\) | 17.0217 | 0.644741 | ||||||||
\(698\) | −80.4926 | −3.04669 | ||||||||
\(699\) | 46.6333 | 1.76383 | ||||||||
\(700\) | −97.9006 | −3.70030 | ||||||||
\(701\) | 1.49731 | 0.0565528 | 0.0282764 | − | 0.999600i | \(-0.490998\pi\) | ||||
0.0282764 | + | 0.999600i | \(0.490998\pi\) | |||||||
\(702\) | −15.4716 | −0.583938 | ||||||||
\(703\) | −10.9949 | −0.414681 | ||||||||
\(704\) | −31.7794 | −1.19773 | ||||||||
\(705\) | 107.308 | 4.04147 | ||||||||
\(706\) | −5.13468 | −0.193246 | ||||||||
\(707\) | −9.96466 | −0.374760 | ||||||||
\(708\) | 68.8390 | 2.58713 | ||||||||
\(709\) | 36.4475 | 1.36881 | 0.684407 | − | 0.729100i | \(-0.260061\pi\) | ||||
0.684407 | + | 0.729100i | \(0.260061\pi\) | |||||||
\(710\) | −61.2176 | −2.29746 | ||||||||
\(711\) | 14.9174 | 0.559447 | ||||||||
\(712\) | 109.417 | 4.10058 | ||||||||
\(713\) | −47.9676 | −1.79640 | ||||||||
\(714\) | 53.1893 | 1.99056 | ||||||||
\(715\) | −12.7687 | −0.477523 | ||||||||
\(716\) | −25.3418 | −0.947068 | ||||||||
\(717\) | 82.0030 | 3.06246 | ||||||||
\(718\) | −32.9439 | −1.22946 | ||||||||
\(719\) | −23.9022 | −0.891400 | −0.445700 | − | 0.895182i | \(-0.647045\pi\) | ||||
−0.445700 | + | 0.895182i | \(0.647045\pi\) | |||||||
\(720\) | 189.528 | 7.06329 | ||||||||
\(721\) | −17.8446 | −0.664568 | ||||||||
\(722\) | −3.43796 | −0.127948 | ||||||||
\(723\) | 23.7032 | 0.881531 | ||||||||
\(724\) | −84.6594 | −3.14634 | ||||||||
\(725\) | −59.4240 | −2.20695 | ||||||||
\(726\) | −5.39651 | −0.200283 | ||||||||
\(727\) | 33.4843 | 1.24187 | 0.620933 | − | 0.783864i | \(-0.286754\pi\) | ||||
0.620933 | + | 0.783864i | \(0.286754\pi\) | |||||||
\(728\) | 16.9960 | 0.629913 | ||||||||
\(729\) | −42.4888 | −1.57366 | ||||||||
\(730\) | 9.11529 | 0.337372 | ||||||||
\(731\) | 34.5154 | 1.27660 | ||||||||
\(732\) | 2.90594 | 0.107407 | ||||||||
\(733\) | −37.7822 | −1.39552 | −0.697759 | − | 0.716332i | \(-0.745820\pi\) | ||||
−0.697759 | + | 0.716332i | \(0.745820\pi\) | |||||||
\(734\) | 9.47528 | 0.349739 | ||||||||
\(735\) | −20.2909 | −0.748442 | ||||||||
\(736\) | −97.7275 | −3.60228 | ||||||||
\(737\) | −38.9951 | −1.43640 | ||||||||
\(738\) | −71.5718 | −2.63459 | ||||||||
\(739\) | 18.4077 | 0.677139 | 0.338569 | − | 0.940941i | \(-0.390057\pi\) | ||||
0.338569 | + | 0.940941i | \(0.390057\pi\) | |||||||
\(740\) | 44.3465 | 1.63021 | ||||||||
\(741\) | −12.8079 | −0.470508 | ||||||||
\(742\) | 48.4548 | 1.77883 | ||||||||
\(743\) | −22.2932 | −0.817857 | −0.408929 | − | 0.912566i | \(-0.634098\pi\) | ||||
−0.408929 | + | 0.912566i | \(0.634098\pi\) | |||||||
\(744\) | 117.502 | 4.30783 | ||||||||
\(745\) | 48.8561 | 1.78995 | ||||||||
\(746\) | 15.0152 | 0.549744 | ||||||||
\(747\) | −34.1638 | −1.24999 | ||||||||
\(748\) | −52.8334 | −1.93178 | ||||||||
\(749\) | 18.6092 | 0.679966 | ||||||||
\(750\) | −108.540 | −3.96333 | ||||||||
\(751\) | 41.3400 | 1.50852 | 0.754260 | − | 0.656576i | \(-0.227996\pi\) | ||||
0.754260 | + | 0.656576i | \(0.227996\pi\) | |||||||
\(752\) | 101.376 | 3.69681 | ||||||||
\(753\) | −37.7563 | −1.37592 | ||||||||
\(754\) | 17.4940 | 0.637094 | ||||||||
\(755\) | −25.6801 | −0.934596 | ||||||||
\(756\) | −64.8644 | −2.35910 | ||||||||
\(757\) | −13.7432 | −0.499504 | −0.249752 | − | 0.968310i | \(-0.580349\pi\) | ||||
−0.249752 | + | 0.968310i | \(0.580349\pi\) | |||||||
\(758\) | −54.5237 | −1.98039 | ||||||||
\(759\) | −85.0840 | −3.08835 | ||||||||
\(760\) | 126.666 | 4.59464 | ||||||||
\(761\) | 10.2563 | 0.371791 | 0.185895 | − | 0.982570i | \(-0.440481\pi\) | ||||
0.185895 | + | 0.982570i | \(0.440481\pi\) | |||||||
\(762\) | −58.7809 | −2.12941 | ||||||||
\(763\) | 13.0689 | 0.473128 | ||||||||
\(764\) | 100.107 | 3.62174 | ||||||||
\(765\) | 59.9230 | 2.16652 | ||||||||
\(766\) | 12.1485 | 0.438942 | ||||||||
\(767\) | 4.96930 | 0.179431 | ||||||||
\(768\) | −37.9920 | −1.37092 | ||||||||
\(769\) | 3.08183 | 0.111134 | 0.0555669 | − | 0.998455i | \(-0.482303\pi\) | ||||
0.0555669 | + | 0.998455i | \(0.482303\pi\) | |||||||
\(770\) | −75.4968 | −2.72072 | ||||||||
\(771\) | 0.729152 | 0.0262598 | ||||||||
\(772\) | 95.6947 | 3.44413 | ||||||||
\(773\) | 13.8242 | 0.497222 | 0.248611 | − | 0.968603i | \(-0.420026\pi\) | ||||
0.248611 | + | 0.968603i | \(0.420026\pi\) | |||||||
\(774\) | −145.129 | −5.21654 | ||||||||
\(775\) | −48.8590 | −1.75507 | ||||||||
\(776\) | 58.8466 | 2.11247 | ||||||||
\(777\) | −15.6348 | −0.560895 | ||||||||
\(778\) | 26.5750 | 0.952759 | ||||||||
\(779\) | −24.2346 | −0.868293 | ||||||||
\(780\) | 51.6588 | 1.84968 | ||||||||
\(781\) | −21.4384 | −0.767128 | ||||||||
\(782\) | −72.5694 | −2.59507 | ||||||||
\(783\) | −39.3716 | −1.40703 | ||||||||
\(784\) | −19.1692 | −0.684614 | ||||||||
\(785\) | 12.0388 | 0.429684 | ||||||||
\(786\) | 20.8159 | 0.742479 | ||||||||
\(787\) | 28.5067 | 1.01615 | 0.508077 | − | 0.861312i | \(-0.330357\pi\) | ||||
0.508077 | + | 0.861312i | \(0.330357\pi\) | |||||||
\(788\) | −76.0832 | −2.71035 | ||||||||
\(789\) | 44.9776 | 1.60125 | ||||||||
\(790\) | −28.7320 | −1.02224 | ||||||||
\(791\) | 8.26631 | 0.293916 | ||||||||
\(792\) | 131.003 | 4.65500 | ||||||||
\(793\) | 0.209772 | 0.00744921 | ||||||||
\(794\) | 31.4840 | 1.11733 | ||||||||
\(795\) | 86.8497 | 3.08024 | ||||||||
\(796\) | −91.7469 | −3.25188 | ||||||||
\(797\) | 40.0833 | 1.41982 | 0.709912 | − | 0.704290i | \(-0.248735\pi\) | ||||
0.709912 | + | 0.704290i | \(0.248735\pi\) | |||||||
\(798\) | −75.7283 | −2.68075 | ||||||||
\(799\) | 32.0520 | 1.13392 | ||||||||
\(800\) | −99.5436 | −3.51940 | ||||||||
\(801\) | −73.6977 | −2.60398 | ||||||||
\(802\) | 49.0159 | 1.73081 | ||||||||
\(803\) | 3.19218 | 0.112650 | ||||||||
\(804\) | 157.764 | 5.56390 | ||||||||
\(805\) | −73.5296 | −2.59158 | ||||||||
\(806\) | 14.3837 | 0.506646 | ||||||||
\(807\) | −16.6112 | −0.584741 | ||||||||
\(808\) | −33.3033 | −1.17161 | ||||||||
\(809\) | −23.9235 | −0.841107 | −0.420553 | − | 0.907268i | \(-0.638164\pi\) | ||||
−0.420553 | + | 0.907268i | \(0.638164\pi\) | |||||||
\(810\) | −15.0619 | −0.529221 | ||||||||
\(811\) | −36.5835 | −1.28462 | −0.642311 | − | 0.766444i | \(-0.722024\pi\) | ||||
−0.642311 | + | 0.766444i | \(0.722024\pi\) | |||||||
\(812\) | 73.3433 | 2.57384 | ||||||||
\(813\) | 87.6748 | 3.07489 | ||||||||
\(814\) | 21.9022 | 0.767670 | ||||||||
\(815\) | 84.7210 | 2.96765 | ||||||||
\(816\) | 90.0654 | 3.15292 | ||||||||
\(817\) | −49.1412 | −1.71923 | ||||||||
\(818\) | −7.29684 | −0.255128 | ||||||||
\(819\) | −11.4476 | −0.400011 | ||||||||
\(820\) | 97.7469 | 3.41347 | ||||||||
\(821\) | −28.2665 | −0.986509 | −0.493254 | − | 0.869885i | \(-0.664193\pi\) | ||||
−0.493254 | + | 0.869885i | \(0.664193\pi\) | |||||||
\(822\) | 56.8358 | 1.98238 | ||||||||
\(823\) | −34.0266 | −1.18609 | −0.593047 | − | 0.805168i | \(-0.702075\pi\) | ||||
−0.593047 | + | 0.805168i | \(0.702075\pi\) | |||||||
\(824\) | −59.6392 | −2.07763 | ||||||||
\(825\) | −86.6651 | −3.01729 | ||||||||
\(826\) | 29.3817 | 1.02232 | ||||||||
\(827\) | −0.299380 | −0.0104105 | −0.00520524 | − | 0.999986i | \(-0.501657\pi\) | ||||
−0.00520524 | + | 0.999986i | \(0.501657\pi\) | |||||||
\(828\) | 216.363 | 7.51913 | ||||||||
\(829\) | 6.31373 | 0.219285 | 0.109642 | − | 0.993971i | \(-0.465029\pi\) | ||||
0.109642 | + | 0.993971i | \(0.465029\pi\) | |||||||
\(830\) | 65.8018 | 2.28402 | ||||||||
\(831\) | 62.0330 | 2.15190 | ||||||||
\(832\) | 9.28119 | 0.321768 | ||||||||
\(833\) | −6.06072 | −0.209991 | ||||||||
\(834\) | −91.2797 | −3.16076 | ||||||||
\(835\) | −31.4318 | −1.08774 | ||||||||
\(836\) | 75.2215 | 2.60159 | ||||||||
\(837\) | −32.3717 | −1.11893 | ||||||||
\(838\) | −59.6118 | −2.05926 | ||||||||
\(839\) | −50.6110 | −1.74729 | −0.873643 | − | 0.486568i | \(-0.838249\pi\) | ||||
−0.873643 | + | 0.486568i | \(0.838249\pi\) | |||||||
\(840\) | 180.119 | 6.21469 | ||||||||
\(841\) | 15.5181 | 0.535107 | ||||||||
\(842\) | −98.1724 | −3.38325 | ||||||||
\(843\) | −30.8633 | −1.06299 | ||||||||
\(844\) | −63.1956 | −2.17528 | ||||||||
\(845\) | 3.72911 | 0.128285 | ||||||||
\(846\) | −134.771 | −4.63351 | ||||||||
\(847\) | −1.63322 | −0.0561180 | ||||||||
\(848\) | 82.0485 | 2.81756 | ||||||||
\(849\) | −55.5262 | −1.90565 | ||||||||
\(850\) | −73.9179 | −2.53536 | ||||||||
\(851\) | 21.3315 | 0.731233 | ||||||||
\(852\) | 86.7342 | 2.97147 | ||||||||
\(853\) | −55.9334 | −1.91512 | −0.957562 | − | 0.288228i | \(-0.906934\pi\) | ||||
−0.957562 | + | 0.288228i | \(0.906934\pi\) | |||||||
\(854\) | 1.24030 | 0.0424423 | ||||||||
\(855\) | −85.3152 | −2.91772 | ||||||||
\(856\) | 62.1947 | 2.12577 | ||||||||
\(857\) | −26.7680 | −0.914378 | −0.457189 | − | 0.889370i | \(-0.651144\pi\) | ||||
−0.457189 | + | 0.889370i | \(0.651144\pi\) | |||||||
\(858\) | 25.5136 | 0.871020 | ||||||||
\(859\) | 54.1769 | 1.84849 | 0.924246 | − | 0.381798i | \(-0.124695\pi\) | ||||
0.924246 | + | 0.381798i | \(0.124695\pi\) | |||||||
\(860\) | 198.205 | 6.75872 | ||||||||
\(861\) | −34.4616 | −1.17445 | ||||||||
\(862\) | 95.2572 | 3.24447 | ||||||||
\(863\) | −15.5228 | −0.528403 | −0.264201 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264201 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(864\) | −65.9529 | −2.24376 | ||||||||
\(865\) | −46.1686 | −1.56978 | ||||||||
\(866\) | −75.7604 | −2.57444 | ||||||||
\(867\) | −19.8363 | −0.673676 | ||||||||
\(868\) | 60.3035 | 2.04683 | ||||||||
\(869\) | −10.0620 | −0.341329 | ||||||||
\(870\) | 185.397 | 6.28554 | ||||||||
\(871\) | 11.3885 | 0.385885 | ||||||||
\(872\) | 43.6783 | 1.47913 | ||||||||
\(873\) | −39.6360 | −1.34148 | ||||||||
\(874\) | 103.321 | 3.49487 | ||||||||
\(875\) | −32.8490 | −1.11050 | ||||||||
\(876\) | −12.9147 | −0.436348 | ||||||||
\(877\) | 48.2164 | 1.62815 | 0.814076 | − | 0.580758i | \(-0.197244\pi\) | ||||
0.814076 | + | 0.580758i | \(0.197244\pi\) | |||||||
\(878\) | −95.1665 | −3.21172 | ||||||||
\(879\) | 26.5738 | 0.896311 | ||||||||
\(880\) | −127.839 | −4.30944 | ||||||||
\(881\) | −22.8612 | −0.770214 | −0.385107 | − | 0.922872i | \(-0.625836\pi\) | ||||
−0.385107 | + | 0.922872i | \(0.625836\pi\) | |||||||
\(882\) | 25.4838 | 0.858084 | ||||||||
\(883\) | −12.1253 | −0.408048 | −0.204024 | − | 0.978966i | \(-0.565402\pi\) | ||||
−0.204024 | + | 0.978966i | \(0.565402\pi\) | |||||||
\(884\) | 15.4300 | 0.518967 | ||||||||
\(885\) | 52.6633 | 1.77026 | ||||||||
\(886\) | 30.5535 | 1.02646 | ||||||||
\(887\) | −40.5122 | −1.36027 | −0.680133 | − | 0.733089i | \(-0.738078\pi\) | ||||
−0.680133 | + | 0.733089i | \(0.738078\pi\) | |||||||
\(888\) | −52.2537 | −1.75352 | ||||||||
\(889\) | −17.7897 | −0.596646 | ||||||||
\(890\) | 141.947 | 4.75807 | ||||||||
\(891\) | −5.27468 | −0.176708 | ||||||||
\(892\) | −75.5723 | −2.53035 | ||||||||
\(893\) | −45.6340 | −1.52708 | ||||||||
\(894\) | −97.6211 | −3.26494 | ||||||||
\(895\) | −19.3870 | −0.648036 | ||||||||
\(896\) | 4.46714 | 0.149237 | ||||||||
\(897\) | 24.8488 | 0.829678 | ||||||||
\(898\) | −85.8767 | −2.86574 | ||||||||
\(899\) | 36.6032 | 1.22079 | ||||||||
\(900\) | 220.383 | 7.34611 | ||||||||
\(901\) | 25.9412 | 0.864227 | ||||||||
\(902\) | 48.2759 | 1.60741 | ||||||||
\(903\) | −69.8790 | −2.32543 | ||||||||
\(904\) | 27.6272 | 0.918867 | ||||||||
\(905\) | −64.7662 | −2.15290 | ||||||||
\(906\) | 51.3124 | 1.70474 | ||||||||
\(907\) | 8.51435 | 0.282714 | 0.141357 | − | 0.989959i | \(-0.454853\pi\) | ||||
0.141357 | + | 0.989959i | \(0.454853\pi\) | |||||||
\(908\) | 52.5370 | 1.74350 | ||||||||
\(909\) | 22.4314 | 0.744002 | ||||||||
\(910\) | 22.0489 | 0.730913 | ||||||||
\(911\) | 29.3978 | 0.973994 | 0.486997 | − | 0.873404i | \(-0.338092\pi\) | ||||
0.486997 | + | 0.873404i | \(0.338092\pi\) | |||||||
\(912\) | −128.231 | −4.24614 | ||||||||
\(913\) | 23.0438 | 0.762640 | ||||||||
\(914\) | 74.1377 | 2.45226 | ||||||||
\(915\) | 2.22310 | 0.0734935 | ||||||||
\(916\) | −26.3837 | −0.871742 | ||||||||
\(917\) | 6.29980 | 0.208038 | ||||||||
\(918\) | −48.9745 | −1.61640 | ||||||||
\(919\) | 38.3293 | 1.26437 | 0.632184 | − | 0.774818i | \(-0.282159\pi\) | ||||
0.632184 | + | 0.774818i | \(0.282159\pi\) | |||||||
\(920\) | −245.747 | −8.10203 | ||||||||
\(921\) | 46.0558 | 1.51759 | ||||||||
\(922\) | 9.67792 | 0.318725 | ||||||||
\(923\) | 6.26110 | 0.206087 | ||||||||
\(924\) | 106.965 | 3.51890 | ||||||||
\(925\) | 21.7279 | 0.714408 | ||||||||
\(926\) | 108.168 | 3.55462 | ||||||||
\(927\) | 40.1699 | 1.31935 | ||||||||
\(928\) | 74.5741 | 2.44801 | ||||||||
\(929\) | −44.0705 | −1.44591 | −0.722954 | − | 0.690897i | \(-0.757216\pi\) | ||||
−0.722954 | + | 0.690897i | \(0.757216\pi\) | |||||||
\(930\) | 152.435 | 4.99854 | ||||||||
\(931\) | 8.62894 | 0.282802 | ||||||||
\(932\) | 79.9870 | 2.62006 | ||||||||
\(933\) | −19.1616 | −0.627323 | ||||||||
\(934\) | 20.9615 | 0.685881 | ||||||||
\(935\) | −40.4187 | −1.32183 | ||||||||
\(936\) | −38.2595 | −1.25055 | ||||||||
\(937\) | −18.8931 | −0.617210 | −0.308605 | − | 0.951190i | \(-0.599862\pi\) | ||||
−0.308605 | + | 0.951190i | \(0.599862\pi\) | |||||||
\(938\) | 67.3363 | 2.19861 | ||||||||
\(939\) | 98.4629 | 3.21322 | ||||||||
\(940\) | 184.059 | 6.00334 | ||||||||
\(941\) | −46.8173 | −1.52620 | −0.763100 | − | 0.646280i | \(-0.776324\pi\) | ||||
−0.763100 | + | 0.646280i | \(0.776324\pi\) | |||||||
\(942\) | −24.0552 | −0.783760 | ||||||||
\(943\) | 47.0180 | 1.53112 | ||||||||
\(944\) | 49.7519 | 1.61929 | ||||||||
\(945\) | −49.6226 | −1.61422 | ||||||||
\(946\) | 97.8907 | 3.18270 | ||||||||
\(947\) | −10.9288 | −0.355138 | −0.177569 | − | 0.984108i | \(-0.556823\pi\) | ||||
−0.177569 | + | 0.984108i | \(0.556823\pi\) | |||||||
\(948\) | 40.7080 | 1.32213 | ||||||||
\(949\) | −0.932277 | −0.0302630 | ||||||||
\(950\) | 105.240 | 3.41445 | ||||||||
\(951\) | 5.66031 | 0.183548 | ||||||||
\(952\) | 53.7998 | 1.74366 | ||||||||
\(953\) | −13.1711 | −0.426654 | −0.213327 | − | 0.976981i | \(-0.568430\pi\) | ||||
−0.213327 | + | 0.976981i | \(0.568430\pi\) | |||||||
\(954\) | −109.076 | −3.53148 | ||||||||
\(955\) | 76.5838 | 2.47819 | ||||||||
\(956\) | 140.654 | 4.54908 | ||||||||
\(957\) | 64.9261 | 2.09876 | ||||||||
\(958\) | 64.4323 | 2.08171 | ||||||||
\(959\) | 17.2010 | 0.555449 | ||||||||
\(960\) | 98.3596 | 3.17454 | ||||||||
\(961\) | −0.904506 | −0.0291776 | ||||||||
\(962\) | −6.39653 | −0.206232 | ||||||||
\(963\) | −41.8911 | −1.34992 | ||||||||
\(964\) | 40.6565 | 1.30946 | ||||||||
\(965\) | 73.2085 | 2.35666 | ||||||||
\(966\) | 146.922 | 4.72714 | ||||||||
\(967\) | −46.1107 | −1.48282 | −0.741410 | − | 0.671053i | \(-0.765842\pi\) | ||||
−0.741410 | + | 0.671053i | \(0.765842\pi\) | |||||||
\(968\) | −5.45845 | −0.175441 | ||||||||
\(969\) | −40.5426 | −1.30242 | ||||||||
\(970\) | 76.3417 | 2.45118 | ||||||||
\(971\) | 34.7972 | 1.11670 | 0.558348 | − | 0.829607i | \(-0.311435\pi\) | ||||
0.558348 | + | 0.829607i | \(0.311435\pi\) | |||||||
\(972\) | −64.9514 | −2.08332 | ||||||||
\(973\) | −27.6252 | −0.885623 | ||||||||
\(974\) | −32.2943 | −1.03478 | ||||||||
\(975\) | 25.3106 | 0.810587 | ||||||||
\(976\) | 2.10021 | 0.0672259 | ||||||||
\(977\) | −23.8448 | −0.762862 | −0.381431 | − | 0.924397i | \(-0.624569\pi\) | ||||
−0.381431 | + | 0.924397i | \(0.624569\pi\) | |||||||
\(978\) | −169.284 | −5.41310 | ||||||||
\(979\) | 49.7098 | 1.58873 | ||||||||
\(980\) | −34.8037 | −1.11176 | ||||||||
\(981\) | −29.4194 | −0.939290 | ||||||||
\(982\) | 23.2568 | 0.742154 | ||||||||
\(983\) | −16.4683 | −0.525257 | −0.262629 | − | 0.964897i | \(-0.584589\pi\) | ||||
−0.262629 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(984\) | −115.176 | −3.67167 | ||||||||
\(985\) | −58.2052 | −1.85457 | ||||||||
\(986\) | 55.3763 | 1.76354 | ||||||||
\(987\) | −64.8917 | −2.06553 | ||||||||
\(988\) | −21.9685 | −0.698910 | ||||||||
\(989\) | 95.3400 | 3.03164 | ||||||||
\(990\) | 169.950 | 5.40137 | ||||||||
\(991\) | 30.4390 | 0.966927 | 0.483464 | − | 0.875365i | \(-0.339379\pi\) | ||||
0.483464 | + | 0.875365i | \(0.339379\pi\) | |||||||
\(992\) | 61.3155 | 1.94677 | ||||||||
\(993\) | 56.0611 | 1.77905 | ||||||||
\(994\) | 37.0197 | 1.17419 | ||||||||
\(995\) | −70.1883 | −2.22512 | ||||||||
\(996\) | −93.2292 | −2.95408 | ||||||||
\(997\) | 10.2714 | 0.325298 | 0.162649 | − | 0.986684i | \(-0.447996\pi\) | ||||
0.162649 | + | 0.986684i | \(0.447996\pi\) | |||||||
\(998\) | −36.9828 | −1.17067 | ||||||||
\(999\) | 14.3959 | 0.455465 |
(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 | 8021.2.a.d.1.15 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.d.1.15 | ✓ | 174 | 1.1 | even | 1 | trivial |