Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43959 | −1.72505 | −0.862527 | − | 0.506011i | \(-0.831119\pi\) | ||||
−0.862527 | + | 0.506011i | \(0.831119\pi\) | |||||||
\(3\) | 2.16595 | 1.25051 | 0.625255 | − | 0.780421i | \(-0.284995\pi\) | ||||
0.625255 | + | 0.780421i | \(0.284995\pi\) | |||||||
\(4\) | 3.95162 | 1.97581 | ||||||||
\(5\) | −1.55175 | −0.693963 | −0.346982 | − | 0.937872i | \(-0.612793\pi\) | ||||
−0.346982 | + | 0.937872i | \(0.612793\pi\) | |||||||
\(6\) | −5.28403 | −2.15720 | ||||||||
\(7\) | −2.38051 | −0.899748 | −0.449874 | − | 0.893092i | \(-0.648531\pi\) | ||||
−0.449874 | + | 0.893092i | \(0.648531\pi\) | |||||||
\(8\) | −4.76117 | −1.68333 | ||||||||
\(9\) | 1.69132 | 0.563775 | ||||||||
\(10\) | 3.78564 | 1.19712 | ||||||||
\(11\) | −0.331488 | −0.0999475 | −0.0499738 | − | 0.998751i | \(-0.515914\pi\) | ||||
−0.0499738 | + | 0.998751i | \(0.515914\pi\) | |||||||
\(12\) | 8.55900 | 2.47077 | ||||||||
\(13\) | 2.10394 | 0.583528 | 0.291764 | − | 0.956490i | \(-0.405758\pi\) | ||||
0.291764 | + | 0.956490i | \(0.405758\pi\) | |||||||
\(14\) | 5.80748 | 1.55211 | ||||||||
\(15\) | −3.36101 | −0.867808 | ||||||||
\(16\) | 3.71207 | 0.928018 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −4.12615 | −0.972542 | ||||||||
\(19\) | 5.24243 | 1.20270 | 0.601348 | − | 0.798987i | \(-0.294630\pi\) | ||||
0.601348 | + | 0.798987i | \(0.294630\pi\) | |||||||
\(20\) | −6.13193 | −1.37114 | ||||||||
\(21\) | −5.15606 | −1.12514 | ||||||||
\(22\) | 0.808697 | 0.172415 | ||||||||
\(23\) | −4.52995 | −0.944560 | −0.472280 | − | 0.881449i | \(-0.656569\pi\) | ||||
−0.472280 | + | 0.881449i | \(0.656569\pi\) | |||||||
\(24\) | −10.3124 | −2.10502 | ||||||||
\(25\) | −2.59207 | −0.518415 | ||||||||
\(26\) | −5.13276 | −1.00662 | ||||||||
\(27\) | −2.83452 | −0.545504 | ||||||||
\(28\) | −9.40687 | −1.77773 | ||||||||
\(29\) | 2.32694 | 0.432102 | 0.216051 | − | 0.976382i | \(-0.430682\pi\) | ||||
0.216051 | + | 0.976382i | \(0.430682\pi\) | |||||||
\(30\) | 8.19949 | 1.49702 | ||||||||
\(31\) | −6.94962 | −1.24819 | −0.624094 | − | 0.781349i | \(-0.714532\pi\) | ||||
−0.624094 | + | 0.781349i | \(0.714532\pi\) | |||||||
\(32\) | 0.466385 | 0.0824460 | ||||||||
\(33\) | −0.717986 | −0.124985 | ||||||||
\(34\) | −2.43959 | −0.418387 | ||||||||
\(35\) | 3.69395 | 0.624392 | ||||||||
\(36\) | 6.68347 | 1.11391 | ||||||||
\(37\) | −1.77681 | −0.292107 | −0.146053 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146053 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(38\) | −12.7894 | −2.07472 | ||||||||
\(39\) | 4.55702 | 0.729708 | ||||||||
\(40\) | 7.38813 | 1.16817 | ||||||||
\(41\) | 10.3883 | 1.62238 | 0.811191 | − | 0.584781i | \(-0.198820\pi\) | ||||
0.811191 | + | 0.584781i | \(0.198820\pi\) | |||||||
\(42\) | 12.5787 | 1.94093 | ||||||||
\(43\) | −5.51062 | −0.840362 | −0.420181 | − | 0.907440i | \(-0.638033\pi\) | ||||
−0.420181 | + | 0.907440i | \(0.638033\pi\) | |||||||
\(44\) | −1.30992 | −0.197477 | ||||||||
\(45\) | −2.62451 | −0.391239 | ||||||||
\(46\) | 11.0512 | 1.62942 | ||||||||
\(47\) | −10.5314 | −1.53616 | −0.768079 | − | 0.640355i | \(-0.778787\pi\) | ||||
−0.768079 | + | 0.640355i | \(0.778787\pi\) | |||||||
\(48\) | 8.04015 | 1.16049 | ||||||||
\(49\) | −1.33317 | −0.190453 | ||||||||
\(50\) | 6.32361 | 0.894294 | ||||||||
\(51\) | 2.16595 | 0.303293 | ||||||||
\(52\) | 8.31398 | 1.15294 | ||||||||
\(53\) | 12.7771 | 1.75506 | 0.877532 | − | 0.479519i | \(-0.159189\pi\) | ||||
0.877532 | + | 0.479519i | \(0.159189\pi\) | |||||||
\(54\) | 6.91508 | 0.941024 | ||||||||
\(55\) | 0.514387 | 0.0693599 | ||||||||
\(56\) | 11.3340 | 1.51457 | ||||||||
\(57\) | 11.3548 | 1.50398 | ||||||||
\(58\) | −5.67680 | −0.745400 | ||||||||
\(59\) | 7.29560 | 0.949806 | 0.474903 | − | 0.880038i | \(-0.342483\pi\) | ||||
0.474903 | + | 0.880038i | \(0.342483\pi\) | |||||||
\(60\) | −13.2814 | −1.71462 | ||||||||
\(61\) | 4.86741 | 0.623209 | 0.311604 | − | 0.950212i | \(-0.399134\pi\) | ||||
0.311604 | + | 0.950212i | \(0.399134\pi\) | |||||||
\(62\) | 16.9542 | 2.15319 | ||||||||
\(63\) | −4.02621 | −0.507255 | ||||||||
\(64\) | −8.56193 | −1.07024 | ||||||||
\(65\) | −3.26479 | −0.404947 | ||||||||
\(66\) | 1.75160 | 0.215606 | ||||||||
\(67\) | −7.11782 | −0.869580 | −0.434790 | − | 0.900532i | \(-0.643177\pi\) | ||||
−0.434790 | + | 0.900532i | \(0.643177\pi\) | |||||||
\(68\) | 3.95162 | 0.479205 | ||||||||
\(69\) | −9.81163 | −1.18118 | ||||||||
\(70\) | −9.01175 | −1.07711 | ||||||||
\(71\) | 12.7376 | 1.51168 | 0.755839 | − | 0.654758i | \(-0.227229\pi\) | ||||
0.755839 | + | 0.654758i | \(0.227229\pi\) | |||||||
\(72\) | −8.05267 | −0.949017 | ||||||||
\(73\) | 1.53418 | 0.179562 | 0.0897811 | − | 0.995962i | \(-0.471383\pi\) | ||||
0.0897811 | + | 0.995962i | \(0.471383\pi\) | |||||||
\(74\) | 4.33471 | 0.503899 | ||||||||
\(75\) | −5.61430 | −0.648283 | ||||||||
\(76\) | 20.7161 | 2.37630 | ||||||||
\(77\) | 0.789112 | 0.0899276 | ||||||||
\(78\) | −11.1173 | −1.25879 | ||||||||
\(79\) | 13.5494 | 1.52443 | 0.762213 | − | 0.647326i | \(-0.224113\pi\) | ||||
0.762213 | + | 0.647326i | \(0.224113\pi\) | |||||||
\(80\) | −5.76020 | −0.644010 | ||||||||
\(81\) | −11.2134 | −1.24593 | ||||||||
\(82\) | −25.3433 | −2.79870 | ||||||||
\(83\) | 5.47710 | 0.601190 | 0.300595 | − | 0.953752i | \(-0.402815\pi\) | ||||
0.300595 | + | 0.953752i | \(0.402815\pi\) | |||||||
\(84\) | −20.3748 | −2.22307 | ||||||||
\(85\) | −1.55175 | −0.168311 | ||||||||
\(86\) | 13.4437 | 1.44967 | ||||||||
\(87\) | 5.04003 | 0.540348 | ||||||||
\(88\) | 1.57827 | 0.168244 | ||||||||
\(89\) | 10.2065 | 1.08189 | 0.540946 | − | 0.841057i | \(-0.318066\pi\) | ||||
0.540946 | + | 0.841057i | \(0.318066\pi\) | |||||||
\(90\) | 6.40274 | 0.674908 | ||||||||
\(91\) | −5.00845 | −0.525029 | ||||||||
\(92\) | −17.9007 | −1.86627 | ||||||||
\(93\) | −15.0525 | −1.56087 | ||||||||
\(94\) | 25.6923 | 2.64995 | ||||||||
\(95\) | −8.13494 | −0.834628 | ||||||||
\(96\) | 1.01016 | 0.103100 | ||||||||
\(97\) | −14.7667 | −1.49933 | −0.749667 | − | 0.661816i | \(-0.769786\pi\) | ||||
−0.749667 | + | 0.661816i | \(0.769786\pi\) | |||||||
\(98\) | 3.25240 | 0.328542 | ||||||||
\(99\) | −0.560654 | −0.0563479 | ||||||||
\(100\) | −10.2429 | −1.02429 | ||||||||
\(101\) | −16.6313 | −1.65488 | −0.827438 | − | 0.561558i | \(-0.810202\pi\) | ||||
−0.827438 | + | 0.561558i | \(0.810202\pi\) | |||||||
\(102\) | −5.28403 | −0.523197 | ||||||||
\(103\) | 11.2320 | 1.10672 | 0.553362 | − | 0.832941i | \(-0.313345\pi\) | ||||
0.553362 | + | 0.832941i | \(0.313345\pi\) | |||||||
\(104\) | −10.0172 | −0.982269 | ||||||||
\(105\) | 8.00091 | 0.780809 | ||||||||
\(106\) | −31.1708 | −3.02758 | ||||||||
\(107\) | 2.82459 | 0.273063 | 0.136532 | − | 0.990636i | \(-0.456405\pi\) | ||||
0.136532 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(108\) | −11.2010 | −1.07781 | ||||||||
\(109\) | 5.72740 | 0.548586 | 0.274293 | − | 0.961646i | \(-0.411556\pi\) | ||||
0.274293 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(110\) | −1.25490 | −0.119650 | ||||||||
\(111\) | −3.84849 | −0.365282 | ||||||||
\(112\) | −8.83662 | −0.834982 | ||||||||
\(113\) | 3.53328 | 0.332383 | 0.166192 | − | 0.986093i | \(-0.446853\pi\) | ||||
0.166192 | + | 0.986093i | \(0.446853\pi\) | |||||||
\(114\) | −27.7012 | −2.59445 | ||||||||
\(115\) | 7.02935 | 0.655490 | ||||||||
\(116\) | 9.19519 | 0.853752 | ||||||||
\(117\) | 3.55845 | 0.328979 | ||||||||
\(118\) | −17.7983 | −1.63847 | ||||||||
\(119\) | −2.38051 | −0.218221 | ||||||||
\(120\) | 16.0023 | 1.46080 | ||||||||
\(121\) | −10.8901 | −0.990010 | ||||||||
\(122\) | −11.8745 | −1.07507 | ||||||||
\(123\) | 22.5005 | 2.02880 | ||||||||
\(124\) | −27.4623 | −2.46618 | ||||||||
\(125\) | 11.7810 | 1.05372 | ||||||||
\(126\) | 9.82233 | 0.875043 | ||||||||
\(127\) | −3.49919 | −0.310503 | −0.155251 | − | 0.987875i | \(-0.549619\pi\) | ||||
−0.155251 | + | 0.987875i | \(0.549619\pi\) | |||||||
\(128\) | 19.9549 | 1.76378 | ||||||||
\(129\) | −11.9357 | −1.05088 | ||||||||
\(130\) | 7.96476 | 0.698556 | ||||||||
\(131\) | −17.2951 | −1.51108 | −0.755539 | − | 0.655104i | \(-0.772625\pi\) | ||||
−0.755539 | + | 0.655104i | \(0.772625\pi\) | |||||||
\(132\) | −2.83721 | −0.246947 | ||||||||
\(133\) | −12.4797 | −1.08212 | ||||||||
\(134\) | 17.3646 | 1.50007 | ||||||||
\(135\) | 4.39847 | 0.378560 | ||||||||
\(136\) | −4.76117 | −0.408267 | ||||||||
\(137\) | −8.67248 | −0.740940 | −0.370470 | − | 0.928844i | \(-0.620803\pi\) | ||||
−0.370470 | + | 0.928844i | \(0.620803\pi\) | |||||||
\(138\) | 23.9364 | 2.03760 | ||||||||
\(139\) | 8.75419 | 0.742520 | 0.371260 | − | 0.928529i | \(-0.378926\pi\) | ||||
0.371260 | + | 0.928529i | \(0.378926\pi\) | |||||||
\(140\) | 14.5971 | 1.23368 | ||||||||
\(141\) | −22.8104 | −1.92098 | ||||||||
\(142\) | −31.0746 | −2.60772 | ||||||||
\(143\) | −0.697432 | −0.0583222 | ||||||||
\(144\) | 6.27831 | 0.523193 | ||||||||
\(145\) | −3.61083 | −0.299863 | ||||||||
\(146\) | −3.74278 | −0.309754 | ||||||||
\(147\) | −2.88758 | −0.238164 | ||||||||
\(148\) | −7.02130 | −0.577147 | ||||||||
\(149\) | 4.48786 | 0.367660 | 0.183830 | − | 0.982958i | \(-0.441150\pi\) | ||||
0.183830 | + | 0.982958i | \(0.441150\pi\) | |||||||
\(150\) | 13.6966 | 1.11832 | ||||||||
\(151\) | −3.82712 | −0.311447 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(152\) | −24.9601 | −2.02453 | ||||||||
\(153\) | 1.69132 | 0.136735 | ||||||||
\(154\) | −1.92511 | −0.155130 | ||||||||
\(155\) | 10.7841 | 0.866197 | ||||||||
\(156\) | 18.0076 | 1.44176 | ||||||||
\(157\) | −2.12060 | −0.169242 | −0.0846212 | − | 0.996413i | \(-0.526968\pi\) | ||||
−0.0846212 | + | 0.996413i | \(0.526968\pi\) | |||||||
\(158\) | −33.0550 | −2.62972 | ||||||||
\(159\) | 27.6744 | 2.19472 | ||||||||
\(160\) | −0.723712 | −0.0572145 | ||||||||
\(161\) | 10.7836 | 0.849866 | ||||||||
\(162\) | 27.3561 | 2.14930 | ||||||||
\(163\) | 4.53145 | 0.354931 | 0.177465 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177465 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(164\) | 41.0507 | 3.20552 | ||||||||
\(165\) | 1.11413 | 0.0867353 | ||||||||
\(166\) | −13.3619 | −1.03708 | ||||||||
\(167\) | 6.19738 | 0.479568 | 0.239784 | − | 0.970826i | \(-0.422923\pi\) | ||||
0.239784 | + | 0.970826i | \(0.422923\pi\) | |||||||
\(168\) | 24.5488 | 1.89398 | ||||||||
\(169\) | −8.57343 | −0.659495 | ||||||||
\(170\) | 3.78564 | 0.290345 | ||||||||
\(171\) | 8.86666 | 0.678050 | ||||||||
\(172\) | −21.7759 | −1.66040 | ||||||||
\(173\) | 3.11966 | 0.237183 | 0.118592 | − | 0.992943i | \(-0.462162\pi\) | ||||
0.118592 | + | 0.992943i | \(0.462162\pi\) | |||||||
\(174\) | −12.2956 | −0.932130 | ||||||||
\(175\) | 6.17046 | 0.466443 | ||||||||
\(176\) | −1.23051 | −0.0927531 | ||||||||
\(177\) | 15.8019 | 1.18774 | ||||||||
\(178\) | −24.8998 | −1.86632 | ||||||||
\(179\) | 19.3913 | 1.44938 | 0.724688 | − | 0.689077i | \(-0.241984\pi\) | ||||
0.724688 | + | 0.689077i | \(0.241984\pi\) | |||||||
\(180\) | −10.3711 | −0.773014 | ||||||||
\(181\) | 8.82501 | 0.655958 | 0.327979 | − | 0.944685i | \(-0.393633\pi\) | ||||
0.327979 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(182\) | 12.2186 | 0.905703 | ||||||||
\(183\) | 10.5426 | 0.779328 | ||||||||
\(184\) | 21.5678 | 1.59000 | ||||||||
\(185\) | 2.75717 | 0.202711 | ||||||||
\(186\) | 36.7220 | 2.69259 | ||||||||
\(187\) | −0.331488 | −0.0242408 | ||||||||
\(188\) | −41.6160 | −3.03516 | ||||||||
\(189\) | 6.74761 | 0.490816 | ||||||||
\(190\) | 19.8460 | 1.43978 | ||||||||
\(191\) | 22.7893 | 1.64898 | 0.824490 | − | 0.565877i | \(-0.191462\pi\) | ||||
0.824490 | + | 0.565877i | \(0.191462\pi\) | |||||||
\(192\) | −18.5447 | −1.33835 | ||||||||
\(193\) | −10.7670 | −0.775023 | −0.387511 | − | 0.921865i | \(-0.626665\pi\) | ||||
−0.387511 | + | 0.921865i | \(0.626665\pi\) | |||||||
\(194\) | 36.0248 | 2.58643 | ||||||||
\(195\) | −7.07136 | −0.506391 | ||||||||
\(196\) | −5.26819 | −0.376300 | ||||||||
\(197\) | 15.3605 | 1.09439 | 0.547195 | − | 0.837005i | \(-0.315696\pi\) | ||||
0.547195 | + | 0.837005i | \(0.315696\pi\) | |||||||
\(198\) | 1.36777 | 0.0972031 | ||||||||
\(199\) | 11.0101 | 0.780487 | 0.390244 | − | 0.920712i | \(-0.372391\pi\) | ||||
0.390244 | + | 0.920712i | \(0.372391\pi\) | |||||||
\(200\) | 12.3413 | 0.872661 | ||||||||
\(201\) | −15.4168 | −1.08742 | ||||||||
\(202\) | 40.5736 | 2.85475 | ||||||||
\(203\) | −5.53931 | −0.388783 | ||||||||
\(204\) | 8.55900 | 0.599250 | ||||||||
\(205\) | −16.1201 | −1.12587 | ||||||||
\(206\) | −27.4016 | −1.90916 | ||||||||
\(207\) | −7.66162 | −0.532519 | ||||||||
\(208\) | 7.80998 | 0.541525 | ||||||||
\(209\) | −1.73781 | −0.120207 | ||||||||
\(210\) | −19.5190 | −1.34694 | ||||||||
\(211\) | −8.86005 | −0.609951 | −0.304976 | − | 0.952360i | \(-0.598648\pi\) | ||||
−0.304976 | + | 0.952360i | \(0.598648\pi\) | |||||||
\(212\) | 50.4901 | 3.46767 | ||||||||
\(213\) | 27.5890 | 1.89037 | ||||||||
\(214\) | −6.89084 | −0.471048 | ||||||||
\(215\) | 8.55110 | 0.583180 | ||||||||
\(216\) | 13.4956 | 0.918261 | ||||||||
\(217\) | 16.5436 | 1.12305 | ||||||||
\(218\) | −13.9725 | −0.946340 | ||||||||
\(219\) | 3.32295 | 0.224544 | ||||||||
\(220\) | 2.03266 | 0.137042 | ||||||||
\(221\) | 2.10394 | 0.141526 | ||||||||
\(222\) | 9.38874 | 0.630131 | ||||||||
\(223\) | 17.8274 | 1.19381 | 0.596907 | − | 0.802311i | \(-0.296396\pi\) | ||||
0.596907 | + | 0.802311i | \(0.296396\pi\) | |||||||
\(224\) | −1.11023 | −0.0741806 | ||||||||
\(225\) | −4.38404 | −0.292269 | ||||||||
\(226\) | −8.61978 | −0.573379 | ||||||||
\(227\) | 7.98163 | 0.529759 | 0.264880 | − | 0.964281i | \(-0.414668\pi\) | ||||
0.264880 | + | 0.964281i | \(0.414668\pi\) | |||||||
\(228\) | 44.8700 | 2.97159 | ||||||||
\(229\) | 21.9464 | 1.45026 | 0.725129 | − | 0.688613i | \(-0.241780\pi\) | ||||
0.725129 | + | 0.688613i | \(0.241780\pi\) | |||||||
\(230\) | −17.1488 | −1.13076 | ||||||||
\(231\) | 1.70917 | 0.112455 | ||||||||
\(232\) | −11.0790 | −0.727369 | ||||||||
\(233\) | −20.4183 | −1.33765 | −0.668825 | − | 0.743420i | \(-0.733202\pi\) | ||||
−0.668825 | + | 0.743420i | \(0.733202\pi\) | |||||||
\(234\) | −8.68117 | −0.567506 | ||||||||
\(235\) | 16.3420 | 1.06604 | ||||||||
\(236\) | 28.8295 | 1.87664 | ||||||||
\(237\) | 29.3473 | 1.90631 | ||||||||
\(238\) | 5.80748 | 0.376443 | ||||||||
\(239\) | −12.9302 | −0.836383 | −0.418192 | − | 0.908359i | \(-0.637336\pi\) | ||||
−0.418192 | + | 0.908359i | \(0.637336\pi\) | |||||||
\(240\) | −12.4763 | −0.805341 | ||||||||
\(241\) | −1.52327 | −0.0981223 | −0.0490611 | − | 0.998796i | \(-0.515623\pi\) | ||||
−0.0490611 | + | 0.998796i | \(0.515623\pi\) | |||||||
\(242\) | 26.5675 | 1.70782 | ||||||||
\(243\) | −15.7840 | −1.01255 | ||||||||
\(244\) | 19.2342 | 1.23134 | ||||||||
\(245\) | 2.06875 | 0.132168 | ||||||||
\(246\) | −54.8922 | −3.49980 | ||||||||
\(247\) | 11.0298 | 0.701808 | ||||||||
\(248\) | 33.0883 | 2.10111 | ||||||||
\(249\) | 11.8631 | 0.751794 | ||||||||
\(250\) | −28.7409 | −1.81773 | ||||||||
\(251\) | −4.23907 | −0.267568 | −0.133784 | − | 0.991011i | \(-0.542713\pi\) | ||||
−0.133784 | + | 0.991011i | \(0.542713\pi\) | |||||||
\(252\) | −15.9101 | −1.00224 | ||||||||
\(253\) | 1.50163 | 0.0944064 | ||||||||
\(254\) | 8.53660 | 0.535634 | ||||||||
\(255\) | −3.36101 | −0.210474 | ||||||||
\(256\) | −31.5579 | −1.97237 | ||||||||
\(257\) | −16.9061 | −1.05457 | −0.527286 | − | 0.849688i | \(-0.676790\pi\) | ||||
−0.527286 | + | 0.849688i | \(0.676790\pi\) | |||||||
\(258\) | 29.1183 | 1.81283 | ||||||||
\(259\) | 4.22972 | 0.262822 | ||||||||
\(260\) | −12.9012 | −0.800099 | ||||||||
\(261\) | 3.93561 | 0.243608 | ||||||||
\(262\) | 42.1930 | 2.60669 | ||||||||
\(263\) | 19.2945 | 1.18975 | 0.594876 | − | 0.803818i | \(-0.297201\pi\) | ||||
0.594876 | + | 0.803818i | \(0.297201\pi\) | |||||||
\(264\) | 3.41845 | 0.210391 | ||||||||
\(265\) | −19.8268 | −1.21795 | ||||||||
\(266\) | 30.4453 | 1.86672 | ||||||||
\(267\) | 22.1068 | 1.35292 | ||||||||
\(268\) | −28.1269 | −1.71812 | ||||||||
\(269\) | −6.66760 | −0.406531 | −0.203265 | − | 0.979124i | \(-0.565155\pi\) | ||||
−0.203265 | + | 0.979124i | \(0.565155\pi\) | |||||||
\(270\) | −10.7305 | −0.653036 | ||||||||
\(271\) | 26.7375 | 1.62419 | 0.812093 | − | 0.583528i | \(-0.198328\pi\) | ||||
0.812093 | + | 0.583528i | \(0.198328\pi\) | |||||||
\(272\) | 3.71207 | 0.225077 | ||||||||
\(273\) | −10.8480 | −0.656553 | ||||||||
\(274\) | 21.1573 | 1.27816 | ||||||||
\(275\) | 0.859243 | 0.0518143 | ||||||||
\(276\) | −38.7719 | −2.33379 | ||||||||
\(277\) | 5.83031 | 0.350309 | 0.175155 | − | 0.984541i | \(-0.443957\pi\) | ||||
0.175155 | + | 0.984541i | \(0.443957\pi\) | |||||||
\(278\) | −21.3567 | −1.28089 | ||||||||
\(279\) | −11.7541 | −0.703697 | ||||||||
\(280\) | −17.5875 | −1.05106 | ||||||||
\(281\) | 3.63894 | 0.217081 | 0.108540 | − | 0.994092i | \(-0.465382\pi\) | ||||
0.108540 | + | 0.994092i | \(0.465382\pi\) | |||||||
\(282\) | 55.6481 | 3.31379 | ||||||||
\(283\) | −24.9066 | −1.48054 | −0.740272 | − | 0.672308i | \(-0.765303\pi\) | ||||
−0.740272 | + | 0.672308i | \(0.765303\pi\) | |||||||
\(284\) | 50.3343 | 2.98679 | ||||||||
\(285\) | −17.6199 | −1.04371 | ||||||||
\(286\) | 1.70145 | 0.100609 | ||||||||
\(287\) | −24.7295 | −1.45974 | ||||||||
\(288\) | 0.788808 | 0.0464810 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 8.80896 | 0.517280 | ||||||||
\(291\) | −31.9839 | −1.87493 | ||||||||
\(292\) | 6.06250 | 0.354781 | ||||||||
\(293\) | 24.0302 | 1.40386 | 0.701929 | − | 0.712247i | \(-0.252322\pi\) | ||||
0.701929 | + | 0.712247i | \(0.252322\pi\) | |||||||
\(294\) | 7.04453 | 0.410845 | ||||||||
\(295\) | −11.3209 | −0.659131 | ||||||||
\(296\) | 8.45971 | 0.491711 | ||||||||
\(297\) | 0.939611 | 0.0545218 | ||||||||
\(298\) | −10.9486 | −0.634233 | ||||||||
\(299\) | −9.53075 | −0.551178 | ||||||||
\(300\) | −22.1856 | −1.28088 | ||||||||
\(301\) | 13.1181 | 0.756114 | ||||||||
\(302\) | 9.33662 | 0.537262 | ||||||||
\(303\) | −36.0225 | −2.06944 | ||||||||
\(304\) | 19.4603 | 1.11612 | ||||||||
\(305\) | −7.55301 | −0.432484 | ||||||||
\(306\) | −4.12615 | −0.235876 | ||||||||
\(307\) | −1.58616 | −0.0905268 | −0.0452634 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452634 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(308\) | 3.11827 | 0.177680 | ||||||||
\(309\) | 24.3279 | 1.38397 | ||||||||
\(310\) | −26.3087 | −1.49424 | ||||||||
\(311\) | 0.859062 | 0.0487130 | 0.0243565 | − | 0.999703i | \(-0.492246\pi\) | ||||
0.0243565 | + | 0.999703i | \(0.492246\pi\) | |||||||
\(312\) | −21.6967 | −1.22834 | ||||||||
\(313\) | 5.90864 | 0.333976 | 0.166988 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166988 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(314\) | 5.17341 | 0.291952 | ||||||||
\(315\) | 6.24767 | 0.352017 | ||||||||
\(316\) | 53.5421 | 3.01198 | ||||||||
\(317\) | 19.0085 | 1.06762 | 0.533812 | − | 0.845603i | \(-0.320759\pi\) | ||||
0.533812 | + | 0.845603i | \(0.320759\pi\) | |||||||
\(318\) | −67.5144 | −3.78602 | ||||||||
\(319\) | −0.771354 | −0.0431876 | ||||||||
\(320\) | 13.2860 | 0.742708 | ||||||||
\(321\) | 6.11790 | 0.341468 | ||||||||
\(322\) | −26.3076 | −1.46606 | ||||||||
\(323\) | 5.24243 | 0.291697 | ||||||||
\(324\) | −44.3111 | −2.46173 | ||||||||
\(325\) | −5.45357 | −0.302510 | ||||||||
\(326\) | −11.0549 | −0.612275 | ||||||||
\(327\) | 12.4052 | 0.686012 | ||||||||
\(328\) | −49.4605 | −2.73100 | ||||||||
\(329\) | 25.0700 | 1.38215 | ||||||||
\(330\) | −2.71804 | −0.149623 | ||||||||
\(331\) | −10.7889 | −0.593012 | −0.296506 | − | 0.955031i | \(-0.595821\pi\) | ||||
−0.296506 | + | 0.955031i | \(0.595821\pi\) | |||||||
\(332\) | 21.6434 | 1.18784 | ||||||||
\(333\) | −3.00517 | −0.164682 | ||||||||
\(334\) | −15.1191 | −0.827281 | ||||||||
\(335\) | 11.0451 | 0.603456 | ||||||||
\(336\) | −19.1396 | −1.04415 | ||||||||
\(337\) | −1.75569 | −0.0956388 | −0.0478194 | − | 0.998856i | \(-0.515227\pi\) | ||||
−0.0478194 | + | 0.998856i | \(0.515227\pi\) | |||||||
\(338\) | 20.9157 | 1.13766 | ||||||||
\(339\) | 7.65290 | 0.415648 | ||||||||
\(340\) | −6.13193 | −0.332550 | ||||||||
\(341\) | 2.30372 | 0.124753 | ||||||||
\(342\) | −21.6310 | −1.16967 | ||||||||
\(343\) | 19.8372 | 1.07111 | ||||||||
\(344\) | 26.2370 | 1.41460 | ||||||||
\(345\) | 15.2252 | 0.819697 | ||||||||
\(346\) | −7.61071 | −0.409154 | ||||||||
\(347\) | 28.4412 | 1.52680 | 0.763401 | − | 0.645924i | \(-0.223528\pi\) | ||||
0.763401 | + | 0.645924i | \(0.223528\pi\) | |||||||
\(348\) | 19.9163 | 1.06763 | ||||||||
\(349\) | −10.9018 | −0.583562 | −0.291781 | − | 0.956485i | \(-0.594248\pi\) | ||||
−0.291781 | + | 0.956485i | \(0.594248\pi\) | |||||||
\(350\) | −15.0534 | −0.804639 | ||||||||
\(351\) | −5.96367 | −0.318317 | ||||||||
\(352\) | −0.154601 | −0.00824027 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −38.5502 | −2.04892 | ||||||||
\(355\) | −19.7656 | −1.04905 | ||||||||
\(356\) | 40.3324 | 2.13761 | ||||||||
\(357\) | −5.15606 | −0.272887 | ||||||||
\(358\) | −47.3070 | −2.50025 | ||||||||
\(359\) | 33.1572 | 1.74997 | 0.874985 | − | 0.484150i | \(-0.160871\pi\) | ||||
0.874985 | + | 0.484150i | \(0.160871\pi\) | |||||||
\(360\) | 12.4957 | 0.658583 | ||||||||
\(361\) | 8.48312 | 0.446480 | ||||||||
\(362\) | −21.5294 | −1.13156 | ||||||||
\(363\) | −23.5874 | −1.23802 | ||||||||
\(364\) | −19.7915 | −1.03736 | ||||||||
\(365\) | −2.38066 | −0.124610 | ||||||||
\(366\) | −25.7196 | −1.34438 | ||||||||
\(367\) | 18.1359 | 0.946685 | 0.473343 | − | 0.880878i | \(-0.343047\pi\) | ||||
0.473343 | + | 0.880878i | \(0.343047\pi\) | |||||||
\(368\) | −16.8155 | −0.876568 | ||||||||
\(369\) | 17.5700 | 0.914658 | ||||||||
\(370\) | −6.72638 | −0.349688 | ||||||||
\(371\) | −30.4159 | −1.57912 | ||||||||
\(372\) | −59.4818 | −3.08399 | ||||||||
\(373\) | 27.4929 | 1.42353 | 0.711765 | − | 0.702418i | \(-0.247896\pi\) | ||||
0.711765 | + | 0.702418i | \(0.247896\pi\) | |||||||
\(374\) | 0.808697 | 0.0418167 | ||||||||
\(375\) | 25.5170 | 1.31769 | ||||||||
\(376\) | 50.1416 | 2.58585 | ||||||||
\(377\) | 4.89575 | 0.252144 | ||||||||
\(378\) | −16.4614 | −0.846684 | ||||||||
\(379\) | 33.4884 | 1.72019 | 0.860093 | − | 0.510138i | \(-0.170406\pi\) | ||||
0.860093 | + | 0.510138i | \(0.170406\pi\) | |||||||
\(380\) | −32.1462 | −1.64907 | ||||||||
\(381\) | −7.57905 | −0.388287 | ||||||||
\(382\) | −55.5968 | −2.84458 | ||||||||
\(383\) | 7.98791 | 0.408163 | 0.204082 | − | 0.978954i | \(-0.434579\pi\) | ||||
0.204082 | + | 0.978954i | \(0.434579\pi\) | |||||||
\(384\) | 43.2212 | 2.20562 | ||||||||
\(385\) | −1.22450 | −0.0624065 | ||||||||
\(386\) | 26.2670 | 1.33696 | ||||||||
\(387\) | −9.32025 | −0.473775 | ||||||||
\(388\) | −58.3525 | −2.96240 | ||||||||
\(389\) | −22.7428 | −1.15310 | −0.576552 | − | 0.817060i | \(-0.695602\pi\) | ||||
−0.576552 | + | 0.817060i | \(0.695602\pi\) | |||||||
\(390\) | 17.2512 | 0.873551 | ||||||||
\(391\) | −4.52995 | −0.229089 | ||||||||
\(392\) | 6.34745 | 0.320595 | ||||||||
\(393\) | −37.4602 | −1.88962 | ||||||||
\(394\) | −37.4734 | −1.88788 | ||||||||
\(395\) | −21.0253 | −1.05790 | ||||||||
\(396\) | −2.21549 | −0.111333 | ||||||||
\(397\) | 17.1611 | 0.861291 | 0.430645 | − | 0.902521i | \(-0.358286\pi\) | ||||
0.430645 | + | 0.902521i | \(0.358286\pi\) | |||||||
\(398\) | −26.8602 | −1.34638 | ||||||||
\(399\) | −27.0303 | −1.35321 | ||||||||
\(400\) | −9.62196 | −0.481098 | ||||||||
\(401\) | 11.0439 | 0.551507 | 0.275754 | − | 0.961228i | \(-0.411073\pi\) | ||||
0.275754 | + | 0.961228i | \(0.411073\pi\) | |||||||
\(402\) | 37.6108 | 1.87585 | ||||||||
\(403\) | −14.6216 | −0.728353 | ||||||||
\(404\) | −65.7206 | −3.26972 | ||||||||
\(405\) | 17.4004 | 0.864632 | ||||||||
\(406\) | 13.5137 | 0.670672 | ||||||||
\(407\) | 0.588994 | 0.0291953 | ||||||||
\(408\) | −10.3124 | −0.510541 | ||||||||
\(409\) | −34.7777 | −1.71964 | −0.859822 | − | 0.510594i | \(-0.829426\pi\) | ||||
−0.859822 | + | 0.510594i | \(0.829426\pi\) | |||||||
\(410\) | 39.3264 | 1.94219 | ||||||||
\(411\) | −18.7841 | −0.926553 | ||||||||
\(412\) | 44.3847 | 2.18668 | ||||||||
\(413\) | −17.3672 | −0.854587 | ||||||||
\(414\) | 18.6912 | 0.918624 | ||||||||
\(415\) | −8.49908 | −0.417204 | ||||||||
\(416\) | 0.981247 | 0.0481096 | ||||||||
\(417\) | 18.9611 | 0.928529 | ||||||||
\(418\) | 4.23954 | 0.207363 | ||||||||
\(419\) | −2.52776 | −0.123489 | −0.0617447 | − | 0.998092i | \(-0.519666\pi\) | ||||
−0.0617447 | + | 0.998092i | \(0.519666\pi\) | |||||||
\(420\) | 31.6166 | 1.54273 | ||||||||
\(421\) | −30.6821 | −1.49536 | −0.747678 | − | 0.664061i | \(-0.768831\pi\) | ||||
−0.747678 | + | 0.664061i | \(0.768831\pi\) | |||||||
\(422\) | 21.6149 | 1.05220 | ||||||||
\(423\) | −17.8120 | −0.866047 | ||||||||
\(424\) | −60.8337 | −2.95434 | ||||||||
\(425\) | −2.59207 | −0.125734 | ||||||||
\(426\) | −67.3060 | −3.26099 | ||||||||
\(427\) | −11.5869 | −0.560731 | ||||||||
\(428\) | 11.1617 | 0.539521 | ||||||||
\(429\) | −1.51060 | −0.0729325 | ||||||||
\(430\) | −20.8612 | −1.00602 | ||||||||
\(431\) | −41.0083 | −1.97530 | −0.987650 | − | 0.156675i | \(-0.949923\pi\) | ||||
−0.987650 | + | 0.156675i | \(0.949923\pi\) | |||||||
\(432\) | −10.5219 | −0.506237 | ||||||||
\(433\) | −19.2570 | −0.925433 | −0.462717 | − | 0.886506i | \(-0.653125\pi\) | ||||
−0.462717 | + | 0.886506i | \(0.653125\pi\) | |||||||
\(434\) | −40.3598 | −1.93733 | ||||||||
\(435\) | −7.82086 | −0.374982 | ||||||||
\(436\) | 22.6325 | 1.08390 | ||||||||
\(437\) | −23.7480 | −1.13602 | ||||||||
\(438\) | −8.10665 | −0.387351 | ||||||||
\(439\) | −5.31344 | −0.253597 | −0.126798 | − | 0.991929i | \(-0.540470\pi\) | ||||
−0.126798 | + | 0.991929i | \(0.540470\pi\) | |||||||
\(440\) | −2.44908 | −0.116755 | ||||||||
\(441\) | −2.25483 | −0.107373 | ||||||||
\(442\) | −5.13276 | −0.244141 | ||||||||
\(443\) | −3.88221 | −0.184450 | −0.0922248 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922248 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(444\) | −15.2078 | −0.721728 | ||||||||
\(445\) | −15.8380 | −0.750793 | ||||||||
\(446\) | −43.4917 | −2.05939 | ||||||||
\(447\) | 9.72046 | 0.459762 | ||||||||
\(448\) | 20.3818 | 0.962948 | ||||||||
\(449\) | 27.8395 | 1.31383 | 0.656914 | − | 0.753965i | \(-0.271861\pi\) | ||||
0.656914 | + | 0.753965i | \(0.271861\pi\) | |||||||
\(450\) | 10.6953 | 0.504180 | ||||||||
\(451\) | −3.44361 | −0.162153 | ||||||||
\(452\) | 13.9622 | 0.656726 | ||||||||
\(453\) | −8.28934 | −0.389467 | ||||||||
\(454\) | −19.4719 | −0.913863 | ||||||||
\(455\) | 7.77186 | 0.364351 | ||||||||
\(456\) | −54.0622 | −2.53170 | ||||||||
\(457\) | 7.88687 | 0.368932 | 0.184466 | − | 0.982839i | \(-0.440944\pi\) | ||||
0.184466 | + | 0.982839i | \(0.440944\pi\) | |||||||
\(458\) | −53.5403 | −2.50177 | ||||||||
\(459\) | −2.83452 | −0.132304 | ||||||||
\(460\) | 27.7773 | 1.29512 | ||||||||
\(461\) | 40.1192 | 1.86854 | 0.934269 | − | 0.356568i | \(-0.116053\pi\) | ||||
0.934269 | + | 0.356568i | \(0.116053\pi\) | |||||||
\(462\) | −4.16969 | −0.193992 | ||||||||
\(463\) | 19.2785 | 0.895949 | 0.447974 | − | 0.894046i | \(-0.352146\pi\) | ||||
0.447974 | + | 0.894046i | \(0.352146\pi\) | |||||||
\(464\) | 8.63777 | 0.400998 | ||||||||
\(465\) | 23.3577 | 1.08319 | ||||||||
\(466\) | 49.8125 | 2.30752 | ||||||||
\(467\) | 38.9346 | 1.80168 | 0.900838 | − | 0.434155i | \(-0.142953\pi\) | ||||
0.900838 | + | 0.434155i | \(0.142953\pi\) | |||||||
\(468\) | 14.0616 | 0.649999 | ||||||||
\(469\) | 16.9440 | 0.782403 | ||||||||
\(470\) | −39.8679 | −1.83897 | ||||||||
\(471\) | −4.59311 | −0.211639 | ||||||||
\(472\) | −34.7356 | −1.59883 | ||||||||
\(473\) | 1.82671 | 0.0839921 | ||||||||
\(474\) | −71.5954 | −3.28849 | ||||||||
\(475\) | −13.5888 | −0.623496 | ||||||||
\(476\) | −9.40687 | −0.431163 | ||||||||
\(477\) | 21.6101 | 0.989460 | ||||||||
\(478\) | 31.5444 | 1.44281 | ||||||||
\(479\) | 22.0684 | 1.00833 | 0.504165 | − | 0.863607i | \(-0.331800\pi\) | ||||
0.504165 | + | 0.863607i | \(0.331800\pi\) | |||||||
\(480\) | −1.56752 | −0.0715473 | ||||||||
\(481\) | −3.73831 | −0.170452 | ||||||||
\(482\) | 3.71615 | 0.169266 | ||||||||
\(483\) | 23.3567 | 1.06277 | ||||||||
\(484\) | −43.0336 | −1.95607 | ||||||||
\(485\) | 22.9142 | 1.04048 | ||||||||
\(486\) | 38.5067 | 1.74670 | ||||||||
\(487\) | −11.5562 | −0.523662 | −0.261831 | − | 0.965114i | \(-0.584326\pi\) | ||||
−0.261831 | + | 0.965114i | \(0.584326\pi\) | |||||||
\(488\) | −23.1746 | −1.04906 | ||||||||
\(489\) | 9.81489 | 0.443845 | ||||||||
\(490\) | −5.04691 | −0.227996 | ||||||||
\(491\) | −21.5999 | −0.974788 | −0.487394 | − | 0.873182i | \(-0.662053\pi\) | ||||
−0.487394 | + | 0.873182i | \(0.662053\pi\) | |||||||
\(492\) | 88.9136 | 4.00853 | ||||||||
\(493\) | 2.32694 | 0.104800 | ||||||||
\(494\) | −26.9082 | −1.21066 | ||||||||
\(495\) | 0.869995 | 0.0391034 | ||||||||
\(496\) | −25.7975 | −1.15834 | ||||||||
\(497\) | −30.3220 | −1.36013 | ||||||||
\(498\) | −28.9412 | −1.29688 | ||||||||
\(499\) | 18.1598 | 0.812943 | 0.406471 | − | 0.913664i | \(-0.366759\pi\) | ||||
0.406471 | + | 0.913664i | \(0.366759\pi\) | |||||||
\(500\) | 46.5540 | 2.08196 | ||||||||
\(501\) | 13.4232 | 0.599704 | ||||||||
\(502\) | 10.3416 | 0.461569 | ||||||||
\(503\) | 22.4046 | 0.998974 | 0.499487 | − | 0.866321i | \(-0.333522\pi\) | ||||
0.499487 | + | 0.866321i | \(0.333522\pi\) | |||||||
\(504\) | 19.1695 | 0.853876 | ||||||||
\(505\) | 25.8076 | 1.14842 | ||||||||
\(506\) | −3.66336 | −0.162856 | ||||||||
\(507\) | −18.5696 | −0.824704 | ||||||||
\(508\) | −13.8275 | −0.613494 | ||||||||
\(509\) | 26.3574 | 1.16827 | 0.584136 | − | 0.811656i | \(-0.301433\pi\) | ||||
0.584136 | + | 0.811656i | \(0.301433\pi\) | |||||||
\(510\) | 8.19949 | 0.363080 | ||||||||
\(511\) | −3.65213 | −0.161561 | ||||||||
\(512\) | 37.0788 | 1.63867 | ||||||||
\(513\) | −14.8598 | −0.656076 | ||||||||
\(514\) | 41.2440 | 1.81919 | ||||||||
\(515\) | −17.4293 | −0.768025 | ||||||||
\(516\) | −47.1654 | −2.07634 | ||||||||
\(517\) | 3.49103 | 0.153535 | ||||||||
\(518\) | −10.3188 | −0.453383 | ||||||||
\(519\) | 6.75702 | 0.296600 | ||||||||
\(520\) | 15.5442 | 0.681658 | ||||||||
\(521\) | −21.1260 | −0.925547 | −0.462773 | − | 0.886477i | \(-0.653146\pi\) | ||||
−0.462773 | + | 0.886477i | \(0.653146\pi\) | |||||||
\(522\) | −9.60130 | −0.420238 | ||||||||
\(523\) | 23.7845 | 1.04002 | 0.520011 | − | 0.854159i | \(-0.325928\pi\) | ||||
0.520011 | + | 0.854159i | \(0.325928\pi\) | |||||||
\(524\) | −68.3436 | −2.98560 | ||||||||
\(525\) | 13.3649 | 0.583291 | ||||||||
\(526\) | −47.0708 | −2.05239 | ||||||||
\(527\) | −6.94962 | −0.302730 | ||||||||
\(528\) | −2.66522 | −0.115989 | ||||||||
\(529\) | −2.47955 | −0.107806 | ||||||||
\(530\) | 48.3693 | 2.10103 | ||||||||
\(531\) | 12.3392 | 0.535477 | ||||||||
\(532\) | −49.3149 | −2.13807 | ||||||||
\(533\) | 21.8564 | 0.946706 | ||||||||
\(534\) | −53.9317 | −2.33385 | ||||||||
\(535\) | −4.38305 | −0.189496 | ||||||||
\(536\) | 33.8891 | 1.46379 | ||||||||
\(537\) | 42.0006 | 1.81246 | ||||||||
\(538\) | 16.2662 | 0.701287 | ||||||||
\(539\) | 0.441931 | 0.0190353 | ||||||||
\(540\) | 17.3811 | 0.747962 | ||||||||
\(541\) | 41.4113 | 1.78041 | 0.890205 | − | 0.455561i | \(-0.150561\pi\) | ||||
0.890205 | + | 0.455561i | \(0.150561\pi\) | |||||||
\(542\) | −65.2286 | −2.80181 | ||||||||
\(543\) | 19.1145 | 0.820281 | ||||||||
\(544\) | 0.466385 | 0.0199961 | ||||||||
\(545\) | −8.88749 | −0.380698 | ||||||||
\(546\) | 26.4648 | 1.13259 | ||||||||
\(547\) | 15.4934 | 0.662452 | 0.331226 | − | 0.943551i | \(-0.392538\pi\) | ||||
0.331226 | + | 0.943551i | \(0.392538\pi\) | |||||||
\(548\) | −34.2704 | −1.46396 | ||||||||
\(549\) | 8.23238 | 0.351349 | ||||||||
\(550\) | −2.09620 | −0.0893824 | ||||||||
\(551\) | 12.1988 | 0.519688 | ||||||||
\(552\) | 46.7148 | 1.98831 | ||||||||
\(553\) | −32.2545 | −1.37160 | ||||||||
\(554\) | −14.2236 | −0.604303 | ||||||||
\(555\) | 5.97188 | 0.253492 | ||||||||
\(556\) | 34.5932 | 1.46708 | ||||||||
\(557\) | −37.9758 | −1.60909 | −0.804543 | − | 0.593895i | \(-0.797590\pi\) | ||||
−0.804543 | + | 0.593895i | \(0.797590\pi\) | |||||||
\(558\) | 28.6751 | 1.21392 | ||||||||
\(559\) | −11.5940 | −0.490375 | ||||||||
\(560\) | 13.7122 | 0.579447 | ||||||||
\(561\) | −0.717986 | −0.0303134 | ||||||||
\(562\) | −8.87754 | −0.374476 | ||||||||
\(563\) | −5.40724 | −0.227888 | −0.113944 | − | 0.993487i | \(-0.536348\pi\) | ||||
−0.113944 | + | 0.993487i | \(0.536348\pi\) | |||||||
\(564\) | −90.1380 | −3.79549 | ||||||||
\(565\) | −5.48277 | −0.230662 | ||||||||
\(566\) | 60.7620 | 2.55402 | ||||||||
\(567\) | 26.6936 | 1.12103 | ||||||||
\(568\) | −60.6459 | −2.54465 | ||||||||
\(569\) | 28.2550 | 1.18451 | 0.592256 | − | 0.805750i | \(-0.298237\pi\) | ||||
0.592256 | + | 0.805750i | \(0.298237\pi\) | |||||||
\(570\) | 42.9853 | 1.80046 | ||||||||
\(571\) | −15.9031 | −0.665522 | −0.332761 | − | 0.943011i | \(-0.607980\pi\) | ||||
−0.332761 | + | 0.943011i | \(0.607980\pi\) | |||||||
\(572\) | −2.75599 | −0.115234 | ||||||||
\(573\) | 49.3605 | 2.06206 | ||||||||
\(574\) | 60.3299 | 2.51812 | ||||||||
\(575\) | 11.7420 | 0.489674 | ||||||||
\(576\) | −14.4810 | −0.603375 | ||||||||
\(577\) | −7.60304 | −0.316519 | −0.158259 | − | 0.987398i | \(-0.550588\pi\) | ||||
−0.158259 | + | 0.987398i | \(0.550588\pi\) | |||||||
\(578\) | −2.43959 | −0.101474 | ||||||||
\(579\) | −23.3207 | −0.969173 | ||||||||
\(580\) | −14.2686 | −0.592473 | ||||||||
\(581\) | −13.0383 | −0.540919 | ||||||||
\(582\) | 78.0278 | 3.23436 | ||||||||
\(583\) | −4.23545 | −0.175414 | ||||||||
\(584\) | −7.30448 | −0.302262 | ||||||||
\(585\) | −5.52182 | −0.228299 | ||||||||
\(586\) | −58.6239 | −2.42173 | ||||||||
\(587\) | 0.467879 | 0.0193114 | 0.00965572 | − | 0.999953i | \(-0.496926\pi\) | ||||
0.00965572 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(588\) | −11.4106 | −0.470566 | ||||||||
\(589\) | −36.4329 | −1.50119 | ||||||||
\(590\) | 27.6185 | 1.13704 | ||||||||
\(591\) | 33.2700 | 1.36854 | ||||||||
\(592\) | −6.59566 | −0.271080 | ||||||||
\(593\) | −40.2234 | −1.65178 | −0.825889 | − | 0.563832i | \(-0.809326\pi\) | ||||
−0.825889 | + | 0.563832i | \(0.809326\pi\) | |||||||
\(594\) | −2.29227 | −0.0940530 | ||||||||
\(595\) | 3.69395 | 0.151437 | ||||||||
\(596\) | 17.7343 | 0.726426 | ||||||||
\(597\) | 23.8473 | 0.976007 | ||||||||
\(598\) | 23.2512 | 0.950811 | ||||||||
\(599\) | 13.1977 | 0.539243 | 0.269621 | − | 0.962966i | \(-0.413101\pi\) | ||||
0.269621 | + | 0.962966i | \(0.413101\pi\) | |||||||
\(600\) | 26.7306 | 1.09127 | ||||||||
\(601\) | 45.1815 | 1.84299 | 0.921496 | − | 0.388389i | \(-0.126968\pi\) | ||||
0.921496 | + | 0.388389i | \(0.126968\pi\) | |||||||
\(602\) | −32.0028 | −1.30434 | ||||||||
\(603\) | −12.0385 | −0.490247 | ||||||||
\(604\) | −15.1233 | −0.615360 | ||||||||
\(605\) | 16.8987 | 0.687031 | ||||||||
\(606\) | 87.8803 | 3.56989 | ||||||||
\(607\) | −37.8514 | −1.53634 | −0.768171 | − | 0.640245i | \(-0.778833\pi\) | ||||
−0.768171 | + | 0.640245i | \(0.778833\pi\) | |||||||
\(608\) | 2.44499 | 0.0991575 | ||||||||
\(609\) | −11.9978 | −0.486177 | ||||||||
\(610\) | 18.4263 | 0.746058 | ||||||||
\(611\) | −22.1574 | −0.896392 | ||||||||
\(612\) | 6.68347 | 0.270163 | ||||||||
\(613\) | −22.6989 | −0.916798 | −0.458399 | − | 0.888746i | \(-0.651577\pi\) | ||||
−0.458399 | + | 0.888746i | \(0.651577\pi\) | |||||||
\(614\) | 3.86958 | 0.156164 | ||||||||
\(615\) | −34.9152 | −1.40792 | ||||||||
\(616\) | −3.75709 | −0.151377 | ||||||||
\(617\) | −35.0940 | −1.41283 | −0.706415 | − | 0.707798i | \(-0.749689\pi\) | ||||
−0.706415 | + | 0.707798i | \(0.749689\pi\) | |||||||
\(618\) | −59.3503 | −2.38742 | ||||||||
\(619\) | 42.7451 | 1.71807 | 0.859035 | − | 0.511916i | \(-0.171064\pi\) | ||||
0.859035 | + | 0.511916i | \(0.171064\pi\) | |||||||
\(620\) | 42.6145 | 1.71144 | ||||||||
\(621\) | 12.8402 | 0.515261 | ||||||||
\(622\) | −2.09576 | −0.0840325 | ||||||||
\(623\) | −24.2968 | −0.973430 | ||||||||
\(624\) | 16.9160 | 0.677182 | ||||||||
\(625\) | −5.32077 | −0.212831 | ||||||||
\(626\) | −14.4147 | −0.576127 | ||||||||
\(627\) | −3.76400 | −0.150320 | ||||||||
\(628\) | −8.37981 | −0.334391 | ||||||||
\(629\) | −1.77681 | −0.0708462 | ||||||||
\(630\) | −15.2418 | −0.607248 | ||||||||
\(631\) | 43.0293 | 1.71297 | 0.856485 | − | 0.516172i | \(-0.172643\pi\) | ||||
0.856485 | + | 0.516172i | \(0.172643\pi\) | |||||||
\(632\) | −64.5109 | −2.56611 | ||||||||
\(633\) | −19.1904 | −0.762750 | ||||||||
\(634\) | −46.3730 | −1.84171 | ||||||||
\(635\) | 5.42986 | 0.215477 | ||||||||
\(636\) | 109.359 | 4.33636 | ||||||||
\(637\) | −2.80492 | −0.111135 | ||||||||
\(638\) | 1.88179 | 0.0745009 | ||||||||
\(639\) | 21.5434 | 0.852246 | ||||||||
\(640\) | −30.9649 | −1.22400 | ||||||||
\(641\) | 22.7599 | 0.898961 | 0.449480 | − | 0.893290i | \(-0.351609\pi\) | ||||
0.449480 | + | 0.893290i | \(0.351609\pi\) | |||||||
\(642\) | −14.9252 | −0.589051 | ||||||||
\(643\) | 46.8753 | 1.84858 | 0.924290 | − | 0.381690i | \(-0.124658\pi\) | ||||
0.924290 | + | 0.381690i | \(0.124658\pi\) | |||||||
\(644\) | 42.6127 | 1.67917 | ||||||||
\(645\) | 18.5212 | 0.729273 | ||||||||
\(646\) | −12.7894 | −0.503193 | ||||||||
\(647\) | 3.43619 | 0.135091 | 0.0675453 | − | 0.997716i | \(-0.478483\pi\) | ||||
0.0675453 | + | 0.997716i | \(0.478483\pi\) | |||||||
\(648\) | 53.3888 | 2.09731 | ||||||||
\(649\) | −2.41841 | −0.0949308 | ||||||||
\(650\) | 13.3045 | 0.521846 | ||||||||
\(651\) | 35.8326 | 1.40439 | ||||||||
\(652\) | 17.9066 | 0.701276 | ||||||||
\(653\) | −25.9230 | −1.01445 | −0.507223 | − | 0.861815i | \(-0.669328\pi\) | ||||
−0.507223 | + | 0.861815i | \(0.669328\pi\) | |||||||
\(654\) | −30.2638 | −1.18341 | ||||||||
\(655\) | 26.8376 | 1.04863 | ||||||||
\(656\) | 38.5622 | 1.50560 | ||||||||
\(657\) | 2.59480 | 0.101233 | ||||||||
\(658\) | −61.1607 | −2.38429 | ||||||||
\(659\) | −7.01835 | −0.273396 | −0.136698 | − | 0.990613i | \(-0.543649\pi\) | ||||
−0.136698 | + | 0.990613i | \(0.543649\pi\) | |||||||
\(660\) | 4.40264 | 0.171372 | ||||||||
\(661\) | 42.6116 | 1.65740 | 0.828700 | − | 0.559693i | \(-0.189081\pi\) | ||||
0.828700 | + | 0.559693i | \(0.189081\pi\) | |||||||
\(662\) | 26.3205 | 1.02298 | ||||||||
\(663\) | 4.55702 | 0.176980 | ||||||||
\(664\) | −26.0774 | −1.01200 | ||||||||
\(665\) | 19.3653 | 0.750955 | ||||||||
\(666\) | 7.33140 | 0.284086 | ||||||||
\(667\) | −10.5409 | −0.408147 | ||||||||
\(668\) | 24.4897 | 0.947536 | ||||||||
\(669\) | 38.6133 | 1.49288 | ||||||||
\(670\) | −26.9455 | −1.04099 | ||||||||
\(671\) | −1.61349 | −0.0622882 | ||||||||
\(672\) | −2.40471 | −0.0927636 | ||||||||
\(673\) | −19.6109 | −0.755946 | −0.377973 | − | 0.925817i | \(-0.623379\pi\) | ||||
−0.377973 | + | 0.925817i | \(0.623379\pi\) | |||||||
\(674\) | 4.28318 | 0.164982 | ||||||||
\(675\) | 7.34729 | 0.282797 | ||||||||
\(676\) | −33.8790 | −1.30304 | ||||||||
\(677\) | −37.3753 | −1.43645 | −0.718224 | − | 0.695812i | \(-0.755045\pi\) | ||||
−0.718224 | + | 0.695812i | \(0.755045\pi\) | |||||||
\(678\) | −18.6700 | −0.717016 | ||||||||
\(679\) | 35.1523 | 1.34902 | ||||||||
\(680\) | 7.38813 | 0.283322 | ||||||||
\(681\) | 17.2878 | 0.662469 | ||||||||
\(682\) | −5.62014 | −0.215206 | ||||||||
\(683\) | 31.0519 | 1.18817 | 0.594084 | − | 0.804403i | \(-0.297515\pi\) | ||||
0.594084 | + | 0.804403i | \(0.297515\pi\) | |||||||
\(684\) | 35.0377 | 1.33970 | ||||||||
\(685\) | 13.4575 | 0.514185 | ||||||||
\(686\) | −48.3947 | −1.84772 | ||||||||
\(687\) | 47.5347 | 1.81356 | ||||||||
\(688\) | −20.4558 | −0.779871 | ||||||||
\(689\) | 26.8822 | 1.02413 | ||||||||
\(690\) | −37.1433 | −1.41402 | ||||||||
\(691\) | −37.1209 | −1.41215 | −0.706073 | − | 0.708139i | \(-0.749535\pi\) | ||||
−0.706073 | + | 0.708139i | \(0.749535\pi\) | |||||||
\(692\) | 12.3277 | 0.468629 | ||||||||
\(693\) | 1.33464 | 0.0506989 | ||||||||
\(694\) | −69.3850 | −2.63382 | ||||||||
\(695\) | −13.5843 | −0.515282 | ||||||||
\(696\) | −23.9964 | −0.909582 | ||||||||
\(697\) | 10.3883 | 0.393485 | ||||||||
\(698\) | 26.5960 | 1.00668 | ||||||||
\(699\) | −44.2250 | −1.67274 | ||||||||
\(700\) | 24.3833 | 0.921603 | ||||||||
\(701\) | 50.5494 | 1.90922 | 0.954611 | − | 0.297854i | \(-0.0962709\pi\) | ||||
0.954611 | + | 0.297854i | \(0.0962709\pi\) | |||||||
\(702\) | 14.5489 | 0.549114 | ||||||||
\(703\) | −9.31483 | −0.351316 | ||||||||
\(704\) | 2.83818 | 0.106968 | ||||||||
\(705\) | 35.3960 | 1.33309 | ||||||||
\(706\) | 2.43959 | 0.0918154 | ||||||||
\(707\) | 39.5910 | 1.48897 | ||||||||
\(708\) | 62.4431 | 2.34675 | ||||||||
\(709\) | 1.08277 | 0.0406644 | 0.0203322 | − | 0.999793i | \(-0.493528\pi\) | ||||
0.0203322 | + | 0.999793i | \(0.493528\pi\) | |||||||
\(710\) | 48.2200 | 1.80967 | ||||||||
\(711\) | 22.9164 | 0.859433 | ||||||||
\(712\) | −48.5951 | −1.82118 | ||||||||
\(713\) | 31.4814 | 1.17899 | ||||||||
\(714\) | 12.5787 | 0.470746 | ||||||||
\(715\) | 1.08224 | 0.0404735 | ||||||||
\(716\) | 76.6272 | 2.86369 | ||||||||
\(717\) | −28.0061 | −1.04591 | ||||||||
\(718\) | −80.8901 | −3.01879 | ||||||||
\(719\) | −51.0688 | −1.90454 | −0.952272 | − | 0.305250i | \(-0.901260\pi\) | ||||
−0.952272 | + | 0.305250i | \(0.901260\pi\) | |||||||
\(720\) | −9.74237 | −0.363077 | ||||||||
\(721\) | −26.7379 | −0.995772 | ||||||||
\(722\) | −20.6954 | −0.770202 | ||||||||
\(723\) | −3.29932 | −0.122703 | ||||||||
\(724\) | 34.8731 | 1.29605 | ||||||||
\(725\) | −6.03161 | −0.224008 | ||||||||
\(726\) | 57.5437 | 2.13565 | ||||||||
\(727\) | 30.7699 | 1.14119 | 0.570596 | − | 0.821231i | \(-0.306712\pi\) | ||||
0.570596 | + | 0.821231i | \(0.306712\pi\) | |||||||
\(728\) | 23.8461 | 0.883794 | ||||||||
\(729\) | −0.547221 | −0.0202674 | ||||||||
\(730\) | 5.80785 | 0.214958 | ||||||||
\(731\) | −5.51062 | −0.203818 | ||||||||
\(732\) | 41.6602 | 1.53981 | ||||||||
\(733\) | 28.6093 | 1.05671 | 0.528355 | − | 0.849023i | \(-0.322809\pi\) | ||||
0.528355 | + | 0.849023i | \(0.322809\pi\) | |||||||
\(734\) | −44.2442 | −1.63308 | ||||||||
\(735\) | 4.48080 | 0.165277 | ||||||||
\(736\) | −2.11270 | −0.0778752 | ||||||||
\(737\) | 2.35947 | 0.0869123 | ||||||||
\(738\) | −42.8637 | −1.57783 | ||||||||
\(739\) | 30.7075 | 1.12959 | 0.564797 | − | 0.825230i | \(-0.308955\pi\) | ||||
0.564797 | + | 0.825230i | \(0.308955\pi\) | |||||||
\(740\) | 10.8953 | 0.400519 | ||||||||
\(741\) | 23.8899 | 0.877618 | ||||||||
\(742\) | 74.2025 | 2.72406 | ||||||||
\(743\) | −45.4232 | −1.66642 | −0.833208 | − | 0.552960i | \(-0.813498\pi\) | ||||
−0.833208 | + | 0.552960i | \(0.813498\pi\) | |||||||
\(744\) | 71.6674 | 2.62746 | ||||||||
\(745\) | −6.96403 | −0.255142 | ||||||||
\(746\) | −67.0716 | −2.45567 | ||||||||
\(747\) | 9.26355 | 0.338936 | ||||||||
\(748\) | −1.30992 | −0.0478953 | ||||||||
\(749\) | −6.72395 | −0.245688 | ||||||||
\(750\) | −62.2511 | −2.27309 | ||||||||
\(751\) | −23.9748 | −0.874851 | −0.437426 | − | 0.899255i | \(-0.644110\pi\) | ||||
−0.437426 | + | 0.899255i | \(0.644110\pi\) | |||||||
\(752\) | −39.0932 | −1.42558 | ||||||||
\(753\) | −9.18160 | −0.334596 | ||||||||
\(754\) | −11.9436 | −0.434962 | ||||||||
\(755\) | 5.93873 | 0.216133 | ||||||||
\(756\) | 26.6640 | 0.969760 | ||||||||
\(757\) | 4.67479 | 0.169908 | 0.0849540 | − | 0.996385i | \(-0.472926\pi\) | ||||
0.0849540 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(758\) | −81.6982 | −2.96741 | ||||||||
\(759\) | 3.25244 | 0.118056 | ||||||||
\(760\) | 38.7318 | 1.40495 | ||||||||
\(761\) | 2.06117 | 0.0747174 | 0.0373587 | − | 0.999302i | \(-0.488106\pi\) | ||||
0.0373587 | + | 0.999302i | \(0.488106\pi\) | |||||||
\(762\) | 18.4898 | 0.669815 | ||||||||
\(763\) | −13.6341 | −0.493589 | ||||||||
\(764\) | 90.0549 | 3.25807 | ||||||||
\(765\) | −2.62451 | −0.0948894 | ||||||||
\(766\) | −19.4873 | −0.704103 | ||||||||
\(767\) | 15.3495 | 0.554239 | ||||||||
\(768\) | −68.3528 | −2.46647 | ||||||||
\(769\) | −35.6933 | −1.28713 | −0.643567 | − | 0.765390i | \(-0.722546\pi\) | ||||
−0.643567 | + | 0.765390i | \(0.722546\pi\) | |||||||
\(770\) | 2.98729 | 0.107654 | ||||||||
\(771\) | −36.6177 | −1.31875 | ||||||||
\(772\) | −42.5469 | −1.53130 | ||||||||
\(773\) | 31.8253 | 1.14468 | 0.572339 | − | 0.820017i | \(-0.306036\pi\) | ||||
0.572339 | + | 0.820017i | \(0.306036\pi\) | |||||||
\(774\) | 22.7376 | 0.817287 | ||||||||
\(775\) | 18.0139 | 0.647079 | ||||||||
\(776\) | 70.3068 | 2.52387 | ||||||||
\(777\) | 9.16136 | 0.328662 | ||||||||
\(778\) | 55.4832 | 1.98917 | ||||||||
\(779\) | 54.4601 | 1.95123 | ||||||||
\(780\) | −27.9433 | −1.00053 | ||||||||
\(781\) | −4.22237 | −0.151088 | ||||||||
\(782\) | 11.0512 | 0.395192 | ||||||||
\(783\) | −6.59577 | −0.235713 | ||||||||
\(784\) | −4.94883 | −0.176744 | ||||||||
\(785\) | 3.29064 | 0.117448 | ||||||||
\(786\) | 91.3877 | 3.25969 | ||||||||
\(787\) | 12.6426 | 0.450660 | 0.225330 | − | 0.974282i | \(-0.427654\pi\) | ||||
0.225330 | + | 0.974282i | \(0.427654\pi\) | |||||||
\(788\) | 60.6988 | 2.16231 | ||||||||
\(789\) | 41.7909 | 1.48780 | ||||||||
\(790\) | 51.2931 | 1.82493 | ||||||||
\(791\) | −8.41101 | −0.299061 | ||||||||
\(792\) | 2.66937 | 0.0948519 | ||||||||
\(793\) | 10.2408 | 0.363660 | ||||||||
\(794\) | −41.8661 | −1.48577 | ||||||||
\(795\) | −42.9438 | −1.52306 | ||||||||
\(796\) | 43.5079 | 1.54210 | ||||||||
\(797\) | 2.72698 | 0.0965946 | 0.0482973 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482973 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(798\) | 65.9430 | 2.33436 | ||||||||
\(799\) | −10.5314 | −0.372573 | ||||||||
\(800\) | −1.20890 | −0.0427412 | ||||||||
\(801\) | 17.2626 | 0.609943 | ||||||||
\(802\) | −26.9427 | −0.951379 | ||||||||
\(803\) | −0.508563 | −0.0179468 | ||||||||
\(804\) | −60.9214 | −2.14853 | ||||||||
\(805\) | −16.7334 | −0.589776 | ||||||||
\(806\) | 35.6707 | 1.25645 | ||||||||
\(807\) | −14.4417 | −0.508371 | ||||||||
\(808\) | 79.1843 | 2.78570 | ||||||||
\(809\) | 6.76133 | 0.237716 | 0.118858 | − | 0.992911i | \(-0.462077\pi\) | ||||
0.118858 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(810\) | −42.4499 | −1.49154 | ||||||||
\(811\) | 20.9359 | 0.735160 | 0.367580 | − | 0.929992i | \(-0.380186\pi\) | ||||
0.367580 | + | 0.929992i | \(0.380186\pi\) | |||||||
\(812\) | −21.8893 | −0.768162 | ||||||||
\(813\) | 57.9119 | 2.03106 | ||||||||
\(814\) | −1.43691 | −0.0503635 | ||||||||
\(815\) | −7.03168 | −0.246309 | ||||||||
\(816\) | 8.04015 | 0.281461 | ||||||||
\(817\) | −28.8891 | −1.01070 | ||||||||
\(818\) | 84.8434 | 2.96648 | ||||||||
\(819\) | −8.47092 | −0.295998 | ||||||||
\(820\) | −63.7004 | −2.22451 | ||||||||
\(821\) | 0.350697 | 0.0122394 | 0.00611970 | − | 0.999981i | \(-0.498052\pi\) | ||||
0.00611970 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(822\) | 45.8257 | 1.59835 | ||||||||
\(823\) | −53.5640 | −1.86712 | −0.933561 | − | 0.358418i | \(-0.883316\pi\) | ||||
−0.933561 | + | 0.358418i | \(0.883316\pi\) | |||||||
\(824\) | −53.4775 | −1.86298 | ||||||||
\(825\) | 1.86107 | 0.0647943 | ||||||||
\(826\) | 42.3690 | 1.47421 | ||||||||
\(827\) | 47.7563 | 1.66065 | 0.830325 | − | 0.557280i | \(-0.188155\pi\) | ||||
0.830325 | + | 0.557280i | \(0.188155\pi\) | |||||||
\(828\) | −30.2758 | −1.05216 | ||||||||
\(829\) | −29.1769 | −1.01335 | −0.506677 | − | 0.862136i | \(-0.669126\pi\) | ||||
−0.506677 | + | 0.862136i | \(0.669126\pi\) | |||||||
\(830\) | 20.7343 | 0.719699 | ||||||||
\(831\) | 12.6281 | 0.438065 | ||||||||
\(832\) | −18.0138 | −0.624516 | ||||||||
\(833\) | −1.33317 | −0.0461917 | ||||||||
\(834\) | −46.2574 | −1.60176 | ||||||||
\(835\) | −9.61678 | −0.332803 | ||||||||
\(836\) | −6.86715 | −0.237505 | ||||||||
\(837\) | 19.6988 | 0.680892 | ||||||||
\(838\) | 6.16672 | 0.213026 | ||||||||
\(839\) | −43.5378 | −1.50309 | −0.751546 | − | 0.659681i | \(-0.770692\pi\) | ||||
−0.751546 | + | 0.659681i | \(0.770692\pi\) | |||||||
\(840\) | −38.0936 | −1.31436 | ||||||||
\(841\) | −23.5853 | −0.813288 | ||||||||
\(842\) | 74.8520 | 2.57957 | ||||||||
\(843\) | 7.88175 | 0.271462 | ||||||||
\(844\) | −35.0116 | −1.20515 | ||||||||
\(845\) | 13.3038 | 0.457665 | ||||||||
\(846\) | 43.4539 | 1.49398 | ||||||||
\(847\) | 25.9240 | 0.890760 | ||||||||
\(848\) | 47.4293 | 1.62873 | ||||||||
\(849\) | −53.9463 | −1.85143 | ||||||||
\(850\) | 6.32361 | 0.216898 | ||||||||
\(851\) | 8.04888 | 0.275912 | ||||||||
\(852\) | 109.021 | 3.73501 | ||||||||
\(853\) | 43.1562 | 1.47764 | 0.738820 | − | 0.673903i | \(-0.235383\pi\) | ||||
0.738820 | + | 0.673903i | \(0.235383\pi\) | |||||||
\(854\) | 28.2674 | 0.967291 | ||||||||
\(855\) | −13.7588 | −0.470542 | ||||||||
\(856\) | −13.4483 | −0.459654 | ||||||||
\(857\) | 32.1463 | 1.09810 | 0.549048 | − | 0.835791i | \(-0.314990\pi\) | ||||
0.549048 | + | 0.835791i | \(0.314990\pi\) | |||||||
\(858\) | 3.68525 | 0.125813 | ||||||||
\(859\) | 32.1165 | 1.09580 | 0.547900 | − | 0.836544i | \(-0.315427\pi\) | ||||
0.547900 | + | 0.836544i | \(0.315427\pi\) | |||||||
\(860\) | 33.7907 | 1.15225 | ||||||||
\(861\) | −53.5627 | −1.82541 | ||||||||
\(862\) | 100.044 | 3.40750 | ||||||||
\(863\) | 9.50292 | 0.323483 | 0.161741 | − | 0.986833i | \(-0.448289\pi\) | ||||
0.161741 | + | 0.986833i | \(0.448289\pi\) | |||||||
\(864\) | −1.32198 | −0.0449746 | ||||||||
\(865\) | −4.84093 | −0.164597 | ||||||||
\(866\) | 46.9793 | 1.59642 | ||||||||
\(867\) | 2.16595 | 0.0735594 | ||||||||
\(868\) | 65.3742 | 2.21894 | ||||||||
\(869\) | −4.49147 | −0.152363 | ||||||||
\(870\) | 19.0797 | 0.646864 | ||||||||
\(871\) | −14.9755 | −0.507424 | ||||||||
\(872\) | −27.2691 | −0.923448 | ||||||||
\(873\) | −24.9753 | −0.845286 | ||||||||
\(874\) | 57.9354 | 1.95969 | ||||||||
\(875\) | −28.0448 | −0.948086 | ||||||||
\(876\) | 13.1310 | 0.443657 | ||||||||
\(877\) | −36.3148 | −1.22626 | −0.613131 | − | 0.789981i | \(-0.710090\pi\) | ||||
−0.613131 | + | 0.789981i | \(0.710090\pi\) | |||||||
\(878\) | 12.9626 | 0.437468 | ||||||||
\(879\) | 52.0481 | 1.75554 | ||||||||
\(880\) | 1.90944 | 0.0643672 | ||||||||
\(881\) | −14.8202 | −0.499307 | −0.249653 | − | 0.968335i | \(-0.580317\pi\) | ||||
−0.249653 | + | 0.968335i | \(0.580317\pi\) | |||||||
\(882\) | 5.50086 | 0.185224 | ||||||||
\(883\) | 45.2575 | 1.52304 | 0.761518 | − | 0.648144i | \(-0.224454\pi\) | ||||
0.761518 | + | 0.648144i | \(0.224454\pi\) | |||||||
\(884\) | 8.31398 | 0.279629 | ||||||||
\(885\) | −24.5206 | −0.824249 | ||||||||
\(886\) | 9.47103 | 0.318185 | ||||||||
\(887\) | 21.1357 | 0.709667 | 0.354834 | − | 0.934929i | \(-0.384538\pi\) | ||||
0.354834 | + | 0.934929i | \(0.384538\pi\) | |||||||
\(888\) | 18.3233 | 0.614889 | ||||||||
\(889\) | 8.32985 | 0.279374 | ||||||||
\(890\) | 38.6383 | 1.29516 | ||||||||
\(891\) | 3.71711 | 0.124528 | ||||||||
\(892\) | 70.4473 | 2.35875 | ||||||||
\(893\) | −55.2100 | −1.84753 | ||||||||
\(894\) | −23.7140 | −0.793115 | ||||||||
\(895\) | −30.0905 | −1.00581 | ||||||||
\(896\) | −47.5028 | −1.58696 | ||||||||
\(897\) | −20.6431 | −0.689253 | ||||||||
\(898\) | −67.9172 | −2.26642 | ||||||||
\(899\) | −16.1714 | −0.539345 | ||||||||
\(900\) | −17.3241 | −0.577469 | ||||||||
\(901\) | 12.7771 | 0.425665 | ||||||||
\(902\) | 8.40100 | 0.279723 | ||||||||
\(903\) | 28.4131 | 0.945528 | ||||||||
\(904\) | −16.8225 | −0.559509 | ||||||||
\(905\) | −13.6942 | −0.455210 | ||||||||
\(906\) | 20.2226 | 0.671852 | ||||||||
\(907\) | −21.3776 | −0.709833 | −0.354917 | − | 0.934898i | \(-0.615491\pi\) | ||||
−0.354917 | + | 0.934898i | \(0.615491\pi\) | |||||||
\(908\) | 31.5404 | 1.04670 | ||||||||
\(909\) | −28.1289 | −0.932977 | ||||||||
\(910\) | −18.9602 | −0.628524 | ||||||||
\(911\) | 32.7938 | 1.08651 | 0.543254 | − | 0.839569i | \(-0.317192\pi\) | ||||
0.543254 | + | 0.839569i | \(0.317192\pi\) | |||||||
\(912\) | 42.1499 | 1.39572 | ||||||||
\(913\) | −1.81559 | −0.0600874 | ||||||||
\(914\) | −19.2408 | −0.636428 | ||||||||
\(915\) | −16.3594 | −0.540825 | ||||||||
\(916\) | 86.7238 | 2.86543 | ||||||||
\(917\) | 41.1711 | 1.35959 | ||||||||
\(918\) | 6.91508 | 0.228232 | ||||||||
\(919\) | −40.7384 | −1.34383 | −0.671917 | − | 0.740626i | \(-0.734529\pi\) | ||||
−0.671917 | + | 0.740626i | \(0.734529\pi\) | |||||||
\(920\) | −33.4679 | −1.10340 | ||||||||
\(921\) | −3.43553 | −0.113205 | ||||||||
\(922\) | −97.8747 | −3.22333 | ||||||||
\(923\) | 26.7992 | 0.882107 | ||||||||
\(924\) | 6.75401 | 0.222190 | ||||||||
\(925\) | 4.60564 | 0.151432 | ||||||||
\(926\) | −47.0318 | −1.54556 | ||||||||
\(927\) | 18.9970 | 0.623943 | ||||||||
\(928\) | 1.08525 | 0.0356251 | ||||||||
\(929\) | 36.9734 | 1.21306 | 0.606529 | − | 0.795061i | \(-0.292561\pi\) | ||||
0.606529 | + | 0.795061i | \(0.292561\pi\) | |||||||
\(930\) | −56.9833 | −1.86856 | ||||||||
\(931\) | −6.98907 | −0.229057 | ||||||||
\(932\) | −80.6855 | −2.64294 | ||||||||
\(933\) | 1.86068 | 0.0609160 | ||||||||
\(934\) | −94.9845 | −3.10799 | ||||||||
\(935\) | 0.514387 | 0.0168222 | ||||||||
\(936\) | −16.9424 | −0.553778 | ||||||||
\(937\) | −38.3520 | −1.25290 | −0.626452 | − | 0.779460i | \(-0.715494\pi\) | ||||
−0.626452 | + | 0.779460i | \(0.715494\pi\) | |||||||
\(938\) | −41.3366 | −1.34969 | ||||||||
\(939\) | 12.7978 | 0.417640 | ||||||||
\(940\) | 64.5775 | 2.10629 | ||||||||
\(941\) | −16.1699 | −0.527123 | −0.263561 | − | 0.964643i | \(-0.584897\pi\) | ||||
−0.263561 | + | 0.964643i | \(0.584897\pi\) | |||||||
\(942\) | 11.2053 | 0.365089 | ||||||||
\(943\) | −47.0586 | −1.53244 | ||||||||
\(944\) | 27.0818 | 0.881437 | ||||||||
\(945\) | −10.4706 | −0.340608 | ||||||||
\(946\) | −4.45643 | −0.144891 | ||||||||
\(947\) | 40.4147 | 1.31330 | 0.656650 | − | 0.754195i | \(-0.271973\pi\) | ||||
0.656650 | + | 0.754195i | \(0.271973\pi\) | |||||||
\(948\) | 115.969 | 3.76651 | ||||||||
\(949\) | 3.22782 | 0.104780 | ||||||||
\(950\) | 33.1511 | 1.07556 | ||||||||
\(951\) | 41.1714 | 1.33507 | ||||||||
\(952\) | 11.3340 | 0.367337 | ||||||||
\(953\) | 43.5794 | 1.41167 | 0.705837 | − | 0.708374i | \(-0.250571\pi\) | ||||
0.705837 | + | 0.708374i | \(0.250571\pi\) | |||||||
\(954\) | −52.7200 | −1.70687 | ||||||||
\(955\) | −35.3633 | −1.14433 | ||||||||
\(956\) | −51.0952 | −1.65254 | ||||||||
\(957\) | −1.67071 | −0.0540065 | ||||||||
\(958\) | −53.8379 | −1.73942 | ||||||||
\(959\) | 20.6449 | 0.666660 | ||||||||
\(960\) | 28.7767 | 0.928764 | ||||||||
\(961\) | 17.2972 | 0.557974 | ||||||||
\(962\) | 9.11997 | 0.294040 | ||||||||
\(963\) | 4.77729 | 0.153946 | ||||||||
\(964\) | −6.01938 | −0.193871 | ||||||||
\(965\) | 16.7076 | 0.537837 | ||||||||
\(966\) | −56.9808 | −1.83333 | ||||||||
\(967\) | 23.2942 | 0.749092 | 0.374546 | − | 0.927208i | \(-0.377799\pi\) | ||||
0.374546 | + | 0.927208i | \(0.377799\pi\) | |||||||
\(968\) | 51.8496 | 1.66651 | ||||||||
\(969\) | 11.3548 | 0.364770 | ||||||||
\(970\) | −55.9015 | −1.79489 | ||||||||
\(971\) | 49.7542 | 1.59669 | 0.798343 | − | 0.602202i | \(-0.205710\pi\) | ||||
0.798343 | + | 0.602202i | \(0.205710\pi\) | |||||||
\(972\) | −62.3726 | −2.00060 | ||||||||
\(973\) | −20.8394 | −0.668081 | ||||||||
\(974\) | 28.1925 | 0.903345 | ||||||||
\(975\) | −11.8121 | −0.378292 | ||||||||
\(976\) | 18.0682 | 0.578349 | ||||||||
\(977\) | −45.3176 | −1.44984 | −0.724919 | − | 0.688834i | \(-0.758123\pi\) | ||||
−0.724919 | + | 0.688834i | \(0.758123\pi\) | |||||||
\(978\) | −23.9443 | −0.765656 | ||||||||
\(979\) | −3.38335 | −0.108132 | ||||||||
\(980\) | 8.17491 | 0.261138 | ||||||||
\(981\) | 9.68689 | 0.309279 | ||||||||
\(982\) | 52.6949 | 1.68156 | ||||||||
\(983\) | 11.2505 | 0.358836 | 0.179418 | − | 0.983773i | \(-0.442579\pi\) | ||||
0.179418 | + | 0.983773i | \(0.442579\pi\) | |||||||
\(984\) | −107.129 | −3.41514 | ||||||||
\(985\) | −23.8356 | −0.759466 | ||||||||
\(986\) | −5.67680 | −0.180786 | ||||||||
\(987\) | 54.3003 | 1.72840 | ||||||||
\(988\) | 43.5855 | 1.38664 | ||||||||
\(989\) | 24.9628 | 0.793772 | ||||||||
\(990\) | −2.12244 | −0.0674554 | ||||||||
\(991\) | −26.8400 | −0.852602 | −0.426301 | − | 0.904581i | \(-0.640184\pi\) | ||||
−0.426301 | + | 0.904581i | \(0.640184\pi\) | |||||||
\(992\) | −3.24120 | −0.102908 | ||||||||
\(993\) | −23.3682 | −0.741567 | ||||||||
\(994\) | 73.9735 | 2.34630 | ||||||||
\(995\) | −17.0850 | −0.541630 | ||||||||
\(996\) | 46.8785 | 1.48540 | ||||||||
\(997\) | 18.6420 | 0.590398 | 0.295199 | − | 0.955436i | \(-0.404614\pi\) | ||||
0.295199 | + | 0.955436i | \(0.404614\pi\) | |||||||
\(998\) | −44.3025 | −1.40237 | ||||||||
\(999\) | 5.03642 | 0.159345 |
(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 | 6001.2.a.d.1.11 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.11 | ✓ | 121 | 1.1 | even | 1 | trivial |