Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33180 | −1.64883 | −0.824414 | − | 0.565987i | \(-0.808495\pi\) | ||||
−0.824414 | + | 0.565987i | \(0.808495\pi\) | |||||||
\(3\) | −3.18012 | −1.83604 | −0.918022 | − | 0.396530i | \(-0.870214\pi\) | ||||
−0.918022 | + | 0.396530i | \(0.870214\pi\) | |||||||
\(4\) | 3.43727 | 1.71863 | ||||||||
\(5\) | 0.827568 | 0.370099 | 0.185050 | − | 0.982729i | \(-0.440755\pi\) | ||||
0.185050 | + | 0.982729i | \(0.440755\pi\) | |||||||
\(6\) | 7.41539 | 3.02732 | ||||||||
\(7\) | −0.00201560 | −0.000761824 0 | −0.000380912 | − | 1.00000i | \(-0.500121\pi\) | ||||
−0.000380912 | 1.00000i | \(0.500121\pi\) | ||||||||
\(8\) | −3.35142 | −1.18490 | ||||||||
\(9\) | 7.11317 | 2.37106 | ||||||||
\(10\) | −1.92972 | −0.610230 | ||||||||
\(11\) | −4.05689 | −1.22320 | −0.611600 | − | 0.791167i | \(-0.709474\pi\) | ||||
−0.611600 | + | 0.791167i | \(0.709474\pi\) | |||||||
\(12\) | −10.9309 | −3.15549 | ||||||||
\(13\) | −2.74850 | −0.762298 | −0.381149 | − | 0.924514i | \(-0.624471\pi\) | ||||
−0.381149 | + | 0.924514i | \(0.624471\pi\) | |||||||
\(14\) | 0.00469996 | 0.00125612 | ||||||||
\(15\) | −2.63176 | −0.679519 | ||||||||
\(16\) | 0.940277 | 0.235069 | ||||||||
\(17\) | −4.33812 | −1.05215 | −0.526074 | − | 0.850439i | \(-0.676336\pi\) | ||||
−0.526074 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(18\) | −16.5865 | −3.90946 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.84457 | 0.636066 | ||||||||
\(21\) | 0.00640985 | 0.00139874 | ||||||||
\(22\) | 9.45985 | 2.01685 | ||||||||
\(23\) | 1.63671 | 0.341277 | 0.170639 | − | 0.985334i | \(-0.445417\pi\) | ||||
0.170639 | + | 0.985334i | \(0.445417\pi\) | |||||||
\(24\) | 10.6579 | 2.17554 | ||||||||
\(25\) | −4.31513 | −0.863026 | ||||||||
\(26\) | 6.40895 | 1.25690 | ||||||||
\(27\) | −13.0804 | −2.51732 | ||||||||
\(28\) | −0.00692815 | −0.00130930 | ||||||||
\(29\) | 8.93765 | 1.65968 | 0.829840 | − | 0.558001i | \(-0.188432\pi\) | ||||
0.829840 | + | 0.558001i | \(0.188432\pi\) | |||||||
\(30\) | 6.13674 | 1.12041 | ||||||||
\(31\) | 8.03527 | 1.44318 | 0.721588 | − | 0.692322i | \(-0.243412\pi\) | ||||
0.721588 | + | 0.692322i | \(0.243412\pi\) | |||||||
\(32\) | 4.51030 | 0.797315 | ||||||||
\(33\) | 12.9014 | 2.24585 | ||||||||
\(34\) | 10.1156 | 1.73481 | ||||||||
\(35\) | −0.00166804 | −0.000281951 0 | ||||||||
\(36\) | 24.4499 | 4.07498 | ||||||||
\(37\) | −2.00336 | −0.329350 | −0.164675 | − | 0.986348i | \(-0.552657\pi\) | ||||
−0.164675 | + | 0.986348i | \(0.552657\pi\) | |||||||
\(38\) | 2.33180 | 0.378267 | ||||||||
\(39\) | 8.74057 | 1.39961 | ||||||||
\(40\) | −2.77352 | −0.438532 | ||||||||
\(41\) | 2.15390 | 0.336383 | 0.168191 | − | 0.985754i | \(-0.446207\pi\) | ||||
0.168191 | + | 0.985754i | \(0.446207\pi\) | |||||||
\(42\) | −0.0149464 | −0.00230629 | ||||||||
\(43\) | 4.53692 | 0.691875 | 0.345937 | − | 0.938258i | \(-0.387561\pi\) | ||||
0.345937 | + | 0.938258i | \(0.387561\pi\) | |||||||
\(44\) | −13.9446 | −2.10223 | ||||||||
\(45\) | 5.88663 | 0.877527 | ||||||||
\(46\) | −3.81647 | −0.562707 | ||||||||
\(47\) | −1.81610 | −0.264906 | −0.132453 | − | 0.991189i | \(-0.542285\pi\) | ||||
−0.132453 | + | 0.991189i | \(0.542285\pi\) | |||||||
\(48\) | −2.99019 | −0.431597 | ||||||||
\(49\) | −7.00000 | −0.999999 | ||||||||
\(50\) | 10.0620 | 1.42298 | ||||||||
\(51\) | 13.7957 | 1.93179 | ||||||||
\(52\) | −9.44734 | −1.31011 | ||||||||
\(53\) | −9.98836 | −1.37201 | −0.686003 | − | 0.727599i | \(-0.740636\pi\) | ||||
−0.686003 | + | 0.727599i | \(0.740636\pi\) | |||||||
\(54\) | 30.5008 | 4.15063 | ||||||||
\(55\) | −3.35735 | −0.452706 | ||||||||
\(56\) | 0.00675511 | 0.000902689 0 | ||||||||
\(57\) | 3.18012 | 0.421217 | ||||||||
\(58\) | −20.8408 | −2.73653 | ||||||||
\(59\) | 1.65878 | 0.215955 | 0.107978 | − | 0.994153i | \(-0.465563\pi\) | ||||
0.107978 | + | 0.994153i | \(0.465563\pi\) | |||||||
\(60\) | −9.04608 | −1.16784 | ||||||||
\(61\) | −5.47696 | −0.701253 | −0.350627 | − | 0.936515i | \(-0.614031\pi\) | ||||
−0.350627 | + | 0.936515i | \(0.614031\pi\) | |||||||
\(62\) | −18.7366 | −2.37955 | ||||||||
\(63\) | −0.0143373 | −0.00180633 | ||||||||
\(64\) | −12.3976 | −1.54971 | ||||||||
\(65\) | −2.27457 | −0.282126 | ||||||||
\(66\) | −30.0835 | −3.70302 | ||||||||
\(67\) | 10.1927 | 1.24524 | 0.622618 | − | 0.782526i | \(-0.286069\pi\) | ||||
0.622618 | + | 0.782526i | \(0.286069\pi\) | |||||||
\(68\) | −14.9113 | −1.80826 | ||||||||
\(69\) | −5.20493 | −0.626600 | ||||||||
\(70\) | 0.00388954 | 0.000464888 0 | ||||||||
\(71\) | 10.4802 | 1.24377 | 0.621885 | − | 0.783108i | \(-0.286367\pi\) | ||||
0.621885 | + | 0.783108i | \(0.286367\pi\) | |||||||
\(72\) | −23.8392 | −2.80947 | ||||||||
\(73\) | −0.992383 | −0.116150 | −0.0580748 | − | 0.998312i | \(-0.518496\pi\) | ||||
−0.0580748 | + | 0.998312i | \(0.518496\pi\) | |||||||
\(74\) | 4.67142 | 0.543041 | ||||||||
\(75\) | 13.7226 | 1.58455 | ||||||||
\(76\) | −3.43727 | −0.394282 | ||||||||
\(77\) | 0.00817707 | 0.000931863 0 | ||||||||
\(78\) | −20.3812 | −2.30772 | ||||||||
\(79\) | −0.206703 | −0.0232559 | −0.0116280 | − | 0.999932i | \(-0.503701\pi\) | ||||
−0.0116280 | + | 0.999932i | \(0.503701\pi\) | |||||||
\(80\) | 0.778143 | 0.0869990 | ||||||||
\(81\) | 20.2577 | 2.25085 | ||||||||
\(82\) | −5.02245 | −0.554637 | ||||||||
\(83\) | −5.35096 | −0.587344 | −0.293672 | − | 0.955906i | \(-0.594877\pi\) | ||||
−0.293672 | + | 0.955906i | \(0.594877\pi\) | |||||||
\(84\) | 0.0220324 | 0.00240393 | ||||||||
\(85\) | −3.59008 | −0.389399 | ||||||||
\(86\) | −10.5792 | −1.14078 | ||||||||
\(87\) | −28.4228 | −3.04725 | ||||||||
\(88\) | 13.5963 | 1.44937 | ||||||||
\(89\) | 8.77864 | 0.930534 | 0.465267 | − | 0.885170i | \(-0.345958\pi\) | ||||
0.465267 | + | 0.885170i | \(0.345958\pi\) | |||||||
\(90\) | −13.7264 | −1.44689 | ||||||||
\(91\) | 0.00553988 | 0.000580737 0 | ||||||||
\(92\) | 5.62580 | 0.586530 | ||||||||
\(93\) | −25.5531 | −2.64974 | ||||||||
\(94\) | 4.23478 | 0.436784 | ||||||||
\(95\) | −0.827568 | −0.0849066 | ||||||||
\(96\) | −14.3433 | −1.46391 | ||||||||
\(97\) | −7.70688 | −0.782515 | −0.391258 | − | 0.920281i | \(-0.627960\pi\) | ||||
−0.391258 | + | 0.920281i | \(0.627960\pi\) | |||||||
\(98\) | 16.3226 | 1.64883 | ||||||||
\(99\) | −28.8574 | −2.90028 | ||||||||
\(100\) | −14.8323 | −1.48323 | ||||||||
\(101\) | 0.582809 | 0.0579917 | 0.0289958 | − | 0.999580i | \(-0.490769\pi\) | ||||
0.0289958 | + | 0.999580i | \(0.490769\pi\) | |||||||
\(102\) | −32.1688 | −3.18519 | ||||||||
\(103\) | −1.54942 | −0.152669 | −0.0763344 | − | 0.997082i | \(-0.524322\pi\) | ||||
−0.0763344 | + | 0.997082i | \(0.524322\pi\) | |||||||
\(104\) | 9.21137 | 0.903250 | ||||||||
\(105\) | 0.00530458 | 0.000517674 0 | ||||||||
\(106\) | 23.2908 | 2.26220 | ||||||||
\(107\) | 4.47606 | 0.432717 | 0.216358 | − | 0.976314i | \(-0.430582\pi\) | ||||
0.216358 | + | 0.976314i | \(0.430582\pi\) | |||||||
\(108\) | −44.9608 | −4.32635 | ||||||||
\(109\) | −1.62513 | −0.155660 | −0.0778298 | − | 0.996967i | \(-0.524799\pi\) | ||||
−0.0778298 | + | 0.996967i | \(0.524799\pi\) | |||||||
\(110\) | 7.82866 | 0.746434 | ||||||||
\(111\) | 6.37092 | 0.604701 | ||||||||
\(112\) | −0.00189522 | −0.000179081 0 | ||||||||
\(113\) | −2.81778 | −0.265075 | −0.132537 | − | 0.991178i | \(-0.542312\pi\) | ||||
−0.132537 | + | 0.991178i | \(0.542312\pi\) | |||||||
\(114\) | −7.41539 | −0.694515 | ||||||||
\(115\) | 1.35449 | 0.126306 | ||||||||
\(116\) | 30.7211 | 2.85238 | ||||||||
\(117\) | −19.5506 | −1.80745 | ||||||||
\(118\) | −3.86794 | −0.356073 | ||||||||
\(119\) | 0.00874390 | 0.000801552 0 | ||||||||
\(120\) | 8.82014 | 0.805165 | ||||||||
\(121\) | 5.45839 | 0.496217 | ||||||||
\(122\) | 12.7712 | 1.15625 | ||||||||
\(123\) | −6.84966 | −0.617613 | ||||||||
\(124\) | 27.6194 | 2.48029 | ||||||||
\(125\) | −7.70890 | −0.689505 | ||||||||
\(126\) | 0.0334316 | 0.00297833 | ||||||||
\(127\) | 0.470587 | 0.0417578 | 0.0208789 | − | 0.999782i | \(-0.493354\pi\) | ||||
0.0208789 | + | 0.999782i | \(0.493354\pi\) | |||||||
\(128\) | 19.8882 | 1.75788 | ||||||||
\(129\) | −14.4280 | −1.27031 | ||||||||
\(130\) | 5.30384 | 0.465177 | ||||||||
\(131\) | 9.27777 | 0.810602 | 0.405301 | − | 0.914183i | \(-0.367167\pi\) | ||||
0.405301 | + | 0.914183i | \(0.367167\pi\) | |||||||
\(132\) | 44.3456 | 3.85979 | ||||||||
\(133\) | 0.00201560 | 0.000174775 0 | ||||||||
\(134\) | −23.7673 | −2.05318 | ||||||||
\(135\) | −10.8249 | −0.931659 | ||||||||
\(136\) | 14.5388 | 1.24669 | ||||||||
\(137\) | −2.33737 | −0.199695 | −0.0998474 | − | 0.995003i | \(-0.531835\pi\) | ||||
−0.0998474 | + | 0.995003i | \(0.531835\pi\) | |||||||
\(138\) | 12.1368 | 1.03315 | ||||||||
\(139\) | 10.6382 | 0.902317 | 0.451158 | − | 0.892444i | \(-0.351011\pi\) | ||||
0.451158 | + | 0.892444i | \(0.351011\pi\) | |||||||
\(140\) | −0.00573351 | −0.000484570 0 | ||||||||
\(141\) | 5.77542 | 0.486378 | ||||||||
\(142\) | −24.4377 | −2.05076 | ||||||||
\(143\) | 11.1504 | 0.932442 | ||||||||
\(144\) | 6.68835 | 0.557362 | ||||||||
\(145\) | 7.39651 | 0.614247 | ||||||||
\(146\) | 2.31403 | 0.191511 | ||||||||
\(147\) | 22.2608 | 1.83604 | ||||||||
\(148\) | −6.88607 | −0.566032 | ||||||||
\(149\) | 18.5949 | 1.52335 | 0.761675 | − | 0.647959i | \(-0.224377\pi\) | ||||
0.761675 | + | 0.647959i | \(0.224377\pi\) | |||||||
\(150\) | −31.9984 | −2.61266 | ||||||||
\(151\) | −8.14825 | −0.663095 | −0.331548 | − | 0.943438i | \(-0.607571\pi\) | ||||
−0.331548 | + | 0.943438i | \(0.607571\pi\) | |||||||
\(152\) | 3.35142 | 0.271836 | ||||||||
\(153\) | −30.8577 | −2.49470 | ||||||||
\(154\) | −0.0190672 | −0.00153648 | ||||||||
\(155\) | 6.64973 | 0.534119 | ||||||||
\(156\) | 30.0437 | 2.40542 | ||||||||
\(157\) | 17.9009 | 1.42865 | 0.714324 | − | 0.699815i | \(-0.246734\pi\) | ||||
0.714324 | + | 0.699815i | \(0.246734\pi\) | |||||||
\(158\) | 0.481989 | 0.0383450 | ||||||||
\(159\) | 31.7642 | 2.51906 | ||||||||
\(160\) | 3.73258 | 0.295086 | ||||||||
\(161\) | −0.00329894 | −0.000259993 0 | ||||||||
\(162\) | −47.2367 | −3.71127 | ||||||||
\(163\) | 4.52406 | 0.354352 | 0.177176 | − | 0.984179i | \(-0.443304\pi\) | ||||
0.177176 | + | 0.984179i | \(0.443304\pi\) | |||||||
\(164\) | 7.40353 | 0.578119 | ||||||||
\(165\) | 10.6768 | 0.831187 | ||||||||
\(166\) | 12.4773 | 0.968430 | ||||||||
\(167\) | 9.81727 | 0.759683 | 0.379842 | − | 0.925052i | \(-0.375979\pi\) | ||||
0.379842 | + | 0.925052i | \(0.375979\pi\) | |||||||
\(168\) | −0.0214821 | −0.00165738 | ||||||||
\(169\) | −5.44573 | −0.418902 | ||||||||
\(170\) | 8.37134 | 0.642052 | ||||||||
\(171\) | −7.11317 | −0.543958 | ||||||||
\(172\) | 15.5946 | 1.18908 | ||||||||
\(173\) | 23.5554 | 1.79089 | 0.895443 | − | 0.445175i | \(-0.146859\pi\) | ||||
0.895443 | + | 0.445175i | \(0.146859\pi\) | |||||||
\(174\) | 66.2762 | 5.02438 | ||||||||
\(175\) | 0.00869757 | 0.000657475 0 | ||||||||
\(176\) | −3.81460 | −0.287537 | ||||||||
\(177\) | −5.27513 | −0.396503 | ||||||||
\(178\) | −20.4700 | −1.53429 | ||||||||
\(179\) | 12.4215 | 0.928425 | 0.464213 | − | 0.885724i | \(-0.346337\pi\) | ||||
0.464213 | + | 0.885724i | \(0.346337\pi\) | |||||||
\(180\) | 20.2339 | 1.50815 | ||||||||
\(181\) | 1.65180 | 0.122777 | 0.0613885 | − | 0.998114i | \(-0.480447\pi\) | ||||
0.0613885 | + | 0.998114i | \(0.480447\pi\) | |||||||
\(182\) | −0.0129179 | −0.000957535 0 | ||||||||
\(183\) | 17.4174 | 1.28753 | ||||||||
\(184\) | −5.48529 | −0.404381 | ||||||||
\(185\) | −1.65791 | −0.121892 | ||||||||
\(186\) | 59.5846 | 4.36896 | ||||||||
\(187\) | 17.5993 | 1.28699 | ||||||||
\(188\) | −6.24243 | −0.455276 | ||||||||
\(189\) | 0.0263648 | 0.00191776 | ||||||||
\(190\) | 1.92972 | 0.139996 | ||||||||
\(191\) | −18.9683 | −1.37250 | −0.686248 | − | 0.727368i | \(-0.740743\pi\) | ||||
−0.686248 | + | 0.727368i | \(0.740743\pi\) | |||||||
\(192\) | 39.4260 | 2.84533 | ||||||||
\(193\) | −0.794447 | −0.0571855 | −0.0285928 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285928 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(194\) | 17.9709 | 1.29023 | ||||||||
\(195\) | 7.23341 | 0.517995 | ||||||||
\(196\) | −24.0609 | −1.71863 | ||||||||
\(197\) | −8.99506 | −0.640871 | −0.320436 | − | 0.947270i | \(-0.603829\pi\) | ||||
−0.320436 | + | 0.947270i | \(0.603829\pi\) | |||||||
\(198\) | 67.2895 | 4.78206 | ||||||||
\(199\) | −24.2584 | −1.71964 | −0.859818 | − | 0.510601i | \(-0.829423\pi\) | ||||
−0.859818 | + | 0.510601i | \(0.829423\pi\) | |||||||
\(200\) | 14.4618 | 1.02260 | ||||||||
\(201\) | −32.4140 | −2.28631 | ||||||||
\(202\) | −1.35899 | −0.0956183 | ||||||||
\(203\) | −0.0180147 | −0.00126439 | ||||||||
\(204\) | 47.4196 | 3.32004 | ||||||||
\(205\) | 1.78250 | 0.124495 | ||||||||
\(206\) | 3.61293 | 0.251725 | ||||||||
\(207\) | 11.6422 | 0.809187 | ||||||||
\(208\) | −2.58435 | −0.179193 | ||||||||
\(209\) | 4.05689 | 0.280621 | ||||||||
\(210\) | −0.0123692 | −0.000853556 0 | ||||||||
\(211\) | −7.02109 | −0.483352 | −0.241676 | − | 0.970357i | \(-0.577697\pi\) | ||||
−0.241676 | + | 0.970357i | \(0.577697\pi\) | |||||||
\(212\) | −34.3327 | −2.35798 | ||||||||
\(213\) | −33.3283 | −2.28362 | ||||||||
\(214\) | −10.4372 | −0.713476 | ||||||||
\(215\) | 3.75461 | 0.256062 | ||||||||
\(216\) | 43.8378 | 2.98278 | ||||||||
\(217\) | −0.0161959 | −0.00109945 | ||||||||
\(218\) | 3.78948 | 0.256656 | ||||||||
\(219\) | 3.15590 | 0.213256 | ||||||||
\(220\) | −11.5401 | −0.778035 | ||||||||
\(221\) | 11.9233 | 0.802049 | ||||||||
\(222\) | −14.8557 | −0.997047 | ||||||||
\(223\) | −5.77160 | −0.386495 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(224\) | −0.00909095 | −0.000607414 0 | ||||||||
\(225\) | −30.6943 | −2.04628 | ||||||||
\(226\) | 6.57049 | 0.437062 | ||||||||
\(227\) | 5.43681 | 0.360854 | 0.180427 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180427 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(228\) | 10.9309 | 0.723918 | ||||||||
\(229\) | 21.7057 | 1.43435 | 0.717176 | − | 0.696892i | \(-0.245435\pi\) | ||||
0.717176 | + | 0.696892i | \(0.245435\pi\) | |||||||
\(230\) | −3.15838 | −0.208258 | ||||||||
\(231\) | −0.0260041 | −0.00171094 | ||||||||
\(232\) | −29.9538 | −1.96656 | ||||||||
\(233\) | −10.3642 | −0.678984 | −0.339492 | − | 0.940609i | \(-0.610255\pi\) | ||||
−0.339492 | + | 0.940609i | \(0.610255\pi\) | |||||||
\(234\) | 45.5879 | 2.98017 | ||||||||
\(235\) | −1.50295 | −0.0980415 | ||||||||
\(236\) | 5.70168 | 0.371148 | ||||||||
\(237\) | 0.657341 | 0.0426989 | ||||||||
\(238\) | −0.0203890 | −0.00132162 | ||||||||
\(239\) | 4.02776 | 0.260534 | 0.130267 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130267 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(240\) | −2.47459 | −0.159734 | ||||||||
\(241\) | −30.3531 | −1.95522 | −0.977608 | − | 0.210433i | \(-0.932513\pi\) | ||||
−0.977608 | + | 0.210433i | \(0.932513\pi\) | |||||||
\(242\) | −12.7279 | −0.818177 | ||||||||
\(243\) | −25.1807 | −1.61534 | ||||||||
\(244\) | −18.8258 | −1.20520 | ||||||||
\(245\) | −5.79297 | −0.370099 | ||||||||
\(246\) | 15.9720 | 1.01834 | ||||||||
\(247\) | 2.74850 | 0.174883 | ||||||||
\(248\) | −26.9295 | −1.71003 | ||||||||
\(249\) | 17.0167 | 1.07839 | ||||||||
\(250\) | 17.9756 | 1.13688 | ||||||||
\(251\) | 17.6655 | 1.11504 | 0.557520 | − | 0.830164i | \(-0.311753\pi\) | ||||
0.557520 | + | 0.830164i | \(0.311753\pi\) | |||||||
\(252\) | −0.0492811 | −0.00310442 | ||||||||
\(253\) | −6.63995 | −0.417450 | ||||||||
\(254\) | −1.09731 | −0.0688515 | ||||||||
\(255\) | 11.4169 | 0.714954 | ||||||||
\(256\) | −21.5798 | −1.34874 | ||||||||
\(257\) | −5.52698 | −0.344764 | −0.172382 | − | 0.985030i | \(-0.555146\pi\) | ||||
−0.172382 | + | 0.985030i | \(0.555146\pi\) | |||||||
\(258\) | 33.6431 | 2.09453 | ||||||||
\(259\) | 0.00403796 | 0.000250907 0 | ||||||||
\(260\) | −7.81831 | −0.484871 | ||||||||
\(261\) | 63.5750 | 3.93520 | ||||||||
\(262\) | −21.6339 | −1.33654 | ||||||||
\(263\) | −11.4711 | −0.707341 | −0.353670 | − | 0.935370i | \(-0.615067\pi\) | ||||
−0.353670 | + | 0.935370i | \(0.615067\pi\) | |||||||
\(264\) | −43.2380 | −2.66111 | ||||||||
\(265\) | −8.26604 | −0.507779 | ||||||||
\(266\) | −0.00469996 | −0.000288173 0 | ||||||||
\(267\) | −27.9171 | −1.70850 | ||||||||
\(268\) | 35.0350 | 2.14011 | ||||||||
\(269\) | 24.6020 | 1.50001 | 0.750006 | − | 0.661431i | \(-0.230051\pi\) | ||||
0.750006 | + | 0.661431i | \(0.230051\pi\) | |||||||
\(270\) | 25.2414 | 1.53614 | ||||||||
\(271\) | 8.29400 | 0.503825 | 0.251912 | − | 0.967750i | \(-0.418941\pi\) | ||||
0.251912 | + | 0.967750i | \(0.418941\pi\) | |||||||
\(272\) | −4.07903 | −0.247327 | ||||||||
\(273\) | −0.0176175 | −0.00106626 | ||||||||
\(274\) | 5.45026 | 0.329262 | ||||||||
\(275\) | 17.5060 | 1.05565 | ||||||||
\(276\) | −17.8907 | −1.07690 | ||||||||
\(277\) | −18.4444 | −1.10821 | −0.554107 | − | 0.832445i | \(-0.686940\pi\) | ||||
−0.554107 | + | 0.832445i | \(0.686940\pi\) | |||||||
\(278\) | −24.8060 | −1.48777 | ||||||||
\(279\) | 57.1562 | 3.42185 | ||||||||
\(280\) | 0.00559031 | 0.000334085 0 | ||||||||
\(281\) | −31.9354 | −1.90511 | −0.952553 | − | 0.304373i | \(-0.901553\pi\) | ||||
−0.952553 | + | 0.304373i | \(0.901553\pi\) | |||||||
\(282\) | −13.4671 | −0.801954 | ||||||||
\(283\) | 14.6555 | 0.871181 | 0.435591 | − | 0.900145i | \(-0.356540\pi\) | ||||
0.435591 | + | 0.900145i | \(0.356540\pi\) | |||||||
\(284\) | 36.0232 | 2.13759 | ||||||||
\(285\) | 2.63176 | 0.155892 | ||||||||
\(286\) | −26.0004 | −1.53744 | ||||||||
\(287\) | −0.00434140 | −0.000256264 0 | ||||||||
\(288\) | 32.0825 | 1.89048 | ||||||||
\(289\) | 1.81925 | 0.107014 | ||||||||
\(290\) | −17.2471 | −1.01279 | ||||||||
\(291\) | 24.5088 | 1.43673 | ||||||||
\(292\) | −3.41109 | −0.199619 | ||||||||
\(293\) | 2.12337 | 0.124049 | 0.0620243 | − | 0.998075i | \(-0.480244\pi\) | ||||
0.0620243 | + | 0.998075i | \(0.480244\pi\) | |||||||
\(294\) | −51.9077 | −3.02732 | ||||||||
\(295\) | 1.37275 | 0.0799249 | ||||||||
\(296\) | 6.71408 | 0.390248 | ||||||||
\(297\) | 53.0657 | 3.07918 | ||||||||
\(298\) | −43.3594 | −2.51174 | ||||||||
\(299\) | −4.49849 | −0.260155 | ||||||||
\(300\) | 47.1684 | 2.72327 | ||||||||
\(301\) | −0.00914462 | −0.000527087 0 | ||||||||
\(302\) | 19.0001 | 1.09333 | ||||||||
\(303\) | −1.85340 | −0.106475 | ||||||||
\(304\) | −0.940277 | −0.0539286 | ||||||||
\(305\) | −4.53256 | −0.259533 | ||||||||
\(306\) | 71.9539 | 4.11333 | ||||||||
\(307\) | 5.93479 | 0.338716 | 0.169358 | − | 0.985555i | \(-0.445831\pi\) | ||||
0.169358 | + | 0.985555i | \(0.445831\pi\) | |||||||
\(308\) | 0.0281068 | 0.00160153 | ||||||||
\(309\) | 4.92734 | 0.280306 | ||||||||
\(310\) | −15.5058 | −0.880670 | ||||||||
\(311\) | 32.0456 | 1.81714 | 0.908568 | − | 0.417736i | \(-0.137176\pi\) | ||||
0.908568 | + | 0.417736i | \(0.137176\pi\) | |||||||
\(312\) | −29.2933 | −1.65841 | ||||||||
\(313\) | −2.18698 | −0.123616 | −0.0618078 | − | 0.998088i | \(-0.519687\pi\) | ||||
−0.0618078 | + | 0.998088i | \(0.519687\pi\) | |||||||
\(314\) | −41.7412 | −2.35559 | ||||||||
\(315\) | −0.0118651 | −0.000668521 0 | ||||||||
\(316\) | −0.710494 | −0.0399684 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | −74.0676 | −4.15350 | ||||||||
\(319\) | −36.2591 | −2.03012 | ||||||||
\(320\) | −10.2599 | −0.573545 | ||||||||
\(321\) | −14.2344 | −0.794487 | ||||||||
\(322\) | 0.00769246 | 0.000428684 0 | ||||||||
\(323\) | 4.33812 | 0.241379 | ||||||||
\(324\) | 69.6310 | 3.86839 | ||||||||
\(325\) | 11.8602 | 0.657883 | ||||||||
\(326\) | −10.5492 | −0.584265 | ||||||||
\(327\) | 5.16812 | 0.285798 | ||||||||
\(328\) | −7.21861 | −0.398581 | ||||||||
\(329\) | 0.00366053 | 0.000201812 0 | ||||||||
\(330\) | −24.8961 | −1.37048 | ||||||||
\(331\) | −1.40645 | −0.0773057 | −0.0386528 | − | 0.999253i | \(-0.512307\pi\) | ||||
−0.0386528 | + | 0.999253i | \(0.512307\pi\) | |||||||
\(332\) | −18.3927 | −1.00943 | ||||||||
\(333\) | −14.2502 | −0.780907 | ||||||||
\(334\) | −22.8919 | −1.25259 | ||||||||
\(335\) | 8.43514 | 0.460861 | ||||||||
\(336\) | 0.00602703 | 0.000328801 0 | ||||||||
\(337\) | −5.17619 | −0.281965 | −0.140982 | − | 0.990012i | \(-0.545026\pi\) | ||||
−0.140982 | + | 0.990012i | \(0.545026\pi\) | |||||||
\(338\) | 12.6983 | 0.690698 | ||||||||
\(339\) | 8.96088 | 0.486688 | ||||||||
\(340\) | −12.3401 | −0.669235 | ||||||||
\(341\) | −32.5982 | −1.76529 | ||||||||
\(342\) | 16.5865 | 0.896893 | ||||||||
\(343\) | 0.0282184 | 0.00152365 | ||||||||
\(344\) | −15.2051 | −0.819805 | ||||||||
\(345\) | −4.30743 | −0.231904 | ||||||||
\(346\) | −54.9265 | −2.95286 | ||||||||
\(347\) | −2.52961 | −0.135796 | −0.0678982 | − | 0.997692i | \(-0.521629\pi\) | ||||
−0.0678982 | + | 0.997692i | \(0.521629\pi\) | |||||||
\(348\) | −97.6968 | −5.23710 | ||||||||
\(349\) | −1.63079 | −0.0872939 | −0.0436470 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436470 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(350\) | −0.0202810 | −0.00108406 | ||||||||
\(351\) | 35.9514 | 1.91895 | ||||||||
\(352\) | −18.2978 | −0.975276 | ||||||||
\(353\) | 5.37407 | 0.286033 | 0.143016 | − | 0.989720i | \(-0.454320\pi\) | ||||
0.143016 | + | 0.989720i | \(0.454320\pi\) | |||||||
\(354\) | 12.3005 | 0.653765 | ||||||||
\(355\) | 8.67307 | 0.460319 | ||||||||
\(356\) | 30.1745 | 1.59925 | ||||||||
\(357\) | −0.0278067 | −0.00147168 | ||||||||
\(358\) | −28.9644 | −1.53081 | ||||||||
\(359\) | 33.1690 | 1.75059 | 0.875297 | − | 0.483586i | \(-0.160666\pi\) | ||||
0.875297 | + | 0.483586i | \(0.160666\pi\) | |||||||
\(360\) | −19.7285 | −1.03979 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −3.85165 | −0.202438 | ||||||||
\(363\) | −17.3583 | −0.911077 | ||||||||
\(364\) | 0.0190420 | 0.000998074 0 | ||||||||
\(365\) | −0.821264 | −0.0429869 | ||||||||
\(366\) | −40.6138 | −2.12292 | ||||||||
\(367\) | 7.16564 | 0.374043 | 0.187022 | − | 0.982356i | \(-0.440117\pi\) | ||||
0.187022 | + | 0.982356i | \(0.440117\pi\) | |||||||
\(368\) | 1.53896 | 0.0802237 | ||||||||
\(369\) | 15.3211 | 0.797582 | ||||||||
\(370\) | 3.86591 | 0.200979 | ||||||||
\(371\) | 0.0201325 | 0.00104523 | ||||||||
\(372\) | −87.8329 | −4.55393 | ||||||||
\(373\) | 6.19041 | 0.320527 | 0.160264 | − | 0.987074i | \(-0.448766\pi\) | ||||
0.160264 | + | 0.987074i | \(0.448766\pi\) | |||||||
\(374\) | −41.0379 | −2.12202 | ||||||||
\(375\) | 24.5152 | 1.26596 | ||||||||
\(376\) | 6.08651 | 0.313888 | ||||||||
\(377\) | −24.5652 | −1.26517 | ||||||||
\(378\) | −0.0614773 | −0.00316205 | ||||||||
\(379\) | 2.72449 | 0.139948 | 0.0699738 | − | 0.997549i | \(-0.477708\pi\) | ||||
0.0699738 | + | 0.997549i | \(0.477708\pi\) | |||||||
\(380\) | −2.84457 | −0.145923 | ||||||||
\(381\) | −1.49652 | −0.0766692 | ||||||||
\(382\) | 44.2301 | 2.26301 | ||||||||
\(383\) | −11.8848 | −0.607283 | −0.303642 | − | 0.952786i | \(-0.598203\pi\) | ||||
−0.303642 | + | 0.952786i | \(0.598203\pi\) | |||||||
\(384\) | −63.2468 | −3.22755 | ||||||||
\(385\) | 0.00676708 | 0.000344882 0 | ||||||||
\(386\) | 1.85249 | 0.0942891 | ||||||||
\(387\) | 32.2719 | 1.64047 | ||||||||
\(388\) | −26.4906 | −1.34486 | ||||||||
\(389\) | −0.457178 | −0.0231798 | −0.0115899 | − | 0.999933i | \(-0.503689\pi\) | ||||
−0.0115899 | + | 0.999933i | \(0.503689\pi\) | |||||||
\(390\) | −16.8668 | −0.854086 | ||||||||
\(391\) | −7.10022 | −0.359074 | ||||||||
\(392\) | 23.4599 | 1.18490 | ||||||||
\(393\) | −29.5044 | −1.48830 | ||||||||
\(394\) | 20.9746 | 1.05669 | ||||||||
\(395\) | −0.171061 | −0.00860700 | ||||||||
\(396\) | −99.1905 | −4.98451 | ||||||||
\(397\) | 8.49801 | 0.426503 | 0.213251 | − | 0.976997i | \(-0.431595\pi\) | ||||
0.213251 | + | 0.976997i | \(0.431595\pi\) | |||||||
\(398\) | 56.5657 | 2.83538 | ||||||||
\(399\) | −0.00640985 | −0.000320894 0 | ||||||||
\(400\) | −4.05742 | −0.202871 | ||||||||
\(401\) | 19.1177 | 0.954693 | 0.477347 | − | 0.878715i | \(-0.341599\pi\) | ||||
0.477347 | + | 0.878715i | \(0.341599\pi\) | |||||||
\(402\) | 75.5828 | 3.76973 | ||||||||
\(403\) | −22.0850 | −1.10013 | ||||||||
\(404\) | 2.00327 | 0.0996665 | ||||||||
\(405\) | 16.7646 | 0.833039 | ||||||||
\(406\) | 0.0420066 | 0.00208475 | ||||||||
\(407\) | 8.12741 | 0.402861 | ||||||||
\(408\) | −46.2352 | −2.28898 | ||||||||
\(409\) | −5.95756 | −0.294582 | −0.147291 | − | 0.989093i | \(-0.547055\pi\) | ||||
−0.147291 | + | 0.989093i | \(0.547055\pi\) | |||||||
\(410\) | −4.15642 | −0.205271 | ||||||||
\(411\) | 7.43311 | 0.366648 | ||||||||
\(412\) | −5.32577 | −0.262382 | ||||||||
\(413\) | −0.00334344 | −0.000164520 0 | ||||||||
\(414\) | −27.1472 | −1.33421 | ||||||||
\(415\) | −4.42828 | −0.217376 | ||||||||
\(416\) | −12.3966 | −0.607792 | ||||||||
\(417\) | −33.8306 | −1.65669 | ||||||||
\(418\) | −9.45985 | −0.462696 | ||||||||
\(419\) | 17.8748 | 0.873243 | 0.436621 | − | 0.899645i | \(-0.356175\pi\) | ||||
0.436621 | + | 0.899645i | \(0.356175\pi\) | |||||||
\(420\) | 0.0182333 | 0.000889692 0 | ||||||||
\(421\) | 21.6663 | 1.05595 | 0.527976 | − | 0.849259i | \(-0.322951\pi\) | ||||
0.527976 | + | 0.849259i | \(0.322951\pi\) | |||||||
\(422\) | 16.3717 | 0.796964 | ||||||||
\(423\) | −12.9182 | −0.628106 | ||||||||
\(424\) | 33.4751 | 1.62570 | ||||||||
\(425\) | 18.7195 | 0.908031 | ||||||||
\(426\) | 77.7148 | 3.76529 | ||||||||
\(427\) | 0.0110394 | 0.000534232 0 | ||||||||
\(428\) | 15.3854 | 0.743682 | ||||||||
\(429\) | −35.4596 | −1.71200 | ||||||||
\(430\) | −8.75499 | −0.422203 | ||||||||
\(431\) | −25.6505 | −1.23554 | −0.617770 | − | 0.786359i | \(-0.711964\pi\) | ||||
−0.617770 | + | 0.786359i | \(0.711964\pi\) | |||||||
\(432\) | −12.2992 | −0.591744 | ||||||||
\(433\) | 5.37919 | 0.258508 | 0.129254 | − | 0.991612i | \(-0.458742\pi\) | ||||
0.129254 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(434\) | 0.0377654 | 0.00181280 | ||||||||
\(435\) | −23.5218 | −1.12778 | ||||||||
\(436\) | −5.58602 | −0.267522 | ||||||||
\(437\) | −1.63671 | −0.0782943 | ||||||||
\(438\) | −7.35891 | −0.351622 | ||||||||
\(439\) | 26.6127 | 1.27015 | 0.635077 | − | 0.772449i | \(-0.280968\pi\) | ||||
0.635077 | + | 0.772449i | \(0.280968\pi\) | |||||||
\(440\) | 11.2519 | 0.536413 | ||||||||
\(441\) | −49.7922 | −2.37105 | ||||||||
\(442\) | −27.8027 | −1.32244 | ||||||||
\(443\) | 7.78093 | 0.369683 | 0.184842 | − | 0.982768i | \(-0.440823\pi\) | ||||
0.184842 | + | 0.982768i | \(0.440823\pi\) | |||||||
\(444\) | 21.8985 | 1.03926 | ||||||||
\(445\) | 7.26492 | 0.344390 | ||||||||
\(446\) | 13.4582 | 0.637264 | ||||||||
\(447\) | −59.1339 | −2.79694 | ||||||||
\(448\) | 0.0249887 | 0.00118060 | ||||||||
\(449\) | −6.85465 | −0.323491 | −0.161746 | − | 0.986832i | \(-0.551712\pi\) | ||||
−0.161746 | + | 0.986832i | \(0.551712\pi\) | |||||||
\(450\) | 71.5727 | 3.37397 | ||||||||
\(451\) | −8.73814 | −0.411463 | ||||||||
\(452\) | −9.68547 | −0.455566 | ||||||||
\(453\) | 25.9124 | 1.21747 | ||||||||
\(454\) | −12.6775 | −0.594986 | ||||||||
\(455\) | 0.00458462 | 0.000214930 0 | ||||||||
\(456\) | −10.6579 | −0.499102 | ||||||||
\(457\) | −37.7910 | −1.76779 | −0.883893 | − | 0.467689i | \(-0.845087\pi\) | ||||
−0.883893 | + | 0.467689i | \(0.845087\pi\) | |||||||
\(458\) | −50.6132 | −2.36500 | ||||||||
\(459\) | 56.7442 | 2.64859 | ||||||||
\(460\) | 4.65573 | 0.217075 | ||||||||
\(461\) | −41.0479 | −1.91179 | −0.955896 | − | 0.293706i | \(-0.905111\pi\) | ||||
−0.955896 | + | 0.293706i | \(0.905111\pi\) | |||||||
\(462\) | 0.0606362 | 0.00282105 | ||||||||
\(463\) | 23.5339 | 1.09371 | 0.546857 | − | 0.837226i | \(-0.315824\pi\) | ||||
0.546857 | + | 0.837226i | \(0.315824\pi\) | |||||||
\(464\) | 8.40387 | 0.390140 | ||||||||
\(465\) | −21.1469 | −0.980666 | ||||||||
\(466\) | 24.1673 | 1.11953 | ||||||||
\(467\) | 3.20274 | 0.148205 | 0.0741027 | − | 0.997251i | \(-0.476391\pi\) | ||||
0.0741027 | + | 0.997251i | \(0.476391\pi\) | |||||||
\(468\) | −67.2005 | −3.10635 | ||||||||
\(469\) | −0.0205444 | −0.000948651 0 | ||||||||
\(470\) | 3.50456 | 0.161654 | ||||||||
\(471\) | −56.9270 | −2.62306 | ||||||||
\(472\) | −5.55927 | −0.255886 | ||||||||
\(473\) | −18.4058 | −0.846301 | ||||||||
\(474\) | −1.53278 | −0.0704031 | ||||||||
\(475\) | 4.31513 | 0.197992 | ||||||||
\(476\) | 0.0300551 | 0.00137757 | ||||||||
\(477\) | −71.0489 | −3.25310 | ||||||||
\(478\) | −9.39190 | −0.429576 | ||||||||
\(479\) | 21.0787 | 0.963112 | 0.481556 | − | 0.876415i | \(-0.340072\pi\) | ||||
0.481556 | + | 0.876415i | \(0.340072\pi\) | |||||||
\(480\) | −11.8700 | −0.541791 | ||||||||
\(481\) | 5.50623 | 0.251063 | ||||||||
\(482\) | 70.7773 | 3.22382 | ||||||||
\(483\) | 0.0104910 | 0.000477359 0 | ||||||||
\(484\) | 18.7620 | 0.852816 | ||||||||
\(485\) | −6.37797 | −0.289609 | ||||||||
\(486\) | 58.7162 | 2.66342 | ||||||||
\(487\) | −27.8917 | −1.26389 | −0.631947 | − | 0.775011i | \(-0.717744\pi\) | ||||
−0.631947 | + | 0.775011i | \(0.717744\pi\) | |||||||
\(488\) | 18.3556 | 0.830918 | ||||||||
\(489\) | −14.3871 | −0.650605 | ||||||||
\(490\) | 13.5080 | 0.610230 | ||||||||
\(491\) | 1.94346 | 0.0877072 | 0.0438536 | − | 0.999038i | \(-0.486036\pi\) | ||||
0.0438536 | + | 0.999038i | \(0.486036\pi\) | |||||||
\(492\) | −23.5441 | −1.06145 | ||||||||
\(493\) | −38.7726 | −1.74623 | ||||||||
\(494\) | −6.40895 | −0.288352 | ||||||||
\(495\) | −23.8814 | −1.07339 | ||||||||
\(496\) | 7.55538 | 0.339246 | ||||||||
\(497\) | −0.0211239 | −0.000947535 0 | ||||||||
\(498\) | −39.6795 | −1.77808 | ||||||||
\(499\) | −20.6892 | −0.926178 | −0.463089 | − | 0.886312i | \(-0.653259\pi\) | ||||
−0.463089 | + | 0.886312i | \(0.653259\pi\) | |||||||
\(500\) | −26.4976 | −1.18501 | ||||||||
\(501\) | −31.2201 | −1.39481 | ||||||||
\(502\) | −41.1924 | −1.83851 | ||||||||
\(503\) | 34.6230 | 1.54376 | 0.771882 | − | 0.635765i | \(-0.219315\pi\) | ||||
0.771882 | + | 0.635765i | \(0.219315\pi\) | |||||||
\(504\) | 0.0480502 | 0.00214033 | ||||||||
\(505\) | 0.482314 | 0.0214627 | ||||||||
\(506\) | 15.4830 | 0.688303 | ||||||||
\(507\) | 17.3181 | 0.769123 | ||||||||
\(508\) | 1.61753 | 0.0717664 | ||||||||
\(509\) | 36.8624 | 1.63390 | 0.816949 | − | 0.576709i | \(-0.195663\pi\) | ||||
0.816949 | + | 0.576709i | \(0.195663\pi\) | |||||||
\(510\) | −26.6219 | −1.17884 | ||||||||
\(511\) | 0.00200025 | 8.84856e−5 0 | ||||||||
\(512\) | 10.5434 | 0.465959 | ||||||||
\(513\) | 13.0804 | 0.577513 | ||||||||
\(514\) | 12.8878 | 0.568456 | ||||||||
\(515\) | −1.28225 | −0.0565026 | ||||||||
\(516\) | −49.5928 | −2.18320 | ||||||||
\(517\) | 7.36773 | 0.324033 | ||||||||
\(518\) | −0.00941570 | −0.000413702 0 | ||||||||
\(519\) | −74.9091 | −3.28815 | ||||||||
\(520\) | 7.62303 | 0.334292 | ||||||||
\(521\) | 15.6930 | 0.687521 | 0.343760 | − | 0.939057i | \(-0.388299\pi\) | ||||
0.343760 | + | 0.939057i | \(0.388299\pi\) | |||||||
\(522\) | −148.244 | −6.48846 | ||||||||
\(523\) | 27.1603 | 1.18764 | 0.593819 | − | 0.804599i | \(-0.297620\pi\) | ||||
0.593819 | + | 0.804599i | \(0.297620\pi\) | |||||||
\(524\) | 31.8902 | 1.39313 | ||||||||
\(525\) | −0.0276593 | −0.00120715 | ||||||||
\(526\) | 26.7483 | 1.16628 | ||||||||
\(527\) | −34.8579 | −1.51843 | ||||||||
\(528\) | 12.1309 | 0.527930 | ||||||||
\(529\) | −20.3212 | −0.883530 | ||||||||
\(530\) | 19.2747 | 0.837240 | ||||||||
\(531\) | 11.7992 | 0.512042 | ||||||||
\(532\) | 0.00692815 | 0.000300373 0 | ||||||||
\(533\) | −5.92000 | −0.256424 | ||||||||
\(534\) | 65.0971 | 2.81703 | ||||||||
\(535\) | 3.70424 | 0.160148 | ||||||||
\(536\) | −34.1600 | −1.47549 | ||||||||
\(537\) | −39.5018 | −1.70463 | ||||||||
\(538\) | −57.3669 | −2.47326 | ||||||||
\(539\) | 28.3982 | 1.22320 | ||||||||
\(540\) | −37.2081 | −1.60118 | ||||||||
\(541\) | 9.23382 | 0.396993 | 0.198496 | − | 0.980102i | \(-0.436394\pi\) | ||||
0.198496 | + | 0.980102i | \(0.436394\pi\) | |||||||
\(542\) | −19.3399 | −0.830721 | ||||||||
\(543\) | −5.25291 | −0.225424 | ||||||||
\(544\) | −19.5662 | −0.838894 | ||||||||
\(545\) | −1.34491 | −0.0576095 | ||||||||
\(546\) | 0.0410804 | 0.00175808 | ||||||||
\(547\) | −14.9271 | −0.638238 | −0.319119 | − | 0.947715i | \(-0.603387\pi\) | ||||
−0.319119 | + | 0.947715i | \(0.603387\pi\) | |||||||
\(548\) | −8.03416 | −0.343202 | ||||||||
\(549\) | −38.9586 | −1.66271 | ||||||||
\(550\) | −40.8205 | −1.74059 | ||||||||
\(551\) | −8.93765 | −0.380757 | ||||||||
\(552\) | 17.4439 | 0.742460 | ||||||||
\(553\) | 0.000416631 0 | 1.77169e−5 0 | ||||||||
\(554\) | 43.0085 | 1.82726 | ||||||||
\(555\) | 5.27236 | 0.223799 | ||||||||
\(556\) | 36.5662 | 1.55075 | ||||||||
\(557\) | −30.6559 | −1.29893 | −0.649466 | − | 0.760391i | \(-0.725007\pi\) | ||||
−0.649466 | + | 0.760391i | \(0.725007\pi\) | |||||||
\(558\) | −133.277 | −5.64205 | ||||||||
\(559\) | −12.4698 | −0.527414 | ||||||||
\(560\) | −0.00156842 | −6.62780e−5 0 | ||||||||
\(561\) | −55.9678 | −2.36296 | ||||||||
\(562\) | 74.4668 | 3.14119 | ||||||||
\(563\) | 0.0412890 | 0.00174012 | 0.000870061 | − | 1.00000i | \(-0.499723\pi\) | ||||
0.000870061 | 1.00000i | \(0.499723\pi\) | ||||||||
\(564\) | 19.8517 | 0.835907 | ||||||||
\(565\) | −2.33190 | −0.0981039 | ||||||||
\(566\) | −34.1737 | −1.43643 | ||||||||
\(567\) | −0.0408313 | −0.00171475 | ||||||||
\(568\) | −35.1235 | −1.47375 | ||||||||
\(569\) | −17.0592 | −0.715157 | −0.357579 | − | 0.933883i | \(-0.616398\pi\) | ||||
−0.357579 | + | 0.933883i | \(0.616398\pi\) | |||||||
\(570\) | −6.13674 | −0.257040 | ||||||||
\(571\) | 3.11814 | 0.130490 | 0.0652452 | − | 0.997869i | \(-0.479217\pi\) | ||||
0.0652452 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(572\) | 38.3269 | 1.60253 | ||||||||
\(573\) | 60.3214 | 2.51996 | ||||||||
\(574\) | 0.0101232 | 0.000422536 0 | ||||||||
\(575\) | −7.06261 | −0.294531 | ||||||||
\(576\) | −88.1865 | −3.67444 | ||||||||
\(577\) | −26.2736 | −1.09378 | −0.546891 | − | 0.837204i | \(-0.684189\pi\) | ||||
−0.546891 | + | 0.837204i | \(0.684189\pi\) | |||||||
\(578\) | −4.24211 | −0.176448 | ||||||||
\(579\) | 2.52644 | 0.104995 | ||||||||
\(580\) | 25.4238 | 1.05567 | ||||||||
\(581\) | 0.0107854 | 0.000447453 0 | ||||||||
\(582\) | −57.1495 | −2.36892 | ||||||||
\(583\) | 40.5217 | 1.67824 | ||||||||
\(584\) | 3.32589 | 0.137626 | ||||||||
\(585\) | −16.1794 | −0.668936 | ||||||||
\(586\) | −4.95127 | −0.204535 | ||||||||
\(587\) | 34.4625 | 1.42242 | 0.711211 | − | 0.702979i | \(-0.248147\pi\) | ||||
0.711211 | + | 0.702979i | \(0.248147\pi\) | |||||||
\(588\) | 76.5165 | 3.15549 | ||||||||
\(589\) | −8.03527 | −0.331087 | ||||||||
\(590\) | −3.20098 | −0.131782 | ||||||||
\(591\) | 28.6054 | 1.17667 | ||||||||
\(592\) | −1.88371 | −0.0774200 | ||||||||
\(593\) | −17.0831 | −0.701518 | −0.350759 | − | 0.936466i | \(-0.614076\pi\) | ||||
−0.350759 | + | 0.936466i | \(0.614076\pi\) | |||||||
\(594\) | −123.738 | −5.07705 | ||||||||
\(595\) | 0.00723617 | 0.000296654 0 | ||||||||
\(596\) | 63.9155 | 2.61808 | ||||||||
\(597\) | 77.1448 | 3.15733 | ||||||||
\(598\) | 10.4896 | 0.428950 | ||||||||
\(599\) | −1.59196 | −0.0650456 | −0.0325228 | − | 0.999471i | \(-0.510354\pi\) | ||||
−0.0325228 | + | 0.999471i | \(0.510354\pi\) | |||||||
\(600\) | −45.9903 | −1.87754 | ||||||||
\(601\) | 16.6771 | 0.680274 | 0.340137 | − | 0.940376i | \(-0.389527\pi\) | ||||
0.340137 | + | 0.940376i | \(0.389527\pi\) | |||||||
\(602\) | 0.0213234 | 0.000869076 0 | ||||||||
\(603\) | 72.5024 | 2.95252 | ||||||||
\(604\) | −28.0077 | −1.13962 | ||||||||
\(605\) | 4.51719 | 0.183650 | ||||||||
\(606\) | 4.32176 | 0.175559 | ||||||||
\(607\) | 3.69644 | 0.150034 | 0.0750170 | − | 0.997182i | \(-0.476099\pi\) | ||||
0.0750170 | + | 0.997182i | \(0.476099\pi\) | |||||||
\(608\) | −4.51030 | −0.182917 | ||||||||
\(609\) | 0.0572890 | 0.00232147 | ||||||||
\(610\) | 10.5690 | 0.427926 | ||||||||
\(611\) | 4.99156 | 0.201937 | ||||||||
\(612\) | −106.066 | −4.28748 | ||||||||
\(613\) | −13.8680 | −0.560123 | −0.280062 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280062 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(614\) | −13.8387 | −0.558485 | ||||||||
\(615\) | −5.66856 | −0.228578 | ||||||||
\(616\) | −0.0274048 | −0.00110417 | ||||||||
\(617\) | −36.0640 | −1.45188 | −0.725941 | − | 0.687757i | \(-0.758596\pi\) | ||||
−0.725941 | + | 0.687757i | \(0.758596\pi\) | |||||||
\(618\) | −11.4895 | −0.462177 | ||||||||
\(619\) | −21.5245 | −0.865142 | −0.432571 | − | 0.901600i | \(-0.642394\pi\) | ||||
−0.432571 | + | 0.901600i | \(0.642394\pi\) | |||||||
\(620\) | 22.8569 | 0.917955 | ||||||||
\(621\) | −21.4087 | −0.859103 | ||||||||
\(622\) | −74.7237 | −2.99615 | ||||||||
\(623\) | −0.0176942 | −0.000708904 0 | ||||||||
\(624\) | 8.21856 | 0.329006 | ||||||||
\(625\) | 15.1960 | 0.607841 | ||||||||
\(626\) | 5.09959 | 0.203821 | ||||||||
\(627\) | −12.9014 | −0.515233 | ||||||||
\(628\) | 61.5302 | 2.45532 | ||||||||
\(629\) | 8.69079 | 0.346525 | ||||||||
\(630\) | 0.0276669 | 0.00110228 | ||||||||
\(631\) | −21.9135 | −0.872365 | −0.436182 | − | 0.899858i | \(-0.643670\pi\) | ||||
−0.436182 | + | 0.899858i | \(0.643670\pi\) | |||||||
\(632\) | 0.692748 | 0.0275560 | ||||||||
\(633\) | 22.3279 | 0.887455 | ||||||||
\(634\) | 2.33180 | 0.0926074 | ||||||||
\(635\) | 0.389443 | 0.0154546 | ||||||||
\(636\) | 109.182 | 4.32935 | ||||||||
\(637\) | 19.2395 | 0.762297 | ||||||||
\(638\) | 84.5488 | 3.34732 | ||||||||
\(639\) | 74.5474 | 2.94905 | ||||||||
\(640\) | 16.4588 | 0.650591 | ||||||||
\(641\) | −2.31263 | −0.0913434 | −0.0456717 | − | 0.998957i | \(-0.514543\pi\) | ||||
−0.0456717 | + | 0.998957i | \(0.514543\pi\) | |||||||
\(642\) | 33.1917 | 1.30997 | ||||||||
\(643\) | −43.2236 | −1.70457 | −0.852287 | − | 0.523075i | \(-0.824785\pi\) | ||||
−0.852287 | + | 0.523075i | \(0.824785\pi\) | |||||||
\(644\) | −0.0113394 | −0.000446833 0 | ||||||||
\(645\) | −11.9401 | −0.470142 | ||||||||
\(646\) | −10.1156 | −0.397993 | ||||||||
\(647\) | −16.5179 | −0.649385 | −0.324693 | − | 0.945820i | \(-0.605261\pi\) | ||||
−0.324693 | + | 0.945820i | \(0.605261\pi\) | |||||||
\(648\) | −67.8918 | −2.66704 | ||||||||
\(649\) | −6.72951 | −0.264156 | ||||||||
\(650\) | −27.6554 | −1.08474 | ||||||||
\(651\) | 0.0515048 | 0.00201863 | ||||||||
\(652\) | 15.5504 | 0.609001 | ||||||||
\(653\) | 26.9470 | 1.05452 | 0.527258 | − | 0.849705i | \(-0.323220\pi\) | ||||
0.527258 | + | 0.849705i | \(0.323220\pi\) | |||||||
\(654\) | −12.0510 | −0.471231 | ||||||||
\(655\) | 7.67798 | 0.300004 | ||||||||
\(656\) | 2.02526 | 0.0790732 | ||||||||
\(657\) | −7.05899 | −0.275397 | ||||||||
\(658\) | −0.00853561 | −0.000332753 0 | ||||||||
\(659\) | −14.1584 | −0.551532 | −0.275766 | − | 0.961225i | \(-0.588932\pi\) | ||||
−0.275766 | + | 0.961225i | \(0.588932\pi\) | |||||||
\(660\) | 36.6990 | 1.42851 | ||||||||
\(661\) | −46.0427 | −1.79085 | −0.895426 | − | 0.445210i | \(-0.853129\pi\) | ||||
−0.895426 | + | 0.445210i | \(0.853129\pi\) | |||||||
\(662\) | 3.27956 | 0.127464 | ||||||||
\(663\) | −37.9176 | −1.47260 | ||||||||
\(664\) | 17.9333 | 0.695947 | ||||||||
\(665\) | 0.00166804 | 6.46840e−5 0 | ||||||||
\(666\) | 33.2286 | 1.28758 | ||||||||
\(667\) | 14.6283 | 0.566411 | ||||||||
\(668\) | 33.7446 | 1.30562 | ||||||||
\(669\) | 18.3544 | 0.709622 | ||||||||
\(670\) | −19.6690 | −0.759881 | ||||||||
\(671\) | 22.2195 | 0.857773 | ||||||||
\(672\) | 0.0289103 | 0.00111524 | ||||||||
\(673\) | 28.3368 | 1.09230 | 0.546151 | − | 0.837687i | \(-0.316092\pi\) | ||||
0.546151 | + | 0.837687i | \(0.316092\pi\) | |||||||
\(674\) | 12.0698 | 0.464912 | ||||||||
\(675\) | 56.4435 | 2.17251 | ||||||||
\(676\) | −18.7184 | −0.719940 | ||||||||
\(677\) | −11.3945 | −0.437924 | −0.218962 | − | 0.975733i | \(-0.570267\pi\) | ||||
−0.218962 | + | 0.975733i | \(0.570267\pi\) | |||||||
\(678\) | −20.8949 | −0.802465 | ||||||||
\(679\) | 0.0155340 | 0.000596139 0 | ||||||||
\(680\) | 12.0319 | 0.461401 | ||||||||
\(681\) | −17.2897 | −0.662544 | ||||||||
\(682\) | 76.0124 | 2.91066 | ||||||||
\(683\) | −24.1339 | −0.923460 | −0.461730 | − | 0.887021i | \(-0.652771\pi\) | ||||
−0.461730 | + | 0.887021i | \(0.652771\pi\) | |||||||
\(684\) | −24.4499 | −0.934864 | ||||||||
\(685\) | −1.93433 | −0.0739069 | ||||||||
\(686\) | −0.0657994 | −0.00251223 | ||||||||
\(687\) | −69.0267 | −2.63353 | ||||||||
\(688\) | 4.26597 | 0.162638 | ||||||||
\(689\) | 27.4530 | 1.04588 | ||||||||
\(690\) | 10.0440 | 0.382370 | ||||||||
\(691\) | −22.7535 | −0.865585 | −0.432793 | − | 0.901494i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901494i | \(0.642472\pi\) | |||||||
\(692\) | 80.9664 | 3.07788 | ||||||||
\(693\) | 0.0581649 | 0.00220950 | ||||||||
\(694\) | 5.89853 | 0.223905 | ||||||||
\(695\) | 8.80379 | 0.333947 | ||||||||
\(696\) | 95.2566 | 3.61069 | ||||||||
\(697\) | −9.34386 | −0.353924 | ||||||||
\(698\) | 3.80266 | 0.143933 | ||||||||
\(699\) | 32.9595 | 1.24664 | ||||||||
\(700\) | 0.0298959 | 0.00112996 | ||||||||
\(701\) | 24.6133 | 0.929630 | 0.464815 | − | 0.885408i | \(-0.346121\pi\) | ||||
0.464815 | + | 0.885408i | \(0.346121\pi\) | |||||||
\(702\) | −83.8314 | −3.16401 | ||||||||
\(703\) | 2.00336 | 0.0755580 | ||||||||
\(704\) | 50.2959 | 1.89560 | ||||||||
\(705\) | 4.77955 | 0.180008 | ||||||||
\(706\) | −12.5312 | −0.471619 | ||||||||
\(707\) | −0.00117471 | −4.41795e−5 0 | ||||||||
\(708\) | −18.1320 | −0.681444 | ||||||||
\(709\) | 21.2668 | 0.798692 | 0.399346 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399346 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(710\) | −20.2238 | −0.758987 | ||||||||
\(711\) | −1.47031 | −0.0551411 | ||||||||
\(712\) | −29.4209 | −1.10259 | ||||||||
\(713\) | 13.1514 | 0.492523 | ||||||||
\(714\) | 0.0648394 | 0.00242655 | ||||||||
\(715\) | 9.22770 | 0.345096 | ||||||||
\(716\) | 42.6960 | 1.59562 | ||||||||
\(717\) | −12.8088 | −0.478352 | ||||||||
\(718\) | −77.3434 | −2.88643 | ||||||||
\(719\) | 0.878476 | 0.0327616 | 0.0163808 | − | 0.999866i | \(-0.494786\pi\) | ||||
0.0163808 | + | 0.999866i | \(0.494786\pi\) | |||||||
\(720\) | 5.53506 | 0.206280 | ||||||||
\(721\) | 0.00312301 | 0.000116307 0 | ||||||||
\(722\) | −2.33180 | −0.0867804 | ||||||||
\(723\) | 96.5266 | 3.58986 | ||||||||
\(724\) | 5.67766 | 0.211009 | ||||||||
\(725\) | −38.5671 | −1.43235 | ||||||||
\(726\) | 40.4761 | 1.50221 | ||||||||
\(727\) | −8.41128 | −0.311957 | −0.155979 | − | 0.987760i | \(-0.549853\pi\) | ||||
−0.155979 | + | 0.987760i | \(0.549853\pi\) | |||||||
\(728\) | −0.0185664 | −0.000688118 0 | ||||||||
\(729\) | 19.3047 | 0.714988 | ||||||||
\(730\) | 1.91502 | 0.0708780 | ||||||||
\(731\) | −19.6817 | −0.727954 | ||||||||
\(732\) | 59.8683 | 2.21280 | ||||||||
\(733\) | −10.4213 | −0.384918 | −0.192459 | − | 0.981305i | \(-0.561646\pi\) | ||||
−0.192459 | + | 0.981305i | \(0.561646\pi\) | |||||||
\(734\) | −16.7088 | −0.616733 | ||||||||
\(735\) | 18.4223 | 0.679518 | ||||||||
\(736\) | 7.38204 | 0.272105 | ||||||||
\(737\) | −41.3507 | −1.52317 | ||||||||
\(738\) | −35.7256 | −1.31508 | ||||||||
\(739\) | −34.8685 | −1.28266 | −0.641329 | − | 0.767266i | \(-0.721617\pi\) | ||||
−0.641329 | + | 0.767266i | \(0.721617\pi\) | |||||||
\(740\) | −5.69869 | −0.209488 | ||||||||
\(741\) | −8.74057 | −0.321093 | ||||||||
\(742\) | −0.0469449 | −0.00172340 | ||||||||
\(743\) | −28.4787 | −1.04478 | −0.522392 | − | 0.852706i | \(-0.674960\pi\) | ||||
−0.522392 | + | 0.852706i | \(0.674960\pi\) | |||||||
\(744\) | 85.6391 | 3.13968 | ||||||||
\(745\) | 15.3885 | 0.563791 | ||||||||
\(746\) | −14.4348 | −0.528494 | ||||||||
\(747\) | −38.0623 | −1.39263 | ||||||||
\(748\) | 60.4934 | 2.21186 | ||||||||
\(749\) | −0.00902193 | −0.000329654 0 | ||||||||
\(750\) | −57.1645 | −2.08735 | ||||||||
\(751\) | 17.2874 | 0.630828 | 0.315414 | − | 0.948954i | \(-0.397857\pi\) | ||||
0.315414 | + | 0.948954i | \(0.397857\pi\) | |||||||
\(752\) | −1.70764 | −0.0622712 | ||||||||
\(753\) | −56.1786 | −2.04726 | ||||||||
\(754\) | 57.2809 | 2.08605 | ||||||||
\(755\) | −6.74323 | −0.245411 | ||||||||
\(756\) | 0.0906228 | 0.00329592 | ||||||||
\(757\) | −25.4403 | −0.924643 | −0.462322 | − | 0.886712i | \(-0.652983\pi\) | ||||
−0.462322 | + | 0.886712i | \(0.652983\pi\) | |||||||
\(758\) | −6.35295 | −0.230749 | ||||||||
\(759\) | 21.1158 | 0.766456 | ||||||||
\(760\) | 2.77352 | 0.100606 | ||||||||
\(761\) | −15.0480 | −0.545490 | −0.272745 | − | 0.962086i | \(-0.587932\pi\) | ||||
−0.272745 | + | 0.962086i | \(0.587932\pi\) | |||||||
\(762\) | 3.48959 | 0.126414 | ||||||||
\(763\) | 0.00327562 | 0.000118585 0 | ||||||||
\(764\) | −65.1990 | −2.35882 | ||||||||
\(765\) | −25.5369 | −0.923288 | ||||||||
\(766\) | 27.7128 | 1.00131 | ||||||||
\(767\) | −4.55917 | −0.164622 | ||||||||
\(768\) | 68.6265 | 2.47635 | ||||||||
\(769\) | 21.5857 | 0.778401 | 0.389201 | − | 0.921153i | \(-0.372751\pi\) | ||||
0.389201 | + | 0.921153i | \(0.372751\pi\) | |||||||
\(770\) | −0.0157794 | −0.000568651 0 | ||||||||
\(771\) | 17.5765 | 0.633001 | ||||||||
\(772\) | −2.73073 | −0.0982810 | ||||||||
\(773\) | −41.4298 | −1.49013 | −0.745063 | − | 0.666994i | \(-0.767581\pi\) | ||||
−0.745063 | + | 0.666994i | \(0.767581\pi\) | |||||||
\(774\) | −75.2515 | −2.70486 | ||||||||
\(775\) | −34.6732 | −1.24550 | ||||||||
\(776\) | 25.8290 | 0.927206 | ||||||||
\(777\) | −0.0128412 | −0.000460676 0 | ||||||||
\(778\) | 1.06605 | 0.0382196 | ||||||||
\(779\) | −2.15390 | −0.0771715 | ||||||||
\(780\) | 24.8632 | 0.890245 | ||||||||
\(781\) | −42.5171 | −1.52138 | ||||||||
\(782\) | 16.5563 | 0.592051 | ||||||||
\(783\) | −116.908 | −4.17795 | ||||||||
\(784\) | −6.58193 | −0.235069 | ||||||||
\(785\) | 14.8142 | 0.528742 | ||||||||
\(786\) | 68.7983 | 2.45395 | ||||||||
\(787\) | −6.40974 | −0.228482 | −0.114241 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114241 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(788\) | −30.9184 | −1.10142 | ||||||||
\(789\) | 36.4796 | 1.29871 | ||||||||
\(790\) | 0.398879 | 0.0141915 | ||||||||
\(791\) | 0.00567951 | 0.000201940 0 | ||||||||
\(792\) | 96.7130 | 3.43655 | ||||||||
\(793\) | 15.0534 | 0.534564 | ||||||||
\(794\) | −19.8156 | −0.703230 | ||||||||
\(795\) | 26.2870 | 0.932304 | ||||||||
\(796\) | −83.3828 | −2.95542 | ||||||||
\(797\) | −23.0604 | −0.816841 | −0.408421 | − | 0.912794i | \(-0.633920\pi\) | ||||
−0.408421 | + | 0.912794i | \(0.633920\pi\) | |||||||
\(798\) | 0.0149464 | 0.000529098 0 | ||||||||
\(799\) | 7.87846 | 0.278720 | ||||||||
\(800\) | −19.4625 | −0.688104 | ||||||||
\(801\) | 62.4440 | 2.20635 | ||||||||
\(802\) | −44.5786 | −1.57412 | ||||||||
\(803\) | 4.02599 | 0.142074 | ||||||||
\(804\) | −111.416 | −3.92933 | ||||||||
\(805\) | −0.00273010 | −9.62233e−5 0 | ||||||||
\(806\) | 51.4976 | 1.81393 | ||||||||
\(807\) | −78.2374 | −2.75409 | ||||||||
\(808\) | −1.95324 | −0.0687146 | ||||||||
\(809\) | 26.7526 | 0.940572 | 0.470286 | − | 0.882514i | \(-0.344151\pi\) | ||||
0.470286 | + | 0.882514i | \(0.344151\pi\) | |||||||
\(810\) | −39.0916 | −1.37354 | ||||||||
\(811\) | −50.8350 | −1.78506 | −0.892530 | − | 0.450989i | \(-0.851071\pi\) | ||||
−0.892530 | + | 0.450989i | \(0.851071\pi\) | |||||||
\(812\) | −0.0619214 | −0.00217302 | ||||||||
\(813\) | −26.3759 | −0.925044 | ||||||||
\(814\) | −18.9514 | −0.664248 | ||||||||
\(815\) | 3.74397 | 0.131145 | ||||||||
\(816\) | 12.9718 | 0.454104 | ||||||||
\(817\) | −4.53692 | −0.158727 | ||||||||
\(818\) | 13.8918 | 0.485715 | ||||||||
\(819\) | 0.0394061 | 0.00137696 | ||||||||
\(820\) | 6.12692 | 0.213961 | ||||||||
\(821\) | −12.0830 | −0.421699 | −0.210850 | − | 0.977519i | \(-0.567623\pi\) | ||||
−0.210850 | + | 0.977519i | \(0.567623\pi\) | |||||||
\(822\) | −17.3325 | −0.604540 | ||||||||
\(823\) | −6.46816 | −0.225466 | −0.112733 | − | 0.993625i | \(-0.535960\pi\) | ||||
−0.112733 | + | 0.993625i | \(0.535960\pi\) | |||||||
\(824\) | 5.19274 | 0.180898 | ||||||||
\(825\) | −55.6713 | −1.93823 | ||||||||
\(826\) | 0.00779622 | 0.000271265 0 | ||||||||
\(827\) | 38.1714 | 1.32735 | 0.663675 | − | 0.748021i | \(-0.268996\pi\) | ||||
0.663675 | + | 0.748021i | \(0.268996\pi\) | |||||||
\(828\) | 40.0173 | 1.39070 | ||||||||
\(829\) | 20.4881 | 0.711581 | 0.355790 | − | 0.934566i | \(-0.384212\pi\) | ||||
0.355790 | + | 0.934566i | \(0.384212\pi\) | |||||||
\(830\) | 10.3258 | 0.358415 | ||||||||
\(831\) | 58.6553 | 2.03473 | ||||||||
\(832\) | 34.0750 | 1.18134 | ||||||||
\(833\) | 30.3668 | 1.05215 | ||||||||
\(834\) | 78.8861 | 2.73160 | ||||||||
\(835\) | 8.12445 | 0.281158 | ||||||||
\(836\) | 13.9446 | 0.482285 | ||||||||
\(837\) | −105.104 | −3.63294 | ||||||||
\(838\) | −41.6804 | −1.43983 | ||||||||
\(839\) | −47.0709 | −1.62507 | −0.812534 | − | 0.582914i | \(-0.801912\pi\) | ||||
−0.812534 | + | 0.582914i | \(0.801912\pi\) | |||||||
\(840\) | −0.0177779 | −0.000613394 0 | ||||||||
\(841\) | 50.8816 | 1.75454 | ||||||||
\(842\) | −50.5214 | −1.74108 | ||||||||
\(843\) | 101.558 | 3.49786 | ||||||||
\(844\) | −24.1334 | −0.830704 | ||||||||
\(845\) | −4.50671 | −0.155036 | ||||||||
\(846\) | 30.1227 | 1.03564 | ||||||||
\(847\) | −0.0110019 | −0.000378031 0 | ||||||||
\(848\) | −9.39182 | −0.322516 | ||||||||
\(849\) | −46.6064 | −1.59953 | ||||||||
\(850\) | −43.6501 | −1.49719 | ||||||||
\(851\) | −3.27891 | −0.112400 | ||||||||
\(852\) | −114.558 | −3.92470 | ||||||||
\(853\) | −11.8014 | −0.404073 | −0.202036 | − | 0.979378i | \(-0.564756\pi\) | ||||
−0.202036 | + | 0.979378i | \(0.564756\pi\) | |||||||
\(854\) | −0.0257415 | −0.000880857 0 | ||||||||
\(855\) | −5.88663 | −0.201318 | ||||||||
\(856\) | −15.0011 | −0.512728 | ||||||||
\(857\) | −28.6238 | −0.977769 | −0.488885 | − | 0.872348i | \(-0.662596\pi\) | ||||
−0.488885 | + | 0.872348i | \(0.662596\pi\) | |||||||
\(858\) | 82.6845 | 2.82280 | ||||||||
\(859\) | −37.6687 | −1.28524 | −0.642619 | − | 0.766186i | \(-0.722152\pi\) | ||||
−0.642619 | + | 0.766186i | \(0.722152\pi\) | |||||||
\(860\) | 12.9056 | 0.440078 | ||||||||
\(861\) | 0.0138062 | 0.000470513 0 | ||||||||
\(862\) | 59.8117 | 2.03719 | ||||||||
\(863\) | −27.8120 | −0.946732 | −0.473366 | − | 0.880866i | \(-0.656961\pi\) | ||||
−0.473366 | + | 0.880866i | \(0.656961\pi\) | |||||||
\(864\) | −58.9964 | −2.00710 | ||||||||
\(865\) | 19.4937 | 0.662806 | ||||||||
\(866\) | −12.5432 | −0.426234 | ||||||||
\(867\) | −5.78542 | −0.196483 | ||||||||
\(868\) | −0.0556695 | −0.00188955 | ||||||||
\(869\) | 0.838573 | 0.0284466 | ||||||||
\(870\) | 54.8480 | 1.85952 | ||||||||
\(871\) | −28.0147 | −0.949240 | ||||||||
\(872\) | 5.44650 | 0.184442 | ||||||||
\(873\) | −54.8204 | −1.85539 | ||||||||
\(874\) | 3.81647 | 0.129094 | ||||||||
\(875\) | 0.0155380 | 0.000525282 0 | ||||||||
\(876\) | 10.8477 | 0.366509 | ||||||||
\(877\) | −19.5619 | −0.660557 | −0.330278 | − | 0.943884i | \(-0.607143\pi\) | ||||
−0.330278 | + | 0.943884i | \(0.607143\pi\) | |||||||
\(878\) | −62.0553 | −2.09427 | ||||||||
\(879\) | −6.75258 | −0.227759 | ||||||||
\(880\) | −3.15684 | −0.106417 | ||||||||
\(881\) | 38.5665 | 1.29934 | 0.649669 | − | 0.760217i | \(-0.274907\pi\) | ||||
0.649669 | + | 0.760217i | \(0.274907\pi\) | |||||||
\(882\) | 116.105 | 3.90946 | ||||||||
\(883\) | −47.2299 | −1.58941 | −0.794706 | − | 0.606995i | \(-0.792375\pi\) | ||||
−0.794706 | + | 0.606995i | \(0.792375\pi\) | |||||||
\(884\) | 40.9837 | 1.37843 | ||||||||
\(885\) | −4.36553 | −0.146746 | ||||||||
\(886\) | −18.1435 | −0.609544 | ||||||||
\(887\) | −35.5561 | −1.19386 | −0.596928 | − | 0.802295i | \(-0.703612\pi\) | ||||
−0.596928 | + | 0.802295i | \(0.703612\pi\) | |||||||
\(888\) | −21.3516 | −0.716512 | ||||||||
\(889\) | −0.000948514 0 | −3.18121e−5 0 | ||||||||
\(890\) | −16.9403 | −0.567840 | ||||||||
\(891\) | −82.1832 | −2.75324 | ||||||||
\(892\) | −19.8385 | −0.664243 | ||||||||
\(893\) | 1.81610 | 0.0607735 | ||||||||
\(894\) | 137.888 | 4.61167 | ||||||||
\(895\) | 10.2796 | 0.343610 | ||||||||
\(896\) | −0.0400866 | −0.00133920 | ||||||||
\(897\) | 14.3058 | 0.477655 | ||||||||
\(898\) | 15.9836 | 0.533381 | ||||||||
\(899\) | 71.8164 | 2.39521 | ||||||||
\(900\) | −105.504 | −3.51681 | ||||||||
\(901\) | 43.3306 | 1.44355 | ||||||||
\(902\) | 20.3756 | 0.678432 | ||||||||
\(903\) | 0.0290810 | 0.000967755 0 | ||||||||
\(904\) | 9.44355 | 0.314088 | ||||||||
\(905\) | 1.36697 | 0.0454397 | ||||||||
\(906\) | −60.4225 | −2.00740 | ||||||||
\(907\) | −7.90809 | −0.262584 | −0.131292 | − | 0.991344i | \(-0.541913\pi\) | ||||
−0.131292 | + | 0.991344i | \(0.541913\pi\) | |||||||
\(908\) | 18.6878 | 0.620176 | ||||||||
\(909\) | 4.14562 | 0.137502 | ||||||||
\(910\) | −0.0106904 | −0.000354383 0 | ||||||||
\(911\) | −18.5754 | −0.615430 | −0.307715 | − | 0.951479i | \(-0.599564\pi\) | ||||
−0.307715 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(912\) | 2.99019 | 0.0990152 | ||||||||
\(913\) | 21.7083 | 0.718439 | ||||||||
\(914\) | 88.1208 | 2.91478 | ||||||||
\(915\) | 14.4141 | 0.476515 | ||||||||
\(916\) | 74.6082 | 2.46513 | ||||||||
\(917\) | −0.0187003 | −0.000617537 0 | ||||||||
\(918\) | −132.316 | −4.36707 | ||||||||
\(919\) | −56.8714 | −1.87601 | −0.938007 | − | 0.346616i | \(-0.887331\pi\) | ||||
−0.938007 | + | 0.346616i | \(0.887331\pi\) | |||||||
\(920\) | −4.53944 | −0.149661 | ||||||||
\(921\) | −18.8733 | −0.621898 | ||||||||
\(922\) | 95.7153 | 3.15222 | ||||||||
\(923\) | −28.8049 | −0.948123 | ||||||||
\(924\) | −0.0893830 | −0.00294048 | ||||||||
\(925\) | 8.64475 | 0.284238 | ||||||||
\(926\) | −54.8763 | −1.80335 | ||||||||
\(927\) | −11.0213 | −0.361986 | ||||||||
\(928\) | 40.3115 | 1.32329 | ||||||||
\(929\) | 37.4640 | 1.22915 | 0.614576 | − | 0.788857i | \(-0.289327\pi\) | ||||
0.614576 | + | 0.788857i | \(0.289327\pi\) | |||||||
\(930\) | 49.3103 | 1.61695 | ||||||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | −35.6247 | −1.16692 | ||||||||
\(933\) | −101.909 | −3.33634 | ||||||||
\(934\) | −7.46814 | −0.244365 | ||||||||
\(935\) | 14.5646 | 0.476313 | ||||||||
\(936\) | 65.5221 | 2.14166 | ||||||||
\(937\) | 30.3303 | 0.990849 | 0.495424 | − | 0.868651i | \(-0.335013\pi\) | ||||
0.495424 | + | 0.868651i | \(0.335013\pi\) | |||||||
\(938\) | 0.0479053 | 0.00156416 | ||||||||
\(939\) | 6.95487 | 0.226964 | ||||||||
\(940\) | −5.16603 | −0.168497 | ||||||||
\(941\) | 14.5932 | 0.475723 | 0.237862 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237862 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(942\) | 132.742 | 4.32497 | ||||||||
\(943\) | 3.52530 | 0.114800 | ||||||||
\(944\) | 1.55972 | 0.0507644 | ||||||||
\(945\) | 0.0218186 | 0.000709760 0 | ||||||||
\(946\) | 42.9186 | 1.39540 | ||||||||
\(947\) | 54.6702 | 1.77654 | 0.888271 | − | 0.459320i | \(-0.151907\pi\) | ||||
0.888271 | + | 0.459320i | \(0.151907\pi\) | |||||||
\(948\) | 2.25946 | 0.0733838 | ||||||||
\(949\) | 2.72757 | 0.0885406 | ||||||||
\(950\) | −10.0620 | −0.326454 | ||||||||
\(951\) | 3.18012 | 0.103122 | ||||||||
\(952\) | −0.0293044 | −0.000949762 0 | ||||||||
\(953\) | −1.81395 | −0.0587597 | −0.0293799 | − | 0.999568i | \(-0.509353\pi\) | ||||
−0.0293799 | + | 0.999568i | \(0.509353\pi\) | |||||||
\(954\) | 165.671 | 5.36381 | ||||||||
\(955\) | −15.6975 | −0.507960 | ||||||||
\(956\) | 13.8445 | 0.447762 | ||||||||
\(957\) | 115.308 | 3.72739 | ||||||||
\(958\) | −49.1513 | −1.58801 | ||||||||
\(959\) | 0.00471119 | 0.000152132 0 | ||||||||
\(960\) | 32.6277 | 1.05305 | ||||||||
\(961\) | 33.5655 | 1.08276 | ||||||||
\(962\) | −12.8394 | −0.413959 | ||||||||
\(963\) | 31.8390 | 1.02600 | ||||||||
\(964\) | −104.332 | −3.36030 | ||||||||
\(965\) | −0.657458 | −0.0211643 | ||||||||
\(966\) | −0.0244630 | −0.000787083 0 | ||||||||
\(967\) | −45.3912 | −1.45968 | −0.729841 | − | 0.683617i | \(-0.760406\pi\) | ||||
−0.729841 | + | 0.683617i | \(0.760406\pi\) | |||||||
\(968\) | −18.2933 | −0.587970 | ||||||||
\(969\) | −13.7957 | −0.443183 | ||||||||
\(970\) | 14.8721 | 0.477515 | ||||||||
\(971\) | 34.0361 | 1.09227 | 0.546135 | − | 0.837697i | \(-0.316098\pi\) | ||||
0.546135 | + | 0.837697i | \(0.316098\pi\) | |||||||
\(972\) | −86.5528 | −2.77618 | ||||||||
\(973\) | −0.0214422 | −0.000687407 0 | ||||||||
\(974\) | 65.0378 | 2.08394 | ||||||||
\(975\) | −37.7167 | −1.20790 | ||||||||
\(976\) | −5.14986 | −0.164843 | ||||||||
\(977\) | 17.2891 | 0.553126 | 0.276563 | − | 0.960996i | \(-0.410804\pi\) | ||||
0.276563 | + | 0.960996i | \(0.410804\pi\) | |||||||
\(978\) | 33.5477 | 1.07274 | ||||||||
\(979\) | −35.6140 | −1.13823 | ||||||||
\(980\) | −19.9120 | −0.636065 | ||||||||
\(981\) | −11.5598 | −0.369078 | ||||||||
\(982\) | −4.53175 | −0.144614 | ||||||||
\(983\) | −28.9745 | −0.924142 | −0.462071 | − | 0.886843i | \(-0.652893\pi\) | ||||
−0.462071 | + | 0.886843i | \(0.652893\pi\) | |||||||
\(984\) | 22.9561 | 0.731812 | ||||||||
\(985\) | −7.44402 | −0.237186 | ||||||||
\(986\) | 90.4097 | 2.87923 | ||||||||
\(987\) | −0.0116409 | −0.000370535 0 | ||||||||
\(988\) | 9.44734 | 0.300560 | ||||||||
\(989\) | 7.42562 | 0.236121 | ||||||||
\(990\) | 55.6866 | 1.76984 | ||||||||
\(991\) | 37.3319 | 1.18589 | 0.592943 | − | 0.805244i | \(-0.297966\pi\) | ||||
0.592943 | + | 0.805244i | \(0.297966\pi\) | |||||||
\(992\) | 36.2414 | 1.15067 | ||||||||
\(993\) | 4.47269 | 0.141937 | ||||||||
\(994\) | 0.0492565 | 0.00156232 | ||||||||
\(995\) | −20.0755 | −0.636436 | ||||||||
\(996\) | 58.4910 | 1.85336 | ||||||||
\(997\) | 10.7772 | 0.341316 | 0.170658 | − | 0.985330i | \(-0.445411\pi\) | ||||
0.170658 | + | 0.985330i | \(0.445411\pi\) | |||||||
\(998\) | 48.2431 | 1.52711 | ||||||||
\(999\) | 26.2047 | 0.829079 |
(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 | 6023.2.a.b.1.8 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.8 | ✓ | 99 | 1.1 | even | 1 | trivial |