Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.3 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 3.78471 | − | 3.26741i | 0.756942 | − | 0.653482i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 3.72268 | + | 3.72268i | 0.531811 | + | 0.531811i | 0.921111 | − | 0.389300i | \(-0.127283\pi\) |
−0.389300 | + | 0.921111i | \(0.627283\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 7.05212 | + | 0.517301i | 0.705212 | + | 0.0517301i | ||||
\(11\) | 11.8026 | 1.07296 | 0.536482 | − | 0.843912i | \(-0.319753\pi\) | ||||
0.536482 | + | 0.843912i | \(0.319753\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 17.6286 | − | 17.6286i | 1.35604 | − | 1.35604i | 0.477305 | − | 0.878738i | \(-0.341614\pi\) |
0.878738 | − | 0.477305i | \(-0.158386\pi\) | |||||||
\(14\) | 7.44536i | 0.531811i | ||||||||
\(15\) | −0.633562 | + | 8.63705i | −0.0422375 | + | 0.575803i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −20.6341 | − | 20.6341i | −1.21377 | − | 1.21377i | −0.969777 | − | 0.243994i | \(-0.921542\pi\) |
−0.243994 | − | 0.969777i | \(-0.578458\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 6.19835i | − | 0.326229i | −0.986607 | − | 0.163114i | \(-0.947846\pi\) | ||
0.986607 | − | 0.163114i | \(-0.0521540\pi\) | |||||||
\(20\) | 6.53482 | + | 7.56942i | 0.326741 | + | 0.378471i | ||||
\(21\) | −9.11866 | −0.434222 | ||||||||
\(22\) | 11.8026 | + | 11.8026i | 0.536482 | + | 0.536482i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 3.64807 | − | 24.7324i | 0.145923 | − | 0.989296i | ||||
\(26\) | 35.2571 | 1.35604 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −7.44536 | + | 7.44536i | −0.265906 | + | 0.265906i | ||||
\(29\) | 0.0875899i | 0.00302034i | 0.999999 | + | 0.00151017i | \(0.000480702\pi\) | ||||
−0.999999 | + | 0.00151017i | \(0.999519\pi\) | |||||||
\(30\) | −9.27061 | + | 8.00349i | −0.309020 | + | 0.266783i | ||||
\(31\) | −0.753876 | −0.0243186 | −0.0121593 | − | 0.999926i | \(-0.503871\pi\) | ||||
−0.0121593 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −14.4552 | + | 14.4552i | −0.438036 | + | 0.438036i | ||||
\(34\) | − | 41.2682i | − | 1.21377i | ||||||
\(35\) | 26.2528 | + | 1.92575i | 0.750079 | + | 0.0550213i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 28.5265 | + | 28.5265i | 0.770986 | + | 0.770986i | 0.978279 | − | 0.207293i | \(-0.0664652\pi\) |
−0.207293 | + | 0.978279i | \(0.566465\pi\) | |||||||
\(38\) | 6.19835 | − | 6.19835i | 0.163114 | − | 0.163114i | ||||
\(39\) | 43.1810i | 1.10720i | ||||||||
\(40\) | −1.03460 | + | 14.1042i | −0.0258651 | + | 0.352606i | ||||
\(41\) | 57.1315 | 1.39345 | 0.696725 | − | 0.717338i | \(-0.254640\pi\) | ||||
0.696725 | + | 0.717338i | \(0.254640\pi\) | |||||||
\(42\) | −9.11866 | − | 9.11866i | −0.217111 | − | 0.217111i | ||||
\(43\) | −1.66664 | + | 1.66664i | −0.0387592 | + | 0.0387592i | −0.726221 | − | 0.687462i | \(-0.758725\pi\) |
0.687462 | + | 0.726221i | \(0.258725\pi\) | |||||||
\(44\) | 23.6052i | 0.536482i | ||||||||
\(45\) | −9.80223 | − | 11.3541i | −0.217827 | − | 0.252314i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 40.7708 | + | 40.7708i | 0.867464 | + | 0.867464i | 0.992191 | − | 0.124727i | \(-0.0398054\pi\) |
−0.124727 | + | 0.992191i | \(0.539805\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 21.2833i | − | 0.434354i | ||||||
\(50\) | 28.3805 | − | 21.0843i | 0.567609 | − | 0.421687i | ||||
\(51\) | 50.5430 | 0.991040 | ||||||||
\(52\) | 35.2571 | + | 35.2571i | 0.678021 | + | 0.678021i | ||||
\(53\) | 7.42708 | − | 7.42708i | 0.140134 | − | 0.140134i | −0.633560 | − | 0.773694i | \(-0.718407\pi\) |
0.773694 | + | 0.633560i | \(0.218407\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 44.6694 | − | 38.5639i | 0.812172 | − | 0.701162i | ||||
\(56\) | −14.8907 | −0.265906 | ||||||||
\(57\) | 7.59140 | + | 7.59140i | 0.133182 | + | 0.133182i | ||||
\(58\) | −0.0875899 | + | 0.0875899i | −0.00151017 | + | 0.00151017i | ||||
\(59\) | 106.957i | 1.81283i | 0.422391 | + | 0.906413i | \(0.361191\pi\) | ||||
−0.422391 | + | 0.906413i | \(0.638809\pi\) | |||||||
\(60\) | −17.2741 | − | 1.26712i | −0.287902 | − | 0.0211187i | ||||
\(61\) | −91.1049 | −1.49352 | −0.746761 | − | 0.665092i | \(-0.768392\pi\) | ||||
−0.746761 | + | 0.665092i | \(0.768392\pi\) | |||||||
\(62\) | −0.753876 | − | 0.753876i | −0.0121593 | − | 0.0121593i | ||||
\(63\) | 11.1680 | − | 11.1680i | 0.177270 | − | 0.177270i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 9.11928 | − | 124.319i | 0.140297 | − | 1.91260i | ||||
\(66\) | −28.9104 | −0.438036 | ||||||||
\(67\) | 22.3209 | + | 22.3209i | 0.333148 | + | 0.333148i | 0.853781 | − | 0.520633i | \(-0.174304\pi\) |
−0.520633 | + | 0.853781i | \(0.674304\pi\) | |||||||
\(68\) | 41.2682 | − | 41.2682i | 0.606885 | − | 0.606885i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | 24.3270 | + | 28.1785i | 0.347529 | + | 0.402550i | ||||
\(71\) | −123.707 | −1.74235 | −0.871177 | − | 0.490969i | \(-0.836643\pi\) | ||||
−0.871177 | + | 0.490969i | \(0.836643\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 14.6619 | − | 14.6619i | 0.200848 | − | 0.200848i | −0.599515 | − | 0.800363i | \(-0.704640\pi\) |
0.800363 | + | 0.599515i | \(0.204640\pi\) | |||||||
\(74\) | 57.0530i | 0.770986i | ||||||||
\(75\) | 25.8229 | + | 34.7588i | 0.344306 | + | 0.463451i | ||||
\(76\) | 12.3967 | 0.163114 | ||||||||
\(77\) | 43.9373 | + | 43.9373i | 0.570614 | + | 0.570614i | ||||
\(78\) | −43.1810 | + | 43.1810i | −0.553602 | + | 0.553602i | ||||
\(79\) | − | 22.2431i | − | 0.281558i | −0.990041 | − | 0.140779i | \(-0.955039\pi\) | ||
0.990041 | − | 0.140779i | \(-0.0449607\pi\) | |||||||
\(80\) | −15.1388 | + | 13.0696i | −0.189236 | + | 0.163370i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 57.1315 | + | 57.1315i | 0.696725 | + | 0.696725i | ||||
\(83\) | 4.59002 | − | 4.59002i | 0.0553014 | − | 0.0553014i | −0.678915 | − | 0.734217i | \(-0.737550\pi\) |
0.734217 | + | 0.678915i | \(0.237550\pi\) | |||||||
\(84\) | − | 18.2373i | − | 0.217111i | ||||||
\(85\) | −145.514 | − | 10.6741i | −1.71193 | − | 0.125577i | ||||
\(86\) | −3.33329 | −0.0387592 | ||||||||
\(87\) | −0.107275 | − | 0.107275i | −0.00123305 | − | 0.00123305i | ||||
\(88\) | −23.6052 | + | 23.6052i | −0.268241 | + | 0.268241i | ||||
\(89\) | 30.0252i | 0.337361i | 0.985671 | + | 0.168681i | \(0.0539507\pi\) | ||||
−0.985671 | + | 0.168681i | \(0.946049\pi\) | |||||||
\(90\) | 1.55190 | − | 21.1564i | 0.0172434 | − | 0.235071i | ||||
\(91\) | 131.251 | 1.44232 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 0.923306 | − | 0.923306i | 0.00992802 | − | 0.00992802i | ||||
\(94\) | 81.5417i | 0.867464i | ||||||||
\(95\) | −20.2525 | − | 23.4590i | −0.213185 | − | 0.246936i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 120.850 | + | 120.850i | 1.24587 | + | 1.24587i | 0.957526 | + | 0.288347i | \(0.0931056\pi\) |
0.288347 | + | 0.957526i | \(0.406894\pi\) | |||||||
\(98\) | 21.2833 | − | 21.2833i | 0.217177 | − | 0.217177i | ||||
\(99\) | − | 35.4078i | − | 0.357655i | ||||||
\(100\) | 49.4648 | + | 7.29614i | 0.494648 | + | 0.0729614i | ||||
\(101\) | −6.35681 | −0.0629387 | −0.0314693 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314693 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(102\) | 50.5430 | + | 50.5430i | 0.495520 | + | 0.495520i | ||||
\(103\) | 128.811 | − | 128.811i | 1.25059 | − | 1.25059i | 0.295136 | − | 0.955455i | \(-0.404635\pi\) |
0.955455 | − | 0.295136i | \(-0.0953649\pi\) | |||||||
\(104\) | 70.5142i | 0.678021i | ||||||||
\(105\) | −34.5115 | + | 29.7944i | −0.328681 | + | 0.283756i | ||||
\(106\) | 14.8542 | 0.140134 | ||||||||
\(107\) | 47.4520 | + | 47.4520i | 0.443477 | + | 0.443477i | 0.893179 | − | 0.449702i | \(-0.148470\pi\) |
−0.449702 | + | 0.893179i | \(0.648470\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 145.890i | 1.33844i | 0.743062 | + | 0.669222i | \(0.233373\pi\) | ||||
−0.743062 | + | 0.669222i | \(0.766627\pi\) | |||||||
\(110\) | 83.2334 | + | 6.10550i | 0.756667 | + | 0.0555046i | ||||
\(111\) | −69.8754 | −0.629508 | ||||||||
\(112\) | −14.8907 | − | 14.8907i | −0.132953 | − | 0.132953i | ||||
\(113\) | −94.3049 | + | 94.3049i | −0.834557 | + | 0.834557i | −0.988136 | − | 0.153580i | \(-0.950920\pi\) |
0.153580 | + | 0.988136i | \(0.450920\pi\) | |||||||
\(114\) | 15.1828i | 0.133182i | ||||||||
\(115\) | −1.75425 | + | 23.9149i | −0.0152544 | + | 0.207956i | ||||
\(116\) | −0.175180 | −0.00151017 | ||||||||
\(117\) | −52.8857 | − | 52.8857i | −0.452014 | − | 0.452014i | ||||
\(118\) | −106.957 | + | 106.957i | −0.906413 | + | 0.906413i | ||||
\(119\) | − | 153.628i | − | 1.29099i | ||||||
\(120\) | −16.0070 | − | 18.5412i | −0.133391 | − | 0.154510i | ||||
\(121\) | 18.3014 | 0.151252 | ||||||||
\(122\) | −91.1049 | − | 91.1049i | −0.746761 | − | 0.746761i | ||||
\(123\) | −69.9715 | + | 69.9715i | −0.568874 | + | 0.568874i | ||||
\(124\) | − | 1.50775i | − | 0.0121593i | ||||||
\(125\) | −67.0040 | − | 105.525i | −0.536032 | − | 0.844198i | ||||
\(126\) | 22.3361 | 0.177270 | ||||||||
\(127\) | 10.3220 | + | 10.3220i | 0.0812757 | + | 0.0812757i | 0.746576 | − | 0.665300i | \(-0.231696\pi\) |
−0.665300 | + | 0.746576i | \(0.731696\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 4.08243i | − | 0.0316467i | ||||||
\(130\) | 133.438 | − | 115.199i | 1.02645 | − | 0.886149i | ||||
\(131\) | −184.410 | −1.40771 | −0.703856 | − | 0.710343i | \(-0.748540\pi\) | ||||
−0.703856 | + | 0.710343i | \(0.748540\pi\) | |||||||
\(132\) | −28.9104 | − | 28.9104i | −0.219018 | − | 0.219018i | ||||
\(133\) | 23.0745 | − | 23.0745i | 0.173492 | − | 0.173492i | ||||
\(134\) | 44.6418i | 0.333148i | ||||||||
\(135\) | 25.9111 | + | 1.90069i | 0.191934 | + | 0.0140792i | ||||
\(136\) | 82.5364 | 0.606885 | ||||||||
\(137\) | −171.020 | − | 171.020i | −1.24832 | − | 1.24832i | −0.956461 | − | 0.291859i | \(-0.905726\pi\) |
−0.291859 | − | 0.956461i | \(-0.594274\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | 83.8444i | 0.603197i | 0.953435 | + | 0.301599i | \(0.0975203\pi\) | ||||
−0.953435 | + | 0.301599i | \(0.902480\pi\) | |||||||
\(140\) | −3.85149 | + | 52.5056i | −0.0275107 | + | 0.375040i | ||||
\(141\) | −99.8677 | −0.708282 | ||||||||
\(142\) | −123.707 | − | 123.707i | −0.871177 | − | 0.871177i | ||||
\(143\) | 208.063 | − | 208.063i | 1.45498 | − | 1.45498i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 0.286192 | + | 0.331502i | 0.00197374 | + | 0.00228622i | ||||
\(146\) | 29.3239 | 0.200848 | ||||||||
\(147\) | 26.0666 | + | 26.0666i | 0.177324 | + | 0.177324i | ||||
\(148\) | −57.0530 | + | 57.0530i | −0.385493 | + | 0.385493i | ||||
\(149\) | − | 117.040i | − | 0.785504i | −0.919644 | − | 0.392752i | \(-0.871523\pi\) | ||
0.919644 | − | 0.392752i | \(-0.128477\pi\) | |||||||
\(150\) | −8.93591 | + | 60.5818i | −0.0595728 | + | 0.403878i | ||||
\(151\) | 39.9086 | 0.264295 | 0.132148 | − | 0.991230i | \(-0.457813\pi\) | ||||
0.132148 | + | 0.991230i | \(0.457813\pi\) | |||||||
\(152\) | 12.3967 | + | 12.3967i | 0.0815572 | + | 0.0815572i | ||||
\(153\) | −61.9023 | + | 61.9023i | −0.404590 | + | 0.404590i | ||||
\(154\) | 87.8746i | 0.570614i | ||||||||
\(155\) | −2.85320 | + | 2.46322i | −0.0184078 | + | 0.0158918i | ||||
\(156\) | −86.3619 | −0.553602 | ||||||||
\(157\) | −56.3304 | − | 56.3304i | −0.358793 | − | 0.358793i | 0.504575 | − | 0.863368i | \(-0.331649\pi\) |
−0.863368 | + | 0.504575i | \(0.831649\pi\) | |||||||
\(158\) | 22.2431 | − | 22.2431i | 0.140779 | − | 0.140779i | ||||
\(159\) | 18.1926i | 0.114419i | ||||||||
\(160\) | −28.2085 | − | 2.06921i | −0.176303 | − | 0.0129325i | ||||
\(161\) | −25.2484 | −0.156823 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 104.950 | − | 104.950i | 0.643867 | − | 0.643867i | −0.307637 | − | 0.951504i | \(-0.599538\pi\) |
0.951504 | + | 0.307637i | \(0.0995382\pi\) | |||||||
\(164\) | 114.263i | 0.696725i | ||||||||
\(165\) | −7.47768 | + | 101.940i | −0.0453193 | + | 0.617816i | ||||
\(166\) | 9.18003 | 0.0553014 | ||||||||
\(167\) | −173.661 | − | 173.661i | −1.03989 | − | 1.03989i | −0.999171 | − | 0.0407150i | \(-0.987036\pi\) |
−0.0407150 | − | 0.999171i | \(-0.512964\pi\) | |||||||
\(168\) | 18.2373 | − | 18.2373i | 0.108556 | − | 0.108556i | ||||
\(169\) | − | 452.532i | − | 2.67770i | ||||||
\(170\) | −134.840 | − | 156.188i | −0.793177 | − | 0.918754i | ||||
\(171\) | −18.5951 | −0.108743 | ||||||||
\(172\) | −3.33329 | − | 3.33329i | −0.0193796 | − | 0.0193796i | ||||
\(173\) | −151.999 | + | 151.999i | −0.878608 | + | 0.878608i | −0.993391 | − | 0.114783i | \(-0.963383\pi\) |
0.114783 | + | 0.993391i | \(0.463383\pi\) | |||||||
\(174\) | − | 0.214551i | − | 0.00123305i | ||||||
\(175\) | 105.651 | − | 78.4902i | 0.603722 | − | 0.448515i | ||||
\(176\) | −47.2104 | −0.268241 | ||||||||
\(177\) | −130.995 | − | 130.995i | −0.740084 | − | 0.740084i | ||||
\(178\) | −30.0252 | + | 30.0252i | −0.168681 | + | 0.168681i | ||||
\(179\) | − | 133.690i | − | 0.746874i | −0.927656 | − | 0.373437i | \(-0.878179\pi\) | ||
0.927656 | − | 0.373437i | \(-0.121821\pi\) | |||||||
\(180\) | 22.7083 | − | 19.6045i | 0.126157 | − | 0.108914i | ||||
\(181\) | 269.565 | 1.48931 | 0.744655 | − | 0.667450i | \(-0.232614\pi\) | ||||
0.744655 | + | 0.667450i | \(0.232614\pi\) | |||||||
\(182\) | 131.251 | + | 131.251i | 0.721159 | + | 0.721159i | ||||
\(183\) | 111.580 | − | 111.580i | 0.609728 | − | 0.609728i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 201.172 | + | 14.7568i | 1.08742 | + | 0.0797665i | ||||
\(186\) | 1.84661 | 0.00992802 | ||||||||
\(187\) | −243.536 | − | 243.536i | −1.30233 | − | 1.30233i | ||||
\(188\) | −81.5417 | + | 81.5417i | −0.433732 | + | 0.433732i | ||||
\(189\) | 27.3560i | 0.144741i | ||||||||
\(190\) | 3.20642 | − | 43.7115i | 0.0168759 | − | 0.230061i | ||||
\(191\) | −322.402 | −1.68797 | −0.843986 | − | 0.536366i | \(-0.819797\pi\) | ||||
−0.843986 | + | 0.536366i | \(0.819797\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −89.8376 | + | 89.8376i | −0.465480 | + | 0.465480i | −0.900447 | − | 0.434967i | \(-0.856760\pi\) |
0.434967 | + | 0.900447i | \(0.356760\pi\) | |||||||
\(194\) | 241.699i | 1.24587i | ||||||||
\(195\) | 141.090 | + | 163.427i | 0.723538 | + | 0.838090i | ||||
\(196\) | 42.5666 | 0.217177 | ||||||||
\(197\) | −43.4072 | − | 43.4072i | −0.220341 | − | 0.220341i | 0.588301 | − | 0.808642i | \(-0.299797\pi\) |
−0.808642 | + | 0.588301i | \(0.799797\pi\) | |||||||
\(198\) | 35.4078 | − | 35.4078i | 0.178827 | − | 0.178827i | ||||
\(199\) | 241.437i | 1.21325i | 0.794989 | + | 0.606624i | \(0.207477\pi\) | ||||
−0.794989 | + | 0.606624i | \(0.792523\pi\) | |||||||
\(200\) | 42.1687 | + | 56.7609i | 0.210843 | + | 0.283805i | ||||
\(201\) | −54.6749 | −0.272014 | ||||||||
\(202\) | −6.35681 | − | 6.35681i | −0.0314693 | − | 0.0314693i | ||||
\(203\) | −0.326069 | + | 0.326069i | −0.00160625 | + | 0.00160625i | ||||
\(204\) | 101.086i | 0.495520i | ||||||||
\(205\) | 216.226 | − | 186.672i | 1.05476 | − | 0.910595i | ||||
\(206\) | 257.622 | 1.25059 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | −70.5142 | + | 70.5142i | −0.339011 | + | 0.339011i | ||||
\(209\) | − | 73.1567i | − | 0.350032i | ||||||
\(210\) | −64.3059 | − | 4.71710i | −0.306219 | − | 0.0224624i | ||||
\(211\) | −52.1391 | −0.247105 | −0.123552 | − | 0.992338i | \(-0.539429\pi\) | ||||
−0.123552 | + | 0.992338i | \(0.539429\pi\) | |||||||
\(212\) | 14.8542 | + | 14.8542i | 0.0700668 | + | 0.0700668i | ||||
\(213\) | 151.510 | − | 151.510i | 0.711313 | − | 0.711313i | ||||
\(214\) | 94.9040i | 0.443477i | ||||||||
\(215\) | −0.862158 | + | 11.7534i | −0.00401003 | + | 0.0546669i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −2.80644 | − | 2.80644i | −0.0129329 | − | 0.0129329i | ||||
\(218\) | −145.890 | + | 145.890i | −0.669222 | + | 0.669222i | ||||
\(219\) | 35.9142i | 0.163992i | ||||||||
\(220\) | 77.1279 | + | 89.3389i | 0.350581 | + | 0.406086i | ||||
\(221\) | −727.499 | −3.29185 | ||||||||
\(222\) | −69.8754 | − | 69.8754i | −0.314754 | − | 0.314754i | ||||
\(223\) | 280.452 | − | 280.452i | 1.25763 | − | 1.25763i | 0.305410 | − | 0.952221i | \(-0.401206\pi\) |
0.952221 | − | 0.305410i | \(-0.0987935\pi\) | |||||||
\(224\) | − | 29.7814i | − | 0.132953i | ||||||
\(225\) | −74.1972 | − | 10.9442i | −0.329765 | − | 0.0486410i | ||||
\(226\) | −188.610 | −0.834557 | ||||||||
\(227\) | 144.396 | + | 144.396i | 0.636105 | + | 0.636105i | 0.949592 | − | 0.313487i | \(-0.101497\pi\) |
−0.313487 | + | 0.949592i | \(0.601497\pi\) | |||||||
\(228\) | −15.1828 | + | 15.1828i | −0.0665912 | + | 0.0665912i | ||||
\(229\) | 362.796i | 1.58426i | 0.610351 | + | 0.792131i | \(0.291028\pi\) | ||||
−0.610351 | + | 0.792131i | \(0.708972\pi\) | |||||||
\(230\) | −25.6692 | + | 22.1606i | −0.111605 | + | 0.0963506i | ||||
\(231\) | −107.624 | −0.465905 | ||||||||
\(232\) | −0.175180 | − | 0.175180i | −0.000755085 | − | 0.000755085i | ||||
\(233\) | −88.1385 | + | 88.1385i | −0.378277 | + | 0.378277i | −0.870480 | − | 0.492203i | \(-0.836192\pi\) |
0.492203 | + | 0.870480i | \(0.336192\pi\) | |||||||
\(234\) | − | 105.771i | − | 0.452014i | ||||||
\(235\) | 287.521 | + | 21.0908i | 1.22349 | + | 0.0897481i | ||||
\(236\) | −213.914 | −0.906413 | ||||||||
\(237\) | 27.2421 | + | 27.2421i | 0.114946 | + | 0.114946i | ||||
\(238\) | 153.628 | − | 153.628i | 0.645497 | − | 0.645497i | ||||
\(239\) | 296.594i | 1.24098i | 0.784214 | + | 0.620490i | \(0.213066\pi\) | ||||
−0.784214 | + | 0.620490i | \(0.786934\pi\) | |||||||
\(240\) | 2.53425 | − | 34.5482i | 0.0105594 | − | 0.143951i | ||||
\(241\) | −286.041 | −1.18689 | −0.593445 | − | 0.804874i | \(-0.702233\pi\) | ||||
−0.593445 | + | 0.804874i | \(0.702233\pi\) | |||||||
\(242\) | 18.3014 | + | 18.3014i | 0.0756258 | + | 0.0756258i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 182.210i | − | 0.746761i | ||||||
\(245\) | −69.5413 | − | 80.5512i | −0.283842 | − | 0.328780i | ||||
\(246\) | −139.943 | −0.568874 | ||||||||
\(247\) | −109.268 | − | 109.268i | −0.442380 | − | 0.442380i | ||||
\(248\) | 1.50775 | − | 1.50775i | 0.00607965 | − | 0.00607965i | ||||
\(249\) | 11.2432i | 0.0451534i | ||||||||
\(250\) | 38.5207 | − | 172.529i | 0.154083 | − | 0.690115i | ||||
\(251\) | 181.698 | 0.723897 | 0.361949 | − | 0.932198i | \(-0.382112\pi\) | ||||
0.361949 | + | 0.932198i | \(0.382112\pi\) | |||||||
\(252\) | 22.3361 | + | 22.3361i | 0.0886352 | + | 0.0886352i | ||||
\(253\) | −40.0246 | + | 40.0246i | −0.158200 | + | 0.158200i | ||||
\(254\) | 20.6440i | 0.0812757i | ||||||||
\(255\) | 191.291 | − | 165.145i | 0.750160 | − | 0.647627i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 196.253 | + | 196.253i | 0.763631 | + | 0.763631i | 0.976977 | − | 0.213346i | \(-0.0684361\pi\) |
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(258\) | 4.08243 | − | 4.08243i | 0.0158234 | − | 0.0158234i | ||||
\(259\) | 212.390i | 0.820039i | ||||||||
\(260\) | 248.637 | + | 18.2386i | 0.956298 | + | 0.0701483i | ||||
\(261\) | 0.262770 | 0.00100678 | ||||||||
\(262\) | −184.410 | − | 184.410i | −0.703856 | − | 0.703856i | ||||
\(263\) | 231.129 | − | 231.129i | 0.878816 | − | 0.878816i | −0.114596 | − | 0.993412i | \(-0.536557\pi\) |
0.993412 | + | 0.114596i | \(0.0365575\pi\) | |||||||
\(264\) | − | 57.8207i | − | 0.219018i | ||||||
\(265\) | 3.84204 | − | 52.3767i | 0.0144983 | − | 0.197648i | ||||
\(266\) | 46.1489 | 0.173492 | ||||||||
\(267\) | −36.7732 | − | 36.7732i | −0.137727 | − | 0.137727i | ||||
\(268\) | −44.6418 | + | 44.6418i | −0.166574 | + | 0.166574i | ||||
\(269\) | − | 275.606i | − | 1.02456i | −0.858820 | − | 0.512278i | \(-0.828802\pi\) | ||
0.858820 | − | 0.512278i | \(-0.171198\pi\) | |||||||
\(270\) | 24.0105 | + | 27.8118i | 0.0889276 | + | 0.103007i | ||||
\(271\) | −31.3910 | −0.115834 | −0.0579170 | − | 0.998321i | \(-0.518446\pi\) | ||||
−0.0579170 | + | 0.998321i | \(0.518446\pi\) | |||||||
\(272\) | 82.5364 | + | 82.5364i | 0.303443 | + | 0.303443i | ||||
\(273\) | −160.749 | + | 160.749i | −0.588824 | + | 0.588824i | ||||
\(274\) | − | 342.040i | − | 1.24832i | ||||||
\(275\) | 43.0567 | − | 291.907i | 0.156570 | − | 1.06148i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | −15.9302 | − | 15.9302i | −0.0575096 | − | 0.0575096i | 0.677767 | − | 0.735277i | \(-0.262948\pi\) |
−0.735277 | + | 0.677767i | \(0.762948\pi\) | |||||||
\(278\) | −83.8444 | + | 83.8444i | −0.301599 | + | 0.301599i | ||||
\(279\) | 2.26163i | 0.00810619i | ||||||||
\(280\) | −56.3571 | + | 48.6541i | −0.201275 | + | 0.173765i | ||||
\(281\) | −48.1708 | −0.171426 | −0.0857131 | − | 0.996320i | \(-0.527317\pi\) | ||||
−0.0857131 | + | 0.996320i | \(0.527317\pi\) | |||||||
\(282\) | −99.8677 | − | 99.8677i | −0.354141 | − | 0.354141i | ||||
\(283\) | −136.406 | + | 136.406i | −0.482000 | + | 0.482000i | −0.905770 | − | 0.423770i | \(-0.860706\pi\) |
0.423770 | + | 0.905770i | \(0.360706\pi\) | |||||||
\(284\) | − | 247.414i | − | 0.871177i | ||||||
\(285\) | 53.5355 | + | 3.92704i | 0.187844 | + | 0.0137791i | ||||
\(286\) | 416.126 | 1.45498 | ||||||||
\(287\) | 212.682 | + | 212.682i | 0.741053 | + | 0.741053i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 562.532i | 1.94648i | ||||||||
\(290\) | −0.0453104 | + | 0.617694i | −0.000156243 | + | 0.00212998i | ||||
\(291\) | −296.020 | −1.01725 | ||||||||
\(292\) | 29.3239 | + | 29.3239i | 0.100424 | + | 0.100424i | ||||
\(293\) | 96.8737 | − | 96.8737i | 0.330627 | − | 0.330627i | −0.522198 | − | 0.852825i | \(-0.674888\pi\) |
0.852825 | + | 0.522198i | \(0.174888\pi\) | |||||||
\(294\) | 52.1333i | 0.177324i | ||||||||
\(295\) | 349.472 | + | 404.801i | 1.18465 | + | 1.37221i | ||||
\(296\) | −114.106 | −0.385493 | ||||||||
\(297\) | 43.3655 | + | 43.3655i | 0.146012 | + | 0.146012i | ||||
\(298\) | 117.040 | − | 117.040i | 0.392752 | − | 0.392752i | ||||
\(299\) | 119.563i | 0.399875i | ||||||||
\(300\) | −69.5177 | + | 51.6458i | −0.231726 | + | 0.172153i | ||||
\(301\) | −12.4088 | −0.0412251 | ||||||||
\(302\) | 39.9086 | + | 39.9086i | 0.132148 | + | 0.132148i | ||||
\(303\) | 7.78547 | − | 7.78547i | 0.0256946 | − | 0.0256946i | ||||
\(304\) | 24.7934i | 0.0815572i | ||||||||
\(305\) | −344.806 | + | 297.677i | −1.13051 | + | 0.975990i | ||||
\(306\) | −123.805 | −0.404590 | ||||||||
\(307\) | 95.1467 | + | 95.1467i | 0.309924 | + | 0.309924i | 0.844880 | − | 0.534956i | \(-0.179672\pi\) |
−0.534956 | + | 0.844880i | \(0.679672\pi\) | |||||||
\(308\) | −87.8746 | + | 87.8746i | −0.285307 | + | 0.285307i | ||||
\(309\) | 315.521i | 1.02110i | ||||||||
\(310\) | −5.31643 | − | 0.389981i | −0.0171498 | − | 0.00125800i | ||||
\(311\) | −374.486 | −1.20414 | −0.602068 | − | 0.798445i | \(-0.705656\pi\) | ||||
−0.602068 | + | 0.798445i | \(0.705656\pi\) | |||||||
\(312\) | −86.3619 | − | 86.3619i | −0.276801 | − | 0.276801i | ||||
\(313\) | 276.544 | − | 276.544i | 0.883528 | − | 0.883528i | −0.110363 | − | 0.993891i | \(-0.535201\pi\) |
0.993891 | + | 0.110363i | \(0.0352015\pi\) | |||||||
\(314\) | − | 112.661i | − | 0.358793i | ||||||
\(315\) | 5.77724 | − | 78.7583i | 0.0183404 | − | 0.250026i | ||||
\(316\) | 44.4862 | 0.140779 | ||||||||
\(317\) | 119.954 | + | 119.954i | 0.378403 | + | 0.378403i | 0.870526 | − | 0.492123i | \(-0.163779\pi\) |
−0.492123 | + | 0.870526i | \(0.663779\pi\) | |||||||
\(318\) | −18.1926 | + | 18.1926i | −0.0572093 | + | 0.0572093i | ||||
\(319\) | 1.03379i | 0.00324072i | ||||||||
\(320\) | −26.1393 | − | 30.2777i | −0.0816852 | − | 0.0946178i | ||||
\(321\) | −116.233 | −0.362097 | ||||||||
\(322\) | −25.2484 | − | 25.2484i | −0.0784113 | − | 0.0784113i | ||||
\(323\) | −127.897 | + | 127.897i | −0.395967 | + | 0.395967i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −371.686 | − | 500.307i | −1.14365 | − | 1.53941i | ||||
\(326\) | 209.901 | 0.643867 | ||||||||
\(327\) | −178.679 | − | 178.679i | −0.546418 | − | 0.546418i | ||||
\(328\) | −114.263 | + | 114.263i | −0.348363 | + | 0.348363i | ||||
\(329\) | 303.553i | 0.922655i | ||||||||
\(330\) | −109.417 | + | 94.4620i | −0.331568 | + | 0.286248i | ||||
\(331\) | −28.1304 | −0.0849862 | −0.0424931 | − | 0.999097i | \(-0.513530\pi\) | ||||
−0.0424931 | + | 0.999097i | \(0.513530\pi\) | |||||||
\(332\) | 9.18003 | + | 9.18003i | 0.0276507 | + | 0.0276507i | ||||
\(333\) | 85.5795 | − | 85.5795i | 0.256995 | − | 0.256995i | ||||
\(334\) | − | 347.322i | − | 1.03989i | ||||||
\(335\) | 157.410 | + | 11.5466i | 0.469880 | + | 0.0344676i | ||||
\(336\) | 36.4747 | 0.108556 | ||||||||
\(337\) | −3.26452 | − | 3.26452i | −0.00968699 | − | 0.00968699i | 0.702247 | − | 0.711934i | \(-0.252180\pi\) |
−0.711934 | + | 0.702247i | \(0.752180\pi\) | |||||||
\(338\) | 452.532 | − | 452.532i | 1.33885 | − | 1.33885i | ||||
\(339\) | − | 230.999i | − | 0.681413i | ||||||
\(340\) | 21.3481 | − | 291.028i | 0.0627885 | − | 0.855966i | ||||
\(341\) | −8.89770 | −0.0260930 | ||||||||
\(342\) | −18.5951 | − | 18.5951i | −0.0543715 | − | 0.0543715i | ||||
\(343\) | 261.642 | − | 261.642i | 0.762805 | − | 0.762805i | ||||
\(344\) | − | 6.66658i | − | 0.0193796i | ||||||
\(345\) | −27.1411 | − | 31.4382i | −0.0786700 | − | 0.0911251i | ||||
\(346\) | −303.998 | −0.878608 | ||||||||
\(347\) | −298.180 | − | 298.180i | −0.859309 | − | 0.859309i | 0.131947 | − | 0.991257i | \(-0.457877\pi\) |
−0.991257 | + | 0.131947i | \(0.957877\pi\) | |||||||
\(348\) | 0.214551 | − | 0.214551i | 0.000616524 | − | 0.000616524i | ||||
\(349\) | − | 330.198i | − | 0.946127i | −0.881028 | − | 0.473063i | \(-0.843148\pi\) | ||
0.881028 | − | 0.473063i | \(-0.156852\pi\) | |||||||
\(350\) | 184.142 | + | 27.1612i | 0.526119 | + | 0.0776034i | ||||
\(351\) | 129.543 | 0.369068 | ||||||||
\(352\) | −47.2104 | − | 47.2104i | −0.134120 | − | 0.134120i | ||||
\(353\) | −121.953 | + | 121.953i | −0.345476 | + | 0.345476i | −0.858421 | − | 0.512946i | \(-0.828554\pi\) |
0.512946 | + | 0.858421i | \(0.328554\pi\) | |||||||
\(354\) | − | 261.990i | − | 0.740084i | ||||||
\(355\) | −468.196 | + | 404.202i | −1.31886 | + | 1.13860i | ||||
\(356\) | −60.0503 | −0.168681 | ||||||||
\(357\) | 188.155 | + | 188.155i | 0.527046 | + | 0.527046i | ||||
\(358\) | 133.690 | − | 133.690i | 0.373437 | − | 0.373437i | ||||
\(359\) | − | 14.1715i | − | 0.0394748i | −0.999805 | − | 0.0197374i | \(-0.993717\pi\) | ||
0.999805 | − | 0.0197374i | \(-0.00628302\pi\) | |||||||
\(360\) | 42.3127 | + | 3.10381i | 0.117535 | + | 0.00862169i | ||||
\(361\) | 322.580 | 0.893575 | ||||||||
\(362\) | 269.565 | + | 269.565i | 0.744655 | + | 0.744655i | ||||
\(363\) | −22.4146 | + | 22.4146i | −0.0617482 | + | 0.0617482i | ||||
\(364\) | 262.502i | 0.721159i | ||||||||
\(365\) | 7.58464 | − | 103.398i | 0.0207798 | − | 0.283281i | ||||
\(366\) | 223.160 | 0.609728 | ||||||||
\(367\) | −63.9505 | − | 63.9505i | −0.174252 | − | 0.174252i | 0.614593 | − | 0.788845i | \(-0.289320\pi\) |
−0.788845 | + | 0.614593i | \(0.789320\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 171.394i | − | 0.464483i | ||||||
\(370\) | 186.416 | + | 215.929i | 0.503826 | + | 0.583592i | ||||
\(371\) | 55.2973 | 0.149049 | ||||||||
\(372\) | 1.84661 | + | 1.84661i | 0.00496401 | + | 0.00496401i | ||||
\(373\) | −160.697 | + | 160.697i | −0.430824 | + | 0.430824i | −0.888909 | − | 0.458085i | \(-0.848536\pi\) |
0.458085 | + | 0.888909i | \(0.348536\pi\) | |||||||
\(374\) | − | 487.072i | − | 1.30233i | ||||||
\(375\) | 211.304 | + | 47.1781i | 0.563476 | + | 0.125808i | ||||
\(376\) | −163.083 | −0.433732 | ||||||||
\(377\) | 1.54408 | + | 1.54408i | 0.00409571 | + | 0.00409571i | ||||
\(378\) | −27.3560 | + | 27.3560i | −0.0723703 | + | 0.0723703i | ||||
\(379\) | − | 201.845i | − | 0.532573i | −0.963894 | − | 0.266287i | \(-0.914203\pi\) | ||
0.963894 | − | 0.266287i | \(-0.0857968\pi\) | |||||||
\(380\) | 46.9179 | − | 40.5051i | 0.123468 | − | 0.106592i | ||||
\(381\) | −25.2837 | −0.0663613 | ||||||||
\(382\) | −322.402 | − | 322.402i | −0.843986 | − | 0.843986i | ||||
\(383\) | 177.891 | − | 177.891i | 0.464466 | − | 0.464466i | −0.435650 | − | 0.900116i | \(-0.643481\pi\) |
0.900116 | + | 0.435650i | \(0.143481\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 309.851 | + | 22.7288i | 0.804808 | + | 0.0590359i | ||||
\(386\) | −179.675 | −0.465480 | ||||||||
\(387\) | 4.99993 | + | 4.99993i | 0.0129197 | + | 0.0129197i | ||||
\(388\) | −241.699 | + | 241.699i | −0.622936 | + | 0.622936i | ||||
\(389\) | 501.474i | 1.28914i | 0.764547 | + | 0.644568i | \(0.222963\pi\) | ||||
−0.764547 | + | 0.644568i | \(0.777037\pi\) | |||||||
\(390\) | −22.3376 | + | 304.517i | −0.0572758 | + | 0.780814i | ||||
\(391\) | 139.947 | 0.357921 | ||||||||
\(392\) | 42.5666 | + | 42.5666i | 0.108588 | + | 0.108588i | ||||
\(393\) | 225.856 | − | 225.856i | 0.574696 | − | 0.574696i | ||||
\(394\) | − | 86.8144i | − | 0.220341i | ||||||
\(395\) | −72.6773 | − | 84.1836i | −0.183993 | − | 0.213123i | ||||
\(396\) | 70.8156 | 0.178827 | ||||||||
\(397\) | −379.320 | − | 379.320i | −0.955467 | − | 0.955467i | 0.0435831 | − | 0.999050i | \(-0.486123\pi\) |
−0.999050 | + | 0.0435831i | \(0.986123\pi\) | |||||||
\(398\) | −241.437 | + | 241.437i | −0.606624 | + | 0.606624i | ||||
\(399\) | 56.5207i | 0.141656i | ||||||||
\(400\) | −14.5923 | + | 98.9296i | −0.0364807 | + | 0.247324i | ||||
\(401\) | 179.175 | 0.446820 | 0.223410 | − | 0.974725i | \(-0.428281\pi\) | ||||
0.223410 | + | 0.974725i | \(0.428281\pi\) | |||||||
\(402\) | −54.6749 | − | 54.6749i | −0.136007 | − | 0.136007i | ||||
\(403\) | −13.2897 | + | 13.2897i | −0.0329770 | + | 0.0329770i | ||||
\(404\) | − | 12.7136i | − | 0.0314693i | ||||||
\(405\) | −34.0624 | + | 29.4067i | −0.0841047 | + | 0.0726091i | ||||
\(406\) | −0.652138 | −0.00160625 | ||||||||
\(407\) | 336.687 | + | 336.687i | 0.827241 | + | 0.827241i | ||||
\(408\) | −101.086 | + | 101.086i | −0.247760 | + | 0.247760i | ||||
\(409\) | 384.881i | 0.941029i | 0.882392 | + | 0.470514i | \(0.155932\pi\) | ||||
−0.882392 | + | 0.470514i | \(0.844068\pi\) | |||||||
\(410\) | 402.898 | + | 29.5542i | 0.982678 | + | 0.0720834i | ||||
\(411\) | 418.911 | 1.01925 | ||||||||
\(412\) | 257.622 | + | 257.622i | 0.625296 | + | 0.625296i | ||||
\(413\) | −398.166 | + | 398.166i | −0.964082 | + | 0.964082i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 2.37442 | − | 32.3693i | 0.00572150 | − | 0.0779984i | ||||
\(416\) | −141.028 | −0.339011 | ||||||||
\(417\) | −102.688 | − | 102.688i | −0.246254 | − | 0.246254i | ||||
\(418\) | 73.1567 | − | 73.1567i | 0.175016 | − | 0.175016i | ||||
\(419\) | 375.801i | 0.896900i | 0.893808 | + | 0.448450i | \(0.148024\pi\) | ||||
−0.893808 | + | 0.448450i | \(0.851976\pi\) | |||||||
\(420\) | −59.5888 | − | 69.0230i | −0.141878 | − | 0.164341i | ||||
\(421\) | 109.575 | 0.260274 | 0.130137 | − | 0.991496i | \(-0.458458\pi\) | ||||
0.130137 | + | 0.991496i | \(0.458458\pi\) | |||||||
\(422\) | −52.1391 | − | 52.1391i | −0.123552 | − | 0.123552i | ||||
\(423\) | 122.312 | − | 122.312i | 0.289155 | − | 0.289155i | ||||
\(424\) | 29.7083i | 0.0700668i | ||||||||
\(425\) | −585.606 | + | 435.056i | −1.37790 | + | 1.02366i | ||||
\(426\) | 303.019 | 0.711313 | ||||||||
\(427\) | −339.154 | − | 339.154i | −0.794272 | − | 0.794272i | ||||
\(428\) | −94.9040 | + | 94.9040i | −0.221738 | + | 0.221738i | ||||
\(429\) | 509.648i | 1.18799i | ||||||||
\(430\) | −12.6155 | + | 10.8912i | −0.0293385 | + | 0.0253284i | ||||
\(431\) | −720.493 | −1.67168 | −0.835839 | − | 0.548975i | \(-0.815018\pi\) | ||||
−0.835839 | + | 0.548975i | \(0.815018\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −10.2464 | + | 10.2464i | −0.0236638 | + | 0.0236638i | −0.718840 | − | 0.695176i | \(-0.755326\pi\) |
0.695176 | + | 0.718840i | \(0.255326\pi\) | |||||||
\(434\) | − | 5.61288i | − | 0.0129329i | ||||||
\(435\) | −0.756518 | − | 0.0554936i | −0.00173912 | − | 0.000127572i | ||||
\(436\) | −291.781 | −0.669222 | ||||||||
\(437\) | 21.0196 | + | 21.0196i | 0.0480998 | + | 0.0480998i | ||||
\(438\) | −35.9142 | + | 35.9142i | −0.0819960 | + | 0.0819960i | ||||
\(439\) | 627.889i | 1.43027i | 0.698985 | + | 0.715136i | \(0.253635\pi\) | ||||
−0.698985 | + | 0.715136i | \(0.746365\pi\) | |||||||
\(440\) | −12.2110 | + | 166.467i | −0.0277523 | + | 0.378334i | ||||
\(441\) | −63.8500 | −0.144785 | ||||||||
\(442\) | −727.499 | − | 727.499i | −1.64593 | − | 1.64593i | ||||
\(443\) | −253.351 | + | 253.351i | −0.571898 | + | 0.571898i | −0.932658 | − | 0.360761i | \(-0.882517\pi\) |
0.360761 | + | 0.932658i | \(0.382517\pi\) | |||||||
\(444\) | − | 139.751i | − | 0.314754i | ||||||
\(445\) | 98.1045 | + | 113.637i | 0.220460 | + | 0.255363i | ||||
\(446\) | 560.903 | 1.25763 | ||||||||
\(447\) | 143.344 | + | 143.344i | 0.320681 | + | 0.320681i | ||||
\(448\) | 29.7814 | − | 29.7814i | 0.0664764 | − | 0.0664764i | ||||
\(449\) | 86.2603i | 0.192116i | 0.995376 | + | 0.0960582i | \(0.0306235\pi\) | ||||
−0.995376 | + | 0.0960582i | \(0.969377\pi\) | |||||||
\(450\) | −63.2530 | − | 85.1414i | −0.140562 | − | 0.189203i | ||||
\(451\) | 674.300 | 1.49512 | ||||||||
\(452\) | −188.610 | − | 188.610i | −0.417278 | − | 0.417278i | ||||
\(453\) | −48.8778 | + | 48.8778i | −0.107898 | + | 0.107898i | ||||
\(454\) | 288.792i | 0.636105i | ||||||||
\(455\) | 496.747 | − | 428.850i | 1.09175 | − | 0.942528i | ||||
\(456\) | −30.3656 | −0.0665912 | ||||||||
\(457\) | 302.229 | + | 302.229i | 0.661333 | + | 0.661333i | 0.955694 | − | 0.294361i | \(-0.0951068\pi\) |
−0.294361 | + | 0.955694i | \(0.595107\pi\) | |||||||
\(458\) | −362.796 | + | 362.796i | −0.792131 | + | 0.792131i | ||||
\(459\) | − | 151.629i | − | 0.330347i | ||||||
\(460\) | −47.8298 | − | 3.50851i | −0.103978 | − | 0.00762719i | ||||
\(461\) | −592.540 | −1.28534 | −0.642668 | − | 0.766145i | \(-0.722172\pi\) | ||||
−0.642668 | + | 0.766145i | \(0.722172\pi\) | |||||||
\(462\) | −107.624 | − | 107.624i | −0.232952 | − | 0.232952i | ||||
\(463\) | −210.922 | + | 210.922i | −0.455554 | + | 0.455554i | −0.897193 | − | 0.441639i | \(-0.854397\pi\) |
0.441639 | + | 0.897193i | \(0.354397\pi\) | |||||||
\(464\) | − | 0.350360i | − | 0.000755085i | ||||||
\(465\) | 0.477627 | − | 6.51126i | 0.00102716 | − | 0.0140027i | ||||
\(466\) | −176.277 | −0.378277 | ||||||||
\(467\) | −75.0504 | − | 75.0504i | −0.160707 | − | 0.160707i | 0.622173 | − | 0.782880i | \(-0.286250\pi\) |
−0.782880 | + | 0.622173i | \(0.786250\pi\) | |||||||
\(468\) | 105.771 | − | 105.771i | 0.226007 | − | 0.226007i | ||||
\(469\) | 166.187i | 0.354344i | ||||||||
\(470\) | 266.430 | + | 308.612i | 0.566872 | + | 0.656620i | ||||
\(471\) | 137.981 | 0.292953 | ||||||||
\(472\) | −213.914 | − | 213.914i | −0.453207 | − | 0.453207i | ||||
\(473\) | −19.6707 | + | 19.6707i | −0.0415872 | + | 0.0415872i | ||||
\(474\) | 54.4842i | 0.114946i | ||||||||
\(475\) | −153.300 | − | 22.6120i | −0.322737 | − | 0.0476043i | ||||
\(476\) | 307.257 | 0.645497 | ||||||||
\(477\) | −22.2813 | − | 22.2813i | −0.0467112 | − | 0.0467112i | ||||
\(478\) | −296.594 | + | 296.594i | −0.620490 | + | 0.620490i | ||||
\(479\) | 582.683i | 1.21646i | 0.793762 | + | 0.608229i | \(0.208120\pi\) | ||||
−0.793762 | + | 0.608229i | \(0.791880\pi\) | |||||||
\(480\) | 37.0824 | − | 32.0139i | 0.0772551 | − | 0.0666957i | ||||
\(481\) | 1005.76 | 2.09098 | ||||||||
\(482\) | −286.041 | − | 286.041i | −0.593445 | − | 0.593445i | ||||
\(483\) | 30.9229 | − | 30.9229i | 0.0640226 | − | 0.0640226i | ||||
\(484\) | 36.6029i | 0.0756258i | ||||||||
\(485\) | 852.246 | + | 62.5157i | 1.75721 | + | 0.128898i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 324.456 | + | 324.456i | 0.666234 | + | 0.666234i | 0.956842 | − | 0.290608i | \(-0.0938575\pi\) |
−0.290608 | + | 0.956842i | \(0.593858\pi\) | |||||||
\(488\) | 182.210 | − | 182.210i | 0.373381 | − | 0.373381i | ||||
\(489\) | 257.075i | 0.525715i | ||||||||
\(490\) | 11.0099 | − | 150.093i | 0.0224692 | − | 0.306311i | ||||
\(491\) | 371.828 | 0.757288 | 0.378644 | − | 0.925542i | \(-0.376390\pi\) | ||||
0.378644 | + | 0.925542i | \(0.376390\pi\) | |||||||
\(492\) | −139.943 | − | 139.943i | −0.284437 | − | 0.284437i | ||||
\(493\) | 1.80734 | − | 1.80734i | 0.00366600 | − | 0.00366600i | ||||
\(494\) | − | 218.536i | − | 0.442380i | ||||||
\(495\) | −115.692 | − | 134.008i | −0.233721 | − | 0.270724i | ||||
\(496\) | 3.01550 | 0.00607965 | ||||||||
\(497\) | −460.522 | − | 460.522i | −0.926604 | − | 0.926604i | ||||
\(498\) | −11.2432 | + | 11.2432i | −0.0225767 | + | 0.0225767i | ||||
\(499\) | − | 116.928i | − | 0.234325i | −0.993113 | − | 0.117163i | \(-0.962620\pi\) | ||
0.993113 | − | 0.117163i | \(-0.0373799\pi\) | |||||||
\(500\) | 211.049 | − | 134.008i | 0.422099 | − | 0.268016i | ||||
\(501\) | 425.381 | 0.849063 | ||||||||
\(502\) | 181.698 | + | 181.698i | 0.361949 | + | 0.361949i | ||||
\(503\) | −97.5611 | + | 97.5611i | −0.193959 | + | 0.193959i | −0.797404 | − | 0.603446i | \(-0.793794\pi\) |
0.603446 | + | 0.797404i | \(0.293794\pi\) | |||||||
\(504\) | 44.6721i | 0.0886352i | ||||||||
\(505\) | −24.0587 | + | 20.7703i | −0.0476410 | + | 0.0411293i | ||||
\(506\) | −80.0491 | −0.158200 | ||||||||
\(507\) | 554.236 | + | 554.236i | 1.09317 | + | 1.09317i | ||||
\(508\) | −20.6440 | + | 20.6440i | −0.0406379 | + | 0.0406379i | ||||
\(509\) | − | 442.972i | − | 0.870278i | −0.900363 | − | 0.435139i | \(-0.856699\pi\) | ||
0.900363 | − | 0.435139i | \(-0.143301\pi\) | |||||||
\(510\) | 356.435 | + | 26.1460i | 0.698893 | + | 0.0512666i | ||||
\(511\) | 109.163 | 0.213627 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 22.7742 | − | 22.7742i | 0.0443941 | − | 0.0443941i | ||||
\(514\) | 392.506i | 0.763631i | ||||||||
\(515\) | 66.6340 | − | 908.390i | 0.129386 | − | 1.76386i | ||||
\(516\) | 8.16486 | 0.0158234 | ||||||||
\(517\) | 481.202 | + | 481.202i | 0.930758 | + | 0.930758i | ||||
\(518\) | −212.390 | + | 212.390i | −0.410019 | + | 0.410019i | ||||
\(519\) | − | 372.320i | − | 0.717380i | ||||||
\(520\) | 230.399 | + | 266.876i | 0.443075 | + | 0.513223i | ||||
\(521\) | −666.249 | −1.27879 | −0.639394 | − | 0.768879i | \(-0.720815\pi\) | ||||
−0.639394 | + | 0.768879i | \(0.720815\pi\) | |||||||
\(522\) | 0.262770 | + | 0.262770i | 0.000503390 | + | 0.000503390i | ||||
\(523\) | −57.5211 | + | 57.5211i | −0.109983 | + | 0.109983i | −0.759957 | − | 0.649974i | \(-0.774780\pi\) |
0.649974 | + | 0.759957i | \(0.274780\pi\) | |||||||
\(524\) | − | 368.821i | − | 0.703856i | ||||||
\(525\) | −33.2655 | + | 225.526i | −0.0633629 | + | 0.429574i | ||||
\(526\) | 462.257 | 0.878816 | ||||||||
\(527\) | 15.5556 | + | 15.5556i | 0.0295172 | + | 0.0295172i | ||||
\(528\) | 57.8207 | − | 57.8207i | 0.109509 | − | 0.109509i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 56.2187 | − | 48.5346i | 0.106073 | − | 0.0915748i | ||||
\(531\) | 320.870 | 0.604276 | ||||||||
\(532\) | 46.1489 | + | 46.1489i | 0.0867461 | + | 0.0867461i | ||||
\(533\) | 1007.15 | − | 1007.15i | 1.88958 | − | 1.88958i | ||||
\(534\) | − | 73.5464i | − | 0.137727i | ||||||
\(535\) | 334.637 | + | 24.5470i | 0.625490 | + | 0.0458822i | ||||
\(536\) | −89.2837 | −0.166574 | ||||||||
\(537\) | 163.737 | + | 163.737i | 0.304910 | + | 0.304910i | ||||
\(538\) | 275.606 | − | 275.606i | 0.512278 | − | 0.512278i | ||||
\(539\) | − | 251.199i | − | 0.466046i | ||||||
\(540\) | −3.80137 | + | 51.8223i | −0.00703958 | + | 0.0959672i | ||||
\(541\) | 487.704 | 0.901487 | 0.450743 | − | 0.892654i | \(-0.351159\pi\) | ||||
0.450743 | + | 0.892654i | \(0.351159\pi\) | |||||||
\(542\) | −31.3910 | − | 31.3910i | −0.0579170 | − | 0.0579170i | ||||
\(543\) | −330.148 | + | 330.148i | −0.608008 | + | 0.608008i | ||||
\(544\) | 165.073i | 0.303443i | ||||||||
\(545\) | 476.684 | + | 552.153i | 0.874650 | + | 1.01313i | ||||
\(546\) | −321.498 | −0.588824 | ||||||||
\(547\) | −151.290 | − | 151.290i | −0.276582 | − | 0.276582i | 0.555161 | − | 0.831743i | \(-0.312657\pi\) |
−0.831743 | + | 0.555161i | \(0.812657\pi\) | |||||||
\(548\) | 342.040 | − | 342.040i | 0.624160 | − | 0.624160i | ||||
\(549\) | 273.315i | 0.497841i | ||||||||
\(550\) | 334.963 | − | 248.850i | 0.609024 | − | 0.452454i | ||||
\(551\) | 0.542913 | 0.000985323 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | 82.8039 | − | 82.8039i | 0.149736 | − | 0.149736i | ||||
\(554\) | − | 31.8603i | − | 0.0575096i | ||||||
\(555\) | −264.458 | + | 228.311i | −0.476501 | + | 0.411372i | ||||
\(556\) | −167.689 | −0.301599 | ||||||||
\(557\) | −54.8204 | − | 54.8204i | −0.0984208 | − | 0.0984208i | 0.656182 | − | 0.754603i | \(-0.272170\pi\) |
−0.754603 | + | 0.656182i | \(0.772170\pi\) | |||||||
\(558\) | −2.26163 | + | 2.26163i | −0.00405310 | + | 0.00405310i | ||||
\(559\) | 58.7611i | 0.105118i | ||||||||
\(560\) | −105.011 | − | 7.70299i | −0.187520 | − | 0.0137553i | ||||
\(561\) | 596.539 | 1.06335 | ||||||||
\(562\) | −48.1708 | − | 48.1708i | −0.0857131 | − | 0.0857131i | ||||
\(563\) | 393.961 | − | 393.961i | 0.699753 | − | 0.699753i | −0.264604 | − | 0.964357i | \(-0.585241\pi\) |
0.964357 | + | 0.264604i | \(0.0852412\pi\) | |||||||
\(564\) | − | 199.735i | − | 0.354141i | ||||||
\(565\) | −48.7841 | + | 665.050i | −0.0863435 | + | 1.17708i | ||||
\(566\) | −272.812 | −0.482000 | ||||||||
\(567\) | −33.5041 | − | 33.5041i | −0.0590901 | − | 0.0590901i | ||||
\(568\) | 247.414 | − | 247.414i | 0.435589 | − | 0.435589i | ||||
\(569\) | 928.406i | 1.63165i | 0.578302 | + | 0.815823i | \(0.303716\pi\) | ||||
−0.578302 | + | 0.815823i | \(0.696284\pi\) | |||||||
\(570\) | 49.6084 | + | 57.4625i | 0.0870323 | + | 0.100811i | ||||
\(571\) | −817.767 | −1.43217 | −0.716083 | − | 0.698015i | \(-0.754067\pi\) | ||||
−0.716083 | + | 0.698015i | \(0.754067\pi\) | |||||||
\(572\) | 416.126 | + | 416.126i | 0.727492 | + | 0.727492i | ||||
\(573\) | 394.861 | − | 394.861i | 0.689111 | − | 0.689111i | ||||
\(574\) | 425.364i | 0.741053i | ||||||||
\(575\) | 71.5004 | + | 96.2429i | 0.124349 | + | 0.167379i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 259.934 | + | 259.934i | 0.450491 | + | 0.450491i | 0.895518 | − | 0.445026i | \(-0.146806\pi\) |
−0.445026 | + | 0.895518i | \(0.646806\pi\) | |||||||
\(578\) | −562.532 | + | 562.532i | −0.973240 | + | 0.973240i | ||||
\(579\) | − | 220.056i | − | 0.380063i | ||||||
\(580\) | −0.663005 | + | 0.572384i | −0.00114311 | + | 0.000986869i | ||||
\(581\) | 34.1743 | 0.0588198 | ||||||||
\(582\) | −296.020 | − | 296.020i | −0.508625 | − | 0.508625i | ||||
\(583\) | 87.6589 | − | 87.6589i | 0.150358 | − | 0.150358i | ||||
\(584\) | 58.6477i | 0.100424i | ||||||||
\(585\) | −372.956 | − | 27.3578i | −0.637532 | − | 0.0467655i | ||||
\(586\) | 193.747 | 0.330627 | ||||||||
\(587\) | 331.058 | + | 331.058i | 0.563984 | + | 0.563984i | 0.930437 | − | 0.366453i | \(-0.119428\pi\) |
−0.366453 | + | 0.930437i | \(0.619428\pi\) | |||||||
\(588\) | −52.1333 | + | 52.1333i | −0.0886620 | + | 0.0886620i | ||||
\(589\) | 4.67279i | 0.00793343i | ||||||||
\(590\) | −55.3289 | + | 754.272i | −0.0937778 | + | 1.27843i | ||||
\(591\) | 106.325 | 0.179908 | ||||||||
\(592\) | −114.106 | − | 114.106i | −0.192747 | − | 0.192747i | ||||
\(593\) | 614.053 | − | 614.053i | 1.03550 | − | 1.03550i | 0.0361568 | − | 0.999346i | \(-0.488488\pi\) |
0.999346 | − | 0.0361568i | \(-0.0115116\pi\) | |||||||
\(594\) | 86.7311i | 0.146012i | ||||||||
\(595\) | −501.967 | − | 581.439i | −0.843641 | − | 0.977208i | ||||
\(596\) | 234.080 | 0.392752 | ||||||||
\(597\) | −295.698 | − | 295.698i | −0.495307 | − | 0.495307i | ||||
\(598\) | −119.563 | + | 119.563i | −0.199938 | + | 0.199938i | ||||
\(599\) | − | 536.579i | − | 0.895791i | −0.894086 | − | 0.447895i | \(-0.852174\pi\) | ||
0.894086 | − | 0.447895i | \(-0.147826\pi\) | |||||||
\(600\) | −121.164 | − | 17.8718i | −0.201939 | − | 0.0297864i | ||||
\(601\) | −764.010 | −1.27123 | −0.635616 | − | 0.772006i | \(-0.719254\pi\) | ||||
−0.635616 | + | 0.772006i | \(0.719254\pi\) | |||||||
\(602\) | −12.4088 | − | 12.4088i | −0.0206126 | − | 0.0206126i | ||||
\(603\) | 66.9628 | − | 66.9628i | 0.111049 | − | 0.111049i | ||||
\(604\) | 79.8172i | 0.132148i | ||||||||
\(605\) | 69.2657 | − | 59.7983i | 0.114489 | − | 0.0988402i | ||||
\(606\) | 15.5709 | 0.0256946 | ||||||||
\(607\) | −375.415 | − | 375.415i | −0.618476 | − | 0.618476i | 0.326665 | − | 0.945140i | \(-0.394075\pi\) |
−0.945140 | + | 0.326665i | \(0.894075\pi\) | |||||||
\(608\) | −24.7934 | + | 24.7934i | −0.0407786 | + | 0.0407786i | ||||
\(609\) | − | 0.798703i | − | 0.00131150i | ||||||
\(610\) | −642.483 | − | 47.1287i | −1.05325 | − | 0.0772601i | ||||
\(611\) | 1437.46 | 2.35264 | ||||||||
\(612\) | −123.805 | − | 123.805i | −0.202295 | − | 0.202295i | ||||
\(613\) | −195.776 | + | 195.776i | −0.319374 | + | 0.319374i | −0.848527 | − | 0.529153i | \(-0.822510\pi\) |
0.529153 | + | 0.848527i | \(0.322510\pi\) | |||||||
\(614\) | 190.293i | 0.309924i | ||||||||
\(615\) | −36.1963 | + | 493.447i | −0.0588558 | + | 0.802353i | ||||
\(616\) | −175.749 | −0.285307 | ||||||||
\(617\) | −124.149 | − | 124.149i | −0.201214 | − | 0.201214i | 0.599306 | − | 0.800520i | \(-0.295443\pi\) |
−0.800520 | + | 0.599306i | \(0.795443\pi\) | |||||||
\(618\) | −315.521 | + | 315.521i | −0.510552 | + | 0.510552i | ||||
\(619\) | − | 144.829i | − | 0.233972i | −0.993134 | − | 0.116986i | \(-0.962677\pi\) | ||
0.993134 | − | 0.116986i | \(-0.0373232\pi\) | |||||||
\(620\) | −4.92644 | − | 5.70641i | −0.00794588 | − | 0.00920388i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | −374.486 | − | 374.486i | −0.602068 | − | 0.602068i | ||||
\(623\) | −111.774 | + | 111.774i | −0.179413 | + | 0.179413i | ||||
\(624\) | − | 172.724i | − | 0.276801i | ||||||
\(625\) | −598.383 | − | 180.451i | −0.957413 | − | 0.288722i | ||||
\(626\) | 553.088 | 0.883528 | ||||||||
\(627\) | 89.5983 | + | 89.5983i | 0.142900 | + | 0.142900i | ||||
\(628\) | 112.661 | − | 112.661i | 0.179396 | − | 0.179396i | ||||
\(629\) | − | 1177.24i | − | 1.87160i | ||||||
\(630\) | 84.5356 | − | 72.9811i | 0.134183 | − | 0.115843i | ||||
\(631\) | 990.046 | 1.56901 | 0.784506 | − | 0.620122i | \(-0.212917\pi\) | ||||
0.784506 | + | 0.620122i | \(0.212917\pi\) | |||||||
\(632\) | 44.4862 | + | 44.4862i | 0.0703895 | + | 0.0703895i | ||||
\(633\) | 63.8570 | − | 63.8570i | 0.100880 | − | 0.100880i | ||||
\(634\) | 239.907i | 0.378403i | ||||||||
\(635\) | 72.7921 | + | 5.33959i | 0.114633 | + | 0.00840881i | ||||
\(636\) | −36.3851 | −0.0572093 | ||||||||
\(637\) | −375.194 | − | 375.194i | −0.589002 | − | 0.589002i | ||||
\(638\) | −1.03379 | + | 1.03379i | −0.00162036 | + | 0.00162036i | ||||
\(639\) | 371.121i | 0.580785i | ||||||||
\(640\) | 4.13841 | − | 56.4170i | 0.00646627 | − | 0.0881515i | ||||
\(641\) | −1189.18 | −1.85519 | −0.927595 | − | 0.373587i | \(-0.878128\pi\) | ||||
−0.927595 | + | 0.373587i | \(0.878128\pi\) | |||||||
\(642\) | −116.233 | − | 116.233i | −0.181049 | − | 0.181049i | ||||
\(643\) | 44.5224 | − | 44.5224i | 0.0692416 | − | 0.0692416i | −0.671638 | − | 0.740880i | \(-0.734409\pi\) |
0.740880 | + | 0.671638i | \(0.234409\pi\) | |||||||
\(644\) | − | 50.4969i | − | 0.0784113i | ||||||
\(645\) | −13.3390 | − | 15.4508i | −0.0206806 | − | 0.0239547i | ||||
\(646\) | −255.795 | −0.395967 | ||||||||
\(647\) | 360.032 | + | 360.032i | 0.556464 | + | 0.556464i | 0.928299 | − | 0.371835i | \(-0.121271\pi\) |
−0.371835 | + | 0.928299i | \(0.621271\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 1262.37i | 1.94510i | ||||||||
\(650\) | 128.620 | − | 871.993i | 0.197878 | − | 1.34153i | ||||
\(651\) | 6.87434 | 0.0105597 | ||||||||
\(652\) | 209.901 | + | 209.901i | 0.321934 | + | 0.321934i | ||||
\(653\) | 712.901 | − | 712.901i | 1.09173 | − | 1.09173i | 0.0963890 | − | 0.995344i | \(-0.469271\pi\) |
0.995344 | − | 0.0963890i | \(-0.0307293\pi\) | |||||||
\(654\) | − | 357.357i | − | 0.546418i | ||||||
\(655\) | −697.940 | + | 602.544i | −1.06556 | + | 0.919914i | ||||
\(656\) | −228.526 | −0.348363 | ||||||||
\(657\) | −43.9858 | − | 43.9858i | −0.0669495 | − | 0.0669495i | ||||
\(658\) | −303.553 | + | 303.553i | −0.461327 | + | 0.461327i | ||||
\(659\) | 1012.88i | 1.53699i | 0.639854 | + | 0.768497i | \(0.278995\pi\) | ||||
−0.639854 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(660\) | −203.879 | − | 14.9554i | −0.308908 | − | 0.0226596i | ||||
\(661\) | −913.639 | −1.38221 | −0.691104 | − | 0.722756i | \(-0.742875\pi\) | ||||
−0.691104 | + | 0.722756i | \(0.742875\pi\) | |||||||
\(662\) | −28.1304 | − | 28.1304i | −0.0424931 | − | 0.0424931i | ||||
\(663\) | 891.001 | − | 891.001i | 1.34389 | − | 1.34389i | ||||
\(664\) | 18.3601i | 0.0276507i | ||||||||
\(665\) | 11.9365 | − | 162.724i | 0.0179496 | − | 0.244698i | ||||
\(666\) | 171.159 | 0.256995 | ||||||||
\(667\) | −0.297032 | − | 0.297032i | −0.000445325 | − | 0.000445325i | ||||
\(668\) | 347.322 | − | 347.322i | 0.519943 | − | 0.519943i | ||||
\(669\) | 686.964i | 1.02685i | ||||||||
\(670\) | 145.863 | + | 168.956i | 0.217706 | + | 0.252174i | ||||
\(671\) | −1075.27 | −1.60250 | ||||||||
\(672\) | 36.4747 | + | 36.4747i | 0.0542778 | + | 0.0542778i | ||||
\(673\) | −493.188 | + | 493.188i | −0.732820 | + | 0.732820i | −0.971178 | − | 0.238357i | \(-0.923391\pi\) |
0.238357 | + | 0.971178i | \(0.423391\pi\) | |||||||
\(674\) | − | 6.52903i | − | 0.00968699i | ||||||
\(675\) | 104.277 | − | 77.4688i | 0.154484 | − | 0.114769i | ||||
\(676\) | 905.064 | 1.33885 | ||||||||
\(677\) | −415.571 | − | 415.571i | −0.613842 | − | 0.613842i | 0.330103 | − | 0.943945i | \(-0.392917\pi\) |
−0.943945 | + | 0.330103i | \(0.892917\pi\) | |||||||
\(678\) | 230.999 | − | 230.999i | 0.340706 | − | 0.340706i | ||||
\(679\) | 899.769i | 1.32514i | ||||||||
\(680\) | 312.376 | − | 269.680i | 0.459377 | − | 0.396589i | ||||
\(681\) | −353.696 | −0.519378 | ||||||||
\(682\) | −8.89770 | − | 8.89770i | −0.0130465 | − | 0.0130465i | ||||
\(683\) | 236.634 | − | 236.634i | 0.346463 | − | 0.346463i | −0.512327 | − | 0.858790i | \(-0.671217\pi\) |
0.858790 | + | 0.512327i | \(0.171217\pi\) | |||||||
\(684\) | − | 37.1901i | − | 0.0543715i | ||||||
\(685\) | −1206.05 | − | 88.4688i | −1.76066 | − | 0.129152i | ||||
\(686\) | 523.284 | 0.762805 | ||||||||
\(687\) | −444.333 | − | 444.333i | −0.646772 | − | 0.646772i | ||||
\(688\) | 6.66658 | − | 6.66658i | 0.00968979 | − | 0.00968979i | ||||
\(689\) | − | 261.858i | − | 0.380054i | ||||||
\(690\) | 4.29703 | − | 58.5793i | 0.00622758 | − | 0.0848976i | ||||
\(691\) | −81.6305 | −0.118134 | −0.0590670 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590670 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(692\) | −303.998 | − | 303.998i | −0.439304 | − | 0.439304i | ||||
\(693\) | 131.812 | − | 131.812i | 0.190205 | − | 0.190205i | ||||
\(694\) | − | 596.361i | − | 0.859309i | ||||||
\(695\) | 273.954 | + | 317.327i | 0.394179 | + | 0.456586i | ||||
\(696\) | 0.429101 | 0.000616524 | ||||||||
\(697\) | −1178.86 | − | 1178.86i | −1.69133 | − | 1.69133i | ||||
\(698\) | 330.198 | − | 330.198i | 0.473063 | − | 0.473063i | ||||
\(699\) | − | 215.894i | − | 0.308862i | ||||||
\(700\) | 156.980 | + | 211.303i | 0.224258 | + | 0.301861i | ||||
\(701\) | 1277.39 | 1.82224 | 0.911122 | − | 0.412137i | \(-0.135218\pi\) | ||||
0.911122 | + | 0.412137i | \(0.135218\pi\) | |||||||
\(702\) | 129.543 | + | 129.543i | 0.184534 | + | 0.184534i | ||||
\(703\) | 176.817 | − | 176.817i | 0.251518 | − | 0.251518i | ||||
\(704\) | − | 94.4208i | − | 0.134120i | ||||||
\(705\) | −377.970 | + | 326.309i | −0.536128 | + | 0.462849i | ||||
\(706\) | −243.906 | −0.345476 | ||||||||
\(707\) | −23.6644 | − | 23.6644i | −0.0334715 | − | 0.0334715i | ||||
\(708\) | 261.990 | − | 261.990i | 0.370042 | − | 0.370042i | ||||
\(709\) | − | 1056.16i | − | 1.48965i | −0.667260 | − | 0.744825i | \(-0.732533\pi\) | ||
0.667260 | − | 0.744825i | \(-0.267467\pi\) | |||||||
\(710\) | −872.398 | − | 63.9939i | −1.22873 | − | 0.0901322i | ||||
\(711\) | −66.7293 | −0.0938527 | ||||||||
\(712\) | −60.0503 | − | 60.0503i | −0.0843404 | − | 0.0843404i | ||||
\(713\) | 2.55652 | − | 2.55652i | 0.00358558 | − | 0.00358558i | ||||
\(714\) | 376.311i | 0.527046i | ||||||||
\(715\) | 107.631 | − | 1467.28i | 0.150533 | − | 2.05215i | ||||
\(716\) | 267.381 | 0.373437 | ||||||||
\(717\) | −363.252 | − | 363.252i | −0.506628 | − | 0.506628i | ||||
\(718\) | 14.1715 | − | 14.1715i | 0.0197374 | − | 0.0197374i | ||||
\(719\) | 532.010i | 0.739931i | 0.929046 | + | 0.369965i | \(0.120630\pi\) | ||||
−0.929046 | + | 0.369965i | \(0.879370\pi\) | |||||||
\(720\) | 39.2089 | + | 45.4165i | 0.0544568 | + | 0.0630785i | ||||
\(721\) | 959.043 | 1.33016 | ||||||||
\(722\) | 322.580 | + | 322.580i | 0.446787 | + | 0.446787i | ||||
\(723\) | 350.327 | − | 350.327i | 0.484546 | − | 0.484546i | ||||
\(724\) | 539.130i | 0.744655i | ||||||||
\(725\) | 2.16631 | + | 0.319534i | 0.00298801 | + | 0.000440737i | ||||
\(726\) | −44.8292 | −0.0617482 | ||||||||
\(727\) | 310.493 | + | 310.493i | 0.427087 | + | 0.427087i | 0.887635 | − | 0.460548i | \(-0.152347\pi\) |
−0.460548 | + | 0.887635i | \(0.652347\pi\) | |||||||
\(728\) | −262.502 | + | 262.502i | −0.360579 | + | 0.360579i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 110.982 | − | 95.8131i | 0.152031 | − | 0.131251i | ||||
\(731\) | 68.7794 | 0.0940895 | ||||||||
\(732\) | 223.160 | + | 223.160i | 0.304864 | + | 0.304864i | ||||
\(733\) | −737.954 | + | 737.954i | −1.00676 | + | 1.00676i | −0.00678219 | + | 0.999977i | \(0.502159\pi\) |
−0.999977 | + | 0.00678219i | \(0.997841\pi\) | |||||||
\(734\) | − | 127.901i | − | 0.174252i | ||||||
\(735\) | 183.825 | + | 13.4843i | 0.250102 | + | 0.0183460i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 263.445 | + | 263.445i | 0.357456 | + | 0.357456i | ||||
\(738\) | 171.394 | − | 171.394i | 0.232242 | − | 0.232242i | ||||
\(739\) | 258.876i | 0.350306i | 0.984541 | + | 0.175153i | \(0.0560421\pi\) | ||||
−0.984541 | + | 0.175153i | \(0.943958\pi\) | |||||||
\(740\) | −29.5136 | + | 402.345i | −0.0398832 | + | 0.543709i | ||||
\(741\) | 267.651 | 0.361202 | ||||||||
\(742\) | 55.2973 | + | 55.2973i | 0.0745247 | + | 0.0745247i | ||||
\(743\) | −570.017 | + | 570.017i | −0.767183 | + | 0.767183i | −0.977610 | − | 0.210427i | \(-0.932515\pi\) |
0.210427 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(744\) | 3.69322i | 0.00496401i | ||||||||
\(745\) | −382.418 | − | 442.963i | −0.513313 | − | 0.594581i | ||||
\(746\) | −321.395 | −0.430824 | ||||||||
\(747\) | −13.7700 | − | 13.7700i | −0.0184338 | − | 0.0184338i | ||||
\(748\) | 487.072 | − | 487.072i | 0.651166 | − | 0.651166i | ||||
\(749\) | 353.297i | 0.471692i | ||||||||
\(750\) | 164.126 | + | 258.482i | 0.218834 | + | 0.344642i | ||||
\(751\) | −739.550 | −0.984754 | −0.492377 | − | 0.870382i | \(-0.663872\pi\) | ||||
−0.492377 | + | 0.870382i | \(0.663872\pi\) | |||||||
\(752\) | −163.083 | − | 163.083i | −0.216866 | − | 0.216866i | ||||
\(753\) | −222.534 | + | 222.534i | −0.295530 | + | 0.295530i | ||||
\(754\) | 3.08817i | 0.00409571i | ||||||||
\(755\) | 151.042 | − | 130.398i | 0.200056 | − | 0.172712i | ||||
\(756\) | −54.7120 | −0.0723703 | ||||||||
\(757\) | −383.596 | − | 383.596i | −0.506732 | − | 0.506732i | 0.406789 | − | 0.913522i | \(-0.366648\pi\) |
−0.913522 | + | 0.406789i | \(0.866648\pi\) | |||||||
\(758\) | 201.845 | − | 201.845i | 0.266287 | − | 0.266287i | ||||
\(759\) | − | 98.0398i | − | 0.129170i | ||||||
\(760\) | 87.4230 | + | 6.41283i | 0.115030 | + | 0.00843793i | ||||
\(761\) | −619.693 | −0.814314 | −0.407157 | − | 0.913358i | \(-0.633480\pi\) | ||||
−0.407157 | + | 0.913358i | \(0.633480\pi\) | |||||||
\(762\) | −25.2837 | − | 25.2837i | −0.0331807 | − | 0.0331807i | ||||
\(763\) | −543.103 | + | 543.103i | −0.711800 | + | 0.711800i | ||||
\(764\) | − | 644.805i | − | 0.843986i | ||||||
\(765\) | −32.0222 | + | 436.543i | −0.0418590 | + | 0.570644i | ||||
\(766\) | 355.781 | 0.464466 | ||||||||
\(767\) | 1885.49 | + | 1885.49i | 2.45827 | + | 2.45827i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 587.333i | 0.763762i | 0.924211 | + | 0.381881i | \(0.124724\pi\) | ||||
−0.924211 | + | 0.381881i | \(0.875276\pi\) | |||||||
\(770\) | 287.122 | + | 332.580i | 0.372886 | + | 0.431922i | ||||
\(771\) | −480.720 | −0.623502 | ||||||||
\(772\) | −179.675 | − | 179.675i | −0.232740 | − | 0.232740i | ||||
\(773\) | 541.479 | − | 541.479i | 0.700490 | − | 0.700490i | −0.264026 | − | 0.964516i | \(-0.585050\pi\) |
0.964516 | + | 0.264026i | \(0.0850504\pi\) | |||||||
\(774\) | 9.99987i | 0.0129197i | ||||||||
\(775\) | −2.75019 | + | 18.6452i | −0.00354864 | + | 0.0240583i | ||||
\(776\) | −483.399 | −0.622936 | ||||||||
\(777\) | −260.124 | − | 260.124i | −0.334779 | − | 0.334779i | ||||
\(778\) | −501.474 | + | 501.474i | −0.644568 | + | 0.644568i | ||||
\(779\) | − | 354.121i | − | 0.454584i | ||||||
\(780\) | −326.855 | + | 282.180i | −0.419045 | + | 0.361769i | ||||
\(781\) | −1460.07 | −1.86948 | ||||||||
\(782\) | 139.947 | + | 139.947i | 0.178961 | + | 0.178961i | ||||
\(783\) | −0.321826 | + | 0.321826i | −0.000411016 | + | 0.000411016i | ||||
\(784\) | 85.1333i | 0.108588i | ||||||||
\(785\) | −397.249 | − | 29.1398i | −0.506050 | − | 0.0371208i | ||||
\(786\) | 451.711 | 0.574696 | ||||||||
\(787\) | 748.081 | + | 748.081i | 0.950548 | + | 0.950548i | 0.998834 | − | 0.0482856i | \(-0.0153758\pi\) |
−0.0482856 | + | 0.998834i | \(0.515376\pi\) | |||||||
\(788\) | 86.8144 | − | 86.8144i | 0.110171 | − | 0.110171i | ||||
\(789\) | 566.147i | 0.717550i | ||||||||
\(790\) | 11.5064 | − | 156.861i | 0.0145650 | − | 0.198558i | ||||
\(791\) | −702.134 | −0.887653 | ||||||||
\(792\) | 70.8156 | + | 70.8156i | 0.0894137 | + | 0.0894137i | ||||
\(793\) | −1606.05 | + | 1606.05i | −2.02528 | + | 2.02528i | ||||
\(794\) | − | 758.641i | − | 0.955467i | ||||||
\(795\) | 59.4426 | + | 68.8536i | 0.0747705 | + | 0.0866083i | ||||
\(796\) | −482.873 | −0.606624 | ||||||||
\(797\) | 521.090 | + | 521.090i | 0.653814 | + | 0.653814i | 0.953909 | − | 0.300095i | \(-0.0970184\pi\) |
−0.300095 | + | 0.953909i | \(0.597018\pi\) | |||||||
\(798\) | −56.5207 | + | 56.5207i | −0.0708279 | + | 0.0708279i | ||||
\(799\) | − | 1682.54i | − | 2.10581i | ||||||
\(800\) | −113.522 | + | 84.3373i | −0.141902 | + | 0.105422i | ||||
\(801\) | 90.0755 | 0.112454 | ||||||||
\(802\) | 179.175 | + | 179.175i | 0.223410 | + | 0.223410i | ||||
\(803\) | 173.049 | − | 173.049i | 0.215503 | − | 0.215503i | ||||
\(804\) | − | 109.350i | − | 0.136007i | ||||||
\(805\) | −95.5580 | + | 82.4970i | −0.118706 | + | 0.102481i | ||||
\(806\) | −26.5795 | −0.0329770 | ||||||||
\(807\) | 337.547 | + | 337.547i | 0.418273 | + | 0.418273i | ||||
\(808\) | 12.7136 | − | 12.7136i | 0.0157347 | − | 0.0157347i | ||||
\(809\) | − | 1423.19i | − | 1.75920i | −0.475718 | − | 0.879598i | \(-0.657812\pi\) | ||
0.475718 | − | 0.879598i | \(-0.342188\pi\) | |||||||
\(810\) | −63.4691 | − | 4.65571i | −0.0783569 | − | 0.00574779i | ||||
\(811\) | 619.095 | 0.763372 | 0.381686 | − | 0.924292i | \(-0.375344\pi\) | ||||
0.381686 | + | 0.924292i | \(0.375344\pi\) | |||||||
\(812\) | −0.652138 | − | 0.652138i | −0.000803126 | − | 0.000803126i | ||||
\(813\) | 38.4460 | − | 38.4460i | 0.0472890 | − | 0.0472890i | ||||
\(814\) | 673.374i | 0.827241i | ||||||||
\(815\) | 54.2909 | − | 740.122i | 0.0666147 | − | 0.908126i | ||||
\(816\) | −202.172 | −0.247760 | ||||||||
\(817\) | 10.3304 | + | 10.3304i | 0.0126444 | + | 0.0126444i | ||||
\(818\) | −384.881 | + | 384.881i | −0.470514 | + | 0.470514i | ||||
\(819\) | − | 393.753i | − | 0.480773i | ||||||
\(820\) | 373.344 | + | 432.452i | 0.455297 | + | 0.527381i | ||||
\(821\) | −1268.52 | −1.54510 | −0.772548 | − | 0.634957i | \(-0.781018\pi\) | ||||
−0.772548 | + | 0.634957i | \(0.781018\pi\) | |||||||
\(822\) | 418.911 | + | 418.911i | 0.509625 | + | 0.509625i | ||||
\(823\) | 908.627 | − | 908.627i | 1.10404 | − | 1.10404i | 0.110125 | − | 0.993918i | \(-0.464875\pi\) |
0.993918 | − | 0.110125i | \(-0.0351250\pi\) | |||||||
\(824\) | 515.244i | 0.625296i | ||||||||
\(825\) | 304.778 | + | 410.245i | 0.369428 | + | 0.497266i | ||||
\(826\) | −796.332 | −0.964082 | ||||||||
\(827\) | −692.885 | − | 692.885i | −0.837829 | − | 0.837829i | 0.150744 | − | 0.988573i | \(-0.451833\pi\) |
−0.988573 | + | 0.150744i | \(0.951833\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | 513.279i | 0.619155i | 0.950874 | + | 0.309577i | \(0.100188\pi\) | ||||
−0.950874 | + | 0.309577i | \(0.899812\pi\) | |||||||
\(830\) | 34.7438 | − | 29.9949i | 0.0418600 | − | 0.0361385i | ||||
\(831\) | 39.0208 | 0.0469564 | ||||||||
\(832\) | −141.028 | − | 141.028i | −0.169505 | − | 0.169505i | ||||
\(833\) | −439.162 | + | 439.162i | −0.527206 | + | 0.527206i | ||||
\(834\) | − | 205.376i | − | 0.246254i | ||||||
\(835\) | −1224.68 | − | 89.8350i | −1.46668 | − | 0.107587i | ||||
\(836\) | 146.313 | 0.175016 | ||||||||
\(837\) | −2.76992 | − | 2.76992i | −0.00330934 | − | 0.00330934i | ||||
\(838\) | −375.801 | + | 375.801i | −0.448450 | + | 0.448450i | ||||
\(839\) | − | 888.628i | − | 1.05915i | −0.848263 | − | 0.529575i | \(-0.822351\pi\) | ||
0.848263 | − | 0.529575i | \(-0.177649\pi\) | |||||||
\(840\) | 9.43419 | − | 128.612i | 0.0112312 | − | 0.153109i | ||||
\(841\) | 840.992 | 0.999991 | ||||||||
\(842\) | 109.575 | + | 109.575i | 0.130137 | + | 0.130137i | ||||
\(843\) | 58.9969 | − | 58.9969i | 0.0699844 | − | 0.0699844i | ||||
\(844\) | − | 104.278i | − | 0.123552i | ||||||
\(845\) | −1478.61 | − | 1712.70i | −1.74983 | − | 2.02687i | ||||
\(846\) | 244.625 | 0.289155 | ||||||||
\(847\) | 68.1304 | + | 68.1304i | 0.0804373 | + | 0.0804373i | ||||
\(848\) | −29.7083 | + | 29.7083i | −0.0350334 | + | 0.0350334i | ||||
\(849\) | − | 334.125i | − | 0.393551i | ||||||
\(850\) | −1020.66 | − | 150.549i | −1.20078 | − | 0.177117i | ||||
\(851\) | −193.476 | −0.227352 | ||||||||
\(852\) | 303.019 | + | 303.019i | 0.355657 | + | 0.355657i | ||||
\(853\) | −34.9834 | + | 34.9834i | −0.0410122 | + | 0.0410122i | −0.727315 | − | 0.686303i | \(-0.759232\pi\) |
0.686303 | + | 0.727315i | \(0.259232\pi\) | |||||||
\(854\) | − | 678.308i | − | 0.794272i | ||||||
\(855\) | −70.3769 | + | 60.7576i | −0.0823122 | + | 0.0710616i | ||||
\(856\) | −189.808 | −0.221738 | ||||||||
\(857\) | 58.3631 | + | 58.3631i | 0.0681016 | + | 0.0681016i | 0.740337 | − | 0.672236i | \(-0.234666\pi\) |
−0.672236 | + | 0.740337i | \(0.734666\pi\) | |||||||
\(858\) | −509.648 | + | 509.648i | −0.593995 | + | 0.593995i | ||||
\(859\) | − | 1424.70i | − | 1.65856i | −0.558834 | − | 0.829280i | \(-0.688751\pi\) | ||
0.558834 | − | 0.829280i | \(-0.311249\pi\) | |||||||
\(860\) | −23.5068 | − | 1.72432i | −0.0273334 | − | 0.00200502i | ||||
\(861\) | −520.963 | −0.605067 | ||||||||
\(862\) | −720.493 | − | 720.493i | −0.835839 | − | 0.835839i | ||||
\(863\) | −683.671 | + | 683.671i | −0.792203 | + | 0.792203i | −0.981852 | − | 0.189649i | \(-0.939265\pi\) |
0.189649 | + | 0.981852i | \(0.439265\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | −78.6293 | + | 1071.92i | −0.0909010 | + | 1.23921i | ||||
\(866\) | −20.4928 | −0.0236638 | ||||||||
\(867\) | −688.959 | − | 688.959i | −0.794647 | − | 0.794647i | ||||
\(868\) | 5.61288 | − | 5.61288i | 0.00646645 | − | 0.00646645i | ||||
\(869\) | − | 262.526i | − | 0.302102i | ||||||
\(870\) | −0.701024 | − | 0.812012i | −0.000805775 | − | 0.000933347i | ||||
\(871\) | 786.971 | 0.903526 | ||||||||
\(872\) | −291.781 | − | 291.781i | −0.334611 | − | 0.334611i | ||||
\(873\) | 362.549 | − | 362.549i | 0.415291 | − | 0.415291i | ||||
\(874\) | 42.0393i | 0.0480998i | ||||||||
\(875\) | 143.400 | − | 642.269i | 0.163886 | − | 0.734022i | ||||
\(876\) | −71.8285 | −0.0819960 | ||||||||
\(877\) | 621.453 | + | 621.453i | 0.708612 | + | 0.708612i | 0.966243 | − | 0.257631i | \(-0.0829420\pi\) |
−0.257631 | + | 0.966243i | \(0.582942\pi\) | |||||||
\(878\) | −627.889 | + | 627.889i | −0.715136 | + | 0.715136i | ||||
\(879\) | 237.291i | 0.269956i | ||||||||
\(880\) | −178.678 | + | 154.256i | −0.203043 | + | 0.175291i | ||||
\(881\) | 1514.77 | 1.71938 | 0.859689 | − | 0.510818i | \(-0.170657\pi\) | ||||
0.859689 | + | 0.510818i | \(0.170657\pi\) | |||||||
\(882\) | −63.8500 | − | 63.8500i | −0.0723923 | − | 0.0723923i | ||||
\(883\) | 725.056 | − | 725.056i | 0.821128 | − | 0.821128i | −0.165142 | − | 0.986270i | \(-0.552808\pi\) |
0.986270 | + | 0.165142i | \(0.0528081\pi\) | |||||||
\(884\) | − | 1455.00i | − | 1.64593i | ||||||
\(885\) | −923.791 | − | 67.7638i | −1.04383 | − | 0.0765692i | ||||
\(886\) | −506.701 | −0.571898 | ||||||||
\(887\) | 13.7391 | + | 13.7391i | 0.0154894 | + | 0.0154894i | 0.714809 | − | 0.699320i | \(-0.246514\pi\) |
−0.699320 | + | 0.714809i | \(0.746514\pi\) | |||||||
\(888\) | 139.751 | − | 139.751i | 0.157377 | − | 0.157377i | ||||
\(889\) | 76.8511i | 0.0864467i | ||||||||
\(890\) | −15.5321 | + | 211.741i | −0.0174518 | + | 0.237911i | ||||
\(891\) | −106.223 | −0.119218 | ||||||||
\(892\) | 560.903 | + | 560.903i | 0.628815 | + | 0.628815i | ||||
\(893\) | 252.712 | − | 252.712i | 0.282992 | − | 0.282992i | ||||
\(894\) | 286.688i | 0.320681i | ||||||||
\(895\) | −436.822 | − | 505.980i | −0.488069 | − | 0.565341i | ||||
\(896\) | 59.5629 | 0.0664764 | ||||||||
\(897\) | −146.434 | − | 146.434i | −0.163248 | − | 0.163248i | ||||
\(898\) | −86.2603 | + | 86.2603i | −0.0960582 | + | 0.0960582i | ||||
\(899\) | − | 0.0660319i | − | 7.34504e-5i | ||||||
\(900\) | 21.8884 | − | 148.394i | 0.0243205 | − | 0.164883i | ||||
\(901\) | −306.502 | −0.340180 | ||||||||
\(902\) | 674.300 | + | 674.300i | 0.747561 | + | 0.747561i | ||||
\(903\) | 15.1976 | − | 15.1976i | 0.0168301 | − | 0.0168301i | ||||
\(904\) | − | 377.220i | − | 0.417278i | ||||||
\(905\) | 1020.23 | − | 880.779i | 1.12732 | − | 0.973237i | ||||
\(906\) | −97.7557 | −0.107898 | ||||||||
\(907\) | 16.3128 | + | 16.3128i | 0.0179854 | + | 0.0179854i | 0.716042 | − | 0.698057i | \(-0.245952\pi\) |
−0.698057 | + | 0.716042i | \(0.745952\pi\) | |||||||
\(908\) | −288.792 | + | 288.792i | −0.318053 | + | 0.318053i | ||||
\(909\) | 19.0704i | 0.0209796i | ||||||||
\(910\) | 925.597 | + | 67.8963i | 1.01714 | + | 0.0746113i | ||||
\(911\) | 1548.82 | 1.70013 | 0.850065 | − | 0.526678i | \(-0.176563\pi\) | ||||
0.850065 | + | 0.526678i | \(0.176563\pi\) | |||||||
\(912\) | −30.3656 | − | 30.3656i | −0.0332956 | − | 0.0332956i | ||||
\(913\) | 54.1741 | − | 54.1741i | 0.0593364 | − | 0.0593364i | ||||
\(914\) | 604.459i | 0.661333i | ||||||||
\(915\) | 57.7206 | − | 786.877i | 0.0630826 | − | 0.859975i | ||||
\(916\) | −725.592 | −0.792131 | ||||||||
\(917\) | −686.500 | − | 686.500i | −0.748637 | − | 0.748637i | ||||
\(918\) | 151.629 | − | 151.629i | 0.165173 | − | 0.165173i | ||||
\(919\) | − | 222.682i | − | 0.242310i | −0.992634 | − | 0.121155i | \(-0.961340\pi\) | ||
0.992634 | − | 0.121155i | \(-0.0386597\pi\) | |||||||
\(920\) | −44.3213 | − | 51.3383i | −0.0481753 | − | 0.0558025i | ||||
\(921\) | −233.061 | −0.253052 | ||||||||
\(922\) | −592.540 | − | 592.540i | −0.642668 | − | 0.642668i | ||||
\(923\) | −2180.78 | + | 2180.78i | −2.36271 | + | 2.36271i | ||||
\(924\) | − | 215.248i | − | 0.232952i | ||||||
\(925\) | 809.595 | − | 601.462i | 0.875238 | − | 0.650229i | ||||
\(926\) | −421.843 | −0.455554 | ||||||||
\(927\) | −386.433 | − | 386.433i | −0.416864 | − | 0.416864i | ||||
\(928\) | 0.350360 | − | 0.350360i | 0.000377543 | − | 0.000377543i | ||||
\(929\) | − | 461.755i | − | 0.497045i | −0.968626 | − | 0.248522i | \(-0.920055\pi\) | ||
0.968626 | − | 0.248522i | \(-0.0799450\pi\) | |||||||
\(930\) | 6.98889 | − | 6.03364i | 0.00751494 | − | 0.00648778i | ||||
\(931\) | −131.921 | −0.141699 | ||||||||
\(932\) | −176.277 | − | 176.277i | −0.189138 | − | 0.189138i | ||||
\(933\) | 458.650 | − | 458.650i | 0.491587 | − | 0.491587i | ||||
\(934\) | − | 150.101i | − | 0.160707i | ||||||
\(935\) | −1717.45 | − | 125.982i | −1.83684 | − | 0.134740i | ||||
\(936\) | 211.543 | 0.226007 | ||||||||
\(937\) | 316.509 | + | 316.509i | 0.337789 | + | 0.337789i | 0.855535 | − | 0.517745i | \(-0.173229\pi\) |
−0.517745 | + | 0.855535i | \(0.673229\pi\) | |||||||
\(938\) | −166.187 | + | 166.187i | −0.177172 | + | 0.177172i | ||||
\(939\) | 677.392i | 0.721397i | ||||||||
\(940\) | −42.1816 | + | 575.042i | −0.0448741 | + | 0.611746i | ||||
\(941\) | 595.796 | 0.633152 | 0.316576 | − | 0.948567i | \(-0.397467\pi\) | ||||
0.316576 | + | 0.948567i | \(0.397467\pi\) | |||||||
\(942\) | 137.981 | + | 137.981i | 0.146476 | + | 0.146476i | ||||
\(943\) | −193.742 | + | 193.742i | −0.205453 | + | 0.205453i | ||||
\(944\) | − | 427.827i | − | 0.453207i | ||||||
\(945\) | 89.3832 | + | 103.535i | 0.0945854 | + | 0.109560i | ||||
\(946\) | −39.3415 | −0.0415872 | ||||||||
\(947\) | −72.4252 | − | 72.4252i | −0.0764786 | − | 0.0764786i | 0.667833 | − | 0.744311i | \(-0.267222\pi\) |
−0.744311 | + | 0.667833i | \(0.767222\pi\) | |||||||
\(948\) | −54.4842 | + | 54.4842i | −0.0574728 | + | 0.0574728i | ||||
\(949\) | − | 516.937i | − | 0.544718i | ||||||
\(950\) | −130.688 | − | 175.912i | −0.137566 | − | 0.185171i | ||||
\(951\) | −293.825 | −0.308965 | ||||||||
\(952\) | 307.257 | + | 307.257i | 0.322749 | + | 0.322749i | ||||
\(953\) | −241.669 | + | 241.669i | −0.253587 | + | 0.253587i | −0.822440 | − | 0.568852i | \(-0.807388\pi\) |
0.568852 | + | 0.822440i | \(0.307388\pi\) | |||||||
\(954\) | − | 44.5625i | − | 0.0467112i | ||||||
\(955\) | −1220.20 | + | 1053.42i | −1.27770 | + | 1.10306i | ||||
\(956\) | −593.189 | −0.620490 | ||||||||
\(957\) | −1.26613 | − | 1.26613i | −0.00132302 | − | 0.00132302i | ||||
\(958\) | −582.683 | + | 582.683i | −0.608229 | + | 0.608229i | ||||
\(959\) | − | 1273.30i | − | 1.32774i | ||||||
\(960\) | 69.0964 | + | 5.06850i | 0.0719754 | + | 0.00527968i | ||||
\(961\) | −960.432 | −0.999409 | ||||||||
\(962\) | 1005.76 | + | 1005.76i | 1.04549 | + | 1.04549i | ||||
\(963\) | 142.356 | − | 142.356i | 0.147826 | − | 0.147826i | ||||
\(964\) | − | 572.081i | − | 0.593445i | ||||||
\(965\) | −46.4731 | + | 633.546i | −0.0481587 | + | 0.656524i | ||||
\(966\) | 61.8458 | 0.0640226 | ||||||||
\(967\) | −855.265 | − | 855.265i | −0.884452 | − | 0.884452i | 0.109532 | − | 0.993983i | \(-0.465065\pi\) |
−0.993983 | + | 0.109532i | \(0.965065\pi\) | |||||||
\(968\) | −36.6029 | + | 36.6029i | −0.0378129 | + | 0.0378129i | ||||
\(969\) | − | 313.283i | − | 0.323306i | ||||||
\(970\) | 789.731 | + | 914.762i | 0.814155 | + | 0.943054i | ||||
\(971\) | −1220.33 | −1.25678 | −0.628390 | − | 0.777899i | \(-0.716286\pi\) | ||||
−0.628390 | + | 0.777899i | \(0.716286\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −312.126 | + | 312.126i | −0.320787 | + | 0.320787i | ||||
\(974\) | 648.912i | 0.666234i | ||||||||
\(975\) | 1067.97 | + | 157.527i | 1.09535 | + | 0.161566i | ||||
\(976\) | 364.420 | 0.373381 | ||||||||
\(977\) | −319.958 | − | 319.958i | −0.327490 | − | 0.327490i | 0.524141 | − | 0.851631i | \(-0.324386\pi\) |
−0.851631 | + | 0.524141i | \(0.824386\pi\) | |||||||
\(978\) | −257.075 | + | 257.075i | −0.262858 | + | 0.262858i | ||||
\(979\) | 354.375i | 0.361977i | ||||||||
\(980\) | 161.102 | − | 139.083i | 0.164390 | − | 0.141921i | ||||
\(981\) | 437.671 | 0.446148 | ||||||||
\(982\) | 371.828 | + | 371.828i | 0.378644 | + | 0.378644i | ||||
\(983\) | −749.299 | + | 749.299i | −0.762258 | + | 0.762258i | −0.976730 | − | 0.214472i | \(-0.931197\pi\) |
0.214472 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(984\) | − | 279.886i | − | 0.284437i | ||||||
\(985\) | −306.113 | − | 22.4546i | −0.310774 | − | 0.0227965i | ||||
\(986\) | 3.61468 | 0.00366600 | ||||||||
\(987\) | −371.776 | − | 371.776i | −0.376672 | − | 0.376672i | ||||
\(988\) | 218.536 | − | 218.536i | 0.221190 | − | 0.221190i | ||||
\(989\) | − | 11.3037i | − | 0.0114295i | ||||||
\(990\) | 18.3165 | − | 249.700i | 0.0185015 | − | 0.252222i | ||||
\(991\) | −1463.17 | −1.47646 | −0.738230 | − | 0.674549i | \(-0.764338\pi\) | ||||
−0.738230 | + | 0.674549i | \(0.764338\pi\) | |||||||
\(992\) | 3.01550 | + | 3.01550i | 0.00303982 | + | 0.00303982i | ||||
\(993\) | 34.4526 | − | 34.4526i | 0.0346955 | − | 0.0346955i | ||||
\(994\) | − | 921.044i | − | 0.926604i | ||||||
\(995\) | 788.872 | + | 913.767i | 0.792836 | + | 0.918359i | ||||
\(996\) | −22.4864 | −0.0225767 | ||||||||
\(997\) | 174.886 | + | 174.886i | 0.175413 | + | 0.175413i | 0.789353 | − | 0.613940i | \(-0.210416\pi\) |
−0.613940 | + | 0.789353i | \(0.710416\pi\) | |||||||
\(998\) | 116.928 | − | 116.928i | 0.117163 | − | 0.117163i | ||||
\(999\) | 209.626i | 0.209836i |
(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 | 690.3.k.a.277.3 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.3 | yes | 40 | 5.3 | odd | 4 | inner |