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 | 553.3 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.a.277.3 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | −0.389300 | − | 0.921111i | \(-0.627283\pi\) |
0.921111 | + | 0.389300i | \(0.127283\pi\) | |||||||
\(8\) | −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 | 0.878738 | + | 0.477305i | \(0.158386\pi\) |
0.477305 | + | 0.878738i | \(0.341614\pi\) | |||||||
\(14\) | − | 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 | −0.243994 | + | 0.969777i | \(0.578458\pi\) |
−0.969777 | + | 0.243994i | \(0.921542\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 6.19835i | 0.326229i | 0.986607 | + | 0.163114i | \(0.0521540\pi\) | ||||
−0.986607 | + | 0.163114i | \(0.947846\pi\) | |||||||
\(20\) | 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 | \(-0.999519\pi\) | ||
0.999999 | − | 0.00151017i | \(-0.000480702\pi\) | |||||||
\(30\) | −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 | −0.207293 | − | 0.978279i | \(-0.566465\pi\) |
0.978279 | + | 0.207293i | \(0.0664652\pi\) | |||||||
\(38\) | 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 | 0.687462 | − | 0.726221i | \(-0.258725\pi\) |
−0.726221 | + | 0.687462i | \(0.758725\pi\) | |||||||
\(44\) | − | 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 | −0.124727 | − | 0.992191i | \(-0.539805\pi\) |
0.992191 | + | 0.124727i | \(0.0398054\pi\) | |||||||
\(48\) | 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 | 0.773694 | − | 0.633560i | \(-0.218407\pi\) |
−0.633560 | + | 0.773694i | \(0.718407\pi\) | |||||||
\(54\) | − | 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 | \(-0.638809\pi\) | ||
0.422391 | − | 0.906413i | \(-0.361191\pi\) | |||||||
\(60\) | −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 | −0.520633 | − | 0.853781i | \(-0.674304\pi\) |
0.853781 | + | 0.520633i | \(0.174304\pi\) | |||||||
\(68\) | 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 | 0.800363 | − | 0.599515i | \(-0.204640\pi\) |
−0.599515 | + | 0.800363i | \(0.704640\pi\) | |||||||
\(74\) | − | 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 | \(0.0449607\pi\) | ||||
−0.990041 | + | 0.140779i | \(0.955039\pi\) | |||||||
\(80\) | −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 | 0.734217 | − | 0.678915i | \(-0.237550\pi\) |
−0.678915 | + | 0.734217i | \(0.737550\pi\) | |||||||
\(84\) | 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 | \(-0.946049\pi\) | ||
0.985671 | − | 0.168681i | \(-0.0539507\pi\) | |||||||
\(90\) | 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 | 0.288347 | − | 0.957526i | \(-0.406894\pi\) |
0.957526 | − | 0.288347i | \(-0.0931056\pi\) | |||||||
\(98\) | 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 | 0.955455 | + | 0.295136i | \(0.0953649\pi\) |
0.295136 | + | 0.955455i | \(0.404635\pi\) | |||||||
\(104\) | − | 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 | −0.449702 | − | 0.893179i | \(-0.648470\pi\) |
0.893179 | + | 0.449702i | \(0.148470\pi\) | |||||||
\(108\) | −7.34847 | − | 7.34847i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 145.890i | − | 1.33844i | −0.743062 | − | 0.669222i | \(-0.766627\pi\) | ||
0.743062 | − | 0.669222i | \(-0.233373\pi\) | |||||||
\(110\) | 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 | 0.153580 | − | 0.988136i | \(-0.450920\pi\) |
−0.988136 | + | 0.153580i | \(0.950920\pi\) | |||||||
\(114\) | − | 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 | −0.665300 | − | 0.746576i | \(-0.731696\pi\) |
0.746576 | + | 0.665300i | \(0.231696\pi\) | |||||||
\(128\) | 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 | −0.291859 | + | 0.956461i | \(0.594274\pi\) |
−0.956461 | + | 0.291859i | \(0.905726\pi\) | |||||||
\(138\) | 8.30662 | + | 8.30662i | 0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 83.8444i | − | 0.603197i | −0.953435 | − | 0.301599i | \(-0.902480\pi\) | ||
0.953435 | − | 0.301599i | \(-0.0975203\pi\) | |||||||
\(140\) | −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 | \(0.128477\pi\) | ||||
−0.919644 | + | 0.392752i | \(0.871523\pi\) | |||||||
\(150\) | −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 | −0.863368 | − | 0.504575i | \(-0.831649\pi\) |
0.504575 | + | 0.863368i | \(0.331649\pi\) | |||||||
\(158\) | 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 | 0.951504 | − | 0.307637i | \(-0.0995382\pi\) |
−0.307637 | + | 0.951504i | \(0.599538\pi\) | |||||||
\(164\) | − | 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 | −0.0407150 | + | 0.999171i | \(0.512964\pi\) |
−0.999171 | + | 0.0407150i | \(0.987036\pi\) | |||||||
\(168\) | 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 | 0.114783 | − | 0.993391i | \(-0.463383\pi\) |
−0.993391 | + | 0.114783i | \(0.963383\pi\) | |||||||
\(174\) | 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 | \(0.121821\pi\) | ||||
−0.927656 | + | 0.373437i | \(0.878179\pi\) | |||||||
\(180\) | 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 | 0.434967 | − | 0.900447i | \(-0.356760\pi\) |
−0.900447 | + | 0.434967i | \(0.856760\pi\) | |||||||
\(194\) | − | 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 | −0.808642 | − | 0.588301i | \(-0.799797\pi\) |
0.588301 | + | 0.808642i | \(0.299797\pi\) | |||||||
\(198\) | 35.4078 | + | 35.4078i | 0.178827 | + | 0.178827i | ||||
\(199\) | − | 241.437i | − | 1.21325i | −0.794989 | − | 0.606624i | \(-0.792523\pi\) | ||
0.794989 | − | 0.606624i | \(-0.207477\pi\) | |||||||
\(200\) | 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 | 0.952221 | + | 0.305410i | \(0.0987935\pi\) |
0.305410 | + | 0.952221i | \(0.401206\pi\) | |||||||
\(224\) | 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 | −0.313487 | − | 0.949592i | \(-0.601497\pi\) |
0.949592 | + | 0.313487i | \(0.101497\pi\) | |||||||
\(228\) | −15.1828 | − | 15.1828i | −0.0665912 | − | 0.0665912i | ||||
\(229\) | − | 362.796i | − | 1.58426i | −0.610351 | − | 0.792131i | \(-0.708972\pi\) | ||
0.610351 | − | 0.792131i | \(-0.291028\pi\) | |||||||
\(230\) | −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 | 0.492203 | − | 0.870480i | \(-0.336192\pi\) |
−0.870480 | + | 0.492203i | \(0.836192\pi\) | |||||||
\(234\) | 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 | \(-0.786934\pi\) | ||
0.784214 | − | 0.620490i | \(-0.213066\pi\) | |||||||
\(240\) | 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 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) |
0.976977 | + | 0.213346i | \(0.0684361\pi\) | |||||||
\(258\) | 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 | 0.993412 | − | 0.114596i | \(-0.0365575\pi\) |
−0.114596 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(264\) | 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 | \(0.171198\pi\) | ||||
−0.858820 | + | 0.512278i | \(0.828802\pi\) | |||||||
\(270\) | 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 | −0.735277 | − | 0.677767i | \(-0.762948\pi\) |
0.677767 | + | 0.735277i | \(0.262948\pi\) | |||||||
\(278\) | −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 | 0.423770 | − | 0.905770i | \(-0.360706\pi\) |
−0.905770 | + | 0.423770i | \(0.860706\pi\) | |||||||
\(284\) | 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 | 0.852825 | − | 0.522198i | \(-0.174888\pi\) |
−0.522198 | + | 0.852825i | \(0.674888\pi\) | |||||||
\(294\) | − | 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 | −0.534956 | − | 0.844880i | \(-0.679672\pi\) |
0.844880 | + | 0.534956i | \(0.179672\pi\) | |||||||
\(308\) | −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 | 0.993891 | − | 0.110363i | \(-0.0352015\pi\) |
−0.110363 | + | 0.993891i | \(0.535201\pi\) | |||||||
\(314\) | 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 | −0.492123 | − | 0.870526i | \(-0.663779\pi\) |
0.870526 | + | 0.492123i | \(0.163779\pi\) | |||||||
\(318\) | −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 | −0.711934 | − | 0.702247i | \(-0.752180\pi\) |
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(338\) | 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 | −0.991257 | − | 0.131947i | \(-0.957877\pi\) |
0.131947 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(348\) | 0.214551 | + | 0.214551i | 0.000616524 | + | 0.000616524i | ||||
\(349\) | 330.198i | 0.946127i | 0.881028 | + | 0.473063i | \(0.156852\pi\) | ||||
−0.881028 | + | 0.473063i | \(0.843148\pi\) | |||||||
\(350\) | 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 | 0.512946 | − | 0.858421i | \(-0.328554\pi\) |
−0.858421 | + | 0.512946i | \(0.828554\pi\) | |||||||
\(354\) | 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 | \(0.00628302\pi\) | ||||
−0.999805 | + | 0.0197374i | \(0.993717\pi\) | |||||||
\(360\) | 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 | −0.788845 | − | 0.614593i | \(-0.789320\pi\) |
0.614593 | + | 0.788845i | \(0.289320\pi\) | |||||||
\(368\) | 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 | 0.458085 | − | 0.888909i | \(-0.348536\pi\) |
−0.888909 | + | 0.458085i | \(0.848536\pi\) | |||||||
\(374\) | 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 | \(0.0857968\pi\) | ||||
−0.963894 | + | 0.266287i | \(0.914203\pi\) | |||||||
\(380\) | 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 | 0.900116 | − | 0.435650i | \(-0.143481\pi\) |
−0.435650 | + | 0.900116i | \(0.643481\pi\) | |||||||
\(384\) | − | 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 | \(-0.777037\pi\) | ||
0.764547 | − | 0.644568i | \(-0.222963\pi\) | |||||||
\(390\) | −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 | −0.999050 | − | 0.0435831i | \(-0.986123\pi\) |
0.0435831 | + | 0.999050i | \(0.486123\pi\) | |||||||
\(398\) | −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 | \(-0.844068\pi\) | ||
0.882392 | − | 0.470514i | \(-0.155932\pi\) | |||||||
\(410\) | 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 | \(-0.851976\pi\) | ||
0.893808 | − | 0.448450i | \(-0.148024\pi\) | |||||||
\(420\) | −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 | 0.695176 | − | 0.718840i | \(-0.255326\pi\) |
−0.718840 | + | 0.695176i | \(0.755326\pi\) | |||||||
\(434\) | 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 | \(-0.746365\pi\) | ||
0.698985 | − | 0.715136i | \(-0.253635\pi\) | |||||||
\(440\) | −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 | 0.360761 | − | 0.932658i | \(-0.382517\pi\) |
−0.932658 | + | 0.360761i | \(0.882517\pi\) | |||||||
\(444\) | 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 | \(-0.969377\pi\) | ||
0.995376 | − | 0.0960582i | \(-0.0306235\pi\) | |||||||
\(450\) | −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 | −0.294361 | − | 0.955694i | \(-0.595107\pi\) |
0.955694 | + | 0.294361i | \(0.0951068\pi\) | |||||||
\(458\) | −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 | 0.441639 | − | 0.897193i | \(-0.354397\pi\) |
−0.897193 | + | 0.441639i | \(0.854397\pi\) | |||||||
\(464\) | 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 | −0.782880 | − | 0.622173i | \(-0.786250\pi\) |
0.622173 | + | 0.782880i | \(0.286250\pi\) | |||||||
\(468\) | 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 | \(-0.791880\pi\) | ||
0.793762 | − | 0.608229i | \(-0.208120\pi\) | |||||||
\(480\) | 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 | −0.290608 | − | 0.956842i | \(-0.593858\pi\) |
0.956842 | + | 0.290608i | \(0.0938575\pi\) | |||||||
\(488\) | 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 | \(0.0373799\pi\) | ||||
−0.993113 | + | 0.117163i | \(0.962620\pi\) | |||||||
\(500\) | 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 | 0.603446 | − | 0.797404i | \(-0.293794\pi\) |
−0.797404 | + | 0.603446i | \(0.793794\pi\) | |||||||
\(504\) | − | 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 | \(0.143301\pi\) | ||||
−0.900363 | + | 0.435139i | \(0.856699\pi\) | |||||||
\(510\) | 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 | 0.649974 | − | 0.759957i | \(-0.274780\pi\) |
−0.759957 | + | 0.649974i | \(0.774780\pi\) | |||||||
\(524\) | 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 | −0.831743 | − | 0.555161i | \(-0.812657\pi\) |
0.555161 | + | 0.831743i | \(0.312657\pi\) | |||||||
\(548\) | 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 | −0.754603 | − | 0.656182i | \(-0.772170\pi\) |
0.656182 | + | 0.754603i | \(0.272170\pi\) | |||||||
\(558\) | −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 | 0.964357 | − | 0.264604i | \(-0.0852412\pi\) |
−0.264604 | + | 0.964357i | \(0.585241\pi\) | |||||||
\(564\) | 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 | \(-0.696284\pi\) | ||
0.578302 | − | 0.815823i | \(-0.303716\pi\) | |||||||
\(570\) | 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 | −0.445026 | − | 0.895518i | \(-0.646806\pi\) |
0.895518 | + | 0.445026i | \(0.146806\pi\) | |||||||
\(578\) | −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 | −0.366453 | − | 0.930437i | \(-0.619428\pi\) |
0.930437 | + | 0.366453i | \(0.119428\pi\) | |||||||
\(588\) | −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 | 0.999346 | + | 0.0361568i | \(0.0115116\pi\) |
0.0361568 | + | 0.999346i | \(0.488488\pi\) | |||||||
\(594\) | − | 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 | \(0.147826\pi\) | ||||
−0.894086 | + | 0.447895i | \(0.852174\pi\) | |||||||
\(600\) | −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 | −0.945140 | − | 0.326665i | \(-0.894075\pi\) |
0.326665 | + | 0.945140i | \(0.394075\pi\) | |||||||
\(608\) | −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 | 0.529153 | − | 0.848527i | \(-0.322510\pi\) |
−0.848527 | + | 0.529153i | \(0.822510\pi\) | |||||||
\(614\) | − | 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 | −0.800520 | − | 0.599306i | \(-0.795443\pi\) |
0.599306 | + | 0.800520i | \(0.295443\pi\) | |||||||
\(618\) | −315.521 | − | 315.521i | −0.510552 | − | 0.510552i | ||||
\(619\) | 144.829i | 0.233972i | 0.993134 | + | 0.116986i | \(0.0373232\pi\) | ||||
−0.993134 | + | 0.116986i | \(0.962677\pi\) | |||||||
\(620\) | −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 | 0.740880 | − | 0.671638i | \(-0.234409\pi\) |
−0.671638 | + | 0.740880i | \(0.734409\pi\) | |||||||
\(644\) | 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 | −0.371835 | − | 0.928299i | \(-0.621271\pi\) |
0.928299 | + | 0.371835i | \(0.121271\pi\) | |||||||
\(648\) | 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 | 0.995344 | + | 0.0963890i | \(0.0307293\pi\) |
0.0963890 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(654\) | 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 | \(-0.721005\pi\) | ||
0.639854 | − | 0.768497i | \(-0.278995\pi\) | |||||||
\(660\) | −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 | 0.238357 | − | 0.971178i | \(-0.423391\pi\) |
−0.971178 | + | 0.238357i | \(0.923391\pi\) | |||||||
\(674\) | 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 | −0.943945 | − | 0.330103i | \(-0.892917\pi\) |
0.330103 | + | 0.943945i | \(0.392917\pi\) | |||||||
\(678\) | 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 | 0.858790 | − | 0.512327i | \(-0.171217\pi\) |
−0.512327 | + | 0.858790i | \(0.671217\pi\) | |||||||
\(684\) | 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 | \(0.267467\pi\) | ||||
−0.667260 | + | 0.744825i | \(0.732533\pi\) | |||||||
\(710\) | −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 | \(-0.879370\pi\) | ||
0.929046 | − | 0.369965i | \(-0.120630\pi\) | |||||||
\(720\) | 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 | −0.460548 | − | 0.887635i | \(-0.652347\pi\) |
0.887635 | + | 0.460548i | \(0.152347\pi\) | |||||||
\(728\) | −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 | −0.999977 | − | 0.00678219i | \(-0.997841\pi\) |
−0.00678219 | − | 0.999977i | \(-0.502159\pi\) | |||||||
\(734\) | 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 | \(-0.943958\pi\) | ||
0.984541 | − | 0.175153i | \(-0.0560421\pi\) | |||||||
\(740\) | −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 | 0.210427 | − | 0.977610i | \(-0.432515\pi\) |
−0.977610 | + | 0.210427i | \(0.932515\pi\) | |||||||
\(744\) | − | 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 | −0.913522 | − | 0.406789i | \(-0.866648\pi\) |
0.406789 | + | 0.913522i | \(0.366648\pi\) | |||||||
\(758\) | 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 | \(-0.875276\pi\) | ||
0.924211 | − | 0.381881i | \(-0.124724\pi\) | |||||||
\(770\) | 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 | 0.964516 | − | 0.264026i | \(-0.0850504\pi\) |
−0.264026 | + | 0.964516i | \(0.585050\pi\) | |||||||
\(774\) | − | 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 | −0.0482856 | − | 0.998834i | \(-0.515376\pi\) |
0.998834 | + | 0.0482856i | \(0.0153758\pi\) | |||||||
\(788\) | 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 | −0.300095 | − | 0.953909i | \(-0.597018\pi\) |
0.953909 | + | 0.300095i | \(0.0970184\pi\) | |||||||
\(798\) | −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 | \(0.342188\pi\) | ||||
−0.475718 | + | 0.879598i | \(0.657812\pi\) | |||||||
\(810\) | −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 | 0.993918 | + | 0.110125i | \(0.0351250\pi\) |
0.110125 | + | 0.993918i | \(0.464875\pi\) | |||||||
\(824\) | − | 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 | −0.988573 | − | 0.150744i | \(-0.951833\pi\) |
0.150744 | + | 0.988573i | \(0.451833\pi\) | |||||||
\(828\) | −20.3470 | − | 20.3470i | −0.0245737 | − | 0.0245737i | ||||
\(829\) | − | 513.279i | − | 0.619155i | −0.950874 | − | 0.309577i | \(-0.899812\pi\) | ||
0.950874 | − | 0.309577i | \(-0.100188\pi\) | |||||||
\(830\) | 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 | \(0.177649\pi\) | ||||
−0.848263 | + | 0.529575i | \(0.822351\pi\) | |||||||
\(840\) | 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 | 0.686303 | − | 0.727315i | \(-0.259232\pi\) |
−0.727315 | + | 0.686303i | \(0.759232\pi\) | |||||||
\(854\) | 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 | −0.672236 | − | 0.740337i | \(-0.734666\pi\) |
0.740337 | + | 0.672236i | \(0.234666\pi\) | |||||||
\(858\) | −509.648 | − | 509.648i | −0.593995 | − | 0.593995i | ||||
\(859\) | 1424.70i | 1.65856i | 0.558834 | + | 0.829280i | \(0.311249\pi\) | ||||
−0.558834 | + | 0.829280i | \(0.688751\pi\) | |||||||
\(860\) | −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 | 0.189649 | − | 0.981852i | \(-0.439265\pi\) |
−0.981852 | + | 0.189649i | \(0.939265\pi\) | |||||||
\(864\) | 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 | −0.257631 | − | 0.966243i | \(-0.582942\pi\) |
0.966243 | + | 0.257631i | \(0.0829420\pi\) | |||||||
\(878\) | −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 | 0.986270 | − | 0.165142i | \(-0.0528081\pi\) |
−0.165142 | + | 0.986270i | \(0.552808\pi\) | |||||||
\(884\) | 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 | −0.699320 | − | 0.714809i | \(-0.746514\pi\) |
0.714809 | + | 0.699320i | \(0.246514\pi\) | |||||||
\(888\) | 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 | −0.698057 | − | 0.716042i | \(-0.745952\pi\) |
0.716042 | + | 0.698057i | \(0.245952\pi\) | |||||||
\(908\) | −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 | \(0.0386597\pi\) | ||||
−0.992634 | + | 0.121155i | \(0.961340\pi\) | |||||||
\(920\) | −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 | \(0.0799450\pi\) | ||||
−0.968626 | + | 0.248522i | \(0.920055\pi\) | |||||||
\(930\) | 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 | −0.517745 | − | 0.855535i | \(-0.673229\pi\) |
0.855535 | + | 0.517745i | \(0.173229\pi\) | |||||||
\(938\) | −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 | −0.744311 | − | 0.667833i | \(-0.767222\pi\) |
0.667833 | + | 0.744311i | \(0.267222\pi\) | |||||||
\(948\) | −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 | 0.568852 | − | 0.822440i | \(-0.307388\pi\) |
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(954\) | 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 | −0.993983 | − | 0.109532i | \(-0.965065\pi\) |
0.109532 | + | 0.993983i | \(0.465065\pi\) | |||||||
\(968\) | −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 | −0.851631 | − | 0.524141i | \(-0.824386\pi\) |
0.524141 | + | 0.851631i | \(0.324386\pi\) | |||||||
\(978\) | −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 | 0.214472 | − | 0.976730i | \(-0.431197\pi\) |
−0.976730 | + | 0.214472i | \(0.931197\pi\) | |||||||
\(984\) | 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 | −0.613940 | − | 0.789353i | \(-0.710416\pi\) |
0.789353 | + | 0.613940i | \(0.210416\pi\) | |||||||
\(998\) | 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.553.3 | yes | 40 | |
5.2 | odd | 4 | inner | 690.3.k.a.277.3 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.3 | ✓ | 40 | 5.2 | odd | 4 | inner | |
690.3.k.a.553.3 | yes | 40 | 1.1 | even | 1 | trivial |