Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Character | \(\chi\) | \(=\) | 475.226 |
Dual form | 475.2.l.f.351.2 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.256855 | + | 1.45670i | −0.181624 | + | 1.03004i | 0.748593 | + | 0.663030i | \(0.230730\pi\) |
−0.930217 | + | 0.367010i | \(0.880381\pi\) | |||||||
\(3\) | 1.90225 | + | 1.59617i | 1.09826 | + | 0.921552i | 0.997307 | − | 0.0733394i | \(-0.0233656\pi\) |
0.100955 | + | 0.994891i | \(0.467810\pi\) | |||||||
\(4\) | −0.176607 | − | 0.0642796i | −0.0883034 | − | 0.0321398i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.81374 | + | 2.36101i | −1.14871 | + | 0.963879i | ||||
\(7\) | 1.62494 | + | 2.81448i | 0.614169 | + | 1.06377i | 0.990530 | + | 0.137298i | \(0.0438419\pi\) |
−0.376361 | + | 0.926473i | \(0.622825\pi\) | |||||||
\(8\) | −1.34017 | + | 2.32124i | −0.473822 | + | 0.820684i | ||||
\(9\) | 0.549824 | + | 3.11821i | 0.183275 | + | 1.03940i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.09200 | − | 3.62344i | 0.630760 | − | 1.09251i | −0.356636 | − | 0.934243i | \(-0.616076\pi\) |
0.987397 | − | 0.158265i | \(-0.0505902\pi\) | |||||||
\(12\) | −0.233348 | − | 0.404171i | −0.0673618 | − | 0.116674i | ||||
\(13\) | 1.36673 | − | 1.14682i | 0.379062 | − | 0.318070i | −0.433272 | − | 0.901263i | \(-0.642641\pi\) |
0.812334 | + | 0.583193i | \(0.198197\pi\) | |||||||
\(14\) | −4.51721 | + | 1.64413i | −1.20728 | + | 0.439412i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.32506 | − | 2.79006i | −0.831266 | − | 0.697515i | ||||
\(17\) | 1.09959 | − | 6.23606i | 0.266689 | − | 1.51247i | −0.497495 | − | 0.867467i | \(-0.665747\pi\) |
0.764183 | − | 0.644999i | \(-0.223142\pi\) | |||||||
\(18\) | −4.68351 | −1.10391 | ||||||||
\(19\) | −4.09399 | − | 1.49640i | −0.939226 | − | 0.343298i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.40136 | + | 7.94751i | −0.305802 | + | 1.73429i | ||||
\(22\) | 4.74092 | + | 3.97810i | 1.01077 | + | 0.848134i | ||||
\(23\) | −1.34721 | − | 0.490346i | −0.280914 | − | 0.102244i | 0.197721 | − | 0.980258i | \(-0.436646\pi\) |
−0.478635 | + | 0.878014i | \(0.658868\pi\) | |||||||
\(24\) | −6.25444 | + | 2.27643i | −1.27668 | + | 0.464675i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.31952 | + | 2.28547i | 0.258779 | + | 0.448218i | ||||
\(27\) | −0.206494 | + | 0.357658i | −0.0397398 | + | 0.0688313i | ||||
\(28\) | −0.106062 | − | 0.601506i | −0.0200438 | − | 0.113674i | ||||
\(29\) | −0.0589345 | − | 0.334234i | −0.0109439 | − | 0.0620657i | 0.978847 | − | 0.204595i | \(-0.0655877\pi\) |
−0.989791 | + | 0.142529i | \(0.954477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38932 | + | 2.40638i | 0.249530 | + | 0.432199i | 0.963395 | − | 0.268084i | \(-0.0863906\pi\) |
−0.713866 | + | 0.700283i | \(0.753057\pi\) | |||||||
\(32\) | 0.811808 | − | 0.681187i | 0.143509 | − | 0.120418i | ||||
\(33\) | 9.76313 | − | 3.55349i | 1.69954 | − | 0.618583i | ||||
\(34\) | 8.80161 | + | 3.20352i | 1.50946 | + | 0.549400i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.103335 | − | 0.586040i | 0.0172224 | − | 0.0976733i | ||||
\(37\) | −2.70482 | −0.444670 | −0.222335 | − | 0.974970i | \(-0.571368\pi\) | ||||
−0.222335 | + | 0.974970i | \(0.571368\pi\) | |||||||
\(38\) | 3.23137 | − | 5.57935i | 0.524197 | − | 0.905090i | ||||
\(39\) | 4.43037 | 0.709427 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.46819 | − | 4.58835i | −0.853987 | − | 0.716581i | 0.106677 | − | 0.994294i | \(-0.465979\pi\) |
−0.960664 | + | 0.277713i | \(0.910423\pi\) | |||||||
\(42\) | −11.2172 | − | 4.08271i | −1.73085 | − | 0.629977i | ||||
\(43\) | −9.29755 | + | 3.38403i | −1.41786 | + | 0.516060i | −0.933427 | − | 0.358767i | \(-0.883197\pi\) |
−0.484436 | + | 0.874827i | \(0.660975\pi\) | |||||||
\(44\) | −0.602374 | + | 0.505452i | −0.0908113 | + | 0.0761997i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.06032 | − | 1.83654i | 0.156336 | − | 0.270782i | ||||
\(47\) | −0.0773501 | − | 0.438674i | −0.0112827 | − | 0.0639872i | 0.978647 | − | 0.205550i | \(-0.0658984\pi\) |
−0.989929 | + | 0.141563i | \(0.954787\pi\) | |||||||
\(48\) | −1.87167 | − | 10.6148i | −0.270152 | − | 1.53211i | ||||
\(49\) | −1.78085 | + | 3.08452i | −0.254407 | + | 0.440645i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0455 | − | 10.1074i | 1.68671 | − | 1.41532i | ||||
\(52\) | −0.315090 | + | 0.114683i | −0.0436952 | + | 0.0159037i | ||||
\(53\) | 6.80087 | + | 2.47532i | 0.934172 | + | 0.340011i | 0.763862 | − | 0.645380i | \(-0.223301\pi\) |
0.170310 | + | 0.985391i | \(0.445523\pi\) | |||||||
\(54\) | −0.467960 | − | 0.392665i | −0.0636813 | − | 0.0534350i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.71078 | −1.16403 | ||||||||
\(57\) | −5.39926 | − | 9.38125i | −0.715150 | − | 1.24258i | ||||
\(58\) | 0.502015 | 0.0659178 | ||||||||
\(59\) | 0.545712 | − | 3.09489i | 0.0710457 | − | 0.402920i | −0.928459 | − | 0.371436i | \(-0.878866\pi\) |
0.999504 | − | 0.0314842i | \(-0.0100234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.88074 | + | 1.04850i | 0.368841 | + | 0.134247i | 0.519789 | − | 0.854295i | \(-0.326010\pi\) |
−0.150948 | + | 0.988542i | \(0.548233\pi\) | |||||||
\(62\) | −3.86222 | + | 1.40573i | −0.490503 | + | 0.178528i | ||||
\(63\) | −7.88269 | + | 6.61436i | −0.993126 | + | 0.833331i | ||||
\(64\) | −3.55679 | − | 6.16055i | −0.444599 | − | 0.770068i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.66865 | + | 15.1347i | 0.328488 | + | 1.86295i | ||||
\(67\) | 1.48513 | + | 8.42261i | 0.181438 | + | 1.02899i | 0.930447 | + | 0.366426i | \(0.119419\pi\) |
−0.749009 | + | 0.662559i | \(0.769470\pi\) | |||||||
\(68\) | −0.595046 | + | 1.03065i | −0.0721599 | + | 0.124985i | ||||
\(69\) | −1.78006 | − | 3.08315i | −0.214294 | − | 0.371167i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1153 | + | 4.40959i | −1.43782 | + | 0.523322i | −0.939161 | − | 0.343478i | \(-0.888395\pi\) |
−0.498656 | + | 0.866800i | \(0.666173\pi\) | |||||||
\(72\) | −7.97498 | − | 2.90266i | −0.939861 | − | 0.342081i | ||||
\(73\) | −1.39594 | − | 1.17133i | −0.163382 | − | 0.137094i | 0.557431 | − | 0.830223i | \(-0.311787\pi\) |
−0.720813 | + | 0.693129i | \(0.756232\pi\) | |||||||
\(74\) | 0.694747 | − | 3.94011i | 0.0807627 | − | 0.458028i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.626839 | + | 0.527435i | 0.0719034 | + | 0.0605010i | ||||
\(77\) | 13.5974 | 1.54957 | ||||||||
\(78\) | −1.13796 | + | 6.45371i | −0.128849 | + | 0.730739i | ||||
\(79\) | 0.535235 | + | 0.449116i | 0.0602187 | + | 0.0505295i | 0.672400 | − | 0.740188i | \(-0.265263\pi\) |
−0.612182 | + | 0.790717i | \(0.709708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.96239 | − | 2.89807i | 0.884710 | − | 0.322008i | ||||
\(82\) | 8.08837 | − | 6.78695i | 0.893211 | − | 0.749493i | ||||
\(83\) | 0.276493 | + | 0.478899i | 0.0303490 | + | 0.0525660i | 0.880801 | − | 0.473487i | \(-0.157005\pi\) |
−0.850452 | + | 0.526053i | \(0.823671\pi\) | |||||||
\(84\) | 0.758353 | − | 1.31351i | 0.0827431 | − | 0.143315i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.54139 | − | 14.4129i | −0.274045 | − | 1.55419i | ||||
\(87\) | 0.421388 | − | 0.729865i | 0.0451775 | − | 0.0782497i | ||||
\(88\) | 5.60726 | + | 9.71206i | 0.597736 | + | 1.03531i | ||||
\(89\) | 5.23109 | − | 4.38940i | 0.554494 | − | 0.465276i | −0.321965 | − | 0.946751i | \(-0.604343\pi\) |
0.876459 | + | 0.481476i | \(0.159899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.44854 | + | 1.98311i | 0.571162 | + | 0.207886i | ||||
\(92\) | 0.206408 | + | 0.173197i | 0.0215195 | + | 0.0180570i | ||||
\(93\) | −1.19816 | + | 6.79513i | −0.124244 | + | 0.704622i | ||||
\(94\) | 0.658883 | 0.0679586 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.63155 | 0.268582 | ||||||||
\(97\) | −2.29226 | + | 13.0001i | −0.232744 | + | 1.31996i | 0.614569 | + | 0.788863i | \(0.289330\pi\) |
−0.847313 | + | 0.531094i | \(0.821781\pi\) | |||||||
\(98\) | −4.03579 | − | 3.38643i | −0.407676 | − | 0.342081i | ||||
\(99\) | 12.4489 | + | 4.53102i | 1.25116 | + | 0.455385i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2339 | − | 11.1046i | 1.31683 | − | 1.10495i | 0.329857 | − | 0.944031i | \(-0.392999\pi\) |
0.986968 | − | 0.160916i | \(-0.0514450\pi\) | |||||||
\(102\) | 11.6294 | + | 20.1428i | 1.15149 | + | 1.99443i | ||||
\(103\) | −6.91430 | + | 11.9759i | −0.681286 | + | 1.18002i | 0.293302 | + | 0.956020i | \(0.405246\pi\) |
−0.974589 | + | 0.224003i | \(0.928088\pi\) | |||||||
\(104\) | 0.830401 | + | 4.70944i | 0.0814275 | + | 0.461798i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.35262 | + | 9.27101i | −0.519893 | + | 0.900481i | ||||
\(107\) | 1.63230 | + | 2.82722i | 0.157800 | + | 0.273318i | 0.934075 | − | 0.357077i | \(-0.116226\pi\) |
−0.776275 | + | 0.630394i | \(0.782893\pi\) | |||||||
\(108\) | 0.0594584 | − | 0.0498915i | 0.00572138 | − | 0.00480081i | ||||
\(109\) | 3.02669 | − | 1.10163i | 0.289905 | − | 0.105517i | −0.192974 | − | 0.981204i | \(-0.561813\pi\) |
0.482879 | + | 0.875687i | \(0.339591\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.14524 | − | 4.31737i | −0.488364 | − | 0.409786i | ||||
\(112\) | 2.44953 | − | 13.8920i | 0.231459 | − | 1.31267i | ||||
\(113\) | 4.71007 | 0.443086 | 0.221543 | − | 0.975151i | \(-0.428891\pi\) | ||||
0.221543 | + | 0.975151i | \(0.428891\pi\) | |||||||
\(114\) | 15.0525 | − | 5.45547i | 1.40979 | − | 0.510952i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0110762 | + | 0.0628163i | −0.00102840 | + | 0.00583234i | ||||
\(117\) | 4.32748 | + | 3.63119i | 0.400076 | + | 0.335704i | ||||
\(118\) | 4.36815 | + | 1.58988i | 0.402121 | + | 0.146360i | ||||
\(119\) | 19.3380 | − | 7.03845i | 1.77271 | − | 0.645214i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.25289 | − | 5.63416i | −0.295717 | − | 0.512197i | ||||
\(122\) | −2.26729 | + | 3.92705i | −0.205270 | + | 0.355539i | ||||
\(123\) | −3.07803 | − | 17.4564i | −0.277536 | − | 1.57399i | ||||
\(124\) | −0.0906829 | − | 0.514288i | −0.00814356 | − | 0.0461844i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.61042 | − | 13.1816i | −0.677990 | − | 1.17431i | ||||
\(127\) | 0.453507 | − | 0.380538i | 0.0402423 | − | 0.0337673i | −0.622445 | − | 0.782664i | \(-0.713860\pi\) |
0.662687 | + | 0.748897i | \(0.269416\pi\) | |||||||
\(128\) | 11.8793 | − | 4.32371i | 1.04999 | − | 0.382165i | ||||
\(129\) | −23.0877 | − | 8.40325i | −2.03276 | − | 0.739865i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.56830 | + | 20.2369i | −0.311764 | + | 1.76810i | 0.278053 | + | 0.960566i | \(0.410311\pi\) |
−0.589817 | + | 0.807537i | \(0.700800\pi\) | |||||||
\(132\) | −1.95265 | −0.169957 | ||||||||
\(133\) | −2.44090 | − | 13.9540i | −0.211653 | − | 1.20997i | ||||
\(134\) | −12.6507 | −1.09285 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.0018 | + | 10.9098i | 1.11489 | + | 0.935506i | ||||
\(137\) | −8.22613 | − | 2.99407i | −0.702806 | − | 0.255800i | −0.0341973 | − | 0.999415i | \(-0.510887\pi\) |
−0.668608 | + | 0.743615i | \(0.733110\pi\) | |||||||
\(138\) | 4.94843 | − | 1.80108i | 0.421238 | − | 0.153318i | ||||
\(139\) | 5.89041 | − | 4.94264i | 0.499618 | − | 0.419229i | −0.357840 | − | 0.933783i | \(-0.616487\pi\) |
0.857458 | + | 0.514553i | \(0.172042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.553061 | − | 0.957930i | 0.0465762 | − | 0.0806723i | ||||
\(142\) | −3.31158 | − | 18.7809i | −0.277901 | − | 1.57606i | ||||
\(143\) | −1.29625 | − | 7.35139i | −0.108398 | − | 0.614754i | ||||
\(144\) | 6.87178 | − | 11.9023i | 0.572649 | − | 0.991857i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.06483 | − | 1.73260i | 0.170887 | − | 0.143391i | ||||
\(147\) | −8.31104 | + | 3.02497i | −0.685483 | + | 0.249495i | ||||
\(148\) | 0.477690 | + | 0.173865i | 0.0392659 | + | 0.0142916i | ||||
\(149\) | −11.4457 | − | 9.60412i | −0.937672 | − | 0.786800i | 0.0395067 | − | 0.999219i | \(-0.487421\pi\) |
−0.977179 | + | 0.212419i | \(0.931866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1424 | 1.06951 | 0.534757 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534757 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(152\) | 8.96017 | − | 7.49772i | 0.726765 | − | 0.608145i | ||||
\(153\) | 20.0499 | 1.62094 | ||||||||
\(154\) | −3.49257 | + | 19.8074i | −0.281440 | + | 1.59612i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.782434 | − | 0.284783i | −0.0626449 | − | 0.0228009i | ||||
\(157\) | −10.1836 | + | 3.70654i | −0.812742 | + | 0.295814i | −0.714756 | − | 0.699374i | \(-0.753462\pi\) |
−0.0979861 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(158\) | −0.791704 | + | 0.664318i | −0.0629846 | + | 0.0528503i | ||||
\(159\) | 8.98590 | + | 15.5640i | 0.712628 | + | 1.23431i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.809073 | − | 4.58848i | −0.0637639 | − | 0.361623i | ||||
\(162\) | 2.17644 | + | 12.3432i | 0.170997 | + | 0.969772i | ||||
\(163\) | −4.22277 | + | 7.31405i | −0.330753 | + | 0.572881i | −0.982660 | − | 0.185418i | \(-0.940636\pi\) |
0.651907 | + | 0.758299i | \(0.273969\pi\) | |||||||
\(164\) | 0.670782 | + | 1.16183i | 0.0523792 | + | 0.0907235i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.768630 | + | 0.279758i | −0.0596573 | + | 0.0217135i | ||||
\(167\) | 18.7011 | + | 6.80663i | 1.44713 | + | 0.526713i | 0.941788 | − | 0.336206i | \(-0.109144\pi\) |
0.505343 | + | 0.862919i | \(0.331366\pi\) | |||||||
\(168\) | −16.5700 | − | 13.9039i | −1.27841 | − | 1.07271i | ||||
\(169\) | −1.70468 | + | 9.66772i | −0.131129 | + | 0.743671i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.41512 | − | 13.5887i | 0.184689 | − | 1.03915i | ||||
\(172\) | 1.85954 | 0.141788 | ||||||||
\(173\) | 2.03534 | − | 11.5430i | 0.154744 | − | 0.877597i | −0.804275 | − | 0.594257i | \(-0.797446\pi\) |
0.959019 | − | 0.283340i | \(-0.0914426\pi\) | |||||||
\(174\) | 0.954956 | + | 0.801304i | 0.0723951 | + | 0.0607467i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.0656 | + | 6.21138i | −1.28637 | + | 0.468200i | ||||
\(177\) | 5.97806 | − | 5.01619i | 0.449339 | − | 0.377040i | ||||
\(178\) | 5.05040 | + | 8.74755i | 0.378544 | + | 0.655657i | ||||
\(179\) | −3.54189 | + | 6.13473i | −0.264733 | + | 0.458532i | −0.967494 | − | 0.252895i | \(-0.918617\pi\) |
0.702760 | + | 0.711427i | \(0.251951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.61176 | + | 9.14076i | 0.119801 | + | 0.679427i | 0.984260 | + | 0.176724i | \(0.0565500\pi\) |
−0.864459 | + | 0.502703i | \(0.832339\pi\) | |||||||
\(182\) | −4.28827 | + | 7.42750i | −0.317868 | + | 0.550563i | ||||
\(183\) | 3.80628 | + | 6.59268i | 0.281369 | + | 0.487345i | ||||
\(184\) | 2.94371 | − | 2.47007i | 0.217013 | − | 0.182096i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.59069 | − | 3.49073i | −0.703224 | − | 0.255952i | ||||
\(187\) | −20.2957 | − | 17.0301i | −1.48417 | − | 1.24536i | ||||
\(188\) | −0.0145373 | + | 0.0824448i | −0.00106024 | + | 0.00601291i | ||||
\(189\) | −1.34216 | −0.0976277 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12426 | 0.587850 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(192\) | 3.06741 | − | 17.3961i | 0.221371 | − | 1.25546i | ||||
\(193\) | 5.91649 | + | 4.96452i | 0.425878 | + | 0.357354i | 0.830394 | − | 0.557177i | \(-0.188115\pi\) |
−0.404516 | + | 0.914531i | \(0.632560\pi\) | |||||||
\(194\) | −18.3484 | − | 6.67827i | −1.31734 | − | 0.479472i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.512781 | − | 0.430275i | 0.0366272 | − | 0.0307339i | ||||
\(197\) | −1.78381 | − | 3.08965i | −0.127091 | − | 0.220129i | 0.795457 | − | 0.606010i | \(-0.207231\pi\) |
−0.922548 | + | 0.385881i | \(0.873897\pi\) | |||||||
\(198\) | −9.79788 | + | 16.9704i | −0.696305 | + | 1.20604i | ||||
\(199\) | −1.52279 | − | 8.63615i | −0.107947 | − | 0.612201i | −0.990002 | − | 0.141053i | \(-0.954951\pi\) |
0.882055 | − | 0.471147i | \(-0.156160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6189 | + | 18.3924i | −0.748997 | + | 1.29730i | ||||
\(202\) | 12.7768 | + | 22.1301i | 0.898974 | + | 1.55707i | ||||
\(203\) | 0.844928 | − | 0.708979i | 0.0593023 | − | 0.0497606i | ||||
\(204\) | −2.77702 | + | 1.01075i | −0.194430 | + | 0.0707668i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.6693 | − | 13.1481i | −1.09173 | − | 0.916073i | ||||
\(207\) | 0.788270 | − | 4.47050i | 0.0547885 | − | 0.310721i | ||||
\(208\) | −7.74414 | −0.536960 | ||||||||
\(209\) | −13.9867 | + | 11.7039i | −0.967483 | + | 0.809574i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.05203 | − | 11.6376i | 0.141267 | − | 0.801167i | −0.829021 | − | 0.559217i | \(-0.811102\pi\) |
0.970289 | − | 0.241950i | \(-0.0777870\pi\) | |||||||
\(212\) | −1.04197 | − | 0.874315i | −0.0715627 | − | 0.0600482i | ||||
\(213\) | −30.0847 | − | 10.9499i | −2.06137 | − | 0.750277i | ||||
\(214\) | −4.53767 | + | 1.65158i | −0.310189 | + | 0.112899i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.553474 | − | 0.958646i | −0.0376592 | − | 0.0652276i | ||||
\(217\) | −4.51513 | + | 7.82043i | −0.306507 | + | 0.530886i | ||||
\(218\) | 0.827314 | + | 4.69193i | 0.0560328 | + | 0.317778i | ||||
\(219\) | −0.785770 | − | 4.45633i | −0.0530974 | − | 0.301131i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.64880 | − | 9.78401i | −0.379979 | − | 0.658144i | ||||
\(222\) | 7.61067 | − | 6.38611i | 0.510795 | − | 0.428608i | ||||
\(223\) | −8.36101 | + | 3.04316i | −0.559895 | + | 0.203785i | −0.606437 | − | 0.795131i | \(-0.707402\pi\) |
0.0465426 | + | 0.998916i | \(0.485180\pi\) | |||||||
\(224\) | 3.23632 | + | 1.17792i | 0.216236 | + | 0.0787034i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.20980 | + | 6.86114i | −0.0804750 | + | 0.456396i | ||||
\(227\) | −26.4080 | −1.75276 | −0.876380 | − | 0.481620i | \(-0.840049\pi\) | ||||
−0.876380 | + | 0.481620i | \(0.840049\pi\) | |||||||
\(228\) | 0.350523 | + | 2.00386i | 0.0232140 | + | 0.132709i | ||||
\(229\) | 21.7852 | 1.43961 | 0.719804 | − | 0.694177i | \(-0.244232\pi\) | ||||
0.719804 | + | 0.694177i | \(0.244232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.8657 | + | 21.7039i | 1.70184 | + | 1.42801i | ||||
\(232\) | 0.854821 | + | 0.311129i | 0.0561217 | + | 0.0204266i | ||||
\(233\) | −9.39780 | + | 3.42052i | −0.615670 | + | 0.224086i | −0.630982 | − | 0.775797i | \(-0.717348\pi\) |
0.0153122 | + | 0.999883i | \(0.495126\pi\) | |||||||
\(234\) | −6.40108 | + | 5.37114i | −0.418452 | + | 0.351123i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.295315 | + | 0.511500i | −0.0192234 | + | 0.0332958i | ||||
\(237\) | 0.301282 | + | 1.70866i | 0.0195704 | + | 0.110989i | ||||
\(238\) | 5.28583 | + | 29.9774i | 0.342630 | + | 1.94315i | ||||
\(239\) | −8.91823 | + | 15.4468i | −0.576872 | + | 0.999172i | 0.418963 | + | 0.908003i | \(0.362394\pi\) |
−0.995835 | + | 0.0911689i | \(0.970940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.1332 | + | 11.0201i | −0.845984 | + | 0.709864i | −0.958901 | − | 0.283740i | \(-0.908425\pi\) |
0.112918 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(242\) | 9.04279 | − | 3.29131i | 0.581293 | − | 0.211573i | ||||
\(243\) | 20.9365 | + | 7.62027i | 1.34308 | + | 0.488840i | ||||
\(244\) | −0.441361 | − | 0.370346i | −0.0282552 | − | 0.0237090i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.2192 | 1.67168 | ||||||||
\(247\) | −7.31147 | + | 2.64990i | −0.465218 | + | 0.168609i | ||||
\(248\) | −7.44772 | −0.472931 | ||||||||
\(249\) | −0.238450 | + | 1.35232i | −0.0151111 | + | 0.0856995i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.11112 | − | 3.31618i | −0.575089 | − | 0.209315i | 0.0380697 | − | 0.999275i | \(-0.487879\pi\) |
−0.613159 | + | 0.789960i | \(0.710101\pi\) | |||||||
\(252\) | 1.81731 | − | 0.661445i | 0.114480 | − | 0.0416671i | ||||
\(253\) | −4.59511 | + | 3.85575i | −0.288892 | + | 0.242409i | ||||
\(254\) | 0.437843 | + | 0.758366i | 0.0274727 | + | 0.0475841i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.776555 | + | 4.40406i | 0.0485347 | + | 0.275254i | ||||
\(257\) | −1.74528 | − | 9.89795i | −0.108867 | − | 0.617417i | −0.989605 | − | 0.143813i | \(-0.954064\pi\) |
0.880738 | − | 0.473605i | \(-0.157047\pi\) | |||||||
\(258\) | 18.1712 | − | 31.4734i | 1.13129 | − | 1.95945i | ||||
\(259\) | −4.39517 | − | 7.61265i | −0.273102 | − | 0.473027i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00981 | − | 0.367540i | 0.0625055 | − | 0.0227501i | ||||
\(262\) | −28.5624 | − | 10.3959i | −1.76459 | − | 0.642259i | ||||
\(263\) | −16.7232 | − | 14.0324i | −1.03120 | − | 0.865276i | −0.0402026 | − | 0.999192i | \(-0.512800\pi\) |
−0.990993 | + | 0.133916i | \(0.957245\pi\) | |||||||
\(264\) | −4.83575 | + | 27.4249i | −0.297620 | + | 1.68789i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.9537 | + | 0.0285081i | 1.28475 | + | 0.00174794i | ||||
\(267\) | 16.9571 | 1.03776 | ||||||||
\(268\) | 0.279117 | − | 1.58295i | 0.0170498 | − | 0.0966943i | ||||
\(269\) | 11.8393 | + | 9.93433i | 0.721853 | + | 0.605707i | 0.927897 | − | 0.372836i | \(-0.121615\pi\) |
−0.206044 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.85182 | + | 1.76592i | −0.294727 | + | 0.107272i | −0.485152 | − | 0.874430i | \(-0.661236\pi\) |
0.190425 | + | 0.981702i | \(0.439013\pi\) | |||||||
\(272\) | −21.0552 | + | 17.6674i | −1.27666 | + | 1.07124i | ||||
\(273\) | 7.19908 | + | 12.4692i | 0.435708 | + | 0.754669i | ||||
\(274\) | 6.47437 | − | 11.2139i | 0.391131 | − | 0.677459i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.116186 | + | 0.658926i | 0.00699360 | + | 0.0396627i | ||||
\(277\) | 2.78515 | − | 4.82402i | 0.167343 | − | 0.289847i | −0.770142 | − | 0.637873i | \(-0.779814\pi\) |
0.937485 | + | 0.348026i | \(0.113148\pi\) | |||||||
\(278\) | 5.68695 | + | 9.85009i | 0.341081 | + | 0.590769i | ||||
\(279\) | −6.73971 | + | 5.65529i | −0.403496 | + | 0.338573i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.6282 | − | 9.32789i | −1.52885 | − | 0.556455i | −0.565509 | − | 0.824742i | \(-0.691320\pi\) |
−0.963339 | + | 0.268287i | \(0.913542\pi\) | |||||||
\(282\) | 1.25336 | + | 1.05169i | 0.0746363 | + | 0.0626273i | ||||
\(283\) | 2.61267 | − | 14.8172i | 0.155307 | − | 0.880792i | −0.803197 | − | 0.595714i | \(-0.796869\pi\) |
0.958504 | − | 0.285078i | \(-0.0920196\pi\) | |||||||
\(284\) | 2.42308 | 0.143784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0417 | 0.652910 | ||||||||
\(287\) | 4.02834 | − | 22.8459i | 0.237786 | − | 1.34855i | ||||
\(288\) | 2.57044 | + | 2.15685i | 0.151464 | + | 0.127094i | ||||
\(289\) | −21.7045 | − | 7.89981i | −1.27674 | − | 0.464694i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.1108 | + | 21.0705i | −1.47202 | + | 1.23517i | ||||
\(292\) | 0.171240 | + | 0.296596i | 0.0100210 | + | 0.0173570i | ||||
\(293\) | −3.91441 | + | 6.77995i | −0.228682 | + | 0.396089i | −0.957418 | − | 0.288706i | \(-0.906775\pi\) |
0.728736 | + | 0.684795i | \(0.240108\pi\) | |||||||
\(294\) | −2.27173 | − | 12.8836i | −0.132490 | − | 0.751389i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.62492 | − | 6.27855i | 0.210694 | − | 0.364933i | ||||
\(297\) | 0.863969 | + | 1.49644i | 0.0501325 | + | 0.0868321i | ||||
\(298\) | 16.9302 | − | 14.2061i | 0.980740 | − | 0.822938i | ||||
\(299\) | −2.40361 | + | 0.874843i | −0.139004 | + | 0.0505935i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6322 | − | 20.6689i | −1.41978 | − | 1.19133i | ||||
\(302\) | −3.37569 | + | 19.1445i | −0.194249 | + | 1.10164i | ||||
\(303\) | 42.8990 | 2.46449 | ||||||||
\(304\) | 9.43773 | + | 16.3981i | 0.541291 | + | 0.940496i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.14992 | + | 29.2066i | −0.294401 | + | 1.66963i | ||||
\(307\) | 12.0381 | + | 10.1011i | 0.687049 | + | 0.576503i | 0.918057 | − | 0.396449i | \(-0.129758\pi\) |
−0.231008 | + | 0.972952i | \(0.574202\pi\) | |||||||
\(308\) | −2.40140 | − | 0.874039i | −0.136833 | − | 0.0498030i | ||||
\(309\) | −32.2684 | + | 11.7447i | −1.83568 | + | 0.668134i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.99061 | − | 15.5722i | −0.509810 | − | 0.883018i | −0.999935 | − | 0.0113654i | \(-0.996382\pi\) |
0.490125 | − | 0.871652i | \(-0.336951\pi\) | |||||||
\(312\) | −5.93746 | + | 10.2840i | −0.336142 | + | 0.582216i | ||||
\(313\) | −3.68143 | − | 20.8784i | −0.208087 | − | 1.18012i | −0.892508 | − | 0.451031i | \(-0.851056\pi\) |
0.684422 | − | 0.729087i | \(-0.260055\pi\) | |||||||
\(314\) | −2.78359 | − | 15.7865i | −0.157087 | − | 0.890884i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0656572 | − | 0.113722i | −0.00369351 | − | 0.00639734i | ||||
\(317\) | −2.34748 | + | 1.96977i | −0.131848 | + | 0.110633i | −0.706327 | − | 0.707886i | \(-0.749649\pi\) |
0.574479 | + | 0.818519i | \(0.305205\pi\) | |||||||
\(318\) | −24.9802 | + | 9.09203i | −1.40082 | + | 0.509856i | ||||
\(319\) | −1.33437 | − | 0.485670i | −0.0747102 | − | 0.0271923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.40771 | + | 7.98350i | −0.0785706 | + | 0.445596i | ||||
\(322\) | 6.89184 | 0.384067 | ||||||||
\(323\) | −13.8333 | + | 23.8850i | −0.769708 | + | 1.32899i | ||||
\(324\) | −1.59250 | −0.0884722 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.56972 | − | 8.02995i | −0.530018 | − | 0.444738i | ||||
\(327\) | 7.51590 | + | 2.73556i | 0.415630 | + | 0.151277i | ||||
\(328\) | 17.9790 | − | 6.54382i | 0.992724 | − | 0.361322i | ||||
\(329\) | 1.10895 | − | 0.930518i | 0.0611383 | − | 0.0513011i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9754 | − | 22.4741i | 0.713195 | − | 1.23529i | −0.250457 | − | 0.968128i | \(-0.580581\pi\) |
0.963652 | − | 0.267162i | \(-0.0860858\pi\) | |||||||
\(332\) | −0.0180470 | − | 0.102350i | −0.000990459 | − | 0.00561717i | ||||
\(333\) | −1.48718 | − | 8.43420i | −0.0814968 | − | 0.462191i | ||||
\(334\) | −14.7187 | + | 25.4935i | −0.805369 | + | 1.39494i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 26.8336 | − | 22.5161i | 1.46389 | − | 1.22835i | ||||
\(337\) | 9.45093 | − | 3.43986i | 0.514825 | − | 0.187381i | −0.0715252 | − | 0.997439i | \(-0.522787\pi\) |
0.586350 | + | 0.810058i | \(0.300564\pi\) | |||||||
\(338\) | −13.6451 | − | 4.96641i | −0.742195 | − | 0.270137i | ||||
\(339\) | 8.95971 | + | 7.51809i | 0.486624 | + | 0.408326i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6258 | 0.629574 | ||||||||
\(342\) | 19.1743 | + | 7.00842i | 1.03683 | + | 0.378972i | ||||
\(343\) | 11.1741 | 0.603343 | ||||||||
\(344\) | 4.60514 | − | 26.1171i | 0.248293 | − | 1.40814i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2918 | + | 5.92975i | 0.875855 | + | 0.318785i | ||||
\(347\) | 6.40683 | − | 2.33190i | 0.343937 | − | 0.125183i | −0.164276 | − | 0.986414i | \(-0.552529\pi\) |
0.508213 | + | 0.861232i | \(0.330306\pi\) | |||||||
\(348\) | −0.121335 | + | 0.101812i | −0.00650426 | + | 0.00545772i | ||||
\(349\) | −15.7983 | − | 27.3634i | −0.845663 | − | 1.46473i | −0.885044 | − | 0.465507i | \(-0.845872\pi\) |
0.0393817 | − | 0.999224i | \(-0.487461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.127948 | + | 0.725632i | 0.00682938 | + | 0.0387314i | ||||
\(352\) | −0.769945 | − | 4.36658i | −0.0410382 | − | 0.232739i | ||||
\(353\) | −3.15328 | + | 5.46165i | −0.167832 | + | 0.290694i | −0.937658 | − | 0.347561i | \(-0.887010\pi\) |
0.769825 | + | 0.638255i | \(0.220343\pi\) | |||||||
\(354\) | 5.77157 | + | 9.99666i | 0.306756 | + | 0.531316i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.20600 | + | 0.438946i | −0.0639176 | + | 0.0232641i | ||||
\(357\) | 48.0202 | + | 17.4779i | 2.54150 | + | 0.925030i | ||||
\(358\) | −8.02670 | − | 6.73520i | −0.424224 | − | 0.355966i | ||||
\(359\) | 0.725269 | − | 4.11321i | 0.0382782 | − | 0.217087i | −0.959669 | − | 0.281134i | \(-0.909290\pi\) |
0.997947 | + | 0.0640469i | \(0.0204007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5216 | + | 12.2525i | 0.764293 | + | 0.644870i | ||||
\(362\) | −13.7293 | −0.721596 | ||||||||
\(363\) | 2.80532 | − | 15.9097i | 0.147241 | − | 0.835045i | ||||
\(364\) | −0.834776 | − | 0.700460i | −0.0437542 | − | 0.0367141i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5812 | + | 3.85124i | −0.553088 | + | 0.201308i | ||||
\(367\) | 12.6941 | − | 10.6516i | 0.662627 | − | 0.556010i | −0.248246 | − | 0.968697i | \(-0.579854\pi\) |
0.910873 | + | 0.412687i | \(0.135410\pi\) | |||||||
\(368\) | 3.11148 | + | 5.38924i | 0.162197 | + | 0.280933i | ||||
\(369\) | 11.3009 | − | 19.5737i | 0.588302 | − | 1.01897i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.08428 | + | 23.1631i | 0.212045 | + | 1.20257i | ||||
\(372\) | 0.648392 | − | 1.12305i | 0.0336176 | − | 0.0582274i | ||||
\(373\) | −18.5002 | − | 32.0433i | −0.957905 | − | 1.65914i | −0.727576 | − | 0.686028i | \(-0.759353\pi\) |
−0.230330 | − | 0.973113i | \(-0.573980\pi\) | |||||||
\(374\) | 30.0207 | − | 25.1904i | 1.55233 | − | 1.30256i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.12193 | + | 0.408350i | 0.0578592 | + | 0.0210590i | ||||
\(377\) | −0.463853 | − | 0.389219i | −0.0238897 | − | 0.0200458i | ||||
\(378\) | 0.344740 | − | 1.95512i | 0.0177315 | − | 0.100561i | ||||
\(379\) | 31.5147 | 1.61880 | 0.809400 | − | 0.587257i | \(-0.199792\pi\) | ||||
0.809400 | + | 0.587257i | \(0.199792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.47009 | 0.0753148 | ||||||||
\(382\) | −2.08676 | + | 11.8346i | −0.106768 | + | 0.605510i | ||||
\(383\) | 2.37331 | + | 1.99144i | 0.121270 | + | 0.101758i | 0.701406 | − | 0.712762i | \(-0.252556\pi\) |
−0.580136 | + | 0.814520i | \(0.697000\pi\) | |||||||
\(384\) | 29.4987 | + | 10.7367i | 1.50535 | + | 0.547903i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.75148 | + | 7.34337i | −0.445439 | + | 0.373768i | ||||
\(387\) | −15.6641 | − | 27.1311i | −0.796253 | − | 1.37915i | ||||
\(388\) | 1.24047 | − | 2.14856i | 0.0629753 | − | 0.109076i | ||||
\(389\) | 4.52037 | + | 25.6363i | 0.229192 | + | 1.29981i | 0.854507 | + | 0.519439i | \(0.173859\pi\) |
−0.625316 | + | 0.780372i | \(0.715030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.53920 | + | 7.86213i | −0.229557 | + | 0.397605i | ||||
\(392\) | −4.77328 | − | 8.26756i | −0.241087 | − | 0.417575i | ||||
\(393\) | −39.0893 | + | 32.7999i | −1.97180 | + | 1.65453i | ||||
\(394\) | 4.95887 | − | 1.80488i | 0.249824 | − | 0.0909285i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.90730 | − | 1.60042i | −0.0958457 | − | 0.0804241i | ||||
\(397\) | −2.19851 | + | 12.4684i | −0.110340 | + | 0.625770i | 0.878612 | + | 0.477536i | \(0.158470\pi\) |
−0.988952 | + | 0.148234i | \(0.952641\pi\) | |||||||
\(398\) | 12.9714 | 0.650197 | ||||||||
\(399\) | 17.6298 | − | 30.4400i | 0.882595 | − | 1.52391i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.60135 | + | 9.08170i | −0.0799675 | + | 0.453518i | 0.918362 | + | 0.395741i | \(0.129512\pi\) |
−0.998330 | + | 0.0577770i | \(0.981599\pi\) | |||||||
\(402\) | −24.0647 | − | 20.1926i | −1.20024 | − | 1.00712i | ||||
\(403\) | 4.65851 | + | 1.69556i | 0.232057 | + | 0.0844618i | ||||
\(404\) | −3.05100 | + | 1.11047i | −0.151793 | + | 0.0552481i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.815744 | + | 1.41291i | 0.0404847 | + | 0.0701215i | ||||
\(407\) | −5.65847 | + | 9.80076i | −0.280480 | + | 0.485806i | ||||
\(408\) | 7.31866 | + | 41.5062i | 0.362328 | + | 2.05486i | ||||
\(409\) | 5.98343 | + | 33.9337i | 0.295861 | + | 1.67791i | 0.663680 | + | 0.748016i | \(0.268993\pi\) |
−0.367819 | + | 0.929897i | \(0.619895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.8691 | − | 18.8258i | −0.536132 | − | 0.928607i | ||||
\(412\) | 1.99092 | − | 1.67058i | 0.0980856 | − | 0.0823036i | ||||
\(413\) | 9.59724 | − | 3.49311i | 0.472249 | − | 0.171885i | ||||
\(414\) | 6.30969 | + | 2.29654i | 0.310104 | + | 0.112869i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.328320 | − | 1.86199i | 0.0160972 | − | 0.0912917i | ||||
\(417\) | 19.0943 | 0.935053 | ||||||||
\(418\) | −13.4564 | − | 23.3806i | −0.658176 | − | 1.14358i | ||||
\(419\) | −7.86047 | −0.384009 | −0.192005 | − | 0.981394i | \(-0.561499\pi\) | ||||
−0.192005 | + | 0.981394i | \(0.561499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.03752 | + | 6.74428i | 0.391725 | + | 0.328696i | 0.817285 | − | 0.576234i | \(-0.195478\pi\) |
−0.425560 | + | 0.904930i | \(0.639923\pi\) | |||||||
\(422\) | 16.4254 | + | 5.97836i | 0.799577 | + | 0.291022i | ||||
\(423\) | 1.32535 | − | 0.482387i | 0.0644406 | − | 0.0234545i | ||||
\(424\) | −14.8601 | + | 12.4691i | −0.721672 | + | 0.605555i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.6781 | − | 41.0117i | 1.14721 | − | 1.98702i | ||||
\(427\) | 1.73004 | + | 9.81153i | 0.0837223 | + | 0.474813i | ||||
\(428\) | −0.106542 | − | 0.604230i | −0.00514991 | − | 0.0292066i | ||||
\(429\) | 9.26832 | − | 16.0532i | 0.447479 | − | 0.775056i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.8988 | − | 19.2144i | 1.10300 | − | 0.925525i | 0.105375 | − | 0.994433i | \(-0.466396\pi\) |
0.997623 | + | 0.0689073i | \(0.0219513\pi\) | |||||||
\(432\) | 1.68449 | − | 0.613105i | 0.0810452 | − | 0.0294980i | ||||
\(433\) | 6.38969 | + | 2.32566i | 0.307069 | + | 0.111764i | 0.490959 | − | 0.871183i | \(-0.336647\pi\) |
−0.183890 | + | 0.982947i | \(0.558869\pi\) | |||||||
\(434\) | −10.2323 | − | 8.58589i | −0.491165 | − | 0.412136i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.605347 | −0.0289908 | ||||||||
\(437\) | 4.78173 | + | 4.02345i | 0.228741 | + | 0.192468i | ||||
\(438\) | 6.69335 | 0.319820 | ||||||||
\(439\) | 1.38329 | − | 7.84504i | 0.0660209 | − | 0.374423i | −0.933839 | − | 0.357693i | \(-0.883563\pi\) |
0.999860 | − | 0.0167300i | \(-0.00532558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5973 | − | 3.85711i | −0.504634 | − | 0.183672i | ||||
\(442\) | 15.7033 | − | 5.71552i | 0.746928 | − | 0.271859i | ||||
\(443\) | 16.6916 | − | 14.0059i | 0.793041 | − | 0.665440i | −0.153455 | − | 0.988156i | \(-0.549040\pi\) |
0.946496 | + | 0.322715i | \(0.104596\pi\) | |||||||
\(444\) | 0.631165 | + | 1.09321i | 0.0299538 | + | 0.0518815i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.28539 | − | 12.9611i | −0.108217 | − | 0.613726i | ||||
\(447\) | −6.44278 | − | 36.5388i | −0.304733 | − | 1.72823i | ||||
\(448\) | 11.5591 | − | 20.0210i | 0.546118 | − | 0.945904i | ||||
\(449\) | −9.39185 | − | 16.2672i | −0.443229 | − | 0.767695i | 0.554698 | − | 0.832052i | \(-0.312834\pi\) |
−0.997927 | + | 0.0643569i | \(0.979500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.0651 | + | 10.2148i | −1.32153 | + | 0.480998i | ||||
\(452\) | −0.831830 | − | 0.302761i | −0.0391260 | − | 0.0142407i | ||||
\(453\) | 25.0001 | + | 20.9776i | 1.17461 | + | 0.985612i | ||||
\(454\) | 6.78303 | − | 38.4685i | 0.318343 | − | 1.80541i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 29.0121 | + | 0.0394717i | 1.35862 | + | 0.00184843i | ||||
\(457\) | −28.2368 | −1.32086 | −0.660431 | − | 0.750887i | \(-0.729627\pi\) | ||||
−0.660431 | + | 0.750887i | \(0.729627\pi\) | |||||||
\(458\) | −5.59564 | + | 31.7345i | −0.261467 | + | 1.48285i | ||||
\(459\) | 2.00332 | + | 1.68098i | 0.0935069 | + | 0.0784616i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.184187 | − | 0.0670386i | 0.00857845 | − | 0.00312230i | −0.337727 | − | 0.941244i | \(-0.609658\pi\) |
0.346306 | + | 0.938122i | \(0.387436\pi\) | |||||||
\(462\) | −38.2597 | + | 32.1037i | −1.78000 | + | 1.49360i | ||||
\(463\) | 6.98206 | + | 12.0933i | 0.324484 | + | 0.562022i | 0.981408 | − | 0.191935i | \(-0.0614761\pi\) |
−0.656924 | + | 0.753957i | \(0.728143\pi\) | |||||||
\(464\) | −0.736571 | + | 1.27578i | −0.0341945 | + | 0.0592266i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.56879 | − | 14.5683i | −0.118997 | − | 0.674865i | ||||
\(467\) | −16.0512 | + | 27.8016i | −0.742763 | + | 1.28650i | 0.208470 | + | 0.978029i | \(0.433152\pi\) |
−0.951233 | + | 0.308474i | \(0.900182\pi\) | |||||||
\(468\) | −0.530851 | − | 0.919462i | −0.0245386 | − | 0.0425021i | ||||
\(469\) | −21.2920 | + | 17.8661i | −0.983172 | + | 0.824979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2881 | − | 9.20410i | −1.16521 | − | 0.424102i | ||||
\(472\) | 6.45264 | + | 5.41441i | 0.297007 | + | 0.249218i | ||||
\(473\) | −7.18859 | + | 40.7685i | −0.330532 | + | 1.87454i | ||||
\(474\) | −2.56638 | −0.117878 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.86765 | −0.177273 | ||||||||
\(477\) | −3.97926 | + | 22.5675i | −0.182198 | + | 1.03330i | ||||
\(478\) | −20.2107 | − | 16.9588i | −0.924414 | − | 0.775675i | ||||
\(479\) | 1.86271 | + | 0.677972i | 0.0851095 | + | 0.0309773i | 0.384224 | − | 0.923240i | \(-0.374469\pi\) |
−0.299114 | + | 0.954217i | \(0.596691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.69675 | + | 3.10194i | −0.168557 | + | 0.141436i | ||||
\(482\) | −12.6796 | − | 21.9616i | −0.577538 | − | 1.00033i | ||||
\(483\) | 5.78496 | − | 10.0198i | 0.263225 | − | 0.455919i | ||||
\(484\) | 0.212320 | + | 1.20413i | 0.00965091 | + | 0.0547330i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.4781 | + | 28.5409i | −0.747460 | + | 1.29464i | ||||
\(487\) | 4.29458 | + | 7.43843i | 0.194606 | + | 0.337068i | 0.946771 | − | 0.321907i | \(-0.104324\pi\) |
−0.752165 | + | 0.658975i | \(0.770990\pi\) | |||||||
\(488\) | −6.29452 | + | 5.28173i | −0.284939 | + | 0.239093i | ||||
\(489\) | −19.7072 | + | 7.17285i | −0.891192 | + | 0.324367i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8407 | + | 16.6483i | 0.895398 | + | 0.751328i | 0.969285 | − | 0.245938i | \(-0.0790961\pi\) |
−0.0738874 | + | 0.997267i | \(0.523541\pi\) | |||||||
\(492\) | −0.578488 | + | 3.28077i | −0.0260802 | + | 0.147908i | ||||
\(493\) | −2.14910 | −0.0967908 | ||||||||
\(494\) | −1.98211 | − | 11.3312i | −0.0891794 | − | 0.509817i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.09435 | − | 11.8777i | 0.0940391 | − | 0.533322i | ||||
\(497\) | −32.0972 | − | 26.9328i | −1.43976 | − | 1.20810i | ||||
\(498\) | −1.90867 | − | 0.694698i | −0.0855294 | − | 0.0311302i | ||||
\(499\) | 19.9251 | − | 7.25214i | 0.891970 | − | 0.324650i | 0.144939 | − | 0.989441i | \(-0.453701\pi\) |
0.747030 | + | 0.664790i | \(0.231479\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.7094 | + | 42.7980i | 1.10394 | + | 1.91207i | ||||
\(502\) | 7.17090 | − | 12.4204i | 0.320053 | − | 0.554348i | ||||
\(503\) | −4.43084 | − | 25.1285i | −0.197561 | − | 1.12043i | −0.908724 | − | 0.417398i | \(-0.862942\pi\) |
0.711162 | − | 0.703028i | \(-0.248169\pi\) | |||||||
\(504\) | −4.78940 | − | 27.1620i | −0.213337 | − | 1.20989i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.43639 | − | 7.68405i | −0.197221 | − | 0.341597i | ||||
\(507\) | −18.6741 | + | 15.6694i | −0.829346 | + | 0.695904i | ||||
\(508\) | −0.104553 | + | 0.0380543i | −0.00463880 | + | 0.00168839i | ||||
\(509\) | 16.0130 | + | 5.82825i | 0.709763 | + | 0.258333i | 0.671574 | − | 0.740938i | \(-0.265619\pi\) |
0.0381894 | + | 0.999271i | \(0.487841\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02837 | − | 5.83218i | 0.0454924 | − | 0.258000i | ||||
\(512\) | 18.6685 | 0.825039 | ||||||||
\(513\) | 1.38059 | − | 1.15525i | 0.0609543 | − | 0.0510056i | ||||
\(514\) | 14.8666 | 0.655738 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.53729 | + | 2.96814i | 0.155721 | + | 0.130665i | ||||
\(517\) | −1.75133 | − | 0.637430i | −0.0770232 | − | 0.0280342i | ||||
\(518\) | 12.2183 | − | 4.44708i | 0.536839 | − | 0.195393i | ||||
\(519\) | 22.2963 | − | 18.7088i | 0.978700 | − | 0.821227i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8909 | + | 18.8635i | −0.477137 | + | 0.826426i | −0.999657 | − | 0.0262016i | \(-0.991659\pi\) |
0.522520 | + | 0.852627i | \(0.324992\pi\) | |||||||
\(522\) | 0.276020 | + | 1.56539i | 0.0120811 | + | 0.0685152i | ||||
\(523\) | 3.03633 | + | 17.2199i | 0.132769 | + | 0.752973i | 0.976387 | + | 0.216028i | \(0.0693104\pi\) |
−0.843618 | + | 0.536944i | \(0.819578\pi\) | |||||||
\(524\) | 1.93100 | − | 3.34460i | 0.0843563 | − | 0.146109i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7364 | − | 20.7563i | 1.07856 | − | 0.905018i | ||||
\(527\) | 16.5340 | − | 6.01788i | 0.720232 | − | 0.262143i | ||||
\(528\) | −42.3775 | − | 15.4241i | −1.84424 | − | 0.671249i | ||||
\(529\) | −16.0445 | − | 13.4629i | −0.697586 | − | 0.585344i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.95056 | 0.431817 | ||||||||
\(532\) | −0.465879 | + | 2.62127i | −0.0201984 | + | 0.113647i | ||||
\(533\) | −12.7355 | −0.551637 | ||||||||
\(534\) | −4.35551 | + | 24.7013i | −0.188481 | + | 1.06893i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.5413 | − | 7.84038i | −0.930441 | − | 0.338653i | ||||
\(537\) | −16.5297 | + | 6.01630i | −0.713307 | + | 0.259623i | ||||
\(538\) | −17.5123 | + | 14.6945i | −0.755008 | + | 0.633527i | ||||
\(539\) | 7.45104 | + | 12.9056i | 0.320939 | + | 0.555883i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.57157 | + | 14.5841i | 0.110560 | + | 0.627018i | 0.988853 | + | 0.148895i | \(0.0475717\pi\) |
−0.878293 | + | 0.478123i | \(0.841317\pi\) | |||||||
\(542\) | −1.32619 | − | 7.52121i | −0.0569648 | − | 0.323064i | ||||
\(543\) | −11.5243 | + | 19.9606i | −0.494554 | + | 0.856592i | ||||
\(544\) | −3.35527 | − | 5.81150i | −0.143856 | − | 0.249166i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20.0129 | + | 7.28411i | −0.856474 | + | 0.311731i | ||||
\(547\) | −24.9709 | − | 9.08867i | −1.06768 | − | 0.388603i | −0.252371 | − | 0.967631i | \(-0.581210\pi\) |
−0.815308 | + | 0.579027i | \(0.803433\pi\) | |||||||
\(548\) | 1.26033 | + | 1.05754i | 0.0538388 | + | 0.0451761i | ||||
\(549\) | −1.68555 | + | 9.55924i | −0.0719376 | + | 0.407979i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.258871 | + | 1.45654i | −0.0110283 | + | 0.0620507i | ||||
\(552\) | 9.54231 | 0.406148 | ||||||||
\(553\) | −0.394301 | + | 2.23619i | −0.0167674 | + | 0.0950926i | ||||
\(554\) | 6.31176 | + | 5.29619i | 0.268161 | + | 0.225014i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.35800 | + | 0.494271i | −0.0575919 | + | 0.0209618i | ||||
\(557\) | 12.3143 | − | 10.3330i | 0.521775 | − | 0.437821i | −0.343475 | − | 0.939162i | \(-0.611604\pi\) |
0.865250 | + | 0.501340i | \(0.167160\pi\) | |||||||
\(558\) | −6.50691 | − | 11.2703i | −0.275460 | − | 0.477110i | ||||
\(559\) | −8.82633 | + | 15.2877i | −0.373314 | + | 0.646599i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.4244 | − | 64.7908i | −0.482337 | − | 2.73547i | ||||
\(562\) | 20.1706 | − | 34.9365i | 0.850847 | − | 1.47371i | ||||
\(563\) | −1.01573 | − | 1.75929i | −0.0428078 | − | 0.0741452i | 0.843828 | − | 0.536614i | \(-0.180297\pi\) |
−0.886635 | + | 0.462469i | \(0.846964\pi\) | |||||||
\(564\) | −0.159250 | + | 0.133626i | −0.00670562 | + | 0.00562669i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.9131 | + | 7.61175i | 0.879044 | + | 0.319946i | ||||
\(567\) | 21.0950 | + | 17.7008i | 0.885905 | + | 0.743362i | ||||
\(568\) | 6.00077 | − | 34.0321i | 0.251787 | − | 1.42795i | ||||
\(569\) | −12.8224 | −0.537543 | −0.268772 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268772 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9168 | 0.540551 | 0.270276 | − | 0.962783i | \(-0.412885\pi\) | ||||
0.270276 | + | 0.962783i | \(0.412885\pi\) | |||||||
\(572\) | −0.243618 | + | 1.38163i | −0.0101862 | + | 0.0577688i | ||||
\(573\) | 15.4543 | + | 12.9677i | 0.645614 | + | 0.541735i | ||||
\(574\) | 32.2448 | + | 11.7362i | 1.34587 | + | 0.489858i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.2543 | − | 14.4780i | 0.718928 | − | 0.603252i | ||||
\(577\) | −4.05680 | − | 7.02658i | −0.168887 | − | 0.292520i | 0.769142 | − | 0.639078i | \(-0.220684\pi\) |
−0.938029 | + | 0.346558i | \(0.887351\pi\) | |||||||
\(578\) | 17.0825 | − | 29.5878i | 0.710540 | − | 1.23069i | ||||
\(579\) | 3.33037 | + | 18.8875i | 0.138406 | + | 0.784937i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.898567 | + | 1.55636i | −0.0372788 | + | 0.0645689i | ||||
\(582\) | −24.2435 | − | 41.9909i | −1.00492 | − | 1.74058i | ||||
\(583\) | 23.1966 | − | 19.4642i | 0.960703 | − | 0.806126i | ||||
\(584\) | 4.58975 | − | 1.67053i | 0.189925 | − | 0.0691271i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.87090 | − | 7.44357i | −0.366454 | − | 0.307491i | ||||
\(587\) | −5.65427 | + | 32.0670i | −0.233377 | + | 1.32355i | 0.612629 | + | 0.790371i | \(0.290112\pi\) |
−0.846005 | + | 0.533174i | \(0.820999\pi\) | |||||||
\(588\) | 1.66223 | 0.0685492 | ||||||||
\(589\) | −2.08697 | − | 11.9307i | −0.0859921 | − | 0.491595i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.53837 | − | 8.72455i | 0.0632802 | − | 0.358880i | ||||
\(592\) | 8.99370 | + | 7.54661i | 0.369639 | + | 0.310164i | ||||
\(593\) | 10.7832 | + | 3.92476i | 0.442812 | + | 0.161171i | 0.553797 | − | 0.832652i | \(-0.313178\pi\) |
−0.110985 | + | 0.993822i | \(0.535401\pi\) | |||||||
\(594\) | −2.40177 | + | 0.874173i | −0.0985459 | + | 0.0358678i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.40405 | + | 2.43188i | 0.0575120 | + | 0.0996138i | ||||
\(597\) | 10.8881 | − | 18.8587i | 0.445620 | − | 0.771836i | ||||
\(598\) | −0.657002 | − | 3.72604i | −0.0268668 | − | 0.152369i | ||||
\(599\) | 5.76684 | + | 32.7054i | 0.235627 | + | 1.33631i | 0.841290 | + | 0.540584i | \(0.181797\pi\) |
−0.605663 | + | 0.795721i | \(0.707092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6590 | − | 23.6581i | −0.557163 | − | 0.965034i | −0.997732 | − | 0.0673154i | \(-0.978557\pi\) |
0.440569 | − | 0.897719i | \(-0.354777\pi\) | |||||||
\(602\) | 36.4352 | − | 30.5728i | 1.48499 | − | 1.24605i | ||||
\(603\) | −25.4469 | + | 9.26191i | −1.03628 | + | 0.377174i | ||||
\(604\) | −2.32104 | − | 0.844789i | −0.0944417 | − | 0.0343740i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.0188 | + | 62.4909i | −0.447609 | + | 2.53852i | ||||
\(607\) | 25.7405 | 1.04478 | 0.522388 | − | 0.852708i | \(-0.325041\pi\) | ||||
0.522388 | + | 0.852708i | \(0.325041\pi\) | |||||||
\(608\) | −4.34286 | + | 1.57399i | −0.176126 | + | 0.0638335i | ||||
\(609\) | 2.73892 | 0.110986 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.608796 | − | 0.510841i | −0.0246293 | − | 0.0206664i | ||||
\(612\) | −3.54095 | − | 1.28880i | −0.143134 | − | 0.0520967i | ||||
\(613\) | −38.1551 | + | 13.8873i | −1.54107 | + | 0.560904i | −0.966302 | − | 0.257411i | \(-0.917131\pi\) |
−0.574770 | + | 0.818315i | \(0.694908\pi\) | |||||||
\(614\) | −17.8063 | + | 14.9413i | −0.718606 | + | 0.602982i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.2229 | + | 31.5630i | −0.734222 | + | 1.27171i | ||||
\(617\) | 2.46776 | + | 13.9954i | 0.0993485 | + | 0.563433i | 0.993328 | + | 0.115325i | \(0.0367910\pi\) |
−0.893979 | + | 0.448108i | \(0.852098\pi\) | |||||||
\(618\) | −8.82021 | − | 50.0219i | −0.354801 | − | 2.01218i | ||||
\(619\) | 14.7818 | − | 25.6028i | 0.594129 | − | 1.02906i | −0.399540 | − | 0.916716i | \(-0.630830\pi\) |
0.993669 | − | 0.112346i | \(-0.0358364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.453568 | − | 0.380589i | 0.0182010 | − | 0.0152725i | ||||
\(622\) | 24.9932 | − | 9.09680i | 1.00214 | − | 0.364748i | ||||
\(623\) | 20.8541 | + | 7.59026i | 0.835500 | + | 0.304097i | ||||
\(624\) | −14.7313 | − | 12.3610i | −0.589723 | − | 0.494836i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.3591 | 1.25336 | ||||||||
\(627\) | −45.2877 | − | 0.0616150i | −1.80861 | − | 0.00246067i | ||||
\(628\) | 2.03675 | 0.0812753 | ||||||||
\(629\) | −2.97418 | + | 16.8674i | −0.118588 | + | 0.672548i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.60465 | + | 0.584045i | 0.0638801 | + | 0.0232505i | 0.373763 | − | 0.927524i | \(-0.378067\pi\) |
−0.309882 | + | 0.950775i | \(0.600290\pi\) | |||||||
\(632\) | −1.75981 | + | 0.640520i | −0.0700017 | + | 0.0254785i | ||||
\(633\) | 22.4791 | − | 18.8622i | 0.893465 | − | 0.749706i | ||||
\(634\) | −2.26640 | − | 3.92552i | −0.0900102 | − | 0.155902i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.586521 | − | 3.32633i | −0.0232571 | − | 0.131897i | ||||
\(637\) | 1.10345 | + | 6.25800i | 0.0437204 | + | 0.247951i | ||||
\(638\) | 1.05021 | − | 1.81902i | 0.0415783 | − | 0.0720158i | ||||
\(639\) | −20.4113 | − | 35.3534i | −0.807459 | − | 1.39856i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.59543 | + | 0.944659i | −0.102513 | + | 0.0373118i | −0.392768 | − | 0.919638i | \(-0.628482\pi\) |
0.290254 | + | 0.956950i | \(0.406260\pi\) | |||||||
\(642\) | −11.2680 | − | 4.10121i | −0.444711 | − | 0.161862i | ||||
\(643\) | 16.6209 | + | 13.9466i | 0.655465 | + | 0.550000i | 0.908724 | − | 0.417398i | \(-0.137058\pi\) |
−0.253259 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(644\) | −0.152058 | + | 0.862364i | −0.00599193 | + | 0.0339819i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.2400 | − | 26.2860i | −1.22912 | − | 1.03421i | ||||
\(647\) | −28.0268 | −1.10185 | −0.550923 | − | 0.834556i | \(-0.685724\pi\) | ||||
−0.550923 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(648\) | −3.94383 | + | 22.3666i | −0.154928 | + | 0.878642i | ||||
\(649\) | −10.0725 | − | 8.45185i | −0.395381 | − | 0.331764i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.0717 | + | 7.66946i | −0.825864 | + | 0.300590i | ||||
\(652\) | 1.21591 | − | 1.02027i | 0.0476189 | − | 0.0399570i | ||||
\(653\) | −3.79654 | − | 6.57580i | −0.148570 | − | 0.257331i | 0.782129 | − | 0.623116i | \(-0.214134\pi\) |
−0.930699 | + | 0.365785i | \(0.880800\pi\) | |||||||
\(654\) | −5.91538 | + | 10.2457i | −0.231310 | + | 0.400640i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.38029 | + | 30.5131i | 0.210065 | + | 1.19134i | ||||
\(657\) | 2.88494 | − | 4.99686i | 0.112552 | − | 0.194946i | ||||
\(658\) | 1.07064 | + | 1.85441i | 0.0417380 | + | 0.0722924i | ||||
\(659\) | 5.50322 | − | 4.61775i | 0.214375 | − | 0.179882i | −0.529277 | − | 0.848449i | \(-0.677537\pi\) |
0.743652 | + | 0.668567i | \(0.233092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1268 | + | 9.87335i | 1.05511 | + | 0.384029i | 0.810589 | − | 0.585615i | \(-0.199147\pi\) |
0.244521 | + | 0.969644i | \(0.421369\pi\) | |||||||
\(662\) | 29.4052 | + | 24.6739i | 1.14287 | + | 0.958978i | ||||
\(663\) | 4.87157 | − | 27.6281i | 0.189196 | − | 1.07298i | ||||
\(664\) | −1.48219 | −0.0575201 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.6681 | 0.490877 | ||||||||
\(667\) | −0.0844929 | + | 0.479183i | −0.00327158 | + | 0.0185540i | ||||
\(668\) | −2.86521 | − | 2.40419i | −0.110858 | − | 0.0930210i | ||||
\(669\) | −20.7621 | − | 7.55679i | −0.802710 | − | 0.292162i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.82569 | − | 8.24473i | 0.379316 | − | 0.318284i | ||||
\(672\) | 4.27611 | + | 7.40644i | 0.164954 | + | 0.285709i | ||||
\(673\) | 11.6595 | − | 20.1949i | 0.449442 | − | 0.778457i | −0.548907 | − | 0.835883i | \(-0.684956\pi\) |
0.998350 | + | 0.0574263i | \(0.0182894\pi\) | |||||||
\(674\) | 2.58331 | + | 14.6507i | 0.0995054 | + | 0.564323i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.922496 | − | 1.59781i | 0.0354806 | − | 0.0614542i | ||||
\(677\) | −8.75493 | − | 15.1640i | −0.336479 | − | 0.582799i | 0.647289 | − | 0.762245i | \(-0.275903\pi\) |
−0.983768 | + | 0.179446i | \(0.942570\pi\) | |||||||
\(678\) | −13.2529 | + | 11.1205i | −0.508975 | + | 0.427081i | ||||
\(679\) | −40.3132 | + | 14.6728i | −1.54708 | + | 0.563090i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −50.2345 | − | 42.1518i | −1.92499 | − | 1.61526i | ||||
\(682\) | −2.98615 | + | 16.9353i | −0.114346 | + | 0.648487i | ||||
\(683\) | −22.0114 | −0.842243 | −0.421122 | − | 0.907004i | \(-0.638363\pi\) | ||||
−0.421122 | + | 0.907004i | \(0.638363\pi\) | |||||||
\(684\) | −1.30000 | + | 2.24461i | −0.0497068 | + | 0.0858249i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.87012 | + | 16.2772i | −0.109582 | + | 0.621468i | ||||
\(687\) | 41.4409 | + | 34.7730i | 1.58107 | + | 1.32667i | ||||
\(688\) | 40.3566 | + | 14.6886i | 1.53858 | + | 0.559997i | ||||
\(689\) | 12.1337 | − | 4.41629i | 0.462256 | − | 0.168247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.32811 | + | 2.30036i | 0.0505238 | + | 0.0875098i | 0.890181 | − | 0.455607i | \(-0.150578\pi\) |
−0.839657 | + | 0.543116i | \(0.817244\pi\) | |||||||
\(692\) | −1.10143 | + | 1.90774i | −0.0418702 | + | 0.0725214i | ||||
\(693\) | 7.47621 | + | 42.3997i | 0.283998 | + | 1.61063i | ||||
\(694\) | 1.75124 | + | 9.93178i | 0.0664762 | + | 0.377005i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.12946 | + | 1.95629i | 0.0428122 | + | 0.0741529i | ||||
\(697\) | −34.6260 | + | 29.0546i | −1.31155 | + | 1.10052i | ||||
\(698\) | 43.9181 | − | 15.9849i | 1.66232 | − | 0.605037i | ||||
\(699\) | −23.3367 | − | 8.49385i | −0.882674 | − | 0.321267i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.27931 | + | 7.25535i | −0.0483190 | + | 0.274031i | −0.999389 | − | 0.0349439i | \(-0.988875\pi\) |
0.951070 | + | 0.308975i | \(0.0999859\pi\) | |||||||
\(702\) | −1.08989 | −0.0411352 | ||||||||
\(703\) | 11.0735 | + | 4.04750i | 0.417646 | + | 0.152654i | ||||
\(704\) | −29.7632 | −1.12174 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.14603 | − | 5.99623i | −0.268944 | − | 0.225671i | ||||
\(707\) | 52.7579 | + | 19.2023i | 1.98416 | + | 0.722177i | ||||
\(708\) | −1.37821 | + | 0.501626i | −0.0517961 | + | 0.0188522i | ||||
\(709\) | −4.58997 | + | 3.85144i | −0.172380 | + | 0.144644i | −0.724896 | − | 0.688858i | \(-0.758112\pi\) |
0.552516 | + | 0.833502i | \(0.313668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.10615 | + | 1.91591i | −0.0414839 | + | 0.0718523i | ||||
\(712\) | 3.17833 | + | 18.0252i | 0.119113 | + | 0.675522i | ||||
\(713\) | −0.691759 | − | 3.92316i | −0.0259066 | − | 0.146923i | ||||
\(714\) | −37.7943 | + | 65.4616i | −1.41441 | + | 2.44984i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.01986 | − | 0.855765i | 0.0381140 | − | 0.0319814i | ||||
\(717\) | −41.6205 | + | 15.1486i | −1.55435 | + | 0.565736i | ||||
\(718\) | 5.80541 | + | 2.11300i | 0.216656 | + | 0.0788563i | ||||
\(719\) | 10.4040 | + | 8.73002i | 0.388005 | + | 0.325575i | 0.815835 | − | 0.578284i | \(-0.196278\pi\) |
−0.427831 | + | 0.903859i | \(0.640722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.9412 | −1.67370 | ||||||||
\(722\) | −21.5782 | + | 18.0064i | −0.803056 | + | 0.670128i | ||||
\(723\) | −42.5725 | −1.58329 | ||||||||
\(724\) | 0.302916 | − | 1.71792i | 0.0112578 | − | 0.0638461i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.4551 | + | 8.17299i | 0.833387 | + | 0.303328i | ||||
\(727\) | 38.7574 | − | 14.1065i | 1.43743 | − | 0.523183i | 0.498381 | − | 0.866958i | \(-0.333928\pi\) |
0.939052 | + | 0.343776i | \(0.111706\pi\) | |||||||
\(728\) | −11.9052 | + | 9.98969i | −0.441238 | + | 0.370242i | ||||
\(729\) | 14.9530 | + | 25.8994i | 0.553816 | + | 0.959237i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8796 | + | 61.7011i | 0.402395 | + | 2.28210i | ||||
\(732\) | −0.248441 | − | 1.40898i | −0.00918264 | − | 0.0520773i | ||||
\(733\) | 0.0619240 | − | 0.107256i | 0.00228722 | − | 0.00396158i | −0.864880 | − | 0.501979i | \(-0.832605\pi\) |
0.867167 | + | 0.498018i | \(0.165939\pi\) | |||||||
\(734\) | 12.2556 | + | 21.2274i | 0.452364 | + | 0.783517i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.42770 | + | 0.519639i | −0.0526256 | + | 0.0191541i | ||||
\(737\) | 33.6257 | + | 12.2388i | 1.23862 | + | 0.450821i | ||||
\(738\) | 25.6103 | + | 21.4896i | 0.942729 | + | 0.791043i | ||||
\(739\) | −6.34049 | + | 35.9587i | −0.233239 | + | 1.32276i | 0.613053 | + | 0.790042i | \(0.289941\pi\) |
−0.846291 | + | 0.532720i | \(0.821170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1379 | − | 6.62962i | −0.666313 | − | 0.243545i | ||||
\(742\) | −34.7907 | −1.27721 | ||||||||
\(743\) | 1.57359 | − | 8.92430i | 0.0577296 | − | 0.327401i | −0.942242 | − | 0.334933i | \(-0.891286\pi\) |
0.999972 | + | 0.00753195i | \(0.00239752\pi\) | |||||||
\(744\) | −14.1674 | − | 11.8879i | −0.519402 | − | 0.435830i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 51.4293 | − | 18.7187i | 1.88296 | − | 0.685341i | ||||
\(747\) | −1.34129 | + | 1.12547i | −0.0490751 | + | 0.0411789i | ||||
\(748\) | 2.48967 | + | 4.31223i | 0.0910312 | + | 0.157671i | ||||
\(749\) | −5.30476 | + | 9.18812i | −0.193832 | + | 0.335727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.709544 | − | 4.02402i | −0.0258916 | − | 0.146839i | 0.969121 | − | 0.246584i | \(-0.0793082\pi\) |
−0.995013 | + | 0.0997456i | \(0.968197\pi\) | |||||||
\(752\) | −0.966732 | + | 1.67443i | −0.0352531 | + | 0.0610602i | ||||
\(753\) | −12.0384 | − | 20.8511i | −0.438704 | − | 0.759857i | ||||
\(754\) | 0.686117 | − | 0.575721i | 0.0249869 | − | 0.0209665i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.237035 | + | 0.0862735i | 0.00862086 | + | 0.00313774i | ||||
\(757\) | −26.3977 | − | 22.1503i | −0.959441 | − | 0.805066i | 0.0214214 | − | 0.999771i | \(-0.493181\pi\) |
−0.980862 | + | 0.194704i | \(0.937625\pi\) | |||||||
\(758\) | −8.09470 | + | 45.9073i | −0.294013 | + | 1.66743i | ||||
\(759\) | −14.8955 | −0.540671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5813 | 0.746072 | 0.373036 | − | 0.927817i | \(-0.378317\pi\) | ||||
0.373036 | + | 0.927817i | \(0.378317\pi\) | |||||||
\(762\) | −0.377599 | + | 2.14147i | −0.0136790 | + | 0.0775773i | ||||
\(763\) | 8.01868 | + | 6.72848i | 0.290296 | + | 0.243587i | ||||
\(764\) | −1.43480 | − | 0.522224i | −0.0519092 | − | 0.0188934i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.51052 | + | 2.94568i | −0.126840 | + | 0.106432i | ||||
\(767\) | −2.80344 | − | 4.85570i | −0.101226 | − | 0.175329i | ||||
\(768\) | −5.55245 | + | 9.61713i | −0.200357 | + | 0.347028i | ||||
\(769\) | −5.27109 | − | 29.8939i | −0.190081 | − | 1.07800i | −0.919252 | − | 0.393669i | \(-0.871206\pi\) |
0.729172 | − | 0.684331i | \(-0.239906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.4789 | − | 21.6141i | 0.449417 | − | 0.778413i | ||||
\(772\) | −0.725774 | − | 1.25708i | −0.0261212 | − | 0.0452432i | ||||
\(773\) | 14.9551 | − | 12.5488i | 0.537898 | − | 0.451350i | −0.332921 | − | 0.942955i | \(-0.608034\pi\) |
0.870818 | + | 0.491605i | \(0.163590\pi\) | |||||||
\(774\) | 43.5452 | − | 15.8491i | 1.56520 | − | 0.569686i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27.1043 | − | 22.7432i | −0.972988 | − | 0.816434i | ||||
\(777\) | 3.79043 | − | 21.4966i | 0.135981 | − | 0.771186i | ||||
\(778\) | −38.5054 | −1.38048 | ||||||||
\(779\) | 15.5207 | + | 26.9673i | 0.556087 | + | 0.966204i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.36716 | + | 53.1238i | −0.335183 | + | 1.90092i | ||||
\(782\) | −10.2868 | − | 8.63167i | −0.367856 | − | 0.308668i | ||||
\(783\) | 0.131711 | + | 0.0479389i | 0.00470697 | + | 0.00171320i | ||||
\(784\) | 14.5274 | − | 5.28754i | 0.518836 | − | 0.188841i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37.7392 | − | 65.3661i | −1.34611 | − | 2.33153i | ||||
\(787\) | 17.6118 | − | 30.5046i | 0.627793 | − | 1.08737i | −0.360200 | − | 0.932875i | \(-0.617292\pi\) |
0.987994 | − | 0.154495i | \(-0.0493750\pi\) | |||||||
\(788\) | 0.116432 | + | 0.660316i | 0.00414770 | + | 0.0235228i | ||||
\(789\) | −9.41343 | − | 53.3862i | −0.335127 | − | 1.90060i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.65357 | + | 13.2564i | 0.272129 | + | 0.471342i | ||||
\(792\) | −27.2012 | + | 22.8245i | −0.966554 | + | 0.811035i | ||||
\(793\) | 5.13963 | − | 1.87067i | 0.182514 | − | 0.0664295i | ||||
\(794\) | −17.5979 | − | 6.40513i | −0.624528 | − | 0.227309i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.286194 | + | 1.62309i | −0.0101439 | + | 0.0575288i | ||||
\(797\) | 28.7940 | 1.01994 | 0.509969 | − | 0.860193i | \(-0.329657\pi\) | ||||
0.509969 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(798\) | 39.8136 | + | 33.5000i | 1.40939 | + | 1.18589i | ||||
\(799\) | −2.82065 | −0.0997874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.5633 | + | 13.8982i | 0.585234 | + | 0.491070i | ||||
\(802\) | −12.8180 | − | 4.66536i | −0.452618 | − | 0.164740i | ||||
\(803\) | −7.16455 | + | 2.60768i | −0.252832 | + | 0.0920232i | ||||
\(804\) | 3.05762 | − | 2.56565i | 0.107834 | − | 0.0904834i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.66648 | + | 6.35052i | −0.129146 | + | 0.223688i | ||||
\(807\) | 6.66429 | + | 37.7951i | 0.234594 | + | 1.33045i | ||||
\(808\) | 8.04072 | + | 45.6012i | 0.282872 | + | 1.60425i | ||||
\(809\) | 24.0034 | − | 41.5751i | 0.843915 | − | 1.46170i | −0.0426458 | − | 0.999090i | \(-0.513579\pi\) |
0.886560 | − | 0.462613i | \(-0.153088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.37613 | + | 6.18931i | −0.259011 | + | 0.217336i | −0.763041 | − | 0.646350i | \(-0.776295\pi\) |
0.504030 | + | 0.863686i | \(0.331850\pi\) | |||||||
\(812\) | −0.194793 | + | 0.0708988i | −0.00683589 | + | 0.00248806i | ||||
\(813\) | −12.0481 | − | 4.38513i | −0.422544 | − | 0.153793i | ||||
\(814\) | −12.8233 | − | 10.7601i | −0.449458 | − | 0.377140i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −68.2523 | −2.38931 | ||||||||
\(817\) | 43.1280 | + | 0.0586768i | 1.50886 | + | 0.00205284i | ||||
\(818\) | −50.9680 | −1.78205 | ||||||||
\(819\) | −3.18800 | + | 18.0800i | −0.111398 | + | 0.631768i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.1743 | + | 8.79872i | 0.843688 | + | 0.307077i | 0.727464 | − | 0.686146i | \(-0.240699\pi\) |
0.116224 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(822\) | 30.2152 | − | 10.9974i | 1.05388 | − | 0.383580i | ||||
\(823\) | −10.3098 | + | 8.65091i | −0.359376 | + | 0.301552i | −0.804542 | − | 0.593896i | \(-0.797589\pi\) |
0.445166 | + | 0.895448i | \(0.353145\pi\) | |||||||
\(824\) | −18.5327 | − | 32.0996i | −0.645617 | − | 1.11824i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.62330 | + | 14.8775i | 0.0912764 | + | 0.517654i | ||||
\(827\) | 0.0299383 | + | 0.169788i | 0.00104106 | + | 0.00590412i | 0.985324 | − | 0.170695i | \(-0.0546014\pi\) |
−0.984283 | + | 0.176599i | \(0.943490\pi\) | |||||||
\(828\) | −0.426576 | + | 0.738851i | −0.0148245 | + | 0.0256769i | ||||
\(829\) | 21.1895 | + | 36.7014i | 0.735943 | + | 1.27469i | 0.954308 | + | 0.298824i | \(0.0965942\pi\) |
−0.218365 | + | 0.975867i | \(0.570072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9980 | − | 4.73089i | 0.450896 | − | 0.164113i | ||||
\(832\) | −11.9262 | − | 4.34078i | −0.413467 | − | 0.150490i | ||||
\(833\) | 17.2770 | + | 14.4971i | 0.598614 | + | 0.502296i | ||||
\(834\) | −4.90447 | + | 27.8147i | −0.169828 | + | 0.963143i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.22247 | − | 1.16792i | 0.111452 | − | 0.0403934i | ||||
\(837\) | −1.14755 | −0.0396651 | ||||||||
\(838\) | 2.01900 | − | 11.4503i | 0.0697452 | − | 0.395545i | ||||
\(839\) | 34.5791 | + | 29.0153i | 1.19380 | + | 1.00172i | 0.999785 | + | 0.0207231i | \(0.00659684\pi\) |
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1428 | − | 9.87919i | 0.935960 | − | 0.340662i | ||||
\(842\) | −11.8888 | + | 9.97593i | −0.409717 | + | 0.343793i | ||||
\(843\) | −33.8621 | − | 58.6509i | −1.16627 | − | 2.02005i | ||||
\(844\) | −1.11046 | + | 1.92338i | −0.0382237 | + | 0.0662055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.362270 | + | 2.05453i | 0.0124551 | + | 0.0706363i | ||||
\(847\) | 10.5715 | − | 18.3103i | 0.363240 | − | 0.629151i | ||||
\(848\) | −15.7070 | − | 27.2054i | −0.539382 | − | 0.934238i | ||||
\(849\) | 28.6208 | − | 24.0157i | 0.982263 | − | 0.824217i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.64397 | + | 1.32630i | 0.124914 | + | 0.0454649i | ||||
\(852\) | 4.60930 | + | 3.86766i | 0.157912 | + | 0.132504i | ||||
\(853\) | −8.04694 | + | 45.6364i | −0.275522 | + | 1.56256i | 0.461778 | + | 0.886996i | \(0.347212\pi\) |
−0.737299 | + | 0.675566i | \(0.763899\pi\) | |||||||
\(854\) | −14.7368 | −0.504283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.75023 | −0.299077 | ||||||||
\(857\) | 3.80174 | − | 21.5607i | 0.129865 | − | 0.736501i | −0.848434 | − | 0.529302i | \(-0.822454\pi\) |
0.978299 | − | 0.207199i | \(-0.0664349\pi\) | |||||||
\(858\) | 21.0040 | + | 17.6245i | 0.717066 | + | 0.601690i | ||||
\(859\) | −31.3876 | − | 11.4242i | −1.07093 | − | 0.389787i | −0.254406 | − | 0.967097i | \(-0.581880\pi\) |
−0.816525 | + | 0.577310i | \(0.804102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.1289 | − | 37.0285i | 1.50391 | − | 1.26193i | ||||
\(862\) | 22.1079 | + | 38.2920i | 0.752998 | + | 1.30423i | ||||
\(863\) | 13.5627 | − | 23.4913i | 0.461680 | − | 0.799653i | −0.537365 | − | 0.843350i | \(-0.680580\pi\) |
0.999045 | + | 0.0436971i | \(0.0139137\pi\) | |||||||
\(864\) | 0.0759988 | + | 0.431011i | 0.00258553 | + | 0.0146633i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.02900 | + | 8.71049i | −0.170892 | + | 0.295994i | ||||
\(867\) | −28.6779 | − | 49.6716i | −0.973953 | − | 1.68694i | ||||
\(868\) | 1.30010 | − | 1.09091i | 0.0441282 | − | 0.0370279i | ||||
\(869\) | 2.74705 | − | 0.999846i | 0.0931875 | − | 0.0339175i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6890 | + | 9.80822i | 0.396066 | + | 0.332339i | ||||
\(872\) | −1.49914 | + | 8.50206i | −0.0507674 | + | 0.287916i | ||||
\(873\) | −41.7973 | −1.41462 | ||||||||
\(874\) | −7.08916 | + | 5.93209i | −0.239794 | + | 0.200656i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.147679 | + | 0.837527i | −0.00498960 | + | 0.0282974i | ||||
\(877\) | −37.5992 | − | 31.5495i | −1.26963 | − | 1.06535i | −0.994586 | − | 0.103920i | \(-0.966861\pi\) |
−0.275049 | − | 0.961430i | \(-0.588694\pi\) | |||||||
\(878\) | 11.0725 | + | 4.03008i | 0.373680 | + | 0.136008i | ||||
\(879\) | −18.2682 | + | 6.64906i | −0.616169 | + | 0.224267i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.9889 | − | 32.8898i | −0.639753 | − | 1.10808i | −0.985487 | − | 0.169751i | \(-0.945704\pi\) |
0.345734 | − | 0.938332i | \(-0.387630\pi\) | |||||||
\(882\) | 8.34062 | − | 14.4464i | 0.280843 | − | 0.486435i | ||||
\(883\) | 5.76686 | + | 32.7055i | 0.194070 | + | 1.10063i | 0.913737 | + | 0.406307i | \(0.133184\pi\) |
−0.719666 | + | 0.694320i | \(0.755705\pi\) | |||||||
\(884\) | 0.368704 | + | 2.09103i | 0.0124009 | + | 0.0703288i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1150 | + | 27.9121i | 0.541395 | + | 0.937724i | ||||
\(887\) | 20.1106 | − | 16.8748i | 0.675248 | − | 0.566601i | −0.239365 | − | 0.970930i | \(-0.576939\pi\) |
0.914614 | + | 0.404329i | \(0.132495\pi\) | |||||||
\(888\) | 16.9172 | − | 6.15734i | 0.567703 | − | 0.206627i | ||||
\(889\) | 1.80794 | + | 0.658035i | 0.0606362 | + | 0.0220698i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.15629 | − | 34.9140i | 0.206243 | − | 1.16966i | ||||
\(892\) | 1.67222 | 0.0559902 | ||||||||
\(893\) | −0.339762 | + | 1.91167i | −0.0113697 | + | 0.0639718i | ||||
\(894\) | 54.8808 | 1.83549 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31.4721 | + | 26.4082i | 1.05141 | + | 0.882236i | ||||
\(897\) | −5.96866 | − | 2.17242i | −0.199288 | − | 0.0725348i | ||||
\(898\) | 26.1087 | − | 9.50278i | 0.871258 | − | 0.317112i | ||||
\(899\) | 0.722415 | − | 0.606178i | 0.0240939 | − | 0.0202172i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9143 | − | 39.6888i | 0.763387 | − | 1.32223i | ||||
\(902\) | −7.67129 | − | 43.5060i | −0.255426 | − | 1.44859i | ||||
\(903\) | −13.8654 | − | 78.6346i | −0.461412 | − | 2.61680i | ||||
\(904\) | −6.31229 | + | 10.9332i | −0.209944 | + | 0.363633i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −36.9793 | + | 31.0294i | −1.22856 | + | 1.03088i | ||||
\(907\) | −7.44950 | + | 2.71140i | −0.247357 | + | 0.0900305i | −0.462723 | − | 0.886503i | \(-0.653128\pi\) |
0.215366 | + | 0.976533i | \(0.430905\pi\) | |||||||
\(908\) | 4.66383 | + | 1.69750i | 0.154775 | + | 0.0563334i | ||||
\(909\) | 41.9027 | + | 35.1606i | 1.38983 | + | 1.16620i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.619746 | −0.0205331 | −0.0102665 | − | 0.999947i | \(-0.503268\pi\) | ||||
−0.0102665 | + | 0.999947i | \(0.503268\pi\) | |||||||
\(912\) | −8.22135 | + | 46.2575i | −0.272236 | + | 1.53174i | ||||
\(913\) | 2.31369 | 0.0765718 | ||||||||
\(914\) | 7.25277 | − | 41.1325i | 0.239900 | − | 1.36054i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.84742 | − | 1.40035i | −0.127122 | − | 0.0462687i | ||||
\(917\) | −62.7544 | + | 22.8407i | −2.07233 | + | 0.754268i | ||||
\(918\) | −2.96325 | + | 2.48646i | −0.0978017 | + | 0.0820654i | ||||
\(919\) | 17.5287 | + | 30.3606i | 0.578219 | + | 1.00150i | 0.995684 | + | 0.0928113i | \(0.0295853\pi\) |
−0.417465 | + | 0.908693i | \(0.637081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.77620 | + | 38.4297i | 0.223283 | + | 1.26630i | ||||
\(922\) | 0.0503456 | + | 0.285524i | 0.00165804 | + | 0.00940324i | ||||
\(923\) | −11.5012 | + | 19.9207i | −0.378568 | + | 0.655699i | ||||
\(924\) | −3.17294 | − | 5.49569i | −0.104382 | − | 0.180795i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.4096 | + | 7.06452i | −0.637840 | + | 0.232155i | ||||
\(927\) | −41.1451 | − | 14.9756i | −1.35138 | − | 0.491863i | ||||
\(928\) | −0.275519 | − | 0.231188i | −0.00904437 | − | 0.00758912i | ||||
\(929\) | 2.09132 | − | 11.8605i | 0.0686140 | − | 0.389129i | −0.931090 | − | 0.364790i | \(-0.881141\pi\) |
0.999704 | − | 0.0243392i | \(-0.00774816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9065 | − | 9.96313i | 0.390218 | − | 0.326528i | ||||
\(932\) | 1.87959 | 0.0615679 | ||||||||
\(933\) | 7.75357 | − | 43.9727i | 0.253841 | − | 1.43960i | ||||
\(934\) | −36.3756 | − | 30.5228i | −1.19025 | − | 0.998735i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.2284 | + | 5.17873i | −0.465071 | + | 0.169272i | ||||
\(937\) | 11.4374 | − | 9.59711i | 0.373643 | − | 0.313524i | −0.436558 | − | 0.899676i | \(-0.643802\pi\) |
0.810201 | + | 0.586152i | \(0.199358\pi\) | |||||||
\(938\) | −20.5565 | − | 35.6049i | −0.671194 | − | 1.16254i | ||||
\(939\) | 26.3226 | − | 45.5921i | 0.859006 | − | 1.48784i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.37221 | + | 19.1248i | 0.109931 | + | 0.623450i | 0.989136 | + | 0.147006i | \(0.0469635\pi\) |
−0.879205 | + | 0.476444i | \(0.841925\pi\) | |||||||
\(942\) | 19.9029 | − | 34.4729i | 0.648473 | − | 1.12319i | ||||
\(943\) | 5.11694 | + | 8.86280i | 0.166630 | + | 0.288612i | ||||
\(944\) | −10.4494 | + | 8.76813i | −0.340101 | + | 0.285378i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −57.5409 | − | 20.9432i | −1.87082 | − | 0.680922i | ||||
\(947\) | 12.8212 | + | 10.7583i | 0.416634 | + | 0.349598i | 0.826881 | − | 0.562377i | \(-0.190113\pi\) |
−0.410247 | + | 0.911975i | \(0.634557\pi\) | |||||||
\(948\) | 0.0566233 | − | 0.321127i | 0.00183904 | − | 0.0104297i | ||||
\(949\) | −3.25117 | −0.105538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.60959 | −0.246758 | ||||||||
\(952\) | −9.57824 | + | 54.3209i | −0.310433 | + | 1.76055i | ||||
\(953\) | −40.7361 | − | 34.1817i | −1.31957 | − | 1.10725i | −0.986396 | − | 0.164389i | \(-0.947435\pi\) |
−0.333177 | − | 0.942864i | \(-0.608121\pi\) | |||||||
\(954\) | −31.8520 | − | 11.5932i | −1.03125 | − | 0.375343i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.56794 | − | 2.15475i | 0.0830530 | − | 0.0696897i | ||||
\(957\) | −1.76308 | − | 3.05375i | −0.0569923 | − | 0.0987136i | ||||
\(958\) | −1.46605 | + | 2.53927i | −0.0473658 | + | 0.0820400i | ||||
\(959\) | −4.94022 | − | 28.0174i | −0.159528 | − | 0.904729i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.6396 | − | 20.1603i | 0.375470 | − | 0.650332i | ||||
\(962\) | −3.56906 | − | 6.18179i | −0.115071 | − | 0.199309i | ||||
\(963\) | −7.91839 | + | 6.64432i | −0.255167 | + | 0.214110i | ||||
\(964\) | 3.02778 | − | 1.10202i | 0.0975181 | − | 0.0354937i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.1100 | + | 11.0006i | 0.421807 | + | 0.353938i | ||||
\(967\) | 5.21432 | − | 29.5719i | 0.167681 | − | 0.950967i | −0.778576 | − | 0.627551i | \(-0.784057\pi\) |
0.946257 | − | 0.323416i | \(-0.104831\pi\) | |||||||
\(968\) | 17.4377 | 0.560469 | ||||||||
\(969\) | −64.4390 | + | 23.3546i | −2.07008 | + | 0.750259i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.19210 | − | 23.7746i | 0.134531 | − | 0.762962i | −0.840654 | − | 0.541572i | \(-0.817829\pi\) |
0.975185 | − | 0.221390i | \(-0.0710595\pi\) | |||||||
\(972\) | −3.20770 | − | 2.69158i | −0.102887 | − | 0.0863325i | ||||
\(973\) | 23.4825 | + | 8.54693i | 0.752814 | + | 0.274002i | ||||
\(974\) | −11.9386 | + | 4.34531i | −0.382538 | + | 0.139233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.65325 | − | 11.5238i | −0.212965 | − | 0.368867i | ||||
\(977\) | 4.78840 | − | 8.29375i | 0.153195 | − | 0.265341i | −0.779206 | − | 0.626768i | \(-0.784377\pi\) |
0.932400 | + | 0.361428i | \(0.117711\pi\) | |||||||
\(978\) | −5.38677 | − | 30.5499i | −0.172250 | − | 0.976877i | ||||
\(979\) | −4.96134 | − | 28.1372i | −0.158565 | − | 0.899267i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.09925 | + | 8.83216i | 0.162806 | + | 0.281989i | ||||
\(982\) | −29.3477 | + | 24.6257i | −0.936524 | + | 0.785837i | ||||
\(983\) | −29.2916 | + | 10.6613i | −0.934257 | + | 0.340042i | −0.763896 | − | 0.645340i | \(-0.776716\pi\) |
−0.170362 | + | 0.985382i | \(0.554494\pi\) | |||||||
\(984\) | 44.6455 | + | 16.2497i | 1.42325 | + | 0.518020i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.552008 | − | 3.13060i | 0.0175795 | − | 0.0996985i | ||||
\(987\) | 3.59476 | 0.114422 | ||||||||
\(988\) | 1.46159 | + | 0.00198853i | 0.0464994 | + | 6.32636e-5i | ||||
\(989\) | 14.1851 | 0.451061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2791 | − | 31.2808i | −1.18421 | − | 0.993669i | −0.999942 | − | 0.0107922i | \(-0.996565\pi\) |
−0.184266 | − | 0.982876i | \(-0.558991\pi\) | |||||||
\(992\) | 2.76706 | + | 1.00713i | 0.0878542 | + | 0.0319763i | ||||
\(993\) | 60.5551 | − | 22.0403i | 1.92166 | − | 0.699426i | ||||
\(994\) | 47.4772 | − | 39.8381i | 1.50589 | − | 1.26359i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.129038 | − | 0.223501i | 0.00408873 | − | 0.00708189i | ||||
\(997\) | 5.53857 | + | 31.4108i | 0.175408 | + | 0.994790i | 0.937672 | + | 0.347523i | \(0.112977\pi\) |
−0.762263 | + | 0.647267i | \(0.775912\pi\) | |||||||
\(998\) | 5.44631 | + | 30.8876i | 0.172400 | + | 0.977729i | ||||
\(999\) | 0.558529 | − | 0.967401i | 0.0176711 | − | 0.0306072i |
(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 | 475.2.l.f.226.2 | 48 | ||
5.2 | odd | 4 | 95.2.p.a.74.2 | yes | 48 | ||
5.3 | odd | 4 | 95.2.p.a.74.7 | yes | 48 | ||
5.4 | even | 2 | inner | 475.2.l.f.226.7 | 48 | ||
15.2 | even | 4 | 855.2.da.b.739.7 | 48 | |||
15.8 | even | 4 | 855.2.da.b.739.2 | 48 | |||
19.3 | odd | 18 | 9025.2.a.ct.1.18 | 24 | |||
19.9 | even | 9 | inner | 475.2.l.f.351.2 | 48 | ||
19.16 | even | 9 | 9025.2.a.cu.1.7 | 24 | |||
95.3 | even | 36 | 1805.2.b.l.1084.7 | 24 | |||
95.9 | even | 18 | inner | 475.2.l.f.351.7 | 48 | ||
95.22 | even | 36 | 1805.2.b.l.1084.18 | 24 | |||
95.28 | odd | 36 | 95.2.p.a.9.2 | ✓ | 48 | ||
95.47 | odd | 36 | 95.2.p.a.9.7 | yes | 48 | ||
95.54 | even | 18 | 9025.2.a.cu.1.18 | 24 | |||
95.73 | odd | 36 | 1805.2.b.k.1084.18 | 24 | |||
95.79 | odd | 18 | 9025.2.a.ct.1.7 | 24 | |||
95.92 | odd | 36 | 1805.2.b.k.1084.7 | 24 | |||
285.47 | even | 36 | 855.2.da.b.199.2 | 48 | |||
285.218 | even | 36 | 855.2.da.b.199.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.2 | ✓ | 48 | 95.28 | odd | 36 | ||
95.2.p.a.9.7 | yes | 48 | 95.47 | odd | 36 | ||
95.2.p.a.74.2 | yes | 48 | 5.2 | odd | 4 | ||
95.2.p.a.74.7 | yes | 48 | 5.3 | odd | 4 | ||
475.2.l.f.226.2 | 48 | 1.1 | even | 1 | trivial | ||
475.2.l.f.226.7 | 48 | 5.4 | even | 2 | inner | ||
475.2.l.f.351.2 | 48 | 19.9 | even | 9 | inner | ||
475.2.l.f.351.7 | 48 | 95.9 | even | 18 | inner | ||
855.2.da.b.199.2 | 48 | 285.47 | even | 36 | |||
855.2.da.b.199.7 | 48 | 285.218 | even | 36 | |||
855.2.da.b.739.2 | 48 | 15.8 | even | 4 | |||
855.2.da.b.739.7 | 48 | 15.2 | even | 4 | |||
1805.2.b.k.1084.7 | 24 | 95.92 | odd | 36 | |||
1805.2.b.k.1084.18 | 24 | 95.73 | odd | 36 | |||
1805.2.b.l.1084.7 | 24 | 95.3 | even | 36 | |||
1805.2.b.l.1084.18 | 24 | 95.22 | even | 36 | |||
9025.2.a.ct.1.7 | 24 | 95.79 | odd | 18 | |||
9025.2.a.ct.1.18 | 24 | 19.3 | odd | 18 | |||
9025.2.a.cu.1.7 | 24 | 19.16 | even | 9 | |||
9025.2.a.cu.1.18 | 24 | 95.54 | even | 18 |